Properties

Label 375.2.g.e.226.2
Level $375$
Weight $2$
Character 375.226
Analytic conductor $2.994$
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] = [375,2,Mod(76,375)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(375, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("375.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.g (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: \(2.99439007580\)
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: \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 226.2
Root \(1.53655i\) of defining polynomial
Character \(\chi\) \(=\) 375.226
Dual form 375.2.g.e.151.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.474819 + 1.46134i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.292036 - 0.212177i) q^{4} +(1.24309 - 0.903160i) q^{6} -1.49550 q^{7} +(-2.03746 + 1.48030i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.474819 + 1.46134i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.292036 - 0.212177i) q^{4} +(1.24309 - 0.903160i) q^{6} -1.49550 q^{7} +(-2.03746 + 1.48030i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.728123 + 2.24093i) q^{11} +(0.111548 + 0.343309i) q^{12} +(-0.417020 - 1.28346i) q^{13} +(0.710090 - 2.18543i) q^{14} +(-1.41890 - 4.36692i) q^{16} +(-1.77502 + 1.28963i) q^{17} -1.53655 q^{18} +(-4.62004 + 3.35666i) q^{19} +(1.20988 + 0.879031i) q^{21} +(-2.92904 - 2.12807i) q^{22} +(-2.71781 + 8.36455i) q^{23} +2.51844 q^{24} +2.07358 q^{26} +(0.309017 - 0.951057i) q^{27} +(0.436739 + 0.317309i) q^{28} +(-6.39137 - 4.64360i) q^{29} +(2.99107 - 2.17314i) q^{31} +2.01841 q^{32} +(1.90625 - 1.38497i) q^{33} +(-1.04178 - 3.20626i) q^{34} +(0.111548 - 0.343309i) q^{36} +(-3.01321 - 9.27372i) q^{37} +(-2.71154 - 8.34527i) q^{38} +(-0.417020 + 1.28346i) q^{39} +(0.573380 + 1.76468i) q^{41} +(-1.85904 + 1.35067i) q^{42} +8.01874 q^{43} +(0.688111 - 0.499942i) q^{44} +(-10.9330 - 7.94330i) q^{46} +(5.39046 + 3.91640i) q^{47} +(-1.41890 + 4.36692i) q^{48} -4.76349 q^{49} +2.19405 q^{51} +(-0.150535 + 0.463298i) q^{52} +(3.37484 + 2.45196i) q^{53} +(1.24309 + 0.903160i) q^{54} +(3.04701 - 2.21378i) q^{56} +5.71069 q^{57} +(9.82064 - 7.13511i) q^{58} +(3.41917 + 10.5231i) q^{59} +(-3.78151 + 11.6383i) q^{61} +(1.75549 + 5.40283i) q^{62} +(-0.462134 - 1.42230i) q^{63} +(1.87942 - 5.78425i) q^{64} +(1.11879 + 3.44330i) q^{66} +(3.48976 - 2.53546i) q^{67} +0.792000 q^{68} +(7.11531 - 5.16958i) q^{69} +(-4.67410 - 3.39593i) q^{71} +(-2.03746 - 1.48030i) q^{72} +(-2.14051 + 6.58781i) q^{73} +14.9828 q^{74} +2.06142 q^{76} +(1.08890 - 3.35130i) q^{77} +(-1.67756 - 1.21882i) q^{78} +(8.63118 + 6.27092i) q^{79} +(-0.809017 + 0.587785i) q^{81} -2.85106 q^{82} +(0.181222 - 0.131666i) q^{83} +(-0.166819 - 0.513417i) q^{84} +(-3.80745 + 11.7181i) q^{86} +(2.44129 + 7.51351i) q^{87} +(-1.83373 - 5.64364i) q^{88} +(0.132620 - 0.408162i) q^{89} +(0.623652 + 1.91940i) q^{91} +(2.56846 - 1.86610i) q^{92} -3.69717 q^{93} +(-8.28270 + 6.01773i) q^{94} +(-1.63293 - 1.18639i) q^{96} +(10.1083 + 7.34411i) q^{97} +(2.26180 - 6.96109i) q^{98} -2.35626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.474819 + 1.46134i −0.335748 + 1.03333i 0.630605 + 0.776104i \(0.282807\pi\)
−0.966353 + 0.257221i \(0.917193\pi\)
\(3\) −0.809017 0.587785i −0.467086 0.339358i
\(4\) −0.292036 0.212177i −0.146018 0.106088i
\(5\) 0 0
\(6\) 1.24309 0.903160i 0.507490 0.368713i
\(7\) −1.49550 −0.565244 −0.282622 0.959231i \(-0.591204\pi\)
−0.282622 + 0.959231i \(0.591204\pi\)
\(8\) −2.03746 + 1.48030i −0.720350 + 0.523365i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) 0 0
\(11\) −0.728123 + 2.24093i −0.219537 + 0.675666i 0.779263 + 0.626697i \(0.215594\pi\)
−0.998800 + 0.0489693i \(0.984406\pi\)
\(12\) 0.111548 + 0.343309i 0.0322011 + 0.0991048i
\(13\) −0.417020 1.28346i −0.115661 0.355967i 0.876424 0.481541i \(-0.159923\pi\)
−0.992084 + 0.125574i \(0.959923\pi\)
\(14\) 0.710090 2.18543i 0.189780 0.584081i
\(15\) 0 0
\(16\) −1.41890 4.36692i −0.354724 1.09173i
\(17\) −1.77502 + 1.28963i −0.430507 + 0.312781i −0.781851 0.623465i \(-0.785724\pi\)
0.351345 + 0.936246i \(0.385724\pi\)
\(18\) −1.53655 −0.362168
\(19\) −4.62004 + 3.35666i −1.05991 + 0.770070i −0.974072 0.226239i \(-0.927357\pi\)
−0.0858386 + 0.996309i \(0.527357\pi\)
\(20\) 0 0
\(21\) 1.20988 + 0.879031i 0.264018 + 0.191820i
\(22\) −2.92904 2.12807i −0.624474 0.453707i
\(23\) −2.71781 + 8.36455i −0.566702 + 1.74413i 0.0961375 + 0.995368i \(0.469351\pi\)
−0.662840 + 0.748762i \(0.730649\pi\)
\(24\) 2.51844 0.514074
\(25\) 0 0
\(26\) 2.07358 0.406662
\(27\) 0.309017 0.951057i 0.0594703 0.183031i
\(28\) 0.436739 + 0.317309i 0.0825359 + 0.0599658i
\(29\) −6.39137 4.64360i −1.18685 0.862296i −0.193920 0.981017i \(-0.562120\pi\)
−0.992928 + 0.118722i \(0.962120\pi\)
\(30\) 0 0
\(31\) 2.99107 2.17314i 0.537213 0.390308i −0.285836 0.958279i \(-0.592271\pi\)
0.823049 + 0.567971i \(0.192271\pi\)
\(32\) 2.01841 0.356808
\(33\) 1.90625 1.38497i 0.331836 0.241093i
\(34\) −1.04178 3.20626i −0.178663 0.549869i
\(35\) 0 0
\(36\) 0.111548 0.343309i 0.0185913 0.0572182i
\(37\) −3.01321 9.27372i −0.495369 1.52459i −0.816380 0.577515i \(-0.804023\pi\)
0.321011 0.947076i \(-0.395977\pi\)
\(38\) −2.71154 8.34527i −0.439870 1.35378i
\(39\) −0.417020 + 1.28346i −0.0667767 + 0.205518i
\(40\) 0 0
\(41\) 0.573380 + 1.76468i 0.0895468 + 0.275597i 0.985794 0.167958i \(-0.0537172\pi\)
−0.896247 + 0.443555i \(0.853717\pi\)
\(42\) −1.85904 + 1.35067i −0.286856 + 0.208413i
\(43\) 8.01874 1.22285 0.611423 0.791304i \(-0.290597\pi\)
0.611423 + 0.791304i \(0.290597\pi\)
\(44\) 0.688111 0.499942i 0.103737 0.0753691i
\(45\) 0 0
\(46\) −10.9330 7.94330i −1.61198 1.17118i
\(47\) 5.39046 + 3.91640i 0.786280 + 0.571266i 0.906857 0.421438i \(-0.138475\pi\)
−0.120577 + 0.992704i \(0.538475\pi\)
\(48\) −1.41890 + 4.36692i −0.204800 + 0.630310i
\(49\) −4.76349 −0.680499
\(50\) 0 0
\(51\) 2.19405 0.307228
\(52\) −0.150535 + 0.463298i −0.0208754 + 0.0642478i
\(53\) 3.37484 + 2.45196i 0.463569 + 0.336803i 0.794930 0.606701i \(-0.207508\pi\)
−0.331360 + 0.943504i \(0.607508\pi\)
\(54\) 1.24309 + 0.903160i 0.169163 + 0.122904i
\(55\) 0 0
\(56\) 3.04701 2.21378i 0.407174 0.295829i
\(57\) 5.71069 0.756399
\(58\) 9.82064 7.13511i 1.28951 0.936886i
\(59\) 3.41917 + 10.5231i 0.445138 + 1.36999i 0.882332 + 0.470627i \(0.155972\pi\)
−0.437195 + 0.899367i \(0.644028\pi\)
\(60\) 0 0
\(61\) −3.78151 + 11.6383i −0.484173 + 1.49013i 0.349003 + 0.937122i \(0.386520\pi\)
−0.833175 + 0.553009i \(0.813480\pi\)
\(62\) 1.75549 + 5.40283i 0.222947 + 0.686161i
\(63\) −0.462134 1.42230i −0.0582234 0.179193i
\(64\) 1.87942 5.78425i 0.234927 0.723031i
\(65\) 0 0
\(66\) 1.11879 + 3.44330i 0.137714 + 0.423841i
\(67\) 3.48976 2.53546i 0.426342 0.309756i −0.353842 0.935305i \(-0.615125\pi\)
0.780185 + 0.625549i \(0.215125\pi\)
\(68\) 0.792000 0.0960442
\(69\) 7.11531 5.16958i 0.856583 0.622344i
\(70\) 0 0
\(71\) −4.67410 3.39593i −0.554713 0.403023i 0.274807 0.961499i \(-0.411386\pi\)
−0.829520 + 0.558477i \(0.811386\pi\)
\(72\) −2.03746 1.48030i −0.240117 0.174455i
\(73\) −2.14051 + 6.58781i −0.250528 + 0.771045i 0.744150 + 0.668012i \(0.232855\pi\)
−0.994678 + 0.103033i \(0.967145\pi\)
\(74\) 14.9828 1.74172
\(75\) 0 0
\(76\) 2.06142 0.236461
\(77\) 1.08890 3.35130i 0.124092 0.381917i
\(78\) −1.67756 1.21882i −0.189946 0.138004i
\(79\) 8.63118 + 6.27092i 0.971084 + 0.705534i 0.955698 0.294348i \(-0.0951024\pi\)
0.0153858 + 0.999882i \(0.495102\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −2.85106 −0.314846
\(83\) 0.181222 0.131666i 0.0198917 0.0144522i −0.577795 0.816182i \(-0.696087\pi\)
0.597687 + 0.801730i \(0.296087\pi\)
\(84\) −0.166819 0.513417i −0.0182015 0.0560184i
\(85\) 0 0
\(86\) −3.80745 + 11.7181i −0.410568 + 1.26360i
\(87\) 2.44129 + 7.51351i 0.261733 + 0.805533i
\(88\) −1.83373 5.64364i −0.195476 0.601615i
\(89\) 0.132620 0.408162i 0.0140577 0.0432651i −0.943782 0.330570i \(-0.892759\pi\)
0.957839 + 0.287304i \(0.0927592\pi\)
\(90\) 0 0
\(91\) 0.623652 + 1.91940i 0.0653765 + 0.201208i
\(92\) 2.56846 1.86610i 0.267780 0.194554i
\(93\) −3.69717 −0.383379
\(94\) −8.28270 + 6.01773i −0.854295 + 0.620682i
\(95\) 0 0
\(96\) −1.63293 1.18639i −0.166660 0.121086i
\(97\) 10.1083 + 7.34411i 1.02634 + 0.745682i 0.967573 0.252590i \(-0.0812824\pi\)
0.0587692 + 0.998272i \(0.481282\pi\)
\(98\) 2.26180 6.96109i 0.228476 0.703177i
\(99\) −2.35626 −0.236813
\(100\) 0 0
\(101\) 8.19767 0.815698 0.407849 0.913049i \(-0.366279\pi\)
0.407849 + 0.913049i \(0.366279\pi\)
\(102\) −1.04178 + 3.20626i −0.103151 + 0.317467i
\(103\) 2.02258 + 1.46949i 0.199291 + 0.144794i 0.682955 0.730460i \(-0.260694\pi\)
−0.483664 + 0.875254i \(0.660694\pi\)
\(104\) 2.74956 + 1.99767i 0.269617 + 0.195888i
\(105\) 0 0
\(106\) −5.18559 + 3.76755i −0.503669 + 0.365937i
\(107\) 1.81004 0.174983 0.0874914 0.996165i \(-0.472115\pi\)
0.0874914 + 0.996165i \(0.472115\pi\)
\(108\) −0.292036 + 0.212177i −0.0281012 + 0.0204167i
\(109\) −0.910913 2.80350i −0.0872496 0.268527i 0.897907 0.440186i \(-0.145087\pi\)
−0.985156 + 0.171659i \(0.945087\pi\)
\(110\) 0 0
\(111\) −3.01321 + 9.27372i −0.286002 + 0.880223i
\(112\) 2.12196 + 6.53071i 0.200506 + 0.617094i
\(113\) −4.27571 13.1593i −0.402225 1.23792i −0.923191 0.384342i \(-0.874428\pi\)
0.520966 0.853577i \(-0.325572\pi\)
\(114\) −2.71154 + 8.34527i −0.253959 + 0.781606i
\(115\) 0 0
\(116\) 0.881247 + 2.71220i 0.0818217 + 0.251821i
\(117\) 1.09177 0.793220i 0.100934 0.0733332i
\(118\) −17.0014 −1.56510
\(119\) 2.65454 1.92864i 0.243341 0.176798i
\(120\) 0 0
\(121\) 4.40757 + 3.20229i 0.400689 + 0.291117i
\(122\) −15.2120 11.0522i −1.37723 1.00062i
\(123\) 0.573380 1.76468i 0.0516999 0.159116i
\(124\) −1.33459 −0.119850
\(125\) 0 0
\(126\) 2.29790 0.204713
\(127\) −1.77374 + 5.45902i −0.157394 + 0.484410i −0.998396 0.0566233i \(-0.981967\pi\)
0.841001 + 0.541033i \(0.181967\pi\)
\(128\) 10.8262 + 7.86572i 0.956914 + 0.695238i
\(129\) −6.48730 4.71330i −0.571175 0.414983i
\(130\) 0 0
\(131\) 3.52534 2.56131i 0.308010 0.223783i −0.423032 0.906115i \(-0.639034\pi\)
0.731042 + 0.682332i \(0.239034\pi\)
\(132\) −0.850553 −0.0740311
\(133\) 6.90926 5.01987i 0.599108 0.435278i
\(134\) 2.04817 + 6.30363i 0.176935 + 0.544550i
\(135\) 0 0
\(136\) 1.70750 5.25514i 0.146417 0.450624i
\(137\) −0.610187 1.87796i −0.0521318 0.160445i 0.921601 0.388138i \(-0.126882\pi\)
−0.973733 + 0.227693i \(0.926882\pi\)
\(138\) 4.17604 + 12.8525i 0.355488 + 1.09408i
\(139\) 0.518869 1.59692i 0.0440099 0.135449i −0.926637 0.375957i \(-0.877314\pi\)
0.970647 + 0.240508i \(0.0773141\pi\)
\(140\) 0 0
\(141\) −2.05897 6.33687i −0.173397 0.533661i
\(142\) 7.18197 5.21801i 0.602698 0.437885i
\(143\) 3.17978 0.265907
\(144\) 3.71472 2.69890i 0.309560 0.224909i
\(145\) 0 0
\(146\) −8.61070 6.25604i −0.712627 0.517754i
\(147\) 3.85375 + 2.79991i 0.317852 + 0.230933i
\(148\) −1.08770 + 3.34759i −0.0894083 + 0.275171i
\(149\) −7.38524 −0.605023 −0.302511 0.953146i \(-0.597825\pi\)
−0.302511 + 0.953146i \(0.597825\pi\)
\(150\) 0 0
\(151\) −4.26137 −0.346785 −0.173393 0.984853i \(-0.555473\pi\)
−0.173393 + 0.984853i \(0.555473\pi\)
\(152\) 4.44428 13.6781i 0.360479 1.10944i
\(153\) −1.77502 1.28963i −0.143502 0.104260i
\(154\) 4.38037 + 3.18253i 0.352980 + 0.256455i
\(155\) 0 0
\(156\) 0.394104 0.286334i 0.0315536 0.0229250i
\(157\) −16.0573 −1.28152 −0.640758 0.767743i \(-0.721380\pi\)
−0.640758 + 0.767743i \(0.721380\pi\)
\(158\) −13.2622 + 9.63557i −1.05509 + 0.766565i
\(159\) −1.28907 3.96736i −0.102230 0.314632i
\(160\) 0 0
\(161\) 4.06447 12.5092i 0.320325 0.985859i
\(162\) −0.474819 1.46134i −0.0373053 0.114814i
\(163\) 6.88916 + 21.2026i 0.539600 + 1.66072i 0.733493 + 0.679697i \(0.237889\pi\)
−0.193893 + 0.981023i \(0.562111\pi\)
\(164\) 0.206976 0.637008i 0.0161621 0.0497420i
\(165\) 0 0
\(166\) 0.106361 + 0.327345i 0.00825520 + 0.0254069i
\(167\) −5.23111 + 3.80062i −0.404795 + 0.294101i −0.771491 0.636240i \(-0.780489\pi\)
0.366696 + 0.930341i \(0.380489\pi\)
\(168\) −3.76631 −0.290577
\(169\) 9.04387 6.57075i 0.695682 0.505443i
\(170\) 0 0
\(171\) −4.62004 3.35666i −0.353303 0.256690i
\(172\) −2.34176 1.70139i −0.178558 0.129730i
\(173\) 3.65198 11.2396i 0.277655 0.854533i −0.710850 0.703344i \(-0.751690\pi\)
0.988505 0.151190i \(-0.0483104\pi\)
\(174\) −12.1390 −0.920254
\(175\) 0 0
\(176\) 10.8191 0.815520
\(177\) 3.41917 10.5231i 0.257000 0.790966i
\(178\) 0.533494 + 0.387606i 0.0399871 + 0.0290523i
\(179\) −12.6001 9.15450i −0.941775 0.684240i 0.00707213 0.999975i \(-0.497749\pi\)
−0.948847 + 0.315735i \(0.897749\pi\)
\(180\) 0 0
\(181\) 11.7952 8.56974i 0.876733 0.636984i −0.0556522 0.998450i \(-0.517724\pi\)
0.932385 + 0.361466i \(0.117724\pi\)
\(182\) −3.10103 −0.229864
\(183\) 9.90012 7.19286i 0.731838 0.531711i
\(184\) −6.84463 21.0656i −0.504593 1.55298i
\(185\) 0 0
\(186\) 1.75549 5.40283i 0.128719 0.396155i
\(187\) −1.59754 4.91672i −0.116824 0.359546i
\(188\) −0.743241 2.28746i −0.0542064 0.166830i
\(189\) −0.462134 + 1.42230i −0.0336153 + 0.103457i
\(190\) 0 0
\(191\) −6.48577 19.9611i −0.469294 1.44434i −0.853501 0.521091i \(-0.825525\pi\)
0.384207 0.923247i \(-0.374475\pi\)
\(192\) −4.92037 + 3.57486i −0.355097 + 0.257993i
\(193\) −22.7094 −1.63466 −0.817328 0.576173i \(-0.804546\pi\)
−0.817328 + 0.576173i \(0.804546\pi\)
\(194\) −15.5319 + 11.2846i −1.11512 + 0.810185i
\(195\) 0 0
\(196\) 1.39111 + 1.01070i 0.0993651 + 0.0721930i
\(197\) 1.09494 + 0.795517i 0.0780109 + 0.0566782i 0.626107 0.779737i \(-0.284647\pi\)
−0.548096 + 0.836415i \(0.684647\pi\)
\(198\) 1.11879 3.44330i 0.0795093 0.244704i
\(199\) −8.96061 −0.635201 −0.317600 0.948225i \(-0.602877\pi\)
−0.317600 + 0.948225i \(0.602877\pi\)
\(200\) 0 0
\(201\) −4.31358 −0.304257
\(202\) −3.89241 + 11.9796i −0.273869 + 0.842882i
\(203\) 9.55827 + 6.94449i 0.670859 + 0.487408i
\(204\) −0.640742 0.465526i −0.0448609 0.0325933i
\(205\) 0 0
\(206\) −3.10780 + 2.25795i −0.216530 + 0.157319i
\(207\) −8.79501 −0.611295
\(208\) −5.01304 + 3.64219i −0.347592 + 0.252540i
\(209\) −4.15808 12.7973i −0.287621 0.885205i
\(210\) 0 0
\(211\) 1.80461 5.55401i 0.124234 0.382354i −0.869527 0.493886i \(-0.835576\pi\)
0.993761 + 0.111532i \(0.0355759\pi\)
\(212\) −0.465325 1.43212i −0.0319586 0.0983586i
\(213\) 1.78535 + 5.49473i 0.122330 + 0.376493i
\(214\) −0.859440 + 2.64508i −0.0587501 + 0.180814i
\(215\) 0 0
\(216\) 0.778240 + 2.39518i 0.0529525 + 0.162971i
\(217\) −4.47314 + 3.24993i −0.303656 + 0.220619i
\(218\) 4.52939 0.306769
\(219\) 5.60393 4.07149i 0.378678 0.275126i
\(220\) 0 0
\(221\) 2.39541 + 1.74036i 0.161132 + 0.117070i
\(222\) −12.1214 8.80668i −0.813532 0.591066i
\(223\) 2.41681 7.43818i 0.161842 0.498098i −0.836948 0.547283i \(-0.815662\pi\)
0.998790 + 0.0491848i \(0.0156623\pi\)
\(224\) −3.01853 −0.201684
\(225\) 0 0
\(226\) 21.2604 1.41422
\(227\) −5.03975 + 15.5107i −0.334500 + 1.02948i 0.632468 + 0.774586i \(0.282042\pi\)
−0.966968 + 0.254898i \(0.917958\pi\)
\(228\) −1.66773 1.21167i −0.110448 0.0802451i
\(229\) 17.5628 + 12.7601i 1.16058 + 0.843211i 0.989851 0.142107i \(-0.0453877\pi\)
0.170729 + 0.985318i \(0.445388\pi\)
\(230\) 0 0
\(231\) −2.85079 + 2.07122i −0.187568 + 0.136276i
\(232\) 19.8961 1.30624
\(233\) −10.9493 + 7.95512i −0.717312 + 0.521157i −0.885524 0.464593i \(-0.846201\pi\)
0.168213 + 0.985751i \(0.446201\pi\)
\(234\) 0.640771 + 1.97209i 0.0418885 + 0.128920i
\(235\) 0 0
\(236\) 1.23424 3.79860i 0.0803421 0.247268i
\(237\) −3.29682 10.1466i −0.214151 0.659090i
\(238\) 1.55797 + 4.79495i 0.100988 + 0.310810i
\(239\) −3.25514 + 10.0183i −0.210557 + 0.648028i 0.788882 + 0.614545i \(0.210660\pi\)
−0.999439 + 0.0334838i \(0.989340\pi\)
\(240\) 0 0
\(241\) 6.02082 + 18.5302i 0.387835 + 1.19363i 0.934403 + 0.356219i \(0.115934\pi\)
−0.546567 + 0.837415i \(0.684066\pi\)
\(242\) −6.77244 + 4.92047i −0.435349 + 0.316300i
\(243\) 1.00000 0.0641500
\(244\) 3.57371 2.59645i 0.228783 0.166221i
\(245\) 0 0
\(246\) 2.30655 + 1.67581i 0.147060 + 0.106846i
\(247\) 6.23478 + 4.52983i 0.396709 + 0.288226i
\(248\) −2.87728 + 8.85537i −0.182708 + 0.562317i
\(249\) −0.224003 −0.0141956
\(250\) 0 0
\(251\) −20.9446 −1.32201 −0.661007 0.750380i \(-0.729871\pi\)
−0.661007 + 0.750380i \(0.729871\pi\)
\(252\) −0.166819 + 0.513417i −0.0105086 + 0.0323422i
\(253\) −16.7655 12.1808i −1.05404 0.765803i
\(254\) −7.13529 5.18409i −0.447708 0.325279i
\(255\) 0 0
\(256\) −6.79428 + 4.93633i −0.424643 + 0.308521i
\(257\) 1.67121 0.104247 0.0521237 0.998641i \(-0.483401\pi\)
0.0521237 + 0.998641i \(0.483401\pi\)
\(258\) 9.96804 7.24220i 0.620583 0.450880i
\(259\) 4.50625 + 13.8688i 0.280005 + 0.861766i
\(260\) 0 0
\(261\) 2.44129 7.51351i 0.151112 0.465074i
\(262\) 2.06905 + 6.36789i 0.127826 + 0.393409i
\(263\) −2.33514 7.18682i −0.143991 0.443158i 0.852889 0.522092i \(-0.174848\pi\)
−0.996880 + 0.0789341i \(0.974848\pi\)
\(264\) −1.83373 + 5.64364i −0.112858 + 0.347342i
\(265\) 0 0
\(266\) 4.05510 + 12.4803i 0.248634 + 0.765218i
\(267\) −0.347203 + 0.252258i −0.0212485 + 0.0154379i
\(268\) −1.55710 −0.0951151
\(269\) 9.12904 6.63264i 0.556608 0.404399i −0.273608 0.961841i \(-0.588217\pi\)
0.830216 + 0.557442i \(0.188217\pi\)
\(270\) 0 0
\(271\) 8.87912 + 6.45106i 0.539368 + 0.391874i 0.823850 0.566808i \(-0.191822\pi\)
−0.284482 + 0.958681i \(0.591822\pi\)
\(272\) 8.15029 + 5.92153i 0.494184 + 0.359045i
\(273\) 0.623652 1.91940i 0.0377452 0.116168i
\(274\) 3.03407 0.183295
\(275\) 0 0
\(276\) −3.17479 −0.191100
\(277\) 1.77719 5.46964i 0.106781 0.328639i −0.883363 0.468689i \(-0.844726\pi\)
0.990144 + 0.140050i \(0.0447265\pi\)
\(278\) 2.08727 + 1.51649i 0.125186 + 0.0909531i
\(279\) 2.99107 + 2.17314i 0.179071 + 0.130103i
\(280\) 0 0
\(281\) −6.87633 + 4.99595i −0.410208 + 0.298033i −0.773686 0.633569i \(-0.781589\pi\)
0.363478 + 0.931603i \(0.381589\pi\)
\(282\) 10.2380 0.609663
\(283\) −13.9352 + 10.1245i −0.828360 + 0.601839i −0.919095 0.394036i \(-0.871078\pi\)
0.0907350 + 0.995875i \(0.471078\pi\)
\(284\) 0.644468 + 1.98347i 0.0382421 + 0.117697i
\(285\) 0 0
\(286\) −1.50982 + 4.64675i −0.0892776 + 0.274768i
\(287\) −0.857487 2.63907i −0.0506158 0.155780i
\(288\) 0.623723 + 1.91962i 0.0367532 + 0.113115i
\(289\) −3.76573 + 11.5897i −0.221513 + 0.681748i
\(290\) 0 0
\(291\) −3.86103 11.8830i −0.226337 0.696595i
\(292\) 2.02289 1.46971i 0.118380 0.0860084i
\(293\) −9.38764 −0.548432 −0.274216 0.961668i \(-0.588418\pi\)
−0.274216 + 0.961668i \(0.588418\pi\)
\(294\) −5.92146 + 4.30219i −0.345347 + 0.250909i
\(295\) 0 0
\(296\) 19.8672 + 14.4344i 1.15476 + 0.838980i
\(297\) 1.90625 + 1.38497i 0.110612 + 0.0803642i
\(298\) 3.50665 10.7924i 0.203135 0.625185i
\(299\) 11.8689 0.686397
\(300\) 0 0
\(301\) −11.9920 −0.691207
\(302\) 2.02338 6.22732i 0.116432 0.358342i
\(303\) −6.63205 4.81847i −0.381001 0.276814i
\(304\) 21.2136 + 15.4126i 1.21668 + 0.883973i
\(305\) 0 0
\(306\) 2.72741 1.98158i 0.155916 0.113279i
\(307\) −10.6465 −0.607627 −0.303814 0.952731i \(-0.598260\pi\)
−0.303814 + 0.952731i \(0.598260\pi\)
\(308\) −1.02907 + 0.747662i −0.0586366 + 0.0426020i
\(309\) −0.772559 2.37769i −0.0439493 0.135262i
\(310\) 0 0
\(311\) −8.45383 + 26.0182i −0.479373 + 1.47536i 0.360596 + 0.932722i \(0.382573\pi\)
−0.839969 + 0.542635i \(0.817427\pi\)
\(312\) −1.05024 3.23230i −0.0594581 0.182993i
\(313\) 0.616517 + 1.89744i 0.0348476 + 0.107250i 0.966967 0.254900i \(-0.0820427\pi\)
−0.932120 + 0.362150i \(0.882043\pi\)
\(314\) 7.62433 23.4653i 0.430266 1.32422i
\(315\) 0 0
\(316\) −1.19007 3.66267i −0.0669469 0.206041i
\(317\) 6.99699 5.08361i 0.392990 0.285524i −0.373690 0.927554i \(-0.621907\pi\)
0.766680 + 0.642030i \(0.221907\pi\)
\(318\) 6.40975 0.359441
\(319\) 15.0597 10.9415i 0.843182 0.612607i
\(320\) 0 0
\(321\) −1.46435 1.06391i −0.0817321 0.0593818i
\(322\) 16.3503 + 11.8792i 0.911165 + 0.662000i
\(323\) 3.87184 11.9163i 0.215435 0.663040i
\(324\) 0.360976 0.0200542
\(325\) 0 0
\(326\) −34.2554 −1.89723
\(327\) −0.910913 + 2.80350i −0.0503736 + 0.155034i
\(328\) −3.78049 2.74669i −0.208743 0.151661i
\(329\) −8.06141 5.85696i −0.444440 0.322905i
\(330\) 0 0
\(331\) 3.19020 2.31782i 0.175349 0.127399i −0.496649 0.867952i \(-0.665436\pi\)
0.671998 + 0.740553i \(0.265436\pi\)
\(332\) −0.0808598 −0.00443776
\(333\) 7.88870 5.73148i 0.432298 0.314083i
\(334\) −3.07018 9.44905i −0.167993 0.517029i
\(335\) 0 0
\(336\) 2.12196 6.53071i 0.115762 0.356279i
\(337\) −1.22207 3.76115i −0.0665706 0.204883i 0.912238 0.409661i \(-0.134353\pi\)
−0.978809 + 0.204778i \(0.934353\pi\)
\(338\) 5.30792 + 16.3361i 0.288713 + 0.888567i
\(339\) −4.27571 + 13.1593i −0.232224 + 0.714713i
\(340\) 0 0
\(341\) 2.69199 + 8.28511i 0.145780 + 0.448664i
\(342\) 7.09891 5.15766i 0.383865 0.278894i
\(343\) 17.5923 0.949893
\(344\) −16.3379 + 11.8701i −0.880878 + 0.639995i
\(345\) 0 0
\(346\) 14.6909 + 10.6736i 0.789789 + 0.573815i
\(347\) −8.08690 5.87548i −0.434127 0.315412i 0.349170 0.937060i \(-0.386464\pi\)
−0.783297 + 0.621647i \(0.786464\pi\)
\(348\) 0.881247 2.71220i 0.0472398 0.145389i
\(349\) 18.4534 0.987789 0.493895 0.869522i \(-0.335573\pi\)
0.493895 + 0.869522i \(0.335573\pi\)
\(350\) 0 0
\(351\) −1.34951 −0.0720313
\(352\) −1.46965 + 4.52312i −0.0783327 + 0.241083i
\(353\) 7.54326 + 5.48050i 0.401487 + 0.291697i 0.770146 0.637867i \(-0.220183\pi\)
−0.368659 + 0.929565i \(0.620183\pi\)
\(354\) 13.7544 + 9.99316i 0.731038 + 0.531130i
\(355\) 0 0
\(356\) −0.125332 + 0.0910592i −0.00664260 + 0.00482613i
\(357\) −3.28119 −0.173659
\(358\) 19.3606 14.0663i 1.02324 0.743428i
\(359\) 8.94412 + 27.5272i 0.472052 + 1.45283i 0.849892 + 0.526957i \(0.176667\pi\)
−0.377839 + 0.925871i \(0.623333\pi\)
\(360\) 0 0
\(361\) 4.20632 12.9457i 0.221385 0.681354i
\(362\) 6.92273 + 21.3060i 0.363850 + 1.11982i
\(363\) −1.68354 5.18141i −0.0883631 0.271954i
\(364\) 0.225124 0.692860i 0.0117997 0.0363157i
\(365\) 0 0
\(366\) 5.81047 + 17.8828i 0.303718 + 0.934748i
\(367\) −3.23501 + 2.35037i −0.168866 + 0.122688i −0.669008 0.743255i \(-0.733281\pi\)
0.500142 + 0.865943i \(0.333281\pi\)
\(368\) 40.3836 2.10514
\(369\) −1.50113 + 1.09063i −0.0781456 + 0.0567761i
\(370\) 0 0
\(371\) −5.04705 3.66690i −0.262030 0.190376i
\(372\) 1.07971 + 0.784453i 0.0559802 + 0.0406720i
\(373\) 0.980386 3.01732i 0.0507625 0.156231i −0.922462 0.386088i \(-0.873826\pi\)
0.973224 + 0.229857i \(0.0738260\pi\)
\(374\) 7.94355 0.410751
\(375\) 0 0
\(376\) −16.7803 −0.865377
\(377\) −3.29453 + 10.1395i −0.169677 + 0.522212i
\(378\) −1.85904 1.35067i −0.0956187 0.0694711i
\(379\) −23.0736 16.7640i −1.18521 0.861107i −0.192462 0.981304i \(-0.561647\pi\)
−0.992750 + 0.120198i \(0.961647\pi\)
\(380\) 0 0
\(381\) 4.64372 3.37386i 0.237905 0.172848i
\(382\) 32.2497 1.65004
\(383\) −9.27224 + 6.73667i −0.473789 + 0.344228i −0.798916 0.601442i \(-0.794593\pi\)
0.325127 + 0.945670i \(0.394593\pi\)
\(384\) −4.13526 12.7270i −0.211026 0.649472i
\(385\) 0 0
\(386\) 10.7828 33.1862i 0.548832 1.68913i
\(387\) 2.47793 + 7.62628i 0.125960 + 0.387665i
\(388\) −1.39374 4.28949i −0.0707564 0.217766i
\(389\) 10.5827 32.5702i 0.536564 1.65137i −0.203681 0.979037i \(-0.565291\pi\)
0.740245 0.672337i \(-0.234709\pi\)
\(390\) 0 0
\(391\) −5.96301 18.3522i −0.301562 0.928113i
\(392\) 9.70541 7.05140i 0.490197 0.356149i
\(393\) −4.35756 −0.219810
\(394\) −1.68242 + 1.22235i −0.0847591 + 0.0615811i
\(395\) 0 0
\(396\) 0.688111 + 0.499942i 0.0345789 + 0.0251230i
\(397\) −16.2073 11.7753i −0.813422 0.590986i 0.101399 0.994846i \(-0.467668\pi\)
−0.914821 + 0.403860i \(0.867668\pi\)
\(398\) 4.25467 13.0945i 0.213267 0.656369i
\(399\) −8.54031 −0.427550
\(400\) 0 0
\(401\) 4.98200 0.248789 0.124395 0.992233i \(-0.460301\pi\)
0.124395 + 0.992233i \(0.460301\pi\)
\(402\) 2.04817 6.30363i 0.102154 0.314396i
\(403\) −4.03647 2.93267i −0.201071 0.146087i
\(404\) −2.39401 1.73935i −0.119107 0.0865361i
\(405\) 0 0
\(406\) −14.6867 + 10.6705i −0.728890 + 0.529570i
\(407\) 22.9758 1.13887
\(408\) −4.47029 + 3.24785i −0.221312 + 0.160793i
\(409\) 7.37286 + 22.6913i 0.364565 + 1.12201i 0.950253 + 0.311478i \(0.100824\pi\)
−0.585689 + 0.810536i \(0.699176\pi\)
\(410\) 0 0
\(411\) −0.610187 + 1.87796i −0.0300983 + 0.0926330i
\(412\) −0.278875 0.858290i −0.0137392 0.0422849i
\(413\) −5.11335 15.7373i −0.251612 0.774381i
\(414\) 4.17604 12.8525i 0.205241 0.631667i
\(415\) 0 0
\(416\) −0.841718 2.59054i −0.0412686 0.127012i
\(417\) −1.35842 + 0.986948i −0.0665220 + 0.0483311i
\(418\) 20.6755 1.01127
\(419\) −0.390391 + 0.283636i −0.0190719 + 0.0138565i −0.597280 0.802033i \(-0.703752\pi\)
0.578208 + 0.815889i \(0.303752\pi\)
\(420\) 0 0
\(421\) 14.3344 + 10.4146i 0.698616 + 0.507575i 0.879481 0.475933i \(-0.157890\pi\)
−0.180865 + 0.983508i \(0.557890\pi\)
\(422\) 7.25945 + 5.27430i 0.353385 + 0.256749i
\(423\) −2.05897 + 6.33687i −0.100111 + 0.308109i
\(424\) −10.5057 −0.510203
\(425\) 0 0
\(426\) −8.87740 −0.430112
\(427\) 5.65523 17.4050i 0.273676 0.842288i
\(428\) −0.528596 0.384047i −0.0255506 0.0185636i
\(429\) −2.57250 1.86903i −0.124201 0.0902375i
\(430\) 0 0
\(431\) −21.6866 + 15.7562i −1.04461 + 0.758952i −0.971180 0.238349i \(-0.923394\pi\)
−0.0734279 + 0.997301i \(0.523394\pi\)
\(432\) −4.59165 −0.220916
\(433\) −7.46816 + 5.42593i −0.358897 + 0.260754i −0.752592 0.658487i \(-0.771197\pi\)
0.393695 + 0.919241i \(0.371197\pi\)
\(434\) −2.62532 8.07992i −0.126020 0.387848i
\(435\) 0 0
\(436\) −0.328818 + 1.01200i −0.0157475 + 0.0484659i
\(437\) −15.5205 47.7673i −0.742448 2.28502i
\(438\) 3.28899 + 10.1225i 0.157154 + 0.483671i
\(439\) 0.309760 0.953343i 0.0147840 0.0455006i −0.943392 0.331679i \(-0.892385\pi\)
0.958176 + 0.286178i \(0.0923850\pi\)
\(440\) 0 0
\(441\) −1.47200 4.53035i −0.0700952 0.215731i
\(442\) −3.68065 + 2.67415i −0.175071 + 0.127196i
\(443\) 26.2872 1.24894 0.624471 0.781048i \(-0.285315\pi\)
0.624471 + 0.781048i \(0.285315\pi\)
\(444\) 2.84763 2.06893i 0.135143 0.0981869i
\(445\) 0 0
\(446\) 9.72219 + 7.06358i 0.460359 + 0.334470i
\(447\) 5.97479 + 4.34094i 0.282598 + 0.205319i
\(448\) −2.81066 + 8.65032i −0.132791 + 0.408689i
\(449\) 4.75449 0.224378 0.112189 0.993687i \(-0.464214\pi\)
0.112189 + 0.993687i \(0.464214\pi\)
\(450\) 0 0
\(451\) −4.37202 −0.205870
\(452\) −1.54343 + 4.75019i −0.0725968 + 0.223430i
\(453\) 3.44752 + 2.50477i 0.161979 + 0.117684i
\(454\) −20.2736 14.7296i −0.951485 0.691294i
\(455\) 0 0
\(456\) −11.6353 + 8.45353i −0.544872 + 0.395873i
\(457\) −15.9703 −0.747059 −0.373529 0.927618i \(-0.621852\pi\)
−0.373529 + 0.927618i \(0.621852\pi\)
\(458\) −26.9860 + 19.6065i −1.26097 + 0.916151i
\(459\) 0.677999 + 2.08667i 0.0316463 + 0.0973972i
\(460\) 0 0
\(461\) 12.2852 37.8100i 0.572180 1.76099i −0.0734077 0.997302i \(-0.523387\pi\)
0.645588 0.763686i \(-0.276613\pi\)
\(462\) −1.67315 5.14944i −0.0778421 0.239573i
\(463\) 8.07181 + 24.8425i 0.375129 + 1.15453i 0.943392 + 0.331681i \(0.107616\pi\)
−0.568263 + 0.822847i \(0.692384\pi\)
\(464\) −11.2095 + 34.4994i −0.520389 + 1.60159i
\(465\) 0 0
\(466\) −6.42623 19.7779i −0.297689 0.916194i
\(467\) 3.11637 2.26417i 0.144208 0.104773i −0.513342 0.858184i \(-0.671593\pi\)
0.657550 + 0.753411i \(0.271593\pi\)
\(468\) −0.487140 −0.0225181
\(469\) −5.21893 + 3.79177i −0.240988 + 0.175088i
\(470\) 0 0
\(471\) 12.9907 + 9.43827i 0.598578 + 0.434893i
\(472\) −22.5438 16.3790i −1.03766 0.753906i
\(473\) −5.83863 + 17.9695i −0.268460 + 0.826236i
\(474\) 16.3930 0.752956
\(475\) 0 0
\(476\) −1.18443 −0.0542884
\(477\) −1.28907 + 3.96736i −0.0590226 + 0.181653i
\(478\) −13.0945 9.51374i −0.598930 0.435148i
\(479\) 11.5445 + 8.38758i 0.527483 + 0.383239i 0.819415 0.573200i \(-0.194298\pi\)
−0.291933 + 0.956439i \(0.594298\pi\)
\(480\) 0 0
\(481\) −10.6458 + 7.73466i −0.485409 + 0.352670i
\(482\) −29.9377 −1.36363
\(483\) −10.6409 + 7.73108i −0.484179 + 0.351776i
\(484\) −0.607720 1.87037i −0.0276236 0.0850167i
\(485\) 0 0
\(486\) −0.474819 + 1.46134i −0.0215382 + 0.0662879i
\(487\) 7.67049 + 23.6073i 0.347583 + 1.06975i 0.960186 + 0.279360i \(0.0901223\pi\)
−0.612604 + 0.790390i \(0.709878\pi\)
\(488\) −9.52349 29.3103i −0.431108 1.32681i
\(489\) 6.88916 21.2026i 0.311538 0.958817i
\(490\) 0 0
\(491\) 3.55040 + 10.9270i 0.160227 + 0.493129i 0.998653 0.0518868i \(-0.0165235\pi\)
−0.838426 + 0.545016i \(0.816524\pi\)
\(492\) −0.541871 + 0.393693i −0.0244295 + 0.0177490i
\(493\) 17.3334 0.780656
\(494\) −9.58003 + 6.96030i −0.431026 + 0.313159i
\(495\) 0 0
\(496\) −13.7340 9.97831i −0.616673 0.448039i
\(497\) 6.99010 + 5.07860i 0.313549 + 0.227806i
\(498\) 0.106361 0.327345i 0.00476614 0.0146687i
\(499\) −4.17487 −0.186893 −0.0934465 0.995624i \(-0.529788\pi\)
−0.0934465 + 0.995624i \(0.529788\pi\)
\(500\) 0 0
\(501\) 6.46601 0.288880
\(502\) 9.94491 30.6073i 0.443863 1.36607i
\(503\) −31.3221 22.7569i −1.39658 1.01468i −0.995106 0.0988094i \(-0.968497\pi\)
−0.401478 0.915869i \(-0.631503\pi\)
\(504\) 3.04701 + 2.21378i 0.135725 + 0.0986097i
\(505\) 0 0
\(506\) 25.7610 18.7164i 1.14521 0.832047i
\(507\) −11.1788 −0.496469
\(508\) 1.67627 1.21788i 0.0743726 0.0540349i
\(509\) 9.32603 + 28.7026i 0.413369 + 1.27222i 0.913702 + 0.406385i \(0.133211\pi\)
−0.500333 + 0.865833i \(0.666789\pi\)
\(510\) 0 0
\(511\) 3.20112 9.85205i 0.141609 0.435829i
\(512\) 4.28289 + 13.1814i 0.189279 + 0.582540i
\(513\) 1.76470 + 5.43119i 0.0779134 + 0.239793i
\(514\) −0.793523 + 2.44221i −0.0350008 + 0.107721i
\(515\) 0 0
\(516\) 0.894473 + 2.75291i 0.0393770 + 0.121190i
\(517\) −12.7013 + 9.22804i −0.558603 + 0.405849i
\(518\) −22.4067 −0.984496
\(519\) −9.56100 + 6.94647i −0.419681 + 0.304916i
\(520\) 0 0
\(521\) 20.6183 + 14.9801i 0.903304 + 0.656288i 0.939312 0.343063i \(-0.111464\pi\)
−0.0360088 + 0.999351i \(0.511464\pi\)
\(522\) 9.82064 + 7.13511i 0.429838 + 0.312295i
\(523\) −1.20263 + 3.70132i −0.0525874 + 0.161847i −0.973901 0.226973i \(-0.927117\pi\)
0.921314 + 0.388820i \(0.127117\pi\)
\(524\) −1.57298 −0.0687158
\(525\) 0 0
\(526\) 11.6112 0.506271
\(527\) −2.50668 + 7.71476i −0.109193 + 0.336060i
\(528\) −8.75283 6.35931i −0.380918 0.276753i
\(529\) −43.9719 31.9474i −1.91182 1.38902i
\(530\) 0 0
\(531\) −8.95150 + 6.50365i −0.388462 + 0.282234i
\(532\) −3.08285 −0.133659
\(533\) 2.02578 1.47182i 0.0877463 0.0637514i
\(534\) −0.203777 0.627160i −0.00881828 0.0271399i
\(535\) 0 0
\(536\) −3.35700 + 10.3318i −0.145000 + 0.446265i
\(537\) 4.81281 + 14.8123i 0.207688 + 0.639198i
\(538\) 5.35792 + 16.4900i 0.230996 + 0.710933i
\(539\) 3.46841 10.6747i 0.149395 0.459790i
\(540\) 0 0
\(541\) 12.4270 + 38.2465i 0.534280 + 1.64435i 0.745199 + 0.666842i \(0.232354\pi\)
−0.210919 + 0.977504i \(0.567646\pi\)
\(542\) −13.6432 + 9.91235i −0.586025 + 0.425772i
\(543\) −14.5797 −0.625675
\(544\) −3.58273 + 2.60300i −0.153608 + 0.111603i
\(545\) 0 0
\(546\) 2.50879 + 1.82274i 0.107366 + 0.0780061i
\(547\) 5.96992 + 4.33740i 0.255255 + 0.185454i 0.708053 0.706160i \(-0.249574\pi\)
−0.452797 + 0.891613i \(0.649574\pi\)
\(548\) −0.220263 + 0.677900i −0.00940917 + 0.0289584i
\(549\) −12.2372 −0.522272
\(550\) 0 0
\(551\) 45.1154 1.92198
\(552\) −6.84463 + 21.0656i −0.291327 + 0.896611i
\(553\) −12.9079 9.37814i −0.548900 0.398799i
\(554\) 7.14917 + 5.19418i 0.303739 + 0.220679i
\(555\) 0 0
\(556\) −0.490357 + 0.356265i −0.0207958 + 0.0151090i
\(557\) −1.52499 −0.0646160 −0.0323080 0.999478i \(-0.510286\pi\)
−0.0323080 + 0.999478i \(0.510286\pi\)
\(558\) −4.59592 + 3.33913i −0.194561 + 0.141357i
\(559\) −3.34398 10.2917i −0.141435 0.435293i
\(560\) 0 0
\(561\) −1.59754 + 4.91672i −0.0674481 + 0.207584i
\(562\) −4.03578 12.4209i −0.170239 0.523942i
\(563\) −4.26305 13.1203i −0.179666 0.552955i 0.820150 0.572149i \(-0.193890\pi\)
−0.999816 + 0.0191938i \(0.993890\pi\)
\(564\) −0.743241 + 2.28746i −0.0312961 + 0.0963194i
\(565\) 0 0
\(566\) −8.17867 25.1714i −0.343775 1.05803i
\(567\) 1.20988 0.879031i 0.0508103 0.0369158i
\(568\) 14.5503 0.610516
\(569\) 6.87586 4.99561i 0.288251 0.209427i −0.434257 0.900789i \(-0.642989\pi\)
0.722508 + 0.691362i \(0.242989\pi\)
\(570\) 0 0
\(571\) −31.8130 23.1135i −1.33133 0.967269i −0.999715 0.0238553i \(-0.992406\pi\)
−0.331617 0.943414i \(-0.607594\pi\)
\(572\) −0.928611 0.674675i −0.0388272 0.0282096i
\(573\) −6.48577 + 19.9611i −0.270947 + 0.833889i
\(574\) 4.26374 0.177965
\(575\) 0 0
\(576\) 6.08192 0.253413
\(577\) −7.59664 + 23.3800i −0.316252 + 0.973324i 0.658984 + 0.752157i \(0.270987\pi\)
−0.975236 + 0.221167i \(0.929013\pi\)
\(578\) −15.1485 11.0060i −0.630095 0.457791i
\(579\) 18.3723 + 13.3482i 0.763525 + 0.554734i
\(580\) 0 0
\(581\) −0.271017 + 0.196905i −0.0112437 + 0.00816901i
\(582\) 19.1985 0.795802
\(583\) −7.95197 + 5.77745i −0.329337 + 0.239277i
\(584\) −5.39074 16.5910i −0.223070 0.686540i
\(585\) 0 0
\(586\) 4.45743 13.7186i 0.184135 0.566708i
\(587\) 2.85615 + 8.79033i 0.117886 + 0.362816i 0.992538 0.121936i \(-0.0389101\pi\)
−0.874652 + 0.484751i \(0.838910\pi\)
\(588\) −0.531357 1.63535i −0.0219128 0.0674407i
\(589\) −6.52439 + 20.0800i −0.268833 + 0.827383i
\(590\) 0 0
\(591\) −0.418228 1.28717i −0.0172036 0.0529472i
\(592\) −36.2221 + 26.3169i −1.48872 + 1.08162i
\(593\) 6.07888 0.249630 0.124815 0.992180i \(-0.460166\pi\)
0.124815 + 0.992180i \(0.460166\pi\)
\(594\) −2.92904 + 2.12807i −0.120180 + 0.0873160i
\(595\) 0 0
\(596\) 2.15676 + 1.56698i 0.0883442 + 0.0641858i
\(597\) 7.24929 + 5.26692i 0.296694 + 0.215560i
\(598\) −5.63559 + 17.3446i −0.230456 + 0.709272i
\(599\) 6.40129 0.261550 0.130775 0.991412i \(-0.458254\pi\)
0.130775 + 0.991412i \(0.458254\pi\)
\(600\) 0 0
\(601\) −38.4675 −1.56912 −0.784560 0.620052i \(-0.787111\pi\)
−0.784560 + 0.620052i \(0.787111\pi\)
\(602\) 5.69403 17.5244i 0.232071 0.714242i
\(603\) 3.48976 + 2.53546i 0.142114 + 0.103252i
\(604\) 1.24447 + 0.904162i 0.0506369 + 0.0367898i
\(605\) 0 0
\(606\) 10.1905 7.40380i 0.413959 0.300759i
\(607\) −5.22464 −0.212062 −0.106031 0.994363i \(-0.533814\pi\)
−0.106031 + 0.994363i \(0.533814\pi\)
\(608\) −9.32514 + 6.77511i −0.378184 + 0.274767i
\(609\) −3.65093 11.2364i −0.147943 0.455323i
\(610\) 0 0
\(611\) 2.77860 8.55164i 0.112410 0.345962i
\(612\) 0.244742 + 0.753237i 0.00989309 + 0.0304478i
\(613\) −9.21343 28.3560i −0.372127 1.14529i −0.945397 0.325922i \(-0.894325\pi\)
0.573270 0.819367i \(-0.305675\pi\)
\(614\) 5.05516 15.5582i 0.204010 0.627877i
\(615\) 0 0
\(616\) 2.74234 + 8.44005i 0.110492 + 0.340059i
\(617\) 18.8521 13.6969i 0.758958 0.551415i −0.139633 0.990203i \(-0.544592\pi\)
0.898591 + 0.438788i \(0.144592\pi\)
\(618\) 3.84145 0.154526
\(619\) 0.191326 0.139007i 0.00769006 0.00558715i −0.583934 0.811801i \(-0.698487\pi\)
0.591624 + 0.806214i \(0.298487\pi\)
\(620\) 0 0
\(621\) 7.11531 + 5.16958i 0.285528 + 0.207448i
\(622\) −34.0075 24.7079i −1.36358 0.990696i
\(623\) −0.198333 + 0.610405i −0.00794603 + 0.0244554i
\(624\) 6.19646 0.248057
\(625\) 0 0
\(626\) −3.06555 −0.122524
\(627\) −4.15808 + 12.7973i −0.166058 + 0.511073i
\(628\) 4.68932 + 3.40699i 0.187124 + 0.135954i
\(629\) 17.3082 + 12.5751i 0.690123 + 0.501404i
\(630\) 0 0
\(631\) 14.4643 10.5090i 0.575816 0.418355i −0.261397 0.965231i \(-0.584183\pi\)
0.837213 + 0.546876i \(0.184183\pi\)
\(632\) −26.8685 −1.06877
\(633\) −4.72452 + 3.43257i −0.187783 + 0.136432i
\(634\) 4.10659 + 12.6388i 0.163094 + 0.501951i
\(635\) 0 0
\(636\) −0.465325 + 1.43212i −0.0184513 + 0.0567873i
\(637\) 1.98647 + 6.11374i 0.0787069 + 0.242235i
\(638\) 8.83867 + 27.2026i 0.349926 + 1.07696i
\(639\) 1.78535 5.49473i 0.0706272 0.217368i
\(640\) 0 0
\(641\) 3.35839 + 10.3361i 0.132648 + 0.408250i 0.995217 0.0976905i \(-0.0311455\pi\)
−0.862568 + 0.505940i \(0.831146\pi\)
\(642\) 2.25004 1.63475i 0.0888021 0.0645185i
\(643\) −3.09039 −0.121873 −0.0609366 0.998142i \(-0.519409\pi\)
−0.0609366 + 0.998142i \(0.519409\pi\)
\(644\) −3.84112 + 2.79074i −0.151361 + 0.109970i
\(645\) 0 0
\(646\) 15.5754 + 11.3162i 0.612805 + 0.445229i
\(647\) −4.47957 3.25460i −0.176110 0.127951i 0.496238 0.868186i \(-0.334714\pi\)
−0.672348 + 0.740235i \(0.734714\pi\)
\(648\) 0.778240 2.39518i 0.0305721 0.0940914i
\(649\) −26.0712 −1.02338
\(650\) 0 0
\(651\) 5.52910 0.216703
\(652\) 2.48682 7.65366i 0.0973915 0.299740i
\(653\) 31.4509 + 22.8504i 1.23077 + 0.894206i 0.996948 0.0780738i \(-0.0248770\pi\)
0.233821 + 0.972280i \(0.424877\pi\)
\(654\) −3.66436 2.66231i −0.143288 0.104105i
\(655\) 0 0
\(656\) 6.89265 5.00780i 0.269113 0.195522i
\(657\) −6.92684 −0.270242
\(658\) 12.3867 8.99949i 0.482885 0.350837i
\(659\) −6.34687 19.5337i −0.247239 0.760923i −0.995260 0.0972484i \(-0.968996\pi\)
0.748021 0.663675i \(-0.231004\pi\)
\(660\) 0 0
\(661\) 11.8741 36.5447i 0.461848 1.42142i −0.401055 0.916054i \(-0.631356\pi\)
0.862903 0.505369i \(-0.168644\pi\)
\(662\) 1.87236 + 5.76252i 0.0727712 + 0.223967i
\(663\) −0.914964 2.81597i −0.0355342 0.109363i
\(664\) −0.174328 + 0.536526i −0.00676524 + 0.0208213i
\(665\) 0 0
\(666\) 4.62995 + 14.2495i 0.179407 + 0.552157i
\(667\) 56.2122 40.8405i 2.17654 1.58135i
\(668\) 2.33408 0.0903081
\(669\) −6.32730 + 4.59705i −0.244627 + 0.177732i
\(670\) 0 0
\(671\) −23.3272 16.9482i −0.900537 0.654278i
\(672\) 2.44204 + 1.77424i 0.0942037 + 0.0684430i
\(673\) 4.01164 12.3466i 0.154637 0.475925i −0.843487 0.537150i \(-0.819501\pi\)
0.998124 + 0.0612254i \(0.0195009\pi\)
\(674\) 6.07660 0.234062
\(675\) 0 0
\(676\) −4.03529 −0.155204
\(677\) −2.23715 + 6.88524i −0.0859807 + 0.264621i −0.984798 0.173701i \(-0.944427\pi\)
0.898818 + 0.438323i \(0.144427\pi\)
\(678\) −17.2000 12.4965i −0.660563 0.479927i
\(679\) −15.1169 10.9831i −0.580134 0.421492i
\(680\) 0 0
\(681\) 13.1942 9.58617i 0.505604 0.367343i
\(682\) −13.3856 −0.512561
\(683\) 20.1283 14.6241i 0.770188 0.559575i −0.131830 0.991272i \(-0.542085\pi\)
0.902018 + 0.431698i \(0.142085\pi\)
\(684\) 0.637015 + 1.96053i 0.0243569 + 0.0749627i
\(685\) 0 0
\(686\) −8.35314 + 25.7083i −0.318924 + 0.981548i
\(687\) −6.70838 20.6463i −0.255941 0.787704i
\(688\) −11.3778 35.0172i −0.433774 1.33502i
\(689\) 1.73961 5.35397i 0.0662739 0.203970i
\(690\) 0 0
\(691\) −10.2812 31.6422i −0.391114 1.20373i −0.931947 0.362595i \(-0.881891\pi\)
0.540832 0.841130i \(-0.318109\pi\)
\(692\) −3.45130 + 2.50751i −0.131199 + 0.0953213i
\(693\) 3.52377 0.133857
\(694\) 12.4259 9.02794i 0.471681 0.342696i
\(695\) 0 0
\(696\) −16.0963 11.6946i −0.610127 0.443283i
\(697\) −3.29355 2.39290i −0.124752 0.0906377i
\(698\) −8.76204 + 26.9668i −0.331648 + 1.02071i
\(699\) 13.5341 0.511905
\(700\) 0 0
\(701\) −13.2163 −0.499173 −0.249586 0.968353i \(-0.580295\pi\)
−0.249586 + 0.968353i \(0.580295\pi\)
\(702\) 0.640771 1.97209i 0.0241844 0.0744318i
\(703\) 45.0499 + 32.7307i 1.69909 + 1.23446i
\(704\) 11.5937 + 8.42328i 0.436952 + 0.317464i
\(705\) 0 0
\(706\) −11.5906 + 8.42104i −0.436217 + 0.316930i
\(707\) −12.2596 −0.461069
\(708\) −3.23128 + 2.34766i −0.121439 + 0.0882306i
\(709\) 1.93157 + 5.94475i 0.0725415 + 0.223260i 0.980753 0.195251i \(-0.0625522\pi\)
−0.908212 + 0.418511i \(0.862552\pi\)
\(710\) 0 0
\(711\) −3.29682 + 10.1466i −0.123640 + 0.380526i
\(712\) 0.333995 + 1.02793i 0.0125170 + 0.0385233i
\(713\) 10.0482 + 30.9252i 0.376308 + 1.15816i
\(714\) 1.55797 4.79495i 0.0583057 0.179446i
\(715\) 0 0
\(716\) 1.73731 + 5.34689i 0.0649263 + 0.199823i
\(717\) 8.52206 6.19164i 0.318262 0.231231i
\(718\) −44.4735 −1.65973
\(719\) −22.2492 + 16.1650i −0.829757 + 0.602854i −0.919491 0.393112i \(-0.871398\pi\)
0.0897336 + 0.995966i \(0.471398\pi\)
\(720\) 0 0
\(721\) −3.02477 2.19762i −0.112648 0.0818437i
\(722\) 16.9209 + 12.2938i 0.629731 + 0.457526i
\(723\) 6.02082 18.5302i 0.223917 0.689145i
\(724\) −5.26293 −0.195595
\(725\) 0 0
\(726\) 8.37120 0.310684
\(727\) 6.81063 20.9610i 0.252592 0.777399i −0.741702 0.670729i \(-0.765981\pi\)
0.994295 0.106670i \(-0.0340188\pi\)
\(728\) −4.11196 2.98751i −0.152399 0.110725i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) 0 0
\(731\) −14.2335 + 10.3412i −0.526443 + 0.382484i
\(732\) −4.41735 −0.163270
\(733\) 28.0838 20.4041i 1.03730 0.753641i 0.0675414 0.997716i \(-0.478485\pi\)
0.969756 + 0.244076i \(0.0784845\pi\)
\(734\) −1.89865 5.84345i −0.0700806 0.215686i
\(735\) 0 0
\(736\) −5.48565 + 16.8831i −0.202204 + 0.622319i
\(737\) 3.14082 + 9.66645i 0.115694 + 0.356068i
\(738\) −0.881025 2.71151i −0.0324310 0.0998122i
\(739\) −2.34418 + 7.21465i −0.0862321 + 0.265395i −0.984870 0.173297i \(-0.944558\pi\)
0.898638 + 0.438692i \(0.144558\pi\)
\(740\) 0 0
\(741\) −2.38147 7.32942i −0.0874856 0.269253i
\(742\) 7.75503 5.63436i 0.284696 0.206844i
\(743\) −27.5328 −1.01008 −0.505040 0.863096i \(-0.668522\pi\)
−0.505040 + 0.863096i \(0.668522\pi\)
\(744\) 7.53283 5.47292i 0.276167 0.200647i
\(745\) 0 0
\(746\) 3.94383 + 2.86536i 0.144394 + 0.104908i
\(747\) 0.181222 + 0.131666i 0.00663057 + 0.00481739i
\(748\) −0.576674 + 1.77482i −0.0210853 + 0.0648938i
\(749\) −2.70690 −0.0989081
\(750\) 0 0
\(751\) 4.24930 0.155059 0.0775296 0.996990i \(-0.475297\pi\)
0.0775296 + 0.996990i \(0.475297\pi\)
\(752\) 9.45408 29.0967i 0.344755 1.06105i
\(753\) 16.9446 + 12.3109i 0.617494 + 0.448636i
\(754\) −13.2530 9.62888i −0.482646 0.350663i
\(755\) 0 0
\(756\) 0.436739 0.317309i 0.0158840 0.0115404i
\(757\) 45.6609 1.65957 0.829787 0.558081i \(-0.188462\pi\)
0.829787 + 0.558081i \(0.188462\pi\)
\(758\) 35.4537 25.7586i 1.28774 0.935595i
\(759\) 6.40385 + 19.7090i 0.232445 + 0.715392i
\(760\) 0 0
\(761\) −12.3999 + 38.1628i −0.449495 + 1.38340i 0.427984 + 0.903786i \(0.359224\pi\)
−0.877479 + 0.479616i \(0.840776\pi\)
\(762\) 2.72544 + 8.38804i 0.0987323 + 0.303867i
\(763\) 1.36227 + 4.19262i 0.0493173 + 0.151783i
\(764\) −2.34121 + 7.20550i −0.0847020 + 0.260686i
\(765\) 0 0
\(766\) −5.44196 16.7486i −0.196626 0.605152i
\(767\) 12.0801 8.77671i 0.436187 0.316909i
\(768\) 8.39819 0.303044
\(769\) 30.6092 22.2389i 1.10380 0.801954i 0.122120 0.992515i \(-0.461031\pi\)
0.981675 + 0.190561i \(0.0610307\pi\)
\(770\) 0 0
\(771\) −1.35204 0.982314i −0.0486925 0.0353772i
\(772\) 6.63195 + 4.81840i 0.238689 + 0.173418i
\(773\) 8.10082 24.9318i 0.291366 0.896733i −0.693052 0.720888i \(-0.743734\pi\)
0.984418 0.175845i \(-0.0562658\pi\)
\(774\) −12.3212 −0.442875
\(775\) 0 0
\(776\) −31.4667 −1.12959
\(777\) 4.50625 13.8688i 0.161661 0.497541i
\(778\) 42.5713 + 30.9299i 1.52626 + 1.10889i
\(779\) −8.57247 6.22826i −0.307140 0.223151i
\(780\) 0 0
\(781\) 11.0134 8.00168i 0.394089 0.286323i
\(782\) 29.6503 1.06029
\(783\) −6.39137 + 4.64360i −0.228409 + 0.165949i
\(784\) 6.75891 + 20.8018i 0.241390 + 0.742921i
\(785\) 0 0
\(786\) 2.06905 6.36789i 0.0738007 0.227135i
\(787\) 0.745515 + 2.29446i 0.0265747 + 0.0817887i 0.963464 0.267837i \(-0.0863088\pi\)
−0.936890 + 0.349626i \(0.886309\pi\)
\(788\) −0.150970 0.464639i −0.00537810 0.0165521i
\(789\) −2.33514 + 7.18682i −0.0831331 + 0.255858i
\(790\) 0 0
\(791\) 6.39430 + 19.6796i 0.227355 + 0.699727i
\(792\) 4.80077 3.48796i 0.170588 0.123939i
\(793\) 16.5142 0.586437
\(794\) 24.9033 18.0933i 0.883785 0.642108i
\(795\) 0 0
\(796\) 2.61682 + 1.90123i 0.0927508 + 0.0673874i
\(797\) 6.56299 + 4.76829i 0.232473 + 0.168902i 0.697923 0.716172i \(-0.254108\pi\)
−0.465450 + 0.885074i \(0.654108\pi\)
\(798\) 4.05510 12.4803i 0.143549 0.441799i
\(799\) −14.6189 −0.517180
\(800\) 0 0
\(801\) 0.429167 0.0151639
\(802\) −2.36555 + 7.28041i −0.0835304 + 0.257080i
\(803\) −13.2043 9.59348i −0.465969 0.338546i
\(804\) 1.25972 + 0.915242i 0.0444270 + 0.0322781i
\(805\) 0 0
\(806\) 6.20223 4.50618i 0.218464 0.158724i
\(807\) −11.2841 −0.397220
\(808\) −16.7024 + 12.1350i −0.587589 + 0.426908i
\(809\) −12.5798 38.7166i −0.442282 1.36120i −0.885437 0.464759i \(-0.846141\pi\)
0.443155 0.896445i \(-0.353859\pi\)
\(810\) 0 0
\(811\) −15.2960 + 47.0763i −0.537116 + 1.65307i 0.201915 + 0.979403i \(0.435283\pi\)
−0.739032 + 0.673671i \(0.764717\pi\)
\(812\) −1.31790 4.05608i −0.0462493 0.142341i
\(813\) −3.39152 10.4380i −0.118946 0.366078i
\(814\) −10.9093 + 33.5755i −0.382372 + 1.17682i
\(815\) 0 0
\(816\) −3.11313 9.58124i −0.108981 0.335410i
\(817\) −37.0469 + 26.9162i −1.29611 + 0.941678i
\(818\) −36.6606 −1.28181
\(819\) −1.63274 + 1.18626i −0.0570527 + 0.0414512i
\(820\) 0 0
\(821\) −34.1498 24.8113i −1.19183 0.865919i −0.198378 0.980126i \(-0.563567\pi\)
−0.993457 + 0.114207i \(0.963567\pi\)
\(822\) −2.45462 1.78338i −0.0856146 0.0622027i
\(823\) 15.2144 46.8252i 0.530342 1.63222i −0.223162 0.974781i \(-0.571638\pi\)
0.753504 0.657443i \(-0.228362\pi\)
\(824\) −6.29622 −0.219339
\(825\) 0 0
\(826\) 25.4255 0.884666
\(827\) −15.7602 + 48.5050i −0.548036 + 1.68668i 0.165623 + 0.986189i \(0.447037\pi\)
−0.713659 + 0.700493i \(0.752963\pi\)
\(828\) 2.56846 + 1.86610i 0.0892602 + 0.0648513i
\(829\) 30.9321 + 22.4735i 1.07432 + 0.780537i 0.976683 0.214686i \(-0.0688727\pi\)
0.0976336 + 0.995222i \(0.468873\pi\)
\(830\) 0 0
\(831\) −4.65275 + 3.38042i −0.161402 + 0.117266i
\(832\) −8.20758 −0.284547
\(833\) 8.45531 6.14314i 0.292959 0.212847i
\(834\) −0.797267 2.45374i −0.0276071 0.0849659i
\(835\) 0 0
\(836\) −1.50097 + 4.61951i −0.0519121 + 0.159769i
\(837\) −1.14249 3.51622i −0.0394902 0.121538i
\(838\) −0.229124 0.705171i −0.00791496 0.0243597i
\(839\) −5.16324 + 15.8908i −0.178255 + 0.548612i −0.999767 0.0215787i \(-0.993131\pi\)
0.821512 + 0.570191i \(0.193131\pi\)
\(840\) 0 0
\(841\) 10.3251 + 31.7774i 0.356038 + 1.09577i
\(842\) −22.0255 + 16.0025i −0.759049 + 0.551481i
\(843\) 8.49962 0.292742
\(844\) −1.70544 + 1.23908i −0.0587037 + 0.0426507i
\(845\) 0 0
\(846\) −8.28270 6.01773i −0.284765 0.206894i
\(847\) −6.59151 4.78901i −0.226487 0.164552i
\(848\) 5.91897 18.2167i 0.203258 0.625564i
\(849\) 17.2248 0.591154
\(850\) 0 0
\(851\) 85.7599 2.93981
\(852\) 0.644468 1.98347i 0.0220791 0.0679525i
\(853\) −14.7762 10.7355i −0.505928 0.367578i 0.305349 0.952241i \(-0.401227\pi\)
−0.811277 + 0.584662i \(0.801227\pi\)
\(854\) 22.7495 + 16.5285i 0.778471 + 0.565593i
\(855\) 0 0
\(856\) −3.68787 + 2.67940i −0.126049 + 0.0915799i
\(857\) 53.4773 1.82675 0.913375 0.407119i \(-0.133466\pi\)
0.913375 + 0.407119i \(0.133466\pi\)
\(858\) 3.95276 2.87185i 0.134945 0.0980433i
\(859\) −5.79639 17.8395i −0.197770 0.608674i −0.999933 0.0115690i \(-0.996317\pi\)
0.802163 0.597105i \(-0.203683\pi\)
\(860\) 0 0
\(861\) −0.857487 + 2.63907i −0.0292231 + 0.0899394i
\(862\) −12.7281 39.1730i −0.433520 1.33424i
\(863\) 15.8329 + 48.7286i 0.538957 + 1.65874i 0.734939 + 0.678133i \(0.237211\pi\)
−0.195982 + 0.980607i \(0.562789\pi\)
\(864\) 0.623723 1.91962i 0.0212195 0.0653069i
\(865\) 0 0
\(866\) −4.38313 13.4899i −0.148945 0.458405i
\(867\) 9.85880 7.16284i 0.334822 0.243263i
\(868\) 1.99588 0.0677444
\(869\) −20.3373 + 14.7759i −0.689895 + 0.501238i
\(870\) 0 0
\(871\) −4.70946 3.42162i −0.159574 0.115937i
\(872\) 6.00597 + 4.36359i 0.203388 + 0.147770i
\(873\) −3.86103 + 11.8830i −0.130676 + 0.402179i
\(874\) 77.1739 2.61045
\(875\) 0 0
\(876\) −2.50042 −0.0844815
\(877\) 1.87359 5.76631i 0.0632666 0.194715i −0.914427 0.404751i \(-0.867358\pi\)
0.977694 + 0.210036i \(0.0673582\pi\)
\(878\) 1.24608 + 0.905331i 0.0420532 + 0.0305534i
\(879\) 7.59476 + 5.51791i 0.256165 + 0.186115i
\(880\) 0 0
\(881\) −18.3403 + 13.3250i −0.617899 + 0.448930i −0.852187 0.523237i \(-0.824724\pi\)
0.234288 + 0.972167i \(0.424724\pi\)
\(882\) 7.31933 0.246455
\(883\) −4.48114 + 3.25574i −0.150802 + 0.109564i −0.660628 0.750713i \(-0.729710\pi\)
0.509826 + 0.860278i \(0.329710\pi\)
\(884\) −0.330280 1.01650i −0.0111085 0.0341885i
\(885\) 0 0
\(886\) −12.4817 + 38.4146i −0.419329 + 1.29056i
\(887\) 3.39041 + 10.4346i 0.113839 + 0.350360i 0.991703 0.128550i \(-0.0410322\pi\)
−0.877864 + 0.478909i \(0.841032\pi\)
\(888\) −7.58859 23.3553i −0.254656 0.783752i
\(889\) 2.65263 8.16394i 0.0889662 0.273810i
\(890\) 0 0
\(891\) −0.728123 2.24093i −0.0243930 0.0750740i
\(892\) −2.28401 + 1.65943i −0.0764742 + 0.0555617i
\(893\) −38.0502 −1.27330
\(894\) −9.18054 + 6.67005i −0.307043 + 0.223080i
\(895\) 0 0
\(896\) −16.1906 11.7632i −0.540890 0.392980i
\(897\) −9.60216 6.97638i −0.320607 0.232934i
\(898\) −2.25752 + 6.94794i −0.0753345 + 0.231856i
\(899\) −29.2083 −0.974151
\(900\) 0 0
\(901\) −9.15254 −0.304915
\(902\) 2.07592 6.38902i 0.0691205 0.212731i
\(903\) 9.70173 + 7.04872i 0.322853 + 0.234567i
\(904\) 28.1912 + 20.4821i 0.937627 + 0.681226i
\(905\) 0 0
\(906\) −5.29727 + 3.84869i −0.175990 + 0.127864i
\(907\) 19.3907 0.643856 0.321928 0.946764i \(-0.395669\pi\)
0.321928 + 0.946764i \(0.395669\pi\)
\(908\) 4.76281 3.46038i 0.158059 0.114837i
\(909\) 2.53322 + 7.79645i 0.0840216 + 0.258592i
\(910\) 0 0
\(911\) −4.23940 + 13.0475i −0.140458 + 0.432284i −0.996399 0.0847888i \(-0.972978\pi\)
0.855941 + 0.517073i \(0.172978\pi\)
\(912\) −8.10288 24.9381i −0.268313 0.825783i
\(913\) 0.163102 + 0.501975i 0.00539788 + 0.0166130i
\(914\) 7.58300 23.3381i 0.250823 0.771955i
\(915\) 0 0
\(916\) −2.42157 7.45282i −0.0800108 0.246248i
\(917\) −5.27213 + 3.83043i −0.174101 + 0.126492i
\(918\) −3.37126 −0.111268
\(919\) 26.2209 19.0506i 0.864947 0.628421i −0.0642792 0.997932i \(-0.520475\pi\)
0.929226 + 0.369511i \(0.120475\pi\)
\(920\) 0 0
\(921\) 8.61319 + 6.25785i 0.283814 + 0.206203i
\(922\) 49.4202 + 35.9058i 1.62757 + 1.18250i
\(923\) −2.40934 + 7.41518i −0.0793043 + 0.244073i
\(924\) 1.27200 0.0418457
\(925\) 0 0
\(926\) −40.1360 −1.31895
\(927\) −0.772559 + 2.37769i −0.0253742 + 0.0780936i
\(928\) −12.9004 9.37270i −0.423477 0.307674i
\(929\) 3.50664 + 2.54772i 0.115049 + 0.0835880i 0.643822 0.765175i \(-0.277348\pi\)
−0.528773 + 0.848763i \(0.677348\pi\)
\(930\) 0 0
\(931\) 22.0075 15.9894i 0.721268 0.524032i
\(932\) 4.88548 0.160029
\(933\) 22.1324 16.0801i 0.724582 0.526440i
\(934\) 1.82902 + 5.62915i 0.0598474 + 0.184192i
\(935\) 0 0
\(936\) −1.05024 + 3.23230i −0.0343281 + 0.105651i
\(937\) 16.8700 + 51.9206i 0.551120 + 1.69617i 0.705977 + 0.708235i \(0.250508\pi\)
−0.154857 + 0.987937i \(0.549492\pi\)
\(938\) −3.06303 9.42705i −0.100012 0.307804i
\(939\) 0.616517 1.89744i 0.0201193 0.0619208i
\(940\) 0 0
\(941\) 1.30978 + 4.03108i 0.0426975 + 0.131409i 0.970133 0.242574i \(-0.0779917\pi\)
−0.927435 + 0.373983i \(0.877992\pi\)
\(942\) −19.9608 + 14.5023i −0.650357 + 0.472512i
\(943\) −16.3191 −0.531423
\(944\) 41.1022 29.8625i 1.33776 0.971940i
\(945\) 0 0
\(946\) −23.4872 17.0645i −0.763636 0.554814i
\(947\) −10.1992 7.41018i −0.331431 0.240798i 0.409607 0.912262i \(-0.365666\pi\)
−0.741037 + 0.671464i \(0.765666\pi\)
\(948\) −1.19007 + 3.66267i −0.0386518 + 0.118958i
\(949\) 9.34781 0.303443
\(950\) 0 0
\(951\) −8.64876 −0.280455
\(952\) −2.55356 + 7.85903i −0.0827612 + 0.254713i
\(953\) 25.2118 + 18.3174i 0.816690 + 0.593360i 0.915762 0.401720i \(-0.131588\pi\)
−0.0990725 + 0.995080i \(0.531588\pi\)
\(954\) −5.18559 3.76755i −0.167890 0.121979i
\(955\) 0 0
\(956\) 3.07626 2.23503i 0.0994934 0.0722862i
\(957\) −18.6148 −0.601732
\(958\) −17.7387 + 12.8879i −0.573111 + 0.416390i
\(959\) 0.912532 + 2.80848i 0.0294672 + 0.0906907i
\(960\) 0 0
\(961\) −5.35555 + 16.4827i −0.172760 + 0.531700i
\(962\) −6.24814 19.2298i −0.201448 0.619994i
\(963\) 0.559332 + 1.72145i 0.0180242 + 0.0554729i
\(964\) 2.17337 6.68896i 0.0699997 0.215437i
\(965\) 0 0
\(966\) −6.24525 19.2209i −0.200938 0.618422i
\(967\) −1.25647 + 0.912880i −0.0404054 + 0.0293562i −0.607805 0.794087i \(-0.707950\pi\)
0.567399 + 0.823443i \(0.307950\pi\)
\(968\) −13.7206 −0.440997
\(969\) −10.1366 + 7.36467i −0.325635 + 0.236587i
\(970\) 0 0
\(971\) 30.9548 + 22.4900i 0.993388 + 0.721739i 0.960660 0.277725i \(-0.0895806\pi\)
0.0327278 + 0.999464i \(0.489581\pi\)
\(972\) −0.292036 0.212177i −0.00936706 0.00680557i
\(973\) −0.775967 + 2.38818i −0.0248764 + 0.0765616i
\(974\) −38.1405 −1.22210
\(975\) 0 0
\(976\) 56.1890 1.79857
\(977\) −6.29348 + 19.3693i −0.201346 + 0.619680i 0.798497 + 0.601998i \(0.205629\pi\)
−0.999844 + 0.0176817i \(0.994371\pi\)
\(978\) 27.7132 + 20.1348i 0.886172 + 0.643841i
\(979\) 0.818100 + 0.594384i 0.0261466 + 0.0189966i
\(980\) 0 0
\(981\) 2.38480 1.73266i 0.0761408 0.0553195i
\(982\) −17.6539 −0.563359
\(983\) 10.7241 7.79150i 0.342045 0.248510i −0.403479 0.914989i \(-0.632199\pi\)
0.745524 + 0.666479i \(0.232199\pi\)
\(984\) 1.44402 + 4.44424i 0.0460337 + 0.141677i
\(985\) 0 0
\(986\) −8.23022 + 25.3300i −0.262103 + 0.806671i
\(987\) 3.07919 + 9.47676i 0.0980116 + 0.301649i
\(988\) −0.859655 2.64575i −0.0273493 0.0841724i
\(989\) −21.7934 + 67.0732i −0.692990 + 2.13280i
\(990\) 0 0
\(991\) −0.692448 2.13113i −0.0219963 0.0676977i 0.939456 0.342670i \(-0.111331\pi\)
−0.961452 + 0.274972i \(0.911331\pi\)
\(992\) 6.03721 4.38629i 0.191682 0.139265i
\(993\) −3.94331 −0.125137
\(994\) −10.7406 + 7.80351i −0.340671 + 0.247512i
\(995\) 0 0
\(996\) 0.0654169 + 0.0475282i 0.00207281 + 0.00150599i
\(997\) 11.3589 + 8.25272i 0.359740 + 0.261366i 0.752943 0.658085i \(-0.228633\pi\)
−0.393204 + 0.919451i \(0.628633\pi\)
\(998\) 1.98231 6.10092i 0.0627489 0.193121i
\(999\) −9.75097 −0.308507
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 375.2.g.e.226.2 16
5.2 odd 4 375.2.i.c.274.1 16
5.3 odd 4 75.2.i.a.4.4 16
5.4 even 2 375.2.g.d.226.3 16
15.8 even 4 225.2.m.b.154.1 16
25.6 even 5 inner 375.2.g.e.151.2 16
25.8 odd 20 375.2.i.c.349.1 16
25.9 even 10 1875.2.a.p.1.6 8
25.12 odd 20 1875.2.b.h.1249.4 16
25.13 odd 20 1875.2.b.h.1249.13 16
25.16 even 5 1875.2.a.m.1.3 8
25.17 odd 20 75.2.i.a.19.4 yes 16
25.19 even 10 375.2.g.d.151.3 16
75.17 even 20 225.2.m.b.19.1 16
75.41 odd 10 5625.2.a.bd.1.6 8
75.59 odd 10 5625.2.a.t.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.i.a.4.4 16 5.3 odd 4
75.2.i.a.19.4 yes 16 25.17 odd 20
225.2.m.b.19.1 16 75.17 even 20
225.2.m.b.154.1 16 15.8 even 4
375.2.g.d.151.3 16 25.19 even 10
375.2.g.d.226.3 16 5.4 even 2
375.2.g.e.151.2 16 25.6 even 5 inner
375.2.g.e.226.2 16 1.1 even 1 trivial
375.2.i.c.274.1 16 5.2 odd 4
375.2.i.c.349.1 16 25.8 odd 20
1875.2.a.m.1.3 8 25.16 even 5
1875.2.a.p.1.6 8 25.9 even 10
1875.2.b.h.1249.4 16 25.12 odd 20
1875.2.b.h.1249.13 16 25.13 odd 20
5625.2.a.t.1.3 8 75.59 odd 10
5625.2.a.bd.1.6 8 75.41 odd 10