Properties

Label 1690.2.e.n.991.1
Level $1690$
Weight $2$
Character 1690.991
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(191,1690)]
 
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, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1690.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1690.e (of order \(3\), 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 \(\Q(\zeta_{3})\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 130)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1690.991
Dual form 1690.2.e.n.191.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.366025 - 0.633975i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.366025 - 0.633975i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.23205 - 2.13397i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +0.732051 q^{12} -3.00000 q^{14} +(-0.366025 - 0.633975i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.09808 - 7.09808i) q^{17} +2.46410 q^{18} +(-0.232051 + 0.401924i) q^{19} +(-0.500000 + 0.866025i) q^{20} +2.19615 q^{21} +(-1.50000 + 2.59808i) q^{22} +(4.73205 + 8.19615i) q^{23} +(0.366025 + 0.633975i) q^{24} +1.00000 q^{25} -4.00000 q^{27} +(-1.50000 - 2.59808i) q^{28} +(1.26795 + 2.19615i) q^{29} +(0.366025 - 0.633975i) q^{30} -4.73205 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.09808 - 1.90192i) q^{33} +8.19615 q^{34} +(-1.50000 + 2.59808i) q^{35} +(1.23205 + 2.13397i) q^{36} +(-0.401924 - 0.696152i) q^{37} -0.464102 q^{38} -1.00000 q^{40} +(5.19615 + 9.00000i) q^{41} +(1.09808 + 1.90192i) q^{42} +(1.00000 - 1.73205i) q^{43} -3.00000 q^{44} +(1.23205 - 2.13397i) q^{45} +(-4.73205 + 8.19615i) q^{46} +3.00000 q^{47} +(-0.366025 + 0.633975i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} -6.00000 q^{51} +0.464102 q^{53} +(-2.00000 - 3.46410i) q^{54} +(1.50000 + 2.59808i) q^{55} +(1.50000 - 2.59808i) q^{56} +0.339746 q^{57} +(-1.26795 + 2.19615i) q^{58} +(-5.19615 + 9.00000i) q^{59} +0.732051 q^{60} +(-3.09808 + 5.36603i) q^{61} +(-2.36603 - 4.09808i) q^{62} +(3.69615 + 6.40192i) q^{63} +1.00000 q^{64} +2.19615 q^{66} +(4.09808 + 7.09808i) q^{68} +(3.46410 - 6.00000i) q^{69} -3.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(-1.23205 + 2.13397i) q^{72} +11.6603 q^{73} +(0.401924 - 0.696152i) q^{74} +(-0.366025 - 0.633975i) q^{75} +(-0.232051 - 0.401924i) q^{76} -9.00000 q^{77} -4.19615 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(-5.19615 + 9.00000i) q^{82} +8.19615 q^{83} +(-1.09808 + 1.90192i) q^{84} +(4.09808 - 7.09808i) q^{85} +2.00000 q^{86} +(0.928203 - 1.60770i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(3.40192 + 5.89230i) q^{89} +2.46410 q^{90} -9.46410 q^{92} +(1.73205 + 3.00000i) q^{93} +(1.50000 + 2.59808i) q^{94} +(-0.232051 + 0.401924i) q^{95} -0.732051 q^{96} +(4.56218 - 7.90192i) q^{97} +(1.00000 - 1.73205i) q^{98} +7.39230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 6 q^{11} - 4 q^{12} - 12 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 6 q^{19} - 2 q^{20} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 2 q^{24} + 4 q^{25} - 16 q^{27} - 6 q^{28} + 12 q^{29} - 2 q^{30} - 12 q^{31} + 2 q^{32} - 6 q^{33} + 12 q^{34} - 6 q^{35} - 2 q^{36} - 12 q^{37} + 12 q^{38} - 4 q^{40} - 6 q^{42} + 4 q^{43} - 12 q^{44} - 2 q^{45} - 12 q^{46} + 12 q^{47} + 2 q^{48} - 4 q^{49} + 2 q^{50} - 24 q^{51} - 12 q^{53} - 8 q^{54} + 6 q^{55} + 6 q^{56} + 36 q^{57} - 12 q^{58} - 4 q^{60} - 2 q^{61} - 6 q^{62} - 6 q^{63} + 4 q^{64} - 12 q^{66} + 6 q^{68} - 12 q^{70} - 12 q^{71} + 2 q^{72} + 12 q^{73} + 12 q^{74} + 2 q^{75} + 6 q^{76} - 36 q^{77} + 4 q^{79} - 2 q^{80} - 2 q^{81} + 12 q^{83} + 6 q^{84} + 6 q^{85} + 8 q^{86} - 24 q^{87} - 6 q^{88} + 24 q^{89} - 4 q^{90} - 24 q^{92} + 6 q^{94} + 6 q^{95} + 4 q^{96} - 6 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.366025 0.633975i −0.211325 0.366025i 0.740805 0.671721i \(-0.234444\pi\)
−0.952129 + 0.305695i \(0.901111\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.00000 0.447214
\(6\) 0.366025 0.633975i 0.149429 0.258819i
\(7\) −1.50000 + 2.59808i −0.566947 + 0.981981i 0.429919 + 0.902867i \(0.358542\pi\)
−0.996866 + 0.0791130i \(0.974791\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.23205 2.13397i 0.410684 0.711325i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0.732051 0.211325
\(13\) 0 0
\(14\) −3.00000 −0.801784
\(15\) −0.366025 0.633975i −0.0945074 0.163692i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.09808 7.09808i 0.993929 1.72154i 0.401685 0.915778i \(-0.368425\pi\)
0.592244 0.805759i \(-0.298242\pi\)
\(18\) 2.46410 0.580794
\(19\) −0.232051 + 0.401924i −0.0532361 + 0.0922076i −0.891415 0.453187i \(-0.850287\pi\)
0.838179 + 0.545395i \(0.183620\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) 2.19615 0.479240
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) 4.73205 + 8.19615i 0.986701 + 1.70902i 0.634120 + 0.773234i \(0.281362\pi\)
0.352581 + 0.935781i \(0.385304\pi\)
\(24\) 0.366025 + 0.633975i 0.0747146 + 0.129410i
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) −1.50000 2.59808i −0.283473 0.490990i
\(29\) 1.26795 + 2.19615i 0.235452 + 0.407815i 0.959404 0.282035i \(-0.0910095\pi\)
−0.723952 + 0.689851i \(0.757676\pi\)
\(30\) 0.366025 0.633975i 0.0668268 0.115747i
\(31\) −4.73205 −0.849901 −0.424951 0.905216i \(-0.639709\pi\)
−0.424951 + 0.905216i \(0.639709\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 1.09808 1.90192i 0.191151 0.331082i
\(34\) 8.19615 1.40563
\(35\) −1.50000 + 2.59808i −0.253546 + 0.439155i
\(36\) 1.23205 + 2.13397i 0.205342 + 0.355662i
\(37\) −0.401924 0.696152i −0.0660759 0.114447i 0.831095 0.556131i \(-0.187715\pi\)
−0.897171 + 0.441684i \(0.854381\pi\)
\(38\) −0.464102 −0.0752872
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 5.19615 + 9.00000i 0.811503 + 1.40556i 0.911812 + 0.410608i \(0.134683\pi\)
−0.100309 + 0.994956i \(0.531983\pi\)
\(42\) 1.09808 + 1.90192i 0.169437 + 0.293473i
\(43\) 1.00000 1.73205i 0.152499 0.264135i −0.779647 0.626219i \(-0.784601\pi\)
0.932145 + 0.362084i \(0.117935\pi\)
\(44\) −3.00000 −0.452267
\(45\) 1.23205 2.13397i 0.183663 0.318114i
\(46\) −4.73205 + 8.19615i −0.697703 + 1.20846i
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) −0.366025 + 0.633975i −0.0528312 + 0.0915064i
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) −6.00000 −0.840168
\(52\) 0 0
\(53\) 0.464102 0.0637493 0.0318746 0.999492i \(-0.489852\pi\)
0.0318746 + 0.999492i \(0.489852\pi\)
\(54\) −2.00000 3.46410i −0.272166 0.471405i
\(55\) 1.50000 + 2.59808i 0.202260 + 0.350325i
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) 0.339746 0.0450005
\(58\) −1.26795 + 2.19615i −0.166490 + 0.288369i
\(59\) −5.19615 + 9.00000i −0.676481 + 1.17170i 0.299552 + 0.954080i \(0.403163\pi\)
−0.976034 + 0.217620i \(0.930171\pi\)
\(60\) 0.732051 0.0945074
\(61\) −3.09808 + 5.36603i −0.396668 + 0.687049i −0.993313 0.115456i \(-0.963167\pi\)
0.596645 + 0.802506i \(0.296500\pi\)
\(62\) −2.36603 4.09808i −0.300486 0.520456i
\(63\) 3.69615 + 6.40192i 0.465671 + 0.806567i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 2.19615 0.270328
\(67\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(68\) 4.09808 + 7.09808i 0.496965 + 0.860768i
\(69\) 3.46410 6.00000i 0.417029 0.722315i
\(70\) −3.00000 −0.358569
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −1.23205 + 2.13397i −0.145199 + 0.251491i
\(73\) 11.6603 1.36473 0.682365 0.731012i \(-0.260952\pi\)
0.682365 + 0.731012i \(0.260952\pi\)
\(74\) 0.401924 0.696152i 0.0467227 0.0809261i
\(75\) −0.366025 0.633975i −0.0422650 0.0732051i
\(76\) −0.232051 0.401924i −0.0266181 0.0461038i
\(77\) −9.00000 −1.02565
\(78\) 0 0
\(79\) −4.19615 −0.472104 −0.236052 0.971740i \(-0.575854\pi\)
−0.236052 + 0.971740i \(0.575854\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −2.23205 3.86603i −0.248006 0.429558i
\(82\) −5.19615 + 9.00000i −0.573819 + 0.993884i
\(83\) 8.19615 0.899645 0.449822 0.893118i \(-0.351487\pi\)
0.449822 + 0.893118i \(0.351487\pi\)
\(84\) −1.09808 + 1.90192i −0.119810 + 0.207517i
\(85\) 4.09808 7.09808i 0.444499 0.769894i
\(86\) 2.00000 0.215666
\(87\) 0.928203 1.60770i 0.0995138 0.172363i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 3.40192 + 5.89230i 0.360603 + 0.624583i 0.988060 0.154068i \(-0.0492375\pi\)
−0.627457 + 0.778651i \(0.715904\pi\)
\(90\) 2.46410 0.259739
\(91\) 0 0
\(92\) −9.46410 −0.986701
\(93\) 1.73205 + 3.00000i 0.179605 + 0.311086i
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) −0.232051 + 0.401924i −0.0238079 + 0.0412365i
\(96\) −0.732051 −0.0747146
\(97\) 4.56218 7.90192i 0.463219 0.802319i −0.535900 0.844281i \(-0.680028\pi\)
0.999119 + 0.0419625i \(0.0133610\pi\)
\(98\) 1.00000 1.73205i 0.101015 0.174964i
\(99\) 7.39230 0.742955
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 5.36603 + 9.29423i 0.533939 + 0.924810i 0.999214 + 0.0396438i \(0.0126223\pi\)
−0.465274 + 0.885167i \(0.654044\pi\)
\(102\) −3.00000 5.19615i −0.297044 0.514496i
\(103\) 9.19615 0.906124 0.453062 0.891479i \(-0.350332\pi\)
0.453062 + 0.891479i \(0.350332\pi\)
\(104\) 0 0
\(105\) 2.19615 0.214323
\(106\) 0.232051 + 0.401924i 0.0225388 + 0.0390383i
\(107\) −8.83013 15.2942i −0.853641 1.47855i −0.877900 0.478843i \(-0.841056\pi\)
0.0242598 0.999706i \(-0.492277\pi\)
\(108\) 2.00000 3.46410i 0.192450 0.333333i
\(109\) 8.53590 0.817591 0.408795 0.912626i \(-0.365949\pi\)
0.408795 + 0.912626i \(0.365949\pi\)
\(110\) −1.50000 + 2.59808i −0.143019 + 0.247717i
\(111\) −0.294229 + 0.509619i −0.0279269 + 0.0483709i
\(112\) 3.00000 0.283473
\(113\) −3.46410 + 6.00000i −0.325875 + 0.564433i −0.981689 0.190490i \(-0.938992\pi\)
0.655814 + 0.754923i \(0.272326\pi\)
\(114\) 0.169873 + 0.294229i 0.0159101 + 0.0275570i
\(115\) 4.73205 + 8.19615i 0.441266 + 0.764295i
\(116\) −2.53590 −0.235452
\(117\) 0 0
\(118\) −10.3923 −0.956689
\(119\) 12.2942 + 21.2942i 1.12701 + 1.95204i
\(120\) 0.366025 + 0.633975i 0.0334134 + 0.0578737i
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −6.19615 −0.560973
\(123\) 3.80385 6.58846i 0.342981 0.594061i
\(124\) 2.36603 4.09808i 0.212475 0.368018i
\(125\) 1.00000 0.0894427
\(126\) −3.69615 + 6.40192i −0.329279 + 0.570329i
\(127\) 5.40192 + 9.35641i 0.479343 + 0.830247i 0.999719 0.0236904i \(-0.00754158\pi\)
−0.520376 + 0.853937i \(0.674208\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −1.46410 −0.128907
\(130\) 0 0
\(131\) 6.12436 0.535087 0.267544 0.963546i \(-0.413788\pi\)
0.267544 + 0.963546i \(0.413788\pi\)
\(132\) 1.09808 + 1.90192i 0.0955753 + 0.165541i
\(133\) −0.696152 1.20577i −0.0603641 0.104554i
\(134\) 0 0
\(135\) −4.00000 −0.344265
\(136\) −4.09808 + 7.09808i −0.351407 + 0.608655i
\(137\) −1.09808 + 1.90192i −0.0938150 + 0.162492i −0.909113 0.416549i \(-0.863240\pi\)
0.815298 + 0.579041i \(0.196573\pi\)
\(138\) 6.92820 0.589768
\(139\) −0.598076 + 1.03590i −0.0507282 + 0.0878638i −0.890274 0.455424i \(-0.849488\pi\)
0.839546 + 0.543288i \(0.182821\pi\)
\(140\) −1.50000 2.59808i −0.126773 0.219578i
\(141\) −1.09808 1.90192i −0.0924747 0.160171i
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) −2.46410 −0.205342
\(145\) 1.26795 + 2.19615i 0.105297 + 0.182381i
\(146\) 5.83013 + 10.0981i 0.482505 + 0.835723i
\(147\) −0.732051 + 1.26795i −0.0603785 + 0.104579i
\(148\) 0.803848 0.0660759
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0.366025 0.633975i 0.0298858 0.0517638i
\(151\) −23.6603 −1.92544 −0.962722 0.270492i \(-0.912813\pi\)
−0.962722 + 0.270492i \(0.912813\pi\)
\(152\) 0.232051 0.401924i 0.0188218 0.0326003i
\(153\) −10.0981 17.4904i −0.816381 1.41401i
\(154\) −4.50000 7.79423i −0.362620 0.628077i
\(155\) −4.73205 −0.380087
\(156\) 0 0
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) −2.09808 3.63397i −0.166914 0.289103i
\(159\) −0.169873 0.294229i −0.0134718 0.0233338i
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) −28.3923 −2.23763
\(162\) 2.23205 3.86603i 0.175366 0.303744i
\(163\) 5.36603 9.29423i 0.420300 0.727980i −0.575669 0.817683i \(-0.695258\pi\)
0.995969 + 0.0897026i \(0.0285917\pi\)
\(164\) −10.3923 −0.811503
\(165\) 1.09808 1.90192i 0.0854851 0.148065i
\(166\) 4.09808 + 7.09808i 0.318072 + 0.550918i
\(167\) 1.50000 + 2.59808i 0.116073 + 0.201045i 0.918208 0.396098i \(-0.129636\pi\)
−0.802135 + 0.597143i \(0.796303\pi\)
\(168\) −2.19615 −0.169437
\(169\) 0 0
\(170\) 8.19615 0.628616
\(171\) 0.571797 + 0.990381i 0.0437264 + 0.0757363i
\(172\) 1.00000 + 1.73205i 0.0762493 + 0.132068i
\(173\) −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i \(0.359807\pi\)
−0.996544 + 0.0830722i \(0.973527\pi\)
\(174\) 1.85641 0.140734
\(175\) −1.50000 + 2.59808i −0.113389 + 0.196396i
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) 7.60770 0.571829
\(178\) −3.40192 + 5.89230i −0.254985 + 0.441647i
\(179\) −4.73205 8.19615i −0.353690 0.612609i 0.633203 0.773986i \(-0.281740\pi\)
−0.986893 + 0.161377i \(0.948407\pi\)
\(180\) 1.23205 + 2.13397i 0.0918316 + 0.159057i
\(181\) −14.5885 −1.08435 −0.542176 0.840265i \(-0.682399\pi\)
−0.542176 + 0.840265i \(0.682399\pi\)
\(182\) 0 0
\(183\) 4.53590 0.335303
\(184\) −4.73205 8.19615i −0.348851 0.604228i
\(185\) −0.401924 0.696152i −0.0295500 0.0511821i
\(186\) −1.73205 + 3.00000i −0.127000 + 0.219971i
\(187\) 24.5885 1.79809
\(188\) −1.50000 + 2.59808i −0.109399 + 0.189484i
\(189\) 6.00000 10.3923i 0.436436 0.755929i
\(190\) −0.464102 −0.0336695
\(191\) 11.3660 19.6865i 0.822417 1.42447i −0.0814609 0.996677i \(-0.525959\pi\)
0.903878 0.427791i \(-0.140708\pi\)
\(192\) −0.366025 0.633975i −0.0264156 0.0457532i
\(193\) −8.19615 14.1962i −0.589972 1.02186i −0.994235 0.107219i \(-0.965805\pi\)
0.404263 0.914643i \(-0.367528\pi\)
\(194\) 9.12436 0.655091
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) −10.7942 18.6962i −0.769057 1.33205i −0.938075 0.346433i \(-0.887393\pi\)
0.169018 0.985613i \(-0.445940\pi\)
\(198\) 3.69615 + 6.40192i 0.262674 + 0.454965i
\(199\) −3.19615 + 5.53590i −0.226569 + 0.392429i −0.956789 0.290783i \(-0.906084\pi\)
0.730220 + 0.683212i \(0.239418\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) −5.36603 + 9.29423i −0.377552 + 0.653940i
\(203\) −7.60770 −0.533956
\(204\) 3.00000 5.19615i 0.210042 0.363803i
\(205\) 5.19615 + 9.00000i 0.362915 + 0.628587i
\(206\) 4.59808 + 7.96410i 0.320363 + 0.554885i
\(207\) 23.3205 1.62089
\(208\) 0 0
\(209\) −1.39230 −0.0963077
\(210\) 1.09808 + 1.90192i 0.0757745 + 0.131245i
\(211\) 8.79423 + 15.2321i 0.605420 + 1.04862i 0.991985 + 0.126356i \(0.0403280\pi\)
−0.386565 + 0.922262i \(0.626339\pi\)
\(212\) −0.232051 + 0.401924i −0.0159373 + 0.0276042i
\(213\) 4.39230 0.300956
\(214\) 8.83013 15.2942i 0.603615 1.04549i
\(215\) 1.00000 1.73205i 0.0681994 0.118125i
\(216\) 4.00000 0.272166
\(217\) 7.09808 12.2942i 0.481849 0.834587i
\(218\) 4.26795 + 7.39230i 0.289062 + 0.500670i
\(219\) −4.26795 7.39230i −0.288401 0.499526i
\(220\) −3.00000 −0.202260
\(221\) 0 0
\(222\) −0.588457 −0.0394947
\(223\) 3.23205 + 5.59808i 0.216434 + 0.374875i 0.953715 0.300711i \(-0.0972240\pi\)
−0.737281 + 0.675586i \(0.763891\pi\)
\(224\) 1.50000 + 2.59808i 0.100223 + 0.173591i
\(225\) 1.23205 2.13397i 0.0821367 0.142265i
\(226\) −6.92820 −0.460857
\(227\) 8.19615 14.1962i 0.543998 0.942232i −0.454672 0.890659i \(-0.650243\pi\)
0.998669 0.0515725i \(-0.0164233\pi\)
\(228\) −0.169873 + 0.294229i −0.0112501 + 0.0194858i
\(229\) −1.26795 −0.0837884 −0.0418942 0.999122i \(-0.513339\pi\)
−0.0418942 + 0.999122i \(0.513339\pi\)
\(230\) −4.73205 + 8.19615i −0.312022 + 0.540438i
\(231\) 3.29423 + 5.70577i 0.216744 + 0.375412i
\(232\) −1.26795 2.19615i −0.0832449 0.144184i
\(233\) −4.73205 −0.310007 −0.155003 0.987914i \(-0.549539\pi\)
−0.155003 + 0.987914i \(0.549539\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) −5.19615 9.00000i −0.338241 0.585850i
\(237\) 1.53590 + 2.66025i 0.0997673 + 0.172802i
\(238\) −12.2942 + 21.2942i −0.796916 + 1.38030i
\(239\) −2.19615 −0.142057 −0.0710286 0.997474i \(-0.522628\pi\)
−0.0710286 + 0.997474i \(0.522628\pi\)
\(240\) −0.366025 + 0.633975i −0.0236268 + 0.0409229i
\(241\) 4.33013 7.50000i 0.278928 0.483117i −0.692191 0.721715i \(-0.743354\pi\)
0.971119 + 0.238597i \(0.0766876\pi\)
\(242\) 2.00000 0.128565
\(243\) −7.63397 + 13.2224i −0.489720 + 0.848219i
\(244\) −3.09808 5.36603i −0.198334 0.343525i
\(245\) −1.00000 1.73205i −0.0638877 0.110657i
\(246\) 7.60770 0.485049
\(247\) 0 0
\(248\) 4.73205 0.300486
\(249\) −3.00000 5.19615i −0.190117 0.329293i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 8.59808 14.8923i 0.542706 0.939994i −0.456042 0.889958i \(-0.650733\pi\)
0.998747 0.0500355i \(-0.0159335\pi\)
\(252\) −7.39230 −0.465671
\(253\) −14.1962 + 24.5885i −0.892504 + 1.54586i
\(254\) −5.40192 + 9.35641i −0.338947 + 0.587073i
\(255\) −6.00000 −0.375735
\(256\) −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 \(0.975585\pi\)
\(258\) −0.732051 1.26795i −0.0455755 0.0789391i
\(259\) 2.41154 0.149846
\(260\) 0 0
\(261\) 6.24871 0.386786
\(262\) 3.06218 + 5.30385i 0.189182 + 0.327673i
\(263\) −1.79423 3.10770i −0.110637 0.191629i 0.805390 0.592745i \(-0.201956\pi\)
−0.916027 + 0.401116i \(0.868622\pi\)
\(264\) −1.09808 + 1.90192i −0.0675819 + 0.117055i
\(265\) 0.464102 0.0285095
\(266\) 0.696152 1.20577i 0.0426838 0.0739306i
\(267\) 2.49038 4.31347i 0.152409 0.263980i
\(268\) 0 0
\(269\) 13.5622 23.4904i 0.826901 1.43223i −0.0735575 0.997291i \(-0.523435\pi\)
0.900458 0.434943i \(-0.143231\pi\)
\(270\) −2.00000 3.46410i −0.121716 0.210819i
\(271\) 4.73205 + 8.19615i 0.287452 + 0.497881i 0.973201 0.229957i \(-0.0738586\pi\)
−0.685749 + 0.727838i \(0.740525\pi\)
\(272\) −8.19615 −0.496965
\(273\) 0 0
\(274\) −2.19615 −0.132674
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 3.46410 + 6.00000i 0.208514 + 0.361158i
\(277\) −0.500000 + 0.866025i −0.0300421 + 0.0520344i −0.880656 0.473757i \(-0.842897\pi\)
0.850613 + 0.525792i \(0.176231\pi\)
\(278\) −1.19615 −0.0717405
\(279\) −5.83013 + 10.0981i −0.349041 + 0.604556i
\(280\) 1.50000 2.59808i 0.0896421 0.155265i
\(281\) −10.3923 −0.619953 −0.309976 0.950744i \(-0.600321\pi\)
−0.309976 + 0.950744i \(0.600321\pi\)
\(282\) 1.09808 1.90192i 0.0653895 0.113258i
\(283\) −4.80385 8.32051i −0.285559 0.494603i 0.687186 0.726482i \(-0.258846\pi\)
−0.972745 + 0.231879i \(0.925513\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 0.339746 0.0201248
\(286\) 0 0
\(287\) −31.1769 −1.84032
\(288\) −1.23205 2.13397i −0.0725993 0.125746i
\(289\) −25.0885 43.4545i −1.47579 2.55615i
\(290\) −1.26795 + 2.19615i −0.0744565 + 0.128963i
\(291\) −6.67949 −0.391559
\(292\) −5.83013 + 10.0981i −0.341182 + 0.590945i
\(293\) −5.59808 + 9.69615i −0.327043 + 0.566455i −0.981924 0.189277i \(-0.939386\pi\)
0.654881 + 0.755732i \(0.272719\pi\)
\(294\) −1.46410 −0.0853881
\(295\) −5.19615 + 9.00000i −0.302532 + 0.524000i
\(296\) 0.401924 + 0.696152i 0.0233613 + 0.0404630i
\(297\) −6.00000 10.3923i −0.348155 0.603023i
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 0.732051 0.0422650
\(301\) 3.00000 + 5.19615i 0.172917 + 0.299501i
\(302\) −11.8301 20.4904i −0.680747 1.17909i
\(303\) 3.92820 6.80385i 0.225669 0.390871i
\(304\) 0.464102 0.0266181
\(305\) −3.09808 + 5.36603i −0.177395 + 0.307258i
\(306\) 10.0981 17.4904i 0.577269 0.999859i
\(307\) −27.4641 −1.56746 −0.783730 0.621102i \(-0.786685\pi\)
−0.783730 + 0.621102i \(0.786685\pi\)
\(308\) 4.50000 7.79423i 0.256411 0.444117i
\(309\) −3.36603 5.83013i −0.191486 0.331664i
\(310\) −2.36603 4.09808i −0.134381 0.232755i
\(311\) 9.12436 0.517395 0.258697 0.965958i \(-0.416707\pi\)
0.258697 + 0.965958i \(0.416707\pi\)
\(312\) 0 0
\(313\) 26.3923 1.49178 0.745891 0.666068i \(-0.232024\pi\)
0.745891 + 0.666068i \(0.232024\pi\)
\(314\) −6.50000 11.2583i −0.366816 0.635344i
\(315\) 3.69615 + 6.40192i 0.208255 + 0.360708i
\(316\) 2.09808 3.63397i 0.118026 0.204427i
\(317\) 23.1962 1.30283 0.651413 0.758723i \(-0.274177\pi\)
0.651413 + 0.758723i \(0.274177\pi\)
\(318\) 0.169873 0.294229i 0.00952600 0.0164995i
\(319\) −3.80385 + 6.58846i −0.212975 + 0.368883i
\(320\) 1.00000 0.0559017
\(321\) −6.46410 + 11.1962i −0.360791 + 0.624908i
\(322\) −14.1962 24.5885i −0.791121 1.37026i
\(323\) 1.90192 + 3.29423i 0.105826 + 0.183296i
\(324\) 4.46410 0.248006
\(325\) 0 0
\(326\) 10.7321 0.594393
\(327\) −3.12436 5.41154i −0.172777 0.299259i
\(328\) −5.19615 9.00000i −0.286910 0.496942i
\(329\) −4.50000 + 7.79423i −0.248093 + 0.429710i
\(330\) 2.19615 0.120894
\(331\) 6.46410 11.1962i 0.355299 0.615396i −0.631870 0.775074i \(-0.717712\pi\)
0.987169 + 0.159678i \(0.0510457\pi\)
\(332\) −4.09808 + 7.09808i −0.224911 + 0.389558i
\(333\) −1.98076 −0.108545
\(334\) −1.50000 + 2.59808i −0.0820763 + 0.142160i
\(335\) 0 0
\(336\) −1.09808 1.90192i −0.0599050 0.103758i
\(337\) −6.19615 −0.337526 −0.168763 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(338\) 0 0
\(339\) 5.07180 0.275462
\(340\) 4.09808 + 7.09808i 0.222249 + 0.384947i
\(341\) −7.09808 12.2942i −0.384382 0.665770i
\(342\) −0.571797 + 0.990381i −0.0309192 + 0.0535537i
\(343\) −15.0000 −0.809924
\(344\) −1.00000 + 1.73205i −0.0539164 + 0.0933859i
\(345\) 3.46410 6.00000i 0.186501 0.323029i
\(346\) −15.0000 −0.806405
\(347\) 14.3660 24.8827i 0.771209 1.33577i −0.165692 0.986178i \(-0.552986\pi\)
0.936901 0.349595i \(-0.113681\pi\)
\(348\) 0.928203 + 1.60770i 0.0497569 + 0.0861815i
\(349\) −2.02628 3.50962i −0.108464 0.187866i 0.806684 0.590983i \(-0.201260\pi\)
−0.915148 + 0.403117i \(0.867927\pi\)
\(350\) −3.00000 −0.160357
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) −4.90192 8.49038i −0.260903 0.451897i 0.705579 0.708631i \(-0.250687\pi\)
−0.966482 + 0.256734i \(0.917354\pi\)
\(354\) 3.80385 + 6.58846i 0.202172 + 0.350173i
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) −6.80385 −0.360603
\(357\) 9.00000 15.5885i 0.476331 0.825029i
\(358\) 4.73205 8.19615i 0.250097 0.433180i
\(359\) 1.60770 0.0848509 0.0424255 0.999100i \(-0.486492\pi\)
0.0424255 + 0.999100i \(0.486492\pi\)
\(360\) −1.23205 + 2.13397i −0.0649348 + 0.112470i
\(361\) 9.39230 + 16.2679i 0.494332 + 0.856208i
\(362\) −7.29423 12.6340i −0.383376 0.664027i
\(363\) −1.46410 −0.0768454
\(364\) 0 0
\(365\) 11.6603 0.610326
\(366\) 2.26795 + 3.92820i 0.118548 + 0.205330i
\(367\) 2.80385 + 4.85641i 0.146360 + 0.253502i 0.929879 0.367865i \(-0.119911\pi\)
−0.783520 + 0.621367i \(0.786578\pi\)
\(368\) 4.73205 8.19615i 0.246675 0.427254i
\(369\) 25.6077 1.33308
\(370\) 0.401924 0.696152i 0.0208950 0.0361912i
\(371\) −0.696152 + 1.20577i −0.0361424 + 0.0626005i
\(372\) −3.46410 −0.179605
\(373\) 0.196152 0.339746i 0.0101564 0.0175914i −0.860903 0.508770i \(-0.830100\pi\)
0.871059 + 0.491179i \(0.163434\pi\)
\(374\) 12.2942 + 21.2942i 0.635719 + 1.10110i
\(375\) −0.366025 0.633975i −0.0189015 0.0327383i
\(376\) −3.00000 −0.154713
\(377\) 0 0
\(378\) 12.0000 0.617213
\(379\) −14.8923 25.7942i −0.764966 1.32496i −0.940264 0.340445i \(-0.889422\pi\)
0.175298 0.984515i \(-0.443911\pi\)
\(380\) −0.232051 0.401924i −0.0119040 0.0206183i
\(381\) 3.95448 6.84936i 0.202594 0.350904i
\(382\) 22.7321 1.16307
\(383\) 11.1962 19.3923i 0.572097 0.990900i −0.424254 0.905543i \(-0.639464\pi\)
0.996350 0.0853571i \(-0.0272031\pi\)
\(384\) 0.366025 0.633975i 0.0186787 0.0323524i
\(385\) −9.00000 −0.458682
\(386\) 8.19615 14.1962i 0.417173 0.722565i
\(387\) −2.46410 4.26795i −0.125257 0.216952i
\(388\) 4.56218 + 7.90192i 0.231609 + 0.401159i
\(389\) −22.7321 −1.15256 −0.576280 0.817252i \(-0.695496\pi\)
−0.576280 + 0.817252i \(0.695496\pi\)
\(390\) 0 0
\(391\) 77.5692 3.92284
\(392\) 1.00000 + 1.73205i 0.0505076 + 0.0874818i
\(393\) −2.24167 3.88269i −0.113077 0.195856i
\(394\) 10.7942 18.6962i 0.543805 0.941899i
\(395\) −4.19615 −0.211131
\(396\) −3.69615 + 6.40192i −0.185739 + 0.321709i
\(397\) 5.59808 9.69615i 0.280959 0.486636i −0.690662 0.723178i \(-0.742681\pi\)
0.971621 + 0.236542i \(0.0760140\pi\)
\(398\) −6.39230 −0.320417
\(399\) −0.509619 + 0.882686i −0.0255129 + 0.0441896i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −2.59808 4.50000i −0.129742 0.224719i 0.793835 0.608134i \(-0.208081\pi\)
−0.923576 + 0.383414i \(0.874748\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −10.7321 −0.533939
\(405\) −2.23205 3.86603i −0.110911 0.192104i
\(406\) −3.80385 6.58846i −0.188782 0.326980i
\(407\) 1.20577 2.08846i 0.0597679 0.103521i
\(408\) 6.00000 0.297044
\(409\) −8.13397 + 14.0885i −0.402199 + 0.696629i −0.993991 0.109461i \(-0.965087\pi\)
0.591792 + 0.806091i \(0.298421\pi\)
\(410\) −5.19615 + 9.00000i −0.256620 + 0.444478i
\(411\) 1.60770 0.0793018
\(412\) −4.59808 + 7.96410i −0.226531 + 0.392363i
\(413\) −15.5885 27.0000i −0.767058 1.32858i
\(414\) 11.6603 + 20.1962i 0.573070 + 0.992587i
\(415\) 8.19615 0.402333
\(416\) 0 0
\(417\) 0.875644 0.0428805
\(418\) −0.696152 1.20577i −0.0340499 0.0589762i
\(419\) 8.66025 + 15.0000i 0.423081 + 0.732798i 0.996239 0.0866469i \(-0.0276152\pi\)
−0.573158 + 0.819445i \(0.694282\pi\)
\(420\) −1.09808 + 1.90192i −0.0535806 + 0.0928044i
\(421\) −2.87564 −0.140150 −0.0700752 0.997542i \(-0.522324\pi\)
−0.0700752 + 0.997542i \(0.522324\pi\)
\(422\) −8.79423 + 15.2321i −0.428096 + 0.741485i
\(423\) 3.69615 6.40192i 0.179713 0.311272i
\(424\) −0.464102 −0.0225388
\(425\) 4.09808 7.09808i 0.198786 0.344307i
\(426\) 2.19615 + 3.80385i 0.106404 + 0.184297i
\(427\) −9.29423 16.0981i −0.449779 0.779041i
\(428\) 17.6603 0.853641
\(429\) 0 0
\(430\) 2.00000 0.0964486
\(431\) 4.09808 + 7.09808i 0.197397 + 0.341902i 0.947684 0.319211i \(-0.103418\pi\)
−0.750286 + 0.661113i \(0.770084\pi\)
\(432\) 2.00000 + 3.46410i 0.0962250 + 0.166667i
\(433\) 4.19615 7.26795i 0.201654 0.349275i −0.747407 0.664366i \(-0.768702\pi\)
0.949062 + 0.315091i \(0.102035\pi\)
\(434\) 14.1962 0.681437
\(435\) 0.928203 1.60770i 0.0445039 0.0770831i
\(436\) −4.26795 + 7.39230i −0.204398 + 0.354027i
\(437\) −4.39230 −0.210112
\(438\) 4.26795 7.39230i 0.203931 0.353218i
\(439\) −1.70577 2.95448i −0.0814120 0.141010i 0.822445 0.568845i \(-0.192610\pi\)
−0.903857 + 0.427835i \(0.859276\pi\)
\(440\) −1.50000 2.59808i −0.0715097 0.123858i
\(441\) −4.92820 −0.234676
\(442\) 0 0
\(443\) −22.3923 −1.06389 −0.531945 0.846779i \(-0.678539\pi\)
−0.531945 + 0.846779i \(0.678539\pi\)
\(444\) −0.294229 0.509619i −0.0139635 0.0241854i
\(445\) 3.40192 + 5.89230i 0.161267 + 0.279322i
\(446\) −3.23205 + 5.59808i −0.153042 + 0.265077i
\(447\) −4.39230 −0.207749
\(448\) −1.50000 + 2.59808i −0.0708683 + 0.122748i
\(449\) −7.79423 + 13.5000i −0.367832 + 0.637104i −0.989226 0.146394i \(-0.953233\pi\)
0.621394 + 0.783498i \(0.286567\pi\)
\(450\) 2.46410 0.116159
\(451\) −15.5885 + 27.0000i −0.734032 + 1.27138i
\(452\) −3.46410 6.00000i −0.162938 0.282216i
\(453\) 8.66025 + 15.0000i 0.406894 + 0.704761i
\(454\) 16.3923 0.769329
\(455\) 0 0
\(456\) −0.339746 −0.0159101
\(457\) −9.16987 15.8827i −0.428949 0.742961i 0.567832 0.823145i \(-0.307783\pi\)
−0.996780 + 0.0801841i \(0.974449\pi\)
\(458\) −0.633975 1.09808i −0.0296237 0.0513097i
\(459\) −16.3923 + 28.3923i −0.765127 + 1.32524i
\(460\) −9.46410 −0.441266
\(461\) −15.2942 + 26.4904i −0.712323 + 1.23378i 0.251660 + 0.967816i \(0.419024\pi\)
−0.963983 + 0.265964i \(0.914310\pi\)
\(462\) −3.29423 + 5.70577i −0.153261 + 0.265457i
\(463\) 12.9282 0.600825 0.300412 0.953809i \(-0.402876\pi\)
0.300412 + 0.953809i \(0.402876\pi\)
\(464\) 1.26795 2.19615i 0.0588631 0.101954i
\(465\) 1.73205 + 3.00000i 0.0803219 + 0.139122i
\(466\) −2.36603 4.09808i −0.109604 0.189840i
\(467\) 37.8564 1.75179 0.875893 0.482506i \(-0.160273\pi\)
0.875893 + 0.482506i \(0.160273\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.50000 + 2.59808i 0.0691898 + 0.119840i
\(471\) 4.75833 + 8.24167i 0.219252 + 0.379756i
\(472\) 5.19615 9.00000i 0.239172 0.414259i
\(473\) 6.00000 0.275880
\(474\) −1.53590 + 2.66025i −0.0705461 + 0.122190i
\(475\) −0.232051 + 0.401924i −0.0106472 + 0.0184415i
\(476\) −24.5885 −1.12701
\(477\) 0.571797 0.990381i 0.0261808 0.0453464i
\(478\) −1.09808 1.90192i −0.0502248 0.0869920i
\(479\) −20.4904 35.4904i −0.936229 1.62160i −0.772427 0.635104i \(-0.780957\pi\)
−0.163803 0.986493i \(-0.552376\pi\)
\(480\) −0.732051 −0.0334134
\(481\) 0 0
\(482\) 8.66025 0.394464
\(483\) 10.3923 + 18.0000i 0.472866 + 0.819028i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 4.56218 7.90192i 0.207158 0.358808i
\(486\) −15.2679 −0.692568
\(487\) −7.62436 + 13.2058i −0.345493 + 0.598411i −0.985443 0.170005i \(-0.945621\pi\)
0.639951 + 0.768416i \(0.278955\pi\)
\(488\) 3.09808 5.36603i 0.140243 0.242909i
\(489\) −7.85641 −0.355279
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) 10.3301 + 17.8923i 0.466192 + 0.807468i 0.999254 0.0386076i \(-0.0122922\pi\)
−0.533062 + 0.846076i \(0.678959\pi\)
\(492\) 3.80385 + 6.58846i 0.171491 + 0.297031i
\(493\) 20.7846 0.936092
\(494\) 0 0
\(495\) 7.39230 0.332259
\(496\) 2.36603 + 4.09808i 0.106238 + 0.184009i
\(497\) −9.00000 15.5885i −0.403705 0.699238i
\(498\) 3.00000 5.19615i 0.134433 0.232845i
\(499\) −25.8564 −1.15749 −0.578746 0.815508i \(-0.696458\pi\)
−0.578746 + 0.815508i \(0.696458\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 1.09808 1.90192i 0.0490584 0.0849717i
\(502\) 17.1962 0.767502
\(503\) 13.3301 23.0885i 0.594361 1.02946i −0.399276 0.916831i \(-0.630738\pi\)
0.993637 0.112633i \(-0.0359283\pi\)
\(504\) −3.69615 6.40192i −0.164640 0.285164i
\(505\) 5.36603 + 9.29423i 0.238785 + 0.413588i
\(506\) −28.3923 −1.26219
\(507\) 0 0
\(508\) −10.8038 −0.479343
\(509\) 11.1962 + 19.3923i 0.496261 + 0.859549i 0.999991 0.00431237i \(-0.00137267\pi\)
−0.503730 + 0.863861i \(0.668039\pi\)
\(510\) −3.00000 5.19615i −0.132842 0.230089i
\(511\) −17.4904 + 30.2942i −0.773729 + 1.34014i
\(512\) −1.00000 −0.0441942
\(513\) 0.928203 1.60770i 0.0409812 0.0709815i
\(514\) 6.92820 12.0000i 0.305590 0.529297i
\(515\) 9.19615 0.405231
\(516\) 0.732051 1.26795i 0.0322267 0.0558184i
\(517\) 4.50000 + 7.79423i 0.197910 + 0.342790i
\(518\) 1.20577 + 2.08846i 0.0529786 + 0.0917615i
\(519\) 10.9808 0.482002
\(520\) 0 0
\(521\) 6.46410 0.283197 0.141599 0.989924i \(-0.454776\pi\)
0.141599 + 0.989924i \(0.454776\pi\)
\(522\) 3.12436 + 5.41154i 0.136749 + 0.236857i
\(523\) 1.19615 + 2.07180i 0.0523041 + 0.0905933i 0.890992 0.454019i \(-0.150010\pi\)
−0.838688 + 0.544612i \(0.816677\pi\)
\(524\) −3.06218 + 5.30385i −0.133772 + 0.231700i
\(525\) 2.19615 0.0958479
\(526\) 1.79423 3.10770i 0.0782321 0.135502i
\(527\) −19.3923 + 33.5885i −0.844742 + 1.46314i
\(528\) −2.19615 −0.0955753
\(529\) −33.2846 + 57.6506i −1.44716 + 2.50655i
\(530\) 0.232051 + 0.401924i 0.0100796 + 0.0174585i
\(531\) 12.8038 + 22.1769i 0.555640 + 0.962396i
\(532\) 1.39230 0.0603641
\(533\) 0 0
\(534\) 4.98076 0.215539
\(535\) −8.83013 15.2942i −0.381760 0.661227i
\(536\) 0 0
\(537\) −3.46410 + 6.00000i −0.149487 + 0.258919i
\(538\) 27.1244 1.16941
\(539\) 3.00000 5.19615i 0.129219 0.223814i
\(540\) 2.00000 3.46410i 0.0860663 0.149071i
\(541\) 22.0526 0.948114 0.474057 0.880494i \(-0.342789\pi\)
0.474057 + 0.880494i \(0.342789\pi\)
\(542\) −4.73205 + 8.19615i −0.203259 + 0.352055i
\(543\) 5.33975 + 9.24871i 0.229150 + 0.396900i
\(544\) −4.09808 7.09808i −0.175704 0.304328i
\(545\) 8.53590 0.365638
\(546\) 0 0
\(547\) −6.78461 −0.290089 −0.145044 0.989425i \(-0.546333\pi\)
−0.145044 + 0.989425i \(0.546333\pi\)
\(548\) −1.09808 1.90192i −0.0469075 0.0812462i
\(549\) 7.63397 + 13.2224i 0.325810 + 0.564320i
\(550\) −1.50000 + 2.59808i −0.0639602 + 0.110782i
\(551\) −1.17691 −0.0501382
\(552\) −3.46410 + 6.00000i −0.147442 + 0.255377i
\(553\) 6.29423 10.9019i 0.267658 0.463597i
\(554\) −1.00000 −0.0424859
\(555\) −0.294229 + 0.509619i −0.0124893 + 0.0216321i
\(556\) −0.598076 1.03590i −0.0253641 0.0439319i
\(557\) −3.40192 5.89230i −0.144144 0.249665i 0.784909 0.619611i \(-0.212710\pi\)
−0.929053 + 0.369946i \(0.879376\pi\)
\(558\) −11.6603 −0.493618
\(559\) 0 0
\(560\) 3.00000 0.126773
\(561\) −9.00000 15.5885i −0.379980 0.658145i
\(562\) −5.19615 9.00000i −0.219186 0.379642i
\(563\) 7.26795 12.5885i 0.306308 0.530540i −0.671244 0.741236i \(-0.734240\pi\)
0.977552 + 0.210696i \(0.0675731\pi\)
\(564\) 2.19615 0.0924747
\(565\) −3.46410 + 6.00000i −0.145736 + 0.252422i
\(566\) 4.80385 8.32051i 0.201921 0.349737i
\(567\) 13.3923 0.562424
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) −13.6244 23.5981i −0.571163 0.989283i −0.996447 0.0842230i \(-0.973159\pi\)
0.425284 0.905060i \(-0.360174\pi\)
\(570\) 0.169873 + 0.294229i 0.00711520 + 0.0123239i
\(571\) 38.3731 1.60586 0.802931 0.596071i \(-0.203272\pi\)
0.802931 + 0.596071i \(0.203272\pi\)
\(572\) 0 0
\(573\) −16.6410 −0.695188
\(574\) −15.5885 27.0000i −0.650650 1.12696i
\(575\) 4.73205 + 8.19615i 0.197340 + 0.341803i
\(576\) 1.23205 2.13397i 0.0513355 0.0889156i
\(577\) 26.4449 1.10091 0.550457 0.834863i \(-0.314453\pi\)
0.550457 + 0.834863i \(0.314453\pi\)
\(578\) 25.0885 43.4545i 1.04354 1.80747i
\(579\) −6.00000 + 10.3923i −0.249351 + 0.431889i
\(580\) −2.53590 −0.105297
\(581\) −12.2942 + 21.2942i −0.510051 + 0.883433i
\(582\) −3.33975 5.78461i −0.138437 0.239780i
\(583\) 0.696152 + 1.20577i 0.0288317 + 0.0499379i
\(584\) −11.6603 −0.482505
\(585\) 0 0
\(586\) −11.1962 −0.462509
\(587\) −15.0000 25.9808i −0.619116 1.07234i −0.989647 0.143521i \(-0.954158\pi\)
0.370531 0.928820i \(-0.379176\pi\)
\(588\) −0.732051 1.26795i −0.0301893 0.0522893i
\(589\) 1.09808 1.90192i 0.0452454 0.0783674i
\(590\) −10.3923 −0.427844
\(591\) −7.90192 + 13.6865i −0.325042 + 0.562989i
\(592\) −0.401924 + 0.696152i −0.0165190 + 0.0286117i
\(593\) −20.7846 −0.853522 −0.426761 0.904365i \(-0.640345\pi\)
−0.426761 + 0.904365i \(0.640345\pi\)
\(594\) 6.00000 10.3923i 0.246183 0.426401i
\(595\) 12.2942 + 21.2942i 0.504014 + 0.872978i
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 4.67949 0.191519
\(598\) 0 0
\(599\) −19.8564 −0.811311 −0.405655 0.914026i \(-0.632957\pi\)
−0.405655 + 0.914026i \(0.632957\pi\)
\(600\) 0.366025 + 0.633975i 0.0149429 + 0.0258819i
\(601\) 18.8923 + 32.7224i 0.770633 + 1.33478i 0.937216 + 0.348748i \(0.113393\pi\)
−0.166583 + 0.986027i \(0.553273\pi\)
\(602\) −3.00000 + 5.19615i −0.122271 + 0.211779i
\(603\) 0 0
\(604\) 11.8301 20.4904i 0.481361 0.833742i
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 7.85641 0.319145
\(607\) 18.7942 32.5526i 0.762834 1.32127i −0.178550 0.983931i \(-0.557141\pi\)
0.941384 0.337337i \(-0.109526\pi\)
\(608\) 0.232051 + 0.401924i 0.00941090 + 0.0163002i
\(609\) 2.78461 + 4.82309i 0.112838 + 0.195441i
\(610\) −6.19615 −0.250875
\(611\) 0 0
\(612\) 20.1962 0.816381
\(613\) −19.4545 33.6962i −0.785759 1.36097i −0.928545 0.371221i \(-0.878939\pi\)
0.142785 0.989754i \(-0.454394\pi\)
\(614\) −13.7321 23.7846i −0.554180 0.959869i
\(615\) 3.80385 6.58846i 0.153386 0.265672i
\(616\) 9.00000 0.362620
\(617\) 9.00000 15.5885i 0.362326 0.627568i −0.626017 0.779809i \(-0.715316\pi\)
0.988343 + 0.152242i \(0.0486493\pi\)
\(618\) 3.36603 5.83013i 0.135401 0.234522i
\(619\) −31.3923 −1.26176 −0.630882 0.775879i \(-0.717307\pi\)
−0.630882 + 0.775879i \(0.717307\pi\)
\(620\) 2.36603 4.09808i 0.0950219 0.164583i
\(621\) −18.9282 32.7846i −0.759563 1.31560i
\(622\) 4.56218 + 7.90192i 0.182927 + 0.316838i
\(623\) −20.4115 −0.817771
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 13.1962 + 22.8564i 0.527424 + 0.913526i
\(627\) 0.509619 + 0.882686i 0.0203522 + 0.0352511i
\(628\) 6.50000 11.2583i 0.259378 0.449256i
\(629\) −6.58846 −0.262699
\(630\) −3.69615 + 6.40192i −0.147258 + 0.255059i
\(631\) 10.3923 18.0000i 0.413711 0.716569i −0.581581 0.813488i \(-0.697566\pi\)
0.995292 + 0.0969198i \(0.0308990\pi\)
\(632\) 4.19615 0.166914
\(633\) 6.43782 11.1506i 0.255880 0.443198i
\(634\) 11.5981 + 20.0885i 0.460618 + 0.797815i
\(635\) 5.40192 + 9.35641i 0.214369 + 0.371298i
\(636\) 0.339746 0.0134718
\(637\) 0 0
\(638\) −7.60770 −0.301192
\(639\) 7.39230 + 12.8038i 0.292435 + 0.506512i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 16.0359 27.7750i 0.633380 1.09705i −0.353476 0.935444i \(-0.615000\pi\)
0.986856 0.161603i \(-0.0516663\pi\)
\(642\) −12.9282 −0.510235
\(643\) −5.36603 + 9.29423i −0.211615 + 0.366529i −0.952220 0.305412i \(-0.901206\pi\)
0.740605 + 0.671941i \(0.234539\pi\)
\(644\) 14.1962 24.5885i 0.559407 0.968921i
\(645\) −1.46410 −0.0576489
\(646\) −1.90192 + 3.29423i −0.0748302 + 0.129610i
\(647\) −0.401924 0.696152i −0.0158013 0.0273686i 0.858017 0.513622i \(-0.171697\pi\)
−0.873818 + 0.486253i \(0.838363\pi\)
\(648\) 2.23205 + 3.86603i 0.0876832 + 0.151872i
\(649\) −31.1769 −1.22380
\(650\) 0 0
\(651\) −10.3923 −0.407307
\(652\) 5.36603 + 9.29423i 0.210150 + 0.363990i
\(653\) −0.696152 1.20577i −0.0272425 0.0471855i 0.852083 0.523407i \(-0.175339\pi\)
−0.879325 + 0.476222i \(0.842006\pi\)
\(654\) 3.12436 5.41154i 0.122172 0.211608i
\(655\) 6.12436 0.239298
\(656\) 5.19615 9.00000i 0.202876 0.351391i
\(657\) 14.3660 24.8827i 0.560472 0.970766i
\(658\) −9.00000 −0.350857
\(659\) 2.66025 4.60770i 0.103629 0.179490i −0.809548 0.587053i \(-0.800288\pi\)
0.913177 + 0.407563i \(0.133621\pi\)
\(660\) 1.09808 + 1.90192i 0.0427426 + 0.0740323i
\(661\) 17.9545 + 31.0981i 0.698348 + 1.20957i 0.969039 + 0.246909i \(0.0794147\pi\)
−0.270690 + 0.962666i \(0.587252\pi\)
\(662\) 12.9282 0.502469
\(663\) 0 0
\(664\) −8.19615 −0.318072
\(665\) −0.696152 1.20577i −0.0269956 0.0467578i
\(666\) −0.990381 1.71539i −0.0383765 0.0664700i
\(667\) −12.0000 + 20.7846i −0.464642 + 0.804783i
\(668\) −3.00000 −0.116073
\(669\) 2.36603 4.09808i 0.0914758 0.158441i
\(670\) 0 0
\(671\) −18.5885 −0.717599
\(672\) 1.09808 1.90192i 0.0423592 0.0733683i
\(673\) 12.1962 + 21.1244i 0.470127 + 0.814284i 0.999416 0.0341573i \(-0.0108747\pi\)
−0.529289 + 0.848441i \(0.677541\pi\)
\(674\) −3.09808 5.36603i −0.119333 0.206692i
\(675\) −4.00000 −0.153960
\(676\) 0 0
\(677\) −25.8564 −0.993742 −0.496871 0.867824i \(-0.665518\pi\)
−0.496871 + 0.867824i \(0.665518\pi\)
\(678\) 2.53590 + 4.39230i 0.0973906 + 0.168685i
\(679\) 13.6865 + 23.7058i 0.525241 + 0.909744i
\(680\) −4.09808 + 7.09808i −0.157154 + 0.272199i
\(681\) −12.0000 −0.459841
\(682\) 7.09808 12.2942i 0.271799 0.470770i
\(683\) −15.5885 + 27.0000i −0.596476 + 1.03313i 0.396861 + 0.917879i \(0.370099\pi\)
−0.993337 + 0.115248i \(0.963234\pi\)
\(684\) −1.14359 −0.0437264
\(685\) −1.09808 + 1.90192i −0.0419553 + 0.0726688i
\(686\) −7.50000 12.9904i −0.286351 0.495975i
\(687\) 0.464102 + 0.803848i 0.0177066 + 0.0306687i
\(688\) −2.00000 −0.0762493
\(689\) 0 0
\(690\) 6.92820 0.263752
\(691\) 18.3564 + 31.7942i 0.698311 + 1.20951i 0.969052 + 0.246857i \(0.0793979\pi\)
−0.270741 + 0.962652i \(0.587269\pi\)
\(692\) −7.50000 12.9904i −0.285107 0.493820i
\(693\) −11.0885 + 19.2058i −0.421216 + 0.729567i
\(694\) 28.7321 1.09065
\(695\) −0.598076 + 1.03590i −0.0226863 + 0.0392939i
\(696\) −0.928203 + 1.60770i −0.0351835 + 0.0609395i
\(697\) 85.1769 3.22631
\(698\) 2.02628 3.50962i 0.0766958 0.132841i
\(699\) 1.73205 + 3.00000i 0.0655122 + 0.113470i
\(700\) −1.50000 2.59808i −0.0566947 0.0981981i
\(701\) −35.9090 −1.35626 −0.678131 0.734941i \(-0.737210\pi\)
−0.678131 + 0.734941i \(0.737210\pi\)
\(702\) 0 0
\(703\) 0.373067 0.0140705
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) −1.09808 1.90192i −0.0413559 0.0716306i
\(706\) 4.90192 8.49038i 0.184486 0.319540i
\(707\) −32.1962 −1.21086
\(708\) −3.80385 + 6.58846i −0.142957 + 0.247609i
\(709\) −5.49038 + 9.50962i −0.206196 + 0.357141i −0.950513 0.310685i \(-0.899442\pi\)
0.744317 + 0.667826i \(0.232775\pi\)
\(710\) −6.00000 −0.225176
\(711\) −5.16987 + 8.95448i −0.193885 + 0.335819i
\(712\) −3.40192 5.89230i −0.127492 0.220823i
\(713\) −22.3923 38.7846i −0.838598 1.45250i
\(714\) 18.0000 0.673633
\(715\) 0 0
\(716\) 9.46410 0.353690
\(717\) 0.803848 + 1.39230i 0.0300202 + 0.0519966i
\(718\) 0.803848 + 1.39230i 0.0299993 + 0.0519604i
\(719\) 12.9282 22.3923i 0.482141 0.835092i −0.517649 0.855593i \(-0.673193\pi\)
0.999790 + 0.0205009i \(0.00652609\pi\)
\(720\) −2.46410 −0.0918316
\(721\) −13.7942 + 23.8923i −0.513724 + 0.889796i
\(722\) −9.39230 + 16.2679i −0.349545 + 0.605430i
\(723\) −6.33975 −0.235778
\(724\) 7.29423 12.6340i 0.271088 0.469538i
\(725\) 1.26795 + 2.19615i 0.0470905 + 0.0815631i
\(726\) −0.732051 1.26795i −0.0271690 0.0470580i
\(727\) −34.3731 −1.27483 −0.637413 0.770522i \(-0.719996\pi\)
−0.637413 + 0.770522i \(0.719996\pi\)
\(728\) 0 0
\(729\) −2.21539 −0.0820515
\(730\) 5.83013 + 10.0981i 0.215783 + 0.373747i
\(731\) −8.19615 14.1962i −0.303146 0.525064i
\(732\) −2.26795 + 3.92820i −0.0838258 + 0.145191i
\(733\) −14.9090 −0.550675 −0.275338 0.961348i \(-0.588790\pi\)
−0.275338 + 0.961348i \(0.588790\pi\)
\(734\) −2.80385 + 4.85641i −0.103492 + 0.179253i
\(735\) −0.732051 + 1.26795i −0.0270021 + 0.0467690i
\(736\) 9.46410 0.348851
\(737\) 0 0
\(738\) 12.8038 + 22.1769i 0.471316 + 0.816344i
\(739\) 16.2846 + 28.2058i 0.599039 + 1.03757i 0.992963 + 0.118423i \(0.0377839\pi\)
−0.393924 + 0.919143i \(0.628883\pi\)
\(740\) 0.803848 0.0295500
\(741\) 0 0
\(742\) −1.39230 −0.0511131
\(743\) 6.80385 + 11.7846i 0.249609 + 0.432335i 0.963417 0.268006i \(-0.0863646\pi\)
−0.713808 + 0.700341i \(0.753031\pi\)
\(744\) −1.73205 3.00000i −0.0635001 0.109985i
\(745\) 3.00000 5.19615i 0.109911 0.190372i
\(746\) 0.392305 0.0143633
\(747\) 10.0981 17.4904i 0.369469 0.639940i
\(748\) −12.2942 + 21.2942i −0.449522 + 0.778594i
\(749\) 52.9808 1.93587
\(750\) 0.366025 0.633975i 0.0133654 0.0231495i
\(751\) −10.1962 17.6603i −0.372063 0.644432i 0.617820 0.786320i \(-0.288016\pi\)
−0.989883 + 0.141888i \(0.954683\pi\)
\(752\) −1.50000 2.59808i −0.0546994 0.0947421i
\(753\) −12.5885 −0.458749
\(754\) 0 0
\(755\) −23.6603 −0.861085
\(756\) 6.00000 + 10.3923i 0.218218 + 0.377964i
\(757\) 18.8923 + 32.7224i 0.686652 + 1.18932i 0.972914 + 0.231166i \(0.0742539\pi\)
−0.286262 + 0.958151i \(0.592413\pi\)
\(758\) 14.8923 25.7942i 0.540913 0.936889i
\(759\) 20.7846 0.754434
\(760\) 0.232051 0.401924i 0.00841737 0.0145793i
\(761\) −9.40192 + 16.2846i −0.340819 + 0.590317i −0.984585 0.174906i \(-0.944038\pi\)
0.643766 + 0.765223i \(0.277371\pi\)
\(762\) 7.90897 0.286512
\(763\) −12.8038 + 22.1769i −0.463530 + 0.802858i
\(764\) 11.3660 + 19.6865i 0.411208 + 0.712234i
\(765\) −10.0981 17.4904i −0.365097 0.632366i
\(766\) 22.3923 0.809067
\(767\) 0 0
\(768\) 0.732051 0.0264156
\(769\) 19.0526 + 33.0000i 0.687053 + 1.19001i 0.972787 + 0.231701i \(0.0744293\pi\)
−0.285734 + 0.958309i \(0.592237\pi\)
\(770\) −4.50000 7.79423i −0.162169 0.280885i
\(771\) −5.07180 + 8.78461i −0.182656 + 0.316370i
\(772\) 16.3923 0.589972
\(773\) 1.20577 2.08846i 0.0433686 0.0751166i −0.843526 0.537088i \(-0.819524\pi\)
0.886895 + 0.461971i \(0.152858\pi\)
\(774\) 2.46410 4.26795i 0.0885703 0.153408i
\(775\) −4.73205 −0.169980
\(776\) −4.56218 + 7.90192i −0.163773 + 0.283663i
\(777\) −0.882686 1.52886i −0.0316662 0.0548474i
\(778\) −11.3660 19.6865i −0.407492 0.705796i
\(779\) −4.82309 −0.172805
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 38.7846 + 67.1769i 1.38693 + 2.40224i
\(783\) −5.07180 8.78461i −0.181251 0.313936i
\(784\) −1.00000 + 1.73205i −0.0357143 + 0.0618590i
\(785\) −13.0000 −0.463990
\(786\) 2.24167 3.88269i 0.0799577 0.138491i
\(787\) 21.4186 37.0981i 0.763490 1.32240i −0.177551 0.984112i \(-0.556818\pi\)
0.941041 0.338292i \(-0.109849\pi\)
\(788\) 21.5885 0.769057
\(789\) −1.31347 + 2.27499i −0.0467606 + 0.0809918i
\(790\) −2.09808 3.63397i −0.0746462 0.129291i
\(791\) −10.3923 18.0000i −0.369508 0.640006i
\(792\) −7.39230 −0.262674
\(793\) 0 0
\(794\) 11.1962 0.397337
\(795\) −0.169873 0.294229i −0.00602477 0.0104352i
\(796\) −3.19615 5.53590i −0.113285 0.196215i
\(797\) −6.46410 + 11.1962i −0.228970 + 0.396588i −0.957503 0.288423i \(-0.906869\pi\)
0.728533 + 0.685011i \(0.240203\pi\)
\(798\) −1.01924 −0.0360806
\(799\) 12.2942 21.2942i 0.434939 0.753336i
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) 16.7654 0.592375
\(802\) 2.59808 4.50000i 0.0917413 0.158901i
\(803\) 17.4904 + 30.2942i 0.617222 + 1.06906i
\(804\) 0 0
\(805\) −28.3923 −1.00070
\(806\) 0 0
\(807\) −19.8564 −0.698979
\(808\) −5.36603 9.29423i −0.188776 0.326970i
\(809\) −12.0000 20.7846i −0.421898 0.730748i 0.574228 0.818696i \(-0.305302\pi\)
−0.996125 + 0.0879478i \(0.971969\pi\)
\(810\) 2.23205 3.86603i 0.0784263 0.135838i
\(811\) −43.3923 −1.52371 −0.761855 0.647748i \(-0.775711\pi\)
−0.761855 + 0.647748i \(0.775711\pi\)
\(812\) 3.80385 6.58846i 0.133489 0.231210i
\(813\) 3.46410 6.00000i 0.121491 0.210429i
\(814\) 2.41154 0.0845245
\(815\) 5.36603 9.29423i 0.187964 0.325563i
\(816\) 3.00000 + 5.19615i 0.105021 + 0.181902i
\(817\) 0.464102 + 0.803848i 0.0162369 + 0.0281231i
\(818\) −16.2679 −0.568796
\(819\) 0 0
\(820\) −10.3923 −0.362915
\(821\) −10.0981 17.4904i −0.352425 0.610419i 0.634249 0.773129i \(-0.281310\pi\)
−0.986674 + 0.162711i \(0.947976\pi\)
\(822\) 0.803848 + 1.39230i 0.0280374 + 0.0485622i
\(823\) −13.5981 + 23.5526i −0.473999 + 0.820991i −0.999557 0.0297674i \(-0.990523\pi\)
0.525558 + 0.850758i \(0.323857\pi\)
\(824\) −9.19615 −0.320363
\(825\) 1.09808 1.90192i 0.0382301 0.0662165i
\(826\) 15.5885 27.0000i 0.542392 0.939450i
\(827\) −42.5885 −1.48095 −0.740473 0.672086i \(-0.765398\pi\)
−0.740473 + 0.672086i \(0.765398\pi\)
\(828\) −11.6603 + 20.1962i −0.405222 + 0.701865i
\(829\) −10.0000 17.3205i −0.347314 0.601566i 0.638457 0.769657i \(-0.279573\pi\)
−0.985771 + 0.168091i \(0.946240\pi\)
\(830\) 4.09808 + 7.09808i 0.142246 + 0.246378i
\(831\) 0.732051 0.0253946
\(832\) 0 0
\(833\) −16.3923 −0.567960
\(834\) 0.437822 + 0.758330i 0.0151605 + 0.0262588i
\(835\) 1.50000 + 2.59808i 0.0519096 + 0.0899101i
\(836\) 0.696152 1.20577i 0.0240769 0.0417025i
\(837\) 18.9282 0.654254
\(838\) −8.66025 + 15.0000i −0.299164 + 0.518166i
\(839\) −10.9019 + 18.8827i −0.376376 + 0.651903i −0.990532 0.137282i \(-0.956163\pi\)
0.614156 + 0.789185i \(0.289497\pi\)
\(840\) −2.19615 −0.0757745
\(841\) 11.2846 19.5455i 0.389124 0.673983i
\(842\) −1.43782 2.49038i −0.0495506 0.0858242i
\(843\) 3.80385 + 6.58846i 0.131011 + 0.226919i
\(844\) −17.5885 −0.605420
\(845\) 0 0
\(846\) 7.39230 0.254153
\(847\) 3.00000 + 5.19615i 0.103081 + 0.178542i
\(848\) −0.232051 0.401924i −0.00796866 0.0138021i
\(849\) −3.51666 + 6.09103i −0.120691 + 0.209044i
\(850\) 8.19615 0.281126
\(851\) 3.80385 6.58846i 0.130394 0.225849i
\(852\) −2.19615 + 3.80385i −0.0752389 + 0.130318i
\(853\) 13.8564 0.474434 0.237217 0.971457i \(-0.423765\pi\)
0.237217 + 0.971457i \(0.423765\pi\)
\(854\) 9.29423 16.0981i 0.318042 0.550865i
\(855\) 0.571797 + 0.990381i 0.0195550 + 0.0338703i
\(856\) 8.83013 + 15.2942i 0.301808 + 0.522746i
\(857\) 16.7321 0.571556 0.285778 0.958296i \(-0.407748\pi\)
0.285778 + 0.958296i \(0.407748\pi\)
\(858\) 0 0
\(859\) −20.3731 −0.695120 −0.347560 0.937658i \(-0.612990\pi\)
−0.347560 + 0.937658i \(0.612990\pi\)
\(860\) 1.00000 + 1.73205i 0.0340997 + 0.0590624i
\(861\) 11.4115 + 19.7654i 0.388904 + 0.673602i
\(862\) −4.09808 + 7.09808i −0.139581 + 0.241761i
\(863\) −43.1769 −1.46976 −0.734880 0.678198i \(-0.762761\pi\)
−0.734880 + 0.678198i \(0.762761\pi\)
\(864\) −2.00000 + 3.46410i −0.0680414 + 0.117851i
\(865\) −7.50000 + 12.9904i −0.255008 + 0.441686i
\(866\) 8.39230 0.285182
\(867\) −18.3660 + 31.8109i −0.623743 + 1.08035i
\(868\) 7.09808 + 12.2942i 0.240924 + 0.417293i
\(869\) −6.29423 10.9019i −0.213517 0.369822i
\(870\) 1.85641 0.0629381
\(871\) 0 0
\(872\) −8.53590 −0.289062
\(873\) −11.2417 19.4711i −0.380473 0.658998i
\(874\) −2.19615 3.80385i −0.0742860 0.128667i
\(875\) −1.50000 + 2.59808i −0.0507093 + 0.0878310i
\(876\) 8.53590 0.288401
\(877\) −13.7321 + 23.7846i −0.463698 + 0.803149i −0.999142 0.0414220i \(-0.986811\pi\)
0.535443 + 0.844571i \(0.320145\pi\)
\(878\) 1.70577 2.95448i 0.0575670 0.0997090i
\(879\) 8.19615 0.276449
\(880\) 1.50000 2.59808i 0.0505650 0.0875811i
\(881\) 13.1603 + 22.7942i 0.443380 + 0.767957i 0.997938 0.0641883i \(-0.0204458\pi\)
−0.554558 + 0.832145i \(0.687112\pi\)
\(882\) −2.46410 4.26795i −0.0829706 0.143709i
\(883\) −4.58846 −0.154414 −0.0772069 0.997015i \(-0.524600\pi\)
−0.0772069 + 0.997015i \(0.524600\pi\)
\(884\) 0 0
\(885\) 7.60770 0.255730
\(886\) −11.1962 19.3923i −0.376142 0.651497i
\(887\) 20.3827 + 35.3038i 0.684384 + 1.18539i 0.973630 + 0.228133i \(0.0732620\pi\)
−0.289246 + 0.957255i \(0.593405\pi\)
\(888\) 0.294229 0.509619i 0.00987367 0.0171017i
\(889\) −32.4115 −1.08705
\(890\) −3.40192 + 5.89230i −0.114033 + 0.197511i
\(891\) 6.69615 11.5981i 0.224330 0.388550i
\(892\) −6.46410 −0.216434
\(893\) −0.696152 + 1.20577i −0.0232959 + 0.0403496i
\(894\) −2.19615 3.80385i −0.0734503 0.127220i
\(895\) −4.73205 8.19615i −0.158175 0.273967i
\(896\) −3.00000 −0.100223
\(897\) 0 0
\(898\) −15.5885 −0.520194
\(899\) −6.00000 10.3923i −0.200111 0.346603i
\(900\) 1.23205 + 2.13397i 0.0410684 + 0.0711325i
\(901\) 1.90192 3.29423i 0.0633623 0.109747i
\(902\) −31.1769 −1.03808
\(903\) 2.19615 3.80385i 0.0730834 0.126584i
\(904\) 3.46410 6.00000i 0.115214 0.199557i
\(905\) −14.5885 −0.484937
\(906\) −8.66025 + 15.0000i −0.287718 + 0.498342i
\(907\) 2.29423 + 3.97372i 0.0761786 + 0.131945i 0.901598 0.432574i \(-0.142395\pi\)
−0.825420 + 0.564520i \(0.809061\pi\)
\(908\) 8.19615 + 14.1962i 0.271999 + 0.471116i
\(909\) 26.4449 0.877121
\(910\) 0 0
\(911\) −21.4641 −0.711137 −0.355569 0.934650i \(-0.615713\pi\)
−0.355569 + 0.934650i \(0.615713\pi\)
\(912\) −0.169873 0.294229i −0.00562506 0.00974288i
\(913\) 12.2942 + 21.2942i 0.406880 + 0.704736i
\(914\) 9.16987 15.8827i 0.303312 0.525353i
\(915\) 4.53590 0.149952
\(916\) 0.633975 1.09808i 0.0209471 0.0362815i
\(917\) −9.18653 + 15.9115i −0.303366 + 0.525445i
\(918\) −32.7846 −1.08205
\(919\) −15.3923 + 26.6603i −0.507745 + 0.879441i 0.492215 + 0.870474i \(0.336188\pi\)
−0.999960 + 0.00896670i \(0.997146\pi\)
\(920\) −4.73205 8.19615i −0.156011 0.270219i
\(921\) 10.0526 + 17.4115i 0.331243 + 0.573730i
\(922\) −30.5885 −1.00738
\(923\) 0 0
\(924\) −6.58846 −0.216744
\(925\) −0.401924 0.696152i −0.0132152 0.0228894i
\(926\) 6.46410 + 11.1962i 0.212424 + 0.367928i
\(927\) 11.3301 19.6244i 0.372130 0.644548i
\(928\) 2.53590 0.0832449
\(929\) −1.60770 + 2.78461i −0.0527468 + 0.0913601i −0.891193 0.453624i \(-0.850131\pi\)
0.838446 + 0.544984i \(0.183464\pi\)
\(930\) −1.73205 + 3.00000i −0.0567962 + 0.0983739i
\(931\) 0.928203 0.0304206
\(932\) 2.36603 4.09808i 0.0775017 0.134237i
\(933\) −3.33975 5.78461i −0.109338 0.189380i
\(934\) 18.9282 + 32.7846i 0.619350 + 1.07275i
\(935\) 24.5885 0.804129
\(936\) 0 0
\(937\) −9.60770 −0.313870 −0.156935 0.987609i \(-0.550161\pi\)
−0.156935 + 0.987609i \(0.550161\pi\)
\(938\) 0 0
\(939\) −9.66025 16.7321i −0.315250 0.546030i
\(940\) −1.50000 + 2.59808i −0.0489246 + 0.0847399i
\(941\) −3.21539 −0.104819 −0.0524094 0.998626i \(-0.516690\pi\)
−0.0524094 + 0.998626i \(0.516690\pi\)
\(942\) −4.75833 + 8.24167i −0.155035 + 0.268528i
\(943\) −49.1769 + 85.1769i −1.60142 + 2.77374i
\(944\) 10.3923 0.338241
\(945\) 6.00000 10.3923i 0.195180 0.338062i
\(946\) 3.00000 + 5.19615i 0.0975384 + 0.168941i
\(947\) 7.68653 + 13.3135i 0.249779 + 0.432630i 0.963464 0.267837i \(-0.0863088\pi\)
−0.713686 + 0.700466i \(0.752975\pi\)
\(948\) −3.07180 −0.0997673
\(949\) 0 0
\(950\) −0.464102 −0.0150574
\(951\) −8.49038 14.7058i −0.275319 0.476867i
\(952\) −12.2942 21.2942i −0.398458 0.690150i
\(953\) −3.29423 + 5.70577i −0.106711 + 0.184828i −0.914436 0.404731i \(-0.867365\pi\)
0.807725 + 0.589559i \(0.200698\pi\)
\(954\) 1.14359 0.0370252
\(955\) 11.3660 19.6865i 0.367796 0.637041i
\(956\) 1.09808 1.90192i 0.0355143 0.0615126i
\(957\) 5.56922 0.180027
\(958\) 20.4904 35.4904i 0.662014 1.14664i
\(959\) −3.29423 5.70577i −0.106376 0.184249i
\(960\) −0.366025 0.633975i −0.0118134 0.0204614i
\(961\) −8.60770 −0.277668
\(962\) 0 0
\(963\) −43.5167 −1.40230
\(964\) 4.33013 + 7.50000i 0.139464 + 0.241559i
\(965\) −8.19615 14.1962i −0.263843 0.456990i
\(966\) −10.3923 + 18.0000i −0.334367 + 0.579141i
\(967\) 44.5692 1.43325 0.716625 0.697459i \(-0.245686\pi\)
0.716625 + 0.697459i \(0.245686\pi\)
\(968\) −1.00000 + 1.73205i −0.0321412 + 0.0556702i
\(969\) 1.39230 2.41154i 0.0447273 0.0774699i
\(970\) 9.12436 0.292965
\(971\) −23.3827 + 40.5000i −0.750386 + 1.29971i 0.197250 + 0.980353i \(0.436799\pi\)
−0.947636 + 0.319354i \(0.896534\pi\)
\(972\) −7.63397 13.2224i −0.244860 0.424110i
\(973\) −1.79423 3.10770i −0.0575203 0.0996281i
\(974\) −15.2487 −0.488600
\(975\) 0 0
\(976\) 6.19615 0.198334
\(977\) −8.19615 14.1962i −0.262218 0.454175i 0.704613 0.709592i \(-0.251121\pi\)
−0.966831 + 0.255417i \(0.917787\pi\)
\(978\) −3.92820 6.80385i −0.125610 0.217563i
\(979\) −10.2058 + 17.6769i −0.326178 + 0.564957i
\(980\) 2.00000 0.0638877
\(981\) 10.5167 18.2154i 0.335771 0.581573i
\(982\) −10.3301 + 17.8923i −0.329648 + 0.570966i
\(983\) 44.5692 1.42154 0.710769 0.703426i \(-0.248347\pi\)
0.710769 + 0.703426i \(0.248347\pi\)
\(984\) −3.80385 + 6.58846i −0.121262 + 0.210032i
\(985\) −10.7942 18.6962i −0.343933 0.595709i
\(986\) 10.3923 + 18.0000i 0.330958 + 0.573237i
\(987\) 6.58846 0.209713
\(988\) 0 0
\(989\) 18.9282 0.601882
\(990\) 3.69615 + 6.40192i 0.117471 + 0.203466i
\(991\) 5.58846 + 9.67949i 0.177523 + 0.307479i 0.941032 0.338319i \(-0.109858\pi\)
−0.763508 + 0.645798i \(0.776525\pi\)
\(992\) −2.36603 + 4.09808i −0.0751214 + 0.130114i
\(993\) −9.46410 −0.300334
\(994\) 9.00000 15.5885i 0.285463 0.494436i
\(995\) −3.19615 + 5.53590i −0.101325 + 0.175500i
\(996\) 6.00000 0.190117
\(997\) −20.2846 + 35.1340i −0.642420 + 1.11270i 0.342471 + 0.939528i \(0.388736\pi\)
−0.984891 + 0.173176i \(0.944597\pi\)
\(998\) −12.9282 22.3923i −0.409235 0.708816i
\(999\) 1.60770 + 2.78461i 0.0508652 + 0.0881012i
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.e.n.991.1 4
13.2 odd 12 1690.2.d.f.1351.4 4
13.3 even 3 1690.2.a.j.1.2 2
13.4 even 6 1690.2.e.l.191.1 4
13.5 odd 4 1690.2.l.g.361.2 4
13.6 odd 12 130.2.l.a.121.1 yes 4
13.7 odd 12 1690.2.l.g.1161.2 4
13.8 odd 4 130.2.l.a.101.1 4
13.9 even 3 inner 1690.2.e.n.191.1 4
13.10 even 6 1690.2.a.m.1.2 2
13.11 odd 12 1690.2.d.f.1351.2 4
13.12 even 2 1690.2.e.l.991.1 4
39.8 even 4 1170.2.bs.c.361.2 4
39.32 even 12 1170.2.bs.c.901.2 4
52.19 even 12 1040.2.da.a.641.2 4
52.47 even 4 1040.2.da.a.881.2 4
65.8 even 4 650.2.n.b.49.1 4
65.19 odd 12 650.2.m.a.251.2 4
65.29 even 6 8450.2.a.bm.1.1 2
65.32 even 12 650.2.n.b.199.1 4
65.34 odd 4 650.2.m.a.101.2 4
65.47 even 4 650.2.n.a.49.2 4
65.49 even 6 8450.2.a.bf.1.1 2
65.58 even 12 650.2.n.a.199.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.2.l.a.101.1 4 13.8 odd 4
130.2.l.a.121.1 yes 4 13.6 odd 12
650.2.m.a.101.2 4 65.34 odd 4
650.2.m.a.251.2 4 65.19 odd 12
650.2.n.a.49.2 4 65.47 even 4
650.2.n.a.199.2 4 65.58 even 12
650.2.n.b.49.1 4 65.8 even 4
650.2.n.b.199.1 4 65.32 even 12
1040.2.da.a.641.2 4 52.19 even 12
1040.2.da.a.881.2 4 52.47 even 4
1170.2.bs.c.361.2 4 39.8 even 4
1170.2.bs.c.901.2 4 39.32 even 12
1690.2.a.j.1.2 2 13.3 even 3
1690.2.a.m.1.2 2 13.10 even 6
1690.2.d.f.1351.2 4 13.11 odd 12
1690.2.d.f.1351.4 4 13.2 odd 12
1690.2.e.l.191.1 4 13.4 even 6
1690.2.e.l.991.1 4 13.12 even 2
1690.2.e.n.191.1 4 13.9 even 3 inner
1690.2.e.n.991.1 4 1.1 even 1 trivial
1690.2.l.g.361.2 4 13.5 odd 4
1690.2.l.g.1161.2 4 13.7 odd 12
8450.2.a.bf.1.1 2 65.49 even 6
8450.2.a.bm.1.1 2 65.29 even 6