Properties

Label 225.2.e.d.151.2
Level $225$
Weight $2$
Character 225.151
Analytic conductor $1.797$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(76,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.2
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 225.151
Dual form 225.2.e.d.76.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 + 0.448288i) q^{2} +(1.67303 + 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-0.633975 + 0.633975i) q^{6} +(1.67303 - 2.89778i) q^{7} -1.93185 q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.258819 + 0.448288i) q^{2} +(1.67303 + 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-0.633975 + 0.633975i) q^{6} +(1.67303 - 2.89778i) q^{7} -1.93185 q^{8} +(2.59808 + 1.50000i) q^{9} +(-0.633975 + 1.09808i) q^{11} +(0.776457 + 2.89778i) q^{12} +(-1.22474 - 2.12132i) q^{13} +(0.866025 + 1.50000i) q^{14} +(-1.23205 + 2.13397i) q^{16} -5.27792 q^{17} +(-1.34486 + 0.776457i) q^{18} -0.732051 q^{19} +(4.09808 - 4.09808i) q^{21} +(-0.328169 - 0.568406i) q^{22} +(0.258819 + 0.448288i) q^{23} +(-3.23205 - 0.866025i) q^{24} +1.26795 q^{26} +(3.67423 + 3.67423i) q^{27} +5.79555 q^{28} +(0.232051 - 0.401924i) q^{29} +(-0.366025 - 0.633975i) q^{31} +(-2.56961 - 4.45069i) q^{32} +(-1.55291 + 1.55291i) q^{33} +(1.36603 - 2.36603i) q^{34} +5.19615i q^{36} +4.24264 q^{37} +(0.189469 - 0.328169i) q^{38} +(-1.09808 - 4.09808i) q^{39} +(-3.86603 - 6.69615i) q^{41} +(0.776457 + 2.89778i) q^{42} +(-0.328169 + 0.568406i) q^{43} -2.19615 q^{44} -0.267949 q^{46} +(-1.48356 + 2.56961i) q^{47} +(-3.01790 + 3.01790i) q^{48} +(-2.09808 - 3.63397i) q^{49} +(-8.83013 - 2.36603i) q^{51} +(2.12132 - 3.67423i) q^{52} +1.03528 q^{53} +(-2.59808 + 0.696152i) q^{54} +(-3.23205 + 5.59808i) q^{56} +(-1.22474 - 0.328169i) q^{57} +(0.120118 + 0.208051i) q^{58} +(-4.73205 - 8.19615i) q^{59} +(3.33013 - 5.76795i) q^{61} +0.378937 q^{62} +(8.69333 - 5.01910i) q^{63} -2.26795 q^{64} +(-0.294229 - 1.09808i) q^{66} +(-3.79435 - 6.57201i) q^{67} +(-4.57081 - 7.91688i) q^{68} +(0.232051 + 0.866025i) q^{69} +14.1962 q^{71} +(-5.01910 - 2.89778i) q^{72} -8.48528 q^{73} +(-1.09808 + 1.90192i) q^{74} +(-0.633975 - 1.09808i) q^{76} +(2.12132 + 3.67423i) q^{77} +(2.12132 + 0.568406i) q^{78} +(-3.73205 + 6.46410i) q^{79} +(4.50000 + 7.79423i) q^{81} +4.00240 q^{82} +(-3.98382 + 6.90018i) q^{83} +(9.69615 + 2.59808i) q^{84} +(-0.169873 - 0.294229i) q^{86} +(0.568406 - 0.568406i) q^{87} +(1.22474 - 2.12132i) q^{88} +13.3923 q^{89} -8.19615 q^{91} +(-0.448288 + 0.776457i) q^{92} +(-0.328169 - 1.22474i) q^{93} +(-0.767949 - 1.33013i) q^{94} +(-2.30385 - 8.59808i) q^{96} +(-7.58871 + 13.1440i) q^{97} +2.17209 q^{98} +(-3.29423 + 1.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{6} - 12 q^{11} + 4 q^{16} + 8 q^{19} + 12 q^{21} - 12 q^{24} + 24 q^{26} - 12 q^{29} + 4 q^{31} + 4 q^{34} + 12 q^{39} - 24 q^{41} + 24 q^{44} - 16 q^{46} + 4 q^{49} - 36 q^{51} - 12 q^{56} - 24 q^{59} - 8 q^{61} - 32 q^{64} + 60 q^{66} - 12 q^{69} + 72 q^{71} + 12 q^{74} - 12 q^{76} - 16 q^{79} + 36 q^{81} + 36 q^{84} - 36 q^{86} + 24 q^{89} - 24 q^{91} - 20 q^{94} - 60 q^{96} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 + 0.448288i −0.183013 + 0.316987i −0.942905 0.333062i \(-0.891918\pi\)
0.759892 + 0.650049i \(0.225252\pi\)
\(3\) 1.67303 + 0.448288i 0.965926 + 0.258819i
\(4\) 0.866025 + 1.50000i 0.433013 + 0.750000i
\(5\) 0 0
\(6\) −0.633975 + 0.633975i −0.258819 + 0.258819i
\(7\) 1.67303 2.89778i 0.632347 1.09526i −0.354724 0.934971i \(-0.615425\pi\)
0.987071 0.160286i \(-0.0512416\pi\)
\(8\) −1.93185 −0.683013
\(9\) 2.59808 + 1.50000i 0.866025 + 0.500000i
\(10\) 0 0
\(11\) −0.633975 + 1.09808i −0.191151 + 0.331082i −0.945632 0.325239i \(-0.894555\pi\)
0.754481 + 0.656322i \(0.227889\pi\)
\(12\) 0.776457 + 2.89778i 0.224144 + 0.836516i
\(13\) −1.22474 2.12132i −0.339683 0.588348i 0.644690 0.764444i \(-0.276986\pi\)
−0.984373 + 0.176096i \(0.943653\pi\)
\(14\) 0.866025 + 1.50000i 0.231455 + 0.400892i
\(15\) 0 0
\(16\) −1.23205 + 2.13397i −0.308013 + 0.533494i
\(17\) −5.27792 −1.28008 −0.640041 0.768340i \(-0.721083\pi\)
−0.640041 + 0.768340i \(0.721083\pi\)
\(18\) −1.34486 + 0.776457i −0.316987 + 0.183013i
\(19\) −0.732051 −0.167944 −0.0839720 0.996468i \(-0.526761\pi\)
−0.0839720 + 0.996468i \(0.526761\pi\)
\(20\) 0 0
\(21\) 4.09808 4.09808i 0.894274 0.894274i
\(22\) −0.328169 0.568406i −0.0699660 0.121185i
\(23\) 0.258819 + 0.448288i 0.0539675 + 0.0934745i 0.891747 0.452534i \(-0.149480\pi\)
−0.837780 + 0.546009i \(0.816147\pi\)
\(24\) −3.23205 0.866025i −0.659740 0.176777i
\(25\) 0 0
\(26\) 1.26795 0.248665
\(27\) 3.67423 + 3.67423i 0.707107 + 0.707107i
\(28\) 5.79555 1.09526
\(29\) 0.232051 0.401924i 0.0430908 0.0746354i −0.843676 0.536853i \(-0.819613\pi\)
0.886766 + 0.462218i \(0.152946\pi\)
\(30\) 0 0
\(31\) −0.366025 0.633975i −0.0657401 0.113865i 0.831282 0.555851i \(-0.187607\pi\)
−0.897022 + 0.441986i \(0.854274\pi\)
\(32\) −2.56961 4.45069i −0.454247 0.786779i
\(33\) −1.55291 + 1.55291i −0.270328 + 0.270328i
\(34\) 1.36603 2.36603i 0.234271 0.405770i
\(35\) 0 0
\(36\) 5.19615i 0.866025i
\(37\) 4.24264 0.697486 0.348743 0.937218i \(-0.386609\pi\)
0.348743 + 0.937218i \(0.386609\pi\)
\(38\) 0.189469 0.328169i 0.0307359 0.0532361i
\(39\) −1.09808 4.09808i −0.175833 0.656217i
\(40\) 0 0
\(41\) −3.86603 6.69615i −0.603772 1.04576i −0.992244 0.124303i \(-0.960331\pi\)
0.388473 0.921460i \(-0.373003\pi\)
\(42\) 0.776457 + 2.89778i 0.119810 + 0.447137i
\(43\) −0.328169 + 0.568406i −0.0500454 + 0.0866811i −0.889963 0.456033i \(-0.849270\pi\)
0.839918 + 0.542714i \(0.182603\pi\)
\(44\) −2.19615 −0.331082
\(45\) 0 0
\(46\) −0.267949 −0.0395070
\(47\) −1.48356 + 2.56961i −0.216400 + 0.374816i −0.953705 0.300744i \(-0.902765\pi\)
0.737305 + 0.675560i \(0.236098\pi\)
\(48\) −3.01790 + 3.01790i −0.435596 + 0.435596i
\(49\) −2.09808 3.63397i −0.299725 0.519139i
\(50\) 0 0
\(51\) −8.83013 2.36603i −1.23647 0.331310i
\(52\) 2.12132 3.67423i 0.294174 0.509525i
\(53\) 1.03528 0.142206 0.0711031 0.997469i \(-0.477348\pi\)
0.0711031 + 0.997469i \(0.477348\pi\)
\(54\) −2.59808 + 0.696152i −0.353553 + 0.0947343i
\(55\) 0 0
\(56\) −3.23205 + 5.59808i −0.431901 + 0.748074i
\(57\) −1.22474 0.328169i −0.162221 0.0434671i
\(58\) 0.120118 + 0.208051i 0.0157723 + 0.0273184i
\(59\) −4.73205 8.19615i −0.616061 1.06705i −0.990197 0.139675i \(-0.955394\pi\)
0.374137 0.927373i \(-0.377939\pi\)
\(60\) 0 0
\(61\) 3.33013 5.76795i 0.426379 0.738510i −0.570169 0.821527i \(-0.693122\pi\)
0.996548 + 0.0830172i \(0.0264556\pi\)
\(62\) 0.378937 0.0481251
\(63\) 8.69333 5.01910i 1.09526 0.632347i
\(64\) −2.26795 −0.283494
\(65\) 0 0
\(66\) −0.294229 1.09808i −0.0362170 0.135164i
\(67\) −3.79435 6.57201i −0.463554 0.802899i 0.535581 0.844484i \(-0.320093\pi\)
−0.999135 + 0.0415848i \(0.986759\pi\)
\(68\) −4.57081 7.91688i −0.554292 0.960062i
\(69\) 0.232051 + 0.866025i 0.0279356 + 0.104257i
\(70\) 0 0
\(71\) 14.1962 1.68477 0.842387 0.538874i \(-0.181150\pi\)
0.842387 + 0.538874i \(0.181150\pi\)
\(72\) −5.01910 2.89778i −0.591506 0.341506i
\(73\) −8.48528 −0.993127 −0.496564 0.868000i \(-0.665405\pi\)
−0.496564 + 0.868000i \(0.665405\pi\)
\(74\) −1.09808 + 1.90192i −0.127649 + 0.221094i
\(75\) 0 0
\(76\) −0.633975 1.09808i −0.0727219 0.125958i
\(77\) 2.12132 + 3.67423i 0.241747 + 0.418718i
\(78\) 2.12132 + 0.568406i 0.240192 + 0.0643593i
\(79\) −3.73205 + 6.46410i −0.419889 + 0.727268i −0.995928 0.0901537i \(-0.971264\pi\)
0.576039 + 0.817422i \(0.304597\pi\)
\(80\) 0 0
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) 4.00240 0.441992
\(83\) −3.98382 + 6.90018i −0.437281 + 0.757393i −0.997479 0.0709657i \(-0.977392\pi\)
0.560198 + 0.828359i \(0.310725\pi\)
\(84\) 9.69615 + 2.59808i 1.05794 + 0.283473i
\(85\) 0 0
\(86\) −0.169873 0.294229i −0.0183179 0.0317275i
\(87\) 0.568406 0.568406i 0.0609395 0.0609395i
\(88\) 1.22474 2.12132i 0.130558 0.226134i
\(89\) 13.3923 1.41958 0.709791 0.704413i \(-0.248789\pi\)
0.709791 + 0.704413i \(0.248789\pi\)
\(90\) 0 0
\(91\) −8.19615 −0.859190
\(92\) −0.448288 + 0.776457i −0.0467372 + 0.0809513i
\(93\) −0.328169 1.22474i −0.0340296 0.127000i
\(94\) −0.767949 1.33013i −0.0792079 0.137192i
\(95\) 0 0
\(96\) −2.30385 8.59808i −0.235135 0.877537i
\(97\) −7.58871 + 13.1440i −0.770516 + 1.33457i 0.166764 + 0.985997i \(0.446668\pi\)
−0.937280 + 0.348577i \(0.886665\pi\)
\(98\) 2.17209 0.219414
\(99\) −3.29423 + 1.90192i −0.331082 + 0.191151i
\(100\) 0 0
\(101\) −4.73205 + 8.19615i −0.470857 + 0.815548i −0.999444 0.0333310i \(-0.989388\pi\)
0.528588 + 0.848879i \(0.322722\pi\)
\(102\) 3.34607 3.34607i 0.331310 0.331310i
\(103\) 0.328169 + 0.568406i 0.0323355 + 0.0560067i 0.881740 0.471735i \(-0.156372\pi\)
−0.849405 + 0.527742i \(0.823039\pi\)
\(104\) 2.36603 + 4.09808i 0.232008 + 0.401849i
\(105\) 0 0
\(106\) −0.267949 + 0.464102i −0.0260255 + 0.0450775i
\(107\) 10.3156 0.997246 0.498623 0.866819i \(-0.333839\pi\)
0.498623 + 0.866819i \(0.333839\pi\)
\(108\) −2.32937 + 8.69333i −0.224144 + 0.836516i
\(109\) 12.6603 1.21263 0.606316 0.795224i \(-0.292647\pi\)
0.606316 + 0.795224i \(0.292647\pi\)
\(110\) 0 0
\(111\) 7.09808 + 1.90192i 0.673720 + 0.180523i
\(112\) 4.12252 + 7.14042i 0.389542 + 0.674706i
\(113\) 8.62398 + 14.9372i 0.811276 + 1.40517i 0.911971 + 0.410254i \(0.134560\pi\)
−0.100695 + 0.994917i \(0.532107\pi\)
\(114\) 0.464102 0.464102i 0.0434671 0.0434671i
\(115\) 0 0
\(116\) 0.803848 0.0746354
\(117\) 7.34847i 0.679366i
\(118\) 4.89898 0.450988
\(119\) −8.83013 + 15.2942i −0.809456 + 1.40202i
\(120\) 0 0
\(121\) 4.69615 + 8.13397i 0.426923 + 0.739452i
\(122\) 1.72380 + 2.98571i 0.156066 + 0.270314i
\(123\) −3.46618 12.9360i −0.312535 1.16640i
\(124\) 0.633975 1.09808i 0.0569326 0.0986102i
\(125\) 0 0
\(126\) 5.19615i 0.462910i
\(127\) −17.3867 −1.54282 −0.771409 0.636340i \(-0.780447\pi\)
−0.771409 + 0.636340i \(0.780447\pi\)
\(128\) 5.72620 9.91808i 0.506130 0.876642i
\(129\) −0.803848 + 0.803848i −0.0707748 + 0.0707748i
\(130\) 0 0
\(131\) −6.46410 11.1962i −0.564771 0.978212i −0.997071 0.0764824i \(-0.975631\pi\)
0.432300 0.901730i \(-0.357702\pi\)
\(132\) −3.67423 0.984508i −0.319801 0.0856904i
\(133\) −1.22474 + 2.12132i −0.106199 + 0.183942i
\(134\) 3.92820 0.339345
\(135\) 0 0
\(136\) 10.1962 0.874313
\(137\) 7.86611 13.6245i 0.672047 1.16402i −0.305276 0.952264i \(-0.598749\pi\)
0.977323 0.211755i \(-0.0679180\pi\)
\(138\) −0.448288 0.120118i −0.0381608 0.0102252i
\(139\) 4.00000 + 6.92820i 0.339276 + 0.587643i 0.984297 0.176522i \(-0.0564848\pi\)
−0.645021 + 0.764165i \(0.723151\pi\)
\(140\) 0 0
\(141\) −3.63397 + 3.63397i −0.306036 + 0.306036i
\(142\) −3.67423 + 6.36396i −0.308335 + 0.534052i
\(143\) 3.10583 0.259722
\(144\) −6.40192 + 3.69615i −0.533494 + 0.308013i
\(145\) 0 0
\(146\) 2.19615 3.80385i 0.181755 0.314809i
\(147\) −1.88108 7.02030i −0.155149 0.579025i
\(148\) 3.67423 + 6.36396i 0.302020 + 0.523114i
\(149\) −2.13397 3.69615i −0.174822 0.302801i 0.765278 0.643700i \(-0.222602\pi\)
−0.940100 + 0.340900i \(0.889268\pi\)
\(150\) 0 0
\(151\) −4.29423 + 7.43782i −0.349459 + 0.605281i −0.986154 0.165835i \(-0.946968\pi\)
0.636694 + 0.771116i \(0.280301\pi\)
\(152\) 1.41421 0.114708
\(153\) −13.7124 7.91688i −1.10858 0.640041i
\(154\) −2.19615 −0.176971
\(155\) 0 0
\(156\) 5.19615 5.19615i 0.416025 0.416025i
\(157\) 6.45189 + 11.1750i 0.514917 + 0.891863i 0.999850 + 0.0173114i \(0.00551066\pi\)
−0.484933 + 0.874551i \(0.661156\pi\)
\(158\) −1.93185 3.34607i −0.153690 0.266199i
\(159\) 1.73205 + 0.464102i 0.137361 + 0.0368057i
\(160\) 0 0
\(161\) 1.73205 0.136505
\(162\) −4.65874 −0.366025
\(163\) −10.4543 −0.818844 −0.409422 0.912345i \(-0.634270\pi\)
−0.409422 + 0.912345i \(0.634270\pi\)
\(164\) 6.69615 11.5981i 0.522882 0.905658i
\(165\) 0 0
\(166\) −2.06218 3.57180i −0.160056 0.277225i
\(167\) 4.96833 + 8.60540i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(168\) −7.91688 + 7.91688i −0.610800 + 0.610800i
\(169\) 3.50000 6.06218i 0.269231 0.466321i
\(170\) 0 0
\(171\) −1.90192 1.09808i −0.145444 0.0839720i
\(172\) −1.13681 −0.0866811
\(173\) 5.27792 9.14162i 0.401273 0.695025i −0.592607 0.805492i \(-0.701901\pi\)
0.993880 + 0.110467i \(0.0352347\pi\)
\(174\) 0.107695 + 0.401924i 0.00816435 + 0.0304698i
\(175\) 0 0
\(176\) −1.56218 2.70577i −0.117754 0.203955i
\(177\) −4.24264 15.8338i −0.318896 1.19014i
\(178\) −3.46618 + 6.00361i −0.259801 + 0.449989i
\(179\) −6.58846 −0.492444 −0.246222 0.969213i \(-0.579189\pi\)
−0.246222 + 0.969213i \(0.579189\pi\)
\(180\) 0 0
\(181\) 1.53590 0.114162 0.0570812 0.998370i \(-0.481821\pi\)
0.0570812 + 0.998370i \(0.481821\pi\)
\(182\) 2.12132 3.67423i 0.157243 0.272352i
\(183\) 8.15711 8.15711i 0.602991 0.602991i
\(184\) −0.500000 0.866025i −0.0368605 0.0638442i
\(185\) 0 0
\(186\) 0.633975 + 0.169873i 0.0464853 + 0.0124557i
\(187\) 3.34607 5.79555i 0.244689 0.423813i
\(188\) −5.13922 −0.374816
\(189\) 16.7942 4.50000i 1.22160 0.327327i
\(190\) 0 0
\(191\) −8.83013 + 15.2942i −0.638926 + 1.10665i 0.346743 + 0.937960i \(0.387287\pi\)
−0.985669 + 0.168691i \(0.946046\pi\)
\(192\) −3.79435 1.01669i −0.273834 0.0733736i
\(193\) 1.88108 + 3.25813i 0.135403 + 0.234526i 0.925751 0.378133i \(-0.123434\pi\)
−0.790348 + 0.612658i \(0.790100\pi\)
\(194\) −3.92820 6.80385i −0.282029 0.488488i
\(195\) 0 0
\(196\) 3.63397 6.29423i 0.259570 0.449588i
\(197\) 15.9353 1.13534 0.567671 0.823255i \(-0.307845\pi\)
0.567671 + 0.823255i \(0.307845\pi\)
\(198\) 1.96902i 0.139932i
\(199\) −26.5885 −1.88481 −0.942403 0.334480i \(-0.891439\pi\)
−0.942403 + 0.334480i \(0.891439\pi\)
\(200\) 0 0
\(201\) −3.40192 12.6962i −0.239953 0.895518i
\(202\) −2.44949 4.24264i −0.172345 0.298511i
\(203\) −0.776457 1.34486i −0.0544966 0.0943909i
\(204\) −4.09808 15.2942i −0.286923 1.07081i
\(205\) 0 0
\(206\) −0.339746 −0.0236712
\(207\) 1.55291i 0.107935i
\(208\) 6.03579 0.418507
\(209\) 0.464102 0.803848i 0.0321026 0.0556033i
\(210\) 0 0
\(211\) −5.56218 9.63397i −0.382916 0.663230i 0.608562 0.793507i \(-0.291747\pi\)
−0.991478 + 0.130276i \(0.958414\pi\)
\(212\) 0.896575 + 1.55291i 0.0615771 + 0.106655i
\(213\) 23.7506 + 6.36396i 1.62737 + 0.436051i
\(214\) −2.66987 + 4.62436i −0.182509 + 0.316114i
\(215\) 0 0
\(216\) −7.09808 7.09808i −0.482963 0.482963i
\(217\) −2.44949 −0.166282
\(218\) −3.27671 + 5.67544i −0.221927 + 0.384389i
\(219\) −14.1962 3.80385i −0.959287 0.257040i
\(220\) 0 0
\(221\) 6.46410 + 11.1962i 0.434823 + 0.753135i
\(222\) −2.68973 + 2.68973i −0.180523 + 0.180523i
\(223\) −2.24144 + 3.88229i −0.150098 + 0.259977i −0.931263 0.364347i \(-0.881292\pi\)
0.781165 + 0.624324i \(0.214626\pi\)
\(224\) −17.1962 −1.14897
\(225\) 0 0
\(226\) −8.92820 −0.593895
\(227\) −13.1948 + 22.8541i −0.875769 + 1.51688i −0.0198279 + 0.999803i \(0.506312\pi\)
−0.855941 + 0.517073i \(0.827021\pi\)
\(228\) −0.568406 2.12132i −0.0376436 0.140488i
\(229\) −3.03590 5.25833i −0.200618 0.347480i 0.748110 0.663575i \(-0.230962\pi\)
−0.948728 + 0.316095i \(0.897628\pi\)
\(230\) 0 0
\(231\) 1.90192 + 7.09808i 0.125137 + 0.467019i
\(232\) −0.448288 + 0.776457i −0.0294315 + 0.0509769i
\(233\) 7.07107 0.463241 0.231621 0.972806i \(-0.425597\pi\)
0.231621 + 0.972806i \(0.425597\pi\)
\(234\) 3.29423 + 1.90192i 0.215350 + 0.124333i
\(235\) 0 0
\(236\) 8.19615 14.1962i 0.533524 0.924091i
\(237\) −9.14162 + 9.14162i −0.593812 + 0.593812i
\(238\) −4.57081 7.91688i −0.296282 0.513175i
\(239\) 0.464102 + 0.803848i 0.0300202 + 0.0519966i 0.880645 0.473776i \(-0.157109\pi\)
−0.850625 + 0.525773i \(0.823776\pi\)
\(240\) 0 0
\(241\) −4.86603 + 8.42820i −0.313448 + 0.542908i −0.979106 0.203348i \(-0.934818\pi\)
0.665658 + 0.746257i \(0.268151\pi\)
\(242\) −4.86181 −0.312529
\(243\) 4.03459 + 15.0573i 0.258819 + 0.965926i
\(244\) 11.5359 0.738510
\(245\) 0 0
\(246\) 6.69615 + 1.79423i 0.426931 + 0.114396i
\(247\) 0.896575 + 1.55291i 0.0570477 + 0.0988096i
\(248\) 0.707107 + 1.22474i 0.0449013 + 0.0777714i
\(249\) −9.75833 + 9.75833i −0.618409 + 0.618409i
\(250\) 0 0
\(251\) −12.5885 −0.794576 −0.397288 0.917694i \(-0.630049\pi\)
−0.397288 + 0.917694i \(0.630049\pi\)
\(252\) 15.0573 + 8.69333i 0.948520 + 0.547628i
\(253\) −0.656339 −0.0412637
\(254\) 4.50000 7.79423i 0.282355 0.489053i
\(255\) 0 0
\(256\) 0.696152 + 1.20577i 0.0435095 + 0.0753607i
\(257\) −8.38375 14.5211i −0.522964 0.905800i −0.999643 0.0267223i \(-0.991493\pi\)
0.476679 0.879077i \(-0.341840\pi\)
\(258\) −0.152304 0.568406i −0.00948203 0.0353874i
\(259\) 7.09808 12.2942i 0.441053 0.763926i
\(260\) 0 0
\(261\) 1.20577 0.696152i 0.0746354 0.0430908i
\(262\) 6.69213 0.413441
\(263\) −10.8840 + 18.8516i −0.671136 + 1.16244i 0.306446 + 0.951888i \(0.400860\pi\)
−0.977582 + 0.210554i \(0.932473\pi\)
\(264\) 3.00000 3.00000i 0.184637 0.184637i
\(265\) 0 0
\(266\) −0.633975 1.09808i −0.0388715 0.0673274i
\(267\) 22.4058 + 6.00361i 1.37121 + 0.367415i
\(268\) 6.57201 11.3831i 0.401450 0.695331i
\(269\) 6.80385 0.414838 0.207419 0.978252i \(-0.433494\pi\)
0.207419 + 0.978252i \(0.433494\pi\)
\(270\) 0 0
\(271\) 21.5167 1.30704 0.653522 0.756908i \(-0.273291\pi\)
0.653522 + 0.756908i \(0.273291\pi\)
\(272\) 6.50266 11.2629i 0.394282 0.682916i
\(273\) −13.7124 3.67423i −0.829914 0.222375i
\(274\) 4.07180 + 7.05256i 0.245986 + 0.426061i
\(275\) 0 0
\(276\) −1.09808 + 1.09808i −0.0660964 + 0.0660964i
\(277\) 6.12372 10.6066i 0.367939 0.637289i −0.621304 0.783569i \(-0.713397\pi\)
0.989243 + 0.146281i \(0.0467302\pi\)
\(278\) −4.14110 −0.248367
\(279\) 2.19615i 0.131480i
\(280\) 0 0
\(281\) 9.86603 17.0885i 0.588558 1.01941i −0.405864 0.913934i \(-0.633029\pi\)
0.994422 0.105478i \(-0.0336374\pi\)
\(282\) −0.688524 2.56961i −0.0410010 0.153018i
\(283\) −8.36516 14.4889i −0.497257 0.861275i 0.502738 0.864439i \(-0.332326\pi\)
−0.999995 + 0.00316407i \(0.998993\pi\)
\(284\) 12.2942 + 21.2942i 0.729528 + 1.26358i
\(285\) 0 0
\(286\) −0.803848 + 1.39230i −0.0475325 + 0.0823287i
\(287\) −25.8719 −1.52717
\(288\) 15.4176i 0.908494i
\(289\) 10.8564 0.638612
\(290\) 0 0
\(291\) −18.5885 + 18.5885i −1.08967 + 1.08967i
\(292\) −7.34847 12.7279i −0.430037 0.744845i
\(293\) −6.88160 11.9193i −0.402027 0.696332i 0.591943 0.805980i \(-0.298361\pi\)
−0.993970 + 0.109648i \(0.965028\pi\)
\(294\) 3.63397 + 0.973721i 0.211938 + 0.0567885i
\(295\) 0 0
\(296\) −8.19615 −0.476392
\(297\) −6.36396 + 1.70522i −0.369274 + 0.0989468i
\(298\) 2.20925 0.127979
\(299\) 0.633975 1.09808i 0.0366637 0.0635034i
\(300\) 0 0
\(301\) 1.09808 + 1.90192i 0.0632921 + 0.109625i
\(302\) −2.22286 3.85010i −0.127911 0.221548i
\(303\) −11.5911 + 11.5911i −0.665892 + 0.665892i
\(304\) 0.901924 1.56218i 0.0517289 0.0895970i
\(305\) 0 0
\(306\) 7.09808 4.09808i 0.405770 0.234271i
\(307\) 3.82654 0.218392 0.109196 0.994020i \(-0.465172\pi\)
0.109196 + 0.994020i \(0.465172\pi\)
\(308\) −3.67423 + 6.36396i −0.209359 + 0.362620i
\(309\) 0.294229 + 1.09808i 0.0167381 + 0.0624674i
\(310\) 0 0
\(311\) 5.02628 + 8.70577i 0.285014 + 0.493659i 0.972613 0.232432i \(-0.0746684\pi\)
−0.687598 + 0.726091i \(0.741335\pi\)
\(312\) 2.12132 + 7.91688i 0.120096 + 0.448205i
\(313\) 7.02030 12.1595i 0.396811 0.687296i −0.596520 0.802598i \(-0.703450\pi\)
0.993330 + 0.115302i \(0.0367836\pi\)
\(314\) −6.67949 −0.376946
\(315\) 0 0
\(316\) −12.9282 −0.727268
\(317\) −2.01978 + 3.49837i −0.113442 + 0.196488i −0.917156 0.398528i \(-0.869521\pi\)
0.803714 + 0.595016i \(0.202854\pi\)
\(318\) −0.656339 + 0.656339i −0.0368057 + 0.0368057i
\(319\) 0.294229 + 0.509619i 0.0164736 + 0.0285332i
\(320\) 0 0
\(321\) 17.2583 + 4.62436i 0.963266 + 0.258106i
\(322\) −0.448288 + 0.776457i −0.0249821 + 0.0432703i
\(323\) 3.86370 0.214982
\(324\) −7.79423 + 13.5000i −0.433013 + 0.750000i
\(325\) 0 0
\(326\) 2.70577 4.68653i 0.149859 0.259563i
\(327\) 21.1810 + 5.67544i 1.17131 + 0.313852i
\(328\) 7.46859 + 12.9360i 0.412384 + 0.714270i
\(329\) 4.96410 + 8.59808i 0.273680 + 0.474027i
\(330\) 0 0
\(331\) 4.19615 7.26795i 0.230641 0.399483i −0.727356 0.686261i \(-0.759251\pi\)
0.957997 + 0.286778i \(0.0925842\pi\)
\(332\) −13.8004 −0.757393
\(333\) 11.0227 + 6.36396i 0.604040 + 0.348743i
\(334\) −5.14359 −0.281445
\(335\) 0 0
\(336\) 3.69615 + 13.7942i 0.201642 + 0.752537i
\(337\) 3.34607 + 5.79555i 0.182272 + 0.315704i 0.942654 0.333772i \(-0.108322\pi\)
−0.760382 + 0.649476i \(0.774988\pi\)
\(338\) 1.81173 + 3.13801i 0.0985453 + 0.170685i
\(339\) 7.73205 + 28.8564i 0.419947 + 1.56726i
\(340\) 0 0
\(341\) 0.928203 0.0502650
\(342\) 0.984508 0.568406i 0.0532361 0.0307359i
\(343\) 9.38186 0.506573
\(344\) 0.633975 1.09808i 0.0341816 0.0592043i
\(345\) 0 0
\(346\) 2.73205 + 4.73205i 0.146876 + 0.254397i
\(347\) −4.94975 8.57321i −0.265716 0.460234i 0.702035 0.712143i \(-0.252275\pi\)
−0.967751 + 0.251909i \(0.918942\pi\)
\(348\) 1.34486 + 0.360355i 0.0720922 + 0.0193171i
\(349\) −14.2321 + 24.6506i −0.761824 + 1.31952i 0.180085 + 0.983651i \(0.442363\pi\)
−0.941909 + 0.335867i \(0.890971\pi\)
\(350\) 0 0
\(351\) 3.29423 12.2942i 0.175833 0.656217i
\(352\) 6.51626 0.347318
\(353\) 10.1769 17.6269i 0.541662 0.938185i −0.457147 0.889391i \(-0.651129\pi\)
0.998809 0.0487943i \(-0.0155379\pi\)
\(354\) 8.19615 + 2.19615i 0.435621 + 0.116724i
\(355\) 0 0
\(356\) 11.5981 + 20.0885i 0.614697 + 1.06469i
\(357\) −21.6293 + 21.6293i −1.14474 + 1.14474i
\(358\) 1.70522 2.95352i 0.0901236 0.156099i
\(359\) 20.1962 1.06591 0.532956 0.846143i \(-0.321081\pi\)
0.532956 + 0.846143i \(0.321081\pi\)
\(360\) 0 0
\(361\) −18.4641 −0.971795
\(362\) −0.397520 + 0.688524i −0.0208932 + 0.0361880i
\(363\) 4.21046 + 15.7136i 0.220992 + 0.824752i
\(364\) −7.09808 12.2942i −0.372040 0.644393i
\(365\) 0 0
\(366\) 1.54552 + 5.76795i 0.0807855 + 0.301496i
\(367\) 17.2987 29.9623i 0.902986 1.56402i 0.0793890 0.996844i \(-0.474703\pi\)
0.823597 0.567175i \(-0.191964\pi\)
\(368\) −1.27551 −0.0664907
\(369\) 23.1962i 1.20754i
\(370\) 0 0
\(371\) 1.73205 3.00000i 0.0899236 0.155752i
\(372\) 1.55291 1.55291i 0.0805149 0.0805149i
\(373\) 13.6245 + 23.5983i 0.705450 + 1.22187i 0.966529 + 0.256557i \(0.0825883\pi\)
−0.261079 + 0.965317i \(0.584078\pi\)
\(374\) 1.73205 + 3.00000i 0.0895622 + 0.155126i
\(375\) 0 0
\(376\) 2.86603 4.96410i 0.147804 0.256004i
\(377\) −1.13681 −0.0585488
\(378\) −2.32937 + 8.69333i −0.119810 + 0.447137i
\(379\) 19.4641 0.999804 0.499902 0.866082i \(-0.333369\pi\)
0.499902 + 0.866082i \(0.333369\pi\)
\(380\) 0 0
\(381\) −29.0885 7.79423i −1.49025 0.399310i
\(382\) −4.57081 7.91688i −0.233863 0.405063i
\(383\) −5.32868 9.22955i −0.272283 0.471608i 0.697163 0.716913i \(-0.254445\pi\)
−0.969446 + 0.245305i \(0.921112\pi\)
\(384\) 14.0263 14.0263i 0.715776 0.715776i
\(385\) 0 0
\(386\) −1.94744 −0.0991221
\(387\) −1.70522 + 0.984508i −0.0866811 + 0.0500454i
\(388\) −26.2880 −1.33457
\(389\) −0.0621778 + 0.107695i −0.00315254 + 0.00546036i −0.867597 0.497267i \(-0.834337\pi\)
0.864445 + 0.502728i \(0.167670\pi\)
\(390\) 0 0
\(391\) −1.36603 2.36603i −0.0690829 0.119655i
\(392\) 4.05317 + 7.02030i 0.204716 + 0.354579i
\(393\) −5.79555 21.6293i −0.292347 1.09105i
\(394\) −4.12436 + 7.14359i −0.207782 + 0.359889i
\(395\) 0 0
\(396\) −5.70577 3.29423i −0.286726 0.165541i
\(397\) 29.3939 1.47524 0.737618 0.675218i \(-0.235950\pi\)
0.737618 + 0.675218i \(0.235950\pi\)
\(398\) 6.88160 11.9193i 0.344943 0.597459i
\(399\) −3.00000 + 3.00000i −0.150188 + 0.150188i
\(400\) 0 0
\(401\) 8.53590 + 14.7846i 0.426262 + 0.738308i 0.996537 0.0831457i \(-0.0264967\pi\)
−0.570275 + 0.821454i \(0.693163\pi\)
\(402\) 6.57201 + 1.76097i 0.327782 + 0.0878290i
\(403\) −0.896575 + 1.55291i −0.0446616 + 0.0773562i
\(404\) −16.3923 −0.815548
\(405\) 0 0
\(406\) 0.803848 0.0398943
\(407\) −2.68973 + 4.65874i −0.133325 + 0.230925i
\(408\) 17.0585 + 4.57081i 0.844521 + 0.226289i
\(409\) 8.26795 + 14.3205i 0.408824 + 0.708104i 0.994758 0.102255i \(-0.0326057\pi\)
−0.585934 + 0.810358i \(0.699272\pi\)
\(410\) 0 0
\(411\) 19.2679 19.2679i 0.950418 0.950418i
\(412\) −0.568406 + 0.984508i −0.0280034 + 0.0485032i
\(413\) −31.6675 −1.55826
\(414\) −0.696152 0.401924i −0.0342140 0.0197535i
\(415\) 0 0
\(416\) −6.29423 + 10.9019i −0.308600 + 0.534511i
\(417\) 3.58630 + 13.3843i 0.175622 + 0.655430i
\(418\) 0.240237 + 0.416102i 0.0117504 + 0.0203522i
\(419\) −11.0263 19.0981i −0.538669 0.933002i −0.998976 0.0452423i \(-0.985594\pi\)
0.460307 0.887760i \(-0.347739\pi\)
\(420\) 0 0
\(421\) 9.73205 16.8564i 0.474311 0.821531i −0.525256 0.850944i \(-0.676031\pi\)
0.999567 + 0.0294132i \(0.00936385\pi\)
\(422\) 5.75839 0.280314
\(423\) −7.70882 + 4.45069i −0.374816 + 0.216400i
\(424\) −2.00000 −0.0971286
\(425\) 0 0
\(426\) −9.00000 + 9.00000i −0.436051 + 0.436051i
\(427\) −11.1428 19.2999i −0.539239 0.933989i
\(428\) 8.93357 + 15.4734i 0.431820 + 0.747935i
\(429\) 5.19615 + 1.39230i 0.250873 + 0.0672211i
\(430\) 0 0
\(431\) −6.00000 −0.289010 −0.144505 0.989504i \(-0.546159\pi\)
−0.144505 + 0.989504i \(0.546159\pi\)
\(432\) −12.3676 + 3.31388i −0.595035 + 0.159439i
\(433\) 13.5601 0.651658 0.325829 0.945429i \(-0.394357\pi\)
0.325829 + 0.945429i \(0.394357\pi\)
\(434\) 0.633975 1.09808i 0.0304318 0.0527093i
\(435\) 0 0
\(436\) 10.9641 + 18.9904i 0.525085 + 0.909474i
\(437\) −0.189469 0.328169i −0.00906352 0.0156985i
\(438\) 5.37945 5.37945i 0.257040 0.257040i
\(439\) 12.6603 21.9282i 0.604241 1.04658i −0.387930 0.921689i \(-0.626810\pi\)
0.992171 0.124887i \(-0.0398569\pi\)
\(440\) 0 0
\(441\) 12.5885i 0.599450i
\(442\) −6.69213 −0.318312
\(443\) 0.827225 1.43280i 0.0393027 0.0680742i −0.845705 0.533651i \(-0.820820\pi\)
0.885008 + 0.465577i \(0.154153\pi\)
\(444\) 3.29423 + 12.2942i 0.156337 + 0.583458i
\(445\) 0 0
\(446\) −1.16025 2.00962i −0.0549396 0.0951582i
\(447\) −1.91327 7.14042i −0.0904945 0.337730i
\(448\) −3.79435 + 6.57201i −0.179266 + 0.310498i
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 9.80385 0.461645
\(452\) −14.9372 + 25.8719i −0.702586 + 1.21691i
\(453\) −10.5187 + 10.5187i −0.494210 + 0.494210i
\(454\) −6.83013 11.8301i −0.320554 0.555215i
\(455\) 0 0
\(456\) 2.36603 + 0.633975i 0.110799 + 0.0296886i
\(457\) −12.3998 + 21.4770i −0.580036 + 1.00465i 0.415438 + 0.909621i \(0.363628\pi\)
−0.995474 + 0.0950304i \(0.969705\pi\)
\(458\) 3.14299 0.146862
\(459\) −19.3923 19.3923i −0.905155 0.905155i
\(460\) 0 0
\(461\) 18.3564 31.7942i 0.854943 1.48080i −0.0217547 0.999763i \(-0.506925\pi\)
0.876698 0.481042i \(-0.159741\pi\)
\(462\) −3.67423 0.984508i −0.170941 0.0458035i
\(463\) −17.0585 29.5462i −0.792776 1.37313i −0.924242 0.381807i \(-0.875302\pi\)
0.131467 0.991321i \(-0.458031\pi\)
\(464\) 0.571797 + 0.990381i 0.0265450 + 0.0459773i
\(465\) 0 0
\(466\) −1.83013 + 3.16987i −0.0847790 + 0.146842i
\(467\) −25.3543 −1.17326 −0.586629 0.809856i \(-0.699545\pi\)
−0.586629 + 0.809856i \(0.699545\pi\)
\(468\) 11.0227 6.36396i 0.509525 0.294174i
\(469\) −25.3923 −1.17251
\(470\) 0 0
\(471\) 5.78461 + 21.5885i 0.266541 + 0.994744i
\(472\) 9.14162 + 15.8338i 0.420777 + 0.728807i
\(473\) −0.416102 0.720710i −0.0191324 0.0331383i
\(474\) −1.73205 6.46410i −0.0795557 0.296906i
\(475\) 0 0
\(476\) −30.5885 −1.40202
\(477\) 2.68973 + 1.55291i 0.123154 + 0.0711031i
\(478\) −0.480473 −0.0219763
\(479\) −2.07180 + 3.58846i −0.0946628 + 0.163961i −0.909468 0.415774i \(-0.863511\pi\)
0.814805 + 0.579735i \(0.196844\pi\)
\(480\) 0 0
\(481\) −5.19615 9.00000i −0.236924 0.410365i
\(482\) −2.51884 4.36276i −0.114730 0.198718i
\(483\) 2.89778 + 0.776457i 0.131853 + 0.0353300i
\(484\) −8.13397 + 14.0885i −0.369726 + 0.640384i
\(485\) 0 0
\(486\) −7.79423 2.08846i −0.353553 0.0947343i
\(487\) −15.8338 −0.717496 −0.358748 0.933435i \(-0.616796\pi\)
−0.358748 + 0.933435i \(0.616796\pi\)
\(488\) −6.43331 + 11.1428i −0.291222 + 0.504412i
\(489\) −17.4904 4.68653i −0.790942 0.211932i
\(490\) 0 0
\(491\) −16.8564 29.1962i −0.760719 1.31760i −0.942480 0.334261i \(-0.891513\pi\)
0.181761 0.983343i \(-0.441820\pi\)
\(492\) 16.4022 16.4022i 0.739466 0.739466i
\(493\) −1.22474 + 2.12132i −0.0551597 + 0.0955395i
\(494\) −0.928203 −0.0417618
\(495\) 0 0
\(496\) 1.80385 0.0809951
\(497\) 23.7506 41.1373i 1.06536 1.84526i
\(498\) −1.84890 6.90018i −0.0828511 0.309205i
\(499\) −11.9282 20.6603i −0.533980 0.924880i −0.999212 0.0396914i \(-0.987363\pi\)
0.465232 0.885189i \(-0.345971\pi\)
\(500\) 0 0
\(501\) 4.45448 + 16.6244i 0.199012 + 0.742721i
\(502\) 3.25813 5.64325i 0.145418 0.251871i
\(503\) −2.48665 −0.110874 −0.0554372 0.998462i \(-0.517655\pi\)
−0.0554372 + 0.998462i \(0.517655\pi\)
\(504\) −16.7942 + 9.69615i −0.748074 + 0.431901i
\(505\) 0 0
\(506\) 0.169873 0.294229i 0.00755178 0.0130801i
\(507\) 8.57321 8.57321i 0.380750 0.380750i
\(508\) −15.0573 26.0800i −0.668059 1.15711i
\(509\) −8.42820 14.5981i −0.373574 0.647048i 0.616539 0.787324i \(-0.288534\pi\)
−0.990112 + 0.140276i \(0.955201\pi\)
\(510\) 0 0
\(511\) −14.1962 + 24.5885i −0.628001 + 1.08773i
\(512\) 22.1841 0.980408
\(513\) −2.68973 2.68973i −0.118754 0.118754i
\(514\) 8.67949 0.382836
\(515\) 0 0
\(516\) −1.90192 0.509619i −0.0837275 0.0224347i
\(517\) −1.88108 3.25813i −0.0827300 0.143293i
\(518\) 3.67423 + 6.36396i 0.161437 + 0.279616i
\(519\) 12.9282 12.9282i 0.567485 0.567485i
\(520\) 0 0
\(521\) −19.3923 −0.849592 −0.424796 0.905289i \(-0.639654\pi\)
−0.424796 + 0.905289i \(0.639654\pi\)
\(522\) 0.720710i 0.0315446i
\(523\) 35.1894 1.53873 0.769363 0.638812i \(-0.220574\pi\)
0.769363 + 0.638812i \(0.220574\pi\)
\(524\) 11.1962 19.3923i 0.489106 0.847157i
\(525\) 0 0
\(526\) −5.63397 9.75833i −0.245653 0.425483i
\(527\) 1.93185 + 3.34607i 0.0841528 + 0.145757i
\(528\) −1.40061 5.22715i −0.0609537 0.227482i
\(529\) 11.3660 19.6865i 0.494175 0.855936i
\(530\) 0 0
\(531\) 28.3923i 1.23212i
\(532\) −4.24264 −0.183942
\(533\) −9.46979 + 16.4022i −0.410182 + 0.710456i
\(534\) −8.49038 + 8.49038i −0.367415 + 0.367415i
\(535\) 0 0
\(536\) 7.33013 + 12.6962i 0.316613 + 0.548390i
\(537\) −11.0227 2.95352i −0.475665 0.127454i
\(538\) −1.76097 + 3.05008i −0.0759206 + 0.131498i
\(539\) 5.32051 0.229171
\(540\) 0 0
\(541\) 0.607695 0.0261269 0.0130634 0.999915i \(-0.495842\pi\)
0.0130634 + 0.999915i \(0.495842\pi\)
\(542\) −5.56892 + 9.64566i −0.239206 + 0.414316i
\(543\) 2.56961 + 0.688524i 0.110272 + 0.0295474i
\(544\) 13.5622 + 23.4904i 0.581474 + 1.00714i
\(545\) 0 0
\(546\) 5.19615 5.19615i 0.222375 0.222375i
\(547\) −13.0239 + 22.5581i −0.556862 + 0.964513i 0.440894 + 0.897559i \(0.354661\pi\)
−0.997756 + 0.0669541i \(0.978672\pi\)
\(548\) 27.2490 1.16402
\(549\) 17.3038 9.99038i 0.738510 0.426379i
\(550\) 0 0
\(551\) −0.169873 + 0.294229i −0.00723683 + 0.0125346i
\(552\) −0.448288 1.67303i −0.0190804 0.0712090i
\(553\) 12.4877 + 21.6293i 0.531030 + 0.919772i
\(554\) 3.16987 + 5.49038i 0.134675 + 0.233264i
\(555\) 0 0
\(556\) −6.92820 + 12.0000i −0.293821 + 0.508913i
\(557\) 31.1127 1.31829 0.659144 0.752017i \(-0.270919\pi\)
0.659144 + 0.752017i \(0.270919\pi\)
\(558\) 0.984508 + 0.568406i 0.0416776 + 0.0240625i
\(559\) 1.60770 0.0679983
\(560\) 0 0
\(561\) 8.19615 8.19615i 0.346042 0.346042i
\(562\) 5.10703 + 8.84564i 0.215427 + 0.373131i
\(563\) 4.58939 + 7.94906i 0.193420 + 0.335013i 0.946381 0.323052i \(-0.104709\pi\)
−0.752962 + 0.658065i \(0.771375\pi\)
\(564\) −8.59808 2.30385i −0.362044 0.0970095i
\(565\) 0 0
\(566\) 8.66025 0.364018
\(567\) 30.1146 1.26469
\(568\) −27.4249 −1.15072
\(569\) −14.6603 + 25.3923i −0.614590 + 1.06450i 0.375867 + 0.926674i \(0.377345\pi\)
−0.990456 + 0.137827i \(0.955988\pi\)
\(570\) 0 0
\(571\) 0.732051 + 1.26795i 0.0306354 + 0.0530620i 0.880937 0.473234i \(-0.156914\pi\)
−0.850301 + 0.526296i \(0.823580\pi\)
\(572\) 2.68973 + 4.65874i 0.112463 + 0.194792i
\(573\) −21.6293 + 21.6293i −0.903577 + 0.903577i
\(574\) 6.69615 11.5981i 0.279492 0.484094i
\(575\) 0 0
\(576\) −5.89230 3.40192i −0.245513 0.141747i
\(577\) −13.8647 −0.577196 −0.288598 0.957450i \(-0.593189\pi\)
−0.288598 + 0.957450i \(0.593189\pi\)
\(578\) −2.80984 + 4.86679i −0.116874 + 0.202432i
\(579\) 1.68653 + 6.29423i 0.0700899 + 0.261579i
\(580\) 0 0
\(581\) 13.3301 + 23.0885i 0.553027 + 0.957871i
\(582\) −3.52193 13.1440i −0.145989 0.544837i
\(583\) −0.656339 + 1.13681i −0.0271828 + 0.0470819i
\(584\) 16.3923 0.678318
\(585\) 0 0
\(586\) 7.12436 0.294304
\(587\) 2.43091 4.21046i 0.100334 0.173784i −0.811488 0.584369i \(-0.801342\pi\)
0.911822 + 0.410585i \(0.134675\pi\)
\(588\) 8.90138 8.90138i 0.367087 0.367087i
\(589\) 0.267949 + 0.464102i 0.0110407 + 0.0191230i
\(590\) 0 0
\(591\) 26.6603 + 7.14359i 1.09666 + 0.293848i
\(592\) −5.22715 + 9.05369i −0.214834 + 0.372104i
\(593\) 19.1427 0.786094 0.393047 0.919518i \(-0.371421\pi\)
0.393047 + 0.919518i \(0.371421\pi\)
\(594\) 0.882686 3.29423i 0.0362170 0.135164i
\(595\) 0 0
\(596\) 3.69615 6.40192i 0.151400 0.262233i
\(597\) −44.4834 11.9193i −1.82058 0.487824i
\(598\) 0.328169 + 0.568406i 0.0134198 + 0.0232439i
\(599\) 10.8564 + 18.8038i 0.443581 + 0.768304i 0.997952 0.0639650i \(-0.0203746\pi\)
−0.554371 + 0.832269i \(0.687041\pi\)
\(600\) 0 0
\(601\) 1.53590 2.66025i 0.0626506 0.108514i −0.832999 0.553275i \(-0.813378\pi\)
0.895649 + 0.444761i \(0.146711\pi\)
\(602\) −1.13681 −0.0463330
\(603\) 22.7661i 0.927108i
\(604\) −14.8756 −0.605281
\(605\) 0 0
\(606\) −2.19615 8.19615i −0.0892126 0.332946i
\(607\) 10.4865 + 18.1631i 0.425633 + 0.737218i 0.996479 0.0838387i \(-0.0267180\pi\)
−0.570846 + 0.821057i \(0.693385\pi\)
\(608\) 1.88108 + 3.25813i 0.0762880 + 0.132135i
\(609\) −0.696152 2.59808i −0.0282095 0.105279i
\(610\) 0 0
\(611\) 7.26795 0.294030
\(612\) 27.4249i 1.10858i
\(613\) 9.62209 0.388633 0.194316 0.980939i \(-0.437751\pi\)
0.194316 + 0.980939i \(0.437751\pi\)
\(614\) −0.990381 + 1.71539i −0.0399685 + 0.0692275i
\(615\) 0 0
\(616\) −4.09808 7.09808i −0.165116 0.285990i
\(617\) 9.00292 + 15.5935i 0.362444 + 0.627771i 0.988362 0.152117i \(-0.0486091\pi\)
−0.625919 + 0.779888i \(0.715276\pi\)
\(618\) −0.568406 0.152304i −0.0228646 0.00612656i
\(619\) −15.0981 + 26.1506i −0.606843 + 1.05108i 0.384914 + 0.922952i \(0.374231\pi\)
−0.991757 + 0.128130i \(0.959102\pi\)
\(620\) 0 0
\(621\) −0.696152 + 2.59808i −0.0279356 + 0.104257i
\(622\) −5.20359 −0.208645
\(623\) 22.4058 38.8079i 0.897668 1.55481i
\(624\) 10.0981 + 2.70577i 0.404247 + 0.108318i
\(625\) 0 0
\(626\) 3.63397 + 6.29423i 0.145243 + 0.251568i
\(627\) 1.13681 1.13681i 0.0453999 0.0453999i
\(628\) −11.1750 + 19.3557i −0.445931 + 0.772376i
\(629\) −22.3923 −0.892840
\(630\) 0 0
\(631\) 1.32051 0.0525686 0.0262843 0.999655i \(-0.491632\pi\)
0.0262843 + 0.999655i \(0.491632\pi\)
\(632\) 7.20977 12.4877i 0.286789 0.496733i
\(633\) −4.98691 18.6114i −0.198212 0.739737i
\(634\) −1.04552 1.81089i −0.0415228 0.0719196i
\(635\) 0 0
\(636\) 0.803848 + 3.00000i 0.0318746 + 0.118958i
\(637\) −5.13922 + 8.90138i −0.203623 + 0.352686i
\(638\) −0.304608 −0.0120595
\(639\) 36.8827 + 21.2942i 1.45906 + 0.842387i
\(640\) 0 0
\(641\) −6.52628 + 11.3038i −0.257773 + 0.446475i −0.965645 0.259865i \(-0.916322\pi\)
0.707872 + 0.706340i \(0.249655\pi\)
\(642\) −6.53983 + 6.53983i −0.258106 + 0.258106i
\(643\) 6.48408 + 11.2308i 0.255707 + 0.442898i 0.965087 0.261928i \(-0.0843584\pi\)
−0.709380 + 0.704826i \(0.751025\pi\)
\(644\) 1.50000 + 2.59808i 0.0591083 + 0.102379i
\(645\) 0 0
\(646\) −1.00000 + 1.73205i −0.0393445 + 0.0681466i
\(647\) 19.4572 0.764942 0.382471 0.923967i \(-0.375073\pi\)
0.382471 + 0.923967i \(0.375073\pi\)
\(648\) −8.69333 15.0573i −0.341506 0.591506i
\(649\) 12.0000 0.471041
\(650\) 0 0
\(651\) −4.09808 1.09808i −0.160616 0.0430370i
\(652\) −9.05369 15.6814i −0.354570 0.614133i
\(653\) −24.2683 42.0339i −0.949691 1.64491i −0.746076 0.665861i \(-0.768064\pi\)
−0.203615 0.979051i \(-0.565269\pi\)
\(654\) −8.02628 + 8.02628i −0.313852 + 0.313852i
\(655\) 0 0
\(656\) 19.0526 0.743877
\(657\) −22.0454 12.7279i −0.860073 0.496564i
\(658\) −5.13922 −0.200348
\(659\) 6.12436 10.6077i 0.238571 0.413217i −0.721733 0.692171i \(-0.756654\pi\)
0.960304 + 0.278954i \(0.0899877\pi\)
\(660\) 0 0
\(661\) −5.39230 9.33975i −0.209736 0.363274i 0.741895 0.670516i \(-0.233927\pi\)
−0.951631 + 0.307242i \(0.900594\pi\)
\(662\) 2.17209 + 3.76217i 0.0844206 + 0.146221i
\(663\) 5.79555 + 21.6293i 0.225081 + 0.840013i
\(664\) 7.69615 13.3301i 0.298669 0.517309i
\(665\) 0 0
\(666\) −5.70577 + 3.29423i −0.221094 + 0.127649i
\(667\) 0.240237 0.00930200
\(668\) −8.60540 + 14.9050i −0.332953 + 0.576691i
\(669\) −5.49038 + 5.49038i −0.212270 + 0.212270i
\(670\) 0 0
\(671\) 4.22243 + 7.31347i 0.163005 + 0.282333i
\(672\) −28.7697 7.70882i −1.10982 0.297374i
\(673\) −20.4046 + 35.3417i −0.786538 + 1.36232i 0.141538 + 0.989933i \(0.454795\pi\)
−0.928076 + 0.372391i \(0.878538\pi\)
\(674\) −3.46410 −0.133432
\(675\) 0 0
\(676\) 12.1244 0.466321
\(677\) −1.84392 + 3.19376i −0.0708676 + 0.122746i −0.899282 0.437370i \(-0.855910\pi\)
0.828414 + 0.560116i \(0.189243\pi\)
\(678\) −14.9372 4.00240i −0.573659 0.153711i
\(679\) 25.3923 + 43.9808i 0.974467 + 1.68783i
\(680\) 0 0
\(681\) −32.3205 + 32.3205i −1.23852 + 1.23852i
\(682\) −0.240237 + 0.416102i −0.00919914 + 0.0159334i
\(683\) −0.101536 −0.00388517 −0.00194258 0.999998i \(-0.500618\pi\)
−0.00194258 + 0.999998i \(0.500618\pi\)
\(684\) 3.80385i 0.145444i
\(685\) 0 0
\(686\) −2.42820 + 4.20577i −0.0927092 + 0.160577i
\(687\) −2.72191 10.1583i −0.103847 0.387564i
\(688\) −0.808643 1.40061i −0.0308292 0.0533978i
\(689\) −1.26795 2.19615i −0.0483050 0.0836667i
\(690\) 0 0
\(691\) 14.1244 24.4641i 0.537316 0.930658i −0.461732 0.887020i \(-0.652772\pi\)
0.999047 0.0436386i \(-0.0138950\pi\)
\(692\) 18.2832 0.695025
\(693\) 12.7279i 0.483494i
\(694\) 5.12436 0.194518
\(695\) 0 0
\(696\) −1.09808 + 1.09808i −0.0416225 + 0.0416225i
\(697\) 20.4046 + 35.3417i 0.772878 + 1.33866i
\(698\) −7.36705 12.7601i −0.278847 0.482977i
\(699\) 11.8301 + 3.16987i 0.447456 + 0.119896i
\(700\) 0 0
\(701\) −12.8038 −0.483595 −0.241797 0.970327i \(-0.577737\pi\)
−0.241797 + 0.970327i \(0.577737\pi\)
\(702\) 4.65874 + 4.65874i 0.175833 + 0.175833i
\(703\) −3.10583 −0.117139
\(704\) 1.43782 2.49038i 0.0541900 0.0938598i
\(705\) 0 0
\(706\) 5.26795 + 9.12436i 0.198262 + 0.343400i
\(707\) 15.8338 + 27.4249i 0.595489 + 1.03142i
\(708\) 20.0764 20.0764i 0.754517 0.754517i
\(709\) −4.89230 + 8.47372i −0.183734 + 0.318237i −0.943149 0.332369i \(-0.892152\pi\)
0.759415 + 0.650607i \(0.225485\pi\)
\(710\) 0 0
\(711\) −19.3923 + 11.1962i −0.727268 + 0.419889i
\(712\) −25.8719 −0.969592
\(713\) 0.189469 0.328169i 0.00709566 0.0122900i
\(714\) −4.09808 15.2942i −0.153367 0.572372i
\(715\) 0 0
\(716\) −5.70577 9.88269i −0.213235 0.369333i
\(717\) 0.416102 + 1.55291i 0.0155396 + 0.0579946i
\(718\) −5.22715 + 9.05369i −0.195075 + 0.337881i
\(719\) 40.3923 1.50638 0.753189 0.657804i \(-0.228514\pi\)
0.753189 + 0.657804i \(0.228514\pi\)
\(720\) 0 0
\(721\) 2.19615 0.0817890
\(722\) 4.77886 8.27723i 0.177851 0.308047i
\(723\) −11.9193 + 11.9193i −0.443283 + 0.443283i
\(724\) 1.33013 + 2.30385i 0.0494338 + 0.0856218i
\(725\) 0 0
\(726\) −8.13397 2.17949i −0.301880 0.0808885i
\(727\) 0.688524 1.19256i 0.0255360 0.0442296i −0.852975 0.521952i \(-0.825204\pi\)
0.878511 + 0.477722i \(0.158537\pi\)
\(728\) 15.8338 0.586838
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 1.73205 3.00000i 0.0640622 0.110959i
\(732\) 19.2999 + 5.17140i 0.713346 + 0.191141i
\(733\) −3.76217 6.51626i −0.138959 0.240684i 0.788144 0.615491i \(-0.211042\pi\)
−0.927103 + 0.374807i \(0.877709\pi\)
\(734\) 8.95448 + 15.5096i 0.330516 + 0.572470i
\(735\) 0 0
\(736\) 1.33013 2.30385i 0.0490291 0.0849209i
\(737\) 9.62209 0.354434
\(738\) 10.3986 + 6.00361i 0.382776 + 0.220996i
\(739\) −18.1436 −0.667423 −0.333711 0.942675i \(-0.608301\pi\)
−0.333711 + 0.942675i \(0.608301\pi\)
\(740\) 0 0
\(741\) 0.803848 + 3.00000i 0.0295301 + 0.110208i
\(742\) 0.896575 + 1.55291i 0.0329143 + 0.0570093i
\(743\) 16.3328 + 28.2893i 0.599193 + 1.03783i 0.992941 + 0.118613i \(0.0378449\pi\)
−0.393748 + 0.919218i \(0.628822\pi\)
\(744\) 0.633975 + 2.36603i 0.0232426 + 0.0867427i
\(745\) 0 0
\(746\) −14.1051 −0.516425
\(747\) −20.7005 + 11.9515i −0.757393 + 0.437281i
\(748\) 11.5911 0.423813
\(749\) 17.2583 29.8923i 0.630606 1.09224i
\(750\) 0 0
\(751\) 12.2224 + 21.1699i 0.446003 + 0.772500i 0.998121 0.0612659i \(-0.0195138\pi\)
−0.552119 + 0.833766i \(0.686180\pi\)
\(752\) −3.65565 6.33178i −0.133308 0.230896i
\(753\) −21.0609 5.64325i −0.767502 0.205651i
\(754\) 0.294229 0.509619i 0.0107152 0.0185592i
\(755\) 0 0
\(756\) 21.2942 + 21.2942i 0.774464 + 0.774464i
\(757\) 7.34847 0.267085 0.133542 0.991043i \(-0.457365\pi\)
0.133542 + 0.991043i \(0.457365\pi\)
\(758\) −5.03768 + 8.72552i −0.182977 + 0.316925i
\(759\) −1.09808 0.294229i −0.0398576 0.0106798i
\(760\) 0 0
\(761\) −7.96410 13.7942i −0.288698 0.500040i 0.684801 0.728730i \(-0.259889\pi\)
−0.973499 + 0.228690i \(0.926556\pi\)
\(762\) 11.0227 11.0227i 0.399310 0.399310i
\(763\) 21.1810 36.6866i 0.766804 1.32814i
\(764\) −30.5885 −1.10665
\(765\) 0 0
\(766\) 5.51666 0.199325
\(767\) −11.5911 + 20.0764i −0.418531 + 0.724916i
\(768\) 0.624153 + 2.32937i 0.0225222 + 0.0840540i
\(769\) −20.8205 36.0622i −0.750807 1.30044i −0.947432 0.319957i \(-0.896332\pi\)
0.196625 0.980479i \(-0.437002\pi\)
\(770\) 0 0
\(771\) −7.51666 28.0526i −0.270706 1.01029i
\(772\) −3.25813 + 5.64325i −0.117263 + 0.203105i
\(773\) −2.07055 −0.0744726 −0.0372363 0.999306i \(-0.511855\pi\)
−0.0372363 + 0.999306i \(0.511855\pi\)
\(774\) 1.01924i 0.0366357i
\(775\) 0 0
\(776\) 14.6603 25.3923i 0.526272 0.911531i
\(777\) 17.3867 17.3867i 0.623743 0.623743i
\(778\) −0.0321856 0.0557471i −0.00115391 0.00199863i
\(779\) 2.83013 + 4.90192i 0.101400 + 0.175630i
\(780\) 0 0
\(781\) −9.00000 + 15.5885i −0.322045 + 0.557799i
\(782\) 1.41421 0.0505722
\(783\) 2.32937 0.624153i 0.0832449 0.0223054i
\(784\) 10.3397 0.369277
\(785\) 0 0
\(786\) 11.1962 + 3.00000i 0.399354 + 0.107006i
\(787\) −13.0561 22.6138i −0.465399 0.806095i 0.533820 0.845598i \(-0.320756\pi\)
−0.999219 + 0.0395027i \(0.987423\pi\)
\(788\) 13.8004 + 23.9029i 0.491618 + 0.851507i
\(789\) −26.6603 + 26.6603i −0.949130 + 0.949130i
\(790\) 0 0
\(791\) 57.7128 2.05203
\(792\) 6.36396 3.67423i 0.226134 0.130558i
\(793\) −16.3142 −0.579335
\(794\) −7.60770 + 13.1769i −0.269987 + 0.467631i
\(795\) 0 0
\(796\) −23.0263 39.8827i −0.816145 1.41360i
\(797\) −26.3388 45.6202i −0.932969 1.61595i −0.778217 0.627996i \(-0.783875\pi\)
−0.154752 0.987953i \(-0.549458\pi\)
\(798\) −0.568406 2.12132i −0.0201214 0.0750939i
\(799\) 7.83013 13.5622i 0.277010 0.479795i
\(800\) 0 0
\(801\) 34.7942 + 20.0885i 1.22939 + 0.709791i
\(802\) −8.83701 −0.312046
\(803\) 5.37945 9.31749i 0.189837 0.328807i
\(804\) 16.0981 16.0981i 0.567735 0.567735i
\(805\) 0 0
\(806\) −0.464102 0.803848i −0.0163473 0.0283143i
\(807\) 11.3831 + 3.05008i 0.400703 + 0.107368i
\(808\) 9.14162 15.8338i 0.321601 0.557029i
\(809\) −25.1769 −0.885173 −0.442587 0.896726i \(-0.645939\pi\)
−0.442587 + 0.896726i \(0.645939\pi\)
\(810\) 0 0
\(811\) −39.5692 −1.38946 −0.694732 0.719269i \(-0.744477\pi\)
−0.694732 + 0.719269i \(0.744477\pi\)
\(812\) 1.34486 2.32937i 0.0471954 0.0817449i
\(813\) 35.9981 + 9.64566i 1.26251 + 0.338288i
\(814\) −1.39230 2.41154i −0.0488003 0.0845245i
\(815\) 0 0
\(816\) 15.9282 15.9282i 0.557599 0.557599i
\(817\) 0.240237 0.416102i 0.00840482 0.0145576i
\(818\) −8.55961 −0.299280
\(819\) −21.2942 12.2942i −0.744081 0.429595i
\(820\) 0 0
\(821\) −14.7224 + 25.5000i −0.513816 + 0.889956i 0.486055 + 0.873928i \(0.338435\pi\)
−0.999872 + 0.0160280i \(0.994898\pi\)
\(822\) 3.65067 + 13.6245i 0.127332 + 0.475209i
\(823\) 9.58991 + 16.6102i 0.334283 + 0.578995i 0.983347 0.181739i \(-0.0581725\pi\)
−0.649064 + 0.760734i \(0.724839\pi\)
\(824\) −0.633975 1.09808i −0.0220856 0.0382533i
\(825\) 0 0
\(826\) 8.19615 14.1962i 0.285181 0.493947i
\(827\) −23.8014 −0.827656 −0.413828 0.910355i \(-0.635808\pi\)
−0.413828 + 0.910355i \(0.635808\pi\)
\(828\) −2.32937 + 1.34486i −0.0809513 + 0.0467372i
\(829\) 0.411543 0.0142935 0.00714673 0.999974i \(-0.497725\pi\)
0.00714673 + 0.999974i \(0.497725\pi\)
\(830\) 0 0
\(831\) 15.0000 15.0000i 0.520344 0.520344i
\(832\) 2.77766 + 4.81105i 0.0962980 + 0.166793i
\(833\) 11.0735 + 19.1798i 0.383673 + 0.664541i
\(834\) −6.92820 1.85641i −0.239904 0.0642821i
\(835\) 0 0
\(836\) 1.60770 0.0556033
\(837\) 0.984508 3.67423i 0.0340296 0.127000i
\(838\) 11.4152 0.394333
\(839\) −2.36603 + 4.09808i −0.0816843 + 0.141481i −0.903974 0.427588i \(-0.859363\pi\)
0.822289 + 0.569070i \(0.192697\pi\)
\(840\) 0 0
\(841\) 14.3923 + 24.9282i 0.496286 + 0.859593i
\(842\) 5.03768 + 8.72552i 0.173610 + 0.300701i
\(843\) 24.1667 24.1667i 0.832346 0.832346i
\(844\) 9.63397 16.6865i 0.331615 0.574374i
\(845\) 0 0
\(846\) 4.60770i 0.158416i
\(847\) 31.4273 1.07985
\(848\) −1.27551 + 2.20925i −0.0438013 + 0.0758661i
\(849\) −7.50000 27.9904i −0.257399 0.960627i
\(850\) 0 0
\(851\) 1.09808 + 1.90192i 0.0376416 + 0.0651971i
\(852\) 11.0227 + 41.1373i 0.377632 + 1.40934i
\(853\) 21.7172 37.6154i 0.743584 1.28793i −0.207269 0.978284i \(-0.566458\pi\)
0.950853 0.309641i \(-0.100209\pi\)
\(854\) 11.5359 0.394750
\(855\) 0 0
\(856\) −19.9282 −0.681132
\(857\) 6.88160 11.9193i 0.235071 0.407155i −0.724222 0.689567i \(-0.757801\pi\)
0.959293 + 0.282412i \(0.0911344\pi\)
\(858\) −1.96902 + 1.96902i −0.0672211 + 0.0672211i
\(859\) −18.2224 31.5622i −0.621741 1.07689i −0.989161 0.146832i \(-0.953092\pi\)
0.367420 0.930055i \(-0.380241\pi\)
\(860\) 0 0
\(861\) −43.2846 11.5981i −1.47514 0.395261i
\(862\) 1.55291 2.68973i 0.0528925 0.0916124i
\(863\) −44.9131 −1.52886 −0.764429 0.644708i \(-0.776979\pi\)
−0.764429 + 0.644708i \(0.776979\pi\)
\(864\) 6.91154 25.7942i 0.235135 0.877537i
\(865\) 0 0
\(866\) −3.50962 + 6.07884i −0.119262 + 0.206567i
\(867\) 18.1631 + 4.86679i 0.616852 + 0.165285i
\(868\) −2.12132 3.67423i −0.0720023 0.124712i
\(869\) −4.73205 8.19615i −0.160524 0.278035i
\(870\) 0 0
\(871\) −9.29423 + 16.0981i −0.314923 + 0.545463i
\(872\) −24.4577 −0.828243
\(873\) −39.4321 + 22.7661i −1.33457 + 0.770516i
\(874\) 0.196152 0.00663495
\(875\) 0 0
\(876\) −6.58846 24.5885i −0.222603 0.830767i
\(877\) −14.6090 25.3035i −0.493311 0.854440i 0.506659 0.862146i \(-0.330880\pi\)
−0.999970 + 0.00770656i \(0.997547\pi\)
\(878\) 6.55343 + 11.3509i 0.221168 + 0.383073i
\(879\) −6.16987 23.0263i −0.208105 0.776657i
\(880\) 0 0
\(881\) −39.5885 −1.33377 −0.666885 0.745161i \(-0.732373\pi\)
−0.666885 + 0.745161i \(0.732373\pi\)
\(882\) 5.64325 + 3.25813i 0.190018 + 0.109707i
\(883\) −54.4336 −1.83184 −0.915919 0.401364i \(-0.868536\pi\)
−0.915919 + 0.401364i \(0.868536\pi\)
\(884\) −11.1962 + 19.3923i −0.376567 + 0.652234i
\(885\) 0 0
\(886\) 0.428203 + 0.741670i 0.0143858 + 0.0249169i
\(887\) −4.29341 7.43640i −0.144159 0.249690i 0.784900 0.619622i \(-0.212714\pi\)
−0.929059 + 0.369932i \(0.879381\pi\)
\(888\) −13.7124 3.67423i −0.460159 0.123299i
\(889\) −29.0885 + 50.3827i −0.975596 + 1.68978i
\(890\) 0 0
\(891\) −11.4115 −0.382301
\(892\) −7.76457 −0.259977
\(893\) 1.08604 1.88108i 0.0363431 0.0629481i
\(894\) 3.69615 + 0.990381i 0.123618 + 0.0331233i
\(895\) 0 0
\(896\) −19.1603 33.1865i −0.640099 1.10868i
\(897\) 1.55291 1.55291i 0.0518503 0.0518503i
\(898\) 3.10583 5.37945i 0.103643 0.179515i
\(899\) −0.339746 −0.0113312
\(900\) 0 0
\(901\) −5.46410 −0.182036
\(902\) −2.53742 + 4.39494i −0.0844869 + 0.146336i
\(903\) 0.984508 + 3.67423i 0.0327624 + 0.122271i
\(904\) −16.6603 28.8564i −0.554112 0.959750i
\(905\) 0 0
\(906\) −1.99296 7.43782i −0.0662116 0.247105i
\(907\) 5.76337 9.98245i 0.191370 0.331462i −0.754335 0.656490i \(-0.772040\pi\)
0.945704 + 0.325028i \(0.105374\pi\)
\(908\) −45.7081 −1.51688
\(909\) −24.5885 + 14.1962i −0.815548 + 0.470857i
\(910\) 0 0
\(911\) −24.9282 + 43.1769i −0.825908 + 1.43051i 0.0753150 + 0.997160i \(0.476004\pi\)
−0.901223 + 0.433355i \(0.857330\pi\)
\(912\) 2.20925 2.20925i 0.0731557 0.0731557i
\(913\) −5.05128 8.74908i −0.167173 0.289552i
\(914\) −6.41858 11.1173i −0.212308 0.367728i
\(915\) 0 0
\(916\) 5.25833 9.10770i 0.173740 0.300927i
\(917\) −43.2586 −1.42853
\(918\) 13.7124 3.67423i 0.452578 0.121268i
\(919\) 47.1769 1.55622 0.778111 0.628126i \(-0.216178\pi\)
0.778111 + 0.628126i \(0.216178\pi\)
\(920\) 0 0
\(921\) 6.40192 + 1.71539i 0.210951 + 0.0565240i
\(922\) 9.50198 + 16.4579i 0.312931 + 0.542012i
\(923\) −17.3867 30.1146i −0.572289 0.991234i
\(924\) −9.00000 + 9.00000i −0.296078 + 0.296078i
\(925\) 0 0
\(926\) 17.6603 0.580352
\(927\) 1.96902i 0.0646710i
\(928\) −2.38512 −0.0782954
\(929\) 1.73205 3.00000i 0.0568267 0.0984268i −0.836213 0.548405i \(-0.815235\pi\)
0.893039 + 0.449979i \(0.148568\pi\)
\(930\) 0 0
\(931\) 1.53590 + 2.66025i 0.0503370 + 0.0871863i
\(932\) 6.12372 + 10.6066i 0.200589 + 0.347431i
\(933\) 4.50644 + 16.8183i 0.147534 + 0.550605i
\(934\) 6.56218 11.3660i 0.214721 0.371908i
\(935\) 0 0
\(936\) 14.1962i 0.464016i
\(937\) 28.5617 0.933069 0.466535 0.884503i \(-0.345502\pi\)
0.466535 + 0.884503i \(0.345502\pi\)
\(938\) 6.57201 11.3831i 0.214584 0.371670i
\(939\) 17.1962 17.1962i 0.561175 0.561175i
\(940\) 0 0
\(941\) −13.1603 22.7942i −0.429012 0.743071i 0.567774 0.823185i \(-0.307805\pi\)
−0.996786 + 0.0801141i \(0.974472\pi\)
\(942\) −11.1750 2.99433i −0.364101 0.0975607i
\(943\) 2.00120 3.46618i 0.0651681 0.112874i
\(944\) 23.3205 0.759018
\(945\) 0 0
\(946\) 0.430781 0.0140059
\(947\) −2.38014 + 4.12252i −0.0773441 + 0.133964i −0.902103 0.431520i \(-0.857977\pi\)
0.824759 + 0.565484i \(0.191311\pi\)
\(948\) −21.6293 5.79555i −0.702487 0.188231i
\(949\) 10.3923 + 18.0000i 0.337348 + 0.584305i
\(950\) 0 0
\(951\) −4.94744 + 4.94744i −0.160432 + 0.160432i
\(952\) 17.0585 29.5462i 0.552869 0.957597i
\(953\) 51.1619 1.65730 0.828648 0.559770i \(-0.189111\pi\)
0.828648 + 0.559770i \(0.189111\pi\)
\(954\) −1.39230 + 0.803848i −0.0450775 + 0.0260255i
\(955\) 0 0
\(956\) −0.803848 + 1.39230i −0.0259983 + 0.0450304i
\(957\) 0.263798 + 0.984508i 0.00852738 + 0.0318246i
\(958\) −1.07244 1.85752i −0.0346490 0.0600138i
\(959\) −26.3205 45.5885i −0.849934 1.47213i
\(960\) 0 0
\(961\) 15.2321 26.3827i 0.491356 0.851054i
\(962\) 5.37945 0.173441
\(963\) 26.8007 + 15.4734i 0.863641 + 0.498623i
\(964\) −16.8564 −0.542908
\(965\) 0 0
\(966\) −1.09808 + 1.09808i −0.0353300 + 0.0353300i
\(967\) −27.9611 48.4300i −0.899168 1.55740i −0.828560 0.559900i \(-0.810840\pi\)
−0.0706076 0.997504i \(-0.522494\pi\)
\(968\) −9.07227 15.7136i −0.291594 0.505055i
\(969\) 6.46410 + 1.73205i 0.207657 + 0.0556415i
\(970\) 0 0
\(971\) 38.1962 1.22577 0.612886 0.790171i \(-0.290008\pi\)
0.612886 + 0.790171i \(0.290008\pi\)
\(972\) −19.0919 + 19.0919i −0.612372 + 0.612372i
\(973\) 26.7685 0.858159
\(974\) 4.09808 7.09808i 0.131311 0.227437i
\(975\) 0 0
\(976\) 8.20577 + 14.2128i 0.262660 + 0.454941i
\(977\) 7.77817 + 13.4722i 0.248846 + 0.431014i 0.963206 0.268765i \(-0.0866154\pi\)
−0.714360 + 0.699778i \(0.753282\pi\)
\(978\) 6.62776 6.62776i 0.211932 0.211932i
\(979\) −8.49038 + 14.7058i −0.271354 + 0.469998i
\(980\) 0 0
\(981\) 32.8923 + 18.9904i 1.05017 + 0.606316i
\(982\) 17.4510 0.556885
\(983\) −16.7117 + 28.9456i −0.533022 + 0.923221i 0.466234 + 0.884661i \(0.345610\pi\)
−0.999256 + 0.0385597i \(0.987723\pi\)
\(984\) 6.69615 + 24.9904i 0.213466 + 0.796664i
\(985\) 0 0
\(986\) −0.633975 1.09808i −0.0201899 0.0349699i
\(987\) 4.45069 + 16.6102i 0.141667 + 0.528709i
\(988\) −1.55291 + 2.68973i −0.0494048 + 0.0855716i
\(989\) −0.339746 −0.0108033
\(990\) 0 0
\(991\) 38.9282 1.23660 0.618298 0.785944i \(-0.287823\pi\)
0.618298 + 0.785944i \(0.287823\pi\)
\(992\) −1.88108 + 3.25813i −0.0597245 + 0.103446i
\(993\) 10.2784 10.2784i 0.326176 0.326176i
\(994\) 12.2942 + 21.2942i 0.389949 + 0.675412i
\(995\) 0 0
\(996\) −23.0885 6.18653i −0.731586 0.196028i
\(997\) 5.13922 8.90138i 0.162761 0.281910i −0.773097 0.634288i \(-0.781294\pi\)
0.935858 + 0.352378i \(0.114627\pi\)
\(998\) 12.3490 0.390900
\(999\) 15.5885 + 15.5885i 0.493197 + 0.493197i
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 225.2.e.d.151.2 8
3.2 odd 2 675.2.e.d.451.3 8
5.2 odd 4 45.2.j.a.34.2 yes 8
5.3 odd 4 45.2.j.a.34.3 yes 8
5.4 even 2 inner 225.2.e.d.151.3 8
9.2 odd 6 2025.2.a.r.1.2 4
9.4 even 3 inner 225.2.e.d.76.2 8
9.5 odd 6 675.2.e.d.226.3 8
9.7 even 3 2025.2.a.t.1.3 4
15.2 even 4 135.2.j.a.19.3 8
15.8 even 4 135.2.j.a.19.2 8
15.14 odd 2 675.2.e.d.451.2 8
20.3 even 4 720.2.by.d.529.3 8
20.7 even 4 720.2.by.d.529.2 8
45.2 even 12 405.2.b.c.244.2 4
45.4 even 6 inner 225.2.e.d.76.3 8
45.7 odd 12 405.2.b.d.244.3 4
45.13 odd 12 45.2.j.a.4.2 8
45.14 odd 6 675.2.e.d.226.2 8
45.22 odd 12 45.2.j.a.4.3 yes 8
45.23 even 12 135.2.j.a.64.3 8
45.29 odd 6 2025.2.a.r.1.3 4
45.32 even 12 135.2.j.a.64.2 8
45.34 even 6 2025.2.a.t.1.2 4
45.38 even 12 405.2.b.c.244.3 4
45.43 odd 12 405.2.b.d.244.2 4
60.23 odd 4 2160.2.by.c.289.1 8
60.47 odd 4 2160.2.by.c.289.3 8
180.23 odd 12 2160.2.by.c.1009.3 8
180.67 even 12 720.2.by.d.49.3 8
180.103 even 12 720.2.by.d.49.2 8
180.167 odd 12 2160.2.by.c.1009.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.2.j.a.4.2 8 45.13 odd 12
45.2.j.a.4.3 yes 8 45.22 odd 12
45.2.j.a.34.2 yes 8 5.2 odd 4
45.2.j.a.34.3 yes 8 5.3 odd 4
135.2.j.a.19.2 8 15.8 even 4
135.2.j.a.19.3 8 15.2 even 4
135.2.j.a.64.2 8 45.32 even 12
135.2.j.a.64.3 8 45.23 even 12
225.2.e.d.76.2 8 9.4 even 3 inner
225.2.e.d.76.3 8 45.4 even 6 inner
225.2.e.d.151.2 8 1.1 even 1 trivial
225.2.e.d.151.3 8 5.4 even 2 inner
405.2.b.c.244.2 4 45.2 even 12
405.2.b.c.244.3 4 45.38 even 12
405.2.b.d.244.2 4 45.43 odd 12
405.2.b.d.244.3 4 45.7 odd 12
675.2.e.d.226.2 8 45.14 odd 6
675.2.e.d.226.3 8 9.5 odd 6
675.2.e.d.451.2 8 15.14 odd 2
675.2.e.d.451.3 8 3.2 odd 2
720.2.by.d.49.2 8 180.103 even 12
720.2.by.d.49.3 8 180.67 even 12
720.2.by.d.529.2 8 20.7 even 4
720.2.by.d.529.3 8 20.3 even 4
2025.2.a.r.1.2 4 9.2 odd 6
2025.2.a.r.1.3 4 45.29 odd 6
2025.2.a.t.1.2 4 45.34 even 6
2025.2.a.t.1.3 4 9.7 even 3
2160.2.by.c.289.1 8 60.23 odd 4
2160.2.by.c.289.3 8 60.47 odd 4
2160.2.by.c.1009.1 8 180.167 odd 12
2160.2.by.c.1009.3 8 180.23 odd 12