Properties

Label 1170.2.m.a.577.1
Level $1170$
Weight $2$
Character 1170.577
Analytic conductor $9.342$
Analytic rank $1$
Dimension $2$
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1170,2,Mod(73,1170)] 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("1170.73"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,-2,0,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(1\)
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: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 130)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 577.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.577
Dual form 1170.2.m.a.73.1

$q$-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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -2.00000i q^{7} -1.00000 q^{8} +(1.00000 + 2.00000i) q^{10} +(-1.00000 - 1.00000i) q^{11} +(-3.00000 - 2.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(-5.00000 + 5.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(-1.00000 - 2.00000i) q^{20} +(1.00000 + 1.00000i) q^{22} +(5.00000 + 5.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(3.00000 + 2.00000i) q^{26} -2.00000i q^{28} -4.00000i q^{29} +(1.00000 - 1.00000i) q^{31} -1.00000 q^{32} +(5.00000 - 5.00000i) q^{34} +(-4.00000 + 2.00000i) q^{35} +8.00000i q^{37} +(3.00000 + 3.00000i) q^{38} +(1.00000 + 2.00000i) q^{40} +(-1.00000 + 1.00000i) q^{41} +(5.00000 + 5.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(-5.00000 - 5.00000i) q^{46} +2.00000i q^{47} +3.00000 q^{49} +(3.00000 - 4.00000i) q^{50} +(-3.00000 - 2.00000i) q^{52} +(1.00000 - 1.00000i) q^{53} +(-1.00000 + 3.00000i) q^{55} +2.00000i q^{56} +4.00000i q^{58} +(-3.00000 + 3.00000i) q^{59} +2.00000 q^{61} +(-1.00000 + 1.00000i) q^{62} +1.00000 q^{64} +(-1.00000 + 8.00000i) q^{65} -12.0000 q^{67} +(-5.00000 + 5.00000i) q^{68} +(4.00000 - 2.00000i) q^{70} +(-1.00000 + 1.00000i) q^{71} -6.00000 q^{73} -8.00000i q^{74} +(-3.00000 - 3.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} +14.0000i q^{79} +(-1.00000 - 2.00000i) q^{80} +(1.00000 - 1.00000i) q^{82} -6.00000i q^{83} +(15.0000 + 5.00000i) q^{85} +(-5.00000 - 5.00000i) q^{86} +(1.00000 + 1.00000i) q^{88} +(7.00000 - 7.00000i) q^{89} +(-4.00000 + 6.00000i) q^{91} +(5.00000 + 5.00000i) q^{92} -2.00000i q^{94} +(-3.00000 + 9.00000i) q^{95} -2.00000 q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 2 q^{8} + 2 q^{10} - 2 q^{11} - 6 q^{13} + 2 q^{16} - 10 q^{17} - 6 q^{19} - 2 q^{20} + 2 q^{22} + 10 q^{23} - 6 q^{25} + 6 q^{26} + 2 q^{31} - 2 q^{32} + 10 q^{34} - 8 q^{35}+ \cdots - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) 0 0
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.00000 + 2.00000i 0.316228 + 0.632456i
\(11\) −1.00000 1.00000i −0.301511 0.301511i 0.540094 0.841605i \(-0.318389\pi\)
−0.841605 + 0.540094i \(0.818389\pi\)
\(12\) 0 0
\(13\) −3.00000 2.00000i −0.832050 0.554700i
\(14\) 2.00000i 0.534522i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −5.00000 + 5.00000i −1.21268 + 1.21268i −0.242536 + 0.970143i \(0.577979\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 0 0
\(19\) −3.00000 3.00000i −0.688247 0.688247i 0.273597 0.961844i \(-0.411786\pi\)
−0.961844 + 0.273597i \(0.911786\pi\)
\(20\) −1.00000 2.00000i −0.223607 0.447214i
\(21\) 0 0
\(22\) 1.00000 + 1.00000i 0.213201 + 0.213201i
\(23\) 5.00000 + 5.00000i 1.04257 + 1.04257i 0.999053 + 0.0435195i \(0.0138571\pi\)
0.0435195 + 0.999053i \(0.486143\pi\)
\(24\) 0 0
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 3.00000 + 2.00000i 0.588348 + 0.392232i
\(27\) 0 0
\(28\) 2.00000i 0.377964i
\(29\) 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 \(0.209465\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 5.00000 5.00000i 0.857493 0.857493i
\(35\) −4.00000 + 2.00000i −0.676123 + 0.338062i
\(36\) 0 0
\(37\) 8.00000i 1.31519i 0.753371 + 0.657596i \(0.228427\pi\)
−0.753371 + 0.657596i \(0.771573\pi\)
\(38\) 3.00000 + 3.00000i 0.486664 + 0.486664i
\(39\) 0 0
\(40\) 1.00000 + 2.00000i 0.158114 + 0.316228i
\(41\) −1.00000 + 1.00000i −0.156174 + 0.156174i −0.780869 0.624695i \(-0.785223\pi\)
0.624695 + 0.780869i \(0.285223\pi\)
\(42\) 0 0
\(43\) 5.00000 + 5.00000i 0.762493 + 0.762493i 0.976772 0.214280i \(-0.0687403\pi\)
−0.214280 + 0.976772i \(0.568740\pi\)
\(44\) −1.00000 1.00000i −0.150756 0.150756i
\(45\) 0 0
\(46\) −5.00000 5.00000i −0.737210 0.737210i
\(47\) 2.00000i 0.291730i 0.989305 + 0.145865i \(0.0465965\pi\)
−0.989305 + 0.145865i \(0.953403\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 3.00000 4.00000i 0.424264 0.565685i
\(51\) 0 0
\(52\) −3.00000 2.00000i −0.416025 0.277350i
\(53\) 1.00000 1.00000i 0.137361 0.137361i −0.635083 0.772444i \(-0.719034\pi\)
0.772444 + 0.635083i \(0.219034\pi\)
\(54\) 0 0
\(55\) −1.00000 + 3.00000i −0.134840 + 0.404520i
\(56\) 2.00000i 0.267261i
\(57\) 0 0
\(58\) 4.00000i 0.525226i
\(59\) −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
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.00000 + 8.00000i −0.124035 + 0.992278i
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) −5.00000 + 5.00000i −0.606339 + 0.606339i
\(69\) 0 0
\(70\) 4.00000 2.00000i 0.478091 0.239046i
\(71\) −1.00000 + 1.00000i −0.118678 + 0.118678i −0.763952 0.645273i \(-0.776743\pi\)
0.645273 + 0.763952i \(0.276743\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 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
\(78\) 0 0
\(79\) 14.0000i 1.57512i 0.616236 + 0.787562i \(0.288657\pi\)
−0.616236 + 0.787562i \(0.711343\pi\)
\(80\) −1.00000 2.00000i −0.111803 0.223607i
\(81\) 0 0
\(82\) 1.00000 1.00000i 0.110432 0.110432i
\(83\) 6.00000i 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) 0 0
\(85\) 15.0000 + 5.00000i 1.62698 + 0.542326i
\(86\) −5.00000 5.00000i −0.539164 0.539164i
\(87\) 0 0
\(88\) 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
\(93\) 0 0
\(94\) 2.00000i 0.206284i
\(95\) −3.00000 + 9.00000i −0.307794 + 0.923381i
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −5.00000 5.00000i −0.492665 0.492665i 0.416480 0.909145i \(-0.363264\pi\)
−0.909145 + 0.416480i \(0.863264\pi\)
\(104\) 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 −0.952632 0.304125i \(-0.901636\pi\)
−0.304125 0.952632i \(-0.598364\pi\)
\(108\) 0 0
\(109\) −13.0000 13.0000i −1.24517 1.24517i −0.957826 0.287348i \(-0.907226\pi\)
−0.287348 0.957826i \(-0.592774\pi\)
\(110\) 1.00000 3.00000i 0.0953463 0.286039i
\(111\) 0 0
\(112\) 2.00000i 0.188982i
\(113\) −9.00000 + 9.00000i −0.846649 + 0.846649i −0.989713 0.143065i \(-0.954304\pi\)
0.143065 + 0.989713i \(0.454304\pi\)
\(114\) 0 0
\(115\) 5.00000 15.0000i 0.466252 1.39876i
\(116\) 4.00000i 0.371391i
\(117\) 0 0
\(118\) 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
\(122\) −2.00000 −0.181071
\(123\) 0 0
\(124\) 1.00000 1.00000i 0.0898027 0.0898027i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 0 0
\(127\) −15.0000 + 15.0000i −1.33103 + 1.33103i −0.426589 + 0.904445i \(0.640285\pi\)
−0.904445 + 0.426589i \(0.859715\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 1.00000 8.00000i 0.0877058 0.701646i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) −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
\(137\) 12.0000i 1.02523i 0.858619 + 0.512615i \(0.171323\pi\)
−0.858619 + 0.512615i \(0.828677\pi\)
\(138\) 0 0
\(139\) 14.0000i 1.18746i 0.804663 + 0.593732i \(0.202346\pi\)
−0.804663 + 0.593732i \(0.797654\pi\)
\(140\) −4.00000 + 2.00000i −0.338062 + 0.169031i
\(141\) 0 0
\(142\) 1.00000 1.00000i 0.0839181 0.0839181i
\(143\) 1.00000 + 5.00000i 0.0836242 + 0.418121i
\(144\) 0 0
\(145\) −8.00000 + 4.00000i −0.664364 + 0.332182i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 8.00000i 0.657596i
\(149\) 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
\(153\) 0 0
\(154\) 2.00000 2.00000i 0.161165 0.161165i
\(155\) −3.00000 1.00000i −0.240966 0.0803219i
\(156\) 0 0
\(157\) 3.00000 + 3.00000i 0.239426 + 0.239426i 0.816612 0.577186i \(-0.195849\pi\)
−0.577186 + 0.816612i \(0.695849\pi\)
\(158\) 14.0000i 1.11378i
\(159\) 0 0
\(160\) 1.00000 + 2.00000i 0.0790569 + 0.158114i
\(161\) 10.0000 10.0000i 0.788110 0.788110i
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −1.00000 + 1.00000i −0.0780869 + 0.0780869i
\(165\) 0 0
\(166\) 6.00000i 0.465690i
\(167\) 2.00000i 0.154765i 0.997001 + 0.0773823i \(0.0246562\pi\)
−0.997001 + 0.0773823i \(0.975344\pi\)
\(168\) 0 0
\(169\) 5.00000 + 12.0000i 0.384615 + 0.923077i
\(170\) −15.0000 5.00000i −1.15045 0.383482i
\(171\) 0 0
\(172\) 5.00000 + 5.00000i 0.381246 + 0.381246i
\(173\) −15.0000 15.0000i −1.14043 1.14043i −0.988372 0.152057i \(-0.951410\pi\)
−0.152057 0.988372i \(-0.548590\pi\)
\(174\) 0 0
\(175\) 8.00000 + 6.00000i 0.604743 + 0.453557i
\(176\) −1.00000 1.00000i −0.0753778 0.0753778i
\(177\) 0 0
\(178\) −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 \(-0.266738\pi\)
\(182\) 4.00000 6.00000i 0.296500 0.444750i
\(183\) 0 0
\(184\) −5.00000 5.00000i −0.368605 0.368605i
\(185\) 16.0000 8.00000i 1.17634 0.588172i
\(186\) 0 0
\(187\) 10.0000 0.731272
\(188\) 2.00000i 0.145865i
\(189\) 0 0
\(190\) 3.00000 9.00000i 0.217643 0.652929i
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 3.00000 4.00000i 0.212132 0.282843i
\(201\) 0 0
\(202\) 0 0
\(203\) −8.00000 −0.561490
\(204\) 0 0
\(205\) 3.00000 + 1.00000i 0.209529 + 0.0698430i
\(206\) 5.00000 + 5.00000i 0.348367 + 0.348367i
\(207\) 0 0
\(208\) −3.00000 2.00000i −0.208013 0.138675i
\(209\) 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
\(213\) 0 0
\(214\) 13.0000 + 13.0000i 0.888662 + 0.888662i
\(215\) 5.00000 15.0000i 0.340997 1.02299i
\(216\) 0 0
\(217\) −2.00000 2.00000i −0.135769 0.135769i
\(218\) 13.0000 + 13.0000i 0.880471 + 0.880471i
\(219\) 0 0
\(220\) −1.00000 + 3.00000i −0.0674200 + 0.202260i
\(221\) 25.0000 5.00000i 1.68168 0.336336i
\(222\) 0 0
\(223\) 6.00000i 0.401790i 0.979613 + 0.200895i \(0.0643850\pi\)
−0.979613 + 0.200895i \(0.935615\pi\)
\(224\) 2.00000i 0.133631i
\(225\) 0 0
\(226\) 9.00000 9.00000i 0.598671 0.598671i
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 0 0
\(229\) 3.00000 3.00000i 0.198246 0.198246i −0.601002 0.799248i \(-0.705232\pi\)
0.799248 + 0.601002i \(0.205232\pi\)
\(230\) −5.00000 + 15.0000i −0.329690 + 0.989071i
\(231\) 0 0
\(232\) 4.00000i 0.262613i
\(233\) −5.00000 5.00000i −0.327561 0.327561i 0.524097 0.851658i \(-0.324403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 0 0
\(235\) 4.00000 2.00000i 0.260931 0.130466i
\(236\) −3.00000 + 3.00000i −0.195283 + 0.195283i
\(237\) 0 0
\(238\) −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 \(0.735496\pi\)
\(242\) 9.00000i 0.578542i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −3.00000 6.00000i −0.191663 0.383326i
\(246\) 0 0
\(247\) 3.00000 + 15.0000i 0.190885 + 0.954427i
\(248\) −1.00000 + 1.00000i −0.0635001 + 0.0635001i
\(249\) 0 0
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) 30.0000i 1.89358i −0.321847 0.946792i \(-0.604304\pi\)
0.321847 0.946792i \(-0.395696\pi\)
\(252\) 0 0
\(253\) 10.0000i 0.628695i
\(254\) 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 \(-0.519869\pi\)
0.998053 + 0.0623783i \(0.0198685\pi\)
\(258\) 0 0
\(259\) 16.0000 0.994192
\(260\) −1.00000 + 8.00000i −0.0620174 + 0.496139i
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) −9.00000 + 9.00000i −0.554964 + 0.554964i −0.927869 0.372906i \(-0.878362\pi\)
0.372906 + 0.927869i \(0.378362\pi\)
\(264\) 0 0
\(265\) −3.00000 1.00000i −0.184289 0.0614295i
\(266\) 6.00000 6.00000i 0.367884 0.367884i
\(267\) 0 0
\(268\) −12.0000 −0.733017
\(269\) 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
\(273\) 0 0
\(274\) 12.0000i 0.724947i
\(275\) 7.00000 1.00000i 0.422116 0.0603023i
\(276\) 0 0
\(277\) −5.00000 + 5.00000i −0.300421 + 0.300421i −0.841178 0.540758i \(-0.818138\pi\)
0.540758 + 0.841178i \(0.318138\pi\)
\(278\) 14.0000i 0.839664i
\(279\) 0 0
\(280\) 4.00000 2.00000i 0.239046 0.119523i
\(281\) −21.0000 21.0000i −1.25275 1.25275i −0.954480 0.298275i \(-0.903589\pi\)
−0.298275 0.954480i \(-0.596411\pi\)
\(282\) 0 0
\(283\) −15.0000 15.0000i −0.891657 0.891657i 0.103022 0.994679i \(-0.467149\pi\)
−0.994679 + 0.103022i \(0.967149\pi\)
\(284\) −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
\(288\) 0 0
\(289\) 33.0000i 1.94118i
\(290\) 8.00000 4.00000i 0.469776 0.234888i
\(291\) 0 0
\(292\) −6.00000 −0.351123
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 0 0
\(295\) 9.00000 + 3.00000i 0.524000 + 0.174667i
\(296\) 8.00000i 0.464991i
\(297\) 0 0
\(298\) −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
\(305\) −2.00000 4.00000i −0.114520 0.229039i
\(306\) 0 0
\(307\) 2.00000i 0.114146i −0.998370 0.0570730i \(-0.981823\pi\)
0.998370 0.0570730i \(-0.0181768\pi\)
\(308\) −2.00000 + 2.00000i −0.113961 + 0.113961i
\(309\) 0 0
\(310\) 3.00000 + 1.00000i 0.170389 + 0.0567962i
\(311\) 10.0000i 0.567048i 0.958965 + 0.283524i \(0.0915036\pi\)
−0.958965 + 0.283524i \(0.908496\pi\)
\(312\) 0 0
\(313\) 9.00000 9.00000i 0.508710 0.508710i −0.405420 0.914130i \(-0.632875\pi\)
0.914130 + 0.405420i \(0.132875\pi\)
\(314\) −3.00000 3.00000i −0.169300 0.169300i
\(315\) 0 0
\(316\) 14.0000i 0.787562i
\(317\) 2.00000 0.112331 0.0561656 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) 0 0
\(319\) −4.00000 + 4.00000i −0.223957 + 0.223957i
\(320\) −1.00000 2.00000i −0.0559017 0.111803i
\(321\) 0 0
\(322\) −10.0000 + 10.0000i −0.557278 + 0.557278i
\(323\) 30.0000 1.66924
\(324\) 0 0
\(325\) 17.0000 6.00000i 0.942990 0.332820i
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) 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 \(0.363749\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 0 0
\(334\) 2.00000i 0.109435i
\(335\) 12.0000 + 24.0000i 0.655630 + 1.31126i
\(336\) 0 0
\(337\) 5.00000 5.00000i 0.272367 0.272367i −0.557685 0.830053i \(-0.688310\pi\)
0.830053 + 0.557685i \(0.188310\pi\)
\(338\) −5.00000 12.0000i −0.271964 0.652714i
\(339\) 0 0
\(340\) 15.0000 + 5.00000i 0.813489 + 0.271163i
\(341\) −2.00000 −0.108306
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) −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 0.869577 0.493797i \(-0.164392\pi\)
−0.493797 + 0.869577i \(0.664392\pi\)
\(348\) 0 0
\(349\) 3.00000 3.00000i 0.160586 0.160586i −0.622240 0.782826i \(-0.713777\pi\)
0.782826 + 0.622240i \(0.213777\pi\)
\(350\) −8.00000 6.00000i −0.427618 0.320713i
\(351\) 0 0
\(352\) 1.00000 + 1.00000i 0.0533002 + 0.0533002i
\(353\) 16.0000i 0.851594i −0.904819 0.425797i \(-0.859994\pi\)
0.904819 0.425797i \(-0.140006\pi\)
\(354\) 0 0
\(355\) 3.00000 + 1.00000i 0.159223 + 0.0530745i
\(356\) 7.00000 7.00000i 0.370999 0.370999i
\(357\) 0 0
\(358\) 20.0000 1.05703
\(359\) −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
\(362\) 20.0000i 1.05118i
\(363\) 0 0
\(364\) −4.00000 + 6.00000i −0.209657 + 0.314485i
\(365\) 6.00000 + 12.0000i 0.314054 + 0.628109i
\(366\) 0 0
\(367\) 3.00000 + 3.00000i 0.156599 + 0.156599i 0.781058 0.624459i \(-0.214680\pi\)
−0.624459 + 0.781058i \(0.714680\pi\)
\(368\) 5.00000 + 5.00000i 0.260643 + 0.260643i
\(369\) 0 0
\(370\) −16.0000 + 8.00000i −0.831800 + 0.415900i
\(371\) −2.00000 2.00000i −0.103835 0.103835i
\(372\) 0 0
\(373\) −1.00000 + 1.00000i −0.0517780 + 0.0517780i −0.732522 0.680744i \(-0.761657\pi\)
0.680744 + 0.732522i \(0.261657\pi\)
\(374\) −10.0000 −0.517088
\(375\) 0 0
\(376\) 2.00000i 0.103142i
\(377\) −8.00000 + 12.0000i −0.412021 + 0.618031i
\(378\) 0 0
\(379\) 17.0000 + 17.0000i 0.873231 + 0.873231i 0.992823 0.119592i \(-0.0381586\pi\)
−0.119592 + 0.992823i \(0.538159\pi\)
\(380\) −3.00000 + 9.00000i −0.153897 + 0.461690i
\(381\) 0 0
\(382\) −8.00000 −0.409316
\(383\) 6.00000i 0.306586i −0.988181 0.153293i \(-0.951012\pi\)
0.988181 0.153293i \(-0.0489878\pi\)
\(384\) 0 0
\(385\) 6.00000 + 2.00000i 0.305788 + 0.101929i
\(386\) −14.0000 −0.712581
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) 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
\(392\) −3.00000 −0.151523
\(393\) 0 0
\(394\) 18.0000 0.906827
\(395\) 28.0000 14.0000i 1.40883 0.704416i
\(396\) 0 0
\(397\) 8.00000i 0.401508i 0.979642 + 0.200754i \(0.0643393\pi\)
−0.979642 + 0.200754i \(0.935661\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) −1.00000 1.00000i −0.0499376 0.0499376i 0.681697 0.731635i \(-0.261242\pi\)
−0.731635 + 0.681697i \(0.761242\pi\)
\(402\) 0 0
\(403\) −5.00000 + 1.00000i −0.249068 + 0.0498135i
\(404\) 0 0
\(405\) 0 0
\(406\) 8.00000 0.397033
\(407\) 8.00000 8.00000i 0.396545 0.396545i
\(408\) 0 0
\(409\) −3.00000 3.00000i −0.148340 0.148340i 0.629036 0.777376i \(-0.283450\pi\)
−0.777376 + 0.629036i \(0.783450\pi\)
\(410\) −3.00000 1.00000i −0.148159 0.0493865i
\(411\) 0 0
\(412\) −5.00000 5.00000i −0.246332 0.246332i
\(413\) 6.00000 + 6.00000i 0.295241 + 0.295241i
\(414\) 0 0
\(415\) −12.0000 + 6.00000i −0.589057 + 0.294528i
\(416\) 3.00000 + 2.00000i 0.147087 + 0.0980581i
\(417\) 0 0
\(418\) 6.00000i 0.293470i
\(419\) 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 \(0.350383\pi\)
\(422\) −12.0000 −0.584151
\(423\) 0 0
\(424\) −1.00000 + 1.00000i −0.0485643 + 0.0485643i
\(425\) −5.00000 35.0000i −0.242536 1.69775i
\(426\) 0 0
\(427\) 4.00000i 0.193574i
\(428\) −13.0000 13.0000i −0.628379 0.628379i
\(429\) 0 0
\(430\) −5.00000 + 15.0000i −0.241121 + 0.723364i
\(431\) −21.0000 + 21.0000i −1.01153 + 1.01153i −0.0116017 + 0.999933i \(0.503693\pi\)
−0.999933 + 0.0116017i \(0.996307\pi\)
\(432\) 0 0
\(433\) −15.0000 15.0000i −0.720854 0.720854i 0.247925 0.968779i \(-0.420251\pi\)
−0.968779 + 0.247925i \(0.920251\pi\)
\(434\) 2.00000 + 2.00000i 0.0960031 + 0.0960031i
\(435\) 0 0
\(436\) −13.0000 13.0000i −0.622587 0.622587i
\(437\) 30.0000i 1.43509i
\(438\) 0 0
\(439\) 40.0000 1.90910 0.954548 0.298057i \(-0.0963387\pi\)
0.954548 + 0.298057i \(0.0963387\pi\)
\(440\) 1.00000 3.00000i 0.0476731 0.143019i
\(441\) 0 0
\(442\) −25.0000 + 5.00000i −1.18913 + 0.237826i
\(443\) −19.0000 + 19.0000i −0.902717 + 0.902717i −0.995670 0.0929532i \(-0.970369\pi\)
0.0929532 + 0.995670i \(0.470369\pi\)
\(444\) 0 0
\(445\) −21.0000 7.00000i −0.995495 0.331832i
\(446\) 6.00000i 0.284108i
\(447\) 0 0
\(448\) 2.00000i 0.0944911i
\(449\) 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
\(453\) 0 0
\(454\) −12.0000 −0.563188
\(455\) 16.0000 + 2.00000i 0.750092 + 0.0937614i
\(456\) 0 0
\(457\) 38.0000 1.77757 0.888783 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) −3.00000 + 3.00000i −0.140181 + 0.140181i
\(459\) 0 0
\(460\) 5.00000 15.0000i 0.233126 0.699379i
\(461\) −11.0000 + 11.0000i −0.512321 + 0.512321i −0.915237 0.402916i \(-0.867997\pi\)
0.402916 + 0.915237i \(0.367997\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 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 \(-0.697688\pi\)
0.813265 + 0.581893i \(0.197688\pi\)
\(468\) 0 0
\(469\) 24.0000i 1.10822i
\(470\) −4.00000 + 2.00000i −0.184506 + 0.0922531i
\(471\) 0 0
\(472\) 3.00000 3.00000i 0.138086 0.138086i
\(473\) 10.0000i 0.459800i
\(474\) 0 0
\(475\) 21.0000 3.00000i 0.963546 0.137649i
\(476\) 10.0000 + 10.0000i 0.458349 + 0.458349i
\(477\) 0 0
\(478\) 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
\(483\) 0 0
\(484\) 9.00000i 0.409091i
\(485\) 2.00000 + 4.00000i 0.0908153 + 0.181631i
\(486\) 0 0
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 0 0
\(490\) 3.00000 + 6.00000i 0.135526 + 0.271052i
\(491\) 10.0000i 0.451294i 0.974209 + 0.225647i \(0.0724495\pi\)
−0.974209 + 0.225647i \(0.927550\pi\)
\(492\) 0 0
\(493\) 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
\(498\) 0 0
\(499\) −23.0000 23.0000i −1.02962 1.02962i −0.999548 0.0300737i \(-0.990426\pi\)
−0.0300737 0.999548i \(-0.509574\pi\)
\(500\) 11.0000 + 2.00000i 0.491935 + 0.0894427i
\(501\) 0 0
\(502\) 30.0000i 1.33897i
\(503\) −9.00000 + 9.00000i −0.401290 + 0.401290i −0.878688 0.477397i \(-0.841580\pi\)
0.477397 + 0.878688i \(0.341580\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 10.0000i 0.444554i
\(507\) 0 0
\(508\) −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
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −15.0000 + 15.0000i −0.661622 + 0.661622i
\(515\) −5.00000 + 15.0000i −0.220326 + 0.660979i
\(516\) 0 0
\(517\) 2.00000 2.00000i 0.0879599 0.0879599i
\(518\) −16.0000 −0.703000
\(519\) 0 0
\(520\) 1.00000 8.00000i 0.0438529 0.350823i
\(521\) −22.0000 −0.963837 −0.481919 0.876216i \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) −21.0000 + 21.0000i −0.918266 + 0.918266i −0.996903 0.0786374i \(-0.974943\pi\)
0.0786374 + 0.996903i \(0.474943\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 9.00000 9.00000i 0.392419 0.392419i
\(527\) 10.0000i 0.435607i
\(528\) 0 0
\(529\) 27.0000i 1.17391i
\(530\) 3.00000 + 1.00000i 0.130312 + 0.0434372i
\(531\) 0 0
\(532\) −6.00000 + 6.00000i −0.260133 + 0.260133i
\(533\) 5.00000 1.00000i 0.216574 0.0433148i
\(534\) 0 0
\(535\) −13.0000 + 39.0000i −0.562039 + 1.68612i
\(536\) 12.0000 0.518321
\(537\) 0 0
\(538\) 16.0000i 0.689809i
\(539\) −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
\(543\) 0 0
\(544\) 5.00000 5.00000i 0.214373 0.214373i
\(545\) −13.0000 + 39.0000i −0.556859 + 1.67058i
\(546\) 0 0
\(547\) −7.00000 7.00000i −0.299298 0.299298i 0.541441 0.840739i \(-0.317879\pi\)
−0.840739 + 0.541441i \(0.817879\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 0 0
\(550\) −7.00000 + 1.00000i −0.298481 + 0.0426401i
\(551\) −12.0000 + 12.0000i −0.511217 + 0.511217i
\(552\) 0 0
\(553\) 28.0000 1.19068
\(554\) 5.00000 5.00000i 0.212430 0.212430i
\(555\) 0 0
\(556\) 14.0000i 0.593732i
\(557\) 8.00000i 0.338971i −0.985533 0.169485i \(-0.945789\pi\)
0.985533 0.169485i \(-0.0542106\pi\)
\(558\) 0 0
\(559\) −5.00000 25.0000i −0.211477 1.05739i
\(560\) −4.00000 + 2.00000i −0.169031 + 0.0845154i
\(561\) 0 0
\(562\) 21.0000 + 21.0000i 0.885832 + 0.885832i
\(563\) −5.00000 5.00000i −0.210725 0.210725i 0.593851 0.804575i \(-0.297607\pi\)
−0.804575 + 0.593851i \(0.797607\pi\)
\(564\) 0 0
\(565\) 27.0000 + 9.00000i 1.13590 + 0.378633i
\(566\) 15.0000 + 15.0000i 0.630497 + 0.630497i
\(567\) 0 0
\(568\) 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 \(-0.0671001\pi\)
\(572\) 1.00000 + 5.00000i 0.0418121 + 0.209061i
\(573\) 0 0
\(574\) −2.00000 2.00000i −0.0834784 0.0834784i
\(575\) −35.0000 + 5.00000i −1.45960 + 0.208514i
\(576\) 0 0
\(577\) −22.0000 −0.915872 −0.457936 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) 33.0000i 1.37262i
\(579\) 0 0
\(580\) −8.00000 + 4.00000i −0.332182 + 0.166091i
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) −2.00000 −0.0828315
\(584\) 6.00000 0.248282
\(585\) 0 0
\(586\) −26.0000 −1.07405
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) −6.00000 −0.247226
\(590\) −9.00000 3.00000i −0.370524 0.123508i
\(591\) 0 0
\(592\) 8.00000i 0.328798i
\(593\) −14.0000 −0.574911 −0.287456 0.957794i \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) 0 0
\(595\) 10.0000 30.0000i 0.409960 1.22988i
\(596\) 13.0000 + 13.0000i 0.532501 + 0.532501i
\(597\) 0 0
\(598\) 5.00000 + 25.0000i 0.204465 + 1.02233i
\(599\) 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
\(603\) 0 0
\(604\) −9.00000 9.00000i −0.366205 0.366205i
\(605\) −18.0000 + 9.00000i −0.731804 + 0.365902i
\(606\) 0 0
\(607\) 3.00000 + 3.00000i 0.121766 + 0.121766i 0.765364 0.643598i \(-0.222559\pi\)
−0.643598 + 0.765364i \(0.722559\pi\)
\(608\) 3.00000 + 3.00000i 0.121666 + 0.121666i
\(609\) 0 0
\(610\) 2.00000 + 4.00000i 0.0809776 + 0.161955i
\(611\) 4.00000 6.00000i 0.161823 0.242734i
\(612\) 0 0
\(613\) 4.00000i 0.161558i −0.996732 0.0807792i \(-0.974259\pi\)
0.996732 0.0807792i \(-0.0257409\pi\)
\(614\) 2.00000i 0.0807134i
\(615\) 0 0
\(616\) 2.00000 2.00000i 0.0805823 0.0805823i
\(617\) −38.0000 −1.52982 −0.764911 0.644136i \(-0.777217\pi\)
−0.764911 + 0.644136i \(0.777217\pi\)
\(618\) 0 0
\(619\) 3.00000 3.00000i 0.120580 0.120580i −0.644242 0.764822i \(-0.722827\pi\)
0.764822 + 0.644242i \(0.222827\pi\)
\(620\) −3.00000 1.00000i −0.120483 0.0401610i
\(621\) 0 0
\(622\) 10.0000i 0.400963i
\(623\) −14.0000 14.0000i −0.560898 0.560898i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) −9.00000 + 9.00000i −0.359712 + 0.359712i
\(627\) 0 0
\(628\) 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 \(0.649790\pi\)
\(632\) 14.0000i 0.556890i
\(633\) 0 0
\(634\) −2.00000 −0.0794301
\(635\) 45.0000 + 15.0000i 1.78577 + 0.595257i
\(636\) 0 0
\(637\) −9.00000 6.00000i −0.356593 0.237729i
\(638\) 4.00000 4.00000i 0.158362 0.158362i
\(639\) 0 0
\(640\) 1.00000 + 2.00000i 0.0395285 + 0.0790569i
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 46.0000i 1.81406i 0.421063 + 0.907031i \(0.361657\pi\)
−0.421063 + 0.907031i \(0.638343\pi\)
\(644\) 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 \(-0.794388\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(648\) 0 0
\(649\) 6.00000 0.235521
\(650\) −17.0000 + 6.00000i −0.666795 + 0.235339i
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) 21.0000 21.0000i 0.821794 0.821794i −0.164572 0.986365i \(-0.552624\pi\)
0.986365 + 0.164572i \(0.0526242\pi\)
\(654\) 0 0
\(655\) 12.0000 + 24.0000i 0.468879 + 0.937758i
\(656\) −1.00000 + 1.00000i −0.0390434 + 0.0390434i
\(657\) 0 0
\(658\) −4.00000 −0.155936
\(659\) 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
\(663\) 0 0
\(664\) 6.00000i 0.232845i
\(665\) 18.0000 + 6.00000i 0.698010 + 0.232670i
\(666\) 0 0
\(667\) 20.0000 20.0000i 0.774403 0.774403i
\(668\) 2.00000i 0.0773823i
\(669\) 0 0
\(670\) −12.0000 24.0000i −0.463600 0.927201i
\(671\) −2.00000 2.00000i −0.0772091 0.0772091i
\(672\) 0 0
\(673\) 5.00000 + 5.00000i 0.192736 + 0.192736i 0.796877 0.604141i \(-0.206484\pi\)
−0.604141 + 0.796877i \(0.706484\pi\)
\(674\) −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 0.109973 0.993935i \(-0.464924\pi\)
−0.993935 + 0.109973i \(0.964924\pi\)
\(678\) 0 0
\(679\) 4.00000i 0.153506i
\(680\) −15.0000 5.00000i −0.575224 0.191741i
\(681\) 0 0
\(682\) 2.00000 0.0765840
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 24.0000 12.0000i 0.916993 0.458496i
\(686\) 20.0000i 0.763604i
\(687\) 0 0
\(688\) 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
\(693\) 0 0
\(694\) −7.00000 7.00000i −0.265716 0.265716i
\(695\) 28.0000 14.0000i 1.06210 0.531050i
\(696\) 0 0
\(697\) 10.0000i 0.378777i
\(698\) −3.00000 + 3.00000i −0.113552 + 0.113552i
\(699\) 0 0
\(700\) 8.00000 + 6.00000i 0.302372 + 0.226779i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 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
\(708\) 0 0
\(709\) 3.00000 3.00000i 0.112667 0.112667i −0.648526 0.761193i \(-0.724614\pi\)
0.761193 + 0.648526i \(0.224614\pi\)
\(710\) −3.00000 1.00000i −0.112588 0.0375293i
\(711\) 0 0
\(712\) −7.00000 + 7.00000i −0.262336 + 0.262336i
\(713\) 10.0000 0.374503
\(714\) 0 0
\(715\) 9.00000 7.00000i 0.336581 0.261785i
\(716\) −20.0000 −0.747435
\(717\) 0 0
\(718\) 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
\(722\) 1.00000i 0.0372161i
\(723\) 0 0
\(724\) 20.0000i 0.743294i
\(725\) 16.0000 + 12.0000i 0.594225 + 0.445669i
\(726\) 0 0
\(727\) −35.0000 + 35.0000i −1.29808 + 1.29808i −0.368418 + 0.929660i \(0.620100\pi\)
−0.929660 + 0.368418i \(0.879900\pi\)
\(728\) 4.00000 6.00000i 0.148250 0.222375i
\(729\) 0 0
\(730\) −6.00000 12.0000i −0.222070 0.444140i
\(731\) −50.0000 −1.84932
\(732\) 0 0
\(733\) 44.0000i 1.62518i −0.582838 0.812589i \(-0.698058\pi\)
0.582838 0.812589i \(-0.301942\pi\)
\(734\) −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
\(738\) 0 0
\(739\) −37.0000 + 37.0000i −1.36107 + 1.36107i −0.488507 + 0.872560i \(0.662458\pi\)
−0.872560 + 0.488507i \(0.837542\pi\)
\(740\) 16.0000 8.00000i 0.588172 0.294086i
\(741\) 0 0
\(742\) 2.00000 + 2.00000i 0.0734223 + 0.0734223i
\(743\) 6.00000i 0.220119i −0.993925 0.110059i \(-0.964896\pi\)
0.993925 0.110059i \(-0.0351041\pi\)
\(744\) 0 0
\(745\) 13.0000 39.0000i 0.476283 1.42885i
\(746\) 1.00000 1.00000i 0.0366126 0.0366126i
\(747\) 0 0
\(748\) 10.0000 0.365636
\(749\) −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 \(-0.0584036\pi\)
\(752\) 2.00000i 0.0729325i
\(753\) 0 0
\(754\) 8.00000 12.0000i 0.291343 0.437014i
\(755\) −9.00000 + 27.0000i −0.327544 + 0.982631i
\(756\) 0 0
\(757\) −17.0000 17.0000i −0.617876 0.617876i 0.327111 0.944986i \(-0.393925\pi\)
−0.944986 + 0.327111i \(0.893925\pi\)
\(758\) −17.0000 17.0000i −0.617468 0.617468i
\(759\) 0 0
\(760\) 3.00000 9.00000i 0.108821 0.326464i
\(761\) 19.0000 + 19.0000i 0.688749 + 0.688749i 0.961956 0.273206i \(-0.0880841\pi\)
−0.273206 + 0.961956i \(0.588084\pi\)
\(762\) 0 0
\(763\) −26.0000 + 26.0000i −0.941263 + 0.941263i
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 6.00000i 0.216789i
\(767\) 15.0000 3.00000i 0.541619 0.108324i
\(768\) 0 0
\(769\) −23.0000 23.0000i −0.829401 0.829401i 0.158033 0.987434i \(-0.449485\pi\)
−0.987434 + 0.158033i \(0.949485\pi\)
\(770\) −6.00000 2.00000i −0.216225 0.0720750i
\(771\) 0 0
\(772\) 14.0000 0.503871
\(773\) 24.0000i 0.863220i 0.902060 + 0.431610i \(0.142054\pi\)
−0.902060 + 0.431610i \(0.857946\pi\)
\(774\) 0 0
\(775\) 1.00000 + 7.00000i 0.0359211 + 0.251447i
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) −10.0000 −0.358517
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) 2.00000 0.0715656
\(782\) 50.0000 1.78800
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) 3.00000 9.00000i 0.107075 0.321224i
\(786\) 0 0
\(787\) 42.0000i 1.49714i −0.663057 0.748569i \(-0.730741\pi\)
0.663057 0.748569i \(-0.269259\pi\)
\(788\) −18.0000 −0.641223
\(789\) 0 0
\(790\) −28.0000 + 14.0000i −0.996195 + 0.498098i
\(791\) 18.0000 + 18.0000i 0.640006 + 0.640006i
\(792\) 0 0
\(793\) −6.00000 4.00000i −0.213066 0.142044i
\(794\) 8.00000i 0.283909i
\(795\) 0 0
\(796\) 0 0
\(797\) 5.00000 5.00000i 0.177109 0.177109i −0.612985 0.790094i \(-0.710032\pi\)
0.790094 + 0.612985i \(0.210032\pi\)
\(798\) 0 0
\(799\) −10.0000 10.0000i −0.353775 0.353775i
\(800\) 3.00000 4.00000i 0.106066 0.141421i
\(801\) 0 0
\(802\) 1.00000 + 1.00000i 0.0353112 + 0.0353112i
\(803\) 6.00000 + 6.00000i 0.211735 + 0.211735i
\(804\) 0 0
\(805\) −30.0000 10.0000i −1.05736 0.352454i
\(806\) 5.00000 1.00000i 0.176117 0.0352235i
\(807\) 0 0
\(808\) 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 \(0.161942\pi\)
\(812\) −8.00000 −0.280745
\(813\) 0 0
\(814\) −8.00000 + 8.00000i −0.280400 + 0.280400i
\(815\) −4.00000 8.00000i −0.140114 0.280228i
\(816\) 0 0
\(817\) 30.0000i 1.04957i
\(818\) 3.00000 + 3.00000i 0.104893 + 0.104893i
\(819\) 0 0
\(820\) 3.00000 + 1.00000i 0.104765 + 0.0349215i
\(821\) 29.0000 29.0000i 1.01211 1.01211i 0.0121812 0.999926i \(-0.496123\pi\)
0.999926 0.0121812i \(-0.00387748\pi\)
\(822\) 0 0
\(823\) 15.0000 + 15.0000i 0.522867 + 0.522867i 0.918436 0.395569i \(-0.129453\pi\)
−0.395569 + 0.918436i \(0.629453\pi\)
\(824\) 5.00000 + 5.00000i 0.174183 + 0.174183i
\(825\) 0 0
\(826\) −6.00000 6.00000i −0.208767 0.208767i
\(827\) 2.00000i 0.0695468i 0.999395 + 0.0347734i \(0.0110710\pi\)
−0.999395 + 0.0347734i \(0.988929\pi\)
\(828\) 0 0
\(829\) −30.0000 −1.04194 −0.520972 0.853574i \(-0.674430\pi\)
−0.520972 + 0.853574i \(0.674430\pi\)
\(830\) 12.0000 6.00000i 0.416526 0.208263i
\(831\) 0 0
\(832\) −3.00000 2.00000i −0.104006 0.0693375i
\(833\) −15.0000 + 15.0000i −0.519719 + 0.519719i
\(834\) 0 0
\(835\) 4.00000 2.00000i 0.138426 0.0692129i
\(836\) 6.00000i 0.207514i
\(837\) 0 0
\(838\) 26.0000i 0.898155i
\(839\) −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
\(843\) 0 0
\(844\) 12.0000 0.413057
\(845\) 19.0000 22.0000i 0.653620 0.756823i
\(846\) 0 0
\(847\) −18.0000 −0.618487
\(848\) 1.00000 1.00000i 0.0343401 0.0343401i
\(849\) 0 0
\(850\) 5.00000 + 35.0000i 0.171499 + 1.20049i
\(851\) −40.0000 + 40.0000i −1.37118 + 1.37118i
\(852\) 0 0
\(853\) −26.0000 −0.890223 −0.445112 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 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 \(-0.788537\pi\)
0.616533 + 0.787329i \(0.288537\pi\)
\(858\) 0 0
\(859\) 26.0000i 0.887109i −0.896248 0.443554i \(-0.853717\pi\)
0.896248 0.443554i \(-0.146283\pi\)
\(860\) 5.00000 15.0000i 0.170499 0.511496i
\(861\) 0 0
\(862\) 21.0000 21.0000i 0.715263 0.715263i
\(863\) 46.0000i 1.56586i −0.622111 0.782929i \(-0.713725\pi\)
0.622111 0.782929i \(-0.286275\pi\)
\(864\) 0 0
\(865\) −15.0000 + 45.0000i −0.510015 + 1.53005i
\(866\) 15.0000 + 15.0000i 0.509721 + 0.509721i
\(867\) 0 0
\(868\) −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
\(873\) 0 0
\(874\) 30.0000i 1.01477i
\(875\) 4.00000 22.0000i 0.135225 0.743736i
\(876\) 0 0
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) −40.0000 −1.34993
\(879\) 0 0
\(880\) −1.00000 + 3.00000i −0.0337100 + 0.101130i
\(881\) 20.0000i 0.673817i −0.941537 0.336909i \(-0.890619\pi\)
0.941537 0.336909i \(-0.109381\pi\)
\(882\) 0 0
\(883\) 5.00000 + 5.00000i 0.168263 + 0.168263i 0.786216 0.617952i \(-0.212037\pi\)
−0.617952 + 0.786216i \(0.712037\pi\)
\(884\) 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 0.206238 0.978502i \(-0.433878\pi\)
−0.978502 + 0.206238i \(0.933878\pi\)
\(888\) 0 0
\(889\) 30.0000 + 30.0000i 1.00617 + 1.00617i
\(890\) 21.0000 + 7.00000i 0.703922 + 0.234641i
\(891\) 0 0
\(892\) 6.00000i 0.200895i
\(893\) 6.00000 6.00000i 0.200782 0.200782i
\(894\) 0 0
\(895\) 20.0000 + 40.0000i 0.668526 + 1.33705i
\(896\) 2.00000i 0.0668153i
\(897\) 0 0
\(898\) −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
\(902\) −2.00000 −0.0665927
\(903\) 0 0
\(904\) 9.00000 9.00000i 0.299336 0.299336i
\(905\) −40.0000 + 20.0000i −1.32964 + 0.664822i
\(906\) 0 0
\(907\) 35.0000 35.0000i 1.16216 1.16216i 0.178153 0.984003i \(-0.442988\pi\)
0.984003 0.178153i \(-0.0570122\pi\)
\(908\) 12.0000 0.398234
\(909\) 0 0
\(910\) −16.0000 2.00000i −0.530395 0.0662994i
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) 0 0
\(913\) −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
\(917\) 24.0000i 0.792550i
\(918\) 0 0
\(919\) 14.0000i 0.461817i 0.972975 + 0.230909i \(0.0741699\pi\)
−0.972975 + 0.230909i \(0.925830\pi\)
\(920\) −5.00000 + 15.0000i −0.164845 + 0.494535i
\(921\) 0 0
\(922\) 11.0000 11.0000i 0.362266 0.362266i
\(923\) 5.00000 1.00000i 0.164577 0.0329154i
\(924\) 0 0
\(925\) −32.0000 24.0000i −1.05215 0.789115i
\(926\) 16.0000 0.525793
\(927\) 0 0
\(928\) 4.00000i 0.131306i
\(929\) −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
\(933\) 0 0
\(934\) −5.00000 + 5.00000i −0.163605 + 0.163605i
\(935\) −10.0000 20.0000i −0.327035 0.654070i
\(936\) 0 0
\(937\) 33.0000 + 33.0000i 1.07806 + 1.07806i 0.996683 + 0.0813798i \(0.0259327\pi\)
0.0813798 + 0.996683i \(0.474067\pi\)
\(938\) 24.0000i 0.783628i
\(939\) 0 0
\(940\) 4.00000 2.00000i 0.130466 0.0652328i
\(941\) 29.0000 29.0000i 0.945373 0.945373i −0.0532103 0.998583i \(-0.516945\pi\)
0.998583 + 0.0532103i \(0.0169454\pi\)
\(942\) 0 0
\(943\) −10.0000 −0.325645
\(944\) −3.00000 + 3.00000i −0.0976417 + 0.0976417i
\(945\) 0 0
\(946\) 10.0000i 0.325128i
\(947\) 38.0000i 1.23483i −0.786636 0.617417i \(-0.788179\pi\)
0.786636 0.617417i \(-0.211821\pi\)
\(948\) 0 0
\(949\) 18.0000 + 12.0000i 0.584305 + 0.389536i
\(950\) −21.0000 + 3.00000i −0.681330 + 0.0973329i
\(951\) 0 0
\(952\) −10.0000 10.0000i −0.324102 0.324102i
\(953\) 35.0000 + 35.0000i 1.13376 + 1.13376i 0.989546 + 0.144215i \(0.0460656\pi\)
0.144215 + 0.989546i \(0.453934\pi\)
\(954\) 0 0
\(955\) −8.00000 16.0000i −0.258874 0.517748i
\(956\) −7.00000 7.00000i −0.226396 0.226396i
\(957\) 0 0
\(958\) 13.0000 13.0000i 0.420011 0.420011i
\(959\) 24.0000 0.775000
\(960\) 0 0
\(961\) 29.0000i 0.935484i
\(962\) −16.0000 + 24.0000i −0.515861 + 0.773791i
\(963\) 0 0
\(964\) 1.00000 + 1.00000i 0.0322078 + 0.0322078i
\(965\) −14.0000 28.0000i −0.450676 0.901352i
\(966\) 0 0
\(967\) 48.0000 1.54358 0.771788 0.635880i \(-0.219363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(968\) 9.00000i 0.289271i
\(969\) 0 0
\(970\) −2.00000 4.00000i −0.0642161 0.128432i
\(971\) −12.0000 −0.385098 −0.192549 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 0 0
\(973\) 28.0000 0.897639
\(974\) 32.0000 1.02535
\(975\) 0 0
\(976\) 2.00000 0.0640184
\(977\) 22.0000 0.703842 0.351921 0.936030i \(-0.385529\pi\)
0.351921 + 0.936030i \(0.385529\pi\)
\(978\) 0 0
\(979\) −14.0000 −0.447442
\(980\) −3.00000 6.00000i −0.0958315 0.191663i
\(981\) 0 0
\(982\) 10.0000i 0.319113i
\(983\) −24.0000 −0.765481 −0.382741 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 0 0
\(985\) 18.0000 + 36.0000i 0.573528 + 1.14706i
\(986\) −20.0000 20.0000i −0.636930 0.636930i
\(987\) 0 0
\(988\) 3.00000 + 15.0000i 0.0954427 + 0.477214i
\(989\) 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
\(993\) 0 0
\(994\) −2.00000 2.00000i −0.0634361 0.0634361i
\(995\) 0 0
\(996\) 0 0
\(997\) −17.0000 17.0000i −0.538395 0.538395i 0.384662 0.923057i \(-0.374318\pi\)
−0.923057 + 0.384662i \(0.874318\pi\)
\(998\) 23.0000 + 23.0000i 0.728052 + 0.728052i
\(999\) 0 0
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 1170.2.m.a.577.1 2
3.2 odd 2 130.2.g.c.57.1 2
5.3 odd 4 1170.2.w.c.343.1 2
12.11 even 2 1040.2.bg.f.577.1 2
13.8 odd 4 1170.2.w.c.307.1 2
15.2 even 4 650.2.j.d.343.1 2
15.8 even 4 130.2.j.b.83.1 yes 2
15.14 odd 2 650.2.g.b.57.1 2
39.8 even 4 130.2.j.b.47.1 yes 2
60.23 odd 4 1040.2.cd.e.993.1 2
65.8 even 4 inner 1170.2.m.a.73.1 2
156.47 odd 4 1040.2.cd.e.177.1 2
195.8 odd 4 130.2.g.c.73.1 yes 2
195.47 odd 4 650.2.g.b.593.1 2
195.164 even 4 650.2.j.d.307.1 2
780.203 even 4 1040.2.bg.f.593.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.2.g.c.57.1 2 3.2 odd 2
130.2.g.c.73.1 yes 2 195.8 odd 4
130.2.j.b.47.1 yes 2 39.8 even 4
130.2.j.b.83.1 yes 2 15.8 even 4
650.2.g.b.57.1 2 15.14 odd 2
650.2.g.b.593.1 2 195.47 odd 4
650.2.j.d.307.1 2 195.164 even 4
650.2.j.d.343.1 2 15.2 even 4
1040.2.bg.f.577.1 2 12.11 even 2
1040.2.bg.f.593.1 2 780.203 even 4
1040.2.cd.e.177.1 2 156.47 odd 4
1040.2.cd.e.993.1 2 60.23 odd 4
1170.2.m.a.73.1 2 65.8 even 4 inner
1170.2.m.a.577.1 2 1.1 even 1 trivial
1170.2.w.c.307.1 2 13.8 odd 4
1170.2.w.c.343.1 2 5.3 odd 4