Properties

Label 1638.2.bj.c.1135.1
Level $1638$
Weight $2$
Character 1638.1135
Analytic conductor $13.079$
Analytic rank $0$
Dimension $4$
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] = [1638,2,Mod(127,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.127");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.bj (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: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 182)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1135.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1638.1135
Dual form 1638.2.bj.c.127.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(-0.633975 - 0.366025i) q^{11} +(2.59808 - 2.50000i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.86603 + 4.96410i) q^{17} +(-1.26795 + 0.732051i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.366025 + 0.633975i) q^{22} +(-0.633975 + 1.09808i) q^{23} +4.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(-1.50000 + 2.59808i) q^{29} -5.26795i q^{31} +(0.866025 - 0.500000i) q^{32} -5.73205i q^{34} +(0.500000 + 0.866025i) q^{35} +(4.50000 + 2.59808i) q^{37} +1.46410 q^{38} -1.00000 q^{40} +(2.13397 + 1.23205i) q^{41} +(-6.09808 - 10.5622i) q^{43} -0.732051i q^{44} +(1.09808 - 0.633975i) q^{46} -2.92820i q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.46410 - 2.00000i) q^{50} +(3.46410 + 1.00000i) q^{52} -1.53590 q^{53} +(-0.366025 + 0.633975i) q^{55} +(0.500000 + 0.866025i) q^{56} +(2.59808 - 1.50000i) q^{58} +(9.29423 - 5.36603i) q^{59} +(5.86603 + 10.1603i) q^{61} +(-2.63397 + 4.56218i) q^{62} -1.00000 q^{64} +(-2.50000 - 2.59808i) q^{65} +(10.0981 + 5.83013i) q^{67} +(-2.86603 + 4.96410i) q^{68} -1.00000i q^{70} +(12.0000 - 6.92820i) q^{71} -11.3923i q^{73} +(-2.59808 - 4.50000i) q^{74} +(-1.26795 - 0.732051i) q^{76} +0.732051 q^{77} -3.80385 q^{79} +(0.866025 + 0.500000i) q^{80} +(-1.23205 - 2.13397i) q^{82} -3.80385i q^{83} +(4.96410 - 2.86603i) q^{85} +12.1962i q^{86} +(-0.366025 + 0.633975i) q^{88} +(-2.19615 - 1.26795i) q^{89} +(-1.00000 + 3.46410i) q^{91} -1.26795 q^{92} +(-1.46410 + 2.53590i) q^{94} +(0.732051 + 1.26795i) q^{95} +(-4.73205 + 2.73205i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 2 q^{10} - 6 q^{11} + 4 q^{14} - 2 q^{16} + 8 q^{17} - 12 q^{19} - 2 q^{22} - 6 q^{23} + 16 q^{25} - 14 q^{26} - 6 q^{29} + 2 q^{35} + 18 q^{37} - 8 q^{38} - 4 q^{40} + 12 q^{41} - 14 q^{43} - 6 q^{46} + 2 q^{49} - 20 q^{53} + 2 q^{55} + 2 q^{56} + 6 q^{59} + 20 q^{61} - 14 q^{62} - 4 q^{64} - 10 q^{65} + 30 q^{67} - 8 q^{68} + 48 q^{71} - 12 q^{76} - 4 q^{77} - 36 q^{79} + 2 q^{82} + 6 q^{85} + 2 q^{88} + 12 q^{89} - 4 q^{91} - 12 q^{92} + 8 q^{94} - 4 q^{95} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i −0.974679 0.223607i \(-0.928217\pi\)
0.974679 0.223607i \(-0.0717831\pi\)
\(6\) 0 0
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −0.633975 0.366025i −0.191151 0.110361i 0.401371 0.915916i \(-0.368534\pi\)
−0.592521 + 0.805555i \(0.701867\pi\)
\(12\) 0 0
\(13\) 2.59808 2.50000i 0.720577 0.693375i
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.86603 + 4.96410i 0.695113 + 1.20397i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) 0 0
\(19\) −1.26795 + 0.732051i −0.290887 + 0.167944i −0.638342 0.769753i \(-0.720379\pi\)
0.347455 + 0.937697i \(0.387046\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 0 0
\(22\) 0.366025 + 0.633975i 0.0780369 + 0.135164i
\(23\) −0.633975 + 1.09808i −0.132193 + 0.228965i −0.924522 0.381130i \(-0.875535\pi\)
0.792329 + 0.610094i \(0.208868\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) −3.50000 + 0.866025i −0.686406 + 0.169842i
\(27\) 0 0
\(28\) −0.866025 0.500000i −0.163663 0.0944911i
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) 5.26795i 0.946152i −0.881022 0.473076i \(-0.843144\pi\)
0.881022 0.473076i \(-0.156856\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 5.73205i 0.983039i
\(35\) 0.500000 + 0.866025i 0.0845154 + 0.146385i
\(36\) 0 0
\(37\) 4.50000 + 2.59808i 0.739795 + 0.427121i 0.821995 0.569495i \(-0.192861\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 1.46410 0.237509
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 2.13397 + 1.23205i 0.333271 + 0.192414i 0.657292 0.753636i \(-0.271702\pi\)
−0.324021 + 0.946050i \(0.605035\pi\)
\(42\) 0 0
\(43\) −6.09808 10.5622i −0.929948 1.61072i −0.783404 0.621513i \(-0.786518\pi\)
−0.146544 0.989204i \(-0.546815\pi\)
\(44\) 0.732051i 0.110361i
\(45\) 0 0
\(46\) 1.09808 0.633975i 0.161903 0.0934745i
\(47\) 2.92820i 0.427122i −0.976930 0.213561i \(-0.931494\pi\)
0.976930 0.213561i \(-0.0685063\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −3.46410 2.00000i −0.489898 0.282843i
\(51\) 0 0
\(52\) 3.46410 + 1.00000i 0.480384 + 0.138675i
\(53\) −1.53590 −0.210972 −0.105486 0.994421i \(-0.533640\pi\)
−0.105486 + 0.994421i \(0.533640\pi\)
\(54\) 0 0
\(55\) −0.366025 + 0.633975i −0.0493549 + 0.0854851i
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 0 0
\(58\) 2.59808 1.50000i 0.341144 0.196960i
\(59\) 9.29423 5.36603i 1.21001 0.698597i 0.247245 0.968953i \(-0.420475\pi\)
0.962760 + 0.270356i \(0.0871414\pi\)
\(60\) 0 0
\(61\) 5.86603 + 10.1603i 0.751068 + 1.30089i 0.947306 + 0.320331i \(0.103794\pi\)
−0.196238 + 0.980556i \(0.562873\pi\)
\(62\) −2.63397 + 4.56218i −0.334515 + 0.579397i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −2.50000 2.59808i −0.310087 0.322252i
\(66\) 0 0
\(67\) 10.0981 + 5.83013i 1.23368 + 0.712263i 0.967794 0.251742i \(-0.0810035\pi\)
0.265882 + 0.964006i \(0.414337\pi\)
\(68\) −2.86603 + 4.96410i −0.347557 + 0.601986i
\(69\) 0 0
\(70\) 1.00000i 0.119523i
\(71\) 12.0000 6.92820i 1.42414 0.822226i 0.427489 0.904021i \(-0.359398\pi\)
0.996649 + 0.0817942i \(0.0260650\pi\)
\(72\) 0 0
\(73\) 11.3923i 1.33337i −0.745340 0.666684i \(-0.767713\pi\)
0.745340 0.666684i \(-0.232287\pi\)
\(74\) −2.59808 4.50000i −0.302020 0.523114i
\(75\) 0 0
\(76\) −1.26795 0.732051i −0.145444 0.0839720i
\(77\) 0.732051 0.0834249
\(78\) 0 0
\(79\) −3.80385 −0.427966 −0.213983 0.976837i \(-0.568644\pi\)
−0.213983 + 0.976837i \(0.568644\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) 0 0
\(82\) −1.23205 2.13397i −0.136057 0.235658i
\(83\) 3.80385i 0.417527i −0.977966 0.208763i \(-0.933056\pi\)
0.977966 0.208763i \(-0.0669438\pi\)
\(84\) 0 0
\(85\) 4.96410 2.86603i 0.538432 0.310864i
\(86\) 12.1962i 1.31514i
\(87\) 0 0
\(88\) −0.366025 + 0.633975i −0.0390184 + 0.0675819i
\(89\) −2.19615 1.26795i −0.232792 0.134402i 0.379068 0.925369i \(-0.376245\pi\)
−0.611859 + 0.790967i \(0.709578\pi\)
\(90\) 0 0
\(91\) −1.00000 + 3.46410i −0.104828 + 0.363137i
\(92\) −1.26795 −0.132193
\(93\) 0 0
\(94\) −1.46410 + 2.53590i −0.151011 + 0.261558i
\(95\) 0.732051 + 1.26795i 0.0751068 + 0.130089i
\(96\) 0 0
\(97\) −4.73205 + 2.73205i −0.480467 + 0.277398i −0.720611 0.693340i \(-0.756139\pi\)
0.240144 + 0.970737i \(0.422805\pi\)
\(98\) −0.866025 + 0.500000i −0.0874818 + 0.0505076i
\(99\) 0 0
\(100\) 2.00000 + 3.46410i 0.200000 + 0.346410i
\(101\) −0.598076 + 1.03590i −0.0595108 + 0.103076i −0.894246 0.447576i \(-0.852287\pi\)
0.834735 + 0.550652i \(0.185621\pi\)
\(102\) 0 0
\(103\) 8.39230 0.826918 0.413459 0.910523i \(-0.364320\pi\)
0.413459 + 0.910523i \(0.364320\pi\)
\(104\) −2.50000 2.59808i −0.245145 0.254762i
\(105\) 0 0
\(106\) 1.33013 + 0.767949i 0.129193 + 0.0745898i
\(107\) 5.46410 9.46410i 0.528235 0.914929i −0.471224 0.882014i \(-0.656187\pi\)
0.999458 0.0329154i \(-0.0104792\pi\)
\(108\) 0 0
\(109\) 10.0000i 0.957826i 0.877862 + 0.478913i \(0.158969\pi\)
−0.877862 + 0.478913i \(0.841031\pi\)
\(110\) 0.633975 0.366025i 0.0604471 0.0348992i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 5.69615 + 9.86603i 0.535849 + 0.928118i 0.999122 + 0.0419019i \(0.0133417\pi\)
−0.463273 + 0.886216i \(0.653325\pi\)
\(114\) 0 0
\(115\) 1.09808 + 0.633975i 0.102396 + 0.0591184i
\(116\) −3.00000 −0.278543
\(117\) 0 0
\(118\) −10.7321 −0.987965
\(119\) −4.96410 2.86603i −0.455058 0.262728i
\(120\) 0 0
\(121\) −5.23205 9.06218i −0.475641 0.823834i
\(122\) 11.7321i 1.06217i
\(123\) 0 0
\(124\) 4.56218 2.63397i 0.409696 0.236538i
\(125\) 9.00000i 0.804984i
\(126\) 0 0
\(127\) 4.92820 8.53590i 0.437307 0.757438i −0.560173 0.828375i \(-0.689266\pi\)
0.997481 + 0.0709368i \(0.0225989\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0.866025 + 3.50000i 0.0759555 + 0.306970i
\(131\) 5.07180 0.443125 0.221562 0.975146i \(-0.428884\pi\)
0.221562 + 0.975146i \(0.428884\pi\)
\(132\) 0 0
\(133\) 0.732051 1.26795i 0.0634769 0.109945i
\(134\) −5.83013 10.0981i −0.503646 0.872341i
\(135\) 0 0
\(136\) 4.96410 2.86603i 0.425668 0.245760i
\(137\) 5.30385 3.06218i 0.453138 0.261620i −0.256016 0.966672i \(-0.582410\pi\)
0.709155 + 0.705053i \(0.249077\pi\)
\(138\) 0 0
\(139\) 0.169873 + 0.294229i 0.0144084 + 0.0249561i 0.873140 0.487470i \(-0.162080\pi\)
−0.858731 + 0.512426i \(0.828747\pi\)
\(140\) −0.500000 + 0.866025i −0.0422577 + 0.0731925i
\(141\) 0 0
\(142\) −13.8564 −1.16280
\(143\) −2.56218 + 0.633975i −0.214260 + 0.0530156i
\(144\) 0 0
\(145\) 2.59808 + 1.50000i 0.215758 + 0.124568i
\(146\) −5.69615 + 9.86603i −0.471417 + 0.816518i
\(147\) 0 0
\(148\) 5.19615i 0.427121i
\(149\) 14.8923 8.59808i 1.22003 0.704382i 0.255102 0.966914i \(-0.417891\pi\)
0.964923 + 0.262532i \(0.0845576\pi\)
\(150\) 0 0
\(151\) 12.3923i 1.00847i −0.863566 0.504236i \(-0.831774\pi\)
0.863566 0.504236i \(-0.168226\pi\)
\(152\) 0.732051 + 1.26795i 0.0593772 + 0.102844i
\(153\) 0 0
\(154\) −0.633975 0.366025i −0.0510871 0.0294952i
\(155\) −5.26795 −0.423132
\(156\) 0 0
\(157\) 13.7321 1.09594 0.547968 0.836499i \(-0.315401\pi\)
0.547968 + 0.836499i \(0.315401\pi\)
\(158\) 3.29423 + 1.90192i 0.262075 + 0.151309i
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 1.26795i 0.0999284i
\(162\) 0 0
\(163\) −0.633975 + 0.366025i −0.0496567 + 0.0286693i −0.524623 0.851335i \(-0.675794\pi\)
0.474966 + 0.880004i \(0.342460\pi\)
\(164\) 2.46410i 0.192414i
\(165\) 0 0
\(166\) −1.90192 + 3.29423i −0.147618 + 0.255682i
\(167\) 4.56218 + 2.63397i 0.353032 + 0.203823i 0.666020 0.745934i \(-0.267997\pi\)
−0.312988 + 0.949757i \(0.601330\pi\)
\(168\) 0 0
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) −5.73205 −0.439628
\(171\) 0 0
\(172\) 6.09808 10.5622i 0.464974 0.805359i
\(173\) 10.4641 + 18.1244i 0.795571 + 1.37797i 0.922476 + 0.386054i \(0.126162\pi\)
−0.126905 + 0.991915i \(0.540504\pi\)
\(174\) 0 0
\(175\) −3.46410 + 2.00000i −0.261861 + 0.151186i
\(176\) 0.633975 0.366025i 0.0477876 0.0275902i
\(177\) 0 0
\(178\) 1.26795 + 2.19615i 0.0950368 + 0.164609i
\(179\) −8.19615 + 14.1962i −0.612609 + 1.06107i 0.378190 + 0.925728i \(0.376547\pi\)
−0.990799 + 0.135342i \(0.956787\pi\)
\(180\) 0 0
\(181\) 3.19615 0.237568 0.118784 0.992920i \(-0.462100\pi\)
0.118784 + 0.992920i \(0.462100\pi\)
\(182\) 2.59808 2.50000i 0.192582 0.185312i
\(183\) 0 0
\(184\) 1.09808 + 0.633975i 0.0809513 + 0.0467372i
\(185\) 2.59808 4.50000i 0.191014 0.330847i
\(186\) 0 0
\(187\) 4.19615i 0.306853i
\(188\) 2.53590 1.46410i 0.184949 0.106781i
\(189\) 0 0
\(190\) 1.46410i 0.106217i
\(191\) 3.56218 + 6.16987i 0.257750 + 0.446436i 0.965639 0.259888i \(-0.0836855\pi\)
−0.707889 + 0.706324i \(0.750352\pi\)
\(192\) 0 0
\(193\) −20.0885 11.5981i −1.44600 0.834848i −0.447759 0.894154i \(-0.647778\pi\)
−0.998240 + 0.0593065i \(0.981111\pi\)
\(194\) 5.46410 0.392300
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −6.12436 3.53590i −0.436342 0.251922i 0.265703 0.964055i \(-0.414396\pi\)
−0.702045 + 0.712133i \(0.747729\pi\)
\(198\) 0 0
\(199\) −2.73205 4.73205i −0.193670 0.335446i 0.752794 0.658256i \(-0.228706\pi\)
−0.946464 + 0.322810i \(0.895372\pi\)
\(200\) 4.00000i 0.282843i
\(201\) 0 0
\(202\) 1.03590 0.598076i 0.0728856 0.0420805i
\(203\) 3.00000i 0.210559i
\(204\) 0 0
\(205\) 1.23205 2.13397i 0.0860502 0.149043i
\(206\) −7.26795 4.19615i −0.506382 0.292360i
\(207\) 0 0
\(208\) 0.866025 + 3.50000i 0.0600481 + 0.242681i
\(209\) 1.07180 0.0741377
\(210\) 0 0
\(211\) 10.6340 18.4186i 0.732073 1.26799i −0.223923 0.974607i \(-0.571886\pi\)
0.955996 0.293381i \(-0.0947804\pi\)
\(212\) −0.767949 1.33013i −0.0527430 0.0913535i
\(213\) 0 0
\(214\) −9.46410 + 5.46410i −0.646953 + 0.373518i
\(215\) −10.5622 + 6.09808i −0.720335 + 0.415885i
\(216\) 0 0
\(217\) 2.63397 + 4.56218i 0.178806 + 0.309701i
\(218\) 5.00000 8.66025i 0.338643 0.586546i
\(219\) 0 0
\(220\) −0.732051 −0.0493549
\(221\) 19.8564 + 5.73205i 1.33569 + 0.385579i
\(222\) 0 0
\(223\) 10.7321 + 6.19615i 0.718671 + 0.414925i 0.814263 0.580496i \(-0.197141\pi\)
−0.0955922 + 0.995421i \(0.530474\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 11.3923i 0.757805i
\(227\) −1.09808 + 0.633975i −0.0728819 + 0.0420784i −0.535998 0.844219i \(-0.680065\pi\)
0.463116 + 0.886298i \(0.346731\pi\)
\(228\) 0 0
\(229\) 24.3923i 1.61189i 0.591991 + 0.805944i \(0.298342\pi\)
−0.591991 + 0.805944i \(0.701658\pi\)
\(230\) −0.633975 1.09808i −0.0418030 0.0724050i
\(231\) 0 0
\(232\) 2.59808 + 1.50000i 0.170572 + 0.0984798i
\(233\) −4.39230 −0.287749 −0.143875 0.989596i \(-0.545956\pi\)
−0.143875 + 0.989596i \(0.545956\pi\)
\(234\) 0 0
\(235\) −2.92820 −0.191015
\(236\) 9.29423 + 5.36603i 0.605003 + 0.349299i
\(237\) 0 0
\(238\) 2.86603 + 4.96410i 0.185777 + 0.321775i
\(239\) 29.5167i 1.90927i −0.297772 0.954637i \(-0.596244\pi\)
0.297772 0.954637i \(-0.403756\pi\)
\(240\) 0 0
\(241\) −13.3301 + 7.69615i −0.858669 + 0.495753i −0.863566 0.504235i \(-0.831774\pi\)
0.00489737 + 0.999988i \(0.498441\pi\)
\(242\) 10.4641i 0.672658i
\(243\) 0 0
\(244\) −5.86603 + 10.1603i −0.375534 + 0.650444i
\(245\) −0.866025 0.500000i −0.0553283 0.0319438i
\(246\) 0 0
\(247\) −1.46410 + 5.07180i −0.0931586 + 0.322711i
\(248\) −5.26795 −0.334515
\(249\) 0 0
\(250\) −4.50000 + 7.79423i −0.284605 + 0.492950i
\(251\) −11.4641 19.8564i −0.723608 1.25333i −0.959545 0.281557i \(-0.909149\pi\)
0.235937 0.971768i \(-0.424184\pi\)
\(252\) 0 0
\(253\) 0.803848 0.464102i 0.0505375 0.0291778i
\(254\) −8.53590 + 4.92820i −0.535590 + 0.309223i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.669873 + 1.16025i −0.0417855 + 0.0723747i −0.886162 0.463376i \(-0.846638\pi\)
0.844376 + 0.535751i \(0.179971\pi\)
\(258\) 0 0
\(259\) −5.19615 −0.322873
\(260\) 1.00000 3.46410i 0.0620174 0.214834i
\(261\) 0 0
\(262\) −4.39230 2.53590i −0.271357 0.156668i
\(263\) −10.2942 + 17.8301i −0.634769 + 1.09945i 0.351795 + 0.936077i \(0.385572\pi\)
−0.986564 + 0.163376i \(0.947762\pi\)
\(264\) 0 0
\(265\) 1.53590i 0.0943495i
\(266\) −1.26795 + 0.732051i −0.0777430 + 0.0448849i
\(267\) 0 0
\(268\) 11.6603i 0.712263i
\(269\) −14.3923 24.9282i −0.877514 1.51990i −0.854060 0.520174i \(-0.825867\pi\)
−0.0234543 0.999725i \(-0.507466\pi\)
\(270\) 0 0
\(271\) 6.16987 + 3.56218i 0.374793 + 0.216387i 0.675550 0.737314i \(-0.263906\pi\)
−0.300757 + 0.953701i \(0.597239\pi\)
\(272\) −5.73205 −0.347557
\(273\) 0 0
\(274\) −6.12436 −0.369986
\(275\) −2.53590 1.46410i −0.152920 0.0882886i
\(276\) 0 0
\(277\) 4.69615 + 8.13397i 0.282164 + 0.488723i 0.971918 0.235321i \(-0.0756143\pi\)
−0.689753 + 0.724045i \(0.742281\pi\)
\(278\) 0.339746i 0.0203766i
\(279\) 0 0
\(280\) 0.866025 0.500000i 0.0517549 0.0298807i
\(281\) 16.6603i 0.993867i −0.867789 0.496934i \(-0.834459\pi\)
0.867789 0.496934i \(-0.165541\pi\)
\(282\) 0 0
\(283\) −5.29423 + 9.16987i −0.314709 + 0.545092i −0.979376 0.202048i \(-0.935240\pi\)
0.664666 + 0.747140i \(0.268574\pi\)
\(284\) 12.0000 + 6.92820i 0.712069 + 0.411113i
\(285\) 0 0
\(286\) 2.53590 + 0.732051i 0.149951 + 0.0432871i
\(287\) −2.46410 −0.145451
\(288\) 0 0
\(289\) −7.92820 + 13.7321i −0.466365 + 0.807768i
\(290\) −1.50000 2.59808i −0.0880830 0.152564i
\(291\) 0 0
\(292\) 9.86603 5.69615i 0.577365 0.333342i
\(293\) −15.0622 + 8.69615i −0.879942 + 0.508035i −0.870639 0.491922i \(-0.836294\pi\)
−0.00930260 + 0.999957i \(0.502961\pi\)
\(294\) 0 0
\(295\) −5.36603 9.29423i −0.312422 0.541131i
\(296\) 2.59808 4.50000i 0.151010 0.261557i
\(297\) 0 0
\(298\) −17.1962 −0.996146
\(299\) 1.09808 + 4.43782i 0.0635034 + 0.256646i
\(300\) 0 0
\(301\) 10.5622 + 6.09808i 0.608794 + 0.351487i
\(302\) −6.19615 + 10.7321i −0.356549 + 0.617560i
\(303\) 0 0
\(304\) 1.46410i 0.0839720i
\(305\) 10.1603 5.86603i 0.581774 0.335888i
\(306\) 0 0
\(307\) 23.5167i 1.34217i 0.741382 + 0.671083i \(0.234171\pi\)
−0.741382 + 0.671083i \(0.765829\pi\)
\(308\) 0.366025 + 0.633975i 0.0208562 + 0.0361241i
\(309\) 0 0
\(310\) 4.56218 + 2.63397i 0.259114 + 0.149600i
\(311\) −10.1962 −0.578171 −0.289085 0.957303i \(-0.593351\pi\)
−0.289085 + 0.957303i \(0.593351\pi\)
\(312\) 0 0
\(313\) −32.0000 −1.80875 −0.904373 0.426742i \(-0.859661\pi\)
−0.904373 + 0.426742i \(0.859661\pi\)
\(314\) −11.8923 6.86603i −0.671122 0.387472i
\(315\) 0 0
\(316\) −1.90192 3.29423i −0.106992 0.185315i
\(317\) 7.05256i 0.396111i 0.980191 + 0.198056i \(0.0634627\pi\)
−0.980191 + 0.198056i \(0.936537\pi\)
\(318\) 0 0
\(319\) 1.90192 1.09808i 0.106487 0.0614805i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) −0.633975 + 1.09808i −0.0353300 + 0.0611934i
\(323\) −7.26795 4.19615i −0.404400 0.233480i
\(324\) 0 0
\(325\) 10.3923 10.0000i 0.576461 0.554700i
\(326\) 0.732051 0.0405445
\(327\) 0 0
\(328\) 1.23205 2.13397i 0.0680286 0.117829i
\(329\) 1.46410 + 2.53590i 0.0807185 + 0.139809i
\(330\) 0 0
\(331\) 3.75833 2.16987i 0.206577 0.119267i −0.393143 0.919477i \(-0.628612\pi\)
0.599719 + 0.800210i \(0.295279\pi\)
\(332\) 3.29423 1.90192i 0.180794 0.104382i
\(333\) 0 0
\(334\) −2.63397 4.56218i −0.144125 0.249631i
\(335\) 5.83013 10.0981i 0.318534 0.551717i
\(336\) 0 0
\(337\) −6.32051 −0.344300 −0.172150 0.985071i \(-0.555071\pi\)
−0.172150 + 0.985071i \(0.555071\pi\)
\(338\) −6.92820 + 11.0000i −0.376845 + 0.598321i
\(339\) 0 0
\(340\) 4.96410 + 2.86603i 0.269216 + 0.155432i
\(341\) −1.92820 + 3.33975i −0.104418 + 0.180857i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −10.5622 + 6.09808i −0.569474 + 0.328786i
\(345\) 0 0
\(346\) 20.9282i 1.12511i
\(347\) 14.4904 + 25.0981i 0.777884 + 1.34734i 0.933159 + 0.359464i \(0.117040\pi\)
−0.155275 + 0.987871i \(0.549626\pi\)
\(348\) 0 0
\(349\) −1.73205 1.00000i −0.0927146 0.0535288i 0.452926 0.891548i \(-0.350380\pi\)
−0.545640 + 0.838019i \(0.683714\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) −0.732051 −0.0390184
\(353\) 31.3301 + 18.0885i 1.66753 + 0.962751i 0.968961 + 0.247213i \(0.0795147\pi\)
0.698573 + 0.715539i \(0.253819\pi\)
\(354\) 0 0
\(355\) −6.92820 12.0000i −0.367711 0.636894i
\(356\) 2.53590i 0.134402i
\(357\) 0 0
\(358\) 14.1962 8.19615i 0.750290 0.433180i
\(359\) 16.3923i 0.865153i 0.901597 + 0.432576i \(0.142395\pi\)
−0.901597 + 0.432576i \(0.857605\pi\)
\(360\) 0 0
\(361\) −8.42820 + 14.5981i −0.443590 + 0.768320i
\(362\) −2.76795 1.59808i −0.145480 0.0839930i
\(363\) 0 0
\(364\) −3.50000 + 0.866025i −0.183450 + 0.0453921i
\(365\) −11.3923 −0.596300
\(366\) 0 0
\(367\) −16.9545 + 29.3660i −0.885017 + 1.53289i −0.0393224 + 0.999227i \(0.512520\pi\)
−0.845694 + 0.533667i \(0.820813\pi\)
\(368\) −0.633975 1.09808i −0.0330482 0.0572412i
\(369\) 0 0
\(370\) −4.50000 + 2.59808i −0.233944 + 0.135068i
\(371\) 1.33013 0.767949i 0.0690568 0.0398699i
\(372\) 0 0
\(373\) 16.2321 + 28.1147i 0.840464 + 1.45573i 0.889503 + 0.456929i \(0.151051\pi\)
−0.0490394 + 0.998797i \(0.515616\pi\)
\(374\) −2.09808 + 3.63397i −0.108489 + 0.187908i
\(375\) 0 0
\(376\) −2.92820 −0.151011
\(377\) 2.59808 + 10.5000i 0.133808 + 0.540778i
\(378\) 0 0
\(379\) 19.2224 + 11.0981i 0.987390 + 0.570070i 0.904493 0.426488i \(-0.140249\pi\)
0.0828969 + 0.996558i \(0.473583\pi\)
\(380\) −0.732051 + 1.26795i −0.0375534 + 0.0650444i
\(381\) 0 0
\(382\) 7.12436i 0.364514i
\(383\) −28.2224 + 16.2942i −1.44210 + 0.832596i −0.997990 0.0633765i \(-0.979813\pi\)
−0.444109 + 0.895973i \(0.646480\pi\)
\(384\) 0 0
\(385\) 0.732051i 0.0373088i
\(386\) 11.5981 + 20.0885i 0.590327 + 1.02248i
\(387\) 0 0
\(388\) −4.73205 2.73205i −0.240233 0.138699i
\(389\) 24.3205 1.23310 0.616549 0.787316i \(-0.288530\pi\)
0.616549 + 0.787316i \(0.288530\pi\)
\(390\) 0 0
\(391\) −7.26795 −0.367556
\(392\) −0.866025 0.500000i −0.0437409 0.0252538i
\(393\) 0 0
\(394\) 3.53590 + 6.12436i 0.178136 + 0.308541i
\(395\) 3.80385i 0.191392i
\(396\) 0 0
\(397\) −25.5167 + 14.7321i −1.28064 + 0.739380i −0.976966 0.213394i \(-0.931548\pi\)
−0.303678 + 0.952775i \(0.598215\pi\)
\(398\) 5.46410i 0.273891i
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 28.6244 + 16.5263i 1.42943 + 0.825283i 0.997076 0.0764198i \(-0.0243489\pi\)
0.432356 + 0.901703i \(0.357682\pi\)
\(402\) 0 0
\(403\) −13.1699 13.6865i −0.656038 0.681775i
\(404\) −1.19615 −0.0595108
\(405\) 0 0
\(406\) −1.50000 + 2.59808i −0.0744438 + 0.128940i
\(407\) −1.90192 3.29423i −0.0942749 0.163289i
\(408\) 0 0
\(409\) 22.7942 13.1603i 1.12710 0.650733i 0.183898 0.982945i \(-0.441129\pi\)
0.943204 + 0.332213i \(0.107795\pi\)
\(410\) −2.13397 + 1.23205i −0.105389 + 0.0608467i
\(411\) 0 0
\(412\) 4.19615 + 7.26795i 0.206730 + 0.358066i
\(413\) −5.36603 + 9.29423i −0.264045 + 0.457339i
\(414\) 0 0
\(415\) −3.80385 −0.186724
\(416\) 1.00000 3.46410i 0.0490290 0.169842i
\(417\) 0 0
\(418\) −0.928203 0.535898i −0.0453999 0.0262116i
\(419\) 2.56218 4.43782i 0.125171 0.216802i −0.796629 0.604469i \(-0.793386\pi\)
0.921800 + 0.387667i \(0.126719\pi\)
\(420\) 0 0
\(421\) 14.1244i 0.688379i −0.938900 0.344189i \(-0.888154\pi\)
0.938900 0.344189i \(-0.111846\pi\)
\(422\) −18.4186 + 10.6340i −0.896603 + 0.517654i
\(423\) 0 0
\(424\) 1.53590i 0.0745898i
\(425\) 11.4641 + 19.8564i 0.556091 + 0.963177i
\(426\) 0 0
\(427\) −10.1603 5.86603i −0.491689 0.283877i
\(428\) 10.9282 0.528235
\(429\) 0 0
\(430\) 12.1962 0.588151
\(431\) −22.9808 13.2679i −1.10694 0.639095i −0.168908 0.985632i \(-0.554024\pi\)
−0.938036 + 0.346537i \(0.887357\pi\)
\(432\) 0 0
\(433\) 10.8660 + 18.8205i 0.522188 + 0.904456i 0.999667 + 0.0258127i \(0.00821735\pi\)
−0.477479 + 0.878643i \(0.658449\pi\)
\(434\) 5.26795i 0.252870i
\(435\) 0 0
\(436\) −8.66025 + 5.00000i −0.414751 + 0.239457i
\(437\) 1.85641i 0.0888040i
\(438\) 0 0
\(439\) −9.63397 + 16.6865i −0.459805 + 0.796405i −0.998950 0.0458077i \(-0.985414\pi\)
0.539146 + 0.842212i \(0.318747\pi\)
\(440\) 0.633975 + 0.366025i 0.0302236 + 0.0174496i
\(441\) 0 0
\(442\) −14.3301 14.8923i −0.681615 0.708355i
\(443\) −35.3205 −1.67813 −0.839064 0.544033i \(-0.816897\pi\)
−0.839064 + 0.544033i \(0.816897\pi\)
\(444\) 0 0
\(445\) −1.26795 + 2.19615i −0.0601066 + 0.104108i
\(446\) −6.19615 10.7321i −0.293396 0.508177i
\(447\) 0 0
\(448\) 0.866025 0.500000i 0.0409159 0.0236228i
\(449\) −15.5885 + 9.00000i −0.735665 + 0.424736i −0.820491 0.571660i \(-0.806300\pi\)
0.0848262 + 0.996396i \(0.472967\pi\)
\(450\) 0 0
\(451\) −0.901924 1.56218i −0.0424699 0.0735601i
\(452\) −5.69615 + 9.86603i −0.267924 + 0.464059i
\(453\) 0 0
\(454\) 1.26795 0.0595078
\(455\) 3.46410 + 1.00000i 0.162400 + 0.0468807i
\(456\) 0 0
\(457\) −12.3564 7.13397i −0.578008 0.333713i 0.182333 0.983237i \(-0.441635\pi\)
−0.760341 + 0.649524i \(0.774968\pi\)
\(458\) 12.1962 21.1244i 0.569889 0.987076i
\(459\) 0 0
\(460\) 1.26795i 0.0591184i
\(461\) −7.20577 + 4.16025i −0.335606 + 0.193762i −0.658327 0.752732i \(-0.728736\pi\)
0.322721 + 0.946494i \(0.395402\pi\)
\(462\) 0 0
\(463\) 3.94744i 0.183453i 0.995784 + 0.0917266i \(0.0292386\pi\)
−0.995784 + 0.0917266i \(0.970761\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) 0 0
\(466\) 3.80385 + 2.19615i 0.176210 + 0.101735i
\(467\) −24.7321 −1.14446 −0.572231 0.820092i \(-0.693922\pi\)
−0.572231 + 0.820092i \(0.693922\pi\)
\(468\) 0 0
\(469\) −11.6603 −0.538421
\(470\) 2.53590 + 1.46410i 0.116972 + 0.0675340i
\(471\) 0 0
\(472\) −5.36603 9.29423i −0.246991 0.427802i
\(473\) 8.92820i 0.410519i
\(474\) 0 0
\(475\) −5.07180 + 2.92820i −0.232710 + 0.134355i
\(476\) 5.73205i 0.262728i
\(477\) 0 0
\(478\) −14.7583 + 25.5622i −0.675030 + 1.16919i
\(479\) −27.8827 16.0981i −1.27399 0.735540i −0.298256 0.954486i \(-0.596405\pi\)
−0.975737 + 0.218946i \(0.929738\pi\)
\(480\) 0 0
\(481\) 18.1865 4.50000i 0.829235 0.205182i
\(482\) 15.3923 0.701100
\(483\) 0 0
\(484\) 5.23205 9.06218i 0.237820 0.411917i
\(485\) 2.73205 + 4.73205i 0.124056 + 0.214871i
\(486\) 0 0
\(487\) 27.1244 15.6603i 1.22912 0.709634i 0.262276 0.964993i \(-0.415527\pi\)
0.966846 + 0.255359i \(0.0821937\pi\)
\(488\) 10.1603 5.86603i 0.459933 0.265542i
\(489\) 0 0
\(490\) 0.500000 + 0.866025i 0.0225877 + 0.0391230i
\(491\) 13.8564 24.0000i 0.625331 1.08310i −0.363146 0.931732i \(-0.618297\pi\)
0.988477 0.151373i \(-0.0483693\pi\)
\(492\) 0 0
\(493\) −17.1962 −0.774476
\(494\) 3.80385 3.66025i 0.171143 0.164683i
\(495\) 0 0
\(496\) 4.56218 + 2.63397i 0.204848 + 0.118269i
\(497\) −6.92820 + 12.0000i −0.310772 + 0.538274i
\(498\) 0 0
\(499\) 11.2679i 0.504423i −0.967672 0.252211i \(-0.918842\pi\)
0.967672 0.252211i \(-0.0811578\pi\)
\(500\) 7.79423 4.50000i 0.348569 0.201246i
\(501\) 0 0
\(502\) 22.9282i 1.02334i
\(503\) 10.3660 + 17.9545i 0.462198 + 0.800551i 0.999070 0.0431129i \(-0.0137275\pi\)
−0.536872 + 0.843664i \(0.680394\pi\)
\(504\) 0 0
\(505\) 1.03590 + 0.598076i 0.0460969 + 0.0266140i
\(506\) −0.928203 −0.0412637
\(507\) 0 0
\(508\) 9.85641 0.437307
\(509\) 23.7224 + 13.6962i 1.05148 + 0.607071i 0.923063 0.384649i \(-0.125678\pi\)
0.128415 + 0.991720i \(0.459011\pi\)
\(510\) 0 0
\(511\) 5.69615 + 9.86603i 0.251983 + 0.436447i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 1.16025 0.669873i 0.0511766 0.0295468i
\(515\) 8.39230i 0.369809i
\(516\) 0 0
\(517\) −1.07180 + 1.85641i −0.0471376 + 0.0816447i
\(518\) 4.50000 + 2.59808i 0.197719 + 0.114153i
\(519\) 0 0
\(520\) −2.59808 + 2.50000i −0.113933 + 0.109632i
\(521\) −44.3731 −1.94402 −0.972010 0.234941i \(-0.924510\pi\)
−0.972010 + 0.234941i \(0.924510\pi\)
\(522\) 0 0
\(523\) −10.7321 + 18.5885i −0.469280 + 0.812816i −0.999383 0.0351165i \(-0.988820\pi\)
0.530103 + 0.847933i \(0.322153\pi\)
\(524\) 2.53590 + 4.39230i 0.110781 + 0.191879i
\(525\) 0 0
\(526\) 17.8301 10.2942i 0.777430 0.448850i
\(527\) 26.1506 15.0981i 1.13914 0.657683i
\(528\) 0 0
\(529\) 10.6962 + 18.5263i 0.465050 + 0.805490i
\(530\) 0.767949 1.33013i 0.0333576 0.0577770i
\(531\) 0 0
\(532\) 1.46410 0.0634769
\(533\) 8.62436 2.13397i 0.373562 0.0924327i
\(534\) 0 0
\(535\) −9.46410 5.46410i −0.409169 0.236234i
\(536\) 5.83013 10.0981i 0.251823 0.436170i
\(537\) 0 0
\(538\) 28.7846i 1.24099i
\(539\) −0.633975 + 0.366025i −0.0273072 + 0.0157658i
\(540\) 0 0
\(541\) 8.26795i 0.355467i −0.984079 0.177733i \(-0.943124\pi\)
0.984079 0.177733i \(-0.0568765\pi\)
\(542\) −3.56218 6.16987i −0.153009 0.265019i
\(543\) 0 0
\(544\) 4.96410 + 2.86603i 0.212834 + 0.122880i
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) −30.4449 −1.30173 −0.650864 0.759194i \(-0.725593\pi\)
−0.650864 + 0.759194i \(0.725593\pi\)
\(548\) 5.30385 + 3.06218i 0.226569 + 0.130810i
\(549\) 0 0
\(550\) 1.46410 + 2.53590i 0.0624295 + 0.108131i
\(551\) 4.39230i 0.187118i
\(552\) 0 0
\(553\) 3.29423 1.90192i 0.140085 0.0808780i
\(554\) 9.39230i 0.399041i
\(555\) 0 0
\(556\) −0.169873 + 0.294229i −0.00720422 + 0.0124781i
\(557\) −22.6244 13.0622i −0.958625 0.553462i −0.0628752 0.998021i \(-0.520027\pi\)
−0.895749 + 0.444559i \(0.853360\pi\)
\(558\) 0 0
\(559\) −42.2487 12.1962i −1.78693 0.515842i
\(560\) −1.00000 −0.0422577
\(561\) 0 0
\(562\) −8.33013 + 14.4282i −0.351385 + 0.608617i
\(563\) 14.2224 + 24.6340i 0.599404 + 1.03820i 0.992909 + 0.118876i \(0.0379290\pi\)
−0.393505 + 0.919322i \(0.628738\pi\)
\(564\) 0 0
\(565\) 9.86603 5.69615i 0.415067 0.239639i
\(566\) 9.16987 5.29423i 0.385439 0.222533i
\(567\) 0 0
\(568\) −6.92820 12.0000i −0.290701 0.503509i
\(569\) 5.66025 9.80385i 0.237290 0.410999i −0.722646 0.691219i \(-0.757074\pi\)
0.959936 + 0.280220i \(0.0904074\pi\)
\(570\) 0 0
\(571\) 5.46410 0.228666 0.114333 0.993443i \(-0.463527\pi\)
0.114333 + 0.993443i \(0.463527\pi\)
\(572\) −1.83013 1.90192i −0.0765215 0.0795234i
\(573\) 0 0
\(574\) 2.13397 + 1.23205i 0.0890704 + 0.0514248i
\(575\) −2.53590 + 4.39230i −0.105754 + 0.183172i
\(576\) 0 0
\(577\) 34.1769i 1.42280i −0.702786 0.711402i \(-0.748061\pi\)
0.702786 0.711402i \(-0.251939\pi\)
\(578\) 13.7321 7.92820i 0.571178 0.329770i
\(579\) 0 0
\(580\) 3.00000i 0.124568i
\(581\) 1.90192 + 3.29423i 0.0789051 + 0.136668i
\(582\) 0 0
\(583\) 0.973721 + 0.562178i 0.0403274 + 0.0232830i
\(584\) −11.3923 −0.471417
\(585\) 0 0
\(586\) 17.3923 0.718469
\(587\) 24.9282 + 14.3923i 1.02890 + 0.594034i 0.916668 0.399648i \(-0.130868\pi\)
0.112229 + 0.993682i \(0.464201\pi\)
\(588\) 0 0
\(589\) 3.85641 + 6.67949i 0.158900 + 0.275224i
\(590\) 10.7321i 0.441832i
\(591\) 0 0
\(592\) −4.50000 + 2.59808i −0.184949 + 0.106780i
\(593\) 3.14359i 0.129092i −0.997915 0.0645460i \(-0.979440\pi\)
0.997915 0.0645460i \(-0.0205599\pi\)
\(594\) 0 0
\(595\) −2.86603 + 4.96410i −0.117496 + 0.203508i
\(596\) 14.8923 + 8.59808i 0.610013 + 0.352191i
\(597\) 0 0
\(598\) 1.26795 4.39230i 0.0518503 0.179615i
\(599\) −30.9282 −1.26369 −0.631846 0.775094i \(-0.717703\pi\)
−0.631846 + 0.775094i \(0.717703\pi\)
\(600\) 0 0
\(601\) 11.5263 19.9641i 0.470167 0.814353i −0.529251 0.848465i \(-0.677527\pi\)
0.999418 + 0.0341125i \(0.0108604\pi\)
\(602\) −6.09808 10.5622i −0.248539 0.430482i
\(603\) 0 0
\(604\) 10.7321 6.19615i 0.436681 0.252118i
\(605\) −9.06218 + 5.23205i −0.368430 + 0.212713i
\(606\) 0 0
\(607\) 4.92820 + 8.53590i 0.200030 + 0.346461i 0.948538 0.316664i \(-0.102563\pi\)
−0.748508 + 0.663126i \(0.769230\pi\)
\(608\) −0.732051 + 1.26795i −0.0296886 + 0.0514221i
\(609\) 0 0
\(610\) −11.7321 −0.475017
\(611\) −7.32051 7.60770i −0.296156 0.307774i
\(612\) 0 0
\(613\) 13.8397 + 7.99038i 0.558982 + 0.322728i 0.752737 0.658322i \(-0.228733\pi\)
−0.193755 + 0.981050i \(0.562067\pi\)
\(614\) 11.7583 20.3660i 0.474528 0.821906i
\(615\) 0 0
\(616\) 0.732051i 0.0294952i
\(617\) 28.7487 16.5981i 1.15738 0.668213i 0.206705 0.978403i \(-0.433726\pi\)
0.950675 + 0.310190i \(0.100393\pi\)
\(618\) 0 0
\(619\) 34.0526i 1.36869i −0.729159 0.684344i \(-0.760089\pi\)
0.729159 0.684344i \(-0.239911\pi\)
\(620\) −2.63397 4.56218i −0.105783 0.183221i
\(621\) 0 0
\(622\) 8.83013 + 5.09808i 0.354056 + 0.204414i
\(623\) 2.53590 0.101599
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 27.7128 + 16.0000i 1.10763 + 0.639489i
\(627\) 0 0
\(628\) 6.86603 + 11.8923i 0.273984 + 0.474555i
\(629\) 29.7846i 1.18759i
\(630\) 0 0
\(631\) 9.12436 5.26795i 0.363235 0.209714i −0.307264 0.951624i \(-0.599413\pi\)
0.670499 + 0.741911i \(0.266080\pi\)
\(632\) 3.80385i 0.151309i
\(633\) 0 0
\(634\) 3.52628 6.10770i 0.140046 0.242568i
\(635\) −8.53590 4.92820i −0.338737 0.195570i
\(636\) 0 0
\(637\) −0.866025 3.50000i −0.0343132 0.138675i
\(638\) −2.19615 −0.0869465
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −22.2321 38.5070i −0.878113 1.52094i −0.853409 0.521242i \(-0.825469\pi\)
−0.0247042 0.999695i \(-0.507864\pi\)
\(642\) 0 0
\(643\) 30.9282 17.8564i 1.21969 0.704188i 0.254838 0.966984i \(-0.417978\pi\)
0.964851 + 0.262796i \(0.0846446\pi\)
\(644\) 1.09808 0.633975i 0.0432703 0.0249821i
\(645\) 0 0
\(646\) 4.19615 + 7.26795i 0.165095 + 0.285954i
\(647\) 6.92820 12.0000i 0.272376 0.471769i −0.697094 0.716980i \(-0.745524\pi\)
0.969470 + 0.245211i \(0.0788573\pi\)
\(648\) 0 0
\(649\) −7.85641 −0.308391
\(650\) −14.0000 + 3.46410i −0.549125 + 0.135873i
\(651\) 0 0
\(652\) −0.633975 0.366025i −0.0248284 0.0143347i
\(653\) 6.19615 10.7321i 0.242474 0.419978i −0.718944 0.695068i \(-0.755374\pi\)
0.961418 + 0.275090i \(0.0887077\pi\)
\(654\) 0 0
\(655\) 5.07180i 0.198171i
\(656\) −2.13397 + 1.23205i −0.0833177 + 0.0481035i
\(657\) 0 0
\(658\) 2.92820i 0.114153i
\(659\) 4.39230 + 7.60770i 0.171100 + 0.296354i 0.938805 0.344450i \(-0.111935\pi\)
−0.767705 + 0.640804i \(0.778601\pi\)
\(660\) 0 0
\(661\) 1.66987 + 0.964102i 0.0649505 + 0.0374992i 0.532124 0.846667i \(-0.321394\pi\)
−0.467173 + 0.884166i \(0.654727\pi\)
\(662\) −4.33975 −0.168669
\(663\) 0 0
\(664\) −3.80385 −0.147618
\(665\) −1.26795 0.732051i −0.0491690 0.0283877i
\(666\) 0 0
\(667\) −1.90192 3.29423i −0.0736428 0.127553i
\(668\) 5.26795i 0.203823i
\(669\) 0 0
\(670\) −10.0981 + 5.83013i −0.390123 + 0.225237i
\(671\) 8.58846i 0.331554i
\(672\) 0 0
\(673\) 10.8923 18.8660i 0.419867 0.727232i −0.576058 0.817409i \(-0.695410\pi\)
0.995926 + 0.0901768i \(0.0287432\pi\)
\(674\) 5.47372 + 3.16025i 0.210840 + 0.121728i
\(675\) 0 0
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) −27.8564 −1.07061 −0.535304 0.844659i \(-0.679803\pi\)
−0.535304 + 0.844659i \(0.679803\pi\)
\(678\) 0 0
\(679\) 2.73205 4.73205i 0.104846 0.181599i
\(680\) −2.86603 4.96410i −0.109907 0.190365i
\(681\) 0 0
\(682\) 3.33975 1.92820i 0.127885 0.0738347i
\(683\) −5.66025 + 3.26795i −0.216584 + 0.125045i −0.604367 0.796706i \(-0.706574\pi\)
0.387784 + 0.921750i \(0.373241\pi\)
\(684\) 0 0
\(685\) −3.06218 5.30385i −0.117000 0.202650i
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) 0 0
\(688\) 12.1962 0.464974
\(689\) −3.99038 + 3.83975i −0.152021 + 0.146283i
\(690\) 0 0
\(691\) 5.07180 + 2.92820i 0.192940 + 0.111394i 0.593358 0.804938i \(-0.297802\pi\)
−0.400418 + 0.916333i \(0.631135\pi\)
\(692\) −10.4641 + 18.1244i −0.397785 + 0.688985i
\(693\) 0 0
\(694\) 28.9808i 1.10009i
\(695\) 0.294229 0.169873i 0.0111607 0.00644365i
\(696\) 0 0
\(697\) 14.1244i 0.534998i
\(698\) 1.00000 + 1.73205i 0.0378506 + 0.0655591i
\(699\) 0 0
\(700\) −3.46410 2.00000i −0.130931 0.0755929i
\(701\) 14.5359 0.549013 0.274507 0.961585i \(-0.411485\pi\)
0.274507 + 0.961585i \(0.411485\pi\)
\(702\) 0 0
\(703\) −7.60770 −0.286930
\(704\) 0.633975 + 0.366025i 0.0238938 + 0.0137951i
\(705\) 0 0
\(706\) −18.0885 31.3301i −0.680768 1.17912i
\(707\) 1.19615i 0.0449859i
\(708\) 0 0
\(709\) −5.64359 + 3.25833i −0.211950 + 0.122369i −0.602217 0.798332i \(-0.705716\pi\)
0.390268 + 0.920702i \(0.372383\pi\)
\(710\) 13.8564i 0.520022i
\(711\) 0 0
\(712\) −1.26795 + 2.19615i −0.0475184 + 0.0823043i
\(713\) 5.78461 + 3.33975i 0.216635 + 0.125074i
\(714\) 0 0
\(715\) 0.633975 + 2.56218i 0.0237093 + 0.0958200i
\(716\) −16.3923 −0.612609
\(717\) 0 0
\(718\) 8.19615 14.1962i 0.305878 0.529796i
\(719\) 3.09808 + 5.36603i 0.115539 + 0.200119i 0.917995 0.396592i \(-0.129807\pi\)
−0.802456 + 0.596711i \(0.796474\pi\)
\(720\) 0 0
\(721\) −7.26795 + 4.19615i −0.270673 + 0.156273i
\(722\) 14.5981 8.42820i 0.543284 0.313665i
\(723\) 0 0
\(724\) 1.59808 + 2.76795i 0.0593920 + 0.102870i
\(725\) −6.00000 + 10.3923i −0.222834 + 0.385961i
\(726\) 0 0
\(727\) −53.8564 −1.99742 −0.998712 0.0507424i \(-0.983841\pi\)
−0.998712 + 0.0507424i \(0.983841\pi\)
\(728\) 3.46410 + 1.00000i 0.128388 + 0.0370625i
\(729\) 0 0
\(730\) 9.86603 + 5.69615i 0.365158 + 0.210824i
\(731\) 34.9545 60.5429i 1.29284 2.23926i
\(732\) 0 0
\(733\) 2.46410i 0.0910137i 0.998964 + 0.0455068i \(0.0144903\pi\)
−0.998964 + 0.0455068i \(0.985510\pi\)
\(734\) 29.3660 16.9545i 1.08392 0.625801i
\(735\) 0 0
\(736\) 1.26795i 0.0467372i
\(737\) −4.26795 7.39230i −0.157212 0.272299i
\(738\) 0 0
\(739\) 5.66025 + 3.26795i 0.208216 + 0.120213i 0.600482 0.799638i \(-0.294975\pi\)
−0.392266 + 0.919852i \(0.628309\pi\)
\(740\) 5.19615 0.191014
\(741\) 0 0
\(742\) −1.53590 −0.0563846
\(743\) 4.39230 + 2.53590i 0.161138 + 0.0930331i 0.578401 0.815753i \(-0.303677\pi\)
−0.417262 + 0.908786i \(0.637010\pi\)
\(744\) 0 0
\(745\) −8.59808 14.8923i −0.315009 0.545612i
\(746\) 32.4641i 1.18860i
\(747\) 0 0
\(748\) 3.63397 2.09808i 0.132871 0.0767133i
\(749\) 10.9282i 0.399308i
\(750\) 0 0
\(751\) 3.22243 5.58142i 0.117588 0.203669i −0.801223 0.598366i \(-0.795817\pi\)
0.918811 + 0.394697i \(0.129150\pi\)
\(752\) 2.53590 + 1.46410i 0.0924747 + 0.0533903i
\(753\) 0 0
\(754\) 3.00000 10.3923i 0.109254 0.378465i
\(755\) −12.3923 −0.451002
\(756\) 0 0
\(757\) 22.1962 38.4449i 0.806733 1.39730i −0.108382 0.994109i \(-0.534567\pi\)
0.915115 0.403193i \(-0.132100\pi\)
\(758\) −11.0981 19.2224i −0.403100 0.698190i
\(759\) 0 0
\(760\) 1.26795 0.732051i 0.0459934 0.0265543i
\(761\) −15.8038 + 9.12436i −0.572889 + 0.330758i −0.758302 0.651903i \(-0.773971\pi\)
0.185413 + 0.982661i \(0.440638\pi\)
\(762\) 0 0
\(763\) −5.00000 8.66025i −0.181012 0.313522i
\(764\) −3.56218 + 6.16987i −0.128875 + 0.223218i
\(765\) 0 0
\(766\) 32.5885 1.17747
\(767\) 10.7321 37.1769i 0.387512 1.34238i
\(768\) 0 0
\(769\) 0.339746 + 0.196152i 0.0122516 + 0.00707344i 0.506113 0.862467i \(-0.331082\pi\)
−0.493862 + 0.869540i \(0.664415\pi\)
\(770\) −0.366025 + 0.633975i −0.0131906 + 0.0228469i
\(771\) 0 0
\(772\) 23.1962i 0.834848i
\(773\) −40.0526 + 23.1244i −1.44059 + 0.831725i −0.997889 0.0649438i \(-0.979313\pi\)
−0.442701 + 0.896669i \(0.645980\pi\)
\(774\) 0 0
\(775\) 21.0718i 0.756921i
\(776\) 2.73205 + 4.73205i 0.0980749 + 0.169871i
\(777\) 0 0
\(778\) −21.0622 12.1603i −0.755116 0.435966i
\(779\) −3.60770 −0.129259
\(780\) 0 0
\(781\) −10.1436 −0.362966
\(782\) 6.29423 + 3.63397i 0.225081 + 0.129951i
\(783\) 0 0
\(784\) 0.500000 + 0.866025i 0.0178571 + 0.0309295i
\(785\) 13.7321i 0.490118i
\(786\) 0 0
\(787\) −38.9545 + 22.4904i −1.38858 + 0.801696i −0.993155 0.116804i \(-0.962735\pi\)
−0.395422 + 0.918499i \(0.629402\pi\)
\(788\) 7.07180i 0.251922i
\(789\) 0 0
\(790\) 1.90192 3.29423i 0.0676674 0.117203i
\(791\) −9.86603 5.69615i −0.350795 0.202532i
\(792\) 0 0
\(793\) 40.6410 + 11.7321i 1.44320 + 0.416617i
\(794\) 29.4641 1.04564
\(795\) 0 0
\(796\) 2.73205 4.73205i 0.0968350 0.167723i
\(797\) 4.46410 + 7.73205i 0.158127 + 0.273883i 0.934193 0.356768i \(-0.116121\pi\)
−0.776067 + 0.630651i \(0.782788\pi\)
\(798\) 0 0
\(799\) 14.5359 8.39230i 0.514243 0.296898i
\(800\) 3.46410 2.00000i 0.122474 0.0707107i
\(801\) 0 0
\(802\) −16.5263 28.6244i −0.583563 1.01076i
\(803\) −4.16987 + 7.22243i −0.147152 + 0.254874i
\(804\) 0 0
\(805\) −1.26795 −0.0446893
\(806\) 4.56218 + 18.4378i 0.160696 + 0.649445i
\(807\) 0 0
\(808\) 1.03590 + 0.598076i 0.0364428 + 0.0210402i
\(809\) −3.62436 + 6.27757i −0.127426 + 0.220708i −0.922678 0.385570i \(-0.874005\pi\)
0.795253 + 0.606278i \(0.207338\pi\)
\(810\) 0 0
\(811\) 20.8756i 0.733043i 0.930410 + 0.366522i \(0.119451\pi\)
−0.930410 + 0.366522i \(0.880549\pi\)
\(812\) 2.59808 1.50000i 0.0911746 0.0526397i
\(813\) 0 0
\(814\) 3.80385i 0.133325i
\(815\) 0.366025 + 0.633975i 0.0128213 + 0.0222072i
\(816\) 0 0
\(817\) 15.4641 + 8.92820i 0.541020 + 0.312358i
\(818\) −26.3205 −0.920275
\(819\) 0 0
\(820\) 2.46410 0.0860502
\(821\) 26.7846 + 15.4641i 0.934789 + 0.539701i 0.888323 0.459219i \(-0.151871\pi\)
0.0464662 + 0.998920i \(0.485204\pi\)
\(822\) 0 0
\(823\) 1.12436 + 1.94744i 0.0391926 + 0.0678835i 0.884956 0.465674i \(-0.154188\pi\)
−0.845764 + 0.533558i \(0.820855\pi\)
\(824\) 8.39230i 0.292360i
\(825\) 0 0
\(826\) 9.29423 5.36603i 0.323388 0.186708i
\(827\) 20.4449i 0.710938i −0.934688 0.355469i \(-0.884321\pi\)
0.934688 0.355469i \(-0.115679\pi\)
\(828\) 0 0
\(829\) −3.20577 + 5.55256i −0.111341 + 0.192848i −0.916311 0.400467i \(-0.868848\pi\)
0.804970 + 0.593315i \(0.202181\pi\)
\(830\) 3.29423 + 1.90192i 0.114344 + 0.0660167i
\(831\) 0 0
\(832\) −2.59808 + 2.50000i −0.0900721 + 0.0866719i
\(833\) 5.73205 0.198604
\(834\) 0 0
\(835\) 2.63397 4.56218i 0.0911524 0.157881i
\(836\) 0.535898 + 0.928203i 0.0185344 + 0.0321026i
\(837\) 0 0
\(838\) −4.43782 + 2.56218i −0.153302 + 0.0885090i
\(839\) −27.4641 + 15.8564i −0.948166 + 0.547424i −0.892511 0.451026i \(-0.851058\pi\)
−0.0556553 + 0.998450i \(0.517725\pi\)
\(840\) 0 0
\(841\) 10.0000 + 17.3205i 0.344828 + 0.597259i
\(842\) −7.06218 + 12.2321i −0.243379 + 0.421544i
\(843\) 0 0
\(844\) 21.2679 0.732073
\(845\) −12.9904 0.500000i −0.446883 0.0172005i
\(846\) 0 0
\(847\) 9.06218 + 5.23205i 0.311380 + 0.179775i
\(848\) 0.767949 1.33013i 0.0263715 0.0456767i
\(849\) 0 0
\(850\) 22.9282i 0.786431i
\(851\) −5.70577 + 3.29423i −0.195591 + 0.112925i
\(852\) 0 0
\(853\) 19.0000i 0.650548i 0.945620 + 0.325274i \(0.105456\pi\)
−0.945620 + 0.325274i \(0.894544\pi\)
\(854\) 5.86603 + 10.1603i 0.200731 + 0.347677i
\(855\) 0 0
\(856\) −9.46410 5.46410i −0.323476 0.186759i
\(857\) −0.947441 −0.0323640 −0.0161820 0.999869i \(-0.505151\pi\)
−0.0161820 + 0.999869i \(0.505151\pi\)
\(858\) 0 0
\(859\) −32.8372 −1.12039 −0.560195 0.828361i \(-0.689274\pi\)
−0.560195 + 0.828361i \(0.689274\pi\)
\(860\) −10.5622 6.09808i −0.360167 0.207943i
\(861\) 0 0
\(862\) 13.2679 + 22.9808i 0.451908 + 0.782728i
\(863\) 44.4449i 1.51292i −0.654040 0.756460i \(-0.726927\pi\)
0.654040 0.756460i \(-0.273073\pi\)
\(864\) 0 0
\(865\) 18.1244 10.4641i 0.616247 0.355790i
\(866\) 21.7321i 0.738485i
\(867\) 0 0
\(868\) −2.63397 + 4.56218i −0.0894029 + 0.154850i
\(869\) 2.41154 + 1.39230i 0.0818060 + 0.0472307i
\(870\) 0 0
\(871\) 40.8109 10.0981i 1.38282 0.342160i
\(872\) 10.0000 0.338643
\(873\) 0 0
\(874\) −0.928203 + 1.60770i −0.0313969 + 0.0543811i
\(875\) 4.50000 + 7.79423i 0.152128 + 0.263493i
\(876\) 0 0
\(877\) 1.62436 0.937822i 0.0548506 0.0316680i −0.472324 0.881425i \(-0.656585\pi\)
0.527175 + 0.849757i \(0.323251\pi\)
\(878\) 16.6865 9.63397i 0.563143 0.325131i
\(879\) 0 0
\(880\) −0.366025 0.633975i −0.0123387 0.0213713i
\(881\) 17.1865 29.7679i 0.579029 1.00291i −0.416562 0.909107i \(-0.636765\pi\)
0.995591 0.0938004i \(-0.0299015\pi\)
\(882\) 0 0
\(883\) 23.5167 0.791399 0.395699 0.918380i \(-0.370502\pi\)
0.395699 + 0.918380i \(0.370502\pi\)
\(884\) 4.96410 + 20.0622i 0.166961 + 0.674764i
\(885\) 0 0
\(886\) 30.5885 + 17.6603i 1.02764 + 0.593308i
\(887\) 1.46410 2.53590i 0.0491597 0.0851471i −0.840398 0.541969i \(-0.817679\pi\)
0.889558 + 0.456822i \(0.151012\pi\)
\(888\) 0 0
\(889\) 9.85641i 0.330573i
\(890\) 2.19615 1.26795i 0.0736152 0.0425018i
\(891\) 0 0
\(892\) 12.3923i 0.414925i
\(893\) 2.14359 + 3.71281i 0.0717326 + 0.124245i
\(894\) 0 0
\(895\) 14.1962 + 8.19615i 0.474525 + 0.273967i
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 18.0000 0.600668
\(899\) 13.6865 + 7.90192i 0.456471 + 0.263544i
\(900\) 0 0
\(901\) −4.40192 7.62436i −0.146649 0.254004i
\(902\) 1.80385i 0.0600616i
\(903\) 0 0
\(904\) 9.86603 5.69615i 0.328139 0.189451i
\(905\) 3.19615i 0.106244i
\(906\) 0 0
\(907\) −11.0263 + 19.0981i −0.366122 + 0.634141i −0.988955 0.148213i \(-0.952648\pi\)
0.622834 + 0.782354i \(0.285981\pi\)
\(908\) −1.09808 0.633975i −0.0364409 0.0210392i
\(909\) 0 0
\(910\) −2.50000 2.59808i −0.0828742 0.0861254i
\(911\) 40.1051 1.32874 0.664371 0.747403i \(-0.268700\pi\)
0.664371 + 0.747403i \(0.268700\pi\)
\(912\) 0 0
\(913\) −1.39230 + 2.41154i −0.0460786 + 0.0798104i
\(914\) 7.13397 + 12.3564i 0.235971 + 0.408714i
\(915\) 0 0
\(916\) −21.1244 + 12.1962i −0.697968 + 0.402972i
\(917\) −4.39230 + 2.53590i −0.145047 + 0.0837427i
\(918\) 0 0
\(919\) −0.392305 0.679492i −0.0129409 0.0224144i 0.859482 0.511165i \(-0.170786\pi\)
−0.872423 + 0.488751i \(0.837453\pi\)
\(920\) 0.633975 1.09808i 0.0209015 0.0362025i
\(921\) 0 0
\(922\) 8.32051 0.274021
\(923\) 13.8564 48.0000i 0.456089 1.57994i
\(924\) 0 0
\(925\) 18.0000 + 10.3923i 0.591836 + 0.341697i
\(926\) 1.97372 3.41858i 0.0648605 0.112342i
\(927\) 0 0
\(928\) 3.00000i 0.0984798i
\(929\) 47.7224 27.5526i 1.56572 0.903970i 0.569063 0.822294i \(-0.307306\pi\)
0.996659 0.0816764i \(-0.0260274\pi\)
\(930\) 0 0
\(931\) 1.46410i 0.0479840i
\(932\) −2.19615 3.80385i −0.0719374 0.124599i
\(933\) 0 0
\(934\) 21.4186 + 12.3660i 0.700837 + 0.404629i
\(935\) −4.19615 −0.137229
\(936\) 0 0
\(937\) 55.5885 1.81600 0.907998 0.418975i \(-0.137610\pi\)
0.907998 + 0.418975i \(0.137610\pi\)
\(938\) 10.0981 + 5.83013i 0.329714 + 0.190360i
\(939\) 0 0
\(940\) −1.46410 2.53590i −0.0477537 0.0827119i
\(941\) 11.3205i 0.369038i −0.982829 0.184519i \(-0.940927\pi\)
0.982829 0.184519i \(-0.0590727\pi\)
\(942\) 0 0
\(943\) −2.70577 + 1.56218i −0.0881120 + 0.0508715i
\(944\) 10.7321i 0.349299i
\(945\) 0 0
\(946\) 4.46410 7.73205i 0.145140 0.251391i
\(947\) −46.0070 26.5622i −1.49503 0.863155i −0.495044 0.868868i \(-0.664848\pi\)
−0.999984 + 0.00571294i \(0.998182\pi\)
\(948\) 0 0
\(949\) −28.4808 29.5981i −0.924525 0.960794i
\(950\) 5.85641 0.190007
\(951\) 0 0
\(952\) −2.86603 + 4.96410i −0.0928884 + 0.160887i
\(953\) −18.5885 32.1962i −0.602139 1.04294i −0.992497 0.122272i \(-0.960982\pi\)
0.390357 0.920663i \(-0.372351\pi\)
\(954\) 0 0
\(955\) 6.16987 3.56218i 0.199652 0.115269i
\(956\) 25.5622 14.7583i 0.826740 0.477319i
\(957\) 0 0
\(958\) 16.0981 + 27.8827i 0.520105 + 0.900849i
\(959\) −3.06218 + 5.30385i −0.0988829 + 0.171270i
\(960\) 0 0
\(961\) 3.24871 0.104797
\(962\) −18.0000 5.19615i −0.580343 0.167531i
\(963\) 0 0
\(964\) −13.3301 7.69615i −0.429334 0.247876i
\(965\) −11.5981 + 20.0885i −0.373355 + 0.646670i
\(966\) 0 0
\(967\) 13.5167i 0.434666i −0.976097 0.217333i \(-0.930264\pi\)
0.976097 0.217333i \(-0.0697358\pi\)
\(968\) −9.06218 + 5.23205i −0.291269 + 0.168164i
\(969\) 0 0
\(970\) 5.46410i 0.175442i
\(971\) −10.1962 17.6603i −0.327210 0.566745i 0.654747 0.755848i \(-0.272775\pi\)
−0.981957 + 0.189104i \(0.939442\pi\)
\(972\) 0 0
\(973\) −0.294229 0.169873i −0.00943254 0.00544588i
\(974\) −31.3205 −1.00357
\(975\) 0 0
\(976\) −11.7321 −0.375534
\(977\) −20.8923 12.0622i −0.668404 0.385903i 0.127068 0.991894i \(-0.459443\pi\)
−0.795472 + 0.605991i \(0.792777\pi\)
\(978\) 0 0
\(979\) 0.928203 + 1.60770i 0.0296655 + 0.0513822i
\(980\) 1.00000i 0.0319438i
\(981\) 0 0
\(982\) −24.0000 + 13.8564i −0.765871 + 0.442176i
\(983\) 44.1051i 1.40673i 0.710826 + 0.703367i \(0.248321\pi\)
−0.710826 + 0.703367i \(0.751679\pi\)
\(984\) 0 0
\(985\) −3.53590 + 6.12436i −0.112663 + 0.195138i
\(986\) 14.8923 + 8.59808i 0.474268 + 0.273819i
\(987\) 0 0
\(988\) −5.12436 + 1.26795i −0.163027 + 0.0403388i
\(989\) 15.4641 0.491730
\(990\) 0 0
\(991\) 22.6865 39.2942i 0.720661 1.24822i −0.240074 0.970755i \(-0.577172\pi\)
0.960735 0.277468i \(-0.0894951\pi\)
\(992\) −2.63397 4.56218i −0.0836288 0.144849i
\(993\) 0 0
\(994\) 12.0000 6.92820i 0.380617 0.219749i
\(995\) −4.73205 + 2.73205i −0.150016 + 0.0866118i
\(996\) 0 0
\(997\) 10.9904 + 19.0359i 0.348069 + 0.602873i 0.985906 0.167298i \(-0.0535042\pi\)
−0.637838 + 0.770171i \(0.720171\pi\)
\(998\) −5.63397 + 9.75833i −0.178340 + 0.308895i
\(999\) 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 1638.2.bj.c.1135.1 4
3.2 odd 2 182.2.m.a.43.2 4
12.11 even 2 1456.2.cc.b.225.2 4
13.10 even 6 inner 1638.2.bj.c.127.1 4
21.2 odd 6 1274.2.o.b.459.1 4
21.5 even 6 1274.2.o.a.459.1 4
21.11 odd 6 1274.2.v.a.667.1 4
21.17 even 6 1274.2.v.b.667.1 4
21.20 even 2 1274.2.m.a.589.2 4
39.17 odd 6 2366.2.d.k.337.4 4
39.20 even 12 2366.2.a.s.1.2 2
39.23 odd 6 182.2.m.a.127.2 yes 4
39.32 even 12 2366.2.a.q.1.2 2
39.35 odd 6 2366.2.d.k.337.2 4
156.23 even 6 1456.2.cc.b.673.2 4
273.23 odd 6 1274.2.v.a.361.1 4
273.62 even 6 1274.2.m.a.491.2 4
273.101 even 6 1274.2.o.a.569.2 4
273.179 odd 6 1274.2.o.b.569.2 4
273.257 even 6 1274.2.v.b.361.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.m.a.43.2 4 3.2 odd 2
182.2.m.a.127.2 yes 4 39.23 odd 6
1274.2.m.a.491.2 4 273.62 even 6
1274.2.m.a.589.2 4 21.20 even 2
1274.2.o.a.459.1 4 21.5 even 6
1274.2.o.a.569.2 4 273.101 even 6
1274.2.o.b.459.1 4 21.2 odd 6
1274.2.o.b.569.2 4 273.179 odd 6
1274.2.v.a.361.1 4 273.23 odd 6
1274.2.v.a.667.1 4 21.11 odd 6
1274.2.v.b.361.1 4 273.257 even 6
1274.2.v.b.667.1 4 21.17 even 6
1456.2.cc.b.225.2 4 12.11 even 2
1456.2.cc.b.673.2 4 156.23 even 6
1638.2.bj.c.127.1 4 13.10 even 6 inner
1638.2.bj.c.1135.1 4 1.1 even 1 trivial
2366.2.a.q.1.2 2 39.32 even 12
2366.2.a.s.1.2 2 39.20 even 12
2366.2.d.k.337.2 4 39.35 odd 6
2366.2.d.k.337.4 4 39.17 odd 6