Properties

Label 162.7.d.f.107.3
Level $162$
Weight $7$
Character 162.107
Analytic conductor $37.269$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,7,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not 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: \(37.2687615464\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.3
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.7.d.f.53.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(21.4919 - 12.4084i) q^{5} +(3.09808 - 5.36603i) q^{7} +181.019i q^{8} +O(q^{10})\) \(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(21.4919 - 12.4084i) q^{5} +(3.09808 - 5.36603i) q^{7} +181.019i q^{8} +140.385 q^{10} +(113.360 + 65.4483i) q^{11} +(461.004 + 798.482i) q^{13} +(30.3548 - 17.5254i) q^{14} +(-512.000 + 886.810i) q^{16} +3384.11i q^{17} +5403.30 q^{19} +(687.742 + 397.068i) q^{20} +(370.232 + 641.260i) q^{22} +(-2045.32 + 1180.87i) q^{23} +(-7504.56 + 12998.3i) q^{25} +5215.66i q^{26} +198.277 q^{28} +(30256.9 + 17468.8i) q^{29} +(-2330.16 - 4035.96i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-9571.71 + 16578.7i) q^{34} -153.768i q^{35} +6916.74 q^{37} +(26470.6 + 15282.8i) q^{38} +(2246.16 + 3890.46i) q^{40} +(-46637.1 + 26926.0i) q^{41} +(-61566.4 + 106636. i) q^{43} +4188.69i q^{44} -13360.0 q^{46} +(83183.9 + 48026.3i) q^{47} +(58805.3 + 101854. i) q^{49} +(-73529.4 + 42452.2i) q^{50} +(-14752.1 + 25551.4i) q^{52} -132310. i q^{53} +3248.43 q^{55} +(971.354 + 560.812i) q^{56} +(98818.5 + 171159. i) q^{58} +(-25181.5 + 14538.6i) q^{59} +(-160333. + 277705. i) q^{61} -26362.8i q^{62} -32768.0 q^{64} +(19815.7 + 11440.6i) q^{65} +(264909. + 458837. i) q^{67} +(-93783.3 + 54145.8i) q^{68} +(434.923 - 753.308i) q^{70} -628518. i q^{71} -68777.7 q^{73} +(33885.0 + 19563.5i) q^{74} +(86452.7 + 149741. i) q^{76} +(702.395 - 405.528i) q^{77} +(-235877. + 408551. i) q^{79} +25412.4i q^{80} -304633. q^{82} +(29055.1 + 16775.0i) q^{83} +(41991.3 + 72731.1i) q^{85} +(-603225. + 348272. i) q^{86} +(-11847.4 + 20520.3i) q^{88} -1.01543e6i q^{89} +5712.90 q^{91} +(-65450.3 - 37787.7i) q^{92} +(271678. + 470559. i) q^{94} +(116127. - 67046.1i) q^{95} +(-209094. + 362162. i) q^{97} +665306. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 128 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 128 q^{4} + 4 q^{7} + 5280 q^{10} - 3836 q^{13} - 4096 q^{16} + 20488 q^{19} + 27072 q^{22} + 25700 q^{25} + 256 q^{28} + 40096 q^{31} - 60528 q^{34} - 40400 q^{37} + 84480 q^{40} - 184940 q^{43} + 325440 q^{46} + 470484 q^{49} + 122752 q^{52} + 1899720 q^{55} - 24624 q^{58} - 609056 q^{61} - 262144 q^{64} + 2008972 q^{67} - 8160 q^{70} + 1051648 q^{73} + 327808 q^{76} + 848716 q^{79} + 1411584 q^{82} + 987840 q^{85} - 866304 q^{88} + 70520 q^{91} + 1965408 q^{94} - 3621728 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.89898 + 2.82843i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 16.0000 + 27.7128i 0.250000 + 0.433013i
\(5\) 21.4919 12.4084i 0.171936 0.0992670i −0.411563 0.911381i \(-0.635017\pi\)
0.583498 + 0.812114i \(0.301684\pi\)
\(6\) 0 0
\(7\) 3.09808 5.36603i 0.00903229 0.0156444i −0.861474 0.507802i \(-0.830458\pi\)
0.870506 + 0.492157i \(0.163792\pi\)
\(8\) 181.019i 0.353553i
\(9\) 0 0
\(10\) 140.385 0.140385
\(11\) 113.360 + 65.4483i 0.0851689 + 0.0491723i 0.541980 0.840392i \(-0.317675\pi\)
−0.456811 + 0.889564i \(0.651008\pi\)
\(12\) 0 0
\(13\) 461.004 + 798.482i 0.209833 + 0.363442i 0.951662 0.307148i \(-0.0993746\pi\)
−0.741829 + 0.670589i \(0.766041\pi\)
\(14\) 30.3548 17.5254i 0.0110623 0.00638680i
\(15\) 0 0
\(16\) −512.000 + 886.810i −0.125000 + 0.216506i
\(17\) 3384.11i 0.688808i 0.938822 + 0.344404i \(0.111919\pi\)
−0.938822 + 0.344404i \(0.888081\pi\)
\(18\) 0 0
\(19\) 5403.30 0.787767 0.393884 0.919160i \(-0.371131\pi\)
0.393884 + 0.919160i \(0.371131\pi\)
\(20\) 687.742 + 397.068i 0.0859678 + 0.0496335i
\(21\) 0 0
\(22\) 370.232 + 641.260i 0.0347701 + 0.0602235i
\(23\) −2045.32 + 1180.87i −0.168104 + 0.0970549i −0.581692 0.813409i \(-0.697609\pi\)
0.413588 + 0.910464i \(0.364276\pi\)
\(24\) 0 0
\(25\) −7504.56 + 12998.3i −0.480292 + 0.831890i
\(26\) 5215.66i 0.296749i
\(27\) 0 0
\(28\) 198.277 0.00903229
\(29\) 30256.9 + 17468.8i 1.24060 + 0.716258i 0.969215 0.246214i \(-0.0791867\pi\)
0.271380 + 0.962472i \(0.412520\pi\)
\(30\) 0 0
\(31\) −2330.16 4035.96i −0.0782170 0.135476i 0.824264 0.566206i \(-0.191589\pi\)
−0.902481 + 0.430730i \(0.858256\pi\)
\(32\) −5016.55 + 2896.31i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −9571.71 + 16578.7i −0.243530 + 0.421807i
\(35\) 153.768i 0.00358643i
\(36\) 0 0
\(37\) 6916.74 0.136551 0.0682757 0.997666i \(-0.478250\pi\)
0.0682757 + 0.997666i \(0.478250\pi\)
\(38\) 26470.6 + 15282.8i 0.482407 + 0.278518i
\(39\) 0 0
\(40\) 2246.16 + 3890.46i 0.0350962 + 0.0607884i
\(41\) −46637.1 + 26926.0i −0.676675 + 0.390679i −0.798601 0.601860i \(-0.794426\pi\)
0.121926 + 0.992539i \(0.461093\pi\)
\(42\) 0 0
\(43\) −61566.4 + 106636.i −0.774352 + 1.34122i 0.160805 + 0.986986i \(0.448591\pi\)
−0.935158 + 0.354231i \(0.884743\pi\)
\(44\) 4188.69i 0.0491723i
\(45\) 0 0
\(46\) −13360.0 −0.137256
\(47\) 83183.9 + 48026.3i 0.801209 + 0.462578i 0.843894 0.536510i \(-0.180258\pi\)
−0.0426847 + 0.999089i \(0.513591\pi\)
\(48\) 0 0
\(49\) 58805.3 + 101854.i 0.499837 + 0.865743i
\(50\) −73529.4 + 42452.2i −0.588235 + 0.339618i
\(51\) 0 0
\(52\) −14752.1 + 25551.4i −0.104917 + 0.181721i
\(53\) 132310.i 0.888722i −0.895848 0.444361i \(-0.853431\pi\)
0.895848 0.444361i \(-0.146569\pi\)
\(54\) 0 0
\(55\) 3248.43 0.0195247
\(56\) 971.354 + 560.812i 0.00553113 + 0.00319340i
\(57\) 0 0
\(58\) 98818.5 + 171159.i 0.506471 + 0.877233i
\(59\) −25181.5 + 14538.6i −0.122610 + 0.0707889i −0.560051 0.828458i \(-0.689218\pi\)
0.437441 + 0.899247i \(0.355885\pi\)
\(60\) 0 0
\(61\) −160333. + 277705.i −0.706372 + 1.22347i 0.259822 + 0.965657i \(0.416336\pi\)
−0.966194 + 0.257816i \(0.916997\pi\)
\(62\) 26362.8i 0.110616i
\(63\) 0 0
\(64\) −32768.0 −0.125000
\(65\) 19815.7 + 11440.6i 0.0721556 + 0.0416590i
\(66\) 0 0
\(67\) 264909. + 458837.i 0.880791 + 1.52558i 0.850463 + 0.526036i \(0.176322\pi\)
0.0303290 + 0.999540i \(0.490345\pi\)
\(68\) −93783.3 + 54145.8i −0.298262 + 0.172202i
\(69\) 0 0
\(70\) 434.923 753.308i 0.00126800 0.00219623i
\(71\) 628518.i 1.75607i −0.478594 0.878036i \(-0.658854\pi\)
0.478594 0.878036i \(-0.341146\pi\)
\(72\) 0 0
\(73\) −68777.7 −0.176799 −0.0883994 0.996085i \(-0.528175\pi\)
−0.0883994 + 0.996085i \(0.528175\pi\)
\(74\) 33885.0 + 19563.5i 0.0836203 + 0.0482782i
\(75\) 0 0
\(76\) 86452.7 + 149741.i 0.196942 + 0.341113i
\(77\) 702.395 405.528i 0.00153854 0.000888277i
\(78\) 0 0
\(79\) −235877. + 408551.i −0.478415 + 0.828638i −0.999694 0.0247478i \(-0.992122\pi\)
0.521279 + 0.853386i \(0.325455\pi\)
\(80\) 25412.4i 0.0496335i
\(81\) 0 0
\(82\) −304633. −0.552503
\(83\) 29055.1 + 16775.0i 0.0508146 + 0.0293378i 0.525192 0.850984i \(-0.323993\pi\)
−0.474377 + 0.880322i \(0.657327\pi\)
\(84\) 0 0
\(85\) 41991.3 + 72731.1i 0.0683759 + 0.118431i
\(86\) −603225. + 348272.i −0.948384 + 0.547550i
\(87\) 0 0
\(88\) −11847.4 + 20520.3i −0.0173850 + 0.0301118i
\(89\) 1.01543e6i 1.44039i −0.693772 0.720195i \(-0.744053\pi\)
0.693772 0.720195i \(-0.255947\pi\)
\(90\) 0 0
\(91\) 5712.90 0.00758110
\(92\) −65450.3 37787.7i −0.0840520 0.0485275i
\(93\) 0 0
\(94\) 271678. + 470559.i 0.327092 + 0.566540i
\(95\) 116127. 67046.1i 0.135445 0.0781993i
\(96\) 0 0
\(97\) −209094. + 362162.i −0.229101 + 0.396815i −0.957542 0.288294i \(-0.906912\pi\)
0.728441 + 0.685109i \(0.240245\pi\)
\(98\) 665306.i 0.706876i
\(99\) 0 0
\(100\) −480292. −0.480292
\(101\) 581679. + 335833.i 0.564572 + 0.325956i 0.754979 0.655749i \(-0.227647\pi\)
−0.190406 + 0.981705i \(0.560981\pi\)
\(102\) 0 0
\(103\) −350999. 607949.i −0.321214 0.556359i 0.659525 0.751683i \(-0.270758\pi\)
−0.980739 + 0.195324i \(0.937424\pi\)
\(104\) −144541. + 83450.6i −0.128496 + 0.0741872i
\(105\) 0 0
\(106\) 374230. 648185.i 0.314211 0.544229i
\(107\) 350565.i 0.286166i 0.989711 + 0.143083i \(0.0457016\pi\)
−0.989711 + 0.143083i \(0.954298\pi\)
\(108\) 0 0
\(109\) 724369. 0.559345 0.279673 0.960095i \(-0.409774\pi\)
0.279673 + 0.960095i \(0.409774\pi\)
\(110\) 15914.0 + 9187.95i 0.0119564 + 0.00690304i
\(111\) 0 0
\(112\) 3172.43 + 5494.81i 0.00225807 + 0.00391110i
\(113\) 1.09419e6 631732.i 0.758330 0.437822i −0.0703658 0.997521i \(-0.522417\pi\)
0.828696 + 0.559699i \(0.189083\pi\)
\(114\) 0 0
\(115\) −29305.3 + 50758.2i −0.0192687 + 0.0333744i
\(116\) 1.11800e6i 0.716258i
\(117\) 0 0
\(118\) −164485. −0.100111
\(119\) 18159.2 + 10484.2i 0.0107760 + 0.00622151i
\(120\) 0 0
\(121\) −877214. 1.51938e6i −0.495164 0.857650i
\(122\) −1.57094e6 + 906981.i −0.865126 + 0.499481i
\(123\) 0 0
\(124\) 74565.2 129151.i 0.0391085 0.0677379i
\(125\) 760240.i 0.389243i
\(126\) 0 0
\(127\) 2.67398e6 1.30541 0.652706 0.757611i \(-0.273634\pi\)
0.652706 + 0.757611i \(0.273634\pi\)
\(128\) −160530. 92681.9i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 64717.9 + 112095.i 0.0294574 + 0.0510217i
\(131\) 3.10743e6 1.79407e6i 1.38225 0.798043i 0.389825 0.920889i \(-0.372535\pi\)
0.992426 + 0.122846i \(0.0392021\pi\)
\(132\) 0 0
\(133\) 16739.8 28994.2i 0.00711534 0.0123241i
\(134\) 2.99711e6i 1.24563i
\(135\) 0 0
\(136\) −612590. −0.243530
\(137\) −1.32548e6 765268.i −0.515481 0.297613i 0.219603 0.975589i \(-0.429524\pi\)
−0.735084 + 0.677976i \(0.762857\pi\)
\(138\) 0 0
\(139\) −1.76383e6 3.05504e6i −0.656769 1.13756i −0.981447 0.191732i \(-0.938589\pi\)
0.324679 0.945824i \(-0.394744\pi\)
\(140\) 4261.35 2460.29i 0.00155297 0.000896609i
\(141\) 0 0
\(142\) 1.77772e6 3.07909e6i 0.620865 1.07537i
\(143\) 120688.i 0.0412719i
\(144\) 0 0
\(145\) 867039. 0.284403
\(146\) −336941. 194533.i −0.108267 0.0625078i
\(147\) 0 0
\(148\) 110668. + 191682.i 0.0341379 + 0.0591285i
\(149\) 2.07440e6 1.19765e6i 0.627094 0.362053i −0.152532 0.988299i \(-0.548743\pi\)
0.779626 + 0.626246i \(0.215409\pi\)
\(150\) 0 0
\(151\) 1.50837e6 2.61258e6i 0.438105 0.758820i −0.559438 0.828872i \(-0.688983\pi\)
0.997543 + 0.0700517i \(0.0223164\pi\)
\(152\) 978101.i 0.278518i
\(153\) 0 0
\(154\) 4588.02 0.00125621
\(155\) −100159. 57827.1i −0.0268966 0.0155287i
\(156\) 0 0
\(157\) −2.79226e6 4.83633e6i −0.721533 1.24973i −0.960385 0.278676i \(-0.910104\pi\)
0.238852 0.971056i \(-0.423229\pi\)
\(158\) −2.31111e6 + 1.33432e6i −0.585936 + 0.338290i
\(159\) 0 0
\(160\) −71877.0 + 124495.i −0.0175481 + 0.0303942i
\(161\) 14633.7i 0.00350651i
\(162\) 0 0
\(163\) −2.46039e6 −0.568121 −0.284061 0.958806i \(-0.591682\pi\)
−0.284061 + 0.958806i \(0.591682\pi\)
\(164\) −1.49239e6 861631.i −0.338338 0.195339i
\(165\) 0 0
\(166\) 94893.6 + 164361.i 0.0207450 + 0.0359313i
\(167\) 3.48381e6 2.01138e6i 0.748005 0.431861i −0.0769675 0.997034i \(-0.524524\pi\)
0.824973 + 0.565173i \(0.191190\pi\)
\(168\) 0 0
\(169\) 1.98836e6 3.44393e6i 0.411940 0.713501i
\(170\) 475078.i 0.0966981i
\(171\) 0 0
\(172\) −3.94025e6 −0.774352
\(173\) −3.58412e6 2.06929e6i −0.692220 0.399653i 0.112223 0.993683i \(-0.464203\pi\)
−0.804443 + 0.594030i \(0.797536\pi\)
\(174\) 0 0
\(175\) 46499.4 + 80539.4i 0.00867628 + 0.0150278i
\(176\) −116080. + 67019.1i −0.0212922 + 0.0122931i
\(177\) 0 0
\(178\) 2.87207e6 4.97457e6i 0.509254 0.882055i
\(179\) 4.64610e6i 0.810083i −0.914298 0.405042i \(-0.867257\pi\)
0.914298 0.405042i \(-0.132743\pi\)
\(180\) 0 0
\(181\) 2.01455e6 0.339737 0.169868 0.985467i \(-0.445666\pi\)
0.169868 + 0.985467i \(0.445666\pi\)
\(182\) 27987.4 + 16158.5i 0.00464246 + 0.00268032i
\(183\) 0 0
\(184\) −213760. 370243.i −0.0343141 0.0594337i
\(185\) 148654. 85825.5i 0.0234780 0.0135551i
\(186\) 0 0
\(187\) −221484. + 383622.i −0.0338703 + 0.0586650i
\(188\) 3.07368e6i 0.462578i
\(189\) 0 0
\(190\) 758540. 0.110591
\(191\) −3.29614e6 1.90303e6i −0.473049 0.273115i 0.244466 0.969658i \(-0.421387\pi\)
−0.717515 + 0.696543i \(0.754721\pi\)
\(192\) 0 0
\(193\) 647738. + 1.12191e6i 0.0901005 + 0.156059i 0.907553 0.419937i \(-0.137948\pi\)
−0.817453 + 0.575996i \(0.804614\pi\)
\(194\) −2.04870e6 + 1.18282e6i −0.280590 + 0.161999i
\(195\) 0 0
\(196\) −1.88177e6 + 3.25932e6i −0.249918 + 0.432871i
\(197\) 5.99463e6i 0.784086i −0.919947 0.392043i \(-0.871769\pi\)
0.919947 0.392043i \(-0.128231\pi\)
\(198\) 0 0
\(199\) −1.04921e6 −0.133139 −0.0665694 0.997782i \(-0.521205\pi\)
−0.0665694 + 0.997782i \(0.521205\pi\)
\(200\) −2.35294e6 1.35847e6i −0.294118 0.169809i
\(201\) 0 0
\(202\) 1.89976e6 + 3.29047e6i 0.230486 + 0.399213i
\(203\) 187476. 108239.i 0.0224108 0.0129389i
\(204\) 0 0
\(205\) −668215. + 1.15738e6i −0.0775630 + 0.134343i
\(206\) 3.97110e6i 0.454265i
\(207\) 0 0
\(208\) −944135. −0.104917
\(209\) 612517. + 353637.i 0.0670933 + 0.0387363i
\(210\) 0 0
\(211\) 2.77104e6 + 4.79958e6i 0.294982 + 0.510923i 0.974981 0.222290i \(-0.0713532\pi\)
−0.679999 + 0.733213i \(0.738020\pi\)
\(212\) 3.66669e6 2.11696e6i 0.384828 0.222180i
\(213\) 0 0
\(214\) −991549. + 1.71741e6i −0.101175 + 0.175240i
\(215\) 3.05576e6i 0.307471i
\(216\) 0 0
\(217\) −28876.1 −0.00282592
\(218\) 3.54867e6 + 2.04882e6i 0.342528 + 0.197758i
\(219\) 0 0
\(220\) 51974.9 + 90023.1i 0.00488119 + 0.00845446i
\(221\) −2.70215e6 + 1.56009e6i −0.250342 + 0.144535i
\(222\) 0 0
\(223\) −2.06883e6 + 3.58332e6i −0.186557 + 0.323125i −0.944100 0.329659i \(-0.893066\pi\)
0.757543 + 0.652785i \(0.226399\pi\)
\(224\) 35891.9i 0.00319340i
\(225\) 0 0
\(226\) 7.14723e6 0.619174
\(227\) 1.27830e7 + 7.38025e6i 1.09283 + 0.630948i 0.934329 0.356410i \(-0.116000\pi\)
0.158504 + 0.987358i \(0.449333\pi\)
\(228\) 0 0
\(229\) 7.31735e6 + 1.26740e7i 0.609323 + 1.05538i 0.991352 + 0.131228i \(0.0418919\pi\)
−0.382030 + 0.924150i \(0.624775\pi\)
\(230\) −287132. + 165776.i −0.0235992 + 0.0136250i
\(231\) 0 0
\(232\) −3.16219e6 + 5.47708e6i −0.253235 + 0.438617i
\(233\) 1.51778e6i 0.119989i 0.998199 + 0.0599946i \(0.0191083\pi\)
−0.998199 + 0.0599946i \(0.980892\pi\)
\(234\) 0 0
\(235\) 2.38371e6 0.183675
\(236\) −805809. 465234.i −0.0613050 0.0353945i
\(237\) 0 0
\(238\) 59307.8 + 102724.i 0.00439927 + 0.00761977i
\(239\) −1.20904e7 + 6.98040e6i −0.885619 + 0.511312i −0.872507 0.488602i \(-0.837507\pi\)
−0.0131121 + 0.999914i \(0.504174\pi\)
\(240\) 0 0
\(241\) −1.26582e7 + 2.19246e7i −0.904317 + 1.56632i −0.0824864 + 0.996592i \(0.526286\pi\)
−0.821831 + 0.569731i \(0.807047\pi\)
\(242\) 9.92454e6i 0.700268i
\(243\) 0 0
\(244\) −1.02613e7 −0.706372
\(245\) 2.52768e6 + 1.45936e6i 0.171879 + 0.0992346i
\(246\) 0 0
\(247\) 2.49094e6 + 4.31443e6i 0.165300 + 0.286308i
\(248\) 730587. 421805.i 0.0478979 0.0276539i
\(249\) 0 0
\(250\) −2.15028e6 + 3.72440e6i −0.137618 + 0.238361i
\(251\) 3.58400e6i 0.226645i 0.993558 + 0.113323i \(0.0361494\pi\)
−0.993558 + 0.113323i \(0.963851\pi\)
\(252\) 0 0
\(253\) −309143. −0.0190896
\(254\) 1.30998e7 + 7.56317e6i 0.799398 + 0.461533i
\(255\) 0 0
\(256\) −524288. 908093.i −0.0312500 0.0541266i
\(257\) −2.00837e7 + 1.15953e7i −1.18316 + 0.683098i −0.956743 0.290933i \(-0.906034\pi\)
−0.226417 + 0.974031i \(0.572701\pi\)
\(258\) 0 0
\(259\) 21428.6 37115.4i 0.00123337 0.00213626i
\(260\) 732199.i 0.0416590i
\(261\) 0 0
\(262\) 2.02976e7 1.12860
\(263\) 1.72997e7 + 9.98800e6i 0.950981 + 0.549049i 0.893386 0.449291i \(-0.148323\pi\)
0.0575954 + 0.998340i \(0.481657\pi\)
\(264\) 0 0
\(265\) −1.64176e6 2.84360e6i −0.0882208 0.152803i
\(266\) 164016. 94694.7i 0.00871448 0.00503131i
\(267\) 0 0
\(268\) −8.47710e6 + 1.46828e7i −0.440396 + 0.762788i
\(269\) 1.05394e7i 0.541453i 0.962656 + 0.270726i \(0.0872639\pi\)
−0.962656 + 0.270726i \(0.912736\pi\)
\(270\) 0 0
\(271\) −2.76838e7 −1.39097 −0.695485 0.718540i \(-0.744811\pi\)
−0.695485 + 0.718540i \(0.744811\pi\)
\(272\) −3.00106e6 1.73267e6i −0.149131 0.0861010i
\(273\) 0 0
\(274\) −4.32901e6 7.49806e6i −0.210444 0.364500i
\(275\) −1.70143e6 + 982322.i −0.0818119 + 0.0472341i
\(276\) 0 0
\(277\) −4.08298e6 + 7.07192e6i −0.192104 + 0.332735i −0.945947 0.324320i \(-0.894865\pi\)
0.753843 + 0.657055i \(0.228198\pi\)
\(278\) 1.99555e7i 0.928811i
\(279\) 0 0
\(280\) 27835.1 0.00126800
\(281\) 3.85847e6 + 2.22769e6i 0.173899 + 0.100400i 0.584423 0.811449i \(-0.301321\pi\)
−0.410524 + 0.911850i \(0.634654\pi\)
\(282\) 0 0
\(283\) 1.59414e7 + 2.76112e7i 0.703341 + 1.21822i 0.967287 + 0.253685i \(0.0816426\pi\)
−0.263946 + 0.964537i \(0.585024\pi\)
\(284\) 1.74180e7 1.00563e7i 0.760402 0.439018i
\(285\) 0 0
\(286\) −341356. + 591246.i −0.0145918 + 0.0252738i
\(287\) 333675.i 0.0141149i
\(288\) 0 0
\(289\) 1.26854e7 0.525544
\(290\) 4.24760e6 + 2.45236e6i 0.174161 + 0.100552i
\(291\) 0 0
\(292\) −1.10044e6 1.90602e6i −0.0441997 0.0765561i
\(293\) −3.09320e7 + 1.78586e7i −1.22972 + 0.709977i −0.966971 0.254888i \(-0.917962\pi\)
−0.262746 + 0.964865i \(0.584628\pi\)
\(294\) 0 0
\(295\) −360800. + 624924.i −0.0140540 + 0.0243423i
\(296\) 1.25206e6i 0.0482782i
\(297\) 0 0
\(298\) 1.35499e7 0.512020
\(299\) −1.88580e6 1.08877e6i −0.0705476 0.0407307i
\(300\) 0 0
\(301\) 381475. + 660734.i 0.0139884 + 0.0242285i
\(302\) 1.47790e7 8.53265e6i 0.536567 0.309787i
\(303\) 0 0
\(304\) −2.76649e6 + 4.79170e6i −0.0984709 + 0.170557i
\(305\) 7.95789e6i 0.280478i
\(306\) 0 0
\(307\) −5.01121e6 −0.173192 −0.0865959 0.996244i \(-0.527599\pi\)
−0.0865959 + 0.996244i \(0.527599\pi\)
\(308\) 22476.6 + 12976.9i 0.000769270 + 0.000444138i
\(309\) 0 0
\(310\) −327119. 566587.i −0.0109805 0.0190187i
\(311\) 2.52550e7 1.45810e7i 0.839587 0.484736i −0.0175371 0.999846i \(-0.505583\pi\)
0.857124 + 0.515111i \(0.172249\pi\)
\(312\) 0 0
\(313\) 1.53413e7 2.65719e7i 0.500298 0.866541i −0.499702 0.866197i \(-0.666557\pi\)
1.00000 0.000343995i \(-0.000109497\pi\)
\(314\) 3.15908e7i 1.02040i
\(315\) 0 0
\(316\) −1.50961e7 −0.478415
\(317\) −4.39431e7 2.53706e7i −1.37947 0.796439i −0.387377 0.921922i \(-0.626619\pi\)
−0.992096 + 0.125483i \(0.959952\pi\)
\(318\) 0 0
\(319\) 2.28661e6 + 3.96052e6i 0.0704401 + 0.122006i
\(320\) −704248. + 406598.i −0.0214919 + 0.0124084i
\(321\) 0 0
\(322\) −41390.3 + 71690.0i −0.00123974 + 0.00214729i
\(323\) 1.82854e7i 0.542620i
\(324\) 0 0
\(325\) −1.38385e7 −0.403125
\(326\) −1.20534e7 6.95903e6i −0.347902 0.200861i
\(327\) 0 0
\(328\) −4.87412e6 8.44223e6i −0.138126 0.239241i
\(329\) 515420. 297578.i 0.0144735 0.00835628i
\(330\) 0 0
\(331\) 2.10713e7 3.64966e7i 0.581042 1.00639i −0.414314 0.910134i \(-0.635978\pi\)
0.995356 0.0962608i \(-0.0306883\pi\)
\(332\) 1.07360e6i 0.0293378i
\(333\) 0 0
\(334\) 2.27561e7 0.610744
\(335\) 1.13868e7 + 6.57419e6i 0.302879 + 0.174867i
\(336\) 0 0
\(337\) −30716.4 53202.3i −0.000802565 0.00139008i 0.865624 0.500695i \(-0.166922\pi\)
−0.866426 + 0.499305i \(0.833589\pi\)
\(338\) 1.94818e7 1.12478e7i 0.504521 0.291286i
\(339\) 0 0
\(340\) −1.34372e6 + 2.32740e6i −0.0341879 + 0.0592153i
\(341\) 610021.i 0.0153844i
\(342\) 0 0
\(343\) 1.45770e6 0.0361233
\(344\) −1.93032e7 1.11447e7i −0.474192 0.273775i
\(345\) 0 0
\(346\) −1.17057e7 2.02748e7i −0.282598 0.489473i
\(347\) −2.10694e7 + 1.21644e7i −0.504271 + 0.291141i −0.730476 0.682939i \(-0.760702\pi\)
0.226205 + 0.974080i \(0.427368\pi\)
\(348\) 0 0
\(349\) 1.26014e7 2.18263e7i 0.296444 0.513456i −0.678876 0.734253i \(-0.737532\pi\)
0.975320 + 0.220797i \(0.0708658\pi\)
\(350\) 526081.i 0.0122701i
\(351\) 0 0
\(352\) −758234. −0.0173850
\(353\) −5.98516e7 3.45553e7i −1.36067 0.785581i −0.370954 0.928651i \(-0.620969\pi\)
−0.989713 + 0.143070i \(0.954303\pi\)
\(354\) 0 0
\(355\) −7.79888e6 1.35081e7i −0.174320 0.301931i
\(356\) 2.81404e7 1.62469e7i 0.623707 0.360097i
\(357\) 0 0
\(358\) 1.31412e7 2.27612e7i 0.286408 0.496073i
\(359\) 1.41061e7i 0.304876i 0.988313 + 0.152438i \(0.0487124\pi\)
−0.988313 + 0.152438i \(0.951288\pi\)
\(360\) 0 0
\(361\) −1.78503e7 −0.379423
\(362\) 9.86925e6 + 5.69801e6i 0.208046 + 0.120115i
\(363\) 0 0
\(364\) 91406.4 + 158320.i 0.00189527 + 0.00328271i
\(365\) −1.47817e6 + 853420.i −0.0303980 + 0.0175503i
\(366\) 0 0
\(367\) 4.07223e7 7.05331e7i 0.823823 1.42690i −0.0789923 0.996875i \(-0.525170\pi\)
0.902815 0.430028i \(-0.141496\pi\)
\(368\) 2.41842e6i 0.0485275i
\(369\) 0 0
\(370\) 971005. 0.0191697
\(371\) −709980. 409907.i −0.0139035 0.00802719i
\(372\) 0 0
\(373\) −3.79860e7 6.57937e7i −0.731977 1.26782i −0.956037 0.293246i \(-0.905265\pi\)
0.224060 0.974575i \(-0.428069\pi\)
\(374\) −2.17010e6 + 1.25291e6i −0.0414824 + 0.0239499i
\(375\) 0 0
\(376\) −8.69368e6 + 1.50579e7i −0.163546 + 0.283270i
\(377\) 3.22127e7i 0.601179i
\(378\) 0 0
\(379\) −4.48086e7 −0.823083 −0.411541 0.911391i \(-0.635009\pi\)
−0.411541 + 0.911391i \(0.635009\pi\)
\(380\) 3.71607e6 + 2.14548e6i 0.0677226 + 0.0390996i
\(381\) 0 0
\(382\) −1.07652e7 1.86458e7i −0.193121 0.334496i
\(383\) 7.76185e7 4.48131e7i 1.38156 0.797643i 0.389214 0.921147i \(-0.372747\pi\)
0.992344 + 0.123504i \(0.0394133\pi\)
\(384\) 0 0
\(385\) 10063.9 17431.2i 0.000176353 0.000305453i
\(386\) 7.32832e6i 0.127421i
\(387\) 0 0
\(388\) −1.33820e7 −0.229101
\(389\) 3.03701e7 + 1.75342e7i 0.515938 + 0.297877i 0.735271 0.677773i \(-0.237055\pi\)
−0.219333 + 0.975650i \(0.570388\pi\)
\(390\) 0 0
\(391\) −3.99619e6 6.92160e6i −0.0668522 0.115791i
\(392\) −1.84375e7 + 1.06449e7i −0.306086 + 0.176719i
\(393\) 0 0
\(394\) 1.69554e7 2.93676e7i 0.277216 0.480152i
\(395\) 1.17074e7i 0.189963i
\(396\) 0 0
\(397\) 8.17666e7 1.30679 0.653393 0.757019i \(-0.273345\pi\)
0.653393 + 0.757019i \(0.273345\pi\)
\(398\) −5.14008e6 2.96762e6i −0.0815305 0.0470717i
\(399\) 0 0
\(400\) −7.68467e6 1.33102e7i −0.120073 0.207973i
\(401\) −5.28941e7 + 3.05384e7i −0.820303 + 0.473602i −0.850521 0.525941i \(-0.823713\pi\)
0.0302179 + 0.999543i \(0.490380\pi\)
\(402\) 0 0
\(403\) 2.14843e6 3.72119e6i 0.0328251 0.0568547i
\(404\) 2.14933e7i 0.325956i
\(405\) 0 0
\(406\) 1.22459e6 0.0182984
\(407\) 784080. + 452689.i 0.0116299 + 0.00671455i
\(408\) 0 0
\(409\) −3.34641e7 5.79615e7i −0.489113 0.847168i 0.510809 0.859694i \(-0.329346\pi\)
−0.999922 + 0.0125261i \(0.996013\pi\)
\(410\) −6.54714e6 + 3.78000e6i −0.0949949 + 0.0548453i
\(411\) 0 0
\(412\) 1.12320e7 1.94544e7i 0.160607 0.278180i
\(413\) 180166.i 0.00255755i
\(414\) 0 0
\(415\) 832601. 0.0116491
\(416\) −4.62530e6 2.67042e6i −0.0642480 0.0370936i
\(417\) 0 0
\(418\) 2.00047e6 + 3.46492e6i 0.0273907 + 0.0474421i
\(419\) 8.43503e7 4.86997e7i 1.14669 0.662040i 0.198609 0.980079i \(-0.436358\pi\)
0.948078 + 0.318039i \(0.103024\pi\)
\(420\) 0 0
\(421\) −3.79673e7 + 6.57613e7i −0.508819 + 0.881300i 0.491129 + 0.871087i \(0.336584\pi\)
−0.999948 + 0.0102133i \(0.996749\pi\)
\(422\) 3.13507e7i 0.417167i
\(423\) 0 0
\(424\) 2.39507e7 0.314211
\(425\) −4.39877e7 2.53963e7i −0.573012 0.330829i
\(426\) 0 0
\(427\) 993448. + 1.72070e6i 0.0127603 + 0.0221015i
\(428\) −9.71515e6 + 5.60905e6i −0.123913 + 0.0715415i
\(429\) 0 0
\(430\) −8.64299e6 + 1.49701e7i −0.108707 + 0.188287i
\(431\) 1.10356e8i 1.37836i 0.724590 + 0.689180i \(0.242029\pi\)
−0.724590 + 0.689180i \(0.757971\pi\)
\(432\) 0 0
\(433\) 7.04803e7 0.868168 0.434084 0.900872i \(-0.357072\pi\)
0.434084 + 0.900872i \(0.357072\pi\)
\(434\) −141463. 81673.9i −0.00173051 0.000999112i
\(435\) 0 0
\(436\) 1.15899e7 + 2.00743e7i 0.139836 + 0.242204i
\(437\) −1.10515e7 + 6.38057e6i −0.132427 + 0.0764567i
\(438\) 0 0
\(439\) 5.59868e6 9.69720e6i 0.0661747 0.114618i −0.831040 0.556213i \(-0.812254\pi\)
0.897214 + 0.441595i \(0.145587\pi\)
\(440\) 588029.i 0.00690304i
\(441\) 0 0
\(442\) −1.76504e7 −0.204403
\(443\) 1.34069e8 + 7.74049e7i 1.54212 + 0.890343i 0.998705 + 0.0508793i \(0.0162024\pi\)
0.543415 + 0.839464i \(0.317131\pi\)
\(444\) 0 0
\(445\) −1.25998e7 2.18236e7i −0.142983 0.247654i
\(446\) −2.02703e7 + 1.17031e7i −0.228484 + 0.131915i
\(447\) 0 0
\(448\) −101518. + 175834.i −0.00112904 + 0.00195555i
\(449\) 9.20846e7i 1.01730i −0.860974 0.508648i \(-0.830145\pi\)
0.860974 0.508648i \(-0.169855\pi\)
\(450\) 0 0
\(451\) −7.04904e6 −0.0768423
\(452\) 3.50142e7 + 2.02154e7i 0.379165 + 0.218911i
\(453\) 0 0
\(454\) 4.17490e7 + 7.23114e7i 0.446147 + 0.772750i
\(455\) 122781. 70887.8i 0.00130346 0.000752553i
\(456\) 0 0
\(457\) −4.18331e7 + 7.24571e7i −0.438300 + 0.759159i −0.997559 0.0698349i \(-0.977753\pi\)
0.559258 + 0.828994i \(0.311086\pi\)
\(458\) 8.27864e7i 0.861712i
\(459\) 0 0
\(460\) −1.87554e6 −0.0192687
\(461\) −1.03069e8 5.95070e7i −1.05203 0.607387i −0.128809 0.991669i \(-0.541116\pi\)
−0.923216 + 0.384282i \(0.874449\pi\)
\(462\) 0 0
\(463\) 5.67866e7 + 9.83573e7i 0.572141 + 0.990977i 0.996346 + 0.0854109i \(0.0272203\pi\)
−0.424205 + 0.905566i \(0.639446\pi\)
\(464\) −3.09830e7 + 1.78881e7i −0.310149 + 0.179065i
\(465\) 0 0
\(466\) −4.29294e6 + 7.43559e6i −0.0424226 + 0.0734781i
\(467\) 1.34722e8i 1.32278i −0.750044 0.661388i \(-0.769968\pi\)
0.750044 0.661388i \(-0.230032\pi\)
\(468\) 0 0
\(469\) 3.28284e6 0.0318223
\(470\) 1.16778e7 + 6.74215e6i 0.112478 + 0.0649389i
\(471\) 0 0
\(472\) −2.63176e6 4.55834e6i −0.0250277 0.0433492i
\(473\) −1.39583e7 + 8.05884e6i −0.131901 + 0.0761534i
\(474\) 0 0
\(475\) −4.05494e7 + 7.02336e7i −0.378358 + 0.655336i
\(476\) 670991.i 0.00622151i
\(477\) 0 0
\(478\) −7.89742e7 −0.723105
\(479\) 1.39409e8 + 8.04877e7i 1.26848 + 0.732357i 0.974700 0.223516i \(-0.0717536\pi\)
0.293779 + 0.955873i \(0.405087\pi\)
\(480\) 0 0
\(481\) 3.18864e6 + 5.52289e6i 0.0286530 + 0.0496285i
\(482\) −1.24025e8 + 7.16056e7i −1.10756 + 0.639449i
\(483\) 0 0
\(484\) 2.80708e7 4.86201e7i 0.247582 0.428825i
\(485\) 1.03781e7i 0.0909687i
\(486\) 0 0
\(487\) 1.14964e7 0.0995351 0.0497676 0.998761i \(-0.484152\pi\)
0.0497676 + 0.998761i \(0.484152\pi\)
\(488\) −5.02700e7 2.90234e7i −0.432563 0.249740i
\(489\) 0 0
\(490\) 8.25537e6 + 1.42987e7i 0.0701695 + 0.121537i
\(491\) 1.20638e8 6.96503e7i 1.01915 0.588408i 0.105294 0.994441i \(-0.466422\pi\)
0.913858 + 0.406033i \(0.133088\pi\)
\(492\) 0 0
\(493\) −5.91164e7 + 1.02393e8i −0.493364 + 0.854532i
\(494\) 2.81818e7i 0.233769i
\(495\) 0 0
\(496\) 4.77217e6 0.0391085
\(497\) −3.37264e6 1.94720e6i −0.0274727 0.0158614i
\(498\) 0 0
\(499\) 4.67348e7 + 8.09470e7i 0.376130 + 0.651477i 0.990496 0.137545i \(-0.0439211\pi\)
−0.614365 + 0.789022i \(0.710588\pi\)
\(500\) −2.10684e7 + 1.21638e7i −0.168547 + 0.0973107i
\(501\) 0 0
\(502\) −1.01371e7 + 1.75579e7i −0.0801313 + 0.138791i
\(503\) 2.32808e8i 1.82934i −0.404200 0.914671i \(-0.632450\pi\)
0.404200 0.914671i \(-0.367550\pi\)
\(504\) 0 0
\(505\) 1.66686e7 0.129427
\(506\) −1.51449e6 874389.i −0.0116900 0.00674921i
\(507\) 0 0
\(508\) 4.27837e7 + 7.41036e7i 0.326353 + 0.565260i
\(509\) −1.48895e8 + 8.59645e7i −1.12908 + 0.651877i −0.943705 0.330790i \(-0.892685\pi\)
−0.185380 + 0.982667i \(0.559352\pi\)
\(510\) 0 0
\(511\) −213079. + 369063.i −0.00159690 + 0.00276591i
\(512\) 5.93164e6i 0.0441942i
\(513\) 0 0
\(514\) −1.31186e8 −0.966046
\(515\) −1.50873e7 8.71067e6i −0.110456 0.0637719i
\(516\) 0 0
\(517\) 6.28648e6 + 1.08885e7i 0.0454921 + 0.0787946i
\(518\) 209956. 121218.i 0.00151057 0.000872126i
\(519\) 0 0
\(520\) −2.07097e6 + 3.58703e6i −0.0147287 + 0.0255108i
\(521\) 2.02142e8i 1.42937i −0.699447 0.714684i \(-0.746570\pi\)
0.699447 0.714684i \(-0.253430\pi\)
\(522\) 0 0
\(523\) −8.40337e7 −0.587419 −0.293710 0.955895i \(-0.594890\pi\)
−0.293710 + 0.955895i \(0.594890\pi\)
\(524\) 9.94376e7 + 5.74103e7i 0.691125 + 0.399021i
\(525\) 0 0
\(526\) 5.65006e7 + 9.78620e7i 0.388236 + 0.672445i
\(527\) 1.36581e7 7.88553e6i 0.0933168 0.0538765i
\(528\) 0 0
\(529\) −7.12291e7 + 1.23372e8i −0.481161 + 0.833395i
\(530\) 1.85743e7i 0.124763i
\(531\) 0 0
\(532\) 1.07135e6 0.00711534
\(533\) −4.29998e7 2.48259e7i −0.283978 0.163955i
\(534\) 0 0
\(535\) 4.34995e6 + 7.53433e6i 0.0284068 + 0.0492021i
\(536\) −8.30583e7 + 4.79537e7i −0.539372 + 0.311407i
\(537\) 0 0
\(538\) −2.98100e7 + 5.16325e7i −0.191432 + 0.331571i
\(539\) 1.53948e7i 0.0983125i
\(540\) 0 0
\(541\) 5.27746e7 0.333299 0.166649 0.986016i \(-0.446705\pi\)
0.166649 + 0.986016i \(0.446705\pi\)
\(542\) −1.35622e8 7.83016e7i −0.851792 0.491782i
\(543\) 0 0
\(544\) −9.80144e6 1.69766e7i −0.0608826 0.105452i
\(545\) 1.55681e7 8.98824e6i 0.0961713 0.0555246i
\(546\) 0 0
\(547\) −3.12323e7 + 5.40959e7i −0.190828 + 0.330523i −0.945525 0.325550i \(-0.894451\pi\)
0.754697 + 0.656073i \(0.227784\pi\)
\(548\) 4.89771e7i 0.297613i
\(549\) 0 0
\(550\) −1.11137e7 −0.0667991
\(551\) 1.63487e8 + 9.43892e7i 0.977300 + 0.564245i
\(552\) 0 0
\(553\) 1.46153e6 + 2.53144e6i 0.00864236 + 0.0149690i
\(554\) −4.00048e7 + 2.30968e7i −0.235279 + 0.135838i
\(555\) 0 0
\(556\) 5.64426e7 9.77614e7i 0.328384 0.568778i
\(557\) 1.98446e8i 1.14836i −0.818730 0.574178i \(-0.805322\pi\)
0.818730 0.574178i \(-0.194678\pi\)
\(558\) 0 0
\(559\) −1.13529e8 −0.649939
\(560\) 136363. + 78729.4i 0.000776486 + 0.000448304i
\(561\) 0 0
\(562\) 1.26017e7 + 2.18268e7i 0.0709938 + 0.122965i
\(563\) 8.55525e7 4.93937e7i 0.479410 0.276788i −0.240760 0.970585i \(-0.577397\pi\)
0.720171 + 0.693797i \(0.244063\pi\)
\(564\) 0 0
\(565\) 1.56775e7 2.71543e7i 0.0869226 0.150554i
\(566\) 1.80356e8i 0.994674i
\(567\) 0 0
\(568\) 1.13774e8 0.620865
\(569\) −1.42132e8 8.20597e7i −0.771531 0.445444i 0.0618893 0.998083i \(-0.480287\pi\)
−0.833421 + 0.552639i \(0.813621\pi\)
\(570\) 0 0
\(571\) 9.76077e7 + 1.69061e8i 0.524295 + 0.908106i 0.999600 + 0.0282845i \(0.00900442\pi\)
−0.475305 + 0.879821i \(0.657662\pi\)
\(572\) −3.34459e6 + 1.93100e6i −0.0178713 + 0.0103180i
\(573\) 0 0
\(574\) −943775. + 1.63467e6i −0.00499037 + 0.00864357i
\(575\) 3.54476e7i 0.186459i
\(576\) 0 0
\(577\) 1.93319e8 1.00634 0.503172 0.864186i \(-0.332166\pi\)
0.503172 + 0.864186i \(0.332166\pi\)
\(578\) 6.21453e7 + 3.58796e7i 0.321829 + 0.185808i
\(579\) 0 0
\(580\) 1.38726e7 + 2.40281e7i 0.0711008 + 0.123150i
\(581\) 180030. 103940.i 0.000917944 0.000529975i
\(582\) 0 0
\(583\) 8.65948e6 1.49987e7i 0.0437005 0.0756915i
\(584\) 1.24501e7i 0.0625078i
\(585\) 0 0
\(586\) −2.02047e8 −1.00406
\(587\) 2.90014e7 + 1.67440e7i 0.143385 + 0.0827835i 0.569976 0.821661i \(-0.306952\pi\)
−0.426591 + 0.904445i \(0.640286\pi\)
\(588\) 0 0
\(589\) −1.25906e7 2.18075e7i −0.0616168 0.106723i
\(590\) −3.53510e6 + 2.04099e6i −0.0172126 + 0.00993769i
\(591\) 0 0
\(592\) −3.54137e6 + 6.13383e6i −0.0170689 + 0.0295642i
\(593\) 3.75231e8i 1.79943i 0.436479 + 0.899715i \(0.356225\pi\)
−0.436479 + 0.899715i \(0.643775\pi\)
\(594\) 0 0
\(595\) 520369. 0.00247036
\(596\) 6.63806e7 + 3.83249e7i 0.313547 + 0.181026i
\(597\) 0 0
\(598\) −6.15900e6 1.06677e7i −0.0288009 0.0498847i
\(599\) 2.57196e8 1.48492e8i 1.19670 0.690913i 0.236879 0.971539i \(-0.423875\pi\)
0.959817 + 0.280626i \(0.0905421\pi\)
\(600\) 0 0
\(601\) −7.77944e7 + 1.34744e8i −0.358365 + 0.620706i −0.987688 0.156438i \(-0.949999\pi\)
0.629323 + 0.777144i \(0.283332\pi\)
\(602\) 4.31590e6i 0.0197825i
\(603\) 0 0
\(604\) 9.65360e7 0.438105
\(605\) −3.77060e7 2.17696e7i −0.170273 0.0983069i
\(606\) 0 0
\(607\) −1.11404e8 1.92958e8i −0.498122 0.862773i 0.501875 0.864940i \(-0.332644\pi\)
−0.999998 + 0.00216674i \(0.999310\pi\)
\(608\) −2.71059e7 + 1.56496e7i −0.120602 + 0.0696294i
\(609\) 0 0
\(610\) −2.25083e7 + 3.89855e7i −0.0991639 + 0.171757i
\(611\) 8.85611e7i 0.388257i
\(612\) 0 0
\(613\) 1.22144e8 0.530262 0.265131 0.964212i \(-0.414585\pi\)
0.265131 + 0.964212i \(0.414585\pi\)
\(614\) −2.45498e7 1.41738e7i −0.106058 0.0612326i
\(615\) 0 0
\(616\) 73408.4 + 127147.i 0.000314053 + 0.000543956i
\(617\) −3.26624e8 + 1.88577e8i −1.39057 + 0.802846i −0.993378 0.114890i \(-0.963348\pi\)
−0.397191 + 0.917736i \(0.630015\pi\)
\(618\) 0 0
\(619\) 2.18072e8 3.77712e8i 0.919450 1.59253i 0.119198 0.992871i \(-0.461968\pi\)
0.800252 0.599663i \(-0.204699\pi\)
\(620\) 3.70093e6i 0.0155287i
\(621\) 0 0
\(622\) 1.64965e8 0.685520
\(623\) −5.44882e6 3.14588e6i −0.0225340 0.0130100i
\(624\) 0 0
\(625\) −1.07825e8 1.86759e8i −0.441653 0.764966i
\(626\) 1.50313e8 8.67834e7i 0.612737 0.353764i
\(627\) 0 0
\(628\) 8.93522e7 1.54763e8i 0.360767 0.624866i
\(629\) 2.34070e7i 0.0940577i
\(630\) 0 0
\(631\) −8.46175e7 −0.336800 −0.168400 0.985719i \(-0.553860\pi\)
−0.168400 + 0.985719i \(0.553860\pi\)
\(632\) −7.39556e7 4.26983e7i −0.292968 0.169145i
\(633\) 0 0
\(634\) −1.43518e8 2.48580e8i −0.563167 0.975434i
\(635\) 5.74691e7 3.31798e7i 0.224447 0.129584i
\(636\) 0 0
\(637\) −5.42189e7 + 9.39099e7i −0.209765 + 0.363323i
\(638\) 2.58700e7i 0.0996173i
\(639\) 0 0
\(640\) −4.60013e6 −0.0175481
\(641\) −9.93835e7 5.73791e7i −0.377347 0.217861i 0.299317 0.954154i \(-0.403241\pi\)
−0.676663 + 0.736293i \(0.736575\pi\)
\(642\) 0 0
\(643\) −1.03843e7 1.79862e7i −0.0390612 0.0676560i 0.845834 0.533446i \(-0.179103\pi\)
−0.884895 + 0.465790i \(0.845770\pi\)
\(644\) −405540. + 234139.i −0.00151836 + 0.000876628i
\(645\) 0 0
\(646\) −5.17188e7 + 8.95796e7i −0.191845 + 0.332286i
\(647\) 5.18773e8i 1.91542i 0.287734 + 0.957710i \(0.407098\pi\)
−0.287734 + 0.957710i \(0.592902\pi\)
\(648\) 0 0
\(649\) −3.80610e6 −0.0139234
\(650\) −6.77946e7 3.91413e7i −0.246863 0.142526i
\(651\) 0 0
\(652\) −3.93662e7 6.81843e7i −0.142030 0.246004i
\(653\) 1.08224e8 6.24831e7i 0.388673 0.224400i −0.292912 0.956139i \(-0.594624\pi\)
0.681585 + 0.731739i \(0.261291\pi\)
\(654\) 0 0
\(655\) 4.45231e7 7.71162e7i 0.158439 0.274424i
\(656\) 5.51444e7i 0.195339i
\(657\) 0 0
\(658\) 3.36671e6 0.0118176
\(659\) 4.37563e8 + 2.52627e8i 1.52892 + 0.882721i 0.999408 + 0.0344179i \(0.0109577\pi\)
0.529511 + 0.848303i \(0.322376\pi\)
\(660\) 0 0
\(661\) −2.09467e8 3.62807e8i −0.725289 1.25624i −0.958855 0.283896i \(-0.908373\pi\)
0.233567 0.972341i \(-0.424960\pi\)
\(662\) 2.06456e8 1.19197e8i 0.711629 0.410859i
\(663\) 0 0
\(664\) −3.03659e6 + 5.25954e6i −0.0103725 + 0.0179657i
\(665\) 830856.i 0.00282528i
\(666\) 0 0
\(667\) −8.25134e7 −0.278065
\(668\) 1.11482e8 + 6.43641e7i 0.374003 + 0.215931i
\(669\) 0 0
\(670\) 3.71893e7 + 6.44137e7i 0.123650 + 0.214168i
\(671\) −3.63506e7 + 2.09871e7i −0.120322 + 0.0694679i
\(672\) 0 0
\(673\) 1.99125e8 3.44894e8i 0.653250 1.13146i −0.329079 0.944302i \(-0.606738\pi\)
0.982329 0.187160i \(-0.0599284\pi\)
\(674\) 347516.i 0.00113500i
\(675\) 0 0
\(676\) 1.27255e8 0.411940
\(677\) −4.73100e8 2.73145e8i −1.52471 0.880292i −0.999571 0.0292753i \(-0.990680\pi\)
−0.525139 0.851017i \(-0.675987\pi\)
\(678\) 0 0
\(679\) 1.29558e6 + 2.24401e6i 0.00413862 + 0.00716829i
\(680\) −1.31657e7 + 7.60124e6i −0.0418715 + 0.0241745i
\(681\) 0 0
\(682\) 1.72540e6 2.98848e6i 0.00543922 0.00942101i
\(683\) 3.24992e7i 0.102002i 0.998699 + 0.0510012i \(0.0162412\pi\)
−0.998699 + 0.0510012i \(0.983759\pi\)
\(684\) 0 0
\(685\) −3.79829e7 −0.118173
\(686\) 7.14126e6 + 4.12301e6i 0.0221209 + 0.0127715i
\(687\) 0 0
\(688\) −6.30440e7 1.09195e8i −0.193588 0.335304i
\(689\) 1.05647e8 6.09955e7i 0.322999 0.186483i
\(690\) 0 0
\(691\) 1.43850e8 2.49156e8i 0.435989 0.755156i −0.561386 0.827554i \(-0.689732\pi\)
0.997376 + 0.0723981i \(0.0230652\pi\)
\(692\) 1.32435e8i 0.399653i
\(693\) 0 0
\(694\) −1.37625e8 −0.411736
\(695\) −7.58163e7 4.37725e7i −0.225844 0.130391i
\(696\) 0 0
\(697\) −9.11205e7 1.57825e8i −0.269103 0.466099i
\(698\) 1.23468e8 7.12843e7i 0.363068 0.209618i
\(699\) 0 0
\(700\) −1.48798e6 + 2.57726e6i −0.00433814 + 0.00751388i
\(701\) 2.82907e8i 0.821278i 0.911798 + 0.410639i \(0.134694\pi\)
−0.911798 + 0.410639i \(0.865306\pi\)
\(702\) 0 0
\(703\) 3.73732e7 0.107571
\(704\) −3.71457e6 2.14461e6i −0.0106461 0.00614654i
\(705\) 0 0
\(706\) −1.95475e8 3.38572e8i −0.555490 0.962137i
\(707\) 3.60417e6 2.08087e6i 0.0101988 0.00588826i
\(708\) 0 0
\(709\) 1.19975e8 2.07803e8i 0.336629 0.583059i −0.647167 0.762348i \(-0.724046\pi\)
0.983796 + 0.179289i \(0.0573798\pi\)
\(710\) 8.82343e7i 0.246526i
\(711\) 0 0
\(712\) 1.83812e8 0.509254
\(713\) 9.53187e6 + 5.50323e6i 0.0262972 + 0.0151827i
\(714\) 0 0
\(715\) 1.49754e6 + 2.59381e6i 0.00409694 + 0.00709611i
\(716\) 1.28757e8 7.43376e7i 0.350776 0.202521i
\(717\) 0 0
\(718\) −3.98980e7 + 6.91054e7i −0.107790 + 0.186698i
\(719\) 2.12836e7i 0.0572611i −0.999590 0.0286305i \(-0.990885\pi\)
0.999590 0.0286305i \(-0.00911463\pi\)
\(720\) 0 0
\(721\) −4.34969e6 −0.0116052
\(722\) −8.74482e7 5.04882e7i −0.232348 0.134146i
\(723\) 0 0
\(724\) 3.22328e7 + 5.58289e7i 0.0849342 + 0.147110i
\(725\) −4.54129e8 + 2.62192e8i −1.19170 + 0.688026i
\(726\) 0 0
\(727\) 8.88685e7 1.53925e8i 0.231283 0.400595i −0.726903 0.686741i \(-0.759041\pi\)
0.958186 + 0.286146i \(0.0923742\pi\)
\(728\) 1.03414e6i 0.00268032i
\(729\) 0 0
\(730\) −9.65535e6 −0.0248199
\(731\) −3.60869e8 2.08348e8i −0.923841 0.533380i
\(732\) 0 0
\(733\) 2.61308e8 + 4.52599e8i 0.663501 + 1.14922i 0.979690 + 0.200520i \(0.0642633\pi\)
−0.316189 + 0.948696i \(0.602403\pi\)
\(734\) 3.98995e8 2.30360e8i 1.00897 0.582531i
\(735\) 0 0
\(736\) 6.84031e6 1.18478e7i 0.0171570 0.0297169i
\(737\) 6.93515e7i 0.173242i
\(738\) 0 0
\(739\) −5.12661e8 −1.27027 −0.635137 0.772400i \(-0.719056\pi\)
−0.635137 + 0.772400i \(0.719056\pi\)
\(740\) 4.75693e6 + 2.74642e6i 0.0117390 + 0.00677753i
\(741\) 0 0
\(742\) −2.31879e6 4.01625e6i −0.00567608 0.00983127i
\(743\) 9.47357e7 5.46957e7i 0.230966 0.133348i −0.380052 0.924965i \(-0.624094\pi\)
0.611017 + 0.791617i \(0.290761\pi\)
\(744\) 0 0
\(745\) 2.97219e7 5.14798e7i 0.0718798 0.124500i
\(746\) 4.29763e8i 1.03517i
\(747\) 0 0
\(748\) −1.41750e7 −0.0338703
\(749\) 1.88114e6 + 1.08608e6i 0.00447689 + 0.00258473i
\(750\) 0 0
\(751\) 1.80758e8 + 3.13082e8i 0.426755 + 0.739161i 0.996583 0.0826034i \(-0.0263235\pi\)
−0.569828 + 0.821764i \(0.692990\pi\)
\(752\) −8.51803e7 + 4.91789e7i −0.200302 + 0.115645i
\(753\) 0 0
\(754\) −9.11114e7 + 1.57810e8i −0.212549 + 0.368145i
\(755\) 7.48659e7i 0.173958i
\(756\) 0 0
\(757\) 8.46631e7 0.195167 0.0975835 0.995227i \(-0.468889\pi\)
0.0975835 + 0.995227i \(0.468889\pi\)
\(758\) −2.19516e8 1.26738e8i −0.504033 0.291004i
\(759\) 0 0
\(760\) 1.21366e7 + 2.10213e7i 0.0276476 + 0.0478871i
\(761\) −8.57072e7 + 4.94831e7i −0.194475 + 0.112280i −0.594076 0.804409i \(-0.702482\pi\)
0.399601 + 0.916689i \(0.369149\pi\)
\(762\) 0 0
\(763\) 2.24415e6 3.88698e6i 0.00505217 0.00875062i
\(764\) 1.21794e8i 0.273115i
\(765\) 0 0
\(766\) 5.07002e8 1.12804
\(767\) −2.32175e7 1.34047e7i −0.0514553 0.0297077i
\(768\) 0 0
\(769\) 2.70757e7 + 4.68965e7i 0.0595390 + 0.103124i 0.894259 0.447551i \(-0.147704\pi\)
−0.834720 + 0.550675i \(0.814370\pi\)
\(770\) 98605.5 56929.9i 0.000215988 0.000124701i
\(771\) 0 0
\(772\) −2.07276e7 + 3.59013e7i −0.0450503 + 0.0780293i
\(773\) 9.36821e7i 0.202823i 0.994845 + 0.101412i \(0.0323359\pi\)
−0.994845 + 0.101412i \(0.967664\pi\)
\(774\) 0 0
\(775\) 6.99474e7 0.150268
\(776\) −6.55583e7 3.78501e7i −0.140295 0.0809995i
\(777\) 0 0
\(778\) 9.91884e7 + 1.71799e8i 0.210631 + 0.364824i
\(779\) −2.51994e8 + 1.45489e8i −0.533063 + 0.307764i
\(780\) 0 0
\(781\) 4.11354e7 7.12486e7i 0.0863501 0.149563i
\(782\) 4.52117e7i 0.0945432i
\(783\) 0 0
\(784\) −1.20433e8 −0.249918
\(785\) −1.20022e8 6.92947e7i −0.248114 0.143249i
\(786\) 0 0
\(787\) 1.59674e8 + 2.76563e8i 0.327574 + 0.567374i 0.982030 0.188726i \(-0.0604357\pi\)
−0.654456 + 0.756100i \(0.727102\pi\)
\(788\) 1.66128e8 9.59140e7i 0.339519 0.196021i
\(789\) 0 0
\(790\) −3.31135e7 + 5.73543e7i −0.0671621 + 0.116328i
\(791\) 7.82862e6i 0.0158181i
\(792\) 0 0
\(793\) −2.95656e8 −0.592881
\(794\) 4.00573e8 + 2.31271e8i 0.800240 + 0.462019i
\(795\) 0 0
\(796\) −1.67874e7 2.90767e7i −0.0332847 0.0576508i
\(797\) −2.16214e8 + 1.24831e8i −0.427080 + 0.246575i −0.698102 0.715998i \(-0.745972\pi\)
0.271022 + 0.962573i \(0.412638\pi\)
\(798\) 0 0
\(799\) −1.62526e8 + 2.81504e8i −0.318627 + 0.551879i
\(800\) 8.69422e7i 0.169809i
\(801\) 0 0
\(802\) −3.45503e8 −0.669775
\(803\) −7.79663e6 4.50139e6i −0.0150578 0.00869360i
\(804\) 0 0
\(805\) 181580. + 314506.i 0.000348081 + 0.000602894i
\(806\) 2.10502e7 1.21533e7i 0.0402023 0.0232108i
\(807\) 0 0
\(808\) −6.07922e7 + 1.05295e8i −0.115243 + 0.199606i
\(809\) 3.16268e8i 0.597323i −0.954359 0.298661i \(-0.903460\pi\)
0.954359 0.298661i \(-0.0965401\pi\)
\(810\) 0 0
\(811\) 1.23239e8 0.231038 0.115519 0.993305i \(-0.463147\pi\)
0.115519 + 0.993305i \(0.463147\pi\)
\(812\) 5.99924e6 + 3.46366e6i 0.0112054 + 0.00646945i
\(813\) 0 0
\(814\) 2.56080e6 + 4.43543e6i 0.00474790 + 0.00822361i
\(815\) −5.28786e7 + 3.05294e7i −0.0976802 + 0.0563957i
\(816\) 0 0
\(817\) −3.32662e8 + 5.76187e8i −0.610009 + 1.05657i
\(818\) 3.78603e8i 0.691710i
\(819\) 0 0
\(820\) −4.27658e7 −0.0775630
\(821\) 4.83629e8 + 2.79223e8i 0.873943 + 0.504571i 0.868656 0.495415i \(-0.164984\pi\)
0.00528613 + 0.999986i \(0.498317\pi\)
\(822\) 0 0
\(823\) 2.33574e8 + 4.04562e8i 0.419010 + 0.725747i 0.995840 0.0911171i \(-0.0290438\pi\)
−0.576830 + 0.816864i \(0.695710\pi\)
\(824\) 1.10050e8 6.35377e7i 0.196703 0.113566i
\(825\) 0 0
\(826\) −509587. + 882631.i −0.000904229 + 0.00156617i
\(827\) 2.65712e8i 0.469780i −0.972022 0.234890i \(-0.924527\pi\)
0.972022 0.234890i \(-0.0754730\pi\)
\(828\) 0 0
\(829\) −4.35459e8 −0.764335 −0.382167 0.924093i \(-0.624822\pi\)
−0.382167 + 0.924093i \(0.624822\pi\)
\(830\) 4.07889e6 + 2.35495e6i 0.00713359 + 0.00411858i
\(831\) 0 0
\(832\) −1.51062e7 2.61646e7i −0.0262292 0.0454302i
\(833\) −3.44685e8 + 1.99004e8i −0.596330 + 0.344291i
\(834\) 0 0
\(835\) 4.99158e7 8.64568e7i 0.0857391 0.148504i
\(836\) 2.26327e7i 0.0387363i
\(837\) 0 0
\(838\) 5.50974e8 0.936266
\(839\) 7.95763e8 + 4.59434e8i 1.34740 + 0.777925i 0.987881 0.155211i \(-0.0496059\pi\)
0.359524 + 0.933136i \(0.382939\pi\)
\(840\) 0 0
\(841\) 3.12907e8 + 5.41972e8i 0.526051 + 0.911147i
\(842\) −3.72002e8 + 2.14775e8i −0.623173 + 0.359789i
\(843\) 0 0
\(844\) −8.86732e7 + 1.53586e8i −0.147491 + 0.255462i
\(845\) 9.86891e7i 0.163568i
\(846\) 0 0
\(847\) −1.08707e7 −0.0178899
\(848\) 1.17334e8 + 6.77428e7i 0.192414 + 0.111090i
\(849\) 0 0
\(850\) −1.43663e8 2.48832e8i −0.233931 0.405181i
\(851\) −1.41470e7 + 8.16775e6i −0.0229548 + 0.0132530i
\(852\) 0 0
\(853\) −3.48121e8 + 6.02964e8i −0.560897 + 0.971503i 0.436521 + 0.899694i \(0.356210\pi\)
−0.997418 + 0.0718085i \(0.977123\pi\)
\(854\) 1.12396e7i 0.0180458i
\(855\) 0 0
\(856\) −6.34591e7 −0.101175
\(857\) −2.23831e8 1.29229e8i −0.355614 0.205314i 0.311541 0.950233i \(-0.399155\pi\)
−0.667155 + 0.744919i \(0.732488\pi\)
\(858\) 0 0
\(859\) −1.96911e8 3.41061e8i −0.310664 0.538087i 0.667842 0.744303i \(-0.267218\pi\)
−0.978506 + 0.206217i \(0.933885\pi\)
\(860\) −8.46836e7 + 4.88921e7i −0.133139 + 0.0768676i
\(861\) 0 0
\(862\) −3.12133e8 + 5.40630e8i −0.487324 + 0.844069i
\(863\) 4.97185e8i 0.773545i 0.922175 + 0.386773i \(0.126410\pi\)
−0.922175 + 0.386773i \(0.873590\pi\)
\(864\) 0 0
\(865\) −1.02706e8 −0.158690
\(866\) 3.45281e8 + 1.99348e8i 0.531642 + 0.306944i
\(867\) 0 0
\(868\) −462018. 800238.i −0.000706479 0.00122366i
\(869\) −5.34780e7 + 3.08755e7i −0.0814921 + 0.0470495i
\(870\) 0 0
\(871\) −2.44248e8 + 4.23051e8i −0.369639 + 0.640233i
\(872\) 1.31125e8i 0.197758i
\(873\) 0 0
\(874\) −7.21879e7 −0.108126
\(875\) 4.07947e6 + 2.35528e6i 0.00608946 + 0.00351575i
\(876\) 0 0
\(877\) −2.87178e7 4.97407e7i −0.0425748 0.0737417i 0.843953 0.536417i \(-0.180223\pi\)
−0.886528 + 0.462676i \(0.846889\pi\)
\(878\) 5.48556e7 3.16709e7i 0.0810471 0.0467926i
\(879\) 0 0
\(880\) −1.66320e6 + 2.88074e6i −0.00244059 + 0.00422723i
\(881\) 2.82313e8i 0.412861i −0.978461 0.206430i \(-0.933815\pi\)
0.978461 0.206430i \(-0.0661847\pi\)
\(882\) 0 0
\(883\) 5.96066e8 0.865789 0.432895 0.901445i \(-0.357492\pi\)
0.432895 + 0.901445i \(0.357492\pi\)
\(884\) −8.64688e7 4.99228e7i −0.125171 0.0722674i
\(885\) 0 0
\(886\) 4.37868e8 + 7.58410e8i 0.629568 + 1.09044i
\(887\) −7.03514e8 + 4.06174e8i −1.00810 + 0.582025i −0.910634 0.413214i \(-0.864406\pi\)
−0.0974628 + 0.995239i \(0.531073\pi\)
\(888\) 0 0
\(889\) 8.28421e6 1.43487e7i 0.0117909 0.0204224i
\(890\) 1.42551e8i 0.202209i
\(891\) 0 0
\(892\) −1.32405e8 −0.186557
\(893\) 4.49467e8 + 2.59500e8i 0.631166 + 0.364404i
\(894\) 0 0
\(895\) −5.76506e7 9.98537e7i −0.0804145 0.139282i
\(896\) −994667. + 574271.i −0.00138278 + 0.000798349i
\(897\) 0 0
\(898\) 2.60454e8 4.51120e8i 0.359669 0.622965i
\(899\) 1.62821e8i 0.224094i
\(900\) 0 0
\(901\) 4.47753e8 0.612158
\(902\) −3.45331e7 1.99377e7i −0.0470561 0.0271678i
\(903\) 0 0
\(904\) 1.14356e8 + 1.98070e8i 0.154793 + 0.268110i
\(905\) 4.32966e7 2.49973e7i 0.0584128 0.0337247i
\(906\) 0 0
\(907\) −4.94339e8 + 8.56220e8i −0.662526 + 1.14753i 0.317424 + 0.948284i \(0.397182\pi\)
−0.979950 + 0.199245i \(0.936151\pi\)
\(908\) 4.72336e8i 0.630948i
\(909\) 0 0
\(910\) 802004. 0.00106427
\(911\) 4.44753e8 + 2.56778e8i 0.588252 + 0.339628i 0.764406 0.644735i \(-0.223032\pi\)
−0.176154 + 0.984363i \(0.556366\pi\)
\(912\) 0 0
\(913\) 2.19579e6 + 3.80322e6i 0.00288521 + 0.00499734i
\(914\) −4.09879e8 + 2.36644e8i −0.536806 + 0.309925i
\(915\) 0 0
\(916\) −2.34155e8 + 4.05569e8i −0.304661 + 0.527689i
\(917\) 2.22327e7i 0.0288326i
\(918\) 0 0
\(919\) −5.30833e8 −0.683929 −0.341965 0.939713i \(-0.611092\pi\)
−0.341965 + 0.939713i \(0.611092\pi\)
\(920\) −9.18822e6 5.30482e6i −0.0117996 0.00681251i
\(921\) 0 0
\(922\) −3.36623e8 5.83047e8i −0.429487 0.743894i
\(923\) 5.01860e8 2.89749e8i 0.638230 0.368482i
\(924\) 0 0
\(925\) −5.19071e7 + 8.99058e7i −0.0655846 + 0.113596i
\(926\) 6.42467e8i 0.809129i
\(927\) 0 0
\(928\) −2.02380e8 −0.253235
\(929\) 7.91295e8 + 4.56854e8i 0.986941 + 0.569810i 0.904358 0.426774i \(-0.140350\pi\)
0.0825823 + 0.996584i \(0.473683\pi\)
\(930\) 0 0
\(931\) 3.17742e8 + 5.50346e8i 0.393755 + 0.682004i
\(932\) −4.20621e7 + 2.42845e7i −0.0519569 + 0.0299973i
\(933\) 0 0
\(934\) 3.81050e8 6.59998e8i 0.467672 0.810032i
\(935\) 1.09931e7i 0.0134488i
\(936\) 0 0
\(937\) 9.47917e8 1.15226 0.576131 0.817357i \(-0.304562\pi\)
0.576131 + 0.817357i \(0.304562\pi\)
\(938\) 1.60826e7 + 9.28527e6i 0.0194871 + 0.0112509i
\(939\) 0 0
\(940\) 3.81394e7 + 6.60594e7i 0.0459188 + 0.0795336i
\(941\) 8.63034e8 4.98273e8i 1.03576 0.597996i 0.117131 0.993117i \(-0.462630\pi\)
0.918629 + 0.395120i \(0.129297\pi\)
\(942\) 0 0
\(943\) 6.35920e7 1.10145e8i 0.0758346 0.131349i
\(944\) 2.97750e7i 0.0353945i
\(945\) 0 0
\(946\) −9.11754e7 −0.107697
\(947\) −1.28817e9 7.43725e8i −1.51678 0.875714i −0.999806 0.0197138i \(-0.993724\pi\)
−0.516975 0.856000i \(-0.672942\pi\)
\(948\) 0 0
\(949\) −3.17068e7 5.49178e7i −0.0370983 0.0642561i
\(950\) −3.97301e8 + 2.29382e8i −0.463392 + 0.267540i
\(951\) 0 0
\(952\) −1.89785e6 + 3.28717e6i −0.00219964 + 0.00380988i
\(953\) 4.53743e8i 0.524241i 0.965035 + 0.262121i \(0.0844218\pi\)
−0.965035 + 0.262121i \(0.915578\pi\)
\(954\) 0 0
\(955\) −9.44541e7 −0.108445
\(956\) −3.86893e8 2.23373e8i −0.442810 0.255656i
\(957\) 0 0
\(958\) 4.55307e8 + 7.88615e8i 0.517855 + 0.896950i
\(959\) −8.21289e6 + 4.74172e6i −0.00931194 + 0.00537625i
\(960\) 0 0
\(961\) 4.32893e8 7.49792e8i 0.487764 0.844832i
\(962\) 3.60754e7i 0.0405215i
\(963\) 0 0
\(964\) −8.10125e8 −0.904317
\(965\) 2.78423e7 + 1.60747e7i 0.0309830 + 0.0178880i
\(966\) 0 0
\(967\) −5.04639e8 8.74060e8i −0.558086 0.966634i −0.997656 0.0684252i \(-0.978203\pi\)
0.439570 0.898208i \(-0.355131\pi\)
\(968\) 2.75037e8 1.58793e8i 0.303225 0.175067i
\(969\) 0 0
\(970\) −2.93537e7 + 5.08420e7i −0.0321623 + 0.0557067i
\(971\) 6.88293e8i 0.751823i −0.926656 0.375912i \(-0.877330\pi\)
0.926656 0.375912i \(-0.122670\pi\)
\(972\) 0 0
\(973\) −2.18579e7 −0.0237285
\(974\) 5.63208e7 + 3.25168e7i 0.0609526 + 0.0351910i
\(975\) 0 0
\(976\) −1.64181e8 2.84370e8i −0.176593 0.305868i
\(977\) 6.66620e8 3.84873e8i 0.714816 0.412699i −0.0980254 0.995184i \(-0.531253\pi\)
0.812842 + 0.582484i \(0.197919\pi\)
\(978\) 0 0
\(979\) 6.64582e7 1.15109e8i 0.0708272 0.122676i
\(980\) 9.33988e7i 0.0992346i
\(981\) 0 0
\(982\) 7.88003e8 0.832135
\(983\) −7.49309e8 4.32614e8i −0.788861 0.455449i 0.0507003 0.998714i \(-0.483855\pi\)
−0.839561 + 0.543265i \(0.817188\pi\)
\(984\) 0 0
\(985\) −7.43836e7 1.28836e8i −0.0778338 0.134812i
\(986\) −5.79220e8 + 3.34413e8i −0.604245 + 0.348861i
\(987\) 0 0
\(988\) −7.97100e7 + 1.38062e8i −0.0826499 + 0.143154i
\(989\) 2.90807e8i 0.300619i
\(990\) 0 0
\(991\) 1.48536e9 1.52620 0.763101 0.646280i \(-0.223676\pi\)
0.763101 + 0.646280i \(0.223676\pi\)
\(992\) 2.33788e7 + 1.34977e7i 0.0239490 + 0.0138269i
\(993\) 0 0
\(994\) −1.10150e7 1.90785e7i −0.0112157 0.0194261i
\(995\) −2.25496e7 + 1.30190e7i −0.0228913 + 0.0132163i
\(996\) 0 0
\(997\) 2.94090e8 5.09379e8i 0.296753 0.513991i −0.678638 0.734473i \(-0.737430\pi\)
0.975391 + 0.220482i \(0.0707630\pi\)
\(998\) 5.28744e8i 0.531929i
\(999\) 0 0
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 162.7.d.f.107.3 8
3.2 odd 2 inner 162.7.d.f.107.2 8
9.2 odd 6 162.7.b.a.161.4 yes 4
9.4 even 3 inner 162.7.d.f.53.2 8
9.5 odd 6 inner 162.7.d.f.53.3 8
9.7 even 3 162.7.b.a.161.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.7.b.a.161.1 4 9.7 even 3
162.7.b.a.161.4 yes 4 9.2 odd 6
162.7.d.f.53.2 8 9.4 even 3 inner
162.7.d.f.53.3 8 9.5 odd 6 inner
162.7.d.f.107.2 8 3.2 odd 2 inner
162.7.d.f.107.3 8 1.1 even 1 trivial