Properties

Label 91.2.bc.a.76.6
Level $91$
Weight $2$
Character 91.76
Analytic conductor $0.727$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,2,Mod(6,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.6");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 76.6
Character \(\chi\) \(=\) 91.76
Dual form 91.2.bc.a.6.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.218036 - 0.813723i) q^{2} +(1.24122 - 0.716618i) q^{3} +(1.11745 + 0.645157i) q^{4} +(-1.01306 + 1.01306i) q^{5} +(-0.312498 - 1.16626i) q^{6} +(-2.62506 + 0.330214i) q^{7} +(1.96000 - 1.96000i) q^{8} +(-0.472916 + 0.819114i) q^{9} +O(q^{10})\) \(q+(0.218036 - 0.813723i) q^{2} +(1.24122 - 0.716618i) q^{3} +(1.11745 + 0.645157i) q^{4} +(-1.01306 + 1.01306i) q^{5} +(-0.312498 - 1.16626i) q^{6} +(-2.62506 + 0.330214i) q^{7} +(1.96000 - 1.96000i) q^{8} +(-0.472916 + 0.819114i) q^{9} +(0.603466 + 1.04523i) q^{10} +(-4.68859 - 1.25630i) q^{11} +1.84933 q^{12} +(1.04975 - 3.44935i) q^{13} +(-0.303657 + 2.20807i) q^{14} +(-0.531452 + 1.98341i) q^{15} +(0.122771 + 0.212645i) q^{16} +(1.49151 - 2.58338i) q^{17} +(0.563419 + 0.563419i) q^{18} +(1.62522 + 6.06542i) q^{19} +(-1.78562 + 0.478455i) q^{20} +(-3.02164 + 2.29104i) q^{21} +(-2.04457 + 3.54129i) q^{22} +(-1.02242 + 0.590296i) q^{23} +(1.02822 - 3.83736i) q^{24} +2.94742i q^{25} +(-2.57793 - 1.60629i) q^{26} +5.65531i q^{27} +(-3.14641 - 1.32458i) q^{28} +(-2.77911 - 4.81356i) q^{29} +(1.49807 + 0.864909i) q^{30} +(4.79337 - 4.79337i) q^{31} +(5.55461 - 1.48835i) q^{32} +(-6.71986 + 1.80058i) q^{33} +(-1.77695 - 1.77695i) q^{34} +(2.32482 - 2.99387i) q^{35} +(-1.05692 + 0.610210i) q^{36} +(5.40165 + 1.44737i) q^{37} +5.28993 q^{38} +(-1.16890 - 5.03367i) q^{39} +3.97118i q^{40} +(4.71621 + 1.26371i) q^{41} +(1.20544 + 2.95831i) q^{42} +(-2.90941 - 1.67975i) q^{43} +(-4.42873 - 4.42873i) q^{44} +(-0.350719 - 1.30890i) q^{45} +(0.257412 + 0.960674i) q^{46} +(-4.12822 - 4.12822i) q^{47} +(0.304771 + 0.175960i) q^{48} +(6.78192 - 1.73367i) q^{49} +(2.39839 + 0.642646i) q^{50} -4.27539i q^{51} +(3.39841 - 3.17721i) q^{52} +5.79315 q^{53} +(4.60186 + 1.23306i) q^{54} +(6.02252 - 3.47711i) q^{55} +(-4.49790 + 5.79233i) q^{56} +(6.36385 + 6.36385i) q^{57} +(-4.52285 + 1.21190i) q^{58} +(-10.7576 + 2.88250i) q^{59} +(-1.87348 + 1.87348i) q^{60} +(-7.95118 - 4.59062i) q^{61} +(-2.85534 - 4.94560i) q^{62} +(0.970951 - 2.30639i) q^{63} -4.35335i q^{64} +(2.43094 + 4.55785i) q^{65} +5.86070i q^{66} +(-0.508485 + 1.89769i) q^{67} +(3.33337 - 1.92452i) q^{68} +(-0.846033 + 1.46537i) q^{69} +(-1.92929 - 2.54453i) q^{70} +(-3.19094 + 0.855010i) q^{71} +(0.678548 + 2.53237i) q^{72} +(-0.353010 - 0.353010i) q^{73} +(2.35552 - 4.07987i) q^{74} +(2.11218 + 3.65840i) q^{75} +(-2.09705 + 7.82630i) q^{76} +(12.7227 + 1.74964i) q^{77} +(-4.35088 - 0.146360i) q^{78} -6.95423 q^{79} +(-0.339796 - 0.0910481i) q^{80} +(2.63395 + 4.56214i) q^{81} +(2.05661 - 3.56216i) q^{82} +(3.22886 - 3.22886i) q^{83} +(-4.85460 + 0.610674i) q^{84} +(1.10612 + 4.12811i) q^{85} +(-2.00121 + 2.00121i) q^{86} +(-6.89897 - 3.98312i) q^{87} +(-11.6520 + 6.72727i) q^{88} +(-0.0636346 + 0.237487i) q^{89} -1.14155 q^{90} +(-1.61663 + 9.40141i) q^{91} -1.52333 q^{92} +(2.51461 - 9.38464i) q^{93} +(-4.25933 + 2.45913i) q^{94} +(-7.79107 - 4.49818i) q^{95} +(5.82791 - 5.82791i) q^{96} +(2.43374 + 9.08284i) q^{97} +(0.0679801 - 5.89661i) q^{98} +(3.24636 - 3.24636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9} - 4 q^{11} - 32 q^{14} - 8 q^{15} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{22} - 12 q^{23} + 24 q^{28} + 4 q^{29} + 12 q^{30} + 4 q^{32} - 20 q^{35} + 4 q^{37} - 36 q^{39} - 28 q^{42} - 48 q^{43} + 24 q^{44} + 84 q^{46} + 24 q^{49} - 44 q^{50} + 72 q^{53} + 60 q^{56} - 92 q^{57} - 16 q^{58} + 76 q^{60} + 48 q^{63} + 4 q^{65} - 56 q^{67} + 56 q^{70} + 84 q^{71} - 128 q^{72} - 24 q^{74} + 148 q^{78} - 80 q^{79} + 28 q^{81} - 64 q^{84} + 36 q^{85} - 48 q^{86} - 228 q^{88} - 48 q^{91} + 24 q^{92} + 108 q^{93} - 84 q^{95} - 32 q^{98} - 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.218036 0.813723i 0.154175 0.575389i −0.845000 0.534767i \(-0.820399\pi\)
0.999175 0.0406221i \(-0.0129340\pi\)
\(3\) 1.24122 0.716618i 0.716618 0.413740i −0.0968883 0.995295i \(-0.530889\pi\)
0.813507 + 0.581555i \(0.197556\pi\)
\(4\) 1.11745 + 0.645157i 0.558723 + 0.322579i
\(5\) −1.01306 + 1.01306i −0.453054 + 0.453054i −0.896367 0.443313i \(-0.853803\pi\)
0.443313 + 0.896367i \(0.353803\pi\)
\(6\) −0.312498 1.16626i −0.127577 0.476123i
\(7\) −2.62506 + 0.330214i −0.992181 + 0.124809i
\(8\) 1.96000 1.96000i 0.692963 0.692963i
\(9\) −0.472916 + 0.819114i −0.157639 + 0.273038i
\(10\) 0.603466 + 1.04523i 0.190833 + 0.330532i
\(11\) −4.68859 1.25630i −1.41366 0.378790i −0.530431 0.847728i \(-0.677970\pi\)
−0.883231 + 0.468938i \(0.844637\pi\)
\(12\) 1.84933 0.533855
\(13\) 1.04975 3.44935i 0.291147 0.956678i
\(14\) −0.303657 + 2.20807i −0.0811556 + 0.590133i
\(15\) −0.531452 + 1.98341i −0.137220 + 0.512113i
\(16\) 0.122771 + 0.212645i 0.0306927 + 0.0531613i
\(17\) 1.49151 2.58338i 0.361745 0.626561i −0.626503 0.779419i \(-0.715514\pi\)
0.988248 + 0.152858i \(0.0488477\pi\)
\(18\) 0.563419 + 0.563419i 0.132799 + 0.132799i
\(19\) 1.62522 + 6.06542i 0.372852 + 1.39150i 0.856458 + 0.516217i \(0.172660\pi\)
−0.483606 + 0.875286i \(0.660673\pi\)
\(20\) −1.78562 + 0.478455i −0.399277 + 0.106986i
\(21\) −3.02164 + 2.29104i −0.659377 + 0.499945i
\(22\) −2.04457 + 3.54129i −0.435903 + 0.755006i
\(23\) −1.02242 + 0.590296i −0.213190 + 0.123085i −0.602793 0.797898i \(-0.705945\pi\)
0.389603 + 0.920983i \(0.372612\pi\)
\(24\) 1.02822 3.83736i 0.209884 0.783297i
\(25\) 2.94742i 0.589485i
\(26\) −2.57793 1.60629i −0.505575 0.315019i
\(27\) 5.65531i 1.08837i
\(28\) −3.14641 1.32458i −0.594615 0.250323i
\(29\) −2.77911 4.81356i −0.516068 0.893856i −0.999826 0.0186541i \(-0.994062\pi\)
0.483758 0.875202i \(-0.339271\pi\)
\(30\) 1.49807 + 0.864909i 0.273508 + 0.157910i
\(31\) 4.79337 4.79337i 0.860914 0.860914i −0.130530 0.991444i \(-0.541668\pi\)
0.991444 + 0.130530i \(0.0416680\pi\)
\(32\) 5.55461 1.48835i 0.981926 0.263106i
\(33\) −6.71986 + 1.80058i −1.16978 + 0.313441i
\(34\) −1.77695 1.77695i −0.304744 0.304744i
\(35\) 2.32482 2.99387i 0.392966 0.506056i
\(36\) −1.05692 + 0.610210i −0.176153 + 0.101702i
\(37\) 5.40165 + 1.44737i 0.888027 + 0.237946i 0.673867 0.738853i \(-0.264632\pi\)
0.214160 + 0.976799i \(0.431299\pi\)
\(38\) 5.28993 0.858140
\(39\) −1.16890 5.03367i −0.187174 0.806033i
\(40\) 3.97118i 0.627899i
\(41\) 4.71621 + 1.26371i 0.736549 + 0.197358i 0.607544 0.794286i \(-0.292155\pi\)
0.129005 + 0.991644i \(0.458822\pi\)
\(42\) 1.20544 + 2.95831i 0.186004 + 0.456477i
\(43\) −2.90941 1.67975i −0.443681 0.256159i 0.261477 0.965210i \(-0.415790\pi\)
−0.705158 + 0.709050i \(0.749124\pi\)
\(44\) −4.42873 4.42873i −0.667656 0.667656i
\(45\) −0.350719 1.30890i −0.0522822 0.195120i
\(46\) 0.257412 + 0.960674i 0.0379533 + 0.141644i
\(47\) −4.12822 4.12822i −0.602163 0.602163i 0.338723 0.940886i \(-0.390005\pi\)
−0.940886 + 0.338723i \(0.890005\pi\)
\(48\) 0.304771 + 0.175960i 0.0439899 + 0.0253976i
\(49\) 6.78192 1.73367i 0.968845 0.247667i
\(50\) 2.39839 + 0.642646i 0.339183 + 0.0908839i
\(51\) 4.27539i 0.598674i
\(52\) 3.39841 3.17721i 0.471275 0.440600i
\(53\) 5.79315 0.795751 0.397875 0.917439i \(-0.369748\pi\)
0.397875 + 0.917439i \(0.369748\pi\)
\(54\) 4.60186 + 1.23306i 0.626234 + 0.167799i
\(55\) 6.02252 3.47711i 0.812077 0.468853i
\(56\) −4.49790 + 5.79233i −0.601057 + 0.774033i
\(57\) 6.36385 + 6.36385i 0.842913 + 0.842913i
\(58\) −4.52285 + 1.21190i −0.593880 + 0.159130i
\(59\) −10.7576 + 2.88250i −1.40053 + 0.375270i −0.878534 0.477681i \(-0.841478\pi\)
−0.521992 + 0.852950i \(0.674811\pi\)
\(60\) −1.87348 + 1.87348i −0.241865 + 0.241865i
\(61\) −7.95118 4.59062i −1.01804 0.587768i −0.104508 0.994524i \(-0.533327\pi\)
−0.913537 + 0.406756i \(0.866660\pi\)
\(62\) −2.85534 4.94560i −0.362629 0.628092i
\(63\) 0.970951 2.30639i 0.122328 0.290578i
\(64\) 4.35335i 0.544169i
\(65\) 2.43094 + 4.55785i 0.301521 + 0.565332i
\(66\) 5.86070i 0.721402i
\(67\) −0.508485 + 1.89769i −0.0621214 + 0.231840i −0.990006 0.141028i \(-0.954959\pi\)
0.927884 + 0.372869i \(0.121626\pi\)
\(68\) 3.33337 1.92452i 0.404231 0.233383i
\(69\) −0.846033 + 1.46537i −0.101850 + 0.176410i
\(70\) −1.92929 2.54453i −0.230594 0.304130i
\(71\) −3.19094 + 0.855010i −0.378695 + 0.101471i −0.443145 0.896450i \(-0.646137\pi\)
0.0644501 + 0.997921i \(0.479471\pi\)
\(72\) 0.678548 + 2.53237i 0.0799676 + 0.298443i
\(73\) −0.353010 0.353010i −0.0413167 0.0413167i 0.686147 0.727463i \(-0.259301\pi\)
−0.727463 + 0.686147i \(0.759301\pi\)
\(74\) 2.35552 4.07987i 0.273823 0.474275i
\(75\) 2.11218 + 3.65840i 0.243893 + 0.422436i
\(76\) −2.09705 + 7.82630i −0.240548 + 0.897738i
\(77\) 12.7227 + 1.74964i 1.44989 + 0.199390i
\(78\) −4.35088 0.146360i −0.492640 0.0165720i
\(79\) −6.95423 −0.782412 −0.391206 0.920303i \(-0.627942\pi\)
−0.391206 + 0.920303i \(0.627942\pi\)
\(80\) −0.339796 0.0910481i −0.0379904 0.0101795i
\(81\) 2.63395 + 4.56214i 0.292662 + 0.506905i
\(82\) 2.05661 3.56216i 0.227115 0.393374i
\(83\) 3.22886 3.22886i 0.354413 0.354413i −0.507335 0.861749i \(-0.669369\pi\)
0.861749 + 0.507335i \(0.169369\pi\)
\(84\) −4.85460 + 0.610674i −0.529680 + 0.0666300i
\(85\) 1.10612 + 4.12811i 0.119976 + 0.447756i
\(86\) −2.00121 + 2.00121i −0.215796 + 0.215796i
\(87\) −6.89897 3.98312i −0.739648 0.427036i
\(88\) −11.6520 + 6.72727i −1.24210 + 0.717129i
\(89\) −0.0636346 + 0.237487i −0.00674525 + 0.0251736i −0.969216 0.246210i \(-0.920815\pi\)
0.962471 + 0.271384i \(0.0874813\pi\)
\(90\) −1.14155 −0.120330
\(91\) −1.61663 + 9.40141i −0.169468 + 0.985536i
\(92\) −1.52333 −0.158819
\(93\) 2.51461 9.38464i 0.260752 0.973141i
\(94\) −4.25933 + 2.45913i −0.439316 + 0.253639i
\(95\) −7.79107 4.49818i −0.799347 0.461503i
\(96\) 5.82791 5.82791i 0.594809 0.594809i
\(97\) 2.43374 + 9.08284i 0.247109 + 0.922223i 0.972312 + 0.233688i \(0.0750793\pi\)
−0.725203 + 0.688535i \(0.758254\pi\)
\(98\) 0.0679801 5.89661i 0.00686703 0.595647i
\(99\) 3.24636 3.24636i 0.326272 0.326272i
\(100\) −1.90155 + 3.29359i −0.190155 + 0.329359i
\(101\) 7.14344 + 12.3728i 0.710799 + 1.23114i 0.964558 + 0.263872i \(0.0849996\pi\)
−0.253759 + 0.967267i \(0.581667\pi\)
\(102\) −3.47898 0.932190i −0.344470 0.0923006i
\(103\) −7.45130 −0.734198 −0.367099 0.930182i \(-0.619649\pi\)
−0.367099 + 0.930182i \(0.619649\pi\)
\(104\) −4.70322 8.81822i −0.461189 0.864698i
\(105\) 0.740146 5.38206i 0.0722309 0.525235i
\(106\) 1.26312 4.71402i 0.122685 0.457866i
\(107\) 2.34132 + 4.05528i 0.226344 + 0.392039i 0.956722 0.291004i \(-0.0939894\pi\)
−0.730378 + 0.683043i \(0.760656\pi\)
\(108\) −3.64857 + 6.31950i −0.351083 + 0.608094i
\(109\) −3.04192 3.04192i −0.291363 0.291363i 0.546256 0.837619i \(-0.316053\pi\)
−0.837619 + 0.546256i \(0.816053\pi\)
\(110\) −1.51627 5.65880i −0.144571 0.539546i
\(111\) 7.74185 2.07442i 0.734824 0.196895i
\(112\) −0.392500 0.517667i −0.0370877 0.0489149i
\(113\) 2.02372 3.50518i 0.190375 0.329740i −0.754999 0.655725i \(-0.772363\pi\)
0.945375 + 0.325986i \(0.105696\pi\)
\(114\) 6.56597 3.79086i 0.614959 0.355047i
\(115\) 0.437769 1.63378i 0.0408222 0.152351i
\(116\) 7.17186i 0.665890i
\(117\) 2.32897 + 2.49112i 0.215314 + 0.230304i
\(118\) 9.38223i 0.863705i
\(119\) −3.06225 + 7.27405i −0.280716 + 0.666811i
\(120\) 2.84582 + 4.92911i 0.259787 + 0.449964i
\(121\) 10.8783 + 6.28058i 0.988935 + 0.570962i
\(122\) −5.46914 + 5.46914i −0.495153 + 0.495153i
\(123\) 6.75945 1.81119i 0.609479 0.163309i
\(124\) 8.44880 2.26385i 0.758725 0.203300i
\(125\) −8.05121 8.05121i −0.720122 0.720122i
\(126\) −1.66506 1.29296i −0.148335 0.115186i
\(127\) 10.6871 6.17021i 0.948328 0.547518i 0.0557671 0.998444i \(-0.482240\pi\)
0.892561 + 0.450926i \(0.148906\pi\)
\(128\) 7.56681 + 2.02752i 0.668817 + 0.179209i
\(129\) −4.81496 −0.423933
\(130\) 4.23886 0.984335i 0.371773 0.0863319i
\(131\) 6.71360i 0.586570i −0.956025 0.293285i \(-0.905251\pi\)
0.956025 0.293285i \(-0.0947485\pi\)
\(132\) −8.67073 2.32332i −0.754690 0.202219i
\(133\) −6.26921 15.3854i −0.543609 1.33409i
\(134\) 1.43333 + 0.827533i 0.123821 + 0.0714879i
\(135\) −5.72916 5.72916i −0.493088 0.493088i
\(136\) −2.14005 7.98678i −0.183508 0.684860i
\(137\) 5.66652 + 21.1477i 0.484124 + 1.80677i 0.583976 + 0.811771i \(0.301496\pi\)
−0.0998520 + 0.995002i \(0.531837\pi\)
\(138\) 1.00794 + 1.00794i 0.0858017 + 0.0858017i
\(139\) 3.49682 + 2.01889i 0.296597 + 0.171240i 0.640913 0.767614i \(-0.278556\pi\)
−0.344316 + 0.938854i \(0.611889\pi\)
\(140\) 4.52937 1.84561i 0.382802 0.155983i
\(141\) −8.08239 2.16567i −0.680660 0.182382i
\(142\) 2.78296i 0.233541i
\(143\) −9.25526 + 14.8538i −0.773964 + 1.24214i
\(144\) −0.232241 −0.0193534
\(145\) 7.69182 + 2.06102i 0.638771 + 0.171158i
\(146\) −0.364221 + 0.210283i −0.0301432 + 0.0174032i
\(147\) 7.17547 7.01191i 0.591823 0.578332i
\(148\) 5.10227 + 5.10227i 0.419404 + 0.419404i
\(149\) −2.74006 + 0.734196i −0.224474 + 0.0601477i −0.369303 0.929309i \(-0.620404\pi\)
0.144829 + 0.989457i \(0.453737\pi\)
\(150\) 3.43746 0.921064i 0.280667 0.0752045i
\(151\) 11.8387 11.8387i 0.963421 0.963421i −0.0359335 0.999354i \(-0.511440\pi\)
0.999354 + 0.0359335i \(0.0114404\pi\)
\(152\) 15.0736 + 8.70277i 1.22263 + 0.705888i
\(153\) 1.41072 + 2.44344i 0.114050 + 0.197541i
\(154\) 4.19773 9.97126i 0.338263 0.803507i
\(155\) 9.71192i 0.780080i
\(156\) 1.94132 6.37898i 0.155430 0.510727i
\(157\) 2.86867i 0.228945i −0.993426 0.114472i \(-0.963482\pi\)
0.993426 0.114472i \(-0.0365177\pi\)
\(158\) −1.51628 + 5.65882i −0.120628 + 0.450191i
\(159\) 7.19058 4.15148i 0.570250 0.329234i
\(160\) −4.11936 + 7.13494i −0.325664 + 0.564067i
\(161\) 2.48900 1.88718i 0.196161 0.148731i
\(162\) 4.28662 1.14860i 0.336789 0.0902422i
\(163\) −6.23736 23.2781i −0.488548 1.82328i −0.563525 0.826099i \(-0.690555\pi\)
0.0749773 0.997185i \(-0.476112\pi\)
\(164\) 4.45482 + 4.45482i 0.347863 + 0.347863i
\(165\) 4.98352 8.63170i 0.387966 0.671977i
\(166\) −1.92339 3.33141i −0.149284 0.258567i
\(167\) −2.53997 + 9.47931i −0.196549 + 0.733531i 0.795311 + 0.606201i \(0.207307\pi\)
−0.991860 + 0.127330i \(0.959359\pi\)
\(168\) −1.43198 + 10.4128i −0.110480 + 0.803368i
\(169\) −10.7961 7.24189i −0.830466 0.557069i
\(170\) 3.60031 0.276131
\(171\) −5.73687 1.53719i −0.438709 0.117552i
\(172\) −2.16740 3.75405i −0.165263 0.286244i
\(173\) 2.61883 4.53595i 0.199106 0.344862i −0.749133 0.662420i \(-0.769529\pi\)
0.948239 + 0.317558i \(0.102863\pi\)
\(174\) −4.74539 + 4.74539i −0.359747 + 0.359747i
\(175\) −0.973282 7.73717i −0.0735732 0.584875i
\(176\) −0.308475 1.15124i −0.0232522 0.0867783i
\(177\) −11.2869 + 11.2869i −0.848379 + 0.848379i
\(178\) 0.179374 + 0.103562i 0.0134447 + 0.00776229i
\(179\) −19.5491 + 11.2867i −1.46117 + 0.843605i −0.999065 0.0432226i \(-0.986238\pi\)
−0.462101 + 0.886827i \(0.652904\pi\)
\(180\) 0.452538 1.68890i 0.0337302 0.125883i
\(181\) −22.4803 −1.67095 −0.835474 0.549530i \(-0.814807\pi\)
−0.835474 + 0.549530i \(0.814807\pi\)
\(182\) 7.29766 + 3.36534i 0.540939 + 0.249455i
\(183\) −13.1589 −0.972733
\(184\) −0.846966 + 3.16092i −0.0624392 + 0.233026i
\(185\) −6.93846 + 4.00592i −0.510126 + 0.294521i
\(186\) −7.08822 4.09239i −0.519733 0.300068i
\(187\) −10.2386 + 10.2386i −0.748721 + 0.748721i
\(188\) −1.94971 7.27641i −0.142197 0.530687i
\(189\) −1.86746 14.8456i −0.135838 1.07986i
\(190\) −5.35901 + 5.35901i −0.388783 + 0.388783i
\(191\) −12.3354 + 21.3655i −0.892557 + 1.54595i −0.0557571 + 0.998444i \(0.517757\pi\)
−0.836800 + 0.547509i \(0.815576\pi\)
\(192\) −3.11969 5.40346i −0.225144 0.389961i
\(193\) 3.32194 + 0.890112i 0.239119 + 0.0640717i 0.376388 0.926462i \(-0.377166\pi\)
−0.137269 + 0.990534i \(0.543833\pi\)
\(194\) 7.92156 0.568735
\(195\) 6.28357 + 3.91524i 0.449976 + 0.280376i
\(196\) 8.69691 + 2.43813i 0.621208 + 0.174152i
\(197\) −1.03338 + 3.85664i −0.0736255 + 0.274774i −0.992918 0.118801i \(-0.962095\pi\)
0.919293 + 0.393575i \(0.128762\pi\)
\(198\) −1.93382 3.34947i −0.137430 0.238036i
\(199\) −0.511550 + 0.886031i −0.0362628 + 0.0628091i −0.883587 0.468267i \(-0.844879\pi\)
0.847324 + 0.531076i \(0.178212\pi\)
\(200\) 5.77694 + 5.77694i 0.408491 + 0.408491i
\(201\) 0.728780 + 2.71984i 0.0514042 + 0.191843i
\(202\) 11.6256 3.11506i 0.817972 0.219175i
\(203\) 8.88485 + 11.7182i 0.623594 + 0.822457i
\(204\) 2.75830 4.77751i 0.193119 0.334493i
\(205\) −6.05801 + 3.49759i −0.423110 + 0.244282i
\(206\) −1.62465 + 6.06329i −0.113195 + 0.422450i
\(207\) 1.11664i 0.0776119i
\(208\) 0.862367 0.200256i 0.0597944 0.0138853i
\(209\) 30.4800i 2.10835i
\(210\) −4.21813 1.77576i −0.291078 0.122539i
\(211\) 2.70061 + 4.67759i 0.185918 + 0.322019i 0.943885 0.330273i \(-0.107141\pi\)
−0.757968 + 0.652292i \(0.773808\pi\)
\(212\) 6.47353 + 3.73750i 0.444604 + 0.256692i
\(213\) −3.34794 + 3.34794i −0.229397 + 0.229397i
\(214\) 3.81037 1.02099i 0.260472 0.0697932i
\(215\) 4.64909 1.24572i 0.317065 0.0849573i
\(216\) 11.0844 + 11.0844i 0.754197 + 0.754197i
\(217\) −11.0001 + 14.1657i −0.746732 + 0.961632i
\(218\) −3.13853 + 1.81203i −0.212568 + 0.122726i
\(219\) −0.691136 0.185189i −0.0467026 0.0125139i
\(220\) 8.97312 0.604968
\(221\) −7.34527 7.85665i −0.494096 0.528496i
\(222\) 6.75202i 0.453166i
\(223\) 16.6138 + 4.45165i 1.11254 + 0.298105i 0.767862 0.640616i \(-0.221321\pi\)
0.344680 + 0.938720i \(0.387987\pi\)
\(224\) −14.0897 + 5.74124i −0.941410 + 0.383603i
\(225\) −2.41428 1.39388i −0.160952 0.0929256i
\(226\) −2.41100 2.41100i −0.160377 0.160377i
\(227\) 2.57850 + 9.62310i 0.171141 + 0.638707i 0.997177 + 0.0750896i \(0.0239243\pi\)
−0.826036 + 0.563618i \(0.809409\pi\)
\(228\) 3.00557 + 11.2169i 0.199049 + 0.742860i
\(229\) 2.94885 + 2.94885i 0.194865 + 0.194865i 0.797795 0.602929i \(-0.206000\pi\)
−0.602929 + 0.797795i \(0.706000\pi\)
\(230\) −1.23399 0.712446i −0.0813671 0.0469773i
\(231\) 17.0455 6.94563i 1.12151 0.456989i
\(232\) −14.8816 3.98752i −0.977026 0.261793i
\(233\) 6.32614i 0.414439i −0.978294 0.207220i \(-0.933559\pi\)
0.978294 0.207220i \(-0.0664414\pi\)
\(234\) 2.53488 1.35198i 0.165710 0.0883820i
\(235\) 8.36426 0.545624
\(236\) −13.8807 3.71933i −0.903560 0.242108i
\(237\) −8.63172 + 4.98353i −0.560691 + 0.323715i
\(238\) 5.25138 + 4.07783i 0.340397 + 0.264327i
\(239\) 7.84175 + 7.84175i 0.507241 + 0.507241i 0.913679 0.406438i \(-0.133229\pi\)
−0.406438 + 0.913679i \(0.633229\pi\)
\(240\) −0.487009 + 0.130494i −0.0314363 + 0.00842332i
\(241\) 13.5060 3.61892i 0.869996 0.233115i 0.203910 0.978990i \(-0.434635\pi\)
0.666086 + 0.745875i \(0.267968\pi\)
\(242\) 7.48251 7.48251i 0.480994 0.480994i
\(243\) −8.15430 4.70789i −0.523099 0.302011i
\(244\) −5.92334 10.2595i −0.379203 0.656799i
\(245\) −5.11417 + 8.62679i −0.326733 + 0.551145i
\(246\) 5.89523i 0.375866i
\(247\) 22.6278 + 0.761183i 1.43978 + 0.0484329i
\(248\) 18.7900i 1.19316i
\(249\) 1.69386 6.32158i 0.107344 0.400614i
\(250\) −8.30691 + 4.79600i −0.525375 + 0.303325i
\(251\) 13.1784 22.8256i 0.831813 1.44074i −0.0647865 0.997899i \(-0.520637\pi\)
0.896599 0.442843i \(-0.146030\pi\)
\(252\) 2.57297 1.95085i 0.162082 0.122892i
\(253\) 5.53531 1.48318i 0.348002 0.0932468i
\(254\) −2.69066 10.0417i −0.168827 0.630071i
\(255\) 4.33122 + 4.33122i 0.271231 + 0.271231i
\(256\) 7.65303 13.2554i 0.478314 0.828465i
\(257\) −5.39025 9.33618i −0.336234 0.582375i 0.647487 0.762077i \(-0.275820\pi\)
−0.983721 + 0.179702i \(0.942487\pi\)
\(258\) −1.04984 + 3.91804i −0.0653599 + 0.243927i
\(259\) −14.6576 2.01573i −0.910781 0.125251i
\(260\) −0.224087 + 6.66149i −0.0138973 + 0.413128i
\(261\) 5.25714 0.325409
\(262\) −5.46301 1.46381i −0.337506 0.0904345i
\(263\) 7.74562 + 13.4158i 0.477616 + 0.827254i 0.999671 0.0256573i \(-0.00816786\pi\)
−0.522055 + 0.852912i \(0.674835\pi\)
\(264\) −9.64177 + 16.7000i −0.593410 + 1.02782i
\(265\) −5.86881 + 5.86881i −0.360518 + 0.360518i
\(266\) −13.8864 + 1.74681i −0.851430 + 0.107104i
\(267\) 0.0912034 + 0.340376i 0.00558156 + 0.0208307i
\(268\) −1.79252 + 1.79252i −0.109495 + 0.109495i
\(269\) 22.6324 + 13.0668i 1.37992 + 0.796697i 0.992149 0.125060i \(-0.0399122\pi\)
0.387770 + 0.921756i \(0.373246\pi\)
\(270\) −5.91112 + 3.41279i −0.359739 + 0.207696i
\(271\) −1.70363 + 6.35804i −0.103488 + 0.386223i −0.998169 0.0604821i \(-0.980736\pi\)
0.894681 + 0.446706i \(0.147403\pi\)
\(272\) 0.732458 0.0444118
\(273\) 4.73064 + 12.8277i 0.286311 + 0.776369i
\(274\) 18.4439 1.11424
\(275\) 3.70286 13.8193i 0.223291 0.833333i
\(276\) −1.89079 + 1.09165i −0.113812 + 0.0657096i
\(277\) −25.2681 14.5885i −1.51821 0.876540i −0.999770 0.0214270i \(-0.993179\pi\)
−0.518442 0.855113i \(-0.673488\pi\)
\(278\) 2.40525 2.40525i 0.144258 0.144258i
\(279\) 1.65946 + 6.19317i 0.0993490 + 0.370776i
\(280\) −1.31134 10.4246i −0.0783677 0.622990i
\(281\) 8.85369 8.85369i 0.528167 0.528167i −0.391859 0.920025i \(-0.628168\pi\)
0.920025 + 0.391859i \(0.128168\pi\)
\(282\) −3.52451 + 6.10463i −0.209882 + 0.363526i
\(283\) −15.9706 27.6618i −0.949351 1.64432i −0.746795 0.665054i \(-0.768409\pi\)
−0.202556 0.979271i \(-0.564925\pi\)
\(284\) −4.11732 1.10323i −0.244318 0.0654648i
\(285\) −12.8939 −0.763769
\(286\) 10.0689 + 10.7699i 0.595386 + 0.636837i
\(287\) −12.7976 1.75995i −0.755421 0.103886i
\(288\) −1.40773 + 5.25373i −0.0829514 + 0.309579i
\(289\) 4.05077 + 7.01614i 0.238281 + 0.412714i
\(290\) 3.35420 5.80964i 0.196965 0.341154i
\(291\) 9.52974 + 9.52974i 0.558643 + 0.558643i
\(292\) −0.166722 0.622216i −0.00975668 0.0364124i
\(293\) −12.4822 + 3.34459i −0.729218 + 0.195393i −0.604281 0.796771i \(-0.706540\pi\)
−0.124937 + 0.992165i \(0.539873\pi\)
\(294\) −4.14124 7.36770i −0.241522 0.429693i
\(295\) 7.97798 13.8183i 0.464496 0.804531i
\(296\) 13.4241 7.75039i 0.780258 0.450482i
\(297\) 7.10479 26.5154i 0.412262 1.53858i
\(298\) 2.38973i 0.138433i
\(299\) 0.962853 + 4.14635i 0.0556832 + 0.239790i
\(300\) 5.45075i 0.314699i
\(301\) 8.19206 + 3.44872i 0.472183 + 0.198781i
\(302\) −7.05216 12.2147i −0.405806 0.702877i
\(303\) 17.7332 + 10.2382i 1.01874 + 0.588171i
\(304\) −1.09025 + 1.09025i −0.0625303 + 0.0625303i
\(305\) 12.7056 3.40445i 0.727520 0.194938i
\(306\) 2.29587 0.615177i 0.131246 0.0351674i
\(307\) 5.42520 + 5.42520i 0.309632 + 0.309632i 0.844767 0.535135i \(-0.179739\pi\)
−0.535135 + 0.844767i \(0.679739\pi\)
\(308\) 13.0881 + 10.1633i 0.745765 + 0.579106i
\(309\) −9.24869 + 5.33974i −0.526140 + 0.303767i
\(310\) 7.90282 + 2.11755i 0.448850 + 0.120269i
\(311\) 0.483376 0.0274097 0.0137049 0.999906i \(-0.495637\pi\)
0.0137049 + 0.999906i \(0.495637\pi\)
\(312\) −12.1570 7.57493i −0.688256 0.428846i
\(313\) 0.445328i 0.0251715i 0.999921 + 0.0125857i \(0.00400627\pi\)
−0.999921 + 0.0125857i \(0.995994\pi\)
\(314\) −2.33430 0.625474i −0.131732 0.0352976i
\(315\) 1.35288 + 3.32014i 0.0762261 + 0.187069i
\(316\) −7.77097 4.48657i −0.437151 0.252389i
\(317\) −17.5588 17.5588i −0.986201 0.986201i 0.0137052 0.999906i \(-0.495637\pi\)
−0.999906 + 0.0137052i \(0.995637\pi\)
\(318\) −1.81035 6.75631i −0.101519 0.378875i
\(319\) 6.98281 + 26.0602i 0.390962 + 1.45909i
\(320\) 4.41020 + 4.41020i 0.246538 + 0.246538i
\(321\) 5.81218 + 3.35567i 0.324404 + 0.187295i
\(322\) −0.992951 2.43683i −0.0553350 0.135799i
\(323\) 18.0933 + 4.84809i 1.00674 + 0.269755i
\(324\) 6.79726i 0.377625i
\(325\) 10.1667 + 3.09405i 0.563947 + 0.171627i
\(326\) −20.3019 −1.12442
\(327\) −5.95559 1.59579i −0.329345 0.0882476i
\(328\) 11.7206 6.76690i 0.647163 0.373640i
\(329\) 12.2000 + 9.47364i 0.672610 + 0.522299i
\(330\) −5.93723 5.93723i −0.326834 0.326834i
\(331\) −14.3822 + 3.85370i −0.790518 + 0.211819i −0.631417 0.775444i \(-0.717526\pi\)
−0.159101 + 0.987262i \(0.550860\pi\)
\(332\) 5.69120 1.52495i 0.312345 0.0836926i
\(333\) −3.74009 + 3.74009i −0.204956 + 0.204956i
\(334\) 7.15973 + 4.13367i 0.391763 + 0.226184i
\(335\) −1.40735 2.43760i −0.0768917 0.133180i
\(336\) −0.858148 0.361266i −0.0468158 0.0197087i
\(337\) 7.23643i 0.394194i 0.980384 + 0.197097i \(0.0631513\pi\)
−0.980384 + 0.197097i \(0.936849\pi\)
\(338\) −8.24683 + 7.20601i −0.448568 + 0.391955i
\(339\) 5.80093i 0.315063i
\(340\) −1.42725 + 5.32656i −0.0774033 + 0.288873i
\(341\) −28.4960 + 16.4522i −1.54315 + 0.890936i
\(342\) −2.50169 + 4.33306i −0.135276 + 0.234305i
\(343\) −17.2305 + 6.79047i −0.930359 + 0.366651i
\(344\) −8.99474 + 2.41013i −0.484964 + 0.129946i
\(345\) −0.627427 2.34159i −0.0337795 0.126067i
\(346\) −3.12001 3.12001i −0.167733 0.167733i
\(347\) 6.28405 10.8843i 0.337345 0.584299i −0.646587 0.762840i \(-0.723804\pi\)
0.983933 + 0.178541i \(0.0571376\pi\)
\(348\) −5.13948 8.90185i −0.275505 0.477189i
\(349\) 4.81774 17.9800i 0.257888 0.962450i −0.708574 0.705637i \(-0.750661\pi\)
0.966461 0.256813i \(-0.0826723\pi\)
\(350\) −6.50813 0.895005i −0.347874 0.0478400i
\(351\) 19.5072 + 5.93665i 1.04122 + 0.316875i
\(352\) −27.9131 −1.48777
\(353\) 6.04570 + 1.61994i 0.321780 + 0.0862207i 0.416093 0.909322i \(-0.363399\pi\)
−0.0943134 + 0.995543i \(0.530066\pi\)
\(354\) 6.72348 + 11.6454i 0.357349 + 0.618947i
\(355\) 2.36643 4.09878i 0.125597 0.217541i
\(356\) −0.224325 + 0.224325i −0.0118892 + 0.0118892i
\(357\) 1.41179 + 11.2232i 0.0747201 + 0.593993i
\(358\) 4.92181 + 18.3684i 0.260126 + 0.970802i
\(359\) −1.66592 + 1.66592i −0.0879237 + 0.0879237i −0.749701 0.661777i \(-0.769803\pi\)
0.661777 + 0.749701i \(0.269803\pi\)
\(360\) −3.25285 1.87804i −0.171440 0.0989812i
\(361\) −17.6935 + 10.2153i −0.931236 + 0.537649i
\(362\) −4.90153 + 18.2928i −0.257619 + 0.961446i
\(363\) 18.0031 0.944918
\(364\) −7.87188 + 9.46258i −0.412599 + 0.495974i
\(365\) 0.715239 0.0374373
\(366\) −2.86912 + 10.7077i −0.149971 + 0.559700i
\(367\) 16.7399 9.66481i 0.873818 0.504499i 0.00520293 0.999986i \(-0.498344\pi\)
0.868615 + 0.495487i \(0.165011\pi\)
\(368\) −0.251047 0.144942i −0.0130867 0.00755563i
\(369\) −3.26549 + 3.26549i −0.169995 + 0.169995i
\(370\) 1.74687 + 6.51943i 0.0908157 + 0.338929i
\(371\) −15.2074 + 1.91298i −0.789529 + 0.0993171i
\(372\) 8.86450 8.86450i 0.459603 0.459603i
\(373\) 4.17375 7.22914i 0.216108 0.374311i −0.737507 0.675340i \(-0.763997\pi\)
0.953615 + 0.301029i \(0.0973302\pi\)
\(374\) 6.09900 + 10.5638i 0.315372 + 0.546240i
\(375\) −15.7630 4.22367i −0.813996 0.218110i
\(376\) −16.1826 −0.834554
\(377\) −19.5210 + 4.53311i −1.00538 + 0.233467i
\(378\) −12.4873 1.71727i −0.642280 0.0883270i
\(379\) −4.99923 + 18.6574i −0.256793 + 0.958365i 0.710291 + 0.703908i \(0.248563\pi\)
−0.967084 + 0.254457i \(0.918103\pi\)
\(380\) −5.80407 10.0529i −0.297742 0.515705i
\(381\) 8.84337 15.3172i 0.453060 0.784723i
\(382\) 14.6960 + 14.6960i 0.751915 + 0.751915i
\(383\) −6.09034 22.7295i −0.311202 1.16142i −0.927474 0.373888i \(-0.878024\pi\)
0.616272 0.787533i \(-0.288642\pi\)
\(384\) 10.8450 2.90592i 0.553433 0.148292i
\(385\) −14.6613 + 11.1163i −0.747210 + 0.566542i
\(386\) 1.44861 2.50906i 0.0737323 0.127708i
\(387\) 2.75181 1.58876i 0.139882 0.0807612i
\(388\) −3.14029 + 11.7197i −0.159424 + 0.594979i
\(389\) 27.9585i 1.41755i −0.705434 0.708775i \(-0.749248\pi\)
0.705434 0.708775i \(-0.250752\pi\)
\(390\) 4.55597 4.25942i 0.230700 0.215684i
\(391\) 3.52174i 0.178102i
\(392\) 9.89455 16.6905i 0.499750 0.842998i
\(393\) −4.81109 8.33305i −0.242687 0.420347i
\(394\) 2.91292 + 1.68177i 0.146751 + 0.0847266i
\(395\) 7.04504 7.04504i 0.354475 0.354475i
\(396\) 5.72205 1.53322i 0.287544 0.0770471i
\(397\) 11.5874 3.10484i 0.581556 0.155827i 0.0439649 0.999033i \(-0.486001\pi\)
0.537591 + 0.843206i \(0.319334\pi\)
\(398\) 0.609447 + 0.609447i 0.0305488 + 0.0305488i
\(399\) −18.8070 14.6041i −0.941525 0.731119i
\(400\) −0.626756 + 0.361858i −0.0313378 + 0.0180929i
\(401\) 19.1246 + 5.12441i 0.955035 + 0.255901i 0.702497 0.711686i \(-0.252068\pi\)
0.252537 + 0.967587i \(0.418735\pi\)
\(402\) 2.37210 0.118310
\(403\) −11.5022 21.5658i −0.572965 1.07427i
\(404\) 18.4346i 0.917154i
\(405\) −7.29007 1.95337i −0.362246 0.0970636i
\(406\) 11.4726 4.67481i 0.569375 0.232007i
\(407\) −23.5078 13.5722i −1.16524 0.672751i
\(408\) −8.37974 8.37974i −0.414859 0.414859i
\(409\) 4.60743 + 17.1952i 0.227823 + 0.850247i 0.981254 + 0.192720i \(0.0617308\pi\)
−0.753431 + 0.657527i \(0.771602\pi\)
\(410\) 1.52521 + 5.69214i 0.0753245 + 0.281115i
\(411\) 22.1883 + 22.1883i 1.09447 + 1.09447i
\(412\) −8.32642 4.80726i −0.410213 0.236837i
\(413\) 27.2877 11.1191i 1.34274 0.547134i
\(414\) −0.908636 0.243468i −0.0446570 0.0119658i
\(415\) 6.54205i 0.321137i
\(416\) 0.697079 20.7222i 0.0341771 1.01599i
\(417\) 5.78710 0.283396
\(418\) −24.8023 6.64576i −1.21312 0.325055i
\(419\) −8.03474 + 4.63886i −0.392523 + 0.226623i −0.683253 0.730182i \(-0.739435\pi\)
0.290730 + 0.956805i \(0.406102\pi\)
\(420\) 4.29935 5.53664i 0.209787 0.270161i
\(421\) −13.2205 13.2205i −0.644329 0.644329i 0.307288 0.951617i \(-0.400579\pi\)
−0.951617 + 0.307288i \(0.900579\pi\)
\(422\) 4.39510 1.17766i 0.213950 0.0573277i
\(423\) 5.33379 1.42918i 0.259338 0.0694893i
\(424\) 11.3546 11.3546i 0.551426 0.551426i
\(425\) 7.61431 + 4.39612i 0.369348 + 0.213243i
\(426\) 1.99432 + 3.45427i 0.0966253 + 0.167360i
\(427\) 22.3883 + 9.42507i 1.08344 + 0.456111i
\(428\) 6.04208i 0.292055i
\(429\) −0.843312 + 25.0693i −0.0407155 + 1.21036i
\(430\) 4.05468i 0.195534i
\(431\) 1.53438 5.72637i 0.0739083 0.275830i −0.919075 0.394082i \(-0.871063\pi\)
0.992984 + 0.118252i \(0.0377292\pi\)
\(432\) −1.20258 + 0.694307i −0.0578589 + 0.0334049i
\(433\) −6.32385 + 10.9532i −0.303905 + 0.526379i −0.977017 0.213162i \(-0.931624\pi\)
0.673112 + 0.739541i \(0.264957\pi\)
\(434\) 9.12857 + 12.0396i 0.438185 + 0.577921i
\(435\) 11.0242 2.95393i 0.528570 0.141630i
\(436\) −1.43666 5.36170i −0.0688036 0.256779i
\(437\) −5.24205 5.24205i −0.250761 0.250761i
\(438\) −0.301386 + 0.522015i −0.0144008 + 0.0249429i
\(439\) 12.8788 + 22.3067i 0.614670 + 1.06464i 0.990442 + 0.137928i \(0.0440442\pi\)
−0.375772 + 0.926712i \(0.622622\pi\)
\(440\) 4.98901 18.6192i 0.237842 0.887638i
\(441\) −1.78720 + 6.37504i −0.0851050 + 0.303574i
\(442\) −7.99468 + 4.26398i −0.380268 + 0.202817i
\(443\) 17.2441 0.819293 0.409647 0.912244i \(-0.365652\pi\)
0.409647 + 0.912244i \(0.365652\pi\)
\(444\) 9.98942 + 2.67666i 0.474077 + 0.127029i
\(445\) −0.176123 0.305054i −0.00834904 0.0144610i
\(446\) 7.24482 12.5484i 0.343052 0.594184i
\(447\) −2.87487 + 2.87487i −0.135977 + 0.135977i
\(448\) 1.43754 + 11.4278i 0.0679173 + 0.539914i
\(449\) −1.50842 5.62952i −0.0711870 0.265673i 0.921155 0.389197i \(-0.127247\pi\)
−0.992342 + 0.123523i \(0.960581\pi\)
\(450\) −1.66064 + 1.66064i −0.0782831 + 0.0782831i
\(451\) −20.5248 11.8500i −0.966474 0.557994i
\(452\) 4.52278 2.61123i 0.212734 0.122822i
\(453\) 6.21060 23.1783i 0.291800 1.08901i
\(454\) 8.39274 0.393891
\(455\) −7.88644 11.1619i −0.369722 0.523279i
\(456\) 24.9463 1.16822
\(457\) 5.74697 21.4480i 0.268832 1.00329i −0.691031 0.722825i \(-0.742843\pi\)
0.959863 0.280469i \(-0.0904901\pi\)
\(458\) 3.04250 1.75659i 0.142167 0.0820801i
\(459\) 14.6098 + 8.43498i 0.681928 + 0.393711i
\(460\) 1.54323 1.54323i 0.0719533 0.0719533i
\(461\) −5.52093 20.6044i −0.257135 0.959642i −0.966890 0.255193i \(-0.917861\pi\)
0.709755 0.704449i \(-0.248806\pi\)
\(462\) −1.93529 15.3847i −0.0900376 0.715761i
\(463\) −5.14657 + 5.14657i −0.239181 + 0.239181i −0.816511 0.577330i \(-0.804095\pi\)
0.577330 + 0.816511i \(0.304095\pi\)
\(464\) 0.682387 1.18193i 0.0316790 0.0548697i
\(465\) 6.95974 + 12.0546i 0.322750 + 0.559020i
\(466\) −5.14772 1.37933i −0.238464 0.0638962i
\(467\) 28.5108 1.31932 0.659661 0.751563i \(-0.270700\pi\)
0.659661 + 0.751563i \(0.270700\pi\)
\(468\) 0.995337 + 4.28624i 0.0460095 + 0.198131i
\(469\) 0.708161 5.14948i 0.0326998 0.237781i
\(470\) 1.82371 6.80619i 0.0841216 0.313946i
\(471\) −2.05574 3.56065i −0.0947235 0.164066i
\(472\) −15.4352 + 26.7346i −0.710465 + 1.23056i
\(473\) 11.5308 + 11.5308i 0.530184 + 0.530184i
\(474\) 2.17318 + 8.11042i 0.0998175 + 0.372524i
\(475\) −17.8774 + 4.79022i −0.820270 + 0.219791i
\(476\) −8.11481 + 6.15272i −0.371942 + 0.282010i
\(477\) −2.73967 + 4.74526i −0.125441 + 0.217270i
\(478\) 8.09080 4.67123i 0.370065 0.213657i
\(479\) −8.52110 + 31.8012i −0.389339 + 1.45303i 0.441873 + 0.897078i \(0.354314\pi\)
−0.831212 + 0.555955i \(0.812352\pi\)
\(480\) 11.8080i 0.538961i
\(481\) 10.6629 17.1128i 0.486184 0.780278i
\(482\) 11.7792i 0.536527i
\(483\) 1.73700 4.12607i 0.0790364 0.187743i
\(484\) 8.10392 + 14.0364i 0.368360 + 0.638018i
\(485\) −11.6670 6.73593i −0.529770 0.305863i
\(486\) −5.60885 + 5.60885i −0.254423 + 0.254423i
\(487\) 13.6913 3.66858i 0.620414 0.166239i 0.0650979 0.997879i \(-0.479264\pi\)
0.555316 + 0.831640i \(0.312597\pi\)
\(488\) −24.5819 + 6.58670i −1.11277 + 0.298166i
\(489\) −24.4235 24.4235i −1.10447 1.10447i
\(490\) 5.90474 + 6.04248i 0.266749 + 0.272971i
\(491\) −25.7788 + 14.8834i −1.16338 + 0.671678i −0.952112 0.305750i \(-0.901093\pi\)
−0.211269 + 0.977428i \(0.567759\pi\)
\(492\) 8.72182 + 2.33700i 0.393210 + 0.105360i
\(493\) −16.5803 −0.746741
\(494\) 5.55309 18.2468i 0.249845 0.820964i
\(495\) 6.57751i 0.295637i
\(496\) 1.60777 + 0.430801i 0.0721911 + 0.0193435i
\(497\) 8.09408 3.29815i 0.363069 0.147942i
\(498\) −4.77470 2.75667i −0.213959 0.123529i
\(499\) 13.0693 + 13.0693i 0.585064 + 0.585064i 0.936291 0.351226i \(-0.114235\pi\)
−0.351226 + 0.936291i \(0.614235\pi\)
\(500\) −3.80249 14.1911i −0.170052 0.634644i
\(501\) 3.64039 + 13.5861i 0.162640 + 0.606982i
\(502\) −15.7004 15.7004i −0.700743 0.700743i
\(503\) 5.05931 + 2.92099i 0.225583 + 0.130241i 0.608533 0.793529i \(-0.291758\pi\)
−0.382949 + 0.923769i \(0.625092\pi\)
\(504\) −2.61746 6.42358i −0.116591 0.286129i
\(505\) −19.7711 5.29765i −0.879802 0.235742i
\(506\) 4.82759i 0.214613i
\(507\) −18.5900 1.25212i −0.825609 0.0556086i
\(508\) 15.9230 0.706470
\(509\) 28.3274 + 7.59031i 1.25559 + 0.336435i 0.824494 0.565871i \(-0.191460\pi\)
0.431097 + 0.902306i \(0.358127\pi\)
\(510\) 4.46878 2.58005i 0.197881 0.114246i
\(511\) 1.04324 + 0.810104i 0.0461503 + 0.0358369i
\(512\) 1.96096 + 1.96096i 0.0866629 + 0.0866629i
\(513\) −34.3018 + 9.19115i −1.51446 + 0.405799i
\(514\) −8.77234 + 2.35054i −0.386931 + 0.103678i
\(515\) 7.54860 7.54860i 0.332631 0.332631i
\(516\) −5.38045 3.10640i −0.236861 0.136752i
\(517\) 14.1692 + 24.5418i 0.623162 + 1.07935i
\(518\) −4.83614 + 11.4877i −0.212488 + 0.504743i
\(519\) 7.50681i 0.329513i
\(520\) 13.6980 + 4.16874i 0.600698 + 0.182811i
\(521\) 41.0128i 1.79680i 0.439173 + 0.898402i \(0.355271\pi\)
−0.439173 + 0.898402i \(0.644729\pi\)
\(522\) 1.14625 4.27786i 0.0501699 0.187237i
\(523\) 38.4309 22.1881i 1.68047 0.970217i 0.719114 0.694892i \(-0.244548\pi\)
0.961351 0.275325i \(-0.0887854\pi\)
\(524\) 4.33133 7.50208i 0.189215 0.327730i
\(525\) −6.75266 8.90606i −0.294710 0.388692i
\(526\) 12.6056 3.37766i 0.549630 0.147273i
\(527\) −5.23370 19.5325i −0.227984 0.850847i
\(528\) −1.20789 1.20789i −0.0525666 0.0525666i
\(529\) −10.8031 + 18.7115i −0.469700 + 0.813544i
\(530\) 3.49597 + 6.05520i 0.151855 + 0.263021i
\(531\) 2.72636 10.1749i 0.118314 0.441554i
\(532\) 2.92054 21.2370i 0.126621 0.920741i
\(533\) 9.30979 14.9413i 0.403252 0.647180i
\(534\) 0.296857 0.0128463
\(535\) −6.48014 1.73635i −0.280161 0.0750688i
\(536\) 2.72284 + 4.71610i 0.117609 + 0.203705i
\(537\) −16.1765 + 28.0185i −0.698066 + 1.20909i
\(538\) 15.5674 15.5674i 0.671160 0.671160i
\(539\) −33.9756 0.391695i −1.46343 0.0168715i
\(540\) −2.70581 10.0982i −0.116440 0.434559i
\(541\) −4.85001 + 4.85001i −0.208518 + 0.208518i −0.803637 0.595119i \(-0.797105\pi\)
0.595119 + 0.803637i \(0.297105\pi\)
\(542\) 4.80223 + 2.77257i 0.206273 + 0.119092i
\(543\) −27.9030 + 16.1098i −1.19743 + 0.691338i
\(544\) 4.43980 16.5696i 0.190355 0.710414i
\(545\) 6.16329 0.264006
\(546\) 11.4697 1.05252i 0.490856 0.0450436i
\(547\) −16.7670 −0.716904 −0.358452 0.933548i \(-0.616695\pi\)
−0.358452 + 0.933548i \(0.616695\pi\)
\(548\) −7.31159 + 27.2872i −0.312336 + 1.16565i
\(549\) 7.52048 4.34195i 0.320966 0.185310i
\(550\) −10.4377 6.02620i −0.445065 0.256958i
\(551\) 24.6796 24.6796i 1.05139 1.05139i
\(552\) 1.21390 + 4.53035i 0.0516672 + 0.192824i
\(553\) 18.2553 2.29639i 0.776294 0.0976523i
\(554\) −17.3804 + 17.3804i −0.738422 + 0.738422i
\(555\) −5.74144 + 9.94446i −0.243710 + 0.422119i
\(556\) 2.60501 + 4.51200i 0.110477 + 0.191352i
\(557\) −38.0545 10.1967i −1.61242 0.432046i −0.663657 0.748037i \(-0.730996\pi\)
−0.948762 + 0.315991i \(0.897663\pi\)
\(558\) 5.40135 0.228657
\(559\) −8.84819 + 8.27227i −0.374238 + 0.349880i
\(560\) 0.922052 + 0.126802i 0.0389638 + 0.00535834i
\(561\) −5.37118 + 20.0455i −0.226772 + 0.846323i
\(562\) −5.27402 9.13488i −0.222471 0.385332i
\(563\) −1.05586 + 1.82880i −0.0444991 + 0.0770748i −0.887417 0.460967i \(-0.847503\pi\)
0.842918 + 0.538042i \(0.180836\pi\)
\(564\) −7.63443 7.63443i −0.321467 0.321467i
\(565\) 1.50081 + 5.60110i 0.0631395 + 0.235640i
\(566\) −25.9912 + 6.96433i −1.09249 + 0.292733i
\(567\) −8.42078 11.1061i −0.353640 0.466414i
\(568\) −4.57841 + 7.93005i −0.192106 + 0.332737i
\(569\) 31.5451 18.2126i 1.32244 0.763512i 0.338323 0.941030i \(-0.390140\pi\)
0.984117 + 0.177518i \(0.0568069\pi\)
\(570\) −2.81134 + 10.4921i −0.117754 + 0.439465i
\(571\) 15.2042i 0.636275i 0.948045 + 0.318138i \(0.103057\pi\)
−0.948045 + 0.318138i \(0.896943\pi\)
\(572\) −19.9253 + 10.6272i −0.833118 + 0.444346i
\(573\) 35.3590i 1.47715i
\(574\) −4.22246 + 10.0300i −0.176242 + 0.418645i
\(575\) −1.73985 3.01351i −0.0725568 0.125672i
\(576\) 3.56589 + 2.05877i 0.148579 + 0.0857820i
\(577\) 8.00711 8.00711i 0.333341 0.333341i −0.520513 0.853854i \(-0.674259\pi\)
0.853854 + 0.520513i \(0.174259\pi\)
\(578\) 6.59241 1.76643i 0.274208 0.0734739i
\(579\) 4.76113 1.27574i 0.197866 0.0530180i
\(580\) 7.26551 + 7.26551i 0.301684 + 0.301684i
\(581\) −7.40975 + 9.54218i −0.307408 + 0.395876i
\(582\) 9.83240 5.67674i 0.407566 0.235308i
\(583\) −27.1617 7.27796i −1.12492 0.301422i
\(584\) −1.38380 −0.0572619
\(585\) −4.88303 0.164261i −0.201889 0.00679137i
\(586\) 10.8863i 0.449709i
\(587\) −3.32195 0.890113i −0.137111 0.0367389i 0.189611 0.981859i \(-0.439277\pi\)
−0.326722 + 0.945120i \(0.605944\pi\)
\(588\) 12.5420 3.20612i 0.517223 0.132218i
\(589\) 36.8641 + 21.2835i 1.51896 + 0.876971i
\(590\) −9.50475 9.50475i −0.391304 0.391304i
\(591\) 1.48108 + 5.52747i 0.0609236 + 0.227370i
\(592\) 0.355389 + 1.32633i 0.0146064 + 0.0545119i
\(593\) −32.9017 32.9017i −1.35111 1.35111i −0.884422 0.466687i \(-0.845447\pi\)
−0.466687 0.884422i \(-0.654553\pi\)
\(594\) −20.0271 11.5627i −0.821722 0.474422i
\(595\) −4.26680 10.4713i −0.174922 0.429281i
\(596\) −3.53554 0.947344i −0.144821 0.0388047i
\(597\) 1.46635i 0.0600135i
\(598\) 3.58392 + 0.120560i 0.146557 + 0.00493008i
\(599\) 7.61769 0.311251 0.155625 0.987816i \(-0.450261\pi\)
0.155625 + 0.987816i \(0.450261\pi\)
\(600\) 11.3103 + 3.03059i 0.461742 + 0.123723i
\(601\) −32.3774 + 18.6931i −1.32070 + 0.762508i −0.983841 0.179045i \(-0.942699\pi\)
−0.336863 + 0.941554i \(0.609366\pi\)
\(602\) 4.59247 5.91412i 0.187175 0.241042i
\(603\) −1.31396 1.31396i −0.0535085 0.0535085i
\(604\) 20.8669 5.59128i 0.849064 0.227506i
\(605\) −17.3829 + 4.65774i −0.706717 + 0.189364i
\(606\) 12.1976 12.1976i 0.495492 0.495492i
\(607\) −16.4375 9.49020i −0.667178 0.385195i 0.127829 0.991796i \(-0.459199\pi\)
−0.795006 + 0.606601i \(0.792533\pi\)
\(608\) 18.0550 + 31.2722i 0.732226 + 1.26825i
\(609\) 19.4255 + 8.17782i 0.787162 + 0.331382i
\(610\) 11.0811i 0.448661i
\(611\) −18.5733 + 9.90610i −0.751394 + 0.400758i
\(612\) 3.64055i 0.147160i
\(613\) −1.13756 + 4.24543i −0.0459456 + 0.171471i −0.985086 0.172062i \(-0.944957\pi\)
0.939141 + 0.343533i \(0.111624\pi\)
\(614\) 5.59750 3.23172i 0.225897 0.130421i
\(615\) −5.01288 + 8.68256i −0.202139 + 0.350115i
\(616\) 28.3657 21.5071i 1.14289 0.866548i
\(617\) 23.9468 6.41652i 0.964061 0.258319i 0.257743 0.966214i \(-0.417021\pi\)
0.706318 + 0.707894i \(0.250355\pi\)
\(618\) 2.32851 + 8.69013i 0.0936666 + 0.349568i
\(619\) −17.2383 17.2383i −0.692866 0.692866i 0.269995 0.962862i \(-0.412978\pi\)
−0.962862 + 0.269995i \(0.912978\pi\)
\(620\) −6.26572 + 10.8525i −0.251637 + 0.435849i
\(621\) −3.33831 5.78211i −0.133962 0.232028i
\(622\) 0.105394 0.393334i 0.00422590 0.0157713i
\(623\) 0.0886230 0.644433i 0.00355061 0.0258186i
\(624\) 0.926879 0.866550i 0.0371049 0.0346898i
\(625\) 1.57557 0.0630229
\(626\) 0.362374 + 0.0970978i 0.0144834 + 0.00388081i
\(627\) −21.8426 37.8324i −0.872307 1.51088i
\(628\) 1.85074 3.20558i 0.0738527 0.127917i
\(629\) 11.7957 11.7957i 0.470327 0.470327i
\(630\) 2.99665 0.376957i 0.119389 0.0150183i
\(631\) 0.701056 + 2.61638i 0.0279086 + 0.104156i 0.978475 0.206364i \(-0.0661633\pi\)
−0.950567 + 0.310521i \(0.899497\pi\)
\(632\) −13.6303 + 13.6303i −0.542183 + 0.542183i
\(633\) 6.70410 + 3.87061i 0.266464 + 0.153843i
\(634\) −18.1165 + 10.4595i −0.719497 + 0.415402i
\(635\) −4.57589 + 17.0775i −0.181589 + 0.677698i
\(636\) 10.7134 0.424815
\(637\) 1.13927 25.2131i 0.0451394 0.998981i
\(638\) 22.7283 0.899822
\(639\) 0.808695 3.01809i 0.0319915 0.119394i
\(640\) −9.71961 + 5.61162i −0.384202 + 0.221819i
\(641\) 2.71103 + 1.56522i 0.107079 + 0.0618223i 0.552583 0.833458i \(-0.313642\pi\)
−0.445504 + 0.895280i \(0.646975\pi\)
\(642\) 3.99785 3.99785i 0.157783 0.157783i
\(643\) 0.747638 + 2.79022i 0.0294840 + 0.110036i 0.979100 0.203381i \(-0.0651930\pi\)
−0.949616 + 0.313417i \(0.898526\pi\)
\(644\) 3.99885 0.503027i 0.157577 0.0198220i
\(645\) 4.87783 4.87783i 0.192064 0.192064i
\(646\) 7.89001 13.6659i 0.310428 0.537677i
\(647\) −8.86801 15.3598i −0.348637 0.603857i 0.637370 0.770558i \(-0.280022\pi\)
−0.986008 + 0.166700i \(0.946689\pi\)
\(648\) 14.1043 + 3.77924i 0.554070 + 0.148463i
\(649\) 54.0594 2.12202
\(650\) 4.73441 7.59827i 0.185699 0.298029i
\(651\) −3.50206 + 25.4656i −0.137256 + 0.998076i
\(652\) 8.04815 30.0361i 0.315190 1.17631i
\(653\) 11.0978 + 19.2219i 0.434289 + 0.752211i 0.997237 0.0742811i \(-0.0236662\pi\)
−0.562948 + 0.826492i \(0.690333\pi\)
\(654\) −2.59707 + 4.49826i −0.101553 + 0.175896i
\(655\) 6.80127 + 6.80127i 0.265748 + 0.265748i
\(656\) 0.310292 + 1.15803i 0.0121149 + 0.0452133i
\(657\) 0.456099 0.122211i 0.0177941 0.00476792i
\(658\) 10.3690 7.86185i 0.404225 0.306487i
\(659\) 14.4500 25.0282i 0.562893 0.974960i −0.434349 0.900745i \(-0.643021\pi\)
0.997242 0.0742153i \(-0.0236452\pi\)
\(660\) 11.1376 6.43031i 0.433531 0.250299i
\(661\) −1.00395 + 3.74678i −0.0390490 + 0.145733i −0.982698 0.185215i \(-0.940702\pi\)
0.943649 + 0.330948i \(0.107368\pi\)
\(662\) 12.5434i 0.487513i
\(663\) −14.7473 4.48807i −0.572738 0.174302i
\(664\) 12.6571i 0.491191i
\(665\) 21.9374 + 9.23528i 0.850697 + 0.358129i
\(666\) 2.22792 + 3.85887i 0.0863302 + 0.149528i
\(667\) 5.68285 + 3.28099i 0.220041 + 0.127041i
\(668\) −8.95393 + 8.95393i −0.346438 + 0.346438i
\(669\) 23.8115 6.38027i 0.920606 0.246676i
\(670\) −2.29039 + 0.613707i −0.0884853 + 0.0237096i
\(671\) 31.5126 + 31.5126i 1.21653 + 1.21653i
\(672\) −13.3742 + 17.2231i −0.515920 + 0.664396i
\(673\) 14.8015 8.54566i 0.570557 0.329411i −0.186815 0.982395i \(-0.559816\pi\)
0.757372 + 0.652984i \(0.226483\pi\)
\(674\) 5.88845 + 1.57781i 0.226815 + 0.0607748i
\(675\) −16.6686 −0.641575
\(676\) −7.39185 15.0576i −0.284302 0.579138i
\(677\) 30.5733i 1.17503i −0.809214 0.587514i \(-0.800107\pi\)
0.809214 0.587514i \(-0.199893\pi\)
\(678\) −4.72035 1.26481i −0.181284 0.0485749i
\(679\) −9.38801 23.0394i −0.360279 0.884170i
\(680\) 10.2591 + 5.92308i 0.393417 + 0.227140i
\(681\) 10.0966 + 10.0966i 0.386902 + 0.386902i
\(682\) 7.17436 + 26.7751i 0.274720 + 1.02527i
\(683\) 1.64019 + 6.12129i 0.0627603 + 0.234224i 0.990180 0.139797i \(-0.0446451\pi\)
−0.927420 + 0.374022i \(0.877978\pi\)
\(684\) −5.41891 5.41891i −0.207197 0.207197i
\(685\) −27.1644 15.6834i −1.03790 0.599231i
\(686\) 1.76869 + 15.5014i 0.0675289 + 0.591847i
\(687\) 5.77337 + 1.54697i 0.220268 + 0.0590206i
\(688\) 0.824896i 0.0314489i
\(689\) 6.08135 19.9826i 0.231681 0.761278i
\(690\) −2.04221 −0.0777455
\(691\) −4.60739 1.23455i −0.175273 0.0469643i 0.170115 0.985424i \(-0.445586\pi\)
−0.345388 + 0.938460i \(0.612253\pi\)
\(692\) 5.85280 3.37912i 0.222490 0.128455i
\(693\) −7.44992 + 9.59391i −0.282999 + 0.364442i
\(694\) −7.48665 7.48665i −0.284189 0.284189i
\(695\) −5.58774 + 1.49723i −0.211955 + 0.0567932i
\(696\) −21.3289 + 5.71506i −0.808469 + 0.216629i
\(697\) 10.2989 10.2989i 0.390100 0.390100i
\(698\) −13.5803 7.84061i −0.514023 0.296771i
\(699\) −4.53343 7.85213i −0.171470 0.296995i
\(700\) 3.90411 9.27379i 0.147561 0.350516i
\(701\) 29.4647i 1.11287i 0.830892 + 0.556433i \(0.187831\pi\)
−0.830892 + 0.556433i \(0.812169\pi\)
\(702\) 9.08406 14.5790i 0.342856 0.550250i
\(703\) 35.1156i 1.32441i
\(704\) −5.46913 + 20.4111i −0.206126 + 0.769271i
\(705\) 10.3819 5.99398i 0.391004 0.225746i
\(706\) 2.63637 4.56632i 0.0992209 0.171856i
\(707\) −22.8377 30.1205i −0.858898 1.13280i
\(708\) −19.8944 + 5.33069i −0.747677 + 0.200340i
\(709\) −4.33842 16.1912i −0.162933 0.608073i −0.998295 0.0583730i \(-0.981409\pi\)
0.835362 0.549700i \(-0.185258\pi\)
\(710\) −2.81931 2.81931i −0.105807 0.105807i
\(711\) 3.28876 5.69631i 0.123338 0.213628i
\(712\) 0.340751 + 0.590198i 0.0127702 + 0.0221186i
\(713\) −2.07134 + 7.73035i −0.0775723 + 0.289504i
\(714\) 9.44037 + 1.29825i 0.353297 + 0.0485858i
\(715\) −5.67164 24.4239i −0.212107 0.913402i
\(716\) −29.1267 −1.08852
\(717\) 15.3529 + 4.11379i 0.573364 + 0.153632i
\(718\) 0.992364 + 1.71882i 0.0370347 + 0.0641460i
\(719\) 8.96395 15.5260i 0.334299 0.579023i −0.649051 0.760745i \(-0.724834\pi\)
0.983350 + 0.181722i \(0.0581672\pi\)
\(720\) 0.235274 0.235274i 0.00876814 0.00876814i
\(721\) 19.5601 2.46052i 0.728457 0.0916347i
\(722\) 4.45463 + 16.6249i 0.165784 + 0.618715i
\(723\) 14.1705 14.1705i 0.527007 0.527007i
\(724\) −25.1205 14.5033i −0.933597 0.539012i
\(725\) 14.1876 8.19122i 0.526914 0.304214i
\(726\) 3.92534 14.6496i 0.145683 0.543696i
\(727\) 32.6548 1.21110 0.605549 0.795808i \(-0.292954\pi\)
0.605549 + 0.795808i \(0.292954\pi\)
\(728\) 15.2582 + 21.5953i 0.565505 + 0.800376i
\(729\) −29.2988 −1.08514
\(730\) 0.155948 0.582007i 0.00577190 0.0215410i
\(731\) −8.67885 + 5.01074i −0.320999 + 0.185329i
\(732\) −14.7043 8.48955i −0.543488 0.313783i
\(733\) −25.0843 + 25.0843i −0.926510 + 0.926510i −0.997479 0.0709685i \(-0.977391\pi\)
0.0709685 + 0.997479i \(0.477391\pi\)
\(734\) −4.21456 15.7290i −0.155562 0.580567i
\(735\) −0.165698 + 14.3726i −0.00611186 + 0.530143i
\(736\) −4.80059 + 4.80059i −0.176952 + 0.176952i
\(737\) 4.76816 8.25869i 0.175637 0.304213i
\(738\) 1.94521 + 3.36920i 0.0716041 + 0.124022i
\(739\) 13.8732 + 3.71731i 0.510333 + 0.136743i 0.504791 0.863241i \(-0.331569\pi\)
0.00554159 + 0.999985i \(0.498236\pi\)
\(740\) −10.3378 −0.380025
\(741\) 28.6316 15.2707i 1.05181 0.560984i
\(742\) −1.75913 + 12.7917i −0.0645797 + 0.469599i
\(743\) 6.76509 25.2477i 0.248187 0.926247i −0.723568 0.690254i \(-0.757499\pi\)
0.971755 0.235993i \(-0.0758344\pi\)
\(744\) −13.4652 23.3225i −0.493659 0.855043i
\(745\) 2.03206 3.51962i 0.0744487 0.128949i
\(746\) −4.97249 4.97249i −0.182056 0.182056i
\(747\) 1.11783 + 4.17178i 0.0408991 + 0.152638i
\(748\) −18.0466 + 4.83557i −0.659849 + 0.176806i
\(749\) −7.48523 9.87224i −0.273504 0.360724i
\(750\) −6.87380 + 11.9058i −0.250996 + 0.434737i
\(751\) 10.2898 5.94079i 0.375479 0.216783i −0.300371 0.953823i \(-0.597110\pi\)
0.675849 + 0.737040i \(0.263777\pi\)
\(752\) 0.371022 1.38467i 0.0135298 0.0504938i
\(753\) 37.7755i 1.37662i
\(754\) −0.567598 + 16.8731i −0.0206707 + 0.614482i
\(755\) 23.9866i 0.872963i
\(756\) 7.49093 17.7939i 0.272442 0.647158i
\(757\) 21.1088 + 36.5615i 0.767212 + 1.32885i 0.939069 + 0.343729i \(0.111690\pi\)
−0.171857 + 0.985122i \(0.554977\pi\)
\(758\) 14.0919 + 8.13598i 0.511842 + 0.295512i
\(759\) 5.80765 5.80765i 0.210805 0.210805i
\(760\) −24.0869 + 6.45406i −0.873723 + 0.234114i
\(761\) −27.8046 + 7.45021i −1.00792 + 0.270070i −0.724758 0.689003i \(-0.758048\pi\)
−0.283157 + 0.959074i \(0.591382\pi\)
\(762\) −10.5358 10.5358i −0.381670 0.381670i
\(763\) 8.98972 + 6.98075i 0.325450 + 0.252720i
\(764\) −27.5682 + 15.9165i −0.997383 + 0.575840i
\(765\) −3.90449 1.04621i −0.141167 0.0378257i
\(766\) −19.8234 −0.716249
\(767\) −1.35004 + 40.1328i −0.0487470 + 1.44911i
\(768\) 21.9372i 0.791591i
\(769\) −33.9039 9.08451i −1.22260 0.327596i −0.410909 0.911676i \(-0.634789\pi\)
−0.811696 + 0.584081i \(0.801455\pi\)
\(770\) 5.84893 + 14.3540i 0.210781 + 0.517283i
\(771\) −13.3810 7.72550i −0.481903 0.278227i
\(772\) 3.13783 + 3.13783i 0.112933 + 0.112933i
\(773\) −7.86544 29.3542i −0.282900 1.05580i −0.950360 0.311152i \(-0.899285\pi\)
0.667460 0.744646i \(-0.267381\pi\)
\(774\) −0.692815 2.58562i −0.0249027 0.0929382i
\(775\) 14.1281 + 14.1281i 0.507496 + 0.507496i
\(776\) 22.5725 + 13.0322i 0.810304 + 0.467829i
\(777\) −19.6378 + 8.00196i −0.704504 + 0.287069i
\(778\) −22.7505 6.09597i −0.815643 0.218551i
\(779\) 30.6596i 1.09849i
\(780\) 4.49561 + 8.42896i 0.160968 + 0.301805i
\(781\) 16.0352 0.573783
\(782\) 2.86572 + 0.767867i 0.102478 + 0.0274589i
\(783\) 27.2222 15.7167i 0.972842 0.561670i
\(784\) 1.20128 + 1.22930i 0.0429028 + 0.0439035i
\(785\) 2.90613 + 2.90613i 0.103724 + 0.103724i
\(786\) −7.82979 + 2.09799i −0.279279 + 0.0748327i
\(787\) 9.81284 2.62934i 0.349790 0.0937260i −0.0796460 0.996823i \(-0.525379\pi\)
0.429436 + 0.903097i \(0.358712\pi\)
\(788\) −3.64289 + 3.64289i −0.129772 + 0.129772i
\(789\) 19.2280 + 11.1013i 0.684536 + 0.395217i
\(790\) −4.19664 7.26879i −0.149310 0.258612i
\(791\) −4.15492 + 9.86958i −0.147732 + 0.350922i
\(792\) 12.7257i 0.452189i
\(793\) −24.1814 + 22.6075i −0.858706 + 0.802814i
\(794\) 10.1059i 0.358646i
\(795\) −3.07878 + 11.4902i −0.109193 + 0.407514i
\(796\) −1.14326 + 0.660061i −0.0405217 + 0.0233952i
\(797\) −18.3972 + 31.8649i −0.651662 + 1.12871i 0.331057 + 0.943611i \(0.392595\pi\)
−0.982719 + 0.185101i \(0.940739\pi\)
\(798\) −15.9843 + 12.1194i −0.565837 + 0.429023i
\(799\) −16.8221 + 4.50746i −0.595122 + 0.159462i
\(800\) 4.38681 + 16.3718i 0.155097 + 0.578831i
\(801\) −0.164436 0.164436i −0.00581004 0.00581004i
\(802\) 8.33970 14.4448i 0.294485 0.510063i
\(803\) 1.21163 + 2.09860i 0.0427575 + 0.0740582i
\(804\) −0.940356 + 3.50946i −0.0331638 + 0.123769i
\(805\) −0.609676 + 4.43333i −0.0214882 + 0.156254i
\(806\) −20.0565 + 4.65746i −0.706460 + 0.164052i
\(807\) 37.4556 1.31850
\(808\) 38.2518 + 10.2495i 1.34569 + 0.360577i
\(809\) 9.38058 + 16.2476i 0.329804 + 0.571237i 0.982473 0.186407i \(-0.0596841\pi\)
−0.652669 + 0.757643i \(0.726351\pi\)
\(810\) −3.17900 + 5.50619i −0.111699 + 0.193468i
\(811\) 3.85841 3.85841i 0.135487 0.135487i −0.636111 0.771598i \(-0.719458\pi\)
0.771598 + 0.636111i \(0.219458\pi\)
\(812\) 2.36825 + 18.8266i 0.0831093 + 0.660683i
\(813\) 2.44171 + 9.11258i 0.0856344 + 0.319592i
\(814\) −16.1696 + 16.1696i −0.566744 + 0.566744i
\(815\) 29.9009 + 17.2633i 1.04738 + 0.604707i
\(816\) 0.909141 0.524893i 0.0318263 0.0183749i
\(817\) 5.45994 20.3768i 0.191019 0.712893i
\(818\) 14.9967 0.524347
\(819\) −6.93630 5.77028i −0.242374 0.201630i
\(820\) −9.02599 −0.315201
\(821\) −0.535196 + 1.99738i −0.0186785 + 0.0697089i −0.974636 0.223796i \(-0.928155\pi\)
0.955958 + 0.293505i \(0.0948217\pi\)
\(822\) 22.8929 13.2173i 0.798483 0.461005i
\(823\) −23.4776 13.5548i −0.818379 0.472491i 0.0314782 0.999504i \(-0.489979\pi\)
−0.849857 + 0.527013i \(0.823312\pi\)
\(824\) −14.6045 + 14.6045i −0.508772 + 0.508772i
\(825\) −5.30707 19.8063i −0.184769 0.689566i
\(826\) −3.09815 24.6290i −0.107798 0.856951i
\(827\) −18.8233 + 18.8233i −0.654550 + 0.654550i −0.954085 0.299535i \(-0.903168\pi\)
0.299535 + 0.954085i \(0.403168\pi\)
\(828\) 0.720409 1.24778i 0.0250359 0.0433635i
\(829\) 2.50749 + 4.34310i 0.0870887 + 0.150842i 0.906279 0.422679i \(-0.138910\pi\)
−0.819191 + 0.573521i \(0.805577\pi\)
\(830\) 5.32342 + 1.42641i 0.184778 + 0.0495112i
\(831\) −41.8177 −1.45064
\(832\) −15.0162 4.56991i −0.520594 0.158433i
\(833\) 5.63661 20.1060i 0.195297 0.696633i
\(834\) 1.26180 4.70910i 0.0436925 0.163063i
\(835\) −7.02996 12.1762i −0.243282 0.421376i
\(836\) 19.6644 34.0598i 0.680108 1.17798i
\(837\) 27.1080 + 27.1080i 0.936989 + 0.936989i
\(838\) 2.02288 + 7.54949i 0.0698792 + 0.260793i
\(839\) 1.91166 0.512227i 0.0659978 0.0176840i −0.225669 0.974204i \(-0.572457\pi\)
0.291667 + 0.956520i \(0.405790\pi\)
\(840\) −9.09813 11.9995i −0.313915 0.414022i
\(841\) −0.946916 + 1.64011i −0.0326523 + 0.0565554i
\(842\) −13.6404 + 7.87529i −0.470079 + 0.271400i
\(843\) 4.64466 17.3341i 0.159970 0.597018i
\(844\) 6.96927i 0.239892i
\(845\) 18.2735 3.60058i 0.628628 0.123864i
\(846\) 4.65184i 0.159934i
\(847\) −30.6301 12.8948i −1.05246 0.443069i
\(848\) 0.711230 + 1.23189i 0.0244238 + 0.0423032i
\(849\) −39.6459 22.8896i −1.36065 0.785569i
\(850\) 5.23743 5.23743i 0.179642 0.179642i
\(851\) −6.37714 + 1.70875i −0.218606 + 0.0585752i
\(852\) −5.90109 + 1.58119i −0.202168 + 0.0541708i
\(853\) −0.494551 0.494551i −0.0169331 0.0169331i 0.698590 0.715523i \(-0.253811\pi\)
−0.715523 + 0.698590i \(0.753811\pi\)
\(854\) 12.5509 16.1628i 0.429481 0.553081i
\(855\) 7.36904 4.25452i 0.252016 0.145502i
\(856\) 12.5373 + 3.35937i 0.428517 + 0.114821i
\(857\) 15.3761 0.525236 0.262618 0.964900i \(-0.415414\pi\)
0.262618 + 0.964900i \(0.415414\pi\)
\(858\) 20.2156 + 6.15225i 0.690149 + 0.210034i
\(859\) 33.1503i 1.13108i 0.824723 + 0.565538i \(0.191331\pi\)
−0.824723 + 0.565538i \(0.808669\pi\)
\(860\) 5.99879 + 1.60737i 0.204557 + 0.0548109i
\(861\) −17.1459 + 6.98655i −0.584331 + 0.238101i
\(862\) −4.32513 2.49712i −0.147315 0.0850521i
\(863\) 18.6818 + 18.6818i 0.635935 + 0.635935i 0.949550 0.313615i \(-0.101540\pi\)
−0.313615 + 0.949550i \(0.601540\pi\)
\(864\) 8.41711 + 31.4131i 0.286356 + 1.06869i
\(865\) 1.94215 + 7.24822i 0.0660352 + 0.246447i
\(866\) 7.53407 + 7.53407i 0.256018 + 0.256018i
\(867\) 10.0558 + 5.80571i 0.341513 + 0.197172i
\(868\) −21.4311 + 8.73266i −0.727418 + 0.296406i
\(869\) 32.6055 + 8.73662i 1.10607 + 0.296370i
\(870\) 9.61472i 0.325969i
\(871\) 6.01203 + 3.74604i 0.203710 + 0.126930i
\(872\) −11.9243 −0.403808
\(873\) −8.59084 2.30191i −0.290756 0.0779078i
\(874\) −5.40854 + 3.12262i −0.182947 + 0.105624i
\(875\) 23.7936 + 18.4763i 0.804369 + 0.624613i
\(876\) −0.652830 0.652830i −0.0220571 0.0220571i
\(877\) −13.9428 + 3.73595i −0.470813 + 0.126154i −0.486422 0.873724i \(-0.661698\pi\)
0.0156084 + 0.999878i \(0.495031\pi\)
\(878\) 20.9595 5.61608i 0.707349 0.189534i
\(879\) −13.0964 + 13.0964i −0.441729 + 0.441729i
\(880\) 1.47878 + 0.853774i 0.0498497 + 0.0287807i
\(881\) −2.13690 3.70122i −0.0719941 0.124697i 0.827781 0.561051i \(-0.189603\pi\)
−0.899775 + 0.436354i \(0.856270\pi\)
\(882\) 4.79784 + 2.84428i 0.161552 + 0.0957719i
\(883\) 32.6002i 1.09708i −0.836123 0.548542i \(-0.815183\pi\)
0.836123 0.548542i \(-0.184817\pi\)
\(884\) −3.13916 13.5182i −0.105581 0.454667i
\(885\) 22.8687i 0.768722i
\(886\) 3.75985 14.0319i 0.126315 0.471412i
\(887\) −15.4078 + 8.89570i −0.517343 + 0.298688i −0.735847 0.677148i \(-0.763216\pi\)
0.218504 + 0.975836i \(0.429882\pi\)
\(888\) 11.1081 19.2399i 0.372765 0.645648i
\(889\) −26.0169 + 19.7262i −0.872578 + 0.661597i
\(890\) −0.286631 + 0.0768025i −0.00960789 + 0.00257443i
\(891\) −6.61809 24.6990i −0.221714 0.827449i
\(892\) 15.6930 + 15.6930i 0.525440 + 0.525440i
\(893\) 18.3301 31.7487i 0.613394 1.06243i
\(894\) 1.71252 + 2.96618i 0.0572754 + 0.0992039i
\(895\) 8.37031 31.2384i 0.279789 1.04418i
\(896\) −20.5329 2.82370i −0.685955 0.0943332i
\(897\) 4.16647 + 4.45654i 0.139114 + 0.148799i
\(898\) −4.90976 −0.163841
\(899\) −36.3945 9.75187i −1.21382 0.325243i
\(900\) −1.79855 3.11518i −0.0599516 0.103839i
\(901\) 8.64057 14.9659i 0.287859 0.498587i
\(902\) −14.1178 + 14.1178i −0.470070 + 0.470070i
\(903\) 12.6396 1.58997i 0.420618 0.0529108i
\(904\) −2.90366 10.8366i −0.0965744 0.360421i
\(905\) 22.7739 22.7739i 0.757029 0.757029i
\(906\) −17.5066 10.1074i −0.581617 0.335797i
\(907\) 28.0724 16.2076i 0.932129 0.538165i 0.0446448 0.999003i \(-0.485784\pi\)
0.887484 + 0.460838i \(0.152451\pi\)
\(908\) −3.32708 + 12.4168i −0.110413 + 0.412067i
\(909\) −13.5130 −0.448197
\(910\) −10.8022 + 3.98368i −0.358091 + 0.132058i
\(911\) −15.2599 −0.505585 −0.252792 0.967521i \(-0.581349\pi\)
−0.252792 + 0.967521i \(0.581349\pi\)
\(912\) −0.571948 + 2.13454i −0.0189391 + 0.0706816i
\(913\) −19.1952 + 11.0824i −0.635269 + 0.366773i
\(914\) −16.1997 9.35288i −0.535838 0.309366i
\(915\) 13.3307 13.3307i 0.440700 0.440700i
\(916\) 1.39271 + 5.19765i 0.0460163 + 0.171735i
\(917\) 2.21693 + 17.6236i 0.0732094 + 0.581984i
\(918\) 10.0492 10.0492i 0.331673 0.331673i
\(919\) −6.10555 + 10.5751i −0.201404 + 0.348841i −0.948981 0.315334i \(-0.897884\pi\)
0.747577 + 0.664175i \(0.231217\pi\)
\(920\) −2.34417 4.06022i −0.0772851 0.133862i
\(921\) 10.6217 + 2.84606i 0.349995 + 0.0937810i
\(922\) −17.9700 −0.591811
\(923\) −0.400449 + 11.9042i −0.0131809 + 0.391832i
\(924\) 23.5284 + 3.23565i 0.774028 + 0.106445i
\(925\) −4.26601 + 15.9210i −0.140266 + 0.523478i
\(926\) 3.06574 + 5.31002i 0.100747 + 0.174498i
\(927\) 3.52384 6.10346i 0.115738 0.200464i
\(928\) −22.6012 22.6012i −0.741920 0.741920i
\(929\) 9.42897 + 35.1894i 0.309354 + 1.15453i 0.929132 + 0.369749i \(0.120556\pi\)
−0.619777 + 0.784778i \(0.712777\pi\)
\(930\) 11.3266 3.03496i 0.371414 0.0995201i
\(931\) 21.5376 + 38.3176i 0.705865 + 1.25581i
\(932\) 4.08135 7.06911i 0.133689 0.231556i
\(933\) 0.599976 0.346396i 0.0196423 0.0113405i
\(934\) 6.21639 23.1999i 0.203407 0.759124i
\(935\) 20.7446i 0.678421i
\(936\) 9.44736 + 0.317802i 0.308797 + 0.0103877i
\(937\) 37.8200i 1.23553i −0.786365 0.617763i \(-0.788039\pi\)
0.786365 0.617763i \(-0.211961\pi\)
\(938\) −4.03584 1.69902i −0.131775 0.0554750i
\(939\) 0.319131 + 0.552750i 0.0104144 + 0.0180383i
\(940\) 9.34660 + 5.39626i 0.304853 + 0.176007i
\(941\) 17.5606 17.5606i 0.572458 0.572458i −0.360357 0.932815i \(-0.617345\pi\)
0.932815 + 0.360357i \(0.117345\pi\)
\(942\) −3.34561 + 0.896453i −0.109006 + 0.0292080i
\(943\) −5.56792 + 1.49192i −0.181316 + 0.0485836i
\(944\) −1.93368 1.93368i −0.0629358 0.0629358i
\(945\) 16.9313 + 13.1476i 0.550774 + 0.427690i
\(946\) 11.8970 6.86871i 0.386804 0.223321i
\(947\) −24.3265 6.51827i −0.790505 0.211815i −0.159094 0.987263i \(-0.550857\pi\)
−0.631411 + 0.775448i \(0.717524\pi\)
\(948\) −12.8606 −0.417694
\(949\) −1.58823 + 0.847084i −0.0515560 + 0.0274975i
\(950\) 15.5917i 0.505860i
\(951\) −34.3773 9.21137i −1.11476 0.298699i
\(952\) 8.25512 + 20.2591i 0.267550 + 0.656602i
\(953\) 15.6650 + 9.04419i 0.507439 + 0.292970i 0.731780 0.681541i \(-0.238690\pi\)
−0.224341 + 0.974511i \(0.572023\pi\)
\(954\) 3.26398 + 3.26398i 0.105675 + 0.105675i
\(955\) −9.14805 34.1410i −0.296024 1.10478i
\(956\) 3.70357 + 13.8219i 0.119782 + 0.447032i
\(957\) 27.3424 + 27.3424i 0.883855 + 0.883855i
\(958\) 24.0194 + 13.8676i 0.776033 + 0.448043i
\(959\) −21.8583 53.6430i −0.705840 1.73222i
\(960\) 8.63446 + 2.31360i 0.278676 + 0.0746710i
\(961\) 14.9527i 0.482346i
\(962\) −11.6002 12.4078i −0.374006 0.400045i
\(963\) −4.42899 −0.142722
\(964\) 17.4270 + 4.66954i 0.561285 + 0.150396i
\(965\) −4.26706 + 2.46359i −0.137361 + 0.0793057i
\(966\) −2.97875 2.31307i −0.0958396 0.0744219i
\(967\) −2.32489 2.32489i −0.0747635 0.0747635i 0.668736 0.743500i \(-0.266836\pi\)
−0.743500 + 0.668736i \(0.766836\pi\)
\(968\) 33.6313 9.01148i 1.08095 0.289640i
\(969\) 25.9320 6.94846i 0.833056 0.223217i
\(970\) −8.02501 + 8.02501i −0.257667 + 0.257667i
\(971\) −12.8317 7.40841i −0.411790 0.237747i 0.279768 0.960068i \(-0.409742\pi\)
−0.691559 + 0.722320i \(0.743076\pi\)
\(972\) −6.07466 10.5216i −0.194845 0.337481i
\(973\) −9.84605 4.14502i −0.315650 0.132883i
\(974\) 11.9408i 0.382609i
\(975\) 14.8364 3.44525i 0.475144 0.110336i
\(976\) 2.25438i 0.0721608i
\(977\) −4.87838 + 18.2064i −0.156073 + 0.582474i 0.842938 + 0.538011i \(0.180824\pi\)
−0.999011 + 0.0444625i \(0.985842\pi\)
\(978\) −25.1992 + 14.5487i −0.805780 + 0.465217i
\(979\) 0.596712 1.03354i 0.0190710 0.0330320i
\(980\) −11.2804 + 6.34052i −0.360341 + 0.202540i
\(981\) 3.93025 1.05311i 0.125483 0.0336231i
\(982\) 6.49024 + 24.2219i 0.207112 + 0.772952i
\(983\) 3.43860 + 3.43860i 0.109674 + 0.109674i 0.759814 0.650140i \(-0.225290\pi\)
−0.650140 + 0.759814i \(0.725290\pi\)
\(984\) 9.69857 16.7984i 0.309179 0.535514i
\(985\) −2.86012 4.95388i −0.0911311 0.157844i
\(986\) −3.61512 + 13.4918i −0.115129 + 0.429666i
\(987\) 21.9319 + 3.01610i 0.698101 + 0.0960035i
\(988\) 24.7943 + 15.4491i 0.788812 + 0.491501i
\(989\) 3.96619 0.126118
\(990\) 5.35228 + 1.43414i 0.170106 + 0.0455799i
\(991\) 8.04617 + 13.9364i 0.255595 + 0.442703i 0.965057 0.262040i \(-0.0843953\pi\)
−0.709462 + 0.704744i \(0.751062\pi\)
\(992\) 19.4911 33.7595i 0.618842 1.07187i
\(993\) −15.0898 + 15.0898i −0.478862 + 0.478862i
\(994\) −0.918975 7.30546i −0.0291481 0.231715i
\(995\) −0.379371 1.41583i −0.0120269 0.0448849i
\(996\) 5.97122 5.97122i 0.189205 0.189205i
\(997\) 22.1768 + 12.8038i 0.702346 + 0.405500i 0.808221 0.588880i \(-0.200431\pi\)
−0.105875 + 0.994379i \(0.533764\pi\)
\(998\) 13.4844 7.78523i 0.426842 0.246437i
\(999\) −8.18532 + 30.5480i −0.258972 + 0.966497i
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 91.2.bc.a.76.6 yes 32
3.2 odd 2 819.2.fm.g.622.4 32
7.2 even 3 637.2.x.b.570.4 32
7.3 odd 6 637.2.bb.b.362.6 32
7.4 even 3 637.2.bb.b.362.5 32
7.5 odd 6 637.2.x.b.570.3 32
7.6 odd 2 inner 91.2.bc.a.76.5 yes 32
13.6 odd 12 inner 91.2.bc.a.6.5 32
21.20 even 2 819.2.fm.g.622.3 32
39.32 even 12 819.2.fm.g.370.3 32
91.6 even 12 inner 91.2.bc.a.6.6 yes 32
91.19 even 12 637.2.bb.b.227.5 32
91.32 odd 12 637.2.x.b.19.4 32
91.45 even 12 637.2.x.b.19.3 32
91.58 odd 12 637.2.bb.b.227.6 32
273.188 odd 12 819.2.fm.g.370.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.bc.a.6.5 32 13.6 odd 12 inner
91.2.bc.a.6.6 yes 32 91.6 even 12 inner
91.2.bc.a.76.5 yes 32 7.6 odd 2 inner
91.2.bc.a.76.6 yes 32 1.1 even 1 trivial
637.2.x.b.19.3 32 91.45 even 12
637.2.x.b.19.4 32 91.32 odd 12
637.2.x.b.570.3 32 7.5 odd 6
637.2.x.b.570.4 32 7.2 even 3
637.2.bb.b.227.5 32 91.19 even 12
637.2.bb.b.227.6 32 91.58 odd 12
637.2.bb.b.362.5 32 7.4 even 3
637.2.bb.b.362.6 32 7.3 odd 6
819.2.fm.g.370.3 32 39.32 even 12
819.2.fm.g.370.4 32 273.188 odd 12
819.2.fm.g.622.3 32 21.20 even 2
819.2.fm.g.622.4 32 3.2 odd 2