Properties

Label 546.2.by.b.397.1
Level $546$
Weight $2$
Character 546.397
Analytic conductor $4.360$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(19,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.by (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: \(4.35983195036\)
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 397.1
Character \(\chi\) \(=\) 546.397
Dual form 546.2.by.b.535.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.13407 - 4.23240i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(0.0297166 + 2.64558i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.13407 - 4.23240i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(0.0297166 + 2.64558i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +4.38171 q^{10} +(-2.28221 + 2.28221i) q^{11} +(0.500000 - 0.866025i) q^{12} +(2.90215 + 2.13951i) q^{13} +(-2.56313 - 0.656024i) q^{14} +(4.23240 - 1.13407i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.17072 + 5.49185i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-3.82276 + 3.82276i) q^{19} +(-1.13407 + 4.23240i) q^{20} +(-2.64558 + 0.0297166i) q^{21} +(-1.61377 - 2.79513i) q^{22} +(1.71950 - 0.992755i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-12.2970 + 7.09968i) q^{25} +(-2.81774 + 2.24952i) q^{26} -1.00000i q^{27} +(1.29706 - 2.30600i) q^{28} +(-1.73874 + 3.01158i) q^{29} +4.38171i q^{30} +(8.25065 + 2.21076i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-2.28221 - 2.28221i) q^{33} +(-4.48408 - 4.48408i) q^{34} +(11.1635 - 3.12605i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-0.173808 - 0.0465718i) q^{37} +(-2.70310 - 4.68191i) q^{38} +(-2.13951 + 2.90215i) q^{39} +(-3.79467 - 2.19085i) q^{40} +(0.00297886 + 0.0111173i) q^{41} +(0.656024 - 2.56313i) q^{42} +(-2.69459 + 1.55572i) q^{43} +(3.11756 - 0.835348i) q^{44} +(1.13407 + 4.23240i) q^{45} +(0.513888 + 1.91786i) q^{46} +(3.71124 - 0.994423i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-6.99823 + 0.157236i) q^{49} +(-3.67507 - 13.7155i) q^{50} +(-5.49185 - 3.17072i) q^{51} +(-1.44358 - 3.30395i) q^{52} +(-6.19883 - 10.7367i) q^{53} +(0.965926 + 0.258819i) q^{54} +(12.2474 + 7.07106i) q^{55} +(1.89172 + 1.84970i) q^{56} +(-3.82276 - 3.82276i) q^{57} +(-2.45895 - 2.45895i) q^{58} +(6.22342 - 1.66756i) q^{59} +(-4.23240 - 1.13407i) q^{60} +5.70985i q^{61} +(-4.27085 + 7.39733i) q^{62} +(-0.0297166 - 2.64558i) q^{63} -1.00000i q^{64} +(5.76403 - 14.7094i) q^{65} +(2.79513 - 1.61377i) q^{66} +(-3.75578 - 3.75578i) q^{67} +(5.49185 - 3.17072i) q^{68} +(0.992755 + 1.71950i) q^{69} +(0.130210 + 11.5922i) q^{70} +(1.61017 - 6.00925i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(0.931045 - 3.47471i) q^{73} +(0.0899699 - 0.155832i) q^{74} +(-7.09968 - 12.2970i) q^{75} +(5.22199 - 1.39923i) q^{76} +(-6.10560 - 5.96997i) q^{77} +(-2.24952 - 2.81774i) q^{78} +(-7.63746 + 13.2285i) q^{79} +(3.09834 - 3.09834i) q^{80} +1.00000 q^{81} -0.0115094 q^{82} +(1.17696 - 1.17696i) q^{83} +(2.30600 + 1.29706i) q^{84} +(26.8396 + 7.19164i) q^{85} +(-0.805301 - 3.00543i) q^{86} +(-3.01158 - 1.73874i) q^{87} +3.22754i q^{88} +(-4.61404 + 17.2198i) q^{89} -4.38171 q^{90} +(-5.57401 + 7.74147i) q^{91} -1.98551 q^{92} +(-2.21076 + 8.25065i) q^{93} +3.84215i q^{94} +(20.5148 + 11.8442i) q^{95} +(-0.258819 - 0.965926i) q^{96} +(-2.25048 - 0.603015i) q^{97} +(1.65940 - 6.80047i) q^{98} +(2.28221 - 2.28221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 + 0.965926i −0.183013 + 0.683013i
\(3\) 1.00000i 0.577350i
\(4\) −0.866025 0.500000i −0.433013 0.250000i
\(5\) −1.13407 4.23240i −0.507171 1.89279i −0.446848 0.894610i \(-0.647453\pi\)
−0.0603236 0.998179i \(-0.519213\pi\)
\(6\) −0.965926 0.258819i −0.394338 0.105662i
\(7\) 0.0297166 + 2.64558i 0.0112318 + 0.999937i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −1.00000 −0.333333
\(10\) 4.38171 1.38562
\(11\) −2.28221 + 2.28221i −0.688113 + 0.688113i −0.961815 0.273702i \(-0.911752\pi\)
0.273702 + 0.961815i \(0.411752\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 2.90215 + 2.13951i 0.804913 + 0.593393i
\(14\) −2.56313 0.656024i −0.685025 0.175330i
\(15\) 4.23240 1.13407i 1.09280 0.292815i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −3.17072 + 5.49185i −0.769013 + 1.33197i 0.169085 + 0.985601i \(0.445919\pi\)
−0.938098 + 0.346369i \(0.887415\pi\)
\(18\) 0.258819 0.965926i 0.0610042 0.227671i
\(19\) −3.82276 + 3.82276i −0.877002 + 0.877002i −0.993223 0.116221i \(-0.962922\pi\)
0.116221 + 0.993223i \(0.462922\pi\)
\(20\) −1.13407 + 4.23240i −0.253586 + 0.946394i
\(21\) −2.64558 + 0.0297166i −0.577314 + 0.00648470i
\(22\) −1.61377 2.79513i −0.344056 0.595923i
\(23\) 1.71950 0.992755i 0.358541 0.207004i −0.309900 0.950769i \(-0.600295\pi\)
0.668441 + 0.743766i \(0.266962\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) −12.2970 + 7.09968i −2.45940 + 1.41994i
\(26\) −2.81774 + 2.24952i −0.552604 + 0.441167i
\(27\) 1.00000i 0.192450i
\(28\) 1.29706 2.30600i 0.245121 0.435793i
\(29\) −1.73874 + 3.01158i −0.322876 + 0.559237i −0.981080 0.193602i \(-0.937983\pi\)
0.658204 + 0.752839i \(0.271316\pi\)
\(30\) 4.38171i 0.799987i
\(31\) 8.25065 + 2.21076i 1.48186 + 0.397063i 0.906980 0.421174i \(-0.138382\pi\)
0.574881 + 0.818237i \(0.305048\pi\)
\(32\) −0.965926 + 0.258819i −0.170753 + 0.0457532i
\(33\) −2.28221 2.28221i −0.397282 0.397282i
\(34\) −4.48408 4.48408i −0.769013 0.769013i
\(35\) 11.1635 3.12605i 1.88697 0.528399i
\(36\) 0.866025 + 0.500000i 0.144338 + 0.0833333i
\(37\) −0.173808 0.0465718i −0.0285739 0.00765636i 0.244504 0.969648i \(-0.421375\pi\)
−0.273078 + 0.961992i \(0.588042\pi\)
\(38\) −2.70310 4.68191i −0.438501 0.759506i
\(39\) −2.13951 + 2.90215i −0.342596 + 0.464717i
\(40\) −3.79467 2.19085i −0.599990 0.346404i
\(41\) 0.00297886 + 0.0111173i 0.000465220 + 0.00173623i 0.966158 0.257951i \(-0.0830473\pi\)
−0.965693 + 0.259687i \(0.916381\pi\)
\(42\) 0.656024 2.56313i 0.101227 0.395499i
\(43\) −2.69459 + 1.55572i −0.410921 + 0.237245i −0.691185 0.722677i \(-0.742911\pi\)
0.280264 + 0.959923i \(0.409578\pi\)
\(44\) 3.11756 0.835348i 0.469990 0.125933i
\(45\) 1.13407 + 4.23240i 0.169057 + 0.630930i
\(46\) 0.513888 + 1.91786i 0.0757687 + 0.282772i
\(47\) 3.71124 0.994423i 0.541339 0.145051i 0.0222199 0.999753i \(-0.492927\pi\)
0.519120 + 0.854702i \(0.326260\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) −6.99823 + 0.157236i −0.999748 + 0.0224622i
\(50\) −3.67507 13.7155i −0.519733 1.93967i
\(51\) −5.49185 3.17072i −0.769013 0.443990i
\(52\) −1.44358 3.30395i −0.200189 0.458175i
\(53\) −6.19883 10.7367i −0.851475 1.47480i −0.879877 0.475202i \(-0.842375\pi\)
0.0284016 0.999597i \(-0.490958\pi\)
\(54\) 0.965926 + 0.258819i 0.131446 + 0.0352208i
\(55\) 12.2474 + 7.07106i 1.65144 + 0.953461i
\(56\) 1.89172 + 1.84970i 0.252792 + 0.247176i
\(57\) −3.82276 3.82276i −0.506337 0.506337i
\(58\) −2.45895 2.45895i −0.322876 0.322876i
\(59\) 6.22342 1.66756i 0.810220 0.217098i 0.170154 0.985418i \(-0.445574\pi\)
0.640066 + 0.768320i \(0.278907\pi\)
\(60\) −4.23240 1.13407i −0.546401 0.146408i
\(61\) 5.70985i 0.731071i 0.930797 + 0.365535i \(0.119114\pi\)
−0.930797 + 0.365535i \(0.880886\pi\)
\(62\) −4.27085 + 7.39733i −0.542399 + 0.939462i
\(63\) −0.0297166 2.64558i −0.00374394 0.333312i
\(64\) 1.00000i 0.125000i
\(65\) 5.76403 14.7094i 0.714940 1.82448i
\(66\) 2.79513 1.61377i 0.344056 0.198641i
\(67\) −3.75578 3.75578i −0.458842 0.458842i 0.439433 0.898275i \(-0.355179\pi\)
−0.898275 + 0.439433i \(0.855179\pi\)
\(68\) 5.49185 3.17072i 0.665985 0.384507i
\(69\) 0.992755 + 1.71950i 0.119514 + 0.207004i
\(70\) 0.130210 + 11.5922i 0.0155630 + 1.38553i
\(71\) 1.61017 6.00925i 0.191092 0.713167i −0.802151 0.597121i \(-0.796311\pi\)
0.993244 0.116046i \(-0.0370220\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) 0.931045 3.47471i 0.108971 0.406684i −0.889795 0.456361i \(-0.849153\pi\)
0.998765 + 0.0496772i \(0.0158193\pi\)
\(74\) 0.0899699 0.155832i 0.0104588 0.0181151i
\(75\) −7.09968 12.2970i −0.819801 1.41994i
\(76\) 5.22199 1.39923i 0.599004 0.160503i
\(77\) −6.10560 5.96997i −0.695798 0.680341i
\(78\) −2.24952 2.81774i −0.254708 0.319046i
\(79\) −7.63746 + 13.2285i −0.859282 + 1.48832i 0.0133334 + 0.999911i \(0.495756\pi\)
−0.872615 + 0.488408i \(0.837578\pi\)
\(80\) 3.09834 3.09834i 0.346404 0.346404i
\(81\) 1.00000 0.111111
\(82\) −0.0115094 −0.00127101
\(83\) 1.17696 1.17696i 0.129188 0.129188i −0.639556 0.768744i \(-0.720882\pi\)
0.768744 + 0.639556i \(0.220882\pi\)
\(84\) 2.30600 + 1.29706i 0.251605 + 0.141521i
\(85\) 26.8396 + 7.19164i 2.91116 + 0.780043i
\(86\) −0.805301 3.00543i −0.0868379 0.324083i
\(87\) −3.01158 1.73874i −0.322876 0.186412i
\(88\) 3.22754i 0.344056i
\(89\) −4.61404 + 17.2198i −0.489088 + 1.82530i 0.0718142 + 0.997418i \(0.477121\pi\)
−0.560902 + 0.827882i \(0.689546\pi\)
\(90\) −4.38171 −0.461873
\(91\) −5.57401 + 7.74147i −0.584315 + 0.811527i
\(92\) −1.98551 −0.207004
\(93\) −2.21076 + 8.25065i −0.229245 + 0.855553i
\(94\) 3.84215i 0.396288i
\(95\) 20.5148 + 11.8442i 2.10477 + 1.21519i
\(96\) −0.258819 0.965926i −0.0264156 0.0985844i
\(97\) −2.25048 0.603015i −0.228502 0.0612269i 0.142751 0.989759i \(-0.454405\pi\)
−0.371253 + 0.928532i \(0.621072\pi\)
\(98\) 1.65940 6.80047i 0.167625 0.686951i
\(99\) 2.28221 2.28221i 0.229371 0.229371i
\(100\) 14.1994 1.41994
\(101\) −8.32192 −0.828062 −0.414031 0.910263i \(-0.635879\pi\)
−0.414031 + 0.910263i \(0.635879\pi\)
\(102\) 4.48408 4.48408i 0.443990 0.443990i
\(103\) −1.19202 + 2.06463i −0.117453 + 0.203434i −0.918758 0.394822i \(-0.870806\pi\)
0.801305 + 0.598256i \(0.204140\pi\)
\(104\) 3.56499 0.539271i 0.349576 0.0528798i
\(105\) 3.12605 + 11.1635i 0.305071 + 1.08944i
\(106\) 11.9752 3.20875i 1.16314 0.311662i
\(107\) 2.13236 + 3.69335i 0.206143 + 0.357050i 0.950496 0.310736i \(-0.100576\pi\)
−0.744353 + 0.667786i \(0.767242\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 4.84556 18.0839i 0.464120 1.73212i −0.195668 0.980670i \(-0.562688\pi\)
0.659789 0.751451i \(-0.270646\pi\)
\(110\) −9.99999 + 9.99999i −0.953461 + 0.953461i
\(111\) 0.0465718 0.173808i 0.00442040 0.0164972i
\(112\) −2.27629 + 1.34853i −0.215089 + 0.127424i
\(113\) 3.88176 + 6.72341i 0.365166 + 0.632486i 0.988803 0.149228i \(-0.0476790\pi\)
−0.623637 + 0.781714i \(0.714346\pi\)
\(114\) 4.68191 2.70310i 0.438501 0.253169i
\(115\) −6.15178 6.15178i −0.573656 0.573656i
\(116\) 3.01158 1.73874i 0.279619 0.161438i
\(117\) −2.90215 2.13951i −0.268304 0.197798i
\(118\) 6.44295i 0.593122i
\(119\) −14.6234 8.22522i −1.34052 0.754005i
\(120\) 2.19085 3.79467i 0.199997 0.346404i
\(121\) 0.583014i 0.0530013i
\(122\) −5.51529 1.47782i −0.499331 0.133795i
\(123\) −0.0111173 + 0.00297886i −0.00100241 + 0.000268595i
\(124\) −6.03990 6.03990i −0.542399 0.542399i
\(125\) 28.5027 + 28.5027i 2.54936 + 2.54936i
\(126\) 2.56313 + 0.656024i 0.228342 + 0.0584432i
\(127\) −0.607656 0.350830i −0.0539207 0.0311311i 0.472797 0.881171i \(-0.343244\pi\)
−0.526718 + 0.850040i \(0.676578\pi\)
\(128\) 0.965926 + 0.258819i 0.0853766 + 0.0228766i
\(129\) −1.55572 2.69459i −0.136974 0.237245i
\(130\) 12.7164 + 9.37471i 1.11530 + 0.822216i
\(131\) 6.17726 + 3.56644i 0.539710 + 0.311602i 0.744961 0.667108i \(-0.232468\pi\)
−0.205252 + 0.978709i \(0.565801\pi\)
\(132\) 0.835348 + 3.11756i 0.0727077 + 0.271349i
\(133\) −10.2270 9.99985i −0.886797 0.867097i
\(134\) 4.59988 2.65574i 0.397369 0.229421i
\(135\) −4.23240 + 1.13407i −0.364267 + 0.0976052i
\(136\) 1.64129 + 6.12537i 0.140739 + 0.525246i
\(137\) −0.234204 0.874063i −0.0200094 0.0746762i 0.955199 0.295964i \(-0.0956408\pi\)
−0.975209 + 0.221287i \(0.928974\pi\)
\(138\) −1.91786 + 0.513888i −0.163259 + 0.0437451i
\(139\) 17.7912 10.2718i 1.50903 0.871239i 0.509085 0.860716i \(-0.329984\pi\)
0.999945 0.0105224i \(-0.00334944\pi\)
\(140\) −11.2309 2.87450i −0.949183 0.242940i
\(141\) 0.994423 + 3.71124i 0.0837455 + 0.312542i
\(142\) 5.38775 + 3.11062i 0.452130 + 0.261037i
\(143\) −11.5061 + 1.74052i −0.962192 + 0.145549i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 14.7181 + 3.94370i 1.22227 + 0.327507i
\(146\) 3.11534 + 1.79864i 0.257827 + 0.148857i
\(147\) −0.157236 6.99823i −0.0129686 0.577205i
\(148\) 0.127237 + 0.127237i 0.0104588 + 0.0104588i
\(149\) −5.11347 5.11347i −0.418912 0.418912i 0.465917 0.884829i \(-0.345725\pi\)
−0.884829 + 0.465917i \(0.845725\pi\)
\(150\) 13.7155 3.67507i 1.11987 0.300068i
\(151\) −3.27255 0.876878i −0.266317 0.0713593i 0.123190 0.992383i \(-0.460688\pi\)
−0.389506 + 0.921024i \(0.627354\pi\)
\(152\) 5.40620i 0.438501i
\(153\) 3.17072 5.49185i 0.256338 0.443990i
\(154\) 7.34679 4.35242i 0.592021 0.350728i
\(155\) 37.4272i 3.00623i
\(156\) 3.30395 1.44358i 0.264527 0.115579i
\(157\) −1.58306 + 0.913980i −0.126342 + 0.0729436i −0.561839 0.827247i \(-0.689906\pi\)
0.435497 + 0.900190i \(0.356573\pi\)
\(158\) −10.8010 10.8010i −0.859282 0.859282i
\(159\) 10.7367 6.19883i 0.851475 0.491599i
\(160\) 2.19085 + 3.79467i 0.173202 + 0.299995i
\(161\) 2.67752 + 4.51959i 0.211018 + 0.356193i
\(162\) −0.258819 + 0.965926i −0.0203347 + 0.0758903i
\(163\) 8.10494 8.10494i 0.634828 0.634828i −0.314447 0.949275i \(-0.601819\pi\)
0.949275 + 0.314447i \(0.101819\pi\)
\(164\) 0.00297886 0.0111173i 0.000232610 0.000868113i
\(165\) −7.07106 + 12.2474i −0.550481 + 0.953461i
\(166\) 0.832238 + 1.44148i 0.0645942 + 0.111880i
\(167\) −9.75066 + 2.61268i −0.754529 + 0.202175i −0.615526 0.788117i \(-0.711056\pi\)
−0.139003 + 0.990292i \(0.544390\pi\)
\(168\) −1.84970 + 1.89172i −0.142707 + 0.145950i
\(169\) 3.84499 + 12.4184i 0.295769 + 0.955260i
\(170\) −13.8932 + 24.0637i −1.06556 + 1.84560i
\(171\) 3.82276 3.82276i 0.292334 0.292334i
\(172\) 3.11145 0.237245
\(173\) −10.9280 −0.830842 −0.415421 0.909629i \(-0.636366\pi\)
−0.415421 + 0.909629i \(0.636366\pi\)
\(174\) 2.45895 2.45895i 0.186412 0.186412i
\(175\) −19.1482 32.3218i −1.44747 2.44330i
\(176\) −3.11756 0.835348i −0.234995 0.0629667i
\(177\) 1.66756 + 6.22342i 0.125341 + 0.467781i
\(178\) −15.4389 8.91365i −1.15719 0.668106i
\(179\) 10.0398i 0.750411i −0.926942 0.375205i \(-0.877572\pi\)
0.926942 0.375205i \(-0.122428\pi\)
\(180\) 1.13407 4.23240i 0.0845285 0.315465i
\(181\) −0.280875 −0.0208773 −0.0104386 0.999946i \(-0.503323\pi\)
−0.0104386 + 0.999946i \(0.503323\pi\)
\(182\) −6.03503 7.38772i −0.447346 0.547614i
\(183\) −5.70985 −0.422084
\(184\) 0.513888 1.91786i 0.0378843 0.141386i
\(185\) 0.788443i 0.0579675i
\(186\) −7.39733 4.27085i −0.542399 0.313154i
\(187\) −5.29731 19.7698i −0.387378 1.44571i
\(188\) −3.71124 0.994423i −0.270670 0.0725257i
\(189\) 2.64558 0.0297166i 0.192438 0.00216157i
\(190\) −16.7502 + 16.7502i −1.21519 + 1.21519i
\(191\) 3.98098 0.288053 0.144027 0.989574i \(-0.453995\pi\)
0.144027 + 0.989574i \(0.453995\pi\)
\(192\) 1.00000 0.0721688
\(193\) 17.3308 17.3308i 1.24750 1.24750i 0.290675 0.956822i \(-0.406120\pi\)
0.956822 0.290675i \(-0.0938799\pi\)
\(194\) 1.16494 2.01773i 0.0836375 0.144864i
\(195\) 14.7094 + 5.76403i 1.05337 + 0.412771i
\(196\) 6.13927 + 3.36295i 0.438519 + 0.240210i
\(197\) 3.65004 0.978025i 0.260054 0.0696814i −0.126436 0.991975i \(-0.540354\pi\)
0.386491 + 0.922293i \(0.373687\pi\)
\(198\) 1.61377 + 2.79513i 0.114685 + 0.198641i
\(199\) −1.78708 + 3.09532i −0.126683 + 0.219421i −0.922390 0.386261i \(-0.873766\pi\)
0.795707 + 0.605682i \(0.207100\pi\)
\(200\) −3.67507 + 13.7155i −0.259866 + 0.969835i
\(201\) 3.75578 3.75578i 0.264913 0.264913i
\(202\) 2.15387 8.03835i 0.151546 0.565577i
\(203\) −8.01907 4.51049i −0.562828 0.316574i
\(204\) 3.17072 + 5.49185i 0.221995 + 0.384507i
\(205\) 0.0436746 0.0252155i 0.00305036 0.00176113i
\(206\) −1.68576 1.68576i −0.117453 0.117453i
\(207\) −1.71950 + 0.992755i −0.119514 + 0.0690013i
\(208\) −0.401793 + 3.58309i −0.0278593 + 0.248443i
\(209\) 17.4487i 1.20695i
\(210\) −11.5922 + 0.130210i −0.799936 + 0.00898531i
\(211\) −7.71910 + 13.3699i −0.531405 + 0.920420i 0.467924 + 0.883769i \(0.345002\pi\)
−0.999328 + 0.0366508i \(0.988331\pi\)
\(212\) 12.3977i 0.851475i
\(213\) 6.00925 + 1.61017i 0.411747 + 0.110327i
\(214\) −4.11940 + 1.10379i −0.281596 + 0.0754535i
\(215\) 9.64030 + 9.64030i 0.657463 + 0.657463i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) −5.60356 + 21.8935i −0.380394 + 1.48623i
\(218\) 16.2136 + 9.36090i 1.09812 + 0.634000i
\(219\) 3.47471 + 0.931045i 0.234799 + 0.0629142i
\(220\) −7.07106 12.2474i −0.476731 0.825722i
\(221\) −20.9518 + 9.15441i −1.40937 + 0.615792i
\(222\) 0.155832 + 0.0899699i 0.0104588 + 0.00603838i
\(223\) 5.78209 + 21.5790i 0.387197 + 1.44504i 0.834674 + 0.550744i \(0.185656\pi\)
−0.447477 + 0.894295i \(0.647677\pi\)
\(224\) −0.713432 2.54775i −0.0476682 0.170229i
\(225\) 12.2970 7.09968i 0.819801 0.473312i
\(226\) −7.49899 + 2.00935i −0.498826 + 0.133660i
\(227\) 5.98281 + 22.3281i 0.397093 + 1.48197i 0.818186 + 0.574953i \(0.194980\pi\)
−0.421093 + 0.907017i \(0.638354\pi\)
\(228\) 1.39923 + 5.22199i 0.0926662 + 0.345835i
\(229\) 13.7806 3.69250i 0.910646 0.244007i 0.227064 0.973880i \(-0.427087\pi\)
0.683583 + 0.729873i \(0.260421\pi\)
\(230\) 7.53436 4.34996i 0.496801 0.286828i
\(231\) 5.96997 6.10560i 0.392795 0.401719i
\(232\) 0.900038 + 3.35899i 0.0590904 + 0.220528i
\(233\) 1.76570 + 1.01943i 0.115675 + 0.0667851i 0.556721 0.830699i \(-0.312059\pi\)
−0.441046 + 0.897484i \(0.645392\pi\)
\(234\) 2.81774 2.24952i 0.184201 0.147056i
\(235\) −8.41760 14.5797i −0.549104 0.951075i
\(236\) −6.22342 1.66756i −0.405110 0.108549i
\(237\) −13.2285 7.63746i −0.859282 0.496107i
\(238\) 11.7298 11.9963i 0.760328 0.777602i
\(239\) 7.26823 + 7.26823i 0.470143 + 0.470143i 0.901961 0.431818i \(-0.142128\pi\)
−0.431818 + 0.901961i \(0.642128\pi\)
\(240\) 3.09834 + 3.09834i 0.199997 + 0.199997i
\(241\) 10.6061 2.84189i 0.683198 0.183062i 0.0995053 0.995037i \(-0.468274\pi\)
0.583693 + 0.811975i \(0.301607\pi\)
\(242\) −0.563149 0.150895i −0.0362006 0.00969991i
\(243\) 1.00000i 0.0641500i
\(244\) 2.85492 4.94487i 0.182768 0.316563i
\(245\) 8.60197 + 29.4410i 0.549560 + 1.88092i
\(246\) 0.0115094i 0.000733816i
\(247\) −19.2731 + 2.91541i −1.22632 + 0.185503i
\(248\) 7.39733 4.27085i 0.469731 0.271199i
\(249\) 1.17696 + 1.17696i 0.0745869 + 0.0745869i
\(250\) −34.9086 + 20.1545i −2.20781 + 1.27468i
\(251\) −6.53973 11.3271i −0.412784 0.714963i 0.582409 0.812896i \(-0.302110\pi\)
−0.995193 + 0.0979333i \(0.968777\pi\)
\(252\) −1.29706 + 2.30600i −0.0817069 + 0.145264i
\(253\) −1.65859 + 6.18995i −0.104275 + 0.389159i
\(254\) 0.496149 0.496149i 0.0311311 0.0311311i
\(255\) −7.19164 + 26.8396i −0.450358 + 1.68076i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.0323063 + 0.0559561i 0.00201521 + 0.00349044i 0.867031 0.498254i \(-0.166025\pi\)
−0.865016 + 0.501744i \(0.832692\pi\)
\(258\) 3.00543 0.805301i 0.187110 0.0501359i
\(259\) 0.118045 0.461209i 0.00733494 0.0286581i
\(260\) −12.3465 + 9.85674i −0.765698 + 0.611289i
\(261\) 1.73874 3.01158i 0.107625 0.186412i
\(262\) −5.04371 + 5.04371i −0.311602 + 0.311602i
\(263\) −3.99899 −0.246588 −0.123294 0.992370i \(-0.539346\pi\)
−0.123294 + 0.992370i \(0.539346\pi\)
\(264\) −3.22754 −0.198641
\(265\) −38.4121 + 38.4121i −2.35964 + 2.35964i
\(266\) 12.3061 7.29042i 0.754533 0.447004i
\(267\) −17.2198 4.61404i −1.05384 0.282375i
\(268\) 1.37471 + 5.13050i 0.0839739 + 0.313395i
\(269\) −3.72107 2.14836i −0.226878 0.130988i 0.382253 0.924058i \(-0.375148\pi\)
−0.609131 + 0.793070i \(0.708482\pi\)
\(270\) 4.38171i 0.266662i
\(271\) 1.97318 7.36399i 0.119862 0.447331i −0.879743 0.475450i \(-0.842285\pi\)
0.999605 + 0.0281194i \(0.00895187\pi\)
\(272\) −6.34145 −0.384507
\(273\) −7.74147 5.57401i −0.468535 0.337355i
\(274\) 0.904896 0.0546668
\(275\) 11.8614 44.2674i 0.715270 2.66942i
\(276\) 1.98551i 0.119514i
\(277\) −1.10751 0.639421i −0.0665438 0.0384191i 0.466359 0.884596i \(-0.345566\pi\)
−0.532903 + 0.846176i \(0.678899\pi\)
\(278\) 5.31705 + 19.8435i 0.318895 + 1.19013i
\(279\) −8.25065 2.21076i −0.493954 0.132354i
\(280\) 5.68332 10.1042i 0.339644 0.603843i
\(281\) 7.17377 7.17377i 0.427951 0.427951i −0.459979 0.887930i \(-0.652143\pi\)
0.887930 + 0.459979i \(0.152143\pi\)
\(282\) −3.84215 −0.228797
\(283\) −4.33819 −0.257878 −0.128939 0.991653i \(-0.541157\pi\)
−0.128939 + 0.991653i \(0.541157\pi\)
\(284\) −4.39908 + 4.39908i −0.261037 + 0.261037i
\(285\) −11.8442 + 20.5148i −0.701590 + 1.21519i
\(286\) 1.29680 11.5646i 0.0766815 0.683827i
\(287\) −0.0293232 + 0.00821120i −0.00173089 + 0.000484692i
\(288\) 0.965926 0.258819i 0.0569177 0.0152511i
\(289\) −11.6070 20.1039i −0.682763 1.18258i
\(290\) −7.61865 + 13.1959i −0.447382 + 0.774889i
\(291\) 0.603015 2.25048i 0.0353494 0.131926i
\(292\) −2.54366 + 2.54366i −0.148857 + 0.148857i
\(293\) 4.70535 17.5606i 0.274890 1.02590i −0.681026 0.732260i \(-0.738466\pi\)
0.955915 0.293643i \(-0.0948676\pi\)
\(294\) 6.80047 + 1.65940i 0.396611 + 0.0967781i
\(295\) −14.1156 24.4489i −0.821840 1.42347i
\(296\) −0.155832 + 0.0899699i −0.00905757 + 0.00522939i
\(297\) 2.28221 + 2.28221i 0.132427 + 0.132427i
\(298\) 6.26270 3.61577i 0.362789 0.209456i
\(299\) 7.11427 + 0.797765i 0.411429 + 0.0461359i
\(300\) 14.1994i 0.819801i
\(301\) −4.19587 7.08254i −0.241846 0.408231i
\(302\) 1.69400 2.93409i 0.0974786 0.168838i
\(303\) 8.32192i 0.478082i
\(304\) −5.22199 1.39923i −0.299502 0.0802513i
\(305\) 24.1664 6.47536i 1.38376 0.370778i
\(306\) 4.48408 + 4.48408i 0.256338 + 0.256338i
\(307\) 7.72652 + 7.72652i 0.440976 + 0.440976i 0.892340 0.451364i \(-0.149062\pi\)
−0.451364 + 0.892340i \(0.649062\pi\)
\(308\) 2.30263 + 8.22294i 0.131204 + 0.468546i
\(309\) −2.06463 1.19202i −0.117453 0.0678114i
\(310\) 36.1519 + 9.68688i 2.05329 + 0.550178i
\(311\) 5.76925 + 9.99263i 0.327144 + 0.566630i 0.981944 0.189172i \(-0.0605804\pi\)
−0.654800 + 0.755802i \(0.727247\pi\)
\(312\) 0.539271 + 3.56499i 0.0305302 + 0.201828i
\(313\) −15.6924 9.06000i −0.886986 0.512101i −0.0140304 0.999902i \(-0.504466\pi\)
−0.872955 + 0.487800i \(0.837799\pi\)
\(314\) −0.473111 1.76567i −0.0266992 0.0996428i
\(315\) −11.1635 + 3.12605i −0.628991 + 0.176133i
\(316\) 13.2285 7.63746i 0.744160 0.429641i
\(317\) −23.9680 + 6.42219i −1.34617 + 0.360706i −0.858721 0.512443i \(-0.828741\pi\)
−0.487453 + 0.873149i \(0.662074\pi\)
\(318\) 3.20875 + 11.9752i 0.179938 + 0.671537i
\(319\) −2.90490 10.8412i −0.162643 0.606993i
\(320\) −4.23240 + 1.13407i −0.236599 + 0.0633964i
\(321\) −3.69335 + 2.13236i −0.206143 + 0.119017i
\(322\) −5.05858 + 1.41653i −0.281904 + 0.0789399i
\(323\) −8.87314 33.1150i −0.493714 1.84257i
\(324\) −0.866025 0.500000i −0.0481125 0.0277778i
\(325\) −50.8777 5.70521i −2.82218 0.316468i
\(326\) 5.73106 + 9.92648i 0.317414 + 0.549777i
\(327\) 18.0839 + 4.84556i 1.00004 + 0.267960i
\(328\) 0.00996747 + 0.00575472i 0.000550362 + 0.000317751i
\(329\) 2.74111 + 9.78884i 0.151123 + 0.539676i
\(330\) −9.99999 9.99999i −0.550481 0.550481i
\(331\) 9.11773 + 9.11773i 0.501156 + 0.501156i 0.911797 0.410641i \(-0.134695\pi\)
−0.410641 + 0.911797i \(0.634695\pi\)
\(332\) −1.60776 + 0.430798i −0.0882373 + 0.0236431i
\(333\) 0.173808 + 0.0465718i 0.00952464 + 0.00255212i
\(334\) 10.0946i 0.552354i
\(335\) −11.6367 + 20.1553i −0.635780 + 1.10120i
\(336\) −1.34853 2.27629i −0.0735682 0.124182i
\(337\) 10.2939i 0.560743i −0.959892 0.280372i \(-0.909542\pi\)
0.959892 0.280372i \(-0.0904577\pi\)
\(338\) −12.9904 + 0.499867i −0.706584 + 0.0271892i
\(339\) −6.72341 + 3.88176i −0.365166 + 0.210829i
\(340\) −19.6479 19.6479i −1.06556 1.06556i
\(341\) −23.8752 + 13.7843i −1.29291 + 0.746463i
\(342\) 2.70310 + 4.68191i 0.146167 + 0.253169i
\(343\) −0.623944 18.5097i −0.0336898 0.999432i
\(344\) −0.805301 + 3.00543i −0.0434189 + 0.162042i
\(345\) 6.15178 6.15178i 0.331201 0.331201i
\(346\) 2.82838 10.5557i 0.152055 0.567475i
\(347\) −13.6113 + 23.5755i −0.730694 + 1.26560i 0.225893 + 0.974152i \(0.427470\pi\)
−0.956587 + 0.291447i \(0.905863\pi\)
\(348\) 1.73874 + 3.01158i 0.0932062 + 0.161438i
\(349\) 20.4872 5.48954i 1.09666 0.293848i 0.335254 0.942128i \(-0.391178\pi\)
0.761402 + 0.648280i \(0.224511\pi\)
\(350\) 36.1764 10.1303i 1.93371 0.541486i
\(351\) 2.13951 2.90215i 0.114199 0.154906i
\(352\) 1.61377 2.79513i 0.0860141 0.148981i
\(353\) 2.52442 2.52442i 0.134362 0.134362i −0.636727 0.771089i \(-0.719712\pi\)
0.771089 + 0.636727i \(0.219712\pi\)
\(354\) −6.44295 −0.342439
\(355\) −27.2596 −1.44679
\(356\) 12.6058 12.6058i 0.668106 0.668106i
\(357\) 8.22522 14.6234i 0.435325 0.773952i
\(358\) 9.69771 + 2.59849i 0.512540 + 0.137335i
\(359\) 4.70401 + 17.5556i 0.248268 + 0.926549i 0.971713 + 0.236167i \(0.0758911\pi\)
−0.723444 + 0.690383i \(0.757442\pi\)
\(360\) 3.79467 + 2.19085i 0.199997 + 0.115468i
\(361\) 10.2270i 0.538266i
\(362\) 0.0726959 0.271305i 0.00382081 0.0142595i
\(363\) −0.583014 −0.0306003
\(364\) 8.69797 3.91731i 0.455898 0.205323i
\(365\) −15.7622 −0.825033
\(366\) 1.47782 5.51529i 0.0772467 0.288289i
\(367\) 0.354772i 0.0185190i −0.999957 0.00925948i \(-0.997053\pi\)
0.999957 0.00925948i \(-0.00294743\pi\)
\(368\) 1.71950 + 0.992755i 0.0896353 + 0.0517510i
\(369\) −0.00297886 0.0111173i −0.000155073 0.000578742i
\(370\) −0.761578 0.204064i −0.0395925 0.0106088i
\(371\) 28.2206 16.7186i 1.46514 0.867986i
\(372\) 6.03990 6.03990i 0.313154 0.313154i
\(373\) 21.2008 1.09773 0.548867 0.835909i \(-0.315059\pi\)
0.548867 + 0.835909i \(0.315059\pi\)
\(374\) 20.4672 1.05834
\(375\) −28.5027 + 28.5027i −1.47187 + 1.47187i
\(376\) 1.92108 3.32740i 0.0990720 0.171598i
\(377\) −11.4894 + 5.02003i −0.591734 + 0.258545i
\(378\) −0.656024 + 2.56313i −0.0337422 + 0.131833i
\(379\) 10.3631 2.77679i 0.532317 0.142634i 0.0173592 0.999849i \(-0.494474\pi\)
0.514958 + 0.857215i \(0.327807\pi\)
\(380\) −11.8442 20.5148i −0.607595 1.05239i
\(381\) 0.350830 0.607656i 0.0179736 0.0311311i
\(382\) −1.03035 + 3.84533i −0.0527174 + 0.196744i
\(383\) −10.3753 + 10.3753i −0.530153 + 0.530153i −0.920618 0.390465i \(-0.872314\pi\)
0.390465 + 0.920618i \(0.372314\pi\)
\(384\) −0.258819 + 0.965926i −0.0132078 + 0.0492922i
\(385\) −18.3431 + 32.6117i −0.934853 + 1.66205i
\(386\) 12.2547 + 21.2258i 0.623748 + 1.08036i
\(387\) 2.69459 1.55572i 0.136974 0.0790818i
\(388\) 1.64747 + 1.64747i 0.0836375 + 0.0836375i
\(389\) 6.90619 3.98729i 0.350158 0.202164i −0.314597 0.949225i \(-0.601869\pi\)
0.664755 + 0.747062i \(0.268536\pi\)
\(390\) −9.37471 + 12.7164i −0.474707 + 0.643919i
\(391\) 12.5910i 0.636755i
\(392\) −4.83732 + 5.05968i −0.244321 + 0.255552i
\(393\) −3.56644 + 6.17726i −0.179903 + 0.311602i
\(394\) 3.77880i 0.190373i
\(395\) 64.6497 + 17.3228i 3.25288 + 0.871606i
\(396\) −3.11756 + 0.835348i −0.156663 + 0.0419778i
\(397\) 15.2081 + 15.2081i 0.763274 + 0.763274i 0.976913 0.213638i \(-0.0685315\pi\)
−0.213638 + 0.976913i \(0.568531\pi\)
\(398\) −2.52732 2.52732i −0.126683 0.126683i
\(399\) 9.99985 10.2270i 0.500618 0.511993i
\(400\) −12.2970 7.09968i −0.614850 0.354984i
\(401\) −21.0329 5.63574i −1.05033 0.281436i −0.307943 0.951405i \(-0.599641\pi\)
−0.742389 + 0.669969i \(0.766307\pi\)
\(402\) 2.65574 + 4.59988i 0.132456 + 0.229421i
\(403\) 19.2147 + 24.0683i 0.957154 + 1.19893i
\(404\) 7.20699 + 4.16096i 0.358561 + 0.207015i
\(405\) −1.13407 4.23240i −0.0563524 0.210310i
\(406\) 6.43228 6.57843i 0.319229 0.326482i
\(407\) 0.502955 0.290381i 0.0249305 0.0143936i
\(408\) −6.12537 + 1.64129i −0.303251 + 0.0812558i
\(409\) 8.36755 + 31.2281i 0.413749 + 1.54413i 0.787329 + 0.616534i \(0.211464\pi\)
−0.373580 + 0.927598i \(0.621870\pi\)
\(410\) 0.0130525 + 0.0487126i 0.000644618 + 0.00240575i
\(411\) 0.874063 0.234204i 0.0431143 0.0115525i
\(412\) 2.06463 1.19202i 0.101717 0.0587264i
\(413\) 4.59661 + 16.4150i 0.226184 + 0.807730i
\(414\) −0.513888 1.91786i −0.0252562 0.0942575i
\(415\) −6.31614 3.64662i −0.310047 0.179006i
\(416\) −3.35701 1.31548i −0.164591 0.0644965i
\(417\) 10.2718 + 17.7912i 0.503010 + 0.871239i
\(418\) 16.8542 + 4.51606i 0.824364 + 0.220888i
\(419\) 4.47379 + 2.58295i 0.218559 + 0.126185i 0.605283 0.796010i \(-0.293060\pi\)
−0.386724 + 0.922196i \(0.626393\pi\)
\(420\) 2.87450 11.2309i 0.140261 0.548011i
\(421\) 10.2156 + 10.2156i 0.497877 + 0.497877i 0.910777 0.412899i \(-0.135484\pi\)
−0.412899 + 0.910777i \(0.635484\pi\)
\(422\) −10.9165 10.9165i −0.531405 0.531405i
\(423\) −3.71124 + 0.994423i −0.180446 + 0.0483505i
\(424\) −11.9752 3.20875i −0.581568 0.155831i
\(425\) 90.0445i 4.36780i
\(426\) −3.11062 + 5.38775i −0.150710 + 0.261037i
\(427\) −15.1059 + 0.169677i −0.731025 + 0.00821126i
\(428\) 4.26472i 0.206143i
\(429\) −1.74052 11.5061i −0.0840329 0.555522i
\(430\) −11.8069 + 6.81672i −0.569380 + 0.328732i
\(431\) −3.04921 3.04921i −0.146875 0.146875i 0.629845 0.776720i \(-0.283118\pi\)
−0.776720 + 0.629845i \(0.783118\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) −19.0775 33.0433i −0.916808 1.58796i −0.804233 0.594314i \(-0.797424\pi\)
−0.112575 0.993643i \(-0.535910\pi\)
\(434\) −19.6972 11.0791i −0.945495 0.531813i
\(435\) −3.94370 + 14.7181i −0.189086 + 0.705679i
\(436\) −13.2383 + 13.2383i −0.634000 + 0.634000i
\(437\) −2.77818 + 10.3683i −0.132899 + 0.495984i
\(438\) −1.79864 + 3.11534i −0.0859424 + 0.148857i
\(439\) 9.88117 + 17.1147i 0.471602 + 0.816839i 0.999472 0.0324860i \(-0.0103424\pi\)
−0.527870 + 0.849325i \(0.677009\pi\)
\(440\) 13.6602 3.66025i 0.651226 0.174496i
\(441\) 6.99823 0.157236i 0.333249 0.00748741i
\(442\) −3.41976 22.6072i −0.162661 1.07532i
\(443\) −13.7162 + 23.7572i −0.651677 + 1.12874i 0.331039 + 0.943617i \(0.392601\pi\)
−0.982716 + 0.185120i \(0.940733\pi\)
\(444\) −0.127237 + 0.127237i −0.00603838 + 0.00603838i
\(445\) 78.1140 3.70296
\(446\) −22.3403 −1.05784
\(447\) 5.11347 5.11347i 0.241859 0.241859i
\(448\) 2.64558 0.0297166i 0.124992 0.00140398i
\(449\) −21.2137 5.68419i −1.00114 0.268253i −0.279214 0.960229i \(-0.590074\pi\)
−0.721921 + 0.691975i \(0.756741\pi\)
\(450\) 3.67507 + 13.7155i 0.173244 + 0.646556i
\(451\) −0.0321704 0.0185736i −0.00151484 0.000874596i
\(452\) 7.76353i 0.365166i
\(453\) 0.876878 3.27255i 0.0411993 0.153758i
\(454\) −23.1158 −1.08488
\(455\) 39.0864 + 14.8121i 1.83240 + 0.694402i
\(456\) −5.40620 −0.253169
\(457\) −2.30088 + 8.58700i −0.107631 + 0.401683i −0.998630 0.0523209i \(-0.983338\pi\)
0.891000 + 0.454004i \(0.150005\pi\)
\(458\) 14.2667i 0.666639i
\(459\) 5.49185 + 3.17072i 0.256338 + 0.147997i
\(460\) 2.25171 + 8.40349i 0.104986 + 0.391815i
\(461\) 12.8354 + 3.43922i 0.597802 + 0.160181i 0.545017 0.838425i \(-0.316523\pi\)
0.0527857 + 0.998606i \(0.483190\pi\)
\(462\) 4.35242 + 7.34679i 0.202493 + 0.341804i
\(463\) 16.8995 16.8995i 0.785385 0.785385i −0.195349 0.980734i \(-0.562584\pi\)
0.980734 + 0.195349i \(0.0625838\pi\)
\(464\) −3.47748 −0.161438
\(465\) 37.4272 1.73565
\(466\) −1.44169 + 1.44169i −0.0667851 + 0.0667851i
\(467\) 5.72210 9.91096i 0.264787 0.458625i −0.702721 0.711466i \(-0.748032\pi\)
0.967508 + 0.252841i \(0.0813650\pi\)
\(468\) 1.44358 + 3.30395i 0.0667297 + 0.152725i
\(469\) 9.82463 10.0479i 0.453659 0.463967i
\(470\) 16.2616 4.35727i 0.750089 0.200986i
\(471\) −0.913980 1.58306i −0.0421140 0.0729436i
\(472\) 3.22148 5.57976i 0.148280 0.256829i
\(473\) 2.59914 9.70012i 0.119509 0.446012i
\(474\) 10.8010 10.8010i 0.496107 0.496107i
\(475\) 19.8682 74.1490i 0.911614 3.40219i
\(476\) 8.55162 + 14.4349i 0.391963 + 0.661624i
\(477\) 6.19883 + 10.7367i 0.283825 + 0.491599i
\(478\) −8.90173 + 5.13942i −0.407156 + 0.235071i
\(479\) 23.3756 + 23.3756i 1.06806 + 1.06806i 0.997508 + 0.0705478i \(0.0224747\pi\)
0.0705478 + 0.997508i \(0.477525\pi\)
\(480\) −3.79467 + 2.19085i −0.173202 + 0.0999983i
\(481\) −0.404778 0.507024i −0.0184563 0.0231183i
\(482\) 10.9802i 0.500136i
\(483\) −4.51959 + 2.67752i −0.205648 + 0.121831i
\(484\) 0.291507 0.504905i 0.0132503 0.0229502i
\(485\) 10.2088i 0.463559i
\(486\) −0.965926 0.258819i −0.0438153 0.0117403i
\(487\) −36.3247 + 9.73317i −1.64603 + 0.441052i −0.958497 0.285102i \(-0.907972\pi\)
−0.687532 + 0.726154i \(0.741306\pi\)
\(488\) 4.03747 + 4.03747i 0.182768 + 0.182768i
\(489\) 8.10494 + 8.10494i 0.366518 + 0.366518i
\(490\) −30.6642 + 0.688960i −1.38527 + 0.0311241i
\(491\) −14.7584 8.52076i −0.666036 0.384536i 0.128537 0.991705i \(-0.458972\pi\)
−0.794573 + 0.607168i \(0.792305\pi\)
\(492\) 0.0111173 + 0.00297886i 0.000501205 + 0.000134298i
\(493\) −11.0261 19.0978i −0.496592 0.860122i
\(494\) 2.17218 19.3709i 0.0977308 0.871540i
\(495\) −12.2474 7.07106i −0.550481 0.317820i
\(496\) 2.21076 + 8.25065i 0.0992658 + 0.370465i
\(497\) 15.9458 + 4.08128i 0.715268 + 0.183070i
\(498\) −1.44148 + 0.832238i −0.0645942 + 0.0372935i
\(499\) −0.641641 + 0.171927i −0.0287238 + 0.00769651i −0.273152 0.961971i \(-0.588066\pi\)
0.244429 + 0.969667i \(0.421400\pi\)
\(500\) −10.4327 38.9354i −0.466565 1.74125i
\(501\) −2.61268 9.75066i −0.116726 0.435628i
\(502\) 12.6338 3.38521i 0.563873 0.151089i
\(503\) 28.3846 16.3878i 1.26561 0.730698i 0.291452 0.956585i \(-0.405862\pi\)
0.974153 + 0.225888i \(0.0725282\pi\)
\(504\) −1.89172 1.84970i −0.0842641 0.0823921i
\(505\) 9.43763 + 35.2217i 0.419969 + 1.56735i
\(506\) −5.54976 3.20415i −0.246717 0.142442i
\(507\) −12.4184 + 3.84499i −0.551519 + 0.170762i
\(508\) 0.350830 + 0.607656i 0.0155656 + 0.0269604i
\(509\) 29.7239 + 7.96450i 1.31749 + 0.353020i 0.848036 0.529938i \(-0.177785\pi\)
0.469452 + 0.882958i \(0.344451\pi\)
\(510\) −24.0637 13.8932i −1.06556 0.615201i
\(511\) 9.22030 + 2.35990i 0.407882 + 0.104396i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 3.82276 + 3.82276i 0.168779 + 0.168779i
\(514\) −0.0624109 + 0.0167230i −0.00275283 + 0.000737618i
\(515\) 10.0902 + 2.70366i 0.444627 + 0.119137i
\(516\) 3.11145i 0.136974i
\(517\) −6.20034 + 10.7393i −0.272691 + 0.472314i
\(518\) 0.414941 + 0.233392i 0.0182315 + 0.0102547i
\(519\) 10.9280i 0.479687i
\(520\) −6.32536 14.4769i −0.277386 0.634855i
\(521\) −25.3802 + 14.6533i −1.11193 + 0.641972i −0.939328 0.343020i \(-0.888550\pi\)
−0.172600 + 0.984992i \(0.555217\pi\)
\(522\) 2.45895 + 2.45895i 0.107625 + 0.107625i
\(523\) 30.5087 17.6142i 1.33405 0.770217i 0.348136 0.937444i \(-0.386815\pi\)
0.985918 + 0.167227i \(0.0534814\pi\)
\(524\) −3.56644 6.17726i −0.155801 0.269855i
\(525\) 32.3218 19.1482i 1.41064 0.835697i
\(526\) 1.03501 3.86273i 0.0451288 0.168423i
\(527\) −38.3017 + 38.3017i −1.66845 + 1.66845i
\(528\) 0.835348 3.11756i 0.0363538 0.135674i
\(529\) −9.52887 + 16.5045i −0.414299 + 0.717587i
\(530\) −27.1615 47.0451i −1.17982 2.04351i
\(531\) −6.22342 + 1.66756i −0.270073 + 0.0723659i
\(532\) 3.85696 + 13.7736i 0.167220 + 0.597163i
\(533\) −0.0151404 + 0.0386373i −0.000655803 + 0.00167357i
\(534\) 8.91365 15.4389i 0.385731 0.668106i
\(535\) 13.2135 13.2135i 0.571270 0.571270i
\(536\) −5.31148 −0.229421
\(537\) 10.0398 0.433250
\(538\) 3.03824 3.03824i 0.130988 0.130988i
\(539\) 15.6126 16.3303i 0.672483 0.703396i
\(540\) 4.23240 + 1.13407i 0.182134 + 0.0488026i
\(541\) 0.956053 + 3.56804i 0.0411039 + 0.153402i 0.983428 0.181301i \(-0.0580308\pi\)
−0.942324 + 0.334703i \(0.891364\pi\)
\(542\) 6.60238 + 3.81188i 0.283596 + 0.163734i
\(543\) 0.280875i 0.0120535i
\(544\) 1.64129 6.12537i 0.0703696 0.262623i
\(545\) −82.0335 −3.51393
\(546\) 7.38772 6.03503i 0.316165 0.258275i
\(547\) −21.9784 −0.939729 −0.469864 0.882739i \(-0.655697\pi\)
−0.469864 + 0.882739i \(0.655697\pi\)
\(548\) −0.234204 + 0.874063i −0.0100047 + 0.0373381i
\(549\) 5.70985i 0.243690i
\(550\) 39.6890 + 22.9145i 1.69235 + 0.977076i
\(551\) −4.86579 18.1594i −0.207290 0.773615i
\(552\) 1.91786 + 0.513888i 0.0816294 + 0.0218725i
\(553\) −35.2240 19.8124i −1.49788 0.842511i
\(554\) 0.904278 0.904278i 0.0384191 0.0384191i
\(555\) −0.788443 −0.0334676
\(556\) −20.5435 −0.871239
\(557\) −5.80587 + 5.80587i −0.246002 + 0.246002i −0.819328 0.573325i \(-0.805653\pi\)
0.573325 + 0.819328i \(0.305653\pi\)
\(558\) 4.27085 7.39733i 0.180800 0.313154i
\(559\) −11.1486 1.25016i −0.471536 0.0528760i
\(560\) 8.28898 + 8.10484i 0.350273 + 0.342492i
\(561\) 19.7698 5.29731i 0.834683 0.223653i
\(562\) 5.07262 + 8.78604i 0.213976 + 0.370617i
\(563\) 4.82462 8.35649i 0.203334 0.352184i −0.746267 0.665647i \(-0.768156\pi\)
0.949601 + 0.313463i \(0.101489\pi\)
\(564\) 0.994423 3.71124i 0.0418727 0.156271i
\(565\) 24.0540 24.0540i 1.01196 1.01196i
\(566\) 1.12281 4.19037i 0.0471950 0.176134i
\(567\) 0.0297166 + 2.64558i 0.00124798 + 0.111104i
\(568\) −3.11062 5.38775i −0.130519 0.226065i
\(569\) 21.0536 12.1553i 0.882613 0.509577i 0.0110936 0.999938i \(-0.496469\pi\)
0.871519 + 0.490362i \(0.163135\pi\)
\(570\) −16.7502 16.7502i −0.701590 0.701590i
\(571\) 17.5708 10.1445i 0.735315 0.424534i −0.0850485 0.996377i \(-0.527105\pi\)
0.820363 + 0.571843i \(0.193771\pi\)
\(572\) 10.8349 + 4.24574i 0.453029 + 0.177523i
\(573\) 3.98098i 0.166308i
\(574\) −0.000342022 0.0304492i −1.42757e−5 0.00127093i
\(575\) −14.0965 + 24.4158i −0.587864 + 1.01821i
\(576\) 1.00000i 0.0416667i
\(577\) −31.4207 8.41915i −1.30806 0.350494i −0.463568 0.886061i \(-0.653431\pi\)
−0.844492 + 0.535568i \(0.820098\pi\)
\(578\) 22.4230 6.00821i 0.932672 0.249909i
\(579\) 17.3308 + 17.3308i 0.720243 + 0.720243i
\(580\) −10.7744 10.7744i −0.447382 0.447382i
\(581\) 3.14873 + 3.07878i 0.130631 + 0.127729i
\(582\) 2.01773 + 1.16494i 0.0836375 + 0.0482882i
\(583\) 38.6505 + 10.3564i 1.60074 + 0.428917i
\(584\) −1.79864 3.11534i −0.0744283 0.128914i
\(585\) −5.76403 + 14.7094i −0.238313 + 0.608161i
\(586\) 15.7444 + 9.09005i 0.650396 + 0.375506i
\(587\) 9.53490 + 35.5847i 0.393548 + 1.46874i 0.824240 + 0.566241i \(0.191603\pi\)
−0.430692 + 0.902499i \(0.641731\pi\)
\(588\) −3.36295 + 6.13927i −0.138686 + 0.253179i
\(589\) −39.9915 + 23.0891i −1.64782 + 0.951370i
\(590\) 27.2692 7.30676i 1.12265 0.300814i
\(591\) 0.978025 + 3.65004i 0.0402306 + 0.150142i
\(592\) −0.0465718 0.173808i −0.00191409 0.00714348i
\(593\) −32.4894 + 8.70551i −1.33418 + 0.357493i −0.854272 0.519826i \(-0.825997\pi\)
−0.479908 + 0.877319i \(0.659330\pi\)
\(594\) −2.79513 + 1.61377i −0.114685 + 0.0662137i
\(595\) −18.2285 + 71.2201i −0.747296 + 2.91974i
\(596\) 1.87166 + 6.98514i 0.0766662 + 0.286122i
\(597\) −3.09532 1.78708i −0.126683 0.0731405i
\(598\) −2.61189 + 6.66538i −0.106808 + 0.272568i
\(599\) −4.56535 7.90742i −0.186535 0.323088i 0.757558 0.652768i \(-0.226393\pi\)
−0.944093 + 0.329680i \(0.893059\pi\)
\(600\) −13.7155 3.67507i −0.559934 0.150034i
\(601\) 39.0133 + 22.5243i 1.59139 + 0.918787i 0.993070 + 0.117527i \(0.0374968\pi\)
0.598316 + 0.801260i \(0.295837\pi\)
\(602\) 7.92718 2.21980i 0.323088 0.0904724i
\(603\) 3.75578 + 3.75578i 0.152947 + 0.152947i
\(604\) 2.39568 + 2.39568i 0.0974786 + 0.0974786i
\(605\) 2.46755 0.661179i 0.100320 0.0268807i
\(606\) 8.03835 + 2.15387i 0.326536 + 0.0874950i
\(607\) 19.4589i 0.789811i 0.918722 + 0.394906i \(0.129223\pi\)
−0.918722 + 0.394906i \(0.870777\pi\)
\(608\) 2.70310 4.68191i 0.109625 0.189877i
\(609\) 4.51049 8.01907i 0.182774 0.324949i
\(610\) 25.0189i 1.01298i
\(611\) 12.8982 + 5.05426i 0.521803 + 0.204473i
\(612\) −5.49185 + 3.17072i −0.221995 + 0.128169i
\(613\) −10.2738 10.2738i −0.414956 0.414956i 0.468505 0.883461i \(-0.344793\pi\)
−0.883461 + 0.468505i \(0.844793\pi\)
\(614\) −9.46302 + 5.46348i −0.381896 + 0.220488i
\(615\) 0.0252155 + 0.0436746i 0.00101679 + 0.00176113i
\(616\) −8.53872 + 0.0959114i −0.344035 + 0.00386438i
\(617\) 4.14330 15.4630i 0.166803 0.622518i −0.831000 0.556272i \(-0.812231\pi\)
0.997803 0.0662456i \(-0.0211021\pi\)
\(618\) 1.68576 1.68576i 0.0678114 0.0678114i
\(619\) 11.1300 41.5376i 0.447351 1.66954i −0.262301 0.964986i \(-0.584481\pi\)
0.709652 0.704552i \(-0.248852\pi\)
\(620\) −18.7136 + 32.4129i −0.751557 + 1.30174i
\(621\) −0.992755 1.71950i −0.0398379 0.0690013i
\(622\) −11.1453 + 2.98638i −0.446887 + 0.119743i
\(623\) −45.6937 11.6951i −1.83068 0.468555i
\(624\) −3.58309 0.401793i −0.143439 0.0160846i
\(625\) 52.8126 91.4740i 2.11250 3.65896i
\(626\) 12.8128 12.8128i 0.512101 0.512101i
\(627\) 17.4487 0.696835
\(628\) 1.82796 0.0729436
\(629\) 0.806864 0.806864i 0.0321718 0.0321718i
\(630\) −0.130210 11.5922i −0.00518767 0.461843i
\(631\) −4.52314 1.21197i −0.180063 0.0482478i 0.167661 0.985845i \(-0.446379\pi\)
−0.347724 + 0.937597i \(0.613045\pi\)
\(632\) 3.95344 + 14.7544i 0.157259 + 0.586900i
\(633\) −13.3699 7.71910i −0.531405 0.306807i
\(634\) 24.8135i 0.985468i
\(635\) −0.795731 + 2.96971i −0.0315776 + 0.117849i
\(636\) −12.3977 −0.491599
\(637\) −20.6464 14.5165i −0.818039 0.575163i
\(638\) 11.2237 0.444350
\(639\) −1.61017 + 6.00925i −0.0636975 + 0.237722i
\(640\) 4.38171i 0.173202i
\(641\) 6.21840 + 3.59019i 0.245612 + 0.141804i 0.617753 0.786372i \(-0.288043\pi\)
−0.372141 + 0.928176i \(0.621376\pi\)
\(642\) −1.10379 4.11940i −0.0435631 0.162580i
\(643\) −29.2307 7.83235i −1.15275 0.308878i −0.368682 0.929556i \(-0.620191\pi\)
−0.784066 + 0.620678i \(0.786858\pi\)
\(644\) −0.0590026 5.25284i −0.00232503 0.206991i
\(645\) −9.64030 + 9.64030i −0.379586 + 0.379586i
\(646\) 34.2832 1.34885
\(647\) 18.5164 0.727956 0.363978 0.931408i \(-0.381418\pi\)
0.363978 + 0.931408i \(0.381418\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) −10.3974 + 18.0089i −0.408135 + 0.706910i
\(650\) 18.6789 47.6674i 0.732647 1.86967i
\(651\) −21.8935 5.60356i −0.858074 0.219621i
\(652\) −11.0716 + 2.96661i −0.433595 + 0.116182i
\(653\) 4.68214 + 8.10970i 0.183226 + 0.317357i 0.942977 0.332857i \(-0.108013\pi\)
−0.759751 + 0.650214i \(0.774679\pi\)
\(654\) −9.36090 + 16.2136i −0.366040 + 0.634000i
\(655\) 8.08919 30.1893i 0.316071 1.17959i
\(656\) −0.00813841 + 0.00813841i −0.000317751 + 0.000317751i
\(657\) −0.931045 + 3.47471i −0.0363235 + 0.135561i
\(658\) −10.1647 + 0.114176i −0.396263 + 0.00445104i
\(659\) 16.2208 + 28.0953i 0.631874 + 1.09444i 0.987168 + 0.159683i \(0.0510473\pi\)
−0.355294 + 0.934754i \(0.615619\pi\)
\(660\) 12.2474 7.07106i 0.476731 0.275241i
\(661\) −2.95795 2.95795i −0.115051 0.115051i 0.647238 0.762288i \(-0.275924\pi\)
−0.762288 + 0.647238i \(0.775924\pi\)
\(662\) −11.1669 + 6.44721i −0.434014 + 0.250578i
\(663\) −9.15441 20.9518i −0.355528 0.813701i
\(664\) 1.66448i 0.0645942i
\(665\) −30.7252 + 54.6255i −1.19147 + 2.11829i
\(666\) −0.0899699 + 0.155832i −0.00348626 + 0.00603838i
\(667\) 6.90457i 0.267346i
\(668\) 9.75066 + 2.61268i 0.377264 + 0.101088i
\(669\) −21.5790 + 5.78209i −0.834294 + 0.223548i
\(670\) −16.4567 16.4567i −0.635780 0.635780i
\(671\) −13.0311 13.0311i −0.503059 0.503059i
\(672\) 2.54775 0.713432i 0.0982815 0.0275212i
\(673\) 24.5261 + 14.1601i 0.945412 + 0.545834i 0.891653 0.452720i \(-0.149546\pi\)
0.0537590 + 0.998554i \(0.482880\pi\)
\(674\) 9.94312 + 2.66425i 0.382995 + 0.102623i
\(675\) 7.09968 + 12.2970i 0.273267 + 0.473312i
\(676\) 2.87932 12.6771i 0.110743 0.487582i
\(677\) 23.0893 + 13.3306i 0.887395 + 0.512337i 0.873089 0.487560i \(-0.162113\pi\)
0.0143051 + 0.999898i \(0.495446\pi\)
\(678\) −2.00935 7.49899i −0.0771686 0.287997i
\(679\) 1.52845 5.97176i 0.0586566 0.229175i
\(680\) 24.0637 13.8932i 0.922801 0.532779i
\(681\) −22.3281 + 5.98281i −0.855616 + 0.229262i
\(682\) −7.13529 26.6293i −0.273224 1.01969i
\(683\) 7.10257 + 26.5071i 0.271772 + 1.01427i 0.957974 + 0.286856i \(0.0926102\pi\)
−0.686201 + 0.727412i \(0.740723\pi\)
\(684\) −5.22199 + 1.39923i −0.199668 + 0.0535008i
\(685\) −3.43378 + 1.98250i −0.131198 + 0.0757473i
\(686\) 18.0405 + 4.18799i 0.688791 + 0.159898i
\(687\) 3.69250 + 13.7806i 0.140877 + 0.525762i
\(688\) −2.69459 1.55572i −0.102730 0.0593114i
\(689\) 4.98130 44.4220i 0.189772 1.69234i
\(690\) 4.34996 + 7.53436i 0.165600 + 0.286828i
\(691\) 17.7212 + 4.74839i 0.674148 + 0.180637i 0.579623 0.814885i \(-0.303200\pi\)
0.0945254 + 0.995522i \(0.469867\pi\)
\(692\) 9.46394 + 5.46401i 0.359765 + 0.207710i
\(693\) 6.10560 + 5.96997i 0.231933 + 0.226780i
\(694\) −19.2493 19.2493i −0.730694 0.730694i
\(695\) −63.6507 63.6507i −2.41441 2.41441i
\(696\) −3.35899 + 0.900038i −0.127322 + 0.0341158i
\(697\) −0.0704996 0.0188903i −0.00267036 0.000715522i
\(698\) 21.2099i 0.802808i
\(699\) −1.01943 + 1.76570i −0.0385584 + 0.0667851i
\(700\) 0.421957 + 37.5656i 0.0159485 + 1.41985i
\(701\) 41.7640i 1.57740i 0.614775 + 0.788702i \(0.289247\pi\)
−0.614775 + 0.788702i \(0.710753\pi\)
\(702\) 2.24952 + 2.81774i 0.0849026 + 0.106349i
\(703\) 0.842462 0.486396i 0.0317740 0.0183448i
\(704\) 2.28221 + 2.28221i 0.0860141 + 0.0860141i
\(705\) 14.5797 8.41760i 0.549104 0.317025i
\(706\) 1.78504 + 3.09178i 0.0671808 + 0.116361i
\(707\) −0.247299 22.0163i −0.00930064 0.828009i
\(708\) 1.66756 6.22342i 0.0626707 0.233890i
\(709\) 6.08452 6.08452i 0.228509 0.228509i −0.583561 0.812070i \(-0.698341\pi\)
0.812070 + 0.583561i \(0.198341\pi\)
\(710\) 7.05531 26.3308i 0.264781 0.988176i
\(711\) 7.63746 13.2285i 0.286427 0.496107i
\(712\) 8.91365 + 15.4389i 0.334053 + 0.578597i
\(713\) 16.3818 4.38948i 0.613502 0.164387i
\(714\) 11.9963 + 11.7298i 0.448949 + 0.438975i
\(715\) 20.4153 + 46.7248i 0.763490 + 1.74741i
\(716\) −5.01990 + 8.69473i −0.187603 + 0.324937i
\(717\) −7.26823 + 7.26823i −0.271437 + 0.271437i
\(718\) −18.1749 −0.678281
\(719\) −17.1045 −0.637891 −0.318946 0.947773i \(-0.603329\pi\)
−0.318946 + 0.947773i \(0.603329\pi\)
\(720\) −3.09834 + 3.09834i −0.115468 + 0.115468i
\(721\) −5.49758 3.09222i −0.204741 0.115160i
\(722\) 9.87857 + 2.64696i 0.367642 + 0.0985095i
\(723\) 2.84189 + 10.6061i 0.105691 + 0.394444i
\(724\) 0.243245 + 0.140438i 0.00904013 + 0.00521932i
\(725\) 49.3780i 1.83385i
\(726\) 0.150895 0.563149i 0.00560025 0.0209004i
\(727\) 45.6775 1.69409 0.847043 0.531525i \(-0.178381\pi\)
0.847043 + 0.531525i \(0.178381\pi\)
\(728\) 1.53263 + 9.41547i 0.0568029 + 0.348961i
\(729\) −1.00000 −0.0370370
\(730\) 4.07957 15.2252i 0.150992 0.563508i
\(731\) 19.7311i 0.729780i
\(732\) 4.94487 + 2.85492i 0.182768 + 0.105521i
\(733\) 8.90463 + 33.2325i 0.328900 + 1.22747i 0.910333 + 0.413877i \(0.135826\pi\)
−0.581433 + 0.813594i \(0.697508\pi\)
\(734\) 0.342684 + 0.0918218i 0.0126487 + 0.00338920i
\(735\) −29.4410 + 8.60197i −1.08595 + 0.317288i
\(736\) −1.40397 + 1.40397i −0.0517510 + 0.0517510i
\(737\) 17.1430 0.631470
\(738\) 0.0115094 0.000423669
\(739\) 1.55885 1.55885i 0.0573432 0.0573432i −0.677854 0.735197i \(-0.737090\pi\)
0.735197 + 0.677854i \(0.237090\pi\)
\(740\) 0.394222 0.682812i 0.0144919 0.0251007i
\(741\) −2.91541 19.2731i −0.107100 0.708015i
\(742\) 8.84489 + 31.5861i 0.324706 + 1.15956i
\(743\) −22.1382 + 5.93191i −0.812172 + 0.217621i −0.640921 0.767607i \(-0.721447\pi\)
−0.171251 + 0.985227i \(0.554781\pi\)
\(744\) 4.27085 + 7.39733i 0.156577 + 0.271199i
\(745\) −15.8433 + 27.4413i −0.580452 + 1.00537i
\(746\) −5.48717 + 20.4784i −0.200899 + 0.749767i
\(747\) −1.17696 + 1.17696i −0.0430628 + 0.0430628i
\(748\) −5.29731 + 19.7698i −0.193689 + 0.722857i
\(749\) −9.70771 + 5.75109i −0.354712 + 0.210140i
\(750\) −20.1545 34.9086i −0.735937 1.27468i
\(751\) −32.6576 + 18.8548i −1.19169 + 0.688023i −0.958690 0.284453i \(-0.908188\pi\)
−0.233001 + 0.972476i \(0.574855\pi\)
\(752\) 2.71681 + 2.71681i 0.0990720 + 0.0990720i
\(753\) 11.3271 6.53973i 0.412784 0.238321i
\(754\) −1.87530 12.3972i −0.0682945 0.451479i
\(755\) 14.8452i 0.540273i
\(756\) −2.30600 1.29706i −0.0838685 0.0471735i
\(757\) −14.6011 + 25.2898i −0.530685 + 0.919173i 0.468674 + 0.883371i \(0.344732\pi\)
−0.999359 + 0.0358019i \(0.988601\pi\)
\(758\) 10.7287i 0.389683i
\(759\) −6.18995 1.65859i −0.224681 0.0602031i
\(760\) 22.8812 6.13101i 0.829990 0.222395i
\(761\) −21.3286 21.3286i −0.773161 0.773161i 0.205497 0.978658i \(-0.434119\pi\)
−0.978658 + 0.205497i \(0.934119\pi\)
\(762\) 0.496149 + 0.496149i 0.0179736 + 0.0179736i
\(763\) 47.9864 + 12.2819i 1.73722 + 0.444636i
\(764\) −3.44763 1.99049i −0.124731 0.0720133i
\(765\) −26.8396 7.19164i −0.970387 0.260014i
\(766\) −7.33644 12.7071i −0.265076 0.459126i
\(767\) 21.6291 + 8.47555i 0.780980 + 0.306034i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) −5.78494 21.5897i −0.208610 0.778544i −0.988319 0.152401i \(-0.951299\pi\)
0.779709 0.626143i \(-0.215367\pi\)
\(770\) −26.7530 26.1586i −0.964110 0.942692i
\(771\) −0.0559561 + 0.0323063i −0.00201521 + 0.00116348i
\(772\) −23.6743 + 6.34351i −0.852056 + 0.228308i
\(773\) 0.119844 + 0.447264i 0.00431049 + 0.0160870i 0.968048 0.250767i \(-0.0806827\pi\)
−0.963737 + 0.266854i \(0.914016\pi\)
\(774\) 0.805301 + 3.00543i 0.0289460 + 0.108028i
\(775\) −117.154 + 31.3913i −4.20830 + 1.12761i
\(776\) −2.01773 + 1.16494i −0.0724322 + 0.0418188i
\(777\) 0.461209 + 0.118045i 0.0165458 + 0.00423483i
\(778\) 2.06397 + 7.70285i 0.0739970 + 0.276161i
\(779\) −0.0538862 0.0311112i −0.00193067 0.00111467i
\(780\) −9.85674 12.3465i −0.352928 0.442076i
\(781\) 10.0396 + 17.3891i 0.359246 + 0.622232i
\(782\) −12.1620 3.25879i −0.434912 0.116534i
\(783\) 3.01158 + 1.73874i 0.107625 + 0.0621375i
\(784\) −3.63529 5.98203i −0.129832 0.213644i
\(785\) 5.66363 + 5.66363i 0.202144 + 0.202144i
\(786\) −5.04371 5.04371i −0.179903 0.179903i
\(787\) −21.0823 + 5.64900i −0.751505 + 0.201365i −0.614185 0.789162i \(-0.710515\pi\)
−0.137319 + 0.990527i \(0.543849\pi\)
\(788\) −3.65004 0.978025i −0.130027 0.0348407i
\(789\) 3.99899i 0.142368i
\(790\) −33.4651 + 57.9633i −1.19064 + 2.06224i
\(791\) −17.6720 + 10.4693i −0.628344 + 0.372247i
\(792\) 3.22754i 0.114685i
\(793\) −12.2163 + 16.5709i −0.433813 + 0.588448i
\(794\) −18.6261 + 10.7538i −0.661015 + 0.381637i
\(795\) −38.4121 38.4121i −1.36234 1.36234i
\(796\) 3.09532 1.78708i 0.109711 0.0633415i
\(797\) −8.23632 14.2657i −0.291745 0.505318i 0.682477 0.730907i \(-0.260903\pi\)
−0.974223 + 0.225589i \(0.927569\pi\)
\(798\) 7.29042 + 12.3061i 0.258078 + 0.435630i
\(799\) −6.30608 + 23.5346i −0.223093 + 0.832595i
\(800\) 10.0405 10.0405i 0.354984 0.354984i
\(801\) 4.61404 17.2198i 0.163029 0.608433i
\(802\) 10.8874 18.8576i 0.384448 0.665884i
\(803\) 5.80518 + 10.0549i 0.204860 + 0.354828i
\(804\) −5.13050 + 1.37471i −0.180939 + 0.0484824i
\(805\) 16.0922 16.4579i 0.567177 0.580063i
\(806\) −28.2213 + 12.3307i −0.994054 + 0.434329i
\(807\) 2.14836 3.72107i 0.0756259 0.130988i
\(808\) −5.88448 + 5.88448i −0.207015 + 0.207015i
\(809\) 17.0828 0.600601 0.300300 0.953845i \(-0.402913\pi\)
0.300300 + 0.953845i \(0.402913\pi\)
\(810\) 4.38171 0.153958
\(811\) 18.8226 18.8226i 0.660952 0.660952i −0.294653 0.955604i \(-0.595204\pi\)
0.955604 + 0.294653i \(0.0952040\pi\)
\(812\) 4.68948 + 7.91573i 0.164568 + 0.277788i
\(813\) 7.36399 + 1.97318i 0.258267 + 0.0692023i
\(814\) 0.150312 + 0.560973i 0.00526844 + 0.0196621i
\(815\) −43.4949 25.1118i −1.52356 0.879629i
\(816\) 6.34145i 0.221995i
\(817\) 4.35362 16.2479i 0.152314 0.568444i
\(818\) −32.3297 −1.13038
\(819\) 5.57401 7.74147i 0.194772 0.270509i
\(820\) −0.0504310 −0.00176113
\(821\) −0.988460 + 3.68898i −0.0344975 + 0.128746i −0.981027 0.193870i \(-0.937896\pi\)
0.946530 + 0.322617i \(0.104563\pi\)
\(822\) 0.904896i 0.0315619i
\(823\) 15.7907 + 9.11678i 0.550430 + 0.317791i 0.749295 0.662236i \(-0.230392\pi\)
−0.198865 + 0.980027i \(0.563726\pi\)
\(824\) 0.617033 + 2.30280i 0.0214954 + 0.0802217i
\(825\) 44.2674 + 11.8614i 1.54119 + 0.412961i
\(826\) −17.0454 + 0.191463i −0.593085 + 0.00666184i
\(827\) 0.844609 0.844609i 0.0293699 0.0293699i −0.692269 0.721639i \(-0.743389\pi\)
0.721639 + 0.692269i \(0.243389\pi\)
\(828\) 1.98551 0.0690013
\(829\) 22.0384 0.765426 0.382713 0.923867i \(-0.374990\pi\)
0.382713 + 0.923867i \(0.374990\pi\)
\(830\) 5.15710 5.15710i 0.179006 0.179006i
\(831\) 0.639421 1.10751i 0.0221813 0.0384191i
\(832\) 2.13951 2.90215i 0.0741742 0.100614i
\(833\) 21.3260 38.9318i 0.738900 1.34891i
\(834\) −19.8435 + 5.31705i −0.687124 + 0.184114i
\(835\) 22.1159 + 38.3058i 0.765351 + 1.32563i
\(836\) −8.72436 + 15.1110i −0.301738 + 0.522626i
\(837\) 2.21076 8.25065i 0.0764149 0.285184i
\(838\) −3.65284 + 3.65284i −0.126185 + 0.126185i
\(839\) −12.2092 + 45.5653i −0.421508 + 1.57309i 0.349925 + 0.936778i \(0.386207\pi\)
−0.771433 + 0.636311i \(0.780460\pi\)
\(840\) 10.1042 + 5.68332i 0.348629 + 0.196093i
\(841\) 8.45357 + 14.6420i 0.291502 + 0.504897i
\(842\) −12.5115 + 7.22351i −0.431174 + 0.248939i
\(843\) 7.17377 + 7.17377i 0.247078 + 0.247078i
\(844\) 13.3699 7.71910i 0.460210 0.265702i
\(845\) 48.1991 30.3569i 1.65810 1.04431i
\(846\) 3.84215i 0.132096i
\(847\) −1.54241 + 0.0173252i −0.0529980 + 0.000595301i
\(848\) 6.19883 10.7367i 0.212869 0.368700i
\(849\) 4.33819i 0.148886i
\(850\) 86.9763 + 23.3052i 2.98326 + 0.799363i
\(851\) −0.345099 + 0.0924689i −0.0118298 + 0.00316979i
\(852\) −4.39908 4.39908i −0.150710 0.150710i
\(853\) −17.7773 17.7773i −0.608682 0.608682i 0.333919 0.942602i \(-0.391629\pi\)
−0.942602 + 0.333919i \(0.891629\pi\)
\(854\) 3.74579 14.6351i 0.128178 0.500802i
\(855\) −20.5148 11.8442i −0.701590 0.405063i
\(856\) 4.11940 + 1.10379i 0.140798 + 0.0377267i
\(857\) 6.86537 + 11.8912i 0.234517 + 0.406195i 0.959132 0.282959i \(-0.0913160\pi\)
−0.724616 + 0.689153i \(0.757983\pi\)
\(858\) 11.5646 + 1.29680i 0.394808 + 0.0442721i
\(859\) 27.2083 + 15.7087i 0.928334 + 0.535974i 0.886284 0.463141i \(-0.153278\pi\)
0.0420501 + 0.999116i \(0.486611\pi\)
\(860\) −3.52860 13.1689i −0.120324 0.449056i
\(861\) −0.00821120 0.0293232i −0.000279837 0.000999331i
\(862\) 3.73450 2.15611i 0.127198 0.0734375i
\(863\) 55.8578 14.9670i 1.90142 0.509484i 0.904952 0.425513i \(-0.139906\pi\)
0.996468 0.0839709i \(-0.0267603\pi\)
\(864\) 0.258819 + 0.965926i 0.00880520 + 0.0328615i
\(865\) 12.3931 + 46.2518i 0.421379 + 1.57261i
\(866\) 36.8550 9.87526i 1.25238 0.335575i
\(867\) 20.1039 11.6070i 0.682763 0.394194i
\(868\) 15.7996 16.1585i 0.536272 0.548457i
\(869\) −12.7599 47.6205i −0.432849 1.61541i
\(870\) −13.1959 7.61865i −0.447382 0.258296i
\(871\) −2.86432 18.9354i −0.0970539 0.641601i
\(872\) −9.36090 16.2136i −0.317000 0.549060i
\(873\) 2.25048 + 0.603015i 0.0761673 + 0.0204090i
\(874\) −9.29598 5.36704i −0.314441 0.181543i
\(875\) −74.5593 + 76.2533i −2.52057 + 2.57783i
\(876\) −2.54366 2.54366i −0.0859424 0.0859424i
\(877\) −25.5733 25.5733i −0.863548 0.863548i 0.128200 0.991748i \(-0.459080\pi\)
−0.991748 + 0.128200i \(0.959080\pi\)
\(878\) −19.0890 + 5.11487i −0.644221 + 0.172618i
\(879\) 17.5606 + 4.70535i 0.592305 + 0.158708i
\(880\) 14.1421i 0.476731i
\(881\) −8.96533 + 15.5284i −0.302050 + 0.523165i −0.976600 0.215063i \(-0.931004\pi\)
0.674550 + 0.738229i \(0.264337\pi\)
\(882\) −1.65940 + 6.80047i −0.0558748 + 0.228984i
\(883\) 15.9776i 0.537689i 0.963184 + 0.268844i \(0.0866417\pi\)
−0.963184 + 0.268844i \(0.913358\pi\)
\(884\) 22.7220 + 2.54795i 0.764224 + 0.0856968i
\(885\) 24.4489 14.1156i 0.821840 0.474490i
\(886\) −19.3976 19.3976i −0.651677 0.651677i
\(887\) 26.4145 15.2504i 0.886910 0.512058i 0.0139798 0.999902i \(-0.495550\pi\)
0.872931 + 0.487844i \(0.162217\pi\)
\(888\) −0.0899699 0.155832i −0.00301919 0.00522939i
\(889\) 0.910093 1.61803i 0.0305235 0.0542670i
\(890\) −20.2174 + 75.4523i −0.677689 + 2.52917i
\(891\) −2.28221 + 2.28221i −0.0764570 + 0.0764570i
\(892\) 5.78209 21.5790i 0.193599 0.722520i
\(893\) −10.3857 + 17.9886i −0.347545 + 0.601966i
\(894\) 3.61577 + 6.26270i 0.120930 + 0.209456i
\(895\) −42.4925 + 11.3858i −1.42037 + 0.380587i
\(896\) −0.656024 + 2.56313i −0.0219162 + 0.0856281i
\(897\) −0.797765 + 7.11427i −0.0266366 + 0.237539i
\(898\) 10.9810 19.0197i 0.366441 0.634694i
\(899\) −21.0036 + 21.0036i −0.700510 + 0.700510i
\(900\) −14.1994 −0.473312
\(901\) 78.6192 2.61918
\(902\) 0.0262670 0.0262670i 0.000874596 0.000874596i
\(903\) 7.08254 4.19587i 0.235692 0.139630i
\(904\) 7.49899 + 2.00935i 0.249413 + 0.0668300i
\(905\) 0.318532 + 1.18878i 0.0105884 + 0.0395163i
\(906\) 2.93409 + 1.69400i 0.0974786 + 0.0562793i
\(907\) 8.03721i 0.266871i 0.991057 + 0.133436i \(0.0426009\pi\)
−0.991057 + 0.133436i \(0.957399\pi\)
\(908\) 5.98281 22.3281i 0.198546 0.740985i
\(909\) 8.32192 0.276021
\(910\) −24.4237 + 33.9209i −0.809638 + 1.12447i
\(911\) −35.0854 −1.16243 −0.581216 0.813750i \(-0.697423\pi\)
−0.581216 + 0.813750i \(0.697423\pi\)
\(912\) 1.39923 5.22199i 0.0463331 0.172917i
\(913\) 5.37215i 0.177792i
\(914\) −7.69890 4.44496i −0.254657 0.147026i
\(915\) 6.47536 + 24.1664i 0.214069 + 0.798916i
\(916\) −13.7806 3.69250i −0.455323 0.122003i
\(917\) −9.25176 + 16.4484i −0.305520 + 0.543175i
\(918\) −4.48408 + 4.48408i −0.147997 + 0.147997i
\(919\) 3.32817 0.109786 0.0548932 0.998492i \(-0.482518\pi\)
0.0548932 + 0.998492i \(0.482518\pi\)
\(920\) −8.69993 −0.286828
\(921\) −7.72652 + 7.72652i −0.254598 + 0.254598i
\(922\) −6.64407 + 11.5079i −0.218811 + 0.378992i
\(923\) 17.5298 13.9948i 0.577001 0.460644i
\(924\) −8.22294 + 2.30263i −0.270515 + 0.0757508i
\(925\) 2.46797 0.661290i 0.0811463 0.0217431i
\(926\) 11.9497 + 20.6975i 0.392693 + 0.680164i
\(927\) 1.19202 2.06463i 0.0391509 0.0678114i
\(928\) 0.900038 3.35899i 0.0295452 0.110264i
\(929\) −19.7186 + 19.7186i −0.646948 + 0.646948i −0.952254 0.305306i \(-0.901241\pi\)
0.305306 + 0.952254i \(0.401241\pi\)
\(930\) −9.68688 + 36.1519i −0.317645 + 1.18547i
\(931\) 26.1515 27.3537i 0.857082 0.896480i
\(932\) −1.01943 1.76570i −0.0333925 0.0578376i
\(933\) −9.99263 + 5.76925i −0.327144 + 0.188877i
\(934\) 8.09226 + 8.09226i 0.264787 + 0.264787i
\(935\) −77.6665 + 44.8407i −2.53996 + 1.46645i
\(936\) −3.56499 + 0.539271i −0.116525 + 0.0176266i
\(937\) 18.5913i 0.607351i −0.952776 0.303676i \(-0.901786\pi\)
0.952776 0.303676i \(-0.0982139\pi\)
\(938\) 7.16268 + 12.0904i 0.233870 + 0.394767i
\(939\) 9.06000 15.6924i 0.295662 0.512101i
\(940\) 16.8352i 0.549104i
\(941\) −27.0611 7.25100i −0.882167 0.236376i −0.210825 0.977524i \(-0.567615\pi\)
−0.671342 + 0.741148i \(0.734282\pi\)
\(942\) 1.76567 0.473111i 0.0575288 0.0154148i
\(943\) 0.0161589 + 0.0161589i 0.000526206 + 0.000526206i
\(944\) 4.55586 + 4.55586i 0.148280 + 0.148280i
\(945\) −3.12605 11.1635i −0.101690 0.363148i
\(946\) 8.69689 + 5.02115i 0.282760 + 0.163252i
\(947\) −29.2741 7.84398i −0.951282 0.254895i −0.250376 0.968149i \(-0.580554\pi\)
−0.700906 + 0.713254i \(0.747221\pi\)
\(948\) 7.63746 + 13.2285i 0.248053 + 0.429641i
\(949\) 10.1362 8.09215i 0.329035 0.262682i
\(950\) 66.4801 + 38.3823i 2.15690 + 1.24529i
\(951\) −6.42219 23.9680i −0.208254 0.777214i
\(952\) −16.1564 + 4.52419i −0.523632 + 0.146630i
\(953\) −23.0230 + 13.2923i −0.745789 + 0.430581i −0.824170 0.566342i \(-0.808358\pi\)
0.0783816 + 0.996923i \(0.475025\pi\)
\(954\) −11.9752 + 3.20875i −0.387712 + 0.103887i
\(955\) −4.51470 16.8491i −0.146092 0.545224i
\(956\) −2.66036 9.92859i −0.0860421 0.321113i
\(957\) 10.8412 2.90490i 0.350448 0.0939022i
\(958\) −28.6291 + 16.5290i −0.924964 + 0.534028i
\(959\) 2.30545 0.645582i 0.0744468 0.0208469i
\(960\) −1.13407 4.23240i −0.0366019 0.136600i
\(961\) 36.3390 + 20.9803i 1.17223 + 0.676785i
\(962\) 0.594511 0.259758i 0.0191678 0.00837494i
\(963\) −2.13236 3.69335i −0.0687143 0.119017i
\(964\) −10.6061 2.84189i −0.341599 0.0915312i
\(965\) −93.0052 53.6966i −2.99394 1.72855i
\(966\) −1.41653 5.05858i −0.0455760 0.162757i
\(967\) 24.4165 + 24.4165i 0.785182 + 0.785182i 0.980700 0.195518i \(-0.0626387\pi\)
−0.195518 + 0.980700i \(0.562639\pi\)
\(968\) 0.412253 + 0.412253i 0.0132503 + 0.0132503i
\(969\) 33.1150 8.87314i 1.06381 0.285046i
\(970\) −9.86096 2.64224i −0.316616 0.0848371i
\(971\) 28.1935i 0.904772i 0.891822 + 0.452386i \(0.149427\pi\)
−0.891822 + 0.452386i \(0.850573\pi\)
\(972\) 0.500000 0.866025i 0.0160375 0.0277778i
\(973\) 27.7035 + 46.7629i 0.888133 + 1.49915i
\(974\) 37.6061i 1.20498i
\(975\) 5.70521 50.8777i 0.182713 1.62939i
\(976\) −4.94487 + 2.85492i −0.158281 + 0.0913839i
\(977\) −11.1254 11.1254i −0.355932 0.355932i 0.506379 0.862311i \(-0.330984\pi\)
−0.862311 + 0.506379i \(0.830984\pi\)
\(978\) −9.92648 + 5.73106i −0.317414 + 0.183259i
\(979\) −28.7691 49.8296i −0.919465 1.59256i
\(980\) 7.27100 29.7977i 0.232264 0.951852i
\(981\) −4.84556 + 18.0839i −0.154707 + 0.577374i
\(982\) 12.0502 12.0502i 0.384536 0.384536i
\(983\) 12.3821 46.2105i 0.394926 1.47388i −0.426979 0.904261i \(-0.640422\pi\)
0.821906 0.569624i \(-0.192911\pi\)
\(984\) −0.00575472 + 0.00996747i −0.000183454 + 0.000317751i
\(985\) −8.27879 14.3393i −0.263784 0.456888i
\(986\) 21.3008 5.70754i 0.678357 0.181765i
\(987\) −9.78884 + 2.74111i −0.311582 + 0.0872506i
\(988\) 18.1487 + 7.11173i 0.577387 + 0.226254i
\(989\) −3.08890 + 5.35014i −0.0982214 + 0.170125i
\(990\) 9.99999 9.99999i 0.317820 0.317820i
\(991\) −8.86301 −0.281543 −0.140771 0.990042i \(-0.544958\pi\)
−0.140771 + 0.990042i \(0.544958\pi\)
\(992\) −8.54170 −0.271199
\(993\) −9.11773 + 9.11773i −0.289343 + 0.289343i
\(994\) −8.06929 + 14.3462i −0.255942 + 0.455033i
\(995\) 15.1273 + 4.05335i 0.479568 + 0.128500i
\(996\) −0.430798 1.60776i −0.0136504 0.0509438i
\(997\) −18.1663 10.4883i −0.575334 0.332169i 0.183943 0.982937i \(-0.441114\pi\)
−0.759277 + 0.650768i \(0.774447\pi\)
\(998\) 0.664275i 0.0210273i
\(999\) −0.0465718 + 0.173808i −0.00147347 + 0.00549906i
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 546.2.by.b.397.1 40
7.3 odd 6 546.2.cg.b.241.1 yes 40
13.2 odd 12 546.2.cg.b.145.1 yes 40
91.80 even 12 inner 546.2.by.b.535.1 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.by.b.397.1 40 1.1 even 1 trivial
546.2.by.b.535.1 yes 40 91.80 even 12 inner
546.2.cg.b.145.1 yes 40 13.2 odd 12
546.2.cg.b.241.1 yes 40 7.3 odd 6