Properties

Label 625.2.d.m.501.1
Level $625$
Weight $2$
Character 625.501
Analytic conductor $4.991$
Analytic rank $0$
Dimension $16$
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] = [625,2,Mod(126,625)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(625, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("625.126");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.d (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 501.1
Root \(-1.51514i\) of defining polynomial
Character \(\chi\) \(=\) 625.501
Dual form 625.2.d.m.126.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.622258 + 1.91511i) q^{2} +(-2.44781 - 1.77844i) q^{3} +(-1.66242 - 1.20782i) q^{4} +(4.92909 - 3.58119i) q^{6} +0.369971 q^{7} +(0.0893841 - 0.0649413i) q^{8} +(1.90189 + 5.85342i) q^{9} +O(q^{10})\) \(q+(-0.622258 + 1.91511i) q^{2} +(-2.44781 - 1.77844i) q^{3} +(-1.66242 - 1.20782i) q^{4} +(4.92909 - 3.58119i) q^{6} +0.369971 q^{7} +(0.0893841 - 0.0649413i) q^{8} +(1.90189 + 5.85342i) q^{9} +(-0.539645 + 1.66086i) q^{11} +(1.92126 + 5.91304i) q^{12} +(0.344932 + 1.06159i) q^{13} +(-0.230218 + 0.708537i) q^{14} +(-1.20123 - 3.69700i) q^{16} +(-4.43988 + 3.22576i) q^{17} -12.3934 q^{18} +(3.03559 - 2.20548i) q^{19} +(-0.905621 - 0.657972i) q^{21} +(-2.84493 - 2.06696i) q^{22} +(2.23920 - 6.89154i) q^{23} -0.334290 q^{24} -2.24770 q^{26} +(2.94954 - 9.07774i) q^{27} +(-0.615049 - 0.446859i) q^{28} +(-3.39208 - 2.46449i) q^{29} +(-0.247303 + 0.179676i) q^{31} +8.04862 q^{32} +(4.27469 - 3.10574i) q^{33} +(-3.41495 - 10.5101i) q^{34} +(3.90813 - 12.0280i) q^{36} +(-2.84900 - 8.76833i) q^{37} +(2.33483 + 7.18587i) q^{38} +(1.04365 - 3.21202i) q^{39} +(-1.29367 - 3.98151i) q^{41} +(1.82362 - 1.32494i) q^{42} +7.17118 q^{43} +(2.90314 - 2.10925i) q^{44} +(11.8047 + 8.57663i) q^{46} +(-0.655524 - 0.476266i) q^{47} +(-3.63451 + 11.1859i) q^{48} -6.86312 q^{49} +16.6048 q^{51} +(0.708789 - 2.18143i) q^{52} +(3.16737 + 2.30123i) q^{53} +(15.5495 + 11.2974i) q^{54} +(0.0330695 - 0.0240264i) q^{56} -11.3529 q^{57} +(6.83052 - 4.96266i) q^{58} +(-0.573962 - 1.76647i) q^{59} +(2.99399 - 9.21454i) q^{61} +(-0.190214 - 0.585419i) q^{62} +(0.703645 + 2.16560i) q^{63} +(-2.60586 + 8.02002i) q^{64} +(3.28789 + 10.1191i) q^{66} +(10.0885 - 7.32972i) q^{67} +11.2771 q^{68} +(-17.7373 + 12.8869i) q^{69} +(-9.44666 - 6.86340i) q^{71} +(0.550127 + 0.399691i) q^{72} +(1.06035 - 3.26343i) q^{73} +18.5652 q^{74} -7.71026 q^{76} +(-0.199653 + 0.614470i) q^{77} +(5.50196 + 3.99741i) q^{78} +(-4.60610 - 3.34653i) q^{79} +(-8.42651 + 6.12222i) q^{81} +8.43005 q^{82} +(-5.77129 + 4.19309i) q^{83} +(0.710813 + 2.18766i) q^{84} +(-4.46232 + 13.7336i) q^{86} +(3.92023 + 12.0652i) q^{87} +(0.0596226 + 0.183499i) q^{88} +(0.472794 - 1.45511i) q^{89} +(0.127615 + 0.392758i) q^{91} +(-12.0462 + 8.75210i) q^{92} +0.924896 q^{93} +(1.32001 - 0.959043i) q^{94} +(-19.7015 - 14.3140i) q^{96} +(-5.17562 - 3.76031i) q^{97} +(4.27063 - 13.1437i) q^{98} -10.7480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9} - 3 q^{11} + 15 q^{12} - 5 q^{13} - q^{14} + q^{16} - 25 q^{17} - 10 q^{18} + 10 q^{19} + 7 q^{21} - 35 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} + 35 q^{28} - 8 q^{31} + 60 q^{32} - 6 q^{34} + q^{36} - 5 q^{37} - 35 q^{38} + q^{39} - 8 q^{41} - 10 q^{42} - 31 q^{44} + 42 q^{46} - 5 q^{47} - 25 q^{48} - 8 q^{49} - 28 q^{51} + 15 q^{52} - 10 q^{53} + 50 q^{54} + 35 q^{56} - 20 q^{57} + 35 q^{58} - 15 q^{59} + 17 q^{61} + 5 q^{62} + 10 q^{63} + 37 q^{64} + 44 q^{66} - 10 q^{67} + 80 q^{68} - 9 q^{69} - 13 q^{71} + 20 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 45 q^{77} + 5 q^{78} - 55 q^{79} - 19 q^{81} - 90 q^{82} - 15 q^{83} + 59 q^{84} + 7 q^{86} - 60 q^{87} + 40 q^{88} - 28 q^{91} + 45 q^{92} - 80 q^{93} + 4 q^{94} - 43 q^{96} + 40 q^{97} + 45 q^{98} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.622258 + 1.91511i −0.440003 + 1.35419i 0.447869 + 0.894099i \(0.352183\pi\)
−0.887872 + 0.460091i \(0.847817\pi\)
\(3\) −2.44781 1.77844i −1.41325 1.02678i −0.992841 0.119447i \(-0.961888\pi\)
−0.420406 0.907336i \(-0.638112\pi\)
\(4\) −1.66242 1.20782i −0.831211 0.603910i
\(5\) 0 0
\(6\) 4.92909 3.58119i 2.01229 1.46202i
\(7\) 0.369971 0.139836 0.0699180 0.997553i \(-0.477726\pi\)
0.0699180 + 0.997553i \(0.477726\pi\)
\(8\) 0.0893841 0.0649413i 0.0316020 0.0229602i
\(9\) 1.90189 + 5.85342i 0.633964 + 1.95114i
\(10\) 0 0
\(11\) −0.539645 + 1.66086i −0.162709 + 0.500767i −0.998860 0.0477321i \(-0.984801\pi\)
0.836151 + 0.548499i \(0.184801\pi\)
\(12\) 1.92126 + 5.91304i 0.554621 + 1.70695i
\(13\) 0.344932 + 1.06159i 0.0956668 + 0.294432i 0.987427 0.158076i \(-0.0505292\pi\)
−0.891760 + 0.452509i \(0.850529\pi\)
\(14\) −0.230218 + 0.708537i −0.0615283 + 0.189365i
\(15\) 0 0
\(16\) −1.20123 3.69700i −0.300307 0.924250i
\(17\) −4.43988 + 3.22576i −1.07683 + 0.782363i −0.977127 0.212655i \(-0.931789\pi\)
−0.0997024 + 0.995017i \(0.531789\pi\)
\(18\) −12.3934 −2.92116
\(19\) 3.03559 2.20548i 0.696411 0.505972i −0.182350 0.983234i \(-0.558370\pi\)
0.878761 + 0.477261i \(0.158370\pi\)
\(20\) 0 0
\(21\) −0.905621 0.657972i −0.197623 0.143581i
\(22\) −2.84493 2.06696i −0.606541 0.440678i
\(23\) 2.23920 6.89154i 0.466905 1.43699i −0.389666 0.920956i \(-0.627410\pi\)
0.856571 0.516029i \(-0.172590\pi\)
\(24\) −0.334290 −0.0682366
\(25\) 0 0
\(26\) −2.24770 −0.440811
\(27\) 2.94954 9.07774i 0.567639 1.74701i
\(28\) −0.615049 0.446859i −0.116233 0.0844484i
\(29\) −3.39208 2.46449i −0.629893 0.457644i 0.226470 0.974018i \(-0.427281\pi\)
−0.856363 + 0.516374i \(0.827281\pi\)
\(30\) 0 0
\(31\) −0.247303 + 0.179676i −0.0444170 + 0.0322708i −0.609772 0.792577i \(-0.708739\pi\)
0.565355 + 0.824848i \(0.308739\pi\)
\(32\) 8.04862 1.42281
\(33\) 4.27469 3.10574i 0.744127 0.540640i
\(34\) −3.41495 10.5101i −0.585659 1.80247i
\(35\) 0 0
\(36\) 3.90813 12.0280i 0.651355 2.00467i
\(37\) −2.84900 8.76833i −0.468373 1.44150i −0.854690 0.519138i \(-0.826253\pi\)
0.386317 0.922366i \(-0.373747\pi\)
\(38\) 2.33483 + 7.18587i 0.378760 + 1.16570i
\(39\) 1.04365 3.21202i 0.167117 0.514334i
\(40\) 0 0
\(41\) −1.29367 3.98151i −0.202038 0.621808i −0.999822 0.0188649i \(-0.993995\pi\)
0.797785 0.602943i \(-0.206005\pi\)
\(42\) 1.82362 1.32494i 0.281391 0.204443i
\(43\) 7.17118 1.09359 0.546797 0.837265i \(-0.315847\pi\)
0.546797 + 0.837265i \(0.315847\pi\)
\(44\) 2.90314 2.10925i 0.437664 0.317982i
\(45\) 0 0
\(46\) 11.8047 + 8.57663i 1.74051 + 1.26456i
\(47\) −0.655524 0.476266i −0.0956181 0.0694706i 0.538949 0.842338i \(-0.318822\pi\)
−0.634567 + 0.772868i \(0.718822\pi\)
\(48\) −3.63451 + 11.1859i −0.524597 + 1.61454i
\(49\) −6.86312 −0.980446
\(50\) 0 0
\(51\) 16.6048 2.32514
\(52\) 0.708789 2.18143i 0.0982913 0.302510i
\(53\) 3.16737 + 2.30123i 0.435072 + 0.316098i 0.783674 0.621173i \(-0.213343\pi\)
−0.348602 + 0.937271i \(0.613343\pi\)
\(54\) 15.5495 + 11.2974i 2.11602 + 1.53738i
\(55\) 0 0
\(56\) 0.0330695 0.0240264i 0.00441910 0.00321067i
\(57\) −11.3529 −1.50372
\(58\) 6.83052 4.96266i 0.896891 0.651630i
\(59\) −0.573962 1.76647i −0.0747235 0.229975i 0.906718 0.421738i \(-0.138580\pi\)
−0.981441 + 0.191762i \(0.938580\pi\)
\(60\) 0 0
\(61\) 2.99399 9.21454i 0.383341 1.17980i −0.554336 0.832293i \(-0.687028\pi\)
0.937677 0.347508i \(-0.112972\pi\)
\(62\) −0.190214 0.585419i −0.0241572 0.0743483i
\(63\) 0.703645 + 2.16560i 0.0886509 + 0.272840i
\(64\) −2.60586 + 8.02002i −0.325733 + 1.00250i
\(65\) 0 0
\(66\) 3.28789 + 10.1191i 0.404711 + 1.24557i
\(67\) 10.0885 7.32972i 1.23251 0.895468i 0.235430 0.971891i \(-0.424350\pi\)
0.997075 + 0.0764234i \(0.0243501\pi\)
\(68\) 11.2771 1.36755
\(69\) −17.7373 + 12.8869i −2.13532 + 1.55140i
\(70\) 0 0
\(71\) −9.44666 6.86340i −1.12111 0.814535i −0.136735 0.990608i \(-0.543661\pi\)
−0.984377 + 0.176072i \(0.943661\pi\)
\(72\) 0.550127 + 0.399691i 0.0648331 + 0.0471040i
\(73\) 1.06035 3.26343i 0.124105 0.381955i −0.869632 0.493700i \(-0.835644\pi\)
0.993737 + 0.111745i \(0.0356440\pi\)
\(74\) 18.5652 2.15816
\(75\) 0 0
\(76\) −7.71026 −0.884427
\(77\) −0.199653 + 0.614470i −0.0227526 + 0.0700253i
\(78\) 5.50196 + 3.99741i 0.622974 + 0.452617i
\(79\) −4.60610 3.34653i −0.518227 0.376514i 0.297709 0.954657i \(-0.403778\pi\)
−0.815936 + 0.578143i \(0.803778\pi\)
\(80\) 0 0
\(81\) −8.42651 + 6.12222i −0.936279 + 0.680246i
\(82\) 8.43005 0.930943
\(83\) −5.77129 + 4.19309i −0.633482 + 0.460251i −0.857605 0.514309i \(-0.828048\pi\)
0.224123 + 0.974561i \(0.428048\pi\)
\(84\) 0.710813 + 2.18766i 0.0775560 + 0.238693i
\(85\) 0 0
\(86\) −4.46232 + 13.7336i −0.481185 + 1.48093i
\(87\) 3.92023 + 12.0652i 0.420292 + 1.29353i
\(88\) 0.0596226 + 0.183499i 0.00635579 + 0.0195611i
\(89\) 0.472794 1.45511i 0.0501160 0.154241i −0.922867 0.385120i \(-0.874160\pi\)
0.972983 + 0.230879i \(0.0741601\pi\)
\(90\) 0 0
\(91\) 0.127615 + 0.392758i 0.0133777 + 0.0411722i
\(92\) −12.0462 + 8.75210i −1.25591 + 0.912470i
\(93\) 0.924896 0.0959072
\(94\) 1.32001 0.959043i 0.136149 0.0989178i
\(95\) 0 0
\(96\) −19.7015 14.3140i −2.01078 1.46092i
\(97\) −5.17562 3.76031i −0.525504 0.381801i 0.293169 0.956061i \(-0.405290\pi\)
−0.818673 + 0.574259i \(0.805290\pi\)
\(98\) 4.27063 13.1437i 0.431399 1.32771i
\(99\) −10.7480 −1.08022
\(100\) 0 0
\(101\) −12.2487 −1.21879 −0.609396 0.792866i \(-0.708588\pi\)
−0.609396 + 0.792866i \(0.708588\pi\)
\(102\) −10.3325 + 31.8002i −1.02307 + 3.14869i
\(103\) 6.20298 + 4.50673i 0.611197 + 0.444061i 0.849836 0.527048i \(-0.176701\pi\)
−0.238638 + 0.971109i \(0.576701\pi\)
\(104\) 0.0997725 + 0.0724889i 0.00978350 + 0.00710813i
\(105\) 0 0
\(106\) −6.37804 + 4.63392i −0.619490 + 0.450086i
\(107\) −0.758003 −0.0732789 −0.0366394 0.999329i \(-0.511665\pi\)
−0.0366394 + 0.999329i \(0.511665\pi\)
\(108\) −15.8677 + 11.5285i −1.52687 + 1.10933i
\(109\) −1.00999 3.10843i −0.0967394 0.297733i 0.890964 0.454075i \(-0.150030\pi\)
−0.987703 + 0.156341i \(0.950030\pi\)
\(110\) 0 0
\(111\) −8.62012 + 26.5300i −0.818186 + 2.51812i
\(112\) −0.444420 1.36778i −0.0419937 0.129243i
\(113\) 0.262033 + 0.806455i 0.0246500 + 0.0758649i 0.962625 0.270839i \(-0.0873010\pi\)
−0.937975 + 0.346704i \(0.887301\pi\)
\(114\) 7.06442 21.7420i 0.661644 2.03633i
\(115\) 0 0
\(116\) 2.66240 + 8.19404i 0.247198 + 0.760797i
\(117\) −5.55791 + 4.03806i −0.513829 + 0.373319i
\(118\) 3.74015 0.344309
\(119\) −1.64263 + 1.19344i −0.150580 + 0.109403i
\(120\) 0 0
\(121\) 6.43196 + 4.67309i 0.584723 + 0.424826i
\(122\) 15.7839 + 11.4676i 1.42900 + 1.03823i
\(123\) −3.91422 + 12.0467i −0.352933 + 1.08622i
\(124\) 0.628139 0.0564086
\(125\) 0 0
\(126\) −4.58521 −0.408483
\(127\) 4.42590 13.6215i 0.392735 1.20872i −0.537976 0.842960i \(-0.680811\pi\)
0.930711 0.365755i \(-0.119189\pi\)
\(128\) −0.714803 0.519335i −0.0631803 0.0459032i
\(129\) −17.5537 12.7535i −1.54552 1.12288i
\(130\) 0 0
\(131\) 13.4512 9.77284i 1.17523 0.853857i 0.183608 0.983000i \(-0.441222\pi\)
0.991626 + 0.129142i \(0.0412224\pi\)
\(132\) −10.8575 −0.945025
\(133\) 1.12308 0.815966i 0.0973834 0.0707532i
\(134\) 7.75960 + 23.8816i 0.670327 + 2.06306i
\(135\) 0 0
\(136\) −0.187369 + 0.576664i −0.0160668 + 0.0494485i
\(137\) −0.949265 2.92154i −0.0811012 0.249604i 0.902282 0.431147i \(-0.141891\pi\)
−0.983383 + 0.181543i \(0.941891\pi\)
\(138\) −13.6427 41.9880i −1.16135 3.57426i
\(139\) −4.85775 + 14.9506i −0.412029 + 1.26809i 0.502852 + 0.864372i \(0.332284\pi\)
−0.914881 + 0.403723i \(0.867716\pi\)
\(140\) 0 0
\(141\) 0.757590 + 2.33162i 0.0638006 + 0.196358i
\(142\) 19.0225 13.8206i 1.59633 1.15980i
\(143\) −1.94929 −0.163008
\(144\) 19.3555 14.0626i 1.61296 1.17188i
\(145\) 0 0
\(146\) 5.59002 + 4.06139i 0.462633 + 0.336123i
\(147\) 16.7996 + 12.2057i 1.38561 + 1.00671i
\(148\) −5.85432 + 18.0177i −0.481222 + 1.48105i
\(149\) 14.8504 1.21660 0.608298 0.793709i \(-0.291853\pi\)
0.608298 + 0.793709i \(0.291853\pi\)
\(150\) 0 0
\(151\) −0.712013 −0.0579428 −0.0289714 0.999580i \(-0.509223\pi\)
−0.0289714 + 0.999580i \(0.509223\pi\)
\(152\) 0.128106 0.394270i 0.0103908 0.0319795i
\(153\) −27.3259 19.8534i −2.20917 1.60506i
\(154\) −1.05254 0.764717i −0.0848164 0.0616227i
\(155\) 0 0
\(156\) −5.61452 + 4.07919i −0.449522 + 0.326597i
\(157\) −22.0704 −1.76141 −0.880704 0.473667i \(-0.842930\pi\)
−0.880704 + 0.473667i \(0.842930\pi\)
\(158\) 9.27517 6.73881i 0.737893 0.536111i
\(159\) −3.66053 11.2660i −0.290299 0.893449i
\(160\) 0 0
\(161\) 0.828439 2.54967i 0.0652901 0.200942i
\(162\) −6.48128 19.9473i −0.509218 1.56721i
\(163\) −4.06725 12.5177i −0.318572 0.980462i −0.974259 0.225430i \(-0.927621\pi\)
0.655688 0.755032i \(-0.272379\pi\)
\(164\) −2.65832 + 8.18148i −0.207580 + 0.638866i
\(165\) 0 0
\(166\) −4.43901 13.6619i −0.344534 1.06037i
\(167\) −8.42033 + 6.11773i −0.651585 + 0.473404i −0.863811 0.503816i \(-0.831929\pi\)
0.212226 + 0.977221i \(0.431929\pi\)
\(168\) −0.123678 −0.00954194
\(169\) 9.50922 6.90886i 0.731479 0.531450i
\(170\) 0 0
\(171\) 18.6830 + 13.5740i 1.42872 + 1.03803i
\(172\) −11.9215 8.66149i −0.909008 0.660433i
\(173\) −2.84063 + 8.74256i −0.215969 + 0.664684i 0.783114 + 0.621878i \(0.213630\pi\)
−0.999083 + 0.0428065i \(0.986370\pi\)
\(174\) −25.5457 −1.93661
\(175\) 0 0
\(176\) 6.78842 0.511697
\(177\) −1.73662 + 5.34476i −0.130532 + 0.401736i
\(178\) 2.49250 + 1.81091i 0.186821 + 0.135733i
\(179\) 17.5454 + 12.7475i 1.31141 + 0.952792i 0.999997 + 0.00251665i \(0.000801074\pi\)
0.311409 + 0.950276i \(0.399199\pi\)
\(180\) 0 0
\(181\) −8.71149 + 6.32927i −0.647520 + 0.470451i −0.862425 0.506184i \(-0.831056\pi\)
0.214906 + 0.976635i \(0.431056\pi\)
\(182\) −0.831586 −0.0616413
\(183\) −23.7162 + 17.2309i −1.75315 + 1.27374i
\(184\) −0.247397 0.761410i −0.0182384 0.0561319i
\(185\) 0 0
\(186\) −0.575524 + 1.77128i −0.0421995 + 0.129877i
\(187\) −2.96157 9.11478i −0.216572 0.666539i
\(188\) 0.514514 + 1.58351i 0.0375248 + 0.115489i
\(189\) 1.09124 3.35851i 0.0793764 0.244295i
\(190\) 0 0
\(191\) −1.18644 3.65150i −0.0858480 0.264213i 0.898913 0.438128i \(-0.144358\pi\)
−0.984761 + 0.173915i \(0.944358\pi\)
\(192\) 20.6418 14.9972i 1.48969 1.08233i
\(193\) −10.5334 −0.758208 −0.379104 0.925354i \(-0.623768\pi\)
−0.379104 + 0.925354i \(0.623768\pi\)
\(194\) 10.4220 7.57202i 0.748255 0.543639i
\(195\) 0 0
\(196\) 11.4094 + 8.28942i 0.814958 + 0.592101i
\(197\) 7.80946 + 5.67390i 0.556401 + 0.404249i 0.830140 0.557555i \(-0.188260\pi\)
−0.273739 + 0.961804i \(0.588260\pi\)
\(198\) 6.68805 20.5837i 0.475299 1.46282i
\(199\) −15.8462 −1.12331 −0.561654 0.827372i \(-0.689835\pi\)
−0.561654 + 0.827372i \(0.689835\pi\)
\(200\) 0 0
\(201\) −37.7302 −2.66129
\(202\) 7.62186 23.4577i 0.536272 1.65048i
\(203\) −1.25497 0.911790i −0.0880817 0.0639951i
\(204\) −27.6043 20.0557i −1.93269 1.40418i
\(205\) 0 0
\(206\) −12.4907 + 9.07506i −0.870272 + 0.632289i
\(207\) 44.5978 3.09976
\(208\) 3.51036 2.55042i 0.243400 0.176840i
\(209\) 2.02485 + 6.23185i 0.140062 + 0.431066i
\(210\) 0 0
\(211\) 2.24070 6.89617i 0.154256 0.474752i −0.843828 0.536613i \(-0.819704\pi\)
0.998085 + 0.0618609i \(0.0197035\pi\)
\(212\) −2.48603 7.65123i −0.170742 0.525489i
\(213\) 10.9175 + 33.6006i 0.748056 + 2.30228i
\(214\) 0.471674 1.45166i 0.0322429 0.0992336i
\(215\) 0 0
\(216\) −0.325879 1.00295i −0.0221733 0.0682423i
\(217\) −0.0914951 + 0.0664751i −0.00621109 + 0.00451262i
\(218\) 6.58147 0.445753
\(219\) −8.39935 + 6.10249i −0.567576 + 0.412368i
\(220\) 0 0
\(221\) −4.95590 3.60067i −0.333370 0.242207i
\(222\) −45.4441 33.0170i −3.05001 2.21596i
\(223\) 7.06578 21.7462i 0.473159 1.45624i −0.375264 0.926918i \(-0.622448\pi\)
0.848424 0.529317i \(-0.177552\pi\)
\(224\) 2.97776 0.198960
\(225\) 0 0
\(226\) −1.70751 −0.113582
\(227\) −0.205626 + 0.632850i −0.0136478 + 0.0420037i −0.957649 0.287940i \(-0.907030\pi\)
0.944001 + 0.329944i \(0.107030\pi\)
\(228\) 18.8733 + 13.7122i 1.24991 + 0.908115i
\(229\) 18.9902 + 13.7972i 1.25491 + 0.911744i 0.998496 0.0548231i \(-0.0174595\pi\)
0.256412 + 0.966567i \(0.417459\pi\)
\(230\) 0 0
\(231\) 1.58151 1.14904i 0.104056 0.0756010i
\(232\) −0.463245 −0.0304135
\(233\) −14.4242 + 10.4798i −0.944959 + 0.686553i −0.949609 0.313436i \(-0.898520\pi\)
0.00465012 + 0.999989i \(0.498520\pi\)
\(234\) −4.27489 13.1567i −0.279458 0.860083i
\(235\) 0 0
\(236\) −1.17942 + 3.62987i −0.0767734 + 0.236284i
\(237\) 5.32328 + 16.3834i 0.345784 + 1.06421i
\(238\) −1.26343 3.88845i −0.0818963 0.252051i
\(239\) −7.37641 + 22.7023i −0.477140 + 1.46849i 0.365909 + 0.930651i \(0.380758\pi\)
−0.843049 + 0.537837i \(0.819242\pi\)
\(240\) 0 0
\(241\) −1.30197 4.00704i −0.0838670 0.258116i 0.900326 0.435217i \(-0.143328\pi\)
−0.984193 + 0.177101i \(0.943328\pi\)
\(242\) −12.9518 + 9.41006i −0.832576 + 0.604902i
\(243\) 2.87982 0.184741
\(244\) −16.1068 + 11.7023i −1.03113 + 0.749160i
\(245\) 0 0
\(246\) −20.6352 14.9923i −1.31565 0.955877i
\(247\) 3.38839 + 2.46181i 0.215598 + 0.156641i
\(248\) −0.0104365 + 0.0321204i −0.000662721 + 0.00203965i
\(249\) 21.5842 1.36784
\(250\) 0 0
\(251\) 19.5741 1.23551 0.617755 0.786371i \(-0.288042\pi\)
0.617755 + 0.786371i \(0.288042\pi\)
\(252\) 1.44590 4.45001i 0.0910830 0.280325i
\(253\) 10.2375 + 7.43797i 0.643625 + 0.467621i
\(254\) 23.3327 + 16.9522i 1.46403 + 1.06368i
\(255\) 0 0
\(256\) −12.2051 + 8.86753i −0.762819 + 0.554220i
\(257\) −18.4169 −1.14881 −0.574407 0.818570i \(-0.694767\pi\)
−0.574407 + 0.818570i \(0.694767\pi\)
\(258\) 35.3474 25.6814i 2.20063 1.59885i
\(259\) −1.05405 3.24403i −0.0654954 0.201574i
\(260\) 0 0
\(261\) 7.97432 24.5424i 0.493598 1.51914i
\(262\) 10.3460 + 31.8417i 0.639179 + 1.96719i
\(263\) −1.33635 4.11285i −0.0824026 0.253609i 0.901364 0.433063i \(-0.142567\pi\)
−0.983766 + 0.179453i \(0.942567\pi\)
\(264\) 0.180398 0.555208i 0.0111027 0.0341707i
\(265\) 0 0
\(266\) 0.863821 + 2.65857i 0.0529643 + 0.163007i
\(267\) −3.74514 + 2.72100i −0.229199 + 0.166523i
\(268\) −25.6243 −1.56526
\(269\) −3.83389 + 2.78548i −0.233756 + 0.169834i −0.698497 0.715613i \(-0.746148\pi\)
0.464741 + 0.885447i \(0.346148\pi\)
\(270\) 0 0
\(271\) −8.06208 5.85745i −0.489737 0.355815i 0.315346 0.948977i \(-0.397879\pi\)
−0.805083 + 0.593162i \(0.797879\pi\)
\(272\) 17.2590 + 12.5394i 1.04648 + 0.760311i
\(273\) 0.386120 1.18835i 0.0233690 0.0719225i
\(274\) 6.18577 0.373696
\(275\) 0 0
\(276\) 45.0520 2.71181
\(277\) −5.44155 + 16.7474i −0.326951 + 1.00625i 0.643601 + 0.765361i \(0.277440\pi\)
−0.970552 + 0.240891i \(0.922560\pi\)
\(278\) −25.6094 18.6063i −1.53595 1.11593i
\(279\) −1.52206 1.10584i −0.0911236 0.0662051i
\(280\) 0 0
\(281\) 20.6270 14.9864i 1.23051 0.894014i 0.233577 0.972338i \(-0.424957\pi\)
0.996928 + 0.0783239i \(0.0249568\pi\)
\(282\) −4.93674 −0.293979
\(283\) 13.0255 9.46360i 0.774287 0.562553i −0.128972 0.991648i \(-0.541168\pi\)
0.903259 + 0.429096i \(0.141168\pi\)
\(284\) 7.41458 + 22.8197i 0.439974 + 1.35410i
\(285\) 0 0
\(286\) 1.21296 3.73311i 0.0717240 0.220744i
\(287\) −0.478621 1.47305i −0.0282521 0.0869511i
\(288\) 15.3076 + 47.1119i 0.902008 + 2.77610i
\(289\) 4.05372 12.4761i 0.238454 0.733887i
\(290\) 0 0
\(291\) 5.98147 + 18.4091i 0.350640 + 1.07916i
\(292\) −5.70438 + 4.14448i −0.333824 + 0.242537i
\(293\) 24.9049 1.45496 0.727481 0.686128i \(-0.240691\pi\)
0.727481 + 0.686128i \(0.240691\pi\)
\(294\) −33.8289 + 24.5782i −1.97294 + 1.43343i
\(295\) 0 0
\(296\) −0.824082 0.598731i −0.0478988 0.0348005i
\(297\) 13.4851 + 9.79752i 0.782487 + 0.568510i
\(298\) −9.24081 + 28.4403i −0.535306 + 1.64750i
\(299\) 8.08836 0.467762
\(300\) 0 0
\(301\) 2.65313 0.152924
\(302\) 0.443056 1.36359i 0.0254950 0.0784655i
\(303\) 29.9826 + 21.7836i 1.72245 + 1.25144i
\(304\) −11.8001 8.57327i −0.676782 0.491711i
\(305\) 0 0
\(306\) 55.0254 39.9783i 3.14559 2.28541i
\(307\) 1.74743 0.0997311 0.0498655 0.998756i \(-0.484121\pi\)
0.0498655 + 0.998756i \(0.484121\pi\)
\(308\) 1.07408 0.780363i 0.0612012 0.0444653i
\(309\) −7.16879 22.0633i −0.407818 1.25513i
\(310\) 0 0
\(311\) 5.66312 17.4293i 0.321126 0.988324i −0.652033 0.758190i \(-0.726084\pi\)
0.973159 0.230133i \(-0.0739162\pi\)
\(312\) −0.115307 0.354879i −0.00652798 0.0200911i
\(313\) 1.02210 + 3.14569i 0.0577724 + 0.177805i 0.975778 0.218761i \(-0.0702016\pi\)
−0.918006 + 0.396566i \(0.870202\pi\)
\(314\) 13.7335 42.2673i 0.775025 2.38528i
\(315\) 0 0
\(316\) 3.61528 + 11.1267i 0.203375 + 0.625925i
\(317\) 0.808243 0.587223i 0.0453954 0.0329817i −0.564856 0.825189i \(-0.691068\pi\)
0.610252 + 0.792208i \(0.291068\pi\)
\(318\) 23.8534 1.33763
\(319\) 5.92368 4.30380i 0.331662 0.240967i
\(320\) 0 0
\(321\) 1.85545 + 1.34806i 0.103561 + 0.0752416i
\(322\) 4.36741 + 3.17311i 0.243386 + 0.176830i
\(323\) −6.36328 + 19.5842i −0.354063 + 1.08969i
\(324\) 21.4030 1.18905
\(325\) 0 0
\(326\) 26.5037 1.46790
\(327\) −3.05589 + 9.40506i −0.168991 + 0.520101i
\(328\) −0.374198 0.271871i −0.0206616 0.0150116i
\(329\) −0.242525 0.176205i −0.0133709 0.00971449i
\(330\) 0 0
\(331\) 11.4888 8.34711i 0.631482 0.458798i −0.225431 0.974259i \(-0.572379\pi\)
0.856913 + 0.515461i \(0.172379\pi\)
\(332\) 14.6588 0.804508
\(333\) 45.9062 33.3528i 2.51564 1.82772i
\(334\) −6.47653 19.9327i −0.354380 1.09067i
\(335\) 0 0
\(336\) −1.34467 + 4.13846i −0.0733575 + 0.225771i
\(337\) 4.06450 + 12.5092i 0.221407 + 0.681422i 0.998636 + 0.0522040i \(0.0166246\pi\)
−0.777229 + 0.629218i \(0.783375\pi\)
\(338\) 7.31405 + 22.5103i 0.397832 + 1.22440i
\(339\) 0.792825 2.44006i 0.0430603 0.132526i
\(340\) 0 0
\(341\) −0.164961 0.507697i −0.00893312 0.0274933i
\(342\) −37.6213 + 27.3335i −2.03433 + 1.47803i
\(343\) −5.12896 −0.276938
\(344\) 0.640989 0.465706i 0.0345598 0.0251092i
\(345\) 0 0
\(346\) −14.9754 10.8803i −0.805082 0.584926i
\(347\) −10.9601 7.96299i −0.588370 0.427476i 0.253362 0.967372i \(-0.418464\pi\)
−0.841732 + 0.539896i \(0.818464\pi\)
\(348\) 8.05554 24.7924i 0.431822 1.32901i
\(349\) −32.0976 −1.71814 −0.859072 0.511854i \(-0.828959\pi\)
−0.859072 + 0.511854i \(0.828959\pi\)
\(350\) 0 0
\(351\) 10.6542 0.568681
\(352\) −4.34340 + 13.3676i −0.231504 + 0.712496i
\(353\) −14.8149 10.7637i −0.788518 0.572892i 0.119005 0.992894i \(-0.462029\pi\)
−0.907523 + 0.420002i \(0.862029\pi\)
\(354\) −9.15519 6.65164i −0.486593 0.353531i
\(355\) 0 0
\(356\) −2.54349 + 1.84796i −0.134805 + 0.0979415i
\(357\) 6.14332 0.325139
\(358\) −35.3307 + 25.6692i −1.86728 + 1.35666i
\(359\) −4.46111 13.7299i −0.235448 0.724635i −0.997062 0.0766035i \(-0.975592\pi\)
0.761613 0.648032i \(-0.224408\pi\)
\(360\) 0 0
\(361\) −1.52069 + 4.68020i −0.0800364 + 0.246327i
\(362\) −6.70047 20.6219i −0.352169 1.08386i
\(363\) −7.43342 22.8777i −0.390153 1.20077i
\(364\) 0.262232 0.807066i 0.0137447 0.0423017i
\(365\) 0 0
\(366\) −18.2414 56.1413i −0.953495 2.93455i
\(367\) −8.42431 + 6.12062i −0.439745 + 0.319494i −0.785534 0.618819i \(-0.787611\pi\)
0.345788 + 0.938312i \(0.387611\pi\)
\(368\) −28.1678 −1.46835
\(369\) 20.8450 15.1448i 1.08515 0.788407i
\(370\) 0 0
\(371\) 1.17184 + 0.851389i 0.0608387 + 0.0442019i
\(372\) −1.53757 1.11711i −0.0797192 0.0579194i
\(373\) 3.09711 9.53194i 0.160363 0.493545i −0.838302 0.545206i \(-0.816451\pi\)
0.998665 + 0.0516608i \(0.0164515\pi\)
\(374\) 19.2987 0.997912
\(375\) 0 0
\(376\) −0.0895228 −0.00461679
\(377\) 1.44624 4.45108i 0.0744853 0.229242i
\(378\) 5.75289 + 4.17972i 0.295896 + 0.214981i
\(379\) −11.5685 8.40503i −0.594236 0.431738i 0.249592 0.968351i \(-0.419703\pi\)
−0.843828 + 0.536613i \(0.819703\pi\)
\(380\) 0 0
\(381\) −35.0589 + 25.4718i −1.79612 + 1.30496i
\(382\) 7.73131 0.395568
\(383\) −4.07506 + 2.96070i −0.208226 + 0.151285i −0.687011 0.726647i \(-0.741077\pi\)
0.478785 + 0.877932i \(0.341077\pi\)
\(384\) 0.826099 + 2.54247i 0.0421567 + 0.129745i
\(385\) 0 0
\(386\) 6.55447 20.1726i 0.333614 1.02676i
\(387\) 13.6388 + 41.9759i 0.693299 + 2.13375i
\(388\) 4.06229 + 12.5024i 0.206231 + 0.634715i
\(389\) 3.13115 9.63668i 0.158755 0.488599i −0.839767 0.542948i \(-0.817308\pi\)
0.998522 + 0.0543486i \(0.0173082\pi\)
\(390\) 0 0
\(391\) 12.2887 + 37.8207i 0.621467 + 1.91268i
\(392\) −0.613454 + 0.445700i −0.0309841 + 0.0225113i
\(393\) −50.3064 −2.53762
\(394\) −15.7257 + 11.4254i −0.792248 + 0.575602i
\(395\) 0 0
\(396\) 17.8678 + 12.9817i 0.897889 + 0.652355i
\(397\) −15.9117 11.5605i −0.798584 0.580205i 0.111914 0.993718i \(-0.464302\pi\)
−0.910498 + 0.413513i \(0.864302\pi\)
\(398\) 9.86044 30.3473i 0.494259 1.52117i
\(399\) −4.20024 −0.210275
\(400\) 0 0
\(401\) −23.0931 −1.15321 −0.576606 0.817022i \(-0.695623\pi\)
−0.576606 + 0.817022i \(0.695623\pi\)
\(402\) 23.4780 72.2577i 1.17097 3.60389i
\(403\) −0.276045 0.200559i −0.0137508 0.00999054i
\(404\) 20.3625 + 14.7942i 1.01307 + 0.736041i
\(405\) 0 0
\(406\) 2.52710 1.83604i 0.125418 0.0911213i
\(407\) 16.1004 0.798066
\(408\) 1.48421 1.07834i 0.0734792 0.0533858i
\(409\) 11.9385 + 36.7429i 0.590321 + 1.81682i 0.576762 + 0.816913i \(0.304316\pi\)
0.0135592 + 0.999908i \(0.495684\pi\)
\(410\) 0 0
\(411\) −2.87216 + 8.83959i −0.141673 + 0.436025i
\(412\) −4.86865 14.9842i −0.239861 0.738217i
\(413\) −0.212349 0.653545i −0.0104490 0.0321588i
\(414\) −27.7513 + 85.4098i −1.36390 + 4.19766i
\(415\) 0 0
\(416\) 2.77622 + 8.54434i 0.136116 + 0.418921i
\(417\) 38.4797 27.9571i 1.88436 1.36907i
\(418\) −13.1947 −0.645373
\(419\) 8.72857 6.34167i 0.426418 0.309811i −0.353797 0.935322i \(-0.615110\pi\)
0.780215 + 0.625511i \(0.215110\pi\)
\(420\) 0 0
\(421\) −26.2567 19.0766i −1.27967 0.929736i −0.280128 0.959963i \(-0.590377\pi\)
−0.999543 + 0.0302271i \(0.990377\pi\)
\(422\) 11.8127 + 8.58240i 0.575031 + 0.417785i
\(423\) 1.54105 4.74286i 0.0749284 0.230606i
\(424\) 0.432557 0.0210068
\(425\) 0 0
\(426\) −71.1426 −3.44687
\(427\) 1.10769 3.40912i 0.0536048 0.164979i
\(428\) 1.26012 + 0.915532i 0.0609102 + 0.0442539i
\(429\) 4.77150 + 3.46670i 0.230370 + 0.167374i
\(430\) 0 0
\(431\) −11.1580 + 8.10676i −0.537462 + 0.390489i −0.823141 0.567836i \(-0.807781\pi\)
0.285680 + 0.958325i \(0.407781\pi\)
\(432\) −37.1035 −1.78514
\(433\) 17.0800 12.4093i 0.820812 0.596355i −0.0961332 0.995368i \(-0.530647\pi\)
0.916945 + 0.399014i \(0.130647\pi\)
\(434\) −0.0703738 0.216588i −0.00337805 0.0103966i
\(435\) 0 0
\(436\) −2.07539 + 6.38741i −0.0993933 + 0.305901i
\(437\) −8.40189 25.8584i −0.401917 1.23697i
\(438\) −6.46039 19.8830i −0.308689 0.950048i
\(439\) 11.2314 34.5668i 0.536047 1.64978i −0.205329 0.978693i \(-0.565827\pi\)
0.741376 0.671090i \(-0.234173\pi\)
\(440\) 0 0
\(441\) −13.0529 40.1727i −0.621567 1.91299i
\(442\) 9.97954 7.25056i 0.474678 0.344874i
\(443\) 6.38810 0.303508 0.151754 0.988418i \(-0.451508\pi\)
0.151754 + 0.988418i \(0.451508\pi\)
\(444\) 46.3738 33.6925i 2.20080 1.59898i
\(445\) 0 0
\(446\) 37.2498 + 27.0635i 1.76383 + 1.28150i
\(447\) −36.3511 26.4106i −1.71935 1.24918i
\(448\) −0.964095 + 2.96718i −0.0455492 + 0.140186i
\(449\) −35.1628 −1.65943 −0.829717 0.558185i \(-0.811498\pi\)
−0.829717 + 0.558185i \(0.811498\pi\)
\(450\) 0 0
\(451\) 7.31084 0.344254
\(452\) 0.538443 1.65716i 0.0253262 0.0779462i
\(453\) 1.74287 + 1.26627i 0.0818874 + 0.0594947i
\(454\) −1.08403 0.787593i −0.0508760 0.0369636i
\(455\) 0 0
\(456\) −1.01477 + 0.737271i −0.0475208 + 0.0345259i
\(457\) 22.2994 1.04312 0.521561 0.853214i \(-0.325350\pi\)
0.521561 + 0.853214i \(0.325350\pi\)
\(458\) −38.2400 + 27.7830i −1.78684 + 1.29821i
\(459\) 16.1871 + 49.8186i 0.755547 + 2.32533i
\(460\) 0 0
\(461\) −0.582623 + 1.79313i −0.0271355 + 0.0835144i −0.963707 0.266962i \(-0.913980\pi\)
0.936572 + 0.350476i \(0.113980\pi\)
\(462\) 1.21643 + 3.74377i 0.0565932 + 0.174176i
\(463\) −3.99100 12.2830i −0.185478 0.570842i 0.814479 0.580194i \(-0.197023\pi\)
−0.999956 + 0.00935195i \(0.997023\pi\)
\(464\) −5.03655 + 15.5009i −0.233816 + 0.719612i
\(465\) 0 0
\(466\) −11.0944 34.1451i −0.513938 1.58174i
\(467\) 2.11813 1.53891i 0.0980155 0.0712125i −0.537698 0.843137i \(-0.680706\pi\)
0.635714 + 0.771925i \(0.280706\pi\)
\(468\) 14.1168 0.652551
\(469\) 3.73245 2.71179i 0.172349 0.125219i
\(470\) 0 0
\(471\) 54.0242 + 39.2509i 2.48930 + 1.80858i
\(472\) −0.166020 0.120621i −0.00764170 0.00555202i
\(473\) −3.86989 + 11.9103i −0.177938 + 0.547636i
\(474\) −34.6885 −1.59329
\(475\) 0 0
\(476\) 4.17221 0.191233
\(477\) −7.44606 + 22.9166i −0.340932 + 1.04928i
\(478\) −38.8874 28.2533i −1.77867 1.29228i
\(479\) −5.44724 3.95765i −0.248891 0.180830i 0.456344 0.889803i \(-0.349159\pi\)
−0.705235 + 0.708974i \(0.749159\pi\)
\(480\) 0 0
\(481\) 8.32566 6.04895i 0.379617 0.275808i
\(482\) 8.48409 0.386440
\(483\) −6.56231 + 4.76779i −0.298595 + 0.216942i
\(484\) −5.04838 15.5373i −0.229472 0.706241i
\(485\) 0 0
\(486\) −1.79199 + 5.51519i −0.0812865 + 0.250174i
\(487\) −1.71750 5.28592i −0.0778274 0.239528i 0.904572 0.426321i \(-0.140191\pi\)
−0.982399 + 0.186793i \(0.940191\pi\)
\(488\) −0.330790 1.01807i −0.0149741 0.0460857i
\(489\) −12.3061 + 37.8744i −0.556503 + 1.71274i
\(490\) 0 0
\(491\) −1.71566 5.28026i −0.0774266 0.238295i 0.904850 0.425730i \(-0.139983\pi\)
−0.982277 + 0.187435i \(0.939983\pi\)
\(492\) 21.0574 15.2991i 0.949339 0.689735i
\(493\) 23.0103 1.03633
\(494\) −6.82310 + 4.95727i −0.306986 + 0.223038i
\(495\) 0 0
\(496\) 0.961330 + 0.698447i 0.0431650 + 0.0313612i
\(497\) −3.49499 2.53926i −0.156772 0.113901i
\(498\) −13.4310 + 41.3362i −0.601856 + 1.85232i
\(499\) 19.2580 0.862107 0.431054 0.902326i \(-0.358142\pi\)
0.431054 + 0.902326i \(0.358142\pi\)
\(500\) 0 0
\(501\) 31.4914 1.40693
\(502\) −12.1802 + 37.4867i −0.543628 + 1.67311i
\(503\) −25.2061 18.3133i −1.12389 0.816551i −0.139093 0.990279i \(-0.544419\pi\)
−0.984794 + 0.173728i \(0.944419\pi\)
\(504\) 0.203531 + 0.147874i 0.00906601 + 0.00658684i
\(505\) 0 0
\(506\) −20.6149 + 14.9776i −0.916445 + 0.665836i
\(507\) −35.5638 −1.57944
\(508\) −23.8101 + 17.2990i −1.05640 + 0.767521i
\(509\) −6.55889 20.1862i −0.290718 0.894737i −0.984626 0.174674i \(-0.944113\pi\)
0.693909 0.720063i \(-0.255887\pi\)
\(510\) 0 0
\(511\) 0.392300 1.20737i 0.0173543 0.0534111i
\(512\) −9.93366 30.5727i −0.439010 1.35113i
\(513\) −11.0672 34.0614i −0.488630 1.50385i
\(514\) 11.4601 35.2704i 0.505482 1.55571i
\(515\) 0 0
\(516\) 13.7777 + 42.4035i 0.606530 + 1.86671i
\(517\) 1.14476 0.831717i 0.0503465 0.0365789i
\(518\) 6.86858 0.301788
\(519\) 22.5015 16.3483i 0.987704 0.717609i
\(520\) 0 0
\(521\) −19.4241 14.1124i −0.850986 0.618277i 0.0744320 0.997226i \(-0.476286\pi\)
−0.925418 + 0.378949i \(0.876286\pi\)
\(522\) 42.0395 + 30.5434i 1.84002 + 1.33685i
\(523\) 7.05145 21.7021i 0.308338 0.948968i −0.670072 0.742296i \(-0.733737\pi\)
0.978410 0.206672i \(-0.0662632\pi\)
\(524\) −34.1654 −1.49252
\(525\) 0 0
\(526\) 8.70813 0.379692
\(527\) 0.518404 1.59548i 0.0225820 0.0695003i
\(528\) −16.6168 12.0728i −0.723153 0.525402i
\(529\) −23.8719 17.3440i −1.03791 0.754085i
\(530\) 0 0
\(531\) 9.24829 6.71928i 0.401342 0.291592i
\(532\) −2.85257 −0.123675
\(533\) 3.78051 2.74670i 0.163752 0.118973i
\(534\) −2.88058 8.86553i −0.124655 0.383649i
\(535\) 0 0
\(536\) 0.425749 1.31032i 0.0183895 0.0565972i
\(537\) −20.2773 62.4070i −0.875028 2.69306i
\(538\) −2.94885 9.07562i −0.127134 0.391278i
\(539\) 3.70365 11.3987i 0.159527 0.490975i
\(540\) 0 0
\(541\) 8.50020 + 26.1609i 0.365452 + 1.12475i 0.949697 + 0.313169i \(0.101391\pi\)
−0.584245 + 0.811577i \(0.698609\pi\)
\(542\) 16.2344 11.7950i 0.697326 0.506637i
\(543\) 32.5803 1.39816
\(544\) −35.7349 + 25.9629i −1.53212 + 1.11315i
\(545\) 0 0
\(546\) 2.03557 + 1.47893i 0.0871143 + 0.0632922i
\(547\) −0.196772 0.142963i −0.00841338 0.00611267i 0.583571 0.812062i \(-0.301655\pi\)
−0.591984 + 0.805950i \(0.701655\pi\)
\(548\) −1.95061 + 6.00337i −0.0833261 + 0.256451i
\(549\) 59.6308 2.54498
\(550\) 0 0
\(551\) −15.7323 −0.670220
\(552\) −0.748541 + 2.30377i −0.0318600 + 0.0980550i
\(553\) −1.70413 1.23812i −0.0724668 0.0526502i
\(554\) −28.6871 20.8424i −1.21880 0.885508i
\(555\) 0 0
\(556\) 26.1333 18.9870i 1.10830 0.805226i
\(557\) 27.7280 1.17487 0.587436 0.809271i \(-0.300138\pi\)
0.587436 + 0.809271i \(0.300138\pi\)
\(558\) 3.06493 2.22680i 0.129749 0.0942682i
\(559\) 2.47357 + 7.61285i 0.104621 + 0.321989i
\(560\) 0 0
\(561\) −8.96072 + 27.5783i −0.378322 + 1.16436i
\(562\) 15.8654 + 48.8285i 0.669239 + 2.05971i
\(563\) −3.83333 11.7978i −0.161556 0.497217i 0.837210 0.546881i \(-0.184185\pi\)
−0.998766 + 0.0496637i \(0.984185\pi\)
\(564\) 1.55675 4.79118i 0.0655509 0.201745i
\(565\) 0 0
\(566\) 10.0186 + 30.8342i 0.421115 + 1.29606i
\(567\) −3.11757 + 2.26505i −0.130926 + 0.0951230i
\(568\) −1.29010 −0.0541313
\(569\) 21.5259 15.6394i 0.902411 0.655640i −0.0366734 0.999327i \(-0.511676\pi\)
0.939084 + 0.343688i \(0.111676\pi\)
\(570\) 0 0
\(571\) −10.4540 7.59530i −0.437488 0.317854i 0.347148 0.937810i \(-0.387150\pi\)
−0.784636 + 0.619957i \(0.787150\pi\)
\(572\) 3.24054 + 2.35439i 0.135494 + 0.0984421i
\(573\) −3.58978 + 11.0482i −0.149965 + 0.461545i
\(574\) 3.11888 0.130179
\(575\) 0 0
\(576\) −51.9006 −2.16253
\(577\) −8.75852 + 26.9560i −0.364622 + 1.12219i 0.585595 + 0.810604i \(0.300861\pi\)
−0.950217 + 0.311588i \(0.899139\pi\)
\(578\) 21.3706 + 15.5267i 0.888901 + 0.645825i
\(579\) 25.7837 + 18.7330i 1.07153 + 0.778516i
\(580\) 0 0
\(581\) −2.13521 + 1.55132i −0.0885836 + 0.0643597i
\(582\) −38.9775 −1.61567
\(583\) −5.53127 + 4.01870i −0.229082 + 0.166438i
\(584\) −0.117153 0.360559i −0.00484781 0.0149200i
\(585\) 0 0
\(586\) −15.4973 + 47.6958i −0.640187 + 1.97029i
\(587\) 2.59230 + 7.97827i 0.106996 + 0.329299i 0.990194 0.139702i \(-0.0446143\pi\)
−0.883198 + 0.469000i \(0.844614\pi\)
\(588\) −13.1859 40.5819i −0.543776 1.67357i
\(589\) −0.354437 + 1.09085i −0.0146043 + 0.0449475i
\(590\) 0 0
\(591\) −9.02540 27.7773i −0.371255 1.14261i
\(592\) −28.9942 + 21.0655i −1.19165 + 0.865787i
\(593\) −30.9031 −1.26904 −0.634518 0.772908i \(-0.718801\pi\)
−0.634518 + 0.772908i \(0.718801\pi\)
\(594\) −27.1546 + 19.7290i −1.11417 + 0.809490i
\(595\) 0 0
\(596\) −24.6877 17.9367i −1.01125 0.734714i
\(597\) 38.7886 + 28.1816i 1.58751 + 1.15339i
\(598\) −5.03305 + 15.4901i −0.205817 + 0.633439i
\(599\) 32.6384 1.33357 0.666784 0.745251i \(-0.267671\pi\)
0.666784 + 0.745251i \(0.267671\pi\)
\(600\) 0 0
\(601\) 16.9351 0.690796 0.345398 0.938456i \(-0.387744\pi\)
0.345398 + 0.938456i \(0.387744\pi\)
\(602\) −1.65093 + 5.08105i −0.0672870 + 0.207088i
\(603\) 62.0911 + 45.1118i 2.52855 + 1.83710i
\(604\) 1.18367 + 0.859984i 0.0481627 + 0.0349922i
\(605\) 0 0
\(606\) −60.3750 + 43.8650i −2.45257 + 1.78189i
\(607\) −36.3044 −1.47355 −0.736775 0.676138i \(-0.763652\pi\)
−0.736775 + 0.676138i \(0.763652\pi\)
\(608\) 24.4323 17.7511i 0.990860 0.719902i
\(609\) 1.45037 + 4.46378i 0.0587720 + 0.180882i
\(610\) 0 0
\(611\) 0.279489 0.860178i 0.0113069 0.0347991i
\(612\) 21.4478 + 66.0096i 0.866977 + 2.66828i
\(613\) 9.51589 + 29.2869i 0.384343 + 1.18289i 0.936956 + 0.349449i \(0.113631\pi\)
−0.552612 + 0.833439i \(0.686369\pi\)
\(614\) −1.08735 + 3.34653i −0.0438820 + 0.135055i
\(615\) 0 0
\(616\) 0.0220586 + 0.0678895i 0.000888768 + 0.00273535i
\(617\) −28.5776 + 20.7628i −1.15049 + 0.835879i −0.988546 0.150921i \(-0.951776\pi\)
−0.161943 + 0.986800i \(0.551776\pi\)
\(618\) 46.7145 1.87913
\(619\) −3.19641 + 2.32233i −0.128475 + 0.0933423i −0.650167 0.759792i \(-0.725301\pi\)
0.521692 + 0.853134i \(0.325301\pi\)
\(620\) 0 0
\(621\) −55.9550 40.6537i −2.24540 1.63138i
\(622\) 29.8551 + 21.6910i 1.19708 + 0.869731i
\(623\) 0.174920 0.538349i 0.00700802 0.0215685i
\(624\) −13.1285 −0.525560
\(625\) 0 0
\(626\) −6.66037 −0.266202
\(627\) 6.12652 18.8555i 0.244670 0.753016i
\(628\) 36.6903 + 26.6571i 1.46410 + 1.06373i
\(629\) 40.9338 + 29.7401i 1.63214 + 1.18582i
\(630\) 0 0
\(631\) −10.9434 + 7.95086i −0.435651 + 0.316519i −0.783904 0.620882i \(-0.786775\pi\)
0.348254 + 0.937400i \(0.386775\pi\)
\(632\) −0.629040 −0.0250219
\(633\) −17.7493 + 12.8956i −0.705470 + 0.512554i
\(634\) 0.621663 + 1.91328i 0.0246894 + 0.0759861i
\(635\) 0 0
\(636\) −7.52191 + 23.1501i −0.298263 + 0.917959i
\(637\) −2.36731 7.28582i −0.0937962 0.288675i
\(638\) 4.55622 + 14.0226i 0.180382 + 0.555160i
\(639\) 22.2078 68.3487i 0.878528 2.70383i
\(640\) 0 0
\(641\) −11.1638 34.3587i −0.440945 1.35709i −0.886870 0.462019i \(-0.847125\pi\)
0.445925 0.895070i \(-0.352875\pi\)
\(642\) −3.73626 + 2.71455i −0.147459 + 0.107135i
\(643\) −7.35135 −0.289909 −0.144954 0.989438i \(-0.546304\pi\)
−0.144954 + 0.989438i \(0.546304\pi\)
\(644\) −4.45676 + 3.23803i −0.175621 + 0.127596i
\(645\) 0 0
\(646\) −33.5463 24.3728i −1.31986 0.958936i
\(647\) −35.3544 25.6864i −1.38992 1.00984i −0.995874 0.0907489i \(-0.971074\pi\)
−0.394049 0.919089i \(-0.628926\pi\)
\(648\) −0.355611 + 1.09446i −0.0139697 + 0.0429943i
\(649\) 3.24359 0.127322
\(650\) 0 0
\(651\) 0.342185 0.0134113
\(652\) −8.35766 + 25.7222i −0.327311 + 1.00736i
\(653\) 28.9988 + 21.0689i 1.13481 + 0.824489i 0.986388 0.164435i \(-0.0525801\pi\)
0.148424 + 0.988924i \(0.452580\pi\)
\(654\) −16.1102 11.7048i −0.629959 0.457692i
\(655\) 0 0
\(656\) −13.1656 + 9.56540i −0.514032 + 0.373466i
\(657\) 21.1189 0.823925
\(658\) 0.488366 0.354819i 0.0190385 0.0138323i
\(659\) 0.0211105 + 0.0649714i 0.000822348 + 0.00253093i 0.951467 0.307751i \(-0.0995765\pi\)
−0.950645 + 0.310282i \(0.899576\pi\)
\(660\) 0 0
\(661\) −8.14485 + 25.0673i −0.316798 + 0.975003i 0.658210 + 0.752834i \(0.271314\pi\)
−0.975008 + 0.222169i \(0.928686\pi\)
\(662\) 8.83666 + 27.1964i 0.343446 + 1.05702i
\(663\) 5.72754 + 17.6275i 0.222439 + 0.684597i
\(664\) −0.243557 + 0.749591i −0.00945184 + 0.0290898i
\(665\) 0 0
\(666\) 35.3089 + 108.670i 1.36819 + 4.21086i
\(667\) −24.5796 + 17.8581i −0.951727 + 0.691470i
\(668\) 21.3873 0.827498
\(669\) −55.9701 + 40.6647i −2.16393 + 1.57219i
\(670\) 0 0
\(671\) 13.6883 + 9.94516i 0.528433 + 0.383929i
\(672\) −7.28900 5.29577i −0.281179 0.204289i
\(673\) −1.56889 + 4.82854i −0.0604762 + 0.186126i −0.976730 0.214471i \(-0.931197\pi\)
0.916254 + 0.400597i \(0.131197\pi\)
\(674\) −26.4858 −1.02019
\(675\) 0 0
\(676\) −24.1530 −0.928962
\(677\) 11.9129 36.6640i 0.457848 1.40911i −0.409910 0.912126i \(-0.634440\pi\)
0.867758 0.496986i \(-0.165560\pi\)
\(678\) 4.17966 + 3.03670i 0.160519 + 0.116624i
\(679\) −1.91483 1.39121i −0.0734844 0.0533896i
\(680\) 0 0
\(681\) 1.62882 1.18341i 0.0624165 0.0453483i
\(682\) 1.07494 0.0411618
\(683\) −29.6208 + 21.5207i −1.13341 + 0.823468i −0.986187 0.165635i \(-0.947032\pi\)
−0.147220 + 0.989104i \(0.547032\pi\)
\(684\) −14.6641 45.1313i −0.560694 1.72564i
\(685\) 0 0
\(686\) 3.19154 9.82254i 0.121853 0.375026i
\(687\) −21.9470 67.5459i −0.837331 2.57704i
\(688\) −8.61421 26.5118i −0.328414 1.01075i
\(689\) −1.35044 + 4.15622i −0.0514475 + 0.158339i
\(690\) 0 0
\(691\) 9.07794 + 27.9390i 0.345341 + 1.06285i 0.961401 + 0.275151i \(0.0887280\pi\)
−0.616060 + 0.787699i \(0.711272\pi\)
\(692\) 15.2818 11.1029i 0.580926 0.422067i
\(693\) −3.97647 −0.151053
\(694\) 22.0701 16.0348i 0.837768 0.608674i
\(695\) 0 0
\(696\) 1.13394 + 0.823853i 0.0429818 + 0.0312281i
\(697\) 18.5872 + 13.5044i 0.704039 + 0.511514i
\(698\) 19.9730 61.4705i 0.755989 2.32669i
\(699\) 53.9454 2.04040
\(700\) 0 0
\(701\) −0.566147 −0.0213831 −0.0106915 0.999943i \(-0.503403\pi\)
−0.0106915 + 0.999943i \(0.503403\pi\)
\(702\) −6.62969 + 20.4041i −0.250221 + 0.770102i
\(703\) −27.9868 20.3336i −1.05554 0.766896i
\(704\) −11.9139 8.65593i −0.449021 0.326233i
\(705\) 0 0
\(706\) 29.8323 21.6745i 1.12275 0.815729i
\(707\) −4.53167 −0.170431
\(708\) 9.34250 6.78772i 0.351113 0.255098i
\(709\) 0.203104 + 0.625089i 0.00762772 + 0.0234757i 0.954798 0.297256i \(-0.0960714\pi\)
−0.947170 + 0.320731i \(0.896071\pi\)
\(710\) 0 0
\(711\) 10.8283 33.3262i 0.406094 1.24983i
\(712\) −0.0522365 0.160767i −0.00195764 0.00602501i
\(713\) 0.684485 + 2.10663i 0.0256342 + 0.0788939i
\(714\) −3.82273 + 11.7652i −0.143062 + 0.440300i
\(715\) 0 0
\(716\) −13.7712 42.3834i −0.514655 1.58394i
\(717\) 58.4307 42.4524i 2.18214 1.58541i
\(718\) 29.0702 1.08489
\(719\) −28.4007 + 20.6343i −1.05917 + 0.769530i −0.973934 0.226831i \(-0.927163\pi\)
−0.0852327 + 0.996361i \(0.527163\pi\)
\(720\) 0 0
\(721\) 2.29492 + 1.66736i 0.0854674 + 0.0620957i
\(722\) −8.01686 5.82459i −0.298357 0.216769i
\(723\) −3.93931 + 12.1240i −0.146505 + 0.450895i
\(724\) 22.1268 0.822336
\(725\) 0 0
\(726\) 48.4389 1.79774
\(727\) −12.7371 + 39.2007i −0.472392 + 1.45387i 0.377052 + 0.926192i \(0.376938\pi\)
−0.849443 + 0.527680i \(0.823062\pi\)
\(728\) 0.0369130 + 0.0268188i 0.00136809 + 0.000993972i
\(729\) 18.2303 + 13.2451i 0.675195 + 0.490558i
\(730\) 0 0
\(731\) −31.8392 + 23.1325i −1.17761 + 0.855587i
\(732\) 60.2382 2.22647
\(733\) 32.4482 23.5750i 1.19850 0.870763i 0.204365 0.978895i \(-0.434487\pi\)
0.994137 + 0.108132i \(0.0344870\pi\)
\(734\) −6.47959 19.9421i −0.239166 0.736077i
\(735\) 0 0
\(736\) 18.0224 55.4674i 0.664316 2.04455i
\(737\) 6.72941 + 20.7110i 0.247881 + 0.762899i
\(738\) 16.0330 + 49.3446i 0.590184 + 1.81640i
\(739\) −8.82040 + 27.1464i −0.324464 + 0.998597i 0.647218 + 0.762305i \(0.275932\pi\)
−0.971682 + 0.236292i \(0.924068\pi\)
\(740\) 0 0
\(741\) −3.91597 12.0521i −0.143857 0.442745i
\(742\) −2.35969 + 1.71442i −0.0866270 + 0.0629382i
\(743\) 29.6851 1.08904 0.544520 0.838748i \(-0.316712\pi\)
0.544520 + 0.838748i \(0.316712\pi\)
\(744\) 0.0826709 0.0600640i 0.00303086 0.00220205i
\(745\) 0 0
\(746\) 16.3275 + 11.8627i 0.597794 + 0.434323i
\(747\) −35.5203 25.8070i −1.29962 0.944228i
\(748\) −6.08564 + 18.7297i −0.222513 + 0.684824i
\(749\) −0.280439 −0.0102470
\(750\) 0 0
\(751\) 45.2113 1.64978 0.824892 0.565290i \(-0.191236\pi\)
0.824892 + 0.565290i \(0.191236\pi\)
\(752\) −0.973322 + 2.99558i −0.0354934 + 0.109237i
\(753\) −47.9139 34.8115i −1.74608 1.26860i
\(754\) 7.62438 + 5.53944i 0.277664 + 0.201734i
\(755\) 0 0
\(756\) −5.87058 + 4.26523i −0.213511 + 0.155125i
\(757\) 5.69813 0.207102 0.103551 0.994624i \(-0.466980\pi\)
0.103551 + 0.994624i \(0.466980\pi\)
\(758\) 23.2952 16.9250i 0.846120 0.614742i
\(759\) −11.8315 36.4135i −0.429455 1.32173i
\(760\) 0 0
\(761\) −12.8645 + 39.5927i −0.466336 + 1.43524i 0.390958 + 0.920409i \(0.372144\pi\)
−0.857294 + 0.514827i \(0.827856\pi\)
\(762\) −26.9657 82.9917i −0.976863 3.00647i
\(763\) −0.373667 1.15003i −0.0135277 0.0416338i
\(764\) −2.43798 + 7.50334i −0.0882032 + 0.271461i
\(765\) 0 0
\(766\) −3.13434 9.64652i −0.113248 0.348543i
\(767\) 1.67729 1.21863i 0.0605636 0.0440020i
\(768\) 45.6462 1.64712
\(769\) 12.8845 9.36110i 0.464625 0.337570i −0.330718 0.943730i \(-0.607291\pi\)
0.795343 + 0.606160i \(0.207291\pi\)
\(770\) 0 0
\(771\) 45.0811 + 32.7534i 1.62356 + 1.17958i
\(772\) 17.5109 + 12.7224i 0.630231 + 0.457890i
\(773\) −14.7809 + 45.4909i −0.531632 + 1.63619i 0.219184 + 0.975683i \(0.429660\pi\)
−0.750816 + 0.660511i \(0.770340\pi\)
\(774\) −88.8755 −3.19456
\(775\) 0 0
\(776\) −0.706817 −0.0253732
\(777\) −3.18920 + 9.81535i −0.114412 + 0.352124i
\(778\) 16.5070 + 11.9930i 0.591803 + 0.429970i
\(779\) −12.7082 9.23305i −0.455319 0.330808i
\(780\) 0 0
\(781\) 16.4970 11.9857i 0.590308 0.428884i
\(782\) −80.0778 −2.86358
\(783\) −32.3770 + 23.5233i −1.15706 + 0.840654i
\(784\) 8.24417 + 25.3730i 0.294435 + 0.906177i
\(785\) 0 0
\(786\) 31.3036 96.3425i 1.11656 3.43642i
\(787\) 12.5325 + 38.5711i 0.446736 + 1.37491i 0.880569 + 0.473919i \(0.157161\pi\)
−0.433832 + 0.900994i \(0.642839\pi\)
\(788\) −6.12956 18.8649i −0.218357 0.672032i
\(789\) −4.04333 + 12.4441i −0.143946 + 0.443022i
\(790\) 0 0
\(791\) 0.0969448 + 0.298365i 0.00344696 + 0.0106087i
\(792\) −0.960703 + 0.697991i −0.0341371 + 0.0248020i
\(793\) 10.8148 0.384044
\(794\) 32.0409 23.2790i 1.13709 0.826142i
\(795\) 0 0
\(796\) 26.3431 + 19.1394i 0.933707 + 0.678378i
\(797\) −22.5163 16.3590i −0.797567 0.579466i 0.112632 0.993637i \(-0.464072\pi\)
−0.910199 + 0.414170i \(0.864072\pi\)
\(798\) 2.61363 8.04394i 0.0925216 0.284752i
\(799\) 4.44678 0.157316
\(800\) 0 0
\(801\) 9.41656 0.332718
\(802\) 14.3698 44.2258i 0.507417 1.56167i
\(803\) 4.84787 + 3.52218i 0.171078 + 0.124295i
\(804\) 62.7236 + 45.5714i 2.21209 + 1.60718i
\(805\) 0 0
\(806\) 0.555864 0.403859i 0.0195795 0.0142253i
\(807\) 14.3385 0.504738
\(808\) −1.09484 + 0.795447i −0.0385163 + 0.0279837i
\(809\) −2.54848 7.84342i −0.0895998 0.275760i 0.896209 0.443632i \(-0.146310\pi\)
−0.985809 + 0.167872i \(0.946310\pi\)
\(810\) 0 0
\(811\) −5.67232 + 17.4576i −0.199182 + 0.613019i 0.800720 + 0.599039i \(0.204450\pi\)
−0.999902 + 0.0139809i \(0.995550\pi\)
\(812\) 0.985014 + 3.03156i 0.0345672 + 0.106387i
\(813\) 9.31736 + 28.6759i 0.326774 + 1.00571i
\(814\) −10.0186 + 30.8341i −0.351152 + 1.08073i
\(815\) 0 0
\(816\) −19.9462 61.3881i −0.698257 2.14901i
\(817\) 21.7687 15.8159i 0.761591 0.553328i
\(818\) −77.7957 −2.72006
\(819\) −2.05627 + 1.49397i −0.0718518 + 0.0522034i
\(820\) 0 0
\(821\) 12.8338 + 9.32434i 0.447904 + 0.325422i 0.788768 0.614691i \(-0.210719\pi\)
−0.340863 + 0.940113i \(0.610719\pi\)
\(822\) −15.1416 11.0010i −0.528124 0.383705i
\(823\) −10.0339 + 30.8812i −0.349761 + 1.07645i 0.609225 + 0.792998i \(0.291481\pi\)
−0.958986 + 0.283455i \(0.908519\pi\)
\(824\) 0.847120 0.0295108
\(825\) 0 0
\(826\) 1.38375 0.0481468
\(827\) 8.89801 27.3853i 0.309414 0.952279i −0.668579 0.743641i \(-0.733097\pi\)
0.977993 0.208638i \(-0.0669029\pi\)
\(828\) −74.1403 53.8661i −2.57655 1.87198i
\(829\) 6.95127 + 5.05039i 0.241428 + 0.175407i 0.701919 0.712257i \(-0.252327\pi\)
−0.460491 + 0.887664i \(0.652327\pi\)
\(830\) 0 0
\(831\) 43.1041 31.3170i 1.49527 1.08637i
\(832\) −9.41283 −0.326331
\(833\) 30.4715 22.1388i 1.05577 0.767064i
\(834\) 29.5968 + 91.0895i 1.02485 + 3.15417i
\(835\) 0 0
\(836\) 4.16080 12.8056i 0.143904 0.442892i
\(837\) 0.901625 + 2.77492i 0.0311647 + 0.0959151i
\(838\) 6.71361 + 20.6624i 0.231918 + 0.713769i
\(839\) −14.5405 + 44.7511i −0.501994 + 1.54498i 0.303771 + 0.952745i \(0.401754\pi\)
−0.805766 + 0.592235i \(0.798246\pi\)
\(840\) 0 0
\(841\) −3.52901 10.8612i −0.121690 0.374524i
\(842\) 52.8722 38.4139i 1.82210 1.32383i
\(843\) −77.1436 −2.65697
\(844\) −12.0543 + 8.75799i −0.414927 + 0.301462i
\(845\) 0 0
\(846\) 8.12420 + 5.90257i 0.279316 + 0.202935i
\(847\) 2.37964 + 1.72891i 0.0817654 + 0.0594061i
\(848\) 4.70291 14.4741i 0.161499 0.497041i
\(849\) −48.7145 −1.67188
\(850\) 0 0
\(851\) −66.8067 −2.29011
\(852\) 22.4340 69.0449i 0.768577 2.36544i
\(853\) 15.1198 + 10.9852i 0.517693 + 0.376126i 0.815734 0.578427i \(-0.196333\pi\)
−0.298041 + 0.954553i \(0.596333\pi\)
\(854\) 5.83958 + 4.24270i 0.199826 + 0.145182i
\(855\) 0 0
\(856\) −0.0677534 + 0.0492257i −0.00231576 + 0.00168250i
\(857\) 3.06228 0.104606 0.0523028 0.998631i \(-0.483344\pi\)
0.0523028 + 0.998631i \(0.483344\pi\)
\(858\) −9.60823 + 6.98079i −0.328020 + 0.238320i
\(859\) 5.24289 + 16.1360i 0.178885 + 0.550552i 0.999790 0.0205136i \(-0.00653012\pi\)
−0.820904 + 0.571066i \(0.806530\pi\)
\(860\) 0 0
\(861\) −1.44815 + 4.45694i −0.0493527 + 0.151892i
\(862\) −8.58221 26.4133i −0.292311 0.899642i
\(863\) −6.76653 20.8252i −0.230335 0.708899i −0.997706 0.0676953i \(-0.978435\pi\)
0.767371 0.641204i \(-0.221565\pi\)
\(864\) 23.7397 73.0633i 0.807641 2.48566i
\(865\) 0 0
\(866\) 13.1371 + 40.4319i 0.446418 + 1.37393i
\(867\) −32.1107 + 23.3298i −1.09054 + 0.792322i
\(868\) 0.232393 0.00788795
\(869\) 8.04377 5.84414i 0.272866 0.198249i
\(870\) 0 0
\(871\) 11.2610 + 8.18160i 0.381565 + 0.277223i
\(872\) −0.292142 0.212254i −0.00989319 0.00718782i
\(873\) 12.1672 37.4467i 0.411797 1.26738i
\(874\) 54.7499 1.85194
\(875\) 0 0
\(876\) 21.3340 0.720808
\(877\) 14.4719 44.5399i 0.488681 1.50401i −0.337896 0.941183i \(-0.609715\pi\)
0.826578 0.562823i \(-0.190285\pi\)
\(878\) 59.2105 + 43.0189i 1.99826 + 1.45182i
\(879\) −60.9626 44.2919i −2.05622 1.49393i
\(880\) 0 0
\(881\) −0.0227639 + 0.0165389i −0.000766934 + 0.000557210i −0.588169 0.808738i \(-0.700151\pi\)
0.587402 + 0.809296i \(0.300151\pi\)
\(882\) 85.0576 2.86404
\(883\) 23.6813 17.2055i 0.796938 0.579010i −0.113076 0.993586i \(-0.536070\pi\)
0.910014 + 0.414577i \(0.136070\pi\)
\(884\) 3.88983 + 11.9717i 0.130829 + 0.402651i
\(885\) 0 0
\(886\) −3.97505 + 12.2339i −0.133544 + 0.411007i
\(887\) 6.14316 + 18.9067i 0.206267 + 0.634825i 0.999659 + 0.0261137i \(0.00831320\pi\)
−0.793392 + 0.608711i \(0.791687\pi\)
\(888\) 0.952392 + 2.93116i 0.0319602 + 0.0983634i
\(889\) 1.63746 5.03958i 0.0549186 0.169022i
\(890\) 0 0
\(891\) −5.62080 17.2991i −0.188304 0.579540i
\(892\) −38.0119 + 27.6172i −1.27273 + 0.924693i
\(893\) −3.04030 −0.101740
\(894\) 73.1991 53.1823i 2.44815 1.77868i
\(895\) 0 0
\(896\) −0.264457 0.192139i −0.00883488 0.00641892i
\(897\) −19.7988 14.3847i −0.661063 0.480290i
\(898\) 21.8803 67.3407i 0.730156 2.24719i
\(899\) 1.28168 0.0427465
\(900\) 0 0
\(901\) −21.4860 −0.715801
\(902\) −4.54923 + 14.0011i −0.151473 + 0.466186i
\(903\) −6.49437 4.71843i −0.216119 0.157020i
\(904\) 0.0757939 + 0.0550675i 0.00252087 + 0.00183152i
\(905\) 0 0
\(906\) −3.50957 + 2.54986i −0.116598 + 0.0847133i
\(907\) −14.2958 −0.474685 −0.237343 0.971426i \(-0.576276\pi\)
−0.237343 + 0.971426i \(0.576276\pi\)
\(908\) 1.10621 0.803706i 0.0367107 0.0266719i
\(909\) −23.2957 71.6968i −0.772670 2.37803i
\(910\) 0 0
\(911\) 5.99507 18.4509i 0.198626 0.611307i −0.801290 0.598277i \(-0.795852\pi\)
0.999915 0.0130299i \(-0.00414767\pi\)
\(912\) 13.6374 + 41.9716i 0.451579 + 1.38982i
\(913\) −3.84967 11.8481i −0.127406 0.392114i
\(914\) −13.8760 + 42.7059i −0.458977 + 1.41258i
\(915\) 0 0
\(916\) −14.9052 45.8735i −0.492482 1.51570i
\(917\) 4.97655 3.61567i 0.164340 0.119400i
\(918\) −105.481 −3.48139
\(919\) −3.47808 + 2.52697i −0.114731 + 0.0833571i −0.643671 0.765302i \(-0.722590\pi\)
0.528940 + 0.848659i \(0.322590\pi\)
\(920\) 0 0
\(921\) −4.27738 3.10770i −0.140945 0.102402i
\(922\) −3.07151 2.23158i −0.101155 0.0734932i
\(923\) 4.02767 12.3959i 0.132572 0.408016i
\(924\) −4.01697 −0.132149
\(925\) 0 0
\(926\) 26.0069 0.854639
\(927\) −14.5824 + 44.8799i −0.478948 + 1.47405i
\(928\) −27.3015 19.8357i −0.896216 0.651139i
\(929\) −34.8134 25.2934i −1.14219 0.829849i −0.154766 0.987951i \(-0.549462\pi\)
−0.987423 + 0.158102i \(0.949462\pi\)
\(930\) 0 0
\(931\) −20.8336 + 15.1365i −0.682794 + 0.496079i
\(932\) 36.6368 1.20008
\(933\) −44.8592 + 32.5921i −1.46862 + 1.06702i
\(934\) 1.62917 + 5.01407i 0.0533081 + 0.164065i
\(935\) 0 0
\(936\) −0.234552 + 0.721876i −0.00766656 + 0.0235953i
\(937\) 5.24737 + 16.1497i 0.171424 + 0.527589i 0.999452 0.0330976i \(-0.0105372\pi\)
−0.828028 + 0.560687i \(0.810537\pi\)
\(938\) 2.87083 + 8.83551i 0.0937359 + 0.288490i
\(939\) 3.09253 9.51781i 0.100921 0.310602i
\(940\) 0 0
\(941\) −5.57614 17.1616i −0.181777 0.559452i 0.818101 0.575074i \(-0.195027\pi\)
−0.999878 + 0.0156227i \(0.995027\pi\)
\(942\) −108.787 + 79.0383i −3.54447 + 2.57521i
\(943\) −30.3355 −0.987860
\(944\) −5.84119 + 4.24387i −0.190115 + 0.138126i
\(945\) 0 0
\(946\) −20.4015 14.8226i −0.663310 0.481923i
\(947\) −5.83198 4.23718i −0.189514 0.137690i 0.488983 0.872294i \(-0.337368\pi\)
−0.678496 + 0.734604i \(0.737368\pi\)
\(948\) 10.9386 33.6656i 0.355270 1.09341i
\(949\) 3.83017 0.124333
\(950\) 0 0
\(951\) −3.02277 −0.0980200
\(952\) −0.0693213 + 0.213349i −0.00224672 + 0.00691468i
\(953\) −11.1644 8.11145i −0.361652 0.262755i 0.392089 0.919927i \(-0.371753\pi\)
−0.753741 + 0.657172i \(0.771753\pi\)
\(954\) −39.2546 28.5201i −1.27091 0.923373i
\(955\) 0 0
\(956\) 39.6830 28.8314i 1.28344 0.932473i
\(957\) −22.1541 −0.716141
\(958\) 10.9689 7.96941i 0.354391 0.257480i
\(959\) −0.351201 1.08089i −0.0113409 0.0349036i
\(960\) 0 0
\(961\) −9.55065 + 29.3939i −0.308086 + 0.948190i
\(962\) 6.40371 + 19.7086i 0.206464 + 0.635431i
\(963\) −1.44164 4.43691i −0.0464561 0.142977i
\(964\) −2.67537 + 8.23393i −0.0861677 + 0.265197i
\(965\) 0 0
\(966\) −5.04742 15.5344i −0.162398 0.499810i
\(967\) −12.0508 + 8.75541i −0.387527 + 0.281555i −0.764441 0.644693i \(-0.776985\pi\)
0.376914 + 0.926248i \(0.376985\pi\)
\(968\) 0.878391 0.0282326
\(969\) 50.4054 36.6217i 1.61926 1.17646i
\(970\) 0 0
\(971\) −32.1938 23.3902i −1.03315 0.750627i −0.0642130 0.997936i \(-0.520454\pi\)
−0.968937 + 0.247309i \(0.920454\pi\)
\(972\) −4.78748 3.47831i −0.153559 0.111567i
\(973\) −1.79723 + 5.53130i −0.0576165 + 0.177325i
\(974\) 11.1919 0.358611
\(975\) 0 0
\(976\) −37.6626 −1.20555
\(977\) 9.56800 29.4473i 0.306107 0.942102i −0.673154 0.739502i \(-0.735061\pi\)
0.979262 0.202600i \(-0.0649390\pi\)
\(978\) −64.8762 47.1353i −2.07451 1.50722i
\(979\) 2.16159 + 1.57048i 0.0690846 + 0.0501929i
\(980\) 0 0
\(981\) 16.2740 11.8238i 0.519590 0.377504i
\(982\) 11.1799 0.356764
\(983\) 22.4542 16.3139i 0.716177 0.520333i −0.168984 0.985619i \(-0.554049\pi\)
0.885160 + 0.465286i \(0.154049\pi\)
\(984\) 0.432461 + 1.33098i 0.0137864 + 0.0424301i
\(985\) 0 0
\(986\) −14.3183 + 44.0673i −0.455989 + 1.40339i
\(987\) 0.280287 + 0.862634i 0.00892163 + 0.0274579i
\(988\) −2.65951 8.18513i −0.0846103 0.260404i
\(989\) 16.0577 49.4204i 0.510604 1.57148i
\(990\) 0 0
\(991\) 4.64082 + 14.2830i 0.147420 + 0.453713i 0.997314 0.0732405i \(-0.0233341\pi\)
−0.849894 + 0.526954i \(0.823334\pi\)
\(992\) −1.99045 + 1.44615i −0.0631968 + 0.0459152i
\(993\) −42.9673 −1.36353
\(994\) 7.03776 5.11323i 0.223224 0.162182i
\(995\) 0 0
\(996\) −35.8821 26.0699i −1.13697 0.826055i
\(997\) 14.4926 + 10.5295i 0.458984 + 0.333471i 0.793133 0.609049i \(-0.208449\pi\)
−0.334149 + 0.942520i \(0.608449\pi\)
\(998\) −11.9835 + 36.8813i −0.379330 + 1.16746i
\(999\) −87.9999 −2.78419
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 625.2.d.m.501.1 16
5.2 odd 4 625.2.e.j.124.2 32
5.3 odd 4 625.2.e.j.124.7 32
5.4 even 2 625.2.d.q.501.4 16
25.2 odd 20 625.2.e.k.249.2 32
25.3 odd 20 625.2.e.k.374.2 32
25.4 even 10 625.2.d.p.251.1 16
25.6 even 5 inner 625.2.d.m.126.1 16
25.8 odd 20 625.2.e.j.499.2 32
25.9 even 10 625.2.a.e.1.8 8
25.11 even 5 625.2.d.n.376.4 16
25.12 odd 20 625.2.b.d.624.4 16
25.13 odd 20 625.2.b.d.624.13 16
25.14 even 10 625.2.d.p.376.1 16
25.16 even 5 625.2.a.g.1.1 yes 8
25.17 odd 20 625.2.e.j.499.7 32
25.19 even 10 625.2.d.q.126.4 16
25.21 even 5 625.2.d.n.251.4 16
25.22 odd 20 625.2.e.k.374.7 32
25.23 odd 20 625.2.e.k.249.7 32
75.41 odd 10 5625.2.a.s.1.8 8
75.59 odd 10 5625.2.a.be.1.1 8
100.59 odd 10 10000.2.a.bn.1.7 8
100.91 odd 10 10000.2.a.be.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
625.2.a.e.1.8 8 25.9 even 10
625.2.a.g.1.1 yes 8 25.16 even 5
625.2.b.d.624.4 16 25.12 odd 20
625.2.b.d.624.13 16 25.13 odd 20
625.2.d.m.126.1 16 25.6 even 5 inner
625.2.d.m.501.1 16 1.1 even 1 trivial
625.2.d.n.251.4 16 25.21 even 5
625.2.d.n.376.4 16 25.11 even 5
625.2.d.p.251.1 16 25.4 even 10
625.2.d.p.376.1 16 25.14 even 10
625.2.d.q.126.4 16 25.19 even 10
625.2.d.q.501.4 16 5.4 even 2
625.2.e.j.124.2 32 5.2 odd 4
625.2.e.j.124.7 32 5.3 odd 4
625.2.e.j.499.2 32 25.8 odd 20
625.2.e.j.499.7 32 25.17 odd 20
625.2.e.k.249.2 32 25.2 odd 20
625.2.e.k.249.7 32 25.23 odd 20
625.2.e.k.374.2 32 25.3 odd 20
625.2.e.k.374.7 32 25.22 odd 20
5625.2.a.s.1.8 8 75.41 odd 10
5625.2.a.be.1.1 8 75.59 odd 10
10000.2.a.be.1.2 8 100.91 odd 10
10000.2.a.bn.1.7 8 100.59 odd 10