Properties

Label 1690.2.l.g.361.1
Level $1690$
Weight $2$
Character 1690.361
Analytic conductor $13.495$
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] = [1690,2,Mod(361,1690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1690, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1690.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1690.l (of order \(6\), degree \(2\), 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: \(13.4947179416\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
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 130)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1690.361
Dual form 1690.2.l.g.1161.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(1.36603 + 2.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-2.36603 - 1.36603i) q^{6} +(2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(1.36603 + 2.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-2.36603 - 1.36603i) q^{6} +(2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(-2.23205 + 3.86603i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.59808 - 1.50000i) q^{11} +2.73205 q^{12} -3.00000 q^{14} +(-2.36603 + 1.36603i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.09808 - 1.90192i) q^{17} -4.46410i q^{18} +(5.59808 + 3.23205i) q^{19} +(0.866025 + 0.500000i) q^{20} +8.19615i q^{21} +(-1.50000 + 2.59808i) q^{22} +(-1.26795 - 2.19615i) q^{23} +(-2.36603 + 1.36603i) q^{24} -1.00000 q^{25} -4.00000 q^{27} +(2.59808 - 1.50000i) q^{28} +(4.73205 + 8.19615i) q^{29} +(1.36603 - 2.36603i) q^{30} -1.26795i q^{31} +(0.866025 + 0.500000i) q^{32} +(7.09808 + 4.09808i) q^{33} +2.19615i q^{34} +(-1.50000 + 2.59808i) q^{35} +(2.23205 + 3.86603i) q^{36} +(-9.69615 + 5.59808i) q^{37} -6.46410 q^{38} -1.00000 q^{40} +(9.00000 - 5.19615i) q^{41} +(-4.09808 - 7.09808i) q^{42} +(-1.00000 + 1.73205i) q^{43} -3.00000i q^{44} +(-3.86603 - 2.23205i) q^{45} +(2.19615 + 1.26795i) q^{46} -3.00000i q^{47} +(1.36603 - 2.36603i) q^{48} +(1.00000 + 1.73205i) q^{49} +(0.866025 - 0.500000i) q^{50} +6.00000 q^{51} -6.46410 q^{53} +(3.46410 - 2.00000i) q^{54} +(1.50000 + 2.59808i) q^{55} +(-1.50000 + 2.59808i) q^{56} +17.6603i q^{57} +(-8.19615 - 4.73205i) q^{58} +(-9.00000 - 5.19615i) q^{59} +2.73205i q^{60} +(2.09808 - 3.63397i) q^{61} +(0.633975 + 1.09808i) q^{62} +(-11.5981 + 6.69615i) q^{63} -1.00000 q^{64} -8.19615 q^{66} +(-1.09808 - 1.90192i) q^{68} +(3.46410 - 6.00000i) q^{69} -3.00000i q^{70} +(-5.19615 - 3.00000i) q^{71} +(-3.86603 - 2.23205i) q^{72} +5.66025i q^{73} +(5.59808 - 9.69615i) q^{74} +(-1.36603 - 2.36603i) q^{75} +(5.59808 - 3.23205i) q^{76} +9.00000 q^{77} +6.19615 q^{79} +(0.866025 - 0.500000i) q^{80} +(1.23205 + 2.13397i) q^{81} +(-5.19615 + 9.00000i) q^{82} -2.19615i q^{83} +(7.09808 + 4.09808i) q^{84} +(1.90192 + 1.09808i) q^{85} -2.00000i q^{86} +(-12.9282 + 22.3923i) q^{87} +(1.50000 + 2.59808i) q^{88} +(14.8923 - 8.59808i) q^{89} +4.46410 q^{90} -2.53590 q^{92} +(3.00000 - 1.73205i) q^{93} +(1.50000 + 2.59808i) q^{94} +(-3.23205 + 5.59808i) q^{95} +2.73205i q^{96} +(-13.0981 - 7.56218i) q^{97} +(-1.73205 - 1.00000i) q^{98} +13.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9} - 2 q^{10} + 4 q^{12} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{17} + 12 q^{19} - 6 q^{22} - 12 q^{23} - 6 q^{24} - 4 q^{25} - 16 q^{27} + 12 q^{29} + 2 q^{30} + 18 q^{33} - 6 q^{35} + 2 q^{36} - 18 q^{37} - 12 q^{38} - 4 q^{40} + 36 q^{41} - 6 q^{42} - 4 q^{43} - 12 q^{45} - 12 q^{46} + 2 q^{48} + 4 q^{49} + 24 q^{51} - 12 q^{53} + 6 q^{55} - 6 q^{56} - 12 q^{58} - 36 q^{59} - 2 q^{61} + 6 q^{62} - 36 q^{63} - 4 q^{64} - 12 q^{66} + 6 q^{68} - 12 q^{72} + 12 q^{74} - 2 q^{75} + 12 q^{76} + 36 q^{77} + 4 q^{79} - 2 q^{81} + 18 q^{84} + 18 q^{85} - 24 q^{87} + 6 q^{88} + 18 q^{89} + 4 q^{90} - 24 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} - 42 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 1.36603 + 2.36603i 0.788675 + 1.36603i 0.926779 + 0.375608i \(0.122566\pi\)
−0.138104 + 0.990418i \(0.544101\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) −2.36603 1.36603i −0.965926 0.557678i
\(7\) 2.59808 + 1.50000i 0.981981 + 0.566947i 0.902867 0.429919i \(-0.141458\pi\)
0.0791130 + 0.996866i \(0.474791\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.23205 + 3.86603i −0.744017 + 1.28868i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 2.59808 1.50000i 0.783349 0.452267i −0.0542666 0.998526i \(-0.517282\pi\)
0.837616 + 0.546259i \(0.183949\pi\)
\(12\) 2.73205 0.788675
\(13\) 0 0
\(14\) −3.00000 −0.801784
\(15\) −2.36603 + 1.36603i −0.610905 + 0.352706i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.09808 1.90192i 0.266323 0.461284i −0.701587 0.712584i \(-0.747525\pi\)
0.967909 + 0.251300i \(0.0808580\pi\)
\(18\) 4.46410i 1.05220i
\(19\) 5.59808 + 3.23205i 1.28429 + 0.741483i 0.977629 0.210337i \(-0.0674560\pi\)
0.306658 + 0.951820i \(0.400789\pi\)
\(20\) 0.866025 + 0.500000i 0.193649 + 0.111803i
\(21\) 8.19615i 1.78855i
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) −1.26795 2.19615i −0.264386 0.457929i 0.703017 0.711173i \(-0.251836\pi\)
−0.967402 + 0.253244i \(0.918503\pi\)
\(24\) −2.36603 + 1.36603i −0.482963 + 0.278839i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 2.59808 1.50000i 0.490990 0.283473i
\(29\) 4.73205 + 8.19615i 0.878720 + 1.52199i 0.852747 + 0.522325i \(0.174935\pi\)
0.0259731 + 0.999663i \(0.491732\pi\)
\(30\) 1.36603 2.36603i 0.249401 0.431975i
\(31\) 1.26795i 0.227730i −0.993496 0.113865i \(-0.963677\pi\)
0.993496 0.113865i \(-0.0363232\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 7.09808 + 4.09808i 1.23562 + 0.713384i
\(34\) 2.19615i 0.376637i
\(35\) −1.50000 + 2.59808i −0.253546 + 0.439155i
\(36\) 2.23205 + 3.86603i 0.372008 + 0.644338i
\(37\) −9.69615 + 5.59808i −1.59404 + 0.920318i −0.601433 + 0.798923i \(0.705403\pi\)
−0.992604 + 0.121395i \(0.961263\pi\)
\(38\) −6.46410 −1.04862
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 9.00000 5.19615i 1.40556 0.811503i 0.410608 0.911812i \(-0.365317\pi\)
0.994956 + 0.100309i \(0.0319833\pi\)
\(42\) −4.09808 7.09808i −0.632347 1.09526i
\(43\) −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i \(-0.882065\pi\)
0.779647 + 0.626219i \(0.215399\pi\)
\(44\) 3.00000i 0.452267i
\(45\) −3.86603 2.23205i −0.576313 0.332734i
\(46\) 2.19615 + 1.26795i 0.323805 + 0.186949i
\(47\) 3.00000i 0.437595i −0.975770 0.218797i \(-0.929787\pi\)
0.975770 0.218797i \(-0.0702134\pi\)
\(48\) 1.36603 2.36603i 0.197169 0.341506i
\(49\) 1.00000 + 1.73205i 0.142857 + 0.247436i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) 6.00000 0.840168
\(52\) 0 0
\(53\) −6.46410 −0.887913 −0.443956 0.896048i \(-0.646425\pi\)
−0.443956 + 0.896048i \(0.646425\pi\)
\(54\) 3.46410 2.00000i 0.471405 0.272166i
\(55\) 1.50000 + 2.59808i 0.202260 + 0.350325i
\(56\) −1.50000 + 2.59808i −0.200446 + 0.347183i
\(57\) 17.6603i 2.33916i
\(58\) −8.19615 4.73205i −1.07621 0.621349i
\(59\) −9.00000 5.19615i −1.17170 0.676481i −0.217620 0.976034i \(-0.569829\pi\)
−0.954080 + 0.299552i \(0.903163\pi\)
\(60\) 2.73205i 0.352706i
\(61\) 2.09808 3.63397i 0.268631 0.465283i −0.699877 0.714263i \(-0.746762\pi\)
0.968509 + 0.248980i \(0.0800954\pi\)
\(62\) 0.633975 + 1.09808i 0.0805149 + 0.139456i
\(63\) −11.5981 + 6.69615i −1.46122 + 0.843636i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −8.19615 −1.00888
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) −1.09808 1.90192i −0.133161 0.230642i
\(69\) 3.46410 6.00000i 0.417029 0.722315i
\(70\) 3.00000i 0.358569i
\(71\) −5.19615 3.00000i −0.616670 0.356034i 0.158901 0.987294i \(-0.449205\pi\)
−0.775571 + 0.631260i \(0.782538\pi\)
\(72\) −3.86603 2.23205i −0.455615 0.263050i
\(73\) 5.66025i 0.662483i 0.943546 + 0.331241i \(0.107467\pi\)
−0.943546 + 0.331241i \(0.892533\pi\)
\(74\) 5.59808 9.69615i 0.650763 1.12715i
\(75\) −1.36603 2.36603i −0.157735 0.273205i
\(76\) 5.59808 3.23205i 0.642143 0.370742i
\(77\) 9.00000 1.02565
\(78\) 0 0
\(79\) 6.19615 0.697122 0.348561 0.937286i \(-0.386670\pi\)
0.348561 + 0.937286i \(0.386670\pi\)
\(80\) 0.866025 0.500000i 0.0968246 0.0559017i
\(81\) 1.23205 + 2.13397i 0.136895 + 0.237108i
\(82\) −5.19615 + 9.00000i −0.573819 + 0.993884i
\(83\) 2.19615i 0.241059i −0.992710 0.120530i \(-0.961541\pi\)
0.992710 0.120530i \(-0.0384592\pi\)
\(84\) 7.09808 + 4.09808i 0.774464 + 0.447137i
\(85\) 1.90192 + 1.09808i 0.206293 + 0.119103i
\(86\) 2.00000i 0.215666i
\(87\) −12.9282 + 22.3923i −1.38605 + 2.40071i
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 14.8923 8.59808i 1.57858 0.911394i 0.583523 0.812096i \(-0.301674\pi\)
0.995058 0.0992979i \(-0.0316597\pi\)
\(90\) 4.46410 0.470558
\(91\) 0 0
\(92\) −2.53590 −0.264386
\(93\) 3.00000 1.73205i 0.311086 0.179605i
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) −3.23205 + 5.59808i −0.331601 + 0.574351i
\(96\) 2.73205i 0.278839i
\(97\) −13.0981 7.56218i −1.32991 0.767823i −0.344623 0.938741i \(-0.611993\pi\)
−0.985285 + 0.170918i \(0.945327\pi\)
\(98\) −1.73205 1.00000i −0.174964 0.101015i
\(99\) 13.3923i 1.34598i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −3.63397 6.29423i −0.361594 0.626299i 0.626629 0.779317i \(-0.284434\pi\)
−0.988223 + 0.153018i \(0.951101\pi\)
\(102\) −5.19615 + 3.00000i −0.514496 + 0.297044i
\(103\) 1.19615 0.117860 0.0589302 0.998262i \(-0.481231\pi\)
0.0589302 + 0.998262i \(0.481231\pi\)
\(104\) 0 0
\(105\) −8.19615 −0.799863
\(106\) 5.59808 3.23205i 0.543733 0.313925i
\(107\) −0.169873 0.294229i −0.0164222 0.0284442i 0.857697 0.514155i \(-0.171894\pi\)
−0.874120 + 0.485710i \(0.838561\pi\)
\(108\) −2.00000 + 3.46410i −0.192450 + 0.333333i
\(109\) 15.4641i 1.48119i 0.671950 + 0.740596i \(0.265457\pi\)
−0.671950 + 0.740596i \(0.734543\pi\)
\(110\) −2.59808 1.50000i −0.247717 0.143019i
\(111\) −26.4904 15.2942i −2.51436 1.45166i
\(112\) 3.00000i 0.283473i
\(113\) 3.46410 6.00000i 0.325875 0.564433i −0.655814 0.754923i \(-0.727674\pi\)
0.981689 + 0.190490i \(0.0610077\pi\)
\(114\) −8.83013 15.2942i −0.827017 1.43244i
\(115\) 2.19615 1.26795i 0.204792 0.118237i
\(116\) 9.46410 0.878720
\(117\) 0 0
\(118\) 10.3923 0.956689
\(119\) 5.70577 3.29423i 0.523047 0.301981i
\(120\) −1.36603 2.36603i −0.124700 0.215988i
\(121\) −1.00000 + 1.73205i −0.0909091 + 0.157459i
\(122\) 4.19615i 0.379902i
\(123\) 24.5885 + 14.1962i 2.21707 + 1.28002i
\(124\) −1.09808 0.633975i −0.0986102 0.0569326i
\(125\) 1.00000i 0.0894427i
\(126\) 6.69615 11.5981i 0.596541 1.03324i
\(127\) −10.5981 18.3564i −0.940427 1.62887i −0.764658 0.644436i \(-0.777092\pi\)
−0.175769 0.984431i \(-0.556241\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −5.46410 −0.481087
\(130\) 0 0
\(131\) −18.1244 −1.58353 −0.791766 0.610824i \(-0.790838\pi\)
−0.791766 + 0.610824i \(0.790838\pi\)
\(132\) 7.09808 4.09808i 0.617808 0.356692i
\(133\) 9.69615 + 16.7942i 0.840763 + 1.45624i
\(134\) 0 0
\(135\) 4.00000i 0.344265i
\(136\) 1.90192 + 1.09808i 0.163089 + 0.0941593i
\(137\) −7.09808 4.09808i −0.606430 0.350122i 0.165137 0.986271i \(-0.447193\pi\)
−0.771567 + 0.636148i \(0.780527\pi\)
\(138\) 6.92820i 0.589768i
\(139\) 4.59808 7.96410i 0.390004 0.675506i −0.602446 0.798160i \(-0.705807\pi\)
0.992450 + 0.122653i \(0.0391404\pi\)
\(140\) 1.50000 + 2.59808i 0.126773 + 0.219578i
\(141\) 7.09808 4.09808i 0.597766 0.345120i
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) 4.46410 0.372008
\(145\) −8.19615 + 4.73205i −0.680653 + 0.392975i
\(146\) −2.83013 4.90192i −0.234223 0.405686i
\(147\) −2.73205 + 4.73205i −0.225336 + 0.390293i
\(148\) 11.1962i 0.920318i
\(149\) 5.19615 + 3.00000i 0.425685 + 0.245770i 0.697507 0.716578i \(-0.254293\pi\)
−0.271821 + 0.962348i \(0.587626\pi\)
\(150\) 2.36603 + 1.36603i 0.193185 + 0.111536i
\(151\) 6.33975i 0.515921i 0.966155 + 0.257961i \(0.0830505\pi\)
−0.966155 + 0.257961i \(0.916950\pi\)
\(152\) −3.23205 + 5.59808i −0.262154 + 0.454064i
\(153\) 4.90192 + 8.49038i 0.396297 + 0.686407i
\(154\) −7.79423 + 4.50000i −0.628077 + 0.362620i
\(155\) 1.26795 0.101844
\(156\) 0 0
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) −5.36603 + 3.09808i −0.426898 + 0.246470i
\(159\) −8.83013 15.2942i −0.700275 1.21291i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 7.60770i 0.599570i
\(162\) −2.13397 1.23205i −0.167661 0.0967991i
\(163\) −6.29423 3.63397i −0.493002 0.284635i 0.232817 0.972521i \(-0.425206\pi\)
−0.725819 + 0.687886i \(0.758539\pi\)
\(164\) 10.3923i 0.811503i
\(165\) −4.09808 + 7.09808i −0.319035 + 0.552584i
\(166\) 1.09808 + 1.90192i 0.0852272 + 0.147618i
\(167\) 2.59808 1.50000i 0.201045 0.116073i −0.396098 0.918208i \(-0.629636\pi\)
0.597143 + 0.802135i \(0.296303\pi\)
\(168\) −8.19615 −0.632347
\(169\) 0 0
\(170\) −2.19615 −0.168437
\(171\) −24.9904 + 14.4282i −1.91106 + 1.10335i
\(172\) 1.00000 + 1.73205i 0.0762493 + 0.132068i
\(173\) 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i \(-0.640193\pi\)
0.996544 0.0830722i \(-0.0264732\pi\)
\(174\) 25.8564i 1.96017i
\(175\) −2.59808 1.50000i −0.196396 0.113389i
\(176\) −2.59808 1.50000i −0.195837 0.113067i
\(177\) 28.3923i 2.13410i
\(178\) −8.59808 + 14.8923i −0.644453 + 1.11623i
\(179\) 1.26795 + 2.19615i 0.0947710 + 0.164148i 0.909513 0.415675i \(-0.136455\pi\)
−0.814742 + 0.579824i \(0.803121\pi\)
\(180\) −3.86603 + 2.23205i −0.288157 + 0.166367i
\(181\) −16.5885 −1.23301 −0.616505 0.787351i \(-0.711452\pi\)
−0.616505 + 0.787351i \(0.711452\pi\)
\(182\) 0 0
\(183\) 11.4641 0.847451
\(184\) 2.19615 1.26795i 0.161903 0.0934745i
\(185\) −5.59808 9.69615i −0.411579 0.712875i
\(186\) −1.73205 + 3.00000i −0.127000 + 0.219971i
\(187\) 6.58846i 0.481796i
\(188\) −2.59808 1.50000i −0.189484 0.109399i
\(189\) −10.3923 6.00000i −0.755929 0.436436i
\(190\) 6.46410i 0.468955i
\(191\) 9.63397 16.6865i 0.697090 1.20740i −0.272381 0.962189i \(-0.587811\pi\)
0.969471 0.245206i \(-0.0788555\pi\)
\(192\) −1.36603 2.36603i −0.0985844 0.170753i
\(193\) 3.80385 2.19615i 0.273807 0.158083i −0.356809 0.934177i \(-0.616135\pi\)
0.630616 + 0.776095i \(0.282802\pi\)
\(194\) 15.1244 1.08587
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) −8.30385 + 4.79423i −0.591625 + 0.341575i −0.765740 0.643151i \(-0.777627\pi\)
0.174115 + 0.984725i \(0.444294\pi\)
\(198\) −6.69615 11.5981i −0.475875 0.824239i
\(199\) −7.19615 + 12.4641i −0.510122 + 0.883557i 0.489810 + 0.871829i \(0.337066\pi\)
−0.999931 + 0.0117273i \(0.996267\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 6.29423 + 3.63397i 0.442860 + 0.255686i
\(203\) 28.3923i 1.99275i
\(204\) 3.00000 5.19615i 0.210042 0.363803i
\(205\) 5.19615 + 9.00000i 0.362915 + 0.628587i
\(206\) −1.03590 + 0.598076i −0.0721745 + 0.0416699i
\(207\) 11.3205 0.786830
\(208\) 0 0
\(209\) 19.3923 1.34139
\(210\) 7.09808 4.09808i 0.489814 0.282794i
\(211\) −6.79423 11.7679i −0.467734 0.810139i 0.531586 0.847004i \(-0.321596\pi\)
−0.999320 + 0.0368651i \(0.988263\pi\)
\(212\) −3.23205 + 5.59808i −0.221978 + 0.384477i
\(213\) 16.3923i 1.12318i
\(214\) 0.294229 + 0.169873i 0.0201131 + 0.0116123i
\(215\) −1.73205 1.00000i −0.118125 0.0681994i
\(216\) 4.00000i 0.272166i
\(217\) 1.90192 3.29423i 0.129111 0.223627i
\(218\) −7.73205 13.3923i −0.523681 0.907041i
\(219\) −13.3923 + 7.73205i −0.904968 + 0.522484i
\(220\) 3.00000 0.202260
\(221\) 0 0
\(222\) 30.5885 2.05296
\(223\) 0.401924 0.232051i 0.0269148 0.0155393i −0.486482 0.873690i \(-0.661720\pi\)
0.513397 + 0.858151i \(0.328387\pi\)
\(224\) 1.50000 + 2.59808i 0.100223 + 0.173591i
\(225\) 2.23205 3.86603i 0.148803 0.257735i
\(226\) 6.92820i 0.460857i
\(227\) −3.80385 2.19615i −0.252470 0.145764i 0.368425 0.929658i \(-0.379897\pi\)
−0.620895 + 0.783894i \(0.713231\pi\)
\(228\) 15.2942 + 8.83013i 1.01289 + 0.584789i
\(229\) 4.73205i 0.312703i 0.987701 + 0.156351i \(0.0499732\pi\)
−0.987701 + 0.156351i \(0.950027\pi\)
\(230\) −1.26795 + 2.19615i −0.0836061 + 0.144810i
\(231\) 12.2942 + 21.2942i 0.808901 + 1.40106i
\(232\) −8.19615 + 4.73205i −0.538104 + 0.310674i
\(233\) 1.26795 0.0830661 0.0415331 0.999137i \(-0.486776\pi\)
0.0415331 + 0.999137i \(0.486776\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) −9.00000 + 5.19615i −0.585850 + 0.338241i
\(237\) 8.46410 + 14.6603i 0.549802 + 0.952286i
\(238\) −3.29423 + 5.70577i −0.213533 + 0.369850i
\(239\) 8.19615i 0.530165i 0.964226 + 0.265083i \(0.0853992\pi\)
−0.964226 + 0.265083i \(0.914601\pi\)
\(240\) 2.36603 + 1.36603i 0.152726 + 0.0881766i
\(241\) 7.50000 + 4.33013i 0.483117 + 0.278928i 0.721715 0.692191i \(-0.243354\pi\)
−0.238597 + 0.971119i \(0.576688\pi\)
\(242\) 2.00000i 0.128565i
\(243\) −9.36603 + 16.2224i −0.600831 + 1.04067i
\(244\) −2.09808 3.63397i −0.134316 0.232641i
\(245\) −1.73205 + 1.00000i −0.110657 + 0.0638877i
\(246\) −28.3923 −1.81023
\(247\) 0 0
\(248\) 1.26795 0.0805149
\(249\) 5.19615 3.00000i 0.329293 0.190117i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −3.40192 + 5.89230i −0.214728 + 0.371919i −0.953188 0.302378i \(-0.902220\pi\)
0.738461 + 0.674296i \(0.235553\pi\)
\(252\) 13.3923i 0.843636i
\(253\) −6.58846 3.80385i −0.414213 0.239146i
\(254\) 18.3564 + 10.5981i 1.15178 + 0.664982i
\(255\) 6.00000i 0.375735i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.92820 12.0000i −0.432169 0.748539i 0.564890 0.825166i \(-0.308918\pi\)
−0.997060 + 0.0766265i \(0.975585\pi\)
\(258\) 4.73205 2.73205i 0.294605 0.170090i
\(259\) −33.5885 −2.08709
\(260\) 0 0
\(261\) −42.2487 −2.61513
\(262\) 15.6962 9.06218i 0.969712 0.559863i
\(263\) 13.7942 + 23.8923i 0.850589 + 1.47326i 0.880678 + 0.473715i \(0.157087\pi\)
−0.0300894 + 0.999547i \(0.509579\pi\)
\(264\) −4.09808 + 7.09808i −0.252219 + 0.436856i
\(265\) 6.46410i 0.397087i
\(266\) −16.7942 9.69615i −1.02972 0.594509i
\(267\) 40.6865 + 23.4904i 2.48998 + 1.43759i
\(268\) 0 0
\(269\) 1.43782 2.49038i 0.0876656 0.151841i −0.818858 0.573996i \(-0.805393\pi\)
0.906524 + 0.422154i \(0.138726\pi\)
\(270\) 2.00000 + 3.46410i 0.121716 + 0.210819i
\(271\) 2.19615 1.26795i 0.133407 0.0770224i −0.431811 0.901964i \(-0.642125\pi\)
0.565218 + 0.824942i \(0.308792\pi\)
\(272\) −2.19615 −0.133161
\(273\) 0 0
\(274\) 8.19615 0.495148
\(275\) −2.59808 + 1.50000i −0.156670 + 0.0904534i
\(276\) −3.46410 6.00000i −0.208514 0.361158i
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) 9.19615i 0.551549i
\(279\) 4.90192 + 2.83013i 0.293471 + 0.169435i
\(280\) −2.59808 1.50000i −0.155265 0.0896421i
\(281\) 10.3923i 0.619953i −0.950744 0.309976i \(-0.899679\pi\)
0.950744 0.309976i \(-0.100321\pi\)
\(282\) −4.09808 + 7.09808i −0.244037 + 0.422684i
\(283\) 15.1962 + 26.3205i 0.903317 + 1.56459i 0.823160 + 0.567810i \(0.192209\pi\)
0.0801576 + 0.996782i \(0.474458\pi\)
\(284\) −5.19615 + 3.00000i −0.308335 + 0.178017i
\(285\) −17.6603 −1.04610
\(286\) 0 0
\(287\) 31.1769 1.84032
\(288\) −3.86603 + 2.23205i −0.227808 + 0.131525i
\(289\) 6.08846 + 10.5455i 0.358145 + 0.620325i
\(290\) 4.73205 8.19615i 0.277876 0.481295i
\(291\) 41.3205i 2.42225i
\(292\) 4.90192 + 2.83013i 0.286863 + 0.165621i
\(293\) 0.696152 + 0.401924i 0.0406697 + 0.0234806i 0.520197 0.854046i \(-0.325859\pi\)
−0.479527 + 0.877527i \(0.659192\pi\)
\(294\) 5.46410i 0.318673i
\(295\) 5.19615 9.00000i 0.302532 0.524000i
\(296\) −5.59808 9.69615i −0.325382 0.563577i
\(297\) −10.3923 + 6.00000i −0.603023 + 0.348155i
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) −2.73205 −0.157735
\(301\) −5.19615 + 3.00000i −0.299501 + 0.172917i
\(302\) −3.16987 5.49038i −0.182406 0.315936i
\(303\) 9.92820 17.1962i 0.570360 0.987893i
\(304\) 6.46410i 0.370742i
\(305\) 3.63397 + 2.09808i 0.208081 + 0.120135i
\(306\) −8.49038 4.90192i −0.485363 0.280224i
\(307\) 20.5359i 1.17205i 0.810295 + 0.586023i \(0.199307\pi\)
−0.810295 + 0.586023i \(0.800693\pi\)
\(308\) 4.50000 7.79423i 0.256411 0.444117i
\(309\) 1.63397 + 2.83013i 0.0929536 + 0.161000i
\(310\) −1.09808 + 0.633975i −0.0623665 + 0.0360073i
\(311\) 15.1244 0.857624 0.428812 0.903394i \(-0.358932\pi\)
0.428812 + 0.903394i \(0.358932\pi\)
\(312\) 0 0
\(313\) 5.60770 0.316966 0.158483 0.987362i \(-0.449340\pi\)
0.158483 + 0.987362i \(0.449340\pi\)
\(314\) 11.2583 6.50000i 0.635344 0.366816i
\(315\) −6.69615 11.5981i −0.377285 0.653478i
\(316\) 3.09808 5.36603i 0.174280 0.301863i
\(317\) 12.8038i 0.719136i 0.933119 + 0.359568i \(0.117076\pi\)
−0.933119 + 0.359568i \(0.882924\pi\)
\(318\) 15.2942 + 8.83013i 0.857658 + 0.495169i
\(319\) 24.5885 + 14.1962i 1.37669 + 0.794832i
\(320\) 1.00000i 0.0559017i
\(321\) 0.464102 0.803848i 0.0259036 0.0448664i
\(322\) 3.80385 + 6.58846i 0.211980 + 0.367160i
\(323\) 12.2942 7.09808i 0.684069 0.394948i
\(324\) 2.46410 0.136895
\(325\) 0 0
\(326\) 7.26795 0.402534
\(327\) −36.5885 + 21.1244i −2.02335 + 1.16818i
\(328\) 5.19615 + 9.00000i 0.286910 + 0.496942i
\(329\) 4.50000 7.79423i 0.248093 0.429710i
\(330\) 8.19615i 0.451183i
\(331\) −0.803848 0.464102i −0.0441835 0.0255093i 0.477746 0.878498i \(-0.341454\pi\)
−0.521929 + 0.852989i \(0.674787\pi\)
\(332\) −1.90192 1.09808i −0.104382 0.0602648i
\(333\) 49.9808i 2.73893i
\(334\) −1.50000 + 2.59808i −0.0820763 + 0.142160i
\(335\) 0 0
\(336\) 7.09808 4.09808i 0.387232 0.223568i
\(337\) −4.19615 −0.228579 −0.114289 0.993447i \(-0.536459\pi\)
−0.114289 + 0.993447i \(0.536459\pi\)
\(338\) 0 0
\(339\) 18.9282 1.02804
\(340\) 1.90192 1.09808i 0.103146 0.0595515i
\(341\) −1.90192 3.29423i −0.102995 0.178392i
\(342\) 14.4282 24.9904i 0.780188 1.35133i
\(343\) 15.0000i 0.809924i
\(344\) −1.73205 1.00000i −0.0933859 0.0539164i
\(345\) 6.00000 + 3.46410i 0.323029 + 0.186501i
\(346\) 15.0000i 0.806405i
\(347\) 12.6340 21.8827i 0.678227 1.17472i −0.297287 0.954788i \(-0.596082\pi\)
0.975514 0.219936i \(-0.0705848\pi\)
\(348\) 12.9282 + 22.3923i 0.693024 + 1.20035i
\(349\) 29.4904 17.0263i 1.57858 0.911396i 0.583527 0.812094i \(-0.301672\pi\)
0.995057 0.0993018i \(-0.0316609\pi\)
\(350\) 3.00000 0.160357
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) 17.4904 10.0981i 0.930919 0.537466i 0.0438169 0.999040i \(-0.486048\pi\)
0.887102 + 0.461573i \(0.152715\pi\)
\(354\) 14.1962 + 24.5885i 0.754517 + 1.30686i
\(355\) 3.00000 5.19615i 0.159223 0.275783i
\(356\) 17.1962i 0.911394i
\(357\) 15.5885 + 9.00000i 0.825029 + 0.476331i
\(358\) −2.19615 1.26795i −0.116070 0.0670132i
\(359\) 22.3923i 1.18182i −0.806737 0.590910i \(-0.798769\pi\)
0.806737 0.590910i \(-0.201231\pi\)
\(360\) 2.23205 3.86603i 0.117639 0.203757i
\(361\) 11.3923 + 19.7321i 0.599595 + 1.03853i
\(362\) 14.3660 8.29423i 0.755062 0.435935i
\(363\) −5.46410 −0.286791
\(364\) 0 0
\(365\) −5.66025 −0.296271
\(366\) −9.92820 + 5.73205i −0.518955 + 0.299619i
\(367\) 13.1962 + 22.8564i 0.688834 + 1.19309i 0.972216 + 0.234088i \(0.0752102\pi\)
−0.283382 + 0.959007i \(0.591456\pi\)
\(368\) −1.26795 + 2.19615i −0.0660964 + 0.114482i
\(369\) 46.3923i 2.41509i
\(370\) 9.69615 + 5.59808i 0.504079 + 0.291030i
\(371\) −16.7942 9.69615i −0.871913 0.503399i
\(372\) 3.46410i 0.179605i
\(373\) −10.1962 + 17.6603i −0.527937 + 0.914413i 0.471533 + 0.881848i \(0.343701\pi\)
−0.999470 + 0.0325648i \(0.989632\pi\)
\(374\) 3.29423 + 5.70577i 0.170341 + 0.295038i
\(375\) 2.36603 1.36603i 0.122181 0.0705412i
\(376\) 3.00000 0.154713
\(377\) 0 0
\(378\) 12.0000 0.617213
\(379\) −10.2058 + 5.89230i −0.524235 + 0.302667i −0.738666 0.674072i \(-0.764544\pi\)
0.214430 + 0.976739i \(0.431210\pi\)
\(380\) 3.23205 + 5.59808i 0.165801 + 0.287175i
\(381\) 28.9545 50.1506i 1.48338 2.56929i
\(382\) 19.2679i 0.985834i
\(383\) 1.39230 + 0.803848i 0.0711435 + 0.0410747i 0.535150 0.844757i \(-0.320255\pi\)
−0.464006 + 0.885832i \(0.653589\pi\)
\(384\) 2.36603 + 1.36603i 0.120741 + 0.0697097i
\(385\) 9.00000i 0.458682i
\(386\) −2.19615 + 3.80385i −0.111781 + 0.193611i
\(387\) −4.46410 7.73205i −0.226923 0.393042i
\(388\) −13.0981 + 7.56218i −0.664954 + 0.383911i
\(389\) 19.2679 0.976924 0.488462 0.872585i \(-0.337558\pi\)
0.488462 + 0.872585i \(0.337558\pi\)
\(390\) 0 0
\(391\) −5.56922 −0.281648
\(392\) −1.73205 + 1.00000i −0.0874818 + 0.0505076i
\(393\) −24.7583 42.8827i −1.24889 2.16315i
\(394\) 4.79423 8.30385i 0.241530 0.418342i
\(395\) 6.19615i 0.311762i
\(396\) 11.5981 + 6.69615i 0.582825 + 0.336494i
\(397\) −0.696152 0.401924i −0.0349389 0.0201720i 0.482429 0.875935i \(-0.339755\pi\)
−0.517368 + 0.855763i \(0.673088\pi\)
\(398\) 14.3923i 0.721421i
\(399\) −26.4904 + 45.8827i −1.32618 + 2.29701i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 4.50000 2.59808i 0.224719 0.129742i −0.383414 0.923576i \(-0.625252\pi\)
0.608134 + 0.793835i \(0.291919\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −7.26795 −0.361594
\(405\) −2.13397 + 1.23205i −0.106038 + 0.0612211i
\(406\) −14.1962 24.5885i −0.704543 1.22030i
\(407\) −16.7942 + 29.0885i −0.832459 + 1.44186i
\(408\) 6.00000i 0.297044i
\(409\) −17.0885 9.86603i −0.844970 0.487844i 0.0139806 0.999902i \(-0.495550\pi\)
−0.858950 + 0.512059i \(0.828883\pi\)
\(410\) −9.00000 5.19615i −0.444478 0.256620i
\(411\) 22.3923i 1.10453i
\(412\) 0.598076 1.03590i 0.0294651 0.0510351i
\(413\) −15.5885 27.0000i −0.767058 1.32858i
\(414\) −9.80385 + 5.66025i −0.481833 + 0.278186i
\(415\) 2.19615 0.107805
\(416\) 0 0
\(417\) 25.1244 1.23034
\(418\) −16.7942 + 9.69615i −0.821433 + 0.474254i
\(419\) −8.66025 15.0000i −0.423081 0.732798i 0.573158 0.819445i \(-0.305718\pi\)
−0.996239 + 0.0866469i \(0.972385\pi\)
\(420\) −4.09808 + 7.09808i −0.199966 + 0.346351i
\(421\) 27.1244i 1.32196i −0.750403 0.660980i \(-0.770141\pi\)
0.750403 0.660980i \(-0.229859\pi\)
\(422\) 11.7679 + 6.79423i 0.572855 + 0.330738i
\(423\) 11.5981 + 6.69615i 0.563918 + 0.325578i
\(424\) 6.46410i 0.313925i
\(425\) −1.09808 + 1.90192i −0.0532645 + 0.0922569i
\(426\) 8.19615 + 14.1962i 0.397105 + 0.687806i
\(427\) 10.9019 6.29423i 0.527581 0.304599i
\(428\) −0.339746 −0.0164222
\(429\) 0 0
\(430\) 2.00000 0.0964486
\(431\) 1.90192 1.09808i 0.0916124 0.0528925i −0.453494 0.891259i \(-0.649823\pi\)
0.545106 + 0.838367i \(0.316489\pi\)
\(432\) 2.00000 + 3.46410i 0.0962250 + 0.166667i
\(433\) 6.19615 10.7321i 0.297768 0.515749i −0.677857 0.735194i \(-0.737091\pi\)
0.975625 + 0.219444i \(0.0704245\pi\)
\(434\) 3.80385i 0.182591i
\(435\) −22.3923 12.9282i −1.07363 0.619860i
\(436\) 13.3923 + 7.73205i 0.641375 + 0.370298i
\(437\) 16.3923i 0.784150i
\(438\) 7.73205 13.3923i 0.369452 0.639909i
\(439\) 17.2942 + 29.9545i 0.825408 + 1.42965i 0.901607 + 0.432557i \(0.142388\pi\)
−0.0761982 + 0.997093i \(0.524278\pi\)
\(440\) −2.59808 + 1.50000i −0.123858 + 0.0715097i
\(441\) −8.92820 −0.425153
\(442\) 0 0
\(443\) −1.60770 −0.0763839 −0.0381920 0.999270i \(-0.512160\pi\)
−0.0381920 + 0.999270i \(0.512160\pi\)
\(444\) −26.4904 + 15.2942i −1.25718 + 0.725832i
\(445\) 8.59808 + 14.8923i 0.407588 + 0.705963i
\(446\) −0.232051 + 0.401924i −0.0109879 + 0.0190316i
\(447\) 16.3923i 0.775329i
\(448\) −2.59808 1.50000i −0.122748 0.0708683i
\(449\) −13.5000 7.79423i −0.637104 0.367832i 0.146394 0.989226i \(-0.453233\pi\)
−0.783498 + 0.621394i \(0.786567\pi\)
\(450\) 4.46410i 0.210440i
\(451\) 15.5885 27.0000i 0.734032 1.27138i
\(452\) −3.46410 6.00000i −0.162938 0.282216i
\(453\) −15.0000 + 8.66025i −0.704761 + 0.406894i
\(454\) 4.39230 0.206141
\(455\) 0 0
\(456\) −17.6603 −0.827017
\(457\) 30.8827 17.8301i 1.44463 0.834058i 0.446477 0.894795i \(-0.352678\pi\)
0.998154 + 0.0607368i \(0.0193450\pi\)
\(458\) −2.36603 4.09808i −0.110557 0.191491i
\(459\) −4.39230 + 7.60770i −0.205015 + 0.355097i
\(460\) 2.53590i 0.118237i
\(461\) 0.509619 + 0.294229i 0.0237353 + 0.0137036i 0.511821 0.859092i \(-0.328971\pi\)
−0.488085 + 0.872796i \(0.662305\pi\)
\(462\) −21.2942 12.2942i −0.990697 0.571979i
\(463\) 0.928203i 0.0431373i 0.999767 + 0.0215686i \(0.00686604\pi\)
−0.999767 + 0.0215686i \(0.993134\pi\)
\(464\) 4.73205 8.19615i 0.219680 0.380497i
\(465\) 1.73205 + 3.00000i 0.0803219 + 0.139122i
\(466\) −1.09808 + 0.633975i −0.0508674 + 0.0293683i
\(467\) −10.1436 −0.469390 −0.234695 0.972069i \(-0.575409\pi\)
−0.234695 + 0.972069i \(0.575409\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2.59808 + 1.50000i −0.119840 + 0.0691898i
\(471\) −17.7583 30.7583i −0.818261 1.41727i
\(472\) 5.19615 9.00000i 0.239172 0.414259i
\(473\) 6.00000i 0.275880i
\(474\) −14.6603 8.46410i −0.673368 0.388769i
\(475\) −5.59808 3.23205i −0.256857 0.148297i
\(476\) 6.58846i 0.301981i
\(477\) 14.4282 24.9904i 0.660622 1.14423i
\(478\) −4.09808 7.09808i −0.187442 0.324658i
\(479\) 9.50962 5.49038i 0.434506 0.250862i −0.266759 0.963763i \(-0.585953\pi\)
0.701264 + 0.712901i \(0.252619\pi\)
\(480\) −2.73205 −0.124700
\(481\) 0 0
\(482\) −8.66025 −0.394464
\(483\) 18.0000 10.3923i 0.819028 0.472866i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 7.56218 13.0981i 0.343381 0.594753i
\(486\) 18.7321i 0.849703i
\(487\) 28.7942 + 16.6244i 1.30479 + 0.753321i 0.981222 0.192883i \(-0.0617838\pi\)
0.323569 + 0.946204i \(0.395117\pi\)
\(488\) 3.63397 + 2.09808i 0.164502 + 0.0949754i
\(489\) 19.8564i 0.897938i
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) −1.66987 2.89230i −0.0753603 0.130528i 0.825883 0.563842i \(-0.190677\pi\)
−0.901243 + 0.433314i \(0.857344\pi\)
\(492\) 24.5885 14.1962i 1.10853 0.640012i
\(493\) 20.7846 0.936092
\(494\) 0 0
\(495\) −13.3923 −0.601939
\(496\) −1.09808 + 0.633975i −0.0493051 + 0.0284663i
\(497\) −9.00000 15.5885i −0.403705 0.699238i
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 1.85641i 0.0831042i 0.999136 + 0.0415521i \(0.0132302\pi\)
−0.999136 + 0.0415521i \(0.986770\pi\)
\(500\) −0.866025 0.500000i −0.0387298 0.0223607i
\(501\) 7.09808 + 4.09808i 0.317119 + 0.183089i
\(502\) 6.80385i 0.303671i
\(503\) 4.66987 8.08846i 0.208219 0.360646i −0.742934 0.669364i \(-0.766567\pi\)
0.951154 + 0.308718i \(0.0998999\pi\)
\(504\) −6.69615 11.5981i −0.298270 0.516619i
\(505\) 6.29423 3.63397i 0.280089 0.161710i
\(506\) 7.60770 0.338203
\(507\) 0 0
\(508\) −21.1962 −0.940427
\(509\) −1.39230 + 0.803848i −0.0617128 + 0.0356299i −0.530539 0.847661i \(-0.678010\pi\)
0.468826 + 0.883290i \(0.344677\pi\)
\(510\) −3.00000 5.19615i −0.132842 0.230089i
\(511\) −8.49038 + 14.7058i −0.375592 + 0.650545i
\(512\) 1.00000i 0.0441942i
\(513\) −22.3923 12.9282i −0.988644 0.570794i
\(514\) 12.0000 + 6.92820i 0.529297 + 0.305590i
\(515\) 1.19615i 0.0527088i
\(516\) −2.73205 + 4.73205i −0.120272 + 0.208317i
\(517\) −4.50000 7.79423i −0.197910 0.342790i
\(518\) 29.0885 16.7942i 1.27807 0.737896i
\(519\) 40.9808 1.79886
\(520\) 0 0
\(521\) −0.464102 −0.0203327 −0.0101663 0.999948i \(-0.503236\pi\)
−0.0101663 + 0.999948i \(0.503236\pi\)
\(522\) 36.5885 21.1244i 1.60143 0.924588i
\(523\) −9.19615 15.9282i −0.402120 0.696492i 0.591862 0.806039i \(-0.298393\pi\)
−0.993982 + 0.109548i \(0.965060\pi\)
\(524\) −9.06218 + 15.6962i −0.395883 + 0.685690i
\(525\) 8.19615i 0.357709i
\(526\) −23.8923 13.7942i −1.04175 0.601457i
\(527\) −2.41154 1.39230i −0.105048 0.0606498i
\(528\) 8.19615i 0.356692i
\(529\) 8.28461 14.3494i 0.360200 0.623885i
\(530\) 3.23205 + 5.59808i 0.140391 + 0.243165i
\(531\) 40.1769 23.1962i 1.74353 1.00663i
\(532\) 19.3923 0.840763
\(533\) 0 0
\(534\) −46.9808 −2.03306
\(535\) 0.294229 0.169873i 0.0127206 0.00734425i
\(536\) 0 0
\(537\) −3.46410 + 6.00000i −0.149487 + 0.258919i
\(538\) 2.87564i 0.123978i
\(539\) 5.19615 + 3.00000i 0.223814 + 0.129219i
\(540\) −3.46410 2.00000i −0.149071 0.0860663i
\(541\) 16.0526i 0.690153i 0.938574 + 0.345077i \(0.112147\pi\)
−0.938574 + 0.345077i \(0.887853\pi\)
\(542\) −1.26795 + 2.19615i −0.0544631 + 0.0943328i
\(543\) −22.6603 39.2487i −0.972445 1.68432i
\(544\) 1.90192 1.09808i 0.0815443 0.0470796i
\(545\) −15.4641 −0.662409
\(546\) 0 0
\(547\) 34.7846 1.48728 0.743641 0.668579i \(-0.233097\pi\)
0.743641 + 0.668579i \(0.233097\pi\)
\(548\) −7.09808 + 4.09808i −0.303215 + 0.175061i
\(549\) 9.36603 + 16.2224i 0.399732 + 0.692357i
\(550\) 1.50000 2.59808i 0.0639602 0.110782i
\(551\) 61.1769i 2.60622i
\(552\) 6.00000 + 3.46410i 0.255377 + 0.147442i
\(553\) 16.0981 + 9.29423i 0.684560 + 0.395231i
\(554\) 1.00000i 0.0424859i
\(555\) 15.2942 26.4904i 0.649204 1.12445i
\(556\) −4.59808 7.96410i −0.195002 0.337753i
\(557\) −14.8923 + 8.59808i −0.631007 + 0.364312i −0.781142 0.624353i \(-0.785363\pi\)
0.150135 + 0.988666i \(0.452029\pi\)
\(558\) −5.66025 −0.239618
\(559\) 0 0
\(560\) 3.00000 0.126773
\(561\) 15.5885 9.00000i 0.658145 0.379980i
\(562\) 5.19615 + 9.00000i 0.219186 + 0.379642i
\(563\) −10.7321 + 18.5885i −0.452302 + 0.783410i −0.998529 0.0542274i \(-0.982730\pi\)
0.546227 + 0.837637i \(0.316064\pi\)
\(564\) 8.19615i 0.345120i
\(565\) 6.00000 + 3.46410i 0.252422 + 0.145736i
\(566\) −26.3205 15.1962i −1.10633 0.638742i
\(567\) 7.39230i 0.310448i
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) −10.6244 18.4019i −0.445396 0.771449i 0.552684 0.833391i \(-0.313604\pi\)
−0.998080 + 0.0619424i \(0.980270\pi\)
\(570\) 15.2942 8.83013i 0.640605 0.369853i
\(571\) 34.3731 1.43847 0.719234 0.694768i \(-0.244493\pi\)
0.719234 + 0.694768i \(0.244493\pi\)
\(572\) 0 0
\(573\) 52.6410 2.19911
\(574\) −27.0000 + 15.5885i −1.12696 + 0.650650i
\(575\) 1.26795 + 2.19615i 0.0528771 + 0.0915859i
\(576\) 2.23205 3.86603i 0.0930021 0.161084i
\(577\) 32.4449i 1.35070i −0.737499 0.675349i \(-0.763993\pi\)
0.737499 0.675349i \(-0.236007\pi\)
\(578\) −10.5455 6.08846i −0.438636 0.253246i
\(579\) 10.3923 + 6.00000i 0.431889 + 0.249351i
\(580\) 9.46410i 0.392975i
\(581\) 3.29423 5.70577i 0.136668 0.236715i
\(582\) 20.6603 + 35.7846i 0.856395 + 1.48332i
\(583\) −16.7942 + 9.69615i −0.695546 + 0.401574i
\(584\) −5.66025 −0.234223
\(585\) 0 0
\(586\) −0.803848 −0.0332066
\(587\) 25.9808 15.0000i 1.07234 0.619116i 0.143521 0.989647i \(-0.454158\pi\)
0.928820 + 0.370531i \(0.120824\pi\)
\(588\) 2.73205 + 4.73205i 0.112668 + 0.195146i
\(589\) 4.09808 7.09808i 0.168858 0.292471i
\(590\) 10.3923i 0.427844i
\(591\) −22.6865 13.0981i −0.933199 0.538783i
\(592\) 9.69615 + 5.59808i 0.398509 + 0.230080i
\(593\) 20.7846i 0.853522i −0.904365 0.426761i \(-0.859655\pi\)
0.904365 0.426761i \(-0.140345\pi\)
\(594\) 6.00000 10.3923i 0.246183 0.426401i
\(595\) 3.29423 + 5.70577i 0.135050 + 0.233914i
\(596\) 5.19615 3.00000i 0.212843 0.122885i
\(597\) −39.3205 −1.60928
\(598\) 0 0
\(599\) 7.85641 0.321004 0.160502 0.987036i \(-0.448689\pi\)
0.160502 + 0.987036i \(0.448689\pi\)
\(600\) 2.36603 1.36603i 0.0965926 0.0557678i
\(601\) −1.89230 3.27757i −0.0771887 0.133695i 0.824847 0.565356i \(-0.191261\pi\)
−0.902036 + 0.431661i \(0.857928\pi\)
\(602\) 3.00000 5.19615i 0.122271 0.211779i
\(603\) 0 0
\(604\) 5.49038 + 3.16987i 0.223400 + 0.128980i
\(605\) −1.73205 1.00000i −0.0704179 0.0406558i
\(606\) 19.8564i 0.806611i
\(607\) 3.20577 5.55256i 0.130118 0.225371i −0.793604 0.608435i \(-0.791798\pi\)
0.923722 + 0.383064i \(0.125131\pi\)
\(608\) 3.23205 + 5.59808i 0.131077 + 0.227032i
\(609\) −67.1769 + 38.7846i −2.72215 + 1.57163i
\(610\) −4.19615 −0.169897
\(611\) 0 0
\(612\) 9.80385 0.396297
\(613\) −23.3038 + 13.4545i −0.941234 + 0.543421i −0.890347 0.455283i \(-0.849538\pi\)
−0.0508868 + 0.998704i \(0.516205\pi\)
\(614\) −10.2679 17.7846i −0.414381 0.717728i
\(615\) −14.1962 + 24.5885i −0.572444 + 0.991502i
\(616\) 9.00000i 0.362620i
\(617\) 15.5885 + 9.00000i 0.627568 + 0.362326i 0.779809 0.626017i \(-0.215316\pi\)
−0.152242 + 0.988343i \(0.548649\pi\)
\(618\) −2.83013 1.63397i −0.113844 0.0657281i
\(619\) 10.6077i 0.426359i 0.977013 + 0.213180i \(0.0683820\pi\)
−0.977013 + 0.213180i \(0.931618\pi\)
\(620\) 0.633975 1.09808i 0.0254610 0.0440998i
\(621\) 5.07180 + 8.78461i 0.203524 + 0.352514i
\(622\) −13.0981 + 7.56218i −0.525185 + 0.303216i
\(623\) 51.5885 2.06685
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −4.85641 + 2.80385i −0.194101 + 0.112064i
\(627\) 26.4904 + 45.8827i 1.05792 + 1.83238i
\(628\) −6.50000 + 11.2583i −0.259378 + 0.449256i
\(629\) 24.5885i 0.980406i
\(630\) 11.5981 + 6.69615i 0.462078 + 0.266781i
\(631\) 18.0000 + 10.3923i 0.716569 + 0.413711i 0.813488 0.581581i \(-0.197566\pi\)
−0.0969198 + 0.995292i \(0.530899\pi\)
\(632\) 6.19615i 0.246470i
\(633\) 18.5622 32.1506i 0.737780 1.27787i
\(634\) −6.40192 11.0885i −0.254253 0.440379i
\(635\) 18.3564 10.5981i 0.728452 0.420572i
\(636\) −17.6603 −0.700275
\(637\) 0 0
\(638\) −28.3923 −1.12406
\(639\) 23.1962 13.3923i 0.917626 0.529791i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −22.9641 + 39.7750i −0.907027 + 1.57102i −0.0888552 + 0.996045i \(0.528321\pi\)
−0.818172 + 0.574973i \(0.805012\pi\)
\(642\) 0.928203i 0.0366333i
\(643\) −6.29423 3.63397i −0.248220 0.143310i 0.370729 0.928741i \(-0.379108\pi\)
−0.618949 + 0.785431i \(0.712441\pi\)
\(644\) −6.58846 3.80385i −0.259622 0.149893i
\(645\) 5.46410i 0.215149i
\(646\) −7.09808 + 12.2942i −0.279270 + 0.483710i
\(647\) 5.59808 + 9.69615i 0.220083 + 0.381195i 0.954833 0.297143i \(-0.0960338\pi\)
−0.734750 + 0.678338i \(0.762700\pi\)
\(648\) −2.13397 + 1.23205i −0.0838304 + 0.0483995i
\(649\) −31.1769 −1.22380
\(650\) 0 0
\(651\) 10.3923 0.407307
\(652\) −6.29423 + 3.63397i −0.246501 + 0.142317i
\(653\) 9.69615 + 16.7942i 0.379440 + 0.657209i 0.990981 0.134004i \(-0.0427834\pi\)
−0.611541 + 0.791213i \(0.709450\pi\)
\(654\) 21.1244 36.5885i 0.826028 1.43072i
\(655\) 18.1244i 0.708177i
\(656\) −9.00000 5.19615i −0.351391 0.202876i
\(657\) −21.8827 12.6340i −0.853725 0.492898i
\(658\) 9.00000i 0.350857i
\(659\) −14.6603 + 25.3923i −0.571082 + 0.989144i 0.425373 + 0.905018i \(0.360143\pi\)
−0.996455 + 0.0841255i \(0.973190\pi\)
\(660\) 4.09808 + 7.09808i 0.159517 + 0.276292i
\(661\) −25.9019 + 14.9545i −1.00747 + 0.581662i −0.910449 0.413621i \(-0.864264\pi\)
−0.0970187 + 0.995283i \(0.530931\pi\)
\(662\) 0.928203 0.0360756
\(663\) 0 0
\(664\) 2.19615 0.0852272
\(665\) −16.7942 + 9.69615i −0.651252 + 0.376001i
\(666\) 24.9904 + 43.2846i 0.968358 + 1.67724i
\(667\) 12.0000 20.7846i 0.464642 0.804783i
\(668\) 3.00000i 0.116073i
\(669\) 1.09808 + 0.633975i 0.0424541 + 0.0245109i
\(670\) 0 0
\(671\) 12.5885i 0.485972i
\(672\) −4.09808 + 7.09808i −0.158087 + 0.273814i
\(673\) −1.80385 3.12436i −0.0695332 0.120435i 0.829163 0.559007i \(-0.188818\pi\)
−0.898696 + 0.438572i \(0.855484\pi\)
\(674\) 3.63397 2.09808i 0.139975 0.0808149i
\(675\) 4.00000 0.153960
\(676\) 0 0
\(677\) 1.85641 0.0713475 0.0356737 0.999363i \(-0.488642\pi\)
0.0356737 + 0.999363i \(0.488642\pi\)
\(678\) −16.3923 + 9.46410i −0.629543 + 0.363467i
\(679\) −22.6865 39.2942i −0.870629 1.50797i
\(680\) −1.09808 + 1.90192i −0.0421093 + 0.0729354i
\(681\) 12.0000i 0.459841i
\(682\) 3.29423 + 1.90192i 0.126143 + 0.0728284i
\(683\) −27.0000 15.5885i −1.03313 0.596476i −0.115248 0.993337i \(-0.536766\pi\)
−0.917879 + 0.396861i \(0.870099\pi\)
\(684\) 28.8564i 1.10335i
\(685\) 4.09808 7.09808i 0.156579 0.271204i
\(686\) 7.50000 + 12.9904i 0.286351 + 0.495975i
\(687\) −11.1962 + 6.46410i −0.427160 + 0.246621i
\(688\) 2.00000 0.0762493
\(689\) 0 0
\(690\) −6.92820 −0.263752
\(691\) 16.2058 9.35641i 0.616497 0.355934i −0.159007 0.987277i \(-0.550829\pi\)
0.775504 + 0.631343i \(0.217496\pi\)
\(692\) −7.50000 12.9904i −0.285107 0.493820i
\(693\) −20.0885 + 34.7942i −0.763097 + 1.32172i
\(694\) 25.2679i 0.959158i
\(695\) 7.96410 + 4.59808i 0.302096 + 0.174415i
\(696\) −22.3923 12.9282i −0.848778 0.490042i
\(697\) 22.8231i 0.864486i
\(698\) −17.0263 + 29.4904i −0.644454 + 1.11623i
\(699\) 1.73205 + 3.00000i 0.0655122 + 0.113470i
\(700\) −2.59808 + 1.50000i −0.0981981 + 0.0566947i
\(701\) −29.9090 −1.12965 −0.564823 0.825212i \(-0.691056\pi\)
−0.564823 + 0.825212i \(0.691056\pi\)
\(702\) 0 0
\(703\) −72.3731 −2.72960
\(704\) −2.59808 + 1.50000i −0.0979187 + 0.0565334i
\(705\) 4.09808 + 7.09808i 0.154342 + 0.267329i
\(706\) −10.0981 + 17.4904i −0.380046 + 0.658259i
\(707\) 21.8038i 0.820018i
\(708\) −24.5885 14.1962i −0.924091 0.533524i
\(709\) −35.4904 20.4904i −1.33287 0.769532i −0.347131 0.937817i \(-0.612844\pi\)
−0.985738 + 0.168284i \(0.946177\pi\)
\(710\) 6.00000i 0.225176i
\(711\) −13.8301 + 23.9545i −0.518670 + 0.898363i
\(712\) 8.59808 + 14.8923i 0.322227 + 0.558113i
\(713\) −2.78461 + 1.60770i −0.104284 + 0.0602087i
\(714\) −18.0000 −0.673633
\(715\) 0 0
\(716\) 2.53590 0.0947710
\(717\) −19.3923 + 11.1962i −0.724219 + 0.418128i
\(718\) 11.1962 + 19.3923i 0.417837 + 0.723714i
\(719\) 0.928203 1.60770i 0.0346161 0.0599569i −0.848198 0.529679i \(-0.822312\pi\)
0.882814 + 0.469722i \(0.155646\pi\)
\(720\) 4.46410i 0.166367i
\(721\) 3.10770 + 1.79423i 0.115737 + 0.0668206i
\(722\) −19.7321 11.3923i −0.734351 0.423978i
\(723\) 23.6603i 0.879934i
\(724\) −8.29423 + 14.3660i −0.308253 + 0.533909i
\(725\) −4.73205 8.19615i −0.175744 0.304397i
\(726\) 4.73205 2.73205i 0.175623 0.101396i
\(727\) −38.3731 −1.42318 −0.711589 0.702596i \(-0.752024\pi\)
−0.711589 + 0.702596i \(0.752024\pi\)
\(728\) 0 0
\(729\) −43.7846 −1.62165
\(730\) 4.90192 2.83013i 0.181428 0.104748i
\(731\) 2.19615 + 3.80385i 0.0812276 + 0.140690i
\(732\) 5.73205 9.92820i 0.211863 0.366957i
\(733\) 50.9090i 1.88037i 0.340670 + 0.940183i \(0.389346\pi\)
−0.340670 + 0.940183i \(0.610654\pi\)
\(734\) −22.8564 13.1962i −0.843645 0.487079i
\(735\) −4.73205 2.73205i −0.174544 0.100773i
\(736\) 2.53590i 0.0934745i
\(737\) 0 0
\(738\) −23.1962 40.1769i −0.853862 1.47893i
\(739\) −43.7942 + 25.2846i −1.61100 + 0.930109i −0.621857 + 0.783131i \(0.713622\pi\)
−0.989140 + 0.146979i \(0.953045\pi\)
\(740\) −11.1962 −0.411579
\(741\) 0 0
\(742\) 19.3923 0.711914
\(743\) −29.7846 + 17.1962i −1.09269 + 0.630866i −0.934292 0.356509i \(-0.883967\pi\)
−0.158400 + 0.987375i \(0.550633\pi\)
\(744\) 1.73205 + 3.00000i 0.0635001 + 0.109985i
\(745\) −3.00000 + 5.19615i −0.109911 + 0.190372i
\(746\) 20.3923i 0.746615i
\(747\) 8.49038 + 4.90192i 0.310647 + 0.179352i
\(748\) −5.70577 3.29423i −0.208624 0.120449i
\(749\) 1.01924i 0.0372421i
\(750\) −1.36603 + 2.36603i −0.0498802 + 0.0863950i
\(751\) −0.196152 0.339746i −0.00715770 0.0123975i 0.862424 0.506186i \(-0.168945\pi\)
−0.869582 + 0.493788i \(0.835612\pi\)
\(752\) −2.59808 + 1.50000i −0.0947421 + 0.0546994i
\(753\) −18.5885 −0.677401
\(754\) 0 0
\(755\) −6.33975 −0.230727
\(756\) −10.3923 + 6.00000i −0.377964 + 0.218218i
\(757\) −1.89230 3.27757i −0.0687770 0.119125i 0.829586 0.558379i \(-0.188576\pi\)
−0.898363 + 0.439253i \(0.855243\pi\)
\(758\) 5.89230 10.2058i 0.214018 0.370690i
\(759\) 20.7846i 0.754434i
\(760\) −5.59808 3.23205i −0.203064 0.117239i
\(761\) 25.2846 + 14.5981i 0.916566 + 0.529180i 0.882538 0.470241i \(-0.155833\pi\)
0.0340283 + 0.999421i \(0.489166\pi\)
\(762\) 57.9090i 2.09782i
\(763\) −23.1962 + 40.1769i −0.839757 + 1.45450i
\(764\) −9.63397 16.6865i −0.348545 0.603698i
\(765\) −8.49038 + 4.90192i −0.306970 + 0.177229i
\(766\) −1.60770 −0.0580884
\(767\) 0 0
\(768\) −2.73205 −0.0985844
\(769\) 33.0000 19.0526i 1.19001 0.687053i 0.231701 0.972787i \(-0.425571\pi\)
0.958309 + 0.285734i \(0.0922374\pi\)
\(770\) −4.50000 7.79423i −0.162169 0.280885i
\(771\) 18.9282 32.7846i 0.681683 1.18071i
\(772\) 4.39230i 0.158083i
\(773\) 29.0885 + 16.7942i 1.04624 + 0.604046i 0.921594 0.388155i \(-0.126887\pi\)
0.124645 + 0.992201i \(0.460221\pi\)
\(774\) 7.73205 + 4.46410i 0.277923 + 0.160459i
\(775\) 1.26795i 0.0455461i
\(776\) 7.56218 13.0981i 0.271466 0.470194i
\(777\) −45.8827 79.4711i −1.64603 2.85101i
\(778\) −16.6865 + 9.63397i −0.598241 + 0.345395i
\(779\) 67.1769 2.40686
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 4.82309 2.78461i 0.172473 0.0995774i
\(783\) −18.9282 32.7846i −0.676439 1.17163i
\(784\) 1.00000 1.73205i 0.0357143 0.0618590i
\(785\) 13.0000i 0.463990i
\(786\) 42.8827 + 24.7583i 1.52957 + 0.883100i
\(787\) 31.9019 + 18.4186i 1.13718 + 0.656552i 0.945731 0.324951i \(-0.105348\pi\)
0.191450 + 0.981502i \(0.438681\pi\)
\(788\) 9.58846i 0.341575i
\(789\) −37.6865 + 65.2750i −1.34168 + 2.32385i
\(790\) −3.09808 5.36603i −0.110225 0.190915i
\(791\) 18.0000 10.3923i 0.640006 0.369508i
\(792\) −13.3923 −0.475875
\(793\) 0 0
\(794\) 0.803848 0.0285275
\(795\) 15.2942 8.83013i 0.542430 0.313172i
\(796\) 7.19615 + 12.4641i 0.255061 + 0.441778i
\(797\) −0.464102 + 0.803848i −0.0164393 + 0.0284737i −0.874128 0.485696i \(-0.838566\pi\)
0.857689 + 0.514169i \(0.171900\pi\)
\(798\) 52.9808i 1.87550i
\(799\) −5.70577 3.29423i −0.201856 0.116541i
\(800\) −0.866025 0.500000i −0.0306186 0.0176777i
\(801\) 76.7654i 2.71237i
\(802\) −2.59808 + 4.50000i −0.0917413 + 0.158901i
\(803\) 8.49038 + 14.7058i 0.299619 + 0.518955i
\(804\) 0 0
\(805\) 7.60770 0.268136
\(806\) 0 0
\(807\) 7.85641 0.276559
\(808\) 6.29423 3.63397i 0.221430 0.127843i
\(809\) −12.0000 20.7846i −0.421898 0.730748i 0.574228 0.818696i \(-0.305302\pi\)
−0.996125 + 0.0879478i \(0.971969\pi\)
\(810\) 1.23205 2.13397i 0.0432899 0.0749802i
\(811\) 22.6077i 0.793864i −0.917848 0.396932i \(-0.870075\pi\)
0.917848 0.396932i \(-0.129925\pi\)
\(812\) 24.5885 + 14.1962i 0.862886 + 0.498187i
\(813\) 6.00000 + 3.46410i 0.210429 + 0.121491i
\(814\) 33.5885i 1.17727i
\(815\) 3.63397 6.29423i 0.127293 0.220477i
\(816\) −3.00000 5.19615i −0.105021 0.181902i
\(817\) −11.1962 + 6.46410i −0.391704 + 0.226150i
\(818\) 19.7321 0.689915
\(819\) 0 0
\(820\) 10.3923 0.362915
\(821\) 8.49038 4.90192i 0.296316 0.171078i −0.344471 0.938797i \(-0.611942\pi\)
0.640787 + 0.767719i \(0.278608\pi\)
\(822\) 11.1962 + 19.3923i 0.390511 + 0.676384i
\(823\) 8.40192 14.5526i 0.292873 0.507270i −0.681615 0.731711i \(-0.738722\pi\)
0.974488 + 0.224441i \(0.0720555\pi\)
\(824\) 1.19615i 0.0416699i
\(825\) −7.09808 4.09808i −0.247123 0.142677i
\(826\) 27.0000 + 15.5885i 0.939450 + 0.542392i
\(827\) 11.4115i 0.396818i 0.980119 + 0.198409i \(0.0635775\pi\)
−0.980119 + 0.198409i \(0.936423\pi\)
\(828\) 5.66025 9.80385i 0.196707 0.340707i
\(829\) 10.0000 + 17.3205i 0.347314 + 0.601566i 0.985771 0.168091i \(-0.0537604\pi\)
−0.638457 + 0.769657i \(0.720427\pi\)
\(830\) −1.90192 + 1.09808i −0.0660167 + 0.0381148i
\(831\) 2.73205 0.0947738
\(832\) 0 0
\(833\) 4.39230 0.152184
\(834\) −21.7583 + 12.5622i −0.753429 + 0.434993i
\(835\) 1.50000 + 2.59808i 0.0519096 + 0.0899101i
\(836\) 9.69615 16.7942i 0.335348 0.580841i
\(837\) 5.07180i 0.175307i
\(838\) 15.0000 + 8.66025i 0.518166 + 0.299164i
\(839\) 27.8827 + 16.0981i 0.962617 + 0.555767i 0.896978 0.442076i \(-0.145758\pi\)
0.0656397 + 0.997843i \(0.479091\pi\)
\(840\) 8.19615i 0.282794i
\(841\) −30.2846 + 52.4545i −1.04430 + 1.80878i
\(842\) 13.5622 + 23.4904i 0.467384 + 0.809532i
\(843\) 24.5885 14.1962i 0.846871 0.488941i
\(844\) −13.5885 −0.467734
\(845\) 0 0
\(846\) −13.3923 −0.460437
\(847\) −5.19615 + 3.00000i −0.178542 + 0.103081i
\(848\) 3.23205 + 5.59808i 0.110989 + 0.192239i
\(849\) −41.5167 + 71.9090i −1.42485 + 2.46791i
\(850\) 2.19615i 0.0753274i
\(851\) 24.5885 + 14.1962i 0.842881 + 0.486638i
\(852\) −14.1962 8.19615i −0.486352 0.280796i
\(853\) 13.8564i 0.474434i 0.971457 + 0.237217i \(0.0762353\pi\)
−0.971457 + 0.237217i \(0.923765\pi\)
\(854\) −6.29423 + 10.9019i −0.215384 + 0.373056i
\(855\) −14.4282 24.9904i −0.493434 0.854653i
\(856\) 0.294229 0.169873i 0.0100565 0.00580614i
\(857\) −13.2679 −0.453225 −0.226612 0.973985i \(-0.572765\pi\)
−0.226612 + 0.973985i \(0.572765\pi\)
\(858\) 0 0
\(859\) 52.3731 1.78695 0.893473 0.449117i \(-0.148261\pi\)
0.893473 + 0.449117i \(0.148261\pi\)
\(860\) −1.73205 + 1.00000i −0.0590624 + 0.0340997i
\(861\) 42.5885 + 73.7654i 1.45141 + 2.51392i
\(862\) −1.09808 + 1.90192i −0.0374006 + 0.0647798i
\(863\) 19.1769i 0.652790i 0.945234 + 0.326395i \(0.105834\pi\)
−0.945234 + 0.326395i \(0.894166\pi\)
\(864\) −3.46410 2.00000i −0.117851 0.0680414i
\(865\) 12.9904 + 7.50000i 0.441686 + 0.255008i
\(866\) 12.3923i 0.421108i
\(867\) −16.6340 + 28.8109i −0.564919 + 0.978469i
\(868\) −1.90192 3.29423i −0.0645555 0.111813i
\(869\) 16.0981 9.29423i 0.546090 0.315285i
\(870\) 25.8564 0.876614
\(871\) 0 0
\(872\) −15.4641 −0.523681
\(873\) 58.4711 33.7583i 1.97895 1.14255i
\(874\) 8.19615 + 14.1962i 0.277239 + 0.480192i
\(875\) 1.50000 2.59808i 0.0507093 0.0878310i
\(876\) 15.4641i 0.522484i
\(877\) −17.7846 10.2679i −0.600544 0.346724i 0.168712 0.985665i \(-0.446039\pi\)
−0.769255 + 0.638941i \(0.779373\pi\)
\(878\) −29.9545 17.2942i −1.01091 0.583652i
\(879\) 2.19615i 0.0740744i
\(880\) 1.50000 2.59808i 0.0505650 0.0875811i
\(881\) 4.16025 + 7.20577i 0.140163 + 0.242769i 0.927558 0.373680i \(-0.121904\pi\)
−0.787395 + 0.616449i \(0.788571\pi\)
\(882\) 7.73205 4.46410i 0.260352 0.150314i
\(883\) −26.5885 −0.894773 −0.447386 0.894341i \(-0.647645\pi\)
−0.447386 + 0.894341i \(0.647645\pi\)
\(884\) 0 0
\(885\) 28.3923 0.954397
\(886\) 1.39230 0.803848i 0.0467754 0.0270058i
\(887\) −26.3827 45.6962i −0.885844 1.53433i −0.844743 0.535172i \(-0.820247\pi\)
−0.0411005 0.999155i \(-0.513086\pi\)
\(888\) 15.2942 26.4904i 0.513241 0.888959i
\(889\) 63.5885i 2.13269i
\(890\) −14.8923 8.59808i −0.499191 0.288208i
\(891\) 6.40192 + 3.69615i 0.214473 + 0.123826i
\(892\) 0.464102i 0.0155393i
\(893\) 9.69615 16.7942i 0.324469 0.561997i
\(894\) −8.19615 14.1962i −0.274120 0.474790i
\(895\) −2.19615 + 1.26795i −0.0734093 + 0.0423829i
\(896\) 3.00000 0.100223
\(897\) 0 0
\(898\) 15.5885 0.520194
\(899\) 10.3923 6.00000i 0.346603 0.200111i
\(900\) −2.23205 3.86603i −0.0744017 0.128868i
\(901\) −7.09808 + 12.2942i −0.236471 + 0.409580i
\(902\) 31.1769i 1.03808i
\(903\) −14.1962 8.19615i −0.472418 0.272751i
\(904\) 6.00000 + 3.46410i 0.199557 + 0.115214i
\(905\) 16.5885i 0.551419i
\(906\) 8.66025 15.0000i 0.287718 0.498342i
\(907\) 13.2942 + 23.0263i 0.441428 + 0.764575i 0.997796 0.0663609i \(-0.0211389\pi\)
−0.556368 + 0.830936i \(0.687806\pi\)
\(908\) −3.80385 + 2.19615i −0.126235 + 0.0728819i
\(909\) 32.4449 1.07613
\(910\) 0 0
\(911\) −14.5359 −0.481596 −0.240798 0.970575i \(-0.577409\pi\)
−0.240798 + 0.970575i \(0.577409\pi\)
\(912\) 15.2942 8.83013i 0.506443 0.292395i
\(913\) −3.29423 5.70577i −0.109023 0.188833i
\(914\) −17.8301 + 30.8827i −0.589768 + 1.02151i
\(915\) 11.4641i 0.378992i
\(916\) 4.09808 + 2.36603i 0.135404 + 0.0781757i
\(917\) −47.0885 27.1865i −1.55500 0.897778i
\(918\) 8.78461i 0.289935i
\(919\) 5.39230 9.33975i 0.177876 0.308090i −0.763277 0.646071i \(-0.776411\pi\)
0.941153 + 0.337982i \(0.109744\pi\)
\(920\) 1.26795 + 2.19615i 0.0418030 + 0.0724050i
\(921\) −48.5885 + 28.0526i −1.60104 + 0.924363i
\(922\) −0.588457 −0.0193798
\(923\) 0 0
\(924\) 24.5885 0.808901
\(925\) 9.69615 5.59808i 0.318808 0.184064i
\(926\) −0.464102 0.803848i −0.0152513 0.0264161i
\(927\) −2.66987 + 4.62436i −0.0876901 + 0.151884i
\(928\) 9.46410i 0.310674i
\(929\) −38.7846 22.3923i −1.27248 0.734668i −0.297027 0.954869i \(-0.595995\pi\)
−0.975454 + 0.220201i \(0.929329\pi\)
\(930\) −3.00000 1.73205i −0.0983739 0.0567962i
\(931\) 12.9282i 0.423705i
\(932\) 0.633975 1.09808i 0.0207665 0.0359687i
\(933\) 20.6603 + 35.7846i 0.676386 + 1.17154i
\(934\) 8.78461 5.07180i 0.287441 0.165954i
\(935\) 6.58846 0.215466
\(936\) 0 0
\(937\) −30.3923 −0.992873 −0.496437 0.868073i \(-0.665359\pi\)
−0.496437 + 0.868073i \(0.665359\pi\)
\(938\) 0 0
\(939\) 7.66025 + 13.2679i 0.249983 + 0.432983i
\(940\) 1.50000 2.59808i 0.0489246 0.0847399i
\(941\) 44.7846i 1.45994i −0.683481 0.729968i \(-0.739535\pi\)
0.683481 0.729968i \(-0.260465\pi\)
\(942\) 30.7583 + 17.7583i 1.00216 + 0.578598i
\(943\) −22.8231 13.1769i −0.743222 0.429099i
\(944\) 10.3923i 0.338241i
\(945\) 6.00000 10.3923i 0.195180 0.338062i
\(946\) −3.00000 5.19615i −0.0975384 0.168941i
\(947\) −49.6865 + 28.6865i −1.61460 + 0.932187i −0.626309 + 0.779575i \(0.715435\pi\)
−0.988286 + 0.152612i \(0.951231\pi\)
\(948\) 16.9282 0.549802
\(949\) 0 0
\(950\) 6.46410 0.209723
\(951\) −30.2942 + 17.4904i −0.982358 + 0.567164i
\(952\) 3.29423 + 5.70577i 0.106767 + 0.184925i
\(953\) −12.2942 + 21.2942i −0.398249 + 0.689788i −0.993510 0.113745i \(-0.963715\pi\)
0.595261 + 0.803533i \(0.297049\pi\)
\(954\) 28.8564i 0.934261i
\(955\) 16.6865 + 9.63397i 0.539964 + 0.311748i
\(956\) 7.09808 + 4.09808i 0.229568 + 0.132541i
\(957\) 77.5692i 2.50746i
\(958\) −5.49038 + 9.50962i −0.177386 + 0.307242i
\(959\) −12.2942 21.2942i −0.397001 0.687627i
\(960\) 2.36603 1.36603i 0.0763631 0.0440883i
\(961\) 29.3923 0.948139
\(962\) 0 0
\(963\) 1.51666 0.0488737
\(964\) 7.50000 4.33013i 0.241559 0.139464i
\(965\) 2.19615 + 3.80385i 0.0706966 + 0.122450i
\(966\) −10.3923 + 18.0000i −0.334367 + 0.579141i
\(967\) 38.5692i 1.24030i −0.784482 0.620151i \(-0.787071\pi\)
0.784482 0.620151i \(-0.212929\pi\)
\(968\) −1.73205 1.00000i −0.0556702 0.0321412i
\(969\) 33.5885 + 19.3923i 1.07902 + 0.622971i
\(970\) 15.1244i 0.485614i
\(971\) 23.3827 40.5000i 0.750386 1.29971i −0.197250 0.980353i \(-0.563201\pi\)
0.947636 0.319354i \(-0.103466\pi\)
\(972\) 9.36603 + 16.2224i 0.300415 + 0.520335i
\(973\) 23.8923 13.7942i 0.765952 0.442223i
\(974\) −33.2487 −1.06536
\(975\) 0 0
\(976\) −4.19615 −0.134316
\(977\) −3.80385 + 2.19615i −0.121696 + 0.0702611i −0.559612 0.828755i \(-0.689050\pi\)
0.437916 + 0.899016i \(0.355717\pi\)
\(978\) 9.92820 + 17.1962i 0.317469 + 0.549872i
\(979\) 25.7942 44.6769i 0.824387 1.42788i
\(980\) 2.00000i 0.0638877i
\(981\) −59.7846 34.5167i −1.90878 1.10203i
\(982\) 2.89230 + 1.66987i 0.0922972 + 0.0532878i
\(983\) 38.5692i 1.23017i 0.788462 + 0.615084i \(0.210878\pi\)
−0.788462 + 0.615084i \(0.789122\pi\)
\(984\) −14.1962 + 24.5885i −0.452557 + 0.783851i
\(985\) −4.79423 8.30385i −0.152757 0.264583i
\(986\) −18.0000 + 10.3923i −0.573237 + 0.330958i
\(987\) 24.5885 0.782659
\(988\) 0 0
\(989\) 5.07180 0.161274
\(990\) 11.5981 6.69615i 0.368611 0.212818i
\(991\) −25.5885 44.3205i −0.812844 1.40789i −0.910866 0.412703i \(-0.864585\pi\)
0.0980215 0.995184i \(-0.468749\pi\)
\(992\) 0.633975 1.09808i 0.0201287 0.0348640i
\(993\) 2.53590i 0.0804743i
\(994\) 15.5885 + 9.00000i 0.494436 + 0.285463i
\(995\) −12.4641 7.19615i −0.395139 0.228133i
\(996\) 6.00000i 0.190117i
\(997\) 21.2846 36.8660i 0.674090 1.16756i −0.302644 0.953104i \(-0.597869\pi\)
0.976734 0.214455i \(-0.0687975\pi\)
\(998\) −0.928203 1.60770i −0.0293818 0.0508907i
\(999\) 38.7846 22.3923i 1.22709 0.708461i
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 1690.2.l.g.361.1 4
13.2 odd 12 1690.2.a.j.1.1 2
13.3 even 3 1690.2.d.f.1351.1 4
13.4 even 6 inner 1690.2.l.g.1161.1 4
13.5 odd 4 1690.2.e.n.991.2 4
13.6 odd 12 1690.2.e.n.191.2 4
13.7 odd 12 1690.2.e.l.191.2 4
13.8 odd 4 1690.2.e.l.991.2 4
13.9 even 3 130.2.l.a.121.2 yes 4
13.10 even 6 1690.2.d.f.1351.3 4
13.11 odd 12 1690.2.a.m.1.1 2
13.12 even 2 130.2.l.a.101.2 4
39.35 odd 6 1170.2.bs.c.901.1 4
39.38 odd 2 1170.2.bs.c.361.1 4
52.35 odd 6 1040.2.da.a.641.1 4
52.51 odd 2 1040.2.da.a.881.1 4
65.9 even 6 650.2.m.a.251.1 4
65.12 odd 4 650.2.n.b.49.2 4
65.22 odd 12 650.2.n.a.199.1 4
65.24 odd 12 8450.2.a.bf.1.2 2
65.38 odd 4 650.2.n.a.49.1 4
65.48 odd 12 650.2.n.b.199.2 4
65.54 odd 12 8450.2.a.bm.1.2 2
65.64 even 2 650.2.m.a.101.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.2.l.a.101.2 4 13.12 even 2
130.2.l.a.121.2 yes 4 13.9 even 3
650.2.m.a.101.1 4 65.64 even 2
650.2.m.a.251.1 4 65.9 even 6
650.2.n.a.49.1 4 65.38 odd 4
650.2.n.a.199.1 4 65.22 odd 12
650.2.n.b.49.2 4 65.12 odd 4
650.2.n.b.199.2 4 65.48 odd 12
1040.2.da.a.641.1 4 52.35 odd 6
1040.2.da.a.881.1 4 52.51 odd 2
1170.2.bs.c.361.1 4 39.38 odd 2
1170.2.bs.c.901.1 4 39.35 odd 6
1690.2.a.j.1.1 2 13.2 odd 12
1690.2.a.m.1.1 2 13.11 odd 12
1690.2.d.f.1351.1 4 13.3 even 3
1690.2.d.f.1351.3 4 13.10 even 6
1690.2.e.l.191.2 4 13.7 odd 12
1690.2.e.l.991.2 4 13.8 odd 4
1690.2.e.n.191.2 4 13.6 odd 12
1690.2.e.n.991.2 4 13.5 odd 4
1690.2.l.g.361.1 4 1.1 even 1 trivial
1690.2.l.g.1161.1 4 13.4 even 6 inner
8450.2.a.bf.1.2 2 65.24 odd 12
8450.2.a.bm.1.2 2 65.54 odd 12