Properties

Label 400.2.q.a.149.1
Level $400$
Weight $2$
Character 400.149
Analytic conductor $3.194$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,2,Mod(149,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.q (of order \(4\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 149.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 400.149
Dual form 400.2.q.a.349.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 - 1.00000i) q^{3} -2.00000i q^{4} +2.00000 q^{6} -2.00000 q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 - 1.00000i) q^{3} -2.00000i q^{4} +2.00000 q^{6} -2.00000 q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(-2.00000 + 2.00000i) q^{12} +(-1.00000 - 1.00000i) q^{13} +(2.00000 - 2.00000i) q^{14} -4.00000 q^{16} +2.00000i q^{17} +(1.00000 + 1.00000i) q^{18} +(-3.00000 + 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} -2.00000 q^{22} -6.00000 q^{23} -4.00000i q^{24} +2.00000 q^{26} +(-4.00000 + 4.00000i) q^{27} +4.00000i q^{28} +(-3.00000 + 3.00000i) q^{29} -8.00000 q^{31} +(4.00000 - 4.00000i) q^{32} -2.00000i q^{33} +(-2.00000 - 2.00000i) q^{34} -2.00000 q^{36} +(3.00000 - 3.00000i) q^{37} -6.00000i q^{38} +2.00000i q^{39} -4.00000 q^{42} +(-5.00000 + 5.00000i) q^{43} +(2.00000 - 2.00000i) q^{44} +(6.00000 - 6.00000i) q^{46} -8.00000i q^{47} +(4.00000 + 4.00000i) q^{48} -3.00000 q^{49} +(2.00000 - 2.00000i) q^{51} +(-2.00000 + 2.00000i) q^{52} +(5.00000 - 5.00000i) q^{53} -8.00000i q^{54} +(-4.00000 - 4.00000i) q^{56} +6.00000 q^{57} -6.00000i q^{58} +(3.00000 + 3.00000i) q^{59} +(-9.00000 + 9.00000i) q^{61} +(8.00000 - 8.00000i) q^{62} +2.00000i q^{63} +8.00000i q^{64} +(2.00000 + 2.00000i) q^{66} +(5.00000 + 5.00000i) q^{67} +4.00000 q^{68} +(6.00000 + 6.00000i) q^{69} -10.0000i q^{71} +(2.00000 - 2.00000i) q^{72} +4.00000 q^{73} +6.00000i q^{74} +(6.00000 + 6.00000i) q^{76} +(-2.00000 - 2.00000i) q^{77} +(-2.00000 - 2.00000i) q^{78} +5.00000 q^{81} +(-1.00000 - 1.00000i) q^{83} +(4.00000 - 4.00000i) q^{84} -10.0000i q^{86} +6.00000 q^{87} +4.00000i q^{88} -4.00000i q^{89} +(2.00000 + 2.00000i) q^{91} +12.0000i q^{92} +(8.00000 + 8.00000i) q^{93} +(8.00000 + 8.00000i) q^{94} -8.00000 q^{96} +2.00000i q^{97} +(3.00000 - 3.00000i) q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 2 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 2 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 8 q^{16} + 2 q^{18} - 6 q^{19} + 4 q^{21} - 4 q^{22} - 12 q^{23} + 4 q^{26} - 8 q^{27} - 6 q^{29} - 16 q^{31} + 8 q^{32} - 4 q^{34} - 4 q^{36} + 6 q^{37} - 8 q^{42} - 10 q^{43} + 4 q^{44} + 12 q^{46} + 8 q^{48} - 6 q^{49} + 4 q^{51} - 4 q^{52} + 10 q^{53} - 8 q^{56} + 12 q^{57} + 6 q^{59} - 18 q^{61} + 16 q^{62} + 4 q^{66} + 10 q^{67} + 8 q^{68} + 12 q^{69} + 4 q^{72} + 8 q^{73} + 12 q^{76} - 4 q^{77} - 4 q^{78} + 10 q^{81} - 2 q^{83} + 8 q^{84} + 12 q^{87} + 4 q^{91} + 16 q^{93} + 16 q^{94} - 16 q^{96} + 6 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.707107 + 0.707107i
\(3\) −1.00000 1.00000i −0.577350 0.577350i 0.356822 0.934172i \(-0.383860\pi\)
−0.934172 + 0.356822i \(0.883860\pi\)
\(4\) 2.00000i 1.00000i
\(5\) 0 0
\(6\) 2.00000 0.816497
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 1.00000 + 1.00000i 0.301511 + 0.301511i 0.841605 0.540094i \(-0.181611\pi\)
−0.540094 + 0.841605i \(0.681611\pi\)
\(12\) −2.00000 + 2.00000i −0.577350 + 0.577350i
\(13\) −1.00000 1.00000i −0.277350 0.277350i 0.554700 0.832050i \(-0.312833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 2.00000 2.00000i 0.534522 0.534522i
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 1.00000 + 1.00000i 0.235702 + 0.235702i
\(19\) −3.00000 + 3.00000i −0.688247 + 0.688247i −0.961844 0.273597i \(-0.911786\pi\)
0.273597 + 0.961844i \(0.411786\pi\)
\(20\) 0 0
\(21\) 2.00000 + 2.00000i 0.436436 + 0.436436i
\(22\) −2.00000 −0.426401
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 4.00000i 0.816497i
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) −4.00000 + 4.00000i −0.769800 + 0.769800i
\(28\) 4.00000i 0.755929i
\(29\) −3.00000 + 3.00000i −0.557086 + 0.557086i −0.928477 0.371391i \(-0.878881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 4.00000 4.00000i 0.707107 0.707107i
\(33\) 2.00000i 0.348155i
\(34\) −2.00000 2.00000i −0.342997 0.342997i
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 2.00000i 0.320256i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −4.00000 −0.617213
\(43\) −5.00000 + 5.00000i −0.762493 + 0.762493i −0.976772 0.214280i \(-0.931260\pi\)
0.214280 + 0.976772i \(0.431260\pi\)
\(44\) 2.00000 2.00000i 0.301511 0.301511i
\(45\) 0 0
\(46\) 6.00000 6.00000i 0.884652 0.884652i
\(47\) 8.00000i 1.16692i −0.812142 0.583460i \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) 4.00000 + 4.00000i 0.577350 + 0.577350i
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) 2.00000 2.00000i 0.280056 0.280056i
\(52\) −2.00000 + 2.00000i −0.277350 + 0.277350i
\(53\) 5.00000 5.00000i 0.686803 0.686803i −0.274721 0.961524i \(-0.588586\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 8.00000i 1.08866i
\(55\) 0 0
\(56\) −4.00000 4.00000i −0.534522 0.534522i
\(57\) 6.00000 0.794719
\(58\) 6.00000i 0.787839i
\(59\) 3.00000 + 3.00000i 0.390567 + 0.390567i 0.874889 0.484323i \(-0.160934\pi\)
−0.484323 + 0.874889i \(0.660934\pi\)
\(60\) 0 0
\(61\) −9.00000 + 9.00000i −1.15233 + 1.15233i −0.166248 + 0.986084i \(0.553165\pi\)
−0.986084 + 0.166248i \(0.946835\pi\)
\(62\) 8.00000 8.00000i 1.01600 1.01600i
\(63\) 2.00000i 0.251976i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 2.00000 + 2.00000i 0.246183 + 0.246183i
\(67\) 5.00000 + 5.00000i 0.610847 + 0.610847i 0.943167 0.332320i \(-0.107831\pi\)
−0.332320 + 0.943167i \(0.607831\pi\)
\(68\) 4.00000 0.485071
\(69\) 6.00000 + 6.00000i 0.722315 + 0.722315i
\(70\) 0 0
\(71\) 10.0000i 1.18678i −0.804914 0.593391i \(-0.797789\pi\)
0.804914 0.593391i \(-0.202211\pi\)
\(72\) 2.00000 2.00000i 0.235702 0.235702i
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 6.00000i 0.697486i
\(75\) 0 0
\(76\) 6.00000 + 6.00000i 0.688247 + 0.688247i
\(77\) −2.00000 2.00000i −0.227921 0.227921i
\(78\) −2.00000 2.00000i −0.226455 0.226455i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) −1.00000 1.00000i −0.109764 0.109764i 0.650092 0.759856i \(-0.274731\pi\)
−0.759856 + 0.650092i \(0.774731\pi\)
\(84\) 4.00000 4.00000i 0.436436 0.436436i
\(85\) 0 0
\(86\) 10.0000i 1.07833i
\(87\) 6.00000 0.643268
\(88\) 4.00000i 0.426401i
\(89\) 4.00000i 0.423999i −0.977270 0.212000i \(-0.932002\pi\)
0.977270 0.212000i \(-0.0679975\pi\)
\(90\) 0 0
\(91\) 2.00000 + 2.00000i 0.209657 + 0.209657i
\(92\) 12.0000i 1.25109i
\(93\) 8.00000 + 8.00000i 0.829561 + 0.829561i
\(94\) 8.00000 + 8.00000i 0.825137 + 0.825137i
\(95\) 0 0
\(96\) −8.00000 −0.816497
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) 3.00000 3.00000i 0.303046 0.303046i
\(99\) 1.00000 1.00000i 0.100504 0.100504i
\(100\) 0 0
\(101\) 11.0000 + 11.0000i 1.09454 + 1.09454i 0.995037 + 0.0995037i \(0.0317255\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 4.00000i 0.396059i
\(103\) −6.00000 −0.591198 −0.295599 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) 4.00000i 0.392232i
\(105\) 0 0
\(106\) 10.0000i 0.971286i
\(107\) −7.00000 + 7.00000i −0.676716 + 0.676716i −0.959256 0.282540i \(-0.908823\pi\)
0.282540 + 0.959256i \(0.408823\pi\)
\(108\) 8.00000 + 8.00000i 0.769800 + 0.769800i
\(109\) −3.00000 + 3.00000i −0.287348 + 0.287348i −0.836031 0.548683i \(-0.815129\pi\)
0.548683 + 0.836031i \(0.315129\pi\)
\(110\) 0 0
\(111\) −6.00000 −0.569495
\(112\) 8.00000 0.755929
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) −6.00000 + 6.00000i −0.561951 + 0.561951i
\(115\) 0 0
\(116\) 6.00000 + 6.00000i 0.557086 + 0.557086i
\(117\) −1.00000 + 1.00000i −0.0924500 + 0.0924500i
\(118\) −6.00000 −0.552345
\(119\) 4.00000i 0.366679i
\(120\) 0 0
\(121\) 9.00000i 0.818182i
\(122\) 18.0000i 1.62964i
\(123\) 0 0
\(124\) 16.0000i 1.43684i
\(125\) 0 0
\(126\) −2.00000 2.00000i −0.178174 0.178174i
\(127\) 8.00000i 0.709885i −0.934888 0.354943i \(-0.884500\pi\)
0.934888 0.354943i \(-0.115500\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) 10.0000 0.880451
\(130\) 0 0
\(131\) 11.0000 11.0000i 0.961074 0.961074i −0.0381958 0.999270i \(-0.512161\pi\)
0.999270 + 0.0381958i \(0.0121611\pi\)
\(132\) −4.00000 −0.348155
\(133\) 6.00000 6.00000i 0.520266 0.520266i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) −4.00000 + 4.00000i −0.342997 + 0.342997i
\(137\) 8.00000 0.683486 0.341743 0.939793i \(-0.388983\pi\)
0.341743 + 0.939793i \(0.388983\pi\)
\(138\) −12.0000 −1.02151
\(139\) 3.00000 + 3.00000i 0.254457 + 0.254457i 0.822795 0.568338i \(-0.192414\pi\)
−0.568338 + 0.822795i \(0.692414\pi\)
\(140\) 0 0
\(141\) −8.00000 + 8.00000i −0.673722 + 0.673722i
\(142\) 10.0000 + 10.0000i 0.839181 + 0.839181i
\(143\) 2.00000i 0.167248i
\(144\) 4.00000i 0.333333i
\(145\) 0 0
\(146\) −4.00000 + 4.00000i −0.331042 + 0.331042i
\(147\) 3.00000 + 3.00000i 0.247436 + 0.247436i
\(148\) −6.00000 6.00000i −0.493197 0.493197i
\(149\) −7.00000 7.00000i −0.573462 0.573462i 0.359632 0.933094i \(-0.382902\pi\)
−0.933094 + 0.359632i \(0.882902\pi\)
\(150\) 0 0
\(151\) 10.0000i 0.813788i −0.913475 0.406894i \(-0.866612\pi\)
0.913475 0.406894i \(-0.133388\pi\)
\(152\) −12.0000 −0.973329
\(153\) 2.00000 0.161690
\(154\) 4.00000 0.322329
\(155\) 0 0
\(156\) 4.00000 0.320256
\(157\) −15.0000 15.0000i −1.19713 1.19713i −0.975022 0.222108i \(-0.928706\pi\)
−0.222108 0.975022i \(-0.571294\pi\)
\(158\) 0 0
\(159\) −10.0000 −0.793052
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) −5.00000 + 5.00000i −0.392837 + 0.392837i
\(163\) −1.00000 1.00000i −0.0783260 0.0783260i 0.666858 0.745184i \(-0.267639\pi\)
−0.745184 + 0.666858i \(0.767639\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 2.00000 0.155230
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 8.00000i 0.617213i
\(169\) 11.0000i 0.846154i
\(170\) 0 0
\(171\) 3.00000 + 3.00000i 0.229416 + 0.229416i
\(172\) 10.0000 + 10.0000i 0.762493 + 0.762493i
\(173\) −1.00000 1.00000i −0.0760286 0.0760286i 0.668070 0.744099i \(-0.267121\pi\)
−0.744099 + 0.668070i \(0.767121\pi\)
\(174\) −6.00000 + 6.00000i −0.454859 + 0.454859i
\(175\) 0 0
\(176\) −4.00000 4.00000i −0.301511 0.301511i
\(177\) 6.00000i 0.450988i
\(178\) 4.00000 + 4.00000i 0.299813 + 0.299813i
\(179\) 17.0000 17.0000i 1.27064 1.27064i 0.324887 0.945753i \(-0.394674\pi\)
0.945753 0.324887i \(-0.105326\pi\)
\(180\) 0 0
\(181\) −9.00000 9.00000i −0.668965 0.668965i 0.288512 0.957476i \(-0.406840\pi\)
−0.957476 + 0.288512i \(0.906840\pi\)
\(182\) −4.00000 −0.296500
\(183\) 18.0000 1.33060
\(184\) −12.0000 12.0000i −0.884652 0.884652i
\(185\) 0 0
\(186\) −16.0000 −1.17318
\(187\) −2.00000 + 2.00000i −0.146254 + 0.146254i
\(188\) −16.0000 −1.16692
\(189\) 8.00000 8.00000i 0.581914 0.581914i
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 8.00000 8.00000i 0.577350 0.577350i
\(193\) 14.0000i 1.00774i 0.863779 + 0.503871i \(0.168091\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) −2.00000 2.00000i −0.143592 0.143592i
\(195\) 0 0
\(196\) 6.00000i 0.428571i
\(197\) −17.0000 + 17.0000i −1.21120 + 1.21120i −0.240567 + 0.970632i \(0.577334\pi\)
−0.970632 + 0.240567i \(0.922666\pi\)
\(198\) 2.00000i 0.142134i
\(199\) 14.0000i 0.992434i −0.868199 0.496217i \(-0.834722\pi\)
0.868199 0.496217i \(-0.165278\pi\)
\(200\) 0 0
\(201\) 10.0000i 0.705346i
\(202\) −22.0000 −1.54791
\(203\) 6.00000 6.00000i 0.421117 0.421117i
\(204\) −4.00000 4.00000i −0.280056 0.280056i
\(205\) 0 0
\(206\) 6.00000 6.00000i 0.418040 0.418040i
\(207\) 6.00000i 0.417029i
\(208\) 4.00000 + 4.00000i 0.277350 + 0.277350i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −9.00000 + 9.00000i −0.619586 + 0.619586i −0.945425 0.325840i \(-0.894353\pi\)
0.325840 + 0.945425i \(0.394353\pi\)
\(212\) −10.0000 10.0000i −0.686803 0.686803i
\(213\) −10.0000 + 10.0000i −0.685189 + 0.685189i
\(214\) 14.0000i 0.957020i
\(215\) 0 0
\(216\) −16.0000 −1.08866
\(217\) 16.0000 1.08615
\(218\) 6.00000i 0.406371i
\(219\) −4.00000 4.00000i −0.270295 0.270295i
\(220\) 0 0
\(221\) 2.00000 2.00000i 0.134535 0.134535i
\(222\) 6.00000 6.00000i 0.402694 0.402694i
\(223\) 24.0000i 1.60716i 0.595198 + 0.803579i \(0.297074\pi\)
−0.595198 + 0.803579i \(0.702926\pi\)
\(224\) −8.00000 + 8.00000i −0.534522 + 0.534522i
\(225\) 0 0
\(226\) 6.00000 + 6.00000i 0.399114 + 0.399114i
\(227\) −15.0000 15.0000i −0.995585 0.995585i 0.00440533 0.999990i \(-0.498598\pi\)
−0.999990 + 0.00440533i \(0.998598\pi\)
\(228\) 12.0000i 0.794719i
\(229\) −7.00000 7.00000i −0.462573 0.462573i 0.436925 0.899498i \(-0.356068\pi\)
−0.899498 + 0.436925i \(0.856068\pi\)
\(230\) 0 0
\(231\) 4.00000i 0.263181i
\(232\) −12.0000 −0.787839
\(233\) 4.00000 0.262049 0.131024 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) 2.00000i 0.130744i
\(235\) 0 0
\(236\) 6.00000 6.00000i 0.390567 0.390567i
\(237\) 0 0
\(238\) 4.00000 + 4.00000i 0.259281 + 0.259281i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 9.00000 + 9.00000i 0.578542 + 0.578542i
\(243\) 7.00000 + 7.00000i 0.449050 + 0.449050i
\(244\) 18.0000 + 18.0000i 1.15233 + 1.15233i
\(245\) 0 0
\(246\) 0 0
\(247\) 6.00000 0.381771
\(248\) −16.0000 16.0000i −1.01600 1.01600i
\(249\) 2.00000i 0.126745i
\(250\) 0 0
\(251\) 21.0000 + 21.0000i 1.32551 + 1.32551i 0.909243 + 0.416265i \(0.136661\pi\)
0.416265 + 0.909243i \(0.363339\pi\)
\(252\) 4.00000 0.251976
\(253\) −6.00000 6.00000i −0.377217 0.377217i
\(254\) 8.00000 + 8.00000i 0.501965 + 0.501965i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 22.0000i 1.37232i 0.727450 + 0.686161i \(0.240706\pi\)
−0.727450 + 0.686161i \(0.759294\pi\)
\(258\) −10.0000 + 10.0000i −0.622573 + 0.622573i
\(259\) −6.00000 + 6.00000i −0.372822 + 0.372822i
\(260\) 0 0
\(261\) 3.00000 + 3.00000i 0.185695 + 0.185695i
\(262\) 22.0000i 1.35916i
\(263\) −6.00000 −0.369976 −0.184988 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) 4.00000 4.00000i 0.246183 0.246183i
\(265\) 0 0
\(266\) 12.0000i 0.735767i
\(267\) −4.00000 + 4.00000i −0.244796 + 0.244796i
\(268\) 10.0000 10.0000i 0.610847 0.610847i
\(269\) −3.00000 + 3.00000i −0.182913 + 0.182913i −0.792624 0.609711i \(-0.791286\pi\)
0.609711 + 0.792624i \(0.291286\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 8.00000i 0.485071i
\(273\) 4.00000i 0.242091i
\(274\) −8.00000 + 8.00000i −0.483298 + 0.483298i
\(275\) 0 0
\(276\) 12.0000 12.0000i 0.722315 0.722315i
\(277\) 3.00000 3.00000i 0.180253 0.180253i −0.611213 0.791466i \(-0.709318\pi\)
0.791466 + 0.611213i \(0.209318\pi\)
\(278\) −6.00000 −0.359856
\(279\) 8.00000i 0.478947i
\(280\) 0 0
\(281\) 20.0000i 1.19310i −0.802576 0.596550i \(-0.796538\pi\)
0.802576 0.596550i \(-0.203462\pi\)
\(282\) 16.0000i 0.952786i
\(283\) 15.0000 15.0000i 0.891657 0.891657i −0.103022 0.994679i \(-0.532851\pi\)
0.994679 + 0.103022i \(0.0328511\pi\)
\(284\) −20.0000 −1.18678
\(285\) 0 0
\(286\) 2.00000 + 2.00000i 0.118262 + 0.118262i
\(287\) 0 0
\(288\) −4.00000 4.00000i −0.235702 0.235702i
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 2.00000 2.00000i 0.117242 0.117242i
\(292\) 8.00000i 0.468165i
\(293\) −15.0000 + 15.0000i −0.876309 + 0.876309i −0.993151 0.116841i \(-0.962723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) −6.00000 −0.349927
\(295\) 0 0
\(296\) 12.0000 0.697486
\(297\) −8.00000 −0.464207
\(298\) 14.0000 0.810998
\(299\) 6.00000 + 6.00000i 0.346989 + 0.346989i
\(300\) 0 0
\(301\) 10.0000 10.0000i 0.576390 0.576390i
\(302\) 10.0000 + 10.0000i 0.575435 + 0.575435i
\(303\) 22.0000i 1.26387i
\(304\) 12.0000 12.0000i 0.688247 0.688247i
\(305\) 0 0
\(306\) −2.00000 + 2.00000i −0.114332 + 0.114332i
\(307\) 5.00000 + 5.00000i 0.285365 + 0.285365i 0.835244 0.549879i \(-0.185326\pi\)
−0.549879 + 0.835244i \(0.685326\pi\)
\(308\) −4.00000 + 4.00000i −0.227921 + 0.227921i
\(309\) 6.00000 + 6.00000i 0.341328 + 0.341328i
\(310\) 0 0
\(311\) 30.0000i 1.70114i 0.525859 + 0.850572i \(0.323744\pi\)
−0.525859 + 0.850572i \(0.676256\pi\)
\(312\) −4.00000 + 4.00000i −0.226455 + 0.226455i
\(313\) −16.0000 −0.904373 −0.452187 0.891923i \(-0.649356\pi\)
−0.452187 + 0.891923i \(0.649356\pi\)
\(314\) 30.0000 1.69300
\(315\) 0 0
\(316\) 0 0
\(317\) 5.00000 + 5.00000i 0.280828 + 0.280828i 0.833439 0.552611i \(-0.186369\pi\)
−0.552611 + 0.833439i \(0.686369\pi\)
\(318\) 10.0000 10.0000i 0.560772 0.560772i
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) 14.0000 0.781404
\(322\) −12.0000 + 12.0000i −0.668734 + 0.668734i
\(323\) −6.00000 6.00000i −0.333849 0.333849i
\(324\) 10.0000i 0.555556i
\(325\) 0 0
\(326\) 2.00000 0.110770
\(327\) 6.00000 0.331801
\(328\) 0 0
\(329\) 16.0000i 0.882109i
\(330\) 0 0
\(331\) 1.00000 + 1.00000i 0.0549650 + 0.0549650i 0.734055 0.679090i \(-0.237625\pi\)
−0.679090 + 0.734055i \(0.737625\pi\)
\(332\) −2.00000 + 2.00000i −0.109764 + 0.109764i
\(333\) −3.00000 3.00000i −0.164399 0.164399i
\(334\) 2.00000 2.00000i 0.109435 0.109435i
\(335\) 0 0
\(336\) −8.00000 8.00000i −0.436436 0.436436i
\(337\) 18.0000i 0.980522i −0.871576 0.490261i \(-0.836901\pi\)
0.871576 0.490261i \(-0.163099\pi\)
\(338\) 11.0000 + 11.0000i 0.598321 + 0.598321i
\(339\) −6.00000 + 6.00000i −0.325875 + 0.325875i
\(340\) 0 0
\(341\) −8.00000 8.00000i −0.433224 0.433224i
\(342\) −6.00000 −0.324443
\(343\) 20.0000 1.07990
\(344\) −20.0000 −1.07833
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) 13.0000 13.0000i 0.697877 0.697877i −0.266076 0.963952i \(-0.585727\pi\)
0.963952 + 0.266076i \(0.0857271\pi\)
\(348\) 12.0000i 0.643268i
\(349\) −3.00000 + 3.00000i −0.160586 + 0.160586i −0.782826 0.622240i \(-0.786223\pi\)
0.622240 + 0.782826i \(0.286223\pi\)
\(350\) 0 0
\(351\) 8.00000 0.427008
\(352\) 8.00000 0.426401
\(353\) 6.00000i 0.319348i −0.987170 0.159674i \(-0.948956\pi\)
0.987170 0.159674i \(-0.0510443\pi\)
\(354\) 6.00000 + 6.00000i 0.318896 + 0.318896i
\(355\) 0 0
\(356\) −8.00000 −0.423999
\(357\) −4.00000 + 4.00000i −0.211702 + 0.211702i
\(358\) 34.0000i 1.79696i
\(359\) 26.0000i 1.37223i 0.727494 + 0.686114i \(0.240685\pi\)
−0.727494 + 0.686114i \(0.759315\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 18.0000 0.946059
\(363\) −9.00000 + 9.00000i −0.472377 + 0.472377i
\(364\) 4.00000 4.00000i 0.209657 0.209657i
\(365\) 0 0
\(366\) −18.0000 + 18.0000i −0.940875 + 0.940875i
\(367\) 8.00000i 0.417597i −0.977959 0.208798i \(-0.933045\pi\)
0.977959 0.208798i \(-0.0669552\pi\)
\(368\) 24.0000 1.25109
\(369\) 0 0
\(370\) 0 0
\(371\) −10.0000 + 10.0000i −0.519174 + 0.519174i
\(372\) 16.0000 16.0000i 0.829561 0.829561i
\(373\) 5.00000 5.00000i 0.258890 0.258890i −0.565712 0.824603i \(-0.691399\pi\)
0.824603 + 0.565712i \(0.191399\pi\)
\(374\) 4.00000i 0.206835i
\(375\) 0 0
\(376\) 16.0000 16.0000i 0.825137 0.825137i
\(377\) 6.00000 0.309016
\(378\) 16.0000i 0.822951i
\(379\) 3.00000 + 3.00000i 0.154100 + 0.154100i 0.779946 0.625847i \(-0.215246\pi\)
−0.625847 + 0.779946i \(0.715246\pi\)
\(380\) 0 0
\(381\) −8.00000 + 8.00000i −0.409852 + 0.409852i
\(382\) 8.00000 8.00000i 0.409316 0.409316i
\(383\) 16.0000i 0.817562i −0.912633 0.408781i \(-0.865954\pi\)
0.912633 0.408781i \(-0.134046\pi\)
\(384\) 16.0000i 0.816497i
\(385\) 0 0
\(386\) −14.0000 14.0000i −0.712581 0.712581i
\(387\) 5.00000 + 5.00000i 0.254164 + 0.254164i
\(388\) 4.00000 0.203069
\(389\) 13.0000 + 13.0000i 0.659126 + 0.659126i 0.955173 0.296047i \(-0.0956686\pi\)
−0.296047 + 0.955173i \(0.595669\pi\)
\(390\) 0 0
\(391\) 12.0000i 0.606866i
\(392\) −6.00000 6.00000i −0.303046 0.303046i
\(393\) −22.0000 −1.10975
\(394\) 34.0000i 1.71290i
\(395\) 0 0
\(396\) −2.00000 2.00000i −0.100504 0.100504i
\(397\) 5.00000 + 5.00000i 0.250943 + 0.250943i 0.821357 0.570414i \(-0.193217\pi\)
−0.570414 + 0.821357i \(0.693217\pi\)
\(398\) 14.0000 + 14.0000i 0.701757 + 0.701757i
\(399\) −12.0000 −0.600751
\(400\) 0 0
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 10.0000 + 10.0000i 0.498755 + 0.498755i
\(403\) 8.00000 + 8.00000i 0.398508 + 0.398508i
\(404\) 22.0000 22.0000i 1.09454 1.09454i
\(405\) 0 0
\(406\) 12.0000i 0.595550i
\(407\) 6.00000 0.297409
\(408\) 8.00000 0.396059
\(409\) 16.0000i 0.791149i 0.918434 + 0.395575i \(0.129455\pi\)
−0.918434 + 0.395575i \(0.870545\pi\)
\(410\) 0 0
\(411\) −8.00000 8.00000i −0.394611 0.394611i
\(412\) 12.0000i 0.591198i
\(413\) −6.00000 6.00000i −0.295241 0.295241i
\(414\) −6.00000 6.00000i −0.294884 0.294884i
\(415\) 0 0
\(416\) −8.00000 −0.392232
\(417\) 6.00000i 0.293821i
\(418\) 6.00000 6.00000i 0.293470 0.293470i
\(419\) −3.00000 + 3.00000i −0.146560 + 0.146560i −0.776579 0.630020i \(-0.783047\pi\)
0.630020 + 0.776579i \(0.283047\pi\)
\(420\) 0 0
\(421\) −9.00000 9.00000i −0.438633 0.438633i 0.452919 0.891552i \(-0.350383\pi\)
−0.891552 + 0.452919i \(0.850383\pi\)
\(422\) 18.0000i 0.876226i
\(423\) −8.00000 −0.388973
\(424\) 20.0000 0.971286
\(425\) 0 0
\(426\) 20.0000i 0.969003i
\(427\) 18.0000 18.0000i 0.871081 0.871081i
\(428\) 14.0000 + 14.0000i 0.676716 + 0.676716i
\(429\) −2.00000 + 2.00000i −0.0965609 + 0.0965609i
\(430\) 0 0
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 16.0000 16.0000i 0.769800 0.769800i
\(433\) 14.0000i 0.672797i 0.941720 + 0.336399i \(0.109209\pi\)
−0.941720 + 0.336399i \(0.890791\pi\)
\(434\) −16.0000 + 16.0000i −0.768025 + 0.768025i
\(435\) 0 0
\(436\) 6.00000 + 6.00000i 0.287348 + 0.287348i
\(437\) 18.0000 18.0000i 0.861057 0.861057i
\(438\) 8.00000 0.382255
\(439\) 14.0000i 0.668184i −0.942541 0.334092i \(-0.891570\pi\)
0.942541 0.334092i \(-0.108430\pi\)
\(440\) 0 0
\(441\) 3.00000i 0.142857i
\(442\) 4.00000i 0.190261i
\(443\) 15.0000 15.0000i 0.712672 0.712672i −0.254422 0.967093i \(-0.581885\pi\)
0.967093 + 0.254422i \(0.0818852\pi\)
\(444\) 12.0000i 0.569495i
\(445\) 0 0
\(446\) −24.0000 24.0000i −1.13643 1.13643i
\(447\) 14.0000i 0.662177i
\(448\) 16.0000i 0.755929i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −12.0000 −0.564433
\(453\) −10.0000 + 10.0000i −0.469841 + 0.469841i
\(454\) 30.0000 1.40797
\(455\) 0 0
\(456\) 12.0000 + 12.0000i 0.561951 + 0.561951i
\(457\) −32.0000 −1.49690 −0.748448 0.663193i \(-0.769201\pi\)
−0.748448 + 0.663193i \(0.769201\pi\)
\(458\) 14.0000 0.654177
\(459\) −8.00000 8.00000i −0.373408 0.373408i
\(460\) 0 0
\(461\) 11.0000 11.0000i 0.512321 0.512321i −0.402916 0.915237i \(-0.632003\pi\)
0.915237 + 0.402916i \(0.132003\pi\)
\(462\) −4.00000 4.00000i −0.186097 0.186097i
\(463\) 16.0000i 0.743583i −0.928316 0.371792i \(-0.878744\pi\)
0.928316 0.371792i \(-0.121256\pi\)
\(464\) 12.0000 12.0000i 0.557086 0.557086i
\(465\) 0 0
\(466\) −4.00000 + 4.00000i −0.185296 + 0.185296i
\(467\) 5.00000 + 5.00000i 0.231372 + 0.231372i 0.813265 0.581893i \(-0.197688\pi\)
−0.581893 + 0.813265i \(0.697688\pi\)
\(468\) 2.00000 + 2.00000i 0.0924500 + 0.0924500i
\(469\) −10.0000 10.0000i −0.461757 0.461757i
\(470\) 0 0
\(471\) 30.0000i 1.38233i
\(472\) 12.0000i 0.552345i
\(473\) −10.0000 −0.459800
\(474\) 0 0
\(475\) 0 0
\(476\) −8.00000 −0.366679
\(477\) −5.00000 5.00000i −0.228934 0.228934i
\(478\) 0 0
\(479\) 40.0000 1.82765 0.913823 0.406112i \(-0.133116\pi\)
0.913823 + 0.406112i \(0.133116\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 18.0000 18.0000i 0.819878 0.819878i
\(483\) −12.0000 12.0000i −0.546019 0.546019i
\(484\) −18.0000 −0.818182
\(485\) 0 0
\(486\) −14.0000 −0.635053
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) −36.0000 −1.62964
\(489\) 2.00000i 0.0904431i
\(490\) 0 0
\(491\) −19.0000 19.0000i −0.857458 0.857458i 0.133580 0.991038i \(-0.457353\pi\)
−0.991038 + 0.133580i \(0.957353\pi\)
\(492\) 0 0
\(493\) −6.00000 6.00000i −0.270226 0.270226i
\(494\) −6.00000 + 6.00000i −0.269953 + 0.269953i
\(495\) 0 0
\(496\) 32.0000 1.43684
\(497\) 20.0000i 0.897123i
\(498\) −2.00000 2.00000i −0.0896221 0.0896221i
\(499\) −23.0000 + 23.0000i −1.02962 + 1.02962i −0.0300737 + 0.999548i \(0.509574\pi\)
−0.999548 + 0.0300737i \(0.990426\pi\)
\(500\) 0 0
\(501\) 2.00000 + 2.00000i 0.0893534 + 0.0893534i
\(502\) −42.0000 −1.87455
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) −4.00000 + 4.00000i −0.178174 + 0.178174i
\(505\) 0 0
\(506\) 12.0000 0.533465
\(507\) −11.0000 + 11.0000i −0.488527 + 0.488527i
\(508\) −16.0000 −0.709885
\(509\) −23.0000 + 23.0000i −1.01946 + 1.01946i −0.0196502 + 0.999807i \(0.506255\pi\)
−0.999807 + 0.0196502i \(0.993745\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 24.0000i 1.05963i
\(514\) −22.0000 22.0000i −0.970378 0.970378i
\(515\) 0 0
\(516\) 20.0000i 0.880451i
\(517\) 8.00000 8.00000i 0.351840 0.351840i
\(518\) 12.0000i 0.527250i
\(519\) 2.00000i 0.0877903i
\(520\) 0 0
\(521\) 40.0000i 1.75243i 0.481919 + 0.876216i \(0.339940\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) −6.00000 −0.262613
\(523\) −25.0000 + 25.0000i −1.09317 + 1.09317i −0.0979859 + 0.995188i \(0.531240\pi\)
−0.995188 + 0.0979859i \(0.968760\pi\)
\(524\) −22.0000 22.0000i −0.961074 0.961074i
\(525\) 0 0
\(526\) 6.00000 6.00000i 0.261612 0.261612i
\(527\) 16.0000i 0.696971i
\(528\) 8.00000i 0.348155i
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 3.00000 3.00000i 0.130189 0.130189i
\(532\) −12.0000 12.0000i −0.520266 0.520266i
\(533\) 0 0
\(534\) 8.00000i 0.346194i
\(535\) 0 0
\(536\) 20.0000i 0.863868i
\(537\) −34.0000 −1.46721
\(538\) 6.00000i 0.258678i
\(539\) −3.00000 3.00000i −0.129219 0.129219i
\(540\) 0 0
\(541\) −9.00000 + 9.00000i −0.386940 + 0.386940i −0.873595 0.486654i \(-0.838217\pi\)
0.486654 + 0.873595i \(0.338217\pi\)
\(542\) 8.00000 8.00000i 0.343629 0.343629i
\(543\) 18.0000i 0.772454i
\(544\) 8.00000 + 8.00000i 0.342997 + 0.342997i
\(545\) 0 0
\(546\) 4.00000 + 4.00000i 0.171184 + 0.171184i
\(547\) 5.00000 + 5.00000i 0.213785 + 0.213785i 0.805873 0.592088i \(-0.201696\pi\)
−0.592088 + 0.805873i \(0.701696\pi\)
\(548\) 16.0000i 0.683486i
\(549\) 9.00000 + 9.00000i 0.384111 + 0.384111i
\(550\) 0 0
\(551\) 18.0000i 0.766826i
\(552\) 24.0000i 1.02151i
\(553\) 0 0
\(554\) 6.00000i 0.254916i
\(555\) 0 0
\(556\) 6.00000 6.00000i 0.254457 0.254457i
\(557\) 25.0000 + 25.0000i 1.05928 + 1.05928i 0.998128 + 0.0611558i \(0.0194786\pi\)
0.0611558 + 0.998128i \(0.480521\pi\)
\(558\) −8.00000 8.00000i −0.338667 0.338667i
\(559\) 10.0000 0.422955
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 20.0000 + 20.0000i 0.843649 + 0.843649i
\(563\) 19.0000 + 19.0000i 0.800755 + 0.800755i 0.983213 0.182459i \(-0.0584057\pi\)
−0.182459 + 0.983213i \(0.558406\pi\)
\(564\) 16.0000 + 16.0000i 0.673722 + 0.673722i
\(565\) 0 0
\(566\) 30.0000i 1.26099i
\(567\) −10.0000 −0.419961
\(568\) 20.0000 20.0000i 0.839181 0.839181i
\(569\) 24.0000i 1.00613i −0.864248 0.503066i \(-0.832205\pi\)
0.864248 0.503066i \(-0.167795\pi\)
\(570\) 0 0
\(571\) 1.00000 + 1.00000i 0.0418487 + 0.0418487i 0.727721 0.685873i \(-0.240579\pi\)
−0.685873 + 0.727721i \(0.740579\pi\)
\(572\) −4.00000 −0.167248
\(573\) 8.00000 + 8.00000i 0.334205 + 0.334205i
\(574\) 0 0
\(575\) 0 0
\(576\) 8.00000 0.333333
\(577\) 18.0000i 0.749350i −0.927156 0.374675i \(-0.877754\pi\)
0.927156 0.374675i \(-0.122246\pi\)
\(578\) −13.0000 + 13.0000i −0.540729 + 0.540729i
\(579\) 14.0000 14.0000i 0.581820 0.581820i
\(580\) 0 0
\(581\) 2.00000 + 2.00000i 0.0829740 + 0.0829740i
\(582\) 4.00000i 0.165805i
\(583\) 10.0000 0.414158
\(584\) 8.00000 + 8.00000i 0.331042 + 0.331042i
\(585\) 0 0
\(586\) 30.0000i 1.23929i
\(587\) −7.00000 + 7.00000i −0.288921 + 0.288921i −0.836653 0.547733i \(-0.815491\pi\)
0.547733 + 0.836653i \(0.315491\pi\)
\(588\) 6.00000 6.00000i 0.247436 0.247436i
\(589\) 24.0000 24.0000i 0.988903 0.988903i
\(590\) 0 0
\(591\) 34.0000 1.39857
\(592\) −12.0000 + 12.0000i −0.493197 + 0.493197i
\(593\) 34.0000i 1.39621i 0.715994 + 0.698106i \(0.245974\pi\)
−0.715994 + 0.698106i \(0.754026\pi\)
\(594\) 8.00000 8.00000i 0.328244 0.328244i
\(595\) 0 0
\(596\) −14.0000 + 14.0000i −0.573462 + 0.573462i
\(597\) −14.0000 + 14.0000i −0.572982 + 0.572982i
\(598\) −12.0000 −0.490716
\(599\) 14.0000i 0.572024i −0.958226 0.286012i \(-0.907670\pi\)
0.958226 0.286012i \(-0.0923298\pi\)
\(600\) 0 0
\(601\) 20.0000i 0.815817i 0.913023 + 0.407909i \(0.133742\pi\)
−0.913023 + 0.407909i \(0.866258\pi\)
\(602\) 20.0000i 0.815139i
\(603\) 5.00000 5.00000i 0.203616 0.203616i
\(604\) −20.0000 −0.813788
\(605\) 0 0
\(606\) 22.0000 + 22.0000i 0.893689 + 0.893689i
\(607\) 32.0000i 1.29884i 0.760430 + 0.649420i \(0.224988\pi\)
−0.760430 + 0.649420i \(0.775012\pi\)
\(608\) 24.0000i 0.973329i
\(609\) −12.0000 −0.486265
\(610\) 0 0
\(611\) −8.00000 + 8.00000i −0.323645 + 0.323645i
\(612\) 4.00000i 0.161690i
\(613\) 25.0000 25.0000i 1.00974 1.00974i 0.00978840 0.999952i \(-0.496884\pi\)
0.999952 0.00978840i \(-0.00311579\pi\)
\(614\) −10.0000 −0.403567
\(615\) 0 0
\(616\) 8.00000i 0.322329i
\(617\) −12.0000 −0.483102 −0.241551 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) −12.0000 −0.482711
\(619\) −17.0000 17.0000i −0.683288 0.683288i 0.277452 0.960740i \(-0.410510\pi\)
−0.960740 + 0.277452i \(0.910510\pi\)
\(620\) 0 0
\(621\) 24.0000 24.0000i 0.963087 0.963087i
\(622\) −30.0000 30.0000i −1.20289 1.20289i
\(623\) 8.00000i 0.320513i
\(624\) 8.00000i 0.320256i
\(625\) 0 0
\(626\) 16.0000 16.0000i 0.639489 0.639489i
\(627\) 6.00000 + 6.00000i 0.239617 + 0.239617i
\(628\) −30.0000 + 30.0000i −1.19713 + 1.19713i
\(629\) 6.00000 + 6.00000i 0.239236 + 0.239236i
\(630\) 0 0
\(631\) 10.0000i 0.398094i −0.979990 0.199047i \(-0.936215\pi\)
0.979990 0.199047i \(-0.0637846\pi\)
\(632\) 0 0
\(633\) 18.0000 0.715436
\(634\) −10.0000 −0.397151
\(635\) 0 0
\(636\) 20.0000i 0.793052i
\(637\) 3.00000 + 3.00000i 0.118864 + 0.118864i
\(638\) 6.00000 6.00000i 0.237542 0.237542i
\(639\) −10.0000 −0.395594
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −14.0000 + 14.0000i −0.552536 + 0.552536i
\(643\) −21.0000 21.0000i −0.828159 0.828159i 0.159103 0.987262i \(-0.449140\pi\)
−0.987262 + 0.159103i \(0.949140\pi\)
\(644\) 24.0000i 0.945732i
\(645\) 0 0
\(646\) 12.0000 0.472134
\(647\) −42.0000 −1.65119 −0.825595 0.564263i \(-0.809160\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(648\) 10.0000 + 10.0000i 0.392837 + 0.392837i
\(649\) 6.00000i 0.235521i
\(650\) 0 0
\(651\) −16.0000 16.0000i −0.627089 0.627089i
\(652\) −2.00000 + 2.00000i −0.0783260 + 0.0783260i
\(653\) 19.0000 + 19.0000i 0.743527 + 0.743527i 0.973255 0.229728i \(-0.0737835\pi\)
−0.229728 + 0.973255i \(0.573784\pi\)
\(654\) −6.00000 + 6.00000i −0.234619 + 0.234619i
\(655\) 0 0
\(656\) 0 0
\(657\) 4.00000i 0.156055i
\(658\) −16.0000 16.0000i −0.623745 0.623745i
\(659\) 17.0000 17.0000i 0.662226 0.662226i −0.293678 0.955904i \(-0.594879\pi\)
0.955904 + 0.293678i \(0.0948794\pi\)
\(660\) 0 0
\(661\) −9.00000 9.00000i −0.350059 0.350059i 0.510072 0.860132i \(-0.329619\pi\)
−0.860132 + 0.510072i \(0.829619\pi\)
\(662\) −2.00000 −0.0777322
\(663\) −4.00000 −0.155347
\(664\) 4.00000i 0.155230i
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 18.0000 18.0000i 0.696963 0.696963i
\(668\) 4.00000i 0.154765i
\(669\) 24.0000 24.0000i 0.927894 0.927894i
\(670\) 0 0
\(671\) −18.0000 −0.694882
\(672\) 16.0000 0.617213
\(673\) 14.0000i 0.539660i 0.962908 + 0.269830i \(0.0869676\pi\)
−0.962908 + 0.269830i \(0.913032\pi\)
\(674\) 18.0000 + 18.0000i 0.693334 + 0.693334i
\(675\) 0 0
\(676\) −22.0000 −0.846154
\(677\) 3.00000 3.00000i 0.115299 0.115299i −0.647103 0.762402i \(-0.724020\pi\)
0.762402 + 0.647103i \(0.224020\pi\)
\(678\) 12.0000i 0.460857i
\(679\) 4.00000i 0.153506i
\(680\) 0 0
\(681\) 30.0000i 1.14960i
\(682\) 16.0000 0.612672
\(683\) −5.00000 + 5.00000i −0.191320 + 0.191320i −0.796266 0.604946i \(-0.793195\pi\)
0.604946 + 0.796266i \(0.293195\pi\)
\(684\) 6.00000 6.00000i 0.229416 0.229416i
\(685\) 0 0
\(686\) −20.0000 + 20.0000i −0.763604 + 0.763604i
\(687\) 14.0000i 0.534133i
\(688\) 20.0000 20.0000i 0.762493 0.762493i
\(689\) −10.0000 −0.380970
\(690\) 0 0
\(691\) −9.00000 + 9.00000i −0.342376 + 0.342376i −0.857260 0.514884i \(-0.827835\pi\)
0.514884 + 0.857260i \(0.327835\pi\)
\(692\) −2.00000 + 2.00000i −0.0760286 + 0.0760286i
\(693\) −2.00000 + 2.00000i −0.0759737 + 0.0759737i
\(694\) 26.0000i 0.986947i
\(695\) 0 0
\(696\) 12.0000 + 12.0000i 0.454859 + 0.454859i
\(697\) 0 0
\(698\) 6.00000i 0.227103i
\(699\) −4.00000 4.00000i −0.151294 0.151294i
\(700\) 0 0
\(701\) 31.0000 31.0000i 1.17085 1.17085i 0.188847 0.982006i \(-0.439525\pi\)
0.982006 0.188847i \(-0.0604752\pi\)
\(702\) −8.00000 + 8.00000i −0.301941 + 0.301941i
\(703\) 18.0000i 0.678883i
\(704\) −8.00000 + 8.00000i −0.301511 + 0.301511i
\(705\) 0 0
\(706\) 6.00000 + 6.00000i 0.225813 + 0.225813i
\(707\) −22.0000 22.0000i −0.827395 0.827395i
\(708\) −12.0000 −0.450988
\(709\) −27.0000 27.0000i −1.01401 1.01401i −0.999901 0.0141058i \(-0.995510\pi\)
−0.0141058 0.999901i \(-0.504490\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 8.00000 8.00000i 0.299813 0.299813i
\(713\) 48.0000 1.79761
\(714\) 8.00000i 0.299392i
\(715\) 0 0
\(716\) −34.0000 34.0000i −1.27064 1.27064i
\(717\) 0 0
\(718\) −26.0000 26.0000i −0.970311 0.970311i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) −1.00000 1.00000i −0.0372161 0.0372161i
\(723\) 18.0000 + 18.0000i 0.669427 + 0.669427i
\(724\) −18.0000 + 18.0000i −0.668965 + 0.668965i
\(725\) 0 0
\(726\) 18.0000i 0.668043i
\(727\) −2.00000 −0.0741759 −0.0370879 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) 8.00000i 0.296500i
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) −10.0000 10.0000i −0.369863 0.369863i
\(732\) 36.0000i 1.33060i
\(733\) −21.0000 21.0000i −0.775653 0.775653i 0.203436 0.979088i \(-0.434789\pi\)
−0.979088 + 0.203436i \(0.934789\pi\)
\(734\) 8.00000 + 8.00000i 0.295285 + 0.295285i
\(735\) 0 0
\(736\) −24.0000 + 24.0000i −0.884652 + 0.884652i
\(737\) 10.0000i 0.368355i
\(738\) 0 0
\(739\) −23.0000 + 23.0000i −0.846069 + 0.846069i −0.989640 0.143571i \(-0.954141\pi\)
0.143571 + 0.989640i \(0.454141\pi\)
\(740\) 0 0
\(741\) −6.00000 6.00000i −0.220416 0.220416i
\(742\) 20.0000i 0.734223i
\(743\) −46.0000 −1.68758 −0.843788 0.536676i \(-0.819680\pi\)
−0.843788 + 0.536676i \(0.819680\pi\)
\(744\) 32.0000i 1.17318i
\(745\) 0 0
\(746\) 10.0000i 0.366126i
\(747\) −1.00000 + 1.00000i −0.0365881 + 0.0365881i
\(748\) 4.00000 + 4.00000i 0.146254 + 0.146254i
\(749\) 14.0000 14.0000i 0.511549 0.511549i
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 32.0000i 1.16692i
\(753\) 42.0000i 1.53057i
\(754\) −6.00000 + 6.00000i −0.218507 + 0.218507i
\(755\) 0 0
\(756\) −16.0000 16.0000i −0.581914 0.581914i
\(757\) 23.0000 23.0000i 0.835949 0.835949i −0.152374 0.988323i \(-0.548692\pi\)
0.988323 + 0.152374i \(0.0486917\pi\)
\(758\) −6.00000 −0.217930
\(759\) 12.0000i 0.435572i
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 16.0000i 0.579619i
\(763\) 6.00000 6.00000i 0.217215 0.217215i
\(764\) 16.0000i 0.578860i
\(765\) 0 0
\(766\) 16.0000 + 16.0000i 0.578103 + 0.578103i
\(767\) 6.00000i 0.216647i
\(768\) −16.0000 16.0000i −0.577350 0.577350i
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) 22.0000 22.0000i 0.792311 0.792311i
\(772\) 28.0000 1.00774
\(773\) 5.00000 5.00000i 0.179838 0.179838i −0.611448 0.791285i \(-0.709412\pi\)
0.791285 + 0.611448i \(0.209412\pi\)
\(774\) −10.0000 −0.359443
\(775\) 0 0
\(776\) −4.00000 + 4.00000i −0.143592 + 0.143592i
\(777\) 12.0000 0.430498
\(778\) −26.0000 −0.932145
\(779\) 0 0
\(780\) 0 0
\(781\) 10.0000 10.0000i 0.357828 0.357828i
\(782\) 12.0000 + 12.0000i 0.429119 + 0.429119i
\(783\) 24.0000i 0.857690i
\(784\) 12.0000 0.428571
\(785\) 0 0
\(786\) 22.0000 22.0000i 0.784714 0.784714i
\(787\) −15.0000 15.0000i −0.534692 0.534692i 0.387273 0.921965i \(-0.373417\pi\)
−0.921965 + 0.387273i \(0.873417\pi\)
\(788\) 34.0000 + 34.0000i 1.21120 + 1.21120i
\(789\) 6.00000 + 6.00000i 0.213606 + 0.213606i
\(790\) 0 0
\(791\) 12.0000i 0.426671i
\(792\) 4.00000 0.142134
\(793\) 18.0000 0.639199
\(794\) −10.0000 −0.354887
\(795\) 0 0
\(796\) −28.0000 −0.992434
\(797\) 25.0000 + 25.0000i 0.885545 + 0.885545i 0.994091 0.108546i \(-0.0346195\pi\)
−0.108546 + 0.994091i \(0.534619\pi\)
\(798\) 12.0000 12.0000i 0.424795 0.424795i
\(799\) 16.0000 0.566039
\(800\) 0 0
\(801\) −4.00000 −0.141333
\(802\) 18.0000 18.0000i 0.635602 0.635602i
\(803\) 4.00000 + 4.00000i 0.141157 + 0.141157i
\(804\) −20.0000 −0.705346
\(805\) 0 0
\(806\) −16.0000 −0.563576
\(807\) 6.00000 0.211210
\(808\) 44.0000i 1.54791i
\(809\) 16.0000i 0.562530i 0.959630 + 0.281265i \(0.0907540\pi\)
−0.959630 + 0.281265i \(0.909246\pi\)
\(810\) 0 0
\(811\) −39.0000 39.0000i −1.36948 1.36948i −0.861187 0.508288i \(-0.830278\pi\)
−0.508288 0.861187i \(-0.669722\pi\)
\(812\) −12.0000 12.0000i −0.421117 0.421117i
\(813\) 8.00000 + 8.00000i 0.280572 + 0.280572i
\(814\) −6.00000 + 6.00000i −0.210300 + 0.210300i
\(815\) 0 0
\(816\) −8.00000 + 8.00000i −0.280056 + 0.280056i
\(817\) 30.0000i 1.04957i
\(818\) −16.0000 16.0000i −0.559427 0.559427i
\(819\) 2.00000 2.00000i 0.0698857 0.0698857i
\(820\) 0 0
\(821\) 11.0000 + 11.0000i 0.383903 + 0.383903i 0.872506 0.488603i \(-0.162493\pi\)
−0.488603 + 0.872506i \(0.662493\pi\)
\(822\) 16.0000 0.558064
\(823\) 34.0000 1.18517 0.592583 0.805510i \(-0.298108\pi\)
0.592583 + 0.805510i \(0.298108\pi\)
\(824\) −12.0000 12.0000i −0.418040 0.418040i
\(825\) 0 0
\(826\) 12.0000 0.417533
\(827\) 33.0000 33.0000i 1.14752 1.14752i 0.160484 0.987038i \(-0.448695\pi\)
0.987038 0.160484i \(-0.0513055\pi\)
\(828\) 12.0000 0.417029
\(829\) −23.0000 + 23.0000i −0.798823 + 0.798823i −0.982910 0.184087i \(-0.941067\pi\)
0.184087 + 0.982910i \(0.441067\pi\)
\(830\) 0 0
\(831\) −6.00000 −0.208138
\(832\) 8.00000 8.00000i 0.277350 0.277350i
\(833\) 6.00000i 0.207888i
\(834\) 6.00000 + 6.00000i 0.207763 + 0.207763i
\(835\) 0 0
\(836\) 12.0000i 0.415029i
\(837\) 32.0000 32.0000i 1.10608 1.10608i
\(838\) 6.00000i 0.207267i
\(839\) 14.0000i 0.483334i −0.970359 0.241667i \(-0.922306\pi\)
0.970359 0.241667i \(-0.0776941\pi\)
\(840\) 0 0
\(841\) 11.0000i 0.379310i
\(842\) 18.0000 0.620321
\(843\) −20.0000 + 20.0000i −0.688837 + 0.688837i
\(844\) 18.0000 + 18.0000i 0.619586 + 0.619586i
\(845\) 0 0
\(846\) 8.00000 8.00000i 0.275046 0.275046i
\(847\) 18.0000i 0.618487i
\(848\) −20.0000 + 20.0000i −0.686803 + 0.686803i
\(849\) −30.0000 −1.02960
\(850\) 0 0
\(851\) −18.0000 + 18.0000i −0.617032 + 0.617032i
\(852\) 20.0000 + 20.0000i 0.685189 + 0.685189i
\(853\) 5.00000 5.00000i 0.171197 0.171197i −0.616308 0.787505i \(-0.711372\pi\)
0.787505 + 0.616308i \(0.211372\pi\)
\(854\) 36.0000i 1.23189i
\(855\) 0 0
\(856\) −28.0000 −0.957020
\(857\) 8.00000 0.273275 0.136637 0.990621i \(-0.456370\pi\)
0.136637 + 0.990621i \(0.456370\pi\)
\(858\) 4.00000i 0.136558i
\(859\) 3.00000 + 3.00000i 0.102359 + 0.102359i 0.756432 0.654073i \(-0.226941\pi\)
−0.654073 + 0.756432i \(0.726941\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −32.0000 + 32.0000i −1.08992 + 1.08992i
\(863\) 24.0000i 0.816970i 0.912765 + 0.408485i \(0.133943\pi\)
−0.912765 + 0.408485i \(0.866057\pi\)
\(864\) 32.0000i 1.08866i
\(865\) 0 0
\(866\) −14.0000 14.0000i −0.475739 0.475739i
\(867\) −13.0000 13.0000i −0.441503 0.441503i
\(868\) 32.0000i 1.08615i
\(869\) 0 0
\(870\) 0 0
\(871\) 10.0000i 0.338837i
\(872\) −12.0000 −0.406371
\(873\) 2.00000 0.0676897
\(874\) 36.0000i 1.21772i
\(875\) 0 0
\(876\) −8.00000 + 8.00000i −0.270295 + 0.270295i
\(877\) 5.00000 + 5.00000i 0.168838 + 0.168838i 0.786468 0.617630i \(-0.211907\pi\)
−0.617630 + 0.786468i \(0.711907\pi\)
\(878\) 14.0000 + 14.0000i 0.472477 + 0.472477i
\(879\) 30.0000 1.01187
\(880\) 0 0
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) −3.00000 3.00000i −0.101015 0.101015i
\(883\) −21.0000 21.0000i −0.706706 0.706706i 0.259135 0.965841i \(-0.416563\pi\)
−0.965841 + 0.259135i \(0.916563\pi\)
\(884\) −4.00000 4.00000i −0.134535 0.134535i
\(885\) 0 0
\(886\) 30.0000i 1.00787i
\(887\) −2.00000 −0.0671534 −0.0335767 0.999436i \(-0.510690\pi\)
−0.0335767 + 0.999436i \(0.510690\pi\)
\(888\) −12.0000 12.0000i −0.402694 0.402694i
\(889\) 16.0000i 0.536623i
\(890\) 0 0
\(891\) 5.00000 + 5.00000i 0.167506 + 0.167506i
\(892\) 48.0000 1.60716
\(893\) 24.0000 + 24.0000i 0.803129 + 0.803129i
\(894\) −14.0000 14.0000i −0.468230 0.468230i
\(895\) 0 0
\(896\) 16.0000 + 16.0000i 0.534522 + 0.534522i
\(897\) 12.0000i 0.400668i
\(898\) 30.0000 30.0000i 1.00111 1.00111i
\(899\) 24.0000 24.0000i 0.800445 0.800445i
\(900\) 0 0
\(901\) 10.0000 + 10.0000i 0.333148 + 0.333148i
\(902\) 0 0
\(903\) −20.0000 −0.665558
\(904\) 12.0000 12.0000i 0.399114 0.399114i
\(905\) 0 0
\(906\) 20.0000i 0.664455i
\(907\) −27.0000 + 27.0000i −0.896520 + 0.896520i −0.995127 0.0986062i \(-0.968562\pi\)
0.0986062 + 0.995127i \(0.468562\pi\)
\(908\) −30.0000 + 30.0000i −0.995585 + 0.995585i
\(909\) 11.0000 11.0000i 0.364847 0.364847i
\(910\) 0 0
\(911\) −8.00000 −0.265052 −0.132526 0.991180i \(-0.542309\pi\)
−0.132526 + 0.991180i \(0.542309\pi\)
\(912\) −24.0000 −0.794719
\(913\) 2.00000i 0.0661903i
\(914\) 32.0000 32.0000i 1.05847 1.05847i
\(915\) 0 0
\(916\) −14.0000 + 14.0000i −0.462573 + 0.462573i
\(917\) −22.0000 + 22.0000i −0.726504 + 0.726504i
\(918\) 16.0000 0.528079
\(919\) 26.0000i 0.857661i 0.903385 + 0.428830i \(0.141074\pi\)
−0.903385 + 0.428830i \(0.858926\pi\)
\(920\) 0 0
\(921\) 10.0000i 0.329511i
\(922\) 22.0000i 0.724531i
\(923\) −10.0000 + 10.0000i −0.329154 + 0.329154i
\(924\) 8.00000 0.263181
\(925\) 0 0
\(926\) 16.0000 + 16.0000i 0.525793 + 0.525793i
\(927\) 6.00000i 0.197066i
\(928\) 24.0000i 0.787839i
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) 9.00000 9.00000i 0.294963 0.294963i
\(932\) 8.00000i 0.262049i
\(933\) 30.0000 30.0000i 0.982156 0.982156i
\(934\) −10.0000 −0.327210
\(935\) 0 0
\(936\) −4.00000 −0.130744
\(937\) 28.0000 0.914720 0.457360 0.889282i \(-0.348795\pi\)
0.457360 + 0.889282i \(0.348795\pi\)
\(938\) 20.0000 0.653023
\(939\) 16.0000 + 16.0000i 0.522140 + 0.522140i
\(940\) 0 0
\(941\) −29.0000 + 29.0000i −0.945373 + 0.945373i −0.998583 0.0532103i \(-0.983055\pi\)
0.0532103 + 0.998583i \(0.483055\pi\)
\(942\) −30.0000 30.0000i −0.977453 0.977453i
\(943\) 0 0
\(944\) −12.0000 12.0000i −0.390567 0.390567i
\(945\) 0 0
\(946\) 10.0000 10.0000i 0.325128 0.325128i
\(947\) 5.00000 + 5.00000i 0.162478 + 0.162478i 0.783664 0.621185i \(-0.213349\pi\)
−0.621185 + 0.783664i \(0.713349\pi\)
\(948\) 0 0
\(949\) −4.00000 4.00000i −0.129845 0.129845i
\(950\) 0 0
\(951\) 10.0000i 0.324272i
\(952\) 8.00000 8.00000i 0.259281 0.259281i
\(953\) 24.0000 0.777436 0.388718 0.921357i \(-0.372918\pi\)
0.388718 + 0.921357i \(0.372918\pi\)
\(954\) 10.0000 0.323762
\(955\) 0 0
\(956\) 0 0
\(957\) 6.00000 + 6.00000i 0.193952 + 0.193952i
\(958\) −40.0000 + 40.0000i −1.29234 + 1.29234i
\(959\) −16.0000 −0.516667
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 6.00000 6.00000i 0.193448 0.193448i
\(963\) 7.00000 + 7.00000i 0.225572 + 0.225572i
\(964\) 36.0000i 1.15948i
\(965\) 0 0
\(966\) 24.0000 0.772187
\(967\) −2.00000 −0.0643157 −0.0321578 0.999483i \(-0.510238\pi\)
−0.0321578 + 0.999483i \(0.510238\pi\)
\(968\) 18.0000 18.0000i 0.578542 0.578542i
\(969\) 12.0000i 0.385496i
\(970\) 0 0
\(971\) −19.0000 19.0000i −0.609739 0.609739i 0.333139 0.942878i \(-0.391892\pi\)
−0.942878 + 0.333139i \(0.891892\pi\)
\(972\) 14.0000 14.0000i 0.449050 0.449050i
\(973\) −6.00000 6.00000i −0.192351 0.192351i
\(974\) 2.00000 2.00000i 0.0640841 0.0640841i
\(975\) 0 0
\(976\) 36.0000 36.0000i 1.15233 1.15233i
\(977\) 2.00000i 0.0639857i 0.999488 + 0.0319928i \(0.0101854\pi\)
−0.999488 + 0.0319928i \(0.989815\pi\)
\(978\) −2.00000 2.00000i −0.0639529 0.0639529i
\(979\) 4.00000 4.00000i 0.127841 0.127841i
\(980\) 0 0
\(981\) 3.00000 + 3.00000i 0.0957826 + 0.0957826i
\(982\) 38.0000 1.21263
\(983\) 34.0000 1.08443 0.542216 0.840239i \(-0.317586\pi\)
0.542216 + 0.840239i \(0.317586\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 12.0000 0.382158
\(987\) 16.0000 16.0000i 0.509286 0.509286i
\(988\) 12.0000i 0.381771i
\(989\) 30.0000 30.0000i 0.953945 0.953945i
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) −32.0000 + 32.0000i −1.01600 + 1.01600i
\(993\) 2.00000i 0.0634681i
\(994\) −20.0000 20.0000i −0.634361 0.634361i
\(995\) 0 0
\(996\) 4.00000 0.126745
\(997\) −37.0000 + 37.0000i −1.17180 + 1.17180i −0.190022 + 0.981780i \(0.560856\pi\)
−0.981780 + 0.190022i \(0.939144\pi\)
\(998\) 46.0000i 1.45610i
\(999\) 24.0000i 0.759326i
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 400.2.q.a.149.1 2
4.3 odd 2 1600.2.q.b.49.1 2
5.2 odd 4 16.2.e.a.5.1 2
5.3 odd 4 400.2.l.c.101.1 2
5.4 even 2 400.2.q.b.149.1 2
15.2 even 4 144.2.k.a.37.1 2
16.3 odd 4 1600.2.q.a.849.1 2
16.13 even 4 400.2.q.b.349.1 2
20.3 even 4 1600.2.l.a.1201.1 2
20.7 even 4 64.2.e.a.49.1 2
20.19 odd 2 1600.2.q.a.49.1 2
35.2 odd 12 784.2.x.f.165.1 4
35.12 even 12 784.2.x.c.165.1 4
35.17 even 12 784.2.x.c.373.1 4
35.27 even 4 784.2.m.b.197.1 2
35.32 odd 12 784.2.x.f.373.1 4
40.27 even 4 128.2.e.a.97.1 2
40.37 odd 4 128.2.e.b.97.1 2
60.47 odd 4 576.2.k.a.433.1 2
80.3 even 4 1600.2.l.a.401.1 2
80.13 odd 4 400.2.l.c.301.1 2
80.19 odd 4 1600.2.q.b.849.1 2
80.27 even 4 128.2.e.a.33.1 2
80.29 even 4 inner 400.2.q.a.349.1 2
80.37 odd 4 128.2.e.b.33.1 2
80.67 even 4 64.2.e.a.17.1 2
80.77 odd 4 16.2.e.a.13.1 yes 2
120.77 even 4 1152.2.k.b.865.1 2
120.107 odd 4 1152.2.k.a.865.1 2
160.27 even 8 1024.2.b.b.513.2 2
160.37 odd 8 1024.2.b.e.513.1 2
160.67 even 8 1024.2.a.e.1.2 2
160.77 odd 8 1024.2.a.b.1.2 2
160.107 even 8 1024.2.b.b.513.1 2
160.117 odd 8 1024.2.b.e.513.2 2
160.147 even 8 1024.2.a.e.1.1 2
160.157 odd 8 1024.2.a.b.1.1 2
240.77 even 4 144.2.k.a.109.1 2
240.107 odd 4 1152.2.k.a.289.1 2
240.197 even 4 1152.2.k.b.289.1 2
240.227 odd 4 576.2.k.a.145.1 2
480.77 even 8 9216.2.a.d.1.2 2
480.227 odd 8 9216.2.a.s.1.1 2
480.317 even 8 9216.2.a.d.1.1 2
480.467 odd 8 9216.2.a.s.1.2 2
560.157 even 12 784.2.x.c.765.1 4
560.237 even 4 784.2.m.b.589.1 2
560.317 odd 12 784.2.x.f.557.1 4
560.397 even 12 784.2.x.c.557.1 4
560.557 odd 12 784.2.x.f.765.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.2.e.a.5.1 2 5.2 odd 4
16.2.e.a.13.1 yes 2 80.77 odd 4
64.2.e.a.17.1 2 80.67 even 4
64.2.e.a.49.1 2 20.7 even 4
128.2.e.a.33.1 2 80.27 even 4
128.2.e.a.97.1 2 40.27 even 4
128.2.e.b.33.1 2 80.37 odd 4
128.2.e.b.97.1 2 40.37 odd 4
144.2.k.a.37.1 2 15.2 even 4
144.2.k.a.109.1 2 240.77 even 4
400.2.l.c.101.1 2 5.3 odd 4
400.2.l.c.301.1 2 80.13 odd 4
400.2.q.a.149.1 2 1.1 even 1 trivial
400.2.q.a.349.1 2 80.29 even 4 inner
400.2.q.b.149.1 2 5.4 even 2
400.2.q.b.349.1 2 16.13 even 4
576.2.k.a.145.1 2 240.227 odd 4
576.2.k.a.433.1 2 60.47 odd 4
784.2.m.b.197.1 2 35.27 even 4
784.2.m.b.589.1 2 560.237 even 4
784.2.x.c.165.1 4 35.12 even 12
784.2.x.c.373.1 4 35.17 even 12
784.2.x.c.557.1 4 560.397 even 12
784.2.x.c.765.1 4 560.157 even 12
784.2.x.f.165.1 4 35.2 odd 12
784.2.x.f.373.1 4 35.32 odd 12
784.2.x.f.557.1 4 560.317 odd 12
784.2.x.f.765.1 4 560.557 odd 12
1024.2.a.b.1.1 2 160.157 odd 8
1024.2.a.b.1.2 2 160.77 odd 8
1024.2.a.e.1.1 2 160.147 even 8
1024.2.a.e.1.2 2 160.67 even 8
1024.2.b.b.513.1 2 160.107 even 8
1024.2.b.b.513.2 2 160.27 even 8
1024.2.b.e.513.1 2 160.37 odd 8
1024.2.b.e.513.2 2 160.117 odd 8
1152.2.k.a.289.1 2 240.107 odd 4
1152.2.k.a.865.1 2 120.107 odd 4
1152.2.k.b.289.1 2 240.197 even 4
1152.2.k.b.865.1 2 120.77 even 4
1600.2.l.a.401.1 2 80.3 even 4
1600.2.l.a.1201.1 2 20.3 even 4
1600.2.q.a.49.1 2 20.19 odd 2
1600.2.q.a.849.1 2 16.3 odd 4
1600.2.q.b.49.1 2 4.3 odd 2
1600.2.q.b.849.1 2 80.19 odd 4
9216.2.a.d.1.1 2 480.317 even 8
9216.2.a.d.1.2 2 480.77 even 8
9216.2.a.s.1.1 2 480.227 odd 8
9216.2.a.s.1.2 2 480.467 odd 8