Properties

Label 273.2.bt.b.145.6
Level $273$
Weight $2$
Character 273.145
Analytic conductor $2.180$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(136,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bt (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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.6
Character \(\chi\) \(=\) 273.145
Dual form 273.2.bt.b.241.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.465913 - 0.465913i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.56585i q^{4} +(-3.81958 + 1.02345i) q^{5} +(0.636449 - 0.170536i) q^{6} +(-2.61148 + 0.424440i) q^{7} +(1.66138 + 1.66138i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.465913 - 0.465913i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.56585i q^{4} +(-3.81958 + 1.02345i) q^{5} +(0.636449 - 0.170536i) q^{6} +(-2.61148 + 0.424440i) q^{7} +(1.66138 + 1.66138i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.30275 + 2.25643i) q^{10} +(2.60034 - 0.696760i) q^{11} +(-0.782925 + 1.35607i) q^{12} +(0.360197 + 3.58751i) q^{13} +(-1.01897 + 1.41448i) q^{14} +(-3.81958 - 1.02345i) q^{15} -1.58358 q^{16} +3.34664 q^{17} +(0.636449 + 0.170536i) q^{18} +(-1.71776 + 6.41075i) q^{19} +(-1.60257 - 5.98088i) q^{20} +(-2.47383 - 0.938166i) q^{21} +(0.886905 - 1.53616i) q^{22} -6.53430i q^{23} +(0.608106 + 2.26948i) q^{24} +(9.21158 - 5.31831i) q^{25} +(1.83929 + 1.50365i) q^{26} +1.00000i q^{27} +(-0.664609 - 4.08919i) q^{28} +(-1.95916 - 3.39337i) q^{29} +(-2.25643 + 1.30275i) q^{30} +(0.378198 - 1.41145i) q^{31} +(-4.06057 + 4.06057i) q^{32} +(2.60034 + 0.696760i) q^{33} +(1.55924 - 1.55924i) q^{34} +(9.54037 - 4.29391i) q^{35} +(-1.35607 + 0.782925i) q^{36} +(1.48339 + 1.48339i) q^{37} +(2.18653 + 3.78718i) q^{38} +(-1.48182 + 3.28698i) q^{39} +(-8.04609 - 4.64541i) q^{40} +(0.717157 - 2.67647i) q^{41} +(-1.58970 + 0.715487i) q^{42} +(9.41379 + 5.43505i) q^{43} +(1.09102 + 4.07175i) q^{44} +(-2.79612 - 2.79612i) q^{45} +(-3.04442 - 3.04442i) q^{46} +(0.473614 + 1.76755i) q^{47} +(-1.37142 - 0.791792i) q^{48} +(6.63970 - 2.21684i) q^{49} +(1.81393 - 6.76967i) q^{50} +(2.89827 + 1.67332i) q^{51} +(-5.61751 + 0.564014i) q^{52} +(3.90136 + 6.75735i) q^{53} +(0.465913 + 0.465913i) q^{54} +(-9.21911 + 5.32265i) q^{55} +(-5.04381 - 3.63350i) q^{56} +(-4.69300 + 4.69300i) q^{57} +(-2.49382 - 0.668217i) q^{58} +(-0.420268 + 0.420268i) q^{59} +(1.60257 - 5.98088i) q^{60} +(4.75223 - 2.74370i) q^{61} +(-0.481407 - 0.833822i) q^{62} +(-1.67332 - 2.04939i) q^{63} +0.616576i q^{64} +(-5.04745 - 13.3341i) q^{65} +(1.53616 - 0.886905i) q^{66} +(-0.853301 - 3.18456i) q^{67} +5.24033i q^{68} +(3.26715 - 5.65887i) q^{69} +(2.44439 - 6.44557i) q^{70} +(-0.629931 - 2.35094i) q^{71} +(-0.608106 + 2.26948i) q^{72} +(-2.50120 - 0.670194i) q^{73} +1.38226 q^{74} +10.6366 q^{75} +(-10.0383 - 2.68975i) q^{76} +(-6.49502 + 2.92327i) q^{77} +(0.841048 + 2.22184i) q^{78} +(-6.72164 + 11.6422i) q^{79} +(6.04862 - 1.62072i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.912868 - 1.58113i) q^{82} +(0.485609 + 0.485609i) q^{83} +(1.46903 - 3.87365i) q^{84} +(-12.7827 + 3.42512i) q^{85} +(6.91827 - 1.85375i) q^{86} -3.91833i q^{87} +(5.47773 + 3.16257i) q^{88} +(5.80764 - 5.80764i) q^{89} -2.60550 q^{90} +(-2.46333 - 9.21586i) q^{91} +10.2317 q^{92} +(1.03326 - 1.03326i) q^{93} +(1.04419 + 0.602863i) q^{94} -26.2444i q^{95} +(-5.54684 + 1.48627i) q^{96} +(-7.37323 + 1.97565i) q^{97} +(2.06067 - 4.12638i) q^{98} +(1.90358 + 1.90358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 2 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 2 q^{7} + 20 q^{9} - 8 q^{11} + 24 q^{12} - 18 q^{14} - 64 q^{16} + 8 q^{17} - 14 q^{19} - 14 q^{20} - 8 q^{21} + 4 q^{22} + 18 q^{24} - 24 q^{25} - 10 q^{26} - 2 q^{28} + 8 q^{29} - 8 q^{31} + 10 q^{32} - 8 q^{33} + 24 q^{34} - 22 q^{35} + 12 q^{37} + 8 q^{38} - 24 q^{39} - 30 q^{40} + 2 q^{41} + 6 q^{42} - 66 q^{43} + 28 q^{44} + 40 q^{46} + 10 q^{47} - 24 q^{48} + 38 q^{49} - 20 q^{50} + 40 q^{52} - 8 q^{53} + 42 q^{55} + 20 q^{56} - 14 q^{57} - 48 q^{58} - 26 q^{59} + 14 q^{60} - 12 q^{61} - 24 q^{62} - 4 q^{63} - 44 q^{65} - 18 q^{66} + 46 q^{67} - 4 q^{69} + 32 q^{70} - 6 q^{71} - 18 q^{72} + 10 q^{73} + 40 q^{74} + 48 q^{75} + 64 q^{76} - 24 q^{77} + 8 q^{78} + 34 q^{80} - 20 q^{81} + 24 q^{82} + 12 q^{83} + 20 q^{84} + 2 q^{85} + 12 q^{86} - 84 q^{88} - 16 q^{89} + 26 q^{91} + 236 q^{92} + 22 q^{93} + 30 q^{94} + 26 q^{96} + 62 q^{97} - 14 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.465913 0.465913i 0.329450 0.329450i −0.522927 0.852377i \(-0.675160\pi\)
0.852377 + 0.522927i \(0.175160\pi\)
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 1.56585i 0.782925i
\(5\) −3.81958 + 1.02345i −1.70817 + 0.457702i −0.974974 0.222320i \(-0.928637\pi\)
−0.733192 + 0.680021i \(0.761970\pi\)
\(6\) 0.636449 0.170536i 0.259829 0.0696211i
\(7\) −2.61148 + 0.424440i −0.987048 + 0.160423i
\(8\) 1.66138 + 1.66138i 0.587385 + 0.587385i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −1.30275 + 2.25643i −0.411966 + 0.713546i
\(11\) 2.60034 0.696760i 0.784033 0.210081i 0.155471 0.987840i \(-0.450310\pi\)
0.628562 + 0.777759i \(0.283644\pi\)
\(12\) −0.782925 + 1.35607i −0.226011 + 0.391462i
\(13\) 0.360197 + 3.58751i 0.0999006 + 0.994997i
\(14\) −1.01897 + 1.41448i −0.272332 + 0.378035i
\(15\) −3.81958 1.02345i −0.986210 0.264254i
\(16\) −1.58358 −0.395896
\(17\) 3.34664 0.811678 0.405839 0.913944i \(-0.366979\pi\)
0.405839 + 0.913944i \(0.366979\pi\)
\(18\) 0.636449 + 0.170536i 0.150013 + 0.0401957i
\(19\) −1.71776 + 6.41075i −0.394080 + 1.47073i 0.429261 + 0.903181i \(0.358774\pi\)
−0.823341 + 0.567547i \(0.807893\pi\)
\(20\) −1.60257 5.98088i −0.358346 1.33737i
\(21\) −2.47383 0.938166i −0.539834 0.204725i
\(22\) 0.886905 1.53616i 0.189089 0.327511i
\(23\) 6.53430i 1.36250i −0.732053 0.681248i \(-0.761438\pi\)
0.732053 0.681248i \(-0.238562\pi\)
\(24\) 0.608106 + 2.26948i 0.124129 + 0.463256i
\(25\) 9.21158 5.31831i 1.84232 1.06366i
\(26\) 1.83929 + 1.50365i 0.360715 + 0.294890i
\(27\) 1.00000i 0.192450i
\(28\) −0.664609 4.08919i −0.125599 0.772785i
\(29\) −1.95916 3.39337i −0.363808 0.630133i 0.624776 0.780804i \(-0.285190\pi\)
−0.988584 + 0.150670i \(0.951857\pi\)
\(30\) −2.25643 + 1.30275i −0.411966 + 0.237849i
\(31\) 0.378198 1.41145i 0.0679263 0.253504i −0.923610 0.383333i \(-0.874776\pi\)
0.991536 + 0.129829i \(0.0414428\pi\)
\(32\) −4.06057 + 4.06057i −0.717814 + 0.717814i
\(33\) 2.60034 + 0.696760i 0.452662 + 0.121290i
\(34\) 1.55924 1.55924i 0.267408 0.267408i
\(35\) 9.54037 4.29391i 1.61262 0.725803i
\(36\) −1.35607 + 0.782925i −0.226011 + 0.130487i
\(37\) 1.48339 + 1.48339i 0.243868 + 0.243868i 0.818448 0.574580i \(-0.194835\pi\)
−0.574580 + 0.818448i \(0.694835\pi\)
\(38\) 2.18653 + 3.78718i 0.354702 + 0.614362i
\(39\) −1.48182 + 3.28698i −0.237281 + 0.526338i
\(40\) −8.04609 4.64541i −1.27220 0.734505i
\(41\) 0.717157 2.67647i 0.112001 0.417994i −0.887044 0.461685i \(-0.847245\pi\)
0.999045 + 0.0436912i \(0.0139118\pi\)
\(42\) −1.58970 + 0.715487i −0.245295 + 0.110402i
\(43\) 9.41379 + 5.43505i 1.43559 + 0.828838i 0.997539 0.0701122i \(-0.0223357\pi\)
0.438051 + 0.898950i \(0.355669\pi\)
\(44\) 1.09102 + 4.07175i 0.164478 + 0.613839i
\(45\) −2.79612 2.79612i −0.416821 0.416821i
\(46\) −3.04442 3.04442i −0.448875 0.448875i
\(47\) 0.473614 + 1.76755i 0.0690838 + 0.257824i 0.991827 0.127592i \(-0.0407247\pi\)
−0.922743 + 0.385416i \(0.874058\pi\)
\(48\) −1.37142 0.791792i −0.197948 0.114285i
\(49\) 6.63970 2.21684i 0.948529 0.316691i
\(50\) 1.81393 6.76967i 0.256528 0.957375i
\(51\) 2.89827 + 1.67332i 0.405839 + 0.234311i
\(52\) −5.61751 + 0.564014i −0.779008 + 0.0782147i
\(53\) 3.90136 + 6.75735i 0.535892 + 0.928193i 0.999120 + 0.0419532i \(0.0133580\pi\)
−0.463227 + 0.886240i \(0.653309\pi\)
\(54\) 0.465913 + 0.465913i 0.0634028 + 0.0634028i
\(55\) −9.21911 + 5.32265i −1.24310 + 0.717707i
\(56\) −5.04381 3.63350i −0.674008 0.485547i
\(57\) −4.69300 + 4.69300i −0.621603 + 0.621603i
\(58\) −2.49382 0.668217i −0.327454 0.0877411i
\(59\) −0.420268 + 0.420268i −0.0547142 + 0.0547142i −0.733934 0.679220i \(-0.762318\pi\)
0.679220 + 0.733934i \(0.262318\pi\)
\(60\) 1.60257 5.98088i 0.206891 0.772128i
\(61\) 4.75223 2.74370i 0.608461 0.351295i −0.163902 0.986477i \(-0.552408\pi\)
0.772363 + 0.635181i \(0.219075\pi\)
\(62\) −0.481407 0.833822i −0.0611388 0.105896i
\(63\) −1.67332 2.04939i −0.210818 0.258199i
\(64\) 0.616576i 0.0770720i
\(65\) −5.04745 13.3341i −0.626059 1.65390i
\(66\) 1.53616 0.886905i 0.189089 0.109170i
\(67\) −0.853301 3.18456i −0.104247 0.389056i 0.894011 0.448044i \(-0.147879\pi\)
−0.998259 + 0.0589879i \(0.981213\pi\)
\(68\) 5.24033i 0.635483i
\(69\) 3.26715 5.65887i 0.393319 0.681248i
\(70\) 2.44439 6.44557i 0.292161 0.770393i
\(71\) −0.629931 2.35094i −0.0747591 0.279005i 0.918419 0.395608i \(-0.129466\pi\)
−0.993179 + 0.116603i \(0.962799\pi\)
\(72\) −0.608106 + 2.26948i −0.0716660 + 0.267461i
\(73\) −2.50120 0.670194i −0.292743 0.0784402i 0.109459 0.993991i \(-0.465088\pi\)
−0.402202 + 0.915551i \(0.631755\pi\)
\(74\) 1.38226 0.160685
\(75\) 10.6366 1.22821
\(76\) −10.0383 2.68975i −1.15147 0.308535i
\(77\) −6.49502 + 2.92327i −0.740177 + 0.333137i
\(78\) 0.841048 + 2.22184i 0.0952299 + 0.251574i
\(79\) −6.72164 + 11.6422i −0.756244 + 1.30985i 0.188510 + 0.982071i \(0.439634\pi\)
−0.944754 + 0.327781i \(0.893699\pi\)
\(80\) 6.04862 1.62072i 0.676256 0.181202i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −0.912868 1.58113i −0.100809 0.174607i
\(83\) 0.485609 + 0.485609i 0.0533025 + 0.0533025i 0.733256 0.679953i \(-0.238000\pi\)
−0.679953 + 0.733256i \(0.738000\pi\)
\(84\) 1.46903 3.87365i 0.160284 0.422650i
\(85\) −12.7827 + 3.42512i −1.38648 + 0.371507i
\(86\) 6.91827 1.85375i 0.746017 0.199895i
\(87\) 3.91833i 0.420089i
\(88\) 5.47773 + 3.16257i 0.583928 + 0.337131i
\(89\) 5.80764 5.80764i 0.615609 0.615609i −0.328793 0.944402i \(-0.606642\pi\)
0.944402 + 0.328793i \(0.106642\pi\)
\(90\) −2.60550 −0.274644
\(91\) −2.46333 9.21586i −0.258227 0.966084i
\(92\) 10.2317 1.06673
\(93\) 1.03326 1.03326i 0.107144 0.107144i
\(94\) 1.04419 + 0.602863i 0.107700 + 0.0621806i
\(95\) 26.2444i 2.69262i
\(96\) −5.54684 + 1.48627i −0.566122 + 0.151692i
\(97\) −7.37323 + 1.97565i −0.748638 + 0.200597i −0.612914 0.790150i \(-0.710003\pi\)
−0.135724 + 0.990747i \(0.543336\pi\)
\(98\) 2.06067 4.12638i 0.208159 0.416827i
\(99\) 1.90358 + 1.90358i 0.191317 + 0.191317i
\(100\) 8.32767 + 14.4239i 0.832767 + 1.44239i
\(101\) −6.78046 + 11.7441i −0.674681 + 1.16858i 0.301882 + 0.953345i \(0.402385\pi\)
−0.976562 + 0.215236i \(0.930948\pi\)
\(102\) 2.12996 0.570722i 0.210898 0.0565099i
\(103\) 2.89216 5.00937i 0.284973 0.493588i −0.687630 0.726062i \(-0.741349\pi\)
0.972603 + 0.232474i \(0.0746820\pi\)
\(104\) −5.36179 + 6.55864i −0.525767 + 0.643127i
\(105\) 10.4092 + 1.05155i 1.01583 + 0.102621i
\(106\) 4.96603 + 1.33064i 0.482343 + 0.129244i
\(107\) 6.76933 0.654416 0.327208 0.944952i \(-0.393892\pi\)
0.327208 + 0.944952i \(0.393892\pi\)
\(108\) −1.56585 −0.150674
\(109\) 4.02199 + 1.07769i 0.385237 + 0.103224i 0.446239 0.894914i \(-0.352763\pi\)
−0.0610023 + 0.998138i \(0.519430\pi\)
\(110\) −1.81541 + 6.77520i −0.173092 + 0.645990i
\(111\) 0.542959 + 2.02635i 0.0515354 + 0.192333i
\(112\) 4.13551 0.672136i 0.390769 0.0635109i
\(113\) −8.98623 + 15.5646i −0.845353 + 1.46420i 0.0399604 + 0.999201i \(0.487277\pi\)
−0.885314 + 0.464994i \(0.846057\pi\)
\(114\) 4.37306i 0.409574i
\(115\) 6.68754 + 24.9583i 0.623617 + 2.32737i
\(116\) 5.31351 3.06776i 0.493347 0.284834i
\(117\) −2.92678 + 2.10570i −0.270581 + 0.194672i
\(118\) 0.391617i 0.0360513i
\(119\) −8.73969 + 1.42045i −0.801166 + 0.130212i
\(120\) −4.64541 8.04609i −0.424066 0.734505i
\(121\) −3.24997 + 1.87637i −0.295452 + 0.170579i
\(122\) 0.935801 3.49246i 0.0847234 0.316192i
\(123\) 1.95931 1.95931i 0.176665 0.176665i
\(124\) 2.21012 + 0.592201i 0.198475 + 0.0531812i
\(125\) −15.7607 + 15.7607i −1.40968 + 1.40968i
\(126\) −1.73446 0.175218i −0.154518 0.0156096i
\(127\) 10.5135 6.07000i 0.932926 0.538625i 0.0451906 0.998978i \(-0.485610\pi\)
0.887736 + 0.460353i \(0.152277\pi\)
\(128\) −7.83386 7.83386i −0.692422 0.692422i
\(129\) 5.43505 + 9.41379i 0.478530 + 0.828838i
\(130\) −8.56423 3.86088i −0.751132 0.338621i
\(131\) −12.0751 6.97154i −1.05500 0.609107i −0.130958 0.991388i \(-0.541805\pi\)
−0.924046 + 0.382281i \(0.875139\pi\)
\(132\) −1.09102 + 4.07175i −0.0949612 + 0.354400i
\(133\) 1.76491 17.4707i 0.153037 1.51490i
\(134\) −1.88130 1.08617i −0.162519 0.0938305i
\(135\) −1.02345 3.81958i −0.0880847 0.328737i
\(136\) 5.56002 + 5.56002i 0.476768 + 0.476768i
\(137\) 11.0067 + 11.0067i 0.940363 + 0.940363i 0.998319 0.0579565i \(-0.0184585\pi\)
−0.0579565 + 0.998319i \(0.518458\pi\)
\(138\) −1.11433 4.15875i −0.0948584 0.354016i
\(139\) −12.6736 7.31710i −1.07496 0.620629i −0.145428 0.989369i \(-0.546456\pi\)
−0.929532 + 0.368740i \(0.879789\pi\)
\(140\) 6.72362 + 14.9388i 0.568249 + 1.26256i
\(141\) −0.473614 + 1.76755i −0.0398855 + 0.148855i
\(142\) −1.38883 0.801839i −0.116548 0.0672888i
\(143\) 3.43627 + 9.07780i 0.287355 + 0.759124i
\(144\) −0.791792 1.37142i −0.0659827 0.114285i
\(145\) 10.9561 + 10.9561i 0.909857 + 0.909857i
\(146\) −1.47759 + 0.853089i −0.122286 + 0.0706021i
\(147\) 6.85857 + 1.40001i 0.565685 + 0.115471i
\(148\) −2.32277 + 2.32277i −0.190930 + 0.190930i
\(149\) −2.71328 0.727021i −0.222280 0.0595599i 0.145960 0.989291i \(-0.453373\pi\)
−0.368240 + 0.929731i \(0.620040\pi\)
\(150\) 4.95574 4.95574i 0.404634 0.404634i
\(151\) 2.18280 8.14633i 0.177634 0.662939i −0.818454 0.574572i \(-0.805169\pi\)
0.996088 0.0883669i \(-0.0281648\pi\)
\(152\) −13.5045 + 7.79684i −1.09536 + 0.632407i
\(153\) 1.67332 + 2.89827i 0.135280 + 0.234311i
\(154\) −1.66413 + 4.38811i −0.134099 + 0.353604i
\(155\) 5.77822i 0.464118i
\(156\) −5.14691 2.32030i −0.412083 0.185773i
\(157\) 15.0399 8.68326i 1.20031 0.693000i 0.239687 0.970850i \(-0.422955\pi\)
0.960624 + 0.277850i \(0.0896220\pi\)
\(158\) 2.29256 + 8.55597i 0.182387 + 0.680676i
\(159\) 7.80271i 0.618795i
\(160\) 11.3538 19.6654i 0.897600 1.55469i
\(161\) 2.77342 + 17.0642i 0.218576 + 1.34485i
\(162\) 0.170536 + 0.636449i 0.0133986 + 0.0500042i
\(163\) 6.14618 22.9379i 0.481406 1.79663i −0.114318 0.993444i \(-0.536468\pi\)
0.595725 0.803189i \(-0.296865\pi\)
\(164\) 4.19094 + 1.12296i 0.327258 + 0.0876884i
\(165\) −10.6453 −0.828736
\(166\) 0.452504 0.0351211
\(167\) 20.3791 + 5.46055i 1.57698 + 0.422550i 0.937989 0.346665i \(-0.112686\pi\)
0.638989 + 0.769216i \(0.279353\pi\)
\(168\) −2.55132 5.66861i −0.196839 0.437343i
\(169\) −12.7405 + 2.58442i −0.980040 + 0.198802i
\(170\) −4.35983 + 7.55145i −0.334384 + 0.579170i
\(171\) −6.41075 + 1.71776i −0.490242 + 0.131360i
\(172\) −8.51048 + 14.7406i −0.648918 + 1.12396i
\(173\) −7.97561 13.8142i −0.606375 1.05027i −0.991833 0.127546i \(-0.959290\pi\)
0.385458 0.922725i \(-0.374043\pi\)
\(174\) −1.82560 1.82560i −0.138398 0.138398i
\(175\) −21.7986 + 17.7984i −1.64782 + 1.34544i
\(176\) −4.11786 + 1.10338i −0.310396 + 0.0831702i
\(177\) −0.574097 + 0.153829i −0.0431517 + 0.0115625i
\(178\) 5.41171i 0.405625i
\(179\) −2.50208 1.44457i −0.187014 0.107973i 0.403570 0.914949i \(-0.367769\pi\)
−0.590584 + 0.806976i \(0.701103\pi\)
\(180\) 4.37831 4.37831i 0.326340 0.326340i
\(181\) 16.0175 1.19057 0.595284 0.803515i \(-0.297040\pi\)
0.595284 + 0.803515i \(0.297040\pi\)
\(182\) −5.44149 3.14609i −0.403350 0.233204i
\(183\) 5.48741 0.405641
\(184\) 10.8559 10.8559i 0.800310 0.800310i
\(185\) −7.18411 4.14775i −0.528186 0.304948i
\(186\) 0.962815i 0.0705970i
\(187\) 8.70240 2.33180i 0.636383 0.170518i
\(188\) −2.76772 + 0.741609i −0.201857 + 0.0540874i
\(189\) −0.424440 2.61148i −0.0308735 0.189958i
\(190\) −12.2276 12.2276i −0.887084 0.887084i
\(191\) −10.6868 18.5100i −0.773267 1.33934i −0.935763 0.352628i \(-0.885288\pi\)
0.162497 0.986709i \(-0.448045\pi\)
\(192\) −0.308288 + 0.533970i −0.0222488 + 0.0385360i
\(193\) 8.98686 2.40802i 0.646888 0.173333i 0.0795667 0.996830i \(-0.474646\pi\)
0.567322 + 0.823496i \(0.307980\pi\)
\(194\) −2.51480 + 4.35577i −0.180552 + 0.312726i
\(195\) 2.29585 14.0714i 0.164409 1.00768i
\(196\) 3.47123 + 10.3968i 0.247945 + 0.742627i
\(197\) −2.84864 0.763291i −0.202957 0.0543823i 0.155908 0.987772i \(-0.450170\pi\)
−0.358865 + 0.933389i \(0.616836\pi\)
\(198\) 1.77381 0.126059
\(199\) −5.64689 −0.400297 −0.200149 0.979766i \(-0.564142\pi\)
−0.200149 + 0.979766i \(0.564142\pi\)
\(200\) 24.1396 + 6.46819i 1.70693 + 0.457370i
\(201\) 0.853301 3.18456i 0.0601872 0.224622i
\(202\) 2.31262 + 8.63083i 0.162716 + 0.607263i
\(203\) 6.55661 + 8.03019i 0.460184 + 0.563609i
\(204\) −2.62016 + 4.53826i −0.183448 + 0.317742i
\(205\) 10.9569i 0.765266i
\(206\) −0.986436 3.68143i −0.0687283 0.256497i
\(207\) 5.65887 3.26715i 0.393319 0.227083i
\(208\) −0.570402 5.68113i −0.0395503 0.393916i
\(209\) 17.8670i 1.23589i
\(210\) 5.33969 4.35983i 0.368474 0.300857i
\(211\) 4.36155 + 7.55442i 0.300261 + 0.520068i 0.976195 0.216895i \(-0.0695928\pi\)
−0.675934 + 0.736962i \(0.736259\pi\)
\(212\) −10.5810 + 6.10894i −0.726705 + 0.419563i
\(213\) 0.629931 2.35094i 0.0431622 0.161083i
\(214\) 3.15392 3.15392i 0.215598 0.215598i
\(215\) −41.5192 11.1250i −2.83159 0.758721i
\(216\) −1.66138 + 1.66138i −0.113042 + 0.113042i
\(217\) −0.388580 + 3.84651i −0.0263785 + 0.261118i
\(218\) 2.37601 1.37179i 0.160924 0.0929093i
\(219\) −1.83100 1.83100i −0.123728 0.123728i
\(220\) −8.33448 14.4357i −0.561910 0.973257i
\(221\) 1.20545 + 12.0061i 0.0810872 + 0.807618i
\(222\) 1.19708 + 0.691132i 0.0803424 + 0.0463857i
\(223\) 2.60725 9.73040i 0.174595 0.651596i −0.822026 0.569450i \(-0.807156\pi\)
0.996620 0.0821456i \(-0.0261773\pi\)
\(224\) 8.88064 12.3276i 0.593363 0.823671i
\(225\) 9.21158 + 5.31831i 0.614105 + 0.354554i
\(226\) 3.06495 + 11.4386i 0.203878 + 0.760882i
\(227\) −3.08511 3.08511i −0.204766 0.204766i 0.597273 0.802038i \(-0.296251\pi\)
−0.802038 + 0.597273i \(0.796251\pi\)
\(228\) −7.34853 7.34853i −0.486668 0.486668i
\(229\) 4.36901 + 16.3054i 0.288713 + 1.07749i 0.946083 + 0.323923i \(0.105002\pi\)
−0.657371 + 0.753567i \(0.728331\pi\)
\(230\) 14.7442 + 8.51257i 0.972204 + 0.561302i
\(231\) −7.08649 0.715888i −0.466257 0.0471020i
\(232\) 2.38276 8.89258i 0.156436 0.583827i
\(233\) 3.04241 + 1.75654i 0.199315 + 0.115075i 0.596336 0.802735i \(-0.296623\pi\)
−0.397021 + 0.917810i \(0.629956\pi\)
\(234\) −0.382554 + 2.34470i −0.0250083 + 0.153278i
\(235\) −3.61801 6.26658i −0.236013 0.408787i
\(236\) −0.658076 0.658076i −0.0428371 0.0428371i
\(237\) −11.6422 + 6.72164i −0.756244 + 0.436617i
\(238\) −3.41013 + 4.73374i −0.221046 + 0.306843i
\(239\) 15.0576 15.0576i 0.973998 0.973998i −0.0256726 0.999670i \(-0.508173\pi\)
0.999670 + 0.0256726i \(0.00817273\pi\)
\(240\) 6.04862 + 1.62072i 0.390437 + 0.104617i
\(241\) 7.77594 7.77594i 0.500892 0.500892i −0.410823 0.911715i \(-0.634759\pi\)
0.911715 + 0.410823i \(0.134759\pi\)
\(242\) −0.639978 + 2.38843i −0.0411393 + 0.153534i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 4.29623 + 7.44128i 0.275038 + 0.476379i
\(245\) −23.0920 + 15.2628i −1.47529 + 0.975104i
\(246\) 1.82574i 0.116405i
\(247\) −23.6174 3.85334i −1.50274 0.245182i
\(248\) 2.97328 1.71663i 0.188804 0.109006i
\(249\) 0.177745 + 0.663355i 0.0112642 + 0.0420384i
\(250\) 14.6862i 0.928837i
\(251\) 11.0284 19.1018i 0.696107 1.20569i −0.273700 0.961815i \(-0.588247\pi\)
0.969806 0.243877i \(-0.0784193\pi\)
\(252\) 3.20904 2.62016i 0.202150 0.165055i
\(253\) −4.55284 16.9914i −0.286235 1.06824i
\(254\) 2.07031 7.72650i 0.129903 0.484803i
\(255\) −12.7827 3.42512i −0.800486 0.214489i
\(256\) −8.53295 −0.533310
\(257\) 6.63988 0.414184 0.207092 0.978321i \(-0.433600\pi\)
0.207092 + 0.978321i \(0.433600\pi\)
\(258\) 6.91827 + 1.85375i 0.430713 + 0.115409i
\(259\) −4.50346 3.24424i −0.279832 0.201587i
\(260\) 20.8793 7.90354i 1.29488 0.490157i
\(261\) 1.95916 3.39337i 0.121269 0.210044i
\(262\) −8.87407 + 2.37780i −0.548242 + 0.146901i
\(263\) −0.526039 + 0.911126i −0.0324369 + 0.0561824i −0.881788 0.471646i \(-0.843660\pi\)
0.849351 + 0.527828i \(0.176993\pi\)
\(264\) 3.16257 + 5.47773i 0.194643 + 0.337131i
\(265\) −21.8173 21.8173i −1.34023 1.34023i
\(266\) −7.31752 8.96211i −0.448666 0.549502i
\(267\) 7.93338 2.12574i 0.485515 0.130093i
\(268\) 4.98655 1.33614i 0.304602 0.0816178i
\(269\) 6.98179i 0.425687i −0.977086 0.212844i \(-0.931727\pi\)
0.977086 0.212844i \(-0.0682725\pi\)
\(270\) −2.25643 1.30275i −0.137322 0.0792829i
\(271\) 17.8972 17.8972i 1.08718 1.08718i 0.0913570 0.995818i \(-0.470880\pi\)
0.995818 0.0913570i \(-0.0291204\pi\)
\(272\) −5.29968 −0.321340
\(273\) 2.47462 9.21283i 0.149771 0.557586i
\(274\) 10.2563 0.619606
\(275\) 20.2477 20.2477i 1.22098 1.22098i
\(276\) 8.86094 + 5.11587i 0.533366 + 0.307939i
\(277\) 26.1098i 1.56878i 0.620265 + 0.784392i \(0.287025\pi\)
−0.620265 + 0.784392i \(0.712975\pi\)
\(278\) −9.31393 + 2.49566i −0.558612 + 0.149680i
\(279\) 1.41145 0.378198i 0.0845015 0.0226421i
\(280\) 22.9839 + 8.71634i 1.37355 + 0.520901i
\(281\) −13.0103 13.0103i −0.776131 0.776131i 0.203039 0.979171i \(-0.434918\pi\)
−0.979171 + 0.203039i \(0.934918\pi\)
\(282\) 0.602863 + 1.04419i 0.0359000 + 0.0621806i
\(283\) −3.14855 + 5.45344i −0.187162 + 0.324174i −0.944303 0.329078i \(-0.893262\pi\)
0.757141 + 0.653251i \(0.226596\pi\)
\(284\) 3.68121 0.986378i 0.218440 0.0585308i
\(285\) 13.1222 22.7283i 0.777292 1.34631i
\(286\) 5.83047 + 2.62846i 0.344763 + 0.155424i
\(287\) −0.736845 + 7.29394i −0.0434946 + 0.430548i
\(288\) −5.54684 1.48627i −0.326850 0.0875793i
\(289\) −5.80003 −0.341178
\(290\) 10.2092 0.599506
\(291\) −7.37323 1.97565i −0.432226 0.115815i
\(292\) 1.04942 3.91650i 0.0614128 0.229196i
\(293\) −3.07465 11.4748i −0.179623 0.670362i −0.995718 0.0924444i \(-0.970532\pi\)
0.816095 0.577918i \(-0.196135\pi\)
\(294\) 3.84778 2.54321i 0.224407 0.148323i
\(295\) 1.17512 2.03537i 0.0684182 0.118504i
\(296\) 4.92894i 0.286489i
\(297\) 0.696760 + 2.60034i 0.0404301 + 0.150887i
\(298\) −1.60288 + 0.925424i −0.0928524 + 0.0536084i
\(299\) 23.4419 2.35363i 1.35568 0.136114i
\(300\) 16.6553i 0.961596i
\(301\) −26.8908 10.1980i −1.54996 0.587801i
\(302\) −2.77849 4.81248i −0.159884 0.276927i
\(303\) −11.7441 + 6.78046i −0.674681 + 0.389527i
\(304\) 2.72021 10.1520i 0.156015 0.582255i
\(305\) −15.3435 + 15.3435i −0.878564 + 0.878564i
\(306\) 2.12996 + 0.570722i 0.121762 + 0.0326260i
\(307\) 14.8912 14.8912i 0.849885 0.849885i −0.140234 0.990118i \(-0.544785\pi\)
0.990118 + 0.140234i \(0.0447854\pi\)
\(308\) −4.57740 10.1702i −0.260821 0.579503i
\(309\) 5.00937 2.89216i 0.284973 0.164529i
\(310\) 2.69215 + 2.69215i 0.152904 + 0.152904i
\(311\) −10.6266 18.4058i −0.602580 1.04370i −0.992429 0.122820i \(-0.960806\pi\)
0.389849 0.920879i \(-0.372527\pi\)
\(312\) −7.92276 + 2.99905i −0.448538 + 0.169788i
\(313\) 4.47455 + 2.58338i 0.252916 + 0.146021i 0.621099 0.783732i \(-0.286687\pi\)
−0.368183 + 0.929754i \(0.620020\pi\)
\(314\) 2.96162 11.0529i 0.167134 0.623752i
\(315\) 8.48882 + 6.11525i 0.478291 + 0.344555i
\(316\) −18.2300 10.5251i −1.02552 0.592082i
\(317\) 1.63753 + 6.11134i 0.0919728 + 0.343247i 0.996543 0.0830772i \(-0.0264748\pi\)
−0.904570 + 0.426325i \(0.859808\pi\)
\(318\) 3.63539 + 3.63539i 0.203862 + 0.203862i
\(319\) −7.45887 7.45887i −0.417616 0.417616i
\(320\) −0.631036 2.35506i −0.0352760 0.131652i
\(321\) 5.86241 + 3.38467i 0.327208 + 0.188914i
\(322\) 9.24262 + 6.65828i 0.515071 + 0.371051i
\(323\) −5.74870 + 21.4545i −0.319866 + 1.19376i
\(324\) −1.35607 0.782925i −0.0753370 0.0434958i
\(325\) 22.3975 + 31.1310i 1.24239 + 1.72684i
\(326\) −7.82347 13.5506i −0.433302 0.750501i
\(327\) 2.94430 + 2.94430i 0.162820 + 0.162820i
\(328\) 5.63808 3.25515i 0.311311 0.179736i
\(329\) −1.98706 4.41492i −0.109550 0.243402i
\(330\) −4.95979 + 4.95979i −0.273027 + 0.273027i
\(331\) 5.28778 + 1.41686i 0.290642 + 0.0778774i 0.401194 0.915993i \(-0.368595\pi\)
−0.110552 + 0.993870i \(0.535262\pi\)
\(332\) −0.760391 + 0.760391i −0.0417319 + 0.0417319i
\(333\) −0.542959 + 2.02635i −0.0297540 + 0.111043i
\(334\) 12.0390 6.95073i 0.658746 0.380327i
\(335\) 6.51850 + 11.2904i 0.356144 + 0.616859i
\(336\) 3.91752 + 1.48567i 0.213718 + 0.0810497i
\(337\) 23.5704i 1.28396i 0.766722 + 0.641980i \(0.221887\pi\)
−0.766722 + 0.641980i \(0.778113\pi\)
\(338\) −4.73186 + 7.14009i −0.257379 + 0.388370i
\(339\) −15.5646 + 8.98623i −0.845353 + 0.488065i
\(340\) −5.36323 20.0158i −0.290862 1.08551i
\(341\) 3.93378i 0.213026i
\(342\) −2.18653 + 3.78718i −0.118234 + 0.204787i
\(343\) −16.3986 + 8.60739i −0.885439 + 0.464755i
\(344\) 6.61018 + 24.6695i 0.356397 + 1.33009i
\(345\) −6.68754 + 24.9583i −0.360045 + 1.34371i
\(346\) −10.1521 2.72026i −0.545783 0.146242i
\(347\) 17.0371 0.914600 0.457300 0.889313i \(-0.348817\pi\)
0.457300 + 0.889313i \(0.348817\pi\)
\(348\) 6.13551 0.328898
\(349\) 16.3863 + 4.39071i 0.877140 + 0.235029i 0.669173 0.743107i \(-0.266649\pi\)
0.207967 + 0.978136i \(0.433315\pi\)
\(350\) −1.86372 + 18.4488i −0.0996202 + 0.986129i
\(351\) −3.58751 + 0.360197i −0.191487 + 0.0192259i
\(352\) −7.72963 + 13.3881i −0.411990 + 0.713588i
\(353\) −33.5283 + 8.98387i −1.78453 + 0.478163i −0.991397 0.130887i \(-0.958217\pi\)
−0.793132 + 0.609050i \(0.791551\pi\)
\(354\) −0.195808 + 0.339150i −0.0104071 + 0.0180256i
\(355\) 4.81214 + 8.33487i 0.255402 + 0.442369i
\(356\) 9.09389 + 9.09389i 0.481975 + 0.481975i
\(357\) −8.27901 3.13970i −0.438172 0.166171i
\(358\) −1.83880 + 0.492704i −0.0971835 + 0.0260402i
\(359\) −16.1282 + 4.32153i −0.851212 + 0.228081i −0.657946 0.753065i \(-0.728575\pi\)
−0.193266 + 0.981146i \(0.561908\pi\)
\(360\) 9.29083i 0.489670i
\(361\) −21.6926 12.5242i −1.14171 0.659169i
\(362\) 7.46275 7.46275i 0.392233 0.392233i
\(363\) −3.75274 −0.196968
\(364\) 14.4306 3.85721i 0.756371 0.202173i
\(365\) 10.2394 0.535956
\(366\) 2.55666 2.55666i 0.133639 0.133639i
\(367\) −3.39078 1.95767i −0.176997 0.102189i 0.408884 0.912586i \(-0.365918\pi\)
−0.585881 + 0.810397i \(0.699251\pi\)
\(368\) 10.3476i 0.539407i
\(369\) 2.67647 0.717157i 0.139331 0.0373337i
\(370\) −5.27966 + 1.41468i −0.274476 + 0.0735458i
\(371\) −13.0564 15.9908i −0.677855 0.830201i
\(372\) 1.61792 + 1.61792i 0.0838854 + 0.0838854i
\(373\) 14.2114 + 24.6148i 0.735836 + 1.27451i 0.954356 + 0.298673i \(0.0965439\pi\)
−0.218520 + 0.975833i \(0.570123\pi\)
\(374\) 2.96815 5.14098i 0.153479 0.265834i
\(375\) −21.5295 + 5.76880i −1.11178 + 0.297900i
\(376\) −2.14972 + 3.72342i −0.110863 + 0.192021i
\(377\) 11.4681 8.25081i 0.590637 0.424938i
\(378\) −1.41448 1.01897i −0.0727529 0.0524103i
\(379\) 13.2091 + 3.53938i 0.678508 + 0.181806i 0.581584 0.813486i \(-0.302433\pi\)
0.0969237 + 0.995292i \(0.469100\pi\)
\(380\) 41.0948 2.10812
\(381\) 12.1400 0.621951
\(382\) −13.6032 3.64496i −0.695999 0.186492i
\(383\) −7.85471 + 29.3142i −0.401357 + 1.49789i 0.409320 + 0.912391i \(0.365766\pi\)
−0.810677 + 0.585494i \(0.800901\pi\)
\(384\) −2.86739 10.7013i −0.146326 0.546096i
\(385\) 21.8164 17.8130i 1.11187 0.907834i
\(386\) 3.06517 5.30903i 0.156013 0.270222i
\(387\) 10.8701i 0.552559i
\(388\) −3.09357 11.5454i −0.157052 0.586127i
\(389\) −15.8430 + 9.14693i −0.803270 + 0.463768i −0.844613 0.535377i \(-0.820170\pi\)
0.0413436 + 0.999145i \(0.486836\pi\)
\(390\) −5.48640 7.62573i −0.277815 0.386144i
\(391\) 21.8679i 1.10591i
\(392\) 14.7140 + 7.34804i 0.743172 + 0.371132i
\(393\) −6.97154 12.0751i −0.351668 0.609107i
\(394\) −1.68285 + 0.971593i −0.0847806 + 0.0489481i
\(395\) 13.7586 51.3476i 0.692268 2.58358i
\(396\) −2.98073 + 2.98073i −0.149787 + 0.149787i
\(397\) −2.24081 0.600424i −0.112463 0.0301344i 0.202149 0.979355i \(-0.435208\pi\)
−0.314612 + 0.949220i \(0.601874\pi\)
\(398\) −2.63096 + 2.63096i −0.131878 + 0.131878i
\(399\) 10.2638 14.2476i 0.513832 0.713271i
\(400\) −14.5873 + 8.42198i −0.729365 + 0.421099i
\(401\) −9.50376 9.50376i −0.474595 0.474595i 0.428803 0.903398i \(-0.358936\pi\)
−0.903398 + 0.428803i \(0.858936\pi\)
\(402\) −1.08617 1.88130i −0.0541731 0.0938305i
\(403\) 5.19983 + 0.848389i 0.259022 + 0.0422613i
\(404\) −18.3895 10.6172i −0.914911 0.528224i
\(405\) 1.02345 3.81958i 0.0508557 0.189796i
\(406\) 6.79618 + 0.686561i 0.337289 + 0.0340734i
\(407\) 4.89089 + 2.82376i 0.242433 + 0.139969i
\(408\) 2.03511 + 7.59513i 0.100753 + 0.376015i
\(409\) −14.4716 14.4716i −0.715573 0.715573i 0.252122 0.967695i \(-0.418872\pi\)
−0.967695 + 0.252122i \(0.918872\pi\)
\(410\) 5.10498 + 5.10498i 0.252117 + 0.252117i
\(411\) 4.02872 + 15.0354i 0.198722 + 0.741641i
\(412\) 7.84392 + 4.52869i 0.386442 + 0.223113i
\(413\) 0.919145 1.27590i 0.0452281 0.0627830i
\(414\) 1.11433 4.15875i 0.0547665 0.204392i
\(415\) −2.35182 1.35782i −0.115446 0.0666529i
\(416\) −16.0299 13.1047i −0.785933 0.642513i
\(417\) −7.31710 12.6736i −0.358320 0.620629i
\(418\) 8.32448 + 8.32448i 0.407164 + 0.407164i
\(419\) −25.2902 + 14.6013i −1.23551 + 0.713321i −0.968173 0.250282i \(-0.919477\pi\)
−0.267336 + 0.963604i \(0.586143\pi\)
\(420\) −1.64657 + 16.2992i −0.0803442 + 0.795318i
\(421\) −27.2327 + 27.2327i −1.32724 + 1.32724i −0.419470 + 0.907769i \(0.637784\pi\)
−0.907769 + 0.419470i \(0.862216\pi\)
\(422\) 5.55181 + 1.48760i 0.270258 + 0.0724154i
\(423\) −1.29394 + 1.29394i −0.0629134 + 0.0629134i
\(424\) −4.74488 + 17.7081i −0.230432 + 0.859982i
\(425\) 30.8278 17.7984i 1.49537 0.863351i
\(426\) −0.801839 1.38883i −0.0388492 0.0672888i
\(427\) −11.2458 + 9.18218i −0.544225 + 0.444357i
\(428\) 10.5998i 0.512358i
\(429\) −1.56300 + 9.57974i −0.0754624 + 0.462514i
\(430\) −24.5277 + 14.1610i −1.18283 + 0.682906i
\(431\) −2.22337 8.29771i −0.107096 0.399687i 0.891479 0.453063i \(-0.149669\pi\)
−0.998575 + 0.0533757i \(0.983002\pi\)
\(432\) 1.58358i 0.0761902i
\(433\) −7.61560 + 13.1906i −0.365983 + 0.633900i −0.988933 0.148361i \(-0.952600\pi\)
0.622951 + 0.782261i \(0.285934\pi\)
\(434\) 1.61110 + 1.97318i 0.0773351 + 0.0947159i
\(435\) 4.01022 + 14.9664i 0.192275 + 0.717582i
\(436\) −1.68750 + 6.29784i −0.0808166 + 0.301612i
\(437\) 41.8898 + 11.2243i 2.00386 + 0.536933i
\(438\) −1.70618 −0.0815243
\(439\) −2.86626 −0.136799 −0.0683996 0.997658i \(-0.521789\pi\)
−0.0683996 + 0.997658i \(0.521789\pi\)
\(440\) −24.1593 6.47348i −1.15175 0.308611i
\(441\) 5.23969 + 4.64173i 0.249509 + 0.221035i
\(442\) 6.15544 + 5.03217i 0.292784 + 0.239356i
\(443\) 10.5160 18.2142i 0.499628 0.865382i −0.500372 0.865811i \(-0.666803\pi\)
1.00000 0.000429119i \(0.000136593\pi\)
\(444\) −3.17296 + 0.850192i −0.150582 + 0.0403483i
\(445\) −16.2389 + 28.1266i −0.769797 + 1.33333i
\(446\) −3.31877 5.74828i −0.157148 0.272189i
\(447\) −1.98626 1.98626i −0.0939468 0.0939468i
\(448\) −0.261699 1.61018i −0.0123641 0.0760737i
\(449\) 6.15599 1.64949i 0.290519 0.0778444i −0.110616 0.993863i \(-0.535282\pi\)
0.401135 + 0.916019i \(0.368616\pi\)
\(450\) 6.76967 1.81393i 0.319125 0.0855093i
\(451\) 7.45941i 0.351250i
\(452\) −24.3718 14.0711i −1.14635 0.661848i
\(453\) 5.96353 5.96353i 0.280191 0.280191i
\(454\) −2.87479 −0.134920
\(455\) 18.8409 + 32.6796i 0.883274 + 1.53204i
\(456\) −15.5937 −0.730241
\(457\) −11.3160 + 11.3160i −0.529342 + 0.529342i −0.920376 0.391034i \(-0.872117\pi\)
0.391034 + 0.920376i \(0.372117\pi\)
\(458\) 9.63248 + 5.56131i 0.450096 + 0.259863i
\(459\) 3.34664i 0.156208i
\(460\) −39.0809 + 10.4717i −1.82216 + 0.488245i
\(461\) 29.9787 8.03276i 1.39625 0.374123i 0.519250 0.854622i \(-0.326211\pi\)
0.876995 + 0.480499i \(0.159545\pi\)
\(462\) −3.63523 + 2.96815i −0.169126 + 0.138091i
\(463\) −2.20061 2.20061i −0.102271 0.102271i 0.654120 0.756391i \(-0.273039\pi\)
−0.756391 + 0.654120i \(0.773039\pi\)
\(464\) 3.10250 + 5.37369i 0.144030 + 0.249467i
\(465\) −2.88911 + 5.00408i −0.133979 + 0.232059i
\(466\) 2.23590 0.599107i 0.103576 0.0277531i
\(467\) −2.25883 + 3.91240i −0.104526 + 0.181044i −0.913544 0.406739i \(-0.866666\pi\)
0.809018 + 0.587783i \(0.199999\pi\)
\(468\) −3.29720 4.58290i −0.152413 0.211845i
\(469\) 3.58004 + 7.95426i 0.165311 + 0.367294i
\(470\) −4.60536 1.23400i −0.212430 0.0569203i
\(471\) 17.3665 0.800207
\(472\) −1.39645 −0.0642767
\(473\) 28.2660 + 7.57386i 1.29967 + 0.348246i
\(474\) −2.29256 + 8.55597i −0.105301 + 0.392989i
\(475\) 18.2711 + 68.1887i 0.838336 + 3.12871i
\(476\) −2.22421 13.6850i −0.101946 0.627253i
\(477\) −3.90136 + 6.75735i −0.178631 + 0.309398i
\(478\) 14.0311i 0.641768i
\(479\) 8.06385 + 30.0947i 0.368447 + 1.37506i 0.862688 + 0.505737i \(0.168779\pi\)
−0.494241 + 0.869325i \(0.664554\pi\)
\(480\) 19.6654 11.3538i 0.897600 0.518230i
\(481\) −4.78738 + 5.85600i −0.218286 + 0.267011i
\(482\) 7.24583i 0.330038i
\(483\) −6.13026 + 16.1648i −0.278937 + 0.735522i
\(484\) −2.93811 5.08896i −0.133551 0.231316i
\(485\) 26.1406 15.0923i 1.18698 0.685306i
\(486\) −0.170536 + 0.636449i −0.00773567 + 0.0288699i
\(487\) 6.77624 6.77624i 0.307061 0.307061i −0.536708 0.843768i \(-0.680332\pi\)
0.843768 + 0.536708i \(0.180332\pi\)
\(488\) 12.4536 + 3.33693i 0.563747 + 0.151056i
\(489\) 16.7917 16.7917i 0.759346 0.759346i
\(490\) −3.64774 + 17.8700i −0.164788 + 0.807285i
\(491\) −0.411322 + 0.237477i −0.0185627 + 0.0107172i −0.509253 0.860617i \(-0.670078\pi\)
0.490690 + 0.871334i \(0.336745\pi\)
\(492\) 3.06798 + 3.06798i 0.138315 + 0.138315i
\(493\) −6.55661 11.3564i −0.295295 0.511466i
\(494\) −12.7990 + 9.20834i −0.575853 + 0.414303i
\(495\) −9.21911 5.32265i −0.414368 0.239236i
\(496\) −0.598908 + 2.23515i −0.0268918 + 0.100361i
\(497\) 2.64289 + 5.87206i 0.118550 + 0.263398i
\(498\) 0.391880 + 0.226252i 0.0175605 + 0.0101386i
\(499\) −0.915629 3.41717i −0.0409892 0.152974i 0.942398 0.334493i \(-0.108565\pi\)
−0.983387 + 0.181520i \(0.941898\pi\)
\(500\) −24.6788 24.6788i −1.10367 1.10367i
\(501\) 14.9185 + 14.9185i 0.666509 + 0.666509i
\(502\) −3.76148 14.0380i −0.167883 0.626548i
\(503\) 10.2816 + 5.93609i 0.458434 + 0.264677i 0.711386 0.702802i \(-0.248068\pi\)
−0.252951 + 0.967479i \(0.581401\pi\)
\(504\) 0.624800 6.18482i 0.0278308 0.275494i
\(505\) 13.8789 51.7969i 0.617605 2.30493i
\(506\) −10.0378 5.79530i −0.446233 0.257633i
\(507\) −12.3258 4.13208i −0.547409 0.183512i
\(508\) 9.50471 + 16.4626i 0.421703 + 0.730411i
\(509\) −8.27892 8.27892i −0.366957 0.366957i 0.499409 0.866366i \(-0.333550\pi\)
−0.866366 + 0.499409i \(0.833550\pi\)
\(510\) −7.55145 + 4.35983i −0.334384 + 0.193057i
\(511\) 6.81629 + 0.688592i 0.301535 + 0.0304615i
\(512\) 11.6921 11.6921i 0.516723 0.516723i
\(513\) −6.41075 1.71776i −0.283042 0.0758408i
\(514\) 3.09361 3.09361i 0.136453 0.136453i
\(515\) −5.91998 + 22.0937i −0.260865 + 0.973563i
\(516\) −14.7406 + 8.51048i −0.648918 + 0.374653i
\(517\) 2.46312 + 4.26625i 0.108328 + 0.187629i
\(518\) −3.60976 + 0.586688i −0.158604 + 0.0257776i
\(519\) 15.9512i 0.700181i
\(520\) 13.7673 30.5387i 0.603737 1.33921i
\(521\) 11.1559 6.44088i 0.488750 0.282180i −0.235306 0.971921i \(-0.575609\pi\)
0.724056 + 0.689741i \(0.242276\pi\)
\(522\) −0.668217 2.49382i −0.0292470 0.109151i
\(523\) 38.5009i 1.68353i −0.539847 0.841763i \(-0.681518\pi\)
0.539847 0.841763i \(-0.318482\pi\)
\(524\) 10.9164 18.9077i 0.476885 0.825988i
\(525\) −27.7773 + 4.51460i −1.21230 + 0.197033i
\(526\) 0.179417 + 0.669594i 0.00782296 + 0.0291957i
\(527\) 1.26569 4.72362i 0.0551343 0.205764i
\(528\) −4.11786 1.10338i −0.179207 0.0480184i
\(529\) −19.6971 −0.856395
\(530\) −20.3300 −0.883078
\(531\) −0.574097 0.153829i −0.0249137 0.00667560i
\(532\) 27.3564 + 2.76359i 1.18605 + 0.119817i
\(533\) 9.86018 + 1.60876i 0.427092 + 0.0696829i
\(534\) 2.70586 4.68668i 0.117094 0.202813i
\(535\) −25.8560 + 6.92809i −1.11785 + 0.299527i
\(536\) 3.87311 6.70842i 0.167293 0.289759i
\(537\) −1.44457 2.50208i −0.0623380 0.107973i
\(538\) −3.25291 3.25291i −0.140243 0.140243i
\(539\) 15.7209 10.3908i 0.677147 0.447564i
\(540\) 5.98088 1.60257i 0.257376 0.0689637i
\(541\) −0.150417 + 0.0403040i −0.00646691 + 0.00173280i −0.262051 0.965054i \(-0.584399\pi\)
0.255584 + 0.966787i \(0.417732\pi\)
\(542\) 16.6771i 0.716341i
\(543\) 13.8715 + 8.00873i 0.595284 + 0.343687i
\(544\) −13.5892 + 13.5892i −0.582634 + 0.582634i
\(545\) −16.4653 −0.705295
\(546\) −3.13942 5.44534i −0.134355 0.233039i
\(547\) 43.5439 1.86180 0.930902 0.365270i \(-0.119023\pi\)
0.930902 + 0.365270i \(0.119023\pi\)
\(548\) −17.2348 + 17.2348i −0.736233 + 0.736233i
\(549\) 4.75223 + 2.74370i 0.202820 + 0.117098i
\(550\) 18.8673i 0.804505i
\(551\) 25.1194 6.73073i 1.07012 0.286739i
\(552\) 14.8295 3.97355i 0.631185 0.169125i
\(553\) 12.6120 33.2564i 0.536318 1.41421i
\(554\) 12.1649 + 12.1649i 0.516837 + 0.516837i
\(555\) −4.14775 7.18411i −0.176062 0.304948i
\(556\) 11.4575 19.8449i 0.485905 0.841613i
\(557\) 19.0951 5.11653i 0.809087 0.216794i 0.169517 0.985527i \(-0.445779\pi\)
0.639570 + 0.768733i \(0.279113\pi\)
\(558\) 0.481407 0.833822i 0.0203796 0.0352985i
\(559\) −16.1075 + 35.7298i −0.681275 + 1.51121i
\(560\) −15.1080 + 6.79977i −0.638428 + 0.287343i
\(561\) 8.70240 + 2.33180i 0.367416 + 0.0984487i
\(562\) −12.1234 −0.511394
\(563\) −18.4608 −0.778031 −0.389016 0.921231i \(-0.627185\pi\)
−0.389016 + 0.921231i \(0.627185\pi\)
\(564\) −2.76772 0.741609i −0.116542 0.0312274i
\(565\) 18.3940 68.6472i 0.773840 2.88801i
\(566\) 1.07388 + 4.00778i 0.0451386 + 0.168460i
\(567\) 0.938166 2.47383i 0.0393993 0.103891i
\(568\) 2.85924 4.95234i 0.119971 0.207796i
\(569\) 24.4291i 1.02412i −0.858949 0.512061i \(-0.828882\pi\)
0.858949 0.512061i \(-0.171118\pi\)
\(570\) −4.47562 16.7032i −0.187463 0.699621i
\(571\) −4.47758 + 2.58513i −0.187381 + 0.108184i −0.590756 0.806850i \(-0.701170\pi\)
0.403375 + 0.915035i \(0.367837\pi\)
\(572\) −14.2145 + 5.38068i −0.594337 + 0.224978i
\(573\) 21.3735i 0.892892i
\(574\) 3.05504 + 3.74165i 0.127515 + 0.156173i
\(575\) −34.7514 60.1912i −1.44923 2.51015i
\(576\) −0.533970 + 0.308288i −0.0222488 + 0.0128453i
\(577\) 3.87429 14.4591i 0.161289 0.601939i −0.837195 0.546904i \(-0.815806\pi\)
0.998484 0.0550348i \(-0.0175270\pi\)
\(578\) −2.70231 + 2.70231i −0.112401 + 0.112401i
\(579\) 8.98686 + 2.40802i 0.373481 + 0.100074i
\(580\) −17.1557 + 17.1557i −0.712350 + 0.712350i
\(581\) −1.47427 1.06205i −0.0611632 0.0440612i
\(582\) −4.35577 + 2.51480i −0.180552 + 0.104242i
\(583\) 14.8531 + 14.8531i 0.615153 + 0.615153i
\(584\) −3.04199 5.26888i −0.125878 0.218028i
\(585\) 9.02398 11.0383i 0.373096 0.456377i
\(586\) −6.77876 3.91372i −0.280028 0.161674i
\(587\) −6.32266 + 23.5965i −0.260964 + 0.973931i 0.703710 + 0.710487i \(0.251525\pi\)
−0.964675 + 0.263444i \(0.915141\pi\)
\(588\) −2.19221 + 10.7395i −0.0904052 + 0.442889i
\(589\) 8.39882 + 4.84906i 0.346068 + 0.199802i
\(590\) −0.400801 1.49581i −0.0165007 0.0615815i
\(591\) −2.08535 2.08535i −0.0857799 0.0857799i
\(592\) −2.34908 2.34908i −0.0965464 0.0965464i
\(593\) 10.0617 + 37.5507i 0.413184 + 1.54202i 0.788446 + 0.615105i \(0.210886\pi\)
−0.375262 + 0.926919i \(0.622447\pi\)
\(594\) 1.53616 + 0.886905i 0.0630296 + 0.0363901i
\(595\) 31.9281 14.3702i 1.30893 0.589119i
\(596\) 1.13841 4.24859i 0.0466309 0.174029i
\(597\) −4.89035 2.82344i −0.200149 0.115556i
\(598\) 9.82530 12.0185i 0.401787 0.491472i
\(599\) −9.62419 16.6696i −0.393234 0.681101i 0.599640 0.800270i \(-0.295310\pi\)
−0.992874 + 0.119169i \(0.961977\pi\)
\(600\) 17.6714 + 17.6714i 0.721433 + 0.721433i
\(601\) 29.6061 17.0931i 1.20766 0.697243i 0.245412 0.969419i \(-0.421077\pi\)
0.962247 + 0.272176i \(0.0877434\pi\)
\(602\) −17.2802 + 7.77742i −0.704287 + 0.316984i
\(603\) 2.33126 2.33126i 0.0949364 0.0949364i
\(604\) 12.7559 + 3.41794i 0.519031 + 0.139074i
\(605\) 10.4931 10.4931i 0.426606 0.426606i
\(606\) −2.31262 + 8.63083i −0.0939440 + 0.350604i
\(607\) −26.1668 + 15.1074i −1.06208 + 0.613191i −0.926006 0.377508i \(-0.876781\pi\)
−0.136071 + 0.990699i \(0.543448\pi\)
\(608\) −19.0562 33.0063i −0.772832 1.33858i
\(609\) 1.66310 + 10.2327i 0.0673920 + 0.414648i
\(610\) 14.2974i 0.578887i
\(611\) −6.17053 + 2.33576i −0.249633 + 0.0944949i
\(612\) −4.53826 + 2.62016i −0.183448 + 0.105914i
\(613\) −2.16481 8.07919i −0.0874360 0.326316i 0.908328 0.418258i \(-0.137359\pi\)
−0.995764 + 0.0919422i \(0.970692\pi\)
\(614\) 13.8760i 0.559990i
\(615\) −5.47847 + 9.48899i −0.220913 + 0.382633i
\(616\) −15.6473 5.93403i −0.630449 0.239089i
\(617\) −7.87008 29.3715i −0.316837 1.18245i −0.922267 0.386554i \(-0.873665\pi\)
0.605429 0.795899i \(-0.293002\pi\)
\(618\) 0.986436 3.68143i 0.0396803 0.148089i
\(619\) −8.20212 2.19775i −0.329671 0.0883351i 0.0901871 0.995925i \(-0.471253\pi\)
−0.419858 + 0.907590i \(0.637920\pi\)
\(620\) −9.04782 −0.363369
\(621\) 6.53430 0.262212
\(622\) −13.5266 3.62444i −0.542367 0.145327i
\(623\) −12.7016 + 17.6316i −0.508878 + 0.706393i
\(624\) 2.34658 5.20520i 0.0939385 0.208375i
\(625\) 17.4772 30.2714i 0.699089 1.21086i
\(626\) 3.28838 0.881119i 0.131430 0.0352166i
\(627\) −8.93351 + 15.4733i −0.356770 + 0.617944i
\(628\) 13.5967 + 23.5501i 0.542567 + 0.939753i
\(629\) 4.96437 + 4.96437i 0.197942 + 0.197942i
\(630\) 6.80423 1.10588i 0.271087 0.0440593i
\(631\) −32.0135 + 8.57800i −1.27444 + 0.341485i −0.831730 0.555180i \(-0.812649\pi\)
−0.442709 + 0.896665i \(0.645983\pi\)
\(632\) −30.5093 + 8.17494i −1.21359 + 0.325182i
\(633\) 8.72310i 0.346712i
\(634\) 3.61030 + 2.08441i 0.143383 + 0.0827825i
\(635\) −33.9449 + 33.9449i −1.34706 + 1.34706i
\(636\) −12.2179 −0.484470
\(637\) 10.3445 + 23.0215i 0.409865 + 0.912146i
\(638\) −6.95037 −0.275168
\(639\) 1.72100 1.72100i 0.0680819 0.0680819i
\(640\) 37.9396 + 21.9044i 1.49969 + 0.865849i
\(641\) 1.08742i 0.0429504i 0.999769 + 0.0214752i \(0.00683629\pi\)
−0.999769 + 0.0214752i \(0.993164\pi\)
\(642\) 4.30834 1.15442i 0.170036 0.0455611i
\(643\) 22.6036 6.05661i 0.891398 0.238849i 0.216080 0.976376i \(-0.430673\pi\)
0.675318 + 0.737526i \(0.264006\pi\)
\(644\) −26.7200 + 4.34276i −1.05292 + 0.171129i
\(645\) −30.3942 30.3942i −1.19677 1.19677i
\(646\) 7.31752 + 12.6743i 0.287904 + 0.498664i
\(647\) −2.47922 + 4.29413i −0.0974681 + 0.168820i −0.910636 0.413209i \(-0.864408\pi\)
0.813168 + 0.582029i \(0.197741\pi\)
\(648\) −2.26948 + 0.608106i −0.0891537 + 0.0238887i
\(649\) −0.800015 + 1.38567i −0.0314033 + 0.0543922i
\(650\) 24.9396 + 4.06907i 0.978213 + 0.159602i
\(651\) −2.25978 + 3.13689i −0.0885676 + 0.122944i
\(652\) 35.9173 + 9.62400i 1.40663 + 0.376905i
\(653\) −27.1187 −1.06124 −0.530619 0.847610i \(-0.678040\pi\)
−0.530619 + 0.847610i \(0.678040\pi\)
\(654\) 2.74358 0.107282
\(655\) 53.2567 + 14.2701i 2.08091 + 0.557578i
\(656\) −1.13568 + 4.23841i −0.0443408 + 0.165482i
\(657\) −0.670194 2.50120i −0.0261467 0.0975810i
\(658\) −2.98276 1.13117i −0.116280 0.0440977i
\(659\) 2.99955 5.19537i 0.116846 0.202383i −0.801670 0.597766i \(-0.796055\pi\)
0.918516 + 0.395384i \(0.129388\pi\)
\(660\) 16.6690i 0.648838i
\(661\) −6.77360 25.2794i −0.263463 0.983256i −0.963185 0.268841i \(-0.913359\pi\)
0.699722 0.714415i \(-0.253307\pi\)
\(662\) 3.12378 1.80351i 0.121409 0.0700955i
\(663\) −4.95910 + 11.0003i −0.192596 + 0.427217i
\(664\) 1.61356i 0.0626183i
\(665\) 11.1392 + 68.5368i 0.431959 + 2.65774i
\(666\) 0.691132 + 1.19708i 0.0267808 + 0.0463857i
\(667\) −22.1733 + 12.8018i −0.858554 + 0.495687i
\(668\) −8.55040 + 31.9105i −0.330825 + 1.23466i
\(669\) 7.12315 7.12315i 0.275397 0.275397i
\(670\) 8.29739 + 2.22328i 0.320556 + 0.0858927i
\(671\) 10.4457 10.4457i 0.403253 0.403253i
\(672\) 13.8546 6.23567i 0.534455 0.240546i
\(673\) −32.5368 + 18.7852i −1.25420 + 0.724114i −0.971941 0.235223i \(-0.924418\pi\)
−0.282262 + 0.959337i \(0.591085\pi\)
\(674\) 10.9817 + 10.9817i 0.423001 + 0.423001i
\(675\) 5.31831 + 9.21158i 0.204702 + 0.354554i
\(676\) −4.04682 19.9497i −0.155647 0.767297i
\(677\) 6.13983 + 3.54483i 0.235973 + 0.136239i 0.613324 0.789831i \(-0.289832\pi\)
−0.377352 + 0.926070i \(0.623165\pi\)
\(678\) −3.06495 + 11.4386i −0.117709 + 0.439295i
\(679\) 18.4165 8.28888i 0.706762 0.318098i
\(680\) −26.9273 15.5465i −1.03262 0.596181i
\(681\) −1.12923 4.21434i −0.0432721 0.161494i
\(682\) −1.83280 1.83280i −0.0701815 0.0701815i
\(683\) 0.0180371 + 0.0180371i 0.000690170 + 0.000690170i 0.707452 0.706762i \(-0.249845\pi\)
−0.706762 + 0.707452i \(0.749845\pi\)
\(684\) −2.68975 10.0383i −0.102845 0.383823i
\(685\) −53.3056 30.7760i −2.03670 1.17589i
\(686\) −3.63001 + 11.6506i −0.138594 + 0.444822i
\(687\) −4.36901 + 16.3054i −0.166688 + 0.622089i
\(688\) −14.9075 8.60687i −0.568344 0.328134i
\(689\) −22.8368 + 16.4301i −0.870013 + 0.625939i
\(690\) 8.51257 + 14.7442i 0.324068 + 0.561302i
\(691\) 8.23261 + 8.23261i 0.313183 + 0.313183i 0.846142 0.532958i \(-0.178920\pi\)
−0.532958 + 0.846142i \(0.678920\pi\)
\(692\) 21.6309 12.4886i 0.822284 0.474746i
\(693\) −5.77914 4.16322i −0.219531 0.158148i
\(694\) 7.93781 7.93781i 0.301315 0.301315i
\(695\) 55.8965 + 14.9774i 2.12027 + 0.568126i
\(696\) 6.50982 6.50982i 0.246754 0.246754i
\(697\) 2.40006 8.95716i 0.0909089 0.339276i
\(698\) 9.68030 5.58892i 0.366405 0.211544i
\(699\) 1.75654 + 3.04241i 0.0664384 + 0.115075i
\(700\) −27.8697 34.1333i −1.05337 1.29012i
\(701\) 23.4707i 0.886478i 0.896404 + 0.443239i \(0.146171\pi\)
−0.896404 + 0.443239i \(0.853829\pi\)
\(702\) −1.50365 + 1.83929i −0.0567516 + 0.0694196i
\(703\) −12.0578 + 6.96155i −0.454767 + 0.262560i
\(704\) 0.429605 + 1.60331i 0.0161914 + 0.0604270i
\(705\) 7.23602i 0.272524i
\(706\) −11.4356 + 19.8070i −0.430383 + 0.745445i
\(707\) 12.7224 33.5474i 0.478475 1.26168i
\(708\) −0.240873 0.898949i −0.00905255 0.0337846i
\(709\) 8.01632 29.9173i 0.301059 1.12357i −0.635225 0.772327i \(-0.719093\pi\)
0.936285 0.351242i \(-0.114241\pi\)
\(710\) 6.12537 + 1.64129i 0.229881 + 0.0615964i
\(711\) −13.4433 −0.504162
\(712\) 19.2974 0.723199
\(713\) −9.22286 2.47126i −0.345399 0.0925493i
\(714\) −5.32013 + 2.39447i −0.199101 + 0.0896110i
\(715\) −22.4158 31.1565i −0.838303 1.16519i
\(716\) 2.26199 3.91788i 0.0845344 0.146418i
\(717\) 20.5691 5.51148i 0.768168 0.205830i
\(718\) −5.50087 + 9.52778i −0.205291 + 0.355574i
\(719\) 9.21852 + 15.9669i 0.343793 + 0.595466i 0.985134 0.171790i \(-0.0549549\pi\)
−0.641341 + 0.767256i \(0.721622\pi\)
\(720\) 4.42790 + 4.42790i 0.165018 + 0.165018i
\(721\) −5.42666 + 14.3094i −0.202099 + 0.532912i
\(722\) −15.9421 + 4.27166i −0.593302 + 0.158975i
\(723\) 10.6221 2.84619i 0.395041 0.105851i
\(724\) 25.0809i 0.932125i
\(725\) −36.0940 20.8389i −1.34050 0.773936i
\(726\) −1.74845 + 1.74845i −0.0648911 + 0.0648911i
\(727\) 43.1639 1.60086 0.800430 0.599426i \(-0.204605\pi\)
0.800430 + 0.599426i \(0.204605\pi\)
\(728\) 11.2185 19.4035i 0.415785 0.719143i
\(729\) −1.00000 −0.0370370
\(730\) 4.77068 4.77068i 0.176571 0.176571i
\(731\) 31.5045 + 18.1892i 1.16524 + 0.672750i
\(732\) 8.59245i 0.317586i
\(733\) −3.91767 + 1.04974i −0.144702 + 0.0387729i −0.330443 0.943826i \(-0.607198\pi\)
0.185741 + 0.982599i \(0.440532\pi\)
\(734\) −2.49191 + 0.667706i −0.0919781 + 0.0246455i
\(735\) −27.6297 + 1.67196i −1.01914 + 0.0616712i
\(736\) 26.5330 + 26.5330i 0.978018 + 0.978018i
\(737\) −4.43775 7.68641i −0.163467 0.283133i
\(738\) 0.912868 1.58113i 0.0336031 0.0582023i
\(739\) −41.3654 + 11.0838i −1.52165 + 0.407725i −0.920285 0.391248i \(-0.872043\pi\)
−0.601366 + 0.798973i \(0.705377\pi\)
\(740\) 6.49475 11.2492i 0.238752 0.413530i
\(741\) −18.5266 15.1458i −0.680591 0.556394i
\(742\) −13.5335 1.36717i −0.496830 0.0501905i
\(743\) 28.2948 + 7.58157i 1.03804 + 0.278141i 0.737299 0.675567i \(-0.236101\pi\)
0.300736 + 0.953707i \(0.402768\pi\)
\(744\) 3.43325 0.125869
\(745\) 11.1076 0.406953
\(746\) 18.0896 + 4.84710i 0.662308 + 0.177465i
\(747\) −0.177745 + 0.663355i −0.00650336 + 0.0242709i
\(748\) 3.65125 + 13.6267i 0.133503 + 0.498240i
\(749\) −17.6780 + 2.87317i −0.645940 + 0.104984i
\(750\) −7.34310 + 12.7186i −0.268132 + 0.464419i
\(751\) 13.1918i 0.481377i −0.970602 0.240688i \(-0.922627\pi\)
0.970602 0.240688i \(-0.0773732\pi\)
\(752\) −0.750008 2.79907i −0.0273500 0.102072i
\(753\) 19.1018 11.0284i 0.696107 0.401897i
\(754\) 1.49897 9.18730i 0.0545893 0.334582i
\(755\) 33.3495i 1.21371i
\(756\) 4.08919 0.664609i 0.148722 0.0241716i
\(757\) 23.1688 + 40.1295i 0.842083 + 1.45853i 0.888130 + 0.459592i \(0.152004\pi\)
−0.0460469 + 0.998939i \(0.514662\pi\)
\(758\) 7.80336 4.50527i 0.283431 0.163639i
\(759\) 4.55284 16.9914i 0.165258 0.616750i
\(760\) 43.6018 43.6018i 1.58160 1.58160i
\(761\) 1.55165 + 0.415762i 0.0562471 + 0.0150714i 0.286833 0.957981i \(-0.407398\pi\)
−0.230586 + 0.973052i \(0.574064\pi\)
\(762\) 5.65619 5.65619i 0.204902 0.204902i
\(763\) −10.9608 1.10728i −0.396807 0.0400861i
\(764\) 28.9839 16.7339i 1.04860 0.605410i
\(765\) −9.35761 9.35761i −0.338325 0.338325i
\(766\) 9.99826 + 17.3175i 0.361252 + 0.625706i
\(767\) −1.65910 1.35634i −0.0599065 0.0489745i
\(768\) −7.38975 4.26648i −0.266655 0.153953i
\(769\) −3.99954 + 14.9265i −0.144227 + 0.538263i 0.855562 + 0.517701i \(0.173212\pi\)
−0.999789 + 0.0205616i \(0.993455\pi\)
\(770\) 1.86525 18.4639i 0.0672188 0.665391i
\(771\) 5.75030 + 3.31994i 0.207092 + 0.119565i
\(772\) 3.77060 + 14.0721i 0.135707 + 0.506465i
\(773\) 12.2384 + 12.2384i 0.440185 + 0.440185i 0.892074 0.451889i \(-0.149250\pi\)
−0.451889 + 0.892074i \(0.649250\pi\)
\(774\) 5.06453 + 5.06453i 0.182041 + 0.182041i
\(775\) −4.02274 15.0131i −0.144501 0.539286i
\(776\) −15.5320 8.96741i −0.557567 0.321911i
\(777\) −2.27799 5.06133i −0.0817226 0.181574i
\(778\) −3.11976 + 11.6431i −0.111849 + 0.417426i
\(779\) 15.9263 + 9.19503i 0.570617 + 0.329446i
\(780\) 22.0337 + 3.59496i 0.788934 + 0.128720i
\(781\) −3.27608 5.67433i −0.117227 0.203043i
\(782\) −10.1886 10.1886i −0.364342 0.364342i
\(783\) 3.39337 1.95916i 0.121269 0.0700148i
\(784\) −10.5145 + 3.51055i −0.375519 + 0.125377i
\(785\) −48.5590 + 48.5590i −1.73314 + 1.73314i
\(786\) −8.87407 2.37780i −0.316528 0.0848133i
\(787\) 10.1433 10.1433i 0.361569 0.361569i −0.502821 0.864390i \(-0.667705\pi\)
0.864390 + 0.502821i \(0.167705\pi\)
\(788\) 1.19520 4.46054i 0.0425772 0.158900i
\(789\) −0.911126 + 0.526039i −0.0324369 + 0.0187275i
\(790\) −17.5132 30.3338i −0.623093 1.07923i
\(791\) 16.8612 44.4608i 0.599514 1.58085i
\(792\) 6.32514i 0.224754i
\(793\) 11.5548 + 16.0604i 0.410323 + 0.570323i
\(794\) −1.32377 + 0.764279i −0.0469788 + 0.0271232i
\(795\) −7.98570 29.8030i −0.283224 1.05700i
\(796\) 8.84218i 0.313403i
\(797\) −25.7962 + 44.6803i −0.913747 + 1.58266i −0.105022 + 0.994470i \(0.533491\pi\)
−0.808725 + 0.588187i \(0.799842\pi\)
\(798\) −1.85610 11.4202i −0.0657053 0.404270i
\(799\) 1.58501 + 5.91536i 0.0560738 + 0.209270i
\(800\) −15.8089 + 58.9996i −0.558928 + 2.08595i
\(801\) 7.93338 + 2.12574i 0.280312 + 0.0751095i
\(802\) −8.85586 −0.312711
\(803\) −6.97094 −0.245999
\(804\) 4.98655 + 1.33614i 0.175862 + 0.0471221i
\(805\) −28.0577 62.3396i −0.988904 2.19718i
\(806\) 2.81795 2.02740i 0.0992580 0.0714120i
\(807\) 3.49090 6.04641i 0.122885 0.212844i
\(808\) −30.7763 + 8.24647i −1.08270 + 0.290110i
\(809\) −1.14846 + 1.98918i −0.0403776 + 0.0699360i −0.885508 0.464624i \(-0.846189\pi\)
0.845130 + 0.534560i \(0.179523\pi\)
\(810\) −1.30275 2.25643i −0.0457740 0.0792829i
\(811\) 8.78392 + 8.78392i 0.308445 + 0.308445i 0.844306 0.535861i \(-0.180013\pi\)
−0.535861 + 0.844306i \(0.680013\pi\)
\(812\) −12.5741 + 10.2667i −0.441263 + 0.360289i
\(813\) 24.4480 6.55082i 0.857428 0.229747i
\(814\) 3.59436 0.963106i 0.125982 0.0337568i
\(815\) 93.9033i 3.28929i
\(816\) −4.58966 2.64984i −0.160670 0.0927629i
\(817\) −51.0134 + 51.0134i −1.78473 + 1.78473i
\(818\) −13.4850 −0.471492
\(819\) 6.74950 6.74124i 0.235847 0.235558i
\(820\) −17.1569 −0.599145
\(821\) −22.8312 + 22.8312i −0.796816 + 0.796816i −0.982592 0.185776i \(-0.940520\pi\)
0.185776 + 0.982592i \(0.440520\pi\)
\(822\) 8.88222 + 5.12815i 0.309803 + 0.178865i
\(823\) 11.3716i 0.396388i −0.980163 0.198194i \(-0.936492\pi\)
0.980163 0.198194i \(-0.0635077\pi\)
\(824\) 13.1274 3.51748i 0.457315 0.122537i
\(825\) 27.6588 7.41116i 0.962957 0.258024i
\(826\) −0.166218 1.02270i −0.00578346 0.0355843i
\(827\) −20.9552 20.9552i −0.728685 0.728685i 0.241673 0.970358i \(-0.422304\pi\)
−0.970358 + 0.241673i \(0.922304\pi\)
\(828\) 5.11587 + 8.86094i 0.177789 + 0.307939i
\(829\) −18.1000 + 31.3501i −0.628638 + 1.08883i 0.359188 + 0.933265i \(0.383054\pi\)
−0.987825 + 0.155567i \(0.950280\pi\)
\(830\) −1.72837 + 0.463116i −0.0599927 + 0.0160750i
\(831\) −13.0549 + 22.6117i −0.452869 + 0.784392i
\(832\) −2.21197 + 0.222089i −0.0766864 + 0.00769954i
\(833\) 22.2207 7.41895i 0.769900 0.257051i
\(834\) −9.31393 2.49566i −0.322515 0.0864177i
\(835\) −83.4279 −2.88714
\(836\) −27.9771 −0.967607
\(837\) 1.41145 + 0.378198i 0.0487870 + 0.0130724i
\(838\) −4.98010 + 18.5860i −0.172035 + 0.642043i
\(839\) 2.14726 + 8.01368i 0.0741316 + 0.276663i 0.993035 0.117820i \(-0.0375905\pi\)
−0.918903 + 0.394483i \(0.870924\pi\)
\(840\) 15.5465 + 19.0405i 0.536406 + 0.656961i
\(841\) 6.82335 11.8184i 0.235288 0.407531i
\(842\) 25.3761i 0.874519i
\(843\) −4.76211 17.7724i −0.164016 0.612115i
\(844\) −11.8291 + 6.82953i −0.407174 + 0.235082i
\(845\) 46.0183 22.9107i 1.58308 0.788152i
\(846\) 1.20573i 0.0414537i
\(847\) 7.69084 6.27953i 0.264260 0.215767i
\(848\) −6.17812 10.7008i −0.212158 0.367468i
\(849\) −5.45344 + 3.14855i −0.187162 + 0.108058i
\(850\) 6.07055 22.6556i 0.208218 0.777081i
\(851\) 9.69293 9.69293i 0.332269 0.332269i
\(852\) 3.68121 + 0.986378i 0.126116 + 0.0337927i
\(853\) −0.875083 + 0.875083i −0.0299623 + 0.0299623i −0.721929 0.691967i \(-0.756744\pi\)
0.691967 + 0.721929i \(0.256744\pi\)
\(854\) −0.961491 + 9.51769i −0.0329015 + 0.325689i
\(855\) 22.7283 13.1222i 0.777292 0.448770i
\(856\) 11.2464 + 11.2464i 0.384394 + 0.384394i
\(857\) 1.31117 + 2.27101i 0.0447886 + 0.0775761i 0.887551 0.460710i \(-0.152405\pi\)
−0.842762 + 0.538286i \(0.819072\pi\)
\(858\) 3.73511 + 5.19155i 0.127514 + 0.177237i
\(859\) 6.83308 + 3.94508i 0.233142 + 0.134605i 0.612021 0.790842i \(-0.290357\pi\)
−0.378879 + 0.925446i \(0.623690\pi\)
\(860\) 17.4201 65.0128i 0.594022 2.21692i
\(861\) −4.28509 + 5.94831i −0.146036 + 0.202718i
\(862\) −4.90191 2.83012i −0.166960 0.0963943i
\(863\) 5.89346 + 21.9947i 0.200616 + 0.748708i 0.990741 + 0.135763i \(0.0433485\pi\)
−0.790126 + 0.612945i \(0.789985\pi\)
\(864\) −4.06057 4.06057i −0.138143 0.138143i
\(865\) 44.6016 + 44.6016i 1.51650 + 1.51650i
\(866\) 2.59747 + 9.69389i 0.0882656 + 0.329412i
\(867\) −5.02297 2.90001i −0.170589 0.0984896i
\(868\) −6.02306 0.608458i −0.204436 0.0206524i
\(869\) −9.36674 + 34.9571i −0.317745 + 1.18584i
\(870\) 8.84144 + 5.10461i 0.299753 + 0.173062i
\(871\) 11.1173 4.20830i 0.376696 0.142593i
\(872\) 4.89160 + 8.47249i 0.165650 + 0.286915i
\(873\) −5.39758 5.39758i −0.182680 0.182680i
\(874\) 24.7466 14.2874i 0.837065 0.483280i
\(875\) 34.4693 47.8482i 1.16527 1.61756i
\(876\) 2.86708 2.86708i 0.0968695 0.0968695i
\(877\) 37.1561 + 9.95594i 1.25467 + 0.336188i 0.824139 0.566387i \(-0.191659\pi\)
0.430532 + 0.902575i \(0.358326\pi\)
\(878\) −1.33543 + 1.33543i −0.0450686 + 0.0450686i
\(879\) 3.07465 11.4748i 0.103705 0.387034i
\(880\) 14.5992 8.42887i 0.492140 0.284137i
\(881\) −20.4737 35.4615i −0.689777 1.19473i −0.971910 0.235354i \(-0.924375\pi\)
0.282133 0.959375i \(-0.408958\pi\)
\(882\) 4.60388 0.278596i 0.155021 0.00938081i
\(883\) 2.58549i 0.0870086i −0.999053 0.0435043i \(-0.986148\pi\)
0.999053 0.0435043i \(-0.0138522\pi\)
\(884\) −18.7998 + 1.88755i −0.632304 + 0.0634852i
\(885\) 2.03537 1.17512i 0.0684182 0.0395013i
\(886\) −3.58670 13.3858i −0.120498 0.449703i
\(887\) 58.2818i 1.95691i −0.206456 0.978456i \(-0.566193\pi\)
0.206456 0.978456i \(-0.433807\pi\)
\(888\) −2.46447 + 4.26859i −0.0827023 + 0.143245i
\(889\) −24.8796 + 20.3141i −0.834435 + 0.681312i
\(890\) 5.53863 + 20.6704i 0.185655 + 0.692875i
\(891\) −0.696760 + 2.60034i −0.0233423 + 0.0871148i
\(892\) 15.2363 + 4.08257i 0.510151 + 0.136694i
\(893\) −12.1449 −0.406413
\(894\) −1.85085 −0.0619016
\(895\) 11.0353 + 2.95691i 0.368870 + 0.0988385i
\(896\) 23.7830 + 17.1330i 0.794535 + 0.572373i
\(897\) 21.4781 + 9.68264i 0.717133 + 0.323294i
\(898\) 2.09964 3.63668i 0.0700658 0.121358i
\(899\) −5.53054 + 1.48190i −0.184454 + 0.0494242i
\(900\) −8.32767 + 14.4239i −0.277589 + 0.480798i
\(901\) 13.0564 + 22.6144i 0.434972 + 0.753394i
\(902\) −3.47544 3.47544i −0.115720 0.115720i
\(903\) −18.1892 22.2771i −0.605297 0.741336i
\(904\) −40.7882 + 10.9292i −1.35660 + 0.363499i
\(905\) −61.1799 + 16.3931i −2.03369 + 0.544925i
\(906\) 5.55697i 0.184618i
\(907\) −31.6596 18.2787i −1.05124 0.606934i −0.128244 0.991743i \(-0.540934\pi\)
−0.922996 + 0.384809i \(0.874267\pi\)
\(908\) 4.83081 4.83081i 0.160316 0.160316i
\(909\) −13.5609 −0.449787
\(910\) 24.0041 + 6.44762i 0.795727 + 0.213737i
\(911\) −0.732987 −0.0242849 −0.0121425 0.999926i \(-0.503865\pi\)
−0.0121425 + 0.999926i \(0.503865\pi\)
\(912\) 7.43175 7.43175i 0.246090 0.246090i
\(913\) 1.60110 + 0.924398i 0.0529888 + 0.0305931i
\(914\) 10.5446i 0.348784i
\(915\) −20.9596 + 5.61610i −0.692902 + 0.185662i
\(916\) −25.5318 + 6.84122i −0.843594 + 0.226040i
\(917\) 34.4929 + 13.0809i 1.13905 + 0.431971i
\(918\) 1.55924 + 1.55924i 0.0514627 + 0.0514627i
\(919\) −16.5464 28.6593i −0.545817 0.945382i −0.998555 0.0537388i \(-0.982886\pi\)
0.452738 0.891643i \(-0.350447\pi\)
\(920\) −30.3545 + 52.5756i −1.00076 + 1.73337i
\(921\) 20.3417 5.45055i 0.670283 0.179602i
\(922\) 10.2249 17.7100i 0.336739 0.583249i
\(923\) 8.20712 3.10669i 0.270141 0.102258i
\(924\) 1.12097 11.0964i 0.0368773 0.365044i
\(925\) 21.5535 + 5.77524i 0.708675 + 0.189889i
\(926\) −2.05058 −0.0673864
\(927\) 5.78432 0.189982
\(928\) 21.7343 + 5.82370i 0.713464 + 0.191172i
\(929\) −1.90230 + 7.09947i −0.0624123 + 0.232926i −0.990085 0.140468i \(-0.955139\pi\)
0.927673 + 0.373394i \(0.121806\pi\)
\(930\) 0.985395 + 3.67754i 0.0323124 + 0.120591i
\(931\) 2.80621 + 46.3735i 0.0919697 + 1.51983i
\(932\) −2.75048 + 4.76396i −0.0900948 + 0.156049i
\(933\) 21.2532i 0.695799i
\(934\) 0.770423 + 2.87526i 0.0252090 + 0.0940814i
\(935\) −30.8530 + 17.8130i −1.00900 + 0.582547i
\(936\) −8.36084 1.36413i −0.273283 0.0445879i
\(937\) 47.7381i 1.55954i −0.626068 0.779768i \(-0.715337\pi\)
0.626068 0.779768i \(-0.284663\pi\)
\(938\) 5.37399 + 2.03801i 0.175467 + 0.0665434i
\(939\) 2.58338 + 4.47455i 0.0843054 + 0.146021i
\(940\) 9.81252 5.66526i 0.320049 0.184780i
\(941\) 9.60732 35.8550i 0.313190 1.16884i −0.612473 0.790491i \(-0.709825\pi\)
0.925663 0.378349i \(-0.123508\pi\)
\(942\) 8.09130 8.09130i 0.263629 0.263629i
\(943\) −17.4888 4.68612i −0.569515 0.152601i
\(944\) 0.665530 0.665530i 0.0216611 0.0216611i
\(945\) 4.29391 + 9.54037i 0.139681 + 0.310348i
\(946\) 16.6983 9.64075i 0.542908 0.313448i
\(947\) −4.69464 4.69464i −0.152555 0.152555i 0.626703 0.779258i \(-0.284404\pi\)
−0.779258 + 0.626703i \(0.784404\pi\)
\(948\) −10.5251 18.2300i −0.341839 0.592082i
\(949\) 1.50341 9.21448i 0.0488026 0.299115i
\(950\) 40.2828 + 23.2573i 1.30695 + 0.754565i
\(951\) −1.63753 + 6.11134i −0.0531005 + 0.198174i
\(952\) −16.8798 12.1600i −0.547078 0.394108i
\(953\) 17.6451 + 10.1874i 0.571581 + 0.330003i 0.757781 0.652509i \(-0.226284\pi\)
−0.186199 + 0.982512i \(0.559617\pi\)
\(954\) 1.33064 + 4.96603i 0.0430812 + 0.160781i
\(955\) 59.7630 + 59.7630i 1.93389 + 1.93389i
\(956\) 23.5780 + 23.5780i 0.762567 + 0.762567i
\(957\) −2.73013 10.1890i −0.0882527 0.329364i
\(958\) 17.7786 + 10.2645i 0.574400 + 0.331630i
\(959\) −33.4154 24.0721i −1.07904 0.777327i
\(960\) 0.631036 2.35506i 0.0203666 0.0760091i
\(961\) 24.9976 + 14.4324i 0.806375 + 0.465561i
\(962\) 0.497887 + 4.95889i 0.0160525 + 0.159881i
\(963\) 3.38467 + 5.86241i 0.109069 + 0.188914i
\(964\) 12.1760 + 12.1760i 0.392161 + 0.392161i
\(965\) −31.8615 + 18.3952i −1.02566 + 0.592164i
\(966\) 4.67521 + 10.3875i 0.150422 + 0.334214i
\(967\) −20.9933 + 20.9933i −0.675099 + 0.675099i −0.958887 0.283788i \(-0.908409\pi\)
0.283788 + 0.958887i \(0.408409\pi\)
\(968\) −8.51678 2.28206i −0.273740 0.0733483i
\(969\) −15.7058 + 15.7058i −0.504541 + 0.504541i
\(970\) 5.14756 19.2110i 0.165278 0.616827i
\(971\) 33.4886 19.3346i 1.07470 0.620478i 0.145237 0.989397i \(-0.453605\pi\)
0.929461 + 0.368919i \(0.120272\pi\)
\(972\) −0.782925 1.35607i −0.0251123 0.0434958i
\(973\) 36.2026 + 13.7293i 1.16060 + 0.440142i
\(974\) 6.31428i 0.202323i
\(975\) 3.83127 + 38.1590i 0.122699 + 1.22207i
\(976\) −7.52556 + 4.34488i −0.240887 + 0.139076i
\(977\) −14.6444 54.6538i −0.468517 1.74853i −0.644959 0.764217i \(-0.723125\pi\)
0.176442 0.984311i \(-0.443541\pi\)
\(978\) 15.6469i 0.500334i
\(979\) 11.0553 19.1484i 0.353330 0.611985i
\(980\) −23.8992 36.1586i −0.763433 1.15504i
\(981\) 1.07769 + 4.02199i 0.0344080 + 0.128412i
\(982\) −0.0809967 + 0.302284i −0.00258471 + 0.00964626i
\(983\) 20.3918 + 5.46396i 0.650396 + 0.174273i 0.568908 0.822401i \(-0.307366\pi\)
0.0814882 + 0.996674i \(0.474033\pi\)
\(984\) 6.51030 0.207541
\(985\) 11.6618 0.371576
\(986\) −8.34590 2.23628i −0.265788 0.0712176i
\(987\) 0.486616 4.81696i 0.0154892 0.153325i
\(988\) 6.03375 36.9813i 0.191959 1.17653i
\(989\) 35.5143 61.5125i 1.12929 1.95599i
\(990\) −6.77520 + 1.81541i −0.215330 + 0.0576975i
\(991\) −18.0056 + 31.1866i −0.571967 + 0.990676i 0.424397 + 0.905476i \(0.360486\pi\)
−0.996364 + 0.0851997i \(0.972847\pi\)
\(992\) 4.19560 + 7.26700i 0.133211 + 0.230727i
\(993\) 3.87092 + 3.87092i 0.122840 + 0.122840i
\(994\) 3.96723 + 1.50452i 0.125833 + 0.0477204i
\(995\) 21.5687 5.77932i 0.683774 0.183217i
\(996\) −1.03871 + 0.278322i −0.0329129 + 0.00881898i
\(997\) 32.6185i 1.03304i −0.856275 0.516520i \(-0.827227\pi\)
0.856275 0.516520i \(-0.172773\pi\)
\(998\) −2.01871 1.16550i −0.0639011 0.0368933i
\(999\) −1.48339 + 1.48339i −0.0469324 + 0.0469324i
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 273.2.bt.b.145.6 40
3.2 odd 2 819.2.et.d.145.5 40
7.3 odd 6 273.2.cg.b.262.6 yes 40
13.7 odd 12 273.2.cg.b.124.6 yes 40
21.17 even 6 819.2.gh.d.262.5 40
39.20 even 12 819.2.gh.d.397.5 40
91.59 even 12 inner 273.2.bt.b.241.6 yes 40
273.59 odd 12 819.2.et.d.514.5 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bt.b.145.6 40 1.1 even 1 trivial
273.2.bt.b.241.6 yes 40 91.59 even 12 inner
273.2.cg.b.124.6 yes 40 13.7 odd 12
273.2.cg.b.262.6 yes 40 7.3 odd 6
819.2.et.d.145.5 40 3.2 odd 2
819.2.et.d.514.5 40 273.59 odd 12
819.2.gh.d.262.5 40 21.17 even 6
819.2.gh.d.397.5 40 39.20 even 12