Properties

Label 429.2.j.a.122.18
Level $429$
Weight $2$
Character 429.122
Analytic conductor $3.426$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(122,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.122");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.j (of order \(4\), degree \(2\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 122.18
Character \(\chi\) \(=\) 429.122
Dual form 429.2.j.a.320.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.680371 - 0.680371i) q^{2} +(-0.131936 + 1.72702i) q^{3} -1.07419i q^{4} +(-1.70906 - 1.70906i) q^{5} +(1.26478 - 1.08525i) q^{6} +(2.81165 + 2.81165i) q^{7} +(-2.09159 + 2.09159i) q^{8} +(-2.96519 - 0.455712i) q^{9} +O(q^{10})\) \(q+(-0.680371 - 0.680371i) q^{2} +(-0.131936 + 1.72702i) q^{3} -1.07419i q^{4} +(-1.70906 - 1.70906i) q^{5} +(1.26478 - 1.08525i) q^{6} +(2.81165 + 2.81165i) q^{7} +(-2.09159 + 2.09159i) q^{8} +(-2.96519 - 0.455712i) q^{9} +2.32560i q^{10} +(0.707107 - 0.707107i) q^{11} +(1.85515 + 0.141724i) q^{12} +(3.50480 - 0.846407i) q^{13} -3.82593i q^{14} +(3.17707 - 2.72610i) q^{15} +0.697738 q^{16} +5.81944 q^{17} +(1.70737 + 2.32748i) q^{18} +(1.64641 - 1.64641i) q^{19} +(-1.83586 + 1.83586i) q^{20} +(-5.22673 + 4.48481i) q^{21} -0.962190 q^{22} +0.839365 q^{23} +(-3.33626 - 3.88817i) q^{24} +0.841793i q^{25} +(-2.96043 - 1.80869i) q^{26} +(1.17824 - 5.06081i) q^{27} +(3.02024 - 3.02024i) q^{28} +0.447682i q^{29} +(-4.01635 - 0.306830i) q^{30} +(2.48598 - 2.48598i) q^{31} +(3.70846 + 3.70846i) q^{32} +(1.12789 + 1.31448i) q^{33} +(-3.95938 - 3.95938i) q^{34} -9.61057i q^{35} +(-0.489521 + 3.18517i) q^{36} +(5.15681 + 5.15681i) q^{37} -2.24035 q^{38} +(0.999353 + 6.16452i) q^{39} +7.14932 q^{40} +(5.85508 + 5.85508i) q^{41} +(6.60745 + 0.504778i) q^{42} -4.97364i q^{43} +(-0.759567 - 0.759567i) q^{44} +(4.28885 + 5.84653i) q^{45} +(-0.571080 - 0.571080i) q^{46} +(2.83286 - 2.83286i) q^{47} +(-0.0920567 + 1.20501i) q^{48} +8.81074i q^{49} +(0.572732 - 0.572732i) q^{50} +(-0.767793 + 10.0503i) q^{51} +(-0.909202 - 3.76482i) q^{52} +1.33071i q^{53} +(-4.24487 + 2.64159i) q^{54} -2.41698 q^{55} -11.7616 q^{56} +(2.62617 + 3.06061i) q^{57} +(0.304590 - 0.304590i) q^{58} +(9.10853 - 9.10853i) q^{59} +(-2.92834 - 3.41278i) q^{60} -13.8044 q^{61} -3.38278 q^{62} +(-7.05576 - 9.61836i) q^{63} -6.44174i q^{64} +(-7.43648 - 4.54335i) q^{65} +(0.126947 - 1.66172i) q^{66} +(-10.4347 + 10.4347i) q^{67} -6.25118i q^{68} +(-0.110742 + 1.44960i) q^{69} +(-6.53876 + 6.53876i) q^{70} +(0.802258 + 0.802258i) q^{71} +(7.15512 - 5.24879i) q^{72} +(7.40166 + 7.40166i) q^{73} -7.01709i q^{74} +(-1.45379 - 0.111063i) q^{75} +(-1.76856 - 1.76856i) q^{76} +3.97627 q^{77} +(3.51423 - 4.87409i) q^{78} -10.1499 q^{79} +(-1.19248 - 1.19248i) q^{80} +(8.58465 + 2.70254i) q^{81} -7.96726i q^{82} +(-7.43639 - 7.43639i) q^{83} +(4.81754 + 5.61450i) q^{84} +(-9.94579 - 9.94579i) q^{85} +(-3.38392 + 3.38392i) q^{86} +(-0.773154 - 0.0590653i) q^{87} +2.95796i q^{88} +(-9.42130 + 9.42130i) q^{89} +(1.05980 - 6.89582i) q^{90} +(12.2341 + 7.47446i) q^{91} -0.901637i q^{92} +(3.96534 + 4.62132i) q^{93} -3.85479 q^{94} -5.62765 q^{95} +(-6.89386 + 5.91530i) q^{96} +(-6.07376 + 6.07376i) q^{97} +(5.99458 - 5.99458i) q^{98} +(-2.41894 + 1.77447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.680371 0.680371i −0.481095 0.481095i 0.424386 0.905481i \(-0.360490\pi\)
−0.905481 + 0.424386i \(0.860490\pi\)
\(3\) −0.131936 + 1.72702i −0.0761732 + 0.997095i
\(4\) 1.07419i 0.537095i
\(5\) −1.70906 1.70906i −0.764316 0.764316i 0.212783 0.977099i \(-0.431747\pi\)
−0.977099 + 0.212783i \(0.931747\pi\)
\(6\) 1.26478 1.08525i 0.516344 0.443051i
\(7\) 2.81165 + 2.81165i 1.06270 + 1.06270i 0.997898 + 0.0648056i \(0.0206427\pi\)
0.0648056 + 0.997898i \(0.479357\pi\)
\(8\) −2.09159 + 2.09159i −0.739489 + 0.739489i
\(9\) −2.96519 0.455712i −0.988395 0.151904i
\(10\) 2.32560i 0.735418i
\(11\) 0.707107 0.707107i 0.213201 0.213201i
\(12\) 1.85515 + 0.141724i 0.535534 + 0.0409122i
\(13\) 3.50480 0.846407i 0.972056 0.234751i
\(14\) 3.82593i 1.02252i
\(15\) 3.17707 2.72610i 0.820316 0.703875i
\(16\) 0.697738 0.174434
\(17\) 5.81944 1.41142 0.705710 0.708500i \(-0.250628\pi\)
0.705710 + 0.708500i \(0.250628\pi\)
\(18\) 1.70737 + 2.32748i 0.402432 + 0.548592i
\(19\) 1.64641 1.64641i 0.377713 0.377713i −0.492563 0.870277i \(-0.663940\pi\)
0.870277 + 0.492563i \(0.163940\pi\)
\(20\) −1.83586 + 1.83586i −0.410510 + 0.410510i
\(21\) −5.22673 + 4.48481i −1.14057 + 0.978666i
\(22\) −0.962190 −0.205140
\(23\) 0.839365 0.175020 0.0875098 0.996164i \(-0.472109\pi\)
0.0875098 + 0.996164i \(0.472109\pi\)
\(24\) −3.33626 3.88817i −0.681011 0.793670i
\(25\) 0.841793i 0.168359i
\(26\) −2.96043 1.80869i −0.580589 0.354714i
\(27\) 1.17824 5.06081i 0.226752 0.973953i
\(28\) 3.02024 3.02024i 0.570773 0.570773i
\(29\) 0.447682i 0.0831324i 0.999136 + 0.0415662i \(0.0132347\pi\)
−0.999136 + 0.0415662i \(0.986765\pi\)
\(30\) −4.01635 0.306830i −0.733281 0.0560192i
\(31\) 2.48598 2.48598i 0.446495 0.446495i −0.447693 0.894188i \(-0.647754\pi\)
0.894188 + 0.447693i \(0.147754\pi\)
\(32\) 3.70846 + 3.70846i 0.655569 + 0.655569i
\(33\) 1.12789 + 1.31448i 0.196341 + 0.228821i
\(34\) −3.95938 3.95938i −0.679028 0.679028i
\(35\) 9.61057i 1.62448i
\(36\) −0.489521 + 3.18517i −0.0815868 + 0.530862i
\(37\) 5.15681 + 5.15681i 0.847774 + 0.847774i 0.989855 0.142081i \(-0.0453795\pi\)
−0.142081 + 0.989855i \(0.545379\pi\)
\(38\) −2.24035 −0.363432
\(39\) 0.999353 + 6.16452i 0.160024 + 0.987113i
\(40\) 7.14932 1.13041
\(41\) 5.85508 + 5.85508i 0.914410 + 0.914410i 0.996615 0.0822051i \(-0.0261963\pi\)
−0.0822051 + 0.996615i \(0.526196\pi\)
\(42\) 6.60745 + 0.504778i 1.01955 + 0.0778889i
\(43\) 4.97364i 0.758473i −0.925300 0.379237i \(-0.876187\pi\)
0.925300 0.379237i \(-0.123813\pi\)
\(44\) −0.759567 0.759567i −0.114509 0.114509i
\(45\) 4.28885 + 5.84653i 0.639344 + 0.871549i
\(46\) −0.571080 0.571080i −0.0842011 0.0842011i
\(47\) 2.83286 2.83286i 0.413215 0.413215i −0.469642 0.882857i \(-0.655617\pi\)
0.882857 + 0.469642i \(0.155617\pi\)
\(48\) −0.0920567 + 1.20501i −0.0132872 + 0.173928i
\(49\) 8.81074i 1.25868i
\(50\) 0.572732 0.572732i 0.0809966 0.0809966i
\(51\) −0.767793 + 10.0503i −0.107512 + 1.40732i
\(52\) −0.909202 3.76482i −0.126084 0.522086i
\(53\) 1.33071i 0.182787i 0.995815 + 0.0913937i \(0.0291322\pi\)
−0.995815 + 0.0913937i \(0.970868\pi\)
\(54\) −4.24487 + 2.64159i −0.577653 + 0.359475i
\(55\) −2.41698 −0.325906
\(56\) −11.7616 −1.57172
\(57\) 2.62617 + 3.06061i 0.347844 + 0.405388i
\(58\) 0.304590 0.304590i 0.0399946 0.0399946i
\(59\) 9.10853 9.10853i 1.18583 1.18583i 0.207621 0.978209i \(-0.433428\pi\)
0.978209 0.207621i \(-0.0665720\pi\)
\(60\) −2.92834 3.41278i −0.378048 0.440587i
\(61\) −13.8044 −1.76747 −0.883734 0.467990i \(-0.844978\pi\)
−0.883734 + 0.467990i \(0.844978\pi\)
\(62\) −3.38278 −0.429613
\(63\) −7.05576 9.61836i −0.888942 1.21180i
\(64\) 6.44174i 0.805217i
\(65\) −7.43648 4.54335i −0.922382 0.563534i
\(66\) 0.126947 1.66172i 0.0156262 0.204544i
\(67\) −10.4347 + 10.4347i −1.27480 + 1.27480i −0.331260 + 0.943540i \(0.607474\pi\)
−0.943540 + 0.331260i \(0.892526\pi\)
\(68\) 6.25118i 0.758067i
\(69\) −0.110742 + 1.44960i −0.0133318 + 0.174511i
\(70\) −6.53876 + 6.53876i −0.781531 + 0.781531i
\(71\) 0.802258 + 0.802258i 0.0952105 + 0.0952105i 0.753108 0.657897i \(-0.228554\pi\)
−0.657897 + 0.753108i \(0.728554\pi\)
\(72\) 7.15512 5.24879i 0.843239 0.618576i
\(73\) 7.40166 + 7.40166i 0.866299 + 0.866299i 0.992061 0.125762i \(-0.0401374\pi\)
−0.125762 + 0.992061i \(0.540137\pi\)
\(74\) 7.01709i 0.815720i
\(75\) −1.45379 0.111063i −0.167870 0.0128244i
\(76\) −1.76856 1.76856i −0.202868 0.202868i
\(77\) 3.97627 0.453138
\(78\) 3.51423 4.87409i 0.397908 0.551882i
\(79\) −10.1499 −1.14196 −0.570978 0.820965i \(-0.693436\pi\)
−0.570978 + 0.820965i \(0.693436\pi\)
\(80\) −1.19248 1.19248i −0.133323 0.133323i
\(81\) 8.58465 + 2.70254i 0.953850 + 0.300282i
\(82\) 7.96726i 0.879837i
\(83\) −7.43639 7.43639i −0.816250 0.816250i 0.169313 0.985562i \(-0.445845\pi\)
−0.985562 + 0.169313i \(0.945845\pi\)
\(84\) 4.81754 + 5.61450i 0.525637 + 0.612592i
\(85\) −9.94579 9.94579i −1.07877 1.07877i
\(86\) −3.38392 + 3.38392i −0.364898 + 0.364898i
\(87\) −0.773154 0.0590653i −0.0828909 0.00633246i
\(88\) 2.95796i 0.315319i
\(89\) −9.42130 + 9.42130i −0.998656 + 0.998656i −0.999999 0.00134288i \(-0.999573\pi\)
0.00134288 + 0.999999i \(0.499573\pi\)
\(90\) 1.05980 6.89582i 0.111713 0.726883i
\(91\) 12.2341 + 7.47446i 1.28248 + 0.783536i
\(92\) 0.901637i 0.0940021i
\(93\) 3.96534 + 4.62132i 0.411187 + 0.479209i
\(94\) −3.85479 −0.397591
\(95\) −5.62765 −0.577385
\(96\) −6.89386 + 5.91530i −0.703602 + 0.603728i
\(97\) −6.07376 + 6.07376i −0.616696 + 0.616696i −0.944683 0.327986i \(-0.893630\pi\)
0.327986 + 0.944683i \(0.393630\pi\)
\(98\) 5.99458 5.99458i 0.605544 0.605544i
\(99\) −2.41894 + 1.77447i −0.243113 + 0.178341i
\(100\) 0.904246 0.0904246
\(101\) −1.43632 −0.142919 −0.0714597 0.997443i \(-0.522766\pi\)
−0.0714597 + 0.997443i \(0.522766\pi\)
\(102\) 7.36030 6.31554i 0.728779 0.625331i
\(103\) 2.87211i 0.282997i −0.989938 0.141499i \(-0.954808\pi\)
0.989938 0.141499i \(-0.0451921\pi\)
\(104\) −5.56026 + 9.10094i −0.545228 + 0.892420i
\(105\) 16.5976 + 1.26798i 1.61976 + 0.123742i
\(106\) 0.905379 0.905379i 0.0879382 0.0879382i
\(107\) 6.76615i 0.654108i −0.945006 0.327054i \(-0.893944\pi\)
0.945006 0.327054i \(-0.106056\pi\)
\(108\) −5.43626 1.26565i −0.523105 0.121787i
\(109\) 8.32125 8.32125i 0.797031 0.797031i −0.185595 0.982626i \(-0.559421\pi\)
0.982626 + 0.185595i \(0.0594213\pi\)
\(110\) 1.64444 + 1.64444i 0.156792 + 0.156792i
\(111\) −9.58627 + 8.22553i −0.909888 + 0.780733i
\(112\) 1.96179 + 1.96179i 0.185372 + 0.185372i
\(113\) 6.35372i 0.597708i −0.954299 0.298854i \(-0.903396\pi\)
0.954299 0.298854i \(-0.0966044\pi\)
\(114\) 0.295582 3.86912i 0.0276838 0.362376i
\(115\) −1.43453 1.43453i −0.133770 0.133770i
\(116\) 0.480895 0.0446500
\(117\) −10.7781 + 0.912579i −0.996435 + 0.0843680i
\(118\) −12.3944 −1.14099
\(119\) 16.3622 + 16.3622i 1.49992 + 1.49992i
\(120\) −0.943252 + 12.3470i −0.0861067 + 1.12712i
\(121\) 1.00000i 0.0909091i
\(122\) 9.39210 + 9.39210i 0.850320 + 0.850320i
\(123\) −10.8843 + 9.33934i −0.981407 + 0.842100i
\(124\) −2.67041 2.67041i −0.239810 0.239810i
\(125\) −7.10664 + 7.10664i −0.635637 + 0.635637i
\(126\) −1.74352 + 11.3446i −0.155325 + 1.01066i
\(127\) 7.46419i 0.662340i −0.943571 0.331170i \(-0.892557\pi\)
0.943571 0.331170i \(-0.107443\pi\)
\(128\) 3.03415 3.03415i 0.268183 0.268183i
\(129\) 8.58957 + 0.656202i 0.756270 + 0.0577754i
\(130\) 1.96840 + 8.15074i 0.172640 + 0.714867i
\(131\) 1.76387i 0.154110i 0.997027 + 0.0770550i \(0.0245517\pi\)
−0.997027 + 0.0770550i \(0.975448\pi\)
\(132\) 1.41200 1.21157i 0.122899 0.105454i
\(133\) 9.25828 0.802795
\(134\) 14.1989 1.22660
\(135\) −10.6629 + 6.63556i −0.917718 + 0.571098i
\(136\) −12.1719 + 12.1719i −1.04373 + 1.04373i
\(137\) −13.5834 + 13.5834i −1.16051 + 1.16051i −0.176148 + 0.984364i \(0.556364\pi\)
−0.984364 + 0.176148i \(0.943636\pi\)
\(138\) 1.06161 0.910919i 0.0903703 0.0775426i
\(139\) −13.6260 −1.15574 −0.577870 0.816129i \(-0.696116\pi\)
−0.577870 + 0.816129i \(0.696116\pi\)
\(140\) −10.3236 −0.872501
\(141\) 4.51864 + 5.26615i 0.380538 + 0.443490i
\(142\) 1.09167i 0.0916106i
\(143\) 1.87976 3.07677i 0.157194 0.257292i
\(144\) −2.06892 0.317967i −0.172410 0.0264973i
\(145\) 0.765116 0.765116i 0.0635394 0.0635394i
\(146\) 10.0718i 0.833545i
\(147\) −15.2163 1.16245i −1.25502 0.0958775i
\(148\) 5.53939 5.53939i 0.455335 0.455335i
\(149\) −4.01381 4.01381i −0.328824 0.328824i 0.523315 0.852139i \(-0.324695\pi\)
−0.852139 + 0.523315i \(0.824695\pi\)
\(150\) 0.913555 + 1.06468i 0.0745915 + 0.0869310i
\(151\) 16.4170 + 16.4170i 1.33599 + 1.33599i 0.899904 + 0.436089i \(0.143637\pi\)
0.436089 + 0.899904i \(0.356363\pi\)
\(152\) 6.88725i 0.558630i
\(153\) −17.2557 2.65198i −1.39504 0.214400i
\(154\) −2.70534 2.70534i −0.218003 0.218003i
\(155\) −8.49739 −0.682527
\(156\) 6.62186 1.07349i 0.530173 0.0859483i
\(157\) 14.4641 1.15436 0.577182 0.816616i \(-0.304152\pi\)
0.577182 + 0.816616i \(0.304152\pi\)
\(158\) 6.90572 + 6.90572i 0.549390 + 0.549390i
\(159\) −2.29817 0.175569i −0.182256 0.0139235i
\(160\) 12.6760i 1.00212i
\(161\) 2.36000 + 2.36000i 0.185994 + 0.185994i
\(162\) −4.00202 7.67948i −0.314429 0.603357i
\(163\) −2.49100 2.49100i −0.195110 0.195110i 0.602790 0.797900i \(-0.294056\pi\)
−0.797900 + 0.602790i \(0.794056\pi\)
\(164\) 6.28947 6.28947i 0.491125 0.491125i
\(165\) 0.318886 4.17417i 0.0248253 0.324959i
\(166\) 10.1190i 0.785388i
\(167\) 5.44439 5.44439i 0.421300 0.421300i −0.464351 0.885651i \(-0.653712\pi\)
0.885651 + 0.464351i \(0.153712\pi\)
\(168\) 1.55178 20.3126i 0.119723 1.56715i
\(169\) 11.5672 5.93297i 0.889784 0.456382i
\(170\) 13.5337i 1.03798i
\(171\) −5.63221 + 4.13163i −0.430706 + 0.315954i
\(172\) −5.34263 −0.407372
\(173\) 4.69200 0.356726 0.178363 0.983965i \(-0.442920\pi\)
0.178363 + 0.983965i \(0.442920\pi\)
\(174\) 0.485846 + 0.566218i 0.0368319 + 0.0429249i
\(175\) −2.36683 + 2.36683i −0.178915 + 0.178915i
\(176\) 0.493375 0.493375i 0.0371896 0.0371896i
\(177\) 14.5289 + 16.9324i 1.09206 + 1.27271i
\(178\) 12.8200 0.960897
\(179\) 18.4698 1.38050 0.690250 0.723571i \(-0.257501\pi\)
0.690250 + 0.723571i \(0.257501\pi\)
\(180\) 6.28028 4.60704i 0.468104 0.343388i
\(181\) 13.9573i 1.03744i −0.854944 0.518720i \(-0.826409\pi\)
0.854944 0.518720i \(-0.173591\pi\)
\(182\) −3.23830 13.4091i −0.240038 0.993949i
\(183\) 1.82129 23.8404i 0.134634 1.76233i
\(184\) −1.75561 + 1.75561i −0.129425 + 0.129425i
\(185\) 17.6266i 1.29593i
\(186\) 0.446310 5.84212i 0.0327250 0.428365i
\(187\) 4.11496 4.11496i 0.300916 0.300916i
\(188\) −3.04303 3.04303i −0.221936 0.221936i
\(189\) 17.5420 10.9164i 1.27599 0.794053i
\(190\) 3.82889 + 3.82889i 0.277777 + 0.277777i
\(191\) 9.05696i 0.655339i −0.944792 0.327669i \(-0.893737\pi\)
0.944792 0.327669i \(-0.106263\pi\)
\(192\) 11.1250 + 0.849896i 0.802878 + 0.0613360i
\(193\) −15.2790 15.2790i −1.09980 1.09980i −0.994433 0.105371i \(-0.966397\pi\)
−0.105371 0.994433i \(-0.533603\pi\)
\(194\) 8.26482 0.593379
\(195\) 8.82760 12.2435i 0.632157 0.876776i
\(196\) 9.46441 0.676029
\(197\) 14.7409 + 14.7409i 1.05024 + 1.05024i 0.998669 + 0.0515755i \(0.0164243\pi\)
0.0515755 + 0.998669i \(0.483576\pi\)
\(198\) 2.85307 + 0.438481i 0.202759 + 0.0311615i
\(199\) 8.62346i 0.611301i 0.952144 + 0.305651i \(0.0988739\pi\)
−0.952144 + 0.305651i \(0.901126\pi\)
\(200\) −1.76069 1.76069i −0.124499 0.124499i
\(201\) −16.6442 19.3976i −1.17399 1.36820i
\(202\) 0.977233 + 0.977233i 0.0687579 + 0.0687579i
\(203\) −1.25872 + 1.25872i −0.0883451 + 0.0883451i
\(204\) 10.7959 + 0.824755i 0.755864 + 0.0577444i
\(205\) 20.0134i 1.39780i
\(206\) −1.95410 + 1.95410i −0.136149 + 0.136149i
\(207\) −2.48887 0.382508i −0.172989 0.0265862i
\(208\) 2.44543 0.590570i 0.169560 0.0409487i
\(209\) 2.32838i 0.161058i
\(210\) −10.4299 12.1553i −0.719729 0.838792i
\(211\) −6.84506 −0.471233 −0.235617 0.971846i \(-0.575711\pi\)
−0.235617 + 0.971846i \(0.575711\pi\)
\(212\) 1.42944 0.0981742
\(213\) −1.49136 + 1.27967i −0.102186 + 0.0876814i
\(214\) −4.60349 + 4.60349i −0.314688 + 0.314688i
\(215\) −8.50027 + 8.50027i −0.579713 + 0.579713i
\(216\) 8.12075 + 13.0495i 0.552547 + 0.887908i
\(217\) 13.9794 0.948984
\(218\) −11.3231 −0.766896
\(219\) −13.7594 + 11.8063i −0.929771 + 0.797793i
\(220\) 2.59629i 0.175042i
\(221\) 20.3959 4.92561i 1.37198 0.331333i
\(222\) 12.1186 + 0.925806i 0.813350 + 0.0621360i
\(223\) −8.92553 + 8.92553i −0.597698 + 0.597698i −0.939699 0.342001i \(-0.888895\pi\)
0.342001 + 0.939699i \(0.388895\pi\)
\(224\) 20.8538i 1.39335i
\(225\) 0.383615 2.49607i 0.0255743 0.166405i
\(226\) −4.32289 + 4.32289i −0.287555 + 0.287555i
\(227\) −1.70381 1.70381i −0.113086 0.113086i 0.648300 0.761385i \(-0.275480\pi\)
−0.761385 + 0.648300i \(0.775480\pi\)
\(228\) 3.28767 2.82100i 0.217732 0.186825i
\(229\) 4.35502 + 4.35502i 0.287788 + 0.287788i 0.836205 0.548417i \(-0.184769\pi\)
−0.548417 + 0.836205i \(0.684769\pi\)
\(230\) 1.95202i 0.128713i
\(231\) −0.524613 + 6.86710i −0.0345170 + 0.451822i
\(232\) −0.936367 0.936367i −0.0614755 0.0614755i
\(233\) 1.44883 0.0949157 0.0474578 0.998873i \(-0.484888\pi\)
0.0474578 + 0.998873i \(0.484888\pi\)
\(234\) 7.95400 + 6.71221i 0.519969 + 0.438791i
\(235\) −9.68307 −0.631654
\(236\) −9.78429 9.78429i −0.636903 0.636903i
\(237\) 1.33914 17.5291i 0.0869865 1.13864i
\(238\) 22.2648i 1.44321i
\(239\) −8.31725 8.31725i −0.537998 0.537998i 0.384943 0.922941i \(-0.374221\pi\)
−0.922941 + 0.384943i \(0.874221\pi\)
\(240\) 2.21676 1.90210i 0.143091 0.122780i
\(241\) 0.461259 + 0.461259i 0.0297123 + 0.0297123i 0.721807 0.692095i \(-0.243312\pi\)
−0.692095 + 0.721807i \(0.743312\pi\)
\(242\) −0.680371 + 0.680371i −0.0437359 + 0.0437359i
\(243\) −5.79996 + 14.4693i −0.372067 + 0.928206i
\(244\) 14.8285i 0.949298i
\(245\) 15.0581 15.0581i 0.962028 0.962028i
\(246\) 13.7596 + 1.05117i 0.877281 + 0.0670200i
\(247\) 4.37681 7.16388i 0.278490 0.455827i
\(248\) 10.3993i 0.660356i
\(249\) 13.8239 11.8617i 0.876054 0.751702i
\(250\) 9.67031 0.611604
\(251\) −22.7631 −1.43680 −0.718398 0.695632i \(-0.755124\pi\)
−0.718398 + 0.695632i \(0.755124\pi\)
\(252\) −10.3319 + 7.57923i −0.650851 + 0.477446i
\(253\) 0.593520 0.593520i 0.0373143 0.0373143i
\(254\) −5.07842 + 5.07842i −0.318648 + 0.318648i
\(255\) 18.4888 15.8643i 1.15781 0.993464i
\(256\) −17.0122 −1.06326
\(257\) −11.4934 −0.716939 −0.358469 0.933542i \(-0.616701\pi\)
−0.358469 + 0.933542i \(0.616701\pi\)
\(258\) −5.39764 6.29056i −0.336042 0.391633i
\(259\) 28.9983i 1.80186i
\(260\) −4.88042 + 7.98819i −0.302671 + 0.495407i
\(261\) 0.204014 1.32746i 0.0126281 0.0821677i
\(262\) 1.20009 1.20009i 0.0741416 0.0741416i
\(263\) 18.6484i 1.14991i 0.818186 + 0.574954i \(0.194980\pi\)
−0.818186 + 0.574954i \(0.805020\pi\)
\(264\) −5.10844 0.390261i −0.314403 0.0240189i
\(265\) 2.27427 2.27427i 0.139707 0.139707i
\(266\) −6.29907 6.29907i −0.386221 0.386221i
\(267\) −15.0278 17.5138i −0.919684 1.07183i
\(268\) 11.2088 + 11.2088i 0.684688 + 0.684688i
\(269\) 4.24668i 0.258925i 0.991584 + 0.129462i \(0.0413251\pi\)
−0.991584 + 0.129462i \(0.958675\pi\)
\(270\) 11.7694 + 2.74010i 0.716262 + 0.166757i
\(271\) −5.07172 5.07172i −0.308085 0.308085i 0.536081 0.844166i \(-0.319904\pi\)
−0.844166 + 0.536081i \(0.819904\pi\)
\(272\) 4.06044 0.246200
\(273\) −14.5226 + 20.1423i −0.878950 + 1.21907i
\(274\) 18.4836 1.11663
\(275\) 0.595238 + 0.595238i 0.0358942 + 0.0358942i
\(276\) 1.55714 + 0.118958i 0.0937290 + 0.00716045i
\(277\) 32.4203i 1.94795i −0.226666 0.973973i \(-0.572782\pi\)
0.226666 0.973973i \(-0.427218\pi\)
\(278\) 9.27072 + 9.27072i 0.556021 + 0.556021i
\(279\) −8.50428 + 6.23850i −0.509138 + 0.373489i
\(280\) 20.1014 + 20.1014i 1.20129 + 1.20129i
\(281\) 13.4081 13.4081i 0.799862 0.799862i −0.183212 0.983074i \(-0.558649\pi\)
0.983074 + 0.183212i \(0.0586493\pi\)
\(282\) 0.508585 6.65730i 0.0302858 0.396436i
\(283\) 11.7358i 0.697622i −0.937193 0.348811i \(-0.886586\pi\)
0.937193 0.348811i \(-0.113414\pi\)
\(284\) 0.861777 0.861777i 0.0511371 0.0511371i
\(285\) 0.742489 9.71906i 0.0439813 0.575707i
\(286\) −3.37228 + 0.814405i −0.199407 + 0.0481568i
\(287\) 32.9249i 1.94349i
\(288\) −9.30629 12.6863i −0.548378 0.747545i
\(289\) 16.8659 0.992109
\(290\) −1.04113 −0.0611370
\(291\) −9.68814 11.2908i −0.567929 0.661880i
\(292\) 7.95079 7.95079i 0.465285 0.465285i
\(293\) −23.6422 + 23.6422i −1.38119 + 1.38119i −0.538683 + 0.842509i \(0.681078\pi\)
−0.842509 + 0.538683i \(0.818922\pi\)
\(294\) 9.56185 + 11.1436i 0.557658 + 0.649911i
\(295\) −31.1341 −1.81270
\(296\) −21.5719 −1.25384
\(297\) −2.74539 4.41167i −0.159304 0.255991i
\(298\) 5.46176i 0.316391i
\(299\) 2.94180 0.710444i 0.170129 0.0410861i
\(300\) −0.119302 + 1.56165i −0.00688793 + 0.0901619i
\(301\) 13.9841 13.9841i 0.806032 0.806032i
\(302\) 22.3392i 1.28548i
\(303\) 0.189503 2.48056i 0.0108866 0.142504i
\(304\) 1.14877 1.14877i 0.0658862 0.0658862i
\(305\) 23.5925 + 23.5925i 1.35090 + 1.35090i
\(306\) 9.93596 + 13.5446i 0.568001 + 0.774295i
\(307\) 1.93714 + 1.93714i 0.110558 + 0.110558i 0.760222 0.649664i \(-0.225090\pi\)
−0.649664 + 0.760222i \(0.725090\pi\)
\(308\) 4.27127i 0.243378i
\(309\) 4.96019 + 0.378935i 0.282175 + 0.0215568i
\(310\) 5.78138 + 5.78138i 0.328360 + 0.328360i
\(311\) 2.50035 0.141782 0.0708908 0.997484i \(-0.477416\pi\)
0.0708908 + 0.997484i \(0.477416\pi\)
\(312\) −14.9839 10.8034i −0.848296 0.611623i
\(313\) −0.146508 −0.00828113 −0.00414056 0.999991i \(-0.501318\pi\)
−0.00414056 + 0.999991i \(0.501318\pi\)
\(314\) −9.84099 9.84099i −0.555359 0.555359i
\(315\) −4.37965 + 28.4971i −0.246765 + 1.60563i
\(316\) 10.9029i 0.613339i
\(317\) 6.82979 + 6.82979i 0.383599 + 0.383599i 0.872397 0.488798i \(-0.162564\pi\)
−0.488798 + 0.872397i \(0.662564\pi\)
\(318\) 1.44415 + 1.68306i 0.0809842 + 0.0943812i
\(319\) 0.316559 + 0.316559i 0.0177239 + 0.0177239i
\(320\) −11.0093 + 11.0093i −0.615440 + 0.615440i
\(321\) 11.6853 + 0.892698i 0.652208 + 0.0498255i
\(322\) 3.21135i 0.178962i
\(323\) 9.58120 9.58120i 0.533112 0.533112i
\(324\) 2.90304 9.22155i 0.161280 0.512308i
\(325\) 0.712500 + 2.95031i 0.0395224 + 0.163654i
\(326\) 3.38961i 0.187733i
\(327\) 13.2731 + 15.4688i 0.734003 + 0.855428i
\(328\) −24.4929 −1.35239
\(329\) 15.9300 0.878250
\(330\) −3.05695 + 2.62302i −0.168279 + 0.144393i
\(331\) 11.9272 11.9272i 0.655577 0.655577i −0.298753 0.954330i \(-0.596571\pi\)
0.954330 + 0.298753i \(0.0965707\pi\)
\(332\) −7.98809 + 7.98809i −0.438403 + 0.438403i
\(333\) −12.9409 17.6409i −0.709155 0.966716i
\(334\) −7.40842 −0.405371
\(335\) 35.6671 1.94870
\(336\) −3.64689 + 3.12922i −0.198954 + 0.170713i
\(337\) 17.9076i 0.975489i 0.872986 + 0.487744i \(0.162180\pi\)
−0.872986 + 0.487744i \(0.837820\pi\)
\(338\) −11.9066 3.83336i −0.647634 0.208507i
\(339\) 10.9730 + 0.838284i 0.595971 + 0.0455294i
\(340\) −10.6837 + 10.6837i −0.579403 + 0.579403i
\(341\) 3.51571i 0.190386i
\(342\) 6.64304 + 1.02095i 0.359215 + 0.0552067i
\(343\) −5.09118 + 5.09118i −0.274898 + 0.274898i
\(344\) 10.4028 + 10.4028i 0.560883 + 0.560883i
\(345\) 2.66672 2.28819i 0.143571 0.123192i
\(346\) −3.19230 3.19230i −0.171619 0.171619i
\(347\) 22.8397i 1.22610i 0.790045 + 0.613049i \(0.210057\pi\)
−0.790045 + 0.613049i \(0.789943\pi\)
\(348\) −0.0634473 + 0.830514i −0.00340113 + 0.0445202i
\(349\) 18.4046 + 18.4046i 0.985178 + 0.985178i 0.999892 0.0147141i \(-0.00468380\pi\)
−0.0147141 + 0.999892i \(0.504684\pi\)
\(350\) 3.22064 0.172151
\(351\) −0.154024 18.7344i −0.00822119 0.999966i
\(352\) 5.24455 0.279536
\(353\) −14.0280 14.0280i −0.746637 0.746637i 0.227209 0.973846i \(-0.427040\pi\)
−0.973846 + 0.227209i \(0.927040\pi\)
\(354\) 1.63526 21.4053i 0.0869132 1.13768i
\(355\) 2.74222i 0.145542i
\(356\) 10.1203 + 10.1203i 0.536373 + 0.536373i
\(357\) −30.4166 + 26.0991i −1.60982 + 1.38131i
\(358\) −12.5663 12.5663i −0.664152 0.664152i
\(359\) 1.62278 1.62278i 0.0856470 0.0856470i −0.662985 0.748632i \(-0.730711\pi\)
0.748632 + 0.662985i \(0.230711\pi\)
\(360\) −21.1991 3.25803i −1.11729 0.171713i
\(361\) 13.5786i 0.714665i
\(362\) −9.49616 + 9.49616i −0.499107 + 0.499107i
\(363\) 1.72702 + 0.131936i 0.0906450 + 0.00692484i
\(364\) 8.02898 13.1417i 0.420833 0.688812i
\(365\) 25.2998i 1.32425i
\(366\) −17.4595 + 14.9812i −0.912622 + 0.783078i
\(367\) 18.1285 0.946300 0.473150 0.880982i \(-0.343117\pi\)
0.473150 + 0.880982i \(0.343117\pi\)
\(368\) 0.585657 0.0305295
\(369\) −14.6932 20.0296i −0.764896 1.04270i
\(370\) −11.9926 + 11.9926i −0.623468 + 0.623468i
\(371\) −3.74150 + 3.74150i −0.194249 + 0.194249i
\(372\) 4.96418 4.25953i 0.257381 0.220846i
\(373\) −23.6499 −1.22454 −0.612272 0.790647i \(-0.709744\pi\)
−0.612272 + 0.790647i \(0.709744\pi\)
\(374\) −5.59941 −0.289538
\(375\) −11.3357 13.2109i −0.585372 0.682209i
\(376\) 11.8504i 0.611136i
\(377\) 0.378921 + 1.56903i 0.0195154 + 0.0808093i
\(378\) −19.3623 4.50785i −0.995889 0.231859i
\(379\) 5.85006 5.85006i 0.300497 0.300497i −0.540711 0.841208i \(-0.681845\pi\)
0.841208 + 0.540711i \(0.181845\pi\)
\(380\) 6.04516i 0.310110i
\(381\) 12.8908 + 0.984794i 0.660415 + 0.0504525i
\(382\) −6.16210 + 6.16210i −0.315280 + 0.315280i
\(383\) −8.71544 8.71544i −0.445338 0.445338i 0.448463 0.893801i \(-0.351972\pi\)
−0.893801 + 0.448463i \(0.851972\pi\)
\(384\) 4.83972 + 5.64034i 0.246976 + 0.287832i
\(385\) −6.79570 6.79570i −0.346341 0.346341i
\(386\) 20.7907i 1.05822i
\(387\) −2.26655 + 14.7478i −0.115215 + 0.749671i
\(388\) 6.52436 + 6.52436i 0.331224 + 0.331224i
\(389\) −31.6941 −1.60696 −0.803478 0.595334i \(-0.797020\pi\)
−0.803478 + 0.595334i \(0.797020\pi\)
\(390\) −14.3362 + 2.32409i −0.725941 + 0.117685i
\(391\) 4.88463 0.247026
\(392\) −18.4285 18.4285i −0.930778 0.930778i
\(393\) −3.04624 0.232718i −0.153662 0.0117391i
\(394\) 20.0586i 1.01054i
\(395\) 17.3469 + 17.3469i 0.872816 + 0.872816i
\(396\) 1.90611 + 2.59840i 0.0957858 + 0.130574i
\(397\) 11.6917 + 11.6917i 0.586788 + 0.586788i 0.936760 0.349972i \(-0.113809\pi\)
−0.349972 + 0.936760i \(0.613809\pi\)
\(398\) 5.86716 5.86716i 0.294094 0.294094i
\(399\) −1.22150 + 15.9892i −0.0611515 + 0.800462i
\(400\) 0.587351i 0.0293676i
\(401\) −4.20239 + 4.20239i −0.209857 + 0.209857i −0.804207 0.594349i \(-0.797410\pi\)
0.594349 + 0.804207i \(0.297410\pi\)
\(402\) −1.87335 + 24.5218i −0.0934341 + 1.22304i
\(403\) 6.60870 10.8170i 0.329203 0.538833i
\(404\) 1.54288i 0.0767613i
\(405\) −10.0529 19.2905i −0.499533 0.958554i
\(406\) 1.71280 0.0850048
\(407\) 7.29282 0.361492
\(408\) −19.4152 22.6270i −0.961193 1.12020i
\(409\) −19.5100 + 19.5100i −0.964708 + 0.964708i −0.999398 0.0346902i \(-0.988956\pi\)
0.0346902 + 0.999398i \(0.488956\pi\)
\(410\) −13.6166 + 13.6166i −0.672474 + 0.672474i
\(411\) −21.6667 25.2510i −1.06874 1.24554i
\(412\) −3.08519 −0.151996
\(413\) 51.2200 2.52037
\(414\) 1.43311 + 1.95361i 0.0704335 + 0.0960145i
\(415\) 25.4185i 1.24775i
\(416\) 16.1363 + 9.85853i 0.791145 + 0.483354i
\(417\) 1.79775 23.5323i 0.0880364 1.15238i
\(418\) −1.58416 + 1.58416i −0.0774840 + 0.0774840i
\(419\) 12.1343i 0.592799i −0.955064 0.296400i \(-0.904214\pi\)
0.955064 0.296400i \(-0.0957861\pi\)
\(420\) 1.36205 17.8290i 0.0664613 0.869966i
\(421\) −20.0518 + 20.0518i −0.977263 + 0.977263i −0.999747 0.0224841i \(-0.992842\pi\)
0.0224841 + 0.999747i \(0.492842\pi\)
\(422\) 4.65718 + 4.65718i 0.226708 + 0.226708i
\(423\) −9.69092 + 7.10899i −0.471189 + 0.345651i
\(424\) −2.78331 2.78331i −0.135169 0.135169i
\(425\) 4.89876i 0.237625i
\(426\) 1.88533 + 0.144030i 0.0913445 + 0.00697828i
\(427\) −38.8130 38.8130i −1.87829 1.87829i
\(428\) −7.26813 −0.351318
\(429\) 5.06562 + 3.65232i 0.244571 + 0.176336i
\(430\) 11.5667 0.557795
\(431\) 1.23158 + 1.23158i 0.0593231 + 0.0593231i 0.736146 0.676823i \(-0.236644\pi\)
−0.676823 + 0.736146i \(0.736644\pi\)
\(432\) 0.822100 3.53112i 0.0395533 0.169891i
\(433\) 31.1338i 1.49620i −0.663588 0.748098i \(-0.730967\pi\)
0.663588 0.748098i \(-0.269033\pi\)
\(434\) −9.51119 9.51119i −0.456552 0.456552i
\(435\) 1.22042 + 1.42232i 0.0585148 + 0.0681948i
\(436\) −8.93860 8.93860i −0.428081 0.428081i
\(437\) 1.38194 1.38194i 0.0661073 0.0661073i
\(438\) 17.3941 + 1.32883i 0.831123 + 0.0634938i
\(439\) 15.2593i 0.728286i 0.931343 + 0.364143i \(0.118638\pi\)
−0.931343 + 0.364143i \(0.881362\pi\)
\(440\) 5.05533 5.05533i 0.241004 0.241004i
\(441\) 4.01516 26.1255i 0.191198 1.24407i
\(442\) −17.2281 10.5256i −0.819455 0.500650i
\(443\) 15.4602i 0.734534i −0.930115 0.367267i \(-0.880293\pi\)
0.930115 0.367267i \(-0.119707\pi\)
\(444\) 8.83578 + 10.2975i 0.419328 + 0.488696i
\(445\) 32.2032 1.52658
\(446\) 12.1454 0.575099
\(447\) 7.46148 6.40235i 0.352916 0.302821i
\(448\) 18.1119 18.1119i 0.855707 0.855707i
\(449\) −0.400323 + 0.400323i −0.0188924 + 0.0188924i −0.716490 0.697597i \(-0.754252\pi\)
0.697597 + 0.716490i \(0.254252\pi\)
\(450\) −1.95926 + 1.43726i −0.0923603 + 0.0677529i
\(451\) 8.28034 0.389906
\(452\) −6.82510 −0.321026
\(453\) −30.5184 + 26.1864i −1.43388 + 1.23034i
\(454\) 2.31844i 0.108810i
\(455\) −8.13446 33.6831i −0.381349 1.57909i
\(456\) −11.8944 0.908675i −0.557007 0.0425526i
\(457\) 2.95148 2.95148i 0.138065 0.138065i −0.634697 0.772761i \(-0.718875\pi\)
0.772761 + 0.634697i \(0.218875\pi\)
\(458\) 5.92607i 0.276907i
\(459\) 6.85667 29.4510i 0.320042 1.37466i
\(460\) −1.54095 + 1.54095i −0.0718474 + 0.0718474i
\(461\) −10.4663 10.4663i −0.487462 0.487462i 0.420042 0.907505i \(-0.362015\pi\)
−0.907505 + 0.420042i \(0.862015\pi\)
\(462\) 5.02911 4.31524i 0.233975 0.200763i
\(463\) −10.9144 10.9144i −0.507235 0.507235i 0.406442 0.913677i \(-0.366769\pi\)
−0.913677 + 0.406442i \(0.866769\pi\)
\(464\) 0.312364i 0.0145012i
\(465\) 1.12111 14.6752i 0.0519903 0.680544i
\(466\) −0.985739 0.985739i −0.0456635 0.0456635i
\(467\) −24.0805 −1.11431 −0.557155 0.830408i \(-0.688107\pi\)
−0.557155 + 0.830408i \(0.688107\pi\)
\(468\) 0.980283 + 11.5777i 0.0453136 + 0.535180i
\(469\) −58.6773 −2.70947
\(470\) 6.58808 + 6.58808i 0.303886 + 0.303886i
\(471\) −1.90834 + 24.9798i −0.0879316 + 1.15101i
\(472\) 38.1027i 1.75382i
\(473\) −3.51690 3.51690i −0.161707 0.161707i
\(474\) −12.8374 + 11.0152i −0.589642 + 0.505945i
\(475\) 1.38594 + 1.38594i 0.0635913 + 0.0635913i
\(476\) 17.5761 17.5761i 0.805600 0.805600i
\(477\) 0.606421 3.94581i 0.0277661 0.180666i
\(478\) 11.3176i 0.517657i
\(479\) 1.49406 1.49406i 0.0682652 0.0682652i −0.672150 0.740415i \(-0.734629\pi\)
0.740415 + 0.672150i \(0.234629\pi\)
\(480\) 21.8917 + 1.67242i 0.999213 + 0.0763351i
\(481\) 22.4383 + 13.7088i 1.02310 + 0.625067i
\(482\) 0.627655i 0.0285889i
\(483\) −4.38713 + 3.76439i −0.199621 + 0.171286i
\(484\) −1.07419 −0.0488268
\(485\) 20.7609 0.942702
\(486\) 13.7906 5.89837i 0.625555 0.267555i
\(487\) 13.5688 13.5688i 0.614860 0.614860i −0.329348 0.944209i \(-0.606829\pi\)
0.944209 + 0.329348i \(0.106829\pi\)
\(488\) 28.8731 28.8731i 1.30702 1.30702i
\(489\) 4.63065 3.97335i 0.209405 0.179681i
\(490\) −20.4902 −0.925654
\(491\) −5.19051 −0.234244 −0.117122 0.993118i \(-0.537367\pi\)
−0.117122 + 0.993118i \(0.537367\pi\)
\(492\) 10.0322 + 11.6918i 0.452288 + 0.527109i
\(493\) 2.60526i 0.117335i
\(494\) −7.85196 + 1.89625i −0.353276 + 0.0853161i
\(495\) 7.16680 + 1.10145i 0.322124 + 0.0495063i
\(496\) 1.73456 1.73456i 0.0778841 0.0778841i
\(497\) 4.51134i 0.202361i
\(498\) −17.4757 1.33506i −0.783106 0.0598255i
\(499\) 1.21906 1.21906i 0.0545728 0.0545728i −0.679294 0.733866i \(-0.737714\pi\)
0.733866 + 0.679294i \(0.237714\pi\)
\(500\) 7.63388 + 7.63388i 0.341397 + 0.341397i
\(501\) 8.68426 + 10.1209i 0.387984 + 0.452168i
\(502\) 15.4874 + 15.4874i 0.691236 + 0.691236i
\(503\) 4.14083i 0.184630i −0.995730 0.0923152i \(-0.970573\pi\)
0.995730 0.0923152i \(-0.0294267\pi\)
\(504\) 34.8754 + 5.35991i 1.55348 + 0.238750i
\(505\) 2.45477 + 2.45477i 0.109236 + 0.109236i
\(506\) −0.807629 −0.0359035
\(507\) 8.72022 + 20.7595i 0.387279 + 0.921963i
\(508\) −8.01795 −0.355739
\(509\) −26.1591 26.1591i −1.15948 1.15948i −0.984587 0.174893i \(-0.944042\pi\)
−0.174893 0.984587i \(-0.555958\pi\)
\(510\) −23.3729 1.78558i −1.03497 0.0790666i
\(511\) 41.6218i 1.84124i
\(512\) 5.50630 + 5.50630i 0.243346 + 0.243346i
\(513\) −6.39232 10.2720i −0.282228 0.453522i
\(514\) 7.81978 + 7.81978i 0.344916 + 0.344916i
\(515\) −4.90862 + 4.90862i −0.216300 + 0.216300i
\(516\) 0.704885 9.22683i 0.0310308 0.406188i
\(517\) 4.00627i 0.176195i
\(518\) 19.7296 19.7296i 0.866868 0.866868i
\(519\) −0.619043 + 8.10316i −0.0271730 + 0.355689i
\(520\) 25.0569 6.05124i 1.09882 0.265364i
\(521\) 28.4750i 1.24751i 0.781620 + 0.623755i \(0.214394\pi\)
−0.781620 + 0.623755i \(0.785606\pi\)
\(522\) −1.04197 + 0.764360i −0.0456058 + 0.0334551i
\(523\) 0.443046 0.0193730 0.00968652 0.999953i \(-0.496917\pi\)
0.00968652 + 0.999953i \(0.496917\pi\)
\(524\) 1.89473 0.0827717
\(525\) −3.77529 4.39983i −0.164767 0.192024i
\(526\) 12.6878 12.6878i 0.553215 0.553215i
\(527\) 14.4670 14.4670i 0.630192 0.630192i
\(528\) 0.786974 + 0.917162i 0.0342487 + 0.0399143i
\(529\) −22.2955 −0.969368
\(530\) −3.09470 −0.134425
\(531\) −31.1594 + 22.8576i −1.35220 + 0.991937i
\(532\) 9.94515i 0.431177i
\(533\) 25.4767 + 15.5651i 1.10352 + 0.674199i
\(534\) −1.69141 + 22.1403i −0.0731947 + 0.958106i
\(535\) −11.5638 + 11.5638i −0.499946 + 0.499946i
\(536\) 43.6502i 1.88540i
\(537\) −2.43683 + 31.8977i −0.105157 + 1.37649i
\(538\) 2.88932 2.88932i 0.124567 0.124567i
\(539\) 6.23014 + 6.23014i 0.268351 + 0.268351i
\(540\) 7.12784 + 11.4540i 0.306734 + 0.492901i
\(541\) −15.0944 15.0944i −0.648960 0.648960i 0.303782 0.952742i \(-0.401751\pi\)
−0.952742 + 0.303782i \(0.901751\pi\)
\(542\) 6.90131i 0.296437i
\(543\) 24.1045 + 1.84147i 1.03443 + 0.0790251i
\(544\) 21.5812 + 21.5812i 0.925284 + 0.925284i
\(545\) −28.4431 −1.21837
\(546\) 23.5850 3.82345i 1.00935 0.163629i
\(547\) −19.0040 −0.812553 −0.406277 0.913750i \(-0.633173\pi\)
−0.406277 + 0.913750i \(0.633173\pi\)
\(548\) 14.5912 + 14.5912i 0.623305 + 0.623305i
\(549\) 40.9325 + 6.29081i 1.74696 + 0.268485i
\(550\) 0.809966i 0.0345371i
\(551\) 0.737069 + 0.737069i 0.0314002 + 0.0314002i
\(552\) −2.80034 3.26359i −0.119190 0.138908i
\(553\) −28.5380 28.5380i −1.21356 1.21356i
\(554\) −22.0578 + 22.0578i −0.937147 + 0.937147i
\(555\) 30.4415 + 2.32558i 1.29217 + 0.0987155i
\(556\) 14.6369i 0.620741i
\(557\) 15.7586 15.7586i 0.667715 0.667715i −0.289471 0.957187i \(-0.593480\pi\)
0.957187 + 0.289471i \(0.0934795\pi\)
\(558\) 10.0306 + 1.54157i 0.424628 + 0.0652599i
\(559\) −4.20973 17.4316i −0.178052 0.737278i
\(560\) 6.70566i 0.283366i
\(561\) 6.56371 + 7.64953i 0.277120 + 0.322963i
\(562\) −18.2450 −0.769620
\(563\) −5.81745 −0.245176 −0.122588 0.992458i \(-0.539119\pi\)
−0.122588 + 0.992458i \(0.539119\pi\)
\(564\) 5.65685 4.85388i 0.238196 0.204385i
\(565\) −10.8589 + 10.8589i −0.456838 + 0.456838i
\(566\) −7.98471 + 7.98471i −0.335622 + 0.335622i
\(567\) 16.5384 + 31.7356i 0.694549 + 1.33277i
\(568\) −3.35599 −0.140814
\(569\) −31.5587 −1.32301 −0.661505 0.749940i \(-0.730082\pi\)
−0.661505 + 0.749940i \(0.730082\pi\)
\(570\) −7.11774 + 6.10740i −0.298129 + 0.255811i
\(571\) 41.1432i 1.72179i −0.508783 0.860895i \(-0.669904\pi\)
0.508783 0.860895i \(-0.330096\pi\)
\(572\) −3.30503 2.01922i −0.138190 0.0844280i
\(573\) 15.6415 + 1.19494i 0.653435 + 0.0499193i
\(574\) 22.4011 22.4011i 0.935006 0.935006i
\(575\) 0.706572i 0.0294661i
\(576\) −2.93557 + 19.1009i −0.122316 + 0.795873i
\(577\) −27.0379 + 27.0379i −1.12560 + 1.12560i −0.134721 + 0.990884i \(0.543014\pi\)
−0.990884 + 0.134721i \(0.956986\pi\)
\(578\) −11.4750 11.4750i −0.477299 0.477299i
\(579\) 28.4029 24.3712i 1.18038 1.01283i
\(580\) −0.821880 0.821880i −0.0341267 0.0341267i
\(581\) 41.8170i 1.73486i
\(582\) −1.09043 + 14.2735i −0.0451996 + 0.591655i
\(583\) 0.940956 + 0.940956i 0.0389704 + 0.0389704i
\(584\) −30.9625 −1.28124
\(585\) 19.9801 + 16.8608i 0.826075 + 0.697107i
\(586\) 32.1709 1.32897
\(587\) −18.7881 18.7881i −0.775467 0.775467i 0.203589 0.979056i \(-0.434739\pi\)
−0.979056 + 0.203589i \(0.934739\pi\)
\(588\) −1.24870 + 16.3452i −0.0514953 + 0.674065i
\(589\) 8.18590i 0.337294i
\(590\) 21.1828 + 21.1828i 0.872081 + 0.872081i
\(591\) −27.4026 + 23.5129i −1.12719 + 0.967193i
\(592\) 3.59810 + 3.59810i 0.147881 + 0.147881i
\(593\) −16.9522 + 16.9522i −0.696145 + 0.696145i −0.963577 0.267431i \(-0.913825\pi\)
0.267431 + 0.963577i \(0.413825\pi\)
\(594\) −1.13369 + 4.86946i −0.0465158 + 0.199796i
\(595\) 55.9281i 2.29283i
\(596\) −4.31159 + 4.31159i −0.176610 + 0.176610i
\(597\) −14.8929 1.13774i −0.609525 0.0465648i
\(598\) −2.48488 1.51815i −0.101614 0.0620818i
\(599\) 37.6173i 1.53700i 0.639848 + 0.768501i \(0.278997\pi\)
−0.639848 + 0.768501i \(0.721003\pi\)
\(600\) 3.27304 2.80844i 0.133621 0.114654i
\(601\) 18.6933 0.762516 0.381258 0.924469i \(-0.375491\pi\)
0.381258 + 0.924469i \(0.375491\pi\)
\(602\) −19.0288 −0.775557
\(603\) 35.6960 26.1856i 1.45365 1.06636i
\(604\) 17.6349 17.6349i 0.717555 0.717555i
\(605\) −1.70906 + 1.70906i −0.0694833 + 0.0694833i
\(606\) −1.81663 + 1.55877i −0.0737956 + 0.0633206i
\(607\) 40.8474 1.65795 0.828973 0.559289i \(-0.188926\pi\)
0.828973 + 0.559289i \(0.188926\pi\)
\(608\) 12.2113 0.495235
\(609\) −2.00777 2.33991i −0.0813589 0.0948179i
\(610\) 32.1034i 1.29983i
\(611\) 7.53084 12.3263i 0.304665 0.498670i
\(612\) −2.84873 + 18.5359i −0.115153 + 0.749270i
\(613\) 11.4619 11.4619i 0.462943 0.462943i −0.436676 0.899619i \(-0.643844\pi\)
0.899619 + 0.436676i \(0.143844\pi\)
\(614\) 2.63595i 0.106378i
\(615\) 34.5635 + 2.64049i 1.39374 + 0.106475i
\(616\) −8.31673 + 8.31673i −0.335091 + 0.335091i
\(617\) 7.74289 + 7.74289i 0.311717 + 0.311717i 0.845574 0.533858i \(-0.179258\pi\)
−0.533858 + 0.845574i \(0.679258\pi\)
\(618\) −3.11695 3.63259i −0.125382 0.146124i
\(619\) 1.84445 + 1.84445i 0.0741349 + 0.0741349i 0.743202 0.669067i \(-0.233306\pi\)
−0.669067 + 0.743202i \(0.733306\pi\)
\(620\) 9.12781i 0.366582i
\(621\) 0.988970 4.24786i 0.0396860 0.170461i
\(622\) −1.70116 1.70116i −0.0682105 0.0682105i
\(623\) −52.9788 −2.12255
\(624\) 0.697286 + 4.30122i 0.0279138 + 0.172187i
\(625\) 28.5004 1.14001
\(626\) 0.0996799 + 0.0996799i 0.00398401 + 0.00398401i
\(627\) 4.02116 + 0.307197i 0.160590 + 0.0122683i
\(628\) 15.5372i 0.620003i
\(629\) 30.0097 + 30.0097i 1.19657 + 1.19657i
\(630\) 22.3684 16.4088i 0.891179 0.653744i
\(631\) 10.4263 + 10.4263i 0.415063 + 0.415063i 0.883498 0.468435i \(-0.155182\pi\)
−0.468435 + 0.883498i \(0.655182\pi\)
\(632\) 21.2295 21.2295i 0.844464 0.844464i
\(633\) 0.903109 11.8215i 0.0358953 0.469864i
\(634\) 9.29359i 0.369096i
\(635\) −12.7568 + 12.7568i −0.506237 + 0.506237i
\(636\) −0.188594 + 2.46867i −0.00747825 + 0.0978890i
\(637\) 7.45748 + 30.8799i 0.295476 + 1.22350i
\(638\) 0.430755i 0.0170538i
\(639\) −2.01325 2.74444i −0.0796428 0.108568i
\(640\) −10.3711 −0.409954
\(641\) 12.0658 0.476572 0.238286 0.971195i \(-0.423414\pi\)
0.238286 + 0.971195i \(0.423414\pi\)
\(642\) −7.34295 8.55769i −0.289803 0.337745i
\(643\) −18.1964 + 18.1964i −0.717595 + 0.717595i −0.968112 0.250517i \(-0.919399\pi\)
0.250517 + 0.968112i \(0.419399\pi\)
\(644\) 2.53509 2.53509i 0.0998964 0.0998964i
\(645\) −13.5586 15.8016i −0.533870 0.622188i
\(646\) −13.0376 −0.512956
\(647\) −38.9982 −1.53318 −0.766588 0.642139i \(-0.778047\pi\)
−0.766588 + 0.642139i \(0.778047\pi\)
\(648\) −23.6082 + 12.3030i −0.927417 + 0.483307i
\(649\) 12.8814i 0.505640i
\(650\) 1.52254 2.49207i 0.0597191 0.0977472i
\(651\) −1.84439 + 24.1427i −0.0722872 + 0.946226i
\(652\) −2.67580 + 2.67580i −0.104793 + 0.104793i
\(653\) 40.6601i 1.59115i 0.605853 + 0.795577i \(0.292832\pi\)
−0.605853 + 0.795577i \(0.707168\pi\)
\(654\) 1.49392 19.5552i 0.0584169 0.764668i
\(655\) 3.01456 3.01456i 0.117789 0.117789i
\(656\) 4.08531 + 4.08531i 0.159505 + 0.159505i
\(657\) −18.5743 25.3203i −0.724652 0.987840i
\(658\) −10.8383 10.8383i −0.422522 0.422522i
\(659\) 33.9929i 1.32418i −0.749426 0.662088i \(-0.769670\pi\)
0.749426 0.662088i \(-0.230330\pi\)
\(660\) −4.48385 0.342545i −0.174534 0.0133335i
\(661\) 24.0884 + 24.0884i 0.936932 + 0.936932i 0.998126 0.0611940i \(-0.0194908\pi\)
−0.0611940 + 0.998126i \(0.519491\pi\)
\(662\) −16.2298 −0.630790
\(663\) 5.81567 + 35.8740i 0.225862 + 1.39323i
\(664\) 31.1078 1.20722
\(665\) −15.8230 15.8230i −0.613589 0.613589i
\(666\) −3.19777 + 20.8070i −0.123911 + 0.806254i
\(667\) 0.375768i 0.0145498i
\(668\) −5.84831 5.84831i −0.226278 0.226278i
\(669\) −14.2370 16.5922i −0.550433 0.641490i
\(670\) −24.2669 24.2669i −0.937510 0.937510i
\(671\) −9.76116 + 9.76116i −0.376825 + 0.376825i
\(672\) −36.0149 2.75136i −1.38930 0.106136i
\(673\) 8.09382i 0.311994i −0.987758 0.155997i \(-0.950141\pi\)
0.987758 0.155997i \(-0.0498590\pi\)
\(674\) 12.1838 12.1838i 0.469303 0.469303i
\(675\) 4.26015 + 0.991832i 0.163973 + 0.0381756i
\(676\) −6.37313 12.4254i −0.245121 0.477898i
\(677\) 6.76042i 0.259824i 0.991526 + 0.129912i \(0.0414695\pi\)
−0.991526 + 0.129912i \(0.958530\pi\)
\(678\) −6.89537 8.03606i −0.264815 0.308623i
\(679\) −34.1545 −1.31073
\(680\) 41.6050 1.59548
\(681\) 3.16730 2.71772i 0.121371 0.104143i
\(682\) −2.39199 + 2.39199i −0.0915939 + 0.0915939i
\(683\) 27.1344 27.1344i 1.03827 1.03827i 0.0390311 0.999238i \(-0.487573\pi\)
0.999238 0.0390311i \(-0.0124271\pi\)
\(684\) 4.43816 + 6.05007i 0.169697 + 0.231330i
\(685\) 46.4299 1.77400
\(686\) 6.92778 0.264504
\(687\) −8.09579 + 6.94662i −0.308874 + 0.265030i
\(688\) 3.47030i 0.132304i
\(689\) 1.12633 + 4.66388i 0.0429096 + 0.177680i
\(690\) −3.37118 0.257542i −0.128339 0.00980445i
\(691\) −33.4914 + 33.4914i −1.27407 + 1.27407i −0.330142 + 0.943931i \(0.607097\pi\)
−0.943931 + 0.330142i \(0.892903\pi\)
\(692\) 5.04009i 0.191596i
\(693\) −11.7904 1.81203i −0.447880 0.0688334i
\(694\) 15.5395 15.5395i 0.589870 0.589870i
\(695\) 23.2876 + 23.2876i 0.883350 + 0.883350i
\(696\) 1.74066 1.49358i 0.0659797 0.0566141i
\(697\) 34.0733 + 34.0733i 1.29062 + 1.29062i
\(698\) 25.0440i 0.947929i
\(699\) −0.191152 + 2.50215i −0.00723003 + 0.0946399i
\(700\) 2.54242 + 2.54242i 0.0960945 + 0.0960945i
\(701\) 14.5002 0.547667 0.273833 0.961777i \(-0.411708\pi\)
0.273833 + 0.961777i \(0.411708\pi\)
\(702\) −12.6415 + 12.8511i −0.477124 + 0.485034i
\(703\) 16.9805 0.640431
\(704\) −4.55500 4.55500i −0.171673 0.171673i
\(705\) 1.27754 16.7228i 0.0481151 0.629818i
\(706\) 19.0885i 0.718407i
\(707\) −4.03844 4.03844i −0.151881 0.151881i
\(708\) 18.1886 15.6068i 0.683568 0.586538i
\(709\) 11.0696 + 11.0696i 0.415726 + 0.415726i 0.883728 0.468002i \(-0.155026\pi\)
−0.468002 + 0.883728i \(0.655026\pi\)
\(710\) −1.86573 + 1.86573i −0.0700195 + 0.0700195i
\(711\) 30.0964 + 4.62544i 1.12870 + 0.173468i
\(712\) 39.4110i 1.47699i
\(713\) 2.08664 2.08664i 0.0781454 0.0781454i
\(714\) 38.4517 + 2.93752i 1.43902 + 0.109934i
\(715\) −8.47102 + 2.04575i −0.316798 + 0.0765067i
\(716\) 19.8401i 0.741459i
\(717\) 15.4614 13.2667i 0.577416 0.495454i
\(718\) −2.20818 −0.0824087
\(719\) −44.7034 −1.66715 −0.833577 0.552403i \(-0.813711\pi\)
−0.833577 + 0.552403i \(0.813711\pi\)
\(720\) 2.99249 + 4.07934i 0.111524 + 0.152028i
\(721\) 8.07537 8.07537i 0.300742 0.300742i
\(722\) 9.23852 9.23852i 0.343822 0.343822i
\(723\) −0.857460 + 0.735747i −0.0318893 + 0.0273627i
\(724\) −14.9928 −0.557203
\(725\) −0.376855 −0.0139961
\(726\) −1.08525 1.26478i −0.0402774 0.0469404i
\(727\) 16.6524i 0.617603i 0.951126 + 0.308802i \(0.0999279\pi\)
−0.951126 + 0.308802i \(0.900072\pi\)
\(728\) −41.2221 + 9.95514i −1.52779 + 0.368962i
\(729\) −24.2235 11.9257i −0.897167 0.441691i
\(730\) −17.2133 + 17.2133i −0.637092 + 0.637092i
\(731\) 28.9438i 1.07053i
\(732\) −25.6091 1.95641i −0.946540 0.0723111i
\(733\) 14.9699 14.9699i 0.552926 0.552926i −0.374358 0.927284i \(-0.622137\pi\)
0.927284 + 0.374358i \(0.122137\pi\)
\(734\) −12.3341 12.3341i −0.455261 0.455261i
\(735\) 24.0189 + 27.9924i 0.885952 + 1.03251i
\(736\) 3.11275 + 3.11275i 0.114738 + 0.114738i
\(737\) 14.7569i 0.543576i
\(738\) −3.63077 + 23.6244i −0.133651 + 0.869627i
\(739\) −26.7056 26.7056i −0.982382 0.982382i 0.0174654 0.999847i \(-0.494440\pi\)
−0.999847 + 0.0174654i \(0.994440\pi\)
\(740\) −18.9343 −0.696040
\(741\) 11.7947 + 8.50400i 0.433289 + 0.312402i
\(742\) 5.09122 0.186904
\(743\) −5.55684 5.55684i −0.203861 0.203861i 0.597791 0.801652i \(-0.296045\pi\)
−0.801652 + 0.597791i \(0.796045\pi\)
\(744\) −17.9598 1.37204i −0.658438 0.0503015i
\(745\) 13.7197i 0.502651i
\(746\) 16.0907 + 16.0907i 0.589122 + 0.589122i
\(747\) 18.6614 + 25.4391i 0.682786 + 0.930769i
\(748\) −4.42025 4.42025i −0.161620 0.161620i
\(749\) 19.0240 19.0240i 0.695123 0.695123i
\(750\) −1.27586 + 16.7008i −0.0465878 + 0.609827i
\(751\) 48.9900i 1.78767i 0.448395 + 0.893835i \(0.351996\pi\)
−0.448395 + 0.893835i \(0.648004\pi\)
\(752\) 1.97659 1.97659i 0.0720789 0.0720789i
\(753\) 3.00328 39.3124i 0.109445 1.43262i
\(754\) 0.809718 1.32533i 0.0294882 0.0482657i
\(755\) 56.1152i 2.04224i
\(756\) −11.7263 18.8434i −0.426482 0.685329i
\(757\) 27.6161 1.00372 0.501862 0.864948i \(-0.332648\pi\)
0.501862 + 0.864948i \(0.332648\pi\)
\(758\) −7.96043 −0.289136
\(759\) 0.946714 + 1.10333i 0.0343635 + 0.0400483i
\(760\) 11.7707 11.7707i 0.426970 0.426970i
\(761\) −10.9476 + 10.9476i −0.396849 + 0.396849i −0.877120 0.480271i \(-0.840538\pi\)
0.480271 + 0.877120i \(0.340538\pi\)
\(762\) −8.10050 9.44055i −0.293450 0.341995i
\(763\) 46.7929 1.69402
\(764\) −9.72890 −0.351979
\(765\) 24.9587 + 34.0235i 0.902383 + 1.23012i
\(766\) 11.8595i 0.428500i
\(767\) 24.2140 39.6331i 0.874318 1.43107i
\(768\) 2.24452 29.3803i 0.0809920 1.06017i
\(769\) −30.2179 + 30.2179i −1.08969 + 1.08969i −0.0941269 + 0.995560i \(0.530006\pi\)
−0.995560 + 0.0941269i \(0.969994\pi\)
\(770\) 9.24720i 0.333246i
\(771\) 1.51639 19.8493i 0.0546115 0.714856i
\(772\) −16.4125 + 16.4125i −0.590699 + 0.590699i
\(773\) 1.22643 + 1.22643i 0.0441117 + 0.0441117i 0.728819 0.684707i \(-0.240070\pi\)
−0.684707 + 0.728819i \(0.740070\pi\)
\(774\) 11.5761 8.49187i 0.416093 0.305234i
\(775\) 2.09268 + 2.09268i 0.0751713 + 0.0751713i
\(776\) 25.4076i 0.912080i
\(777\) −50.0805 3.82591i −1.79663 0.137254i
\(778\) 21.5638 + 21.5638i 0.773099 + 0.773099i
\(779\) 19.2798 0.690770
\(780\) −13.1518 9.48251i −0.470912 0.339528i
\(781\) 1.13456 0.0405979
\(782\) −3.32336 3.32336i −0.118843 0.118843i
\(783\) 2.26563 + 0.527475i 0.0809670 + 0.0188504i
\(784\) 6.14759i 0.219557i
\(785\) −24.7201 24.7201i −0.882299 0.882299i
\(786\) 1.91424 + 2.23091i 0.0682786 + 0.0795738i
\(787\) −8.45316 8.45316i −0.301323 0.301323i 0.540209 0.841531i \(-0.318345\pi\)
−0.841531 + 0.540209i \(0.818345\pi\)
\(788\) 15.8345 15.8345i 0.564081 0.564081i
\(789\) −32.2061 2.46039i −1.14657 0.0875922i
\(790\) 23.6046i 0.839815i
\(791\) 17.8644 17.8644i 0.635186 0.635186i
\(792\) 1.34797 8.77089i 0.0478982 0.311660i
\(793\) −48.3815 + 11.6841i −1.71808 + 0.414915i
\(794\) 15.9094i 0.564602i
\(795\) 3.62765 + 4.22777i 0.128660 + 0.149944i
\(796\) 9.26324 0.328327
\(797\) 31.6461 1.12096 0.560481 0.828168i \(-0.310616\pi\)
0.560481 + 0.828168i \(0.310616\pi\)
\(798\) 11.7097 10.0475i 0.414518 0.355679i
\(799\) 16.4856 16.4856i 0.583220 0.583220i
\(800\) −3.12176 + 3.12176i −0.110371 + 0.110371i
\(801\) 32.2293 23.6425i 1.13877 0.835367i
\(802\) 5.71838 0.201923
\(803\) 10.4675 0.369391
\(804\) −20.8367 + 17.8790i −0.734854 + 0.630544i
\(805\) 8.06678i 0.284316i
\(806\) −11.8559 + 2.86321i −0.417608 + 0.100852i
\(807\) −7.33410 0.560290i −0.258172 0.0197231i
\(808\) 3.00420 3.00420i 0.105687 0.105687i
\(809\) 32.5336i 1.14382i 0.820317 + 0.571909i \(0.193797\pi\)
−0.820317 + 0.571909i \(0.806203\pi\)
\(810\) −6.28501 + 19.9644i −0.220833 + 0.701479i
\(811\) 7.10405 7.10405i 0.249457 0.249457i −0.571291 0.820748i \(-0.693557\pi\)
0.820748 + 0.571291i \(0.193557\pi\)
\(812\) 1.35211 + 1.35211i 0.0474497 + 0.0474497i
\(813\) 9.42810 8.08982i 0.330658 0.283722i
\(814\) −4.96183 4.96183i −0.173912 0.173912i
\(815\) 8.51454i 0.298251i
\(816\) −0.535718 + 7.01246i −0.0187539 + 0.245485i
\(817\) −8.18867 8.18867i −0.286485 0.286485i
\(818\) 26.5481 0.928233
\(819\) −32.8701 27.7384i −1.14857 0.969257i
\(820\) −21.4982 −0.750750
\(821\) 37.6418 + 37.6418i 1.31371 + 1.31371i 0.918662 + 0.395044i \(0.129271\pi\)
0.395044 + 0.918662i \(0.370729\pi\)
\(822\) −2.43865 + 31.9215i −0.0850576 + 1.11339i
\(823\) 26.1139i 0.910274i 0.890422 + 0.455137i \(0.150410\pi\)
−0.890422 + 0.455137i \(0.849590\pi\)
\(824\) 6.00728 + 6.00728i 0.209274 + 0.209274i
\(825\) −1.10652 + 0.949454i −0.0385241 + 0.0330557i
\(826\) −34.8486 34.8486i −1.21254 1.21254i
\(827\) 5.04334 5.04334i 0.175374 0.175374i −0.613962 0.789336i \(-0.710425\pi\)
0.789336 + 0.613962i \(0.210425\pi\)
\(828\) −0.410886 + 2.67352i −0.0142793 + 0.0929113i
\(829\) 29.9527i 1.04030i 0.854075 + 0.520150i \(0.174124\pi\)
−0.854075 + 0.520150i \(0.825876\pi\)
\(830\) 17.2940 17.2940i 0.600284 0.600284i
\(831\) 55.9904 + 4.27740i 1.94229 + 0.148381i
\(832\) −5.45233 22.5770i −0.189026 0.782716i
\(833\) 51.2736i 1.77652i
\(834\) −17.2338 + 14.7876i −0.596759 + 0.512051i
\(835\) −18.6096 −0.644013
\(836\) −2.50112 −0.0865031
\(837\) −9.65199 15.5101i −0.333621 0.536109i
\(838\) −8.25583 + 8.25583i −0.285193 + 0.285193i
\(839\) −17.9945 + 17.9945i −0.621239 + 0.621239i −0.945848 0.324609i \(-0.894767\pi\)
0.324609 + 0.945848i \(0.394767\pi\)
\(840\) −37.3676 + 32.0634i −1.28930 + 1.10629i
\(841\) 28.7996 0.993089
\(842\) 27.2853 0.940313
\(843\) 21.3871 + 24.9251i 0.736610 + 0.858466i
\(844\) 7.35289i 0.253097i
\(845\) −29.9089 9.62924i −1.02890 0.331256i
\(846\) 11.4302 + 1.75667i 0.392977 + 0.0603957i
\(847\) 2.81165 2.81165i 0.0966094 0.0966094i
\(848\) 0.928489i 0.0318844i
\(849\) 20.2680 + 1.54837i 0.695595 + 0.0531401i
\(850\) 3.33298 3.33298i 0.114320 0.114320i
\(851\) 4.32844 + 4.32844i 0.148377 + 0.148377i
\(852\) 1.37461 + 1.60200i 0.0470932 + 0.0548838i
\(853\) −1.31174 1.31174i −0.0449131 0.0449131i 0.684294 0.729207i \(-0.260111\pi\)
−0.729207 + 0.684294i \(0.760111\pi\)
\(854\) 52.8146i 1.80728i
\(855\) 16.6870 + 2.56459i 0.570685 + 0.0877070i
\(856\) 14.1520 + 14.1520i 0.483706 + 0.483706i
\(857\) −23.4162 −0.799881 −0.399941 0.916541i \(-0.630969\pi\)
−0.399941 + 0.916541i \(0.630969\pi\)
\(858\) −0.961568 5.93144i −0.0328274 0.202496i
\(859\) −37.7480 −1.28794 −0.643972 0.765049i \(-0.722715\pi\)
−0.643972 + 0.765049i \(0.722715\pi\)
\(860\) 9.13090 + 9.13090i 0.311361 + 0.311361i
\(861\) −56.8619 4.34397i −1.93785 0.148042i
\(862\) 1.67586i 0.0570802i
\(863\) 14.4849 + 14.4849i 0.493073 + 0.493073i 0.909273 0.416200i \(-0.136638\pi\)
−0.416200 + 0.909273i \(0.636638\pi\)
\(864\) 23.1372 14.3984i 0.787145 0.489842i
\(865\) −8.01892 8.01892i −0.272651 0.272651i
\(866\) −21.1826 + 21.1826i −0.719813 + 0.719813i
\(867\) −2.22521 + 29.1276i −0.0755721 + 0.989226i
\(868\) 15.0165i 0.509694i
\(869\) −7.17709 + 7.17709i −0.243466 + 0.243466i
\(870\) 0.137362 1.79804i 0.00465701 0.0609594i
\(871\) −27.7394 + 45.4034i −0.939915 + 1.53844i
\(872\) 34.8093i 1.17879i
\(873\) 20.7777 15.2419i 0.703218 0.515861i
\(874\) −1.88047 −0.0636078
\(875\) −39.9627 −1.35099
\(876\) 12.6822 + 14.7802i 0.428491 + 0.499375i
\(877\) 29.9739 29.9739i 1.01215 1.01215i 0.0122215 0.999925i \(-0.496110\pi\)
0.999925 0.0122215i \(-0.00389031\pi\)
\(878\) 10.3820 10.3820i 0.350375 0.350375i
\(879\) −37.7112 43.9498i −1.27197 1.48239i
\(880\) −1.68642 −0.0568492
\(881\) 6.12371 0.206313 0.103157 0.994665i \(-0.467106\pi\)
0.103157 + 0.994665i \(0.467106\pi\)
\(882\) −20.5068 + 15.0432i −0.690501 + 0.506532i
\(883\) 23.1902i 0.780412i 0.920728 + 0.390206i \(0.127596\pi\)
−0.920728 + 0.390206i \(0.872404\pi\)
\(884\) −5.29104 21.9091i −0.177957 0.736883i
\(885\) 4.10771 53.7692i 0.138079 1.80743i
\(886\) −10.5186 + 10.5186i −0.353381 + 0.353381i
\(887\) 34.4025i 1.15512i −0.816347 0.577561i \(-0.804005\pi\)
0.816347 0.577561i \(-0.195995\pi\)
\(888\) 2.84610 37.2550i 0.0955089 1.25020i
\(889\) 20.9867 20.9867i 0.703871 0.703871i
\(890\) −21.9101 21.9101i −0.734430 0.734430i
\(891\) 7.98125 4.15928i 0.267382 0.139341i
\(892\) 9.58772 + 9.58772i 0.321020 + 0.321020i
\(893\) 9.32812i 0.312154i
\(894\) −9.43256 0.720602i −0.315472 0.0241005i
\(895\) −31.5661 31.5661i −1.05514 1.05514i
\(896\) 17.0619 0.569999
\(897\) 0.838821 + 5.17428i 0.0280074 + 0.172764i
\(898\) 0.544737 0.0181781
\(899\) 1.11293 + 1.11293i 0.0371182 + 0.0371182i
\(900\) −2.68126 0.412075i −0.0893752 0.0137358i
\(901\) 7.74400i 0.257990i
\(902\) −5.63370 5.63370i −0.187582 0.187582i
\(903\) 22.3059 + 25.9959i 0.742292 + 0.865088i
\(904\) 13.2894 + 13.2894i 0.441999 + 0.441999i
\(905\) −23.8539 + 23.8539i −0.792932 + 0.792932i
\(906\) 38.5803 + 2.94735i 1.28174 + 0.0979191i
\(907\) 33.8818i 1.12503i −0.826788 0.562514i \(-0.809834\pi\)
0.826788 0.562514i \(-0.190166\pi\)
\(908\) −1.83021 + 1.83021i −0.0607378 + 0.0607378i
\(909\) 4.25896 + 0.654549i 0.141261 + 0.0217100i
\(910\) −17.3826 + 28.4515i −0.576226 + 0.943157i
\(911\) 23.1786i 0.767942i −0.923345 0.383971i \(-0.874556\pi\)
0.923345 0.383971i \(-0.125444\pi\)
\(912\) 1.83238 + 2.13550i 0.0606760 + 0.0707136i
\(913\) −10.5166 −0.348050
\(914\) −4.01621 −0.132844
\(915\) −43.8574 + 37.6320i −1.44988 + 1.24408i
\(916\) 4.67812 4.67812i 0.154569 0.154569i
\(917\) −4.95938 + 4.95938i −0.163773 + 0.163773i
\(918\) −24.7027 + 15.3726i −0.815312 + 0.507370i
\(919\) −10.8639 −0.358367 −0.179183 0.983816i \(-0.557346\pi\)
−0.179183 + 0.983816i \(0.557346\pi\)
\(920\) 6.00089 0.197843
\(921\) −3.60105 + 3.08989i −0.118659 + 0.101815i
\(922\) 14.2419i 0.469032i
\(923\) 3.49079 + 2.13271i 0.114901 + 0.0701991i
\(924\) 7.37656 + 0.563534i 0.242671 + 0.0185389i
\(925\) −4.34097 + 4.34097i −0.142730 + 0.142730i
\(926\) 14.8517i 0.488056i
\(927\) −1.30885 + 8.51634i −0.0429884 + 0.279713i
\(928\) −1.66021 + 1.66021i −0.0544990 + 0.0544990i
\(929\) −31.1696 31.1696i −1.02264 1.02264i −0.999738 0.0229025i \(-0.992709\pi\)
−0.0229025 0.999738i \(-0.507291\pi\)
\(930\) −10.7473 + 9.22178i −0.352419 + 0.302394i
\(931\) 14.5061 + 14.5061i 0.475419 + 0.475419i
\(932\) 1.55631i 0.0509787i
\(933\) −0.329885 + 4.31814i −0.0108000 + 0.141370i
\(934\) 16.3837 + 16.3837i 0.536090 + 0.536090i
\(935\) −14.0655 −0.459990
\(936\) 20.6346 24.4521i 0.674463 0.799242i
\(937\) 32.1756 1.05113 0.525565 0.850753i \(-0.323854\pi\)
0.525565 + 0.850753i \(0.323854\pi\)
\(938\) 39.9224 + 39.9224i 1.30351 + 1.30351i
\(939\) 0.0193297 0.253022i 0.000630800 0.00825707i
\(940\) 10.4015i 0.339258i
\(941\) −7.54952 7.54952i −0.246107 0.246107i 0.573264 0.819371i \(-0.305677\pi\)
−0.819371 + 0.573264i \(0.805677\pi\)
\(942\) 18.2939 15.6972i 0.596049 0.511442i
\(943\) 4.91455 + 4.91455i 0.160040 + 0.160040i
\(944\) 6.35537 6.35537i 0.206850 0.206850i
\(945\) −48.6372 11.3235i −1.58217 0.368354i
\(946\) 4.78559i 0.155593i
\(947\) 36.5257 36.5257i 1.18693 1.18693i 0.209014 0.977913i \(-0.432975\pi\)
0.977913 0.209014i \(-0.0670255\pi\)
\(948\) −18.8296 1.43849i −0.611557 0.0467200i
\(949\) 32.2061 + 19.6765i 1.04546 + 0.638726i
\(950\) 1.88591i 0.0611870i
\(951\) −12.6963 + 10.8941i −0.411705 + 0.353265i
\(952\) −68.4461 −2.21835
\(953\) 3.69885 0.119817 0.0599087 0.998204i \(-0.480919\pi\)
0.0599087 + 0.998204i \(0.480919\pi\)
\(954\) −3.09721 + 2.27203i −0.100276 + 0.0735595i
\(955\) −15.4789 + 15.4789i −0.500886 + 0.500886i
\(956\) −8.93430 + 8.93430i −0.288956 + 0.288956i
\(957\) −0.588468 + 0.504937i −0.0190225 + 0.0163223i
\(958\) −2.03303 −0.0656841
\(959\) −76.3838 −2.46656
\(960\) −17.5608 20.4659i −0.566772 0.660532i
\(961\) 18.6398i 0.601284i
\(962\) −5.93931 24.5935i −0.191491 0.792925i
\(963\) −3.08341 + 20.0629i −0.0993616 + 0.646518i
\(964\) 0.495480 0.495480i 0.0159583 0.0159583i
\(965\) 52.2254i 1.68120i
\(966\) 5.54606 + 0.423693i 0.178442 + 0.0136321i
\(967\) 15.1872 15.1872i 0.488386 0.488386i −0.419411 0.907797i \(-0.637763\pi\)
0.907797 + 0.419411i \(0.137763\pi\)
\(968\) 2.09159 + 2.09159i 0.0672263 + 0.0672263i
\(969\) 15.2828 + 17.8110i 0.490955 + 0.572172i
\(970\) −14.1251 14.1251i −0.453530 0.453530i
\(971\) 31.7994i 1.02049i 0.860029 + 0.510246i \(0.170446\pi\)
−0.860029 + 0.510246i \(0.829554\pi\)
\(972\) 15.5428 + 6.23025i 0.498534 + 0.199836i
\(973\) −38.3114 38.3114i −1.22821 1.22821i
\(974\) −18.4636 −0.591613
\(975\) −5.18925 + 0.841249i −0.166189 + 0.0269415i
\(976\) −9.63183 −0.308307
\(977\) 8.96922 + 8.96922i 0.286951 + 0.286951i 0.835873 0.548922i \(-0.184962\pi\)
−0.548922 + 0.835873i \(0.684962\pi\)
\(978\) −5.85391 0.447211i −0.187188 0.0143002i
\(979\) 13.3237i 0.425828i
\(980\) −16.1753 16.1753i −0.516700 0.516700i
\(981\) −28.4661 + 20.8820i −0.908854 + 0.666710i
\(982\) 3.53148 + 3.53148i 0.112694 + 0.112694i
\(983\) 18.4004 18.4004i 0.586881 0.586881i −0.349905 0.936785i \(-0.613786\pi\)
0.936785 + 0.349905i \(0.113786\pi\)
\(984\) 3.23149 42.2996i 0.103016 1.34846i
\(985\) 50.3862i 1.60544i
\(986\) 1.77254 1.77254i 0.0564492 0.0564492i
\(987\) −2.10174 + 27.5114i −0.0668991 + 0.875698i
\(988\) −7.69537 4.70152i −0.244822 0.149575i
\(989\) 4.17470i 0.132748i
\(990\) −4.12669 5.62547i −0.131155 0.178789i
\(991\) 27.3003 0.867221 0.433611 0.901100i \(-0.357239\pi\)
0.433611 + 0.901100i \(0.357239\pi\)
\(992\) 18.4383 0.585417
\(993\) 19.0248 + 22.1721i 0.603735 + 0.703610i
\(994\) 3.06938 3.06938i 0.0973550 0.0973550i
\(995\) 14.7380 14.7380i 0.467227 0.467227i
\(996\) −12.7417 14.8495i −0.403735 0.470524i
\(997\) −25.6515 −0.812391 −0.406196 0.913786i \(-0.633145\pi\)
−0.406196 + 0.913786i \(0.633145\pi\)
\(998\) −1.65883 −0.0525094
\(999\) 32.1735 20.0217i 1.01793 0.633457i
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 429.2.j.a.122.18 96
3.2 odd 2 inner 429.2.j.a.122.31 yes 96
13.8 odd 4 inner 429.2.j.a.320.31 yes 96
39.8 even 4 inner 429.2.j.a.320.18 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.j.a.122.18 96 1.1 even 1 trivial
429.2.j.a.122.31 yes 96 3.2 odd 2 inner
429.2.j.a.320.18 yes 96 39.8 even 4 inner
429.2.j.a.320.31 yes 96 13.8 odd 4 inner