Properties

Label 966.2.g.d.643.3
Level $966$
Weight $2$
Character 966.643
Analytic conductor $7.714$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(643,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.643");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.g (of order \(2\), degree \(1\), 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: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 3x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 643.3
Root \(-1.32288 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 966.643
Dual form 966.2.g.d.643.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.64575 q^{5} -1.00000i q^{6} -2.64575 q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.64575 q^{5} -1.00000i q^{6} -2.64575 q^{7} -1.00000 q^{8} -1.00000 q^{9} +2.64575 q^{10} +1.00000i q^{12} +5.00000i q^{13} +2.64575 q^{14} -2.64575i q^{15} +1.00000 q^{16} -5.29150 q^{17} +1.00000 q^{18} +5.29150 q^{19} -2.64575 q^{20} -2.64575i q^{21} +(4.00000 - 2.64575i) q^{23} -1.00000i q^{24} +2.00000 q^{25} -5.00000i q^{26} -1.00000i q^{27} -2.64575 q^{28} -1.00000 q^{29} +2.64575i q^{30} -4.00000i q^{31} -1.00000 q^{32} +5.29150 q^{34} +7.00000 q^{35} -1.00000 q^{36} -7.93725i q^{37} -5.29150 q^{38} -5.00000 q^{39} +2.64575 q^{40} -9.00000i q^{41} +2.64575i q^{42} +2.64575i q^{43} +2.64575 q^{45} +(-4.00000 + 2.64575i) q^{46} -13.0000i q^{47} +1.00000i q^{48} +7.00000 q^{49} -2.00000 q^{50} -5.29150i q^{51} +5.00000i q^{52} -5.29150i q^{53} +1.00000i q^{54} +2.64575 q^{56} +5.29150i q^{57} +1.00000 q^{58} +14.0000i q^{59} -2.64575i q^{60} +10.5830 q^{61} +4.00000i q^{62} +2.64575 q^{63} +1.00000 q^{64} -13.2288i q^{65} +5.29150i q^{67} -5.29150 q^{68} +(2.64575 + 4.00000i) q^{69} -7.00000 q^{70} +6.00000 q^{71} +1.00000 q^{72} +4.00000i q^{73} +7.93725i q^{74} +2.00000i q^{75} +5.29150 q^{76} +5.00000 q^{78} -5.29150i q^{79} -2.64575 q^{80} +1.00000 q^{81} +9.00000i q^{82} -15.8745 q^{83} -2.64575i q^{84} +14.0000 q^{85} -2.64575i q^{86} -1.00000i q^{87} -2.64575 q^{90} -13.2288i q^{91} +(4.00000 - 2.64575i) q^{92} +4.00000 q^{93} +13.0000i q^{94} -14.0000 q^{95} -1.00000i q^{96} +2.64575 q^{97} -7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9} + 4 q^{16} + 4 q^{18} + 16 q^{23} + 8 q^{25} - 4 q^{29} - 4 q^{32} + 28 q^{35} - 4 q^{36} - 20 q^{39} - 16 q^{46} + 28 q^{49} - 8 q^{50} + 4 q^{58} + 4 q^{64} - 28 q^{70} + 24 q^{71} + 4 q^{72} + 20 q^{78} + 4 q^{81} + 56 q^{85} + 16 q^{92} + 16 q^{93} - 56 q^{95} - 28 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) −2.64575 −1.18322 −0.591608 0.806226i \(-0.701507\pi\)
−0.591608 + 0.806226i \(0.701507\pi\)
\(6\) 1.00000i 0.408248i
\(7\) −2.64575 −1.00000
\(8\) −1.00000 −0.353553
\(9\) −1.00000 −0.333333
\(10\) 2.64575 0.836660
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 5.00000i 1.38675i 0.720577 + 0.693375i \(0.243877\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) 2.64575 0.707107
\(15\) 2.64575i 0.683130i
\(16\) 1.00000 0.250000
\(17\) −5.29150 −1.28338 −0.641689 0.766965i \(-0.721766\pi\)
−0.641689 + 0.766965i \(0.721766\pi\)
\(18\) 1.00000 0.235702
\(19\) 5.29150 1.21395 0.606977 0.794719i \(-0.292382\pi\)
0.606977 + 0.794719i \(0.292382\pi\)
\(20\) −2.64575 −0.591608
\(21\) 2.64575i 0.577350i
\(22\) 0 0
\(23\) 4.00000 2.64575i 0.834058 0.551677i
\(24\) 1.00000i 0.204124i
\(25\) 2.00000 0.400000
\(26\) 5.00000i 0.980581i
\(27\) 1.00000i 0.192450i
\(28\) −2.64575 −0.500000
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 2.64575i 0.483046i
\(31\) 4.00000i 0.718421i −0.933257 0.359211i \(-0.883046\pi\)
0.933257 0.359211i \(-0.116954\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 5.29150 0.907485
\(35\) 7.00000 1.18322
\(36\) −1.00000 −0.166667
\(37\) 7.93725i 1.30488i −0.757842 0.652438i \(-0.773746\pi\)
0.757842 0.652438i \(-0.226254\pi\)
\(38\) −5.29150 −0.858395
\(39\) −5.00000 −0.800641
\(40\) 2.64575 0.418330
\(41\) 9.00000i 1.40556i −0.711405 0.702782i \(-0.751941\pi\)
0.711405 0.702782i \(-0.248059\pi\)
\(42\) 2.64575i 0.408248i
\(43\) 2.64575i 0.403473i 0.979440 + 0.201737i \(0.0646585\pi\)
−0.979440 + 0.201737i \(0.935341\pi\)
\(44\) 0 0
\(45\) 2.64575 0.394405
\(46\) −4.00000 + 2.64575i −0.589768 + 0.390095i
\(47\) 13.0000i 1.89624i −0.317905 0.948122i \(-0.602979\pi\)
0.317905 0.948122i \(-0.397021\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 7.00000 1.00000
\(50\) −2.00000 −0.282843
\(51\) 5.29150i 0.740959i
\(52\) 5.00000i 0.693375i
\(53\) 5.29150i 0.726844i −0.931625 0.363422i \(-0.881608\pi\)
0.931625 0.363422i \(-0.118392\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0 0
\(56\) 2.64575 0.353553
\(57\) 5.29150i 0.700877i
\(58\) 1.00000 0.131306
\(59\) 14.0000i 1.82264i 0.411693 + 0.911322i \(0.364937\pi\)
−0.411693 + 0.911322i \(0.635063\pi\)
\(60\) 2.64575i 0.341565i
\(61\) 10.5830 1.35501 0.677507 0.735516i \(-0.263060\pi\)
0.677507 + 0.735516i \(0.263060\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 2.64575 0.333333
\(64\) 1.00000 0.125000
\(65\) 13.2288i 1.64083i
\(66\) 0 0
\(67\) 5.29150i 0.646460i 0.946320 + 0.323230i \(0.104769\pi\)
−0.946320 + 0.323230i \(0.895231\pi\)
\(68\) −5.29150 −0.641689
\(69\) 2.64575 + 4.00000i 0.318511 + 0.481543i
\(70\) −7.00000 −0.836660
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 1.00000 0.117851
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) 7.93725i 0.922687i
\(75\) 2.00000i 0.230940i
\(76\) 5.29150 0.606977
\(77\) 0 0
\(78\) 5.00000 0.566139
\(79\) 5.29150i 0.595341i −0.954669 0.297670i \(-0.903790\pi\)
0.954669 0.297670i \(-0.0962096\pi\)
\(80\) −2.64575 −0.295804
\(81\) 1.00000 0.111111
\(82\) 9.00000i 0.993884i
\(83\) −15.8745 −1.74245 −0.871227 0.490881i \(-0.836675\pi\)
−0.871227 + 0.490881i \(0.836675\pi\)
\(84\) 2.64575i 0.288675i
\(85\) 14.0000 1.51851
\(86\) 2.64575i 0.285299i
\(87\) 1.00000i 0.107211i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −2.64575 −0.278887
\(91\) 13.2288i 1.38675i
\(92\) 4.00000 2.64575i 0.417029 0.275839i
\(93\) 4.00000 0.414781
\(94\) 13.0000i 1.34085i
\(95\) −14.0000 −1.43637
\(96\) 1.00000i 0.102062i
\(97\) 2.64575 0.268635 0.134318 0.990938i \(-0.457116\pi\)
0.134318 + 0.990938i \(0.457116\pi\)
\(98\) −7.00000 −0.707107
\(99\) 0 0
\(100\) 2.00000 0.200000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 5.29150i 0.523937i
\(103\) 2.64575 0.260694 0.130347 0.991468i \(-0.458391\pi\)
0.130347 + 0.991468i \(0.458391\pi\)
\(104\) 5.00000i 0.490290i
\(105\) 7.00000i 0.683130i
\(106\) 5.29150i 0.513956i
\(107\) 5.29150i 0.511549i 0.966736 + 0.255774i \(0.0823304\pi\)
−0.966736 + 0.255774i \(0.917670\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 18.5203i 1.77392i −0.461847 0.886960i \(-0.652813\pi\)
0.461847 0.886960i \(-0.347187\pi\)
\(110\) 0 0
\(111\) 7.93725 0.753371
\(112\) −2.64575 −0.250000
\(113\) 2.64575i 0.248891i −0.992226 0.124446i \(-0.960285\pi\)
0.992226 0.124446i \(-0.0397153\pi\)
\(114\) 5.29150i 0.495595i
\(115\) −10.5830 + 7.00000i −0.986870 + 0.652753i
\(116\) −1.00000 −0.0928477
\(117\) 5.00000i 0.462250i
\(118\) 14.0000i 1.28880i
\(119\) 14.0000 1.28338
\(120\) 2.64575i 0.241523i
\(121\) 11.0000 1.00000
\(122\) −10.5830 −0.958140
\(123\) 9.00000 0.811503
\(124\) 4.00000i 0.359211i
\(125\) 7.93725 0.709930
\(126\) −2.64575 −0.235702
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.64575 −0.232945
\(130\) 13.2288i 1.16024i
\(131\) 22.0000i 1.92215i −0.276289 0.961074i \(-0.589105\pi\)
0.276289 0.961074i \(-0.410895\pi\)
\(132\) 0 0
\(133\) −14.0000 −1.21395
\(134\) 5.29150i 0.457116i
\(135\) 2.64575i 0.227710i
\(136\) 5.29150 0.453743
\(137\) 7.93725i 0.678125i −0.940764 0.339063i \(-0.889890\pi\)
0.940764 0.339063i \(-0.110110\pi\)
\(138\) −2.64575 4.00000i −0.225221 0.340503i
\(139\) 5.00000i 0.424094i −0.977259 0.212047i \(-0.931987\pi\)
0.977259 0.212047i \(-0.0680131\pi\)
\(140\) 7.00000 0.591608
\(141\) 13.0000 1.09480
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) 2.64575 0.219718
\(146\) 4.00000i 0.331042i
\(147\) 7.00000i 0.577350i
\(148\) 7.93725i 0.652438i
\(149\) 15.8745i 1.30049i 0.759724 + 0.650245i \(0.225334\pi\)
−0.759724 + 0.650245i \(0.774666\pi\)
\(150\) 2.00000i 0.163299i
\(151\) −5.00000 −0.406894 −0.203447 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(152\) −5.29150 −0.429198
\(153\) 5.29150 0.427793
\(154\) 0 0
\(155\) 10.5830i 0.850047i
\(156\) −5.00000 −0.400320
\(157\) 10.5830 0.844616 0.422308 0.906452i \(-0.361220\pi\)
0.422308 + 0.906452i \(0.361220\pi\)
\(158\) 5.29150i 0.420969i
\(159\) 5.29150 0.419643
\(160\) 2.64575 0.209165
\(161\) −10.5830 + 7.00000i −0.834058 + 0.551677i
\(162\) −1.00000 −0.0785674
\(163\) −18.0000 −1.40987 −0.704934 0.709273i \(-0.749024\pi\)
−0.704934 + 0.709273i \(0.749024\pi\)
\(164\) 9.00000i 0.702782i
\(165\) 0 0
\(166\) 15.8745 1.23210
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 2.64575i 0.204124i
\(169\) −12.0000 −0.923077
\(170\) −14.0000 −1.07375
\(171\) −5.29150 −0.404651
\(172\) 2.64575i 0.201737i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 1.00000i 0.0758098i
\(175\) −5.29150 −0.400000
\(176\) 0 0
\(177\) −14.0000 −1.05230
\(178\) 0 0
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 2.64575 0.197203
\(181\) −15.8745 −1.17994 −0.589971 0.807424i \(-0.700861\pi\)
−0.589971 + 0.807424i \(0.700861\pi\)
\(182\) 13.2288i 0.980581i
\(183\) 10.5830i 0.782318i
\(184\) −4.00000 + 2.64575i −0.294884 + 0.195047i
\(185\) 21.0000i 1.54395i
\(186\) −4.00000 −0.293294
\(187\) 0 0
\(188\) 13.0000i 0.948122i
\(189\) 2.64575i 0.192450i
\(190\) 14.0000 1.01567
\(191\) 15.8745i 1.14864i 0.818631 + 0.574320i \(0.194733\pi\)
−0.818631 + 0.574320i \(0.805267\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 19.0000 1.36765 0.683825 0.729646i \(-0.260315\pi\)
0.683825 + 0.729646i \(0.260315\pi\)
\(194\) −2.64575 −0.189954
\(195\) 13.2288 0.947331
\(196\) 7.00000 0.500000
\(197\) −1.00000 −0.0712470 −0.0356235 0.999365i \(-0.511342\pi\)
−0.0356235 + 0.999365i \(0.511342\pi\)
\(198\) 0 0
\(199\) −13.2288 −0.937762 −0.468881 0.883261i \(-0.655343\pi\)
−0.468881 + 0.883261i \(0.655343\pi\)
\(200\) −2.00000 −0.141421
\(201\) −5.29150 −0.373234
\(202\) 0 0
\(203\) 2.64575 0.185695
\(204\) 5.29150i 0.370479i
\(205\) 23.8118i 1.66309i
\(206\) −2.64575 −0.184338
\(207\) −4.00000 + 2.64575i −0.278019 + 0.183892i
\(208\) 5.00000i 0.346688i
\(209\) 0 0
\(210\) 7.00000i 0.483046i
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 5.29150i 0.363422i
\(213\) 6.00000i 0.411113i
\(214\) 5.29150i 0.361720i
\(215\) 7.00000i 0.477396i
\(216\) 1.00000i 0.0680414i
\(217\) 10.5830i 0.718421i
\(218\) 18.5203i 1.25435i
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) 26.4575i 1.77972i
\(222\) −7.93725 −0.532714
\(223\) 28.0000i 1.87502i −0.347960 0.937509i \(-0.613126\pi\)
0.347960 0.937509i \(-0.386874\pi\)
\(224\) 2.64575 0.176777
\(225\) −2.00000 −0.133333
\(226\) 2.64575i 0.175993i
\(227\) −7.93725 −0.526814 −0.263407 0.964685i \(-0.584846\pi\)
−0.263407 + 0.964685i \(0.584846\pi\)
\(228\) 5.29150i 0.350438i
\(229\) 10.5830 0.699345 0.349672 0.936872i \(-0.386293\pi\)
0.349672 + 0.936872i \(0.386293\pi\)
\(230\) 10.5830 7.00000i 0.697823 0.461566i
\(231\) 0 0
\(232\) 1.00000 0.0656532
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 5.00000i 0.326860i
\(235\) 34.3948i 2.24367i
\(236\) 14.0000i 0.911322i
\(237\) 5.29150 0.343720
\(238\) −14.0000 −0.907485
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 2.64575i 0.170783i
\(241\) −23.8118 −1.53385 −0.766925 0.641736i \(-0.778214\pi\)
−0.766925 + 0.641736i \(0.778214\pi\)
\(242\) −11.0000 −0.707107
\(243\) 1.00000i 0.0641500i
\(244\) 10.5830 0.677507
\(245\) −18.5203 −1.18322
\(246\) −9.00000 −0.573819
\(247\) 26.4575i 1.68345i
\(248\) 4.00000i 0.254000i
\(249\) 15.8745i 1.00601i
\(250\) −7.93725 −0.501996
\(251\) 18.5203 1.16899 0.584494 0.811398i \(-0.301293\pi\)
0.584494 + 0.811398i \(0.301293\pi\)
\(252\) 2.64575 0.166667
\(253\) 0 0
\(254\) 13.0000 0.815693
\(255\) 14.0000i 0.876714i
\(256\) 1.00000 0.0625000
\(257\) 6.00000i 0.374270i −0.982334 0.187135i \(-0.940080\pi\)
0.982334 0.187135i \(-0.0599201\pi\)
\(258\) 2.64575 0.164717
\(259\) 21.0000i 1.30488i
\(260\) 13.2288i 0.820413i
\(261\) 1.00000 0.0618984
\(262\) 22.0000i 1.35916i
\(263\) 23.8118i 1.46830i 0.678989 + 0.734148i \(0.262418\pi\)
−0.678989 + 0.734148i \(0.737582\pi\)
\(264\) 0 0
\(265\) 14.0000i 0.860013i
\(266\) 14.0000 0.858395
\(267\) 0 0
\(268\) 5.29150i 0.323230i
\(269\) 10.0000i 0.609711i −0.952399 0.304855i \(-0.901392\pi\)
0.952399 0.304855i \(-0.0986081\pi\)
\(270\) 2.64575i 0.161015i
\(271\) 14.0000i 0.850439i −0.905090 0.425220i \(-0.860197\pi\)
0.905090 0.425220i \(-0.139803\pi\)
\(272\) −5.29150 −0.320844
\(273\) 13.2288 0.800641
\(274\) 7.93725i 0.479507i
\(275\) 0 0
\(276\) 2.64575 + 4.00000i 0.159256 + 0.240772i
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 5.00000i 0.299880i
\(279\) 4.00000i 0.239474i
\(280\) −7.00000 −0.418330
\(281\) 7.93725i 0.473497i −0.971571 0.236748i \(-0.923918\pi\)
0.971571 0.236748i \(-0.0760817\pi\)
\(282\) −13.0000 −0.774139
\(283\) 10.5830 0.629094 0.314547 0.949242i \(-0.398147\pi\)
0.314547 + 0.949242i \(0.398147\pi\)
\(284\) 6.00000 0.356034
\(285\) 14.0000i 0.829288i
\(286\) 0 0
\(287\) 23.8118i 1.40556i
\(288\) 1.00000 0.0589256
\(289\) 11.0000 0.647059
\(290\) −2.64575 −0.155364
\(291\) 2.64575i 0.155097i
\(292\) 4.00000i 0.234082i
\(293\) 21.1660 1.23653 0.618266 0.785969i \(-0.287836\pi\)
0.618266 + 0.785969i \(0.287836\pi\)
\(294\) 7.00000i 0.408248i
\(295\) 37.0405i 2.15658i
\(296\) 7.93725i 0.461344i
\(297\) 0 0
\(298\) 15.8745i 0.919586i
\(299\) 13.2288 + 20.0000i 0.765039 + 1.15663i
\(300\) 2.00000i 0.115470i
\(301\) 7.00000i 0.403473i
\(302\) 5.00000 0.287718
\(303\) 0 0
\(304\) 5.29150 0.303488
\(305\) −28.0000 −1.60328
\(306\) −5.29150 −0.302495
\(307\) 21.0000i 1.19853i −0.800549 0.599267i \(-0.795459\pi\)
0.800549 0.599267i \(-0.204541\pi\)
\(308\) 0 0
\(309\) 2.64575i 0.150512i
\(310\) 10.5830i 0.601074i
\(311\) 24.0000i 1.36092i 0.732787 + 0.680458i \(0.238219\pi\)
−0.732787 + 0.680458i \(0.761781\pi\)
\(312\) 5.00000 0.283069
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) −10.5830 −0.597234
\(315\) −7.00000 −0.394405
\(316\) 5.29150i 0.297670i
\(317\) 27.0000 1.51647 0.758236 0.651981i \(-0.226062\pi\)
0.758236 + 0.651981i \(0.226062\pi\)
\(318\) −5.29150 −0.296733
\(319\) 0 0
\(320\) −2.64575 −0.147902
\(321\) −5.29150 −0.295343
\(322\) 10.5830 7.00000i 0.589768 0.390095i
\(323\) −28.0000 −1.55796
\(324\) 1.00000 0.0555556
\(325\) 10.0000i 0.554700i
\(326\) 18.0000 0.996928
\(327\) 18.5203 1.02417
\(328\) 9.00000i 0.496942i
\(329\) 34.3948i 1.89624i
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) −15.8745 −0.871227
\(333\) 7.93725i 0.434959i
\(334\) 0 0
\(335\) 14.0000i 0.764902i
\(336\) 2.64575i 0.144338i
\(337\) 26.4575i 1.44123i 0.693334 + 0.720616i \(0.256141\pi\)
−0.693334 + 0.720616i \(0.743859\pi\)
\(338\) 12.0000 0.652714
\(339\) 2.64575 0.143697
\(340\) 14.0000 0.759257
\(341\) 0 0
\(342\) 5.29150 0.286132
\(343\) −18.5203 −1.00000
\(344\) 2.64575i 0.142649i
\(345\) −7.00000 10.5830i −0.376867 0.569770i
\(346\) 0 0
\(347\) −11.0000 −0.590511 −0.295255 0.955418i \(-0.595405\pi\)
−0.295255 + 0.955418i \(0.595405\pi\)
\(348\) 1.00000i 0.0536056i
\(349\) 30.0000i 1.60586i −0.596071 0.802932i \(-0.703272\pi\)
0.596071 0.802932i \(-0.296728\pi\)
\(350\) 5.29150 0.282843
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 25.0000i 1.33062i −0.746569 0.665308i \(-0.768300\pi\)
0.746569 0.665308i \(-0.231700\pi\)
\(354\) 14.0000 0.744092
\(355\) −15.8745 −0.842531
\(356\) 0 0
\(357\) 14.0000i 0.740959i
\(358\) −9.00000 −0.475665
\(359\) 23.8118i 1.25674i −0.777916 0.628368i \(-0.783723\pi\)
0.777916 0.628368i \(-0.216277\pi\)
\(360\) −2.64575 −0.139443
\(361\) 9.00000 0.473684
\(362\) 15.8745 0.834346
\(363\) 11.0000i 0.577350i
\(364\) 13.2288i 0.693375i
\(365\) 10.5830i 0.553940i
\(366\) 10.5830i 0.553183i
\(367\) −18.5203 −0.966750 −0.483375 0.875413i \(-0.660589\pi\)
−0.483375 + 0.875413i \(0.660589\pi\)
\(368\) 4.00000 2.64575i 0.208514 0.137919i
\(369\) 9.00000i 0.468521i
\(370\) 21.0000i 1.09174i
\(371\) 14.0000i 0.726844i
\(372\) 4.00000 0.207390
\(373\) 21.1660i 1.09593i −0.836500 0.547967i \(-0.815402\pi\)
0.836500 0.547967i \(-0.184598\pi\)
\(374\) 0 0
\(375\) 7.93725i 0.409878i
\(376\) 13.0000i 0.670424i
\(377\) 5.00000i 0.257513i
\(378\) 2.64575i 0.136083i
\(379\) 23.8118i 1.22313i 0.791195 + 0.611564i \(0.209459\pi\)
−0.791195 + 0.611564i \(0.790541\pi\)
\(380\) −14.0000 −0.718185
\(381\) 13.0000i 0.666010i
\(382\) 15.8745i 0.812210i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) −19.0000 −0.967075
\(387\) 2.64575i 0.134491i
\(388\) 2.64575 0.134318
\(389\) 21.1660i 1.07316i −0.843850 0.536580i \(-0.819716\pi\)
0.843850 0.536580i \(-0.180284\pi\)
\(390\) −13.2288 −0.669864
\(391\) −21.1660 + 14.0000i −1.07041 + 0.708010i
\(392\) −7.00000 −0.353553
\(393\) 22.0000 1.10975
\(394\) 1.00000 0.0503793
\(395\) 14.0000i 0.704416i
\(396\) 0 0
\(397\) 34.0000i 1.70641i −0.521575 0.853206i \(-0.674655\pi\)
0.521575 0.853206i \(-0.325345\pi\)
\(398\) 13.2288 0.663098
\(399\) 14.0000i 0.700877i
\(400\) 2.00000 0.100000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 5.29150 0.263916
\(403\) 20.0000 0.996271
\(404\) 0 0
\(405\) −2.64575 −0.131468
\(406\) −2.64575 −0.131306
\(407\) 0 0
\(408\) 5.29150i 0.261968i
\(409\) 18.0000i 0.890043i 0.895520 + 0.445021i \(0.146804\pi\)
−0.895520 + 0.445021i \(0.853196\pi\)
\(410\) 23.8118i 1.17598i
\(411\) 7.93725 0.391516
\(412\) 2.64575 0.130347
\(413\) 37.0405i 1.82264i
\(414\) 4.00000 2.64575i 0.196589 0.130032i
\(415\) 42.0000 2.06170
\(416\) 5.00000i 0.245145i
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) 15.8745 0.775520 0.387760 0.921760i \(-0.373249\pi\)
0.387760 + 0.921760i \(0.373249\pi\)
\(420\) 7.00000i 0.341565i
\(421\) 29.1033i 1.41841i −0.705004 0.709203i \(-0.749055\pi\)
0.705004 0.709203i \(-0.250945\pi\)
\(422\) 16.0000 0.778868
\(423\) 13.0000i 0.632082i
\(424\) 5.29150i 0.256978i
\(425\) −10.5830 −0.513351
\(426\) 6.00000i 0.290701i
\(427\) −28.0000 −1.35501
\(428\) 5.29150i 0.255774i
\(429\) 0 0
\(430\) 7.00000i 0.337570i
\(431\) 13.2288i 0.637207i −0.947888 0.318603i \(-0.896786\pi\)
0.947888 0.318603i \(-0.103214\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −13.2288 −0.635733 −0.317867 0.948135i \(-0.602966\pi\)
−0.317867 + 0.948135i \(0.602966\pi\)
\(434\) 10.5830i 0.508001i
\(435\) 2.64575i 0.126854i
\(436\) 18.5203i 0.886960i
\(437\) 21.1660 14.0000i 1.01251 0.669711i
\(438\) 4.00000 0.191127
\(439\) 6.00000i 0.286364i −0.989696 0.143182i \(-0.954267\pi\)
0.989696 0.143182i \(-0.0457335\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) 26.4575i 1.25846i
\(443\) 3.00000 0.142534 0.0712672 0.997457i \(-0.477296\pi\)
0.0712672 + 0.997457i \(0.477296\pi\)
\(444\) 7.93725 0.376685
\(445\) 0 0
\(446\) 28.0000i 1.32584i
\(447\) −15.8745 −0.750838
\(448\) −2.64575 −0.125000
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 2.00000 0.0942809
\(451\) 0 0
\(452\) 2.64575i 0.124446i
\(453\) 5.00000i 0.234920i
\(454\) 7.93725 0.372514
\(455\) 35.0000i 1.64083i
\(456\) 5.29150i 0.247797i
\(457\) 5.29150i 0.247526i −0.992312 0.123763i \(-0.960504\pi\)
0.992312 0.123763i \(-0.0394963\pi\)
\(458\) −10.5830 −0.494511
\(459\) 5.29150i 0.246986i
\(460\) −10.5830 + 7.00000i −0.493435 + 0.326377i
\(461\) 12.0000i 0.558896i −0.960161 0.279448i \(-0.909849\pi\)
0.960161 0.279448i \(-0.0901514\pi\)
\(462\) 0 0
\(463\) 19.0000 0.883005 0.441502 0.897260i \(-0.354446\pi\)
0.441502 + 0.897260i \(0.354446\pi\)
\(464\) −1.00000 −0.0464238
\(465\) −10.5830 −0.490775
\(466\) 18.0000 0.833834
\(467\) −13.2288 −0.612154 −0.306077 0.952007i \(-0.599016\pi\)
−0.306077 + 0.952007i \(0.599016\pi\)
\(468\) 5.00000i 0.231125i
\(469\) 14.0000i 0.646460i
\(470\) 34.3948i 1.58651i
\(471\) 10.5830i 0.487639i
\(472\) 14.0000i 0.644402i
\(473\) 0 0
\(474\) −5.29150 −0.243047
\(475\) 10.5830 0.485582
\(476\) 14.0000 0.641689
\(477\) 5.29150i 0.242281i
\(478\) 20.0000 0.914779
\(479\) 5.29150 0.241775 0.120887 0.992666i \(-0.461426\pi\)
0.120887 + 0.992666i \(0.461426\pi\)
\(480\) 2.64575i 0.120761i
\(481\) 39.6863 1.80954
\(482\) 23.8118 1.08460
\(483\) −7.00000 10.5830i −0.318511 0.481543i
\(484\) 11.0000 0.500000
\(485\) −7.00000 −0.317854
\(486\) 1.00000i 0.0453609i
\(487\) −23.0000 −1.04223 −0.521115 0.853487i \(-0.674484\pi\)
−0.521115 + 0.853487i \(0.674484\pi\)
\(488\) −10.5830 −0.479070
\(489\) 18.0000i 0.813988i
\(490\) 18.5203 0.836660
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 9.00000 0.405751
\(493\) 5.29150 0.238317
\(494\) 26.4575i 1.19038i
\(495\) 0 0
\(496\) 4.00000i 0.179605i
\(497\) −15.8745 −0.712069
\(498\) 15.8745i 0.711354i
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 7.93725 0.354965
\(501\) 0 0
\(502\) −18.5203 −0.826600
\(503\) 26.4575 1.17968 0.589841 0.807519i \(-0.299190\pi\)
0.589841 + 0.807519i \(0.299190\pi\)
\(504\) −2.64575 −0.117851
\(505\) 0 0
\(506\) 0 0
\(507\) 12.0000i 0.532939i
\(508\) −13.0000 −0.576782
\(509\) 20.0000i 0.886484i −0.896402 0.443242i \(-0.853828\pi\)
0.896402 0.443242i \(-0.146172\pi\)
\(510\) 14.0000i 0.619930i
\(511\) 10.5830i 0.468165i
\(512\) −1.00000 −0.0441942
\(513\) 5.29150i 0.233626i
\(514\) 6.00000i 0.264649i
\(515\) −7.00000 −0.308457
\(516\) −2.64575 −0.116473
\(517\) 0 0
\(518\) 21.0000i 0.922687i
\(519\) 0 0
\(520\) 13.2288i 0.580119i
\(521\) 15.8745 0.695475 0.347737 0.937592i \(-0.386950\pi\)
0.347737 + 0.937592i \(0.386950\pi\)
\(522\) −1.00000 −0.0437688
\(523\) −21.1660 −0.925525 −0.462763 0.886482i \(-0.653142\pi\)
−0.462763 + 0.886482i \(0.653142\pi\)
\(524\) 22.0000i 0.961074i
\(525\) 5.29150i 0.230940i
\(526\) 23.8118i 1.03824i
\(527\) 21.1660i 0.922006i
\(528\) 0 0
\(529\) 9.00000 21.1660i 0.391304 0.920261i
\(530\) 14.0000i 0.608121i
\(531\) 14.0000i 0.607548i
\(532\) −14.0000 −0.606977
\(533\) 45.0000 1.94917
\(534\) 0 0
\(535\) 14.0000i 0.605273i
\(536\) 5.29150i 0.228558i
\(537\) 9.00000i 0.388379i
\(538\) 10.0000i 0.431131i
\(539\) 0 0
\(540\) 2.64575i 0.113855i
\(541\) −24.0000 −1.03184 −0.515920 0.856637i \(-0.672550\pi\)
−0.515920 + 0.856637i \(0.672550\pi\)
\(542\) 14.0000i 0.601351i
\(543\) 15.8745i 0.681240i
\(544\) 5.29150 0.226871
\(545\) 49.0000i 2.09893i
\(546\) −13.2288 −0.566139
\(547\) −34.0000 −1.45374 −0.726868 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) 7.93725i 0.339063i
\(549\) −10.5830 −0.451672
\(550\) 0 0
\(551\) −5.29150 −0.225426
\(552\) −2.64575 4.00000i −0.112611 0.170251i
\(553\) 14.0000i 0.595341i
\(554\) −2.00000 −0.0849719
\(555\) −21.0000 −0.891400
\(556\) 5.00000i 0.212047i
\(557\) 31.7490i 1.34525i 0.739984 + 0.672624i \(0.234833\pi\)
−0.739984 + 0.672624i \(0.765167\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −13.2288 −0.559517
\(560\) 7.00000 0.295804
\(561\) 0 0
\(562\) 7.93725i 0.334813i
\(563\) 23.8118 1.00355 0.501773 0.864999i \(-0.332681\pi\)
0.501773 + 0.864999i \(0.332681\pi\)
\(564\) 13.0000 0.547399
\(565\) 7.00000i 0.294492i
\(566\) −10.5830 −0.444837
\(567\) −2.64575 −0.111111
\(568\) −6.00000 −0.251754
\(569\) 23.8118i 0.998241i 0.866533 + 0.499120i \(0.166343\pi\)
−0.866533 + 0.499120i \(0.833657\pi\)
\(570\) 14.0000i 0.586395i
\(571\) 26.4575i 1.10721i −0.832779 0.553606i \(-0.813251\pi\)
0.832779 0.553606i \(-0.186749\pi\)
\(572\) 0 0
\(573\) −15.8745 −0.663167
\(574\) 23.8118i 0.993884i
\(575\) 8.00000 5.29150i 0.333623 0.220671i
\(576\) −1.00000 −0.0416667
\(577\) 10.0000i 0.416305i 0.978096 + 0.208153i \(0.0667451\pi\)
−0.978096 + 0.208153i \(0.933255\pi\)
\(578\) −11.0000 −0.457540
\(579\) 19.0000i 0.789613i
\(580\) 2.64575 0.109859
\(581\) 42.0000 1.74245
\(582\) 2.64575i 0.109670i
\(583\) 0 0
\(584\) 4.00000i 0.165521i
\(585\) 13.2288i 0.546942i
\(586\) −21.1660 −0.874360
\(587\) 2.00000i 0.0825488i −0.999148 0.0412744i \(-0.986858\pi\)
0.999148 0.0412744i \(-0.0131418\pi\)
\(588\) 7.00000i 0.288675i
\(589\) 21.1660i 0.872130i
\(590\) 37.0405i 1.52493i
\(591\) 1.00000i 0.0411345i
\(592\) 7.93725i 0.326219i
\(593\) 21.0000i 0.862367i 0.902264 + 0.431183i \(0.141904\pi\)
−0.902264 + 0.431183i \(0.858096\pi\)
\(594\) 0 0
\(595\) −37.0405 −1.51851
\(596\) 15.8745i 0.650245i
\(597\) 13.2288i 0.541417i
\(598\) −13.2288 20.0000i −0.540964 0.817861i
\(599\) −46.0000 −1.87951 −0.939755 0.341850i \(-0.888947\pi\)
−0.939755 + 0.341850i \(0.888947\pi\)
\(600\) 2.00000i 0.0816497i
\(601\) 2.00000i 0.0815817i 0.999168 + 0.0407909i \(0.0129877\pi\)
−0.999168 + 0.0407909i \(0.987012\pi\)
\(602\) 7.00000i 0.285299i
\(603\) 5.29150i 0.215487i
\(604\) −5.00000 −0.203447
\(605\) −29.1033 −1.18322
\(606\) 0 0
\(607\) 14.0000i 0.568242i 0.958788 + 0.284121i \(0.0917018\pi\)
−0.958788 + 0.284121i \(0.908298\pi\)
\(608\) −5.29150 −0.214599
\(609\) 2.64575i 0.107211i
\(610\) 28.0000 1.13369
\(611\) 65.0000 2.62962
\(612\) 5.29150 0.213896
\(613\) 13.2288i 0.534304i 0.963654 + 0.267152i \(0.0860827\pi\)
−0.963654 + 0.267152i \(0.913917\pi\)
\(614\) 21.0000i 0.847491i
\(615\) −23.8118 −0.960183
\(616\) 0 0
\(617\) 21.1660i 0.852111i −0.904697 0.426056i \(-0.859903\pi\)
0.904697 0.426056i \(-0.140097\pi\)
\(618\) 2.64575i 0.106428i
\(619\) −21.1660 −0.850734 −0.425367 0.905021i \(-0.639855\pi\)
−0.425367 + 0.905021i \(0.639855\pi\)
\(620\) 10.5830i 0.425024i
\(621\) −2.64575 4.00000i −0.106170 0.160514i
\(622\) 24.0000i 0.962312i
\(623\) 0 0
\(624\) −5.00000 −0.200160
\(625\) −31.0000 −1.24000
\(626\) 0 0
\(627\) 0 0
\(628\) 10.5830 0.422308
\(629\) 42.0000i 1.67465i
\(630\) 7.00000 0.278887
\(631\) 31.7490i 1.26391i −0.775006 0.631954i \(-0.782253\pi\)
0.775006 0.631954i \(-0.217747\pi\)
\(632\) 5.29150i 0.210485i
\(633\) 16.0000i 0.635943i
\(634\) −27.0000 −1.07231
\(635\) 34.3948 1.36491
\(636\) 5.29150 0.209822
\(637\) 35.0000i 1.38675i
\(638\) 0 0
\(639\) −6.00000 −0.237356
\(640\) 2.64575 0.104583
\(641\) 2.64575i 0.104501i −0.998634 0.0522504i \(-0.983361\pi\)
0.998634 0.0522504i \(-0.0166394\pi\)
\(642\) 5.29150 0.208839
\(643\) 31.7490 1.25206 0.626029 0.779799i \(-0.284679\pi\)
0.626029 + 0.779799i \(0.284679\pi\)
\(644\) −10.5830 + 7.00000i −0.417029 + 0.275839i
\(645\) 7.00000 0.275625
\(646\) 28.0000 1.10165
\(647\) 24.0000i 0.943537i 0.881722 + 0.471769i \(0.156384\pi\)
−0.881722 + 0.471769i \(0.843616\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 10.0000i 0.392232i
\(651\) −10.5830 −0.414781
\(652\) −18.0000 −0.704934
\(653\) −3.00000 −0.117399 −0.0586995 0.998276i \(-0.518695\pi\)
−0.0586995 + 0.998276i \(0.518695\pi\)
\(654\) −18.5203 −0.724199
\(655\) 58.2065i 2.27432i
\(656\) 9.00000i 0.351391i
\(657\) 4.00000i 0.156055i
\(658\) 34.3948i 1.34085i
\(659\) 42.3320i 1.64902i 0.565846 + 0.824511i \(0.308550\pi\)
−0.565846 + 0.824511i \(0.691450\pi\)
\(660\) 0 0
\(661\) 26.4575 1.02908 0.514539 0.857467i \(-0.327963\pi\)
0.514539 + 0.857467i \(0.327963\pi\)
\(662\) −4.00000 −0.155464
\(663\) 26.4575 1.02752
\(664\) 15.8745 0.616050
\(665\) 37.0405 1.43637
\(666\) 7.93725i 0.307562i
\(667\) −4.00000 + 2.64575i −0.154881 + 0.102444i
\(668\) 0 0
\(669\) 28.0000 1.08254
\(670\) 14.0000i 0.540867i
\(671\) 0 0
\(672\) 2.64575i 0.102062i
\(673\) −29.0000 −1.11787 −0.558934 0.829212i \(-0.688789\pi\)
−0.558934 + 0.829212i \(0.688789\pi\)
\(674\) 26.4575i 1.01911i
\(675\) 2.00000i 0.0769800i
\(676\) −12.0000 −0.461538
\(677\) 31.7490 1.22021 0.610107 0.792319i \(-0.291126\pi\)
0.610107 + 0.792319i \(0.291126\pi\)
\(678\) −2.64575 −0.101609
\(679\) −7.00000 −0.268635
\(680\) −14.0000 −0.536875
\(681\) 7.93725i 0.304156i
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −5.29150 −0.202326
\(685\) 21.0000i 0.802369i
\(686\) 18.5203 0.707107
\(687\) 10.5830i 0.403767i
\(688\) 2.64575i 0.100868i
\(689\) 26.4575 1.00795
\(690\) 7.00000 + 10.5830i 0.266485 + 0.402888i
\(691\) 35.0000i 1.33146i −0.746191 0.665731i \(-0.768120\pi\)
0.746191 0.665731i \(-0.231880\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 11.0000 0.417554
\(695\) 13.2288i 0.501795i
\(696\) 1.00000i 0.0379049i
\(697\) 47.6235i 1.80387i
\(698\) 30.0000i 1.13552i
\(699\) 18.0000i 0.680823i
\(700\) −5.29150 −0.200000
\(701\) 10.5830i 0.399715i 0.979825 + 0.199857i \(0.0640479\pi\)
−0.979825 + 0.199857i \(0.935952\pi\)
\(702\) −5.00000 −0.188713
\(703\) 42.0000i 1.58406i
\(704\) 0 0
\(705\) −34.3948 −1.29538
\(706\) 25.0000i 0.940887i
\(707\) 0 0
\(708\) −14.0000 −0.526152
\(709\) 42.3320i 1.58981i −0.606732 0.794906i \(-0.707520\pi\)
0.606732 0.794906i \(-0.292480\pi\)
\(710\) 15.8745 0.595760
\(711\) 5.29150i 0.198447i
\(712\) 0 0
\(713\) −10.5830 16.0000i −0.396337 0.599205i
\(714\) 14.0000i 0.523937i
\(715\) 0 0
\(716\) 9.00000 0.336346
\(717\) 20.0000i 0.746914i
\(718\) 23.8118i 0.888647i
\(719\) 21.0000i 0.783168i −0.920142 0.391584i \(-0.871927\pi\)
0.920142 0.391584i \(-0.128073\pi\)
\(720\) 2.64575 0.0986013
\(721\) −7.00000 −0.260694
\(722\) −9.00000 −0.334945
\(723\) 23.8118i 0.885569i
\(724\) −15.8745 −0.589971
\(725\) −2.00000 −0.0742781
\(726\) 11.0000i 0.408248i
\(727\) 47.6235 1.76626 0.883129 0.469130i \(-0.155432\pi\)
0.883129 + 0.469130i \(0.155432\pi\)
\(728\) 13.2288i 0.490290i
\(729\) −1.00000 −0.0370370
\(730\) 10.5830i 0.391695i
\(731\) 14.0000i 0.517809i
\(732\) 10.5830i 0.391159i
\(733\) −37.0405 −1.36812 −0.684061 0.729424i \(-0.739788\pi\)
−0.684061 + 0.729424i \(0.739788\pi\)
\(734\) 18.5203 0.683595
\(735\) 18.5203i 0.683130i
\(736\) −4.00000 + 2.64575i −0.147442 + 0.0975237i
\(737\) 0 0
\(738\) 9.00000i 0.331295i
\(739\) 40.0000 1.47142 0.735712 0.677295i \(-0.236848\pi\)
0.735712 + 0.677295i \(0.236848\pi\)
\(740\) 21.0000i 0.771975i
\(741\) −26.4575 −0.971941
\(742\) 14.0000i 0.513956i
\(743\) 15.8745i 0.582379i −0.956665 0.291190i \(-0.905949\pi\)
0.956665 0.291190i \(-0.0940511\pi\)
\(744\) −4.00000 −0.146647
\(745\) 42.0000i 1.53876i
\(746\) 21.1660i 0.774943i
\(747\) 15.8745 0.580818
\(748\) 0 0
\(749\) 14.0000i 0.511549i
\(750\) 7.93725i 0.289828i
\(751\) 15.8745i 0.579269i 0.957137 + 0.289635i \(0.0935338\pi\)
−0.957137 + 0.289635i \(0.906466\pi\)
\(752\) 13.0000i 0.474061i
\(753\) 18.5203i 0.674916i
\(754\) 5.00000i 0.182089i
\(755\) 13.2288 0.481444
\(756\) 2.64575i 0.0962250i
\(757\) 52.9150i 1.92323i −0.274403 0.961615i \(-0.588480\pi\)
0.274403 0.961615i \(-0.411520\pi\)
\(758\) 23.8118i 0.864882i
\(759\) 0 0
\(760\) 14.0000 0.507833
\(761\) 6.00000i 0.217500i −0.994069 0.108750i \(-0.965315\pi\)
0.994069 0.108750i \(-0.0346848\pi\)
\(762\) 13.0000i 0.470940i
\(763\) 49.0000i 1.77392i
\(764\) 15.8745i 0.574320i
\(765\) −14.0000 −0.506171
\(766\) 0 0
\(767\) −70.0000 −2.52755
\(768\) 1.00000i 0.0360844i
\(769\) 29.1033 1.04949 0.524745 0.851259i \(-0.324161\pi\)
0.524745 + 0.851259i \(0.324161\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) 19.0000 0.683825
\(773\) −34.3948 −1.23709 −0.618547 0.785748i \(-0.712278\pi\)
−0.618547 + 0.785748i \(0.712278\pi\)
\(774\) 2.64575i 0.0950996i
\(775\) 8.00000i 0.287368i
\(776\) −2.64575 −0.0949769
\(777\) −21.0000 −0.753371
\(778\) 21.1660i 0.758838i
\(779\) 47.6235i 1.70629i
\(780\) 13.2288 0.473665
\(781\) 0 0
\(782\) 21.1660 14.0000i 0.756895 0.500639i
\(783\) 1.00000i 0.0357371i
\(784\) 7.00000 0.250000
\(785\) −28.0000 −0.999363
\(786\) −22.0000 −0.784714
\(787\) 42.3320 1.50897 0.754487 0.656315i \(-0.227886\pi\)
0.754487 + 0.656315i \(0.227886\pi\)
\(788\) −1.00000 −0.0356235