Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,3,Mod(11,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.j (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.08720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 11.20 | ||
Character | \(\chi\) | \(=\) | 150.11 |
Dual form | 150.3.j.a.41.20 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.831254 | + | 1.14412i | 0.415627 | + | 0.572061i | ||||
\(3\) | 2.98083 | − | 0.338569i | 0.993611 | − | 0.112856i | ||||
\(4\) | −0.618034 | + | 1.90211i | −0.154508 | + | 0.475528i | ||||
\(5\) | −1.16748 | − | 4.86179i | −0.233496 | − | 0.972358i | ||||
\(6\) | 2.86519 | + | 3.12900i | 0.477532 | + | 0.521501i | ||||
\(7\) | 6.03242 | 0.861775 | 0.430887 | − | 0.902406i | \(-0.358201\pi\) | ||||
0.430887 | + | 0.902406i | \(0.358201\pi\) | |||||||
\(8\) | −2.68999 | + | 0.874032i | −0.336249 | + | 0.109254i | ||||
\(9\) | 8.77074 | − | 2.01844i | 0.974527 | − | 0.224271i | ||||
\(10\) | 4.59201 | − | 5.37712i | 0.459201 | − | 0.537712i | ||||
\(11\) | 3.18447 | + | 4.38305i | 0.289497 | + | 0.398459i | 0.928851 | − | 0.370454i | \(-0.120798\pi\) |
−0.639353 | + | 0.768913i | \(0.720798\pi\) | |||||||
\(12\) | −1.19826 | + | 5.87913i | −0.0998550 | + | 0.489928i | ||||
\(13\) | 10.2465 | + | 7.44455i | 0.788196 | + | 0.572658i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.119231 | + | 0.992866i | \(0.538043\pi\) | |||||||
\(14\) | 5.01447 | + | 6.90183i | 0.358177 | + | 0.492988i | ||||
\(15\) | −5.12611 | − | 14.0969i | −0.341741 | − | 0.939794i | ||||
\(16\) | −3.23607 | − | 2.35114i | −0.202254 | − | 0.146946i | ||||
\(17\) | −29.2114 | + | 9.49135i | −1.71832 | + | 0.558314i | −0.991682 | − | 0.128711i | \(-0.958916\pi\) |
−0.726633 | + | 0.687026i | \(0.758916\pi\) | |||||||
\(18\) | 9.60005 | + | 8.35697i | 0.533336 | + | 0.464276i | ||||
\(19\) | −5.28636 | − | 16.2697i | −0.278229 | − | 0.856302i | −0.988347 | − | 0.152219i | \(-0.951358\pi\) |
0.710117 | − | 0.704083i | \(-0.248642\pi\) | |||||||
\(20\) | 9.96921 | + | 0.784075i | 0.498461 | + | 0.0392037i | ||||
\(21\) | 17.9816 | − | 2.04239i | 0.856269 | − | 0.0972567i | ||||
\(22\) | −2.36764 | + | 7.28685i | −0.107620 | + | 0.331221i | ||||
\(23\) | −4.21551 | − | 5.80215i | −0.183283 | − | 0.252268i | 0.707482 | − | 0.706731i | \(-0.249831\pi\) |
−0.890765 | + | 0.454464i | \(0.849831\pi\) | |||||||
\(24\) | −7.72251 | + | 3.51609i | −0.321771 | + | 0.146504i | ||||
\(25\) | −22.2740 | + | 11.3521i | −0.890960 | + | 0.454083i | ||||
\(26\) | 17.9116i | 0.688909i | ||||||||
\(27\) | 25.4607 | − | 8.98613i | 0.942991 | − | 0.332820i | ||||
\(28\) | −3.72824 | + | 11.4743i | −0.133151 | + | 0.409798i | ||||
\(29\) | −37.6522 | − | 12.2340i | −1.29835 | − | 0.421860i | −0.423345 | − | 0.905969i | \(-0.639144\pi\) |
−0.875008 | + | 0.484108i | \(0.839144\pi\) | |||||||
\(30\) | 11.8675 | − | 17.5830i | 0.395583 | − | 0.586100i | ||||
\(31\) | 10.1306 | + | 31.1789i | 0.326795 | + | 1.00577i | 0.970624 | + | 0.240601i | \(0.0773446\pi\) |
−0.643829 | + | 0.765169i | \(0.722655\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 10.9763 | + | 11.9870i | 0.332617 | + | 0.363242i | ||||
\(34\) | −35.1413 | − | 25.5317i | −1.03357 | − | 0.750931i | ||||
\(35\) | −7.04272 | − | 29.3284i | −0.201221 | − | 0.837953i | ||||
\(36\) | −1.58132 | + | 17.9304i | −0.0439256 | + | 0.498067i | ||||
\(37\) | 10.6591 | + | 7.74430i | 0.288084 | + | 0.209305i | 0.722436 | − | 0.691438i | \(-0.243022\pi\) |
−0.434352 | + | 0.900743i | \(0.643022\pi\) | |||||||
\(38\) | 14.2203 | − | 19.5725i | 0.374218 | − | 0.515066i | ||||
\(39\) | 33.0638 | + | 18.7218i | 0.847789 | + | 0.480047i | ||||
\(40\) | 7.38987 | + | 12.0578i | 0.184747 | + | 0.301444i | ||||
\(41\) | 27.3403 | − | 37.6306i | 0.666836 | − | 0.917821i | −0.332848 | − | 0.942981i | \(-0.608010\pi\) |
0.999683 | + | 0.0251600i | \(0.00800952\pi\) | |||||||
\(42\) | 17.2841 | + | 18.8755i | 0.411525 | + | 0.449416i | ||||
\(43\) | 2.54995 | 0.0593013 | 0.0296506 | − | 0.999560i | \(-0.490561\pi\) | ||||
0.0296506 | + | 0.999560i | \(0.490561\pi\) | |||||||
\(44\) | −10.3052 | + | 3.34835i | −0.234208 | + | 0.0760989i | ||||
\(45\) | −20.0529 | − | 40.2850i | −0.445619 | − | 0.895223i | ||||
\(46\) | 3.13422 | − | 9.64612i | 0.0681351 | − | 0.209698i | ||||
\(47\) | −61.8997 | − | 20.1124i | −1.31702 | − | 0.427924i | −0.435547 | − | 0.900166i | \(-0.643445\pi\) |
−0.881469 | + | 0.472242i | \(0.843445\pi\) | |||||||
\(48\) | −10.4422 | − | 5.91273i | −0.217546 | − | 0.123182i | ||||
\(49\) | −12.6099 | −0.257345 | ||||||||
\(50\) | −31.5035 | − | 16.0477i | −0.630070 | − | 0.320955i | ||||
\(51\) | −83.8607 | + | 38.1822i | −1.64433 | + | 0.748670i | ||||
\(52\) | −20.4931 | + | 14.8891i | −0.394098 | + | 0.286329i | ||||
\(53\) | 54.8364 | + | 17.8174i | 1.03465 | + | 0.336178i | 0.776626 | − | 0.629961i | \(-0.216929\pi\) |
0.258022 | + | 0.966139i | \(0.416929\pi\) | |||||||
\(54\) | 31.4456 | + | 21.6605i | 0.582325 | + | 0.401120i | ||||
\(55\) | 17.5917 | − | 20.5993i | 0.319848 | − | 0.374534i | ||||
\(56\) | −16.2272 | + | 5.27253i | −0.289771 | + | 0.0941523i | ||||
\(57\) | −21.2662 | − | 46.7076i | −0.373091 | − | 0.819431i | ||||
\(58\) | −17.3014 | − | 53.2483i | −0.298300 | − | 0.918074i | ||||
\(59\) | −42.1001 | + | 57.9458i | −0.713561 | + | 0.982133i | 0.286152 | + | 0.958184i | \(0.407624\pi\) |
−0.999713 | + | 0.0239487i | \(0.992376\pi\) | |||||||
\(60\) | 29.9820 | − | 1.03807i | 0.499701 | − | 0.0173012i | ||||
\(61\) | −47.8917 | + | 34.7953i | −0.785109 | + | 0.570415i | −0.906508 | − | 0.422188i | \(-0.861262\pi\) |
0.121399 | + | 0.992604i | \(0.461262\pi\) | |||||||
\(62\) | −27.2513 | + | 37.5083i | −0.439538 | + | 0.604972i | ||||
\(63\) | 52.9088 | − | 12.1761i | 0.839822 | − | 0.193271i | ||||
\(64\) | 6.47214 | − | 4.70228i | 0.101127 | − | 0.0734732i | ||||
\(65\) | 24.2312 | − | 58.5079i | 0.372788 | − | 0.900122i | ||||
\(66\) | −4.59044 | + | 22.5225i | −0.0695522 | + | 0.341250i | ||||
\(67\) | −33.9509 | − | 104.490i | −0.506730 | − | 1.55956i | −0.797842 | − | 0.602867i | \(-0.794025\pi\) |
0.291112 | − | 0.956689i | \(-0.405975\pi\) | |||||||
\(68\) | − | 61.4293i | − | 0.903372i | ||||||
\(69\) | −14.5302 | − | 15.8680i | −0.210582 | − | 0.229971i | ||||
\(70\) | 27.7010 | − | 32.4371i | 0.395728 | − | 0.463387i | ||||
\(71\) | −30.3355 | − | 9.85659i | −0.427260 | − | 0.138825i | 0.0874902 | − | 0.996165i | \(-0.472115\pi\) |
−0.514750 | + | 0.857340i | \(0.672115\pi\) | |||||||
\(72\) | −21.8291 | + | 13.0955i | −0.303181 | + | 0.181882i | ||||
\(73\) | 41.8731 | − | 30.4226i | 0.573604 | − | 0.416748i | −0.262808 | − | 0.964848i | \(-0.584649\pi\) |
0.836413 | + | 0.548100i | \(0.184649\pi\) | |||||||
\(74\) | 18.6328i | 0.251795i | ||||||||
\(75\) | −62.5516 | + | 41.3799i | −0.834021 | + | 0.551732i | ||||
\(76\) | 34.2140 | 0.450185 | ||||||||
\(77\) | 19.2101 | + | 26.4404i | 0.249482 | + | 0.343382i | ||||
\(78\) | 6.06432 | + | 53.3916i | 0.0777477 | + | 0.684507i | ||||
\(79\) | −22.8375 | + | 70.2866i | −0.289082 | + | 0.889704i | 0.696063 | + | 0.717981i | \(0.254934\pi\) |
−0.985145 | + | 0.171723i | \(0.945066\pi\) | |||||||
\(80\) | −7.65271 | + | 18.4780i | −0.0956589 | + | 0.230975i | ||||
\(81\) | 72.8518 | − | 35.4064i | 0.899405 | − | 0.437116i | ||||
\(82\) | 65.7808 | 0.802205 | ||||||||
\(83\) | 94.2433 | − | 30.6215i | 1.13546 | − | 0.368934i | 0.319812 | − | 0.947481i | \(-0.396380\pi\) |
0.815649 | + | 0.578547i | \(0.196380\pi\) | |||||||
\(84\) | −7.22841 | + | 35.4654i | −0.0860525 | + | 0.422207i | ||||
\(85\) | 80.2485 | + | 130.939i | 0.944101 | + | 1.54045i | ||||
\(86\) | 2.11966 | + | 2.91746i | 0.0246472 | + | 0.0339240i | ||||
\(87\) | −116.377 | − | 23.7195i | −1.33767 | − | 0.272638i | ||||
\(88\) | −12.3971 | − | 9.00705i | −0.140877 | − | 0.102353i | ||||
\(89\) | 77.7962 | + | 107.077i | 0.874114 | + | 1.20312i | 0.978016 | + | 0.208528i | \(0.0668671\pi\) |
−0.103902 | + | 0.994588i | \(0.533133\pi\) | |||||||
\(90\) | 29.4220 | − | 56.4300i | 0.326911 | − | 0.627000i | ||||
\(91\) | 61.8115 | + | 44.9087i | 0.679247 | + | 0.493502i | ||||
\(92\) | 13.6417 | − | 4.43245i | 0.148279 | − | 0.0481788i | ||||
\(93\) | 40.7539 | + | 89.5092i | 0.438214 | + | 0.962464i | ||||
\(94\) | −28.4433 | − | 87.5395i | −0.302588 | − | 0.931271i | ||||
\(95\) | −72.9283 | + | 44.6957i | −0.767667 | + | 0.470481i | ||||
\(96\) | −1.91524 | − | 16.8621i | −0.0199504 | − | 0.175647i | ||||
\(97\) | 16.8097 | − | 51.7350i | 0.173296 | − | 0.533351i | −0.826255 | − | 0.563296i | \(-0.809533\pi\) |
0.999552 | + | 0.0299448i | \(0.00953316\pi\) | |||||||
\(98\) | −10.4820 | − | 14.4273i | −0.106959 | − | 0.147217i | ||||
\(99\) | 36.7771 | + | 32.0149i | 0.371486 | + | 0.323383i | ||||
\(100\) | −7.82684 | − | 49.3836i | −0.0782684 | − | 0.493836i | ||||
\(101\) | 100.836i | 0.998378i | 0.866493 | + | 0.499189i | \(0.166369\pi\) | ||||
−0.866493 | + | 0.499189i | \(0.833631\pi\) | |||||||
\(102\) | −113.395 | − | 64.2079i | −1.11171 | − | 0.629489i | ||||
\(103\) | −23.3279 | + | 71.7959i | −0.226485 | + | 0.697048i | 0.771653 | + | 0.636044i | \(0.219430\pi\) |
−0.998138 | + | 0.0610041i | \(0.980570\pi\) | |||||||
\(104\) | −34.0699 | − | 11.0700i | −0.327596 | − | 0.106442i | ||||
\(105\) | −30.9229 | − | 85.0385i | −0.294503 | − | 0.809891i | ||||
\(106\) | 25.1976 | + | 77.5503i | 0.237713 | + | 0.731607i | ||||
\(107\) | 42.2165i | 0.394547i | 0.980349 | + | 0.197273i | \(0.0632087\pi\) | ||||
−0.980349 | + | 0.197273i | \(0.936791\pi\) | |||||||
\(108\) | 1.35702 | + | 53.9829i | 0.0125650 | + | 0.499842i | ||||
\(109\) | 101.895 | + | 74.0307i | 0.934812 | + | 0.679181i | 0.947166 | − | 0.320743i | \(-0.103933\pi\) |
−0.0123541 | + | 0.999924i | \(0.503933\pi\) | |||||||
\(110\) | 38.1913 | + | 3.00373i | 0.347194 | + | 0.0273067i | ||||
\(111\) | 34.3950 | + | 19.4756i | 0.309865 | + | 0.175456i | ||||
\(112\) | −19.5213 | − | 14.1831i | −0.174298 | − | 0.126635i | ||||
\(113\) | 38.2362 | − | 52.6276i | 0.338373 | − | 0.465731i | −0.605592 | − | 0.795775i | \(-0.707064\pi\) |
0.943965 | + | 0.330044i | \(0.107064\pi\) | |||||||
\(114\) | 35.7616 | − | 63.1570i | 0.313698 | − | 0.554009i | ||||
\(115\) | −23.2873 | + | 27.2688i | −0.202498 | + | 0.237120i | ||||
\(116\) | 46.5407 | − | 64.0578i | 0.401213 | − | 0.552222i | ||||
\(117\) | 104.896 | + | 44.6123i | 0.896549 | + | 0.381301i | ||||
\(118\) | −101.293 | −0.858416 | ||||||||
\(119\) | −176.215 | + | 57.2558i | −1.48080 | + | 0.481141i | ||||
\(120\) | 26.1104 | + | 33.4402i | 0.217586 | + | 0.278669i | ||||
\(121\) | 28.3208 | − | 87.1624i | 0.234056 | − | 0.720351i | ||||
\(122\) | −79.6203 | − | 25.8702i | −0.652625 | − | 0.212051i | ||||
\(123\) | 68.7562 | − | 121.427i | 0.558994 | − | 0.987214i | ||||
\(124\) | −65.5668 | −0.528765 | ||||||||
\(125\) | 81.1958 | + | 95.0381i | 0.649566 | + | 0.760305i | ||||
\(126\) | 57.9116 | + | 50.4128i | 0.459616 | + | 0.400101i | ||||
\(127\) | 120.084 | − | 87.2464i | 0.945546 | − | 0.686979i | −0.00420341 | − | 0.999991i | \(-0.501338\pi\) |
0.949749 | + | 0.313012i | \(0.101338\pi\) | |||||||
\(128\) | 10.7600 | + | 3.49613i | 0.0840623 | + | 0.0273135i | ||||
\(129\) | 7.60099 | − | 0.863336i | 0.0589224 | − | 0.00669253i | ||||
\(130\) | 87.0825 | − | 20.9114i | 0.669866 | − | 0.160857i | ||||
\(131\) | 145.285 | − | 47.2060i | 1.10905 | − | 0.360351i | 0.303470 | − | 0.952841i | \(-0.401855\pi\) |
0.805578 | + | 0.592490i | \(0.201855\pi\) | |||||||
\(132\) | −29.5843 | + | 13.4699i | −0.224124 | + | 0.102045i | ||||
\(133\) | −31.8895 | − | 98.1459i | −0.239771 | − | 0.737939i | ||||
\(134\) | 91.3278 | − | 125.702i | 0.681551 | − | 0.938074i | ||||
\(135\) | −73.4135 | − | 113.294i | −0.543804 | − | 0.839212i | ||||
\(136\) | 70.2826 | − | 51.0633i | 0.516784 | − | 0.375466i | ||||
\(137\) | 64.1108 | − | 88.2409i | 0.467962 | − | 0.644094i | −0.508174 | − | 0.861254i | \(-0.669679\pi\) |
0.976136 | + | 0.217160i | \(0.0696793\pi\) | |||||||
\(138\) | 6.07670 | − | 29.8146i | 0.0440340 | − | 0.216048i | ||||
\(139\) | −174.671 | + | 126.906i | −1.25662 | + | 0.912990i | −0.998587 | − | 0.0531448i | \(-0.983076\pi\) |
−0.258037 | + | 0.966135i | \(0.583076\pi\) | |||||||
\(140\) | 60.1385 | + | 4.72987i | 0.429561 | + | 0.0337848i | ||||
\(141\) | −191.322 | − | 38.9945i | −1.35690 | − | 0.276557i | ||||
\(142\) | −13.9393 | − | 42.9008i | −0.0981643 | − | 0.302118i | ||||
\(143\) | 68.6181i | 0.479847i | ||||||||
\(144\) | −33.1283 | − | 14.0895i | −0.230058 | − | 0.0978434i | ||||
\(145\) | −15.5207 | + | 197.340i | −0.107039 | + | 1.36097i | ||||
\(146\) | 69.6144 | + | 22.6191i | 0.476811 | + | 0.154925i | ||||
\(147\) | −37.5880 | + | 4.26932i | −0.255700 | + | 0.0290430i | ||||
\(148\) | −21.3182 | + | 15.4886i | −0.144042 | + | 0.104653i | ||||
\(149\) | − | 188.713i | − | 1.26653i | −0.773936 | − | 0.633264i | \(-0.781715\pi\) | ||
0.773936 | − | 0.633264i | \(-0.218285\pi\) | |||||||
\(150\) | −99.3400 | − | 37.1695i | −0.662266 | − | 0.247797i | ||||
\(151\) | −131.965 | −0.873944 | −0.436972 | − | 0.899475i | \(-0.643949\pi\) | ||||
−0.436972 | + | 0.899475i | \(0.643949\pi\) | |||||||
\(152\) | 28.4405 | + | 39.1451i | 0.187109 | + | 0.257533i | ||||
\(153\) | −237.048 | + | 142.207i | −1.54933 | + | 0.929460i | ||||
\(154\) | −14.2826 | + | 43.9574i | −0.0927443 | + | 0.285437i | ||||
\(155\) | 139.758 | − | 85.6537i | 0.901664 | − | 0.552604i | ||||
\(156\) | −56.0455 | + | 51.3203i | −0.359266 | + | 0.328976i | ||||
\(157\) | 130.779 | 0.832987 | 0.416494 | − | 0.909139i | \(-0.363259\pi\) | ||||
0.416494 | + | 0.909139i | \(0.363259\pi\) | |||||||
\(158\) | −99.4003 | + | 32.2971i | −0.629116 | + | 0.204412i | ||||
\(159\) | 169.490 | + | 34.5449i | 1.06598 | + | 0.217263i | ||||
\(160\) | −27.5024 | + | 6.60426i | −0.171890 | + | 0.0412766i | ||||
\(161\) | −25.4297 | − | 35.0010i | −0.157949 | − | 0.217398i | ||||
\(162\) | 101.068 | + | 53.9198i | 0.623874 | + | 0.332838i | ||||
\(163\) | −227.827 | − | 165.526i | −1.39771 | − | 1.01550i | −0.994969 | − | 0.100182i | \(-0.968057\pi\) |
−0.402741 | − | 0.915314i | \(-0.631943\pi\) | |||||||
\(164\) | 54.6805 | + | 75.2613i | 0.333418 | + | 0.458910i | ||||
\(165\) | 45.4635 | − | 67.3592i | 0.275536 | − | 0.408238i | ||||
\(166\) | 113.375 | + | 82.3717i | 0.682981 | + | 0.496215i | ||||
\(167\) | 15.3004 | − | 4.97139i | 0.0916190 | − | 0.0297688i | −0.262849 | − | 0.964837i | \(-0.584662\pi\) |
0.354468 | + | 0.935068i | \(0.384662\pi\) | |||||||
\(168\) | −46.5854 | + | 21.2106i | −0.277294 | + | 0.126253i | ||||
\(169\) | −2.65348 | − | 8.16657i | −0.0157011 | − | 0.0483229i | ||||
\(170\) | −83.1028 | + | 200.657i | −0.488840 | + | 1.18034i | ||||
\(171\) | −79.2047 | − | 132.027i | −0.463185 | − | 0.772091i | ||||
\(172\) | −1.57596 | + | 4.85030i | −0.00916255 | + | 0.0281994i | ||||
\(173\) | 88.5080 | + | 121.821i | 0.511607 | + | 0.704167i | 0.984189 | − | 0.177120i | \(-0.0566780\pi\) |
−0.472582 | + | 0.881287i | \(0.656678\pi\) | |||||||
\(174\) | −69.6009 | − | 152.867i | −0.400005 | − | 0.878544i | ||||
\(175\) | −134.366 | + | 68.4805i | −0.767806 | + | 0.391317i | ||||
\(176\) | − | 21.6710i | − | 0.123131i | ||||||
\(177\) | −105.875 | + | 186.981i | −0.598163 | + | 1.05639i | ||||
\(178\) | −57.8411 | + | 178.017i | −0.324950 | + | 1.00009i | ||||
\(179\) | −79.5307 | − | 25.8411i | −0.444305 | − | 0.144364i | 0.0783158 | − | 0.996929i | \(-0.475046\pi\) |
−0.522621 | + | 0.852565i | \(0.675046\pi\) | |||||||
\(180\) | 89.0200 | − | 13.2453i | 0.494556 | − | 0.0735850i | ||||
\(181\) | −22.7871 | − | 70.1314i | −0.125896 | − | 0.387467i | 0.868168 | − | 0.496271i | \(-0.165298\pi\) |
−0.994063 | + | 0.108804i | \(0.965298\pi\) | |||||||
\(182\) | 108.050i | 0.593684i | ||||||||
\(183\) | −130.977 | + | 119.934i | −0.715719 | + | 0.655376i | ||||
\(184\) | 16.4110 | + | 11.9233i | 0.0891900 | + | 0.0648004i | ||||
\(185\) | 25.2069 | − | 60.8636i | 0.136253 | − | 0.328993i | ||||
\(186\) | −68.5326 | + | 121.032i | −0.368455 | + | 0.650712i | ||||
\(187\) | −134.624 | − | 97.8099i | −0.719913 | − | 0.523048i | ||||
\(188\) | 76.5123 | − | 105.310i | 0.406980 | − | 0.560160i | ||||
\(189\) | 153.590 | − | 54.2081i | 0.812645 | − | 0.286815i | ||||
\(190\) | −111.759 | − | 46.2855i | −0.588207 | − | 0.243608i | ||||
\(191\) | −3.92026 | + | 5.39577i | −0.0205249 | + | 0.0282501i | −0.819156 | − | 0.573571i | \(-0.805558\pi\) |
0.798631 | + | 0.601821i | \(0.205558\pi\) | |||||||
\(192\) | 17.7003 | − | 16.2080i | 0.0921891 | − | 0.0844166i | ||||
\(193\) | 291.040 | 1.50798 | 0.753990 | − | 0.656886i | \(-0.228127\pi\) | ||||
0.753990 | + | 0.656886i | \(0.228127\pi\) | |||||||
\(194\) | 73.1644 | − | 23.7726i | 0.377136 | − | 0.122539i | ||||
\(195\) | 52.4203 | − | 182.606i | 0.268822 | − | 0.936443i | ||||
\(196\) | 7.79334 | − | 23.9854i | 0.0397619 | − | 0.122375i | ||||
\(197\) | 152.080 | + | 49.4136i | 0.771977 | + | 0.250831i | 0.668411 | − | 0.743792i | \(-0.266975\pi\) |
0.103566 | + | 0.994623i | \(0.466975\pi\) | |||||||
\(198\) | −6.05793 | + | 68.6900i | −0.0305956 | + | 0.346919i | ||||
\(199\) | −261.398 | −1.31356 | −0.656779 | − | 0.754083i | \(-0.728082\pi\) | ||||
−0.656779 | + | 0.754083i | \(0.728082\pi\) | |||||||
\(200\) | 49.9948 | − | 50.0052i | 0.249974 | − | 0.250026i | ||||
\(201\) | −136.579 | − | 299.973i | −0.679499 | − | 1.49240i | ||||
\(202\) | −115.369 | + | 83.8205i | −0.571134 | + | 0.414953i | ||||
\(203\) | −227.134 | − | 73.8004i | −1.11889 | − | 0.363549i | ||||
\(204\) | −20.7981 | − | 183.110i | −0.101951 | − | 0.897600i | ||||
\(205\) | −214.871 | − | 88.9896i | −1.04815 | − | 0.434096i | ||||
\(206\) | −101.535 | + | 32.9907i | −0.492887 | + | 0.160149i | ||||
\(207\) | −48.6844 | − | 42.3804i | −0.235191 | − | 0.204736i | ||||
\(208\) | −15.6553 | − | 48.1822i | −0.0752660 | − | 0.231645i | ||||
\(209\) | 54.4768 | − | 74.9809i | 0.260655 | − | 0.358760i | ||||
\(210\) | 71.5898 | − | 106.068i | 0.340904 | − | 0.505087i | ||||
\(211\) | 312.392 | − | 226.966i | 1.48053 | − | 1.07567i | 0.503146 | − | 0.864202i | \(-0.332176\pi\) |
0.977385 | − | 0.211467i | \(-0.0678240\pi\) | |||||||
\(212\) | −67.7815 | + | 93.2932i | −0.319724 | + | 0.440062i | ||||
\(213\) | −93.7621 | − | 19.1102i | −0.440198 | − | 0.0897193i | ||||
\(214\) | −48.3009 | + | 35.0926i | −0.225705 | + | 0.163984i | ||||
\(215\) | −2.97702 | − | 12.3973i | −0.0138466 | − | 0.0576621i | ||||
\(216\) | −60.6351 | + | 46.4261i | −0.280718 | + | 0.214936i | ||||
\(217\) | 61.1123 | + | 188.084i | 0.281623 | + | 0.866747i | ||||
\(218\) | 178.118i | 0.817056i | ||||||||
\(219\) | 114.517 | − | 104.862i | 0.522907 | − | 0.478820i | ||||
\(220\) | 28.3100 | + | 46.1924i | 0.128682 | + | 0.209966i | ||||
\(221\) | −369.974 | − | 120.212i | −1.67409 | − | 0.543946i | ||||
\(222\) | 6.30849 | + | 55.5413i | 0.0284166 | + | 0.250186i | ||||
\(223\) | 239.756 | − | 174.193i | 1.07514 | − | 0.781133i | 0.0983083 | − | 0.995156i | \(-0.468657\pi\) |
0.976829 | + | 0.214023i | \(0.0686569\pi\) | |||||||
\(224\) | − | 34.1245i | − | 0.152342i | ||||||
\(225\) | −172.446 | + | 144.525i | −0.766427 | + | 0.642332i | ||||
\(226\) | 91.9963 | 0.407063 | ||||||||
\(227\) | 158.259 | + | 217.825i | 0.697178 | + | 0.959583i | 0.999979 | + | 0.00652938i | \(0.00207838\pi\) |
−0.302801 | + | 0.953054i | \(0.597922\pi\) | |||||||
\(228\) | 101.986 | − | 11.5838i | 0.447309 | − | 0.0508062i | ||||
\(229\) | −19.2902 | + | 59.3692i | −0.0842368 | + | 0.259254i | −0.984300 | − | 0.176506i | \(-0.943520\pi\) |
0.900063 | + | 0.435760i | \(0.143520\pi\) | |||||||
\(230\) | −50.5566 | − | 3.97625i | −0.219811 | − | 0.0172881i | ||||
\(231\) | 66.2140 | + | 72.3105i | 0.286640 | + | 0.313033i | ||||
\(232\) | 111.977 | 0.482660 | ||||||||
\(233\) | −118.262 | + | 38.4255i | −0.507560 | + | 0.164916i | −0.551592 | − | 0.834114i | \(-0.685980\pi\) |
0.0440320 | + | 0.999030i | \(0.485980\pi\) | |||||||
\(234\) | 36.1535 | + | 157.098i | 0.154502 | + | 0.671360i | ||||
\(235\) | −25.5159 | + | 324.424i | −0.108578 | + | 1.38053i | ||||
\(236\) | −84.2002 | − | 115.892i | −0.356781 | − | 0.491066i | ||||
\(237\) | −44.2780 | + | 217.245i | −0.186827 | + | 0.916645i | ||||
\(238\) | −211.987 | − | 154.018i | −0.890703 | − | 0.647133i | ||||
\(239\) | −28.5359 | − | 39.2763i | −0.119397 | − | 0.164336i | 0.745135 | − | 0.666914i | \(-0.232385\pi\) |
−0.864532 | + | 0.502578i | \(0.832385\pi\) | |||||||
\(240\) | −16.5554 | + | 57.6708i | −0.0689808 | + | 0.240295i | ||||
\(241\) | 155.430 | + | 112.927i | 0.644940 | + | 0.468576i | 0.861544 | − | 0.507683i | \(-0.169498\pi\) |
−0.216604 | + | 0.976260i | \(0.569498\pi\) | |||||||
\(242\) | 123.266 | − | 40.0517i | 0.509365 | − | 0.165503i | ||||
\(243\) | 205.172 | − | 130.206i | 0.844328 | − | 0.535827i | ||||
\(244\) | −36.5860 | − | 112.600i | −0.149943 | − | 0.461476i | ||||
\(245\) | 14.7218 | + | 61.3066i | 0.0600889 | + | 0.250231i | ||||
\(246\) | 196.082 | − | 22.2713i | 0.797080 | − | 0.0905339i | ||||
\(247\) | 66.9540 | − | 206.063i | 0.271069 | − | 0.834264i | ||||
\(248\) | −54.5027 | − | 75.0165i | −0.219769 | − | 0.302486i | ||||
\(249\) | 270.556 | − | 123.185i | 1.08657 | − | 0.494721i | ||||
\(250\) | −41.2410 | + | 171.899i | −0.164964 | + | 0.687595i | ||||
\(251\) | 177.231i | 0.706100i | 0.935604 | + | 0.353050i | \(0.114856\pi\) | ||||
−0.935604 | + | 0.353050i | \(0.885144\pi\) | |||||||
\(252\) | −9.53920 | + | 108.164i | −0.0378540 | + | 0.429221i | ||||
\(253\) | 12.0069 | − | 36.9536i | 0.0474583 | − | 0.146062i | ||||
\(254\) | 199.641 | + | 64.8673i | 0.785989 | + | 0.255383i | ||||
\(255\) | 283.539 | + | 363.136i | 1.11192 | + | 1.42406i | ||||
\(256\) | 4.94427 | + | 15.2169i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | − | 428.597i | − | 1.66769i | −0.551996 | − | 0.833847i | \(-0.686134\pi\) | ||
0.551996 | − | 0.833847i | \(-0.313866\pi\) | |||||||
\(258\) | 7.30612 | + | 7.97882i | 0.0283183 | + | 0.0309256i | ||||
\(259\) | 64.3003 | + | 46.7169i | 0.248264 | + | 0.180374i | ||||
\(260\) | 96.3130 | + | 82.2504i | 0.370434 | + | 0.316348i | ||||
\(261\) | −354.931 | − | 31.3022i | −1.35989 | − | 0.119932i | ||||
\(262\) | 174.778 | + | 126.984i | 0.667093 | + | 0.484672i | ||||
\(263\) | −46.7684 | + | 64.3712i | −0.177827 | + | 0.244757i | −0.888621 | − | 0.458643i | \(-0.848336\pi\) |
0.710794 | + | 0.703400i | \(0.248336\pi\) | |||||||
\(264\) | −40.0033 | − | 22.6512i | −0.151528 | − | 0.0858001i | ||||
\(265\) | 22.6042 | − | 287.404i | 0.0852990 | − | 1.08454i | ||||
\(266\) | 85.7827 | − | 118.070i | 0.322491 | − | 0.443871i | ||||
\(267\) | 268.151 | + | 292.840i | 1.00431 | + | 1.09678i | ||||
\(268\) | 219.735 | 0.819907 | ||||||||
\(269\) | 71.6202 | − | 23.2708i | 0.266246 | − | 0.0865086i | −0.172852 | − | 0.984948i | \(-0.555298\pi\) |
0.439098 | + | 0.898439i | \(0.355298\pi\) | |||||||
\(270\) | 68.5966 | − | 178.170i | 0.254061 | − | 0.659888i | ||||
\(271\) | −95.3791 | + | 293.547i | −0.351953 | + | 1.08320i | 0.605803 | + | 0.795615i | \(0.292852\pi\) |
−0.957755 | + | 0.287584i | \(0.907148\pi\) | |||||||
\(272\) | 116.845 | + | 37.9654i | 0.429579 | + | 0.139579i | ||||
\(273\) | 199.455 | + | 112.938i | 0.730603 | + | 0.413692i | ||||
\(274\) | 154.251 | 0.562959 | ||||||||
\(275\) | −120.688 | − | 61.4776i | −0.438864 | − | 0.223555i | ||||
\(276\) | 39.1629 | − | 17.8310i | 0.141895 | − | 0.0646053i | ||||
\(277\) | 108.377 | − | 78.7407i | 0.391254 | − | 0.284263i | −0.374715 | − | 0.927140i | \(-0.622260\pi\) |
0.765969 | + | 0.642877i | \(0.222260\pi\) | |||||||
\(278\) | −290.391 | − | 94.3539i | −1.04457 | − | 0.339402i | ||||
\(279\) | 151.786 | + | 253.014i | 0.544035 | + | 0.906860i | ||||
\(280\) | 44.5788 | + | 72.7376i | 0.159210 | + | 0.259777i | ||||
\(281\) | −176.332 | + | 57.2937i | −0.627516 | + | 0.203892i | −0.605474 | − | 0.795865i | \(-0.707017\pi\) |
−0.0220414 | + | 0.999757i | \(0.507017\pi\) | |||||||
\(282\) | −114.423 | − | 251.311i | −0.405755 | − | 0.891172i | ||||
\(283\) | −37.9724 | − | 116.867i | −0.134178 | − | 0.412957i | 0.861283 | − | 0.508125i | \(-0.169661\pi\) |
−0.995461 | + | 0.0951678i | \(0.969661\pi\) | |||||||
\(284\) | 37.4967 | − | 51.6098i | 0.132031 | − | 0.181725i | ||||
\(285\) | −202.255 | + | 157.922i | −0.709665 | + | 0.554112i | ||||
\(286\) | −78.5075 | + | 57.0391i | −0.274502 | + | 0.199437i | ||||
\(287\) | 164.928 | − | 227.004i | 0.574662 | − | 0.790954i | ||||
\(288\) | −11.4180 | − | 49.6148i | −0.0396458 | − | 0.172274i | ||||
\(289\) | 529.412 | − | 384.640i | 1.83187 | − | 1.33093i | ||||
\(290\) | −238.683 | + | 146.282i | −0.823045 | + | 0.504421i | ||||
\(291\) | 32.5911 | − | 159.905i | 0.111997 | − | 0.549501i | ||||
\(292\) | 31.9882 | + | 98.4496i | 0.109549 | + | 0.337156i | ||||
\(293\) | 216.859i | 0.740133i | 0.929005 | + | 0.370067i | \(0.120665\pi\) | ||||
−0.929005 | + | 0.370067i | \(0.879335\pi\) | |||||||
\(294\) | −36.1298 | − | 39.4564i | −0.122890 | − | 0.134205i | ||||
\(295\) | 330.871 | + | 137.031i | 1.12160 | + | 0.464513i | ||||
\(296\) | −35.4417 | − | 11.5157i | −0.119735 | − | 0.0389044i | ||||
\(297\) | 120.466 | + | 82.9796i | 0.405608 | + | 0.279393i | ||||
\(298\) | 215.911 | − | 156.868i | 0.724532 | − | 0.526403i | ||||
\(299\) | − | 90.8346i | − | 0.303795i | ||||||
\(300\) | −40.0503 | − | 144.554i | −0.133501 | − | 0.481848i | ||||
\(301\) | 15.3824 | 0.0511043 | ||||||||
\(302\) | −109.697 | − | 150.985i | −0.363235 | − | 0.499949i | ||||
\(303\) | 34.1400 | + | 300.576i | 0.112673 | + | 0.992000i | ||||
\(304\) | −21.1454 | + | 65.0790i | −0.0695573 | + | 0.214076i | ||||
\(305\) | 225.080 | + | 192.216i | 0.737968 | + | 0.630218i | ||||
\(306\) | −359.749 | − | 153.001i | −1.17565 | − | 0.500004i | ||||
\(307\) | −101.826 | −0.331679 | −0.165840 | − | 0.986153i | \(-0.553033\pi\) | ||||
−0.165840 | + | 0.986153i | \(0.553033\pi\) | |||||||
\(308\) | −62.1651 | + | 20.1987i | −0.201835 | + | 0.0655801i | ||||
\(309\) | −45.2288 | + | 221.910i | −0.146371 | + | 0.718155i | ||||
\(310\) | 214.173 | + | 88.7002i | 0.690879 | + | 0.286130i | ||||
\(311\) | −67.7199 | − | 93.2084i | −0.217749 | − | 0.299706i | 0.686143 | − | 0.727467i | \(-0.259302\pi\) |
−0.903892 | + | 0.427761i | \(0.859302\pi\) | |||||||
\(312\) | −105.305 | − | 21.4628i | −0.337515 | − | 0.0687910i | ||||
\(313\) | −417.997 | − | 303.692i | −1.33545 | − | 0.970263i | −0.999598 | − | 0.0283498i | \(-0.990975\pi\) |
−0.335855 | − | 0.941914i | \(-0.609025\pi\) | |||||||
\(314\) | 108.711 | + | 149.627i | 0.346212 | + | 0.476520i | ||||
\(315\) | −120.967 | − | 243.016i | −0.384023 | − | 0.771480i | ||||
\(316\) | −119.579 | − | 86.8791i | −0.378414 | − | 0.274934i | ||||
\(317\) | −247.370 | + | 80.3755i | −0.780348 | + | 0.253550i | −0.671989 | − | 0.740561i | \(-0.734560\pi\) |
−0.108359 | + | 0.994112i | \(0.534560\pi\) | |||||||
\(318\) | 101.366 | + | 222.633i | 0.318761 | + | 0.700105i | ||||
\(319\) | −66.2805 | − | 203.990i | −0.207776 | − | 0.639468i | ||||
\(320\) | −30.4176 | − | 25.9763i | −0.0950549 | − | 0.0811761i | ||||
\(321\) | 14.2932 | + | 125.840i | 0.0445271 | + | 0.392026i | ||||
\(322\) | 18.9069 | − | 58.1895i | 0.0587171 | − | 0.180713i | ||||
\(323\) | 308.843 | + | 425.086i | 0.956172 | + | 1.31606i | ||||
\(324\) | 22.3220 | + | 160.455i | 0.0688951 | + | 0.495231i | ||||
\(325\) | −312.743 | − | 49.5004i | −0.962285 | − | 0.152309i | ||||
\(326\) | − | 398.256i | − | 1.22164i | ||||||
\(327\) | 328.795 | + | 186.175i | 1.00549 | + | 0.569342i | ||||
\(328\) | −40.6548 | + | 125.122i | −0.123947 | + | 0.381471i | ||||
\(329\) | −373.405 | − | 121.327i | −1.13497 | − | 0.368774i | ||||
\(330\) | 114.859 | − | 3.97677i | 0.348057 | − | 0.0120508i | ||||
\(331\) | −30.9481 | − | 95.2485i | −0.0934989 | − | 0.287760i | 0.893361 | − | 0.449340i | \(-0.148341\pi\) |
−0.986860 | + | 0.161580i | \(0.948341\pi\) | |||||||
\(332\) | 198.187i | 0.596947i | ||||||||
\(333\) | 109.120 | + | 46.4085i | 0.327687 | + | 0.139365i | ||||
\(334\) | 18.4064 | + | 13.3730i | 0.0551089 | + | 0.0400390i | ||||
\(335\) | −468.373 | + | 287.052i | −1.39813 | + | 0.856873i | ||||
\(336\) | −62.9918 | − | 35.6681i | −0.187476 | − | 0.106155i | ||||
\(337\) | 62.3359 | + | 45.2897i | 0.184973 | + | 0.134391i | 0.676418 | − | 0.736518i | \(-0.263531\pi\) |
−0.491445 | + | 0.870908i | \(0.663531\pi\) | |||||||
\(338\) | 7.13785 | − | 9.82440i | 0.0211179 | − | 0.0290663i | ||||
\(339\) | 96.1576 | − | 169.820i | 0.283651 | − | 0.500943i | ||||
\(340\) | −298.656 | + | 71.7174i | −0.878401 | + | 0.210933i | ||||
\(341\) | −104.398 | + | 143.691i | −0.306152 | + | 0.421382i | ||||
\(342\) | 85.2164 | − | 200.368i | 0.249171 | − | 0.585872i | ||||
\(343\) | −371.657 | −1.08355 | ||||||||
\(344\) | −6.85936 | + | 2.22874i | −0.0199400 | + | 0.00647890i | ||||
\(345\) | −60.1833 | + | 89.1682i | −0.174444 | + | 0.258458i | ||||
\(346\) | −65.8054 | + | 202.528i | −0.190189 | + | 0.585341i | ||||
\(347\) | −153.183 | − | 49.7722i | −0.441450 | − | 0.143436i | 0.0798548 | − | 0.996807i | \(-0.474554\pi\) |
−0.521304 | + | 0.853371i | \(0.674554\pi\) | |||||||
\(348\) | 117.042 | − | 206.703i | 0.336328 | − | 0.593974i | ||||
\(349\) | −434.522 | −1.24505 | −0.622525 | − | 0.782600i | \(-0.713893\pi\) | ||||
−0.622525 | + | 0.782600i | \(0.713893\pi\) | |||||||
\(350\) | −190.042 | − | 96.8067i | −0.542978 | − | 0.276590i | ||||
\(351\) | 327.782 | + | 97.4671i | 0.933853 | + | 0.277684i | ||||
\(352\) | 24.7943 | − | 18.0141i | 0.0704383 | − | 0.0511764i | ||||
\(353\) | −423.819 | − | 137.707i | −1.20062 | − | 0.390105i | −0.360631 | − | 0.932708i | \(-0.617439\pi\) |
−0.839989 | + | 0.542603i | \(0.817439\pi\) | |||||||
\(354\) | −301.938 | + | 34.2947i | −0.852932 | + | 0.0968777i | ||||
\(355\) | −12.5047 | + | 158.992i | −0.0352244 | + | 0.447865i | ||||
\(356\) | −251.754 | + | 81.7997i | −0.707173 | + | 0.229775i | ||||
\(357\) | −505.883 | + | 230.331i | −1.41704 | + | 0.645185i | ||||
\(358\) | −36.5448 | − | 112.473i | −0.102080 | − | 0.314171i | ||||
\(359\) | 312.127 | − | 429.606i | 0.869435 | − | 1.19667i | −0.109802 | − | 0.993954i | \(-0.535022\pi\) |
0.979237 | − | 0.202721i | \(-0.0649785\pi\) | |||||||
\(360\) | 89.1525 | + | 90.8396i | 0.247646 | + | 0.252332i | ||||
\(361\) | 55.2963 | − | 40.1751i | 0.153175 | − | 0.111288i | ||||
\(362\) | 61.2971 | − | 84.3683i | 0.169329 | − | 0.233061i | ||||
\(363\) | 54.9091 | − | 269.405i | 0.151265 | − | 0.742163i | ||||
\(364\) | −123.623 | + | 89.8174i | −0.339624 | + | 0.246751i | ||||
\(365\) | −196.794 | − | 168.061i | −0.539162 | − | 0.460440i | ||||
\(366\) | −246.094 | − | 50.1578i | −0.672387 | − | 0.137043i | ||||
\(367\) | −149.005 | − | 458.591i | −0.406008 | − | 1.24957i | −0.920050 | − | 0.391800i | \(-0.871852\pi\) |
0.514042 | − | 0.857765i | \(-0.328148\pi\) | |||||||
\(368\) | 28.6874i | 0.0779549i | ||||||||
\(369\) | 163.839 | − | 385.233i | 0.444009 | − | 1.04399i | ||||
\(370\) | 90.5888 | − | 21.7534i | 0.244835 | − | 0.0587930i | ||||
\(371\) | 330.796 | + | 107.482i | 0.891634 | + | 0.289709i | ||||
\(372\) | −195.444 | + | 22.1989i | −0.525387 | + | 0.0596745i | ||||
\(373\) | −309.458 | + | 224.834i | −0.829645 | + | 0.602772i | −0.919459 | − | 0.393186i | \(-0.871373\pi\) |
0.0898138 | + | 0.995959i | \(0.471373\pi\) | |||||||
\(374\) | − | 235.331i | − | 0.629227i | ||||||
\(375\) | 274.208 | + | 255.803i | 0.731222 | + | 0.682140i | ||||
\(376\) | 184.089 | 0.489598 | ||||||||
\(377\) | −294.729 | − | 405.660i | −0.781775 | − | 1.07602i | ||||
\(378\) | 189.693 | + | 130.665i | 0.501833 | + | 0.345675i | ||||
\(379\) | −160.496 | + | 493.956i | −0.423473 | + | 1.30331i | 0.480977 | + | 0.876733i | \(0.340282\pi\) |
−0.904449 | + | 0.426581i | \(0.859718\pi\) | |||||||
\(380\) | −39.9441 | − | 166.341i | −0.105116 | − | 0.437741i | ||||
\(381\) | 328.412 | − | 300.724i | 0.861975 | − | 0.789301i | ||||
\(382\) | −9.43216 | −0.0246915 | ||||||||
\(383\) | 493.379 | − | 160.308i | 1.28820 | − | 0.418560i | 0.416736 | − | 0.909028i | \(-0.363174\pi\) |
0.871459 | + | 0.490468i | \(0.163174\pi\) | |||||||
\(384\) | 33.2574 | + | 6.77838i | 0.0866078 | + | 0.0176520i | ||||
\(385\) | 106.120 | − | 124.264i | 0.275637 | − | 0.322763i | ||||
\(386\) | 241.928 | + | 332.986i | 0.626757 | + | 0.862657i | ||||
\(387\) | 22.3650 | − | 5.14692i | 0.0577907 | − | 0.0132995i | ||||
\(388\) | 88.0169 | + | 63.9480i | 0.226848 | + | 0.164815i | ||||
\(389\) | 360.915 | + | 496.757i | 0.927803 | + | 1.27701i | 0.960710 | + | 0.277553i | \(0.0895233\pi\) |
−0.0329076 | + | 0.999458i | \(0.510477\pi\) | |||||||
\(390\) | 252.499 | − | 91.8170i | 0.647432 | − | 0.235428i | ||||
\(391\) | 178.211 | + | 129.478i | 0.455783 | + | 0.331145i | ||||
\(392\) | 33.9205 | − | 11.0214i | 0.0865319 | − | 0.0281159i | ||||
\(393\) | 417.089 | − | 189.902i | 1.06129 | − | 0.483212i | ||||
\(394\) | 69.8814 | + | 215.073i | 0.177364 | + | 0.545870i | ||||
\(395\) | 368.381 | + | 28.9730i | 0.932610 | + | 0.0733495i | ||||
\(396\) | −83.6255 | + | 50.1679i | −0.211176 | + | 0.126687i | ||||
\(397\) | −173.188 | + | 533.018i | −0.436242 | + | 1.34261i | 0.455567 | + | 0.890202i | \(0.349437\pi\) |
−0.891809 | + | 0.452413i | \(0.850563\pi\) | |||||||
\(398\) | −217.288 | − | 299.072i | −0.545950 | − | 0.751436i | ||||
\(399\) | −128.287 | − | 281.760i | −0.321520 | − | 0.706165i | ||||
\(400\) | 98.7705 | + | 15.6332i | 0.246926 | + | 0.0390831i | ||||
\(401\) | 102.563i | 0.255767i | 0.991789 | + | 0.127884i | \(0.0408184\pi\) | ||||
−0.991789 | + | 0.127884i | \(0.959182\pi\) | |||||||
\(402\) | 229.674 | − | 405.617i | 0.571329 | − | 1.00900i | ||||
\(403\) | −128.309 | + | 394.894i | −0.318384 | + | 0.979886i | ||||
\(404\) | −191.802 | − | 62.3202i | −0.474757 | − | 0.154258i | ||||
\(405\) | −257.191 | − | 312.854i | −0.635040 | − | 0.772479i | ||||
\(406\) | −104.369 | − | 321.216i | −0.257068 | − | 0.791173i | ||||
\(407\) | 71.3809i | 0.175383i | ||||||||
\(408\) | 192.212 | − | 176.007i | 0.471109 | − | 0.431389i | ||||
\(409\) | 123.035 | + | 89.3900i | 0.300819 | + | 0.218558i | 0.727947 | − | 0.685634i | \(-0.240475\pi\) |
−0.427128 | + | 0.904191i | \(0.640475\pi\) | |||||||
\(410\) | −76.7976 | − | 319.812i | −0.187311 | − | 0.780030i | ||||
\(411\) | 161.228 | − | 284.738i | 0.392282 | − | 0.692792i | ||||
\(412\) | −122.147 | − | 88.7447i | −0.296472 | − | 0.215400i | ||||
\(413\) | −253.966 | + | 349.554i | −0.614929 | + | 0.846377i | ||||
\(414\) | 8.01931 | − | 90.9299i | 0.0193703 | − | 0.219637i | ||||
\(415\) | −258.902 | − | 422.441i | −0.623861 | − | 1.01793i | ||||
\(416\) | 42.1128 | − | 57.9632i | 0.101233 | − | 0.139335i | ||||
\(417\) | −477.698 | + | 437.423i | −1.14556 | + | 1.04898i | ||||
\(418\) | 131.071 | 0.313568 | ||||||||
\(419\) | −274.209 | + | 89.0960i | −0.654437 | + | 0.212640i | −0.617370 | − | 0.786673i | \(-0.711802\pi\) |
−0.0370676 | + | 0.999313i | \(0.511802\pi\) | |||||||
\(420\) | 180.864 | − | 6.26208i | 0.430629 | − | 0.0149097i | ||||
\(421\) | −59.6285 | + | 183.518i | −0.141636 | + | 0.435909i | −0.996563 | − | 0.0828382i | \(-0.973602\pi\) |
0.854928 | + | 0.518747i | \(0.173602\pi\) | |||||||
\(422\) | 519.354 | + | 168.748i | 1.23070 | + | 0.399878i | ||||
\(423\) | −583.502 | − | 51.4604i | −1.37944 | − | 0.121656i | ||||
\(424\) | −163.082 | −0.384628 | ||||||||
\(425\) | 542.907 | − | 543.019i | 1.27743 | − | 1.27769i | ||||
\(426\) | −56.0757 | − | 123.161i | −0.131633 | − | 0.289110i | ||||
\(427\) | −288.903 | + | 209.900i | −0.676587 | + | 0.491569i | ||||
\(428\) | −80.3006 | − | 26.0912i | −0.187618 | − | 0.0609608i | ||||
\(429\) | 23.2320 | + | 204.539i | 0.0541538 | + | 0.476781i | ||||
\(430\) | 11.7094 | − | 13.7114i | 0.0272312 | − | 0.0318870i | ||||
\(431\) | 340.186 | − | 110.533i | 0.789294 | − | 0.256457i | 0.113491 | − | 0.993539i | \(-0.463797\pi\) |
0.675804 | + | 0.737082i | \(0.263797\pi\) | |||||||
\(432\) | −103.520 | − | 30.7821i | −0.239630 | − | 0.0712548i | ||||
\(433\) | 153.149 | + | 471.344i | 0.353693 | + | 1.08855i | 0.956764 | + | 0.290867i | \(0.0939437\pi\) |
−0.603071 | + | 0.797688i | \(0.706056\pi\) | |||||||
\(434\) | −164.392 | + | 226.266i | −0.378782 | + | 0.521349i | ||||
\(435\) | 20.5486 | + | 593.493i | 0.0472381 | + | 1.36435i | ||||
\(436\) | −203.789 | + | 148.061i | −0.467406 | + | 0.339590i | ||||
\(437\) | −72.1148 | + | 99.2575i | −0.165022 | + | 0.227134i | ||||
\(438\) | 215.167 | + | 43.8544i | 0.491249 | + | 0.100124i | ||||
\(439\) | −70.5959 | + | 51.2909i | −0.160811 | + | 0.116836i | −0.665280 | − | 0.746594i | \(-0.731688\pi\) |
0.504470 | + | 0.863429i | \(0.331688\pi\) | |||||||
\(440\) | −29.3170 | + | 70.7878i | −0.0666295 | + | 0.160881i | ||||
\(441\) | −110.598 | + | 25.4523i | −0.250789 | + | 0.0577149i | ||||
\(442\) | −170.005 | − | 523.223i | −0.384628 | − | 1.18376i | ||||
\(443\) | − | 676.337i | − | 1.52672i | −0.645973 | − | 0.763360i | \(-0.723548\pi\) | ||
0.645973 | − | 0.763360i | \(-0.276452\pi\) | |||||||
\(444\) | −58.3021 | + | 53.3866i | −0.131311 | + | 0.120240i | ||||
\(445\) | 429.762 | − | 503.239i | 0.965756 | − | 1.13087i | ||||
\(446\) | 398.595 | + | 129.511i | 0.893712 | + | 0.290385i | ||||
\(447\) | −63.8923 | − | 562.521i | −0.142936 | − | 1.25844i | ||||
\(448\) | 39.0427 | − | 28.3661i | 0.0871488 | − | 0.0633173i | ||||
\(449\) | 520.153i | 1.15847i | 0.815160 | + | 0.579235i | \(0.196649\pi\) | ||||
−0.815160 | + | 0.579235i | \(0.803351\pi\) | |||||||
\(450\) | −308.700 | − | 77.1627i | −0.686001 | − | 0.171473i | ||||
\(451\) | 252.001 | 0.558761 | ||||||||
\(452\) | 76.4723 | + | 105.255i | 0.169187 | + | 0.232865i | ||||
\(453\) | −393.367 | + | 44.6794i | −0.868360 | + | 0.0986301i | ||||
\(454\) | −117.665 | + | 362.136i | −0.259175 | + | 0.797657i | ||||
\(455\) | 146.173 | − | 352.944i | 0.321259 | − | 0.775702i | ||||
\(456\) | 98.0298 | + | 107.056i | 0.214978 | + | 0.234772i | ||||
\(457\) | 521.866 | 1.14194 | 0.570969 | − | 0.820971i | \(-0.306568\pi\) | ||||
0.570969 | + | 0.820971i | \(0.306568\pi\) | |||||||
\(458\) | −83.9607 | + | 27.2805i | −0.183320 | + | 0.0595644i | ||||
\(459\) | −658.452 | + | 504.154i | −1.43454 | + | 1.09837i | ||||
\(460\) | −37.4760 | − | 61.1482i | −0.0814696 | − | 0.132931i | ||||
\(461\) | 510.674 | + | 702.882i | 1.10775 | + | 1.52469i | 0.824687 | + | 0.565590i | \(0.191351\pi\) |
0.283066 | + | 0.959101i | \(0.408649\pi\) | |||||||
\(462\) | −27.6915 | + | 135.865i | −0.0599383 | + | 0.294081i | ||||
\(463\) | −643.127 | − | 467.259i | −1.38904 | − | 1.00920i | −0.995970 | − | 0.0896923i | \(-0.971412\pi\) |
−0.393074 | − | 0.919507i | \(-0.628588\pi\) | |||||||
\(464\) | 93.0814 | + | 128.116i | 0.200607 | + | 0.276111i | ||||
\(465\) | 387.595 | − | 302.637i | 0.833538 | − | 0.650832i | ||||
\(466\) | −142.269 | − | 103.364i | −0.305298 | − | 0.221812i | ||||
\(467\) | 50.8482 | − | 16.5216i | 0.108883 | − | 0.0353781i | −0.254069 | − | 0.967186i | \(-0.581769\pi\) |
0.362952 | + | 0.931808i | \(0.381769\pi\) | |||||||
\(468\) | −149.687 | + | 171.953i | −0.319844 | + | 0.367420i | ||||
\(469\) | −204.806 | − | 630.329i | −0.436687 | − | 1.34399i | ||||
\(470\) | −392.391 | + | 240.486i | −0.834876 | + | 0.511672i | ||||
\(471\) | 389.831 | − | 44.2777i | 0.827666 | − | 0.0940079i | ||||
\(472\) | 62.6025 | − | 192.671i | 0.132633 | − | 0.408201i | ||||
\(473\) | 8.12026 | + | 11.1766i | 0.0171676 | + | 0.0236291i | ||||
\(474\) | −285.361 | + | 129.926i | −0.602028 | + | 0.274106i | ||||
\(475\) | 302.443 | + | 302.381i | 0.636723 | + | 0.636591i | ||||
\(476\) | − | 370.567i | − | 0.778503i | ||||||
\(477\) | 516.919 | + | 45.5882i | 1.08369 | + | 0.0955728i | ||||
\(478\) | 21.2163 | − | 65.2971i | 0.0443856 | − | 0.136605i | ||||
\(479\) | −270.562 | − | 87.9110i | −0.564848 | − | 0.183530i | 0.0126533 | − | 0.999920i | \(-0.495972\pi\) |
−0.577501 | + | 0.816390i | \(0.695972\pi\) | |||||||
\(480\) | −79.7442 | + | 28.9977i | −0.166134 | + | 0.0604118i | ||||
\(481\) | 51.5663 | + | 158.705i | 0.107206 | + | 0.329947i | ||||
\(482\) | 271.702i | 0.563698i | ||||||||
\(483\) | −87.6521 | − | 95.7225i | −0.181474 | − | 0.198183i | ||||
\(484\) | 148.290 | + | 107.739i | 0.306383 | + | 0.222601i | ||||
\(485\) | −271.150 | − | 21.3258i | −0.559072 | − | 0.0439708i | ||||
\(486\) | 319.521 | + | 126.507i | 0.657451 | + | 0.260303i | ||||
\(487\) | 357.514 | + | 259.749i | 0.734115 | + | 0.533366i | 0.890863 | − | 0.454273i | \(-0.150101\pi\) |
−0.156747 | + | 0.987639i | \(0.550101\pi\) | |||||||
\(488\) | 98.4161 | − | 135.458i | 0.201672 | − | 0.277578i | ||||
\(489\) | −735.156 | − | 416.270i | −1.50339 | − | 0.851268i | ||||
\(490\) | −57.9048 | + | 67.8049i | −0.118173 | + | 0.138377i | ||||
\(491\) | −449.208 | + | 618.282i | −0.914884 | + | 1.25923i | 0.0505873 | + | 0.998720i | \(0.483891\pi\) |
−0.965471 | + | 0.260510i | \(0.916109\pi\) | |||||||
\(492\) | 188.475 | + | 205.828i | 0.383079 | + | 0.418350i | ||||
\(493\) | 1215.99 | 2.46651 | ||||||||
\(494\) | 291.417 | − | 94.6873i | 0.589914 | − | 0.191675i | ||||
\(495\) | 112.713 | − | 216.179i | 0.227704 | − | 0.436726i | ||||
\(496\) | 40.5225 | − | 124.716i | 0.0816987 | − | 0.251443i | ||||
\(497\) | −182.996 | − | 59.4591i | −0.368202 | − | 0.119636i | ||||
\(498\) | 365.840 | + | 207.151i | 0.734619 | + | 0.415966i | ||||
\(499\) | −280.284 | −0.561691 | −0.280846 | − | 0.959753i | \(-0.590615\pi\) | ||||
−0.280846 | + | 0.959753i | \(0.590615\pi\) | |||||||
\(500\) | −230.955 | + | 95.7067i | −0.461910 | + | 0.191413i | ||||
\(501\) | 43.9247 | − | 19.9991i | 0.0876741 | − | 0.0399184i | ||||
\(502\) | −202.774 | + | 147.324i | −0.403933 | + | 0.293474i | ||||
\(503\) | 274.463 | + | 89.1785i | 0.545652 | + | 0.177293i | 0.568855 | − | 0.822438i | \(-0.307386\pi\) |
−0.0232030 | + | 0.999731i | \(0.507386\pi\) | |||||||
\(504\) | −131.682 | + | 78.9975i | −0.261274 | + | 0.156741i | ||||
\(505\) | 490.244 | − | 117.724i | 0.970781 | − | 0.233117i | ||||
\(506\) | 52.2603 | − | 16.9804i | 0.103281 | − | 0.0335581i | ||||
\(507\) | −10.6745 | − | 23.4448i | −0.0210543 | − | 0.0462422i | ||||
\(508\) | 91.7363 | + | 282.335i | 0.180583 | + | 0.555778i | ||||
\(509\) | −214.224 | + | 294.854i | −0.420873 | + | 0.579282i | −0.965828 | − | 0.259183i | \(-0.916547\pi\) |
0.544955 | + | 0.838465i | \(0.316547\pi\) | |||||||
\(510\) | −179.779 | + | 626.262i | −0.352509 | + | 1.22797i | ||||
\(511\) | 252.596 | − | 183.522i | 0.494318 | − | 0.359143i | ||||
\(512\) | −13.3001 | + | 18.3060i | −0.0259767 | + | 0.0357538i | ||||
\(513\) | −280.797 | − | 366.736i | −0.547362 | − | 0.714885i | ||||
\(514\) | 490.368 | − | 356.273i | 0.954023 | − | 0.693139i | ||||
\(515\) | 376.292 | + | 29.5952i | 0.730663 | + | 0.0574664i | ||||
\(516\) | −3.05551 | + | 14.9915i | −0.00592153 | + | 0.0290533i | ||||
\(517\) | −108.964 | − | 335.357i | −0.210762 | − | 0.648660i | ||||
\(518\) | 112.401i | 0.216990i | ||||||||
\(519\) | 305.073 | + | 333.162i | 0.587808 | + | 0.641930i | ||||
\(520\) | −14.0441 | + | 178.565i | −0.0270078 | + | 0.343394i | ||||
\(521\) | −163.048 | − | 52.9776i | −0.312953 | − | 0.101685i | 0.148329 | − | 0.988938i | \(-0.452610\pi\) |
−0.461282 | + | 0.887253i | \(0.652610\pi\) | |||||||
\(522\) | −259.225 | − | 432.105i | −0.496599 | − | 0.827788i | ||||
\(523\) | −20.2180 | + | 14.6892i | −0.0386577 | + | 0.0280864i | −0.606946 | − | 0.794743i | \(-0.707606\pi\) |
0.568289 | + | 0.822829i | \(0.307606\pi\) | |||||||
\(524\) | 305.524i | 0.583061i | ||||||||
\(525\) | −377.338 | + | 249.621i | −0.718738 | + | 0.475469i | ||||
\(526\) | −112.525 | −0.213926 | ||||||||
\(527\) | −591.859 | − | 814.624i | −1.12307 | − | 1.54578i | ||||
\(528\) | −7.33713 | − | 64.5976i | −0.0138961 | − | 0.122344i | ||||
\(529\) | 147.576 | − | 454.191i | 0.278971 | − | 0.858584i | ||||
\(530\) | 347.616 | − | 213.044i | 0.655879 | − | 0.401970i | ||||
\(531\) | −252.289 | + | 593.204i | −0.475121 | + | 1.11715i | ||||
\(532\) | 206.393 | 0.387958 | ||||||||
\(533\) | 560.287 | − | 182.048i | 1.05119 | − | 0.341554i | ||||
\(534\) | −112.144 | + | 550.222i | −0.210007 | + | 1.03038i | ||||
\(535\) | 205.248 | − | 49.2869i | 0.383641 | − | 0.0921250i | ||||
\(536\) | 182.656 | + | 251.404i | 0.340775 | + | 0.469037i | ||||
\(537\) | −245.817 | − | 50.1013i | −0.457759 | − | 0.0932986i | ||||
\(538\) | 86.1592 | + | 62.5983i | 0.160147 | + | 0.116354i | ||||
\(539\) | −40.1558 | − | 55.2697i | −0.0745006 | − | 0.102541i | ||||
\(540\) | 260.869 | − | 69.6215i | 0.483091 | − | 0.128929i | ||||
\(541\) | −118.186 | − | 85.8674i | −0.218459 | − | 0.158720i | 0.473174 | − | 0.880969i | \(-0.343108\pi\) |
−0.691633 | + | 0.722249i | \(0.743108\pi\) | |||||||
\(542\) | −415.138 | + | 134.886i | −0.765937 | + | 0.248868i | ||||
\(543\) | −91.6689 | − | 201.335i | −0.168819 | − | 0.370783i | ||||
\(544\) | 53.6912 | + | 165.244i | 0.0986970 | + | 0.303758i | ||||
\(545\) | 240.962 | − | 581.819i | 0.442132 | − | 1.06756i | ||||
\(546\) | 36.5826 | + | 322.081i | 0.0670010 | + | 0.589891i | ||||
\(547\) | −64.7619 | + | 199.317i | −0.118395 | + | 0.364382i | −0.992640 | − | 0.121103i | \(-0.961357\pi\) |
0.874245 | + | 0.485485i | \(0.161357\pi\) | |||||||
\(548\) | 128.222 | + | 176.482i | 0.233981 | + | 0.322047i | ||||
\(549\) | −349.813 | + | 401.847i | −0.637183 | + | 0.731962i | ||||
\(550\) | −29.9840 | − | 189.185i | −0.0545164 | − | 0.343973i | ||||
\(551\) | 677.265i | 1.22916i | ||||||||
\(552\) | 52.9552 | + | 29.9850i | 0.0959334 | + | 0.0543207i | ||||
\(553\) | −137.766 | + | 423.999i | −0.249124 | + | 0.766725i | ||||
\(554\) | 180.178 | + | 58.5434i | 0.325231 | + | 0.105674i | ||||
\(555\) | 54.5309 | − | 189.959i | 0.0982539 | − | 0.342268i | ||||
\(556\) | −133.437 | − | 410.675i | −0.239994 | − | 0.738625i | ||||
\(557\) | 656.487i | 1.17861i | 0.807910 | + | 0.589306i | \(0.200599\pi\) | ||||
−0.807910 | + | 0.589306i | \(0.799401\pi\) | |||||||
\(558\) | −163.306 | + | 383.980i | −0.292664 | + | 0.688137i | ||||
\(559\) | 26.1282 | + | 18.9833i | 0.0467410 | + | 0.0339593i | ||||
\(560\) | −46.1644 | + | 111.467i | −0.0824364 | + | 0.199048i | ||||
\(561\) | −434.407 | − | 245.976i | −0.774343 | − | 0.438459i | ||||
\(562\) | −212.128 | − | 154.120i | −0.377451 | − | 0.274234i | ||||
\(563\) | 401.927 | − | 553.206i | 0.713903 | − | 0.982603i | −0.285801 | − | 0.958289i | \(-0.592260\pi\) |
0.999704 | − | 0.0243143i | \(-0.00774025\pi\) | |||||||
\(564\) | 192.416 | − | 339.817i | 0.341163 | − | 0.602512i | ||||
\(565\) | −300.504 | − | 124.455i | −0.531865 | − | 0.220274i | ||||
\(566\) | 102.145 | − | 140.591i | 0.180469 | − | 0.248394i | ||||
\(567\) | 439.473 | − | 213.586i | 0.775085 | − | 0.376695i | ||||
\(568\) | 90.2172 | 0.158833 | ||||||||
\(569\) | 468.726 | − | 152.298i | 0.823772 | − | 0.267660i | 0.133352 | − | 0.991069i | \(-0.457426\pi\) |
0.690420 | + | 0.723409i | \(0.257426\pi\) | |||||||
\(570\) | −348.807 | − | 100.131i | −0.611942 | − | 0.175668i | ||||
\(571\) | 83.1517 | − | 255.915i | 0.145625 | − | 0.448187i | −0.851466 | − | 0.524410i | \(-0.824286\pi\) |
0.997091 | + | 0.0762228i | \(0.0242860\pi\) | |||||||
\(572\) | −130.519 | − | 42.4083i | −0.228181 | − | 0.0741404i | ||||
\(573\) | −9.85880 | + | 17.4112i | −0.0172056 | + | 0.0303860i | ||||
\(574\) | 396.817 | 0.691320 | ||||||||
\(575\) | 159.763 | + | 81.3823i | 0.277848 | + | 0.141534i | ||||
\(576\) | 47.2742 | − | 54.3061i | 0.0820732 | − | 0.0942814i | ||||
\(577\) | −607.971 | + | 441.717i | −1.05368 | + | 0.765540i | −0.972908 | − | 0.231193i | \(-0.925737\pi\) |
−0.0807676 | + | 0.996733i | \(0.525737\pi\) | |||||||
\(578\) | 880.151 | + | 285.978i | 1.52275 | + | 0.494772i | ||||
\(579\) | 867.543 | − | 98.5372i | 1.49835 | − | 0.170185i | ||||
\(580\) | −365.771 | − | 151.485i | −0.630639 | − | 0.261181i | ||||
\(581\) | 568.515 | − | 184.722i | 0.978512 | − | 0.317938i | ||||
\(582\) | 210.042 | − | 95.6332i | 0.360897 | − | 0.164318i | ||||
\(583\) | 96.5302 | + | 297.089i | 0.165575 | + | 0.509587i | ||||
\(584\) | −86.0481 | + | 118.435i | −0.147343 | + | 0.202800i | ||||
\(585\) | 94.4313 | − | 562.067i | 0.161421 | − | 0.960798i | ||||
\(586\) | −248.113 | + | 180.265i | −0.423402 | + | 0.307619i | ||||
\(587\) | 68.4199 | − | 94.1720i | 0.116559 | − | 0.160429i | −0.746751 | − | 0.665104i | \(-0.768387\pi\) |
0.863310 | + | 0.504674i | \(0.168387\pi\) | |||||||
\(588\) | 15.1099 | − | 74.1352i | 0.0256971 | − | 0.126080i | ||||
\(589\) | 453.718 | − | 329.646i | 0.770319 | − | 0.559670i | ||||
\(590\) | 118.257 | + | 492.465i | 0.200436 | + | 0.834687i | ||||
\(591\) | 470.054 | + | 95.8044i | 0.795353 | + | 0.162106i | ||||
\(592\) | −16.2857 | − | 50.1221i | −0.0275096 | − | 0.0846658i | ||||
\(593\) | 145.831i | 0.245921i | 0.992412 | + | 0.122960i | \(0.0392388\pi\) | ||||
−0.992412 | + | 0.122960i | \(0.960761\pi\) | |||||||
\(594\) | 5.19865 | + | 206.805i | 0.00875194 | + | 0.348156i | ||||
\(595\) | 484.093 | + | 789.876i | 0.813602 | + | 1.32752i | ||||
\(596\) | 358.953 | + | 116.631i | 0.602270 | + | 0.195689i | ||||
\(597\) | −779.184 | + | 88.5013i | −1.30517 | + | 0.148243i | ||||
\(598\) | 103.926 | − | 75.5066i | 0.173789 | − | 0.126265i | ||||
\(599\) | − | 107.299i | − | 0.179130i | −0.995981 | − | 0.0895649i | \(-0.971452\pi\) | ||
0.995981 | − | 0.0895649i | \(-0.0285477\pi\) | |||||||
\(600\) | 132.096 | − | 165.984i | 0.220160 | − | 0.276640i | ||||
\(601\) | −920.464 | −1.53155 | −0.765777 | − | 0.643107i | \(-0.777645\pi\) | ||||
−0.765777 | + | 0.643107i | \(0.777645\pi\) | |||||||
\(602\) | 12.7867 | + | 17.5994i | 0.0212403 | + | 0.0292348i | ||||
\(603\) | −508.682 | − | 847.929i | −0.843585 | − | 1.40618i | ||||
\(604\) | 81.5592 | − | 251.013i | 0.135032 | − | 0.415585i | ||||
\(605\) | −456.829 | − | 35.9295i | −0.755090 | − | 0.0593875i | ||||
\(606\) | −315.517 | + | 288.915i | −0.520655 | + | 0.476758i | ||||
\(607\) | −75.1335 | −0.123778 | −0.0618892 | − | 0.998083i | \(-0.519713\pi\) | ||||
−0.0618892 | + | 0.998083i | \(0.519713\pi\) | |||||||
\(608\) | −92.0355 | + | 29.9042i | −0.151374 | + | 0.0491845i | ||||
\(609\) | −702.036 | − | 143.086i | −1.15277 | − | 0.234952i | ||||
\(610\) | −32.8205 | + | 417.300i | −0.0538041 | + | 0.684098i | ||||
\(611\) | −484.531 | − | 666.899i | −0.793012 | − | 1.09149i | ||||
\(612\) | −123.991 | − | 538.780i | −0.202600 | − | 0.880360i | ||||
\(613\) | 948.446 | + | 689.086i | 1.54722 | + | 1.12412i | 0.945597 | + | 0.325340i | \(0.105479\pi\) |
0.601623 | + | 0.798780i | \(0.294521\pi\) | |||||||
\(614\) | −84.6429 | − | 116.501i | −0.137855 | − | 0.189741i | ||||
\(615\) | −670.625 | − | 192.514i | −1.09045 | − | 0.313032i | ||||
\(616\) | −74.7848 | − | 54.3343i | −0.121404 | − | 0.0882050i | ||||
\(617\) | −268.772 | + | 87.3293i | −0.435611 | + | 0.141539i | −0.518610 | − | 0.855011i | \(-0.673550\pi\) |
0.0829989 | + | 0.996550i | \(0.473550\pi\) | |||||||
\(618\) | −291.489 | + | 132.716i | −0.471665 | + | 0.214751i | ||||
\(619\) | 82.0044 | + | 252.384i | 0.132479 | + | 0.407728i | 0.995189 | − | 0.0979701i | \(-0.0312350\pi\) |
−0.862710 | + | 0.505698i | \(0.831235\pi\) | |||||||
\(620\) | 76.5479 | + | 318.772i | 0.123464 | + | 0.514149i | ||||
\(621\) | −159.469 | − | 109.846i | −0.256794 | − | 0.176886i | ||||
\(622\) | 50.3495 | − | 154.960i | 0.0809477 | − | 0.249131i | ||||
\(623\) | 469.299 | + | 645.935i | 0.753289 | + | 1.03681i | ||||
\(624\) | −62.9789 | − | 138.323i | −0.100928 | − | 0.221671i | ||||
\(625\) | 367.261 | − | 505.712i | 0.587618 | − | 0.809139i | ||||
\(626\) | − | 730.685i | − | 1.16723i | ||||||
\(627\) | 137.000 | − | 241.950i | 0.218501 | − | 0.385885i | ||||
\(628\) | −80.8259 | + | 248.756i | −0.128704 | + | 0.396109i | ||||
\(629\) | −384.871 | − | 125.052i | −0.611877 | − | 0.198811i | ||||
\(630\) | 177.486 | − | 340.410i | 0.281724 | − | 0.540333i | ||||
\(631\) | 115.403 | + | 355.175i | 0.182890 | + | 0.562876i | 0.999906 | − | 0.0137386i | \(-0.00437328\pi\) |
−0.817016 | + | 0.576615i | \(0.804373\pi\) | |||||||
\(632\) | − | 209.031i | − | 0.330746i | ||||||
\(633\) | 854.345 | − | 782.314i | 1.34968 | − | 1.23588i | ||||
\(634\) | −297.587 | − | 216.210i | −0.469380 | − | 0.341025i | ||||
\(635\) | −564.369 | − | 481.966i | −0.888771 | − | 0.759002i | ||||
\(636\) | −170.459 | + | 301.040i | −0.268017 | + | 0.473334i | ||||
\(637\) | −129.208 | − | 93.8750i | −0.202838 | − | 0.147370i | ||||
\(638\) | 178.294 | − | 245.401i | 0.279458 | − | 0.384641i | ||||
\(639\) | −285.959 | − | 25.2194i | −0.447511 | − | 0.0394670i | ||||
\(640\) | 4.43540 | − | 56.3944i | 0.00693031 | − | 0.0881162i | ||||
\(641\) | 195.404 | − | 268.951i | 0.304843 | − | 0.419580i | −0.628922 | − | 0.777469i | \(-0.716503\pi\) |
0.933764 | + | 0.357889i | \(0.116503\pi\) | |||||||
\(642\) | −132.096 | + | 120.959i | −0.205756 | + | 0.188409i | ||||
\(643\) | −894.132 | −1.39056 | −0.695282 | − | 0.718737i | \(-0.744720\pi\) | ||||
−0.695282 | + | 0.718737i | \(0.744720\pi\) | |||||||
\(644\) | 82.2924 | − | 26.7384i | 0.127783 | − | 0.0415193i | ||||
\(645\) | −13.0714 | − | 35.9465i | −0.0202657 | − | 0.0557310i | ||||
\(646\) | −229.624 | + | 706.710i | −0.355455 | + | 1.09398i | ||||
\(647\) | 890.975 | + | 289.495i | 1.37709 | + | 0.447443i | 0.901711 | − | 0.432340i | \(-0.142312\pi\) |
0.475376 | + | 0.879783i | \(0.342312\pi\) | |||||||
\(648\) | −165.025 | + | 158.918i | −0.254668 | + | 0.245243i | ||||
\(649\) | −388.046 | −0.597914 | ||||||||
\(650\) | −203.334 | − | 398.963i | −0.312822 | − | 0.613790i | ||||
\(651\) | 245.845 | + | 539.957i | 0.377642 | + | 0.829427i | ||||
\(652\) | 455.654 | − | 331.052i | 0.698855 | − | 0.507748i | ||||
\(653\) | −261.706 | − | 85.0333i | −0.400774 | − | 0.130219i | 0.101693 | − | 0.994816i | \(-0.467574\pi\) |
−0.502467 | + | 0.864596i | \(0.667574\pi\) | |||||||
\(654\) | 60.3053 | + | 530.941i | 0.0922100 | + | 0.811836i | ||||
\(655\) | −399.123 | − | 651.234i | −0.609348 | − | 0.994251i | ||||
\(656\) | −176.950 | + | 57.4945i | −0.269741 | + | 0.0876441i | ||||
\(657\) | 305.852 | − | 351.347i | 0.465528 | − | 0.534775i | ||||
\(658\) | −171.582 | − | 528.075i | −0.260763 | − | 0.802546i | ||||
\(659\) | −135.648 | + | 186.703i | −0.205839 | + | 0.283313i | −0.899438 | − | 0.437048i | \(-0.856024\pi\) |
0.693599 | + | 0.720361i | \(0.256024\pi\) | |||||||
\(660\) | 100.027 | + | 128.107i | 0.151556 | + | 0.194102i | ||||
\(661\) | −437.717 | + | 318.020i | −0.662204 | + | 0.481120i | −0.867407 | − | 0.497600i | \(-0.834215\pi\) |
0.205202 | + | 0.978720i | \(0.434215\pi\) | |||||||
\(662\) | 83.2503 | − | 114.584i | 0.125756 | − | 0.173088i | ||||
\(663\) | −1143.53 | − | 233.070i | −1.72478 | − | 0.351539i | ||||
\(664\) | −226.750 | + | 164.743i | −0.341491 | + | 0.248107i | ||||
\(665\) | −439.934 | + | 269.623i | −0.661556 | + | 0.405449i | ||||
\(666\) | 37.6091 | + | 163.424i | 0.0564702 | + | 0.245381i | ||||
\(667\) | 87.7401 | + | 270.036i | 0.131544 | + | 0.404852i | ||||
\(668\) | 32.1755i | 0.0481670i | ||||||||
\(669\) | 655.695 | − | 600.413i | 0.980112 | − | 0.897478i | ||||
\(670\) | −717.760 | − | 297.262i | −1.07128 | − | 0.443675i | ||||
\(671\) | −305.019 | − | 99.1068i | −0.454574 | − | 0.147700i | ||||
\(672\) | −11.5535 | − | 101.720i | −0.0171927 | − | 0.151368i | ||||
\(673\) | 707.647 | − | 514.136i | 1.05148 | − | 0.763946i | 0.0789883 | − | 0.996876i | \(-0.474831\pi\) |
0.972494 | + | 0.232929i | \(0.0748310\pi\) | |||||||
\(674\) | 108.967i | 0.161672i | ||||||||
\(675\) | −465.101 | + | 489.189i | −0.689039 | + | 0.724724i | ||||
\(676\) | 17.1737 | 0.0254049 | ||||||||
\(677\) | −563.162 | − | 775.126i | −0.831849 | − | 1.14494i | −0.987576 | − | 0.157142i | \(-0.949772\pi\) |
0.155727 | − | 0.987800i | \(-0.450228\pi\) | |||||||
\(678\) | 274.226 | − | 31.1471i | 0.404463 | − | 0.0459397i | ||||
\(679\) | 101.403 | − | 312.088i | 0.149342 | − | 0.459628i | ||||
\(680\) | −330.313 | − | 282.084i | −0.485754 | − | 0.414829i | ||||
\(681\) | 545.494 | + | 595.720i | 0.801019 | + | 0.874772i | ||||
\(682\) | −251.182 | −0.368302 | ||||||||
\(683\) | −720.816 | + | 234.207i | −1.05537 | + | 0.342910i | −0.784773 | − | 0.619783i | \(-0.787220\pi\) |
−0.270595 | + | 0.962693i | \(0.587220\pi\) | |||||||
\(684\) | 300.082 | − | 69.0588i | 0.438717 | − | 0.100963i | ||||
\(685\) | −503.857 | − | 208.674i | −0.735557 | − | 0.304633i | ||||
\(686\) | −308.941 | − | 425.221i | −0.450352 | − | 0.619856i | ||||
\(687\) | −37.4004 | + | 183.501i | −0.0544401 | + | 0.267104i | ||||
\(688\) | −8.25183 | − | 5.99530i | −0.0119939 | − | 0.00871410i | ||||
\(689\) | 429.241 | + | 590.799i | 0.622991 | + | 0.857473i | ||||
\(690\) | −152.047 | + | 5.26433i | −0.220358 | + | 0.00762947i | ||||
\(691\) | −834.128 | − | 606.029i | −1.20713 | − | 0.877032i | −0.212164 | − | 0.977234i | \(-0.568051\pi\) |
−0.994967 | + | 0.100202i | \(0.968051\pi\) | |||||||
\(692\) | −286.418 | + | 93.0629i | −0.413899 | + | 0.134484i | ||||
\(693\) | 221.855 | + | 193.128i | 0.320137 | + | 0.278683i | ||||
\(694\) | −70.3885 | − | 216.633i | −0.101424 | − | 0.312152i | ||||
\(695\) | 820.913 | + | 701.052i | 1.18117 | + | 1.00871i | ||||
\(696\) | 333.785 | − | 37.9120i | 0.479577 | − | 0.0544713i | ||||
\(697\) | −441.481 | + | 1358.74i | −0.633401 | + | 1.94941i | ||||
\(698\) | −361.198 | − | 497.147i | −0.517476 | − | 0.712245i | ||||
\(699\) | −339.508 | + | 154.580i | −0.485706 | + | 0.221144i | ||||
\(700\) | −47.2148 | − | 297.903i | −0.0674497 | − | 0.425575i | ||||
\(701\) | 569.513i | 0.812429i | 0.913778 | + | 0.406214i | \(0.133151\pi\) | ||||
−0.913778 | + | 0.406214i | \(0.866849\pi\) | |||||||
\(702\) | 160.956 | + | 456.043i | 0.229282 | + | 0.649634i | ||||
\(703\) | 69.6498 | − | 214.360i | 0.0990751 | − | 0.304922i | ||||
\(704\) | 41.2207 | + | 13.3934i | 0.0585521 | + | 0.0190247i | ||||
\(705\) | 33.7815 | + | 975.694i | 0.0479171 | + | 1.38396i | ||||
\(706\) | −194.747 | − | 599.371i | −0.275846 | − | 0.848967i | ||||
\(707\) | 608.287i | 0.860377i | ||||||||
\(708\) | −290.224 | − | 316.946i | −0.409921 | − | 0.447664i | ||||
\(709\) | 845.717 | + | 614.450i | 1.19283 | + | 0.866643i | 0.993561 | − | 0.113302i | \(-0.0361427\pi\) |
0.199271 | + | 0.979944i | \(0.436143\pi\) | |||||||
\(710\) | −192.301 | + | 117.856i | −0.270846 | + | 0.165994i | ||||
\(711\) | −58.4328 | + | 662.562i | −0.0821840 | + | 0.931874i | ||||
\(712\) | −302.860 | − | 220.041i | −0.425365 | − | 0.309046i | ||||
\(713\) | 138.199 | − | 190.214i | 0.193827 | − | 0.266780i | ||||
\(714\) | −684.044 | − | 387.329i | −0.958045 | − | 0.542478i | ||||
\(715\) | 333.607 | − | 80.1102i | 0.466583 | − | 0.112042i | ||||
\(716\) | 98.3053 | − | 135.306i | 0.137298 | − | 0.188974i | ||||
\(717\) | −98.3584 | − | 107.415i | −0.137180 | − | 0.149811i | ||||
\(718\) | 750.979 | 1.04593 | ||||||||
\(719\) | −552.024 | + | 179.363i | −0.767766 | + | 0.249462i | −0.666608 | − | 0.745408i | \(-0.732255\pi\) |
−0.101158 | + | 0.994870i | \(0.532255\pi\) | |||||||
\(720\) | −29.8233 | + | 177.512i | −0.0414213 | + | 0.246545i | ||||
\(721\) | −140.724 | + | 433.103i | −0.195179 | + | 0.600698i | ||||
\(722\) | 91.9306 | + | 29.8701i | 0.127328 | + | 0.0413713i | ||||
\(723\) | 501.546 | + | 283.992i | 0.693701 | + | 0.392797i | ||||
\(724\) | 147.481 | 0.203703 | ||||||||
\(725\) | 977.546 | − | 154.932i | 1.34834 | − | 0.213699i | ||||
\(726\) | 353.876 | − | 161.121i | 0.487433 | − | 0.221930i | ||||
\(727\) | 199.702 | − | 145.092i | 0.274694 | − | 0.199577i | −0.441906 | − | 0.897061i | \(-0.645698\pi\) |
0.716600 | + | 0.697485i | \(0.245698\pi\) | |||||||
\(728\) | −205.524 | − | 66.7789i | −0.282314 | − | 0.0917292i | ||||
\(729\) | 567.499 | − | 457.587i | 0.778462 | − | 0.627691i | ||||
\(730\) | 28.6959 | − | 364.858i | 0.0393095 | − | 0.499805i | ||||
\(731\) | −74.4876 | + | 24.2025i | −0.101898 | + | 0.0331088i | ||||
\(732\) | −147.180 | − | 323.255i | −0.201065 | − | 0.441606i | ||||
\(733\) | 100.092 | + | 308.051i | 0.136551 | + | 0.420261i | 0.995828 | − | 0.0912495i | \(-0.0290861\pi\) |
−0.859277 | + | 0.511511i | \(0.829086\pi\) | |||||||
\(734\) | 400.823 | − | 551.685i | 0.546080 | − | 0.751615i | ||||
\(735\) | 64.6397 | + | 177.760i | 0.0879451 | + | 0.241851i | ||||
\(736\) | −32.8219 | + | 23.8465i | −0.0445950 | + | 0.0324002i | ||||
\(737\) | 349.870 | − | 481.555i | 0.474722 | − | 0.653399i | ||||
\(738\) | 576.946 | − | 132.774i | 0.781770 | − | 0.179911i | ||||
\(739\) | −233.638 | + | 169.748i | −0.316154 | + | 0.229699i | −0.734533 | − | 0.678573i | \(-0.762599\pi\) |
0.418379 | + | 0.908273i | \(0.362599\pi\) | |||||||
\(740\) | 100.191 | + | 85.5621i | 0.135393 | + | 0.115624i | ||||
\(741\) | 129.812 | − | 636.909i | 0.175185 | − | 0.859526i | ||||
\(742\) | 152.003 | + | 467.816i | 0.204855 | + | 0.630480i | ||||
\(743\) | − | 206.430i | − | 0.277833i | −0.990304 | − | 0.138916i | \(-0.955638\pi\) | ||
0.990304 | − | 0.138916i | \(-0.0443619\pi\) | |||||||
\(744\) | −187.862 | − | 205.159i | −0.252502 | − | 0.275751i | ||||
\(745\) | −917.482 | + | 220.318i | −1.23152 | + | 0.295729i | ||||
\(746\) | −514.476 | − | 167.163i | −0.689646 | − | 0.224079i | ||||
\(747\) | 764.776 | − | 458.797i | 1.02380 | − | 0.614187i | ||||
\(748\) | 269.248 | − | 195.620i | 0.359957 | − | 0.261524i | ||||
\(749\) | 254.668i | 0.340010i | ||||||||
\(750\) | −64.7330 | + | 526.365i | −0.0863107 | + | 0.701819i | ||||
\(751\) | 31.5104 | 0.0419579 | 0.0209789 | − | 0.999780i | \(-0.493322\pi\) | ||||
0.0209789 | + | 0.999780i | \(0.493322\pi\) | |||||||
\(752\) | 153.025 | + | 210.620i | 0.203490 | + | 0.280080i | ||||
\(753\) | 60.0050 | + | 528.297i | 0.0796879 | + | 0.701589i | ||||
\(754\) | 219.130 | − | 674.413i | 0.290623 | − | 0.894447i | ||||
\(755\) | 154.067 | + | 641.588i | 0.204062 | + | 0.849786i | ||||
\(756\) | 8.18613 | + | 325.648i | 0.0108282 | + | 0.430751i | ||||
\(757\) | −196.725 | −0.259875 | −0.129937 | − | 0.991522i | \(-0.541478\pi\) | ||||
−0.129937 | + | 0.991522i | \(0.541478\pi\) | |||||||
\(758\) | −698.560 | + | 226.976i | −0.921583 | + | 0.299440i | ||||
\(759\) | 23.2794 | − | 114.218i | 0.0306711 | − | 0.150484i | ||||
\(760\) | 157.111 | − | 183.973i | 0.206725 | − | 0.242070i | ||||
\(761\) | −660.543 | − | 909.160i | −0.867994 | − | 1.19469i | −0.979604 | − | 0.200939i | \(-0.935601\pi\) |
0.111610 | − | 0.993752i | \(-0.464399\pi\) | |||||||
\(762\) | 617.059 | + | 125.766i | 0.809789 | + | 0.165048i | ||||
\(763\) | 614.671 | + | 446.584i | 0.805597 | + | 0.585301i | ||||
\(764\) | −7.84052 | − | 10.7915i | −0.0102625 | − | 0.0141251i | ||||
\(765\) | 968.130 | + | 986.451i | 1.26553 | + | 1.28948i | ||||
\(766\) | 593.536 | + | 431.229i | 0.774851 | + | 0.562962i | ||||
\(767\) | −862.762 | + | 280.328i | −1.12485 | + | 0.365487i | ||||
\(768\) | 19.8900 | + | 43.6851i | 0.0258985 | + | 0.0568816i | ||||
\(769\) | 118.743 | + | 365.453i | 0.154412 | + | 0.475231i | 0.998101 | − | 0.0616013i | \(-0.0196207\pi\) |
−0.843689 | + | 0.536832i | \(0.819621\pi\) | |||||||
\(770\) | 230.386 | + | 18.1198i | 0.299203 | + | 0.0235322i | ||||
\(771\) | −145.110 | − | 1277.58i | −0.188210 | − | 1.65704i | ||||
\(772\) | −179.873 | + | 553.591i | −0.232996 | + | 0.717087i | ||||
\(773\) | −396.060 | − | 545.129i | −0.512367 | − | 0.705213i | 0.471949 | − | 0.881626i | \(-0.343551\pi\) |
−0.984316 | + | 0.176413i | \(0.943551\pi\) | |||||||
\(774\) | 24.4797 | + | 21.3099i | 0.0316275 | + | 0.0275322i | ||||
\(775\) | −579.594 | − | 579.474i | −0.747864 | − | 0.747709i | ||||
\(776\) | 153.859i | 0.198272i | ||||||||
\(777\) | 207.485 | + | 117.485i | 0.267034 | + | 0.151204i | ||||
\(778\) | −268.339 | + | 825.863i | −0.344909 | + | 1.06152i | ||||
\(779\) | −756.771 | − | 245.890i | −0.971465 | − | 0.315648i | ||||
\(780\) | 314.940 | + | 212.566i | 0.403770 | + | 0.272521i | ||||
\(781\) | −53.4005 | − | 164.350i | −0.0683745 | − | 0.210435i | ||||
\(782\) | 311.524i | 0.398369i | ||||||||
\(783\) | −1068.59 | + | 26.8622i | −1.36474 | + | 0.0343068i | ||||
\(784\) | 40.8064 | + | 29.6476i | 0.0520490 | + | 0.0378158i | ||||
\(785\) | −152.682 | − | 635.820i | −0.194499 | − | 0.809962i | ||||
\(786\) | 563.978 | + | 319.343i | 0.717530 | + | 0.406289i | ||||
\(787\) | 212.191 | + | 154.166i | 0.269621 | + | 0.195891i | 0.714378 | − | 0.699760i | \(-0.246710\pi\) |
−0.444757 | + | 0.895651i | \(0.646710\pi\) | |||||||
\(788\) | −187.981 | + | 258.733i | −0.238554 | + | 0.328342i | ||||
\(789\) | −117.615 | + | 207.714i | −0.149068 | + | 0.263262i | ||||
\(790\) | 273.070 | + | 445.557i | 0.345658 | + | 0.563996i | ||||
\(791\) | 230.657 | − | 317.472i | 0.291601 | − | 0.401355i | ||||
\(792\) | −126.912 | − | 53.9756i | −0.160243 | − | 0.0681511i | ||||
\(793\) | −749.760 | −0.945473 | ||||||||
\(794\) | −753.801 | + | 244.925i | −0.949372 | + | 0.308470i | ||||
\(795\) | −29.9267 | − | 864.357i | −0.0376437 | − | 1.08724i | ||||
\(796\) | 161.553 | − | 497.209i | 0.202956 | − | 0.624634i | ||||
\(797\) | 1160.09 | + | 376.937i | 1.45558 | + | 0.472945i | 0.926715 | − | 0.375764i | \(-0.122620\pi\) |
0.528860 | + | 0.848709i | \(0.322620\pi\) | |||||||
\(798\) | 215.729 | − | 380.990i | 0.270337 | − | 0.477431i | ||||
\(799\) | 1999.07 | 2.50196 | ||||||||
\(800\) | 64.2170 | + | 126.001i | 0.0802712 | + | 0.157501i | ||||
\(801\) | 898.459 | + | 782.120i | 1.12167 | + | 0.976430i | ||||
\(802\) | −117.344 | + | 85.2557i | −0.146315 | + | 0.106304i | ||||
\(803\) | 266.687 | + | 86.6520i | 0.332114 | + | 0.107910i | ||||
\(804\) | 654.994 | − | 74.3955i | 0.814669 | − | 0.0925317i | ||||
\(805\) | −140.479 | + | 164.497i | −0.174508 | + | 0.204344i | ||||
\(806\) | −558.464 | + | 181.456i | −0.692884 | + | 0.225132i | ||||
\(807\) | 205.609 | − | 93.6148i | 0.254782 | − | 0.116003i | ||||
\(808\) | −88.1341 | − | 271.249i | −0.109077 | − | 0.335704i | ||||
\(809\) | 840.152 | − | 1156.37i | 1.03851 | − | 1.42938i | 0.140143 | − | 0.990131i | \(-0.455244\pi\) |
0.898364 | − | 0.439251i | \(-0.144756\pi\) | |||||||
\(810\) | 144.152 | − | 554.320i | 0.177966 | − | 0.684345i | ||||
\(811\) | 476.063 | − | 345.880i | 0.587007 | − | 0.426486i | −0.254236 | − | 0.967142i | \(-0.581824\pi\) |
0.841243 | + | 0.540657i | \(0.181824\pi\) | |||||||
\(812\) | 280.753 | − | 386.424i | 0.345755 | − | 0.475891i | ||||
\(813\) | −184.923 | + | 907.307i | −0.227458 | + | 1.11600i | ||||
\(814\) | −81.6685 | + | 59.3356i | −0.100330 | + | 0.0728939i | ||||
\(815\) | −538.769 | + | 1300.89i | −0.661066 | + | 1.59619i | ||||
\(816\) | 361.151 | + | 73.6082i | 0.442587 | + | 0.0902062i | ||||
\(817\) | −13.4800 | − | 41.4871i | −0.0164994 | − | 0.0507798i | ||||
\(818\) | 215.073i | 0.262925i | ||||||||
\(819\) | 632.778 | + | 269.120i | 0.772623 | + | 0.328596i | ||||
\(820\) | 302.066 | − | 353.711i | 0.368373 | − | 0.431355i | ||||
\(821\) | −237.171 | − | 77.0614i | −0.288880 | − | 0.0938629i | 0.160992 | − | 0.986956i | \(-0.448531\pi\) |
−0.449873 | + | 0.893093i | \(0.648531\pi\) | |||||||
\(822\) | 459.796 | − | 52.2246i | 0.559363 | − | 0.0635335i | ||||
\(823\) | −404.466 | + | 293.861i | −0.491453 | + | 0.357061i | −0.805743 | − | 0.592266i | \(-0.798234\pi\) |
0.314290 | + | 0.949327i | \(0.398234\pi\) | |||||||
\(824\) | − | 213.520i | − | 0.259126i | ||||||
\(825\) | −380.564 | − | 142.394i | −0.461290 | − | 0.172598i | ||||
\(826\) | −611.042 | −0.739761 | ||||||||
\(827\) | 393.018 | + | 540.943i | 0.475234 | + | 0.654103i | 0.977580 | − | 0.210563i | \(-0.0675298\pi\) |
−0.502347 | + | 0.864666i | \(0.667530\pi\) | |||||||
\(828\) | 110.701 | − | 66.4107i | 0.133697 | − | 0.0802062i | ||||
\(829\) | −219.753 | + | 676.330i | −0.265082 | + | 0.815839i | 0.726592 | + | 0.687069i | \(0.241103\pi\) |
−0.991675 | + | 0.128770i | \(0.958897\pi\) | |||||||
\(830\) | 268.111 | − | 647.372i | 0.323025 | − | 0.779966i | ||||
\(831\) | 296.396 | − | 271.406i | 0.356673 | − | 0.326602i | ||||
\(832\) | 101.323 | 0.121783 | ||||||||
\(833\) | 368.352 | − | 119.685i | 0.442199 | − | 0.143679i | ||||
\(834\) | −897.554 | − | 182.936i | −1.07620 | − | 0.219347i | ||||
\(835\) | −42.0327 | − | 68.5832i | −0.0503386 | − | 0.0821356i | ||||
\(836\) | 108.954 | + | 149.962i | 0.130327 | + | 0.179380i | ||||
\(837\) | 538.111 | + | 702.802i | 0.642904 | + | 0.839668i | ||||
\(838\) | −329.874 | − | 239.668i | −0.393645 | − | 0.286000i | ||||
\(839\) | −711.944 | − | 979.907i | −0.848562 | − | 1.16795i | −0.984178 | − | 0.177184i | \(-0.943301\pi\) |
0.135615 | − | 0.990762i | \(-0.456699\pi\) | |||||||
\(840\) | 157.509 | + | 201.726i | 0.187510 | + | 0.240149i | ||||
\(841\) | 587.638 | + | 426.944i | 0.698737 | + | 0.507662i | ||||
\(842\) | −259.533 | + | 84.3275i | −0.308234 | + | 0.100151i | ||||
\(843\) | −506.218 | + | 230.484i | −0.600496 | + | 0.273409i | ||||
\(844\) | 238.646 | + | 734.478i | 0.282756 | + | 0.870234i | ||||
\(845\) | −36.6063 | + | 22.4350i | −0.0433210 | + | 0.0265502i | ||||
\(846\) | −426.162 | − | 710.375i | −0.503737 | − | 0.839687i | ||||
\(847\) | 170.843 | − | 525.801i | 0.201704 | − | 0.620780i | ||||
\(848\) | −135.563 | − | 186.586i | −0.159862 | − | 0.220031i | ||||
\(849\) | −152.757 | − | 335.505i | −0.179926 | − | 0.395176i | ||||
\(850\) | 1072.57 | + | 169.765i | 1.26185 | + | 0.199724i | ||||
\(851\) | − | 94.4920i | − | 0.111036i | ||||||
\(852\) | 94.2980 | − | 166.535i | 0.110678 | − | 0.195464i | ||||
\(853\) | 250.095 | − | 769.715i | 0.293195 | − | 0.902362i | −0.690627 | − | 0.723212i | \(-0.742665\pi\) |
0.983822 | − | 0.179150i | \(-0.0573349\pi\) | |||||||
\(854\) | −480.303 | − | 156.060i | −0.562416 | − | 0.182740i | ||||
\(855\) | −549.420 | + | 539.216i | −0.642597 | + | 0.630662i | ||||
\(856\) | −36.8986 | − | 113.562i | −0.0431058 | − | 0.132666i | ||||
\(857\) | 787.176i | 0.918525i | 0.888301 | + | 0.459262i | \(0.151886\pi\) | ||||
−0.888301 | + | 0.459262i | \(0.848114\pi\) | |||||||
\(858\) | −214.706 | + | 196.604i | −0.250240 | + | 0.229142i | ||||
\(859\) | −1007.39 | − | 731.913i | −1.17275 | − | 0.852052i | −0.181413 | − | 0.983407i | \(-0.558067\pi\) |
−0.991335 | + | 0.131355i | \(0.958067\pi\) | |||||||
\(860\) | 25.4210 | + | 1.99936i | 0.0295594 | + | 0.00232483i | ||||
\(861\) | 414.766 | − | 732.501i | 0.481726 | − | 0.850756i | ||||
\(862\) | 409.244 | + | 297.333i | 0.474761 | + | 0.344934i | ||||
\(863\) | −482.115 | + | 663.574i | −0.558650 | + | 0.768916i | −0.991154 | − | 0.132716i | \(-0.957630\pi\) |
0.432504 | + | 0.901632i | \(0.357630\pi\) | |||||||
\(864\) | −50.8332 | − | 144.028i | −0.0588347 | − | 0.166699i | ||||
\(865\) | 488.936 | − | 572.531i | 0.565244 | − | 0.661885i | ||||
\(866\) | −411.970 | + | 567.028i | −0.475716 | + | 0.654767i | ||||
\(867\) | 1447.86 | − | 1325.79i | 1.66997 | − | 1.52917i | ||||
\(868\) | −395.527 | −0.455676 | ||||||||
\(869\) | −380.795 | + | 123.728i | −0.438199 | + | 0.142380i | ||||
\(870\) | −661.948 | + | 516.853i | −0.760859 | + | 0.594084i | ||||
\(871\) | 430.003 | − | 1323.41i | 0.493689 | − | 1.51942i | ||||
\(872\) | −338.801 | − | 110.083i | −0.388533 | − | 0.126242i | ||||
\(873\) | 43.0099 | − | 487.684i | 0.0492668 | − | 0.558630i | ||||
\(874\) | −173.508 | −0.198522 | ||||||||
\(875\) | 489.807 | + | 573.310i | 0.559780 | + | 0.655212i | ||||
\(876\) | 128.684 | + | 282.632i | 0.146899 | + | 0.322639i | ||||
\(877\) | −351.891 | + | 255.664i | −0.401244 | + | 0.291521i | −0.770048 | − | 0.637986i | \(-0.779768\pi\) |
0.368803 | + | 0.929507i | \(0.379768\pi\) | |||||||
\(878\) | −117.366 | − | 38.1346i | −0.133674 | − | 0.0434335i | ||||
\(879\) | 73.4218 | + | 646.421i | 0.0835288 | + | 0.735405i | ||||
\(880\) | −105.360 | + | 25.3004i | −0.119727 | + | 0.0287505i | ||||
\(881\) | −34.1578 | + | 11.0986i | −0.0387717 | + | 0.0125977i | −0.328339 | − | 0.944560i | \(-0.606489\pi\) |
0.289567 | + | 0.957158i | \(0.406489\pi\) | |||||||
\(882\) | −121.056 | − | 105.380i | −0.137251 | − | 0.119479i | ||||
\(883\) | 260.046 | + | 800.340i | 0.294503 | + | 0.906387i | 0.983388 | + | 0.181516i | \(0.0581005\pi\) |
−0.688885 | + | 0.724871i | \(0.741899\pi\) | |||||||
\(884\) | 457.314 | − | 629.438i | 0.517323 | − | 0.712034i | ||||
\(885\) | 1032.67 | + | 296.445i | 1.16686 | + | 0.334966i | ||||
\(886\) | 773.812 | − | 562.208i | 0.873377 | − | 0.634546i | ||||
\(887\) | −265.811 | + | 365.858i | −0.299675 | + | 0.412467i | −0.932126 | − | 0.362133i | \(-0.882049\pi\) |
0.632452 | + | 0.774600i | \(0.282049\pi\) | |||||||
\(888\) | −109.545 | − | 22.3269i | −0.123361 | − | 0.0251430i | ||||
\(889\) | 724.399 | − | 526.307i | 0.814847 | − | 0.592021i | ||||
\(890\) | 933.008 | + | 73.3807i | 1.04832 | + | 0.0824503i | ||||
\(891\) | 387.182 | + | 206.563i | 0.434548 | + | 0.231832i | ||||
\(892\) | 183.157 | + | 563.699i | 0.205333 | + | 0.631950i | ||||
\(893\) | 1113.41i | 1.24682i | ||||||||
\(894\) | 590.483 | − | 540.699i | 0.660495 | − | 0.604809i | ||||
\(895\) | −32.7835 | + | 416.830i | −0.0366297 | + | 0.465732i | ||||
\(896\) | 64.9087 | + | 21.0901i | 0.0724428 | + | 0.0235381i | ||||
\(897\) | −30.7538 | − | 270.763i | −0.0342852 | − | 0.301854i | ||||
\(898\) | −595.119 | + | 432.379i | −0.662716 | + | 0.481491i | ||||
\(899\) | − | 1297.89i | − | 1.44371i | ||||||
\(900\) | −168.325 | − | 417.333i | −0.187028 | − | 0.463703i | ||||
\(901\) | −1770.96 | −1.96554 | ||||||||
\(902\) | 209.477 | + | 288.320i | 0.232236 | + | 0.319646i | ||||
\(903\) | 45.8524 | − | 5.20801i | 0.0507778 | − | 0.00576745i | ||||
\(904\) | −56.8569 | + | 174.987i | −0.0628948 | + | 0.193570i | ||||
\(905\) | −314.361 | + | 192.663i | −0.347360 | + | 0.212887i | ||||
\(906\) | −378.107 | − | 412.920i | −0.417336 | − | 0.455762i | ||||
\(907\) | 424.060 | 0.467542 | 0.233771 | − | 0.972292i | \(-0.424893\pi\) | ||||
0.233771 | + | 0.972292i | \(0.424893\pi\) | |||||||
\(908\) | −512.138 | + | 166.404i | −0.564029 | + | 0.183264i | ||||
\(909\) | 203.531 | + | 884.408i | 0.223907 | + | 0.972947i | ||||
\(910\) | 525.319 | − | 126.147i | 0.577273 | − | 0.138623i | ||||
\(911\) | −265.355 | − | 365.229i | −0.291279 | − | 0.400910i | 0.638150 | − | 0.769912i | \(-0.279700\pi\) |
−0.929429 | + | 0.369001i | \(0.879700\pi\) | |||||||
\(912\) | −40.9973 | + | 201.149i | −0.0449532 | + | 0.220558i | ||||
\(913\) | 434.331 | + | 315.560i | 0.475718 | + | 0.345629i | ||||
\(914\) | 433.803 | + | 597.079i | 0.474620 | + | 0.653259i | ||||
\(915\) | 736.005 | + | 496.760i | 0.804377 | + | 0.542907i | ||||
\(916\) | −101.005 | − | 73.3843i | −0.110267 | − | 0.0801139i | ||||
\(917\) | 876.422 | − | 284.767i | 0.955749 | − | 0.310542i | ||||
\(918\) | −1124.15 | − | 334.271i | −1.22457 | − | 0.364129i | ||||
\(919\) | 69.7294 | + | 214.605i | 0.0758753 | + | 0.233520i | 0.981800 | − | 0.189919i | \(-0.0608227\pi\) |
−0.905924 | + | 0.423439i | \(0.860823\pi\) | |||||||
\(920\) | 38.8090 | − | 93.7068i | 0.0421836 | − | 0.101855i | ||||
\(921\) | −303.525 | + | 34.4750i | −0.329560 | + | 0.0374321i | ||||
\(922\) | −379.684 | + | 1168.55i | −0.411805 | + | 1.26740i | ||||
\(923\) | −237.456 | − | 326.830i | −0.257265 | − | 0.354095i | ||||
\(924\) | −178.465 | + | 81.2561i | −0.193144 | + | 0.0879395i | ||||
\(925\) | −325.335 | − | 51.4934i | −0.351713 | − | 0.0556686i | ||||
\(926\) | − | 1124.23i | − | 1.21407i | ||||||
\(927\) | −59.6876 | + | 676.790i | −0.0643879 | + | 0.730086i | ||||
\(928\) | −69.2057 | + | 212.993i | −0.0745751 | + | 0.229519i | ||||
\(929\) | 247.159 | + | 80.3069i | 0.266049 | + | 0.0864444i | 0.439004 | − | 0.898485i | \(-0.355332\pi\) |
−0.172955 | + | 0.984930i | \(0.555332\pi\) | |||||||
\(930\) | 668.444 | + | 191.888i | 0.718757 | + | 0.206332i | ||||
\(931\) | 66.6604 | + | 205.160i | 0.0716008 | + | 0.220365i | ||||
\(932\) | − | 248.695i | − | 0.266840i | ||||||
\(933\) | −233.419 | − | 254.911i | −0.250181 | − | 0.273216i | ||||
\(934\) | 61.1704 | + | 44.4429i | 0.0654930 | + | 0.0475834i | ||||
\(935\) | −318.361 | + | 768.703i | −0.340493 | + | 0.822143i | ||||
\(936\) | −321.163 | − | 28.3240i | −0.343123 | − | 0.0302607i | ||||
\(937\) | −0.344734 | − | 0.250464i | −0.000367912 | − | 0.000267304i | 0.587601 | − | 0.809151i | \(-0.300072\pi\) |
−0.587969 | + | 0.808883i | \(0.700072\pi\) | |||||||
\(938\) | 550.928 | − | 758.287i | 0.587343 | − | 0.808409i | ||||
\(939\) | −1348.80 | − | 763.736i | −1.43642 | − | 0.813350i | ||||
\(940\) | −601.322 | − | 249.039i | −0.639704 | − | 0.264935i | ||||
\(941\) | 140.562 | − | 193.466i | 0.149375 | − | 0.205597i | −0.727772 | − | 0.685819i | \(-0.759444\pi\) |
0.877147 | + | 0.480223i | \(0.159444\pi\) | |||||||
\(942\) | 374.707 | + | 409.208i | 0.397778 | + | 0.434403i | ||||
\(943\) | −333.592 | −0.353756 | ||||||||
\(944\) | 272.478 | − | 88.5334i | 0.288642 | − | 0.0937854i | ||||
\(945\) | −442.861 | − | 683.435i | −0.468636 | − | 0.723212i | ||||
\(946\) | −6.03738 | + | 18.5811i | −0.00638201 | + | 0.0196418i | ||||
\(947\) | −944.144 | − | 306.771i | −0.996984 | − | 0.323940i | −0.235325 | − | 0.971917i | \(-0.575615\pi\) |
−0.761660 | + | 0.647977i | \(0.775615\pi\) | |||||||
\(948\) | −385.859 | − | 218.486i | −0.407024 | − | 0.230471i | ||||
\(949\) | 655.538 | 0.690767 | ||||||||
\(950\) | −94.5535 | + | 597.388i | −0.0995300 | + | 0.628829i | ||||
\(951\) | −710.157 | + | 323.338i | −0.746748 | + | 0.339998i | ||||
\(952\) | 423.975 | − | 308.036i | 0.445351 | − | 0.323567i | ||||
\(953\) | −382.635 | − | 124.326i | −0.401506 | − | 0.130457i | 0.101301 | − | 0.994856i | \(-0.467699\pi\) |
−0.502807 | + | 0.864399i | \(0.667699\pi\) | |||||||
\(954\) | 377.532 | + | 629.314i | 0.395736 | + | 0.659658i | ||||
\(955\) | 30.8099 | + | 12.7600i | 0.0322617 | + | 0.0133613i | ||||
\(956\) | 92.3440 | − | 30.0044i | 0.0965941 | − | 0.0313853i | ||||
\(957\) | −266.636 | − | 585.621i | −0.278616 | − | 0.611934i | ||||
\(958\) | −124.325 | − | 382.633i | −0.129776 | − | 0.399408i | ||||
\(959\) | 386.743 | − | 532.307i | 0.403278 | − | 0.555064i | ||||
\(960\) | −99.4646 | − | 67.1327i | −0.103609 | − | 0.0699299i | ||||
\(961\) | −92.0277 | + | 66.8620i | −0.0957624 | + | 0.0695755i | ||||
\(962\) | −138.713 | + | 190.922i | −0.144192 | + | 0.198464i | ||||
\(963\) | 85.2113 | + | 370.270i | 0.0884853 | + | 0.384496i | ||||
\(964\) | −310.861 | + | 225.854i | −0.322470 | + | 0.234288i | ||||
\(965\) | −339.783 | − | 1414.98i | −0.352107 | − | 1.46630i | ||||
\(966\) | 36.6572 | − | 179.855i | 0.0379474 | − | 0.186185i | ||||
\(967\) | −156.898 | − | 482.881i | −0.162252 | − | 0.499360i | 0.836571 | − | 0.547858i | \(-0.184557\pi\) |
−0.998823 | + | 0.0484980i | \(0.984557\pi\) | |||||||
\(968\) | 259.220i | 0.267789i | ||||||||
\(969\) | 1064.53 | + | 1162.55i | 1.09859 | + | 1.19974i | ||||
\(970\) | −200.995 | − | 327.956i | −0.207211 | − | 0.338099i | ||||
\(971\) | −918.296 | − | 298.372i | −0.945722 | − | 0.307284i | −0.204746 | − | 0.978815i | \(-0.565637\pi\) |
−0.740976 | + | 0.671532i | \(0.765637\pi\) | |||||||
\(972\) | 120.863 | + | 470.731i | 0.124345 | + | 0.484292i | ||||
\(973\) | −1053.69 | + | 765.549i | −1.08293 | + | 0.786792i | ||||
\(974\) | 624.958i | 0.641640i | ||||||||
\(975\) | −948.993 | − | 41.6674i | −0.973326 | − | 0.0427358i | ||||
\(976\) | 236.789 | 0.242612 | ||||||||
\(977\) | 146.478 | + | 201.610i | 0.149927 | + | 0.206357i | 0.877374 | − | 0.479807i | \(-0.159293\pi\) |
−0.727447 | + | 0.686164i | \(0.759293\pi\) | |||||||
\(978\) | −134.837 | − | 1187.13i | −0.137870 | − | 1.21384i | ||||
\(979\) | −221.585 | + | 681.969i | −0.226338 | + | 0.696597i | ||||
\(980\) | −125.711 | − | 9.88709i | −0.128276 | − | 0.0100889i | ||||
\(981\) | 1043.12 | + | 443.637i | 1.06332 | + | 0.452229i | ||||
\(982\) | −1080.80 | −1.10061 | ||||||||
\(983\) | −90.6916 | + | 29.4675i | −0.0922600 | + | 0.0299771i | −0.354783 | − | 0.934949i | \(-0.615445\pi\) |
0.262523 | + | 0.964926i | \(0.415445\pi\) | |||||||
\(984\) | −78.8225 | + | 386.734i | −0.0801041 | + | 0.393022i | ||||
\(985\) | 62.6891 | − | 797.068i | 0.0636438 | − | 0.809206i | ||||
\(986\) | 1010.80 | + | 1391.24i | 1.02515 | + | 1.41100i | ||||
\(987\) | −1154.14 | − | 235.231i | −1.16934 | − | 0.238330i | ||||
\(988\) | 350.576 | + | 254.708i | 0.354834 | + | 0.257802i | ||||
\(989\) | −10.7494 | − | 14.7952i | −0.0108689 | − | 0.0149598i | ||||
\(990\) | 341.029 | − | 50.7418i | 0.344474 | − | 0.0512543i | ||||
\(991\) | 277.389 | + | 201.535i | 0.279908 | + | 0.203365i | 0.718877 | − | 0.695137i | \(-0.244656\pi\) |
−0.438969 | + | 0.898502i | \(0.644656\pi\) | |||||||
\(992\) | 176.374 | − | 57.3075i | 0.177797 | − | 0.0577697i | ||||
\(993\) | −124.499 | − | 273.442i | −0.125377 | − | 0.275370i | ||||
\(994\) | −84.0879 | − | 258.796i | −0.0845955 | − | 0.260358i | ||||
\(995\) | 305.177 | + | 1270.86i | 0.306710 | + | 1.27725i | ||||
\(996\) | 67.0998 | + | 590.761i | 0.0673693 | + | 0.593134i | ||||
\(997\) | 603.529 | − | 1857.47i | 0.605345 | − | 1.86306i | 0.110944 | − | 0.993827i | \(-0.464613\pi\) |
0.494401 | − | 0.869234i | \(-0.335387\pi\) | |||||||
\(998\) | −232.987 | − | 320.679i | −0.233454 | − | 0.321322i | ||||
\(999\) | 340.980 | + | 101.391i | 0.341321 | + | 0.101493i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 150.3.j.a.11.20 | yes | 80 | |
3.2 | odd | 2 | inner | 150.3.j.a.11.3 | ✓ | 80 | |
25.16 | even | 5 | inner | 150.3.j.a.41.3 | yes | 80 | |
75.41 | odd | 10 | inner | 150.3.j.a.41.20 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.3.j.a.11.3 | ✓ | 80 | 3.2 | odd | 2 | inner | |
150.3.j.a.11.20 | yes | 80 | 1.1 | even | 1 | trivial | |
150.3.j.a.41.3 | yes | 80 | 25.16 | even | 5 | inner | |
150.3.j.a.41.20 | yes | 80 | 75.41 | odd | 10 | inner |