Properties

Label 804.2.l.a.431.9
Level $804$
Weight $2$
Character 804.431
Analytic conductor $6.420$
Analytic rank $0$
Dimension $264$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [804,2,Mod(431,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.431");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.l (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(264\)
Relative dimension: \(132\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 431.9
Character \(\chi\) \(=\) 804.431
Dual form 804.2.l.a.707.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39349 - 0.241196i) q^{2} +(1.40279 + 1.01597i) q^{3} +(1.88365 + 0.672210i) q^{4} +2.69591i q^{5} +(-1.70973 - 1.75409i) q^{6} +(-2.30125 + 1.32862i) q^{7} +(-2.46272 - 1.39105i) q^{8} +(0.935617 + 2.85037i) q^{9} +O(q^{10})\) \(q+(-1.39349 - 0.241196i) q^{2} +(1.40279 + 1.01597i) q^{3} +(1.88365 + 0.672210i) q^{4} +2.69591i q^{5} +(-1.70973 - 1.75409i) q^{6} +(-2.30125 + 1.32862i) q^{7} +(-2.46272 - 1.39105i) q^{8} +(0.935617 + 2.85037i) q^{9} +(0.650241 - 3.75673i) q^{10} +(-1.81317 - 3.14050i) q^{11} +(1.95941 + 2.85669i) q^{12} +(-1.62861 + 2.82084i) q^{13} +(3.52723 - 1.29638i) q^{14} +(-2.73895 + 3.78178i) q^{15} +(3.09627 + 2.53242i) q^{16} +(-5.74370 - 3.31613i) q^{17} +(-0.616278 - 4.19764i) q^{18} +(2.90835 + 1.67914i) q^{19} +(-1.81221 + 5.07814i) q^{20} +(-4.57799 - 0.474217i) q^{21} +(1.76916 + 4.81359i) q^{22} +(0.748332 - 1.29615i) q^{23} +(-2.04141 - 4.45339i) q^{24} -2.26790 q^{25} +(2.94984 - 3.53801i) q^{26} +(-1.58342 + 4.94902i) q^{27} +(-5.22785 + 0.955742i) q^{28} +(-7.51302 + 4.33764i) q^{29} +(4.72886 - 4.60926i) q^{30} +(1.29744 - 0.749075i) q^{31} +(-3.70382 - 4.27571i) q^{32} +(0.647160 - 6.24756i) q^{33} +(7.20398 + 6.00636i) q^{34} +(-3.58185 - 6.20394i) q^{35} +(-0.153675 + 5.99803i) q^{36} +(-0.403643 + 0.699131i) q^{37} +(-3.64777 - 3.04135i) q^{38} +(-5.15048 + 2.30241i) q^{39} +(3.75014 - 6.63926i) q^{40} +(5.57648 - 3.21958i) q^{41} +(6.26503 + 1.76501i) q^{42} -6.46571i q^{43} +(-1.30430 - 7.13442i) q^{44} +(-7.68433 + 2.52233i) q^{45} +(-1.35542 + 1.62568i) q^{46} +(2.55148 + 4.41929i) q^{47} +(1.77055 + 6.69815i) q^{48} +(0.0304862 - 0.0528036i) q^{49} +(3.16031 + 0.547009i) q^{50} +(-4.68810 - 10.4872i) q^{51} +(-4.96393 + 4.21870i) q^{52} -3.44533i q^{53} +(3.40017 - 6.51451i) q^{54} +(8.46648 - 4.88812i) q^{55} +(7.51550 - 0.0708840i) q^{56} +(2.37384 + 5.31026i) q^{57} +(11.5156 - 4.23237i) q^{58} +8.67316 q^{59} +(-7.70138 + 5.28239i) q^{60} +(-2.11204 + 3.65817i) q^{61} +(-1.98864 + 0.730895i) q^{62} +(-5.94016 - 5.31632i) q^{63} +(4.12997 + 6.85152i) q^{64} +(-7.60471 - 4.39058i) q^{65} +(-2.40870 + 8.54984i) q^{66} +(-6.46115 - 5.02528i) q^{67} +(-8.58998 - 10.1074i) q^{68} +(2.36660 - 1.05794i) q^{69} +(3.49491 + 9.50908i) q^{70} +(2.90810 + 5.03697i) q^{71} +(1.66085 - 8.32115i) q^{72} +(-3.55746 + 6.16170i) q^{73} +(0.731102 - 0.876877i) q^{74} +(-3.18138 - 2.30412i) q^{75} +(4.34958 + 5.11793i) q^{76} +(8.34508 + 4.81803i) q^{77} +(7.73249 - 1.96613i) q^{78} +(6.69700 - 3.86652i) q^{79} +(-6.82715 + 8.34724i) q^{80} +(-7.24924 + 5.33371i) q^{81} +(-8.54733 + 3.14144i) q^{82} +(-3.57387 + 6.19012i) q^{83} +(-8.30456 - 3.97063i) q^{84} +(8.93997 - 15.4845i) q^{85} +(-1.55950 + 9.00993i) q^{86} +(-14.9461 - 1.54820i) q^{87} +(0.0967350 + 10.2564i) q^{88} +15.3183i q^{89} +(11.3164 - 1.66143i) q^{90} -8.65526i q^{91} +(2.28088 - 1.93845i) q^{92} +(2.58106 + 0.267362i) q^{93} +(-2.48955 - 6.77366i) q^{94} +(-4.52679 + 7.84064i) q^{95} +(-0.851680 - 9.76087i) q^{96} +(-8.07260 + 13.9821i) q^{97} +(-0.0552183 + 0.0662284i) q^{98} +(7.25515 - 8.10650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39349 0.241196i −0.985349 0.170551i
\(3\) 1.40279 + 1.01597i 0.809899 + 0.586570i
\(4\) 1.88365 + 0.672210i 0.941825 + 0.336105i
\(5\) 2.69591i 1.20565i 0.797875 + 0.602823i \(0.205957\pi\)
−0.797875 + 0.602823i \(0.794043\pi\)
\(6\) −1.70973 1.75409i −0.697993 0.716105i
\(7\) −2.30125 + 1.32862i −0.869789 + 0.502173i −0.867278 0.497824i \(-0.834133\pi\)
−0.00251083 + 0.999997i \(0.500799\pi\)
\(8\) −2.46272 1.39105i −0.870703 0.491810i
\(9\) 0.935617 + 2.85037i 0.311872 + 0.950124i
\(10\) 0.650241 3.75673i 0.205624 1.18798i
\(11\) −1.81317 3.14050i −0.546690 0.946895i −0.998498 0.0547799i \(-0.982554\pi\)
0.451808 0.892115i \(-0.350779\pi\)
\(12\) 1.95941 + 2.85669i 0.565634 + 0.824657i
\(13\) −1.62861 + 2.82084i −0.451696 + 0.782360i −0.998492 0.0549061i \(-0.982514\pi\)
0.546796 + 0.837266i \(0.315847\pi\)
\(14\) 3.52723 1.29638i 0.942692 0.346472i
\(15\) −2.73895 + 3.78178i −0.707195 + 0.976451i
\(16\) 3.09627 + 2.53242i 0.774067 + 0.633104i
\(17\) −5.74370 3.31613i −1.39305 0.804279i −0.399400 0.916777i \(-0.630782\pi\)
−0.993652 + 0.112497i \(0.964115\pi\)
\(18\) −0.616278 4.19764i −0.145258 0.989394i
\(19\) 2.90835 + 1.67914i 0.667221 + 0.385220i 0.795023 0.606579i \(-0.207459\pi\)
−0.127802 + 0.991800i \(0.540792\pi\)
\(20\) −1.81221 + 5.07814i −0.405223 + 1.13551i
\(21\) −4.57799 0.474217i −0.999000 0.103483i
\(22\) 1.76916 + 4.81359i 0.377186 + 1.02626i
\(23\) 0.748332 1.29615i 0.156038 0.270266i −0.777399 0.629008i \(-0.783461\pi\)
0.933436 + 0.358743i \(0.116794\pi\)
\(24\) −2.04141 4.45339i −0.416700 0.909044i
\(25\) −2.26790 −0.453581
\(26\) 2.94984 3.53801i 0.578510 0.693860i
\(27\) −1.58342 + 4.94902i −0.304729 + 0.952439i
\(28\) −5.22785 + 0.955742i −0.987971 + 0.180618i
\(29\) −7.51302 + 4.33764i −1.39513 + 0.805480i −0.993878 0.110486i \(-0.964759\pi\)
−0.401255 + 0.915966i \(0.631426\pi\)
\(30\) 4.72886 4.60926i 0.863369 0.841532i
\(31\) 1.29744 0.749075i 0.233026 0.134538i −0.378941 0.925421i \(-0.623712\pi\)
0.611967 + 0.790883i \(0.290378\pi\)
\(32\) −3.70382 4.27571i −0.654749 0.755846i
\(33\) 0.647160 6.24756i 0.112656 1.08756i
\(34\) 7.20398 + 6.00636i 1.23547 + 1.03008i
\(35\) −3.58185 6.20394i −0.605442 1.04866i
\(36\) −0.153675 + 5.99803i −0.0256126 + 0.999672i
\(37\) −0.403643 + 0.699131i −0.0663585 + 0.114936i −0.897296 0.441430i \(-0.854471\pi\)
0.830937 + 0.556366i \(0.187805\pi\)
\(38\) −3.64777 3.04135i −0.591746 0.493372i
\(39\) −5.15048 + 2.30241i −0.824736 + 0.368681i
\(40\) 3.75014 6.63926i 0.592949 1.04976i
\(41\) 5.57648 3.21958i 0.870899 0.502814i 0.00325234 0.999995i \(-0.498965\pi\)
0.867647 + 0.497181i \(0.165631\pi\)
\(42\) 6.26503 + 1.76501i 0.966715 + 0.272347i
\(43\) 6.46571i 0.986012i −0.870026 0.493006i \(-0.835898\pi\)
0.870026 0.493006i \(-0.164102\pi\)
\(44\) −1.30430 7.13442i −0.196630 1.07555i
\(45\) −7.68433 + 2.52233i −1.14551 + 0.376007i
\(46\) −1.35542 + 1.62568i −0.199846 + 0.239694i
\(47\) 2.55148 + 4.41929i 0.372171 + 0.644620i 0.989899 0.141772i \(-0.0452800\pi\)
−0.617728 + 0.786392i \(0.711947\pi\)
\(48\) 1.77055 + 6.69815i 0.255556 + 0.966794i
\(49\) 0.0304862 0.0528036i 0.00435517 0.00754338i
\(50\) 3.16031 + 0.547009i 0.446935 + 0.0773588i
\(51\) −4.68810 10.4872i −0.656466 1.46851i
\(52\) −4.96393 + 4.21870i −0.688373 + 0.585029i
\(53\) 3.44533i 0.473253i −0.971601 0.236626i \(-0.923958\pi\)
0.971601 0.236626i \(-0.0760417\pi\)
\(54\) 3.40017 6.51451i 0.462704 0.886513i
\(55\) 8.46648 4.88812i 1.14162 0.659114i
\(56\) 7.51550 0.0708840i 1.00430 0.00947228i
\(57\) 2.37384 + 5.31026i 0.314423 + 0.703361i
\(58\) 11.5156 4.23237i 1.51207 0.555737i
\(59\) 8.67316 1.12915 0.564575 0.825382i \(-0.309040\pi\)
0.564575 + 0.825382i \(0.309040\pi\)
\(60\) −7.70138 + 5.28239i −0.994244 + 0.681954i
\(61\) −2.11204 + 3.65817i −0.270420 + 0.468380i −0.968969 0.247181i \(-0.920496\pi\)
0.698550 + 0.715561i \(0.253829\pi\)
\(62\) −1.98864 + 0.730895i −0.252558 + 0.0928238i
\(63\) −5.94016 5.31632i −0.748389 0.669794i
\(64\) 4.12997 + 6.85152i 0.516246 + 0.856440i
\(65\) −7.60471 4.39058i −0.943249 0.544585i
\(66\) −2.40870 + 8.54984i −0.296491 + 1.05241i
\(67\) −6.46115 5.02528i −0.789356 0.613936i
\(68\) −8.58998 10.1074i −1.04169 1.22570i
\(69\) 2.36660 1.05794i 0.284905 0.127361i
\(70\) 3.49491 + 9.50908i 0.417722 + 1.13655i
\(71\) 2.90810 + 5.03697i 0.345127 + 0.597778i 0.985377 0.170389i \(-0.0545024\pi\)
−0.640249 + 0.768167i \(0.721169\pi\)
\(72\) 1.66085 8.32115i 0.195733 0.980657i
\(73\) −3.55746 + 6.16170i −0.416369 + 0.721172i −0.995571 0.0940117i \(-0.970031\pi\)
0.579202 + 0.815184i \(0.303364\pi\)
\(74\) 0.731102 0.876877i 0.0849888 0.101935i
\(75\) −3.18138 2.30412i −0.367355 0.266057i
\(76\) 4.34958 + 5.11793i 0.498931 + 0.587066i
\(77\) 8.34508 + 4.81803i 0.951010 + 0.549066i
\(78\) 7.73249 1.96613i 0.875532 0.222620i
\(79\) 6.69700 3.86652i 0.753472 0.435017i −0.0734752 0.997297i \(-0.523409\pi\)
0.826947 + 0.562280i \(0.190076\pi\)
\(80\) −6.82715 + 8.34724i −0.763299 + 0.933250i
\(81\) −7.24924 + 5.33371i −0.805471 + 0.592635i
\(82\) −8.54733 + 3.14144i −0.943895 + 0.346914i
\(83\) −3.57387 + 6.19012i −0.392283 + 0.679454i −0.992750 0.120195i \(-0.961648\pi\)
0.600467 + 0.799649i \(0.294981\pi\)
\(84\) −8.30456 3.97063i −0.906102 0.433231i
\(85\) 8.93997 15.4845i 0.969676 1.67953i
\(86\) −1.55950 + 9.00993i −0.168166 + 0.971565i
\(87\) −14.9461 1.54820i −1.60239 0.165985i
\(88\) 0.0967350 + 10.2564i 0.0103120 + 1.09333i
\(89\) 15.3183i 1.62374i 0.583841 + 0.811868i \(0.301549\pi\)
−0.583841 + 0.811868i \(0.698451\pi\)
\(90\) 11.3164 1.66143i 1.19286 0.175130i
\(91\) 8.65526i 0.907317i
\(92\) 2.28088 1.93845i 0.237798 0.202098i
\(93\) 2.58106 + 0.267362i 0.267644 + 0.0277242i
\(94\) −2.48955 6.77366i −0.256778 0.698650i
\(95\) −4.52679 + 7.84064i −0.464439 + 0.804432i
\(96\) −0.851680 9.76087i −0.0869242 0.996215i
\(97\) −8.07260 + 13.9821i −0.819648 + 1.41967i 0.0862938 + 0.996270i \(0.472498\pi\)
−0.905942 + 0.423402i \(0.860836\pi\)
\(98\) −0.0552183 + 0.0662284i −0.00557789 + 0.00669008i
\(99\) 7.25515 8.10650i 0.729170 0.814734i
\(100\) −4.27194 1.52451i −0.427194 0.152451i
\(101\) −13.0530 + 7.53614i −1.29882 + 0.749874i −0.980200 0.198008i \(-0.936553\pi\)
−0.318620 + 0.947882i \(0.603219\pi\)
\(102\) 4.00336 + 15.7447i 0.396392 + 1.55895i
\(103\) −7.75882 + 4.47956i −0.764499 + 0.441384i −0.830909 0.556409i \(-0.812179\pi\)
0.0664097 + 0.997792i \(0.478846\pi\)
\(104\) 7.93474 4.68145i 0.778065 0.459054i
\(105\) 1.27844 12.3418i 0.124763 1.20444i
\(106\) −0.831000 + 4.80105i −0.0807139 + 0.466319i
\(107\) −16.7910 −1.62325 −0.811625 0.584178i \(-0.801417\pi\)
−0.811625 + 0.584178i \(0.801417\pi\)
\(108\) −6.30938 + 8.25782i −0.607121 + 0.794610i
\(109\) 0.323228 0.0309596 0.0154798 0.999880i \(-0.495072\pi\)
0.0154798 + 0.999880i \(0.495072\pi\)
\(110\) −12.9770 + 4.76949i −1.23731 + 0.454753i
\(111\) −1.27652 + 0.570642i −0.121162 + 0.0541629i
\(112\) −10.4899 1.71393i −0.991202 0.161951i
\(113\) 7.11304 4.10672i 0.669139 0.386327i −0.126612 0.991952i \(-0.540410\pi\)
0.795750 + 0.605625i \(0.207077\pi\)
\(114\) −2.02712 7.97238i −0.189857 0.746682i
\(115\) 3.49429 + 2.01743i 0.325845 + 0.188126i
\(116\) −17.0677 + 3.12027i −1.58470 + 0.289710i
\(117\) −9.56420 2.00293i −0.884210 0.185171i
\(118\) −12.0860 2.09193i −1.11261 0.192578i
\(119\) 17.6236 1.61555
\(120\) 12.0059 5.50344i 1.09598 0.502393i
\(121\) −1.07514 + 1.86220i −0.0977399 + 0.169291i
\(122\) 3.82546 4.58822i 0.346340 0.415398i
\(123\) 11.0936 + 1.14914i 1.00028 + 0.103615i
\(124\) 2.94745 0.538845i 0.264689 0.0483897i
\(125\) 7.36547i 0.658788i
\(126\) 6.99530 + 8.84100i 0.623191 + 0.787619i
\(127\) 3.74329 2.16119i 0.332163 0.191775i −0.324638 0.945838i \(-0.605242\pi\)
0.656801 + 0.754064i \(0.271909\pi\)
\(128\) −4.10252 10.5437i −0.362615 0.931939i
\(129\) 6.56896 9.07001i 0.578364 0.798570i
\(130\) 9.53813 + 7.95248i 0.836549 + 0.697478i
\(131\) 3.64660 0.318605 0.159302 0.987230i \(-0.449076\pi\)
0.159302 + 0.987230i \(0.449076\pi\)
\(132\) 5.41870 11.3332i 0.471637 0.986427i
\(133\) −8.92377 −0.773789
\(134\) 7.79150 + 8.56111i 0.673083 + 0.739567i
\(135\) −13.3421 4.26875i −1.14830 0.367395i
\(136\) 9.53223 + 16.1565i 0.817382 + 1.38541i
\(137\) 12.2871i 1.04976i −0.851177 0.524879i \(-0.824111\pi\)
0.851177 0.524879i \(-0.175889\pi\)
\(138\) −3.55301 + 0.903416i −0.302452 + 0.0769039i
\(139\) 8.56693i 0.726638i 0.931665 + 0.363319i \(0.118356\pi\)
−0.931665 + 0.363319i \(0.881644\pi\)
\(140\) −2.57659 14.0938i −0.217762 1.19114i
\(141\) −0.910681 + 8.79154i −0.0766932 + 0.740381i
\(142\) −2.83752 7.72040i −0.238119 0.647882i
\(143\) 11.8118 0.987750
\(144\) −4.32141 + 11.1949i −0.360117 + 0.932907i
\(145\) −11.6939 20.2544i −0.971124 1.68204i
\(146\) 6.44347 7.72824i 0.533266 0.639594i
\(147\) 0.0964124 0.0430992i 0.00795196 0.00355476i
\(148\) −1.23028 + 1.04558i −0.101129 + 0.0859464i
\(149\) 21.5265i 1.76352i 0.471696 + 0.881761i \(0.343642\pi\)
−0.471696 + 0.881761i \(0.656358\pi\)
\(150\) 3.87749 + 3.97811i 0.316596 + 0.324812i
\(151\) 12.1761 + 7.02986i 0.990875 + 0.572082i 0.905536 0.424270i \(-0.139469\pi\)
0.0853396 + 0.996352i \(0.472802\pi\)
\(152\) −4.82669 8.18090i −0.391496 0.663559i
\(153\) 4.07830 19.4743i 0.329711 1.57440i
\(154\) −10.4667 8.72670i −0.843433 0.703217i
\(155\) 2.01944 + 3.49776i 0.162205 + 0.280947i
\(156\) −11.2494 + 0.874739i −0.900673 + 0.0700352i
\(157\) −2.24187 + 3.88302i −0.178920 + 0.309899i −0.941511 0.336982i \(-0.890594\pi\)
0.762591 + 0.646881i \(0.223927\pi\)
\(158\) −10.2648 + 3.77268i −0.816625 + 0.300138i
\(159\) 3.50035 4.83306i 0.277596 0.383287i
\(160\) 11.5269 9.98515i 0.911283 0.789395i
\(161\) 3.97701i 0.313432i
\(162\) 11.3882 5.68400i 0.894745 0.446578i
\(163\) 17.8072 10.2810i 1.39477 0.805269i 0.400929 0.916109i \(-0.368687\pi\)
0.993838 + 0.110840i \(0.0353540\pi\)
\(164\) 12.6684 2.31600i 0.989233 0.180849i
\(165\) 16.8428 + 1.74468i 1.31121 + 0.135823i
\(166\) 6.47319 7.76389i 0.502417 0.602595i
\(167\) 11.0224 + 19.0914i 0.852939 + 1.47733i 0.878544 + 0.477662i \(0.158516\pi\)
−0.0256045 + 0.999672i \(0.508151\pi\)
\(168\) 10.6147 + 7.53608i 0.818938 + 0.581421i
\(169\) 1.19525 + 2.07023i 0.0919420 + 0.159248i
\(170\) −16.1926 + 19.4212i −1.24191 + 1.48954i
\(171\) −2.06506 + 9.86091i −0.157919 + 0.754083i
\(172\) 4.34631 12.1791i 0.331403 0.928650i
\(173\) 12.0229 + 6.94145i 0.914087 + 0.527749i 0.881744 0.471728i \(-0.156370\pi\)
0.0323433 + 0.999477i \(0.489703\pi\)
\(174\) 20.4538 + 5.76234i 1.55060 + 0.436842i
\(175\) 5.21900 3.01319i 0.394520 0.227776i
\(176\) 2.33899 14.3155i 0.176308 1.07907i
\(177\) 12.1666 + 8.81166i 0.914497 + 0.662325i
\(178\) 3.69471 21.3459i 0.276930 1.59995i
\(179\) 3.63905 0.271995 0.135998 0.990709i \(-0.456576\pi\)
0.135998 + 0.990709i \(0.456576\pi\)
\(180\) −16.1701 0.414294i −1.20525 0.0308797i
\(181\) −3.05055 5.28371i −0.226746 0.392735i 0.730096 0.683345i \(-0.239475\pi\)
−0.956842 + 0.290609i \(0.906142\pi\)
\(182\) −2.08761 + 12.0610i −0.154744 + 0.894024i
\(183\) −6.67933 + 2.98586i −0.493750 + 0.220721i
\(184\) −3.64594 + 2.15108i −0.268782 + 0.158580i
\(185\) −1.88479 1.08818i −0.138572 0.0800049i
\(186\) −3.53221 0.995109i −0.258994 0.0729649i
\(187\) 24.0508i 1.75877i
\(188\) 1.83540 + 10.0395i 0.133860 + 0.732207i
\(189\) −2.93155 13.4927i −0.213239 0.981448i
\(190\) 8.19919 9.83403i 0.594832 0.713436i
\(191\) −0.838003 + 1.45146i −0.0606358 + 0.105024i −0.894750 0.446568i \(-0.852646\pi\)
0.834114 + 0.551592i \(0.185979\pi\)
\(192\) −1.16747 + 13.8071i −0.0842551 + 0.996444i
\(193\) 13.3286 0.959411 0.479706 0.877429i \(-0.340743\pi\)
0.479706 + 0.877429i \(0.340743\pi\)
\(194\) 14.6215 17.5370i 1.04977 1.25908i
\(195\) −6.20709 13.8852i −0.444499 0.994340i
\(196\) 0.0929204 0.0789704i 0.00663717 0.00564074i
\(197\) −2.07867 + 1.20012i −0.148099 + 0.0855049i −0.572218 0.820101i \(-0.693917\pi\)
0.424119 + 0.905606i \(0.360584\pi\)
\(198\) −12.0653 + 9.54644i −0.857441 + 0.678436i
\(199\) −8.55685 4.94030i −0.606579 0.350209i 0.165046 0.986286i \(-0.447223\pi\)
−0.771625 + 0.636077i \(0.780556\pi\)
\(200\) 5.58521 + 3.15477i 0.394934 + 0.223076i
\(201\) −3.95809 13.6137i −0.279182 0.960238i
\(202\) 20.0069 7.35324i 1.40768 0.517372i
\(203\) 11.5262 19.9640i 0.808981 1.40120i
\(204\) −1.78112 22.9057i −0.124703 1.60372i
\(205\) 8.67968 + 15.0337i 0.606215 + 1.05000i
\(206\) 11.8923 4.37084i 0.828577 0.304531i
\(207\) 4.39466 + 0.920326i 0.305450 + 0.0639671i
\(208\) −12.1862 + 4.60975i −0.844958 + 0.319629i
\(209\) 12.1782i 0.842385i
\(210\) −4.75830 + 16.8899i −0.328354 + 1.16552i
\(211\) −12.0232 6.94158i −0.827710 0.477878i 0.0253583 0.999678i \(-0.491927\pi\)
−0.853068 + 0.521800i \(0.825261\pi\)
\(212\) 2.31599 6.48980i 0.159063 0.445721i
\(213\) −1.03797 + 10.0203i −0.0711203 + 0.686581i
\(214\) 23.3982 + 4.04993i 1.59947 + 0.276848i
\(215\) 17.4309 1.18878
\(216\) 10.7838 9.98543i 0.733747 0.679422i
\(217\) −1.99048 + 3.44761i −0.135123 + 0.234039i
\(218\) −0.450416 0.0779612i −0.0305060 0.00528020i
\(219\) −11.2504 + 5.02928i −0.760235 + 0.339847i
\(220\) 19.2337 3.51626i 1.29674 0.237066i
\(221\) 18.7085 10.8014i 1.25847 0.726579i
\(222\) 1.91646 0.487294i 0.128624 0.0327051i
\(223\) 7.10950i 0.476087i −0.971254 0.238044i \(-0.923494\pi\)
0.971254 0.238044i \(-0.0765061\pi\)
\(224\) 14.2042 + 4.91847i 0.949059 + 0.328629i
\(225\) −2.12189 6.46437i −0.141459 0.430958i
\(226\) −10.9025 + 4.00705i −0.725223 + 0.266545i
\(227\) −10.1557 17.5902i −0.674059 1.16750i −0.976743 0.214414i \(-0.931216\pi\)
0.302684 0.953091i \(-0.402117\pi\)
\(228\) 0.901876 + 11.5984i 0.0597282 + 0.768122i
\(229\) 11.5651 20.0313i 0.764243 1.32371i −0.176404 0.984318i \(-0.556446\pi\)
0.940646 0.339389i \(-0.110220\pi\)
\(230\) −4.38268 3.65409i −0.288985 0.240943i
\(231\) 6.81139 + 15.2370i 0.448156 + 1.00252i
\(232\) 24.5363 0.231420i 1.61089 0.0151934i
\(233\) 1.61526 0.932569i 0.105819 0.0610946i −0.446156 0.894955i \(-0.647208\pi\)
0.551975 + 0.833860i \(0.313874\pi\)
\(234\) 12.8445 + 5.09791i 0.839674 + 0.333261i
\(235\) −11.9140 + 6.87855i −0.777183 + 0.448707i
\(236\) 16.3372 + 5.83019i 1.06346 + 0.379513i
\(237\) 13.3227 + 1.38005i 0.865404 + 0.0896438i
\(238\) −24.5583 4.25073i −1.59188 0.275534i
\(239\) −11.5345 19.9783i −0.746104 1.29229i −0.949677 0.313230i \(-0.898589\pi\)
0.203574 0.979060i \(-0.434744\pi\)
\(240\) −18.0576 + 4.77323i −1.16561 + 0.308110i
\(241\) 3.39895 0.218946 0.109473 0.993990i \(-0.465084\pi\)
0.109473 + 0.993990i \(0.465084\pi\)
\(242\) 1.94735 2.33564i 0.125181 0.150141i
\(243\) −15.5880 + 0.117052i −0.999972 + 0.00750890i
\(244\) −6.43741 + 5.47097i −0.412113 + 0.350243i
\(245\) 0.142354 + 0.0821879i 0.00909464 + 0.00525079i
\(246\) −15.1817 4.27705i −0.967949 0.272695i
\(247\) −9.47315 + 5.46933i −0.602762 + 0.348005i
\(248\) −4.23722 + 0.0399642i −0.269064 + 0.00253773i
\(249\) −11.3023 + 5.05248i −0.716257 + 0.320188i
\(250\) 1.77652 10.2637i 0.112357 0.649136i
\(251\) −12.7223 + 22.0357i −0.803026 + 1.39088i 0.114590 + 0.993413i \(0.463445\pi\)
−0.917616 + 0.397469i \(0.869889\pi\)
\(252\) −7.61549 14.0071i −0.479731 0.882366i
\(253\) −5.42740 −0.341218
\(254\) −5.73752 + 2.10874i −0.360004 + 0.132314i
\(255\) 28.2726 12.6387i 1.77050 0.791465i
\(256\) 3.17374 + 15.6821i 0.198359 + 0.980129i
\(257\) 14.0099 8.08863i 0.873915 0.504555i 0.00526747 0.999986i \(-0.498323\pi\)
0.868647 + 0.495431i \(0.164990\pi\)
\(258\) −11.3414 + 11.0546i −0.706088 + 0.688229i
\(259\) 2.14516i 0.133294i
\(260\) −11.3732 13.3823i −0.705337 0.829934i
\(261\) −19.3932 17.3565i −1.20041 1.07434i
\(262\) −5.08151 0.879545i −0.313937 0.0543385i
\(263\) 20.4917 1.26357 0.631786 0.775143i \(-0.282322\pi\)
0.631786 + 0.775143i \(0.282322\pi\)
\(264\) −10.2844 + 14.4858i −0.632963 + 0.891537i
\(265\) 9.28829 0.570575
\(266\) 12.4352 + 2.15238i 0.762452 + 0.131971i
\(267\) −15.5629 + 21.4883i −0.952434 + 1.31506i
\(268\) −8.79250 13.8091i −0.537088 0.843526i
\(269\) 23.6053i 1.43924i −0.694368 0.719620i \(-0.744316\pi\)
0.694368 0.719620i \(-0.255684\pi\)
\(270\) 17.5625 + 9.16653i 1.06882 + 0.557857i
\(271\) 4.52570i 0.274917i −0.990508 0.137458i \(-0.956107\pi\)
0.990508 0.137458i \(-0.0438933\pi\)
\(272\) −9.38622 24.8131i −0.569123 1.50451i
\(273\) 8.79347 12.1415i 0.532205 0.734835i
\(274\) −2.96360 + 17.1220i −0.179037 + 1.03438i
\(275\) 4.11209 + 7.12234i 0.247968 + 0.429493i
\(276\) 5.16899 0.401934i 0.311137 0.0241936i
\(277\) −10.8617 −0.652614 −0.326307 0.945264i \(-0.605804\pi\)
−0.326307 + 0.945264i \(0.605804\pi\)
\(278\) 2.06631 11.9380i 0.123929 0.715992i
\(279\) 3.34905 + 2.99733i 0.200502 + 0.179445i
\(280\) 0.191097 + 20.2611i 0.0114202 + 1.21083i
\(281\) 17.3942 + 10.0425i 1.03765 + 0.599088i 0.919167 0.393869i \(-0.128863\pi\)
0.118483 + 0.992956i \(0.462197\pi\)
\(282\) 3.38951 12.0313i 0.201843 0.716454i
\(283\) 26.0264i 1.54711i 0.633731 + 0.773553i \(0.281522\pi\)
−0.633731 + 0.773553i \(0.718478\pi\)
\(284\) 2.09193 + 11.4427i 0.124133 + 0.679001i
\(285\) −14.3160 + 6.39966i −0.848004 + 0.379083i
\(286\) −16.4596 2.84895i −0.973278 0.168462i
\(287\) −8.55523 + 14.8181i −0.504999 + 0.874684i
\(288\) 8.72201 14.5577i 0.513950 0.857820i
\(289\) 13.4934 + 23.3713i 0.793730 + 1.37478i
\(290\) 11.4101 + 31.0449i 0.670022 + 1.82302i
\(291\) −25.5295 + 11.4125i −1.49657 + 0.669010i
\(292\) −10.8430 + 9.21512i −0.634536 + 0.539274i
\(293\) 29.4487i 1.72041i 0.509948 + 0.860205i \(0.329665\pi\)
−0.509948 + 0.860205i \(0.670335\pi\)
\(294\) −0.144745 + 0.0368042i −0.00844173 + 0.00214646i
\(295\) 23.3820i 1.36135i
\(296\) 1.96658 1.16027i 0.114305 0.0674396i
\(297\) 18.4134 4.00067i 1.06845 0.232143i
\(298\) 5.19211 29.9971i 0.300771 1.73768i
\(299\) 2.43748 + 4.22185i 0.140963 + 0.244156i
\(300\) −4.44376 6.47871i −0.256561 0.374049i
\(301\) 8.59050 + 14.8792i 0.495148 + 0.857622i
\(302\) −15.2717 12.7329i −0.878789 0.732696i
\(303\) −25.9670 2.68982i −1.49177 0.154526i
\(304\) 4.75276 + 12.5642i 0.272589 + 0.720607i
\(305\) −9.86207 5.69387i −0.564701 0.326030i
\(306\) −10.3802 + 26.1537i −0.593397 + 1.49511i
\(307\) 8.01545 + 4.62772i 0.457466 + 0.264118i 0.710978 0.703214i \(-0.248252\pi\)
−0.253512 + 0.967332i \(0.581586\pi\)
\(308\) 12.4805 + 14.6851i 0.711141 + 0.836763i
\(309\) −15.4350 1.59886i −0.878069 0.0909558i
\(310\) −1.97042 5.36119i −0.111913 0.304495i
\(311\) 28.8183 1.63413 0.817067 0.576543i \(-0.195599\pi\)
0.817067 + 0.576543i \(0.195599\pi\)
\(312\) 15.8869 + 1.49437i 0.899421 + 0.0846018i
\(313\) −25.6878 −1.45196 −0.725980 0.687716i \(-0.758614\pi\)
−0.725980 + 0.687716i \(0.758614\pi\)
\(314\) 4.06059 4.87024i 0.229153 0.274844i
\(315\) 14.3323 16.0141i 0.807534 0.902292i
\(316\) 15.2139 2.78137i 0.855850 0.156464i
\(317\) 16.3826 + 9.45851i 0.920140 + 0.531243i 0.883680 0.468092i \(-0.155059\pi\)
0.0364600 + 0.999335i \(0.488392\pi\)
\(318\) −6.04343 + 5.89057i −0.338899 + 0.330327i
\(319\) 27.2447 + 15.7297i 1.52541 + 0.880696i
\(320\) −18.4711 + 11.1340i −1.03256 + 0.622409i
\(321\) −23.5542 17.0592i −1.31467 0.952150i
\(322\) 0.959238 5.54194i 0.0534563 0.308840i
\(323\) −11.1365 19.2889i −0.619650 1.07326i
\(324\) −17.2404 + 5.17383i −0.957800 + 0.287435i
\(325\) 3.69354 6.39739i 0.204881 0.354864i
\(326\) −27.2940 + 10.0315i −1.51167 + 0.555592i
\(327\) 0.453419 + 0.328389i 0.0250742 + 0.0181600i
\(328\) −18.2119 + 0.171769i −1.00558 + 0.00948437i
\(329\) −11.7432 6.77991i −0.647421 0.373789i
\(330\) −23.0496 6.49363i −1.26884 0.357462i
\(331\) 2.34917 1.35629i 0.129122 0.0745486i −0.434048 0.900890i \(-0.642915\pi\)
0.563170 + 0.826341i \(0.309582\pi\)
\(332\) −10.8930 + 9.25762i −0.597830 + 0.508078i
\(333\) −2.37044 0.496415i −0.129899 0.0272034i
\(334\) −10.7549 29.2623i −0.588481 1.60116i
\(335\) 13.5477 17.4187i 0.740189 0.951683i
\(336\) −12.9738 13.0617i −0.707778 0.712573i
\(337\) 11.3754 19.7027i 0.619657 1.07328i −0.369891 0.929075i \(-0.620605\pi\)
0.989548 0.144202i \(-0.0460615\pi\)
\(338\) −1.16624 3.17314i −0.0634349 0.172596i
\(339\) 14.1504 + 1.46578i 0.768542 + 0.0796103i
\(340\) 27.2486 23.1578i 1.47776 1.25591i
\(341\) −4.70493 2.71639i −0.254786 0.147101i
\(342\) 5.25607 13.2430i 0.284215 0.716101i
\(343\) 18.4387i 0.995598i
\(344\) −8.99412 + 15.9232i −0.484930 + 0.858523i
\(345\) 2.85210 + 6.38012i 0.153552 + 0.343494i
\(346\) −15.0796 12.5727i −0.810687 0.675915i
\(347\) −10.9382 18.9454i −0.587191 1.01704i −0.994598 0.103798i \(-0.966900\pi\)
0.407407 0.913247i \(-0.366433\pi\)
\(348\) −27.1124 12.9632i −1.45338 0.694899i
\(349\) 14.7072 0.787259 0.393630 0.919269i \(-0.371219\pi\)
0.393630 + 0.919269i \(0.371219\pi\)
\(350\) −7.99942 + 2.94006i −0.427587 + 0.157153i
\(351\) −11.3816 12.5266i −0.607505 0.668620i
\(352\) −6.71221 + 19.3844i −0.357762 + 1.03319i
\(353\) −21.9805 12.6905i −1.16990 0.675445i −0.216247 0.976339i \(-0.569382\pi\)
−0.953658 + 0.300894i \(0.902715\pi\)
\(354\) −14.8287 15.2135i −0.788138 0.808589i
\(355\) −13.5792 + 7.83995i −0.720709 + 0.416101i
\(356\) −10.2971 + 28.8543i −0.545746 + 1.52927i
\(357\) 24.7221 + 17.9050i 1.30843 + 0.947632i
\(358\) −5.07099 0.877723i −0.268010 0.0463891i
\(359\) 4.03521 0.212970 0.106485 0.994314i \(-0.466040\pi\)
0.106485 + 0.994314i \(0.466040\pi\)
\(360\) 22.4330 + 4.47748i 1.18232 + 0.235984i
\(361\) −3.86100 6.68745i −0.203210 0.351971i
\(362\) 2.97651 + 8.09860i 0.156442 + 0.425653i
\(363\) −3.40012 + 1.51995i −0.178460 + 0.0797769i
\(364\) 5.81815 16.3035i 0.304954 0.854534i
\(365\) −16.6114 9.59057i −0.869478 0.501993i
\(366\) 10.0278 2.54974i 0.524160 0.133277i
\(367\) −7.35243 + 4.24493i −0.383794 + 0.221583i −0.679468 0.733706i \(-0.737789\pi\)
0.295674 + 0.955289i \(0.404456\pi\)
\(368\) 5.59942 2.11814i 0.291890 0.110415i
\(369\) 14.3944 + 12.8827i 0.749345 + 0.670649i
\(370\) 2.36398 + 1.97098i 0.122897 + 0.102466i
\(371\) 4.57755 + 7.92855i 0.237655 + 0.411630i
\(372\) 4.68209 + 2.23863i 0.242755 + 0.116068i
\(373\) 13.6229 + 23.5956i 0.705368 + 1.22173i 0.966559 + 0.256446i \(0.0825514\pi\)
−0.261191 + 0.965287i \(0.584115\pi\)
\(374\) 5.80094 33.5146i 0.299960 1.73300i
\(375\) −7.48308 + 10.3322i −0.386425 + 0.533551i
\(376\) −0.136125 14.4327i −0.00702011 0.744310i
\(377\) 28.2574i 1.45533i
\(378\) 0.830724 + 19.5090i 0.0427278 + 1.00344i
\(379\) −23.0310 13.2970i −1.18303 0.683020i −0.226313 0.974055i \(-0.572667\pi\)
−0.956713 + 0.291035i \(0.906001\pi\)
\(380\) −13.7974 + 11.7261i −0.707794 + 0.601534i
\(381\) 7.44673 + 0.771378i 0.381508 + 0.0395189i
\(382\) 1.51784 1.82048i 0.0776594 0.0931440i
\(383\) −11.3469 + 19.6535i −0.579801 + 1.00425i 0.415701 + 0.909502i \(0.363536\pi\)
−0.995502 + 0.0947435i \(0.969797\pi\)
\(384\) 4.95709 18.9586i 0.252965 0.967475i
\(385\) −12.9890 + 22.4975i −0.661979 + 1.14658i
\(386\) −18.5733 3.21480i −0.945355 0.163629i
\(387\) 18.4297 6.04943i 0.936833 0.307510i
\(388\) −24.6049 + 20.9110i −1.24912 + 1.06159i
\(389\) −15.6531 9.03733i −0.793645 0.458211i 0.0475993 0.998867i \(-0.484843\pi\)
−0.841244 + 0.540655i \(0.818176\pi\)
\(390\) 5.30049 + 20.8461i 0.268401 + 1.05558i
\(391\) −8.59639 + 4.96313i −0.434738 + 0.250996i
\(392\) −0.148531 + 0.0876327i −0.00750197 + 0.00442612i
\(393\) 5.11540 + 3.70483i 0.258038 + 0.186884i
\(394\) 3.18607 1.17099i 0.160512 0.0589937i
\(395\) 10.4238 + 18.0545i 0.524476 + 0.908420i
\(396\) 19.1154 10.3928i 0.960586 0.522258i
\(397\) 36.5930 1.83655 0.918274 0.395945i \(-0.129583\pi\)
0.918274 + 0.395945i \(0.129583\pi\)
\(398\) 10.7323 + 8.94815i 0.537963 + 0.448530i
\(399\) −12.5181 9.06627i −0.626691 0.453881i
\(400\) −7.02204 5.74328i −0.351102 0.287164i
\(401\) 17.8898i 0.893373i 0.894691 + 0.446687i \(0.147396\pi\)
−0.894691 + 0.446687i \(0.852604\pi\)
\(402\) 2.23199 + 19.9253i 0.111322 + 0.993784i
\(403\) 4.87981i 0.243081i
\(404\) −29.6531 + 5.42110i −1.47530 + 0.269710i
\(405\) −14.3792 19.5433i −0.714507 0.971113i
\(406\) −20.8769 + 25.0396i −1.03610 + 1.24269i
\(407\) 2.92749 0.145110
\(408\) −3.04278 + 32.3485i −0.150640 + 1.60149i
\(409\) −0.518494 0.898057i −0.0256379 0.0444061i 0.852922 0.522039i \(-0.174828\pi\)
−0.878560 + 0.477633i \(0.841495\pi\)
\(410\) −8.46903 23.0428i −0.418255 1.13800i
\(411\) 12.4833 17.2362i 0.615756 0.850197i
\(412\) −17.6261 + 3.22236i −0.868375 + 0.158754i
\(413\) −19.9591 + 11.5234i −0.982122 + 0.567028i
\(414\) −5.90195 2.34244i −0.290065 0.115125i
\(415\) −16.6880 9.63481i −0.819181 0.472954i
\(416\) 18.0932 3.48441i 0.887091 0.170837i
\(417\) −8.70373 + 12.0176i −0.426224 + 0.588503i
\(418\) −2.93734 + 16.9703i −0.143670 + 0.830043i
\(419\) −0.732705 + 1.26908i −0.0357950 + 0.0619988i −0.883368 0.468680i \(-0.844730\pi\)
0.847573 + 0.530679i \(0.178063\pi\)
\(420\) 10.7044 22.3883i 0.522323 1.09244i
\(421\) 13.9150 24.1015i 0.678175 1.17463i −0.297355 0.954767i \(-0.596104\pi\)
0.975530 0.219867i \(-0.0705623\pi\)
\(422\) 15.0799 + 12.5730i 0.734080 + 0.612044i
\(423\) −10.2094 + 11.4074i −0.496399 + 0.554648i
\(424\) −4.79262 + 8.48488i −0.232750 + 0.412062i
\(425\) 13.0262 + 7.52066i 0.631862 + 0.364806i
\(426\) 3.86326 13.7129i 0.187176 0.664392i
\(427\) 11.2245i 0.543189i
\(428\) −31.6284 11.2871i −1.52882 0.545583i
\(429\) 16.5694 + 12.0004i 0.799978 + 0.579384i
\(430\) −24.2899 4.20427i −1.17136 0.202748i
\(431\) −1.99565 3.45656i −0.0961269 0.166497i 0.813951 0.580933i \(-0.197312\pi\)
−0.910078 + 0.414436i \(0.863979\pi\)
\(432\) −17.4357 + 11.3136i −0.838873 + 0.544326i
\(433\) 7.51625 + 13.0185i 0.361208 + 0.625631i 0.988160 0.153427i \(-0.0490311\pi\)
−0.626952 + 0.779058i \(0.715698\pi\)
\(434\) 3.60527 4.32413i 0.173058 0.207565i
\(435\) 4.17381 40.2932i 0.200119 1.93191i
\(436\) 0.608848 + 0.217277i 0.0291585 + 0.0104057i
\(437\) 4.35282 2.51310i 0.208224 0.120218i
\(438\) 16.8905 4.29471i 0.807058 0.205209i
\(439\) −14.6600 8.46393i −0.699682 0.403961i 0.107547 0.994200i \(-0.465700\pi\)
−0.807229 + 0.590239i \(0.799034\pi\)
\(440\) −27.6502 + 0.260788i −1.31817 + 0.0124326i
\(441\) 0.179033 + 0.0374930i 0.00852540 + 0.00178538i
\(442\) −28.6755 + 10.5392i −1.36395 + 0.501300i
\(443\) 18.6986 + 32.3869i 0.888398 + 1.53875i 0.841769 + 0.539838i \(0.181514\pi\)
0.0466285 + 0.998912i \(0.485152\pi\)
\(444\) −2.78811 + 0.216800i −0.132318 + 0.0102889i
\(445\) −41.2967 −1.95765
\(446\) −1.71478 + 9.90704i −0.0811973 + 0.469112i
\(447\) −21.8703 + 30.1971i −1.03443 + 1.42827i
\(448\) −18.6072 10.2799i −0.879106 0.485678i
\(449\) 30.9710 17.8811i 1.46161 0.843861i 0.462524 0.886607i \(-0.346944\pi\)
0.999086 + 0.0427459i \(0.0136106\pi\)
\(450\) 1.39766 + 9.51985i 0.0658863 + 0.448770i
\(451\) −20.2222 11.6753i −0.952224 0.549767i
\(452\) 16.1590 2.95415i 0.760058 0.138952i
\(453\) 9.93832 + 22.2319i 0.466943 + 1.04455i
\(454\) 9.90925 + 26.9614i 0.465064 + 1.26536i
\(455\) 23.3337 1.09390
\(456\) 1.54073 16.3798i 0.0721511 0.767055i
\(457\) −10.2530 17.7587i −0.479614 0.830716i 0.520112 0.854098i \(-0.325890\pi\)
−0.999727 + 0.0233816i \(0.992557\pi\)
\(458\) −20.9473 + 25.1241i −0.978805 + 1.17397i
\(459\) 25.5063 23.1749i 1.19053 1.08171i
\(460\) 5.22589 + 6.14903i 0.243658 + 0.286700i
\(461\) 21.7865i 1.01470i 0.861741 + 0.507348i \(0.169374\pi\)
−0.861741 + 0.507348i \(0.830626\pi\)
\(462\) −5.81652 22.8755i −0.270609 1.06427i
\(463\) −29.7470 17.1745i −1.38246 0.798165i −0.390012 0.920810i \(-0.627529\pi\)
−0.992451 + 0.122645i \(0.960862\pi\)
\(464\) −34.2470 5.59558i −1.58988 0.259768i
\(465\) −0.720783 + 6.95830i −0.0334255 + 0.322683i
\(466\) −2.47578 + 0.909936i −0.114688 + 0.0421520i
\(467\) −8.95602 + 15.5123i −0.414435 + 0.717823i −0.995369 0.0961280i \(-0.969354\pi\)
0.580934 + 0.813951i \(0.302688\pi\)
\(468\) −16.6692 10.2020i −0.770534 0.471586i
\(469\) 21.5454 + 2.97996i 0.994875 + 0.137602i
\(470\) 18.2611 6.71160i 0.842324 0.309583i
\(471\) −7.08989 + 3.16939i −0.326685 + 0.146038i
\(472\) −21.3596 12.0648i −0.983153 0.555327i
\(473\) −20.3055 + 11.7234i −0.933649 + 0.539043i
\(474\) −18.2323 5.13647i −0.837436 0.235926i
\(475\) −6.59586 3.80812i −0.302639 0.174729i
\(476\) 33.1966 + 11.8467i 1.52156 + 0.542994i
\(477\) 9.82048 3.22351i 0.449649 0.147594i
\(478\) 11.2545 + 30.6217i 0.514771 + 1.40060i
\(479\) 8.56023 14.8268i 0.391127 0.677452i −0.601472 0.798894i \(-0.705419\pi\)
0.992598 + 0.121443i \(0.0387520\pi\)
\(480\) 26.3144 2.29605i 1.20108 0.104800i
\(481\) −1.31476 2.27722i −0.0599477 0.103833i
\(482\) −4.73642 0.819813i −0.215738 0.0373415i
\(483\) −4.04051 + 5.57889i −0.183850 + 0.253848i
\(484\) −3.27697 + 2.78500i −0.148953 + 0.126591i
\(485\) −37.6945 21.7630i −1.71162 0.988205i
\(486\) 21.7500 + 3.59665i 0.986602 + 0.163148i
\(487\) 15.2610 + 8.81097i 0.691544 + 0.399263i 0.804190 0.594372i \(-0.202599\pi\)
−0.112646 + 0.993635i \(0.535933\pi\)
\(488\) 10.2901 6.07108i 0.465809 0.274825i
\(489\) 35.4248 + 3.66952i 1.60197 + 0.165941i
\(490\) −0.178545 0.148863i −0.00806586 0.00672496i
\(491\) −8.04678 −0.363146 −0.181573 0.983377i \(-0.558119\pi\)
−0.181573 + 0.983377i \(0.558119\pi\)
\(492\) 20.1240 + 9.62181i 0.907259 + 0.433784i
\(493\) 57.5367 2.59132
\(494\) 14.5200 5.33658i 0.653284 0.240104i
\(495\) 21.8543 + 19.5592i 0.982280 + 0.879121i
\(496\) 5.91418 + 0.966310i 0.265554 + 0.0433886i
\(497\) −13.3845 7.72753i −0.600376 0.346627i
\(498\) 16.9684 4.31452i 0.760371 0.193338i
\(499\) 36.7784 + 21.2340i 1.64643 + 0.950564i 0.978477 + 0.206358i \(0.0661610\pi\)
0.667949 + 0.744207i \(0.267172\pi\)
\(500\) −4.95114 + 13.8740i −0.221422 + 0.620462i
\(501\) −3.93415 + 37.9795i −0.175765 + 1.69680i
\(502\) 23.0434 27.6381i 1.02848 1.23355i
\(503\) −14.7585 25.5625i −0.658050 1.13978i −0.981120 0.193401i \(-0.938048\pi\)
0.323070 0.946375i \(-0.395285\pi\)
\(504\) 7.23367 + 21.3557i 0.322213 + 0.951256i
\(505\) −20.3167 35.1896i −0.904083 1.56592i
\(506\) 7.56305 + 1.30907i 0.336218 + 0.0581951i
\(507\) −0.426611 + 4.11842i −0.0189464 + 0.182905i
\(508\) 8.50382 1.55465i 0.377296 0.0689762i
\(509\) 35.2449i 1.56220i 0.624404 + 0.781102i \(0.285342\pi\)
−0.624404 + 0.781102i \(0.714658\pi\)
\(510\) −42.4461 + 10.7927i −1.87954 + 0.477908i
\(511\) 18.9061i 0.836357i
\(512\) −0.640141 22.6184i −0.0282905 0.999600i
\(513\) −12.9152 + 11.7347i −0.570221 + 0.518100i
\(514\) −21.4737 + 7.89232i −0.947163 + 0.348115i
\(515\) −12.0765 20.9170i −0.532152 0.921715i
\(516\) 18.4706 12.6690i 0.813121 0.557721i
\(517\) 9.25251 16.0258i 0.406925 0.704814i
\(518\) −0.517404 + 2.98927i −0.0227334 + 0.131341i
\(519\) 9.81332 + 21.9523i 0.430757 + 0.963599i
\(520\) 12.6208 + 21.3913i 0.553457 + 0.938071i
\(521\) 9.66600i 0.423475i −0.977327 0.211738i \(-0.932088\pi\)
0.977327 0.211738i \(-0.0679122\pi\)
\(522\) 22.8380 + 28.8638i 0.999591 + 1.26333i
\(523\) −18.6802 10.7850i −0.816830 0.471597i 0.0324923 0.999472i \(-0.489656\pi\)
−0.849322 + 0.527875i \(0.822989\pi\)
\(524\) 6.86891 + 2.45128i 0.300070 + 0.107085i
\(525\) 10.3825 + 1.07548i 0.453127 + 0.0469377i
\(526\) −28.5550 4.94251i −1.24506 0.215504i
\(527\) −9.93612 −0.432824
\(528\) 17.8252 17.7052i 0.775742 0.770522i
\(529\) 10.3800 + 17.9787i 0.451304 + 0.781682i
\(530\) −12.9432 2.24030i −0.562215 0.0973123i
\(531\) 8.11475 + 24.7217i 0.352150 + 1.07283i
\(532\) −16.8093 5.99865i −0.728773 0.260074i
\(533\) 20.9738i 0.908476i
\(534\) 26.8697 26.1901i 1.16277 1.13336i
\(535\) 45.2670i 1.95707i
\(536\) 8.92159 + 21.3636i 0.385354 + 0.922769i
\(537\) 5.10480 + 3.69716i 0.220289 + 0.159544i
\(538\) −5.69350 + 32.8938i −0.245464 + 1.41815i
\(539\) −0.221106 −0.00952371
\(540\) −22.2623 17.0095i −0.958017 0.731972i
\(541\) −15.7176 −0.675753 −0.337876 0.941191i \(-0.609709\pi\)
−0.337876 + 0.941191i \(0.609709\pi\)
\(542\) −1.09158 + 6.30654i −0.0468874 + 0.270889i
\(543\) 1.08881 10.5112i 0.0467254 0.451078i
\(544\) 7.09484 + 36.8408i 0.304189 + 1.57953i
\(545\) 0.871392i 0.0373263i
\(546\) −15.1821 + 14.7981i −0.649734 + 0.633301i
\(547\) 26.4585 15.2758i 1.13128 0.653147i 0.187026 0.982355i \(-0.440115\pi\)
0.944257 + 0.329208i \(0.106782\pi\)
\(548\) 8.25951 23.1446i 0.352829 0.988687i
\(549\) −12.4032 2.59747i −0.529356 0.110857i
\(550\) −4.01229 10.9168i −0.171084 0.465492i
\(551\) −29.1340 −1.24115
\(552\) −7.29990 0.686647i −0.310704 0.0292256i
\(553\) −10.2743 + 17.7956i −0.436908 + 0.756746i
\(554\) 15.1357 + 2.61979i 0.643052 + 0.111304i
\(555\) −1.53840 3.44138i −0.0653013 0.146078i
\(556\) −5.75878 + 16.1371i −0.244227 + 0.684365i
\(557\) 7.61456 4.39627i 0.322639 0.186276i −0.329929 0.944006i \(-0.607025\pi\)
0.652568 + 0.757730i \(0.273692\pi\)
\(558\) −3.94393 4.98453i −0.166960 0.211012i
\(559\) 18.2387 + 10.5301i 0.771416 + 0.445377i
\(560\) 4.62060 28.2798i 0.195256 1.19504i
\(561\) −24.4348 + 33.7381i −1.03164 + 1.42442i
\(562\) −21.8165 18.1896i −0.920272 0.767283i
\(563\) 19.2290 0.810405 0.405203 0.914227i \(-0.367201\pi\)
0.405203 + 0.914227i \(0.367201\pi\)
\(564\) −7.62517 + 15.9480i −0.321077 + 0.671532i
\(565\) 11.0713 + 19.1761i 0.465774 + 0.806744i
\(566\) 6.27745 36.2676i 0.263861 1.52444i
\(567\) 9.59579 21.9057i 0.402985 0.919953i
\(568\) −0.155151 16.4499i −0.00650999 0.690224i
\(569\) −0.932104 + 0.538150i −0.0390758 + 0.0225604i −0.519411 0.854525i \(-0.673848\pi\)
0.480335 + 0.877085i \(0.340515\pi\)
\(570\) 21.4928 5.46493i 0.900233 0.228901i
\(571\) 20.8988 12.0659i 0.874589 0.504944i 0.00571856 0.999984i \(-0.498180\pi\)
0.868871 + 0.495039i \(0.164846\pi\)
\(572\) 22.2492 + 7.93999i 0.930287 + 0.331988i
\(573\) −2.65018 + 1.18471i −0.110713 + 0.0494919i
\(574\) 15.4957 18.5854i 0.646779 0.775741i
\(575\) −1.69715 + 2.93954i −0.0707758 + 0.122587i
\(576\) −15.6653 + 18.1823i −0.652722 + 0.757598i
\(577\) −12.0012 20.7867i −0.499617 0.865363i 0.500383 0.865804i \(-0.333193\pi\)
−1.00000 0.000441740i \(0.999859\pi\)
\(578\) −13.1659 35.8223i −0.547630 1.49001i
\(579\) 18.6971 + 13.5414i 0.777026 + 0.562762i
\(580\) −8.41196 46.0129i −0.349288 1.91058i
\(581\) 18.9933i 0.787975i
\(582\) 38.3279 9.74556i 1.58874 0.403967i
\(583\) −10.8200 + 6.24696i −0.448121 + 0.258723i
\(584\) 17.3322 10.2259i 0.717213 0.423152i
\(585\) 5.39970 25.7842i 0.223250 1.06604i
\(586\) 7.10290 41.0366i 0.293418 1.69520i
\(587\) −5.05511 + 8.75571i −0.208647 + 0.361387i −0.951289 0.308302i \(-0.900239\pi\)
0.742642 + 0.669689i \(0.233573\pi\)
\(588\) 0.210579 0.0163743i 0.00868413 0.000675267i
\(589\) 5.03120 0.207307
\(590\) 5.63965 32.5827i 0.232181 1.34141i
\(591\) −4.13521 0.428350i −0.170100 0.0176200i
\(592\) −3.02028 + 1.14250i −0.124133 + 0.0469566i
\(593\) 18.2024 + 10.5091i 0.747481 + 0.431558i 0.824783 0.565449i \(-0.191297\pi\)
−0.0773019 + 0.997008i \(0.524631\pi\)
\(594\) −26.6239 + 1.13368i −1.09239 + 0.0465156i
\(595\) 47.5114i 1.94778i
\(596\) −14.4704 + 40.5484i −0.592729 + 1.66093i
\(597\) −6.98424 15.6237i −0.285846 0.639434i
\(598\) −2.37833 6.47103i −0.0972570 0.264620i
\(599\) 4.45915 + 7.72348i 0.182196 + 0.315573i 0.942628 0.333845i \(-0.108346\pi\)
−0.760432 + 0.649418i \(0.775013\pi\)
\(600\) 4.62971 + 10.0999i 0.189007 + 0.412325i
\(601\) 14.7922 25.6209i 0.603387 1.04510i −0.388917 0.921273i \(-0.627151\pi\)
0.992304 0.123825i \(-0.0395161\pi\)
\(602\) −8.38201 22.8060i −0.341625 0.929505i
\(603\) 8.27877 23.1184i 0.337137 0.941455i
\(604\) 18.2099 + 21.4267i 0.740951 + 0.871839i
\(605\) −5.02030 2.89847i −0.204104 0.117840i
\(606\) 35.5361 + 10.0114i 1.44356 + 0.406685i
\(607\) −14.9898 + 8.65439i −0.608419 + 0.351271i −0.772346 0.635201i \(-0.780917\pi\)
0.163927 + 0.986472i \(0.447584\pi\)
\(608\) −3.59250 18.6545i −0.145695 0.756540i
\(609\) 36.4516 16.2949i 1.47709 0.660303i
\(610\) 12.3694 + 10.3131i 0.500822 + 0.417564i
\(611\) −16.6215 −0.672433
\(612\) 20.7729 33.9413i 0.839695 1.37200i
\(613\) −18.8470 + 32.6439i −0.761222 + 1.31848i 0.180999 + 0.983483i \(0.442067\pi\)
−0.942221 + 0.334992i \(0.891266\pi\)
\(614\) −10.0533 8.38200i −0.405718 0.338270i
\(615\) −3.09798 + 29.9073i −0.124923 + 1.20598i
\(616\) −13.8495 23.4739i −0.558011 0.945789i
\(617\) 2.25497i 0.0907817i 0.998969 + 0.0453909i \(0.0144533\pi\)
−0.998969 + 0.0453909i \(0.985547\pi\)
\(618\) 21.1230 + 5.95087i 0.849692 + 0.239379i
\(619\) 10.7960 + 6.23307i 0.433928 + 0.250528i 0.701019 0.713143i \(-0.252729\pi\)
−0.267091 + 0.963671i \(0.586062\pi\)
\(620\) 1.45268 + 7.94605i 0.0583408 + 0.319121i
\(621\) 5.22974 + 5.75585i 0.209862 + 0.230974i
\(622\) −40.1581 6.95085i −1.61019 0.278704i
\(623\) −20.3523 35.2512i −0.815396 1.41231i
\(624\) −21.7779 5.91426i −0.871815 0.236760i
\(625\) −31.1961 −1.24785
\(626\) 35.7958 + 6.19579i 1.43069 + 0.247634i
\(627\) 12.3727 17.0834i 0.494117 0.682246i
\(628\) −6.83310 + 5.80725i −0.272670 + 0.231735i
\(629\) 4.63681 2.67707i 0.184882 0.106742i
\(630\) −23.8345 + 18.8587i −0.949589 + 0.751347i
\(631\) −9.32817 5.38562i −0.371349 0.214398i 0.302699 0.953086i \(-0.402112\pi\)
−0.674048 + 0.738688i \(0.735446\pi\)
\(632\) −21.8713 + 0.206284i −0.869996 + 0.00820555i
\(633\) −9.81351 21.9527i −0.390052 0.872542i
\(634\) −20.5477 17.1318i −0.816054 0.680390i
\(635\) 5.82636 + 10.0916i 0.231212 + 0.400471i
\(636\) 9.84226 6.75083i 0.390271 0.267688i
\(637\) 0.0993004 + 0.171993i 0.00393442 + 0.00681462i
\(638\) −34.1714 28.4906i −1.35286 1.12795i
\(639\) −11.6364 + 13.0018i −0.460328 + 0.514344i
\(640\) 28.4248 11.0600i 1.12359 0.437185i
\(641\) 17.8141 10.2850i 0.703613 0.406231i −0.105078 0.994464i \(-0.533509\pi\)
0.808692 + 0.588233i \(0.200176\pi\)
\(642\) 28.7081 + 29.4530i 1.13302 + 1.16242i
\(643\) 12.5057i 0.493175i 0.969121 + 0.246588i \(0.0793093\pi\)
−0.969121 + 0.246588i \(0.920691\pi\)
\(644\) −2.67338 + 7.49129i −0.105346 + 0.295198i
\(645\) 24.4519 + 17.7093i 0.962792 + 0.697302i
\(646\) 10.8662 + 29.5651i 0.427524 + 1.16322i
\(647\) 7.61005 13.1810i 0.299182 0.518198i −0.676767 0.736197i \(-0.736620\pi\)
0.975949 + 0.217999i \(0.0699530\pi\)
\(648\) 25.2723 3.05138i 0.992790 0.119869i
\(649\) −15.7259 27.2380i −0.617295 1.06919i
\(650\) −6.68994 + 8.02386i −0.262401 + 0.314722i
\(651\) −6.29488 + 2.81400i −0.246716 + 0.110289i
\(652\) 40.4535 7.39560i 1.58428 0.289634i
\(653\) −8.75547 5.05498i −0.342628 0.197816i 0.318805 0.947820i \(-0.396718\pi\)
−0.661434 + 0.750004i \(0.730052\pi\)
\(654\) −0.552631 0.566971i −0.0216096 0.0221703i
\(655\) 9.83088i 0.384124i
\(656\) 25.4196 + 4.15327i 0.992468 + 0.162158i
\(657\) −20.8916 4.37509i −0.815057 0.170689i
\(658\) 14.7287 + 12.2802i 0.574186 + 0.478731i
\(659\) −13.1025 22.6942i −0.510401 0.884040i −0.999927 0.0120520i \(-0.996164\pi\)
0.489526 0.871988i \(-0.337170\pi\)
\(660\) 30.5532 + 14.6083i 1.18928 + 0.568627i
\(661\) −43.6516 −1.69785 −0.848926 0.528512i \(-0.822750\pi\)
−0.848926 + 0.528512i \(0.822750\pi\)
\(662\) −3.60068 + 1.32338i −0.139945 + 0.0514345i
\(663\) 37.2179 + 3.85526i 1.44542 + 0.149726i
\(664\) 17.4122 10.2731i 0.675724 0.398674i
\(665\) 24.0576i 0.932915i
\(666\) 3.18346 + 1.26349i 0.123356 + 0.0489593i
\(667\) 12.9840i 0.502742i
\(668\) 7.92894 + 43.3708i 0.306780 + 1.67807i
\(669\) 7.22302 9.97310i 0.279258 0.385582i
\(670\) −23.0799 + 21.0051i −0.891655 + 0.811500i
\(671\) 15.3179 0.591343
\(672\) 14.9285 + 21.3306i 0.575878 + 0.822846i
\(673\) −27.9399 −1.07700 −0.538501 0.842625i \(-0.681009\pi\)
−0.538501 + 0.842625i \(0.681009\pi\)
\(674\) −20.6038 + 24.7120i −0.793627 + 0.951869i
\(675\) 3.59104 11.2239i 0.138219 0.432008i
\(676\) 0.859797 + 4.70304i 0.0330691 + 0.180886i
\(677\) 39.2175 22.6422i 1.50725 0.870211i 0.507286 0.861778i \(-0.330649\pi\)
0.999964 0.00843376i \(-0.00268458\pi\)
\(678\) −19.3649 5.45557i −0.743705 0.209520i
\(679\) 42.9018i 1.64642i
\(680\) −43.5563 + 25.6980i −1.67031 + 0.985473i
\(681\) 3.62481 34.9932i 0.138903 1.34094i
\(682\) 5.90111 + 4.92009i 0.225965 + 0.188400i
\(683\) −14.3250 + 24.8117i −0.548132 + 0.949393i 0.450270 + 0.892892i \(0.351328\pi\)
−0.998403 + 0.0565004i \(0.982006\pi\)
\(684\) −10.5185 + 17.1863i −0.402183 + 0.657136i
\(685\) 33.1248 1.26564
\(686\) −4.44735 + 25.6942i −0.169800 + 0.981011i
\(687\) 36.5745 16.3499i 1.39541 0.623787i
\(688\) 16.3739 20.0196i 0.624248 0.763239i
\(689\) 9.71873 + 5.61111i 0.370254 + 0.213766i
\(690\) −2.43552 9.57857i −0.0927188 0.364650i
\(691\) 30.1341 17.3979i 1.14636 0.661848i 0.198359 0.980129i \(-0.436439\pi\)
0.947996 + 0.318281i \(0.103106\pi\)
\(692\) 17.9809 + 21.1572i 0.683531 + 0.804276i
\(693\) −5.92539 + 28.2944i −0.225087 + 1.07482i
\(694\) 10.6727 + 29.0386i 0.405130 + 1.10229i
\(695\) −23.0956 −0.876068
\(696\) 34.6543 + 24.6035i 1.31357 + 0.932593i
\(697\) −42.7062 −1.61761
\(698\) −20.4944 3.54732i −0.775725 0.134268i
\(699\) 3.21332 + 0.332855i 0.121539 + 0.0125897i
\(700\) 11.8563 2.16753i 0.448125 0.0819250i
\(701\) 11.7067 6.75886i 0.442155 0.255279i −0.262356 0.964971i \(-0.584499\pi\)
0.704511 + 0.709693i \(0.251166\pi\)
\(702\) 12.8388 + 20.2009i 0.484571 + 0.762435i
\(703\) −2.34787 + 1.35554i −0.0885517 + 0.0511253i
\(704\) 14.0289 25.3931i 0.528733 0.957038i
\(705\) −23.7012 2.45511i −0.892637 0.0924648i
\(706\) 27.5688 + 22.9857i 1.03757 + 0.865077i
\(707\) 20.0254 34.6850i 0.753133 1.30446i
\(708\) 16.9943 + 24.7766i 0.638685 + 0.931161i
\(709\) 4.18449 7.24774i 0.157152 0.272195i −0.776689 0.629885i \(-0.783102\pi\)
0.933840 + 0.357690i \(0.116436\pi\)
\(710\) 20.8135 7.64967i 0.781116 0.287087i
\(711\) 17.2868 + 15.4714i 0.648307 + 0.580222i
\(712\) 21.3085 37.7247i 0.798570 1.41379i
\(713\) 2.24223i 0.0839721i
\(714\) −30.1314 30.9133i −1.12764 1.15690i
\(715\) 31.8434i 1.19088i
\(716\) 6.85469 + 2.44620i 0.256172 + 0.0914189i
\(717\) 4.11692 39.7440i 0.153749 1.48427i
\(718\) −5.62304 0.973276i −0.209850 0.0363223i
\(719\) 4.30385 7.45449i 0.160507 0.278006i −0.774544 0.632520i \(-0.782021\pi\)
0.935050 + 0.354515i \(0.115354\pi\)
\(720\) −30.1803 11.6501i −1.12476 0.434174i
\(721\) 11.9033 20.6171i 0.443302 0.767821i
\(722\) 3.76729 + 10.2502i 0.140204 + 0.381472i
\(723\) 4.76800 + 3.45323i 0.177324 + 0.128427i
\(724\) −2.19441 12.0033i −0.0815544 0.446098i
\(725\) 17.0388 9.83736i 0.632806 0.365350i
\(726\) 5.10466 1.29795i 0.189452 0.0481715i
\(727\) 22.5344 + 13.0102i 0.835755 + 0.482523i 0.855819 0.517276i \(-0.173054\pi\)
−0.0200643 + 0.999799i \(0.506387\pi\)
\(728\) −12.0399 + 21.3155i −0.446228 + 0.790003i
\(729\) −21.9856 15.6727i −0.814280 0.580472i
\(730\) 20.8346 + 17.3710i 0.771124 + 0.642929i
\(731\) −21.4411 + 37.1371i −0.793029 + 1.37357i
\(732\) −14.5886 + 1.13439i −0.539211 + 0.0419284i
\(733\) 0.535517 + 0.927542i 0.0197798 + 0.0342595i 0.875746 0.482772i \(-0.160370\pi\)
−0.855966 + 0.517032i \(0.827037\pi\)
\(734\) 11.2694 4.14190i 0.415962 0.152880i
\(735\) 0.116191 + 0.259919i 0.00428578 + 0.00958725i
\(736\) −8.31365 + 1.60105i −0.306445 + 0.0590155i
\(737\) −4.06673 + 29.4029i −0.149800 + 1.08307i
\(738\) −16.9513 21.4239i −0.623986 0.788625i
\(739\) −3.80731 2.19815i −0.140054 0.0808603i 0.428336 0.903620i \(-0.359100\pi\)
−0.568390 + 0.822759i \(0.692433\pi\)
\(740\) −2.81879 3.31673i −0.103621 0.121925i
\(741\) −18.8455 1.95213i −0.692305 0.0717132i
\(742\) −4.46646 12.1525i −0.163969 0.446131i
\(743\) −0.903673 + 1.56521i −0.0331525 + 0.0574219i −0.882126 0.471014i \(-0.843888\pi\)
0.848973 + 0.528436i \(0.177221\pi\)
\(744\) −5.98452 4.24882i −0.219403 0.155769i
\(745\) −58.0335 −2.12618
\(746\) −13.2923 36.1661i −0.486665 1.32413i
\(747\) −20.9879 4.39527i −0.767908 0.160815i
\(748\) −16.1672 + 45.3032i −0.591130 + 1.65645i
\(749\) 38.6403 22.3090i 1.41189 0.815153i
\(750\) 12.9197 12.5929i 0.471761 0.459829i
\(751\) 20.2715i 0.739716i 0.929088 + 0.369858i \(0.120594\pi\)
−0.929088 + 0.369858i \(0.879406\pi\)
\(752\) −3.29142 + 20.1447i −0.120026 + 0.734602i
\(753\) −40.2343 + 17.9859i −1.46622 + 0.655443i
\(754\) −6.81556 + 39.3765i −0.248208 + 1.43401i
\(755\) −18.9518 + 32.8256i −0.689728 + 1.19464i
\(756\) 3.54789 27.3861i 0.129036 0.996022i
\(757\) 1.28056 + 2.21800i 0.0465428 + 0.0806145i 0.888358 0.459151i \(-0.151846\pi\)
−0.841815 + 0.539765i \(0.818513\pi\)
\(758\) 28.8864 + 24.0843i 1.04920 + 0.874780i
\(759\) −7.61348 5.51407i −0.276352 0.200148i
\(760\) 22.0549 13.0123i 0.800016 0.472005i
\(761\) 21.9523i 0.795769i 0.917435 + 0.397885i \(0.130256\pi\)
−0.917435 + 0.397885i \(0.869744\pi\)
\(762\) −10.1909 2.87103i −0.369178 0.104007i
\(763\) −0.743826 + 0.429448i −0.0269283 + 0.0155471i
\(764\) −2.55419 + 2.17073i −0.0924074 + 0.0785344i
\(765\) 52.5009 + 10.9947i 1.89817 + 0.397514i
\(766\) 20.5522 24.6501i 0.742582 0.890646i
\(767\) −14.1252 + 24.4656i −0.510032 + 0.883401i
\(768\) −11.4804 + 25.2230i −0.414263 + 0.910157i
\(769\) 6.10165 + 10.5684i 0.220031 + 0.381105i 0.954817 0.297194i \(-0.0960508\pi\)
−0.734786 + 0.678299i \(0.762717\pi\)
\(770\) 23.5263 28.2173i 0.847831 1.01688i
\(771\) 27.8707 + 2.88702i 1.00374 + 0.103973i
\(772\) 25.1063 + 8.95960i 0.903597 + 0.322463i
\(773\) −28.9447 + 16.7112i −1.04107 + 0.601062i −0.920136 0.391599i \(-0.871922\pi\)
−0.120933 + 0.992661i \(0.538589\pi\)
\(774\) −27.1407 + 3.98467i −0.975554 + 0.143226i
\(775\) −2.94246 + 1.69883i −0.105696 + 0.0610238i
\(776\) 39.3304 23.2047i 1.41188 0.833001i
\(777\) 2.17942 3.00920i 0.0781861 0.107955i
\(778\) 19.6328 + 16.3689i 0.703868 + 0.586855i
\(779\) 21.6245 0.774777
\(780\) −2.35821 30.3273i −0.0844376 1.08589i
\(781\) 10.5457 18.2657i 0.377355 0.653599i
\(782\) 13.1761 4.84267i 0.471176 0.173174i
\(783\) −9.57083 44.0504i −0.342034 1.57423i
\(784\) 0.228114 0.0862905i 0.00814693 0.00308180i
\(785\) −10.4683 6.04386i −0.373628 0.215714i
\(786\) −6.23468 6.39647i −0.222384 0.228154i
\(787\) −9.94926 5.74421i −0.354653 0.204759i 0.312080 0.950056i \(-0.398974\pi\)
−0.666733 + 0.745297i \(0.732308\pi\)
\(788\) −4.72221 + 0.863302i −0.168222 + 0.0307539i
\(789\) 28.7455 + 20.8189i 1.02337 + 0.741173i
\(790\) −10.1708 27.6730i −0.361860 0.984560i
\(791\) −10.9126 + 18.9011i −0.388006 + 0.672046i
\(792\) −29.1439 + 9.87175i −1.03558 + 0.350777i
\(793\) −6.87940 11.9155i −0.244295 0.423131i
\(794\) −50.9921 8.82608i −1.80964 0.313226i
\(795\) 13.0295 + 9.43661i 0.462108 + 0.334682i
\(796\) −12.7972 15.0578i −0.453584 0.533709i
\(797\) −42.9834 + 24.8165i −1.52255 + 0.879045i −0.522906 + 0.852391i \(0.675152\pi\)
−0.999645 + 0.0266541i \(0.991515\pi\)
\(798\) 15.2572 + 15.6531i 0.540099 + 0.554114i
\(799\) 33.8441i 1.19732i
\(800\) 8.39991 + 9.69691i 0.296982 + 0.342837i
\(801\) −43.6628 + 14.3321i −1.54275 + 0.506398i
\(802\) 4.31494 24.9293i 0.152366 0.880284i
\(803\) 25.8010 0.910499
\(804\) 1.69563 28.3041i 0.0598004 0.998210i
\(805\) −10.7216 −0.377888
\(806\) 1.17699 6.79999i 0.0414577 0.239519i
\(807\) 23.9822 33.1132i 0.844215 1.16564i
\(808\) 42.6290 0.402064i 1.49968 0.0141446i
\(809\) 12.7782i 0.449257i −0.974445 0.224628i \(-0.927883\pi\)
0.974445 0.224628i \(-0.0721168\pi\)
\(810\) 15.3235 + 30.7016i 0.538414 + 1.07875i
\(811\) −13.0695 + 7.54568i −0.458932 + 0.264965i −0.711595 0.702590i \(-0.752027\pi\)
0.252663 + 0.967554i \(0.418694\pi\)
\(812\) 35.1313 29.8571i 1.23287 1.04778i
\(813\) 4.59797 6.34859i 0.161258 0.222655i
\(814\) −4.07944 0.706098i −0.142984 0.0247487i
\(815\) 27.7166 + 48.0065i 0.970869 + 1.68159i
\(816\) 12.0424 44.3435i 0.421569 1.55233i
\(817\) 10.8568 18.8046i 0.379832 0.657888i
\(818\) 0.505910 + 1.37650i 0.0176887 + 0.0481280i
\(819\) 24.6707 8.09800i 0.862064 0.282967i
\(820\) 6.24371 + 34.1527i 0.218040 + 1.19266i
\(821\) 23.9170 + 13.8085i 0.834708 + 0.481919i 0.855462 0.517866i \(-0.173273\pi\)
−0.0207538 + 0.999785i \(0.506607\pi\)
\(822\) −21.5527 + 21.0076i −0.751736 + 0.732723i
\(823\) −16.9467 9.78416i −0.590724 0.341054i 0.174660 0.984629i \(-0.444117\pi\)
−0.765384 + 0.643574i \(0.777451\pi\)
\(824\) 25.3391 0.238991i 0.882728 0.00832564i
\(825\) −1.46770 + 14.1689i −0.0510987 + 0.493297i
\(826\) 30.5922 11.2437i 1.06444 0.391218i
\(827\) 17.4936 30.2998i 0.608312 1.05363i −0.383206 0.923663i \(-0.625180\pi\)
0.991519 0.129965i \(-0.0414866\pi\)
\(828\) 7.65934 + 4.68770i 0.266181 + 0.162909i
\(829\) −12.4727 −0.433193 −0.216597 0.976261i \(-0.569496\pi\)
−0.216597 + 0.976261i \(0.569496\pi\)
\(830\) 20.9307 + 17.4511i 0.726516 + 0.605737i
\(831\) −15.2366 11.0351i −0.528551 0.382803i
\(832\) −26.0532 + 0.491495i −0.903231 + 0.0170395i
\(833\) −0.350207 + 0.202192i −0.0121340 + 0.00700555i
\(834\) 15.0272 14.6471i 0.520349 0.507188i
\(835\) −51.4685 + 29.7154i −1.78114 + 1.02834i
\(836\) 8.18632 22.9395i 0.283130 0.793379i
\(837\) 1.65280 + 7.60713i 0.0571292 + 0.262941i
\(838\) 1.32712 1.59173i 0.0458445 0.0549855i
\(839\) −16.1231 27.9260i −0.556631 0.964112i −0.997775 0.0666762i \(-0.978761\pi\)
0.441144 0.897436i \(-0.354573\pi\)
\(840\) −20.3165 + 28.6161i −0.700987 + 0.987349i
\(841\) 23.1303 40.0629i 0.797597 1.38148i
\(842\) −25.2036 + 30.2290i −0.868575 + 1.04176i
\(843\) 14.1974 + 31.7595i 0.488985 + 1.09385i
\(844\) −17.9812 21.1576i −0.618940 0.728275i
\(845\) −5.58113 + 3.22227i −0.191997 + 0.110849i
\(846\) 16.9782 13.4337i 0.583722 0.461860i
\(847\) 5.71383i 0.196329i
\(848\) 8.72501 10.6677i 0.299618 0.366329i
\(849\) −26.4420 + 36.5094i −0.907486 + 1.25300i
\(850\) −16.3379 13.6219i −0.560386 0.467226i
\(851\) 0.604118 + 1.04636i 0.0207089 + 0.0358689i
\(852\) −8.69092 + 18.1770i −0.297746 + 0.622735i
\(853\) −5.18959 + 8.98864i −0.177688 + 0.307765i −0.941088 0.338161i \(-0.890195\pi\)
0.763400 + 0.645926i \(0.223529\pi\)
\(854\) −2.70729 + 15.6412i −0.0926417 + 0.535231i
\(855\) −26.5841 5.56722i −0.909156 0.190395i
\(856\) 41.3516 + 23.3572i 1.41337 + 0.798331i
\(857\) 11.0582i 0.377740i −0.982002 0.188870i \(-0.939518\pi\)
0.982002 0.188870i \(-0.0604825\pi\)
\(858\) −20.1949 20.7189i −0.689442 0.707333i
\(859\) −41.4210 + 23.9144i −1.41327 + 0.815950i −0.995695 0.0926932i \(-0.970452\pi\)
−0.417573 + 0.908644i \(0.637119\pi\)
\(860\) 32.8338 + 11.7173i 1.11962 + 0.399555i
\(861\) −27.0559 + 12.0948i −0.922061 + 0.412188i
\(862\) 1.94721 + 5.29804i 0.0663223 + 0.180452i
\(863\) −36.9722 −1.25855 −0.629274 0.777184i \(-0.716648\pi\)
−0.629274 + 0.777184i \(0.716648\pi\)
\(864\) 27.0253 11.5600i 0.919419 0.393280i
\(865\) −18.7135 + 32.4127i −0.636278 + 1.10207i
\(866\) −7.33383 19.9541i −0.249214 0.678069i
\(867\) −4.81611 + 46.4938i −0.163564 + 1.57901i
\(868\) −6.06688 + 5.15607i −0.205923 + 0.175008i
\(869\) −24.2856 14.0213i −0.823831 0.475639i
\(870\) −15.5347 + 55.1416i −0.526677 + 1.86947i
\(871\) 24.6982 10.0416i 0.836868 0.340248i
\(872\) −0.796019 0.449626i −0.0269566 0.0152262i
\(873\) −47.4072 9.92798i −1.60449 0.336011i
\(874\) −6.67178 + 2.45211i −0.225676 + 0.0829439i
\(875\) −9.78594 16.9498i −0.330825 0.573006i
\(876\) −24.5726 + 1.91074i −0.830232 + 0.0645578i
\(877\) −3.07553 + 5.32697i −0.103853 + 0.179879i −0.913269 0.407357i \(-0.866451\pi\)
0.809416 + 0.587236i \(0.199784\pi\)
\(878\) 18.3871 + 15.3304i 0.620534 + 0.517374i
\(879\) −29.9189 + 41.3102i −1.00914 + 1.39336i
\(880\) 38.5932 + 6.30570i 1.30098 + 0.212565i
\(881\) 14.4267 + 8.32923i 0.486046 + 0.280619i 0.722933 0.690918i \(-0.242794\pi\)
−0.236886 + 0.971537i \(0.576127\pi\)
\(882\) −0.240439 0.0954284i −0.00809599 0.00321324i
\(883\) 29.1625 16.8370i 0.981396 0.566609i 0.0787048 0.996898i \(-0.474922\pi\)
0.902691 + 0.430289i \(0.141588\pi\)
\(884\) 42.5011 7.76994i 1.42947 0.261331i
\(885\) −23.7554 + 32.8000i −0.798529 + 1.10256i
\(886\) −18.2448 49.6410i −0.612946 1.66772i
\(887\) −21.4466 + 37.1466i −0.720106 + 1.24726i 0.240850 + 0.970562i \(0.422574\pi\)
−0.960957 + 0.276699i \(0.910760\pi\)
\(888\) 3.93750 + 0.370371i 0.132134 + 0.0124288i
\(889\) −5.74282 + 9.94685i −0.192608 + 0.333607i
\(890\) 57.5467 + 9.96059i 1.92897 + 0.333880i
\(891\) 29.8946 + 13.0953i 1.00151 + 0.438709i
\(892\) 4.77907 13.3918i 0.160015 0.448390i
\(893\) 17.1371i 0.573472i
\(894\) 37.7595 36.8045i 1.26287 1.23093i
\(895\) 9.81052i 0.327930i
\(896\) 23.4495 + 18.8129i 0.783393 + 0.628495i
\(897\) −0.869994 + 8.39875i −0.0290483 + 0.280426i
\(898\) −47.4707 + 17.4471i −1.58412 + 0.582218i
\(899\) −6.49844 + 11.2556i −0.216735 + 0.375396i
\(900\) 0.348521 13.6030i 0.0116174 0.453432i
\(901\) −11.4252 + 19.7890i −0.380627 + 0.659266i
\(902\) 25.3634 + 21.1469i 0.844509 + 0.704115i
\(903\) −3.06615 + 29.6000i −0.102035 + 0.985026i
\(904\) −23.2301 + 0.219099i −0.772620 + 0.00728713i
\(905\) 14.2444 8.22400i 0.473499 0.273375i
\(906\) −8.48673 33.3771i −0.281953 1.10888i
\(907\) −37.5266 + 21.6660i −1.24605 + 0.719407i −0.970319 0.241828i \(-0.922253\pi\)
−0.275730 + 0.961235i \(0.588920\pi\)
\(908\) −7.30549 39.9606i −0.242441 1.32614i
\(909\) −33.6934 30.1549i −1.11754 1.00018i
\(910\) −32.5154 5.62800i −1.07788 0.186567i
\(911\) −28.9203 −0.958172 −0.479086 0.877768i \(-0.659032\pi\)
−0.479086 + 0.877768i \(0.659032\pi\)
\(912\) −6.09774 + 22.4535i −0.201916 + 0.743511i
\(913\) 25.9201 0.857829
\(914\) 10.0041 + 27.2196i 0.330908 + 0.900344i
\(915\) −8.04959 18.0068i −0.266111 0.595288i
\(916\) 35.2498 29.9578i 1.16469 0.989834i
\(917\) −8.39172 + 4.84496i −0.277119 + 0.159995i
\(918\) −41.1325 + 26.1420i −1.35757 + 0.862816i
\(919\) 13.8299 + 7.98469i 0.456206 + 0.263391i 0.710448 0.703750i \(-0.248492\pi\)
−0.254242 + 0.967141i \(0.581826\pi\)
\(920\) −5.79912 9.82910i −0.191191 0.324056i
\(921\) 6.54234 + 14.6351i 0.215577 + 0.482245i
\(922\) 5.25480 30.3593i 0.173058 0.999830i
\(923\) −18.9446 −0.623570
\(924\) 2.58780 + 33.2798i 0.0851323 + 1.09483i
\(925\) 0.915424 1.58556i 0.0300990 0.0521329i
\(926\) 37.3099 + 31.1074i 1.22608 + 1.02225i
\(927\) −20.0277 17.9244i −0.657795 0.588714i
\(928\) 46.3734 + 16.0577i 1.52228 + 0.527118i
\(929\) 20.0684i 0.658422i −0.944256 0.329211i \(-0.893217\pi\)
0.944256 0.329211i \(-0.106783\pi\)
\(930\) 2.68272 9.52249i 0.0879698 0.312255i
\(931\) 0.177329 0.102381i 0.00581173 0.00335540i
\(932\) 3.66946 0.670841i 0.120197 0.0219741i
\(933\) 40.4259 + 29.2784i 1.32348 + 0.958533i
\(934\) 16.2217 19.4561i 0.530789 0.636623i
\(935\) −64.8386 −2.12045
\(936\) 20.7678 + 18.2369i 0.678815 + 0.596092i
\(937\) 57.0219 1.86282 0.931412 0.363966i \(-0.118578\pi\)
0.931412 + 0.363966i \(0.118578\pi\)
\(938\) −29.3046 9.34922i −0.956831 0.305263i
\(939\) −36.0345 26.0980i −1.17594 0.851676i
\(940\) −27.0656 + 4.94806i −0.882783 + 0.161388i
\(941\) 37.5791i 1.22504i 0.790454 + 0.612522i \(0.209845\pi\)
−0.790454 + 0.612522i \(0.790155\pi\)
\(942\) 10.6442 2.70647i 0.346805 0.0881816i
\(943\) 9.63726i 0.313832i
\(944\) 26.8544 + 21.9640i 0.874037 + 0.714869i
\(945\) 36.3750 7.90319i 1.18328 0.257091i
\(946\) 31.1233 11.4389i 1.01190 0.371910i
\(947\) 2.98264 0.0969228 0.0484614 0.998825i \(-0.484568\pi\)
0.0484614 + 0.998825i \(0.484568\pi\)
\(948\) 24.1676 + 11.5552i 0.784929 + 0.375295i
\(949\) −11.5874 20.0700i −0.376144 0.651501i
\(950\) 8.27279 + 6.89749i 0.268405 + 0.223784i
\(951\) 13.3718 + 29.9125i 0.433609 + 0.969979i
\(952\) −43.4019 24.5152i −1.40666 0.794543i
\(953\) 29.9705i 0.970841i 0.874281 + 0.485420i \(0.161333\pi\)
−0.874281 + 0.485420i \(0.838667\pi\)
\(954\) −14.4623 + 2.12328i −0.468233 + 0.0687437i
\(955\) −3.91301 2.25918i −0.126622 0.0731053i
\(956\) −8.29730 45.3857i −0.268354 1.46788i
\(957\) 22.2376 + 49.7452i 0.718839 + 1.60803i
\(958\) −15.5048 + 18.5963i −0.500937 + 0.600819i
\(959\) 16.3249 + 28.2756i 0.527160 + 0.913067i
\(960\) −37.2227 3.14740i −1.20136 0.101582i
\(961\) −14.3778 + 24.9030i −0.463799 + 0.803324i
\(962\) 1.28285 + 3.49041i 0.0413607 + 0.112535i
\(963\) −15.7100 47.8607i −0.506247 1.54229i
\(964\) 6.40243 + 2.28481i 0.206208 + 0.0735888i
\(965\) 35.9326i 1.15671i
\(966\) 6.97604 6.79959i 0.224450 0.218773i
\(967\) −9.48674 + 5.47717i −0.305073 + 0.176134i −0.644720 0.764419i \(-0.723026\pi\)
0.339647 + 0.940553i \(0.389693\pi\)
\(968\) 5.23817 3.09049i 0.168361 0.0993322i
\(969\) 3.97486 38.3725i 0.127691 1.23270i
\(970\) 47.2780 + 39.4183i 1.51800 + 1.26565i
\(971\) −25.5428 44.2414i −0.819706 1.41977i −0.905899 0.423494i \(-0.860803\pi\)
0.0861926 0.996278i \(-0.472530\pi\)
\(972\) −29.4410 10.2579i −0.944322 0.329023i
\(973\) −11.3822 19.7146i −0.364898 0.632022i
\(974\) −19.1410 15.9589i −0.613317 0.511357i
\(975\) 11.6808 5.22166i 0.374085 0.167227i
\(976\) −15.8035 + 5.97809i −0.505856 + 0.191354i
\(977\) −15.0360 8.68103i −0.481044 0.277731i 0.239807 0.970820i \(-0.422916\pi\)
−0.720851 + 0.693090i \(0.756249\pi\)
\(978\) −48.4792 13.6578i −1.55019 0.436728i
\(979\) 48.1070 27.7746i 1.53751 0.887680i
\(980\) 0.212897 + 0.250505i 0.00680073 + 0.00800208i
\(981\) 0.302417 + 0.921320i 0.00965544 + 0.0294155i
\(982\) 11.2131 + 1.94085i 0.357825 + 0.0619350i
\(983\) −11.4476 −0.365122 −0.182561 0.983195i \(-0.558439\pi\)
−0.182561 + 0.983195i \(0.558439\pi\)
\(984\) −25.7219 18.2617i −0.819984 0.582163i
\(985\) −3.23541 5.60389i −0.103089 0.178555i
\(986\) −80.1771 13.8776i −2.55336 0.441954i
\(987\) −9.58496 21.4414i −0.305093 0.682489i
\(988\) −21.5206 + 3.93434i −0.684662 + 0.125168i
\(989\) −8.38052 4.83850i −0.266485 0.153855i
\(990\) −25.7363 32.5268i −0.817953 1.03377i
\(991\) 29.2457i 0.929021i −0.885568 0.464511i \(-0.846230\pi\)
0.885568 0.464511i \(-0.153770\pi\)
\(992\) −8.00830 2.77302i −0.254264 0.0880436i
\(993\) 4.67333 + 0.484092i 0.148304 + 0.0153622i
\(994\) 16.7873 + 13.9966i 0.532462 + 0.443944i
\(995\) 13.3186 23.0685i 0.422227 0.731319i
\(996\) −24.6860 + 1.91955i −0.782205 + 0.0608232i
\(997\) −18.5302 −0.586856 −0.293428 0.955981i \(-0.594796\pi\)
−0.293428 + 0.955981i \(0.594796\pi\)
\(998\) −46.1289 38.4602i −1.46018 1.21744i
\(999\) −2.82087 3.10465i −0.0892485 0.0982269i
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 804.2.l.a.431.9 264
3.2 odd 2 inner 804.2.l.a.431.124 yes 264
4.3 odd 2 inner 804.2.l.a.431.38 yes 264
12.11 even 2 inner 804.2.l.a.431.95 yes 264
67.37 even 3 inner 804.2.l.a.707.95 yes 264
201.104 odd 6 inner 804.2.l.a.707.38 yes 264
268.171 odd 6 inner 804.2.l.a.707.124 yes 264
804.707 even 6 inner 804.2.l.a.707.9 yes 264
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.l.a.431.9 264 1.1 even 1 trivial
804.2.l.a.431.38 yes 264 4.3 odd 2 inner
804.2.l.a.431.95 yes 264 12.11 even 2 inner
804.2.l.a.431.124 yes 264 3.2 odd 2 inner
804.2.l.a.707.9 yes 264 804.707 even 6 inner
804.2.l.a.707.38 yes 264 201.104 odd 6 inner
804.2.l.a.707.95 yes 264 67.37 even 3 inner
804.2.l.a.707.124 yes 264 268.171 odd 6 inner