Properties

Label 429.2.f.a.131.2
Level $429$
Weight $2$
Character 429.131
Analytic conductor $3.426$
Analytic rank $0$
Dimension $48$
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] = [429,2,Mod(131,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.131");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.f (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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 131.2
Character \(\chi\) \(=\) 429.131
Dual form 429.2.f.a.131.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.70555 q^{2} +(-1.68970 + 0.380676i) q^{3} +5.32000 q^{4} -2.40031i q^{5} +(4.57157 - 1.02994i) q^{6} -4.64879i q^{7} -8.98243 q^{8} +(2.71017 - 1.28646i) q^{9} +O(q^{10})\) \(q-2.70555 q^{2} +(-1.68970 + 0.380676i) q^{3} +5.32000 q^{4} -2.40031i q^{5} +(4.57157 - 1.02994i) q^{6} -4.64879i q^{7} -8.98243 q^{8} +(2.71017 - 1.28646i) q^{9} +6.49415i q^{10} +(-0.588530 - 3.26399i) q^{11} +(-8.98921 + 2.02520i) q^{12} -1.00000i q^{13} +12.5775i q^{14} +(0.913739 + 4.05580i) q^{15} +13.6624 q^{16} +2.96873 q^{17} +(-7.33251 + 3.48057i) q^{18} +0.907622i q^{19} -12.7696i q^{20} +(1.76968 + 7.85505i) q^{21} +(1.59230 + 8.83089i) q^{22} -0.745744i q^{23} +(15.1776 - 3.41940i) q^{24} -0.761477 q^{25} +2.70555i q^{26} +(-4.08965 + 3.20542i) q^{27} -24.7316i q^{28} +4.15417 q^{29} +(-2.47217 - 10.9732i) q^{30} -2.63982 q^{31} -18.9995 q^{32} +(2.23696 + 5.29113i) q^{33} -8.03206 q^{34} -11.1585 q^{35} +(14.4181 - 6.84395i) q^{36} -9.06415 q^{37} -2.45562i q^{38} +(0.380676 + 1.68970i) q^{39} +21.5606i q^{40} +4.58710 q^{41} +(-4.78796 - 21.2522i) q^{42} -6.71382i q^{43} +(-3.13098 - 17.3644i) q^{44} +(-3.08789 - 6.50525i) q^{45} +2.01765i q^{46} +6.35638i q^{47} +(-23.0854 + 5.20095i) q^{48} -14.6112 q^{49} +2.06021 q^{50} +(-5.01627 + 1.13013i) q^{51} -5.32000i q^{52} -6.81627i q^{53} +(11.0648 - 8.67243i) q^{54} +(-7.83458 + 1.41265i) q^{55} +41.7574i q^{56} +(-0.345510 - 1.53361i) q^{57} -11.2393 q^{58} -5.61923i q^{59} +(4.86109 + 21.5769i) q^{60} +5.76709i q^{61} +7.14217 q^{62} +(-5.98046 - 12.5990i) q^{63} +24.0793 q^{64} -2.40031 q^{65} +(-6.05221 - 14.3154i) q^{66} +8.08809 q^{67} +15.7937 q^{68} +(0.283887 + 1.26008i) q^{69} +30.1899 q^{70} +0.0134651i q^{71} +(-24.3439 + 11.5555i) q^{72} +4.80852i q^{73} +24.5235 q^{74} +(1.28667 - 0.289876i) q^{75} +4.82855i q^{76} +(-15.1736 + 2.73595i) q^{77} +(-1.02994 - 4.57157i) q^{78} -8.17275i q^{79} -32.7940i q^{80} +(5.69006 - 6.97303i) q^{81} -12.4106 q^{82} -1.87173 q^{83} +(9.41470 + 41.7889i) q^{84} -7.12587i q^{85} +18.1646i q^{86} +(-7.01931 + 1.58139i) q^{87} +(5.28643 + 29.3186i) q^{88} +6.88831i q^{89} +(8.35444 + 17.6003i) q^{90} -4.64879 q^{91} -3.96736i q^{92} +(4.46051 - 1.00492i) q^{93} -17.1975i q^{94} +2.17857 q^{95} +(32.1035 - 7.23265i) q^{96} +13.4578 q^{97} +39.5314 q^{98} +(-5.79400 - 8.08886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70555 −1.91311 −0.956556 0.291547i \(-0.905830\pi\)
−0.956556 + 0.291547i \(0.905830\pi\)
\(3\) −1.68970 + 0.380676i −0.975549 + 0.219783i
\(4\) 5.32000 2.66000
\(5\) 2.40031i 1.07345i −0.843757 0.536725i \(-0.819661\pi\)
0.843757 0.536725i \(-0.180339\pi\)
\(6\) 4.57157 1.02994i 1.86633 0.420470i
\(7\) 4.64879i 1.75708i −0.477673 0.878538i \(-0.658519\pi\)
0.477673 0.878538i \(-0.341481\pi\)
\(8\) −8.98243 −3.17577
\(9\) 2.71017 1.28646i 0.903391 0.428819i
\(10\) 6.49415i 2.05363i
\(11\) −0.588530 3.26399i −0.177448 0.984130i
\(12\) −8.98921 + 2.02520i −2.59496 + 0.584624i
\(13\) 1.00000i 0.277350i
\(14\) 12.5775i 3.36148i
\(15\) 0.913739 + 4.05580i 0.235926 + 1.04720i
\(16\) 13.6624 3.41561
\(17\) 2.96873 0.720024 0.360012 0.932948i \(-0.382773\pi\)
0.360012 + 0.932948i \(0.382773\pi\)
\(18\) −7.33251 + 3.48057i −1.72829 + 0.820378i
\(19\) 0.907622i 0.208223i 0.994566 + 0.104111i \(0.0331999\pi\)
−0.994566 + 0.104111i \(0.966800\pi\)
\(20\) 12.7696i 2.85538i
\(21\) 1.76968 + 7.85505i 0.386176 + 1.71411i
\(22\) 1.59230 + 8.83089i 0.339479 + 1.88275i
\(23\) 0.745744i 0.155498i −0.996973 0.0777492i \(-0.975227\pi\)
0.996973 0.0777492i \(-0.0247734\pi\)
\(24\) 15.1776 3.41940i 3.09812 0.697981i
\(25\) −0.761477 −0.152295
\(26\) 2.70555i 0.530602i
\(27\) −4.08965 + 3.20542i −0.787054 + 0.616884i
\(28\) 24.7316i 4.67382i
\(29\) 4.15417 0.771411 0.385705 0.922622i \(-0.373958\pi\)
0.385705 + 0.922622i \(0.373958\pi\)
\(30\) −2.47217 10.9732i −0.451354 2.00342i
\(31\) −2.63982 −0.474126 −0.237063 0.971494i \(-0.576185\pi\)
−0.237063 + 0.971494i \(0.576185\pi\)
\(32\) −18.9995 −3.35867
\(33\) 2.23696 + 5.29113i 0.389405 + 0.921067i
\(34\) −8.03206 −1.37749
\(35\) −11.1585 −1.88613
\(36\) 14.4181 6.84395i 2.40302 1.14066i
\(37\) −9.06415 −1.49014 −0.745069 0.666988i \(-0.767583\pi\)
−0.745069 + 0.666988i \(0.767583\pi\)
\(38\) 2.45562i 0.398354i
\(39\) 0.380676 + 1.68970i 0.0609569 + 0.270569i
\(40\) 21.5606i 3.40903i
\(41\) 4.58710 0.716385 0.358192 0.933648i \(-0.383393\pi\)
0.358192 + 0.933648i \(0.383393\pi\)
\(42\) −4.78796 21.2522i −0.738798 3.27929i
\(43\) 6.71382i 1.02385i −0.859031 0.511924i \(-0.828933\pi\)
0.859031 0.511924i \(-0.171067\pi\)
\(44\) −3.13098 17.3644i −0.472013 2.61779i
\(45\) −3.08789 6.50525i −0.460315 0.969745i
\(46\) 2.01765i 0.297486i
\(47\) 6.35638i 0.927173i 0.886052 + 0.463587i \(0.153438\pi\)
−0.886052 + 0.463587i \(0.846562\pi\)
\(48\) −23.0854 + 5.20095i −3.33209 + 0.750693i
\(49\) −14.6112 −2.08732
\(50\) 2.06021 0.291358
\(51\) −5.01627 + 1.13013i −0.702418 + 0.158249i
\(52\) 5.32000i 0.737752i
\(53\) 6.81627i 0.936287i −0.883652 0.468143i \(-0.844923\pi\)
0.883652 0.468143i \(-0.155077\pi\)
\(54\) 11.0648 8.67243i 1.50572 1.18017i
\(55\) −7.83458 + 1.41265i −1.05641 + 0.190482i
\(56\) 41.7574i 5.58007i
\(57\) −0.345510 1.53361i −0.0457639 0.203132i
\(58\) −11.2393 −1.47580
\(59\) 5.61923i 0.731561i −0.930701 0.365781i \(-0.880802\pi\)
0.930701 0.365781i \(-0.119198\pi\)
\(60\) 4.86109 + 21.5769i 0.627565 + 2.78556i
\(61\) 5.76709i 0.738400i 0.929350 + 0.369200i \(0.120368\pi\)
−0.929350 + 0.369200i \(0.879632\pi\)
\(62\) 7.14217 0.907056
\(63\) −5.98046 12.5990i −0.753467 1.58733i
\(64\) 24.0793 3.00991
\(65\) −2.40031 −0.297722
\(66\) −6.05221 14.3154i −0.744976 1.76210i
\(67\) 8.08809 0.988117 0.494059 0.869429i \(-0.335513\pi\)
0.494059 + 0.869429i \(0.335513\pi\)
\(68\) 15.7937 1.91526
\(69\) 0.283887 + 1.26008i 0.0341760 + 0.151696i
\(70\) 30.1899 3.60839
\(71\) 0.0134651i 0.00159802i 1.00000 0.000799009i \(0.000254333\pi\)
−1.00000 0.000799009i \(0.999746\pi\)
\(72\) −24.3439 + 11.5555i −2.86896 + 1.36183i
\(73\) 4.80852i 0.562795i 0.959591 + 0.281398i \(0.0907980\pi\)
−0.959591 + 0.281398i \(0.909202\pi\)
\(74\) 24.5235 2.85080
\(75\) 1.28667 0.289876i 0.148572 0.0334720i
\(76\) 4.82855i 0.553873i
\(77\) −15.1736 + 2.73595i −1.72919 + 0.311790i
\(78\) −1.02994 4.57157i −0.116617 0.517628i
\(79\) 8.17275i 0.919506i −0.888047 0.459753i \(-0.847938\pi\)
0.888047 0.459753i \(-0.152062\pi\)
\(80\) 32.7940i 3.66648i
\(81\) 5.69006 6.97303i 0.632229 0.774781i
\(82\) −12.4106 −1.37052
\(83\) −1.87173 −0.205449 −0.102724 0.994710i \(-0.532756\pi\)
−0.102724 + 0.994710i \(0.532756\pi\)
\(84\) 9.41470 + 41.7889i 1.02723 + 4.55954i
\(85\) 7.12587i 0.772910i
\(86\) 18.1646i 1.95874i
\(87\) −7.01931 + 1.58139i −0.752549 + 0.169543i
\(88\) 5.28643 + 29.3186i 0.563536 + 3.12537i
\(89\) 6.88831i 0.730159i 0.930976 + 0.365080i \(0.118958\pi\)
−0.930976 + 0.365080i \(0.881042\pi\)
\(90\) 8.35444 + 17.6003i 0.880635 + 1.85523i
\(91\) −4.64879 −0.487325
\(92\) 3.96736i 0.413626i
\(93\) 4.46051 1.00492i 0.462533 0.104205i
\(94\) 17.1975i 1.77379i
\(95\) 2.17857 0.223517
\(96\) 32.1035 7.23265i 3.27655 0.738179i
\(97\) 13.4578 1.36643 0.683217 0.730215i \(-0.260580\pi\)
0.683217 + 0.730215i \(0.260580\pi\)
\(98\) 39.5314 3.99327
\(99\) −5.79400 8.08886i −0.582319 0.812961i
\(100\) −4.05106 −0.405106
\(101\) 5.10627 0.508093 0.254046 0.967192i \(-0.418238\pi\)
0.254046 + 0.967192i \(0.418238\pi\)
\(102\) 13.5718 3.05761i 1.34381 0.302749i
\(103\) −3.16632 −0.311987 −0.155993 0.987758i \(-0.549858\pi\)
−0.155993 + 0.987758i \(0.549858\pi\)
\(104\) 8.98243i 0.880800i
\(105\) 18.8545 4.24778i 1.84002 0.414541i
\(106\) 18.4418i 1.79122i
\(107\) −12.6023 −1.21831 −0.609156 0.793050i \(-0.708492\pi\)
−0.609156 + 0.793050i \(0.708492\pi\)
\(108\) −21.7570 + 17.0528i −2.09357 + 1.64091i
\(109\) 14.0453i 1.34529i 0.739963 + 0.672647i \(0.234843\pi\)
−0.739963 + 0.672647i \(0.765157\pi\)
\(110\) 21.1969 3.82200i 2.02104 0.364414i
\(111\) 15.3157 3.45050i 1.45370 0.327507i
\(112\) 63.5137i 6.00148i
\(113\) 2.86467i 0.269486i 0.990881 + 0.134743i \(0.0430208\pi\)
−0.990881 + 0.134743i \(0.956979\pi\)
\(114\) 0.934794 + 4.14926i 0.0875515 + 0.388614i
\(115\) −1.79002 −0.166920
\(116\) 22.1002 2.05195
\(117\) −1.28646 2.71017i −0.118933 0.250555i
\(118\) 15.2031i 1.39956i
\(119\) 13.8010i 1.26514i
\(120\) −8.20760 36.4310i −0.749248 3.32568i
\(121\) −10.3073 + 3.84191i −0.937024 + 0.349265i
\(122\) 15.6031i 1.41264i
\(123\) −7.75082 + 1.74620i −0.698868 + 0.157449i
\(124\) −14.0439 −1.26118
\(125\) 10.1738i 0.909969i
\(126\) 16.1804 + 34.0872i 1.44147 + 3.03673i
\(127\) 10.8973i 0.966976i 0.875351 + 0.483488i \(0.160630\pi\)
−0.875351 + 0.483488i \(0.839370\pi\)
\(128\) −27.1487 −2.39963
\(129\) 2.55579 + 11.3443i 0.225025 + 0.998814i
\(130\) 6.49415 0.569575
\(131\) −21.5642 −1.88407 −0.942036 0.335512i \(-0.891091\pi\)
−0.942036 + 0.335512i \(0.891091\pi\)
\(132\) 11.9006 + 28.1488i 1.03582 + 2.45004i
\(133\) 4.21934 0.365863
\(134\) −21.8827 −1.89038
\(135\) 7.69400 + 9.81643i 0.662194 + 0.844864i
\(136\) −26.6665 −2.28663
\(137\) 21.2168i 1.81267i 0.422555 + 0.906337i \(0.361133\pi\)
−0.422555 + 0.906337i \(0.638867\pi\)
\(138\) −0.768070 3.40922i −0.0653825 0.290212i
\(139\) 15.4534i 1.31074i −0.755309 0.655369i \(-0.772513\pi\)
0.755309 0.655369i \(-0.227487\pi\)
\(140\) −59.3633 −5.01712
\(141\) −2.41972 10.7404i −0.203777 0.904503i
\(142\) 0.0364306i 0.00305719i
\(143\) −3.26399 + 0.588530i −0.272949 + 0.0492154i
\(144\) 37.0275 17.5761i 3.08563 1.46468i
\(145\) 9.97129i 0.828071i
\(146\) 13.0097i 1.07669i
\(147\) 24.6886 5.56213i 2.03628 0.458757i
\(148\) −48.2213 −3.96377
\(149\) −12.6919 −1.03976 −0.519880 0.854239i \(-0.674023\pi\)
−0.519880 + 0.854239i \(0.674023\pi\)
\(150\) −3.48114 + 0.784274i −0.284234 + 0.0640357i
\(151\) 4.45438i 0.362492i 0.983438 + 0.181246i \(0.0580131\pi\)
−0.983438 + 0.181246i \(0.941987\pi\)
\(152\) 8.15266i 0.661268i
\(153\) 8.04578 3.81914i 0.650463 0.308760i
\(154\) 41.0529 7.40225i 3.30814 0.596490i
\(155\) 6.33638i 0.508950i
\(156\) 2.02520 + 8.98921i 0.162145 + 0.719713i
\(157\) 13.7663 1.09867 0.549335 0.835602i \(-0.314881\pi\)
0.549335 + 0.835602i \(0.314881\pi\)
\(158\) 22.1118i 1.75912i
\(159\) 2.59479 + 11.5175i 0.205780 + 0.913393i
\(160\) 45.6047i 3.60536i
\(161\) −3.46681 −0.273223
\(162\) −15.3948 + 18.8659i −1.20953 + 1.48224i
\(163\) −9.13240 −0.715305 −0.357653 0.933855i \(-0.616423\pi\)
−0.357653 + 0.933855i \(0.616423\pi\)
\(164\) 24.4034 1.90558
\(165\) 12.7003 5.36940i 0.988719 0.418007i
\(166\) 5.06405 0.393046
\(167\) 5.90115 0.456644 0.228322 0.973586i \(-0.426676\pi\)
0.228322 + 0.973586i \(0.426676\pi\)
\(168\) −15.8960 70.5575i −1.22641 5.44363i
\(169\) −1.00000 −0.0769231
\(170\) 19.2794i 1.47866i
\(171\) 1.16762 + 2.45981i 0.0892898 + 0.188107i
\(172\) 35.7175i 2.72344i
\(173\) 13.0937 0.995497 0.497748 0.867322i \(-0.334160\pi\)
0.497748 + 0.867322i \(0.334160\pi\)
\(174\) 18.9911 4.27854i 1.43971 0.324355i
\(175\) 3.53994i 0.267595i
\(176\) −8.04075 44.5940i −0.606094 3.36140i
\(177\) 2.13910 + 9.49481i 0.160785 + 0.713674i
\(178\) 18.6367i 1.39688i
\(179\) 22.5404i 1.68475i 0.538893 + 0.842374i \(0.318843\pi\)
−0.538893 + 0.842374i \(0.681157\pi\)
\(180\) −16.4276 34.6079i −1.22444 2.57952i
\(181\) 2.44801 0.181959 0.0909796 0.995853i \(-0.471000\pi\)
0.0909796 + 0.995853i \(0.471000\pi\)
\(182\) 12.5775 0.932308
\(183\) −2.19539 9.74465i −0.162288 0.720345i
\(184\) 6.69860i 0.493827i
\(185\) 21.7568i 1.59959i
\(186\) −12.0681 + 2.71885i −0.884878 + 0.199356i
\(187\) −1.74719 9.68992i −0.127767 0.708597i
\(188\) 33.8160i 2.46628i
\(189\) 14.9013 + 19.0119i 1.08391 + 1.38291i
\(190\) −5.89424 −0.427613
\(191\) 19.6329i 1.42059i −0.703907 0.710293i \(-0.748563\pi\)
0.703907 0.710293i \(-0.251437\pi\)
\(192\) −40.6867 + 9.16639i −2.93631 + 0.661528i
\(193\) 15.8242i 1.13905i −0.821974 0.569526i \(-0.807127\pi\)
0.821974 0.569526i \(-0.192873\pi\)
\(194\) −36.4108 −2.61414
\(195\) 4.05580 0.913739i 0.290442 0.0654342i
\(196\) −77.7317 −5.55226
\(197\) −5.90304 −0.420574 −0.210287 0.977640i \(-0.567440\pi\)
−0.210287 + 0.977640i \(0.567440\pi\)
\(198\) 15.6759 + 21.8848i 1.11404 + 1.55529i
\(199\) 9.39740 0.666164 0.333082 0.942898i \(-0.391911\pi\)
0.333082 + 0.942898i \(0.391911\pi\)
\(200\) 6.83992 0.483655
\(201\) −13.6664 + 3.07894i −0.963957 + 0.217172i
\(202\) −13.8153 −0.972039
\(203\) 19.3119i 1.35543i
\(204\) −26.6866 + 6.01227i −1.86843 + 0.420943i
\(205\) 11.0104i 0.769003i
\(206\) 8.56663 0.596865
\(207\) −0.959367 2.02110i −0.0666806 0.140476i
\(208\) 13.6624i 0.947319i
\(209\) 2.96247 0.534163i 0.204918 0.0369488i
\(210\) −51.0119 + 11.4926i −3.52016 + 0.793063i
\(211\) 0.229443i 0.0157955i 0.999969 + 0.00789775i \(0.00251396\pi\)
−0.999969 + 0.00789775i \(0.997486\pi\)
\(212\) 36.2626i 2.49052i
\(213\) −0.00512585 0.0227521i −0.000351218 0.00155895i
\(214\) 34.0962 2.33077
\(215\) −16.1152 −1.09905
\(216\) 36.7351 28.7925i 2.49950 1.95908i
\(217\) 12.2720i 0.833075i
\(218\) 38.0002i 2.57370i
\(219\) −1.83049 8.12496i −0.123693 0.549034i
\(220\) −41.6800 + 7.51532i −2.81006 + 0.506683i
\(221\) 2.96873i 0.199699i
\(222\) −41.4374 + 9.33551i −2.78110 + 0.626558i
\(223\) 5.90391 0.395355 0.197678 0.980267i \(-0.436660\pi\)
0.197678 + 0.980267i \(0.436660\pi\)
\(224\) 88.3246i 5.90144i
\(225\) −2.06373 + 0.979607i −0.137582 + 0.0653071i
\(226\) 7.75052i 0.515557i
\(227\) 2.05068 0.136108 0.0680541 0.997682i \(-0.478321\pi\)
0.0680541 + 0.997682i \(0.478321\pi\)
\(228\) −1.83811 8.15881i −0.121732 0.540330i
\(229\) 14.9772 0.989722 0.494861 0.868972i \(-0.335219\pi\)
0.494861 + 0.868972i \(0.335219\pi\)
\(230\) 4.84298 0.319337
\(231\) 24.5973 10.3992i 1.61838 0.684214i
\(232\) −37.3146 −2.44982
\(233\) 10.9417 0.716814 0.358407 0.933565i \(-0.383320\pi\)
0.358407 + 0.933565i \(0.383320\pi\)
\(234\) 3.48057 + 7.33251i 0.227532 + 0.479341i
\(235\) 15.2573 0.995274
\(236\) 29.8943i 1.94595i
\(237\) 3.11117 + 13.8095i 0.202092 + 0.897023i
\(238\) 37.3393i 2.42035i
\(239\) 21.9971 1.42287 0.711436 0.702751i \(-0.248045\pi\)
0.711436 + 0.702751i \(0.248045\pi\)
\(240\) 12.4839 + 55.4120i 0.805832 + 3.57683i
\(241\) 3.54849i 0.228578i −0.993448 0.114289i \(-0.963541\pi\)
0.993448 0.114289i \(-0.0364590\pi\)
\(242\) 27.8868 10.3945i 1.79263 0.668183i
\(243\) −6.96003 + 13.9484i −0.446486 + 0.894790i
\(244\) 30.6809i 1.96414i
\(245\) 35.0714i 2.24063i
\(246\) 20.9702 4.72443i 1.33701 0.301218i
\(247\) 0.907622 0.0577506
\(248\) 23.7120 1.50571
\(249\) 3.16265 0.712521i 0.200425 0.0451542i
\(250\) 27.5256i 1.74087i
\(251\) 15.5158i 0.979346i −0.871906 0.489673i \(-0.837116\pi\)
0.871906 0.489673i \(-0.162884\pi\)
\(252\) −31.8160 67.0268i −2.00422 4.22229i
\(253\) −2.43410 + 0.438893i −0.153031 + 0.0275930i
\(254\) 29.4831i 1.84993i
\(255\) 2.71265 + 12.0406i 0.169873 + 0.754011i
\(256\) 25.2935 1.58085
\(257\) 7.59761i 0.473926i 0.971519 + 0.236963i \(0.0761520\pi\)
−0.971519 + 0.236963i \(0.923848\pi\)
\(258\) −6.91482 30.6927i −0.430498 1.91084i
\(259\) 42.1373i 2.61828i
\(260\) −12.7696 −0.791940
\(261\) 11.2585 5.34416i 0.696885 0.330795i
\(262\) 58.3430 3.60444
\(263\) −6.37999 −0.393407 −0.196703 0.980463i \(-0.563024\pi\)
−0.196703 + 0.980463i \(0.563024\pi\)
\(264\) −20.0934 47.5272i −1.23666 2.92510i
\(265\) −16.3611 −1.00506
\(266\) −11.4156 −0.699938
\(267\) −2.62221 11.6392i −0.160477 0.712306i
\(268\) 43.0286 2.62839
\(269\) 27.4691i 1.67482i −0.546576 0.837409i \(-0.684069\pi\)
0.546576 0.837409i \(-0.315931\pi\)
\(270\) −20.8165 26.5588i −1.26685 1.61632i
\(271\) 10.7347i 0.652088i −0.945355 0.326044i \(-0.894284\pi\)
0.945355 0.326044i \(-0.105716\pi\)
\(272\) 40.5601 2.45932
\(273\) 7.85505 1.76968i 0.475409 0.107106i
\(274\) 57.4031i 3.46785i
\(275\) 0.448152 + 2.48545i 0.0270246 + 0.149878i
\(276\) 1.51028 + 6.70365i 0.0909081 + 0.403512i
\(277\) 12.1941i 0.732671i −0.930483 0.366336i \(-0.880612\pi\)
0.930483 0.366336i \(-0.119388\pi\)
\(278\) 41.8099i 2.50759i
\(279\) −7.15437 + 3.39601i −0.428321 + 0.203314i
\(280\) 100.231 5.98993
\(281\) −29.1873 −1.74117 −0.870583 0.492022i \(-0.836258\pi\)
−0.870583 + 0.492022i \(0.836258\pi\)
\(282\) 6.54668 + 29.0586i 0.389849 + 1.73042i
\(283\) 11.3887i 0.676989i 0.940968 + 0.338494i \(0.109918\pi\)
−0.940968 + 0.338494i \(0.890082\pi\)
\(284\) 0.0716346i 0.00425073i
\(285\) −3.68113 + 0.829330i −0.218052 + 0.0491253i
\(286\) 8.83089 1.59230i 0.522181 0.0941545i
\(287\) 21.3244i 1.25874i
\(288\) −51.4919 + 24.4420i −3.03419 + 1.44026i
\(289\) −8.18662 −0.481566
\(290\) 26.9778i 1.58419i
\(291\) −22.7397 + 5.12307i −1.33302 + 0.300320i
\(292\) 25.5814i 1.49704i
\(293\) 16.9662 0.991178 0.495589 0.868557i \(-0.334952\pi\)
0.495589 + 0.868557i \(0.334952\pi\)
\(294\) −66.7961 + 15.0486i −3.89563 + 0.877654i
\(295\) −13.4879 −0.785294
\(296\) 81.4181 4.73233
\(297\) 12.8693 + 11.4621i 0.746755 + 0.665099i
\(298\) 34.3385 1.98918
\(299\) −0.745744 −0.0431275
\(300\) 6.84508 1.54214i 0.395201 0.0890355i
\(301\) −31.2111 −1.79898
\(302\) 12.0516i 0.693489i
\(303\) −8.62806 + 1.94383i −0.495669 + 0.111670i
\(304\) 12.4003i 0.711207i
\(305\) 13.8428 0.792636
\(306\) −21.7683 + 10.3329i −1.24441 + 0.590692i
\(307\) 27.4337i 1.56572i 0.622196 + 0.782862i \(0.286241\pi\)
−0.622196 + 0.782862i \(0.713759\pi\)
\(308\) −80.7235 + 14.5553i −4.59965 + 0.829363i
\(309\) 5.35013 1.20534i 0.304358 0.0685694i
\(310\) 17.1434i 0.973680i
\(311\) 4.04707i 0.229488i 0.993395 + 0.114744i \(0.0366048\pi\)
−0.993395 + 0.114744i \(0.963395\pi\)
\(312\) −3.41940 15.1776i −0.193585 0.859263i
\(313\) 24.0372 1.35866 0.679332 0.733831i \(-0.262270\pi\)
0.679332 + 0.733831i \(0.262270\pi\)
\(314\) −37.2454 −2.10188
\(315\) −30.2415 + 14.3549i −1.70392 + 0.808809i
\(316\) 43.4790i 2.44589i
\(317\) 4.26641i 0.239625i −0.992797 0.119813i \(-0.961771\pi\)
0.992797 0.119813i \(-0.0382294\pi\)
\(318\) −7.02033 31.1610i −0.393681 1.74742i
\(319\) −2.44486 13.5592i −0.136886 0.759168i
\(320\) 57.7976i 3.23099i
\(321\) 21.2941 4.79740i 1.18852 0.267765i
\(322\) 9.37962 0.522706
\(323\) 2.69449i 0.149925i
\(324\) 30.2711 37.0966i 1.68173 2.06092i
\(325\) 0.761477i 0.0422391i
\(326\) 24.7082 1.36846
\(327\) −5.34670 23.7323i −0.295673 1.31240i
\(328\) −41.2033 −2.27507
\(329\) 29.5495 1.62911
\(330\) −34.3614 + 14.5272i −1.89153 + 0.799694i
\(331\) −10.1438 −0.557556 −0.278778 0.960356i \(-0.589929\pi\)
−0.278778 + 0.960356i \(0.589929\pi\)
\(332\) −9.95758 −0.546493
\(333\) −24.5654 + 11.6606i −1.34618 + 0.638999i
\(334\) −15.9658 −0.873612
\(335\) 19.4139i 1.06069i
\(336\) 24.1781 + 107.319i 1.31902 + 5.85473i
\(337\) 10.7437i 0.585245i 0.956228 + 0.292622i \(0.0945279\pi\)
−0.956228 + 0.292622i \(0.905472\pi\)
\(338\) 2.70555 0.147163
\(339\) −1.09051 4.84044i −0.0592285 0.262896i
\(340\) 37.9097i 2.05594i
\(341\) 1.55361 + 8.61635i 0.0841329 + 0.466601i
\(342\) −3.15904 6.65515i −0.170822 0.359869i
\(343\) 35.3829i 1.91050i
\(344\) 60.3064i 3.25151i
\(345\) 3.02459 0.681416i 0.162838 0.0366862i
\(346\) −35.4257 −1.90450
\(347\) 15.0847 0.809788 0.404894 0.914364i \(-0.367308\pi\)
0.404894 + 0.914364i \(0.367308\pi\)
\(348\) −37.3427 + 8.41302i −2.00178 + 0.450985i
\(349\) 20.5817i 1.10171i −0.834600 0.550856i \(-0.814301\pi\)
0.834600 0.550856i \(-0.185699\pi\)
\(350\) 9.57749i 0.511939i
\(351\) 3.20542 + 4.08965i 0.171093 + 0.218290i
\(352\) 11.1818 + 62.0142i 0.595991 + 3.30537i
\(353\) 19.7474i 1.05105i −0.850779 0.525524i \(-0.823869\pi\)
0.850779 0.525524i \(-0.176131\pi\)
\(354\) −5.78745 25.6887i −0.307600 1.36534i
\(355\) 0.0323205 0.00171539
\(356\) 36.6458i 1.94223i
\(357\) 5.25371 + 23.3196i 0.278056 + 1.23420i
\(358\) 60.9842i 3.22311i
\(359\) 15.2603 0.805408 0.402704 0.915330i \(-0.368070\pi\)
0.402704 + 0.915330i \(0.368070\pi\)
\(360\) 27.7368 + 58.4329i 1.46186 + 3.07969i
\(361\) 18.1762 0.956643
\(362\) −6.62322 −0.348109
\(363\) 15.9537 10.4154i 0.837350 0.546667i
\(364\) −24.7316 −1.29629
\(365\) 11.5419 0.604133
\(366\) 5.93974 + 26.3646i 0.310475 + 1.37810i
\(367\) 15.8794 0.828898 0.414449 0.910073i \(-0.363974\pi\)
0.414449 + 0.910073i \(0.363974\pi\)
\(368\) 10.1887i 0.531121i
\(369\) 12.4318 5.90110i 0.647175 0.307199i
\(370\) 58.8640i 3.06019i
\(371\) −31.6874 −1.64513
\(372\) 23.7299 5.34616i 1.23034 0.277185i
\(373\) 19.6181i 1.01579i −0.861420 0.507894i \(-0.830424\pi\)
0.861420 0.507894i \(-0.169576\pi\)
\(374\) 4.72711 + 26.2166i 0.244433 + 1.35563i
\(375\) 3.87290 + 17.1906i 0.199996 + 0.887719i
\(376\) 57.0958i 2.94449i
\(377\) 4.15417i 0.213951i
\(378\) −40.3163 51.4377i −2.07364 2.64567i
\(379\) −12.0138 −0.617106 −0.308553 0.951207i \(-0.599845\pi\)
−0.308553 + 0.951207i \(0.599845\pi\)
\(380\) 11.5900 0.594555
\(381\) −4.14833 18.4131i −0.212525 0.943333i
\(382\) 53.1177i 2.71774i
\(383\) 20.5930i 1.05225i −0.850407 0.526125i \(-0.823644\pi\)
0.850407 0.526125i \(-0.176356\pi\)
\(384\) 45.8731 10.3348i 2.34095 0.527398i
\(385\) 6.56712 + 36.4213i 0.334691 + 1.85620i
\(386\) 42.8132i 2.17913i
\(387\) −8.63703 18.1956i −0.439045 0.924935i
\(388\) 71.5957 3.63472
\(389\) 9.37067i 0.475112i −0.971374 0.237556i \(-0.923654\pi\)
0.971374 0.237556i \(-0.0763463\pi\)
\(390\) −10.9732 + 2.47217i −0.555648 + 0.125183i
\(391\) 2.21392i 0.111963i
\(392\) 131.244 6.62883
\(393\) 36.4370 8.20896i 1.83800 0.414087i
\(394\) 15.9710 0.804606
\(395\) −19.6171 −0.987044
\(396\) −30.8241 43.0327i −1.54897 2.16248i
\(397\) 8.54019 0.428620 0.214310 0.976766i \(-0.431250\pi\)
0.214310 + 0.976766i \(0.431250\pi\)
\(398\) −25.4251 −1.27445
\(399\) −7.12942 + 1.60620i −0.356918 + 0.0804106i
\(400\) −10.4036 −0.520181
\(401\) 0.437486i 0.0218470i −0.999940 0.0109235i \(-0.996523\pi\)
0.999940 0.0109235i \(-0.00347713\pi\)
\(402\) 36.9752 8.33023i 1.84416 0.415474i
\(403\) 2.63982i 0.131499i
\(404\) 27.1654 1.35153
\(405\) −16.7374 13.6579i −0.831689 0.678667i
\(406\) 52.2492i 2.59308i
\(407\) 5.33452 + 29.5853i 0.264423 + 1.46649i
\(408\) 45.0583 10.1513i 2.23072 0.502563i
\(409\) 14.4152i 0.712783i 0.934337 + 0.356392i \(0.115993\pi\)
−0.934337 + 0.356392i \(0.884007\pi\)
\(410\) 29.7893i 1.47119i
\(411\) −8.07673 35.8500i −0.398395 1.76835i
\(412\) −16.8448 −0.829885
\(413\) −26.1226 −1.28541
\(414\) 2.59562 + 5.46818i 0.127568 + 0.268746i
\(415\) 4.49272i 0.220539i
\(416\) 18.9995i 0.931527i
\(417\) 5.88272 + 26.1116i 0.288078 + 1.27869i
\(418\) −8.01511 + 1.44520i −0.392032 + 0.0706873i
\(419\) 40.5181i 1.97944i 0.143017 + 0.989720i \(0.454320\pi\)
−0.143017 + 0.989720i \(0.545680\pi\)
\(420\) 100.306 22.5982i 4.89444 1.10268i
\(421\) −14.5428 −0.708771 −0.354386 0.935099i \(-0.615310\pi\)
−0.354386 + 0.935099i \(0.615310\pi\)
\(422\) 0.620769i 0.0302186i
\(423\) 8.17720 + 17.2269i 0.397589 + 0.837600i
\(424\) 61.2267i 2.97343i
\(425\) −2.26062 −0.109656
\(426\) 0.0138683 + 0.0615568i 0.000671919 + 0.00298244i
\(427\) 26.8100 1.29742
\(428\) −67.0444 −3.24071
\(429\) 5.29113 2.23696i 0.255458 0.108002i
\(430\) 43.6006 2.10261
\(431\) 18.9139 0.911049 0.455524 0.890223i \(-0.349452\pi\)
0.455524 + 0.890223i \(0.349452\pi\)
\(432\) −55.8746 + 43.7938i −2.68827 + 2.10703i
\(433\) −29.8901 −1.43643 −0.718213 0.695824i \(-0.755040\pi\)
−0.718213 + 0.695824i \(0.755040\pi\)
\(434\) 33.2024i 1.59377i
\(435\) 3.79583 + 16.8485i 0.181996 + 0.807824i
\(436\) 74.7210i 3.57849i
\(437\) 0.676854 0.0323783
\(438\) 4.95248 + 21.9825i 0.236639 + 1.05036i
\(439\) 28.1904i 1.34545i −0.739891 0.672727i \(-0.765123\pi\)
0.739891 0.672727i \(-0.234877\pi\)
\(440\) 70.3736 12.6891i 3.35493 0.604927i
\(441\) −39.5989 + 18.7967i −1.88566 + 0.895080i
\(442\) 8.03206i 0.382046i
\(443\) 18.4814i 0.878079i 0.898468 + 0.439039i \(0.144681\pi\)
−0.898468 + 0.439039i \(0.855319\pi\)
\(444\) 81.4795 18.3567i 3.86685 0.871170i
\(445\) 16.5341 0.783790
\(446\) −15.9733 −0.756359
\(447\) 21.4455 4.83150i 1.01434 0.228522i
\(448\) 111.939i 5.28864i
\(449\) 27.7393i 1.30910i −0.756019 0.654550i \(-0.772858\pi\)
0.756019 0.654550i \(-0.227142\pi\)
\(450\) 5.58354 2.65037i 0.263210 0.124940i
\(451\) −2.69965 14.9722i −0.127121 0.705016i
\(452\) 15.2401i 0.716832i
\(453\) −1.69568 7.52657i −0.0796698 0.353629i
\(454\) −5.54821 −0.260390
\(455\) 11.1585i 0.523119i
\(456\) 3.10352 + 13.7755i 0.145336 + 0.645099i
\(457\) 9.88017i 0.462175i 0.972933 + 0.231088i \(0.0742284\pi\)
−0.972933 + 0.231088i \(0.925772\pi\)
\(458\) −40.5216 −1.89345
\(459\) −12.1411 + 9.51604i −0.566698 + 0.444171i
\(460\) −9.52289 −0.444007
\(461\) 0.122017 0.00568292 0.00284146 0.999996i \(-0.499096\pi\)
0.00284146 + 0.999996i \(0.499096\pi\)
\(462\) −66.5492 + 28.1354i −3.09615 + 1.30898i
\(463\) −32.4447 −1.50784 −0.753918 0.656969i \(-0.771838\pi\)
−0.753918 + 0.656969i \(0.771838\pi\)
\(464\) 56.7561 2.63483
\(465\) −2.41211 10.7066i −0.111859 0.496506i
\(466\) −29.6033 −1.37135
\(467\) 2.06150i 0.0953948i 0.998862 + 0.0476974i \(0.0151883\pi\)
−0.998862 + 0.0476974i \(0.984812\pi\)
\(468\) −6.84395 14.4181i −0.316362 0.666478i
\(469\) 37.5998i 1.73620i
\(470\) −41.2793 −1.90407
\(471\) −23.2609 + 5.24050i −1.07181 + 0.241469i
\(472\) 50.4743i 2.32327i
\(473\) −21.9138 + 3.95128i −1.00760 + 0.181680i
\(474\) −8.41742 37.3623i −0.386625 1.71611i
\(475\) 0.691134i 0.0317114i
\(476\) 73.4214i 3.36526i
\(477\) −8.76883 18.4733i −0.401497 0.845833i
\(478\) −59.5142 −2.72212
\(479\) 19.1463 0.874815 0.437408 0.899263i \(-0.355897\pi\)
0.437408 + 0.899263i \(0.355897\pi\)
\(480\) −17.3606 77.0582i −0.792399 3.51721i
\(481\) 9.06415i 0.413290i
\(482\) 9.60062i 0.437296i
\(483\) 5.85786 1.31973i 0.266542 0.0600498i
\(484\) −54.8347 + 20.4390i −2.49249 + 0.929045i
\(485\) 32.3029i 1.46680i
\(486\) 18.8307 37.7381i 0.854179 1.71184i
\(487\) 7.65812 0.347022 0.173511 0.984832i \(-0.444489\pi\)
0.173511 + 0.984832i \(0.444489\pi\)
\(488\) 51.8025i 2.34499i
\(489\) 15.4310 3.47649i 0.697815 0.157212i
\(490\) 94.8874i 4.28658i
\(491\) −15.4009 −0.695031 −0.347516 0.937674i \(-0.612975\pi\)
−0.347516 + 0.937674i \(0.612975\pi\)
\(492\) −41.2344 + 9.28978i −1.85899 + 0.418815i
\(493\) 12.3326 0.555434
\(494\) −2.45562 −0.110483
\(495\) −19.4157 + 13.9074i −0.872673 + 0.625090i
\(496\) −36.0663 −1.61943
\(497\) 0.0625966 0.00280784
\(498\) −8.55672 + 1.92776i −0.383436 + 0.0863850i
\(499\) −14.3159 −0.640868 −0.320434 0.947271i \(-0.603829\pi\)
−0.320434 + 0.947271i \(0.603829\pi\)
\(500\) 54.1244i 2.42052i
\(501\) −9.97116 + 2.24642i −0.445479 + 0.100363i
\(502\) 41.9787i 1.87360i
\(503\) 12.7139 0.566885 0.283442 0.958989i \(-0.408524\pi\)
0.283442 + 0.958989i \(0.408524\pi\)
\(504\) 53.7191 + 113.170i 2.39284 + 5.04098i
\(505\) 12.2566i 0.545412i
\(506\) 6.58559 1.18745i 0.292765 0.0527885i
\(507\) 1.68970 0.380676i 0.0750422 0.0169064i
\(508\) 57.9735i 2.57216i
\(509\) 10.7626i 0.477045i −0.971137 0.238523i \(-0.923337\pi\)
0.971137 0.238523i \(-0.0766631\pi\)
\(510\) −7.33921 32.5764i −0.324986 1.44251i
\(511\) 22.3538 0.988874
\(512\) −14.1356 −0.624712
\(513\) −2.90931 3.71186i −0.128449 0.163883i
\(514\) 20.5557i 0.906674i
\(515\) 7.60014i 0.334902i
\(516\) 13.5968 + 60.3519i 0.598566 + 2.65685i
\(517\) 20.7472 3.74092i 0.912459 0.164526i
\(518\) 114.005i 5.00907i
\(519\) −22.1244 + 4.98446i −0.971155 + 0.218794i
\(520\) 21.5606 0.945495
\(521\) 13.0706i 0.572632i −0.958135 0.286316i \(-0.907569\pi\)
0.958135 0.286316i \(-0.0924307\pi\)
\(522\) −30.4605 + 14.4589i −1.33322 + 0.632849i
\(523\) 4.52508i 0.197868i −0.995094 0.0989339i \(-0.968457\pi\)
0.995094 0.0989339i \(-0.0315432\pi\)
\(524\) −114.722 −5.01163
\(525\) −1.34757 5.98144i −0.0588128 0.261052i
\(526\) 17.2614 0.752632
\(527\) −7.83693 −0.341382
\(528\) 30.5623 + 72.2896i 1.33005 + 3.14600i
\(529\) 22.4439 0.975820
\(530\) 44.2659 1.92279
\(531\) −7.22889 15.2291i −0.313707 0.660885i
\(532\) 22.4469 0.973197
\(533\) 4.58710i 0.198689i
\(534\) 7.09453 + 31.4904i 0.307010 + 1.36272i
\(535\) 30.2495i 1.30780i
\(536\) −72.6507 −3.13803
\(537\) −8.58058 38.0865i −0.370279 1.64355i
\(538\) 74.3189i 3.20412i
\(539\) 8.59913 + 47.6908i 0.370391 + 2.05419i
\(540\) 40.9321 + 52.2234i 1.76144 + 2.24734i
\(541\) 8.78739i 0.377799i −0.981996 0.188900i \(-0.939508\pi\)
0.981996 0.188900i \(-0.0604921\pi\)
\(542\) 29.0434i 1.24752i
\(543\) −4.13640 + 0.931899i −0.177510 + 0.0399916i
\(544\) −56.4045 −2.41832
\(545\) 33.7130 1.44411
\(546\) −21.2522 + 4.78796i −0.909512 + 0.204906i
\(547\) 43.5328i 1.86133i −0.365875 0.930664i \(-0.619230\pi\)
0.365875 0.930664i \(-0.380770\pi\)
\(548\) 112.873i 4.82172i
\(549\) 7.41910 + 15.6298i 0.316640 + 0.667064i
\(550\) −1.21250 6.72452i −0.0517011 0.286734i
\(551\) 3.77042i 0.160625i
\(552\) −2.55000 11.3186i −0.108535 0.481753i
\(553\) −37.9933 −1.61564
\(554\) 32.9917i 1.40168i
\(555\) −8.28227 36.7624i −0.351563 1.56048i
\(556\) 82.2119i 3.48656i
\(557\) −15.9263 −0.674817 −0.337409 0.941358i \(-0.609550\pi\)
−0.337409 + 0.941358i \(0.609550\pi\)
\(558\) 19.3565 9.18808i 0.819426 0.388963i
\(559\) −6.71382 −0.283964
\(560\) −152.452 −6.44229
\(561\) 6.64094 + 15.7079i 0.280381 + 0.663190i
\(562\) 78.9676 3.33105
\(563\) −25.5134 −1.07526 −0.537630 0.843181i \(-0.680680\pi\)
−0.537630 + 0.843181i \(0.680680\pi\)
\(564\) −12.8729 57.1388i −0.542048 2.40598i
\(565\) 6.87610 0.289280
\(566\) 30.8127i 1.29516i
\(567\) −32.4161 26.4519i −1.36135 1.11087i
\(568\) 0.120950i 0.00507494i
\(569\) −39.9270 −1.67383 −0.836913 0.547336i \(-0.815642\pi\)
−0.836913 + 0.547336i \(0.815642\pi\)
\(570\) 9.95950 2.24379i 0.417157 0.0939822i
\(571\) 24.5956i 1.02929i −0.857402 0.514647i \(-0.827923\pi\)
0.857402 0.514647i \(-0.172077\pi\)
\(572\) −17.3644 + 3.13098i −0.726044 + 0.130913i
\(573\) 7.47376 + 33.1737i 0.312221 + 1.38585i
\(574\) 57.6943i 2.40812i
\(575\) 0.567867i 0.0236817i
\(576\) 65.2589 30.9769i 2.71912 1.29070i
\(577\) 38.2383 1.59188 0.795941 0.605374i \(-0.206976\pi\)
0.795941 + 0.605374i \(0.206976\pi\)
\(578\) 22.1493 0.921290
\(579\) 6.02389 + 26.7382i 0.250344 + 1.11120i
\(580\) 53.0473i 2.20267i
\(581\) 8.70125i 0.360989i
\(582\) 61.5234 13.8607i 2.55023 0.574545i
\(583\) −22.2482 + 4.01158i −0.921428 + 0.166143i
\(584\) 43.1923i 1.78731i
\(585\) −6.50525 + 3.08789i −0.268959 + 0.127669i
\(586\) −45.9030 −1.89624
\(587\) 7.39147i 0.305079i 0.988297 + 0.152539i \(0.0487451\pi\)
−0.988297 + 0.152539i \(0.951255\pi\)
\(588\) 131.343 29.5906i 5.41650 1.22029i
\(589\) 2.39596i 0.0987238i
\(590\) 36.4921 1.50236
\(591\) 9.97437 2.24715i 0.410291 0.0924352i
\(592\) −123.838 −5.08972
\(593\) −10.0660 −0.413362 −0.206681 0.978408i \(-0.566266\pi\)
−0.206681 + 0.978408i \(0.566266\pi\)
\(594\) −34.8187 31.0113i −1.42863 1.27241i
\(595\) −33.1267 −1.35806
\(596\) −67.5209 −2.76576
\(597\) −15.8788 + 3.57736i −0.649875 + 0.146412i
\(598\) 2.01765 0.0825078
\(599\) 4.65033i 0.190008i −0.995477 0.0950038i \(-0.969714\pi\)
0.995477 0.0950038i \(-0.0302863\pi\)
\(600\) −11.5574 + 2.60379i −0.471829 + 0.106299i
\(601\) 8.64295i 0.352553i −0.984341 0.176277i \(-0.943595\pi\)
0.984341 0.176277i \(-0.0564053\pi\)
\(602\) 84.4432 3.44165
\(603\) 21.9201 10.4050i 0.892656 0.423723i
\(604\) 23.6973i 0.964230i
\(605\) 9.22177 + 24.7406i 0.374918 + 1.00585i
\(606\) 23.3436 5.25914i 0.948271 0.213638i
\(607\) 32.9707i 1.33824i −0.743155 0.669120i \(-0.766671\pi\)
0.743155 0.669120i \(-0.233329\pi\)
\(608\) 17.2444i 0.699352i
\(609\) 7.35156 + 32.6313i 0.297900 + 1.32229i
\(610\) −37.4524 −1.51640
\(611\) 6.35638 0.257152
\(612\) 42.8036 20.3179i 1.73023 0.821301i
\(613\) 23.5803i 0.952398i −0.879338 0.476199i \(-0.842014\pi\)
0.879338 0.476199i \(-0.157986\pi\)
\(614\) 74.2232i 2.99541i
\(615\) 4.19141 + 18.6044i 0.169014 + 0.750200i
\(616\) 136.296 24.5755i 5.49151 0.990175i
\(617\) 12.0090i 0.483465i −0.970343 0.241732i \(-0.922284\pi\)
0.970343 0.241732i \(-0.0777156\pi\)
\(618\) −14.4750 + 3.26111i −0.582271 + 0.131181i
\(619\) 33.8834 1.36189 0.680944 0.732336i \(-0.261570\pi\)
0.680944 + 0.732336i \(0.261570\pi\)
\(620\) 33.7096i 1.35381i
\(621\) 2.39042 + 3.04984i 0.0959245 + 0.122386i
\(622\) 10.9496i 0.439037i
\(623\) 32.0223 1.28295
\(624\) 5.20095 + 23.0854i 0.208205 + 0.924155i
\(625\) −28.2275 −1.12910
\(626\) −65.0339 −2.59928
\(627\) −4.80234 + 2.03032i −0.191787 + 0.0810830i
\(628\) 73.2368 2.92247
\(629\) −26.9091 −1.07293
\(630\) 81.8199 38.8380i 3.25978 1.54734i
\(631\) 26.8591 1.06924 0.534621 0.845092i \(-0.320454\pi\)
0.534621 + 0.845092i \(0.320454\pi\)
\(632\) 73.4112i 2.92014i
\(633\) −0.0873433 0.387689i −0.00347159 0.0154093i
\(634\) 11.5430i 0.458430i
\(635\) 26.1568 1.03800
\(636\) 13.8043 + 61.2729i 0.547376 + 2.42963i
\(637\) 14.6112i 0.578917i
\(638\) 6.61468 + 36.6850i 0.261878 + 1.45237i
\(639\) 0.0173223 + 0.0364929i 0.000685260 + 0.00144364i
\(640\) 65.1651i 2.57588i
\(641\) 20.2051i 0.798053i 0.916939 + 0.399027i \(0.130652\pi\)
−0.916939 + 0.399027i \(0.869348\pi\)
\(642\) −57.6124 + 12.9796i −2.27378 + 0.512264i
\(643\) −25.2247 −0.994765 −0.497382 0.867531i \(-0.665705\pi\)
−0.497382 + 0.867531i \(0.665705\pi\)
\(644\) −18.4434 −0.726772
\(645\) 27.2299 6.13468i 1.07218 0.241553i
\(646\) 7.29008i 0.286824i
\(647\) 27.8084i 1.09326i 0.837374 + 0.546631i \(0.184090\pi\)
−0.837374 + 0.546631i \(0.815910\pi\)
\(648\) −51.1106 + 62.6348i −2.00781 + 2.46053i
\(649\) −18.3411 + 3.30708i −0.719951 + 0.129814i
\(650\) 2.06021i 0.0808083i
\(651\) −4.67164 20.7359i −0.183096 0.812705i
\(652\) −48.5844 −1.90271
\(653\) 34.9648i 1.36828i −0.729351 0.684140i \(-0.760178\pi\)
0.729351 0.684140i \(-0.239822\pi\)
\(654\) 14.4658 + 64.2090i 0.565656 + 2.51077i
\(655\) 51.7607i 2.02246i
\(656\) 62.6709 2.44689
\(657\) 6.18595 + 13.0319i 0.241337 + 0.508424i
\(658\) −79.9475 −3.11668
\(659\) 50.7710 1.97776 0.988879 0.148720i \(-0.0475152\pi\)
0.988879 + 0.148720i \(0.0475152\pi\)
\(660\) 67.5658 28.5652i 2.62999 1.11190i
\(661\) −17.8821 −0.695532 −0.347766 0.937581i \(-0.613060\pi\)
−0.347766 + 0.937581i \(0.613060\pi\)
\(662\) 27.4447 1.06667
\(663\) 1.13013 + 5.01627i 0.0438904 + 0.194816i
\(664\) 16.8126 0.652457
\(665\) 10.1277i 0.392736i
\(666\) 66.4629 31.5484i 2.57539 1.22248i
\(667\) 3.09795i 0.119953i
\(668\) 31.3941 1.21467
\(669\) −9.97584 + 2.24748i −0.385688 + 0.0868925i
\(670\) 52.5253i 2.02923i
\(671\) 18.8237 3.39410i 0.726682 0.131028i
\(672\) −33.6230 149.242i −1.29704 5.75714i
\(673\) 34.4034i 1.32615i 0.748552 + 0.663077i \(0.230750\pi\)
−0.748552 + 0.663077i \(0.769250\pi\)
\(674\) 29.0675i 1.11964i
\(675\) 3.11418 2.44085i 0.119865 0.0939485i
\(676\) −5.32000 −0.204615
\(677\) 32.3052 1.24159 0.620795 0.783973i \(-0.286810\pi\)
0.620795 + 0.783973i \(0.286810\pi\)
\(678\) 2.95043 + 13.0960i 0.113311 + 0.502951i
\(679\) 62.5625i 2.40093i
\(680\) 64.0077i 2.45458i
\(681\) −3.46503 + 0.780643i −0.132780 + 0.0299143i
\(682\) −4.20338 23.3120i −0.160956 0.892661i
\(683\) 27.4993i 1.05223i −0.850413 0.526116i \(-0.823648\pi\)
0.850413 0.526116i \(-0.176352\pi\)
\(684\) 6.21172 + 13.0862i 0.237511 + 0.500364i
\(685\) 50.9269 1.94582
\(686\) 95.7301i 3.65499i
\(687\) −25.3070 + 5.70146i −0.965522 + 0.217524i
\(688\) 91.7270i 3.49706i
\(689\) −6.81627 −0.259679
\(690\) −8.18318 + 1.84360i −0.311528 + 0.0701848i
\(691\) 35.6772 1.35722 0.678612 0.734497i \(-0.262582\pi\)
0.678612 + 0.734497i \(0.262582\pi\)
\(692\) 69.6586 2.64802
\(693\) −37.6034 + 26.9350i −1.42843 + 1.02318i
\(694\) −40.8124 −1.54922
\(695\) −37.0928 −1.40701
\(696\) 63.0505 14.2048i 2.38992 0.538430i
\(697\) 13.6179 0.515814
\(698\) 55.6848i 2.10770i
\(699\) −18.4882 + 4.16524i −0.699287 + 0.157544i
\(700\) 18.8325i 0.711802i
\(701\) −33.0189 −1.24711 −0.623554 0.781780i \(-0.714312\pi\)
−0.623554 + 0.781780i \(0.714312\pi\)
\(702\) −8.67243 11.0648i −0.327320 0.417613i
\(703\) 8.22683i 0.310281i
\(704\) −14.1714 78.5945i −0.534104 2.96214i
\(705\) −25.7802 + 5.80807i −0.970939 + 0.218745i
\(706\) 53.4276i 2.01077i
\(707\) 23.7379i 0.892757i
\(708\) 11.3800 + 50.5124i 0.427688 + 1.89837i
\(709\) 27.3389 1.02673 0.513367 0.858169i \(-0.328398\pi\)
0.513367 + 0.858169i \(0.328398\pi\)
\(710\) −0.0874447 −0.00328174
\(711\) −10.5139 22.1495i −0.394301 0.830673i
\(712\) 61.8738i 2.31882i
\(713\) 1.96863i 0.0737258i
\(714\) −14.2142 63.0922i −0.531952 2.36117i
\(715\) 1.41265 + 7.83458i 0.0528302 + 0.292997i
\(716\) 119.915i 4.48143i
\(717\) −37.1685 + 8.37375i −1.38808 + 0.312724i
\(718\) −41.2875 −1.54084
\(719\) 27.5207i 1.02635i 0.858285 + 0.513174i \(0.171530\pi\)
−0.858285 + 0.513174i \(0.828470\pi\)
\(720\) −42.1881 88.8774i −1.57226 3.31227i
\(721\) 14.7195i 0.548184i
\(722\) −49.1767 −1.83017
\(723\) 1.35082 + 5.99588i 0.0502377 + 0.222989i
\(724\) 13.0234 0.484012
\(725\) −3.16331 −0.117482
\(726\) −43.1634 + 28.1794i −1.60195 + 1.04584i
\(727\) 23.5273 0.872580 0.436290 0.899806i \(-0.356292\pi\)
0.436290 + 0.899806i \(0.356292\pi\)
\(728\) 41.7574 1.54763
\(729\) 6.45055 26.2181i 0.238909 0.971042i
\(730\) −31.2273 −1.15577
\(731\) 19.9315i 0.737195i
\(732\) −11.6795 51.8416i −0.431686 1.91612i
\(733\) 40.4706i 1.49482i 0.664365 + 0.747408i \(0.268702\pi\)
−0.664365 + 0.747408i \(0.731298\pi\)
\(734\) −42.9625 −1.58578
\(735\) −13.3508 59.2601i −0.492453 2.18584i
\(736\) 14.1688i 0.522268i
\(737\) −4.76008 26.3994i −0.175340 0.972436i
\(738\) −33.6349 + 15.9657i −1.23812 + 0.587706i
\(739\) 21.7703i 0.800832i 0.916333 + 0.400416i \(0.131134\pi\)
−0.916333 + 0.400416i \(0.868866\pi\)
\(740\) 115.746i 4.25491i
\(741\) −1.53361 + 0.345510i −0.0563386 + 0.0126926i
\(742\) 85.7318 3.14731
\(743\) 19.9234 0.730918 0.365459 0.930827i \(-0.380912\pi\)
0.365459 + 0.930827i \(0.380912\pi\)
\(744\) −40.0662 + 9.02659i −1.46890 + 0.330931i
\(745\) 30.4644i 1.11613i
\(746\) 53.0778i 1.94332i
\(747\) −5.07270 + 2.40789i −0.185600 + 0.0881002i
\(748\) −9.29505 51.5504i −0.339861 1.88487i
\(749\) 58.5855i 2.14067i
\(750\) −10.4783 46.5100i −0.382615 1.69831i
\(751\) 16.4501 0.600272 0.300136 0.953896i \(-0.402968\pi\)
0.300136 + 0.953896i \(0.402968\pi\)
\(752\) 86.8436i 3.16686i
\(753\) 5.90647 + 26.2170i 0.215244 + 0.955399i
\(754\) 11.2393i 0.409312i
\(755\) 10.6919 0.389118
\(756\) 79.2750 + 101.144i 2.88321 + 3.67855i
\(757\) −35.7661 −1.29994 −0.649970 0.759960i \(-0.725219\pi\)
−0.649970 + 0.759960i \(0.725219\pi\)
\(758\) 32.5039 1.18059
\(759\) 3.94583 1.66820i 0.143224 0.0605519i
\(760\) −19.5689 −0.709838
\(761\) 35.0961 1.27223 0.636117 0.771593i \(-0.280540\pi\)
0.636117 + 0.771593i \(0.280540\pi\)
\(762\) 11.2235 + 49.8176i 0.406585 + 1.80470i
\(763\) 65.2935 2.36378
\(764\) 104.447i 3.77876i
\(765\) −9.16712 19.3123i −0.331438 0.698239i
\(766\) 55.7153i 2.01307i
\(767\) −5.61923 −0.202899
\(768\) −42.7385 + 9.62864i −1.54219 + 0.347444i
\(769\) 39.6385i 1.42940i 0.699431 + 0.714700i \(0.253437\pi\)
−0.699431 + 0.714700i \(0.746563\pi\)
\(770\) −17.7677 98.5396i −0.640303 3.55112i
\(771\) −2.89223 12.8377i −0.104161 0.462338i
\(772\) 84.1848i 3.02988i
\(773\) 8.43042i 0.303221i −0.988440 0.151611i \(-0.951554\pi\)
0.988440 0.151611i \(-0.0484459\pi\)
\(774\) 23.3679 + 49.2291i 0.839943 + 1.76950i
\(775\) 2.01016 0.0722072
\(776\) −120.884 −4.33948
\(777\) −16.0406 71.1994i −0.575455 2.55426i
\(778\) 25.3528i 0.908943i
\(779\) 4.16335i 0.149168i
\(780\) 21.5769 4.86109i 0.772576 0.174055i
\(781\) 0.0439501 0.00792464i 0.00157266 0.000283566i
\(782\) 5.98986i 0.214197i
\(783\) −16.9891 + 13.3159i −0.607142 + 0.475871i
\(784\) −199.624 −7.12945
\(785\) 33.0434i 1.17937i
\(786\) −98.5821 + 22.2098i −3.51631 + 0.792196i
\(787\) 18.8892i 0.673328i 0.941625 + 0.336664i \(0.109299\pi\)
−0.941625 + 0.336664i \(0.890701\pi\)
\(788\) −31.4042 −1.11873
\(789\) 10.7803 2.42871i 0.383788 0.0864643i
\(790\) 53.0751 1.88833
\(791\) 13.3173 0.473507
\(792\) 52.0442 + 72.6576i 1.84931 + 2.58178i
\(793\) 5.76709 0.204795
\(794\) −23.1059 −0.819998
\(795\) 27.6454 6.22829i 0.980482 0.220895i
\(796\) 49.9942 1.77200
\(797\) 7.57802i 0.268427i −0.990952 0.134214i \(-0.957149\pi\)
0.990952 0.134214i \(-0.0428508\pi\)
\(798\) 19.2890 4.34566i 0.682824 0.153835i
\(799\) 18.8704i 0.667587i
\(800\) 14.4677 0.511510
\(801\) 8.86151 + 18.6685i 0.313106 + 0.659619i
\(802\) 1.18364i 0.0417958i
\(803\) 15.6950 2.82996i 0.553864 0.0998671i
\(804\) −72.7055 + 16.3800i −2.56413 + 0.577677i
\(805\) 8.32140i 0.293291i
\(806\) 7.14217i 0.251572i
\(807\) 10.4568 + 46.4145i 0.368097 + 1.63387i
\(808\) −45.8667 −1.61359
\(809\) 22.3252 0.784914 0.392457 0.919770i \(-0.371625\pi\)
0.392457 + 0.919770i \(0.371625\pi\)
\(810\) 45.2839 + 36.9521i 1.59112 + 1.29837i
\(811\) 42.1574i 1.48035i −0.672416 0.740174i \(-0.734743\pi\)
0.672416 0.740174i \(-0.265257\pi\)
\(812\) 102.739i 3.60544i
\(813\) 4.08645 + 18.1385i 0.143318 + 0.636144i
\(814\) −14.4328 80.0445i −0.505870 2.80556i
\(815\) 21.9206i 0.767844i
\(816\) −68.5344 + 15.4402i −2.39918 + 0.540517i
\(817\) 6.09361 0.213189
\(818\) 39.0009i 1.36364i
\(819\) −12.5990 + 5.98046i −0.440245 + 0.208974i
\(820\) 58.5756i 2.04555i
\(821\) −20.9868 −0.732443 −0.366221 0.930528i \(-0.619349\pi\)
−0.366221 + 0.930528i \(0.619349\pi\)
\(822\) 21.8520 + 96.9941i 0.762176 + 3.38306i
\(823\) −8.85694 −0.308733 −0.154367 0.988014i \(-0.549334\pi\)
−0.154367 + 0.988014i \(0.549334\pi\)
\(824\) 28.4412 0.990797
\(825\) −1.70339 4.02907i −0.0593046 0.140274i
\(826\) 70.6760 2.45913
\(827\) −11.5953 −0.403209 −0.201605 0.979467i \(-0.564616\pi\)
−0.201605 + 0.979467i \(0.564616\pi\)
\(828\) −5.10384 10.7522i −0.177371 0.373666i
\(829\) −10.6080 −0.368430 −0.184215 0.982886i \(-0.558974\pi\)
−0.184215 + 0.982886i \(0.558974\pi\)
\(830\) 12.1553i 0.421916i
\(831\) 4.64199 + 20.6043i 0.161029 + 0.714757i
\(832\) 24.0793i 0.834798i
\(833\) −43.3768 −1.50292
\(834\) −15.9160 70.6461i −0.551126 2.44627i
\(835\) 14.1646i 0.490185i
\(836\) 15.7604 2.84175i 0.545083 0.0982839i
\(837\) 10.7960 8.46174i 0.373163 0.292480i
\(838\) 109.624i 3.78689i
\(839\) 14.1872i 0.489795i −0.969549 0.244897i \(-0.921246\pi\)
0.969549 0.244897i \(-0.0787543\pi\)
\(840\) −169.360 + 38.1554i −5.84346 + 1.31649i
\(841\) −11.7428 −0.404926
\(842\) 39.3462 1.35596
\(843\) 49.3177 11.1109i 1.69859 0.382679i
\(844\) 1.22064i 0.0420160i
\(845\) 2.40031i 0.0825731i
\(846\) −22.1238 46.6082i −0.760633 1.60242i
\(847\) 17.8602 + 47.9163i 0.613685 + 1.64642i
\(848\) 93.1268i 3.19799i
\(849\) −4.33541 19.2435i −0.148791 0.660436i
\(850\) 6.11623 0.209785
\(851\) 6.75954i 0.231714i
\(852\) −0.0272696 0.121041i −0.000934240 0.00414680i
\(853\) 4.40579i 0.150851i −0.997151 0.0754256i \(-0.975968\pi\)
0.997151 0.0754256i \(-0.0240315\pi\)
\(854\) −72.5357 −2.48212
\(855\) 5.90431 2.80264i 0.201923 0.0958482i
\(856\) 113.200 3.86908
\(857\) 4.94679 0.168979 0.0844895 0.996424i \(-0.473074\pi\)
0.0844895 + 0.996424i \(0.473074\pi\)
\(858\) −14.3154 + 6.05221i −0.488720 + 0.206619i
\(859\) −27.1208 −0.925351 −0.462676 0.886528i \(-0.653111\pi\)
−0.462676 + 0.886528i \(0.653111\pi\)
\(860\) −85.7331 −2.92347
\(861\) 8.11770 + 36.0319i 0.276650 + 1.22796i
\(862\) −51.1724 −1.74294
\(863\) 17.0607i 0.580752i −0.956913 0.290376i \(-0.906220\pi\)
0.956913 0.290376i \(-0.0937805\pi\)
\(864\) 77.7014 60.9014i 2.64346 2.07191i
\(865\) 31.4289i 1.06862i
\(866\) 80.8691 2.74804
\(867\) 13.8329 3.11645i 0.469791 0.105840i
\(868\) 65.2869i 2.21598i
\(869\) −26.6758 + 4.80991i −0.904913 + 0.163165i
\(870\) −10.2698 45.5845i −0.348179 1.54546i
\(871\) 8.08809i 0.274054i
\(872\) 126.161i 4.27235i
\(873\) 36.4730 17.3129i 1.23442 0.585953i
\(874\) −1.83126 −0.0619434
\(875\) −47.2956 −1.59888
\(876\) −9.73821 43.2248i −0.329023 1.46043i
\(877\) 48.8134i 1.64831i 0.566363 + 0.824156i \(0.308350\pi\)
−0.566363 + 0.824156i \(0.691650\pi\)
\(878\) 76.2705i 2.57401i
\(879\) −28.6678 + 6.45863i −0.966942 + 0.217844i
\(880\) −107.039 + 19.3003i −3.60830 + 0.650612i
\(881\) 23.2768i 0.784215i 0.919919 + 0.392107i \(0.128254\pi\)
−0.919919 + 0.392107i \(0.871746\pi\)
\(882\) 107.137 50.8553i 3.60748 1.71239i
\(883\) 6.19019 0.208317 0.104158 0.994561i \(-0.466785\pi\)
0.104158 + 0.994561i \(0.466785\pi\)
\(884\) 15.7937i 0.531199i
\(885\) 22.7905 5.13451i 0.766093 0.172595i
\(886\) 50.0024i 1.67986i
\(887\) 0.793840 0.0266545 0.0133273 0.999911i \(-0.495758\pi\)
0.0133273 + 0.999911i \(0.495758\pi\)
\(888\) −137.572 + 30.9939i −4.61662 + 1.04009i
\(889\) 50.6591 1.69905
\(890\) −44.7337 −1.49948
\(891\) −26.1087 14.4685i −0.874674 0.484712i
\(892\) 31.4088 1.05165
\(893\) −5.76919 −0.193059
\(894\) −58.0218 + 13.0719i −1.94054 + 0.437188i
\(895\) 54.1039 1.80849
\(896\) 126.208i 4.21632i
\(897\) 1.26008 0.283887i 0.0420730 0.00947871i
\(898\) 75.0501i 2.50445i
\(899\) −10.9663 −0.365746
\(900\) −10.9791 + 5.21151i −0.365969 + 0.173717i
\(901\) 20.2357i 0.674149i
\(902\) 7.30403 + 40.5082i 0.243197 + 1.34877i
\(903\) 52.7374 11.8813i 1.75499 0.395385i
\(904\) 25.7317i 0.855825i
\(905\) 5.87598i 0.195324i
\(906\) 4.58774 + 20.3635i 0.152417 + 0.676532i
\(907\) 10.9991 0.365219 0.182609 0.983186i \(-0.441546\pi\)
0.182609 + 0.983186i \(0.441546\pi\)
\(908\) 10.9096 0.362048
\(909\) 13.8389 6.56899i 0.459006 0.217880i
\(910\) 30.1899i 1.00079i
\(911\) 7.69798i 0.255046i 0.991836 + 0.127523i \(0.0407026\pi\)
−0.991836 + 0.127523i \(0.959297\pi\)
\(912\) −4.72050 20.9528i −0.156311 0.693817i
\(913\) 1.10157 + 6.10929i 0.0364565 + 0.202188i
\(914\) 26.7313i 0.884193i
\(915\) −23.3902 + 5.26961i −0.773255 + 0.174208i
\(916\) 79.6788 2.63266
\(917\) 100.247i 3.31046i
\(918\) 32.8483 25.7461i 1.08416 0.849749i
\(919\) 26.3226i 0.868301i 0.900840 + 0.434151i \(0.142951\pi\)
−0.900840 + 0.434151i \(0.857049\pi\)
\(920\) 16.0787 0.530099
\(921\) −10.4433 46.3547i −0.344120 1.52744i
\(922\) −0.330124 −0.0108721
\(923\) 0.0134651 0.000443211
\(924\) 130.858 55.3235i 4.30490 1.82001i
\(925\) 6.90214 0.226941
\(926\) 87.7809 2.88466
\(927\) −8.58126 + 4.07333i −0.281846 + 0.133786i
\(928\) −78.9272 −2.59091
\(929\) 47.6720i 1.56407i −0.623236 0.782034i \(-0.714182\pi\)
0.623236 0.782034i \(-0.285818\pi\)
\(930\) 6.52608 + 28.9672i 0.213999 + 0.949872i
\(931\) 13.2615i 0.434627i
\(932\) 58.2099 1.90673
\(933\) −1.54062 6.83834i −0.0504377 0.223877i
\(934\) 5.57749i 0.182501i
\(935\) −23.2588 + 4.19379i −0.760644 + 0.137152i
\(936\) 11.5555 + 24.3439i 0.377703 + 0.795707i
\(937\) 36.0674i 1.17827i −0.808034 0.589135i \(-0.799469\pi\)
0.808034 0.589135i \(-0.200531\pi\)
\(938\) 101.728i 3.32154i
\(939\) −40.6157 + 9.15038i −1.32544 + 0.298611i
\(940\) 81.1687 2.64743
\(941\) 5.65441 0.184329 0.0921643 0.995744i \(-0.470622\pi\)
0.0921643 + 0.995744i \(0.470622\pi\)
\(942\) 62.9336 14.1784i 2.05049 0.461958i
\(943\) 3.42080i 0.111397i
\(944\) 76.7723i 2.49872i
\(945\) 45.6345 35.7677i 1.48449 1.16352i
\(946\) 59.2890 10.6904i 1.92765 0.347575i
\(947\) 10.0116i 0.325333i −0.986681 0.162666i \(-0.947991\pi\)
0.986681 0.162666i \(-0.0520094\pi\)
\(948\) 16.5514 + 73.4665i 0.537565 + 2.38608i
\(949\) 4.80852 0.156091
\(950\) 1.86990i 0.0606675i
\(951\) 1.62412 + 7.20895i 0.0526657 + 0.233766i
\(952\) 123.967i 4.01778i
\(953\) 10.1129 0.327588 0.163794 0.986495i \(-0.447627\pi\)
0.163794 + 0.986495i \(0.447627\pi\)
\(954\) 23.7245 + 49.9804i 0.768110 + 1.61817i
\(955\) −47.1250 −1.52493
\(956\) 117.025 3.78484
\(957\) 9.29272 + 21.9803i 0.300391 + 0.710521i
\(958\) −51.8012 −1.67362
\(959\) 98.6324 3.18501
\(960\) 22.0022 + 97.6607i 0.710117 + 3.15198i
\(961\) −24.0313 −0.775205
\(962\) 24.5235i 0.790670i
\(963\) −34.1545 + 16.2123i −1.10061 + 0.522435i
\(964\) 18.8780i 0.608019i
\(965\) −37.9830 −1.22271
\(966\) −15.8487 + 3.57059i −0.509925 + 0.114882i
\(967\) 24.8226i 0.798243i −0.916898 0.399121i \(-0.869315\pi\)
0.916898 0.399121i \(-0.130685\pi\)
\(968\) 92.5843 34.5097i 2.97577 1.10918i
\(969\) −1.02573 4.55288i −0.0329511 0.146260i
\(970\) 87.3972i 2.80615i
\(971\) 39.0524i 1.25325i 0.779320 + 0.626626i \(0.215565\pi\)
−0.779320 + 0.626626i \(0.784435\pi\)
\(972\) −37.0274 + 74.2055i −1.18765 + 2.38014i
\(973\) −71.8394 −2.30306
\(974\) −20.7194 −0.663893
\(975\) −0.289876 1.28667i −0.00928346 0.0412063i
\(976\) 78.7924i 2.52208i
\(977\) 4.91859i 0.157360i 0.996900 + 0.0786799i \(0.0250705\pi\)
−0.996900 + 0.0786799i \(0.974930\pi\)
\(978\) −41.7494 + 9.40581i −1.33500 + 0.300765i
\(979\) 22.4834 4.05398i 0.718572 0.129566i
\(980\) 186.580i 5.96008i
\(981\) 18.0686 + 38.0651i 0.576887 + 1.21533i
\(982\) 41.6678 1.32967
\(983\) 37.1938i 1.18630i −0.805093 0.593148i \(-0.797885\pi\)
0.805093 0.593148i \(-0.202115\pi\)
\(984\) 69.6212 15.6851i 2.21944 0.500023i
\(985\) 14.1691i 0.451466i
\(986\) −33.3666 −1.06261
\(987\) −49.9297 + 11.2488i −1.58928 + 0.358052i
\(988\) 4.82855 0.153617
\(989\) −5.00679 −0.159207
\(990\) 52.5303 37.6271i 1.66952 1.19587i
\(991\) −15.4387 −0.490425 −0.245213 0.969469i \(-0.578858\pi\)
−0.245213 + 0.969469i \(0.578858\pi\)
\(992\) 50.1553 1.59243
\(993\) 17.1400 3.86151i 0.543923 0.122541i
\(994\) −0.169358 −0.00537171
\(995\) 22.5567i 0.715094i
\(996\) 16.8253 3.79061i 0.533131 0.120110i
\(997\) 29.8330i 0.944821i −0.881379 0.472411i \(-0.843384\pi\)
0.881379 0.472411i \(-0.156616\pi\)
\(998\) 38.7324 1.22605
\(999\) 37.0692 29.0544i 1.17282 0.919241i
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 429.2.f.a.131.2 yes 48
3.2 odd 2 inner 429.2.f.a.131.47 yes 48
11.10 odd 2 inner 429.2.f.a.131.48 yes 48
33.32 even 2 inner 429.2.f.a.131.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.f.a.131.1 48 33.32 even 2 inner
429.2.f.a.131.2 yes 48 1.1 even 1 trivial
429.2.f.a.131.47 yes 48 3.2 odd 2 inner
429.2.f.a.131.48 yes 48 11.10 odd 2 inner