Properties

Label 91.2.bc.a.41.6
Level $91$
Weight $2$
Character 91.41
Analytic conductor $0.727$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 41.6
Character \(\chi\) \(=\) 91.41
Dual form 91.2.bc.a.20.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.112775 - 0.0302180i) q^{2} +(2.25055 - 1.29935i) q^{3} +(-1.72025 - 0.993184i) q^{4} +(1.24841 + 1.24841i) q^{5} +(-0.293070 + 0.0785278i) q^{6} +(-2.63771 - 0.206123i) q^{7} +(0.329103 + 0.329103i) q^{8} +(1.87664 - 3.25044i) q^{9} +O(q^{10})\) \(q+(-0.112775 - 0.0302180i) q^{2} +(2.25055 - 1.29935i) q^{3} +(-1.72025 - 0.993184i) q^{4} +(1.24841 + 1.24841i) q^{5} +(-0.293070 + 0.0785278i) q^{6} +(-2.63771 - 0.206123i) q^{7} +(0.329103 + 0.329103i) q^{8} +(1.87664 - 3.25044i) q^{9} +(-0.103066 - 0.178515i) q^{10} +(-0.506699 + 1.89103i) q^{11} -5.16199 q^{12} +(1.85749 + 3.09026i) q^{13} +(0.291240 + 0.102952i) q^{14} +(4.43175 + 1.18748i) q^{15} +(1.95920 + 3.39343i) q^{16} +(2.13907 - 3.70498i) q^{17} +(-0.309861 + 0.309861i) q^{18} +(-4.12248 + 1.10462i) q^{19} +(-0.907674 - 3.38749i) q^{20} +(-6.20412 + 2.96343i) q^{21} +(0.114286 - 0.197949i) q^{22} +(-5.53927 + 3.19810i) q^{23} +(1.16828 + 0.313041i) q^{24} -1.88292i q^{25} +(-0.116097 - 0.404635i) q^{26} -1.95756i q^{27} +(4.33279 + 2.97431i) q^{28} +(-3.57954 - 6.19995i) q^{29} +(-0.463908 - 0.267837i) q^{30} +(3.02628 + 3.02628i) q^{31} +(-0.359327 - 1.34103i) q^{32} +(1.31676 + 4.91422i) q^{33} +(-0.353191 + 0.353191i) q^{34} +(-3.03563 - 3.55028i) q^{35} +(-6.45657 + 3.72770i) q^{36} +(-0.732202 + 2.73261i) q^{37} +0.498293 q^{38} +(8.19572 + 4.54125i) q^{39} +0.821715i q^{40} +(2.94901 - 11.0059i) q^{41} +(0.789220 - 0.146725i) q^{42} +(-1.55234 - 0.896243i) q^{43} +(2.74978 - 2.74978i) q^{44} +(6.40072 - 1.71507i) q^{45} +(0.721333 - 0.193281i) q^{46} +(4.68665 - 4.68665i) q^{47} +(8.81854 + 5.09139i) q^{48} +(6.91503 + 1.08738i) q^{49} +(-0.0568982 + 0.212347i) q^{50} -11.1176i q^{51} +(-0.126138 - 7.16084i) q^{52} +4.27793 q^{53} +(-0.0591537 + 0.220765i) q^{54} +(-2.99335 + 1.72821i) q^{55} +(-0.800244 - 0.935915i) q^{56} +(-7.84255 + 7.84255i) q^{57} +(0.216333 + 0.807367i) q^{58} +(0.436704 + 1.62980i) q^{59} +(-6.44431 - 6.44431i) q^{60} +(-2.66960 - 1.54129i) q^{61} +(-0.249841 - 0.432737i) q^{62} +(-5.62002 + 8.18690i) q^{63} -7.67470i q^{64} +(-1.53901 + 6.17685i) q^{65} -0.593993i q^{66} +(-0.0190380 - 0.00510122i) q^{67} +(-7.35945 + 4.24898i) q^{68} +(-8.31093 + 14.3949i) q^{69} +(0.235061 + 0.492115i) q^{70} +(1.23109 + 4.59449i) q^{71} +(1.68734 - 0.452121i) q^{72} +(-0.698492 + 0.698492i) q^{73} +(0.165148 - 0.286046i) q^{74} +(-2.44658 - 4.23761i) q^{75} +(8.18877 + 2.19417i) q^{76} +(1.72631 - 4.88353i) q^{77} +(-0.787046 - 0.759799i) q^{78} -5.93719 q^{79} +(-1.79052 + 6.68230i) q^{80} +(3.08636 + 5.34573i) q^{81} +(-0.665151 + 1.15208i) q^{82} +(-9.87683 - 9.87683i) q^{83} +(13.6158 + 1.06400i) q^{84} +(7.29580 - 1.95490i) q^{85} +(0.147983 + 0.147983i) q^{86} +(-16.1119 - 9.30218i) q^{87} +(-0.789099 + 0.455587i) q^{88} +(7.76240 + 2.07993i) q^{89} -0.773669 q^{90} +(-4.26255 - 8.53409i) q^{91} +12.7052 q^{92} +(10.7430 + 2.87857i) q^{93} +(-0.670159 + 0.386917i) q^{94} +(-6.52558 - 3.76755i) q^{95} +(-2.55115 - 2.55115i) q^{96} +(-14.2676 + 3.82300i) q^{97} +(-0.746985 - 0.331588i) q^{98} +(5.19577 + 5.19577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9} - 4 q^{11} - 32 q^{14} - 8 q^{15} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{22} - 12 q^{23} + 24 q^{28} + 4 q^{29} + 12 q^{30} + 4 q^{32} - 20 q^{35} + 4 q^{37} - 36 q^{39} - 28 q^{42} - 48 q^{43} + 24 q^{44} + 84 q^{46} + 24 q^{49} - 44 q^{50} + 72 q^{53} + 60 q^{56} - 92 q^{57} - 16 q^{58} + 76 q^{60} + 48 q^{63} + 4 q^{65} - 56 q^{67} + 56 q^{70} + 84 q^{71} - 128 q^{72} - 24 q^{74} + 148 q^{78} - 80 q^{79} + 28 q^{81} - 64 q^{84} + 36 q^{85} - 48 q^{86} - 228 q^{88} - 48 q^{91} + 24 q^{92} + 108 q^{93} - 84 q^{95} - 32 q^{98} - 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.112775 0.0302180i −0.0797441 0.0213674i 0.218726 0.975786i \(-0.429810\pi\)
−0.298471 + 0.954419i \(0.596476\pi\)
\(3\) 2.25055 1.29935i 1.29935 0.750182i 0.319062 0.947734i \(-0.396632\pi\)
0.980292 + 0.197552i \(0.0632990\pi\)
\(4\) −1.72025 0.993184i −0.860123 0.496592i
\(5\) 1.24841 + 1.24841i 0.558308 + 0.558308i 0.928825 0.370518i \(-0.120820\pi\)
−0.370518 + 0.928825i \(0.620820\pi\)
\(6\) −0.293070 + 0.0785278i −0.119645 + 0.0320589i
\(7\) −2.63771 0.206123i −0.996961 0.0779070i
\(8\) 0.329103 + 0.329103i 0.116356 + 0.116356i
\(9\) 1.87664 3.25044i 0.625547 1.08348i
\(10\) −0.103066 0.178515i −0.0325922 0.0564514i
\(11\) −0.506699 + 1.89103i −0.152775 + 0.570166i 0.846510 + 0.532373i \(0.178699\pi\)
−0.999286 + 0.0377930i \(0.987967\pi\)
\(12\) −5.16199 −1.49014
\(13\) 1.85749 + 3.09026i 0.515175 + 0.857085i
\(14\) 0.291240 + 0.102952i 0.0778371 + 0.0275151i
\(15\) 4.43175 + 1.18748i 1.14427 + 0.306607i
\(16\) 1.95920 + 3.39343i 0.489800 + 0.848358i
\(17\) 2.13907 3.70498i 0.518801 0.898589i −0.480960 0.876742i \(-0.659712\pi\)
0.999761 0.0218471i \(-0.00695471\pi\)
\(18\) −0.309861 + 0.309861i −0.0730348 + 0.0730348i
\(19\) −4.12248 + 1.10462i −0.945762 + 0.253416i −0.698563 0.715549i \(-0.746177\pi\)
−0.247199 + 0.968965i \(0.579510\pi\)
\(20\) −0.907674 3.38749i −0.202962 0.757465i
\(21\) −6.20412 + 2.96343i −1.35385 + 0.646673i
\(22\) 0.114286 0.197949i 0.0243659 0.0422030i
\(23\) −5.53927 + 3.19810i −1.15502 + 0.666850i −0.950105 0.311930i \(-0.899024\pi\)
−0.204913 + 0.978780i \(0.565691\pi\)
\(24\) 1.16828 + 0.313041i 0.238475 + 0.0638992i
\(25\) 1.88292i 0.376585i
\(26\) −0.116097 0.404635i −0.0227685 0.0793554i
\(27\) 1.95756i 0.376733i
\(28\) 4.33279 + 2.97431i 0.818821 + 0.562092i
\(29\) −3.57954 6.19995i −0.664704 1.15130i −0.979365 0.202097i \(-0.935224\pi\)
0.314661 0.949204i \(-0.398109\pi\)
\(30\) −0.463908 0.267837i −0.0846976 0.0489002i
\(31\) 3.02628 + 3.02628i 0.543535 + 0.543535i 0.924563 0.381028i \(-0.124430\pi\)
−0.381028 + 0.924563i \(0.624430\pi\)
\(32\) −0.359327 1.34103i −0.0635206 0.237062i
\(33\) 1.31676 + 4.91422i 0.229219 + 0.855456i
\(34\) −0.353191 + 0.353191i −0.0605718 + 0.0605718i
\(35\) −3.03563 3.55028i −0.513115 0.600107i
\(36\) −6.45657 + 3.72770i −1.07609 + 0.621284i
\(37\) −0.732202 + 2.73261i −0.120373 + 0.449239i −0.999633 0.0271042i \(-0.991371\pi\)
0.879259 + 0.476343i \(0.158038\pi\)
\(38\) 0.498293 0.0808338
\(39\) 8.19572 + 4.54125i 1.31236 + 0.727181i
\(40\) 0.821715i 0.129925i
\(41\) 2.94901 11.0059i 0.460558 1.71883i −0.210654 0.977561i \(-0.567559\pi\)
0.671212 0.741266i \(-0.265774\pi\)
\(42\) 0.789220 0.146725i 0.121779 0.0226402i
\(43\) −1.55234 0.896243i −0.236730 0.136676i 0.376943 0.926236i \(-0.376975\pi\)
−0.613673 + 0.789561i \(0.710309\pi\)
\(44\) 2.74978 2.74978i 0.414545 0.414545i
\(45\) 6.40072 1.71507i 0.954163 0.255667i
\(46\) 0.721333 0.193281i 0.106355 0.0284977i
\(47\) 4.68665 4.68665i 0.683618 0.683618i −0.277196 0.960814i \(-0.589405\pi\)
0.960814 + 0.277196i \(0.0894050\pi\)
\(48\) 8.81854 + 5.09139i 1.27285 + 0.734878i
\(49\) 6.91503 + 1.08738i 0.987861 + 0.155340i
\(50\) −0.0568982 + 0.212347i −0.00804663 + 0.0300304i
\(51\) 11.1176i 1.55678i
\(52\) −0.126138 7.16084i −0.0174922 0.993030i
\(53\) 4.27793 0.587619 0.293809 0.955864i \(-0.405077\pi\)
0.293809 + 0.955864i \(0.405077\pi\)
\(54\) −0.0591537 + 0.220765i −0.00804980 + 0.0300423i
\(55\) −2.99335 + 1.72821i −0.403624 + 0.233032i
\(56\) −0.800244 0.935915i −0.106937 0.125067i
\(57\) −7.84255 + 7.84255i −1.03877 + 1.03877i
\(58\) 0.216333 + 0.807367i 0.0284060 + 0.106013i
\(59\) 0.436704 + 1.62980i 0.0568541 + 0.212182i 0.988509 0.151162i \(-0.0483015\pi\)
−0.931655 + 0.363344i \(0.881635\pi\)
\(60\) −6.44431 6.44431i −0.831956 0.831956i
\(61\) −2.66960 1.54129i −0.341807 0.197342i 0.319264 0.947666i \(-0.396564\pi\)
−0.661071 + 0.750323i \(0.729898\pi\)
\(62\) −0.249841 0.432737i −0.0317298 0.0549577i
\(63\) −5.62002 + 8.18690i −0.708057 + 1.03145i
\(64\) 7.67470i 0.959338i
\(65\) −1.53901 + 6.17685i −0.190891 + 0.766144i
\(66\) 0.593993i 0.0731154i
\(67\) −0.0190380 0.00510122i −0.00232586 0.000623213i 0.257656 0.966237i \(-0.417050\pi\)
−0.259982 + 0.965614i \(0.583717\pi\)
\(68\) −7.35945 + 4.24898i −0.892465 + 0.515265i
\(69\) −8.31093 + 14.3949i −1.00052 + 1.73295i
\(70\) 0.235061 + 0.492115i 0.0280952 + 0.0588189i
\(71\) 1.23109 + 4.59449i 0.146104 + 0.545266i 0.999704 + 0.0243373i \(0.00774758\pi\)
−0.853600 + 0.520929i \(0.825586\pi\)
\(72\) 1.68734 0.452121i 0.198855 0.0532830i
\(73\) −0.698492 + 0.698492i −0.0817523 + 0.0817523i −0.746800 0.665048i \(-0.768411\pi\)
0.665048 + 0.746800i \(0.268411\pi\)
\(74\) 0.165148 0.286046i 0.0191981 0.0332521i
\(75\) −2.44658 4.23761i −0.282507 0.489317i
\(76\) 8.18877 + 2.19417i 0.939316 + 0.251689i
\(77\) 1.72631 4.88353i 0.196731 0.556530i
\(78\) −0.787046 0.759799i −0.0891154 0.0860303i
\(79\) −5.93719 −0.667987 −0.333993 0.942575i \(-0.608396\pi\)
−0.333993 + 0.942575i \(0.608396\pi\)
\(80\) −1.79052 + 6.68230i −0.200186 + 0.747104i
\(81\) 3.08636 + 5.34573i 0.342929 + 0.593970i
\(82\) −0.665151 + 1.15208i −0.0734536 + 0.127225i
\(83\) −9.87683 9.87683i −1.08412 1.08412i −0.996120 0.0880033i \(-0.971951\pi\)
−0.0880033 0.996120i \(-0.528049\pi\)
\(84\) 13.6158 + 1.06400i 1.48561 + 0.116092i
\(85\) 7.29580 1.95490i 0.791340 0.212039i
\(86\) 0.147983 + 0.147983i 0.0159574 + 0.0159574i
\(87\) −16.1119 9.30218i −1.72737 0.997299i
\(88\) −0.789099 + 0.455587i −0.0841183 + 0.0485657i
\(89\) 7.76240 + 2.07993i 0.822813 + 0.220472i 0.645576 0.763696i \(-0.276617\pi\)
0.177237 + 0.984168i \(0.443284\pi\)
\(90\) −0.773669 −0.0815519
\(91\) −4.26255 8.53409i −0.446836 0.894616i
\(92\) 12.7052 1.32461
\(93\) 10.7430 + 2.87857i 1.11400 + 0.298494i
\(94\) −0.670159 + 0.386917i −0.0691216 + 0.0399074i
\(95\) −6.52558 3.76755i −0.669511 0.386542i
\(96\) −2.55115 2.55115i −0.260376 0.260376i
\(97\) −14.2676 + 3.82300i −1.44866 + 0.388167i −0.895557 0.444946i \(-0.853223\pi\)
−0.553102 + 0.833113i \(0.686556\pi\)
\(98\) −0.746985 0.331588i −0.0754569 0.0334955i
\(99\) 5.19577 + 5.19577i 0.522194 + 0.522194i
\(100\) −1.87009 + 3.23909i −0.187009 + 0.323909i
\(101\) 8.00479 + 13.8647i 0.796506 + 1.37959i 0.921878 + 0.387480i \(0.126654\pi\)
−0.125372 + 0.992110i \(0.540012\pi\)
\(102\) −0.335953 + 1.25379i −0.0332643 + 0.124144i
\(103\) 11.8151 1.16418 0.582088 0.813126i \(-0.302236\pi\)
0.582088 + 0.813126i \(0.302236\pi\)
\(104\) −0.405710 + 1.62832i −0.0397831 + 0.159670i
\(105\) −11.4449 4.04572i −1.11691 0.394822i
\(106\) −0.482444 0.129271i −0.0468591 0.0125559i
\(107\) −3.99556 6.92051i −0.386265 0.669031i 0.605679 0.795709i \(-0.292902\pi\)
−0.991944 + 0.126678i \(0.959568\pi\)
\(108\) −1.94422 + 3.36749i −0.187083 + 0.324037i
\(109\) −8.75647 + 8.75647i −0.838718 + 0.838718i −0.988690 0.149972i \(-0.952082\pi\)
0.149972 + 0.988690i \(0.452082\pi\)
\(110\) 0.389799 0.104446i 0.0371659 0.00995857i
\(111\) 1.90278 + 7.10127i 0.180604 + 0.674022i
\(112\) −4.46833 9.35472i −0.422218 0.883938i
\(113\) 4.27217 7.39961i 0.401892 0.696097i −0.592063 0.805892i \(-0.701686\pi\)
0.993954 + 0.109795i \(0.0350195\pi\)
\(114\) 1.12143 0.647459i 0.105032 0.0606401i
\(115\) −10.9079 2.92275i −1.01716 0.272548i
\(116\) 14.2206i 1.32035i
\(117\) 13.5306 0.238340i 1.25090 0.0220346i
\(118\) 0.196998i 0.0181351i
\(119\) −6.40593 + 9.33175i −0.587230 + 0.855440i
\(120\) 1.06770 + 1.84931i 0.0974671 + 0.168818i
\(121\) 6.20705 + 3.58364i 0.564277 + 0.325785i
\(122\) 0.254490 + 0.254490i 0.0230404 + 0.0230404i
\(123\) −7.66362 28.6010i −0.691005 2.57887i
\(124\) −2.20029 8.21159i −0.197592 0.737422i
\(125\) 8.59274 8.59274i 0.768558 0.768558i
\(126\) 0.881192 0.753453i 0.0785028 0.0671229i
\(127\) −5.29483 + 3.05697i −0.469840 + 0.271262i −0.716173 0.697923i \(-0.754108\pi\)
0.246333 + 0.969185i \(0.420774\pi\)
\(128\) −0.950568 + 3.54757i −0.0840191 + 0.313564i
\(129\) −4.65815 −0.410127
\(130\) 0.360215 0.650090i 0.0315929 0.0570166i
\(131\) 5.76435i 0.503634i 0.967775 + 0.251817i \(0.0810280\pi\)
−0.967775 + 0.251817i \(0.918972\pi\)
\(132\) 2.61557 9.76146i 0.227657 0.849626i
\(133\) 11.1016 2.06392i 0.962630 0.178964i
\(134\) 0.00199287 + 0.00115058i 0.000172157 + 9.93951e-5i
\(135\) 2.44385 2.44385i 0.210333 0.210333i
\(136\) 1.92330 0.515346i 0.164921 0.0441905i
\(137\) −6.06188 + 1.62427i −0.517901 + 0.138771i −0.508296 0.861183i \(-0.669724\pi\)
−0.00960548 + 0.999954i \(0.503058\pi\)
\(138\) 1.37225 1.37225i 0.116814 0.116814i
\(139\) 18.1314 + 10.4682i 1.53789 + 0.887900i 0.998962 + 0.0455477i \(0.0145033\pi\)
0.538927 + 0.842353i \(0.318830\pi\)
\(140\) 1.69594 + 9.12229i 0.143333 + 0.770975i
\(141\) 4.45791 16.6371i 0.375424 1.40110i
\(142\) 0.555346i 0.0466036i
\(143\) −6.78495 + 1.94673i −0.567386 + 0.162794i
\(144\) 14.7069 1.22557
\(145\) 3.27135 12.2089i 0.271671 1.01389i
\(146\) 0.0998797 0.0576656i 0.00826610 0.00477244i
\(147\) 16.9755 6.53786i 1.40011 0.539234i
\(148\) 3.97356 3.97356i 0.326624 0.326624i
\(149\) 4.00070 + 14.9308i 0.327750 + 1.22318i 0.911518 + 0.411260i \(0.134911\pi\)
−0.583768 + 0.811921i \(0.698422\pi\)
\(150\) 0.147862 + 0.551828i 0.0120729 + 0.0450566i
\(151\) 3.12599 + 3.12599i 0.254390 + 0.254390i 0.822768 0.568378i \(-0.192429\pi\)
−0.568378 + 0.822768i \(0.692429\pi\)
\(152\) −1.72026 0.993190i −0.139531 0.0805583i
\(153\) −8.02854 13.9058i −0.649069 1.12422i
\(154\) −0.342256 + 0.498576i −0.0275797 + 0.0401764i
\(155\) 7.55609i 0.606920i
\(156\) −9.58835 15.9519i −0.767682 1.27718i
\(157\) 6.93064i 0.553125i 0.960996 + 0.276563i \(0.0891953\pi\)
−0.960996 + 0.276563i \(0.910805\pi\)
\(158\) 0.669569 + 0.179410i 0.0532680 + 0.0142731i
\(159\) 9.62768 5.55854i 0.763525 0.440821i
\(160\) 1.22557 2.12274i 0.0968896 0.167818i
\(161\) 15.2702 7.29389i 1.20346 0.574839i
\(162\) −0.186527 0.696129i −0.0146550 0.0546931i
\(163\) −12.4944 + 3.34785i −0.978634 + 0.262224i −0.712469 0.701703i \(-0.752423\pi\)
−0.266165 + 0.963928i \(0.585757\pi\)
\(164\) −16.0039 + 16.0039i −1.24969 + 1.24969i
\(165\) −4.49112 + 7.77885i −0.349633 + 0.605583i
\(166\) 0.815404 + 1.41232i 0.0632876 + 0.109617i
\(167\) 0.900490 + 0.241286i 0.0696820 + 0.0186712i 0.293492 0.955962i \(-0.405183\pi\)
−0.223810 + 0.974633i \(0.571849\pi\)
\(168\) −3.01707 1.06652i −0.232772 0.0822839i
\(169\) −6.09946 + 11.4803i −0.469189 + 0.883098i
\(170\) −0.881858 −0.0676355
\(171\) −4.14593 + 15.4728i −0.317047 + 1.18324i
\(172\) 1.78027 + 3.08352i 0.135744 + 0.235116i
\(173\) 0.263780 0.456880i 0.0200548 0.0347360i −0.855824 0.517267i \(-0.826949\pi\)
0.875879 + 0.482531i \(0.160283\pi\)
\(174\) 1.53592 + 1.53592i 0.116438 + 0.116438i
\(175\) −0.388113 + 4.96660i −0.0293386 + 0.375440i
\(176\) −7.40979 + 1.98545i −0.558534 + 0.149659i
\(177\) 3.10051 + 3.10051i 0.233049 + 0.233049i
\(178\) −0.812555 0.469129i −0.0609036 0.0351627i
\(179\) 7.16206 4.13502i 0.535317 0.309066i −0.207862 0.978158i \(-0.566650\pi\)
0.743179 + 0.669093i \(0.233317\pi\)
\(180\) −12.7142 3.40676i −0.947660 0.253925i
\(181\) −14.9785 −1.11334 −0.556672 0.830732i \(-0.687922\pi\)
−0.556672 + 0.830732i \(0.687922\pi\)
\(182\) 0.222826 + 1.09124i 0.0165170 + 0.0808881i
\(183\) −8.01075 −0.592171
\(184\) −2.87550 0.770488i −0.211985 0.0568011i
\(185\) −4.32553 + 2.49734i −0.318019 + 0.183608i
\(186\) −1.12456 0.649263i −0.0824565 0.0476063i
\(187\) 5.92234 + 5.92234i 0.433085 + 0.433085i
\(188\) −12.7169 + 3.40748i −0.927475 + 0.248516i
\(189\) −0.403498 + 5.16348i −0.0293502 + 0.375588i
\(190\) 0.622076 + 0.622076i 0.0451301 + 0.0451301i
\(191\) 7.26461 12.5827i 0.525649 0.910450i −0.473905 0.880576i \(-0.657156\pi\)
0.999554 0.0298741i \(-0.00951063\pi\)
\(192\) −9.97216 17.2723i −0.719678 1.24652i
\(193\) 5.06711 18.9107i 0.364738 1.36122i −0.503037 0.864265i \(-0.667784\pi\)
0.867775 0.496957i \(-0.165549\pi\)
\(194\) 1.72456 0.123816
\(195\) 4.56229 + 15.9010i 0.326712 + 1.13869i
\(196\) −10.8156 8.73846i −0.772541 0.624176i
\(197\) −21.0175 5.63163i −1.49744 0.401237i −0.585196 0.810892i \(-0.698982\pi\)
−0.912240 + 0.409655i \(0.865649\pi\)
\(198\) −0.428948 0.742960i −0.0304840 0.0527999i
\(199\) 9.64065 16.6981i 0.683408 1.18370i −0.290527 0.956867i \(-0.593830\pi\)
0.973934 0.226830i \(-0.0728362\pi\)
\(200\) 0.619676 0.619676i 0.0438177 0.0438177i
\(201\) −0.0494742 + 0.0132566i −0.00348964 + 0.000935047i
\(202\) −0.483778 1.80548i −0.0340385 0.127033i
\(203\) 8.16384 + 17.0915i 0.572989 + 1.19959i
\(204\) −11.0419 + 19.1251i −0.773085 + 1.33902i
\(205\) 17.4215 10.0583i 1.21677 0.702501i
\(206\) −1.33245 0.357029i −0.0928363 0.0248754i
\(207\) 24.0067i 1.66858i
\(208\) −6.84741 + 12.3577i −0.474782 + 0.856853i
\(209\) 8.35542i 0.577957i
\(210\) 1.16845 + 0.802099i 0.0806305 + 0.0553501i
\(211\) 1.51130 + 2.61764i 0.104042 + 0.180206i 0.913346 0.407184i \(-0.133489\pi\)
−0.809304 + 0.587389i \(0.800156\pi\)
\(212\) −7.35909 4.24877i −0.505424 0.291807i
\(213\) 8.74050 + 8.74050i 0.598889 + 0.598889i
\(214\) 0.241476 + 0.901200i 0.0165070 + 0.0616048i
\(215\) −0.819079 3.05685i −0.0558607 0.208475i
\(216\) 0.644241 0.644241i 0.0438350 0.0438350i
\(217\) −7.35865 8.60622i −0.499538 0.584228i
\(218\) 1.25212 0.722910i 0.0848040 0.0489616i
\(219\) −0.664401 + 2.47958i −0.0448961 + 0.167554i
\(220\) 6.86574 0.462888
\(221\) 15.4227 0.271670i 1.03744 0.0182745i
\(222\) 0.858345i 0.0576084i
\(223\) −1.13865 + 4.24949i −0.0762495 + 0.284567i −0.993514 0.113712i \(-0.963726\pi\)
0.917264 + 0.398279i \(0.130392\pi\)
\(224\) 0.671384 + 3.61130i 0.0448587 + 0.241290i
\(225\) −6.12033 3.53357i −0.408022 0.235571i
\(226\) −0.705396 + 0.705396i −0.0469223 + 0.0469223i
\(227\) 3.95917 1.06086i 0.262780 0.0704116i −0.125024 0.992154i \(-0.539901\pi\)
0.387803 + 0.921742i \(0.373234\pi\)
\(228\) 21.2802 5.70202i 1.40932 0.377625i
\(229\) −9.60039 + 9.60039i −0.634412 + 0.634412i −0.949171 0.314760i \(-0.898076\pi\)
0.314760 + 0.949171i \(0.398076\pi\)
\(230\) 1.14182 + 0.659228i 0.0752892 + 0.0434682i
\(231\) −2.46030 13.2337i −0.161876 0.870714i
\(232\) 0.862385 3.21846i 0.0566183 0.211303i
\(233\) 16.3500i 1.07113i 0.844495 + 0.535563i \(0.179900\pi\)
−0.844495 + 0.535563i \(0.820100\pi\)
\(234\) −1.53311 0.381988i −0.100223 0.0249713i
\(235\) 11.7018 0.763339
\(236\) 0.867456 3.23739i 0.0564666 0.210736i
\(237\) −13.3619 + 7.71452i −0.867951 + 0.501112i
\(238\) 1.00442 0.858816i 0.0651067 0.0556688i
\(239\) 6.11495 6.11495i 0.395543 0.395543i −0.481115 0.876658i \(-0.659768\pi\)
0.876658 + 0.481115i \(0.159768\pi\)
\(240\) 4.65303 + 17.3653i 0.300352 + 1.12093i
\(241\) −3.47625 12.9736i −0.223925 0.835700i −0.982832 0.184501i \(-0.940933\pi\)
0.758907 0.651199i \(-0.225734\pi\)
\(242\) −0.591711 0.591711i −0.0380366 0.0380366i
\(243\) 18.9779 + 10.9569i 1.21743 + 0.702885i
\(244\) 3.06158 + 5.30281i 0.195997 + 0.339478i
\(245\) 7.27531 + 9.99032i 0.464803 + 0.638258i
\(246\) 3.45707i 0.220414i
\(247\) −11.0710 10.6877i −0.704432 0.680045i
\(248\) 1.99192i 0.126487i
\(249\) −35.0618 9.39478i −2.22195 0.595370i
\(250\) −1.22870 + 0.709393i −0.0777101 + 0.0448659i
\(251\) 1.74301 3.01899i 0.110018 0.190557i −0.805759 0.592243i \(-0.798242\pi\)
0.915777 + 0.401686i \(0.131576\pi\)
\(252\) 17.7989 8.50175i 1.12123 0.535560i
\(253\) −3.24095 12.0954i −0.203756 0.760430i
\(254\) 0.689501 0.184751i 0.0432631 0.0115923i
\(255\) 13.8794 13.8794i 0.869163 0.869163i
\(256\) −7.46030 + 12.9216i −0.466269 + 0.807601i
\(257\) −6.72396 11.6462i −0.419429 0.726472i 0.576453 0.817130i \(-0.304436\pi\)
−0.995882 + 0.0906578i \(0.971103\pi\)
\(258\) 0.525324 + 0.140760i 0.0327052 + 0.00876334i
\(259\) 2.49459 7.05692i 0.155006 0.438496i
\(260\) 8.78223 9.09717i 0.544651 0.564183i
\(261\) −26.8701 −1.66322
\(262\) 0.174187 0.650076i 0.0107613 0.0401618i
\(263\) −10.2679 17.7846i −0.633147 1.09664i −0.986904 0.161306i \(-0.948430\pi\)
0.353757 0.935337i \(-0.384904\pi\)
\(264\) −1.18394 + 2.05064i −0.0728663 + 0.126208i
\(265\) 5.34063 + 5.34063i 0.328072 + 0.328072i
\(266\) −1.31435 0.102709i −0.0805881 0.00629752i
\(267\) 20.1722 5.40513i 1.23452 0.330788i
\(268\) 0.0276836 + 0.0276836i 0.00169104 + 0.00169104i
\(269\) 9.29875 + 5.36864i 0.566955 + 0.327332i 0.755932 0.654650i \(-0.227184\pi\)
−0.188977 + 0.981981i \(0.560517\pi\)
\(270\) −0.349454 + 0.201757i −0.0212671 + 0.0122786i
\(271\) 1.44767 + 0.387901i 0.0879396 + 0.0235633i 0.302521 0.953143i \(-0.402172\pi\)
−0.214581 + 0.976706i \(0.568839\pi\)
\(272\) 16.7635 1.01643
\(273\) −20.6819 13.6678i −1.25172 0.827214i
\(274\) 0.732712 0.0442647
\(275\) 3.56065 + 0.954075i 0.214716 + 0.0575329i
\(276\) 28.5937 16.5086i 1.72114 0.993699i
\(277\) 4.07919 + 2.35512i 0.245095 + 0.141506i 0.617516 0.786558i \(-0.288139\pi\)
−0.372421 + 0.928064i \(0.621472\pi\)
\(278\) −1.72845 1.72845i −0.103666 0.103666i
\(279\) 15.5160 4.15749i 0.928916 0.248902i
\(280\) 0.169374 2.16745i 0.0101220 0.129530i
\(281\) 8.01227 + 8.01227i 0.477972 + 0.477972i 0.904483 0.426511i \(-0.140257\pi\)
−0.426511 + 0.904483i \(0.640257\pi\)
\(282\) −1.00548 + 1.74155i −0.0598757 + 0.103708i
\(283\) 3.93934 + 6.82313i 0.234169 + 0.405593i 0.959031 0.283301i \(-0.0914297\pi\)
−0.724862 + 0.688894i \(0.758096\pi\)
\(284\) 2.44540 9.12636i 0.145108 0.541550i
\(285\) −19.5815 −1.15991
\(286\) 0.824001 0.0145147i 0.0487242 0.000858275i
\(287\) −10.0472 + 28.4224i −0.593067 + 1.67772i
\(288\) −5.03325 1.34865i −0.296587 0.0794703i
\(289\) −0.651246 1.12799i −0.0383086 0.0663525i
\(290\) −0.737855 + 1.27800i −0.0433284 + 0.0750469i
\(291\) −27.1426 + 27.1426i −1.59113 + 1.59113i
\(292\) 1.89531 0.507847i 0.110915 0.0297195i
\(293\) −3.16216 11.8013i −0.184735 0.689442i −0.994687 0.102945i \(-0.967173\pi\)
0.809952 0.586497i \(-0.199493\pi\)
\(294\) −2.11198 + 0.224343i −0.123173 + 0.0130839i
\(295\) −1.48948 + 2.57986i −0.0867210 + 0.150205i
\(296\) −1.14028 + 0.658343i −0.0662776 + 0.0382654i
\(297\) 3.70180 + 0.991894i 0.214800 + 0.0575556i
\(298\) 1.80472i 0.104545i
\(299\) −20.1721 11.1774i −1.16658 0.646404i
\(300\) 9.71963i 0.561163i
\(301\) 3.90988 + 2.68400i 0.225362 + 0.154703i
\(302\) −0.258073 0.446996i −0.0148504 0.0257217i
\(303\) 36.0303 + 20.8021i 2.06989 + 1.19505i
\(304\) −11.8252 11.8252i −0.678221 0.678221i
\(305\) −1.40859 5.25694i −0.0806558 0.301011i
\(306\) 0.485213 + 1.81084i 0.0277378 + 0.103519i
\(307\) 7.97207 7.97207i 0.454990 0.454990i −0.442017 0.897007i \(-0.645737\pi\)
0.897007 + 0.442017i \(0.145737\pi\)
\(308\) −7.81992 + 6.68634i −0.445581 + 0.380989i
\(309\) 26.5904 15.3520i 1.51268 0.873345i
\(310\) 0.228330 0.852140i 0.0129683 0.0483983i
\(311\) 13.0428 0.739588 0.369794 0.929114i \(-0.379428\pi\)
0.369794 + 0.929114i \(0.379428\pi\)
\(312\) 1.20270 + 4.19178i 0.0680894 + 0.237313i
\(313\) 3.57391i 0.202009i −0.994886 0.101005i \(-0.967794\pi\)
0.994886 0.101005i \(-0.0322057\pi\)
\(314\) 0.209430 0.781604i 0.0118188 0.0441085i
\(315\) −17.2368 + 3.20452i −0.971181 + 0.180554i
\(316\) 10.2134 + 5.89673i 0.574551 + 0.331717i
\(317\) 23.4565 23.4565i 1.31745 1.31745i 0.401662 0.915788i \(-0.368433\pi\)
0.915788 0.401662i \(-0.131567\pi\)
\(318\) −1.25373 + 0.335936i −0.0703058 + 0.0188384i
\(319\) 13.5380 3.62750i 0.757983 0.203101i
\(320\) 9.58121 9.58121i 0.535606 0.535606i
\(321\) −17.9844 10.3833i −1.00379 0.579539i
\(322\) −1.94251 + 0.361135i −0.108252 + 0.0201253i
\(323\) −4.72570 + 17.6366i −0.262945 + 0.981324i
\(324\) 12.2613i 0.681183i
\(325\) 5.81873 3.49751i 0.322765 0.194007i
\(326\) 1.51022 0.0836434
\(327\) −8.32910 + 31.0846i −0.460600 + 1.71898i
\(328\) 4.59260 2.65154i 0.253584 0.146407i
\(329\) −13.3280 + 11.3960i −0.734799 + 0.628282i
\(330\) 0.741549 0.741549i 0.0408209 0.0408209i
\(331\) −0.245395 0.915826i −0.0134881 0.0503383i 0.958854 0.283900i \(-0.0916285\pi\)
−0.972342 + 0.233562i \(0.924962\pi\)
\(332\) 7.18106 + 26.8001i 0.394112 + 1.47085i
\(333\) 7.50812 + 7.50812i 0.411442 + 0.411442i
\(334\) −0.0942618 0.0544221i −0.00515778 0.00297784i
\(335\) −0.0173989 0.0301357i −0.000950602 0.00164649i
\(336\) −22.2113 15.2473i −1.21173 0.831808i
\(337\) 14.1901i 0.772982i 0.922293 + 0.386491i \(0.126313\pi\)
−0.922293 + 0.386491i \(0.873687\pi\)
\(338\) 1.03478 1.11038i 0.0562846 0.0603965i
\(339\) 22.2042i 1.20597i
\(340\) −14.4921 3.88316i −0.785947 0.210594i
\(341\) −7.25617 + 4.18935i −0.392944 + 0.226866i
\(342\) 0.935117 1.61967i 0.0505654 0.0875818i
\(343\) −18.0157 4.29355i −0.972756 0.231830i
\(344\) −0.215923 0.805837i −0.0116418 0.0434478i
\(345\) −28.3463 + 7.59538i −1.52612 + 0.408921i
\(346\) −0.0435539 + 0.0435539i −0.00234147 + 0.00234147i
\(347\) −6.92103 + 11.9876i −0.371540 + 0.643527i −0.989803 0.142445i \(-0.954504\pi\)
0.618262 + 0.785972i \(0.287837\pi\)
\(348\) 18.4776 + 32.0041i 0.990502 + 1.71560i
\(349\) −14.7875 3.96231i −0.791559 0.212098i −0.159684 0.987168i \(-0.551048\pi\)
−0.631875 + 0.775071i \(0.717714\pi\)
\(350\) 0.193851 0.548382i 0.0103617 0.0293123i
\(351\) 6.04939 3.63615i 0.322892 0.194084i
\(352\) 2.71798 0.144869
\(353\) 4.07649 15.2137i 0.216970 0.809742i −0.768494 0.639857i \(-0.778994\pi\)
0.985464 0.169885i \(-0.0543398\pi\)
\(354\) −0.255970 0.443353i −0.0136046 0.0235639i
\(355\) −4.19892 + 7.27274i −0.222856 + 0.385997i
\(356\) −11.2875 11.2875i −0.598235 0.598235i
\(357\) −2.29160 + 29.3251i −0.121284 + 1.55205i
\(358\) −0.932655 + 0.249904i −0.0492924 + 0.0132078i
\(359\) −4.68787 4.68787i −0.247416 0.247416i 0.572493 0.819910i \(-0.305976\pi\)
−0.819910 + 0.572493i \(0.805976\pi\)
\(360\) 2.67093 + 1.54206i 0.140771 + 0.0812739i
\(361\) −0.679814 + 0.392491i −0.0357797 + 0.0206574i
\(362\) 1.68920 + 0.452621i 0.0887826 + 0.0237892i
\(363\) 18.6257 0.977594
\(364\) −1.14330 + 18.9142i −0.0599250 + 0.991375i
\(365\) −1.74402 −0.0912859
\(366\) 0.903414 + 0.242069i 0.0472222 + 0.0126531i
\(367\) −28.4547 + 16.4284i −1.48533 + 0.857553i −0.999860 0.0167033i \(-0.994683\pi\)
−0.485465 + 0.874256i \(0.661350\pi\)
\(368\) −21.7051 12.5314i −1.13145 0.653246i
\(369\) −30.2396 30.2396i −1.57421 1.57421i
\(370\) 0.563277 0.150930i 0.0292834 0.00784646i
\(371\) −11.2839 0.881778i −0.585833 0.0457796i
\(372\) −15.6216 15.6216i −0.809943 0.809943i
\(373\) −3.93986 + 6.82405i −0.203998 + 0.353336i −0.949813 0.312818i \(-0.898727\pi\)
0.745815 + 0.666153i \(0.232060\pi\)
\(374\) −0.488932 0.846855i −0.0252821 0.0437899i
\(375\) 8.17336 30.5034i 0.422070 1.57519i
\(376\) 3.08478 0.159086
\(377\) 12.5105 22.5781i 0.644324 1.16283i
\(378\) 0.201535 0.570120i 0.0103658 0.0293238i
\(379\) 10.8095 + 2.89639i 0.555245 + 0.148778i 0.525521 0.850781i \(-0.323870\pi\)
0.0297243 + 0.999558i \(0.490537\pi\)
\(380\) 7.48374 + 12.9622i 0.383908 + 0.664947i
\(381\) −7.94417 + 13.7597i −0.406992 + 0.704931i
\(382\) −1.19949 + 1.19949i −0.0613713 + 0.0613713i
\(383\) −2.32841 + 0.623897i −0.118976 + 0.0318796i −0.317816 0.948152i \(-0.602949\pi\)
0.198840 + 0.980032i \(0.436283\pi\)
\(384\) 2.47025 + 9.21909i 0.126059 + 0.470460i
\(385\) 8.25182 3.94153i 0.420552 0.200879i
\(386\) −1.14289 + 1.97954i −0.0581715 + 0.100756i
\(387\) −5.82637 + 3.36386i −0.296171 + 0.170994i
\(388\) 28.3408 + 7.59389i 1.43879 + 0.385522i
\(389\) 16.8210i 0.852858i 0.904521 + 0.426429i \(0.140229\pi\)
−0.904521 + 0.426429i \(0.859771\pi\)
\(390\) −0.0340163 1.93110i −0.00172248 0.0977852i
\(391\) 27.3638i 1.38385i
\(392\) 1.91790 + 2.63362i 0.0968685 + 0.133018i
\(393\) 7.48993 + 12.9729i 0.377817 + 0.654398i
\(394\) 2.20008 + 1.27022i 0.110838 + 0.0639926i
\(395\) −7.41208 7.41208i −0.372942 0.372942i
\(396\) −3.77764 14.0984i −0.189834 0.708469i
\(397\) 6.08873 + 22.7234i 0.305585 + 1.14046i 0.932441 + 0.361322i \(0.117675\pi\)
−0.626856 + 0.779135i \(0.715659\pi\)
\(398\) −1.59181 + 1.59181i −0.0797903 + 0.0797903i
\(399\) 22.3029 19.0698i 1.11654 0.954686i
\(400\) 6.38957 3.68902i 0.319479 0.184451i
\(401\) 2.23318 8.33434i 0.111520 0.416197i −0.887483 0.460840i \(-0.847548\pi\)
0.999003 + 0.0446427i \(0.0142149\pi\)
\(402\) 0.00598005 0.000298258
\(403\) −3.73071 + 14.9733i −0.185840 + 0.745872i
\(404\) 31.8009i 1.58216i
\(405\) −2.82063 + 10.5267i −0.140158 + 0.523078i
\(406\) −0.404208 2.17419i −0.0200605 0.107903i
\(407\) −4.79644 2.76922i −0.237751 0.137265i
\(408\) 3.65885 3.65885i 0.181140 0.181140i
\(409\) 12.9780 3.47744i 0.641720 0.171948i 0.0767375 0.997051i \(-0.475550\pi\)
0.564982 + 0.825103i \(0.308883\pi\)
\(410\) −2.26865 + 0.607883i −0.112041 + 0.0300212i
\(411\) −11.5320 + 11.5320i −0.568833 + 0.568833i
\(412\) −20.3249 11.7346i −1.00133 0.578121i
\(413\) −0.815960 4.38896i −0.0401508 0.215967i
\(414\) 0.725437 2.70737i 0.0356533 0.133060i
\(415\) 24.6608i 1.21055i
\(416\) 3.47668 3.60136i 0.170458 0.176571i
\(417\) 54.4075 2.66435
\(418\) −0.252484 + 0.942285i −0.0123494 + 0.0460886i
\(419\) 15.0514 8.68991i 0.735308 0.424530i −0.0850532 0.996376i \(-0.527106\pi\)
0.820361 + 0.571846i \(0.193773\pi\)
\(420\) 15.6699 + 18.3265i 0.764612 + 0.894243i
\(421\) −21.2490 + 21.2490i −1.03561 + 1.03561i −0.0362722 + 0.999342i \(0.511548\pi\)
−0.999342 + 0.0362722i \(0.988452\pi\)
\(422\) −0.0913368 0.340874i −0.00444621 0.0165935i
\(423\) −6.43850 24.0288i −0.313051 1.16832i
\(424\) 1.40788 + 1.40788i 0.0683727 + 0.0683727i
\(425\) −6.97619 4.02771i −0.338395 0.195372i
\(426\) −0.721591 1.24983i −0.0349612 0.0605546i
\(427\) 6.72393 + 4.61575i 0.325394 + 0.223372i
\(428\) 15.8733i 0.767265i
\(429\) −12.7404 + 13.1973i −0.615111 + 0.637170i
\(430\) 0.369487i 0.0178183i
\(431\) 23.3087 + 6.24554i 1.12274 + 0.300837i 0.771991 0.635633i \(-0.219261\pi\)
0.350748 + 0.936470i \(0.385927\pi\)
\(432\) 6.64286 3.83525i 0.319605 0.184524i
\(433\) 2.27124 3.93391i 0.109149 0.189051i −0.806277 0.591538i \(-0.798521\pi\)
0.915426 + 0.402487i \(0.131854\pi\)
\(434\) 0.569811 + 1.19293i 0.0273518 + 0.0572626i
\(435\) −8.50129 31.7273i −0.407606 1.52121i
\(436\) 23.7601 6.36649i 1.13790 0.304900i
\(437\) 19.3029 19.3029i 0.923381 0.923381i
\(438\) 0.149856 0.259558i 0.00716039 0.0124022i
\(439\) −8.50036 14.7231i −0.405700 0.702693i 0.588703 0.808350i \(-0.299639\pi\)
−0.994403 + 0.105657i \(0.966306\pi\)
\(440\) −1.55388 0.416362i −0.0740785 0.0198493i
\(441\) 16.5115 20.4362i 0.786262 0.973154i
\(442\) −1.74750 0.435405i −0.0831203 0.0207101i
\(443\) −36.6165 −1.73970 −0.869851 0.493315i \(-0.835785\pi\)
−0.869851 + 0.493315i \(0.835785\pi\)
\(444\) 3.77962 14.1057i 0.179373 0.669429i
\(445\) 7.09408 + 12.2873i 0.336292 + 0.582474i
\(446\) 0.256823 0.444830i 0.0121609 0.0210633i
\(447\) 28.4042 + 28.4042i 1.34347 + 1.34347i
\(448\) −1.58193 + 20.2436i −0.0747392 + 0.956422i
\(449\) −32.7480 + 8.77481i −1.54547 + 0.414109i −0.928030 0.372505i \(-0.878499\pi\)
−0.617445 + 0.786614i \(0.711832\pi\)
\(450\) 0.583444 + 0.583444i 0.0275038 + 0.0275038i
\(451\) 19.3181 + 11.1533i 0.909654 + 0.525189i
\(452\) −14.6984 + 8.48610i −0.691353 + 0.399153i
\(453\) 11.0970 + 2.97342i 0.521381 + 0.139704i
\(454\) −0.478554 −0.0224596
\(455\) 5.33266 15.9755i 0.249999 0.748943i
\(456\) −5.16202 −0.241734
\(457\) −2.18565 0.585644i −0.102241 0.0273953i 0.207336 0.978270i \(-0.433521\pi\)
−0.309577 + 0.950874i \(0.600187\pi\)
\(458\) 1.37279 0.792582i 0.0641463 0.0370349i
\(459\) −7.25273 4.18737i −0.338528 0.195449i
\(460\) 15.8614 + 15.8614i 0.739540 + 0.739540i
\(461\) 24.5455 6.57694i 1.14320 0.306319i 0.362961 0.931804i \(-0.381766\pi\)
0.780235 + 0.625486i \(0.215099\pi\)
\(462\) −0.122435 + 1.56678i −0.00569621 + 0.0728932i
\(463\) −22.6265 22.6265i −1.05154 1.05154i −0.998597 0.0529442i \(-0.983139\pi\)
−0.0529442 0.998597i \(-0.516861\pi\)
\(464\) 14.0261 24.2939i 0.651144 1.12781i
\(465\) 9.81804 + 17.0053i 0.455301 + 0.788604i
\(466\) 0.494066 1.84388i 0.0228871 0.0854160i
\(467\) 11.2941 0.522627 0.261314 0.965254i \(-0.415844\pi\)
0.261314 + 0.965254i \(0.415844\pi\)
\(468\) −23.5126 13.0283i −1.08687 0.602235i
\(469\) 0.0491652 + 0.0173797i 0.00227024 + 0.000802520i
\(470\) −1.31967 0.353604i −0.0608718 0.0163105i
\(471\) 9.00535 + 15.5977i 0.414945 + 0.718705i
\(472\) −0.392653 + 0.680095i −0.0180733 + 0.0313039i
\(473\) 2.48139 2.48139i 0.114094 0.114094i
\(474\) 1.74001 0.466235i 0.0799215 0.0214149i
\(475\) 2.07991 + 7.76231i 0.0954326 + 0.356159i
\(476\) 20.2879 9.69063i 0.929895 0.444169i
\(477\) 8.02814 13.9051i 0.367583 0.636673i
\(478\) −0.874396 + 0.504833i −0.0399939 + 0.0230905i
\(479\) −19.3716 5.19059i −0.885109 0.237164i −0.212499 0.977161i \(-0.568160\pi\)
−0.672610 + 0.739997i \(0.734827\pi\)
\(480\) 6.36978i 0.290739i
\(481\) −9.80456 + 2.81311i −0.447049 + 0.128267i
\(482\) 1.56814i 0.0714269i
\(483\) 24.8889 36.2566i 1.13249 1.64973i
\(484\) −7.11843 12.3295i −0.323565 0.560431i
\(485\) −22.5846 13.0392i −1.02551 0.592081i
\(486\) −1.80914 1.80914i −0.0820643 0.0820643i
\(487\) −8.13109 30.3456i −0.368455 1.37509i −0.862676 0.505756i \(-0.831213\pi\)
0.494221 0.869336i \(-0.335453\pi\)
\(488\) −0.371329 1.38582i −0.0168093 0.0627331i
\(489\) −23.7691 + 23.7691i −1.07488 + 1.07488i
\(490\) −0.518587 1.34651i −0.0234274 0.0608290i
\(491\) −16.8341 + 9.71919i −0.759714 + 0.438621i −0.829193 0.558962i \(-0.811200\pi\)
0.0694792 + 0.997583i \(0.477866\pi\)
\(492\) −15.2228 + 56.8122i −0.686296 + 2.56129i
\(493\) −30.6276 −1.37940
\(494\) 0.925574 + 1.53986i 0.0416436 + 0.0692814i
\(495\) 12.9729i 0.583091i
\(496\) −4.34038 + 16.1985i −0.194889 + 0.727336i
\(497\) −2.30023 12.3727i −0.103179 0.554991i
\(498\) 3.67021 + 2.11900i 0.164466 + 0.0949545i
\(499\) 11.8051 11.8051i 0.528471 0.528471i −0.391645 0.920116i \(-0.628094\pi\)
0.920116 + 0.391645i \(0.128094\pi\)
\(500\) −23.3158 + 6.24745i −1.04271 + 0.279394i
\(501\) 2.34011 0.627031i 0.104548 0.0280137i
\(502\) −0.287797 + 0.287797i −0.0128450 + 0.0128450i
\(503\) −25.9585 14.9871i −1.15743 0.668243i −0.206743 0.978395i \(-0.566287\pi\)
−0.950687 + 0.310153i \(0.899620\pi\)
\(504\) −4.54391 + 0.844766i −0.202402 + 0.0376289i
\(505\) −7.31560 + 27.3022i −0.325540 + 1.21493i
\(506\) 1.46199i 0.0649935i
\(507\) 1.18981 + 33.7622i 0.0528413 + 1.49943i
\(508\) 12.1445 0.538827
\(509\) 3.62928 13.5446i 0.160865 0.600356i −0.837667 0.546182i \(-0.816081\pi\)
0.998532 0.0541739i \(-0.0172525\pi\)
\(510\) −1.98466 + 1.14585i −0.0878824 + 0.0507389i
\(511\) 1.98639 1.69844i 0.0878729 0.0751348i
\(512\) 6.42580 6.42580i 0.283983 0.283983i
\(513\) 2.16235 + 8.07001i 0.0954702 + 0.356300i
\(514\) 0.406370 + 1.51659i 0.0179242 + 0.0668940i
\(515\) 14.7501 + 14.7501i 0.649969 + 0.649969i
\(516\) 8.01316 + 4.62640i 0.352760 + 0.203666i
\(517\) 6.48785 + 11.2373i 0.285335 + 0.494215i
\(518\) −0.494574 + 0.720464i −0.0217303 + 0.0316554i
\(519\) 1.37097i 0.0601791i
\(520\) −2.53932 + 1.52633i −0.111356 + 0.0669339i
\(521\) 0.875247i 0.0383452i 0.999816 + 0.0191726i \(0.00610321\pi\)
−0.999816 + 0.0191726i \(0.993897\pi\)
\(522\) 3.03028 + 0.811961i 0.132632 + 0.0355386i
\(523\) 11.7198 6.76640i 0.512469 0.295874i −0.221379 0.975188i \(-0.571056\pi\)
0.733848 + 0.679314i \(0.237722\pi\)
\(524\) 5.72506 9.91610i 0.250100 0.433187i
\(525\) 5.57991 + 11.6819i 0.243527 + 0.509839i
\(526\) 0.620553 + 2.31593i 0.0270574 + 0.100980i
\(527\) 17.6857 4.73887i 0.770401 0.206428i
\(528\) −14.0963 + 14.0963i −0.613462 + 0.613462i
\(529\) 8.95568 15.5117i 0.389377 0.674421i
\(530\) −0.440907 0.763674i −0.0191518 0.0331719i
\(531\) 6.11711 + 1.63908i 0.265460 + 0.0711298i
\(532\) −21.1473 7.47548i −0.916853 0.324103i
\(533\) 39.4888 11.3301i 1.71045 0.490759i
\(534\) −2.43826 −0.105514
\(535\) 3.65155 13.6278i 0.157870 0.589180i
\(536\) −0.00458664 0.00794430i −0.000198113 0.000343141i
\(537\) 10.7457 18.6121i 0.463711 0.803171i
\(538\) −0.886440 0.886440i −0.0382171 0.0382171i
\(539\) −5.56010 + 12.5255i −0.239491 + 0.539512i
\(540\) −6.63121 + 1.77683i −0.285362 + 0.0764625i
\(541\) 8.68791 + 8.68791i 0.373522 + 0.373522i 0.868758 0.495236i \(-0.164918\pi\)
−0.495236 + 0.868758i \(0.664918\pi\)
\(542\) −0.151539 0.0874914i −0.00650918 0.00375808i
\(543\) −33.7098 + 19.4624i −1.44663 + 0.835211i
\(544\) −5.73710 1.53725i −0.245976 0.0659091i
\(545\) −21.8634 −0.936526
\(546\) 1.91939 + 2.16636i 0.0821422 + 0.0927115i
\(547\) 16.2786 0.696022 0.348011 0.937490i \(-0.386857\pi\)
0.348011 + 0.937490i \(0.386857\pi\)
\(548\) 12.0411 + 3.22641i 0.514371 + 0.137825i
\(549\) −10.0198 + 5.78491i −0.427633 + 0.246894i
\(550\) −0.372723 0.215192i −0.0158930 0.00917582i
\(551\) 21.6051 + 21.6051i 0.920410 + 0.920410i
\(552\) −7.47258 + 2.00227i −0.318054 + 0.0852224i
\(553\) 15.6606 + 1.22379i 0.665956 + 0.0520408i
\(554\) −0.388865 0.388865i −0.0165213 0.0165213i
\(555\) −6.48987 + 11.2408i −0.275480 + 0.477145i
\(556\) −20.7937 36.0157i −0.881849 1.52741i
\(557\) 2.13873 7.98185i 0.0906210 0.338202i −0.905698 0.423923i \(-0.860653\pi\)
0.996319 + 0.0857210i \(0.0273194\pi\)
\(558\) −1.87545 −0.0793940
\(559\) −0.113826 6.46190i −0.00481433 0.273309i
\(560\) 6.10024 17.2569i 0.257782 0.729237i
\(561\) 21.0237 + 5.63329i 0.887623 + 0.237838i
\(562\) −0.661470 1.14570i −0.0279024 0.0483285i
\(563\) −14.0767 + 24.3815i −0.593261 + 1.02756i 0.400528 + 0.916284i \(0.368827\pi\)
−0.993790 + 0.111274i \(0.964507\pi\)
\(564\) −24.1924 + 24.1924i −1.01869 + 1.01869i
\(565\) 14.5712 3.90435i 0.613016 0.164257i
\(566\) −0.238078 0.888519i −0.0100072 0.0373472i
\(567\) −7.03904 14.7366i −0.295612 0.618881i
\(568\) −1.10691 + 1.91722i −0.0464448 + 0.0804447i
\(569\) −8.62645 + 4.98048i −0.361640 + 0.208793i −0.669800 0.742542i \(-0.733620\pi\)
0.308160 + 0.951335i \(0.400287\pi\)
\(570\) 2.20831 + 0.591715i 0.0924959 + 0.0247842i
\(571\) 5.15214i 0.215610i 0.994172 + 0.107805i \(0.0343823\pi\)
−0.994172 + 0.107805i \(0.965618\pi\)
\(572\) 13.6052 + 3.38986i 0.568864 + 0.141737i
\(573\) 37.7572i 1.57733i
\(574\) 1.99194 2.90174i 0.0831421 0.121116i
\(575\) 6.02177 + 10.4300i 0.251125 + 0.434962i
\(576\) −24.9461 14.4027i −1.03942 0.600111i
\(577\) 9.50342 + 9.50342i 0.395633 + 0.395633i 0.876689 0.481057i \(-0.159747\pi\)
−0.481057 + 0.876689i \(0.659747\pi\)
\(578\) 0.0393588 + 0.146889i 0.00163711 + 0.00610978i
\(579\) −13.1679 49.1434i −0.547240 2.04233i
\(580\) −17.7532 + 17.7532i −0.737161 + 0.737161i
\(581\) 24.0164 + 28.0881i 0.996368 + 1.16529i
\(582\) 3.88120 2.24081i 0.160881 0.0928847i
\(583\) −2.16762 + 8.08967i −0.0897737 + 0.335040i
\(584\) −0.459752 −0.0190247
\(585\) 17.1893 + 16.5942i 0.710690 + 0.686085i
\(586\) 1.42645i 0.0589263i
\(587\) −9.73498 + 36.3314i −0.401806 + 1.49956i 0.408066 + 0.912952i \(0.366203\pi\)
−0.809872 + 0.586607i \(0.800463\pi\)
\(588\) −35.6953 5.61306i −1.47205 0.231479i
\(589\) −15.8186 9.13289i −0.651795 0.376314i
\(590\) 0.245935 0.245935i 0.0101250 0.0101250i
\(591\) −54.6184 + 14.6350i −2.24670 + 0.602001i
\(592\) −10.7075 + 2.86906i −0.440074 + 0.117918i
\(593\) −25.8396 + 25.8396i −1.06110 + 1.06110i −0.0630974 + 0.998007i \(0.520098\pi\)
−0.998007 + 0.0630974i \(0.979902\pi\)
\(594\) −0.387498 0.223722i −0.0158992 0.00917944i
\(595\) −19.6471 + 3.65264i −0.805454 + 0.149744i
\(596\) 7.94687 29.6581i 0.325517 1.21484i
\(597\) 50.1065i 2.05072i
\(598\) 1.93716 + 1.87009i 0.0792162 + 0.0764738i
\(599\) 5.32027 0.217381 0.108690 0.994076i \(-0.465334\pi\)
0.108690 + 0.994076i \(0.465334\pi\)
\(600\) 0.589432 2.19979i 0.0240635 0.0898061i
\(601\) 21.4564 12.3879i 0.875225 0.505312i 0.00614424 0.999981i \(-0.498044\pi\)
0.869081 + 0.494669i \(0.164711\pi\)
\(602\) −0.359833 0.420838i −0.0146657 0.0171521i
\(603\) −0.0523087 + 0.0523087i −0.00213017 + 0.00213017i
\(604\) −2.27279 8.48216i −0.0924785 0.345134i
\(605\) 3.27510 + 12.2228i 0.133152 + 0.496929i
\(606\) −3.43473 3.43473i −0.139526 0.139526i
\(607\) −19.5367 11.2795i −0.792971 0.457822i 0.0480365 0.998846i \(-0.484704\pi\)
−0.841007 + 0.541024i \(0.818037\pi\)
\(608\) 2.96263 + 5.13143i 0.120151 + 0.208107i
\(609\) 40.5810 + 27.8575i 1.64443 + 1.12884i
\(610\) 0.635418i 0.0257273i
\(611\) 23.1884 + 5.77758i 0.938102 + 0.233736i
\(612\) 31.8953i 1.28929i
\(613\) −22.2201 5.95385i −0.897459 0.240474i −0.219535 0.975605i \(-0.570454\pi\)
−0.677925 + 0.735131i \(0.737121\pi\)
\(614\) −1.13995 + 0.658151i −0.0460047 + 0.0265608i
\(615\) 26.1385 45.2733i 1.05401 1.82560i
\(616\) 2.17532 1.03905i 0.0876462 0.0418647i
\(617\) 7.79350 + 29.0858i 0.313755 + 1.17095i 0.925143 + 0.379618i \(0.123945\pi\)
−0.611389 + 0.791330i \(0.709389\pi\)
\(618\) −3.46265 + 0.927815i −0.139288 + 0.0373222i
\(619\) −7.55579 + 7.55579i −0.303693 + 0.303693i −0.842457 0.538764i \(-0.818891\pi\)
0.538764 + 0.842457i \(0.318891\pi\)
\(620\) 7.50459 12.9983i 0.301392 0.522026i
\(621\) 6.26048 + 10.8435i 0.251224 + 0.435133i
\(622\) −1.47090 0.394127i −0.0589778 0.0158031i
\(623\) −20.0462 7.08625i −0.803135 0.283905i
\(624\) 0.646624 + 36.7088i 0.0258857 + 1.46953i
\(625\) 12.0400 0.481599
\(626\) −0.107997 + 0.403049i −0.00431641 + 0.0161091i
\(627\) −10.8566 18.8043i −0.433573 0.750970i
\(628\) 6.88340 11.9224i 0.274678 0.475755i
\(629\) 8.55805 + 8.55805i 0.341232 + 0.341232i
\(630\) 2.04071 + 0.159471i 0.0813040 + 0.00635346i
\(631\) 13.6759 3.66444i 0.544428 0.145879i 0.0238855 0.999715i \(-0.492396\pi\)
0.520543 + 0.853836i \(0.325730\pi\)
\(632\) −1.95395 1.95395i −0.0777240 0.0777240i
\(633\) 6.80249 + 3.92742i 0.270375 + 0.156101i
\(634\) −3.35413 + 1.93651i −0.133209 + 0.0769085i
\(635\) −10.4265 2.79377i −0.413763 0.110867i
\(636\) −22.0826 −0.875633
\(637\) 9.48429 + 23.3891i 0.375781 + 0.926708i
\(638\) −1.63637 −0.0647844
\(639\) 17.2444 + 4.62063i 0.682179 + 0.182789i
\(640\) −5.61554 + 3.24213i −0.221974 + 0.128157i
\(641\) −32.0667 18.5137i −1.26656 0.731248i −0.292224 0.956350i \(-0.594395\pi\)
−0.974335 + 0.225102i \(0.927729\pi\)
\(642\) 1.71443 + 1.71443i 0.0676632 + 0.0676632i
\(643\) 33.2886 8.91965i 1.31277 0.351757i 0.466507 0.884517i \(-0.345512\pi\)
0.846266 + 0.532761i \(0.178845\pi\)
\(644\) −33.5127 2.61883i −1.32058 0.103196i
\(645\) −5.81530 5.81530i −0.228977 0.228977i
\(646\) 1.06588 1.84617i 0.0419366 0.0726364i
\(647\) −3.03363 5.25440i −0.119264 0.206572i 0.800212 0.599717i \(-0.204720\pi\)
−0.919476 + 0.393145i \(0.871387\pi\)
\(648\) −0.743567 + 2.77503i −0.0292101 + 0.109013i
\(649\) −3.30328 −0.129665
\(650\) −0.761896 + 0.218602i −0.0298840 + 0.00857428i
\(651\) −27.7435 9.80721i −1.08735 0.384375i
\(652\) 24.8184 + 6.65007i 0.971964 + 0.260437i
\(653\) −15.1009 26.1555i −0.590943 1.02354i −0.994106 0.108416i \(-0.965422\pi\)
0.403162 0.915129i \(-0.367911\pi\)
\(654\) 1.87863 3.25389i 0.0734603 0.127237i
\(655\) −7.19630 + 7.19630i −0.281183 + 0.281183i
\(656\) 43.1253 11.5554i 1.68376 0.451162i
\(657\) 0.959586 + 3.58123i 0.0374370 + 0.139717i
\(658\) 1.84744 0.882439i 0.0720206 0.0344010i
\(659\) 4.37179 7.57216i 0.170301 0.294969i −0.768224 0.640181i \(-0.778859\pi\)
0.938525 + 0.345211i \(0.112193\pi\)
\(660\) 15.4517 8.92102i 0.601455 0.347250i
\(661\) −17.3494 4.64874i −0.674812 0.180815i −0.0948903 0.995488i \(-0.530250\pi\)
−0.579921 + 0.814673i \(0.696917\pi\)
\(662\) 0.110698i 0.00430239i
\(663\) 34.3564 20.6509i 1.33429 0.802015i
\(664\) 6.50100i 0.252288i
\(665\) 16.4360 + 11.2828i 0.637361 + 0.437527i
\(666\) −0.619849 1.07361i −0.0240187 0.0416015i
\(667\) 39.6561 + 22.8955i 1.53549 + 0.886516i
\(668\) −1.30942 1.30942i −0.0506631 0.0506631i
\(669\) 2.95901 + 11.0432i 0.114402 + 0.426954i
\(670\) 0.00105152 + 0.00392433i 4.06238e−5 + 0.000151610i
\(671\) 4.26731 4.26731i 0.164738 0.164738i
\(672\) 6.20334 + 7.25504i 0.239299 + 0.279869i
\(673\) 22.0524 12.7319i 0.850057 0.490780i −0.0106133 0.999944i \(-0.503378\pi\)
0.860670 + 0.509163i \(0.170045\pi\)
\(674\) 0.428796 1.60029i 0.0165166 0.0616408i
\(675\) −3.68594 −0.141872
\(676\) 21.8946 13.6910i 0.842100 0.526577i
\(677\) 21.8547i 0.839946i 0.907537 + 0.419973i \(0.137961\pi\)
−0.907537 + 0.419973i \(0.862039\pi\)
\(678\) −0.670968 + 2.50409i −0.0257684 + 0.0961689i
\(679\) 38.4219 7.14309i 1.47450 0.274127i
\(680\) 3.04444 + 1.75771i 0.116749 + 0.0674050i
\(681\) 7.53188 7.53188i 0.288622 0.288622i
\(682\) 0.944911 0.253188i 0.0361825 0.00969507i
\(683\) 30.9579 8.29515i 1.18457 0.317405i 0.387833 0.921729i \(-0.373224\pi\)
0.796738 + 0.604324i \(0.206557\pi\)
\(684\) 22.4994 22.4994i 0.860286 0.860286i
\(685\) −9.59550 5.53997i −0.366625 0.211671i
\(686\) 1.90198 + 1.02860i 0.0726180 + 0.0392723i
\(687\) −9.13183 + 34.0804i −0.348401 + 1.30025i
\(688\) 7.02368i 0.267775i
\(689\) 7.94621 + 13.2199i 0.302726 + 0.503639i
\(690\) 3.42628 0.130436
\(691\) 7.27863 27.1642i 0.276892 1.03337i −0.677671 0.735365i \(-0.737011\pi\)
0.954563 0.298010i \(-0.0963227\pi\)
\(692\) −0.907533 + 0.523964i −0.0344992 + 0.0199181i
\(693\) −12.6340 14.7759i −0.479925 0.561290i
\(694\) 1.14276 1.14276i 0.0433786 0.0433786i
\(695\) 9.56691 + 35.7042i 0.362894 + 1.35434i
\(696\) −2.24109 8.36385i −0.0849482 0.317031i
\(697\) −34.4683 34.4683i −1.30558 1.30558i
\(698\) 1.54794 + 0.893701i 0.0585902 + 0.0338271i
\(699\) 21.2445 + 36.7965i 0.803540 + 1.39177i
\(700\) 5.60040 8.15831i 0.211675 0.308355i
\(701\) 41.8411i 1.58032i −0.612904 0.790158i \(-0.709999\pi\)
0.612904 0.790158i \(-0.290001\pi\)
\(702\) −0.792098 + 0.227268i −0.0298958 + 0.00857766i
\(703\) 12.0740i 0.455378i
\(704\) 14.5131 + 3.88876i 0.546981 + 0.146563i
\(705\) 26.3354 15.2047i 0.991847 0.572643i
\(706\) −0.919455 + 1.59254i −0.0346041 + 0.0599361i
\(707\) −18.2565 38.2210i −0.686606 1.43745i
\(708\) −2.25426 8.41303i −0.0847204 0.316181i
\(709\) −36.1012 + 9.67328i −1.35581 + 0.363288i −0.862275 0.506440i \(-0.830961\pi\)
−0.493532 + 0.869727i \(0.664295\pi\)
\(710\) 0.693302 0.693302i 0.0260192 0.0260192i
\(711\) −11.1420 + 19.2985i −0.417857 + 0.723750i
\(712\) 1.87012 + 3.23914i 0.0700857 + 0.121392i
\(713\) −26.4417 7.08503i −0.990249 0.265336i
\(714\) 1.14458 3.23790i 0.0428349 0.121175i
\(715\) −10.9008 6.04011i −0.407665 0.225887i
\(716\) −16.4273 −0.613918
\(717\) 5.81649 21.7075i 0.217221 0.810680i
\(718\) 0.387018 + 0.670334i 0.0144434 + 0.0250166i
\(719\) −14.7469 + 25.5425i −0.549968 + 0.952573i 0.448308 + 0.893879i \(0.352027\pi\)
−0.998276 + 0.0586936i \(0.981307\pi\)
\(720\) 18.3602 + 18.3602i 0.684246 + 0.684246i
\(721\) −31.1648 2.43536i −1.16064 0.0906975i
\(722\) 0.0885265 0.0237206i 0.00329461 0.000882789i
\(723\) −24.6807 24.6807i −0.917886 0.917886i
\(724\) 25.7667 + 14.8764i 0.957612 + 0.552878i
\(725\) −11.6740 + 6.74000i −0.433562 + 0.250317i
\(726\) −2.10051 0.562831i −0.0779574 0.0208886i
\(727\) 3.04387 0.112891 0.0564455 0.998406i \(-0.482023\pi\)
0.0564455 + 0.998406i \(0.482023\pi\)
\(728\) 1.40578 4.21142i 0.0521017 0.156086i
\(729\) 38.4293 1.42331
\(730\) 0.196682 + 0.0527007i 0.00727952 + 0.00195054i
\(731\) −6.64113 + 3.83426i −0.245631 + 0.141815i
\(732\) 13.7805 + 7.95615i 0.509340 + 0.294068i
\(733\) −0.928339 0.928339i −0.0342890 0.0342890i 0.689754 0.724043i \(-0.257718\pi\)
−0.724043 + 0.689754i \(0.757718\pi\)
\(734\) 3.70542 0.992865i 0.136770 0.0366473i
\(735\) 29.3544 + 13.0305i 1.08275 + 0.480637i
\(736\) 6.27914 + 6.27914i 0.231452 + 0.231452i
\(737\) 0.0192931 0.0334166i 0.000710669 0.00123091i
\(738\) 2.49650 + 4.32406i 0.0918974 + 0.159171i
\(739\) −7.76649 + 28.9849i −0.285695 + 1.06623i 0.662635 + 0.748942i \(0.269438\pi\)
−0.948330 + 0.317285i \(0.897229\pi\)
\(740\) 9.92129 0.364714
\(741\) −38.8030 9.66809i −1.42546 0.355166i
\(742\) 1.24590 + 0.440421i 0.0457385 + 0.0161684i
\(743\) −39.4397 10.5678i −1.44690 0.387697i −0.551958 0.833872i \(-0.686119\pi\)
−0.894946 + 0.446175i \(0.852786\pi\)
\(744\) 2.58820 + 4.48290i 0.0948881 + 0.164351i
\(745\) −13.6453 + 23.6344i −0.499926 + 0.865897i
\(746\) 0.650528 0.650528i 0.0238175 0.0238175i
\(747\) −50.6393 + 13.5688i −1.85280 + 0.496455i
\(748\) −4.30591 16.0699i −0.157440 0.587573i
\(749\) 9.11265 + 19.0779i 0.332969 + 0.697090i
\(750\) −1.84350 + 3.19304i −0.0673153 + 0.116593i
\(751\) −31.0690 + 17.9377i −1.13372 + 0.654556i −0.944869 0.327448i \(-0.893811\pi\)
−0.188856 + 0.982005i \(0.560478\pi\)
\(752\) 25.0859 + 6.72175i 0.914789 + 0.245117i
\(753\) 9.05917i 0.330135i
\(754\) −2.09314 + 2.16820i −0.0762277 + 0.0789614i
\(755\) 7.80507i 0.284056i
\(756\) 5.82241 8.48171i 0.211759 0.308477i
\(757\) −0.439138 0.760610i −0.0159607 0.0276448i 0.857935 0.513759i \(-0.171747\pi\)
−0.873895 + 0.486114i \(0.838414\pi\)
\(758\) −1.13152 0.653282i −0.0410986 0.0237283i
\(759\) −23.0101 23.0101i −0.835213 0.835213i
\(760\) −0.907679 3.38750i −0.0329250 0.122878i
\(761\) 9.46773 + 35.3341i 0.343205 + 1.28086i 0.894695 + 0.446677i \(0.147393\pi\)
−0.551490 + 0.834181i \(0.685941\pi\)
\(762\) 1.31170 1.31170i 0.0475178 0.0475178i
\(763\) 24.9019 21.2921i 0.901511 0.770827i
\(764\) −24.9938 + 14.4302i −0.904245 + 0.522066i
\(765\) 7.33730 27.3832i 0.265281 0.990041i
\(766\) 0.281440 0.0101689
\(767\) −4.22535 + 4.37687i −0.152568 + 0.158040i
\(768\) 38.7743i 1.39915i
\(769\) −7.85943 + 29.3318i −0.283418 + 1.05773i 0.666569 + 0.745443i \(0.267762\pi\)
−0.949987 + 0.312288i \(0.898904\pi\)
\(770\) −1.04971 + 0.195153i −0.0378288 + 0.00703282i
\(771\) −30.2652 17.4736i −1.08997 0.629297i
\(772\) −27.4985 + 27.4985i −0.989692 + 0.989692i
\(773\) 19.1599 5.13389i 0.689134 0.184653i 0.102776 0.994705i \(-0.467228\pi\)
0.586359 + 0.810052i \(0.300561\pi\)
\(774\) 0.758719 0.203298i 0.0272716 0.00730740i
\(775\) 5.69824 5.69824i 0.204687 0.204687i
\(776\) −5.95369 3.43737i −0.213725 0.123394i
\(777\) −3.55525 19.1233i −0.127544 0.686044i
\(778\) 0.508297 1.89699i 0.0182233 0.0680104i
\(779\) 48.6290i 1.74231i
\(780\) 7.94437 31.8848i 0.284454 1.14166i
\(781\) −9.31209 −0.333213
\(782\) 0.826882 3.08596i 0.0295692 0.110354i
\(783\) −12.1368 + 7.00718i −0.433733 + 0.250416i
\(784\) 9.85795 + 25.5961i 0.352070 + 0.914145i
\(785\) −8.65231 + 8.65231i −0.308814 + 0.308814i
\(786\) −0.452662 1.68936i −0.0161459 0.0602574i
\(787\) −2.27486 8.48989i −0.0810900 0.302632i 0.913455 0.406940i \(-0.133404\pi\)
−0.994545 + 0.104308i \(0.966737\pi\)
\(788\) 30.5620 + 30.5620i 1.08873 + 1.08873i
\(789\) −46.2169 26.6833i −1.64536 0.949951i
\(790\) 0.611921 + 1.05988i 0.0217712 + 0.0377087i
\(791\) −12.7940 + 18.6374i −0.454901 + 0.662671i
\(792\) 3.41989i 0.121521i
\(793\) −0.195750 11.1127i −0.00695128 0.394624i
\(794\) 2.74663i 0.0974743i
\(795\) 18.9587 + 5.07997i 0.672396 + 0.180168i
\(796\) −33.1686 + 19.1499i −1.17563 + 0.678750i
\(797\) −12.3887 + 21.4579i −0.438832 + 0.760079i −0.997600 0.0692450i \(-0.977941\pi\)
0.558768 + 0.829324i \(0.311274\pi\)
\(798\) −3.09147 + 1.47666i −0.109437 + 0.0522731i
\(799\) −7.33886 27.3890i −0.259630 0.968953i
\(800\) −2.52505 + 0.676585i −0.0892739 + 0.0239209i
\(801\) 21.3279 21.3279i 0.753585 0.753585i
\(802\) −0.503695 + 0.872425i −0.0177861 + 0.0308064i
\(803\) −0.966941 1.67479i −0.0341226 0.0591021i
\(804\) 0.0982740 + 0.0263324i 0.00346586 + 0.000928674i
\(805\) 28.1693 + 9.95773i 0.992838 + 0.350964i
\(806\) 0.873195 1.57588i 0.0307570 0.0555080i
\(807\) 27.9030 0.982234
\(808\) −1.92852 + 7.19733i −0.0678450 + 0.253201i
\(809\) −3.75373 6.50166i −0.131974 0.228586i 0.792463 0.609920i \(-0.208798\pi\)
−0.924438 + 0.381334i \(0.875465\pi\)
\(810\) 0.636195 1.10192i 0.0223536 0.0387176i
\(811\) −32.4572 32.4572i −1.13973 1.13973i −0.988499 0.151229i \(-0.951677\pi\)
−0.151229 0.988499i \(-0.548323\pi\)
\(812\) 2.93118 37.5098i 0.102864 1.31633i
\(813\) 3.76207 1.00804i 0.131941 0.0353536i
\(814\) 0.457239 + 0.457239i 0.0160262 + 0.0160262i
\(815\) −19.7777 11.4186i −0.692781 0.399977i
\(816\) 37.7270 21.7817i 1.32071 0.762511i
\(817\) 7.38949 + 1.98001i 0.258526 + 0.0692717i
\(818\) −1.56868 −0.0548475
\(819\) −35.7388 2.16028i −1.24882 0.0754863i
\(820\) −39.9589 −1.39543
\(821\) 30.4367 + 8.15549i 1.06225 + 0.284629i 0.747305 0.664482i \(-0.231348\pi\)
0.314944 + 0.949110i \(0.398014\pi\)
\(822\) 1.64900 0.952052i 0.0575156 0.0332066i
\(823\) 27.4139 + 15.8274i 0.955590 + 0.551710i 0.894813 0.446442i \(-0.147309\pi\)
0.0607767 + 0.998151i \(0.480642\pi\)
\(824\) 3.88839 + 3.88839i 0.135459 + 0.135459i
\(825\) 9.25310 2.47936i 0.322152 0.0863203i
\(826\) −0.0406057 + 0.519623i −0.00141285 + 0.0180800i
\(827\) 25.1824 + 25.1824i 0.875678 + 0.875678i 0.993084 0.117406i \(-0.0374580\pi\)
−0.117406 + 0.993084i \(0.537458\pi\)
\(828\) 23.8431 41.2975i 0.828606 1.43519i
\(829\) −1.05432 1.82614i −0.0366182 0.0634246i 0.847135 0.531377i \(-0.178325\pi\)
−0.883754 + 0.467952i \(0.844992\pi\)
\(830\) −0.745200 + 2.78112i −0.0258663 + 0.0965342i
\(831\) 12.2405 0.424620
\(832\) 23.7169 14.2557i 0.822234 0.494227i
\(833\) 18.8205 23.2940i 0.652090 0.807091i
\(834\) −6.13582 1.64409i −0.212466 0.0569302i
\(835\) 0.822960 + 1.42541i 0.0284797 + 0.0493283i
\(836\) −8.29847 + 14.3734i −0.287009 + 0.497114i
\(837\) 5.92412 5.92412i 0.204768 0.204768i
\(838\) −1.96001 + 0.525184i −0.0677076 + 0.0181422i
\(839\) 6.14897 + 22.9483i 0.212286 + 0.792262i 0.987104 + 0.160078i \(0.0511746\pi\)
−0.774818 + 0.632184i \(0.782159\pi\)
\(840\) −2.43510 5.09802i −0.0840188 0.175898i
\(841\) −11.1262 + 19.2712i −0.383663 + 0.664525i
\(842\) 3.03847 1.75426i 0.104713 0.0604558i
\(843\) 28.4428 + 7.62121i 0.979621 + 0.262489i
\(844\) 6.00398i 0.206666i
\(845\) −21.9468 + 6.71748i −0.754992 + 0.231088i
\(846\) 2.90442i 0.0998559i
\(847\) −15.6337 10.7320i −0.537181 0.368756i
\(848\) 8.38131 + 14.5169i 0.287815 + 0.498511i
\(849\) 17.7313 + 10.2372i 0.608537 + 0.351339i
\(850\) 0.665032 + 0.665032i 0.0228104 + 0.0228104i
\(851\) −4.68331 17.4783i −0.160542 0.599150i
\(852\) −6.35488 23.7167i −0.217715 0.812522i
\(853\) 4.73993 4.73993i 0.162292 0.162292i −0.621289 0.783581i \(-0.713391\pi\)
0.783581 + 0.621289i \(0.213391\pi\)
\(854\) −0.618814 0.723726i −0.0211754 0.0247654i
\(855\) −24.4924 + 14.1407i −0.837621 + 0.483601i
\(856\) 0.962612 3.59252i 0.0329014 0.122790i
\(857\) 11.3220 0.386751 0.193376 0.981125i \(-0.438056\pi\)
0.193376 + 0.981125i \(0.438056\pi\)
\(858\) 1.83559 1.10334i 0.0626661 0.0376672i
\(859\) 48.4452i 1.65293i −0.562988 0.826465i \(-0.690348\pi\)
0.562988 0.826465i \(-0.309652\pi\)
\(860\) −1.62699 + 6.07202i −0.0554800 + 0.207054i
\(861\) 14.3191 + 77.0208i 0.487993 + 2.62486i
\(862\) −2.43991 1.40868i −0.0831038 0.0479800i
\(863\) −13.2582 + 13.2582i −0.451313 + 0.451313i −0.895790 0.444477i \(-0.853390\pi\)
0.444477 + 0.895790i \(0.353390\pi\)
\(864\) −2.62514 + 0.703405i −0.0893091 + 0.0239303i
\(865\) 0.899682 0.241069i 0.0305901 0.00819660i
\(866\) −0.375015 + 0.375015i −0.0127435 + 0.0127435i
\(867\) −2.93132 1.69240i −0.0995529 0.0574769i
\(868\) 4.11113 + 22.1133i 0.139541 + 0.750575i
\(869\) 3.00837 11.2274i 0.102052 0.380863i
\(870\) 3.83494i 0.130017i
\(871\) −0.0195988 0.0683079i −0.000664080 0.00231452i
\(872\) −5.76357 −0.195179
\(873\) −14.3488 + 53.5505i −0.485634 + 1.81241i
\(874\) −2.76018 + 1.59359i −0.0933645 + 0.0539040i
\(875\) −24.4363 + 20.8940i −0.826098 + 0.706346i
\(876\) 3.60561 3.60561i 0.121822 0.121822i
\(877\) 1.83431 + 6.84575i 0.0619403 + 0.231164i 0.989956 0.141377i \(-0.0451530\pi\)
−0.928015 + 0.372542i \(0.878486\pi\)
\(878\) 0.513728 + 1.91726i 0.0173375 + 0.0647044i
\(879\) −22.4507 22.4507i −0.757244 0.757244i
\(880\) −11.7291 6.77183i −0.395389 0.228278i
\(881\) 12.1808 + 21.0977i 0.410380 + 0.710800i 0.994931 0.100557i \(-0.0320626\pi\)
−0.584551 + 0.811357i \(0.698729\pi\)
\(882\) −2.47963 + 1.80576i −0.0834935 + 0.0608030i
\(883\) 4.51673i 0.152000i −0.997108 0.0760000i \(-0.975785\pi\)
0.997108 0.0760000i \(-0.0242149\pi\)
\(884\) −26.8006 14.8502i −0.901401 0.499467i
\(885\) 7.74145i 0.260226i
\(886\) 4.12943 + 1.10648i 0.138731 + 0.0371729i
\(887\) −38.3035 + 22.1145i −1.28611 + 0.742533i −0.977957 0.208805i \(-0.933042\pi\)
−0.308148 + 0.951338i \(0.599709\pi\)
\(888\) −1.71084 + 2.96326i −0.0574121 + 0.0994406i
\(889\) 14.5963 6.97202i 0.489545 0.233834i
\(890\) −0.428738 1.60007i −0.0143713 0.0536346i
\(891\) −11.6728 + 3.12771i −0.391052 + 0.104782i
\(892\) 6.17928 6.17928i 0.206898 0.206898i
\(893\) −14.1437 + 24.4976i −0.473300 + 0.819780i
\(894\) −2.34497 4.06161i −0.0784276 0.135841i
\(895\) 14.1034 + 3.77900i 0.471426 + 0.126318i
\(896\) 3.23856 9.16152i 0.108193 0.306065i
\(897\) −59.9216 + 1.05552i −2.00073 + 0.0352427i
\(898\) 3.95832 0.132091
\(899\) 7.93007 29.5954i 0.264483 0.987063i
\(900\) 7.01898 + 12.1572i 0.233966 + 0.405241i
\(901\) 9.15079 15.8496i 0.304857 0.528028i
\(902\) −1.84157 1.84157i −0.0613176 0.0613176i
\(903\) 12.2868 + 0.960150i 0.408881 + 0.0319518i
\(904\) 3.84122 1.02925i 0.127757 0.0342324i
\(905\) −18.6994 18.6994i −0.621589 0.621589i
\(906\) −1.16161 0.670657i −0.0385920 0.0222811i
\(907\) 29.3466 16.9433i 0.974439 0.562593i 0.0738526 0.997269i \(-0.476471\pi\)
0.900587 + 0.434676i \(0.143137\pi\)
\(908\) −7.86438 2.10725i −0.260989 0.0699317i
\(909\) 60.0885 1.99301
\(910\) −1.08414 + 1.64050i −0.0359389 + 0.0543820i
\(911\) 4.66390 0.154522 0.0772610 0.997011i \(-0.475383\pi\)
0.0772610 + 0.997011i \(0.475383\pi\)
\(912\) −41.9783 11.2480i −1.39004 0.372460i
\(913\) 23.6819 13.6728i 0.783757 0.452502i
\(914\) 0.228791 + 0.132092i 0.00756772 + 0.00436923i
\(915\) −10.0007 10.0007i −0.330614 0.330614i
\(916\) 26.0500 6.98007i 0.860716 0.230628i
\(917\) 1.18816 15.2047i 0.0392366 0.502103i
\(918\) 0.691394 + 0.691394i 0.0228194 + 0.0228194i
\(919\) −12.0900 + 20.9405i −0.398812 + 0.690763i −0.993580 0.113135i \(-0.963911\pi\)
0.594767 + 0.803898i \(0.297244\pi\)
\(920\) −2.62793 4.55170i −0.0866402 0.150065i
\(921\) 7.58297 28.3000i 0.249867 0.932518i
\(922\) −2.96686 −0.0977084
\(923\) −11.9115 + 12.3386i −0.392070 + 0.406131i
\(924\) −8.91118 + 25.2088i −0.293156 + 0.829307i
\(925\) 5.14530 + 1.37868i 0.169177 + 0.0453307i
\(926\) 1.86798 + 3.23543i 0.0613856 + 0.106323i
\(927\) 22.1727 38.4043i 0.728247 1.26136i
\(928\) −7.02806 + 7.02806i −0.230708 + 0.230708i
\(929\) 15.0006 4.01941i 0.492155 0.131872i −0.00420200 0.999991i \(-0.501338\pi\)
0.496357 + 0.868119i \(0.334671\pi\)
\(930\) −0.593364 2.21446i −0.0194572 0.0726151i
\(931\) −29.7082 + 3.15573i −0.973647 + 0.103425i
\(932\) 16.2386 28.1261i 0.531913 0.921300i
\(933\) 29.3534 16.9472i 0.960987 0.554826i
\(934\) −1.27369 0.341285i −0.0416765 0.0111672i
\(935\) 14.7871i 0.483589i
\(936\) 4.53139 + 4.37451i 0.148113 + 0.142985i
\(937\) 25.4720i 0.832134i −0.909334 0.416067i \(-0.863408\pi\)
0.909334 0.416067i \(-0.136592\pi\)
\(938\) −0.00501944 0.00344568i −0.000163891 0.000112505i
\(939\) −4.64378 8.04326i −0.151544 0.262482i
\(940\) −20.1299 11.6220i −0.656565 0.379068i
\(941\) 12.6726 + 12.6726i 0.413116 + 0.413116i 0.882823 0.469706i \(-0.155640\pi\)
−0.469706 + 0.882823i \(0.655640\pi\)
\(942\) −0.544248 2.03116i −0.0177326 0.0661788i
\(943\) 18.8625 + 70.3957i 0.614246 + 2.29240i
\(944\) −4.67503 + 4.67503i −0.152159 + 0.152159i
\(945\) −6.94990 + 5.94243i −0.226080 + 0.193307i
\(946\) −0.354822 + 0.204856i −0.0115362 + 0.00666046i
\(947\) 3.21690 12.0056i 0.104535 0.390130i −0.893757 0.448552i \(-0.851940\pi\)
0.998292 + 0.0584214i \(0.0186067\pi\)
\(948\) 30.6478 0.995393
\(949\) −3.45597 0.861083i −0.112185 0.0279519i
\(950\) 0.938247i 0.0304408i
\(951\) 22.3117 83.2684i 0.723506 2.70016i
\(952\) −5.17932 + 0.962898i −0.167863 + 0.0312077i
\(953\) 25.0716 + 14.4751i 0.812147 + 0.468893i 0.847701 0.530474i \(-0.177986\pi\)
−0.0355538 + 0.999368i \(0.511320\pi\)
\(954\) −1.32556 + 1.32556i −0.0429166 + 0.0429166i
\(955\) 24.7776 6.63914i 0.801785 0.214838i
\(956\) −16.5925 + 4.44594i −0.536639 + 0.143792i
\(957\) 25.7545 25.7545i 0.832525 0.832525i
\(958\) 2.02778 + 1.17074i 0.0655147 + 0.0378249i
\(959\) 16.3243 3.03488i 0.527138 0.0980013i
\(960\) 9.11358 34.0123i 0.294140 1.09774i
\(961\) 12.6833i 0.409139i
\(962\) 1.19072 0.0209745i 0.0383903 0.000676243i
\(963\) −29.9929 −0.966509
\(964\) −6.90512 + 25.7703i −0.222399 + 0.830004i
\(965\) 29.9342 17.2825i 0.963617 0.556344i
\(966\) −3.90246 + 3.33675i −0.125560 + 0.107358i
\(967\) 20.8937 20.8937i 0.671895 0.671895i −0.286258 0.958153i \(-0.592411\pi\)
0.958153 + 0.286258i \(0.0924113\pi\)
\(968\) 0.863372 + 3.22215i 0.0277498 + 0.103564i
\(969\) 12.2807 + 45.8323i 0.394513 + 1.47234i
\(970\) 2.15297 + 2.15297i 0.0691276 + 0.0691276i
\(971\) 35.5507 + 20.5252i 1.14088 + 0.658685i 0.946647 0.322271i \(-0.104446\pi\)
0.194229 + 0.980956i \(0.437780\pi\)
\(972\) −21.7644 37.6971i −0.698094 1.20913i
\(973\) −45.6677 31.3494i −1.46404 1.00501i
\(974\) 3.66794i 0.117528i
\(975\) 8.55082 15.4319i 0.273845 0.494216i
\(976\) 12.0788i 0.386633i
\(977\) −22.0546 5.90951i −0.705589 0.189062i −0.111856 0.993724i \(-0.535680\pi\)
−0.593733 + 0.804662i \(0.702346\pi\)
\(978\) 3.39882 1.96231i 0.108682 0.0627478i
\(979\) −7.86639 + 13.6250i −0.251411 + 0.435457i
\(980\) −2.59309 24.4115i −0.0828334 0.779798i
\(981\) 12.0296 + 44.8951i 0.384076 + 1.43339i
\(982\) 2.19217 0.587390i 0.0699549 0.0187444i
\(983\) 21.0430 21.0430i 0.671167 0.671167i −0.286818 0.957985i \(-0.592598\pi\)
0.957985 + 0.286818i \(0.0925976\pi\)
\(984\) 6.89057 11.9348i 0.219663 0.380468i
\(985\) −19.2080 33.2692i −0.612017 1.06004i
\(986\) 3.45403 + 0.925505i 0.109999 + 0.0294741i
\(987\) −15.1880 + 42.9651i −0.483438 + 1.36759i
\(988\) 8.42998 + 29.3811i 0.268193 + 0.934737i
\(989\) 11.4651 0.364569
\(990\) 0.392017 1.46303i 0.0124591 0.0464981i
\(991\) 1.24883 + 2.16303i 0.0396703 + 0.0687110i 0.885179 0.465251i \(-0.154036\pi\)
−0.845509 + 0.533962i \(0.820703\pi\)
\(992\) 2.97089 5.14574i 0.0943259 0.163377i
\(993\) −1.74225 1.74225i −0.0552888 0.0552888i
\(994\) −0.114469 + 1.46484i −0.00363075 + 0.0464620i
\(995\) 32.8817 8.81062i 1.04242 0.279315i
\(996\) 50.9841 + 50.9841i 1.61549 + 1.61549i
\(997\) 5.16724 + 2.98331i 0.163648 + 0.0944823i 0.579587 0.814910i \(-0.303214\pi\)
−0.415939 + 0.909392i \(0.636547\pi\)
\(998\) −1.68806 + 0.974599i −0.0534345 + 0.0308504i
\(999\) 5.34926 + 1.43333i 0.169243 + 0.0453486i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 91.2.bc.a.41.6 yes 32
3.2 odd 2 819.2.fm.g.496.3 32
7.2 even 3 637.2.x.b.80.4 32
7.3 odd 6 637.2.bb.b.509.4 32
7.4 even 3 637.2.bb.b.509.3 32
7.5 odd 6 637.2.x.b.80.3 32
7.6 odd 2 inner 91.2.bc.a.41.5 yes 32
13.7 odd 12 inner 91.2.bc.a.20.5 32
21.20 even 2 819.2.fm.g.496.4 32
39.20 even 12 819.2.fm.g.748.4 32
91.20 even 12 inner 91.2.bc.a.20.6 yes 32
91.33 even 12 637.2.bb.b.423.3 32
91.46 odd 12 637.2.x.b.215.4 32
91.59 even 12 637.2.x.b.215.3 32
91.72 odd 12 637.2.bb.b.423.4 32
273.20 odd 12 819.2.fm.g.748.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.bc.a.20.5 32 13.7 odd 12 inner
91.2.bc.a.20.6 yes 32 91.20 even 12 inner
91.2.bc.a.41.5 yes 32 7.6 odd 2 inner
91.2.bc.a.41.6 yes 32 1.1 even 1 trivial
637.2.x.b.80.3 32 7.5 odd 6
637.2.x.b.80.4 32 7.2 even 3
637.2.x.b.215.3 32 91.59 even 12
637.2.x.b.215.4 32 91.46 odd 12
637.2.bb.b.423.3 32 91.33 even 12
637.2.bb.b.423.4 32 91.72 odd 12
637.2.bb.b.509.3 32 7.4 even 3
637.2.bb.b.509.4 32 7.3 odd 6
819.2.fm.g.496.3 32 3.2 odd 2
819.2.fm.g.496.4 32 21.20 even 2
819.2.fm.g.748.3 32 273.20 odd 12
819.2.fm.g.748.4 32 39.20 even 12