Properties

Label 234.2.h.a.55.1
Level $234$
Weight $2$
Character 234.55
Analytic conductor $1.868$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [234,2,Mod(55,234)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(234, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("234.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 234.h (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.86849940730\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 234.55
Dual form 234.2.h.a.217.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(3.00000 + 5.19615i) q^{11} +(-3.50000 + 0.866025i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.50000 - 2.59808i) q^{20} +(3.00000 - 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} +4.00000 q^{25} +(2.50000 + 2.59808i) q^{26} +(-1.00000 - 1.73205i) q^{28} +(1.50000 + 2.59808i) q^{29} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(3.00000 - 5.19615i) q^{35} +(3.50000 + 6.06218i) q^{37} +2.00000 q^{38} -3.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} +(5.00000 - 8.66025i) q^{43} -6.00000 q^{44} +(-3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(1.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(1.00000 - 3.46410i) q^{52} -3.00000 q^{53} +(-9.00000 - 15.5885i) q^{55} +(-1.00000 + 1.73205i) q^{56} +(1.50000 - 2.59808i) q^{58} +(3.50000 - 6.06218i) q^{61} +(2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +(10.5000 - 2.59808i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-1.50000 - 2.59808i) q^{68} -6.00000 q^{70} +(3.00000 - 5.19615i) q^{71} -13.0000 q^{73} +(3.50000 - 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} -12.0000 q^{77} -4.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-1.50000 + 2.59808i) q^{82} +6.00000 q^{83} +(4.50000 - 7.79423i) q^{85} -10.0000 q^{86} +(3.00000 + 5.19615i) q^{88} +(9.00000 + 15.5885i) q^{89} +(2.00000 - 6.92820i) q^{91} +6.00000 q^{92} +(3.00000 + 5.19615i) q^{94} +(3.00000 - 5.19615i) q^{95} +(-7.00000 + 12.1244i) q^{97} +(1.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 6 q^{5} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 6 q^{5} - 2 q^{7} + 2 q^{8} + 3 q^{10} + 6 q^{11} - 7 q^{13} + 4 q^{14} - q^{16} - 3 q^{17} - 2 q^{19} + 3 q^{20} + 6 q^{22} - 6 q^{23} + 8 q^{25} + 5 q^{26} - 2 q^{28} + 3 q^{29} - 8 q^{31} - q^{32} + 6 q^{34} + 6 q^{35} + 7 q^{37} + 4 q^{38} - 6 q^{40} - 3 q^{41} + 10 q^{43} - 12 q^{44} - 6 q^{46} - 12 q^{47} + 3 q^{49} - 4 q^{50} + 2 q^{52} - 6 q^{53} - 18 q^{55} - 2 q^{56} + 3 q^{58} + 7 q^{61} + 4 q^{62} + 2 q^{64} + 21 q^{65} + 10 q^{67} - 3 q^{68} - 12 q^{70} + 6 q^{71} - 26 q^{73} + 7 q^{74} - 2 q^{76} - 24 q^{77} - 8 q^{79} + 3 q^{80} - 3 q^{82} + 12 q^{83} + 9 q^{85} - 20 q^{86} + 6 q^{88} + 18 q^{89} + 4 q^{91} + 12 q^{92} + 6 q^{94} + 6 q^{95} - 14 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/234\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(209\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 0 0
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i \(0.193114\pi\)
0.0829925 + 0.996550i \(0.473552\pi\)
\(12\) 0 0
\(13\) −3.50000 + 0.866025i −0.970725 + 0.240192i
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) 0 0
\(22\) 3.00000 5.19615i 0.639602 1.10782i
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 2.50000 + 2.59808i 0.490290 + 0.509525i
\(27\) 0 0
\(28\) −1.00000 1.73205i −0.188982 0.327327i
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) 3.00000 5.19615i 0.507093 0.878310i
\(36\) 0 0
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 2.00000 0.324443
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) −6.00000 −0.904534
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) 1.00000 3.46410i 0.138675 0.480384i
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) 0 0
\(55\) −9.00000 15.5885i −1.21356 2.10195i
\(56\) −1.00000 + 1.73205i −0.133631 + 0.231455i
\(57\) 0 0
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) 2.00000 + 3.46410i 0.254000 + 0.439941i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 10.5000 2.59808i 1.30236 0.322252i
\(66\) 0 0
\(67\) 5.00000 + 8.66025i 0.610847 + 1.05802i 0.991098 + 0.133135i \(0.0425044\pi\)
−0.380251 + 0.924883i \(0.624162\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 0 0
\(70\) −6.00000 −0.717137
\(71\) 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) 0 0
\(73\) −13.0000 −1.52153 −0.760767 0.649025i \(-0.775177\pi\)
−0.760767 + 0.649025i \(0.775177\pi\)
\(74\) 3.50000 6.06218i 0.406867 0.704714i
\(75\) 0 0
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) −12.0000 −1.36753
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 1.50000 + 2.59808i 0.167705 + 0.290474i
\(81\) 0 0
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 4.50000 7.79423i 0.488094 0.845403i
\(86\) −10.0000 −1.07833
\(87\) 0 0
\(88\) 3.00000 + 5.19615i 0.319801 + 0.553912i
\(89\) 9.00000 + 15.5885i 0.953998 + 1.65237i 0.736644 + 0.676280i \(0.236409\pi\)
0.217354 + 0.976093i \(0.430258\pi\)
\(90\) 0 0
\(91\) 2.00000 6.92820i 0.209657 0.726273i
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 3.00000 5.19615i 0.307794 0.533114i
\(96\) 0 0
\(97\) −7.00000 + 12.1244i −0.710742 + 1.23104i 0.253837 + 0.967247i \(0.418307\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) 1.50000 2.59808i 0.151523 0.262445i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) 7.50000 + 12.9904i 0.746278 + 1.29259i 0.949595 + 0.313478i \(0.101494\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) −3.50000 + 0.866025i −0.343203 + 0.0849208i
\(105\) 0 0
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) −9.00000 + 15.5885i −0.858116 + 1.48630i
\(111\) 0 0
\(112\) 2.00000 0.188982
\(113\) −1.50000 + 2.59808i −0.141108 + 0.244406i −0.927914 0.372794i \(-0.878400\pi\)
0.786806 + 0.617200i \(0.211733\pi\)
\(114\) 0 0
\(115\) 9.00000 + 15.5885i 0.839254 + 1.45363i
\(116\) −3.00000 −0.278543
\(117\) 0 0
\(118\) 0 0
\(119\) −3.00000 5.19615i −0.275010 0.476331i
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) −7.00000 −0.633750
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) 2.00000 + 3.46410i 0.177471 + 0.307389i 0.941014 0.338368i \(-0.109875\pi\)
−0.763542 + 0.645758i \(0.776542\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −7.50000 7.79423i −0.657794 0.683599i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) 5.00000 8.66025i 0.431934 0.748132i
\(135\) 0 0
\(136\) −1.50000 + 2.59808i −0.128624 + 0.222783i
\(137\) 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i \(-0.707721\pi\)
0.991694 + 0.128618i \(0.0410540\pi\)
\(138\) 0 0
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 3.00000 + 5.19615i 0.253546 + 0.439155i
\(141\) 0 0
\(142\) −6.00000 −0.503509
\(143\) −15.0000 15.5885i −1.25436 1.30357i
\(144\) 0 0
\(145\) −4.50000 7.79423i −0.373705 0.647275i
\(146\) 6.50000 + 11.2583i 0.537944 + 0.931746i
\(147\) 0 0
\(148\) −7.00000 −0.575396
\(149\) −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i \(-0.953515\pi\)
0.620701 + 0.784047i \(0.286848\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) 0 0
\(154\) 6.00000 + 10.3923i 0.483494 + 0.837436i
\(155\) 12.0000 0.963863
\(156\) 0 0
\(157\) 5.00000 0.399043 0.199522 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) 0 0
\(160\) 1.50000 2.59808i 0.118585 0.205396i
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) −9.00000 −0.690268
\(171\) 0 0
\(172\) 5.00000 + 8.66025i 0.381246 + 0.660338i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 0 0
\(175\) −4.00000 + 6.92820i −0.302372 + 0.523723i
\(176\) 3.00000 5.19615i 0.226134 0.391675i
\(177\) 0 0
\(178\) 9.00000 15.5885i 0.674579 1.16840i
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) −7.00000 + 1.73205i −0.518875 + 0.128388i
\(183\) 0 0
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) −10.5000 18.1865i −0.771975 1.33710i
\(186\) 0 0
\(187\) −18.0000 −1.31629
\(188\) 3.00000 5.19615i 0.218797 0.378968i
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) 0 0
\(193\) −11.5000 19.9186i −0.827788 1.43377i −0.899770 0.436365i \(-0.856266\pi\)
0.0719816 0.997406i \(-0.477068\pi\)
\(194\) 14.0000 1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 3.00000 + 5.19615i 0.213741 + 0.370211i 0.952882 0.303340i \(-0.0981018\pi\)
−0.739141 + 0.673550i \(0.764768\pi\)
\(198\) 0 0
\(199\) 5.00000 8.66025i 0.354441 0.613909i −0.632581 0.774494i \(-0.718005\pi\)
0.987022 + 0.160585i \(0.0513380\pi\)
\(200\) 4.00000 0.282843
\(201\) 0 0
\(202\) 7.50000 12.9904i 0.527698 0.914000i
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) −7.00000 12.1244i −0.487713 0.844744i
\(207\) 0 0
\(208\) 2.50000 + 2.59808i 0.173344 + 0.180144i
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 1.50000 2.59808i 0.103020 0.178437i
\(213\) 0 0
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) −15.0000 + 25.9808i −1.02299 + 1.77187i
\(216\) 0 0
\(217\) 4.00000 6.92820i 0.271538 0.470317i
\(218\) −7.00000 12.1244i −0.474100 0.821165i
\(219\) 0 0
\(220\) 18.0000 1.21356
\(221\) 3.00000 10.3923i 0.201802 0.699062i
\(222\) 0 0
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) −1.00000 1.73205i −0.0668153 0.115728i
\(225\) 0 0
\(226\) 3.00000 0.199557
\(227\) 9.00000 15.5885i 0.597351 1.03464i −0.395860 0.918311i \(-0.629553\pi\)
0.993210 0.116331i \(-0.0371134\pi\)
\(228\) 0 0
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 9.00000 15.5885i 0.593442 1.02787i
\(231\) 0 0
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 18.0000 1.17419
\(236\) 0 0
\(237\) 0 0
\(238\) −3.00000 + 5.19615i −0.194461 + 0.336817i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 25.0000 1.60706
\(243\) 0 0
\(244\) 3.50000 + 6.06218i 0.224065 + 0.388091i
\(245\) −4.50000 7.79423i −0.287494 0.497955i
\(246\) 0 0
\(247\) 2.00000 6.92820i 0.127257 0.440831i
\(248\) −4.00000 −0.254000
\(249\) 0 0
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) −6.00000 + 10.3923i −0.378717 + 0.655956i −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) 0 0
\(253\) 18.0000 31.1769i 1.13165 1.96008i
\(254\) 2.00000 3.46410i 0.125491 0.217357i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 0 0
\(259\) −14.0000 −0.869918
\(260\) −3.00000 + 10.3923i −0.186052 + 0.644503i
\(261\) 0 0
\(262\) 0 0
\(263\) −3.00000 5.19615i −0.184988 0.320408i 0.758585 0.651575i \(-0.225891\pi\)
−0.943572 + 0.331166i \(0.892558\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) −2.00000 + 3.46410i −0.122628 + 0.212398i
\(267\) 0 0
\(268\) −10.0000 −0.610847
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) −9.00000 −0.543710
\(275\) 12.0000 + 20.7846i 0.723627 + 1.25336i
\(276\) 0 0
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) 3.00000 5.19615i 0.179284 0.310530i
\(281\) −9.00000 −0.536895 −0.268447 0.963294i \(-0.586511\pi\)
−0.268447 + 0.963294i \(0.586511\pi\)
\(282\) 0 0
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 0 0
\(286\) −6.00000 + 20.7846i −0.354787 + 1.22902i
\(287\) 6.00000 0.354169
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) −4.50000 + 7.79423i −0.264249 + 0.457693i
\(291\) 0 0
\(292\) 6.50000 11.2583i 0.380384 0.658844i
\(293\) −10.5000 + 18.1865i −0.613417 + 1.06247i 0.377244 + 0.926114i \(0.376872\pi\)
−0.990660 + 0.136355i \(0.956461\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.50000 + 6.06218i 0.203433 + 0.352357i
\(297\) 0 0
\(298\) 9.00000 0.521356
\(299\) 15.0000 + 15.5885i 0.867472 + 0.901504i
\(300\) 0 0
\(301\) 10.0000 + 17.3205i 0.576390 + 0.998337i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 0 0
\(304\) 2.00000 0.114708
\(305\) −10.5000 + 18.1865i −0.601228 + 1.04136i
\(306\) 0 0
\(307\) −10.0000 −0.570730 −0.285365 0.958419i \(-0.592115\pi\)
−0.285365 + 0.958419i \(0.592115\pi\)
\(308\) 6.00000 10.3923i 0.341882 0.592157i
\(309\) 0 0
\(310\) −6.00000 10.3923i −0.340777 0.590243i
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −2.50000 4.33013i −0.141083 0.244363i
\(315\) 0 0
\(316\) 2.00000 3.46410i 0.112509 0.194871i
\(317\) −3.00000 −0.168497 −0.0842484 0.996445i \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) 0 0
\(319\) −9.00000 + 15.5885i −0.503903 + 0.872786i
\(320\) −3.00000 −0.167705
\(321\) 0 0
\(322\) −6.00000 10.3923i −0.334367 0.579141i
\(323\) −3.00000 5.19615i −0.166924 0.289122i
\(324\) 0 0
\(325\) −14.0000 + 3.46410i −0.776580 + 0.192154i
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) −1.50000 2.59808i −0.0828236 0.143455i
\(329\) 6.00000 10.3923i 0.330791 0.572946i
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) −3.00000 + 5.19615i −0.164646 + 0.285176i
\(333\) 0 0
\(334\) 0 0
\(335\) −15.0000 25.9808i −0.819538 1.41948i
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) −11.0000 6.92820i −0.598321 0.376845i
\(339\) 0 0
\(340\) 4.50000 + 7.79423i 0.244047 + 0.422701i
\(341\) −12.0000 20.7846i −0.649836 1.12555i
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 5.00000 8.66025i 0.269582 0.466930i
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) −15.0000 + 25.9808i −0.805242 + 1.39472i 0.110885 + 0.993833i \(0.464631\pi\)
−0.916127 + 0.400887i \(0.868702\pi\)
\(348\) 0 0
\(349\) 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) 8.00000 0.427618
\(351\) 0 0
\(352\) −6.00000 −0.319801
\(353\) −7.50000 12.9904i −0.399185 0.691408i 0.594441 0.804139i \(-0.297373\pi\)
−0.993626 + 0.112731i \(0.964040\pi\)
\(354\) 0 0
\(355\) −9.00000 + 15.5885i −0.477670 + 0.827349i
\(356\) −18.0000 −0.953998
\(357\) 0 0
\(358\) 3.00000 5.19615i 0.158555 0.274625i
\(359\) −6.00000 −0.316668 −0.158334 0.987386i \(-0.550612\pi\)
−0.158334 + 0.987386i \(0.550612\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 3.50000 + 6.06218i 0.183956 + 0.318621i
\(363\) 0 0
\(364\) 5.00000 + 5.19615i 0.262071 + 0.272352i
\(365\) 39.0000 2.04135
\(366\) 0 0
\(367\) −1.00000 1.73205i −0.0521996 0.0904123i 0.838745 0.544524i \(-0.183290\pi\)
−0.890945 + 0.454112i \(0.849957\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) 0 0
\(370\) −10.5000 + 18.1865i −0.545869 + 0.945473i
\(371\) 3.00000 5.19615i 0.155752 0.269771i
\(372\) 0 0
\(373\) −14.5000 + 25.1147i −0.750782 + 1.30039i 0.196663 + 0.980471i \(0.436990\pi\)
−0.947444 + 0.319921i \(0.896344\pi\)
\(374\) 9.00000 + 15.5885i 0.465379 + 0.806060i
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) −7.50000 7.79423i −0.386270 0.401423i
\(378\) 0 0
\(379\) −10.0000 17.3205i −0.513665 0.889695i −0.999874 0.0158521i \(-0.994954\pi\)
0.486209 0.873843i \(-0.338379\pi\)
\(380\) 3.00000 + 5.19615i 0.153897 + 0.266557i
\(381\) 0 0
\(382\) 12.0000 0.613973
\(383\) 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i \(-0.623227\pi\)
0.990702 0.136047i \(-0.0434398\pi\)
\(384\) 0 0
\(385\) 36.0000 1.83473
\(386\) −11.5000 + 19.9186i −0.585335 + 1.01383i
\(387\) 0 0
\(388\) −7.00000 12.1244i −0.355371 0.615521i
\(389\) −39.0000 −1.97738 −0.988689 0.149979i \(-0.952080\pi\)
−0.988689 + 0.149979i \(0.952080\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 1.50000 + 2.59808i 0.0757614 + 0.131223i
\(393\) 0 0
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) 12.0000 0.603786
\(396\) 0 0
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) −10.0000 −0.501255
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) 14.0000 3.46410i 0.697390 0.172559i
\(404\) −15.0000 −0.746278
\(405\) 0 0
\(406\) 3.00000 + 5.19615i 0.148888 + 0.257881i
\(407\) −21.0000 + 36.3731i −1.04093 + 1.80295i
\(408\) 0 0
\(409\) 0.500000 0.866025i 0.0247234 0.0428222i −0.853399 0.521258i \(-0.825463\pi\)
0.878122 + 0.478436i \(0.158796\pi\)
\(410\) 4.50000 7.79423i 0.222239 0.384930i
\(411\) 0 0
\(412\) −7.00000 + 12.1244i −0.344865 + 0.597324i
\(413\) 0 0
\(414\) 0 0
\(415\) −18.0000 −0.883585
\(416\) 1.00000 3.46410i 0.0490290 0.169842i
\(417\) 0 0
\(418\) 6.00000 + 10.3923i 0.293470 + 0.508304i
\(419\) 12.0000 + 20.7846i 0.586238 + 1.01539i 0.994720 + 0.102628i \(0.0327251\pi\)
−0.408481 + 0.912767i \(0.633942\pi\)
\(420\) 0 0
\(421\) 29.0000 1.41337 0.706687 0.707527i \(-0.250189\pi\)
0.706687 + 0.707527i \(0.250189\pi\)
\(422\) 8.00000 13.8564i 0.389434 0.674519i
\(423\) 0 0
\(424\) −3.00000 −0.145693
\(425\) −6.00000 + 10.3923i −0.291043 + 0.504101i
\(426\) 0 0
\(427\) 7.00000 + 12.1244i 0.338754 + 0.586739i
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) 30.0000 1.44673
\(431\) −3.00000 5.19615i −0.144505 0.250290i 0.784683 0.619897i \(-0.212826\pi\)
−0.929188 + 0.369607i \(0.879492\pi\)
\(432\) 0 0
\(433\) 6.50000 11.2583i 0.312370 0.541041i −0.666505 0.745501i \(-0.732210\pi\)
0.978875 + 0.204460i \(0.0655438\pi\)
\(434\) −8.00000 −0.384012
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 12.0000 0.574038
\(438\) 0 0
\(439\) −7.00000 12.1244i −0.334092 0.578664i 0.649218 0.760602i \(-0.275096\pi\)
−0.983310 + 0.181938i \(0.941763\pi\)
\(440\) −9.00000 15.5885i −0.429058 0.743151i
\(441\) 0 0
\(442\) −10.5000 + 2.59808i −0.499434 + 0.123578i
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 0 0
\(445\) −27.0000 46.7654i −1.27992 2.21689i
\(446\) −4.00000 + 6.92820i −0.189405 + 0.328060i
\(447\) 0 0
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) 9.00000 15.5885i 0.424736 0.735665i −0.571660 0.820491i \(-0.693700\pi\)
0.996396 + 0.0848262i \(0.0270335\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) −1.50000 2.59808i −0.0705541 0.122203i
\(453\) 0 0
\(454\) −18.0000 −0.844782
\(455\) −6.00000 + 20.7846i −0.281284 + 0.974398i
\(456\) 0 0
\(457\) −5.50000 9.52628i −0.257279 0.445621i 0.708233 0.705979i \(-0.249493\pi\)
−0.965512 + 0.260358i \(0.916159\pi\)
\(458\) 11.0000 + 19.0526i 0.513996 + 0.890268i
\(459\) 0 0
\(460\) −18.0000 −0.839254
\(461\) 7.50000 12.9904i 0.349310 0.605022i −0.636817 0.771015i \(-0.719749\pi\)
0.986127 + 0.165992i \(0.0530827\pi\)
\(462\) 0 0
\(463\) 38.0000 1.76601 0.883005 0.469364i \(-0.155517\pi\)
0.883005 + 0.469364i \(0.155517\pi\)
\(464\) 1.50000 2.59808i 0.0696358 0.120613i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) 18.0000 0.832941 0.416470 0.909149i \(-0.363267\pi\)
0.416470 + 0.909149i \(0.363267\pi\)
\(468\) 0 0
\(469\) −20.0000 −0.923514
\(470\) −9.00000 15.5885i −0.415139 0.719042i
\(471\) 0 0
\(472\) 0 0
\(473\) 60.0000 2.75880
\(474\) 0 0
\(475\) −4.00000 + 6.92820i −0.183533 + 0.317888i
\(476\) 6.00000 0.275010
\(477\) 0 0
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) −17.5000 18.1865i −0.797931 0.829235i
\(482\) −1.00000 −0.0455488
\(483\) 0 0
\(484\) −12.5000 21.6506i −0.568182 0.984120i
\(485\) 21.0000 36.3731i 0.953561 1.65162i
\(486\) 0 0
\(487\) −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i \(-0.847762\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(488\) 3.50000 6.06218i 0.158438 0.274422i
\(489\) 0 0
\(490\) −4.50000 + 7.79423i −0.203289 + 0.352107i
\(491\) −9.00000 15.5885i −0.406164 0.703497i 0.588292 0.808649i \(-0.299801\pi\)
−0.994456 + 0.105151i \(0.966467\pi\)
\(492\) 0 0
\(493\) −9.00000 −0.405340
\(494\) −7.00000 + 1.73205i −0.314945 + 0.0779287i
\(495\) 0 0
\(496\) 2.00000 + 3.46410i 0.0898027 + 0.155543i
\(497\) 6.00000 + 10.3923i 0.269137 + 0.466159i
\(498\) 0 0
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) 0 0
\(502\) 12.0000 0.535586
\(503\) 3.00000 5.19615i 0.133763 0.231685i −0.791361 0.611349i \(-0.790627\pi\)
0.925124 + 0.379664i \(0.123960\pi\)
\(504\) 0 0
\(505\) −22.5000 38.9711i −1.00124 1.73419i
\(506\) −36.0000 −1.60040
\(507\) 0 0
\(508\) −4.00000 −0.177471
\(509\) 1.50000 + 2.59808i 0.0664863 + 0.115158i 0.897352 0.441315i \(-0.145488\pi\)
−0.830866 + 0.556473i \(0.812154\pi\)
\(510\) 0 0
\(511\) 13.0000 22.5167i 0.575086 0.996078i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −1.50000 + 2.59808i −0.0661622 + 0.114596i
\(515\) −42.0000 −1.85074
\(516\) 0 0
\(517\) −18.0000 31.1769i −0.791639 1.37116i
\(518\) 7.00000 + 12.1244i 0.307562 + 0.532714i
\(519\) 0 0
\(520\) 10.5000 2.59808i 0.460455 0.113933i
\(521\) −33.0000 −1.44576 −0.722878 0.690976i \(-0.757181\pi\)
−0.722878 + 0.690976i \(0.757181\pi\)
\(522\) 0 0
\(523\) 17.0000 + 29.4449i 0.743358 + 1.28753i 0.950958 + 0.309320i \(0.100101\pi\)
−0.207600 + 0.978214i \(0.566565\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −3.00000 + 5.19615i −0.130806 + 0.226563i
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) −4.50000 7.79423i −0.195468 0.338560i
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) 7.50000 + 7.79423i 0.324861 + 0.337606i
\(534\) 0 0
\(535\) 9.00000 + 15.5885i 0.389104 + 0.673948i
\(536\) 5.00000 + 8.66025i 0.215967 + 0.374066i
\(537\) 0 0
\(538\) −18.0000 −0.776035
\(539\) −9.00000 + 15.5885i −0.387657 + 0.671442i
\(540\) 0 0
\(541\) 29.0000 1.24681 0.623404 0.781900i \(-0.285749\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) −42.0000 −1.79908
\(546\) 0 0
\(547\) −34.0000 −1.45374 −0.726868 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) 4.50000 + 7.79423i 0.192230 + 0.332953i
\(549\) 0 0
\(550\) 12.0000 20.7846i 0.511682 0.886259i
\(551\) −6.00000 −0.255609
\(552\) 0 0
\(553\) 4.00000 6.92820i 0.170097 0.294617i
\(554\) 17.0000 0.722261
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) 1.50000 + 2.59808i 0.0635570 + 0.110084i 0.896053 0.443947i \(-0.146422\pi\)
−0.832496 + 0.554031i \(0.813089\pi\)
\(558\) 0 0
\(559\) −10.0000 + 34.6410i −0.422955 + 1.46516i
\(560\) −6.00000 −0.253546
\(561\) 0 0
\(562\) 4.50000 + 7.79423i 0.189821 + 0.328780i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) 4.50000 7.79423i 0.189316 0.327906i
\(566\) −7.00000 + 12.1244i −0.294232 + 0.509625i
\(567\) 0 0
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) 21.0000 5.19615i 0.878054 0.217262i
\(573\) 0 0
\(574\) −3.00000 5.19615i −0.125218 0.216883i
\(575\) −12.0000 20.7846i −0.500435 0.866778i
\(576\) 0 0
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 0 0
\(580\) 9.00000 0.373705
\(581\) −6.00000 + 10.3923i −0.248922 + 0.431145i
\(582\) 0 0
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) −13.0000 −0.537944
\(585\) 0 0
\(586\) 21.0000 0.867502
\(587\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) 0 0
\(589\) 4.00000 6.92820i 0.164817 0.285472i
\(590\) 0 0
\(591\) 0 0
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) −9.00000 −0.369586 −0.184793 0.982777i \(-0.559161\pi\)
−0.184793 + 0.982777i \(0.559161\pi\)
\(594\) 0 0
\(595\) 9.00000 + 15.5885i 0.368964 + 0.639064i
\(596\) −4.50000 7.79423i −0.184327 0.319264i
\(597\) 0 0
\(598\) 6.00000 20.7846i 0.245358 0.849946i
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) 18.5000 + 32.0429i 0.754631 + 1.30706i 0.945558 + 0.325455i \(0.105517\pi\)
−0.190927 + 0.981604i \(0.561149\pi\)
\(602\) 10.0000 17.3205i 0.407570 0.705931i
\(603\) 0 0
\(604\) 5.00000 8.66025i 0.203447 0.352381i
\(605\) 37.5000 64.9519i 1.52459 2.64067i
\(606\) 0 0
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) −1.00000 1.73205i −0.0405554 0.0702439i
\(609\) 0 0
\(610\) 21.0000 0.850265
\(611\) 21.0000 5.19615i 0.849569 0.210214i
\(612\) 0 0
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) 5.00000 + 8.66025i 0.201784 + 0.349499i
\(615\) 0 0
\(616\) −12.0000 −0.483494
\(617\) −7.50000 + 12.9904i −0.301939 + 0.522973i −0.976575 0.215177i \(-0.930967\pi\)
0.674636 + 0.738150i \(0.264300\pi\)
\(618\) 0 0
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) −6.00000 + 10.3923i −0.240966 + 0.417365i
\(621\) 0 0
\(622\) −15.0000 25.9808i −0.601445 1.04173i
\(623\) −36.0000 −1.44231
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 5.00000 + 8.66025i 0.199840 + 0.346133i
\(627\) 0 0
\(628\) −2.50000 + 4.33013i −0.0997609 + 0.172791i
\(629\) −21.0000 −0.837325
\(630\) 0 0
\(631\) −10.0000 + 17.3205i −0.398094 + 0.689519i −0.993491 0.113913i \(-0.963661\pi\)
0.595397 + 0.803432i \(0.296995\pi\)
\(632\) −4.00000 −0.159111
\(633\) 0 0
\(634\) 1.50000 + 2.59808i 0.0595726 + 0.103183i
\(635\) −6.00000 10.3923i −0.238103 0.412406i
\(636\) 0 0
\(637\) −7.50000 7.79423i −0.297161 0.308819i
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) −1.50000 + 2.59808i −0.0592464 + 0.102618i −0.894127 0.447813i \(-0.852203\pi\)
0.834881 + 0.550431i \(0.185536\pi\)
\(642\) 0 0
\(643\) 8.00000 13.8564i 0.315489 0.546443i −0.664052 0.747686i \(-0.731165\pi\)
0.979541 + 0.201243i \(0.0644981\pi\)
\(644\) −6.00000 + 10.3923i −0.236433 + 0.409514i
\(645\) 0 0
\(646\) −3.00000 + 5.19615i −0.118033 + 0.204440i
\(647\) 12.0000 + 20.7846i 0.471769 + 0.817127i 0.999478 0.0322975i \(-0.0102824\pi\)
−0.527710 + 0.849425i \(0.676949\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 10.0000 + 10.3923i 0.392232 + 0.407620i
\(651\) 0 0
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 21.0000 + 36.3731i 0.821794 + 1.42339i 0.904345 + 0.426801i \(0.140360\pi\)
−0.0825519 + 0.996587i \(0.526307\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) 0 0
\(658\) −12.0000 −0.467809
\(659\) 12.0000 20.7846i 0.467454 0.809653i −0.531855 0.846836i \(-0.678505\pi\)
0.999309 + 0.0371821i \(0.0118382\pi\)
\(660\) 0 0
\(661\) −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i \(-0.197668\pi\)
−0.910541 + 0.413419i \(0.864334\pi\)
\(662\) −4.00000 −0.155464
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 6.00000 + 10.3923i 0.232670 + 0.402996i
\(666\) 0 0
\(667\) 9.00000 15.5885i 0.348481 0.603587i
\(668\) 0 0
\(669\) 0 0
\(670\) −15.0000 + 25.9808i −0.579501 + 1.00372i
\(671\) 42.0000 1.62139
\(672\) 0 0
\(673\) 6.50000 + 11.2583i 0.250557 + 0.433977i 0.963679 0.267063i \(-0.0860531\pi\)
−0.713123 + 0.701039i \(0.752720\pi\)
\(674\) −11.5000 19.9186i −0.442963 0.767235i
\(675\) 0 0
\(676\) −0.500000 + 12.9904i −0.0192308 + 0.499630i
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 0 0
\(679\) −14.0000 24.2487i −0.537271 0.930580i
\(680\) 4.50000 7.79423i 0.172567 0.298895i
\(681\) 0 0
\(682\) −12.0000 + 20.7846i −0.459504 + 0.795884i
\(683\) −24.0000 + 41.5692i −0.918334 + 1.59060i −0.116390 + 0.993204i \(0.537132\pi\)
−0.801945 + 0.597398i \(0.796201\pi\)
\(684\) 0 0
\(685\) −13.5000 + 23.3827i −0.515808 + 0.893407i
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 0 0
\(688\) −10.0000 −0.381246
\(689\) 10.5000 2.59808i 0.400018 0.0989788i
\(690\) 0 0
\(691\) −13.0000 22.5167i −0.494543 0.856574i 0.505437 0.862864i \(-0.331331\pi\)
−0.999980 + 0.00628943i \(0.997998\pi\)
\(692\) −3.00000 5.19615i −0.114043 0.197528i
\(693\) 0 0
\(694\) 30.0000 1.13878
\(695\) −6.00000 + 10.3923i −0.227593 + 0.394203i
\(696\) 0 0
\(697\) 9.00000 0.340899
\(698\) 5.00000 8.66025i 0.189253 0.327795i
\(699\) 0 0
\(700\) −4.00000 6.92820i −0.151186 0.261861i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) −14.0000 −0.528020
\(704\) 3.00000 + 5.19615i 0.113067 + 0.195837i
\(705\) 0 0
\(706\) −7.50000 + 12.9904i −0.282266 + 0.488899i
\(707\) −30.0000 −1.12827
\(708\) 0 0
\(709\) −2.50000 + 4.33013i −0.0938895 + 0.162621i −0.909145 0.416481i \(-0.863263\pi\)
0.815255 + 0.579102i \(0.196597\pi\)
\(710\) 18.0000 0.675528
\(711\) 0 0
\(712\) 9.00000 + 15.5885i 0.337289 + 0.584202i
\(713\) 12.0000 + 20.7846i 0.449404 + 0.778390i
\(714\) 0 0
\(715\) 45.0000 + 46.7654i 1.68290 + 1.74893i
\(716\) −6.00000 −0.224231
\(717\) 0 0
\(718\) 3.00000 + 5.19615i 0.111959 + 0.193919i
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 0 0
\(721\) −14.0000 + 24.2487i −0.521387 + 0.903069i
\(722\) 7.50000 12.9904i 0.279121 0.483452i
\(723\) 0 0
\(724\) 3.50000 6.06218i 0.130076 0.225299i
\(725\) 6.00000 + 10.3923i 0.222834 + 0.385961i
\(726\) 0 0
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) 2.00000 6.92820i 0.0741249 0.256776i
\(729\) 0 0
\(730\) −19.5000 33.7750i −0.721727 1.25007i
\(731\) 15.0000 + 25.9808i 0.554795 + 0.960933i
\(732\) 0 0
\(733\) −31.0000 −1.14501 −0.572506 0.819901i \(-0.694029\pi\)
−0.572506 + 0.819901i \(0.694029\pi\)
\(734\) −1.00000 + 1.73205i −0.0369107 + 0.0639312i
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) −30.0000 + 51.9615i −1.10506 + 1.91403i
\(738\) 0 0
\(739\) 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) 21.0000 0.771975
\(741\) 0 0
\(742\) −6.00000 −0.220267
\(743\) −18.0000 31.1769i −0.660356 1.14377i −0.980522 0.196409i \(-0.937072\pi\)
0.320166 0.947361i \(-0.396261\pi\)
\(744\) 0 0
\(745\) 13.5000 23.3827i 0.494602 0.856675i
\(746\) 29.0000 1.06177
\(747\) 0 0
\(748\) 9.00000 15.5885i 0.329073 0.569970i
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −7.00000 12.1244i −0.255434 0.442424i 0.709580 0.704625i \(-0.248885\pi\)
−0.965013 + 0.262201i \(0.915552\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) −3.00000 + 10.3923i −0.109254 + 0.378465i
\(755\) 30.0000 1.09181
\(756\) 0 0
\(757\) 17.0000 + 29.4449i 0.617876 + 1.07019i 0.989873 + 0.141958i \(0.0453398\pi\)
−0.371997 + 0.928234i \(0.621327\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) 0 0
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) −15.0000 + 25.9808i −0.543750 + 0.941802i 0.454935 + 0.890525i \(0.349663\pi\)
−0.998684 + 0.0512772i \(0.983671\pi\)
\(762\) 0 0
\(763\) −14.0000 + 24.2487i −0.506834 + 0.877862i
\(764\) −6.00000 10.3923i −0.217072 0.375980i
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) 0 0
\(769\) −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(770\) −18.0000 31.1769i −0.648675 1.12354i
\(771\) 0 0
\(772\) 23.0000 0.827788
\(773\) −15.0000 + 25.9808i −0.539513 + 0.934463i 0.459418 + 0.888220i \(0.348058\pi\)
−0.998930 + 0.0462427i \(0.985275\pi\)
\(774\) 0 0
\(775\) −16.0000 −0.574737
\(776\) −7.00000 + 12.1244i −0.251285 + 0.435239i
\(777\) 0 0
\(778\) 19.5000 + 33.7750i 0.699109 + 1.21089i
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) −9.00000 15.5885i −0.321839 0.557442i
\(783\) 0 0
\(784\) 1.50000 2.59808i 0.0535714 0.0927884i
\(785\) −15.0000 −0.535373
\(786\) 0 0
\(787\) 14.0000 24.2487i 0.499046 0.864373i −0.500953 0.865474i \(-0.667017\pi\)
0.999999 + 0.00110111i \(0.000350496\pi\)
\(788\) −6.00000 −0.213741
\(789\) 0 0
\(790\) −6.00000 10.3923i −0.213470 0.369742i
\(791\) −3.00000 5.19615i −0.106668 0.184754i
\(792\) 0 0
\(793\) −7.00000 + 24.2487i −0.248577 + 0.861097i
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) 5.00000 + 8.66025i 0.177220 + 0.306955i
\(797\) 15.0000 25.9808i 0.531327 0.920286i −0.468004 0.883726i \(-0.655027\pi\)
0.999331 0.0365596i \(-0.0116399\pi\)
\(798\) 0 0
\(799\) 9.00000 15.5885i 0.318397 0.551480i
\(800\) −2.00000 + 3.46410i −0.0707107 + 0.122474i
\(801\) 0 0
\(802\) −1.50000 + 2.59808i −0.0529668 + 0.0917413i
\(803\) −39.0000 67.5500i −1.37628 2.38379i
\(804\) 0 0
\(805\) −36.0000 −1.26883
\(806\) −10.0000 10.3923i −0.352235 0.366053i
\(807\) 0 0
\(808\) 7.50000 + 12.9904i 0.263849 + 0.457000i
\(809\) −25.5000 44.1673i −0.896532 1.55284i −0.831897 0.554930i \(-0.812745\pi\)
−0.0646355 0.997909i \(-0.520588\pi\)
\(810\) 0 0
\(811\) −4.00000 −0.140459 −0.0702295 0.997531i \(-0.522373\pi\)
−0.0702295 + 0.997531i \(0.522373\pi\)
\(812\) 3.00000 5.19615i 0.105279 0.182349i
\(813\) 0 0
\(814\) 42.0000 1.47210
\(815\) −6.00000 + 10.3923i −0.210171 + 0.364027i
\(816\) 0 0
\(817\) 10.0000 + 17.3205i 0.349856 + 0.605968i
\(818\) −1.00000 −0.0349642
\(819\) 0 0
\(820\) −9.00000 −0.314294
\(821\) 9.00000 + 15.5885i 0.314102 + 0.544041i 0.979246 0.202674i \(-0.0649632\pi\)
−0.665144 + 0.746715i \(0.731630\pi\)
\(822\) 0 0
\(823\) 20.0000 34.6410i 0.697156 1.20751i −0.272292 0.962215i \(-0.587782\pi\)
0.969448 0.245295i \(-0.0788849\pi\)
\(824\) 14.0000 0.487713
\(825\) 0 0
\(826\) 0 0
\(827\) 48.0000 1.66912 0.834562 0.550914i \(-0.185721\pi\)
0.834562 + 0.550914i \(0.185721\pi\)
\(828\) 0 0
\(829\) −8.50000 14.7224i −0.295217 0.511331i 0.679818 0.733381i \(-0.262059\pi\)
−0.975035 + 0.222049i \(0.928725\pi\)
\(830\) 9.00000 + 15.5885i 0.312395 + 0.541083i
\(831\) 0 0
\(832\) −3.50000 + 0.866025i −0.121341 + 0.0300240i
\(833\) −9.00000 −0.311832
\(834\) 0 0
\(835\) 0 0
\(836\) 6.00000 10.3923i 0.207514 0.359425i
\(837\) 0 0
\(838\) 12.0000 20.7846i 0.414533 0.717992i
\(839\) −6.00000 + 10.3923i −0.207143 + 0.358782i −0.950813 0.309764i \(-0.899750\pi\)
0.743670 + 0.668546i \(0.233083\pi\)
\(840\) 0 0
\(841\) 10.0000 17.3205i 0.344828 0.597259i
\(842\) −14.5000 25.1147i −0.499703 0.865511i
\(843\) 0 0
\(844\) −16.0000 −0.550743
\(845\) −34.5000 + 18.1865i −1.18684 + 0.625636i
\(846\) 0 0
\(847\) −25.0000 43.3013i −0.859010 1.48785i
\(848\) 1.50000 + 2.59808i 0.0515102 + 0.0892183i
\(849\) 0 0
\(850\) 12.0000 0.411597
\(851\) 21.0000 36.3731i 0.719871 1.24685i
\(852\) 0 0
\(853\) −19.0000 −0.650548 −0.325274 0.945620i \(-0.605456\pi\)
−0.325274 + 0.945620i \(0.605456\pi\)
\(854\) 7.00000 12.1244i 0.239535 0.414887i
\(855\) 0 0
\(856\) −3.00000 5.19615i −0.102538 0.177601i
\(857\) −21.0000 −0.717346 −0.358673 0.933463i \(-0.616771\pi\)
−0.358673 + 0.933463i \(0.616771\pi\)
\(858\) 0 0
\(859\) 26.0000 0.887109 0.443554 0.896248i \(-0.353717\pi\)
0.443554 + 0.896248i \(0.353717\pi\)
\(860\) −15.0000 25.9808i −0.511496 0.885937i
\(861\) 0 0
\(862\) −3.00000 + 5.19615i −0.102180 + 0.176982i
\(863\) −18.0000 −0.612727 −0.306364 0.951915i \(-0.599112\pi\)
−0.306364 + 0.951915i \(0.599112\pi\)
\(864\) 0 0
\(865\) 9.00000 15.5885i 0.306009 0.530023i
\(866\) −13.0000 −0.441758
\(867\) 0 0
\(868\) 4.00000 + 6.92820i 0.135769 + 0.235159i
\(869\) −12.0000 20.7846i −0.407072 0.705070i
\(870\) 0 0
\(871\) −25.0000 25.9808i −0.847093 0.880325i
\(872\) 14.0000 0.474100
\(873\) 0 0
\(874\) −6.00000 10.3923i −0.202953 0.351525i
\(875\) −3.00000 + 5.19615i −0.101419 + 0.175662i
\(876\) 0 0
\(877\) −20.5000 + 35.5070i −0.692236 + 1.19899i 0.278868 + 0.960329i \(0.410041\pi\)
−0.971104 + 0.238658i \(0.923292\pi\)
\(878\) −7.00000 + 12.1244i −0.236239 + 0.409177i
\(879\) 0 0
\(880\) −9.00000 + 15.5885i −0.303390 + 0.525487i
\(881\) 16.5000 + 28.5788i 0.555899 + 0.962846i 0.997833 + 0.0657979i \(0.0209593\pi\)
−0.441934 + 0.897048i \(0.645707\pi\)
\(882\) 0 0
\(883\) 8.00000 0.269221 0.134611 0.990899i \(-0.457022\pi\)
0.134611 + 0.990899i \(0.457022\pi\)
\(884\) 7.50000 + 7.79423i 0.252252 + 0.262148i
\(885\) 0 0
\(886\) −18.0000 31.1769i −0.604722 1.04741i
\(887\) −24.0000 41.5692i −0.805841 1.39576i −0.915722 0.401813i \(-0.868380\pi\)
0.109881 0.993945i \(-0.464953\pi\)
\(888\) 0 0
\(889\) −8.00000 −0.268311
\(890\) −27.0000 + 46.7654i −0.905042 + 1.56758i
\(891\) 0 0
\(892\) 8.00000 0.267860
\(893\) 6.00000 10.3923i 0.200782 0.347765i
\(894\) 0 0
\(895\) −9.00000 15.5885i −0.300837 0.521065i
\(896\) 2.00000 0.0668153
\(897\) 0 0
\(898\) −18.0000 −0.600668
\(899\) −6.00000 10.3923i −0.200111 0.346603i
\(900\) 0 0
\(901\) 4.50000 7.79423i 0.149917 0.259663i
\(902\) −18.0000 −0.599334
\(903\) 0 0
\(904\) −1.50000 + 2.59808i −0.0498893 + 0.0864107i
\(905\) 21.0000 0.698064
\(906\) 0 0
\(907\) −22.0000 38.1051i −0.730498 1.26526i −0.956671 0.291172i \(-0.905955\pi\)
0.226173 0.974087i \(-0.427379\pi\)
\(908\) 9.00000 + 15.5885i 0.298675 + 0.517321i
\(909\) 0 0
\(910\) 21.0000 5.19615i 0.696143 0.172251i
\(911\) 24.0000 0.795155 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(912\) 0 0
\(913\) 18.0000 + 31.1769i 0.595713 + 1.03181i
\(914\) −5.50000 + 9.52628i −0.181924 + 0.315101i
\(915\) 0 0
\(916\) 11.0000 19.0526i 0.363450 0.629514i
\(917\) 0 0
\(918\) 0 0
\(919\) 8.00000 13.8564i 0.263896 0.457081i −0.703378 0.710816i \(-0.748326\pi\)
0.967274 + 0.253735i \(0.0816592\pi\)
\(920\) 9.00000 + 15.5885i 0.296721 + 0.513936i
\(921\) 0 0
\(922\) −15.0000 −0.493999
\(923\) −6.00000 + 20.7846i −0.197492 + 0.684134i
\(924\) 0 0
\(925\) 14.0000 + 24.2487i 0.460317 + 0.797293i
\(926\) −19.0000 32.9090i −0.624379 1.08146i
\(927\) 0 0
\(928\) −3.00000 −0.0984798
\(929\) 16.5000 28.5788i 0.541347 0.937641i −0.457480 0.889220i \(-0.651248\pi\)
0.998827 0.0484211i \(-0.0154190\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) −3.00000 + 5.19615i −0.0982683 + 0.170206i
\(933\) 0 0
\(934\) −9.00000 15.5885i −0.294489 0.510070i
\(935\) 54.0000 1.76599
\(936\) 0 0
\(937\) 47.0000 1.53542 0.767712 0.640796i \(-0.221395\pi\)
0.767712 + 0.640796i \(0.221395\pi\)
\(938\) 10.0000 + 17.3205i 0.326512 + 0.565535i
\(939\) 0 0
\(940\) −9.00000 + 15.5885i −0.293548 + 0.508439i
\(941\) −42.0000 −1.36916 −0.684580 0.728937i \(-0.740015\pi\)
−0.684580 + 0.728937i \(0.740015\pi\)
\(942\) 0 0
\(943\) −9.00000 + 15.5885i −0.293080 + 0.507630i
\(944\) 0 0
\(945\) 0 0
\(946\) −30.0000 51.9615i −0.975384 1.68941i
\(947\) 12.0000 + 20.7846i 0.389948 + 0.675409i 0.992442 0.122714i \(-0.0391598\pi\)
−0.602494 + 0.798123i \(0.705826\pi\)
\(948\) 0 0
\(949\) 45.5000 11.2583i 1.47699 0.365461i
\(950\) 8.00000 0.259554
\(951\) 0 0
\(952\) −3.00000 5.19615i −0.0972306 0.168408i
\(953\) 27.0000 46.7654i 0.874616 1.51488i 0.0174443 0.999848i \(-0.494447\pi\)
0.857171 0.515031i \(-0.172220\pi\)
\(954\) 0 0
\(955\) 18.0000 31.1769i 0.582466 1.00886i
\(956\) 3.00000 5.19615i 0.0970269 0.168056i
\(957\) 0 0
\(958\) 0 0
\(959\) 9.00000 + 15.5885i 0.290625 + 0.503378i
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −7.00000 + 24.2487i −0.225689 + 0.781810i
\(963\) 0 0
\(964\) 0.500000 + 0.866025i 0.0161039 + 0.0278928i
\(965\) 34.5000 + 59.7558i 1.11059 + 1.92361i
\(966\) 0 0
\(967\) −22.0000 −0.707472 −0.353736 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) −12.5000 + 21.6506i −0.401765 + 0.695878i
\(969\) 0 0
\(970\) −42.0000 −1.34854
\(971\) 30.0000 51.9615i 0.962746 1.66752i 0.247193 0.968966i \(-0.420492\pi\)
0.715553 0.698558i \(-0.246175\pi\)
\(972\) 0 0
\(973\) 4.00000 + 6.92820i 0.128234 + 0.222108i
\(974\) 2.00000 0.0640841
\(975\) 0 0
\(976\) −7.00000 −0.224065
\(977\) −1.50000 2.59808i −0.0479893 0.0831198i 0.841033 0.540984i \(-0.181948\pi\)
−0.889022 + 0.457864i \(0.848615\pi\)
\(978\) 0 0
\(979\) −54.0000 + 93.5307i −1.72585 + 2.98926i
\(980\) 9.00000 0.287494
\(981\) 0 0
\(982\) −9.00000 + 15.5885i −0.287202 + 0.497448i
\(983\) 36.0000 1.14822 0.574111 0.818778i \(-0.305348\pi\)
0.574111 + 0.818778i \(0.305348\pi\)
\(984\) 0 0
\(985\) −9.00000 15.5885i −0.286764 0.496690i
\(986\) 4.50000 + 7.79423i 0.143309 + 0.248219i
\(987\) 0 0
\(988\) 5.00000 + 5.19615i 0.159071 + 0.165312i
\(989\) −60.0000 −1.90789
\(990\) 0 0
\(991\) −19.0000 32.9090i −0.603555 1.04539i −0.992278 0.124033i \(-0.960417\pi\)
0.388723 0.921355i \(-0.372916\pi\)
\(992\) 2.00000 3.46410i 0.0635001 0.109985i
\(993\) 0 0
\(994\) 6.00000 10.3923i 0.190308 0.329624i
\(995\) −15.0000 + 25.9808i −0.475532 + 0.823646i
\(996\) 0 0
\(997\) −2.50000 + 4.33013i −0.0791758 + 0.137136i −0.902895 0.429862i \(-0.858562\pi\)
0.823719 + 0.566999i \(0.191896\pi\)
\(998\) −16.0000 27.7128i −0.506471 0.877234i
\(999\) 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 234.2.h.a.55.1 2
3.2 odd 2 78.2.e.a.55.1 2
4.3 odd 2 1872.2.t.c.289.1 2
12.11 even 2 624.2.q.g.289.1 2
13.2 odd 12 3042.2.b.h.1351.1 2
13.3 even 3 3042.2.a.i.1.1 1
13.9 even 3 inner 234.2.h.a.217.1 2
13.10 even 6 3042.2.a.h.1.1 1
13.11 odd 12 3042.2.b.h.1351.2 2
15.2 even 4 1950.2.z.g.1849.1 4
15.8 even 4 1950.2.z.g.1849.2 4
15.14 odd 2 1950.2.i.m.601.1 2
39.2 even 12 1014.2.b.c.337.2 2
39.5 even 4 1014.2.i.b.361.2 4
39.8 even 4 1014.2.i.b.361.1 4
39.11 even 12 1014.2.b.c.337.1 2
39.17 odd 6 1014.2.e.a.529.1 2
39.20 even 12 1014.2.i.b.823.2 4
39.23 odd 6 1014.2.a.f.1.1 1
39.29 odd 6 1014.2.a.c.1.1 1
39.32 even 12 1014.2.i.b.823.1 4
39.35 odd 6 78.2.e.a.61.1 yes 2
39.38 odd 2 1014.2.e.a.991.1 2
52.35 odd 6 1872.2.t.c.1153.1 2
156.23 even 6 8112.2.a.c.1.1 1
156.35 even 6 624.2.q.g.529.1 2
156.107 even 6 8112.2.a.m.1.1 1
195.74 odd 6 1950.2.i.m.451.1 2
195.113 even 12 1950.2.z.g.1699.1 4
195.152 even 12 1950.2.z.g.1699.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.2.e.a.55.1 2 3.2 odd 2
78.2.e.a.61.1 yes 2 39.35 odd 6
234.2.h.a.55.1 2 1.1 even 1 trivial
234.2.h.a.217.1 2 13.9 even 3 inner
624.2.q.g.289.1 2 12.11 even 2
624.2.q.g.529.1 2 156.35 even 6
1014.2.a.c.1.1 1 39.29 odd 6
1014.2.a.f.1.1 1 39.23 odd 6
1014.2.b.c.337.1 2 39.11 even 12
1014.2.b.c.337.2 2 39.2 even 12
1014.2.e.a.529.1 2 39.17 odd 6
1014.2.e.a.991.1 2 39.38 odd 2
1014.2.i.b.361.1 4 39.8 even 4
1014.2.i.b.361.2 4 39.5 even 4
1014.2.i.b.823.1 4 39.32 even 12
1014.2.i.b.823.2 4 39.20 even 12
1872.2.t.c.289.1 2 4.3 odd 2
1872.2.t.c.1153.1 2 52.35 odd 6
1950.2.i.m.451.1 2 195.74 odd 6
1950.2.i.m.601.1 2 15.14 odd 2
1950.2.z.g.1699.1 4 195.113 even 12
1950.2.z.g.1699.2 4 195.152 even 12
1950.2.z.g.1849.1 4 15.2 even 4
1950.2.z.g.1849.2 4 15.8 even 4
3042.2.a.h.1.1 1 13.10 even 6
3042.2.a.i.1.1 1 13.3 even 3
3042.2.b.h.1351.1 2 13.2 odd 12
3042.2.b.h.1351.2 2 13.11 odd 12
8112.2.a.c.1.1 1 156.23 even 6
8112.2.a.m.1.1 1 156.107 even 6