Properties

Label 287.2.c.b.204.2
Level $287$
Weight $2$
Character 287.204
Analytic conductor $2.292$
Analytic rank $0$
Dimension $12$
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] = [287,2,Mod(204,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.204");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 113x^{8} + 290x^{6} + 258x^{4} + 49x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 204.2
Root \(-2.72816i\) of defining polynomial
Character \(\chi\) \(=\) 287.204
Dual form 287.2.c.b.204.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.72816 q^{2} +1.72816i q^{3} +5.44285 q^{4} -1.58817 q^{5} -4.71469i q^{6} +1.00000i q^{7} -9.39263 q^{8} +0.0134697 q^{9} +O(q^{10})\) \(q-2.72816 q^{2} +1.72816i q^{3} +5.44285 q^{4} -1.58817 q^{5} -4.71469i q^{6} +1.00000i q^{7} -9.39263 q^{8} +0.0134697 q^{9} +4.33279 q^{10} +6.33279i q^{11} +9.40610i q^{12} -2.36161i q^{13} -2.72816i q^{14} -2.74461i q^{15} +14.7389 q^{16} -3.29792i q^{17} -0.0367475 q^{18} +3.34626i q^{19} -8.64418 q^{20} -1.72816 q^{21} -17.2768i q^{22} -2.17141 q^{23} -16.2319i q^{24} -2.47771 q^{25} +6.44285i q^{26} +5.20775i q^{27} +5.44285i q^{28} +1.97861i q^{29} +7.48774i q^{30} -7.04449 q^{31} -21.4247 q^{32} -10.9441 q^{33} +8.99726i q^{34} -1.58817i q^{35} +0.0733135 q^{36} -6.69440 q^{37} -9.12911i q^{38} +4.08124 q^{39} +14.9171 q^{40} +(1.38002 - 6.25264i) q^{41} +4.71469 q^{42} -6.85467 q^{43} +34.4684i q^{44} -0.0213922 q^{45} +5.92394 q^{46} -4.19130i q^{47} +25.4711i q^{48} -1.00000 q^{49} +6.75958 q^{50} +5.69933 q^{51} -12.8539i q^{52} +3.14492i q^{53} -14.2076i q^{54} -10.0576i q^{55} -9.39263i q^{56} -5.78286 q^{57} -5.39795i q^{58} -7.58817 q^{59} -14.9385i q^{60} +14.2054 q^{61} +19.2185 q^{62} +0.0134697i q^{63} +28.9723 q^{64} +3.75064i q^{65} +29.8571 q^{66} +14.0207i q^{67} -17.9501i q^{68} -3.75254i q^{69} +4.33279i q^{70} -1.84675i q^{71} -0.126516 q^{72} +6.52220 q^{73} +18.2634 q^{74} -4.28187i q^{75} +18.2132i q^{76} -6.33279 q^{77} -11.1343 q^{78} +6.15260i q^{79} -23.4079 q^{80} -8.95941 q^{81} +(-3.76491 + 17.0582i) q^{82} +10.7760 q^{83} -9.40610 q^{84} +5.23767i q^{85} +18.7006 q^{86} -3.41935 q^{87} -59.4815i q^{88} +10.2497i q^{89} +0.0583613 q^{90} +2.36161 q^{91} -11.8186 q^{92} -12.1740i q^{93} +11.4345i q^{94} -5.31443i q^{95} -37.0254i q^{96} +9.34775i q^{97} +2.72816 q^{98} +0.0853007i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9} - 4 q^{10} + 28 q^{16} - 40 q^{18} + 2 q^{20} + 8 q^{21} + 16 q^{23} + 34 q^{25} - 6 q^{31} - 42 q^{32} + 18 q^{33} - 36 q^{36} - 10 q^{37} + 10 q^{39} + 38 q^{40} - 2 q^{41} + 32 q^{42} - 50 q^{43} + 6 q^{45} - 8 q^{46} - 12 q^{49} + 18 q^{50} - 2 q^{51} - 50 q^{57} - 70 q^{59} + 52 q^{61} + 68 q^{62} + 8 q^{64} + 92 q^{66} + 2 q^{72} - 64 q^{73} + 18 q^{74} - 20 q^{77} - 12 q^{78} - 32 q^{80} - 4 q^{81} - 56 q^{82} + 60 q^{83} - 20 q^{84} + 48 q^{86} - 20 q^{87} - 42 q^{90} + 14 q^{91} + 56 q^{92} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72816 −1.92910 −0.964550 0.263902i \(-0.914990\pi\)
−0.964550 + 0.263902i \(0.914990\pi\)
\(3\) 1.72816i 0.997753i 0.866673 + 0.498876i \(0.166254\pi\)
−0.866673 + 0.498876i \(0.833746\pi\)
\(4\) 5.44285 2.72142
\(5\) −1.58817 −0.710252 −0.355126 0.934818i \(-0.615562\pi\)
−0.355126 + 0.934818i \(0.615562\pi\)
\(6\) 4.71469i 1.92476i
\(7\) 1.00000i 0.377964i
\(8\) −9.39263 −3.32080
\(9\) 0.0134697 0.00448990
\(10\) 4.33279 1.37015
\(11\) 6.33279i 1.90941i 0.297559 + 0.954703i \(0.403827\pi\)
−0.297559 + 0.954703i \(0.596173\pi\)
\(12\) 9.40610i 2.71531i
\(13\) 2.36161i 0.654993i −0.944852 0.327496i \(-0.893795\pi\)
0.944852 0.327496i \(-0.106205\pi\)
\(14\) 2.72816i 0.729131i
\(15\) 2.74461i 0.708656i
\(16\) 14.7389 3.68472
\(17\) 3.29792i 0.799864i −0.916545 0.399932i \(-0.869034\pi\)
0.916545 0.399932i \(-0.130966\pi\)
\(18\) −0.0367475 −0.00866146
\(19\) 3.34626i 0.767684i 0.923399 + 0.383842i \(0.125399\pi\)
−0.923399 + 0.383842i \(0.874601\pi\)
\(20\) −8.64418 −1.93290
\(21\) −1.72816 −0.377115
\(22\) 17.2768i 3.68343i
\(23\) −2.17141 −0.452770 −0.226385 0.974038i \(-0.572691\pi\)
−0.226385 + 0.974038i \(0.572691\pi\)
\(24\) 16.2319i 3.31333i
\(25\) −2.47771 −0.495542
\(26\) 6.44285i 1.26355i
\(27\) 5.20775i 1.00223i
\(28\) 5.44285i 1.02860i
\(29\) 1.97861i 0.367418i 0.982981 + 0.183709i \(0.0588104\pi\)
−0.982981 + 0.183709i \(0.941190\pi\)
\(30\) 7.48774i 1.36707i
\(31\) −7.04449 −1.26523 −0.632614 0.774467i \(-0.718018\pi\)
−0.632614 + 0.774467i \(0.718018\pi\)
\(32\) −21.4247 −3.78740
\(33\) −10.9441 −1.90512
\(34\) 8.99726i 1.54302i
\(35\) 1.58817i 0.268450i
\(36\) 0.0733135 0.0122189
\(37\) −6.69440 −1.10055 −0.550276 0.834983i \(-0.685477\pi\)
−0.550276 + 0.834983i \(0.685477\pi\)
\(38\) 9.12911i 1.48094i
\(39\) 4.08124 0.653521
\(40\) 14.9171 2.35860
\(41\) 1.38002 6.25264i 0.215523 0.976499i
\(42\) 4.71469 0.727492
\(43\) −6.85467 −1.04533 −0.522664 0.852539i \(-0.675062\pi\)
−0.522664 + 0.852539i \(0.675062\pi\)
\(44\) 34.4684i 5.19630i
\(45\) −0.0213922 −0.00318896
\(46\) 5.92394 0.873438
\(47\) 4.19130i 0.611364i −0.952134 0.305682i \(-0.901116\pi\)
0.952134 0.305682i \(-0.0988844\pi\)
\(48\) 25.4711i 3.67644i
\(49\) −1.00000 −0.142857
\(50\) 6.75958 0.955949
\(51\) 5.69933 0.798066
\(52\) 12.8539i 1.78251i
\(53\) 3.14492i 0.431988i 0.976395 + 0.215994i \(0.0692992\pi\)
−0.976395 + 0.215994i \(0.930701\pi\)
\(54\) 14.2076i 1.93341i
\(55\) 10.0576i 1.35616i
\(56\) 9.39263i 1.25514i
\(57\) −5.78286 −0.765958
\(58\) 5.39795i 0.708786i
\(59\) −7.58817 −0.987896 −0.493948 0.869491i \(-0.664447\pi\)
−0.493948 + 0.869491i \(0.664447\pi\)
\(60\) 14.9385i 1.92855i
\(61\) 14.2054 1.81882 0.909408 0.415905i \(-0.136535\pi\)
0.909408 + 0.415905i \(0.136535\pi\)
\(62\) 19.2185 2.44075
\(63\) 0.0134697i 0.00169702i
\(64\) 28.9723 3.62154
\(65\) 3.75064i 0.465210i
\(66\) 29.8571 3.67516
\(67\) 14.0207i 1.71291i 0.516225 + 0.856453i \(0.327337\pi\)
−0.516225 + 0.856453i \(0.672663\pi\)
\(68\) 17.9501i 2.17677i
\(69\) 3.75254i 0.451752i
\(70\) 4.33279i 0.517867i
\(71\) 1.84675i 0.219169i −0.993977 0.109585i \(-0.965048\pi\)
0.993977 0.109585i \(-0.0349520\pi\)
\(72\) −0.126516 −0.0149100
\(73\) 6.52220 0.763365 0.381683 0.924293i \(-0.375345\pi\)
0.381683 + 0.924293i \(0.375345\pi\)
\(74\) 18.2634 2.12307
\(75\) 4.28187i 0.494428i
\(76\) 18.2132i 2.08919i
\(77\) −6.33279 −0.721688
\(78\) −11.1343 −1.26071
\(79\) 6.15260i 0.692221i 0.938194 + 0.346111i \(0.112498\pi\)
−0.938194 + 0.346111i \(0.887502\pi\)
\(80\) −23.4079 −2.61708
\(81\) −8.95941 −0.995490
\(82\) −3.76491 + 17.0582i −0.415764 + 1.88376i
\(83\) 10.7760 1.18282 0.591412 0.806370i \(-0.298571\pi\)
0.591412 + 0.806370i \(0.298571\pi\)
\(84\) −9.40610 −1.02629
\(85\) 5.23767i 0.568105i
\(86\) 18.7006 2.01654
\(87\) −3.41935 −0.366592
\(88\) 59.4815i 6.34075i
\(89\) 10.2497i 1.08646i 0.839583 + 0.543231i \(0.182799\pi\)
−0.839583 + 0.543231i \(0.817201\pi\)
\(90\) 0.0583613 0.00615182
\(91\) 2.36161 0.247564
\(92\) −11.8186 −1.23218
\(93\) 12.1740i 1.26238i
\(94\) 11.4345i 1.17938i
\(95\) 5.31443i 0.545249i
\(96\) 37.0254i 3.77888i
\(97\) 9.34775i 0.949120i 0.880223 + 0.474560i \(0.157393\pi\)
−0.880223 + 0.474560i \(0.842607\pi\)
\(98\) 2.72816 0.275586
\(99\) 0.0853007i 0.00857305i
\(100\) −13.4858 −1.34858
\(101\) 6.38598i 0.635429i −0.948186 0.317714i \(-0.897085\pi\)
0.948186 0.317714i \(-0.102915\pi\)
\(102\) −15.5487 −1.53955
\(103\) 10.3206 1.01692 0.508460 0.861085i \(-0.330215\pi\)
0.508460 + 0.861085i \(0.330215\pi\)
\(104\) 22.1817i 2.17510i
\(105\) 2.74461 0.267847
\(106\) 8.57985i 0.833348i
\(107\) −0.924553 −0.0893799 −0.0446900 0.999001i \(-0.514230\pi\)
−0.0446900 + 0.999001i \(0.514230\pi\)
\(108\) 28.3450i 2.72750i
\(109\) 5.30372i 0.508004i −0.967204 0.254002i \(-0.918253\pi\)
0.967204 0.254002i \(-0.0817470\pi\)
\(110\) 27.4386i 2.61617i
\(111\) 11.5690i 1.09808i
\(112\) 14.7389i 1.39269i
\(113\) 4.49971 0.423297 0.211649 0.977346i \(-0.432117\pi\)
0.211649 + 0.977346i \(0.432117\pi\)
\(114\) 15.7766 1.47761
\(115\) 3.44857 0.321581
\(116\) 10.7693i 0.999901i
\(117\) 0.0318102i 0.00294085i
\(118\) 20.7017 1.90575
\(119\) 3.29792 0.302320
\(120\) 25.7791i 2.35330i
\(121\) −29.1042 −2.64583
\(122\) −38.7546 −3.50868
\(123\) 10.8056 + 2.38489i 0.974304 + 0.215038i
\(124\) −38.3421 −3.44322
\(125\) 11.8759 1.06221
\(126\) 0.0367475i 0.00327373i
\(127\) 5.13749 0.455879 0.227939 0.973675i \(-0.426801\pi\)
0.227939 + 0.973675i \(0.426801\pi\)
\(128\) −36.1916 −3.19892
\(129\) 11.8460i 1.04298i
\(130\) 10.2324i 0.897437i
\(131\) 10.2845 0.898557 0.449278 0.893392i \(-0.351681\pi\)
0.449278 + 0.893392i \(0.351681\pi\)
\(132\) −59.5668 −5.18462
\(133\) −3.34626 −0.290157
\(134\) 38.2508i 3.30437i
\(135\) 8.27081i 0.711838i
\(136\) 30.9762i 2.65618i
\(137\) 20.4701i 1.74888i 0.485135 + 0.874439i \(0.338770\pi\)
−0.485135 + 0.874439i \(0.661230\pi\)
\(138\) 10.2375i 0.871475i
\(139\) −11.9165 −1.01074 −0.505371 0.862902i \(-0.668644\pi\)
−0.505371 + 0.862902i \(0.668644\pi\)
\(140\) 8.64418i 0.730566i
\(141\) 7.24322 0.609989
\(142\) 5.03823i 0.422799i
\(143\) 14.9556 1.25065
\(144\) 0.198528 0.0165440
\(145\) 3.14237i 0.260960i
\(146\) −17.7936 −1.47261
\(147\) 1.72816i 0.142536i
\(148\) −36.4366 −2.99507
\(149\) 3.94015i 0.322790i −0.986890 0.161395i \(-0.948401\pi\)
0.986890 0.161395i \(-0.0515993\pi\)
\(150\) 11.6816i 0.953800i
\(151\) 9.16632i 0.745944i 0.927843 + 0.372972i \(0.121661\pi\)
−0.927843 + 0.372972i \(0.878339\pi\)
\(152\) 31.4301i 2.54932i
\(153\) 0.0444221i 0.00359131i
\(154\) 17.2768 1.39221
\(155\) 11.1879 0.898631
\(156\) 22.2135 1.77851
\(157\) 21.9129i 1.74884i 0.485172 + 0.874419i \(0.338757\pi\)
−0.485172 + 0.874419i \(0.661243\pi\)
\(158\) 16.7853i 1.33536i
\(159\) −5.43492 −0.431018
\(160\) 34.0262 2.69001
\(161\) 2.17141i 0.171131i
\(162\) 24.4427 1.92040
\(163\) 15.6921 1.22910 0.614548 0.788879i \(-0.289338\pi\)
0.614548 + 0.788879i \(0.289338\pi\)
\(164\) 7.51122 34.0322i 0.586528 2.65747i
\(165\) 17.3810 1.35311
\(166\) −29.3987 −2.28178
\(167\) 8.82477i 0.682881i −0.939903 0.341441i \(-0.889085\pi\)
0.939903 0.341441i \(-0.110915\pi\)
\(168\) 16.2319 1.25232
\(169\) 7.42280 0.570984
\(170\) 14.2892i 1.09593i
\(171\) 0.0450731i 0.00344682i
\(172\) −37.3089 −2.84478
\(173\) −4.49306 −0.341601 −0.170800 0.985306i \(-0.554635\pi\)
−0.170800 + 0.985306i \(0.554635\pi\)
\(174\) 9.32852 0.707193
\(175\) 2.47771i 0.187297i
\(176\) 93.3382i 7.03563i
\(177\) 13.1136i 0.985676i
\(178\) 27.9627i 2.09589i
\(179\) 5.96309i 0.445702i 0.974852 + 0.222851i \(0.0715364\pi\)
−0.974852 + 0.222851i \(0.928464\pi\)
\(180\) −0.116435 −0.00867852
\(181\) 21.3416i 1.58631i −0.609023 0.793153i \(-0.708438\pi\)
0.609023 0.793153i \(-0.291562\pi\)
\(182\) −6.44285 −0.477576
\(183\) 24.5492i 1.81473i
\(184\) 20.3952 1.50356
\(185\) 10.6319 0.781670
\(186\) 33.2126i 2.43526i
\(187\) 20.8850 1.52727
\(188\) 22.8126i 1.66378i
\(189\) −5.20775 −0.378808
\(190\) 14.4986i 1.05184i
\(191\) 1.04897i 0.0759009i 0.999280 + 0.0379504i \(0.0120829\pi\)
−0.999280 + 0.0379504i \(0.987917\pi\)
\(192\) 50.0688i 3.61340i
\(193\) 10.6726i 0.768230i −0.923285 0.384115i \(-0.874507\pi\)
0.923285 0.384115i \(-0.125493\pi\)
\(194\) 25.5021i 1.83095i
\(195\) −6.48171 −0.464165
\(196\) −5.44285 −0.388775
\(197\) −4.36309 −0.310857 −0.155429 0.987847i \(-0.549676\pi\)
−0.155429 + 0.987847i \(0.549676\pi\)
\(198\) 0.232714i 0.0165383i
\(199\) 14.7840i 1.04801i −0.851715 0.524006i \(-0.824437\pi\)
0.851715 0.524006i \(-0.175563\pi\)
\(200\) 23.2722 1.64559
\(201\) −24.2301 −1.70906
\(202\) 17.4220i 1.22581i
\(203\) −1.97861 −0.138871
\(204\) 31.0206 2.17188
\(205\) −2.19171 + 9.93028i −0.153075 + 0.693561i
\(206\) −28.1563 −1.96174
\(207\) −0.0292482 −0.00203289
\(208\) 34.8075i 2.41347i
\(209\) −21.1911 −1.46582
\(210\) −7.48774 −0.516703
\(211\) 16.9879i 1.16950i −0.811215 0.584748i \(-0.801193\pi\)
0.811215 0.584748i \(-0.198807\pi\)
\(212\) 17.1173i 1.17562i
\(213\) 3.19148 0.218677
\(214\) 2.52233 0.172423
\(215\) 10.8864 0.742447
\(216\) 48.9145i 3.32821i
\(217\) 7.04449i 0.478211i
\(218\) 14.4694i 0.979990i
\(219\) 11.2714i 0.761650i
\(220\) 54.7417i 3.69069i
\(221\) −7.78841 −0.523905
\(222\) 31.5620i 2.11830i
\(223\) −10.8872 −0.729060 −0.364530 0.931192i \(-0.618770\pi\)
−0.364530 + 0.931192i \(0.618770\pi\)
\(224\) 21.4247i 1.43150i
\(225\) −0.0333740 −0.00222493
\(226\) −12.2759 −0.816582
\(227\) 9.19154i 0.610064i −0.952342 0.305032i \(-0.901333\pi\)
0.952342 0.305032i \(-0.0986671\pi\)
\(228\) −31.4752 −2.08450
\(229\) 16.1981i 1.07040i 0.844725 + 0.535201i \(0.179764\pi\)
−0.844725 + 0.535201i \(0.820236\pi\)
\(230\) −9.40824 −0.620361
\(231\) 10.9441i 0.720066i
\(232\) 18.5843i 1.22012i
\(233\) 20.6673i 1.35396i 0.736000 + 0.676981i \(0.236712\pi\)
−0.736000 + 0.676981i \(0.763288\pi\)
\(234\) 0.0867832i 0.00567320i
\(235\) 6.65650i 0.434222i
\(236\) −41.3013 −2.68848
\(237\) −10.6327 −0.690666
\(238\) −8.99726 −0.583206
\(239\) 9.88334i 0.639300i 0.947536 + 0.319650i \(0.103565\pi\)
−0.947536 + 0.319650i \(0.896435\pi\)
\(240\) 40.4525i 2.61120i
\(241\) −6.78526 −0.437077 −0.218538 0.975828i \(-0.570129\pi\)
−0.218538 + 0.975828i \(0.570129\pi\)
\(242\) 79.4008 5.10408
\(243\) 0.139980i 0.00897973i
\(244\) 77.3179 4.94977
\(245\) 1.58817 0.101465
\(246\) −29.4793 6.50635i −1.87953 0.414830i
\(247\) 7.90255 0.502827
\(248\) 66.1663 4.20156
\(249\) 18.6227i 1.18017i
\(250\) −32.3993 −2.04911
\(251\) 24.1079 1.52168 0.760840 0.648940i \(-0.224787\pi\)
0.760840 + 0.648940i \(0.224787\pi\)
\(252\) 0.0733135i 0.00461832i
\(253\) 13.7511i 0.864522i
\(254\) −14.0159 −0.879435
\(255\) −9.05152 −0.566828
\(256\) 40.7917 2.54948
\(257\) 3.52723i 0.220022i 0.993930 + 0.110011i \(0.0350887\pi\)
−0.993930 + 0.110011i \(0.964911\pi\)
\(258\) 32.3177i 2.01201i
\(259\) 6.69440i 0.415970i
\(260\) 20.4142i 1.26603i
\(261\) 0.0266513i 0.00164967i
\(262\) −28.0576 −1.73341
\(263\) 14.5722i 0.898558i 0.893392 + 0.449279i \(0.148319\pi\)
−0.893392 + 0.449279i \(0.851681\pi\)
\(264\) 102.793 6.32650
\(265\) 4.99468i 0.306821i
\(266\) 9.12911 0.559742
\(267\) −17.7130 −1.08402
\(268\) 76.3127i 4.66154i
\(269\) 2.97762 0.181548 0.0907742 0.995872i \(-0.471066\pi\)
0.0907742 + 0.995872i \(0.471066\pi\)
\(270\) 22.5641i 1.37321i
\(271\) 1.44928 0.0880376 0.0440188 0.999031i \(-0.485984\pi\)
0.0440188 + 0.999031i \(0.485984\pi\)
\(272\) 48.6077i 2.94728i
\(273\) 4.08124i 0.247008i
\(274\) 55.8457i 3.37376i
\(275\) 15.6908i 0.946191i
\(276\) 20.4245i 1.22941i
\(277\) 13.5089 0.811669 0.405834 0.913947i \(-0.366981\pi\)
0.405834 + 0.913947i \(0.366981\pi\)
\(278\) 32.5100 1.94982
\(279\) −0.0948872 −0.00568075
\(280\) 14.9171i 0.891468i
\(281\) 6.61575i 0.394663i 0.980337 + 0.197331i \(0.0632275\pi\)
−0.980337 + 0.197331i \(0.936773\pi\)
\(282\) −19.7607 −1.17673
\(283\) 8.21936 0.488590 0.244295 0.969701i \(-0.421443\pi\)
0.244295 + 0.969701i \(0.421443\pi\)
\(284\) 10.0516i 0.596452i
\(285\) 9.18418 0.544024
\(286\) −40.8012 −2.41262
\(287\) 6.25264 + 1.38002i 0.369082 + 0.0814599i
\(288\) −0.288585 −0.0170050
\(289\) 6.12370 0.360218
\(290\) 8.57288i 0.503417i
\(291\) −16.1544 −0.946987
\(292\) 35.4993 2.07744
\(293\) 25.7737i 1.50572i 0.658182 + 0.752859i \(0.271326\pi\)
−0.658182 + 0.752859i \(0.728674\pi\)
\(294\) 4.71469i 0.274966i
\(295\) 12.0513 0.701655
\(296\) 62.8780 3.65471
\(297\) −32.9796 −1.91367
\(298\) 10.7494i 0.622693i
\(299\) 5.12802i 0.296561i
\(300\) 23.3056i 1.34555i
\(301\) 6.85467i 0.395097i
\(302\) 25.0072i 1.43900i
\(303\) 11.0360 0.634001
\(304\) 49.3201i 2.82870i
\(305\) −22.5606 −1.29182
\(306\) 0.121190i 0.00692799i
\(307\) −30.6173 −1.74742 −0.873711 0.486446i \(-0.838293\pi\)
−0.873711 + 0.486446i \(0.838293\pi\)
\(308\) −34.4684 −1.96402
\(309\) 17.8357i 1.01464i
\(310\) −30.5223 −1.73355
\(311\) 16.1116i 0.913605i 0.889568 + 0.456802i \(0.151005\pi\)
−0.889568 + 0.456802i \(0.848995\pi\)
\(312\) −38.3335 −2.17021
\(313\) 4.23750i 0.239517i −0.992803 0.119759i \(-0.961788\pi\)
0.992803 0.119759i \(-0.0382121\pi\)
\(314\) 59.7818i 3.37368i
\(315\) 0.0213922i 0.00120531i
\(316\) 33.4876i 1.88383i
\(317\) 7.39882i 0.415559i −0.978176 0.207780i \(-0.933376\pi\)
0.978176 0.207780i \(-0.0666237\pi\)
\(318\) 14.8273 0.831475
\(319\) −12.5301 −0.701551
\(320\) −46.0131 −2.57221
\(321\) 1.59777i 0.0891790i
\(322\) 5.92394i 0.330128i
\(323\) 11.0357 0.614042
\(324\) −48.7647 −2.70915
\(325\) 5.85138i 0.324576i
\(326\) −42.8104 −2.37105
\(327\) 9.16566 0.506862
\(328\) −12.9620 + 58.7288i −0.715706 + 3.24275i
\(329\) 4.19130 0.231074
\(330\) −47.4182 −2.61029
\(331\) 4.76900i 0.262128i −0.991374 0.131064i \(-0.958161\pi\)
0.991374 0.131064i \(-0.0418393\pi\)
\(332\) 58.6523 3.21896
\(333\) −0.0901715 −0.00494137
\(334\) 24.0754i 1.31735i
\(335\) 22.2674i 1.21660i
\(336\) −25.4711 −1.38956
\(337\) −8.17118 −0.445113 −0.222556 0.974920i \(-0.571440\pi\)
−0.222556 + 0.974920i \(0.571440\pi\)
\(338\) −20.2506 −1.10149
\(339\) 7.77621i 0.422346i
\(340\) 28.5078i 1.54605i
\(341\) 44.6112i 2.41583i
\(342\) 0.122966i 0.00664926i
\(343\) 1.00000i 0.0539949i
\(344\) 64.3834 3.47132
\(345\) 5.95967i 0.320858i
\(346\) 12.2578 0.658982
\(347\) 2.85656i 0.153348i −0.997056 0.0766742i \(-0.975570\pi\)
0.997056 0.0766742i \(-0.0244301\pi\)
\(348\) −18.6110 −0.997653
\(349\) −2.88634 −0.154502 −0.0772512 0.997012i \(-0.524614\pi\)
−0.0772512 + 0.997012i \(0.524614\pi\)
\(350\) 6.75958i 0.361315i
\(351\) 12.2987 0.656455
\(352\) 135.678i 7.23168i
\(353\) −7.30891 −0.389014 −0.194507 0.980901i \(-0.562311\pi\)
−0.194507 + 0.980901i \(0.562311\pi\)
\(354\) 35.7759i 1.90147i
\(355\) 2.93296i 0.155665i
\(356\) 55.7873i 2.95672i
\(357\) 5.69933i 0.301641i
\(358\) 16.2683i 0.859804i
\(359\) 33.3194 1.75853 0.879265 0.476334i \(-0.158035\pi\)
0.879265 + 0.476334i \(0.158035\pi\)
\(360\) 0.200929 0.0105899
\(361\) 7.80258 0.410662
\(362\) 58.2231i 3.06014i
\(363\) 50.2966i 2.63989i
\(364\) 12.8539 0.673727
\(365\) −10.3584 −0.542182
\(366\) 66.9741i 3.50079i
\(367\) −27.0498 −1.41199 −0.705994 0.708218i \(-0.749499\pi\)
−0.705994 + 0.708218i \(0.749499\pi\)
\(368\) −32.0041 −1.66833
\(369\) 0.0185884 0.0842213i 0.000967675 0.00438438i
\(370\) −29.0054 −1.50792
\(371\) −3.14492 −0.163276
\(372\) 66.2612i 3.43548i
\(373\) 23.6784 1.22602 0.613010 0.790075i \(-0.289958\pi\)
0.613010 + 0.790075i \(0.289958\pi\)
\(374\) −56.9777 −2.94625
\(375\) 20.5234i 1.05982i
\(376\) 39.3673i 2.03021i
\(377\) 4.67270 0.240656
\(378\) 14.2076 0.730759
\(379\) −0.144696 −0.00743253 −0.00371627 0.999993i \(-0.501183\pi\)
−0.00371627 + 0.999993i \(0.501183\pi\)
\(380\) 28.9256i 1.48385i
\(381\) 8.87840i 0.454854i
\(382\) 2.86176i 0.146420i
\(383\) 24.5984i 1.25692i −0.777841 0.628461i \(-0.783685\pi\)
0.777841 0.628461i \(-0.216315\pi\)
\(384\) 62.5448i 3.19173i
\(385\) 10.0576 0.512580
\(386\) 29.1165i 1.48199i
\(387\) −0.0923304 −0.00469342
\(388\) 50.8784i 2.58296i
\(389\) 12.4897 0.633253 0.316626 0.948550i \(-0.397450\pi\)
0.316626 + 0.948550i \(0.397450\pi\)
\(390\) 17.6831 0.895420
\(391\) 7.16114i 0.362154i
\(392\) 9.39263 0.474399
\(393\) 17.7732i 0.896537i
\(394\) 11.9032 0.599675
\(395\) 9.77139i 0.491652i
\(396\) 0.464279i 0.0233309i
\(397\) 3.02007i 0.151573i 0.997124 + 0.0757865i \(0.0241467\pi\)
−0.997124 + 0.0757865i \(0.975853\pi\)
\(398\) 40.3332i 2.02172i
\(399\) 5.78286i 0.289505i
\(400\) −36.5187 −1.82593
\(401\) −4.21447 −0.210460 −0.105230 0.994448i \(-0.533558\pi\)
−0.105230 + 0.994448i \(0.533558\pi\)
\(402\) 66.1034 3.29694
\(403\) 16.6363i 0.828715i
\(404\) 34.7579i 1.72927i
\(405\) 14.2291 0.707049
\(406\) 5.39795 0.267896
\(407\) 42.3942i 2.10140i
\(408\) −53.5317 −2.65022
\(409\) 2.29691 0.113575 0.0567875 0.998386i \(-0.481914\pi\)
0.0567875 + 0.998386i \(0.481914\pi\)
\(410\) 5.97932 27.0914i 0.295298 1.33795i
\(411\) −35.3756 −1.74495
\(412\) 56.1735 2.76747
\(413\) 7.58817i 0.373390i
\(414\) 0.0797938 0.00392165
\(415\) −17.1142 −0.840103
\(416\) 50.5969i 2.48072i
\(417\) 20.5936i 1.00847i
\(418\) 57.8127 2.82771
\(419\) −26.3559 −1.28757 −0.643784 0.765207i \(-0.722636\pi\)
−0.643784 + 0.765207i \(0.722636\pi\)
\(420\) 14.9385 0.728925
\(421\) 34.8204i 1.69704i 0.529163 + 0.848520i \(0.322506\pi\)
−0.529163 + 0.848520i \(0.677494\pi\)
\(422\) 46.3457i 2.25607i
\(423\) 0.0564555i 0.00274496i
\(424\) 29.5391i 1.43455i
\(425\) 8.17129i 0.396366i
\(426\) −8.70686 −0.421849
\(427\) 14.2054i 0.687448i
\(428\) −5.03220 −0.243241
\(429\) 25.8456i 1.24784i
\(430\) −29.6998 −1.43225
\(431\) −19.3419 −0.931668 −0.465834 0.884872i \(-0.654246\pi\)
−0.465834 + 0.884872i \(0.654246\pi\)
\(432\) 76.7565i 3.69295i
\(433\) 26.3927 1.26835 0.634176 0.773189i \(-0.281339\pi\)
0.634176 + 0.773189i \(0.281339\pi\)
\(434\) 19.2185i 0.922516i
\(435\) 5.43051 0.260373
\(436\) 28.8673i 1.38249i
\(437\) 7.26608i 0.347584i
\(438\) 30.7501i 1.46930i
\(439\) 25.8188i 1.23226i −0.787643 0.616132i \(-0.788699\pi\)
0.787643 0.616132i \(-0.211301\pi\)
\(440\) 94.4669i 4.50353i
\(441\) −0.0134697 −0.000641414
\(442\) 21.2480 1.01066
\(443\) 16.8943 0.802671 0.401335 0.915931i \(-0.368546\pi\)
0.401335 + 0.915931i \(0.368546\pi\)
\(444\) 62.9681i 2.98834i
\(445\) 16.2782i 0.771662i
\(446\) 29.7020 1.40643
\(447\) 6.80920 0.322064
\(448\) 28.9723i 1.36881i
\(449\) −0.826112 −0.0389866 −0.0194933 0.999810i \(-0.506205\pi\)
−0.0194933 + 0.999810i \(0.506205\pi\)
\(450\) 0.0910495 0.00429212
\(451\) 39.5967 + 8.73935i 1.86453 + 0.411520i
\(452\) 24.4912 1.15197
\(453\) −15.8408 −0.744268
\(454\) 25.0760i 1.17687i
\(455\) −3.75064 −0.175833
\(456\) 54.3162 2.54359
\(457\) 32.8865i 1.53836i −0.639030 0.769182i \(-0.720664\pi\)
0.639030 0.769182i \(-0.279336\pi\)
\(458\) 44.1910i 2.06491i
\(459\) 17.1748 0.801650
\(460\) 18.7700 0.875157
\(461\) −3.69324 −0.172012 −0.0860058 0.996295i \(-0.527410\pi\)
−0.0860058 + 0.996295i \(0.527410\pi\)
\(462\) 29.8571i 1.38908i
\(463\) 25.9484i 1.20592i −0.797770 0.602962i \(-0.793987\pi\)
0.797770 0.602962i \(-0.206013\pi\)
\(464\) 29.1625i 1.35383i
\(465\) 19.3344i 0.896611i
\(466\) 56.3838i 2.61193i
\(467\) −11.9439 −0.552697 −0.276349 0.961057i \(-0.589124\pi\)
−0.276349 + 0.961057i \(0.589124\pi\)
\(468\) 0.173138i 0.00800331i
\(469\) −14.0207 −0.647418
\(470\) 18.1600i 0.837658i
\(471\) −37.8689 −1.74491
\(472\) 71.2729 3.28060
\(473\) 43.4092i 1.99596i
\(474\) 29.0076 1.33236
\(475\) 8.29104i 0.380419i
\(476\) 17.9501 0.822741
\(477\) 0.0423612i 0.00193959i
\(478\) 26.9633i 1.23327i
\(479\) 9.64918i 0.440882i −0.975400 0.220441i \(-0.929250\pi\)
0.975400 0.220441i \(-0.0707497\pi\)
\(480\) 58.8026i 2.68396i
\(481\) 15.8096i 0.720854i
\(482\) 18.5113 0.843165
\(483\) 3.75254 0.170746
\(484\) −158.410 −7.20043
\(485\) 14.8458i 0.674115i
\(486\) 0.381888i 0.0173228i
\(487\) 27.8889 1.26377 0.631884 0.775063i \(-0.282282\pi\)
0.631884 + 0.775063i \(0.282282\pi\)
\(488\) −133.426 −6.03992
\(489\) 27.1184i 1.22633i
\(490\) −4.33279 −0.195735
\(491\) 22.4897 1.01495 0.507474 0.861667i \(-0.330579\pi\)
0.507474 + 0.861667i \(0.330579\pi\)
\(492\) 58.8130 + 12.9806i 2.65149 + 0.585210i
\(493\) 6.52530 0.293885
\(494\) −21.5594 −0.970004
\(495\) 0.135472i 0.00608903i
\(496\) −103.828 −4.66201
\(497\) 1.84675 0.0828381
\(498\) 50.8056i 2.27666i
\(499\) 14.0838i 0.630479i 0.949012 + 0.315239i \(0.102085\pi\)
−0.949012 + 0.315239i \(0.897915\pi\)
\(500\) 64.6386 2.89073
\(501\) 15.2506 0.681346
\(502\) −65.7703 −2.93547
\(503\) 35.4759i 1.58179i 0.611951 + 0.790896i \(0.290385\pi\)
−0.611951 + 0.790896i \(0.709615\pi\)
\(504\) 0.126516i 0.00563547i
\(505\) 10.1420i 0.451315i
\(506\) 37.5151i 1.66775i
\(507\) 12.8278i 0.569701i
\(508\) 27.9626 1.24064
\(509\) 17.5946i 0.779866i 0.920843 + 0.389933i \(0.127502\pi\)
−0.920843 + 0.389933i \(0.872498\pi\)
\(510\) 24.6940 1.09347
\(511\) 6.52220i 0.288525i
\(512\) −38.9031 −1.71929
\(513\) −17.4265 −0.769397
\(514\) 9.62284i 0.424445i
\(515\) −16.3909 −0.722270
\(516\) 64.4757i 2.83839i
\(517\) 26.5426 1.16734
\(518\) 18.2634i 0.802446i
\(519\) 7.76471i 0.340833i
\(520\) 35.2284i 1.54487i
\(521\) 1.16311i 0.0509567i −0.999675 0.0254783i \(-0.991889\pi\)
0.999675 0.0254783i \(-0.00811088\pi\)
\(522\) 0.0727089i 0.00318238i
\(523\) −11.6390 −0.508937 −0.254468 0.967081i \(-0.581900\pi\)
−0.254468 + 0.967081i \(0.581900\pi\)
\(524\) 55.9767 2.44535
\(525\) 4.28187 0.186876
\(526\) 39.7552i 1.73341i
\(527\) 23.2322i 1.01201i
\(528\) −161.303 −7.01982
\(529\) −18.2850 −0.795000
\(530\) 13.6263i 0.591888i
\(531\) −0.102210 −0.00443556
\(532\) −18.2132 −0.789640
\(533\) −14.7663 3.25906i −0.639600 0.141166i
\(534\) 48.3239 2.09118
\(535\) 1.46835 0.0634823
\(536\) 131.692i 5.68821i
\(537\) −10.3052 −0.444701
\(538\) −8.12340 −0.350225
\(539\) 6.33279i 0.272772i
\(540\) 45.0167i 1.93721i
\(541\) 25.9764 1.11681 0.558406 0.829568i \(-0.311413\pi\)
0.558406 + 0.829568i \(0.311413\pi\)
\(542\) −3.95387 −0.169833
\(543\) 36.8816 1.58274
\(544\) 70.6572i 3.02940i
\(545\) 8.42322i 0.360811i
\(546\) 11.1343i 0.476502i
\(547\) 40.6869i 1.73964i 0.493365 + 0.869822i \(0.335767\pi\)
−0.493365 + 0.869822i \(0.664233\pi\)
\(548\) 111.416i 4.75944i
\(549\) 0.191343 0.00816631
\(550\) 42.8070i 1.82530i
\(551\) −6.62093 −0.282061
\(552\) 35.2462i 1.50018i
\(553\) −6.15260 −0.261635
\(554\) −36.8543 −1.56579
\(555\) 18.3735i 0.779913i
\(556\) −64.8595 −2.75066
\(557\) 27.9485i 1.18422i −0.805858 0.592108i \(-0.798296\pi\)
0.805858 0.592108i \(-0.201704\pi\)
\(558\) 0.258867 0.0109587
\(559\) 16.1881i 0.684682i
\(560\) 23.4079i 0.989164i
\(561\) 36.0927i 1.52383i
\(562\) 18.0488i 0.761343i
\(563\) 0.912204i 0.0384448i −0.999815 0.0192224i \(-0.993881\pi\)
0.999815 0.0192224i \(-0.00611906\pi\)
\(564\) 39.4238 1.66004
\(565\) −7.14632 −0.300648
\(566\) −22.4237 −0.942539
\(567\) 8.95941i 0.376260i
\(568\) 17.3459i 0.727816i
\(569\) −21.4934 −0.901049 −0.450524 0.892764i \(-0.648763\pi\)
−0.450524 + 0.892764i \(0.648763\pi\)
\(570\) −25.0559 −1.04948
\(571\) 41.2697i 1.72708i 0.504277 + 0.863542i \(0.331759\pi\)
−0.504277 + 0.863542i \(0.668241\pi\)
\(572\) 81.4009 3.40354
\(573\) −1.81279 −0.0757303
\(574\) −17.0582 3.76491i −0.711996 0.157144i
\(575\) 5.38011 0.224366
\(576\) 0.390249 0.0162604
\(577\) 22.6298i 0.942089i 0.882109 + 0.471045i \(0.156123\pi\)
−0.882109 + 0.471045i \(0.843877\pi\)
\(578\) −16.7064 −0.694896
\(579\) 18.4439 0.766504
\(580\) 17.1034i 0.710182i
\(581\) 10.7760i 0.447065i
\(582\) 44.0717 1.82683
\(583\) −19.9161 −0.824841
\(584\) −61.2606 −2.53498
\(585\) 0.0505201i 0.00208875i
\(586\) 70.3148i 2.90468i
\(587\) 0.556658i 0.0229758i −0.999934 0.0114879i \(-0.996343\pi\)
0.999934 0.0114879i \(-0.00365678\pi\)
\(588\) 9.40610i 0.387901i
\(589\) 23.5727i 0.971294i
\(590\) −32.8779 −1.35356
\(591\) 7.54011i 0.310159i
\(592\) −98.6679 −4.05523
\(593\) 4.65161i 0.191019i −0.995429 0.0955094i \(-0.969552\pi\)
0.995429 0.0955094i \(-0.0304480\pi\)
\(594\) 89.9735 3.69166
\(595\) −5.23767 −0.214724
\(596\) 21.4456i 0.878447i
\(597\) 25.5491 1.04566
\(598\) 13.9900i 0.572096i
\(599\) −6.12297 −0.250178 −0.125089 0.992146i \(-0.539922\pi\)
−0.125089 + 0.992146i \(0.539922\pi\)
\(600\) 40.2180i 1.64189i
\(601\) 32.2061i 1.31371i −0.754016 0.656857i \(-0.771886\pi\)
0.754016 0.656857i \(-0.228114\pi\)
\(602\) 18.7006i 0.762181i
\(603\) 0.188855i 0.00769078i
\(604\) 49.8908i 2.03003i
\(605\) 46.2224 1.87921
\(606\) −30.1079 −1.22305
\(607\) −36.7385 −1.49117 −0.745586 0.666410i \(-0.767830\pi\)
−0.745586 + 0.666410i \(0.767830\pi\)
\(608\) 71.6927i 2.90752i
\(609\) 3.41935i 0.138559i
\(610\) 61.5490 2.49205
\(611\) −9.89821 −0.400439
\(612\) 0.241782i 0.00977347i
\(613\) 17.6423 0.712564 0.356282 0.934378i \(-0.384044\pi\)
0.356282 + 0.934378i \(0.384044\pi\)
\(614\) 83.5288 3.37095
\(615\) −17.1611 3.78761i −0.692002 0.152731i
\(616\) 59.4815 2.39658
\(617\) −8.87689 −0.357370 −0.178685 0.983906i \(-0.557184\pi\)
−0.178685 + 0.983906i \(0.557184\pi\)
\(618\) 48.6585i 1.95733i
\(619\) 9.61795 0.386578 0.193289 0.981142i \(-0.438084\pi\)
0.193289 + 0.981142i \(0.438084\pi\)
\(620\) 60.8938 2.44555
\(621\) 11.3082i 0.453781i
\(622\) 43.9550i 1.76243i
\(623\) −10.2497 −0.410644
\(624\) 60.1529 2.40804
\(625\) −6.47242 −0.258897
\(626\) 11.5606i 0.462053i
\(627\) 36.6216i 1.46253i
\(628\) 119.268i 4.75933i
\(629\) 22.0776i 0.880292i
\(630\) 0.0583613i 0.00232517i
\(631\) 13.1951 0.525290 0.262645 0.964893i \(-0.415405\pi\)
0.262645 + 0.964893i \(0.415405\pi\)
\(632\) 57.7891i 2.29873i
\(633\) 29.3578 1.16687
\(634\) 20.1852i 0.801655i
\(635\) −8.15922 −0.323789
\(636\) −29.5815 −1.17298
\(637\) 2.36161i 0.0935704i
\(638\) 34.1841 1.35336
\(639\) 0.0248752i 0.000984048i
\(640\) 57.4785 2.27204
\(641\) 21.9177i 0.865698i −0.901466 0.432849i \(-0.857508\pi\)
0.901466 0.432849i \(-0.142492\pi\)
\(642\) 4.35898i 0.172035i
\(643\) 23.0816i 0.910251i −0.890427 0.455125i \(-0.849594\pi\)
0.890427 0.455125i \(-0.150406\pi\)
\(644\) 11.8186i 0.465720i
\(645\) 18.8134i 0.740778i
\(646\) −30.1071 −1.18455
\(647\) −1.06211 −0.0417558 −0.0208779 0.999782i \(-0.506646\pi\)
−0.0208779 + 0.999782i \(0.506646\pi\)
\(648\) 84.1524 3.30582
\(649\) 48.0543i 1.88630i
\(650\) 15.9635i 0.626140i
\(651\) 12.1740 0.477136
\(652\) 85.4094 3.34489
\(653\) 5.96470i 0.233417i 0.993166 + 0.116708i \(0.0372343\pi\)
−0.993166 + 0.116708i \(0.962766\pi\)
\(654\) −25.0054 −0.977788
\(655\) −16.3335 −0.638202
\(656\) 20.3399 92.1570i 0.794140 3.59813i
\(657\) 0.0878521 0.00342744
\(658\) −11.4345 −0.445764
\(659\) 30.3564i 1.18252i 0.806482 + 0.591259i \(0.201369\pi\)
−0.806482 + 0.591259i \(0.798631\pi\)
\(660\) 94.6024 3.68239
\(661\) −22.2278 −0.864561 −0.432281 0.901739i \(-0.642291\pi\)
−0.432281 + 0.901739i \(0.642291\pi\)
\(662\) 13.0106i 0.505671i
\(663\) 13.4596i 0.522728i
\(664\) −101.215 −3.92792
\(665\) 5.31443 0.206085
\(666\) 0.246002 0.00953239
\(667\) 4.29636i 0.166356i
\(668\) 48.0319i 1.85841i
\(669\) 18.8148i 0.727421i
\(670\) 60.7489i 2.34693i
\(671\) 89.9598i 3.47286i
\(672\) 37.0254 1.42828
\(673\) 2.72867i 0.105183i 0.998616 + 0.0525913i \(0.0167481\pi\)
−0.998616 + 0.0525913i \(0.983252\pi\)
\(674\) 22.2923 0.858666
\(675\) 12.9033i 0.496648i
\(676\) 40.4011 1.55389
\(677\) 44.7433 1.71962 0.859812 0.510611i \(-0.170581\pi\)
0.859812 + 0.510611i \(0.170581\pi\)
\(678\) 21.2147i 0.814747i
\(679\) −9.34775 −0.358734
\(680\) 49.1955i 1.88656i
\(681\) 15.8844 0.608693
\(682\) 121.706i 4.66038i
\(683\) 10.6927i 0.409143i −0.978852 0.204572i \(-0.934420\pi\)
0.978852 0.204572i \(-0.0655802\pi\)
\(684\) 0.245326i 0.00938027i
\(685\) 32.5100i 1.24214i
\(686\) 2.72816i 0.104162i
\(687\) −27.9929 −1.06800
\(688\) −101.030 −3.85174
\(689\) 7.42708 0.282949
\(690\) 16.2589i 0.618967i
\(691\) 30.0511i 1.14320i 0.820533 + 0.571599i \(0.193677\pi\)
−0.820533 + 0.571599i \(0.806323\pi\)
\(692\) −24.4550 −0.929641
\(693\) −0.0853007 −0.00324031
\(694\) 7.79316i 0.295824i
\(695\) 18.9254 0.717882
\(696\) 32.1167 1.21738
\(697\) −20.6207 4.55119i −0.781066 0.172389i
\(698\) 7.87440 0.298051
\(699\) −35.7164 −1.35092
\(700\) 13.4858i 0.509715i
\(701\) −42.2827 −1.59699 −0.798497 0.601999i \(-0.794371\pi\)
−0.798497 + 0.601999i \(0.794371\pi\)
\(702\) −33.5527 −1.26637
\(703\) 22.4012i 0.844876i
\(704\) 183.476i 6.91499i
\(705\) −11.5035 −0.433246
\(706\) 19.9399 0.750447
\(707\) 6.38598 0.240170
\(708\) 71.3751i 2.68244i
\(709\) 46.1118i 1.73177i −0.500247 0.865883i \(-0.666757\pi\)
0.500247 0.865883i \(-0.333243\pi\)
\(710\) 8.00158i 0.300294i
\(711\) 0.0828737i 0.00310801i
\(712\) 96.2712i 3.60792i
\(713\) 15.2965 0.572857
\(714\) 15.5487i 0.581895i
\(715\) −23.7520 −0.888275
\(716\) 32.4562i 1.21294i
\(717\) −17.0800 −0.637863
\(718\) −90.9005 −3.39238
\(719\) 11.9585i 0.445976i 0.974821 + 0.222988i \(0.0715811\pi\)
−0.974821 + 0.222988i \(0.928419\pi\)
\(720\) −0.315297 −0.0117504
\(721\) 10.3206i 0.384360i
\(722\) −21.2867 −0.792208
\(723\) 11.7260i 0.436095i
\(724\) 116.159i 4.31701i
\(725\) 4.90241i 0.182071i
\(726\) 137.217i 5.09260i
\(727\) 21.6176i 0.801753i −0.916132 0.400877i \(-0.868706\pi\)
0.916132 0.400877i \(-0.131294\pi\)
\(728\) −22.1817 −0.822110
\(729\) −27.1201 −1.00445
\(730\) 28.2593 1.04592
\(731\) 22.6062i 0.836120i
\(732\) 133.618i 4.93865i
\(733\) 33.4999 1.23735 0.618673 0.785649i \(-0.287671\pi\)
0.618673 + 0.785649i \(0.287671\pi\)
\(734\) 73.7961 2.72386
\(735\) 2.74461i 0.101237i
\(736\) 46.5219 1.71482
\(737\) −88.7903 −3.27063
\(738\) −0.0507122 + 0.229769i −0.00186674 + 0.00845791i
\(739\) 1.23982 0.0456073 0.0228037 0.999740i \(-0.492741\pi\)
0.0228037 + 0.999740i \(0.492741\pi\)
\(740\) 57.8676 2.12725
\(741\) 13.6569i 0.501697i
\(742\) 8.57985 0.314976
\(743\) 12.6353 0.463542 0.231771 0.972770i \(-0.425548\pi\)
0.231771 + 0.972770i \(0.425548\pi\)
\(744\) 114.346i 4.19212i
\(745\) 6.25764i 0.229262i
\(746\) −64.5984 −2.36512
\(747\) 0.145150 0.00531076
\(748\) 113.674 4.15634
\(749\) 0.924553i 0.0337824i
\(750\) 55.9911i 2.04451i
\(751\) 35.1470i 1.28253i −0.767318 0.641267i \(-0.778409\pi\)
0.767318 0.641267i \(-0.221591\pi\)
\(752\) 61.7750i 2.25270i
\(753\) 41.6623i 1.51826i
\(754\) −12.7479 −0.464250
\(755\) 14.5577i 0.529809i
\(756\) −28.3450 −1.03090
\(757\) 36.7182i 1.33455i 0.744813 + 0.667273i \(0.232539\pi\)
−0.744813 + 0.667273i \(0.767461\pi\)
\(758\) 0.394753 0.0143381
\(759\) 23.7640 0.862579
\(760\) 49.9165i 1.81066i
\(761\) −22.2613 −0.806973 −0.403486 0.914986i \(-0.632202\pi\)
−0.403486 + 0.914986i \(0.632202\pi\)
\(762\) 24.2217i 0.877458i
\(763\) 5.30372 0.192008
\(764\) 5.70939i 0.206558i
\(765\) 0.0705499i 0.00255074i
\(766\) 67.1084i 2.42473i
\(767\) 17.9203i 0.647065i
\(768\) 70.4946i 2.54375i
\(769\) 30.1091 1.08576 0.542882 0.839809i \(-0.317333\pi\)
0.542882 + 0.839809i \(0.317333\pi\)
\(770\) −27.4386 −0.988819
\(771\) −6.09561 −0.219528
\(772\) 58.0893i 2.09068i
\(773\) 34.6738i 1.24713i −0.781771 0.623566i \(-0.785683\pi\)
0.781771 0.623566i \(-0.214317\pi\)
\(774\) 0.251892 0.00905407
\(775\) 17.4542 0.626973
\(776\) 87.8000i 3.15184i
\(777\) 11.5690 0.415035
\(778\) −34.0739 −1.22161
\(779\) 20.9229 + 4.61789i 0.749642 + 0.165453i
\(780\) −35.2789 −1.26319
\(781\) 11.6951 0.418483
\(782\) 19.5367i 0.698631i
\(783\) −10.3041 −0.368238
\(784\) −14.7389 −0.526389
\(785\) 34.8014i 1.24212i
\(786\) 48.4880i 1.72951i
\(787\) −22.1393 −0.789182 −0.394591 0.918857i \(-0.629114\pi\)
−0.394591 + 0.918857i \(0.629114\pi\)
\(788\) −23.7476 −0.845975
\(789\) −25.1830 −0.896538
\(790\) 26.6579i 0.948445i
\(791\) 4.49971i 0.159991i
\(792\) 0.801198i 0.0284693i
\(793\) 33.5476i 1.19131i
\(794\) 8.23923i 0.292399i
\(795\) 8.63160 0.306131
\(796\) 80.4672i 2.85208i
\(797\) −15.9924 −0.566481 −0.283241 0.959049i \(-0.591410\pi\)
−0.283241 + 0.959049i \(0.591410\pi\)
\(798\) 15.7766i 0.558484i
\(799\) −13.8226 −0.489008
\(800\) 53.0843 1.87681
\(801\) 0.138060i 0.00487811i
\(802\) 11.4977 0.405999
\(803\) 41.3037i 1.45757i
\(804\) −131.880 −4.65107
\(805\) 3.44857i 0.121546i
\(806\) 45.3866i 1.59867i
\(807\) 5.14579i 0.181140i
\(808\) 59.9812i 2.11013i
\(809\) 16.6457i 0.585233i 0.956230 + 0.292616i \(0.0945259\pi\)
−0.956230 + 0.292616i \(0.905474\pi\)
\(810\) −38.8192 −1.36397
\(811\) 28.3191 0.994419 0.497210 0.867630i \(-0.334358\pi\)
0.497210 + 0.867630i \(0.334358\pi\)
\(812\) −10.7693 −0.377927
\(813\) 2.50459i 0.0878397i
\(814\) 115.658i 4.05381i
\(815\) −24.9217 −0.872969
\(816\) 84.0018 2.94065
\(817\) 22.9375i 0.802481i
\(818\) −6.26634 −0.219097
\(819\) 0.0318102 0.00111154
\(820\) −11.9291 + 54.0490i −0.416583 + 1.88747i
\(821\) −28.3525 −0.989509 −0.494755 0.869033i \(-0.664742\pi\)
−0.494755 + 0.869033i \(0.664742\pi\)
\(822\) 96.5101 3.36618
\(823\) 14.0767i 0.490681i −0.969437 0.245341i \(-0.921100\pi\)
0.969437 0.245341i \(-0.0788998\pi\)
\(824\) −96.9377 −3.37699
\(825\) 27.1162 0.944064
\(826\) 20.7017i 0.720305i
\(827\) 6.68674i 0.232521i −0.993219 0.116260i \(-0.962909\pi\)
0.993219 0.116260i \(-0.0370907\pi\)
\(828\) −0.159194 −0.00553236
\(829\) 16.4614 0.571729 0.285865 0.958270i \(-0.407719\pi\)
0.285865 + 0.958270i \(0.407719\pi\)
\(830\) 46.6902 1.62064
\(831\) 23.3454i 0.809845i
\(832\) 68.4214i 2.37208i
\(833\) 3.29792i 0.114266i
\(834\) 56.1825i 1.94544i
\(835\) 14.0153i 0.485018i
\(836\) −115.340 −3.98912
\(837\) 36.6859i 1.26805i
\(838\) 71.9029 2.48385
\(839\) 14.2042i 0.490384i −0.969475 0.245192i \(-0.921149\pi\)
0.969475 0.245192i \(-0.0788510\pi\)
\(840\) −25.7791 −0.889465
\(841\) 25.0851 0.865004
\(842\) 94.9954i 3.27376i
\(843\) −11.4331 −0.393776
\(844\) 92.4625i 3.18269i
\(845\) −11.7887 −0.405543
\(846\) 0.154020i 0.00529530i
\(847\) 29.1042i 1.00003i
\(848\) 46.3527i 1.59176i
\(849\) 14.2043i 0.487492i
\(850\) 22.2926i 0.764629i
\(851\) 14.5363 0.498297
\(852\) 17.3707 0.595111
\(853\) 20.2084 0.691921 0.345961 0.938249i \(-0.387553\pi\)
0.345961 + 0.938249i \(0.387553\pi\)
\(854\) 38.7546i 1.32616i
\(855\) 0.0715838i 0.00244811i
\(856\) 8.68398 0.296812
\(857\) −37.1260 −1.26820 −0.634100 0.773251i \(-0.718629\pi\)
−0.634100 + 0.773251i \(0.718629\pi\)
\(858\) 70.5109i 2.40720i
\(859\) −42.1440 −1.43794 −0.718968 0.695043i \(-0.755385\pi\)
−0.718968 + 0.695043i \(0.755385\pi\)
\(860\) 59.2530 2.02051
\(861\) −2.38489 + 10.8056i −0.0812768 + 0.368252i
\(862\) 52.7679 1.79728
\(863\) −14.1793 −0.482669 −0.241334 0.970442i \(-0.577585\pi\)
−0.241334 + 0.970442i \(0.577585\pi\)
\(864\) 111.575i 3.79585i
\(865\) 7.13575 0.242623
\(866\) −72.0034 −2.44678
\(867\) 10.5827i 0.359408i
\(868\) 38.3421i 1.30141i
\(869\) −38.9631 −1.32173
\(870\) −14.8153 −0.502286
\(871\) 33.1115 1.12194
\(872\) 49.8159i 1.68698i
\(873\) 0.125911i 0.00426146i
\(874\) 19.8230i 0.670524i
\(875\) 11.8759i 0.401478i
\(876\) 61.3484i 2.07277i
\(877\) 35.0845 1.18472 0.592360 0.805674i \(-0.298196\pi\)
0.592360 + 0.805674i \(0.298196\pi\)
\(878\) 70.4377i 2.37716i
\(879\) −44.5411 −1.50233
\(880\) 148.237i 4.99707i
\(881\) 45.4290 1.53054 0.765271 0.643708i \(-0.222605\pi\)
0.765271 + 0.643708i \(0.222605\pi\)
\(882\) 0.0367475 0.00123735
\(883\) 41.0997i 1.38311i 0.722322 + 0.691557i \(0.243075\pi\)
−0.722322 + 0.691557i \(0.756925\pi\)
\(884\) −42.3911 −1.42577
\(885\) 20.8266i 0.700078i
\(886\) −46.0902 −1.54843
\(887\) 11.4933i 0.385908i −0.981208 0.192954i \(-0.938193\pi\)
0.981208 0.192954i \(-0.0618069\pi\)
\(888\) 108.663i 3.64649i
\(889\) 5.13749i 0.172306i
\(890\) 44.4096i 1.48861i
\(891\) 56.7380i 1.90080i
\(892\) −59.2573 −1.98408
\(893\) 14.0251 0.469334
\(894\) −18.5766 −0.621294
\(895\) 9.47042i 0.316561i
\(896\) 36.1916i 1.20908i
\(897\) −8.86203 −0.295894
\(898\) 2.25376 0.0752091
\(899\) 13.9383i 0.464868i
\(900\) −0.181650 −0.00605498
\(901\) 10.3717 0.345532
\(902\) −108.026 23.8423i −3.59687 0.793863i
\(903\) 11.8460 0.394209
\(904\) −42.2641 −1.40568
\(905\) 33.8941i 1.12668i
\(906\) 43.2163 1.43577
\(907\) 2.28582 0.0758995 0.0379497 0.999280i \(-0.487917\pi\)
0.0379497 + 0.999280i \(0.487917\pi\)
\(908\) 50.0281i 1.66024i
\(909\) 0.0860173i 0.00285301i
\(910\) 10.2324 0.339199
\(911\) −13.0710 −0.433063 −0.216532 0.976276i \(-0.569474\pi\)
−0.216532 + 0.976276i \(0.569474\pi\)
\(912\) −85.2329 −2.82234
\(913\) 68.2423i 2.25849i
\(914\) 89.7195i 2.96766i
\(915\) 38.9884i 1.28892i
\(916\) 88.1639i 2.91302i
\(917\) 10.2845i 0.339623i
\(918\) −46.8555 −1.54646
\(919\) 10.5657i 0.348530i 0.984699 + 0.174265i \(0.0557549\pi\)
−0.984699 + 0.174265i \(0.944245\pi\)
\(920\) −32.3911 −1.06790
\(921\) 52.9115i 1.74349i
\(922\) 10.0758 0.331827
\(923\) −4.36131 −0.143554
\(924\) 59.5668i 1.95960i
\(925\) 16.5868 0.545369
\(926\) 70.7913i 2.32634i
\(927\) 0.139016 0.00456587
\(928\) 42.3912i 1.39156i
\(929\) 14.8268i 0.486452i −0.969970 0.243226i \(-0.921794\pi\)
0.969970 0.243226i \(-0.0782056\pi\)
\(930\) 52.7473i 1.72965i
\(931\) 3.34626i 0.109669i
\(932\) 112.489i 3.68471i
\(933\) −27.8434 −0.911552
\(934\) 32.5848 1.06621
\(935\) −33.1690 −1.08474
\(936\) 0.298781i 0.00976597i
\(937\) 21.1237i 0.690081i 0.938588 + 0.345041i \(0.112135\pi\)
−0.938588 + 0.345041i \(0.887865\pi\)
\(938\) 38.2508 1.24893
\(939\) 7.32306 0.238979
\(940\) 36.2303i 1.18170i
\(941\) −25.2099 −0.821820 −0.410910 0.911676i \(-0.634789\pi\)
−0.410910 + 0.911676i \(0.634789\pi\)
\(942\) 103.312 3.36610
\(943\) −2.99658 + 13.5770i −0.0975821 + 0.442129i
\(944\) −111.841 −3.64012
\(945\) 8.27081 0.269049
\(946\) 118.427i 3.85040i
\(947\) −16.8971 −0.549083 −0.274542 0.961575i \(-0.588526\pi\)
−0.274542 + 0.961575i \(0.588526\pi\)
\(948\) −57.8719 −1.87959
\(949\) 15.4029i 0.499999i
\(950\) 22.6193i 0.733866i
\(951\) 12.7863 0.414625
\(952\) −30.9762 −1.00394
\(953\) 37.4437 1.21292 0.606460 0.795114i \(-0.292589\pi\)
0.606460 + 0.795114i \(0.292589\pi\)
\(954\) 0.115568i 0.00374165i
\(955\) 1.66595i 0.0539088i
\(956\) 53.7935i 1.73981i
\(957\) 21.6540i 0.699974i
\(958\) 26.3245i 0.850505i
\(959\) −20.4701 −0.661014
\(960\) 79.5178i 2.56643i
\(961\) 18.6248 0.600801
\(962\) 43.1310i 1.39060i
\(963\) −0.0124535 −0.000401307
\(964\) −36.9311 −1.18947
\(965\) 16.9499i 0.545637i
\(966\) −10.2375 −0.329386
\(967\) 25.2099i 0.810695i 0.914163 + 0.405347i \(0.132849\pi\)
−0.914163 + 0.405347i \(0.867151\pi\)
\(968\) 273.365 8.78627
\(969\) 19.0714i 0.612662i
\(970\) 40.5018i 1.30043i
\(971\) 46.8483i 1.50343i 0.659487 + 0.751716i \(0.270774\pi\)
−0.659487 + 0.751716i \(0.729226\pi\)
\(972\) 0.761891i 0.0244377i
\(973\) 11.9165i 0.382025i
\(974\) −76.0854 −2.43793
\(975\) −10.1121 −0.323847
\(976\) 209.372 6.70183
\(977\) 17.0743i 0.546256i −0.961978 0.273128i \(-0.911942\pi\)
0.961978 0.273128i \(-0.0880582\pi\)
\(978\) 73.9832i 2.36572i
\(979\) −64.9089 −2.07450
\(980\) 8.64418 0.276128
\(981\) 0.0714395i 0.00228089i
\(982\) −61.3555 −1.95793
\(983\) −11.6164 −0.370507 −0.185253 0.982691i \(-0.559311\pi\)
−0.185253 + 0.982691i \(0.559311\pi\)
\(984\) −101.493 22.4004i −3.23547 0.714098i
\(985\) 6.92934 0.220787
\(986\) −17.8020 −0.566933
\(987\) 7.24322i 0.230554i
\(988\) 43.0124 1.36841
\(989\) 14.8843 0.473293
\(990\) 0.369590i 0.0117463i
\(991\) 15.3988i 0.489160i −0.969629 0.244580i \(-0.921350\pi\)
0.969629 0.244580i \(-0.0786500\pi\)
\(992\) 150.926 4.79192
\(993\) 8.24159 0.261539
\(994\) −5.03823 −0.159803
\(995\) 23.4796i 0.744353i
\(996\) 101.360i 3.21173i
\(997\) 2.32934i 0.0737708i −0.999320 0.0368854i \(-0.988256\pi\)
0.999320 0.0368854i \(-0.0117437\pi\)
\(998\) 38.4229i 1.21626i
\(999\) 34.8628i 1.10301i
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 287.2.c.b.204.2 yes 12
41.40 even 2 inner 287.2.c.b.204.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.c.b.204.1 12 41.40 even 2 inner
287.2.c.b.204.2 yes 12 1.1 even 1 trivial