Properties

Label 1170.2.e.a.469.2
Level $1170$
Weight $2$
Character 1170.469
Analytic conductor $9.342$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 469.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.469
Dual form 1170.2.e.a.469.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +(-1.00000 - 2.00000i) q^{10} -2.00000 q^{11} -1.00000i q^{13} +2.00000 q^{14} +1.00000 q^{16} +2.00000i q^{17} +4.00000 q^{19} +(2.00000 - 1.00000i) q^{20} -2.00000i q^{22} +(3.00000 - 4.00000i) q^{25} +1.00000 q^{26} +2.00000i q^{28} +4.00000 q^{29} +8.00000 q^{31} +1.00000i q^{32} -2.00000 q^{34} +(2.00000 + 4.00000i) q^{35} -6.00000i q^{37} +4.00000i q^{38} +(1.00000 + 2.00000i) q^{40} +6.00000 q^{41} +4.00000i q^{43} +2.00000 q^{44} -8.00000i q^{47} +3.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +1.00000i q^{52} -2.00000i q^{53} +(4.00000 - 2.00000i) q^{55} -2.00000 q^{56} +4.00000i q^{58} +10.0000 q^{59} -14.0000 q^{61} +8.00000i q^{62} -1.00000 q^{64} +(1.00000 + 2.00000i) q^{65} +16.0000i q^{67} -2.00000i q^{68} +(-4.00000 + 2.00000i) q^{70} +4.00000 q^{71} +8.00000i q^{73} +6.00000 q^{74} -4.00000 q^{76} +4.00000i q^{77} +8.00000 q^{79} +(-2.00000 + 1.00000i) q^{80} +6.00000i q^{82} -12.0000i q^{83} +(-2.00000 - 4.00000i) q^{85} -4.00000 q^{86} +2.00000i q^{88} +6.00000 q^{89} -2.00000 q^{91} +8.00000 q^{94} +(-8.00000 + 4.00000i) q^{95} -12.0000i q^{97} +3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 4 q^{5} + O(q^{10}) \) \( 2 q - 2 q^{4} - 4 q^{5} - 2 q^{10} - 4 q^{11} + 4 q^{14} + 2 q^{16} + 8 q^{19} + 4 q^{20} + 6 q^{25} + 2 q^{26} + 8 q^{29} + 16 q^{31} - 4 q^{34} + 4 q^{35} + 2 q^{40} + 12 q^{41} + 4 q^{44} + 6 q^{49} + 8 q^{50} + 8 q^{55} - 4 q^{56} + 20 q^{59} - 28 q^{61} - 2 q^{64} + 2 q^{65} - 8 q^{70} + 8 q^{71} + 12 q^{74} - 8 q^{76} + 16 q^{79} - 4 q^{80} - 4 q^{85} - 8 q^{86} + 12 q^{89} - 4 q^{91} + 16 q^{94} - 16 q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 0 0
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.00000 2.00000i −0.316228 0.632456i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 2.00000 1.00000i 0.447214 0.223607i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 2.00000i 0.377964i
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 2.00000 + 4.00000i 0.338062 + 0.676123i
\(36\) 0 0
\(37\) 6.00000i 0.986394i −0.869918 0.493197i \(-0.835828\pi\)
0.869918 0.493197i \(-0.164172\pi\)
\(38\) 4.00000i 0.648886i
\(39\) 0 0
\(40\) 1.00000 + 2.00000i 0.158114 + 0.316228i
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) 0 0
\(47\) 8.00000i 1.16692i −0.812142 0.583460i \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 0 0
\(52\) 1.00000i 0.138675i
\(53\) 2.00000i 0.274721i −0.990521 0.137361i \(-0.956138\pi\)
0.990521 0.137361i \(-0.0438619\pi\)
\(54\) 0 0
\(55\) 4.00000 2.00000i 0.539360 0.269680i
\(56\) −2.00000 −0.267261
\(57\) 0 0
\(58\) 4.00000i 0.525226i
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) 0 0
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 8.00000i 1.01600i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.00000 + 2.00000i 0.124035 + 0.248069i
\(66\) 0 0
\(67\) 16.0000i 1.95471i 0.211604 + 0.977356i \(0.432131\pi\)
−0.211604 + 0.977356i \(0.567869\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 0 0
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0 0
\(73\) 8.00000i 0.936329i 0.883641 + 0.468165i \(0.155085\pi\)
−0.883641 + 0.468165i \(0.844915\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 4.00000i 0.455842i
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −2.00000 + 1.00000i −0.223607 + 0.111803i
\(81\) 0 0
\(82\) 6.00000i 0.662589i
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) −2.00000 4.00000i −0.216930 0.433861i
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 2.00000i 0.213201i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) 0 0
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) −8.00000 + 4.00000i −0.820783 + 0.410391i
\(96\) 0 0
\(97\) 12.0000i 1.21842i −0.793011 0.609208i \(-0.791488\pi\)
0.793011 0.609208i \(-0.208512\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 0 0
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) −4.00000 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 4.00000i 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) 0 0
\(109\) 18.0000 1.72409 0.862044 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) 2.00000 + 4.00000i 0.190693 + 0.381385i
\(111\) 0 0
\(112\) 2.00000i 0.188982i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.00000 −0.371391
\(117\) 0 0
\(118\) 10.0000i 0.920575i
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 14.0000i 1.26750i
\(123\) 0 0
\(124\) −8.00000 −0.718421
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) 6.00000i 0.532414i −0.963916 0.266207i \(-0.914230\pi\)
0.963916 0.266207i \(-0.0857705\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −2.00000 + 1.00000i −0.175412 + 0.0877058i
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) 8.00000i 0.693688i
\(134\) −16.0000 −1.38219
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) 14.0000i 1.19610i −0.801459 0.598050i \(-0.795942\pi\)
0.801459 0.598050i \(-0.204058\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −2.00000 4.00000i −0.169031 0.338062i
\(141\) 0 0
\(142\) 4.00000i 0.335673i
\(143\) 2.00000i 0.167248i
\(144\) 0 0
\(145\) −8.00000 + 4.00000i −0.664364 + 0.332182i
\(146\) −8.00000 −0.662085
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) 12.0000 0.983078 0.491539 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 4.00000i 0.324443i
\(153\) 0 0
\(154\) −4.00000 −0.322329
\(155\) −16.0000 + 8.00000i −1.28515 + 0.642575i
\(156\) 0 0
\(157\) 10.0000i 0.798087i −0.916932 0.399043i \(-0.869342\pi\)
0.916932 0.399043i \(-0.130658\pi\)
\(158\) 8.00000i 0.636446i
\(159\) 0 0
\(160\) −1.00000 2.00000i −0.0790569 0.158114i
\(161\) 0 0
\(162\) 0 0
\(163\) 8.00000i 0.626608i −0.949653 0.313304i \(-0.898564\pi\)
0.949653 0.313304i \(-0.101436\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 4.00000 2.00000i 0.306786 0.153393i
\(171\) 0 0
\(172\) 4.00000i 0.304997i
\(173\) 14.0000i 1.06440i −0.846619 0.532200i \(-0.821365\pi\)
0.846619 0.532200i \(-0.178635\pi\)
\(174\) 0 0
\(175\) −8.00000 6.00000i −0.604743 0.453557i
\(176\) −2.00000 −0.150756
\(177\) 0 0
\(178\) 6.00000i 0.449719i
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 2.00000i 0.148250i
\(183\) 0 0
\(184\) 0 0
\(185\) 6.00000 + 12.0000i 0.441129 + 0.882258i
\(186\) 0 0
\(187\) 4.00000i 0.292509i
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) −4.00000 8.00000i −0.290191 0.580381i
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 10.0000i 0.712470i 0.934396 + 0.356235i \(0.115940\pi\)
−0.934396 + 0.356235i \(0.884060\pi\)
\(198\) 0 0
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) 0 0
\(202\) 4.00000i 0.281439i
\(203\) 8.00000i 0.561490i
\(204\) 0 0
\(205\) −12.0000 + 6.00000i −0.838116 + 0.419058i
\(206\) −6.00000 −0.418040
\(207\) 0 0
\(208\) 1.00000i 0.0693375i
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 2.00000i 0.137361i
\(213\) 0 0
\(214\) 4.00000 0.273434
\(215\) −4.00000 8.00000i −0.272798 0.545595i
\(216\) 0 0
\(217\) 16.0000i 1.08615i
\(218\) 18.0000i 1.21911i
\(219\) 0 0
\(220\) −4.00000 + 2.00000i −0.269680 + 0.134840i
\(221\) 2.00000 0.134535
\(222\) 0 0
\(223\) 14.0000i 0.937509i −0.883328 0.468755i \(-0.844703\pi\)
0.883328 0.468755i \(-0.155297\pi\)
\(224\) 2.00000 0.133631
\(225\) 0 0
\(226\) 6.00000 0.399114
\(227\) 12.0000i 0.796468i 0.917284 + 0.398234i \(0.130377\pi\)
−0.917284 + 0.398234i \(0.869623\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.00000i 0.262613i
\(233\) 14.0000i 0.917170i 0.888650 + 0.458585i \(0.151644\pi\)
−0.888650 + 0.458585i \(0.848356\pi\)
\(234\) 0 0
\(235\) 8.00000 + 16.0000i 0.521862 + 1.04372i
\(236\) −10.0000 −0.650945
\(237\) 0 0
\(238\) 4.00000i 0.259281i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 0 0
\(244\) 14.0000 0.896258
\(245\) −6.00000 + 3.00000i −0.383326 + 0.191663i
\(246\) 0 0
\(247\) 4.00000i 0.254514i
\(248\) 8.00000i 0.508001i
\(249\) 0 0
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 6.00000 0.376473
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i −0.827541 0.561405i \(-0.810261\pi\)
0.827541 0.561405i \(-0.189739\pi\)
\(258\) 0 0
\(259\) −12.0000 −0.745644
\(260\) −1.00000 2.00000i −0.0620174 0.124035i
\(261\) 0 0
\(262\) 6.00000i 0.370681i
\(263\) 8.00000i 0.493301i 0.969104 + 0.246651i \(0.0793300\pi\)
−0.969104 + 0.246651i \(0.920670\pi\)
\(264\) 0 0
\(265\) 2.00000 + 4.00000i 0.122859 + 0.245718i
\(266\) 8.00000 0.490511
\(267\) 0 0
\(268\) 16.0000i 0.977356i
\(269\) −20.0000 −1.21942 −0.609711 0.792624i \(-0.708714\pi\)
−0.609711 + 0.792624i \(0.708714\pi\)
\(270\) 0 0
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) −6.00000 + 8.00000i −0.361814 + 0.482418i
\(276\) 0 0
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 0 0
\(280\) 4.00000 2.00000i 0.239046 0.119523i
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) 16.0000i 0.951101i 0.879688 + 0.475551i \(0.157751\pi\)
−0.879688 + 0.475551i \(0.842249\pi\)
\(284\) −4.00000 −0.237356
\(285\) 0 0
\(286\) −2.00000 −0.118262
\(287\) 12.0000i 0.708338i
\(288\) 0 0
\(289\) 13.0000 0.764706
\(290\) −4.00000 8.00000i −0.234888 0.469776i
\(291\) 0 0
\(292\) 8.00000i 0.468165i
\(293\) 26.0000i 1.51894i −0.650545 0.759468i \(-0.725459\pi\)
0.650545 0.759468i \(-0.274541\pi\)
\(294\) 0 0
\(295\) −20.0000 + 10.0000i −1.16445 + 0.582223i
\(296\) −6.00000 −0.348743
\(297\) 0 0
\(298\) 12.0000i 0.695141i
\(299\) 0 0
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 16.0000i 0.920697i
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) 28.0000 14.0000i 1.60328 0.801638i
\(306\) 0 0
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) 4.00000i 0.227921i
\(309\) 0 0
\(310\) −8.00000 16.0000i −0.454369 0.908739i
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 0 0
\(313\) 20.0000i 1.13047i −0.824931 0.565233i \(-0.808786\pi\)
0.824931 0.565233i \(-0.191214\pi\)
\(314\) 10.0000 0.564333
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 18.0000i 1.01098i −0.862832 0.505490i \(-0.831312\pi\)
0.862832 0.505490i \(-0.168688\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 2.00000 1.00000i 0.111803 0.0559017i
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000i 0.445132i
\(324\) 0 0
\(325\) −4.00000 3.00000i −0.221880 0.166410i
\(326\) 8.00000 0.443079
\(327\) 0 0
\(328\) 6.00000i 0.331295i
\(329\) −16.0000 −0.882109
\(330\) 0 0
\(331\) −12.0000 −0.659580 −0.329790 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 12.0000i 0.658586i
\(333\) 0 0
\(334\) −12.0000 −0.656611
\(335\) −16.0000 32.0000i −0.874173 1.74835i
\(336\) 0 0
\(337\) 20.0000i 1.08947i −0.838608 0.544735i \(-0.816630\pi\)
0.838608 0.544735i \(-0.183370\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 0 0
\(340\) 2.00000 + 4.00000i 0.108465 + 0.216930i
\(341\) −16.0000 −0.866449
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 14.0000 0.752645
\(347\) 12.0000i 0.644194i 0.946707 + 0.322097i \(0.104388\pi\)
−0.946707 + 0.322097i \(0.895612\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 6.00000 8.00000i 0.320713 0.427618i
\(351\) 0 0
\(352\) 2.00000i 0.106600i
\(353\) 34.0000i 1.80964i 0.425797 + 0.904819i \(0.359994\pi\)
−0.425797 + 0.904819i \(0.640006\pi\)
\(354\) 0 0
\(355\) −8.00000 + 4.00000i −0.424596 + 0.212298i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 18.0000i 0.951330i
\(359\) 32.0000 1.68890 0.844448 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 6.00000i 0.315353i
\(363\) 0 0
\(364\) 2.00000 0.104828
\(365\) −8.00000 16.0000i −0.418739 0.837478i
\(366\) 0 0
\(367\) 10.0000i 0.521996i 0.965339 + 0.260998i \(0.0840516\pi\)
−0.965339 + 0.260998i \(0.915948\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −12.0000 + 6.00000i −0.623850 + 0.311925i
\(371\) −4.00000 −0.207670
\(372\) 0 0
\(373\) 22.0000i 1.13912i −0.821951 0.569558i \(-0.807114\pi\)
0.821951 0.569558i \(-0.192886\pi\)
\(374\) 4.00000 0.206835
\(375\) 0 0
\(376\) −8.00000 −0.412568
\(377\) 4.00000i 0.206010i
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 8.00000 4.00000i 0.410391 0.205196i
\(381\) 0 0
\(382\) 12.0000i 0.613973i
\(383\) 24.0000i 1.22634i −0.789950 0.613171i \(-0.789894\pi\)
0.789950 0.613171i \(-0.210106\pi\)
\(384\) 0 0
\(385\) −4.00000 8.00000i −0.203859 0.407718i
\(386\) 0 0
\(387\) 0 0
\(388\) 12.0000i 0.609208i
\(389\) 16.0000 0.811232 0.405616 0.914044i \(-0.367057\pi\)
0.405616 + 0.914044i \(0.367057\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.00000i 0.151523i
\(393\) 0 0
\(394\) −10.0000 −0.503793
\(395\) −16.0000 + 8.00000i −0.805047 + 0.402524i
\(396\) 0 0
\(397\) 18.0000i 0.903394i 0.892171 + 0.451697i \(0.149181\pi\)
−0.892171 + 0.451697i \(0.850819\pi\)
\(398\) 24.0000i 1.20301i
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 8.00000i 0.398508i
\(404\) 4.00000 0.199007
\(405\) 0 0
\(406\) 8.00000 0.397033
\(407\) 12.0000i 0.594818i
\(408\) 0 0
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) −6.00000 12.0000i −0.296319 0.592638i
\(411\) 0 0
\(412\) 6.00000i 0.295599i
\(413\) 20.0000i 0.984136i
\(414\) 0 0
\(415\) 12.0000 + 24.0000i 0.589057 + 1.17811i
\(416\) 1.00000 0.0490290
\(417\) 0 0
\(418\) 8.00000i 0.391293i
\(419\) −14.0000 −0.683945 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 4.00000i 0.194717i
\(423\) 0 0
\(424\) −2.00000 −0.0971286
\(425\) 8.00000 + 6.00000i 0.388057 + 0.291043i
\(426\) 0 0
\(427\) 28.0000i 1.35501i
\(428\) 4.00000i 0.193347i
\(429\) 0 0
\(430\) 8.00000 4.00000i 0.385794 0.192897i
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) 12.0000i 0.576683i 0.957528 + 0.288342i \(0.0931039\pi\)
−0.957528 + 0.288342i \(0.906896\pi\)
\(434\) 16.0000 0.768025
\(435\) 0 0
\(436\) −18.0000 −0.862044
\(437\) 0 0
\(438\) 0 0
\(439\) −32.0000 −1.52728 −0.763638 0.645644i \(-0.776589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(440\) −2.00000 4.00000i −0.0953463 0.190693i
\(441\) 0 0
\(442\) 2.00000i 0.0951303i
\(443\) 4.00000i 0.190046i −0.995475 0.0950229i \(-0.969708\pi\)
0.995475 0.0950229i \(-0.0302924\pi\)
\(444\) 0 0
\(445\) −12.0000 + 6.00000i −0.568855 + 0.284427i
\(446\) 14.0000 0.662919
\(447\) 0 0
\(448\) 2.00000i 0.0944911i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) −12.0000 −0.565058
\(452\) 6.00000i 0.282216i
\(453\) 0 0
\(454\) −12.0000 −0.563188
\(455\) 4.00000 2.00000i 0.187523 0.0937614i
\(456\) 0 0
\(457\) 28.0000i 1.30978i 0.755722 + 0.654892i \(0.227286\pi\)
−0.755722 + 0.654892i \(0.772714\pi\)
\(458\) 22.0000i 1.02799i
\(459\) 0 0
\(460\) 0 0
\(461\) −20.0000 −0.931493 −0.465746 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(462\) 0 0
\(463\) 6.00000i 0.278844i 0.990233 + 0.139422i \(0.0445244\pi\)
−0.990233 + 0.139422i \(0.955476\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) −14.0000 −0.648537
\(467\) 28.0000i 1.29569i 0.761774 + 0.647843i \(0.224329\pi\)
−0.761774 + 0.647843i \(0.775671\pi\)
\(468\) 0 0
\(469\) 32.0000 1.47762
\(470\) −16.0000 + 8.00000i −0.738025 + 0.369012i
\(471\) 0 0
\(472\) 10.0000i 0.460287i
\(473\) 8.00000i 0.367840i
\(474\) 0 0
\(475\) 12.0000 16.0000i 0.550598 0.734130i
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) 12.0000i 0.548867i
\(479\) 36.0000 1.64488 0.822441 0.568850i \(-0.192612\pi\)
0.822441 + 0.568850i \(0.192612\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 18.0000i 0.819878i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) 12.0000 + 24.0000i 0.544892 + 1.08978i
\(486\) 0 0
\(487\) 26.0000i 1.17817i 0.808070 + 0.589086i \(0.200512\pi\)
−0.808070 + 0.589086i \(0.799488\pi\)
\(488\) 14.0000i 0.633750i
\(489\) 0 0
\(490\) −3.00000 6.00000i −0.135526 0.271052i
\(491\) 22.0000 0.992846 0.496423 0.868081i \(-0.334646\pi\)
0.496423 + 0.868081i \(0.334646\pi\)
\(492\) 0 0
\(493\) 8.00000i 0.360302i
\(494\) 4.00000 0.179969
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 8.00000i 0.358849i
\(498\) 0 0
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) 2.00000 11.0000i 0.0894427 0.491935i
\(501\) 0 0
\(502\) 18.0000i 0.803379i
\(503\) 36.0000i 1.60516i 0.596544 + 0.802580i \(0.296540\pi\)
−0.596544 + 0.802580i \(0.703460\pi\)
\(504\) 0 0
\(505\) 8.00000 4.00000i 0.355995 0.177998i
\(506\) 0 0
\(507\) 0 0
\(508\) 6.00000i 0.266207i
\(509\) −40.0000 −1.77297 −0.886484 0.462758i \(-0.846860\pi\)
−0.886484 + 0.462758i \(0.846860\pi\)
\(510\) 0 0
\(511\) 16.0000 0.707798
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 18.0000 0.793946
\(515\) −6.00000 12.0000i −0.264392 0.528783i
\(516\) 0 0
\(517\) 16.0000i 0.703679i
\(518\) 12.0000i 0.527250i
\(519\) 0 0
\(520\) 2.00000 1.00000i 0.0877058 0.0438529i
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i 0.936819 + 0.349816i \(0.113756\pi\)
−0.936819 + 0.349816i \(0.886244\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) 16.0000i 0.696971i
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) −4.00000 + 2.00000i −0.173749 + 0.0868744i
\(531\) 0 0
\(532\) 8.00000i 0.346844i
\(533\) 6.00000i 0.259889i
\(534\) 0 0
\(535\) 4.00000 + 8.00000i 0.172935 + 0.345870i
\(536\) 16.0000 0.691095
\(537\) 0 0
\(538\) 20.0000i 0.862261i
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 16.0000i 0.687259i
\(543\) 0 0
\(544\) −2.00000 −0.0857493
\(545\) −36.0000 + 18.0000i −1.54207 + 0.771035i
\(546\) 0 0
\(547\) 20.0000i 0.855138i 0.903983 + 0.427569i \(0.140630\pi\)
−0.903983 + 0.427569i \(0.859370\pi\)
\(548\) 14.0000i 0.598050i
\(549\) 0 0
\(550\) −8.00000 6.00000i −0.341121 0.255841i
\(551\) 16.0000 0.681623
\(552\) 0 0
\(553\) 16.0000i 0.680389i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) 14.0000i 0.593199i −0.955002 0.296600i \(-0.904147\pi\)
0.955002 0.296600i \(-0.0958526\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) 2.00000 + 4.00000i 0.0845154 + 0.169031i
\(561\) 0 0
\(562\) 18.0000i 0.759284i
\(563\) 44.0000i 1.85438i 0.374593 + 0.927189i \(0.377783\pi\)
−0.374593 + 0.927189i \(0.622217\pi\)
\(564\) 0 0
\(565\) 6.00000 + 12.0000i 0.252422 + 0.504844i
\(566\) −16.0000 −0.672530
\(567\) 0 0
\(568\) 4.00000i 0.167836i
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 2.00000i 0.0836242i
\(573\) 0 0
\(574\) 12.0000 0.500870
\(575\) 0 0
\(576\) 0 0
\(577\) 28.0000i 1.16566i −0.812596 0.582828i \(-0.801946\pi\)
0.812596 0.582828i \(-0.198054\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 0 0
\(580\) 8.00000 4.00000i 0.332182 0.166091i
\(581\) −24.0000 −0.995688
\(582\) 0 0
\(583\) 4.00000i 0.165663i
\(584\) 8.00000 0.331042
\(585\) 0 0
\(586\) 26.0000 1.07405
\(587\) 36.0000i 1.48588i 0.669359 + 0.742940i \(0.266569\pi\)
−0.669359 + 0.742940i \(0.733431\pi\)
\(588\) 0 0
\(589\) 32.0000 1.31854
\(590\) −10.0000 20.0000i −0.411693 0.823387i
\(591\) 0 0
\(592\) 6.00000i 0.246598i
\(593\) 34.0000i 1.39621i −0.715994 0.698106i \(-0.754026\pi\)
0.715994 0.698106i \(-0.245974\pi\)
\(594\) 0 0
\(595\) −8.00000 + 4.00000i −0.327968 + 0.163984i
\(596\) −12.0000 −0.491539
\(597\) 0 0
\(598\) 0 0
\(599\) 32.0000 1.30748 0.653742 0.756717i \(-0.273198\pi\)
0.653742 + 0.756717i \(0.273198\pi\)
\(600\) 0 0
\(601\) −46.0000 −1.87638 −0.938190 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 0 0
\(604\) 16.0000 0.651031
\(605\) 14.0000 7.00000i 0.569181 0.284590i
\(606\) 0 0
\(607\) 18.0000i 0.730597i −0.930890 0.365299i \(-0.880967\pi\)
0.930890 0.365299i \(-0.119033\pi\)
\(608\) 4.00000i 0.162221i
\(609\) 0 0
\(610\) 14.0000 + 28.0000i 0.566843 + 1.13369i
\(611\) −8.00000 −0.323645
\(612\) 0 0
\(613\) 2.00000i 0.0807792i −0.999184 0.0403896i \(-0.987140\pi\)
0.999184 0.0403896i \(-0.0128599\pi\)
\(614\) −28.0000 −1.12999
\(615\) 0 0
\(616\) 4.00000 0.161165
\(617\) 46.0000i 1.85189i 0.377658 + 0.925945i \(0.376729\pi\)
−0.377658 + 0.925945i \(0.623271\pi\)
\(618\) 0 0
\(619\) 24.0000 0.964641 0.482321 0.875995i \(-0.339794\pi\)
0.482321 + 0.875995i \(0.339794\pi\)
\(620\) 16.0000 8.00000i 0.642575 0.321288i
\(621\) 0 0
\(622\) 20.0000i 0.801927i
\(623\) 12.0000i 0.480770i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 20.0000 0.799361
\(627\) 0 0
\(628\) 10.0000i 0.399043i
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 8.00000i 0.318223i
\(633\) 0 0
\(634\) 18.0000 0.714871
\(635\) 6.00000 + 12.0000i 0.238103 + 0.476205i
\(636\) 0 0
\(637\) 3.00000i 0.118864i
\(638\) 8.00000i 0.316723i
\(639\) 0 0
\(640\) 1.00000 + 2.00000i 0.0395285 + 0.0790569i
\(641\) 38.0000 1.50091 0.750455 0.660922i \(-0.229834\pi\)
0.750455 + 0.660922i \(0.229834\pi\)
\(642\) 0 0
\(643\) 32.0000i 1.26196i 0.775800 + 0.630978i \(0.217346\pi\)
−0.775800 + 0.630978i \(0.782654\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −8.00000 −0.314756
\(647\) 36.0000i 1.41531i 0.706560 + 0.707653i \(0.250246\pi\)
−0.706560 + 0.707653i \(0.749754\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) 3.00000 4.00000i 0.117670 0.156893i
\(651\) 0 0
\(652\) 8.00000i 0.313304i
\(653\) 34.0000i 1.33052i 0.746611 + 0.665261i \(0.231680\pi\)
−0.746611 + 0.665261i \(0.768320\pi\)
\(654\) 0 0
\(655\) −12.0000 + 6.00000i −0.468879 + 0.234439i
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 16.0000i 0.623745i
\(659\) 10.0000 0.389545 0.194772 0.980848i \(-0.437603\pi\)
0.194772 + 0.980848i \(0.437603\pi\)
\(660\) 0 0
\(661\) 30.0000 1.16686 0.583432 0.812162i \(-0.301709\pi\)
0.583432 + 0.812162i \(0.301709\pi\)
\(662\) 12.0000i 0.466393i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 8.00000 + 16.0000i 0.310227 + 0.620453i
\(666\) 0 0
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 0 0
\(670\) 32.0000 16.0000i 1.23627 0.618134i
\(671\) 28.0000 1.08093
\(672\) 0 0
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) 20.0000 0.770371
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 10.0000i 0.384331i −0.981363 0.192166i \(-0.938449\pi\)
0.981363 0.192166i \(-0.0615511\pi\)
\(678\) 0 0
\(679\) −24.0000 −0.921035
\(680\) −4.00000 + 2.00000i −0.153393 + 0.0766965i
\(681\) 0 0
\(682\) 16.0000i 0.612672i
\(683\) 12.0000i 0.459167i −0.973289 0.229584i \(-0.926264\pi\)
0.973289 0.229584i \(-0.0737364\pi\)
\(684\) 0 0
\(685\) 14.0000 + 28.0000i 0.534913 + 1.06983i
\(686\) 20.0000 0.763604
\(687\) 0 0
\(688\) 4.00000i 0.152499i
\(689\) −2.00000 −0.0761939
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 8.00000 4.00000i 0.303457 0.151729i
\(696\) 0 0
\(697\) 12.0000i 0.454532i
\(698\) 14.0000i 0.529908i
\(699\) 0 0
\(700\) 8.00000 + 6.00000i 0.302372 + 0.226779i
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 0 0
\(703\) 24.0000i 0.905177i
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) −34.0000 −1.27961
\(707\) 8.00000i 0.300871i
\(708\) 0 0
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) −4.00000 8.00000i −0.150117 0.300235i
\(711\) 0 0
\(712\) 6.00000i 0.224860i
\(713\) 0 0
\(714\) 0 0
\(715\) −2.00000 4.00000i −0.0747958 0.149592i
\(716\) 18.0000 0.672692
\(717\) 0 0
\(718\) 32.0000i 1.19423i
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 3.00000i 0.111648i
\(723\) 0 0
\(724\) 6.00000 0.222988
\(725\) 12.0000 16.0000i 0.445669 0.594225i
\(726\) 0 0
\(727\) 34.0000i 1.26099i −0.776193 0.630495i \(-0.782852\pi\)
0.776193 0.630495i \(-0.217148\pi\)
\(728\) 2.00000i 0.0741249i
\(729\) 0 0
\(730\) 16.0000 8.00000i 0.592187 0.296093i
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) 14.0000i 0.517102i 0.965998 + 0.258551i \(0.0832450\pi\)
−0.965998 + 0.258551i \(0.916755\pi\)
\(734\) −10.0000 −0.369107
\(735\) 0 0
\(736\) 0 0
\(737\) 32.0000i 1.17874i
\(738\) 0 0
\(739\) −28.0000 −1.03000 −0.514998 0.857191i \(-0.672207\pi\)
−0.514998 + 0.857191i \(0.672207\pi\)
\(740\) −6.00000 12.0000i −0.220564 0.441129i
\(741\) 0 0
\(742\) 4.00000i 0.146845i
\(743\) 16.0000i 0.586983i −0.955962 0.293492i \(-0.905183\pi\)
0.955962 0.293492i \(-0.0948173\pi\)
\(744\) 0 0
\(745\) −24.0000 + 12.0000i −0.879292 + 0.439646i
\(746\) 22.0000 0.805477
\(747\) 0 0
\(748\) 4.00000i 0.146254i
\(749\) −8.00000 −0.292314
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 0 0
\(754\) 4.00000 0.145671
\(755\) 32.0000 16.0000i 1.16460 0.582300i
\(756\) 0 0
\(757\) 26.0000i 0.944986i 0.881334 + 0.472493i \(0.156646\pi\)
−0.881334 + 0.472493i \(0.843354\pi\)
\(758\) 8.00000i 0.290573i
\(759\) 0 0
\(760\) 4.00000 + 8.00000i 0.145095 + 0.290191i
\(761\) −38.0000 −1.37750 −0.688749 0.724999i \(-0.741840\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 0 0
\(763\) 36.0000i 1.30329i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 24.0000 0.867155
\(767\) 10.0000i 0.361079i
\(768\) 0 0
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 8.00000 4.00000i 0.288300 0.144150i
\(771\) 0 0
\(772\) 0 0
\(773\) 22.0000i 0.791285i −0.918405 0.395643i \(-0.870522\pi\)
0.918405 0.395643i \(-0.129478\pi\)
\(774\) 0 0
\(775\) 24.0000 32.0000i 0.862105 1.14947i
\(776\) −12.0000 −0.430775
\(777\) 0 0
\(778\) 16.0000i 0.573628i
\(779\) 24.0000 0.859889
\(780\) 0 0
\(781\) −8.00000 −0.286263
\(782\) 0 0
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) 10.0000 + 20.0000i 0.356915 + 0.713831i
\(786\) 0 0
\(787\) 8.00000i 0.285169i 0.989783 + 0.142585i \(0.0455413\pi\)
−0.989783 + 0.142585i \(0.954459\pi\)
\(788\) 10.0000i 0.356235i
\(789\) 0 0
\(790\) −8.00000 16.0000i −0.284627 0.569254i
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) 14.0000i 0.497155i
\(794\) −18.0000 −0.638796
\(795\) 0 0
\(796\) −24.0000 −0.850657
\(797\) 14.0000i 0.495905i 0.968772 + 0.247953i \(0.079