Properties

Label 76.7.j.a.13.5
Level $76$
Weight $7$
Character 76.13
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 13.5
Character \(\chi\) \(=\) 76.13
Dual form 76.7.j.a.41.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.50553 + 9.63135i) q^{3} +(35.8010 + 203.037i) q^{5} +(-107.477 + 186.155i) q^{7} +(477.972 + 401.066i) q^{9} +O(q^{10})\) \(q+(-3.50553 + 9.63135i) q^{3} +(35.8010 + 203.037i) q^{5} +(-107.477 + 186.155i) q^{7} +(477.972 + 401.066i) q^{9} +(-1139.35 - 1973.42i) q^{11} +(416.997 + 1145.69i) q^{13} +(-2081.03 - 366.941i) q^{15} +(1100.79 - 923.671i) q^{17} +(-5928.97 + 3448.65i) q^{19} +(-1416.17 - 1687.72i) q^{21} +(344.169 - 1951.88i) q^{23} +(-25259.8 + 9193.81i) q^{25} +(-12009.2 + 6933.50i) q^{27} +(-12446.4 + 14833.0i) q^{29} +(-16009.5 - 9243.09i) q^{31} +(23000.8 - 4055.65i) q^{33} +(-41644.3 - 15157.3i) q^{35} -74669.7i q^{37} -12496.3 q^{39} +(-18646.0 + 51229.4i) q^{41} +(14851.6 + 84227.4i) q^{43} +(-64319.6 + 111405. i) q^{45} +(-62976.8 - 52843.8i) q^{47} +(35721.9 + 61872.2i) q^{49} +(5037.36 + 13840.0i) q^{51} +(-73135.0 - 12895.7i) q^{53} +(359888. - 301982. i) q^{55} +(-12431.0 - 69193.3i) q^{57} +(149404. + 178053. i) q^{59} +(37107.5 - 210447. i) q^{61} +(-126032. + 45871.8i) q^{63} +(-217689. + 125683. i) q^{65} +(204848. - 244129. i) q^{67} +(17592.8 + 10157.2i) q^{69} +(404511. - 71326.1i) q^{71} +(333804. + 121495. i) q^{73} -275515. i q^{75} +489817. q^{77} +(-120930. + 332253. i) q^{79} +(54304.8 + 307978. i) q^{81} +(-105419. + 182591. i) q^{83} +(226949. + 190433. i) q^{85} +(-99230.8 - 171873. i) q^{87} +(427489. + 1.17452e6i) q^{89} +(-258094. - 45508.9i) q^{91} +(145145. - 121791. i) q^{93} +(-912469. - 1.08034e6i) q^{95} +(-624933. - 744766. i) q^{97} +(246892. - 1.40020e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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
\(3\) −3.50553 + 9.63135i −0.129834 + 0.356717i −0.987528 0.157444i \(-0.949674\pi\)
0.857694 + 0.514161i \(0.171897\pi\)
\(4\) 0 0
\(5\) 35.8010 + 203.037i 0.286408 + 1.62430i 0.700213 + 0.713934i \(0.253088\pi\)
−0.413805 + 0.910366i \(0.635800\pi\)
\(6\) 0 0
\(7\) −107.477 + 186.155i −0.313344 + 0.542727i −0.979084 0.203456i \(-0.934783\pi\)
0.665740 + 0.746184i \(0.268116\pi\)
\(8\) 0 0
\(9\) 477.972 + 401.066i 0.655654 + 0.550159i
\(10\) 0 0
\(11\) −1139.35 1973.42i −0.856014 1.48266i −0.875701 0.482854i \(-0.839600\pi\)
0.0196867 0.999806i \(-0.493733\pi\)
\(12\) 0 0
\(13\) 416.997 + 1145.69i 0.189803 + 0.521479i 0.997695 0.0678507i \(-0.0216141\pi\)
−0.807893 + 0.589330i \(0.799392\pi\)
\(14\) 0 0
\(15\) −2081.03 366.941i −0.616601 0.108723i
\(16\) 0 0
\(17\) 1100.79 923.671i 0.224056 0.188006i −0.523849 0.851811i \(-0.675504\pi\)
0.747905 + 0.663806i \(0.231060\pi\)
\(18\) 0 0
\(19\) −5928.97 + 3448.65i −0.864407 + 0.502792i
\(20\) 0 0
\(21\) −1416.17 1687.72i −0.152917 0.182240i
\(22\) 0 0
\(23\) 344.169 1951.88i 0.0282871 0.160424i −0.967392 0.253283i \(-0.918490\pi\)
0.995679 + 0.0928592i \(0.0296006\pi\)
\(24\) 0 0
\(25\) −25259.8 + 9193.81i −1.61663 + 0.588404i
\(26\) 0 0
\(27\) −12009.2 + 6933.50i −0.610130 + 0.352258i
\(28\) 0 0
\(29\) −12446.4 + 14833.0i −0.510327 + 0.608184i −0.958265 0.285880i \(-0.907714\pi\)
0.447938 + 0.894064i \(0.352158\pi\)
\(30\) 0 0
\(31\) −16009.5 9243.09i −0.537394 0.310265i 0.206628 0.978420i \(-0.433751\pi\)
−0.744022 + 0.668155i \(0.767084\pi\)
\(32\) 0 0
\(33\) 23000.8 4055.65i 0.640030 0.112855i
\(34\) 0 0
\(35\) −41644.3 15157.3i −0.971296 0.353523i
\(36\) 0 0
\(37\) 74669.7i 1.47414i −0.675815 0.737071i \(-0.736208\pi\)
0.675815 0.737071i \(-0.263792\pi\)
\(38\) 0 0
\(39\) −12496.3 −0.210663
\(40\) 0 0
\(41\) −18646.0 + 51229.4i −0.270541 + 0.743306i 0.727803 + 0.685786i \(0.240542\pi\)
−0.998344 + 0.0575200i \(0.981681\pi\)
\(42\) 0 0
\(43\) 14851.6 + 84227.4i 0.186796 + 1.05937i 0.923627 + 0.383293i \(0.125210\pi\)
−0.736831 + 0.676077i \(0.763679\pi\)
\(44\) 0 0
\(45\) −64319.6 + 111405.i −0.705839 + 1.22255i
\(46\) 0 0
\(47\) −62976.8 52843.8i −0.606579 0.508980i 0.286974 0.957938i \(-0.407351\pi\)
−0.893553 + 0.448958i \(0.851795\pi\)
\(48\) 0 0
\(49\) 35721.9 + 61872.2i 0.303631 + 0.525905i
\(50\) 0 0
\(51\) 5037.36 + 13840.0i 0.0379745 + 0.104334i
\(52\) 0 0
\(53\) −73135.0 12895.7i −0.491244 0.0866196i −0.0774616 0.996995i \(-0.524682\pi\)
−0.413783 + 0.910376i \(0.635793\pi\)
\(54\) 0 0
\(55\) 359888. 301982.i 2.16312 1.81507i
\(56\) 0 0
\(57\) −12431.0 69193.3i −0.0671248 0.373628i
\(58\) 0 0
\(59\) 149404. + 178053.i 0.727454 + 0.866946i 0.995332 0.0965066i \(-0.0307669\pi\)
−0.267878 + 0.963453i \(0.586322\pi\)
\(60\) 0 0
\(61\) 37107.5 210447.i 0.163483 0.927157i −0.787132 0.616784i \(-0.788435\pi\)
0.950615 0.310373i \(-0.100454\pi\)
\(62\) 0 0
\(63\) −126032. + 45871.8i −0.504032 + 0.183453i
\(64\) 0 0
\(65\) −217689. + 125683.i −0.792677 + 0.457652i
\(66\) 0 0
\(67\) 204848. 244129.i 0.681095 0.811698i −0.309153 0.951012i \(-0.600046\pi\)
0.990248 + 0.139315i \(0.0444900\pi\)
\(68\) 0 0
\(69\) 17592.8 + 10157.2i 0.0535534 + 0.0309190i
\(70\) 0 0
\(71\) 404511. 71326.1i 1.13020 0.199285i 0.422884 0.906184i \(-0.361018\pi\)
0.707314 + 0.706899i \(0.249907\pi\)
\(72\) 0 0
\(73\) 333804. + 121495.i 0.858070 + 0.312312i 0.733326 0.679877i \(-0.237967\pi\)
0.124744 + 0.992189i \(0.460189\pi\)
\(74\) 0 0
\(75\) 275515.i 0.653073i
\(76\) 0 0
\(77\) 489817. 1.07291
\(78\) 0 0
\(79\) −120930. + 332253.i −0.245275 + 0.673889i 0.754569 + 0.656221i \(0.227846\pi\)
−0.999844 + 0.0176674i \(0.994376\pi\)
\(80\) 0 0
\(81\) 54304.8 + 307978.i 0.102184 + 0.579514i
\(82\) 0 0
\(83\) −105419. + 182591.i −0.184367 + 0.319333i −0.943363 0.331762i \(-0.892357\pi\)
0.758996 + 0.651095i \(0.225690\pi\)
\(84\) 0 0
\(85\) 226949. + 190433.i 0.369549 + 0.310088i
\(86\) 0 0
\(87\) −99230.8 171873.i −0.150692 0.261005i
\(88\) 0 0
\(89\) 427489. + 1.17452e6i 0.606394 + 1.66606i 0.738039 + 0.674758i \(0.235752\pi\)
−0.131645 + 0.991297i \(0.542026\pi\)
\(90\) 0 0
\(91\) −258094. 45508.9i −0.342494 0.0603910i
\(92\) 0 0
\(93\) 145145. 121791.i 0.180449 0.151414i
\(94\) 0 0
\(95\) −912469. 1.08034e6i −1.06426 1.26005i
\(96\) 0 0
\(97\) −624933. 744766.i −0.684728 0.816027i 0.305979 0.952038i \(-0.401016\pi\)
−0.990707 + 0.136011i \(0.956572\pi\)
\(98\) 0 0
\(99\) 246892. 1.40020e6i 0.254450 1.44306i
\(100\) 0 0
\(101\) 1.43100e6 520841.i 1.38891 0.505523i 0.464045 0.885811i \(-0.346397\pi\)
0.924868 + 0.380288i \(0.124175\pi\)
\(102\) 0 0
\(103\) −1.47197e6 + 849843.i −1.34706 + 0.777727i −0.987832 0.155522i \(-0.950294\pi\)
−0.359230 + 0.933249i \(0.616961\pi\)
\(104\) 0 0
\(105\) 291970. 347957.i 0.252215 0.300578i
\(106\) 0 0
\(107\) −1.38169e6 797721.i −1.12787 0.651178i −0.184474 0.982837i \(-0.559058\pi\)
−0.943399 + 0.331659i \(0.892392\pi\)
\(108\) 0 0
\(109\) −2.01591e6 + 355460.i −1.55665 + 0.274480i −0.884717 0.466129i \(-0.845648\pi\)
−0.671936 + 0.740609i \(0.734537\pi\)
\(110\) 0 0
\(111\) 719171. + 261757.i 0.525851 + 0.191394i
\(112\) 0 0
\(113\) 2.71799e6i 1.88370i 0.336032 + 0.941850i \(0.390915\pi\)
−0.336032 + 0.941850i \(0.609085\pi\)
\(114\) 0 0
\(115\) 408626. 0.268679
\(116\) 0 0
\(117\) −260184. + 714851.i −0.162452 + 0.446332i
\(118\) 0 0
\(119\) 53637.1 + 304191.i 0.0318291 + 0.180512i
\(120\) 0 0
\(121\) −1.71048e6 + 2.96264e6i −0.965521 + 1.67233i
\(122\) 0 0
\(123\) −428045. 359172.i −0.230024 0.193013i
\(124\) 0 0
\(125\) −1.16031e6 2.00972e6i −0.594081 1.02898i
\(126\) 0 0
\(127\) 404171. + 1.11045e6i 0.197312 + 0.542111i 0.998407 0.0564269i \(-0.0179708\pi\)
−0.801094 + 0.598538i \(0.795749\pi\)
\(128\) 0 0
\(129\) −863286. 152221.i −0.402148 0.0709095i
\(130\) 0 0
\(131\) 804567. 675112.i 0.357889 0.300305i −0.446060 0.895003i \(-0.647173\pi\)
0.803949 + 0.594699i \(0.202729\pi\)
\(132\) 0 0
\(133\) −4758.43 1.47436e6i −0.00202260 0.626684i
\(134\) 0 0
\(135\) −1.83770e6 2.19009e6i −0.746919 0.890144i
\(136\) 0 0
\(137\) −665784. + 3.77585e6i −0.258923 + 1.46843i 0.526874 + 0.849944i \(0.323364\pi\)
−0.785797 + 0.618484i \(0.787747\pi\)
\(138\) 0 0
\(139\) 3.02038e6 1.09933e6i 1.12465 0.409339i 0.288302 0.957540i \(-0.406909\pi\)
0.836347 + 0.548201i \(0.184687\pi\)
\(140\) 0 0
\(141\) 729725. 421307.i 0.260316 0.150294i
\(142\) 0 0
\(143\) 1.78582e6 2.12826e6i 0.610702 0.727807i
\(144\) 0 0
\(145\) −3.45725e6 1.99604e6i −1.13403 0.654735i
\(146\) 0 0
\(147\) −721137. + 127156.i −0.227021 + 0.0400299i
\(148\) 0 0
\(149\) 1.38896e6 + 505541.i 0.419887 + 0.152826i 0.543318 0.839527i \(-0.317168\pi\)
−0.123432 + 0.992353i \(0.539390\pi\)
\(150\) 0 0
\(151\) 1.72947e6i 0.502321i 0.967945 + 0.251161i \(0.0808122\pi\)
−0.967945 + 0.251161i \(0.919188\pi\)
\(152\) 0 0
\(153\) 896600. 0.250337
\(154\) 0 0
\(155\) 1.30354e6 3.58144e6i 0.350049 0.961751i
\(156\) 0 0
\(157\) 598687. + 3.39532e6i 0.154704 + 0.877369i 0.959056 + 0.283216i \(0.0914014\pi\)
−0.804352 + 0.594153i \(0.797488\pi\)
\(158\) 0 0
\(159\) 380579. 659183.i 0.0946790 0.163989i
\(160\) 0 0
\(161\) 326363. + 273851.i 0.0782030 + 0.0656201i
\(162\) 0 0
\(163\) 459958. + 796671.i 0.106208 + 0.183957i 0.914231 0.405194i \(-0.132796\pi\)
−0.808023 + 0.589150i \(0.799463\pi\)
\(164\) 0 0
\(165\) 1.64690e6 + 4.52482e6i 0.366619 + 1.00728i
\(166\) 0 0
\(167\) 8.43458e6 + 1.48724e6i 1.81098 + 0.319325i 0.973767 0.227548i \(-0.0730709\pi\)
0.837215 + 0.546873i \(0.184182\pi\)
\(168\) 0 0
\(169\) 2.55883e6 2.14712e6i 0.530129 0.444831i
\(170\) 0 0
\(171\) −4.21702e6 729549.i −0.843368 0.145904i
\(172\) 0 0
\(173\) 951553. + 1.13402e6i 0.183778 + 0.219019i 0.850066 0.526676i \(-0.176562\pi\)
−0.666287 + 0.745695i \(0.732118\pi\)
\(174\) 0 0
\(175\) 1.00337e6 5.69037e6i 0.187217 1.06176i
\(176\) 0 0
\(177\) −2.23863e6 + 814793.i −0.403703 + 0.146936i
\(178\) 0 0
\(179\) −3.21971e6 + 1.85890e6i −0.561381 + 0.324113i −0.753699 0.657219i \(-0.771733\pi\)
0.192319 + 0.981333i \(0.438399\pi\)
\(180\) 0 0
\(181\) 170137. 202762.i 0.0286922 0.0341940i −0.751508 0.659724i \(-0.770673\pi\)
0.780200 + 0.625530i \(0.215117\pi\)
\(182\) 0 0
\(183\) 1.89681e6 + 1.09512e6i 0.309507 + 0.178694i
\(184\) 0 0
\(185\) 1.51608e7 2.67325e6i 2.39445 0.422206i
\(186\) 0 0
\(187\) −3.07698e6 1.11993e6i −0.470544 0.171264i
\(188\) 0 0
\(189\) 2.98077e6i 0.441512i
\(190\) 0 0
\(191\) −1.12582e6 −0.161573 −0.0807863 0.996731i \(-0.525743\pi\)
−0.0807863 + 0.996731i \(0.525743\pi\)
\(192\) 0 0
\(193\) 3.74939e6 1.03014e7i 0.521541 1.43292i −0.347263 0.937768i \(-0.612889\pi\)
0.868804 0.495155i \(-0.164889\pi\)
\(194\) 0 0
\(195\) −447381. 2.53722e6i −0.0603356 0.342180i
\(196\) 0 0
\(197\) −3.83343e6 + 6.63970e6i −0.501406 + 0.868460i 0.498593 + 0.866836i \(0.333850\pi\)
−0.999999 + 0.00162394i \(0.999483\pi\)
\(198\) 0 0
\(199\) 2.40858e6 + 2.02104e6i 0.305634 + 0.256458i 0.782685 0.622418i \(-0.213850\pi\)
−0.477050 + 0.878876i \(0.658294\pi\)
\(200\) 0 0
\(201\) 1.63319e6 + 2.82876e6i 0.201117 + 0.348344i
\(202\) 0 0
\(203\) −1.42355e6 3.91116e6i −0.170170 0.467539i
\(204\) 0 0
\(205\) −1.10690e7 1.95177e6i −1.28484 0.226551i
\(206\) 0 0
\(207\) 947337. 794910.i 0.106805 0.0896204i
\(208\) 0 0
\(209\) 1.35608e7 + 7.77111e6i 1.48542 + 0.851225i
\(210\) 0 0
\(211\) 5.01952e6 + 5.98203e6i 0.534337 + 0.636797i 0.963908 0.266235i \(-0.0857798\pi\)
−0.429572 + 0.903033i \(0.641335\pi\)
\(212\) 0 0
\(213\) −731055. + 4.14602e6i −0.0756504 + 0.429035i
\(214\) 0 0
\(215\) −1.65696e7 + 6.03084e6i −1.66724 + 0.606824i
\(216\) 0 0
\(217\) 3.44130e6 1.98684e6i 0.336778 0.194439i
\(218\) 0 0
\(219\) −2.34032e6 + 2.78908e6i −0.222814 + 0.265539i
\(220\) 0 0
\(221\) 1.51727e6 + 875994.i 0.140567 + 0.0811567i
\(222\) 0 0
\(223\) −5.38996e6 + 950395.i −0.486039 + 0.0857018i −0.411297 0.911501i \(-0.634924\pi\)
−0.0747414 + 0.997203i \(0.523813\pi\)
\(224\) 0 0
\(225\) −1.57608e7 5.73647e6i −1.38366 0.503613i
\(226\) 0 0
\(227\) 4.70422e6i 0.402170i 0.979574 + 0.201085i \(0.0644468\pi\)
−0.979574 + 0.201085i \(0.935553\pi\)
\(228\) 0 0
\(229\) −1.32193e7 −1.10078 −0.550391 0.834907i \(-0.685521\pi\)
−0.550391 + 0.834907i \(0.685521\pi\)
\(230\) 0 0
\(231\) −1.71707e6 + 4.71761e6i −0.139300 + 0.382724i
\(232\) 0 0
\(233\) −444687. 2.52195e6i −0.0351550 0.199374i 0.962172 0.272443i \(-0.0878317\pi\)
−0.997327 + 0.0730693i \(0.976721\pi\)
\(234\) 0 0
\(235\) 8.47464e6 1.46785e7i 0.653007 1.13104i
\(236\) 0 0
\(237\) −2.77613e6 2.32945e6i −0.208542 0.174988i
\(238\) 0 0
\(239\) 1.07823e7 + 1.86756e7i 0.789804 + 1.36798i 0.926087 + 0.377310i \(0.123151\pi\)
−0.136283 + 0.990670i \(0.543516\pi\)
\(240\) 0 0
\(241\) −8.41303e6 2.31146e7i −0.601037 1.65134i −0.749177 0.662370i \(-0.769551\pi\)
0.148139 0.988966i \(-0.452672\pi\)
\(242\) 0 0
\(243\) −1.31121e7 2.31201e6i −0.913803 0.161128i
\(244\) 0 0
\(245\) −1.12835e7 + 9.46797e6i −0.767265 + 0.643812i
\(246\) 0 0
\(247\) −6.42345e6 5.35468e6i −0.426263 0.355339i
\(248\) 0 0
\(249\) −1.38905e6 1.65540e6i −0.0899744 0.107227i
\(250\) 0 0
\(251\) −682498. + 3.87064e6i −0.0431599 + 0.244772i −0.998753 0.0499162i \(-0.984105\pi\)
0.955594 + 0.294688i \(0.0952157\pi\)
\(252\) 0 0
\(253\) −4.24401e6 + 1.54469e6i −0.262069 + 0.0953852i
\(254\) 0 0
\(255\) −2.62970e6 + 1.51826e6i −0.158594 + 0.0915642i
\(256\) 0 0
\(257\) 8.65124e6 1.03101e7i 0.509658 0.607387i −0.448445 0.893810i \(-0.648022\pi\)
0.958103 + 0.286424i \(0.0924665\pi\)
\(258\) 0 0
\(259\) 1.39002e7 + 8.02527e6i 0.800057 + 0.461913i
\(260\) 0 0
\(261\) −1.18980e7 + 2.09794e6i −0.669196 + 0.117997i
\(262\) 0 0
\(263\) −3.13484e6 1.14099e6i −0.172325 0.0627211i 0.254417 0.967095i \(-0.418116\pi\)
−0.426742 + 0.904374i \(0.640339\pi\)
\(264\) 0 0
\(265\) 1.53108e7i 0.822736i
\(266\) 0 0
\(267\) −1.28108e7 −0.673041
\(268\) 0 0
\(269\) 1.54529e6 4.24565e6i 0.0793876 0.218116i −0.893649 0.448767i \(-0.851863\pi\)
0.973037 + 0.230651i \(0.0740856\pi\)
\(270\) 0 0
\(271\) 735236. + 4.16973e6i 0.0369419 + 0.209508i 0.997692 0.0679092i \(-0.0216328\pi\)
−0.960750 + 0.277417i \(0.910522\pi\)
\(272\) 0 0
\(273\) 1.34307e6 2.32626e6i 0.0660100 0.114333i
\(274\) 0 0
\(275\) 4.69231e7 + 3.93732e7i 2.25626 + 1.89323i
\(276\) 0 0
\(277\) 258430. + 447613.i 0.0121591 + 0.0210603i 0.872041 0.489433i \(-0.162796\pi\)
−0.859882 + 0.510493i \(0.829463\pi\)
\(278\) 0 0
\(279\) −3.94500e6 1.08388e7i −0.181650 0.499079i
\(280\) 0 0
\(281\) −1.21863e7 2.14877e6i −0.549226 0.0968434i −0.107853 0.994167i \(-0.534397\pi\)
−0.441373 + 0.897323i \(0.645509\pi\)
\(282\) 0 0
\(283\) −1.84825e7 + 1.55087e7i −0.815458 + 0.684250i −0.951904 0.306397i \(-0.900876\pi\)
0.136446 + 0.990648i \(0.456432\pi\)
\(284\) 0 0
\(285\) 1.36038e7 5.00116e6i 0.587659 0.216041i
\(286\) 0 0
\(287\) −7.53262e6 8.97703e6i −0.318640 0.379741i
\(288\) 0 0
\(289\) −3.83288e6 + 2.17373e7i −0.158793 + 0.900560i
\(290\) 0 0
\(291\) 9.36382e6 3.40815e6i 0.379992 0.138306i
\(292\) 0 0
\(293\) 3.31594e7 1.91446e7i 1.31827 0.761103i 0.334819 0.942282i \(-0.391325\pi\)
0.983450 + 0.181179i \(0.0579914\pi\)
\(294\) 0 0
\(295\) −3.08025e7 + 3.67090e7i −1.19983 + 1.42990i
\(296\) 0 0
\(297\) 2.73654e7 + 1.57994e7i 1.04456 + 0.603077i
\(298\) 0 0
\(299\) 2.37977e6 419617.i 0.0890268 0.0156978i
\(300\) 0 0
\(301\) −1.72756e7 6.28780e6i −0.633481 0.230568i
\(302\) 0 0
\(303\) 1.56083e7i 0.561083i
\(304\) 0 0
\(305\) 4.40571e7 1.55280
\(306\) 0 0
\(307\) 8.53678e6 2.34546e7i 0.295039 0.810612i −0.700271 0.713877i \(-0.746938\pi\)
0.995310 0.0967356i \(-0.0308401\pi\)
\(308\) 0 0
\(309\) −3.02511e6 1.71562e7i −0.102533 0.581496i
\(310\) 0 0
\(311\) 2.79872e7 4.84753e7i 0.930419 1.61153i 0.147814 0.989015i \(-0.452776\pi\)
0.782605 0.622518i \(-0.213890\pi\)
\(312\) 0 0
\(313\) 2.08333e7 + 1.74812e7i 0.679400 + 0.570084i 0.915831 0.401564i \(-0.131533\pi\)
−0.236431 + 0.971648i \(0.575978\pi\)
\(314\) 0 0
\(315\) −1.38257e7 2.39469e7i −0.442341 0.766156i
\(316\) 0 0
\(317\) −1.35836e7 3.73205e7i −0.426418 1.17157i −0.947971 0.318356i \(-0.896869\pi\)
0.521553 0.853219i \(-0.325353\pi\)
\(318\) 0 0
\(319\) 4.34526e7 + 7.66186e6i 1.33858 + 0.236027i
\(320\) 0 0
\(321\) 1.25267e7 1.05111e7i 0.378723 0.317786i
\(322\) 0 0
\(323\) −3.34112e6 + 9.27266e6i −0.0991481 + 0.275167i
\(324\) 0 0
\(325\) −2.10665e7 2.51061e7i −0.613681 0.731356i
\(326\) 0 0
\(327\) 3.64327e6 2.06620e7i 0.104195 0.590921i
\(328\) 0 0
\(329\) 1.66057e7 6.04399e6i 0.466305 0.169721i
\(330\) 0 0
\(331\) −2.70828e7 + 1.56363e7i −0.746810 + 0.431171i −0.824540 0.565804i \(-0.808566\pi\)
0.0777301 + 0.996974i \(0.475233\pi\)
\(332\) 0 0
\(333\) 2.99475e7 3.56900e7i 0.811013 0.966528i
\(334\) 0 0
\(335\) 5.69010e7 + 3.28518e7i 1.51351 + 0.873826i
\(336\) 0 0
\(337\) −5.54959e7 + 9.78543e6i −1.45001 + 0.255676i −0.842526 0.538655i \(-0.818933\pi\)
−0.607485 + 0.794331i \(0.707822\pi\)
\(338\) 0 0
\(339\) −2.61779e7 9.52797e6i −0.671948 0.244569i
\(340\) 0 0
\(341\) 4.21246e7i 1.06236i
\(342\) 0 0
\(343\) −4.06462e7 −1.00725
\(344\) 0 0
\(345\) −1.43245e6 + 3.93563e6i −0.0348837 + 0.0958422i
\(346\) 0 0
\(347\) 1.04601e7 + 5.93222e7i 0.250350 + 1.41980i 0.807732 + 0.589549i \(0.200695\pi\)
−0.557383 + 0.830256i \(0.688194\pi\)
\(348\) 0 0
\(349\) 9.93827e6 1.72136e7i 0.233795 0.404944i −0.725127 0.688615i \(-0.758219\pi\)
0.958922 + 0.283671i \(0.0915523\pi\)
\(350\) 0 0
\(351\) −1.29514e7 1.08675e7i −0.299500 0.251310i
\(352\) 0 0
\(353\) 2.34329e7 + 4.05869e7i 0.532723 + 0.922703i 0.999270 + 0.0382064i \(0.0121644\pi\)
−0.466547 + 0.884496i \(0.654502\pi\)
\(354\) 0 0
\(355\) 2.89637e7 + 7.95772e7i 0.647396 + 1.77870i
\(356\) 0 0
\(357\) −3.11780e6 549752.i −0.0685241 0.0120827i
\(358\) 0 0
\(359\) 3.28167e7 2.75364e7i 0.709269 0.595147i −0.215125 0.976587i \(-0.569016\pi\)
0.924394 + 0.381439i \(0.124571\pi\)
\(360\) 0 0
\(361\) 2.32595e7 4.08939e7i 0.494400 0.869235i
\(362\) 0 0
\(363\) −2.25381e7 2.68598e7i −0.471191 0.561543i
\(364\) 0 0
\(365\) −1.27175e7 + 7.21243e7i −0.261530 + 1.48321i
\(366\) 0 0
\(367\) −1.05165e7 + 3.82769e6i −0.212751 + 0.0774351i −0.446197 0.894935i \(-0.647222\pi\)
0.233446 + 0.972370i \(0.425000\pi\)
\(368\) 0 0
\(369\) −2.94586e7 + 1.70080e7i −0.586319 + 0.338511i
\(370\) 0 0
\(371\) 1.02609e7 1.22285e7i 0.200939 0.239470i
\(372\) 0 0
\(373\) −5.87279e7 3.39066e7i −1.13167 0.653367i −0.187312 0.982300i \(-0.559978\pi\)
−0.944353 + 0.328933i \(0.893311\pi\)
\(374\) 0 0
\(375\) 2.34239e7 4.13026e6i 0.444186 0.0783220i
\(376\) 0 0
\(377\) −2.21841e7 8.07435e6i −0.414017 0.150690i
\(378\) 0 0
\(379\) 8.41232e7i 1.54525i −0.634863 0.772624i \(-0.718944\pi\)
0.634863 0.772624i \(-0.281056\pi\)
\(380\) 0 0
\(381\) −1.21120e7 −0.218998
\(382\) 0 0
\(383\) 1.79448e7 4.93029e7i 0.319405 0.877559i −0.671258 0.741224i \(-0.734246\pi\)
0.990663 0.136335i \(-0.0435322\pi\)
\(384\) 0 0
\(385\) 1.75359e7 + 9.94513e7i 0.307289 + 1.74272i
\(386\) 0 0
\(387\) −2.66821e7 + 4.62148e7i −0.460349 + 0.797348i
\(388\) 0 0
\(389\) −7.17365e7 6.01940e7i −1.21868 1.02260i −0.998892 0.0470508i \(-0.985018\pi\)
−0.219792 0.975547i \(-0.570538\pi\)
\(390\) 0 0
\(391\) −1.42404e6 2.46651e6i −0.0238227 0.0412622i
\(392\) 0 0
\(393\) 3.68181e6 + 1.01157e7i 0.0606574 + 0.166655i
\(394\) 0 0
\(395\) −7.17893e7 1.26584e7i −1.16485 0.205394i
\(396\) 0 0
\(397\) 2.59318e7 2.17593e7i 0.414439 0.347755i −0.411604 0.911363i \(-0.635031\pi\)
0.826043 + 0.563607i \(0.190587\pi\)
\(398\) 0 0
\(399\) 1.42168e7 + 5.12258e6i 0.223811 + 0.0806436i
\(400\) 0 0
\(401\) 2.98098e6 + 3.55259e6i 0.0462301 + 0.0550949i 0.788664 0.614824i \(-0.210773\pi\)
−0.742434 + 0.669919i \(0.766329\pi\)
\(402\) 0 0
\(403\) 3.91380e6 2.21963e7i 0.0597975 0.339129i
\(404\) 0 0
\(405\) −6.05868e7 + 2.20518e7i −0.912039 + 0.331955i
\(406\) 0 0
\(407\) −1.47355e8 + 8.50753e7i −2.18565 + 1.26189i
\(408\) 0 0
\(409\) 3.72772e7 4.44252e7i 0.544845 0.649321i −0.421422 0.906865i \(-0.638469\pi\)
0.966267 + 0.257544i \(0.0829132\pi\)
\(410\) 0 0
\(411\) −3.40326e7 1.96487e7i −0.490196 0.283015i
\(412\) 0 0
\(413\) −4.92029e7 + 8.67580e6i −0.698459 + 0.123157i
\(414\) 0 0
\(415\) −4.08468e7 1.48670e7i −0.571497 0.208008i
\(416\) 0 0
\(417\) 3.29440e7i 0.454327i
\(418\) 0 0
\(419\) 9.49195e7 1.29037 0.645184 0.764028i \(-0.276781\pi\)
0.645184 + 0.764028i \(0.276781\pi\)
\(420\) 0 0
\(421\) 3.98581e7 1.09509e8i 0.534159 1.46759i −0.319918 0.947445i \(-0.603655\pi\)
0.854078 0.520145i \(-0.174122\pi\)
\(422\) 0 0
\(423\) −8.90729e6 5.05158e7i −0.117686 0.667430i
\(424\) 0 0
\(425\) −1.93136e7 + 3.34522e7i −0.251592 + 0.435770i
\(426\) 0 0
\(427\) 3.51877e7 + 2.95260e7i 0.451967 + 0.379246i
\(428\) 0 0
\(429\) 1.42378e7 + 2.46605e7i 0.180331 + 0.312342i
\(430\) 0 0
\(431\) 4.67963e7 + 1.28572e8i 0.584493 + 1.60588i 0.780415 + 0.625262i \(0.215008\pi\)
−0.195921 + 0.980620i \(0.562770\pi\)
\(432\) 0 0
\(433\) 6.81832e7 + 1.20225e7i 0.839873 + 0.148092i 0.577006 0.816740i \(-0.304221\pi\)
0.262867 + 0.964832i \(0.415332\pi\)
\(434\) 0 0
\(435\) 3.13441e7 2.63008e7i 0.380792 0.319522i
\(436\) 0 0
\(437\) 4.69079e6 + 1.27596e7i 0.0562085 + 0.152894i
\(438\) 0 0
\(439\) −7.52592e7 8.96904e7i −0.889541 1.06011i −0.997820 0.0659929i \(-0.978979\pi\)
0.108279 0.994121i \(-0.465466\pi\)
\(440\) 0 0
\(441\) −7.74076e6 + 4.39000e7i −0.0902543 + 0.511858i
\(442\) 0 0
\(443\) −3.81669e7 + 1.38916e7i −0.439012 + 0.159787i −0.552064 0.833802i \(-0.686160\pi\)
0.113052 + 0.993589i \(0.463937\pi\)
\(444\) 0 0
\(445\) −2.23166e8 + 1.28845e8i −2.53250 + 1.46214i
\(446\) 0 0
\(447\) −9.73810e6 + 1.16054e7i −0.109031 + 0.129939i
\(448\) 0 0
\(449\) 6.98851e7 + 4.03482e7i 0.772050 + 0.445743i 0.833605 0.552360i \(-0.186273\pi\)
−0.0615553 + 0.998104i \(0.519606\pi\)
\(450\) 0 0
\(451\) 1.22342e8 2.15721e7i 1.33366 0.235160i
\(452\) 0 0
\(453\) −1.66571e7 6.06269e6i −0.179186 0.0652185i
\(454\) 0 0
\(455\) 5.40320e7i 0.573610i
\(456\) 0 0
\(457\) 7.81939e7 0.819265 0.409632 0.912251i \(-0.365657\pi\)
0.409632 + 0.912251i \(0.365657\pi\)
\(458\) 0 0
\(459\) −6.81529e6 + 1.87249e7i −0.0704768 + 0.193633i
\(460\) 0 0
\(461\) 1.11644e7 + 6.33165e7i 0.113955 + 0.646270i 0.987262 + 0.159101i \(0.0508594\pi\)
−0.873308 + 0.487169i \(0.838029\pi\)
\(462\) 0 0
\(463\) 3.45247e7 5.97986e7i 0.347846 0.602488i −0.638020 0.770020i \(-0.720246\pi\)
0.985867 + 0.167532i \(0.0535798\pi\)
\(464\) 0 0
\(465\) 2.99245e7 + 2.51097e7i 0.297624 + 0.249737i
\(466\) 0 0
\(467\) −6.59965e7 1.14309e8i −0.647993 1.12236i −0.983602 0.180355i \(-0.942275\pi\)
0.335609 0.942001i \(-0.391058\pi\)
\(468\) 0 0
\(469\) 2.34294e7 + 6.43718e7i 0.227114 + 0.623989i
\(470\) 0 0
\(471\) −3.48003e7 6.13623e6i −0.333058 0.0587271i
\(472\) 0 0
\(473\) 1.49295e8 1.25273e8i 1.41079 1.18379i
\(474\) 0 0
\(475\) 1.18058e8 1.41622e8i 1.10158 1.32145i
\(476\) 0 0
\(477\) −2.97845e7 3.54957e7i −0.274432 0.327055i
\(478\) 0 0
\(479\) −1.33139e6 + 7.55068e6i −0.0121143 + 0.0687036i −0.990266 0.139191i \(-0.955550\pi\)
0.978151 + 0.207894i \(0.0666610\pi\)
\(480\) 0 0
\(481\) 8.55483e7 3.11370e7i 0.768734 0.279796i
\(482\) 0 0
\(483\) −3.78163e6 + 2.18333e6i −0.0335612 + 0.0193766i
\(484\) 0 0
\(485\) 1.28842e8 1.53548e8i 1.12936 1.34592i
\(486\) 0 0
\(487\) −1.63330e8 9.42985e7i −1.41409 0.816428i −0.418324 0.908298i \(-0.637382\pi\)
−0.995771 + 0.0918702i \(0.970716\pi\)
\(488\) 0 0
\(489\) −9.28541e6 + 1.63727e6i −0.0794099 + 0.0140021i
\(490\) 0 0
\(491\) −5.76956e7 2.09995e7i −0.487414 0.177404i 0.0866105 0.996242i \(-0.472396\pi\)
−0.574025 + 0.818838i \(0.694619\pi\)
\(492\) 0 0
\(493\) 2.78243e7i 0.232212i
\(494\) 0 0
\(495\) 2.93131e8 2.41683
\(496\) 0 0
\(497\) −3.01978e7 + 8.29678e7i −0.245984 + 0.675834i
\(498\) 0 0
\(499\) 1.22895e7 + 6.96975e7i 0.0989087 + 0.560939i 0.993479 + 0.114012i \(0.0363703\pi\)
−0.894571 + 0.446927i \(0.852519\pi\)
\(500\) 0 0
\(501\) −4.38918e7 + 7.60229e7i −0.349036 + 0.604549i
\(502\) 0 0
\(503\) 1.78546e8 + 1.49818e8i 1.40296 + 1.17722i 0.959767 + 0.280797i \(0.0905986\pi\)
0.443193 + 0.896426i \(0.353846\pi\)
\(504\) 0 0
\(505\) 1.56981e8 + 2.71900e8i 1.21892 + 2.11123i
\(506\) 0 0
\(507\) 1.17096e7 + 3.21718e7i 0.0898498 + 0.246860i
\(508\) 0 0
\(509\) −1.34170e7 2.36577e6i −0.101742 0.0179399i 0.122545 0.992463i \(-0.460894\pi\)
−0.224287 + 0.974523i \(0.572005\pi\)
\(510\) 0 0
\(511\) −5.84931e7 + 4.90816e7i −0.438371 + 0.367837i
\(512\) 0 0
\(513\) 4.72908e7 8.25240e7i 0.350287 0.611263i
\(514\) 0 0
\(515\) −2.25248e8 2.68440e8i −1.64907 1.96529i
\(516\) 0 0
\(517\) −3.25302e7 + 1.84488e8i −0.235404 + 1.33504i
\(518\) 0 0
\(519\) −1.42578e7 + 5.18942e6i −0.101988 + 0.0371207i
\(520\) 0 0
\(521\) −9.00631e7 + 5.19979e7i −0.636845 + 0.367682i −0.783398 0.621520i \(-0.786515\pi\)
0.146553 + 0.989203i \(0.453182\pi\)
\(522\) 0 0
\(523\) −4.39612e7 + 5.23909e7i −0.307301 + 0.366227i −0.897488 0.441040i \(-0.854610\pi\)
0.590187 + 0.807267i \(0.299054\pi\)
\(524\) 0 0
\(525\) 5.12887e7 + 2.96115e7i 0.354441 + 0.204636i
\(526\) 0 0
\(527\) −2.61607e7 + 4.61283e6i −0.178738 + 0.0315163i
\(528\) 0 0
\(529\) 1.35417e8 + 4.92877e7i 0.914757 + 0.332944i
\(530\) 0 0
\(531\) 1.45025e8i 0.968633i
\(532\) 0 0
\(533\) −6.64683e7 −0.438968
\(534\) 0 0
\(535\) 1.12501e8 3.09095e8i 0.734677 2.01851i
\(536\) 0 0
\(537\) −6.61695e6 3.75266e7i −0.0427302 0.242335i
\(538\) 0 0
\(539\) 8.13999e7 1.40989e8i 0.519825 0.900364i
\(540\) 0 0
\(541\) 1.47761e7 + 1.23986e7i 0.0933185 + 0.0783035i 0.688253 0.725470i \(-0.258378\pi\)
−0.594935 + 0.803774i \(0.702822\pi\)
\(542\) 0 0
\(543\) 1.35645e6 + 2.34944e6i 0.00847235 + 0.0146745i
\(544\) 0 0
\(545\) −1.44343e8 3.96580e8i −0.891675 2.44986i
\(546\) 0 0
\(547\) 4.56979e7 + 8.05778e6i 0.279212 + 0.0492327i 0.311501 0.950246i \(-0.399168\pi\)
−0.0322883 + 0.999479i \(0.510279\pi\)
\(548\) 0 0
\(549\) 1.02140e8 8.57053e7i 0.617273 0.517953i
\(550\) 0 0
\(551\) 2.26402e7 1.30868e8i 0.135340 0.782307i
\(552\) 0 0
\(553\) −4.88536e7 5.82214e7i −0.288882 0.344277i
\(554\) 0 0
\(555\) −2.73994e7 + 1.55390e8i −0.160274 + 0.908957i
\(556\) 0 0
\(557\) −1.37459e8 + 5.00312e7i −0.795443 + 0.289518i −0.707597 0.706616i \(-0.750221\pi\)
−0.0878464 + 0.996134i \(0.527998\pi\)
\(558\) 0 0
\(559\) −9.03053e7 + 5.21378e7i −0.516985 + 0.298481i
\(560\) 0 0
\(561\) 2.15729e7 2.57095e7i 0.122185 0.145615i
\(562\) 0 0
\(563\) 2.82392e8 + 1.63039e8i 1.58244 + 0.913624i 0.994502 + 0.104720i \(0.0333945\pi\)
0.587941 + 0.808904i \(0.299939\pi\)
\(564\) 0 0
\(565\) −5.51853e8 + 9.73066e7i −3.05969 + 0.539507i
\(566\) 0 0
\(567\) −6.31683e7 2.29914e7i −0.346537 0.126129i
\(568\) 0 0
\(569\) 2.75490e7i 0.149544i 0.997201 + 0.0747719i \(0.0238229\pi\)
−0.997201 + 0.0747719i \(0.976177\pi\)
\(570\) 0 0
\(571\) −4.86462e7 −0.261301 −0.130650 0.991429i \(-0.541707\pi\)
−0.130650 + 0.991429i \(0.541707\pi\)
\(572\) 0 0
\(573\) 3.94658e6 1.08431e7i 0.0209777 0.0576357i
\(574\) 0 0
\(575\) 9.25158e6 + 5.24683e7i 0.0486645 + 0.275990i
\(576\) 0 0
\(577\) 5.93258e7 1.02755e8i 0.308828 0.534905i −0.669278 0.743012i \(-0.733397\pi\)
0.978106 + 0.208106i \(0.0667300\pi\)
\(578\) 0 0
\(579\) 8.60725e7 + 7.22234e7i 0.443434 + 0.372085i
\(580\) 0 0
\(581\) −2.26602e7 3.92486e7i −0.115541 0.200122i
\(582\) 0 0
\(583\) 5.78781e7 + 1.59019e8i 0.292085 + 0.802496i
\(584\) 0 0
\(585\) −1.54456e8 2.72348e7i −0.771504 0.136037i
\(586\) 0 0
\(587\) −2.47095e8 + 2.07337e8i −1.22166 + 1.02509i −0.222920 + 0.974837i \(0.571559\pi\)
−0.998736 + 0.0502546i \(0.983997\pi\)
\(588\) 0 0
\(589\) 1.26796e8 409229.i 0.620526 0.00200272i
\(590\) 0 0
\(591\) −5.05111e7 6.01968e7i −0.244695 0.291616i
\(592\) 0 0
\(593\) −1.35949e7 + 7.71004e7i −0.0651945 + 0.369736i 0.934703 + 0.355429i \(0.115665\pi\)
−0.999898 + 0.0143071i \(0.995446\pi\)
\(594\) 0 0
\(595\) −5.98419e7 + 2.17807e7i −0.284089 + 0.103400i
\(596\) 0 0
\(597\) −2.79087e7 + 1.61131e7i −0.131165 + 0.0757279i
\(598\) 0 0
\(599\) −5.51373e7 + 6.57101e7i −0.256546 + 0.305740i −0.878909 0.476989i \(-0.841728\pi\)
0.622363 + 0.782728i \(0.286173\pi\)
\(600\) 0 0
\(601\) 1.79901e8 + 1.03866e8i 0.828726 + 0.478465i 0.853416 0.521230i \(-0.174527\pi\)
−0.0246905 + 0.999695i \(0.507860\pi\)
\(602\) 0 0
\(603\) 1.95823e8 3.45290e7i 0.893126 0.157482i
\(604\) 0 0
\(605\) −6.62763e8 2.41226e8i −2.99290 1.08933i
\(606\) 0 0
\(607\) 4.34484e7i 0.194271i 0.995271 + 0.0971354i \(0.0309680\pi\)
−0.995271 + 0.0971354i \(0.969032\pi\)
\(608\) 0 0
\(609\) 4.26601e7 0.188873
\(610\) 0 0
\(611\) 3.42815e7 9.41876e7i 0.150292 0.412924i
\(612\) 0 0
\(613\) 7.53731e7 + 4.27462e8i 0.327216 + 1.85573i 0.493621 + 0.869677i \(0.335673\pi\)
−0.166404 + 0.986058i \(0.553216\pi\)
\(614\) 0 0
\(615\) 5.76010e7 9.97678e7i 0.247631 0.428909i
\(616\) 0 0
\(617\) 1.67608e8 + 1.40640e8i 0.713576 + 0.598762i 0.925600 0.378503i \(-0.123561\pi\)
−0.212024 + 0.977264i \(0.568005\pi\)
\(618\) 0 0
\(619\) −3.04638e7 5.27649e7i −0.128444 0.222471i 0.794630 0.607094i \(-0.207665\pi\)
−0.923074 + 0.384623i \(0.874331\pi\)
\(620\) 0 0
\(621\) 9.40018e6 + 2.58268e7i 0.0392520 + 0.107844i
\(622\) 0 0
\(623\) −2.64588e8 4.66540e7i −1.09422 0.192941i
\(624\) 0 0
\(625\) 4.47590e7 3.75572e7i 0.183333 0.153834i
\(626\) 0 0
\(627\) −1.22384e8 + 1.03367e8i −0.496504 + 0.419354i
\(628\) 0 0
\(629\) −6.89703e7 8.21956e7i −0.277147 0.330291i
\(630\) 0 0
\(631\) 3.69370e6 2.09480e7i 0.0147019 0.0833786i −0.976574 0.215182i \(-0.930966\pi\)
0.991276 + 0.131803i \(0.0420767\pi\)
\(632\) 0 0
\(633\) −7.52111e7 + 2.73746e7i −0.296532 + 0.107929i
\(634\) 0 0
\(635\) −2.10993e8 + 1.21817e8i −0.824039 + 0.475759i
\(636\) 0 0
\(637\) −5.59904e7 + 6.67267e7i −0.216618 + 0.258156i
\(638\) 0 0
\(639\) 2.21951e8 + 1.28144e8i 0.850658 + 0.491128i
\(640\) 0 0
\(641\) 1.08716e8 1.91695e7i 0.412780 0.0727842i 0.0365980 0.999330i \(-0.488348\pi\)
0.376182 + 0.926546i \(0.377237\pi\)
\(642\) 0 0
\(643\) −4.29688e8 1.56394e8i −1.61629 0.588282i −0.633622 0.773643i \(-0.718433\pi\)
−0.982671 + 0.185360i \(0.940655\pi\)
\(644\) 0 0
\(645\) 1.80729e8i 0.673517i
\(646\) 0 0
\(647\) −2.53626e8 −0.936442 −0.468221 0.883611i \(-0.655105\pi\)
−0.468221 + 0.883611i \(0.655105\pi\)
\(648\) 0 0
\(649\) 1.81149e8 4.97702e8i 0.662675 1.82069i
\(650\) 0 0
\(651\) 7.07236e6 + 4.01093e7i 0.0256343 + 0.145379i
\(652\) 0 0
\(653\) 2.62828e8 4.55232e8i 0.943915 1.63491i 0.186006 0.982549i \(-0.440446\pi\)
0.757909 0.652360i \(-0.226221\pi\)
\(654\) 0 0
\(655\) 1.65877e8 + 1.39188e8i 0.590287 + 0.495309i
\(656\) 0 0
\(657\) 1.10822e8 + 1.91949e8i 0.390776 + 0.676844i
\(658\) 0 0
\(659\) −5.84206e7 1.60509e8i −0.204131 0.560847i 0.794809 0.606859i \(-0.207571\pi\)
−0.998941 + 0.0460125i \(0.985349\pi\)
\(660\) 0 0
\(661\) 3.34371e8 + 5.89586e7i 1.15777 + 0.204147i 0.719368 0.694630i \(-0.244432\pi\)
0.438407 + 0.898777i \(0.355543\pi\)
\(662\) 0 0
\(663\) −1.37558e7 + 1.15425e7i −0.0472004 + 0.0396059i
\(664\) 0 0
\(665\) 2.99180e8 5.37497e7i 1.01734 0.182773i
\(666\) 0 0
\(667\) 2.46686e7 + 2.93989e7i 0.0831317 + 0.0990725i
\(668\) 0 0
\(669\) 9.74105e6 5.52442e7i 0.0325333 0.184505i
\(670\) 0 0
\(671\) −4.57579e8 + 1.66545e8i −1.51460 + 0.551270i
\(672\) 0 0
\(673\) 1.87639e8 1.08333e8i 0.615570 0.355400i −0.159572 0.987186i \(-0.551011\pi\)
0.775142 + 0.631787i \(0.217678\pi\)
\(674\) 0 0
\(675\) 2.39604e8 2.85549e8i 0.779082 0.928473i
\(676\) 0 0
\(677\) 1.49801e8 + 8.64877e7i 0.482780 + 0.278733i 0.721574 0.692337i \(-0.243419\pi\)
−0.238794 + 0.971070i \(0.576752\pi\)
\(678\) 0 0
\(679\) 2.05808e8 3.62895e7i 0.657436 0.115924i
\(680\) 0 0
\(681\) −4.53080e7 1.64908e7i −0.143461 0.0522155i
\(682\) 0 0
\(683\) 3.07375e7i 0.0964733i −0.998836 0.0482366i \(-0.984640\pi\)
0.998836 0.0482366i \(-0.0153602\pi\)
\(684\) 0 0
\(685\) −7.90474e8 −2.45932
\(686\) 0 0
\(687\) 4.63406e7 1.27320e8i 0.142919 0.392668i
\(688\) 0 0
\(689\) −1.57226e7 8.91674e7i −0.0480692 0.272614i
\(690\) 0 0
\(691\) 1.00569e8 1.74191e8i 0.304811 0.527949i −0.672408 0.740181i \(-0.734740\pi\)
0.977219 + 0.212232i \(0.0680733\pi\)
\(692\) 0 0
\(693\) 2.34119e8 + 1.96449e8i 0.703456 + 0.590270i
\(694\) 0 0
\(695\) 3.31337e8 + 5.73893e8i 0.986997 + 1.70953i
\(696\) 0 0
\(697\) 2.67939e7 + 7.36155e7i 0.0791292 + 0.217406i
\(698\) 0 0
\(699\) 2.58486e7 + 4.55781e6i 0.0756843 + 0.0133452i
\(700\) 0 0
\(701\) 1.62068e8 1.35991e8i 0.470481 0.394780i −0.376489 0.926421i \(-0.622869\pi\)
0.846970 + 0.531641i \(0.178424\pi\)
\(702\) 0 0
\(703\) 2.57510e8 + 4.42714e8i 0.741188 + 1.27426i
\(704\) 0 0
\(705\) 1.11666e8 + 1.33078e8i 0.318679 + 0.379787i
\(706\) 0 0
\(707\) −5.68419e7 + 3.22367e8i −0.160846 + 0.912204i
\(708\) 0 0
\(709\) 5.78511e8 2.10561e8i 1.62320 0.590798i 0.639215 0.769028i \(-0.279259\pi\)
0.983989 + 0.178230i \(0.0570370\pi\)
\(710\) 0 0
\(711\) −1.91057e8 + 1.10307e8i −0.531562 + 0.306898i
\(712\) 0 0
\(713\) −2.35514e7 + 2.80674e7i −0.0649752 + 0.0774345i
\(714\) 0 0
\(715\) 4.96050e8 + 2.86395e8i 1.35709 + 0.783514i
\(716\) 0 0
\(717\) −2.17669e8 + 3.83809e7i −0.590525 + 0.104126i
\(718\) 0 0
\(719\) −3.18059e8 1.15764e8i −0.855699 0.311449i −0.123337 0.992365i \(-0.539360\pi\)
−0.732362 + 0.680916i \(0.761582\pi\)
\(720\) 0 0
\(721\) 3.65354e8i 0.974784i
\(722\) 0 0
\(723\) 2.52117e8 0.667095
\(724\) 0 0
\(725\) 1.78021e8 4.89108e8i 0.467150 1.28349i
\(726\) 0 0
\(727\) 9.24146e7 + 5.24109e8i 0.240512 + 1.36401i 0.830688 + 0.556738i \(0.187947\pi\)
−0.590176 + 0.807275i \(0.700942\pi\)
\(728\) 0 0
\(729\) −4.57571e7 + 7.92536e7i −0.118107 + 0.204567i
\(730\) 0 0
\(731\) 9.41468e7 + 7.89986e7i 0.241020 + 0.202240i
\(732\) 0 0
\(733\) −9.26237e7 1.60429e8i −0.235185 0.407353i 0.724141 0.689652i \(-0.242236\pi\)
−0.959327 + 0.282299i \(0.908903\pi\)
\(734\) 0 0
\(735\) −5.16348e7 1.41866e8i −0.130041 0.357285i
\(736\) 0 0
\(737\) −7.15163e8 1.26103e8i −1.78650 0.315008i
\(738\) 0 0
\(739\) 4.00561e8 3.36111e8i 0.992512 0.832816i 0.00658219 0.999978i \(-0.497905\pi\)
0.985929 + 0.167162i \(0.0534604\pi\)
\(740\) 0 0
\(741\) 7.40904e7 4.30955e7i 0.182099 0.105920i
\(742\) 0 0
\(743\) 1.81218e8 + 2.15967e8i 0.441809 + 0.526527i 0.940291 0.340373i \(-0.110553\pi\)
−0.498482 + 0.866900i \(0.666109\pi\)
\(744\) 0 0
\(745\) −5.29176e7 + 3.00110e8i −0.127977 + 0.725792i
\(746\) 0 0
\(747\) −1.23618e8 + 4.49933e7i −0.296565 + 0.107941i
\(748\) 0 0
\(749\) 2.97000e8 1.71473e8i 0.706824 0.408085i
\(750\) 0 0
\(751\) 3.23054e8 3.85001e8i 0.762703 0.908954i −0.235313 0.971920i \(-0.575611\pi\)
0.998016 + 0.0629658i \(0.0200559\pi\)
\(752\) 0 0
\(753\) −3.48870e7 2.01420e7i −0.0817106 0.0471756i
\(754\) 0 0
\(755\) −3.51146e8 + 6.19166e7i −0.815920 + 0.143869i
\(756\) 0 0
\(757\) −3.94069e8 1.43429e8i −0.908416 0.330637i −0.154796 0.987946i \(-0.549472\pi\)
−0.753620 + 0.657310i \(0.771694\pi\)
\(758\) 0 0
\(759\) 4.62906e7i 0.105869i
\(760\) 0 0
\(761\) 6.17896e8 1.40204 0.701022 0.713140i \(-0.252728\pi\)
0.701022 + 0.713140i \(0.252728\pi\)
\(762\) 0 0
\(763\) 1.50493e8 4.13477e8i 0.338800 0.930845i
\(764\) 0 0
\(765\) 3.20991e7 + 1.82043e8i 0.0716983 + 0.406622i
\(766\) 0 0
\(767\) −1.41692e8 + 2.45418e8i −0.314021 + 0.543901i
\(768\) 0 0
\(769\) 3.50631e8 + 2.94214e8i 0.771030 + 0.646971i 0.940973 0.338483i \(-0.109914\pi\)
−0.169942 + 0.985454i \(0.554358\pi\)
\(770\) 0 0
\(771\) 6.89735e7 + 1.19466e8i 0.150494 + 0.260663i
\(772\) 0 0
\(773\) −1.56342e8 4.29547e8i −0.338484 0.929977i −0.985825 0.167777i \(-0.946341\pi\)
0.647341 0.762200i \(-0.275881\pi\)
\(774\) 0 0
\(775\) 4.89376e8 + 8.62902e7i 1.05133 + 0.185377i
\(776\) 0 0
\(777\) −1.26022e8 + 1.05745e8i −0.268647 + 0.225422i
\(778\) 0 0
\(779\) −6.61210e7 3.68041e8i −0.139871 0.778545i
\(780\) 0 0
\(781\) −6.01638e8 7.17004e8i −1.26294 1.50511i
\(782\) 0 0
\(783\) 4.66260e7 2.64429e8i 0.0971276 0.550838i
\(784\) 0 0
\(785\) −6.67944e8 + 2.43112e8i −1.38080 + 0.502571i
\(786\) 0 0
\(787\) −6.44389e8 + 3.72038e8i −1.32198 + 0.763244i −0.984044 0.177926i \(-0.943061\pi\)
−0.337933 + 0.941170i \(0.609728\pi\)
\(788\) 0 0
\(789\) 2.19785e7 2.61930e7i 0.0447473 0.0533278i
\(790\) 0 0
\(791\) −5.05968e8 2.92121e8i −1.02234 0.590246i
\(792\) 0 0
\(793\) 2.56581e8 4.52421e7i 0.514522 0.0907242i
\(794\) 0 0
\(795\) 1.47464e8 + 5.36725e7i 0.293484 + 0.106819i
\(796\) 0 0
\(797\) 3.85024e8i 0.760524i 0.924879 + 0.380262i \(0.124166\pi\)
−0.924879 + 0.380262i \(0.875834\pi\)
\(798\) 0 0
\(799\) −1.18134e8 −0.231599
\(800\) 0 0
\(801\) −2.66731e8 + 7.32838e8i −0.519011 + 1.42597i
\(802\) 0 0
\(803\) −1.40561e8 7.97161e8i −0.271468 1.53957i
\(804\) 0 0
\(805\) −4.39179e7 + 7.60681e7i −0.0841887 + 0.145819i
\(806\) 0 0
\(807\) 3.54743e7 + 2.97664e7i 0.0674983 + 0.0566378i
\(808\) 0 0
\(809\) 2.00969e8 + 3.48088e8i 0.379562 + 0.657420i 0.990998 0.133873i \(-0.0427414\pi\)
−0.611437 + 0.791293i \(0.709408\pi\)
\(810\) 0 0
\(811\) 1.75250e8 + 4.81495e8i 0.328545 + 0.902670i 0.988481 + 0.151348i \(0.0483613\pi\)
−0.659936 + 0.751322i \(0.729417\pi\)
\(812\) 0 0
\(813\) −4.27375e7 7.53578e6i −0.0795312 0.0140235i
\(814\) 0 0
\(815\) −1.45287e8 + 1.21910e8i −0.268382 + 0.225200i
\(816\) 0 0
\(817\) −3.78525e8 4.48164e8i −0.694111 0.821808i
\(818\) 0 0
\(819\) −1.05110e8 1.25265e8i −0.191333 0.228022i
\(820\) 0 0
\(821\) −4.47379e7 + 2.53721e8i −0.0808437 + 0.458487i 0.917333 + 0.398122i \(0.130338\pi\)
−0.998176 + 0.0603657i \(0.980773\pi\)
\(822\) 0 0
\(823\) 1.14575e8 4.17020e7i 0.205538 0.0748096i −0.237200 0.971461i \(-0.576230\pi\)
0.442737 + 0.896651i \(0.354007\pi\)
\(824\) 0 0
\(825\) −5.43707e8 + 3.13910e8i −0.968285 + 0.559040i
\(826\) 0 0
\(827\) −2.78081e8 + 3.31404e8i −0.491648 + 0.585923i −0.953636 0.300963i \(-0.902692\pi\)
0.461988 + 0.886886i \(0.347136\pi\)
\(828\) 0 0
\(829\) −4.22140e8 2.43723e8i −0.740958 0.427792i 0.0814598 0.996677i \(-0.474042\pi\)
−0.822417 + 0.568885i \(0.807375\pi\)
\(830\) 0 0
\(831\) −5.21705e6 + 919907.i −0.00909122 + 0.00160303i
\(832\) 0 0
\(833\) 9.64718e7 + 3.51129e7i 0.166904 + 0.0607479i
\(834\) 0 0
\(835\) 1.76578e9i 3.03304i
\(836\) 0 0
\(837\) 2.56348e8 0.437173
\(838\) 0 0
\(839\) 5.98914e7 1.64550e8i 0.101409 0.278620i −0.878604 0.477551i \(-0.841525\pi\)
0.980014 + 0.198931i \(0.0637469\pi\)
\(840\) 0 0
\(841\) 3.81841e7 + 2.16553e8i 0.0641940 + 0.364062i
\(842\) 0 0
\(843\) 6.34147e7 1.09838e8i 0.105854 0.183345i
\(844\) 0 0
\(845\) 5.27554e8 + 4.42670e8i 0.874372 + 0.733686i
\(846\) 0 0
\(847\) −3.67674e8 6.36830e8i −0.605080 1.04803i
\(848\) 0 0
\(849\) −8.45785e7 2.32378e8i −0.138209 0.379727i
\(850\) 0 0
\(851\) −1.45746e8 2.56990e7i −0.236488 0.0416992i
\(852\) 0 0
\(853\) −6.13974e8 + 5.15186e8i −0.989243 + 0.830074i −0.985458 0.169919i \(-0.945649\pi\)
−0.00378518 + 0.999993i \(0.501205\pi\)
\(854\) 0 0
\(855\) −2.84769e6 8.82332e8i −0.00455610 1.41167i
\(856\) 0 0
\(857\) −5.59895e8 6.67257e8i −0.889537 1.06011i −0.997820 0.0659891i \(-0.978980\pi\)
0.108283 0.994120i \(-0.465465\pi\)
\(858\) 0 0
\(859\) −1.53933e7 + 8.72996e7i −0.0242857 + 0.137731i −0.994540 0.104357i \(-0.966721\pi\)
0.970254 + 0.242089i \(0.0778325\pi\)
\(860\) 0 0
\(861\) 1.12867e8 4.10801e7i 0.176830 0.0643610i
\(862\) 0 0
\(863\) −7.19149e7 + 4.15201e7i −0.111889 + 0.0645990i −0.554900 0.831917i \(-0.687244\pi\)
0.443011 + 0.896516i \(0.353910\pi\)
\(864\) 0 0
\(865\) −1.96181e8 + 2.33800e8i −0.303116 + 0.361240i
\(866\) 0 0
\(867\) −1.95924e8 1.13117e8i −0.300628 0.173568i
\(868\) 0 0
\(869\) 7.93458e8 1.39908e8i 1.20911 0.213198i
\(870\) 0 0
\(871\) 3.65117e8 + 1.32892e8i 0.552557 + 0.201114i
\(872\) 0 0
\(873\) 6.06617e8i 0.911742i
\(874\) 0 0
\(875\) 4.98828e8 0.744606
\(876\) 0 0
\(877\) 1.53914e8 4.22875e8i 0.228181 0.626921i −0.771779 0.635891i \(-0.780633\pi\)
0.999960 + 0.00896940i \(0.00285509\pi\)
\(878\) 0 0
\(879\) 6.81472e7 + 3.86482e8i 0.100342 + 0.569066i
\(880\) 0 0
\(881\) −4.07341e8 + 7.05536e8i −0.595704 + 1.03179i 0.397743 + 0.917497i \(0.369794\pi\)
−0.993447 + 0.114293i \(0.963540\pi\)
\(882\) 0 0
\(883\) −7.50637e8 6.29859e8i −1.09030 0.914874i −0.0935687 0.995613i \(-0.529827\pi\)
−0.996735 + 0.0807392i \(0.974272\pi\)
\(884\) 0 0
\(885\) −2.45579e8 4.25355e8i −0.354291 0.613651i
\(886\) 0 0
\(887\) 3.34105e7 + 9.17947e7i 0.0478754 + 0.131537i 0.961326 0.275413i \(-0.0888146\pi\)
−0.913451 + 0.406950i \(0.866592\pi\)
\(888\) 0 0
\(889\) −2.50156e8 4.41092e7i −0.356045 0.0627803i
\(890\) 0 0
\(891\) 5.45897e8 4.58062e8i 0.771752 0.647577i
\(892\) 0 0
\(893\) 5.55628e8 + 9.61242e7i 0.780242 + 0.134983i
\(894\) 0 0
\(895\) −4.92695e8 5.87171e8i −0.687241 0.819022i
\(896\) 0 0
\(897\) −4.30085e6 + 2.43914e7i −0.00595905 + 0.0337955i
\(898\) 0 0
\(899\) 3.36363e8 1.22426e8i 0.462945 0.168498i
\(900\) 0 0
\(901\) −9.24175e7 + 5.33573e7i −0.126351 + 0.0729490i
\(902\) 0 0
\(903\) 1.21120e8 1.44345e8i 0.164495 0.196038i
\(904\) 0 0
\(905\) 4.72593e7 + 2.72852e7i 0.0637590 + 0.0368113i
\(906\) 0 0
\(907\) −1.24056e9 + 2.18744e8i −1.66263 + 0.293166i −0.924411 0.381397i \(-0.875443\pi\)
−0.738217 + 0.674563i \(0.764332\pi\)
\(908\) 0 0
\(909\) 8.92869e8 + 3.24978e8i 1.18877 + 0.432675i
\(910\) 0 0
\(911\) 4.17943e8i 0.552792i −0.961044 0.276396i \(-0.910860\pi\)
0.961044 0.276396i \(-0.0891401\pi\)
\(912\) 0 0
\(913\) 4.80438e8 0.631284
\(914\) 0 0
\(915\) −1.54443e8 + 4.24330e8i −0.201607 + 0.553911i
\(916\) 0 0
\(917\) 3.92034e7 + 2.22334e8i 0.0508412 + 0.288335i
\(918\) 0 0
\(919\) −2.16746e8 + 3.75416e8i −0.279258 + 0.483689i −0.971201 0.238264i \(-0.923422\pi\)
0.691943 + 0.721952i \(0.256755\pi\)
\(920\) 0 0
\(921\) 1.95974e8 + 1.64442e8i 0.250853 + 0.210491i
\(922\) 0 0
\(923\) 2.50397e8 + 4.33701e8i 0.318438 + 0.551550i
\(924\) 0 0
\(925\) 6.86500e8 + 1.88614e9i 0.867391 + 2.38314i
\(926\) 0 0
\(927\) −1.04440e9 1.84157e8i −1.31108 0.231179i
\(928\) 0 0
\(929\) 5.66904e8 4.75689e8i 0.707070 0.593302i −0.216706 0.976237i \(-0.569531\pi\)
0.923775 + 0.382935i \(0.125087\pi\)
\(930\) 0 0
\(931\) −4.25170e8 2.43646e8i −0.526882 0.301932i
\(932\) 0 0
\(933\) 3.68773e8 + 4.39486e8i 0.454061 + 0.541129i
\(934\) 0 0
\(935\) 1.17229e8 6.64837e8i 0.143416 0.813355i
\(936\) 0 0
\(937\) 2.22024e8 8.08102e7i 0.269887 0.0982308i −0.203532 0.979068i \(-0.565242\pi\)
0.473419 + 0.880838i \(0.343020\pi\)
\(938\) 0 0
\(939\) −2.41400e8 + 1.39372e8i −0.291568 + 0.168337i
\(940\) 0 0
\(941\) 3.17073e8 3.77873e8i 0.380531 0.453500i −0.541450 0.840733i \(-0.682125\pi\)
0.921982 + 0.387233i \(0.126569\pi\)
\(942\) 0 0
\(943\) 9.35763e7 + 5.40263e7i 0.111591 + 0.0644273i
\(944\) 0 0
\(945\) 6.05207e8 1.06714e8i 0.717148 0.126453i
\(946\) 0 0
\(947\) 1.31479e9 + 4.78543e8i 1.54812 + 0.563471i 0.967976 0.251042i \(-0.0807731\pi\)
0.580146 + 0.814512i \(0.302995\pi\)
\(948\) 0 0
\(949\) 4.33099e8i 0.506743i
\(950\) 0 0
\(951\) 4.07065e8 0.473284
\(952\) 0 0
\(953\) −7.54080e7 + 2.07182e8i −0.0871242 + 0.239372i −0.975602 0.219549i \(-0.929541\pi\)
0.888477 + 0.458920i \(0.151764\pi\)
\(954\) 0 0
\(955\) −4.03054e7 2.28583e8i −0.0462757 0.262442i
\(956\) 0 0
\(957\) −2.26118e8 + 3.91648e8i −0.257988 + 0.446849i
\(958\) 0 0
\(959\) −6.31338e8 5.29756e8i −0.715824 0.600648i
\(960\) 0 0
\(961\) −2.72882e8 4.72646e8i −0.307472 0.532557i
\(962\) 0 0
\(963\) −3.40472e8 9.35439e8i −0.381244 1.04746i
\(964\) 0 0
\(965\) 2.22579e9 + 3.92468e8i 2.47687 + 0.436739i
\(966\) 0 0
\(967\) 1.06160e9 8.90789e8i 1.17404 0.985135i 0.174038 0.984739i \(-0.444319\pi\)
1.00000 0.000395594i \(-0.000125922\pi\)
\(968\) 0 0
\(969\) −7.75959e7 6.46850e7i −0.0852839 0.0710939i
\(970\) 0 0
\(971\) 3.08422e8 + 3.67563e8i 0.336889 + 0.401489i 0.907718 0.419580i \(-0.137823\pi\)
−0.570829 + 0.821069i \(0.693378\pi\)
\(972\) 0 0
\(973\) −1.19975e8 + 6.80412e8i −0.130242 + 0.738641i
\(974\) 0 0
\(975\) 3.15655e8 1.14889e8i 0.340564 0.123955i
\(976\) 0 0
\(977\) −3.90385e8 + 2.25389e8i −0.418609 + 0.241684i −0.694482 0.719510i \(-0.744366\pi\)
0.275873 + 0.961194i \(0.411033\pi\)
\(978\) 0 0
\(979\) 1.83075e9 2.18181e9i 1.95111 2.32524i
\(980\) 0 0
\(981\) −1.10611e9 6.38614e8i −1.17163 0.676443i
\(982\) 0 0
\(983\) 2.04256e8 3.60159e7i 0.215038 0.0379170i −0.0650912 0.997879i \(-0.520734\pi\)
0.280129 + 0.959962i \(0.409623\pi\)
\(984\) 0 0
\(985\) −1.48535e9 5.40623e8i −1.55425 0.565699i
\(986\) 0 0
\(987\) 1.81123e8i 0.188374i
\(988\) 0 0
\(989\) 1.69513e8 0.175232
\(990\) 0 0
\(991\) 9.44180e7 2.59411e8i 0.0970139 0.266544i −0.881687 0.471835i \(-0.843592\pi\)
0.978701 + 0.205291i \(0.0658141\pi\)
\(992\) 0 0
\(993\) −5.56590e7 3.15658e8i −0.0568444 0.322380i
\(994\) 0 0
\(995\) −3.24117e8 + 5.61388e8i −0.329028 + 0.569893i
\(996\) 0 0
\(997\) −1.12179e9 9.41292e8i −1.13195 0.949815i −0.132800 0.991143i \(-0.542397\pi\)
−0.999146 + 0.0413280i \(0.986841\pi\)
\(998\) 0 0
\(999\) 5.17723e8 + 8.96722e8i 0.519279 + 0.899418i
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.13.5 60
19.3 odd 18 inner 76.7.j.a.41.5 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.7.j.a.13.5 60 1.1 even 1 trivial
76.7.j.a.41.5 yes 60 19.3 odd 18 inner