Properties

Label 1170.2.e.c.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: \( x^{2} + 1 \) Copy content Toggle raw display
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.c.469.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +4.00000i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +4.00000i q^{7} -1.00000i q^{8} +(1.00000 - 2.00000i) q^{10} +6.00000 q^{11} +1.00000i q^{13} -4.00000 q^{14} +1.00000 q^{16} -4.00000i q^{17} -2.00000 q^{19} +(2.00000 + 1.00000i) q^{20} +6.00000i q^{22} +6.00000i q^{23} +(3.00000 + 4.00000i) q^{25} -1.00000 q^{26} -4.00000i q^{28} -10.0000 q^{29} +4.00000 q^{31} +1.00000i q^{32} +4.00000 q^{34} +(4.00000 - 8.00000i) q^{35} +6.00000i q^{37} -2.00000i q^{38} +(-1.00000 + 2.00000i) q^{40} -10.0000 q^{41} -6.00000 q^{44} -6.00000 q^{46} +8.00000i q^{47} -9.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -1.00000i q^{52} +6.00000i q^{53} +(-12.0000 - 6.00000i) q^{55} +4.00000 q^{56} -10.0000i q^{58} -6.00000 q^{59} -6.00000 q^{61} +4.00000i q^{62} -1.00000 q^{64} +(1.00000 - 2.00000i) q^{65} +12.0000i q^{67} +4.00000i q^{68} +(8.00000 + 4.00000i) q^{70} +2.00000i q^{73} -6.00000 q^{74} +2.00000 q^{76} +24.0000i q^{77} +8.00000 q^{79} +(-2.00000 - 1.00000i) q^{80} -10.0000i q^{82} +4.00000i q^{83} +(-4.00000 + 8.00000i) q^{85} -6.00000i q^{88} +14.0000 q^{89} -4.00000 q^{91} -6.00000i q^{92} -8.00000 q^{94} +(4.00000 + 2.00000i) q^{95} -14.0000i q^{97} -9.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} - 4 q^{5} + 2 q^{10} + 12 q^{11} - 8 q^{14} + 2 q^{16} - 4 q^{19} + 4 q^{20} + 6 q^{25} - 2 q^{26} - 20 q^{29} + 8 q^{31} + 8 q^{34} + 8 q^{35} - 2 q^{40} - 20 q^{41} - 12 q^{44} - 12 q^{46} - 18 q^{49} - 8 q^{50} - 24 q^{55} + 8 q^{56} - 12 q^{59} - 12 q^{61} - 2 q^{64} + 2 q^{65} + 16 q^{70} - 12 q^{74} + 4 q^{76} + 16 q^{79} - 4 q^{80} - 8 q^{85} + 28 q^{89} - 8 q^{91} - 16 q^{94} + 8 q^{95}+O(q^{100}) \) Copy content Toggle raw display

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
\(7\) 4.00000i 1.51186i 0.654654 + 0.755929i \(0.272814\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.00000 2.00000i 0.316228 0.632456i
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) −4.00000 −1.06904
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000i 0.970143i −0.874475 0.485071i \(-0.838794\pi\)
0.874475 0.485071i \(-0.161206\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 2.00000 + 1.00000i 0.447214 + 0.223607i
\(21\) 0 0
\(22\) 6.00000i 1.27920i
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 0 0
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) 4.00000i 0.755929i
\(29\) −10.0000 −1.85695 −0.928477 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) 4.00000 8.00000i 0.676123 1.35225i
\(36\) 0 0
\(37\) 6.00000i 0.986394i 0.869918 + 0.493197i \(0.164172\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) 2.00000i 0.324443i
\(39\) 0 0
\(40\) −1.00000 + 2.00000i −0.158114 + 0.316228i
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −6.00000 −0.904534
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 0 0
\(49\) −9.00000 −1.28571
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 1.00000i 0.138675i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 0 0
\(55\) −12.0000 6.00000i −1.61808 0.809040i
\(56\) 4.00000 0.534522
\(57\) 0 0
\(58\) 10.0000i 1.31306i
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.00000 2.00000i 0.124035 0.248069i
\(66\) 0 0
\(67\) 12.0000i 1.46603i 0.680211 + 0.733017i \(0.261888\pi\)
−0.680211 + 0.733017i \(0.738112\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) 8.00000 + 4.00000i 0.956183 + 0.478091i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) −6.00000 −0.697486
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 24.0000i 2.73505i
\(78\) 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
\(82\) 10.0000i 1.10432i
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) −4.00000 + 8.00000i −0.433861 + 0.867722i
\(86\) 0 0
\(87\) 0 0
\(88\) 6.00000i 0.639602i
\(89\) 14.0000 1.48400 0.741999 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) 4.00000 + 2.00000i 0.410391 + 0.205196i
\(96\) 0 0
\(97\) 14.0000i 1.42148i −0.703452 0.710742i \(-0.748359\pi\)
0.703452 0.710742i \(-0.251641\pi\)
\(98\) 9.00000i 0.909137i
\(99\) 0 0
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 2.00000i 0.197066i −0.995134 0.0985329i \(-0.968585\pi\)
0.995134 0.0985329i \(-0.0314150\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 6.00000 12.0000i 0.572078 1.14416i
\(111\) 0 0
\(112\) 4.00000i 0.377964i
\(113\) 4.00000i 0.376288i 0.982141 + 0.188144i \(0.0602472\pi\)
−0.982141 + 0.188144i \(0.939753\pi\)
\(114\) 0 0
\(115\) 6.00000 12.0000i 0.559503 1.11901i
\(116\) 10.0000 0.928477
\(117\) 0 0
\(118\) 6.00000i 0.552345i
\(119\) 16.0000 1.46672
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 6.00000i 0.543214i
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 10.0000i 0.887357i 0.896186 + 0.443678i \(0.146327\pi\)
−0.896186 + 0.443678i \(0.853673\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 2.00000 + 1.00000i 0.175412 + 0.0877058i
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 0 0
\(133\) 8.00000i 0.693688i
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) −4.00000 −0.342997
\(137\) 14.0000i 1.19610i −0.801459 0.598050i \(-0.795942\pi\)
0.801459 0.598050i \(-0.204058\pi\)
\(138\) 0 0
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −4.00000 + 8.00000i −0.338062 + 0.676123i
\(141\) 0 0
\(142\) 0 0
\(143\) 6.00000i 0.501745i
\(144\) 0 0
\(145\) 20.0000 + 10.0000i 1.66091 + 0.830455i
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) 16.0000 1.31077 0.655386 0.755295i \(-0.272506\pi\)
0.655386 + 0.755295i \(0.272506\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 2.00000i 0.162221i
\(153\) 0 0
\(154\) −24.0000 −1.93398
\(155\) −8.00000 4.00000i −0.642575 0.321288i
\(156\) 0 0
\(157\) 6.00000i 0.478852i −0.970915 0.239426i \(-0.923041\pi\)
0.970915 0.239426i \(-0.0769593\pi\)
\(158\) 8.00000i 0.636446i
\(159\) 0 0
\(160\) 1.00000 2.00000i 0.0790569 0.158114i
\(161\) −24.0000 −1.89146
\(162\) 0 0
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 10.0000 0.780869
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) 16.0000i 1.23812i −0.785345 0.619059i \(-0.787514\pi\)
0.785345 0.619059i \(-0.212486\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) −8.00000 4.00000i −0.613572 0.306786i
\(171\) 0 0
\(172\) 0 0
\(173\) 22.0000i 1.67263i 0.548250 + 0.836315i \(0.315294\pi\)
−0.548250 + 0.836315i \(0.684706\pi\)
\(174\) 0 0
\(175\) −16.0000 + 12.0000i −1.20949 + 0.907115i
\(176\) 6.00000 0.452267
\(177\) 0 0
\(178\) 14.0000i 1.04934i
\(179\) −24.0000 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 0 0
\(184\) 6.00000 0.442326
\(185\) 6.00000 12.0000i 0.441129 0.882258i
\(186\) 0 0
\(187\) 24.0000i 1.75505i
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) −2.00000 + 4.00000i −0.145095 + 0.290191i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 2.00000i 0.143963i −0.997406 0.0719816i \(-0.977068\pi\)
0.997406 0.0719816i \(-0.0229323\pi\)
\(194\) 14.0000 1.00514
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) 6.00000i 0.427482i −0.976890 0.213741i \(-0.931435\pi\)
0.976890 0.213741i \(-0.0685649\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) 0 0
\(202\) 10.0000i 0.703598i
\(203\) 40.0000i 2.80745i
\(204\) 0 0
\(205\) 20.0000 + 10.0000i 1.39686 + 0.698430i
\(206\) 2.00000 0.139347
\(207\) 0 0
\(208\) 1.00000i 0.0693375i
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 16.0000i 1.08615i
\(218\) 4.00000i 0.270914i
\(219\) 0 0
\(220\) 12.0000 + 6.00000i 0.809040 + 0.404520i
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) −4.00000 −0.267261
\(225\) 0 0
\(226\) −4.00000 −0.266076
\(227\) 4.00000i 0.265489i −0.991150 0.132745i \(-0.957621\pi\)
0.991150 0.132745i \(-0.0423790\pi\)
\(228\) 0 0
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) 12.0000 + 6.00000i 0.791257 + 0.395628i
\(231\) 0 0
\(232\) 10.0000i 0.656532i
\(233\) 12.0000i 0.786146i 0.919507 + 0.393073i \(0.128588\pi\)
−0.919507 + 0.393073i \(0.871412\pi\)
\(234\) 0 0
\(235\) 8.00000 16.0000i 0.521862 1.04372i
\(236\) 6.00000 0.390567
\(237\) 0 0
\(238\) 16.0000i 1.03713i
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 25.0000i 1.60706i
\(243\) 0 0
\(244\) 6.00000 0.384111
\(245\) 18.0000 + 9.00000i 1.14998 + 0.574989i
\(246\) 0 0
\(247\) 2.00000i 0.127257i
\(248\) 4.00000i 0.254000i
\(249\) 0 0
\(250\) 11.0000 2.00000i 0.695701 0.126491i
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 0 0
\(253\) 36.0000i 2.26330i
\(254\) −10.0000 −0.627456
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 28.0000i 1.74659i 0.487190 + 0.873296i \(0.338022\pi\)
−0.487190 + 0.873296i \(0.661978\pi\)
\(258\) 0 0
\(259\) −24.0000 −1.49129
\(260\) −1.00000 + 2.00000i −0.0620174 + 0.124035i
\(261\) 0 0
\(262\) 8.00000i 0.494242i
\(263\) 10.0000i 0.616626i 0.951285 + 0.308313i \(0.0997645\pi\)
−0.951285 + 0.308313i \(0.900236\pi\)
\(264\) 0 0
\(265\) 6.00000 12.0000i 0.368577 0.737154i
\(266\) 8.00000 0.490511
\(267\) 0 0
\(268\) 12.0000i 0.733017i
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) 18.0000 + 24.0000i 1.08544 + 1.44725i
\(276\) 0 0
\(277\) 14.0000i 0.841178i 0.907251 + 0.420589i \(0.138177\pi\)
−0.907251 + 0.420589i \(0.861823\pi\)
\(278\) 16.0000i 0.959616i
\(279\) 0 0
\(280\) −8.00000 4.00000i −0.478091 0.239046i
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) 12.0000i 0.713326i −0.934233 0.356663i \(-0.883914\pi\)
0.934233 0.356663i \(-0.116086\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 40.0000i 2.36113i
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) −10.0000 + 20.0000i −0.587220 + 1.17444i
\(291\) 0 0
\(292\) 2.00000i 0.117041i
\(293\) 18.0000i 1.05157i −0.850617 0.525786i \(-0.823771\pi\)
0.850617 0.525786i \(-0.176229\pi\)
\(294\) 0 0
\(295\) 12.0000 + 6.00000i 0.698667 + 0.349334i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) 16.0000i 0.926855i
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) 0 0
\(302\) 16.0000i 0.920697i
\(303\) 0 0
\(304\) −2.00000 −0.114708
\(305\) 12.0000 + 6.00000i 0.687118 + 0.343559i
\(306\) 0 0
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 24.0000i 1.36753i
\(309\) 0 0
\(310\) 4.00000 8.00000i 0.227185 0.454369i
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) 6.00000 0.338600
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 2.00000i 0.112331i 0.998421 + 0.0561656i \(0.0178875\pi\)
−0.998421 + 0.0561656i \(0.982113\pi\)
\(318\) 0 0
\(319\) −60.0000 −3.35936
\(320\) 2.00000 + 1.00000i 0.111803 + 0.0559017i
\(321\) 0 0
\(322\) 24.0000i 1.33747i
\(323\) 8.00000i 0.445132i
\(324\) 0 0
\(325\) −4.00000 + 3.00000i −0.221880 + 0.166410i
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) 10.0000i 0.552158i
\(329\) −32.0000 −1.76422
\(330\) 0 0
\(331\) 2.00000 0.109930 0.0549650 0.998488i \(-0.482495\pi\)
0.0549650 + 0.998488i \(0.482495\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 0 0
\(334\) 16.0000 0.875481
\(335\) 12.0000 24.0000i 0.655630 1.31126i
\(336\) 0 0
\(337\) 16.0000i 0.871576i −0.900049 0.435788i \(-0.856470\pi\)
0.900049 0.435788i \(-0.143530\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 0 0
\(340\) 4.00000 8.00000i 0.216930 0.433861i
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) 8.00000i 0.431959i
\(344\) 0 0
\(345\) 0 0
\(346\) −22.0000 −1.18273
\(347\) 16.0000i 0.858925i 0.903085 + 0.429463i \(0.141297\pi\)
−0.903085 + 0.429463i \(0.858703\pi\)
\(348\) 0 0
\(349\) 4.00000 0.214115 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(350\) −12.0000 16.0000i −0.641427 0.855236i
\(351\) 0 0
\(352\) 6.00000i 0.319801i
\(353\) 26.0000i 1.38384i 0.721974 + 0.691920i \(0.243235\pi\)
−0.721974 + 0.691920i \(0.756765\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) 24.0000i 1.26844i
\(359\) −20.0000 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 6.00000i 0.315353i
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) 2.00000 4.00000i 0.104685 0.209370i
\(366\) 0 0
\(367\) 18.0000i 0.939592i 0.882775 + 0.469796i \(0.155673\pi\)
−0.882775 + 0.469796i \(0.844327\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 0 0
\(370\) 12.0000 + 6.00000i 0.623850 + 0.311925i
\(371\) −24.0000 −1.24602
\(372\) 0 0
\(373\) 18.0000i 0.932005i −0.884783 0.466002i \(-0.845694\pi\)
0.884783 0.466002i \(-0.154306\pi\)
\(374\) 24.0000 1.24101
\(375\) 0 0
\(376\) 8.00000 0.412568
\(377\) 10.0000i 0.515026i
\(378\) 0 0
\(379\) −10.0000 −0.513665 −0.256833 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) −4.00000 2.00000i −0.205196 0.102598i
\(381\) 0 0
\(382\) 0 0
\(383\) 20.0000i 1.02195i −0.859595 0.510976i \(-0.829284\pi\)
0.859595 0.510976i \(-0.170716\pi\)
\(384\) 0 0
\(385\) 24.0000 48.0000i 1.22315 2.44631i
\(386\) 2.00000 0.101797
\(387\) 0 0
\(388\) 14.0000i 0.710742i
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 9.00000i 0.454569i
\(393\) 0 0
\(394\) 6.00000 0.302276
\(395\) −16.0000 8.00000i −0.805047 0.402524i
\(396\) 0 0
\(397\) 10.0000i 0.501886i 0.968002 + 0.250943i \(0.0807406\pi\)
−0.968002 + 0.250943i \(0.919259\pi\)
\(398\) 8.00000i 0.401004i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −30.0000 −1.49813 −0.749064 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 0 0
\(403\) 4.00000i 0.199254i
\(404\) 10.0000 0.497519
\(405\) 0 0
\(406\) 40.0000 1.98517
\(407\) 36.0000i 1.78445i
\(408\) 0 0
\(409\) 34.0000 1.68119 0.840596 0.541663i \(-0.182205\pi\)
0.840596 + 0.541663i \(0.182205\pi\)
\(410\) −10.0000 + 20.0000i −0.493865 + 0.987730i
\(411\) 0 0
\(412\) 2.00000i 0.0985329i
\(413\) 24.0000i 1.18096i
\(414\) 0 0
\(415\) 4.00000 8.00000i 0.196352 0.392705i
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) 12.0000i 0.586939i
\(419\) 8.00000 0.390826 0.195413 0.980721i \(-0.437395\pi\)
0.195413 + 0.980721i \(0.437395\pi\)
\(420\) 0 0
\(421\) 4.00000 0.194948 0.0974740 0.995238i \(-0.468924\pi\)
0.0974740 + 0.995238i \(0.468924\pi\)
\(422\) 4.00000i 0.194717i
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 16.0000 12.0000i 0.776114 0.582086i
\(426\) 0 0
\(427\) 24.0000i 1.16144i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 0 0
\(433\) 16.0000i 0.768911i 0.923144 + 0.384455i \(0.125611\pi\)
−0.923144 + 0.384455i \(0.874389\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) 4.00000 0.191565
\(437\) 12.0000i 0.574038i
\(438\) 0 0
\(439\) 32.0000 1.52728 0.763638 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) −6.00000 + 12.0000i −0.286039 + 0.572078i
\(441\) 0 0
\(442\) 4.00000i 0.190261i
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) −28.0000 14.0000i −1.32733 0.663664i
\(446\) −8.00000 −0.378811
\(447\) 0 0
\(448\) 4.00000i 0.188982i
\(449\) 38.0000 1.79333 0.896665 0.442709i \(-0.145982\pi\)
0.896665 + 0.442709i \(0.145982\pi\)
\(450\) 0 0
\(451\) −60.0000 −2.82529
\(452\) 4.00000i 0.188144i
\(453\) 0 0
\(454\) 4.00000 0.187729
\(455\) 8.00000 + 4.00000i 0.375046 + 0.187523i
\(456\) 0 0
\(457\) 14.0000i 0.654892i −0.944870 0.327446i \(-0.893812\pi\)
0.944870 0.327446i \(-0.106188\pi\)
\(458\) 8.00000i 0.373815i
\(459\) 0 0
\(460\) −6.00000 + 12.0000i −0.279751 + 0.559503i
\(461\) 4.00000 0.186299 0.0931493 0.995652i \(-0.470307\pi\)
0.0931493 + 0.995652i \(0.470307\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i 0.995671 + 0.0929479i \(0.0296290\pi\)
−0.995671 + 0.0929479i \(0.970371\pi\)
\(464\) −10.0000 −0.464238
\(465\) 0 0
\(466\) −12.0000 −0.555889
\(467\) 8.00000i 0.370196i 0.982720 + 0.185098i \(0.0592602\pi\)
−0.982720 + 0.185098i \(0.940740\pi\)
\(468\) 0 0
\(469\) −48.0000 −2.21643
\(470\) 16.0000 + 8.00000i 0.738025 + 0.369012i
\(471\) 0 0
\(472\) 6.00000i 0.276172i
\(473\) 0 0
\(474\) 0 0
\(475\) −6.00000 8.00000i −0.275299 0.367065i
\(476\) −16.0000 −0.733359
\(477\) 0 0
\(478\) 4.00000i 0.182956i
\(479\) −20.0000 −0.913823 −0.456912 0.889512i \(-0.651044\pi\)
−0.456912 + 0.889512i \(0.651044\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 18.0000i 0.819878i
\(483\) 0 0
\(484\) −25.0000 −1.13636
\(485\) −14.0000 + 28.0000i −0.635707 + 1.27141i
\(486\) 0 0
\(487\) 32.0000i 1.45006i −0.688718 0.725029i \(-0.741826\pi\)
0.688718 0.725029i \(-0.258174\pi\)
\(488\) 6.00000i 0.271607i
\(489\) 0 0
\(490\) −9.00000 + 18.0000i −0.406579 + 0.813157i
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 40.0000i 1.80151i
\(494\) 2.00000 0.0899843
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 18.0000 0.805791 0.402895 0.915246i \(-0.368004\pi\)
0.402895 + 0.915246i \(0.368004\pi\)
\(500\) 2.00000 + 11.0000i 0.0894427 + 0.491935i
\(501\) 0 0
\(502\) 20.0000i 0.892644i
\(503\) 14.0000i 0.624229i 0.950044 + 0.312115i \(0.101037\pi\)
−0.950044 + 0.312115i \(0.898963\pi\)
\(504\) 0 0
\(505\) 20.0000 + 10.0000i 0.889988 + 0.444994i
\(506\) −36.0000 −1.60040
\(507\) 0 0
\(508\) 10.0000i 0.443678i
\(509\) 16.0000 0.709188 0.354594 0.935020i \(-0.384619\pi\)
0.354594 + 0.935020i \(0.384619\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −28.0000 −1.23503
\(515\) −2.00000 + 4.00000i −0.0881305 + 0.176261i
\(516\) 0 0
\(517\) 48.0000i 2.11104i
\(518\) 24.0000i 1.05450i
\(519\) 0 0
\(520\) −2.00000 1.00000i −0.0877058 0.0438529i
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i 0.936819 + 0.349816i \(0.113756\pi\)
−0.936819 + 0.349816i \(0.886244\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) −10.0000 −0.436021
\(527\) 16.0000i 0.696971i
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) 12.0000 + 6.00000i 0.521247 + 0.260623i
\(531\) 0 0
\(532\) 8.00000i 0.346844i
\(533\) 10.0000i 0.433148i
\(534\) 0 0
\(535\) 0 0
\(536\) 12.0000 0.518321
\(537\) 0 0
\(538\) 10.0000i 0.431131i
\(539\) −54.0000 −2.32594
\(540\) 0 0
\(541\) −32.0000 −1.37579 −0.687894 0.725811i \(-0.741464\pi\)
−0.687894 + 0.725811i \(0.741464\pi\)
\(542\) 8.00000i 0.343629i
\(543\) 0 0
\(544\) 4.00000 0.171499
\(545\) 8.00000 + 4.00000i 0.342682 + 0.171341i
\(546\) 0 0
\(547\) 36.0000i 1.53925i −0.638497 0.769624i \(-0.720443\pi\)
0.638497 0.769624i \(-0.279557\pi\)
\(548\) 14.0000i 0.598050i
\(549\) 0 0
\(550\) −24.0000 + 18.0000i −1.02336 + 0.767523i
\(551\) 20.0000 0.852029
\(552\) 0 0
\(553\) 32.0000i 1.36078i
\(554\) −14.0000 −0.594803
\(555\) 0 0
\(556\) 16.0000 0.678551
\(557\) 18.0000i 0.762684i −0.924434 0.381342i \(-0.875462\pi\)
0.924434 0.381342i \(-0.124538\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 4.00000 8.00000i 0.169031 0.338062i
\(561\) 0 0
\(562\) 18.0000i 0.759284i
\(563\) 24.0000i 1.01148i −0.862686 0.505740i \(-0.831220\pi\)
0.862686 0.505740i \(-0.168780\pi\)
\(564\) 0 0
\(565\) 4.00000 8.00000i 0.168281 0.336563i
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) 0 0
\(569\) −42.0000 −1.76073 −0.880366 0.474295i \(-0.842703\pi\)
−0.880366 + 0.474295i \(0.842703\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 6.00000i 0.250873i
\(573\) 0 0
\(574\) 40.0000 1.66957
\(575\) −24.0000 + 18.0000i −1.00087 + 0.750652i
\(576\) 0 0
\(577\) 2.00000i 0.0832611i −0.999133 0.0416305i \(-0.986745\pi\)
0.999133 0.0416305i \(-0.0132552\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 0 0
\(580\) −20.0000 10.0000i −0.830455 0.415227i
\(581\) −16.0000 −0.663792
\(582\) 0 0
\(583\) 36.0000i 1.49097i
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) 18.0000 0.743573
\(587\) 28.0000i 1.15568i −0.816149 0.577842i \(-0.803895\pi\)
0.816149 0.577842i \(-0.196105\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) −6.00000 + 12.0000i −0.247016 + 0.494032i
\(591\) 0 0
\(592\) 6.00000i 0.246598i
\(593\) 14.0000i 0.574911i −0.957794 0.287456i \(-0.907191\pi\)
0.957794 0.287456i \(-0.0928094\pi\)
\(594\) 0 0
\(595\) −32.0000 16.0000i −1.31187 0.655936i
\(596\) −16.0000 −0.655386
\(597\) 0 0
\(598\) 6.00000i 0.245358i
\(599\) −32.0000 −1.30748 −0.653742 0.756717i \(-0.726802\pi\)
−0.653742 + 0.756717i \(0.726802\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −16.0000 −0.651031
\(605\) −50.0000 25.0000i −2.03279 1.01639i
\(606\) 0 0
\(607\) 42.0000i 1.70473i −0.522949 0.852364i \(-0.675168\pi\)
0.522949 0.852364i \(-0.324832\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) 0 0
\(610\) −6.00000 + 12.0000i −0.242933 + 0.485866i
\(611\) −8.00000 −0.323645
\(612\) 0 0
\(613\) 38.0000i 1.53481i −0.641165 0.767403i \(-0.721549\pi\)
0.641165 0.767403i \(-0.278451\pi\)
\(614\) −4.00000 −0.161427
\(615\) 0 0
\(616\) 24.0000 0.966988
\(617\) 18.0000i 0.724653i −0.932051 0.362326i \(-0.881983\pi\)
0.932051 0.362326i \(-0.118017\pi\)
\(618\) 0 0
\(619\) 22.0000 0.884255 0.442127 0.896952i \(-0.354224\pi\)
0.442127 + 0.896952i \(0.354224\pi\)
\(620\) 8.00000 + 4.00000i 0.321288 + 0.160644i
\(621\) 0 0
\(622\) 8.00000i 0.320771i
\(623\) 56.0000i 2.24359i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 8.00000 0.319744
\(627\) 0 0
\(628\) 6.00000i 0.239426i
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 8.00000i 0.318223i
\(633\) 0 0
\(634\) −2.00000 −0.0794301
\(635\) 10.0000 20.0000i 0.396838 0.793676i
\(636\) 0 0
\(637\) 9.00000i 0.356593i
\(638\) 60.0000i 2.37542i
\(639\) 0 0
\(640\) −1.00000 + 2.00000i −0.0395285 + 0.0790569i
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 0 0
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 24.0000 0.945732
\(645\) 0 0
\(646\) −8.00000 −0.314756
\(647\) 6.00000i 0.235884i −0.993020 0.117942i \(-0.962370\pi\)
0.993020 0.117942i \(-0.0376297\pi\)
\(648\) 0 0
\(649\) −36.0000 −1.41312
\(650\) −3.00000 4.00000i −0.117670 0.156893i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) 10.0000i 0.391330i 0.980671 + 0.195665i \(0.0626866\pi\)
−0.980671 + 0.195665i \(0.937313\pi\)
\(654\) 0 0
\(655\) −16.0000 8.00000i −0.625172 0.312586i
\(656\) −10.0000 −0.390434
\(657\) 0 0
\(658\) 32.0000i 1.24749i
\(659\) −32.0000 −1.24654 −0.623272 0.782006i \(-0.714197\pi\)
−0.623272 + 0.782006i \(0.714197\pi\)
\(660\) 0 0
\(661\) −32.0000 −1.24466 −0.622328 0.782757i \(-0.713813\pi\)
−0.622328 + 0.782757i \(0.713813\pi\)
\(662\) 2.00000i 0.0777322i
\(663\) 0 0
\(664\) 4.00000 0.155230
\(665\) −8.00000 + 16.0000i −0.310227 + 0.620453i
\(666\) 0 0
\(667\) 60.0000i 2.32321i
\(668\) 16.0000i 0.619059i
\(669\) 0 0
\(670\) 24.0000 + 12.0000i 0.927201 + 0.463600i
\(671\) −36.0000 −1.38976
\(672\) 0 0
\(673\) 44.0000i 1.69608i 0.529936 + 0.848038i \(0.322216\pi\)
−0.529936 + 0.848038i \(0.677784\pi\)
\(674\) 16.0000 0.616297
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 6.00000i 0.230599i 0.993331 + 0.115299i \(0.0367827\pi\)
−0.993331 + 0.115299i \(0.963217\pi\)
\(678\) 0 0
\(679\) 56.0000 2.14908
\(680\) 8.00000 + 4.00000i 0.306786 + 0.153393i
\(681\) 0 0
\(682\) 24.0000i 0.919007i
\(683\) 20.0000i 0.765279i 0.923898 + 0.382639i \(0.124985\pi\)
−0.923898 + 0.382639i \(0.875015\pi\)
\(684\) 0 0
\(685\) −14.0000 + 28.0000i −0.534913 + 1.06983i
\(686\) 8.00000 0.305441
\(687\) 0 0
\(688\) 0 0
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) 18.0000 0.684752 0.342376 0.939563i \(-0.388768\pi\)
0.342376 + 0.939563i \(0.388768\pi\)
\(692\) 22.0000i 0.836315i
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) 32.0000 + 16.0000i 1.21383 + 0.606915i
\(696\) 0 0
\(697\) 40.0000i 1.51511i
\(698\) 4.00000i 0.151402i
\(699\) 0 0
\(700\) 16.0000 12.0000i 0.604743 0.453557i
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) 12.0000i 0.452589i
\(704\) −6.00000 −0.226134
\(705\) 0 0
\(706\) −26.0000 −0.978523
\(707\) 40.0000i 1.50435i
\(708\) 0 0
\(709\) 8.00000 0.300446 0.150223 0.988652i \(-0.452001\pi\)
0.150223 + 0.988652i \(0.452001\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 14.0000i 0.524672i
\(713\) 24.0000i 0.898807i
\(714\) 0 0
\(715\) 6.00000 12.0000i 0.224387 0.448775i
\(716\) 24.0000 0.896922
\(717\) 0 0
\(718\) 20.0000i 0.746393i
\(719\) 8.00000 0.298350 0.149175 0.988811i \(-0.452338\pi\)
0.149175 + 0.988811i \(0.452338\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 15.0000i 0.558242i
\(723\) 0 0
\(724\) −6.00000 −0.222988
\(725\) −30.0000 40.0000i −1.11417 1.48556i
\(726\) 0 0
\(727\) 38.0000i 1.40934i −0.709534 0.704671i \(-0.751095\pi\)
0.709534 0.704671i \(-0.248905\pi\)
\(728\) 4.00000i 0.148250i
\(729\) 0 0
\(730\) 4.00000 + 2.00000i 0.148047 + 0.0740233i
\(731\) 0 0
\(732\) 0 0
\(733\) 18.0000i 0.664845i −0.943131 0.332423i \(-0.892134\pi\)
0.943131 0.332423i \(-0.107866\pi\)
\(734\) −18.0000 −0.664392
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 72.0000i 2.65215i
\(738\) 0 0
\(739\) 2.00000 0.0735712 0.0367856 0.999323i \(-0.488288\pi\)
0.0367856 + 0.999323i \(0.488288\pi\)
\(740\) −6.00000 + 12.0000i −0.220564 + 0.441129i
\(741\) 0 0
\(742\) 24.0000i 0.881068i
\(743\) 36.0000i 1.32071i 0.750953 + 0.660356i \(0.229595\pi\)
−0.750953 + 0.660356i \(0.770405\pi\)
\(744\) 0 0
\(745\) −32.0000 16.0000i −1.17239 0.586195i
\(746\) 18.0000 0.659027
\(747\) 0 0
\(748\) 24.0000i 0.877527i
\(749\) 0 0
\(750\) 0 0
\(751\) −48.0000 −1.75154 −0.875772 0.482724i \(-0.839647\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 0 0
\(754\) 10.0000 0.364179
\(755\) −32.0000 16.0000i −1.16460 0.582300i
\(756\) 0 0
\(757\) 22.0000i 0.799604i 0.916602 + 0.399802i \(0.130921\pi\)
−0.916602 + 0.399802i \(0.869079\pi\)
\(758\) 10.0000i 0.363216i
\(759\) 0 0
\(760\) 2.00000 4.00000i 0.0725476 0.145095i
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) 0 0
\(763\) 16.0000i 0.579239i
\(764\) 0 0
\(765\) 0 0
\(766\) 20.0000 0.722629
\(767\) 6.00000i 0.216647i
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 48.0000 + 24.0000i 1.72980 + 0.864900i
\(771\) 0 0
\(772\) 2.00000i 0.0719816i
\(773\) 18.0000i 0.647415i 0.946157 + 0.323708i \(0.104929\pi\)
−0.946157 + 0.323708i \(0.895071\pi\)
\(774\) 0 0
\(775\) 12.0000 + 16.0000i 0.431053 + 0.574737i
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) 30.0000i 1.07555i
\(779\) 20.0000 0.716574
\(780\) 0 0
\(781\) 0 0
\(782\) 24.0000i 0.858238i
\(783\) 0 0
\(784\) −9.00000 −0.321429
\(785\) −6.00000 + 12.0000i −0.214149 + 0.428298i
\(786\) 0 0
\(787\) 12.0000i 0.427754i 0.976861 + 0.213877i \(0.0686091\pi\)
−0.976861 + 0.213877i \(0.931391\pi\)
\(788\) 6.00000i 0.213741i
\(789\) 0 0
\(790\) 8.00000 16.0000i 0.284627 0.569254i
\(791\) −16.0000 −0.568895
\(792\) 0 0
\(793\) 6.00000i 0.213066i
\(794\) −10.0000 −0.354887
\(795\) 0 0
\(796\) −8.00000 −0.283552