Properties

Label 650.2.j.d.343.1
Level $650$
Weight $2$
Character 650.343
Analytic conductor $5.190$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [650,2,Mod(307,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.307"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 650.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,2,-2,0,-2,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.19027613138\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Copy content comment:defining polynomial
 
Copy content 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 130)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 343.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 650.343
Dual form 650.2.j.d.307.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(1.00000 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 + 1.00000i) q^{6} +2.00000 q^{7} -1.00000i q^{8} -1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{12} +(-2.00000 + 3.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(5.00000 + 5.00000i) q^{17} +1.00000 q^{18} +(3.00000 + 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(-5.00000 + 5.00000i) q^{23} +(1.00000 - 1.00000i) q^{24} +(-3.00000 - 2.00000i) q^{26} +(4.00000 - 4.00000i) q^{27} -2.00000 q^{28} -4.00000i q^{29} +(1.00000 - 1.00000i) q^{31} +1.00000i q^{32} +2.00000i q^{33} +(-5.00000 + 5.00000i) q^{34} +1.00000i q^{36} -8.00000 q^{37} +(-3.00000 + 3.00000i) q^{38} +(-5.00000 + 1.00000i) q^{39} +(1.00000 - 1.00000i) q^{41} +(-2.00000 + 2.00000i) q^{42} +(5.00000 - 5.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(-5.00000 - 5.00000i) q^{46} +2.00000 q^{47} +(1.00000 + 1.00000i) q^{48} -3.00000 q^{49} +10.0000i q^{51} +(2.00000 - 3.00000i) q^{52} +(1.00000 + 1.00000i) q^{53} +(4.00000 + 4.00000i) q^{54} -2.00000i q^{56} +6.00000i q^{57} +4.00000 q^{58} +(-3.00000 + 3.00000i) q^{59} +2.00000 q^{61} +(1.00000 + 1.00000i) q^{62} -2.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} -12.0000i q^{67} +(-5.00000 - 5.00000i) q^{68} -10.0000 q^{69} +(1.00000 - 1.00000i) q^{71} -1.00000 q^{72} +6.00000i q^{73} -8.00000i q^{74} +(-3.00000 - 3.00000i) q^{76} +(2.00000 + 2.00000i) q^{77} +(-1.00000 - 5.00000i) q^{78} -14.0000i q^{79} +5.00000 q^{81} +(1.00000 + 1.00000i) q^{82} +6.00000 q^{83} +(-2.00000 - 2.00000i) q^{84} +(5.00000 + 5.00000i) q^{86} +(4.00000 - 4.00000i) q^{87} +(1.00000 - 1.00000i) q^{88} +(7.00000 - 7.00000i) q^{89} +(-4.00000 + 6.00000i) q^{91} +(5.00000 - 5.00000i) q^{92} +2.00000 q^{93} +2.00000i q^{94} +(-1.00000 + 1.00000i) q^{96} -2.00000i q^{97} -3.00000i q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{16} + 10 q^{17} + 2 q^{18} + 6 q^{19} + 4 q^{21} - 2 q^{22} - 10 q^{23} + 2 q^{24} - 6 q^{26} + 8 q^{27} - 4 q^{28} + 2 q^{31}+ \cdots + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000 + 1.00000i 0.577350 + 0.577350i 0.934172 0.356822i \(-0.116140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) −1.00000 + 1.00000i −0.408248 + 0.408248i
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 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 \(0.681611\pi\)
\(12\) −1.00000 1.00000i −0.288675 0.288675i
\(13\) −2.00000 + 3.00000i −0.554700 + 0.832050i
\(14\) 2.00000i 0.534522i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.00000 + 5.00000i 1.21268 + 1.21268i 0.970143 + 0.242536i \(0.0779791\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.00000 + 3.00000i 0.688247 + 0.688247i 0.961844 0.273597i \(-0.0882135\pi\)
−0.273597 + 0.961844i \(0.588214\pi\)
\(20\) 0 0
\(21\) 2.00000 + 2.00000i 0.436436 + 0.436436i
\(22\) −1.00000 + 1.00000i −0.213201 + 0.213201i
\(23\) −5.00000 + 5.00000i −1.04257 + 1.04257i −0.0435195 + 0.999053i \(0.513857\pi\)
−0.999053 + 0.0435195i \(0.986143\pi\)
\(24\) 1.00000 1.00000i 0.204124 0.204124i
\(25\) 0 0
\(26\) −3.00000 2.00000i −0.588348 0.392232i
\(27\) 4.00000 4.00000i 0.769800 0.769800i
\(28\) −2.00000 −0.377964
\(29\) 4.00000i 0.742781i −0.928477 0.371391i \(-0.878881\pi\)
0.928477 0.371391i \(-0.121119\pi\)
\(30\) 0 0
\(31\) 1.00000 1.00000i 0.179605 0.179605i −0.611578 0.791184i \(-0.709465\pi\)
0.791184 + 0.611578i \(0.209465\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.00000i 0.348155i
\(34\) −5.00000 + 5.00000i −0.857493 + 0.857493i
\(35\) 0 0
\(36\) 1.00000i 0.166667i
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) −3.00000 + 3.00000i −0.486664 + 0.486664i
\(39\) −5.00000 + 1.00000i −0.800641 + 0.160128i
\(40\) 0 0
\(41\) 1.00000 1.00000i 0.156174 0.156174i −0.624695 0.780869i \(-0.714777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) −2.00000 + 2.00000i −0.308607 + 0.308607i
\(43\) 5.00000 5.00000i 0.762493 0.762493i −0.214280 0.976772i \(-0.568740\pi\)
0.976772 + 0.214280i \(0.0687403\pi\)
\(44\) −1.00000 1.00000i −0.150756 0.150756i
\(45\) 0 0
\(46\) −5.00000 5.00000i −0.737210 0.737210i
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 1.00000 + 1.00000i 0.144338 + 0.144338i
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) 10.0000i 1.40028i
\(52\) 2.00000 3.00000i 0.277350 0.416025i
\(53\) 1.00000 + 1.00000i 0.137361 + 0.137361i 0.772444 0.635083i \(-0.219034\pi\)
−0.635083 + 0.772444i \(0.719034\pi\)
\(54\) 4.00000 + 4.00000i 0.544331 + 0.544331i
\(55\) 0 0
\(56\) 2.00000i 0.267261i
\(57\) 6.00000i 0.794719i
\(58\) 4.00000 0.525226
\(59\) −3.00000 + 3.00000i −0.390567 + 0.390567i −0.874889 0.484323i \(-0.839066\pi\)
0.484323 + 0.874889i \(0.339066\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 1.00000 + 1.00000i 0.127000 + 0.127000i
\(63\) 2.00000i 0.251976i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −2.00000 −0.246183
\(67\) 12.0000i 1.46603i −0.680211 0.733017i \(-0.738112\pi\)
0.680211 0.733017i \(-0.261888\pi\)
\(68\) −5.00000 5.00000i −0.606339 0.606339i
\(69\) −10.0000 −1.20386
\(70\) 0 0
\(71\) 1.00000 1.00000i 0.118678 0.118678i −0.645273 0.763952i \(-0.723257\pi\)
0.763952 + 0.645273i \(0.223257\pi\)
\(72\) −1.00000 −0.117851
\(73\) 6.00000i 0.702247i 0.936329 + 0.351123i \(0.114200\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 8.00000i 0.929981i
\(75\) 0 0
\(76\) −3.00000 3.00000i −0.344124 0.344124i
\(77\) 2.00000 + 2.00000i 0.227921 + 0.227921i
\(78\) −1.00000 5.00000i −0.113228 0.566139i
\(79\) 14.0000i 1.57512i −0.616236 0.787562i \(-0.711343\pi\)
0.616236 0.787562i \(-0.288657\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 1.00000 + 1.00000i 0.110432 + 0.110432i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −2.00000 2.00000i −0.218218 0.218218i
\(85\) 0 0
\(86\) 5.00000 + 5.00000i 0.539164 + 0.539164i
\(87\) 4.00000 4.00000i 0.428845 0.428845i
\(88\) 1.00000 1.00000i 0.106600 0.106600i
\(89\) 7.00000 7.00000i 0.741999 0.741999i −0.230964 0.972962i \(-0.574188\pi\)
0.972962 + 0.230964i \(0.0741879\pi\)
\(90\) 0 0
\(91\) −4.00000 + 6.00000i −0.419314 + 0.628971i
\(92\) 5.00000 5.00000i 0.521286 0.521286i
\(93\) 2.00000 0.207390
\(94\) 2.00000i 0.206284i
\(95\) 0 0
\(96\) −1.00000 + 1.00000i −0.102062 + 0.102062i
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 1.00000 1.00000i 0.100504 0.100504i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −10.0000 −0.990148
\(103\) −5.00000 + 5.00000i −0.492665 + 0.492665i −0.909145 0.416480i \(-0.863264\pi\)
0.416480 + 0.909145i \(0.363264\pi\)
\(104\) 3.00000 + 2.00000i 0.294174 + 0.196116i
\(105\) 0 0
\(106\) −1.00000 + 1.00000i −0.0971286 + 0.0971286i
\(107\) −13.0000 + 13.0000i −1.25676 + 1.25676i −0.304125 + 0.952632i \(0.598364\pi\)
−0.952632 + 0.304125i \(0.901636\pi\)
\(108\) −4.00000 + 4.00000i −0.384900 + 0.384900i
\(109\) 13.0000 + 13.0000i 1.24517 + 1.24517i 0.957826 + 0.287348i \(0.0927736\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) 0 0
\(111\) −8.00000 8.00000i −0.759326 0.759326i
\(112\) 2.00000 0.188982
\(113\) −9.00000 9.00000i −0.846649 0.846649i 0.143065 0.989713i \(-0.454304\pi\)
−0.989713 + 0.143065i \(0.954304\pi\)
\(114\) −6.00000 −0.561951
\(115\) 0 0
\(116\) 4.00000i 0.371391i
\(117\) 3.00000 + 2.00000i 0.277350 + 0.184900i
\(118\) −3.00000 3.00000i −0.276172 0.276172i
\(119\) 10.0000 + 10.0000i 0.916698 + 0.916698i
\(120\) 0 0
\(121\) 9.00000i 0.818182i
\(122\) 2.00000i 0.181071i
\(123\) 2.00000 0.180334
\(124\) −1.00000 + 1.00000i −0.0898027 + 0.0898027i
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) −15.0000 15.0000i −1.33103 1.33103i −0.904445 0.426589i \(-0.859715\pi\)
−0.426589 0.904445i \(-0.640285\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 10.0000 0.880451
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 6.00000 + 6.00000i 0.520266 + 0.520266i
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 5.00000 5.00000i 0.428746 0.428746i
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 10.0000i 0.851257i
\(139\) 14.0000i 1.18746i −0.804663 0.593732i \(-0.797654\pi\)
0.804663 0.593732i \(-0.202346\pi\)
\(140\) 0 0
\(141\) 2.00000 + 2.00000i 0.168430 + 0.168430i
\(142\) 1.00000 + 1.00000i 0.0839181 + 0.0839181i
\(143\) −5.00000 + 1.00000i −0.418121 + 0.0836242i
\(144\) 1.00000i 0.0833333i
\(145\) 0 0
\(146\) −6.00000 −0.496564
\(147\) −3.00000 3.00000i −0.247436 0.247436i
\(148\) 8.00000 0.657596
\(149\) 13.0000 + 13.0000i 1.06500 + 1.06500i 0.997735 + 0.0672664i \(0.0214278\pi\)
0.0672664 + 0.997735i \(0.478572\pi\)
\(150\) 0 0
\(151\) −9.00000 9.00000i −0.732410 0.732410i 0.238687 0.971097i \(-0.423283\pi\)
−0.971097 + 0.238687i \(0.923283\pi\)
\(152\) 3.00000 3.00000i 0.243332 0.243332i
\(153\) 5.00000 5.00000i 0.404226 0.404226i
\(154\) −2.00000 + 2.00000i −0.161165 + 0.161165i
\(155\) 0 0
\(156\) 5.00000 1.00000i 0.400320 0.0800641i
\(157\) −3.00000 + 3.00000i −0.239426 + 0.239426i −0.816612 0.577186i \(-0.804151\pi\)
0.577186 + 0.816612i \(0.304151\pi\)
\(158\) 14.0000 1.11378
\(159\) 2.00000i 0.158610i
\(160\) 0 0
\(161\) −10.0000 + 10.0000i −0.788110 + 0.788110i
\(162\) 5.00000i 0.392837i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) −1.00000 + 1.00000i −0.0780869 + 0.0780869i
\(165\) 0 0
\(166\) 6.00000i 0.465690i
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 2.00000 2.00000i 0.154303 0.154303i
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) 0 0
\(171\) 3.00000 3.00000i 0.229416 0.229416i
\(172\) −5.00000 + 5.00000i −0.381246 + 0.381246i
\(173\) 15.0000 15.0000i 1.14043 1.14043i 0.152057 0.988372i \(-0.451410\pi\)
0.988372 0.152057i \(-0.0485898\pi\)
\(174\) 4.00000 + 4.00000i 0.303239 + 0.303239i
\(175\) 0 0
\(176\) 1.00000 + 1.00000i 0.0753778 + 0.0753778i
\(177\) −6.00000 −0.450988
\(178\) 7.00000 + 7.00000i 0.524672 + 0.524672i
\(179\) −20.0000 −1.49487 −0.747435 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 0 0
\(181\) 20.0000i 1.48659i −0.668965 0.743294i \(-0.733262\pi\)
0.668965 0.743294i \(-0.266738\pi\)
\(182\) −6.00000 4.00000i −0.444750 0.296500i
\(183\) 2.00000 + 2.00000i 0.147844 + 0.147844i
\(184\) 5.00000 + 5.00000i 0.368605 + 0.368605i
\(185\) 0 0
\(186\) 2.00000i 0.146647i
\(187\) 10.0000i 0.731272i
\(188\) −2.00000 −0.145865
\(189\) 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 \(0.593466\pi\)
\(192\) −1.00000 1.00000i −0.0721688 0.0721688i
\(193\) 14.0000i 1.00774i −0.863779 0.503871i \(-0.831909\pi\)
0.863779 0.503871i \(-0.168091\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) 1.00000 + 1.00000i 0.0710669 + 0.0710669i
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 12.0000 12.0000i 0.846415 0.846415i
\(202\) 0 0
\(203\) 8.00000i 0.561490i
\(204\) 10.0000i 0.700140i
\(205\) 0 0
\(206\) −5.00000 5.00000i −0.348367 0.348367i
\(207\) 5.00000 + 5.00000i 0.347524 + 0.347524i
\(208\) −2.00000 + 3.00000i −0.138675 + 0.208013i
\(209\) 6.00000i 0.415029i
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −1.00000 1.00000i −0.0686803 0.0686803i
\(213\) 2.00000 0.137038
\(214\) −13.0000 13.0000i −0.888662 0.888662i
\(215\) 0 0
\(216\) −4.00000 4.00000i −0.272166 0.272166i
\(217\) 2.00000 2.00000i 0.135769 0.135769i
\(218\) −13.0000 + 13.0000i −0.880471 + 0.880471i
\(219\) −6.00000 + 6.00000i −0.405442 + 0.405442i
\(220\) 0 0
\(221\) −25.0000 + 5.00000i −1.68168 + 0.336336i
\(222\) 8.00000 8.00000i 0.536925 0.536925i
\(223\) 6.00000 0.401790 0.200895 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) 2.00000i 0.133631i
\(225\) 0 0
\(226\) 9.00000 9.00000i 0.598671 0.598671i
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 6.00000i 0.397360i
\(229\) −3.00000 + 3.00000i −0.198246 + 0.198246i −0.799248 0.601002i \(-0.794768\pi\)
0.601002 + 0.799248i \(0.294768\pi\)
\(230\) 0 0
\(231\) 4.00000i 0.263181i
\(232\) −4.00000 −0.262613
\(233\) 5.00000 5.00000i 0.327561 0.327561i −0.524097 0.851658i \(-0.675597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) −2.00000 + 3.00000i −0.130744 + 0.196116i
\(235\) 0 0
\(236\) 3.00000 3.00000i 0.195283 0.195283i
\(237\) 14.0000 14.0000i 0.909398 0.909398i
\(238\) −10.0000 + 10.0000i −0.648204 + 0.648204i
\(239\) −7.00000 7.00000i −0.452792 0.452792i 0.443488 0.896280i \(-0.353741\pi\)
−0.896280 + 0.443488i \(0.853741\pi\)
\(240\) 0 0
\(241\) 1.00000 + 1.00000i 0.0644157 + 0.0644157i 0.738581 0.674165i \(-0.235496\pi\)
−0.674165 + 0.738581i \(0.735496\pi\)
\(242\) 9.00000 0.578542
\(243\) −7.00000 7.00000i −0.449050 0.449050i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) 2.00000i 0.127515i
\(247\) −15.0000 + 3.00000i −0.954427 + 0.190885i
\(248\) −1.00000 1.00000i −0.0635001 0.0635001i
\(249\) 6.00000 + 6.00000i 0.380235 + 0.380235i
\(250\) 0 0
\(251\) 30.0000i 1.89358i 0.321847 + 0.946792i \(0.395696\pi\)
−0.321847 + 0.946792i \(0.604304\pi\)
\(252\) 2.00000i 0.125988i
\(253\) −10.0000 −0.628695
\(254\) 15.0000 15.0000i 0.941184 0.941184i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −15.0000 15.0000i −0.935674 0.935674i 0.0623783 0.998053i \(-0.480131\pi\)
−0.998053 + 0.0623783i \(0.980131\pi\)
\(258\) 10.0000i 0.622573i
\(259\) −16.0000 −0.994192
\(260\) 0 0
\(261\) −4.00000 −0.247594
\(262\) 12.0000i 0.741362i
\(263\) −9.00000 9.00000i −0.554964 0.554964i 0.372906 0.927869i \(-0.378362\pi\)
−0.927869 + 0.372906i \(0.878362\pi\)
\(264\) 2.00000 0.123091
\(265\) 0 0
\(266\) −6.00000 + 6.00000i −0.367884 + 0.367884i
\(267\) 14.0000 0.856786
\(268\) 12.0000i 0.733017i
\(269\) 16.0000i 0.975537i 0.872973 + 0.487769i \(0.162189\pi\)
−0.872973 + 0.487769i \(0.837811\pi\)
\(270\) 0 0
\(271\) −9.00000 9.00000i −0.546711 0.546711i 0.378777 0.925488i \(-0.376345\pi\)
−0.925488 + 0.378777i \(0.876345\pi\)
\(272\) 5.00000 + 5.00000i 0.303170 + 0.303170i
\(273\) −10.0000 + 2.00000i −0.605228 + 0.121046i
\(274\) 12.0000i 0.724947i
\(275\) 0 0
\(276\) 10.0000 0.601929
\(277\) −5.00000 5.00000i −0.300421 0.300421i 0.540758 0.841178i \(-0.318138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 14.0000 0.839664
\(279\) −1.00000 1.00000i −0.0598684 0.0598684i
\(280\) 0 0
\(281\) 21.0000 + 21.0000i 1.25275 + 1.25275i 0.954480 + 0.298275i \(0.0964112\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) −2.00000 + 2.00000i −0.119098 + 0.119098i
\(283\) −15.0000 + 15.0000i −0.891657 + 0.891657i −0.994679 0.103022i \(-0.967149\pi\)
0.103022 + 0.994679i \(0.467149\pi\)
\(284\) −1.00000 + 1.00000i −0.0593391 + 0.0593391i
\(285\) 0 0
\(286\) −1.00000 5.00000i −0.0591312 0.295656i
\(287\) 2.00000 2.00000i 0.118056 0.118056i
\(288\) 1.00000 0.0589256
\(289\) 33.0000i 1.94118i
\(290\) 0 0
\(291\) 2.00000 2.00000i 0.117242 0.117242i
\(292\) 6.00000i 0.351123i
\(293\) 26.0000i 1.51894i 0.650545 + 0.759468i \(0.274541\pi\)
−0.650545 + 0.759468i \(0.725459\pi\)
\(294\) 3.00000 3.00000i 0.174964 0.174964i
\(295\) 0 0
\(296\) 8.00000i 0.464991i
\(297\) 8.00000 0.464207
\(298\) −13.0000 + 13.0000i −0.753070 + 0.753070i
\(299\) −5.00000 25.0000i −0.289157 1.44579i
\(300\) 0 0
\(301\) 10.0000 10.0000i 0.576390 0.576390i
\(302\) 9.00000 9.00000i 0.517892 0.517892i
\(303\) 0 0
\(304\) 3.00000 + 3.00000i 0.172062 + 0.172062i
\(305\) 0 0
\(306\) 5.00000 + 5.00000i 0.285831 + 0.285831i
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −2.00000 2.00000i −0.113961 0.113961i
\(309\) −10.0000 −0.568880
\(310\) 0 0
\(311\) 10.0000i 0.567048i −0.958965 0.283524i \(-0.908496\pi\)
0.958965 0.283524i \(-0.0915036\pi\)
\(312\) 1.00000 + 5.00000i 0.0566139 + 0.283069i
\(313\) −9.00000 9.00000i −0.508710 0.508710i 0.405420 0.914130i \(-0.367125\pi\)
−0.914130 + 0.405420i \(0.867125\pi\)
\(314\) −3.00000 3.00000i −0.169300 0.169300i
\(315\) 0 0
\(316\) 14.0000i 0.787562i
\(317\) 2.00000i 0.112331i −0.998421 0.0561656i \(-0.982113\pi\)
0.998421 0.0561656i \(-0.0178875\pi\)
\(318\) −2.00000 −0.112154
\(319\) 4.00000 4.00000i 0.223957 0.223957i
\(320\) 0 0
\(321\) −26.0000 −1.45118
\(322\) −10.0000 10.0000i −0.557278 0.557278i
\(323\) 30.0000i 1.66924i
\(324\) −5.00000 −0.277778
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) 26.0000i 1.43780i
\(328\) −1.00000 1.00000i −0.0552158 0.0552158i
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) −9.00000 + 9.00000i −0.494685 + 0.494685i −0.909779 0.415094i \(-0.863749\pi\)
0.415094 + 0.909779i \(0.363749\pi\)
\(332\) −6.00000 −0.329293
\(333\) 8.00000i 0.438397i
\(334\) 2.00000i 0.109435i
\(335\) 0 0
\(336\) 2.00000 + 2.00000i 0.109109 + 0.109109i
\(337\) 5.00000 + 5.00000i 0.272367 + 0.272367i 0.830053 0.557685i \(-0.188310\pi\)
−0.557685 + 0.830053i \(0.688310\pi\)
\(338\) 12.0000 5.00000i 0.652714 0.271964i
\(339\) 18.0000i 0.977626i
\(340\) 0 0
\(341\) 2.00000 0.108306
\(342\) 3.00000 + 3.00000i 0.162221 + 0.162221i
\(343\) −20.0000 −1.07990
\(344\) −5.00000 5.00000i −0.269582 0.269582i
\(345\) 0 0
\(346\) 15.0000 + 15.0000i 0.806405 + 0.806405i
\(347\) 7.00000 7.00000i 0.375780 0.375780i −0.493797 0.869577i \(-0.664392\pi\)
0.869577 + 0.493797i \(0.164392\pi\)
\(348\) −4.00000 + 4.00000i −0.214423 + 0.214423i
\(349\) −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
\(351\) 4.00000 + 20.0000i 0.213504 + 1.06752i
\(352\) −1.00000 + 1.00000i −0.0533002 + 0.0533002i
\(353\) 16.0000 0.851594 0.425797 0.904819i \(-0.359994\pi\)
0.425797 + 0.904819i \(0.359994\pi\)
\(354\) 6.00000i 0.318896i
\(355\) 0 0
\(356\) −7.00000 + 7.00000i −0.370999 + 0.370999i
\(357\) 20.0000i 1.05851i
\(358\) 20.0000i 1.05703i
\(359\) −13.0000 + 13.0000i −0.686114 + 0.686114i −0.961371 0.275257i \(-0.911237\pi\)
0.275257 + 0.961371i \(0.411237\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 20.0000 1.05118
\(363\) 9.00000 9.00000i 0.472377 0.472377i
\(364\) 4.00000 6.00000i 0.209657 0.314485i
\(365\) 0 0
\(366\) −2.00000 + 2.00000i −0.104542 + 0.104542i
\(367\) −3.00000 + 3.00000i −0.156599 + 0.156599i −0.781058 0.624459i \(-0.785320\pi\)
0.624459 + 0.781058i \(0.285320\pi\)
\(368\) −5.00000 + 5.00000i −0.260643 + 0.260643i
\(369\) −1.00000 1.00000i −0.0520579 0.0520579i
\(370\) 0 0
\(371\) 2.00000 + 2.00000i 0.103835 + 0.103835i
\(372\) −2.00000 −0.103695
\(373\) 1.00000 + 1.00000i 0.0517780 + 0.0517780i 0.732522 0.680744i \(-0.238343\pi\)
−0.680744 + 0.732522i \(0.738343\pi\)
\(374\) −10.0000 −0.517088
\(375\) 0 0
\(376\) 2.00000i 0.103142i
\(377\) 12.0000 + 8.00000i 0.618031 + 0.412021i
\(378\) 8.00000 + 8.00000i 0.411476 + 0.411476i
\(379\) −17.0000 17.0000i −0.873231 0.873231i 0.119592 0.992823i \(-0.461841\pi\)
−0.992823 + 0.119592i \(0.961841\pi\)
\(380\) 0 0
\(381\) 30.0000i 1.53695i
\(382\) 8.00000i 0.409316i
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 1.00000 1.00000i 0.0510310 0.0510310i
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) −5.00000 5.00000i −0.254164 0.254164i
\(388\) 2.00000i 0.101535i
\(389\) 10.0000 0.507020 0.253510 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 0 0
\(391\) −50.0000 −2.52861
\(392\) 3.00000i 0.151523i
\(393\) 12.0000 + 12.0000i 0.605320 + 0.605320i
\(394\) −18.0000 −0.906827
\(395\) 0 0
\(396\) −1.00000 + 1.00000i −0.0502519 + 0.0502519i
\(397\) −8.00000 −0.401508 −0.200754 0.979642i \(-0.564339\pi\)
−0.200754 + 0.979642i \(0.564339\pi\)
\(398\) 0 0
\(399\) 12.0000i 0.600751i
\(400\) 0 0
\(401\) 1.00000 + 1.00000i 0.0499376 + 0.0499376i 0.731635 0.681697i \(-0.238758\pi\)
−0.681697 + 0.731635i \(0.738758\pi\)
\(402\) 12.0000 + 12.0000i 0.598506 + 0.598506i
\(403\) 1.00000 + 5.00000i 0.0498135 + 0.249068i
\(404\) 0 0
\(405\) 0 0
\(406\) 8.00000 0.397033
\(407\) −8.00000 8.00000i −0.396545 0.396545i
\(408\) 10.0000 0.495074
\(409\) 3.00000 + 3.00000i 0.148340 + 0.148340i 0.777376 0.629036i \(-0.216550\pi\)
−0.629036 + 0.777376i \(0.716550\pi\)
\(410\) 0 0
\(411\) 12.0000 + 12.0000i 0.591916 + 0.591916i
\(412\) 5.00000 5.00000i 0.246332 0.246332i
\(413\) −6.00000 + 6.00000i −0.295241 + 0.295241i
\(414\) −5.00000 + 5.00000i −0.245737 + 0.245737i
\(415\) 0 0
\(416\) −3.00000 2.00000i −0.147087 0.0980581i
\(417\) 14.0000 14.0000i 0.685583 0.685583i
\(418\) −6.00000 −0.293470
\(419\) 26.0000i 1.27018i 0.772437 + 0.635092i \(0.219038\pi\)
−0.772437 + 0.635092i \(0.780962\pi\)
\(420\) 0 0
\(421\) −9.00000 + 9.00000i −0.438633 + 0.438633i −0.891552 0.452919i \(-0.850383\pi\)
0.452919 + 0.891552i \(0.350383\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 2.00000i 0.0972433i
\(424\) 1.00000 1.00000i 0.0485643 0.0485643i
\(425\) 0 0
\(426\) 2.00000i 0.0969003i
\(427\) 4.00000 0.193574
\(428\) 13.0000 13.0000i 0.628379 0.628379i
\(429\) −6.00000 4.00000i −0.289683 0.193122i
\(430\) 0 0
\(431\) 21.0000 21.0000i 1.01153 1.01153i 0.0116017 0.999933i \(-0.496307\pi\)
0.999933 0.0116017i \(-0.00369302\pi\)
\(432\) 4.00000 4.00000i 0.192450 0.192450i
\(433\) −15.0000 + 15.0000i −0.720854 + 0.720854i −0.968779 0.247925i \(-0.920251\pi\)
0.247925 + 0.968779i \(0.420251\pi\)
\(434\) 2.00000 + 2.00000i 0.0960031 + 0.0960031i
\(435\) 0 0
\(436\) −13.0000 13.0000i −0.622587 0.622587i
\(437\) −30.0000 −1.43509
\(438\) −6.00000 6.00000i −0.286691 0.286691i
\(439\) −40.0000 −1.90910 −0.954548 0.298057i \(-0.903661\pi\)
−0.954548 + 0.298057i \(0.903661\pi\)
\(440\) 0 0
\(441\) 3.00000i 0.142857i
\(442\) −5.00000 25.0000i −0.237826 1.18913i
\(443\) −19.0000 19.0000i −0.902717 0.902717i 0.0929532 0.995670i \(-0.470369\pi\)
−0.995670 + 0.0929532i \(0.970369\pi\)
\(444\) 8.00000 + 8.00000i 0.379663 + 0.379663i
\(445\) 0 0
\(446\) 6.00000i 0.284108i
\(447\) 26.0000i 1.22976i
\(448\) −2.00000 −0.0944911
\(449\) 7.00000 7.00000i 0.330350 0.330350i −0.522369 0.852720i \(-0.674952\pi\)
0.852720 + 0.522369i \(0.174952\pi\)
\(450\) 0 0
\(451\) 2.00000 0.0941763
\(452\) 9.00000 + 9.00000i 0.423324 + 0.423324i
\(453\) 18.0000i 0.845714i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) 38.0000i 1.77757i 0.458329 + 0.888783i \(0.348448\pi\)
−0.458329 + 0.888783i \(0.651552\pi\)
\(458\) −3.00000 3.00000i −0.140181 0.140181i
\(459\) 40.0000 1.86704
\(460\) 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 −0.186097
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) 4.00000i 0.185695i
\(465\) 0 0
\(466\) 5.00000 + 5.00000i 0.231621 + 0.231621i
\(467\) −5.00000 5.00000i −0.231372 0.231372i 0.581893 0.813265i \(-0.302312\pi\)
−0.813265 + 0.581893i \(0.802312\pi\)
\(468\) −3.00000 2.00000i −0.138675 0.0924500i
\(469\) 24.0000i 1.10822i
\(470\) 0 0
\(471\) −6.00000 −0.276465
\(472\) 3.00000 + 3.00000i 0.138086 + 0.138086i
\(473\) 10.0000 0.459800
\(474\) 14.0000 + 14.0000i 0.643041 + 0.643041i
\(475\) 0 0
\(476\) −10.0000 10.0000i −0.458349 0.458349i
\(477\) 1.00000 1.00000i 0.0457869 0.0457869i
\(478\) 7.00000 7.00000i 0.320173 0.320173i
\(479\) −13.0000 + 13.0000i −0.593985 + 0.593985i −0.938705 0.344720i \(-0.887974\pi\)
0.344720 + 0.938705i \(0.387974\pi\)
\(480\) 0 0
\(481\) 16.0000 24.0000i 0.729537 1.09431i
\(482\) −1.00000 + 1.00000i −0.0455488 + 0.0455488i
\(483\) −20.0000 −0.910032
\(484\) 9.00000i 0.409091i
\(485\) 0 0
\(486\) 7.00000 7.00000i 0.317526 0.317526i
\(487\) 32.0000i 1.45006i −0.688718 0.725029i \(-0.741826\pi\)
0.688718 0.725029i \(-0.258174\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) 4.00000 4.00000i 0.180886 0.180886i
\(490\) 0 0
\(491\) 10.0000i 0.451294i −0.974209 0.225647i \(-0.927550\pi\)
0.974209 0.225647i \(-0.0724495\pi\)
\(492\) −2.00000 −0.0901670
\(493\) 20.0000 20.0000i 0.900755 0.900755i
\(494\) −3.00000 15.0000i −0.134976 0.674882i
\(495\) 0 0
\(496\) 1.00000 1.00000i 0.0449013 0.0449013i
\(497\) 2.00000 2.00000i 0.0897123 0.0897123i
\(498\) −6.00000 + 6.00000i −0.268866 + 0.268866i
\(499\) 23.0000 + 23.0000i 1.02962 + 1.02962i 0.999548 + 0.0300737i \(0.00957421\pi\)
0.0300737 + 0.999548i \(0.490426\pi\)
\(500\) 0 0
\(501\) 2.00000 + 2.00000i 0.0893534 + 0.0893534i
\(502\) −30.0000 −1.33897
\(503\) −9.00000 9.00000i −0.401290 0.401290i 0.477397 0.878688i \(-0.341580\pi\)
−0.878688 + 0.477397i \(0.841580\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 0 0
\(506\) 10.0000i 0.444554i
\(507\) 7.00000 17.0000i 0.310881 0.754997i
\(508\) 15.0000 + 15.0000i 0.665517 + 0.665517i
\(509\) 13.0000 + 13.0000i 0.576215 + 0.576215i 0.933858 0.357643i \(-0.116420\pi\)
−0.357643 + 0.933858i \(0.616420\pi\)
\(510\) 0 0
\(511\) 12.0000i 0.530849i
\(512\) 1.00000i 0.0441942i
\(513\) 24.0000 1.05963
\(514\) 15.0000 15.0000i 0.661622 0.661622i
\(515\) 0 0
\(516\) −10.0000 −0.440225
\(517\) 2.00000 + 2.00000i 0.0879599 + 0.0879599i
\(518\) 16.0000i 0.703000i
\(519\) 30.0000 1.31685
\(520\) 0 0
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 4.00000i 0.175075i
\(523\) 21.0000 + 21.0000i 0.918266 + 0.918266i 0.996903 0.0786374i \(-0.0250569\pi\)
−0.0786374 + 0.996903i \(0.525057\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 9.00000 9.00000i 0.392419 0.392419i
\(527\) 10.0000 0.435607
\(528\) 2.00000i 0.0870388i
\(529\) 27.0000i 1.17391i
\(530\) 0 0
\(531\) 3.00000 + 3.00000i 0.130189 + 0.130189i
\(532\) −6.00000 6.00000i −0.260133 0.260133i
\(533\) 1.00000 + 5.00000i 0.0433148 + 0.216574i
\(534\) 14.0000i 0.605839i
\(535\) 0 0
\(536\) −12.0000 −0.518321
\(537\) −20.0000 20.0000i −0.863064 0.863064i
\(538\) −16.0000 −0.689809
\(539\) −3.00000 3.00000i −0.129219 0.129219i
\(540\) 0 0
\(541\) −9.00000 9.00000i −0.386940 0.386940i 0.486654 0.873595i \(-0.338217\pi\)
−0.873595 + 0.486654i \(0.838217\pi\)
\(542\) 9.00000 9.00000i 0.386583 0.386583i
\(543\) 20.0000 20.0000i 0.858282 0.858282i
\(544\) −5.00000 + 5.00000i −0.214373 + 0.214373i
\(545\) 0 0
\(546\) −2.00000 10.0000i −0.0855921 0.427960i
\(547\) 7.00000 7.00000i 0.299298 0.299298i −0.541441 0.840739i \(-0.682121\pi\)
0.840739 + 0.541441i \(0.182121\pi\)
\(548\) −12.0000 −0.512615
\(549\) 2.00000i 0.0853579i
\(550\) 0 0
\(551\) 12.0000 12.0000i 0.511217 0.511217i
\(552\) 10.0000i 0.425628i
\(553\) 28.0000i 1.19068i
\(554\) 5.00000 5.00000i 0.212430 0.212430i
\(555\) 0 0
\(556\) 14.0000i 0.593732i
\(557\) −8.00000 −0.338971 −0.169485 0.985533i \(-0.554211\pi\)
−0.169485 + 0.985533i \(0.554211\pi\)
\(558\) 1.00000 1.00000i 0.0423334 0.0423334i
\(559\) 5.00000 + 25.0000i 0.211477 + 1.05739i
\(560\) 0 0
\(561\) −10.0000 + 10.0000i −0.422200 + 0.422200i
\(562\) −21.0000 + 21.0000i −0.885832 + 0.885832i
\(563\) 5.00000 5.00000i 0.210725 0.210725i −0.593851 0.804575i \(-0.702393\pi\)
0.804575 + 0.593851i \(0.202393\pi\)
\(564\) −2.00000 2.00000i −0.0842152 0.0842152i
\(565\) 0 0
\(566\) −15.0000 15.0000i −0.630497 0.630497i
\(567\) 10.0000 0.419961
\(568\) −1.00000 1.00000i −0.0419591 0.0419591i
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) 10.0000i 0.418487i −0.977864 0.209243i \(-0.932900\pi\)
0.977864 0.209243i \(-0.0671001\pi\)
\(572\) 5.00000 1.00000i 0.209061 0.0418121i
\(573\) −8.00000 8.00000i −0.334205 0.334205i
\(574\) 2.00000 + 2.00000i 0.0834784 + 0.0834784i
\(575\) 0 0
\(576\) 1.00000i 0.0416667i
\(577\) 22.0000i 0.915872i −0.888985 0.457936i \(-0.848589\pi\)
0.888985 0.457936i \(-0.151411\pi\)
\(578\) −33.0000 −1.37262
\(579\) 14.0000 14.0000i 0.581820 0.581820i
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 2.00000 + 2.00000i 0.0829027 + 0.0829027i
\(583\) 2.00000i 0.0828315i
\(584\) 6.00000 0.248282
\(585\) 0 0
\(586\) −26.0000 −1.07405
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 3.00000 + 3.00000i 0.123718 + 0.123718i
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) −18.0000 + 18.0000i −0.740421 + 0.740421i
\(592\) −8.00000 −0.328798
\(593\) 14.0000i 0.574911i −0.957794 0.287456i \(-0.907191\pi\)
0.957794 0.287456i \(-0.0928094\pi\)
\(594\) 8.00000i 0.328244i
\(595\) 0 0
\(596\) −13.0000 13.0000i −0.532501 0.532501i
\(597\) 0 0
\(598\) 25.0000 5.00000i 1.02233 0.204465i
\(599\) 14.0000i 0.572024i −0.958226 0.286012i \(-0.907670\pi\)
0.958226 0.286012i \(-0.0923298\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 10.0000 + 10.0000i 0.407570 + 0.407570i
\(603\) −12.0000 −0.488678
\(604\) 9.00000 + 9.00000i 0.366205 + 0.366205i
\(605\) 0 0
\(606\) 0 0
\(607\) −3.00000 + 3.00000i −0.121766 + 0.121766i −0.765364 0.643598i \(-0.777441\pi\)
0.643598 + 0.765364i \(0.277441\pi\)
\(608\) −3.00000 + 3.00000i −0.121666 + 0.121666i
\(609\) 8.00000 8.00000i 0.324176 0.324176i
\(610\) 0 0
\(611\) −4.00000 + 6.00000i −0.161823 + 0.242734i
\(612\) −5.00000 + 5.00000i −0.202113 + 0.202113i
\(613\) −4.00000 −0.161558 −0.0807792 0.996732i \(-0.525741\pi\)
−0.0807792 + 0.996732i \(0.525741\pi\)
\(614\) 2.00000i 0.0807134i
\(615\) 0 0
\(616\) 2.00000 2.00000i 0.0805823 0.0805823i
\(617\) 38.0000i 1.52982i 0.644136 + 0.764911i \(0.277217\pi\)
−0.644136 + 0.764911i \(0.722783\pi\)
\(618\) 10.0000i 0.402259i
\(619\) −3.00000 + 3.00000i −0.120580 + 0.120580i −0.764822 0.644242i \(-0.777173\pi\)
0.644242 + 0.764822i \(0.277173\pi\)
\(620\) 0 0
\(621\) 40.0000i 1.60514i
\(622\) 10.0000 0.400963
\(623\) 14.0000 14.0000i 0.560898 0.560898i
\(624\) −5.00000 + 1.00000i −0.200160 + 0.0400320i
\(625\) 0 0
\(626\) 9.00000 9.00000i 0.359712 0.359712i
\(627\) −6.00000 + 6.00000i −0.239617 + 0.239617i
\(628\) 3.00000 3.00000i 0.119713 0.119713i
\(629\) −40.0000 40.0000i −1.59490 1.59490i
\(630\) 0 0
\(631\) 11.0000 + 11.0000i 0.437903 + 0.437903i 0.891306 0.453403i \(-0.149790\pi\)
−0.453403 + 0.891306i \(0.649790\pi\)
\(632\) −14.0000 −0.556890
\(633\) 12.0000 + 12.0000i 0.476957 + 0.476957i
\(634\) 2.00000 0.0794301
\(635\) 0 0
\(636\) 2.00000i 0.0793052i
\(637\) 6.00000 9.00000i 0.237729 0.356593i
\(638\) 4.00000 + 4.00000i 0.158362 + 0.158362i
\(639\) −1.00000 1.00000i −0.0395594 0.0395594i
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 26.0000i 1.02614i
\(643\) 46.0000 1.81406 0.907031 0.421063i \(-0.138343\pi\)
0.907031 + 0.421063i \(0.138343\pi\)
\(644\) 10.0000 10.0000i 0.394055 0.394055i
\(645\) 0 0
\(646\) −30.0000 −1.18033
\(647\) 5.00000 + 5.00000i 0.196570 + 0.196570i 0.798528 0.601958i \(-0.205612\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(648\) 5.00000i 0.196419i
\(649\) −6.00000 −0.235521
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) 4.00000i 0.156652i
\(653\) 21.0000 + 21.0000i 0.821794 + 0.821794i 0.986365 0.164572i \(-0.0526242\pi\)
−0.164572 + 0.986365i \(0.552624\pi\)
\(654\) −26.0000 −1.01668
\(655\) 0 0
\(656\) 1.00000 1.00000i 0.0390434 0.0390434i
\(657\) 6.00000 0.234082
\(658\) 4.00000i 0.155936i
\(659\) 14.0000i 0.545363i −0.962104 0.272681i \(-0.912090\pi\)
0.962104 0.272681i \(-0.0879105\pi\)
\(660\) 0 0
\(661\) 31.0000 + 31.0000i 1.20576 + 1.20576i 0.972387 + 0.233373i \(0.0749763\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(662\) −9.00000 9.00000i −0.349795 0.349795i
\(663\) −30.0000 20.0000i −1.16510 0.776736i
\(664\) 6.00000i 0.232845i
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) 20.0000 + 20.0000i 0.774403 + 0.774403i
\(668\) −2.00000 −0.0773823
\(669\) 6.00000 + 6.00000i 0.231973 + 0.231973i
\(670\) 0 0
\(671\) 2.00000 + 2.00000i 0.0772091 + 0.0772091i
\(672\) −2.00000 + 2.00000i −0.0771517 + 0.0771517i
\(673\) 5.00000 5.00000i 0.192736 0.192736i −0.604141 0.796877i \(-0.706484\pi\)
0.796877 + 0.604141i \(0.206484\pi\)
\(674\) −5.00000 + 5.00000i −0.192593 + 0.192593i
\(675\) 0 0
\(676\) 5.00000 + 12.0000i 0.192308 + 0.461538i
\(677\) −23.0000 + 23.0000i −0.883962 + 0.883962i −0.993935 0.109973i \(-0.964924\pi\)
0.109973 + 0.993935i \(0.464924\pi\)
\(678\) 18.0000 0.691286
\(679\) 4.00000i 0.153506i
\(680\) 0 0
\(681\) 12.0000 12.0000i 0.459841 0.459841i
\(682\) 2.00000i 0.0765840i
\(683\) 36.0000i 1.37750i 0.724998 + 0.688751i \(0.241841\pi\)
−0.724998 + 0.688751i \(0.758159\pi\)
\(684\) −3.00000 + 3.00000i −0.114708 + 0.114708i
\(685\) 0 0
\(686\) 20.0000i 0.763604i
\(687\) −6.00000 −0.228914
\(688\) 5.00000 5.00000i 0.190623 0.190623i
\(689\) −5.00000 + 1.00000i −0.190485 + 0.0380970i
\(690\) 0 0
\(691\) −9.00000 + 9.00000i −0.342376 + 0.342376i −0.857260 0.514884i \(-0.827835\pi\)
0.514884 + 0.857260i \(0.327835\pi\)
\(692\) −15.0000 + 15.0000i −0.570214 + 0.570214i
\(693\) 2.00000 2.00000i 0.0759737 0.0759737i
\(694\) 7.00000 + 7.00000i 0.265716 + 0.265716i
\(695\) 0 0
\(696\) −4.00000 4.00000i −0.151620 0.151620i
\(697\) 10.0000 0.378777
\(698\) −3.00000 3.00000i −0.113552 0.113552i
\(699\) 10.0000 0.378235
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −20.0000 + 4.00000i −0.754851 + 0.150970i
\(703\) −24.0000 24.0000i −0.905177 0.905177i
\(704\) −1.00000 1.00000i −0.0376889 0.0376889i
\(705\) 0 0
\(706\) 16.0000i 0.602168i
\(707\) 0 0
\(708\) 6.00000 0.225494
\(709\) −3.00000 + 3.00000i −0.112667 + 0.112667i −0.761193 0.648526i \(-0.775386\pi\)
0.648526 + 0.761193i \(0.275386\pi\)
\(710\) 0 0
\(711\) −14.0000 −0.525041
\(712\) −7.00000 7.00000i −0.262336 0.262336i
\(713\) 10.0000i 0.374503i
\(714\) −20.0000 −0.748481
\(715\) 0 0
\(716\) 20.0000 0.747435
\(717\) 14.0000i 0.522840i
\(718\) −13.0000 13.0000i −0.485156 0.485156i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) −10.0000 + 10.0000i −0.372419 + 0.372419i
\(722\) 1.00000 0.0372161
\(723\) 2.00000i 0.0743808i
\(724\) 20.0000i 0.743294i
\(725\) 0 0
\(726\) 9.00000 + 9.00000i 0.334021 + 0.334021i
\(727\) −35.0000 35.0000i −1.29808 1.29808i −0.929660 0.368418i \(-0.879900\pi\)
−0.368418 0.929660i \(-0.620100\pi\)
\(728\) 6.00000 + 4.00000i 0.222375 + 0.148250i
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 50.0000 1.84932
\(732\) −2.00000 2.00000i −0.0739221 0.0739221i
\(733\) −44.0000 −1.62518 −0.812589 0.582838i \(-0.801942\pi\)
−0.812589 + 0.582838i \(0.801942\pi\)
\(734\) −3.00000 3.00000i −0.110732 0.110732i
\(735\) 0 0
\(736\) −5.00000 5.00000i −0.184302 0.184302i
\(737\) 12.0000 12.0000i 0.442026 0.442026i
\(738\) 1.00000 1.00000i 0.0368105 0.0368105i
\(739\) 37.0000 37.0000i 1.36107 1.36107i 0.488507 0.872560i \(-0.337542\pi\)
0.872560 0.488507i \(-0.162458\pi\)
\(740\) 0 0
\(741\) −18.0000 12.0000i −0.661247 0.440831i
\(742\) −2.00000 + 2.00000i −0.0734223 + 0.0734223i
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 2.00000i 0.0733236i
\(745\) 0 0
\(746\) −1.00000 + 1.00000i −0.0366126 + 0.0366126i
\(747\) 6.00000i 0.219529i
\(748\) 10.0000i 0.365636i
\(749\) −26.0000 + 26.0000i −0.950019 + 0.950019i
\(750\) 0 0
\(751\) 10.0000i 0.364905i −0.983215 0.182453i \(-0.941596\pi\)
0.983215 0.182453i \(-0.0584036\pi\)
\(752\) 2.00000 0.0729325
\(753\) −30.0000 + 30.0000i −1.09326 + 1.09326i
\(754\) −8.00000 + 12.0000i −0.291343 + 0.437014i
\(755\) 0 0
\(756\) −8.00000 + 8.00000i −0.290957 + 0.290957i
\(757\) 17.0000 17.0000i 0.617876 0.617876i −0.327111 0.944986i \(-0.606075\pi\)
0.944986 + 0.327111i \(0.106075\pi\)
\(758\) 17.0000 17.0000i 0.617468 0.617468i
\(759\) −10.0000 10.0000i −0.362977 0.362977i
\(760\) 0 0
\(761\) −19.0000 19.0000i −0.688749 0.688749i 0.273206 0.961956i \(-0.411916\pi\)
−0.961956 + 0.273206i \(0.911916\pi\)
\(762\) 30.0000 1.08679
\(763\) 26.0000 + 26.0000i 0.941263 + 0.941263i
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 6.00000i 0.216789i
\(767\) −3.00000 15.0000i −0.108324 0.541619i
\(768\) 1.00000 + 1.00000i 0.0360844 + 0.0360844i
\(769\) 23.0000 + 23.0000i 0.829401 + 0.829401i 0.987434 0.158033i \(-0.0505151\pi\)
−0.158033 + 0.987434i \(0.550515\pi\)
\(770\) 0 0
\(771\) 30.0000i 1.08042i
\(772\) 14.0000i 0.503871i
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 5.00000 5.00000i 0.179721 0.179721i
\(775\) 0 0
\(776\) −2.00000 −0.0717958
\(777\) −16.0000 16.0000i −0.573997 0.573997i
\(778\) 10.0000i 0.358517i
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) 2.00000 0.0715656
\(782\) 50.0000i 1.78800i
\(783\) −16.0000 16.0000i −0.571793 0.571793i
\(784\) −3.00000 −0.107143
\(785\) 0 0
\(786\) −12.0000 + 12.0000i −0.428026 + 0.428026i
\(787\) 42.0000 1.49714 0.748569 0.663057i \(-0.230741\pi\)
0.748569 + 0.663057i \(0.230741\pi\)
\(788\) 18.0000i 0.641223i
\(789\) 18.0000i 0.640817i
\(790\) 0 0
\(791\) −18.0000 18.0000i −0.640006 0.640006i
\(792\) −1.00000 1.00000i −0.0355335 0.0355335i
\(793\) −4.00000 + 6.00000i −0.142044 + 0.213066i
\(794\) 8.00000i 0.283909i
\(795\) 0 0
\(796\) 0 0
\(797\) −5.00000 5.00000i −0.177109 0.177109i 0.612985 0.790094i \(-0.289968\pi\)
−0.790094 + 0.612985i \(0.789968\pi\)
\(798\) −12.0000 −0.424795
\(799\) 10.0000 + 10.0000i 0.353775 + 0.353775i
\(800\) 0 0
\(801\) −7.00000 7.00000i −0.247333 0.247333i
\(802\) −1.00000 + 1.00000i −0.0353112 + 0.0353112i
\(803\) −6.00000 + 6.00000i −0.211735 + 0.211735i
\(804\) −12.0000 + 12.0000i −0.423207 + 0.423207i
\(805\) 0 0
\(806\) −5.00000 + 1.00000i −0.176117 + 0.0352235i
\(807\) −16.0000 + 16.0000i −0.563227 + 0.563227i
\(808\) 0 0
\(809\) 36.0000i 1.26569i 0.774277 + 0.632846i \(0.218114\pi\)
−0.774277 + 0.632846i \(0.781886\pi\)
\(810\) 0 0
\(811\) 11.0000 11.0000i 0.386262 0.386262i −0.487090 0.873352i \(-0.661942\pi\)
0.873352 + 0.487090i \(0.161942\pi\)
\(812\) 8.00000i 0.280745i
\(813\) 18.0000i 0.631288i
\(814\) 8.00000 8.00000i 0.280400 0.280400i
\(815\) 0 0
\(816\) 10.0000i 0.350070i
\(817\) 30.0000 1.04957
\(818\) −3.00000 + 3.00000i −0.104893 + 0.104893i
\(819\) 6.00000 + 4.00000i 0.209657 + 0.139771i
\(820\) 0 0
\(821\) −29.0000 + 29.0000i −1.01211 + 1.01211i −0.0121812 + 0.999926i \(0.503877\pi\)
−0.999926 + 0.0121812i \(0.996123\pi\)
\(822\) −12.0000 + 12.0000i −0.418548 + 0.418548i
\(823\) 15.0000 15.0000i 0.522867 0.522867i −0.395569 0.918436i \(-0.629453\pi\)
0.918436 + 0.395569i \(0.129453\pi\)
\(824\) 5.00000 + 5.00000i 0.174183 + 0.174183i
\(825\) 0 0
\(826\) −6.00000 6.00000i −0.208767 0.208767i
\(827\) 2.00000 0.0695468 0.0347734 0.999395i \(-0.488929\pi\)
0.0347734 + 0.999395i \(0.488929\pi\)
\(828\) −5.00000 5.00000i −0.173762 0.173762i
\(829\) 30.0000 1.04194 0.520972 0.853574i \(-0.325570\pi\)
0.520972 + 0.853574i \(0.325570\pi\)
\(830\) 0 0
\(831\) 10.0000i 0.346896i
\(832\) 2.00000 3.00000i 0.0693375 0.104006i
\(833\) −15.0000 15.0000i −0.519719 0.519719i
\(834\) 14.0000 + 14.0000i 0.484780 + 0.484780i
\(835\) 0 0
\(836\) 6.00000i 0.207514i
\(837\) 8.00000i 0.276520i
\(838\) −26.0000 −0.898155
\(839\) −13.0000 + 13.0000i −0.448810 + 0.448810i −0.894959 0.446149i \(-0.852795\pi\)
0.446149 + 0.894959i \(0.352795\pi\)
\(840\) 0 0
\(841\) 13.0000 0.448276
\(842\) −9.00000 9.00000i −0.310160 0.310160i
\(843\) 42.0000i 1.44656i
\(844\) −12.0000 −0.413057
\(845\) 0 0
\(846\) 2.00000 0.0687614
\(847\) 18.0000i 0.618487i
\(848\) 1.00000 + 1.00000i 0.0343401 + 0.0343401i
\(849\) −30.0000 −1.02960
\(850\) 0 0
\(851\) 40.0000 40.0000i 1.37118 1.37118i
\(852\) −2.00000 −0.0685189
\(853\) 26.0000i 0.890223i 0.895475 + 0.445112i \(0.146836\pi\)
−0.895475 + 0.445112i \(0.853164\pi\)
\(854\) 4.00000i 0.136877i
\(855\) 0 0
\(856\) 13.0000 + 13.0000i 0.444331 + 0.444331i
\(857\) 5.00000 + 5.00000i 0.170797 + 0.170797i 0.787329 0.616533i \(-0.211463\pi\)
−0.616533 + 0.787329i \(0.711463\pi\)
\(858\) 4.00000 6.00000i 0.136558 0.204837i
\(859\) 26.0000i 0.887109i 0.896248 + 0.443554i \(0.146283\pi\)
−0.896248 + 0.443554i \(0.853717\pi\)
\(860\) 0 0
\(861\) 4.00000 0.136320
\(862\) 21.0000 + 21.0000i 0.715263 + 0.715263i
\(863\) 46.0000 1.56586 0.782929 0.622111i \(-0.213725\pi\)
0.782929 + 0.622111i \(0.213725\pi\)
\(864\) 4.00000 + 4.00000i 0.136083 + 0.136083i
\(865\) 0 0
\(866\) −15.0000 15.0000i −0.509721 0.509721i
\(867\) −33.0000 + 33.0000i −1.12074 + 1.12074i
\(868\) −2.00000 + 2.00000i −0.0678844 + 0.0678844i
\(869\) 14.0000 14.0000i 0.474917 0.474917i
\(870\) 0 0
\(871\) 36.0000 + 24.0000i 1.21981 + 0.813209i
\(872\) 13.0000 13.0000i 0.440236 0.440236i
\(873\) −2.00000 −0.0676897
\(874\) 30.0000i 1.01477i
\(875\) 0 0
\(876\) 6.00000 6.00000i 0.202721 0.202721i
\(877\) 18.0000i 0.607817i 0.952701 + 0.303908i \(0.0982917\pi\)
−0.952701 + 0.303908i \(0.901708\pi\)
\(878\) 40.0000i 1.34993i
\(879\) −26.0000 + 26.0000i −0.876958 + 0.876958i
\(880\) 0 0
\(881\) 20.0000i 0.673817i 0.941537 + 0.336909i \(0.109381\pi\)
−0.941537 + 0.336909i \(0.890619\pi\)
\(882\) −3.00000 −0.101015
\(883\) 5.00000 5.00000i 0.168263 0.168263i −0.617952 0.786216i \(-0.712037\pi\)
0.786216 + 0.617952i \(0.212037\pi\)
\(884\) 25.0000 5.00000i 0.840841 0.168168i
\(885\) 0 0
\(886\) 19.0000 19.0000i 0.638317 0.638317i
\(887\) −23.0000 + 23.0000i −0.772264 + 0.772264i −0.978502 0.206238i \(-0.933878\pi\)
0.206238 + 0.978502i \(0.433878\pi\)
\(888\) −8.00000 + 8.00000i −0.268462 + 0.268462i
\(889\) −30.0000 30.0000i −1.00617 1.00617i
\(890\) 0 0
\(891\) 5.00000 + 5.00000i 0.167506 + 0.167506i
\(892\) −6.00000 −0.200895
\(893\) 6.00000 + 6.00000i 0.200782 + 0.200782i
\(894\) −26.0000 −0.869570
\(895\) 0 0
\(896\) 2.00000i 0.0668153i
\(897\) 20.0000 30.0000i 0.667781 1.00167i
\(898\) 7.00000 + 7.00000i 0.233593 + 0.233593i
\(899\) −4.00000 4.00000i −0.133407 0.133407i
\(900\) 0 0
\(901\) 10.0000i 0.333148i
\(902\) 2.00000i 0.0665927i
\(903\) 20.0000 0.665558
\(904\) −9.00000 + 9.00000i −0.299336 + 0.299336i
\(905\) 0 0
\(906\) 18.0000 0.598010
\(907\) 35.0000 + 35.0000i 1.16216 + 1.16216i 0.984003 + 0.178153i \(0.0570122\pi\)
0.178153 + 0.984003i \(0.442988\pi\)
\(908\) 12.0000i 0.398234i
\(909\) 0 0
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 6.00000i 0.198680i
\(913\) 6.00000 + 6.00000i 0.198571 + 0.198571i
\(914\) −38.0000 −1.25693
\(915\) 0 0
\(916\) 3.00000 3.00000i 0.0991228 0.0991228i
\(917\) 24.0000 0.792550
\(918\) 40.0000i 1.32020i
\(919\) 14.0000i 0.461817i −0.972975 0.230909i \(-0.925830\pi\)
0.972975 0.230909i \(-0.0741699\pi\)
\(920\) 0 0
\(921\) 2.00000 + 2.00000i 0.0659022 + 0.0659022i
\(922\) 11.0000 + 11.0000i 0.362266 + 0.362266i
\(923\) 1.00000 + 5.00000i 0.0329154 + 0.164577i
\(924\) 4.00000i 0.131590i
\(925\) 0 0
\(926\) −16.0000 −0.525793
\(927\) 5.00000 + 5.00000i 0.164222 + 0.164222i
\(928\) 4.00000 0.131306
\(929\) −17.0000 17.0000i −0.557752 0.557752i 0.370915 0.928667i \(-0.379044\pi\)
−0.928667 + 0.370915i \(0.879044\pi\)
\(930\) 0 0
\(931\) −9.00000 9.00000i −0.294963 0.294963i
\(932\) −5.00000 + 5.00000i −0.163780 + 0.163780i
\(933\) 10.0000 10.0000i 0.327385 0.327385i
\(934\) 5.00000 5.00000i 0.163605 0.163605i
\(935\) 0 0
\(936\) 2.00000 3.00000i 0.0653720 0.0980581i
\(937\) −33.0000 + 33.0000i −1.07806 + 1.07806i −0.0813798 + 0.996683i \(0.525933\pi\)
−0.996683 + 0.0813798i \(0.974067\pi\)
\(938\) 24.0000 0.783628
\(939\) 18.0000i 0.587408i
\(940\) 0 0
\(941\) −29.0000 + 29.0000i −0.945373 + 0.945373i −0.998583 0.0532103i \(-0.983055\pi\)
0.0532103 + 0.998583i \(0.483055\pi\)
\(942\) 6.00000i 0.195491i
\(943\) 10.0000i 0.325645i
\(944\) −3.00000 + 3.00000i −0.0976417 + 0.0976417i
\(945\) 0 0
\(946\) 10.0000i 0.325128i
\(947\) −38.0000 −1.23483 −0.617417 0.786636i \(-0.711821\pi\)
−0.617417 + 0.786636i \(0.711821\pi\)
\(948\) −14.0000 + 14.0000i −0.454699 + 0.454699i
\(949\) −18.0000 12.0000i −0.584305 0.389536i
\(950\) 0 0
\(951\) 2.00000 2.00000i 0.0648544 0.0648544i
\(952\) 10.0000 10.0000i 0.324102 0.324102i
\(953\) −35.0000 + 35.0000i −1.13376 + 1.13376i −0.144215 + 0.989546i \(0.546066\pi\)
−0.989546 + 0.144215i \(0.953934\pi\)
\(954\) 1.00000 + 1.00000i 0.0323762 + 0.0323762i
\(955\) 0 0
\(956\) 7.00000 + 7.00000i 0.226396 + 0.226396i
\(957\) 8.00000 0.258603
\(958\) −13.0000 13.0000i −0.420011 0.420011i
\(959\) 24.0000 0.775000
\(960\) 0 0
\(961\) 29.0000i 0.935484i
\(962\) 24.0000 + 16.0000i 0.773791 + 0.515861i
\(963\) 13.0000 + 13.0000i 0.418919 + 0.418919i
\(964\) −1.00000 1.00000i −0.0322078 0.0322078i
\(965\) 0 0
\(966\) 20.0000i 0.643489i
\(967\) 48.0000i 1.54358i 0.635880 + 0.771788i \(0.280637\pi\)
−0.635880 + 0.771788i \(0.719363\pi\)
\(968\) −9.00000 −0.289271
\(969\) −30.0000 + 30.0000i −0.963739 + 0.963739i
\(970\) 0 0
\(971\) 12.0000 0.385098 0.192549 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) 7.00000 + 7.00000i 0.224525 + 0.224525i
\(973\) 28.0000i 0.897639i
\(974\) 32.0000 1.02535
\(975\) 0 0
\(976\) 2.00000 0.0640184
\(977\) 22.0000i 0.703842i −0.936030 0.351921i \(-0.885529\pi\)
0.936030 0.351921i \(-0.114471\pi\)
\(978\) 4.00000 + 4.00000i 0.127906 + 0.127906i
\(979\) 14.0000 0.447442
\(980\) 0 0
\(981\) 13.0000 13.0000i 0.415058 0.415058i
\(982\) 10.0000 0.319113
\(983\) 24.0000i 0.765481i −0.923856 0.382741i \(-0.874980\pi\)
0.923856 0.382741i \(-0.125020\pi\)
\(984\) 2.00000i 0.0637577i
\(985\) 0 0
\(986\) 20.0000 + 20.0000i 0.636930 + 0.636930i
\(987\) 4.00000 + 4.00000i 0.127321 + 0.127321i
\(988\) 15.0000 3.00000i 0.477214 0.0954427i
\(989\) 50.0000i 1.58991i
\(990\) 0 0
\(991\) −8.00000 −0.254128 −0.127064 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 1.00000 + 1.00000i 0.0317500 + 0.0317500i
\(993\) −18.0000 −0.571213
\(994\) 2.00000 + 2.00000i 0.0634361 + 0.0634361i
\(995\) 0 0
\(996\) −6.00000 6.00000i −0.190117 0.190117i
\(997\) 17.0000 17.0000i 0.538395 0.538395i −0.384662 0.923057i \(-0.625682\pi\)
0.923057 + 0.384662i \(0.125682\pi\)
\(998\) −23.0000 + 23.0000i −0.728052 + 0.728052i
\(999\) −32.0000 + 32.0000i −1.01244 + 1.01244i
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 650.2.j.d.343.1 2
5.2 odd 4 650.2.g.b.57.1 2
5.3 odd 4 130.2.g.c.57.1 2
5.4 even 2 130.2.j.b.83.1 yes 2
13.8 odd 4 650.2.g.b.593.1 2
15.8 even 4 1170.2.m.a.577.1 2
15.14 odd 2 1170.2.w.c.343.1 2
20.3 even 4 1040.2.bg.f.577.1 2
20.19 odd 2 1040.2.cd.e.993.1 2
65.8 even 4 130.2.j.b.47.1 yes 2
65.34 odd 4 130.2.g.c.73.1 yes 2
65.47 even 4 inner 650.2.j.d.307.1 2
195.8 odd 4 1170.2.w.c.307.1 2
195.164 even 4 1170.2.m.a.73.1 2
260.99 even 4 1040.2.bg.f.593.1 2
260.203 odd 4 1040.2.cd.e.177.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.2.g.c.57.1 2 5.3 odd 4
130.2.g.c.73.1 yes 2 65.34 odd 4
130.2.j.b.47.1 yes 2 65.8 even 4
130.2.j.b.83.1 yes 2 5.4 even 2
650.2.g.b.57.1 2 5.2 odd 4
650.2.g.b.593.1 2 13.8 odd 4
650.2.j.d.307.1 2 65.47 even 4 inner
650.2.j.d.343.1 2 1.1 even 1 trivial
1040.2.bg.f.577.1 2 20.3 even 4
1040.2.bg.f.593.1 2 260.99 even 4
1040.2.cd.e.177.1 2 260.203 odd 4
1040.2.cd.e.993.1 2 20.19 odd 2
1170.2.m.a.73.1 2 195.164 even 4
1170.2.m.a.577.1 2 15.8 even 4
1170.2.w.c.307.1 2 195.8 odd 4
1170.2.w.c.343.1 2 15.14 odd 2