Properties

Label 864.2.v.a.109.10
Level $864$
Weight $2$
Character 864.109
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
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] = [864,2,Mod(109,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.v (of order \(8\), degree \(4\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 109.10
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.a.325.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.934820 + 1.06118i) q^{2} +(-0.252222 - 1.98403i) q^{4} +(0.930451 - 0.385405i) q^{5} +(-0.938500 + 0.938500i) q^{7} +(2.34121 + 1.58706i) q^{8} +O(q^{10})\) \(q+(-0.934820 + 1.06118i) q^{2} +(-0.252222 - 1.98403i) q^{4} +(0.930451 - 0.385405i) q^{5} +(-0.938500 + 0.938500i) q^{7} +(2.34121 + 1.58706i) q^{8} +(-0.460818 + 1.34766i) q^{10} +(-0.846222 - 2.04296i) q^{11} +(-5.64483 - 2.33816i) q^{13} +(-0.118592 - 1.87325i) q^{14} +(-3.87277 + 1.00083i) q^{16} +7.71645i q^{17} +(-3.36643 - 1.39442i) q^{19} +(-0.999337 - 1.74884i) q^{20} +(2.95902 + 1.01180i) q^{22} +(5.65026 + 5.65026i) q^{23} +(-2.81833 + 2.81833i) q^{25} +(7.75812 - 3.80444i) q^{26} +(2.09872 + 1.62530i) q^{28} +(-0.949070 + 2.29126i) q^{29} +5.39395 q^{31} +(2.55827 - 5.04532i) q^{32} +(-8.18857 - 7.21350i) q^{34} +(-0.511525 + 1.23493i) q^{35} +(-4.01544 + 1.66325i) q^{37} +(4.62674 - 2.26887i) q^{38} +(2.79004 + 0.574368i) q^{40} +(-6.02596 - 6.02596i) q^{41} +(3.38507 + 8.17229i) q^{43} +(-3.83986 + 2.19421i) q^{44} +(-11.2779 + 0.713987i) q^{46} +6.68653i q^{47} +5.23844i q^{49} +(-0.356135 - 5.62540i) q^{50} +(-3.21524 + 11.7893i) q^{52} +(0.589451 + 1.42306i) q^{53} +(-1.57474 - 1.57474i) q^{55} +(-3.68668 + 0.707766i) q^{56} +(-1.54424 - 3.14905i) q^{58} +(-7.21416 + 2.98820i) q^{59} +(-3.05674 + 7.37963i) q^{61} +(-5.04238 + 5.72397i) q^{62} +(2.96249 + 7.43126i) q^{64} -6.15337 q^{65} +(3.77223 - 9.10696i) q^{67} +(15.3097 - 1.94626i) q^{68} +(-0.832305 - 1.69726i) q^{70} +(-1.95353 + 1.95353i) q^{71} +(-8.58563 - 8.58563i) q^{73} +(1.98870 - 5.81596i) q^{74} +(-1.91749 + 7.03081i) q^{76} +(2.71150 + 1.12314i) q^{77} -11.7674i q^{79} +(-3.21769 + 2.42381i) q^{80} +(12.0278 - 0.761461i) q^{82} +(-6.05690 - 2.50885i) q^{83} +(2.97396 + 7.17978i) q^{85} +(-11.8367 - 4.04744i) q^{86} +(1.26112 - 6.12599i) q^{88} +(-5.36845 + 5.36845i) q^{89} +(7.49204 - 3.10330i) q^{91} +(9.78518 - 12.6354i) q^{92} +(-7.09564 - 6.25071i) q^{94} -3.66972 q^{95} -8.31108 q^{97} +(-5.55894 - 4.89700i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.934820 + 1.06118i −0.661018 + 0.750370i
\(3\) 0 0
\(4\) −0.252222 1.98403i −0.126111 0.992016i
\(5\) 0.930451 0.385405i 0.416110 0.172359i −0.164798 0.986327i \(-0.552697\pi\)
0.580909 + 0.813969i \(0.302697\pi\)
\(6\) 0 0
\(7\) −0.938500 + 0.938500i −0.354720 + 0.354720i −0.861862 0.507143i \(-0.830702\pi\)
0.507143 + 0.861862i \(0.330702\pi\)
\(8\) 2.34121 + 1.58706i 0.827741 + 0.561110i
\(9\) 0 0
\(10\) −0.460818 + 1.34766i −0.145724 + 0.426169i
\(11\) −0.846222 2.04296i −0.255145 0.615976i 0.743459 0.668781i \(-0.233184\pi\)
−0.998605 + 0.0528055i \(0.983184\pi\)
\(12\) 0 0
\(13\) −5.64483 2.33816i −1.56559 0.648490i −0.579543 0.814941i \(-0.696769\pi\)
−0.986050 + 0.166451i \(0.946769\pi\)
\(14\) −0.118592 1.87325i −0.0316951 0.500647i
\(15\) 0 0
\(16\) −3.87277 + 1.00083i −0.968192 + 0.250209i
\(17\) 7.71645i 1.87151i 0.352645 + 0.935757i \(0.385282\pi\)
−0.352645 + 0.935757i \(0.614718\pi\)
\(18\) 0 0
\(19\) −3.36643 1.39442i −0.772312 0.319902i −0.0385035 0.999258i \(-0.512259\pi\)
−0.733809 + 0.679356i \(0.762259\pi\)
\(20\) −0.999337 1.74884i −0.223459 0.391052i
\(21\) 0 0
\(22\) 2.95902 + 1.01180i 0.630865 + 0.215717i
\(23\) 5.65026 + 5.65026i 1.17816 + 1.17816i 0.980212 + 0.197948i \(0.0634278\pi\)
0.197948 + 0.980212i \(0.436572\pi\)
\(24\) 0 0
\(25\) −2.81833 + 2.81833i −0.563666 + 0.563666i
\(26\) 7.75812 3.80444i 1.52149 0.746111i
\(27\) 0 0
\(28\) 2.09872 + 1.62530i 0.396622 + 0.307154i
\(29\) −0.949070 + 2.29126i −0.176238 + 0.425476i −0.987172 0.159662i \(-0.948960\pi\)
0.810934 + 0.585138i \(0.198960\pi\)
\(30\) 0 0
\(31\) 5.39395 0.968782 0.484391 0.874852i \(-0.339041\pi\)
0.484391 + 0.874852i \(0.339041\pi\)
\(32\) 2.55827 5.04532i 0.452243 0.891895i
\(33\) 0 0
\(34\) −8.18857 7.21350i −1.40433 1.23710i
\(35\) −0.511525 + 1.23493i −0.0864636 + 0.208741i
\(36\) 0 0
\(37\) −4.01544 + 1.66325i −0.660134 + 0.273436i −0.687495 0.726189i \(-0.741290\pi\)
0.0273609 + 0.999626i \(0.491290\pi\)
\(38\) 4.62674 2.26887i 0.750557 0.368059i
\(39\) 0 0
\(40\) 2.79004 + 0.574368i 0.441144 + 0.0908155i
\(41\) −6.02596 6.02596i −0.941096 0.941096i 0.0572629 0.998359i \(-0.481763\pi\)
−0.998359 + 0.0572629i \(0.981763\pi\)
\(42\) 0 0
\(43\) 3.38507 + 8.17229i 0.516219 + 1.24626i 0.940210 + 0.340596i \(0.110629\pi\)
−0.423991 + 0.905666i \(0.639371\pi\)
\(44\) −3.83986 + 2.19421i −0.578881 + 0.330790i
\(45\) 0 0
\(46\) −11.2779 + 0.713987i −1.66284 + 0.105272i
\(47\) 6.68653i 0.975331i 0.873031 + 0.487666i \(0.162151\pi\)
−0.873031 + 0.487666i \(0.837849\pi\)
\(48\) 0 0
\(49\) 5.23844i 0.748348i
\(50\) −0.356135 5.62540i −0.0503650 0.795552i
\(51\) 0 0
\(52\) −3.21524 + 11.7893i −0.445874 + 1.63488i
\(53\) 0.589451 + 1.42306i 0.0809673 + 0.195472i 0.959179 0.282800i \(-0.0912632\pi\)
−0.878212 + 0.478272i \(0.841263\pi\)
\(54\) 0 0
\(55\) −1.57474 1.57474i −0.212337 0.212337i
\(56\) −3.68668 + 0.707766i −0.492653 + 0.0945792i
\(57\) 0 0
\(58\) −1.54424 3.14905i −0.202768 0.413491i
\(59\) −7.21416 + 2.98820i −0.939204 + 0.389031i −0.799163 0.601115i \(-0.794723\pi\)
−0.140041 + 0.990146i \(0.544723\pi\)
\(60\) 0 0
\(61\) −3.05674 + 7.37963i −0.391376 + 0.944865i 0.598265 + 0.801298i \(0.295857\pi\)
−0.989641 + 0.143566i \(0.954143\pi\)
\(62\) −5.04238 + 5.72397i −0.640382 + 0.726946i
\(63\) 0 0
\(64\) 2.96249 + 7.43126i 0.370311 + 0.928908i
\(65\) −6.15337 −0.763232
\(66\) 0 0
\(67\) 3.77223 9.10696i 0.460851 1.11259i −0.507198 0.861830i \(-0.669319\pi\)
0.968049 0.250762i \(-0.0806813\pi\)
\(68\) 15.3097 1.94626i 1.85657 0.236019i
\(69\) 0 0
\(70\) −0.832305 1.69726i −0.0994795 0.202861i
\(71\) −1.95353 + 1.95353i −0.231842 + 0.231842i −0.813461 0.581619i \(-0.802419\pi\)
0.581619 + 0.813461i \(0.302419\pi\)
\(72\) 0 0
\(73\) −8.58563 8.58563i −1.00487 1.00487i −0.999988 0.00488401i \(-0.998445\pi\)
−0.00488401 0.999988i \(-0.501555\pi\)
\(74\) 1.98870 5.81596i 0.231182 0.676091i
\(75\) 0 0
\(76\) −1.91749 + 7.03081i −0.219951 + 0.806489i
\(77\) 2.71150 + 1.12314i 0.309004 + 0.127994i
\(78\) 0 0
\(79\) 11.7674i 1.32394i −0.749531 0.661969i \(-0.769721\pi\)
0.749531 0.661969i \(-0.230279\pi\)
\(80\) −3.21769 + 2.42381i −0.359749 + 0.270991i
\(81\) 0 0
\(82\) 12.0278 0.761461i 1.32825 0.0840894i
\(83\) −6.05690 2.50885i −0.664831 0.275382i 0.0246390 0.999696i \(-0.492156\pi\)
−0.689470 + 0.724314i \(0.742156\pi\)
\(84\) 0 0
\(85\) 2.97396 + 7.17978i 0.322571 + 0.778756i
\(86\) −11.8367 4.04744i −1.27639 0.436446i
\(87\) 0 0
\(88\) 1.26112 6.12599i 0.134436 0.653033i
\(89\) −5.36845 + 5.36845i −0.569055 + 0.569055i −0.931864 0.362809i \(-0.881818\pi\)
0.362809 + 0.931864i \(0.381818\pi\)
\(90\) 0 0
\(91\) 7.49204 3.10330i 0.785379 0.325315i
\(92\) 9.78518 12.6354i 1.02018 1.31733i
\(93\) 0 0
\(94\) −7.09564 6.25071i −0.731860 0.644711i
\(95\) −3.66972 −0.376505
\(96\) 0 0
\(97\) −8.31108 −0.843862 −0.421931 0.906628i \(-0.638648\pi\)
−0.421931 + 0.906628i \(0.638648\pi\)
\(98\) −5.55894 4.89700i −0.561538 0.494671i
\(99\) 0 0
\(100\) 6.30251 + 4.88082i 0.630251 + 0.488082i
\(101\) 3.21953 1.33357i 0.320355 0.132695i −0.216711 0.976236i \(-0.569533\pi\)
0.537066 + 0.843540i \(0.319533\pi\)
\(102\) 0 0
\(103\) 0.343343 0.343343i 0.0338306 0.0338306i −0.689989 0.723820i \(-0.742385\pi\)
0.723820 + 0.689989i \(0.242385\pi\)
\(104\) −9.50489 14.4328i −0.932032 1.41525i
\(105\) 0 0
\(106\) −2.06116 0.704790i −0.200198 0.0684553i
\(107\) 1.86534 + 4.50334i 0.180330 + 0.435354i 0.988035 0.154233i \(-0.0492906\pi\)
−0.807705 + 0.589587i \(0.799291\pi\)
\(108\) 0 0
\(109\) −6.74343 2.79322i −0.645904 0.267542i 0.0355895 0.999366i \(-0.488669\pi\)
−0.681493 + 0.731824i \(0.738669\pi\)
\(110\) 3.14318 0.198989i 0.299690 0.0189729i
\(111\) 0 0
\(112\) 2.69531 4.57388i 0.254683 0.432191i
\(113\) 2.17091i 0.204222i −0.994773 0.102111i \(-0.967440\pi\)
0.994773 0.102111i \(-0.0325596\pi\)
\(114\) 0 0
\(115\) 7.43493 + 3.07965i 0.693311 + 0.287179i
\(116\) 4.78531 + 1.30508i 0.444304 + 0.121174i
\(117\) 0 0
\(118\) 3.57291 10.4490i 0.328913 0.961907i
\(119\) −7.24189 7.24189i −0.663863 0.663863i
\(120\) 0 0
\(121\) 4.32058 4.32058i 0.392780 0.392780i
\(122\) −4.97364 10.1424i −0.450292 0.918249i
\(123\) 0 0
\(124\) −1.36047 10.7018i −0.122174 0.961048i
\(125\) −3.46315 + 8.36078i −0.309753 + 0.747810i
\(126\) 0 0
\(127\) −0.995355 −0.0883235 −0.0441617 0.999024i \(-0.514062\pi\)
−0.0441617 + 0.999024i \(0.514062\pi\)
\(128\) −10.6553 3.80315i −0.941807 0.336154i
\(129\) 0 0
\(130\) 5.75230 6.52986i 0.504510 0.572707i
\(131\) 4.10132 9.90147i 0.358334 0.865096i −0.637200 0.770698i \(-0.719908\pi\)
0.995535 0.0943974i \(-0.0300924\pi\)
\(132\) 0 0
\(133\) 4.46806 1.85073i 0.387430 0.160479i
\(134\) 6.13780 + 12.5164i 0.530225 + 1.08125i
\(135\) 0 0
\(136\) −12.2465 + 18.0658i −1.05013 + 1.54913i
\(137\) 12.7750 + 12.7750i 1.09144 + 1.09144i 0.995375 + 0.0960676i \(0.0306265\pi\)
0.0960676 + 0.995375i \(0.469374\pi\)
\(138\) 0 0
\(139\) −1.10035 2.65647i −0.0933302 0.225319i 0.870320 0.492487i \(-0.163912\pi\)
−0.963650 + 0.267168i \(0.913912\pi\)
\(140\) 2.57916 + 0.703405i 0.217979 + 0.0594486i
\(141\) 0 0
\(142\) −0.246855 3.89926i −0.0207156 0.327219i
\(143\) 13.5108i 1.12983i
\(144\) 0 0
\(145\) 2.49768i 0.207421i
\(146\) 17.1370 1.08491i 1.41826 0.0897879i
\(147\) 0 0
\(148\) 4.31272 + 7.54725i 0.354504 + 0.620380i
\(149\) 0.247702 + 0.598004i 0.0202925 + 0.0489904i 0.933701 0.358054i \(-0.116560\pi\)
−0.913408 + 0.407044i \(0.866560\pi\)
\(150\) 0 0
\(151\) 13.5472 + 13.5472i 1.10246 + 1.10246i 0.994113 + 0.108344i \(0.0345549\pi\)
0.108344 + 0.994113i \(0.465445\pi\)
\(152\) −5.66848 8.60735i −0.459774 0.698148i
\(153\) 0 0
\(154\) −3.72662 + 1.82746i −0.300300 + 0.147261i
\(155\) 5.01881 2.07886i 0.403120 0.166978i
\(156\) 0 0
\(157\) 4.17046 10.0684i 0.332839 0.803544i −0.665526 0.746375i \(-0.731793\pi\)
0.998365 0.0571689i \(-0.0182074\pi\)
\(158\) 12.4874 + 11.0004i 0.993444 + 0.875147i
\(159\) 0 0
\(160\) 0.435854 5.68039i 0.0344573 0.449075i
\(161\) −10.6055 −0.835834
\(162\) 0 0
\(163\) −2.29505 + 5.54074i −0.179762 + 0.433985i −0.987917 0.154986i \(-0.950467\pi\)
0.808154 + 0.588971i \(0.200467\pi\)
\(164\) −10.4358 + 13.4756i −0.814900 + 1.05227i
\(165\) 0 0
\(166\) 8.32446 4.08216i 0.646103 0.316837i
\(167\) −6.22675 + 6.22675i −0.481840 + 0.481840i −0.905719 0.423879i \(-0.860668\pi\)
0.423879 + 0.905719i \(0.360668\pi\)
\(168\) 0 0
\(169\) 17.2047 + 17.2047i 1.32344 + 1.32344i
\(170\) −10.3992 3.55588i −0.797581 0.272724i
\(171\) 0 0
\(172\) 15.3603 8.77733i 1.17121 0.669265i
\(173\) −0.963826 0.399230i −0.0732783 0.0303529i 0.345743 0.938329i \(-0.387627\pi\)
−0.419022 + 0.907976i \(0.637627\pi\)
\(174\) 0 0
\(175\) 5.29001i 0.399887i
\(176\) 5.32188 + 7.06498i 0.401152 + 0.532543i
\(177\) 0 0
\(178\) −0.678377 10.7154i −0.0508465 0.803157i
\(179\) −9.89224 4.09750i −0.739381 0.306261i −0.0189802 0.999820i \(-0.506042\pi\)
−0.720400 + 0.693558i \(0.756042\pi\)
\(180\) 0 0
\(181\) 1.31664 + 3.17865i 0.0978651 + 0.236267i 0.965228 0.261408i \(-0.0841870\pi\)
−0.867363 + 0.497676i \(0.834187\pi\)
\(182\) −3.71053 + 10.8515i −0.275043 + 0.804364i
\(183\) 0 0
\(184\) 4.26112 + 22.1957i 0.314134 + 1.63629i
\(185\) −3.09514 + 3.09514i −0.227559 + 0.227559i
\(186\) 0 0
\(187\) 15.7644 6.52983i 1.15281 0.477508i
\(188\) 13.2663 1.68649i 0.967544 0.123000i
\(189\) 0 0
\(190\) 3.43052 3.89424i 0.248876 0.282518i
\(191\) 21.8507 1.58106 0.790531 0.612422i \(-0.209805\pi\)
0.790531 + 0.612422i \(0.209805\pi\)
\(192\) 0 0
\(193\) −14.5286 −1.04579 −0.522897 0.852396i \(-0.675149\pi\)
−0.522897 + 0.852396i \(0.675149\pi\)
\(194\) 7.76936 8.81958i 0.557808 0.633209i
\(195\) 0 0
\(196\) 10.3932 1.32125i 0.742373 0.0943750i
\(197\) 15.9169 6.59300i 1.13403 0.469732i 0.264883 0.964280i \(-0.414667\pi\)
0.869150 + 0.494548i \(0.164667\pi\)
\(198\) 0 0
\(199\) 12.3938 12.3938i 0.878574 0.878574i −0.114813 0.993387i \(-0.536627\pi\)
0.993387 + 0.114813i \(0.0366270\pi\)
\(200\) −11.0712 + 2.12543i −0.782849 + 0.150291i
\(201\) 0 0
\(202\) −1.59451 + 4.66316i −0.112190 + 0.328099i
\(203\) −1.25964 3.04105i −0.0884096 0.213440i
\(204\) 0 0
\(205\) −7.92929 3.28442i −0.553806 0.229394i
\(206\) 0.0433860 + 0.685313i 0.00302285 + 0.0477480i
\(207\) 0 0
\(208\) 24.2012 + 3.40563i 1.67805 + 0.236138i
\(209\) 8.05747i 0.557347i
\(210\) 0 0
\(211\) −10.6796 4.42362i −0.735212 0.304535i −0.0165202 0.999864i \(-0.505259\pi\)
−0.718692 + 0.695329i \(0.755259\pi\)
\(212\) 2.67473 1.52842i 0.183701 0.104972i
\(213\) 0 0
\(214\) −6.52263 2.23034i −0.445878 0.152463i
\(215\) 6.29929 + 6.29929i 0.429608 + 0.429608i
\(216\) 0 0
\(217\) −5.06222 + 5.06222i −0.343646 + 0.343646i
\(218\) 9.26802 4.54486i 0.627710 0.307817i
\(219\) 0 0
\(220\) −2.72714 + 3.52151i −0.183864 + 0.237420i
\(221\) 18.0423 43.5580i 1.21366 2.93003i
\(222\) 0 0
\(223\) 12.0545 0.807226 0.403613 0.914930i \(-0.367754\pi\)
0.403613 + 0.914930i \(0.367754\pi\)
\(224\) 2.33409 + 7.13597i 0.155953 + 0.476792i
\(225\) 0 0
\(226\) 2.30373 + 2.02941i 0.153242 + 0.134994i
\(227\) 3.72637 8.99626i 0.247328 0.597103i −0.750647 0.660703i \(-0.770258\pi\)
0.997975 + 0.0636001i \(0.0202582\pi\)
\(228\) 0 0
\(229\) −26.6130 + 11.0235i −1.75864 + 0.728452i −0.761906 + 0.647688i \(0.775736\pi\)
−0.996733 + 0.0807641i \(0.974264\pi\)
\(230\) −10.2184 + 5.01091i −0.673781 + 0.330410i
\(231\) 0 0
\(232\) −5.85833 + 3.85807i −0.384618 + 0.253295i
\(233\) −11.3815 11.3815i −0.745628 0.745628i 0.228027 0.973655i \(-0.426773\pi\)
−0.973655 + 0.228027i \(0.926773\pi\)
\(234\) 0 0
\(235\) 2.57703 + 6.22149i 0.168107 + 0.405845i
\(236\) 7.74826 + 13.5594i 0.504369 + 0.882644i
\(237\) 0 0
\(238\) 14.4548 0.915111i 0.936968 0.0593179i
\(239\) 12.1171i 0.783790i 0.920010 + 0.391895i \(0.128180\pi\)
−0.920010 + 0.391895i \(0.871820\pi\)
\(240\) 0 0
\(241\) 1.31602i 0.0847721i 0.999101 + 0.0423860i \(0.0134959\pi\)
−0.999101 + 0.0423860i \(0.986504\pi\)
\(242\) 0.545964 + 8.62390i 0.0350959 + 0.554365i
\(243\) 0 0
\(244\) 15.4124 + 4.20337i 0.986678 + 0.269093i
\(245\) 2.01892 + 4.87411i 0.128984 + 0.311395i
\(246\) 0 0
\(247\) 15.7425 + 15.7425i 1.00167 + 1.00167i
\(248\) 12.6283 + 8.56052i 0.801901 + 0.543594i
\(249\) 0 0
\(250\) −5.63490 11.4909i −0.356382 0.726746i
\(251\) −9.63552 + 3.99117i −0.608189 + 0.251920i −0.665454 0.746439i \(-0.731762\pi\)
0.0572650 + 0.998359i \(0.481762\pi\)
\(252\) 0 0
\(253\) 6.76188 16.3246i 0.425116 1.02632i
\(254\) 0.930478 1.05625i 0.0583834 0.0662753i
\(255\) 0 0
\(256\) 13.9967 7.75200i 0.874791 0.484500i
\(257\) −8.53035 −0.532109 −0.266054 0.963958i \(-0.585720\pi\)
−0.266054 + 0.963958i \(0.585720\pi\)
\(258\) 0 0
\(259\) 2.20753 5.32945i 0.137169 0.331156i
\(260\) 1.55202 + 12.2085i 0.0962521 + 0.757139i
\(261\) 0 0
\(262\) 6.67328 + 13.6084i 0.412277 + 0.840727i
\(263\) −6.53095 + 6.53095i −0.402715 + 0.402715i −0.879189 0.476473i \(-0.841915\pi\)
0.476473 + 0.879189i \(0.341915\pi\)
\(264\) 0 0
\(265\) 1.09691 + 1.09691i 0.0673827 + 0.0673827i
\(266\) −2.21287 + 6.47153i −0.135680 + 0.396795i
\(267\) 0 0
\(268\) −19.0199 5.18724i −1.16183 0.316861i
\(269\) 22.7725 + 9.43267i 1.38846 + 0.575120i 0.946731 0.322027i \(-0.104364\pi\)
0.441732 + 0.897147i \(0.354364\pi\)
\(270\) 0 0
\(271\) 30.4157i 1.84762i −0.382847 0.923812i \(-0.625056\pi\)
0.382847 0.923812i \(-0.374944\pi\)
\(272\) −7.72289 29.8840i −0.468269 1.81199i
\(273\) 0 0
\(274\) −25.4990 + 1.61430i −1.54045 + 0.0975232i
\(275\) 8.14267 + 3.37281i 0.491022 + 0.203388i
\(276\) 0 0
\(277\) 11.9512 + 28.8527i 0.718077 + 1.73359i 0.678755 + 0.734365i \(0.262520\pi\)
0.0393221 + 0.999227i \(0.487480\pi\)
\(278\) 3.84763 + 1.31565i 0.230766 + 0.0789077i
\(279\) 0 0
\(280\) −3.15749 + 2.07941i −0.188696 + 0.124268i
\(281\) −23.3117 + 23.3117i −1.39066 + 1.39066i −0.566816 + 0.823844i \(0.691825\pi\)
−0.823844 + 0.566816i \(0.808175\pi\)
\(282\) 0 0
\(283\) 22.7460 9.42171i 1.35211 0.560063i 0.415232 0.909716i \(-0.363701\pi\)
0.936879 + 0.349653i \(0.113701\pi\)
\(284\) 4.36860 + 3.38315i 0.259228 + 0.200753i
\(285\) 0 0
\(286\) −14.3374 12.6301i −0.847788 0.746835i
\(287\) 11.3107 0.667651
\(288\) 0 0
\(289\) −42.5436 −2.50257
\(290\) −2.65050 2.33488i −0.155643 0.137109i
\(291\) 0 0
\(292\) −14.8687 + 19.1997i −0.870124 + 1.12357i
\(293\) 10.6254 4.40120i 0.620744 0.257121i −0.0500704 0.998746i \(-0.515945\pi\)
0.670815 + 0.741625i \(0.265945\pi\)
\(294\) 0 0
\(295\) −5.56075 + 5.56075i −0.323759 + 0.323759i
\(296\) −12.0406 2.47873i −0.699848 0.144073i
\(297\) 0 0
\(298\) −0.866149 0.296170i −0.0501747 0.0171567i
\(299\) −18.6835 45.1060i −1.08050 2.60855i
\(300\) 0 0
\(301\) −10.8466 4.49280i −0.625187 0.258961i
\(302\) −27.0403 + 1.71188i −1.55600 + 0.0985074i
\(303\) 0 0
\(304\) 14.4330 + 2.03103i 0.827789 + 0.116488i
\(305\) 8.04447i 0.460625i
\(306\) 0 0
\(307\) −3.33416 1.38105i −0.190290 0.0788209i 0.285504 0.958378i \(-0.407839\pi\)
−0.475794 + 0.879557i \(0.657839\pi\)
\(308\) 1.54444 5.66298i 0.0880028 0.322678i
\(309\) 0 0
\(310\) −2.48563 + 7.26924i −0.141174 + 0.412865i
\(311\) 15.7937 + 15.7937i 0.895577 + 0.895577i 0.995041 0.0994642i \(-0.0317129\pi\)
−0.0994642 + 0.995041i \(0.531713\pi\)
\(312\) 0 0
\(313\) 22.6900 22.6900i 1.28251 1.28251i 0.343279 0.939234i \(-0.388462\pi\)
0.939234 0.343279i \(-0.111538\pi\)
\(314\) 6.78577 + 13.8377i 0.382943 + 0.780909i
\(315\) 0 0
\(316\) −23.3469 + 2.96801i −1.31337 + 0.166963i
\(317\) −0.135667 + 0.327529i −0.00761982 + 0.0183959i −0.927644 0.373467i \(-0.878169\pi\)
0.920024 + 0.391862i \(0.128169\pi\)
\(318\) 0 0
\(319\) 5.48407 0.307049
\(320\) 5.62050 + 5.77267i 0.314195 + 0.322702i
\(321\) 0 0
\(322\) 9.91427 11.2544i 0.552501 0.627185i
\(323\) 10.7600 25.9769i 0.598701 1.44539i
\(324\) 0 0
\(325\) 22.4987 9.31927i 1.24800 0.516940i
\(326\) −3.73429 7.61507i −0.206823 0.421760i
\(327\) 0 0
\(328\) −4.54445 23.6716i −0.250925 1.30704i
\(329\) −6.27531 6.27531i −0.345969 0.345969i
\(330\) 0 0
\(331\) −0.599578 1.44751i −0.0329558 0.0795622i 0.906545 0.422110i \(-0.138710\pi\)
−0.939501 + 0.342547i \(0.888710\pi\)
\(332\) −3.44995 + 12.6499i −0.189341 + 0.694252i
\(333\) 0 0
\(334\) −0.786835 12.4286i −0.0430537 0.680064i
\(335\) 9.92741i 0.542393i
\(336\) 0 0
\(337\) 9.16524i 0.499262i 0.968341 + 0.249631i \(0.0803094\pi\)
−0.968341 + 0.249631i \(0.919691\pi\)
\(338\) −34.3406 + 2.17404i −1.86788 + 0.118252i
\(339\) 0 0
\(340\) 13.4948 7.71134i 0.731859 0.418206i
\(341\) −4.56448 11.0196i −0.247180 0.596746i
\(342\) 0 0
\(343\) −11.4858 11.4858i −0.620173 0.620173i
\(344\) −5.04476 + 24.5053i −0.271995 + 1.32124i
\(345\) 0 0
\(346\) 1.32466 0.649588i 0.0712141 0.0349221i
\(347\) 0.809488 0.335301i 0.0434556 0.0179999i −0.360850 0.932624i \(-0.617513\pi\)
0.404305 + 0.914624i \(0.367513\pi\)
\(348\) 0 0
\(349\) 1.88249 4.54472i 0.100767 0.243273i −0.865454 0.500989i \(-0.832970\pi\)
0.966221 + 0.257716i \(0.0829697\pi\)
\(350\) 5.61367 + 4.94521i 0.300063 + 0.264333i
\(351\) 0 0
\(352\) −12.4722 0.956990i −0.664773 0.0510078i
\(353\) 6.05956 0.322518 0.161259 0.986912i \(-0.448445\pi\)
0.161259 + 0.986912i \(0.448445\pi\)
\(354\) 0 0
\(355\) −1.06476 + 2.57057i −0.0565118 + 0.136432i
\(356\) 12.0052 + 9.29714i 0.636275 + 0.492747i
\(357\) 0 0
\(358\) 13.5957 6.66706i 0.718553 0.352365i
\(359\) 11.1337 11.1337i 0.587616 0.587616i −0.349369 0.936985i \(-0.613604\pi\)
0.936985 + 0.349369i \(0.113604\pi\)
\(360\) 0 0
\(361\) −4.04659 4.04659i −0.212978 0.212978i
\(362\) −4.60395 1.57427i −0.241978 0.0827418i
\(363\) 0 0
\(364\) −8.04671 14.0817i −0.421762 0.738083i
\(365\) −11.2975 4.67956i −0.591336 0.244939i
\(366\) 0 0
\(367\) 33.7822i 1.76341i 0.471797 + 0.881707i \(0.343606\pi\)
−0.471797 + 0.881707i \(0.656394\pi\)
\(368\) −27.5371 16.2272i −1.43547 0.845900i
\(369\) 0 0
\(370\) −0.391113 6.17792i −0.0203330 0.321175i
\(371\) −1.88874 0.782343i −0.0980586 0.0406172i
\(372\) 0 0
\(373\) 0.132294 + 0.319386i 0.00684991 + 0.0165372i 0.927267 0.374400i \(-0.122151\pi\)
−0.920418 + 0.390937i \(0.872151\pi\)
\(374\) −7.80753 + 22.8331i −0.403718 + 1.18067i
\(375\) 0 0
\(376\) −10.6119 + 15.6545i −0.547268 + 0.807322i
\(377\) 10.7147 10.7147i 0.551834 0.551834i
\(378\) 0 0
\(379\) 0.705525 0.292238i 0.0362404 0.0150112i −0.364490 0.931207i \(-0.618757\pi\)
0.400730 + 0.916196i \(0.368757\pi\)
\(380\) 0.925584 + 7.28083i 0.0474815 + 0.373499i
\(381\) 0 0
\(382\) −20.4265 + 23.1876i −1.04511 + 1.18638i
\(383\) 0.0618011 0.00315789 0.00157894 0.999999i \(-0.499497\pi\)
0.00157894 + 0.999999i \(0.499497\pi\)
\(384\) 0 0
\(385\) 2.95578 0.150640
\(386\) 13.5817 15.4176i 0.691289 0.784733i
\(387\) 0 0
\(388\) 2.09624 + 16.4894i 0.106420 + 0.837125i
\(389\) 22.0157 9.11918i 1.11624 0.462361i 0.253156 0.967425i \(-0.418531\pi\)
0.863082 + 0.505064i \(0.168531\pi\)
\(390\) 0 0
\(391\) −43.6000 + 43.6000i −2.20494 + 2.20494i
\(392\) −8.31371 + 12.2643i −0.419906 + 0.619438i
\(393\) 0 0
\(394\) −7.88307 + 23.0541i −0.397143 + 1.16145i
\(395\) −4.53523 10.9490i −0.228192 0.550904i
\(396\) 0 0
\(397\) 2.50388 + 1.03714i 0.125666 + 0.0520525i 0.444630 0.895714i \(-0.353335\pi\)
−0.318964 + 0.947767i \(0.603335\pi\)
\(398\) 1.56613 + 24.7381i 0.0785028 + 1.24001i
\(399\) 0 0
\(400\) 8.09406 13.7354i 0.404703 0.686771i
\(401\) 14.8862i 0.743380i −0.928357 0.371690i \(-0.878778\pi\)
0.928357 0.371690i \(-0.121222\pi\)
\(402\) 0 0
\(403\) −30.4479 12.6119i −1.51672 0.628246i
\(404\) −3.45789 6.05129i −0.172036 0.301063i
\(405\) 0 0
\(406\) 4.40465 + 1.50612i 0.218599 + 0.0747475i
\(407\) 6.79590 + 6.79590i 0.336860 + 0.336860i
\(408\) 0 0
\(409\) 12.5375 12.5375i 0.619938 0.619938i −0.325578 0.945515i \(-0.605559\pi\)
0.945515 + 0.325578i \(0.105559\pi\)
\(410\) 10.8978 5.34409i 0.538206 0.263926i
\(411\) 0 0
\(412\) −0.767802 0.594604i −0.0378269 0.0292941i
\(413\) 3.96606 9.57492i 0.195157 0.471151i
\(414\) 0 0
\(415\) −6.60257 −0.324107
\(416\) −26.2378 + 22.4983i −1.28641 + 1.10307i
\(417\) 0 0
\(418\) −8.55046 7.53229i −0.418217 0.368416i
\(419\) −15.1946 + 36.6829i −0.742303 + 1.79208i −0.146060 + 0.989276i \(0.546659\pi\)
−0.596244 + 0.802803i \(0.703341\pi\)
\(420\) 0 0
\(421\) −11.0470 + 4.57581i −0.538397 + 0.223011i −0.635276 0.772285i \(-0.719114\pi\)
0.0968796 + 0.995296i \(0.469114\pi\)
\(422\) 14.6778 7.19770i 0.714502 0.350378i
\(423\) 0 0
\(424\) −0.878456 + 4.26717i −0.0426616 + 0.207232i
\(425\) −21.7475 21.7475i −1.05491 1.05491i
\(426\) 0 0
\(427\) −4.05703 9.79454i −0.196333 0.473991i
\(428\) 8.46428 4.83674i 0.409137 0.233793i
\(429\) 0 0
\(430\) −12.5734 + 0.796001i −0.606343 + 0.0383866i
\(431\) 27.7654i 1.33741i −0.743527 0.668706i \(-0.766848\pi\)
0.743527 0.668706i \(-0.233152\pi\)
\(432\) 0 0
\(433\) 5.43486i 0.261183i 0.991436 + 0.130591i \(0.0416876\pi\)
−0.991436 + 0.130591i \(0.958312\pi\)
\(434\) −0.639681 10.1042i −0.0307057 0.485018i
\(435\) 0 0
\(436\) −3.84100 + 14.0837i −0.183950 + 0.674487i
\(437\) −11.1424 26.9001i −0.533012 1.28680i
\(438\) 0 0
\(439\) −7.46141 7.46141i −0.356114 0.356114i 0.506265 0.862378i \(-0.331026\pi\)
−0.862378 + 0.506265i \(0.831026\pi\)
\(440\) −1.18758 6.18598i −0.0566157 0.294905i
\(441\) 0 0
\(442\) 29.3567 + 59.8652i 1.39636 + 2.84749i
\(443\) 33.3044 13.7951i 1.58234 0.655427i 0.593558 0.804791i \(-0.297723\pi\)
0.988782 + 0.149365i \(0.0477229\pi\)
\(444\) 0 0
\(445\) −2.92605 + 7.06411i −0.138708 + 0.334871i
\(446\) −11.2687 + 12.7920i −0.533591 + 0.605718i
\(447\) 0 0
\(448\) −9.75453 4.19395i −0.460858 0.198145i
\(449\) −7.32090 −0.345494 −0.172747 0.984966i \(-0.555264\pi\)
−0.172747 + 0.984966i \(0.555264\pi\)
\(450\) 0 0
\(451\) −7.21149 + 17.4101i −0.339576 + 0.819809i
\(452\) −4.30715 + 0.547551i −0.202591 + 0.0257546i
\(453\) 0 0
\(454\) 6.06320 + 12.3643i 0.284560 + 0.580283i
\(455\) 5.77494 5.77494i 0.270733 0.270733i
\(456\) 0 0
\(457\) −13.2198 13.2198i −0.618398 0.618398i 0.326723 0.945120i \(-0.394056\pi\)
−0.945120 + 0.326723i \(0.894056\pi\)
\(458\) 13.1805 38.5463i 0.615883 1.80115i
\(459\) 0 0
\(460\) 4.23487 15.5279i 0.197452 0.723992i
\(461\) −3.91240 1.62057i −0.182219 0.0754774i 0.289709 0.957115i \(-0.406442\pi\)
−0.471927 + 0.881637i \(0.656442\pi\)
\(462\) 0 0
\(463\) 19.9447i 0.926910i −0.886121 0.463455i \(-0.846610\pi\)
0.886121 0.463455i \(-0.153390\pi\)
\(464\) 1.38236 9.82337i 0.0641744 0.456038i
\(465\) 0 0
\(466\) 22.7176 1.43821i 1.05237 0.0666238i
\(467\) −23.4125 9.69779i −1.08340 0.448760i −0.231701 0.972787i \(-0.574429\pi\)
−0.851702 + 0.524027i \(0.824429\pi\)
\(468\) 0 0
\(469\) 5.00665 + 12.0871i 0.231185 + 0.558131i
\(470\) −9.01120 3.08128i −0.415656 0.142129i
\(471\) 0 0
\(472\) −21.6323 4.45330i −0.995707 0.204980i
\(473\) 13.8311 13.8311i 0.635956 0.635956i
\(474\) 0 0
\(475\) 13.4177 5.55778i 0.615645 0.255008i
\(476\) −12.5416 + 16.1947i −0.574842 + 0.742283i
\(477\) 0 0
\(478\) −12.8585 11.3273i −0.588133 0.518099i
\(479\) −15.7464 −0.719470 −0.359735 0.933054i \(-0.617133\pi\)
−0.359735 + 0.933054i \(0.617133\pi\)
\(480\) 0 0
\(481\) 26.5554 1.21082
\(482\) −1.39654 1.23024i −0.0636104 0.0560358i
\(483\) 0 0
\(484\) −9.66192 7.48243i −0.439178 0.340110i
\(485\) −7.73305 + 3.20313i −0.351140 + 0.145447i
\(486\) 0 0
\(487\) −21.8941 + 21.8941i −0.992116 + 0.992116i −0.999969 0.00785353i \(-0.997500\pi\)
0.00785353 + 0.999969i \(0.497500\pi\)
\(488\) −18.8684 + 12.4260i −0.854131 + 0.562498i
\(489\) 0 0
\(490\) −7.05965 2.41397i −0.318923 0.109052i
\(491\) 3.16126 + 7.63197i 0.142666 + 0.344426i 0.979020 0.203763i \(-0.0653173\pi\)
−0.836354 + 0.548189i \(0.815317\pi\)
\(492\) 0 0
\(493\) −17.6804 7.32345i −0.796284 0.329832i
\(494\) −31.4222 + 1.98928i −1.41375 + 0.0895021i
\(495\) 0 0
\(496\) −20.8895 + 5.39845i −0.937967 + 0.242398i
\(497\) 3.66678i 0.164478i
\(498\) 0 0
\(499\) −23.1527 9.59016i −1.03646 0.429314i −0.201418 0.979505i \(-0.564555\pi\)
−0.835039 + 0.550191i \(0.814555\pi\)
\(500\) 17.4615 + 4.76222i 0.780903 + 0.212973i
\(501\) 0 0
\(502\) 4.77212 13.9561i 0.212990 0.622891i
\(503\) 5.59362 + 5.59362i 0.249407 + 0.249407i 0.820727 0.571320i \(-0.193569\pi\)
−0.571320 + 0.820727i \(0.693569\pi\)
\(504\) 0 0
\(505\) 2.48165 2.48165i 0.110432 0.110432i
\(506\) 11.0023 + 22.4362i 0.489111 + 0.997410i
\(507\) 0 0
\(508\) 0.251051 + 1.97482i 0.0111386 + 0.0876183i
\(509\) −13.2327 + 31.9466i −0.586530 + 1.41601i 0.300270 + 0.953854i \(0.402923\pi\)
−0.886800 + 0.462154i \(0.847077\pi\)
\(510\) 0 0
\(511\) 16.1152 0.712896
\(512\) −4.85807 + 22.0998i −0.214698 + 0.976680i
\(513\) 0 0
\(514\) 7.97435 9.05227i 0.351733 0.399279i
\(515\) 0.187137 0.451790i 0.00824626 0.0199082i
\(516\) 0 0
\(517\) 13.6603 5.65829i 0.600780 0.248851i
\(518\) 3.59188 + 7.32467i 0.157818 + 0.321828i
\(519\) 0 0
\(520\) −14.4063 9.76577i −0.631759 0.428257i
\(521\) 15.3045 + 15.3045i 0.670500 + 0.670500i 0.957831 0.287331i \(-0.0927680\pi\)
−0.287331 + 0.957831i \(0.592768\pi\)
\(522\) 0 0
\(523\) 11.5084 + 27.7838i 0.503229 + 1.21490i 0.947716 + 0.319116i \(0.103386\pi\)
−0.444487 + 0.895785i \(0.646614\pi\)
\(524\) −20.6793 5.63979i −0.903379 0.246375i
\(525\) 0 0
\(526\) −0.825274 13.0358i −0.0359837 0.568388i
\(527\) 41.6222i 1.81309i
\(528\) 0 0
\(529\) 40.8509i 1.77613i
\(530\) −2.18944 + 0.138610i −0.0951031 + 0.00602081i
\(531\) 0 0
\(532\) −4.79885 8.39798i −0.208057 0.364099i
\(533\) 19.9258 + 48.1051i 0.863082 + 2.08367i
\(534\) 0 0
\(535\) 3.47122 + 3.47122i 0.150074 + 0.150074i
\(536\) 23.2848 15.3345i 1.00575 0.662350i
\(537\) 0 0
\(538\) −31.2980 + 15.3479i −1.34935 + 0.661697i
\(539\) 10.7019 4.43288i 0.460964 0.190938i
\(540\) 0 0
\(541\) −3.65267 + 8.81833i −0.157041 + 0.379130i −0.982743 0.184976i \(-0.940779\pi\)
0.825702 + 0.564106i \(0.190779\pi\)
\(542\) 32.2767 + 28.4332i 1.38640 + 1.22131i
\(543\) 0 0
\(544\) 38.9320 + 19.7408i 1.66919 + 0.846379i
\(545\) −7.35096 −0.314880
\(546\) 0 0
\(547\) −6.85086 + 16.5394i −0.292921 + 0.707175i 0.707079 + 0.707135i \(0.250013\pi\)
−1.00000 3.99033e-5i \(0.999987\pi\)
\(548\) 22.1239 28.5682i 0.945085 1.22037i
\(549\) 0 0
\(550\) −11.1911 + 5.48791i −0.477190 + 0.234005i
\(551\) 6.38996 6.38996i 0.272221 0.272221i
\(552\) 0 0
\(553\) 11.0437 + 11.0437i 0.469627 + 0.469627i
\(554\) −41.7902 14.2897i −1.77550 0.607111i
\(555\) 0 0
\(556\) −4.99300 + 2.85315i −0.211750 + 0.121000i
\(557\) 3.33392 + 1.38096i 0.141263 + 0.0585130i 0.452195 0.891919i \(-0.350641\pi\)
−0.310932 + 0.950432i \(0.600641\pi\)
\(558\) 0 0
\(559\) 54.0460i 2.28590i
\(560\) 0.745057 5.29455i 0.0314844 0.223736i
\(561\) 0 0
\(562\) −2.94575 46.5303i −0.124259 1.96276i
\(563\) −15.8181 6.55208i −0.666654 0.276137i 0.0235814 0.999722i \(-0.492493\pi\)
−0.690236 + 0.723585i \(0.742493\pi\)
\(564\) 0 0
\(565\) −0.836679 2.01992i −0.0351993 0.0849787i
\(566\) −11.2653 + 32.9453i −0.473515 + 1.38480i
\(567\) 0 0
\(568\) −7.67399 + 1.47325i −0.321994 + 0.0618161i
\(569\) −14.2778 + 14.2778i −0.598558 + 0.598558i −0.939929 0.341371i \(-0.889109\pi\)
0.341371 + 0.939929i \(0.389109\pi\)
\(570\) 0 0
\(571\) −20.4753 + 8.48116i −0.856866 + 0.354926i −0.767481 0.641071i \(-0.778490\pi\)
−0.0893852 + 0.995997i \(0.528490\pi\)
\(572\) 26.8058 3.40771i 1.12081 0.142484i
\(573\) 0 0
\(574\) −10.5735 + 12.0028i −0.441329 + 0.500985i
\(575\) −31.8486 −1.32818
\(576\) 0 0
\(577\) −32.9749 −1.37276 −0.686382 0.727241i \(-0.740802\pi\)
−0.686382 + 0.727241i \(0.740802\pi\)
\(578\) 39.7706 45.1466i 1.65424 1.87785i
\(579\) 0 0
\(580\) 4.95548 0.629970i 0.205765 0.0261581i
\(581\) 8.03895 3.32984i 0.333512 0.138145i
\(582\) 0 0
\(583\) 2.40845 2.40845i 0.0997478 0.0997478i
\(584\) −6.47482 33.7266i −0.267930 1.39562i
\(585\) 0 0
\(586\) −5.26239 + 15.3899i −0.217387 + 0.635749i
\(587\) −6.25478 15.1004i −0.258162 0.623259i 0.740655 0.671886i \(-0.234516\pi\)
−0.998817 + 0.0486267i \(0.984516\pi\)
\(588\) 0 0
\(589\) −18.1584 7.52144i −0.748202 0.309916i
\(590\) −0.702677 11.0993i −0.0289287 0.456950i
\(591\) 0 0
\(592\) 13.8862 10.4602i 0.570720 0.429910i
\(593\) 2.82225i 0.115896i 0.998320 + 0.0579479i \(0.0184557\pi\)
−0.998320 + 0.0579479i \(0.981544\pi\)
\(594\) 0 0
\(595\) −9.52929 3.94716i −0.390663 0.161818i
\(596\) 1.12398 0.642278i 0.0460402 0.0263087i
\(597\) 0 0
\(598\) 65.3314 + 22.3393i 2.67160 + 0.913524i
\(599\) 4.80895 + 4.80895i 0.196488 + 0.196488i 0.798493 0.602004i \(-0.205631\pi\)
−0.602004 + 0.798493i \(0.705631\pi\)
\(600\) 0 0
\(601\) 1.97562 1.97562i 0.0805873 0.0805873i −0.665664 0.746251i \(-0.731852\pi\)
0.746251 + 0.665664i \(0.231852\pi\)
\(602\) 14.9073 7.31026i 0.607576 0.297944i
\(603\) 0 0
\(604\) 23.4612 30.2950i 0.954624 1.23269i
\(605\) 2.35491 5.68526i 0.0957408 0.231139i
\(606\) 0 0
\(607\) −2.25264 −0.0914320 −0.0457160 0.998954i \(-0.514557\pi\)
−0.0457160 + 0.998954i \(0.514557\pi\)
\(608\) −15.6475 + 13.4174i −0.634592 + 0.544148i
\(609\) 0 0
\(610\) −8.53666 7.52013i −0.345639 0.304481i
\(611\) 15.6342 37.7443i 0.632492 1.52697i
\(612\) 0 0
\(613\) 38.1764 15.8132i 1.54193 0.638688i 0.560095 0.828428i \(-0.310764\pi\)
0.981834 + 0.189740i \(0.0607644\pi\)
\(614\) 4.58239 2.24712i 0.184930 0.0906863i
\(615\) 0 0
\(616\) 4.56568 + 6.93281i 0.183957 + 0.279331i
\(617\) 11.7568 + 11.7568i 0.473312 + 0.473312i 0.902985 0.429673i \(-0.141371\pi\)
−0.429673 + 0.902985i \(0.641371\pi\)
\(618\) 0 0
\(619\) 14.6215 + 35.2995i 0.587689 + 1.41881i 0.885706 + 0.464247i \(0.153675\pi\)
−0.298017 + 0.954561i \(0.596325\pi\)
\(620\) −5.39038 9.43314i −0.216483 0.378844i
\(621\) 0 0
\(622\) −31.5242 + 1.99575i −1.26401 + 0.0800221i
\(623\) 10.0766i 0.403710i
\(624\) 0 0
\(625\) 10.8146i 0.432584i
\(626\) 2.86719 + 45.2893i 0.114596 + 1.81012i
\(627\) 0 0
\(628\) −21.0279 5.73485i −0.839103 0.228846i
\(629\) −12.8344 30.9849i −0.511740 1.23545i
\(630\) 0 0
\(631\) 0.538322 + 0.538322i 0.0214302 + 0.0214302i 0.717741 0.696310i \(-0.245176\pi\)
−0.696310 + 0.717741i \(0.745176\pi\)
\(632\) 18.6756 27.5499i 0.742875 1.09588i
\(633\) 0 0
\(634\) −0.220744 0.450149i −0.00876688 0.0178777i
\(635\) −0.926129 + 0.383615i −0.0367523 + 0.0152233i
\(636\) 0 0
\(637\) 12.2483 29.5701i 0.485296 1.17161i
\(638\) −5.12662 + 5.81961i −0.202965 + 0.230400i
\(639\) 0 0
\(640\) −11.3800 + 0.567973i −0.449835 + 0.0224511i
\(641\) 13.2510 0.523384 0.261692 0.965151i \(-0.415719\pi\)
0.261692 + 0.965151i \(0.415719\pi\)
\(642\) 0 0
\(643\) 4.36388 10.5353i 0.172095 0.415473i −0.814174 0.580621i \(-0.802810\pi\)
0.986269 + 0.165147i \(0.0528100\pi\)
\(644\) 2.67495 + 21.0417i 0.105408 + 0.829160i
\(645\) 0 0
\(646\) 17.5076 + 35.7020i 0.688828 + 1.40468i
\(647\) 0.948610 0.948610i 0.0372937 0.0372937i −0.688214 0.725508i \(-0.741605\pi\)
0.725508 + 0.688214i \(0.241605\pi\)
\(648\) 0 0
\(649\) 12.2096 + 12.2096i 0.479267 + 0.479267i
\(650\) −11.1428 + 32.5871i −0.437056 + 1.27817i
\(651\) 0 0
\(652\) 11.5719 + 3.15596i 0.453190 + 0.123597i
\(653\) 42.6127 + 17.6508i 1.66756 + 0.690727i 0.998617 0.0525829i \(-0.0167454\pi\)
0.668947 + 0.743310i \(0.266745\pi\)
\(654\) 0 0
\(655\) 10.7935i 0.421737i
\(656\) 29.3681 + 17.3061i 1.14663 + 0.675691i
\(657\) 0 0
\(658\) 12.5255 0.792971i 0.488297 0.0309132i
\(659\) 7.85964 + 3.25557i 0.306168 + 0.126819i 0.530477 0.847699i \(-0.322013\pi\)
−0.224310 + 0.974518i \(0.572013\pi\)
\(660\) 0 0
\(661\) −4.31440 10.4159i −0.167811 0.405131i 0.817494 0.575937i \(-0.195363\pi\)
−0.985305 + 0.170806i \(0.945363\pi\)
\(662\) 2.09657 + 0.716898i 0.0814855 + 0.0278630i
\(663\) 0 0
\(664\) −10.1987 15.4864i −0.395788 0.600988i
\(665\) 3.44403 3.44403i 0.133554 0.133554i
\(666\) 0 0
\(667\) −18.3087 + 7.58371i −0.708915 + 0.293642i
\(668\) 13.9246 + 10.7835i 0.538759 + 0.417228i
\(669\) 0 0
\(670\) 10.5348 + 9.28035i 0.406995 + 0.358531i
\(671\) 17.6630 0.681871
\(672\) 0 0
\(673\) −6.74887 −0.260150 −0.130075 0.991504i \(-0.541522\pi\)
−0.130075 + 0.991504i \(0.541522\pi\)
\(674\) −9.72601 8.56785i −0.374632 0.330021i
\(675\) 0 0
\(676\) 29.7952 38.4740i 1.14597 1.47977i
\(677\) −11.8633 + 4.91394i −0.455944 + 0.188858i −0.598822 0.800882i \(-0.704364\pi\)
0.142878 + 0.989740i \(0.454364\pi\)
\(678\) 0 0
\(679\) 7.79995 7.79995i 0.299334 0.299334i
\(680\) −4.43208 + 21.5292i −0.169963 + 0.825607i
\(681\) 0 0
\(682\) 15.9608 + 5.45762i 0.611171 + 0.208983i
\(683\) 14.3773 + 34.7099i 0.550132 + 1.32814i 0.917379 + 0.398014i \(0.130300\pi\)
−0.367247 + 0.930123i \(0.619700\pi\)
\(684\) 0 0
\(685\) 16.8101 + 6.96296i 0.642280 + 0.266041i
\(686\) 22.9256 1.45138i 0.875305 0.0554141i
\(687\) 0 0
\(688\) −21.2887 28.2615i −0.811624 1.07746i
\(689\) 9.41116i 0.358537i
\(690\) 0 0
\(691\) −45.7721 18.9594i −1.74125 0.721250i −0.998673 0.0514917i \(-0.983602\pi\)
−0.742579 0.669759i \(-0.766398\pi\)
\(692\) −0.548986 + 2.01296i −0.0208693 + 0.0765211i
\(693\) 0 0
\(694\) −0.400910 + 1.17246i −0.0152183 + 0.0445060i
\(695\) −2.04764 2.04764i −0.0776713 0.0776713i
\(696\) 0 0
\(697\) 46.4990 46.4990i 1.76128 1.76128i
\(698\) 3.06300 + 6.24616i 0.115936 + 0.236421i
\(699\) 0 0
\(700\) −10.4956 + 1.33426i −0.396695 + 0.0504302i
\(701\) 13.2680 32.0317i 0.501124 1.20982i −0.447748 0.894160i \(-0.647774\pi\)
0.948872 0.315661i \(-0.102226\pi\)
\(702\) 0 0
\(703\) 15.8370 0.597302
\(704\) 12.6749 12.3407i 0.477702 0.465109i
\(705\) 0 0
\(706\) −5.66459 + 6.43030i −0.213190 + 0.242008i
\(707\) −1.76997 + 4.27309i −0.0665666 + 0.160706i
\(708\) 0 0
\(709\) 22.1634 9.18039i 0.832365 0.344777i 0.0745263 0.997219i \(-0.476256\pi\)
0.757838 + 0.652442i \(0.226256\pi\)
\(710\) −1.73248 3.53293i −0.0650189 0.132588i
\(711\) 0 0
\(712\) −21.0887 + 4.04860i −0.790332 + 0.151728i
\(713\) 30.4772 + 30.4772i 1.14138 + 1.14138i
\(714\) 0 0
\(715\) 5.20712 + 12.5711i 0.194735 + 0.470132i
\(716\) −5.63453 + 20.6600i −0.210572 + 0.772101i
\(717\) 0 0
\(718\) 1.40690 + 22.2230i 0.0525050 + 0.829354i
\(719\) 30.9298i 1.15349i 0.816925 + 0.576744i \(0.195677\pi\)
−0.816925 + 0.576744i \(0.804323\pi\)
\(720\) 0 0
\(721\) 0.644454i 0.0240007i
\(722\) 8.07700 0.511341i 0.300595 0.0190301i
\(723\) 0 0
\(724\) 5.97446 3.41398i 0.222039 0.126880i
\(725\) −3.78273 9.13232i −0.140487 0.339166i
\(726\) 0 0
\(727\) −1.17119 1.17119i −0.0434369 0.0434369i 0.685055 0.728492i \(-0.259778\pi\)
−0.728492 + 0.685055i \(0.759778\pi\)
\(728\) 22.4655 + 4.62484i 0.832628 + 0.171408i
\(729\) 0 0
\(730\) 15.5270 7.61413i 0.574679 0.281812i
\(731\) −63.0611 + 26.1207i −2.33240 + 0.966111i
\(732\) 0 0
\(733\) 2.77936 6.70998i 0.102658 0.247839i −0.864202 0.503145i \(-0.832176\pi\)
0.966860 + 0.255306i \(0.0821762\pi\)
\(734\) −35.8491 31.5803i −1.32321 1.16565i
\(735\) 0 0
\(736\) 42.9623 14.0525i 1.58361 0.517980i
\(737\) −21.7973 −0.802913
\(738\) 0 0
\(739\) 1.42163 3.43212i 0.0522956 0.126253i −0.895573 0.444915i \(-0.853234\pi\)
0.947868 + 0.318663i \(0.103234\pi\)
\(740\) 6.92153 + 5.36020i 0.254440 + 0.197045i
\(741\) 0 0
\(742\) 2.59584 1.27295i 0.0952964 0.0467316i
\(743\) −15.7962 + 15.7962i −0.579505 + 0.579505i −0.934767 0.355262i \(-0.884392\pi\)
0.355262 + 0.934767i \(0.384392\pi\)
\(744\) 0 0
\(745\) 0.460948 + 0.460948i 0.0168878 + 0.0168878i
\(746\) −0.462598 0.158180i −0.0169369 0.00579138i
\(747\) 0 0
\(748\) −16.9315 29.6301i −0.619078 1.08338i
\(749\) −5.97701 2.47576i −0.218395 0.0904622i
\(750\) 0 0
\(751\) 13.5578i 0.494731i 0.968922 + 0.247366i \(0.0795649\pi\)
−0.968922 + 0.247366i \(0.920435\pi\)
\(752\) −6.69211 25.8954i −0.244036 0.944308i
\(753\) 0 0
\(754\) 1.35394 + 21.3865i 0.0493077 + 0.778851i
\(755\) 17.8262 + 7.38386i 0.648762 + 0.268726i
\(756\) 0 0
\(757\) 16.6598 + 40.2204i 0.605512 + 1.46184i 0.867834 + 0.496855i \(0.165512\pi\)
−0.262322 + 0.964980i \(0.584488\pi\)
\(758\) −0.349421 + 1.02188i −0.0126915 + 0.0371164i
\(759\) 0 0
\(760\) −8.59156 5.82406i −0.311649 0.211261i
\(761\) −4.92005 + 4.92005i −0.178352 + 0.178352i −0.790637 0.612285i \(-0.790250\pi\)
0.612285 + 0.790637i \(0.290250\pi\)
\(762\) 0 0
\(763\) 8.95015 3.70727i 0.324017 0.134212i
\(764\) −5.51123 43.3525i −0.199389 1.56844i
\(765\) 0 0
\(766\) −0.0577729 + 0.0655823i −0.00208742 + 0.00236958i
\(767\) 47.7096 1.72269
\(768\) 0 0
\(769\) 30.1958 1.08889 0.544444 0.838797i \(-0.316741\pi\)
0.544444 + 0.838797i \(0.316741\pi\)
\(770\) −2.76312 + 3.13662i −0.0995760 + 0.113036i
\(771\) 0 0
\(772\) 3.66445 + 28.8253i 0.131886 + 1.03744i
\(773\) −28.5054 + 11.8073i −1.02527 + 0.424679i −0.831002 0.556270i \(-0.812232\pi\)
−0.194265 + 0.980949i \(0.562232\pi\)
\(774\) 0 0
\(775\) −15.2019 + 15.2019i −0.546070 + 0.546070i
\(776\) −19.4579 13.1902i −0.698499 0.473500i
\(777\) 0 0
\(778\) −10.9035 + 31.8875i −0.390911 + 1.14322i
\(779\) 11.8832 + 28.6887i 0.425761 + 1.02788i
\(780\) 0 0
\(781\) 5.64411 + 2.33787i 0.201962 + 0.0836554i
\(782\) −5.50945 87.0257i −0.197017 3.11203i
\(783\) 0 0
\(784\) −5.24281 20.2872i −0.187243 0.724544i
\(785\) 10.9754i 0.391730i
\(786\) 0 0
\(787\) 12.1718 + 5.04174i 0.433879 + 0.179719i 0.588923 0.808189i \(-0.299552\pi\)
−0.155044 + 0.987908i \(0.549552\pi\)
\(788\) −17.0953 29.9168i −0.608996 1.06574i
\(789\) 0 0
\(790\) 15.8585 + 5.42264i 0.564221 + 0.192929i
\(791\) 2.03740 + 2.03740i 0.0724414 + 0.0724414i
\(792\) 0 0
\(793\) 34.5096 34.5096i 1.22547 1.22547i
\(794\) −3.44127 + 1.68753i −0.122126 + 0.0598883i
\(795\) 0 0
\(796\) −27.7157 21.4637i −0.982357 0.760761i
\(797\) −1.91098 + 4.61351i −0.0676903 + 0.163419i −0.954104 0.299474i \(-0.903189\pi\)
0.886414 + 0.462893i \(0.153189\pi\)
\(798\) 0 0
\(799\) −51.5963 −1.82535
\(800\) 7.00932 + 21.4294i 0.247817 + 0.757645i
\(801\) 0 0
\(802\) 15.7970 + 13.9159i 0.557810 + 0.491387i
\(803\) −10.2748 + 24.8054i −0.362588 + 0.875365i
\(804\) 0 0
\(805\) −9.86793 + 4.08743i −0.347799 + 0.144063i
\(806\) 41.8469 20.5209i 1.47400 0.722819i
\(807\) 0 0
\(808\) 9.65404 + 1.98742i 0.339628 + 0.0699170i
\(809\) −18.3954 18.3954i −0.646746 0.646746i 0.305459 0.952205i \(-0.401190\pi\)
−0.952205 + 0.305459i \(0.901190\pi\)
\(810\) 0 0
\(811\) 17.3184 + 41.8102i 0.608130 + 1.46816i 0.865031 + 0.501718i \(0.167299\pi\)
−0.256901 + 0.966438i \(0.582701\pi\)
\(812\) −5.71583 + 3.26619i −0.200586 + 0.114621i
\(813\) 0 0
\(814\) −13.5646 + 0.858755i −0.475441 + 0.0300993i
\(815\) 6.03992i 0.211569i
\(816\) 0 0
\(817\) 32.2317i 1.12764i
\(818\) 1.58428 + 25.0248i 0.0553930 + 0.874973i
\(819\) 0 0
\(820\) −4.51645 + 16.5604i −0.157721 + 0.578313i
\(821\) 8.21305 + 19.8281i 0.286638 + 0.692004i 0.999961 0.00883070i \(-0.00281093\pi\)
−0.713323 + 0.700835i \(0.752811\pi\)
\(822\) 0 0
\(823\) 22.0587 + 22.0587i 0.768918 + 0.768918i 0.977916 0.208998i \(-0.0670202\pi\)
−0.208998 + 0.977916i \(0.567020\pi\)
\(824\) 1.34874 0.258931i 0.0469856 0.00902027i
\(825\) 0 0
\(826\) 6.45319 + 13.1595i 0.224535 + 0.457879i
\(827\) −5.61721 + 2.32672i −0.195329 + 0.0809081i −0.478204 0.878249i \(-0.658712\pi\)
0.282875 + 0.959157i \(0.408712\pi\)
\(828\) 0 0
\(829\) 15.9329 38.4654i 0.553373 1.33596i −0.361558 0.932349i \(-0.617755\pi\)
0.914931 0.403610i \(-0.132245\pi\)
\(830\) 6.17221 7.00654i 0.214241 0.243201i
\(831\) 0 0
\(832\) 0.652794 48.8750i 0.0226315 1.69443i
\(833\) −40.4221 −1.40054
\(834\) 0 0
\(835\) −3.39386 + 8.19351i −0.117449 + 0.283548i
\(836\) 15.9863 2.03227i 0.552897 0.0702877i
\(837\) 0 0
\(838\) −24.7232 50.4162i −0.854047 1.74160i
\(839\) −19.8239 + 19.8239i −0.684399 + 0.684399i −0.960988 0.276590i \(-0.910796\pi\)
0.276590 + 0.960988i \(0.410796\pi\)
\(840\) 0 0
\(841\) 16.1570 + 16.1570i 0.557137 + 0.557137i
\(842\) 5.47116 16.0004i 0.188549 0.551411i
\(843\) 0 0
\(844\) −6.08299 + 22.3044i −0.209385 + 0.767747i
\(845\) 22.6389 + 9.37733i 0.778801 + 0.322590i
\(846\) 0 0
\(847\) 8.10973i 0.278654i
\(848\) −3.70705 4.92124i −0.127301 0.168996i
\(849\) 0 0
\(850\) 43.4081 2.74810i 1.48889 0.0942589i
\(851\) −32.0861 13.2905i −1.09990 0.455592i
\(852\) 0 0
\(853\) −0.282320 0.681580i −0.00966645 0.0233369i 0.918973 0.394321i \(-0.129020\pi\)
−0.928639 + 0.370984i \(0.879020\pi\)
\(854\) 14.1864 + 4.85088i 0.485449 + 0.165994i
\(855\) 0 0
\(856\) −2.77991 + 13.5036i −0.0950154 + 0.461545i
\(857\) −28.6025 + 28.6025i −0.977043 + 0.977043i −0.999742 0.0226993i \(-0.992774\pi\)
0.0226993 + 0.999742i \(0.492774\pi\)
\(858\) 0 0
\(859\) 40.1822 16.6440i 1.37100 0.567886i 0.428939 0.903333i \(-0.358887\pi\)
0.942059 + 0.335447i \(0.108887\pi\)
\(860\) 10.9092 14.0868i 0.372000 0.480356i
\(861\) 0 0
\(862\) 29.4642 + 25.9557i 1.00355 + 0.884053i
\(863\) −24.3873 −0.830152 −0.415076 0.909787i \(-0.636245\pi\)
−0.415076 + 0.909787i \(0.636245\pi\)
\(864\) 0 0
\(865\) −1.05066 −0.0357234
\(866\) −5.76738 5.08062i −0.195984 0.172646i
\(867\) 0 0
\(868\) 11.3204 + 8.76681i 0.384240 + 0.297565i
\(869\) −24.0404 + 9.95785i −0.815514 + 0.337797i
\(870\) 0 0
\(871\) −42.5871 + 42.5871i −1.44301 + 1.44301i
\(872\) −11.3548 17.2417i −0.384521 0.583879i
\(873\) 0 0
\(874\) 38.9620 + 13.3226i 1.31791 + 0.450644i
\(875\) −4.59642 11.0968i −0.155388 0.375139i
\(876\) 0 0
\(877\) −27.2085 11.2701i −0.918765 0.380565i −0.127360 0.991857i \(-0.540650\pi\)
−0.791405 + 0.611292i \(0.790650\pi\)
\(878\) 14.8930 0.942851i 0.502615 0.0318197i
\(879\) 0 0
\(880\) 7.67463 + 4.52254i 0.258712 + 0.152455i
\(881\) 39.5282i 1.33174i 0.746069 + 0.665869i \(0.231939\pi\)
−0.746069 + 0.665869i \(0.768061\pi\)
\(882\) 0 0
\(883\) −4.08879 1.69363i −0.137599 0.0569952i 0.312822 0.949812i \(-0.398726\pi\)
−0.450420 + 0.892817i \(0.648726\pi\)
\(884\) −90.9712 24.8103i −3.05969 0.834459i
\(885\) 0 0
\(886\) −16.4945 + 48.2381i −0.554142 + 1.62059i
\(887\) −8.25045 8.25045i −0.277023 0.277023i 0.554896 0.831919i \(-0.312758\pi\)
−0.831919 + 0.554896i \(0.812758\pi\)
\(888\) 0 0
\(889\) 0.934141 0.934141i 0.0313301 0.0313301i
\(890\) −4.76099 9.70875i −0.159589 0.325438i
\(891\) 0 0
\(892\) −3.04040 23.9164i −0.101800 0.800781i
\(893\) 9.32384 22.5097i 0.312011 0.753260i
\(894\) 0 0
\(895\) −10.7834 −0.360451
\(896\) 13.5693 6.43077i 0.453318 0.214837i
\(897\) 0 0
\(898\) 6.84372 7.76882i 0.228378 0.259249i
\(899\) −5.11924 + 12.3589i −0.170736 + 0.412193i
\(900\) 0 0
\(901\) −10.9810 + 4.54847i −0.365829 + 0.151532i
\(902\) −11.7338 23.9280i −0.390694 0.796716i
\(903\) 0 0
\(904\) 3.44536 5.08254i 0.114591 0.169043i
\(905\) 2.45014 + 2.45014i 0.0814453 + 0.0814453i
\(906\) 0 0
\(907\) −19.7593 47.7031i −0.656096 1.58396i −0.803784 0.594921i \(-0.797183\pi\)
0.147688 0.989034i \(-0.452817\pi\)
\(908\) −18.7888 5.12419i −0.623527 0.170052i
\(909\) 0 0
\(910\) 0.729743 + 11.5268i 0.0241907 + 0.382110i
\(911\) 51.4196i 1.70361i −0.523862 0.851803i \(-0.675509\pi\)
0.523862 0.851803i \(-0.324491\pi\)
\(912\) 0 0
\(913\) 14.4970i 0.479782i
\(914\) 26.3868 1.67051i 0.872799 0.0552554i
\(915\) 0 0
\(916\) 28.5833 + 50.0208i 0.944420 + 1.65273i
\(917\) 5.44344 + 13.1416i 0.179758 + 0.433975i
\(918\) 0 0
\(919\) 15.9328 + 15.9328i 0.525575 + 0.525575i 0.919250 0.393675i \(-0.128796\pi\)
−0.393675 + 0.919250i \(0.628796\pi\)
\(920\) 12.5191 + 19.0098i 0.412743 + 0.626733i
\(921\) 0 0
\(922\) 5.37711 2.63683i 0.177086 0.0868395i
\(923\) 15.5950 6.45967i 0.513317 0.212623i
\(924\) 0 0
\(925\) 6.62925 16.0044i 0.217968 0.526222i
\(926\) 21.1650 + 18.6447i 0.695526 + 0.612704i
\(927\) 0 0
\(928\) 9.13214 + 10.6500i 0.299777 + 0.349604i
\(929\) 25.5885 0.839532 0.419766 0.907632i \(-0.362112\pi\)
0.419766 + 0.907632i \(0.362112\pi\)
\(930\) 0 0
\(931\) 7.30458 17.6348i 0.239398 0.577958i
\(932\) −19.7106 + 25.4520i −0.645643 + 0.833707i
\(933\) 0 0
\(934\) 32.1776 15.7793i 1.05288 0.516315i
\(935\) 12.1514 12.1514i 0.397392 0.397392i
\(936\) 0 0
\(937\) 6.19246 + 6.19246i 0.202299 + 0.202299i 0.800984 0.598685i \(-0.204310\pi\)
−0.598685 + 0.800984i \(0.704310\pi\)
\(938\) −17.5070 5.98631i −0.571623 0.195460i
\(939\) 0 0
\(940\) 11.6937 6.68210i 0.381405 0.217946i
\(941\) −22.7706 9.43189i −0.742300 0.307471i −0.0207048 0.999786i \(-0.506591\pi\)
−0.721596 + 0.692315i \(0.756591\pi\)
\(942\) 0 0
\(943\) 68.0964i 2.21753i
\(944\) 24.9481 18.7928i 0.811990 0.611653i
\(945\) 0 0
\(946\) 1.74775 + 27.6070i 0.0568243 + 0.897581i
\(947\) 35.7353 + 14.8021i 1.16124 + 0.481002i 0.878288 0.478131i \(-0.158686\pi\)
0.282954 + 0.959134i \(0.408686\pi\)
\(948\) 0 0
\(949\) 28.3898 + 68.5390i 0.921571 + 2.22487i
\(950\) −6.64528 + 19.4341i −0.215601 + 0.630526i
\(951\) 0 0
\(952\) −5.46144 28.4481i −0.177006 0.922007i
\(953\) 2.65738 2.65738i 0.0860809 0.0860809i −0.662755 0.748836i \(-0.730613\pi\)
0.748836 + 0.662755i \(0.230613\pi\)
\(954\) 0 0
\(955\) 20.3310 8.42138i 0.657896 0.272509i
\(956\) 24.0407 3.05620i 0.777532 0.0988447i
\(957\) 0 0
\(958\) 14.7200 16.7098i 0.475583 0.539869i
\(959\) −23.9787 −0.774312
\(960\) 0 0
\(961\) −1.90528 −0.0614607
\(962\) −24.8245 + 28.1802i −0.800375 + 0.908565i
\(963\) 0 0
\(964\) 2.61102 0.331929i 0.0840952 0.0106907i
\(965\) −13.5182 + 5.59942i −0.435166 + 0.180252i
\(966\) 0 0
\(967\) −5.32503 + 5.32503i −0.171241 + 0.171241i −0.787525 0.616283i \(-0.788638\pi\)
0.616283 + 0.787525i \(0.288638\pi\)
\(968\) 16.9724 3.25835i 0.545513 0.104727i
\(969\) 0 0
\(970\) 3.82990 11.2005i 0.122971 0.359628i
\(971\) −9.21695 22.2517i −0.295786 0.714090i −0.999992 0.00409432i \(-0.998697\pi\)
0.704206 0.709996i \(-0.251303\pi\)
\(972\) 0 0
\(973\) 3.52578 + 1.46042i 0.113031 + 0.0468190i
\(974\) −2.76662 43.7007i −0.0886481 1.40026i
\(975\) 0 0
\(976\) 4.45227 31.6389i 0.142514 1.01274i
\(977\) 21.7322i 0.695274i 0.937629 + 0.347637i \(0.113016\pi\)
−0.937629 + 0.347637i \(0.886984\pi\)
\(978\) 0 0
\(979\) 15.5104 + 6.42463i 0.495715 + 0.205332i
\(980\) 9.16117 5.23496i 0.292643 0.167225i
\(981\) 0 0
\(982\) −11.0541 3.77984i −0.352752 0.120619i
\(983\) −30.7394 30.7394i −0.980436 0.980436i 0.0193762 0.999812i \(-0.493832\pi\)
−0.999812 + 0.0193762i \(0.993832\pi\)
\(984\) 0 0
\(985\) 12.2689 12.2689i 0.390921 0.390921i
\(986\) 24.2995 11.9160i 0.773854 0.379483i
\(987\) 0 0
\(988\) 27.2631 35.2043i 0.867354 1.12000i
\(989\) −27.0490 + 65.3021i −0.860109 + 2.07649i
\(990\) 0 0
\(991\) 12.5981 0.400192 0.200096 0.979776i \(-0.435875\pi\)
0.200096 + 0.979776i \(0.435875\pi\)
\(992\) 13.7992 27.2142i 0.438125 0.864052i
\(993\) 0 0
\(994\) 3.89113 + 3.42778i 0.123419 + 0.108723i
\(995\) 6.75519 16.3085i 0.214154 0.517013i
\(996\) 0 0
\(997\) 0.0205884 0.00852802i 0.000652043 0.000270085i −0.382357 0.924015i \(-0.624888\pi\)
0.383009 + 0.923744i \(0.374888\pi\)
\(998\) 31.8205 15.6042i 1.00726 0.493942i
\(999\) 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 864.2.v.a.109.10 128
3.2 odd 2 inner 864.2.v.a.109.23 yes 128
32.5 even 8 inner 864.2.v.a.325.10 yes 128
96.5 odd 8 inner 864.2.v.a.325.23 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
864.2.v.a.109.10 128 1.1 even 1 trivial
864.2.v.a.109.23 yes 128 3.2 odd 2 inner
864.2.v.a.325.10 yes 128 32.5 even 8 inner
864.2.v.a.325.23 yes 128 96.5 odd 8 inner