Properties

Label 31.2.d.a.4.1
Level $31$
Weight $2$
Character 31.4
Analytic conductor $0.248$
Analytic rank $0$
Dimension $4$
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] = [31,2,Mod(2,31)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(31, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("31.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 31.d (of order \(5\), 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: \(0.247536246266\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 4.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 31.4
Dual form 31.2.d.a.8.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.190983 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.30902 - 0.951057i) q^{4} -2.61803 q^{5} +0.618034 q^{6} +(-2.42705 + 1.76336i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(1.61803 + 1.17557i) q^{9} +O(q^{10})\) \(q+(-0.190983 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.30902 - 0.951057i) q^{4} -2.61803 q^{5} +0.618034 q^{6} +(-2.42705 + 1.76336i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(1.61803 + 1.17557i) q^{9} +(0.500000 + 1.53884i) q^{10} +(0.618034 - 0.449028i) q^{11} +(0.500000 + 1.53884i) q^{12} +(1.50000 - 4.61653i) q^{13} +(1.50000 + 1.08981i) q^{14} +(0.809017 - 2.48990i) q^{15} +(0.572949 - 1.76336i) q^{16} +(-0.190983 - 0.138757i) q^{17} +(0.381966 - 1.17557i) q^{18} +(1.54508 + 4.75528i) q^{19} +(-3.42705 + 2.48990i) q^{20} +(-0.927051 - 2.85317i) q^{21} +(-0.381966 - 0.277515i) q^{22} +(4.42705 + 3.21644i) q^{23} +(1.80902 - 1.31433i) q^{24} +1.85410 q^{25} -3.00000 q^{26} +(-4.04508 + 2.93893i) q^{27} +(-1.50000 + 4.61653i) q^{28} +(-2.66312 - 8.19624i) q^{29} -1.61803 q^{30} +(-5.54508 + 0.502029i) q^{31} -5.61803 q^{32} +(0.236068 + 0.726543i) q^{33} +(-0.0450850 + 0.138757i) q^{34} +(6.35410 - 4.61653i) q^{35} +3.23607 q^{36} +0.236068 q^{37} +(2.50000 - 1.81636i) q^{38} +(3.92705 + 2.85317i) q^{39} +(4.73607 + 3.44095i) q^{40} +(2.00000 + 6.15537i) q^{41} +(-1.50000 + 1.08981i) q^{42} +(-1.42705 - 4.39201i) q^{43} +(0.381966 - 1.17557i) q^{44} +(-4.23607 - 3.07768i) q^{45} +(1.04508 - 3.21644i) q^{46} +(-1.04508 + 3.21644i) q^{47} +(1.50000 + 1.08981i) q^{48} +(0.618034 - 1.90211i) q^{49} +(-0.354102 - 1.08981i) q^{50} +(0.190983 - 0.138757i) q^{51} +(-2.42705 - 7.46969i) q^{52} +(10.2812 + 7.46969i) q^{53} +(2.50000 + 1.81636i) q^{54} +(-1.61803 + 1.17557i) q^{55} +6.70820 q^{56} -5.00000 q^{57} +(-4.30902 + 3.13068i) q^{58} +(2.92705 - 9.00854i) q^{59} +(-1.30902 - 4.02874i) q^{60} -6.94427 q^{61} +(1.35410 + 3.16344i) q^{62} -6.00000 q^{63} +(-0.0729490 - 0.224514i) q^{64} +(-3.92705 + 12.0862i) q^{65} +(0.381966 - 0.277515i) q^{66} -4.23607 q^{67} -0.381966 q^{68} +(-4.42705 + 3.21644i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(-0.0729490 - 0.0530006i) q^{71} +(-1.38197 - 4.25325i) q^{72} +(6.92705 - 5.03280i) q^{73} +(-0.0450850 - 0.138757i) q^{74} +(-0.572949 + 1.76336i) q^{75} +(6.54508 + 4.75528i) q^{76} +(-0.708204 + 2.17963i) q^{77} +(0.927051 - 2.85317i) q^{78} +(-1.50000 + 4.61653i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.23607 - 2.35114i) q^{82} +(-1.26393 - 3.88998i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(0.500000 + 0.363271i) q^{85} +(-2.30902 + 1.67760i) q^{86} +8.61803 q^{87} -1.70820 q^{88} +(5.16312 - 3.75123i) q^{89} +(-1.00000 + 3.07768i) q^{90} +(4.50000 + 13.8496i) q^{91} +8.85410 q^{92} +(1.23607 - 5.42882i) q^{93} +2.09017 q^{94} +(-4.04508 - 12.4495i) q^{95} +(1.73607 - 5.34307i) q^{96} +(4.28115 - 3.11044i) q^{97} -1.23607 q^{98} +1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} + q^{3} + 3 q^{4} - 6 q^{5} - 2 q^{6} - 3 q^{7} - 5 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3 q^{2} + q^{3} + 3 q^{4} - 6 q^{5} - 2 q^{6} - 3 q^{7} - 5 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} + 6 q^{14} + q^{15} + 9 q^{16} - 3 q^{17} + 6 q^{18} - 5 q^{19} - 7 q^{20} + 3 q^{21} - 6 q^{22} + 11 q^{23} + 5 q^{24} - 6 q^{25} - 12 q^{26} - 5 q^{27} - 6 q^{28} + 5 q^{29} - 2 q^{30} - 11 q^{31} - 18 q^{32} - 8 q^{33} + 11 q^{34} + 12 q^{35} + 4 q^{36} - 8 q^{37} + 10 q^{38} + 9 q^{39} + 10 q^{40} + 8 q^{41} - 6 q^{42} + q^{43} + 6 q^{44} - 8 q^{45} - 7 q^{46} + 7 q^{47} + 6 q^{48} - 2 q^{49} + 12 q^{50} + 3 q^{51} - 3 q^{52} + 21 q^{53} + 10 q^{54} - 2 q^{55} - 20 q^{57} - 15 q^{58} + 5 q^{59} - 3 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 7 q^{64} - 9 q^{65} + 6 q^{66} - 8 q^{67} - 6 q^{68} - 11 q^{69} - 9 q^{70} - 7 q^{71} - 10 q^{72} + 21 q^{73} + 11 q^{74} - 9 q^{75} + 15 q^{76} + 24 q^{77} - 3 q^{78} - 6 q^{80} - q^{81} + 4 q^{82} - 14 q^{83} - 9 q^{84} + 2 q^{85} - 7 q^{86} + 30 q^{87} + 20 q^{88} + 5 q^{89} - 4 q^{90} + 18 q^{91} + 22 q^{92} - 4 q^{93} - 14 q^{94} - 5 q^{95} - 2 q^{96} - 3 q^{97} + 4 q^{98} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/31\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.190983 0.587785i −0.135045 0.415627i 0.860552 0.509363i \(-0.170119\pi\)
−0.995597 + 0.0937362i \(0.970119\pi\)
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i −0.999773 0.0213149i \(-0.993215\pi\)
0.821362 + 0.570408i \(0.193215\pi\)
\(4\) 1.30902 0.951057i 0.654508 0.475528i
\(5\) −2.61803 −1.17082 −0.585410 0.810737i \(-0.699067\pi\)
−0.585410 + 0.810737i \(0.699067\pi\)
\(6\) 0.618034 0.252311
\(7\) −2.42705 + 1.76336i −0.917339 + 0.666486i −0.942860 0.333188i \(-0.891875\pi\)
0.0255212 + 0.999674i \(0.491875\pi\)
\(8\) −1.80902 1.31433i −0.639584 0.464685i
\(9\) 1.61803 + 1.17557i 0.539345 + 0.391857i
\(10\) 0.500000 + 1.53884i 0.158114 + 0.486624i
\(11\) 0.618034 0.449028i 0.186344 0.135387i −0.490702 0.871327i \(-0.663260\pi\)
0.677046 + 0.735940i \(0.263260\pi\)
\(12\) 0.500000 + 1.53884i 0.144338 + 0.444225i
\(13\) 1.50000 4.61653i 0.416025 1.28039i −0.495306 0.868719i \(-0.664944\pi\)
0.911331 0.411675i \(-0.135056\pi\)
\(14\) 1.50000 + 1.08981i 0.400892 + 0.291265i
\(15\) 0.809017 2.48990i 0.208887 0.642889i
\(16\) 0.572949 1.76336i 0.143237 0.440839i
\(17\) −0.190983 0.138757i −0.0463202 0.0336536i 0.564384 0.825512i \(-0.309114\pi\)
−0.610704 + 0.791859i \(0.709114\pi\)
\(18\) 0.381966 1.17557i 0.0900303 0.277085i
\(19\) 1.54508 + 4.75528i 0.354467 + 1.09094i 0.956318 + 0.292328i \(0.0944300\pi\)
−0.601851 + 0.798608i \(0.705570\pi\)
\(20\) −3.42705 + 2.48990i −0.766312 + 0.556758i
\(21\) −0.927051 2.85317i −0.202299 0.622613i
\(22\) −0.381966 0.277515i −0.0814354 0.0591663i
\(23\) 4.42705 + 3.21644i 0.923104 + 0.670674i 0.944295 0.329101i \(-0.106746\pi\)
−0.0211907 + 0.999775i \(0.506746\pi\)
\(24\) 1.80902 1.31433i 0.369264 0.268286i
\(25\) 1.85410 0.370820
\(26\) −3.00000 −0.588348
\(27\) −4.04508 + 2.93893i −0.778477 + 0.565597i
\(28\) −1.50000 + 4.61653i −0.283473 + 0.872441i
\(29\) −2.66312 8.19624i −0.494529 1.52200i −0.817690 0.575659i \(-0.804746\pi\)
0.323161 0.946344i \(-0.395254\pi\)
\(30\) −1.61803 −0.295411
\(31\) −5.54508 + 0.502029i −0.995927 + 0.0901670i
\(32\) −5.61803 −0.993137
\(33\) 0.236068 + 0.726543i 0.0410942 + 0.126475i
\(34\) −0.0450850 + 0.138757i −0.00773201 + 0.0237967i
\(35\) 6.35410 4.61653i 1.07404 0.780335i
\(36\) 3.23607 0.539345
\(37\) 0.236068 0.0388093 0.0194047 0.999812i \(-0.493823\pi\)
0.0194047 + 0.999812i \(0.493823\pi\)
\(38\) 2.50000 1.81636i 0.405554 0.294652i
\(39\) 3.92705 + 2.85317i 0.628831 + 0.456873i
\(40\) 4.73607 + 3.44095i 0.748838 + 0.544063i
\(41\) 2.00000 + 6.15537i 0.312348 + 0.961307i 0.976833 + 0.214005i \(0.0686510\pi\)
−0.664485 + 0.747302i \(0.731349\pi\)
\(42\) −1.50000 + 1.08981i −0.231455 + 0.168162i
\(43\) −1.42705 4.39201i −0.217623 0.669775i −0.998957 0.0456620i \(-0.985460\pi\)
0.781334 0.624113i \(-0.214540\pi\)
\(44\) 0.381966 1.17557i 0.0575835 0.177224i
\(45\) −4.23607 3.07768i −0.631476 0.458794i
\(46\) 1.04508 3.21644i 0.154089 0.474238i
\(47\) −1.04508 + 3.21644i −0.152441 + 0.469166i −0.997893 0.0648863i \(-0.979332\pi\)
0.845451 + 0.534052i \(0.179332\pi\)
\(48\) 1.50000 + 1.08981i 0.216506 + 0.157301i
\(49\) 0.618034 1.90211i 0.0882906 0.271730i
\(50\) −0.354102 1.08981i −0.0500776 0.154123i
\(51\) 0.190983 0.138757i 0.0267430 0.0194299i
\(52\) −2.42705 7.46969i −0.336571 1.03586i
\(53\) 10.2812 + 7.46969i 1.41222 + 1.02604i 0.992994 + 0.118162i \(0.0377001\pi\)
0.419231 + 0.907880i \(0.362300\pi\)
\(54\) 2.50000 + 1.81636i 0.340207 + 0.247175i
\(55\) −1.61803 + 1.17557i −0.218176 + 0.158514i
\(56\) 6.70820 0.896421
\(57\) −5.00000 −0.662266
\(58\) −4.30902 + 3.13068i −0.565802 + 0.411079i
\(59\) 2.92705 9.00854i 0.381070 1.17281i −0.558222 0.829692i \(-0.688516\pi\)
0.939292 0.343120i \(-0.111484\pi\)
\(60\) −1.30902 4.02874i −0.168993 0.520108i
\(61\) −6.94427 −0.889123 −0.444561 0.895748i \(-0.646640\pi\)
−0.444561 + 0.895748i \(0.646640\pi\)
\(62\) 1.35410 + 3.16344i 0.171971 + 0.401757i
\(63\) −6.00000 −0.755929
\(64\) −0.0729490 0.224514i −0.00911863 0.0280642i
\(65\) −3.92705 + 12.0862i −0.487091 + 1.49911i
\(66\) 0.381966 0.277515i 0.0470168 0.0341597i
\(67\) −4.23607 −0.517518 −0.258759 0.965942i \(-0.583314\pi\)
−0.258759 + 0.965942i \(0.583314\pi\)
\(68\) −0.381966 −0.0463202
\(69\) −4.42705 + 3.21644i −0.532954 + 0.387214i
\(70\) −3.92705 2.85317i −0.469372 0.341019i
\(71\) −0.0729490 0.0530006i −0.00865746 0.00629001i 0.583448 0.812150i \(-0.301703\pi\)
−0.592106 + 0.805860i \(0.701703\pi\)
\(72\) −1.38197 4.25325i −0.162866 0.501251i
\(73\) 6.92705 5.03280i 0.810750 0.589044i −0.103298 0.994650i \(-0.532940\pi\)
0.914048 + 0.405606i \(0.132940\pi\)
\(74\) −0.0450850 0.138757i −0.00524102 0.0161302i
\(75\) −0.572949 + 1.76336i −0.0661585 + 0.203615i
\(76\) 6.54508 + 4.75528i 0.750773 + 0.545468i
\(77\) −0.708204 + 2.17963i −0.0807073 + 0.248392i
\(78\) 0.927051 2.85317i 0.104968 0.323058i
\(79\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(80\) −1.50000 + 4.61653i −0.167705 + 0.516143i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 3.23607 2.35114i 0.357364 0.259640i
\(83\) −1.26393 3.88998i −0.138735 0.426981i 0.857418 0.514621i \(-0.172067\pi\)
−0.996152 + 0.0876401i \(0.972067\pi\)
\(84\) −3.92705 2.85317i −0.428476 0.311306i
\(85\) 0.500000 + 0.363271i 0.0542326 + 0.0394023i
\(86\) −2.30902 + 1.67760i −0.248988 + 0.180900i
\(87\) 8.61803 0.923950
\(88\) −1.70820 −0.182095
\(89\) 5.16312 3.75123i 0.547290 0.397629i −0.279496 0.960147i \(-0.590167\pi\)
0.826785 + 0.562518i \(0.190167\pi\)
\(90\) −1.00000 + 3.07768i −0.105409 + 0.324416i
\(91\) 4.50000 + 13.8496i 0.471728 + 1.45183i
\(92\) 8.85410 0.923104
\(93\) 1.23607 5.42882i 0.128174 0.562943i
\(94\) 2.09017 0.215585
\(95\) −4.04508 12.4495i −0.415017 1.27729i
\(96\) 1.73607 5.34307i 0.177187 0.545325i
\(97\) 4.28115 3.11044i 0.434685 0.315817i −0.348834 0.937184i \(-0.613422\pi\)
0.783520 + 0.621367i \(0.213422\pi\)
\(98\) −1.23607 −0.124862
\(99\) 1.52786 0.153556
\(100\) 2.42705 1.76336i 0.242705 0.176336i
\(101\) −3.85410 2.80017i −0.383497 0.278627i 0.379288 0.925279i \(-0.376169\pi\)
−0.762786 + 0.646651i \(0.776169\pi\)
\(102\) −0.118034 0.0857567i −0.0116871 0.00849118i
\(103\) −0.0450850 0.138757i −0.00444235 0.0136722i 0.948811 0.315845i \(-0.102288\pi\)
−0.953253 + 0.302173i \(0.902288\pi\)
\(104\) −8.78115 + 6.37988i −0.861063 + 0.625599i
\(105\) 2.42705 + 7.46969i 0.236856 + 0.728968i
\(106\) 2.42705 7.46969i 0.235736 0.725521i
\(107\) −0.881966 0.640786i −0.0852629 0.0619471i 0.544337 0.838867i \(-0.316781\pi\)
−0.629600 + 0.776919i \(0.716781\pi\)
\(108\) −2.50000 + 7.69421i −0.240563 + 0.740376i
\(109\) −2.60081 + 8.00448i −0.249113 + 0.766690i 0.745820 + 0.666147i \(0.232058\pi\)
−0.994933 + 0.100543i \(0.967942\pi\)
\(110\) 1.00000 + 0.726543i 0.0953463 + 0.0692731i
\(111\) −0.0729490 + 0.224514i −0.00692401 + 0.0213099i
\(112\) 1.71885 + 5.29007i 0.162416 + 0.499864i
\(113\) 1.50000 1.08981i 0.141108 0.102521i −0.514992 0.857195i \(-0.672205\pi\)
0.656100 + 0.754674i \(0.272205\pi\)
\(114\) 0.954915 + 2.93893i 0.0894360 + 0.275256i
\(115\) −11.5902 8.42075i −1.08079 0.785239i
\(116\) −11.2812 8.19624i −1.04743 0.761002i
\(117\) 7.85410 5.70634i 0.726112 0.527551i
\(118\) −5.85410 −0.538914
\(119\) 0.708204 0.0649209
\(120\) −4.73607 + 3.44095i −0.432342 + 0.314115i
\(121\) −3.21885 + 9.90659i −0.292622 + 0.900599i
\(122\) 1.32624 + 4.08174i 0.120072 + 0.369543i
\(123\) −6.47214 −0.583573
\(124\) −6.78115 + 5.93085i −0.608966 + 0.532606i
\(125\) 8.23607 0.736656
\(126\) 1.14590 + 3.52671i 0.102085 + 0.314184i
\(127\) 3.16312 9.73508i 0.280681 0.863849i −0.706979 0.707235i \(-0.749942\pi\)
0.987660 0.156614i \(-0.0500577\pi\)
\(128\) −9.20820 + 6.69015i −0.813898 + 0.591331i
\(129\) 4.61803 0.406595
\(130\) 7.85410 0.688850
\(131\) −0.0729490 + 0.0530006i −0.00637359 + 0.00463068i −0.590967 0.806695i \(-0.701254\pi\)
0.584594 + 0.811326i \(0.301254\pi\)
\(132\) 1.00000 + 0.726543i 0.0870388 + 0.0632374i
\(133\) −12.1353 8.81678i −1.05226 0.764512i
\(134\) 0.809017 + 2.48990i 0.0698884 + 0.215094i
\(135\) 10.5902 7.69421i 0.911457 0.662212i
\(136\) 0.163119 + 0.502029i 0.0139873 + 0.0430486i
\(137\) −2.00000 + 6.15537i −0.170872 + 0.525888i −0.999421 0.0340275i \(-0.989167\pi\)
0.828549 + 0.559916i \(0.189167\pi\)
\(138\) 2.73607 + 1.98787i 0.232910 + 0.169219i
\(139\) 1.80902 5.56758i 0.153439 0.472236i −0.844561 0.535460i \(-0.820138\pi\)
0.997999 + 0.0632239i \(0.0201382\pi\)
\(140\) 3.92705 12.0862i 0.331896 1.02147i
\(141\) −2.73607 1.98787i −0.230418 0.167409i
\(142\) −0.0172209 + 0.0530006i −0.00144515 + 0.00444771i
\(143\) −1.14590 3.52671i −0.0958248 0.294918i
\(144\) 3.00000 2.17963i 0.250000 0.181636i
\(145\) 6.97214 + 21.4580i 0.579004 + 1.78199i
\(146\) −4.28115 3.11044i −0.354311 0.257422i
\(147\) 1.61803 + 1.17557i 0.133453 + 0.0969594i
\(148\) 0.309017 0.224514i 0.0254010 0.0184549i
\(149\) −17.0344 −1.39552 −0.697758 0.716334i \(-0.745819\pi\)
−0.697758 + 0.716334i \(0.745819\pi\)
\(150\) 1.14590 0.0935622
\(151\) 15.7812 11.4657i 1.28425 0.933064i 0.284579 0.958652i \(-0.408146\pi\)
0.999673 + 0.0255888i \(0.00814604\pi\)
\(152\) 3.45492 10.6331i 0.280231 0.862461i
\(153\) −0.145898 0.449028i −0.0117952 0.0363018i
\(154\) 1.41641 0.114137
\(155\) 14.5172 1.31433i 1.16605 0.105569i
\(156\) 7.85410 0.628831
\(157\) 3.00000 + 9.23305i 0.239426 + 0.736878i 0.996503 + 0.0835524i \(0.0266266\pi\)
−0.757077 + 0.653325i \(0.773373\pi\)
\(158\) 0 0
\(159\) −10.2812 + 7.46969i −0.815348 + 0.592385i
\(160\) 14.7082 1.16279
\(161\) −16.4164 −1.29379
\(162\) 0.500000 0.363271i 0.0392837 0.0285413i
\(163\) 10.2812 + 7.46969i 0.805282 + 0.585072i 0.912459 0.409168i \(-0.134181\pi\)
−0.107177 + 0.994240i \(0.534181\pi\)
\(164\) 8.47214 + 6.15537i 0.661563 + 0.480653i
\(165\) −0.618034 1.90211i −0.0481139 0.148079i
\(166\) −2.04508 + 1.48584i −0.158729 + 0.115324i
\(167\) −2.85410 8.78402i −0.220857 0.679728i −0.998686 0.0512518i \(-0.983679\pi\)
0.777829 0.628476i \(-0.216321\pi\)
\(168\) −2.07295 + 6.37988i −0.159931 + 0.492219i
\(169\) −8.54508 6.20837i −0.657314 0.477567i
\(170\) 0.118034 0.363271i 0.00905279 0.0278616i
\(171\) −3.09017 + 9.51057i −0.236311 + 0.727291i
\(172\) −6.04508 4.39201i −0.460933 0.334888i
\(173\) 0.281153 0.865300i 0.0213757 0.0657875i −0.939800 0.341726i \(-0.888989\pi\)
0.961175 + 0.275938i \(0.0889886\pi\)
\(174\) −1.64590 5.06555i −0.124775 0.384019i
\(175\) −4.50000 + 3.26944i −0.340168 + 0.247147i
\(176\) −0.437694 1.34708i −0.0329924 0.101540i
\(177\) 7.66312 + 5.56758i 0.575995 + 0.418485i
\(178\) −3.19098 2.31838i −0.239174 0.173770i
\(179\) −16.0172 + 11.6372i −1.19718 + 0.869805i −0.994005 0.109337i \(-0.965127\pi\)
−0.203179 + 0.979142i \(0.565127\pi\)
\(180\) −8.47214 −0.631476
\(181\) 17.0000 1.26360 0.631800 0.775131i \(-0.282316\pi\)
0.631800 + 0.775131i \(0.282316\pi\)
\(182\) 7.28115 5.29007i 0.539715 0.392126i
\(183\) 2.14590 6.60440i 0.158629 0.488211i
\(184\) −3.78115 11.6372i −0.278750 0.857905i
\(185\) −0.618034 −0.0454388
\(186\) −3.42705 + 0.310271i −0.251284 + 0.0227502i
\(187\) −0.180340 −0.0131878
\(188\) 1.69098 + 5.20431i 0.123328 + 0.379563i
\(189\) 4.63525 14.2658i 0.337165 1.03769i
\(190\) −6.54508 + 4.75528i −0.474830 + 0.344984i
\(191\) −16.0902 −1.16424 −0.582122 0.813102i \(-0.697777\pi\)
−0.582122 + 0.813102i \(0.697777\pi\)
\(192\) 0.236068 0.0170367
\(193\) 1.92705 1.40008i 0.138712 0.100780i −0.516265 0.856429i \(-0.672678\pi\)
0.654977 + 0.755648i \(0.272678\pi\)
\(194\) −2.64590 1.92236i −0.189964 0.138017i
\(195\) −10.2812 7.46969i −0.736249 0.534916i
\(196\) −1.00000 3.07768i −0.0714286 0.219835i
\(197\) −13.2812 + 9.64932i −0.946243 + 0.687486i −0.949915 0.312507i \(-0.898831\pi\)
0.00367232 + 0.999993i \(0.498831\pi\)
\(198\) −0.291796 0.898056i −0.0207370 0.0638221i
\(199\) −8.25329 + 25.4010i −0.585060 + 1.80063i 0.0139686 + 0.999902i \(0.495554\pi\)
−0.599029 + 0.800728i \(0.704446\pi\)
\(200\) −3.35410 2.43690i −0.237171 0.172315i
\(201\) 1.30902 4.02874i 0.0923309 0.284165i
\(202\) −0.909830 + 2.80017i −0.0640154 + 0.197019i
\(203\) 20.9164 + 15.1967i 1.46804 + 1.06660i
\(204\) 0.118034 0.363271i 0.00826403 0.0254341i
\(205\) −5.23607 16.1150i −0.365703 1.12552i
\(206\) −0.0729490 + 0.0530006i −0.00508260 + 0.00369272i
\(207\) 3.38197 + 10.4086i 0.235063 + 0.723449i
\(208\) −7.28115 5.29007i −0.504857 0.366800i
\(209\) 3.09017 + 2.24514i 0.213752 + 0.155300i
\(210\) 3.92705 2.85317i 0.270992 0.196887i
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 20.5623 1.41222
\(213\) 0.0729490 0.0530006i 0.00499838 0.00363154i
\(214\) −0.208204 + 0.640786i −0.0142325 + 0.0438032i
\(215\) 3.73607 + 11.4984i 0.254798 + 0.784187i
\(216\) 11.1803 0.760726
\(217\) 12.5729 10.9964i 0.853507 0.746485i
\(218\) 5.20163 0.352299
\(219\) 2.64590 + 8.14324i 0.178793 + 0.550269i
\(220\) −1.00000 + 3.07768i −0.0674200 + 0.207497i
\(221\) −0.927051 + 0.673542i −0.0623602 + 0.0453073i
\(222\) 0.145898 0.00979203
\(223\) 0.708204 0.0474248 0.0237124 0.999719i \(-0.492451\pi\)
0.0237124 + 0.999719i \(0.492451\pi\)
\(224\) 13.6353 9.90659i 0.911044 0.661912i
\(225\) 3.00000 + 2.17963i 0.200000 + 0.145309i
\(226\) −0.927051 0.673542i −0.0616665 0.0448033i
\(227\) −6.40983 19.7274i −0.425435 1.30936i −0.902577 0.430529i \(-0.858327\pi\)
0.477141 0.878827i \(-0.341673\pi\)
\(228\) −6.54508 + 4.75528i −0.433459 + 0.314926i
\(229\) −2.23607 6.88191i −0.147764 0.454769i 0.849592 0.527440i \(-0.176848\pi\)
−0.997356 + 0.0726703i \(0.976848\pi\)
\(230\) −2.73607 + 8.42075i −0.180411 + 0.555248i
\(231\) −1.85410 1.34708i −0.121991 0.0886316i
\(232\) −5.95492 + 18.3273i −0.390959 + 1.20325i
\(233\) 5.80902 17.8783i 0.380561 1.17125i −0.559088 0.829108i \(-0.688849\pi\)
0.939649 0.342139i \(-0.111151\pi\)
\(234\) −4.85410 3.52671i −0.317323 0.230548i
\(235\) 2.73607 8.42075i 0.178481 0.549309i
\(236\) −4.73607 14.5761i −0.308292 0.948824i
\(237\) 0 0
\(238\) −0.135255 0.416272i −0.00876727 0.0269829i
\(239\) 10.8541 + 7.88597i 0.702093 + 0.510101i 0.880613 0.473836i \(-0.157131\pi\)
−0.178520 + 0.983936i \(0.557131\pi\)
\(240\) −3.92705 2.85317i −0.253490 0.184171i
\(241\) 6.89919 5.01255i 0.444416 0.322887i −0.342971 0.939346i \(-0.611433\pi\)
0.787387 + 0.616459i \(0.211433\pi\)
\(242\) 6.43769 0.413831
\(243\) −16.0000 −1.02640
\(244\) −9.09017 + 6.60440i −0.581938 + 0.422803i
\(245\) −1.61803 + 4.97980i −0.103372 + 0.318148i
\(246\) 1.23607 + 3.80423i 0.0788088 + 0.242549i
\(247\) 24.2705 1.54430
\(248\) 10.6910 + 6.37988i 0.678878 + 0.405123i
\(249\) 4.09017 0.259204
\(250\) −1.57295 4.84104i −0.0994820 0.306174i
\(251\) 0.291796 0.898056i 0.0184180 0.0566848i −0.941425 0.337222i \(-0.890513\pi\)
0.959843 + 0.280537i \(0.0905127\pi\)
\(252\) −7.85410 + 5.70634i −0.494762 + 0.359466i
\(253\) 4.18034 0.262816
\(254\) −6.32624 −0.396943
\(255\) −0.500000 + 0.363271i −0.0313112 + 0.0227489i
\(256\) 5.30902 + 3.85723i 0.331814 + 0.241077i
\(257\) −1.14590 0.832544i −0.0714792 0.0519326i 0.551472 0.834194i \(-0.314066\pi\)
−0.622951 + 0.782261i \(0.714066\pi\)
\(258\) −0.881966 2.71441i −0.0549088 0.168992i
\(259\) −0.572949 + 0.416272i −0.0356013 + 0.0258659i
\(260\) 6.35410 + 19.5559i 0.394065 + 1.21281i
\(261\) 5.32624 16.3925i 0.329686 1.01467i
\(262\) 0.0450850 + 0.0327561i 0.00278536 + 0.00202368i
\(263\) −3.33688 + 10.2699i −0.205761 + 0.633267i 0.793920 + 0.608022i \(0.208037\pi\)
−0.999681 + 0.0252452i \(0.991963\pi\)
\(264\) 0.527864 1.62460i 0.0324878 0.0999871i
\(265\) −26.9164 19.5559i −1.65346 1.20131i
\(266\) −2.86475 + 8.81678i −0.175649 + 0.540591i
\(267\) 1.97214 + 6.06961i 0.120693 + 0.371454i
\(268\) −5.54508 + 4.02874i −0.338720 + 0.246094i
\(269\) −0.427051 1.31433i −0.0260378 0.0801360i 0.937193 0.348811i \(-0.113414\pi\)
−0.963231 + 0.268675i \(0.913414\pi\)
\(270\) −6.54508 4.75528i −0.398321 0.289397i
\(271\) −7.73607 5.62058i −0.469933 0.341426i 0.327482 0.944857i \(-0.393800\pi\)
−0.797415 + 0.603431i \(0.793800\pi\)
\(272\) −0.354102 + 0.257270i −0.0214706 + 0.0155993i
\(273\) −14.5623 −0.881351
\(274\) 4.00000 0.241649
\(275\) 1.14590 0.832544i 0.0691003 0.0502043i
\(276\) −2.73607 + 8.42075i −0.164692 + 0.506870i
\(277\) 4.11803 + 12.6740i 0.247429 + 0.761507i 0.995228 + 0.0975818i \(0.0311108\pi\)
−0.747799 + 0.663925i \(0.768889\pi\)
\(278\) −3.61803 −0.216995
\(279\) −9.56231 5.70634i −0.572480 0.341630i
\(280\) −17.5623 −1.04955
\(281\) 5.88197 + 18.1028i 0.350889 + 1.07992i 0.958355 + 0.285579i \(0.0921859\pi\)
−0.607466 + 0.794345i \(0.707814\pi\)
\(282\) −0.645898 + 1.98787i −0.0384627 + 0.118376i
\(283\) −5.30902 + 3.85723i −0.315588 + 0.229288i −0.734291 0.678835i \(-0.762485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(284\) −0.145898 −0.00865746
\(285\) 13.0902 0.775395
\(286\) −1.85410 + 1.34708i −0.109635 + 0.0796547i
\(287\) −15.7082 11.4127i −0.927226 0.673669i
\(288\) −9.09017 6.60440i −0.535643 0.389168i
\(289\) −5.23607 16.1150i −0.308004 0.947939i
\(290\) 11.2812 8.19624i 0.662452 0.481300i
\(291\) 1.63525 + 5.03280i 0.0958603 + 0.295028i
\(292\) 4.28115 13.1760i 0.250536 0.771069i
\(293\) 6.66312 + 4.84104i 0.389264 + 0.282817i 0.765154 0.643848i \(-0.222663\pi\)
−0.375890 + 0.926664i \(0.622663\pi\)
\(294\) 0.381966 1.17557i 0.0222767 0.0685607i
\(295\) −7.66312 + 23.5847i −0.446164 + 1.37315i
\(296\) −0.427051 0.310271i −0.0248218 0.0180341i
\(297\) −1.18034 + 3.63271i −0.0684903 + 0.210791i
\(298\) 3.25329 + 10.0126i 0.188458 + 0.580014i
\(299\) 21.4894 15.6129i 1.24276 0.902919i
\(300\) 0.927051 + 2.85317i 0.0535233 + 0.164728i
\(301\) 11.2082 + 8.14324i 0.646030 + 0.469368i
\(302\) −9.75329 7.08618i −0.561239 0.407764i
\(303\) 3.85410 2.80017i 0.221412 0.160866i
\(304\) 9.27051 0.531700
\(305\) 18.1803 1.04100
\(306\) −0.236068 + 0.171513i −0.0134951 + 0.00980477i
\(307\) 1.88197 5.79210i 0.107409 0.330572i −0.882879 0.469601i \(-0.844398\pi\)
0.990288 + 0.139028i \(0.0443979\pi\)
\(308\) 1.14590 + 3.52671i 0.0652936 + 0.200953i
\(309\) 0.145898 0.00829985
\(310\) −3.54508 8.28199i −0.201347 0.470386i
\(311\) 16.4721 0.934049 0.467025 0.884244i \(-0.345326\pi\)
0.467025 + 0.884244i \(0.345326\pi\)
\(312\) −3.35410 10.3229i −0.189889 0.584417i
\(313\) 0.381966 1.17557i 0.0215900 0.0664472i −0.939681 0.342052i \(-0.888878\pi\)
0.961271 + 0.275605i \(0.0888781\pi\)
\(314\) 4.85410 3.52671i 0.273933 0.199024i
\(315\) 15.7082 0.885057
\(316\) 0 0
\(317\) −20.9443 + 15.2169i −1.17635 + 0.854666i −0.991755 0.128149i \(-0.959097\pi\)
−0.184593 + 0.982815i \(0.559097\pi\)
\(318\) 6.35410 + 4.61653i 0.356320 + 0.258882i
\(319\) −5.32624 3.86974i −0.298212 0.216664i
\(320\) 0.190983 + 0.587785i 0.0106763 + 0.0328582i
\(321\) 0.881966 0.640786i 0.0492265 0.0357652i
\(322\) 3.13525 + 9.64932i 0.174721 + 0.537736i
\(323\) 0.364745 1.12257i 0.0202950 0.0624615i
\(324\) 1.30902 + 0.951057i 0.0727232 + 0.0528365i
\(325\) 2.78115 8.55951i 0.154271 0.474796i
\(326\) 2.42705 7.46969i 0.134422 0.413708i
\(327\) −6.80902 4.94704i −0.376540 0.273572i
\(328\) 4.47214 13.7638i 0.246932 0.759980i
\(329\) −3.13525 9.64932i −0.172852 0.531984i
\(330\) −1.00000 + 0.726543i −0.0550482 + 0.0399948i
\(331\) 3.48278 + 10.7189i 0.191431 + 0.589164i 1.00000 0.000762014i \(0.000242557\pi\)
−0.808569 + 0.588402i \(0.799757\pi\)
\(332\) −5.35410 3.88998i −0.293845 0.213491i
\(333\) 0.381966 + 0.277515i 0.0209316 + 0.0152077i
\(334\) −4.61803 + 3.35520i −0.252688 + 0.183588i
\(335\) 11.0902 0.605921
\(336\) −5.56231 −0.303449
\(337\) −15.3541 + 11.1554i −0.836391 + 0.607674i −0.921360 0.388710i \(-0.872921\pi\)
0.0849690 + 0.996384i \(0.472921\pi\)
\(338\) −2.01722 + 6.20837i −0.109722 + 0.337691i
\(339\) 0.572949 + 1.76336i 0.0311183 + 0.0957723i
\(340\) 1.00000 0.0542326
\(341\) −3.20163 + 2.80017i −0.173378 + 0.151638i
\(342\) 6.18034 0.334195
\(343\) −4.63525 14.2658i −0.250280 0.770283i
\(344\) −3.19098 + 9.82084i −0.172046 + 0.529504i
\(345\) 11.5902 8.42075i 0.623994 0.453358i
\(346\) −0.562306 −0.0302298
\(347\) 8.12461 0.436152 0.218076 0.975932i \(-0.430022\pi\)
0.218076 + 0.975932i \(0.430022\pi\)
\(348\) 11.2812 8.19624i 0.604733 0.439364i
\(349\) 13.5172 + 9.82084i 0.723560 + 0.525697i 0.887520 0.460770i \(-0.152427\pi\)
−0.163959 + 0.986467i \(0.552427\pi\)
\(350\) 2.78115 + 2.02063i 0.148659 + 0.108007i
\(351\) 7.50000 + 23.0826i 0.400320 + 1.23206i
\(352\) −3.47214 + 2.52265i −0.185065 + 0.134458i
\(353\) −10.0066 30.7971i −0.532596 1.63916i −0.748786 0.662812i \(-0.769363\pi\)
0.216190 0.976351i \(-0.430637\pi\)
\(354\) 1.80902 5.56758i 0.0961482 0.295914i
\(355\) 0.190983 + 0.138757i 0.0101363 + 0.00736447i
\(356\) 3.19098 9.82084i 0.169122 0.520503i
\(357\) −0.218847 + 0.673542i −0.0115826 + 0.0356476i
\(358\) 9.89919 + 7.19218i 0.523188 + 0.380119i
\(359\) −7.82624 + 24.0867i −0.413053 + 1.27125i 0.500928 + 0.865489i \(0.332992\pi\)
−0.913981 + 0.405757i \(0.867008\pi\)
\(360\) 3.61803 + 11.1352i 0.190687 + 0.586875i
\(361\) −4.85410 + 3.52671i −0.255479 + 0.185616i
\(362\) −3.24671 9.99235i −0.170643 0.525186i
\(363\) −8.42705 6.12261i −0.442305 0.321354i
\(364\) 19.0623 + 13.8496i 0.999136 + 0.725915i
\(365\) −18.1353 + 13.1760i −0.949243 + 0.689665i
\(366\) −4.29180 −0.224336
\(367\) −36.2705 −1.89331 −0.946653 0.322256i \(-0.895559\pi\)
−0.946653 + 0.322256i \(0.895559\pi\)
\(368\) 8.20820 5.96361i 0.427882 0.310875i
\(369\) −4.00000 + 12.3107i −0.208232 + 0.640871i
\(370\) 0.118034 + 0.363271i 0.00613629 + 0.0188856i
\(371\) −38.1246 −1.97933
\(372\) −3.54508 8.28199i −0.183804 0.429401i
\(373\) −0.347524 −0.0179941 −0.00899706 0.999960i \(-0.502864\pi\)
−0.00899706 + 0.999960i \(0.502864\pi\)
\(374\) 0.0344419 + 0.106001i 0.00178095 + 0.00548119i
\(375\) −2.54508 + 7.83297i −0.131428 + 0.404493i
\(376\) 6.11803 4.44501i 0.315514 0.229234i
\(377\) −41.8328 −2.15450
\(378\) −9.27051 −0.476824
\(379\) 14.8992 10.8249i 0.765320 0.556037i −0.135218 0.990816i \(-0.543173\pi\)
0.900537 + 0.434779i \(0.143173\pi\)
\(380\) −17.1353 12.4495i −0.879020 0.638645i
\(381\) 8.28115 + 6.01661i 0.424256 + 0.308240i
\(382\) 3.07295 + 9.45756i 0.157226 + 0.483891i
\(383\) 13.6353 9.90659i 0.696729 0.506203i −0.182136 0.983273i \(-0.558301\pi\)
0.878865 + 0.477070i \(0.158301\pi\)
\(384\) −3.51722 10.8249i −0.179487 0.552406i
\(385\) 1.85410 5.70634i 0.0944938 0.290822i
\(386\) −1.19098 0.865300i −0.0606194 0.0440426i
\(387\) 2.85410 8.78402i 0.145082 0.446517i
\(388\) 2.64590 8.14324i 0.134325 0.413410i
\(389\) 23.5172 + 17.0863i 1.19237 + 0.866308i 0.993513 0.113721i \(-0.0362769\pi\)
0.198858 + 0.980028i \(0.436277\pi\)
\(390\) −2.42705 + 7.46969i −0.122899 + 0.378243i
\(391\) −0.399187 1.22857i −0.0201878 0.0621315i
\(392\) −3.61803 + 2.62866i −0.182738 + 0.132767i
\(393\) −0.0278640 0.0857567i −0.00140556 0.00432585i
\(394\) 8.20820 + 5.96361i 0.413523 + 0.300442i
\(395\) 0 0
\(396\) 2.00000 1.45309i 0.100504 0.0730203i
\(397\) 16.2918 0.817662 0.408831 0.912610i \(-0.365937\pi\)
0.408831 + 0.912610i \(0.365937\pi\)
\(398\) 16.5066 0.827400
\(399\) 12.1353 8.81678i 0.607523 0.441391i
\(400\) 1.06231 3.26944i 0.0531153 0.163472i
\(401\) −9.21885 28.3727i −0.460367 1.41686i −0.864717 0.502260i \(-0.832502\pi\)
0.404349 0.914605i \(-0.367498\pi\)
\(402\) −2.61803 −0.130576
\(403\) −6.00000 + 26.3521i −0.298881 + 1.31269i
\(404\) −7.70820 −0.383497
\(405\) −0.809017 2.48990i −0.0402004 0.123724i
\(406\) 4.93769 15.1967i 0.245054 0.754198i
\(407\) 0.145898 0.106001i 0.00723190 0.00525428i
\(408\) −0.527864 −0.0261332
\(409\) −6.18034 −0.305598 −0.152799 0.988257i \(-0.548829\pi\)
−0.152799 + 0.988257i \(0.548829\pi\)
\(410\) −8.47214 + 6.15537i −0.418409 + 0.303992i
\(411\) −5.23607 3.80423i −0.258276 0.187649i
\(412\) −0.190983 0.138757i −0.00940906 0.00683608i
\(413\) 8.78115 + 27.0256i 0.432092 + 1.32984i
\(414\) 5.47214 3.97574i 0.268941 0.195397i
\(415\) 3.30902 + 10.1841i 0.162433 + 0.499918i
\(416\) −8.42705 + 25.9358i −0.413170 + 1.27161i
\(417\) 4.73607 + 3.44095i 0.231926 + 0.168504i
\(418\) 0.729490 2.24514i 0.0356805 0.109813i
\(419\) 1.38197 4.25325i 0.0675135 0.207785i −0.911608 0.411060i \(-0.865159\pi\)
0.979122 + 0.203275i \(0.0651586\pi\)
\(420\) 10.2812 + 7.46969i 0.501669 + 0.364484i
\(421\) 4.56231 14.0413i 0.222353 0.684333i −0.776196 0.630491i \(-0.782853\pi\)
0.998549 0.0538414i \(-0.0171466\pi\)
\(422\) 1.52786 + 4.70228i 0.0743753 + 0.228904i
\(423\) −5.47214 + 3.97574i −0.266064 + 0.193307i
\(424\) −8.78115 27.0256i −0.426450 1.31248i
\(425\) −0.354102 0.257270i −0.0171765 0.0124794i
\(426\) −0.0450850 0.0327561i −0.00218437 0.00158704i
\(427\) 16.8541 12.2452i 0.815627 0.592588i
\(428\) −1.76393 −0.0852629
\(429\) 3.70820 0.179034
\(430\) 6.04508 4.39201i 0.291520 0.211802i
\(431\) 9.03444 27.8052i 0.435174 1.33933i −0.457735 0.889089i \(-0.651339\pi\)
0.892908 0.450238i \(-0.148661\pi\)
\(432\) 2.86475 + 8.81678i 0.137830 + 0.424197i
\(433\) 0.583592 0.0280456 0.0140228 0.999902i \(-0.495536\pi\)
0.0140228 + 0.999902i \(0.495536\pi\)
\(434\) −8.86475 5.29007i −0.425521 0.253931i
\(435\) −22.5623 −1.08178
\(436\) 4.20820 + 12.9515i 0.201536 + 0.620265i
\(437\) −8.45492 + 26.0216i −0.404453 + 1.24478i
\(438\) 4.28115 3.11044i 0.204561 0.148623i
\(439\) 41.8328 1.99657 0.998286 0.0585295i \(-0.0186412\pi\)
0.998286 + 0.0585295i \(0.0186412\pi\)
\(440\) 4.47214 0.213201
\(441\) 3.23607 2.35114i 0.154098 0.111959i
\(442\) 0.572949 + 0.416272i 0.0272524 + 0.0198000i
\(443\) 33.2705 + 24.1724i 1.58073 + 1.14847i 0.915853 + 0.401514i \(0.131516\pi\)
0.664877 + 0.746953i \(0.268484\pi\)
\(444\) 0.118034 + 0.363271i 0.00560165 + 0.0172401i
\(445\) −13.5172 + 9.82084i −0.640778 + 0.465552i
\(446\) −0.135255 0.416272i −0.00640451 0.0197110i
\(447\) 5.26393 16.2007i 0.248975 0.766268i
\(448\) 0.572949 + 0.416272i 0.0270693 + 0.0196670i
\(449\) 7.43769 22.8909i 0.351006 1.08029i −0.607283 0.794486i \(-0.707740\pi\)
0.958289 0.285801i \(-0.0922596\pi\)
\(450\) 0.708204 2.17963i 0.0333851 0.102749i
\(451\) 4.00000 + 2.90617i 0.188353 + 0.136846i
\(452\) 0.927051 2.85317i 0.0436048 0.134202i
\(453\) 6.02786 + 18.5519i 0.283214 + 0.871642i
\(454\) −10.3713 + 7.53521i −0.486750 + 0.353645i
\(455\) −11.7812 36.2587i −0.552309 1.69983i
\(456\) 9.04508 + 6.57164i 0.423575 + 0.307745i
\(457\) 12.7361 + 9.25330i 0.595768 + 0.432851i 0.844374 0.535754i \(-0.179972\pi\)
−0.248606 + 0.968605i \(0.579972\pi\)
\(458\) −3.61803 + 2.62866i −0.169060 + 0.122829i
\(459\) 1.18034 0.0550935
\(460\) −23.1803 −1.08079
\(461\) −8.69098 + 6.31437i −0.404779 + 0.294089i −0.771485 0.636248i \(-0.780486\pi\)
0.366705 + 0.930337i \(0.380486\pi\)
\(462\) −0.437694 + 1.34708i −0.0203634 + 0.0626720i
\(463\) −9.61803 29.6013i −0.446988 1.37569i −0.880289 0.474438i \(-0.842651\pi\)
0.433301 0.901249i \(-0.357349\pi\)
\(464\) −15.9787 −0.741793
\(465\) −3.23607 + 14.2128i −0.150069 + 0.659105i
\(466\) −11.6180 −0.538195
\(467\) −10.1287 31.1729i −0.468699 1.44251i −0.854270 0.519830i \(-0.825995\pi\)
0.385571 0.922678i \(-0.374005\pi\)
\(468\) 4.85410 14.9394i 0.224381 0.690574i
\(469\) 10.2812 7.46969i 0.474740 0.344918i
\(470\) −5.47214 −0.252411
\(471\) −9.70820 −0.447330
\(472\) −17.1353 + 12.4495i −0.788714 + 0.573034i
\(473\) −2.85410 2.07363i −0.131232 0.0953454i
\(474\) 0 0
\(475\) 2.86475 + 8.81678i 0.131444 + 0.404542i
\(476\) 0.927051 0.673542i 0.0424913 0.0308717i
\(477\) 7.85410 + 24.1724i 0.359615 + 1.10678i
\(478\) 2.56231 7.88597i 0.117197 0.360696i
\(479\) 7.23607 + 5.25731i 0.330624 + 0.240213i 0.740696 0.671841i \(-0.234496\pi\)
−0.410071 + 0.912054i \(0.634496\pi\)
\(480\) −4.54508 + 13.9883i −0.207454 + 0.638477i
\(481\) 0.354102 1.08981i 0.0161457 0.0496912i
\(482\) −4.26393 3.09793i −0.194217 0.141107i
\(483\) 5.07295 15.6129i 0.230827 0.710413i
\(484\) 5.20820 + 16.0292i 0.236737 + 0.728600i
\(485\) −11.2082 + 8.14324i −0.508938 + 0.369765i
\(486\) 3.05573 + 9.40456i 0.138611 + 0.426600i
\(487\) −18.5451 13.4738i −0.840358 0.610556i 0.0821126 0.996623i \(-0.473833\pi\)
−0.922471 + 0.386067i \(0.873833\pi\)
\(488\) 12.5623 + 9.12705i 0.568669 + 0.413162i
\(489\) −10.2812 + 7.46969i −0.464930 + 0.337791i
\(490\) 3.23607 0.146191
\(491\) −27.5967 −1.24542 −0.622712 0.782451i \(-0.713969\pi\)
−0.622712 + 0.782451i \(0.713969\pi\)
\(492\) −8.47214 + 6.15537i −0.381953 + 0.277505i
\(493\) −0.628677 + 1.93487i −0.0283142 + 0.0871421i
\(494\) −4.63525 14.2658i −0.208550 0.641851i
\(495\) −4.00000 −0.179787
\(496\) −2.29180 + 10.0656i −0.102905 + 0.451959i
\(497\) 0.270510 0.0121340
\(498\) −0.781153 2.40414i −0.0350043 0.107732i
\(499\) 1.28115 3.94298i 0.0573523 0.176512i −0.918277 0.395940i \(-0.870419\pi\)
0.975629 + 0.219427i \(0.0704189\pi\)
\(500\) 10.7812 7.83297i 0.482148 0.350301i
\(501\) 9.23607 0.412637
\(502\) −0.583592 −0.0260470
\(503\) −10.6353 + 7.72696i −0.474203 + 0.344528i −0.799077 0.601229i \(-0.794678\pi\)
0.324874 + 0.945757i \(0.394678\pi\)
\(504\) 10.8541 + 7.88597i 0.483480 + 0.351269i
\(505\) 10.0902 + 7.33094i 0.449007 + 0.326222i
\(506\) −0.798374 2.45714i −0.0354920 0.109233i
\(507\) 8.54508 6.20837i 0.379501 0.275723i
\(508\) −5.11803 15.7517i −0.227076 0.698868i
\(509\) −0.590170 + 1.81636i −0.0261588 + 0.0805086i −0.963284 0.268486i \(-0.913477\pi\)
0.937125 + 0.348994i \(0.113477\pi\)
\(510\) 0.309017 + 0.224514i 0.0136835 + 0.00994165i
\(511\) −7.93769 + 24.4297i −0.351143 + 1.08071i
\(512\) −5.78115 + 17.7926i −0.255493 + 0.786327i
\(513\) −20.2254 14.6946i −0.892974 0.648784i
\(514\) −0.270510 + 0.832544i −0.0119317 + 0.0367219i
\(515\) 0.118034 + 0.363271i 0.00520120 + 0.0160076i
\(516\) 6.04508 4.39201i 0.266120 0.193348i
\(517\) 0.798374 + 2.45714i 0.0351124 + 0.108065i
\(518\) 0.354102 + 0.257270i 0.0155583 + 0.0113038i
\(519\) 0.736068 + 0.534785i 0.0323098 + 0.0234744i
\(520\) 22.9894 16.7027i 1.00815 0.732464i
\(521\) 31.0689 1.36115 0.680576 0.732677i \(-0.261729\pi\)
0.680576 + 0.732677i \(0.261729\pi\)
\(522\) −10.6525 −0.466246
\(523\) −27.6074 + 20.0579i −1.20719 + 0.877073i −0.994972 0.100150i \(-0.968068\pi\)
−0.212215 + 0.977223i \(0.568068\pi\)
\(524\) −0.0450850 + 0.138757i −0.00196955 + 0.00606164i
\(525\) −1.71885 5.29007i −0.0750166 0.230877i
\(526\) 6.67376 0.290990
\(527\) 1.12868 + 0.673542i 0.0491659 + 0.0293399i
\(528\) 1.41641 0.0616412
\(529\) 2.14590 + 6.60440i 0.0932999 + 0.287148i
\(530\) −6.35410 + 19.5559i −0.276005 + 0.849455i
\(531\) 15.3262 11.1352i 0.665102 0.483225i
\(532\) −24.2705 −1.05226
\(533\) 31.4164 1.36080
\(534\) 3.19098 2.31838i 0.138087 0.100326i
\(535\) 2.30902 + 1.67760i 0.0998275 + 0.0725289i
\(536\) 7.66312 + 5.56758i 0.330996 + 0.240483i
\(537\) −6.11803 18.8294i −0.264013 0.812547i
\(538\) −0.690983 + 0.502029i −0.0297904 + 0.0216440i
\(539\) −0.472136 1.45309i −0.0203363 0.0625888i
\(540\) 6.54508 20.1437i 0.281656 0.866847i
\(541\) −17.7984 12.9313i −0.765212 0.555959i 0.135293 0.990806i \(-0.456803\pi\)
−0.900504 + 0.434847i \(0.856803\pi\)
\(542\) −1.82624 + 5.62058i −0.0784436 + 0.241425i
\(543\) −5.25329 + 16.1680i −0.225440 + 0.693834i
\(544\) 1.07295 + 0.779543i 0.0460023 + 0.0334226i
\(545\) 6.80902 20.9560i 0.291666 0.897656i
\(546\) 2.78115 + 8.55951i 0.119022 + 0.366313i
\(547\) 19.1803 13.9353i 0.820092 0.595832i −0.0966468 0.995319i \(-0.530812\pi\)
0.916739 + 0.399487i \(0.130812\pi\)
\(548\) 3.23607 + 9.95959i 0.138238 + 0.425453i
\(549\) −11.2361 8.16348i −0.479544 0.348409i
\(550\) −0.708204 0.514540i −0.0301979 0.0219401i
\(551\) 34.8607 25.3278i 1.48511 1.07900i
\(552\) 12.2361 0.520802
\(553\) 0 0
\(554\) 6.66312 4.84104i 0.283089 0.205676i
\(555\) 0.190983 0.587785i 0.00810678 0.0249501i
\(556\) −2.92705 9.00854i −0.124135 0.382047i
\(557\) 35.8885 1.52065 0.760323 0.649545i \(-0.225041\pi\)
0.760323 + 0.649545i \(0.225041\pi\)
\(558\) −1.52786 + 6.71040i −0.0646796 + 0.284074i
\(559\) −22.4164 −0.948113
\(560\) −4.50000 13.8496i −0.190160 0.585251i
\(561\) 0.0557281 0.171513i 0.00235284 0.00724130i
\(562\) 9.51722 6.91467i 0.401460 0.291678i
\(563\) −8.56231 −0.360858 −0.180429 0.983588i \(-0.557749\pi\)
−0.180429 + 0.983588i \(0.557749\pi\)
\(564\) −5.47214 −0.230418
\(565\) −3.92705 + 2.85317i −0.165212 + 0.120034i
\(566\) 3.28115 + 2.38390i 0.137917 + 0.100203i
\(567\) −2.42705 1.76336i −0.101927 0.0740540i
\(568\) 0.0623059 + 0.191758i 0.00261430 + 0.00804598i
\(569\) −12.5623 + 9.12705i −0.526639 + 0.382626i −0.819099 0.573652i \(-0.805526\pi\)
0.292460 + 0.956278i \(0.405526\pi\)
\(570\) −2.50000 7.69421i −0.104713 0.322275i
\(571\) 2.16312 6.65740i 0.0905237 0.278603i −0.895538 0.444986i \(-0.853209\pi\)
0.986061 + 0.166383i \(0.0532087\pi\)
\(572\) −4.85410 3.52671i −0.202960 0.147459i
\(573\) 4.97214 15.3027i 0.207714 0.639278i
\(574\) −3.70820 + 11.4127i −0.154777 + 0.476356i
\(575\) 8.20820 + 5.96361i 0.342306 + 0.248700i
\(576\) 0.145898 0.449028i 0.00607908 0.0187095i
\(577\) 12.0451 + 37.0710i 0.501443 + 1.54328i 0.806669 + 0.591004i \(0.201268\pi\)
−0.305225 + 0.952280i \(0.598732\pi\)
\(578\) −8.47214 + 6.15537i −0.352394 + 0.256030i
\(579\) 0.736068 + 2.26538i 0.0305899 + 0.0941462i
\(580\) 29.5344 + 21.4580i 1.22635 + 0.890996i
\(581\) 9.92705 + 7.21242i 0.411843 + 0.299222i
\(582\) 2.64590 1.92236i 0.109676 0.0796843i
\(583\) 9.70820 0.402073
\(584\) −19.1459 −0.792263
\(585\) −20.5623 + 14.9394i −0.850147 + 0.617668i
\(586\) 1.57295 4.84104i 0.0649779 0.199981i
\(587\) 11.1287 + 34.2505i 0.459330 + 1.41367i 0.865976 + 0.500086i \(0.166698\pi\)
−0.406646 + 0.913586i \(0.633302\pi\)
\(588\) 3.23607 0.133453
\(589\) −10.9549 25.5928i −0.451389 1.05453i
\(590\) 15.3262 0.630971
\(591\) −5.07295 15.6129i −0.208673 0.642230i
\(592\) 0.135255 0.416272i 0.00555894 0.0171087i
\(593\) −4.94427 + 3.59222i −0.203037 + 0.147515i −0.684658 0.728865i \(-0.740048\pi\)
0.481621 + 0.876380i \(0.340048\pi\)
\(594\) 2.36068 0.0968599
\(595\) −1.85410 −0.0760108
\(596\) −22.2984 + 16.2007i −0.913377 + 0.663607i
\(597\) −21.6074 15.6987i −0.884332 0.642505i
\(598\) −13.2812 9.64932i −0.543107 0.394590i
\(599\) 9.20820 + 28.3399i 0.376237 + 1.15794i 0.942640 + 0.333810i \(0.108334\pi\)
−0.566403 + 0.824128i \(0.691666\pi\)
\(600\) 3.35410 2.43690i 0.136931 0.0994859i
\(601\) 6.79837 + 20.9232i 0.277311 + 0.853477i 0.988599 + 0.150575i \(0.0481126\pi\)
−0.711287 + 0.702902i \(0.751887\pi\)
\(602\) 2.64590 8.14324i 0.107839 0.331894i
\(603\) −6.85410 4.97980i −0.279121 0.202793i
\(604\) 9.75329 30.0175i 0.396856 1.22140i
\(605\) 8.42705 25.9358i 0.342608 1.05444i
\(606\) −2.38197 1.73060i −0.0967608 0.0703008i
\(607\) −7.85410 + 24.1724i −0.318788 + 0.981129i 0.655379 + 0.755300i \(0.272509\pi\)
−0.974167 + 0.225829i \(0.927491\pi\)
\(608\) −8.68034 26.7153i −0.352034 1.08345i
\(609\) −20.9164 + 15.1967i −0.847576 + 0.615800i
\(610\) −3.47214 10.6861i −0.140583 0.432669i
\(611\) 13.2812 + 9.64932i 0.537298 + 0.390370i
\(612\) −0.618034 0.449028i −0.0249825 0.0181509i
\(613\) −20.2705 + 14.7274i −0.818718 + 0.594834i −0.916345 0.400390i \(-0.868875\pi\)
0.0976269 + 0.995223i \(0.468875\pi\)
\(614\) −3.76393 −0.151900
\(615\) 16.9443 0.683259
\(616\) 4.14590 3.01217i 0.167043 0.121364i
\(617\) −4.39919 + 13.5393i −0.177105 + 0.545072i −0.999723 0.0235215i \(-0.992512\pi\)
0.822619 + 0.568593i \(0.192512\pi\)
\(618\) −0.0278640 0.0857567i −0.00112086 0.00344964i
\(619\) −40.0000 −1.60774 −0.803868 0.594808i \(-0.797228\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(620\) 17.7533 15.5272i 0.712989 0.623586i
\(621\) −27.3607 −1.09795
\(622\) −3.14590 9.68208i −0.126139 0.388216i
\(623\) −5.91641 + 18.2088i −0.237036 + 0.729521i
\(624\) 7.28115 5.29007i 0.291479 0.211772i
\(625\) −30.8328 −1.23331
\(626\) −0.763932 −0.0305329
\(627\) −3.09017 + 2.24514i −0.123410 + 0.0896623i
\(628\) 12.7082 + 9.23305i 0.507113 + 0.368439i
\(629\) −0.0450850 0.0327561i −0.00179766 0.00130607i
\(630\) −3.00000 9.23305i −0.119523 0.367854i
\(631\) 7.06231 5.13107i 0.281146 0.204264i −0.438271 0.898843i \(-0.644409\pi\)
0.719417 + 0.694578i \(0.244409\pi\)
\(632\) 0 0
\(633\) 2.47214 7.60845i 0.0982586 0.302409i
\(634\) 12.9443 + 9.40456i 0.514083 + 0.373503i
\(635\) −8.28115 + 25.4868i −0.328628 + 1.01141i
\(636\) −6.35410 + 19.5559i −0.251957 + 0.775442i
\(637\) −7.85410 5.70634i −0.311191 0.226093i
\(638\) −1.25735 + 3.86974i −0.0497791 + 0.153204i
\(639\) −0.0557281 0.171513i −0.00220457 0.00678497i
\(640\) 24.1074 17.5150i 0.952928 0.692343i
\(641\) −12.6976 39.0791i −0.501523 1.54353i −0.806538 0.591183i \(-0.798661\pi\)
0.305014 0.952348i \(-0.401339\pi\)
\(642\) −0.545085 0.396027i −0.0215128 0.0156300i
\(643\) −6.59017 4.78804i −0.259891 0.188822i 0.450208 0.892924i \(-0.351350\pi\)
−0.710099 + 0.704102i \(0.751350\pi\)
\(644\) −21.4894 + 15.6129i −0.846799 + 0.615236i
\(645\) −12.0902 −0.476050
\(646\) −0.729490 −0.0287014
\(647\) 24.1803 17.5680i 0.950627 0.690671i −0.000327889 1.00000i \(-0.500104\pi\)
0.950955 + 0.309329i \(0.100104\pi\)
\(648\) 0.690983 2.12663i 0.0271444 0.0835418i
\(649\) −2.23607 6.88191i −0.0877733 0.270139i
\(650\) −5.56231 −0.218172
\(651\) 6.57295 + 15.3557i 0.257614 + 0.601836i
\(652\) 20.5623 0.805282
\(653\) 12.2533 + 37.7117i 0.479508 + 1.47577i 0.839780 + 0.542927i \(0.182684\pi\)
−0.360272 + 0.932847i \(0.617316\pi\)
\(654\) −1.60739 + 4.94704i −0.0628540 + 0.193445i
\(655\) 0.190983 0.138757i 0.00746232 0.00542170i
\(656\) 12.0000 0.468521
\(657\) 17.1246 0.668095
\(658\) −5.07295 + 3.68571i −0.197764 + 0.143684i
\(659\) −18.3541 13.3350i −0.714974 0.519459i 0.169800 0.985478i \(-0.445688\pi\)
−0.884775 + 0.466019i \(0.845688\pi\)
\(660\) −2.61803 1.90211i −0.101907 0.0740396i
\(661\) −5.13525 15.8047i −0.199738 0.614731i −0.999889 0.0149316i \(-0.995247\pi\)
0.800150 0.599800i \(-0.204753\pi\)
\(662\) 5.63525 4.09425i 0.219020 0.159128i
\(663\) −0.354102 1.08981i −0.0137522 0.0423249i
\(664\) −2.82624 + 8.69827i −0.109679 + 0.337558i
\(665\) 31.7705 + 23.0826i 1.23201 + 0.895106i
\(666\) 0.0901699 0.277515i 0.00349401 0.0107535i
\(667\) 14.5729 44.8509i 0.564267 1.73663i
\(668\) −12.0902 8.78402i −0.467783 0.339864i
\(669\) −0.218847 + 0.673542i −0.00846112 + 0.0260406i
\(670\) −2.11803 6.51864i −0.0818268 0.251837i
\(671\) −4.29180 + 3.11817i −0.165683 + 0.120376i
\(672\) 5.20820 + 16.0292i 0.200911 + 0.618340i
\(673\) 3.57295 + 2.59590i 0.137727 + 0.100065i 0.654516 0.756049i \(-0.272873\pi\)
−0.516788 + 0.856113i \(0.672873\pi\)
\(674\) 9.48936 + 6.89442i 0.365516 + 0.265563i
\(675\) −7.50000 + 5.44907i −0.288675 + 0.209735i
\(676\) −17.0902 −0.657314
\(677\) 28.6525 1.10120 0.550602 0.834768i \(-0.314398\pi\)
0.550602 + 0.834768i \(0.314398\pi\)
\(678\) 0.927051 0.673542i 0.0356032 0.0258672i
\(679\) −4.90576 + 15.0984i −0.188266 + 0.579423i
\(680\) −0.427051 1.31433i −0.0163767 0.0504022i
\(681\) 20.7426 0.794860
\(682\) 2.25735 + 1.34708i 0.0864386 + 0.0515825i
\(683\) 10.0557 0.384772 0.192386 0.981319i \(-0.438377\pi\)
0.192386 + 0.981319i \(0.438377\pi\)
\(684\) 5.00000 + 15.3884i 0.191180 + 0.588391i
\(685\) 5.23607 16.1150i 0.200060 0.615721i
\(686\) −7.50000 + 5.44907i −0.286351 + 0.208046i
\(687\) 7.23607 0.276073
\(688\) −8.56231 −0.326435
\(689\) 49.9058 36.2587i 1.90126 1.38134i
\(690\) −7.16312 5.20431i −0.272695 0.198125i
\(691\) −3.10081 2.25287i −0.117960 0.0857033i 0.527241 0.849716i \(-0.323227\pi\)
−0.645201 + 0.764013i \(0.723227\pi\)
\(692\) −0.454915 1.40008i −0.0172933 0.0532232i
\(693\) −3.70820 + 2.69417i −0.140863 + 0.102343i
\(694\) −1.55166 4.77553i −0.0589003 0.181277i
\(695\) −4.73607 + 14.5761i −0.179649 + 0.552904i
\(696\) −15.5902 11.3269i −0.590944 0.429346i
\(697\) 0.472136 1.45309i 0.0178834 0.0550395i
\(698\) 3.19098 9.82084i 0.120780 0.371724i
\(699\) 15.2082 + 11.0494i 0.575227 + 0.417927i
\(700\) −2.78115 + 8.55951i −0.105118 + 0.323519i
\(701\) −9.28115 28.5645i −0.350544 1.07886i −0.958548 0.284930i \(-0.908030\pi\)
0.608004 0.793934i \(-0.291970\pi\)
\(702\) 12.1353 8.81678i 0.458016 0.332768i
\(703\) 0.364745 + 1.12257i 0.0137566 + 0.0423385i
\(704\) −0.145898 0.106001i −0.00549874 0.00399507i
\(705\) 7.16312 + 5.20431i 0.269779 + 0.196006i
\(706\) −16.1910 + 11.7634i −0.609356 + 0.442723i
\(707\) 14.2918 0.537498
\(708\) 15.3262 0.575995
\(709\) −3.35410 + 2.43690i −0.125966 + 0.0915196i −0.648984 0.760802i \(-0.724806\pi\)
0.523018 + 0.852321i \(0.324806\pi\)
\(710\) 0.0450850 0.138757i 0.00169201 0.00520747i
\(711\) 0 0
\(712\) −14.2705 −0.534810
\(713\) −26.1631 15.6129i −0.979817 0.584709i
\(714\) 0.437694 0.0163803
\(715\) 3.00000 + 9.23305i 0.112194 + 0.345297i
\(716\) −9.89919 + 30.4666i −0.369950 + 1.13859i
\(717\) −10.8541 + 7.88597i −0.405354 + 0.294507i
\(718\) 15.6525 0.584145
\(719\) −41.3820 −1.54329 −0.771643 0.636055i \(-0.780565\pi\)
−0.771643 + 0.636055i \(0.780565\pi\)
\(720\) −7.85410 + 5.70634i −0.292705 + 0.212663i
\(721\) 0.354102 + 0.257270i 0.0131874 + 0.00958124i
\(722\) 3.00000 + 2.17963i 0.111648 + 0.0811173i
\(723\) 2.63525 + 8.11048i 0.0980062 + 0.301632i
\(724\) 22.2533 16.1680i 0.827037 0.600878i
\(725\) −4.93769 15.1967i −0.183381 0.564390i
\(726\) −1.98936 + 6.12261i −0.0738320 + 0.227231i
\(727\) 19.2812 + 14.0086i 0.715098 + 0.519549i 0.884814 0.465944i \(-0.154285\pi\)
−0.169716 + 0.985493i \(0.554285\pi\)
\(728\) 10.0623 30.9686i 0.372934 1.14777i
\(729\) 4.01722 12.3637i 0.148786 0.457916i
\(730\) 11.2082 + 8.14324i 0.414834 + 0.301395i
\(731\) −0.336881 + 1.03681i −0.0124600 + 0.0383479i
\(732\) −3.47214 10.6861i −0.128334 0.394971i
\(733\) −22.6074 + 16.4252i −0.835023 + 0.606680i −0.920976 0.389619i \(-0.872607\pi\)
0.0859529 + 0.996299i \(0.472607\pi\)
\(734\) 6.92705 + 21.3193i 0.255682 + 0.786909i
\(735\) −4.23607 3.07768i −0.156250 0.113522i
\(736\) −24.8713 18.0701i −0.916769 0.666072i
\(737\) −2.61803 + 1.90211i −0.0964365 + 0.0700652i
\(738\) 8.00000 0.294484
\(739\) 21.7082 0.798549 0.399275 0.916831i \(-0.369262\pi\)
0.399275 + 0.916831i \(0.369262\pi\)
\(740\) −0.809017 + 0.587785i −0.0297401 + 0.0216074i
\(741\) −7.50000 + 23.0826i −0.275519 + 0.847961i
\(742\) 7.28115 + 22.4091i 0.267300 + 0.822663i
\(743\) −3.43769 −0.126117 −0.0630584 0.998010i \(-0.520085\pi\)
−0.0630584 + 0.998010i \(0.520085\pi\)
\(744\) −9.37132 + 8.19624i −0.343569 + 0.300489i
\(745\) 44.5967 1.63390
\(746\) 0.0663712 + 0.204270i 0.00243002 + 0.00747884i
\(747\) 2.52786 7.77997i 0.0924897 0.284654i
\(748\) −0.236068 + 0.171513i −0.00863150 + 0.00627115i
\(749\) 3.27051 0.119502
\(750\) 5.09017 0.185867
\(751\) 32.2254 23.4131i 1.17592 0.854358i 0.184217 0.982886i \(-0.441025\pi\)
0.991706 + 0.128528i \(0.0410252\pi\)
\(752\) 5.07295 + 3.68571i 0.184991 + 0.134404i
\(753\) 0.763932 + 0.555029i 0.0278392 + 0.0202264i
\(754\) 7.98936 + 24.5887i 0.290955 + 0.895468i
\(755\) −41.3156 + 30.0175i −1.50363 + 1.09245i
\(756\) −7.50000 23.0826i −0.272772 0.839507i
\(757\) 13.3262 41.0139i 0.484350 1.49068i −0.348569 0.937283i \(-0.613332\pi\)
0.832920 0.553394i \(-0.186668\pi\)
\(758\) −9.20820 6.69015i −0.334457 0.242997i
\(759\) −1.29180 + 3.97574i −0.0468892 + 0.144310i
\(760\) −9.04508 + 27.8379i −0.328100 + 1.00979i
\(761\) −2.83688 2.06111i −0.102837 0.0747154i 0.535178 0.844739i \(-0.320244\pi\)
−0.638015 + 0.770024i \(0.720244\pi\)
\(762\) 1.95492 6.01661i 0.0708191 0.217959i
\(763\) −7.80244 24.0134i −0.282467 0.869345i
\(764\) −21.0623 + 15.3027i −0.762007 + 0.553631i
\(765\) 0.381966 + 1.17557i 0.0138100 + 0.0425028i
\(766\) −8.42705 6.12261i −0.304482 0.221219i
\(767\) −37.1976 27.0256i −1.34313 0.975838i
\(768\) −5.30902 + 3.85723i −0.191573 + 0.139186i
\(769\) −53.7426 −1.93801 −0.969005 0.247042i \(-0.920541\pi\)
−0.969005 + 0.247042i \(0.920541\pi\)
\(770\) −3.70820 −0.133634
\(771\) 1.14590 0.832544i 0.0412685 0.0299833i
\(772\) 1.19098 3.66547i 0.0428644 0.131923i
\(773\) −5.89919 18.1558i −0.212179 0.653020i −0.999342 0.0362746i \(-0.988451\pi\)
0.787163 0.616745i \(-0.211549\pi\)
\(774\) −5.70820 −0.205177
\(775\) −10.2812 + 0.930812i −0.369310 + 0.0334358i
\(776\) −11.8328 −0.424773
\(777\) −0.218847 0.673542i −0.00785109 0.0241632i
\(778\) 5.55166 17.0863i 0.199037 0.612572i
\(779\) −26.1803 + 19.0211i −0.938008 + 0.681503i
\(780\) −20.5623 −0.736249
\(781\) −0.0688837 −0.00246485
\(782\) −0.645898 + 0.469272i −0.0230973 + 0.0167811i
\(783\) 34.8607 + 25.3278i 1.24582 + 0.905141i
\(784\) −3.00000 2.17963i −0.107143 0.0778438i
\(785\) −7.85410 24.1724i −0.280325 0.862751i
\(786\) −0.0450850 + 0.0327561i −0.00160813 + 0.00116837i
\(787\) 9.66970 + 29.7603i 0.344687 + 1.06084i 0.961751 + 0.273926i \(0.0883222\pi\)
−0.617063 + 0.786913i \(0.711678\pi\)
\(788\) −8.20820 + 25.2623i −0.292405 + 0.899931i
\(789\) −8.73607 6.34712i −0.311012 0.225964i
\(790\) 0 0
\(791\) −1.71885 + 5.29007i −0.0611152 + 0.188093i
\(792\) −2.76393 2.00811i −0.0982120 0.0713552i
\(793\) −10.4164 + 32.0584i −0.369897 + 1.13843i
\(794\) −3.11146 9.57608i −0.110421 0.339842i
\(795\) 26.9164 19.5559i 0.954627 0.693577i
\(796\) 13.3541 + 41.0997i 0.473324 + 1.45674i
\(797\) −7.32624 5.32282i −0.259509 0.188544i 0.450422 0.892816i \(-0.351274\pi\)
−0.709930 + 0.704272i \(0.751274\pi\)
\(798\) −7.50000 5.44907i −0.265497 0.192895i
\(799\) 0.645898 0.469272i 0.0228502 0.0166017i
\(800\) −10.4164 −0.368276
\(801\) 12.7639 0.450991
\(802\) −14.9164 + 10.8374i −0.526717 + 0.382682i
\(803\) 2.02129 6.22088i 0.0713296 0.219530i
\(804\) −2.11803 6.51864i −0.0746973 0.229895i
\(805\) 42.9787 1.51480
\(806\) 16.6353 1.50609i 0.585952 0.0530496i
\(807\) 1.38197 0.0486475
\(808\) 3.29180 + 10.1311i 0.115805 + 0.356411i
\(809\) 16.9336 52.1164i 0.595355 1.83231i 0.0424020 0.999101i \(-0.486499\pi\)
0.552953 0.833213i \(-0.313501\pi\)
\(810\) −1.30902 + 0.951057i −0.0459942 + 0.0334167i
\(811\) 42.7771 1.50211 0.751053 0.660242i \(-0.229546\pi\)
0.751053 + 0.660242i \(0.229546\pi\)
\(812\) 41.8328 1.46804
\(813\) 7.73607 5.62058i 0.271316 0.197122i
\(814\) −0.0901699 0.0655123i −0.00316045 0.00229620i
\(815\) −26.9164 19.5559i −0.942841 0.685014i
\(816\) −0.135255 0.416272i −0.00473487 0.0145724i
\(817\) 18.6803 13.5721i 0.653542 0.474826i
\(818\) 1.18034 + 3.63271i 0.0412696 + 0.127015i
\(819\) −9.00000 + 27.6992i −0.314485 + 0.967887i
\(820\) −22.1803 16.1150i −0.774571 0.562759i
\(821\) −10.0344 + 30.8828i −0.350204 + 1.07782i 0.608534 + 0.793528i \(0.291758\pi\)
−0.958738 + 0.284290i \(0.908242\pi\)
\(822\) −1.23607 + 3.80423i −0.0431128 + 0.132688i
\(823\) 4.95492 + 3.59996i 0.172717 + 0.125487i 0.670786 0.741651i \(-0.265957\pi\)
−0.498068 + 0.867138i \(0.665957\pi\)
\(824\) −0.100813 + 0.310271i −0.00351199 + 0.0108088i
\(825\) 0.437694 + 1.34708i 0.0152386 + 0.0468994i
\(826\) 14.2082 10.3229i 0.494367 0.359178i
\(827\) 0.826238 + 2.54290i 0.0287311 + 0.0884253i 0.964394 0.264470i \(-0.0851971\pi\)
−0.935663 + 0.352896i \(0.885197\pi\)
\(828\) 14.3262 + 10.4086i 0.497871 + 0.361725i
\(829\) 17.5623 + 12.7598i 0.609964 + 0.443165i 0.849402 0.527747i \(-0.176963\pi\)
−0.239438 + 0.970912i \(0.576963\pi\)
\(830\) 5.35410 3.88998i 0.185844 0.135023i
\(831\) −13.3262 −0.462282
\(832\) −1.14590 −0.0397269
\(833\) −0.381966 + 0.277515i −0.0132343 + 0.00961531i
\(834\) 1.11803 3.44095i 0.0387144 0.119151i
\(835\) 7.47214 + 22.9969i 0.258584 + 0.795839i
\(836\) 6.18034 0.213752
\(837\) 20.9549 18.3273i 0.724308 0.633486i
\(838\) −2.76393 −0.0954784
\(839\) 3.45492 + 10.6331i 0.119277 + 0.367097i 0.992815 0.119659i \(-0.0381802\pi\)
−0.873538 + 0.486756i \(0.838180\pi\)
\(840\) 5.42705 16.7027i 0.187251 0.576299i
\(841\) −36.6246 + 26.6093i −1.26292 + 0.917563i
\(842\) −9.12461 −0.314455
\(843\) −19.0344 −0.655581
\(844\) −10.4721 + 7.60845i −0.360466 + 0.261894i
\(845\) 22.3713 + 16.2537i 0.769597 + 0.559145i
\(846\) 3.38197 + 2.45714i 0.116274 + 0.0844783i
\(847\) −9.65654 29.7198i −0.331803 1.02118i
\(848\) 19.0623 13.8496i 0.654602 0.475596i
\(849\) −2.02786 6.24112i −0.0695961 0.214195i
\(850\) −0.0835921 + 0.257270i −0.00286719 + 0.00882429i
\(851\) 1.04508 + 0.759299i 0.0358251 + 0.0260284i
\(852\) 0.0450850 0.138757i 0.00154459 0.00475375i
\(853\) 1.23607 3.80423i 0.0423222 0.130254i −0.927663 0.373419i \(-0.878185\pi\)
0.969985 + 0.243164i \(0.0781855\pi\)
\(854\) −10.4164 7.56796i −0.356442 0.258970i
\(855\) 8.09017 24.8990i 0.276678 0.851527i
\(856\) 0.753289 + 2.31838i 0.0257469 + 0.0792408i
\(857\) 6.61803 4.80828i 0.226068 0.164248i −0.468986 0.883206i \(-0.655381\pi\)
0.695054 + 0.718958i \(0.255381\pi\)
\(858\) −0.708204 2.17963i −0.0241777 0.0744113i
\(859\) −35.0238 25.4463i −1.19500 0.868216i −0.201213 0.979547i \(-0.564488\pi\)
−0.993783 + 0.111332i \(0.964488\pi\)
\(860\) 15.8262 + 11.4984i 0.539670 + 0.392093i
\(861\) 15.7082 11.4127i 0.535334 0.388943i
\(862\) −18.0689 −0.615429
\(863\) 2.49342 0.0848771 0.0424385 0.999099i \(-0.486487\pi\)
0.0424385 + 0.999099i \(0.486487\pi\)
\(864\) 22.7254 16.5110i 0.773135 0.561715i
\(865\) −0.736068 + 2.26538i −0.0250271 + 0.0770254i
\(866\) −0.111456 0.343027i −0.00378744 0.0116565i
\(867\) 16.9443 0.575458
\(868\) 6.00000 26.3521i 0.203653 0.894447i
\(869\) 0 0
\(870\) 4.30902 + 13.2618i 0.146089 + 0.449617i
\(871\) −6.35410 + 19.5559i −0.215301 + 0.662627i
\(872\) 15.2254 11.0619i 0.515598 0.374604i
\(873\) 10.5836 0.358200
\(874\) 16.9098 0.571984
\(875\) −19.9894 + 14.5231i −0.675764 + 0.490971i
\(876\) 11.2082 + 8.14324i 0.378690 + 0.275134i
\(877\) −13.1803 9.57608i −0.445068 0.323361i 0.342577 0.939490i \(-0.388700\pi\)
−0.787646 + 0.616129i \(0.788700\pi\)
\(878\) −7.98936 24.5887i −0.269628 0.829829i
\(879\) −6.66312 + 4.84104i −0.224741 + 0.163284i
\(880\) 1.14590 + 3.52671i 0.0386282 + 0.118885i
\(881\) −4.74671 + 14.6089i −0.159921 + 0.492185i −0.998626 0.0523999i \(-0.983313\pi\)
0.838705 + 0.544585i \(0.183313\pi\)
\(882\) −2.00000 1.45309i −0.0673435 0.0489279i
\(883\) −0.309017 + 0.951057i −0.0103992 + 0.0320056i −0.956121 0.292970i \(-0.905356\pi\)
0.945722 + 0.324976i \(0.105356\pi\)
\(884\) −0.572949 + 1.76336i −0.0192704 + 0.0593081i
\(885\) −20.0623 14.5761i −0.674387 0.489971i
\(886\) 7.85410 24.1724i 0.263864 0.812089i
\(887\) 12.0836 + 37.1895i 0.405727 + 1.24870i 0.920286 + 0.391245i \(0.127956\pi\)
−0.514559 + 0.857455i \(0.672044\pi\)
\(888\) 0.427051 0.310271i 0.0143309 0.0104120i
\(889\) 9.48936 + 29.2052i 0.318263 + 0.979512i
\(890\) 8.35410 + 6.06961i 0.280030 + 0.203454i
\(891\) 0.618034 + 0.449028i 0.0207049 + 0.0150430i
\(892\) 0.927051 0.673542i 0.0310400 0.0225519i
\(893\) −16.9098 −0.565866
\(894\) −10.5279 −0.352104
\(895\) 41.9336 30.4666i 1.40169 1.01838i
\(896\) 10.5517 32.4747i 0.352506 1.08490i
\(897\) 8.20820 + 25.2623i 0.274064 + 0.843482i
\(898\) −14.8754 −0.496398
\(899\) 18.8820 + 44.1119i 0.629749 + 1.47121i
\(900\) 6.00000 0.200000
\(901\) −0.927051 2.85317i −0.0308845 0.0950529i
\(902\) 0.944272 2.90617i 0.0314408 0.0967649i
\(903\) −11.2082 + 8.14324i −0.372986 + 0.270990i
\(904\) −4.14590 −0.137891
\(905\) −44.5066 −1.47945
\(906\) 9.75329 7.08618i 0.324031 0.235423i
\(907\) −42.8156 31.1074i −1.42167 1.03290i −0.991493 0.130157i \(-0.958452\pi\)
−0.430175 0.902745i \(-0.641548\pi\)
\(908\) −27.1525 19.7274i −0.901087 0.654678i
\(909\) −2.94427 9.06154i −0.0976553 0.300552i
\(910\) −19.0623 + 13.8496i −0.631909 + 0.459109i
\(911\) 2.52786 + 7.77997i 0.0837519 + 0.257762i 0.984159 0.177286i \(-0.0567316\pi\)
−0.900408 + 0.435047i \(0.856732\pi\)
\(912\) −2.86475 + 8.81678i −0.0948612 + 0.291953i
\(913\) −2.52786 1.83660i −0.0836601 0.0607826i
\(914\) 3.00658 9.25330i 0.0994488 0.306072i
\(915\) −5.61803 + 17.2905i −0.185726 + 0.571607i
\(916\) −9.47214 6.88191i −0.312968 0.227385i
\(917\) 0.0835921 0.257270i 0.00276046 0.00849581i
\(918\) −0.225425 0.693786i −0.00744013 0.0228984i
\(919\) −7.98936 + 5.80461i −0.263545 + 0.191476i −0.711708 0.702475i \(-0.752078\pi\)
0.448164 + 0.893952i \(0.352078\pi\)
\(920\) 9.89919 + 30.4666i 0.326367 + 1.00445i
\(921\) 4.92705 + 3.57971i 0.162352 + 0.117956i
\(922\) 5.37132 + 3.90249i 0.176895 + 0.128522i
\(923\) −0.354102 + 0.257270i −0.0116554 + 0.00846815i
\(924\) −3.70820 −0.121991
\(925\) 0.437694 0.0143913
\(926\) −15.5623 + 11.3067i −0.511409 + 0.371560i
\(927\) 0.0901699 0.277515i 0.00296157 0.00911477i
\(928\) 14.9615 + 46.0467i 0.491135 + 1.51156i
\(929\) 33.5410 1.10045 0.550223 0.835018i \(-0.314543\pi\)
0.550223 + 0.835018i \(0.314543\pi\)
\(930\) 8.97214 0.812299i 0.294208 0.0266363i
\(931\) 10.0000 0.327737
\(932\) −9.39919 28.9277i −0.307881 0.947559i
\(933\) −5.09017 + 15.6659i −0.166645 + 0.512880i
\(934\) −16.3885 + 11.9070i −0.536250 + 0.389608i
\(935\) 0.472136 0.0154405
\(936\) −21.7082 −0.709555
\(937\) −32.7533 + 23.7967i −1.07000 + 0.777403i −0.975913 0.218161i \(-0.929994\pi\)
−0.0940905 + 0.995564i \(0.529994\pi\)
\(938\) −6.35410 4.61653i −0.207469 0.150735i
\(939\) 1.00000 + 0.726543i 0.0326338 + 0.0237098i
\(940\) −4.42705 13.6251i −0.144394 0.444401i
\(941\) −23.1246 + 16.8010i −0.753841 + 0.547697i −0.897015 0.442000i \(-0.854269\pi\)
0.143174 + 0.989698i \(0.454269\pi\)
\(942\) 1.85410 + 5.70634i 0.0604099 + 0.185923i
\(943\) −10.9443 + 33.6830i −0.356395 + 1.09687i
\(944\) −14.2082 10.3229i −0.462438 0.335981i
\(945\) −12.1353 + 37.3485i −0.394760 + 1.21495i
\(946\) −0.673762 + 2.07363i −0.0219059 + 0.0674194i
\(947\) −17.8541 12.9718i −0.580180 0.421526i 0.258609 0.965982i \(-0.416736\pi\)
−0.838789 + 0.544456i \(0.816736\pi\)
\(948\) 0 0
\(949\) −12.8435 39.5281i −0.416916 1.28314i
\(950\) 4.63525 3.36771i 0.150388 0.109263i
\(951\) −8.00000 24.6215i −0.259418 0.798406i
\(952\) −1.28115 0.930812i −0.0415224 0.0301678i
\(953\) −34.1525 24.8132i −1.10631 0.803779i −0.124229 0.992254i \(-0.539646\pi\)
−0.982078 + 0.188474i \(0.939646\pi\)
\(954\) 12.7082 9.23305i 0.411443 0.298931i
\(955\) 42.1246 1.36312
\(956\) 21.7082 0.702093
\(957\) 5.32624 3.86974i 0.172173 0.125091i
\(958\) 1.70820 5.25731i 0.0551896 0.169856i
\(959\) −6.00000 18.4661i −0.193750 0.596302i
\(960\) −0.618034 −0.0199470
\(961\) 30.4959 5.56758i 0.983740 0.179599i
\(962\) −0.708204 −0.0228334
\(963\) −0.673762 2.07363i −0.0217117 0.0668217i
\(964\) 4.26393 13.1230i 0.137332 0.422664i
\(965\) −5.04508 + 3.66547i −0.162407 + 0.117996i
\(966\) −10.1459 −0.326439
\(967\) 43.6525 1.40377 0.701884 0.712291i \(-0.252342\pi\)
0.701884 + 0.712291i \(0.252342\pi\)
\(968\) 18.8435 13.6906i 0.605652 0.440032i
\(969\) 0.954915 + 0.693786i 0.0306763 + 0.0222876i
\(970\) 6.92705 + 5.03280i 0.222414 + 0.161593i
\(971\) −6.35410 19.5559i −0.203913 0.627579i −0.999756 0.0220767i \(-0.992972\pi\)
0.795843 0.605502i \(-0.207028\pi\)
\(972\) −20.9443 + 15.2169i −0.671788 + 0.488082i
\(973\) 5.42705 + 16.7027i 0.173983 + 0.535465i
\(974\) −4.37790 + 13.4738i −0.140277 + 0.431728i
\(975\) 7.28115 + 5.29007i 0.233184 + 0.169418i
\(976\) −3.97871 + 12.2452i −0.127356 + 0.391960i
\(977\) −1.87539 + 5.77185i −0.0599990 + 0.184658i −0.976564 0.215228i \(-0.930950\pi\)
0.916565 + 0.399886i \(0.130950\pi\)
\(978\) 6.35410 + 4.61653i 0.203182 + 0.147620i
\(979\) 1.50658 4.63677i 0.0481504 0.148192i
\(980\) 2.61803 + 8.05748i 0.0836300 + 0.257387i
\(981\) −13.6180 + 9.89408i −0.434790 + 0.315894i
\(982\) 5.27051 + 16.2210i 0.168189 + 0.517632i
\(983\) −17.0172 12.3637i −0.542765 0.394342i 0.282346 0.959313i \(-0.408887\pi\)
−0.825111 + 0.564971i \(0.808887\pi\)
\(984\) 11.7082 + 8.50651i 0.373244 + 0.271178i
\(985\) 34.7705 25.2623i 1.10788 0.804922i
\(986\) 1.25735 0.0400423
\(987\) 10.1459 0.322947
\(988\) 31.7705 23.0826i 1.01075 0.734356i
\(989\) 7.80902 24.0337i 0.248312 0.764227i
\(990\) 0.763932 + 2.35114i 0.0242794 + 0.0747242i
\(991\) −17.2705 −0.548616 −0.274308 0.961642i \(-0.588449\pi\)
−0.274308 + 0.961642i \(0.588449\pi\)
\(992\) 31.1525 2.82041i 0.989092 0.0895482i
\(993\) −11.2705 −0.357659
\(994\) −0.0516628 0.159002i −0.00163864 0.00504323i
\(995\) 21.6074 66.5007i 0.685000 2.10821i
\(996\) 5.35410 3.88998i 0.169651 0.123259i
\(997\) −27.2492 −0.862992 −0.431496 0.902115i \(-0.642014\pi\)
−0.431496 + 0.902115i \(0.642014\pi\)
\(998\) −2.56231 −0.0811084
\(999\) −0.954915 + 0.693786i −0.0302122 + 0.0219504i
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 31.2.d.a.4.1 4
3.2 odd 2 279.2.i.a.190.1 4
4.3 odd 2 496.2.n.b.97.1 4
5.2 odd 4 775.2.bf.a.624.2 8
5.3 odd 4 775.2.bf.a.624.1 8
5.4 even 2 775.2.k.c.376.1 4
31.2 even 5 961.2.d.f.388.1 4
31.3 odd 30 961.2.c.d.439.1 4
31.4 even 5 961.2.d.f.374.1 4
31.5 even 3 961.2.g.b.844.1 8
31.6 odd 6 961.2.g.c.547.1 8
31.7 even 15 961.2.g.f.816.1 8
31.8 even 5 inner 31.2.d.a.8.1 yes 4
31.9 even 15 961.2.g.b.448.1 8
31.10 even 15 961.2.g.f.338.1 8
31.11 odd 30 961.2.g.g.732.1 8
31.12 odd 30 961.2.g.g.235.1 8
31.13 odd 30 961.2.c.d.521.1 4
31.14 even 15 961.2.g.b.846.1 8
31.15 odd 10 961.2.a.e.1.1 2
31.16 even 5 961.2.a.d.1.1 2
31.17 odd 30 961.2.g.c.846.1 8
31.18 even 15 961.2.c.f.521.1 4
31.19 even 15 961.2.g.f.235.1 8
31.20 even 15 961.2.g.f.732.1 8
31.21 odd 30 961.2.g.g.338.1 8
31.22 odd 30 961.2.g.c.448.1 8
31.23 odd 10 961.2.d.b.628.1 4
31.24 odd 30 961.2.g.g.816.1 8
31.25 even 3 961.2.g.b.547.1 8
31.26 odd 6 961.2.g.c.844.1 8
31.27 odd 10 961.2.d.e.374.1 4
31.28 even 15 961.2.c.f.439.1 4
31.29 odd 10 961.2.d.e.388.1 4
31.30 odd 2 961.2.d.b.531.1 4
93.8 odd 10 279.2.i.a.163.1 4
93.47 odd 10 8649.2.a.g.1.2 2
93.77 even 10 8649.2.a.f.1.2 2
124.39 odd 10 496.2.n.b.225.1 4
155.8 odd 20 775.2.bf.a.349.2 8
155.39 even 10 775.2.k.c.101.1 4
155.132 odd 20 775.2.bf.a.349.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
31.2.d.a.4.1 4 1.1 even 1 trivial
31.2.d.a.8.1 yes 4 31.8 even 5 inner
279.2.i.a.163.1 4 93.8 odd 10
279.2.i.a.190.1 4 3.2 odd 2
496.2.n.b.97.1 4 4.3 odd 2
496.2.n.b.225.1 4 124.39 odd 10
775.2.k.c.101.1 4 155.39 even 10
775.2.k.c.376.1 4 5.4 even 2
775.2.bf.a.349.1 8 155.132 odd 20
775.2.bf.a.349.2 8 155.8 odd 20
775.2.bf.a.624.1 8 5.3 odd 4
775.2.bf.a.624.2 8 5.2 odd 4
961.2.a.d.1.1 2 31.16 even 5
961.2.a.e.1.1 2 31.15 odd 10
961.2.c.d.439.1 4 31.3 odd 30
961.2.c.d.521.1 4 31.13 odd 30
961.2.c.f.439.1 4 31.28 even 15
961.2.c.f.521.1 4 31.18 even 15
961.2.d.b.531.1 4 31.30 odd 2
961.2.d.b.628.1 4 31.23 odd 10
961.2.d.e.374.1 4 31.27 odd 10
961.2.d.e.388.1 4 31.29 odd 10
961.2.d.f.374.1 4 31.4 even 5
961.2.d.f.388.1 4 31.2 even 5
961.2.g.b.448.1 8 31.9 even 15
961.2.g.b.547.1 8 31.25 even 3
961.2.g.b.844.1 8 31.5 even 3
961.2.g.b.846.1 8 31.14 even 15
961.2.g.c.448.1 8 31.22 odd 30
961.2.g.c.547.1 8 31.6 odd 6
961.2.g.c.844.1 8 31.26 odd 6
961.2.g.c.846.1 8 31.17 odd 30
961.2.g.f.235.1 8 31.19 even 15
961.2.g.f.338.1 8 31.10 even 15
961.2.g.f.732.1 8 31.20 even 15
961.2.g.f.816.1 8 31.7 even 15
961.2.g.g.235.1 8 31.12 odd 30
961.2.g.g.338.1 8 31.21 odd 30
961.2.g.g.732.1 8 31.11 odd 30
961.2.g.g.816.1 8 31.24 odd 30
8649.2.a.f.1.2 2 93.77 even 10
8649.2.a.g.1.2 2 93.47 odd 10