Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(99,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.99");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.g (of order \(2\), degree \(1\), 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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.292213762624.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.4 | ||
Root | \(-1.05468 - 1.69931i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.99 |
Dual form | 392.3.g.m.99.3 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.05468 | + | 1.69931i | −0.527338 | + | 0.849655i | ||||
\(3\) | 3.44128 | 1.14709 | 0.573546 | − | 0.819173i | \(-0.305567\pi\) | ||||
0.573546 | + | 0.819173i | \(0.305567\pi\) | |||||||
\(4\) | −1.77532 | − | 3.58445i | −0.443829 | − | 0.896112i | ||||
\(5\) | 4.88287i | 0.976573i | 0.872683 | + | 0.488287i | \(0.162378\pi\) | ||||
−0.872683 | + | 0.488287i | \(0.837622\pi\) | |||||||
\(6\) | −3.62943 | + | 5.84780i | −0.604906 | + | 0.974633i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.96347 | + | 0.763618i | 0.995434 | + | 0.0954523i | ||||
\(9\) | 2.84239 | 0.315821 | ||||||||
\(10\) | −8.29751 | − | 5.14984i | −0.829751 | − | 0.514984i | ||||
\(11\) | −21.4776 | −1.95251 | −0.976253 | − | 0.216632i | \(-0.930493\pi\) | ||||
−0.976253 | + | 0.216632i | \(0.930493\pi\) | |||||||
\(12\) | −6.10935 | − | 12.3351i | −0.509113 | − | 1.02792i | ||||
\(13\) | 13.0760i | 1.00585i | 0.864331 | + | 0.502924i | \(0.167742\pi\) | ||||
−0.864331 | + | 0.502924i | \(0.832258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16.8033i | 1.12022i | ||||||||
\(16\) | −9.69651 | + | 12.7270i | −0.606032 | + | 0.795440i | ||||
\(17\) | 0.234889 | 0.0138170 | 0.00690851 | − | 0.999976i | \(-0.497801\pi\) | ||||
0.00690851 | + | 0.999976i | \(0.497801\pi\) | |||||||
\(18\) | −2.99780 | + | 4.83011i | −0.166545 | + | 0.268339i | ||||
\(19\) | −4.55872 | −0.239933 | −0.119966 | − | 0.992778i | \(-0.538279\pi\) | ||||
−0.119966 | + | 0.992778i | \(0.538279\pi\) | |||||||
\(20\) | 17.5024 | − | 8.66863i | 0.875119 | − | 0.433431i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 22.6519 | − | 36.4971i | 1.02963 | − | 1.65896i | ||||
\(23\) | 10.9523i | 0.476187i | 0.971242 | + | 0.238094i | \(0.0765225\pi\) | ||||
−0.971242 | + | 0.238094i | \(0.923478\pi\) | |||||||
\(24\) | 27.4045 | + | 2.62782i | 1.14185 | + | 0.109493i | ||||
\(25\) | 1.15761 | 0.0463043 | ||||||||
\(26\) | −22.2202 | − | 13.7910i | −0.854624 | − | 0.530422i | ||||
\(27\) | −21.1900 | −0.784816 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.6435i | 1.19460i | 0.802016 | + | 0.597302i | \(0.203761\pi\) | ||||
−0.802016 | + | 0.597302i | \(0.796239\pi\) | |||||||
\(30\) | −28.5540 | − | 17.7220i | −0.951801 | − | 0.590735i | ||||
\(31\) | 34.1079i | 1.10025i | 0.835081 | + | 0.550127i | \(0.185421\pi\) | ||||
−0.835081 | + | 0.550127i | \(0.814579\pi\) | |||||||
\(32\) | −11.4005 | − | 29.9003i | −0.356266 | − | 0.934384i | ||||
\(33\) | −73.9103 | −2.23971 | ||||||||
\(34\) | −0.247732 | + | 0.399150i | −0.00728624 | + | 0.0117397i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.04614 | − | 10.1884i | −0.140171 | − | 0.283011i | ||||
\(37\) | − | 54.2370i | − | 1.46586i | −0.680302 | − | 0.732932i | \(-0.738151\pi\) | ||
0.680302 | − | 0.732932i | \(-0.261849\pi\) | |||||||
\(38\) | 4.80798 | − | 7.74669i | 0.126526 | − | 0.203860i | ||||
\(39\) | 44.9982i | 1.15380i | ||||||||
\(40\) | −3.72865 | + | 38.8846i | −0.0932162 | + | 0.972114i | ||||
\(41\) | 37.8300 | 0.922682 | 0.461341 | − | 0.887223i | \(-0.347368\pi\) | ||||
0.461341 | + | 0.887223i | \(0.347368\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.84714 | −0.112724 | −0.0563621 | − | 0.998410i | \(-0.517950\pi\) | ||||
−0.0563621 | + | 0.998410i | \(0.517950\pi\) | |||||||
\(44\) | 38.1295 | + | 76.9852i | 0.866579 | + | 1.74966i | ||||
\(45\) | 13.8790i | 0.308423i | ||||||||
\(46\) | −18.6114 | − | 11.5511i | −0.404595 | − | 0.251112i | ||||
\(47\) | 72.3368i | 1.53908i | 0.638598 | + | 0.769541i | \(0.279515\pi\) | ||||
−0.638598 | + | 0.769541i | \(0.720485\pi\) | |||||||
\(48\) | −33.3684 | + | 43.7973i | −0.695175 | + | 0.912444i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.22090 | + | 1.96714i | −0.0244180 | + | 0.0393427i | ||||
\(51\) | 0.808319 | 0.0158494 | ||||||||
\(52\) | 46.8703 | − | 23.2141i | 0.901352 | − | 0.446424i | ||||
\(53\) | 21.6707i | 0.408881i | 0.978879 | + | 0.204440i | \(0.0655374\pi\) | ||||
−0.978879 | + | 0.204440i | \(0.934463\pi\) | |||||||
\(54\) | 22.3486 | − | 36.0085i | 0.413864 | − | 0.666823i | ||||
\(55\) | − | 104.872i | − | 1.90677i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.6878 | −0.275225 | ||||||||
\(58\) | −58.8701 | − | 36.5377i | −1.01500 | − | 0.629961i | ||||
\(59\) | −34.9007 | −0.591537 | −0.295768 | − | 0.955260i | \(-0.595576\pi\) | ||||
−0.295768 | + | 0.955260i | \(0.595576\pi\) | |||||||
\(60\) | 60.2305 | − | 29.8312i | 1.00384 | − | 0.497186i | ||||
\(61\) | − | 63.6012i | − | 1.04264i | −0.853360 | − | 0.521321i | \(-0.825439\pi\) | ||
0.853360 | − | 0.521321i | \(-0.174561\pi\) | |||||||
\(62\) | −57.9599 | − | 35.9728i | −0.934837 | − | 0.580206i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 62.8338 | + | 12.1621i | 0.981778 | + | 0.190033i | ||||
\(65\) | −63.8485 | −0.982284 | ||||||||
\(66\) | 77.9514 | − | 125.597i | 1.18108 | − | 1.90298i | ||||
\(67\) | 18.4344 | 0.275140 | 0.137570 | − | 0.990492i | \(-0.456071\pi\) | ||||
0.137570 | + | 0.990492i | \(0.456071\pi\) | |||||||
\(68\) | −0.417002 | − | 0.841948i | −0.00613239 | − | 0.0123816i | ||||
\(69\) | 37.6899i | 0.546231i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 47.5244i | − | 0.669358i | −0.942332 | − | 0.334679i | \(-0.891372\pi\) | ||
0.942332 | − | 0.334679i | \(-0.108628\pi\) | |||||||
\(72\) | 22.6353 | + | 2.17050i | 0.314379 | + | 0.0301459i | ||||
\(73\) | −55.9103 | −0.765894 | −0.382947 | − | 0.923770i | \(-0.625091\pi\) | ||||
−0.382947 | + | 0.923770i | \(0.625091\pi\) | |||||||
\(74\) | 92.1655 | + | 57.2024i | 1.24548 | + | 0.773006i | ||||
\(75\) | 3.98365 | 0.0531153 | ||||||||
\(76\) | 8.09317 | + | 16.3405i | 0.106489 | + | 0.215007i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −76.4660 | − | 47.4586i | −0.980333 | − | 0.608443i | ||||
\(79\) | − | 95.0135i | − | 1.20270i | −0.798985 | − | 0.601351i | \(-0.794629\pi\) | ||
0.798985 | − | 0.601351i | \(-0.205371\pi\) | |||||||
\(80\) | −62.1445 | − | 47.3468i | −0.776806 | − | 0.591835i | ||||
\(81\) | −98.5023 | −1.21608 | ||||||||
\(82\) | −39.8984 | + | 64.2849i | −0.486566 | + | 0.783962i | ||||
\(83\) | −71.5156 | −0.861634 | −0.430817 | − | 0.902439i | \(-0.641775\pi\) | ||||
−0.430817 | + | 0.902439i | \(0.641775\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.14693i | 0.0134933i | ||||||||
\(86\) | 5.11217 | − | 8.23680i | 0.0594438 | − | 0.0957768i | ||||
\(87\) | 119.218i | 1.37032i | ||||||||
\(88\) | −171.036 | − | 16.4007i | −1.94359 | − | 0.186371i | ||||
\(89\) | 159.756 | 1.79501 | 0.897504 | − | 0.441006i | \(-0.145378\pi\) | ||||
0.897504 | + | 0.441006i | \(0.145378\pi\) | |||||||
\(90\) | −23.5848 | − | 14.6379i | −0.262053 | − | 0.162643i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 39.2579 | − | 19.4438i | 0.426717 | − | 0.211346i | ||||
\(93\) | 117.375i | 1.26209i | ||||||||
\(94\) | −122.923 | − | 76.2920i | −1.30769 | − | 0.811617i | ||||
\(95\) | − | 22.2596i | − | 0.234312i | ||||||
\(96\) | −39.2324 | − | 102.895i | −0.408671 | − | 1.07183i | ||||
\(97\) | 90.4794 | 0.932777 | 0.466389 | − | 0.884580i | \(-0.345555\pi\) | ||||
0.466389 | + | 0.884580i | \(0.345555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −61.0477 | −0.616643 | ||||||||
\(100\) | −2.05512 | − | 4.14938i | −0.0205512 | − | 0.0414938i | ||||
\(101\) | 181.147i | 1.79353i | 0.442503 | + | 0.896767i | \(0.354091\pi\) | ||||
−0.442503 | + | 0.896767i | \(0.645909\pi\) | |||||||
\(102\) | −0.852515 | + | 1.37359i | −0.00835799 | + | 0.0134665i | ||||
\(103\) | − | 39.3003i | − | 0.381556i | −0.981633 | − | 0.190778i | \(-0.938899\pi\) | ||
0.981633 | − | 0.190778i | \(-0.0611010\pi\) | |||||||
\(104\) | −9.98509 | + | 104.131i | −0.0960105 | + | 1.00126i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −36.8252 | − | 22.8556i | −0.347408 | − | 0.215618i | ||||
\(107\) | 38.4498 | 0.359344 | 0.179672 | − | 0.983727i | \(-0.442496\pi\) | ||||
0.179672 | + | 0.983727i | \(0.442496\pi\) | |||||||
\(108\) | 37.6190 | + | 75.9546i | 0.348324 | + | 0.703283i | ||||
\(109\) | 27.8786i | 0.255767i | 0.991789 | + | 0.127883i | \(0.0408183\pi\) | ||||
−0.991789 | + | 0.127883i | \(0.959182\pi\) | |||||||
\(110\) | 178.210 | + | 110.606i | 1.62009 | + | 1.00551i | ||||
\(111\) | − | 186.644i | − | 1.68148i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 82.4419 | 0.729574 | 0.364787 | − | 0.931091i | \(-0.381142\pi\) | ||||
0.364787 | + | 0.931091i | \(0.381142\pi\) | |||||||
\(114\) | 16.5456 | − | 26.6585i | 0.145137 | − | 0.233846i | ||||
\(115\) | −53.4786 | −0.465032 | ||||||||
\(116\) | 124.178 | − | 61.5032i | 1.07050 | − | 0.530200i | ||||
\(117\) | 37.1672i | 0.317668i | ||||||||
\(118\) | 36.8089 | − | 59.3071i | 0.311940 | − | 0.502603i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.8313 | + | 133.813i | −0.106928 | + | 1.11511i | ||||
\(121\) | 340.286 | 2.81228 | ||||||||
\(122\) | 108.078 | + | 67.0787i | 0.885887 | + | 0.549825i | ||||
\(123\) | 130.183 | 1.05840 | ||||||||
\(124\) | 122.258 | − | 60.5522i | 0.985951 | − | 0.488325i | ||||
\(125\) | 127.724i | 1.02179i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 25.1408i | 0.197959i | 0.995089 | + | 0.0989796i | \(0.0315579\pi\) | ||||
−0.995089 | + | 0.0989796i | \(0.968442\pi\) | |||||||
\(128\) | −86.9365 | + | 93.9470i | −0.679191 | + | 0.733961i | ||||
\(129\) | −16.6804 | −0.129305 | ||||||||
\(130\) | 67.3395 | − | 108.498i | 0.517996 | − | 0.834603i | ||||
\(131\) | 126.398 | 0.964872 | 0.482436 | − | 0.875931i | \(-0.339752\pi\) | ||||
0.482436 | + | 0.875931i | \(0.339752\pi\) | |||||||
\(132\) | 131.214 | + | 264.928i | 0.994046 | + | 2.00703i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −19.4423 | + | 31.3257i | −0.145092 | + | 0.233774i | ||||
\(135\) | − | 103.468i | − | 0.766431i | ||||||
\(136\) | 1.87053 | + | 0.179366i | 0.0137539 | + | 0.00131887i | ||||
\(137\) | 34.9456 | 0.255078 | 0.127539 | − | 0.991834i | \(-0.459292\pi\) | ||||
0.127539 | + | 0.991834i | \(0.459292\pi\) | |||||||
\(138\) | −64.0469 | − | 39.7507i | −0.464108 | − | 0.288048i | ||||
\(139\) | 119.148 | 0.857177 | 0.428589 | − | 0.903500i | \(-0.359011\pi\) | ||||
0.428589 | + | 0.903500i | \(0.359011\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 248.931i | 1.76547i | ||||||||
\(142\) | 80.7587 | + | 50.1229i | 0.568723 | + | 0.352978i | ||||
\(143\) | − | 280.841i | − | 1.96392i | ||||||
\(144\) | −27.5613 | + | 36.1753i | −0.191398 | + | 0.251217i | ||||
\(145\) | −169.160 | −1.16662 | ||||||||
\(146\) | 58.9673 | − | 95.0090i | 0.403885 | − | 0.650746i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −194.409 | + | 96.2877i | −1.31358 | + | 0.650593i | ||||
\(149\) | 121.932i | 0.818334i | 0.912460 | + | 0.409167i | \(0.134181\pi\) | ||||
−0.912460 | + | 0.409167i | \(0.865819\pi\) | |||||||
\(150\) | −4.20146 | + | 6.76946i | −0.0280097 | + | 0.0451297i | ||||
\(151\) | 220.404i | 1.45963i | 0.683645 | + | 0.729815i | \(0.260394\pi\) | ||||
−0.683645 | + | 0.729815i | \(0.739606\pi\) | |||||||
\(152\) | −36.3033 | − | 3.48112i | −0.238837 | − | 0.0229021i | ||||
\(153\) | 0.667647 | 0.00436371 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −166.544 | −1.07448 | ||||||||
\(156\) | 161.294 | − | 79.8860i | 1.03393 | − | 0.512090i | ||||
\(157\) | − | 6.77014i | − | 0.0431219i | −0.999768 | − | 0.0215610i | \(-0.993136\pi\) | ||
0.999768 | − | 0.0215610i | \(-0.00686360\pi\) | |||||||
\(158\) | 161.457 | + | 100.208i | 1.02188 | + | 0.634231i | ||||
\(159\) | 74.5748i | 0.469024i | ||||||||
\(160\) | 145.999 | − | 55.6672i | 0.912495 | − | 0.347920i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 103.888 | − | 167.386i | 0.641285 | − | 1.03325i | ||||
\(163\) | −207.243 | −1.27143 | −0.635715 | − | 0.771924i | \(-0.719294\pi\) | ||||
−0.635715 | + | 0.771924i | \(0.719294\pi\) | |||||||
\(164\) | −67.1601 | − | 135.600i | −0.409513 | − | 0.826826i | ||||
\(165\) | − | 360.894i | − | 2.18724i | ||||||
\(166\) | 75.4259 | − | 121.527i | 0.454373 | − | 0.732092i | ||||
\(167\) | 165.529i | 0.991193i | 0.868553 | + | 0.495596i | \(0.165050\pi\) | ||||
−0.868553 | + | 0.495596i | \(0.834950\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.98237 | −0.0117300 | ||||||||
\(170\) | −1.94900 | − | 1.20964i | −0.0114647 | − | 0.00711555i | ||||
\(171\) | −12.9577 | −0.0757759 | ||||||||
\(172\) | 8.60521 | + | 17.3743i | 0.0500303 | + | 0.101014i | ||||
\(173\) | − | 88.8530i | − | 0.513601i | −0.966464 | − | 0.256800i | \(-0.917332\pi\) | ||
0.966464 | − | 0.256800i | \(-0.0826683\pi\) | |||||||
\(174\) | −202.588 | − | 125.736i | −1.16430 | − | 0.722623i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 208.258 | − | 273.346i | 1.18328 | − | 1.55310i | ||||
\(177\) | −120.103 | −0.678548 | ||||||||
\(178\) | −168.491 | + | 271.475i | −0.946576 | + | 1.52514i | ||||
\(179\) | 80.3791 | 0.449045 | 0.224523 | − | 0.974469i | \(-0.427918\pi\) | ||||
0.224523 | + | 0.974469i | \(0.427918\pi\) | |||||||
\(180\) | 49.7486 | − | 24.6396i | 0.276381 | − | 0.136887i | ||||
\(181\) | 276.353i | 1.52681i | 0.645919 | + | 0.763406i | \(0.276474\pi\) | ||||
−0.645919 | + | 0.763406i | \(0.723526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 218.869i | − | 1.19601i | ||||||
\(184\) | −8.36338 | + | 87.2184i | −0.0454532 | + | 0.474013i | ||||
\(185\) | 264.832 | 1.43152 | ||||||||
\(186\) | −199.456 | − | 123.792i | −1.07234 | − | 0.665550i | ||||
\(187\) | −5.04485 | −0.0269778 | ||||||||
\(188\) | 259.288 | − | 128.421i | 1.37919 | − | 0.683089i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 37.8260 | + | 23.4767i | 0.199084 | + | 0.123562i | ||||
\(191\) | − | 203.015i | − | 1.06290i | −0.847088 | − | 0.531452i | \(-0.821647\pi\) | ||
0.847088 | − | 0.531452i | \(-0.178353\pi\) | |||||||
\(192\) | 216.228 | + | 41.8532i | 1.12619 | + | 0.217985i | ||||
\(193\) | 87.3328 | 0.452502 | 0.226251 | − | 0.974069i | \(-0.427353\pi\) | ||||
0.226251 | + | 0.974069i | \(0.427353\pi\) | |||||||
\(194\) | −95.4265 | + | 153.753i | −0.491889 | + | 0.792539i | ||||
\(195\) | −219.720 | −1.12677 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 21.6639i | − | 0.109969i | −0.998487 | − | 0.0549845i | \(-0.982489\pi\) | ||
0.998487 | − | 0.0549845i | \(-0.0175109\pi\) | |||||||
\(198\) | 64.3856 | − | 103.739i | 0.325180 | − | 0.523934i | ||||
\(199\) | − | 181.933i | − | 0.914235i | −0.889406 | − | 0.457118i | \(-0.848882\pi\) | ||
0.889406 | − | 0.457118i | \(-0.151118\pi\) | |||||||
\(200\) | 9.21858 | + | 0.883971i | 0.0460929 | + | 0.00441985i | ||||
\(201\) | 63.4378 | 0.315611 | ||||||||
\(202\) | −307.825 | − | 191.051i | −1.52389 | − | 0.945799i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.43502 | − | 2.89738i | −0.00703442 | − | 0.0142028i | ||||
\(205\) | 184.719i | 0.901067i | ||||||||
\(206\) | 66.7834 | + | 41.4491i | 0.324191 | + | 0.201209i | ||||
\(207\) | 31.1307i | 0.150390i | ||||||||
\(208\) | −166.419 | − | 126.792i | −0.800092 | − | 0.609576i | ||||
\(209\) | 97.9103 | 0.468470 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.4204 | −0.101519 | −0.0507594 | − | 0.998711i | \(-0.516164\pi\) | ||||
−0.0507594 | + | 0.998711i | \(0.516164\pi\) | |||||||
\(212\) | 77.6774 | − | 38.4723i | 0.366403 | − | 0.181473i | ||||
\(213\) | − | 163.545i | − | 0.767815i | ||||||
\(214\) | −40.5521 | + | 65.3382i | −0.189496 | + | 0.305319i | ||||
\(215\) | − | 23.6680i | − | 0.110084i | ||||||
\(216\) | −168.746 | − | 16.1811i | −0.781233 | − | 0.0749125i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −47.3744 | − | 29.4029i | −0.217314 | − | 0.134876i | ||||
\(219\) | −192.403 | −0.878552 | ||||||||
\(220\) | −375.909 | + | 186.181i | −1.70868 | + | 0.846278i | ||||
\(221\) | 3.07142i | 0.0138978i | ||||||||
\(222\) | 317.167 | + | 196.850i | 1.42868 | + | 0.886710i | ||||
\(223\) | − | 195.958i | − | 0.878735i | −0.898307 | − | 0.439367i | \(-0.855203\pi\) | ||
0.898307 | − | 0.439367i | \(-0.144797\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.29038 | 0.0146239 | ||||||||
\(226\) | −86.9495 | + | 140.094i | −0.384732 | + | 0.619887i | ||||
\(227\) | 27.2652 | 0.120111 | 0.0600554 | − | 0.998195i | \(-0.480872\pi\) | ||||
0.0600554 | + | 0.998195i | \(0.480872\pi\) | |||||||
\(228\) | 27.8508 | + | 56.2322i | 0.122153 | + | 0.246632i | ||||
\(229\) | 176.347i | 0.770076i | 0.922901 | + | 0.385038i | \(0.125812\pi\) | ||||
−0.922901 | + | 0.385038i | \(0.874188\pi\) | |||||||
\(230\) | 56.4027 | − | 90.8768i | 0.245229 | − | 0.395117i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −26.4544 | + | 275.883i | −0.114028 | + | 1.18915i | ||||
\(233\) | 71.8366 | 0.308312 | 0.154156 | − | 0.988047i | \(-0.450734\pi\) | ||||
0.154156 | + | 0.988047i | \(0.450734\pi\) | |||||||
\(234\) | −63.1586 | − | 39.1994i | −0.269909 | − | 0.167519i | ||||
\(235\) | −353.211 | −1.50303 | ||||||||
\(236\) | 61.9597 | + | 125.100i | 0.262541 | + | 0.530083i | ||||
\(237\) | − | 326.968i | − | 1.37961i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 71.0926i | − | 0.297459i | −0.988878 | − | 0.148729i | \(-0.952482\pi\) | ||
0.988878 | − | 0.148729i | \(-0.0475183\pi\) | |||||||
\(240\) | −213.856 | − | 162.933i | −0.891068 | − | 0.678889i | ||||
\(241\) | −56.1113 | −0.232827 | −0.116413 | − | 0.993201i | \(-0.537140\pi\) | ||||
−0.116413 | + | 0.993201i | \(0.537140\pi\) | |||||||
\(242\) | −358.892 | + | 578.252i | −1.48302 | + | 2.38947i | ||||
\(243\) | −148.264 | −0.610138 | ||||||||
\(244\) | −227.975 | + | 112.912i | −0.934324 | + | 0.462755i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −137.301 | + | 221.222i | −0.558136 | + | 0.899277i | ||||
\(247\) | − | 59.6100i | − | 0.241336i | ||||||
\(248\) | −26.0454 | + | 271.617i | −0.105022 | + | 1.09523i | ||||
\(249\) | −246.105 | −0.988374 | ||||||||
\(250\) | −217.043 | − | 134.708i | −0.868172 | − | 0.538830i | ||||
\(251\) | −368.953 | −1.46993 | −0.734966 | − | 0.678104i | \(-0.762802\pi\) | ||||
−0.734966 | + | 0.678104i | \(0.762802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 235.229i | − | 0.929759i | ||||||
\(254\) | −42.7221 | − | 26.5154i | −0.168197 | − | 0.104391i | ||||
\(255\) | 3.94691i | 0.0154781i | ||||||||
\(256\) | −67.9553 | − | 246.816i | −0.265451 | − | 0.964124i | ||||
\(257\) | −23.7428 | −0.0923845 | −0.0461923 | − | 0.998933i | \(-0.514709\pi\) | ||||
−0.0461923 | + | 0.998933i | \(0.514709\pi\) | |||||||
\(258\) | 17.5924 | − | 28.3451i | 0.0681876 | − | 0.109865i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 113.351 | + | 228.861i | 0.435966 | + | 0.880236i | ||||
\(261\) | 98.4705i | 0.377282i | ||||||||
\(262\) | −133.309 | + | 214.790i | −0.508814 | + | 0.819809i | ||||
\(263\) | − | 73.9707i | − | 0.281257i | −0.990062 | − | 0.140629i | \(-0.955088\pi\) | ||
0.990062 | − | 0.140629i | \(-0.0449124\pi\) | |||||||
\(264\) | −588.583 | − | 56.4393i | −2.22948 | − | 0.213785i | ||||
\(265\) | −105.815 | −0.399302 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 549.764 | 2.05904 | ||||||||
\(268\) | −32.7268 | − | 66.0770i | −0.122115 | − | 0.246556i | ||||
\(269\) | − | 335.593i | − | 1.24756i | −0.781601 | − | 0.623779i | \(-0.785597\pi\) | ||
0.781601 | − | 0.623779i | \(-0.214403\pi\) | |||||||
\(270\) | 175.825 | + | 109.125i | 0.651202 | + | 0.404168i | ||||
\(271\) | − | 187.276i | − | 0.691054i | −0.938409 | − | 0.345527i | \(-0.887700\pi\) | ||
0.938409 | − | 0.345527i | \(-0.112300\pi\) | |||||||
\(272\) | −2.27761 | + | 2.98945i | −0.00837355 | + | 0.0109906i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −36.8564 | + | 59.3835i | −0.134512 | + | 0.216728i | ||||
\(275\) | −24.8626 | −0.0904095 | ||||||||
\(276\) | 135.097 | − | 66.9115i | 0.489484 | − | 0.242433i | ||||
\(277\) | 132.592i | 0.478670i | 0.970937 | + | 0.239335i | \(0.0769294\pi\) | ||||
−0.970937 | + | 0.239335i | \(0.923071\pi\) | |||||||
\(278\) | −125.662 | + | 202.469i | −0.452022 | + | 0.728305i | ||||
\(279\) | 96.9480i | 0.347484i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 331.520 | 1.17979 | 0.589894 | − | 0.807481i | \(-0.299170\pi\) | ||||
0.589894 | + | 0.807481i | \(0.299170\pi\) | |||||||
\(282\) | −423.011 | − | 262.542i | −1.50004 | − | 0.930999i | ||||
\(283\) | 66.7158 | 0.235745 | 0.117873 | − | 0.993029i | \(-0.462393\pi\) | ||||
0.117873 | + | 0.993029i | \(0.462393\pi\) | |||||||
\(284\) | −170.349 | + | 84.3708i | −0.599819 | + | 0.297080i | ||||
\(285\) | − | 76.6016i | − | 0.268778i | ||||||
\(286\) | 477.237 | + | 296.197i | 1.66866 | + | 1.03565i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −32.4048 | − | 84.9884i | −0.112517 | − | 0.295099i | ||||
\(289\) | −288.945 | −0.999809 | ||||||||
\(290\) | 178.409 | − | 287.455i | 0.615203 | − | 0.991224i | ||||
\(291\) | 311.365 | 1.06998 | ||||||||
\(292\) | 99.2584 | + | 200.407i | 0.339926 | + | 0.686327i | ||||
\(293\) | 289.215i | 0.987082i | 0.869723 | + | 0.493541i | \(0.164298\pi\) | ||||
−0.869723 | + | 0.493541i | \(0.835702\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 170.415i | − | 0.577679i | ||||||
\(296\) | 41.4163 | − | 431.915i | 0.139920 | − | 1.45917i | ||||
\(297\) | 455.111 | 1.53236 | ||||||||
\(298\) | −207.200 | − | 128.598i | −0.695302 | − | 0.431539i | ||||
\(299\) | −143.213 | −0.478972 | ||||||||
\(300\) | −7.07223 | − | 14.2792i | −0.0235741 | − | 0.0475973i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −374.535 | − | 232.455i | −1.24018 | − | 0.769719i | ||||
\(303\) | 623.377i | 2.05735i | ||||||||
\(304\) | 44.2037 | − | 58.0191i | 0.145407 | − | 0.190852i | ||||
\(305\) | 310.556 | 1.01822 | ||||||||
\(306\) | −0.704152 | + | 1.13454i | −0.00230115 | + | 0.00370765i | ||||
\(307\) | −0.693177 | −0.00225790 | −0.00112895 | − | 0.999999i | \(-0.500359\pi\) | ||||
−0.00112895 | + | 0.999999i | \(0.500359\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 135.243i | − | 0.437680i | ||||||
\(310\) | 175.650 | − | 283.010i | 0.566614 | − | 0.912937i | ||||
\(311\) | 62.1583i | 0.199866i | 0.994994 | + | 0.0999330i | \(0.0318628\pi\) | ||||
−0.994994 | + | 0.0999330i | \(0.968137\pi\) | |||||||
\(312\) | −34.3615 | + | 358.342i | −0.110133 | + | 1.14853i | ||||
\(313\) | −213.594 | −0.682408 | −0.341204 | − | 0.939989i | \(-0.610835\pi\) | ||||
−0.341204 | + | 0.939989i | \(0.610835\pi\) | |||||||
\(314\) | 11.5046 | + | 7.14031i | 0.0366388 | + | 0.0227398i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −340.571 | + | 168.679i | −1.07776 | + | 0.533794i | ||||
\(317\) | − | 23.4577i | − | 0.0739990i | −0.999315 | − | 0.0369995i | \(-0.988220\pi\) | ||
0.999315 | − | 0.0369995i | \(-0.0117800\pi\) | |||||||
\(318\) | −126.726 | − | 78.6523i | −0.398509 | − | 0.247334i | ||||
\(319\) | − | 744.059i | − | 2.33247i | ||||||
\(320\) | −59.3860 | + | 306.809i | −0.185581 | + | 0.958778i | ||||
\(321\) | 132.317 | 0.412201 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.07079 | −0.00331515 | ||||||||
\(324\) | 174.873 | + | 353.076i | 0.539731 | + | 1.08974i | ||||
\(325\) | 15.1369i | 0.0465751i | ||||||||
\(326\) | 218.574 | − | 352.170i | 0.670473 | − | 1.08028i | ||||
\(327\) | 95.9380i | 0.293388i | ||||||||
\(328\) | 301.258 | + | 28.8877i | 0.918469 | + | 0.0880721i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 613.271 | + | 380.627i | 1.85840 | + | 1.15341i | ||||
\(331\) | 507.406 | 1.53295 | 0.766474 | − | 0.642275i | \(-0.222009\pi\) | ||||
0.766474 | + | 0.642275i | \(0.222009\pi\) | |||||||
\(332\) | 126.963 | + | 256.344i | 0.382418 | + | 0.772120i | ||||
\(333\) | − | 154.163i | − | 0.462951i | ||||||
\(334\) | −281.286 | − | 174.580i | −0.842172 | − | 0.522694i | ||||
\(335\) | 90.0126i | 0.268694i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −342.726 | −1.01699 | −0.508495 | − | 0.861065i | \(-0.669798\pi\) | ||||
−0.508495 | + | 0.861065i | \(0.669798\pi\) | |||||||
\(338\) | 2.09076 | − | 3.36866i | 0.00618567 | − | 0.00996645i | ||||
\(339\) | 283.705 | 0.836889 | ||||||||
\(340\) | 4.11112 | − | 2.03617i | 0.0120915 | − | 0.00598873i | ||||
\(341\) | − | 732.555i | − | 2.14825i | ||||||
\(342\) | 13.6662 | − | 22.0191i | 0.0399595 | − | 0.0643834i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −38.6001 | − | 3.70137i | −0.112210 | − | 0.0107598i | ||||
\(345\) | −184.035 | −0.533434 | ||||||||
\(346\) | 150.989 | + | 93.7111i | 0.436384 | + | 0.270841i | ||||
\(347\) | 136.745 | 0.394079 | 0.197039 | − | 0.980396i | \(-0.436867\pi\) | ||||
0.197039 | + | 0.980396i | \(0.436867\pi\) | |||||||
\(348\) | 427.331 | − | 211.650i | 1.22796 | − | 0.608188i | ||||
\(349\) | 82.0565i | 0.235119i | 0.993066 | + | 0.117559i | \(0.0375071\pi\) | ||||
−0.993066 | + | 0.117559i | \(0.962493\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 277.081i | − | 0.789406i | ||||||
\(352\) | 244.856 | + | 642.186i | 0.695613 | + | 1.82439i | ||||
\(353\) | −507.367 | −1.43730 | −0.718651 | − | 0.695371i | \(-0.755240\pi\) | ||||
−0.718651 | + | 0.695371i | \(0.755240\pi\) | |||||||
\(354\) | 126.670 | − | 204.092i | 0.357824 | − | 0.576532i | ||||
\(355\) | 232.055 | 0.653677 | ||||||||
\(356\) | −283.617 | − | 572.636i | −0.796676 | − | 1.60853i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −84.7740 | + | 136.589i | −0.236799 | + | 0.381534i | ||||
\(359\) | 560.809i | 1.56214i | 0.624442 | + | 0.781071i | \(0.285326\pi\) | ||||
−0.624442 | + | 0.781071i | \(0.714674\pi\) | |||||||
\(360\) | −10.5983 | + | 110.525i | −0.0294397 | + | 0.307014i | ||||
\(361\) | −340.218 | −0.942432 | ||||||||
\(362\) | −469.610 | − | 291.463i | −1.29726 | − | 0.805147i | ||||
\(363\) | 1171.02 | 3.22595 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 273.003i | − | 0.747952i | ||||||
\(366\) | 371.927 | + | 230.836i | 1.01619 | + | 0.630701i | ||||
\(367\) | − | 26.9431i | − | 0.0734145i | −0.999326 | − | 0.0367072i | \(-0.988313\pi\) | ||
0.999326 | − | 0.0367072i | \(-0.0116869\pi\) | |||||||
\(368\) | −139.390 | − | 106.199i | −0.378778 | − | 0.288585i | ||||
\(369\) | 107.528 | 0.291403 | ||||||||
\(370\) | −279.312 | + | 450.032i | −0.754897 | + | 1.21630i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 420.723 | − | 208.377i | 1.13098 | − | 0.560153i | ||||
\(373\) | − | 538.034i | − | 1.44245i | −0.692701 | − | 0.721225i | \(-0.743579\pi\) | ||
0.692701 | − | 0.721225i | \(-0.256421\pi\) | |||||||
\(374\) | 5.32069 | − | 8.57277i | 0.0142264 | − | 0.0229218i | ||||
\(375\) | 439.534i | 1.17209i | ||||||||
\(376\) | −55.2377 | + | 576.052i | −0.146909 | + | 1.53205i | ||||
\(377\) | −453.000 | −1.20159 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −182.132 | −0.480560 | −0.240280 | − | 0.970704i | \(-0.577239\pi\) | ||||
−0.240280 | + | 0.970704i | \(0.577239\pi\) | |||||||
\(380\) | −79.7885 | + | 39.5179i | −0.209970 | + | 0.103994i | ||||
\(381\) | 86.5166i | 0.227078i | ||||||||
\(382\) | 344.985 | + | 214.115i | 0.903102 | + | 0.560510i | ||||
\(383\) | 333.271i | 0.870160i | 0.900392 | + | 0.435080i | \(0.143280\pi\) | ||||
−0.900392 | + | 0.435080i | \(0.856720\pi\) | |||||||
\(384\) | −299.173 | + | 323.298i | −0.779095 | + | 0.841921i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −92.1079 | + | 148.406i | −0.238621 | + | 0.384471i | ||||
\(387\) | −13.7775 | −0.0356007 | ||||||||
\(388\) | −160.629 | − | 324.319i | −0.413993 | − | 0.835873i | ||||
\(389\) | 109.639i | 0.281847i | 0.990020 | + | 0.140924i | \(0.0450072\pi\) | ||||
−0.990020 | + | 0.140924i | \(0.954993\pi\) | |||||||
\(390\) | 231.734 | − | 373.373i | 0.594189 | − | 0.957367i | ||||
\(391\) | 2.57258i | 0.00657948i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 434.971 | 1.10680 | ||||||||
\(394\) | 36.8137 | + | 22.8484i | 0.0934358 | + | 0.0579909i | ||||
\(395\) | 463.938 | 1.17453 | ||||||||
\(396\) | 108.379 | + | 218.822i | 0.273684 | + | 0.552581i | ||||
\(397\) | 310.938i | 0.783219i | 0.920131 | + | 0.391610i | \(0.128082\pi\) | ||||
−0.920131 | + | 0.391610i | \(0.871918\pi\) | |||||||
\(398\) | 309.160 | + | 191.880i | 0.776785 | + | 0.482111i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.2248 | + | 14.7329i | −0.0280619 | + | 0.0368323i | ||||
\(401\) | −423.903 | −1.05711 | −0.528557 | − | 0.848898i | \(-0.677267\pi\) | ||||
−0.528557 | + | 0.848898i | \(0.677267\pi\) | |||||||
\(402\) | −66.9063 | + | 107.801i | −0.166434 | + | 0.268160i | ||||
\(403\) | −445.995 | −1.10669 | ||||||||
\(404\) | 649.311 | − | 321.593i | 1.60721 | − | 0.796022i | ||||
\(405\) | − | 480.974i | − | 1.18759i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1164.88i | 2.86211i | ||||||||
\(408\) | 6.43703 | + | 0.617247i | 0.0157770 | + | 0.00151286i | ||||
\(409\) | −444.543 | −1.08690 | −0.543451 | − | 0.839441i | \(-0.682883\pi\) | ||||
−0.543451 | + | 0.839441i | \(0.682883\pi\) | |||||||
\(410\) | −313.895 | − | 194.818i | −0.765596 | − | 0.475167i | ||||
\(411\) | 120.258 | 0.292598 | ||||||||
\(412\) | −140.870 | + | 69.7703i | −0.341917 | + | 0.169345i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −52.9008 | − | 32.8329i | −0.127780 | − | 0.0793064i | ||||
\(415\) | − | 349.201i | − | 0.841449i | ||||||
\(416\) | 390.977 | − | 149.074i | 0.939849 | − | 0.358350i | ||||
\(417\) | 410.020 | 0.983261 | ||||||||
\(418\) | −103.264 | + | 166.380i | −0.247042 | + | 0.398038i | ||||
\(419\) | −457.129 | −1.09100 | −0.545500 | − | 0.838111i | \(-0.683660\pi\) | ||||
−0.545500 | + | 0.838111i | \(0.683660\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4812i | 0.0605255i | 0.999542 | + | 0.0302628i | \(0.00963441\pi\) | ||||
−0.999542 | + | 0.0302628i | \(0.990366\pi\) | |||||||
\(422\) | 22.5916 | − | 36.4000i | 0.0535347 | − | 0.0862559i | ||||
\(423\) | 205.610i | 0.486075i | ||||||||
\(424\) | −16.5481 | + | 172.574i | −0.0390286 | + | 0.407014i | ||||
\(425\) | 0.271910 | 0.000639787 | ||||||||
\(426\) | 277.913 | + | 172.487i | 0.652378 | + | 0.404898i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −68.2606 | − | 137.821i | −0.159487 | − | 0.322013i | ||||
\(429\) | − | 966.453i | − | 2.25280i | ||||||
\(430\) | 40.2192 | + | 24.9620i | 0.0935331 | + | 0.0580512i | ||||
\(431\) | − | 124.595i | − | 0.289084i | −0.989499 | − | 0.144542i | \(-0.953829\pi\) | ||
0.989499 | − | 0.144542i | \(-0.0461709\pi\) | |||||||
\(432\) | 205.469 | − | 269.687i | 0.475624 | − | 0.624274i | ||||
\(433\) | 272.271 | 0.628802 | 0.314401 | − | 0.949290i | \(-0.398196\pi\) | ||||
0.314401 | + | 0.949290i | \(0.398196\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −582.126 | −1.33822 | ||||||||
\(436\) | 99.9293 | − | 49.4933i | 0.229196 | − | 0.113517i | ||||
\(437\) | − | 49.9285i | − | 0.114253i | ||||||
\(438\) | 202.923 | − | 326.952i | 0.463294 | − | 0.746466i | ||||
\(439\) | − | 255.069i | − | 0.581023i | −0.956871 | − | 0.290512i | \(-0.906174\pi\) | ||
0.956871 | − | 0.290512i | \(-0.0938255\pi\) | |||||||
\(440\) | 80.0823 | − | 835.146i | 0.182005 | − | 1.89806i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.21929 | − | 3.23935i | −0.0118084 | − | 0.00732885i | ||||
\(443\) | 131.274 | 0.296330 | 0.148165 | − | 0.988963i | \(-0.452663\pi\) | ||||
0.148165 | + | 0.988963i | \(0.452663\pi\) | |||||||
\(444\) | −669.017 | + | 331.353i | −1.50680 | + | 0.746290i | ||||
\(445\) | 780.066i | 1.75296i | ||||||||
\(446\) | 332.993 | + | 206.672i | 0.746622 | + | 0.463391i | ||||
\(447\) | 419.601i | 0.938704i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −642.824 | −1.43168 | −0.715839 | − | 0.698265i | \(-0.753956\pi\) | ||||
−0.715839 | + | 0.698265i | \(0.753956\pi\) | |||||||
\(450\) | −3.47028 | + | 5.59137i | −0.00771174 | + | 0.0124253i | ||||
\(451\) | −812.496 | −1.80154 | ||||||||
\(452\) | −146.360 | − | 295.509i | −0.323806 | − | 0.653780i | ||||
\(453\) | 758.472i | 1.67433i | ||||||||
\(454\) | −28.7559 | + | 46.3320i | −0.0633390 | + | 0.102053i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −124.930 | − | 11.9795i | −0.273968 | − | 0.0262709i | ||||
\(457\) | 693.088 | 1.51660 | 0.758302 | − | 0.651903i | \(-0.226029\pi\) | ||||
0.758302 | + | 0.651903i | \(0.226029\pi\) | |||||||
\(458\) | −299.669 | − | 185.990i | −0.654300 | − | 0.406091i | ||||
\(459\) | −4.97731 | −0.0108438 | ||||||||
\(460\) | 94.9415 | + | 191.691i | 0.206394 | + | 0.416720i | ||||
\(461\) | 258.699i | 0.561170i | 0.959829 | + | 0.280585i | \(0.0905285\pi\) | ||||
−0.959829 | + | 0.280585i | \(0.909472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 637.226i | 1.37630i | 0.725569 | + | 0.688150i | \(0.241577\pi\) | ||||
−0.725569 | + | 0.688150i | \(0.758423\pi\) | |||||||
\(464\) | −440.910 | − | 335.921i | −0.950237 | − | 0.723969i | ||||
\(465\) | −573.125 | −1.23253 | ||||||||
\(466\) | −75.7644 | + | 122.073i | −0.162584 | + | 0.261959i | ||||
\(467\) | 199.483 | 0.427159 | 0.213580 | − | 0.976926i | \(-0.431488\pi\) | ||||
0.213580 | + | 0.976926i | \(0.431488\pi\) | |||||||
\(468\) | 133.224 | − | 65.9835i | 0.284666 | − | 0.140990i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 372.524 | − | 600.216i | 0.792603 | − | 1.27705i | ||||
\(471\) | − | 23.2979i | − | 0.0494648i | ||||||
\(472\) | −277.931 | − | 26.6508i | −0.588836 | − | 0.0564636i | ||||
\(473\) | 104.105 | 0.220095 | ||||||||
\(474\) | 555.620 | + | 344.845i | 1.17219 | + | 0.727521i | ||||
\(475\) | −5.27721 | −0.0111099 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 61.5966i | 0.129133i | ||||||||
\(478\) | 120.809 | + | 74.9797i | 0.252737 | + | 0.156861i | ||||
\(479\) | 674.160i | 1.40743i | 0.710481 | + | 0.703716i | \(0.248477\pi\) | ||||
−0.710481 | + | 0.703716i | \(0.751523\pi\) | |||||||
\(480\) | 502.424 | − | 191.566i | 1.04672 | − | 0.399097i | ||||
\(481\) | 709.204 | 1.47444 | ||||||||
\(482\) | 59.1792 | − | 95.3505i | 0.122778 | − | 0.197823i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −604.115 | − | 1219.74i | −1.24817 | − | 2.52012i | ||||
\(485\) | 441.799i | 0.910926i | ||||||||
\(486\) | 156.370 | − | 251.946i | 0.321749 | − | 0.518407i | ||||
\(487\) | − | 401.718i | − | 0.824883i | −0.910984 | − | 0.412442i | \(-0.864676\pi\) | ||
0.910984 | − | 0.412442i | \(-0.135324\pi\) | |||||||
\(488\) | 48.5670 | − | 506.486i | 0.0995226 | − | 1.03788i | ||||
\(489\) | −713.181 | −1.45845 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 428.880 | 0.873482 | 0.436741 | − | 0.899587i | \(-0.356133\pi\) | ||||
0.436741 | + | 0.899587i | \(0.356133\pi\) | |||||||
\(492\) | −231.117 | − | 466.636i | −0.469749 | − | 0.948446i | ||||
\(493\) | 8.13739i | 0.0165059i | ||||||||
\(494\) | 101.296 | + | 62.8692i | 0.205052 | + | 0.127266i | ||||
\(495\) | − | 298.088i | − | 0.602198i | ||||||
\(496\) | −434.093 | − | 330.727i | −0.875187 | − | 0.666789i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 259.561 | − | 418.209i | 0.521207 | − | 0.839778i | ||||
\(499\) | 182.619 | 0.365970 | 0.182985 | − | 0.983116i | \(-0.441424\pi\) | ||||
0.182985 | + | 0.983116i | \(0.441424\pi\) | |||||||
\(500\) | 457.820 | − | 226.751i | 0.915641 | − | 0.453501i | ||||
\(501\) | 569.632i | 1.13699i | ||||||||
\(502\) | 389.126 | − | 626.966i | 0.775152 | − | 1.24894i | ||||
\(503\) | 380.158i | 0.755781i | 0.925850 | + | 0.377891i | \(0.123350\pi\) | ||||
−0.925850 | + | 0.377891i | \(0.876650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −884.516 | −1.75152 | ||||||||
\(506\) | 399.727 | + | 248.090i | 0.789974 | + | 0.490297i | ||||
\(507\) | −6.82188 | −0.0134554 | ||||||||
\(508\) | 90.1160 | − | 44.6329i | 0.177394 | − | 0.0878600i | ||||
\(509\) | 289.538i | 0.568836i | 0.958700 | + | 0.284418i | \(0.0918004\pi\) | ||||
−0.958700 | + | 0.284418i | \(0.908200\pi\) | |||||||
\(510\) | −6.70703 | − | 4.16272i | −0.0131510 | − | 0.00816219i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 491.088 | + | 144.834i | 0.959156 | + | 0.282878i | ||||
\(513\) | 96.5995 | 0.188303 | ||||||||
\(514\) | 25.0410 | − | 40.3464i | 0.0487179 | − | 0.0784950i | ||||
\(515\) | 191.898 | 0.372617 | ||||||||
\(516\) | 29.6129 | + | 59.7899i | 0.0573894 | + | 0.115872i | ||||
\(517\) | − | 1553.62i | − | 3.00507i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 305.768i | − | 0.589148i | ||||||
\(520\) | −508.456 | − | 48.7559i | −0.977799 | − | 0.0937613i | ||||
\(521\) | 738.899 | 1.41823 | 0.709116 | − | 0.705092i | \(-0.249094\pi\) | ||||
0.709116 | + | 0.705092i | \(0.249094\pi\) | |||||||
\(522\) | −167.332 | − | 103.855i | −0.320559 | − | 0.198955i | ||||
\(523\) | −647.126 | −1.23734 | −0.618668 | − | 0.785653i | \(-0.712327\pi\) | ||||
−0.618668 | + | 0.785653i | \(0.712327\pi\) | |||||||
\(524\) | −224.397 | − | 453.068i | −0.428238 | − | 0.864633i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 125.699 | + | 78.0151i | 0.238972 | + | 0.148318i | ||||
\(527\) | 8.01157i | 0.0152022i | ||||||||
\(528\) | 716.672 | − | 940.660i | 1.35733 | − | 1.78155i | ||||
\(529\) | 409.047 | 0.773246 | ||||||||
\(530\) | 111.601 | − | 179.813i | 0.210567 | − | 0.339269i | ||||
\(531\) | −99.2014 | −0.186820 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 494.666i | 0.928078i | ||||||||
\(534\) | −579.823 | + | 934.220i | −1.08581 | + | 1.74948i | ||||
\(535\) | 187.745i | 0.350926i | ||||||||
\(536\) | 146.802 | + | 14.0768i | 0.273884 | + | 0.0262627i | ||||
\(537\) | 276.607 | 0.515097 | ||||||||
\(538\) | 570.277 | + | 353.942i | 1.05999 | + | 0.657885i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −370.876 | + | 183.689i | −0.686807 | + | 0.340164i | ||||
\(541\) | 178.722i | 0.330355i | 0.986264 | + | 0.165178i | \(0.0528198\pi\) | ||||
−0.986264 | + | 0.165178i | \(0.947180\pi\) | |||||||
\(542\) | 318.240 | + | 197.515i | 0.587158 | + | 0.364419i | ||||
\(543\) | 951.008i | 1.75140i | ||||||||
\(544\) | −2.67786 | − | 7.02326i | −0.00492254 | − | 0.0129104i | ||||
\(545\) | −136.127 | −0.249775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 452.236 | 0.826758 | 0.413379 | − | 0.910559i | \(-0.364349\pi\) | ||||
0.413379 | + | 0.910559i | \(0.364349\pi\) | |||||||
\(548\) | −62.0395 | − | 125.261i | −0.113211 | − | 0.228578i | ||||
\(549\) | − | 180.780i | − | 0.329289i | ||||||
\(550\) | 26.2220 | − | 42.2493i | 0.0476764 | − | 0.0768169i | ||||
\(551\) | − | 157.930i | − | 0.286625i | ||||||
\(552\) | −28.7807 | + | 300.143i | −0.0521390 | + | 0.543737i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −225.314 | − | 139.841i | −0.406705 | − | 0.252421i | ||||
\(555\) | 911.360 | 1.64209 | ||||||||
\(556\) | −211.525 | − | 427.078i | −0.380440 | − | 0.768126i | ||||
\(557\) | − | 854.108i | − | 1.53341i | −0.642001 | − | 0.766704i | \(-0.721895\pi\) | ||
0.642001 | − | 0.766704i | \(-0.278105\pi\) | |||||||
\(558\) | −164.745 | − | 102.249i | −0.295242 | − | 0.183241i | ||||
\(559\) | − | 63.3814i | − | 0.113383i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.3607 | −0.0309460 | ||||||||
\(562\) | −349.647 | + | 563.356i | −0.622147 | + | 1.00241i | ||||
\(563\) | −249.654 | −0.443436 | −0.221718 | − | 0.975111i | \(-0.571166\pi\) | ||||
−0.221718 | + | 0.975111i | \(0.571166\pi\) | |||||||
\(564\) | 892.280 | − | 441.931i | 1.58206 | − | 0.783566i | ||||
\(565\) | 402.553i | 0.712483i | ||||||||
\(566\) | −70.3636 | + | 113.371i | −0.124317 | + | 0.200302i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 36.2905 | − | 378.459i | 0.0638917 | − | 0.666301i | ||||
\(569\) | 104.353 | 0.183396 | 0.0916982 | − | 0.995787i | \(-0.470771\pi\) | ||||
0.0916982 | + | 0.995787i | \(0.470771\pi\) | |||||||
\(570\) | 130.170 | + | 80.7899i | 0.228368 | + | 0.141737i | ||||
\(571\) | −649.705 | −1.13784 | −0.568919 | − | 0.822394i | \(-0.692638\pi\) | ||||
−0.568919 | + | 0.822394i | \(0.692638\pi\) | |||||||
\(572\) | −1006.66 | + | 498.582i | −1.75990 | + | 0.871646i | ||||
\(573\) | − | 698.630i | − | 1.21925i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.6785i | 0.0220495i | ||||||||
\(576\) | 178.598 | + | 34.5695i | 0.310066 | + | 0.0600165i | ||||
\(577\) | 346.022 | 0.599692 | 0.299846 | − | 0.953988i | \(-0.403065\pi\) | ||||
0.299846 | + | 0.953988i | \(0.403065\pi\) | |||||||
\(578\) | 304.743 | − | 491.007i | 0.527238 | − | 0.849493i | ||||
\(579\) | 300.537 | 0.519061 | ||||||||
\(580\) | 300.312 | + | 606.344i | 0.517779 | + | 1.04542i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −328.389 | + | 529.106i | −0.564242 | + | 0.909116i | ||||
\(583\) | − | 465.434i | − | 0.798342i | ||||||
\(584\) | −445.240 | − | 42.6941i | −0.762397 | − | 0.0731064i | ||||
\(585\) | −181.482 | −0.310226 | ||||||||
\(586\) | −491.466 | − | 305.028i | −0.838679 | − | 0.520526i | ||||
\(587\) | 1153.54 | 1.96514 | 0.982572 | − | 0.185885i | \(-0.0595150\pi\) | ||||
0.982572 | + | 0.185885i | \(0.0595150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 155.488i | − | 0.263987i | ||||||
\(590\) | 289.589 | + | 179.733i | 0.490828 | + | 0.304632i | ||||
\(591\) | − | 74.5515i | − | 0.126145i | ||||||
\(592\) | 690.276 | + | 525.909i | 1.16601 | + | 0.888360i | ||||
\(593\) | −880.135 | −1.48421 | −0.742104 | − | 0.670285i | \(-0.766172\pi\) | ||||
−0.742104 | + | 0.670285i | \(0.766172\pi\) | |||||||
\(594\) | −479.994 | + | 773.374i | −0.808071 | + | 1.30198i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 437.058 | − | 216.467i | 0.733318 | − | 0.363200i | ||||
\(597\) | − | 626.081i | − | 1.04871i | ||||||
\(598\) | 151.043 | − | 243.363i | 0.252580 | − | 0.406961i | ||||
\(599\) | − | 554.939i | − | 0.926442i | −0.886243 | − | 0.463221i | \(-0.846694\pi\) | ||
0.886243 | − | 0.463221i | \(-0.153306\pi\) | |||||||
\(600\) | 31.7237 | + | 3.04199i | 0.0528728 | + | 0.00506998i | ||||
\(601\) | 666.057 | 1.10825 | 0.554124 | − | 0.832434i | \(-0.313054\pi\) | ||||
0.554124 | + | 0.832434i | \(0.313054\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 52.3977 | 0.0868950 | ||||||||
\(604\) | 790.027 | − | 391.287i | 1.30799 | − | 0.647826i | ||||
\(605\) | 1661.57i | 2.74640i | ||||||||
\(606\) | −1059.31 | − | 657.461i | −1.74804 | − | 1.08492i | ||||
\(607\) | 192.927i | 0.317836i | 0.987292 | + | 0.158918i | \(0.0508006\pi\) | ||||
−0.987292 | + | 0.158918i | \(0.949199\pi\) | |||||||
\(608\) | 51.9718 | + | 136.307i | 0.0854800 | + | 0.224189i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −327.536 | + | 527.732i | −0.536945 | + | 0.865134i | ||||
\(611\) | −945.878 | −1.54808 | ||||||||
\(612\) | −1.18528 | − | 2.39315i | −0.00193674 | − | 0.00391037i | ||||
\(613\) | 608.234i | 0.992226i | 0.868258 | + | 0.496113i | \(0.165240\pi\) | ||||
−0.868258 | + | 0.496113i | \(0.834760\pi\) | |||||||
\(614\) | 0.731077 | − | 1.17792i | 0.00119068 | − | 0.00191844i | ||||
\(615\) | 635.668i | 1.03361i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.884056 | 0.00143283 | 0.000716415 | − | 1.00000i | \(-0.499772\pi\) | ||||
0.000716415 | 1.00000i | \(0.499772\pi\) | ||||||||
\(618\) | 229.820 | + | 142.638i | 0.371877 | + | 0.230805i | ||||
\(619\) | −358.525 | −0.579200 | −0.289600 | − | 0.957148i | \(-0.593522\pi\) | ||||
−0.289600 | + | 0.957148i | \(0.593522\pi\) | |||||||
\(620\) | 295.669 | + | 596.969i | 0.476885 | + | 0.962853i | ||||
\(621\) | − | 232.080i | − | 0.373719i | ||||||
\(622\) | −105.626 | − | 65.5569i | −0.169817 | − | 0.105397i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −572.694 | − | 436.326i | −0.917780 | − | 0.699240i | ||||
\(625\) | −594.720 | −0.951552 | ||||||||
\(626\) | 225.272 | − | 362.962i | 0.359860 | − | 0.579812i | ||||
\(627\) | 336.937 | 0.537379 | ||||||||
\(628\) | −24.2672 | + | 12.0191i | −0.0386421 | + | 0.0191388i | ||||
\(629\) | − | 12.7397i | − | 0.0202539i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 390.515i | − | 0.618883i | −0.950918 | − | 0.309442i | \(-0.899858\pi\) | ||
0.950918 | − | 0.309442i | \(-0.100142\pi\) | |||||||
\(632\) | 72.5540 | − | 756.637i | 0.114801 | − | 1.19721i | ||||
\(633\) | −73.7137 | −0.116451 | ||||||||
\(634\) | 39.8619 | + | 24.7403i | 0.0628737 | + | 0.0390225i | ||||
\(635\) | −122.759 | −0.193322 | ||||||||
\(636\) | 267.309 | − | 132.394i | 0.420298 | − | 0.208166i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1264.39 | + | 784.742i | 1.98180 | + | 1.23000i | ||||
\(639\) | − | 135.083i | − | 0.211397i | ||||||
\(640\) | −458.731 | − | 424.499i | −0.716767 | − | 0.663280i | ||||
\(641\) | −431.936 | −0.673848 | −0.336924 | − | 0.941532i | \(-0.609386\pi\) | ||||
−0.336924 | + | 0.941532i | \(0.609386\pi\) | |||||||
\(642\) | −139.551 | + | 224.847i | −0.217369 | + | 0.350229i | ||||
\(643\) | −49.9370 | −0.0776625 | −0.0388313 | − | 0.999246i | \(-0.512363\pi\) | ||||
−0.0388313 | + | 0.999246i | \(0.512363\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 81.4480i | − | 0.126276i | ||||||
\(646\) | 1.12934 | − | 1.81961i | 0.00174821 | − | 0.00281674i | ||||
\(647\) | 224.141i | 0.346431i | 0.984884 | + | 0.173216i | \(0.0554157\pi\) | ||||
−0.984884 | + | 0.173216i | \(0.944584\pi\) | |||||||
\(648\) | −784.421 | − | 75.2182i | −1.21053 | − | 0.116077i | ||||
\(649\) | 749.582 | 1.15498 | ||||||||
\(650\) | −25.7223 | − | 15.9645i | −0.0395728 | − | 0.0245608i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 367.922 | + | 742.851i | 0.564297 | + | 1.13934i | ||||
\(653\) | 80.7637i | 0.123681i | 0.998086 | + | 0.0618405i | \(0.0196970\pi\) | ||||
−0.998086 | + | 0.0618405i | \(0.980303\pi\) | |||||||
\(654\) | −163.028 | − | 101.183i | −0.249279 | − | 0.154715i | ||||
\(655\) | 617.186i | 0.942268i | ||||||||
\(656\) | −366.819 | + | 481.464i | −0.559175 | + | 0.733939i | ||||
\(657\) | −158.919 | −0.241886 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −940.466 | −1.42711 | −0.713555 | − | 0.700599i | \(-0.752916\pi\) | ||||
−0.713555 | + | 0.700599i | \(0.752916\pi\) | |||||||
\(660\) | −1293.61 | + | 640.701i | −1.96001 | + | 0.970759i | ||||
\(661\) | − | 119.930i | − | 0.181437i | −0.995877 | − | 0.0907184i | \(-0.971084\pi\) | ||
0.995877 | − | 0.0907184i | \(-0.0289163\pi\) | |||||||
\(662\) | −535.149 | + | 862.240i | −0.808382 | + | 1.30248i | ||||
\(663\) | 10.5696i | 0.0159421i | ||||||||
\(664\) | −569.513 | − | 54.6107i | −0.857700 | − | 0.0822450i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 261.970 | + | 162.592i | 0.393349 | + | 0.244132i | ||||
\(667\) | −379.426 | −0.568855 | ||||||||
\(668\) | 593.330 | − | 293.866i | 0.888219 | − | 0.439920i | ||||
\(669\) | − | 674.346i | − | 1.00799i | ||||||
\(670\) | −152.959 | − | 94.9341i | −0.228298 | − | 0.141693i | ||||
\(671\) | 1366.00i | 2.03577i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1085.06 | 1.61227 | 0.806136 | − | 0.591731i | \(-0.201555\pi\) | ||||
0.806136 | + | 0.591731i | \(0.201555\pi\) | |||||||
\(674\) | 361.465 | − | 582.398i | 0.536298 | − | 0.864091i | ||||
\(675\) | −24.5298 | −0.0363404 | ||||||||
\(676\) | 3.51933 | + | 7.10569i | 0.00520611 | + | 0.0105114i | ||||
\(677\) | − | 949.901i | − | 1.40310i | −0.712618 | − | 0.701552i | \(-0.752491\pi\) | ||
0.712618 | − | 0.701552i | \(-0.247509\pi\) | |||||||
\(678\) | −299.217 | + | 482.104i | −0.441324 | + | 0.711068i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.875819 | + | 9.13357i | −0.00128797 | + | 0.0134317i | ||||
\(681\) | 93.8270 | 0.137778 | ||||||||
\(682\) | 1244.84 | + | 772.608i | 1.82528 | + | 1.13286i | ||||
\(683\) | −893.785 | −1.30862 | −0.654308 | − | 0.756228i | \(-0.727040\pi\) | ||||
−0.654308 | + | 0.756228i | \(0.727040\pi\) | |||||||
\(684\) | 23.0040 | + | 46.4461i | 0.0336315 | + | 0.0679037i | ||||
\(685\) | 170.635i | 0.249102i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 606.861i | 0.883349i | ||||||||
\(688\) | 47.0004 | − | 61.6898i | 0.0683145 | − | 0.0896654i | ||||
\(689\) | −283.366 | −0.411272 | ||||||||
\(690\) | 194.097 | − | 312.732i | 0.281300 | − | 0.453235i | ||||
\(691\) | −1208.56 | −1.74901 | −0.874504 | − | 0.485019i | \(-0.838813\pi\) | ||||
−0.874504 | + | 0.485019i | \(0.838813\pi\) | |||||||
\(692\) | −318.489 | + | 157.742i | −0.460244 | + | 0.227951i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −144.222 | + | 232.373i | −0.207813 | + | 0.334831i | ||||
\(695\) | 581.782i | 0.837096i | ||||||||
\(696\) | −91.0371 | + | 949.389i | −0.130800 | + | 1.36407i | ||||
\(697\) | 8.88585 | 0.0127487 | ||||||||
\(698\) | −139.439 | − | 86.5430i | −0.199770 | − | 0.123987i | ||||
\(699\) | 247.210 | 0.353662 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 219.477i | 0.313091i | 0.987671 | + | 0.156546i | \(0.0500358\pi\) | ||||
−0.987671 | + | 0.156546i | \(0.949964\pi\) | |||||||
\(702\) | 470.847 | + | 292.231i | 0.670723 | + | 0.416284i | ||||
\(703\) | 247.251i | 0.351709i | ||||||||
\(704\) | −1349.52 | − | 261.213i | −1.91693 | − | 0.371041i | ||||
\(705\) | −1215.50 | −1.72411 | ||||||||
\(706\) | 535.108 | − | 862.175i | 0.757944 | − | 1.22121i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 213.221 | + | 430.502i | 0.301159 | + | 0.608054i | ||||
\(709\) | 1265.13i | 1.78439i | 0.451651 | + | 0.892195i | \(0.350835\pi\) | ||||
−0.451651 | + | 0.892195i | \(0.649165\pi\) | |||||||
\(710\) | −244.743 | + | 394.334i | −0.344709 | + | 0.555400i | ||||
\(711\) | − | 270.066i | − | 0.379839i | ||||||
\(712\) | 1272.21 | + | 121.992i | 1.78681 | + | 0.171338i | ||||
\(713\) | −373.560 | −0.523927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1371.31 | 1.91792 | ||||||||
\(716\) | −142.698 | − | 288.115i | −0.199299 | − | 0.402395i | ||||
\(717\) | − | 244.650i | − | 0.341213i | ||||||
\(718\) | −952.989 | − | 591.472i | −1.32728 | − | 0.823777i | ||||
\(719\) | − | 1163.47i | − | 1.61818i | −0.587687 | − | 0.809089i | \(-0.699961\pi\) | ||
0.587687 | − | 0.809089i | \(-0.300039\pi\) | |||||||
\(720\) | −176.639 | − | 134.578i | −0.245332 | − | 0.186914i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 358.820 | − | 578.136i | 0.496981 | − | 0.800743i | ||||
\(723\) | −193.094 | −0.267074 | ||||||||
\(724\) | 990.573 | − | 490.614i | 1.36819 | − | 0.677643i | ||||
\(725\) | 40.1036i | 0.0553153i | ||||||||
\(726\) | −1235.05 | + | 1989.93i | −1.70117 | + | 2.74094i | ||||
\(727\) | − | 1303.68i | − | 1.79324i | −0.442803 | − | 0.896619i | \(-0.646016\pi\) | ||
0.442803 | − | 0.896619i | \(-0.353984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 376.305 | 0.516193 | ||||||||
\(730\) | 463.916 | + | 287.929i | 0.635502 | + | 0.394424i | ||||
\(731\) | −1.13854 | −0.00155751 | ||||||||
\(732\) | −784.526 | + | 388.562i | −1.07176 | + | 0.530823i | ||||
\(733\) | 1256.12i | 1.71367i | 0.515589 | + | 0.856836i | \(0.327573\pi\) | ||||
−0.515589 | + | 0.856836i | \(0.672427\pi\) | |||||||
\(734\) | 45.7847 | + | 28.4163i | 0.0623770 | + | 0.0387143i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 327.477 | − | 124.862i | 0.444942 | − | 0.169649i | ||||
\(737\) | −395.925 | −0.537212 | ||||||||
\(738\) | −113.407 | + | 182.723i | −0.153668 | + | 0.247592i | ||||
\(739\) | 687.168 | 0.929862 | 0.464931 | − | 0.885347i | \(-0.346079\pi\) | ||||
0.464931 | + | 0.885347i | \(0.346079\pi\) | |||||||
\(740\) | −470.160 | − | 949.276i | −0.635352 | − | 1.28281i | ||||
\(741\) | − | 205.134i | − | 0.276835i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 362.628i | − | 0.488059i | −0.969768 | − | 0.244030i | \(-0.921531\pi\) | ||
0.969768 | − | 0.244030i | \(-0.0784694\pi\) | |||||||
\(744\) | −89.6295 | + | 934.710i | −0.120470 | + | 1.25633i | ||||
\(745\) | −595.376 | −0.799163 | ||||||||
\(746\) | 914.287 | + | 567.452i | 1.22559 | + | 0.760659i | ||||
\(747\) | −203.275 | −0.272122 | ||||||||
\(748\) | 8.95620 | + | 18.0830i | 0.0119735 | + | 0.0241751i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −746.905 | − | 463.566i | −0.995874 | − | 0.618088i | ||||
\(751\) | 261.366i | 0.348024i | 0.984744 | + | 0.174012i | \(0.0556732\pi\) | ||||
−0.984744 | + | 0.174012i | \(0.944327\pi\) | |||||||
\(752\) | −920.634 | − | 701.415i | −1.22425 | − | 0.932733i | ||||
\(753\) | −1269.67 | −1.68615 | ||||||||
\(754\) | 477.768 | − | 769.787i | 0.633645 | − | 1.02094i | ||||
\(755\) | −1076.20 | −1.42544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1395.34i | − | 1.84325i | −0.388081 | − | 0.921625i | \(-0.626862\pi\) | ||
0.388081 | − | 0.921625i | \(-0.373138\pi\) | |||||||
\(758\) | 192.091 | − | 309.500i | 0.253418 | − | 0.408311i | ||||
\(759\) | − | 809.488i | − | 1.06652i | ||||||
\(760\) | 16.9979 | − | 177.264i | 0.0223656 | − | 0.233242i | ||||
\(761\) | 319.500 | 0.419843 | 0.209921 | − | 0.977718i | \(-0.432679\pi\) | ||||
0.209921 | + | 0.977718i | \(0.432679\pi\) | |||||||
\(762\) | −147.019 | − | 91.2470i | −0.192938 | − | 0.119747i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −727.695 | + | 360.415i | −0.952481 | + | 0.471747i | ||||
\(765\) | 3.26003i | 0.00426148i | ||||||||
\(766\) | −566.331 | − | 351.493i | −0.739336 | − | 0.458868i | ||||
\(767\) | − | 456.362i | − | 0.594996i | ||||||
\(768\) | −233.853 | − | 849.362i | −0.304496 | − | 1.10594i | ||||
\(769\) | −634.936 | −0.825664 | −0.412832 | − | 0.910807i | \(-0.635460\pi\) | ||||
−0.412832 | + | 0.910807i | \(0.635460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −81.7056 | −0.105974 | ||||||||
\(772\) | −155.043 | − | 313.040i | −0.200833 | − | 0.405492i | ||||
\(773\) | − | 96.1663i | − | 0.124407i | −0.998063 | − | 0.0622033i | \(-0.980187\pi\) | ||
0.998063 | − | 0.0622033i | \(-0.0198127\pi\) | |||||||
\(774\) | 14.5308 | − | 23.4122i | 0.0187736 | − | 0.0302484i | ||||
\(775\) | 39.4836i | 0.0509465i | ||||||||
\(776\) | 720.530 | + | 69.0917i | 0.928518 | + | 0.0890358i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −186.310 | − | 115.633i | −0.239473 | − | 0.148629i | ||||
\(779\) | −172.456 | −0.221382 | ||||||||
\(780\) | 390.073 | + | 787.576i | 0.500093 | + | 1.00971i | ||||
\(781\) | 1020.71i | 1.30693i | ||||||||
\(782\) | −4.37161 | − | 2.71324i | −0.00559029 | − | 0.00346961i | ||||
\(783\) | − | 734.098i | − | 0.937545i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.0577 | 0.0421117 | ||||||||
\(786\) | −458.754 | + | 739.151i | −0.583656 | + | 0.940396i | ||||
\(787\) | 1319.25 | 1.67630 | 0.838148 | − | 0.545442i | \(-0.183638\pi\) | ||||
0.838148 | + | 0.545442i | \(0.183638\pi\) | |||||||
\(788\) | −77.6531 | + | 38.4603i | −0.0985445 | + | 0.0488074i | ||||
\(789\) | − | 254.554i | − | 0.322628i | ||||||
\(790\) | −489.305 | + | 788.375i | −0.619373 | + | 0.997943i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −486.152 | − | 46.6171i | −0.613828 | − | 0.0588600i | ||||
\(793\) | 831.651 | 1.04874 | ||||||||
\(794\) | −528.380 | − | 327.939i | −0.665466 | − | 0.413021i | ||||
\(795\) | −364.139 | −0.458036 | ||||||||
\(796\) | −652.128 | + | 322.988i | −0.819257 | + | 0.405764i | ||||
\(797\) | 818.575i | 1.02707i | 0.858068 | + | 0.513535i | \(0.171664\pi\) | ||||
−0.858068 | + | 0.513535i | \(0.828336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.9911i | 0.0212655i | ||||||||
\(800\) | −13.1973 | − | 34.6128i | −0.0164967 | − | 0.0432660i | ||||
\(801\) | 454.088 | 0.566902 | ||||||||
\(802\) | 447.081 | − | 720.343i | 0.557457 | − | 0.898183i | ||||
\(803\) | 1200.82 | 1.49541 | ||||||||
\(804\) | −112.622 | − | 227.389i | −0.140077 | − | 0.282823i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 470.381 | − | 757.885i | 0.583599 | − | 0.940304i | ||||
\(807\) | − | 1154.87i | − | 1.43106i | ||||||
\(808\) | −138.327 | + | 1442.56i | −0.171197 | + | 1.78534i | ||||
\(809\) | 1232.72 | 1.52376 | 0.761881 | − | 0.647717i | \(-0.224276\pi\) | ||||
0.761881 | + | 0.647717i | \(0.224276\pi\) | |||||||
\(810\) | 817.324 | + | 507.272i | 1.00904 | + | 0.626261i | ||||
\(811\) | 1009.05 | 1.24421 | 0.622103 | − | 0.782935i | \(-0.286278\pi\) | ||||
0.622103 | + | 0.782935i | \(0.286278\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 644.468i | − | 0.792703i | ||||||
\(814\) | −1979.49 | − | 1228.57i | −2.43181 | − | 1.50930i | ||||
\(815\) | − | 1011.94i | − | 1.24164i | ||||||
\(816\) | −7.83787 | + | 10.2875i | −0.00960524 | + | 0.0126072i | ||||
\(817\) | 22.0968 | 0.0270462 | ||||||||
\(818\) | 468.849 | − | 755.417i | 0.573165 | − | 0.923493i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 662.114 | − | 327.934i | 0.807457 | − | 0.399919i | ||||
\(821\) | − | 939.093i | − | 1.14384i | −0.820309 | − | 0.571920i | \(-0.806199\pi\) | ||
0.820309 | − | 0.571920i | \(-0.193801\pi\) | |||||||
\(822\) | −126.833 | + | 204.355i | −0.154298 | + | 0.248607i | ||||
\(823\) | − | 911.100i | − | 1.10705i | −0.832833 | − | 0.553524i | \(-0.813283\pi\) | ||
0.832833 | − | 0.553524i | \(-0.186717\pi\) | |||||||
\(824\) | 30.0104 | − | 312.966i | 0.0364204 | − | 0.379814i | ||||
\(825\) | −85.5591 | −0.103708 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −65.6564 | −0.0793910 | −0.0396955 | − | 0.999212i | \(-0.512639\pi\) | ||||
−0.0396955 | + | 0.999212i | \(0.512639\pi\) | |||||||
\(828\) | 111.586 | − | 55.2669i | 0.134766 | − | 0.0667474i | ||||
\(829\) | − | 1515.94i | − | 1.82864i | −0.404997 | − | 0.914318i | \(-0.632728\pi\) | ||
0.404997 | − | 0.914318i | \(-0.367272\pi\) | |||||||
\(830\) | 593.402 | + | 368.294i | 0.714942 | + | 0.443728i | ||||
\(831\) | 456.285i | 0.549079i | ||||||||
\(832\) | −159.032 | + | 821.616i | −0.191144 | + | 0.987519i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −432.438 | + | 696.752i | −0.518511 | + | 0.835433i | ||||
\(835\) | −808.257 | −0.967972 | ||||||||
\(836\) | −173.822 | − | 350.954i | −0.207921 | − | 0.419802i | ||||
\(837\) | − | 722.747i | − | 0.863497i | ||||||
\(838\) | 482.123 | − | 776.804i | 0.575326 | − | 0.926974i | ||||
\(839\) | − | 869.972i | − | 1.03692i | −0.855103 | − | 0.518458i | \(-0.826506\pi\) | ||
0.855103 | − | 0.518458i | \(-0.173494\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −359.174 | −0.427080 | ||||||||
\(842\) | −43.3006 | − | 26.8745i | −0.0514258 | − | 0.0319174i | ||||
\(843\) | 1140.85 | 1.35333 | ||||||||
\(844\) | 38.0280 | + | 76.7804i | 0.0450569 | + | 0.0909721i | ||||
\(845\) | − | 9.67964i | − | 0.0114552i | ||||||
\(846\) | −349.395 | − | 216.852i | −0.412996 | − | 0.256326i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −275.804 | − | 210.130i | −0.325240 | − | 0.247795i | ||||
\(849\) | 229.588 | 0.270421 | ||||||||
\(850\) | −0.286777 | + | 0.462059i | −0.000337384 | + | 0.000543599i | ||||
\(851\) | 594.020 | 0.698026 | ||||||||
\(852\) | −586.217 | + | 290.343i | −0.688048 | + | 0.340778i | ||||
\(853\) | 1643.91i | 1.92721i | 0.267322 | + | 0.963607i | \(0.413861\pi\) | ||||
−0.267322 | + | 0.963607i | \(0.586139\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 63.2706i | − | 0.0740007i | ||||||
\(856\) | 306.194 | + | 29.3610i | 0.357703 | + | 0.0343002i | ||||
\(857\) | −286.059 | −0.333791 | −0.166895 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166895 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(858\) | 1642.30 | + | 1019.29i | 1.91411 | + | 1.18799i | ||||
\(859\) | −719.782 | −0.837930 | −0.418965 | − | 0.908002i | \(-0.637607\pi\) | ||||
−0.418965 | + | 0.908002i | \(0.637607\pi\) | |||||||
\(860\) | −84.8365 | + | 42.0181i | −0.0986471 | + | 0.0488582i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 211.726 | + | 131.408i | 0.245622 | + | 0.152445i | ||||
\(863\) | 1120.47i | 1.29835i | 0.760641 | + | 0.649173i | \(0.224885\pi\) | ||||
−0.760641 | + | 0.649173i | \(0.775115\pi\) | |||||||
\(864\) | 241.578 | + | 633.589i | 0.279604 | + | 0.733320i | ||||
\(865\) | 433.857 | 0.501569 | ||||||||
\(866\) | −287.158 | + | 462.674i | −0.331592 | + | 0.534265i | ||||
\(867\) | −994.339 | −1.14687 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2040.66i | 2.34828i | ||||||||
\(870\) | 613.954 | − | 989.213i | 0.705695 | − | 1.13703i | ||||
\(871\) | 241.048i | 0.276749i | ||||||||
\(872\) | −21.2886 | + | 222.010i | −0.0244135 | + | 0.254599i | ||||
\(873\) | 257.178 | 0.294591 | ||||||||
\(874\) | 84.8441 | + | 52.6584i | 0.0970756 | + | 0.0602499i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 341.576 | + | 689.658i | 0.389927 | + | 0.787281i | ||||
\(877\) | 145.400i | 0.165792i | 0.996558 | + | 0.0828960i | \(0.0264169\pi\) | ||||
−0.996558 | + | 0.0828960i | \(0.973583\pi\) | |||||||
\(878\) | 433.442 | + | 269.016i | 0.493670 | + | 0.306396i | ||||
\(879\) | 995.269i | 1.13227i | ||||||||
\(880\) | 1334.71 | + | 1016.89i | 1.51672 | + | 1.15556i | ||||
\(881\) | −476.080 | −0.540386 | −0.270193 | − | 0.962806i | \(-0.587087\pi\) | ||||
−0.270193 | + | 0.962806i | \(0.587087\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1101.22 | −1.24714 | −0.623568 | − | 0.781769i | \(-0.714318\pi\) | ||||
−0.623568 | + | 0.781769i | \(0.714318\pi\) | |||||||
\(884\) | 11.0093 | − | 5.45273i | 0.0124540 | − | 0.00616825i | ||||
\(885\) | − | 586.447i | − | 0.662652i | ||||||
\(886\) | −138.452 | + | 223.075i | −0.156266 | + | 0.251778i | ||||
\(887\) | 1491.49i | 1.68150i | 0.541427 | + | 0.840748i | \(0.317884\pi\) | ||||
−0.541427 | + | 0.840748i | \(0.682116\pi\) | |||||||
\(888\) | 142.525 | − | 1486.34i | 0.160501 | − | 1.67380i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1325.57 | − | 822.717i | −1.48941 | − | 0.924401i | ||||
\(891\) | 2115.59 | 2.37440 | ||||||||
\(892\) | −702.401 | + | 347.887i | −0.787445 | + | 0.390008i | ||||
\(893\) | − | 329.764i | − | 0.369276i | ||||||
\(894\) | −713.032 | − | 442.543i | −0.797575 | − | 0.495015i | ||||
\(895\) | 392.481i | 0.438526i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −492.834 | −0.549425 | ||||||||
\(898\) | 677.971 | − | 1092.36i | 0.754979 | − | 1.21643i | ||||
\(899\) | −1181.62 | −1.31437 | ||||||||
\(900\) | −5.84145 | − | 11.7942i | −0.00649050 | − | 0.0131046i | ||||
\(901\) | 5.09021i | 0.00564951i | ||||||||
\(902\) | 856.920 | − | 1380.68i | 0.950023 | − | 1.53069i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 656.524 | + | 62.9541i | 0.726243 | + | 0.0696395i | ||||
\(905\) | −1349.40 | −1.49104 | ||||||||
\(906\) | −1288.88 | − | 799.942i | −1.42260 | − | 0.882938i | ||||
\(907\) | 1155.46 | 1.27394 | 0.636969 | − | 0.770889i | \(-0.280188\pi\) | ||||
0.636969 | + | 0.770889i | \(0.280188\pi\) | |||||||
\(908\) | −48.4043 | − | 97.7305i | −0.0533087 | − | 0.107633i | ||||
\(909\) | 514.891i | 0.566436i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 944.690i | − | 1.03698i | −0.855083 | − | 0.518491i | \(-0.826494\pi\) | ||
0.855083 | − | 0.518491i | \(-0.173506\pi\) | |||||||
\(912\) | 152.117 | − | 199.660i | 0.166795 | − | 0.218925i | ||||
\(913\) | 1535.98 | 1.68235 | ||||||||
\(914\) | −730.984 | + | 1177.77i | −0.799764 | + | 1.28859i | ||||
\(915\) | 1068.71 | 1.16799 | ||||||||
\(916\) | 632.108 | − | 313.072i | 0.690074 | − | 0.341782i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.24945 | − | 8.45800i | 0.00571836 | − | 0.00921351i | ||||
\(919\) | 149.150i | 0.162296i | 0.996702 | + | 0.0811478i | \(0.0258586\pi\) | ||||
−0.996702 | + | 0.0811478i | \(0.974141\pi\) | |||||||
\(920\) | −425.876 | − | 40.8373i | −0.462908 | − | 0.0443883i | ||||
\(921\) | −2.38541 | −0.00259003 | ||||||||
\(922\) | −439.611 | − | 272.844i | −0.476801 | − | 0.295926i | ||||
\(923\) | 621.430 | 0.673272 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 62.7851i | − | 0.0678758i | ||||||
\(926\) | −1082.85 | − | 672.068i | −1.16938 | − | 0.725775i | ||||
\(927\) | − | 111.707i | − | 0.120503i | ||||||
\(928\) | 1035.85 | − | 394.954i | 1.11622 | − | 0.425597i | ||||
\(929\) | 58.8399 | 0.0633368 | 0.0316684 | − | 0.999498i | \(-0.489918\pi\) | ||||
0.0316684 | + | 0.999498i | \(0.489918\pi\) | |||||||
\(930\) | 604.462 | − | 973.918i | 0.649959 | − | 1.04722i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −127.533 | − | 257.494i | −0.136838 | − | 0.276282i | ||||
\(933\) | 213.904i | 0.229265i | ||||||||
\(934\) | −210.390 | + | 338.984i | −0.225257 | + | 0.362938i | ||||
\(935\) | − | 24.6333i | − | 0.0263458i | ||||||
\(936\) | −28.3815 | + | 295.980i | −0.0303222 | + | 0.316218i | ||||
\(937\) | 1700.18 | 1.81449 | 0.907246 | − | 0.420601i | \(-0.138181\pi\) | ||||
0.907246 | + | 0.420601i | \(0.138181\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −735.036 | −0.782786 | ||||||||
\(940\) | 627.061 | + | 1266.07i | 0.667086 | + | 1.34688i | ||||
\(941\) | 56.6116i | 0.0601611i | 0.999547 | + | 0.0300805i | \(0.00957637\pi\) | ||||
−0.999547 | + | 0.0300805i | \(0.990424\pi\) | |||||||
\(942\) | 39.5904 | + | 24.5718i | 0.0420281 | + | 0.0260847i | ||||
\(943\) | 414.325i | 0.439369i | ||||||||
\(944\) | 338.415 | − | 444.182i | 0.358490 | − | 0.470532i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −109.797 | + | 176.907i | −0.116064 | + | 0.187005i | ||||
\(947\) | 242.533 | 0.256107 | 0.128053 | − | 0.991767i | \(-0.459127\pi\) | ||||
0.128053 | + | 0.991767i | \(0.459127\pi\) | |||||||
\(948\) | −1172.00 | + | 580.471i | −1.23629 | + | 0.612311i | ||||
\(949\) | − | 731.084i | − | 0.770373i | ||||||
\(950\) | 5.56575 | − | 8.96763i | 0.00585869 | − | 0.00943961i | ||||
\(951\) | − | 80.7244i | − | 0.0848837i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −364.070 | −0.382025 | −0.191013 | − | 0.981588i | \(-0.561177\pi\) | ||||
−0.191013 | + | 0.981588i | \(0.561177\pi\) | |||||||
\(954\) | −104.672 | − | 64.9644i | −0.109719 | − | 0.0680969i | ||||
\(955\) | 991.294 | 1.03800 | ||||||||
\(956\) | −254.828 | + | 126.212i | −0.266556 | + | 0.132021i | ||||
\(957\) | − | 2560.51i | − | 2.67556i | ||||||
\(958\) | −1145.61 | − | 711.021i | −1.19583 | − | 0.742193i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −204.364 | + | 1055.81i | −0.212879 | + | 1.09981i | ||||
\(961\) | −202.348 | −0.210560 | ||||||||
\(962\) | −747.981 | + | 1205.16i | −0.777527 | + | 1.25276i | ||||
\(963\) | 109.290 | 0.113489 | ||||||||
\(964\) | 99.6152 | + | 201.128i | 0.103335 | + | 0.208639i | ||||
\(965\) | 426.435i | 0.441901i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1221.99i | 1.26369i | 0.775093 | + | 0.631847i | \(0.217703\pi\) | ||||
−0.775093 | + | 0.631847i | \(0.782297\pi\) | |||||||
\(968\) | 2709.86 | + | 259.849i | 2.79944 | + | 0.268439i | ||||
\(969\) | −3.68490 | −0.00380279 | ||||||||
\(970\) | −750.754 | − | 465.955i | −0.773973 | − | 0.480366i | ||||
\(971\) | 1088.53 | 1.12104 | 0.560521 | − | 0.828140i | \(-0.310601\pi\) | ||||
0.560521 | + | 0.828140i | \(0.310601\pi\) | |||||||
\(972\) | 263.215 | + | 531.443i | 0.270797 | + | 0.546752i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 682.644 | + | 423.683i | 0.700866 | + | 0.434992i | ||||
\(975\) | 52.0903i | 0.0534259i | ||||||||
\(976\) | 809.455 | + | 616.710i | 0.829360 | + | 0.631875i | ||||
\(977\) | −1061.51 | −1.08650 | −0.543252 | − | 0.839570i | \(-0.682807\pi\) | ||||
−0.543252 | + | 0.839570i | \(0.682807\pi\) | |||||||
\(978\) | 752.175 | − | 1211.92i | 0.769095 | − | 1.23918i | ||||
\(979\) | −3431.17 | −3.50477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 79.2419i | 0.0807766i | ||||||||
\(982\) | −452.329 | + | 728.800i | −0.460621 | + | 0.742159i | ||||
\(983\) | − | 1322.61i | − | 1.34549i | −0.739877 | − | 0.672743i | \(-0.765116\pi\) | ||
0.739877 | − | 0.672743i | \(-0.234884\pi\) | |||||||
\(984\) | 1036.71 | + | 99.4105i | 1.05357 | + | 0.101027i | ||||
\(985\) | 105.782 | 0.107393 | ||||||||
\(986\) | −13.8280 | − | 8.58232i | −0.0140243 | − | 0.00870417i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −213.669 | + | 105.826i | −0.216264 | + | 0.107112i | ||||
\(989\) | − | 53.0874i | − | 0.0536778i | ||||||
\(990\) | 506.544 | + | 314.386i | 0.511660 | + | 0.317562i | ||||
\(991\) | − | 675.806i | − | 0.681944i | −0.940073 | − | 0.340972i | \(-0.889244\pi\) | ||
0.940073 | − | 0.340972i | \(-0.110756\pi\) | |||||||
\(992\) | 1019.84 | − | 388.848i | 1.02806 | − | 0.391984i | ||||
\(993\) | 1746.12 | 1.75843 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 888.354 | 0.892818 | ||||||||
\(996\) | 436.914 | + | 882.151i | 0.438669 | + | 0.885694i | ||||
\(997\) | 409.220i | 0.410452i | 0.978715 | + | 0.205226i | \(0.0657929\pi\) | ||||
−0.978715 | + | 0.205226i | \(0.934207\pi\) | |||||||
\(998\) | −192.604 | + | 310.327i | −0.192990 | + | 0.310949i | ||||
\(999\) | 1149.28i | 1.15043i |
(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 | 392.3.g.m.99.4 | 8 | ||
4.3 | odd | 2 | 1568.3.g.m.687.4 | 8 | |||
7.2 | even | 3 | 392.3.k.n.67.8 | 16 | |||
7.3 | odd | 6 | 392.3.k.o.275.3 | 16 | |||
7.4 | even | 3 | 392.3.k.n.275.3 | 16 | |||
7.5 | odd | 6 | 392.3.k.o.67.8 | 16 | |||
7.6 | odd | 2 | 56.3.g.b.43.4 | yes | 8 | ||
8.3 | odd | 2 | inner | 392.3.g.m.99.3 | 8 | ||
8.5 | even | 2 | 1568.3.g.m.687.3 | 8 | |||
21.20 | even | 2 | 504.3.g.b.379.5 | 8 | |||
28.27 | even | 2 | 224.3.g.b.15.5 | 8 | |||
56.3 | even | 6 | 392.3.k.o.275.8 | 16 | |||
56.11 | odd | 6 | 392.3.k.n.275.8 | 16 | |||
56.13 | odd | 2 | 224.3.g.b.15.6 | 8 | |||
56.19 | even | 6 | 392.3.k.o.67.3 | 16 | |||
56.27 | even | 2 | 56.3.g.b.43.3 | ✓ | 8 | ||
56.51 | odd | 6 | 392.3.k.n.67.3 | 16 | |||
84.83 | odd | 2 | 2016.3.g.b.1135.6 | 8 | |||
112.13 | odd | 4 | 1792.3.d.j.1023.5 | 16 | |||
112.27 | even | 4 | 1792.3.d.j.1023.6 | 16 | |||
112.69 | odd | 4 | 1792.3.d.j.1023.12 | 16 | |||
112.83 | even | 4 | 1792.3.d.j.1023.11 | 16 | |||
168.83 | odd | 2 | 504.3.g.b.379.6 | 8 | |||
168.125 | even | 2 | 2016.3.g.b.1135.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.3 | ✓ | 8 | 56.27 | even | 2 | ||
56.3.g.b.43.4 | yes | 8 | 7.6 | odd | 2 | ||
224.3.g.b.15.5 | 8 | 28.27 | even | 2 | |||
224.3.g.b.15.6 | 8 | 56.13 | odd | 2 | |||
392.3.g.m.99.3 | 8 | 8.3 | odd | 2 | inner | ||
392.3.g.m.99.4 | 8 | 1.1 | even | 1 | trivial | ||
392.3.k.n.67.3 | 16 | 56.51 | odd | 6 | |||
392.3.k.n.67.8 | 16 | 7.2 | even | 3 | |||
392.3.k.n.275.3 | 16 | 7.4 | even | 3 | |||
392.3.k.n.275.8 | 16 | 56.11 | odd | 6 | |||
392.3.k.o.67.3 | 16 | 56.19 | even | 6 | |||
392.3.k.o.67.8 | 16 | 7.5 | odd | 6 | |||
392.3.k.o.275.3 | 16 | 7.3 | odd | 6 | |||
392.3.k.o.275.8 | 16 | 56.3 | even | 6 | |||
504.3.g.b.379.5 | 8 | 21.20 | even | 2 | |||
504.3.g.b.379.6 | 8 | 168.83 | odd | 2 | |||
1568.3.g.m.687.3 | 8 | 8.5 | even | 2 | |||
1568.3.g.m.687.4 | 8 | 4.3 | odd | 2 | |||
1792.3.d.j.1023.5 | 16 | 112.13 | odd | 4 | |||
1792.3.d.j.1023.6 | 16 | 112.27 | even | 4 | |||
1792.3.d.j.1023.11 | 16 | 112.83 | even | 4 | |||
1792.3.d.j.1023.12 | 16 | 112.69 | odd | 4 | |||
2016.3.g.b.1135.3 | 8 | 168.125 | even | 2 | |||
2016.3.g.b.1135.6 | 8 | 84.83 | odd | 2 |