Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,3,Mod(7,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.d (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: | \(0.599456581593\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.64000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(0.831254 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.19 |
Dual form | 22.3.d.a.7.2 |
$q$-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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) |
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 | ||||
\(3\) | −0.295274 | − | 0.908759i | −0.0984246 | − | 0.302920i | 0.889706 | − | 0.456533i | \(-0.150909\pi\) |
−0.988131 | + | 0.153613i | \(0.950909\pi\) | |||||||
\(4\) | −0.618034 | + | 1.90211i | −0.154508 | + | 0.475528i | ||||
\(5\) | −2.42545 | − | 1.76219i | −0.485090 | − | 0.352439i | 0.318203 | − | 0.948023i | \(-0.396921\pi\) |
−0.803293 | + | 0.595584i | \(0.796921\pi\) | |||||||
\(6\) | 0.794285 | − | 1.09324i | 0.132381 | − | 0.182207i | ||||
\(7\) | −3.70473 | − | 1.20374i | −0.529247 | − | 0.171963i | 0.0321910 | − | 0.999482i | \(-0.489752\pi\) |
−0.561438 | + | 0.827519i | \(0.689752\pi\) | |||||||
\(8\) | −2.68999 | + | 0.874032i | −0.336249 | + | 0.109254i | ||||
\(9\) | 6.54250 | − | 4.75340i | 0.726944 | − | 0.528156i | ||||
\(10\) | − | 4.23984i | − | 0.423984i | ||||||
\(11\) | −10.2616 | + | 3.96233i | −0.932871 | + | 0.360212i | ||||
\(12\) | 1.91105 | 0.159254 | ||||||||
\(13\) | 14.4340 | + | 19.8667i | 1.11031 | + | 1.52820i | 0.820965 | + | 0.570978i | \(0.193436\pi\) |
0.289340 | + | 0.957226i | \(0.406564\pi\) | |||||||
\(14\) | −1.70234 | − | 5.23927i | −0.121596 | − | 0.374234i | ||||
\(15\) | −0.885238 | + | 2.72448i | −0.0590158 | + | 0.181632i | ||||
\(16\) | −3.23607 | − | 2.35114i | −0.202254 | − | 0.146946i | ||||
\(17\) | 3.79692 | − | 5.22601i | 0.223348 | − | 0.307412i | −0.682607 | − | 0.730785i | \(-0.739154\pi\) |
0.905955 | + | 0.423373i | \(0.139154\pi\) | |||||||
\(18\) | 10.8770 | + | 3.53414i | 0.604275 | + | 0.196341i | ||||
\(19\) | 14.9139 | − | 4.84581i | 0.784940 | − | 0.255043i | 0.110992 | − | 0.993821i | \(-0.464597\pi\) |
0.673948 | + | 0.738779i | \(0.264597\pi\) | |||||||
\(20\) | 4.85090 | − | 3.52439i | 0.242545 | − | 0.176219i | ||||
\(21\) | 3.72214i | 0.177245i | ||||||||
\(22\) | −13.0634 | − | 8.44680i | −0.593789 | − | 0.383946i | ||||
\(23\) | −30.3518 | −1.31964 | −0.659822 | − | 0.751422i | \(-0.729369\pi\) | ||||
−0.659822 | + | 0.751422i | \(0.729369\pi\) | |||||||
\(24\) | 1.58857 | + | 2.18648i | 0.0661904 | + | 0.0911033i | ||||
\(25\) | −4.94794 | − | 15.2282i | −0.197918 | − | 0.609127i | ||||
\(26\) | −10.7316 | + | 33.0285i | −0.412754 | + | 1.27033i | ||||
\(27\) | −13.2089 | − | 9.59680i | −0.489217 | − | 0.355437i | ||||
\(28\) | 4.57929 | − | 6.30286i | 0.163546 | − | 0.225102i | ||||
\(29\) | −14.2561 | − | 4.63209i | −0.491590 | − | 0.159727i | 0.0527235 | − | 0.998609i | \(-0.483210\pi\) |
−0.544314 | + | 0.838882i | \(0.683210\pi\) | |||||||
\(30\) | −3.85300 | + | 1.25191i | −0.128433 | + | 0.0417305i | ||||
\(31\) | 21.4645 | − | 15.5949i | 0.692404 | − | 0.503061i | −0.185045 | − | 0.982730i | \(-0.559243\pi\) |
0.877450 | + | 0.479669i | \(0.159243\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 6.63078 | + | 8.15533i | 0.200933 | + | 0.247131i | ||||
\(34\) | 9.13540 | 0.268688 | ||||||||
\(35\) | 6.86441 | + | 9.44805i | 0.196126 | + | 0.269944i | ||||
\(36\) | 4.99802 | + | 15.3823i | 0.138834 | + | 0.427287i | ||||
\(37\) | −1.29043 | + | 3.97153i | −0.0348765 | + | 0.107339i | −0.966979 | − | 0.254855i | \(-0.917972\pi\) |
0.932103 | + | 0.362194i | \(0.117972\pi\) | |||||||
\(38\) | 17.9414 | + | 13.0352i | 0.472142 | + | 0.343031i | ||||
\(39\) | 13.7920 | − | 18.9831i | 0.353642 | − | 0.486746i | ||||
\(40\) | 8.06466 | + | 2.62037i | 0.201617 | + | 0.0655092i | ||||
\(41\) | 41.2318 | − | 13.3970i | 1.00565 | − | 0.326757i | 0.240532 | − | 0.970641i | \(-0.422678\pi\) |
0.765123 | + | 0.643884i | \(0.222678\pi\) | |||||||
\(42\) | −4.25858 | + | 3.09404i | −0.101395 | + | 0.0736676i | ||||
\(43\) | 56.0236i | 1.30287i | 0.758703 | + | 0.651437i | \(0.225833\pi\) | ||||
−0.758703 | + | 0.651437i | \(0.774167\pi\) | |||||||
\(44\) | −1.19479 | − | 21.9675i | −0.0271544 | − | 0.499262i | ||||
\(45\) | −24.2449 | −0.538776 | ||||||||
\(46\) | −25.2301 | − | 34.7262i | −0.548480 | − | 0.754918i | ||||
\(47\) | 9.34350 | + | 28.7563i | 0.198798 | + | 0.611837i | 0.999911 | + | 0.0133244i | \(0.00424141\pi\) |
−0.801113 | + | 0.598513i | \(0.795759\pi\) | |||||||
\(48\) | −1.18110 | + | 3.63504i | −0.0246062 | + | 0.0757300i | ||||
\(49\) | −27.3658 | − | 19.8824i | −0.558486 | − | 0.405764i | ||||
\(50\) | 13.3099 | − | 18.3195i | 0.266198 | − | 0.366391i | ||||
\(51\) | −5.87032 | − | 1.90738i | −0.115104 | − | 0.0373996i | ||||
\(52\) | −46.7093 | + | 15.1768i | −0.898256 | + | 0.291861i | ||||
\(53\) | −42.1199 | + | 30.6019i | −0.794714 | + | 0.577394i | −0.909359 | − | 0.416013i | \(-0.863427\pi\) |
0.114644 | + | 0.993407i | \(0.463427\pi\) | |||||||
\(54\) | − | 23.0899i | − | 0.427591i | ||||||
\(55\) | 31.8713 | + | 8.47245i | 0.579479 | + | 0.154044i | ||||
\(56\) | 11.0178 | 0.196746 | ||||||||
\(57\) | −8.80735 | − | 12.1223i | −0.154515 | − | 0.212671i | ||||
\(58\) | −6.55077 | − | 20.1612i | −0.112944 | − | 0.347607i | ||||
\(59\) | 29.1737 | − | 89.7875i | 0.494470 | − | 1.52182i | −0.323312 | − | 0.946293i | \(-0.604796\pi\) |
0.817781 | − | 0.575529i | \(-0.195204\pi\) | |||||||
\(60\) | −4.63516 | − | 3.36764i | −0.0772527 | − | 0.0561274i | ||||
\(61\) | −54.8450 | + | 75.4877i | −0.899098 | + | 1.23750i | 0.0716564 | + | 0.997429i | \(0.477172\pi\) |
−0.970755 | + | 0.240073i | \(0.922828\pi\) | |||||||
\(62\) | 35.6849 | + | 11.5947i | 0.575564 | + | 0.187012i | ||||
\(63\) | −29.9600 | + | 9.73460i | −0.475556 | + | 0.154517i | ||||
\(64\) | 6.47214 | − | 4.70228i | 0.101127 | − | 0.0734732i | ||||
\(65\) | − | 73.6210i | − | 1.13263i | ||||||
\(66\) | −3.81884 | + | 14.3656i | −0.0578612 | + | 0.217660i | ||||
\(67\) | 54.0771 | 0.807121 | 0.403560 | − | 0.914953i | \(-0.367773\pi\) | ||||
0.403560 | + | 0.914953i | \(0.367773\pi\) | |||||||
\(68\) | 7.59384 | + | 10.4520i | 0.111674 | + | 0.153706i | ||||
\(69\) | 8.96210 | + | 27.5825i | 0.129886 | + | 0.399747i | ||||
\(70\) | −5.10366 | + | 15.7075i | −0.0729095 | + | 0.224392i | ||||
\(71\) | 75.9613 | + | 55.1891i | 1.06988 | + | 0.777312i | 0.975890 | − | 0.218262i | \(-0.0700387\pi\) |
0.0939873 | + | 0.995573i | \(0.470039\pi\) | |||||||
\(72\) | −13.4446 | + | 18.5050i | −0.186731 | + | 0.257014i | ||||
\(73\) | −23.3346 | − | 7.58189i | −0.319653 | − | 0.103861i | 0.144796 | − | 0.989462i | \(-0.453747\pi\) |
−0.464449 | + | 0.885600i | \(0.653747\pi\) | |||||||
\(74\) | −5.61660 | + | 1.82494i | −0.0758999 | + | 0.0246614i | ||||
\(75\) | −12.3778 | + | 8.99297i | −0.165037 | + | 0.119906i | ||||
\(76\) | 31.3627i | 0.412667i | ||||||||
\(77\) | 42.7859 | − | 2.32709i | 0.555662 | − | 0.0302219i | ||||
\(78\) | 33.1837 | 0.425432 | ||||||||
\(79\) | −45.4416 | − | 62.5450i | −0.575210 | − | 0.791709i | 0.417950 | − | 0.908470i | \(-0.362749\pi\) |
−0.993160 | + | 0.116761i | \(0.962749\pi\) | |||||||
\(80\) | 3.70576 | + | 11.4052i | 0.0463220 | + | 0.142564i | ||||
\(81\) | 17.6701 | − | 54.3831i | 0.218150 | − | 0.671397i | ||||
\(82\) | 49.6020 | + | 36.0379i | 0.604902 | + | 0.439487i | ||||
\(83\) | −16.8251 | + | 23.1578i | −0.202712 | + | 0.279010i | −0.898254 | − | 0.439476i | \(-0.855164\pi\) |
0.695542 | + | 0.718485i | \(0.255164\pi\) | |||||||
\(84\) | −7.07993 | − | 2.30041i | −0.0842848 | − | 0.0273858i | ||||
\(85\) | −18.4185 | + | 5.98453i | −0.216688 | + | 0.0704062i | ||||
\(86\) | −64.0978 | + | 46.5698i | −0.745324 | + | 0.541509i | ||||
\(87\) | 14.3231i | 0.164633i | ||||||||
\(88\) | 24.1404 | − | 19.6276i | 0.274322 | − | 0.223041i | ||||
\(89\) | 68.2705 | 0.767085 | 0.383542 | − | 0.923523i | \(-0.374704\pi\) | ||||
0.383542 | + | 0.923523i | \(0.374704\pi\) | |||||||
\(90\) | −20.1537 | − | 27.7392i | −0.223930 | − | 0.308213i | ||||
\(91\) | −29.5597 | − | 90.9753i | −0.324831 | − | 0.999728i | ||||
\(92\) | 18.7585 | − | 57.7326i | 0.203896 | − | 0.627528i | ||||
\(93\) | −20.5099 | − | 14.9013i | −0.220537 | − | 0.160229i | ||||
\(94\) | −25.1340 | + | 34.5939i | −0.267383 | + | 0.368021i | ||||
\(95\) | −44.7121 | − | 14.5278i | −0.470654 | − | 0.152925i | ||||
\(96\) | −5.14072 | + | 1.67032i | −0.0535492 | + | 0.0173992i | ||||
\(97\) | −29.1342 | + | 21.1672i | −0.300353 | + | 0.218219i | −0.727746 | − | 0.685847i | \(-0.759432\pi\) |
0.427393 | + | 0.904066i | \(0.359432\pi\) | |||||||
\(98\) | − | 47.8372i | − | 0.488135i | ||||||
\(99\) | −48.3018 | + | 74.7009i | −0.487897 | + | 0.754555i | ||||
\(100\) | 32.0237 | 0.320237 | ||||||||
\(101\) | 1.45687 | + | 2.00522i | 0.0144245 | + | 0.0198536i | 0.816168 | − | 0.577814i | \(-0.196094\pi\) |
−0.801744 | + | 0.597668i | \(0.796094\pi\) | |||||||
\(102\) | −2.69744 | − | 8.30188i | −0.0264455 | − | 0.0813910i | ||||
\(103\) | −9.38014 | + | 28.8691i | −0.0910693 | + | 0.280283i | −0.986209 | − | 0.165502i | \(-0.947075\pi\) |
0.895140 | + | 0.445785i | \(0.147075\pi\) | |||||||
\(104\) | −56.1914 | − | 40.8254i | −0.540302 | − | 0.392552i | ||||
\(105\) | 6.55913 | − | 9.02786i | 0.0624679 | − | 0.0859796i | ||||
\(106\) | −70.0246 | − | 22.7524i | −0.660609 | − | 0.214645i | ||||
\(107\) | −72.8287 | + | 23.6635i | −0.680642 | + | 0.221154i | −0.628876 | − | 0.777505i | \(-0.716485\pi\) |
−0.0517656 | + | 0.998659i | \(0.516485\pi\) | |||||||
\(108\) | 26.4177 | − | 19.1936i | 0.244609 | − | 0.177718i | ||||
\(109\) | − | 12.1116i | − | 0.111116i | −0.998455 | − | 0.0555580i | \(-0.982306\pi\) | ||
0.998455 | − | 0.0555580i | \(-0.0176938\pi\) | |||||||
\(110\) | 16.7997 | + | 43.5075i | 0.152724 | + | 0.395523i | ||||
\(111\) | 3.99020 | 0.0359477 | ||||||||
\(112\) | 9.15859 | + | 12.6057i | 0.0817731 | + | 0.112551i | ||||
\(113\) | 29.3180 | + | 90.2315i | 0.259451 | + | 0.798509i | 0.992920 | + | 0.118786i | \(0.0379001\pi\) |
−0.733469 | + | 0.679723i | \(0.762100\pi\) | |||||||
\(114\) | 6.54823 | − | 20.1534i | 0.0574406 | − | 0.176784i | ||||
\(115\) | 73.6169 | + | 53.4858i | 0.640147 | + | 0.465094i | ||||
\(116\) | 17.6215 | − | 24.2539i | 0.151910 | − | 0.209086i | ||||
\(117\) | 188.868 | + | 61.3671i | 1.61426 | + | 0.524505i | ||||
\(118\) | 126.979 | − | 41.2579i | 1.07609 | − | 0.349643i | ||||
\(119\) | −20.3573 | + | 14.7904i | −0.171070 | + | 0.124289i | ||||
\(120\) | − | 8.10256i | − | 0.0675214i | ||||||
\(121\) | 89.5999 | − | 81.3195i | 0.740495 | − | 0.672062i | ||||
\(122\) | −131.957 | −1.08162 | ||||||||
\(123\) | −24.3494 | − | 33.5140i | −0.197962 | − | 0.272472i | ||||
\(124\) | 16.3974 | + | 50.4661i | 0.132237 | + | 0.406985i | ||||
\(125\) | −37.9950 | + | 116.937i | −0.303960 | + | 0.935493i | ||||
\(126\) | −36.0419 | − | 26.1860i | −0.286047 | − | 0.207825i | ||||
\(127\) | 78.4228 | − | 107.940i | 0.617502 | − | 0.849919i | −0.379666 | − | 0.925124i | \(-0.623961\pi\) |
0.997168 | + | 0.0752049i | \(0.0239611\pi\) | |||||||
\(128\) | 10.7600 | + | 3.49613i | 0.0840623 | + | 0.0273135i | ||||
\(129\) | 50.9119 | − | 16.5423i | 0.394666 | − | 0.128235i | ||||
\(130\) | 84.2315 | − | 61.1978i | 0.647935 | − | 0.470752i | ||||
\(131\) | 42.3750i | 0.323473i | 0.986834 | + | 0.161737i | \(0.0517095\pi\) | ||||
−0.986834 | + | 0.161737i | \(0.948290\pi\) | |||||||
\(132\) | −19.6104 | + | 7.57222i | −0.148564 | + | 0.0573653i | ||||
\(133\) | −61.0849 | −0.459285 | ||||||||
\(134\) | 44.9518 | + | 61.8708i | 0.335461 | + | 0.461723i | ||||
\(135\) | 15.1260 | + | 46.5531i | 0.112045 | + | 0.344838i | ||||
\(136\) | −5.64599 | + | 17.3766i | −0.0415146 | + | 0.127769i | ||||
\(137\) | −110.042 | − | 79.9503i | −0.803227 | − | 0.583579i | 0.108632 | − | 0.994082i | \(-0.465353\pi\) |
−0.911859 | + | 0.410503i | \(0.865353\pi\) | |||||||
\(138\) | −24.1080 | + | 33.1818i | −0.174696 | + | 0.240448i | ||||
\(139\) | −96.2740 | − | 31.2813i | −0.692619 | − | 0.225045i | −0.0585070 | − | 0.998287i | \(-0.518634\pi\) |
−0.634112 | + | 0.773242i | \(0.718634\pi\) | |||||||
\(140\) | −22.2137 | + | 7.21767i | −0.158669 | + | 0.0515548i | ||||
\(141\) | 23.3737 | − | 16.9820i | 0.165771 | − | 0.120440i | ||||
\(142\) | 132.785i | 0.935107i | ||||||||
\(143\) | −226.834 | − | 146.671i | −1.58625 | − | 1.02567i | ||||
\(144\) | −32.3479 | −0.224638 | ||||||||
\(145\) | 26.4149 | + | 36.3569i | 0.182171 | + | 0.250737i | ||||
\(146\) | −10.7224 | − | 33.0002i | −0.0734411 | − | 0.226029i | ||||
\(147\) | −9.98794 | + | 30.7397i | −0.0679452 | + | 0.209114i | ||||
\(148\) | −6.75678 | − | 4.90909i | −0.0456539 | − | 0.0331695i | ||||
\(149\) | 30.3729 | − | 41.8048i | 0.203845 | − | 0.280569i | −0.694839 | − | 0.719165i | \(-0.744524\pi\) |
0.898684 | + | 0.438597i | \(0.144524\pi\) | |||||||
\(150\) | −20.5781 | − | 6.68624i | −0.137188 | − | 0.0445749i | ||||
\(151\) | −79.6932 | + | 25.8939i | −0.527770 | + | 0.171483i | −0.560769 | − | 0.827973i | \(-0.689494\pi\) |
0.0329987 | + | 0.999455i | \(0.489494\pi\) | |||||||
\(152\) | −35.8828 | + | 26.0704i | −0.236071 | + | 0.171516i | ||||
\(153\) | − | 52.2394i | − | 0.341434i | ||||||
\(154\) | 38.2285 | + | 47.0180i | 0.248237 | + | 0.305311i | ||||
\(155\) | −79.5424 | −0.513177 | ||||||||
\(156\) | 27.5841 | + | 37.9662i | 0.176821 | + | 0.243373i | ||||
\(157\) | −71.8482 | − | 221.126i | −0.457632 | − | 1.40845i | −0.868017 | − | 0.496534i | \(-0.834606\pi\) |
0.410386 | − | 0.911912i | \(-0.365394\pi\) | |||||||
\(158\) | 33.7857 | − | 103.982i | 0.213833 | − | 0.658111i | ||||
\(159\) | 40.2466 | + | 29.2409i | 0.253124 | + | 0.183905i | ||||
\(160\) | −9.96847 | + | 13.7204i | −0.0623029 | + | 0.0857526i | ||||
\(161\) | 112.445 | + | 36.5357i | 0.698418 | + | 0.226930i | ||||
\(162\) | 76.9094 | − | 24.9894i | 0.474749 | − | 0.154255i | ||||
\(163\) | 260.206 | − | 189.051i | 1.59636 | − | 1.15982i | 0.702284 | − | 0.711897i | \(-0.252164\pi\) |
0.894072 | − | 0.447923i | \(-0.147836\pi\) | |||||||
\(164\) | 86.7074i | 0.528704i | ||||||||
\(165\) | −1.71136 | − | 31.4651i | −0.0103719 | − | 0.190697i | ||||
\(166\) | −40.4813 | −0.243863 | ||||||||
\(167\) | 73.5229 | + | 101.196i | 0.440257 | + | 0.605961i | 0.970269 | − | 0.242028i | \(-0.0778127\pi\) |
−0.530012 | + | 0.847990i | \(0.677813\pi\) | |||||||
\(168\) | −3.25327 | − | 10.0125i | −0.0193647 | − | 0.0595984i | ||||
\(169\) | −134.121 | + | 412.781i | −0.793613 | + | 2.44249i | ||||
\(170\) | −22.1575 | − | 16.0983i | −0.130338 | − | 0.0946961i | ||||
\(171\) | 74.5398 | − | 102.595i | 0.435905 | − | 0.599972i | ||||
\(172\) | −106.563 | − | 34.6245i | −0.619553 | − | 0.201305i | ||||
\(173\) | 120.522 | − | 39.1600i | 0.696660 | − | 0.226358i | 0.0607851 | − | 0.998151i | \(-0.480640\pi\) |
0.635875 | + | 0.771792i | \(0.280640\pi\) | |||||||
\(174\) | −16.3874 | + | 11.9061i | −0.0941805 | + | 0.0684261i | ||||
\(175\) | 62.3723i | 0.356413i | ||||||||
\(176\) | 42.5232 | + | 11.3040i | 0.241609 | + | 0.0642275i | ||||
\(177\) | −90.2094 | −0.509658 | ||||||||
\(178\) | 56.7501 | + | 78.1099i | 0.318821 | + | 0.438820i | ||||
\(179\) | 61.2907 | + | 188.633i | 0.342406 | + | 1.05382i | 0.962958 | + | 0.269653i | \(0.0869088\pi\) |
−0.620551 | + | 0.784166i | \(0.713091\pi\) | |||||||
\(180\) | 14.9842 | − | 46.1166i | 0.0832454 | − | 0.256203i | ||||
\(181\) | −86.4445 | − | 62.8056i | −0.477594 | − | 0.346992i | 0.322800 | − | 0.946467i | \(-0.395376\pi\) |
−0.800393 | + | 0.599475i | \(0.795376\pi\) | |||||||
\(182\) | 79.5153 | − | 109.443i | 0.436897 | − | 0.601337i | ||||
\(183\) | 84.7944 | + | 27.5514i | 0.463358 | + | 0.150554i | ||||
\(184\) | 81.6463 | − | 26.5285i | 0.443730 | − | 0.144176i | ||||
\(185\) | 10.1285 | − | 7.35877i | 0.0547485 | − | 0.0397771i | ||||
\(186\) | − | 35.8527i | − | 0.192756i | ||||||
\(187\) | −18.2552 | + | 68.6717i | −0.0976214 | + | 0.367229i | ||||
\(188\) | −60.4724 | −0.321662 | ||||||||
\(189\) | 37.3832 | + | 51.4535i | 0.197795 | + | 0.272241i | ||||
\(190\) | −20.5455 | − | 63.2324i | −0.108134 | − | 0.332802i | ||||
\(191\) | 10.6399 | − | 32.7463i | 0.0557064 | − | 0.171447i | −0.919332 | − | 0.393482i | \(-0.871270\pi\) |
0.975039 | + | 0.222036i | \(0.0712702\pi\) | |||||||
\(192\) | −6.18430 | − | 4.49315i | −0.0322099 | − | 0.0234018i | ||||
\(193\) | −125.780 | + | 173.121i | −0.651710 | + | 0.897002i | −0.999172 | − | 0.0406920i | \(-0.987044\pi\) |
0.347461 | + | 0.937694i | \(0.387044\pi\) | |||||||
\(194\) | −48.4358 | − | 15.7378i | −0.249669 | − | 0.0811225i | ||||
\(195\) | −66.9038 | + | 21.7384i | −0.343097 | + | 0.111479i | ||||
\(196\) | 54.7316 | − | 39.7649i | 0.279243 | − | 0.202882i | ||||
\(197\) | − | 271.384i | − | 1.37758i | −0.724960 | − | 0.688791i | \(-0.758142\pi\) | ||
0.724960 | − | 0.688791i | \(-0.241858\pi\) | |||||||
\(198\) | −125.618 | + | 6.83225i | −0.634435 | + | 0.0345063i | ||||
\(199\) | 249.930 | 1.25593 | 0.627966 | − | 0.778241i | \(-0.283888\pi\) | ||||
0.627966 | + | 0.778241i | \(0.283888\pi\) | |||||||
\(200\) | 26.6198 | + | 36.6391i | 0.133099 | + | 0.183195i | ||||
\(201\) | −15.9675 | − | 49.1431i | −0.0794405 | − | 0.244493i | ||||
\(202\) | −1.08318 | + | 3.33369i | −0.00536228 | + | 0.0165034i | ||||
\(203\) | 47.2392 | + | 34.3213i | 0.232705 | + | 0.169070i | ||||
\(204\) | 7.25611 | − | 9.98718i | 0.0355692 | − | 0.0489568i | ||||
\(205\) | −123.614 | − | 40.1646i | −0.602995 | − | 0.195925i | ||||
\(206\) | −40.8271 | + | 13.2655i | −0.198190 | + | 0.0643957i | ||||
\(207\) | −198.577 | + | 144.274i | −0.959308 | + | 0.696978i | ||||
\(208\) | − | 98.2262i | − | 0.472241i | ||||||
\(209\) | −133.839 | + | 108.819i | −0.640378 | + | 0.520666i | ||||
\(210\) | 15.7813 | 0.0751490 | ||||||||
\(211\) | −5.23750 | − | 7.20881i | −0.0248223 | − | 0.0341650i | 0.796425 | − | 0.604737i | \(-0.206722\pi\) |
−0.821248 | + | 0.570572i | \(0.806722\pi\) | |||||||
\(212\) | −32.1767 | − | 99.0297i | −0.151777 | − | 0.467121i | ||||
\(213\) | 27.7242 | − | 85.3265i | 0.130161 | − | 0.400594i | ||||
\(214\) | −87.6131 | − | 63.6546i | −0.409407 | − | 0.297452i | ||||
\(215\) | 98.7243 | − | 135.882i | 0.459183 | − | 0.632011i | ||||
\(216\) | 43.9197 | + | 14.2704i | 0.203332 | + | 0.0660665i | ||||
\(217\) | −98.2924 | + | 31.9371i | −0.452960 | + | 0.147176i | ||||
\(218\) | 13.8572 | − | 10.0679i | 0.0635652 | − | 0.0461828i | ||||
\(219\) | 23.4443i | 0.107052i | ||||||||
\(220\) | −35.8131 | + | 55.3866i | −0.162787 | + | 0.251757i | ||||
\(221\) | 158.628 | 0.717774 | ||||||||
\(222\) | 3.31687 | + | 4.56528i | 0.0149408 | + | 0.0205643i | ||||
\(223\) | −63.9823 | − | 196.917i | −0.286916 | − | 0.883037i | −0.985818 | − | 0.167819i | \(-0.946327\pi\) |
0.698902 | − | 0.715218i | \(-0.253673\pi\) | |||||||
\(224\) | −6.80937 | + | 20.9571i | −0.0303990 | + | 0.0935585i | ||||
\(225\) | −104.758 | − | 76.1108i | −0.465589 | − | 0.338270i | ||||
\(226\) | −78.8652 | + | 108.549i | −0.348961 | + | 0.480304i | ||||
\(227\) | 92.3282 | + | 29.9992i | 0.406732 | + | 0.132155i | 0.505236 | − | 0.862981i | \(-0.331406\pi\) |
−0.0985035 | + | 0.995137i | \(0.531406\pi\) | |||||||
\(228\) | 28.5012 | − | 9.26059i | 0.125005 | − | 0.0406166i | ||||
\(229\) | −46.7820 | + | 33.9891i | −0.204288 | + | 0.148424i | −0.685226 | − | 0.728331i | \(-0.740296\pi\) |
0.480937 | + | 0.876755i | \(0.340296\pi\) | |||||||
\(230\) | 128.687i | 0.559509i | ||||||||
\(231\) | −14.7483 | − | 38.1950i | −0.0638456 | − | 0.165346i | ||||
\(232\) | 42.3975 | 0.182748 | ||||||||
\(233\) | −41.2848 | − | 56.8237i | −0.177188 | − | 0.243879i | 0.711180 | − | 0.703009i | \(-0.248161\pi\) |
−0.888369 | + | 0.459131i | \(0.848161\pi\) | |||||||
\(234\) | 86.7861 | + | 267.100i | 0.370881 | + | 1.14145i | ||||
\(235\) | 28.0120 | − | 86.2122i | 0.119200 | − | 0.366860i | ||||
\(236\) | 152.756 | + | 110.983i | 0.647269 | + | 0.470269i | ||||
\(237\) | −43.4207 | + | 59.7634i | −0.183210 | + | 0.252166i | ||||
\(238\) | −33.8442 | − | 10.9966i | −0.142202 | − | 0.0462043i | ||||
\(239\) | 62.7924 | − | 20.4025i | 0.262730 | − | 0.0853660i | −0.174690 | − | 0.984623i | \(-0.555892\pi\) |
0.437420 | + | 0.899257i | \(0.355892\pi\) | |||||||
\(240\) | 9.27033 | − | 6.73529i | 0.0386264 | − | 0.0280637i | ||||
\(241\) | 49.6438i | 0.205991i | 0.994682 | + | 0.102995i | \(0.0328427\pi\) | ||||
−0.994682 | + | 0.102995i | \(0.967157\pi\) | |||||||
\(242\) | 167.520 | + | 34.9162i | 0.692230 | + | 0.144282i | ||||
\(243\) | −201.582 | −0.829556 | ||||||||
\(244\) | −109.690 | − | 150.975i | −0.449549 | − | 0.618751i | ||||
\(245\) | 31.3378 | + | 96.4477i | 0.127909 | + | 0.393664i | ||||
\(246\) | 18.1037 | − | 55.7173i | 0.0735921 | − | 0.226493i | ||||
\(247\) | 311.536 | + | 226.344i | 1.26128 | + | 0.916374i | ||||
\(248\) | −44.1090 | + | 60.7109i | −0.177859 | + | 0.244802i | ||||
\(249\) | 26.0129 | + | 8.45210i | 0.104469 | + | 0.0339442i | ||||
\(250\) | −165.373 | + | 53.7331i | −0.661494 | + | 0.214932i | ||||
\(251\) | 53.3991 | − | 38.7967i | 0.212746 | − | 0.154569i | −0.476309 | − | 0.879278i | \(-0.658026\pi\) |
0.689055 | + | 0.724709i | \(0.258026\pi\) | |||||||
\(252\) | − | 63.0036i | − | 0.250014i | ||||||
\(253\) | 311.458 | − | 120.264i | 1.23106 | − | 0.475352i | ||||
\(254\) | 188.685 | 0.742856 | ||||||||
\(255\) | 10.8770 | + | 14.9709i | 0.0426549 | + | 0.0587094i | ||||
\(256\) | 4.94427 | + | 15.2169i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 84.1944 | − | 259.124i | 0.327605 | − | 1.00826i | −0.642647 | − | 0.766163i | \(-0.722164\pi\) |
0.970251 | − | 0.242101i | \(-0.0778364\pi\) | |||||||
\(258\) | 61.2472 | + | 44.4987i | 0.237392 | + | 0.172475i | ||||
\(259\) | 9.56137 | − | 13.1601i | 0.0369165 | − | 0.0508112i | ||||
\(260\) | 140.036 | + | 45.5003i | 0.538598 | + | 0.175001i | ||||
\(261\) | −115.289 | + | 37.4596i | −0.441719 | + | 0.143523i | ||||
\(262\) | −48.4822 | + | 35.2244i | −0.185047 | + | 0.134444i | ||||
\(263\) | 66.3839i | 0.252410i | 0.992004 | + | 0.126205i | \(0.0402797\pi\) | ||||
−0.992004 | + | 0.126205i | \(0.959720\pi\) | |||||||
\(264\) | −24.9648 | − | 16.1423i | −0.0945636 | − | 0.0611450i | ||||
\(265\) | 156.086 | 0.589004 | ||||||||
\(266\) | −50.7770 | − | 69.8886i | −0.190891 | − | 0.262739i | ||||
\(267\) | −20.1585 | − | 62.0415i | −0.0755000 | − | 0.232365i | ||||
\(268\) | −33.4215 | + | 102.861i | −0.124707 | + | 0.383809i | ||||
\(269\) | −147.830 | − | 107.405i | −0.549553 | − | 0.399274i | 0.278067 | − | 0.960562i | \(-0.410306\pi\) |
−0.827621 | + | 0.561288i | \(0.810306\pi\) | |||||||
\(270\) | −40.6889 | + | 56.0035i | −0.150700 | + | 0.207420i | ||||
\(271\) | −380.422 | − | 123.607i | −1.40377 | − | 0.456113i | −0.493363 | − | 0.869823i | \(-0.664233\pi\) |
−0.910409 | + | 0.413710i | \(0.864233\pi\) | |||||||
\(272\) | −24.5742 | + | 7.98463i | −0.0903462 | + | 0.0293553i | ||||
\(273\) | −73.9464 | + | 53.7252i | −0.270866 | + | 0.196796i | ||||
\(274\) | − | 192.361i | − | 0.702047i | ||||||
\(275\) | 111.113 | + | 136.660i | 0.404046 | + | 0.496945i | ||||
\(276\) | −58.0039 | −0.210159 | ||||||||
\(277\) | −27.4031 | − | 37.7171i | −0.0989282 | − | 0.136163i | 0.756683 | − | 0.653782i | \(-0.226819\pi\) |
−0.855611 | + | 0.517619i | \(0.826819\pi\) | |||||||
\(278\) | −44.2385 | − | 136.152i | −0.159131 | − | 0.489755i | ||||
\(279\) | 66.3028 | − | 204.059i | 0.237644 | − | 0.731394i | ||||
\(280\) | −26.7231 | − | 19.4155i | −0.0954397 | − | 0.0693410i | ||||
\(281\) | −296.043 | + | 407.468i | −1.05353 | + | 1.45006i | −0.167826 | + | 0.985817i | \(0.553675\pi\) |
−0.885706 | + | 0.464246i | \(0.846325\pi\) | |||||||
\(282\) | 38.8590 | + | 12.6260i | 0.137798 | + | 0.0447732i | ||||
\(283\) | −53.4612 | + | 17.3706i | −0.188909 | + | 0.0613802i | −0.401944 | − | 0.915664i | \(-0.631665\pi\) |
0.213035 | + | 0.977045i | \(0.431665\pi\) | |||||||
\(284\) | −151.923 | + | 110.378i | −0.534939 | + | 0.388656i | ||||
\(285\) | 44.9222i | 0.157622i | ||||||||
\(286\) | −20.7465 | − | 381.446i | −0.0725403 | − | 1.33373i | ||||
\(287\) | −168.879 | −0.588429 | ||||||||
\(288\) | −26.8893 | − | 37.0099i | −0.0933656 | − | 0.128507i | ||||
\(289\) | 76.4113 | + | 235.170i | 0.264399 | + | 0.813737i | ||||
\(290\) | −19.6393 | + | 60.4437i | −0.0677219 | + | 0.208426i | ||||
\(291\) | 27.8385 | + | 20.2259i | 0.0956650 | + | 0.0695047i | ||||
\(292\) | 28.8432 | − | 39.6993i | 0.0987781 | − | 0.135956i | ||||
\(293\) | 177.512 | + | 57.6771i | 0.605843 | + | 0.196850i | 0.595845 | − | 0.803100i | \(-0.296817\pi\) |
0.00999814 | + | 0.999950i | \(0.496817\pi\) | |||||||
\(294\) | −43.4725 | + | 14.1251i | −0.147866 | + | 0.0480445i | ||||
\(295\) | −228.982 | + | 166.365i | −0.776211 | + | 0.563950i | ||||
\(296\) | − | 11.8113i | − | 0.0399030i | ||||||
\(297\) | 173.569 | + | 46.1404i | 0.584409 | + | 0.155355i | ||||
\(298\) | 73.0774 | 0.245226 | ||||||||
\(299\) | −438.098 | − | 602.990i | −1.46521 | − | 2.01669i | ||||
\(300\) | −9.45577 | − | 29.1019i | −0.0315192 | − | 0.0970062i | ||||
\(301\) | 67.4377 | − | 207.552i | 0.224046 | − | 0.689541i | ||||
\(302\) | −95.8711 | − | 69.6545i | −0.317454 | − | 0.230644i | ||||
\(303\) | 1.39208 | − | 1.91604i | 0.00459433 | − | 0.00632355i | ||||
\(304\) | −59.6555 | − | 19.3832i | −0.196235 | − | 0.0637606i | ||||
\(305\) | 266.048 | − | 86.4441i | 0.872288 | − | 0.283423i | ||||
\(306\) | 59.7683 | − | 43.4242i | 0.195321 | − | 0.141909i | ||||
\(307\) | 495.856i | 1.61517i | 0.589755 | + | 0.807583i | \(0.299224\pi\) | ||||
−0.589755 | + | 0.807583i | \(0.700776\pi\) | |||||||
\(308\) | −22.0168 | + | 82.8219i | −0.0714830 | + | 0.268902i | ||||
\(309\) | 29.0048 | 0.0938666 | ||||||||
\(310\) | −66.1199 | − | 91.0063i | −0.213290 | − | 0.293569i | ||||
\(311\) | 114.991 | + | 353.907i | 0.369747 | + | 1.13796i | 0.946955 | + | 0.321366i | \(0.104142\pi\) |
−0.577208 | + | 0.816597i | \(0.695858\pi\) | |||||||
\(312\) | −20.5087 | + | 63.1191i | −0.0657329 | + | 0.202305i | ||||
\(313\) | 198.463 | + | 144.192i | 0.634068 | + | 0.460677i | 0.857807 | − | 0.513972i | \(-0.171826\pi\) |
−0.223739 | + | 0.974649i | \(0.571826\pi\) | |||||||
\(314\) | 193.271 | − | 266.015i | 0.615513 | − | 0.847181i | ||||
\(315\) | 89.8208 | + | 29.1845i | 0.285145 | + | 0.0926493i | ||||
\(316\) | 147.052 | − | 47.7801i | 0.465355 | − | 0.151203i | ||||
\(317\) | 48.6657 | − | 35.3577i | 0.153519 | − | 0.111538i | −0.508374 | − | 0.861136i | \(-0.669753\pi\) |
0.661893 | + | 0.749598i | \(0.269753\pi\) | |||||||
\(318\) | 70.3537i | 0.221238i | ||||||||
\(319\) | 164.644 | − | 8.95484i | 0.516126 | − | 0.0280716i | ||||
\(320\) | −23.9842 | −0.0749506 | ||||||||
\(321\) | 43.0088 | + | 59.1966i | 0.133984 | + | 0.184413i | ||||
\(322\) | 51.6692 | + | 159.022i | 0.160463 | + | 0.493856i | ||||
\(323\) | 31.3025 | − | 96.3391i | 0.0969117 | − | 0.298264i | ||||
\(324\) | 92.5221 | + | 67.2212i | 0.285562 | + | 0.207473i | ||||
\(325\) | 231.115 | − | 318.102i | 0.711122 | − | 0.978776i | ||||
\(326\) | 432.594 | + | 140.558i | 1.32698 | + | 0.431161i | ||||
\(327\) | −11.0066 | + | 3.57625i | −0.0336592 | + | 0.0109365i | ||||
\(328\) | −99.2039 | + | 72.0759i | −0.302451 | + | 0.219744i | ||||
\(329\) | − | 117.782i | − | 0.357999i | ||||||
\(330\) | 34.5773 | − | 28.1135i | 0.104780 | − | 0.0851923i | ||||
\(331\) | −89.7487 | −0.271144 | −0.135572 | − | 0.990767i | \(-0.543287\pi\) | ||||
−0.135572 | + | 0.990767i | \(0.543287\pi\) | |||||||
\(332\) | −33.6502 | − | 46.3156i | −0.101356 | − | 0.139505i | ||||
\(333\) | 10.4357 | + | 32.1177i | 0.0313383 | + | 0.0964495i | ||||
\(334\) | −54.6640 | + | 168.238i | −0.163665 | + | 0.503708i | ||||
\(335\) | −131.161 | − | 95.2943i | −0.391526 | − | 0.284460i | ||||
\(336\) | 8.75127 | − | 12.0451i | 0.0260454 | − | 0.0358485i | ||||
\(337\) | −117.112 | − | 38.0519i | −0.347513 | − | 0.112914i | 0.130060 | − | 0.991506i | \(-0.458483\pi\) |
−0.477572 | + | 0.878592i | \(0.658483\pi\) | |||||||
\(338\) | −583.760 | + | 189.675i | −1.72710 | + | 0.561169i | ||||
\(339\) | 73.3419 | − | 53.2860i | 0.216348 | − | 0.157186i | ||||
\(340\) | − | 38.7327i | − | 0.113920i | ||||||
\(341\) | −158.468 | + | 245.078i | −0.464715 | + | 0.718703i | ||||
\(342\) | 179.343 | 0.524395 | ||||||||
\(343\) | 189.642 | + | 261.020i | 0.552893 | + | 0.760992i | ||||
\(344\) | −48.9664 | − | 150.703i | −0.142344 | − | 0.438090i | ||||
\(345\) | 26.8686 | − | 82.6930i | 0.0778799 | − | 0.239690i | ||||
\(346\) | 144.988 | + | 105.340i | 0.419041 | + | 0.304451i | ||||
\(347\) | −186.940 | + | 257.300i | −0.538731 | + | 0.741500i | −0.988430 | − | 0.151681i | \(-0.951531\pi\) |
0.449698 | + | 0.893180i | \(0.351531\pi\) | |||||||
\(348\) | −27.2442 | − | 8.85217i | −0.0782879 | − | 0.0254373i | ||||
\(349\) | 252.823 | − | 82.1472i | 0.724421 | − | 0.235379i | 0.0764822 | − | 0.997071i | \(-0.475631\pi\) |
0.647939 | + | 0.761692i | \(0.275631\pi\) | |||||||
\(350\) | −71.3616 | + | 51.8472i | −0.203890 | + | 0.148135i | ||||
\(351\) | − | 400.936i | − | 1.14227i | ||||||
\(352\) | 22.4143 | + | 58.0482i | 0.0636770 | + | 0.164910i | ||||
\(353\) | −249.501 | −0.706802 | −0.353401 | − | 0.935472i | \(-0.614975\pi\) | ||||
−0.353401 | + | 0.935472i | \(0.614975\pi\) | |||||||
\(354\) | −74.9869 | − | 103.211i | −0.211828 | − | 0.291556i | ||||
\(355\) | −86.9865 | − | 267.717i | −0.245032 | − | 0.754132i | ||||
\(356\) | −42.1935 | + | 129.858i | −0.118521 | + | 0.364770i | ||||
\(357\) | 19.4519 | + | 14.1327i | 0.0544872 | + | 0.0395873i | ||||
\(358\) | −164.872 | + | 226.926i | −0.460536 | + | 0.633873i | ||||
\(359\) | −535.038 | − | 173.844i | −1.49036 | − | 0.484246i | −0.553169 | − | 0.833069i | \(-0.686581\pi\) |
−0.937189 | + | 0.348823i | \(0.886581\pi\) | |||||||
\(360\) | 65.2187 | − | 21.1908i | 0.181163 | − | 0.0588634i | ||||
\(361\) | −93.1137 | + | 67.6511i | −0.257933 | + | 0.187399i | ||||
\(362\) | − | 151.110i | − | 0.417432i | ||||||
\(363\) | −100.356 | − | 57.4132i | −0.276464 | − | 0.158163i | ||||
\(364\) | 191.314 | 0.525588 | ||||||||
\(365\) | 43.2363 | + | 59.5097i | 0.118456 | + | 0.163040i | ||||
\(366\) | 38.9635 | + | 119.917i | 0.106458 | + | 0.327643i | ||||
\(367\) | 8.68220 | − | 26.7211i | 0.0236572 | − | 0.0728094i | −0.938531 | − | 0.345195i | \(-0.887813\pi\) |
0.962188 | + | 0.272386i | \(0.0878127\pi\) | |||||||
\(368\) | 98.2206 | + | 71.3614i | 0.266904 | + | 0.193917i | ||||
\(369\) | 206.078 | − | 283.641i | 0.558476 | − | 0.768676i | ||||
\(370\) | 16.8387 | + | 5.47122i | 0.0455099 | + | 0.0147871i | ||||
\(371\) | 192.879 | − | 62.6703i | 0.519890 | − | 0.168923i | ||||
\(372\) | 41.0198 | − | 29.8027i | 0.110268 | − | 0.0801147i | ||||
\(373\) | 157.016i | 0.420953i | 0.977599 | + | 0.210477i | \(0.0675016\pi\) | ||||
−0.977599 | + | 0.210477i | \(0.932498\pi\) | |||||||
\(374\) | −93.7436 | + | 36.1975i | −0.250651 | + | 0.0967846i | ||||
\(375\) | 117.486 | 0.313297 | ||||||||
\(376\) | −50.2679 | − | 69.1879i | −0.133691 | − | 0.184010i | ||||
\(377\) | −113.748 | − | 350.081i | −0.301719 | − | 0.928596i | ||||
\(378\) | −27.7942 | + | 85.5419i | −0.0735297 | + | 0.226301i | ||||
\(379\) | −503.479 | − | 365.799i | −1.32844 | − | 0.965169i | −0.999785 | − | 0.0207195i | \(-0.993404\pi\) |
−0.328656 | − | 0.944450i | \(-0.606596\pi\) | |||||||
\(380\) | 55.2672 | − | 76.0688i | 0.145440 | − | 0.200181i | ||||
\(381\) | −121.247 | − | 39.3957i | −0.318235 | − | 0.103401i | ||||
\(382\) | 46.3103 | − | 15.0471i | 0.121231 | − | 0.0393904i | ||||
\(383\) | 278.690 | − | 202.480i | 0.727651 | − | 0.528670i | −0.161168 | − | 0.986927i | \(-0.551526\pi\) |
0.888820 | + | 0.458257i | \(0.151526\pi\) | |||||||
\(384\) | − | 10.8105i | − | 0.0281525i | ||||||
\(385\) | −107.876 | − | 69.7528i | −0.280197 | − | 0.181176i | ||||
\(386\) | −302.627 | −0.784009 | ||||||||
\(387\) | 266.302 | + | 366.534i | 0.688120 | + | 0.947116i | ||||
\(388\) | −22.2566 | − | 68.4986i | −0.0573623 | − | 0.176543i | ||||
\(389\) | −89.6214 | + | 275.826i | −0.230389 | + | 0.709065i | 0.767311 | + | 0.641276i | \(0.221595\pi\) |
−0.997700 | + | 0.0677892i | \(0.978405\pi\) | |||||||
\(390\) | −80.4854 | − | 58.4761i | −0.206373 | − | 0.149939i | ||||
\(391\) | −115.243 | + | 158.619i | −0.294740 | + | 0.405675i | ||||
\(392\) | 90.9918 | + | 29.5650i | 0.232122 | + | 0.0754210i | ||||
\(393\) | 38.5087 | − | 12.5122i | 0.0979865 | − | 0.0318377i | ||||
\(394\) | 310.496 | − | 225.589i | 0.788061 | − | 0.572560i | ||||
\(395\) | 231.777i | 0.586777i | ||||||||
\(396\) | −112.237 | − | 138.043i | −0.283428 | − | 0.348594i | ||||
\(397\) | −238.817 | −0.601554 | −0.300777 | − | 0.953694i | \(-0.597246\pi\) | ||||
−0.300777 | + | 0.953694i | \(0.597246\pi\) | |||||||
\(398\) | 207.756 | + | 285.951i | 0.521999 | + | 0.718470i | ||||
\(399\) | 18.0368 | + | 55.5114i | 0.0452049 | + | 0.139126i | ||||
\(400\) | −19.7918 | + | 60.9127i | −0.0494794 | + | 0.152282i | ||||
\(401\) | 109.555 | + | 79.5964i | 0.273205 | + | 0.198495i | 0.715948 | − | 0.698154i | \(-0.245995\pi\) |
−0.442743 | + | 0.896648i | \(0.645995\pi\) | |||||||
\(402\) | 42.9526 | − | 59.1192i | 0.106847 | − | 0.147063i | ||||
\(403\) | 619.637 | + | 201.332i | 1.53756 | + | 0.499584i | ||||
\(404\) | −4.71455 | + | 1.53185i | −0.0116697 | + | 0.00379170i | ||||
\(405\) | −138.692 | + | 100.765i | −0.342449 | + | 0.248803i | ||||
\(406\) | 82.5771i | 0.203392i | ||||||||
\(407\) | −2.49468 | − | 45.8673i | −0.00612944 | − | 0.112696i | ||||
\(408\) | 17.4582 | 0.0427898 | ||||||||
\(409\) | 178.874 | + | 246.199i | 0.437345 | + | 0.601953i | 0.969619 | − | 0.244618i | \(-0.0786627\pi\) |
−0.532275 | + | 0.846572i | \(0.678663\pi\) | |||||||
\(410\) | −56.8013 | − | 174.816i | −0.138540 | − | 0.426382i | ||||
\(411\) | −40.1630 | + | 123.609i | −0.0977203 | + | 0.300752i | ||||
\(412\) | −49.1151 | − | 35.6842i | −0.119211 | − | 0.0866121i | ||||
\(413\) | −216.161 | + | 297.520i | −0.523393 | + | 0.720388i | ||||
\(414\) | −330.135 | − | 107.267i | −0.797428 | − | 0.259100i | ||||
\(415\) | 81.6170 | − | 26.5190i | 0.196667 | − | 0.0639011i | ||||
\(416\) | 112.383 | − | 81.6509i | 0.270151 | − | 0.196276i | ||||
\(417\) | 96.7264i | 0.231958i | ||||||||
\(418\) | −235.757 | − | 62.6719i | −0.564012 | − | 0.149933i | ||||
\(419\) | 594.131 | 1.41797 | 0.708987 | − | 0.705221i | \(-0.249152\pi\) | ||||
0.708987 | + | 0.705221i | \(0.249152\pi\) | |||||||
\(420\) | 13.1183 | + | 18.0557i | 0.0312339 | + | 0.0429898i | ||||
\(421\) | −78.8474 | − | 242.667i | −0.187286 | − | 0.576407i | 0.812694 | − | 0.582690i | \(-0.198000\pi\) |
−0.999980 | + | 0.00628320i | \(0.998000\pi\) | |||||||
\(422\) | 3.89406 | − | 11.9847i | 0.00922764 | − | 0.0283998i | ||||
\(423\) | 197.820 | + | 143.725i | 0.467660 | + | 0.339775i | ||||
\(424\) | 86.5552 | − | 119.133i | 0.204140 | − | 0.280974i | ||||
\(425\) | −98.3696 | − | 31.9622i | −0.231458 | − | 0.0752052i | ||||
\(426\) | 120.670 | − | 39.2080i | 0.283263 | − | 0.0920376i | ||||
\(427\) | 294.053 | − | 213.642i | 0.688649 | − | 0.500333i | ||||
\(428\) | − | 153.153i | − | 0.357835i | ||||||
\(429\) | −66.3107 | + | 249.445i | −0.154570 | + | 0.581457i | ||||
\(430\) | 237.531 | 0.552398 | ||||||||
\(431\) | 388.839 | + | 535.191i | 0.902178 | + | 1.24174i | 0.969768 | + | 0.244029i | \(0.0784691\pi\) |
−0.0675899 | + | 0.997713i | \(0.521531\pi\) | |||||||
\(432\) | 20.1813 | + | 62.1118i | 0.0467161 | + | 0.143777i | ||||
\(433\) | 33.9998 | − | 104.641i | 0.0785215 | − | 0.241664i | −0.904089 | − | 0.427345i | \(-0.859449\pi\) |
0.982610 | + | 0.185681i | \(0.0594490\pi\) | |||||||
\(434\) | −118.246 | − | 85.9107i | −0.272456 | − | 0.197951i | ||||
\(435\) | 25.2401 | − | 34.7400i | 0.0580232 | − | 0.0798621i | ||||
\(436\) | 23.0377 | + | 7.48541i | 0.0528388 | + | 0.0171684i | ||||
\(437\) | −452.663 | + | 147.079i | −1.03584 | + | 0.336566i | ||||
\(438\) | −26.8232 | + | 19.4882i | −0.0612401 | + | 0.0444936i | ||||
\(439\) | − | 549.236i | − | 1.25111i | −0.780181 | − | 0.625553i | \(-0.784873\pi\) | ||
0.780181 | − | 0.625553i | \(-0.215127\pi\) | |||||||
\(440\) | −93.1389 | + | 5.06574i | −0.211679 | + | 0.0115130i | ||||
\(441\) | −273.550 | −0.620295 | ||||||||
\(442\) | 131.860 | + | 181.490i | 0.298326 | + | 0.410611i | ||||
\(443\) | −10.8704 | − | 33.4556i | −0.0245381 | − | 0.0755205i | 0.938038 | − | 0.346534i | \(-0.112641\pi\) |
−0.962576 | + | 0.271013i | \(0.912641\pi\) | |||||||
\(444\) | −2.46608 | + | 7.58981i | −0.00555423 | + | 0.0170942i | ||||
\(445\) | −165.587 | − | 120.306i | −0.372105 | − | 0.270350i | ||||
\(446\) | 172.112 | − | 236.892i | 0.385901 | − | 0.531148i | ||||
\(447\) | −46.9588 | − | 15.2578i | −0.105053 | − | 0.0341339i | ||||
\(448\) | −29.6378 | + | 9.62991i | −0.0661558 | + | 0.0214953i | ||||
\(449\) | 456.315 | − | 331.532i | 1.01629 | − | 0.738379i | 0.0507723 | − | 0.998710i | \(-0.483832\pi\) |
0.965519 | + | 0.260331i | \(0.0838317\pi\) | |||||||
\(450\) | − | 183.123i | − | 0.406940i | ||||||
\(451\) | −370.020 | + | 300.849i | −0.820444 | + | 0.667070i | ||||
\(452\) | −189.750 | −0.419801 | ||||||||
\(453\) | 47.0627 | + | 64.7762i | 0.103891 | + | 0.142994i | ||||
\(454\) | 42.4253 | + | 130.572i | 0.0934479 | + | 0.287603i | ||||
\(455\) | −88.6205 | + | 272.746i | −0.194770 | + | 0.599441i | ||||
\(456\) | 34.2870 | + | 24.9109i | 0.0751907 | + | 0.0546293i | ||||
\(457\) | 399.901 | − | 550.416i | 0.875056 | − | 1.20441i | −0.102710 | − | 0.994711i | \(-0.532751\pi\) |
0.977766 | − | 0.209700i | \(-0.0672487\pi\) | |||||||
\(458\) | −77.7755 | − | 25.2708i | −0.169816 | − | 0.0551764i | ||||
\(459\) | −100.306 | + | 32.5914i | −0.218531 | + | 0.0710052i | ||||
\(460\) | −147.234 | + | 106.972i | −0.320073 | + | 0.232547i | ||||
\(461\) | 202.839i | 0.439998i | 0.975500 | + | 0.219999i | \(0.0706053\pi\) | ||||
−0.975500 | + | 0.219999i | \(0.929395\pi\) | |||||||
\(462\) | 31.4402 | − | 48.6236i | 0.0680523 | − | 0.105246i | ||||
\(463\) | −746.270 | −1.61182 | −0.805908 | − | 0.592041i | \(-0.798322\pi\) | ||||
−0.805908 | + | 0.592041i | \(0.798322\pi\) | |||||||
\(464\) | 35.2430 | + | 48.5079i | 0.0759548 | + | 0.104543i | ||||
\(465\) | 23.4868 | + | 72.2849i | 0.0505092 | + | 0.155451i | ||||
\(466\) | 30.6951 | − | 94.4698i | 0.0658693 | − | 0.202725i | ||||
\(467\) | −301.368 | − | 218.957i | −0.645328 | − | 0.468858i | 0.216348 | − | 0.976316i | \(-0.430585\pi\) |
−0.861677 | + | 0.507458i | \(0.830585\pi\) | |||||||
\(468\) | −233.454 | + | 321.322i | −0.498834 | + | 0.686586i | ||||
\(469\) | −200.341 | − | 65.0947i | −0.427166 | − | 0.138795i | ||||
\(470\) | 121.922 | − | 39.6150i | 0.259409 | − | 0.0842872i | ||||
\(471\) | −179.735 | + | 130.585i | −0.381604 | + | 0.277251i | ||||
\(472\) | 267.027i | 0.565734i | ||||||||
\(473\) | −221.984 | − | 574.890i | −0.469310 | − | 1.21541i | ||||
\(474\) | −104.470 | −0.220401 | ||||||||
\(475\) | −147.586 | − | 203.134i | −0.310707 | − | 0.427651i | ||||
\(476\) | −15.5516 | − | 47.8629i | −0.0326714 | − | 0.100552i | ||||
\(477\) | −130.106 | + | 400.425i | −0.272759 | + | 0.839466i | ||||
\(478\) | 75.5394 | + | 54.8826i | 0.158032 | + | 0.114817i | ||||
\(479\) | 336.874 | − | 463.668i | 0.703287 | − | 0.967991i | −0.296629 | − | 0.954993i | \(-0.595862\pi\) |
0.999916 | − | 0.0129981i | \(-0.00413753\pi\) | |||||||
\(480\) | 15.4120 | + | 5.00766i | 0.0321083 | + | 0.0104326i | ||||
\(481\) | −97.5271 | + | 31.6885i | −0.202759 | + | 0.0658804i | ||||
\(482\) | −56.7986 | + | 41.2666i | −0.117839 | + | 0.0856153i | ||||
\(483\) | − | 112.974i | − | 0.233900i | ||||||
\(484\) | 99.3031 | + | 220.687i | 0.205172 | + | 0.455966i | ||||
\(485\) | 107.964 | 0.222607 | ||||||||
\(486\) | −167.566 | − | 230.635i | −0.344786 | − | 0.474557i | ||||
\(487\) | 13.0777 | + | 40.2489i | 0.0268535 | + | 0.0826467i | 0.963585 | − | 0.267402i | \(-0.0861651\pi\) |
−0.936732 | + | 0.350049i | \(0.886165\pi\) | |||||||
\(488\) | 81.5541 | − | 250.998i | 0.167119 | − | 0.514339i | ||||
\(489\) | −248.634 | − | 180.643i | −0.508453 | − | 0.369413i | ||||
\(490\) | −84.2984 | + | 116.027i | −0.172038 | + | 0.236789i | ||||
\(491\) | 582.692 | + | 189.328i | 1.18675 | + | 0.385597i | 0.834868 | − | 0.550450i | \(-0.185544\pi\) |
0.351877 | + | 0.936046i | \(0.385544\pi\) | |||||||
\(492\) | 78.7962 | − | 25.6024i | 0.160155 | − | 0.0520375i | ||||
\(493\) | −78.3366 | + | 56.9149i | −0.158898 | + | 0.115446i | ||||
\(494\) | 544.585i | 1.10240i | ||||||||
\(495\) | 248.791 | − | 96.0663i | 0.502608 | − | 0.194073i | ||||
\(496\) | −106.126 | −0.213965 | ||||||||
\(497\) | −214.983 | − | 295.898i | −0.432561 | − | 0.595368i | ||||
\(498\) | 11.9531 | + | 36.7878i | 0.0240021 | + | 0.0738710i | ||||
\(499\) | −143.126 | + | 440.498i | −0.286826 | + | 0.882761i | 0.699019 | + | 0.715103i | \(0.253620\pi\) |
−0.985845 | + | 0.167658i | \(0.946380\pi\) | |||||||
\(500\) | −198.945 | − | 144.542i | −0.397889 | − | 0.289083i | ||||
\(501\) | 70.2530 | − | 96.6950i | 0.140226 | − | 0.193004i | ||||
\(502\) | 88.7765 | + | 28.8452i | 0.176846 | + | 0.0574606i | ||||
\(503\) | 717.814 | − | 233.232i | 1.42707 | − | 0.463682i | 0.509226 | − | 0.860633i | \(-0.329932\pi\) |
0.917840 | + | 0.396951i | \(0.129932\pi\) | |||||||
\(504\) | 72.0839 | − | 52.3720i | 0.143024 | − | 0.103913i | ||||
\(505\) | − | 7.43085i | − | 0.0147145i | ||||||
\(506\) | 396.497 | + | 256.376i | 0.783591 | + | 0.506672i | ||||
\(507\) | 414.721 | 0.817990 | ||||||||
\(508\) | 156.846 | + | 215.879i | 0.308751 | + | 0.424959i | ||||
\(509\) | 216.406 | + | 666.029i | 0.425159 | + | 1.30850i | 0.902842 | + | 0.429972i | \(0.141477\pi\) |
−0.477683 | + | 0.878532i | \(0.658523\pi\) | |||||||
\(510\) | −8.08700 | + | 24.8892i | −0.0158569 | + | 0.0488024i | ||||
\(511\) | 77.3219 | + | 56.1776i | 0.151315 | + | 0.109937i | ||||
\(512\) | −13.3001 | + | 18.3060i | −0.0259767 | + | 0.0357538i | ||||
\(513\) | −243.499 | − | 79.1177i | −0.474658 | − | 0.154226i | ||||
\(514\) | 366.456 | − | 119.069i | 0.712950 | − | 0.231651i | ||||
\(515\) | 73.6240 | − | 53.4910i | 0.142959 | − | 0.103866i | ||||
\(516\) | 107.064i | 0.207488i | ||||||||
\(517\) | −209.821 | − | 258.063i | −0.405844 | − | 0.499156i | ||||
\(518\) | 23.0047 | 0.0444106 | ||||||||
\(519\) | −71.1741 | − | 97.9627i | −0.137137 | − | 0.188753i | ||||
\(520\) | 64.3472 | + | 198.040i | 0.123745 | + | 0.380846i | ||||
\(521\) | 72.6318 | − | 223.538i | 0.139408 | − | 0.429055i | −0.856841 | − | 0.515580i | \(-0.827576\pi\) |
0.996250 | + | 0.0865255i | \(0.0275764\pi\) | |||||||
\(522\) | −138.693 | − | 100.766i | −0.265695 | − | 0.193038i | ||||
\(523\) | −381.075 | + | 524.505i | −0.728633 | + | 1.00288i | 0.270559 | + | 0.962703i | \(0.412791\pi\) |
−0.999193 | + | 0.0401744i | \(0.987209\pi\) | |||||||
\(524\) | −80.6021 | − | 26.1892i | −0.153821 | − | 0.0499794i | ||||
\(525\) | 56.6814 | − | 18.4169i | 0.107965 | − | 0.0350798i | ||||
\(526\) | −75.9513 | + | 55.1819i | −0.144394 | + | 0.104908i | ||||
\(527\) | − | 171.386i | − | 0.325211i | ||||||
\(528\) | −2.28332 | − | 41.9811i | −0.00432446 | − | 0.0795097i | ||||
\(529\) | 392.234 | 0.741463 | ||||||||
\(530\) | 129.747 | + | 178.582i | 0.244806 | + | 0.336947i | ||||
\(531\) | −235.927 | − | 726.109i | −0.444307 | − | 1.36744i | ||||
\(532\) | 37.7525 | − | 116.190i | 0.0709634 | − | 0.218403i | ||||
\(533\) | 861.293 | + | 625.766i | 1.61593 | + | 1.17405i | ||||
\(534\) | 54.2263 | − | 74.6360i | 0.101547 | − | 0.139768i | ||||
\(535\) | 218.342 | + | 70.9436i | 0.408116 | + | 0.132605i | ||||
\(536\) | −145.467 | + | 47.2651i | −0.271394 | + | 0.0881812i | ||||
\(537\) | 153.325 | − | 111.397i | 0.285521 | − | 0.207443i | ||||
\(538\) | − | 258.416i | − | 0.480327i | ||||||
\(539\) | 359.597 | + | 95.5927i | 0.667156 | + | 0.177352i | ||||
\(540\) | −97.8977 | −0.181292 | ||||||||
\(541\) | −194.429 | − | 267.608i | −0.359388 | − | 0.494655i | 0.590590 | − | 0.806972i | \(-0.298895\pi\) |
−0.949978 | + | 0.312317i | \(0.898895\pi\) | |||||||
\(542\) | −174.806 | − | 537.998i | −0.322521 | − | 0.992617i | ||||
\(543\) | −31.5504 | + | 97.1021i | −0.0581038 | + | 0.178825i | ||||
\(544\) | −29.5628 | − | 21.4786i | −0.0543433 | − | 0.0394827i | ||||
\(545\) | −21.3431 | + | 29.3762i | −0.0391616 | + | 0.0539013i | ||||
\(546\) | −122.937 | − | 39.9445i | −0.225158 | − | 0.0731584i | ||||
\(547\) | −575.496 | + | 186.990i | −1.05209 | + | 0.341846i | −0.783490 | − | 0.621404i | \(-0.786562\pi\) |
−0.268604 | + | 0.963251i | \(0.586562\pi\) | |||||||
\(548\) | 220.084 | − | 159.901i | 0.401614 | − | 0.291789i | ||||
\(549\) | 754.578i | 1.37446i | ||||||||
\(550\) | −63.9928 | + | 240.726i | −0.116350 | + | 0.437683i | ||||
\(551\) | −235.060 | −0.426606 | ||||||||
\(552\) | −48.2160 | − | 66.3636i | −0.0873478 | − | 0.120224i | ||||
\(553\) | 93.0609 | + | 286.412i | 0.168284 | + | 0.517924i | ||||
\(554\) | 20.3741 | − | 62.7050i | 0.0367764 | − | 0.113186i | ||||
\(555\) | −9.67803 | − | 7.03150i | −0.0174379 | − | 0.0126694i | ||||
\(556\) | 119.001 | − | 163.791i | 0.214031 | − | 0.294588i | ||||
\(557\) | −242.301 | − | 78.7283i | −0.435010 | − | 0.141343i | 0.0833221 | − | 0.996523i | \(-0.473447\pi\) |
−0.518332 | + | 0.855179i | \(0.673447\pi\) | |||||||
\(558\) | 288.583 | − | 93.7663i | 0.517174 | − | 0.168040i | ||||
\(559\) | −1113.00 | + | 808.642i | −1.99106 | + | 1.44659i | ||||
\(560\) | − | 46.7137i | − | 0.0834174i | ||||||
\(561\) | 67.7964 | − | 3.68738i | 0.120849 | − | 0.00657288i | ||||
\(562\) | −712.280 | −1.26740 | ||||||||
\(563\) | −594.763 | − | 818.621i | −1.05642 | − | 1.45403i | −0.883110 | − | 0.469166i | \(-0.844554\pi\) |
−0.173308 | − | 0.984868i | \(-0.555446\pi\) | |||||||
\(564\) | 17.8559 | + | 54.9549i | 0.0316594 | + | 0.0974377i | ||||
\(565\) | 87.8960 | − | 270.516i | 0.155568 | − | 0.478789i | ||||
\(566\) | −64.3140 | − | 46.7268i | −0.113629 | − | 0.0825562i | ||||
\(567\) | −130.926 | + | 180.204i | −0.230910 | + | 0.317821i | ||||
\(568\) | −252.573 | − | 82.0658i | −0.444670 | − | 0.144482i | ||||
\(569\) | −418.918 | + | 136.115i | −0.736236 | + | 0.239217i | −0.653048 | − | 0.757316i | \(-0.726510\pi\) |
−0.0831875 | + | 0.996534i | \(0.526510\pi\) | |||||||
\(570\) | −51.3965 | + | 37.3418i | −0.0901694 | + | 0.0655119i | ||||
\(571\) | − | 577.275i | − | 1.01099i | −0.862830 | − | 0.505495i | \(-0.831310\pi\) | ||
0.862830 | − | 0.505495i | \(-0.168690\pi\) | |||||||
\(572\) | 419.176 | − | 340.815i | 0.732825 | − | 0.595831i | ||||
\(573\) | −32.9002 | −0.0574175 | ||||||||
\(574\) | −140.381 | − | 193.218i | −0.244567 | − | 0.336618i | ||||
\(575\) | 150.179 | + | 462.203i | 0.261181 | + | 0.803832i | ||||
\(576\) | 19.9921 | − | 61.5293i | 0.0347085 | − | 0.106822i | ||||
\(577\) | 666.510 | + | 484.248i | 1.15513 | + | 0.839251i | 0.989155 | − | 0.146879i | \(-0.0469226\pi\) |
0.165976 | + | 0.986130i | \(0.446923\pi\) | |||||||
\(578\) | −205.546 | + | 282.910i | −0.355616 | + | 0.489463i | ||||
\(579\) | 194.465 | + | 63.1856i | 0.335864 | + | 0.109129i | ||||
\(580\) | −85.4803 | + | 27.7742i | −0.147380 | + | 0.0478866i | ||||
\(581\) | 90.2084 | − | 65.5402i | 0.155264 | − | 0.112806i | ||||
\(582\) | 48.6635i | 0.0836142i | ||||||||
\(583\) | 310.962 | − | 480.916i | 0.533382 | − | 0.824899i | ||||
\(584\) | 69.3969 | 0.118830 | ||||||||
\(585\) | −349.950 | − | 481.665i | −0.598206 | − | 0.823360i | ||||
\(586\) | 81.5678 | + | 251.040i | 0.139194 | + | 0.428395i | ||||
\(587\) | −70.2908 | + | 216.333i | −0.119746 | + | 0.368540i | −0.992907 | − | 0.118891i | \(-0.962066\pi\) |
0.873161 | + | 0.487431i | \(0.162066\pi\) | |||||||
\(588\) | −52.2975 | − | 37.9964i | −0.0889414 | − | 0.0646197i | ||||
\(589\) | 244.549 | − | 336.593i | 0.415194 | − | 0.571465i | ||||
\(590\) | −380.685 | − | 123.692i | −0.645228 | − | 0.209647i | ||||
\(591\) | −246.622 | + | 80.1325i | −0.417297 | + | 0.135588i | ||||
\(592\) | 13.5136 | − | 9.81817i | 0.0228269 | − | 0.0165847i | ||||
\(593\) | 154.112i | 0.259885i | 0.991522 | + | 0.129942i | \(0.0414792\pi\) | ||||
−0.991522 | + | 0.129942i | \(0.958521\pi\) | |||||||
\(594\) | 91.4899 | + | 236.939i | 0.154023 | + | 0.398887i | ||||
\(595\) | 75.4392 | 0.126789 | ||||||||
\(596\) | 60.7459 | + | 83.6095i | 0.101923 | + | 0.140284i | ||||
\(597\) | −73.7979 | − | 227.127i | −0.123615 | − | 0.380446i | ||||
\(598\) | 325.724 | − | 1002.47i | 0.544689 | − | 1.67638i | ||||
\(599\) | −357.063 | − | 259.422i | −0.596099 | − | 0.433091i | 0.248393 | − | 0.968659i | \(-0.420097\pi\) |
−0.844492 | + | 0.535568i | \(0.820097\pi\) | |||||||
\(600\) | 25.4360 | − | 35.0096i | 0.0423933 | − | 0.0583493i | ||||
\(601\) | 1074.30 | + | 349.062i | 1.78753 | + | 0.580802i | 0.999397 | − | 0.0347090i | \(-0.0110504\pi\) |
0.788128 | + | 0.615511i | \(0.211050\pi\) | |||||||
\(602\) | 293.523 | − | 95.3713i | 0.487579 | − | 0.158424i | ||||
\(603\) | 353.799 | − | 257.050i | 0.586731 | − | 0.426285i | ||||
\(604\) | − | 167.589i | − | 0.277465i | ||||||
\(605\) | −360.621 | + | 39.3441i | −0.596067 | + | 0.0650315i | ||||
\(606\) | 3.34935 | 0.00552699 | ||||||||
\(607\) | 156.362 | + | 215.214i | 0.257599 | + | 0.354554i | 0.918154 | − | 0.396223i | \(-0.129679\pi\) |
−0.660556 | + | 0.750777i | \(0.729679\pi\) | |||||||
\(608\) | −27.4120 | − | 84.3655i | −0.0450856 | − | 0.138759i | ||||
\(609\) | 17.2413 | − | 53.0632i | 0.0283108 | − | 0.0871317i | ||||
\(610\) | 320.056 | + | 232.534i | 0.524682 | + | 0.381204i | ||||
\(611\) | −436.429 | + | 600.692i | −0.714286 | + | 0.983130i | ||||
\(612\) | 99.3653 | + | 32.2857i | 0.162362 | + | 0.0527545i | ||||
\(613\) | −206.889 | + | 67.2223i | −0.337503 | + | 0.109661i | −0.472865 | − | 0.881135i | \(-0.656780\pi\) |
0.135362 | + | 0.990796i | \(0.456780\pi\) | |||||||
\(614\) | −567.320 | + | 412.182i | −0.923974 | + | 0.671306i | ||||
\(615\) | 124.195i | 0.201943i | ||||||||
\(616\) | −113.060 | + | 43.6561i | −0.183539 | + | 0.0708704i | ||||
\(617\) | 828.147 | 1.34222 | 0.671108 | − | 0.741360i | \(-0.265819\pi\) | ||||
0.671108 | + | 0.741360i | \(0.265819\pi\) | |||||||
\(618\) | 24.1103 | + | 33.1850i | 0.0390135 | + | 0.0536975i | ||||
\(619\) | 110.604 | + | 340.406i | 0.178683 | + | 0.549928i | 0.999782 | − | 0.0208561i | \(-0.00663920\pi\) |
−0.821100 | + | 0.570784i | \(0.806639\pi\) | |||||||
\(620\) | 49.1599 | − | 151.299i | 0.0792902 | − | 0.244030i | ||||
\(621\) | 400.913 | + | 291.280i | 0.645593 | + | 0.469051i | ||||
\(622\) | −309.326 | + | 425.750i | −0.497308 | + | 0.684486i | ||||
\(623\) | −252.924 | − | 82.1799i | −0.405977 | − | 0.131910i | ||||
\(624\) | −89.2639 | + | 29.0036i | −0.143051 | + | 0.0464802i | ||||
\(625\) | −25.6267 | + | 18.6189i | −0.0410027 | + | 0.0297902i | ||||
\(626\) | 346.926i | 0.554195i | ||||||||
\(627\) | 138.410 | + | 89.4960i | 0.220749 | + | 0.142737i | ||||
\(628\) | 465.011 | 0.740464 | ||||||||
\(629\) | 15.8556 | + | 21.8234i | 0.0252077 | + | 0.0346954i | ||||
\(630\) | 41.2732 | + | 127.026i | 0.0655130 | + | 0.201628i | ||||
\(631\) | 193.271 | − | 594.828i | 0.306293 | − | 0.942674i | −0.672898 | − | 0.739735i | \(-0.734951\pi\) |
0.979191 | − | 0.202939i | \(-0.0650493\pi\) | |||||||
\(632\) | 176.904 | + | 128.528i | 0.279911 | + | 0.203368i | ||||
\(633\) | −5.00457 | + | 6.88820i | −0.00790612 | + | 0.0108818i | ||||
\(634\) | 80.9071 | + | 26.2883i | 0.127614 | + | 0.0414642i | ||||
\(635\) | −380.421 | + | 123.606i | −0.599088 | + | 0.194656i | ||||
\(636\) | −80.4933 | + | 58.4818i | −0.126562 | + | 0.0919525i | ||||
\(637\) | − | 830.650i | − | 1.30400i | ||||||
\(638\) | 147.106 | + | 180.929i | 0.230574 | + | 0.283588i | ||||
\(639\) | 759.313 | 1.18828 | ||||||||
\(640\) | −19.9369 | − | 27.4408i | −0.0311515 | − | 0.0428763i | ||||
\(641\) | −184.027 | − | 566.377i | −0.287094 | − | 0.883583i | −0.985763 | − | 0.168139i | \(-0.946224\pi\) |
0.698670 | − | 0.715444i | \(-0.253776\pi\) | |||||||
\(642\) | −31.9769 | + | 98.4148i | −0.0498082 | + | 0.153294i | ||||
\(643\) | −594.110 | − | 431.646i | −0.923965 | − | 0.671300i | 0.0205425 | − | 0.999789i | \(-0.493461\pi\) |
−0.944508 | + | 0.328489i | \(0.893461\pi\) | |||||||
\(644\) | −138.990 | + | 191.303i | −0.215823 | + | 0.297055i | ||||
\(645\) | −152.635 | − | 49.5941i | −0.236644 | − | 0.0768902i | ||||
\(646\) | 136.244 | − | 44.2684i | 0.210904 | − | 0.0685269i | ||||
\(647\) | −740.468 | + | 537.981i | −1.14446 | + | 0.831501i | −0.987735 | − | 0.156141i | \(-0.950095\pi\) |
−0.156728 | + | 0.987642i | \(0.550095\pi\) | |||||||
\(648\) | 161.735i | 0.249590i | ||||||||
\(649\) | 56.3992 | + | 1036.96i | 0.0869016 | + | 1.59778i | ||||
\(650\) | 556.063 | 0.855482 | ||||||||
\(651\) | 58.0463 | + | 79.8939i | 0.0891649 | + | 0.122725i | ||||
\(652\) | 198.780 | + | 611.781i | 0.304877 | + | 0.938314i | ||||
\(653\) | 146.502 | − | 450.888i | 0.224353 | − | 0.690487i | −0.774004 | − | 0.633181i | \(-0.781749\pi\) |
0.998357 | − | 0.0573062i | \(-0.0182511\pi\) | |||||||
\(654\) | −13.2409 | − | 9.62010i | −0.0202461 | − | 0.0147096i | ||||
\(655\) | 74.6730 | − | 102.779i | 0.114005 | − | 0.156914i | ||||
\(656\) | −164.927 | − | 53.5881i | −0.251414 | − | 0.0816892i | ||||
\(657\) | −188.707 | + | 61.3145i | −0.287225 | + | 0.0933249i | ||||
\(658\) | 134.757 | − | 97.9063i | 0.204797 | − | 0.148794i | ||||
\(659\) | − | 482.603i | − | 0.732326i | −0.930551 | − | 0.366163i | \(-0.880671\pi\) | ||
0.930551 | − | 0.366163i | \(-0.119329\pi\) | |||||||
\(660\) | 60.9078 | + | 16.1913i | 0.0922845 | + | 0.0245323i | ||||
\(661\) | 45.0509 | 0.0681557 | 0.0340779 | − | 0.999419i | \(-0.489151\pi\) | ||||
0.0340779 | + | 0.999419i | \(0.489151\pi\) | |||||||
\(662\) | −74.6040 | − | 102.684i | −0.112695 | − | 0.155111i | ||||
\(663\) | −46.8387 | − | 144.155i | −0.0706466 | − | 0.217428i | ||||
\(664\) | 25.0188 | − | 77.0000i | 0.0376789 | − | 0.115964i | ||||
\(665\) | 148.158 | + | 107.643i | 0.222794 | + | 0.161870i | ||||
\(666\) | −28.0719 | + | 38.6376i | −0.0421500 | + | 0.0580144i | ||||
\(667\) | 432.699 | + | 140.592i | 0.648724 | + | 0.210783i | ||||
\(668\) | −237.925 | + | 77.3065i | −0.356175 | + | 0.115728i | ||||
\(669\) | −160.058 | + | 116.289i | −0.239250 | + | 0.173825i | ||||
\(670\) | − | 229.278i | − | 0.342207i | ||||||
\(671\) | 263.689 | − | 991.936i | 0.392979 | − | 1.47830i | ||||
\(672\) | 21.0556 | 0.0313327 | ||||||||
\(673\) | −179.880 | − | 247.583i | −0.267280 | − | 0.367880i | 0.654189 | − | 0.756331i | \(-0.273010\pi\) |
−0.921469 | + | 0.388451i | \(0.873010\pi\) | |||||||
\(674\) | −53.8135 | − | 165.621i | −0.0798421 | − | 0.245729i | ||||
\(675\) | −80.7852 | + | 248.631i | −0.119682 | + | 0.368343i | ||||
\(676\) | −702.265 | − | 510.225i | −1.03885 | − | 0.754771i | ||||
\(677\) | −64.6416 | + | 88.9715i | −0.0954824 | + | 0.131420i | −0.854085 | − | 0.520133i | \(-0.825882\pi\) |
0.758603 | + | 0.651553i | \(0.225882\pi\) | |||||||
\(678\) | 121.931 | + | 39.6179i | 0.179840 | + | 0.0584335i | ||||
\(679\) | 133.414 | − | 43.3489i | 0.196486 | − | 0.0638422i | ||||
\(680\) | 44.3149 | − | 32.1967i | 0.0651690 | − | 0.0473481i | ||||
\(681\) | − | 92.7621i | − | 0.136215i | ||||||
\(682\) | −412.126 | + | 22.4152i | −0.604290 | + | 0.0328668i | ||||
\(683\) | −490.810 | −0.718610 | −0.359305 | − | 0.933220i | \(-0.616986\pi\) | ||||
−0.359305 | + | 0.933220i | \(0.616986\pi\) | |||||||
\(684\) | 149.080 | + | 205.191i | 0.217953 | + | 0.299986i | ||||
\(685\) | 126.014 | + | 387.831i | 0.183962 | + | 0.566177i | ||||
\(686\) | −140.998 | + | 433.948i | −0.205537 | + | 0.632578i | ||||
\(687\) | 44.7015 | + | 32.4775i | 0.0650676 | + | 0.0472744i | ||||
\(688\) | 131.719 | − | 181.296i | 0.191452 | − | 0.263512i | ||||
\(689\) | −1215.91 | − | 395.074i | −1.76475 | − | 0.573403i | ||||
\(690\) | 116.946 | − | 37.9979i | 0.169486 | − | 0.0550694i | ||||
\(691\) | 632.920 | − | 459.843i | 0.915947 | − | 0.665475i | −0.0265646 | − | 0.999647i | \(-0.508457\pi\) |
0.942512 | + | 0.334172i | \(0.108457\pi\) | |||||||
\(692\) | 253.449i | 0.366256i | ||||||||
\(693\) | 268.865 | − | 218.604i | 0.387973 | − | 0.315445i | ||||
\(694\) | −449.778 | −0.648095 | ||||||||
\(695\) | 178.384 | + | 245.525i | 0.256668 | + | 0.353273i | ||||
\(696\) | −12.5189 | − | 38.5291i | −0.0179869 | − | 0.0553579i | ||||
\(697\) | 86.5408 | − | 266.345i | 0.124162 | − | 0.382131i | ||||
\(698\) | 304.147 | + | 220.975i | 0.435740 | + | 0.316584i | ||||
\(699\) | −39.4487 | + | 54.2965i | −0.0564360 | + | 0.0776775i | ||||
\(700\) | −118.639 | − | 38.5482i | −0.169484 | − | 0.0550688i | ||||
\(701\) | −298.888 | + | 97.1146i | −0.426374 | + | 0.138537i | −0.514340 | − | 0.857586i | \(-0.671963\pi\) |
0.0879664 | + | 0.996123i | \(0.471963\pi\) | |||||||
\(702\) | 458.720 | − | 333.279i | 0.653447 | − | 0.474757i | ||||
\(703\) | 65.4841i | 0.0931495i | ||||||||
\(704\) | −47.7823 | + | 73.8976i | −0.0678726 | + | 0.104968i | ||||
\(705\) | −86.6173 | −0.122861 | ||||||||
\(706\) | −207.399 | − | 285.460i | −0.293766 | − | 0.404334i | ||||
\(707\) | −2.98357 | − | 9.18247i | −0.00422004 | − | 0.0129879i | ||||
\(708\) | 55.7525 | − | 171.589i | 0.0787465 | − | 0.242357i | ||||
\(709\) | −53.5936 | − | 38.9380i | −0.0755904 | − | 0.0549197i | 0.549348 | − | 0.835593i | \(-0.314876\pi\) |
−0.624939 | + | 0.780674i | \(0.714876\pi\) | |||||||
\(710\) | 233.993 | − | 322.064i | 0.329568 | − | 0.453611i | ||||
\(711\) | −594.603 | − | 193.198i | −0.836291 | − | 0.271728i | ||||
\(712\) | −183.647 | + | 59.6706i | −0.257932 | + | 0.0838071i | ||||
\(713\) | −651.488 | + | 473.334i | −0.913728 | + | 0.663862i | ||||
\(714\) | 34.0032i | 0.0476235i | ||||||||
\(715\) | 291.711 | + | 755.468i | 0.407987 | + | 1.05660i | ||||
\(716\) | −396.682 | −0.554025 | ||||||||
\(717\) | −37.0819 | − | 51.0388i | −0.0517181 | − | 0.0711839i | ||||
\(718\) | −245.853 | − | 756.658i | −0.342414 | − | 1.05384i | ||||
\(719\) | −310.081 | + | 954.330i | −0.431267 | + | 1.32730i | 0.465598 | + | 0.884997i | \(0.345839\pi\) |
−0.896864 | + | 0.442306i | \(0.854161\pi\) | |||||||
\(720\) | 78.4582 | + | 57.0032i | 0.108970 | + | 0.0791711i | ||||
\(721\) | 69.5017 | − | 95.6609i | 0.0963963 | − | 0.132678i | ||||
\(722\) | −154.802 | − | 50.2983i | −0.214408 | − | 0.0696652i | ||||
\(723\) | 45.1142 | − | 14.6585i | 0.0623987 | − | 0.0202746i | ||||
\(724\) | 172.889 | − | 125.611i | 0.238797 | − | 0.173496i | ||||
\(725\) | 240.014i | 0.331054i | ||||||||
\(726\) | −17.7338 | − | 162.545i | −0.0244267 | − | 0.223891i | ||||
\(727\) | 364.375 | 0.501204 | 0.250602 | − | 0.968090i | \(-0.419371\pi\) | ||||
0.250602 | + | 0.968090i | \(0.419371\pi\) | |||||||
\(728\) | 159.031 | + | 218.887i | 0.218449 | + | 0.300669i | ||||
\(729\) | −99.5094 | − | 306.258i | −0.136501 | − | 0.420108i | ||||
\(730\) | −32.1460 | + | 98.9353i | −0.0440356 | + | 0.135528i | ||||
\(731\) | 292.780 | + | 212.717i | 0.400519 | + | 0.290994i | ||||
\(732\) | −104.812 | + | 144.261i | −0.143185 | + | 0.197078i | ||||
\(733\) | 900.076 | + | 292.452i | 1.22793 | + | 0.398980i | 0.849965 | − | 0.526838i | \(-0.176623\pi\) |
0.377969 | + | 0.925818i | \(0.376623\pi\) | |||||||
\(734\) | 37.7893 | − | 12.2785i | 0.0514841 | − | 0.0167282i | ||||
\(735\) | 78.3946 | − | 56.9570i | 0.106659 | − | 0.0774925i | ||||
\(736\) | 171.696i | 0.233282i | ||||||||
\(737\) | −554.916 | + | 214.271i | −0.752939 | + | 0.290734i | ||||
\(738\) | 495.823 | 0.671847 | ||||||||
\(739\) | 126.126 | + | 173.598i | 0.170672 | + | 0.234909i | 0.885781 | − | 0.464103i | \(-0.153623\pi\) |
−0.715110 | + | 0.699012i | \(0.753623\pi\) | |||||||
\(740\) | 7.73747 | + | 23.8135i | 0.0104560 | + | 0.0321804i | ||||
\(741\) | 113.704 | − | 349.945i | 0.153447 | − | 0.472261i | ||||
\(742\) | 232.034 | + | 168.583i | 0.312714 | + | 0.227200i | ||||
\(743\) | 25.6695 | − | 35.3310i | 0.0345484 | − | 0.0475518i | −0.791393 | − | 0.611307i | \(-0.790644\pi\) |
0.825942 | + | 0.563755i | \(0.190644\pi\) | |||||||
\(744\) | 68.1958 | + | 22.1582i | 0.0916610 | + | 0.0297825i | ||||
\(745\) | −147.336 | + | 47.8724i | −0.197767 | + | 0.0642583i | ||||
\(746\) | −179.645 | + | 130.520i | −0.240811 | + | 0.174959i | ||||
\(747\) | 231.486i | 0.309888i | ||||||||
\(748\) | −119.339 | − | 77.1649i | −0.159544 | − | 0.103162i | ||||
\(749\) | 298.295 | 0.398258 | ||||||||
\(750\) | 97.6609 | + | 134.419i | 0.130215 | + | 0.179225i | ||||
\(751\) | 157.978 | + | 486.208i | 0.210357 | + | 0.647414i | 0.999451 | + | 0.0331403i | \(0.0105508\pi\) |
−0.789093 | + | 0.614273i | \(0.789449\pi\) | |||||||
\(752\) | 37.3740 | − | 115.025i | 0.0496995 | − | 0.152959i | ||||
\(753\) | −51.0243 | − | 37.0713i | −0.0677613 | − | 0.0492315i | ||||
\(754\) | 305.982 | − | 421.148i | 0.405811 | − | 0.558551i | ||||
\(755\) | 238.922 | + | 77.6305i | 0.316453 | + | 0.102822i | ||||
\(756\) | −120.974 | + | 39.3070i | −0.160019 | + | 0.0519934i | ||||
\(757\) | 700.963 | − | 509.280i | 0.925975 | − | 0.672760i | −0.0190290 | − | 0.999819i | \(-0.506057\pi\) |
0.945004 | + | 0.327059i | \(0.106057\pi\) | |||||||
\(758\) | − | 880.114i | − | 1.16110i | ||||||
\(759\) | −201.256 | − | 247.529i | −0.265160 | − | 0.326126i | ||||
\(760\) | 132.973 | 0.174965 | ||||||||
\(761\) | 770.228 | + | 1060.13i | 1.01213 | + | 1.39307i | 0.917580 | + | 0.397552i | \(0.130140\pi\) |
0.0945463 | + | 0.995520i | \(0.469860\pi\) | |||||||
\(762\) | −55.7139 | − | 171.470i | −0.0731153 | − | 0.225026i | ||||
\(763\) | −14.5793 | + | 44.8703i | −0.0191078 | + | 0.0588078i | ||||
\(764\) | 55.7114 | + | 40.4767i | 0.0729206 | + | 0.0529799i | ||||
\(765\) | −92.0559 | + | 126.704i | −0.120335 | + | 0.165626i | ||||
\(766\) | 463.325 | + | 150.543i | 0.604863 | + | 0.196532i | ||||
\(767\) | 2204.87 | − | 716.406i | 2.87467 | − | 0.934036i | ||||
\(768\) | 12.3686 | − | 8.98631i | 0.0161049 | − | 0.0117009i | ||||
\(769\) | 1207.32i | 1.56999i | 0.619503 | + | 0.784994i | \(0.287334\pi\) | ||||
−0.619503 | + | 0.784994i | \(0.712666\pi\) | |||||||
\(770\) | −9.86649 | − | 181.406i | −0.0128136 | − | 0.235592i | ||||
\(771\) | −260.341 | −0.337667 | ||||||||
\(772\) | −251.560 | − | 346.243i | −0.325855 | − | 0.448501i | ||||
\(773\) | −247.836 | − | 762.760i | −0.320615 | − | 0.986753i | −0.973381 | − | 0.229193i | \(-0.926391\pi\) |
0.652766 | − | 0.757560i | \(-0.273609\pi\) | |||||||
\(774\) | −197.995 | + | 609.365i | −0.255807 | + | 0.787294i | ||||
\(775\) | −343.687 | − | 249.703i | −0.443467 | − | 0.322198i | ||||
\(776\) | 59.8700 | − | 82.4040i | 0.0771521 | − | 0.106191i | ||||
\(777\) | −14.7826 | − | 4.80316i | −0.0190252 | − | 0.00618167i | ||||
\(778\) | −390.077 | + | 126.744i | −0.501385 | + | 0.162910i | ||||
\(779\) | 550.006 | − | 399.603i | 0.706042 | − | 0.512969i | ||||
\(780\) | − | 140.694i | − | 0.180377i | ||||||
\(781\) | −998.160 | − | 265.344i | −1.27805 | − | 0.339749i | ||||
\(782\) | −277.276 | −0.354573 | ||||||||
\(783\) | 143.854 | + | 197.998i | 0.183721 | + | 0.252871i | ||||
\(784\) | 41.8113 | + | 128.682i | 0.0533307 | + | 0.164135i | ||||
\(785\) | −215.402 | + | 662.941i | −0.274398 | + | 0.844510i | ||||
\(786\) | 46.3260 | + | 33.6578i | 0.0589390 | + | 0.0428217i | ||||
\(787\) | −196.270 | + | 270.143i | −0.249390 | + | 0.343256i | −0.915298 | − | 0.402778i | \(-0.868045\pi\) |
0.665907 | + | 0.746034i | \(0.268045\pi\) | |||||||
\(788\) | 516.202 | + | 167.724i | 0.655079 | + | 0.212848i | ||||
\(789\) | 60.3270 | − | 19.6014i | 0.0764601 | − | 0.0248434i | ||||
\(790\) | −265.181 | + | 192.665i | −0.335672 | + | 0.243880i | ||||
\(791\) | − | 369.574i | − | 0.467224i | ||||||
\(792\) | 64.6405 | − | 243.162i | 0.0816168 | − | 0.307023i | ||||
\(793\) | −2291.32 | −2.88943 | ||||||||
\(794\) | −198.518 | − | 273.236i | −0.250022 | − | 0.344126i | ||||
\(795\) | −46.0881 | − | 141.845i | −0.0579725 | − | 0.178421i | ||||
\(796\) | −154.465 | + | 475.396i | −0.194052 | + | 0.597231i | ||||
\(797\) | −651.319 | − | 473.211i | −0.817213 | − | 0.593740i | 0.0986995 | − | 0.995117i | \(-0.468532\pi\) |
−0.915913 | + | 0.401377i | \(0.868532\pi\) | |||||||
\(798\) | −48.5188 | + | 66.7804i | −0.0608005 | + | 0.0836847i | ||||
\(799\) | 185.757 | + | 60.3563i | 0.232487 | + | 0.0755397i | ||||
\(800\) | −86.1436 | + | 27.9898i | −0.107680 | + | 0.0349872i | ||||
\(801\) | 446.660 | − | 324.517i | 0.557628 | − | 0.405140i | ||||
\(802\) | 191.509i | 0.238790i | ||||||||
\(803\) | 269.492 | − | 14.6574i | 0.335607 | − | 0.0182534i | ||||
\(804\) | 103.344 | 0.128537 | ||||||||
\(805\) | −208.347 | − | 286.766i | −0.258817 | − | 0.356231i | ||||
\(806\) | 284.727 | + | 876.299i | 0.353259 | + | 1.08722i | ||||
\(807\) | −53.9547 | + | 166.056i | −0.0668584 | + | 0.205769i | ||||
\(808\) | −5.67161 | − | 4.12066i | −0.00701932 | − | 0.00509983i | ||||
\(809\) | 698.652 | − | 961.612i | 0.863600 | − | 1.18864i | −0.117099 | − | 0.993120i | \(-0.537360\pi\) |
0.980699 | − | 0.195523i | \(-0.0626404\pi\) | |||||||
\(810\) | −230.576 | − | 74.9187i | −0.284662 | − | 0.0924922i | ||||
\(811\) | 838.169 | − | 272.338i | 1.03350 | − | 0.335805i | 0.257328 | − | 0.966324i | \(-0.417158\pi\) |
0.776174 | + | 0.630519i | \(0.217158\pi\) | |||||||
\(812\) | −94.4783 | + | 68.6425i | −0.116353 | + | 0.0845351i | ||||
\(813\) | 382.210i | 0.470123i | ||||||||
\(814\) | 50.4041 | − | 40.9816i | 0.0619215 | − | 0.0503459i | ||||
\(815\) | −964.261 | −1.18314 | ||||||||
\(816\) | 14.5122 | + | 19.9744i | 0.0177846 | + | 0.0244784i | ||||
\(817\) | 271.479 | + | 835.528i | 0.332288 | + | 1.02268i | ||||
\(818\) | −132.992 | + | 409.307i | −0.162582 | + | 0.500376i | ||||
\(819\) | −625.836 | − | 454.696i | −0.764146 | − | 0.555185i | ||||
\(820\) | 152.795 | − | 210.305i | 0.186336 | − | 0.256469i | ||||
\(821\) | −981.725 | − | 318.982i | −1.19577 | − | 0.388528i | −0.357565 | − | 0.933888i | \(-0.616393\pi\) |
−0.838202 | + | 0.545360i | \(0.816393\pi\) | |||||||
\(822\) | −174.810 | + | 56.7991i | −0.212664 | + | 0.0690987i | ||||
\(823\) | −650.900 | + | 472.906i | −0.790886 | + | 0.574613i | −0.908226 | − | 0.418479i | \(-0.862563\pi\) |
0.117340 | + | 0.993092i | \(0.462563\pi\) | |||||||
\(824\) | − | 85.8563i | − | 0.104195i | ||||||
\(825\) | 91.3822 | − | 141.327i | 0.110766 | − | 0.171305i | ||||
\(826\) | −520.085 | −0.629643 | ||||||||
\(827\) | −37.9422 | − | 52.2230i | −0.0458793 | − | 0.0631475i | 0.785461 | − | 0.618911i | \(-0.212426\pi\) |
−0.831340 | + | 0.555764i | \(0.812426\pi\) | |||||||
\(828\) | −151.699 | − | 466.882i | −0.183212 | − | 0.563867i | ||||
\(829\) | 188.558 | − | 580.323i | 0.227453 | − | 0.700028i | −0.770581 | − | 0.637343i | \(-0.780034\pi\) |
0.998033 | − | 0.0626852i | \(-0.0199664\pi\) | |||||||
\(830\) | 98.1854 | + | 71.3359i | 0.118296 | + | 0.0859468i | ||||
\(831\) | −26.1844 | + | 36.0397i | −0.0315095 | + | 0.0433691i | ||||
\(832\) | 186.837 | + | 60.7071i | 0.224564 | + | 0.0729653i | ||||
\(833\) | −207.812 | + | 67.5221i | −0.249474 | + | 0.0810589i | ||||
\(834\) | −110.667 | + | 80.4042i | −0.132694 | + | 0.0964079i | ||||
\(835\) | − | 375.006i | − | 0.449109i | ||||||
\(836\) | −124.269 | − | 321.831i | −0.148648 | − | 0.384965i | ||||
\(837\) | −433.183 | −0.517542 | ||||||||
\(838\) | 493.874 | + | 679.759i | 0.589348 | + | 0.811168i | ||||
\(839\) | −195.113 | − | 600.497i | −0.232554 | − | 0.715729i | −0.997436 | − | 0.0715585i | \(-0.977203\pi\) |
0.764882 | − | 0.644170i | \(-0.222797\pi\) | |||||||
\(840\) | −9.75337 | + | 30.0178i | −0.0116112 | + | 0.0357355i | ||||
\(841\) | −498.603 | − | 362.256i | −0.592869 | − | 0.430745i | ||||
\(842\) | 212.099 | − | 291.929i | 0.251899 | − | 0.346709i | ||||
\(843\) | 457.704 | + | 148.717i | 0.542946 | + | 0.176414i | ||||
\(844\) | 16.9489 | − | 5.50704i | 0.0200817 | − | 0.00652493i | ||||
\(845\) | 1052.70 | − | 764.833i | 1.24580 | − | 0.905128i | ||||
\(846\) | 345.803i | 0.408750i | ||||||||
\(847\) | −429.830 | + | 193.412i | −0.507474 | + | 0.228349i | ||||
\(848\) | 208.252 | 0.245580 | ||||||||
\(849\) | 31.5714 | + | 43.4543i | 0.0371866 | + | 0.0511829i | ||||
\(850\) | −45.2014 | − | 139.116i | −0.0531781 | − | 0.163665i | ||||
\(851\) | 39.1669 | − | 120.543i | 0.0460246 | − | 0.141649i | ||||
\(852\) | 145.166 | + | 105.469i | 0.170383 | + | 0.123790i | ||||
\(853\) | 253.913 | − | 349.481i | 0.297671 | − | 0.409709i | −0.633816 | − | 0.773484i | \(-0.718512\pi\) |
0.931487 | + | 0.363775i | \(0.118512\pi\) | |||||||
\(854\) | 488.866 | + | 158.842i | 0.572442 | + | 0.185998i | ||||
\(855\) | −361.585 | + | 117.486i | −0.422907 | + | 0.137411i | ||||
\(856\) | 175.226 | − | 127.309i | 0.204703 | − | 0.148726i | ||||
\(857\) | 137.536i | 0.160485i | 0.996775 | + | 0.0802425i | \(0.0255695\pi\) | ||||
−0.996775 | + | 0.0802425i | \(0.974431\pi\) | |||||||
\(858\) | −340.517 | + | 131.485i | −0.396873 | + | 0.153246i | ||||
\(859\) | −64.8174 | −0.0754568 | −0.0377284 | − | 0.999288i | \(-0.512012\pi\) | ||||
−0.0377284 | + | 0.999288i | \(0.512012\pi\) | |||||||
\(860\) | 197.449 | + | 271.765i | 0.229591 | + | 0.316006i | ||||
\(861\) | 49.8656 | + | 153.471i | 0.0579159 | + | 0.178247i | ||||
\(862\) | −289.100 | + | 889.759i | −0.335383 | + | 1.03220i | ||||
\(863\) | 817.704 | + | 594.097i | 0.947513 | + | 0.688409i | 0.950217 | − | 0.311588i | \(-0.100861\pi\) |
−0.00270429 | + | 0.999996i | \(0.500861\pi\) | |||||||
\(864\) | −54.2877 | + | 74.7206i | −0.0628330 | + | 0.0864822i | ||||
\(865\) | −361.328 | − | 117.403i | −0.417720 | − | 0.135726i | ||||
\(866\) | 147.984 | − | 48.0830i | 0.170883 | − | 0.0555231i | ||||
\(867\) | 191.151 | − | 138.879i | 0.220474 | − | 0.160183i | ||||
\(868\) | − | 206.701i | − | 0.238135i | ||||||
\(869\) | 714.127 | + | 461.756i | 0.821780 | + | 0.531365i | ||||
\(870\) | 60.7278 | 0.0698020 | ||||||||
\(871\) | 780.547 | + | 1074.33i | 0.896150 | + | 1.23345i | ||||
\(872\) | 10.5860 | + | 32.5803i | 0.0121399 | + | 0.0373627i | ||||
\(873\) | −89.9940 | + | 276.973i | −0.103086 | + | 0.317266i | ||||
\(874\) | −544.555 | − | 395.642i | −0.623060 | − | 0.452680i | ||||
\(875\) | 281.522 | − | 387.482i | 0.321740 | − | 0.442837i | ||||
\(876\) | −44.5937 | − | 14.4894i | −0.0509061 | − | 0.0165404i | ||||
\(877\) | 628.136 | − | 204.094i | 0.716233 | − | 0.232718i | 0.0718438 | − | 0.997416i | \(-0.477112\pi\) |
0.644389 | + | 0.764698i | \(0.277112\pi\) | |||||||
\(878\) | 628.393 | − | 456.554i | 0.715710 | − | 0.519994i | ||||
\(879\) | − | 178.346i | − | 0.202897i | ||||||
\(880\) | −83.2179 | − | 102.351i | −0.0945658 | − | 0.116308i | ||||
\(881\) | 1527.49 | 1.73382 | 0.866909 | − | 0.498466i | \(-0.166103\pi\) | ||||
0.866909 | + | 0.498466i | \(0.166103\pi\) | |||||||
\(882\) | −227.389 | − | 312.975i | −0.257811 | − | 0.354847i | ||||
\(883\) | −0.133623 | − | 0.411250i | −0.000151329 | − | 0.000465742i | 0.950981 | − | 0.309250i | \(-0.100078\pi\) |
−0.951132 | + | 0.308784i | \(0.900078\pi\) | |||||||
\(884\) | −98.0375 | + | 301.728i | −0.110902 | + | 0.341322i | ||||
\(885\) | 218.799 | + | 158.966i | 0.247230 | + | 0.179623i | ||||
\(886\) | 29.2412 | − | 40.2471i | 0.0330037 | − | 0.0454256i | ||||
\(887\) | −939.334 | − | 305.208i | −1.05900 | − | 0.344090i | −0.272806 | − | 0.962069i | \(-0.587952\pi\) |
−0.786195 | + | 0.617979i | \(0.787952\pi\) | |||||||
\(888\) | −10.7336 | + | 3.48756i | −0.0120874 | + | 0.00392743i | ||||
\(889\) | −420.466 | + | 305.486i | −0.472965 | + | 0.343629i | ||||
\(890\) | − | 289.456i | − | 0.325232i | ||||||
\(891\) | 34.1603 | + | 628.072i | 0.0383392 | + | 0.704906i | ||||
\(892\) | 414.102 | 0.464240 | ||||||||
\(893\) | 278.695 | + | 383.591i | 0.312089 | + | 0.429554i | ||||
\(894\) | −21.5778 | − | 66.4098i | −0.0241363 | − | 0.0742839i | ||||
\(895\) | 183.751 | − | 565.527i | 0.205308 | − | 0.631874i | ||||
\(896\) | −35.6543 | − | 25.9044i | −0.0397928 | − | 0.0289112i | ||||
\(897\) | −418.614 | + | 576.172i | −0.466682 | + | 0.642333i | ||||
\(898\) | 758.627 | + | 246.493i | 0.844796 | + | 0.274491i | ||||
\(899\) | −378.238 | + | 122.897i | −0.420732 | + | 0.136704i | ||||
\(900\) | 209.515 | − | 152.222i | 0.232795 | − | 0.169135i | ||||
\(901\) | 336.312i | 0.373265i | ||||||||
\(902\) | −651.789 | − | 173.267i | −0.722604 | − | 0.192092i | ||||
\(903\) | −208.527 | −0.230927 | ||||||||
\(904\) | −157.730 | − | 217.097i | −0.174481 | − | 0.240152i | ||||
\(905\) | 98.9912 | + | 304.664i | 0.109383 | + | 0.336645i | ||||
\(906\) | −34.9909 | + | 107.691i | −0.0386213 | + | 0.118864i | ||||
\(907\) | −581.102 | − | 422.195i | −0.640685 | − | 0.465485i | 0.219400 | − | 0.975635i | \(-0.429590\pi\) |
−0.860086 | + | 0.510150i | \(0.829590\pi\) | |||||||
\(908\) | −114.124 | + | 157.078i | −0.125687 | + | 0.172993i | ||||
\(909\) | 19.0632 | + | 6.19401i | 0.0209716 | + | 0.00681409i | ||||
\(910\) | −385.721 | + | 125.328i | −0.423869 | + | 0.137723i | ||||
\(911\) | −275.435 | + | 200.115i | −0.302343 | + | 0.219665i | −0.728604 | − | 0.684935i | \(-0.759831\pi\) |
0.426261 | + | 0.904600i | \(0.359831\pi\) | |||||||
\(912\) | 59.9358i | 0.0657191i | ||||||||
\(913\) | 80.8935 | − | 304.302i | 0.0886018 | − | 0.333299i | ||||
\(914\) | 962.162 | 1.05269 | ||||||||
\(915\) | −157.114 | − | 216.249i | −0.171709 | − | 0.236337i | ||||
\(916\) | −35.7383 | − | 109.991i | −0.0390156 | − | 0.120078i | ||||
\(917\) | 51.0084 | − | 156.988i | 0.0556253 | − | 0.171197i | ||||
\(918\) | −120.668 | − | 87.6706i | −0.131447 | − | 0.0955017i | ||||
\(919\) | 590.474 | − | 812.718i | 0.642518 | − | 0.884350i | −0.356229 | − | 0.934399i | \(-0.615938\pi\) |
0.998747 | + | 0.0500487i | \(0.0159377\pi\) | |||||||
\(920\) | −244.777 | − | 79.5330i | −0.266062 | − | 0.0864489i | ||||
\(921\) | 450.614 | − | 146.413i | 0.489266 | − | 0.158972i | ||||
\(922\) | −232.073 | + | 168.611i | −0.251706 | + | 0.182875i | ||||
\(923\) | 2305.70i | 2.49804i | ||||||||
\(924\) | 81.7662 | − | 4.44719i | 0.0884915 | − | 0.00481298i | ||||
\(925\) | 66.8642 | 0.0722856 | ||||||||
\(926\) | −620.340 | − | 853.825i | −0.669914 | − | 0.922057i | ||||
\(927\) | 75.8569 | + | 233.464i | 0.0818305 | + | 0.251849i | ||||
\(928\) | −26.2031 | + | 80.6447i | −0.0282361 | + | 0.0869017i | ||||
\(929\) | 273.837 | + | 198.954i | 0.294765 | + | 0.214159i | 0.725332 | − | 0.688399i | \(-0.241686\pi\) |
−0.430567 | + | 0.902559i | \(0.641686\pi\) | |||||||
\(930\) | −63.1793 | + | 86.9589i | −0.0679347 | + | 0.0935042i | ||||
\(931\) | −504.477 | − | 163.914i | −0.541865 | − | 0.176063i | ||||
\(932\) | 133.601 | − | 43.4094i | 0.143348 | − | 0.0465767i | ||||
\(933\) | 287.662 | − | 208.999i | 0.308319 | − | 0.224007i | ||||
\(934\) | − | 526.811i | − | 0.564037i | ||||||
\(935\) | 165.290 | − | 134.391i | 0.176781 | − | 0.143733i | ||||
\(936\) | −561.692 | −0.600098 | ||||||||
\(937\) | 16.1676 | + | 22.2528i | 0.0172547 | + | 0.0237490i | 0.817557 | − | 0.575847i | \(-0.195328\pi\) |
−0.800303 | + | 0.599596i | \(0.795328\pi\) | |||||||
\(938\) | −92.0578 | − | 283.325i | −0.0981426 | − | 0.302052i | ||||
\(939\) | 72.4348 | − | 222.931i | 0.0771404 | − | 0.237414i | ||||
\(940\) | 146.673 | + | 106.564i | 0.156035 | + | 0.113366i | ||||
\(941\) | −389.897 | + | 536.648i | −0.414344 | + | 0.570295i | −0.964271 | − | 0.264917i | \(-0.914655\pi\) |
0.549927 | + | 0.835212i | \(0.314655\pi\) | |||||||
\(942\) | −298.812 | − | 97.0898i | −0.317210 | − | 0.103068i | ||||
\(943\) | −1251.46 | + | 406.625i | −1.32711 | + | 0.431203i | ||||
\(944\) | −305.511 | + | 221.967i | −0.323635 | + | 0.235134i | ||||
\(945\) | − | 190.674i | − | 0.201772i | ||||||
\(946\) | 473.220 | − | 731.856i | 0.500232 | − | 0.773632i | ||||
\(947\) | −730.987 | −0.771898 | −0.385949 | − | 0.922520i | \(-0.626126\pi\) | ||||
−0.385949 | + | 0.922520i | \(0.626126\pi\) | |||||||
\(948\) | −86.8413 | − | 119.527i | −0.0916048 | − | 0.126083i | ||||
\(949\) | −186.185 | − | 573.018i | −0.196191 | − | 0.603813i | ||||
\(950\) | 109.729 | − | 337.712i | 0.115505 | − | 0.355487i | ||||
\(951\) | −46.5013 | − | 33.7852i | −0.0488973 | − | 0.0355260i | ||||
\(952\) | 41.8337 | − | 57.5791i | 0.0439429 | − | 0.0604823i | ||||
\(953\) | 362.664 | + | 117.837i | 0.380550 | + | 0.123648i | 0.493045 | − | 0.870004i | \(-0.335884\pi\) |
−0.112494 | + | 0.993652i | \(0.535884\pi\) | |||||||
\(954\) | −566.287 | + | 183.998i | −0.593592 | + | 0.192870i | ||||
\(955\) | −83.5119 | + | 60.6750i | −0.0874471 | + | 0.0635340i | ||||
\(956\) | 132.048i | 0.138125i | ||||||||
\(957\) | −56.7529 | − | 146.978i | −0.0593029 | − | 0.153582i | ||||
\(958\) | 810.521 | 0.846055 | ||||||||
\(959\) | 311.437 | + | 428.656i | 0.324752 | + | 0.446982i | ||||
\(960\) | 7.08190 | + | 21.7958i | 0.00737698 | + | 0.0227040i | ||||
\(961\) | −79.4400 | + | 244.491i | −0.0826639 | + | 0.254413i | ||||
\(962\) | −117.325 | − | 85.2418i | −0.121960 | − | 0.0886090i | ||||
\(963\) | −363.999 | + | 501.002i | −0.377985 | + | 0.520252i | ||||
\(964\) | −94.4281 | − | 30.6815i | −0.0979544 | − | 0.0318273i | ||||
\(965\) | 610.147 | − | 198.249i | 0.632276 | − | 0.205439i | ||||
\(966\) | 129.256 | − | 93.9098i | 0.133805 | − | 0.0972151i | ||||
\(967\) | − | 1791.77i | − | 1.85292i | −0.376396 | − | 0.926459i | \(-0.622837\pi\) | ||
0.376396 | − | 0.926459i | \(-0.377163\pi\) | |||||||
\(968\) | −169.947 | + | 297.062i | −0.175565 | + | 0.306882i | ||||
\(969\) | −96.7919 | −0.0998884 | ||||||||
\(970\) | 89.7458 | + | 123.524i | 0.0925214 | + | 0.127345i | ||||
\(971\) | −194.009 | − | 597.098i | −0.199803 | − | 0.614931i | −0.999887 | − | 0.0150426i | \(-0.995212\pi\) |
0.800084 | − | 0.599888i | \(-0.204788\pi\) | |||||||
\(972\) | 124.585 | − | 383.432i | 0.128173 | − | 0.394477i | ||||
\(973\) | 319.014 | + | 231.777i | 0.327867 | + | 0.238209i | ||||
\(974\) | −35.1789 | + | 48.4196i | −0.0361179 | + | 0.0497121i | ||||
\(975\) | −357.321 | − | 116.100i | −0.366483 | − | 0.119077i | ||||
\(976\) | 354.964 | − | 115.335i | 0.363693 | − | 0.118171i | ||||
\(977\) | −382.101 | + | 277.613i | −0.391096 | + | 0.284148i | −0.765905 | − | 0.642954i | \(-0.777709\pi\) |
0.374808 | + | 0.927102i | \(0.377709\pi\) | |||||||
\(978\) | − | 434.628i | − | 0.444404i | ||||||
\(979\) | −700.563 | + | 270.510i | −0.715591 | + | 0.276313i | ||||
\(980\) | −202.822 | −0.206962 | ||||||||
\(981\) | −57.5715 | − | 79.2404i | −0.0586866 | − | 0.0807751i | ||||
\(982\) | 267.750 | + | 824.051i | 0.272658 | + | 0.839156i | ||||
\(983\) | 145.406 | − | 447.515i | 0.147921 | − | 0.455254i | −0.849454 | − | 0.527663i | \(-0.823069\pi\) |
0.997375 | + | 0.0724086i | \(0.0230686\pi\) | |||||||
\(984\) | 94.7920 | + | 68.8704i | 0.0963333 | + | 0.0699902i | ||||
\(985\) | −478.230 | + | 658.228i | −0.485513 | + | 0.668251i | ||||
\(986\) | −130.235 | − | 42.3160i | −0.132084 | − | 0.0429168i | ||||
\(987\) | −107.035 | + | 34.7778i | −0.108445 | + | 0.0352359i | ||||
\(988\) | −623.073 | + | 452.689i | −0.630640 | + | 0.458187i | ||||
\(989\) | − | 1700.42i | − | 1.71933i | ||||||
\(990\) | 316.720 | + | 204.792i | 0.319919 | + | 0.206861i | ||||
\(991\) | 1639.02 | 1.65391 | 0.826955 | − | 0.562269i | \(-0.190071\pi\) | ||||
0.826955 | + | 0.562269i | \(0.190071\pi\) | |||||||
\(992\) | −88.2180 | − | 121.422i | −0.0889295 | − | 0.122401i | ||||
\(993\) | 26.5004 | + | 81.5600i | 0.0266873 | + | 0.0821349i | ||||
\(994\) | 159.839 | − | 491.933i | 0.160804 | − | 0.494902i | ||||
\(995\) | −606.194 | − | 440.425i | −0.609240 | − | 0.442639i | ||||
\(996\) | −32.1537 | + | 44.2558i | −0.0322828 | + | 0.0444335i | ||||
\(997\) | 123.947 | + | 40.2729i | 0.124320 | + | 0.0403941i | 0.370516 | − | 0.928826i | \(-0.379181\pi\) |
−0.246196 | + | 0.969220i | \(0.579181\pi\) | |||||||
\(998\) | −622.958 | + | 202.411i | −0.624206 | + | 0.202817i | ||||
\(999\) | 55.1591 | − | 40.0754i | 0.0552143 | − | 0.0401155i |
(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 | 22.3.d.a.19.2 | yes | 8 | |
3.2 | odd | 2 | 198.3.j.a.19.1 | 8 | |||
4.3 | odd | 2 | 176.3.n.b.129.1 | 8 | |||
11.2 | odd | 10 | 242.3.b.d.241.7 | 8 | |||
11.3 | even | 5 | 242.3.d.d.215.2 | 8 | |||
11.4 | even | 5 | 242.3.d.c.161.1 | 8 | |||
11.5 | even | 5 | 242.3.d.e.233.1 | 8 | |||
11.6 | odd | 10 | 242.3.d.d.233.2 | 8 | |||
11.7 | odd | 10 | inner | 22.3.d.a.7.2 | ✓ | 8 | |
11.8 | odd | 10 | 242.3.d.e.215.1 | 8 | |||
11.9 | even | 5 | 242.3.b.d.241.3 | 8 | |||
11.10 | odd | 2 | 242.3.d.c.239.1 | 8 | |||
33.2 | even | 10 | 2178.3.d.l.1693.1 | 8 | |||
33.20 | odd | 10 | 2178.3.d.l.1693.5 | 8 | |||
33.29 | even | 10 | 198.3.j.a.73.1 | 8 | |||
44.7 | even | 10 | 176.3.n.b.161.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.3.d.a.7.2 | ✓ | 8 | 11.7 | odd | 10 | inner | |
22.3.d.a.19.2 | yes | 8 | 1.1 | even | 1 | trivial | |
176.3.n.b.129.1 | 8 | 4.3 | odd | 2 | |||
176.3.n.b.161.1 | 8 | 44.7 | even | 10 | |||
198.3.j.a.19.1 | 8 | 3.2 | odd | 2 | |||
198.3.j.a.73.1 | 8 | 33.29 | even | 10 | |||
242.3.b.d.241.3 | 8 | 11.9 | even | 5 | |||
242.3.b.d.241.7 | 8 | 11.2 | odd | 10 | |||
242.3.d.c.161.1 | 8 | 11.4 | even | 5 | |||
242.3.d.c.239.1 | 8 | 11.10 | odd | 2 | |||
242.3.d.d.215.2 | 8 | 11.3 | even | 5 | |||
242.3.d.d.233.2 | 8 | 11.6 | odd | 10 | |||
242.3.d.e.215.1 | 8 | 11.8 | odd | 10 | |||
242.3.d.e.233.1 | 8 | 11.5 | even | 5 | |||
2178.3.d.l.1693.1 | 8 | 33.2 | even | 10 | |||
2178.3.d.l.1693.5 | 8 | 33.20 | odd | 10 |