Properties

Label 75.3.k.a.37.3
Level $75$
Weight $3$
Character 75.37
Analytic conductor $2.044$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,3,Mod(13,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.13");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.k (of order \(20\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.04360198270\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 37.3
Character \(\chi\) \(=\) 75.37
Dual form 75.3.k.a.73.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.224472 - 1.41726i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(1.84598 - 0.599796i) q^{4} +(-3.76307 - 3.29231i) q^{5} +(-0.768021 + 2.36373i) q^{6} +(-1.57196 - 1.57196i) q^{7} +(-3.87022 - 7.59573i) q^{8} +(1.76336 + 2.42705i) q^{9} +O(q^{10})\) \(q+(-0.224472 - 1.41726i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(1.84598 - 0.599796i) q^{4} +(-3.76307 - 3.29231i) q^{5} +(-0.768021 + 2.36373i) q^{6} +(-1.57196 - 1.57196i) q^{7} +(-3.87022 - 7.59573i) q^{8} +(1.76336 + 2.42705i) q^{9} +(-3.82136 + 6.07229i) q^{10} +(-2.65478 - 1.92881i) q^{11} +(-3.32049 - 0.525913i) q^{12} +(1.08721 - 6.86438i) q^{13} +(-1.87501 + 2.58073i) q^{14} +(3.21858 + 8.03995i) q^{15} +(-3.61523 + 2.62662i) q^{16} +(0.0769625 - 0.0392144i) q^{17} +(3.04394 - 3.04394i) q^{18} +(30.3208 + 9.85181i) q^{19} +(-8.92128 - 3.82046i) q^{20} +(1.18987 + 3.66203i) q^{21} +(-2.13771 + 4.19549i) q^{22} +(26.6636 - 4.22310i) q^{23} +14.7655i q^{24} +(3.32143 + 24.7784i) q^{25} -9.97267 q^{26} +(-0.812857 - 5.13218i) q^{27} +(-3.84465 - 1.95895i) q^{28} +(33.6464 - 10.9324i) q^{29} +(10.6722 - 6.36631i) q^{30} +(2.05994 - 6.33986i) q^{31} +(-19.5779 - 19.5779i) q^{32} +(2.58035 + 5.06422i) q^{33} +(-0.0728530 - 0.100274i) q^{34} +(0.740023 + 11.0907i) q^{35} +(4.71086 + 3.42264i) q^{36} +(-26.2508 - 4.15773i) q^{37} +(7.15643 - 45.1839i) q^{38} +(-7.07556 + 9.73867i) q^{39} +(-10.4436 + 41.3252i) q^{40} +(-53.2182 + 38.6653i) q^{41} +(4.92297 - 2.50838i) q^{42} +(-10.6913 + 10.6913i) q^{43} +(-6.05757 - 1.96822i) q^{44} +(1.35496 - 14.9387i) q^{45} +(-11.9705 - 36.8413i) q^{46} +(-8.60750 + 16.8932i) q^{47} +(7.64468 - 1.21080i) q^{48} -44.0579i q^{49} +(34.3719 - 10.2694i) q^{50} -0.149609 q^{51} +(-2.11025 - 13.3236i) q^{52} +(53.8293 + 27.4274i) q^{53} +(-7.09118 + 2.30406i) q^{54} +(3.63990 + 15.9986i) q^{55} +(-5.85633 + 18.0239i) q^{56} +(-39.0463 - 39.0463i) q^{57} +(-23.0467 - 45.2317i) q^{58} +(-26.7005 - 36.7501i) q^{59} +(10.7638 + 12.9111i) q^{60} +(-58.1403 - 42.2414i) q^{61} +(-9.44764 - 1.49636i) q^{62} +(1.04330 - 6.58713i) q^{63} +(-33.8588 + 46.6026i) q^{64} +(-26.6909 + 22.2517i) q^{65} +(6.59811 - 4.79381i) q^{66} +(114.761 - 58.4735i) q^{67} +(0.118551 - 0.118551i) q^{68} +(-44.4699 - 14.4491i) q^{69} +(15.5524 - 3.53837i) q^{70} +(23.5416 + 72.4536i) q^{71} +(11.6106 - 22.7872i) q^{72} +(-87.6813 + 13.8873i) q^{73} +38.1376i q^{74} +(14.3582 - 40.8515i) q^{75} +61.8807 q^{76} +(1.14119 + 7.20520i) q^{77} +(15.3905 + 7.84186i) q^{78} +(136.696 - 44.4152i) q^{79} +(22.2520 + 2.01829i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(66.7449 + 66.7449i) q^{82} +(66.3235 + 130.167i) q^{83} +(4.39294 + 6.04637i) q^{84} +(-0.418721 - 0.105818i) q^{85} +(17.5523 + 12.7525i) q^{86} +(-60.5219 - 9.58572i) q^{87} +(-4.37615 + 27.6299i) q^{88} +(-35.3179 + 48.6109i) q^{89} +(-21.4762 + 1.43298i) q^{90} +(-12.4995 + 9.08145i) q^{91} +(46.6875 - 23.7885i) q^{92} +(-8.16429 + 8.16429i) q^{93} +(25.8742 + 8.40703i) q^{94} +(-81.6640 - 136.898i) q^{95} +(14.8192 + 45.6087i) q^{96} +(-59.3549 + 116.490i) q^{97} +(-62.4416 + 9.88978i) q^{98} -9.84447i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{20}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.224472 1.41726i −0.112236 0.708631i −0.978066 0.208293i \(-0.933209\pi\)
0.865830 0.500338i \(-0.166791\pi\)
\(3\) −1.54327 0.786335i −0.514423 0.262112i
\(4\) 1.84598 0.599796i 0.461496 0.149949i
\(5\) −3.76307 3.29231i −0.752615 0.658461i
\(6\) −0.768021 + 2.36373i −0.128004 + 0.393954i
\(7\) −1.57196 1.57196i −0.224565 0.224565i 0.585853 0.810418i \(-0.300760\pi\)
−0.810418 + 0.585853i \(0.800760\pi\)
\(8\) −3.87022 7.59573i −0.483777 0.949466i
\(9\) 1.76336 + 2.42705i 0.195928 + 0.269672i
\(10\) −3.82136 + 6.07229i −0.382136 + 0.607229i
\(11\) −2.65478 1.92881i −0.241344 0.175347i 0.460538 0.887640i \(-0.347657\pi\)
−0.701882 + 0.712293i \(0.747657\pi\)
\(12\) −3.32049 0.525913i −0.276707 0.0438261i
\(13\) 1.08721 6.86438i 0.0836316 0.528029i −0.909932 0.414757i \(-0.863867\pi\)
0.993564 0.113272i \(-0.0361333\pi\)
\(14\) −1.87501 + 2.58073i −0.133929 + 0.184338i
\(15\) 3.21858 + 8.03995i 0.214572 + 0.535997i
\(16\) −3.61523 + 2.62662i −0.225952 + 0.164164i
\(17\) 0.0769625 0.0392144i 0.00452721 0.00230673i −0.451725 0.892157i \(-0.649191\pi\)
0.456253 + 0.889850i \(0.349191\pi\)
\(18\) 3.04394 3.04394i 0.169108 0.169108i
\(19\) 30.3208 + 9.85181i 1.59583 + 0.518516i 0.966071 0.258275i \(-0.0831540\pi\)
0.629758 + 0.776791i \(0.283154\pi\)
\(20\) −8.92128 3.82046i −0.446064 0.191023i
\(21\) 1.18987 + 3.66203i 0.0566603 + 0.174382i
\(22\) −2.13771 + 4.19549i −0.0971685 + 0.190704i
\(23\) 26.6636 4.22310i 1.15929 0.183613i 0.452981 0.891520i \(-0.350360\pi\)
0.706306 + 0.707907i \(0.250360\pi\)
\(24\) 14.7655i 0.615230i
\(25\) 3.32143 + 24.7784i 0.132857 + 0.991135i
\(26\) −9.97267 −0.383564
\(27\) −0.812857 5.13218i −0.0301058 0.190081i
\(28\) −3.84465 1.95895i −0.137309 0.0699625i
\(29\) 33.6464 10.9324i 1.16022 0.376978i 0.335236 0.942134i \(-0.391184\pi\)
0.824984 + 0.565156i \(0.191184\pi\)
\(30\) 10.6722 6.36631i 0.355741 0.212210i
\(31\) 2.05994 6.33986i 0.0664498 0.204511i −0.912318 0.409481i \(-0.865710\pi\)
0.978768 + 0.204970i \(0.0657097\pi\)
\(32\) −19.5779 19.5779i −0.611809 0.611809i
\(33\) 2.58035 + 5.06422i 0.0781924 + 0.153461i
\(34\) −0.0728530 0.100274i −0.00214274 0.00294922i
\(35\) 0.740023 + 11.0907i 0.0211435 + 0.316878i
\(36\) 4.71086 + 3.42264i 0.130857 + 0.0950733i
\(37\) −26.2508 4.15773i −0.709482 0.112371i −0.208745 0.977970i \(-0.566938\pi\)
−0.500737 + 0.865599i \(0.666938\pi\)
\(38\) 7.15643 45.1839i 0.188327 1.18905i
\(39\) −7.07556 + 9.73867i −0.181425 + 0.249709i
\(40\) −10.4436 + 41.3252i −0.261089 + 1.03313i
\(41\) −53.2182 + 38.6653i −1.29800 + 0.943056i −0.999934 0.0114880i \(-0.996343\pi\)
−0.298071 + 0.954544i \(0.596343\pi\)
\(42\) 4.92297 2.50838i 0.117213 0.0597233i
\(43\) −10.6913 + 10.6913i −0.248635 + 0.248635i −0.820410 0.571775i \(-0.806255\pi\)
0.571775 + 0.820410i \(0.306255\pi\)
\(44\) −6.05757 1.96822i −0.137672 0.0447324i
\(45\) 1.35496 14.9387i 0.0301102 0.331971i
\(46\) −11.9705 36.8413i −0.260228 0.800899i
\(47\) −8.60750 + 16.8932i −0.183138 + 0.359429i −0.964263 0.264945i \(-0.914646\pi\)
0.781125 + 0.624374i \(0.214646\pi\)
\(48\) 7.64468 1.21080i 0.159264 0.0252250i
\(49\) 44.0579i 0.899141i
\(50\) 34.3719 10.2694i 0.687438 0.205388i
\(51\) −0.149609 −0.00293352
\(52\) −2.11025 13.3236i −0.0405818 0.256224i
\(53\) 53.8293 + 27.4274i 1.01565 + 0.517498i 0.880860 0.473377i \(-0.156965\pi\)
0.134787 + 0.990875i \(0.456965\pi\)
\(54\) −7.09118 + 2.30406i −0.131318 + 0.0426678i
\(55\) 3.63990 + 15.9986i 0.0661799 + 0.290884i
\(56\) −5.85633 + 18.0239i −0.104577 + 0.321856i
\(57\) −39.0463 39.0463i −0.685022 0.685022i
\(58\) −23.0467 45.2317i −0.397357 0.779857i
\(59\) −26.7005 36.7501i −0.452551 0.622882i 0.520393 0.853927i \(-0.325786\pi\)
−0.972943 + 0.231045i \(0.925786\pi\)
\(60\) 10.7638 + 12.9111i 0.179396 + 0.215185i
\(61\) −58.1403 42.2414i −0.953119 0.692482i −0.00157682 0.999999i \(-0.500502\pi\)
−0.951543 + 0.307517i \(0.900502\pi\)
\(62\) −9.44764 1.49636i −0.152381 0.0241348i
\(63\) 1.04330 6.58713i 0.0165603 0.104558i
\(64\) −33.8588 + 46.6026i −0.529043 + 0.728166i
\(65\) −26.6909 + 22.2517i −0.410629 + 0.342334i
\(66\) 6.59811 4.79381i 0.0999714 0.0726335i
\(67\) 114.761 58.4735i 1.71285 0.872739i 0.731167 0.682199i \(-0.238976\pi\)
0.981679 0.190540i \(-0.0610239\pi\)
\(68\) 0.118551 0.118551i 0.00174339 0.00174339i
\(69\) −44.4699 14.4491i −0.644491 0.209408i
\(70\) 15.5524 3.53837i 0.222177 0.0505481i
\(71\) 23.5416 + 72.4536i 0.331572 + 1.02047i 0.968386 + 0.249456i \(0.0802519\pi\)
−0.636814 + 0.771018i \(0.719748\pi\)
\(72\) 11.6106 22.7872i 0.161259 0.316489i
\(73\) −87.6813 + 13.8873i −1.20111 + 0.190238i −0.724751 0.689011i \(-0.758045\pi\)
−0.476363 + 0.879249i \(0.658045\pi\)
\(74\) 38.1376i 0.515373i
\(75\) 14.3582 40.8515i 0.191443 0.544686i
\(76\) 61.8807 0.814219
\(77\) 1.14119 + 7.20520i 0.0148207 + 0.0935741i
\(78\) 15.3905 + 7.84186i 0.197314 + 0.100537i
\(79\) 136.696 44.4152i 1.73033 0.562218i 0.736831 0.676077i \(-0.236321\pi\)
0.993497 + 0.113860i \(0.0363215\pi\)
\(80\) 22.2520 + 2.01829i 0.278150 + 0.0252287i
\(81\) −2.78115 + 8.55951i −0.0343352 + 0.105673i
\(82\) 66.7449 + 66.7449i 0.813962 + 0.813962i
\(83\) 66.3235 + 130.167i 0.799079 + 1.56828i 0.822643 + 0.568558i \(0.192498\pi\)
−0.0235646 + 0.999722i \(0.507502\pi\)
\(84\) 4.39294 + 6.04637i 0.0522970 + 0.0719806i
\(85\) −0.418721 0.105818i −0.00492613 0.00124491i
\(86\) 17.5523 + 12.7525i 0.204096 + 0.148285i
\(87\) −60.5219 9.58572i −0.695654 0.110181i
\(88\) −4.37615 + 27.6299i −0.0497290 + 0.313976i
\(89\) −35.3179 + 48.6109i −0.396830 + 0.546190i −0.959945 0.280189i \(-0.909603\pi\)
0.563115 + 0.826379i \(0.309603\pi\)
\(90\) −21.4762 + 1.43298i −0.238624 + 0.0159220i
\(91\) −12.4995 + 9.08145i −0.137358 + 0.0997961i
\(92\) 46.6875 23.7885i 0.507473 0.258570i
\(93\) −8.16429 + 8.16429i −0.0877881 + 0.0877881i
\(94\) 25.8742 + 8.40703i 0.275257 + 0.0894365i
\(95\) −81.6640 136.898i −0.859621 1.44104i
\(96\) 14.8192 + 45.6087i 0.154366 + 0.475090i
\(97\) −59.3549 + 116.490i −0.611906 + 1.20093i 0.352327 + 0.935877i \(0.385390\pi\)
−0.964233 + 0.265056i \(0.914610\pi\)
\(98\) −62.4416 + 9.88978i −0.637159 + 0.100916i
\(99\) 9.84447i 0.0994391i
\(100\) 20.9933 + 43.7483i 0.209933 + 0.437483i
\(101\) 65.2078 0.645622 0.322811 0.946464i \(-0.395372\pi\)
0.322811 + 0.946464i \(0.395372\pi\)
\(102\) 0.0335832 + 0.212036i 0.000329247 + 0.00207878i
\(103\) −62.1063 31.6447i −0.602974 0.307230i 0.125725 0.992065i \(-0.459874\pi\)
−0.728698 + 0.684835i \(0.759874\pi\)
\(104\) −56.3477 + 18.3085i −0.541805 + 0.176043i
\(105\) 7.57898 17.6979i 0.0721808 0.168551i
\(106\) 26.7886 82.4469i 0.252723 0.777801i
\(107\) 50.9651 + 50.9651i 0.476310 + 0.476310i 0.903949 0.427640i \(-0.140655\pi\)
−0.427640 + 0.903949i \(0.640655\pi\)
\(108\) −4.57878 8.98636i −0.0423961 0.0832071i
\(109\) −58.9479 81.1348i −0.540807 0.744356i 0.447922 0.894072i \(-0.352164\pi\)
−0.988729 + 0.149716i \(0.952164\pi\)
\(110\) 21.8572 8.74993i 0.198702 0.0795448i
\(111\) 37.2427 + 27.0584i 0.335520 + 0.243770i
\(112\) 9.81191 + 1.55405i 0.0876064 + 0.0138755i
\(113\) 2.63188 16.6171i 0.0232910 0.147054i −0.973302 0.229527i \(-0.926282\pi\)
0.996593 + 0.0824736i \(0.0262820\pi\)
\(114\) −46.5740 + 64.1036i −0.408544 + 0.562312i
\(115\) −114.241 71.8929i −0.993398 0.625156i
\(116\) 55.5534 40.3619i 0.478909 0.347947i
\(117\) 18.5773 9.46562i 0.158781 0.0809028i
\(118\) −46.0910 + 46.0910i −0.390601 + 0.390601i
\(119\) −0.182625 0.0593384i −0.00153466 0.000498642i
\(120\) 48.6126 55.5638i 0.405105 0.463031i
\(121\) −34.0635 104.837i −0.281517 0.866419i
\(122\) −46.8162 + 91.8820i −0.383740 + 0.753131i
\(123\) 112.534 17.8236i 0.914909 0.144907i
\(124\) 12.9388i 0.104345i
\(125\) 69.0792 104.178i 0.552634 0.833424i
\(126\) −9.56988 −0.0759515
\(127\) 29.9804 + 189.289i 0.236066 + 1.49046i 0.766229 + 0.642568i \(0.222131\pi\)
−0.530162 + 0.847896i \(0.677869\pi\)
\(128\) −25.0298 12.7533i −0.195545 0.0996353i
\(129\) 24.9065 8.09261i 0.193074 0.0627334i
\(130\) 37.5279 + 32.8331i 0.288676 + 0.252562i
\(131\) 66.1552 203.605i 0.505001 1.55423i −0.295767 0.955260i \(-0.595575\pi\)
0.800768 0.598974i \(-0.204425\pi\)
\(132\) 7.80078 + 7.80078i 0.0590968 + 0.0590968i
\(133\) −32.1763 63.1495i −0.241927 0.474808i
\(134\) −108.633 149.520i −0.810693 1.11582i
\(135\) −13.8379 + 21.9889i −0.102503 + 0.162881i
\(136\) −0.595723 0.432818i −0.00438032 0.00318249i
\(137\) −93.9989 14.8880i −0.686123 0.108671i −0.196367 0.980531i \(-0.562914\pi\)
−0.489757 + 0.871859i \(0.662914\pi\)
\(138\) −10.4960 + 66.2689i −0.0760577 + 0.480209i
\(139\) −23.4198 + 32.2346i −0.168488 + 0.231904i −0.884908 0.465765i \(-0.845779\pi\)
0.716421 + 0.697669i \(0.245779\pi\)
\(140\) 8.01825 + 20.0294i 0.0572732 + 0.143067i
\(141\) 26.5674 19.3023i 0.188421 0.136896i
\(142\) 97.4014 49.6285i 0.685925 0.349496i
\(143\) −16.1264 + 16.1264i −0.112772 + 0.112772i
\(144\) −12.7499 4.14269i −0.0885408 0.0287687i
\(145\) −162.606 69.6349i −1.12142 0.480240i
\(146\) 39.3640 + 121.150i 0.269617 + 0.829795i
\(147\) −34.6443 + 67.9932i −0.235675 + 0.462539i
\(148\) −50.9524 + 8.07006i −0.344273 + 0.0545275i
\(149\) 80.0934i 0.537540i 0.963204 + 0.268770i \(0.0866171\pi\)
−0.963204 + 0.268770i \(0.913383\pi\)
\(150\) −61.1202 11.1794i −0.407468 0.0745291i
\(151\) 24.3022 0.160941 0.0804707 0.996757i \(-0.474358\pi\)
0.0804707 + 0.996757i \(0.474358\pi\)
\(152\) −42.5162 268.437i −0.279712 1.76603i
\(153\) 0.230888 + 0.117643i 0.00150907 + 0.000768909i
\(154\) 9.95550 3.23474i 0.0646461 0.0210048i
\(155\) −28.6245 + 17.0754i −0.184674 + 0.110164i
\(156\) −7.22014 + 22.2213i −0.0462829 + 0.142444i
\(157\) 79.6697 + 79.6697i 0.507451 + 0.507451i 0.913743 0.406292i \(-0.133179\pi\)
−0.406292 + 0.913743i \(0.633179\pi\)
\(158\) −93.6324 183.764i −0.592610 1.16306i
\(159\) −61.5059 84.6556i −0.386830 0.532425i
\(160\) 9.21660 + 138.129i 0.0576037 + 0.863309i
\(161\) −48.5525 35.2755i −0.301568 0.219102i
\(162\) 12.7554 + 2.02025i 0.0787368 + 0.0124707i
\(163\) −33.3800 + 210.753i −0.204785 + 1.29296i 0.644326 + 0.764751i \(0.277138\pi\)
−0.849112 + 0.528213i \(0.822862\pi\)
\(164\) −75.0486 + 103.295i −0.457613 + 0.629851i
\(165\) 6.96293 27.5523i 0.0421996 0.166984i
\(166\) 169.593 123.217i 1.02165 0.742270i
\(167\) −27.5199 + 14.0221i −0.164790 + 0.0839645i −0.534440 0.845206i \(-0.679477\pi\)
0.369650 + 0.929171i \(0.379477\pi\)
\(168\) 23.2107 23.2107i 0.138159 0.138159i
\(169\) 114.791 + 37.2978i 0.679236 + 0.220697i
\(170\) −0.0559802 + 0.617191i −0.000329295 + 0.00363054i
\(171\) 29.5554 + 90.9623i 0.172839 + 0.531943i
\(172\) −13.3234 + 26.1486i −0.0774614 + 0.152027i
\(173\) 84.3603 13.3614i 0.487632 0.0772333i 0.0922226 0.995738i \(-0.470603\pi\)
0.395409 + 0.918505i \(0.370603\pi\)
\(174\) 87.9271i 0.505328i
\(175\) 33.7294 44.1716i 0.192739 0.252409i
\(176\) 14.6639 0.0833177
\(177\) 12.3082 + 77.7107i 0.0695377 + 0.439044i
\(178\) 76.8223 + 39.1429i 0.431586 + 0.219904i
\(179\) 29.3539 9.53765i 0.163988 0.0532830i −0.225872 0.974157i \(-0.572523\pi\)
0.389860 + 0.920874i \(0.372523\pi\)
\(180\) −6.45892 28.3892i −0.0358829 0.157718i
\(181\) −69.8971 + 215.121i −0.386172 + 1.18851i 0.549455 + 0.835523i \(0.314835\pi\)
−0.935627 + 0.352991i \(0.885165\pi\)
\(182\) 15.6766 + 15.6766i 0.0861351 + 0.0861351i
\(183\) 56.5102 + 110.908i 0.308799 + 0.606052i
\(184\) −135.271 186.185i −0.735170 1.01188i
\(185\) 85.0953 + 102.072i 0.459975 + 0.551739i
\(186\) 13.4036 + 9.73829i 0.0720624 + 0.0523564i
\(187\) −0.279956 0.0443407i −0.00149709 0.000237116i
\(188\) −5.75683 + 36.3472i −0.0306215 + 0.193336i
\(189\) −6.78978 + 9.34533i −0.0359248 + 0.0494462i
\(190\) −175.689 + 146.469i −0.924682 + 0.770891i
\(191\) −32.9654 + 23.9507i −0.172593 + 0.125397i −0.670728 0.741703i \(-0.734018\pi\)
0.498135 + 0.867100i \(0.334018\pi\)
\(192\) 88.8984 45.2960i 0.463013 0.235917i
\(193\) 166.613 166.613i 0.863279 0.863279i −0.128438 0.991717i \(-0.540996\pi\)
0.991717 + 0.128438i \(0.0409965\pi\)
\(194\) 178.421 + 57.9725i 0.919696 + 0.298827i
\(195\) 58.6885 13.3524i 0.300967 0.0684739i
\(196\) −26.4258 81.3301i −0.134825 0.414950i
\(197\) −11.6312 + 22.8275i −0.0590415 + 0.115875i −0.918642 0.395092i \(-0.870713\pi\)
0.859600 + 0.510967i \(0.170713\pi\)
\(198\) −13.9522 + 2.20981i −0.0704656 + 0.0111607i
\(199\) 106.010i 0.532713i 0.963875 + 0.266357i \(0.0858199\pi\)
−0.963875 + 0.266357i \(0.914180\pi\)
\(200\) 175.355 121.126i 0.876776 0.605632i
\(201\) −223.086 −1.10988
\(202\) −14.6373 92.4165i −0.0724621 0.457507i
\(203\) −70.0758 35.7054i −0.345201 0.175889i
\(204\) −0.276176 + 0.0897352i −0.00135381 + 0.000439878i
\(205\) 327.562 + 29.7104i 1.59786 + 0.144929i
\(206\) −30.9077 + 95.1242i −0.150038 + 0.461768i
\(207\) 57.2671 + 57.2671i 0.276653 + 0.276653i
\(208\) 14.0996 + 27.6720i 0.0677865 + 0.133039i
\(209\) −61.4927 84.6375i −0.294223 0.404964i
\(210\) −26.7838 6.76871i −0.127542 0.0322320i
\(211\) 33.9133 + 24.6394i 0.160726 + 0.116775i 0.665241 0.746628i \(-0.268329\pi\)
−0.504515 + 0.863403i \(0.668329\pi\)
\(212\) 115.819 + 18.3439i 0.546315 + 0.0865277i
\(213\) 20.6418 130.327i 0.0969097 0.611864i
\(214\) 60.7907 83.6712i 0.284069 0.390987i
\(215\) 75.4312 5.03310i 0.350843 0.0234098i
\(216\) −35.8367 + 26.0369i −0.165911 + 0.120541i
\(217\) −13.2041 + 6.72783i −0.0608484 + 0.0310038i
\(218\) −101.757 + 101.757i −0.466776 + 0.466776i
\(219\) 146.236 + 47.5149i 0.667744 + 0.216963i
\(220\) 16.3151 + 27.3500i 0.0741595 + 0.124318i
\(221\) −0.185508 0.570934i −0.000839402 0.00258341i
\(222\) 29.9889 58.8566i 0.135085 0.265120i
\(223\) 70.9316 11.2345i 0.318079 0.0503788i 0.00464637 0.999989i \(-0.498521\pi\)
0.313433 + 0.949610i \(0.398521\pi\)
\(224\) 61.5511i 0.274782i
\(225\) −54.2815 + 51.7544i −0.241251 + 0.230019i
\(226\) −24.1415 −0.106821
\(227\) −63.7589 402.558i −0.280876 1.77338i −0.575533 0.817779i \(-0.695205\pi\)
0.294657 0.955603i \(-0.404795\pi\)
\(228\) −95.4985 48.6589i −0.418853 0.213416i
\(229\) 285.985 92.9223i 1.24884 0.405774i 0.391338 0.920247i \(-0.372012\pi\)
0.857507 + 0.514473i \(0.172012\pi\)
\(230\) −76.2472 + 178.047i −0.331510 + 0.774118i
\(231\) 3.90454 12.0169i 0.0169028 0.0520213i
\(232\) −213.258 213.258i −0.919215 0.919215i
\(233\) 76.9510 + 151.025i 0.330262 + 0.648176i 0.995107 0.0988059i \(-0.0315023\pi\)
−0.664845 + 0.746982i \(0.731502\pi\)
\(234\) −17.5854 24.2042i −0.0751511 0.103437i
\(235\) 88.0081 35.2317i 0.374503 0.149922i
\(236\) −71.3312 51.8251i −0.302251 0.219598i
\(237\) −245.884 38.9441i −1.03748 0.164321i
\(238\) −0.0431039 + 0.272147i −0.000181109 + 0.00114348i
\(239\) −153.985 + 211.943i −0.644290 + 0.886789i −0.998835 0.0482498i \(-0.984636\pi\)
0.354545 + 0.935039i \(0.384636\pi\)
\(240\) −32.7538 20.6123i −0.136474 0.0858846i
\(241\) −384.321 + 279.225i −1.59469 + 1.15861i −0.697864 + 0.716230i \(0.745866\pi\)
−0.896827 + 0.442381i \(0.854134\pi\)
\(242\) −140.935 + 71.8098i −0.582375 + 0.296735i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) −132.662 43.1045i −0.543697 0.176658i
\(245\) −145.052 + 165.793i −0.592050 + 0.676707i
\(246\) −50.5214 155.489i −0.205372 0.632069i
\(247\) 100.592 197.422i 0.407254 0.799280i
\(248\) −56.1282 + 8.88984i −0.226324 + 0.0358461i
\(249\) 253.036i 1.01621i
\(250\) −163.154 74.5183i −0.652616 0.298073i
\(251\) −162.145 −0.645998 −0.322999 0.946399i \(-0.604691\pi\)
−0.322999 + 0.946399i \(0.604691\pi\)
\(252\) −2.02502 12.7855i −0.00803581 0.0507361i
\(253\) −78.9316 40.2177i −0.311983 0.158963i
\(254\) 261.542 84.9802i 1.02969 0.334568i
\(255\) 0.562991 + 0.492560i 0.00220781 + 0.00193161i
\(256\) −83.6587 + 257.475i −0.326792 + 1.00576i
\(257\) 194.613 + 194.613i 0.757250 + 0.757250i 0.975821 0.218571i \(-0.0701397\pi\)
−0.218571 + 0.975821i \(0.570140\pi\)
\(258\) −17.0602 33.4825i −0.0661247 0.129777i
\(259\) 34.7294 + 47.8009i 0.134090 + 0.184559i
\(260\) −35.9244 + 57.0854i −0.138171 + 0.219559i
\(261\) 85.8639 + 62.3838i 0.328981 + 0.239018i
\(262\) −303.411 48.0556i −1.15806 0.183418i
\(263\) 8.08718 51.0604i 0.0307497 0.194146i −0.967532 0.252750i \(-0.918665\pi\)
0.998281 + 0.0586040i \(0.0186649\pi\)
\(264\) 28.4799 39.1993i 0.107879 0.148482i
\(265\) −112.264 280.434i −0.423638 1.05824i
\(266\) −82.2767 + 59.7775i −0.309311 + 0.224727i
\(267\) 92.7295 47.2480i 0.347301 0.176959i
\(268\) 176.774 176.774i 0.659605 0.659605i
\(269\) 144.928 + 47.0899i 0.538765 + 0.175055i 0.565744 0.824581i \(-0.308589\pi\)
−0.0269794 + 0.999636i \(0.508589\pi\)
\(270\) 34.2703 + 14.6760i 0.126927 + 0.0543555i
\(271\) −67.0716 206.425i −0.247497 0.761717i −0.995216 0.0977016i \(-0.968851\pi\)
0.747719 0.664015i \(-0.231149\pi\)
\(272\) −0.175236 + 0.343920i −0.000644251 + 0.00126441i
\(273\) 26.4312 4.18629i 0.0968176 0.0153344i
\(274\) 136.563i 0.498405i
\(275\) 38.9752 72.1876i 0.141728 0.262500i
\(276\) −90.7571 −0.328830
\(277\) −34.9582 220.717i −0.126203 0.796813i −0.966872 0.255263i \(-0.917838\pi\)
0.840669 0.541550i \(-0.182162\pi\)
\(278\) 50.9420 + 25.9562i 0.183244 + 0.0933677i
\(279\) 19.0196 6.17983i 0.0681705 0.0221499i
\(280\) 81.3782 48.5446i 0.290636 0.173373i
\(281\) 75.8100 233.319i 0.269786 0.830317i −0.720766 0.693179i \(-0.756210\pi\)
0.990552 0.137138i \(-0.0437904\pi\)
\(282\) −33.3201 33.3201i −0.118156 0.118156i
\(283\) −23.3063 45.7411i −0.0823543 0.161630i 0.846157 0.532934i \(-0.178911\pi\)
−0.928511 + 0.371304i \(0.878911\pi\)
\(284\) 86.9148 + 119.628i 0.306038 + 0.421225i
\(285\) 18.3816 + 275.486i 0.0644970 + 0.966618i
\(286\) 26.4753 + 19.2354i 0.0925709 + 0.0672567i
\(287\) 144.437 + 22.8765i 0.503264 + 0.0797092i
\(288\) 12.9937 82.0393i 0.0451172 0.284859i
\(289\) −169.866 + 233.800i −0.587770 + 0.808996i
\(290\) −62.1902 + 246.087i −0.214449 + 0.848576i
\(291\) 183.201 133.103i 0.629557 0.457400i
\(292\) −153.528 + 78.2267i −0.525782 + 0.267900i
\(293\) 237.590 237.590i 0.810886 0.810886i −0.173880 0.984767i \(-0.555631\pi\)
0.984767 + 0.173880i \(0.0556306\pi\)
\(294\) 104.141 + 33.8374i 0.354221 + 0.115093i
\(295\) −20.5166 + 226.199i −0.0695479 + 0.766777i
\(296\) 70.0155 + 215.485i 0.236539 + 0.727991i
\(297\) −7.74105 + 15.1927i −0.0260641 + 0.0511538i
\(298\) 113.513 17.9787i 0.380917 0.0603314i
\(299\) 187.620i 0.627493i
\(300\) 2.00251 84.0231i 0.00667505 0.280077i
\(301\) 33.6125 0.111669
\(302\) −5.45516 34.4425i −0.0180634 0.114048i
\(303\) −100.633 51.2751i −0.332122 0.169225i
\(304\) −135.494 + 44.0245i −0.445702 + 0.144818i
\(305\) 79.7145 + 350.373i 0.261359 + 1.14876i
\(306\) 0.114903 0.353636i 0.000375501 0.00115567i
\(307\) 111.148 + 111.148i 0.362044 + 0.362044i 0.864565 0.502521i \(-0.167594\pi\)
−0.502521 + 0.864565i \(0.667594\pi\)
\(308\) 6.42827 + 12.6162i 0.0208710 + 0.0409617i
\(309\) 70.9633 + 97.6726i 0.229655 + 0.316093i
\(310\) 30.6257 + 36.7354i 0.0987925 + 0.118501i
\(311\) −119.526 86.8408i −0.384328 0.279231i 0.378799 0.925479i \(-0.376337\pi\)
−0.763127 + 0.646248i \(0.776337\pi\)
\(312\) 101.356 + 16.0532i 0.324860 + 0.0514527i
\(313\) 60.0355 379.049i 0.191807 1.21102i −0.684408 0.729099i \(-0.739939\pi\)
0.876215 0.481921i \(-0.160061\pi\)
\(314\) 95.0293 130.797i 0.302641 0.416550i
\(315\) −25.6129 + 21.3530i −0.0813107 + 0.0677873i
\(316\) 225.698 163.979i 0.714235 0.518922i
\(317\) −364.651 + 185.799i −1.15032 + 0.586117i −0.921893 0.387445i \(-0.873358\pi\)
−0.228426 + 0.973561i \(0.573358\pi\)
\(318\) −106.173 + 106.173i −0.333877 + 0.333877i
\(319\) −110.410 35.8745i −0.346114 0.112459i
\(320\) 280.843 63.8955i 0.877635 0.199673i
\(321\) −38.5772 118.729i −0.120178 0.369871i
\(322\) −39.0959 + 76.7300i −0.121416 + 0.238292i
\(323\) 2.71990 0.430789i 0.00842073 0.00133371i
\(324\) 17.4688i 0.0539161i
\(325\) 173.699 + 4.13976i 0.534459 + 0.0127377i
\(326\) 306.185 0.939219
\(327\) 27.1733 + 171.566i 0.0830989 + 0.524666i
\(328\) 499.657 + 254.588i 1.52334 + 0.776182i
\(329\) 40.0859 13.0247i 0.121842 0.0395887i
\(330\) −40.6119 3.68356i −0.123066 0.0111623i
\(331\) −88.5011 + 272.378i −0.267375 + 0.822896i 0.723762 + 0.690050i \(0.242411\pi\)
−0.991137 + 0.132846i \(0.957589\pi\)
\(332\) 200.506 + 200.506i 0.603933 + 0.603933i
\(333\) −36.1986 71.0437i −0.108704 0.213344i
\(334\) 26.0504 + 35.8553i 0.0779952 + 0.107351i
\(335\) −624.366 157.787i −1.86378 0.471007i
\(336\) −13.9204 10.1138i −0.0414298 0.0301005i
\(337\) −288.617 45.7125i −0.856431 0.135645i −0.287248 0.957856i \(-0.592740\pi\)
−0.569183 + 0.822211i \(0.692740\pi\)
\(338\) 27.0934 171.061i 0.0801580 0.506098i
\(339\) −17.1283 + 23.5750i −0.0505259 + 0.0695429i
\(340\) −0.836421 + 0.0558097i −0.00246006 + 0.000164146i
\(341\) −17.6971 + 12.8577i −0.0518976 + 0.0377058i
\(342\) 122.283 62.3063i 0.357553 0.182182i
\(343\) −146.283 + 146.283i −0.426481 + 0.426481i
\(344\) 122.586 + 39.8306i 0.356354 + 0.115787i
\(345\) 119.772 + 200.782i 0.347166 + 0.581976i
\(346\) −37.8731 116.561i −0.109460 0.336883i
\(347\) −107.638 + 211.251i −0.310195 + 0.608792i −0.992496 0.122280i \(-0.960979\pi\)
0.682301 + 0.731072i \(0.260979\pi\)
\(348\) −117.472 + 18.6057i −0.337563 + 0.0534647i
\(349\) 328.355i 0.940846i 0.882441 + 0.470423i \(0.155899\pi\)
−0.882441 + 0.470423i \(0.844101\pi\)
\(350\) −70.1741 37.8880i −0.200497 0.108252i
\(351\) −36.1130 −0.102886
\(352\) 14.2130 + 89.7370i 0.0403777 + 0.254935i
\(353\) −360.052 183.455i −1.01998 0.519704i −0.137719 0.990471i \(-0.543977\pi\)
−0.882257 + 0.470768i \(0.843977\pi\)
\(354\) 107.374 34.8878i 0.303315 0.0985531i
\(355\) 149.951 350.155i 0.422397 0.986351i
\(356\) −36.0396 + 110.918i −0.101235 + 0.311569i
\(357\) 0.235179 + 0.235179i 0.000658766 + 0.000658766i
\(358\) −20.1065 39.4612i −0.0561633 0.110227i
\(359\) −107.677 148.204i −0.299935 0.412825i 0.632275 0.774744i \(-0.282121\pi\)
−0.932209 + 0.361920i \(0.882121\pi\)
\(360\) −118.714 + 47.5240i −0.329761 + 0.132011i
\(361\) 530.235 + 385.238i 1.46880 + 1.06714i
\(362\) 320.573 + 50.7738i 0.885560 + 0.140259i
\(363\) −29.8676 + 188.576i −0.0822798 + 0.519494i
\(364\) −17.6269 + 24.2614i −0.0484256 + 0.0666521i
\(365\) 375.672 + 236.415i 1.02924 + 0.647711i
\(366\) 144.500 104.985i 0.394809 0.286845i
\(367\) 207.864 105.912i 0.566387 0.288589i −0.147256 0.989098i \(-0.547044\pi\)
0.713643 + 0.700510i \(0.247044\pi\)
\(368\) −85.3026 + 85.3026i −0.231801 + 0.231801i
\(369\) −187.685 60.9826i −0.508632 0.165265i
\(370\) 125.561 143.515i 0.339353 0.387877i
\(371\) −41.5026 127.732i −0.111867 0.344291i
\(372\) −10.1742 + 19.9681i −0.0273501 + 0.0536776i
\(373\) −116.272 + 18.4157i −0.311722 + 0.0493719i −0.310335 0.950627i \(-0.600441\pi\)
−0.00138646 + 0.999999i \(0.500441\pi\)
\(374\) 0.406724i 0.00108750i
\(375\) −188.527 + 106.455i −0.502738 + 0.283881i
\(376\) 161.629 0.429864
\(377\) −38.4632 242.847i −0.102024 0.644157i
\(378\) 14.7689 + 7.52513i 0.0390712 + 0.0199078i
\(379\) −522.156 + 169.659i −1.37772 + 0.447648i −0.901919 0.431904i \(-0.857842\pi\)
−0.475801 + 0.879553i \(0.657842\pi\)
\(380\) −232.861 203.730i −0.612793 0.536132i
\(381\) 102.577 315.698i 0.269230 0.828604i
\(382\) 41.3443 + 41.3443i 0.108231 + 0.108231i
\(383\) 37.5805 + 73.7558i 0.0981214 + 0.192574i 0.934849 0.355045i \(-0.115534\pi\)
−0.836728 + 0.547619i \(0.815534\pi\)
\(384\) 28.5993 + 39.3636i 0.0744774 + 0.102509i
\(385\) 19.4274 30.8709i 0.0504607 0.0801841i
\(386\) −273.534 198.734i −0.708637 0.514855i
\(387\) −44.8009 7.09577i −0.115765 0.0183353i
\(388\) −39.6975 + 250.640i −0.102313 + 0.645980i
\(389\) 398.970 549.135i 1.02563 1.41166i 0.117451 0.993079i \(-0.462528\pi\)
0.908180 0.418580i \(-0.137472\pi\)
\(390\) −32.0978 80.1798i −0.0823021 0.205589i
\(391\) 1.88649 1.37062i 0.00482479 0.00350541i
\(392\) −334.652 + 170.514i −0.853704 + 0.434984i
\(393\) −262.197 + 262.197i −0.667167 + 0.667167i
\(394\) 34.9634 + 11.3603i 0.0887396 + 0.0288332i
\(395\) −660.625 282.907i −1.67247 0.716221i
\(396\) −5.90467 18.1727i −0.0149108 0.0458907i
\(397\) 190.293 373.472i 0.479328 0.940735i −0.517070 0.855943i \(-0.672977\pi\)
0.996399 0.0847919i \(-0.0270226\pi\)
\(398\) 150.244 23.7963i 0.377497 0.0597897i
\(399\) 122.758i 0.307664i
\(400\) −77.0911 80.8555i −0.192728 0.202139i
\(401\) −202.262 −0.504394 −0.252197 0.967676i \(-0.581153\pi\)
−0.252197 + 0.967676i \(0.581153\pi\)
\(402\) 50.0767 + 316.172i 0.124569 + 0.786497i
\(403\) −41.2796 21.0330i −0.102431 0.0521911i
\(404\) 120.372 39.1114i 0.297951 0.0968103i
\(405\) 38.6462 23.0536i 0.0954227 0.0569226i
\(406\) −34.8738 + 107.331i −0.0858961 + 0.264361i
\(407\) 61.6708 + 61.6708i 0.151525 + 0.151525i
\(408\) 0.579021 + 1.13639i 0.00141917 + 0.00278528i
\(409\) 182.069 + 250.597i 0.445157 + 0.612706i 0.971348 0.237660i \(-0.0763805\pi\)
−0.526192 + 0.850366i \(0.676381\pi\)
\(410\) −31.4212 470.910i −0.0766371 1.14856i
\(411\) 133.359 + 96.8907i 0.324474 + 0.235744i
\(412\) −133.627 21.1645i −0.324338 0.0513702i
\(413\) −15.7975 + 99.7414i −0.0382506 + 0.241505i
\(414\) 68.3076 94.0173i 0.164994 0.227095i
\(415\) 178.970 708.186i 0.431254 1.70647i
\(416\) −155.675 + 113.105i −0.374219 + 0.271886i
\(417\) 61.4902 31.3308i 0.147459 0.0751339i
\(418\) −106.150 + 106.150i −0.253947 + 0.253947i
\(419\) −724.830 235.512i −1.72991 0.562080i −0.736469 0.676471i \(-0.763509\pi\)
−0.993436 + 0.114390i \(0.963509\pi\)
\(420\) 3.37553 37.2158i 0.00803699 0.0886092i
\(421\) 71.9229 + 221.356i 0.170838 + 0.525786i 0.999419 0.0340835i \(-0.0108512\pi\)
−0.828581 + 0.559870i \(0.810851\pi\)
\(422\) 27.3079 53.5948i 0.0647108 0.127002i
\(423\) −56.1786 + 8.89782i −0.132810 + 0.0210350i
\(424\) 515.022i 1.21467i
\(425\) 1.22729 + 1.77676i 0.00288775 + 0.00418061i
\(426\) −189.341 −0.444463
\(427\) 24.9924 + 157.795i 0.0585301 + 0.369544i
\(428\) 124.649 + 63.5120i 0.291237 + 0.148393i
\(429\) 37.5681 12.2066i 0.0875714 0.0284537i
\(430\) −24.0654 105.776i −0.0559661 0.245991i
\(431\) 239.589 737.380i 0.555892 1.71086i −0.137684 0.990476i \(-0.543966\pi\)
0.693576 0.720383i \(-0.256034\pi\)
\(432\) 16.4190 + 16.4190i 0.0380068 + 0.0380068i
\(433\) 35.8419 + 70.3437i 0.0827758 + 0.162457i 0.928684 0.370872i \(-0.120941\pi\)
−0.845908 + 0.533328i \(0.820941\pi\)
\(434\) 12.4991 + 17.2035i 0.0287997 + 0.0396393i
\(435\) 196.189 + 235.328i 0.451009 + 0.540985i
\(436\) −157.481 114.417i −0.361195 0.262424i
\(437\) 850.066 + 134.637i 1.94523 + 0.308094i
\(438\) 34.5152 217.920i 0.0788018 0.497535i
\(439\) −233.982 + 322.049i −0.532989 + 0.733596i −0.987582 0.157103i \(-0.949785\pi\)
0.454593 + 0.890699i \(0.349785\pi\)
\(440\) 107.434 89.5657i 0.244168 0.203558i
\(441\) 106.931 77.6898i 0.242473 0.176167i
\(442\) −0.767522 + 0.391072i −0.00173648 + 0.000884778i
\(443\) −444.473 + 444.473i −1.00333 + 1.00333i −0.00333156 + 0.999994i \(0.501060\pi\)
−0.999994 + 0.00333156i \(0.998940\pi\)
\(444\) 84.9790 + 27.6113i 0.191394 + 0.0621877i
\(445\) 292.946 66.6491i 0.658306 0.149773i
\(446\) −31.8444 98.0069i −0.0713999 0.219746i
\(447\) 62.9802 123.606i 0.140895 0.276523i
\(448\) 126.482 20.0327i 0.282325 0.0447159i
\(449\) 248.455i 0.553352i −0.960963 0.276676i \(-0.910767\pi\)
0.960963 0.276676i \(-0.0892328\pi\)
\(450\) 85.5342 + 65.3137i 0.190076 + 0.145142i
\(451\) 215.861 0.478627
\(452\) −5.10844 32.2534i −0.0113018 0.0713571i
\(453\) −37.5048 19.1096i −0.0827920 0.0421846i
\(454\) −556.218 + 180.726i −1.22515 + 0.398075i
\(455\) 76.9356 + 6.97818i 0.169089 + 0.0153367i
\(456\) −145.467 + 447.702i −0.319007 + 0.981803i
\(457\) −522.656 522.656i −1.14367 1.14367i −0.987774 0.155893i \(-0.950174\pi\)
−0.155893 0.987774i \(-0.549826\pi\)
\(458\) −195.891 384.458i −0.427710 0.839428i
\(459\) −0.263815 0.363110i −0.000574760 0.000791089i
\(460\) −254.008 64.1919i −0.552190 0.139548i
\(461\) 429.212 + 311.841i 0.931045 + 0.676444i 0.946249 0.323440i \(-0.104840\pi\)
−0.0152033 + 0.999884i \(0.504840\pi\)
\(462\) −17.9076 2.83628i −0.0387610 0.00613914i
\(463\) −63.6099 + 401.617i −0.137386 + 0.867424i 0.818675 + 0.574257i \(0.194709\pi\)
−0.956061 + 0.293167i \(0.905291\pi\)
\(464\) −92.9242 + 127.899i −0.200268 + 0.275645i
\(465\) 57.6022 3.84347i 0.123876 0.00826553i
\(466\) 196.769 142.961i 0.422250 0.306783i
\(467\) −106.525 + 54.2773i −0.228105 + 0.116225i −0.564308 0.825564i \(-0.690857\pi\)
0.336203 + 0.941789i \(0.390857\pi\)
\(468\) 28.6160 28.6160i 0.0611453 0.0611453i
\(469\) −272.316 88.4810i −0.580632 0.188659i
\(470\) −69.6879 116.822i −0.148272 0.248558i
\(471\) −60.3047 185.599i −0.128036 0.394053i
\(472\) −175.807 + 345.040i −0.372472 + 0.731017i
\(473\) 49.0046 7.76157i 0.103604 0.0164092i
\(474\) 357.223i 0.753636i
\(475\) −143.404 + 784.021i −0.301902 + 1.65057i
\(476\) −0.372713 −0.000783011
\(477\) 28.3525 + 179.011i 0.0594392 + 0.375284i
\(478\) 334.944 + 170.662i 0.700719 + 0.357034i
\(479\) −323.344 + 105.061i −0.675040 + 0.219334i −0.626423 0.779484i \(-0.715482\pi\)
−0.0486175 + 0.998817i \(0.515482\pi\)
\(480\) 94.3922 220.418i 0.196650 0.459204i
\(481\) −57.0804 + 175.675i −0.118670 + 0.365229i
\(482\) 482.005 + 482.005i 1.00001 + 1.00001i
\(483\) 47.1912 + 92.6180i 0.0977044 + 0.191756i
\(484\) −125.761 173.096i −0.259837 0.357635i
\(485\) 606.879 242.948i 1.25130 0.500923i
\(486\) −18.0964 13.1478i −0.0372353 0.0270530i
\(487\) 373.620 + 59.1756i 0.767187 + 0.121511i 0.527748 0.849401i \(-0.323036\pi\)
0.239439 + 0.970911i \(0.423036\pi\)
\(488\) −95.8386 + 605.101i −0.196391 + 1.23996i
\(489\) 217.237 299.001i 0.444247 0.611454i
\(490\) 267.532 + 168.361i 0.545985 + 0.343594i
\(491\) −64.7689 + 47.0573i −0.131912 + 0.0958398i −0.651785 0.758404i \(-0.725979\pi\)
0.519873 + 0.854244i \(0.325979\pi\)
\(492\) 197.045 100.399i 0.400498 0.204064i
\(493\) 2.16080 2.16080i 0.00438297 0.00438297i
\(494\) −302.379 98.2489i −0.612103 0.198884i
\(495\) −32.4110 + 37.0455i −0.0654768 + 0.0748393i
\(496\) 9.20522 + 28.3307i 0.0185589 + 0.0571184i
\(497\) 76.8875 150.900i 0.154703 0.303622i
\(498\) −358.618 + 56.7995i −0.720116 + 0.114055i
\(499\) 220.673i 0.442230i −0.975248 0.221115i \(-0.929030\pi\)
0.975248 0.221115i \(-0.0709696\pi\)
\(500\) 65.0335 233.744i 0.130067 0.467488i
\(501\) 53.4966 0.106780
\(502\) 36.3971 + 229.803i 0.0725043 + 0.457774i
\(503\) 120.247 + 61.2690i 0.239060 + 0.121807i 0.569417 0.822049i \(-0.307169\pi\)
−0.330357 + 0.943856i \(0.607169\pi\)
\(504\) −54.0718 + 17.5690i −0.107285 + 0.0348591i
\(505\) −245.382 214.684i −0.485904 0.425117i
\(506\) −39.2810 + 120.894i −0.0776304 + 0.238922i
\(507\) −147.825 147.825i −0.291567 0.291567i
\(508\) 168.878 + 331.442i 0.332437 + 0.652445i
\(509\) 464.907 + 639.890i 0.913374 + 1.25715i 0.966001 + 0.258537i \(0.0832404\pi\)
−0.0526274 + 0.998614i \(0.516760\pi\)
\(510\) 0.571711 0.908472i 0.00112100 0.00178132i
\(511\) 159.661 + 116.001i 0.312449 + 0.227007i
\(512\) 272.706 + 43.1924i 0.532629 + 0.0843601i
\(513\) 25.9148 163.620i 0.0505162 0.318947i
\(514\) 232.133 319.503i 0.451620 0.621601i
\(515\) 129.526 + 323.554i 0.251507 + 0.628261i
\(516\) 41.1230 29.8776i 0.0796958 0.0579024i
\(517\) 55.4348 28.2454i 0.107224 0.0546333i
\(518\) 59.9506 59.9506i 0.115735 0.115735i
\(519\) −140.697 45.7152i −0.271093 0.0880833i
\(520\) 272.317 + 116.618i 0.523687 + 0.224265i
\(521\) 270.466 + 832.408i 0.519128 + 1.59771i 0.775643 + 0.631172i \(0.217426\pi\)
−0.256514 + 0.966540i \(0.582574\pi\)
\(522\) 69.1401 135.695i 0.132452 0.259952i
\(523\) −310.361 + 49.1563i −0.593424 + 0.0939891i −0.445921 0.895072i \(-0.647124\pi\)
−0.147503 + 0.989062i \(0.547124\pi\)
\(524\) 415.530i 0.792997i
\(525\) −86.7872 + 41.6461i −0.165309 + 0.0793260i
\(526\) −74.1814 −0.141029
\(527\) −0.0900749 0.568711i −0.000170920 0.00107915i
\(528\) −22.6303 11.5307i −0.0428605 0.0218385i
\(529\) 190.004 61.7360i 0.359176 0.116703i
\(530\) −372.248 + 222.057i −0.702354 + 0.418976i
\(531\) 42.1118 129.607i 0.0793066 0.244081i
\(532\) −97.2736 97.2736i −0.182845 0.182845i
\(533\) 207.554 + 407.347i 0.389407 + 0.764254i
\(534\) −87.7780 120.816i −0.164378 0.226247i
\(535\) −23.9926 359.578i −0.0448461 0.672109i
\(536\) −888.297 645.386i −1.65727 1.20408i
\(537\) −52.8007 8.36281i −0.0983253 0.0155732i
\(538\) 34.2065 215.971i 0.0635808 0.401433i
\(539\) −84.9794 + 116.964i −0.157661 + 0.217002i
\(540\) −12.3556 + 48.8911i −0.0228807 + 0.0905390i
\(541\) 159.741 116.059i 0.295270 0.214526i −0.430280 0.902695i \(-0.641585\pi\)
0.725550 + 0.688169i \(0.241585\pi\)
\(542\) −277.503 + 141.395i −0.511998 + 0.260876i
\(543\) 277.027 277.027i 0.510179 0.510179i
\(544\) −2.27450 0.739029i −0.00418106 0.00135851i
\(545\) −45.2955 + 499.391i −0.0831110 + 0.916314i
\(546\) −11.8661 36.5202i −0.0217329 0.0668869i
\(547\) 223.030 437.721i 0.407733 0.800222i −0.592251 0.805753i \(-0.701761\pi\)
0.999985 + 0.00553158i \(0.00176076\pi\)
\(548\) −182.450 + 28.8972i −0.332938 + 0.0527322i
\(549\) 215.596i 0.392707i
\(550\) −111.058 39.0339i −0.201923 0.0709707i
\(551\) 1127.89 2.04698
\(552\) 62.3563 + 393.702i 0.112964 + 0.713228i
\(553\) −284.698 145.061i −0.514825 0.262317i
\(554\) −304.967 + 99.0898i −0.550482 + 0.178862i
\(555\) −51.0625 224.437i −0.0920044 0.404392i
\(556\) −23.8984 + 73.5516i −0.0429827 + 0.132287i
\(557\) −490.446 490.446i −0.880514 0.880514i 0.113073 0.993587i \(-0.463931\pi\)
−0.993587 + 0.113073i \(0.963931\pi\)
\(558\) −13.0278 25.5685i −0.0233473 0.0458217i
\(559\) 61.7655 + 85.0129i 0.110493 + 0.152080i
\(560\) −31.8065 38.1518i −0.0567973 0.0681283i
\(561\) 0.397181 + 0.288569i 0.000707987 + 0.000514382i
\(562\) −347.692 55.0689i −0.618668 0.0979874i
\(563\) 74.3177 469.223i 0.132003 0.833434i −0.829473 0.558546i \(-0.811359\pi\)
0.961476 0.274888i \(-0.0886407\pi\)
\(564\) 37.4654 51.5667i 0.0664280 0.0914304i
\(565\) −64.6124 + 53.8662i −0.114358 + 0.0953385i
\(566\) −59.5956 + 43.2987i −0.105293 + 0.0764995i
\(567\) 17.8270 9.08332i 0.0314409 0.0160200i
\(568\) 459.227 459.227i 0.808498 0.808498i
\(569\) 213.907 + 69.5027i 0.375936 + 0.122149i 0.490889 0.871222i \(-0.336672\pi\)
−0.114954 + 0.993371i \(0.536672\pi\)
\(570\) 386.310 87.8906i 0.677737 0.154194i
\(571\) −61.7239 189.967i −0.108098 0.332691i 0.882347 0.470599i \(-0.155962\pi\)
−0.990445 + 0.137908i \(0.955962\pi\)
\(572\) −20.0965 + 39.4416i −0.0351337 + 0.0689538i
\(573\) 69.7077 11.0406i 0.121654 0.0192681i
\(574\) 209.840i 0.365575i
\(575\) 193.203 + 646.654i 0.336005 + 1.12462i
\(576\) −172.812 −0.300021
\(577\) 103.797 + 655.351i 0.179891 + 1.13579i 0.898044 + 0.439905i \(0.144988\pi\)
−0.718153 + 0.695885i \(0.755012\pi\)
\(578\) 369.486 + 188.262i 0.639249 + 0.325714i
\(579\) −388.142 + 126.115i −0.670366 + 0.217815i
\(580\) −341.935 31.0140i −0.589544 0.0534725i
\(581\) 100.359 308.875i 0.172736 0.531626i
\(582\) −229.766 229.766i −0.394787 0.394787i
\(583\) −90.0027 176.640i −0.154379 0.302985i
\(584\) 444.830 + 612.256i 0.761695 + 1.04838i
\(585\) −101.072 25.5425i −0.172772 0.0436623i
\(586\) −390.059 283.395i −0.665630 0.483609i
\(587\) 6.03922 + 0.956518i 0.0102883 + 0.00162950i 0.161576 0.986860i \(-0.448342\pi\)
−0.151288 + 0.988490i \(0.548342\pi\)
\(588\) −23.1706 + 146.294i −0.0394059 + 0.248799i
\(589\) 124.918 171.935i 0.212085 0.291910i
\(590\) 325.189 21.6980i 0.551168 0.0367763i
\(591\) 35.9001 26.0829i 0.0607446 0.0441335i
\(592\) 105.824 53.9198i 0.178756 0.0910808i
\(593\) 291.125 291.125i 0.490935 0.490935i −0.417665 0.908601i \(-0.637152\pi\)
0.908601 + 0.417665i \(0.137152\pi\)
\(594\) 23.2696 + 7.56076i 0.0391745 + 0.0127286i
\(595\) 0.491870 + 0.824552i 0.000826673 + 0.00138580i
\(596\) 48.0397 + 147.851i 0.0806035 + 0.248072i
\(597\) 83.3593 163.602i 0.139630 0.274040i
\(598\) −265.907 + 42.1156i −0.444661 + 0.0704274i
\(599\) 414.898i 0.692651i 0.938114 + 0.346325i \(0.112571\pi\)
−0.938114 + 0.346325i \(0.887429\pi\)
\(600\) −365.866 + 49.0427i −0.609776 + 0.0817378i
\(601\) −996.218 −1.65760 −0.828800 0.559545i \(-0.810976\pi\)
−0.828800 + 0.559545i \(0.810976\pi\)
\(602\) −7.54508 47.6377i −0.0125333 0.0791324i
\(603\) 344.282 + 175.420i 0.570949 + 0.290913i
\(604\) 44.8614 14.5763i 0.0742738 0.0241330i
\(605\) −216.971 + 506.656i −0.358630 + 0.837447i
\(606\) −50.0810 + 154.133i −0.0826418 + 0.254345i
\(607\) −36.4802 36.4802i −0.0600991 0.0600991i 0.676418 0.736518i \(-0.263531\pi\)
−0.736518 + 0.676418i \(0.763531\pi\)
\(608\) −400.739 786.494i −0.659109 1.29358i
\(609\) 80.0693 + 110.206i 0.131477 + 0.180962i
\(610\) 478.677 191.625i 0.784716 0.314140i
\(611\) 106.603 + 77.4515i 0.174473 + 0.126762i
\(612\) 0.496776 + 0.0786816i 0.000811726 + 0.000128565i
\(613\) 121.448 766.790i 0.198120 1.25088i −0.665370 0.746514i \(-0.731726\pi\)
0.863490 0.504366i \(-0.168274\pi\)
\(614\) 132.576 182.475i 0.215921 0.297190i
\(615\) −482.154 303.424i −0.783990 0.493373i
\(616\) 50.3121 36.5539i 0.0816755 0.0593407i
\(617\) −799.539 + 407.386i −1.29585 + 0.660268i −0.959564 0.281492i \(-0.909171\pi\)
−0.336286 + 0.941760i \(0.609171\pi\)
\(618\) 122.498 122.498i 0.198217 0.198217i
\(619\) 490.309 + 159.311i 0.792098 + 0.257368i 0.676997 0.735986i \(-0.263281\pi\)
0.115101 + 0.993354i \(0.463281\pi\)
\(620\) −42.5985 + 48.6897i −0.0687073 + 0.0785317i
\(621\) −43.3474 133.410i −0.0698026 0.214830i
\(622\) −96.2458 + 188.893i −0.154736 + 0.303687i
\(623\) 131.932 20.8960i 0.211769 0.0335410i
\(624\) 53.7923i 0.0862057i
\(625\) −602.936 + 164.599i −0.964698 + 0.263359i
\(626\) −550.688 −0.879694
\(627\) 28.3464 + 178.972i 0.0452096 + 0.285442i
\(628\) 194.855 + 99.2833i 0.310278 + 0.158094i
\(629\) −2.18337 + 0.709421i −0.00347118 + 0.00112786i
\(630\) 36.0122 + 31.5070i 0.0571622 + 0.0500111i
\(631\) 314.889 969.128i 0.499032 1.53586i −0.311547 0.950231i \(-0.600847\pi\)
0.810578 0.585630i \(-0.199153\pi\)
\(632\) −866.408 866.408i −1.37090 1.37090i
\(633\) −32.9624 64.6924i −0.0520734 0.102200i
\(634\) 345.180 + 475.099i 0.544448 + 0.749368i
\(635\) 510.379 811.013i 0.803746 1.27719i
\(636\) −164.315 119.382i −0.258357 0.187707i
\(637\) −302.430 47.9002i −0.474773 0.0751966i
\(638\) −26.0595 + 164.533i −0.0408456 + 0.257889i
\(639\) −134.336 + 184.898i −0.210229 + 0.289356i
\(640\) 52.2011 + 130.397i 0.0815643 + 0.203746i
\(641\) −822.390 + 597.501i −1.28298 + 0.932139i −0.999639 0.0268797i \(-0.991443\pi\)
−0.283341 + 0.959019i \(0.591443\pi\)
\(642\) −159.610 + 81.3253i −0.248614 + 0.126675i
\(643\) −244.880 + 244.880i −0.380839 + 0.380839i −0.871405 0.490565i \(-0.836790\pi\)
0.490565 + 0.871405i \(0.336790\pi\)
\(644\) −110.785 35.9963i −0.172027 0.0558948i
\(645\) −120.368 51.5468i −0.186618 0.0799175i
\(646\) −1.22108 3.75810i −0.00189022 0.00581750i
\(647\) −95.1186 + 186.681i −0.147015 + 0.288533i −0.952757 0.303734i \(-0.901767\pi\)
0.805742 + 0.592266i \(0.201767\pi\)
\(648\) 75.7793 12.0023i 0.116943 0.0185220i
\(649\) 149.064i 0.229682i
\(650\) −33.1235 247.107i −0.0509593 0.380164i
\(651\) 25.6678 0.0394283
\(652\) 64.7900 + 409.068i 0.0993711 + 0.627404i
\(653\) −938.922 478.405i −1.43786 0.732626i −0.450746 0.892652i \(-0.648842\pi\)
−0.987113 + 0.160026i \(0.948842\pi\)
\(654\) 237.054 77.0235i 0.362468 0.117773i
\(655\) −919.276 + 548.376i −1.40347 + 0.837215i
\(656\) 90.8371 279.568i 0.138471 0.426171i
\(657\) −188.319 188.319i −0.286634 0.286634i
\(658\) −27.4576 53.8885i −0.0417288 0.0818975i
\(659\) 285.009 + 392.281i 0.432487 + 0.595268i 0.968522 0.248928i \(-0.0800784\pi\)
−0.536035 + 0.844196i \(0.680078\pi\)
\(660\) −3.67234 55.0375i −0.00556415 0.0833901i
\(661\) 299.590 + 217.665i 0.453237 + 0.329296i 0.790873 0.611981i \(-0.209627\pi\)
−0.337635 + 0.941277i \(0.609627\pi\)
\(662\) 405.898 + 64.2879i 0.613138 + 0.0971116i
\(663\) −0.162657 + 1.02698i −0.000245335 + 0.00154898i
\(664\) 732.028 1007.55i 1.10245 1.51740i
\(665\) −86.8258 + 343.570i −0.130565 + 0.516647i
\(666\) −92.5619 + 67.2502i −0.138982 + 0.100976i
\(667\) 850.965 433.588i 1.27581 0.650057i
\(668\) −42.3908 + 42.3908i −0.0634593 + 0.0634593i
\(669\) −118.301 38.4382i −0.176832 0.0574562i
\(670\) −83.4734 + 920.308i −0.124587 + 1.37359i
\(671\) 72.8741 + 224.283i 0.108605 + 0.334252i
\(672\) 48.3998 94.9899i 0.0720234 0.141354i
\(673\) 408.101 64.6369i 0.606391 0.0960429i 0.154314 0.988022i \(-0.450683\pi\)
0.452077 + 0.891979i \(0.350683\pi\)
\(674\) 419.308i 0.622118i
\(675\) 124.467 37.1875i 0.184396 0.0550925i
\(676\) 234.273 0.346558
\(677\) −142.220 897.942i −0.210074 1.32635i −0.836969 0.547250i \(-0.815675\pi\)
0.626895 0.779104i \(-0.284325\pi\)
\(678\) 37.2568 + 18.9833i 0.0549511 + 0.0279990i
\(679\) 276.421 89.8146i 0.407100 0.132275i
\(680\) 0.816779 + 3.59003i 0.00120115 + 0.00527946i
\(681\) −218.148 + 671.390i −0.320335 + 0.985889i
\(682\) 22.1952 + 22.1952i 0.0325443 + 0.0325443i
\(683\) 187.663 + 368.309i 0.274762 + 0.539252i 0.986613 0.163079i \(-0.0521427\pi\)
−0.711851 + 0.702331i \(0.752143\pi\)
\(684\) 109.118 + 150.188i 0.159529 + 0.219572i
\(685\) 304.709 + 365.498i 0.444831 + 0.533573i
\(686\) 240.158 + 174.485i 0.350084 + 0.254351i
\(687\) −514.420 81.4762i −0.748792 0.118597i
\(688\) 10.5696 66.7336i 0.0153627 0.0969964i
\(689\) 246.796 339.685i 0.358194 0.493012i
\(690\) 257.675 214.819i 0.373441 0.311331i
\(691\) −346.098 + 251.455i −0.500866 + 0.363900i −0.809348 0.587330i \(-0.800179\pi\)
0.308482 + 0.951230i \(0.400179\pi\)
\(692\) 147.713 75.2638i 0.213459 0.108763i
\(693\) −15.4751 + 15.4751i −0.0223305 + 0.0223305i
\(694\) 323.559 + 105.131i 0.466224 + 0.151485i
\(695\) 194.257 44.1959i 0.279506 0.0635913i
\(696\) 161.422 + 496.806i 0.231928 + 0.713802i
\(697\) −2.57957 + 5.06270i −0.00370097 + 0.00726355i
\(698\) 465.365 73.7066i 0.666713 0.105597i
\(699\) 293.581i 0.420002i
\(700\) 35.7698 101.771i 0.0510998 0.145387i
\(701\) 573.168 0.817643 0.408821 0.912614i \(-0.365940\pi\)
0.408821 + 0.912614i \(0.365940\pi\)
\(702\) 8.10636 + 51.1815i 0.0115475 + 0.0729082i
\(703\) −754.984 384.684i −1.07395 0.547203i
\(704\) 179.775 58.4125i 0.255363 0.0829724i
\(705\) −163.524 14.8319i −0.231949 0.0210381i
\(706\) −179.183 + 551.468i −0.253800 + 0.781116i
\(707\) −102.504 102.504i −0.144984 0.144984i
\(708\) 69.3312 + 136.070i 0.0979255 + 0.192190i
\(709\) 536.938 + 739.031i 0.757317 + 1.04236i 0.997432 + 0.0716131i \(0.0228147\pi\)
−0.240115 + 0.970744i \(0.577185\pi\)
\(710\) −529.921 133.920i −0.746367 0.188619i
\(711\) 348.841 + 253.448i 0.490635 + 0.356467i
\(712\) 505.923 + 80.1304i 0.710566 + 0.112543i
\(713\) 28.1517 177.743i 0.0394834 0.249288i
\(714\) 0.280520 0.386102i 0.000392885 0.000540759i
\(715\) 113.778 7.59176i 0.159130 0.0106178i
\(716\) 48.4661 35.2127i 0.0676900 0.0491797i
\(717\) 404.298 206.000i 0.563875 0.287309i
\(718\) −185.874 + 185.874i −0.258877 + 0.258877i
\(719\) 737.539 + 239.641i 1.02579 + 0.333298i 0.773123 0.634257i \(-0.218694\pi\)
0.252663 + 0.967554i \(0.418694\pi\)
\(720\) 34.3397 + 57.5658i 0.0476941 + 0.0799524i
\(721\) 47.8842 + 147.372i 0.0664136 + 0.204400i
\(722\) 426.961 837.957i 0.591358 1.16061i
\(723\) 812.674 128.715i 1.12403 0.178029i
\(724\) 439.034i 0.606400i
\(725\) 382.640 + 797.391i 0.527780 + 1.09985i
\(726\) 273.967 0.377365
\(727\) 174.272 + 1100.31i 0.239713 + 1.51349i 0.754573 + 0.656216i \(0.227844\pi\)
−0.514860 + 0.857274i \(0.672156\pi\)
\(728\) 117.356 + 59.7959i 0.161203 + 0.0821373i
\(729\) −25.6785 + 8.34346i −0.0352243 + 0.0114451i
\(730\) 250.733 585.495i 0.343470 0.802047i
\(731\) −0.403577 + 1.24208i −0.000552089 + 0.00169916i
\(732\) 170.839 + 170.839i 0.233386 + 0.233386i
\(733\) −179.936 353.144i −0.245479 0.481779i 0.735086 0.677974i \(-0.237142\pi\)
−0.980565 + 0.196194i \(0.937142\pi\)
\(734\) −196.765 270.824i −0.268072 0.368970i
\(735\) 354.223 141.804i 0.481937 0.192930i
\(736\) −604.696 439.337i −0.821598 0.596926i
\(737\) −417.449 66.1174i −0.566417 0.0897116i
\(738\) −44.2982 + 279.688i −0.0600247 + 0.378981i
\(739\) 432.274 594.974i 0.584944 0.805106i −0.409283 0.912408i \(-0.634221\pi\)
0.994227 + 0.107301i \(0.0342210\pi\)
\(740\) 218.307 + 137.383i 0.295009 + 0.185652i
\(741\) −310.480 + 225.577i −0.419001 + 0.304422i
\(742\) −171.713 + 87.4923i −0.231419 + 0.117914i
\(743\) 608.093 608.093i 0.818429 0.818429i −0.167451 0.985880i \(-0.553554\pi\)
0.985880 + 0.167451i \(0.0535537\pi\)
\(744\) 93.6113 + 30.4162i 0.125822 + 0.0408819i
\(745\) 263.692 301.397i 0.353949 0.404560i
\(746\) 52.1998 + 160.654i 0.0699729 + 0.215354i
\(747\) −198.971 + 390.502i −0.266360 + 0.522760i
\(748\) −0.543389 + 0.0860644i −0.000726456 + 0.000115059i
\(749\) 160.230i 0.213925i
\(750\) 193.194 + 243.295i 0.257592 + 0.324394i
\(751\) −1051.05 −1.39954 −0.699770 0.714368i \(-0.746714\pi\)
−0.699770 + 0.714368i \(0.746714\pi\)
\(752\) −13.2538 83.6813i −0.0176248 0.111278i
\(753\) 250.234 + 127.501i 0.332316 + 0.169323i
\(754\) −335.544 + 109.025i −0.445019 + 0.144595i
\(755\) −91.4508 80.0102i −0.121127 0.105974i
\(756\) −6.92852 + 21.3238i −0.00916471 + 0.0282061i
\(757\) −636.529 636.529i −0.840857 0.840857i 0.148113 0.988970i \(-0.452680\pi\)
−0.988970 + 0.148113i \(0.952680\pi\)
\(758\) 357.660 + 701.948i 0.471848 + 0.926053i
\(759\) 90.1881 + 124.133i 0.118825 + 0.163548i
\(760\) −723.785 + 1150.12i −0.952348 + 1.51332i
\(761\) −742.006 539.099i −0.975041 0.708409i −0.0184461 0.999830i \(-0.505872\pi\)
−0.956595 + 0.291421i \(0.905872\pi\)
\(762\) −470.453 74.5124i −0.617392 0.0977853i
\(763\) −34.8769 + 220.204i −0.0457102 + 0.288603i
\(764\) −46.4879 + 63.9851i −0.0608480 + 0.0837501i
\(765\) −0.481530 1.20285i −0.000629451 0.00157236i
\(766\) 96.0956 69.8175i 0.125451 0.0911456i
\(767\) −281.295 + 143.327i −0.366748 + 0.186867i
\(768\) 331.570 331.570i 0.431731 0.431731i
\(769\) −797.315 259.063i −1.03682 0.336884i −0.259337 0.965787i \(-0.583504\pi\)
−0.777484 + 0.628903i \(0.783504\pi\)
\(770\) −48.1130 20.6040i −0.0624844 0.0267584i
\(771\) −147.309 453.371i −0.191063 0.588030i
\(772\) 207.631 407.498i 0.268952 0.527847i
\(773\) −576.333 + 91.2823i −0.745580 + 0.118088i −0.517654 0.855590i \(-0.673195\pi\)
−0.227926 + 0.973678i \(0.573195\pi\)
\(774\) 65.0875i 0.0840923i
\(775\) 163.933 + 29.9847i 0.211527 + 0.0386899i
\(776\) 1114.55 1.43627
\(777\) −16.0093 101.079i −0.0206040 0.130088i
\(778\) −867.827 442.180i −1.11546 0.568354i
\(779\) −1994.54 + 648.065i −2.56038 + 0.831919i
\(780\) 100.329 59.8494i 0.128627 0.0767301i
\(781\) 77.2516 237.756i 0.0989137 0.304425i
\(782\) −2.36599 2.36599i −0.00302556 0.00302556i
\(783\) −83.4566 163.793i −0.106586 0.209186i
\(784\) 115.723 + 159.280i 0.147606 + 0.203163i
\(785\) −37.5058 562.100i −0.0477781 0.716051i
\(786\) 430.457 + 312.745i 0.547655 + 0.397895i
\(787\) 1439.16 + 227.941i 1.82867 + 0.289633i 0.973495 0.228709i \(-0.0734504\pi\)
0.855174 + 0.518342i \(0.173450\pi\)
\(788\) −7.77912 + 49.1154i −0.00987198 + 0.0623292i
\(789\) −52.6313 + 72.4407i −0.0667063 + 0.0918133i
\(790\) −252.662 + 999.783i −0.319825 + 1.26555i
\(791\) −30.2585 + 21.9841i −0.0382535 + 0.0277928i
\(792\) −74.7759 + 38.1002i −0.0944140 + 0.0481063i
\(793\) −353.172 + 353.172i −0.445361 + 0.445361i
\(794\) −572.023 185.861i −0.720432 0.234082i
\(795\) −47.2611 + 521.062i −0.0594479 + 0.655423i
\(796\) 63.5844 + 195.693i 0.0798798 + 0.245845i
\(797\) 84.3810 165.607i 0.105873 0.207788i −0.831992 0.554788i \(-0.812800\pi\)
0.937865 + 0.347000i \(0.112800\pi\)
\(798\) 173.980 27.5557i 0.218020 0.0345310i
\(799\) 1.63768i 0.00204966i
\(800\) 420.082 550.135i 0.525102 0.687668i
\(801\) −180.259 −0.225043
\(802\) 45.4022 + 286.658i 0.0566112 + 0.357429i
\(803\) 259.561 + 132.253i 0.323239 + 0.164698i
\(804\) −411.813 + 133.806i −0.512206 + 0.166426i
\(805\) 66.5690 + 292.594i 0.0826944 + 0.363471i
\(806\) −20.5431 + 63.2253i −0.0254878 + 0.0784433i
\(807\) −186.634 186.634i −0.231269 0.231269i
\(808\) −252.368 495.300i −0.312337 0.612995i
\(809\) −665.339 915.760i −0.822421 1.13197i −0.989287 0.145986i \(-0.953365\pi\)
0.166866 0.985980i \(-0.446635\pi\)
\(810\) −41.3481 49.5969i −0.0510470 0.0612307i
\(811\) −380.314 276.315i −0.468945 0.340709i 0.328085 0.944648i \(-0.393597\pi\)
−0.797030 + 0.603940i \(0.793597\pi\)
\(812\) −150.775 23.8803i −0.185683 0.0294093i
\(813\) −58.8098 + 371.310i −0.0723368 + 0.456716i
\(814\) 73.5603 101.247i 0.0903689 0.124382i
\(815\) 819.475 683.182i 1.00549 0.838260i
\(816\) 0.540873 0.392967i 0.000662835 0.000481578i
\(817\) −429.497 + 218.840i −0.525700 + 0.267858i
\(818\) 314.292 314.292i 0.384220 0.384220i
\(819\) −44.0823 14.3232i −0.0538245 0.0174886i
\(820\) 622.494 141.626i 0.759139 0.172714i
\(821\) −192.145 591.361i −0.234038 0.720294i −0.997248 0.0741431i \(-0.976378\pi\)
0.763210 0.646150i \(-0.223622\pi\)
\(822\) 107.384 210.753i 0.130638 0.256391i
\(823\) 725.192 114.859i 0.881156 0.139561i 0.300570 0.953760i \(-0.402823\pi\)
0.580587 + 0.814198i \(0.302823\pi\)
\(824\) 594.214i 0.721134i
\(825\) −116.913 + 80.7574i −0.141712 + 0.0978877i
\(826\) 144.906 0.175431
\(827\) −87.9936 555.570i −0.106401 0.671790i −0.982019 0.188784i \(-0.939545\pi\)
0.875618 0.483005i \(-0.160455\pi\)
\(828\) 140.063 + 71.3654i 0.169158 + 0.0861902i
\(829\) 595.744 193.569i 0.718630 0.233497i 0.0732008 0.997317i \(-0.476679\pi\)
0.645429 + 0.763820i \(0.276679\pi\)
\(830\) −1043.86 94.6796i −1.25766 0.114072i
\(831\) −119.608 + 368.115i −0.143932 + 0.442978i
\(832\) 283.086 + 283.086i 0.340248 + 0.340248i
\(833\) −1.72770 3.39081i −0.00207407 0.00407060i
\(834\) −58.2068 80.1148i −0.0697924 0.0960610i
\(835\) 149.724 + 37.8378i 0.179311 + 0.0453147i
\(836\) −164.280 119.356i −0.196507 0.142771i
\(837\) −34.2117 5.41860i −0.0408742 0.00647384i
\(838\) −171.077 + 1080.14i −0.204150 + 1.28895i
\(839\) 480.122 660.831i 0.572255 0.787641i −0.420565 0.907262i \(-0.638168\pi\)
0.992820 + 0.119622i \(0.0381681\pi\)
\(840\) −163.761 + 10.9268i −0.194953 + 0.0130081i
\(841\) 332.178 241.341i 0.394980 0.286969i
\(842\) 297.575 151.622i 0.353414 0.180074i
\(843\) −300.462 + 300.462i −0.356420 + 0.356420i
\(844\) 77.3819 + 25.1429i 0.0916847 + 0.0297902i
\(845\) −309.171 518.281i −0.365882 0.613351i
\(846\) 25.2211 + 77.6226i 0.0298122 + 0.0917524i
\(847\) −111.252 + 218.345i −0.131349 + 0.257786i
\(848\) −266.647 + 42.2327i −0.314442 + 0.0498027i
\(849\) 88.9174i 0.104732i
\(850\) 2.24264 2.13823i 0.00263840 0.00251557i
\(851\) −717.500 −0.843126
\(852\) −40.0653 252.962i −0.0470250 0.296904i
\(853\) 155.268 + 79.1128i 0.182025 + 0.0927466i 0.542629 0.839973i \(-0.317429\pi\)
−0.360603 + 0.932719i \(0.617429\pi\)
\(854\) 218.027 70.8414i 0.255301 0.0829525i
\(855\) 188.256 439.603i 0.220183 0.514156i
\(856\) 189.871 584.363i 0.221812 0.682667i
\(857\) 316.537 + 316.537i 0.369354 + 0.369354i 0.867242 0.497887i \(-0.165891\pi\)
−0.497887 + 0.867242i \(0.665891\pi\)
\(858\) −25.7330 50.5038i −0.0299918 0.0588623i
\(859\) −524.013 721.242i −0.610027 0.839630i 0.386553 0.922267i \(-0.373666\pi\)
−0.996580 + 0.0826374i \(0.973666\pi\)
\(860\) 136.226 54.5344i 0.158402 0.0634120i
\(861\) −204.916 148.880i −0.237998 0.172915i
\(862\) −1098.84 174.040i −1.27476 0.201902i
\(863\) −64.6532 + 408.204i −0.0749168 + 0.473006i 0.921497 + 0.388386i \(0.126967\pi\)
−0.996413 + 0.0846194i \(0.973033\pi\)
\(864\) −84.5632 + 116.391i −0.0978740 + 0.134712i
\(865\) −361.444 227.460i −0.417854 0.262960i
\(866\) 91.6499 66.5876i 0.105831 0.0768910i
\(867\) 445.993 227.245i 0.514410 0.262105i
\(868\) −20.3392 + 20.3392i −0.0234323 + 0.0234323i
\(869\) −448.566 145.748i −0.516187 0.167719i
\(870\) 289.483 330.876i 0.332739 0.380317i
\(871\) −276.615 851.334i −0.317583 0.977421i
\(872\) −388.137 + 761.761i −0.445111 + 0.873580i
\(873\) −387.392 + 61.3569i −0.443748 + 0.0702828i
\(874\) 1234.99i 1.41303i
\(875\) −272.353 + 55.1737i −0.311260 + 0.0630557i
\(876\) 298.448 0.340694
\(877\) 21.4347 + 135.333i 0.0244409 + 0.154314i 0.996890 0.0787996i \(-0.0251087\pi\)
−0.972450 + 0.233113i \(0.925109\pi\)
\(878\) 508.950 + 259.323i 0.579670 + 0.295357i
\(879\) −553.490 + 179.840i −0.629681 + 0.204596i
\(880\) −55.1814 48.2781i −0.0627061 0.0548615i
\(881\) −212.803 + 654.939i −0.241547 + 0.743404i 0.754639 + 0.656141i \(0.227812\pi\)
−0.996185 + 0.0872634i \(0.972188\pi\)
\(882\) −134.110 134.110i −0.152052 0.152052i
\(883\) 564.040 + 1106.99i 0.638777 + 1.25367i 0.952611 + 0.304192i \(0.0983865\pi\)
−0.313834 + 0.949478i \(0.601613\pi\)
\(884\) −0.684888 0.942668i −0.000774760 0.00106637i
\(885\) 209.531 332.953i 0.236758 0.376219i
\(886\) 729.707 + 530.163i 0.823597 + 0.598379i
\(887\) 583.902 + 92.4810i 0.658289 + 0.104263i 0.476637 0.879100i \(-0.341856\pi\)
0.181652 + 0.983363i \(0.441856\pi\)
\(888\) 61.3910 387.608i 0.0691340 0.436495i
\(889\) 250.426 344.682i 0.281694 0.387718i
\(890\) −160.217 400.220i −0.180020 0.449686i
\(891\) 23.8930 17.3593i 0.0268160 0.0194829i
\(892\) 124.200 63.2831i 0.139238 0.0709452i
\(893\) −427.414 + 427.414i −0.478627 + 0.478627i
\(894\) −189.319 61.5134i −0.211766 0.0688070i
\(895\) −141.862 60.7511i −0.158505 0.0678783i
\(896\) 19.2981 + 59.3934i 0.0215380 + 0.0662873i
\(897\) −147.532 + 289.549i −0.164473 + 0.322797i
\(898\) −352.126 + 55.7712i −0.392122 + 0.0621060i
\(899\) 235.833i 0.262328i
\(900\) −69.1607 + 128.096i −0.0768452 + 0.142328i
\(901\) 5.21838 0.00579177
\(902\) −48.4548 305.931i −0.0537192 0.339170i
\(903\) −51.8731 26.4307i −0.0574453 0.0292699i
\(904\) −136.405 + 44.3205i −0.150890 + 0.0490271i
\(905\) 971.272 579.394i 1.07323 0.640214i
\(906\) −18.6646 + 57.4436i −0.0206011 + 0.0634036i
\(907\) 977.680 + 977.680i 1.07793 + 1.07793i 0.996695 + 0.0812324i \(0.0258856\pi\)
0.0812324 + 0.996695i \(0.474114\pi\)
\(908\) −359.150 704.872i −0.395540 0.776291i
\(909\) 114.985 + 158.263i 0.126496 + 0.174106i
\(910\) −7.38000 110.604i −0.00810989 0.121543i
\(911\) 1069.38 + 776.951i 1.17385 + 0.852855i 0.991465 0.130371i \(-0.0416169\pi\)
0.182389 + 0.983226i \(0.441617\pi\)
\(912\) 243.721 + 38.6016i 0.267238 + 0.0423263i
\(913\) 74.9936 473.491i 0.0821398 0.518610i
\(914\) −623.419 + 858.062i −0.682077 + 0.938799i
\(915\) 152.490 603.402i 0.166655 0.659456i
\(916\) 472.190 343.066i 0.515491 0.374526i
\(917\) −424.050 + 216.064i −0.462432 + 0.235621i
\(918\) −0.455403 + 0.455403i −0.000496081 + 0.000496081i
\(919\) −240.353 78.0956i −0.261538 0.0849788i 0.175313 0.984513i \(-0.443906\pi\)
−0.436851 + 0.899534i \(0.643906\pi\)
\(920\) −103.942 + 1145.98i −0.112981 + 1.24563i
\(921\) −84.1314 258.930i −0.0913479 0.281140i
\(922\) 345.614 678.305i 0.374852 0.735689i
\(923\) 522.944 82.8262i 0.566570 0.0897358i
\(924\) 24.5250i 0.0265422i
\(925\) 15.8313 664.263i 0.0171149 0.718122i
\(926\) 583.475 0.630103
\(927\) −32.7121 206.536i −0.0352881 0.222800i
\(928\) −872.757 444.692i −0.940471 0.479194i
\(929\) 880.302 286.027i 0.947580 0.307887i 0.205848 0.978584i \(-0.434005\pi\)
0.741732 + 0.670697i \(0.234005\pi\)
\(930\) −18.3773 80.7747i −0.0197605 0.0868545i
\(931\) 434.050 1335.87i 0.466219 1.43488i
\(932\) 232.634 + 232.634i 0.249608 + 0.249608i
\(933\) 116.175 + 228.006i 0.124518 + 0.244379i
\(934\) 100.837 + 138.790i 0.107963 + 0.148598i
\(935\) 0.907511 + 1.08856i 0.000970600 + 0.00116423i
\(936\) −143.797 104.474i −0.153629 0.111618i
\(937\) 970.377 + 153.693i 1.03562 + 0.164026i 0.651023 0.759058i \(-0.274340\pi\)
0.384598 + 0.923084i \(0.374340\pi\)
\(938\) −64.2732 + 405.805i −0.0685216 + 0.432628i
\(939\) −390.710 + 537.767i −0.416092 + 0.572701i
\(940\) 141.330 117.824i 0.150351 0.125345i
\(941\) −1067.29 + 775.433i −1.13421 + 0.824052i −0.986302 0.164950i \(-0.947254\pi\)
−0.147908 + 0.989001i \(0.547254\pi\)
\(942\) −249.506 + 127.129i −0.264868 + 0.134957i
\(943\) −1255.70 + 1255.70i −1.33160 + 1.33160i
\(944\) 193.057 + 62.7280i 0.204509 + 0.0664491i
\(945\) 56.3181 12.8131i 0.0595959 0.0135589i
\(946\) −22.0003 67.7101i −0.0232562 0.0715752i
\(947\) −424.436 + 833.002i −0.448190 + 0.879622i 0.550798 + 0.834639i \(0.314323\pi\)
−0.998988 + 0.0449833i \(0.985677\pi\)
\(948\) −477.255 + 75.5898i −0.503434 + 0.0797361i
\(949\) 616.976i 0.650133i
\(950\) 1143.35 + 27.2495i 1.20353 + 0.0286836i
\(951\) 708.855 0.745378
\(952\) 0.256079 + 1.61682i 0.000268991 + 0.00169834i
\(953\) 794.055 + 404.591i 0.833216 + 0.424545i 0.817916 0.575338i \(-0.195130\pi\)
0.0153004 + 0.999883i \(0.495130\pi\)
\(954\) 247.341 80.3658i 0.259267 0.0842409i
\(955\) 202.904 + 18.4037i 0.212465 + 0.0192709i
\(956\) −157.132 + 483.602i −0.164364 + 0.505860i
\(957\) 142.183 + 142.183i 0.148572 + 0.148572i
\(958\) 221.481 + 434.680i 0.231191 + 0.453737i
\(959\) 124.359 + 171.165i 0.129676 + 0.178483i
\(960\) −483.660 122.229i −0.503812 0.127322i
\(961\) 741.515 + 538.742i 0.771608 + 0.560606i
\(962\) 261.791 + 41.4636i 0.272132 + 0.0431015i
\(963\) −33.8253 + 213.565i −0.0351249 + 0.221770i
\(964\) −541.971 + 745.959i −0.562210 + 0.773816i
\(965\) −1175.52 + 78.4356i −1.21815 + 0.0812804i
\(966\) 120.671 87.6725i 0.124918 0.0907583i
\(967\) −624.105 + 317.998i −0.645404 + 0.328850i −0.745871 0.666091i \(-0.767966\pi\)
0.100467 + 0.994940i \(0.467966\pi\)
\(968\) −664.478 + 664.478i −0.686444 + 0.686444i
\(969\) −4.53627 1.47392i −0.00468140 0.00152108i
\(970\) −480.548 805.572i −0.495410 0.830486i
\(971\) −2.06234 6.34723i −0.00212393 0.00653680i 0.949989 0.312284i \(-0.101094\pi\)
−0.952113 + 0.305747i \(0.901094\pi\)
\(972\) 13.7363 26.9591i 0.0141320 0.0277357i
\(973\) 87.4862 13.8565i 0.0899139 0.0142410i
\(974\) 542.801i 0.557290i
\(975\) −264.809 142.975i −0.271599 0.146641i
\(976\) 321.143 0.329040
\(977\) 244.140 + 1541.44i 0.249887 + 1.57772i 0.719271 + 0.694730i \(0.244476\pi\)
−0.469384 + 0.882994i \(0.655524\pi\)
\(978\) −472.526 240.764i −0.483155 0.246180i
\(979\) 187.523 60.9298i 0.191545 0.0622368i
\(980\) −168.322 + 393.053i −0.171757 + 0.401074i
\(981\) 92.9723 286.139i 0.0947729 0.291681i
\(982\) 81.2314 + 81.2314i 0.0827204 + 0.0827204i
\(983\) 165.564 + 324.937i 0.168427 + 0.330556i 0.959757 0.280833i \(-0.0906108\pi\)
−0.791330 + 0.611390i \(0.790611\pi\)
\(984\) −570.913 785.795i −0.580197 0.798572i
\(985\) 118.924 47.6080i 0.120735 0.0483330i
\(986\) −3.54747 2.57738i −0.00359784 0.00261398i
\(987\) −72.1051 11.4203i −0.0730548 0.0115707i
\(988\) 67.2773 424.772i 0.0680944 0.429931i
\(989\) −239.918 + 330.219i −0.242587 + 0.333892i
\(990\) 59.7785 + 37.6192i 0.0603823 + 0.0379992i
\(991\) 367.512 267.013i 0.370850 0.269438i −0.386714 0.922200i \(-0.626390\pi\)
0.757563 + 0.652762i \(0.226390\pi\)
\(992\) −164.450 + 83.7916i −0.165776 + 0.0844673i
\(993\) 350.762 350.762i 0.353234 0.353234i
\(994\) −231.124 75.0968i −0.232519 0.0755501i
\(995\) 349.017 398.923i 0.350771 0.400928i
\(996\) −151.770 467.099i −0.152379 0.468975i
\(997\) −219.351 + 430.501i −0.220011 + 0.431796i −0.974460 0.224563i \(-0.927904\pi\)
0.754448 + 0.656359i \(0.227904\pi\)
\(998\) −312.751 + 49.5349i −0.313378 + 0.0496342i
\(999\) 138.104i 0.138242i
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 75.3.k.a.37.3 80
3.2 odd 2 225.3.r.b.37.8 80
5.2 odd 4 375.3.k.b.43.8 80
5.3 odd 4 375.3.k.c.43.3 80
5.4 even 2 375.3.k.a.82.8 80
25.2 odd 20 375.3.k.a.343.8 80
25.11 even 5 375.3.k.c.157.3 80
25.14 even 10 375.3.k.b.157.8 80
25.23 odd 20 inner 75.3.k.a.73.3 yes 80
75.23 even 20 225.3.r.b.73.8 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.3.k.a.37.3 80 1.1 even 1 trivial
75.3.k.a.73.3 yes 80 25.23 odd 20 inner
225.3.r.b.37.8 80 3.2 odd 2
225.3.r.b.73.8 80 75.23 even 20
375.3.k.a.82.8 80 5.4 even 2
375.3.k.a.343.8 80 25.2 odd 20
375.3.k.b.43.8 80 5.2 odd 4
375.3.k.b.157.8 80 25.14 even 10
375.3.k.c.43.3 80 5.3 odd 4
375.3.k.c.157.3 80 25.11 even 5