Properties

Label 950.2.bb.d.193.5
Level $950$
Weight $2$
Character 950.193
Analytic conductor $7.586$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(143,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([27, 34]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bb (of order \(36\), degree \(12\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(8\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 193.5
Character \(\chi\) \(=\) 950.193
Dual form 950.2.bb.d.507.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0871557 + 0.996195i) q^{2} +(-1.36591 + 2.92920i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.03710 - 1.10542i) q^{6} +(-2.44739 - 0.655775i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(-4.78616 - 5.70392i) q^{9} +O(q^{10})\) \(q+(0.0871557 + 0.996195i) q^{2} +(-1.36591 + 2.92920i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.03710 - 1.10542i) q^{6} +(-2.44739 - 0.655775i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(-4.78616 - 5.70392i) q^{9} +(1.97115 - 3.41412i) q^{11} +(0.836508 - 3.12189i) q^{12} +(-3.34937 + 1.56183i) q^{13} +(0.439976 - 2.49523i) q^{14} +(0.939693 - 0.342020i) q^{16} +(3.64591 - 0.318976i) q^{17} +(5.26508 - 5.26508i) q^{18} +(4.35498 - 0.184704i) q^{19} +(5.26381 - 6.27316i) q^{21} +(3.57293 + 1.66608i) q^{22} +(0.904036 - 1.29110i) q^{23} +(3.18292 + 0.561234i) q^{24} +(-1.84781 - 3.20050i) q^{26} +(13.8797 - 3.71907i) q^{27} +(2.52408 + 0.220828i) q^{28} +(-4.66306 + 3.91277i) q^{29} +(-3.71476 + 2.14472i) q^{31} +(0.422618 + 0.906308i) q^{32} +(7.30826 + 10.4373i) q^{33} +(0.635524 + 3.60423i) q^{34} +(5.70392 + 4.78616i) q^{36} +(-4.92208 - 4.92208i) q^{37} +(0.563563 + 4.32231i) q^{38} -11.9443i q^{39} +(-2.93537 - 8.06485i) q^{41} +(6.70806 + 4.69704i) q^{42} +(-5.02897 + 3.52132i) q^{43} +(-1.34834 + 3.70454i) q^{44} +(1.36498 + 0.788070i) q^{46} +(1.11739 - 12.7719i) q^{47} +(-0.281689 + 3.21972i) q^{48} +(-0.502521 - 0.290131i) q^{49} +(-4.04564 + 11.1153i) q^{51} +(3.02727 - 2.11972i) q^{52} +(-0.774207 - 0.542106i) q^{53} +(4.91461 + 13.5028i) q^{54} +2.53372i q^{56} +(-5.40748 + 13.0089i) q^{57} +(-4.30429 - 4.30429i) q^{58} +(7.62033 + 6.39421i) q^{59} +(-0.438632 - 2.48761i) q^{61} +(-2.46032 - 3.51370i) q^{62} +(7.97309 + 17.0983i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-9.76060 + 8.19011i) q^{66} +(11.4932 + 1.00553i) q^{67} +(-3.53513 + 0.947235i) q^{68} +(2.54706 + 4.41163i) q^{69} +(-5.43677 - 0.958650i) q^{71} +(-4.27082 + 6.09936i) q^{72} +(-5.28326 - 2.46362i) q^{73} +(4.47437 - 5.33234i) q^{74} +(-4.25675 + 0.938133i) q^{76} +(-7.06305 + 7.06305i) q^{77} +(11.8988 - 1.04101i) q^{78} +(14.1589 - 5.15341i) q^{79} +(-4.18566 + 23.7380i) q^{81} +(7.77833 - 3.62709i) q^{82} +(4.68290 - 17.4768i) q^{83} +(-4.09452 + 7.09191i) q^{84} +(-3.94623 - 4.70293i) q^{86} +(-5.09198 - 19.0035i) q^{87} +(-3.80796 - 1.02034i) q^{88} +(-2.15275 - 0.783537i) q^{89} +(9.22140 - 1.62598i) q^{91} +(-0.666105 + 1.42847i) q^{92} +(-1.20829 - 13.8108i) q^{93} +12.8207 q^{94} -3.23202 q^{96} +(0.681237 + 7.78657i) q^{97} +(0.245229 - 0.525895i) q^{98} +(-28.9081 + 5.09728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0871557 + 0.996195i 0.0616284 + 0.704416i
\(3\) −1.36591 + 2.92920i −0.788609 + 1.69118i −0.0681534 + 0.997675i \(0.521711\pi\)
−0.720455 + 0.693502i \(0.756067\pi\)
\(4\) −0.984808 + 0.173648i −0.492404 + 0.0868241i
\(5\) 0 0
\(6\) −3.03710 1.10542i −1.23989 0.451284i
\(7\) −2.44739 0.655775i −0.925025 0.247860i −0.235293 0.971924i \(-0.575605\pi\)
−0.689732 + 0.724065i \(0.742272\pi\)
\(8\) −0.258819 0.965926i −0.0915064 0.341506i
\(9\) −4.78616 5.70392i −1.59539 1.90131i
\(10\) 0 0
\(11\) 1.97115 3.41412i 0.594323 1.02940i −0.399319 0.916812i \(-0.630754\pi\)
0.993642 0.112585i \(-0.0359131\pi\)
\(12\) 0.836508 3.12189i 0.241479 0.901212i
\(13\) −3.34937 + 1.56183i −0.928947 + 0.433175i −0.827373 0.561653i \(-0.810166\pi\)
−0.101574 + 0.994828i \(0.532388\pi\)
\(14\) 0.439976 2.49523i 0.117589 0.666878i
\(15\) 0 0
\(16\) 0.939693 0.342020i 0.234923 0.0855050i
\(17\) 3.64591 0.318976i 0.884263 0.0773630i 0.364030 0.931387i \(-0.381401\pi\)
0.520233 + 0.854024i \(0.325845\pi\)
\(18\) 5.26508 5.26508i 1.24099 1.24099i
\(19\) 4.35498 0.184704i 0.999102 0.0423740i
\(20\) 0 0
\(21\) 5.26381 6.27316i 1.14866 1.36892i
\(22\) 3.57293 + 1.66608i 0.761751 + 0.355210i
\(23\) 0.904036 1.29110i 0.188505 0.269212i −0.713765 0.700386i \(-0.753011\pi\)
0.902269 + 0.431173i \(0.141900\pi\)
\(24\) 3.18292 + 0.561234i 0.649710 + 0.114561i
\(25\) 0 0
\(26\) −1.84781 3.20050i −0.362385 0.627669i
\(27\) 13.8797 3.71907i 2.67116 0.715735i
\(28\) 2.52408 + 0.220828i 0.477006 + 0.0417326i
\(29\) −4.66306 + 3.91277i −0.865908 + 0.726583i −0.963232 0.268670i \(-0.913416\pi\)
0.0973245 + 0.995253i \(0.468972\pi\)
\(30\) 0 0
\(31\) −3.71476 + 2.14472i −0.667190 + 0.385202i −0.795011 0.606595i \(-0.792535\pi\)
0.127821 + 0.991797i \(0.459202\pi\)
\(32\) 0.422618 + 0.906308i 0.0747091 + 0.160214i
\(33\) 7.30826 + 10.4373i 1.27220 + 1.81690i
\(34\) 0.635524 + 3.60423i 0.108991 + 0.618121i
\(35\) 0 0
\(36\) 5.70392 + 4.78616i 0.950654 + 0.797693i
\(37\) −4.92208 4.92208i −0.809186 0.809186i 0.175325 0.984511i \(-0.443902\pi\)
−0.984511 + 0.175325i \(0.943902\pi\)
\(38\) 0.563563 + 4.32231i 0.0914220 + 0.701172i
\(39\) 11.9443i 1.91262i
\(40\) 0 0
\(41\) −2.93537 8.06485i −0.458427 1.25952i −0.926656 0.375911i \(-0.877330\pi\)
0.468229 0.883607i \(-0.344892\pi\)
\(42\) 6.70806 + 4.69704i 1.03508 + 0.724768i
\(43\) −5.02897 + 3.52132i −0.766911 + 0.536997i −0.890307 0.455361i \(-0.849510\pi\)
0.123396 + 0.992357i \(0.460621\pi\)
\(44\) −1.34834 + 3.70454i −0.203270 + 0.558481i
\(45\) 0 0
\(46\) 1.36498 + 0.788070i 0.201255 + 0.116195i
\(47\) 1.11739 12.7719i 0.162989 1.86297i −0.271692 0.962384i \(-0.587583\pi\)
0.434681 0.900584i \(-0.356861\pi\)
\(48\) −0.281689 + 3.21972i −0.0406583 + 0.464727i
\(49\) −0.502521 0.290131i −0.0717887 0.0414472i
\(50\) 0 0
\(51\) −4.04564 + 11.1153i −0.566503 + 1.55645i
\(52\) 3.02727 2.11972i 0.419807 0.293952i
\(53\) −0.774207 0.542106i −0.106346 0.0744639i 0.519194 0.854656i \(-0.326232\pi\)
−0.625540 + 0.780192i \(0.715121\pi\)
\(54\) 4.91461 + 13.5028i 0.668794 + 1.83750i
\(55\) 0 0
\(56\) 2.53372i 0.338583i
\(57\) −5.40748 + 13.0089i −0.716238 + 1.72307i
\(58\) −4.30429 4.30429i −0.565181 0.565181i
\(59\) 7.62033 + 6.39421i 0.992082 + 0.832456i 0.985868 0.167525i \(-0.0535774\pi\)
0.00621438 + 0.999981i \(0.498022\pi\)
\(60\) 0 0
\(61\) −0.438632 2.48761i −0.0561611 0.318506i 0.943766 0.330615i \(-0.107256\pi\)
−0.999927 + 0.0121099i \(0.996145\pi\)
\(62\) −2.46032 3.51370i −0.312461 0.446240i
\(63\) 7.97309 + 17.0983i 1.00451 + 2.15419i
\(64\) −0.866025 + 0.500000i −0.108253 + 0.0625000i
\(65\) 0 0
\(66\) −9.76060 + 8.19011i −1.20145 + 1.00813i
\(67\) 11.4932 + 1.00553i 1.40412 + 0.122845i 0.763896 0.645340i \(-0.223284\pi\)
0.640228 + 0.768185i \(0.278840\pi\)
\(68\) −3.53513 + 0.947235i −0.428697 + 0.114869i
\(69\) 2.54706 + 4.41163i 0.306629 + 0.531098i
\(70\) 0 0
\(71\) −5.43677 0.958650i −0.645226 0.113771i −0.158547 0.987351i \(-0.550681\pi\)
−0.486679 + 0.873581i \(0.661792\pi\)
\(72\) −4.27082 + 6.09936i −0.503321 + 0.718816i
\(73\) −5.28326 2.46362i −0.618359 0.288345i 0.0880868 0.996113i \(-0.471925\pi\)
−0.706446 + 0.707767i \(0.749702\pi\)
\(74\) 4.47437 5.33234i 0.520135 0.619872i
\(75\) 0 0
\(76\) −4.25675 + 0.938133i −0.488283 + 0.107611i
\(77\) −7.06305 + 7.06305i −0.804909 + 0.804909i
\(78\) 11.8988 1.04101i 1.34728 0.117872i
\(79\) 14.1589 5.15341i 1.59300 0.579804i 0.615020 0.788512i \(-0.289148\pi\)
0.977978 + 0.208708i \(0.0669258\pi\)
\(80\) 0 0
\(81\) −4.18566 + 23.7380i −0.465073 + 2.63756i
\(82\) 7.77833 3.62709i 0.858973 0.400545i
\(83\) 4.68290 17.4768i 0.514015 1.91833i 0.142925 0.989734i \(-0.454349\pi\)
0.371090 0.928597i \(-0.378984\pi\)
\(84\) −4.09452 + 7.09191i −0.446748 + 0.773791i
\(85\) 0 0
\(86\) −3.94623 4.70293i −0.425533 0.507130i
\(87\) −5.09198 19.0035i −0.545918 2.03739i
\(88\) −3.80796 1.02034i −0.405930 0.108769i
\(89\) −2.15275 0.783537i −0.228191 0.0830548i 0.225394 0.974268i \(-0.427633\pi\)
−0.453585 + 0.891213i \(0.649855\pi\)
\(90\) 0 0
\(91\) 9.22140 1.62598i 0.966666 0.170449i
\(92\) −0.666105 + 1.42847i −0.0694463 + 0.148928i
\(93\) −1.20829 13.8108i −0.125293 1.43211i
\(94\) 12.8207 1.32235
\(95\) 0 0
\(96\) −3.23202 −0.329867
\(97\) 0.681237 + 7.78657i 0.0691691 + 0.790606i 0.948991 + 0.315303i \(0.102106\pi\)
−0.879822 + 0.475303i \(0.842338\pi\)
\(98\) 0.245229 0.525895i 0.0247719 0.0531234i
\(99\) −28.9081 + 5.09728i −2.90538 + 0.512296i
\(100\) 0 0
\(101\) 14.4675 + 5.26572i 1.43957 + 0.523959i 0.939657 0.342119i \(-0.111145\pi\)
0.499909 + 0.866078i \(0.333367\pi\)
\(102\) −11.4256 3.06148i −1.13130 0.303132i
\(103\) −2.69162 10.0453i −0.265213 0.989790i −0.962120 0.272627i \(-0.912107\pi\)
0.696906 0.717162i \(-0.254559\pi\)
\(104\) 2.37550 + 2.83101i 0.232937 + 0.277603i
\(105\) 0 0
\(106\) 0.472566 0.818509i 0.0458997 0.0795006i
\(107\) −2.20164 + 8.21663i −0.212841 + 0.794332i 0.774075 + 0.633094i \(0.218215\pi\)
−0.986916 + 0.161238i \(0.948451\pi\)
\(108\) −13.0231 + 6.07276i −1.25315 + 0.584351i
\(109\) −1.23485 + 7.00316i −0.118277 + 0.670781i 0.866799 + 0.498658i \(0.166174\pi\)
−0.985075 + 0.172123i \(0.944937\pi\)
\(110\) 0 0
\(111\) 21.1409 7.69466i 2.00661 0.730345i
\(112\) −2.52408 + 0.220828i −0.238503 + 0.0208663i
\(113\) −4.04575 + 4.04575i −0.380592 + 0.380592i −0.871315 0.490723i \(-0.836733\pi\)
0.490723 + 0.871315i \(0.336733\pi\)
\(114\) −13.4307 4.25310i −1.25790 0.398339i
\(115\) 0 0
\(116\) 3.91277 4.66306i 0.363291 0.432954i
\(117\) 24.9392 + 11.6293i 2.30563 + 1.07513i
\(118\) −5.70573 + 8.14862i −0.525255 + 0.750142i
\(119\) −9.13212 1.61024i −0.837140 0.147610i
\(120\) 0 0
\(121\) −2.27083 3.93319i −0.206439 0.357563i
\(122\) 2.43991 0.653772i 0.220899 0.0591898i
\(123\) 27.6330 + 2.41758i 2.49159 + 0.217986i
\(124\) 3.28590 2.75719i 0.295082 0.247603i
\(125\) 0 0
\(126\) −16.3384 + 9.43297i −1.45554 + 0.840356i
\(127\) −1.27125 2.72621i −0.112805 0.241912i 0.841798 0.539793i \(-0.181498\pi\)
−0.954603 + 0.297882i \(0.903720\pi\)
\(128\) −0.573576 0.819152i −0.0506975 0.0724035i
\(129\) −3.44555 19.5407i −0.303364 1.72046i
\(130\) 0 0
\(131\) −13.8905 11.6555i −1.21362 1.01835i −0.999134 0.0416173i \(-0.986749\pi\)
−0.214483 0.976728i \(-0.568807\pi\)
\(132\) −9.00964 9.00964i −0.784189 0.784189i
\(133\) −10.7795 2.40385i −0.934697 0.208440i
\(134\) 11.5372i 0.996658i
\(135\) 0 0
\(136\) −1.25174 3.43912i −0.107336 0.294902i
\(137\) 2.54287 + 1.78054i 0.217252 + 0.152121i 0.677137 0.735857i \(-0.263220\pi\)
−0.459885 + 0.887979i \(0.652109\pi\)
\(138\) −4.17285 + 2.92186i −0.355217 + 0.248725i
\(139\) 5.24754 14.4175i 0.445091 1.22288i −0.491013 0.871152i \(-0.663373\pi\)
0.936104 0.351725i \(-0.114405\pi\)
\(140\) 0 0
\(141\) 35.8851 + 20.7183i 3.02207 + 1.74480i
\(142\) 0.481156 5.49964i 0.0403777 0.461519i
\(143\) −1.26979 + 14.5138i −0.106185 + 1.21370i
\(144\) −6.44838 3.72297i −0.537365 0.310248i
\(145\) 0 0
\(146\) 1.99378 5.47787i 0.165007 0.453352i
\(147\) 1.53625 1.07569i 0.126708 0.0887217i
\(148\) 5.70202 + 3.99260i 0.468703 + 0.328189i
\(149\) 1.25031 + 3.43520i 0.102429 + 0.281422i 0.980312 0.197453i \(-0.0632669\pi\)
−0.877883 + 0.478875i \(0.841045\pi\)
\(150\) 0 0
\(151\) 16.9102i 1.37613i −0.725649 0.688065i \(-0.758460\pi\)
0.725649 0.688065i \(-0.241540\pi\)
\(152\) −1.30556 4.15879i −0.105895 0.337322i
\(153\) −19.2693 19.2693i −1.55783 1.55783i
\(154\) −7.65176 6.42059i −0.616596 0.517386i
\(155\) 0 0
\(156\) 2.07411 + 11.7628i 0.166061 + 0.941781i
\(157\) −5.15180 7.35754i −0.411159 0.587195i 0.559150 0.829067i \(-0.311128\pi\)
−0.970308 + 0.241871i \(0.922239\pi\)
\(158\) 6.36783 + 13.6558i 0.506597 + 1.08640i
\(159\) 2.64543 1.52734i 0.209797 0.121126i
\(160\) 0 0
\(161\) −3.05920 + 2.56697i −0.241098 + 0.202306i
\(162\) −24.0125 2.10082i −1.88660 0.165056i
\(163\) −6.29963 + 1.68798i −0.493425 + 0.132213i −0.496947 0.867781i \(-0.665546\pi\)
0.00352169 + 0.999994i \(0.498879\pi\)
\(164\) 4.29122 + 7.43261i 0.335088 + 0.580389i
\(165\) 0 0
\(166\) 17.8185 + 3.14188i 1.38298 + 0.243857i
\(167\) −6.38626 + 9.12052i −0.494184 + 0.705767i −0.986337 0.164741i \(-0.947321\pi\)
0.492153 + 0.870509i \(0.336210\pi\)
\(168\) −7.42178 3.46083i −0.572603 0.267009i
\(169\) 0.422682 0.503732i 0.0325140 0.0387487i
\(170\) 0 0
\(171\) −21.8972 23.9565i −1.67452 1.83200i
\(172\) 4.34110 4.34110i 0.331006 0.331006i
\(173\) 7.99455 0.699433i 0.607815 0.0531769i 0.220906 0.975295i \(-0.429099\pi\)
0.386908 + 0.922118i \(0.373543\pi\)
\(174\) 18.4874 6.72887i 1.40153 0.510114i
\(175\) 0 0
\(176\) 0.684572 3.88240i 0.0516015 0.292647i
\(177\) −29.1386 + 13.5876i −2.19019 + 1.02130i
\(178\) 0.592931 2.21285i 0.0444421 0.165860i
\(179\) −2.05678 + 3.56245i −0.153731 + 0.266270i −0.932596 0.360921i \(-0.882462\pi\)
0.778865 + 0.627191i \(0.215796\pi\)
\(180\) 0 0
\(181\) −13.3606 15.9226i −0.993087 1.18352i −0.983007 0.183566i \(-0.941236\pi\)
−0.0100800 0.999949i \(-0.503209\pi\)
\(182\) 2.42349 + 9.04460i 0.179641 + 0.670430i
\(183\) 7.88584 + 2.11300i 0.582938 + 0.156198i
\(184\) −1.48109 0.539071i −0.109187 0.0397409i
\(185\) 0 0
\(186\) 13.6529 2.40738i 1.00108 0.176517i
\(187\) 6.09759 13.0763i 0.445900 0.956236i
\(188\) 1.11739 + 12.7719i 0.0814943 + 0.931484i
\(189\) −36.4080 −2.64829
\(190\) 0 0
\(191\) 2.70813 0.195953 0.0979766 0.995189i \(-0.468763\pi\)
0.0979766 + 0.995189i \(0.468763\pi\)
\(192\) −0.281689 3.21972i −0.0203292 0.232363i
\(193\) 5.11958 10.9790i 0.368516 0.790284i −0.631375 0.775478i \(-0.717509\pi\)
0.999890 0.0148063i \(-0.00471317\pi\)
\(194\) −7.69757 + 1.35729i −0.552653 + 0.0974476i
\(195\) 0 0
\(196\) 0.545267 + 0.198461i 0.0389477 + 0.0141758i
\(197\) −20.2186 5.41756i −1.44052 0.385985i −0.547803 0.836608i \(-0.684536\pi\)
−0.892715 + 0.450622i \(0.851202\pi\)
\(198\) −7.59739 28.3539i −0.539923 2.01502i
\(199\) −10.6962 12.7472i −0.758231 0.903625i 0.239504 0.970895i \(-0.423015\pi\)
−0.997735 + 0.0672708i \(0.978571\pi\)
\(200\) 0 0
\(201\) −18.6441 + 32.2926i −1.31506 + 2.27774i
\(202\) −3.98476 + 14.8713i −0.280367 + 1.04634i
\(203\) 13.9782 6.51814i 0.981077 0.457484i
\(204\) 2.05402 11.6490i 0.143811 0.815590i
\(205\) 0 0
\(206\) 9.77245 3.55688i 0.680879 0.247820i
\(207\) −11.6912 + 1.02285i −0.812594 + 0.0710927i
\(208\) −2.61319 + 2.61319i −0.181192 + 0.181192i
\(209\) 7.95370 15.2325i 0.550169 1.05366i
\(210\) 0 0
\(211\) 8.58756 10.2343i 0.591192 0.704555i −0.384643 0.923066i \(-0.625675\pi\)
0.975835 + 0.218510i \(0.0701197\pi\)
\(212\) 0.856581 + 0.399430i 0.0588302 + 0.0274330i
\(213\) 10.2342 14.6160i 0.701237 1.00147i
\(214\) −8.37725 1.47713i −0.572657 0.100975i
\(215\) 0 0
\(216\) −7.18469 12.4442i −0.488856 0.846723i
\(217\) 10.4979 2.81290i 0.712644 0.190952i
\(218\) −7.08414 0.619782i −0.479798 0.0419769i
\(219\) 14.4329 12.1107i 0.975286 0.818362i
\(220\) 0 0
\(221\) −11.7133 + 6.76267i −0.787921 + 0.454907i
\(222\) 9.50793 + 20.3898i 0.638131 + 1.36848i
\(223\) −6.72312 9.60162i −0.450214 0.642972i 0.528323 0.849043i \(-0.322821\pi\)
−0.978537 + 0.206071i \(0.933932\pi\)
\(224\) −0.439976 2.49523i −0.0293971 0.166719i
\(225\) 0 0
\(226\) −4.38296 3.67774i −0.291550 0.244640i
\(227\) 7.27903 + 7.27903i 0.483126 + 0.483126i 0.906129 0.423002i \(-0.139024\pi\)
−0.423002 + 0.906129i \(0.639024\pi\)
\(228\) 3.06635 13.7503i 0.203074 0.910635i
\(229\) 1.66662i 0.110134i −0.998483 0.0550668i \(-0.982463\pi\)
0.998483 0.0550668i \(-0.0175372\pi\)
\(230\) 0 0
\(231\) −11.0416 30.3366i −0.726485 1.99600i
\(232\) 4.98633 + 3.49147i 0.327369 + 0.229226i
\(233\) −2.19866 + 1.53952i −0.144039 + 0.100857i −0.643375 0.765551i \(-0.722466\pi\)
0.499336 + 0.866409i \(0.333577\pi\)
\(234\) −9.41149 + 25.8578i −0.615248 + 1.69038i
\(235\) 0 0
\(236\) −8.61490 4.97382i −0.560782 0.323768i
\(237\) −4.24437 + 48.5133i −0.275701 + 3.15128i
\(238\) 0.808195 9.23771i 0.0523875 0.598792i
\(239\) −2.95516 1.70617i −0.191154 0.110363i 0.401369 0.915917i \(-0.368535\pi\)
−0.592523 + 0.805554i \(0.701868\pi\)
\(240\) 0 0
\(241\) 1.67023 4.58892i 0.107589 0.295599i −0.874202 0.485562i \(-0.838615\pi\)
0.981791 + 0.189964i \(0.0608371\pi\)
\(242\) 3.72031 2.60499i 0.239150 0.167455i
\(243\) −28.5042 19.9589i −1.82855 1.28036i
\(244\) 0.863937 + 2.37365i 0.0553079 + 0.151957i
\(245\) 0 0
\(246\) 27.7386i 1.76855i
\(247\) −14.2980 + 7.42041i −0.909757 + 0.472149i
\(248\) 3.03309 + 3.03309i 0.192601 + 0.192601i
\(249\) 44.7967 + 37.5889i 2.83888 + 2.38210i
\(250\) 0 0
\(251\) 2.11295 + 11.9832i 0.133368 + 0.756370i 0.975982 + 0.217851i \(0.0699047\pi\)
−0.842614 + 0.538519i \(0.818984\pi\)
\(252\) −10.8211 15.4541i −0.681663 0.973515i
\(253\) −2.62598 5.63143i −0.165094 0.354045i
\(254\) 2.60504 1.50402i 0.163454 0.0943705i
\(255\) 0 0
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −22.5912 1.97647i −1.40920 0.123289i −0.642987 0.765877i \(-0.722305\pi\)
−0.766211 + 0.642588i \(0.777861\pi\)
\(258\) 19.1660 5.13552i 1.19323 0.319724i
\(259\) 8.81846 + 15.2740i 0.547952 + 0.949081i
\(260\) 0 0
\(261\) 44.6363 + 7.87058i 2.76292 + 0.487177i
\(262\) 10.4005 14.8535i 0.642545 0.917650i
\(263\) 9.76593 + 4.55393i 0.602193 + 0.280807i 0.699710 0.714427i \(-0.253312\pi\)
−0.0975174 + 0.995234i \(0.531090\pi\)
\(264\) 8.19011 9.76060i 0.504067 0.600723i
\(265\) 0 0
\(266\) 1.45521 10.9479i 0.0892246 0.671261i
\(267\) 5.23560 5.23560i 0.320414 0.320414i
\(268\) −11.4932 + 1.00553i −0.702062 + 0.0614225i
\(269\) 5.02541 1.82910i 0.306405 0.111522i −0.184242 0.982881i \(-0.558983\pi\)
0.490646 + 0.871359i \(0.336761\pi\)
\(270\) 0 0
\(271\) −5.36280 + 30.4140i −0.325767 + 1.84752i 0.178463 + 0.983947i \(0.442888\pi\)
−0.504230 + 0.863570i \(0.668224\pi\)
\(272\) 3.31694 1.54671i 0.201119 0.0937833i
\(273\) −7.83277 + 29.2323i −0.474061 + 1.76922i
\(274\) −1.55214 + 2.68838i −0.0937679 + 0.162411i
\(275\) 0 0
\(276\) −3.27443 3.90232i −0.197098 0.234892i
\(277\) −2.79061 10.4147i −0.167671 0.625758i −0.997684 0.0680138i \(-0.978334\pi\)
0.830013 0.557744i \(-0.188333\pi\)
\(278\) 14.8200 + 3.97101i 0.888844 + 0.238165i
\(279\) 30.0127 + 10.9237i 1.79682 + 0.653987i
\(280\) 0 0
\(281\) −11.8294 + 2.08583i −0.705680 + 0.124430i −0.514960 0.857214i \(-0.672193\pi\)
−0.190720 + 0.981645i \(0.561082\pi\)
\(282\) −17.5119 + 37.5543i −1.04282 + 2.23633i
\(283\) −1.33827 15.2965i −0.0795521 0.909285i −0.926176 0.377092i \(-0.876924\pi\)
0.846624 0.532192i \(-0.178632\pi\)
\(284\) 5.52064 0.327590
\(285\) 0 0
\(286\) −14.5692 −0.861494
\(287\) 1.89524 + 21.6627i 0.111873 + 1.27871i
\(288\) 3.14679 6.74832i 0.185426 0.397648i
\(289\) −3.55082 + 0.626106i −0.208872 + 0.0368298i
\(290\) 0 0
\(291\) −23.7390 8.64027i −1.39160 0.506502i
\(292\) 5.63080 + 1.50877i 0.329518 + 0.0882940i
\(293\) 0.751065 + 2.80301i 0.0438777 + 0.163754i 0.984388 0.176011i \(-0.0563193\pi\)
−0.940511 + 0.339764i \(0.889653\pi\)
\(294\) 1.20549 + 1.43665i 0.0703058 + 0.0837872i
\(295\) 0 0
\(296\) −3.48044 + 6.02830i −0.202296 + 0.350388i
\(297\) 14.6616 54.7180i 0.850755 3.17506i
\(298\) −3.31315 + 1.54495i −0.191926 + 0.0894965i
\(299\) −1.01147 + 5.73631i −0.0584946 + 0.331740i
\(300\) 0 0
\(301\) 14.6170 5.32016i 0.842512 0.306649i
\(302\) 16.8458 1.47382i 0.969368 0.0848087i
\(303\) −35.1856 + 35.1856i −2.02136 + 2.02136i
\(304\) 4.02917 1.66306i 0.231089 0.0953829i
\(305\) 0 0
\(306\) 17.5166 20.8754i 1.00136 1.19337i
\(307\) −21.4864 10.0192i −1.22629 0.571829i −0.301923 0.953332i \(-0.597629\pi\)
−0.924367 + 0.381503i \(0.875406\pi\)
\(308\) 5.72926 8.18223i 0.326455 0.466226i
\(309\) 33.1011 + 5.83662i 1.88306 + 0.332034i
\(310\) 0 0
\(311\) −11.1882 19.3786i −0.634427 1.09886i −0.986636 0.162939i \(-0.947903\pi\)
0.352209 0.935921i \(-0.385431\pi\)
\(312\) −11.5373 + 3.09141i −0.653171 + 0.175017i
\(313\) −8.58311 0.750925i −0.485146 0.0424448i −0.158040 0.987433i \(-0.550518\pi\)
−0.327105 + 0.944988i \(0.606073\pi\)
\(314\) 6.88053 5.77345i 0.388291 0.325815i
\(315\) 0 0
\(316\) −13.0489 + 7.53378i −0.734057 + 0.423808i
\(317\) −7.38229 15.8314i −0.414631 0.889178i −0.997084 0.0763141i \(-0.975685\pi\)
0.582453 0.812864i \(-0.302093\pi\)
\(318\) 1.75210 + 2.50225i 0.0982526 + 0.140319i
\(319\) 4.16712 + 23.6329i 0.233314 + 1.32319i
\(320\) 0 0
\(321\) −21.0609 17.6722i −1.17551 0.986367i
\(322\) −2.82383 2.82383i −0.157366 0.157366i
\(323\) 15.8190 2.06255i 0.880190 0.114763i
\(324\) 24.1042i 1.33912i
\(325\) 0 0
\(326\) −2.23061 6.12854i −0.123542 0.339429i
\(327\) −18.8270 13.1828i −1.04114 0.729011i
\(328\) −7.03032 + 4.92268i −0.388184 + 0.271810i
\(329\) −11.1102 + 30.5249i −0.612523 + 1.68289i
\(330\) 0 0
\(331\) 26.5373 + 15.3213i 1.45862 + 0.842137i 0.998944 0.0459480i \(-0.0146308\pi\)
0.459680 + 0.888085i \(0.347964\pi\)
\(332\) −1.57694 + 18.0245i −0.0865457 + 0.989222i
\(333\) −4.51731 + 51.6331i −0.247547 + 2.82948i
\(334\) −9.64242 5.56705i −0.527609 0.304615i
\(335\) 0 0
\(336\) 2.80081 7.69517i 0.152797 0.419806i
\(337\) −7.96380 + 5.57631i −0.433816 + 0.303761i −0.770010 0.638032i \(-0.779749\pi\)
0.336194 + 0.941793i \(0.390860\pi\)
\(338\) 0.538655 + 0.377170i 0.0292990 + 0.0205153i
\(339\) −6.32469 17.3770i −0.343510 0.943786i
\(340\) 0 0
\(341\) 16.9102i 0.915738i
\(342\) 21.9568 23.9018i 1.18729 1.29246i
\(343\) 13.5809 + 13.5809i 0.733298 + 0.733298i
\(344\) 4.70293 + 3.94623i 0.253565 + 0.212766i
\(345\) 0 0
\(346\) 1.39354 + 7.90317i 0.0749173 + 0.424877i
\(347\) 8.11237 + 11.5857i 0.435495 + 0.621951i 0.975576 0.219662i \(-0.0704953\pi\)
−0.540081 + 0.841613i \(0.681606\pi\)
\(348\) 8.31455 + 17.8306i 0.445707 + 0.955821i
\(349\) 2.06292 1.19103i 0.110426 0.0637542i −0.443770 0.896141i \(-0.646359\pi\)
0.554196 + 0.832386i \(0.313026\pi\)
\(350\) 0 0
\(351\) −40.6798 + 34.1344i −2.17133 + 1.82196i
\(352\) 3.92729 + 0.343593i 0.209325 + 0.0183136i
\(353\) 2.40113 0.643381i 0.127799 0.0342437i −0.194352 0.980932i \(-0.562261\pi\)
0.322152 + 0.946688i \(0.395594\pi\)
\(354\) −16.0755 27.8435i −0.854401 1.47987i
\(355\) 0 0
\(356\) 2.25611 + 0.397812i 0.119573 + 0.0210840i
\(357\) 17.1904 24.5504i 0.909811 1.29935i
\(358\) −3.72816 1.73847i −0.197039 0.0918809i
\(359\) −17.3352 + 20.6593i −0.914916 + 1.09035i 0.0806929 + 0.996739i \(0.474287\pi\)
−0.995608 + 0.0936149i \(0.970158\pi\)
\(360\) 0 0
\(361\) 18.9318 1.60876i 0.996409 0.0846718i
\(362\) 14.6975 14.6975i 0.772485 0.772485i
\(363\) 14.6229 1.27933i 0.767501 0.0671476i
\(364\) −8.79896 + 3.20256i −0.461191 + 0.167860i
\(365\) 0 0
\(366\) −1.41767 + 8.03999i −0.0741027 + 0.420257i
\(367\) −3.32673 + 1.55128i −0.173654 + 0.0809761i −0.507501 0.861651i \(-0.669431\pi\)
0.333847 + 0.942627i \(0.391653\pi\)
\(368\) 0.407935 1.52243i 0.0212651 0.0793623i
\(369\) −31.9522 + 55.3428i −1.66336 + 2.88103i
\(370\) 0 0
\(371\) 1.53928 + 1.83445i 0.0799156 + 0.0952398i
\(372\) 3.58815 + 13.3911i 0.186037 + 0.694298i
\(373\) −30.3773 8.13958i −1.57288 0.421452i −0.636167 0.771552i \(-0.719481\pi\)
−0.936712 + 0.350100i \(0.886148\pi\)
\(374\) 13.5580 + 4.93471i 0.701068 + 0.255168i
\(375\) 0 0
\(376\) −12.6259 + 2.22628i −0.651130 + 0.114812i
\(377\) 9.50718 20.3882i 0.489645 1.05005i
\(378\) −3.17316 36.2694i −0.163210 1.86550i
\(379\) 23.5065 1.20745 0.603723 0.797194i \(-0.293683\pi\)
0.603723 + 0.797194i \(0.293683\pi\)
\(380\) 0 0
\(381\) 9.72203 0.498075
\(382\) 0.236029 + 2.69782i 0.0120763 + 0.138033i
\(383\) −2.24823 + 4.82135i −0.114879 + 0.246359i −0.955337 0.295517i \(-0.904508\pi\)
0.840458 + 0.541876i \(0.182286\pi\)
\(384\) 3.18292 0.561234i 0.162428 0.0286404i
\(385\) 0 0
\(386\) 11.3834 + 4.14322i 0.579400 + 0.210884i
\(387\) 44.1548 + 11.8312i 2.24452 + 0.601416i
\(388\) −2.02301 7.54998i −0.102703 0.383292i
\(389\) −15.7557 18.7770i −0.798848 0.952030i 0.200771 0.979638i \(-0.435655\pi\)
−0.999619 + 0.0276084i \(0.991211\pi\)
\(390\) 0 0
\(391\) 2.88421 4.99559i 0.145861 0.252638i
\(392\) −0.150183 + 0.560489i −0.00758537 + 0.0283090i
\(393\) 53.1144 24.7677i 2.67927 1.24936i
\(394\) 3.63478 20.6139i 0.183118 1.03851i
\(395\) 0 0
\(396\) 27.5838 10.0397i 1.38614 0.504513i
\(397\) 32.4668 2.84048i 1.62946 0.142560i 0.764578 0.644531i \(-0.222947\pi\)
0.864884 + 0.501971i \(0.167392\pi\)
\(398\) 11.7665 11.7665i 0.589799 0.589799i
\(399\) 21.7651 28.2918i 1.08962 1.41636i
\(400\) 0 0
\(401\) −11.1685 + 13.3101i −0.557730 + 0.664676i −0.969064 0.246808i \(-0.920618\pi\)
0.411335 + 0.911484i \(0.365063\pi\)
\(402\) −33.7947 15.7587i −1.68552 0.785973i
\(403\) 9.09239 12.9853i 0.452924 0.646843i
\(404\) −15.1620 2.67348i −0.754340 0.133010i
\(405\) 0 0
\(406\) 7.71162 + 13.3569i 0.382721 + 0.662892i
\(407\) −26.5068 + 7.10246i −1.31389 + 0.352056i
\(408\) 11.7836 + 1.03094i 0.583377 + 0.0510389i
\(409\) −10.1412 + 8.50946i −0.501449 + 0.420766i −0.858108 0.513469i \(-0.828360\pi\)
0.356659 + 0.934235i \(0.383916\pi\)
\(410\) 0 0
\(411\) −8.68888 + 5.01653i −0.428591 + 0.247447i
\(412\) 4.39507 + 9.42526i 0.216530 + 0.464349i
\(413\) −14.4567 20.6463i −0.711369 1.01594i
\(414\) −2.03791 11.5576i −0.100158 0.568023i
\(415\) 0 0
\(416\) −2.83101 2.37550i −0.138801 0.116468i
\(417\) 35.0641 + 35.0641i 1.71710 + 1.71710i
\(418\) 15.8678 + 6.59584i 0.776118 + 0.322613i
\(419\) 5.51559i 0.269454i −0.990883 0.134727i \(-0.956984\pi\)
0.990883 0.134727i \(-0.0430157\pi\)
\(420\) 0 0
\(421\) −4.35404 11.9626i −0.212203 0.583023i 0.787231 0.616658i \(-0.211514\pi\)
−0.999434 + 0.0336350i \(0.989292\pi\)
\(422\) 10.9438 + 7.66291i 0.532734 + 0.373025i
\(423\) −78.1978 + 54.7547i −3.80211 + 2.66226i
\(424\) −0.323254 + 0.888134i −0.0156986 + 0.0431316i
\(425\) 0 0
\(426\) 15.4523 + 8.92141i 0.748668 + 0.432244i
\(427\) −0.557808 + 6.37578i −0.0269942 + 0.308546i
\(428\) 0.741389 8.47411i 0.0358364 0.409612i
\(429\) −40.7793 23.5439i −1.96884 1.13671i
\(430\) 0 0
\(431\) −8.13482 + 22.3502i −0.391840 + 1.07657i 0.574320 + 0.818631i \(0.305266\pi\)
−0.966160 + 0.257942i \(0.916956\pi\)
\(432\) 11.7707 8.24193i 0.566318 0.396540i
\(433\) −11.4226 7.99820i −0.548936 0.384369i 0.265953 0.963986i \(-0.414313\pi\)
−0.814889 + 0.579617i \(0.803202\pi\)
\(434\) 3.71715 + 10.2128i 0.178429 + 0.490230i
\(435\) 0 0
\(436\) 7.11120i 0.340565i
\(437\) 3.69859 5.78969i 0.176928 0.276958i
\(438\) 13.3225 + 13.3225i 0.636573 + 0.636573i
\(439\) −11.1903 9.38976i −0.534083 0.448149i 0.335426 0.942067i \(-0.391120\pi\)
−0.869508 + 0.493918i \(0.835564\pi\)
\(440\) 0 0
\(441\) 0.750263 + 4.25495i 0.0357268 + 0.202617i
\(442\) −7.75782 11.0793i −0.369002 0.526989i
\(443\) −4.32586 9.27683i −0.205528 0.440755i 0.776342 0.630312i \(-0.217073\pi\)
−0.981870 + 0.189556i \(0.939295\pi\)
\(444\) −19.4836 + 11.2488i −0.924649 + 0.533847i
\(445\) 0 0
\(446\) 8.97912 7.53438i 0.425174 0.356763i
\(447\) −11.7702 1.02976i −0.556712 0.0487060i
\(448\) 2.44739 0.655775i 0.115628 0.0309825i
\(449\) −6.29574 10.9045i −0.297114 0.514617i 0.678360 0.734730i \(-0.262691\pi\)
−0.975475 + 0.220112i \(0.929358\pi\)
\(450\) 0 0
\(451\) −33.3204 5.87529i −1.56900 0.276657i
\(452\) 3.28175 4.68682i 0.154360 0.220450i
\(453\) 49.5333 + 23.0978i 2.32728 + 1.08523i
\(454\) −6.61692 + 7.88574i −0.310548 + 0.370096i
\(455\) 0 0
\(456\) 13.9652 + 1.85627i 0.653981 + 0.0869277i
\(457\) 17.8182 17.8182i 0.833499 0.833499i −0.154494 0.987994i \(-0.549375\pi\)
0.987994 + 0.154494i \(0.0493749\pi\)
\(458\) 1.66028 0.145256i 0.0775799 0.00678736i
\(459\) 49.4180 17.9867i 2.30663 0.839546i
\(460\) 0 0
\(461\) 2.41039 13.6700i 0.112263 0.636676i −0.875806 0.482664i \(-0.839669\pi\)
0.988069 0.154012i \(-0.0492195\pi\)
\(462\) 29.2588 13.6436i 1.36124 0.634758i
\(463\) 0.652191 2.43401i 0.0303099 0.113118i −0.949114 0.314934i \(-0.898018\pi\)
0.979423 + 0.201816i \(0.0646843\pi\)
\(464\) −3.04359 + 5.27166i −0.141295 + 0.244731i
\(465\) 0 0
\(466\) −1.72528 2.05611i −0.0799223 0.0952476i
\(467\) 10.3044 + 38.4564i 0.476829 + 1.77955i 0.614330 + 0.789049i \(0.289427\pi\)
−0.137500 + 0.990502i \(0.543907\pi\)
\(468\) −26.5797 7.12201i −1.22865 0.329215i
\(469\) −27.4690 9.99790i −1.26840 0.461660i
\(470\) 0 0
\(471\) 28.5886 5.04095i 1.31729 0.232275i
\(472\) 4.20405 9.01562i 0.193507 0.414977i
\(473\) 2.10940 + 24.1106i 0.0969904 + 1.10861i
\(474\) −48.6986 −2.23680
\(475\) 0 0
\(476\) 9.27300 0.425027
\(477\) 0.613350 + 7.01062i 0.0280834 + 0.320994i
\(478\) 1.44211 3.09262i 0.0659607 0.141453i
\(479\) 3.02245 0.532939i 0.138099 0.0243506i −0.104171 0.994559i \(-0.533219\pi\)
0.242270 + 0.970209i \(0.422108\pi\)
\(480\) 0 0
\(481\) 24.1733 + 8.79838i 1.10221 + 0.401171i
\(482\) 4.71703 + 1.26392i 0.214855 + 0.0575702i
\(483\) −3.34059 12.4673i −0.152002 0.567280i
\(484\) 2.91932 + 3.47911i 0.132696 + 0.158141i
\(485\) 0 0
\(486\) 17.3986 30.1353i 0.789218 1.36696i
\(487\) 3.75668 14.0201i 0.170231 0.635312i −0.827084 0.562079i \(-0.810002\pi\)
0.997315 0.0732327i \(-0.0233316\pi\)
\(488\) −2.28932 + 1.06753i −0.103633 + 0.0483247i
\(489\) 3.66029 20.7585i 0.165524 0.938734i
\(490\) 0 0
\(491\) 11.6629 4.24495i 0.526340 0.191572i −0.0651635 0.997875i \(-0.520757\pi\)
0.591503 + 0.806303i \(0.298535\pi\)
\(492\) −27.6330 + 2.41758i −1.24579 + 0.108993i
\(493\) −15.7530 + 15.7530i −0.709480 + 0.709480i
\(494\) −8.63832 13.5968i −0.388656 0.611750i
\(495\) 0 0
\(496\) −2.75719 + 3.28590i −0.123802 + 0.147541i
\(497\) 12.6772 + 5.91149i 0.568651 + 0.265166i
\(498\) −33.5416 + 47.9024i −1.50304 + 2.14656i
\(499\) −24.0876 4.24730i −1.07831 0.190135i −0.393842 0.919178i \(-0.628854\pi\)
−0.684468 + 0.729043i \(0.739965\pi\)
\(500\) 0 0
\(501\) −17.9928 31.1645i −0.803860 1.39233i
\(502\) −11.7534 + 3.14931i −0.524580 + 0.140561i
\(503\) 10.0264 + 0.877199i 0.447056 + 0.0391124i 0.308462 0.951237i \(-0.400186\pi\)
0.138595 + 0.990349i \(0.455741\pi\)
\(504\) 14.4521 12.1268i 0.643750 0.540170i
\(505\) 0 0
\(506\) 5.38113 3.10680i 0.239221 0.138114i
\(507\) 0.898190 + 1.92617i 0.0398900 + 0.0855444i
\(508\) 1.72534 + 2.46404i 0.0765495 + 0.109324i
\(509\) −1.85157 10.5008i −0.0820694 0.465439i −0.997951 0.0639893i \(-0.979618\pi\)
0.915881 0.401449i \(-0.131493\pi\)
\(510\) 0 0
\(511\) 11.3146 + 9.49407i 0.500528 + 0.419993i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 59.7591 18.7601i 2.63843 0.828279i
\(514\) 22.6775i 1.00026i
\(515\) 0 0
\(516\) 6.78641 + 18.6455i 0.298755 + 0.820823i
\(517\) −41.4022 28.9901i −1.82087 1.27498i
\(518\) −14.4473 + 10.1161i −0.634779 + 0.444477i
\(519\) −8.87106 + 24.3730i −0.389396 + 1.06986i
\(520\) 0 0
\(521\) 19.5360 + 11.2791i 0.855886 + 0.494146i 0.862632 0.505831i \(-0.168814\pi\)
−0.00674670 + 0.999977i \(0.502148\pi\)
\(522\) −3.95032 + 45.1524i −0.172901 + 1.97627i
\(523\) 0.525149 6.00248i 0.0229632 0.262470i −0.976031 0.217631i \(-0.930167\pi\)
0.998994 0.0448390i \(-0.0142775\pi\)
\(524\) 15.7034 + 9.06636i 0.686006 + 0.396066i
\(525\) 0 0
\(526\) −3.68544 + 10.1257i −0.160693 + 0.441500i
\(527\) −12.8596 + 9.00436i −0.560171 + 0.392236i
\(528\) 10.4373 + 7.30826i 0.454224 + 0.318051i
\(529\) 7.01681 + 19.2785i 0.305079 + 0.838197i
\(530\) 0 0
\(531\) 74.0695i 3.21434i
\(532\) 11.0331 + 0.495496i 0.478346 + 0.0214825i
\(533\) 22.4276 + 22.4276i 0.971446 + 0.971446i
\(534\) 5.67199 + 4.75937i 0.245451 + 0.205958i
\(535\) 0 0
\(536\) −2.00341 11.3619i −0.0865339 0.490758i
\(537\) −7.62577 10.8907i −0.329076 0.469969i
\(538\) 2.26013 + 4.84687i 0.0974413 + 0.208963i
\(539\) −1.98108 + 1.14378i −0.0853313 + 0.0492661i
\(540\) 0 0
\(541\) −25.3958 + 21.3096i −1.09185 + 0.916173i −0.996851 0.0793037i \(-0.974730\pi\)
−0.0950024 + 0.995477i \(0.530286\pi\)
\(542\) −30.7656 2.69164i −1.32150 0.115616i
\(543\) 64.8899 17.3872i 2.78469 0.746156i
\(544\) 1.82992 + 3.16951i 0.0784571 + 0.135892i
\(545\) 0 0
\(546\) −29.8037 5.25520i −1.27548 0.224902i
\(547\) 2.03107 2.90067i 0.0868423 0.124024i −0.773380 0.633942i \(-0.781436\pi\)
0.860223 + 0.509919i \(0.170325\pi\)
\(548\) −2.81342 1.31192i −0.120184 0.0560425i
\(549\) −12.0898 + 14.4080i −0.515978 + 0.614919i
\(550\) 0 0
\(551\) −19.5848 + 17.9013i −0.834342 + 0.762622i
\(552\) 3.60208 3.60208i 0.153315 0.153315i
\(553\) −38.0317 + 3.32734i −1.61727 + 0.141493i
\(554\) 10.1318 3.68769i 0.430460 0.156675i
\(555\) 0 0
\(556\) −2.66425 + 15.1097i −0.112989 + 0.640794i
\(557\) −3.50860 + 1.63609i −0.148664 + 0.0693232i −0.495526 0.868593i \(-0.665025\pi\)
0.346862 + 0.937916i \(0.387247\pi\)
\(558\) −8.26639 + 30.8506i −0.349944 + 1.30601i
\(559\) 11.3441 19.6486i 0.479806 0.831048i
\(560\) 0 0
\(561\) 29.9745 + 35.7222i 1.26552 + 1.50819i
\(562\) −3.10889 11.6025i −0.131141 0.489424i
\(563\) 4.19083 + 1.12293i 0.176622 + 0.0473258i 0.346046 0.938217i \(-0.387524\pi\)
−0.169424 + 0.985543i \(0.554191\pi\)
\(564\) −38.9377 14.1722i −1.63957 0.596755i
\(565\) 0 0
\(566\) 15.1217 2.66636i 0.635612 0.112076i
\(567\) 25.8107 55.3513i 1.08395 2.32454i
\(568\) 0.481156 + 5.49964i 0.0201888 + 0.230760i
\(569\) 10.7883 0.452270 0.226135 0.974096i \(-0.427391\pi\)
0.226135 + 0.974096i \(0.427391\pi\)
\(570\) 0 0
\(571\) −20.2403 −0.847029 −0.423514 0.905889i \(-0.639204\pi\)
−0.423514 + 0.905889i \(0.639204\pi\)
\(572\) −1.26979 14.5138i −0.0530925 0.606850i
\(573\) −3.69906 + 7.93265i −0.154530 + 0.331391i
\(574\) −21.4151 + 3.77606i −0.893850 + 0.157610i
\(575\) 0 0
\(576\) 6.99690 + 2.54666i 0.291537 + 0.106111i
\(577\) 15.6233 + 4.18625i 0.650406 + 0.174276i 0.568912 0.822398i \(-0.307364\pi\)
0.0814936 + 0.996674i \(0.474031\pi\)
\(578\) −0.933198 3.48274i −0.0388159 0.144863i
\(579\) 25.1668 + 29.9926i 1.04590 + 1.24645i
\(580\) 0 0
\(581\) −22.9217 + 39.7016i −0.950954 + 1.64710i
\(582\) 6.53841 24.4017i 0.271026 1.01148i
\(583\) −3.37689 + 1.57467i −0.139857 + 0.0652162i
\(584\) −1.01227 + 5.74087i −0.0418880 + 0.237559i
\(585\) 0 0
\(586\) −2.72689 + 0.992506i −0.112647 + 0.0410000i
\(587\) 39.8641 3.48766i 1.64537 0.143951i 0.773534 0.633755i \(-0.218487\pi\)
0.871833 + 0.489804i \(0.162932\pi\)
\(588\) −1.32612 + 1.32612i −0.0546882 + 0.0546882i
\(589\) −15.7816 + 10.0263i −0.650268 + 0.413128i
\(590\) 0 0
\(591\) 43.4860 51.8246i 1.78877 2.13178i
\(592\) −6.30870 2.94179i −0.259286 0.120907i
\(593\) 4.60785 6.58069i 0.189222 0.270237i −0.713320 0.700838i \(-0.752810\pi\)
0.902542 + 0.430601i \(0.141698\pi\)
\(594\) 55.7876 + 9.83686i 2.28899 + 0.403611i
\(595\) 0 0
\(596\) −1.82783 3.16590i −0.0748709 0.129680i
\(597\) 51.9491 13.9197i 2.12614 0.569696i
\(598\) −5.80264 0.507665i −0.237288 0.0207600i
\(599\) −5.00661 + 4.20105i −0.204565 + 0.171650i −0.739314 0.673360i \(-0.764850\pi\)
0.534750 + 0.845010i \(0.320406\pi\)
\(600\) 0 0
\(601\) 6.10772 3.52629i 0.249139 0.143841i −0.370231 0.928940i \(-0.620721\pi\)
0.619370 + 0.785099i \(0.287388\pi\)
\(602\) 6.57388 + 14.0977i 0.267931 + 0.574580i
\(603\) −49.2731 70.3692i −2.00655 2.86566i
\(604\) 2.93642 + 16.6533i 0.119481 + 0.677612i
\(605\) 0 0
\(606\) −38.1183 31.9851i −1.54845 1.29931i
\(607\) 8.39622 + 8.39622i 0.340792 + 0.340792i 0.856665 0.515873i \(-0.172532\pi\)
−0.515873 + 0.856665i \(0.672532\pi\)
\(608\) 2.00789 + 3.86890i 0.0814309 + 0.156904i
\(609\) 49.8482i 2.01995i
\(610\) 0 0
\(611\) 16.2050 + 44.5228i 0.655584 + 1.80120i
\(612\) 22.3227 + 15.6305i 0.902340 + 0.631825i
\(613\) 35.3794 24.7729i 1.42896 1.00057i 0.433936 0.900944i \(-0.357125\pi\)
0.995025 0.0996252i \(-0.0317644\pi\)
\(614\) 8.10846 22.2778i 0.327231 0.899060i
\(615\) 0 0
\(616\) 8.65044 + 4.99433i 0.348536 + 0.201227i
\(617\) 0.949913 10.8576i 0.0382421 0.437109i −0.952804 0.303587i \(-0.901816\pi\)
0.991046 0.133522i \(-0.0426287\pi\)
\(618\) −2.92946 + 33.4839i −0.117840 + 1.34692i
\(619\) 31.1894 + 18.0072i 1.25361 + 0.723770i 0.971824 0.235708i \(-0.0757409\pi\)
0.281783 + 0.959478i \(0.409074\pi\)
\(620\) 0 0
\(621\) 7.74612 21.2823i 0.310841 0.854029i
\(622\) 18.3297 12.8346i 0.734956 0.514622i
\(623\) 4.75479 + 3.32934i 0.190497 + 0.133387i
\(624\) −4.08519 11.2240i −0.163539 0.449318i
\(625\) 0 0
\(626\) 8.61589i 0.344360i
\(627\) 33.7551 + 44.1043i 1.34805 + 1.76136i
\(628\) 6.35116 + 6.35116i 0.253439 + 0.253439i
\(629\) −19.5155 16.3754i −0.778134 0.652932i
\(630\) 0 0
\(631\) −4.49012 25.4647i −0.178749 1.01374i −0.933727 0.357986i \(-0.883464\pi\)
0.754978 0.655750i \(-0.227647\pi\)
\(632\) −8.64240 12.3426i −0.343776 0.490963i
\(633\) 18.2484 + 39.1338i 0.725308 + 1.55543i
\(634\) 15.1277 8.73399i 0.600798 0.346871i
\(635\) 0 0
\(636\) −2.34002 + 1.96351i −0.0927880 + 0.0778584i
\(637\) 2.13626 + 0.186899i 0.0846418 + 0.00740520i
\(638\) −23.1798 + 6.21100i −0.917696 + 0.245896i
\(639\) 20.5532 + 35.5992i 0.813072 + 1.40828i
\(640\) 0 0
\(641\) 20.2511 + 3.57082i 0.799872 + 0.141039i 0.558620 0.829424i \(-0.311331\pi\)
0.241252 + 0.970463i \(0.422442\pi\)
\(642\) 15.7694 22.5210i 0.622368 0.888834i
\(643\) −14.6946 6.85219i −0.579497 0.270224i 0.110690 0.993855i \(-0.464694\pi\)
−0.690187 + 0.723631i \(0.742472\pi\)
\(644\) 2.56697 3.05920i 0.101153 0.120549i
\(645\) 0 0
\(646\) 3.43341 + 15.5790i 0.135086 + 0.612948i
\(647\) −15.8182 + 15.8182i −0.621877 + 0.621877i −0.946011 0.324134i \(-0.894927\pi\)
0.324134 + 0.946011i \(0.394927\pi\)
\(648\) 24.0125 2.10082i 0.943301 0.0825281i
\(649\) 36.8514 13.4128i 1.44654 0.526499i
\(650\) 0 0
\(651\) −6.09962 + 34.5927i −0.239063 + 1.35579i
\(652\) 5.91081 2.75626i 0.231485 0.107943i
\(653\) −7.36581 + 27.4896i −0.288246 + 1.07575i 0.658188 + 0.752854i \(0.271323\pi\)
−0.946434 + 0.322896i \(0.895343\pi\)
\(654\) 11.4918 19.9043i 0.449363 0.778320i
\(655\) 0 0
\(656\) −5.51668 6.57453i −0.215390 0.256692i
\(657\) 11.2342 + 41.9266i 0.438288 + 1.63571i
\(658\) −31.3771 8.40747i −1.22321 0.327757i
\(659\) −37.6974 13.7207i −1.46848 0.534484i −0.520794 0.853682i \(-0.674364\pi\)
−0.947688 + 0.319199i \(0.896586\pi\)
\(660\) 0 0
\(661\) −29.2704 + 5.16115i −1.13848 + 0.200746i −0.710943 0.703250i \(-0.751731\pi\)
−0.427542 + 0.903995i \(0.640620\pi\)
\(662\) −12.9502 + 27.7717i −0.503322 + 1.07938i
\(663\) −3.80994 43.5478i −0.147966 1.69126i
\(664\) −18.0933 −0.702158
\(665\) 0 0
\(666\) −51.8303 −2.00838
\(667\) 0.836195 + 9.55775i 0.0323776 + 0.370077i
\(668\) 4.70547 10.0909i 0.182060 0.390430i
\(669\) 37.3083 6.57846i 1.44242 0.254338i
\(670\) 0 0
\(671\) −9.35761 3.40589i −0.361246 0.131483i
\(672\) 7.91000 + 2.11948i 0.305135 + 0.0817606i
\(673\) −3.54088 13.2147i −0.136491 0.509391i −0.999987 0.00503589i \(-0.998397\pi\)
0.863496 0.504355i \(-0.168270\pi\)
\(674\) −6.24918 7.44749i −0.240710 0.286866i
\(675\) 0 0
\(676\) −0.328788 + 0.569478i −0.0126457 + 0.0219030i
\(677\) −0.691310 + 2.58000i −0.0265692 + 0.0991575i −0.977937 0.208899i \(-0.933012\pi\)
0.951368 + 0.308057i \(0.0996786\pi\)
\(678\) 16.7596 7.81513i 0.643648 0.300138i
\(679\) 3.43899 19.5035i 0.131976 0.748475i
\(680\) 0 0
\(681\) −31.2643 + 11.3793i −1.19805 + 0.436054i
\(682\) −16.8458 + 1.47382i −0.645061 + 0.0564355i
\(683\) −2.33396 + 2.33396i −0.0893066 + 0.0893066i −0.750349 0.661042i \(-0.770114\pi\)
0.661042 + 0.750349i \(0.270114\pi\)
\(684\) 25.7245 + 19.7901i 0.983602 + 0.756694i
\(685\) 0 0
\(686\) −12.3455 + 14.7129i −0.471355 + 0.561739i
\(687\) 4.88188 + 2.27646i 0.186255 + 0.0868523i
\(688\) −3.52132 + 5.02897i −0.134249 + 0.191728i
\(689\) 3.43978 + 0.606526i 0.131045 + 0.0231068i
\(690\) 0 0
\(691\) 15.0419 + 26.0534i 0.572222 + 0.991118i 0.996337 + 0.0855098i \(0.0272519\pi\)
−0.424115 + 0.905608i \(0.639415\pi\)
\(692\) −7.75164 + 2.07705i −0.294673 + 0.0789574i
\(693\) 74.0920 + 6.48221i 2.81452 + 0.246239i
\(694\) −10.8345 + 9.09126i −0.411274 + 0.345100i
\(695\) 0 0
\(696\) −17.0381 + 9.83695i −0.645828 + 0.372869i
\(697\) −13.2746 28.4674i −0.502810 1.07828i
\(698\) 1.36629 + 1.95126i 0.0517148 + 0.0738565i
\(699\) −1.50639 8.54316i −0.0569769 0.323132i
\(700\) 0 0
\(701\) 1.51859 + 1.27425i 0.0573562 + 0.0481276i 0.671015 0.741444i \(-0.265859\pi\)
−0.613659 + 0.789571i \(0.710303\pi\)
\(702\) −37.5500 37.5500i −1.41723 1.41723i
\(703\) −22.3447 20.5265i −0.842747 0.774171i
\(704\) 3.94229i 0.148581i
\(705\) 0 0
\(706\) 0.850205 + 2.33592i 0.0319979 + 0.0879134i
\(707\) −31.9543 22.3747i −1.20177 0.841485i
\(708\) 26.3365 18.4410i 0.989786 0.693056i
\(709\) −0.457833 + 1.25789i −0.0171943 + 0.0472409i −0.947993 0.318292i \(-0.896891\pi\)
0.930799 + 0.365533i \(0.119113\pi\)
\(710\) 0 0
\(711\) −97.1613 56.0961i −3.64383 2.10377i
\(712\) −0.199666 + 2.28219i −0.00748280 + 0.0855287i
\(713\) −0.589238 + 6.73502i −0.0220671 + 0.252228i
\(714\) 25.9552 + 14.9853i 0.971350 + 0.560809i
\(715\) 0 0
\(716\) 1.40692 3.86549i 0.0525792 0.144460i
\(717\) 9.03419 6.32581i 0.337388 0.236242i
\(718\) −22.0915 15.4686i −0.824448 0.577284i
\(719\) 12.0709 + 33.1646i 0.450170 + 1.23683i 0.932605 + 0.360900i \(0.117530\pi\)
−0.482435 + 0.875932i \(0.660247\pi\)
\(720\) 0 0
\(721\) 26.3497i 0.981316i
\(722\) 3.25266 + 18.7195i 0.121051 + 0.696668i
\(723\) 11.1605 + 11.1605i 0.415064 + 0.415064i
\(724\) 15.9226 + 13.3606i 0.591758 + 0.496544i
\(725\) 0 0
\(726\) 2.54893 + 14.4557i 0.0945998 + 0.536502i
\(727\) −5.97690 8.53589i −0.221671 0.316579i 0.692878 0.721055i \(-0.256343\pi\)
−0.914548 + 0.404477i \(0.867454\pi\)
\(728\) −3.95725 8.48636i −0.146666 0.314525i
\(729\) 34.7732 20.0763i 1.28790 0.743567i
\(730\) 0 0
\(731\) −17.2120 + 14.4425i −0.636607 + 0.534177i
\(732\) −8.13296 0.711542i −0.300603 0.0262993i
\(733\) −1.49475 + 0.400516i −0.0552097 + 0.0147934i −0.286318 0.958135i \(-0.592431\pi\)
0.231108 + 0.972928i \(0.425765\pi\)
\(734\) −1.83532 3.17887i −0.0677429 0.117334i
\(735\) 0 0
\(736\) 1.55219 + 0.273694i 0.0572146 + 0.0100885i
\(737\) 26.0879 37.2573i 0.960959 1.37239i
\(738\) −57.9170 27.0071i −2.13195 0.994146i
\(739\) −11.1902 + 13.3359i −0.411638 + 0.490571i −0.931532 0.363660i \(-0.881527\pi\)
0.519894 + 0.854231i \(0.325971\pi\)
\(740\) 0 0
\(741\) −2.20616 52.0172i −0.0810452 1.91090i
\(742\) −1.69331 + 1.69331i −0.0621633 + 0.0621633i
\(743\) −8.20317 + 0.717685i −0.300945 + 0.0263293i −0.236628 0.971600i \(-0.576042\pi\)
−0.0643168 + 0.997930i \(0.520487\pi\)
\(744\) −13.0275 + 4.74161i −0.477610 + 0.173836i
\(745\) 0 0
\(746\) 5.46105 30.9712i 0.199943 1.13393i
\(747\) −122.100 + 56.9360i −4.46739 + 2.08318i
\(748\) −3.73428 + 13.9365i −0.136539 + 0.509569i
\(749\) 10.7765 18.6655i 0.393766 0.682022i
\(750\) 0 0
\(751\) 3.83062 + 4.56515i 0.139781 + 0.166585i 0.831393 0.555684i \(-0.187544\pi\)
−0.691612 + 0.722269i \(0.743099\pi\)
\(752\) −3.31823 12.3838i −0.121003 0.451591i
\(753\) −37.9872 10.1786i −1.38433 0.370930i
\(754\) 21.1392 + 7.69405i 0.769846 + 0.280201i
\(755\) 0 0
\(756\) 35.8548 6.32218i 1.30403 0.229935i
\(757\) −6.60826 + 14.1715i −0.240181 + 0.515070i −0.989038 0.147662i \(-0.952825\pi\)
0.748857 + 0.662732i \(0.230603\pi\)
\(758\) 2.04872 + 23.4170i 0.0744130 + 0.850545i
\(759\) 20.0825 0.728947
\(760\) 0 0
\(761\) 47.0910 1.70705 0.853523 0.521055i \(-0.174461\pi\)
0.853523 + 0.521055i \(0.174461\pi\)
\(762\) 0.847330 + 9.68503i 0.0306955 + 0.350852i
\(763\) 7.61464 16.3297i 0.275669 0.591173i
\(764\) −2.66698 + 0.470261i −0.0964881 + 0.0170135i
\(765\) 0 0
\(766\) −4.99895 1.81947i −0.180619 0.0657400i
\(767\) −35.5100 9.51487i −1.28219 0.343562i
\(768\) 0.836508 + 3.12189i 0.0301849 + 0.112652i
\(769\) 31.2892 + 37.2890i 1.12832 + 1.34468i 0.931290 + 0.364278i \(0.118684\pi\)
0.197027 + 0.980398i \(0.436871\pi\)
\(770\) 0 0
\(771\) 36.6470 63.4744i 1.31981 2.28598i
\(772\) −3.13532 + 11.7012i −0.112843 + 0.421135i
\(773\) −27.1557 + 12.6629i −0.976722 + 0.455453i −0.844376 0.535751i \(-0.820029\pi\)
−0.132346 + 0.991204i \(0.542251\pi\)
\(774\) −7.93788 + 45.0180i −0.285321 + 1.61814i
\(775\) 0 0
\(776\) 7.34493 2.67334i 0.263668 0.0959672i
\(777\) −56.7859 + 4.96813i −2.03718 + 0.178231i
\(778\) 17.3323 17.3323i 0.621393 0.621393i
\(779\) −14.2731 34.5801i −0.511386 1.23896i
\(780\) 0 0
\(781\) −13.9896 + 16.6722i −0.500588 + 0.596577i
\(782\) 5.22796 + 2.43784i 0.186951 + 0.0871768i
\(783\) −50.1702 + 71.6505i −1.79294 + 2.56058i
\(784\) −0.571446 0.100761i −0.0204088 0.00359862i
\(785\) 0 0
\(786\) 29.3027 + 50.7537i 1.04519 + 1.81032i
\(787\) 32.6623 8.75182i 1.16428 0.311969i 0.375608 0.926779i \(-0.377434\pi\)
0.788675 + 0.614810i \(0.210767\pi\)
\(788\) 20.8522 + 1.82433i 0.742829 + 0.0649891i
\(789\) −26.6788 + 22.3861i −0.949789 + 0.796968i
\(790\) 0 0
\(791\) 12.5546 7.24841i 0.446391 0.257724i
\(792\) 12.4056 + 26.6038i 0.440813 + 0.945326i
\(793\) 5.35437 + 7.64684i 0.190139 + 0.271547i
\(794\) 5.65934 + 32.0957i 0.200842 + 1.13903i
\(795\) 0 0
\(796\) 12.7472 + 10.6962i 0.451812 + 0.379116i
\(797\) −8.46761 8.46761i −0.299938 0.299938i 0.541051 0.840989i \(-0.318026\pi\)
−0.840989 + 0.541051i \(0.818026\pi\)
\(798\) 30.0811 + 19.2165i 1.06486 + 0.680257i
\(799\) 46.9215i 1.65996i
\(800\) 0 0
\(801\) 5.83417 + 16.0293i 0.206140 + 0.566366i
\(802\) −14.2329 9.96597i −0.502581 0.351911i
\(803\) −18.8252 + 13.1815i −0.664327 + 0.465167i
\(804\) 12.7533 35.0395i 0.449776 1.23575i
\(805\) 0 0
\(806\) 13.7283 + 7.92605i 0.483559 + 0.279183i
\(807\) −1.50645 + 17.2188i −0.0530297 + 0.606132i
\(808\) 1.34184 15.3374i 0.0472059 0.539566i
\(809\) −2.66522 1.53877i −0.0937041 0.0541001i 0.452416 0.891807i \(-0.350562\pi\)
−0.546120 + 0.837707i \(0.683896\pi\)
\(810\) 0 0
\(811\) 15.4853 42.5455i 0.543762 1.49398i −0.298234 0.954493i \(-0.596398\pi\)
0.841997 0.539482i \(-0.181380\pi\)
\(812\) −12.6340 + 8.84640i −0.443366 + 0.310448i
\(813\) −81.7636 57.2515i −2.86757 2.00790i
\(814\) −9.38565 25.7869i −0.328967 0.903829i
\(815\) 0 0
\(816\) 11.8287i 0.414086i
\(817\) −21.2507 + 16.2642i −0.743467 + 0.569012i
\(818\) −9.36094 9.36094i −0.327297 0.327297i
\(819\) −53.4096 44.8160i −1.86628 1.56600i
\(820\) 0 0
\(821\) 2.49565 + 14.1535i 0.0870987 + 0.493962i 0.996884 + 0.0788822i \(0.0251351\pi\)
−0.909785 + 0.415079i \(0.863754\pi\)
\(822\) −5.75473 8.21860i −0.200719 0.286657i
\(823\) 15.4765 + 33.1894i 0.539476 + 1.15691i 0.967437 + 0.253113i \(0.0814543\pi\)
−0.427961 + 0.903797i \(0.640768\pi\)
\(824\) −9.00634 + 5.19981i −0.313751 + 0.181144i
\(825\) 0 0
\(826\) 19.3078 16.2012i 0.671804 0.563710i
\(827\) 6.42486 + 0.562102i 0.223414 + 0.0195462i 0.198313 0.980139i \(-0.436454\pi\)
0.0251010 + 0.999685i \(0.492009\pi\)
\(828\) 11.3360 3.03746i 0.393952 0.105559i
\(829\) 0.793407 + 1.37422i 0.0275562 + 0.0477287i 0.879475 0.475946i \(-0.157894\pi\)
−0.851918 + 0.523674i \(0.824561\pi\)
\(830\) 0 0
\(831\) 34.3184 + 6.05127i 1.19049 + 0.209916i
\(832\) 2.11972 3.02727i 0.0734880 0.104952i
\(833\) −1.92469 0.897498i −0.0666866 0.0310965i
\(834\) −31.8747 + 37.9868i −1.10373 + 1.31537i
\(835\) 0 0
\(836\) −5.18777 + 16.3823i −0.179423 + 0.566592i
\(837\) −43.5836 + 43.5836i −1.50647 + 1.50647i
\(838\) 5.49460 0.480715i 0.189808 0.0166060i
\(839\) −38.8710 + 14.1479i −1.34198 + 0.488440i −0.910435 0.413653i \(-0.864253\pi\)
−0.431543 + 0.902092i \(0.642031\pi\)
\(840\) 0 0
\(841\) 1.39854 7.93150i 0.0482255 0.273500i
\(842\) 11.5376 5.38009i 0.397613 0.185410i
\(843\) 10.0480 37.4996i 0.346071 1.29156i
\(844\) −6.67994 + 11.5700i −0.229933 + 0.398255i
\(845\) 0 0
\(846\) −61.3617 73.1280i −2.10966 2.51419i
\(847\) 2.97831 + 11.1152i 0.102336 + 0.381922i
\(848\) −0.912928 0.244618i −0.0313501 0.00840022i
\(849\) 46.6346 + 16.9736i 1.60050 + 0.582533i
\(850\) 0 0
\(851\) −10.8046 + 1.90515i −0.370378 + 0.0653077i
\(852\) −7.54070 + 16.1711i −0.258340 + 0.554012i
\(853\) 1.04460 + 11.9398i 0.0357664 + 0.408812i 0.992882 + 0.119105i \(0.0380024\pi\)
−0.957115 + 0.289707i \(0.906442\pi\)
\(854\) −6.40013 −0.219008
\(855\) 0 0
\(856\) 8.50648 0.290746
\(857\) −3.10606 35.5024i −0.106101 1.21274i −0.843443 0.537219i \(-0.819475\pi\)
0.737342 0.675520i \(-0.236081\pi\)
\(858\) 19.9002 42.6761i 0.679382 1.45694i
\(859\) −42.8794 + 7.56079i −1.46303 + 0.257971i −0.847773 0.530359i \(-0.822057\pi\)
−0.615252 + 0.788330i \(0.710946\pi\)
\(860\) 0 0
\(861\) −66.0433 24.0378i −2.25075 0.819206i
\(862\) −22.9742 6.15591i −0.782503 0.209671i
\(863\) 5.41950 + 20.2259i 0.184482 + 0.688496i 0.994741 + 0.102424i \(0.0326598\pi\)
−0.810259 + 0.586072i \(0.800674\pi\)
\(864\) 9.23645 + 11.0076i 0.314231 + 0.374485i
\(865\) 0 0
\(866\) 6.97222 12.0762i 0.236926 0.410367i
\(867\) 3.01611 11.2563i 0.102433 0.382284i
\(868\) −9.84996 + 4.59311i −0.334329 + 0.155900i
\(869\) 10.3148 58.4983i 0.349906 1.98442i
\(870\) 0 0
\(871\) −40.0656 + 14.5827i −1.35757 + 0.494115i
\(872\) 7.08414 0.619782i 0.239899 0.0209885i
\(873\) 41.1535 41.1535i 1.39283 1.39283i
\(874\) 6.09001 + 3.17991i 0.205998 + 0.107562i
\(875\) 0 0
\(876\) −12.1107 + 14.4329i −0.409181 + 0.487643i
\(877\) 27.9030 + 13.0114i 0.942218 + 0.439363i 0.832144 0.554560i \(-0.187113\pi\)
0.110074 + 0.993923i \(0.464891\pi\)
\(878\) 8.37873 11.9661i 0.282768 0.403835i
\(879\) −9.23648 1.62864i −0.311539 0.0549327i
\(880\) 0 0
\(881\) −12.2260 21.1761i −0.411906 0.713442i 0.583192 0.812334i \(-0.301803\pi\)
−0.995098 + 0.0988924i \(0.968470\pi\)
\(882\) −4.17337 + 1.11825i −0.140525 + 0.0376535i
\(883\) 6.08198 + 0.532104i 0.204675 + 0.0179067i 0.189032 0.981971i \(-0.439465\pi\)
0.0156428 + 0.999878i \(0.495021\pi\)
\(884\) 10.3610 8.69393i 0.348479 0.292408i
\(885\) 0 0
\(886\) 8.86450 5.11792i 0.297809 0.171940i
\(887\) 18.7865 + 40.2877i 0.630787 + 1.35273i 0.918656 + 0.395058i \(0.129276\pi\)
−0.287869 + 0.957670i \(0.592947\pi\)
\(888\) −12.9041 18.4290i −0.433035 0.618438i
\(889\) 1.32346 + 7.50573i 0.0443875 + 0.251734i
\(890\) 0 0
\(891\) 72.7941 + 61.0815i 2.43869 + 2.04631i
\(892\) 8.28829 + 8.28829i 0.277512 + 0.277512i
\(893\) 2.50722 55.8277i 0.0839009 1.86820i
\(894\) 11.8152i 0.395158i
\(895\) 0 0
\(896\) 0.866583 + 2.38092i 0.0289505 + 0.0795409i
\(897\) −15.4213 10.7981i −0.514901 0.360537i
\(898\) 10.3143 7.22218i 0.344194 0.241007i
\(899\) 8.93035 24.5359i 0.297844 0.818319i
\(900\) 0 0
\(901\) −2.99561 1.72951i −0.0997981 0.0576185i
\(902\) 2.94887 33.7057i 0.0981865 1.12228i
\(903\) −4.38170 + 50.0831i −0.145814 + 1.66666i
\(904\) 4.95501 + 2.86078i 0.164801 + 0.0951480i
\(905\) 0 0
\(906\) −18.6928 + 51.3579i −0.621025 + 1.70625i
\(907\) 38.1001 26.6780i 1.26509 0.885828i 0.268106 0.963389i \(-0.413602\pi\)
0.996988 + 0.0775610i \(0.0247132\pi\)
\(908\) −8.43244 5.90446i −0.279840 0.195946i
\(909\) −39.2083 107.724i −1.30046 3.57297i
\(910\) 0 0
\(911\) 5.31610i 0.176130i 0.996115 + 0.0880651i \(0.0280684\pi\)
−0.996115 + 0.0880651i \(0.971932\pi\)
\(912\) −0.632056 + 14.0739i −0.0209295 + 0.466032i
\(913\) −50.4374 50.4374i −1.66923 1.66923i
\(914\) 19.3033 + 16.1974i 0.638497 + 0.535763i
\(915\) 0 0
\(916\) 0.289406 + 1.64130i 0.00956225 + 0.0542302i
\(917\) 26.3520 + 37.6345i 0.870219 + 1.24280i
\(918\) 22.2253 + 47.6623i 0.733544 + 1.57309i
\(919\) −50.4140 + 29.1066i −1.66301 + 0.960137i −0.691737 + 0.722150i \(0.743154\pi\)
−0.971268 + 0.237987i \(0.923512\pi\)
\(920\) 0 0
\(921\) 58.6968 49.2525i 1.93413 1.62292i
\(922\) 13.8281 + 1.20980i 0.455403 + 0.0398426i
\(923\) 19.7070 5.28047i 0.648663 0.173809i
\(924\) 16.1418 + 27.9584i 0.531025 + 0.919763i
\(925\) 0 0
\(926\) 2.48159 + 0.437571i 0.0815501 + 0.0143795i
\(927\) −44.4149 + 63.4311i −1.45878 + 2.08335i
\(928\) −5.51687 2.57256i −0.181100 0.0844483i
\(929\) 23.9686 28.5646i 0.786383 0.937175i −0.212820 0.977091i \(-0.568265\pi\)
0.999203 + 0.0399164i \(0.0127092\pi\)
\(930\) 0 0
\(931\) −2.24206 1.17070i −0.0734805 0.0383680i
\(932\) 1.89792 1.89792i 0.0621685 0.0621685i
\(933\) 72.0460 6.30321i 2.35868 0.206358i
\(934\) −37.4120 + 13.6169i −1.22416 + 0.445557i
\(935\) 0 0
\(936\) 4.77834 27.0993i 0.156185 0.885768i
\(937\) 3.59828 1.67790i 0.117551 0.0548147i −0.362953 0.931807i \(-0.618232\pi\)
0.480504 + 0.876993i \(0.340454\pi\)
\(938\) 7.56578 28.2359i 0.247031 0.921934i
\(939\) 13.9234 24.1160i 0.454372 0.786995i
\(940\) 0 0
\(941\) 31.8602 + 37.9696i 1.03861 + 1.23777i 0.970754 + 0.240077i \(0.0771728\pi\)
0.0678605 + 0.997695i \(0.478383\pi\)
\(942\) 7.51343 + 28.0405i 0.244801 + 0.913608i
\(943\) −13.0662 3.50107i −0.425494 0.114011i
\(944\) 9.34772 + 3.40229i 0.304242 + 0.110735i
\(945\) 0 0
\(946\) −23.8350 + 4.20275i −0.774942 + 0.136643i
\(947\) 15.8773 34.0490i 0.515944 1.10644i −0.459899 0.887971i \(-0.652115\pi\)
0.975843 0.218473i \(-0.0701077\pi\)
\(948\) −4.24437 48.5133i −0.137851 1.57564i
\(949\) 21.5433 0.699326
\(950\) 0 0
\(951\) 56.4569 1.83074
\(952\) 0.808195 + 9.23771i 0.0261938 + 0.299396i
\(953\) −4.74708 + 10.1801i −0.153773 + 0.329767i −0.968070 0.250682i \(-0.919345\pi\)
0.814297 + 0.580449i \(0.197123\pi\)
\(954\) −6.93049 + 1.22203i −0.224383 + 0.0395647i
\(955\) 0 0
\(956\) 3.20654 + 1.16709i 0.103707 + 0.0377462i
\(957\) −74.9175 20.0741i −2.42174 0.648903i
\(958\) 0.794334 + 2.96450i 0.0256638 + 0.0957785i
\(959\) −5.05575 6.02521i −0.163259 0.194564i
\(960\) 0 0
\(961\) −6.30038 + 10.9126i −0.203238 + 0.352019i
\(962\) −6.65805 + 24.8482i −0.214664 + 0.801138i
\(963\) 57.4044 26.7681i 1.84983 0.862591i
\(964\) −0.847999 + 4.80924i −0.0273122 + 0.154895i
\(965\) 0 0
\(966\) 12.1287 4.41447i 0.390233 0.142033i
\(967\) 29.3776 2.57021i 0.944721 0.0826524i 0.395625 0.918412i \(-0.370528\pi\)
0.549095 + 0.835760i \(0.314972\pi\)
\(968\) −3.21144 + 3.21144i −0.103219 + 0.103219i
\(969\) −15.5657 + 49.1542i −0.500041 + 1.57906i
\(970\) 0 0
\(971\) −23.8812 + 28.4605i −0.766385 + 0.913342i −0.998234 0.0594102i \(-0.981078\pi\)
0.231849 + 0.972752i \(0.425522\pi\)
\(972\) 31.5370 + 14.7060i 1.01155 + 0.471694i
\(973\) −22.2974 + 31.8440i −0.714822 + 1.02087i
\(974\) 14.2942 + 2.52045i 0.458015 + 0.0807604i
\(975\) 0 0
\(976\) −1.26299 2.18757i −0.0404274 0.0700223i
\(977\) 7.63544 2.04591i 0.244279 0.0654544i −0.134602 0.990900i \(-0.542976\pi\)
0.378881 + 0.925445i \(0.376309\pi\)
\(978\) 20.9986 + 1.83714i 0.671460 + 0.0587451i
\(979\) −6.91848 + 5.80529i −0.221115 + 0.185538i
\(980\) 0 0
\(981\) 45.8557 26.4748i 1.46406 0.845275i
\(982\) 5.24529 + 11.2486i 0.167384 + 0.358956i
\(983\) 5.02927 + 7.18255i 0.160409 + 0.229088i 0.891309 0.453397i \(-0.149788\pi\)
−0.730900 + 0.682485i \(0.760899\pi\)
\(984\) −4.81676 27.3172i −0.153553 0.870840i
\(985\) 0 0
\(986\) −17.0660 14.3201i −0.543493 0.456045i
\(987\) −74.2383 74.2383i −2.36303 2.36303i
\(988\) 12.7922 9.79049i 0.406974 0.311477i
\(989\) 9.67630i 0.307688i
\(990\) 0 0
\(991\) −9.03655 24.8277i −0.287055 0.788678i −0.996475 0.0838918i \(-0.973265\pi\)
0.709419 0.704787i \(-0.248957\pi\)
\(992\) −3.51370 2.46032i −0.111560 0.0781152i
\(993\) −81.1269 + 56.8057i −2.57448 + 1.80267i
\(994\) −4.78410 + 13.1442i −0.151742 + 0.416909i
\(995\) 0 0
\(996\) −50.6434 29.2390i −1.60470 0.926473i
\(997\) 5.05084 57.7314i 0.159962 1.82837i −0.315832 0.948815i \(-0.602284\pi\)
0.475794 0.879557i \(-0.342161\pi\)
\(998\) 2.13176 24.3661i 0.0674797 0.771297i
\(999\) −86.6229 50.0117i −2.74063 1.58230i
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 950.2.bb.d.193.5 yes 96
5.2 odd 4 inner 950.2.bb.d.307.4 yes 96
5.3 odd 4 inner 950.2.bb.d.307.5 yes 96
5.4 even 2 inner 950.2.bb.d.193.4 96
19.13 odd 18 inner 950.2.bb.d.393.4 yes 96
95.13 even 36 inner 950.2.bb.d.507.4 yes 96
95.32 even 36 inner 950.2.bb.d.507.5 yes 96
95.89 odd 18 inner 950.2.bb.d.393.5 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.bb.d.193.4 96 5.4 even 2 inner
950.2.bb.d.193.5 yes 96 1.1 even 1 trivial
950.2.bb.d.307.4 yes 96 5.2 odd 4 inner
950.2.bb.d.307.5 yes 96 5.3 odd 4 inner
950.2.bb.d.393.4 yes 96 19.13 odd 18 inner
950.2.bb.d.393.5 yes 96 95.89 odd 18 inner
950.2.bb.d.507.4 yes 96 95.13 even 36 inner
950.2.bb.d.507.5 yes 96 95.32 even 36 inner