Properties

Label 432.2.l.b.107.7
Level $432$
Weight $2$
Character 432.107
Analytic conductor $3.450$
Analytic rank $0$
Dimension $32$
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] = [432,2,Mod(107,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.l (of order \(4\), degree \(2\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.7
Character \(\chi\) \(=\) 432.107
Dual form 432.2.l.b.323.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.379657 + 1.36230i) q^{2} +(-1.71172 - 1.03441i) q^{4} +(0.463925 - 0.463925i) q^{5} -1.85883 q^{7} +(2.05905 - 1.93916i) q^{8} +O(q^{10})\) \(q+(-0.379657 + 1.36230i) q^{2} +(-1.71172 - 1.03441i) q^{4} +(0.463925 - 0.463925i) q^{5} -1.85883 q^{7} +(2.05905 - 1.93916i) q^{8} +(0.455873 + 0.808137i) q^{10} +(3.73577 + 3.73577i) q^{11} +(-4.31012 + 4.31012i) q^{13} +(0.705716 - 2.53228i) q^{14} +(1.85998 + 3.54125i) q^{16} +6.55700i q^{17} +(-1.31300 - 1.31300i) q^{19} +(-1.27400 + 0.314221i) q^{20} +(-6.50754 + 3.67093i) q^{22} -0.727384i q^{23} +4.56955i q^{25} +(-4.23531 - 7.50805i) q^{26} +(3.18180 + 1.92279i) q^{28} +(0.896599 + 0.896599i) q^{29} -5.25771i q^{31} +(-5.53040 + 1.18939i) q^{32} +(-8.93260 - 2.48941i) q^{34} +(-0.862356 + 0.862356i) q^{35} +(3.98112 + 3.98112i) q^{37} +(2.28719 - 1.29021i) q^{38} +(0.0556200 - 1.85487i) q^{40} +5.10406 q^{41} +(1.09445 - 1.09445i) q^{43} +(-2.53027 - 10.2589i) q^{44} +(0.990915 + 0.276156i) q^{46} -6.81472 q^{47} -3.54476 q^{49} +(-6.22509 - 1.73486i) q^{50} +(11.8362 - 2.91929i) q^{52} +(-0.712025 + 0.712025i) q^{53} +3.46623 q^{55} +(-3.82741 + 3.60456i) q^{56} +(-1.56184 + 0.881037i) q^{58} +(1.86942 + 1.86942i) q^{59} +(5.98625 - 5.98625i) q^{61} +(7.16257 + 1.99612i) q^{62} +(0.479345 - 7.98563i) q^{64} +3.99915i q^{65} +(-8.48245 - 8.48245i) q^{67} +(6.78264 - 11.2238i) q^{68} +(-0.847389 - 1.50219i) q^{70} +12.4124i q^{71} +3.72969i q^{73} +(-6.93493 + 3.91202i) q^{74} +(0.889307 + 3.60567i) q^{76} +(-6.94415 - 6.94415i) q^{77} -0.199069i q^{79} +(2.50577 + 0.779983i) q^{80} +(-1.93779 + 6.95326i) q^{82} +(9.97322 - 9.97322i) q^{83} +(3.04195 + 3.04195i) q^{85} +(1.07545 + 1.90648i) q^{86} +(14.9364 + 0.447882i) q^{88} -7.53220 q^{89} +(8.01178 - 8.01178i) q^{91} +(-0.752415 + 1.24508i) q^{92} +(2.58725 - 9.28369i) q^{94} -1.21827 q^{95} +9.81958 q^{97} +(1.34579 - 4.82903i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.379657 + 1.36230i −0.268458 + 0.963291i
\(3\) 0 0
\(4\) −1.71172 1.03441i −0.855861 0.517206i
\(5\) 0.463925 0.463925i 0.207474 0.207474i −0.595719 0.803193i \(-0.703133\pi\)
0.803193 + 0.595719i \(0.203133\pi\)
\(6\) 0 0
\(7\) −1.85883 −0.702571 −0.351285 0.936268i \(-0.614255\pi\)
−0.351285 + 0.936268i \(0.614255\pi\)
\(8\) 2.05905 1.93916i 0.727983 0.685595i
\(9\) 0 0
\(10\) 0.455873 + 0.808137i 0.144160 + 0.255555i
\(11\) 3.73577 + 3.73577i 1.12638 + 1.12638i 0.990762 + 0.135615i \(0.0433009\pi\)
0.135615 + 0.990762i \(0.456699\pi\)
\(12\) 0 0
\(13\) −4.31012 + 4.31012i −1.19541 + 1.19541i −0.219888 + 0.975525i \(0.570569\pi\)
−0.975525 + 0.219888i \(0.929431\pi\)
\(14\) 0.705716 2.53228i 0.188611 0.676780i
\(15\) 0 0
\(16\) 1.85998 + 3.54125i 0.464995 + 0.885313i
\(17\) 6.55700i 1.59031i 0.606409 + 0.795153i \(0.292609\pi\)
−0.606409 + 0.795153i \(0.707391\pi\)
\(18\) 0 0
\(19\) −1.31300 1.31300i −0.301223 0.301223i 0.540269 0.841492i \(-0.318322\pi\)
−0.841492 + 0.540269i \(0.818322\pi\)
\(20\) −1.27400 + 0.314221i −0.284875 + 0.0702618i
\(21\) 0 0
\(22\) −6.50754 + 3.67093i −1.38741 + 0.782644i
\(23\) 0.727384i 0.151670i −0.997120 0.0758350i \(-0.975838\pi\)
0.997120 0.0758350i \(-0.0241622\pi\)
\(24\) 0 0
\(25\) 4.56955i 0.913909i
\(26\) −4.23531 7.50805i −0.830613 1.47245i
\(27\) 0 0
\(28\) 3.18180 + 1.92279i 0.601303 + 0.363374i
\(29\) 0.896599 + 0.896599i 0.166494 + 0.166494i 0.785436 0.618942i \(-0.212439\pi\)
−0.618942 + 0.785436i \(0.712439\pi\)
\(30\) 0 0
\(31\) 5.25771i 0.944312i −0.881515 0.472156i \(-0.843476\pi\)
0.881515 0.472156i \(-0.156524\pi\)
\(32\) −5.53040 + 1.18939i −0.977646 + 0.210257i
\(33\) 0 0
\(34\) −8.93260 2.48941i −1.53193 0.426930i
\(35\) −0.862356 + 0.862356i −0.145765 + 0.145765i
\(36\) 0 0
\(37\) 3.98112 + 3.98112i 0.654492 + 0.654492i 0.954071 0.299580i \(-0.0968464\pi\)
−0.299580 + 0.954071i \(0.596846\pi\)
\(38\) 2.28719 1.29021i 0.371031 0.209300i
\(39\) 0 0
\(40\) 0.0556200 1.85487i 0.00879430 0.293280i
\(41\) 5.10406 0.797121 0.398560 0.917142i \(-0.369510\pi\)
0.398560 + 0.917142i \(0.369510\pi\)
\(42\) 0 0
\(43\) 1.09445 1.09445i 0.166901 0.166901i −0.618714 0.785616i \(-0.712346\pi\)
0.785616 + 0.618714i \(0.212346\pi\)
\(44\) −2.53027 10.2589i −0.381452 1.54659i
\(45\) 0 0
\(46\) 0.990915 + 0.276156i 0.146102 + 0.0407170i
\(47\) −6.81472 −0.994029 −0.497014 0.867742i \(-0.665570\pi\)
−0.497014 + 0.867742i \(0.665570\pi\)
\(48\) 0 0
\(49\) −3.54476 −0.506394
\(50\) −6.22509 1.73486i −0.880361 0.245346i
\(51\) 0 0
\(52\) 11.8362 2.91929i 1.64138 0.404832i
\(53\) −0.712025 + 0.712025i −0.0978042 + 0.0978042i −0.754316 0.656512i \(-0.772031\pi\)
0.656512 + 0.754316i \(0.272031\pi\)
\(54\) 0 0
\(55\) 3.46623 0.467386
\(56\) −3.82741 + 3.60456i −0.511459 + 0.481679i
\(57\) 0 0
\(58\) −1.56184 + 0.881037i −0.205079 + 0.115686i
\(59\) 1.86942 + 1.86942i 0.243378 + 0.243378i 0.818246 0.574868i \(-0.194947\pi\)
−0.574868 + 0.818246i \(0.694947\pi\)
\(60\) 0 0
\(61\) 5.98625 5.98625i 0.766461 0.766461i −0.211021 0.977482i \(-0.567679\pi\)
0.977482 + 0.211021i \(0.0676787\pi\)
\(62\) 7.16257 + 1.99612i 0.909648 + 0.253508i
\(63\) 0 0
\(64\) 0.479345 7.98563i 0.0599181 0.998203i
\(65\) 3.99915i 0.496033i
\(66\) 0 0
\(67\) −8.48245 8.48245i −1.03630 1.03630i −0.999316 0.0369805i \(-0.988226\pi\)
−0.0369805 0.999316i \(-0.511774\pi\)
\(68\) 6.78264 11.2238i 0.822516 1.36108i
\(69\) 0 0
\(70\) −0.847389 1.50219i −0.101282 0.179546i
\(71\) 12.4124i 1.47308i 0.676394 + 0.736540i \(0.263542\pi\)
−0.676394 + 0.736540i \(0.736458\pi\)
\(72\) 0 0
\(73\) 3.72969i 0.436527i 0.975890 + 0.218264i \(0.0700392\pi\)
−0.975890 + 0.218264i \(0.929961\pi\)
\(74\) −6.93493 + 3.91202i −0.806170 + 0.454763i
\(75\) 0 0
\(76\) 0.889307 + 3.60567i 0.102010 + 0.413599i
\(77\) −6.94415 6.94415i −0.791359 0.791359i
\(78\) 0 0
\(79\) 0.199069i 0.0223970i −0.999937 0.0111985i \(-0.996435\pi\)
0.999937 0.0111985i \(-0.00356468\pi\)
\(80\) 2.50577 + 0.779983i 0.280153 + 0.0872048i
\(81\) 0 0
\(82\) −1.93779 + 6.95326i −0.213993 + 0.767860i
\(83\) 9.97322 9.97322i 1.09470 1.09470i 0.0996837 0.995019i \(-0.468217\pi\)
0.995019 0.0996837i \(-0.0317831\pi\)
\(84\) 0 0
\(85\) 3.04195 + 3.04195i 0.329946 + 0.329946i
\(86\) 1.07545 + 1.90648i 0.115969 + 0.205581i
\(87\) 0 0
\(88\) 14.9364 + 0.447882i 1.59222 + 0.0477444i
\(89\) −7.53220 −0.798412 −0.399206 0.916861i \(-0.630714\pi\)
−0.399206 + 0.916861i \(0.630714\pi\)
\(90\) 0 0
\(91\) 8.01178 8.01178i 0.839863 0.839863i
\(92\) −0.752415 + 1.24508i −0.0784447 + 0.129808i
\(93\) 0 0
\(94\) 2.58725 9.28369i 0.266855 0.957539i
\(95\) −1.21827 −0.124991
\(96\) 0 0
\(97\) 9.81958 0.997027 0.498514 0.866882i \(-0.333879\pi\)
0.498514 + 0.866882i \(0.333879\pi\)
\(98\) 1.34579 4.82903i 0.135946 0.487805i
\(99\) 0 0
\(100\) 4.72680 7.82179i 0.472680 0.782179i
\(101\) 13.6195 13.6195i 1.35519 1.35519i 0.475454 0.879741i \(-0.342284\pi\)
0.879741 0.475454i \(-0.157716\pi\)
\(102\) 0 0
\(103\) 1.29990 0.128083 0.0640414 0.997947i \(-0.479601\pi\)
0.0640414 + 0.997947i \(0.479601\pi\)
\(104\) −0.516742 + 17.2328i −0.0506707 + 1.68981i
\(105\) 0 0
\(106\) −0.699667 1.24032i −0.0679576 0.120470i
\(107\) 10.6692 + 10.6692i 1.03143 + 1.03143i 0.999490 + 0.0319359i \(0.0101672\pi\)
0.0319359 + 0.999490i \(0.489833\pi\)
\(108\) 0 0
\(109\) −8.11473 + 8.11473i −0.777250 + 0.777250i −0.979362 0.202112i \(-0.935220\pi\)
0.202112 + 0.979362i \(0.435220\pi\)
\(110\) −1.31598 + 4.72205i −0.125474 + 0.450229i
\(111\) 0 0
\(112\) −3.45738 6.58258i −0.326692 0.621995i
\(113\) 18.0982i 1.70253i 0.524735 + 0.851266i \(0.324164\pi\)
−0.524735 + 0.851266i \(0.675836\pi\)
\(114\) 0 0
\(115\) −0.337451 0.337451i −0.0314675 0.0314675i
\(116\) −0.607275 2.46218i −0.0563840 0.228608i
\(117\) 0 0
\(118\) −3.25646 + 1.83698i −0.299781 + 0.169107i
\(119\) 12.1883i 1.11730i
\(120\) 0 0
\(121\) 16.9119i 1.53745i
\(122\) 5.88235 + 10.4278i 0.532563 + 0.944088i
\(123\) 0 0
\(124\) −5.43864 + 8.99973i −0.488404 + 0.808200i
\(125\) 4.43955 + 4.43955i 0.397086 + 0.397086i
\(126\) 0 0
\(127\) 17.6229i 1.56378i −0.623416 0.781891i \(-0.714256\pi\)
0.623416 0.781891i \(-0.285744\pi\)
\(128\) 10.6968 + 3.68481i 0.945475 + 0.325694i
\(129\) 0 0
\(130\) −5.44804 1.51830i −0.477825 0.133164i
\(131\) −0.516185 + 0.516185i −0.0450993 + 0.0450993i −0.729297 0.684197i \(-0.760153\pi\)
0.684197 + 0.729297i \(0.260153\pi\)
\(132\) 0 0
\(133\) 2.44064 + 2.44064i 0.211630 + 0.211630i
\(134\) 14.7761 8.33522i 1.27646 0.720054i
\(135\) 0 0
\(136\) 12.7150 + 13.5012i 1.09031 + 1.15772i
\(137\) −9.51987 −0.813338 −0.406669 0.913576i \(-0.633310\pi\)
−0.406669 + 0.913576i \(0.633310\pi\)
\(138\) 0 0
\(139\) 8.85424 8.85424i 0.751007 0.751007i −0.223660 0.974667i \(-0.571801\pi\)
0.974667 + 0.223660i \(0.0718007\pi\)
\(140\) 2.36815 0.584082i 0.200145 0.0493639i
\(141\) 0 0
\(142\) −16.9094 4.71245i −1.41901 0.395460i
\(143\) −32.2032 −2.69297
\(144\) 0 0
\(145\) 0.831909 0.0690863
\(146\) −5.08095 1.41600i −0.420503 0.117189i
\(147\) 0 0
\(148\) −2.69645 10.9327i −0.221647 0.898661i
\(149\) 12.8550 12.8550i 1.05313 1.05313i 0.0546187 0.998507i \(-0.482606\pi\)
0.998507 0.0546187i \(-0.0173943\pi\)
\(150\) 0 0
\(151\) −6.75375 −0.549612 −0.274806 0.961500i \(-0.588614\pi\)
−0.274806 + 0.961500i \(0.588614\pi\)
\(152\) −5.24964 0.157416i −0.425802 0.0127681i
\(153\) 0 0
\(154\) 12.0964 6.82362i 0.974756 0.549863i
\(155\) −2.43918 2.43918i −0.195920 0.195920i
\(156\) 0 0
\(157\) −1.36386 + 1.36386i −0.108848 + 0.108848i −0.759433 0.650585i \(-0.774524\pi\)
0.650585 + 0.759433i \(0.274524\pi\)
\(158\) 0.271192 + 0.0755780i 0.0215749 + 0.00601266i
\(159\) 0 0
\(160\) −2.01390 + 3.11748i −0.159213 + 0.246458i
\(161\) 1.35208i 0.106559i
\(162\) 0 0
\(163\) 4.75407 + 4.75407i 0.372368 + 0.372368i 0.868339 0.495971i \(-0.165188\pi\)
−0.495971 + 0.868339i \(0.665188\pi\)
\(164\) −8.73673 5.27971i −0.682224 0.412276i
\(165\) 0 0
\(166\) 9.80011 + 17.3729i 0.760636 + 1.34840i
\(167\) 18.6718i 1.44487i −0.691439 0.722435i \(-0.743023\pi\)
0.691439 0.722435i \(-0.256977\pi\)
\(168\) 0 0
\(169\) 24.1543i 1.85803i
\(170\) −5.29895 + 2.98916i −0.406411 + 0.229258i
\(171\) 0 0
\(172\) −3.00550 + 0.741278i −0.229167 + 0.0565219i
\(173\) −13.5409 13.5409i −1.02950 1.02950i −0.999552 0.0299462i \(-0.990466\pi\)
−0.0299462 0.999552i \(-0.509534\pi\)
\(174\) 0 0
\(175\) 8.49400i 0.642086i
\(176\) −6.28084 + 20.1778i −0.473436 + 1.52096i
\(177\) 0 0
\(178\) 2.85965 10.2611i 0.214340 0.769103i
\(179\) 13.2637 13.2637i 0.991375 0.991375i −0.00858851 0.999963i \(-0.502734\pi\)
0.999963 + 0.00858851i \(0.00273384\pi\)
\(180\) 0 0
\(181\) 0.588855 + 0.588855i 0.0437692 + 0.0437692i 0.728653 0.684883i \(-0.240147\pi\)
−0.684883 + 0.728653i \(0.740147\pi\)
\(182\) 7.87272 + 13.9562i 0.583565 + 1.03450i
\(183\) 0 0
\(184\) −1.41051 1.49772i −0.103984 0.110413i
\(185\) 3.69388 0.271579
\(186\) 0 0
\(187\) −24.4954 + 24.4954i −1.79128 + 1.79128i
\(188\) 11.6649 + 7.04923i 0.850750 + 0.514118i
\(189\) 0 0
\(190\) 0.462523 1.65964i 0.0335549 0.120403i
\(191\) −8.73890 −0.632325 −0.316162 0.948705i \(-0.602394\pi\)
−0.316162 + 0.948705i \(0.602394\pi\)
\(192\) 0 0
\(193\) −11.8318 −0.851673 −0.425836 0.904800i \(-0.640020\pi\)
−0.425836 + 0.904800i \(0.640020\pi\)
\(194\) −3.72807 + 13.3772i −0.267660 + 0.960428i
\(195\) 0 0
\(196\) 6.06764 + 3.66674i 0.433403 + 0.261910i
\(197\) −6.04244 + 6.04244i −0.430506 + 0.430506i −0.888800 0.458295i \(-0.848460\pi\)
0.458295 + 0.888800i \(0.348460\pi\)
\(198\) 0 0
\(199\) −11.7641 −0.833934 −0.416967 0.908922i \(-0.636907\pi\)
−0.416967 + 0.908922i \(0.636907\pi\)
\(200\) 8.86107 + 9.40891i 0.626572 + 0.665310i
\(201\) 0 0
\(202\) 13.3831 + 23.7246i 0.941635 + 1.66926i
\(203\) −1.66662 1.66662i −0.116974 0.116974i
\(204\) 0 0
\(205\) 2.36790 2.36790i 0.165381 0.165381i
\(206\) −0.493515 + 1.77085i −0.0343848 + 0.123381i
\(207\) 0 0
\(208\) −23.2800 7.24649i −1.61418 0.502453i
\(209\) 9.81012i 0.678580i
\(210\) 0 0
\(211\) 14.2861 + 14.2861i 0.983498 + 0.983498i 0.999866 0.0163680i \(-0.00521031\pi\)
−0.0163680 + 0.999866i \(0.505210\pi\)
\(212\) 1.95532 0.482261i 0.134292 0.0331218i
\(213\) 0 0
\(214\) −18.5852 + 10.4840i −1.27046 + 0.716669i
\(215\) 1.01548i 0.0692553i
\(216\) 0 0
\(217\) 9.77317i 0.663446i
\(218\) −7.97389 14.1355i −0.540060 0.957378i
\(219\) 0 0
\(220\) −5.93322 3.58551i −0.400018 0.241735i
\(221\) −28.2615 28.2615i −1.90107 1.90107i
\(222\) 0 0
\(223\) 25.2083i 1.68807i 0.536286 + 0.844036i \(0.319827\pi\)
−0.536286 + 0.844036i \(0.680173\pi\)
\(224\) 10.2801 2.21088i 0.686866 0.147720i
\(225\) 0 0
\(226\) −24.6551 6.87109i −1.64003 0.457058i
\(227\) 5.31259 5.31259i 0.352609 0.352609i −0.508470 0.861080i \(-0.669789\pi\)
0.861080 + 0.508470i \(0.169789\pi\)
\(228\) 0 0
\(229\) −6.10498 6.10498i −0.403429 0.403429i 0.476011 0.879439i \(-0.342082\pi\)
−0.879439 + 0.476011i \(0.842082\pi\)
\(230\) 0.587826 0.331594i 0.0387601 0.0218647i
\(231\) 0 0
\(232\) 3.58478 + 0.107493i 0.235353 + 0.00705729i
\(233\) −8.03106 −0.526132 −0.263066 0.964778i \(-0.584734\pi\)
−0.263066 + 0.964778i \(0.584734\pi\)
\(234\) 0 0
\(235\) −3.16152 + 3.16152i −0.206235 + 0.206235i
\(236\) −1.26618 5.13369i −0.0824212 0.334175i
\(237\) 0 0
\(238\) 16.6042 + 4.62738i 1.07629 + 0.299948i
\(239\) 16.4509 1.06412 0.532060 0.846706i \(-0.321418\pi\)
0.532060 + 0.846706i \(0.321418\pi\)
\(240\) 0 0
\(241\) 3.21157 0.206876 0.103438 0.994636i \(-0.467016\pi\)
0.103438 + 0.994636i \(0.467016\pi\)
\(242\) −23.0391 6.42072i −1.48101 0.412740i
\(243\) 0 0
\(244\) −16.4390 + 4.05454i −1.05240 + 0.259565i
\(245\) −1.64450 + 1.64450i −0.105063 + 0.105063i
\(246\) 0 0
\(247\) 11.3184 0.720172
\(248\) −10.1955 10.8259i −0.647416 0.687443i
\(249\) 0 0
\(250\) −7.73350 + 4.36249i −0.489110 + 0.275908i
\(251\) −0.155779 0.155779i −0.00983268 0.00983268i 0.702173 0.712006i \(-0.252213\pi\)
−0.712006 + 0.702173i \(0.752213\pi\)
\(252\) 0 0
\(253\) 2.71734 2.71734i 0.170837 0.170837i
\(254\) 24.0077 + 6.69066i 1.50638 + 0.419809i
\(255\) 0 0
\(256\) −9.08094 + 13.1733i −0.567559 + 0.823333i
\(257\) 13.0277i 0.812646i 0.913729 + 0.406323i \(0.133189\pi\)
−0.913729 + 0.406323i \(0.866811\pi\)
\(258\) 0 0
\(259\) −7.40021 7.40021i −0.459827 0.459827i
\(260\) 4.13677 6.84543i 0.256552 0.424535i
\(261\) 0 0
\(262\) −0.507226 0.899172i −0.0313365 0.0555510i
\(263\) 14.3366i 0.884032i 0.897007 + 0.442016i \(0.145736\pi\)
−0.897007 + 0.442016i \(0.854264\pi\)
\(264\) 0 0
\(265\) 0.660652i 0.0405835i
\(266\) −4.25149 + 2.39828i −0.260676 + 0.147048i
\(267\) 0 0
\(268\) 5.74524 + 23.2940i 0.350947 + 1.42290i
\(269\) 9.05831 + 9.05831i 0.552295 + 0.552295i 0.927103 0.374807i \(-0.122291\pi\)
−0.374807 + 0.927103i \(0.622291\pi\)
\(270\) 0 0
\(271\) 25.2882i 1.53615i 0.640360 + 0.768075i \(0.278785\pi\)
−0.640360 + 0.768075i \(0.721215\pi\)
\(272\) −23.2200 + 12.1959i −1.40792 + 0.739485i
\(273\) 0 0
\(274\) 3.61428 12.9689i 0.218347 0.783481i
\(275\) −17.0708 + 17.0708i −1.02941 + 1.02941i
\(276\) 0 0
\(277\) −4.54879 4.54879i −0.273310 0.273310i 0.557121 0.830431i \(-0.311906\pi\)
−0.830431 + 0.557121i \(0.811906\pi\)
\(278\) 8.70056 + 15.4237i 0.521825 + 0.925052i
\(279\) 0 0
\(280\) −0.103388 + 3.44788i −0.00617862 + 0.206050i
\(281\) 18.3548 1.09495 0.547477 0.836820i \(-0.315588\pi\)
0.547477 + 0.836820i \(0.315588\pi\)
\(282\) 0 0
\(283\) 10.0643 10.0643i 0.598259 0.598259i −0.341590 0.939849i \(-0.610965\pi\)
0.939849 + 0.341590i \(0.110965\pi\)
\(284\) 12.8395 21.2466i 0.761887 1.26075i
\(285\) 0 0
\(286\) 12.2262 43.8705i 0.722949 2.59412i
\(287\) −9.48757 −0.560034
\(288\) 0 0
\(289\) −25.9942 −1.52907
\(290\) −0.315840 + 1.13331i −0.0185468 + 0.0665502i
\(291\) 0 0
\(292\) 3.85804 6.38419i 0.225775 0.373606i
\(293\) −0.876200 + 0.876200i −0.0511882 + 0.0511882i −0.732238 0.681049i \(-0.761524\pi\)
0.681049 + 0.732238i \(0.261524\pi\)
\(294\) 0 0
\(295\) 1.73454 0.100989
\(296\) 15.9173 + 0.477297i 0.925175 + 0.0277423i
\(297\) 0 0
\(298\) 12.6319 + 22.3929i 0.731747 + 1.29719i
\(299\) 3.13511 + 3.13511i 0.181308 + 0.181308i
\(300\) 0 0
\(301\) −2.03439 + 2.03439i −0.117260 + 0.117260i
\(302\) 2.56411 9.20063i 0.147548 0.529437i
\(303\) 0 0
\(304\) 2.20751 7.09182i 0.126609 0.406744i
\(305\) 5.55434i 0.318041i
\(306\) 0 0
\(307\) −13.8024 13.8024i −0.787744 0.787744i 0.193380 0.981124i \(-0.438055\pi\)
−0.981124 + 0.193380i \(0.938055\pi\)
\(308\) 4.70333 + 19.0696i 0.267997 + 1.08659i
\(309\) 0 0
\(310\) 4.24895 2.39684i 0.241324 0.136132i
\(311\) 12.4588i 0.706472i −0.935534 0.353236i \(-0.885081\pi\)
0.935534 0.353236i \(-0.114919\pi\)
\(312\) 0 0
\(313\) 12.1941i 0.689249i −0.938741 0.344625i \(-0.888006\pi\)
0.938741 0.344625i \(-0.111994\pi\)
\(314\) −1.34019 2.37579i −0.0756312 0.134073i
\(315\) 0 0
\(316\) −0.205920 + 0.340751i −0.0115839 + 0.0191688i
\(317\) 18.9130 + 18.9130i 1.06226 + 1.06226i 0.997929 + 0.0643287i \(0.0204906\pi\)
0.0643287 + 0.997929i \(0.479509\pi\)
\(318\) 0 0
\(319\) 6.69897i 0.375070i
\(320\) −3.48235 3.92711i −0.194669 0.219532i
\(321\) 0 0
\(322\) −1.84194 0.513327i −0.102647 0.0286066i
\(323\) 8.60934 8.60934i 0.479036 0.479036i
\(324\) 0 0
\(325\) −19.6953 19.6953i −1.09250 1.09250i
\(326\) −8.28138 + 4.67155i −0.458663 + 0.258733i
\(327\) 0 0
\(328\) 10.5095 9.89758i 0.580290 0.546502i
\(329\) 12.6674 0.698375
\(330\) 0 0
\(331\) 0.852960 0.852960i 0.0468829 0.0468829i −0.683277 0.730160i \(-0.739446\pi\)
0.730160 + 0.683277i \(0.239446\pi\)
\(332\) −27.3878 + 6.75495i −1.50310 + 0.370726i
\(333\) 0 0
\(334\) 25.4366 + 7.08888i 1.39183 + 0.387887i
\(335\) −7.87044 −0.430008
\(336\) 0 0
\(337\) 32.9286 1.79374 0.896869 0.442297i \(-0.145836\pi\)
0.896869 + 0.442297i \(0.145836\pi\)
\(338\) 32.9055 + 9.17036i 1.78982 + 0.498802i
\(339\) 0 0
\(340\) −2.06034 8.35361i −0.111738 0.453038i
\(341\) 19.6416 19.6416i 1.06365 1.06365i
\(342\) 0 0
\(343\) 19.6009 1.05835
\(344\) 0.131213 4.37582i 0.00707455 0.235928i
\(345\) 0 0
\(346\) 23.5877 13.3059i 1.26808 0.715330i
\(347\) 13.8785 + 13.8785i 0.745036 + 0.745036i 0.973542 0.228506i \(-0.0733841\pi\)
−0.228506 + 0.973542i \(0.573384\pi\)
\(348\) 0 0
\(349\) 19.2311 19.2311i 1.02942 1.02942i 0.0298648 0.999554i \(-0.490492\pi\)
0.999554 0.0298648i \(-0.00950766\pi\)
\(350\) 11.5714 + 3.22480i 0.618516 + 0.172373i
\(351\) 0 0
\(352\) −25.1036 16.2170i −1.33803 0.864369i
\(353\) 12.1549i 0.646939i 0.946239 + 0.323469i \(0.104849\pi\)
−0.946239 + 0.323469i \(0.895151\pi\)
\(354\) 0 0
\(355\) 5.75842 + 5.75842i 0.305625 + 0.305625i
\(356\) 12.8930 + 7.79141i 0.683330 + 0.412944i
\(357\) 0 0
\(358\) 13.0335 + 23.1048i 0.688840 + 1.22112i
\(359\) 2.82558i 0.149128i −0.997216 0.0745642i \(-0.976243\pi\)
0.997216 0.0745642i \(-0.0237566\pi\)
\(360\) 0 0
\(361\) 15.5521i 0.818530i
\(362\) −1.02576 + 0.578634i −0.0539127 + 0.0304123i
\(363\) 0 0
\(364\) −22.0014 + 5.42645i −1.15319 + 0.284423i
\(365\) 1.73030 + 1.73030i 0.0905678 + 0.0905678i
\(366\) 0 0
\(367\) 9.20981i 0.480748i 0.970680 + 0.240374i \(0.0772701\pi\)
−0.970680 + 0.240374i \(0.922730\pi\)
\(368\) 2.57585 1.35292i 0.134275 0.0705259i
\(369\) 0 0
\(370\) −1.40241 + 5.03217i −0.0729076 + 0.261610i
\(371\) 1.32353 1.32353i 0.0687143 0.0687143i
\(372\) 0 0
\(373\) 15.4719 + 15.4719i 0.801107 + 0.801107i 0.983269 0.182162i \(-0.0583094\pi\)
−0.182162 + 0.983269i \(0.558309\pi\)
\(374\) −24.0703 42.6699i −1.24464 2.20641i
\(375\) 0 0
\(376\) −14.0318 + 13.2148i −0.723636 + 0.681501i
\(377\) −7.72891 −0.398059
\(378\) 0 0
\(379\) −6.10456 + 6.10456i −0.313570 + 0.313570i −0.846291 0.532721i \(-0.821170\pi\)
0.532721 + 0.846291i \(0.321170\pi\)
\(380\) 2.08533 + 1.26019i 0.106975 + 0.0646464i
\(381\) 0 0
\(382\) 3.31778 11.9050i 0.169753 0.609113i
\(383\) −1.66755 −0.0852078 −0.0426039 0.999092i \(-0.513565\pi\)
−0.0426039 + 0.999092i \(0.513565\pi\)
\(384\) 0 0
\(385\) −6.44313 −0.328372
\(386\) 4.49203 16.1185i 0.228638 0.820409i
\(387\) 0 0
\(388\) −16.8084 10.1575i −0.853317 0.515669i
\(389\) −18.2598 + 18.2598i −0.925810 + 0.925810i −0.997432 0.0716217i \(-0.977183\pi\)
0.0716217 + 0.997432i \(0.477183\pi\)
\(390\) 0 0
\(391\) 4.76945 0.241202
\(392\) −7.29883 + 6.87384i −0.368646 + 0.347182i
\(393\) 0 0
\(394\) −5.93756 10.5257i −0.299130 0.530275i
\(395\) −0.0923532 0.0923532i −0.00464679 0.00464679i
\(396\) 0 0
\(397\) 7.45587 7.45587i 0.374199 0.374199i −0.494805 0.869004i \(-0.664760\pi\)
0.869004 + 0.494805i \(0.164760\pi\)
\(398\) 4.46632 16.0262i 0.223876 0.803322i
\(399\) 0 0
\(400\) −16.1819 + 8.49927i −0.809096 + 0.424964i
\(401\) 26.1001i 1.30338i 0.758487 + 0.651688i \(0.225939\pi\)
−0.758487 + 0.651688i \(0.774061\pi\)
\(402\) 0 0
\(403\) 22.6614 + 22.6614i 1.12884 + 1.12884i
\(404\) −37.4011 + 9.22464i −1.86077 + 0.458943i
\(405\) 0 0
\(406\) 2.90318 1.63770i 0.144083 0.0812775i
\(407\) 29.7451i 1.47441i
\(408\) 0 0
\(409\) 26.4012i 1.30546i −0.757592 0.652728i \(-0.773624\pi\)
0.757592 0.652728i \(-0.226376\pi\)
\(410\) 2.32680 + 4.12478i 0.114913 + 0.203708i
\(411\) 0 0
\(412\) −2.22506 1.34463i −0.109621 0.0662452i
\(413\) −3.47494 3.47494i −0.170990 0.170990i
\(414\) 0 0
\(415\) 9.25365i 0.454244i
\(416\) 18.7103 28.9632i 0.917348 1.42004i
\(417\) 0 0
\(418\) 13.3643 + 3.72448i 0.653671 + 0.182170i
\(419\) −12.4672 + 12.4672i −0.609061 + 0.609061i −0.942701 0.333640i \(-0.891723\pi\)
0.333640 + 0.942701i \(0.391723\pi\)
\(420\) 0 0
\(421\) −16.2503 16.2503i −0.791992 0.791992i 0.189826 0.981818i \(-0.439208\pi\)
−0.981818 + 0.189826i \(0.939208\pi\)
\(422\) −24.8858 + 14.0382i −1.21142 + 0.683368i
\(423\) 0 0
\(424\) −0.0853648 + 2.84682i −0.00414568 + 0.138254i
\(425\) −29.9625 −1.45340
\(426\) 0 0
\(427\) −11.1274 + 11.1274i −0.538493 + 0.538493i
\(428\) −7.22631 29.2989i −0.349297 1.41622i
\(429\) 0 0
\(430\) 1.38339 + 0.385534i 0.0667130 + 0.0185921i
\(431\) 25.7670 1.24115 0.620576 0.784146i \(-0.286899\pi\)
0.620576 + 0.784146i \(0.286899\pi\)
\(432\) 0 0
\(433\) 21.5016 1.03330 0.516652 0.856196i \(-0.327178\pi\)
0.516652 + 0.856196i \(0.327178\pi\)
\(434\) −13.3140 3.71045i −0.639092 0.178107i
\(435\) 0 0
\(436\) 22.2841 5.49618i 1.06722 0.263219i
\(437\) −0.955055 + 0.955055i −0.0456865 + 0.0456865i
\(438\) 0 0
\(439\) −22.7689 −1.08670 −0.543349 0.839507i \(-0.682844\pi\)
−0.543349 + 0.839507i \(0.682844\pi\)
\(440\) 7.13713 6.72156i 0.340249 0.320438i
\(441\) 0 0
\(442\) 49.2303 27.7709i 2.34164 1.32093i
\(443\) 10.2897 + 10.2897i 0.488878 + 0.488878i 0.907952 0.419074i \(-0.137645\pi\)
−0.419074 + 0.907952i \(0.637645\pi\)
\(444\) 0 0
\(445\) −3.49438 + 3.49438i −0.165649 + 0.165649i
\(446\) −34.3413 9.57050i −1.62611 0.453176i
\(447\) 0 0
\(448\) −0.891020 + 14.8439i −0.0420967 + 0.701308i
\(449\) 21.5190i 1.01555i −0.861491 0.507773i \(-0.830469\pi\)
0.861491 0.507773i \(-0.169531\pi\)
\(450\) 0 0
\(451\) 19.0676 + 19.0676i 0.897858 + 0.897858i
\(452\) 18.7210 30.9790i 0.880560 1.45713i
\(453\) 0 0
\(454\) 5.22038 + 9.25431i 0.245005 + 0.434326i
\(455\) 7.43373i 0.348498i
\(456\) 0 0
\(457\) 6.79833i 0.318012i −0.987278 0.159006i \(-0.949171\pi\)
0.987278 0.159006i \(-0.0508290\pi\)
\(458\) 10.6346 5.99902i 0.496923 0.280316i
\(459\) 0 0
\(460\) 0.228559 + 0.926687i 0.0106566 + 0.0432070i
\(461\) 19.4466 + 19.4466i 0.905720 + 0.905720i 0.995923 0.0902034i \(-0.0287517\pi\)
−0.0902034 + 0.995923i \(0.528752\pi\)
\(462\) 0 0
\(463\) 10.1469i 0.471566i −0.971806 0.235783i \(-0.924235\pi\)
0.971806 0.235783i \(-0.0757654\pi\)
\(464\) −1.50743 + 4.84274i −0.0699805 + 0.224819i
\(465\) 0 0
\(466\) 3.04905 10.9407i 0.141244 0.506819i
\(467\) 2.71845 2.71845i 0.125795 0.125795i −0.641406 0.767201i \(-0.721649\pi\)
0.767201 + 0.641406i \(0.221649\pi\)
\(468\) 0 0
\(469\) 15.7674 + 15.7674i 0.728072 + 0.728072i
\(470\) −3.10664 5.50722i −0.143299 0.254029i
\(471\) 0 0
\(472\) 7.47434 + 0.224126i 0.344034 + 0.0103162i
\(473\) 8.17719 0.375988
\(474\) 0 0
\(475\) 5.99981 5.99981i 0.275290 0.275290i
\(476\) −12.6078 + 20.8630i −0.577876 + 0.956255i
\(477\) 0 0
\(478\) −6.24570 + 22.4111i −0.285672 + 1.02506i
\(479\) 2.18580 0.0998716 0.0499358 0.998752i \(-0.484098\pi\)
0.0499358 + 0.998752i \(0.484098\pi\)
\(480\) 0 0
\(481\) −34.3182 −1.56478
\(482\) −1.21930 + 4.37513i −0.0555374 + 0.199282i
\(483\) 0 0
\(484\) 17.4939 28.9485i 0.795177 1.31584i
\(485\) 4.55555 4.55555i 0.206857 0.206857i
\(486\) 0 0
\(487\) 6.03958 0.273679 0.136840 0.990593i \(-0.456305\pi\)
0.136840 + 0.990593i \(0.456305\pi\)
\(488\) 0.717693 23.9342i 0.0324884 1.08345i
\(489\) 0 0
\(490\) −1.61596 2.86465i −0.0730016 0.129412i
\(491\) −15.4395 15.4395i −0.696777 0.696777i 0.266937 0.963714i \(-0.413988\pi\)
−0.963714 + 0.266937i \(0.913988\pi\)
\(492\) 0 0
\(493\) −5.87900 + 5.87900i −0.264777 + 0.264777i
\(494\) −4.29710 + 15.4190i −0.193336 + 0.693735i
\(495\) 0 0
\(496\) 18.6189 9.77924i 0.836012 0.439101i
\(497\) 23.0725i 1.03494i
\(498\) 0 0
\(499\) −9.67414 9.67414i −0.433074 0.433074i 0.456599 0.889673i \(-0.349068\pi\)
−0.889673 + 0.456599i \(0.849068\pi\)
\(500\) −3.00695 12.1916i −0.134475 0.545225i
\(501\) 0 0
\(502\) 0.271360 0.153075i 0.0121114 0.00683207i
\(503\) 31.7197i 1.41431i 0.707057 + 0.707156i \(0.250022\pi\)
−0.707057 + 0.707156i \(0.749978\pi\)
\(504\) 0 0
\(505\) 12.6369i 0.562334i
\(506\) 2.67017 + 4.73348i 0.118704 + 0.210429i
\(507\) 0 0
\(508\) −18.2294 + 30.1655i −0.808797 + 1.33838i
\(509\) 4.16082 + 4.16082i 0.184425 + 0.184425i 0.793281 0.608856i \(-0.208371\pi\)
−0.608856 + 0.793281i \(0.708371\pi\)
\(510\) 0 0
\(511\) 6.93285i 0.306691i
\(512\) −14.4984 17.3723i −0.640744 0.767755i
\(513\) 0 0
\(514\) −17.7476 4.94606i −0.782815 0.218161i
\(515\) 0.603055 0.603055i 0.0265738 0.0265738i
\(516\) 0 0
\(517\) −25.4582 25.4582i −1.11965 1.11965i
\(518\) 12.8908 7.27177i 0.566391 0.319503i
\(519\) 0 0
\(520\) 7.75497 + 8.23443i 0.340078 + 0.361104i
\(521\) −0.107484 −0.00470896 −0.00235448 0.999997i \(-0.500749\pi\)
−0.00235448 + 0.999997i \(0.500749\pi\)
\(522\) 0 0
\(523\) −3.02020 + 3.02020i −0.132064 + 0.132064i −0.770049 0.637985i \(-0.779768\pi\)
0.637985 + 0.770049i \(0.279768\pi\)
\(524\) 1.41751 0.349617i 0.0619244 0.0152731i
\(525\) 0 0
\(526\) −19.5307 5.44298i −0.851580 0.237325i
\(527\) 34.4748 1.50174
\(528\) 0 0
\(529\) 22.4709 0.976996
\(530\) −0.900007 0.250821i −0.0390938 0.0108950i
\(531\) 0 0
\(532\) −1.65307 6.70232i −0.0716696 0.290583i
\(533\) −21.9991 + 21.9991i −0.952889 + 0.952889i
\(534\) 0 0
\(535\) 9.89937 0.427987
\(536\) −33.9146 1.01696i −1.46489 0.0439261i
\(537\) 0 0
\(538\) −15.7792 + 8.90109i −0.680289 + 0.383753i
\(539\) −13.2424 13.2424i −0.570391 0.570391i
\(540\) 0 0
\(541\) −5.72807 + 5.72807i −0.246269 + 0.246269i −0.819437 0.573169i \(-0.805714\pi\)
0.573169 + 0.819437i \(0.305714\pi\)
\(542\) −34.4501 9.60084i −1.47976 0.412391i
\(543\) 0 0
\(544\) −7.79884 36.2628i −0.334373 1.55476i
\(545\) 7.52925i 0.322518i
\(546\) 0 0
\(547\) 13.2259 + 13.2259i 0.565500 + 0.565500i 0.930865 0.365365i \(-0.119056\pi\)
−0.365365 + 0.930865i \(0.619056\pi\)
\(548\) 16.2954 + 9.84747i 0.696104 + 0.420663i
\(549\) 0 0
\(550\) −16.7745 29.7365i −0.715266 1.26797i
\(551\) 2.35447i 0.100304i
\(552\) 0 0
\(553\) 0.370036i 0.0157355i
\(554\) 7.92379 4.46984i 0.336650 0.189905i
\(555\) 0 0
\(556\) −24.3149 + 5.99706i −1.03118 + 0.254332i
\(557\) 21.4603 + 21.4603i 0.909301 + 0.909301i 0.996216 0.0869144i \(-0.0277007\pi\)
−0.0869144 + 0.996216i \(0.527701\pi\)
\(558\) 0 0
\(559\) 9.43440i 0.399032i
\(560\) −4.65779 1.44985i −0.196827 0.0612675i
\(561\) 0 0
\(562\) −6.96852 + 25.0047i −0.293949 + 1.05476i
\(563\) −29.5192 + 29.5192i −1.24409 + 1.24409i −0.285797 + 0.958290i \(0.592258\pi\)
−0.958290 + 0.285797i \(0.907742\pi\)
\(564\) 0 0
\(565\) 8.39618 + 8.39618i 0.353230 + 0.353230i
\(566\) 9.88960 + 17.5315i 0.415691 + 0.736906i
\(567\) 0 0
\(568\) 24.0696 + 25.5577i 1.00994 + 1.07238i
\(569\) 11.3544 0.476003 0.238001 0.971265i \(-0.423508\pi\)
0.238001 + 0.971265i \(0.423508\pi\)
\(570\) 0 0
\(571\) −1.37894 + 1.37894i −0.0577066 + 0.0577066i −0.735371 0.677665i \(-0.762992\pi\)
0.677665 + 0.735371i \(0.262992\pi\)
\(572\) 55.1230 + 33.3114i 2.30481 + 1.39282i
\(573\) 0 0
\(574\) 3.60202 12.9249i 0.150345 0.539476i
\(575\) 3.32381 0.138613
\(576\) 0 0
\(577\) 6.63854 0.276366 0.138183 0.990407i \(-0.455874\pi\)
0.138183 + 0.990407i \(0.455874\pi\)
\(578\) 9.86888 35.4119i 0.410491 1.47294i
\(579\) 0 0
\(580\) −1.42400 0.860537i −0.0591282 0.0357319i
\(581\) −18.5385 + 18.5385i −0.769106 + 0.769106i
\(582\) 0 0
\(583\) −5.31992 −0.220329
\(584\) 7.23245 + 7.67960i 0.299281 + 0.317784i
\(585\) 0 0
\(586\) −0.860992 1.52630i −0.0355673 0.0630510i
\(587\) −21.0123 21.0123i −0.867269 0.867269i 0.124900 0.992169i \(-0.460139\pi\)
−0.992169 + 0.124900i \(0.960139\pi\)
\(588\) 0 0
\(589\) −6.90337 + 6.90337i −0.284448 + 0.284448i
\(590\) −0.658531 + 2.36297i −0.0271113 + 0.0972819i
\(591\) 0 0
\(592\) −6.69334 + 21.5030i −0.275094 + 0.883766i
\(593\) 33.0340i 1.35654i −0.734812 0.678271i \(-0.762729\pi\)
0.734812 0.678271i \(-0.237271\pi\)
\(594\) 0 0
\(595\) −5.65447 5.65447i −0.231811 0.231811i
\(596\) −35.3017 + 8.70684i −1.44601 + 0.356646i
\(597\) 0 0
\(598\) −5.46123 + 3.08070i −0.223326 + 0.125979i
\(599\) 16.4107i 0.670522i 0.942125 + 0.335261i \(0.108824\pi\)
−0.942125 + 0.335261i \(0.891176\pi\)
\(600\) 0 0
\(601\) 34.3301i 1.40035i 0.713969 + 0.700177i \(0.246896\pi\)
−0.713969 + 0.700177i \(0.753104\pi\)
\(602\) −1.99908 3.54381i −0.0814762 0.144435i
\(603\) 0 0
\(604\) 11.5605 + 6.98616i 0.470391 + 0.284263i
\(605\) 7.84586 + 7.84586i 0.318980 + 0.318980i
\(606\) 0 0
\(607\) 42.5123i 1.72552i 0.505614 + 0.862760i \(0.331266\pi\)
−0.505614 + 0.862760i \(0.668734\pi\)
\(608\) 8.82309 + 5.69974i 0.357823 + 0.231155i
\(609\) 0 0
\(610\) 7.56668 + 2.10874i 0.306366 + 0.0853805i
\(611\) 29.3723 29.3723i 1.18828 1.18828i
\(612\) 0 0
\(613\) −11.1129 11.1129i −0.448845 0.448845i 0.446126 0.894970i \(-0.352803\pi\)
−0.894970 + 0.446126i \(0.852803\pi\)
\(614\) 24.0432 13.5628i 0.970304 0.547351i
\(615\) 0 0
\(616\) −27.7641 0.832535i −1.11865 0.0335438i
\(617\) 33.8647 1.36334 0.681671 0.731659i \(-0.261254\pi\)
0.681671 + 0.731659i \(0.261254\pi\)
\(618\) 0 0
\(619\) 0.960938 0.960938i 0.0386234 0.0386234i −0.687531 0.726155i \(-0.741306\pi\)
0.726155 + 0.687531i \(0.241306\pi\)
\(620\) 1.65208 + 6.69832i 0.0663491 + 0.269011i
\(621\) 0 0
\(622\) 16.9726 + 4.73005i 0.680538 + 0.189658i
\(623\) 14.0011 0.560941
\(624\) 0 0
\(625\) −18.7285 −0.749140
\(626\) 16.6120 + 4.62956i 0.663948 + 0.185034i
\(627\) 0 0
\(628\) 3.74535 0.923756i 0.149456 0.0368619i
\(629\) −26.1042 + 26.1042i −1.04084 + 1.04084i
\(630\) 0 0
\(631\) −15.2529 −0.607210 −0.303605 0.952798i \(-0.598190\pi\)
−0.303605 + 0.952798i \(0.598190\pi\)
\(632\) −0.386027 0.409893i −0.0153553 0.0163047i
\(633\) 0 0
\(634\) −32.9455 + 18.5847i −1.30843 + 0.738092i
\(635\) −8.17571 8.17571i −0.324443 0.324443i
\(636\) 0 0
\(637\) 15.2784 15.2784i 0.605351 0.605351i
\(638\) −9.12601 2.54331i −0.361302 0.100691i
\(639\) 0 0
\(640\) 6.67200 3.25305i 0.263734 0.128588i
\(641\) 8.86880i 0.350297i −0.984542 0.175148i \(-0.943960\pi\)
0.984542 0.175148i \(-0.0560405\pi\)
\(642\) 0 0
\(643\) −22.1302 22.1302i −0.872730 0.872730i 0.120039 0.992769i \(-0.461698\pi\)
−0.992769 + 0.120039i \(0.961698\pi\)
\(644\) 1.39861 2.31439i 0.0551129 0.0911996i
\(645\) 0 0
\(646\) 8.45990 + 14.9971i 0.332850 + 0.590053i
\(647\) 28.2219i 1.10952i −0.832011 0.554759i \(-0.812810\pi\)
0.832011 0.554759i \(-0.187190\pi\)
\(648\) 0 0
\(649\) 13.9675i 0.548271i
\(650\) 34.3084 19.3535i 1.34569 0.759106i
\(651\) 0 0
\(652\) −3.21998 13.0553i −0.126104 0.511286i
\(653\) −21.7199 21.7199i −0.849964 0.849964i 0.140164 0.990128i \(-0.455237\pi\)
−0.990128 + 0.140164i \(0.955237\pi\)
\(654\) 0 0
\(655\) 0.478942i 0.0187138i
\(656\) 9.49346 + 18.0748i 0.370657 + 0.705701i
\(657\) 0 0
\(658\) −4.80926 + 17.2568i −0.187484 + 0.672739i
\(659\) −18.3081 + 18.3081i −0.713181 + 0.713181i −0.967199 0.254018i \(-0.918248\pi\)
0.254018 + 0.967199i \(0.418248\pi\)
\(660\) 0 0
\(661\) 14.2270 + 14.2270i 0.553366 + 0.553366i 0.927411 0.374045i \(-0.122029\pi\)
−0.374045 + 0.927411i \(0.622029\pi\)
\(662\) 0.838155 + 1.48582i 0.0325758 + 0.0577480i
\(663\) 0 0
\(664\) 1.19569 39.8749i 0.0464018 1.54745i
\(665\) 2.26455 0.0878154
\(666\) 0 0
\(667\) 0.652171 0.652171i 0.0252522 0.0252522i
\(668\) −19.3144 + 31.9610i −0.747296 + 1.23661i
\(669\) 0 0
\(670\) 2.98807 10.7219i 0.115439 0.414223i
\(671\) 44.7265 1.72665
\(672\) 0 0
\(673\) −24.8456 −0.957727 −0.478863 0.877889i \(-0.658951\pi\)
−0.478863 + 0.877889i \(0.658951\pi\)
\(674\) −12.5016 + 44.8587i −0.481543 + 1.72789i
\(675\) 0 0
\(676\) −24.9856 + 41.3455i −0.960983 + 1.59021i
\(677\) 19.3414 19.3414i 0.743350 0.743350i −0.229871 0.973221i \(-0.573830\pi\)
0.973221 + 0.229871i \(0.0738303\pi\)
\(678\) 0 0
\(679\) −18.2529 −0.700482
\(680\) 12.1623 + 0.364700i 0.466405 + 0.0139856i
\(681\) 0 0
\(682\) 19.3007 + 34.2148i 0.739060 + 1.31015i
\(683\) −12.6585 12.6585i −0.484363 0.484363i 0.422159 0.906522i \(-0.361272\pi\)
−0.906522 + 0.422159i \(0.861272\pi\)
\(684\) 0 0
\(685\) −4.41651 + 4.41651i −0.168746 + 0.168746i
\(686\) −7.44161 + 26.7023i −0.284122 + 1.01950i
\(687\) 0 0
\(688\) 5.91136 + 1.84006i 0.225368 + 0.0701516i
\(689\) 6.13783i 0.233833i
\(690\) 0 0
\(691\) −24.0824 24.0824i −0.916137 0.916137i 0.0806084 0.996746i \(-0.474314\pi\)
−0.996746 + 0.0806084i \(0.974314\pi\)
\(692\) 9.17139 + 37.1852i 0.348644 + 1.41357i
\(693\) 0 0
\(694\) −24.1757 + 13.6376i −0.917698 + 0.517676i
\(695\) 8.21540i 0.311628i
\(696\) 0 0
\(697\) 33.4673i 1.26767i
\(698\) 18.8973 + 33.4998i 0.715275 + 1.26799i
\(699\) 0 0
\(700\) −8.78630 + 14.5394i −0.332091 + 0.549536i
\(701\) 22.8729 + 22.8729i 0.863896 + 0.863896i 0.991788 0.127892i \(-0.0408212\pi\)
−0.127892 + 0.991788i \(0.540821\pi\)
\(702\) 0 0
\(703\) 10.4544i 0.394296i
\(704\) 31.6232 28.0417i 1.19184 1.05686i
\(705\) 0 0
\(706\) −16.5586 4.61468i −0.623190 0.173676i
\(707\) −25.3164 + 25.3164i −0.952120 + 0.952120i
\(708\) 0 0
\(709\) 8.29714 + 8.29714i 0.311606 + 0.311606i 0.845531 0.533926i \(-0.179284\pi\)
−0.533926 + 0.845531i \(0.679284\pi\)
\(710\) −10.0309 + 5.65847i −0.376454 + 0.212359i
\(711\) 0 0
\(712\) −15.5092 + 14.6061i −0.581230 + 0.547388i
\(713\) −3.82437 −0.143224
\(714\) 0 0
\(715\) −14.9399 + 14.9399i −0.558720 + 0.558720i
\(716\) −36.4239 + 8.98362i −1.36122 + 0.335734i
\(717\) 0 0
\(718\) 3.84929 + 1.07275i 0.143654 + 0.0400347i
\(719\) −4.37297 −0.163084 −0.0815421 0.996670i \(-0.525985\pi\)
−0.0815421 + 0.996670i \(0.525985\pi\)
\(720\) 0 0
\(721\) −2.41629 −0.0899872
\(722\) 21.1866 + 5.90445i 0.788483 + 0.219741i
\(723\) 0 0
\(724\) −0.398837 1.61707i −0.0148226 0.0600981i
\(725\) −4.09705 + 4.09705i −0.152161 + 0.152161i
\(726\) 0 0
\(727\) 11.7071 0.434193 0.217096 0.976150i \(-0.430341\pi\)
0.217096 + 0.976150i \(0.430341\pi\)
\(728\) 0.960533 32.0327i 0.0355997 1.18721i
\(729\) 0 0
\(730\) −3.01410 + 1.70026i −0.111557 + 0.0629295i
\(731\) 7.17628 + 7.17628i 0.265424 + 0.265424i
\(732\) 0 0
\(733\) 16.9853 16.9853i 0.627367 0.627367i −0.320038 0.947405i \(-0.603696\pi\)
0.947405 + 0.320038i \(0.103696\pi\)
\(734\) −12.5465 3.49657i −0.463100 0.129061i
\(735\) 0 0
\(736\) 0.865145 + 4.02272i 0.0318897 + 0.148280i
\(737\) 63.3769i 2.33452i
\(738\) 0 0
\(739\) −7.66564 7.66564i −0.281985 0.281985i 0.551915 0.833900i \(-0.313897\pi\)
−0.833900 + 0.551915i \(0.813897\pi\)
\(740\) −6.32289 3.82100i −0.232434 0.140463i
\(741\) 0 0
\(742\) 1.30056 + 2.30553i 0.0477450 + 0.0846388i
\(743\) 3.54776i 0.130155i −0.997880 0.0650774i \(-0.979271\pi\)
0.997880 0.0650774i \(-0.0207294\pi\)
\(744\) 0 0
\(745\) 11.9275i 0.436992i
\(746\) −26.9515 + 15.2034i −0.986763 + 0.556636i
\(747\) 0 0
\(748\) 67.2677 16.5910i 2.45955 0.606626i
\(749\) −19.8321 19.8321i −0.724650 0.724650i
\(750\) 0 0
\(751\) 37.9479i 1.38474i −0.721543 0.692370i \(-0.756567\pi\)
0.721543 0.692370i \(-0.243433\pi\)
\(752\) −12.6752 24.1326i −0.462219 0.880027i
\(753\) 0 0
\(754\) 2.93433 10.5291i 0.106862 0.383447i
\(755\) −3.13323 + 3.13323i −0.114030 + 0.114030i
\(756\) 0 0
\(757\) 25.8295 + 25.8295i 0.938789 + 0.938789i 0.998232 0.0594425i \(-0.0189323\pi\)
−0.0594425 + 0.998232i \(0.518932\pi\)
\(758\) −5.99860 10.6339i −0.217879 0.386240i
\(759\) 0 0
\(760\) −2.50847 + 2.36241i −0.0909917 + 0.0856936i
\(761\) −12.7041 −0.460523 −0.230261 0.973129i \(-0.573958\pi\)
−0.230261 + 0.973129i \(0.573958\pi\)
\(762\) 0 0
\(763\) 15.0839 15.0839i 0.546073 0.546073i
\(764\) 14.9586 + 9.03963i 0.541182 + 0.327042i
\(765\) 0 0
\(766\) 0.633096 2.27170i 0.0228747 0.0820799i
\(767\) −16.1149 −0.581875
\(768\) 0 0
\(769\) 0.366691 0.0132232 0.00661161 0.999978i \(-0.497895\pi\)
0.00661161 + 0.999978i \(0.497895\pi\)
\(770\) 2.44618 8.77747i 0.0881541 0.316318i
\(771\) 0 0
\(772\) 20.2528 + 12.2390i 0.728913 + 0.440490i
\(773\) −7.31241 + 7.31241i −0.263009 + 0.263009i −0.826275 0.563266i \(-0.809545\pi\)
0.563266 + 0.826275i \(0.309545\pi\)
\(774\) 0 0
\(775\) 24.0253 0.863016
\(776\) 20.2190 19.0417i 0.725819 0.683557i
\(777\) 0 0
\(778\) −17.9429 31.8078i −0.643284 1.14037i
\(779\) −6.70163 6.70163i −0.240111 0.240111i
\(780\) 0 0
\(781\) −46.3698 + 46.3698i −1.65924 + 1.65924i
\(782\) −1.81075 + 6.49743i −0.0647525 + 0.232347i
\(783\) 0 0
\(784\) −6.59319 12.5529i −0.235471 0.448318i
\(785\) 1.26546i 0.0451661i
\(786\) 0 0
\(787\) 15.3004 + 15.3004i 0.545401 + 0.545401i 0.925107 0.379706i \(-0.123975\pi\)
−0.379706 + 0.925107i \(0.623975\pi\)
\(788\) 16.5933 4.09260i 0.591113 0.145793i
\(789\) 0 0
\(790\) 0.160875 0.0907502i 0.00572369 0.00322875i
\(791\) 33.6413i 1.19615i
\(792\) 0 0
\(793\) 51.6030i 1.83248i
\(794\) 7.32646 + 12.9878i 0.260006 + 0.460920i
\(795\) 0 0
\(796\) 20.1368 + 12.1689i 0.713732 + 0.431316i
\(797\) −8.26831 8.26831i −0.292878 0.292878i 0.545338 0.838216i \(-0.316401\pi\)
−0.838216 + 0.545338i \(0.816401\pi\)
\(798\) 0 0
\(799\) 44.6841i 1.58081i
\(800\) −5.43498 25.2714i −0.192156 0.893480i
\(801\) 0 0
\(802\) −35.5562 9.90907i −1.25553 0.349902i
\(803\) −13.9332 + 13.9332i −0.491694 + 0.491694i
\(804\) 0 0
\(805\) 0.627264 + 0.627264i 0.0221082 + 0.0221082i
\(806\) −39.4751 + 22.2680i −1.39045 + 0.784358i
\(807\) 0 0
\(808\) 1.63285 54.4537i 0.0574434 1.91567i
\(809\) 5.41620 0.190424 0.0952118 0.995457i \(-0.469647\pi\)
0.0952118 + 0.995457i \(0.469647\pi\)
\(810\) 0 0
\(811\) 23.5526 23.5526i 0.827044 0.827044i −0.160063 0.987107i \(-0.551170\pi\)
0.987107 + 0.160063i \(0.0511697\pi\)
\(812\) 1.12882 + 4.57677i 0.0396138 + 0.160613i
\(813\) 0 0
\(814\) −40.5217 11.2929i −1.42028 0.395816i
\(815\) 4.41106 0.154513
\(816\) 0 0
\(817\) −2.87401 −0.100549
\(818\) 35.9664 + 10.0234i 1.25753 + 0.350460i
\(819\) 0 0
\(820\) −6.50258 + 1.60380i −0.227080 + 0.0560072i
\(821\) 0.586621 0.586621i 0.0204732 0.0204732i −0.696796 0.717269i \(-0.745392\pi\)
0.717269 + 0.696796i \(0.245392\pi\)
\(822\) 0 0
\(823\) −42.9664 −1.49772 −0.748858 0.662731i \(-0.769397\pi\)
−0.748858 + 0.662731i \(0.769397\pi\)
\(824\) 2.67655 2.52071i 0.0932421 0.0878130i
\(825\) 0 0
\(826\) 6.05319 3.41462i 0.210617 0.118810i
\(827\) 4.76551 + 4.76551i 0.165713 + 0.165713i 0.785092 0.619379i \(-0.212616\pi\)
−0.619379 + 0.785092i \(0.712616\pi\)
\(828\) 0 0
\(829\) 18.7283 18.7283i 0.650460 0.650460i −0.302644 0.953104i \(-0.597869\pi\)
0.953104 + 0.302644i \(0.0978692\pi\)
\(830\) 12.6062 + 3.51321i 0.437569 + 0.121945i
\(831\) 0 0
\(832\) 32.3530 + 36.4851i 1.12164 + 1.26489i
\(833\) 23.2430i 0.805322i
\(834\) 0 0
\(835\) −8.66233 8.66233i −0.299772 0.299772i
\(836\) −10.1477 + 16.7922i −0.350966 + 0.580770i
\(837\) 0 0
\(838\) −12.2508 21.7173i −0.423196 0.750210i
\(839\) 1.97689i 0.0682499i −0.999418 0.0341249i \(-0.989136\pi\)
0.999418 0.0341249i \(-0.0108644\pi\)
\(840\) 0 0
\(841\) 27.3922i 0.944559i
\(842\) 28.3073 15.9683i 0.975535 0.550303i
\(843\) 0 0
\(844\) −9.67613 39.2316i −0.333066 1.35041i
\(845\) −11.2058 11.2058i −0.385491 0.385491i
\(846\) 0 0
\(847\) 31.4363i 1.08017i
\(848\) −3.84581 1.19711i −0.132066 0.0411088i
\(849\) 0 0
\(850\) 11.3755 40.8179i 0.390175 1.40004i
\(851\) 2.89580 2.89580i 0.0992668 0.0992668i
\(852\) 0 0
\(853\) 23.8260 + 23.8260i 0.815787 + 0.815787i 0.985495 0.169707i \(-0.0542822\pi\)
−0.169707 + 0.985495i \(0.554282\pi\)
\(854\) −10.9343 19.3835i −0.374163 0.663288i
\(855\) 0 0
\(856\) 42.6574 + 1.27913i 1.45800 + 0.0437196i
\(857\) −56.6389 −1.93475 −0.967375 0.253350i \(-0.918468\pi\)
−0.967375 + 0.253350i \(0.918468\pi\)
\(858\) 0 0
\(859\) 10.4303 10.4303i 0.355877 0.355877i −0.506414 0.862291i \(-0.669029\pi\)
0.862291 + 0.506414i \(0.169029\pi\)
\(860\) −1.05043 + 1.73822i −0.0358193 + 0.0592729i
\(861\) 0 0
\(862\) −9.78261 + 35.1024i −0.333197 + 1.19559i
\(863\) −16.2869 −0.554412 −0.277206 0.960810i \(-0.589408\pi\)
−0.277206 + 0.960810i \(0.589408\pi\)
\(864\) 0 0
\(865\) −12.5639 −0.427187
\(866\) −8.16324 + 29.2917i −0.277398 + 0.995372i
\(867\) 0 0
\(868\) 10.1095 16.7289i 0.343138 0.567818i
\(869\) 0.743677 0.743677i 0.0252275 0.0252275i
\(870\) 0 0
\(871\) 73.1209 2.47761
\(872\) −0.972877 + 32.4443i −0.0329458 + 1.09870i
\(873\) 0 0
\(874\) −0.938478 1.66366i −0.0317445 0.0562743i
\(875\) −8.25236 8.25236i −0.278981 0.278981i
\(876\) 0 0
\(877\) −2.12318 + 2.12318i −0.0716946 + 0.0716946i −0.742045 0.670350i \(-0.766144\pi\)
0.670350 + 0.742045i \(0.266144\pi\)
\(878\) 8.64435 31.0180i 0.291733 1.04681i
\(879\) 0 0
\(880\) 6.44713 + 12.2748i 0.217333 + 0.413783i
\(881\) 17.3923i 0.585963i −0.956118 0.292981i \(-0.905353\pi\)
0.956118 0.292981i \(-0.0946474\pi\)
\(882\) 0 0
\(883\) 8.04441 + 8.04441i 0.270716 + 0.270716i 0.829388 0.558672i \(-0.188689\pi\)
−0.558672 + 0.829388i \(0.688689\pi\)
\(884\) 19.1418 + 77.6098i 0.643807 + 2.61030i
\(885\) 0 0
\(886\) −17.9242 + 10.1111i −0.602175 + 0.339689i
\(887\) 42.1906i 1.41662i −0.705901 0.708311i \(-0.749458\pi\)
0.705901 0.708311i \(-0.250542\pi\)
\(888\) 0 0
\(889\) 32.7580i 1.09867i
\(890\) −3.43373 6.08705i −0.115099 0.204038i
\(891\) 0 0
\(892\) 26.0758 43.1496i 0.873082 1.44475i
\(893\) 8.94772 + 8.94772i 0.299424 + 0.299424i
\(894\) 0 0
\(895\) 12.3067i 0.411368i
\(896\) −19.8836 6.84942i −0.664263 0.228823i
\(897\) 0 0
\(898\) 29.3154 + 8.16985i 0.978267 + 0.272631i
\(899\) 4.71405 4.71405i 0.157223 0.157223i
\(900\) 0 0
\(901\) −4.66875 4.66875i −0.155538 0.155538i
\(902\) −33.2149 + 18.7366i −1.10594 + 0.623862i
\(903\) 0 0
\(904\) 35.0952 + 37.2649i 1.16725 + 1.23941i
\(905\) 0.546369 0.0181619
\(906\) 0 0
\(907\) 5.05861 5.05861i 0.167968 0.167968i −0.618117 0.786086i \(-0.712104\pi\)
0.786086 + 0.618117i \(0.212104\pi\)
\(908\) −14.5891 + 3.59827i −0.484156 + 0.119413i
\(909\) 0 0
\(910\) 10.1270 + 2.82226i 0.335706 + 0.0935571i
\(911\) 40.8990 1.35505 0.677523 0.735502i \(-0.263054\pi\)
0.677523 + 0.735502i \(0.263054\pi\)
\(912\) 0 0
\(913\) 74.5152 2.46609
\(914\) 9.26136 + 2.58103i 0.306339 + 0.0853729i
\(915\) 0 0
\(916\) 4.13496 + 16.7651i 0.136623 + 0.553935i
\(917\) 0.959499 0.959499i 0.0316854 0.0316854i
\(918\) 0 0
\(919\) −30.9766 −1.02182 −0.510912 0.859633i \(-0.670692\pi\)
−0.510912 + 0.859633i \(0.670692\pi\)
\(920\) −1.34920 0.0404571i −0.0444818 0.00133383i
\(921\) 0 0
\(922\) −33.8752 + 19.1091i −1.11562 + 0.629325i
\(923\) −53.4990 53.4990i −1.76094 1.76094i
\(924\) 0 0
\(925\) −18.1919 + 18.1919i −0.598146 + 0.598146i
\(926\) 13.8231 + 3.85233i 0.454255 + 0.126595i
\(927\) 0 0
\(928\) −6.02496 3.89214i −0.197779 0.127766i
\(929\) 16.8850i 0.553980i −0.960873 0.276990i \(-0.910663\pi\)
0.960873 0.276990i \(-0.0893368\pi\)
\(930\) 0 0
\(931\) 4.65427 + 4.65427i 0.152538 + 0.152538i
\(932\) 13.7469 + 8.30743i 0.450296 + 0.272119i
\(933\) 0 0
\(934\) 2.67127 + 4.73543i 0.0874067 + 0.154948i
\(935\) 22.7281i 0.743287i
\(936\) 0 0
\(937\) 53.1410i 1.73604i −0.496528 0.868020i \(-0.665392\pi\)
0.496528 0.868020i \(-0.334608\pi\)
\(938\) −27.4662 + 15.4937i −0.896802 + 0.505889i
\(939\) 0 0
\(940\) 8.68195 2.14132i 0.283174 0.0698423i
\(941\) 9.89314 + 9.89314i 0.322507 + 0.322507i 0.849728 0.527221i \(-0.176766\pi\)
−0.527221 + 0.849728i \(0.676766\pi\)
\(942\) 0 0
\(943\) 3.71261i 0.120899i
\(944\) −3.14301 + 10.0972i −0.102296 + 0.328636i
\(945\) 0 0
\(946\) −3.10453 + 11.1398i −0.100937 + 0.362186i
\(947\) 14.3740 14.3740i 0.467093 0.467093i −0.433878 0.900971i \(-0.642855\pi\)
0.900971 + 0.433878i \(0.142855\pi\)
\(948\) 0 0
\(949\) −16.0754 16.0754i −0.521830 0.521830i
\(950\) 5.89568 + 10.4514i 0.191281 + 0.339089i
\(951\) 0 0
\(952\) −23.6351 25.0963i −0.766017 0.813377i
\(953\) −5.12058 −0.165872 −0.0829360 0.996555i \(-0.526430\pi\)
−0.0829360 + 0.996555i \(0.526430\pi\)
\(954\) 0 0
\(955\) −4.05419 + 4.05419i −0.131191 + 0.131191i
\(956\) −28.1594 17.0170i −0.910739 0.550370i
\(957\) 0 0
\(958\) −0.829852 + 2.97771i −0.0268113 + 0.0962054i
\(959\) 17.6958 0.571427
\(960\) 0 0
\(961\) 3.35651 0.108275
\(962\) 13.0291 46.7517i 0.420077 1.50734i
\(963\) 0 0
\(964\) −5.49732 3.32209i −0.177057 0.106997i
\(965\) −5.48907 + 5.48907i −0.176699 + 0.176699i
\(966\) 0 0
\(967\) −52.7411 −1.69604 −0.848019 0.529965i \(-0.822205\pi\)
−0.848019 + 0.529965i \(0.822205\pi\)
\(968\) 32.7949 + 34.8224i 1.05407 + 1.11924i
\(969\) 0 0
\(970\) 4.47648 + 7.93557i 0.143731 + 0.254796i
\(971\) −22.7551 22.7551i −0.730246 0.730246i 0.240423 0.970668i \(-0.422714\pi\)
−0.970668 + 0.240423i \(0.922714\pi\)
\(972\) 0 0
\(973\) −16.4585 + 16.4585i −0.527635 + 0.527635i
\(974\) −2.29297 + 8.22771i −0.0734714 + 0.263633i
\(975\) 0 0
\(976\) 32.3331 + 10.0645i 1.03496 + 0.322157i
\(977\) 16.3452i 0.522929i −0.965213 0.261465i \(-0.915795\pi\)
0.965213 0.261465i \(-0.0842055\pi\)
\(978\) 0 0
\(979\) −28.1386 28.1386i −0.899312 0.899312i
\(980\) 4.51602 1.11384i 0.144259 0.0355802i
\(981\) 0 0
\(982\) 26.8950 15.1716i 0.858255 0.484144i
\(983\) 6.62052i 0.211162i 0.994411 + 0.105581i \(0.0336702\pi\)
−0.994411 + 0.105581i \(0.966330\pi\)
\(984\) 0 0
\(985\) 5.60647i 0.178637i
\(986\) −5.77696 10.2410i −0.183976 0.326138i
\(987\) 0 0
\(988\) −19.3739 11.7079i −0.616367 0.372477i
\(989\) −0.796082 0.796082i −0.0253139 0.0253139i
\(990\) 0 0
\(991\) 41.3701i 1.31417i 0.753818 + 0.657083i \(0.228210\pi\)
−0.753818 + 0.657083i \(0.771790\pi\)
\(992\) 6.25348 + 29.0772i 0.198548 + 0.923203i
\(993\) 0 0
\(994\) 31.4317 + 8.75963i 0.996952 + 0.277839i
\(995\) −5.45765 + 5.45765i −0.173019 + 0.173019i
\(996\) 0 0
\(997\) 1.44258 + 1.44258i 0.0456871 + 0.0456871i 0.729581 0.683894i \(-0.239715\pi\)
−0.683894 + 0.729581i \(0.739715\pi\)
\(998\) 16.8519 9.50623i 0.533439 0.300914i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 432.2.l.b.107.7 32
3.2 odd 2 inner 432.2.l.b.107.10 yes 32
4.3 odd 2 1728.2.l.b.1295.10 32
12.11 even 2 1728.2.l.b.1295.7 32
16.3 odd 4 inner 432.2.l.b.323.10 yes 32
16.13 even 4 1728.2.l.b.431.7 32
48.29 odd 4 1728.2.l.b.431.10 32
48.35 even 4 inner 432.2.l.b.323.7 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.l.b.107.7 32 1.1 even 1 trivial
432.2.l.b.107.10 yes 32 3.2 odd 2 inner
432.2.l.b.323.7 yes 32 48.35 even 4 inner
432.2.l.b.323.10 yes 32 16.3 odd 4 inner
1728.2.l.b.431.7 32 16.13 even 4
1728.2.l.b.431.10 32 48.29 odd 4
1728.2.l.b.1295.7 32 12.11 even 2
1728.2.l.b.1295.10 32 4.3 odd 2