Properties

Label 273.2.cg.a.115.9
Level $273$
Weight $2$
Character 273.115
Analytic conductor $2.180$
Analytic rank $0$
Dimension $36$
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] = [273,2,Mod(19,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 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("273.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.cg (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 115.9
Character \(\chi\) \(=\) 273.115
Dual form 273.2.cg.a.19.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.45222 - 0.657070i) q^{2} +1.00000i q^{3} +(3.84958 - 2.22256i) q^{4} +(-2.20549 - 0.590961i) q^{5} +(0.657070 + 2.45222i) q^{6} +(2.58986 - 0.540936i) q^{7} +(4.38935 - 4.38935i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(2.45222 - 0.657070i) q^{2} +1.00000i q^{3} +(3.84958 - 2.22256i) q^{4} +(-2.20549 - 0.590961i) q^{5} +(0.657070 + 2.45222i) q^{6} +(2.58986 - 0.540936i) q^{7} +(4.38935 - 4.38935i) q^{8} -1.00000 q^{9} -5.79666 q^{10} +(-1.22725 + 1.22725i) q^{11} +(2.22256 + 3.84958i) q^{12} +(1.05331 + 3.44826i) q^{13} +(5.99548 - 3.02821i) q^{14} +(0.590961 - 2.20549i) q^{15} +(3.43442 - 5.94858i) q^{16} +(-3.75960 - 6.51182i) q^{17} +(-2.45222 + 0.657070i) q^{18} +(-4.24907 + 4.24907i) q^{19} +(-9.80368 + 2.62689i) q^{20} +(0.540936 + 2.58986i) q^{21} +(-2.20310 + 3.81588i) q^{22} +(0.0187715 + 0.0108378i) q^{23} +(4.38935 + 4.38935i) q^{24} +(0.184846 + 0.106721i) q^{25} +(4.84871 + 7.76380i) q^{26} -1.00000i q^{27} +(8.76763 - 7.83850i) q^{28} +(0.432921 + 0.749842i) q^{29} -5.79666i q^{30} +(1.55740 + 5.81230i) q^{31} +(1.30008 - 4.85196i) q^{32} +(-1.22725 - 1.22725i) q^{33} +(-13.4981 - 13.4981i) q^{34} +(-6.03160 - 0.337475i) q^{35} +(-3.84958 + 2.22256i) q^{36} +(-2.43056 - 9.07099i) q^{37} +(-7.62770 + 13.2116i) q^{38} +(-3.44826 + 1.05331i) q^{39} +(-12.2746 + 7.08675i) q^{40} +(2.45125 + 0.656811i) q^{41} +(3.02821 + 5.99548i) q^{42} +(1.71095 + 0.987815i) q^{43} +(-1.99677 + 7.45205i) q^{44} +(2.20549 + 0.590961i) q^{45} +(0.0531531 + 0.0142423i) q^{46} +(1.50594 - 5.62025i) q^{47} +(5.94858 + 3.43442i) q^{48} +(6.41478 - 2.80190i) q^{49} +(0.523405 + 0.140246i) q^{50} +(6.51182 - 3.75960i) q^{51} +(11.7188 + 10.9333i) q^{52} +(-6.87167 + 11.9021i) q^{53} +(-0.657070 - 2.45222i) q^{54} +(3.43196 - 1.98144i) q^{55} +(8.99345 - 13.7422i) q^{56} +(-4.24907 - 4.24907i) q^{57} +(1.55432 + 1.55432i) q^{58} +(1.50298 - 5.60919i) q^{59} +(-2.62689 - 9.80368i) q^{60} -3.60438i q^{61} +(7.63818 + 13.2297i) q^{62} +(-2.58986 + 0.540936i) q^{63} +0.985368i q^{64} +(-0.285288 - 8.22760i) q^{65} +(-3.81588 - 2.20310i) q^{66} +(-0.794679 - 0.794679i) q^{67} +(-28.9458 - 16.7119i) q^{68} +(-0.0108378 + 0.0187715i) q^{69} +(-15.0125 + 3.13562i) q^{70} +(12.5434 - 3.36098i) q^{71} +(-4.38935 + 4.38935i) q^{72} +(9.58115 - 2.56726i) q^{73} +(-11.9205 - 20.6470i) q^{74} +(-0.106721 + 0.184846i) q^{75} +(-6.91334 + 25.8009i) q^{76} +(-2.51455 + 3.84228i) q^{77} +(-7.76380 + 4.84871i) q^{78} +(2.16727 + 3.75382i) q^{79} +(-11.0900 + 11.0900i) q^{80} +1.00000 q^{81} +6.44258 q^{82} +(8.64819 - 8.64819i) q^{83} +(7.83850 + 8.76763i) q^{84} +(4.44355 + 16.5836i) q^{85} +(4.84468 + 1.29813i) q^{86} +(-0.749842 + 0.432921i) q^{87} +10.7737i q^{88} +(2.34321 - 0.627860i) q^{89} +5.79666 q^{90} +(4.59323 + 8.36076i) q^{91} +0.0963502 q^{92} +(-5.81230 + 1.55740i) q^{93} -14.7716i q^{94} +(11.8823 - 6.86026i) q^{95} +(4.85196 + 1.30008i) q^{96} +(1.99188 + 7.43379i) q^{97} +(13.8894 - 11.0858i) q^{98} +(1.22725 - 1.22725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.45222 0.657070i 1.73398 0.464619i 0.752886 0.658150i \(-0.228661\pi\)
0.981094 + 0.193532i \(0.0619943\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 3.84958 2.22256i 1.92479 1.11128i
\(5\) −2.20549 0.590961i −0.986327 0.264286i −0.270620 0.962686i \(-0.587229\pi\)
−0.715707 + 0.698401i \(0.753895\pi\)
\(6\) 0.657070 + 2.45222i 0.268248 + 1.00111i
\(7\) 2.58986 0.540936i 0.978876 0.204455i
\(8\) 4.38935 4.38935i 1.55187 1.55187i
\(9\) −1.00000 −0.333333
\(10\) −5.79666 −1.83306
\(11\) −1.22725 + 1.22725i −0.370030 + 0.370030i −0.867488 0.497458i \(-0.834267\pi\)
0.497458 + 0.867488i \(0.334267\pi\)
\(12\) 2.22256 + 3.84958i 0.641597 + 1.11128i
\(13\) 1.05331 + 3.44826i 0.292137 + 0.956377i
\(14\) 5.99548 3.02821i 1.60236 0.809324i
\(15\) 0.590961 2.20549i 0.152585 0.569456i
\(16\) 3.43442 5.94858i 0.858604 1.48715i
\(17\) −3.75960 6.51182i −0.911837 1.57935i −0.811467 0.584398i \(-0.801331\pi\)
−0.100370 0.994950i \(-0.532003\pi\)
\(18\) −2.45222 + 0.657070i −0.577993 + 0.154873i
\(19\) −4.24907 + 4.24907i −0.974803 + 0.974803i −0.999690 0.0248877i \(-0.992077\pi\)
0.0248877 + 0.999690i \(0.492077\pi\)
\(20\) −9.80368 + 2.62689i −2.19217 + 0.587390i
\(21\) 0.540936 + 2.58986i 0.118042 + 0.565154i
\(22\) −2.20310 + 3.81588i −0.469703 + 0.813549i
\(23\) 0.0187715 + 0.0108378i 0.00391414 + 0.00225983i 0.501956 0.864893i \(-0.332614\pi\)
−0.498042 + 0.867153i \(0.665947\pi\)
\(24\) 4.38935 + 4.38935i 0.895972 + 0.895972i
\(25\) 0.184846 + 0.106721i 0.0369691 + 0.0213441i
\(26\) 4.84871 + 7.76380i 0.950909 + 1.52261i
\(27\) 1.00000i 0.192450i
\(28\) 8.76763 7.83850i 1.65693 1.48134i
\(29\) 0.432921 + 0.749842i 0.0803915 + 0.139242i 0.903418 0.428761i \(-0.141050\pi\)
−0.823027 + 0.568003i \(0.807716\pi\)
\(30\) 5.79666i 1.05832i
\(31\) 1.55740 + 5.81230i 0.279718 + 1.04392i 0.952614 + 0.304183i \(0.0983835\pi\)
−0.672896 + 0.739737i \(0.734950\pi\)
\(32\) 1.30008 4.85196i 0.229823 0.857713i
\(33\) −1.22725 1.22725i −0.213637 0.213637i
\(34\) −13.4981 13.4981i −2.31490 2.31490i
\(35\) −6.03160 0.337475i −1.01953 0.0570438i
\(36\) −3.84958 + 2.22256i −0.641597 + 0.370426i
\(37\) −2.43056 9.07099i −0.399582 1.49126i −0.813833 0.581099i \(-0.802623\pi\)
0.414251 0.910163i \(-0.364044\pi\)
\(38\) −7.62770 + 13.2116i −1.23738 + 2.14320i
\(39\) −3.44826 + 1.05331i −0.552164 + 0.168665i
\(40\) −12.2746 + 7.08675i −1.94079 + 1.12051i
\(41\) 2.45125 + 0.656811i 0.382822 + 0.102577i 0.445097 0.895482i \(-0.353169\pi\)
−0.0622757 + 0.998059i \(0.519836\pi\)
\(42\) 3.02821 + 5.99548i 0.467264 + 0.925122i
\(43\) 1.71095 + 0.987815i 0.260917 + 0.150640i 0.624753 0.780823i \(-0.285200\pi\)
−0.363836 + 0.931463i \(0.618533\pi\)
\(44\) −1.99677 + 7.45205i −0.301025 + 1.12344i
\(45\) 2.20549 + 0.590961i 0.328776 + 0.0880952i
\(46\) 0.0531531 + 0.0142423i 0.00783699 + 0.00209992i
\(47\) 1.50594 5.62025i 0.219664 0.819798i −0.764808 0.644258i \(-0.777166\pi\)
0.984472 0.175540i \(-0.0561671\pi\)
\(48\) 5.94858 + 3.43442i 0.858604 + 0.495715i
\(49\) 6.41478 2.80190i 0.916397 0.400271i
\(50\) 0.523405 + 0.140246i 0.0740206 + 0.0198338i
\(51\) 6.51182 3.75960i 0.911837 0.526449i
\(52\) 11.7188 + 10.9333i 1.62510 + 1.51618i
\(53\) −6.87167 + 11.9021i −0.943897 + 1.63488i −0.185952 + 0.982559i \(0.559537\pi\)
−0.757945 + 0.652319i \(0.773796\pi\)
\(54\) −0.657070 2.45222i −0.0894159 0.333705i
\(55\) 3.43196 1.98144i 0.462765 0.267177i
\(56\) 8.99345 13.7422i 1.20180 1.83637i
\(57\) −4.24907 4.24907i −0.562803 0.562803i
\(58\) 1.55432 + 1.55432i 0.204092 + 0.204092i
\(59\) 1.50298 5.60919i 0.195671 0.730254i −0.796421 0.604742i \(-0.793276\pi\)
0.992092 0.125512i \(-0.0400573\pi\)
\(60\) −2.62689 9.80368i −0.339130 1.26565i
\(61\) 3.60438i 0.461494i −0.973014 0.230747i \(-0.925883\pi\)
0.973014 0.230747i \(-0.0741170\pi\)
\(62\) 7.63818 + 13.2297i 0.970050 + 1.68018i
\(63\) −2.58986 + 0.540936i −0.326292 + 0.0681515i
\(64\) 0.985368i 0.123171i
\(65\) −0.285288 8.22760i −0.0353857 1.02051i
\(66\) −3.81588 2.20310i −0.469703 0.271183i
\(67\) −0.794679 0.794679i −0.0970854 0.0970854i 0.656896 0.753981i \(-0.271869\pi\)
−0.753981 + 0.656896i \(0.771869\pi\)
\(68\) −28.9458 16.7119i −3.51019 2.02661i
\(69\) −0.0108378 + 0.0187715i −0.00130471 + 0.00225983i
\(70\) −15.0125 + 3.13562i −1.79434 + 0.374778i
\(71\) 12.5434 3.36098i 1.48862 0.398875i 0.579350 0.815079i \(-0.303306\pi\)
0.909272 + 0.416203i \(0.136640\pi\)
\(72\) −4.38935 + 4.38935i −0.517290 + 0.517290i
\(73\) 9.58115 2.56726i 1.12139 0.300475i 0.349943 0.936771i \(-0.386201\pi\)
0.771445 + 0.636296i \(0.219534\pi\)
\(74\) −11.9205 20.6470i −1.38574 2.40016i
\(75\) −0.106721 + 0.184846i −0.0123230 + 0.0213441i
\(76\) −6.91334 + 25.8009i −0.793014 + 2.95957i
\(77\) −2.51455 + 3.84228i −0.286560 + 0.437868i
\(78\) −7.76380 + 4.84871i −0.879077 + 0.549008i
\(79\) 2.16727 + 3.75382i 0.243837 + 0.422338i 0.961804 0.273739i \(-0.0882606\pi\)
−0.717967 + 0.696077i \(0.754927\pi\)
\(80\) −11.0900 + 11.0900i −1.23990 + 1.23990i
\(81\) 1.00000 0.111111
\(82\) 6.44258 0.711464
\(83\) 8.64819 8.64819i 0.949263 0.949263i −0.0495109 0.998774i \(-0.515766\pi\)
0.998774 + 0.0495109i \(0.0157663\pi\)
\(84\) 7.83850 + 8.76763i 0.855250 + 0.956627i
\(85\) 4.44355 + 16.5836i 0.481971 + 1.79874i
\(86\) 4.84468 + 1.29813i 0.522415 + 0.139981i
\(87\) −0.749842 + 0.432921i −0.0803915 + 0.0464141i
\(88\) 10.7737i 1.14848i
\(89\) 2.34321 0.627860i 0.248379 0.0665530i −0.132481 0.991186i \(-0.542294\pi\)
0.380861 + 0.924632i \(0.375628\pi\)
\(90\) 5.79666 0.611021
\(91\) 4.59323 + 8.36076i 0.481501 + 0.876446i
\(92\) 0.0963502 0.0100452
\(93\) −5.81230 + 1.55740i −0.602708 + 0.161495i
\(94\) 14.7716i 1.52357i
\(95\) 11.8823 6.86026i 1.21910 0.703848i
\(96\) 4.85196 + 1.30008i 0.495201 + 0.132689i
\(97\) 1.99188 + 7.43379i 0.202245 + 0.754787i 0.990272 + 0.139147i \(0.0444360\pi\)
−0.788027 + 0.615641i \(0.788897\pi\)
\(98\) 13.8894 11.0858i 1.40304 1.11984i
\(99\) 1.22725 1.22725i 0.123343 0.123343i
\(100\) 0.948771 0.0948771
\(101\) −4.46176 −0.443961 −0.221981 0.975051i \(-0.571252\pi\)
−0.221981 + 0.975051i \(0.571252\pi\)
\(102\) 13.4981 13.4981i 1.33651 1.33651i
\(103\) −4.23657 7.33795i −0.417441 0.723030i 0.578240 0.815867i \(-0.303740\pi\)
−0.995681 + 0.0928371i \(0.970406\pi\)
\(104\) 19.7590 + 10.5123i 1.93753 + 1.03081i
\(105\) 0.337475 6.03160i 0.0329342 0.588624i
\(106\) −9.03034 + 33.7017i −0.877104 + 3.27340i
\(107\) −5.06882 + 8.77945i −0.490021 + 0.848741i −0.999934 0.0114847i \(-0.996344\pi\)
0.509913 + 0.860226i \(0.329678\pi\)
\(108\) −2.22256 3.84958i −0.213866 0.370426i
\(109\) 3.92728 1.05231i 0.376165 0.100793i −0.0657825 0.997834i \(-0.520954\pi\)
0.441948 + 0.897041i \(0.354288\pi\)
\(110\) 7.11396 7.11396i 0.678290 0.678290i
\(111\) 9.07099 2.43056i 0.860980 0.230699i
\(112\) 5.67686 17.2638i 0.536413 1.63128i
\(113\) −2.30418 + 3.99096i −0.216759 + 0.375438i −0.953815 0.300394i \(-0.902882\pi\)
0.737056 + 0.675831i \(0.236215\pi\)
\(114\) −13.2116 7.62770i −1.23738 0.714400i
\(115\) −0.0349958 0.0349958i −0.00326338 0.00326338i
\(116\) 3.33314 + 1.92439i 0.309474 + 0.178675i
\(117\) −1.05331 3.44826i −0.0973788 0.318792i
\(118\) 14.7425i 1.35716i
\(119\) −13.2593 14.8310i −1.21548 1.35956i
\(120\) −7.08675 12.2746i −0.646929 1.12051i
\(121\) 7.98770i 0.726155i
\(122\) −2.36833 8.83874i −0.214419 0.800222i
\(123\) −0.656811 + 2.45125i −0.0592227 + 0.221022i
\(124\) 18.9135 + 18.9135i 1.69849 + 1.69849i
\(125\) 7.72806 + 7.72806i 0.691219 + 0.691219i
\(126\) −5.99548 + 3.02821i −0.534120 + 0.269775i
\(127\) 2.76191 1.59459i 0.245080 0.141497i −0.372430 0.928060i \(-0.621475\pi\)
0.617509 + 0.786564i \(0.288142\pi\)
\(128\) 3.24761 + 12.1202i 0.287051 + 1.07129i
\(129\) −0.987815 + 1.71095i −0.0869723 + 0.150640i
\(130\) −6.10570 19.9884i −0.535505 1.75310i
\(131\) −7.19475 + 4.15389i −0.628608 + 0.362927i −0.780213 0.625514i \(-0.784889\pi\)
0.151605 + 0.988441i \(0.451556\pi\)
\(132\) −7.45205 1.99677i −0.648618 0.173797i
\(133\) −8.70602 + 13.3030i −0.754908 + 1.15351i
\(134\) −2.47088 1.42657i −0.213452 0.123237i
\(135\) −0.590961 + 2.20549i −0.0508618 + 0.189819i
\(136\) −45.0848 12.0804i −3.86599 1.03589i
\(137\) −4.84610 1.29851i −0.414031 0.110939i 0.0457898 0.998951i \(-0.485420\pi\)
−0.459820 + 0.888012i \(0.652086\pi\)
\(138\) −0.0142423 + 0.0531531i −0.00121239 + 0.00452469i
\(139\) −2.35400 1.35908i −0.199663 0.115276i 0.396835 0.917890i \(-0.370108\pi\)
−0.596498 + 0.802614i \(0.703442\pi\)
\(140\) −23.9692 + 12.1064i −2.02577 + 1.02318i
\(141\) 5.62025 + 1.50594i 0.473310 + 0.126823i
\(142\) 28.5506 16.4837i 2.39592 1.38328i
\(143\) −5.52457 2.93921i −0.461988 0.245789i
\(144\) −3.43442 + 5.94858i −0.286201 + 0.495715i
\(145\) −0.511679 1.90961i −0.0424926 0.158585i
\(146\) 21.8082 12.5910i 1.80486 1.04204i
\(147\) 2.80190 + 6.41478i 0.231097 + 0.529082i
\(148\) −29.5175 29.5175i −2.42632 2.42632i
\(149\) −15.9474 15.9474i −1.30647 1.30647i −0.923948 0.382518i \(-0.875057\pi\)
−0.382518 0.923948i \(-0.624943\pi\)
\(150\) −0.140246 + 0.523405i −0.0114510 + 0.0427358i
\(151\) −5.41469 20.2079i −0.440641 1.64450i −0.727195 0.686431i \(-0.759176\pi\)
0.286553 0.958064i \(-0.407490\pi\)
\(152\) 37.3013i 3.02553i
\(153\) 3.75960 + 6.51182i 0.303946 + 0.526449i
\(154\) −3.64158 + 11.0743i −0.293447 + 0.892396i
\(155\) 13.7394i 1.10357i
\(156\) −10.9333 + 11.7188i −0.875367 + 0.938254i
\(157\) 5.68992 + 3.28508i 0.454105 + 0.262178i 0.709563 0.704643i \(-0.248893\pi\)
−0.255457 + 0.966820i \(0.582226\pi\)
\(158\) 7.78114 + 7.78114i 0.619034 + 0.619034i
\(159\) −11.9021 6.87167i −0.943897 0.544959i
\(160\) −5.73463 + 9.93267i −0.453362 + 0.785246i
\(161\) 0.0544782 + 0.0179141i 0.00429349 + 0.00141183i
\(162\) 2.45222 0.657070i 0.192664 0.0516243i
\(163\) 17.1549 17.1549i 1.34368 1.34368i 0.451310 0.892367i \(-0.350957\pi\)
0.892367 0.451310i \(-0.149043\pi\)
\(164\) 10.8961 2.91960i 0.850843 0.227983i
\(165\) 1.98144 + 3.43196i 0.154255 + 0.267177i
\(166\) 15.5248 26.8897i 1.20496 2.08705i
\(167\) 1.98472 7.40707i 0.153582 0.573176i −0.845641 0.533753i \(-0.820781\pi\)
0.999223 0.0394232i \(-0.0125520\pi\)
\(168\) 13.7422 + 8.99345i 1.06023 + 0.693860i
\(169\) −10.7811 + 7.26421i −0.829312 + 0.558785i
\(170\) 21.7931 + 37.7468i 1.67146 + 2.89505i
\(171\) 4.24907 4.24907i 0.324934 0.324934i
\(172\) 8.78191 0.669614
\(173\) 0.223665 0.0170049 0.00850246 0.999964i \(-0.497294\pi\)
0.00850246 + 0.999964i \(0.497294\pi\)
\(174\) −1.55432 + 1.55432i −0.117832 + 0.117832i
\(175\) 0.536454 + 0.176402i 0.0405521 + 0.0133348i
\(176\) 3.08552 + 11.5153i 0.232580 + 0.867999i
\(177\) 5.60919 + 1.50298i 0.421612 + 0.112971i
\(178\) 5.33351 3.07930i 0.399763 0.230803i
\(179\) 10.8654i 0.812115i 0.913848 + 0.406058i \(0.133097\pi\)
−0.913848 + 0.406058i \(0.866903\pi\)
\(180\) 9.80368 2.62689i 0.730723 0.195797i
\(181\) −0.436016 −0.0324088 −0.0162044 0.999869i \(-0.505158\pi\)
−0.0162044 + 0.999869i \(0.505158\pi\)
\(182\) 16.7572 + 17.4843i 1.24213 + 1.29603i
\(183\) 3.60438 0.266444
\(184\) 0.129966 0.0348242i 0.00958119 0.00256727i
\(185\) 21.4424i 1.57648i
\(186\) −13.2297 + 7.63818i −0.970050 + 0.560059i
\(187\) 12.6056 + 3.37767i 0.921815 + 0.246999i
\(188\) −6.69409 24.9827i −0.488216 1.82205i
\(189\) −0.540936 2.58986i −0.0393473 0.188385i
\(190\) 24.6304 24.6304i 1.78688 1.78688i
\(191\) −8.84445 −0.639962 −0.319981 0.947424i \(-0.603677\pi\)
−0.319981 + 0.947424i \(0.603677\pi\)
\(192\) −0.985368 −0.0711128
\(193\) −6.37156 + 6.37156i −0.458635 + 0.458635i −0.898207 0.439572i \(-0.855130\pi\)
0.439572 + 0.898207i \(0.355130\pi\)
\(194\) 9.76905 + 16.9205i 0.701377 + 1.21482i
\(195\) 8.22760 0.285288i 0.589190 0.0204299i
\(196\) 18.4668 25.0434i 1.31906 1.78881i
\(197\) −3.23591 + 12.0766i −0.230549 + 0.860421i 0.749556 + 0.661941i \(0.230267\pi\)
−0.980105 + 0.198480i \(0.936400\pi\)
\(198\) 2.20310 3.81588i 0.156568 0.271183i
\(199\) −4.17254 7.22706i −0.295784 0.512313i 0.679383 0.733784i \(-0.262247\pi\)
−0.975167 + 0.221471i \(0.928914\pi\)
\(200\) 1.27979 0.342918i 0.0904945 0.0242479i
\(201\) 0.794679 0.794679i 0.0560523 0.0560523i
\(202\) −10.9412 + 2.93169i −0.769820 + 0.206273i
\(203\) 1.52682 + 1.70781i 0.107162 + 0.119864i
\(204\) 16.7119 28.9458i 1.17006 2.02661i
\(205\) −5.01808 2.89719i −0.350478 0.202348i
\(206\) −15.2105 15.2105i −1.05977 1.05977i
\(207\) −0.0187715 0.0108378i −0.00130471 0.000753276i
\(208\) 24.1298 + 5.57706i 1.67310 + 0.386699i
\(209\) 10.4294i 0.721413i
\(210\) −3.13562 15.0125i −0.216378 1.03596i
\(211\) −0.0517275 0.0895946i −0.00356106 0.00616794i 0.864239 0.503081i \(-0.167800\pi\)
−0.867800 + 0.496913i \(0.834467\pi\)
\(212\) 61.0908i 4.19573i
\(213\) 3.36098 + 12.5434i 0.230291 + 0.859456i
\(214\) −6.66114 + 24.8597i −0.455346 + 1.69937i
\(215\) −3.18972 3.18972i −0.217537 0.217537i
\(216\) −4.38935 4.38935i −0.298657 0.298657i
\(217\) 7.17754 + 14.2106i 0.487243 + 0.964679i
\(218\) 8.93911 5.16100i 0.605433 0.349547i
\(219\) 2.56726 + 9.58115i 0.173479 + 0.647434i
\(220\) 8.80774 15.2554i 0.593817 1.02852i
\(221\) 18.4944 19.8231i 1.24407 1.33345i
\(222\) 20.6470 11.9205i 1.38574 0.800055i
\(223\) −25.3112 6.78211i −1.69496 0.454163i −0.723298 0.690536i \(-0.757375\pi\)
−0.971663 + 0.236372i \(0.924041\pi\)
\(224\) 0.742426 13.2692i 0.0496054 0.886583i
\(225\) −0.184846 0.106721i −0.0123230 0.00711471i
\(226\) −3.02802 + 11.3007i −0.201421 + 0.751712i
\(227\) 13.1489 + 3.52323i 0.872722 + 0.233845i 0.667265 0.744821i \(-0.267465\pi\)
0.205458 + 0.978666i \(0.434132\pi\)
\(228\) −25.8009 6.91334i −1.70871 0.457847i
\(229\) −6.29210 + 23.4824i −0.415794 + 1.55176i 0.367447 + 0.930044i \(0.380232\pi\)
−0.783241 + 0.621719i \(0.786435\pi\)
\(230\) −0.108812 0.0628227i −0.00717486 0.00414241i
\(231\) −3.84228 2.51455i −0.252803 0.165445i
\(232\) 5.19156 + 1.39107i 0.340843 + 0.0913285i
\(233\) 8.29904 4.79145i 0.543688 0.313899i −0.202884 0.979203i \(-0.565031\pi\)
0.746572 + 0.665304i \(0.231698\pi\)
\(234\) −4.84871 7.76380i −0.316970 0.507535i
\(235\) −6.64269 + 11.5055i −0.433321 + 0.750535i
\(236\) −6.68091 24.9335i −0.434890 1.62303i
\(237\) −3.75382 + 2.16727i −0.243837 + 0.140779i
\(238\) −42.2598 27.6566i −2.73929 1.79271i
\(239\) 5.64222 + 5.64222i 0.364965 + 0.364965i 0.865637 0.500672i \(-0.166914\pi\)
−0.500672 + 0.865637i \(0.666914\pi\)
\(240\) −11.0900 11.0900i −0.715854 0.715854i
\(241\) 6.56799 24.5121i 0.423081 1.57896i −0.344997 0.938604i \(-0.612120\pi\)
0.768078 0.640357i \(-0.221213\pi\)
\(242\) 5.24848 + 19.5876i 0.337385 + 1.25914i
\(243\) 1.00000i 0.0641500i
\(244\) −8.01095 13.8754i −0.512849 0.888280i
\(245\) −15.8036 + 2.38869i −1.00965 + 0.152608i
\(246\) 6.44258i 0.410764i
\(247\) −19.1275 10.1763i −1.21705 0.647503i
\(248\) 32.3482 + 18.6762i 2.05411 + 1.18594i
\(249\) 8.64819 + 8.64819i 0.548057 + 0.548057i
\(250\) 24.0288 + 13.8730i 1.51971 + 0.877407i
\(251\) −5.75368 + 9.96567i −0.363169 + 0.629027i −0.988481 0.151348i \(-0.951639\pi\)
0.625311 + 0.780375i \(0.284972\pi\)
\(252\) −8.76763 + 7.83850i −0.552309 + 0.493779i
\(253\) −0.0363381 + 0.00973676i −0.00228456 + 0.000612145i
\(254\) 5.72504 5.72504i 0.359221 0.359221i
\(255\) −16.5836 + 4.44355i −1.03850 + 0.278266i
\(256\) 14.9423 + 25.8809i 0.933896 + 1.61756i
\(257\) −13.6912 + 23.7139i −0.854036 + 1.47923i 0.0234997 + 0.999724i \(0.492519\pi\)
−0.877536 + 0.479511i \(0.840814\pi\)
\(258\) −1.29813 + 4.84468i −0.0808179 + 0.301616i
\(259\) −11.2017 22.1778i −0.696037 1.37806i
\(260\) −19.3846 31.0388i −1.20218 1.92494i
\(261\) −0.432921 0.749842i −0.0267972 0.0464141i
\(262\) −14.9137 + 14.9137i −0.921372 + 0.921372i
\(263\) −20.2715 −1.25000 −0.624998 0.780627i \(-0.714900\pi\)
−0.624998 + 0.780627i \(0.714900\pi\)
\(264\) −10.7737 −0.663074
\(265\) 22.1891 22.1891i 1.36307 1.36307i
\(266\) −12.6081 + 38.3423i −0.773052 + 2.35091i
\(267\) 0.627860 + 2.34321i 0.0384244 + 0.143402i
\(268\) −4.82540 1.29296i −0.294758 0.0789803i
\(269\) 1.57225 0.907738i 0.0958617 0.0553458i −0.451303 0.892371i \(-0.649041\pi\)
0.547164 + 0.837025i \(0.315707\pi\)
\(270\) 5.79666i 0.352773i
\(271\) −21.2681 + 5.69876i −1.29194 + 0.346175i −0.838398 0.545059i \(-0.816507\pi\)
−0.453545 + 0.891234i \(0.649841\pi\)
\(272\) −51.6481 −3.13163
\(273\) −8.36076 + 4.59323i −0.506016 + 0.277995i
\(274\) −12.7369 −0.769466
\(275\) −0.357825 + 0.0958790i −0.0215777 + 0.00578172i
\(276\) 0.0963502i 0.00579960i
\(277\) 17.5808 10.1503i 1.05633 0.609873i 0.131916 0.991261i \(-0.457887\pi\)
0.924415 + 0.381388i \(0.124554\pi\)
\(278\) −6.66553 1.78602i −0.399772 0.107119i
\(279\) −1.55740 5.81230i −0.0932392 0.347974i
\(280\) −27.9561 + 24.9935i −1.67070 + 1.49365i
\(281\) −14.1904 + 14.1904i −0.846529 + 0.846529i −0.989698 0.143169i \(-0.954271\pi\)
0.143169 + 0.989698i \(0.454271\pi\)
\(282\) 14.7716 0.879636
\(283\) 6.80207 0.404341 0.202171 0.979350i \(-0.435200\pi\)
0.202171 + 0.979350i \(0.435200\pi\)
\(284\) 40.8167 40.8167i 2.42203 2.42203i
\(285\) 6.86026 + 11.8823i 0.406367 + 0.703848i
\(286\) −15.4787 3.57755i −0.915276 0.211545i
\(287\) 6.70370 + 0.375080i 0.395707 + 0.0221403i
\(288\) −1.30008 + 4.85196i −0.0766078 + 0.285904i
\(289\) −19.7692 + 34.2413i −1.16289 + 2.01419i
\(290\) −2.50950 4.34658i −0.147363 0.255240i
\(291\) −7.43379 + 1.99188i −0.435777 + 0.116766i
\(292\) 31.1775 31.1775i 1.82453 1.82453i
\(293\) −20.5482 + 5.50587i −1.20044 + 0.321656i −0.803004 0.595974i \(-0.796766\pi\)
−0.397435 + 0.917630i \(0.630099\pi\)
\(294\) 11.0858 + 13.8894i 0.646539 + 0.810046i
\(295\) −6.62962 + 11.4828i −0.385991 + 0.668557i
\(296\) −50.4843 29.1471i −2.93434 1.69414i
\(297\) 1.22725 + 1.22725i 0.0712124 + 0.0712124i
\(298\) −49.5852 28.6280i −2.87239 1.65838i
\(299\) −0.0175991 + 0.0761448i −0.00101778 + 0.00440357i
\(300\) 0.948771i 0.0547773i
\(301\) 4.96546 + 1.63279i 0.286204 + 0.0941127i
\(302\) −26.5560 45.9964i −1.52813 2.64679i
\(303\) 4.46176i 0.256321i
\(304\) 10.6829 + 39.8690i 0.612704 + 2.28664i
\(305\) −2.13005 + 7.94945i −0.121966 + 0.455184i
\(306\) 13.4981 + 13.4981i 0.771634 + 0.771634i
\(307\) 17.4862 + 17.4862i 0.997992 + 0.997992i 0.999998 0.00200593i \(-0.000638508\pi\)
−0.00200593 + 0.999998i \(0.500639\pi\)
\(308\) −1.14028 + 20.3799i −0.0649736 + 1.16125i
\(309\) 7.33795 4.23657i 0.417441 0.241010i
\(310\) −9.02773 33.6919i −0.512740 1.91357i
\(311\) −1.90903 + 3.30654i −0.108251 + 0.187497i −0.915062 0.403314i \(-0.867858\pi\)
0.806811 + 0.590810i \(0.201192\pi\)
\(312\) −10.5123 + 19.7590i −0.595141 + 1.11863i
\(313\) −11.1229 + 6.42180i −0.628702 + 0.362981i −0.780249 0.625469i \(-0.784908\pi\)
0.151547 + 0.988450i \(0.451575\pi\)
\(314\) 16.1115 + 4.31705i 0.909223 + 0.243625i
\(315\) 6.03160 + 0.337475i 0.339842 + 0.0190146i
\(316\) 16.6862 + 9.63376i 0.938670 + 0.541941i
\(317\) 2.44740 9.13383i 0.137460 0.513007i −0.862516 0.506030i \(-0.831112\pi\)
0.999976 0.00697710i \(-0.00222090\pi\)
\(318\) −33.7017 9.03034i −1.88990 0.506396i
\(319\) −1.45155 0.388941i −0.0812712 0.0217765i
\(320\) 0.582314 2.17322i 0.0325523 0.121487i
\(321\) −8.77945 5.06882i −0.490021 0.282914i
\(322\) 0.145363 + 0.00813326i 0.00810078 + 0.000453249i
\(323\) 43.6439 + 11.6944i 2.42841 + 0.650692i
\(324\) 3.84958 2.22256i 0.213866 0.123475i
\(325\) −0.173301 + 0.749807i −0.00961299 + 0.0415918i
\(326\) 30.7956 53.3396i 1.70561 2.95421i
\(327\) 1.05231 + 3.92728i 0.0581930 + 0.217179i
\(328\) 13.6424 7.87643i 0.753275 0.434903i
\(329\) 0.859987 15.3703i 0.0474126 0.847392i
\(330\) 7.11396 + 7.11396i 0.391611 + 0.391611i
\(331\) 11.1115 + 11.1115i 0.610743 + 0.610743i 0.943140 0.332397i \(-0.107857\pi\)
−0.332397 + 0.943140i \(0.607857\pi\)
\(332\) 14.0708 52.5131i 0.772237 2.88203i
\(333\) 2.43056 + 9.07099i 0.133194 + 0.497087i
\(334\) 19.4678i 1.06523i
\(335\) 1.28304 + 2.22228i 0.0700997 + 0.121416i
\(336\) 17.2638 + 5.67686i 0.941818 + 0.309698i
\(337\) 1.41323i 0.0769835i 0.999259 + 0.0384917i \(0.0122553\pi\)
−0.999259 + 0.0384917i \(0.987745\pi\)
\(338\) −21.6644 + 24.8973i −1.17839 + 1.35424i
\(339\) −3.99096 2.30418i −0.216759 0.125146i
\(340\) 53.9638 + 53.9638i 2.92660 + 2.92660i
\(341\) −9.04449 5.22184i −0.489786 0.282778i
\(342\) 7.62770 13.2116i 0.412459 0.714400i
\(343\) 15.0977 10.7265i 0.815201 0.579177i
\(344\) 11.8458 3.17407i 0.638683 0.171135i
\(345\) 0.0349958 0.0349958i 0.00188411 0.00188411i
\(346\) 0.548475 0.146963i 0.0294862 0.00790081i
\(347\) −2.75091 4.76472i −0.147677 0.255784i 0.782692 0.622410i \(-0.213846\pi\)
−0.930368 + 0.366626i \(0.880513\pi\)
\(348\) −1.92439 + 3.33314i −0.103158 + 0.178675i
\(349\) −3.51381 + 13.1137i −0.188090 + 0.701960i 0.805858 + 0.592109i \(0.201704\pi\)
−0.993948 + 0.109852i \(0.964962\pi\)
\(350\) 1.43141 + 0.0800892i 0.0765121 + 0.00428095i
\(351\) 3.44826 1.05331i 0.184055 0.0562217i
\(352\) 4.35905 + 7.55010i 0.232338 + 0.402421i
\(353\) −5.48924 + 5.48924i −0.292163 + 0.292163i −0.837934 0.545771i \(-0.816237\pi\)
0.545771 + 0.837934i \(0.316237\pi\)
\(354\) 14.7425 0.783556
\(355\) −29.6505 −1.57369
\(356\) 7.62491 7.62491i 0.404120 0.404120i
\(357\) 14.8310 13.2593i 0.784941 0.701758i
\(358\) 7.13930 + 26.6442i 0.377324 + 1.40819i
\(359\) 22.0147 + 5.89881i 1.16189 + 0.311327i 0.787720 0.616033i \(-0.211261\pi\)
0.374169 + 0.927360i \(0.377928\pi\)
\(360\) 12.2746 7.08675i 0.646929 0.373505i
\(361\) 17.1091i 0.900480i
\(362\) −1.06921 + 0.286493i −0.0561962 + 0.0150577i
\(363\) −7.98770 −0.419246
\(364\) 36.2643 + 21.9767i 1.90077 + 1.15189i
\(365\) −22.6483 −1.18547
\(366\) 8.83874 2.36833i 0.462008 0.123795i
\(367\) 21.2751i 1.11055i −0.831666 0.555276i \(-0.812612\pi\)
0.831666 0.555276i \(-0.187388\pi\)
\(368\) 0.128939 0.0744427i 0.00672139 0.00388059i
\(369\) −2.45125 0.656811i −0.127607 0.0341922i
\(370\) 14.0891 + 52.5814i 0.732460 + 2.73358i
\(371\) −11.3584 + 34.5419i −0.589700 + 1.79333i
\(372\) −18.9135 + 18.9135i −0.980621 + 0.980621i
\(373\) 16.6520 0.862207 0.431104 0.902302i \(-0.358124\pi\)
0.431104 + 0.902302i \(0.358124\pi\)
\(374\) 33.1311 1.71317
\(375\) −7.72806 + 7.72806i −0.399075 + 0.399075i
\(376\) −18.0591 31.2793i −0.931329 1.61311i
\(377\) −2.12965 + 2.28265i −0.109683 + 0.117562i
\(378\) −3.02821 5.99548i −0.155755 0.308374i
\(379\) −4.72716 + 17.6420i −0.242818 + 0.906209i 0.731649 + 0.681681i \(0.238751\pi\)
−0.974468 + 0.224528i \(0.927916\pi\)
\(380\) 30.4947 52.8183i 1.56434 2.70952i
\(381\) 1.59459 + 2.76191i 0.0816932 + 0.141497i
\(382\) −21.6885 + 5.81142i −1.10968 + 0.297338i
\(383\) 18.8703 18.8703i 0.964225 0.964225i −0.0351564 0.999382i \(-0.511193\pi\)
0.999382 + 0.0351564i \(0.0111929\pi\)
\(384\) −12.1202 + 3.24761i −0.618509 + 0.165729i
\(385\) 7.81646 6.98813i 0.398364 0.356148i
\(386\) −11.4379 + 19.8110i −0.582174 + 1.00835i
\(387\) −1.71095 0.987815i −0.0869723 0.0502135i
\(388\) 24.1899 + 24.1899i 1.22806 + 1.22806i
\(389\) 0.958138 + 0.553181i 0.0485795 + 0.0280474i 0.524093 0.851661i \(-0.324404\pi\)
−0.475514 + 0.879708i \(0.657738\pi\)
\(390\) 19.9884 6.10570i 1.01215 0.309174i
\(391\) 0.162983i 0.00824238i
\(392\) 15.8582 40.4552i 0.800959 2.04330i
\(393\) −4.15389 7.19475i −0.209536 0.362927i
\(394\) 31.7406i 1.59907i
\(395\) −2.56154 9.55980i −0.128885 0.481006i
\(396\) 1.99677 7.45205i 0.100342 0.374480i
\(397\) −10.0331 10.0331i −0.503548 0.503548i 0.408990 0.912539i \(-0.365881\pi\)
−0.912539 + 0.408990i \(0.865881\pi\)
\(398\) −14.9807 14.9807i −0.750913 0.750913i
\(399\) −13.3030 8.70602i −0.665981 0.435846i
\(400\) 1.26967 0.733046i 0.0634837 0.0366523i
\(401\) −0.590311 2.20307i −0.0294787 0.110016i 0.949619 0.313407i \(-0.101470\pi\)
−0.979098 + 0.203391i \(0.934804\pi\)
\(402\) 1.42657 2.47088i 0.0711506 0.123237i
\(403\) −18.4019 + 11.4925i −0.916665 + 0.572483i
\(404\) −17.1759 + 9.91652i −0.854533 + 0.493365i
\(405\) −2.20549 0.590961i −0.109592 0.0293651i
\(406\) 4.86625 + 3.18468i 0.241508 + 0.158053i
\(407\) 14.1153 + 8.14948i 0.699670 + 0.403955i
\(408\) 12.0804 45.0848i 0.598071 2.23203i
\(409\) 19.0509 + 5.10468i 0.942008 + 0.252410i 0.696968 0.717102i \(-0.254532\pi\)
0.245041 + 0.969513i \(0.421199\pi\)
\(410\) −14.2091 3.80731i −0.701736 0.188030i
\(411\) 1.29851 4.84610i 0.0640508 0.239041i
\(412\) −32.6180 18.8320i −1.60698 0.927788i
\(413\) 0.858294 15.3400i 0.0422339 0.754834i
\(414\) −0.0531531 0.0142423i −0.00261233 0.000699972i
\(415\) −24.1843 + 13.9628i −1.18716 + 0.685407i
\(416\) 18.1002 0.627617i 0.887436 0.0307715i
\(417\) 1.35908 2.35400i 0.0665545 0.115276i
\(418\) −6.85281 25.5751i −0.335182 1.25092i
\(419\) 11.9093 6.87586i 0.581809 0.335908i −0.180043 0.983659i \(-0.557624\pi\)
0.761852 + 0.647751i \(0.224290\pi\)
\(420\) −12.1064 23.9692i −0.590734 1.16958i
\(421\) −18.9223 18.9223i −0.922215 0.922215i 0.0749709 0.997186i \(-0.476114\pi\)
−0.997186 + 0.0749709i \(0.976114\pi\)
\(422\) −0.185717 0.185717i −0.00904056 0.00904056i
\(423\) −1.50594 + 5.62025i −0.0732214 + 0.273266i
\(424\) 22.0802 + 82.4046i 1.07231 + 4.00192i
\(425\) 1.60491i 0.0778495i
\(426\) 16.4837 + 28.5506i 0.798639 + 1.38328i
\(427\) −1.94974 9.33486i −0.0943545 0.451745i
\(428\) 45.0630i 2.17820i
\(429\) 2.93921 5.52457i 0.141906 0.266729i
\(430\) −9.91777 5.72603i −0.478277 0.276134i
\(431\) 20.1127 + 20.1127i 0.968793 + 0.968793i 0.999528 0.0307350i \(-0.00978479\pi\)
−0.0307350 + 0.999528i \(0.509785\pi\)
\(432\) −5.94858 3.43442i −0.286201 0.165238i
\(433\) 12.8931 22.3315i 0.619602 1.07318i −0.369957 0.929049i \(-0.620628\pi\)
0.989558 0.144132i \(-0.0460391\pi\)
\(434\) 26.9383 + 30.1314i 1.29308 + 1.44635i
\(435\) 1.90961 0.511679i 0.0915589 0.0245331i
\(436\) 12.7796 12.7796i 0.612030 0.612030i
\(437\) −0.125812 + 0.0337112i −0.00601840 + 0.00161262i
\(438\) 12.5910 + 21.8082i 0.601620 + 1.04204i
\(439\) −1.23875 + 2.14557i −0.0591222 + 0.102403i −0.894072 0.447924i \(-0.852164\pi\)
0.834949 + 0.550327i \(0.185497\pi\)
\(440\) 6.36682 23.7613i 0.303526 1.13277i
\(441\) −6.41478 + 2.80190i −0.305466 + 0.133424i
\(442\) 32.3273 60.7627i 1.53765 2.89019i
\(443\) −11.6371 20.1560i −0.552894 0.957641i −0.998064 0.0621947i \(-0.980190\pi\)
0.445170 0.895446i \(-0.353143\pi\)
\(444\) 29.5175 29.5175i 1.40084 1.40084i
\(445\) −5.53897 −0.262572
\(446\) −66.5248 −3.15004
\(447\) 15.9474 15.9474i 0.754288 0.754288i
\(448\) 0.533021 + 2.55197i 0.0251829 + 0.120569i
\(449\) −2.13306 7.96070i −0.100665 0.375688i 0.897152 0.441722i \(-0.145632\pi\)
−0.997817 + 0.0660335i \(0.978966\pi\)
\(450\) −0.523405 0.140246i −0.0246735 0.00661125i
\(451\) −3.81438 + 2.20223i −0.179612 + 0.103699i
\(452\) 20.4847i 0.963520i
\(453\) 20.2079 5.41469i 0.949450 0.254404i
\(454\) 34.5590 1.62193
\(455\) −5.18946 21.1540i −0.243286 0.991716i
\(456\) −37.3013 −1.74679
\(457\) 5.33153 1.42858i 0.249399 0.0668261i −0.131954 0.991256i \(-0.542125\pi\)
0.381352 + 0.924430i \(0.375458\pi\)
\(458\) 61.7184i 2.88391i
\(459\) −6.51182 + 3.75960i −0.303946 + 0.175483i
\(460\) −0.212500 0.0569391i −0.00990785 0.00265480i
\(461\) 8.89222 + 33.1862i 0.414152 + 1.54564i 0.786529 + 0.617554i \(0.211876\pi\)
−0.372377 + 0.928082i \(0.621457\pi\)
\(462\) −11.0743 3.64158i −0.515225 0.169422i
\(463\) 10.3935 10.3935i 0.483025 0.483025i −0.423072 0.906096i \(-0.639048\pi\)
0.906096 + 0.423072i \(0.139048\pi\)
\(464\) 5.94733 0.276098
\(465\) 13.7394 0.637148
\(466\) 17.2027 17.2027i 0.796902 0.796902i
\(467\) 10.6589 + 18.4618i 0.493237 + 0.854311i 0.999970 0.00779214i \(-0.00248034\pi\)
−0.506733 + 0.862103i \(0.669147\pi\)
\(468\) −11.7188 10.9333i −0.541701 0.505394i
\(469\) −2.48798 1.62824i −0.114884 0.0751850i
\(470\) −8.72943 + 32.5787i −0.402658 + 1.50274i
\(471\) −3.28508 + 5.68992i −0.151368 + 0.262178i
\(472\) −18.0236 31.2178i −0.829603 1.43691i
\(473\) −3.31206 + 0.887464i −0.152289 + 0.0408056i
\(474\) −7.78114 + 7.78114i −0.357399 + 0.357399i
\(475\) −1.23888 + 0.331958i −0.0568439 + 0.0152313i
\(476\) −84.0057 27.6236i −3.85039 1.26613i
\(477\) 6.87167 11.9021i 0.314632 0.544959i
\(478\) 17.5433 + 10.1286i 0.802411 + 0.463272i
\(479\) 10.5215 + 10.5215i 0.480740 + 0.480740i 0.905368 0.424628i \(-0.139595\pi\)
−0.424628 + 0.905368i \(0.639595\pi\)
\(480\) −9.93267 5.73463i −0.453362 0.261749i
\(481\) 28.7190 17.9358i 1.30947 0.817803i
\(482\) 64.4246i 2.93446i
\(483\) −0.0179141 + 0.0544782i −0.000815120 + 0.00247885i
\(484\) 17.7531 + 30.7493i 0.806961 + 1.39770i
\(485\) 17.5723i 0.797918i
\(486\) 0.657070 + 2.45222i 0.0298053 + 0.111235i
\(487\) 3.73572 13.9419i 0.169281 0.631767i −0.828174 0.560471i \(-0.810620\pi\)
0.997455 0.0712956i \(-0.0227134\pi\)
\(488\) −15.8209 15.8209i −0.716178 0.716178i
\(489\) 17.1549 + 17.1549i 0.775772 + 0.775772i
\(490\) −37.1843 + 16.2416i −1.67981 + 0.733723i
\(491\) 0.458913 0.264954i 0.0207105 0.0119572i −0.489609 0.871942i \(-0.662860\pi\)
0.510319 + 0.859985i \(0.329527\pi\)
\(492\) 2.91960 + 10.8961i 0.131626 + 0.491235i
\(493\) 3.25522 5.63821i 0.146608 0.253932i
\(494\) −53.5914 12.3864i −2.41119 0.557291i
\(495\) −3.43196 + 1.98144i −0.154255 + 0.0890591i
\(496\) 39.9237 + 10.6975i 1.79263 + 0.480333i
\(497\) 30.6675 15.4896i 1.37562 0.694805i
\(498\) 26.8897 + 15.5248i 1.20496 + 0.695683i
\(499\) 6.57425 24.5354i 0.294304 1.09836i −0.647465 0.762095i \(-0.724171\pi\)
0.941769 0.336261i \(-0.109163\pi\)
\(500\) 46.9259 + 12.5738i 2.09859 + 0.562316i
\(501\) 7.40707 + 1.98472i 0.330923 + 0.0886706i
\(502\) −7.56114 + 28.2186i −0.337470 + 1.25946i
\(503\) −18.0905 10.4445i −0.806615 0.465699i 0.0391641 0.999233i \(-0.487530\pi\)
−0.845779 + 0.533533i \(0.820864\pi\)
\(504\) −8.99345 + 13.7422i −0.400600 + 0.612125i
\(505\) 9.84038 + 2.63672i 0.437891 + 0.117333i
\(506\) −0.0827112 + 0.0477533i −0.00367696 + 0.00212289i
\(507\) −7.26421 10.7811i −0.322615 0.478804i
\(508\) 7.08813 12.2770i 0.314485 0.544704i
\(509\) −2.99323 11.1709i −0.132673 0.495142i 0.867324 0.497744i \(-0.165838\pi\)
−0.999997 + 0.00260275i \(0.999172\pi\)
\(510\) −37.7468 + 21.7931i −1.67146 + 0.965016i
\(511\) 23.4251 11.8316i 1.03627 0.523401i
\(512\) 35.9022 + 35.9022i 1.58667 + 1.58667i
\(513\) 4.24907 + 4.24907i 0.187601 + 0.187601i
\(514\) −17.9922 + 67.1479i −0.793602 + 2.96176i
\(515\) 5.00729 + 18.6875i 0.220647 + 0.823468i
\(516\) 8.78191i 0.386602i
\(517\) 5.04930 + 8.74564i 0.222068 + 0.384633i
\(518\) −42.0413 47.0246i −1.84719 2.06614i
\(519\) 0.223665i 0.00981780i
\(520\) −37.3660 34.8616i −1.63861 1.52878i
\(521\) 24.8573 + 14.3514i 1.08902 + 0.628746i 0.933315 0.359058i \(-0.116902\pi\)
0.155705 + 0.987804i \(0.450235\pi\)
\(522\) −1.55432 1.55432i −0.0680306 0.0680306i
\(523\) −1.33141 0.768693i −0.0582187 0.0336126i 0.470608 0.882342i \(-0.344035\pi\)
−0.528827 + 0.848730i \(0.677368\pi\)
\(524\) −18.4645 + 31.9815i −0.806627 + 1.39712i
\(525\) −0.176402 + 0.536454i −0.00769882 + 0.0234128i
\(526\) −49.7102 + 13.3198i −2.16747 + 0.580771i
\(527\) 31.9935 31.9935i 1.39366 1.39366i
\(528\) −11.5153 + 3.08552i −0.501139 + 0.134280i
\(529\) −11.4998 19.9182i −0.499990 0.866008i
\(530\) 39.8327 68.9923i 1.73022 2.99684i
\(531\) −1.50298 + 5.60919i −0.0652237 + 0.243418i
\(532\) −3.94795 + 70.5606i −0.171165 + 3.05919i
\(533\) 0.317078 + 9.14440i 0.0137342 + 0.396088i
\(534\) 3.07930 + 5.33351i 0.133254 + 0.230803i
\(535\) 16.3676 16.3676i 0.707631 0.707631i
\(536\) −6.97624 −0.301328
\(537\) −10.8654 −0.468875
\(538\) 3.25905 3.25905i 0.140508 0.140508i
\(539\) −4.43391 + 11.3112i −0.190982 + 0.487207i
\(540\) 2.62689 + 9.80368i 0.113043 + 0.421883i
\(541\) −38.2161 10.2400i −1.64304 0.440251i −0.685388 0.728178i \(-0.740367\pi\)
−0.957652 + 0.287927i \(0.907034\pi\)
\(542\) −48.4094 + 27.9492i −2.07936 + 1.20052i
\(543\) 0.436016i 0.0187112i
\(544\) −36.4828 + 9.77555i −1.56419 + 0.419123i
\(545\) −9.28347 −0.397660
\(546\) −17.4843 + 16.7572i −0.748260 + 0.717142i
\(547\) 23.5304 1.00609 0.503043 0.864261i \(-0.332214\pi\)
0.503043 + 0.864261i \(0.332214\pi\)
\(548\) −21.5415 + 5.77203i −0.920207 + 0.246569i
\(549\) 3.60438i 0.153831i
\(550\) −0.814467 + 0.470232i −0.0347290 + 0.0200508i
\(551\) −5.02564 1.34662i −0.214099 0.0573678i
\(552\) 0.0348242 + 0.129966i 0.00148221 + 0.00553170i
\(553\) 7.64350 + 8.54952i 0.325035 + 0.363563i
\(554\) 36.4426 36.4426i 1.54830 1.54830i
\(555\) −21.4424 −0.910179
\(556\) −12.0825 −0.512414
\(557\) −13.1965 + 13.1965i −0.559152 + 0.559152i −0.929066 0.369914i \(-0.879387\pi\)
0.369914 + 0.929066i \(0.379387\pi\)
\(558\) −7.63818 13.2297i −0.323350 0.560059i
\(559\) −1.60409 + 6.94028i −0.0678456 + 0.293542i
\(560\) −22.7225 + 34.7204i −0.960202 + 1.46721i
\(561\) −3.37767 + 12.6056i −0.142605 + 0.532210i
\(562\) −25.4739 + 44.1221i −1.07455 + 1.86118i
\(563\) 5.01839 + 8.69210i 0.211500 + 0.366328i 0.952184 0.305525i \(-0.0988319\pi\)
−0.740684 + 0.671853i \(0.765499\pi\)
\(564\) 24.9827 6.69409i 1.05196 0.281872i
\(565\) 7.44036 7.44036i 0.313018 0.313018i
\(566\) 16.6802 4.46944i 0.701119 0.187864i
\(567\) 2.58986 0.540936i 0.108764 0.0227172i
\(568\) 40.3046 69.8097i 1.69114 2.92915i
\(569\) 9.90569 + 5.71905i 0.415268 + 0.239755i 0.693051 0.720889i \(-0.256266\pi\)
−0.277783 + 0.960644i \(0.589599\pi\)
\(570\) 24.6304 + 24.6304i 1.03165 + 1.03165i
\(571\) −37.6951 21.7633i −1.57749 0.910765i −0.995208 0.0977796i \(-0.968826\pi\)
−0.582284 0.812986i \(-0.697841\pi\)
\(572\) −27.7999 + 0.963949i −1.16237 + 0.0403047i
\(573\) 8.84445i 0.369482i
\(574\) 16.6854 3.48502i 0.696435 0.145462i
\(575\) 0.00231322 + 0.00400662i 9.64681e−5 + 0.000167088i
\(576\) 0.985368i 0.0410570i
\(577\) 0.354101 + 1.32152i 0.0147414 + 0.0550158i 0.972905 0.231206i \(-0.0742672\pi\)
−0.958163 + 0.286222i \(0.907601\pi\)
\(578\) −25.9795 + 96.9568i −1.08060 + 4.03287i
\(579\) −6.37156 6.37156i −0.264793 0.264793i
\(580\) −6.21398 6.21398i −0.258021 0.258021i
\(581\) 17.7195 27.0758i 0.735129 1.12329i
\(582\) −16.9205 + 9.76905i −0.701377 + 0.404940i
\(583\) −6.17359 23.0401i −0.255684 0.954225i
\(584\) 30.7864 53.3236i 1.27395 2.20655i
\(585\) 0.285288 + 8.22760i 0.0117952 + 0.340169i
\(586\) −46.7709 + 27.0032i −1.93209 + 1.11549i
\(587\) −20.9489 5.61323i −0.864652 0.231683i −0.200878 0.979616i \(-0.564380\pi\)
−0.663774 + 0.747933i \(0.731046\pi\)
\(588\) 25.0434 + 18.4668i 1.03277 + 0.761560i
\(589\) −31.3144 18.0794i −1.29029 0.744947i
\(590\) −8.71225 + 32.5145i −0.358678 + 1.33860i
\(591\) −12.0766 3.23591i −0.496764 0.133108i
\(592\) −62.3071 16.6951i −2.56081 0.686166i
\(593\) −1.09310 + 4.07949i −0.0448881 + 0.167525i −0.984731 0.174082i \(-0.944304\pi\)
0.939843 + 0.341606i \(0.110971\pi\)
\(594\) 3.81588 + 2.20310i 0.156568 + 0.0903943i
\(595\) 20.4788 + 40.5455i 0.839550 + 1.66220i
\(596\) −96.8352 25.9469i −3.96652 1.06283i
\(597\) 7.22706 4.17254i 0.295784 0.170771i
\(598\) 0.00687554 + 0.198288i 0.000281162 + 0.00810858i
\(599\) 9.66178 16.7347i 0.394770 0.683761i −0.598302 0.801271i \(-0.704158\pi\)
0.993072 + 0.117510i \(0.0374911\pi\)
\(600\) 0.342918 + 1.27979i 0.0139995 + 0.0522470i
\(601\) −6.96892 + 4.02351i −0.284268 + 0.164122i −0.635354 0.772221i \(-0.719146\pi\)
0.351086 + 0.936343i \(0.385813\pi\)
\(602\) 13.2493 + 0.741312i 0.539999 + 0.0302136i
\(603\) 0.794679 + 0.794679i 0.0323618 + 0.0323618i
\(604\) −65.7576 65.7576i −2.67564 2.67564i
\(605\) 4.72042 17.6168i 0.191912 0.716226i
\(606\) −2.93169 10.9412i −0.119092 0.444456i
\(607\) 44.9749i 1.82547i 0.408547 + 0.912737i \(0.366036\pi\)
−0.408547 + 0.912737i \(0.633964\pi\)
\(608\) 15.0922 + 26.1404i 0.612068 + 1.06013i
\(609\) −1.70781 + 1.52682i −0.0692038 + 0.0618700i
\(610\) 20.8934i 0.845948i
\(611\) 20.9663 0.726999i 0.848207 0.0294112i
\(612\) 28.9458 + 16.7119i 1.17006 + 0.675537i
\(613\) −3.82525 3.82525i −0.154500 0.154500i 0.625624 0.780125i \(-0.284844\pi\)
−0.780125 + 0.625624i \(0.784844\pi\)
\(614\) 54.3697 + 31.3904i 2.19418 + 1.26681i
\(615\) 2.89719 5.01808i 0.116826 0.202348i
\(616\) 5.82787 + 27.9023i 0.234811 + 1.12422i
\(617\) 21.1557 5.66866i 0.851697 0.228212i 0.193540 0.981092i \(-0.438003\pi\)
0.658157 + 0.752881i \(0.271336\pi\)
\(618\) 15.2105 15.2105i 0.611858 0.611858i
\(619\) −6.45170 + 1.72873i −0.259316 + 0.0694834i −0.386135 0.922442i \(-0.626190\pi\)
0.126819 + 0.991926i \(0.459523\pi\)
\(620\) −30.5365 52.8909i −1.22638 2.12415i
\(621\) 0.0108378 0.0187715i 0.000434904 0.000753276i
\(622\) −2.50873 + 9.36272i −0.100591 + 0.375411i
\(623\) 5.72895 2.89360i 0.229526 0.115929i
\(624\) −5.57706 + 24.1298i −0.223261 + 0.965965i
\(625\) −13.0108 22.5354i −0.520433 0.901416i
\(626\) −23.0562 + 23.0562i −0.921510 + 0.921510i
\(627\) 10.4294 0.416508
\(628\) 29.2051 1.16541
\(629\) −49.9307 + 49.9307i −1.99087 + 1.99087i
\(630\) 15.0125 3.13562i 0.598114 0.124926i
\(631\) −5.79046 21.6103i −0.230515 0.860293i −0.980120 0.198407i \(-0.936423\pi\)
0.749605 0.661886i \(-0.230244\pi\)
\(632\) 25.9897 + 6.96392i 1.03382 + 0.277010i
\(633\) 0.0895946 0.0517275i 0.00356106 0.00205598i
\(634\) 24.0063i 0.953411i
\(635\) −7.03371 + 1.88468i −0.279124 + 0.0747911i
\(636\) −61.0908 −2.42241
\(637\) 16.4185 + 19.1686i 0.650523 + 0.759486i
\(638\) −3.81508 −0.151040
\(639\) −12.5434 + 3.36098i −0.496207 + 0.132958i
\(640\) 28.6504i 1.13250i
\(641\) 1.91511 1.10569i 0.0756424 0.0436722i −0.461702 0.887035i \(-0.652761\pi\)
0.537344 + 0.843363i \(0.319428\pi\)
\(642\) −24.8597 6.66114i −0.981134 0.262894i
\(643\) −1.55263 5.79449i −0.0612297 0.228512i 0.928530 0.371258i \(-0.121074\pi\)
−0.989759 + 0.142746i \(0.954407\pi\)
\(644\) 0.249534 0.0521193i 0.00983301 0.00205379i
\(645\) 3.18972 3.18972i 0.125595 0.125595i
\(646\) 114.709 4.51315
\(647\) 1.55351 0.0610747 0.0305373 0.999534i \(-0.490278\pi\)
0.0305373 + 0.999534i \(0.490278\pi\)
\(648\) 4.38935 4.38935i 0.172430 0.172430i
\(649\) 5.03936 + 8.72842i 0.197812 + 0.342621i
\(650\) 0.0677042 + 1.95256i 0.00265558 + 0.0765857i
\(651\) −14.2106 + 7.17754i −0.556958 + 0.281310i
\(652\) 27.9115 104.167i 1.09310 4.07950i
\(653\) −10.9877 + 19.0312i −0.429981 + 0.744749i −0.996871 0.0790445i \(-0.974813\pi\)
0.566890 + 0.823793i \(0.308146\pi\)
\(654\) 5.16100 + 8.93911i 0.201811 + 0.349547i
\(655\) 18.3228 4.90957i 0.715930 0.191833i
\(656\) 12.3257 12.3257i 0.481239 0.481239i
\(657\) −9.58115 + 2.56726i −0.373796 + 0.100158i
\(658\) −7.99048 38.2564i −0.311501 1.49139i
\(659\) 13.5876 23.5344i 0.529298 0.916771i −0.470118 0.882604i \(-0.655789\pi\)
0.999416 0.0341676i \(-0.0108780\pi\)
\(660\) 15.2554 + 8.80774i 0.593817 + 0.342841i
\(661\) 7.66117 + 7.66117i 0.297985 + 0.297985i 0.840224 0.542239i \(-0.182423\pi\)
−0.542239 + 0.840224i \(0.682423\pi\)
\(662\) 34.5488 + 19.9468i 1.34278 + 0.775254i
\(663\) 19.8231 + 18.4944i 0.769865 + 0.718265i
\(664\) 75.9199i 2.94626i
\(665\) 27.0626 24.1947i 1.04944 0.938231i
\(666\) 11.9205 + 20.6470i 0.461912 + 0.800055i
\(667\) 0.0187676i 0.000726684i
\(668\) −8.82230 32.9253i −0.341345 1.27392i
\(669\) 6.78211 25.3112i 0.262211 0.978586i
\(670\) 4.60648 + 4.60648i 0.177964 + 0.177964i
\(671\) 4.42349 + 4.42349i 0.170767 + 0.170767i
\(672\) 13.2692 + 0.742426i 0.511869 + 0.0286397i
\(673\) −33.8958 + 19.5698i −1.30659 + 0.754359i −0.981525 0.191333i \(-0.938719\pi\)
−0.325063 + 0.945692i \(0.605386\pi\)
\(674\) 0.928590 + 3.46555i 0.0357680 + 0.133488i
\(675\) 0.106721 0.184846i 0.00410768 0.00711471i
\(676\) −25.3575 + 51.9257i −0.975288 + 1.99714i
\(677\) 13.3692 7.71873i 0.513822 0.296655i −0.220582 0.975369i \(-0.570796\pi\)
0.734403 + 0.678714i \(0.237462\pi\)
\(678\) −11.3007 3.02802i −0.434001 0.116290i
\(679\) 9.17990 + 18.1750i 0.352292 + 0.697494i
\(680\) 92.2953 + 53.2867i 3.53936 + 2.04345i
\(681\) −3.52323 + 13.1489i −0.135011 + 0.503866i
\(682\) −25.6102 6.86223i −0.980664 0.262768i
\(683\) 45.0831 + 12.0800i 1.72506 + 0.462227i 0.979034 0.203695i \(-0.0652950\pi\)
0.746021 + 0.665922i \(0.231962\pi\)
\(684\) 6.91334 25.8009i 0.264338 0.986523i
\(685\) 9.92069 + 5.72771i 0.379050 + 0.218845i
\(686\) 29.9749 36.2240i 1.14445 1.38304i
\(687\) −23.4824 6.29210i −0.895911 0.240059i
\(688\) 11.7522 6.78514i 0.448049 0.258681i
\(689\) −48.2796 11.1587i −1.83931 0.425114i
\(690\) 0.0628227 0.108812i 0.00239162 0.00414241i
\(691\) −1.25695 4.69099i −0.0478165 0.178454i 0.937888 0.346939i \(-0.112779\pi\)
−0.985704 + 0.168486i \(0.946112\pi\)
\(692\) 0.861017 0.497108i 0.0327310 0.0188972i
\(693\) 2.51455 3.84228i 0.0955199 0.145956i
\(694\) −9.87660 9.87660i −0.374910 0.374910i
\(695\) 4.38857 + 4.38857i 0.166468 + 0.166468i
\(696\) −1.39107 + 5.19156i −0.0527286 + 0.196786i
\(697\) −4.93870 18.4315i −0.187067 0.698142i
\(698\) 34.4665i 1.30458i
\(699\) 4.79145 + 8.29904i 0.181229 + 0.313899i
\(700\) 2.45719 0.513224i 0.0928730 0.0193981i
\(701\) 34.8788i 1.31735i −0.752426 0.658677i \(-0.771116\pi\)
0.752426 0.658677i \(-0.228884\pi\)
\(702\) 7.76380 4.84871i 0.293026 0.183003i
\(703\) 48.8709 + 28.2156i 1.84320 + 1.06417i
\(704\) −1.20930 1.20930i −0.0455770 0.0455770i
\(705\) −11.5055 6.64269i −0.433321 0.250178i
\(706\) −9.85401 + 17.0676i −0.370861 + 0.642349i
\(707\) −11.5553 + 2.41352i −0.434583 + 0.0907699i
\(708\) 24.9335 6.68091i 0.937058 0.251084i
\(709\) −31.3560 + 31.3560i −1.17760 + 1.17760i −0.197246 + 0.980354i \(0.563200\pi\)
−0.980354 + 0.197246i \(0.936800\pi\)
\(710\) −72.7095 + 19.4825i −2.72874 + 0.731164i
\(711\) −2.16727 3.75382i −0.0812789 0.140779i
\(712\) 7.52925 13.0410i 0.282171 0.488734i
\(713\) −0.0337575 + 0.125985i −0.00126423 + 0.00471816i
\(714\) 27.6566 42.2598i 1.03502 1.58153i
\(715\) 10.4475 + 9.74722i 0.390713 + 0.364525i
\(716\) 24.1489 + 41.8271i 0.902487 + 1.56315i
\(717\) −5.64222 + 5.64222i −0.210712 + 0.210712i
\(718\) 57.8607 2.15934
\(719\) −23.4461 −0.874394 −0.437197 0.899366i \(-0.644029\pi\)
−0.437197 + 0.899366i \(0.644029\pi\)
\(720\) 11.0900 11.0900i 0.413299 0.413299i
\(721\) −14.9415 16.7126i −0.556450 0.622409i
\(722\) −11.2419 41.9553i −0.418380 1.56141i
\(723\) 24.5121 + 6.56799i 0.911613 + 0.244266i
\(724\) −1.67848 + 0.969071i −0.0623802 + 0.0360152i
\(725\) 0.184807i 0.00686355i
\(726\) −19.5876 + 5.24848i −0.726964 + 0.194789i
\(727\) 4.34538 0.161161 0.0805806 0.996748i \(-0.474323\pi\)
0.0805806 + 0.996748i \(0.474323\pi\)
\(728\) 56.8596 + 16.5370i 2.10736 + 0.612902i
\(729\) −1.00000 −0.0370370
\(730\) −55.5386 + 14.8815i −2.05558 + 0.550790i
\(731\) 14.8552i 0.549438i
\(732\) 13.8754 8.01095i 0.512849 0.296093i
\(733\) 42.9792 + 11.5162i 1.58747 + 0.425362i 0.941229 0.337768i \(-0.109672\pi\)
0.646245 + 0.763130i \(0.276339\pi\)
\(734\) −13.9792 52.1713i −0.515984 1.92568i
\(735\) −2.38869 15.8036i −0.0881083 0.582923i
\(736\) 0.0769888 0.0769888i 0.00283784 0.00283784i
\(737\) 1.95054 0.0718491
\(738\) −6.44258 −0.237155
\(739\) 20.6855 20.6855i 0.760929 0.760929i −0.215561 0.976490i \(-0.569158\pi\)
0.976490 + 0.215561i \(0.0691581\pi\)
\(740\) 47.6570 + 82.5443i 1.75190 + 3.03439i
\(741\) 10.1763 19.1275i 0.373836 0.702666i
\(742\) −5.15689 + 92.1676i −0.189315 + 3.38358i
\(743\) −2.66460 + 9.94444i −0.0977548 + 0.364826i −0.997423 0.0717489i \(-0.977142\pi\)
0.899668 + 0.436575i \(0.143809\pi\)
\(744\) −18.6762 + 32.3482i −0.684704 + 1.18594i
\(745\) 25.7477 + 44.5963i 0.943323 + 1.63388i
\(746\) 40.8343 10.9415i 1.49505 0.400598i
\(747\) −8.64819 + 8.64819i −0.316421 + 0.316421i
\(748\) 56.0335 15.0141i 2.04879 0.548971i
\(749\) −8.37842 + 25.4795i −0.306141 + 0.931000i
\(750\) −13.8730 + 24.0288i −0.506571 + 0.877407i
\(751\) −18.5810 10.7278i −0.678031 0.391462i 0.121081 0.992643i \(-0.461364\pi\)
−0.799113 + 0.601181i \(0.794697\pi\)
\(752\) −28.2605 28.2605i −1.03055 1.03055i
\(753\) −9.96567 5.75368i −0.363169 0.209676i
\(754\) −3.72251 + 6.99688i −0.135566 + 0.254811i
\(755\) 47.7683i 1.73847i
\(756\) −7.83850 8.76763i −0.285083 0.318876i
\(757\) −18.9933 32.8973i −0.690322 1.19567i −0.971732 0.236085i \(-0.924136\pi\)
0.281410 0.959588i \(-0.409198\pi\)
\(758\) 46.3682i 1.68417i
\(759\) −0.00973676 0.0363381i −0.000353422 0.00131899i
\(760\) 22.0436 82.2677i 0.799604 2.98416i
\(761\) 11.9557 + 11.9557i 0.433393 + 0.433393i 0.889781 0.456388i \(-0.150857\pi\)
−0.456388 + 0.889781i \(0.650857\pi\)
\(762\) 5.72504 + 5.72504i 0.207396 + 0.207396i
\(763\) 9.60188 4.84975i 0.347611 0.175573i
\(764\) −34.0475 + 19.6573i −1.23179 + 0.711177i
\(765\) −4.44355 16.5836i −0.160657 0.599580i
\(766\) 33.8749 58.6731i 1.22395 2.11995i
\(767\) 20.9251 0.725568i 0.755561 0.0261987i
\(768\) −25.8809 + 14.9423i −0.933896 + 0.539185i
\(769\) −35.8744 9.61252i −1.29366 0.346636i −0.454614 0.890689i \(-0.650223\pi\)
−0.839051 + 0.544052i \(0.816889\pi\)
\(770\) 14.5760 22.2724i 0.525282 0.802641i
\(771\) −23.7139 13.6912i −0.854036 0.493078i
\(772\) −10.3667 + 38.6890i −0.373106 + 1.39245i
\(773\) 11.3980 + 3.05409i 0.409958 + 0.109848i 0.457903 0.889002i \(-0.348601\pi\)
−0.0479452 + 0.998850i \(0.515267\pi\)
\(774\) −4.84468 1.29813i −0.174138 0.0466602i
\(775\) −0.332414 + 1.24059i −0.0119407 + 0.0445631i
\(776\) 41.3726 + 23.8865i 1.48519 + 0.857474i
\(777\) 22.1778 11.2017i 0.795625 0.401857i
\(778\) 2.71304 + 0.726958i 0.0972673 + 0.0260627i
\(779\) −13.2064 + 7.62470i −0.473167 + 0.273183i
\(780\) 31.0388 19.3846i 1.11137 0.694079i
\(781\) −11.2691 + 19.5186i −0.403240 + 0.698431i
\(782\) −0.107091 0.399669i −0.00382956 0.0142921i
\(783\) 0.749842 0.432921i 0.0267972 0.0154714i
\(784\) 5.36368 47.7817i 0.191560 1.70649i
\(785\) −10.6077 10.6077i −0.378607 0.378607i
\(786\) −14.9137 14.9137i −0.531954 0.531954i
\(787\) −1.05985 + 3.95541i −0.0377795 + 0.140995i −0.982240 0.187631i \(-0.939919\pi\)
0.944460 + 0.328626i \(0.106586\pi\)
\(788\) 14.3840 + 53.6818i 0.512409 + 1.91234i
\(789\) 20.2715i 0.721685i
\(790\) −12.5629 21.7596i −0.446968 0.774172i
\(791\) −3.80866 + 11.5825i −0.135420 + 0.411825i
\(792\) 10.7737i 0.382826i
\(793\) 12.4289 3.79655i 0.441362 0.134819i
\(794\) −31.1959 18.0110i −1.10710 0.639185i
\(795\) 22.1891 + 22.1891i 0.786966 + 0.786966i
\(796\) −32.1251 18.5475i −1.13864 0.657397i
\(797\) 1.02216 1.77043i 0.0362067 0.0627119i −0.847354 0.531028i \(-0.821806\pi\)
0.883561 + 0.468316i \(0.155139\pi\)
\(798\) −38.3423 12.6081i −1.35730 0.446322i
\(799\) −42.2598 + 11.3235i −1.49504 + 0.400596i
\(800\) 0.758117 0.758117i 0.0268035 0.0268035i
\(801\) −2.34321 + 0.627860i −0.0827931 + 0.0221843i
\(802\) −2.89514 5.01454i −0.102231 0.177069i
\(803\) −8.60781 + 14.9092i −0.303763 + 0.526133i
\(804\) 1.29296 4.82540i 0.0455993 0.170179i
\(805\) −0.109565 0.0717039i −0.00386166 0.00252723i
\(806\) −37.5742 + 40.2735i −1.32349 + 1.41857i
\(807\) 0.907738 + 1.57225i 0.0319539 + 0.0553458i
\(808\) −19.5842 + 19.5842i −0.688970 + 0.688970i
\(809\) −27.1722 −0.955322 −0.477661 0.878544i \(-0.658515\pi\)
−0.477661 + 0.878544i \(0.658515\pi\)
\(810\) −5.79666 −0.203674
\(811\) 18.4741 18.4741i 0.648712 0.648712i −0.303970 0.952682i \(-0.598312\pi\)
0.952682 + 0.303970i \(0.0983122\pi\)
\(812\) 9.67333 + 3.18088i 0.339467 + 0.111627i
\(813\) −5.69876 21.2681i −0.199864 0.745903i
\(814\) 39.9686 + 10.7096i 1.40090 + 0.375370i
\(815\) −47.9730 + 27.6972i −1.68042 + 0.970191i
\(816\) 51.6481i 1.80805i
\(817\) −11.4672 + 3.07263i −0.401187 + 0.107498i
\(818\) 50.0712 1.75070
\(819\) −4.59323 8.36076i −0.160500 0.292149i
\(820\) −25.7567 −0.899462
\(821\) −1.59604 + 0.427657i −0.0557021 + 0.0149253i −0.286562 0.958062i \(-0.592513\pi\)
0.230860 + 0.972987i \(0.425846\pi\)
\(822\) 12.7369i 0.444251i
\(823\) −22.8653 + 13.2013i −0.797033 + 0.460167i −0.842433 0.538802i \(-0.818877\pi\)
0.0453998 + 0.998969i \(0.485544\pi\)
\(824\) −50.8046 13.6131i −1.76986 0.474233i
\(825\) −0.0958790 0.357825i −0.00333808 0.0124579i
\(826\) −7.97476 38.1811i −0.277477 1.32849i
\(827\) 21.2610 21.2610i 0.739319 0.739319i −0.233127 0.972446i \(-0.574896\pi\)
0.972446 + 0.233127i \(0.0748959\pi\)
\(828\) −0.0963502 −0.00334840
\(829\) −28.6228 −0.994111 −0.497056 0.867719i \(-0.665586\pi\)
−0.497056 + 0.867719i \(0.665586\pi\)
\(830\) −50.1306 + 50.1306i −1.74006 + 1.74006i
\(831\) 10.1503 + 17.5808i 0.352110 + 0.609873i
\(832\) −3.39781 + 1.03790i −0.117798 + 0.0359828i
\(833\) −42.3625 31.2378i −1.46777 1.08233i
\(834\) 1.78602 6.66553i 0.0618449 0.230808i
\(835\) −8.75457 + 15.1634i −0.302964 + 0.524750i
\(836\) −23.1798 40.1487i −0.801692 1.38857i
\(837\) 5.81230 1.55740i 0.200903 0.0538317i
\(838\) 24.6864 24.6864i 0.852776 0.852776i
\(839\) −2.96674 + 0.794936i −0.102423 + 0.0274442i −0.309667 0.950845i \(-0.600217\pi\)
0.207243 + 0.978289i \(0.433551\pi\)
\(840\) −24.9935 27.9561i −0.862358 0.964577i
\(841\) 14.1252 24.4655i 0.487074 0.843638i
\(842\) −58.8348 33.9683i −2.02758 1.17062i
\(843\) −14.1904 14.1904i −0.488744 0.488744i
\(844\) −0.398258 0.229935i −0.0137086 0.00791467i
\(845\) 28.0704 9.64999i 0.965652 0.331970i
\(846\) 14.7716i 0.507858i
\(847\) 4.32084 + 20.6871i 0.148466 + 0.710816i
\(848\) 47.2004 + 81.7534i 1.62087 + 2.80742i
\(849\) 6.80207i 0.233446i
\(850\) −1.05454 3.93559i −0.0361703 0.134989i
\(851\) 0.0526837 0.196618i 0.00180597 0.00673999i
\(852\) 40.8167 + 40.8167i 1.39836 + 1.39836i
\(853\) −15.7683 15.7683i −0.539896 0.539896i 0.383603 0.923498i \(-0.374683\pi\)
−0.923498 + 0.383603i \(0.874683\pi\)
\(854\) −10.9148 21.6100i −0.373498 0.739479i
\(855\) −11.8823 + 6.86026i −0.406367 + 0.234616i
\(856\) 16.2873 + 60.7849i 0.556687 + 2.07758i
\(857\) 8.97423 15.5438i 0.306554 0.530967i −0.671052 0.741410i \(-0.734157\pi\)
0.977606 + 0.210443i \(0.0674907\pi\)
\(858\) 3.57755 15.4787i 0.122136 0.528435i
\(859\) −49.1470 + 28.3750i −1.67687 + 0.968144i −0.713239 + 0.700921i \(0.752773\pi\)
−0.963635 + 0.267223i \(0.913894\pi\)
\(860\) −19.3685 5.18976i −0.660459 0.176969i
\(861\) −0.375080 + 6.70370i −0.0127827 + 0.228462i
\(862\) 62.5361 + 36.1052i 2.12999 + 1.22975i
\(863\) −2.21271 + 8.25794i −0.0753215 + 0.281104i −0.993306 0.115513i \(-0.963149\pi\)
0.917985 + 0.396616i \(0.129816\pi\)
\(864\) −4.85196 1.30008i −0.165067 0.0442295i
\(865\) −0.493292 0.132177i −0.0167724 0.00449416i
\(866\) 16.9433 63.2333i 0.575757 2.14875i
\(867\) −34.2413 19.7692i −1.16289 0.671397i
\(868\) 59.2145 + 38.7524i 2.00987 + 1.31534i
\(869\) −7.26667 1.94710i −0.246505 0.0660508i
\(870\) 4.34658 2.50950i 0.147363 0.0850799i
\(871\) 1.90322 3.57731i 0.0644880 0.121212i
\(872\) 12.6192 21.8572i 0.427341 0.740177i
\(873\) −1.99188 7.43379i −0.0674149 0.251596i
\(874\) −0.286368 + 0.165334i −0.00968653 + 0.00559252i
\(875\) 24.1950 + 15.8342i 0.817941 + 0.535295i
\(876\) 31.1775 + 31.1775i 1.05339 + 1.05339i
\(877\) 19.6573 + 19.6573i 0.663781 + 0.663781i 0.956269 0.292488i \(-0.0944831\pi\)
−0.292488 + 0.956269i \(0.594483\pi\)
\(878\) −1.62789 + 6.07536i −0.0549386 + 0.205034i
\(879\) −5.50587 20.5482i −0.185708 0.693073i
\(880\) 27.2204i 0.917598i
\(881\) 7.37078 + 12.7666i 0.248328 + 0.430116i 0.963062 0.269280i \(-0.0867857\pi\)
−0.714734 + 0.699396i \(0.753452\pi\)
\(882\) −13.8894 + 11.0858i −0.467680 + 0.373279i
\(883\) 16.7260i 0.562876i 0.959579 + 0.281438i \(0.0908114\pi\)
−0.959579 + 0.281438i \(0.909189\pi\)
\(884\) 27.1379 117.416i 0.912748 3.94911i
\(885\) −11.4828 6.62962i −0.385991 0.222852i
\(886\) −41.7806 41.7806i −1.40365 1.40365i
\(887\) 15.9425 + 9.20441i 0.535297 + 0.309054i 0.743171 0.669102i \(-0.233321\pi\)
−0.207874 + 0.978156i \(0.566654\pi\)
\(888\) 29.1471 50.4843i 0.978114 1.69414i
\(889\) 6.29039 5.62378i 0.210973 0.188615i
\(890\) −13.5828 + 3.63949i −0.455295 + 0.121996i
\(891\) −1.22725 + 1.22725i −0.0411145 + 0.0411145i
\(892\) −112.511 + 30.1473i −3.76715 + 1.00940i
\(893\) 17.4820 + 30.2797i 0.585012 + 1.01327i
\(894\) 28.6280 49.5852i 0.957465 1.65838i
\(895\) 6.42100 23.9635i 0.214630 0.801011i
\(896\) 14.9671 + 29.6330i 0.500017 + 0.989970i
\(897\) −0.0761448 0.0175991i −0.00254240 0.000587618i
\(898\) −10.4615 18.1198i −0.349104 0.604665i
\(899\) −3.68408 + 3.68408i −0.122871 + 0.122871i
\(900\) −0.948771 −0.0316257
\(901\) 103.339 3.44272
\(902\) −7.90667 + 7.90667i −0.263263 + 0.263263i
\(903\) −1.63279 + 4.96546i −0.0543360 + 0.165240i
\(904\) 7.40386 + 27.6316i 0.246249 + 0.919012i
\(905\) 0.961631 + 0.257668i 0.0319657 + 0.00856518i
\(906\) 45.9964 26.5560i 1.52813 0.882264i
\(907\) 28.8547i 0.958105i 0.877786 + 0.479053i \(0.159020\pi\)
−0.877786 + 0.479053i \(0.840980\pi\)
\(908\) 58.4483 15.6612i 1.93968 0.519735i
\(909\) 4.46176 0.147987
\(910\) −26.6254 48.4644i −0.882622 1.60658i
\(911\) −13.0437 −0.432159 −0.216079 0.976376i \(-0.569327\pi\)
−0.216079 + 0.976376i \(0.569327\pi\)
\(912\) −39.8690 + 10.6829i −1.32019 + 0.353745i
\(913\) 21.2270i 0.702512i
\(914\) 12.1354 7.00638i 0.401403 0.231750i
\(915\) −7.94945 2.13005i −0.262801 0.0704172i
\(916\) 27.9691 + 104.382i 0.924126 + 3.44888i
\(917\) −16.3864 + 14.6499i −0.541127 + 0.483782i
\(918\) −13.4981 + 13.4981i −0.445503 + 0.445503i
\(919\) 6.81332 0.224751 0.112375 0.993666i \(-0.464154\pi\)
0.112375 + 0.993666i \(0.464154\pi\)
\(920\) −0.307218 −0.0101287
\(921\) −17.4862 + 17.4862i −0.576191 + 0.576191i
\(922\) 43.6113 + 75.5370i 1.43626 + 2.48768i
\(923\) 24.8016 + 39.7126i 0.816356 + 1.30716i
\(924\) −20.3799 1.14028i −0.670450 0.0375125i
\(925\) 0.518783 1.93612i 0.0170575 0.0636593i
\(926\) 18.6578 32.3163i 0.613133 1.06198i
\(927\) 4.23657 + 7.33795i 0.139147 + 0.241010i
\(928\) 4.20103 1.12566i 0.137906 0.0369517i
\(929\) 3.62723 3.62723i 0.119006 0.119006i −0.645096 0.764102i \(-0.723183\pi\)
0.764102 + 0.645096i \(0.223183\pi\)
\(930\) 33.6919 9.02773i 1.10480 0.296031i
\(931\) −15.3514 + 39.1623i −0.503120 + 1.28349i
\(932\) 21.2986 36.8902i 0.697658 1.20838i
\(933\) −3.30654 1.90903i −0.108251 0.0624988i
\(934\) 38.2687 + 38.2687i 1.25219 + 1.25219i
\(935\) −25.8056 14.8989i −0.843932 0.487245i
\(936\) −19.7590 10.5123i −0.645843 0.343605i
\(937\) 49.7519i 1.62532i 0.582736 + 0.812662i \(0.301982\pi\)
−0.582736 + 0.812662i \(0.698018\pi\)
\(938\) −7.17093 2.35802i −0.234139 0.0769921i
\(939\) −6.42180 11.1229i −0.209567 0.362981i
\(940\) 59.0551i 1.92616i
\(941\) −14.9061 55.6304i −0.485926 1.81350i −0.575857 0.817551i \(-0.695331\pi\)
0.0899311 0.995948i \(-0.471335\pi\)
\(942\) −4.31705 + 16.1115i −0.140657 + 0.524940i
\(943\) 0.0388954 + 0.0388954i 0.00126661 + 0.00126661i
\(944\) −28.2049 28.2049i −0.917991 0.917991i
\(945\) −0.337475 + 6.03160i −0.0109781 + 0.196208i
\(946\) −7.53877 + 4.35251i −0.245107 + 0.141512i
\(947\) −4.20655 15.6990i −0.136694 0.510151i −0.999985 0.00544363i \(-0.998267\pi\)
0.863291 0.504707i \(-0.168399\pi\)
\(948\) −9.63376 + 16.6862i −0.312890 + 0.541941i
\(949\) 18.9445 + 30.3342i 0.614966 + 0.984690i
\(950\) −2.81989 + 1.62807i −0.0914895 + 0.0528215i
\(951\) 9.13383 + 2.44740i 0.296185 + 0.0793625i
\(952\) −123.298 6.89869i −3.99612 0.223588i
\(953\) 8.84363 + 5.10587i 0.286473 + 0.165395i 0.636350 0.771400i \(-0.280443\pi\)
−0.349877 + 0.936796i \(0.613777\pi\)
\(954\) 9.03034 33.7017i 0.292368 1.09113i
\(955\) 19.5064 + 5.22672i 0.631212 + 0.169133i
\(956\) 34.2603 + 9.18003i 1.10806 + 0.296903i
\(957\) 0.388941 1.45155i 0.0125727 0.0469219i
\(958\) 32.7144 + 18.8877i 1.05695 + 0.610233i
\(959\) −13.2532 0.741530i −0.427967 0.0239453i
\(960\) 2.17322 + 0.582314i 0.0701405 + 0.0187941i
\(961\) −4.51058 + 2.60419i −0.145503 + 0.0840060i
\(962\) 58.6402 62.8530i 1.89064 2.02646i
\(963\) 5.06882 8.77945i 0.163340 0.282914i
\(964\) −29.1955 108.959i −0.940323 3.50933i
\(965\) 17.8178 10.2871i 0.573575 0.331154i
\(966\) −0.00813326 + 0.145363i −0.000261683 + 0.00467699i
\(967\) 13.8579 + 13.8579i 0.445641 + 0.445641i 0.893903 0.448261i \(-0.147957\pi\)
−0.448261 + 0.893903i \(0.647957\pi\)
\(968\) 35.0608 + 35.0608i 1.12690 + 1.12690i
\(969\) −11.6944 + 43.6439i −0.375677 + 1.40205i
\(970\) −11.5462 43.0912i −0.370727 1.38357i
\(971\) 5.48046i 0.175876i 0.996126 + 0.0879381i \(0.0280278\pi\)
−0.996126 + 0.0879381i \(0.971972\pi\)
\(972\) 2.22256 + 3.84958i 0.0712886 + 0.123475i
\(973\) −6.83170 2.24647i −0.219014 0.0720186i
\(974\) 36.6432i 1.17412i
\(975\) −0.749807 0.173301i −0.0240130 0.00555007i
\(976\) −21.4410 12.3790i −0.686309 0.396241i
\(977\) 15.5007 + 15.5007i 0.495912 + 0.495912i 0.910163 0.414251i \(-0.135956\pi\)
−0.414251 + 0.910163i \(0.635956\pi\)
\(978\) 53.3396 + 30.7956i 1.70561 + 0.984736i
\(979\) −2.10516 + 3.64625i −0.0672813 + 0.116535i
\(980\) −55.5282 + 44.3198i −1.77378 + 1.41575i
\(981\) −3.92728 + 1.05231i −0.125388 + 0.0335977i
\(982\) 0.951263 0.951263i 0.0303560 0.0303560i
\(983\) −0.0940093 + 0.0251897i −0.00299843 + 0.000803427i −0.260318 0.965523i \(-0.583827\pi\)
0.257320 + 0.966326i \(0.417161\pi\)
\(984\) 7.87643 + 13.6424i 0.251092 + 0.434903i
\(985\) 14.2736 24.7225i 0.454794 0.787726i
\(986\) 4.27782 15.9650i 0.136234 0.508431i
\(987\) 15.3703 + 0.859987i 0.489242 + 0.0273737i
\(988\) −96.2504 + 3.33744i −3.06213 + 0.106178i
\(989\) 0.0214114 + 0.0370856i 0.000680843 + 0.00117925i
\(990\) −7.11396 + 7.11396i −0.226097 + 0.226097i
\(991\) 9.43469 0.299703 0.149851 0.988709i \(-0.452120\pi\)
0.149851 + 0.988709i \(0.452120\pi\)
\(992\) 30.2258 0.959669
\(993\) −11.1115 + 11.1115i −0.352613 + 0.352613i
\(994\) 65.0256 58.1346i 2.06249 1.84392i
\(995\) 4.93162 + 18.4051i 0.156343 + 0.583479i
\(996\) 52.5131 + 14.0708i 1.66394 + 0.445851i
\(997\) 33.3314 19.2439i 1.05562 0.609461i 0.131400 0.991329i \(-0.458053\pi\)
0.924217 + 0.381869i \(0.124719\pi\)
\(998\) 64.4860i 2.04127i
\(999\) −9.07099 + 2.43056i −0.286993 + 0.0768996i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 273.2.cg.a.115.9 yes 36
3.2 odd 2 819.2.gh.c.388.1 36
7.5 odd 6 273.2.bt.a.271.1 yes 36
13.6 odd 12 273.2.bt.a.136.1 36
21.5 even 6 819.2.et.c.271.9 36
39.32 even 12 819.2.et.c.136.9 36
91.19 even 12 inner 273.2.cg.a.19.9 yes 36
273.110 odd 12 819.2.gh.c.19.1 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bt.a.136.1 36 13.6 odd 12
273.2.bt.a.271.1 yes 36 7.5 odd 6
273.2.cg.a.19.9 yes 36 91.19 even 12 inner
273.2.cg.a.115.9 yes 36 1.1 even 1 trivial
819.2.et.c.136.9 36 39.32 even 12
819.2.et.c.271.9 36 21.5 even 6
819.2.gh.c.19.1 36 273.110 odd 12
819.2.gh.c.388.1 36 3.2 odd 2