Properties

Label 76.7.j.a.21.2
Level $76$
Weight $7$
Character 76.21
Analytic conductor $17.484$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,7,Mod(13,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.13");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), 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: \(17.4841103551\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(10\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 21.2
Character \(\chi\) \(=\) 76.21
Dual form 76.7.j.a.29.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-18.1708 + 21.6552i) q^{3} +(40.6936 - 14.8113i) q^{5} +(179.977 + 311.730i) q^{7} +(-12.1770 - 69.0593i) q^{9} +O(q^{10})\) \(q+(-18.1708 + 21.6552i) q^{3} +(40.6936 - 14.8113i) q^{5} +(179.977 + 311.730i) q^{7} +(-12.1770 - 69.0593i) q^{9} +(451.055 - 781.249i) q^{11} +(880.095 + 1048.86i) q^{13} +(-418.697 + 1150.36i) q^{15} +(-1025.67 + 5816.84i) q^{17} +(-5697.06 - 3819.60i) q^{19} +(-10020.9 - 1766.96i) q^{21} +(-8881.65 - 3232.66i) q^{23} +(-10532.8 + 8838.11i) q^{25} +(-16130.3 - 9312.81i) q^{27} +(9151.84 - 1613.72i) q^{29} +(-43451.8 + 25086.9i) q^{31} +(8722.04 + 23963.6i) q^{33} +(11941.1 + 10019.7i) q^{35} +37981.8i q^{37} -38705.2 q^{39} +(30507.4 - 36357.3i) q^{41} +(691.795 - 251.793i) q^{43} +(-1518.38 - 2629.91i) q^{45} +(10700.2 + 60683.8i) q^{47} +(-5959.27 + 10321.8i) q^{49} +(-107327. - 127908. i) q^{51} +(-22191.6 + 60971.0i) q^{53} +(6783.75 - 38472.6i) q^{55} +(186234. - 53965.5i) q^{57} +(-103188. - 18194.9i) q^{59} +(-42024.7 - 15295.7i) q^{61} +(19336.3 - 16225.0i) q^{63} +(51349.2 + 29646.5i) q^{65} +(497157. - 87662.2i) q^{67} +(231391. - 133593. i) q^{69} +(-75111.0 - 206366. i) q^{71} +(75180.8 + 63084.2i) q^{73} -388686. i q^{75} +324719. q^{77} +(-167089. + 199129. i) q^{79} +(542808. - 197566. i) q^{81} +(471277. + 816276. i) q^{83} +(44416.7 + 251900. i) q^{85} +(-131351. + 227507. i) q^{87} +(-127638. - 152113. i) q^{89} +(-168563. + 463123. i) q^{91} +(246295. - 1.39681e6i) q^{93} +(-288407. - 71052.6i) q^{95} +(-412609. - 72754.2i) q^{97} +(-59445.0 - 21636.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −18.1708 + 21.6552i −0.672994 + 0.802043i −0.989188 0.146652i \(-0.953150\pi\)
0.316195 + 0.948694i \(0.397595\pi\)
\(4\) 0 0
\(5\) 40.6936 14.8113i 0.325549 0.118490i −0.174075 0.984732i \(-0.555694\pi\)
0.499624 + 0.866242i \(0.333471\pi\)
\(6\) 0 0
\(7\) 179.977 + 311.730i 0.524716 + 0.908834i 0.999586 + 0.0287782i \(0.00916166\pi\)
−0.474870 + 0.880056i \(0.657505\pi\)
\(8\) 0 0
\(9\) −12.1770 69.0593i −0.0167037 0.0947315i
\(10\) 0 0
\(11\) 451.055 781.249i 0.338884 0.586964i −0.645339 0.763896i \(-0.723284\pi\)
0.984223 + 0.176932i \(0.0566173\pi\)
\(12\) 0 0
\(13\) 880.095 + 1048.86i 0.400590 + 0.477404i 0.928200 0.372083i \(-0.121356\pi\)
−0.527610 + 0.849487i \(0.676912\pi\)
\(14\) 0 0
\(15\) −418.697 + 1150.36i −0.124058 + 0.340847i
\(16\) 0 0
\(17\) −1025.67 + 5816.84i −0.208766 + 1.18397i 0.682637 + 0.730758i \(0.260833\pi\)
−0.891403 + 0.453212i \(0.850278\pi\)
\(18\) 0 0
\(19\) −5697.06 3819.60i −0.830597 0.556874i
\(20\) 0 0
\(21\) −10020.9 1766.96i −1.08205 0.190795i
\(22\) 0 0
\(23\) −8881.65 3232.66i −0.729979 0.265691i −0.0498230 0.998758i \(-0.515866\pi\)
−0.680156 + 0.733067i \(0.738088\pi\)
\(24\) 0 0
\(25\) −10532.8 + 8838.11i −0.674102 + 0.565639i
\(26\) 0 0
\(27\) −16130.3 9312.81i −0.819502 0.473140i
\(28\) 0 0
\(29\) 9151.84 1613.72i 0.375245 0.0661657i 0.0171546 0.999853i \(-0.494539\pi\)
0.358090 + 0.933687i \(0.383428\pi\)
\(30\) 0 0
\(31\) −43451.8 + 25086.9i −1.45856 + 0.842097i −0.998940 0.0460208i \(-0.985346\pi\)
−0.459615 + 0.888118i \(0.652013\pi\)
\(32\) 0 0
\(33\) 8722.04 + 23963.6i 0.242704 + 0.666823i
\(34\) 0 0
\(35\) 11941.1 + 10019.7i 0.278509 + 0.233696i
\(36\) 0 0
\(37\) 37981.8i 0.749844i 0.927056 + 0.374922i \(0.122330\pi\)
−0.927056 + 0.374922i \(0.877670\pi\)
\(38\) 0 0
\(39\) −38705.2 −0.652493
\(40\) 0 0
\(41\) 30507.4 36357.3i 0.442643 0.527521i −0.497883 0.867244i \(-0.665889\pi\)
0.940525 + 0.339723i \(0.110333\pi\)
\(42\) 0 0
\(43\) 691.795 251.793i 0.00870106 0.00316693i −0.337666 0.941266i \(-0.609637\pi\)
0.346367 + 0.938099i \(0.387415\pi\)
\(44\) 0 0
\(45\) −1518.38 2629.91i −0.0166626 0.0288605i
\(46\) 0 0
\(47\) 10700.2 + 60683.8i 0.103062 + 0.584493i 0.991977 + 0.126420i \(0.0403488\pi\)
−0.888915 + 0.458072i \(0.848540\pi\)
\(48\) 0 0
\(49\) −5959.27 + 10321.8i −0.0506529 + 0.0877334i
\(50\) 0 0
\(51\) −107327. 127908.i −0.809096 0.964243i
\(52\) 0 0
\(53\) −22191.6 + 60971.0i −0.149060 + 0.409539i −0.991641 0.129031i \(-0.958813\pi\)
0.842580 + 0.538571i \(0.181035\pi\)
\(54\) 0 0
\(55\) 6783.75 38472.6i 0.0407739 0.231240i
\(56\) 0 0
\(57\) 186234. 53965.5i 1.00562 0.291401i
\(58\) 0 0
\(59\) −103188. 18194.9i −0.502429 0.0885919i −0.0833113 0.996524i \(-0.526550\pi\)
−0.419118 + 0.907932i \(0.637661\pi\)
\(60\) 0 0
\(61\) −42024.7 15295.7i −0.185146 0.0673877i 0.247783 0.968815i \(-0.420298\pi\)
−0.432930 + 0.901428i \(0.642520\pi\)
\(62\) 0 0
\(63\) 19336.3 16225.0i 0.0773305 0.0648880i
\(64\) 0 0
\(65\) 51349.2 + 29646.5i 0.186979 + 0.107952i
\(66\) 0 0
\(67\) 497157. 87662.2i 1.65299 0.291466i 0.732071 0.681229i \(-0.238554\pi\)
0.920915 + 0.389763i \(0.127443\pi\)
\(68\) 0 0
\(69\) 231391. 133593.i 0.704366 0.406666i
\(70\) 0 0
\(71\) −75111.0 206366.i −0.209859 0.576584i 0.789447 0.613818i \(-0.210367\pi\)
−0.999307 + 0.0372346i \(0.988145\pi\)
\(72\) 0 0
\(73\) 75180.8 + 63084.2i 0.193258 + 0.162163i 0.734282 0.678844i \(-0.237519\pi\)
−0.541024 + 0.841007i \(0.681963\pi\)
\(74\) 0 0
\(75\) 388686.i 0.921330i
\(76\) 0 0
\(77\) 324719. 0.711271
\(78\) 0 0
\(79\) −167089. + 199129.i −0.338897 + 0.403881i −0.908396 0.418110i \(-0.862693\pi\)
0.569500 + 0.821992i \(0.307137\pi\)
\(80\) 0 0
\(81\) 542808. 197566.i 1.02139 0.371755i
\(82\) 0 0
\(83\) 471277. + 816276.i 0.824218 + 1.42759i 0.902515 + 0.430658i \(0.141718\pi\)
−0.0782971 + 0.996930i \(0.524948\pi\)
\(84\) 0 0
\(85\) 44416.7 + 251900.i 0.0723252 + 0.410177i
\(86\) 0 0
\(87\) −131351. + 227507.i −0.199469 + 0.345491i
\(88\) 0 0
\(89\) −127638. 152113.i −0.181055 0.215773i 0.667882 0.744267i \(-0.267201\pi\)
−0.848937 + 0.528494i \(0.822757\pi\)
\(90\) 0 0
\(91\) −168563. + 463123.i −0.223685 + 0.614571i
\(92\) 0 0
\(93\) 246295. 1.39681e6i 0.306201 1.73655i
\(94\) 0 0
\(95\) −288407. 71052.6i −0.336384 0.0828723i
\(96\) 0 0
\(97\) −412609. 72754.2i −0.452089 0.0797155i −0.0570325 0.998372i \(-0.518164\pi\)
−0.395057 + 0.918657i \(0.629275\pi\)
\(98\) 0 0
\(99\) −59445.0 21636.2i −0.0612646 0.0222985i
\(100\) 0 0
\(101\) −38059.7 + 31935.9i −0.0369404 + 0.0309967i −0.661071 0.750323i \(-0.729898\pi\)
0.624131 + 0.781320i \(0.285453\pi\)
\(102\) 0 0
\(103\) −861685. 497494.i −0.788563 0.455277i 0.0508931 0.998704i \(-0.483793\pi\)
−0.839457 + 0.543427i \(0.817127\pi\)
\(104\) 0 0
\(105\) −433958. + 76518.4i −0.374869 + 0.0660995i
\(106\) 0 0
\(107\) −1.51337e6 + 873744.i −1.23536 + 0.713236i −0.968142 0.250401i \(-0.919438\pi\)
−0.267218 + 0.963636i \(0.586104\pi\)
\(108\) 0 0
\(109\) 233335. + 641082.i 0.180177 + 0.495033i 0.996597 0.0824256i \(-0.0262667\pi\)
−0.816420 + 0.577459i \(0.804044\pi\)
\(110\) 0 0
\(111\) −822503. 690162.i −0.601407 0.504640i
\(112\) 0 0
\(113\) 353386.i 0.244914i 0.992474 + 0.122457i \(0.0390773\pi\)
−0.992474 + 0.122457i \(0.960923\pi\)
\(114\) 0 0
\(115\) −409306. −0.269126
\(116\) 0 0
\(117\) 61716.3 73550.7i 0.0385339 0.0459229i
\(118\) 0 0
\(119\) −1.99788e6 + 727170.i −1.18557 + 0.431514i
\(120\) 0 0
\(121\) 478880. + 829445.i 0.270315 + 0.468200i
\(122\) 0 0
\(123\) 232978. + 1.32128e6i 0.125199 + 0.710036i
\(124\) 0 0
\(125\) −636038. + 1.10165e6i −0.325652 + 0.564045i
\(126\) 0 0
\(127\) 64878.6 + 77319.4i 0.0316731 + 0.0377465i 0.781648 0.623719i \(-0.214379\pi\)
−0.749975 + 0.661466i \(0.769935\pi\)
\(128\) 0 0
\(129\) −7117.88 + 19556.2i −0.00331575 + 0.00910994i
\(130\) 0 0
\(131\) 108653. 616200.i 0.0483311 0.274099i −0.951059 0.309008i \(-0.900003\pi\)
0.999391 + 0.0349088i \(0.0111141\pi\)
\(132\) 0 0
\(133\) 165341. 2.46339e6i 0.0702790 1.04708i
\(134\) 0 0
\(135\) −794333. 140062.i −0.322850 0.0569272i
\(136\) 0 0
\(137\) 4.30476e6 + 1.56681e6i 1.67412 + 0.609331i 0.992486 0.122359i \(-0.0390460\pi\)
0.681637 + 0.731690i \(0.261268\pi\)
\(138\) 0 0
\(139\) −1.41797e6 + 1.18982e6i −0.527985 + 0.443032i −0.867405 0.497603i \(-0.834214\pi\)
0.339420 + 0.940635i \(0.389769\pi\)
\(140\) 0 0
\(141\) −1.50855e6 870961.i −0.538148 0.310700i
\(142\) 0 0
\(143\) 1.21639e6 214482.i 0.415972 0.0733472i
\(144\) 0 0
\(145\) 348520. 201218.i 0.114320 0.0660030i
\(146\) 0 0
\(147\) −115234. 316604.i −0.0362769 0.0996699i
\(148\) 0 0
\(149\) 4.84421e6 + 4.06477e6i 1.46441 + 1.22879i 0.921139 + 0.389234i \(0.127260\pi\)
0.543275 + 0.839555i \(0.317184\pi\)
\(150\) 0 0
\(151\) 5.70613e6i 1.65734i −0.559740 0.828668i \(-0.689099\pi\)
0.559740 0.828668i \(-0.310901\pi\)
\(152\) 0 0
\(153\) 414196. 0.115646
\(154\) 0 0
\(155\) −1.39664e6 + 1.66445e6i −0.375051 + 0.446968i
\(156\) 0 0
\(157\) −3.09392e6 + 1.12610e6i −0.799485 + 0.290989i −0.709273 0.704934i \(-0.750977\pi\)
−0.0902122 + 0.995923i \(0.528755\pi\)
\(158\) 0 0
\(159\) −917096. 1.58846e6i −0.228151 0.395170i
\(160\) 0 0
\(161\) −590781. 3.35048e6i −0.141563 0.802842i
\(162\) 0 0
\(163\) −1.41965e6 + 2.45890e6i −0.327807 + 0.567778i −0.982076 0.188483i \(-0.939643\pi\)
0.654270 + 0.756261i \(0.272976\pi\)
\(164\) 0 0
\(165\) 709863. + 845981.i 0.158024 + 0.188325i
\(166\) 0 0
\(167\) 1.48824e6 4.08889e6i 0.319538 0.877923i −0.671095 0.741371i \(-0.734176\pi\)
0.990633 0.136552i \(-0.0436020\pi\)
\(168\) 0 0
\(169\) 512634. 2.90729e6i 0.106206 0.602322i
\(170\) 0 0
\(171\) −194405. + 439946.i −0.0388795 + 0.0879855i
\(172\) 0 0
\(173\) 9.43626e6 + 1.66387e6i 1.82247 + 0.321351i 0.977093 0.212812i \(-0.0682622\pi\)
0.845381 + 0.534163i \(0.179373\pi\)
\(174\) 0 0
\(175\) −4.65078e6 1.69275e6i −0.867784 0.315848i
\(176\) 0 0
\(177\) 2.26903e6 1.90394e6i 0.409186 0.343348i
\(178\) 0 0
\(179\) −2.47613e6 1.42960e6i −0.431733 0.249261i 0.268352 0.963321i \(-0.413521\pi\)
−0.700084 + 0.714060i \(0.746854\pi\)
\(180\) 0 0
\(181\) 5.46878e6 964293.i 0.922262 0.162620i 0.307696 0.951485i \(-0.400442\pi\)
0.614566 + 0.788865i \(0.289331\pi\)
\(182\) 0 0
\(183\) 1.09485e6 632115.i 0.178650 0.103144i
\(184\) 0 0
\(185\) 562559. + 1.54562e6i 0.0888491 + 0.244111i
\(186\) 0 0
\(187\) 4.08177e6 + 3.42501e6i 0.624200 + 0.523766i
\(188\) 0 0
\(189\) 6.70438e6i 0.993055i
\(190\) 0 0
\(191\) 5.02912e6 0.721758 0.360879 0.932613i \(-0.382477\pi\)
0.360879 + 0.932613i \(0.382477\pi\)
\(192\) 0 0
\(193\) 5.35590e6 6.38291e6i 0.745007 0.887865i −0.251794 0.967781i \(-0.581021\pi\)
0.996802 + 0.0799155i \(0.0254650\pi\)
\(194\) 0 0
\(195\) −1.57506e6 + 573273.i −0.212418 + 0.0773139i
\(196\) 0 0
\(197\) 1.34460e6 + 2.32891e6i 0.175871 + 0.304617i 0.940462 0.339898i \(-0.110393\pi\)
−0.764591 + 0.644515i \(0.777059\pi\)
\(198\) 0 0
\(199\) 879101. + 4.98563e6i 0.111553 + 0.632646i 0.988399 + 0.151876i \(0.0485316\pi\)
−0.876847 + 0.480770i \(0.840357\pi\)
\(200\) 0 0
\(201\) −7.13542e6 + 1.23589e7i −0.878681 + 1.52192i
\(202\) 0 0
\(203\) 2.15017e6 + 2.56247e6i 0.257030 + 0.306317i
\(204\) 0 0
\(205\) 702958. 1.93136e6i 0.0815958 0.224183i
\(206\) 0 0
\(207\) −115093. + 652724.i −0.0129759 + 0.0735900i
\(208\) 0 0
\(209\) −5.55375e6 + 2.72798e6i −0.608341 + 0.298815i
\(210\) 0 0
\(211\) 1.36467e7 + 2.40628e6i 1.45272 + 0.256153i 0.843619 0.536943i \(-0.180421\pi\)
0.609097 + 0.793096i \(0.291532\pi\)
\(212\) 0 0
\(213\) 5.83371e6 + 2.12330e6i 0.603679 + 0.219721i
\(214\) 0 0
\(215\) 24422.3 20492.7i 0.00245737 0.00206198i
\(216\) 0 0
\(217\) −1.56407e7 9.03016e6i −1.53065 0.883723i
\(218\) 0 0
\(219\) −2.73220e6 + 481760.i −0.260123 + 0.0458668i
\(220\) 0 0
\(221\) −7.00372e6 + 4.04360e6i −0.648861 + 0.374620i
\(222\) 0 0
\(223\) −5.23237e6 1.43758e7i −0.471829 1.29634i −0.916281 0.400536i \(-0.868824\pi\)
0.444453 0.895802i \(-0.353398\pi\)
\(224\) 0 0
\(225\) 738612. + 619769.i 0.0648438 + 0.0544104i
\(226\) 0 0
\(227\) 4.56799e6i 0.390524i −0.980751 0.195262i \(-0.937444\pi\)
0.980751 0.195262i \(-0.0625557\pi\)
\(228\) 0 0
\(229\) −1.88839e7 −1.57248 −0.786240 0.617922i \(-0.787975\pi\)
−0.786240 + 0.617922i \(0.787975\pi\)
\(230\) 0 0
\(231\) −5.90041e6 + 7.03183e6i −0.478681 + 0.570469i
\(232\) 0 0
\(233\) −1.15903e7 + 4.21852e6i −0.916276 + 0.333497i −0.756756 0.653697i \(-0.773217\pi\)
−0.159520 + 0.987195i \(0.550995\pi\)
\(234\) 0 0
\(235\) 1.33423e6 + 2.31096e6i 0.102808 + 0.178069i
\(236\) 0 0
\(237\) −1.27602e6 7.23669e6i −0.0958548 0.543619i
\(238\) 0 0
\(239\) −7.25128e6 + 1.25596e7i −0.531154 + 0.919987i 0.468184 + 0.883631i \(0.344908\pi\)
−0.999339 + 0.0363558i \(0.988425\pi\)
\(240\) 0 0
\(241\) 3.82187e6 + 4.55473e6i 0.273039 + 0.325395i 0.885087 0.465425i \(-0.154099\pi\)
−0.612048 + 0.790821i \(0.709654\pi\)
\(242\) 0 0
\(243\) −940979. + 2.58532e6i −0.0655784 + 0.180175i
\(244\) 0 0
\(245\) −89625.9 + 508294.i −0.00609446 + 0.0345634i
\(246\) 0 0
\(247\) −1.00775e6 9.33701e6i −0.0668745 0.619608i
\(248\) 0 0
\(249\) −2.62401e7 4.62683e6i −1.69968 0.299699i
\(250\) 0 0
\(251\) 1.97392e7 + 7.18448e6i 1.24827 + 0.454333i 0.879817 0.475313i \(-0.157665\pi\)
0.368453 + 0.929646i \(0.379887\pi\)
\(252\) 0 0
\(253\) −6.53162e6 + 5.48068e6i −0.403329 + 0.338433i
\(254\) 0 0
\(255\) −6.26202e6 3.61538e6i −0.377654 0.218038i
\(256\) 0 0
\(257\) 6.94771e6 1.22507e6i 0.409300 0.0721707i 0.0347928 0.999395i \(-0.488923\pi\)
0.374508 + 0.927224i \(0.377812\pi\)
\(258\) 0 0
\(259\) −1.18401e7 + 6.83587e6i −0.681484 + 0.393455i
\(260\) 0 0
\(261\) −222884. 612369.i −0.0125360 0.0344423i
\(262\) 0 0
\(263\) 1.95721e7 + 1.64230e7i 1.07590 + 0.902786i 0.995574 0.0939830i \(-0.0299599\pi\)
0.0803244 + 0.996769i \(0.474404\pi\)
\(264\) 0 0
\(265\) 2.80982e6i 0.150987i
\(266\) 0 0
\(267\) 5.61332e6 0.294908
\(268\) 0 0
\(269\) −7.37005e6 + 8.78329e6i −0.378629 + 0.451232i −0.921381 0.388661i \(-0.872938\pi\)
0.542752 + 0.839893i \(0.317382\pi\)
\(270\) 0 0
\(271\) 1.51840e7 5.52651e6i 0.762917 0.277679i 0.0688861 0.997625i \(-0.478055\pi\)
0.694030 + 0.719946i \(0.255833\pi\)
\(272\) 0 0
\(273\) −6.96606e6 1.20656e7i −0.342373 0.593008i
\(274\) 0 0
\(275\) 2.15388e6 + 1.22152e7i 0.103567 + 0.587360i
\(276\) 0 0
\(277\) 1.44052e6 2.49506e6i 0.0677767 0.117393i −0.830146 0.557547i \(-0.811743\pi\)
0.897922 + 0.440154i \(0.145076\pi\)
\(278\) 0 0
\(279\) 2.26160e6 + 2.69527e6i 0.104136 + 0.124105i
\(280\) 0 0
\(281\) 2.24951e6 6.18047e6i 0.101384 0.278549i −0.878622 0.477517i \(-0.841537\pi\)
0.980006 + 0.198968i \(0.0637590\pi\)
\(282\) 0 0
\(283\) 5.98103e6 3.39201e7i 0.263886 1.49657i −0.508302 0.861179i \(-0.669727\pi\)
0.772188 0.635394i \(-0.219162\pi\)
\(284\) 0 0
\(285\) 6.77925e6 4.95442e6i 0.292851 0.214022i
\(286\) 0 0
\(287\) 1.68243e7 + 2.96658e6i 0.711690 + 0.125490i
\(288\) 0 0
\(289\) −1.01018e7 3.67675e6i −0.418508 0.152325i
\(290\) 0 0
\(291\) 9.07296e6 7.61312e6i 0.368188 0.308947i
\(292\) 0 0
\(293\) 3.74355e7 + 2.16134e7i 1.48827 + 0.859252i 0.999910 0.0133914i \(-0.00426275\pi\)
0.488358 + 0.872643i \(0.337596\pi\)
\(294\) 0 0
\(295\) −4.46860e6 + 787935.i −0.174063 + 0.0306919i
\(296\) 0 0
\(297\) −1.45512e7 + 8.40117e6i −0.555432 + 0.320679i
\(298\) 0 0
\(299\) −4.42611e6 1.21606e7i −0.165580 0.454928i
\(300\) 0 0
\(301\) 202999. + 170336.i 0.00744379 + 0.00624608i
\(302\) 0 0
\(303\) 1.40449e6i 0.0504884i
\(304\) 0 0
\(305\) −1.93669e6 −0.0682589
\(306\) 0 0
\(307\) 178771. 213050.i 0.00617847 0.00736321i −0.762946 0.646462i \(-0.776248\pi\)
0.769125 + 0.639099i \(0.220692\pi\)
\(308\) 0 0
\(309\) 2.64308e7 9.62003e6i 0.895850 0.326063i
\(310\) 0 0
\(311\) 1.05577e7 + 1.82864e7i 0.350983 + 0.607920i 0.986422 0.164231i \(-0.0525142\pi\)
−0.635439 + 0.772151i \(0.719181\pi\)
\(312\) 0 0
\(313\) 1.65039e6 + 9.35984e6i 0.0538213 + 0.305236i 0.999821 0.0189324i \(-0.00602672\pi\)
−0.945999 + 0.324168i \(0.894916\pi\)
\(314\) 0 0
\(315\) 546549. 946651.i 0.0174863 0.0302871i
\(316\) 0 0
\(317\) 1.11490e7 + 1.32868e7i 0.349991 + 0.417103i 0.912105 0.409957i \(-0.134456\pi\)
−0.562114 + 0.827060i \(0.690012\pi\)
\(318\) 0 0
\(319\) 2.86726e6 7.87774e6i 0.0883274 0.242678i
\(320\) 0 0
\(321\) 8.57811e6 4.86489e7i 0.259344 1.47081i
\(322\) 0 0
\(323\) 2.80613e7 2.92213e7i 0.832722 0.867145i
\(324\) 0 0
\(325\) −1.85398e7 3.26907e6i −0.540077 0.0952301i
\(326\) 0 0
\(327\) −1.81226e7 6.59609e6i −0.518296 0.188644i
\(328\) 0 0
\(329\) −1.69912e7 + 1.42573e7i −0.477129 + 0.400359i
\(330\) 0 0
\(331\) −3.84726e7 2.22121e7i −1.06088 0.612500i −0.135206 0.990818i \(-0.543170\pi\)
−0.925676 + 0.378317i \(0.876503\pi\)
\(332\) 0 0
\(333\) 2.62300e6 462505.i 0.0710338 0.0125252i
\(334\) 0 0
\(335\) 1.89327e7 1.09308e7i 0.503592 0.290749i
\(336\) 0 0
\(337\) −1.16766e7 3.20812e7i −0.305089 0.838226i −0.993595 0.112996i \(-0.963955\pi\)
0.688506 0.725231i \(-0.258267\pi\)
\(338\) 0 0
\(339\) −7.65262e6 6.42131e6i −0.196431 0.164826i
\(340\) 0 0
\(341\) 4.52623e7i 1.14149i
\(342\) 0 0
\(343\) 3.80582e7 0.943118
\(344\) 0 0
\(345\) 7.43744e6 8.86359e6i 0.181120 0.215850i
\(346\) 0 0
\(347\) 7.27757e7 2.64882e7i 1.74180 0.633963i 0.742444 0.669908i \(-0.233666\pi\)
0.999354 + 0.0359455i \(0.0114443\pi\)
\(348\) 0 0
\(349\) 1.09690e7 + 1.89989e7i 0.258043 + 0.446944i 0.965718 0.259595i \(-0.0835891\pi\)
−0.707675 + 0.706538i \(0.750256\pi\)
\(350\) 0 0
\(351\) −4.42836e6 2.51145e7i −0.102405 0.580768i
\(352\) 0 0
\(353\) −3.78160e7 + 6.54992e7i −0.859708 + 1.48906i 0.0124990 + 0.999922i \(0.496021\pi\)
−0.872207 + 0.489136i \(0.837312\pi\)
\(354\) 0 0
\(355\) −6.11308e6 7.28528e6i −0.136639 0.162840i
\(356\) 0 0
\(357\) 2.05562e7 5.64777e7i 0.451792 1.24129i
\(358\) 0 0
\(359\) −1.35791e7 + 7.70110e7i −0.293487 + 1.66445i 0.379804 + 0.925067i \(0.375992\pi\)
−0.673290 + 0.739378i \(0.735120\pi\)
\(360\) 0 0
\(361\) 1.78672e7 + 4.35210e7i 0.379782 + 0.925076i
\(362\) 0 0
\(363\) −2.66634e7 4.70148e6i −0.557437 0.0982911i
\(364\) 0 0
\(365\) 3.99374e6 + 1.45360e6i 0.0821298 + 0.0298928i
\(366\) 0 0
\(367\) −4.41039e7 + 3.70076e7i −0.892234 + 0.748673i −0.968657 0.248402i \(-0.920094\pi\)
0.0764231 + 0.997075i \(0.475650\pi\)
\(368\) 0 0
\(369\) −2.88229e6 1.66409e6i −0.0573666 0.0331206i
\(370\) 0 0
\(371\) −2.30005e7 + 4.05561e6i −0.450417 + 0.0794207i
\(372\) 0 0
\(373\) 8.82867e6 5.09723e6i 0.170125 0.0982218i −0.412520 0.910949i \(-0.635351\pi\)
0.582645 + 0.812727i \(0.302018\pi\)
\(374\) 0 0
\(375\) −1.22991e7 3.37914e7i −0.233227 0.640785i
\(376\) 0 0
\(377\) 9.74705e6 + 8.17874e6i 0.181907 + 0.152638i
\(378\) 0 0
\(379\) 5.59727e7i 1.02815i 0.857744 + 0.514077i \(0.171866\pi\)
−0.857744 + 0.514077i \(0.828134\pi\)
\(380\) 0 0
\(381\) −2.85326e6 −0.0515901
\(382\) 0 0
\(383\) −1.29810e7 + 1.54701e7i −0.231053 + 0.275358i −0.869097 0.494642i \(-0.835299\pi\)
0.638044 + 0.770000i \(0.279744\pi\)
\(384\) 0 0
\(385\) 1.32140e7 4.80949e6i 0.231553 0.0842786i
\(386\) 0 0
\(387\) −25812.6 44708.8i −0.000445348 0.000771365i
\(388\) 0 0
\(389\) −4.62894e6 2.62520e7i −0.0786381 0.445979i −0.998549 0.0538514i \(-0.982850\pi\)
0.919911 0.392128i \(-0.128261\pi\)
\(390\) 0 0
\(391\) 2.79135e7 4.83476e7i 0.466964 0.808806i
\(392\) 0 0
\(393\) 1.13696e7 + 1.35498e7i 0.187313 + 0.223231i
\(394\) 0 0
\(395\) −3.85011e6 + 1.05781e7i −0.0624715 + 0.171639i
\(396\) 0 0
\(397\) −2.16627e6 + 1.22855e7i −0.0346212 + 0.196346i −0.997213 0.0746100i \(-0.976229\pi\)
0.962592 + 0.270956i \(0.0873399\pi\)
\(398\) 0 0
\(399\) 5.03407e7 + 4.83423e7i 0.792502 + 0.761042i
\(400\) 0 0
\(401\) −1.24567e8 2.19646e7i −1.93184 0.340635i −0.932072 0.362272i \(-0.882001\pi\)
−0.999766 + 0.0216372i \(0.993112\pi\)
\(402\) 0 0
\(403\) −6.45543e7 2.34959e7i −0.986303 0.358985i
\(404\) 0 0
\(405\) 1.91626e7 1.60794e7i 0.288463 0.242049i
\(406\) 0 0
\(407\) 2.96733e7 + 1.71319e7i 0.440132 + 0.254110i
\(408\) 0 0
\(409\) −1.23587e8 + 2.17918e7i −1.80636 + 0.318510i −0.972401 0.233315i \(-0.925043\pi\)
−0.833960 + 0.551825i \(0.813932\pi\)
\(410\) 0 0
\(411\) −1.12150e8 + 6.47501e7i −1.61538 + 0.932642i
\(412\) 0 0
\(413\) −1.28997e7 3.54416e7i −0.183117 0.503110i
\(414\) 0 0
\(415\) 3.12681e7 + 2.62370e7i 0.437478 + 0.367088i
\(416\) 0 0
\(417\) 5.23262e7i 0.721624i
\(418\) 0 0
\(419\) −7.88780e7 −1.07229 −0.536147 0.844125i \(-0.680121\pi\)
−0.536147 + 0.844125i \(0.680121\pi\)
\(420\) 0 0
\(421\) 3.85619e7 4.59563e7i 0.516788 0.615884i −0.443030 0.896507i \(-0.646097\pi\)
0.959818 + 0.280623i \(0.0905410\pi\)
\(422\) 0 0
\(423\) 4.06048e6 1.47789e6i 0.0536484 0.0195264i
\(424\) 0 0
\(425\) −4.06067e7 7.03329e7i −0.528970 0.916203i
\(426\) 0 0
\(427\) −2.79535e6 1.58532e7i −0.0359049 0.203627i
\(428\) 0 0
\(429\) −1.74582e7 + 3.02384e7i −0.221119 + 0.382990i
\(430\) 0 0
\(431\) 5.40562e7 + 6.44217e7i 0.675171 + 0.804638i 0.989478 0.144684i \(-0.0462165\pi\)
−0.314307 + 0.949321i \(0.601772\pi\)
\(432\) 0 0
\(433\) 1.79027e6 4.91872e6i 0.0220523 0.0605882i −0.928178 0.372136i \(-0.878625\pi\)
0.950230 + 0.311548i \(0.100848\pi\)
\(434\) 0 0
\(435\) −1.97549e6 + 1.12036e7i −0.0239998 + 0.136109i
\(436\) 0 0
\(437\) 3.82519e7 + 5.23410e7i 0.458362 + 0.627188i
\(438\) 0 0
\(439\) 3.02929e7 + 5.34146e6i 0.358054 + 0.0631345i 0.349782 0.936831i \(-0.386256\pi\)
0.00827199 + 0.999966i \(0.497367\pi\)
\(440\) 0 0
\(441\) 785378. + 285854.i 0.00915721 + 0.00333295i
\(442\) 0 0
\(443\) −7.29809e7 + 6.12383e7i −0.839456 + 0.704388i −0.957441 0.288628i \(-0.906801\pi\)
0.117985 + 0.993015i \(0.462357\pi\)
\(444\) 0 0
\(445\) −7.44705e6 4.29955e6i −0.0845092 0.0487914i
\(446\) 0 0
\(447\) −1.76046e8 + 3.10417e7i −1.97108 + 0.347555i
\(448\) 0 0
\(449\) 4.51922e7 2.60917e7i 0.499257 0.288246i −0.229149 0.973391i \(-0.573594\pi\)
0.728407 + 0.685145i \(0.240261\pi\)
\(450\) 0 0
\(451\) −1.46436e7 4.02330e7i −0.159631 0.438584i
\(452\) 0 0
\(453\) 1.23567e8 + 1.03685e8i 1.32925 + 1.11538i
\(454\) 0 0
\(455\) 2.13428e7i 0.226577i
\(456\) 0 0
\(457\) 9.86379e7 1.03346 0.516732 0.856147i \(-0.327148\pi\)
0.516732 + 0.856147i \(0.327148\pi\)
\(458\) 0 0
\(459\) 7.07154e7 8.42753e7i 0.731267 0.871490i
\(460\) 0 0
\(461\) 1.65163e8 6.01143e7i 1.68581 0.613586i 0.691724 0.722162i \(-0.256851\pi\)
0.994088 + 0.108576i \(0.0346291\pi\)
\(462\) 0 0
\(463\) −6.33406e7 1.09709e8i −0.638174 1.10535i −0.985833 0.167729i \(-0.946357\pi\)
0.347659 0.937621i \(-0.386977\pi\)
\(464\) 0 0
\(465\) −1.06658e7 6.04890e7i −0.106081 0.601614i
\(466\) 0 0
\(467\) 3.61434e7 6.26021e7i 0.354877 0.614665i −0.632220 0.774789i \(-0.717856\pi\)
0.987097 + 0.160124i \(0.0511894\pi\)
\(468\) 0 0
\(469\) 1.16804e8 + 1.39202e8i 1.13224 + 1.34935i
\(470\) 0 0
\(471\) 3.18334e7 8.74615e7i 0.304663 0.837055i
\(472\) 0 0
\(473\) 115324. 654037.i 0.00108978 0.00618043i
\(474\) 0 0
\(475\) 9.37643e7 1.01200e7i 0.874897 0.0944279i
\(476\) 0 0
\(477\) 4.48084e6 + 790093.i 0.0412861 + 0.00727986i
\(478\) 0 0
\(479\) 4.67863e7 + 1.70288e7i 0.425709 + 0.154945i 0.545985 0.837795i \(-0.316156\pi\)
−0.120276 + 0.992741i \(0.538378\pi\)
\(480\) 0 0
\(481\) −3.98375e7 + 3.34276e7i −0.357978 + 0.300380i
\(482\) 0 0
\(483\) 8.32902e7 + 4.80876e7i 0.739184 + 0.426768i
\(484\) 0 0
\(485\) −1.78682e7 + 3.15064e6i −0.156623 + 0.0276168i
\(486\) 0 0
\(487\) −1.23024e7 + 7.10279e6i −0.106513 + 0.0614953i −0.552310 0.833639i \(-0.686254\pi\)
0.445797 + 0.895134i \(0.352920\pi\)
\(488\) 0 0
\(489\) −2.74517e7 7.54230e7i −0.234770 0.645026i
\(490\) 0 0
\(491\) 1.51913e6 + 1.27470e6i 0.0128336 + 0.0107687i 0.649182 0.760633i \(-0.275111\pi\)
−0.636348 + 0.771402i \(0.719556\pi\)
\(492\) 0 0
\(493\) 5.48899e7i 0.458091i
\(494\) 0 0
\(495\) −2.73949e6 −0.0225868
\(496\) 0 0
\(497\) 5.08121e7 6.05555e7i 0.413903 0.493270i
\(498\) 0 0
\(499\) 8.64256e7 3.14564e7i 0.695570 0.253167i 0.0300518 0.999548i \(-0.490433\pi\)
0.665518 + 0.746382i \(0.268211\pi\)
\(500\) 0 0
\(501\) 6.15032e7 + 1.06527e8i 0.489085 + 0.847120i
\(502\) 0 0
\(503\) −2.29460e7 1.30133e8i −0.180303 1.02255i −0.931843 0.362862i \(-0.881799\pi\)
0.751539 0.659688i \(-0.229312\pi\)
\(504\) 0 0
\(505\) −1.07578e6 + 1.86330e6i −0.00835311 + 0.0144680i
\(506\) 0 0
\(507\) 5.36429e7 + 6.39291e7i 0.411612 + 0.490540i
\(508\) 0 0
\(509\) 6.27988e7 1.72538e8i 0.476210 1.30838i −0.436477 0.899715i \(-0.643774\pi\)
0.912687 0.408660i \(-0.134004\pi\)
\(510\) 0 0
\(511\) −6.13439e6 + 3.47899e7i −0.0459736 + 0.260729i
\(512\) 0 0
\(513\) 5.63239e7 + 1.14667e8i 0.417196 + 0.849348i
\(514\) 0 0
\(515\) −4.24336e7 7.48219e6i −0.310662 0.0547781i
\(516\) 0 0
\(517\) 5.22355e7 + 1.90122e7i 0.378002 + 0.137582i
\(518\) 0 0
\(519\) −2.07496e8 + 1.74110e8i −1.48425 + 1.24543i
\(520\) 0 0
\(521\) −6.99790e7 4.04024e7i −0.494829 0.285689i 0.231747 0.972776i \(-0.425556\pi\)
−0.726575 + 0.687087i \(0.758889\pi\)
\(522\) 0 0
\(523\) −1.73842e8 + 3.06531e7i −1.21521 + 0.214274i −0.744262 0.667888i \(-0.767199\pi\)
−0.470946 + 0.882162i \(0.656088\pi\)
\(524\) 0 0
\(525\) 1.21165e8 6.99547e7i 0.837336 0.483436i
\(526\) 0 0
\(527\) −1.01360e8 2.78483e8i −0.692521 1.90269i
\(528\) 0 0
\(529\) −4.49684e7 3.77329e7i −0.303767 0.254891i
\(530\) 0 0
\(531\) 7.34768e6i 0.0490757i
\(532\) 0 0
\(533\) 6.49829e7 0.429159
\(534\) 0 0
\(535\) −4.86432e7 + 5.79707e7i −0.317659 + 0.378571i
\(536\) 0 0
\(537\) 7.59515e7 2.76441e7i 0.490471 0.178517i
\(538\) 0 0
\(539\) 5.37591e6 + 9.31135e6i 0.0343309 + 0.0594629i
\(540\) 0 0
\(541\) −1.13037e7 6.41063e7i −0.0713885 0.404864i −0.999472 0.0324920i \(-0.989656\pi\)
0.928084 0.372372i \(-0.121455\pi\)
\(542\) 0 0
\(543\) −7.84903e7 + 1.35949e8i −0.490249 + 0.849136i
\(544\) 0 0
\(545\) 1.89905e7 + 2.26320e7i 0.117313 + 0.139808i
\(546\) 0 0
\(547\) 9.74719e7 2.67802e8i 0.595549 1.63626i −0.164489 0.986379i \(-0.552597\pi\)
0.760038 0.649879i \(-0.225180\pi\)
\(548\) 0 0
\(549\) −544577. + 3.08845e6i −0.00329111 + 0.0186648i
\(550\) 0 0
\(551\) −5.83024e7 2.57629e7i −0.348523 0.154007i
\(552\) 0 0
\(553\) −9.21469e7 1.62480e7i −0.544886 0.0960780i
\(554\) 0 0
\(555\) −4.36928e7 1.59029e7i −0.255582 0.0930243i
\(556\) 0 0
\(557\) 1.54226e8 1.29411e8i 0.892466 0.748868i −0.0762369 0.997090i \(-0.524291\pi\)
0.968703 + 0.248222i \(0.0798461\pi\)
\(558\) 0 0
\(559\) 872940. + 503992.i 0.00499746 + 0.00288528i
\(560\) 0 0
\(561\) −1.48338e8 + 2.61561e7i −0.840166 + 0.148144i
\(562\) 0 0
\(563\) −2.50670e8 + 1.44724e8i −1.40468 + 0.810991i −0.994868 0.101179i \(-0.967738\pi\)
−0.409810 + 0.912171i \(0.634405\pi\)
\(564\) 0 0
\(565\) 5.23409e6 + 1.43805e7i 0.0290199 + 0.0797315i
\(566\) 0 0
\(567\) 1.59280e8 + 1.33652e8i 0.873803 + 0.733208i
\(568\) 0 0
\(569\) 2.25654e8i 1.22492i 0.790503 + 0.612458i \(0.209819\pi\)
−0.790503 + 0.612458i \(0.790181\pi\)
\(570\) 0 0
\(571\) 1.09355e8 0.587393 0.293696 0.955899i \(-0.405115\pi\)
0.293696 + 0.955899i \(0.405115\pi\)
\(572\) 0 0
\(573\) −9.13833e7 + 1.08906e8i −0.485739 + 0.578881i
\(574\) 0 0
\(575\) 1.22120e8 4.44479e7i 0.642365 0.233802i
\(576\) 0 0
\(577\) −4.18129e6 7.24221e6i −0.0217662 0.0377002i 0.854937 0.518732i \(-0.173596\pi\)
−0.876703 + 0.481031i \(0.840262\pi\)
\(578\) 0 0
\(579\) 4.09018e7 + 2.31966e8i 0.210721 + 1.19506i
\(580\) 0 0
\(581\) −1.69639e8 + 2.93823e8i −0.864960 + 1.49816i
\(582\) 0 0
\(583\) 3.76239e7 + 4.48384e7i 0.189871 + 0.226279i
\(584\) 0 0
\(585\) 1.42208e6 3.90714e6i 0.00710325 0.0195160i
\(586\) 0 0
\(587\) 3.46622e7 1.96579e8i 0.171373 0.971904i −0.770875 0.636987i \(-0.780181\pi\)
0.942248 0.334917i \(-0.108708\pi\)
\(588\) 0 0
\(589\) 3.43370e8 + 2.30468e7i 1.68041 + 0.112788i
\(590\) 0 0
\(591\) −7.48655e7 1.32008e7i −0.362676 0.0639496i
\(592\) 0 0
\(593\) −2.92834e8 1.06583e8i −1.40429 0.511121i −0.474844 0.880070i \(-0.657495\pi\)
−0.929450 + 0.368949i \(0.879718\pi\)
\(594\) 0 0
\(595\) −7.05307e7 + 5.91823e7i −0.334832 + 0.280958i
\(596\) 0 0
\(597\) −1.23939e8 7.15560e7i −0.582483 0.336297i
\(598\) 0 0
\(599\) 2.09749e7 3.69843e6i 0.0975929 0.0172083i −0.124638 0.992202i \(-0.539777\pi\)
0.222231 + 0.974994i \(0.428666\pi\)
\(600\) 0 0
\(601\) −2.61565e8 + 1.51015e8i −1.20492 + 0.695658i −0.961644 0.274300i \(-0.911554\pi\)
−0.243271 + 0.969958i \(0.578221\pi\)
\(602\) 0 0
\(603\) −1.21078e7 3.32658e7i −0.0552220 0.151721i
\(604\) 0 0
\(605\) 3.17725e7 + 2.66603e7i 0.143478 + 0.120392i
\(606\) 0 0
\(607\) 1.69817e8i 0.759301i −0.925130 0.379650i \(-0.876044\pi\)
0.925130 0.379650i \(-0.123956\pi\)
\(608\) 0 0
\(609\) −9.45610e7 −0.418659
\(610\) 0 0
\(611\) −5.42314e7 + 6.46305e7i −0.237754 + 0.283344i
\(612\) 0 0
\(613\) 9.88419e7 3.59755e7i 0.429101 0.156180i −0.118436 0.992962i \(-0.537788\pi\)
0.547537 + 0.836782i \(0.315566\pi\)
\(614\) 0 0
\(615\) 2.90506e7 + 5.03171e7i 0.124891 + 0.216317i
\(616\) 0 0
\(617\) −1.91970e7 1.08872e8i −0.0817294 0.463510i −0.998015 0.0629838i \(-0.979938\pi\)
0.916285 0.400526i \(-0.131173\pi\)
\(618\) 0 0
\(619\) −1.78705e8 + 3.09526e8i −0.753467 + 1.30504i 0.192666 + 0.981264i \(0.438287\pi\)
−0.946133 + 0.323779i \(0.895047\pi\)
\(620\) 0 0
\(621\) 1.13158e8 + 1.34857e8i 0.472510 + 0.563116i
\(622\) 0 0
\(623\) 2.44463e7 6.71656e7i 0.101099 0.277768i
\(624\) 0 0
\(625\) 2.77404e7 1.57324e8i 0.113625 0.644398i
\(626\) 0 0
\(627\) 4.18414e7 1.69837e8i 0.169747 0.689016i
\(628\) 0 0
\(629\) −2.20934e8 3.89567e7i −0.887792 0.156542i
\(630\) 0 0
\(631\) 9.88954e7 + 3.59950e7i 0.393630 + 0.143270i 0.531249 0.847216i \(-0.321723\pi\)
−0.137619 + 0.990485i \(0.543945\pi\)
\(632\) 0 0
\(633\) −3.00081e8 + 2.51797e8i −1.18311 + 0.992751i
\(634\) 0 0
\(635\) 3.78534e6 + 2.18547e6i 0.0147837 + 0.00853539i
\(636\) 0 0
\(637\) −1.60708e7 + 2.83371e6i −0.0621753 + 0.0109632i
\(638\) 0 0
\(639\) −1.33368e7 + 7.70003e6i −0.0511152 + 0.0295114i
\(640\) 0 0
\(641\) −1.71073e8 4.70019e8i −0.649542 1.78460i −0.619425 0.785056i \(-0.712634\pi\)
−0.0301171 0.999546i \(-0.509588\pi\)
\(642\) 0 0
\(643\) 3.76968e8 + 3.16314e8i 1.41799 + 1.18983i 0.952408 + 0.304825i \(0.0985980\pi\)
0.465578 + 0.885007i \(0.345846\pi\)
\(644\) 0 0
\(645\) 901238.i 0.00335862i
\(646\) 0 0
\(647\) −3.22687e8 −1.19143 −0.595716 0.803195i \(-0.703132\pi\)
−0.595716 + 0.803195i \(0.703132\pi\)
\(648\) 0 0
\(649\) −6.07584e7 + 7.24090e7i −0.222265 + 0.264886i
\(650\) 0 0
\(651\) 4.79754e8 1.74616e8i 1.73890 0.632909i
\(652\) 0 0
\(653\) −2.25243e8 3.90133e8i −0.808932 1.40111i −0.913604 0.406605i \(-0.866713\pi\)
0.104672 0.994507i \(-0.466621\pi\)
\(654\) 0 0
\(655\) −4.70523e6 2.66847e7i −0.0167439 0.0949595i
\(656\) 0 0
\(657\) 3.44107e6 5.96011e6i 0.0121338 0.0210164i
\(658\) 0 0
\(659\) 1.19731e7 + 1.42690e7i 0.0418360 + 0.0498582i 0.786557 0.617518i \(-0.211862\pi\)
−0.744721 + 0.667376i \(0.767417\pi\)
\(660\) 0 0
\(661\) −1.63569e8 + 4.49401e8i −0.566364 + 1.55607i 0.243773 + 0.969832i \(0.421615\pi\)
−0.810137 + 0.586240i \(0.800608\pi\)
\(662\) 0 0
\(663\) 3.96986e7 2.25142e8i 0.136218 0.772531i
\(664\) 0 0
\(665\) −2.97576e7 1.02693e8i −0.101189 0.349202i
\(666\) 0 0
\(667\) −8.65001e7 1.52523e7i −0.291500 0.0513994i
\(668\) 0 0
\(669\) 4.06387e8 + 1.47913e8i 1.35726 + 0.494001i
\(670\) 0 0
\(671\) −3.09052e7 + 2.59325e7i −0.102297 + 0.0858376i
\(672\) 0 0
\(673\) −3.09972e8 1.78963e8i −1.01690 0.587107i −0.103694 0.994609i \(-0.533066\pi\)
−0.913204 + 0.407503i \(0.866400\pi\)
\(674\) 0 0
\(675\) 2.52205e8 4.44706e7i 0.820054 0.144598i
\(676\) 0 0
\(677\) −1.56997e8 + 9.06421e7i −0.505970 + 0.292122i −0.731175 0.682190i \(-0.761028\pi\)
0.225206 + 0.974311i \(0.427695\pi\)
\(678\) 0 0
\(679\) −5.15807e7 1.41717e8i −0.164770 0.452702i
\(680\) 0 0
\(681\) 9.89205e7 + 8.30041e7i 0.313217 + 0.262820i
\(682\) 0 0
\(683\) 3.01027e8i 0.944808i 0.881382 + 0.472404i \(0.156614\pi\)
−0.881382 + 0.472404i \(0.843386\pi\)
\(684\) 0 0
\(685\) 1.98383e8 0.617209
\(686\) 0 0
\(687\) 3.43136e8 4.08933e8i 1.05827 1.26120i
\(688\) 0 0
\(689\) −8.34806e7 + 3.03844e7i −0.255228 + 0.0928953i
\(690\) 0 0
\(691\) 3.20424e8 + 5.54991e8i 0.971162 + 1.68210i 0.692060 + 0.721840i \(0.256703\pi\)
0.279101 + 0.960262i \(0.409963\pi\)
\(692\) 0 0
\(693\) −3.95410e6 2.24248e7i −0.0118809 0.0673797i
\(694\) 0 0
\(695\) −4.00795e7 + 6.94198e7i −0.119390 + 0.206790i
\(696\) 0 0
\(697\) 1.80194e8 + 2.14747e8i 0.532160 + 0.634204i
\(698\) 0 0
\(699\) 1.19252e8 3.27643e8i 0.349169 0.959334i
\(700\) 0 0
\(701\) 7.74532e7 4.39259e8i 0.224846 1.27517i −0.638133 0.769926i \(-0.720293\pi\)
0.862979 0.505239i \(-0.168596\pi\)
\(702\) 0 0
\(703\) 1.45075e8 2.16385e8i 0.417569 0.622818i
\(704\) 0 0
\(705\) −7.42883e7 1.30990e7i −0.212008 0.0373828i
\(706\) 0 0
\(707\) −1.68053e7 6.11662e6i −0.0475540 0.0173083i
\(708\) 0 0
\(709\) 2.19435e8 1.84127e8i 0.615696 0.516630i −0.280751 0.959781i \(-0.590584\pi\)
0.896447 + 0.443150i \(0.146139\pi\)
\(710\) 0 0
\(711\) 1.57864e7 + 9.11426e6i 0.0439211 + 0.0253579i
\(712\) 0 0
\(713\) 4.67022e8 8.23485e7i 1.28845 0.227189i
\(714\) 0 0
\(715\) 4.63225e7 2.67443e7i 0.126728 0.0731667i
\(716\) 0 0
\(717\) −1.40218e8 3.85246e8i −0.380405 1.04515i
\(718\) 0 0
\(719\) 4.84586e8 + 4.06616e8i 1.30372 + 1.09395i 0.989489 + 0.144605i \(0.0461912\pi\)
0.314231 + 0.949346i \(0.398253\pi\)
\(720\) 0 0
\(721\) 3.58151e8i 0.955564i
\(722\) 0 0
\(723\) −1.68080e8 −0.444735
\(724\) 0 0
\(725\) −8.21327e7 + 9.78820e7i −0.215527 + 0.256855i
\(726\) 0 0
\(727\) 1.48118e8 5.39107e7i 0.385484 0.140305i −0.142007 0.989866i \(-0.545355\pi\)
0.527490 + 0.849561i \(0.323133\pi\)
\(728\) 0 0
\(729\) 1.71664e8 + 2.97331e8i 0.443096 + 0.767464i
\(730\) 0 0
\(731\) 755088. + 4.28232e6i 0.00193306 + 0.0109629i
\(732\) 0 0
\(733\) −2.93269e8 + 5.07956e8i −0.744652 + 1.28978i 0.205705 + 0.978614i \(0.434051\pi\)
−0.950357 + 0.311162i \(0.899282\pi\)
\(734\) 0 0
\(735\) −9.37860e6 1.11770e7i −0.0236198 0.0281490i
\(736\) 0 0
\(737\) 1.55759e8 4.27944e8i 0.389090 1.06902i
\(738\) 0 0
\(739\) −1.08543e7 + 6.15578e7i −0.0268948 + 0.152528i −0.995298 0.0968627i \(-0.969119\pi\)
0.968403 + 0.249391i \(0.0802303\pi\)
\(740\) 0 0
\(741\) 2.20506e8 + 1.47838e8i 0.541958 + 0.363356i
\(742\) 0 0
\(743\) 7.37754e8 + 1.30086e8i 1.79864 + 0.317150i 0.970088 0.242756i \(-0.0780513\pi\)
0.828557 + 0.559905i \(0.189162\pi\)
\(744\) 0 0
\(745\) 2.57333e8 + 9.36614e7i 0.622338 + 0.226512i
\(746\) 0 0
\(747\) 5.06327e7 4.24859e7i 0.121470 0.101925i
\(748\) 0 0
\(749\) −5.44745e8 3.14509e8i −1.29643 0.748492i
\(750\) 0 0
\(751\) −2.56973e8 + 4.53113e7i −0.606692 + 0.106976i −0.468551 0.883437i \(-0.655224\pi\)
−0.138141 + 0.990413i \(0.544113\pi\)
\(752\) 0 0
\(753\) −5.14259e8 + 2.96908e8i −1.20447 + 0.695403i
\(754\) 0 0
\(755\) −8.45150e7 2.32203e8i −0.196378 0.539544i
\(756\) 0 0
\(757\) 1.66909e8 + 1.40054e8i 0.384763 + 0.322854i 0.814569 0.580067i \(-0.196974\pi\)
−0.429806 + 0.902921i \(0.641418\pi\)
\(758\) 0 0
\(759\) 2.41032e8i 0.551250i
\(760\) 0 0
\(761\) 5.96010e7 0.135238 0.0676191 0.997711i \(-0.478460\pi\)
0.0676191 + 0.997711i \(0.478460\pi\)
\(762\) 0 0
\(763\) −1.57850e8 + 1.88118e8i −0.355361 + 0.423503i
\(764\) 0 0
\(765\) 1.68552e7 6.13477e6i 0.0376486 0.0137030i
\(766\) 0 0
\(767\) −7.17318e7 1.24243e8i −0.158974 0.275351i
\(768\) 0 0
\(769\) 8.06199e7 + 4.57218e8i 0.177281 + 1.00541i 0.935478 + 0.353386i \(0.114970\pi\)
−0.758196 + 0.652026i \(0.773919\pi\)
\(770\) 0 0
\(771\) −9.97166e7 + 1.72714e8i −0.217573 + 0.376847i
\(772\) 0 0
\(773\) 2.45464e8 + 2.92532e8i 0.531434 + 0.633338i 0.963244 0.268626i \(-0.0865697\pi\)
−0.431811 + 0.901964i \(0.642125\pi\)
\(774\) 0 0
\(775\) 2.35951e8 6.48269e8i 0.506892 1.39268i
\(776\) 0 0
\(777\) 6.71122e7 3.80612e8i 0.143067 0.811372i
\(778\) 0 0
\(779\) −3.12673e8 + 9.06037e7i −0.661420 + 0.191661i
\(780\) 0 0
\(781\) −1.95102e8 3.44018e7i −0.409552 0.0722151i
\(782\) 0 0
\(783\) −1.62650e8 5.91997e7i −0.338819 0.123320i
\(784\) 0 0
\(785\) −1.09224e8 + 9.16498e7i −0.225792 + 0.189462i
\(786\) 0 0
\(787\) 2.71653e7 + 1.56839e7i 0.0557302 + 0.0321758i 0.527606 0.849489i \(-0.323090\pi\)
−0.471876 + 0.881665i \(0.656423\pi\)
\(788\) 0 0
\(789\) −7.11284e8 + 1.25419e8i −1.44815 + 0.255347i
\(790\) 0 0
\(791\) −1.10161e8 + 6.36014e7i −0.222586 + 0.128510i
\(792\) 0 0
\(793\) −2.09427e7 5.75396e7i −0.0419965 0.115384i
\(794\) 0 0
\(795\) −6.08470e7 5.10567e7i −0.121098 0.101613i
\(796\) 0 0
\(797\) 5.61520e8i 1.10915i −0.832134 0.554575i \(-0.812881\pi\)
0.832134 0.554575i \(-0.187119\pi\)
\(798\) 0 0
\(799\) −3.63963e8 −0.713538
\(800\) 0 0
\(801\) −8.95057e6 + 1.06669e7i −0.0174162 + 0.0207558i
\(802\) 0 0
\(803\) 8.31951e7 3.02805e7i 0.160676 0.0584813i
\(804\) 0 0
\(805\) −7.36659e7 1.27593e8i −0.141214 0.244591i
\(806\) 0 0
\(807\) −5.62834e7 3.19199e8i −0.107093 0.607353i
\(808\) 0 0
\(809\) −4.46354e8 + 7.73108e8i −0.843013 + 1.46014i 0.0443231 + 0.999017i \(0.485887\pi\)
−0.887336 + 0.461124i \(0.847446\pi\)
\(810\) 0 0
\(811\) −3.67936e8 4.38489e8i −0.689778 0.822045i 0.301551 0.953450i \(-0.402496\pi\)
−0.991329 + 0.131405i \(0.958051\pi\)
\(812\) 0 0
\(813\) −1.56228e8 + 4.29232e8i −0.290728 + 0.798768i
\(814\) 0 0
\(815\) −2.13512e7 + 1.21088e8i −0.0394411 + 0.223681i
\(816\) 0 0
\(817\) −4.90295e6 1.20790e6i −0.00899065 0.00221495i
\(818\) 0 0
\(819\) 3.40355e7 + 6.00138e6i 0.0619556 + 0.0109244i
\(820\) 0 0
\(821\) 1.02256e8 + 3.72181e7i 0.184781 + 0.0672549i 0.432754 0.901512i \(-0.357542\pi\)
−0.247972 + 0.968767i \(0.579764\pi\)
\(822\) 0 0
\(823\) −4.18823e8 + 3.51434e8i −0.751331 + 0.630442i −0.935855 0.352387i \(-0.885370\pi\)
0.184524 + 0.982828i \(0.440926\pi\)
\(824\) 0 0
\(825\) −3.03661e8 1.75319e8i −0.540788 0.312224i
\(826\) 0 0
\(827\) −2.85266e8 + 5.03000e7i −0.504351 + 0.0889307i −0.420034 0.907508i \(-0.637982\pi\)
−0.0843168 + 0.996439i \(0.526871\pi\)
\(828\) 0 0
\(829\) 4.71872e7 2.72436e7i 0.0828249 0.0478190i −0.458016 0.888944i \(-0.651440\pi\)
0.540840 + 0.841125i \(0.318106\pi\)
\(830\) 0 0
\(831\) 2.78554e7 + 7.65320e7i 0.0485407 + 0.133364i
\(832\) 0 0
\(833\) −5.39278e7 4.52508e7i −0.0932991 0.0782873i
\(834\) 0 0
\(835\) 1.88435e8i 0.323669i
\(836\) 0 0
\(837\) 9.34519e8 1.59372
\(838\) 0 0
\(839\) −5.01275e8 + 5.97396e8i −0.848770 + 1.01153i 0.150965 + 0.988539i \(0.451762\pi\)
−0.999736 + 0.0229862i \(0.992683\pi\)
\(840\) 0 0
\(841\) −4.77799e8 + 1.73905e8i −0.803262 + 0.292363i
\(842\) 0 0
\(843\) 9.29636e7 + 1.61018e8i 0.155178 + 0.268776i
\(844\) 0 0
\(845\) −2.21997e7 1.25901e8i −0.0367941 0.208670i
\(846\) 0 0
\(847\) −1.72375e8 + 2.98563e8i −0.283677 + 0.491344i
\(848\) 0 0
\(849\) 6.25865e8 + 7.45876e8i 1.02272 + 1.21883i
\(850\) 0 0
\(851\) 1.22782e8 3.37342e8i 0.199226 0.547370i
\(852\) 0 0
\(853\) −9.69524e7 + 5.49844e8i −0.156211 + 0.885916i 0.801459 + 0.598049i \(0.204057\pi\)
−0.957670 + 0.287867i \(0.907054\pi\)
\(854\) 0 0
\(855\) −1.39490e6 + 2.07824e7i −0.00223175 + 0.0332504i
\(856\) 0 0
\(857\) 3.64855e8 + 6.43338e7i 0.579666 + 0.102211i 0.455791 0.890087i \(-0.349357\pi\)
0.123875 + 0.992298i \(0.460468\pi\)
\(858\) 0 0
\(859\) −1.26302e8 4.59702e7i −0.199265 0.0725266i 0.240460 0.970659i \(-0.422702\pi\)
−0.439725 + 0.898133i \(0.644924\pi\)
\(860\) 0 0
\(861\) −3.69953e8 + 3.10427e8i −0.579612 + 0.486352i
\(862\) 0 0
\(863\) 4.29635e8 + 2.48050e8i 0.668447 + 0.385928i 0.795488 0.605970i \(-0.207215\pi\)
−0.127041 + 0.991897i \(0.540548\pi\)
\(864\) 0 0
\(865\) 4.08639e8 7.20542e7i 0.631382 0.111330i
\(866\) 0 0
\(867\) 2.63178e8 1.51946e8i 0.403824 0.233148i
\(868\) 0 0
\(869\) 8.02032e7 + 2.20357e8i 0.122217 + 0.335789i
\(870\) 0 0
\(871\) 5.29491e8 + 4.44295e8i 0.801316 + 0.672384i
\(872\) 0 0
\(873\) 2.93804e7i 0.0441586i
\(874\) 0 0
\(875\) −4.57890e8 −0.683498
\(876\) 0 0
\(877\) 5.13057e8 6.11437e8i 0.760618 0.906469i −0.237269 0.971444i \(-0.576252\pi\)
0.997887 + 0.0649746i \(0.0206966\pi\)
\(878\) 0 0
\(879\) −1.14828e9 + 4.17938e8i −1.69075 + 0.615383i
\(880\) 0 0
\(881\) −5.17847e8 8.96937e8i −0.757310 1.31170i −0.944218 0.329322i \(-0.893180\pi\)
0.186908 0.982377i \(-0.440153\pi\)
\(882\) 0 0
\(883\) −1.60800e8 9.11941e8i −0.233563 1.32460i −0.845620 0.533786i \(-0.820769\pi\)
0.612057 0.790813i \(-0.290342\pi\)
\(884\) 0 0
\(885\) 6.41353e7 1.11086e8i 0.0925268 0.160261i
\(886\) 0 0
\(887\) 3.48129e8 + 4.14884e8i 0.498849 + 0.594505i 0.955445 0.295169i \(-0.0953759\pi\)
−0.456596 + 0.889674i \(0.650931\pi\)
\(888\) 0 0
\(889\) −1.24261e7 + 3.41404e7i −0.0176860 + 0.0485918i
\(890\) 0 0
\(891\) 9.04878e7 5.13182e8i 0.127925 0.725501i
\(892\) 0 0
\(893\) 1.70828e8 3.86590e8i 0.239886 0.542870i
\(894\) 0 0
\(895\) −1.21937e8 2.15008e7i −0.170085 0.0299906i
\(896\) 0 0
\(897\) 3.43766e8 + 1.25121e8i 0.476306 + 0.173361i
\(898\) 0 0
\(899\) −3.57181e8 + 2.99710e8i −0.491597 + 0.412499i
\(900\) 0 0
\(901\) −3.31897e8 1.91621e8i −0.453763 0.261980i
\(902\) 0 0
\(903\) −7.37732e6 + 1.30082e6i −0.0100192 + 0.00176666i
\(904\) 0 0
\(905\) 2.08262e8 1.20240e8i 0.280973 0.162220i
\(906\) 0 0
\(907\) 5.33048e6 + 1.46454e7i 0.00714405 + 0.0196281i 0.943213 0.332187i \(-0.107787\pi\)
−0.936069 + 0.351816i \(0.885564\pi\)
\(908\) 0 0
\(909\) 2.66892e6 + 2.23949e6i 0.00355340 + 0.00298166i
\(910\) 0 0
\(911\) 4.69164e8i 0.620540i 0.950648 + 0.310270i \(0.100419\pi\)
−0.950648 + 0.310270i \(0.899581\pi\)
\(912\) 0 0
\(913\) 8.50287e8 1.11726
\(914\) 0 0
\(915\) 3.51912e7 4.19392e7i 0.0459378 0.0547466i
\(916\) 0 0
\(917\) 2.11643e8 7.70318e7i 0.274471 0.0998992i
\(918\) 0 0
\(919\) 7.31203e6 + 1.26648e7i 0.00942088 + 0.0163174i 0.870697 0.491819i \(-0.163668\pi\)
−0.861277 + 0.508137i \(0.830335\pi\)
\(920\) 0 0
\(921\) 1.36523e6 + 7.74261e6i 0.00174754 + 0.00991079i
\(922\) 0 0
\(923\) 1.50343e8 2.60402e8i 0.191196 0.331161i
\(924\) 0 0
\(925\) −3.35688e8 4.00057e8i −0.424141 0.505471i
\(926\) 0 0
\(927\) −2.38638e7 + 6.55653e7i −0.0299572 + 0.0823066i
\(928\) 0 0
\(929\) −2.01336e7 + 1.14183e8i −0.0251116 + 0.142415i −0.994786 0.101986i \(-0.967480\pi\)
0.969674 + 0.244401i \(0.0785913\pi\)
\(930\) 0 0
\(931\) 7.33753e7 3.60417e7i 0.0909286 0.0446638i
\(932\) 0 0
\(933\) −5.87836e8 1.03651e8i −0.723787 0.127623i
\(934\) 0 0
\(935\) 2.16831e8 + 7.89200e7i 0.265269 + 0.0965500i
\(936\) 0 0
\(937\) 5.10543e8 4.28396e8i 0.620602 0.520747i −0.277391 0.960757i \(-0.589470\pi\)
0.897993 + 0.440010i \(0.145025\pi\)
\(938\) 0 0
\(939\) −2.32678e8 1.34337e8i −0.281034 0.162255i
\(940\) 0 0
\(941\) −2.14572e8 + 3.78348e7i −0.257516 + 0.0454070i −0.300916 0.953651i \(-0.597292\pi\)
0.0433997 + 0.999058i \(0.486181\pi\)
\(942\) 0 0
\(943\) −3.88486e8 + 2.24293e8i −0.463277 + 0.267473i
\(944\) 0 0
\(945\) −9.93004e7 2.72826e8i −0.117667 0.323288i
\(946\) 0 0
\(947\) −2.80228e8 2.35139e8i −0.329960 0.276869i 0.462724 0.886503i \(-0.346872\pi\)
−0.792684 + 0.609633i \(0.791317\pi\)
\(948\) 0 0
\(949\) 1.34374e8i 0.157223i
\(950\) 0 0
\(951\) −4.90314e8 −0.570076
\(952\) 0 0
\(953\) 6.99232e8 8.33312e8i 0.807872 0.962784i −0.191955 0.981404i \(-0.561483\pi\)
0.999827 + 0.0186199i \(0.00592724\pi\)
\(954\) 0 0
\(955\) 2.04653e8 7.44876e7i 0.234968 0.0855213i
\(956\) 0 0
\(957\) 1.18493e8 + 2.05236e8i 0.135194 + 0.234163i
\(958\) 0 0
\(959\) 2.86340e8 + 1.62391e9i 0.324658 + 1.84123i
\(960\) 0 0
\(961\) 8.14956e8 1.41154e9i 0.918256 1.59047i
\(962\) 0 0
\(963\) 7.87684e7 + 9.38726e7i 0.0882010 + 0.105114i
\(964\) 0 0
\(965\) 1.23412e8 3.39072e8i 0.137333 0.377320i
\(966\) 0 0
\(967\) 8.49043e7 4.81516e8i 0.0938967 0.532514i −0.901183 0.433438i \(-0.857300\pi\)
0.995080 0.0990760i \(-0.0315887\pi\)
\(968\) 0 0
\(969\) 1.22894e8 + 1.13865e9i 0.135071 + 1.25146i
\(970\) 0 0
\(971\) 5.58169e8 + 9.84202e7i 0.609688 + 0.107505i 0.469964 0.882686i \(-0.344267\pi\)
0.139725 + 0.990190i \(0.455378\pi\)
\(972\) 0 0
\(973\) −6.26103e8 2.27883e8i −0.679685 0.247385i
\(974\) 0 0
\(975\) 4.07676e8 3.42081e8i 0.439847 0.369075i
\(976\) 0 0
\(977\) 5.96459e8 + 3.44366e8i 0.639583 + 0.369263i 0.784454 0.620187i \(-0.212943\pi\)
−0.144871 + 0.989451i \(0.546277\pi\)
\(978\) 0 0
\(979\) −1.76410e8 + 3.11059e7i −0.188008 + 0.0331508i
\(980\) 0 0
\(981\) 4.14313e7 2.39204e7i 0.0438856 0.0253374i
\(982\) 0 0
\(983\) 2.28539e8 + 6.27906e8i 0.240603 + 0.661050i 0.999946 + 0.0103605i \(0.00329789\pi\)
−0.759344 + 0.650690i \(0.774480\pi\)
\(984\) 0 0
\(985\) 8.92108e7 + 7.48567e7i 0.0933488 + 0.0783289i
\(986\) 0 0
\(987\) 6.27013e8i 0.652116i
\(988\) 0 0
\(989\) −6.95824e6 −0.00719301
\(990\) 0 0
\(991\) 2.89568e8 3.45094e8i 0.297529 0.354582i −0.596482 0.802627i \(-0.703435\pi\)
0.894011 + 0.448045i \(0.147880\pi\)
\(992\) 0 0
\(993\) 1.18009e9 4.29516e8i 1.20522 0.438664i
\(994\) 0 0
\(995\) 1.09617e8 + 1.89863e8i 0.111278 + 0.192739i
\(996\) 0 0
\(997\) −1.77375e8 1.00594e9i −0.178981 1.01505i −0.933448 0.358713i \(-0.883216\pi\)
0.754467 0.656338i \(-0.227896\pi\)
\(998\) 0 0
\(999\) 3.53718e8 6.12657e8i 0.354781 0.614498i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 76.7.j.a.21.2 60
19.10 odd 18 inner 76.7.j.a.29.2 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.7.j.a.21.2 60 1.1 even 1 trivial
76.7.j.a.29.2 yes 60 19.10 odd 18 inner