Properties

Label 693.2.m.k.190.2
Level $693$
Weight $2$
Character 693.190
Analytic conductor $5.534$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [693,2,Mod(64,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.m (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 190.2
Character \(\chi\) \(=\) 693.190
Dual form 693.2.m.k.631.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.70216 + 1.23669i) q^{2} +(0.749912 - 2.30799i) q^{4} +(-3.03419 - 2.20447i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.277470 + 0.853964i) q^{8} +O(q^{10})\) \(q+(-1.70216 + 1.23669i) q^{2} +(0.749912 - 2.30799i) q^{4} +(-3.03419 - 2.20447i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.277470 + 0.853964i) q^{8} +7.89093 q^{10} +(-1.33588 - 3.03569i) q^{11} +(-2.80385 + 2.03712i) q^{13} +(0.650168 + 2.00101i) q^{14} +(2.39820 + 1.74239i) q^{16} +(1.23523 + 0.897450i) q^{17} +(-1.59455 - 4.90753i) q^{19} +(-7.36326 + 5.34972i) q^{20} +(6.02811 + 3.51516i) q^{22} +4.87487 q^{23} +(2.80154 + 8.62225i) q^{25} +(2.25332 - 6.93501i) q^{26} +(-1.96329 - 1.42642i) q^{28} +(-3.31493 + 10.2023i) q^{29} +(-6.57516 + 4.77714i) q^{31} -8.03275 q^{32} -3.21244 q^{34} +(-3.03419 + 2.20447i) q^{35} +(2.86103 - 8.80533i) q^{37} +(8.78330 + 6.38144i) q^{38} +(1.04064 - 3.20276i) q^{40} +(3.36746 + 10.3640i) q^{41} -0.137677 q^{43} +(-8.00814 + 0.806704i) q^{44} +(-8.29782 + 6.02872i) q^{46} +(0.843708 + 2.59667i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-15.4318 - 11.2118i) q^{50} +(2.59901 + 7.99893i) q^{52} +(-2.26034 + 1.64224i) q^{53} +(-2.63876 + 12.1558i) q^{55} +0.897910 q^{56} +(-6.97458 - 21.4656i) q^{58} +(1.49714 - 4.60772i) q^{59} +(0.240947 + 0.175058i) q^{61} +(5.28414 - 16.2629i) q^{62} +(8.87665 - 6.44926i) q^{64} +12.9982 q^{65} +0.816899 q^{67} +(2.99762 - 2.17790i) q^{68} +(2.43843 - 7.50472i) q^{70} +(4.63563 + 3.36798i) q^{71} +(-0.764866 + 2.35402i) q^{73} +(6.01957 + 18.5263i) q^{74} -12.5223 q^{76} +(-3.29992 + 0.332419i) q^{77} +(-9.24242 + 6.71501i) q^{79} +(-3.43554 - 10.5735i) q^{80} +(-18.5490 - 13.4766i) q^{82} +(-8.61276 - 6.25754i) q^{83} +(-1.76953 - 5.44606i) q^{85} +(0.234348 - 0.170264i) q^{86} +(2.22170 - 1.98311i) q^{88} -8.91589 q^{89} +(1.07098 + 3.29613i) q^{91} +(3.65572 - 11.2512i) q^{92} +(-4.64741 - 3.37654i) q^{94} +(-5.98031 + 18.4055i) q^{95} +(-6.54067 + 4.75207i) q^{97} +2.10399 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70216 + 1.23669i −1.20361 + 0.874474i −0.994635 0.103447i \(-0.967013\pi\)
−0.208975 + 0.977921i \(0.567013\pi\)
\(3\) 0 0
\(4\) 0.749912 2.30799i 0.374956 1.15400i
\(5\) −3.03419 2.20447i −1.35693 0.985867i −0.998634 0.0522596i \(-0.983358\pi\)
−0.358297 0.933608i \(-0.616642\pi\)
\(6\) 0 0
\(7\) 0.309017 0.951057i 0.116797 0.359466i
\(8\) 0.277470 + 0.853964i 0.0981003 + 0.301922i
\(9\) 0 0
\(10\) 7.89093 2.49533
\(11\) −1.33588 3.03569i −0.402784 0.915295i
\(12\) 0 0
\(13\) −2.80385 + 2.03712i −0.777649 + 0.564995i −0.904272 0.426956i \(-0.859586\pi\)
0.126624 + 0.991951i \(0.459586\pi\)
\(14\) 0.650168 + 2.00101i 0.173765 + 0.534793i
\(15\) 0 0
\(16\) 2.39820 + 1.74239i 0.599550 + 0.435599i
\(17\) 1.23523 + 0.897450i 0.299588 + 0.217664i 0.727416 0.686197i \(-0.240721\pi\)
−0.427828 + 0.903860i \(0.640721\pi\)
\(18\) 0 0
\(19\) −1.59455 4.90753i −0.365816 1.12587i −0.949469 0.313862i \(-0.898377\pi\)
0.583653 0.812003i \(-0.301623\pi\)
\(20\) −7.36326 + 5.34972i −1.64648 + 1.19623i
\(21\) 0 0
\(22\) 6.02811 + 3.51516i 1.28520 + 0.749435i
\(23\) 4.87487 1.01648 0.508240 0.861215i \(-0.330296\pi\)
0.508240 + 0.861215i \(0.330296\pi\)
\(24\) 0 0
\(25\) 2.80154 + 8.62225i 0.560308 + 1.72445i
\(26\) 2.25332 6.93501i 0.441913 1.36007i
\(27\) 0 0
\(28\) −1.96329 1.42642i −0.371028 0.269568i
\(29\) −3.31493 + 10.2023i −0.615568 + 1.89452i −0.222907 + 0.974840i \(0.571555\pi\)
−0.392661 + 0.919683i \(0.628445\pi\)
\(30\) 0 0
\(31\) −6.57516 + 4.77714i −1.18093 + 0.857999i −0.992277 0.124044i \(-0.960414\pi\)
−0.188658 + 0.982043i \(0.560414\pi\)
\(32\) −8.03275 −1.42000
\(33\) 0 0
\(34\) −3.21244 −0.550929
\(35\) −3.03419 + 2.20447i −0.512871 + 0.372623i
\(36\) 0 0
\(37\) 2.86103 8.80533i 0.470350 1.44759i −0.381778 0.924254i \(-0.624688\pi\)
0.852128 0.523334i \(-0.175312\pi\)
\(38\) 8.78330 + 6.38144i 1.42484 + 1.03521i
\(39\) 0 0
\(40\) 1.04064 3.20276i 0.164540 0.506401i
\(41\) 3.36746 + 10.3640i 0.525908 + 1.61858i 0.762513 + 0.646973i \(0.223965\pi\)
−0.236605 + 0.971606i \(0.576035\pi\)
\(42\) 0 0
\(43\) −0.137677 −0.0209955 −0.0104978 0.999945i \(-0.503342\pi\)
−0.0104978 + 0.999945i \(0.503342\pi\)
\(44\) −8.00814 + 0.806704i −1.20727 + 0.121615i
\(45\) 0 0
\(46\) −8.29782 + 6.02872i −1.22345 + 0.888886i
\(47\) 0.843708 + 2.59667i 0.123068 + 0.378763i 0.993544 0.113447i \(-0.0361892\pi\)
−0.870477 + 0.492210i \(0.836189\pi\)
\(48\) 0 0
\(49\) −0.809017 0.587785i −0.115574 0.0839693i
\(50\) −15.4318 11.2118i −2.18238 1.58559i
\(51\) 0 0
\(52\) 2.59901 + 7.99893i 0.360418 + 1.10925i
\(53\) −2.26034 + 1.64224i −0.310482 + 0.225579i −0.732103 0.681194i \(-0.761461\pi\)
0.421621 + 0.906772i \(0.361461\pi\)
\(54\) 0 0
\(55\) −2.63876 + 12.1558i −0.355811 + 1.63908i
\(56\) 0.897910 0.119988
\(57\) 0 0
\(58\) −6.97458 21.4656i −0.915808 2.81857i
\(59\) 1.49714 4.60772i 0.194911 0.599875i −0.805067 0.593185i \(-0.797870\pi\)
0.999978 0.00669015i \(-0.00212956\pi\)
\(60\) 0 0
\(61\) 0.240947 + 0.175058i 0.0308501 + 0.0224139i 0.603103 0.797663i \(-0.293931\pi\)
−0.572253 + 0.820077i \(0.693931\pi\)
\(62\) 5.28414 16.2629i 0.671087 2.06539i
\(63\) 0 0
\(64\) 8.87665 6.44926i 1.10958 0.806158i
\(65\) 12.9982 1.61223
\(66\) 0 0
\(67\) 0.816899 0.0998001 0.0499001 0.998754i \(-0.484110\pi\)
0.0499001 + 0.998754i \(0.484110\pi\)
\(68\) 2.99762 2.17790i 0.363515 0.264109i
\(69\) 0 0
\(70\) 2.43843 7.50472i 0.291448 0.896986i
\(71\) 4.63563 + 3.36798i 0.550148 + 0.399706i 0.827840 0.560964i \(-0.189570\pi\)
−0.277692 + 0.960670i \(0.589570\pi\)
\(72\) 0 0
\(73\) −0.764866 + 2.35402i −0.0895208 + 0.275517i −0.985787 0.168000i \(-0.946269\pi\)
0.896266 + 0.443516i \(0.146269\pi\)
\(74\) 6.01957 + 18.5263i 0.699760 + 2.15364i
\(75\) 0 0
\(76\) −12.5223 −1.43641
\(77\) −3.29992 + 0.332419i −0.376061 + 0.0378827i
\(78\) 0 0
\(79\) −9.24242 + 6.71501i −1.03985 + 0.755497i −0.970257 0.242078i \(-0.922171\pi\)
−0.0695961 + 0.997575i \(0.522171\pi\)
\(80\) −3.43554 10.5735i −0.384105 1.18215i
\(81\) 0 0
\(82\) −18.5490 13.4766i −2.04839 1.48825i
\(83\) −8.61276 6.25754i −0.945373 0.686854i 0.00433474 0.999991i \(-0.498620\pi\)
−0.949708 + 0.313137i \(0.898620\pi\)
\(84\) 0 0
\(85\) −1.76953 5.44606i −0.191933 0.590708i
\(86\) 0.234348 0.170264i 0.0252704 0.0183600i
\(87\) 0 0
\(88\) 2.22170 1.98311i 0.236834 0.211400i
\(89\) −8.91589 −0.945082 −0.472541 0.881309i \(-0.656663\pi\)
−0.472541 + 0.881309i \(0.656663\pi\)
\(90\) 0 0
\(91\) 1.07098 + 3.29613i 0.112269 + 0.345528i
\(92\) 3.65572 11.2512i 0.381135 1.17301i
\(93\) 0 0
\(94\) −4.64741 3.37654i −0.479344 0.348264i
\(95\) −5.98031 + 18.4055i −0.613567 + 1.88837i
\(96\) 0 0
\(97\) −6.54067 + 4.75207i −0.664104 + 0.482500i −0.868046 0.496483i \(-0.834625\pi\)
0.203942 + 0.978983i \(0.434625\pi\)
\(98\) 2.10399 0.212535
\(99\) 0 0
\(100\) 22.0010 2.20010
\(101\) −1.39311 + 1.01215i −0.138619 + 0.100713i −0.654934 0.755686i \(-0.727304\pi\)
0.516315 + 0.856399i \(0.327304\pi\)
\(102\) 0 0
\(103\) −0.832485 + 2.56213i −0.0820272 + 0.252454i −0.983656 0.180056i \(-0.942372\pi\)
0.901629 + 0.432510i \(0.142372\pi\)
\(104\) −2.51761 1.82915i −0.246872 0.179363i
\(105\) 0 0
\(106\) 1.81653 5.59070i 0.176437 0.543017i
\(107\) 1.53889 + 4.73620i 0.148770 + 0.457866i 0.997476 0.0709975i \(-0.0226183\pi\)
−0.848707 + 0.528864i \(0.822618\pi\)
\(108\) 0 0
\(109\) 11.2061 1.07335 0.536676 0.843788i \(-0.319680\pi\)
0.536676 + 0.843788i \(0.319680\pi\)
\(110\) −10.5414 23.9544i −1.00508 2.28396i
\(111\) 0 0
\(112\) 2.39820 1.74239i 0.226609 0.164641i
\(113\) −5.07595 15.6222i −0.477505 1.46961i −0.842549 0.538620i \(-0.818946\pi\)
0.365044 0.930990i \(-0.381054\pi\)
\(114\) 0 0
\(115\) −14.7913 10.7465i −1.37929 1.00212i
\(116\) 21.0610 + 15.3017i 1.95546 + 1.42073i
\(117\) 0 0
\(118\) 3.14997 + 9.69460i 0.289978 + 0.892460i
\(119\) 1.23523 0.897450i 0.113234 0.0822691i
\(120\) 0 0
\(121\) −7.43084 + 8.11065i −0.675531 + 0.737332i
\(122\) −0.626624 −0.0567318
\(123\) 0 0
\(124\) 6.09480 + 18.7579i 0.547329 + 1.68450i
\(125\) 4.71228 14.5029i 0.421479 1.29718i
\(126\) 0 0
\(127\) 15.8614 + 11.5240i 1.40747 + 1.02259i 0.993684 + 0.112213i \(0.0357939\pi\)
0.413786 + 0.910374i \(0.364206\pi\)
\(128\) −2.16922 + 6.67618i −0.191734 + 0.590096i
\(129\) 0 0
\(130\) −22.1250 + 16.0748i −1.94049 + 1.40985i
\(131\) 13.3659 1.16778 0.583891 0.811832i \(-0.301530\pi\)
0.583891 + 0.811832i \(0.301530\pi\)
\(132\) 0 0
\(133\) −5.16008 −0.447436
\(134\) −1.39050 + 1.01025i −0.120120 + 0.0872726i
\(135\) 0 0
\(136\) −0.423650 + 1.30386i −0.0363277 + 0.111805i
\(137\) 4.27145 + 3.10339i 0.364935 + 0.265141i 0.755107 0.655601i \(-0.227585\pi\)
−0.390173 + 0.920742i \(0.627585\pi\)
\(138\) 0 0
\(139\) −6.60545 + 20.3295i −0.560267 + 1.72432i 0.121344 + 0.992610i \(0.461280\pi\)
−0.681611 + 0.731714i \(0.738720\pi\)
\(140\) 2.81252 + 8.65604i 0.237701 + 0.731569i
\(141\) 0 0
\(142\) −12.0557 −1.01170
\(143\) 9.92968 + 5.79028i 0.830362 + 0.484208i
\(144\) 0 0
\(145\) 32.5488 23.6481i 2.70303 1.96387i
\(146\) −1.60927 4.95282i −0.133184 0.409898i
\(147\) 0 0
\(148\) −18.1771 13.2064i −1.49415 1.08556i
\(149\) 8.89641 + 6.46362i 0.728822 + 0.529520i 0.889191 0.457537i \(-0.151268\pi\)
−0.160369 + 0.987057i \(0.551268\pi\)
\(150\) 0 0
\(151\) −1.09444 3.36836i −0.0890647 0.274113i 0.896597 0.442848i \(-0.146032\pi\)
−0.985661 + 0.168735i \(0.946032\pi\)
\(152\) 3.74841 2.72338i 0.304036 0.220895i
\(153\) 0 0
\(154\) 5.20590 4.64682i 0.419504 0.374452i
\(155\) 30.4813 2.44832
\(156\) 0 0
\(157\) 3.94277 + 12.1346i 0.314667 + 0.968446i 0.975891 + 0.218257i \(0.0700372\pi\)
−0.661224 + 0.750188i \(0.729963\pi\)
\(158\) 7.42768 22.8601i 0.590915 1.81865i
\(159\) 0 0
\(160\) 24.3729 + 17.7079i 1.92685 + 1.39994i
\(161\) 1.50642 4.63628i 0.118722 0.365390i
\(162\) 0 0
\(163\) 13.1748 9.57207i 1.03193 0.749742i 0.0632373 0.997999i \(-0.479858\pi\)
0.968694 + 0.248256i \(0.0798575\pi\)
\(164\) 26.4452 2.06503
\(165\) 0 0
\(166\) 22.3990 1.73850
\(167\) −4.58131 + 3.32851i −0.354512 + 0.257568i −0.750760 0.660576i \(-0.770312\pi\)
0.396247 + 0.918144i \(0.370312\pi\)
\(168\) 0 0
\(169\) −0.305480 + 0.940172i −0.0234985 + 0.0723209i
\(170\) 9.74714 + 7.08171i 0.747572 + 0.543143i
\(171\) 0 0
\(172\) −0.103245 + 0.317757i −0.00787239 + 0.0242287i
\(173\) −4.14744 12.7645i −0.315324 0.970467i −0.975621 0.219462i \(-0.929570\pi\)
0.660297 0.751004i \(-0.270430\pi\)
\(174\) 0 0
\(175\) 9.06597 0.685323
\(176\) 2.08566 9.60783i 0.157212 0.724217i
\(177\) 0 0
\(178\) 15.1763 11.0262i 1.13751 0.826450i
\(179\) −1.17687 3.62202i −0.0879631 0.270722i 0.897393 0.441232i \(-0.145459\pi\)
−0.985356 + 0.170510i \(0.945459\pi\)
\(180\) 0 0
\(181\) 7.91914 + 5.75359i 0.588625 + 0.427661i 0.841823 0.539753i \(-0.181483\pi\)
−0.253198 + 0.967414i \(0.581483\pi\)
\(182\) −5.89927 4.28607i −0.437283 0.317705i
\(183\) 0 0
\(184\) 1.35263 + 4.16296i 0.0997171 + 0.306898i
\(185\) −28.0920 + 20.4100i −2.06536 + 1.50057i
\(186\) 0 0
\(187\) 1.07425 4.94867i 0.0785572 0.361883i
\(188\) 6.62579 0.483236
\(189\) 0 0
\(190\) −12.5825 38.7250i −0.912831 2.80941i
\(191\) −2.77796 + 8.54967i −0.201006 + 0.618632i 0.798848 + 0.601533i \(0.205443\pi\)
−0.999854 + 0.0170994i \(0.994557\pi\)
\(192\) 0 0
\(193\) 4.73227 + 3.43819i 0.340636 + 0.247487i 0.744930 0.667142i \(-0.232483\pi\)
−0.404294 + 0.914629i \(0.632483\pi\)
\(194\) 5.25642 16.1776i 0.377389 1.16148i
\(195\) 0 0
\(196\) −1.96329 + 1.42642i −0.140235 + 0.101887i
\(197\) −6.19555 −0.441414 −0.220707 0.975340i \(-0.570837\pi\)
−0.220707 + 0.975340i \(0.570837\pi\)
\(198\) 0 0
\(199\) −18.8634 −1.33719 −0.668596 0.743626i \(-0.733105\pi\)
−0.668596 + 0.743626i \(0.733105\pi\)
\(200\) −6.58575 + 4.78482i −0.465683 + 0.338338i
\(201\) 0 0
\(202\) 1.11957 3.44569i 0.0787729 0.242438i
\(203\) 8.67861 + 6.30538i 0.609119 + 0.442551i
\(204\) 0 0
\(205\) 12.6295 38.8697i 0.882084 2.71477i
\(206\) −1.75154 5.39068i −0.122036 0.375587i
\(207\) 0 0
\(208\) −10.2737 −0.712351
\(209\) −12.7676 + 11.3965i −0.883154 + 0.788309i
\(210\) 0 0
\(211\) −0.517917 + 0.376288i −0.0356549 + 0.0259048i −0.605470 0.795868i \(-0.707015\pi\)
0.569815 + 0.821773i \(0.307015\pi\)
\(212\) 2.09521 + 6.44839i 0.143900 + 0.442877i
\(213\) 0 0
\(214\) −8.47667 6.15866i −0.579453 0.420997i
\(215\) 0.417737 + 0.303504i 0.0284894 + 0.0206988i
\(216\) 0 0
\(217\) 2.51149 + 7.72957i 0.170491 + 0.524717i
\(218\) −19.0746 + 13.8585i −1.29190 + 0.938618i
\(219\) 0 0
\(220\) 26.0766 + 15.2060i 1.75808 + 1.02519i
\(221\) −5.29163 −0.355953
\(222\) 0 0
\(223\) −5.16437 15.8943i −0.345832 1.06436i −0.961137 0.276072i \(-0.910967\pi\)
0.615305 0.788289i \(-0.289033\pi\)
\(224\) −2.48226 + 7.63960i −0.165853 + 0.510443i
\(225\) 0 0
\(226\) 27.9599 + 20.3141i 1.85987 + 1.35127i
\(227\) −2.88200 + 8.86988i −0.191285 + 0.588714i 0.808715 + 0.588201i \(0.200164\pi\)
−1.00000 0.000513716i \(0.999836\pi\)
\(228\) 0 0
\(229\) −17.2900 + 12.5619i −1.14256 + 0.830115i −0.987473 0.157786i \(-0.949564\pi\)
−0.155083 + 0.987902i \(0.549564\pi\)
\(230\) 38.4672 2.53646
\(231\) 0 0
\(232\) −9.63220 −0.632385
\(233\) −13.8475 + 10.0608i −0.907177 + 0.659103i −0.940299 0.340348i \(-0.889455\pi\)
0.0331221 + 0.999451i \(0.489455\pi\)
\(234\) 0 0
\(235\) 3.16430 9.73870i 0.206416 0.635283i
\(236\) −9.51187 6.91078i −0.619170 0.449853i
\(237\) 0 0
\(238\) −0.992698 + 3.05521i −0.0643470 + 0.198040i
\(239\) −1.04152 3.20548i −0.0673706 0.207345i 0.911704 0.410848i \(-0.134767\pi\)
−0.979074 + 0.203503i \(0.934767\pi\)
\(240\) 0 0
\(241\) 5.77583 0.372054 0.186027 0.982545i \(-0.440439\pi\)
0.186027 + 0.982545i \(0.440439\pi\)
\(242\) 2.61811 22.9953i 0.168298 1.47819i
\(243\) 0 0
\(244\) 0.584721 0.424825i 0.0374330 0.0271966i
\(245\) 1.15896 + 3.56690i 0.0740430 + 0.227881i
\(246\) 0 0
\(247\) 14.4681 + 10.5117i 0.920584 + 0.668844i
\(248\) −5.90391 4.28944i −0.374899 0.272380i
\(249\) 0 0
\(250\) 9.91459 + 30.5140i 0.627054 + 1.92987i
\(251\) 9.51530 6.91327i 0.600600 0.436362i −0.245492 0.969399i \(-0.578949\pi\)
0.846092 + 0.533037i \(0.178949\pi\)
\(252\) 0 0
\(253\) −6.51225 14.7986i −0.409422 0.930380i
\(254\) −41.2503 −2.58827
\(255\) 0 0
\(256\) 2.21714 + 6.82366i 0.138571 + 0.426479i
\(257\) 4.40845 13.5678i 0.274991 0.846336i −0.714230 0.699911i \(-0.753223\pi\)
0.989222 0.146426i \(-0.0467769\pi\)
\(258\) 0 0
\(259\) −7.49026 5.44200i −0.465422 0.338149i
\(260\) 9.74749 29.9997i 0.604514 1.86050i
\(261\) 0 0
\(262\) −22.7509 + 16.5295i −1.40555 + 1.02119i
\(263\) 4.85285 0.299239 0.149620 0.988744i \(-0.452195\pi\)
0.149620 + 0.988744i \(0.452195\pi\)
\(264\) 0 0
\(265\) 10.4786 0.643693
\(266\) 8.78330 6.38144i 0.538539 0.391271i
\(267\) 0 0
\(268\) 0.612603 1.88540i 0.0374207 0.115169i
\(269\) −5.14102 3.73517i −0.313453 0.227737i 0.419923 0.907560i \(-0.362057\pi\)
−0.733377 + 0.679822i \(0.762057\pi\)
\(270\) 0 0
\(271\) −4.70183 + 14.4708i −0.285616 + 0.879036i 0.700597 + 0.713557i \(0.252917\pi\)
−0.986213 + 0.165479i \(0.947083\pi\)
\(272\) 1.39863 + 4.30453i 0.0848042 + 0.261000i
\(273\) 0 0
\(274\) −11.1086 −0.671098
\(275\) 22.4320 20.0229i 1.35270 1.20743i
\(276\) 0 0
\(277\) 0.306857 0.222945i 0.0184372 0.0133954i −0.578528 0.815662i \(-0.696373\pi\)
0.596966 + 0.802267i \(0.296373\pi\)
\(278\) −13.8978 42.7730i −0.833534 2.56535i
\(279\) 0 0
\(280\) −2.72443 1.97941i −0.162816 0.118293i
\(281\) 4.08025 + 2.96448i 0.243407 + 0.176846i 0.702800 0.711387i \(-0.251933\pi\)
−0.459393 + 0.888233i \(0.651933\pi\)
\(282\) 0 0
\(283\) −9.93028 30.5623i −0.590294 1.81674i −0.576881 0.816828i \(-0.695730\pi\)
−0.0134127 0.999910i \(-0.504270\pi\)
\(284\) 11.2496 8.17330i 0.667540 0.484996i
\(285\) 0 0
\(286\) −24.0627 + 2.42397i −1.42286 + 0.143332i
\(287\) 10.8973 0.643248
\(288\) 0 0
\(289\) −4.53290 13.9508i −0.266641 0.820638i
\(290\) −26.1579 + 80.5058i −1.53605 + 4.72746i
\(291\) 0 0
\(292\) 4.85947 + 3.53061i 0.284379 + 0.206613i
\(293\) −8.28925 + 25.5117i −0.484263 + 1.49041i 0.348783 + 0.937204i \(0.386595\pi\)
−0.833046 + 0.553204i \(0.813405\pi\)
\(294\) 0 0
\(295\) −14.7002 + 10.6803i −0.855878 + 0.621832i
\(296\) 8.31328 0.483200
\(297\) 0 0
\(298\) −23.1366 −1.34027
\(299\) −13.6684 + 9.93069i −0.790465 + 0.574306i
\(300\) 0 0
\(301\) −0.0425445 + 0.130938i −0.00245222 + 0.00754716i
\(302\) 6.02854 + 4.37999i 0.346904 + 0.252040i
\(303\) 0 0
\(304\) 4.72680 14.5476i 0.271100 0.834361i
\(305\) −0.345168 1.06232i −0.0197643 0.0608282i
\(306\) 0 0
\(307\) −5.75200 −0.328284 −0.164142 0.986437i \(-0.552486\pi\)
−0.164142 + 0.986437i \(0.552486\pi\)
\(308\) −1.70743 + 7.86548i −0.0972899 + 0.448177i
\(309\) 0 0
\(310\) −51.8841 + 37.6960i −2.94682 + 2.14099i
\(311\) −5.52543 17.0055i −0.313319 0.964295i −0.976441 0.215784i \(-0.930769\pi\)
0.663122 0.748511i \(-0.269231\pi\)
\(312\) 0 0
\(313\) −15.7763 11.4621i −0.891727 0.647877i 0.0446010 0.999005i \(-0.485798\pi\)
−0.936328 + 0.351128i \(0.885798\pi\)
\(314\) −21.7180 15.7790i −1.22562 0.890463i
\(315\) 0 0
\(316\) 8.56718 + 26.3671i 0.481942 + 1.48326i
\(317\) −14.1666 + 10.2926i −0.795675 + 0.578091i −0.909642 0.415393i \(-0.863644\pi\)
0.113967 + 0.993484i \(0.463644\pi\)
\(318\) 0 0
\(319\) 35.3994 3.56598i 1.98199 0.199657i
\(320\) −41.1506 −2.30039
\(321\) 0 0
\(322\) 3.16948 + 9.75467i 0.176628 + 0.543607i
\(323\) 2.43462 7.49298i 0.135466 0.416921i
\(324\) 0 0
\(325\) −25.4196 18.4685i −1.41003 1.02445i
\(326\) −10.5880 + 32.5864i −0.586413 + 1.80480i
\(327\) 0 0
\(328\) −7.91608 + 5.75137i −0.437092 + 0.317566i
\(329\) 2.73030 0.150526
\(330\) 0 0
\(331\) −17.6231 −0.968652 −0.484326 0.874888i \(-0.660935\pi\)
−0.484326 + 0.874888i \(0.660935\pi\)
\(332\) −20.9012 + 15.1856i −1.14710 + 0.833417i
\(333\) 0 0
\(334\) 3.68178 11.3313i 0.201458 0.620023i
\(335\) −2.47863 1.80083i −0.135422 0.0983897i
\(336\) 0 0
\(337\) 0.494763 1.52272i 0.0269515 0.0829481i −0.936676 0.350197i \(-0.886115\pi\)
0.963628 + 0.267249i \(0.0861146\pi\)
\(338\) −0.642727 1.97811i −0.0349598 0.107595i
\(339\) 0 0
\(340\) −13.8965 −0.753641
\(341\) 23.2856 + 13.5785i 1.26098 + 0.735316i
\(342\) 0 0
\(343\) −0.809017 + 0.587785i −0.0436828 + 0.0317374i
\(344\) −0.0382011 0.117571i −0.00205967 0.00633900i
\(345\) 0 0
\(346\) 22.8454 + 16.5981i 1.22817 + 0.892321i
\(347\) 2.78676 + 2.02470i 0.149601 + 0.108691i 0.660068 0.751206i \(-0.270527\pi\)
−0.510467 + 0.859897i \(0.670527\pi\)
\(348\) 0 0
\(349\) 1.04987 + 3.23117i 0.0561983 + 0.172961i 0.975216 0.221257i \(-0.0710158\pi\)
−0.919017 + 0.394217i \(0.871016\pi\)
\(350\) −15.4318 + 11.2118i −0.824862 + 0.599297i
\(351\) 0 0
\(352\) 10.7308 + 24.3850i 0.571954 + 1.29972i
\(353\) −10.4083 −0.553977 −0.276989 0.960873i \(-0.589336\pi\)
−0.276989 + 0.960873i \(0.589336\pi\)
\(354\) 0 0
\(355\) −6.64076 20.4382i −0.352455 1.08475i
\(356\) −6.68613 + 20.5778i −0.354364 + 1.09062i
\(357\) 0 0
\(358\) 6.48254 + 4.70984i 0.342613 + 0.248923i
\(359\) −7.10580 + 21.8694i −0.375030 + 1.15422i 0.568429 + 0.822732i \(0.307551\pi\)
−0.943459 + 0.331490i \(0.892449\pi\)
\(360\) 0 0
\(361\) −6.16995 + 4.48273i −0.324734 + 0.235933i
\(362\) −20.5951 −1.08245
\(363\) 0 0
\(364\) 8.41057 0.440834
\(365\) 7.51010 5.45640i 0.393096 0.285601i
\(366\) 0 0
\(367\) 6.06776 18.6747i 0.316735 0.974809i −0.658300 0.752756i \(-0.728724\pi\)
0.975035 0.222053i \(-0.0712759\pi\)
\(368\) 11.6909 + 8.49395i 0.609431 + 0.442778i
\(369\) 0 0
\(370\) 22.5762 69.4823i 1.17368 3.61221i
\(371\) 0.863375 + 2.65719i 0.0448242 + 0.137955i
\(372\) 0 0
\(373\) −31.9047 −1.65196 −0.825981 0.563698i \(-0.809378\pi\)
−0.825981 + 0.563698i \(0.809378\pi\)
\(374\) 4.29144 + 9.75197i 0.221905 + 0.504262i
\(375\) 0 0
\(376\) −1.98336 + 1.44099i −0.102284 + 0.0743135i
\(377\) −11.4887 35.3587i −0.591700 1.82107i
\(378\) 0 0
\(379\) 1.39117 + 1.01074i 0.0714594 + 0.0519183i 0.622941 0.782268i \(-0.285937\pi\)
−0.551482 + 0.834187i \(0.685937\pi\)
\(380\) 37.9951 + 27.6050i 1.94911 + 1.41611i
\(381\) 0 0
\(382\) −5.84479 17.9884i −0.299045 0.920367i
\(383\) 7.02258 5.10220i 0.358837 0.260710i −0.393730 0.919226i \(-0.628815\pi\)
0.752567 + 0.658516i \(0.228815\pi\)
\(384\) 0 0
\(385\) 10.7454 + 6.26595i 0.547636 + 0.319342i
\(386\) −12.3071 −0.626414
\(387\) 0 0
\(388\) 6.06282 + 18.6594i 0.307793 + 0.947290i
\(389\) 8.28220 25.4900i 0.419924 1.29239i −0.487847 0.872929i \(-0.662218\pi\)
0.907771 0.419465i \(-0.137782\pi\)
\(390\) 0 0
\(391\) 6.02160 + 4.37495i 0.304526 + 0.221251i
\(392\) 0.277470 0.853964i 0.0140143 0.0431317i
\(393\) 0 0
\(394\) 10.5458 7.66199i 0.531291 0.386005i
\(395\) 42.8462 2.15583
\(396\) 0 0
\(397\) −17.8714 −0.896938 −0.448469 0.893798i \(-0.648031\pi\)
−0.448469 + 0.893798i \(0.648031\pi\)
\(398\) 32.1086 23.3283i 1.60946 1.16934i
\(399\) 0 0
\(400\) −8.30471 + 25.5593i −0.415236 + 1.27796i
\(401\) −23.3916 16.9950i −1.16812 0.848689i −0.177337 0.984150i \(-0.556748\pi\)
−0.990783 + 0.135462i \(0.956748\pi\)
\(402\) 0 0
\(403\) 8.70420 26.7888i 0.433587 1.33444i
\(404\) 1.29133 + 3.97430i 0.0642461 + 0.197729i
\(405\) 0 0
\(406\) −22.5702 −1.12014
\(407\) −30.5523 + 3.07770i −1.51442 + 0.152556i
\(408\) 0 0
\(409\) −22.3760 + 16.2571i −1.10642 + 0.803864i −0.982097 0.188378i \(-0.939677\pi\)
−0.124327 + 0.992241i \(0.539677\pi\)
\(410\) 26.5724 + 81.7813i 1.31232 + 4.03889i
\(411\) 0 0
\(412\) 5.28908 + 3.84274i 0.260574 + 0.189318i
\(413\) −3.91956 2.84773i −0.192869 0.140128i
\(414\) 0 0
\(415\) 12.3382 + 37.9731i 0.605659 + 1.86403i
\(416\) 22.5227 16.3637i 1.10426 0.802295i
\(417\) 0 0
\(418\) 7.63863 35.1882i 0.373618 1.72111i
\(419\) 4.51003 0.220330 0.110165 0.993913i \(-0.464862\pi\)
0.110165 + 0.993913i \(0.464862\pi\)
\(420\) 0 0
\(421\) 11.1075 + 34.1853i 0.541345 + 1.66609i 0.729526 + 0.683953i \(0.239741\pi\)
−0.188181 + 0.982134i \(0.560259\pi\)
\(422\) 0.416225 1.28101i 0.0202615 0.0623585i
\(423\) 0 0
\(424\) −2.02959 1.47458i −0.0985655 0.0716120i
\(425\) −4.27748 + 13.1647i −0.207488 + 0.638583i
\(426\) 0 0
\(427\) 0.240947 0.175058i 0.0116602 0.00847165i
\(428\) 12.0851 0.584158
\(429\) 0 0
\(430\) −1.08640 −0.0523907
\(431\) −17.9771 + 13.0611i −0.865927 + 0.629133i −0.929491 0.368845i \(-0.879753\pi\)
0.0635640 + 0.997978i \(0.479753\pi\)
\(432\) 0 0
\(433\) 7.87661 24.2417i 0.378526 1.16498i −0.562544 0.826768i \(-0.690177\pi\)
0.941069 0.338214i \(-0.109823\pi\)
\(434\) −13.8341 10.0510i −0.664056 0.482465i
\(435\) 0 0
\(436\) 8.40360 25.8636i 0.402460 1.23864i
\(437\) −7.77324 23.9236i −0.371845 1.14442i
\(438\) 0 0
\(439\) 11.1407 0.531715 0.265857 0.964012i \(-0.414345\pi\)
0.265857 + 0.964012i \(0.414345\pi\)
\(440\) −11.1128 + 1.11945i −0.529780 + 0.0533676i
\(441\) 0 0
\(442\) 9.00720 6.54412i 0.428429 0.311272i
\(443\) −4.28027 13.1733i −0.203362 0.625883i −0.999777 0.0211325i \(-0.993273\pi\)
0.796415 0.604751i \(-0.206727\pi\)
\(444\) 0 0
\(445\) 27.0525 + 19.6548i 1.28241 + 0.931726i
\(446\) 28.4470 + 20.6679i 1.34700 + 0.978655i
\(447\) 0 0
\(448\) −3.39058 10.4351i −0.160190 0.493013i
\(449\) 8.64664 6.28215i 0.408060 0.296473i −0.364756 0.931103i \(-0.618848\pi\)
0.772816 + 0.634630i \(0.218848\pi\)
\(450\) 0 0
\(451\) 26.9633 24.0676i 1.26965 1.13330i
\(452\) −39.8624 −1.87497
\(453\) 0 0
\(454\) −6.06369 18.6621i −0.284583 0.875857i
\(455\) 4.01666 12.3620i 0.188304 0.579540i
\(456\) 0 0
\(457\) −25.3852 18.4434i −1.18747 0.862746i −0.194473 0.980908i \(-0.562300\pi\)
−0.992994 + 0.118162i \(0.962300\pi\)
\(458\) 13.8951 42.7649i 0.649278 1.99827i
\(459\) 0 0
\(460\) −35.8950 + 26.0792i −1.67361 + 1.21595i
\(461\) −41.1844 −1.91815 −0.959075 0.283151i \(-0.908620\pi\)
−0.959075 + 0.283151i \(0.908620\pi\)
\(462\) 0 0
\(463\) 35.6274 1.65575 0.827874 0.560915i \(-0.189550\pi\)
0.827874 + 0.560915i \(0.189550\pi\)
\(464\) −25.7263 + 18.6913i −1.19432 + 0.867721i
\(465\) 0 0
\(466\) 11.1285 34.2501i 0.515520 1.58661i
\(467\) 5.22581 + 3.79677i 0.241821 + 0.175694i 0.702094 0.712084i \(-0.252248\pi\)
−0.460273 + 0.887777i \(0.652248\pi\)
\(468\) 0 0
\(469\) 0.252436 0.776917i 0.0116564 0.0358747i
\(470\) 6.65764 + 20.4901i 0.307094 + 0.945139i
\(471\) 0 0
\(472\) 4.35024 0.200236
\(473\) 0.183920 + 0.417944i 0.00845665 + 0.0192171i
\(474\) 0 0
\(475\) 37.8468 27.4973i 1.73653 1.26166i
\(476\) −1.14499 3.52392i −0.0524805 0.161518i
\(477\) 0 0
\(478\) 5.73704 + 4.16820i 0.262406 + 0.190649i
\(479\) −5.50379 3.99874i −0.251475 0.182707i 0.454905 0.890540i \(-0.349673\pi\)
−0.706380 + 0.707833i \(0.749673\pi\)
\(480\) 0 0
\(481\) 9.91561 + 30.5171i 0.452113 + 1.39146i
\(482\) −9.83139 + 7.14293i −0.447808 + 0.325351i
\(483\) 0 0
\(484\) 13.1468 + 23.2326i 0.597584 + 1.05603i
\(485\) 30.3214 1.37682
\(486\) 0 0
\(487\) 8.25829 + 25.4164i 0.374219 + 1.15173i 0.944004 + 0.329933i \(0.107026\pi\)
−0.569786 + 0.821793i \(0.692974\pi\)
\(488\) −0.0826378 + 0.254333i −0.00374084 + 0.0115131i
\(489\) 0 0
\(490\) −6.38390 4.63817i −0.288395 0.209531i
\(491\) 1.88271 5.79438i 0.0849654 0.261497i −0.899544 0.436831i \(-0.856101\pi\)
0.984509 + 0.175335i \(0.0561007\pi\)
\(492\) 0 0
\(493\) −13.2508 + 9.62726i −0.596785 + 0.433590i
\(494\) −37.6268 −1.69291
\(495\) 0 0
\(496\) −24.0922 −1.08177
\(497\) 4.63563 3.36798i 0.207936 0.151075i
\(498\) 0 0
\(499\) 0.462142 1.42233i 0.0206883 0.0636721i −0.940179 0.340680i \(-0.889343\pi\)
0.960868 + 0.277008i \(0.0893428\pi\)
\(500\) −29.9388 21.7518i −1.33890 0.972771i
\(501\) 0 0
\(502\) −7.64699 + 23.5350i −0.341302 + 1.05042i
\(503\) −4.44469 13.6793i −0.198179 0.609932i −0.999925 0.0122669i \(-0.996095\pi\)
0.801746 0.597665i \(-0.203905\pi\)
\(504\) 0 0
\(505\) 6.45820 0.287386
\(506\) 29.3862 + 17.1360i 1.30638 + 0.761786i
\(507\) 0 0
\(508\) 38.4919 27.9660i 1.70780 1.24079i
\(509\) 0.860293 + 2.64771i 0.0381318 + 0.117358i 0.968310 0.249749i \(-0.0803483\pi\)
−0.930179 + 0.367107i \(0.880348\pi\)
\(510\) 0 0
\(511\) 2.00245 + 1.45486i 0.0885830 + 0.0643593i
\(512\) −23.5709 17.1253i −1.04170 0.756837i
\(513\) 0 0
\(514\) 9.27532 + 28.5465i 0.409117 + 1.25913i
\(515\) 8.17404 5.93879i 0.360191 0.261694i
\(516\) 0 0
\(517\) 6.75558 6.03008i 0.297110 0.265203i
\(518\) 19.4797 0.855890
\(519\) 0 0
\(520\) 3.60660 + 11.1000i 0.158160 + 0.486766i
\(521\) −12.5241 + 38.5453i −0.548691 + 1.68870i 0.163356 + 0.986567i \(0.447768\pi\)
−0.712047 + 0.702131i \(0.752232\pi\)
\(522\) 0 0
\(523\) −0.724294 0.526231i −0.0316712 0.0230105i 0.571837 0.820367i \(-0.306231\pi\)
−0.603508 + 0.797357i \(0.706231\pi\)
\(524\) 10.0232 30.8483i 0.437867 1.34762i
\(525\) 0 0
\(526\) −8.26033 + 6.00148i −0.360168 + 0.261677i
\(527\) −12.4091 −0.540549
\(528\) 0 0
\(529\) 0.764354 0.0332328
\(530\) −17.8362 + 12.9588i −0.774756 + 0.562893i
\(531\) 0 0
\(532\) −3.86961 + 11.9094i −0.167769 + 0.516339i
\(533\) −30.5545 22.1991i −1.32346 0.961551i
\(534\) 0 0
\(535\) 5.77154 17.7630i 0.249525 0.767960i
\(536\) 0.226665 + 0.697602i 0.00979042 + 0.0301318i
\(537\) 0 0
\(538\) 13.3701 0.576426
\(539\) −0.703583 + 3.24114i −0.0303055 + 0.139606i
\(540\) 0 0
\(541\) 2.31464 1.68169i 0.0995144 0.0723014i −0.536915 0.843636i \(-0.680411\pi\)
0.636430 + 0.771335i \(0.280411\pi\)
\(542\) −9.89260 30.4463i −0.424924 1.30778i
\(543\) 0 0
\(544\) −9.92233 7.20899i −0.425416 0.309083i
\(545\) −34.0015 24.7035i −1.45646 1.05818i
\(546\) 0 0
\(547\) 8.25667 + 25.4114i 0.353030 + 1.08651i 0.957143 + 0.289615i \(0.0935273\pi\)
−0.604114 + 0.796898i \(0.706473\pi\)
\(548\) 10.3658 7.53120i 0.442806 0.321717i
\(549\) 0 0
\(550\) −13.4206 + 61.8237i −0.572258 + 2.63617i
\(551\) 55.3540 2.35816
\(552\) 0 0
\(553\) 3.53029 + 10.8651i 0.150123 + 0.462031i
\(554\) −0.246606 + 0.758976i −0.0104773 + 0.0322458i
\(555\) 0 0
\(556\) 41.9668 + 30.4907i 1.77979 + 1.29309i
\(557\) 3.53536 10.8807i 0.149798 0.461031i −0.847799 0.530318i \(-0.822073\pi\)
0.997597 + 0.0692874i \(0.0220726\pi\)
\(558\) 0 0
\(559\) 0.386025 0.280464i 0.0163271 0.0118624i
\(560\) −11.1176 −0.469806
\(561\) 0 0
\(562\) −10.6114 −0.447615
\(563\) 9.88153 7.17935i 0.416457 0.302574i −0.359754 0.933047i \(-0.617139\pi\)
0.776211 + 0.630474i \(0.217139\pi\)
\(564\) 0 0
\(565\) −19.0372 + 58.5904i −0.800900 + 2.46492i
\(566\) 54.6991 + 39.7412i 2.29917 + 1.67045i
\(567\) 0 0
\(568\) −1.58989 + 4.89317i −0.0667102 + 0.205313i
\(569\) −6.29680 19.3796i −0.263976 0.812433i −0.991928 0.126805i \(-0.959528\pi\)
0.727952 0.685628i \(-0.240472\pi\)
\(570\) 0 0
\(571\) −20.3621 −0.852129 −0.426065 0.904693i \(-0.640100\pi\)
−0.426065 + 0.904693i \(0.640100\pi\)
\(572\) 20.8103 18.5754i 0.870123 0.776677i
\(573\) 0 0
\(574\) −18.5490 + 13.4766i −0.774220 + 0.562504i
\(575\) 13.6571 + 42.0323i 0.569542 + 1.75287i
\(576\) 0 0
\(577\) −4.89034 3.55304i −0.203588 0.147915i 0.481320 0.876545i \(-0.340157\pi\)
−0.684908 + 0.728630i \(0.740157\pi\)
\(578\) 24.9686 + 18.1408i 1.03856 + 0.754557i
\(579\) 0 0
\(580\) −30.1709 92.8564i −1.25278 3.85565i
\(581\) −8.61276 + 6.25754i −0.357318 + 0.259606i
\(582\) 0 0
\(583\) 8.00488 + 4.66787i 0.331528 + 0.193324i
\(584\) −2.22247 −0.0919665
\(585\) 0 0
\(586\) −17.4405 53.6763i −0.720459 2.21735i
\(587\) −11.2920 + 34.7533i −0.466072 + 1.43442i 0.391557 + 0.920154i \(0.371936\pi\)
−0.857629 + 0.514268i \(0.828064\pi\)
\(588\) 0 0
\(589\) 33.9284 + 24.6504i 1.39800 + 1.01570i
\(590\) 11.8138 36.3592i 0.486368 1.49689i
\(591\) 0 0
\(592\) 22.2037 16.1319i 0.912566 0.663018i
\(593\) −15.6666 −0.643349 −0.321675 0.946850i \(-0.604246\pi\)
−0.321675 + 0.946850i \(0.604246\pi\)
\(594\) 0 0
\(595\) −5.72633 −0.234757
\(596\) 21.5895 15.6857i 0.884340 0.642511i
\(597\) 0 0
\(598\) 10.9847 33.8073i 0.449196 1.38248i
\(599\) 22.9983 + 16.7092i 0.939683 + 0.682720i 0.948344 0.317243i \(-0.102757\pi\)
−0.00866125 + 0.999962i \(0.502757\pi\)
\(600\) 0 0
\(601\) −3.80479 + 11.7099i −0.155201 + 0.477658i −0.998181 0.0602858i \(-0.980799\pi\)
0.842981 + 0.537944i \(0.180799\pi\)
\(602\) −0.0895130 0.275493i −0.00364828 0.0112282i
\(603\) 0 0
\(604\) −8.59487 −0.349720
\(605\) 40.4262 8.22820i 1.64356 0.334524i
\(606\) 0 0
\(607\) 27.1485 19.7245i 1.10192 0.800594i 0.120550 0.992707i \(-0.461534\pi\)
0.981373 + 0.192113i \(0.0615342\pi\)
\(608\) 12.8087 + 39.4210i 0.519460 + 1.59873i
\(609\) 0 0
\(610\) 1.90129 + 1.38137i 0.0769811 + 0.0559301i
\(611\) −7.65535 5.56194i −0.309702 0.225012i
\(612\) 0 0
\(613\) −1.66265 5.11712i −0.0671540 0.206679i 0.911849 0.410527i \(-0.134655\pi\)
−0.979003 + 0.203848i \(0.934655\pi\)
\(614\) 9.79083 7.11346i 0.395126 0.287076i
\(615\) 0 0
\(616\) −1.19950 2.72578i −0.0483293 0.109825i
\(617\) 29.3058 1.17981 0.589904 0.807473i \(-0.299166\pi\)
0.589904 + 0.807473i \(0.299166\pi\)
\(618\) 0 0
\(619\) 1.03779 + 3.19399i 0.0417123 + 0.128377i 0.969744 0.244124i \(-0.0785003\pi\)
−0.928032 + 0.372501i \(0.878500\pi\)
\(620\) 22.8583 70.3506i 0.918012 2.82535i
\(621\) 0 0
\(622\) 30.4358 + 22.1129i 1.22036 + 0.886647i
\(623\) −2.75516 + 8.47951i −0.110383 + 0.339724i
\(624\) 0 0
\(625\) −9.59653 + 6.97229i −0.383861 + 0.278891i
\(626\) 41.0289 1.63984
\(627\) 0 0
\(628\) 30.9633 1.23557
\(629\) 11.4364 8.30902i 0.455998 0.331302i
\(630\) 0 0
\(631\) −9.62320 + 29.6172i −0.383093 + 1.17904i 0.554761 + 0.832010i \(0.312810\pi\)
−0.937854 + 0.347030i \(0.887190\pi\)
\(632\) −8.29886 6.02948i −0.330111 0.239840i
\(633\) 0 0
\(634\) 11.3850 35.0394i 0.452156 1.39159i
\(635\) −22.7222 69.9318i −0.901704 2.77516i
\(636\) 0 0
\(637\) 3.46575 0.137318
\(638\) −55.8456 + 49.8481i −2.21095 + 1.97351i
\(639\) 0 0
\(640\) 21.2992 15.4748i 0.841926 0.611695i
\(641\) −6.57985 20.2507i −0.259888 0.799855i −0.992827 0.119560i \(-0.961852\pi\)
0.732939 0.680295i \(-0.238148\pi\)
\(642\) 0 0
\(643\) −18.4098 13.3755i −0.726011 0.527478i 0.162288 0.986743i \(-0.448113\pi\)
−0.888299 + 0.459265i \(0.848113\pi\)
\(644\) −9.57081 6.95360i −0.377143 0.274010i
\(645\) 0 0
\(646\) 5.12241 + 15.7651i 0.201538 + 0.620271i
\(647\) 34.8543 25.3232i 1.37027 0.995556i 0.372549 0.928013i \(-0.378484\pi\)
0.997716 0.0675433i \(-0.0215161\pi\)
\(648\) 0 0
\(649\) −15.9876 + 1.61052i −0.627569 + 0.0632185i
\(650\) 66.1082 2.59298
\(651\) 0 0
\(652\) −12.2123 37.5856i −0.478270 1.47197i
\(653\) −11.0514 + 34.0126i −0.432473 + 1.33102i 0.463181 + 0.886264i \(0.346708\pi\)
−0.895654 + 0.444752i \(0.853292\pi\)
\(654\) 0 0
\(655\) −40.5546 29.4646i −1.58460 1.15128i
\(656\) −9.98228 + 30.7223i −0.389743 + 1.19950i
\(657\) 0 0
\(658\) −4.64741 + 3.37654i −0.181175 + 0.131631i
\(659\) −16.6988 −0.650495 −0.325247 0.945629i \(-0.605448\pi\)
−0.325247 + 0.945629i \(0.605448\pi\)
\(660\) 0 0
\(661\) 36.5422 1.42133 0.710664 0.703532i \(-0.248395\pi\)
0.710664 + 0.703532i \(0.248395\pi\)
\(662\) 29.9973 21.7943i 1.16588 0.847061i
\(663\) 0 0
\(664\) 2.95393 9.09126i 0.114635 0.352809i
\(665\) 15.6567 + 11.3752i 0.607139 + 0.441113i
\(666\) 0 0
\(667\) −16.1599 + 49.7350i −0.625713 + 1.92575i
\(668\) 4.24661 + 13.0697i 0.164306 + 0.505682i
\(669\) 0 0
\(670\) 6.44609 0.249034
\(671\) 0.209546 0.965297i 0.00808942 0.0372649i
\(672\) 0 0
\(673\) −23.1936 + 16.8512i −0.894049 + 0.649564i −0.936930 0.349516i \(-0.886346\pi\)
0.0428818 + 0.999080i \(0.486346\pi\)
\(674\) 1.04098 + 3.20379i 0.0400969 + 0.123405i
\(675\) 0 0
\(676\) 1.94083 + 1.41009i 0.0746472 + 0.0542343i
\(677\) 8.88350 + 6.45424i 0.341421 + 0.248057i 0.745261 0.666773i \(-0.232325\pi\)
−0.403840 + 0.914829i \(0.632325\pi\)
\(678\) 0 0
\(679\) 2.49831 + 7.68902i 0.0958764 + 0.295077i
\(680\) 4.15975 3.02223i 0.159519 0.115897i
\(681\) 0 0
\(682\) −56.4282 + 5.68432i −2.16075 + 0.217664i
\(683\) −25.3941 −0.971679 −0.485840 0.874048i \(-0.661486\pi\)
−0.485840 + 0.874048i \(0.661486\pi\)
\(684\) 0 0
\(685\) −6.11906 18.8325i −0.233797 0.719554i
\(686\) 0.650168 2.00101i 0.0248235 0.0763990i
\(687\) 0 0
\(688\) −0.330176 0.239887i −0.0125879 0.00914562i
\(689\) 2.99224 9.20918i 0.113995 0.350842i
\(690\) 0 0
\(691\) 21.5170 15.6330i 0.818545 0.594708i −0.0977502 0.995211i \(-0.531165\pi\)
0.916295 + 0.400503i \(0.131165\pi\)
\(692\) −32.5706 −1.23815
\(693\) 0 0
\(694\) −7.24744 −0.275109
\(695\) 64.8579 47.1220i 2.46020 1.78744i
\(696\) 0 0
\(697\) −5.14154 + 15.8240i −0.194750 + 0.599378i
\(698\) −5.78302 4.20161i −0.218890 0.159033i
\(699\) 0 0
\(700\) 6.79868 20.9242i 0.256966 0.790860i
\(701\) 13.9546 + 42.9477i 0.527057 + 1.62211i 0.760213 + 0.649674i \(0.225095\pi\)
−0.233156 + 0.972439i \(0.574905\pi\)
\(702\) 0 0
\(703\) −47.7745 −1.80185
\(704\) −31.4361 18.3313i −1.18479 0.690887i
\(705\) 0 0
\(706\) 17.7166 12.8719i 0.666773 0.484439i
\(707\) 0.532120 + 1.63770i 0.0200124 + 0.0615919i
\(708\) 0 0
\(709\) −34.5641 25.1123i −1.29808 0.943111i −0.298146 0.954520i \(-0.596368\pi\)
−0.999935 + 0.0114097i \(0.996368\pi\)
\(710\) 36.5794 + 26.5765i 1.37280 + 0.997398i
\(711\) 0 0
\(712\) −2.47389 7.61384i −0.0927128 0.285341i
\(713\) −32.0531 + 23.2879i −1.20040 + 0.872139i
\(714\) 0 0
\(715\) −17.3640 39.4584i −0.649378 1.47566i
\(716\) −9.24214 −0.345395
\(717\) 0 0
\(718\) −14.9505 46.0130i −0.557948 1.71719i
\(719\) 4.77125 14.6844i 0.177938 0.547636i −0.821818 0.569751i \(-0.807040\pi\)
0.999755 + 0.0221144i \(0.00703981\pi\)
\(720\) 0 0
\(721\) 2.17947 + 1.58348i 0.0811679 + 0.0589719i
\(722\) 4.95849 15.2607i 0.184536 0.567943i
\(723\) 0 0
\(724\) 19.2179 13.9626i 0.714227 0.518917i
\(725\) −97.2539 −3.61192
\(726\) 0 0
\(727\) 14.8932 0.552357 0.276178 0.961106i \(-0.410932\pi\)
0.276178 + 0.961106i \(0.410932\pi\)
\(728\) −2.51761 + 1.82915i −0.0933088 + 0.0677928i
\(729\) 0 0
\(730\) −6.03550 + 18.5754i −0.223384 + 0.687505i
\(731\) −0.170063 0.123558i −0.00629001 0.00456996i
\(732\) 0 0
\(733\) −2.28260 + 7.02511i −0.0843096 + 0.259478i −0.984321 0.176389i \(-0.943558\pi\)
0.900011 + 0.435867i \(0.143558\pi\)
\(734\) 12.7665 + 39.2913i 0.471220 + 1.45027i
\(735\) 0 0
\(736\) −39.1586 −1.44341
\(737\) −1.09128 2.47985i −0.0401979 0.0913466i
\(738\) 0 0
\(739\) −28.1984 + 20.4874i −1.03730 + 0.753640i −0.969756 0.244077i \(-0.921515\pi\)
−0.0675401 + 0.997717i \(0.521515\pi\)
\(740\) 26.0396 + 80.1417i 0.957235 + 2.94607i
\(741\) 0 0
\(742\) −4.75574 3.45525i −0.174589 0.126846i
\(743\) −2.69669 1.95926i −0.0989321 0.0718783i 0.537219 0.843442i \(-0.319475\pi\)
−0.636152 + 0.771564i \(0.719475\pi\)
\(744\) 0 0
\(745\) −12.7445 39.2237i −0.466924 1.43704i
\(746\) 54.3069 39.4563i 1.98832 1.44460i
\(747\) 0 0
\(748\) −10.6159 6.19044i −0.388156 0.226345i
\(749\) 4.97994 0.181963
\(750\) 0 0
\(751\) 15.8399 + 48.7501i 0.578005 + 1.77892i 0.625711 + 0.780055i \(0.284809\pi\)
−0.0477057 + 0.998861i \(0.515191\pi\)
\(752\) −2.50104 + 7.69740i −0.0912034 + 0.280695i
\(753\) 0 0
\(754\) 63.2836 + 45.9782i 2.30465 + 1.67443i
\(755\) −4.10467 + 12.6329i −0.149384 + 0.459758i
\(756\) 0 0
\(757\) −3.29614 + 2.39479i −0.119800 + 0.0870401i −0.646072 0.763276i \(-0.723589\pi\)
0.526272 + 0.850316i \(0.323589\pi\)
\(758\) −3.61797 −0.131411
\(759\) 0 0
\(760\) −17.3770 −0.630330
\(761\) 4.86330 3.53339i 0.176294 0.128085i −0.496139 0.868243i \(-0.665249\pi\)
0.672433 + 0.740158i \(0.265249\pi\)
\(762\) 0 0
\(763\) 3.46288 10.6577i 0.125365 0.385833i
\(764\) 17.6493 + 12.8230i 0.638531 + 0.463920i
\(765\) 0 0
\(766\) −5.64371 + 17.3696i −0.203916 + 0.627588i
\(767\) 5.18872 + 15.9692i 0.187354 + 0.576616i
\(768\) 0 0
\(769\) 43.2310 1.55895 0.779474 0.626434i \(-0.215486\pi\)
0.779474 + 0.626434i \(0.215486\pi\)
\(770\) −26.0395 + 2.62310i −0.938397 + 0.0945299i
\(771\) 0 0
\(772\) 11.4841 8.34369i 0.413322 0.300296i
\(773\) 2.98056 + 9.17322i 0.107203 + 0.329938i 0.990241 0.139364i \(-0.0445057\pi\)
−0.883038 + 0.469302i \(0.844506\pi\)
\(774\) 0 0
\(775\) −59.6102 43.3094i −2.14126 1.55572i
\(776\) −5.87293 4.26694i −0.210826 0.153174i
\(777\) 0 0
\(778\) 17.4257 + 53.6307i 0.624740 + 1.92275i
\(779\) 45.4919 33.0518i 1.62992 1.18420i
\(780\) 0 0
\(781\) 4.03150 18.5716i 0.144258 0.664542i
\(782\) −15.6602 −0.560008
\(783\) 0 0
\(784\) −0.916031 2.81925i −0.0327154 0.100688i
\(785\) 14.7872 45.5103i 0.527778 1.62433i
\(786\) 0 0
\(787\) 19.5129 + 14.1769i 0.695558 + 0.505353i 0.878483 0.477774i \(-0.158556\pi\)
−0.182924 + 0.983127i \(0.558556\pi\)
\(788\) −4.64611 + 14.2993i −0.165511 + 0.509390i
\(789\) 0 0
\(790\) −72.9312 + 52.9876i −2.59478 + 1.88522i
\(791\) −16.4261 −0.584046
\(792\) 0 0
\(793\) −1.03219 −0.0366543
\(794\) 30.4200 22.1014i 1.07956 0.784349i
\(795\) 0 0
\(796\) −14.1459 + 43.5366i −0.501388 + 1.54311i
\(797\) −34.3079 24.9262i −1.21525 0.882931i −0.219553 0.975601i \(-0.570460\pi\)
−0.995697 + 0.0926701i \(0.970460\pi\)
\(798\) 0 0
\(799\) −1.28820 + 3.96468i −0.0455733 + 0.140260i
\(800\) −22.5041 69.2604i −0.795639 2.44873i
\(801\) 0 0
\(802\) 60.8338 2.14812
\(803\) 8.16783 0.822790i 0.288237 0.0290356i
\(804\) 0 0
\(805\) −14.7913 + 10.7465i −0.521324 + 0.378764i
\(806\) 18.3135 + 56.3633i 0.645067 + 1.98531i
\(807\) 0 0
\(808\) −1.25089 0.908821i −0.0440060 0.0319722i
\(809\) −2.80108 2.03510i −0.0984806 0.0715503i 0.537455 0.843292i \(-0.319386\pi\)
−0.635936 + 0.771742i \(0.719386\pi\)
\(810\) 0 0
\(811\) 4.86848 + 14.9837i 0.170956 + 0.526147i 0.999426 0.0338861i \(-0.0107883\pi\)
−0.828470 + 0.560033i \(0.810788\pi\)
\(812\) 21.0610 15.3017i 0.739095 0.536984i
\(813\) 0 0
\(814\) 48.1987 43.0225i 1.68937 1.50794i
\(815\) −61.0762 −2.13941
\(816\) 0 0
\(817\) 0.219533 + 0.675653i 0.00768049 + 0.0236381i
\(818\) 17.9825 55.3446i 0.628745 1.93508i
\(819\) 0 0
\(820\) −80.2398 58.2976i −2.80210 2.03584i
\(821\) −2.45096 + 7.54328i −0.0855391 + 0.263262i −0.984673 0.174412i \(-0.944198\pi\)
0.899134 + 0.437674i \(0.144198\pi\)
\(822\) 0 0
\(823\) −26.6492 + 19.3618i −0.928932 + 0.674908i −0.945731 0.324950i \(-0.894652\pi\)
0.0167992 + 0.999859i \(0.494652\pi\)
\(824\) −2.41895 −0.0842682
\(825\) 0 0
\(826\) 10.1935 0.354677
\(827\) 24.4141 17.7379i 0.848962 0.616807i −0.0758980 0.997116i \(-0.524182\pi\)
0.924860 + 0.380309i \(0.124182\pi\)
\(828\) 0 0
\(829\) −6.73188 + 20.7186i −0.233808 + 0.719587i 0.763469 + 0.645844i \(0.223494\pi\)
−0.997277 + 0.0737429i \(0.976506\pi\)
\(830\) −67.9627 49.3778i −2.35902 1.71393i
\(831\) 0 0
\(832\) −11.7509 + 36.1656i −0.407389 + 1.25382i
\(833\) −0.471817 1.45210i −0.0163475 0.0503124i
\(834\) 0 0
\(835\) 21.2381 0.734976
\(836\) 16.7283 + 38.0139i 0.578562 + 1.31474i
\(837\) 0 0
\(838\) −7.67681 + 5.57753i −0.265191 + 0.192672i
\(839\) 4.17093 + 12.8368i 0.143996 + 0.443175i 0.996881 0.0789248i \(-0.0251487\pi\)
−0.852884 + 0.522100i \(0.825149\pi\)
\(840\) 0 0
\(841\) −69.6370 50.5943i −2.40128 1.74463i
\(842\) −61.1834 44.4523i −2.10852 1.53193i
\(843\) 0 0
\(844\) 0.480079 + 1.47753i 0.0165250 + 0.0508587i
\(845\) 2.99946 2.17924i 0.103185 0.0749681i
\(846\) 0 0
\(847\) 5.41743 + 9.57348i 0.186145 + 0.328949i
\(848\) −8.28218 −0.284411
\(849\) 0 0
\(850\) −8.99977 27.6984i −0.308690 0.950049i
\(851\) 13.9471 42.9249i 0.478101 1.47145i
\(852\) 0 0
\(853\) −18.2167 13.2352i −0.623729 0.453165i 0.230493 0.973074i \(-0.425966\pi\)
−0.854222 + 0.519909i \(0.825966\pi\)
\(854\) −0.193637 + 0.595955i −0.00662613 + 0.0203931i
\(855\) 0 0
\(856\) −3.61755 + 2.62831i −0.123645 + 0.0898336i
\(857\) −12.2772 −0.419383 −0.209691 0.977768i \(-0.567246\pi\)
−0.209691 + 0.977768i \(0.567246\pi\)
\(858\) 0 0
\(859\) −46.4901 −1.58622 −0.793110 0.609078i \(-0.791540\pi\)
−0.793110 + 0.609078i \(0.791540\pi\)
\(860\) 1.01375 0.736533i 0.0345686 0.0251156i
\(861\) 0 0
\(862\) 14.4473 44.4643i 0.492078 1.51446i
\(863\) 44.0606 + 32.0119i 1.49984 + 1.08970i 0.970445 + 0.241324i \(0.0775815\pi\)
0.529396 + 0.848375i \(0.322419\pi\)
\(864\) 0 0
\(865\) −15.5548 + 47.8728i −0.528879 + 1.62772i
\(866\) 16.5723 + 51.0043i 0.563149 + 1.73320i
\(867\) 0 0
\(868\) 19.7232 0.669448
\(869\) 32.7315 + 19.0867i 1.11034 + 0.647470i
\(870\) 0 0
\(871\) −2.29047 + 1.66412i −0.0776095 + 0.0563866i
\(872\) 3.10936 + 9.56962i 0.105296 + 0.324068i
\(873\) 0 0
\(874\) 42.8174 + 31.1087i 1.44832 + 1.05227i
\(875\) −12.3369 8.96329i −0.417064 0.303015i
\(876\) 0 0
\(877\) −9.10275 28.0154i −0.307378 0.946013i −0.978779 0.204918i \(-0.934307\pi\)
0.671401 0.741094i \(-0.265693\pi\)
\(878\) −18.9632 + 13.7776i −0.639977 + 0.464971i
\(879\) 0 0
\(880\) −27.5084 + 24.5542i −0.927309 + 0.827722i
\(881\) 29.9763 1.00993 0.504964 0.863141i \(-0.331506\pi\)
0.504964 + 0.863141i \(0.331506\pi\)
\(882\) 0 0
\(883\) 9.34912 + 28.7736i 0.314623 + 0.968310i 0.975909 + 0.218176i \(0.0700108\pi\)
−0.661286 + 0.750134i \(0.729989\pi\)
\(884\) −3.96825 + 12.2130i −0.133467 + 0.410769i
\(885\) 0 0
\(886\) 23.5771 + 17.1297i 0.792087 + 0.575485i
\(887\) −14.6213 + 44.9998i −0.490936 + 1.51095i 0.332259 + 0.943188i \(0.392189\pi\)
−0.823195 + 0.567759i \(0.807811\pi\)
\(888\) 0 0
\(889\) 15.8614 11.5240i 0.531974 0.386502i
\(890\) −70.3546 −2.35829
\(891\) 0 0
\(892\) −40.5567 −1.35794
\(893\) 11.3979 8.28105i 0.381416 0.277115i
\(894\) 0 0
\(895\) −4.41379 + 13.5842i −0.147537 + 0.454071i
\(896\) 5.67910 + 4.12610i 0.189725 + 0.137843i
\(897\) 0 0
\(898\) −6.94889 + 21.3865i −0.231887 + 0.713676i
\(899\) −26.9416 82.9178i −0.898554 2.76546i
\(900\) 0 0
\(901\) −4.26588 −0.142117
\(902\) −16.1316 + 74.3122i −0.537124 + 2.47433i
\(903\) 0 0
\(904\) 11.9323 8.66935i 0.396864 0.288338i
\(905\) −11.3446 34.9149i −0.377106 1.16061i
\(906\) 0 0
\(907\) 40.1660 + 29.1823i 1.33369 + 0.968982i 0.999651 + 0.0264221i \(0.00841141\pi\)
0.334038 + 0.942560i \(0.391589\pi\)
\(908\) 18.3104 + 13.3033i 0.607651 + 0.441484i
\(909\) 0 0
\(910\) 8.45100 + 26.0095i 0.280148 + 0.862207i
\(911\) −17.4325 + 12.6655i −0.577564 + 0.419625i −0.837845 0.545908i \(-0.816185\pi\)
0.260281 + 0.965533i \(0.416185\pi\)
\(912\) 0 0
\(913\) −7.49032 + 34.5050i −0.247893 + 1.14195i
\(914\) 66.0185 2.18370
\(915\) 0 0
\(916\) 16.0268 + 49.3255i 0.529542 + 1.62976i
\(917\) 4.13028 12.7117i 0.136394 0.419777i
\(918\) 0 0
\(919\) −35.7654 25.9851i −1.17979 0.857169i −0.187643 0.982237i \(-0.560085\pi\)
−0.992148 + 0.125069i \(0.960085\pi\)
\(920\) 5.07298 15.6130i 0.167251 0.514746i
\(921\) 0 0
\(922\) 70.1026 50.9325i 2.30871 1.67737i
\(923\) −19.8586 −0.653654
\(924\) 0 0
\(925\) 83.9371 2.75983
\(926\) −60.6437 + 44.0602i −1.99287 + 1.44791i
\(927\) 0 0
\(928\) 26.6281 81.9527i 0.874109 2.69023i
\(929\) 1.38218 + 1.00422i 0.0453480 + 0.0329472i 0.610228 0.792226i \(-0.291078\pi\)
−0.564880 + 0.825173i \(0.691078\pi\)
\(930\) 0 0
\(931\) −1.59455 + 4.90753i −0.0522594 + 0.160838i
\(932\) 12.8358 + 39.5045i 0.420450 + 1.29401i
\(933\) 0 0
\(934\) −13.5906 −0.444698
\(935\) −14.1687 + 12.6471i −0.463365 + 0.413603i
\(936\) 0 0
\(937\) 26.9982 19.6153i 0.881991 0.640804i −0.0517861 0.998658i \(-0.516491\pi\)
0.933778 + 0.357854i \(0.116491\pi\)
\(938\) 0.531122 + 1.63462i 0.0173417 + 0.0533724i
\(939\) 0 0
\(940\) −20.1039 14.6063i −0.655717 0.476406i
\(941\) −17.9708 13.0566i −0.585832 0.425632i 0.254990 0.966944i \(-0.417928\pi\)
−0.840822 + 0.541312i \(0.817928\pi\)
\(942\) 0 0
\(943\) 16.4159 + 50.5230i 0.534576 + 1.64525i
\(944\) 11.6189 8.44164i 0.378164 0.274752i
\(945\) 0 0
\(946\) −0.829930 0.483956i −0.0269834 0.0157348i
\(947\) −16.6969 −0.542578 −0.271289 0.962498i \(-0.587450\pi\)
−0.271289 + 0.962498i \(0.587450\pi\)
\(948\) 0 0
\(949\) −2.65084 8.15844i −0.0860498 0.264834i
\(950\) −30.4156 + 93.6097i −0.986813 + 3.03710i
\(951\) 0 0
\(952\) 1.10913 + 0.805830i 0.0359471 + 0.0261171i
\(953\) 5.89802 18.1522i 0.191056 0.588009i −0.808944 0.587885i \(-0.799961\pi\)
1.00000 0.000123576i \(-3.93355e-5\pi\)
\(954\) 0 0
\(955\) 27.2763 19.8174i 0.882640 0.641276i
\(956\) −8.17927 −0.264537
\(957\) 0 0
\(958\) 14.3136 0.462450
\(959\) 4.27145 3.10339i 0.137932 0.100214i
\(960\) 0 0
\(961\) 10.8322 33.3381i 0.349426 1.07542i
\(962\) −54.6183 39.6825i −1.76096 1.27942i
\(963\) 0 0
\(964\) 4.33136 13.3306i 0.139504 0.429348i
\(965\) −6.77921 20.8643i −0.218230 0.671644i
\(966\) 0 0
\(967\) 36.9443 1.18805 0.594024 0.804447i \(-0.297538\pi\)
0.594024 + 0.804447i \(0.297538\pi\)
\(968\) −8.98803 4.09521i −0.288886 0.131625i
\(969\) 0 0
\(970\) −51.6119 + 37.4983i −1.65716 + 1.20400i
\(971\) 9.67373 + 29.7727i 0.310445 + 0.955451i 0.977589 + 0.210522i \(0.0675165\pi\)
−0.667144 + 0.744929i \(0.732484\pi\)
\(972\) 0 0
\(973\) 17.2933 + 12.5643i 0.554398 + 0.402793i
\(974\) −45.4892 33.0499i −1.45757 1.05899i
\(975\) 0 0
\(976\) 0.272818 + 0.839649i 0.00873271 + 0.0268765i
\(977\) −36.1962 + 26.2981i −1.15802 + 0.841350i −0.989526 0.144353i \(-0.953890\pi\)
−0.168492 + 0.985703i \(0.553890\pi\)
\(978\) 0 0
\(979\) 11.9106 + 27.0659i 0.380664 + 0.865029i
\(980\) 9.10149 0.290737
\(981\) 0 0
\(982\) 3.96119 + 12.1913i 0.126407 + 0.389040i
\(983\) −17.6829 + 54.4225i −0.563998 + 1.73581i 0.106913 + 0.994268i \(0.465903\pi\)
−0.670910 + 0.741538i \(0.734097\pi\)
\(984\) 0 0
\(985\) 18.7985 + 13.6579i 0.598969 + 0.435176i
\(986\) 10.6490 32.7743i 0.339134 1.04375i
\(987\) 0 0
\(988\) 35.1107 25.5094i 1.11702 0.811564i
\(989\) −0.671156 −0.0213415
\(990\) 0 0
\(991\) −26.9663 −0.856614 −0.428307 0.903633i \(-0.640890\pi\)
−0.428307 + 0.903633i \(0.640890\pi\)
\(992\) 52.8167 38.3736i 1.67693 1.21836i
\(993\) 0 0
\(994\) −3.72543 + 11.4657i −0.118163 + 0.363670i
\(995\) 57.2352 + 41.5838i 1.81448 + 1.31829i
\(996\) 0 0
\(997\) 7.82755 24.0907i 0.247901 0.762961i −0.747245 0.664549i \(-0.768624\pi\)
0.995146 0.0984118i \(-0.0313762\pi\)
\(998\) 0.972341 + 2.99256i 0.0307789 + 0.0947278i
\(999\) 0 0
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 693.2.m.k.190.2 32
3.2 odd 2 inner 693.2.m.k.190.7 yes 32
11.2 odd 10 7623.2.a.db.1.3 16
11.4 even 5 inner 693.2.m.k.631.2 yes 32
11.9 even 5 7623.2.a.dc.1.14 16
33.2 even 10 7623.2.a.db.1.14 16
33.20 odd 10 7623.2.a.dc.1.3 16
33.26 odd 10 inner 693.2.m.k.631.7 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
693.2.m.k.190.2 32 1.1 even 1 trivial
693.2.m.k.190.7 yes 32 3.2 odd 2 inner
693.2.m.k.631.2 yes 32 11.4 even 5 inner
693.2.m.k.631.7 yes 32 33.26 odd 10 inner
7623.2.a.db.1.3 16 11.2 odd 10
7623.2.a.db.1.14 16 33.2 even 10
7623.2.a.dc.1.3 16 33.20 odd 10
7623.2.a.dc.1.14 16 11.9 even 5