Properties

Label 1134.2.k.d.647.4
Level $1134$
Weight $2$
Character 1134.647
Analytic conductor $9.055$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(647,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.647");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.k (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + 16903 x^{8} - 23292 x^{7} + 26994 x^{6} - 25716 x^{5} + 19962 x^{4} + \cdots + 225 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 647.4
Root \(0.500000 + 1.97090i\) of defining polynomial
Character \(\chi\) \(=\) 1134.647
Dual form 1134.2.k.d.971.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.08560 + 3.61236i) q^{5} +(1.94402 - 1.79465i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.08560 + 3.61236i) q^{5} +(1.94402 - 1.79465i) q^{7} +1.00000i q^{8} +(-3.61236 - 2.08560i) q^{10} +(0.0814333 + 0.0470156i) q^{11} -3.79497i q^{13} +(-0.786244 + 2.52623i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.82627 - 6.62729i) q^{17} +(6.77624 - 3.91226i) q^{19} +4.17119 q^{20} -0.0940311 q^{22} +(3.31685 - 1.91499i) q^{23} +(-6.19941 + 10.7377i) q^{25} +(1.89748 + 3.28654i) q^{26} +(-0.582206 - 2.58090i) q^{28} -2.03174i q^{29} +(-1.45596 - 0.840596i) q^{31} +(0.866025 + 0.500000i) q^{32} +7.65254i q^{34} +(10.5374 + 3.27958i) q^{35} +(-2.18343 - 3.78182i) q^{37} +(-3.91226 + 6.77624i) q^{38} +(-3.61236 + 2.08560i) q^{40} -3.07145 q^{41} -5.12790 q^{43} +(0.0814333 - 0.0470156i) q^{44} +(-1.91499 + 3.31685i) q^{46} +(2.54960 + 4.41603i) q^{47} +(0.558434 - 6.97769i) q^{49} -12.3988i q^{50} +(-3.28654 - 1.89748i) q^{52} +(-6.05506 - 3.49589i) q^{53} +0.392222i q^{55} +(1.79465 + 1.94402i) q^{56} +(1.01587 + 1.75954i) q^{58} +(-5.21303 + 9.02922i) q^{59} +(2.69902 - 1.55828i) q^{61} +1.68119 q^{62} -1.00000 q^{64} +(13.7088 - 7.91477i) q^{65} +(-3.76669 + 6.52409i) q^{67} +(-3.82627 - 6.62729i) q^{68} +(-10.7654 + 2.42849i) q^{70} +8.61322i q^{71} +(-0.129966 - 0.0750360i) q^{73} +(3.78182 + 2.18343i) q^{74} -7.82452i q^{76} +(0.242685 - 0.0547454i) q^{77} +(6.48425 + 11.2311i) q^{79} +(2.08560 - 3.61236i) q^{80} +(2.65995 - 1.53573i) q^{82} -2.58840 q^{83} +31.9202 q^{85} +(4.44089 - 2.56395i) q^{86} +(-0.0470156 + 0.0814333i) q^{88} +(1.37123 + 2.37504i) q^{89} +(-6.81065 - 7.37750i) q^{91} -3.82997i q^{92} +(-4.41603 - 2.54960i) q^{94} +(28.2650 + 16.3188i) q^{95} +4.06398i q^{97} +(3.00523 + 6.32207i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 2.08560 + 3.61236i 0.932707 + 1.61550i 0.778673 + 0.627429i \(0.215893\pi\)
0.154033 + 0.988066i \(0.450774\pi\)
\(6\) 0 0
\(7\) 1.94402 1.79465i 0.734771 0.678315i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −3.61236 2.08560i −1.14233 0.659523i
\(11\) 0.0814333 + 0.0470156i 0.0245531 + 0.0141757i 0.512226 0.858851i \(-0.328821\pi\)
−0.487673 + 0.873026i \(0.662154\pi\)
\(12\) 0 0
\(13\) 3.79497i 1.05253i −0.850319 0.526267i \(-0.823591\pi\)
0.850319 0.526267i \(-0.176409\pi\)
\(14\) −0.786244 + 2.52623i −0.210133 + 0.675162i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.82627 6.62729i 0.928006 1.60735i 0.141353 0.989959i \(-0.454855\pi\)
0.786654 0.617395i \(-0.211812\pi\)
\(18\) 0 0
\(19\) 6.77624 3.91226i 1.55458 0.897534i 0.556815 0.830636i \(-0.312023\pi\)
0.997760 0.0668980i \(-0.0213102\pi\)
\(20\) 4.17119 0.932707
\(21\) 0 0
\(22\) −0.0940311 −0.0200475
\(23\) 3.31685 1.91499i 0.691612 0.399302i −0.112604 0.993640i \(-0.535919\pi\)
0.804216 + 0.594338i \(0.202586\pi\)
\(24\) 0 0
\(25\) −6.19941 + 10.7377i −1.23988 + 2.14754i
\(26\) 1.89748 + 3.28654i 0.372127 + 0.644543i
\(27\) 0 0
\(28\) −0.582206 2.58090i −0.110027 0.487744i
\(29\) 2.03174i 0.377285i −0.982046 0.188642i \(-0.939591\pi\)
0.982046 0.188642i \(-0.0604087\pi\)
\(30\) 0 0
\(31\) −1.45596 0.840596i −0.261497 0.150976i 0.363520 0.931586i \(-0.381575\pi\)
−0.625017 + 0.780611i \(0.714908\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 7.65254i 1.31240i
\(35\) 10.5374 + 3.27958i 1.78114 + 0.554349i
\(36\) 0 0
\(37\) −2.18343 3.78182i −0.358954 0.621727i 0.628832 0.777541i \(-0.283533\pi\)
−0.987786 + 0.155814i \(0.950200\pi\)
\(38\) −3.91226 + 6.77624i −0.634653 + 1.09925i
\(39\) 0 0
\(40\) −3.61236 + 2.08560i −0.571164 + 0.329762i
\(41\) −3.07145 −0.479680 −0.239840 0.970812i \(-0.577095\pi\)
−0.239840 + 0.970812i \(0.577095\pi\)
\(42\) 0 0
\(43\) −5.12790 −0.781997 −0.390999 0.920391i \(-0.627870\pi\)
−0.390999 + 0.920391i \(0.627870\pi\)
\(44\) 0.0814333 0.0470156i 0.0122765 0.00708786i
\(45\) 0 0
\(46\) −1.91499 + 3.31685i −0.282349 + 0.489044i
\(47\) 2.54960 + 4.41603i 0.371897 + 0.644145i 0.989857 0.142065i \(-0.0453741\pi\)
−0.617960 + 0.786209i \(0.712041\pi\)
\(48\) 0 0
\(49\) 0.558434 6.97769i 0.0797763 0.996813i
\(50\) 12.3988i 1.75346i
\(51\) 0 0
\(52\) −3.28654 1.89748i −0.455761 0.263134i
\(53\) −6.05506 3.49589i −0.831726 0.480197i 0.0227173 0.999742i \(-0.492768\pi\)
−0.854443 + 0.519545i \(0.826102\pi\)
\(54\) 0 0
\(55\) 0.392222i 0.0528872i
\(56\) 1.79465 + 1.94402i 0.239821 + 0.259781i
\(57\) 0 0
\(58\) 1.01587 + 1.75954i 0.133390 + 0.231039i
\(59\) −5.21303 + 9.02922i −0.678678 + 1.17550i 0.296701 + 0.954970i \(0.404114\pi\)
−0.975379 + 0.220535i \(0.929220\pi\)
\(60\) 0 0
\(61\) 2.69902 1.55828i 0.345574 0.199517i −0.317160 0.948372i \(-0.602729\pi\)
0.662734 + 0.748855i \(0.269396\pi\)
\(62\) 1.68119 0.213512
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 13.7088 7.91477i 1.70036 0.981706i
\(66\) 0 0
\(67\) −3.76669 + 6.52409i −0.460174 + 0.797045i −0.998969 0.0453920i \(-0.985546\pi\)
0.538795 + 0.842437i \(0.318880\pi\)
\(68\) −3.82627 6.62729i −0.464003 0.803677i
\(69\) 0 0
\(70\) −10.7654 + 2.42849i −1.28671 + 0.290260i
\(71\) 8.61322i 1.02220i 0.859521 + 0.511100i \(0.170762\pi\)
−0.859521 + 0.511100i \(0.829238\pi\)
\(72\) 0 0
\(73\) −0.129966 0.0750360i −0.0152114 0.00878230i 0.492375 0.870383i \(-0.336129\pi\)
−0.507586 + 0.861601i \(0.669462\pi\)
\(74\) 3.78182 + 2.18343i 0.439628 + 0.253819i
\(75\) 0 0
\(76\) 7.82452i 0.897534i
\(77\) 0.242685 0.0547454i 0.0276565 0.00623882i
\(78\) 0 0
\(79\) 6.48425 + 11.2311i 0.729535 + 1.26359i 0.957080 + 0.289825i \(0.0935970\pi\)
−0.227544 + 0.973768i \(0.573070\pi\)
\(80\) 2.08560 3.61236i 0.233177 0.403874i
\(81\) 0 0
\(82\) 2.65995 1.53573i 0.293743 0.169592i
\(83\) −2.58840 −0.284114 −0.142057 0.989858i \(-0.545372\pi\)
−0.142057 + 0.989858i \(0.545372\pi\)
\(84\) 0 0
\(85\) 31.9202 3.46223
\(86\) 4.44089 2.56395i 0.478873 0.276478i
\(87\) 0 0
\(88\) −0.0470156 + 0.0814333i −0.00501188 + 0.00868082i
\(89\) 1.37123 + 2.37504i 0.145350 + 0.251754i 0.929504 0.368813i \(-0.120236\pi\)
−0.784153 + 0.620567i \(0.786902\pi\)
\(90\) 0 0
\(91\) −6.81065 7.37750i −0.713950 0.773372i
\(92\) 3.82997i 0.399302i
\(93\) 0 0
\(94\) −4.41603 2.54960i −0.455479 0.262971i
\(95\) 28.2650 + 16.3188i 2.89992 + 1.67427i
\(96\) 0 0
\(97\) 4.06398i 0.412634i 0.978485 + 0.206317i \(0.0661479\pi\)
−0.978485 + 0.206317i \(0.933852\pi\)
\(98\) 3.00523 + 6.32207i 0.303574 + 0.638626i
\(99\) 0 0
\(100\) 6.19941 + 10.7377i 0.619941 + 1.07377i
\(101\) −6.16567 + 10.6793i −0.613507 + 1.06263i 0.377137 + 0.926157i \(0.376908\pi\)
−0.990644 + 0.136468i \(0.956425\pi\)
\(102\) 0 0
\(103\) −1.57103 + 0.907035i −0.154798 + 0.0893728i −0.575398 0.817873i \(-0.695153\pi\)
0.420600 + 0.907246i \(0.361820\pi\)
\(104\) 3.79497 0.372127
\(105\) 0 0
\(106\) 6.99178 0.679101
\(107\) 2.70445 1.56142i 0.261449 0.150948i −0.363546 0.931576i \(-0.618434\pi\)
0.624996 + 0.780628i \(0.285101\pi\)
\(108\) 0 0
\(109\) 1.12213 1.94358i 0.107480 0.186161i −0.807269 0.590184i \(-0.799055\pi\)
0.914749 + 0.404023i \(0.132388\pi\)
\(110\) −0.196111 0.339674i −0.0186984 0.0323866i
\(111\) 0 0
\(112\) −2.52623 0.786244i −0.238706 0.0742931i
\(113\) 3.58148i 0.336917i 0.985709 + 0.168458i \(0.0538789\pi\)
−0.985709 + 0.168458i \(0.946121\pi\)
\(114\) 0 0
\(115\) 13.8352 + 7.98778i 1.29014 + 0.744864i
\(116\) −1.75954 1.01587i −0.163369 0.0943212i
\(117\) 0 0
\(118\) 10.4261i 0.959796i
\(119\) −4.45535 19.7504i −0.408421 1.81052i
\(120\) 0 0
\(121\) −5.49558 9.51862i −0.499598 0.865329i
\(122\) −1.55828 + 2.69902i −0.141080 + 0.244358i
\(123\) 0 0
\(124\) −1.45596 + 0.840596i −0.130749 + 0.0754878i
\(125\) −30.8619 −2.76037
\(126\) 0 0
\(127\) 9.49968 0.842960 0.421480 0.906838i \(-0.361511\pi\)
0.421480 + 0.906838i \(0.361511\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −7.91477 + 13.7088i −0.694171 + 1.20234i
\(131\) 1.51601 + 2.62581i 0.132455 + 0.229418i 0.924622 0.380886i \(-0.124381\pi\)
−0.792168 + 0.610304i \(0.791047\pi\)
\(132\) 0 0
\(133\) 6.15199 19.7665i 0.533445 1.71397i
\(134\) 7.53337i 0.650784i
\(135\) 0 0
\(136\) 6.62729 + 3.82627i 0.568285 + 0.328100i
\(137\) −3.82389 2.20773i −0.326697 0.188619i 0.327677 0.944790i \(-0.393734\pi\)
−0.654374 + 0.756171i \(0.727068\pi\)
\(138\) 0 0
\(139\) 1.32729i 0.112579i −0.998414 0.0562896i \(-0.982073\pi\)
0.998414 0.0562896i \(-0.0179270\pi\)
\(140\) 8.10888 7.48584i 0.685326 0.632669i
\(141\) 0 0
\(142\) −4.30661 7.45926i −0.361403 0.625968i
\(143\) 0.178423 0.309037i 0.0149204 0.0258430i
\(144\) 0 0
\(145\) 7.33937 4.23739i 0.609502 0.351896i
\(146\) 0.150072 0.0124200
\(147\) 0 0
\(148\) −4.36687 −0.358954
\(149\) −9.16722 + 5.29269i −0.751008 + 0.433594i −0.826058 0.563585i \(-0.809422\pi\)
0.0750503 + 0.997180i \(0.476088\pi\)
\(150\) 0 0
\(151\) 3.86400 6.69264i 0.314448 0.544639i −0.664872 0.746957i \(-0.731514\pi\)
0.979320 + 0.202318i \(0.0648474\pi\)
\(152\) 3.91226 + 6.77624i 0.317326 + 0.549625i
\(153\) 0 0
\(154\) −0.182798 + 0.168753i −0.0147303 + 0.0135985i
\(155\) 7.01257i 0.563264i
\(156\) 0 0
\(157\) −3.37019 1.94578i −0.268970 0.155290i 0.359449 0.933165i \(-0.382965\pi\)
−0.628419 + 0.777875i \(0.716298\pi\)
\(158\) −11.2311 6.48425i −0.893495 0.515859i
\(159\) 0 0
\(160\) 4.17119i 0.329762i
\(161\) 3.01130 9.67538i 0.237323 0.762527i
\(162\) 0 0
\(163\) 8.82699 + 15.2888i 0.691383 + 1.19751i 0.971385 + 0.237511i \(0.0763317\pi\)
−0.280002 + 0.960000i \(0.590335\pi\)
\(164\) −1.53573 + 2.65995i −0.119920 + 0.207708i
\(165\) 0 0
\(166\) 2.24162 1.29420i 0.173984 0.100450i
\(167\) −16.3967 −1.26881 −0.634407 0.772999i \(-0.718756\pi\)
−0.634407 + 0.772999i \(0.718756\pi\)
\(168\) 0 0
\(169\) −1.40178 −0.107829
\(170\) −27.6437 + 15.9601i −2.12017 + 1.22408i
\(171\) 0 0
\(172\) −2.56395 + 4.44089i −0.195499 + 0.338615i
\(173\) 3.92819 + 6.80383i 0.298655 + 0.517286i 0.975829 0.218538i \(-0.0701287\pi\)
−0.677173 + 0.735823i \(0.736795\pi\)
\(174\) 0 0
\(175\) 7.21867 + 32.0001i 0.545680 + 2.41898i
\(176\) 0.0940311i 0.00708786i
\(177\) 0 0
\(178\) −2.37504 1.37123i −0.178017 0.102778i
\(179\) 15.7884 + 9.11541i 1.18008 + 0.681318i 0.956032 0.293261i \(-0.0947406\pi\)
0.224044 + 0.974579i \(0.428074\pi\)
\(180\) 0 0
\(181\) 14.2290i 1.05763i 0.848736 + 0.528817i \(0.177364\pi\)
−0.848736 + 0.528817i \(0.822636\pi\)
\(182\) 9.58695 + 2.98377i 0.710632 + 0.221172i
\(183\) 0 0
\(184\) 1.91499 + 3.31685i 0.141175 + 0.244522i
\(185\) 9.10752 15.7747i 0.669598 1.15978i
\(186\) 0 0
\(187\) 0.623171 0.359788i 0.0455708 0.0263103i
\(188\) 5.09920 0.371897
\(189\) 0 0
\(190\) −32.6376 −2.36778
\(191\) −16.6452 + 9.61013i −1.20441 + 0.695365i −0.961532 0.274693i \(-0.911424\pi\)
−0.242875 + 0.970058i \(0.578091\pi\)
\(192\) 0 0
\(193\) −3.77817 + 6.54399i −0.271959 + 0.471046i −0.969363 0.245631i \(-0.921005\pi\)
0.697405 + 0.716678i \(0.254338\pi\)
\(194\) −2.03199 3.51951i −0.145888 0.252686i
\(195\) 0 0
\(196\) −5.76364 3.97246i −0.411689 0.283747i
\(197\) 2.10437i 0.149930i −0.997186 0.0749651i \(-0.976115\pi\)
0.997186 0.0749651i \(-0.0238845\pi\)
\(198\) 0 0
\(199\) 1.24340 + 0.717876i 0.0881421 + 0.0508889i 0.543423 0.839459i \(-0.317128\pi\)
−0.455281 + 0.890348i \(0.650461\pi\)
\(200\) −10.7377 6.19941i −0.759270 0.438365i
\(201\) 0 0
\(202\) 12.3313i 0.867630i
\(203\) −3.64627 3.94975i −0.255918 0.277218i
\(204\) 0 0
\(205\) −6.40580 11.0952i −0.447401 0.774921i
\(206\) 0.907035 1.57103i 0.0631961 0.109459i
\(207\) 0 0
\(208\) −3.28654 + 1.89748i −0.227880 + 0.131567i
\(209\) 0.735749 0.0508928
\(210\) 0 0
\(211\) −4.36800 −0.300706 −0.150353 0.988632i \(-0.548041\pi\)
−0.150353 + 0.988632i \(0.548041\pi\)
\(212\) −6.05506 + 3.49589i −0.415863 + 0.240099i
\(213\) 0 0
\(214\) −1.56142 + 2.70445i −0.106736 + 0.184873i
\(215\) −10.6947 18.5238i −0.729374 1.26331i
\(216\) 0 0
\(217\) −4.33899 + 0.978800i −0.294550 + 0.0664452i
\(218\) 2.24425i 0.152000i
\(219\) 0 0
\(220\) 0.339674 + 0.196111i 0.0229008 + 0.0132218i
\(221\) −25.1503 14.5206i −1.69180 0.976759i
\(222\) 0 0
\(223\) 17.2931i 1.15803i −0.815315 0.579017i \(-0.803436\pi\)
0.815315 0.579017i \(-0.196564\pi\)
\(224\) 2.58090 0.582206i 0.172444 0.0389002i
\(225\) 0 0
\(226\) −1.79074 3.10165i −0.119118 0.206319i
\(227\) −4.25063 + 7.36231i −0.282124 + 0.488653i −0.971908 0.235362i \(-0.924372\pi\)
0.689784 + 0.724016i \(0.257706\pi\)
\(228\) 0 0
\(229\) −21.0383 + 12.1465i −1.39025 + 0.802662i −0.993343 0.115196i \(-0.963250\pi\)
−0.396909 + 0.917858i \(0.629917\pi\)
\(230\) −15.9756 −1.05340
\(231\) 0 0
\(232\) 2.03174 0.133390
\(233\) 14.2442 8.22389i 0.933168 0.538765i 0.0453562 0.998971i \(-0.485558\pi\)
0.887812 + 0.460206i \(0.152224\pi\)
\(234\) 0 0
\(235\) −10.6349 + 18.4201i −0.693742 + 1.20160i
\(236\) 5.21303 + 9.02922i 0.339339 + 0.587752i
\(237\) 0 0
\(238\) 13.7337 + 14.8767i 0.890220 + 0.964312i
\(239\) 17.8574i 1.15510i −0.816356 0.577549i \(-0.804009\pi\)
0.816356 0.577549i \(-0.195991\pi\)
\(240\) 0 0
\(241\) 7.27380 + 4.19953i 0.468546 + 0.270515i 0.715631 0.698479i \(-0.246139\pi\)
−0.247085 + 0.968994i \(0.579473\pi\)
\(242\) 9.51862 + 5.49558i 0.611880 + 0.353269i
\(243\) 0 0
\(244\) 3.11656i 0.199517i
\(245\) 26.3706 12.5354i 1.68475 0.800856i
\(246\) 0 0
\(247\) −14.8469 25.7156i −0.944686 1.63624i
\(248\) 0.840596 1.45596i 0.0533779 0.0924533i
\(249\) 0 0
\(250\) 26.7272 15.4310i 1.69038 0.975940i
\(251\) −12.3552 −0.779850 −0.389925 0.920847i \(-0.627499\pi\)
−0.389925 + 0.920847i \(0.627499\pi\)
\(252\) 0 0
\(253\) 0.360137 0.0226416
\(254\) −8.22696 + 4.74984i −0.516206 + 0.298031i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.94605 + 12.0309i 0.433283 + 0.750468i 0.997154 0.0753950i \(-0.0240218\pi\)
−0.563871 + 0.825863i \(0.690688\pi\)
\(258\) 0 0
\(259\) −11.0317 3.43343i −0.685476 0.213343i
\(260\) 15.8295i 0.981706i
\(261\) 0 0
\(262\) −2.62581 1.51601i −0.162223 0.0936595i
\(263\) −9.51479 5.49337i −0.586707 0.338736i 0.177087 0.984195i \(-0.443333\pi\)
−0.763794 + 0.645460i \(0.776666\pi\)
\(264\) 0 0
\(265\) 29.1640i 1.79153i
\(266\) 4.55548 + 20.1943i 0.279314 + 1.23819i
\(267\) 0 0
\(268\) 3.76669 + 6.52409i 0.230087 + 0.398522i
\(269\) −10.0800 + 17.4590i −0.614585 + 1.06449i 0.375872 + 0.926672i \(0.377343\pi\)
−0.990457 + 0.137821i \(0.955990\pi\)
\(270\) 0 0
\(271\) −12.1106 + 6.99205i −0.735666 + 0.424737i −0.820491 0.571659i \(-0.806300\pi\)
0.0848253 + 0.996396i \(0.472967\pi\)
\(272\) −7.65254 −0.464003
\(273\) 0 0
\(274\) 4.41545 0.266747
\(275\) −1.00968 + 0.582938i −0.0608859 + 0.0351525i
\(276\) 0 0
\(277\) 9.47254 16.4069i 0.569150 0.985796i −0.427501 0.904015i \(-0.640606\pi\)
0.996650 0.0817810i \(-0.0260608\pi\)
\(278\) 0.663644 + 1.14947i 0.0398028 + 0.0689404i
\(279\) 0 0
\(280\) −3.27958 + 10.5374i −0.195992 + 0.629728i
\(281\) 6.12155i 0.365181i −0.983189 0.182591i \(-0.941552\pi\)
0.983189 0.182591i \(-0.0584483\pi\)
\(282\) 0 0
\(283\) 23.6497 + 13.6542i 1.40583 + 0.811657i 0.994983 0.100047i \(-0.0318993\pi\)
0.410848 + 0.911704i \(0.365233\pi\)
\(284\) 7.45926 + 4.30661i 0.442626 + 0.255550i
\(285\) 0 0
\(286\) 0.356845i 0.0211007i
\(287\) −5.97096 + 5.51219i −0.352455 + 0.325374i
\(288\) 0 0
\(289\) −20.7806 35.9931i −1.22239 2.11724i
\(290\) −4.23739 + 7.33937i −0.248828 + 0.430983i
\(291\) 0 0
\(292\) −0.129966 + 0.0750360i −0.00760569 + 0.00439115i
\(293\) −15.2713 −0.892158 −0.446079 0.894994i \(-0.647180\pi\)
−0.446079 + 0.894994i \(0.647180\pi\)
\(294\) 0 0
\(295\) −43.4890 −2.53203
\(296\) 3.78182 2.18343i 0.219814 0.126910i
\(297\) 0 0
\(298\) 5.29269 9.16722i 0.306598 0.531043i
\(299\) −7.26731 12.5874i −0.420280 0.727946i
\(300\) 0 0
\(301\) −9.96874 + 9.20280i −0.574589 + 0.530441i
\(302\) 7.72799i 0.444696i
\(303\) 0 0
\(304\) −6.77624 3.91226i −0.388644 0.224384i
\(305\) 11.2581 + 6.49988i 0.644638 + 0.372182i
\(306\) 0 0
\(307\) 28.9407i 1.65173i 0.563866 + 0.825866i \(0.309313\pi\)
−0.563866 + 0.825866i \(0.690687\pi\)
\(308\) 0.0739314 0.237544i 0.00421263 0.0135353i
\(309\) 0 0
\(310\) 3.50629 + 6.07307i 0.199144 + 0.344927i
\(311\) −3.22911 + 5.59299i −0.183106 + 0.317149i −0.942937 0.332972i \(-0.891949\pi\)
0.759830 + 0.650121i \(0.225282\pi\)
\(312\) 0 0
\(313\) 23.7283 13.6995i 1.34120 0.774344i 0.354220 0.935162i \(-0.384747\pi\)
0.986984 + 0.160818i \(0.0514132\pi\)
\(314\) 3.89155 0.219613
\(315\) 0 0
\(316\) 12.9685 0.729535
\(317\) −16.8167 + 9.70915i −0.944522 + 0.545320i −0.891375 0.453267i \(-0.850258\pi\)
−0.0531469 + 0.998587i \(0.516925\pi\)
\(318\) 0 0
\(319\) 0.0955235 0.165451i 0.00534829 0.00926350i
\(320\) −2.08560 3.61236i −0.116588 0.201937i
\(321\) 0 0
\(322\) 2.22983 + 9.88477i 0.124264 + 0.550857i
\(323\) 59.8774i 3.33167i
\(324\) 0 0
\(325\) 40.7492 + 23.5266i 2.26036 + 1.30502i
\(326\) −15.2888 8.82699i −0.846768 0.488882i
\(327\) 0 0
\(328\) 3.07145i 0.169592i
\(329\) 12.8817 + 4.00922i 0.710193 + 0.221035i
\(330\) 0 0
\(331\) −6.55931 11.3611i −0.360532 0.624460i 0.627516 0.778603i \(-0.284072\pi\)
−0.988048 + 0.154143i \(0.950738\pi\)
\(332\) −1.29420 + 2.24162i −0.0710286 + 0.123025i
\(333\) 0 0
\(334\) 14.2000 8.19835i 0.776987 0.448594i
\(335\) −31.4231 −1.71683
\(336\) 0 0
\(337\) 23.7311 1.29272 0.646359 0.763034i \(-0.276291\pi\)
0.646359 + 0.763034i \(0.276291\pi\)
\(338\) 1.21398 0.700889i 0.0660315 0.0381233i
\(339\) 0 0
\(340\) 15.9601 27.6437i 0.865557 1.49919i
\(341\) −0.0790422 0.136905i −0.00428038 0.00741383i
\(342\) 0 0
\(343\) −11.4369 14.5670i −0.617536 0.786542i
\(344\) 5.12790i 0.276478i
\(345\) 0 0
\(346\) −6.80383 3.92819i −0.365776 0.211181i
\(347\) −7.21858 4.16765i −0.387514 0.223731i 0.293568 0.955938i \(-0.405157\pi\)
−0.681082 + 0.732207i \(0.738490\pi\)
\(348\) 0 0
\(349\) 18.7486i 1.00359i −0.864987 0.501794i \(-0.832674\pi\)
0.864987 0.501794i \(-0.167326\pi\)
\(350\) −22.2516 24.1036i −1.18940 1.28839i
\(351\) 0 0
\(352\) 0.0470156 + 0.0814333i 0.00250594 + 0.00434041i
\(353\) 9.76869 16.9199i 0.519935 0.900554i −0.479797 0.877380i \(-0.659290\pi\)
0.999731 0.0231739i \(-0.00737714\pi\)
\(354\) 0 0
\(355\) −31.1140 + 17.9637i −1.65136 + 0.953413i
\(356\) 2.74246 0.145350
\(357\) 0 0
\(358\) −18.2308 −0.963529
\(359\) 14.3290 8.27288i 0.756258 0.436626i −0.0716925 0.997427i \(-0.522840\pi\)
0.827951 + 0.560801i \(0.189507\pi\)
\(360\) 0 0
\(361\) 21.1116 36.5663i 1.11114 1.92454i
\(362\) −7.11450 12.3227i −0.373930 0.647665i
\(363\) 0 0
\(364\) −9.79443 + 2.20945i −0.513367 + 0.115807i
\(365\) 0.625979i 0.0327652i
\(366\) 0 0
\(367\) 27.8308 + 16.0681i 1.45276 + 0.838749i 0.998637 0.0521924i \(-0.0166209\pi\)
0.454119 + 0.890941i \(0.349954\pi\)
\(368\) −3.31685 1.91499i −0.172903 0.0998256i
\(369\) 0 0
\(370\) 18.2150i 0.946955i
\(371\) −18.0451 + 4.07065i −0.936853 + 0.211338i
\(372\) 0 0
\(373\) 12.8677 + 22.2875i 0.666264 + 1.15400i 0.978941 + 0.204144i \(0.0654410\pi\)
−0.312677 + 0.949860i \(0.601226\pi\)
\(374\) −0.359788 + 0.623171i −0.0186042 + 0.0322234i
\(375\) 0 0
\(376\) −4.41603 + 2.54960i −0.227740 + 0.131485i
\(377\) −7.71039 −0.397105
\(378\) 0 0
\(379\) −36.3772 −1.86857 −0.934285 0.356527i \(-0.883961\pi\)
−0.934285 + 0.356527i \(0.883961\pi\)
\(380\) 28.2650 16.3188i 1.44996 0.837136i
\(381\) 0 0
\(382\) 9.61013 16.6452i 0.491697 0.851645i
\(383\) 12.5773 + 21.7845i 0.642670 + 1.11314i 0.984834 + 0.173497i \(0.0555066\pi\)
−0.342165 + 0.939640i \(0.611160\pi\)
\(384\) 0 0
\(385\) 0.703902 + 0.762487i 0.0358742 + 0.0388599i
\(386\) 7.55634i 0.384608i
\(387\) 0 0
\(388\) 3.51951 + 2.03199i 0.178676 + 0.103159i
\(389\) 8.39614 + 4.84752i 0.425701 + 0.245779i 0.697514 0.716571i \(-0.254290\pi\)
−0.271812 + 0.962350i \(0.587623\pi\)
\(390\) 0 0
\(391\) 29.3090i 1.48222i
\(392\) 6.97769 + 0.558434i 0.352427 + 0.0282052i
\(393\) 0 0
\(394\) 1.05219 + 1.82244i 0.0530083 + 0.0918131i
\(395\) −27.0471 + 46.8469i −1.36088 + 2.35712i
\(396\) 0 0
\(397\) −11.1844 + 6.45731i −0.561329 + 0.324083i −0.753679 0.657243i \(-0.771722\pi\)
0.192350 + 0.981326i \(0.438389\pi\)
\(398\) −1.43575 −0.0719677
\(399\) 0 0
\(400\) 12.3988 0.619941
\(401\) −24.9194 + 14.3872i −1.24442 + 0.718464i −0.969990 0.243144i \(-0.921821\pi\)
−0.274427 + 0.961608i \(0.588488\pi\)
\(402\) 0 0
\(403\) −3.19004 + 5.52530i −0.158907 + 0.275235i
\(404\) 6.16567 + 10.6793i 0.306754 + 0.531313i
\(405\) 0 0
\(406\) 5.13264 + 1.59745i 0.254729 + 0.0792799i
\(407\) 0.410622i 0.0203538i
\(408\) 0 0
\(409\) −28.7809 16.6167i −1.42312 0.821641i −0.426559 0.904460i \(-0.640274\pi\)
−0.996565 + 0.0828189i \(0.973608\pi\)
\(410\) 11.0952 + 6.40580i 0.547952 + 0.316360i
\(411\) 0 0
\(412\) 1.81407i 0.0893728i
\(413\) 6.07010 + 26.9086i 0.298690 + 1.32408i
\(414\) 0 0
\(415\) −5.39836 9.35024i −0.264995 0.458985i
\(416\) 1.89748 3.28654i 0.0930318 0.161136i
\(417\) 0 0
\(418\) −0.637177 + 0.367874i −0.0311653 + 0.0179933i
\(419\) 2.16604 0.105818 0.0529090 0.998599i \(-0.483151\pi\)
0.0529090 + 0.998599i \(0.483151\pi\)
\(420\) 0 0
\(421\) 12.3865 0.603682 0.301841 0.953358i \(-0.402399\pi\)
0.301841 + 0.953358i \(0.402399\pi\)
\(422\) 3.78280 2.18400i 0.184144 0.106316i
\(423\) 0 0
\(424\) 3.49589 6.05506i 0.169775 0.294060i
\(425\) 47.4412 + 82.1706i 2.30124 + 3.98586i
\(426\) 0 0
\(427\) 2.45038 7.87313i 0.118582 0.381008i
\(428\) 3.12283i 0.150948i
\(429\) 0 0
\(430\) 18.5238 + 10.6947i 0.893297 + 0.515745i
\(431\) 20.2513 + 11.6921i 0.975468 + 0.563187i 0.900899 0.434029i \(-0.142908\pi\)
0.0745695 + 0.997216i \(0.476242\pi\)
\(432\) 0 0
\(433\) 30.6220i 1.47160i −0.677199 0.735800i \(-0.736806\pi\)
0.677199 0.735800i \(-0.263194\pi\)
\(434\) 3.26827 3.01716i 0.156882 0.144828i
\(435\) 0 0
\(436\) −1.12213 1.94358i −0.0537401 0.0930807i
\(437\) 14.9839 25.9528i 0.716775 1.24149i
\(438\) 0 0
\(439\) −26.8443 + 15.4986i −1.28121 + 0.739707i −0.977070 0.212920i \(-0.931703\pi\)
−0.304141 + 0.952627i \(0.598369\pi\)
\(440\) −0.392222 −0.0186984
\(441\) 0 0
\(442\) 29.0411 1.38135
\(443\) 8.70257 5.02443i 0.413472 0.238718i −0.278809 0.960347i \(-0.589940\pi\)
0.692280 + 0.721629i \(0.256606\pi\)
\(444\) 0 0
\(445\) −5.71967 + 9.90676i −0.271138 + 0.469626i
\(446\) 8.64657 + 14.9763i 0.409427 + 0.709148i
\(447\) 0 0
\(448\) −1.94402 + 1.79465i −0.0918464 + 0.0847894i
\(449\) 3.58784i 0.169320i −0.996410 0.0846602i \(-0.973020\pi\)
0.996410 0.0846602i \(-0.0269805\pi\)
\(450\) 0 0
\(451\) −0.250118 0.144406i −0.0117776 0.00679981i
\(452\) 3.10165 + 1.79074i 0.145889 + 0.0842292i
\(453\) 0 0
\(454\) 8.50126i 0.398984i
\(455\) 12.4459 39.9890i 0.583472 1.87471i
\(456\) 0 0
\(457\) −1.28677 2.22875i −0.0601926 0.104257i 0.834359 0.551222i \(-0.185838\pi\)
−0.894551 + 0.446965i \(0.852505\pi\)
\(458\) 12.1465 21.0383i 0.567568 0.983056i
\(459\) 0 0
\(460\) 13.8352 7.98778i 0.645071 0.372432i
\(461\) 17.4108 0.810902 0.405451 0.914117i \(-0.367114\pi\)
0.405451 + 0.914117i \(0.367114\pi\)
\(462\) 0 0
\(463\) 15.8825 0.738121 0.369061 0.929405i \(-0.379679\pi\)
0.369061 + 0.929405i \(0.379679\pi\)
\(464\) −1.75954 + 1.01587i −0.0816846 + 0.0471606i
\(465\) 0 0
\(466\) −8.22389 + 14.2442i −0.380964 + 0.659850i
\(467\) 16.3177 + 28.2631i 0.755093 + 1.30786i 0.945328 + 0.326121i \(0.105742\pi\)
−0.190235 + 0.981739i \(0.560925\pi\)
\(468\) 0 0
\(469\) 4.38597 + 19.4429i 0.202525 + 0.897788i
\(470\) 21.2697i 0.981099i
\(471\) 0 0
\(472\) −9.02922 5.21303i −0.415604 0.239949i
\(473\) −0.417582 0.241091i −0.0192004 0.0110854i
\(474\) 0 0
\(475\) 97.0149i 4.45135i
\(476\) −19.3320 6.01676i −0.886082 0.275778i
\(477\) 0 0
\(478\) 8.92870 + 15.4650i 0.408389 + 0.707351i
\(479\) −5.58651 + 9.67613i −0.255254 + 0.442113i −0.964965 0.262380i \(-0.915493\pi\)
0.709710 + 0.704494i \(0.248826\pi\)
\(480\) 0 0
\(481\) −14.3519 + 8.28606i −0.654389 + 0.377812i
\(482\) −8.39906 −0.382566
\(483\) 0 0
\(484\) −10.9912 −0.499598
\(485\) −14.6805 + 8.47581i −0.666609 + 0.384867i
\(486\) 0 0
\(487\) −16.1951 + 28.0507i −0.733868 + 1.27110i 0.221350 + 0.975194i \(0.428954\pi\)
−0.955218 + 0.295902i \(0.904380\pi\)
\(488\) 1.55828 + 2.69902i 0.0705400 + 0.122179i
\(489\) 0 0
\(490\) −16.5699 + 24.0412i −0.748552 + 1.08607i
\(491\) 33.1341i 1.49532i −0.664081 0.747661i \(-0.731177\pi\)
0.664081 0.747661i \(-0.268823\pi\)
\(492\) 0 0
\(493\) −13.4649 7.77399i −0.606430 0.350123i
\(494\) 25.7156 + 14.8469i 1.15700 + 0.667994i
\(495\) 0 0
\(496\) 1.68119i 0.0754878i
\(497\) 15.4577 + 16.7443i 0.693375 + 0.751083i
\(498\) 0 0
\(499\) 12.0418 + 20.8569i 0.539063 + 0.933685i 0.998955 + 0.0457097i \(0.0145549\pi\)
−0.459892 + 0.887975i \(0.652112\pi\)
\(500\) −15.4310 + 26.7272i −0.690094 + 1.19528i
\(501\) 0 0
\(502\) 10.6999 6.17758i 0.477559 0.275719i
\(503\) 30.1146 1.34274 0.671372 0.741121i \(-0.265705\pi\)
0.671372 + 0.741121i \(0.265705\pi\)
\(504\) 0 0
\(505\) −51.4364 −2.28889
\(506\) −0.311888 + 0.180068i −0.0138651 + 0.00800502i
\(507\) 0 0
\(508\) 4.74984 8.22696i 0.210740 0.365013i
\(509\) −4.94736 8.56907i −0.219288 0.379817i 0.735303 0.677739i \(-0.237040\pi\)
−0.954590 + 0.297921i \(0.903707\pi\)
\(510\) 0 0
\(511\) −0.387320 + 0.0873727i −0.0171340 + 0.00386514i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −12.0309 6.94605i −0.530661 0.306377i
\(515\) −6.55307 3.78341i −0.288763 0.166717i
\(516\) 0 0
\(517\) 0.479483i 0.0210876i
\(518\) 11.2704 2.54242i 0.495195 0.111707i
\(519\) 0 0
\(520\) 7.91477 + 13.7088i 0.347085 + 0.601170i
\(521\) 0.0257283 0.0445628i 0.00112718 0.00195233i −0.865461 0.500976i \(-0.832975\pi\)
0.866588 + 0.499024i \(0.166308\pi\)
\(522\) 0 0
\(523\) −3.58537 + 2.07001i −0.156777 + 0.0905154i −0.576336 0.817213i \(-0.695518\pi\)
0.419559 + 0.907728i \(0.362185\pi\)
\(524\) 3.03202 0.132455
\(525\) 0 0
\(526\) 10.9867 0.479045
\(527\) −11.1418 + 6.43269i −0.485342 + 0.280212i
\(528\) 0 0
\(529\) −4.16565 + 7.21512i −0.181115 + 0.313701i
\(530\) 14.5820 + 25.2568i 0.633402 + 1.09708i
\(531\) 0 0
\(532\) −14.0423 15.2110i −0.608811 0.659482i
\(533\) 11.6561i 0.504880i
\(534\) 0 0
\(535\) 11.2808 + 6.51296i 0.487711 + 0.281580i
\(536\) −6.52409 3.76669i −0.281798 0.162696i
\(537\) 0 0
\(538\) 20.1599i 0.869155i
\(539\) 0.373535 0.541961i 0.0160893 0.0233439i
\(540\) 0 0
\(541\) 9.98675 + 17.2976i 0.429364 + 0.743680i 0.996817 0.0797258i \(-0.0254045\pi\)
−0.567453 + 0.823406i \(0.692071\pi\)
\(542\) 6.99205 12.1106i 0.300334 0.520194i
\(543\) 0 0
\(544\) 6.62729 3.82627i 0.284143 0.164050i
\(545\) 9.36121 0.400990
\(546\) 0 0
\(547\) −7.91405 −0.338381 −0.169190 0.985583i \(-0.554115\pi\)
−0.169190 + 0.985583i \(0.554115\pi\)
\(548\) −3.82389 + 2.20773i −0.163349 + 0.0943094i
\(549\) 0 0
\(550\) 0.582938 1.00968i 0.0248566 0.0430528i
\(551\) −7.94870 13.7676i −0.338626 0.586518i
\(552\) 0 0
\(553\) 32.7614 + 10.1964i 1.39316 + 0.433596i
\(554\) 18.9451i 0.804899i
\(555\) 0 0
\(556\) −1.14947 0.663644i −0.0487482 0.0281448i
\(557\) −30.5833 17.6573i −1.29586 0.748163i −0.316171 0.948702i \(-0.602397\pi\)
−0.979686 + 0.200539i \(0.935731\pi\)
\(558\) 0 0
\(559\) 19.4602i 0.823079i
\(560\) −2.42849 10.7654i −0.102622 0.454922i
\(561\) 0 0
\(562\) 3.06078 + 5.30142i 0.129111 + 0.223627i
\(563\) 18.0983 31.3471i 0.762751 1.32112i −0.178677 0.983908i \(-0.557182\pi\)
0.941428 0.337215i \(-0.109485\pi\)
\(564\) 0 0
\(565\) −12.9376 + 7.46951i −0.544288 + 0.314245i
\(566\) −27.3084 −1.14786
\(567\) 0 0
\(568\) −8.61322 −0.361403
\(569\) −19.1602 + 11.0622i −0.803239 + 0.463750i −0.844602 0.535394i \(-0.820163\pi\)
0.0413637 + 0.999144i \(0.486830\pi\)
\(570\) 0 0
\(571\) 12.0521 20.8748i 0.504363 0.873582i −0.495624 0.868537i \(-0.665061\pi\)
0.999987 0.00504524i \(-0.00160596\pi\)
\(572\) −0.178423 0.309037i −0.00746022 0.0129215i
\(573\) 0 0
\(574\) 2.41491 7.75918i 0.100796 0.323862i
\(575\) 47.4872i 1.98035i
\(576\) 0 0
\(577\) 9.03494 + 5.21633i 0.376129 + 0.217158i 0.676133 0.736780i \(-0.263654\pi\)
−0.300003 + 0.953938i \(0.596988\pi\)
\(578\) 35.9931 + 20.7806i 1.49712 + 0.864361i
\(579\) 0 0
\(580\) 8.47478i 0.351896i
\(581\) −5.03191 + 4.64529i −0.208759 + 0.192719i
\(582\) 0 0
\(583\) −0.328722 0.569364i −0.0136143 0.0235806i
\(584\) 0.0750360 0.129966i 0.00310501 0.00537804i
\(585\) 0 0
\(586\) 13.2253 7.63564i 0.546333 0.315425i
\(587\) 20.1447 0.831460 0.415730 0.909488i \(-0.363526\pi\)
0.415730 + 0.909488i \(0.363526\pi\)
\(588\) 0 0
\(589\) −13.1545 −0.542023
\(590\) 37.6626 21.7445i 1.55055 0.895208i
\(591\) 0 0
\(592\) −2.18343 + 3.78182i −0.0897386 + 0.155432i
\(593\) −9.16661 15.8770i −0.376428 0.651992i 0.614112 0.789219i \(-0.289514\pi\)
−0.990540 + 0.137227i \(0.956181\pi\)
\(594\) 0 0
\(595\) 62.0535 57.2857i 2.54395 2.34848i
\(596\) 10.5854i 0.433594i
\(597\) 0 0
\(598\) 12.5874 + 7.26731i 0.514735 + 0.297183i
\(599\) 13.7613 + 7.94509i 0.562272 + 0.324628i 0.754057 0.656809i \(-0.228094\pi\)
−0.191785 + 0.981437i \(0.561428\pi\)
\(600\) 0 0
\(601\) 40.2556i 1.64206i 0.570884 + 0.821030i \(0.306600\pi\)
−0.570884 + 0.821030i \(0.693400\pi\)
\(602\) 4.03178 12.9542i 0.164323 0.527975i
\(603\) 0 0
\(604\) −3.86400 6.69264i −0.157224 0.272320i
\(605\) 22.9231 39.7040i 0.931957 1.61420i
\(606\) 0 0
\(607\) −6.94932 + 4.01219i −0.282064 + 0.162850i −0.634358 0.773040i \(-0.718735\pi\)
0.352293 + 0.935890i \(0.385402\pi\)
\(608\) 7.82452 0.317326
\(609\) 0 0
\(610\) −12.9998 −0.526345
\(611\) 16.7587 9.67564i 0.677985 0.391435i
\(612\) 0 0
\(613\) 20.4658 35.4478i 0.826606 1.43172i −0.0740802 0.997252i \(-0.523602\pi\)
0.900686 0.434471i \(-0.143065\pi\)
\(614\) −14.4703 25.0634i −0.583975 1.01148i
\(615\) 0 0
\(616\) 0.0547454 + 0.242685i 0.00220576 + 0.00977805i
\(617\) 5.98876i 0.241098i −0.992707 0.120549i \(-0.961534\pi\)
0.992707 0.120549i \(-0.0384655\pi\)
\(618\) 0 0
\(619\) −16.5700 9.56672i −0.666006 0.384519i 0.128556 0.991702i \(-0.458966\pi\)
−0.794562 + 0.607183i \(0.792299\pi\)
\(620\) −6.07307 3.50629i −0.243900 0.140816i
\(621\) 0 0
\(622\) 6.45823i 0.258951i
\(623\) 6.92809 + 2.15625i 0.277568 + 0.0863882i
\(624\) 0 0
\(625\) −33.3684 57.7958i −1.33474 2.31183i
\(626\) −13.6995 + 23.7283i −0.547544 + 0.948374i
\(627\) 0 0
\(628\) −3.37019 + 1.94578i −0.134485 + 0.0776450i
\(629\) −33.4176 −1.33245
\(630\) 0 0
\(631\) 44.6986 1.77942 0.889712 0.456522i \(-0.150905\pi\)
0.889712 + 0.456522i \(0.150905\pi\)
\(632\) −11.2311 + 6.48425i −0.446747 + 0.257930i
\(633\) 0 0
\(634\) 9.70915 16.8167i 0.385599 0.667878i
\(635\) 19.8125 + 34.3162i 0.786235 + 1.36180i
\(636\) 0 0
\(637\) −26.4801 2.11924i −1.04918 0.0839673i
\(638\) 0.191047i 0.00756362i
\(639\) 0 0
\(640\) 3.61236 + 2.08560i 0.142791 + 0.0824404i
\(641\) 23.6804 + 13.6719i 0.935321 + 0.540008i 0.888490 0.458895i \(-0.151755\pi\)
0.0468305 + 0.998903i \(0.485088\pi\)
\(642\) 0 0
\(643\) 0.714773i 0.0281879i −0.999901 0.0140939i \(-0.995514\pi\)
0.999901 0.0140939i \(-0.00448639\pi\)
\(644\) −6.87348 7.44555i −0.270853 0.293396i
\(645\) 0 0
\(646\) 29.9387 + 51.8554i 1.17792 + 2.04022i
\(647\) 6.33080 10.9653i 0.248889 0.431089i −0.714329 0.699810i \(-0.753268\pi\)
0.963218 + 0.268722i \(0.0866011\pi\)
\(648\) 0 0
\(649\) −0.849028 + 0.490187i −0.0333273 + 0.0192415i
\(650\) −47.0531 −1.84558
\(651\) 0 0
\(652\) 17.6540 0.691383
\(653\) 32.8218 18.9497i 1.28442 0.741558i 0.306764 0.951786i \(-0.400754\pi\)
0.977652 + 0.210228i \(0.0674206\pi\)
\(654\) 0 0
\(655\) −6.32357 + 10.9528i −0.247083 + 0.427959i
\(656\) 1.53573 + 2.65995i 0.0599600 + 0.103854i
\(657\) 0 0
\(658\) −13.1605 + 2.96878i −0.513050 + 0.115735i
\(659\) 47.1979i 1.83857i −0.393595 0.919284i \(-0.628769\pi\)
0.393595 0.919284i \(-0.371231\pi\)
\(660\) 0 0
\(661\) −22.0106 12.7078i −0.856112 0.494276i 0.00659651 0.999978i \(-0.497900\pi\)
−0.862708 + 0.505702i \(0.831234\pi\)
\(662\) 11.3611 + 6.55931i 0.441560 + 0.254935i
\(663\) 0 0
\(664\) 2.58840i 0.100450i
\(665\) 84.2343 19.0018i 3.26646 0.736857i
\(666\) 0 0
\(667\) −3.89076 6.73899i −0.150651 0.260935i
\(668\) −8.19835 + 14.2000i −0.317204 + 0.549413i
\(669\) 0 0
\(670\) 27.2132 15.7116i 1.05134 0.606991i
\(671\) 0.293054 0.0113132
\(672\) 0 0
\(673\) 3.57996 0.137997 0.0689987 0.997617i \(-0.478020\pi\)
0.0689987 + 0.997617i \(0.478020\pi\)
\(674\) −20.5518 + 11.8656i −0.791624 + 0.457045i
\(675\) 0 0
\(676\) −0.700889 + 1.21398i −0.0269573 + 0.0466914i
\(677\) −12.0629 20.8936i −0.463617 0.803008i 0.535521 0.844522i \(-0.320115\pi\)
−0.999138 + 0.0415142i \(0.986782\pi\)
\(678\) 0 0
\(679\) 7.29343 + 7.90046i 0.279896 + 0.303192i
\(680\) 31.9202i 1.22408i
\(681\) 0 0
\(682\) 0.136905 + 0.0790422i 0.00524237 + 0.00302668i
\(683\) −12.8920 7.44319i −0.493298 0.284806i 0.232644 0.972562i \(-0.425262\pi\)
−0.725942 + 0.687756i \(0.758596\pi\)
\(684\) 0 0
\(685\) 18.4177i 0.703704i
\(686\) 17.1882 + 6.89690i 0.656247 + 0.263325i
\(687\) 0 0
\(688\) 2.56395 + 4.44089i 0.0977496 + 0.169307i
\(689\) −13.2668 + 22.9787i −0.505424 + 0.875420i
\(690\) 0 0
\(691\) 31.3291 18.0879i 1.19182 0.688095i 0.233097 0.972453i \(-0.425114\pi\)
0.958718 + 0.284359i \(0.0917807\pi\)
\(692\) 7.85639 0.298655
\(693\) 0 0
\(694\) 8.33530 0.316404
\(695\) 4.79464 2.76819i 0.181871 0.105003i
\(696\) 0 0
\(697\) −11.7522 + 20.3554i −0.445146 + 0.771015i
\(698\) 9.37428 + 16.2367i 0.354822 + 0.614569i
\(699\) 0 0
\(700\) 31.3222 + 9.74851i 1.18387 + 0.368459i
\(701\) 23.4537i 0.885834i 0.896563 + 0.442917i \(0.146056\pi\)
−0.896563 + 0.442917i \(0.853944\pi\)
\(702\) 0 0
\(703\) −29.5909 17.0843i −1.11604 0.644348i
\(704\) −0.0814333 0.0470156i −0.00306913 0.00177197i
\(705\) 0 0
\(706\) 19.5374i 0.735299i
\(707\) 7.17937 + 31.8259i 0.270008 + 1.19694i
\(708\) 0 0
\(709\) 9.06708 + 15.7046i 0.340521 + 0.589800i 0.984530 0.175218i \(-0.0560631\pi\)
−0.644008 + 0.765018i \(0.722730\pi\)
\(710\) 17.9637 31.1140i 0.674165 1.16769i
\(711\) 0 0
\(712\) −2.37504 + 1.37123i −0.0890085 + 0.0513891i
\(713\) −6.43892 −0.241140
\(714\) 0 0
\(715\) 1.48847 0.0556656
\(716\) 15.7884 9.11541i 0.590038 0.340659i
\(717\) 0 0
\(718\) −8.27288 + 14.3290i −0.308741 + 0.534755i
\(719\) −16.4312 28.4597i −0.612781 1.06137i −0.990769 0.135558i \(-0.956717\pi\)
0.377988 0.925810i \(-0.376616\pi\)
\(720\) 0 0
\(721\) −1.42630 + 4.58275i −0.0531183 + 0.170671i
\(722\) 42.2232i 1.57138i
\(723\) 0 0
\(724\) 12.3227 + 7.11450i 0.457969 + 0.264408i
\(725\) 21.8162 + 12.5956i 0.810234 + 0.467789i
\(726\) 0 0
\(727\) 7.24873i 0.268840i −0.990924 0.134420i \(-0.957083\pi\)
0.990924 0.134420i \(-0.0429172\pi\)
\(728\) 7.37750 6.81065i 0.273428 0.252420i
\(729\) 0 0
\(730\) 0.312989 + 0.542113i 0.0115843 + 0.0200645i
\(731\) −19.6207 + 33.9841i −0.725698 + 1.25695i
\(732\) 0 0
\(733\) 29.5250 17.0463i 1.09053 0.629619i 0.156814 0.987628i \(-0.449878\pi\)
0.933718 + 0.358010i \(0.116544\pi\)
\(734\) −32.1362 −1.18617
\(735\) 0 0
\(736\) 3.82997 0.141175
\(737\) −0.613468 + 0.354186i −0.0225974 + 0.0130466i
\(738\) 0 0
\(739\) −17.4439 + 30.2137i −0.641683 + 1.11143i 0.343373 + 0.939199i \(0.388430\pi\)
−0.985057 + 0.172229i \(0.944903\pi\)
\(740\) −9.10752 15.7747i −0.334799 0.579889i
\(741\) 0 0
\(742\) 13.5922 12.5478i 0.498984 0.460645i
\(743\) 45.8060i 1.68046i −0.542230 0.840230i \(-0.682420\pi\)
0.542230 0.840230i \(-0.317580\pi\)
\(744\) 0 0
\(745\) −38.2382 22.0768i −1.40094 0.808833i
\(746\) −22.2875 12.8677i −0.816004 0.471120i
\(747\) 0 0
\(748\) 0.719576i 0.0263103i
\(749\) 2.45531 7.88898i 0.0897151 0.288257i
\(750\) 0 0
\(751\) −15.7630 27.3024i −0.575201 0.996277i −0.996020 0.0891324i \(-0.971591\pi\)
0.420819 0.907145i \(-0.361743\pi\)
\(752\) 2.54960 4.41603i 0.0929743 0.161036i
\(753\) 0 0
\(754\) 6.67740 3.85520i 0.243176 0.140398i
\(755\) 32.2349 1.17315
\(756\) 0 0
\(757\) −0.176603 −0.00641874 −0.00320937 0.999995i \(-0.501022\pi\)
−0.00320937 + 0.999995i \(0.501022\pi\)
\(758\) 31.5036 18.1886i 1.14426 0.660639i
\(759\) 0 0
\(760\) −16.3188 + 28.2650i −0.591945 + 1.02528i
\(761\) −19.0504 32.9963i −0.690576 1.19611i −0.971649 0.236427i \(-0.924024\pi\)
0.281073 0.959686i \(-0.409310\pi\)
\(762\) 0 0
\(763\) −1.30662 5.79219i −0.0473027 0.209691i
\(764\) 19.2203i 0.695365i
\(765\) 0 0
\(766\) −21.7845 12.5773i −0.787107 0.454436i
\(767\) 34.2656 + 19.7833i 1.23726 + 0.714332i
\(768\) 0 0
\(769\) 17.6927i 0.638016i −0.947752 0.319008i \(-0.896650\pi\)
0.947752 0.319008i \(-0.103350\pi\)
\(770\) −0.990841 0.308382i −0.0357074 0.0111133i
\(771\) 0 0
\(772\) 3.77817 + 6.54399i 0.135979 + 0.235523i
\(773\) −5.67628 + 9.83160i −0.204162 + 0.353618i −0.949865 0.312659i \(-0.898780\pi\)
0.745704 + 0.666278i \(0.232113\pi\)
\(774\) 0 0
\(775\) 18.0521 10.4224i 0.648452 0.374384i
\(776\) −4.06398 −0.145888
\(777\) 0 0
\(778\) −9.69503 −0.347584
\(779\) −20.8129 + 12.0163i −0.745699 + 0.430529i
\(780\) 0 0
\(781\) −0.404955 + 0.701403i −0.0144904 + 0.0250982i
\(782\) 14.6545 + 25.3823i 0.524044 + 0.907671i
\(783\) 0 0
\(784\) −6.32207 + 3.00523i −0.225788 + 0.107330i
\(785\) 16.2324i 0.579360i
\(786\) 0 0
\(787\) −24.5394 14.1678i −0.874735 0.505028i −0.00581596 0.999983i \(-0.501851\pi\)
−0.868919 + 0.494955i \(0.835185\pi\)
\(788\) −1.82244 1.05219i −0.0649217 0.0374825i
\(789\) 0 0
\(790\) 54.0941i 1.92458i
\(791\) 6.42751 + 6.96246i 0.228536 + 0.247557i
\(792\) 0 0
\(793\) −5.91362 10.2427i −0.209999 0.363729i
\(794\) 6.45731 11.1844i 0.229161 0.396919i
\(795\) 0 0
\(796\) 1.24340 0.717876i 0.0440710 0.0254444i
\(797\) 47.9417 1.69818 0.849091 0.528246i \(-0.177150\pi\)
0.849091 + 0.528246i \(0.177150\pi\)
\(798\) 0 0
\(799\) 39.0218 1.38049
\(800\) −10.7377 + 6.19941i −0.379635 + 0.219182i
\(801\) 0 0
\(802\) 14.3872 24.9194i 0.508031 0.879936i
\(803\) −0.00705572 0.0122209i −0.000248991 0.000431265i
\(804\) 0 0
\(805\) 41.2313 9.30105i 1.45321 0.327819i
\(806\) 6.38007i 0.224728i
\(807\) 0 0
\(808\) −10.6793 6.16567i −0.375695 0.216908i
\(809\) −29.3232 16.9297i −1.03095 0.595218i −0.113692 0.993516i \(-0.536268\pi\)
−0.917256 + 0.398298i \(0.869601\pi\)
\(810\) 0 0
\(811\) 32.8364i 1.15304i 0.817082 + 0.576521i \(0.195590\pi\)
−0.817082 + 0.576521i \(0.804410\pi\)
\(812\) −5.24372 + 1.18289i −0.184018 + 0.0415113i
\(813\) 0 0
\(814\) 0.205311 + 0.355609i 0.00719614 + 0.0124641i
\(815\) −36.8191 + 63.7725i −1.28972 + 2.23385i
\(816\) 0 0
\(817\) −34.7478 + 20.0617i −1.21567 + 0.701869i
\(818\) 33.2333 1.16198
\(819\) 0 0
\(820\) −12.8116 −0.447401
\(821\) −30.0927 + 17.3740i −1.05024 + 0.606357i −0.922717 0.385479i \(-0.874036\pi\)
−0.127524 + 0.991835i \(0.540703\pi\)
\(822\) 0 0
\(823\) −22.1948 + 38.4426i −0.773663 + 1.34002i 0.161880 + 0.986810i \(0.448244\pi\)
−0.935543 + 0.353213i \(0.885089\pi\)
\(824\) −0.907035 1.57103i −0.0315981 0.0547294i
\(825\) 0 0
\(826\) −18.7112 20.2685i −0.651044 0.705230i
\(827\) 13.2991i 0.462456i 0.972900 + 0.231228i \(0.0742743\pi\)
−0.972900 + 0.231228i \(0.925726\pi\)
\(828\) 0 0
\(829\) 1.16441 + 0.672270i 0.0404415 + 0.0233489i 0.520084 0.854115i \(-0.325900\pi\)
−0.479643 + 0.877464i \(0.659234\pi\)
\(830\) 9.35024 + 5.39836i 0.324552 + 0.187380i
\(831\) 0 0
\(832\) 3.79497i 0.131567i
\(833\) −44.1065 30.3994i −1.52820 1.05328i
\(834\) 0 0
\(835\) −34.1969 59.2307i −1.18343 2.04976i
\(836\) 0.367874 0.637177i 0.0127232 0.0220372i
\(837\) 0 0
\(838\) −1.87584 + 1.08302i −0.0648000 + 0.0374123i
\(839\) 3.10045 0.107039 0.0535196 0.998567i \(-0.482956\pi\)
0.0535196 + 0.998567i \(0.482956\pi\)
\(840\) 0 0
\(841\) 24.8720 0.857656
\(842\) −10.7270 + 6.19326i −0.369678 + 0.213434i
\(843\) 0 0
\(844\) −2.18400 + 3.78280i −0.0751764 + 0.130209i
\(845\) −2.92354 5.06372i −0.100573 0.174197i
\(846\) 0 0
\(847\) −27.7662 8.64174i −0.954056 0.296934i
\(848\) 6.99178i 0.240099i
\(849\) 0 0
\(850\) −82.1706 47.4412i −2.81843 1.62722i
\(851\) −14.4843 8.36250i −0.496514 0.286663i
\(852\) 0 0
\(853\) 29.1021i 0.996439i 0.867051 + 0.498219i \(0.166013\pi\)
−0.867051 + 0.498219i \(0.833987\pi\)
\(854\) 1.81448 + 8.04352i 0.0620902 + 0.275244i
\(855\) 0 0
\(856\) 1.56142 + 2.70445i 0.0533681 + 0.0924363i
\(857\) 2.37441 4.11260i 0.0811084 0.140484i −0.822618 0.568595i \(-0.807487\pi\)
0.903726 + 0.428111i \(0.140821\pi\)
\(858\) 0 0
\(859\) −31.2496 + 18.0419i −1.06622 + 0.615583i −0.927147 0.374699i \(-0.877746\pi\)
−0.139075 + 0.990282i \(0.544413\pi\)
\(860\) −21.3894 −0.729374
\(861\) 0 0
\(862\) −23.3841 −0.796467
\(863\) 10.3650 5.98423i 0.352829 0.203706i −0.313102 0.949720i \(-0.601368\pi\)
0.665930 + 0.746014i \(0.268035\pi\)
\(864\) 0 0
\(865\) −16.3852 + 28.3801i −0.557115 + 0.964952i
\(866\) 15.3110 + 26.5194i 0.520289 + 0.901167i
\(867\) 0 0
\(868\) −1.32183 + 4.24707i −0.0448658 + 0.144155i
\(869\) 1.21944i 0.0413668i
\(870\) 0 0
\(871\) 24.7587 + 14.2945i 0.838917 + 0.484349i
\(872\) 1.94358 + 1.12213i 0.0658180 + 0.0380000i
\(873\) 0 0
\(874\) 29.9677i 1.01367i
\(875\) −59.9962 + 55.3865i −2.02824 + 1.87240i
\(876\) 0 0
\(877\) 12.0096 + 20.8013i 0.405537 + 0.702410i 0.994384 0.105834i \(-0.0337514\pi\)
−0.588847 + 0.808244i \(0.700418\pi\)
\(878\) 15.4986 26.8443i 0.523052 0.905953i
\(879\) 0 0
\(880\) 0.339674 0.196111i 0.0114504 0.00661089i
\(881\) 13.4264 0.452348 0.226174 0.974087i \(-0.427378\pi\)
0.226174 + 0.974087i \(0.427378\pi\)
\(882\) 0 0
\(883\) 27.1649 0.914172 0.457086 0.889423i \(-0.348893\pi\)
0.457086 + 0.889423i \(0.348893\pi\)
\(884\) −25.1503 + 14.5206i −0.845898 + 0.488379i
\(885\) 0 0
\(886\) −5.02443 + 8.70257i −0.168799 + 0.292369i
\(887\) −4.12273 7.14078i −0.138428 0.239764i 0.788474 0.615068i \(-0.210872\pi\)
−0.926902 + 0.375304i \(0.877538\pi\)
\(888\) 0 0
\(889\) 18.4676 17.0486i 0.619383 0.571793i
\(890\) 11.4393i 0.383448i
\(891\) 0 0
\(892\) −14.9763 8.64657i −0.501444 0.289509i
\(893\) 34.5534 + 19.9494i 1.15628 + 0.667581i
\(894\) 0 0
\(895\) 76.0442i 2.54188i
\(896\) 0.786244 2.52623i 0.0262666 0.0843953i
\(897\) 0 0
\(898\) 1.79392 + 3.10716i 0.0598638 + 0.103687i
\(899\) −1.70787 + 2.95813i −0.0569608 + 0.0986590i
\(900\) 0 0
\(901\) −46.3365 + 26.7524i −1.54369 + 0.891252i
\(902\) 0.288812 0.00961638
\(903\) 0 0
\(904\) −3.58148 −0.119118
\(905\) −51.4002 + 29.6759i −1.70860 + 0.986461i
\(906\) 0 0
\(907\) 18.6275 32.2638i 0.618517 1.07130i −0.371239 0.928537i \(-0.621067\pi\)
0.989756 0.142766i \(-0.0455997\pi\)
\(908\) 4.25063 + 7.36231i 0.141062 + 0.244327i
\(909\) 0 0
\(910\) 9.21604 + 40.8544i 0.305509 + 1.35431i
\(911\) 15.3829i 0.509657i −0.966986 0.254829i \(-0.917981\pi\)
0.966986 0.254829i \(-0.0820190\pi\)
\(912\) 0 0
\(913\) −0.210782 0.121695i −0.00697588 0.00402753i
\(914\) 2.22875 + 1.28677i 0.0737206 + 0.0425626i
\(915\) 0 0
\(916\) 24.2930i 0.802662i
\(917\) 7.65958 + 2.38391i 0.252942 + 0.0787237i
\(918\) 0 0
\(919\) 25.3211 + 43.8575i 0.835267 + 1.44673i 0.893812 + 0.448441i \(0.148021\pi\)
−0.0585450 + 0.998285i \(0.518646\pi\)
\(920\) −7.98778 + 13.8352i −0.263349 + 0.456134i
\(921\) 0 0
\(922\) −15.0782 + 8.70540i −0.496574 + 0.286697i
\(923\) 32.6869 1.07590
\(924\) 0 0
\(925\) 54.1441 1.78025
\(926\) −13.7546 + 7.94124i −0.452005 + 0.260965i
\(927\) 0 0
\(928\) 1.01587 1.75954i 0.0333476 0.0577597i
\(929\) −15.1981 26.3239i −0.498634 0.863659i 0.501365 0.865236i \(-0.332831\pi\)
−0.999999 + 0.00157664i \(0.999498\pi\)
\(930\) 0 0
\(931\) −23.5145 49.4672i −0.770655 1.62122i
\(932\) 16.4478i 0.538765i
\(933\) 0 0
\(934\) −28.2631 16.3177i −0.924796 0.533931i
\(935\) 2.59937 + 1.50075i 0.0850084 + 0.0490796i
\(936\) 0 0
\(937\) 13.7262i 0.448416i −0.974541 0.224208i \(-0.928020\pi\)
0.974541 0.224208i \(-0.0719796\pi\)
\(938\) −13.5198 14.6450i −0.441437 0.478177i
\(939\) 0 0
\(940\) 10.6349 + 18.4201i 0.346871 + 0.600798i
\(941\) −15.7219 + 27.2311i −0.512520 + 0.887710i 0.487375 + 0.873193i \(0.337954\pi\)
−0.999895 + 0.0145172i \(0.995379\pi\)
\(942\) 0 0
\(943\) −10.1876 + 5.88179i −0.331752 + 0.191537i
\(944\) 10.4261 0.339339
\(945\) 0 0
\(946\) 0.482182 0.0156771
\(947\) −0.726997 + 0.419732i −0.0236242 + 0.0136395i −0.511766 0.859125i \(-0.671008\pi\)
0.488141 + 0.872765i \(0.337675\pi\)
\(948\) 0 0
\(949\) −0.284759 + 0.493217i −0.00924367 + 0.0160105i
\(950\) −48.5075 84.0174i −1.57379 2.72588i
\(951\) 0 0
\(952\) 19.7504 4.45535i 0.640115 0.144399i
\(953\) 41.8952i 1.35712i −0.734545 0.678560i \(-0.762604\pi\)
0.734545 0.678560i \(-0.237396\pi\)
\(954\) 0 0
\(955\) −69.4305 40.0857i −2.24672 1.29714i
\(956\) −15.4650 8.92870i −0.500172 0.288775i
\(957\) 0 0
\(958\) 11.1730i 0.360984i
\(959\) −11.3958 + 2.57070i −0.367991 + 0.0830122i
\(960\) 0 0
\(961\) −14.0868 24.3990i −0.454413 0.787066i
\(962\) 8.28606 14.3519i 0.267153 0.462723i
\(963\) 0 0
\(964\) 7.27380 4.19953i 0.234273 0.135258i
\(965\) −31.5190 −1.01463
\(966\) 0 0
\(967\) −46.6870 −1.50135 −0.750676 0.660671i \(-0.770272\pi\)
−0.750676 + 0.660671i \(0.770272\pi\)
\(968\) 9.51862 5.49558i 0.305940 0.176635i
\(969\) 0 0
\(970\) 8.47581 14.6805i 0.272142 0.471364i
\(971\) 11.6725 + 20.2173i 0.374587 + 0.648804i 0.990265 0.139194i \(-0.0444512\pi\)
−0.615678 + 0.787998i \(0.711118\pi\)
\(972\) 0 0
\(973\) −2.38202 2.58028i −0.0763642 0.0827199i
\(974\) 32.3901i 1.03785i
\(975\) 0 0
\(976\) −2.69902 1.55828i −0.0863935 0.0498793i
\(977\) −27.0245 15.6026i −0.864589 0.499171i 0.000957477 1.00000i \(-0.499695\pi\)
−0.865546 + 0.500829i \(0.833029\pi\)
\(978\) 0 0
\(979\) 0.257877i 0.00824179i
\(980\) 2.32933 29.1053i 0.0744079 0.929734i
\(981\) 0 0
\(982\) 16.5671 + 28.6950i 0.528676 + 0.915693i
\(983\) 1.41367 2.44856i 0.0450892 0.0780968i −0.842600 0.538540i \(-0.818976\pi\)
0.887689 + 0.460443i \(0.152309\pi\)
\(984\) 0 0
\(985\) 7.60174 4.38887i 0.242211 0.139841i
\(986\) 15.5480 0.495148
\(987\) 0 0
\(988\) −29.6938 −0.944686
\(989\) −17.0085 + 9.81986i −0.540839 + 0.312253i
\(990\) 0 0
\(991\) 14.4402 25.0111i 0.458708 0.794505i −0.540185 0.841546i \(-0.681646\pi\)
0.998893 + 0.0470409i \(0.0149791\pi\)
\(992\) −0.840596 1.45596i −0.0266890 0.0462266i
\(993\) 0 0
\(994\) −21.7589 6.77209i −0.690152 0.214798i
\(995\) 5.98879i 0.189857i
\(996\) 0 0
\(997\) 29.6911 + 17.1421i 0.940326 + 0.542897i 0.890062 0.455839i \(-0.150661\pi\)
0.0502633 + 0.998736i \(0.483994\pi\)
\(998\) −20.8569 12.0418i −0.660215 0.381175i
\(999\) 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 1134.2.k.d.647.4 yes 16
3.2 odd 2 1134.2.k.c.647.5 16
7.5 odd 6 1134.2.k.c.971.5 yes 16
9.2 odd 6 1134.2.t.h.1025.4 16
9.4 even 3 1134.2.l.g.269.4 16
9.5 odd 6 1134.2.l.h.269.5 16
9.7 even 3 1134.2.t.g.1025.5 16
21.5 even 6 inner 1134.2.k.d.971.4 yes 16
63.5 even 6 1134.2.t.g.593.5 16
63.40 odd 6 1134.2.t.h.593.4 16
63.47 even 6 1134.2.l.g.215.8 16
63.61 odd 6 1134.2.l.h.215.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1134.2.k.c.647.5 16 3.2 odd 2
1134.2.k.c.971.5 yes 16 7.5 odd 6
1134.2.k.d.647.4 yes 16 1.1 even 1 trivial
1134.2.k.d.971.4 yes 16 21.5 even 6 inner
1134.2.l.g.215.8 16 63.47 even 6
1134.2.l.g.269.4 16 9.4 even 3
1134.2.l.h.215.1 16 63.61 odd 6
1134.2.l.h.269.5 16 9.5 odd 6
1134.2.t.g.593.5 16 63.5 even 6
1134.2.t.g.1025.5 16 9.7 even 3
1134.2.t.h.593.4 16 63.40 odd 6
1134.2.t.h.1025.4 16 9.2 odd 6