Properties

Label 245.2.l.b.117.1
Level $245$
Weight $2$
Character 245.117
Analytic conductor $1.956$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [245,2,Mod(68,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("245.68");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.l (of order \(12\), degree \(4\), not 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: \(1.95633484952\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 117.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 245.117
Dual form 245.2.l.b.178.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.133975i) q^{2} +(0.133975 - 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} -0.267949i q^{6} +(-1.36603 + 1.36603i) q^{8} +(2.36603 + 1.36603i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.133975i) q^{2} +(0.133975 - 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} -0.267949i q^{6} +(-1.36603 + 1.36603i) q^{8} +(2.36603 + 1.36603i) q^{9} +(0.232051 + 1.13397i) q^{10} +(1.36603 + 2.36603i) q^{11} +(0.232051 + 0.866025i) q^{12} +(2.00000 + 2.00000i) q^{13} +(1.09808 + 0.366025i) q^{15} +(1.23205 - 2.13397i) q^{16} +(-3.73205 - 1.00000i) q^{17} +(1.36603 + 0.366025i) q^{18} +(-0.366025 + 0.633975i) q^{19} +(-1.73205 - 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(0.0358984 + 0.133975i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.96410 - 0.598076i) q^{25} +(1.26795 + 0.732051i) q^{26} +(2.09808 - 2.09808i) q^{27} -3.00000i q^{29} +(0.598076 + 0.0358984i) q^{30} +(6.46410 - 3.73205i) q^{31} +(1.33013 - 4.96410i) q^{32} +(1.36603 - 0.366025i) q^{33} -2.00000 q^{34} -4.73205 q^{36} +(-4.73205 + 1.26795i) q^{37} +(-0.0980762 + 0.366025i) q^{38} +(1.26795 - 0.732051i) q^{39} +(-2.86603 - 3.23205i) q^{40} +6.46410i q^{41} +(2.83013 - 2.83013i) q^{43} +(-4.09808 - 2.36603i) q^{44} +(-3.36603 + 5.09808i) q^{45} +(0.0358984 + 0.0621778i) q^{46} +(-2.36603 - 8.83013i) q^{47} +(-0.901924 - 0.901924i) q^{48} +(-2.56218 + 0.366025i) q^{50} +(-1.00000 + 1.73205i) q^{51} +(-4.73205 - 1.26795i) q^{52} +(6.83013 + 1.83013i) q^{53} +(0.767949 - 1.33013i) q^{54} +(-5.46410 + 2.73205i) q^{55} +(0.267949 + 0.267949i) q^{57} +(-0.401924 - 1.50000i) q^{58} +(4.09808 + 7.09808i) q^{59} +(-1.96410 + 0.401924i) q^{60} +(-1.33013 - 0.767949i) q^{61} +(2.73205 - 2.73205i) q^{62} +2.26795i q^{64} +(-4.73205 + 4.19615i) q^{65} +(0.633975 - 0.366025i) q^{66} +(2.86603 - 10.6962i) q^{67} +(6.46410 - 1.73205i) q^{68} +0.0717968 q^{69} +1.26795 q^{71} +(-5.09808 + 1.36603i) q^{72} +(3.46410 - 12.9282i) q^{73} +(-2.19615 + 1.26795i) q^{74} +(-0.964102 + 2.40192i) q^{75} -1.26795i q^{76} +(0.535898 - 0.535898i) q^{78} +(2.83013 + 1.63397i) q^{79} +(4.59808 + 3.03590i) q^{80} +(3.33013 + 5.76795i) q^{81} +(0.866025 + 3.23205i) q^{82} +(2.09808 + 2.09808i) q^{83} +(2.73205 - 8.19615i) q^{85} +(1.03590 - 1.79423i) q^{86} +(-1.50000 - 0.401924i) q^{87} +(-5.09808 - 1.36603i) q^{88} +(0.330127 - 0.571797i) q^{89} +(-1.00000 + 3.00000i) q^{90} +(-0.169873 - 0.169873i) q^{92} +(-1.00000 - 3.73205i) q^{93} +(-2.36603 - 4.09808i) q^{94} +(-1.36603 - 0.901924i) q^{95} +(-2.30385 - 1.33013i) q^{96} +(5.92820 - 5.92820i) q^{97} +7.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 4 q^{5} - 2 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 4 q^{5} - 2 q^{8} + 6 q^{9} - 6 q^{10} + 2 q^{11} - 6 q^{12} + 8 q^{13} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{19} + 4 q^{22} + 14 q^{23} + 2 q^{24} - 6 q^{25} + 12 q^{26} - 2 q^{27} - 8 q^{30} + 12 q^{31} - 12 q^{32} + 2 q^{33} - 8 q^{34} - 12 q^{36} - 12 q^{37} + 10 q^{38} + 12 q^{39} - 8 q^{40} - 6 q^{43} - 6 q^{44} - 10 q^{45} + 14 q^{46} - 6 q^{47} - 14 q^{48} + 14 q^{50} - 4 q^{51} - 12 q^{52} + 10 q^{53} + 10 q^{54} - 8 q^{55} + 8 q^{57} - 12 q^{58} + 6 q^{59} + 6 q^{60} + 12 q^{61} + 4 q^{62} - 12 q^{65} + 6 q^{66} + 8 q^{67} + 12 q^{68} + 28 q^{69} + 12 q^{71} - 10 q^{72} + 12 q^{74} + 10 q^{75} + 16 q^{78} - 6 q^{79} + 8 q^{80} - 4 q^{81} - 2 q^{83} + 4 q^{85} + 18 q^{86} - 6 q^{87} - 10 q^{88} - 16 q^{89} - 4 q^{90} - 18 q^{92} - 4 q^{93} - 6 q^{94} - 2 q^{95} - 30 q^{96} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.133975i 0.353553 0.0947343i −0.0776710 0.996979i \(-0.524748\pi\)
0.431224 + 0.902245i \(0.358082\pi\)
\(3\) 0.133975 0.500000i 0.0773503 0.288675i −0.916406 0.400251i \(-0.868923\pi\)
0.993756 + 0.111576i \(0.0355897\pi\)
\(4\) −1.50000 + 0.866025i −0.750000 + 0.433013i
\(5\) −0.133975 + 2.23205i −0.0599153 + 0.998203i
\(6\) 0.267949i 0.109390i
\(7\) 0 0
\(8\) −1.36603 + 1.36603i −0.482963 + 0.482963i
\(9\) 2.36603 + 1.36603i 0.788675 + 0.455342i
\(10\) 0.232051 + 1.13397i 0.0733809 + 0.358594i
\(11\) 1.36603 + 2.36603i 0.411872 + 0.713384i 0.995094 0.0989291i \(-0.0315417\pi\)
−0.583222 + 0.812313i \(0.698208\pi\)
\(12\) 0.232051 + 0.866025i 0.0669873 + 0.250000i
\(13\) 2.00000 + 2.00000i 0.554700 + 0.554700i 0.927794 0.373094i \(-0.121703\pi\)
−0.373094 + 0.927794i \(0.621703\pi\)
\(14\) 0 0
\(15\) 1.09808 + 0.366025i 0.283522 + 0.0945074i
\(16\) 1.23205 2.13397i 0.308013 0.533494i
\(17\) −3.73205 1.00000i −0.905155 0.242536i −0.223926 0.974606i \(-0.571888\pi\)
−0.681229 + 0.732070i \(0.738554\pi\)
\(18\) 1.36603 + 0.366025i 0.321975 + 0.0862730i
\(19\) −0.366025 + 0.633975i −0.0839720 + 0.145444i −0.904953 0.425512i \(-0.860094\pi\)
0.820981 + 0.570956i \(0.193427\pi\)
\(20\) −1.73205 3.46410i −0.387298 0.774597i
\(21\) 0 0
\(22\) 1.00000 + 1.00000i 0.213201 + 0.213201i
\(23\) 0.0358984 + 0.133975i 0.00748533 + 0.0279356i 0.969567 0.244824i \(-0.0787302\pi\)
−0.962082 + 0.272760i \(0.912064\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −4.96410 0.598076i −0.992820 0.119615i
\(26\) 1.26795 + 0.732051i 0.248665 + 0.143567i
\(27\) 2.09808 2.09808i 0.403775 0.403775i
\(28\) 0 0
\(29\) 3.00000i 0.557086i −0.960424 0.278543i \(-0.910149\pi\)
0.960424 0.278543i \(-0.0898515\pi\)
\(30\) 0.598076 + 0.0358984i 0.109193 + 0.00655412i
\(31\) 6.46410 3.73205i 1.16099 0.670296i 0.209447 0.977820i \(-0.432834\pi\)
0.951540 + 0.307524i \(0.0995004\pi\)
\(32\) 1.33013 4.96410i 0.235135 0.877537i
\(33\) 1.36603 0.366025i 0.237795 0.0637168i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) −4.73205 −0.788675
\(37\) −4.73205 + 1.26795i −0.777944 + 0.208450i −0.625878 0.779921i \(-0.715259\pi\)
−0.152066 + 0.988370i \(0.548593\pi\)
\(38\) −0.0980762 + 0.366025i −0.0159101 + 0.0593772i
\(39\) 1.26795 0.732051i 0.203034 0.117222i
\(40\) −2.86603 3.23205i −0.453158 0.511032i
\(41\) 6.46410i 1.00952i 0.863259 + 0.504762i \(0.168420\pi\)
−0.863259 + 0.504762i \(0.831580\pi\)
\(42\) 0 0
\(43\) 2.83013 2.83013i 0.431590 0.431590i −0.457579 0.889169i \(-0.651283\pi\)
0.889169 + 0.457579i \(0.151283\pi\)
\(44\) −4.09808 2.36603i −0.617808 0.356692i
\(45\) −3.36603 + 5.09808i −0.501777 + 0.759976i
\(46\) 0.0358984 + 0.0621778i 0.00529293 + 0.00916762i
\(47\) −2.36603 8.83013i −0.345120 1.28801i −0.892472 0.451103i \(-0.851031\pi\)
0.547351 0.836903i \(-0.315636\pi\)
\(48\) −0.901924 0.901924i −0.130181 0.130181i
\(49\) 0 0
\(50\) −2.56218 + 0.366025i −0.362347 + 0.0517638i
\(51\) −1.00000 + 1.73205i −0.140028 + 0.242536i
\(52\) −4.73205 1.26795i −0.656217 0.175833i
\(53\) 6.83013 + 1.83013i 0.938190 + 0.251387i 0.695344 0.718677i \(-0.255252\pi\)
0.242846 + 0.970065i \(0.421919\pi\)
\(54\) 0.767949 1.33013i 0.104505 0.181007i
\(55\) −5.46410 + 2.73205i −0.736779 + 0.368390i
\(56\) 0 0
\(57\) 0.267949 + 0.267949i 0.0354907 + 0.0354907i
\(58\) −0.401924 1.50000i −0.0527752 0.196960i
\(59\) 4.09808 + 7.09808i 0.533524 + 0.924091i 0.999233 + 0.0391530i \(0.0124660\pi\)
−0.465709 + 0.884938i \(0.654201\pi\)
\(60\) −1.96410 + 0.401924i −0.253564 + 0.0518881i
\(61\) −1.33013 0.767949i −0.170305 0.0983258i 0.412424 0.910992i \(-0.364682\pi\)
−0.582730 + 0.812666i \(0.698015\pi\)
\(62\) 2.73205 2.73205i 0.346971 0.346971i
\(63\) 0 0
\(64\) 2.26795i 0.283494i
\(65\) −4.73205 + 4.19615i −0.586939 + 0.520469i
\(66\) 0.633975 0.366025i 0.0780369 0.0450546i
\(67\) 2.86603 10.6962i 0.350141 1.30674i −0.536350 0.843996i \(-0.680197\pi\)
0.886490 0.462747i \(-0.153136\pi\)
\(68\) 6.46410 1.73205i 0.783887 0.210042i
\(69\) 0.0717968 0.00864332
\(70\) 0 0
\(71\) 1.26795 0.150478 0.0752389 0.997166i \(-0.476028\pi\)
0.0752389 + 0.997166i \(0.476028\pi\)
\(72\) −5.09808 + 1.36603i −0.600814 + 0.160988i
\(73\) 3.46410 12.9282i 0.405442 1.51313i −0.397796 0.917474i \(-0.630225\pi\)
0.803238 0.595658i \(-0.203109\pi\)
\(74\) −2.19615 + 1.26795i −0.255298 + 0.147396i
\(75\) −0.964102 + 2.40192i −0.111325 + 0.277350i
\(76\) 1.26795i 0.145444i
\(77\) 0 0
\(78\) 0.535898 0.535898i 0.0606785 0.0606785i
\(79\) 2.83013 + 1.63397i 0.318414 + 0.183837i 0.650686 0.759347i \(-0.274482\pi\)
−0.332271 + 0.943184i \(0.607815\pi\)
\(80\) 4.59808 + 3.03590i 0.514081 + 0.339424i
\(81\) 3.33013 + 5.76795i 0.370014 + 0.640883i
\(82\) 0.866025 + 3.23205i 0.0956365 + 0.356920i
\(83\) 2.09808 + 2.09808i 0.230294 + 0.230294i 0.812815 0.582522i \(-0.197934\pi\)
−0.582522 + 0.812815i \(0.697934\pi\)
\(84\) 0 0
\(85\) 2.73205 8.19615i 0.296333 0.888998i
\(86\) 1.03590 1.79423i 0.111704 0.193477i
\(87\) −1.50000 0.401924i −0.160817 0.0430908i
\(88\) −5.09808 1.36603i −0.543457 0.145619i
\(89\) 0.330127 0.571797i 0.0349934 0.0606103i −0.847998 0.529999i \(-0.822192\pi\)
0.882992 + 0.469389i \(0.155526\pi\)
\(90\) −1.00000 + 3.00000i −0.105409 + 0.316228i
\(91\) 0 0
\(92\) −0.169873 0.169873i −0.0177105 0.0177105i
\(93\) −1.00000 3.73205i −0.103695 0.386996i
\(94\) −2.36603 4.09808i −0.244037 0.422684i
\(95\) −1.36603 0.901924i −0.140151 0.0925354i
\(96\) −2.30385 1.33013i −0.235135 0.135756i
\(97\) 5.92820 5.92820i 0.601918 0.601918i −0.338903 0.940821i \(-0.610056\pi\)
0.940821 + 0.338903i \(0.110056\pi\)
\(98\) 0 0
\(99\) 7.46410i 0.750170i
\(100\) 7.96410 3.40192i 0.796410 0.340192i
\(101\) −7.16025 + 4.13397i −0.712472 + 0.411346i −0.811976 0.583691i \(-0.801608\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) −0.267949 + 1.00000i −0.0265309 + 0.0990148i
\(103\) −4.59808 + 1.23205i −0.453062 + 0.121398i −0.478132 0.878288i \(-0.658686\pi\)
0.0250698 + 0.999686i \(0.492019\pi\)
\(104\) −5.46410 −0.535799
\(105\) 0 0
\(106\) 3.66025 0.355515
\(107\) 12.6962 3.40192i 1.22738 0.328876i 0.413823 0.910357i \(-0.364193\pi\)
0.813560 + 0.581481i \(0.197526\pi\)
\(108\) −1.33013 + 4.96410i −0.127992 + 0.477671i
\(109\) −8.76795 + 5.06218i −0.839817 + 0.484869i −0.857202 0.514980i \(-0.827799\pi\)
0.0173849 + 0.999849i \(0.494466\pi\)
\(110\) −2.36603 + 2.09808i −0.225592 + 0.200044i
\(111\) 2.53590i 0.240697i
\(112\) 0 0
\(113\) −7.73205 + 7.73205i −0.727370 + 0.727370i −0.970095 0.242725i \(-0.921959\pi\)
0.242725 + 0.970095i \(0.421959\pi\)
\(114\) 0.169873 + 0.0980762i 0.0159101 + 0.00918568i
\(115\) −0.303848 + 0.0621778i −0.0283339 + 0.00579811i
\(116\) 2.59808 + 4.50000i 0.241225 + 0.417815i
\(117\) 2.00000 + 7.46410i 0.184900 + 0.690056i
\(118\) 3.00000 + 3.00000i 0.276172 + 0.276172i
\(119\) 0 0
\(120\) −2.00000 + 1.00000i −0.182574 + 0.0912871i
\(121\) 1.76795 3.06218i 0.160723 0.278380i
\(122\) −0.767949 0.205771i −0.0695269 0.0186297i
\(123\) 3.23205 + 0.866025i 0.291424 + 0.0780869i
\(124\) −6.46410 + 11.1962i −0.580493 + 1.00544i
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 0 0
\(127\) 0.464102 + 0.464102i 0.0411824 + 0.0411824i 0.727398 0.686216i \(-0.240729\pi\)
−0.686216 + 0.727398i \(0.740729\pi\)
\(128\) 2.96410 + 11.0622i 0.261992 + 0.977768i
\(129\) −1.03590 1.79423i −0.0912058 0.157973i
\(130\) −1.80385 + 2.73205i −0.158208 + 0.239617i
\(131\) 13.3923 + 7.73205i 1.17009 + 0.675552i 0.953702 0.300755i \(-0.0972385\pi\)
0.216390 + 0.976307i \(0.430572\pi\)
\(132\) −1.73205 + 1.73205i −0.150756 + 0.150756i
\(133\) 0 0
\(134\) 5.73205i 0.495174i
\(135\) 4.40192 + 4.96410i 0.378857 + 0.427242i
\(136\) 6.46410 3.73205i 0.554292 0.320021i
\(137\) −3.53590 + 13.1962i −0.302092 + 1.12742i 0.633327 + 0.773884i \(0.281689\pi\)
−0.935420 + 0.353539i \(0.884978\pi\)
\(138\) 0.0358984 0.00961894i 0.00305587 0.000818819i
\(139\) 5.66025 0.480096 0.240048 0.970761i \(-0.422837\pi\)
0.240048 + 0.970761i \(0.422837\pi\)
\(140\) 0 0
\(141\) −4.73205 −0.398511
\(142\) 0.633975 0.169873i 0.0532020 0.0142554i
\(143\) −2.00000 + 7.46410i −0.167248 + 0.624180i
\(144\) 5.83013 3.36603i 0.485844 0.280502i
\(145\) 6.69615 + 0.401924i 0.556085 + 0.0333780i
\(146\) 6.92820i 0.573382i
\(147\) 0 0
\(148\) 6.00000 6.00000i 0.493197 0.493197i
\(149\) 0.696152 + 0.401924i 0.0570310 + 0.0329269i 0.528244 0.849092i \(-0.322850\pi\)
−0.471213 + 0.882019i \(0.656184\pi\)
\(150\) −0.160254 + 1.33013i −0.0130847 + 0.108604i
\(151\) −6.92820 12.0000i −0.563809 0.976546i −0.997159 0.0753205i \(-0.976002\pi\)
0.433350 0.901226i \(-0.357331\pi\)
\(152\) −0.366025 1.36603i −0.0296886 0.110799i
\(153\) −7.46410 7.46410i −0.603437 0.603437i
\(154\) 0 0
\(155\) 7.46410 + 14.9282i 0.599531 + 1.19906i
\(156\) −1.26795 + 2.19615i −0.101517 + 0.175833i
\(157\) 4.63397 + 1.24167i 0.369831 + 0.0990960i 0.438948 0.898513i \(-0.355351\pi\)
−0.0691164 + 0.997609i \(0.522018\pi\)
\(158\) 1.63397 + 0.437822i 0.129992 + 0.0348313i
\(159\) 1.83013 3.16987i 0.145139 0.251387i
\(160\) 10.9019 + 3.63397i 0.861873 + 0.287291i
\(161\) 0 0
\(162\) 2.43782 + 2.43782i 0.191533 + 0.191533i
\(163\) −3.63397 13.5622i −0.284635 1.06227i −0.949106 0.314958i \(-0.898010\pi\)
0.664471 0.747314i \(-0.268657\pi\)
\(164\) −5.59808 9.69615i −0.437136 0.757142i
\(165\) 0.633975 + 3.09808i 0.0493549 + 0.241185i
\(166\) 1.33013 + 0.767949i 0.103238 + 0.0596044i
\(167\) −11.7583 + 11.7583i −0.909887 + 0.909887i −0.996263 0.0863757i \(-0.972471\pi\)
0.0863757 + 0.996263i \(0.472471\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0.267949 4.46410i 0.0205508 0.342381i
\(171\) −1.73205 + 1.00000i −0.132453 + 0.0764719i
\(172\) −1.79423 + 6.69615i −0.136809 + 0.510577i
\(173\) −19.9282 + 5.33975i −1.51511 + 0.405973i −0.918130 0.396280i \(-0.870301\pi\)
−0.596984 + 0.802253i \(0.703634\pi\)
\(174\) −0.803848 −0.0609395
\(175\) 0 0
\(176\) 6.73205 0.507447
\(177\) 4.09808 1.09808i 0.308030 0.0825365i
\(178\) 0.0884573 0.330127i 0.00663015 0.0247441i
\(179\) 6.80385 3.92820i 0.508543 0.293608i −0.223691 0.974660i \(-0.571811\pi\)
0.732235 + 0.681052i \(0.238477\pi\)
\(180\) 0.633975 10.5622i 0.0472537 0.787258i
\(181\) 1.19615i 0.0889093i 0.999011 + 0.0444547i \(0.0141550\pi\)
−0.999011 + 0.0444547i \(0.985845\pi\)
\(182\) 0 0
\(183\) −0.562178 + 0.562178i −0.0415574 + 0.0415574i
\(184\) −0.232051 0.133975i −0.0171070 0.00987674i
\(185\) −2.19615 10.7321i −0.161464 0.789036i
\(186\) −1.00000 1.73205i −0.0733236 0.127000i
\(187\) −2.73205 10.1962i −0.199787 0.745617i
\(188\) 11.1962 + 11.1962i 0.816563 + 0.816563i
\(189\) 0 0
\(190\) −0.803848 0.267949i −0.0583172 0.0194391i
\(191\) −6.63397 + 11.4904i −0.480018 + 0.831415i −0.999737 0.0229220i \(-0.992703\pi\)
0.519720 + 0.854337i \(0.326036\pi\)
\(192\) 1.13397 + 0.303848i 0.0818376 + 0.0219283i
\(193\) −7.83013 2.09808i −0.563625 0.151023i −0.0342537 0.999413i \(-0.510905\pi\)
−0.529371 + 0.848390i \(0.677572\pi\)
\(194\) 2.16987 3.75833i 0.155788 0.269832i
\(195\) 1.46410 + 2.92820i 0.104846 + 0.209693i
\(196\) 0 0
\(197\) −10.1244 10.1244i −0.721330 0.721330i 0.247546 0.968876i \(-0.420376\pi\)
−0.968876 + 0.247546i \(0.920376\pi\)
\(198\) 1.00000 + 3.73205i 0.0710669 + 0.265225i
\(199\) 5.53590 + 9.58846i 0.392429 + 0.679708i 0.992769 0.120037i \(-0.0383014\pi\)
−0.600340 + 0.799745i \(0.704968\pi\)
\(200\) 7.59808 5.96410i 0.537265 0.421726i
\(201\) −4.96410 2.86603i −0.350141 0.202154i
\(202\) −3.02628 + 3.02628i −0.212928 + 0.212928i
\(203\) 0 0
\(204\) 3.46410i 0.242536i
\(205\) −14.4282 0.866025i −1.00771 0.0604858i
\(206\) −2.13397 + 1.23205i −0.148681 + 0.0858410i
\(207\) −0.0980762 + 0.366025i −0.00681677 + 0.0254405i
\(208\) 6.73205 1.80385i 0.466784 0.125074i
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −0.196152 −0.0135037 −0.00675184 0.999977i \(-0.502149\pi\)
−0.00675184 + 0.999977i \(0.502149\pi\)
\(212\) −11.8301 + 3.16987i −0.812496 + 0.217708i
\(213\) 0.169873 0.633975i 0.0116395 0.0434392i
\(214\) 5.89230 3.40192i 0.402790 0.232551i
\(215\) 5.93782 + 6.69615i 0.404956 + 0.456674i
\(216\) 5.73205i 0.390017i
\(217\) 0 0
\(218\) −3.70577 + 3.70577i −0.250987 + 0.250987i
\(219\) −6.00000 3.46410i −0.405442 0.234082i
\(220\) 5.83013 8.83013i 0.393067 0.595327i
\(221\) −5.46410 9.46410i −0.367555 0.636624i
\(222\) 0.339746 + 1.26795i 0.0228023 + 0.0850992i
\(223\) −18.1244 18.1244i −1.21370 1.21370i −0.969802 0.243895i \(-0.921575\pi\)
−0.243895 0.969802i \(-0.578425\pi\)
\(224\) 0 0
\(225\) −10.9282 8.19615i −0.728547 0.546410i
\(226\) −2.83013 + 4.90192i −0.188257 + 0.326071i
\(227\) 19.0263 + 5.09808i 1.26282 + 0.338371i 0.827275 0.561797i \(-0.189890\pi\)
0.435543 + 0.900168i \(0.356556\pi\)
\(228\) −0.633975 0.169873i −0.0419860 0.0112501i
\(229\) 9.19615 15.9282i 0.607699 1.05257i −0.383920 0.923366i \(-0.625426\pi\)
0.991619 0.129199i \(-0.0412406\pi\)
\(230\) −0.143594 + 0.0717968i −0.00946828 + 0.00473414i
\(231\) 0 0
\(232\) 4.09808 + 4.09808i 0.269052 + 0.269052i
\(233\) −1.73205 6.46410i −0.113470 0.423477i 0.885698 0.464263i \(-0.153681\pi\)
−0.999168 + 0.0407854i \(0.987014\pi\)
\(234\) 2.00000 + 3.46410i 0.130744 + 0.226455i
\(235\) 20.0263 4.09808i 1.30637 0.267329i
\(236\) −12.2942 7.09808i −0.800286 0.462045i
\(237\) 1.19615 1.19615i 0.0776984 0.0776984i
\(238\) 0 0
\(239\) 2.39230i 0.154745i 0.997002 + 0.0773727i \(0.0246531\pi\)
−0.997002 + 0.0773727i \(0.975347\pi\)
\(240\) 2.13397 1.89230i 0.137747 0.122148i
\(241\) −21.4641 + 12.3923i −1.38262 + 0.798259i −0.992470 0.122491i \(-0.960912\pi\)
−0.390155 + 0.920749i \(0.627578\pi\)
\(242\) 0.473721 1.76795i 0.0304519 0.113648i
\(243\) 11.9282 3.19615i 0.765195 0.205033i
\(244\) 2.66025 0.170305
\(245\) 0 0
\(246\) 1.73205 0.110432
\(247\) −2.00000 + 0.535898i −0.127257 + 0.0340984i
\(248\) −3.73205 + 13.9282i −0.236985 + 0.884442i
\(249\) 1.33013 0.767949i 0.0842934 0.0486668i
\(250\) −0.473721 5.76795i −0.0299607 0.364797i
\(251\) 21.8564i 1.37956i −0.724017 0.689782i \(-0.757706\pi\)
0.724017 0.689782i \(-0.242294\pi\)
\(252\) 0 0
\(253\) −0.267949 + 0.267949i −0.0168458 + 0.0168458i
\(254\) 0.294229 + 0.169873i 0.0184615 + 0.0106588i
\(255\) −3.73205 2.46410i −0.233710 0.154308i
\(256\) 0.696152 + 1.20577i 0.0435095 + 0.0753607i
\(257\) 0.732051 + 2.73205i 0.0456641 + 0.170421i 0.984992 0.172600i \(-0.0552167\pi\)
−0.939328 + 0.343020i \(0.888550\pi\)
\(258\) −0.758330 0.758330i −0.0472116 0.0472116i
\(259\) 0 0
\(260\) 3.46410 10.3923i 0.214834 0.644503i
\(261\) 4.09808 7.09808i 0.253665 0.439360i
\(262\) 7.73205 + 2.07180i 0.477688 + 0.127996i
\(263\) −15.1603 4.06218i −0.934821 0.250485i −0.240912 0.970547i \(-0.577447\pi\)
−0.693909 + 0.720062i \(0.744113\pi\)
\(264\) −1.36603 + 2.36603i −0.0840731 + 0.145619i
\(265\) −5.00000 + 15.0000i −0.307148 + 0.921443i
\(266\) 0 0
\(267\) −0.241670 0.241670i −0.0147899 0.0147899i
\(268\) 4.96410 + 18.5263i 0.303231 + 1.13167i
\(269\) −11.4282 19.7942i −0.696790 1.20688i −0.969574 0.244800i \(-0.921278\pi\)
0.272784 0.962075i \(-0.412056\pi\)
\(270\) 2.86603 + 1.89230i 0.174421 + 0.115162i
\(271\) −18.4186 10.6340i −1.11885 0.645968i −0.177742 0.984077i \(-0.556879\pi\)
−0.941107 + 0.338109i \(0.890213\pi\)
\(272\) −6.73205 + 6.73205i −0.408191 + 0.408191i
\(273\) 0 0
\(274\) 7.07180i 0.427223i
\(275\) −5.36603 12.5622i −0.323584 0.757528i
\(276\) −0.107695 + 0.0621778i −0.00648249 + 0.00374267i
\(277\) −1.39230 + 5.19615i −0.0836555 + 0.312207i −0.995056 0.0993135i \(-0.968335\pi\)
0.911401 + 0.411520i \(0.135002\pi\)
\(278\) 2.83013 0.758330i 0.169740 0.0454816i
\(279\) 20.3923 1.22086
\(280\) 0 0
\(281\) −0.928203 −0.0553720 −0.0276860 0.999617i \(-0.508814\pi\)
−0.0276860 + 0.999617i \(0.508814\pi\)
\(282\) −2.36603 + 0.633975i −0.140895 + 0.0377526i
\(283\) 0.509619 1.90192i 0.0302937 0.113058i −0.949123 0.314904i \(-0.898028\pi\)
0.979417 + 0.201847i \(0.0646943\pi\)
\(284\) −1.90192 + 1.09808i −0.112858 + 0.0651588i
\(285\) −0.633975 + 0.562178i −0.0375534 + 0.0333005i
\(286\) 4.00000i 0.236525i
\(287\) 0 0
\(288\) 9.92820 9.92820i 0.585025 0.585025i
\(289\) −1.79423 1.03590i −0.105543 0.0609352i
\(290\) 3.40192 0.696152i 0.199768 0.0408795i
\(291\) −2.16987 3.75833i −0.127200 0.220317i
\(292\) 6.00000 + 22.3923i 0.351123 + 1.31041i
\(293\) 2.39230 + 2.39230i 0.139760 + 0.139760i 0.773525 0.633765i \(-0.218492\pi\)
−0.633765 + 0.773525i \(0.718492\pi\)
\(294\) 0 0
\(295\) −16.3923 + 8.19615i −0.954397 + 0.477198i
\(296\) 4.73205 8.19615i 0.275045 0.476392i
\(297\) 7.83013 + 2.09808i 0.454350 + 0.121743i
\(298\) 0.401924 + 0.107695i 0.0232828 + 0.00623861i
\(299\) −0.196152 + 0.339746i −0.0113438 + 0.0196480i
\(300\) −0.633975 4.43782i −0.0366025 0.256218i
\(301\) 0 0
\(302\) −5.07180 5.07180i −0.291849 0.291849i
\(303\) 1.10770 + 4.13397i 0.0636354 + 0.237491i
\(304\) 0.901924 + 1.56218i 0.0517289 + 0.0895970i
\(305\) 1.89230 2.86603i 0.108353 0.164108i
\(306\) −4.73205 2.73205i −0.270513 0.156181i
\(307\) −6.29423 + 6.29423i −0.359231 + 0.359231i −0.863529 0.504299i \(-0.831751\pi\)
0.504299 + 0.863529i \(0.331751\pi\)
\(308\) 0 0
\(309\) 2.46410i 0.140178i
\(310\) 5.73205 + 6.46410i 0.325559 + 0.367136i
\(311\) 13.2224 7.63397i 0.749775 0.432883i −0.0758374 0.997120i \(-0.524163\pi\)
0.825613 + 0.564237i \(0.190830\pi\)
\(312\) −0.732051 + 2.73205i −0.0414442 + 0.154672i
\(313\) 5.19615 1.39230i 0.293704 0.0786977i −0.108958 0.994046i \(-0.534752\pi\)
0.402662 + 0.915349i \(0.368085\pi\)
\(314\) 2.48334 0.140143
\(315\) 0 0
\(316\) −5.66025 −0.318414
\(317\) 9.19615 2.46410i 0.516507 0.138398i 0.00885679 0.999961i \(-0.497181\pi\)
0.507651 + 0.861563i \(0.330514\pi\)
\(318\) 0.490381 1.83013i 0.0274992 0.102628i
\(319\) 7.09808 4.09808i 0.397416 0.229448i
\(320\) −5.06218 0.303848i −0.282984 0.0169856i
\(321\) 6.80385i 0.379754i
\(322\) 0 0
\(323\) 2.00000 2.00000i 0.111283 0.111283i
\(324\) −9.99038 5.76795i −0.555021 0.320442i
\(325\) −8.73205 11.1244i −0.484367 0.617068i
\(326\) −3.63397 6.29423i −0.201267 0.348605i
\(327\) 1.35641 + 5.06218i 0.0750094 + 0.279939i
\(328\) −8.83013 8.83013i −0.487562 0.487562i
\(329\) 0 0
\(330\) 0.732051 + 1.46410i 0.0402981 + 0.0805961i
\(331\) 0.928203 1.60770i 0.0510187 0.0883669i −0.839388 0.543532i \(-0.817087\pi\)
0.890407 + 0.455165i \(0.150420\pi\)
\(332\) −4.96410 1.33013i −0.272440 0.0730002i
\(333\) −12.9282 3.46410i −0.708461 0.189832i
\(334\) −4.30385 + 7.45448i −0.235496 + 0.407891i
\(335\) 23.4904 + 7.83013i 1.28342 + 0.427806i
\(336\) 0 0
\(337\) 9.53590 + 9.53590i 0.519453 + 0.519453i 0.917406 0.397953i \(-0.130279\pi\)
−0.397953 + 0.917406i \(0.630279\pi\)
\(338\) −0.669873 2.50000i −0.0364363 0.135982i
\(339\) 2.83013 + 4.90192i 0.153711 + 0.266236i
\(340\) 3.00000 + 14.6603i 0.162698 + 0.795064i
\(341\) 17.6603 + 10.1962i 0.956356 + 0.552153i
\(342\) −0.732051 + 0.732051i −0.0395848 + 0.0395848i
\(343\) 0 0
\(344\) 7.73205i 0.416884i
\(345\) −0.00961894 + 0.160254i −0.000517866 + 0.00862779i
\(346\) −9.24871 + 5.33975i −0.497214 + 0.287067i
\(347\) −7.79423 + 29.0885i −0.418416 + 1.56155i 0.359477 + 0.933154i \(0.382955\pi\)
−0.777893 + 0.628396i \(0.783712\pi\)
\(348\) 2.59808 0.696152i 0.139272 0.0373177i
\(349\) −6.26795 −0.335516 −0.167758 0.985828i \(-0.553653\pi\)
−0.167758 + 0.985828i \(0.553653\pi\)
\(350\) 0 0
\(351\) 8.39230 0.447948
\(352\) 13.5622 3.63397i 0.722867 0.193691i
\(353\) −3.63397 + 13.5622i −0.193417 + 0.721842i 0.799254 + 0.600993i \(0.205228\pi\)
−0.992671 + 0.120849i \(0.961438\pi\)
\(354\) 1.90192 1.09808i 0.101086 0.0583621i
\(355\) −0.169873 + 2.83013i −0.00901592 + 0.150208i
\(356\) 1.14359i 0.0606103i
\(357\) 0 0
\(358\) 2.87564 2.87564i 0.151983 0.151983i
\(359\) 29.6603 + 17.1244i 1.56541 + 0.903789i 0.996693 + 0.0812542i \(0.0258926\pi\)
0.568715 + 0.822535i \(0.307441\pi\)
\(360\) −2.36603 11.5622i −0.124700 0.609380i
\(361\) 9.23205 + 15.9904i 0.485897 + 0.841599i
\(362\) 0.160254 + 0.598076i 0.00842277 + 0.0314342i
\(363\) −1.29423 1.29423i −0.0679294 0.0679294i
\(364\) 0 0
\(365\) 28.3923 + 9.46410i 1.48612 + 0.495374i
\(366\) −0.205771 + 0.356406i −0.0107558 + 0.0186297i
\(367\) −0.500000 0.133975i −0.0260998 0.00699342i 0.245746 0.969334i \(-0.420967\pi\)
−0.271845 + 0.962341i \(0.587634\pi\)
\(368\) 0.330127 + 0.0884573i 0.0172091 + 0.00461115i
\(369\) −8.83013 + 15.2942i −0.459678 + 0.796186i
\(370\) −2.53590 5.07180i −0.131835 0.263670i
\(371\) 0 0
\(372\) 4.73205 + 4.73205i 0.245345 + 0.245345i
\(373\) 2.07180 + 7.73205i 0.107274 + 0.400350i 0.998593 0.0530251i \(-0.0168863\pi\)
−0.891320 + 0.453376i \(0.850220\pi\)
\(374\) −2.73205 4.73205i −0.141271 0.244689i
\(375\) −5.23205 2.47372i −0.270182 0.127742i
\(376\) 15.2942 + 8.83013i 0.788740 + 0.455379i
\(377\) 6.00000 6.00000i 0.309016 0.309016i
\(378\) 0 0
\(379\) 2.33975i 0.120185i 0.998193 + 0.0600923i \(0.0191395\pi\)
−0.998193 + 0.0600923i \(0.980860\pi\)
\(380\) 2.83013 + 0.169873i 0.145182 + 0.00871430i
\(381\) 0.294229 0.169873i 0.0150738 0.00870286i
\(382\) −1.77757 + 6.63397i −0.0909483 + 0.339424i
\(383\) −30.5526 + 8.18653i −1.56116 + 0.418312i −0.933031 0.359795i \(-0.882847\pi\)
−0.628131 + 0.778107i \(0.716180\pi\)
\(384\) 5.92820 0.302522
\(385\) 0 0
\(386\) −4.19615 −0.213579
\(387\) 10.5622 2.83013i 0.536906 0.143863i
\(388\) −3.75833 + 14.0263i −0.190800 + 0.712076i
\(389\) −4.26795 + 2.46410i −0.216394 + 0.124935i −0.604279 0.796773i \(-0.706539\pi\)
0.387886 + 0.921707i \(0.373206\pi\)
\(390\) 1.12436 + 1.26795i 0.0569340 + 0.0642051i
\(391\) 0.535898i 0.0271015i
\(392\) 0 0
\(393\) 5.66025 5.66025i 0.285522 0.285522i
\(394\) −6.41858 3.70577i −0.323364 0.186694i
\(395\) −4.02628 + 6.09808i −0.202584 + 0.306828i
\(396\) −6.46410 11.1962i −0.324833 0.562628i
\(397\) 0.973721 + 3.63397i 0.0488696 + 0.182384i 0.986046 0.166471i \(-0.0532372\pi\)
−0.937177 + 0.348855i \(0.886571\pi\)
\(398\) 4.05256 + 4.05256i 0.203136 + 0.203136i
\(399\) 0 0
\(400\) −7.39230 + 9.85641i −0.369615 + 0.492820i
\(401\) −5.50000 + 9.52628i −0.274657 + 0.475720i −0.970049 0.242911i \(-0.921898\pi\)
0.695392 + 0.718631i \(0.255231\pi\)
\(402\) −2.86603 0.767949i −0.142944 0.0383018i
\(403\) 20.3923 + 5.46410i 1.01581 + 0.272186i
\(404\) 7.16025 12.4019i 0.356236 0.617019i
\(405\) −13.3205 + 6.66025i −0.661901 + 0.330951i
\(406\) 0 0
\(407\) −9.46410 9.46410i −0.469118 0.469118i
\(408\) −1.00000 3.73205i −0.0495074 0.184764i
\(409\) 10.4282 + 18.0622i 0.515641 + 0.893117i 0.999835 + 0.0181564i \(0.00577967\pi\)
−0.484194 + 0.874961i \(0.660887\pi\)
\(410\) −7.33013 + 1.50000i −0.362009 + 0.0740797i
\(411\) 6.12436 + 3.53590i 0.302092 + 0.174413i
\(412\) 5.83013 5.83013i 0.287230 0.287230i
\(413\) 0 0
\(414\) 0.196152i 0.00964037i
\(415\) −4.96410 + 4.40192i −0.243678 + 0.216082i
\(416\) 12.5885 7.26795i 0.617200 0.356341i
\(417\) 0.758330 2.83013i 0.0371356 0.138592i
\(418\) −1.00000 + 0.267949i −0.0489116 + 0.0131058i
\(419\) −23.8564 −1.16546 −0.582731 0.812665i \(-0.698016\pi\)
−0.582731 + 0.812665i \(0.698016\pi\)
\(420\) 0 0
\(421\) −17.3397 −0.845088 −0.422544 0.906343i \(-0.638863\pi\)
−0.422544 + 0.906343i \(0.638863\pi\)
\(422\) −0.0980762 + 0.0262794i −0.00477428 + 0.00127926i
\(423\) 6.46410 24.1244i 0.314295 1.17297i
\(424\) −11.8301 + 6.83013i −0.574522 + 0.331700i
\(425\) 17.9282 + 7.19615i 0.869646 + 0.349065i
\(426\) 0.339746i 0.0164607i
\(427\) 0 0
\(428\) −16.0981 + 16.0981i −0.778130 + 0.778130i
\(429\) 3.46410 + 2.00000i 0.167248 + 0.0965609i
\(430\) 3.86603 + 2.55256i 0.186436 + 0.123095i
\(431\) −3.09808 5.36603i −0.149229 0.258472i 0.781714 0.623637i \(-0.214346\pi\)
−0.930943 + 0.365165i \(0.881013\pi\)
\(432\) −1.89230 7.06218i −0.0910436 0.339779i
\(433\) 17.5359 + 17.5359i 0.842721 + 0.842721i 0.989212 0.146491i \(-0.0467978\pi\)
−0.146491 + 0.989212i \(0.546798\pi\)
\(434\) 0 0
\(435\) 1.09808 3.29423i 0.0526487 0.157946i
\(436\) 8.76795 15.1865i 0.419909 0.727303i
\(437\) −0.0980762 0.0262794i −0.00469162 0.00125712i
\(438\) −3.46410 0.928203i −0.165521 0.0443513i
\(439\) −1.66025 + 2.87564i −0.0792396 + 0.137247i −0.902922 0.429804i \(-0.858583\pi\)
0.823682 + 0.567051i \(0.191916\pi\)
\(440\) 3.73205 11.1962i 0.177919 0.533756i
\(441\) 0 0
\(442\) −4.00000 4.00000i −0.190261 0.190261i
\(443\) −3.50000 13.0622i −0.166290 0.620603i −0.997872 0.0652010i \(-0.979231\pi\)
0.831582 0.555402i \(-0.187436\pi\)
\(444\) −2.19615 3.80385i −0.104225 0.180523i
\(445\) 1.23205 + 0.813467i 0.0584048 + 0.0385620i
\(446\) −11.4904 6.63397i −0.544085 0.314128i
\(447\) 0.294229 0.294229i 0.0139165 0.0139165i
\(448\) 0 0
\(449\) 33.0526i 1.55985i −0.625875 0.779923i \(-0.715258\pi\)
0.625875 0.779923i \(-0.284742\pi\)
\(450\) −6.56218 2.63397i −0.309344 0.124167i
\(451\) −15.2942 + 8.83013i −0.720177 + 0.415794i
\(452\) 4.90192 18.2942i 0.230567 0.860488i
\(453\) −6.92820 + 1.85641i −0.325515 + 0.0872216i
\(454\) 10.1962 0.478529
\(455\) 0 0
\(456\) −0.732051 −0.0342814
\(457\) −11.7321 + 3.14359i −0.548802 + 0.147051i −0.522557 0.852604i \(-0.675022\pi\)
−0.0262453 + 0.999656i \(0.508355\pi\)
\(458\) 2.46410 9.19615i 0.115140 0.429708i
\(459\) −9.92820 + 5.73205i −0.463409 + 0.267549i
\(460\) 0.401924 0.356406i 0.0187398 0.0166175i
\(461\) 5.60770i 0.261176i 0.991437 + 0.130588i \(0.0416866\pi\)
−0.991437 + 0.130588i \(0.958313\pi\)
\(462\) 0 0
\(463\) −4.75833 + 4.75833i −0.221138 + 0.221138i −0.808978 0.587839i \(-0.799979\pi\)
0.587839 + 0.808978i \(0.299979\pi\)
\(464\) −6.40192 3.69615i −0.297202 0.171590i
\(465\) 8.46410 1.73205i 0.392513 0.0803219i
\(466\) −1.73205 3.00000i −0.0802357 0.138972i
\(467\) −3.64359 13.5981i −0.168605 0.629244i −0.997553 0.0699173i \(-0.977726\pi\)
0.828947 0.559327i \(-0.188940\pi\)
\(468\) −9.46410 9.46410i −0.437478 0.437478i
\(469\) 0 0
\(470\) 9.46410 4.73205i 0.436546 0.218273i
\(471\) 1.24167 2.15064i 0.0572131 0.0990960i
\(472\) −15.2942 4.09808i −0.703974 0.188629i
\(473\) 10.5622 + 2.83013i 0.485649 + 0.130129i
\(474\) 0.437822 0.758330i 0.0201098 0.0348313i
\(475\) 2.19615 2.92820i 0.100766 0.134355i
\(476\) 0 0
\(477\) 13.6603 + 13.6603i 0.625460 + 0.625460i
\(478\) 0.320508 + 1.19615i 0.0146597 + 0.0547107i
\(479\) −6.53590 11.3205i −0.298633 0.517247i 0.677191 0.735808i \(-0.263197\pi\)
−0.975823 + 0.218560i \(0.929864\pi\)
\(480\) 3.27757 4.96410i 0.149600 0.226579i
\(481\) −12.0000 6.92820i −0.547153 0.315899i
\(482\) −9.07180 + 9.07180i −0.413209 + 0.413209i
\(483\) 0 0
\(484\) 6.12436i 0.278380i
\(485\) 12.4378 + 14.0263i 0.564772 + 0.636901i
\(486\) 5.53590 3.19615i 0.251113 0.144980i
\(487\) 7.29423 27.2224i 0.330533 1.23357i −0.578098 0.815967i \(-0.696205\pi\)
0.908631 0.417599i \(-0.137128\pi\)
\(488\) 2.86603 0.767949i 0.129739 0.0347634i
\(489\) −7.26795 −0.328668
\(490\) 0 0
\(491\) 37.7128 1.70196 0.850978 0.525202i \(-0.176010\pi\)
0.850978 + 0.525202i \(0.176010\pi\)
\(492\) −5.59808 + 1.50000i −0.252381 + 0.0676252i
\(493\) −3.00000 + 11.1962i −0.135113 + 0.504249i
\(494\) −0.928203 + 0.535898i −0.0417618 + 0.0241112i
\(495\) −16.6603 1.00000i −0.748823 0.0449467i
\(496\) 18.3923i 0.825839i
\(497\) 0 0
\(498\) 0.562178 0.562178i 0.0251918 0.0251918i
\(499\) −9.97372 5.75833i −0.446485 0.257778i 0.259860 0.965646i \(-0.416324\pi\)
−0.706345 + 0.707868i \(0.749657\pi\)
\(500\) 6.52628 + 18.2321i 0.291864 + 0.815362i
\(501\) 4.30385 + 7.45448i 0.192282 + 0.333042i
\(502\) −2.92820 10.9282i −0.130692 0.487750i
\(503\) 17.6340 + 17.6340i 0.786260 + 0.786260i 0.980879 0.194619i \(-0.0623470\pi\)
−0.194619 + 0.980879i \(0.562347\pi\)
\(504\) 0 0
\(505\) −8.26795 16.5359i −0.367919 0.735838i
\(506\) −0.0980762 + 0.169873i −0.00436002 + 0.00755178i
\(507\) −2.50000 0.669873i −0.111029 0.0297501i
\(508\) −1.09808 0.294229i −0.0487193 0.0130543i
\(509\) 19.4545 33.6962i 0.862305 1.49356i −0.00739389 0.999973i \(-0.502354\pi\)
0.869699 0.493583i \(-0.164313\pi\)
\(510\) −2.19615 0.732051i −0.0972473 0.0324158i
\(511\) 0 0
\(512\) −15.6865 15.6865i −0.693253 0.693253i
\(513\) 0.562178 + 2.09808i 0.0248208 + 0.0926323i
\(514\) 0.732051 + 1.26795i 0.0322894 + 0.0559268i
\(515\) −2.13397 10.4282i −0.0940342 0.459522i
\(516\) 3.10770 + 1.79423i 0.136809 + 0.0789865i
\(517\) 17.6603 17.6603i 0.776697 0.776697i
\(518\) 0 0
\(519\) 10.6795i 0.468778i
\(520\) 0.732051 12.1962i 0.0321026 0.534837i
\(521\) 20.6603 11.9282i 0.905142 0.522584i 0.0262772 0.999655i \(-0.491635\pi\)
0.878865 + 0.477071i \(0.158301\pi\)
\(522\) 1.09808 4.09808i 0.0480615 0.179368i
\(523\) 42.8827 11.4904i 1.87513 0.502439i 0.875307 0.483568i \(-0.160659\pi\)
0.999822 0.0188717i \(-0.00600740\pi\)
\(524\) −26.7846 −1.17009
\(525\) 0 0
\(526\) −8.12436 −0.354239
\(527\) −27.8564 + 7.46410i −1.21344 + 0.325141i
\(528\) 0.901924 3.36603i 0.0392512 0.146487i
\(529\) 19.9019 11.4904i 0.865301 0.499582i
\(530\) −0.490381 + 8.16987i −0.0213008 + 0.354877i
\(531\) 22.3923i 0.971743i
\(532\) 0 0
\(533\) −12.9282 + 12.9282i −0.559983 + 0.559983i
\(534\) −0.153212 0.0884573i −0.00663015 0.00382792i
\(535\) 5.89230 + 28.7942i 0.254747 + 1.24488i
\(536\) 10.6962 + 18.5263i 0.462003 + 0.800213i
\(537\) −1.05256 3.92820i −0.0454213 0.169514i
\(538\) −8.36603 8.36603i −0.360685 0.360685i
\(539\) 0 0
\(540\) −10.9019 3.63397i −0.469144 0.156381i
\(541\) −18.3564 + 31.7942i −0.789204 + 1.36694i 0.137252 + 0.990536i \(0.456173\pi\)
−0.926455 + 0.376404i \(0.877160\pi\)
\(542\) −10.6340 2.84936i −0.456768 0.122391i
\(543\) 0.598076 + 0.160254i 0.0256659 + 0.00687716i
\(544\) −9.92820 + 17.1962i −0.425668 + 0.737279i
\(545\) −10.1244 20.2487i −0.433680 0.867359i
\(546\) 0 0
\(547\) −16.7583 16.7583i −0.716534 0.716534i 0.251359 0.967894i \(-0.419122\pi\)
−0.967894 + 0.251359i \(0.919122\pi\)
\(548\) −6.12436 22.8564i −0.261620 0.976377i
\(549\) −2.09808 3.63397i −0.0895437 0.155094i
\(550\) −4.36603 5.56218i −0.186168 0.237172i
\(551\) 1.90192 + 1.09808i 0.0810247 + 0.0467796i
\(552\) −0.0980762 + 0.0980762i −0.00417440 + 0.00417440i
\(553\) 0 0
\(554\) 2.78461i 0.118307i
\(555\) −5.66025 0.339746i −0.240264 0.0144214i
\(556\) −8.49038 + 4.90192i −0.360072 + 0.207888i
\(557\) 8.36603 31.2224i 0.354480 1.32294i −0.526658 0.850077i \(-0.676555\pi\)
0.881138 0.472860i \(-0.156778\pi\)
\(558\) 10.1962 2.73205i 0.431638 0.115657i
\(559\) 11.3205 0.478806
\(560\) 0 0
\(561\) −5.46410 −0.230695
\(562\) −0.464102 + 0.124356i −0.0195769 + 0.00524563i
\(563\) 6.35641 23.7224i 0.267891 0.999781i −0.692567 0.721354i \(-0.743520\pi\)
0.960457 0.278427i \(-0.0898132\pi\)
\(564\) 7.09808 4.09808i 0.298883 0.172560i
\(565\) −16.2224 18.2942i −0.682483 0.769644i
\(566\) 1.01924i 0.0428418i
\(567\) 0 0
\(568\) −1.73205 + 1.73205i −0.0726752 + 0.0726752i
\(569\) −25.0526 14.4641i −1.05026 0.606367i −0.127536 0.991834i \(-0.540707\pi\)
−0.922722 + 0.385467i \(0.874040\pi\)
\(570\) −0.241670 + 0.366025i −0.0101224 + 0.0153311i
\(571\) 9.02628 + 15.6340i 0.377738 + 0.654261i 0.990733 0.135826i \(-0.0433687\pi\)
−0.612995 + 0.790087i \(0.710035\pi\)
\(572\) −3.46410 12.9282i −0.144841 0.540555i
\(573\) 4.85641 + 4.85641i 0.202879 + 0.202879i
\(574\) 0 0
\(575\) −0.0980762 0.686533i −0.00409006 0.0286304i
\(576\) −3.09808 + 5.36603i −0.129087 + 0.223584i
\(577\) −5.63397 1.50962i −0.234545 0.0628463i 0.139632 0.990204i \(-0.455408\pi\)
−0.374177 + 0.927357i \(0.622075\pi\)
\(578\) −1.03590 0.277568i −0.0430877 0.0115453i
\(579\) −2.09808 + 3.63397i −0.0871931 + 0.151023i
\(580\) −10.3923 + 5.19615i −0.431517 + 0.215758i
\(581\) 0 0
\(582\) −1.58846 1.58846i −0.0658437 0.0658437i
\(583\) 5.00000 + 18.6603i 0.207079 + 0.772829i
\(584\) 12.9282 + 22.3923i 0.534973 + 0.926600i
\(585\) −16.9282 + 3.46410i −0.699895 + 0.143223i
\(586\) 1.51666 + 0.875644i 0.0626527 + 0.0361725i
\(587\) −15.7846 + 15.7846i −0.651501 + 0.651501i −0.953354 0.301854i \(-0.902395\pi\)
0.301854 + 0.953354i \(0.402395\pi\)
\(588\) 0 0
\(589\) 5.46410i 0.225144i
\(590\) −7.09808 + 6.29423i −0.292223 + 0.259129i
\(591\) −6.41858 + 3.70577i −0.264025 + 0.152435i
\(592\) −3.12436 + 11.6603i −0.128410 + 0.479233i
\(593\) −20.7583 + 5.56218i −0.852442 + 0.228411i −0.658481 0.752598i \(-0.728801\pi\)
−0.193962 + 0.981009i \(0.562134\pi\)
\(594\) 4.19615 0.172170
\(595\) 0 0
\(596\) −1.39230 −0.0570310
\(597\) 5.53590 1.48334i 0.226569 0.0607090i
\(598\) −0.0525589 + 0.196152i −0.00214929 + 0.00802127i
\(599\) −15.3397 + 8.85641i −0.626765 + 0.361863i −0.779498 0.626405i \(-0.784526\pi\)
0.152733 + 0.988267i \(0.451193\pi\)
\(600\) −1.96410 4.59808i −0.0801841 0.187716i
\(601\) 41.1769i 1.67964i 0.542864 + 0.839821i \(0.317340\pi\)
−0.542864 + 0.839821i \(0.682660\pi\)
\(602\) 0 0
\(603\) 21.3923 21.3923i 0.871162 0.871162i
\(604\) 20.7846 + 12.0000i 0.845714 + 0.488273i
\(605\) 6.59808 + 4.35641i 0.268250 + 0.177113i
\(606\) 1.10770 + 1.91858i 0.0449970 + 0.0779372i
\(607\) −3.40192 12.6962i −0.138080 0.515321i −0.999966 0.00821951i \(-0.997384\pi\)
0.861886 0.507101i \(-0.169283\pi\)
\(608\) 2.66025 + 2.66025i 0.107888 + 0.107888i
\(609\) 0 0
\(610\) 0.562178 1.68653i 0.0227619 0.0682857i
\(611\) 12.9282 22.3923i 0.523019 0.905896i
\(612\) 17.6603 + 4.73205i 0.713873 + 0.191282i
\(613\) 24.3923 + 6.53590i 0.985196 + 0.263982i 0.715231 0.698888i \(-0.246321\pi\)
0.269965 + 0.962870i \(0.412988\pi\)
\(614\) −2.30385 + 3.99038i −0.0929757 + 0.161039i
\(615\) −2.36603 + 7.09808i −0.0954074 + 0.286222i
\(616\) 0 0
\(617\) 33.9090 + 33.9090i 1.36512 + 1.36512i 0.867249 + 0.497874i \(0.165886\pi\)
0.497874 + 0.867249i \(0.334114\pi\)
\(618\) 0.330127 + 1.23205i 0.0132797 + 0.0495604i
\(619\) −5.09808 8.83013i −0.204909 0.354913i 0.745195 0.666847i \(-0.232357\pi\)
−0.950104 + 0.311934i \(0.899023\pi\)
\(620\) −24.1244 15.9282i −0.968857 0.639692i
\(621\) 0.356406 + 0.205771i 0.0143021 + 0.00825732i
\(622\) 5.58846 5.58846i 0.224077 0.224077i
\(623\) 0 0
\(624\) 3.60770i 0.144423i
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 2.41154 1.39230i 0.0963846 0.0556477i
\(627\) −0.267949 + 1.00000i −0.0107009 + 0.0399362i
\(628\) −8.02628 + 2.15064i −0.320283 + 0.0858197i
\(629\) 18.9282 0.754717
\(630\) 0 0
\(631\) −4.58846 −0.182664 −0.0913318 0.995821i \(-0.529112\pi\)
−0.0913318 + 0.995821i \(0.529112\pi\)
\(632\) −6.09808 + 1.63397i −0.242568 + 0.0649960i
\(633\) −0.0262794 + 0.0980762i −0.00104451 + 0.00389818i
\(634\) 4.26795 2.46410i 0.169502 0.0978620i
\(635\) −1.09808 + 0.973721i −0.0435758 + 0.0386409i
\(636\) 6.33975i 0.251387i
\(637\) 0 0
\(638\) 3.00000 3.00000i 0.118771 0.118771i
\(639\) 3.00000 + 1.73205i 0.118678 + 0.0685189i
\(640\) −25.0885 + 5.13397i −0.991708 + 0.202938i
\(641\) −5.33013 9.23205i −0.210527 0.364644i 0.741352 0.671116i \(-0.234185\pi\)
−0.951880 + 0.306472i \(0.900851\pi\)
\(642\) −0.911543 3.40192i −0.0359757 0.134263i
\(643\) −17.5359 17.5359i −0.691548 0.691548i 0.271024 0.962573i \(-0.412638\pi\)
−0.962573 + 0.271024i \(0.912638\pi\)
\(644\) 0 0
\(645\) 4.14359 2.07180i 0.163154 0.0815769i
\(646\) 0.732051 1.26795i 0.0288022 0.0498868i
\(647\) −39.5526 10.5981i −1.55497 0.416653i −0.623904 0.781501i \(-0.714454\pi\)
−0.931067 + 0.364847i \(0.881121\pi\)
\(648\) −12.4282 3.33013i −0.488226 0.130820i
\(649\) −11.1962 + 19.3923i −0.439487 + 0.761215i
\(650\) −5.85641 4.39230i −0.229707 0.172280i
\(651\) 0 0
\(652\) 17.1962 + 17.1962i 0.673453 + 0.673453i
\(653\) −5.26795 19.6603i −0.206151 0.769365i −0.989096 0.147274i \(-0.952950\pi\)
0.782945 0.622091i \(-0.213717\pi\)
\(654\) 1.35641 + 2.34936i 0.0530397 + 0.0918674i
\(655\) −19.0526 + 28.8564i −0.744445 + 1.12751i
\(656\) 13.7942 + 7.96410i 0.538574 + 0.310946i
\(657\) 25.8564 25.8564i 1.00875 1.00875i
\(658\) 0 0
\(659\) 27.6603i 1.07749i −0.842469 0.538745i \(-0.818899\pi\)
0.842469 0.538745i \(-0.181101\pi\)
\(660\) −3.63397 4.09808i −0.141452 0.159517i
\(661\) 41.7224 24.0885i 1.62281 0.936932i 0.636652 0.771151i \(-0.280319\pi\)
0.986163 0.165781i \(-0.0530145\pi\)
\(662\) 0.248711 0.928203i 0.00966644 0.0360756i
\(663\) −5.46410 + 1.46410i −0.212208 + 0.0568610i
\(664\) −5.73205 −0.222447
\(665\) 0 0
\(666\) −6.92820 −0.268462
\(667\) 0.401924 0.107695i 0.0155626 0.00416997i
\(668\) 7.45448 27.8205i 0.288423 1.07641i
\(669\) −11.4904 + 6.63397i −0.444244 + 0.256484i
\(670\) 12.7942 + 0.767949i 0.494284 + 0.0296685i
\(671\) 4.19615i 0.161991i
\(672\) 0 0
\(673\) 4.39230 4.39230i 0.169311 0.169311i −0.617366 0.786676i \(-0.711800\pi\)
0.786676 + 0.617366i \(0.211800\pi\)
\(674\) 6.04552 + 3.49038i 0.232865 + 0.134444i
\(675\) −11.6699 + 9.16025i −0.449174 + 0.352578i
\(676\) 4.33013 + 7.50000i 0.166543 + 0.288462i
\(677\) 6.92820 + 25.8564i 0.266272 + 0.993742i 0.961467 + 0.274921i \(0.0886516\pi\)
−0.695194 + 0.718822i \(0.744682\pi\)
\(678\) 2.07180 + 2.07180i 0.0795669 + 0.0795669i
\(679\) 0 0
\(680\) 7.46410 + 14.9282i 0.286235 + 0.572470i
\(681\) 5.09808 8.83013i 0.195359 0.338371i
\(682\) 10.1962 + 2.73205i 0.390431 + 0.104616i
\(683\) 17.0622 + 4.57180i 0.652866 + 0.174935i 0.570024 0.821628i \(-0.306934\pi\)
0.0828417 + 0.996563i \(0.473600\pi\)
\(684\) 1.73205 3.00000i 0.0662266 0.114708i
\(685\) −28.9808 9.66025i −1.10730 0.369099i
\(686\) 0 0
\(687\) −6.73205 6.73205i −0.256844 0.256844i
\(688\) −2.55256 9.52628i −0.0973154 0.363186i
\(689\) 10.0000 + 17.3205i 0.380970 + 0.659859i
\(690\) 0.0166605 + 0.0814157i 0.000634254 + 0.00309944i
\(691\) 44.0263 + 25.4186i 1.67484 + 0.966969i 0.964867 + 0.262738i \(0.0846255\pi\)
0.709971 + 0.704231i \(0.248708\pi\)
\(692\) 25.2679 25.2679i 0.960543 0.960543i
\(693\) 0 0
\(694\) 15.5885i 0.591730i
\(695\) −0.758330 + 12.6340i −0.0287651 + 0.479234i
\(696\) 2.59808 1.50000i 0.0984798 0.0568574i
\(697\) 6.46410 24.1244i 0.244845 0.913775i
\(698\) −3.13397 + 0.839746i −0.118623 + 0.0317849i
\(699\) −3.46410 −0.131024
\(700\) 0 0
\(701\) −20.2679 −0.765510 −0.382755 0.923850i \(-0.625025\pi\)
−0.382755 + 0.923850i \(0.625025\pi\)
\(702\) 4.19615 1.12436i 0.158374 0.0424361i
\(703\) 0.928203 3.46410i 0.0350078 0.130651i
\(704\) −5.36603 + 3.09808i −0.202240 + 0.116763i
\(705\) 0.633975 10.5622i 0.0238769 0.397795i
\(706\) 7.26795i 0.273533i
\(707\) 0 0
\(708\) −5.19615 + 5.19615i −0.195283 + 0.195283i
\(709\) 18.9904 + 10.9641i 0.713199 + 0.411765i 0.812244 0.583317i \(-0.198246\pi\)
−0.0990456 + 0.995083i \(0.531579\pi\)
\(710\) 0.294229 + 1.43782i 0.0110422 + 0.0539605i
\(711\) 4.46410 + 7.73205i 0.167417 + 0.289975i
\(712\) 0.330127 + 1.23205i 0.0123720 + 0.0461731i
\(713\) 0.732051 + 0.732051i 0.0274155 + 0.0274155i
\(714\) 0 0
\(715\) −16.3923 5.46410i −0.613037 0.204346i
\(716\) −6.80385 + 11.7846i −0.254272 + 0.440412i
\(717\) 1.19615 + 0.320508i 0.0446711 + 0.0119696i
\(718\) 17.1244 + 4.58846i 0.639075 + 0.171240i
\(719\) −19.2942 + 33.4186i −0.719553 + 1.24630i 0.241624 + 0.970370i \(0.422320\pi\)
−0.961177 + 0.275933i \(0.911013\pi\)
\(720\) 6.73205 + 13.4641i 0.250889 + 0.501777i
\(721\) 0 0
\(722\) 6.75833 + 6.75833i 0.251519 + 0.251519i
\(723\) 3.32051 + 12.3923i 0.123491 + 0.460875i
\(724\) −1.03590 1.79423i −0.0384989 0.0666820i
\(725\) −1.79423 + 14.8923i −0.0666360 + 0.553086i
\(726\) −0.820508 0.473721i −0.0304519 0.0175814i
\(727\) 10.0981 10.0981i 0.374517 0.374517i −0.494602 0.869119i \(-0.664686\pi\)
0.869119 + 0.494602i \(0.164686\pi\)
\(728\) 0 0
\(729\) 13.5885i 0.503276i
\(730\) 15.4641 + 0.928203i 0.572352 + 0.0343543i
\(731\) −13.3923 + 7.73205i −0.495332 + 0.285980i
\(732\) 0.356406 1.33013i 0.0131732 0.0491629i
\(733\) 4.36603 1.16987i 0.161263 0.0432102i −0.177284 0.984160i \(-0.556731\pi\)
0.338547 + 0.940949i \(0.390065\pi\)
\(734\) −0.267949 −0.00989019
\(735\) 0 0
\(736\) 0.712813 0.0262746
\(737\) 29.2224 7.83013i 1.07642 0.288426i
\(738\) −2.36603 + 8.83013i −0.0870946 + 0.325041i
\(739\) −19.5622 + 11.2942i −0.719606 + 0.415465i −0.814608 0.580012i \(-0.803048\pi\)
0.0950014 + 0.995477i \(0.469714\pi\)
\(740\) 12.5885 + 14.1962i 0.462761 + 0.521861i
\(741\) 1.07180i 0.0393734i
\(742\) 0 0
\(743\) −6.16987 + 6.16987i −0.226351 + 0.226351i −0.811166 0.584816i \(-0.801167\pi\)
0.584816 + 0.811166i \(0.301167\pi\)
\(744\) 6.46410 + 3.73205i 0.236985 + 0.136824i
\(745\) −0.990381 + 1.50000i −0.0362848 + 0.0549557i
\(746\) 2.07180 + 3.58846i 0.0758539 + 0.131383i
\(747\) 2.09808 + 7.83013i 0.0767646 + 0.286489i
\(748\) 12.9282 + 12.9282i 0.472702 + 0.472702i
\(749\) 0 0
\(750\) −2.94744 0.535898i −0.107625 0.0195682i
\(751\) 3.19615 5.53590i 0.116629 0.202008i −0.801801 0.597592i \(-0.796124\pi\)
0.918430 + 0.395584i \(0.129458\pi\)
\(752\) −21.7583 5.83013i −0.793445 0.212603i
\(753\) −10.9282 2.92820i −0.398246 0.106710i
\(754\) 2.19615 3.80385i 0.0799792 0.138528i
\(755\) 27.7128 13.8564i 1.00857 0.504286i
\(756\) 0 0
\(757\) 12.7321 + 12.7321i 0.462754 + 0.462754i 0.899557 0.436803i \(-0.143889\pi\)
−0.436803 + 0.899557i \(0.643889\pi\)
\(758\) 0.313467 + 1.16987i 0.0113856 + 0.0424917i
\(759\) 0.0980762 + 0.169873i 0.00355994 + 0.00616600i
\(760\) 3.09808 0.633975i 0.112379 0.0229967i
\(761\) −24.9282 14.3923i −0.903647 0.521721i −0.0252651 0.999681i \(-0.508043\pi\)
−0.878382 + 0.477960i \(0.841376\pi\)
\(762\) 0.124356 0.124356i 0.00450493 0.00450493i
\(763\) 0 0
\(764\) 22.9808i 0.831415i
\(765\) 17.6603 15.6603i 0.638508 0.566198i
\(766\) −14.1795 + 8.18653i −0.512326 + 0.295791i
\(767\) −6.00000 + 22.3923i −0.216647 + 0.808539i
\(768\) 0.696152 0.186533i 0.0251202 0.00673095i
\(769\) −15.1769 −0.547294 −0.273647 0.961830i \(-0.588230\pi\)
−0.273647 + 0.961830i \(0.588230\pi\)
\(770\) 0 0
\(771\) 1.46410 0.0527283
\(772\) 13.5622 3.63397i 0.488113 0.130790i
\(773\) −4.07180 + 15.1962i −0.146452 + 0.546568i 0.853234 + 0.521528i \(0.174638\pi\)
−0.999686 + 0.0250395i \(0.992029\pi\)
\(774\) 4.90192 2.83013i 0.176196 0.101727i
\(775\) −34.3205 + 14.6603i −1.23283 + 0.526612i
\(776\) 16.1962i 0.581408i
\(777\) 0 0
\(778\) −1.80385 + 1.80385i −0.0646711 + 0.0646711i
\(779\) −4.09808 2.36603i −0.146829 0.0847717i
\(780\) −4.73205 3.12436i −0.169435 0.111870i
\(781\) 1.73205 + 3.00000i 0.0619777 + 0.107348i
\(782\) −0.0717968 0.267949i −0.00256745 0.00958184i
\(783\) −6.29423 6.29423i −0.224937 0.224937i
\(784\) 0 0
\(785\) −3.39230 + 10.1769i −0.121077 + 0.363230i
\(786\) 2.07180 3.58846i 0.0738985 0.127996i
\(787\) −31.1865 8.35641i −1.11168 0.297874i −0.344168 0.938908i \(-0.611839\pi\)
−0.767512 + 0.641034i \(0.778506\pi\)
\(788\) 23.9545 + 6.41858i 0.853343 + 0.228653i
\(789\) −4.06218 + 7.03590i −0.144617 + 0.250485i
\(790\) −1.19615 + 3.58846i −0.0425572 + 0.127672i
\(791\) 0 0
\(792\) −10.1962 10.1962i −0.362305 0.362305i
\(793\) −1.12436 4.19615i −0.0399270 0.149010i
\(794\) 0.973721 + 1.68653i 0.0345560 + 0.0598528i
\(795\) 6.83013 + 4.50962i 0.242240 + 0.159940i
\(796\) −16.6077 9.58846i −0.588644 0.339854i
\(797\) −22.5359 + 22.5359i −0.798262 + 0.798262i −0.982821 0.184559i \(-0.940914\pi\)
0.184559 + 0.982821i \(0.440914\pi\)
\(798\) 0 0
\(799\) 35.3205i 1.24955i
\(800\) −9.57180 + 23.8468i −0.338414 + 0.843111i
\(801\) 1.56218 0.901924i 0.0551968 0.0318679i
\(802\) −1.47372 + 5.50000i −0.0520389 + 0.194212i
\(803\) 35.3205 9.46410i 1.24643 0.333981i
\(804\) 9.92820 0.350141
\(805\) 0 0
\(806\) 10.9282 0.384930
\(807\) −11.4282 + 3.06218i −0.402292 + 0.107794i
\(808\) 4.13397 15.4282i 0.145433 0.542762i
\(809\) −3.99038 + 2.30385i −0.140294 + 0.0809990i −0.568504 0.822680i \(-0.692478\pi\)
0.428210 + 0.903679i \(0.359144\pi\)
\(810\) −5.76795 + 5.11474i −0.202665 + 0.179714i
\(811\) 42.9282i 1.50741i −0.657211 0.753707i \(-0.728264\pi\)
0.657211 0.753707i \(-0.271736\pi\)
\(812\) 0 0
\(813\) −7.78461 + 7.78461i −0.273018 + 0.273018i
\(814\) −6.00000 3.46410i −0.210300 0.121417i
\(815\) 30.7583 6.29423i 1.07742 0.220477i
\(816\) 2.46410 + 4.26795i 0.0862608 + 0.149408i
\(817\) 0.758330 + 2.83013i 0.0265306 + 0.0990136i
\(818\) 7.63397 + 7.63397i 0.266916 + 0.266916i
\(819\) 0 0
\(820\) 22.3923 11.1962i 0.781973 0.390987i
\(821\) 24.6603 42.7128i 0.860649 1.49069i −0.0106549 0.999943i \(-0.503392\pi\)
0.871304 0.490744i \(-0.163275\pi\)
\(822\) 3.53590 + 0.947441i 0.123329 + 0.0330458i
\(823\) −53.3827 14.3038i −1.86080 0.498601i −0.860856 0.508849i \(-0.830071\pi\)
−0.999947 + 0.0102479i \(0.996738\pi\)
\(824\) 4.59808 7.96410i 0.160182 0.277443i
\(825\) −7.00000 + 1.00000i −0.243709 + 0.0348155i
\(826\) 0 0
\(827\) −33.2224 33.2224i −1.15526 1.15526i −0.985483 0.169774i \(-0.945696\pi\)
−0.169774 0.985483i \(-0.554304\pi\)
\(828\) −0.169873 0.633975i −0.00590349 0.0220321i
\(829\) 7.26795 + 12.5885i 0.252426 + 0.437215i 0.964193 0.265200i \(-0.0854381\pi\)
−0.711767 + 0.702416i \(0.752105\pi\)
\(830\) −1.89230 + 2.86603i −0.0656829 + 0.0994812i
\(831\) 2.41154 + 1.39230i 0.0836555 + 0.0482985i
\(832\) −4.53590 + 4.53590i −0.157254 + 0.157254i
\(833\) 0 0
\(834\) 1.51666i 0.0525177i
\(835\) −24.6699 27.8205i −0.853736 0.962768i
\(836\) 3.00000 1.73205i 0.103757 0.0599042i
\(837\) 5.73205 21.3923i 0.198129 0.739426i
\(838\) −11.9282 + 3.19615i −0.412053 + 0.110409i
\(839\) −6.87564 −0.237374 −0.118687 0.992932i \(-0.537868\pi\)
−0.118687 + 0.992932i \(0.537868\pi\)
\(840\) 0 0
\(841\) 20.0000 0.689655
\(842\) −8.66987 + 2.32309i −0.298784 + 0.0800588i
\(843\) −0.124356 + 0.464102i −0.00428304 + 0.0159845i
\(844\) 0.294229 0.169873i 0.0101278 0.00584727i
\(845\) 11.1603 + 0.669873i 0.383924 + 0.0230443i
\(846\) 12.9282i 0.444481i
\(847\) 0 0
\(848\) 12.3205 12.3205i 0.423088 0.423088i
\(849\) −0.882686 0.509619i −0.0302937 0.0174901i
\(850\) 9.92820 + 1.19615i 0.340535 + 0.0410277i
\(851\) −0.339746 0.588457i −0.0116463 0.0201721i
\(852\) 0.294229 + 1.09808i 0.0100801 + 0.0376195i
\(853\) 18.1244 + 18.1244i 0.620566 + 0.620566i 0.945676 0.325110i \(-0.105401\pi\)
−0.325110 + 0.945676i \(0.605401\pi\)
\(854\) 0 0
\(855\) −2.00000 4.00000i −0.0683986 0.136797i
\(856\) −12.6962 + 21.9904i −0.433946 + 0.751616i
\(857\) 11.0981 + 2.97372i 0.379103 + 0.101580i 0.443338 0.896354i \(-0.353794\pi\)
−0.0642351 + 0.997935i \(0.520461\pi\)
\(858\) 2.00000 + 0.535898i 0.0682789 + 0.0182953i
\(859\) 17.4641 30.2487i 0.595867 1.03207i −0.397556 0.917578i \(-0.630142\pi\)
0.993424 0.114495i \(-0.0365250\pi\)
\(860\) −14.7058 4.90192i −0.501463 0.167154i
\(861\) 0 0
\(862\) −2.26795 2.26795i −0.0772467 0.0772467i
\(863\) 13.3827 + 49.9449i 0.455552 + 1.70014i 0.686460 + 0.727167i \(0.259164\pi\)
−0.230908 + 0.972976i \(0.574170\pi\)
\(864\) −7.62436 13.2058i −0.259386 0.449269i
\(865\) −9.24871 45.1962i −0.314466 1.53672i
\(866\) 11.1173 + 6.41858i 0.377782 + 0.218112i
\(867\) −0.758330 + 0.758330i −0.0257542 + 0.0257542i
\(868\) 0 0
\(869\) 8.92820i 0.302869i
\(870\) 0.107695 1.79423i 0.00365121 0.0608300i
\(871\) 27.1244 15.6603i 0.919074 0.530627i
\(872\) 5.06218 18.8923i 0.171427 0.639774i
\(873\) 22.1244 5.92820i 0.748796 0.200639i
\(874\) −0.0525589 −0.00177783
\(875\) 0 0
\(876\) 12.0000 0.405442
\(877\) −39.1506 + 10.4904i −1.32202 + 0.354235i −0.849735 0.527209i \(-0.823238\pi\)
−0.472288 + 0.881444i \(0.656572\pi\)
\(878\) −0.444864 + 1.66025i −0.0150134 + 0.0560309i
\(879\) 1.51666 0.875644i 0.0511557 0.0295348i
\(880\) −0.901924 + 15.0263i −0.0304038 + 0.506536i
\(881\) 25.1436i 0.847109i −0.905871 0.423555i \(-0.860782\pi\)
0.905871 0.423555i \(-0.139218\pi\)
\(882\) 0 0
\(883\) 8.07180 8.07180i 0.271638 0.271638i −0.558122 0.829759i \(-0.688478\pi\)
0.829759 + 0.558122i \(0.188478\pi\)
\(884\) 16.3923 + 9.46410i 0.551333 + 0.318312i
\(885\) 1.90192 + 9.29423i 0.0639325 + 0.312422i
\(886\) −3.50000 6.06218i −0.117585 0.203663i
\(887\) −2.91858 10.8923i −0.0979965 0.365728i 0.899460 0.437003i \(-0.143960\pi\)
−0.997457 + 0.0712748i \(0.977293\pi\)
\(888\) −3.46410 3.46410i −0.116248 0.116248i
\(889\) 0 0
\(890\) 0.725009 + 0.241670i 0.0243024 + 0.00810079i
\(891\) −9.09808 + 15.7583i −0.304797 + 0.527924i
\(892\) 42.8827 + 11.4904i 1.43582 + 0.384726i
\(893\) 6.46410 + 1.73205i 0.216313 + 0.0579609i
\(894\) 0.107695 0.186533i 0.00360186 0.00623861i
\(895\) 7.85641 + 15.7128i 0.262611 + 0.525221i
\(896\) 0 0
\(897\) 0.143594 + 0.143594i 0.00479445 + 0.00479445i
\(898\) −4.42820 16.5263i −0.147771 0.551489i
\(899\) −11.1962 19.3923i −0.373413 0.646770i
\(900\) 23.4904 + 2.83013i 0.783013 + 0.0943376i
\(901\) −23.6603 13.6603i −0.788237 0.455089i
\(902\) −6.46410 + 6.46410i −0.215231 + 0.215231i
\(903\) 0 0
\(904\) 21.1244i 0.702586i
\(905\) −2.66987 0.160254i −0.0887496 0.00532702i
\(906\) −3.21539 + 1.85641i −0.106824 + 0.0616750i
\(907\) −8.69615 + 32.4545i −0.288751 + 1.07763i 0.657304 + 0.753626i \(0.271697\pi\)
−0.946055 + 0.324007i \(0.894970\pi\)
\(908\) −32.9545 + 8.83013i −1.09363 + 0.293038i
\(909\) −22.5885 −0.749212
\(910\) 0 0
\(911\) −7.51666 −0.249038 −0.124519 0.992217i \(-0.539739\pi\)
−0.124519 + 0.992217i \(0.539739\pi\)
\(912\) 0.901924 0.241670i 0.0298657 0.00800249i
\(913\) −2.09808 + 7.83013i −0.0694362 + 0.259139i
\(914\) −5.44486 + 3.14359i −0.180100 + 0.103981i
\(915\) −1.17949 1.33013i −0.0389928 0.0439726i
\(916\) 31.8564i 1.05257i
\(917\) 0 0
\(918\) −4.19615 + 4.19615i −0.138494 + 0.138494i
\(919\) −48.6673 28.0981i −1.60539 0.926870i −0.990384 0.138344i \(-0.955822\pi\)
−0.615002 0.788526i \(-0.710845\pi\)
\(920\) 0.330127 0.500000i 0.0108840 0.0164845i
\(921\) 2.30385 + 3.99038i 0.0759144 + 0.131488i
\(922\) 0.751289 + 2.80385i 0.0247424 + 0.0923398i
\(923\) 2.53590 + 2.53590i 0.0834701 + 0.0834701i
\(924\) 0 0
\(925\) 24.2487 3.46410i 0.797293 0.113899i
\(926\) −1.74167 + 3.01666i −0.0572348 + 0.0991336i
\(927\) −12.5622 3.36603i −0.412596 0.110555i
\(928\) −14.8923 3.99038i −0.488864 0.130991i
\(929\) 18.1603 31.4545i 0.595819 1.03199i −0.397612 0.917554i \(-0.630161\pi\)
0.993431 0.114435i \(-0.0365056\pi\)
\(930\) 4.00000 2.00000i 0.131165 0.0655826i
\(931\) 0 0
\(932\) 8.19615 + 8.19615i 0.268474 + 0.268474i
\(933\) −2.04552 7.63397i −0.0669672 0.249925i
\(934\) −3.64359 6.31089i −0.119222 0.206499i
\(935\) 23.1244 4.73205i 0.756247 0.154755i
\(936\) −12.9282 7.46410i −0.422572 0.243972i
\(937\) −17.0718 + 17.0718i −0.557711 + 0.557711i −0.928655 0.370944i \(-0.879034\pi\)
0.370944 + 0.928655i \(0.379034\pi\)
\(938\) 0 0
\(939\) 2.78461i 0.0908723i
\(940\) −26.4904 + 23.4904i −0.864021 + 0.766172i
\(941\) −35.1962 + 20.3205i −1.14736 + 0.662430i −0.948243 0.317546i \(-0.897141\pi\)
−0.199119 + 0.979975i \(0.563808\pi\)
\(942\) 0.332704 1.24167i 0.0108401 0.0404558i
\(943\) −0.866025 + 0.232051i −0.0282017 + 0.00755661i
\(944\) 20.1962 0.657329
\(945\) 0 0
\(946\) 5.66025 0.184031
\(947\) −1.30385 + 0.349365i −0.0423694 + 0.0113528i −0.279941 0.960017i \(-0.590315\pi\)
0.237572 + 0.971370i \(0.423648\pi\)
\(948\) −0.758330 + 2.83013i −0.0246294 + 0.0919183i
\(949\) 32.7846 18.9282i 1.06423 0.614435i
\(950\) 0.705771 1.75833i 0.0228982 0.0570478i
\(951\) 4.92820i 0.159808i
\(952\) 0 0
\(953\) −37.8564 + 37.8564i −1.22629 + 1.22629i −0.260932 + 0.965357i \(0.584030\pi\)
−0.965357 + 0.260932i \(0.915970\pi\)
\(954\) 8.66025 + 5.00000i 0.280386 + 0.161881i
\(955\) −24.7583 16.3468i −0.801161 0.528970i
\(956\) −2.07180 3.58846i −0.0670067 0.116059i
\(957\) −1.09808 4.09808i −0.0354958 0.132472i
\(958\) −4.78461 4.78461i −0.154584 0.154584i
\(959\) 0 0
\(960\) −0.830127 + 2.49038i −0.0267922 + 0.0803767i
\(961\) 12.3564 21.4019i 0.398594 0.690385i
\(962\) −6.92820 1.85641i −0.223374 0.0598529i
\(963\) 34.6865 + 9.29423i 1.11776 + 0.299502i
\(964\) 21.4641 37.1769i 0.691312 1.19739i
\(965\) 5.73205 17.1962i 0.184521 0.553564i
\(966\) 0 0
\(967\) −13.5622 13.5622i −0.436130 0.436130i 0.454577 0.890707i \(-0.349790\pi\)
−0.890707 + 0.454577i \(0.849790\pi\)
\(968\) 1.76795 + 6.59808i 0.0568240 + 0.212070i
\(969\) −0.732051 1.26795i −0.0235169 0.0407324i
\(970\) 8.09808 + 5.34679i 0.260014 + 0.171675i
\(971\) −29.0718 16.7846i −0.932958 0.538644i −0.0452124 0.998977i \(-0.514396\pi\)
−0.887746 + 0.460334i \(0.847730\pi\)
\(972\) −15.1244 + 15.1244i −0.485114 + 0.485114i
\(973\) 0 0
\(974\) 14.5885i 0.467444i
\(975\) −6.73205 + 2.87564i −0.215598 + 0.0920943i
\(976\) −3.27757 + 1.89230i −0.104912 + 0.0605712i
\(977\) −0.150635 + 0.562178i −0.00481924 + 0.0179857i −0.968294 0.249815i \(-0.919630\pi\)
0.963474 + 0.267801i \(0.0862969\pi\)
\(978\) −3.63397 + 0.973721i −0.116202 + 0.0311362i
\(979\) 1.80385 0.0576512
\(980\) 0 0
\(981\) −27.6603 −0.883124
\(982\) 18.8564 5.05256i 0.601732 0.161234i
\(983\) −14.5000 + 54.1147i −0.462478 + 1.72599i 0.202639 + 0.979253i \(0.435048\pi\)
−0.665118 + 0.746739i \(0.731619\pi\)
\(984\) −5.59808 + 3.23205i −0.178460 + 0.103034i
\(985\) 23.9545 21.2417i 0.763253 0.676816i
\(986\) 6.00000i 0.191079i
\(987\) 0 0
\(988\) 2.53590 2.53590i 0.0806777 0.0806777i
\(989\) 0.480762 + 0.277568i 0.0152873 + 0.00882615i
\(990\) −8.46410 + 1.73205i −0.269007 + 0.0550482i
\(991\) −15.8564 27.4641i −0.503695 0.872426i −0.999991 0.00427229i \(-0.998640\pi\)
0.496296 0.868154i \(-0.334693\pi\)
\(992\) −9.92820 37.0526i −0.315221 1.17642i
\(993\) −0.679492 0.679492i −0.0215630 0.0215630i
\(994\) 0 0
\(995\) −22.1436 + 11.0718i −0.701999 + 0.351000i
\(996\) −1.33013 + 2.30385i −0.0421467 + 0.0730002i
\(997\) 39.8827 + 10.6865i 1.26310 + 0.338446i 0.827382 0.561639i \(-0.189829\pi\)
0.435715 + 0.900085i \(0.356496\pi\)
\(998\) −5.75833 1.54294i −0.182277 0.0488409i
\(999\) −7.26795 + 12.5885i −0.229948 + 0.398281i
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 245.2.l.b.117.1 4
5.3 odd 4 245.2.l.a.68.1 4
7.2 even 3 245.2.f.a.97.1 4
7.3 odd 6 245.2.l.a.227.1 4
7.4 even 3 35.2.k.a.17.1 4
7.5 odd 6 245.2.f.b.97.1 4
7.6 odd 2 35.2.k.b.12.1 yes 4
21.11 odd 6 315.2.bz.b.262.1 4
21.20 even 2 315.2.bz.a.82.1 4
28.11 odd 6 560.2.ci.a.17.1 4
28.27 even 2 560.2.ci.b.257.1 4
35.3 even 12 inner 245.2.l.b.178.1 4
35.4 even 6 175.2.o.b.157.1 4
35.13 even 4 35.2.k.a.33.1 yes 4
35.18 odd 12 35.2.k.b.3.1 yes 4
35.23 odd 12 245.2.f.b.48.1 4
35.27 even 4 175.2.o.b.68.1 4
35.32 odd 12 175.2.o.a.143.1 4
35.33 even 12 245.2.f.a.48.1 4
35.34 odd 2 175.2.o.a.82.1 4
105.53 even 12 315.2.bz.a.73.1 4
105.83 odd 4 315.2.bz.b.208.1 4
140.83 odd 4 560.2.ci.a.33.1 4
140.123 even 12 560.2.ci.b.353.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.k.a.17.1 4 7.4 even 3
35.2.k.a.33.1 yes 4 35.13 even 4
35.2.k.b.3.1 yes 4 35.18 odd 12
35.2.k.b.12.1 yes 4 7.6 odd 2
175.2.o.a.82.1 4 35.34 odd 2
175.2.o.a.143.1 4 35.32 odd 12
175.2.o.b.68.1 4 35.27 even 4
175.2.o.b.157.1 4 35.4 even 6
245.2.f.a.48.1 4 35.33 even 12
245.2.f.a.97.1 4 7.2 even 3
245.2.f.b.48.1 4 35.23 odd 12
245.2.f.b.97.1 4 7.5 odd 6
245.2.l.a.68.1 4 5.3 odd 4
245.2.l.a.227.1 4 7.3 odd 6
245.2.l.b.117.1 4 1.1 even 1 trivial
245.2.l.b.178.1 4 35.3 even 12 inner
315.2.bz.a.73.1 4 105.53 even 12
315.2.bz.a.82.1 4 21.20 even 2
315.2.bz.b.208.1 4 105.83 odd 4
315.2.bz.b.262.1 4 21.11 odd 6
560.2.ci.a.17.1 4 28.11 odd 6
560.2.ci.a.33.1 4 140.83 odd 4
560.2.ci.b.257.1 4 28.27 even 2
560.2.ci.b.353.1 4 140.123 even 12