Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,4,Mod(2,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.2");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.d (of order \(8\), 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: | \(1.00303247010\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 15.3 | ||
Root | \(-2.49971i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.15 |
Dual form | 17.4.d.a.8.3 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.47467 | + | 2.47467i | 0.874927 | + | 0.874927i | 0.993004 | − | 0.118077i | \(-0.0376731\pi\) |
−0.118077 | + | 0.993004i | \(0.537673\pi\) | |||||||
\(3\) | −1.08123 | − | 2.61032i | −0.208083 | − | 0.502357i | 0.785038 | − | 0.619447i | \(-0.212643\pi\) |
−0.993121 | + | 0.117090i | \(0.962643\pi\) | |||||||
\(4\) | 4.24796i | 0.530995i | ||||||||
\(5\) | −8.05561 | + | 3.33674i | −0.720515 | + | 0.298447i | −0.712648 | − | 0.701522i | \(-0.752504\pi\) |
−0.00786742 | + | 0.999969i | \(0.502504\pi\) | |||||||
\(6\) | 3.78400 | − | 9.13537i | 0.257468 | − | 0.621583i | ||||
\(7\) | −6.33320 | − | 2.62330i | −0.341961 | − | 0.141645i | 0.205093 | − | 0.978743i | \(-0.434250\pi\) |
−0.547053 | + | 0.837098i | \(0.684250\pi\) | |||||||
\(8\) | 9.28506 | − | 9.28506i | 0.410345 | − | 0.410345i | ||||
\(9\) | 13.4472 | − | 13.4472i | 0.498043 | − | 0.498043i | ||||
\(10\) | −28.1923 | − | 11.6776i | −0.891518 | − | 0.369279i | ||||
\(11\) | −23.6471 | + | 57.0891i | −0.648170 | + | 1.56482i | 0.167227 | + | 0.985918i | \(0.446519\pi\) |
−0.815397 | + | 0.578902i | \(0.803481\pi\) | |||||||
\(12\) | 11.0885 | − | 4.59303i | 0.266749 | − | 0.110491i | ||||
\(13\) | 5.37363i | 0.114644i | 0.998356 | + | 0.0573221i | \(0.0182562\pi\) | ||||
−0.998356 | + | 0.0573221i | \(0.981744\pi\) | |||||||
\(14\) | −9.18078 | − | 22.1644i | −0.175262 | − | 0.423120i | ||||
\(15\) | 17.4200 | + | 17.4200i | 0.299854 | + | 0.299854i | ||||
\(16\) | 79.9385 | 1.24904 | ||||||||
\(17\) | 44.2970 | + | 54.3210i | 0.631977 | + | 0.774987i | ||||
\(18\) | 66.5545 | 0.871502 | ||||||||
\(19\) | −68.4392 | − | 68.4392i | −0.826370 | − | 0.826370i | 0.160643 | − | 0.987013i | \(-0.448643\pi\) |
−0.987013 | + | 0.160643i | \(0.948643\pi\) | |||||||
\(20\) | −14.1743 | − | 34.2199i | −0.158474 | − | 0.382590i | ||||
\(21\) | 19.3681i | 0.201260i | ||||||||
\(22\) | −199.795 | + | 82.7579i | −1.93620 | + | 0.802002i | ||||
\(23\) | 44.5923 | − | 107.655i | 0.404267 | − | 0.975986i | −0.582351 | − | 0.812937i | \(-0.697867\pi\) |
0.986618 | − | 0.163049i | \(-0.0521328\pi\) | |||||||
\(24\) | −34.2763 | − | 14.1977i | −0.291526 | − | 0.120754i | ||||
\(25\) | −34.6294 | + | 34.6294i | −0.277035 | + | 0.277035i | ||||
\(26\) | −13.2979 | + | 13.2979i | −0.100305 | + | 0.100305i | ||||
\(27\) | −120.120 | − | 49.7552i | −0.856187 | − | 0.354644i | ||||
\(28\) | 11.1437 | − | 26.9032i | 0.0752126 | − | 0.181579i | ||||
\(29\) | 182.351 | − | 75.5321i | 1.16764 | − | 0.483653i | 0.287230 | − | 0.957862i | \(-0.407266\pi\) |
0.880413 | + | 0.474208i | \(0.157266\pi\) | |||||||
\(30\) | 86.2172i | 0.524701i | ||||||||
\(31\) | −52.8371 | − | 127.560i | −0.306123 | − | 0.739047i | −0.999824 | − | 0.0187835i | \(-0.994021\pi\) |
0.693700 | − | 0.720264i | \(-0.255979\pi\) | |||||||
\(32\) | 123.541 | + | 123.541i | 0.682473 | + | 0.682473i | ||||
\(33\) | 174.589 | 0.920972 | ||||||||
\(34\) | −24.8060 | + | 244.047i | −0.125123 | + | 1.23099i | ||||
\(35\) | 59.7710 | 0.288661 | ||||||||
\(36\) | 57.1229 | + | 57.1229i | 0.264458 | + | 0.264458i | ||||
\(37\) | 42.6416 | + | 102.946i | 0.189466 | + | 0.457411i | 0.989857 | − | 0.142067i | \(-0.0453749\pi\) |
−0.800391 | + | 0.599478i | \(0.795375\pi\) | |||||||
\(38\) | − | 338.729i | − | 1.44603i | ||||||
\(39\) | 14.0269 | − | 5.81013i | 0.0575924 | − | 0.0238555i | ||||
\(40\) | −43.8149 | + | 105.779i | −0.173194 | + | 0.418127i | ||||
\(41\) | −153.814 | − | 63.7117i | −0.585894 | − | 0.242685i | 0.0699888 | − | 0.997548i | \(-0.477704\pi\) |
−0.655883 | + | 0.754862i | \(0.727704\pi\) | |||||||
\(42\) | −47.9296 | + | 47.9296i | −0.176088 | + | 0.176088i | ||||
\(43\) | −117.300 | + | 117.300i | −0.416000 | + | 0.416000i | −0.883823 | − | 0.467822i | \(-0.845039\pi\) |
0.467822 | + | 0.883823i | \(0.345039\pi\) | |||||||
\(44\) | −242.512 | − | 100.452i | −0.830911 | − | 0.344175i | ||||
\(45\) | −63.4553 | + | 153.195i | −0.210208 | + | 0.507487i | ||||
\(46\) | 376.762 | − | 156.060i | 1.20762 | − | 0.500213i | ||||
\(47\) | 130.994i | 0.406541i | 0.979123 | + | 0.203271i | \(0.0651571\pi\) | ||||
−0.979123 | + | 0.203271i | \(0.934843\pi\) | |||||||
\(48\) | −86.4320 | − | 208.665i | −0.259904 | − | 0.627464i | ||||
\(49\) | −209.310 | − | 209.310i | −0.610233 | − | 0.610233i | ||||
\(50\) | −171.392 | −0.484771 | ||||||||
\(51\) | 93.9001 | − | 174.363i | 0.257816 | − | 0.478740i | ||||
\(52\) | −22.8269 | −0.0608755 | ||||||||
\(53\) | 505.038 | + | 505.038i | 1.30891 | + | 1.30891i | 0.922201 | + | 0.386711i | \(0.126389\pi\) |
0.386711 | + | 0.922201i | \(0.373611\pi\) | |||||||
\(54\) | −174.129 | − | 420.384i | −0.438813 | − | 1.05939i | ||||
\(55\) | − | 538.792i | − | 1.32092i | ||||||
\(56\) | −83.1616 | + | 34.4467i | −0.198445 | + | 0.0821987i | ||||
\(57\) | −104.650 | + | 252.647i | −0.243179 | + | 0.587087i | ||||
\(58\) | 638.174 | + | 264.340i | 1.44476 | + | 0.598441i | ||||
\(59\) | −598.365 | + | 598.365i | −1.32035 | + | 1.32035i | −0.406855 | + | 0.913493i | \(0.633375\pi\) |
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(60\) | −73.9992 | + | 73.9992i | −0.159221 | + | 0.159221i | ||||
\(61\) | 4.61209 | + | 1.91039i | 0.00968061 | + | 0.00400984i | 0.387518 | − | 0.921862i | \(-0.373332\pi\) |
−0.377838 | + | 0.925872i | \(0.623332\pi\) | |||||||
\(62\) | 184.915 | − | 446.423i | 0.378777 | − | 0.914448i | ||||
\(63\) | −120.439 | + | 49.8876i | −0.240856 | + | 0.0997659i | ||||
\(64\) | − | 28.0634i | − | 0.0548113i | ||||||
\(65\) | −17.9304 | − | 43.2878i | −0.0342153 | − | 0.0826030i | ||||
\(66\) | 432.050 | + | 432.050i | 0.805783 | + | 0.805783i | ||||
\(67\) | 314.069 | 0.572681 | 0.286341 | − | 0.958128i | \(-0.407561\pi\) | ||||
0.286341 | + | 0.958128i | \(0.407561\pi\) | |||||||
\(68\) | −230.753 | + | 188.172i | −0.411514 | + | 0.335576i | ||||
\(69\) | −329.230 | −0.574415 | ||||||||
\(70\) | 147.913 | + | 147.913i | 0.252558 | + | 0.252558i | ||||
\(71\) | −45.3357 | − | 109.450i | −0.0757796 | − | 0.182948i | 0.881450 | − | 0.472277i | \(-0.156568\pi\) |
−0.957230 | + | 0.289329i | \(0.906568\pi\) | |||||||
\(72\) | − | 249.715i | − | 0.408739i | ||||||
\(73\) | 601.028 | − | 248.954i | 0.963630 | − | 0.399149i | 0.155293 | − | 0.987868i | \(-0.450368\pi\) |
0.808337 | + | 0.588720i | \(0.200368\pi\) | |||||||
\(74\) | −149.233 | + | 360.280i | −0.234432 | + | 0.565969i | ||||
\(75\) | 127.836 | + | 52.9515i | 0.196817 | + | 0.0815242i | ||||
\(76\) | 290.727 | − | 290.727i | 0.438798 | − | 0.438798i | ||||
\(77\) | 299.524 | − | 299.524i | 0.443297 | − | 0.443297i | ||||
\(78\) | 49.0901 | + | 20.3338i | 0.0712610 | + | 0.0295173i | ||||
\(79\) | −79.7533 | + | 192.542i | −0.113582 | + | 0.274210i | −0.970440 | − | 0.241341i | \(-0.922413\pi\) |
0.856859 | + | 0.515551i | \(0.172413\pi\) | |||||||
\(80\) | −643.953 | + | 266.734i | −0.899952 | + | 0.372772i | ||||
\(81\) | − | 146.115i | − | 0.200432i | ||||||
\(82\) | −222.972 | − | 538.303i | −0.300283 | − | 0.724947i | ||||
\(83\) | −524.977 | − | 524.977i | −0.694262 | − | 0.694262i | 0.268905 | − | 0.963167i | \(-0.413338\pi\) |
−0.963167 | + | 0.268905i | \(0.913338\pi\) | |||||||
\(84\) | −82.2749 | −0.106868 | ||||||||
\(85\) | −538.095 | − | 289.781i | −0.686642 | − | 0.369778i | ||||
\(86\) | −580.555 | −0.727940 | ||||||||
\(87\) | −394.326 | − | 394.326i | −0.485933 | − | 0.485933i | ||||
\(88\) | 310.511 | + | 749.640i | 0.376143 | + | 0.908090i | ||||
\(89\) | 215.527i | 0.256695i | 0.991729 | + | 0.128348i | \(0.0409673\pi\) | ||||
−0.991729 | + | 0.128348i | \(0.959033\pi\) | |||||||
\(90\) | −536.137 | + | 222.075i | −0.627931 | + | 0.260097i | ||||
\(91\) | 14.0966 | − | 34.0323i | 0.0162388 | − | 0.0392038i | ||||
\(92\) | 457.315 | + | 189.426i | 0.518244 | + | 0.214663i | ||||
\(93\) | −275.844 | + | 275.844i | −0.307567 | + | 0.307567i | ||||
\(94\) | −324.167 | + | 324.167i | −0.355694 | + | 0.355694i | ||||
\(95\) | 779.683 | + | 322.955i | 0.842040 | + | 0.348784i | ||||
\(96\) | 188.905 | − | 456.058i | 0.200834 | − | 0.484856i | ||||
\(97\) | 651.973 | − | 270.056i | 0.682452 | − | 0.282681i | −0.0143996 | − | 0.999896i | \(-0.504584\pi\) |
0.696851 | + | 0.717216i | \(0.254584\pi\) | |||||||
\(98\) | − | 1035.94i | − | 1.06782i | ||||||
\(99\) | 449.700 | + | 1085.67i | 0.456531 | + | 1.10216i | ||||
\(100\) | −147.104 | − | 147.104i | −0.147104 | − | 0.147104i | ||||
\(101\) | 546.988 | 0.538884 | 0.269442 | − | 0.963017i | \(-0.413161\pi\) | ||||
0.269442 | + | 0.963017i | \(0.413161\pi\) | |||||||
\(102\) | 663.862 | − | 199.120i | 0.644433 | − | 0.193292i | ||||
\(103\) | 1550.96 | 1.48369 | 0.741846 | − | 0.670570i | \(-0.233950\pi\) | ||||
0.741846 | + | 0.670570i | \(0.233950\pi\) | |||||||
\(104\) | 49.8944 | + | 49.8944i | 0.0470438 | + | 0.0470438i | ||||
\(105\) | −64.6263 | − | 156.022i | −0.0600656 | − | 0.145011i | ||||
\(106\) | 2499.60i | 2.29041i | ||||||||
\(107\) | 227.070 | − | 94.0554i | 0.205156 | − | 0.0849783i | −0.277739 | − | 0.960656i | \(-0.589585\pi\) |
0.482895 | + | 0.875678i | \(0.339585\pi\) | |||||||
\(108\) | 211.358 | − | 510.263i | 0.188314 | − | 0.454631i | ||||
\(109\) | −1841.65 | − | 762.836i | −1.61833 | − | 0.670334i | −0.624477 | − | 0.781043i | \(-0.714688\pi\) |
−0.993853 | + | 0.110708i | \(0.964688\pi\) | |||||||
\(110\) | 1333.33 | − | 1333.33i | 1.15571 | − | 1.15571i | ||||
\(111\) | 222.617 | − | 222.617i | 0.190359 | − | 0.190359i | ||||
\(112\) | −506.267 | − | 209.703i | −0.427122 | − | 0.176920i | ||||
\(113\) | −414.351 | + | 1000.33i | −0.344946 | + | 0.832773i | 0.652255 | + | 0.758000i | \(0.273823\pi\) |
−0.997201 | + | 0.0747730i | \(0.976177\pi\) | |||||||
\(114\) | −884.191 | + | 366.244i | −0.726422 | + | 0.300894i | ||||
\(115\) | 1016.02i | 0.823865i | ||||||||
\(116\) | 320.857 | + | 774.617i | 0.256817 | + | 0.620012i | ||||
\(117\) | 72.2600 | + | 72.2600i | 0.0570977 | + | 0.0570977i | ||||
\(118\) | −2961.51 | −2.31042 | ||||||||
\(119\) | −138.042 | − | 460.230i | −0.106338 | − | 0.354531i | ||||
\(120\) | 323.491 | 0.246088 | ||||||||
\(121\) | −1758.83 | − | 1758.83i | −1.32143 | − | 1.32143i | ||||
\(122\) | 6.68580 | + | 16.1410i | 0.00496151 | + | 0.0119781i | ||||
\(123\) | 470.391i | 0.344827i | ||||||||
\(124\) | 541.870 | − | 224.450i | 0.392430 | − | 0.162550i | ||||
\(125\) | 580.504 | − | 1401.46i | 0.415375 | − | 1.00280i | ||||
\(126\) | −421.503 | − | 174.592i | −0.298019 | − | 0.123444i | ||||
\(127\) | 718.468 | − | 718.468i | 0.501998 | − | 0.501998i | −0.410061 | − | 0.912058i | \(-0.634492\pi\) |
0.912058 | + | 0.410061i | \(0.134492\pi\) | |||||||
\(128\) | 1057.77 | − | 1057.77i | 0.730429 | − | 0.730429i | ||||
\(129\) | 433.018 | + | 179.362i | 0.295543 | + | 0.122418i | ||||
\(130\) | 62.7512 | − | 151.495i | 0.0423357 | − | 0.102207i | ||||
\(131\) | −1024.45 | + | 424.340i | −0.683255 | + | 0.283014i | −0.697187 | − | 0.716889i | \(-0.745565\pi\) |
0.0139317 | + | 0.999903i | \(0.495565\pi\) | |||||||
\(132\) | 741.647i | 0.489031i | ||||||||
\(133\) | 253.903 | + | 612.976i | 0.165535 | + | 0.399637i | ||||
\(134\) | 777.217 | + | 777.217i | 0.501054 | + | 0.501054i | ||||
\(135\) | 1133.66 | 0.722738 | ||||||||
\(136\) | 915.674 | + | 93.0731i | 0.577341 | + | 0.0586835i | ||||
\(137\) | −1975.27 | −1.23182 | −0.615909 | − | 0.787818i | \(-0.711211\pi\) | ||||
−0.615909 | + | 0.787818i | \(0.711211\pi\) | |||||||
\(138\) | −814.734 | − | 814.734i | −0.502571 | − | 0.502571i | ||||
\(139\) | 397.418 | + | 959.451i | 0.242507 | + | 0.585465i | 0.997531 | − | 0.0702334i | \(-0.0223744\pi\) |
−0.755023 | + | 0.655698i | \(0.772374\pi\) | |||||||
\(140\) | 253.905i | 0.153278i | ||||||||
\(141\) | 341.937 | − | 141.635i | 0.204229 | − | 0.0845944i | ||||
\(142\) | 158.662 | − | 383.043i | 0.0937647 | − | 0.226368i | ||||
\(143\) | −306.776 | − | 127.071i | −0.179398 | − | 0.0743090i | ||||
\(144\) | 1074.95 | − | 1074.95i | 0.622075 | − | 0.622075i | ||||
\(145\) | −1216.91 | + | 1216.91i | −0.696960 | + | 0.696960i | ||||
\(146\) | 2103.42 | + | 871.266i | 1.19233 | + | 0.493880i | ||||
\(147\) | −320.054 | + | 772.679i | −0.179576 | + | 0.433534i | ||||
\(148\) | −437.310 | + | 181.140i | −0.242883 | + | 0.100605i | ||||
\(149\) | − | 119.562i | − | 0.0657377i | −0.999460 | − | 0.0328689i | \(-0.989536\pi\) | ||
0.999460 | − | 0.0328689i | \(-0.0104644\pi\) | |||||||
\(150\) | 185.315 | + | 447.390i | 0.100873 | + | 0.243528i | ||||
\(151\) | −1108.64 | − | 1108.64i | −0.597481 | − | 0.597481i | 0.342160 | − | 0.939642i | \(-0.388841\pi\) |
−0.939642 | + | 0.342160i | \(0.888841\pi\) | |||||||
\(152\) | −1270.92 | −0.678194 | ||||||||
\(153\) | 1326.13 | + | 134.794i | 0.700728 | + | 0.0712251i | ||||
\(154\) | 1482.44 | 0.775705 | ||||||||
\(155\) | 851.270 | + | 851.270i | 0.441133 | + | 0.441133i | ||||
\(156\) | 24.6812 | + | 59.5857i | 0.0126672 | + | 0.0305812i | ||||
\(157\) | 2121.62i | 1.07850i | 0.842147 | + | 0.539248i | \(0.181291\pi\) | ||||
−0.842147 | + | 0.539248i | \(0.818709\pi\) | |||||||
\(158\) | −673.839 | + | 279.113i | −0.339290 | + | 0.140538i | ||||
\(159\) | 772.250 | − | 1864.38i | 0.385179 | − | 0.929904i | ||||
\(160\) | −1407.42 | − | 582.972i | −0.695414 | − | 0.288050i | ||||
\(161\) | −564.824 | + | 564.824i | −0.276487 | + | 0.276487i | ||||
\(162\) | 361.586 | − | 361.586i | 0.175363 | − | 0.175363i | ||||
\(163\) | 409.544 | + | 169.639i | 0.196797 | + | 0.0815160i | 0.478905 | − | 0.877867i | \(-0.341034\pi\) |
−0.282108 | + | 0.959383i | \(0.591034\pi\) | |||||||
\(164\) | 270.645 | − | 653.394i | 0.128865 | − | 0.311107i | ||||
\(165\) | −1406.42 | + | 582.559i | −0.663574 | + | 0.274861i | ||||
\(166\) | − | 2598.29i | − | 1.21486i | ||||||
\(167\) | 900.241 | + | 2173.37i | 0.417142 | + | 1.00707i | 0.983171 | + | 0.182685i | \(0.0584790\pi\) |
−0.566029 | + | 0.824385i | \(0.691521\pi\) | |||||||
\(168\) | 179.834 | + | 179.834i | 0.0825862 | + | 0.0825862i | ||||
\(169\) | 2168.12 | 0.986857 | ||||||||
\(170\) | −614.494 | − | 2048.72i | −0.277233 | − | 0.924291i | ||||
\(171\) | −1840.63 | −0.823135 | ||||||||
\(172\) | −498.284 | − | 498.284i | −0.220894 | − | 0.220894i | ||||
\(173\) | −727.203 | − | 1755.62i | −0.319585 | − | 0.771547i | −0.999276 | − | 0.0380481i | \(-0.987886\pi\) |
0.679691 | − | 0.733499i | \(-0.262114\pi\) | |||||||
\(174\) | − | 1951.65i | − | 0.850313i | ||||||
\(175\) | 310.158 | − | 128.472i | 0.133976 | − | 0.0554945i | ||||
\(176\) | −1890.31 | + | 4563.62i | −0.809590 | + | 1.95452i | ||||
\(177\) | 2208.90 | + | 914.956i | 0.938028 | + | 0.388544i | ||||
\(178\) | −533.359 | + | 533.359i | −0.224589 | + | 0.224589i | ||||
\(179\) | −70.5199 | + | 70.5199i | −0.0294464 | + | 0.0294464i | −0.721677 | − | 0.692230i | \(-0.756628\pi\) |
0.692230 | + | 0.721677i | \(0.256628\pi\) | |||||||
\(180\) | −650.764 | − | 269.555i | −0.269473 | − | 0.111619i | ||||
\(181\) | 1484.36 | − | 3583.56i | 0.609567 | − | 1.47162i | −0.253906 | − | 0.967229i | \(-0.581715\pi\) |
0.863473 | − | 0.504395i | \(-0.168285\pi\) | |||||||
\(182\) | 119.103 | − | 49.3341i | 0.0485082 | − | 0.0200928i | ||||
\(183\) | − | 14.1046i | − | 0.00569750i | ||||||
\(184\) | −585.544 | − | 1413.63i | −0.234602 | − | 0.566380i | ||||
\(185\) | −687.007 | − | 687.007i | −0.273026 | − | 0.273026i | ||||
\(186\) | −1365.24 | −0.538197 | ||||||||
\(187\) | −4148.64 | + | 1244.35i | −1.62234 | + | 0.486607i | ||||
\(188\) | −556.457 | −0.215871 | ||||||||
\(189\) | 630.219 | + | 630.219i | 0.242549 | + | 0.242549i | ||||
\(190\) | 1130.25 | + | 2728.66i | 0.431563 | + | 1.04188i | ||||
\(191\) | − | 2326.90i | − | 0.881511i | −0.897627 | − | 0.440756i | \(-0.854711\pi\) | ||
0.897627 | − | 0.440756i | \(-0.145289\pi\) | |||||||
\(192\) | −73.2545 | + | 30.3430i | −0.0275348 | + | 0.0114053i | ||||
\(193\) | −534.412 | + | 1290.18i | −0.199315 | + | 0.481189i | −0.991660 | − | 0.128885i | \(-0.958860\pi\) |
0.792345 | + | 0.610074i | \(0.208860\pi\) | |||||||
\(194\) | 2281.72 | + | 945.117i | 0.844421 | + | 0.349770i | ||||
\(195\) | −93.6083 | + | 93.6083i | −0.0343766 | + | 0.0343766i | ||||
\(196\) | 889.140 | − | 889.140i | 0.324030 | − | 0.324030i | ||||
\(197\) | −1869.77 | − | 774.486i | −0.676223 | − | 0.280101i | 0.0180240 | − | 0.999838i | \(-0.494262\pi\) |
−0.694247 | + | 0.719737i | \(0.744262\pi\) | |||||||
\(198\) | −1573.82 | + | 3799.54i | −0.564881 | + | 1.36374i | ||||
\(199\) | 3827.94 | − | 1585.59i | 1.36360 | − | 0.564820i | 0.423552 | − | 0.905872i | \(-0.360783\pi\) |
0.940045 | + | 0.341052i | \(0.110783\pi\) | |||||||
\(200\) | 643.072i | 0.227360i | ||||||||
\(201\) | −339.581 | − | 819.822i | −0.119165 | − | 0.287691i | ||||
\(202\) | 1353.61 | + | 1353.61i | 0.471484 | + | 0.471484i | ||||
\(203\) | −1353.01 | −0.467795 | ||||||||
\(204\) | 740.688 | + | 398.884i | 0.254208 | + | 0.136899i | ||||
\(205\) | 1451.65 | 0.494575 | ||||||||
\(206\) | 3838.10 | + | 3838.10i | 1.29812 | + | 1.29812i | ||||
\(207\) | −848.018 | − | 2047.30i | −0.284741 | − | 0.687425i | ||||
\(208\) | 429.560i | 0.143195i | ||||||||
\(209\) | 5525.52 | − | 2288.75i | 1.82875 | − | 0.757493i | ||||
\(210\) | 226.173 | − | 546.031i | 0.0743212 | − | 0.179427i | ||||
\(211\) | 2171.62 | + | 899.516i | 0.708535 | + | 0.293485i | 0.707698 | − | 0.706515i | \(-0.249734\pi\) |
0.000836499 | 1.00000i | \(0.499734\pi\) | ||||||||
\(212\) | −2145.38 | + | 2145.38i | −0.695025 | + | 0.695025i | ||||
\(213\) | −236.681 | + | 236.681i | −0.0761368 | + | 0.0761368i | ||||
\(214\) | 794.678 | + | 329.166i | 0.253846 | + | 0.105147i | ||||
\(215\) | 553.521 | − | 1336.32i | 0.175581 | − | 0.423889i | ||||
\(216\) | −1577.30 | + | 653.338i | −0.496859 | + | 0.205806i | ||||
\(217\) | 946.471i | 0.296086i | ||||||||
\(218\) | −2669.70 | − | 6445.24i | −0.829427 | − | 2.00241i | ||||
\(219\) | −1299.70 | − | 1299.70i | −0.401030 | − | 0.401030i | ||||
\(220\) | 2288.77 | 0.701402 | ||||||||
\(221\) | −291.901 | + | 238.036i | −0.0888478 | + | 0.0724526i | ||||
\(222\) | 1101.80 | 0.333100 | ||||||||
\(223\) | −291.603 | − | 291.603i | −0.0875657 | − | 0.0875657i | 0.661967 | − | 0.749533i | \(-0.269722\pi\) |
−0.749533 | + | 0.661967i | \(0.769722\pi\) | |||||||
\(224\) | −458.324 | − | 1106.49i | −0.136710 | − | 0.330048i | ||||
\(225\) | 931.333i | 0.275951i | ||||||||
\(226\) | −3500.87 | + | 1450.11i | −1.03042 | + | 0.426813i | ||||
\(227\) | −733.181 | + | 1770.05i | −0.214374 | + | 0.517545i | −0.994086 | − | 0.108593i | \(-0.965365\pi\) |
0.779712 | + | 0.626138i | \(0.215365\pi\) | |||||||
\(228\) | −1073.23 | − | 444.548i | −0.311740 | − | 0.129127i | ||||
\(229\) | −3439.04 | + | 3439.04i | −0.992394 | + | 0.992394i | −0.999971 | − | 0.00757695i | \(-0.997588\pi\) |
0.00757695 | + | 0.999971i | \(0.497588\pi\) | |||||||
\(230\) | −2514.32 | + | 2514.32i | −0.720822 | + | 0.720822i | ||||
\(231\) | −1105.71 | − | 457.999i | −0.314936 | − | 0.130451i | ||||
\(232\) | 991.815 | − | 2394.45i | 0.280672 | − | 0.677602i | ||||
\(233\) | 513.374 | − | 212.646i | 0.144344 | − | 0.0597894i | −0.309342 | − | 0.950951i | \(-0.600109\pi\) |
0.453686 | + | 0.891162i | \(0.350109\pi\) | |||||||
\(234\) | 357.639i | 0.0999127i | ||||||||
\(235\) | −437.093 | − | 1055.24i | −0.121331 | − | 0.292919i | ||||
\(236\) | −2541.83 | − | 2541.83i | −0.701098 | − | 0.701098i | ||||
\(237\) | 588.828 | 0.161386 | ||||||||
\(238\) | 797.309 | − | 1480.52i | 0.217151 | − | 0.403228i | ||||
\(239\) | −3205.56 | −0.867575 | −0.433787 | − | 0.901015i | \(-0.642823\pi\) | ||||
−0.433787 | + | 0.901015i | \(0.642823\pi\) | |||||||
\(240\) | 1392.53 | + | 1392.53i | 0.374530 | + | 0.374530i | ||||
\(241\) | −341.888 | − | 825.391i | −0.0913815 | − | 0.220614i | 0.871580 | − | 0.490253i | \(-0.163096\pi\) |
−0.962962 | + | 0.269639i | \(0.913096\pi\) | |||||||
\(242\) | − | 8705.02i | − | 2.31231i | ||||||
\(243\) | −3624.64 | + | 1501.37i | −0.956875 | + | 0.396351i | ||||
\(244\) | −8.11525 | + | 19.5920i | −0.00212920 | + | 0.00514035i | ||||
\(245\) | 2384.53 | + | 987.705i | 0.621805 | + | 0.257560i | ||||
\(246\) | −1164.06 | + | 1164.06i | −0.301698 | + | 0.301698i | ||||
\(247\) | 367.767 | − | 367.767i | 0.0947386 | − | 0.0947386i | ||||
\(248\) | −1675.00 | − | 693.807i | −0.428881 | − | 0.177648i | ||||
\(249\) | −802.738 | + | 1937.98i | −0.204303 | + | 0.493231i | ||||
\(250\) | 4904.70 | − | 2031.60i | 1.24080 | − | 0.513957i | ||||
\(251\) | 2431.39i | 0.611427i | 0.952124 | + | 0.305713i | \(0.0988949\pi\) | ||||
−0.952124 | + | 0.305713i | \(0.901105\pi\) | |||||||
\(252\) | −211.921 | − | 511.622i | −0.0529752 | − | 0.127893i | ||||
\(253\) | 5091.47 | + | 5091.47i | 1.26521 | + | 1.26521i | ||||
\(254\) | 3555.94 | 0.878422 | ||||||||
\(255\) | −174.617 | + | 1717.92i | −0.0428821 | + | 0.421884i | ||||
\(256\) | 5010.77 | 1.22333 | ||||||||
\(257\) | 2273.66 | + | 2273.66i | 0.551856 | + | 0.551856i | 0.926976 | − | 0.375120i | \(-0.122399\pi\) |
−0.375120 | + | 0.926976i | \(0.622399\pi\) | |||||||
\(258\) | 627.714 | + | 1515.44i | 0.151472 | + | 0.365686i | ||||
\(259\) | − | 763.838i | − | 0.183253i | ||||||
\(260\) | 183.885 | − | 76.1676i | 0.0438617 | − | 0.0181681i | ||||
\(261\) | 1436.40 | − | 3467.79i | 0.340656 | − | 0.822416i | ||||
\(262\) | −3585.27 | − | 1485.07i | −0.845415 | − | 0.350182i | ||||
\(263\) | 1880.31 | − | 1880.31i | 0.440856 | − | 0.440856i | −0.451444 | − | 0.892300i | \(-0.649091\pi\) |
0.892300 | + | 0.451444i | \(0.149091\pi\) | |||||||
\(264\) | 1621.07 | − | 1621.07i | 0.377917 | − | 0.377917i | ||||
\(265\) | −5753.57 | − | 2383.21i | −1.33373 | − | 0.552450i | ||||
\(266\) | −888.586 | + | 2145.24i | −0.204822 | + | 0.494484i | ||||
\(267\) | 562.596 | − | 233.035i | 0.128953 | − | 0.0534139i | ||||
\(268\) | 1334.15i | 0.304091i | ||||||||
\(269\) | 2186.04 | + | 5277.57i | 0.495484 | + | 1.19620i | 0.951892 | + | 0.306434i | \(0.0991359\pi\) |
−0.456408 | + | 0.889771i | \(0.650864\pi\) | |||||||
\(270\) | 2805.42 | + | 2805.42i | 0.632343 | + | 0.632343i | ||||
\(271\) | 250.885 | 0.0562369 | 0.0281185 | − | 0.999605i | \(-0.491048\pi\) | ||||
0.0281185 | + | 0.999605i | \(0.491048\pi\) | |||||||
\(272\) | 3541.04 | + | 4342.34i | 0.789364 | + | 0.967989i | ||||
\(273\) | −104.077 | −0.0230733 | ||||||||
\(274\) | −4888.14 | − | 4888.14i | −1.07775 | − | 1.07775i | ||||
\(275\) | −1158.08 | − | 2795.85i | −0.253944 | − | 0.613076i | ||||
\(276\) | − | 1398.55i | − | 0.305011i | ||||||
\(277\) | −3407.52 | + | 1411.44i | −0.739126 | + | 0.306156i | −0.720296 | − | 0.693667i | \(-0.755994\pi\) |
−0.0188299 | + | 0.999823i | \(0.505994\pi\) | |||||||
\(278\) | −1390.85 | + | 3357.80i | −0.300063 | + | 0.724415i | ||||
\(279\) | −2425.83 | − | 1004.81i | −0.520540 | − | 0.215615i | ||||
\(280\) | 554.978 | − | 554.978i | 0.118451 | − | 0.118451i | ||||
\(281\) | −2497.50 | + | 2497.50i | −0.530208 | + | 0.530208i | −0.920634 | − | 0.390426i | \(-0.872328\pi\) |
0.390426 | + | 0.920634i | \(0.372328\pi\) | |||||||
\(282\) | 1196.68 | + | 495.681i | 0.252699 | + | 0.104671i | ||||
\(283\) | −301.639 | + | 728.220i | −0.0633589 | + | 0.152962i | −0.952388 | − | 0.304889i | \(-0.901381\pi\) |
0.889029 | + | 0.457851i | \(0.151381\pi\) | |||||||
\(284\) | 464.939 | − | 192.584i | 0.0971445 | − | 0.0402386i | ||||
\(285\) | − | 2384.42i | − | 0.495581i | ||||||
\(286\) | −444.710 | − | 1073.63i | −0.0919450 | − | 0.221975i | ||||
\(287\) | 806.998 | + | 806.998i | 0.165978 | + | 0.165978i | ||||
\(288\) | 3322.54 | 0.679801 | ||||||||
\(289\) | −988.544 | + | 4812.52i | −0.201210 | + | 0.979548i | ||||
\(290\) | −6022.91 | −1.21958 | ||||||||
\(291\) | −1409.87 | − | 1409.87i | −0.284013 | − | 0.284013i | ||||
\(292\) | 1057.55 | + | 2553.14i | 0.211946 | + | 0.511683i | ||||
\(293\) | − | 1413.82i | − | 0.281899i | −0.990017 | − | 0.140949i | \(-0.954985\pi\) | ||
0.990017 | − | 0.140949i | \(-0.0450154\pi\) | |||||||
\(294\) | −2704.15 | + | 1120.10i | −0.536426 | + | 0.222195i | ||||
\(295\) | 2823.61 | − | 6816.79i | 0.557277 | − | 1.34539i | ||||
\(296\) | 1351.79 | + | 559.929i | 0.265443 | + | 0.109950i | ||||
\(297\) | 5680.96 | − | 5680.96i | 1.10991 | − | 1.10991i | ||||
\(298\) | 295.877 | − | 295.877i | 0.0575157 | − | 0.0575157i | ||||
\(299\) | 578.499 | + | 239.622i | 0.111891 | + | 0.0463469i | ||||
\(300\) | −224.936 | + | 543.043i | −0.0432889 | + | 0.104509i | ||||
\(301\) | 1050.59 | − | 435.170i | 0.201180 | − | 0.0833315i | ||||
\(302\) | − | 5487.02i | − | 1.04551i | ||||||
\(303\) | −591.420 | − | 1427.81i | −0.112133 | − | 0.270712i | ||||
\(304\) | −5470.93 | − | 5470.93i | −1.03217 | − | 1.03217i | ||||
\(305\) | −43.5276 | −0.00817175 | ||||||||
\(306\) | 2948.17 | + | 3615.31i | 0.550769 | + | 0.675403i | ||||
\(307\) | 4499.58 | 0.836498 | 0.418249 | − | 0.908333i | \(-0.362644\pi\) | ||||
0.418249 | + | 0.908333i | \(0.362644\pi\) | |||||||
\(308\) | 1272.36 | + | 1272.36i | 0.235388 | + | 0.235388i | ||||
\(309\) | −1676.94 | − | 4048.50i | −0.308731 | − | 0.745343i | ||||
\(310\) | 4213.22i | 0.771919i | ||||||||
\(311\) | −4357.74 | + | 1805.04i | −0.794550 | + | 0.329113i | −0.742771 | − | 0.669545i | \(-0.766489\pi\) |
−0.0517785 | + | 0.998659i | \(0.516489\pi\) | |||||||
\(312\) | 76.2932 | − | 184.188i | 0.0138438 | − | 0.0334218i | ||||
\(313\) | −5701.55 | − | 2361.66i | −1.02962 | − | 0.426482i | −0.197044 | − | 0.980395i | \(-0.563134\pi\) |
−0.832575 | + | 0.553913i | \(0.813134\pi\) | |||||||
\(314\) | −5250.30 | + | 5250.30i | −0.943605 | + | 0.943605i | ||||
\(315\) | 803.750 | − | 803.750i | 0.143766 | − | 0.143766i | ||||
\(316\) | −817.908 | − | 338.789i | −0.145604 | − | 0.0603113i | ||||
\(317\) | 454.194 | − | 1096.52i | 0.0804735 | − | 0.194280i | −0.878522 | − | 0.477702i | \(-0.841470\pi\) |
0.958995 | + | 0.283422i | \(0.0914698\pi\) | |||||||
\(318\) | 6524.77 | − | 2702.65i | 1.15060 | − | 0.476595i | ||||
\(319\) | 12196.3i | 2.14064i | ||||||||
\(320\) | 93.6403 | + | 226.068i | 0.0163583 | + | 0.0394924i | ||||
\(321\) | −491.030 | − | 491.030i | −0.0853789 | − | 0.0853789i | ||||
\(322\) | −2795.50 | −0.483811 | ||||||||
\(323\) | 686.033 | − | 6749.34i | 0.118179 | − | 1.16267i | ||||
\(324\) | 620.690 | 0.106428 | ||||||||
\(325\) | −186.085 | − | 186.085i | −0.0317605 | − | 0.0317605i | ||||
\(326\) | 593.685 | + | 1433.28i | 0.100863 | + | 0.243504i | ||||
\(327\) | 5632.10i | 0.952465i | ||||||||
\(328\) | −2019.74 | + | 836.602i | −0.340004 | + | 0.140834i | ||||
\(329\) | 343.636 | − | 829.611i | 0.0575844 | − | 0.139021i | ||||
\(330\) | −4922.06 | − | 2038.79i | −0.821063 | − | 0.340095i | ||||
\(331\) | 2170.88 | − | 2170.88i | 0.360491 | − | 0.360491i | −0.503503 | − | 0.863994i | \(-0.667956\pi\) |
0.863994 | + | 0.503503i | \(0.167956\pi\) | |||||||
\(332\) | 2230.08 | − | 2230.08i | 0.368649 | − | 0.368649i | ||||
\(333\) | 1957.74 | + | 810.921i | 0.322172 | + | 0.133448i | ||||
\(334\) | −3150.58 | + | 7606.18i | −0.516144 | + | 1.24608i | ||||
\(335\) | −2530.02 | + | 1047.97i | −0.412626 | + | 0.170915i | ||||
\(336\) | 1548.26i | 0.251382i | ||||||||
\(337\) | −1698.14 | − | 4099.67i | −0.274491 | − | 0.662681i | 0.725173 | − | 0.688566i | \(-0.241760\pi\) |
−0.999665 | + | 0.0258852i | \(0.991760\pi\) | |||||||
\(338\) | 5365.39 | + | 5365.39i | 0.863428 | + | 0.863428i | ||||
\(339\) | 3059.20 | 0.490127 | ||||||||
\(340\) | 1230.98 | − | 2285.80i | 0.196350 | − | 0.364603i | ||||
\(341\) | 8531.74 | 1.35490 | ||||||||
\(342\) | −4554.94 | − | 4554.94i | −0.720183 | − | 0.720183i | ||||
\(343\) | 1676.31 | + | 4046.97i | 0.263884 | + | 0.637073i | ||||
\(344\) | 2178.27i | 0.341408i | ||||||||
\(345\) | 2652.15 | − | 1098.55i | 0.413875 | − | 0.171432i | ||||
\(346\) | 2545.00 | − | 6144.17i | 0.395434 | − | 0.954661i | ||||
\(347\) | 8050.88 | + | 3334.79i | 1.24552 | + | 0.515910i | 0.905434 | − | 0.424486i | \(-0.139545\pi\) |
0.340082 | + | 0.940396i | \(0.389545\pi\) | |||||||
\(348\) | 1675.08 | − | 1675.08i | 0.258028 | − | 0.258028i | ||||
\(349\) | 71.3677 | − | 71.3677i | 0.0109462 | − | 0.0109462i | −0.701612 | − | 0.712559i | \(-0.747536\pi\) |
0.712559 | + | 0.701612i | \(0.247536\pi\) | |||||||
\(350\) | 1085.46 | + | 449.613i | 0.165773 | + | 0.0686653i | ||||
\(351\) | 267.366 | − | 645.478i | 0.0406579 | − | 0.0981569i | ||||
\(352\) | −9974.22 | + | 4131.46i | −1.51031 | + | 0.625589i | ||||
\(353\) | − | 8688.88i | − | 1.31009i | −0.755589 | − | 0.655046i | \(-0.772649\pi\) | ||
0.755589 | − | 0.655046i | \(-0.227351\pi\) | |||||||
\(354\) | 3202.08 | + | 7730.50i | 0.480759 | + | 1.16065i | ||||
\(355\) | 730.412 | + | 730.412i | 0.109201 | + | 0.109201i | ||||
\(356\) | −915.551 | −0.136304 | ||||||||
\(357\) | −1052.09 | + | 857.949i | −0.155974 | + | 0.127192i | ||||
\(358\) | −349.026 | −0.0515269 | ||||||||
\(359\) | −1705.20 | − | 1705.20i | −0.250688 | − | 0.250688i | 0.570565 | − | 0.821253i | \(-0.306724\pi\) |
−0.821253 | + | 0.570565i | \(0.806724\pi\) | |||||||
\(360\) | 833.235 | + | 2011.61i | 0.121987 | + | 0.294503i | ||||
\(361\) | 2508.85i | 0.365775i | ||||||||
\(362\) | 12541.4 | − | 5194.82i | 1.82089 | − | 0.754237i | ||||
\(363\) | −2689.41 | + | 6492.80i | −0.388863 | + | 0.938798i | ||||
\(364\) | 144.568 | + | 59.8818i | 0.0208170 | + | 0.00862270i | ||||
\(365\) | −4010.95 | + | 4010.95i | −0.575186 | + | 0.575186i | ||||
\(366\) | 34.9042 | − | 34.9042i | 0.00498490 | − | 0.00498490i | ||||
\(367\) | −2101.09 | − | 870.300i | −0.298845 | − | 0.123786i | 0.228223 | − | 0.973609i | \(-0.426709\pi\) |
−0.527068 | + | 0.849823i | \(0.676709\pi\) | |||||||
\(368\) | 3564.64 | − | 8605.81i | 0.504945 | − | 1.21905i | ||||
\(369\) | −2925.10 | + | 1211.62i | −0.412668 | + | 0.170933i | ||||
\(370\) | − | 3400.23i | − | 0.477755i | ||||||
\(371\) | −1873.64 | − | 4523.37i | −0.262196 | − | 0.632997i | ||||
\(372\) | −1171.77 | − | 1171.77i | −0.163316 | − | 0.163316i | ||||
\(373\) | −9493.93 | −1.31790 | −0.658951 | − | 0.752186i | \(-0.728999\pi\) | ||||
−0.658951 | + | 0.752186i | \(0.728999\pi\) | |||||||
\(374\) | −13345.8 | − | 7187.15i | −1.84518 | − | 0.993687i | ||||
\(375\) | −4285.93 | −0.590198 | ||||||||
\(376\) | 1216.29 | + | 1216.29i | 0.166822 | + | 0.166822i | ||||
\(377\) | 405.881 | + | 979.883i | 0.0554481 | + | 0.133864i | ||||
\(378\) | 3119.17i | 0.424425i | ||||||||
\(379\) | 4931.39 | − | 2042.65i | 0.668360 | − | 0.276844i | −0.0225917 | − | 0.999745i | \(-0.507192\pi\) |
0.690952 | + | 0.722901i | \(0.257192\pi\) | |||||||
\(380\) | −1371.90 | + | 3312.06i | −0.185203 | + | 0.447119i | ||||
\(381\) | −2652.26 | − | 1098.60i | −0.356639 | − | 0.147725i | ||||
\(382\) | 5758.31 | − | 5758.31i | 0.771258 | − | 0.771258i | ||||
\(383\) | 551.137 | − | 551.137i | 0.0735295 | − | 0.0735295i | −0.669386 | − | 0.742915i | \(-0.733443\pi\) |
0.742915 | + | 0.669386i | \(0.233443\pi\) | |||||||
\(384\) | −3904.83 | − | 1617.43i | −0.518926 | − | 0.214946i | ||||
\(385\) | −1413.41 | + | 3412.28i | −0.187102 | + | 0.451703i | ||||
\(386\) | −4515.27 | + | 1870.28i | −0.595391 | + | 0.246619i | ||||
\(387\) | 3154.69i | 0.414372i | ||||||||
\(388\) | 1147.19 | + | 2769.55i | 0.150102 | + | 0.362378i | ||||
\(389\) | −7655.19 | − | 7655.19i | −0.997772 | − | 0.997772i | 0.00222529 | − | 0.999998i | \(-0.499292\pi\) |
−0.999998 | + | 0.00222529i | \(0.999292\pi\) | |||||||
\(390\) | −463.299 | −0.0601540 | ||||||||
\(391\) | 7823.25 | − | 2346.51i | 1.01186 | − | 0.303499i | ||||
\(392\) | −3886.91 | −0.500813 | ||||||||
\(393\) | 2215.33 | + | 2215.33i | 0.284348 | + | 0.284348i | ||||
\(394\) | −2710.48 | − | 6543.67i | −0.346578 | − | 0.836714i | ||||
\(395\) | − | 1817.16i | − | 0.231471i | ||||||
\(396\) | −4611.89 | + | 1910.31i | −0.585243 | + | 0.242416i | ||||
\(397\) | −2337.00 | + | 5642.01i | −0.295442 | + | 0.713260i | 0.704551 | + | 0.709653i | \(0.251148\pi\) |
−0.999993 | + | 0.00360730i | \(0.998852\pi\) | |||||||
\(398\) | 13396.7 | + | 5549.09i | 1.68722 | + | 0.698871i | ||||
\(399\) | 1325.54 | − | 1325.54i | 0.166315 | − | 0.166315i | ||||
\(400\) | −2768.22 | + | 2768.22i | −0.346028 | + | 0.346028i | ||||
\(401\) | 10579.9 | + | 4382.32i | 1.31754 | + | 0.545743i | 0.927075 | − | 0.374875i | \(-0.122314\pi\) |
0.390464 | + | 0.920618i | \(0.372314\pi\) | |||||||
\(402\) | 1188.44 | − | 2869.14i | 0.147447 | − | 0.355969i | ||||
\(403\) | 685.460 | − | 283.927i | 0.0847276 | − | 0.0350953i | ||||
\(404\) | 2323.58i | 0.286145i | ||||||||
\(405\) | 487.548 | + | 1177.04i | 0.0598184 | + | 0.144414i | ||||
\(406\) | −3348.24 | − | 3348.24i | −0.409286 | − | 0.409286i | ||||
\(407\) | −6885.44 | −0.838571 | ||||||||
\(408\) | −747.105 | − | 2490.84i | −0.0906549 | − | 0.302243i | ||||
\(409\) | −7597.11 | −0.918466 | −0.459233 | − | 0.888316i | \(-0.651876\pi\) | ||||
−0.459233 | + | 0.888316i | \(0.651876\pi\) | |||||||
\(410\) | 3592.36 | + | 3592.36i | 0.432717 | + | 0.432717i | ||||
\(411\) | 2135.73 | + | 5156.10i | 0.256320 | + | 0.618812i | ||||
\(412\) | 6588.40i | 0.787833i | ||||||||
\(413\) | 5359.26 | − | 2219.88i | 0.638527 | − | 0.264487i | ||||
\(414\) | 2967.82 | − | 7164.94i | 0.352319 | − | 0.850574i | ||||
\(415\) | 5980.72 | + | 2477.30i | 0.707427 | + | 0.293026i | ||||
\(416\) | −663.862 | + | 663.862i | −0.0782416 | + | 0.0782416i | ||||
\(417\) | 2074.78 | − | 2074.78i | 0.243651 | − | 0.243651i | ||||
\(418\) | 19337.7 | + | 8009.95i | 2.26277 | + | 0.937271i | ||||
\(419\) | 2635.75 | − | 6363.26i | 0.307315 | − | 0.741923i | −0.692476 | − | 0.721441i | \(-0.743480\pi\) |
0.999790 | − | 0.0204818i | \(-0.00652001\pi\) | |||||||
\(420\) | 662.774 | − | 274.530i | 0.0770001 | − | 0.0318945i | ||||
\(421\) | − | 13586.7i | − | 1.57286i | −0.617678 | − | 0.786431i | \(-0.711927\pi\) | ||
0.617678 | − | 0.786431i | \(-0.288073\pi\) | |||||||
\(422\) | 3148.04 | + | 7600.05i | 0.363138 | + | 0.876694i | ||||
\(423\) | 1761.50 | + | 1761.50i | 0.202475 | + | 0.202475i | ||||
\(424\) | 9378.62 | 1.07421 | ||||||||
\(425\) | −3415.08 | − | 347.124i | −0.389778 | − | 0.0396188i | ||||
\(426\) | −1171.42 | −0.133228 | ||||||||
\(427\) | −24.1978 | − | 24.1978i | −0.00274242 | − | 0.00274242i | ||||
\(428\) | 399.543 | + | 964.583i | 0.0451230 | + | 0.108937i | ||||
\(429\) | 938.177i | 0.105584i | ||||||||
\(430\) | 4676.72 | − | 1937.16i | 0.524492 | − | 0.217252i | ||||
\(431\) | −6434.61 | + | 15534.5i | −0.719128 | + | 1.73613i | −0.0433099 | + | 0.999062i | \(0.513790\pi\) |
−0.675819 | + | 0.737068i | \(0.736210\pi\) | |||||||
\(432\) | −9602.19 | − | 3977.36i | −1.06941 | − | 0.442964i | ||||
\(433\) | −175.945 | + | 175.945i | −0.0195274 | + | 0.0195274i | −0.716803 | − | 0.697276i | \(-0.754395\pi\) |
0.697276 | + | 0.716803i | \(0.254395\pi\) | |||||||
\(434\) | −2342.20 | + | 2342.20i | −0.259054 | + | 0.259054i | ||||
\(435\) | 4492.30 | + | 1860.77i | 0.495148 | + | 0.205097i | ||||
\(436\) | 3240.50 | − | 7823.25i | 0.355944 | − | 0.859325i | ||||
\(437\) | −10419.7 | + | 4315.98i | −1.14060 | + | 0.472452i | ||||
\(438\) | − | 6432.66i | − | 0.701745i | ||||||
\(439\) | 3777.10 | + | 9118.74i | 0.410641 | + | 0.991375i | 0.984966 | + | 0.172748i | \(0.0552645\pi\) |
−0.574325 | + | 0.818627i | \(0.694735\pi\) | |||||||
\(440\) | −5002.71 | − | 5002.71i | −0.542034 | − | 0.542034i | ||||
\(441\) | −5629.24 | −0.607844 | ||||||||
\(442\) | −1311.42 | − | 133.298i | −0.141126 | − | 0.0143447i | ||||
\(443\) | −10000.3 | −1.07253 | −0.536264 | − | 0.844051i | \(-0.680165\pi\) | ||||
−0.536264 | + | 0.844051i | \(0.680165\pi\) | |||||||
\(444\) | 945.666 | + | 945.666i | 0.101080 | + | 0.101080i | ||||
\(445\) | −719.159 | − | 1736.20i | −0.0766099 | − | 0.184953i | ||||
\(446\) | − | 1443.24i | − | 0.153227i | ||||||
\(447\) | −312.096 | + | 129.274i | −0.0330238 | + | 0.0136789i | ||||
\(448\) | −73.6186 | + | 177.731i | −0.00776373 | + | 0.0187433i | ||||
\(449\) | −7927.24 | − | 3283.57i | −0.833206 | − | 0.345125i | −0.0750349 | − | 0.997181i | \(-0.523907\pi\) |
−0.758171 | + | 0.652056i | \(0.773907\pi\) | |||||||
\(450\) | −2304.74 | + | 2304.74i | −0.241437 | + | 0.241437i | ||||
\(451\) | 7274.50 | − | 7274.50i | 0.759518 | − | 0.759518i | ||||
\(452\) | −4249.37 | − | 1760.15i | −0.442198 | − | 0.183164i | ||||
\(453\) | −1695.21 | + | 4092.60i | −0.175823 | + | 0.424475i | ||||
\(454\) | −6194.67 | + | 2565.92i | −0.640375 | + | 0.265252i | ||||
\(455\) | 321.187i | 0.0330934i | ||||||||
\(456\) | 1374.16 | + | 3317.52i | 0.141121 | + | 0.340696i | ||||
\(457\) | 5901.41 | + | 5901.41i | 0.604062 | + | 0.604062i | 0.941388 | − | 0.337326i | \(-0.109522\pi\) |
−0.337326 | + | 0.941388i | \(0.609522\pi\) | |||||||
\(458\) | −17021.0 | −1.73655 | ||||||||
\(459\) | −2618.19 | − | 8729.03i | −0.266246 | − | 0.887661i | ||||
\(460\) | −4316.02 | −0.437468 | ||||||||
\(461\) | 6081.73 | + | 6081.73i | 0.614435 | + | 0.614435i | 0.944099 | − | 0.329663i | \(-0.106935\pi\) |
−0.329663 | + | 0.944099i | \(0.606935\pi\) | |||||||
\(462\) | −1602.86 | − | 3869.66i | −0.161411 | − | 0.389681i | ||||
\(463\) | − | 15888.5i | − | 1.59482i | −0.603440 | − | 0.797408i | \(-0.706204\pi\) | ||
0.603440 | − | 0.797408i | \(-0.293796\pi\) | |||||||
\(464\) | 14576.8 | − | 6037.92i | 1.45843 | − | 0.604102i | ||||
\(465\) | 1301.67 | − | 3142.51i | 0.129814 | − | 0.313399i | ||||
\(466\) | 1796.66 | + | 744.200i | 0.178602 | + | 0.0739794i | ||||
\(467\) | −4201.42 | + | 4201.42i | −0.416314 | + | 0.416314i | −0.883931 | − | 0.467617i | \(-0.845113\pi\) |
0.467617 | + | 0.883931i | \(0.345113\pi\) | |||||||
\(468\) | −306.957 | + | 306.957i | −0.0303186 | + | 0.0303186i | ||||
\(469\) | −1989.06 | − | 823.897i | −0.195835 | − | 0.0811173i | ||||
\(470\) | 1529.70 | − | 3693.02i | 0.150127 | − | 0.362439i | ||||
\(471\) | 5538.12 | − | 2293.96i | 0.541790 | − | 0.224417i | ||||
\(472\) | 11111.7i | 1.08360i | ||||||||
\(473\) | −3922.74 | − | 9470.33i | −0.381327 | − | 0.920605i | ||||
\(474\) | 1457.15 | + | 1457.15i | 0.141201 | + | 0.141201i | ||||
\(475\) | 4740.02 | 0.457867 | ||||||||
\(476\) | 1955.04 | − | 586.396i | 0.188254 | − | 0.0564652i | ||||
\(477\) | 13582.7 | 1.30379 | ||||||||
\(478\) | −7932.69 | − | 7932.69i | −0.759064 | − | 0.759064i | ||||
\(479\) | 5707.77 | + | 13779.8i | 0.544456 | + | 1.31443i | 0.921551 | + | 0.388258i | \(0.126923\pi\) |
−0.377094 | + | 0.926175i | \(0.623077\pi\) | |||||||
\(480\) | 4304.15i | 0.409285i | ||||||||
\(481\) | −553.192 | + | 229.140i | −0.0524395 | + | 0.0217212i | ||||
\(482\) | 1196.51 | − | 2888.63i | 0.113069 | − | 0.272974i | ||||
\(483\) | 2085.08 | + | 863.668i | 0.196427 | + | 0.0813628i | ||||
\(484\) | 7471.42 | − | 7471.42i | 0.701673 | − | 0.701673i | ||||
\(485\) | −4350.93 | + | 4350.93i | −0.407352 | + | 0.407352i | ||||
\(486\) | −12685.2 | − | 5254.37i | −1.18397 | − | 0.490418i | ||||
\(487\) | −3146.75 | + | 7596.92i | −0.292798 | + | 0.706878i | −1.00000 | 0.000134144i | \(-0.999957\pi\) | |
0.707202 | + | 0.707012i | \(0.249957\pi\) | |||||||
\(488\) | 60.5616 | − | 25.0854i | 0.00561781 | − | 0.00232697i | ||||
\(489\) | − | 1252.46i | − | 0.115825i | ||||||
\(490\) | 3456.68 | + | 8345.16i | 0.318688 | + | 0.769380i | ||||
\(491\) | −1863.67 | − | 1863.67i | −0.171295 | − | 0.171295i | 0.616253 | − | 0.787548i | \(-0.288650\pi\) |
−0.787548 | + | 0.616253i | \(0.788650\pi\) | |||||||
\(492\) | −1998.20 | −0.183101 | ||||||||
\(493\) | 12180.6 | + | 6559.62i | 1.11275 | + | 0.599250i | ||||
\(494\) | 1820.20 | 0.165779 | ||||||||
\(495\) | −7245.22 | − | 7245.22i | −0.657875 | − | 0.657875i | ||||
\(496\) | −4223.72 | − | 10197.0i | −0.382360 | − | 0.923099i | ||||
\(497\) | 812.097i | 0.0732949i | ||||||||
\(498\) | −6782.37 | + | 2809.35i | −0.610292 | + | 0.252791i | ||||
\(499\) | 4884.55 | − | 11792.3i | 0.438201 | − | 1.05791i | −0.538368 | − | 0.842710i | \(-0.680959\pi\) |
0.976570 | − | 0.215202i | \(-0.0690409\pi\) | |||||||
\(500\) | 5953.35 | + | 2465.96i | 0.532484 | + | 0.220562i | ||||
\(501\) | 4699.84 | − | 4699.84i | 0.419109 | − | 0.419109i | ||||
\(502\) | −6016.89 | + | 6016.89i | −0.534954 | + | 0.534954i | ||||
\(503\) | 5915.75 | + | 2450.38i | 0.524394 | + | 0.217211i | 0.629146 | − | 0.777287i | \(-0.283405\pi\) |
−0.104752 | + | 0.994498i | \(0.533405\pi\) | |||||||
\(504\) | −655.077 | + | 1581.50i | −0.0578958 | + | 0.139773i | ||||
\(505\) | −4406.32 | + | 1825.16i | −0.388274 | + | 0.160828i | ||||
\(506\) | 25199.4i | 2.21393i | ||||||||
\(507\) | −2344.24 | − | 5659.51i | −0.205348 | − | 0.495754i | ||||
\(508\) | 3052.02 | + | 3052.02i | 0.266558 | + | 0.266558i | ||||
\(509\) | 7892.36 | 0.687274 | 0.343637 | − | 0.939103i | \(-0.388341\pi\) | ||||
0.343637 | + | 0.939103i | \(0.388341\pi\) | |||||||
\(510\) | −4683.40 | + | 3819.17i | −0.406637 | + | 0.331599i | ||||
\(511\) | −4459.51 | −0.386061 | ||||||||
\(512\) | 3937.80 | + | 3937.80i | 0.339898 | + | 0.339898i | ||||
\(513\) | 4815.69 | + | 11626.1i | 0.414460 | + | 1.00059i | ||||
\(514\) | 11253.1i | 0.965667i | ||||||||
\(515\) | −12493.9 | + | 5175.14i | −1.06902 | + | 0.442804i | ||||
\(516\) | −761.922 | + | 1839.44i | −0.0650034 | + | 0.156932i | ||||
\(517\) | −7478.33 | − | 3097.63i | −0.636164 | − | 0.263508i | ||||
\(518\) | 1890.25 | − | 1890.25i | 0.160333 | − | 0.160333i | ||||
\(519\) | −3796.47 | + | 3796.47i | −0.321092 | + | 0.321092i | ||||
\(520\) | −568.415 | − | 235.445i | −0.0479358 | − | 0.0198557i | ||||
\(521\) | 3255.41 | − | 7859.25i | 0.273747 | − | 0.660883i | −0.725891 | − | 0.687810i | \(-0.758572\pi\) |
0.999637 | + | 0.0269270i | \(0.00857216\pi\) | |||||||
\(522\) | 12136.2 | − | 5027.00i | 1.01760 | − | 0.421505i | ||||
\(523\) | − | 18757.8i | − | 1.56830i | −0.620571 | − | 0.784150i | \(-0.713099\pi\) | ||
0.620571 | − | 0.784150i | \(-0.286901\pi\) | |||||||
\(524\) | −1802.58 | − | 4351.81i | −0.150279 | − | 0.362805i | ||||
\(525\) | −670.705 | − | 670.705i | −0.0557562 | − | 0.0557562i | ||||
\(526\) | 9306.30 | 0.771433 | ||||||||
\(527\) | 4588.67 | − | 8520.70i | 0.379289 | − | 0.704303i | ||||
\(528\) | 13956.4 | 1.15033 | ||||||||
\(529\) | −997.824 | − | 997.824i | −0.0820107 | − | 0.0820107i | ||||
\(530\) | −8340.53 | − | 20135.8i | −0.683565 | − | 1.65027i | ||||
\(531\) | 16092.6i | 1.31518i | ||||||||
\(532\) | −2603.89 | + | 1078.57i | −0.212205 | + | 0.0878983i | ||||
\(533\) | 342.363 | − | 826.537i | 0.0278225 | − | 0.0671694i | ||||
\(534\) | 1968.92 | + | 815.555i | 0.159557 | + | 0.0660908i | ||||
\(535\) | −1515.35 | + | 1515.35i | −0.122456 | + | 0.122456i | ||||
\(536\) | 2916.15 | − | 2916.15i | 0.234997 | − | 0.234997i | ||||
\(537\) | 260.328 | + | 107.831i | 0.0209199 | + | 0.00866530i | ||||
\(538\) | −7650.50 | + | 18470.0i | −0.613079 | + | 1.48010i | ||||
\(539\) | 16898.9 | − | 6999.75i | 1.35044 | − | 0.559370i | ||||
\(540\) | 4815.73i | 0.383770i | ||||||||
\(541\) | −5127.75 | − | 12379.5i | −0.407503 | − | 0.983800i | −0.985792 | − | 0.167968i | \(-0.946279\pi\) |
0.578289 | − | 0.815832i | \(-0.303721\pi\) | |||||||
\(542\) | 620.858 | + | 620.858i | 0.0492032 | + | 0.0492032i | ||||
\(543\) | −10959.2 | −0.866121 | ||||||||
\(544\) | −1238.37 | + | 12183.4i | −0.0976005 | + | 0.960215i | ||||
\(545\) | 17381.0 | 1.36609 | ||||||||
\(546\) | −257.556 | − | 257.556i | −0.0201875 | − | 0.0201875i | ||||
\(547\) | 2729.96 | + | 6590.70i | 0.213391 | + | 0.515170i | 0.993940 | − | 0.109924i | \(-0.0350606\pi\) |
−0.780549 | + | 0.625094i | \(0.785061\pi\) | |||||||
\(548\) | − | 8390.88i | − | 0.654089i | ||||||
\(549\) | 87.7087 | − | 36.3301i | 0.00681843 | − | 0.00282429i | ||||
\(550\) | 4052.93 | − | 9784.65i | 0.314214 | − | 0.758579i | ||||
\(551\) | −17649.3 | − | 7310.57i | −1.36458 | − | 0.565228i | ||||
\(552\) | −3056.92 | + | 3056.92i | −0.235708 | + | 0.235708i | ||||
\(553\) | 1010.19 | − | 1010.19i | 0.0776809 | − | 0.0776809i | ||||
\(554\) | −11925.3 | − | 4939.63i | −0.914546 | − | 0.378817i | ||||
\(555\) | −1050.50 | + | 2536.13i | −0.0803444 | + | 0.193969i | ||||
\(556\) | −4075.71 | + | 1688.21i | −0.310879 | + | 0.128770i | ||||
\(557\) | − | 5175.60i | − | 0.393712i | −0.980432 | − | 0.196856i | \(-0.936927\pi\) | ||
0.980432 | − | 0.196856i | \(-0.0630731\pi\) | |||||||
\(558\) | −3516.55 | − | 8489.70i | −0.266787 | − | 0.644081i | ||||
\(559\) | −630.324 | − | 630.324i | −0.0476921 | − | 0.0476921i | ||||
\(560\) | 4778.01 | 0.360550 | ||||||||
\(561\) | 7733.78 | + | 9483.86i | 0.582033 | + | 0.713741i | ||||
\(562\) | −12361.0 | −0.927787 | ||||||||
\(563\) | −3938.10 | − | 3938.10i | −0.294798 | − | 0.294798i | 0.544174 | − | 0.838972i | \(-0.316843\pi\) |
−0.838972 | + | 0.544174i | \(0.816843\pi\) | |||||||
\(564\) | 601.659 | + | 1452.53i | 0.0449192 | + | 0.108444i | ||||
\(565\) | − | 9440.87i | − | 0.702974i | ||||||
\(566\) | −2548.56 | + | 1055.65i | −0.189265 | + | 0.0783961i | ||||
\(567\) | −383.303 | + | 925.375i | −0.0283901 | + | 0.0685398i | ||||
\(568\) | −1437.19 | − | 595.305i | −0.106168 | − | 0.0439761i | ||||
\(569\) | −10840.0 | + | 10840.0i | −0.798660 | + | 0.798660i | −0.982884 | − | 0.184224i | \(-0.941023\pi\) |
0.184224 | + | 0.982884i | \(0.441023\pi\) | |||||||
\(570\) | 5900.64 | − | 5900.64i | 0.433597 | − | 0.433597i | ||||
\(571\) | −20588.7 | − | 8528.10i | −1.50895 | − | 0.625026i | −0.533606 | − | 0.845733i | \(-0.679164\pi\) |
−0.975340 | + | 0.220707i | \(0.929164\pi\) | |||||||
\(572\) | 539.791 | − | 1303.17i | 0.0394577 | − | 0.0952592i | ||||
\(573\) | −6073.96 | + | 2515.92i | −0.442833 | + | 0.183428i | ||||
\(574\) | 3994.11i | 0.290437i | ||||||||
\(575\) | 2183.83 | + | 5272.24i | 0.158386 | + | 0.382378i | ||||
\(576\) | −377.373 | − | 377.373i | −0.0272984 | − | 0.0272984i | ||||
\(577\) | 19321.1 | 1.39401 | 0.697007 | − | 0.717064i | \(-0.254515\pi\) | ||||
0.697007 | + | 0.717064i | \(0.254515\pi\) | |||||||
\(578\) | −14355.7 | + | 9463.07i | −1.03308 | + | 0.680989i | ||||
\(579\) | 3945.62 | 0.283203 | ||||||||
\(580\) | −5169.40 | − | 5169.40i | −0.370082 | − | 0.370082i | ||||
\(581\) | 1947.61 | + | 4701.96i | 0.139072 | + | 0.335749i | ||||
\(582\) | − | 6977.91i | − | 0.496982i | ||||||
\(583\) | −40774.9 | + | 16889.5i | −2.89661 | + | 1.19981i | ||||
\(584\) | 3269.03 | − | 7892.13i | 0.231632 | − | 0.559210i | ||||
\(585\) | −823.211 | − | 340.985i | −0.0581805 | − | 0.0240991i | ||||
\(586\) | 3498.74 | − | 3498.74i | 0.246641 | − | 0.246641i | ||||
\(587\) | 16667.4 | − | 16667.4i | 1.17195 | − | 1.17195i | 0.190210 | − | 0.981743i | \(-0.439083\pi\) |
0.981743 | − | 0.190210i | \(-0.0609169\pi\) | |||||||
\(588\) | −3282.31 | − | 1359.58i | −0.230204 | − | 0.0953537i | ||||
\(589\) | −5113.98 | + | 12346.2i | −0.357755 | + | 0.863698i | ||||
\(590\) | 23856.8 | − | 9881.80i | 1.66469 | − | 0.689537i | ||||
\(591\) | 5718.12i | 0.397990i | ||||||||
\(592\) | 3408.70 | + | 8229.34i | 0.236650 | + | 0.571324i | ||||
\(593\) | 19330.9 | + | 19330.9i | 1.33866 | + | 1.33866i | 0.897359 | + | 0.441302i | \(0.145483\pi\) |
0.441302 | + | 0.897359i | \(0.354517\pi\) | |||||||
\(594\) | 28117.0 | 1.94218 | ||||||||
\(595\) | 2647.68 | + | 3246.82i | 0.182427 | + | 0.223709i | ||||
\(596\) | 507.895 | 0.0349064 | ||||||||
\(597\) | −8277.79 | − | 8277.79i | −0.567483 | − | 0.567483i | ||||
\(598\) | 838.608 | + | 2024.58i | 0.0573465 | + | 0.138447i | ||||
\(599\) | − | 3930.83i | − | 0.268129i | −0.990973 | − | 0.134064i | \(-0.957197\pi\) | ||
0.990973 | − | 0.134064i | \(-0.0428029\pi\) | |||||||
\(600\) | 1678.63 | − | 695.309i | 0.114216 | − | 0.0473098i | ||||
\(601\) | −8595.04 | + | 20750.3i | −0.583359 | + | 1.40835i | 0.306391 | + | 0.951906i | \(0.400879\pi\) |
−0.889750 | + | 0.456448i | \(0.849121\pi\) | |||||||
\(602\) | 3676.77 | + | 1522.97i | 0.248927 | + | 0.103109i | ||||
\(603\) | 4223.34 | − | 4223.34i | 0.285220 | − | 0.285220i | ||||
\(604\) | 4709.45 | − | 4709.45i | 0.317259 | − | 0.317259i | ||||
\(605\) | 20037.2 | + | 8299.66i | 1.34649 | + | 0.557734i | ||||
\(606\) | 2069.80 | − | 4996.94i | 0.138746 | − | 0.334961i | ||||
\(607\) | 2057.72 | − | 852.335i | 0.137595 | − | 0.0569938i | −0.312823 | − | 0.949811i | \(-0.601275\pi\) |
0.450419 | + | 0.892818i | \(0.351275\pi\) | |||||||
\(608\) | − | 16910.1i | − | 1.12795i | ||||||
\(609\) | 1462.91 | + | 3531.78i | 0.0973402 | + | 0.235000i | ||||
\(610\) | −107.716 | − | 107.716i | −0.00714969 | − | 0.00714969i | ||||
\(611\) | −703.913 | −0.0466076 | ||||||||
\(612\) | −572.599 | + | 5633.35i | −0.0378201 | + | 0.372083i | ||||
\(613\) | 721.642 | 0.0475479 | 0.0237739 | − | 0.999717i | \(-0.492432\pi\) | ||||
0.0237739 | + | 0.999717i | \(0.492432\pi\) | |||||||
\(614\) | 11135.0 | + | 11135.0i | 0.731874 | + | 0.731874i | ||||
\(615\) | −1569.57 | − | 3789.28i | −0.102913 | − | 0.248453i | ||||
\(616\) | − | 5562.19i | − | 0.363810i | ||||||
\(617\) | 6311.56 | − | 2614.33i | 0.411821 | − | 0.170582i | −0.167147 | − | 0.985932i | \(-0.553455\pi\) |
0.578968 | + | 0.815350i | \(0.303455\pi\) | |||||||
\(618\) | 5868.81 | − | 14168.6i | 0.382004 | − | 0.922239i | ||||
\(619\) | 14869.8 | + | 6159.26i | 0.965536 | + | 0.399938i | 0.809048 | − | 0.587742i | \(-0.199983\pi\) |
0.156487 | + | 0.987680i | \(0.449983\pi\) | |||||||
\(620\) | −3616.16 | + | 3616.16i | −0.234240 | + | 0.234240i | ||||
\(621\) | −10712.8 | + | 10712.8i | −0.692256 | + | 0.692256i | ||||
\(622\) | −15250.8 | − | 6317.10i | −0.983123 | − | 0.407223i | ||||
\(623\) | 565.393 | − | 1364.98i | 0.0363595 | − | 0.0877796i | ||||
\(624\) | 1121.29 | − | 464.453i | 0.0719351 | − | 0.0297965i | ||||
\(625\) | 7104.94i | 0.454716i | ||||||||
\(626\) | −8265.11 | − | 19953.8i | −0.527700 | − | 1.27398i | ||||
\(627\) | −11948.7 | − | 11948.7i | −0.761063 | − | 0.761063i | ||||
\(628\) | −9012.55 | −0.572675 | ||||||||
\(629\) | −3703.23 | + | 6876.53i | −0.234749 | + | 0.435906i | ||||
\(630\) | 3978.03 | 0.251569 | ||||||||
\(631\) | 19184.5 | + | 19184.5i | 1.21034 | + | 1.21034i | 0.970916 | + | 0.239421i | \(0.0769578\pi\) |
0.239421 | + | 0.970916i | \(0.423042\pi\) | |||||||
\(632\) | 1047.25 | + | 2528.27i | 0.0659132 | + | 0.159129i | ||||
\(633\) | − | 6641.23i | − | 0.417007i | ||||||
\(634\) | 3837.51 | − | 1589.55i | 0.240389 | − | 0.0995725i | ||||
\(635\) | −3390.35 | + | 8185.03i | −0.211877 | + | 0.511517i | ||||
\(636\) | 7919.79 | + | 3280.49i | 0.493774 | + | 0.204528i | ||||
\(637\) | 1124.75 | − | 1124.75i | 0.0699597 | − | 0.0699597i | ||||
\(638\) | −30181.9 | + | 30181.9i | −1.87290 | + | 1.87290i | ||||
\(639\) | −2081.43 | − | 862.155i | −0.128857 | − | 0.0533745i | ||||
\(640\) | −4991.49 | + | 12050.5i | −0.308291 | + | 0.744280i | ||||
\(641\) | −12843.5 | + | 5319.95i | −0.791400 | + | 0.327809i | −0.741506 | − | 0.670946i | \(-0.765888\pi\) |
−0.0498939 | + | 0.998755i | \(0.515888\pi\) | |||||||
\(642\) | − | 2430.27i | − | 0.149401i | ||||||
\(643\) | −3378.07 | − | 8155.37i | −0.207182 | − | 0.500181i | 0.785795 | − | 0.618487i | \(-0.212254\pi\) |
−0.992977 | + | 0.118305i | \(0.962254\pi\) | |||||||
\(644\) | −2399.35 | − | 2399.35i | −0.146813 | − | 0.146813i | ||||
\(645\) | −4086.71 | −0.249479 | ||||||||
\(646\) | 18400.1 | − | 15004.7i | 1.12065 | − | 0.913856i | ||||
\(647\) | −14695.4 | −0.892946 | −0.446473 | − | 0.894797i | \(-0.647320\pi\) | ||||
−0.446473 | + | 0.894797i | \(0.647320\pi\) | |||||||
\(648\) | −1356.68 | − | 1356.68i | −0.0822463 | − | 0.0822463i | ||||
\(649\) | −20010.6 | − | 48309.8i | −1.21030 | − | 2.92192i | ||||
\(650\) | − | 920.999i | − | 0.0555762i | ||||||
\(651\) | 2470.60 | − | 1023.35i | 0.148741 | − | 0.0616105i | ||||
\(652\) | −720.617 | + | 1739.72i | −0.0432846 | + | 0.104498i | ||||
\(653\) | 6413.85 | + | 2656.70i | 0.384370 | + | 0.159211i | 0.566497 | − | 0.824064i | \(-0.308298\pi\) |
−0.182127 | + | 0.983275i | \(0.558298\pi\) | |||||||
\(654\) | −13937.6 | + | 13937.6i | −0.833337 | + | 0.833337i | ||||
\(655\) | 6836.64 | − | 6836.64i | 0.407831 | − | 0.407831i | ||||
\(656\) | −12295.6 | − | 5093.02i | −0.731805 | − | 0.303124i | ||||
\(657\) | 4734.39 | − | 11429.8i | 0.281136 | − | 0.678722i | ||||
\(658\) | 2903.40 | − | 1202.63i | 0.172016 | − | 0.0712512i | ||||
\(659\) | 11804.8i | 0.697800i | 0.937160 | + | 0.348900i | \(0.113445\pi\) | ||||
−0.937160 | + | 0.348900i | \(0.886555\pi\) | |||||||
\(660\) | −2474.69 | − | 5974.42i | −0.145950 | − | 0.352354i | ||||
\(661\) | 2731.80 | + | 2731.80i | 0.160748 | + | 0.160748i | 0.782898 | − | 0.622150i | \(-0.213741\pi\) |
−0.622150 | + | 0.782898i | \(0.713741\pi\) | |||||||
\(662\) | 10744.4 | 0.630806 | ||||||||
\(663\) | 936.963 | + | 504.584i | 0.0548848 | + | 0.0295572i | ||||
\(664\) | −9748.88 | −0.569774 | ||||||||
\(665\) | −4090.68 | − | 4090.68i | −0.238541 | − | 0.238541i | ||||
\(666\) | 2837.99 | + | 6851.50i | 0.165120 | + | 0.398634i | ||||
\(667\) | − | 22999.1i | − | 1.33513i | ||||||
\(668\) | −9232.40 | + | 3824.19i | −0.534749 | + | 0.221500i | ||||
\(669\) | −445.887 | + | 1076.47i | −0.0257683 | + | 0.0622102i | ||||
\(670\) | −8854.32 | − | 3667.58i | −0.510556 | − | 0.211479i | ||||
\(671\) | −218.125 | + | 218.125i | −0.0125494 | + | 0.0125494i | ||||
\(672\) | −2392.75 | + | 2392.75i | −0.137355 | + | 0.137355i | ||||
\(673\) | 809.824 | + | 335.440i | 0.0463840 | + | 0.0192129i | 0.405755 | − | 0.913982i | \(-0.367009\pi\) |
−0.359371 | + | 0.933195i | \(0.617009\pi\) | |||||||
\(674\) | 5943.00 | − | 14347.7i | 0.339638 | − | 0.819958i | ||||
\(675\) | 5882.66 | − | 2436.68i | 0.335443 | − | 0.138945i | ||||
\(676\) | 9210.10i | 0.524016i | ||||||||
\(677\) | −7784.19 | − | 18792.7i | −0.441906 | − | 1.06686i | −0.975279 | − | 0.220976i | \(-0.929076\pi\) |
0.533373 | − | 0.845880i | \(-0.320924\pi\) | |||||||
\(678\) | 7570.50 | + | 7570.50i | 0.428825 | + | 0.428825i | ||||
\(679\) | −4837.51 | −0.273412 | ||||||||
\(680\) | −7686.87 | + | 2305.61i | −0.433497 | + | 0.130024i | ||||
\(681\) | 5413.15 | 0.304600 | ||||||||
\(682\) | 21113.2 | + | 21113.2i | 1.18544 | + | 1.18544i | ||||
\(683\) | 11493.8 | + | 27748.5i | 0.643922 | + | 1.55456i | 0.821346 | + | 0.570430i | \(0.193223\pi\) |
−0.177425 | + | 0.984134i | \(0.556777\pi\) | |||||||
\(684\) | − | 7818.90i | − | 0.437080i | ||||||
\(685\) | 15912.0 | − | 6590.98i | 0.887543 | − | 0.367633i | ||||
\(686\) | −5866.60 | + | 14163.2i | −0.326513 | + | 0.788272i | ||||
\(687\) | 12695.4 | + | 5258.61i | 0.705037 | + | 0.292036i | ||||
\(688\) | −9376.76 | + | 9376.76i | −0.519601 | + | 0.519601i | ||||
\(689\) | −2713.89 | + | 2713.89i | −0.150059 | + | 0.150059i | ||||
\(690\) | 9281.74 | + | 3844.62i | 0.512101 | + | 0.212119i | ||||
\(691\) | 4132.11 | − | 9975.80i | 0.227486 | − | 0.549200i | −0.768384 | − | 0.639989i | \(-0.778939\pi\) |
0.995870 | + | 0.0907888i | \(0.0289388\pi\) | |||||||
\(692\) | 7457.82 | − | 3089.13i | 0.409687 | − | 0.169698i | ||||
\(693\) | − | 8055.48i | − | 0.441562i | ||||||
\(694\) | 11670.8 | + | 28175.7i | 0.638352 | + | 1.54112i | ||||
\(695\) | −6402.88 | − | 6402.88i | −0.349461 | − | 0.349461i | ||||
\(696\) | −7322.68 | −0.398801 | ||||||||
\(697\) | −3352.61 | − | 11177.6i | −0.182194 | − | 0.607432i | ||||
\(698\) | 353.223 | 0.0191543 | ||||||||
\(699\) | −1110.15 | − | 1110.15i | −0.0600713 | − | 0.0600713i | ||||
\(700\) | 545.742 | + | 1317.54i | 0.0294673 | + | 0.0711404i | ||||
\(701\) | − | 328.897i | − | 0.0177208i | −0.999961 | − | 0.00886039i | \(-0.997180\pi\) | ||
0.999961 | − | 0.00886039i | \(-0.00282039\pi\) | |||||||
\(702\) | 2258.98 | − | 935.702i | 0.121453 | − | 0.0503074i | ||||
\(703\) | 4127.18 | − | 9963.88i | 0.221422 | − | 0.534559i | ||||
\(704\) | 1602.11 | + | 663.618i | 0.0857698 | + | 0.0355270i | ||||
\(705\) | −2281.91 | + | 2281.91i | −0.121903 | + | 0.121903i | ||||
\(706\) | 21502.1 | − | 21502.1i | 1.14624 | − | 1.14624i | ||||
\(707\) | −3464.18 | − | 1434.91i | −0.184277 | − | 0.0763301i | ||||
\(708\) | −3886.69 | + | 9383.31i | −0.206315 | + | 0.498088i | ||||
\(709\) | 4480.97 | − | 1856.08i | 0.237357 | − | 0.0983167i | −0.260834 | − | 0.965384i | \(-0.583998\pi\) |
0.498192 | + | 0.867067i | \(0.333998\pi\) | |||||||
\(710\) | 3615.06i | 0.191085i | ||||||||
\(711\) | 1516.68 | + | 3661.59i | 0.0800000 | + | 0.193137i | ||||
\(712\) | 2001.18 | + | 2001.18i | 0.105334 | + | 0.105334i | ||||
\(713\) | −16088.7 | −0.845056 | ||||||||
\(714\) | −4726.72 | − | 480.445i | −0.247750 | − | 0.0251824i | ||||
\(715\) | 2895.27 | 0.151436 | ||||||||
\(716\) | −299.565 | − | 299.565i | −0.0156359 | − | 0.0156359i | ||||
\(717\) | 3465.95 | + | 8367.55i | 0.180528 | + | 0.435832i | ||||
\(718\) | − | 8439.60i | − | 0.438667i | ||||||
\(719\) | 30379.9 | − | 12583.8i | 1.57577 | − | 0.652705i | 0.588034 | − | 0.808836i | \(-0.299902\pi\) |
0.987736 | + | 0.156131i | \(0.0499021\pi\) | |||||||
\(720\) | −5072.52 | + | 12246.2i | −0.262558 | + | 0.633871i | ||||
\(721\) | −9822.52 | − | 4068.62i | −0.507365 | − | 0.210157i | ||||
\(722\) | −6208.57 | + | 6208.57i | −0.320026 | + | 0.320026i | ||||
\(723\) | −1784.88 | + | 1784.88i | −0.0918123 | + | 0.0918123i | ||||
\(724\) | 15222.8 | + | 6305.50i | 0.781425 | + | 0.323677i | ||||
\(725\) | −3699.06 | + | 8930.31i | −0.189489 | + | 0.457467i | ||||
\(726\) | −22722.9 | + | 9412.14i | −1.16161 | + | 0.481153i | ||||
\(727\) | 16213.2i | 0.827116i | 0.910478 | + | 0.413558i | \(0.135714\pi\) | ||||
−0.910478 | + | 0.413558i | \(0.864286\pi\) | |||||||
\(728\) | −185.103 | − | 446.879i | −0.00942361 | − | 0.0227506i | ||||
\(729\) | 5048.54 | + | 5048.54i | 0.256492 | + | 0.256492i | ||||
\(730\) | −19851.5 | −1.00649 | ||||||||
\(731\) | −11567.9 | − | 1175.81i | −0.585298 | − | 0.0594922i | ||||
\(732\) | 59.9158 | 0.00302534 | ||||||||
\(733\) | 17579.4 | + | 17579.4i | 0.885826 | + | 0.885826i | 0.994119 | − | 0.108293i | \(-0.0345384\pi\) |
−0.108293 | + | 0.994119i | \(0.534538\pi\) | |||||||
\(734\) | −3045.80 | − | 7353.20i | −0.153164 | − | 0.369771i | ||||
\(735\) | − | 7292.34i | − | 0.365962i | ||||||
\(736\) | 18808.8 | − | 7790.86i | 0.941985 | − | 0.390183i | ||||
\(737\) | −7426.82 | + | 17929.9i | −0.371195 | + | 0.896143i | ||||
\(738\) | −10237.0 | − | 4240.30i | −0.510608 | − | 0.211501i | ||||
\(739\) | 724.084 | − | 724.084i | 0.0360431 | − | 0.0360431i | −0.688856 | − | 0.724899i | \(-0.741887\pi\) |
0.724899 | + | 0.688856i | \(0.241887\pi\) | |||||||
\(740\) | 2918.38 | − | 2918.38i | 0.144975 | − | 0.144975i | ||||
\(741\) | −1357.63 | − | 562.349i | −0.0673061 | − | 0.0278791i | ||||
\(742\) | 6557.20 | − | 15830.5i | 0.324424 | − | 0.783229i | ||||
\(743\) | 6347.67 | − | 2629.29i | 0.313423 | − | 0.129824i | −0.220426 | − | 0.975404i | \(-0.570745\pi\) |
0.533849 | + | 0.845580i | \(0.320745\pi\) | |||||||
\(744\) | 5122.45i | 0.252417i | ||||||||
\(745\) | 398.948 | + | 963.146i | 0.0196192 | + | 0.0473650i | ||||
\(746\) | −23494.3 | − | 23494.3i | −1.15307 | − | 1.15307i | ||||
\(747\) | −14118.9 | −0.691544 | ||||||||
\(748\) | −5285.93 | − | 17623.2i | −0.258386 | − | 0.861456i | ||||
\(749\) | −1684.81 | −0.0821919 | ||||||||
\(750\) | −10606.2 | − | 10606.2i | −0.516380 | − | 0.516380i | ||||
\(751\) | 4656.89 | + | 11242.7i | 0.226275 | + | 0.546275i | 0.995718 | − | 0.0924395i | \(-0.0294665\pi\) |
−0.769444 | + | 0.638715i | \(0.779466\pi\) | |||||||
\(752\) | 10471.5i | 0.507786i | ||||||||
\(753\) | 6346.72 | − | 2628.90i | 0.307155 | − | 0.127228i | ||||
\(754\) | −1420.46 | + | 3429.31i | −0.0686078 | + | 0.165634i | ||||
\(755\) | 12630.0 | + | 5231.51i | 0.608811 | + | 0.252178i | ||||
\(756\) | −2677.14 | + | 2677.14i | −0.128792 | + | 0.128792i | ||||
\(757\) | −19971.1 | + | 19971.1i | −0.958866 | + | 0.958866i | −0.999187 | − | 0.0403208i | \(-0.987162\pi\) |
0.0403208 | + | 0.999187i | \(0.487162\pi\) | |||||||
\(758\) | 17258.4 | + | 7148.67i | 0.826984 | + | 0.342548i | ||||
\(759\) | 7785.33 | − | 18795.4i | 0.372318 | − | 0.898856i | ||||
\(760\) | 10238.1 | − | 4240.74i | 0.488649 | − | 0.202405i | ||||
\(761\) | − | 30505.2i | − | 1.45310i | −0.687112 | − | 0.726552i | \(-0.741122\pi\) | ||
0.687112 | − | 0.726552i | \(-0.258878\pi\) | |||||||
\(762\) | −3844.79 | − | 9282.15i | −0.182785 | − | 0.441282i | ||||
\(763\) | 9662.39 | + | 9662.39i | 0.458456 | + | 0.458456i | ||||
\(764\) | 9884.58 | 0.468078 | ||||||||
\(765\) | −11132.6 | + | 3339.11i | −0.526142 | + | 0.157812i | ||||
\(766\) | 2727.76 | 0.128666 | ||||||||
\(767\) | −3215.39 | − | 3215.39i | −0.151370 | − | 0.151370i | ||||
\(768\) | −5417.80 | − | 13079.7i | −0.254555 | − | 0.614550i | ||||
\(769\) | 20404.5i | 0.956834i | 0.878133 | + | 0.478417i | \(0.158789\pi\) | ||||
−0.878133 | + | 0.478417i | \(0.841211\pi\) | |||||||
\(770\) | −11942.0 | + | 4946.53i | −0.558908 | + | 0.231507i | ||||
\(771\) | 3476.64 | − | 8393.34i | 0.162397 | − | 0.392061i | ||||
\(772\) | −5480.65 | − | 2270.16i | −0.255509 | − | 0.105835i | ||||
\(773\) | 21642.1 | − | 21642.1i | 1.00700 | − | 1.00700i | 0.00702854 | − | 0.999975i | \(-0.497763\pi\) |
0.999975 | − | 0.00702854i | \(-0.00223727\pi\) | |||||||
\(774\) | −7806.81 | + | 7806.81i | −0.362545 | + | 0.362545i | ||||
\(775\) | 6247.05 | + | 2587.61i | 0.289549 | + | 0.119935i | ||||
\(776\) | 3546.12 | − | 8561.09i | 0.164044 | − | 0.396038i | ||||
\(777\) | −1993.86 | + | 825.886i | −0.0920586 | + | 0.0381319i | ||||
\(778\) | − | 37888.1i | − | 1.74596i | ||||||
\(779\) | 6166.51 | + | 14887.3i | 0.283618 | + | 0.684713i | ||||
\(780\) | −397.644 | − | 397.644i | −0.0182538 | − | 0.0182538i | ||||
\(781\) | 7320.46 | 0.335399 | ||||||||
\(782\) | 25166.8 | + | 13553.1i | 1.15085 | + | 0.619767i | ||||
\(783\) | −25662.0 | −1.17124 | ||||||||
\(784\) | −16731.9 | − | 16731.9i | −0.762205 | − | 0.762205i | ||||
\(785\) | −7079.30 | − | 17090.9i | −0.321874 | − | 0.777072i | ||||
\(786\) | 10964.4i | 0.497567i | ||||||||
\(787\) | −33344.2 | + | 13811.6i | −1.51028 | + | 0.625580i | −0.975617 | − | 0.219482i | \(-0.929563\pi\) |
−0.534668 | + | 0.845062i | \(0.679563\pi\) | |||||||
\(788\) | 3289.98 | − | 7942.73i | 0.148732 | − | 0.359071i | ||||
\(789\) | −6941.28 | − | 2875.17i | −0.313202 | − | 0.129732i | ||||
\(790\) | 4496.86 | − | 4496.86i | 0.202520 | − | 0.202520i | ||||
\(791\) | 5248.34 | − | 5248.34i | 0.235916 | − | 0.235916i | ||||
\(792\) | 14256.0 | + | 5905.04i | 0.639603 | + | 0.264932i | ||||
\(793\) | −10.2657 | + | 24.7836i | −0.000459705 | + | 0.00110983i | ||||
\(794\) | −19745.4 | + | 8178.81i | −0.882541 | + | 0.365560i | ||||
\(795\) | 17595.5i | 0.784966i | ||||||||
\(796\) | 6735.50 | + | 16260.9i | 0.299917 | + | 0.724063i | ||||
\(797\) | −15101.8 | − | 15101.8i | −0.671185 | − | 0.671185i | 0.286804 | − | 0.957989i | \(-0.407407\pi\) |
−0.957989 | + | 0.286804i | \(0.907407\pi\) | |||||||
\(798\) | 6560.53 | 0.291028 | ||||||||
\(799\) | −7115.72 | + | 5802.65i | −0.315064 | + | 0.256925i | ||||
\(800\) | −8556.28 | −0.378138 | ||||||||
\(801\) | 2898.23 | + | 2898.23i | 0.127845 | + | 0.127845i | ||||
\(802\) | 15336.9 | + | 37026.5i | 0.675266 | + | 1.63024i | ||||
\(803\) | 40199.2i | 1.76662i | ||||||||
\(804\) | 3482.57 | − | 1442.53i | 0.152762 | − | 0.0632762i | ||||
\(805\) | 2665.33 | − | 6434.67i | 0.116696 | − | 0.281730i | ||||
\(806\) | 2398.91 | + | 993.661i | 0.104836 | + | 0.0434246i | ||||
\(807\) | 11412.5 | − | 11412.5i | 0.497820 | − | 0.497820i | ||||
\(808\) | 5078.81 | − | 5078.81i | 0.221129 | − | 0.221129i | ||||
\(809\) | −24176.9 | − | 10014.4i | −1.05070 | − | 0.435213i | −0.210556 | − | 0.977582i | \(-0.567527\pi\) |
−0.840140 | + | 0.542369i | \(0.817527\pi\) | |||||||
\(810\) | −1706.27 | + | 4119.31i | −0.0740153 | + | 0.178689i | ||||
\(811\) | −18503.7 | + | 7664.48i | −0.801174 | + | 0.331857i | −0.745427 | − | 0.666588i | \(-0.767754\pi\) |
−0.0557475 | + | 0.998445i | \(0.517754\pi\) | |||||||
\(812\) | − | 5747.51i | − | 0.248397i | ||||||
\(813\) | −271.265 | − | 654.892i | −0.0117019 | − | 0.0282510i | ||||
\(814\) | −17039.2 | − | 17039.2i | −0.733689 | − | 0.733689i | ||||
\(815\) | −3865.16 | −0.166124 | ||||||||
\(816\) | 7506.23 | − | 13938.3i | 0.322023 | − | 0.597965i | ||||
\(817\) | 16055.8 | 0.687541 | ||||||||
\(818\) | −18800.3 | − | 18800.3i | −0.803591 | − | 0.803591i | ||||
\(819\) | −268.077 | − | 647.196i | −0.0114376 | − | 0.0276128i | ||||
\(820\) | 6166.56i | 0.262617i | ||||||||
\(821\) | 1997.50 | − | 827.392i | 0.0849126 | − | 0.0351719i | −0.339823 | − | 0.940489i | \(-0.610367\pi\) |
0.424735 | + | 0.905318i | \(0.360367\pi\) | |||||||
\(822\) | −7474.42 | + | 18044.9i | −0.317154 | + | 0.765677i | ||||
\(823\) | 36378.3 | + | 15068.4i | 1.54079 | + | 0.638214i | 0.981621 | − | 0.190842i | \(-0.0611218\pi\) |
0.559165 | + | 0.829056i | \(0.311122\pi\) | |||||||
\(824\) | 14400.7 | − | 14400.7i | 0.608826 | − | 0.608826i | ||||
\(825\) | −6045.91 | + | 6045.91i | −0.255141 | + | 0.255141i | ||||
\(826\) | 18755.8 | + | 7768.92i | 0.790072 | + | 0.327258i | ||||
\(827\) | −8644.75 | + | 20870.3i | −0.363492 | + | 0.877546i | 0.631293 | + | 0.775545i | \(0.282525\pi\) |
−0.994784 | + | 0.102002i | \(0.967475\pi\) | |||||||
\(828\) | 8696.83 | − | 3602.35i | 0.365019 | − | 0.151196i | ||||
\(829\) | 10977.3i | 0.459898i | 0.973203 | + | 0.229949i | \(0.0738560\pi\) | ||||
−0.973203 | + | 0.229949i | \(0.926144\pi\) | |||||||
\(830\) | 8669.81 | + | 20930.8i | 0.362571 | + | 0.875323i | ||||
\(831\) | 7368.63 | + | 7368.63i | 0.307599 | + | 0.307599i | ||||
\(832\) | 150.802 | 0.00628380 | ||||||||
\(833\) | 2098.12 | − | 20641.7i | 0.0872694 | − | 0.858576i | ||||
\(834\) | 10268.8 | 0.426353 | ||||||||
\(835\) | −14504.0 | − | 14504.0i | −0.601115 | − | 0.601115i | ||||
\(836\) | 9722.50 | + | 23472.2i | 0.402225 | + | 0.971056i | ||||
\(837\) | 17951.4i | 0.741327i | ||||||||
\(838\) | 22269.6 | − | 9224.36i | 0.918006 | − | 0.380251i | ||||
\(839\) | 17065.4 | − | 41199.4i | 0.702219 | − | 1.69531i | −0.0163657 | − | 0.999866i | \(-0.505210\pi\) |
0.718584 | − | 0.695440i | \(-0.244790\pi\) | |||||||
\(840\) | −2048.73 | − | 848.612i | −0.0841523 | − | 0.0348570i | ||||
\(841\) | 10301.0 | − | 10301.0i | 0.422362 | − | 0.422362i | ||||
\(842\) | 33622.5 | − | 33622.5i | 1.37614 | − | 1.37614i | ||||
\(843\) | 9219.67 | + | 3818.91i | 0.376681 | + | 0.156026i | ||||
\(844\) | −3821.11 | + | 9224.97i | −0.155839 | + | 0.376228i | ||||
\(845\) | −17465.6 | + | 7234.47i | −0.711045 | + | 0.294525i | ||||
\(846\) | 8718.23i | 0.354301i | ||||||||
\(847\) | 6525.07 | + | 15752.9i | 0.264704 | + | 0.639052i | ||||
\(848\) | 40372.0 | + | 40372.0i | 1.63488 | + | 1.63488i | ||||
\(849\) | 2227.03 | 0.0900254 | ||||||||
\(850\) | −7592.18 | − | 9310.21i | −0.306364 | − | 0.375691i | ||||
\(851\) | 12984.1 | 0.523021 | ||||||||
\(852\) | −1005.41 | − | 1005.41i | −0.0404283 | − | 0.0404283i | ||||
\(853\) | −14188.3 | − | 34253.7i | −0.569519 | − | 1.37494i | −0.901961 | − | 0.431817i | \(-0.857873\pi\) |
0.332443 | − | 0.943123i | \(-0.392127\pi\) | |||||||
\(854\) | − | 119.763i | − | 0.00479883i | ||||||
\(855\) | 14827.4 | − | 6141.69i | 0.593082 | − | 0.245662i | ||||
\(856\) | 1235.05 | − | 2981.67i | 0.0493143 | − | 0.119055i | ||||
\(857\) | −42102.6 | − | 17439.5i | −1.67818 | − | 0.695123i | −0.678940 | − | 0.734194i | \(-0.737560\pi\) |
−0.999236 | + | 0.0390702i | \(0.987560\pi\) | |||||||
\(858\) | −2321.68 | + | 2321.68i | −0.0923784 | + | 0.0923784i | ||||
\(859\) | −48.4609 | + | 48.4609i | −0.00192487 | + | 0.00192487i | −0.708069 | − | 0.706144i | \(-0.750433\pi\) |
0.706144 | + | 0.708069i | \(0.250433\pi\) | |||||||
\(860\) | 5676.62 | + | 2351.33i | 0.225083 | + | 0.0932324i | ||||
\(861\) | 1233.98 | − | 2979.08i | 0.0488429 | − | 0.117917i | ||||
\(862\) | −54366.3 | + | 22519.3i | −2.14817 | + | 0.889802i | ||||
\(863\) | 5064.23i | 0.199755i | 0.995000 | + | 0.0998774i | \(0.0318451\pi\) | ||||
−0.995000 | + | 0.0998774i | \(0.968155\pi\) | |||||||
\(864\) | −8692.88 | − | 20986.5i | −0.342289 | − | 0.826359i | ||||
\(865\) | 11716.1 | + | 11716.1i | 0.460532 | + | 0.460532i | ||||
\(866\) | −870.810 | −0.0341701 | ||||||||
\(867\) | 13631.1 | − | 2623.03i | 0.533951 | − | 0.102748i | ||||
\(868\) | −4020.57 | −0.157220 | ||||||||
\(869\) | −9106.10 | − | 9106.10i | −0.355470 | − | 0.355470i | ||||
\(870\) | 6512.16 | + | 15721.7i | 0.253773 | + | 0.612663i | ||||
\(871\) | 1687.69i | 0.0656546i | ||||||||
\(872\) | −24182.8 | + | 10016.8i | −0.939143 | + | 0.389006i | ||||
\(873\) | 5135.70 | − | 12398.7i | 0.199103 | − | 0.480677i | ||||
\(874\) | −36465.9 | − | 15104.7i | −1.41130 | − | 0.584581i | ||||
\(875\) | −7352.90 | + | 7352.90i | −0.284084 | + | 0.284084i | ||||
\(876\) | 5521.08 | − | 5521.08i | 0.212945 | − | 0.212945i | ||||
\(877\) | −3535.56 | − | 1464.48i | −0.136131 | − | 0.0563875i | 0.313578 | − | 0.949563i | \(-0.398472\pi\) |
−0.449709 | + | 0.893175i | \(0.648472\pi\) | |||||||
\(878\) | −13218.8 | + | 31912.9i | −0.508100 | + | 1.22666i | ||||
\(879\) | −3690.53 | + | 1528.67i | −0.141614 | + | 0.0586583i | ||||
\(880\) | − | 43070.2i | − | 1.64988i | ||||||
\(881\) | 15695.8 | + | 37893.0i | 0.600232 | + | 1.44909i | 0.873343 | + | 0.487105i | \(0.161947\pi\) |
−0.273112 | + | 0.961982i | \(0.588053\pi\) | |||||||
\(882\) | −13930.5 | − | 13930.5i | −0.531819 | − | 0.531819i | ||||
\(883\) | −7085.32 | −0.270034 | −0.135017 | − | 0.990843i | \(-0.543109\pi\) | ||||
−0.135017 | + | 0.990843i | \(0.543109\pi\) | |||||||
\(884\) | −1011.17 | − | 1239.98i | −0.0384719 | − | 0.0471777i | ||||
\(885\) | −20847.0 | −0.791824 | ||||||||
\(886\) | −24747.5 | − | 24747.5i | −0.938383 | − | 0.938383i | ||||
\(887\) | −6602.86 | − | 15940.7i | −0.249946 | − | 0.603424i | 0.748253 | − | 0.663414i | \(-0.230893\pi\) |
−0.998199 | + | 0.0599902i | \(0.980893\pi\) | |||||||
\(888\) | − | 4134.01i | − | 0.156226i | ||||||
\(889\) | −6434.95 | + | 2665.45i | −0.242769 | + | 0.100558i | ||||
\(890\) | 2516.85 | − | 6076.21i | 0.0947921 | − | 0.228848i | ||||
\(891\) | 8341.57 | + | 3455.19i | 0.313640 | + | 0.129914i | ||||
\(892\) | 1238.72 | − | 1238.72i | 0.0464969 | − | 0.0464969i | ||||
\(893\) | 8965.12 | − | 8965.12i | 0.335953 | − | 0.335953i | ||||
\(894\) | −1092.25 | − | 452.423i | −0.0408615 | − | 0.0169254i | ||||
\(895\) | 332.774 | − | 803.387i | 0.0124284 | − | 0.0300048i | ||||
\(896\) | −9473.95 | + | 3924.24i | −0.353239 | + | 0.146317i | ||||
\(897\) | − | 1769.16i | − | 0.0658534i | ||||||
\(898\) | −11491.5 | − | 27743.0i | −0.427035 | − | 1.03095i | ||||
\(899\) | −19269.8 | − | 19269.8i | −0.714886 | − | 0.714886i | ||||
\(900\) | −3956.26 | −0.146528 | ||||||||
\(901\) | −5062.49 | + | 49805.9i | −0.187188 | + | 1.84159i | ||||
\(902\) | 36003.9 | 1.32905 | ||||||||
\(903\) | −2271.87 | − | 2271.87i | −0.0837244 | − | 0.0837244i | ||||
\(904\) | 5440.87 | + | 13135.4i | 0.200178 | + | 0.483271i | ||||
\(905\) | 33820.7i | 1.24225i | ||||||||
\(906\) | −14322.9 | + | 5932.74i | −0.525217 | + | 0.217552i | ||||
\(907\) | 6929.04 | − | 16728.2i | 0.253666 | − | 0.612404i | −0.744828 | − | 0.667256i | \(-0.767469\pi\) |
0.998494 | + | 0.0548519i | \(0.0174687\pi\) | |||||||
\(908\) | −7519.12 | − | 3114.52i | −0.274813 | − | 0.113831i | ||||
\(909\) | 7355.43 | − | 7355.43i | 0.268387 | − | 0.268387i | ||||
\(910\) | −794.832 | + | 794.832i | −0.0289543 | + | 0.0289543i | ||||
\(911\) | −17702.1 | − | 7332.47i | −0.643796 | − | 0.266669i | 0.0368060 | − | 0.999322i | \(-0.488282\pi\) |
−0.680602 | + | 0.732653i | \(0.738282\pi\) | |||||||
\(912\) | −8365.56 | + | 20196.2i | −0.303740 | + | 0.733294i | ||||
\(913\) | 42384.7 | − | 17556.3i | 1.53639 | − | 0.636395i | ||||
\(914\) | 29208.1i | 1.05702i | ||||||||
\(915\) | 47.0635 | + | 113.621i | 0.00170040 | + | 0.00410514i | ||||
\(916\) | −14608.9 | − | 14608.9i | −0.526956 | − | 0.526956i | ||||
\(917\) | 7601.21 | 0.273734 | ||||||||
\(918\) | 15122.3 | − | 28080.6i | 0.543693 | − | 1.00958i | ||||
\(919\) | −13214.6 | −0.474329 | −0.237165 | − | 0.971469i | \(-0.576218\pi\) | ||||
−0.237165 | + | 0.971469i | \(0.576218\pi\) | |||||||
\(920\) | 9433.82 | + | 9433.82i | 0.338069 | + | 0.338069i | ||||
\(921\) | −4865.09 | − | 11745.4i | −0.174061 | − | 0.420220i | ||||
\(922\) | 30100.5i | 1.07517i | ||||||||
\(923\) | 588.143 | − | 243.617i | 0.0209740 | − | 0.00868770i | ||||
\(924\) | 1945.56 | − | 4697.00i | 0.0692687 | − | 0.167229i | ||||
\(925\) | −5041.60 | − | 2088.30i | −0.179207 | − | 0.0742301i | ||||
\(926\) | 39318.7 | − | 39318.7i | 1.39535 | − | 1.39535i | ||||
\(927\) | 20856.0 | − | 20856.0i | 0.738942 | − | 0.738942i | ||||
\(928\) | 31859.0 | + | 13196.4i | 1.12696 | + | 0.466804i | ||||
\(929\) | −3109.06 | + | 7505.93i | −0.109801 | + | 0.265082i | −0.969223 | − | 0.246184i | \(-0.920823\pi\) |
0.859422 | + | 0.511266i | \(0.170823\pi\) | |||||||
\(930\) | 10997.9 | − | 4555.47i | 0.387779 | − | 0.160623i | ||||
\(931\) | 28650.0i | 1.00856i | ||||||||
\(932\) | 903.313 | + | 2180.79i | 0.0317479 | + | 0.0766461i | ||||
\(933\) | 9423.46 | + | 9423.46i | 0.330665 | + | 0.330665i | ||||
\(934\) | −20794.2 | −0.728489 | ||||||||
\(935\) | 29267.7 | − | 23866.9i | 1.02370 | − | 0.834792i | ||||
\(936\) | 1341.88 | 0.0468596 | ||||||||
\(937\) | 8214.97 | + | 8214.97i | 0.286415 | + | 0.286415i | 0.835661 | − | 0.549246i | \(-0.185085\pi\) |
−0.549246 | + | 0.835661i | \(0.685085\pi\) | |||||||
\(938\) | −2883.40 | − | 6961.14i | −0.100369 | − | 0.242313i | ||||
\(939\) | 17436.4i | 0.605980i | ||||||||
\(940\) | 4482.60 | − | 1856.75i | 0.155539 | − | 0.0644262i | ||||
\(941\) | 4902.44 | − | 11835.5i | 0.169835 | − | 0.410019i | −0.815929 | − | 0.578152i | \(-0.803774\pi\) |
0.985764 | + | 0.168133i | \(0.0537740\pi\) | |||||||
\(942\) | 19381.8 | + | 8028.20i | 0.670375 | + | 0.277678i | ||||
\(943\) | −13717.8 | + | 13717.8i | −0.473715 | + | 0.473715i | ||||
\(944\) | −47832.4 | + | 47832.4i | −1.64917 | + | 1.64917i | ||||
\(945\) | −7179.68 | − | 2973.92i | −0.247148 | − | 0.102372i | ||||
\(946\) | 13728.4 | − | 33143.4i | 0.471829 | − | 1.13910i | ||||
\(947\) | 19835.0 | − | 8215.93i | 0.680624 | − | 0.281924i | −0.0154635 | − | 0.999880i | \(-0.504922\pi\) |
0.696088 | + | 0.717957i | \(0.254922\pi\) | |||||||
\(948\) | 2501.31i | 0.0856951i | ||||||||
\(949\) | 1337.79 | + | 3229.70i | 0.0457601 | + | 0.110475i | ||||
\(950\) | 11730.0 | + | 11730.0i | 0.400600 | + | 0.400600i | ||||
\(951\) | −3353.37 | −0.114343 | ||||||||
\(952\) | −5554.99 | − | 2991.54i | −0.189116 | − | 0.101845i | ||||
\(953\) | 15897.5 | 0.540369 | 0.270184 | − | 0.962809i | \(-0.412915\pi\) | ||||
0.270184 | + | 0.962809i | \(0.412915\pi\) | |||||||
\(954\) | 33612.6 | + | 33612.6i | 1.14072 | + | 1.14072i | ||||
\(955\) | 7764.27 | + | 18744.6i | 0.263085 | + | 0.635142i | ||||
\(956\) | − | 13617.1i | − | 0.460678i | ||||||
\(957\) | 31836.4 | − | 13187.1i | 1.07537 | − | 0.445431i | ||||
\(958\) | −19975.5 | + | 48225.2i | −0.673674 | + | 1.62639i | ||||
\(959\) | 12509.8 | + | 5181.73i | 0.421233 | + | 0.174480i | ||||
\(960\) | 488.863 | − | 488.863i | 0.0164354 | − | 0.0164354i | ||||
\(961\) | 7585.60 | − | 7585.60i | 0.254627 | − | 0.254627i | ||||
\(962\) | −1936.01 | − | 801.922i | −0.0648852 | − | 0.0268763i | ||||
\(963\) | 1788.67 | − | 4318.22i | 0.0598535 | − | 0.144499i | ||||
\(964\) | 3506.22 | − | 1452.33i | 0.117145 | − | 0.0485231i | ||||
\(965\) | − | 12176.4i | − | 0.406189i | ||||||
\(966\) | 3022.59 | + | 7297.17i | 0.100673 | + | 0.243046i | ||||
\(967\) | −23469.7 | − | 23469.7i | −0.780492 | − | 0.780492i | 0.199421 | − | 0.979914i | \(-0.436094\pi\) |
−0.979914 | + | 0.199421i | \(0.936094\pi\) | |||||||
\(968\) | −32661.6 | −1.08449 | ||||||||
\(969\) | −18359.7 | + | 5506.83i | −0.608668 | + | 0.182564i | ||||
\(970\) | −21534.2 | −0.712806 | ||||||||
\(971\) | −22510.4 | − | 22510.4i | −0.743968 | − | 0.743968i | 0.229371 | − | 0.973339i | \(-0.426333\pi\) |
−0.973339 | + | 0.229371i | \(0.926333\pi\) | |||||||
\(972\) | −6377.77 | − | 15397.3i | −0.210460 | − | 0.508096i | ||||
\(973\) | − | 7118.94i | − | 0.234556i | ||||||
\(974\) | −26587.0 | + | 11012.7i | −0.874644 | + | 0.362289i | ||||
\(975\) | −284.542 | + | 686.944i | −0.00934628 | + | 0.0225639i | ||||
\(976\) | 368.683 | + | 152.714i | 0.0120915 | + | 0.00500845i | ||||
\(977\) | −10216.1 | + | 10216.1i | −0.334536 | + | 0.334536i | −0.854306 | − | 0.519770i | \(-0.826018\pi\) |
0.519770 | + | 0.854306i | \(0.326018\pi\) | |||||||
\(978\) | 3099.42 | − | 3099.42i | 0.101338 | − | 0.101338i | ||||
\(979\) | −12304.3 | − | 5096.60i | −0.401682 | − | 0.166382i | ||||
\(980\) | −4195.73 | + | 10129.4i | −0.136763 | + | 0.330175i | ||||
\(981\) | −35022.9 | + | 14507.0i | −1.13985 | + | 0.472143i | ||||
\(982\) | − | 9223.90i | − | 0.299742i | ||||||
\(983\) | 2996.76 | + | 7234.81i | 0.0972347 | + | 0.234745i | 0.965011 | − | 0.262210i | \(-0.0844513\pi\) |
−0.867776 | + | 0.496955i | \(0.834451\pi\) | |||||||
\(984\) | 4367.61 | + | 4367.61i | 0.141498 | + | 0.141498i | ||||
\(985\) | 17646.4 | 0.570824 | ||||||||
\(986\) | 13910.0 | + | 46375.7i | 0.449274 | + | 1.49787i | ||||
\(987\) | −2537.10 | −0.0818206 | ||||||||
\(988\) | 1562.26 | + | 1562.26i | 0.0503057 | + | 0.0503057i | ||||
\(989\) | 7397.27 | + | 17858.6i | 0.237836 | + | 0.574186i | ||||
\(990\) | − | 35859.0i | − | 1.15119i | ||||||
\(991\) | 13532.7 | − | 5605.45i | 0.433786 | − | 0.179680i | −0.155095 | − | 0.987899i | \(-0.549569\pi\) |
0.588881 | + | 0.808219i | \(0.299569\pi\) | |||||||
\(992\) | 9231.34 | − | 22286.4i | 0.295459 | − | 0.713301i | ||||
\(993\) | −8013.93 | − | 3319.48i | −0.256107 | − | 0.106083i | ||||
\(994\) | −2009.67 | + | 2009.67i | −0.0641277 | + | 0.0641277i | ||||
\(995\) | −25545.7 | + | 25545.7i | −0.813923 | + | 0.813923i | ||||
\(996\) | −8232.47 | − | 3410.00i | −0.261903 | − | 0.108484i | ||||
\(997\) | 18818.3 | − | 45431.4i | 0.597775 | − | 1.44316i | −0.278068 | − | 0.960561i | \(-0.589694\pi\) |
0.875843 | − | 0.482596i | \(-0.160306\pi\) | |||||||
\(998\) | 41269.8 | − | 17094.5i | 1.30899 | − | 0.542201i | ||||
\(999\) | − | 14487.5i | − | 0.458822i |
(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 | 17.4.d.a.15.3 | yes | 12 | |
3.2 | odd | 2 | 153.4.l.a.100.1 | 12 | |||
17.3 | odd | 16 | 289.4.b.e.288.9 | 12 | |||
17.5 | odd | 16 | 289.4.a.g.1.4 | 12 | |||
17.8 | even | 8 | inner | 17.4.d.a.8.3 | ✓ | 12 | |
17.12 | odd | 16 | 289.4.a.g.1.3 | 12 | |||
17.14 | odd | 16 | 289.4.b.e.288.10 | 12 | |||
51.8 | odd | 8 | 153.4.l.a.127.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.8.3 | ✓ | 12 | 17.8 | even | 8 | inner | |
17.4.d.a.15.3 | yes | 12 | 1.1 | even | 1 | trivial | |
153.4.l.a.100.1 | 12 | 3.2 | odd | 2 | |||
153.4.l.a.127.1 | 12 | 51.8 | odd | 8 | |||
289.4.a.g.1.3 | 12 | 17.12 | odd | 16 | |||
289.4.a.g.1.4 | 12 | 17.5 | odd | 16 | |||
289.4.b.e.288.9 | 12 | 17.3 | odd | 16 | |||
289.4.b.e.288.10 | 12 | 17.14 | odd | 16 |