Properties

Label 531.2.i.b.163.4
Level $531$
Weight $2$
Character 531.163
Analytic conductor $4.240$
Analytic rank $0$
Dimension $140$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [531,2,Mod(19,531)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(531, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([0, 38]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("531.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 531.i (of order \(29\), degree \(28\), 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: \(4.24005634733\)
Analytic rank: \(0\)
Dimension: \(140\)
Relative dimension: \(5\) over \(\Q(\zeta_{29})\)
Twist minimal: no (minimal twist has level 177)
Sato-Tate group: $\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label 163.4
Character \(\chi\) \(=\) 531.163
Dual form 531.2.i.b.316.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.992185 - 0.596978i) q^{2} +(-0.308769 + 0.582400i) q^{4} +(0.793835 - 0.0863348i) q^{5} +(-4.18976 + 1.41169i) q^{7} +(0.166703 + 3.07465i) q^{8} +O(q^{10})\) \(q+(0.992185 - 0.596978i) q^{2} +(-0.308769 + 0.582400i) q^{4} +(0.793835 - 0.0863348i) q^{5} +(-4.18976 + 1.41169i) q^{7} +(0.166703 + 3.07465i) q^{8} +(0.736091 - 0.559562i) q^{10} +(-0.744195 + 1.09760i) q^{11} +(2.28411 + 2.16363i) q^{13} +(-3.31426 + 3.90185i) q^{14} +(1.26104 + 1.85990i) q^{16} +(7.48680 + 2.52260i) q^{17} +(0.837472 + 5.10835i) q^{19} +(-0.194830 + 0.488987i) q^{20} +(-0.0831328 + 1.53329i) q^{22} +(-0.662011 - 2.38435i) q^{23} +(-4.26038 + 0.937781i) q^{25} +(3.55790 + 0.783152i) q^{26} +(0.471496 - 2.87600i) q^{28} +(-6.94296 - 4.17744i) q^{29} +(-0.686795 + 4.18927i) q^{31} +(-3.22765 - 1.49327i) q^{32} +(8.93422 - 1.96657i) q^{34} +(-3.20410 + 1.48237i) q^{35} +(0.435953 - 8.04068i) q^{37} +(3.88050 + 4.56848i) q^{38} +(0.397784 + 2.42637i) q^{40} +(1.62041 - 5.83619i) q^{41} +(6.39177 + 9.42715i) q^{43} +(-0.409461 - 0.772325i) q^{44} +(-2.08024 - 1.97051i) q^{46} +(-3.69898 - 0.402288i) q^{47} +(9.98853 - 7.59308i) q^{49} +(-3.66725 + 3.47380i) q^{50} +(-1.96536 + 0.662206i) q^{52} +(1.10424 + 0.839421i) q^{53} +(-0.496006 + 0.935567i) q^{55} +(-5.03891 - 12.6467i) q^{56} -9.38254 q^{58} +(7.67111 + 0.392457i) q^{59} +(8.88976 - 5.34879i) q^{61} +(1.81947 + 4.56653i) q^{62} +(-8.56172 + 0.931143i) q^{64} +(2.00000 + 1.52036i) q^{65} +(-0.0694302 - 1.28056i) q^{67} +(-3.78085 + 3.58141i) q^{68} +(-2.29411 + 3.38356i) q^{70} +(-0.433685 - 0.0471661i) q^{71} +(-1.39656 + 1.64416i) q^{73} +(-4.36756 - 8.23809i) q^{74} +(-3.23369 - 1.08956i) q^{76} +(1.56851 - 5.64927i) q^{77} +(-1.73950 + 4.36581i) q^{79} +(1.16163 + 1.36758i) q^{80} +(-1.87633 - 6.75792i) q^{82} +(3.34065 - 1.54555i) q^{83} +(6.16107 + 1.35615i) q^{85} +(11.9696 + 5.53773i) q^{86} +(-3.49881 - 2.10516i) q^{88} +(5.98712 + 3.60233i) q^{89} +(-12.6243 - 5.84060i) q^{91} +(1.59305 + 0.350658i) q^{92} +(-3.91022 + 1.80906i) q^{94} +(1.10584 + 3.98289i) q^{95} +(-6.66777 - 7.84990i) q^{97} +(5.37756 - 13.4967i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8} - 116 q^{10} - 2 q^{11} + 4 q^{13} + 43 q^{14} + 7 q^{16} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 6 q^{23} - 57 q^{25} - 12 q^{26} - 10 q^{28} + 4 q^{29} - 12 q^{31} + 150 q^{32} - 2 q^{34} - 6 q^{35} + 12 q^{37} + 12 q^{38} - 66 q^{40} + 4 q^{41} - 60 q^{43} - 20 q^{44} + 76 q^{46} + 25 q^{47} + 31 q^{49} - 137 q^{50} + 118 q^{52} - 48 q^{53} + 93 q^{55} - 228 q^{56} - 120 q^{58} - 57 q^{59} + 72 q^{61} + 179 q^{62} + 249 q^{64} + 39 q^{65} + 40 q^{67} - 94 q^{68} + 94 q^{70} - 30 q^{71} - 205 q^{73} - 66 q^{74} - 216 q^{76} + 46 q^{77} + 4 q^{79} + 356 q^{80} - 28 q^{82} - 4 q^{83} + 50 q^{85} + 18 q^{86} - 162 q^{88} - 26 q^{89} - 198 q^{91} - 10 q^{92} - 4 q^{94} + 326 q^{95} - 20 q^{97} + 143 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).

\(n\) \(119\) \(415\)
\(\chi(n)\) \(1\) \(e\left(\frac{24}{29}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.992185 0.596978i 0.701580 0.422127i −0.119580 0.992825i \(-0.538155\pi\)
0.821160 + 0.570698i \(0.193327\pi\)
\(3\) 0 0
\(4\) −0.308769 + 0.582400i −0.154384 + 0.291200i
\(5\) 0.793835 0.0863348i 0.355014 0.0386101i 0.0711254 0.997467i \(-0.477341\pi\)
0.283888 + 0.958857i \(0.408375\pi\)
\(6\) 0 0
\(7\) −4.18976 + 1.41169i −1.58358 + 0.533570i −0.967230 0.253903i \(-0.918286\pi\)
−0.616349 + 0.787473i \(0.711389\pi\)
\(8\) 0.166703 + 3.07465i 0.0589383 + 1.08705i
\(9\) 0 0
\(10\) 0.736091 0.559562i 0.232772 0.176949i
\(11\) −0.744195 + 1.09760i −0.224383 + 0.330940i −0.923172 0.384388i \(-0.874412\pi\)
0.698789 + 0.715328i \(0.253723\pi\)
\(12\) 0 0
\(13\) 2.28411 + 2.16363i 0.633499 + 0.600082i 0.935543 0.353212i \(-0.114911\pi\)
−0.302045 + 0.953294i \(0.597669\pi\)
\(14\) −3.31426 + 3.90185i −0.885774 + 1.04281i
\(15\) 0 0
\(16\) 1.26104 + 1.85990i 0.315260 + 0.464974i
\(17\) 7.48680 + 2.52260i 1.81582 + 0.611819i 0.999410 + 0.0343397i \(0.0109328\pi\)
0.816405 + 0.577480i \(0.195964\pi\)
\(18\) 0 0
\(19\) 0.837472 + 5.10835i 0.192129 + 1.17194i 0.890085 + 0.455795i \(0.150645\pi\)
−0.697956 + 0.716141i \(0.745907\pi\)
\(20\) −0.194830 + 0.488987i −0.0435654 + 0.109341i
\(21\) 0 0
\(22\) −0.0831328 + 1.53329i −0.0177240 + 0.326899i
\(23\) −0.662011 2.38435i −0.138039 0.497171i 0.861912 0.507057i \(-0.169267\pi\)
−0.999951 + 0.00988634i \(0.996853\pi\)
\(24\) 0 0
\(25\) −4.26038 + 0.937781i −0.852076 + 0.187556i
\(26\) 3.55790 + 0.783152i 0.697761 + 0.153589i
\(27\) 0 0
\(28\) 0.471496 2.87600i 0.0891045 0.543513i
\(29\) −6.94296 4.17744i −1.28928 0.775732i −0.304997 0.952353i \(-0.598655\pi\)
−0.984279 + 0.176622i \(0.943483\pi\)
\(30\) 0 0
\(31\) −0.686795 + 4.18927i −0.123352 + 0.752414i 0.850626 + 0.525771i \(0.176223\pi\)
−0.973978 + 0.226643i \(0.927225\pi\)
\(32\) −3.22765 1.49327i −0.570573 0.263975i
\(33\) 0 0
\(34\) 8.93422 1.96657i 1.53221 0.337264i
\(35\) −3.20410 + 1.48237i −0.541591 + 0.250567i
\(36\) 0 0
\(37\) 0.435953 8.04068i 0.0716702 1.32188i −0.712649 0.701521i \(-0.752505\pi\)
0.784319 0.620358i \(-0.213013\pi\)
\(38\) 3.88050 + 4.56848i 0.629500 + 0.741105i
\(39\) 0 0
\(40\) 0.397784 + 2.42637i 0.0628951 + 0.383643i
\(41\) 1.62041 5.83619i 0.253065 0.911459i −0.722431 0.691443i \(-0.756975\pi\)
0.975496 0.220016i \(-0.0706109\pi\)
\(42\) 0 0
\(43\) 6.39177 + 9.42715i 0.974735 + 1.43763i 0.897704 + 0.440598i \(0.145234\pi\)
0.0770311 + 0.997029i \(0.475456\pi\)
\(44\) −0.409461 0.772325i −0.0617286 0.116432i
\(45\) 0 0
\(46\) −2.08024 1.97051i −0.306715 0.290536i
\(47\) −3.69898 0.402288i −0.539551 0.0586797i −0.165714 0.986174i \(-0.552993\pi\)
−0.373837 + 0.927494i \(0.621958\pi\)
\(48\) 0 0
\(49\) 9.98853 7.59308i 1.42693 1.08473i
\(50\) −3.66725 + 3.47380i −0.518628 + 0.491270i
\(51\) 0 0
\(52\) −1.96536 + 0.662206i −0.272546 + 0.0918315i
\(53\) 1.10424 + 0.839421i 0.151679 + 0.115303i 0.678261 0.734821i \(-0.262734\pi\)
−0.526582 + 0.850124i \(0.676527\pi\)
\(54\) 0 0
\(55\) −0.496006 + 0.935567i −0.0668815 + 0.126152i
\(56\) −5.03891 12.6467i −0.673352 1.68999i
\(57\) 0 0
\(58\) −9.38254 −1.23199
\(59\) 7.67111 + 0.392457i 0.998694 + 0.0510936i
\(60\) 0 0
\(61\) 8.88976 5.34879i 1.13822 0.684843i 0.183696 0.982983i \(-0.441194\pi\)
0.954522 + 0.298140i \(0.0963664\pi\)
\(62\) 1.81947 + 4.56653i 0.231073 + 0.579949i
\(63\) 0 0
\(64\) −8.56172 + 0.931143i −1.07021 + 0.116393i
\(65\) 2.00000 + 1.52036i 0.248070 + 0.188578i
\(66\) 0 0
\(67\) −0.0694302 1.28056i −0.00848225 0.156446i −0.999706 0.0242504i \(-0.992280\pi\)
0.991224 0.132195i \(-0.0422027\pi\)
\(68\) −3.78085 + 3.58141i −0.458495 + 0.434310i
\(69\) 0 0
\(70\) −2.29411 + 3.38356i −0.274199 + 0.404413i
\(71\) −0.433685 0.0471661i −0.0514689 0.00559758i 0.0823483 0.996604i \(-0.473758\pi\)
−0.133817 + 0.991006i \(0.542724\pi\)
\(72\) 0 0
\(73\) −1.39656 + 1.64416i −0.163455 + 0.192434i −0.837792 0.545990i \(-0.816154\pi\)
0.674337 + 0.738424i \(0.264430\pi\)
\(74\) −4.36756 8.23809i −0.507718 0.957659i
\(75\) 0 0
\(76\) −3.23369 1.08956i −0.370930 0.124981i
\(77\) 1.56851 5.64927i 0.178749 0.643794i
\(78\) 0 0
\(79\) −1.73950 + 4.36581i −0.195709 + 0.491191i −0.993779 0.111373i \(-0.964475\pi\)
0.798070 + 0.602565i \(0.205854\pi\)
\(80\) 1.16163 + 1.36758i 0.129875 + 0.152900i
\(81\) 0 0
\(82\) −1.87633 6.75792i −0.207206 0.746288i
\(83\) 3.34065 1.54555i 0.366684 0.169646i −0.227890 0.973687i \(-0.573183\pi\)
0.594574 + 0.804041i \(0.297321\pi\)
\(84\) 0 0
\(85\) 6.16107 + 1.35615i 0.668262 + 0.147096i
\(86\) 11.9696 + 5.53773i 1.29072 + 0.597149i
\(87\) 0 0
\(88\) −3.49881 2.10516i −0.372974 0.224411i
\(89\) 5.98712 + 3.60233i 0.634634 + 0.381846i 0.796216 0.605013i \(-0.206832\pi\)
−0.161582 + 0.986859i \(0.551660\pi\)
\(90\) 0 0
\(91\) −12.6243 5.84060i −1.32338 0.612261i
\(92\) 1.59305 + 0.350658i 0.166087 + 0.0365586i
\(93\) 0 0
\(94\) −3.91022 + 1.80906i −0.403309 + 0.186590i
\(95\) 1.10584 + 3.98289i 0.113457 + 0.408635i
\(96\) 0 0
\(97\) −6.66777 7.84990i −0.677009 0.797037i 0.311167 0.950355i \(-0.399280\pi\)
−0.988177 + 0.153318i \(0.951004\pi\)
\(98\) 5.37756 13.4967i 0.543216 1.36337i
\(99\) 0 0
\(100\) 0.769310 2.77080i 0.0769310 0.277080i
\(101\) −0.188243 0.0634265i −0.0187309 0.00631117i 0.309920 0.950762i \(-0.399698\pi\)
−0.328651 + 0.944451i \(0.606594\pi\)
\(102\) 0 0
\(103\) −2.88236 5.43671i −0.284008 0.535695i 0.699929 0.714212i \(-0.253215\pi\)
−0.983937 + 0.178517i \(0.942870\pi\)
\(104\) −6.27162 + 7.38353i −0.614983 + 0.724014i
\(105\) 0 0
\(106\) 1.59672 + 0.173654i 0.155088 + 0.0168668i
\(107\) 5.57926 8.22880i 0.539368 0.795508i −0.456168 0.889894i \(-0.650778\pi\)
0.995536 + 0.0943857i \(0.0300887\pi\)
\(108\) 0 0
\(109\) 3.79341 3.59331i 0.363343 0.344177i −0.484148 0.874986i \(-0.660871\pi\)
0.847491 + 0.530809i \(0.178112\pi\)
\(110\) 0.0663829 + 1.22436i 0.00632936 + 0.116738i
\(111\) 0 0
\(112\) −7.90906 6.01231i −0.747336 0.568110i
\(113\) 7.13771 0.776273i 0.671459 0.0730256i 0.233963 0.972246i \(-0.424831\pi\)
0.437497 + 0.899220i \(0.355865\pi\)
\(114\) 0 0
\(115\) −0.731380 1.83563i −0.0682015 0.171173i
\(116\) 4.57671 2.75372i 0.424937 0.255676i
\(117\) 0 0
\(118\) 7.84545 4.19009i 0.722232 0.385729i
\(119\) −34.9290 −3.20194
\(120\) 0 0
\(121\) 3.42061 + 8.58508i 0.310964 + 0.780462i
\(122\) 5.62718 10.6140i 0.509461 0.960945i
\(123\) 0 0
\(124\) −2.22777 1.69350i −0.200059 0.152081i
\(125\) −7.08466 + 2.38710i −0.633671 + 0.213509i
\(126\) 0 0
\(127\) 11.3503 10.7516i 1.00718 0.954049i 0.00823195 0.999966i \(-0.497380\pi\)
0.998945 + 0.0459172i \(0.0146210\pi\)
\(128\) −2.27658 + 1.73061i −0.201223 + 0.152966i
\(129\) 0 0
\(130\) 2.89200 + 0.314524i 0.253645 + 0.0275856i
\(131\) −6.01093 5.69385i −0.525177 0.497474i 0.378551 0.925580i \(-0.376422\pi\)
−0.903728 + 0.428106i \(0.859181\pi\)
\(132\) 0 0
\(133\) −10.7202 20.2205i −0.929562 1.75334i
\(134\) −0.833356 1.22911i −0.0719910 0.106179i
\(135\) 0 0
\(136\) −6.50803 + 23.4398i −0.558059 + 2.00995i
\(137\) 1.85540 + 11.3174i 0.158518 + 0.966914i 0.939547 + 0.342420i \(0.111247\pi\)
−0.781029 + 0.624494i \(0.785305\pi\)
\(138\) 0 0
\(139\) 12.1020 + 14.2476i 1.02648 + 1.20847i 0.977775 + 0.209655i \(0.0672342\pi\)
0.0487070 + 0.998813i \(0.484490\pi\)
\(140\) 0.125992 2.32378i 0.0106482 0.196395i
\(141\) 0 0
\(142\) −0.458453 + 0.212103i −0.0384725 + 0.0177993i
\(143\) −4.07463 + 0.896894i −0.340738 + 0.0750020i
\(144\) 0 0
\(145\) −5.87223 2.71678i −0.487662 0.225616i
\(146\) −0.404120 + 2.46502i −0.0334452 + 0.204007i
\(147\) 0 0
\(148\) 4.54828 + 2.73661i 0.373866 + 0.224948i
\(149\) −2.87916 + 17.5621i −0.235870 + 1.43874i 0.557588 + 0.830118i \(0.311727\pi\)
−0.793458 + 0.608625i \(0.791722\pi\)
\(150\) 0 0
\(151\) 12.4650 + 2.74375i 1.01439 + 0.223283i 0.690900 0.722950i \(-0.257214\pi\)
0.323485 + 0.946233i \(0.395145\pi\)
\(152\) −15.5668 + 3.42651i −1.26263 + 0.277926i
\(153\) 0 0
\(154\) −1.81623 6.54149i −0.146356 0.527128i
\(155\) −0.183523 + 3.38488i −0.0147409 + 0.271880i
\(156\) 0 0
\(157\) −7.26263 + 18.2278i −0.579621 + 1.45474i 0.288057 + 0.957613i \(0.406991\pi\)
−0.867678 + 0.497126i \(0.834389\pi\)
\(158\) 0.880387 + 5.37013i 0.0700399 + 0.427224i
\(159\) 0 0
\(160\) −2.69114 0.906750i −0.212753 0.0716849i
\(161\) 6.13964 + 9.05528i 0.483871 + 0.713656i
\(162\) 0 0
\(163\) −7.48651 + 8.81380i −0.586388 + 0.690350i −0.972713 0.232013i \(-0.925469\pi\)
0.386324 + 0.922363i \(0.373745\pi\)
\(164\) 2.89866 + 2.74576i 0.226347 + 0.214408i
\(165\) 0 0
\(166\) 2.39188 3.52777i 0.185646 0.273808i
\(167\) 3.21429 2.44344i 0.248729 0.189079i −0.473380 0.880858i \(-0.656966\pi\)
0.722109 + 0.691780i \(0.243173\pi\)
\(168\) 0 0
\(169\) −0.167915 3.09700i −0.0129165 0.238231i
\(170\) 6.92251 2.33247i 0.530933 0.178892i
\(171\) 0 0
\(172\) −7.46395 + 0.811754i −0.569121 + 0.0618956i
\(173\) 3.10214 5.85125i 0.235851 0.444862i −0.737129 0.675752i \(-0.763819\pi\)
0.972980 + 0.230890i \(0.0741638\pi\)
\(174\) 0 0
\(175\) 16.5261 9.94343i 1.24926 0.751652i
\(176\) −2.97989 −0.224618
\(177\) 0 0
\(178\) 8.09084 0.606434
\(179\) −7.43790 + 4.47524i −0.555935 + 0.334495i −0.765639 0.643270i \(-0.777577\pi\)
0.209705 + 0.977765i \(0.432750\pi\)
\(180\) 0 0
\(181\) 3.00529 5.66857i 0.223381 0.421341i −0.746337 0.665568i \(-0.768189\pi\)
0.969718 + 0.244227i \(0.0785341\pi\)
\(182\) −16.0123 + 1.74144i −1.18691 + 0.129084i
\(183\) 0 0
\(184\) 7.22068 2.43293i 0.532315 0.179358i
\(185\) −0.348115 6.42061i −0.0255940 0.472053i
\(186\) 0 0
\(187\) −8.34045 + 6.34024i −0.609914 + 0.463645i
\(188\) 1.37642 2.03007i 0.100386 0.148058i
\(189\) 0 0
\(190\) 3.47489 + 3.29159i 0.252095 + 0.238797i
\(191\) 16.4433 19.3585i 1.18979 1.40073i 0.294266 0.955723i \(-0.404925\pi\)
0.895526 0.445009i \(-0.146799\pi\)
\(192\) 0 0
\(193\) 0.407806 + 0.601468i 0.0293545 + 0.0432946i 0.842083 0.539348i \(-0.181329\pi\)
−0.812729 + 0.582642i \(0.802019\pi\)
\(194\) −11.3019 3.80805i −0.811427 0.273402i
\(195\) 0 0
\(196\) 1.33806 + 8.16183i 0.0955760 + 0.582988i
\(197\) 0.971271 2.43771i 0.0692002 0.173679i −0.890309 0.455357i \(-0.849512\pi\)
0.959509 + 0.281678i \(0.0908909\pi\)
\(198\) 0 0
\(199\) 0.0527440 0.972806i 0.00373892 0.0689604i −0.996068 0.0885868i \(-0.971765\pi\)
0.999807 + 0.0196264i \(0.00624769\pi\)
\(200\) −3.59356 12.9429i −0.254103 0.915198i
\(201\) 0 0
\(202\) −0.224636 + 0.0494461i −0.0158053 + 0.00347902i
\(203\) 34.9866 + 7.70113i 2.45558 + 0.540513i
\(204\) 0 0
\(205\) 0.782472 4.77287i 0.0546502 0.333351i
\(206\) −6.10543 3.67352i −0.425386 0.255946i
\(207\) 0 0
\(208\) −1.14376 + 6.97664i −0.0793056 + 0.483743i
\(209\) −6.23019 2.88239i −0.430951 0.199379i
\(210\) 0 0
\(211\) −3.55199 + 0.781851i −0.244529 + 0.0538248i −0.335544 0.942025i \(-0.608920\pi\)
0.0910148 + 0.995850i \(0.470989\pi\)
\(212\) −0.829833 + 0.383922i −0.0569932 + 0.0263679i
\(213\) 0 0
\(214\) 0.623251 11.4952i 0.0426045 0.785795i
\(215\) 5.88790 + 6.93177i 0.401551 + 0.472743i
\(216\) 0 0
\(217\) −3.03645 18.5215i −0.206128 1.25732i
\(218\) 1.61864 5.82981i 0.109628 0.394845i
\(219\) 0 0
\(220\) −0.391723 0.577748i −0.0264100 0.0389518i
\(221\) 11.6427 + 21.9605i 0.783175 + 1.47722i
\(222\) 0 0
\(223\) 3.70796 + 3.51237i 0.248304 + 0.235206i 0.801721 0.597698i \(-0.203918\pi\)
−0.553417 + 0.832904i \(0.686677\pi\)
\(224\) 15.6311 + 1.69998i 1.04440 + 0.113585i
\(225\) 0 0
\(226\) 6.61851 5.03126i 0.440257 0.334674i
\(227\) −9.29992 + 8.80935i −0.617257 + 0.584697i −0.931094 0.364780i \(-0.881144\pi\)
0.313836 + 0.949477i \(0.398386\pi\)
\(228\) 0 0
\(229\) 20.8942 7.04007i 1.38073 0.465221i 0.471626 0.881799i \(-0.343667\pi\)
0.909100 + 0.416578i \(0.136771\pi\)
\(230\) −1.82149 1.38466i −0.120106 0.0913019i
\(231\) 0 0
\(232\) 11.6868 22.0436i 0.767273 1.44723i
\(233\) −4.30895 10.8147i −0.282289 0.708492i −0.999927 0.0120755i \(-0.996156\pi\)
0.717638 0.696416i \(-0.245223\pi\)
\(234\) 0 0
\(235\) −2.97111 −0.193814
\(236\) −2.59717 + 4.34648i −0.169061 + 0.282932i
\(237\) 0 0
\(238\) −34.6560 + 20.8518i −2.24642 + 1.35162i
\(239\) 4.80006 + 12.0472i 0.310490 + 0.779271i 0.998561 + 0.0536279i \(0.0170785\pi\)
−0.688071 + 0.725643i \(0.741542\pi\)
\(240\) 0 0
\(241\) −14.3385 + 1.55941i −0.923624 + 0.100450i −0.557557 0.830139i \(-0.688261\pi\)
−0.366066 + 0.930589i \(0.619296\pi\)
\(242\) 8.51898 + 6.47596i 0.547621 + 0.416290i
\(243\) 0 0
\(244\) 0.370254 + 6.82894i 0.0237031 + 0.437178i
\(245\) 7.27370 6.89001i 0.464699 0.440187i
\(246\) 0 0
\(247\) −9.13968 + 13.4800i −0.581544 + 0.857713i
\(248\) −12.9950 1.41329i −0.825184 0.0897442i
\(249\) 0 0
\(250\) −5.60424 + 6.59783i −0.354444 + 0.417283i
\(251\) −3.75643 7.08538i −0.237104 0.447225i 0.736194 0.676770i \(-0.236621\pi\)
−0.973298 + 0.229545i \(0.926276\pi\)
\(252\) 0 0
\(253\) 3.10974 + 1.04779i 0.195508 + 0.0658742i
\(254\) 4.84315 17.4434i 0.303886 1.09450i
\(255\) 0 0
\(256\) 5.14976 12.9249i 0.321860 0.807807i
\(257\) −16.5510 19.4853i −1.03242 1.21546i −0.976161 0.217046i \(-0.930358\pi\)
−0.0562614 0.998416i \(-0.517918\pi\)
\(258\) 0 0
\(259\) 9.52443 + 34.3039i 0.591820 + 2.13154i
\(260\) −1.50300 + 0.695362i −0.0932121 + 0.0431245i
\(261\) 0 0
\(262\) −9.36305 2.06096i −0.578451 0.127327i
\(263\) −20.8210 9.63280i −1.28388 0.593984i −0.345117 0.938560i \(-0.612161\pi\)
−0.938758 + 0.344576i \(0.888023\pi\)
\(264\) 0 0
\(265\) 0.949055 + 0.571027i 0.0583000 + 0.0350779i
\(266\) −22.7076 13.6627i −1.39229 0.837715i
\(267\) 0 0
\(268\) 0.767238 + 0.354962i 0.0468665 + 0.0216828i
\(269\) 29.4845 + 6.49003i 1.79770 + 0.395704i 0.982916 0.184056i \(-0.0589226\pi\)
0.814787 + 0.579760i \(0.196854\pi\)
\(270\) 0 0
\(271\) 6.39160 2.95707i 0.388262 0.179629i −0.216040 0.976384i \(-0.569314\pi\)
0.604302 + 0.796755i \(0.293452\pi\)
\(272\) 4.74940 + 17.1058i 0.287974 + 1.03719i
\(273\) 0 0
\(274\) 8.59716 + 10.1214i 0.519373 + 0.611454i
\(275\) 2.14124 5.37411i 0.129122 0.324071i
\(276\) 0 0
\(277\) −4.24669 + 15.2952i −0.255159 + 0.919000i 0.719349 + 0.694649i \(0.244440\pi\)
−0.974508 + 0.224351i \(0.927974\pi\)
\(278\) 20.5130 + 6.91163i 1.23029 + 0.414532i
\(279\) 0 0
\(280\) −5.09191 9.60436i −0.304300 0.573970i
\(281\) −6.91504 + 8.14101i −0.412517 + 0.485652i −0.928703 0.370824i \(-0.879075\pi\)
0.516187 + 0.856476i \(0.327351\pi\)
\(282\) 0 0
\(283\) −4.66278 0.507108i −0.277174 0.0301445i −0.0315236 0.999503i \(-0.510036\pi\)
−0.245650 + 0.969359i \(0.579001\pi\)
\(284\) 0.161378 0.238015i 0.00957602 0.0141236i
\(285\) 0 0
\(286\) −3.50736 + 3.32235i −0.207395 + 0.196455i
\(287\) 1.44979 + 26.7397i 0.0855781 + 1.57840i
\(288\) 0 0
\(289\) 36.1551 + 27.4844i 2.12677 + 1.61673i
\(290\) −7.44819 + 0.810040i −0.437373 + 0.0475672i
\(291\) 0 0
\(292\) −0.526342 1.32102i −0.0308019 0.0773068i
\(293\) 8.14496 4.90066i 0.475834 0.286300i −0.257365 0.966314i \(-0.582854\pi\)
0.733198 + 0.680015i \(0.238027\pi\)
\(294\) 0 0
\(295\) 6.12348 0.350737i 0.356523 0.0204207i
\(296\) 24.7949 1.44118
\(297\) 0 0
\(298\) 7.62752 + 19.1436i 0.441850 + 1.10896i
\(299\) 3.64673 6.87847i 0.210896 0.397792i
\(300\) 0 0
\(301\) −40.0882 30.4743i −2.31065 1.75651i
\(302\) 14.0055 4.71901i 0.805927 0.271548i
\(303\) 0 0
\(304\) −8.44492 + 7.99946i −0.484350 + 0.458800i
\(305\) 6.59522 5.01356i 0.377641 0.287075i
\(306\) 0 0
\(307\) −9.36164 1.01814i −0.534297 0.0581083i −0.163006 0.986625i \(-0.552119\pi\)
−0.371291 + 0.928517i \(0.621085\pi\)
\(308\) 2.80583 + 2.65782i 0.159877 + 0.151443i
\(309\) 0 0
\(310\) 1.83861 + 3.46799i 0.104426 + 0.196968i
\(311\) −10.1967 15.0390i −0.578203 0.852785i 0.420306 0.907383i \(-0.361923\pi\)
−0.998508 + 0.0545974i \(0.982612\pi\)
\(312\) 0 0
\(313\) −5.64119 + 20.3177i −0.318859 + 1.14843i 0.614333 + 0.789047i \(0.289425\pi\)
−0.933192 + 0.359379i \(0.882989\pi\)
\(314\) 3.67574 + 22.4210i 0.207434 + 1.26529i
\(315\) 0 0
\(316\) −2.00554 2.36111i −0.112821 0.132823i
\(317\) 0.181796 3.35302i 0.0102107 0.188324i −0.988978 0.148060i \(-0.952697\pi\)
0.999189 0.0402646i \(-0.0128201\pi\)
\(318\) 0 0
\(319\) 9.75210 4.51180i 0.546013 0.252612i
\(320\) −6.71620 + 1.47835i −0.375447 + 0.0826422i
\(321\) 0 0
\(322\) 11.4975 + 5.31929i 0.640728 + 0.296432i
\(323\) −6.61633 + 40.3578i −0.368142 + 2.24557i
\(324\) 0 0
\(325\) −11.7602 7.07588i −0.652338 0.392499i
\(326\) −2.16636 + 13.2142i −0.119983 + 0.731866i
\(327\) 0 0
\(328\) 18.2143 + 4.00928i 1.00572 + 0.221376i
\(329\) 16.0657 3.53633i 0.885731 0.194964i
\(330\) 0 0
\(331\) −2.94133 10.5937i −0.161670 0.582282i −0.999348 0.0361174i \(-0.988501\pi\)
0.837678 0.546165i \(-0.183913\pi\)
\(332\) −0.131361 + 2.42281i −0.00720938 + 0.132969i
\(333\) 0 0
\(334\) 1.73049 4.34320i 0.0946881 0.237649i
\(335\) −0.165673 1.01056i −0.00905170 0.0552129i
\(336\) 0 0
\(337\) 25.2273 + 8.50006i 1.37422 + 0.463028i 0.907006 0.421118i \(-0.138362\pi\)
0.467212 + 0.884146i \(0.345259\pi\)
\(338\) −2.01544 2.97256i −0.109626 0.161686i
\(339\) 0 0
\(340\) −2.69217 + 3.16947i −0.146004 + 0.171889i
\(341\) −4.08705 3.87146i −0.221326 0.209651i
\(342\) 0 0
\(343\) −13.7626 + 20.2983i −0.743110 + 1.09601i
\(344\) −27.9197 + 21.2240i −1.50533 + 1.14432i
\(345\) 0 0
\(346\) −0.415173 7.65742i −0.0223199 0.411666i
\(347\) 8.50773 2.86659i 0.456719 0.153886i −0.0815329 0.996671i \(-0.525982\pi\)
0.538252 + 0.842784i \(0.319085\pi\)
\(348\) 0 0
\(349\) 21.2727 2.31354i 1.13870 0.123841i 0.480718 0.876875i \(-0.340376\pi\)
0.657982 + 0.753034i \(0.271410\pi\)
\(350\) 10.4609 19.7314i 0.559161 1.05469i
\(351\) 0 0
\(352\) 4.04101 2.43140i 0.215387 0.129594i
\(353\) −8.75208 −0.465826 −0.232913 0.972498i \(-0.574826\pi\)
−0.232913 + 0.972498i \(0.574826\pi\)
\(354\) 0 0
\(355\) −0.348346 −0.0184883
\(356\) −3.94664 + 2.37461i −0.209171 + 0.125854i
\(357\) 0 0
\(358\) −4.70815 + 8.88052i −0.248834 + 0.469350i
\(359\) −1.85696 + 0.201956i −0.0980065 + 0.0106588i −0.156991 0.987600i \(-0.550179\pi\)
0.0589844 + 0.998259i \(0.481214\pi\)
\(360\) 0 0
\(361\) −7.38848 + 2.48947i −0.388868 + 0.131025i
\(362\) −0.402212 7.41836i −0.0211398 0.389900i
\(363\) 0 0
\(364\) 7.29954 5.54897i 0.382600 0.290845i
\(365\) −0.966689 + 1.42576i −0.0505988 + 0.0746277i
\(366\) 0 0
\(367\) −8.22928 7.79518i −0.429565 0.406905i 0.442133 0.896950i \(-0.354222\pi\)
−0.871698 + 0.490044i \(0.836981\pi\)
\(368\) 3.59982 4.23804i 0.187654 0.220923i
\(369\) 0 0
\(370\) −4.17836 6.16261i −0.217222 0.320379i
\(371\) −5.81150 1.95812i −0.301718 0.101661i
\(372\) 0 0
\(373\) −2.72783 16.6390i −0.141242 0.861537i −0.958464 0.285214i \(-0.907935\pi\)
0.817222 0.576323i \(-0.195513\pi\)
\(374\) −4.49028 + 11.2698i −0.232187 + 0.582745i
\(375\) 0 0
\(376\) 0.620265 11.4401i 0.0319877 0.589979i
\(377\) −6.82008 24.5637i −0.351252 1.26510i
\(378\) 0 0
\(379\) 7.93556 1.74675i 0.407622 0.0897244i −0.00642610 0.999979i \(-0.502046\pi\)
0.414048 + 0.910255i \(0.364114\pi\)
\(380\) −2.66108 0.585749i −0.136511 0.0300483i
\(381\) 0 0
\(382\) 4.75816 29.0235i 0.243448 1.48497i
\(383\) −24.6615 14.8383i −1.26014 0.758204i −0.280676 0.959802i \(-0.590559\pi\)
−0.979468 + 0.201599i \(0.935386\pi\)
\(384\) 0 0
\(385\) 0.757412 4.62001i 0.0386013 0.235457i
\(386\) 0.763682 + 0.353317i 0.0388704 + 0.0179833i
\(387\) 0 0
\(388\) 6.63058 1.45950i 0.336617 0.0740950i
\(389\) 3.20473 1.48267i 0.162486 0.0751742i −0.336960 0.941519i \(-0.609399\pi\)
0.499447 + 0.866345i \(0.333537\pi\)
\(390\) 0 0
\(391\) 1.05840 19.5211i 0.0535258 0.987226i
\(392\) 25.0112 + 29.4454i 1.26326 + 1.48722i
\(393\) 0 0
\(394\) −0.491576 2.99848i −0.0247652 0.151061i
\(395\) −1.00395 + 3.61591i −0.0505143 + 0.181936i
\(396\) 0 0
\(397\) −4.77515 7.04282i −0.239658 0.353469i 0.688771 0.724979i \(-0.258151\pi\)
−0.928429 + 0.371510i \(0.878840\pi\)
\(398\) −0.528412 0.996690i −0.0264869 0.0499595i
\(399\) 0 0
\(400\) −7.11670 6.74129i −0.355835 0.337065i
\(401\) −24.9046 2.70854i −1.24368 0.135258i −0.537482 0.843275i \(-0.680624\pi\)
−0.706195 + 0.708017i \(0.749590\pi\)
\(402\) 0 0
\(403\) −10.6327 + 8.08278i −0.529654 + 0.402632i
\(404\) 0.0950632 0.0900486i 0.00472957 0.00448009i
\(405\) 0 0
\(406\) 39.3106 13.2453i 1.95095 0.657352i
\(407\) 8.50105 + 6.46233i 0.421382 + 0.320326i
\(408\) 0 0
\(409\) −7.67640 + 14.4792i −0.379574 + 0.715952i −0.997529 0.0702616i \(-0.977617\pi\)
0.617955 + 0.786214i \(0.287961\pi\)
\(410\) −2.07294 5.20268i −0.102375 0.256942i
\(411\) 0 0
\(412\) 4.05633 0.199841
\(413\) −32.6941 + 9.18496i −1.60877 + 0.451962i
\(414\) 0 0
\(415\) 2.51849 1.51533i 0.123628 0.0743845i
\(416\) −4.14143 10.3942i −0.203050 0.509618i
\(417\) 0 0
\(418\) −7.90223 + 0.859419i −0.386511 + 0.0420356i
\(419\) 17.9264 + 13.6273i 0.875760 + 0.665735i 0.943286 0.331982i \(-0.107717\pi\)
−0.0675257 + 0.997718i \(0.521510\pi\)
\(420\) 0 0
\(421\) 1.51998 + 28.0343i 0.0740791 + 1.36631i 0.765304 + 0.643669i \(0.222589\pi\)
−0.691225 + 0.722640i \(0.742928\pi\)
\(422\) −3.05748 + 2.89620i −0.148836 + 0.140985i
\(423\) 0 0
\(424\) −2.39684 + 3.53508i −0.116401 + 0.171679i
\(425\) −34.2623 3.72625i −1.66196 0.180749i
\(426\) 0 0
\(427\) −29.6951 + 34.9598i −1.43705 + 1.69182i
\(428\) 3.06975 + 5.79016i 0.148382 + 0.279878i
\(429\) 0 0
\(430\) 9.98000 + 3.36265i 0.481278 + 0.162162i
\(431\) 3.64968 13.1450i 0.175799 0.633170i −0.822157 0.569261i \(-0.807229\pi\)
0.997956 0.0639092i \(-0.0203568\pi\)
\(432\) 0 0
\(433\) −1.95391 + 4.90393i −0.0938987 + 0.235668i −0.968423 0.249314i \(-0.919795\pi\)
0.874524 + 0.484982i \(0.161174\pi\)
\(434\) −14.0697 16.5641i −0.675366 0.795102i
\(435\) 0 0
\(436\) 0.921456 + 3.31879i 0.0441298 + 0.158941i
\(437\) 11.6257 5.37861i 0.556132 0.257294i
\(438\) 0 0
\(439\) −29.8771 6.57644i −1.42595 0.313876i −0.566066 0.824360i \(-0.691535\pi\)
−0.859888 + 0.510484i \(0.829466\pi\)
\(440\) −2.95923 1.36908i −0.141076 0.0652685i
\(441\) 0 0
\(442\) 24.6617 + 14.8384i 1.17304 + 0.705793i
\(443\) 13.4066 + 8.06647i 0.636966 + 0.383250i 0.797102 0.603845i \(-0.206366\pi\)
−0.160135 + 0.987095i \(0.551193\pi\)
\(444\) 0 0
\(445\) 5.06379 + 2.34276i 0.240047 + 0.111058i
\(446\) 5.77579 + 1.27135i 0.273492 + 0.0602001i
\(447\) 0 0
\(448\) 34.5570 15.9878i 1.63267 0.755352i
\(449\) 9.31068 + 33.5340i 0.439398 + 1.58257i 0.769515 + 0.638629i \(0.220498\pi\)
−0.330117 + 0.943940i \(0.607088\pi\)
\(450\) 0 0
\(451\) 5.19993 + 6.12183i 0.244855 + 0.288266i
\(452\) −1.75180 + 4.39669i −0.0823978 + 0.206803i
\(453\) 0 0
\(454\) −3.96825 + 14.2923i −0.186239 + 0.670773i
\(455\) −10.5258 3.54656i −0.493458 0.166265i
\(456\) 0 0
\(457\) −3.79277 7.15393i −0.177418 0.334647i 0.778814 0.627255i \(-0.215822\pi\)
−0.956232 + 0.292608i \(0.905477\pi\)
\(458\) 16.5281 19.4584i 0.772308 0.909231i
\(459\) 0 0
\(460\) 1.29490 + 0.140828i 0.0603748 + 0.00656616i
\(461\) −3.00186 + 4.42741i −0.139811 + 0.206205i −0.891148 0.453714i \(-0.850099\pi\)
0.751337 + 0.659919i \(0.229409\pi\)
\(462\) 0 0
\(463\) −2.09195 + 1.98160i −0.0972214 + 0.0920930i −0.734767 0.678320i \(-0.762708\pi\)
0.637545 + 0.770413i \(0.279950\pi\)
\(464\) −0.985752 18.1811i −0.0457624 0.844038i
\(465\) 0 0
\(466\) −10.7314 8.15779i −0.497122 0.377902i
\(467\) −10.0330 + 1.09115i −0.464272 + 0.0504926i −0.337266 0.941409i \(-0.609502\pi\)
−0.127006 + 0.991902i \(0.540537\pi\)
\(468\) 0 0
\(469\) 2.09866 + 5.26724i 0.0969071 + 0.243218i
\(470\) −2.94789 + 1.77369i −0.135976 + 0.0818140i
\(471\) 0 0
\(472\) 0.0721257 + 23.6514i 0.00331986 + 1.08864i
\(473\) −15.1040 −0.694483
\(474\) 0 0
\(475\) −8.35846 20.9782i −0.383513 0.962544i
\(476\) 10.7850 20.3426i 0.494329 0.932404i
\(477\) 0 0
\(478\) 11.9545 + 9.08756i 0.546785 + 0.415655i
\(479\) 37.0448 12.4818i 1.69262 0.570310i 0.702642 0.711543i \(-0.252003\pi\)
0.989976 + 0.141234i \(0.0451069\pi\)
\(480\) 0 0
\(481\) 18.3928 17.4226i 0.838639 0.794401i
\(482\) −13.2955 + 10.1070i −0.605594 + 0.460360i
\(483\) 0 0
\(484\) −6.05613 0.658644i −0.275279 0.0299383i
\(485\) −5.97083 5.65587i −0.271121 0.256820i
\(486\) 0 0
\(487\) −8.04378 15.1722i −0.364498 0.687517i 0.631645 0.775258i \(-0.282380\pi\)
−0.996143 + 0.0877408i \(0.972035\pi\)
\(488\) 17.9276 + 26.4412i 0.811545 + 1.19694i
\(489\) 0 0
\(490\) 3.10367 11.1784i 0.140209 0.504989i
\(491\) −5.31911 32.4451i −0.240048 1.46423i −0.781716 0.623635i \(-0.785655\pi\)
0.541668 0.840593i \(-0.317793\pi\)
\(492\) 0 0
\(493\) −41.4426 48.7900i −1.86648 2.19739i
\(494\) −1.02098 + 18.8309i −0.0459360 + 0.847240i
\(495\) 0 0
\(496\) −8.65768 + 4.00547i −0.388741 + 0.179851i
\(497\) 1.88362 0.414616i 0.0844918 0.0185981i
\(498\) 0 0
\(499\) −38.9781 18.0332i −1.74490 0.807277i −0.988135 0.153589i \(-0.950917\pi\)
−0.756765 0.653687i \(-0.773221\pi\)
\(500\) 0.797276 4.86317i 0.0356553 0.217487i
\(501\) 0 0
\(502\) −7.95689 4.78750i −0.355133 0.213677i
\(503\) −3.93390 + 23.9957i −0.175404 + 1.06992i 0.741543 + 0.670906i \(0.234095\pi\)
−0.916946 + 0.399010i \(0.869354\pi\)
\(504\) 0 0
\(505\) −0.154910 0.0340982i −0.00689340 0.00151735i
\(506\) 3.71094 0.816840i 0.164972 0.0363130i
\(507\) 0 0
\(508\) 2.75710 + 9.93018i 0.122327 + 0.440580i
\(509\) 2.07068 38.1914i 0.0917813 1.69281i −0.483893 0.875127i \(-0.660778\pi\)
0.575674 0.817679i \(-0.304740\pi\)
\(510\) 0 0
\(511\) 3.53020 8.86012i 0.156167 0.391949i
\(512\) −3.53167 21.5422i −0.156079 0.952041i
\(513\) 0 0
\(514\) −28.0540 9.45248i −1.23741 0.416931i
\(515\) −2.75750 4.06701i −0.121510 0.179214i
\(516\) 0 0
\(517\) 3.19431 3.76063i 0.140486 0.165392i
\(518\) 29.9287 + 28.3499i 1.31499 + 1.24562i
\(519\) 0 0
\(520\) −4.34118 + 6.40276i −0.190373 + 0.280780i
\(521\) 33.7434 25.6510i 1.47832 1.12379i 0.514420 0.857538i \(-0.328007\pi\)
0.963903 0.266254i \(-0.0857860\pi\)
\(522\) 0 0
\(523\) 0.484092 + 8.92856i 0.0211679 + 0.390419i 0.989850 + 0.142115i \(0.0453903\pi\)
−0.968682 + 0.248304i \(0.920127\pi\)
\(524\) 5.17209 1.74268i 0.225944 0.0761293i
\(525\) 0 0
\(526\) −26.4088 + 2.87213i −1.15148 + 0.125231i
\(527\) −15.7097 + 29.6317i −0.684326 + 1.29078i
\(528\) 0 0
\(529\) 14.4609 8.70081i 0.628733 0.378296i
\(530\) 1.28253 0.0557095
\(531\) 0 0
\(532\) 15.0865 0.654082
\(533\) 16.3285 9.82454i 0.707267 0.425548i
\(534\) 0 0
\(535\) 3.71858 7.01399i 0.160768 0.303241i
\(536\) 3.92571 0.426947i 0.169565 0.0184413i
\(537\) 0 0
\(538\) 33.1285 11.1623i 1.42827 0.481240i
\(539\) 0.900795 + 16.6142i 0.0388000 + 0.715624i
\(540\) 0 0
\(541\) −3.00212 + 2.28215i −0.129071 + 0.0981174i −0.667718 0.744414i \(-0.732729\pi\)
0.538647 + 0.842532i \(0.318936\pi\)
\(542\) 4.57634 6.74960i 0.196571 0.289920i
\(543\) 0 0
\(544\) −20.3978 19.3218i −0.874549 0.828417i
\(545\) 2.70112 3.18000i 0.115703 0.136216i
\(546\) 0 0
\(547\) −13.9910 20.6352i −0.598214 0.882300i 0.401219 0.915982i \(-0.368587\pi\)
−0.999433 + 0.0336828i \(0.989276\pi\)
\(548\) −7.16417 2.41389i −0.306038 0.103116i
\(549\) 0 0
\(550\) −1.08372 6.61038i −0.0462098 0.281868i
\(551\) 15.5253 38.9656i 0.661400 1.65999i
\(552\) 0 0
\(553\) 1.12489 20.7473i 0.0478350 0.882265i
\(554\) 4.91739 + 17.7109i 0.208920 + 0.752462i
\(555\) 0 0
\(556\) −12.0346 + 2.64901i −0.510379 + 0.112343i
\(557\) −36.6543 8.06823i −1.55309 0.341862i −0.646183 0.763183i \(-0.723636\pi\)
−0.906912 + 0.421321i \(0.861567\pi\)
\(558\) 0 0
\(559\) −5.79732 + 35.3621i −0.245200 + 1.49566i
\(560\) −6.79756 4.08996i −0.287250 0.172832i
\(561\) 0 0
\(562\) −2.00099 + 12.2055i −0.0844067 + 0.514858i
\(563\) 3.18405 + 1.47310i 0.134192 + 0.0620837i 0.485836 0.874050i \(-0.338515\pi\)
−0.351644 + 0.936134i \(0.614377\pi\)
\(564\) 0 0
\(565\) 5.59914 1.23246i 0.235558 0.0518502i
\(566\) −4.92908 + 2.28043i −0.207184 + 0.0958537i
\(567\) 0 0
\(568\) 0.0727227 1.34129i 0.00305138 0.0562793i
\(569\) 9.96616 + 11.7331i 0.417803 + 0.491876i 0.930293 0.366817i \(-0.119553\pi\)
−0.512490 + 0.858693i \(0.671277\pi\)
\(570\) 0 0
\(571\) −5.59746 34.1430i −0.234246 1.42884i −0.797881 0.602815i \(-0.794046\pi\)
0.563635 0.826024i \(-0.309402\pi\)
\(572\) 0.735768 2.65000i 0.0307640 0.110802i
\(573\) 0 0
\(574\) 17.4015 + 25.6652i 0.726323 + 1.07125i
\(575\) 5.05642 + 9.53742i 0.210867 + 0.397738i
\(576\) 0 0
\(577\) −7.20125 6.82139i −0.299792 0.283978i 0.522986 0.852342i \(-0.324818\pi\)
−0.822778 + 0.568363i \(0.807577\pi\)
\(578\) 52.2801 + 5.68580i 2.17456 + 0.236498i
\(579\) 0 0
\(580\) 3.39541 2.58113i 0.140987 0.107175i
\(581\) −11.8147 + 11.1915i −0.490155 + 0.464300i
\(582\) 0 0
\(583\) −1.74312 + 0.587326i −0.0721927 + 0.0243245i
\(584\) −5.28801 4.01984i −0.218819 0.166342i
\(585\) 0 0
\(586\) 5.15572 9.72472i 0.212981 0.401724i
\(587\) −10.6872 26.8227i −0.441106 1.10709i −0.966599 0.256295i \(-0.917498\pi\)
0.525493 0.850798i \(-0.323881\pi\)
\(588\) 0 0
\(589\) −21.9754 −0.905481
\(590\) 5.86624 4.00358i 0.241509 0.164825i
\(591\) 0 0
\(592\) 15.5046 9.32880i 0.637235 0.383411i
\(593\) 0.0333929 + 0.0838098i 0.00137128 + 0.00344166i 0.929661 0.368417i \(-0.120100\pi\)
−0.928289 + 0.371858i \(0.878721\pi\)
\(594\) 0 0
\(595\) −27.7279 + 3.01559i −1.13673 + 0.123627i
\(596\) −9.33916 7.09945i −0.382547 0.290805i
\(597\) 0 0
\(598\) −0.488059 9.00173i −0.0199582 0.368108i
\(599\) −4.53741 + 4.29806i −0.185393 + 0.175614i −0.774767 0.632246i \(-0.782133\pi\)
0.589374 + 0.807860i \(0.299374\pi\)
\(600\) 0 0
\(601\) −0.938158 + 1.38368i −0.0382683 + 0.0564415i −0.846342 0.532640i \(-0.821200\pi\)
0.808074 + 0.589082i \(0.200510\pi\)
\(602\) −57.9673 6.30433i −2.36257 0.256945i
\(603\) 0 0
\(604\) −5.44676 + 6.41242i −0.221625 + 0.260918i
\(605\) 3.45659 + 6.51982i 0.140530 + 0.265068i
\(606\) 0 0
\(607\) 0.934319 + 0.314809i 0.0379228 + 0.0127777i 0.338199 0.941075i \(-0.390182\pi\)
−0.300276 + 0.953852i \(0.597079\pi\)
\(608\) 4.92507 17.7385i 0.199738 0.719392i
\(609\) 0 0
\(610\) 3.55069 8.91157i 0.143763 0.360819i
\(611\) −7.57847 8.92207i −0.306592 0.360948i
\(612\) 0 0
\(613\) 5.47497 + 19.7190i 0.221132 + 0.796445i 0.987975 + 0.154611i \(0.0494123\pi\)
−0.766844 + 0.641834i \(0.778174\pi\)
\(614\) −9.89628 + 4.57851i −0.399381 + 0.184774i
\(615\) 0 0
\(616\) 17.6310 + 3.88088i 0.710373 + 0.156365i
\(617\) 7.96916 + 3.68693i 0.320826 + 0.148430i 0.573692 0.819071i \(-0.305511\pi\)
−0.252865 + 0.967502i \(0.581373\pi\)
\(618\) 0 0
\(619\) 8.28427 + 4.98448i 0.332973 + 0.200343i 0.672215 0.740356i \(-0.265343\pi\)
−0.339242 + 0.940699i \(0.610171\pi\)
\(620\) −1.91469 1.15203i −0.0768957 0.0462666i
\(621\) 0 0
\(622\) −19.0950 8.83428i −0.765639 0.354222i
\(623\) −30.1700 6.64091i −1.20873 0.266063i
\(624\) 0 0
\(625\) 14.3779 6.65195i 0.575118 0.266078i
\(626\) 6.53213 + 23.5266i 0.261076 + 0.940312i
\(627\) 0 0
\(628\) −8.37342 9.85795i −0.334136 0.393375i
\(629\) 23.5473 59.0992i 0.938891 2.35644i
\(630\) 0 0
\(631\) −2.67131 + 9.62119i −0.106343 + 0.383014i −0.997499 0.0706843i \(-0.977482\pi\)
0.891156 + 0.453698i \(0.149896\pi\)
\(632\) −13.7133 4.62055i −0.545486 0.183796i
\(633\) 0 0
\(634\) −1.82130 3.43534i −0.0723332 0.136435i
\(635\) 8.08204 9.51491i 0.320726 0.377588i
\(636\) 0 0
\(637\) 39.2435 + 4.26799i 1.55488 + 0.169104i
\(638\) 6.98244 10.2983i 0.276437 0.407714i
\(639\) 0 0
\(640\) −1.65782 + 1.57037i −0.0655310 + 0.0620742i
\(641\) 1.42450 + 26.2733i 0.0562642 + 1.03773i 0.881272 + 0.472610i \(0.156688\pi\)
−0.825008 + 0.565122i \(0.808829\pi\)
\(642\) 0 0
\(643\) 4.57009 + 3.47409i 0.180227 + 0.137005i 0.691398 0.722474i \(-0.256995\pi\)
−0.511171 + 0.859479i \(0.670788\pi\)
\(644\) −7.16953 + 0.779733i −0.282519 + 0.0307258i
\(645\) 0 0
\(646\) 17.5281 + 43.9922i 0.689633 + 1.73085i
\(647\) −1.57126 + 0.945395i −0.0617726 + 0.0371673i −0.546105 0.837717i \(-0.683890\pi\)
0.484333 + 0.874884i \(0.339062\pi\)
\(648\) 0 0
\(649\) −6.13956 + 8.12779i −0.240999 + 0.319044i
\(650\) −15.8924 −0.623352
\(651\) 0 0
\(652\) −2.82155 7.08157i −0.110501 0.277336i
\(653\) −16.4492 + 31.0265i −0.643707 + 1.21416i 0.320056 + 0.947399i \(0.396298\pi\)
−0.963763 + 0.266762i \(0.914046\pi\)
\(654\) 0 0
\(655\) −5.26326 4.00103i −0.205653 0.156333i
\(656\) 12.8981 4.34588i 0.503587 0.169678i
\(657\) 0 0
\(658\) 13.8290 13.0996i 0.539112 0.510674i
\(659\) 12.7676 9.70566i 0.497354 0.378079i −0.326214 0.945296i \(-0.605773\pi\)
0.823568 + 0.567217i \(0.191980\pi\)
\(660\) 0 0
\(661\) 16.0604 + 1.74667i 0.624677 + 0.0679377i 0.414983 0.909829i \(-0.363788\pi\)
0.209694 + 0.977767i \(0.432753\pi\)
\(662\) −9.24254 8.75500i −0.359222 0.340273i
\(663\) 0 0
\(664\) 5.30892 + 10.0137i 0.206026 + 0.388606i
\(665\) −10.2558 15.1262i −0.397704 0.586569i
\(666\) 0 0
\(667\) −5.36416 + 19.3200i −0.207701 + 0.748072i
\(668\) 0.430586 + 2.62646i 0.0166599 + 0.101621i
\(669\) 0 0
\(670\) −0.767662 0.903761i −0.0296574 0.0349153i
\(671\) −0.744852 + 13.7380i −0.0287547 + 0.530349i
\(672\) 0 0
\(673\) 31.4438 14.5475i 1.21207 0.560763i 0.293476 0.955966i \(-0.405188\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(674\) 30.1045 6.62649i 1.15958 0.255243i
\(675\) 0 0
\(676\) 1.85554 + 0.858465i 0.0713670 + 0.0330179i
\(677\) 5.73680 34.9929i 0.220483 1.34489i −0.612009 0.790851i \(-0.709638\pi\)
0.832492 0.554037i \(-0.186913\pi\)
\(678\) 0 0
\(679\) 39.0180 + 23.4763i 1.49737 + 0.900939i
\(680\) −3.14263 + 19.1692i −0.120514 + 0.735106i
\(681\) 0 0
\(682\) −6.36628 1.40132i −0.243777 0.0536595i
\(683\) −48.6714 + 10.7134i −1.86236 + 0.409936i −0.995990 0.0894664i \(-0.971484\pi\)
−0.866370 + 0.499403i \(0.833553\pi\)
\(684\) 0 0
\(685\) 2.44997 + 8.82400i 0.0936086 + 0.337148i
\(686\) −1.53740 + 28.3556i −0.0586981 + 1.08262i
\(687\) 0 0
\(688\) −9.47325 + 23.7761i −0.361164 + 0.906454i
\(689\) 0.706013 + 4.30649i 0.0268970 + 0.164064i
\(690\) 0 0
\(691\) −28.1356 9.47999i −1.07033 0.360636i −0.271652 0.962396i \(-0.587570\pi\)
−0.798677 + 0.601760i \(0.794466\pi\)
\(692\) 2.44992 + 3.61337i 0.0931321 + 0.137360i
\(693\) 0 0
\(694\) 6.72995 7.92311i 0.255465 0.300757i
\(695\) 10.8371 + 10.2654i 0.411075 + 0.389391i
\(696\) 0 0
\(697\) 26.8540 39.6067i 1.01717 1.50021i
\(698\) 19.7253 14.9948i 0.746613 0.567560i
\(699\) 0 0
\(700\) 0.688304 + 12.6950i 0.0260155 + 0.479827i
\(701\) −25.8068 + 8.69531i −0.974708 + 0.328417i −0.761195 0.648523i \(-0.775387\pi\)
−0.213513 + 0.976940i \(0.568490\pi\)
\(702\) 0 0
\(703\) 41.4397 4.50684i 1.56293 0.169979i
\(704\) 5.34956 10.0903i 0.201619 0.380294i
\(705\) 0 0
\(706\) −8.68368 + 5.22479i −0.326814 + 0.196638i
\(707\) 0.878231 0.0330293
\(708\) 0 0
\(709\) 26.0629 0.978812 0.489406 0.872056i \(-0.337214\pi\)
0.489406 + 0.872056i \(0.337214\pi\)
\(710\) −0.345624 + 0.207955i −0.0129710 + 0.00780441i
\(711\) 0 0
\(712\) −10.0778 + 19.0088i −0.377683 + 0.712386i
\(713\) 10.4433 1.13578i 0.391106 0.0425353i
\(714\) 0 0
\(715\) −3.15715 + 1.06377i −0.118071 + 0.0397827i
\(716\) −0.309785 5.71365i −0.0115772 0.213529i
\(717\) 0 0
\(718\) −1.72188 + 1.30894i −0.0642600 + 0.0488492i
\(719\) −24.8663 + 36.6750i −0.927356 + 1.36775i 0.00256756 + 0.999997i \(0.499183\pi\)
−0.929924 + 0.367752i \(0.880128\pi\)
\(720\) 0 0
\(721\) 19.7514 + 18.7095i 0.735579 + 0.696778i
\(722\) −5.84458 + 6.88077i −0.217513 + 0.256076i
\(723\) 0 0
\(724\) 2.37344 + 3.50056i 0.0882081 + 0.130097i
\(725\) 33.4972 + 11.2865i 1.24405 + 0.419171i
\(726\) 0 0
\(727\) 2.96185 + 18.0665i 0.109849 + 0.670049i 0.983141 + 0.182851i \(0.0585326\pi\)
−0.873292 + 0.487198i \(0.838019\pi\)
\(728\) 15.8533 39.7888i 0.587562 1.47467i
\(729\) 0 0
\(730\) −0.107987 + 1.99171i −0.00399679 + 0.0737165i
\(731\) 24.0730 + 86.7030i 0.890371 + 3.20683i
\(732\) 0 0
\(733\) −32.1939 + 7.08642i −1.18911 + 0.261743i −0.765098 0.643914i \(-0.777309\pi\)
−0.424012 + 0.905657i \(0.639378\pi\)
\(734\) −12.8185 2.82157i −0.473140 0.104146i
\(735\) 0 0
\(736\) −1.42373 + 8.68439i −0.0524795 + 0.320111i
\(737\) 1.45722 + 0.876782i 0.0536775 + 0.0322967i
\(738\) 0 0
\(739\) −3.02035 + 18.4233i −0.111106 + 0.677714i 0.871271 + 0.490802i \(0.163296\pi\)
−0.982377 + 0.186912i \(0.940152\pi\)
\(740\) 3.84685 + 1.77974i 0.141413 + 0.0654246i
\(741\) 0 0
\(742\) −6.93503 + 1.52652i −0.254593 + 0.0560402i
\(743\) −42.5593 + 19.6900i −1.56135 + 0.722357i −0.994817 0.101683i \(-0.967577\pi\)
−0.566531 + 0.824040i \(0.691715\pi\)
\(744\) 0 0
\(745\) −0.769358 + 14.1900i −0.0281871 + 0.519880i
\(746\) −12.6397 14.8805i −0.462771 0.544816i
\(747\) 0 0
\(748\) −1.11729 6.81515i −0.0408520 0.249186i
\(749\) −11.7592 + 42.3529i −0.429672 + 1.54754i
\(750\) 0 0
\(751\) 0.750798 + 1.10734i 0.0273970 + 0.0404075i 0.841141 0.540816i \(-0.181885\pi\)
−0.813744 + 0.581224i \(0.802574\pi\)
\(752\) −3.91635 7.38702i −0.142815 0.269377i
\(753\) 0 0
\(754\) −21.4308 20.3003i −0.780463 0.739294i
\(755\) 10.1320 + 1.10192i 0.368742 + 0.0401031i
\(756\) 0 0
\(757\) 18.7522 14.2551i 0.681561 0.518109i −0.206144 0.978522i \(-0.566092\pi\)
0.887705 + 0.460413i \(0.152299\pi\)
\(758\) 6.83077 6.47045i 0.248105 0.235017i
\(759\) 0 0
\(760\) −12.0616 + 4.06404i −0.437521 + 0.147418i
\(761\) 36.4550 + 27.7124i 1.32149 + 1.00457i 0.998303 + 0.0582398i \(0.0185488\pi\)
0.323191 + 0.946334i \(0.395244\pi\)
\(762\) 0 0
\(763\) −10.8208 + 20.4102i −0.391740 + 0.738900i
\(764\) 6.19722 + 15.5539i 0.224208 + 0.562719i
\(765\) 0 0
\(766\) −33.3269 −1.20415
\(767\) 16.6726 + 17.4938i 0.602011 + 0.631666i
\(768\) 0 0
\(769\) 6.84073 4.11593i 0.246683 0.148424i −0.386843 0.922146i \(-0.626434\pi\)
0.633526 + 0.773721i \(0.281607\pi\)
\(770\) −2.00655 5.03606i −0.0723110 0.181487i
\(771\) 0 0
\(772\) −0.476213 + 0.0517913i −0.0171393 + 0.00186401i
\(773\) −32.9287 25.0317i −1.18436 0.900328i −0.187721 0.982222i \(-0.560110\pi\)
−0.996641 + 0.0818941i \(0.973903\pi\)
\(774\) 0 0
\(775\) −1.00260 18.4919i −0.0360146 0.664250i
\(776\) 23.0242 21.8097i 0.826520 0.782921i
\(777\) 0 0
\(778\) 2.29457 3.38423i 0.0822642 0.121331i
\(779\) 31.1703 + 3.38998i 1.11679 + 0.121459i
\(780\) 0 0
\(781\) 0.374516 0.440914i 0.0134012 0.0157771i
\(782\) −10.6035 20.0004i −0.379182 0.715213i
\(783\) 0 0
\(784\) 26.7183 + 9.00245i 0.954225 + 0.321516i
\(785\) −4.19164 + 15.0969i −0.149606 + 0.538832i
\(786\) 0 0
\(787\) 4.31562 10.8314i 0.153835 0.386097i −0.831779 0.555106i \(-0.812678\pi\)
0.985614 + 0.169009i \(0.0540568\pi\)
\(788\) 1.11982 + 1.31836i 0.0398920 + 0.0469645i
\(789\) 0 0
\(790\) 1.16251 + 4.18699i 0.0413603 + 0.148966i
\(791\) −28.8094 + 13.3286i −1.02434 + 0.473912i
\(792\) 0 0
\(793\) 31.8780 + 7.01688i 1.13202 + 0.249177i
\(794\) −8.94224 4.13712i −0.317348 0.146821i
\(795\) 0 0
\(796\) 0.550276 + 0.331090i 0.0195040 + 0.0117352i
\(797\) −47.1170 28.3494i −1.66897 1.00419i −0.951526 0.307570i \(-0.900484\pi\)
−0.717444 0.696616i \(-0.754688\pi\)
\(798\) 0 0
\(799\) −26.6787 12.3429i −0.943823 0.436659i
\(800\) 15.1514 + 3.33507i 0.535682 + 0.117912i
\(801\) 0 0
\(802\) −26.3269 + 12.1801i −0.929636 + 0.430095i
\(803\) −0.765322 2.75644i −0.0270076 0.0972727i
\(804\) 0 0
\(805\) 5.65564 + 6.65834i 0.199335 + 0.234676i
\(806\) −5.72438 + 14.3671i −0.201633 + 0.506060i
\(807\) 0 0
\(808\) 0.163634 0.589355i 0.00575661 0.0207334i
\(809\) −28.7012 9.67056i −1.00908 0.339999i −0.234256 0.972175i \(-0.575265\pi\)
−0.774825 + 0.632176i \(0.782162\pi\)
\(810\) 0 0
\(811\) 7.12872 + 13.4462i 0.250323 + 0.472160i 0.976549 0.215297i \(-0.0690720\pi\)
−0.726225 + 0.687457i \(0.758727\pi\)
\(812\) −15.2879 + 17.9983i −0.536500 + 0.631617i
\(813\) 0 0
\(814\) 12.2925 + 1.33689i 0.430851 + 0.0468579i
\(815\) −5.18211 + 7.64305i −0.181522 + 0.267724i
\(816\) 0 0
\(817\) −42.8043 + 40.5464i −1.49753 + 1.41854i
\(818\) 1.02737 + 18.9487i 0.0359211 + 0.662526i
\(819\) 0 0
\(820\) 2.53811 + 1.92942i 0.0886348 + 0.0673784i
\(821\) −4.41732 + 0.480413i −0.154166 + 0.0167665i −0.184876 0.982762i \(-0.559188\pi\)
0.0307107 + 0.999528i \(0.490223\pi\)
\(822\) 0 0
\(823\) 6.28245 + 15.7678i 0.218992 + 0.549629i 0.996894 0.0787568i \(-0.0250951\pi\)
−0.777901 + 0.628386i \(0.783716\pi\)
\(824\) 16.2355 9.76857i 0.565590 0.340304i
\(825\) 0 0
\(826\) −26.9554 + 28.6308i −0.937898 + 0.996194i
\(827\) 31.3425 1.08988 0.544942 0.838474i \(-0.316552\pi\)
0.544942 + 0.838474i \(0.316552\pi\)
\(828\) 0 0
\(829\) −8.84002 22.1868i −0.307027 0.770579i −0.998824 0.0484870i \(-0.984560\pi\)
0.691797 0.722092i \(-0.256819\pi\)
\(830\) 1.59419 3.00697i 0.0553353 0.104373i
\(831\) 0 0
\(832\) −21.5706 16.3975i −0.747825 0.568482i
\(833\) 93.9364 31.6508i 3.25470 1.09664i
\(834\) 0 0
\(835\) 2.34066 2.21719i 0.0810019 0.0767291i
\(836\) 3.60240 2.73847i 0.124591 0.0947120i
\(837\) 0 0
\(838\) 25.9214 + 2.81913i 0.895441 + 0.0973851i
\(839\) 10.2400 + 9.69986i 0.353525 + 0.334876i 0.843767 0.536710i \(-0.180333\pi\)
−0.490242 + 0.871586i \(0.663092\pi\)
\(840\) 0 0
\(841\) 17.1699 + 32.3858i 0.592064 + 1.11675i
\(842\) 18.2440 + 26.9078i 0.628729 + 0.927305i
\(843\) 0 0
\(844\) 0.641393 2.31009i 0.0220776 0.0795165i
\(845\) −0.400676 2.44401i −0.0137837 0.0840766i
\(846\) 0 0
\(847\) −26.4510 31.1405i −0.908868 1.07000i
\(848\) −0.168745 + 3.11232i −0.00579472 + 0.106877i
\(849\) 0 0
\(850\) −36.2190 + 16.7567i −1.24230 + 0.574749i
\(851\) −19.4604 + 4.28356i −0.667093 + 0.146838i
\(852\) 0 0
\(853\) −4.49931 2.08160i −0.154053 0.0712727i 0.341347 0.939937i \(-0.389117\pi\)
−0.495401 + 0.868664i \(0.664979\pi\)
\(854\) −8.59281 + 52.4138i −0.294040 + 1.79356i
\(855\) 0 0
\(856\) 26.2308 + 15.7825i 0.896549 + 0.539435i
\(857\) 6.72149 40.9993i 0.229602 1.40051i −0.580519 0.814247i \(-0.697150\pi\)
0.810121 0.586263i \(-0.199401\pi\)
\(858\) 0 0
\(859\) −42.6648 9.39122i −1.45570 0.320424i −0.584519 0.811380i \(-0.698717\pi\)
−0.871184 + 0.490956i \(0.836648\pi\)
\(860\) −5.85507 + 1.28880i −0.199656 + 0.0439476i
\(861\) 0 0
\(862\) −4.22609 15.2210i −0.143941 0.518429i
\(863\) −0.837052 + 15.4385i −0.0284936 + 0.525533i 0.949093 + 0.314997i \(0.102004\pi\)
−0.977586 + 0.210536i \(0.932479\pi\)
\(864\) 0 0
\(865\) 1.95742 4.91275i 0.0665542 0.167038i
\(866\) 0.988904 + 6.03204i 0.0336043 + 0.204977i
\(867\) 0 0
\(868\) 11.7245 + 3.95045i 0.397956 + 0.134087i
\(869\) −3.49741 5.15829i −0.118641 0.174983i
\(870\) 0 0
\(871\) 2.61208 3.07517i 0.0885068 0.104198i
\(872\) 11.6805 + 11.0644i 0.395553 + 0.374688i
\(873\) 0 0
\(874\) 8.32391 12.2768i 0.281560 0.415270i
\(875\) 26.3131 20.0027i 0.889547 0.676216i
\(876\) 0 0
\(877\) −0.906204 16.7140i −0.0306003 0.564390i −0.973128 0.230263i \(-0.926041\pi\)
0.942528 0.334127i \(-0.108441\pi\)
\(878\) −33.5695 + 11.3109i −1.13292 + 0.381724i
\(879\) 0 0
\(880\) −2.36554 + 0.257268i −0.0797425 + 0.00867252i
\(881\) −13.9870 + 26.3823i −0.471235 + 0.888843i 0.527982 + 0.849256i \(0.322949\pi\)
−0.999216 + 0.0395869i \(0.987396\pi\)
\(882\) 0 0
\(883\) 35.5740 21.4042i 1.19716 0.720307i 0.229683 0.973266i \(-0.426231\pi\)
0.967477 + 0.252958i \(0.0814036\pi\)
\(884\) −16.3847 −0.551078
\(885\) 0 0
\(886\) 18.1173 0.608663
\(887\) 13.1844 7.93278i 0.442688 0.266357i −0.276711 0.960953i \(-0.589245\pi\)
0.719400 + 0.694596i \(0.244417\pi\)
\(888\) 0 0
\(889\) −32.3771 + 61.0697i −1.08589 + 2.04821i
\(890\) 6.42280 0.698521i 0.215293 0.0234145i
\(891\) 0 0
\(892\) −3.19051 + 1.07501i −0.106826 + 0.0359939i
\(893\) −1.04276 19.2326i −0.0348946 0.643593i
\(894\) 0 0
\(895\) −5.51810 + 4.19475i −0.184450 + 0.140215i
\(896\) 7.09522 10.4647i 0.237035 0.349600i
\(897\) 0 0
\(898\) 29.2570 + 27.7137i 0.976318 + 0.924817i
\(899\) 22.2688 26.2169i 0.742706 0.874381i
\(900\) 0 0
\(901\) 6.14969 + 9.07012i 0.204876 + 0.302170i
\(902\) 8.81388 + 2.96974i 0.293470 + 0.0988816i
\(903\) 0 0
\(904\) 3.57664 + 21.8165i 0.118957 + 0.725607i
\(905\) 1.89631 4.75937i 0.0630354 0.158207i
\(906\) 0 0
\(907\) 2.67775 49.3882i 0.0889132 1.63991i −0.525407 0.850851i \(-0.676087\pi\)
0.614321 0.789057i \(-0.289430\pi\)
\(908\) −2.25904 8.13633i −0.0749689 0.270014i
\(909\) 0 0
\(910\) −12.5608 + 2.76484i −0.416386 + 0.0916534i
\(911\) 46.2768 + 10.1863i 1.53322 + 0.337487i 0.899793 0.436317i \(-0.143717\pi\)
0.633425 + 0.773804i \(0.281648\pi\)
\(912\) 0 0
\(913\) −0.789692 + 4.81691i −0.0261350 + 0.159416i
\(914\) −8.03386 4.83381i −0.265737 0.159888i
\(915\) 0 0
\(916\) −2.35134 + 14.3425i −0.0776903 + 0.473890i
\(917\) 33.2223 + 15.3703i 1.09710 + 0.507571i
\(918\) 0 0
\(919\) 12.8102 2.81973i 0.422568 0.0930143i 0.00140458 0.999999i \(-0.499553\pi\)
0.421163 + 0.906985i \(0.361622\pi\)
\(920\) 5.52198 2.55474i 0.182054 0.0842273i
\(921\) 0 0
\(922\) −0.335333 + 6.18485i −0.0110436 + 0.203687i
\(923\) −0.888535 1.04606i −0.0292465 0.0344316i
\(924\) 0 0
\(925\) 5.68307 + 34.6652i 0.186858 + 1.13978i
\(926\) −0.892631 + 3.21497i −0.0293337 + 0.105650i
\(927\) 0 0
\(928\) 16.1714 + 23.8510i 0.530852 + 0.782948i
\(929\) 11.0864 + 20.9112i 0.363733 + 0.686073i 0.996065 0.0886242i \(-0.0282470\pi\)
−0.632332 + 0.774697i \(0.717902\pi\)
\(930\) 0 0
\(931\) 47.1532 + 44.6659i 1.54538 + 1.46387i
\(932\) 7.62893 + 0.829696i 0.249894 + 0.0271776i
\(933\) 0 0
\(934\) −9.30319 + 7.07210i −0.304410 + 0.231406i
\(935\) −6.07356 + 5.75318i −0.198627 + 0.188149i
\(936\) 0 0
\(937\) −6.61401 + 2.22852i −0.216070 + 0.0728025i −0.425255 0.905074i \(-0.639816\pi\)
0.209185 + 0.977876i \(0.432919\pi\)
\(938\) 5.22668 + 3.97322i 0.170657 + 0.129730i
\(939\) 0 0
\(940\) 0.917386 1.73037i 0.0299218 0.0564386i
\(941\) −14.4622 36.2975i −0.471455 1.18326i −0.951947 0.306264i \(-0.900921\pi\)
0.480491 0.877000i \(-0.340458\pi\)
\(942\) 0 0
\(943\) −14.9882 −0.488084
\(944\) 8.94366 + 14.7624i 0.291091 + 0.480475i
\(945\) 0 0
\(946\) −14.9860 + 9.01675i −0.487236 + 0.293160i
\(947\) 14.0994 + 35.3867i 0.458168 + 1.14991i 0.958756 + 0.284229i \(0.0917377\pi\)
−0.500588 + 0.865685i \(0.666883\pi\)
\(948\) 0 0
\(949\) −6.74723 + 0.733806i −0.219025 + 0.0238204i
\(950\) −20.8166 15.8244i −0.675381 0.513411i
\(951\) 0 0
\(952\) −5.82275 107.394i −0.188717 3.48067i
\(953\) −18.4851 + 17.5100i −0.598790 + 0.567204i −0.925894 0.377784i \(-0.876686\pi\)
0.327103 + 0.944989i \(0.393928\pi\)
\(954\) 0 0
\(955\) 11.3819 16.7871i 0.368310 0.543217i
\(956\) −8.49842 0.924259i −0.274859 0.0298927i
\(957\) 0 0
\(958\) 29.3039 34.4992i 0.946765 1.11462i
\(959\) −23.7504 44.7981i −0.766942 1.44661i
\(960\) 0 0
\(961\) 12.2990 + 4.14401i 0.396742 + 0.133678i
\(962\) 7.84815 28.2665i 0.253035 0.911348i
\(963\) 0 0
\(964\) 3.51908 8.83223i 0.113342 0.284467i
\(965\) 0.375658 + 0.442259i 0.0120929 + 0.0142368i
\(966\) 0 0
\(967\) 9.62691 + 34.6730i 0.309581 + 1.11501i 0.940677 + 0.339304i \(0.110192\pi\)
−0.631096 + 0.775705i \(0.717395\pi\)
\(968\) −25.8259 + 11.9483i −0.830075 + 0.384034i
\(969\) 0 0
\(970\) −9.30059 2.04722i −0.298624 0.0657321i
\(971\) −26.1848 12.1144i −0.840312 0.388770i −0.0479711 0.998849i \(-0.515276\pi\)
−0.792340 + 0.610079i \(0.791138\pi\)
\(972\) 0 0
\(973\) −70.8179 42.6097i −2.27032 1.36601i
\(974\) −17.0384 10.2516i −0.545944 0.328484i
\(975\) 0 0
\(976\) 21.1586 + 9.78900i 0.677269 + 0.313338i
\(977\) −26.9648 5.93540i −0.862680 0.189890i −0.238473 0.971149i \(-0.576647\pi\)
−0.624207 + 0.781259i \(0.714578\pi\)
\(978\) 0 0
\(979\) −8.40952 + 3.89066i −0.268769 + 0.124346i
\(980\) 1.76685 + 6.36362i 0.0564400 + 0.203278i
\(981\) 0 0
\(982\) −24.6465 29.0161i −0.786503 0.925943i
\(983\) −1.23721 + 3.10515i −0.0394607 + 0.0990390i −0.947386 0.320092i \(-0.896286\pi\)
0.907926 + 0.419131i \(0.137665\pi\)
\(984\) 0 0
\(985\) 0.560570 2.01899i 0.0178612 0.0643304i
\(986\) −70.2452 23.6684i −2.23706 0.753754i
\(987\) 0 0
\(988\) −5.02872 9.48516i −0.159985 0.301763i
\(989\) 18.2462 21.4811i 0.580195 0.683059i
\(990\) 0 0
\(991\) 3.89177 + 0.423256i 0.123626 + 0.0134452i 0.169723 0.985492i \(-0.445713\pi\)
−0.0460967 + 0.998937i \(0.514678\pi\)
\(992\) 8.47243 12.4959i 0.269000 0.396745i
\(993\) 0 0
\(994\) 1.62138 1.53585i 0.0514271 0.0487143i
\(995\) −0.0421169 0.776801i −0.00133520 0.0246262i
\(996\) 0 0
\(997\) 18.0485 + 13.7201i 0.571603 + 0.434521i 0.850632 0.525761i \(-0.176220\pi\)
−0.279029 + 0.960283i \(0.590013\pi\)
\(998\) −49.4389 + 5.37680i −1.56496 + 0.170200i
\(999\) 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 531.2.i.b.163.4 140
3.2 odd 2 177.2.e.b.163.2 yes 140
59.21 even 29 inner 531.2.i.b.316.4 140
177.80 odd 58 177.2.e.b.139.2 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.2.e.b.139.2 140 177.80 odd 58
177.2.e.b.163.2 yes 140 3.2 odd 2
531.2.i.b.163.4 140 1.1 even 1 trivial
531.2.i.b.316.4 140 59.21 even 29 inner