Properties

Label 1170.2.e.b.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.b.469.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -4.00000i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -4.00000i q^{7} -1.00000i q^{8} +(1.00000 - 2.00000i) q^{10} -2.00000 q^{11} +1.00000i q^{13} +4.00000 q^{14} +1.00000 q^{16} +4.00000i q^{17} -2.00000 q^{19} +(2.00000 + 1.00000i) q^{20} -2.00000i q^{22} +6.00000i q^{23} +(3.00000 + 4.00000i) q^{25} -1.00000 q^{26} +4.00000i q^{28} -2.00000 q^{29} -4.00000 q^{31} +1.00000i q^{32} -4.00000 q^{34} +(-4.00000 + 8.00000i) q^{35} +6.00000i q^{37} -2.00000i q^{38} +(-1.00000 + 2.00000i) q^{40} +6.00000 q^{41} +8.00000i q^{43} +2.00000 q^{44} -6.00000 q^{46} +8.00000i q^{47} -9.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -1.00000i q^{52} -10.0000i q^{53} +(4.00000 + 2.00000i) q^{55} -4.00000 q^{56} -2.00000i q^{58} -14.0000 q^{59} +10.0000 q^{61} -4.00000i q^{62} -1.00000 q^{64} +(1.00000 - 2.00000i) q^{65} -4.00000i q^{67} -4.00000i q^{68} +(-8.00000 - 4.00000i) q^{70} -8.00000 q^{71} +10.0000i q^{73} -6.00000 q^{74} +2.00000 q^{76} +8.00000i q^{77} +8.00000 q^{79} +(-2.00000 - 1.00000i) q^{80} +6.00000i q^{82} -12.0000i q^{83} +(4.00000 - 8.00000i) q^{85} -8.00000 q^{86} +2.00000i q^{88} -18.0000 q^{89} +4.00000 q^{91} -6.00000i q^{92} -8.00000 q^{94} +(4.00000 + 2.00000i) q^{95} -6.00000i q^{97} -9.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} - 4 q^{5} + 2 q^{10} - 4 q^{11} + 8 q^{14} + 2 q^{16} - 4 q^{19} + 4 q^{20} + 6 q^{25} - 2 q^{26} - 4 q^{29} - 8 q^{31} - 8 q^{34} - 8 q^{35} - 2 q^{40} + 12 q^{41} + 4 q^{44} - 12 q^{46} - 18 q^{49} - 8 q^{50} + 8 q^{55} - 8 q^{56} - 28 q^{59} + 20 q^{61} - 2 q^{64} + 2 q^{65} - 16 q^{70} - 16 q^{71} - 12 q^{74} + 4 q^{76} + 16 q^{79} - 4 q^{80} + 8 q^{85} - 16 q^{86} - 36 q^{89} + 8 q^{91} - 16 q^{94} + 8 q^{95}+O(q^{100}) \) 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 \(-0.727186\pi\)
0.654654 0.755929i \(-0.272814\pi\)
\(8\) 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
\(14\) 4.00000 1.06904
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000i 0.970143i 0.874475 + 0.485071i \(0.161206\pi\)
−0.874475 + 0.485071i \(0.838794\pi\)
\(18\) 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
\(22\) 2.00000i 0.426401i
\(23\) 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
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 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
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 8.00000i 1.21999i 0.792406 + 0.609994i \(0.208828\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) 2.00000 0.301511
\(45\) 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
\(53\) 10.0000i 1.37361i −0.726844 0.686803i \(-0.759014\pi\)
0.726844 0.686803i \(-0.240986\pi\)
\(54\) 0 0
\(55\) 4.00000 + 2.00000i 0.539360 + 0.269680i
\(56\) −4.00000 −0.534522
\(57\) 0 0
\(58\) 2.00000i 0.262613i
\(59\) −14.0000 −1.82264 −0.911322 0.411693i \(-0.864937\pi\)
−0.911322 + 0.411693i \(0.864937\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.00000 2.00000i 0.124035 0.248069i
\(66\) 0 0
\(67\) 4.00000i 0.488678i −0.969690 0.244339i \(-0.921429\pi\)
0.969690 0.244339i \(-0.0785709\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) −8.00000 4.00000i −0.956183 0.478091i
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 10.0000i 1.17041i 0.810885 + 0.585206i \(0.198986\pi\)
−0.810885 + 0.585206i \(0.801014\pi\)
\(74\) −6.00000 −0.697486
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 8.00000i 0.911685i
\(78\) 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
\(85\) 4.00000 8.00000i 0.433861 0.867722i
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) 2.00000i 0.213201i
\(89\) −18.0000 −1.90800 −0.953998 0.299813i \(-0.903076\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 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
\(97\) 6.00000i 0.609208i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985241\pi\)
\(98\) 9.00000i 0.909137i
\(99\) 0 0
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 14.0000 1.39305 0.696526 0.717532i \(-0.254728\pi\)
0.696526 + 0.717532i \(0.254728\pi\)
\(102\) 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
\(106\) 10.0000 0.971286
\(107\) 8.00000i 0.773389i −0.922208 0.386695i \(-0.873617\pi\)
0.922208 0.386695i \(-0.126383\pi\)
\(108\) 0 0
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) −2.00000 + 4.00000i −0.190693 + 0.381385i
\(111\) 0 0
\(112\) 4.00000i 0.377964i
\(113\) 12.0000i 1.12887i 0.825479 + 0.564433i \(0.190905\pi\)
−0.825479 + 0.564433i \(0.809095\pi\)
\(114\) 0 0
\(115\) 6.00000 12.0000i 0.559503 1.11901i
\(116\) 2.00000 0.185695
\(117\) 0 0
\(118\) 14.0000i 1.28880i
\(119\) 16.0000 1.46672
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 10.0000i 0.905357i
\(123\) 0 0
\(124\) 4.00000 0.359211
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 18.0000i 1.59724i 0.601834 + 0.798621i \(0.294437\pi\)
−0.601834 + 0.798621i \(0.705563\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 2.00000 + 1.00000i 0.175412 + 0.0877058i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 8.00000i 0.693688i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 4.00000 0.342997
\(137\) 2.00000i 0.170872i 0.996344 + 0.0854358i \(0.0272282\pi\)
−0.996344 + 0.0854358i \(0.972772\pi\)
\(138\) 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
\(142\) 8.00000i 0.671345i
\(143\) 2.00000i 0.167248i
\(144\) 0 0
\(145\) 4.00000 + 2.00000i 0.332182 + 0.166091i
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 2.00000i 0.162221i
\(153\) 0 0
\(154\) −8.00000 −0.644658
\(155\) 8.00000 + 4.00000i 0.642575 + 0.321288i
\(156\) 0 0
\(157\) 10.0000i 0.798087i 0.916932 + 0.399043i \(0.130658\pi\)
−0.916932 + 0.399043i \(0.869342\pi\)
\(158\) 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 \(-0.0500701\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 8.00000 + 4.00000i 0.613572 + 0.306786i
\(171\) 0 0
\(172\) 8.00000i 0.609994i
\(173\) 10.0000i 0.760286i −0.924928 0.380143i \(-0.875875\pi\)
0.924928 0.380143i \(-0.124125\pi\)
\(174\) 0 0
\(175\) 16.0000 12.0000i 1.20949 0.907115i
\(176\) −2.00000 −0.150756
\(177\) 0 0
\(178\) 18.0000i 1.34916i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 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
\(187\) 8.00000i 0.585018i
\(188\) 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
\(193\) 6.00000i 0.431889i 0.976406 + 0.215945i \(0.0692831\pi\)
−0.976406 + 0.215945i \(0.930717\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) 26.0000i 1.85242i 0.377004 + 0.926212i \(0.376954\pi\)
−0.377004 + 0.926212i \(0.623046\pi\)
\(198\) 0 0
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) 0 0
\(202\) 14.0000i 0.985037i
\(203\) 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
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 10.0000i 0.686803i
\(213\) 0 0
\(214\) 8.00000 0.546869
\(215\) 8.00000 16.0000i 0.545595 1.09119i
\(216\) 0 0
\(217\) 16.0000i 1.08615i
\(218\) 12.0000i 0.812743i
\(219\) 0 0
\(220\) −4.00000 2.00000i −0.269680 0.134840i
\(221\) −4.00000 −0.269069
\(222\) 0 0
\(223\) 16.0000i 1.07144i −0.844396 0.535720i \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) 4.00000 0.267261
\(225\) 0 0
\(226\) −12.0000 −0.798228
\(227\) 12.0000i 0.796468i 0.917284 + 0.398234i \(0.130377\pi\)
−0.917284 + 0.398234i \(0.869623\pi\)
\(228\) 0 0
\(229\) 16.0000 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 12.0000 + 6.00000i 0.791257 + 0.395628i
\(231\) 0 0
\(232\) 2.00000i 0.131306i
\(233\) 4.00000i 0.262049i 0.991379 + 0.131024i \(0.0418266\pi\)
−0.991379 + 0.131024i \(0.958173\pi\)
\(234\) 0 0
\(235\) 8.00000 16.0000i 0.521862 1.04372i
\(236\) 14.0000 0.911322
\(237\) 0 0
\(238\) 16.0000i 1.03713i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −30.0000 −1.93247 −0.966235 0.257663i \(-0.917048\pi\)
−0.966235 + 0.257663i \(0.917048\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) 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
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 12.0000i 0.754434i
\(254\) −18.0000 −1.12942
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 12.0000i 0.748539i −0.927320 0.374270i \(-0.877893\pi\)
0.927320 0.374270i \(-0.122107\pi\)
\(258\) 0 0
\(259\) 24.0000 1.49129
\(260\) −1.00000 + 2.00000i −0.0620174 + 0.124035i
\(261\) 0 0
\(262\) 0 0
\(263\) 10.0000i 0.616626i 0.951285 + 0.308313i \(0.0997645\pi\)
−0.951285 + 0.308313i \(0.900236\pi\)
\(264\) 0 0
\(265\) −10.0000 + 20.0000i −0.614295 + 1.22859i
\(266\) −8.00000 −0.490511
\(267\) 0 0
\(268\) 4.00000i 0.244339i
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) −6.00000 8.00000i −0.361814 0.482418i
\(276\) 0 0
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) 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
\(283\) 4.00000i 0.237775i −0.992908 0.118888i \(-0.962067\pi\)
0.992908 0.118888i \(-0.0379328\pi\)
\(284\) 8.00000 0.474713
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) 24.0000i 1.41668i
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) −2.00000 + 4.00000i −0.117444 + 0.234888i
\(291\) 0 0
\(292\) 10.0000i 0.585206i
\(293\) 14.0000i 0.817889i 0.912559 + 0.408944i \(0.134103\pi\)
−0.912559 + 0.408944i \(0.865897\pi\)
\(294\) 0 0
\(295\) 28.0000 + 14.0000i 1.63022 + 0.815112i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) 0 0
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) 32.0000 1.84445
\(302\) 8.00000i 0.460348i
\(303\) 0 0
\(304\) −2.00000 −0.114708
\(305\) −20.0000 10.0000i −1.14520 0.572598i
\(306\) 0 0
\(307\) 28.0000i 1.59804i −0.601302 0.799022i \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 8.00000i 0.455842i
\(309\) 0 0
\(310\) −4.00000 + 8.00000i −0.227185 + 0.454369i
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 0 0
\(313\) 8.00000i 0.452187i 0.974106 + 0.226093i \(0.0725954\pi\)
−0.974106 + 0.226093i \(0.927405\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 30.0000i 1.68497i −0.538721 0.842484i \(-0.681092\pi\)
0.538721 0.842484i \(-0.318908\pi\)
\(318\) 0 0
\(319\) 4.00000 0.223957
\(320\) 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
\(328\) 6.00000i 0.331295i
\(329\) 32.0000 1.76422
\(330\) 0 0
\(331\) 18.0000 0.989369 0.494685 0.869072i \(-0.335284\pi\)
0.494685 + 0.869072i \(0.335284\pi\)
\(332\) 12.0000i 0.658586i
\(333\) 0 0
\(334\) 0 0
\(335\) −4.00000 + 8.00000i −0.218543 + 0.437087i
\(336\) 0 0
\(337\) 32.0000i 1.74315i 0.490261 + 0.871576i \(0.336901\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 0 0
\(340\) −4.00000 + 8.00000i −0.216930 + 0.433861i
\(341\) 8.00000 0.433224
\(342\) 0 0
\(343\) 8.00000i 0.431959i
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) 10.0000 0.537603
\(347\) 24.0000i 1.28839i −0.764862 0.644194i \(-0.777193\pi\)
0.764862 0.644194i \(-0.222807\pi\)
\(348\) 0 0
\(349\) 28.0000 1.49881 0.749403 0.662114i \(-0.230341\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(350\) 12.0000 + 16.0000i 0.641427 + 0.855236i
\(351\) 0 0
\(352\) 2.00000i 0.106600i
\(353\) 26.0000i 1.38384i 0.721974 + 0.691920i \(0.243235\pi\)
−0.721974 + 0.691920i \(0.756765\pi\)
\(354\) 0 0
\(355\) 16.0000 + 8.00000i 0.849192 + 0.424596i
\(356\) 18.0000 0.953998
\(357\) 0 0
\(358\) 0 0
\(359\) 20.0000 1.05556 0.527780 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 6.00000i 0.315353i
\(363\) 0 0
\(364\) −4.00000 −0.209657
\(365\) 10.0000 20.0000i 0.523424 1.04685i
\(366\) 0 0
\(367\) 22.0000i 1.14839i −0.818718 0.574195i \(-0.805315\pi\)
0.818718 0.574195i \(-0.194685\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 0 0
\(370\) 12.0000 + 6.00000i 0.623850 + 0.311925i
\(371\) −40.0000 −2.07670
\(372\) 0 0
\(373\) 2.00000i 0.103556i −0.998659 0.0517780i \(-0.983511\pi\)
0.998659 0.0517780i \(-0.0164888\pi\)
\(374\) 8.00000 0.413670
\(375\) 0 0
\(376\) 8.00000 0.412568
\(377\) 2.00000i 0.103005i
\(378\) 0 0
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) −4.00000 2.00000i −0.205196 0.102598i
\(381\) 0 0
\(382\) 0 0
\(383\) 12.0000i 0.613171i 0.951843 + 0.306586i \(0.0991866\pi\)
−0.951843 + 0.306586i \(0.900813\pi\)
\(384\) 0 0
\(385\) 8.00000 16.0000i 0.407718 0.815436i
\(386\) −6.00000 −0.305392
\(387\) 0 0
\(388\) 6.00000i 0.304604i
\(389\) −26.0000 −1.31825 −0.659126 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 9.00000i 0.454569i
\(393\) 0 0
\(394\) −26.0000 −1.30986
\(395\) −16.0000 8.00000i −0.805047 0.402524i
\(396\) 0 0
\(397\) 6.00000i 0.301131i −0.988600 0.150566i \(-0.951890\pi\)
0.988600 0.150566i \(-0.0481095\pi\)
\(398\) 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
\(403\) 4.00000i 0.199254i
\(404\) −14.0000 −0.696526
\(405\) 0 0
\(406\) −8.00000 −0.397033
\(407\) 12.0000i 0.594818i
\(408\) 0 0
\(409\) 2.00000 0.0988936 0.0494468 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) 6.00000 12.0000i 0.296319 0.592638i
\(411\) 0 0
\(412\) 6.00000i 0.295599i
\(413\) 56.0000i 2.75558i
\(414\) 0 0
\(415\) −12.0000 + 24.0000i −0.589057 + 1.17811i
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) 4.00000i 0.195646i
\(419\) 16.0000 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(420\) 0 0
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) 28.0000i 1.36302i
\(423\) 0 0
\(424\) −10.0000 −0.485643
\(425\) −16.0000 + 12.0000i −0.776114 + 0.582086i
\(426\) 0 0
\(427\) 40.0000i 1.93574i
\(428\) 8.00000i 0.386695i
\(429\) 0 0
\(430\) 16.0000 + 8.00000i 0.771589 + 0.385794i
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) 12.0000 0.574696
\(437\) 12.0000i 0.574038i
\(438\) 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
\(442\) 4.00000i 0.190261i
\(443\) 8.00000i 0.380091i −0.981775 0.190046i \(-0.939136\pi\)
0.981775 0.190046i \(-0.0608636\pi\)
\(444\) 0 0
\(445\) 36.0000 + 18.0000i 1.70656 + 0.853282i
\(446\) 16.0000 0.757622
\(447\) 0 0
\(448\) 4.00000i 0.188982i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) −12.0000 −0.565058
\(452\) 12.0000i 0.564433i
\(453\) 0 0
\(454\) −12.0000 −0.563188
\(455\) −8.00000 4.00000i −0.375046 0.187523i
\(456\) 0 0
\(457\) 26.0000i 1.21623i 0.793849 + 0.608114i \(0.208074\pi\)
−0.793849 + 0.608114i \(0.791926\pi\)
\(458\) 16.0000i 0.747631i
\(459\) 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
\(463\) 36.0000i 1.67306i −0.547920 0.836531i \(-0.684580\pi\)
0.547920 0.836531i \(-0.315420\pi\)
\(464\) −2.00000 −0.0928477
\(465\) 0 0
\(466\) −4.00000 −0.185296
\(467\) 16.0000i 0.740392i −0.928954 0.370196i \(-0.879291\pi\)
0.928954 0.370196i \(-0.120709\pi\)
\(468\) 0 0
\(469\) −16.0000 −0.738811
\(470\) 16.0000 + 8.00000i 0.738025 + 0.369012i
\(471\) 0 0
\(472\) 14.0000i 0.644402i
\(473\) 16.0000i 0.735681i
\(474\) 0 0
\(475\) −6.00000 8.00000i −0.275299 0.367065i
\(476\) −16.0000 −0.733359
\(477\) 0 0
\(478\) 12.0000i 0.548867i
\(479\) −12.0000 −0.548294 −0.274147 0.961688i \(-0.588395\pi\)
−0.274147 + 0.961688i \(0.588395\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 30.0000i 1.36646i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) −6.00000 + 12.0000i −0.272446 + 0.544892i
\(486\) 0 0
\(487\) 40.0000i 1.81257i 0.422664 + 0.906287i \(0.361095\pi\)
−0.422664 + 0.906287i \(0.638905\pi\)
\(488\) 10.0000i 0.452679i
\(489\) 0 0
\(490\) −9.00000 + 18.0000i −0.406579 + 0.813157i
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 0 0
\(493\) 8.00000i 0.360302i
\(494\) 2.00000 0.0899843
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 32.0000i 1.43540i
\(498\) 0 0
\(499\) −30.0000 −1.34298 −0.671492 0.741012i \(-0.734346\pi\)
−0.671492 + 0.741012i \(0.734346\pi\)
\(500\) 2.00000 + 11.0000i 0.0894427 + 0.491935i
\(501\) 0 0
\(502\) 12.0000i 0.535586i
\(503\) 18.0000i 0.802580i −0.915951 0.401290i \(-0.868562\pi\)
0.915951 0.401290i \(-0.131438\pi\)
\(504\) 0 0
\(505\) −28.0000 14.0000i −1.24598 0.622992i
\(506\) 12.0000 0.533465
\(507\) 0 0
\(508\) 18.0000i 0.798621i
\(509\) −16.0000 −0.709188 −0.354594 0.935020i \(-0.615381\pi\)
−0.354594 + 0.935020i \(0.615381\pi\)
\(510\) 0 0
\(511\) 40.0000 1.76950
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 12.0000 0.529297
\(515\) 6.00000 12.0000i 0.264392 0.528783i
\(516\) 0 0
\(517\) 16.0000i 0.703679i
\(518\) 24.0000i 1.05450i
\(519\) 0 0
\(520\) −2.00000 1.00000i −0.0877058 0.0438529i
\(521\) −38.0000 −1.66481 −0.832405 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(522\) 0 0
\(523\) 8.00000i 0.349816i 0.984585 + 0.174908i \(0.0559627\pi\)
−0.984585 + 0.174908i \(0.944037\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −10.0000 −0.436021
\(527\) 16.0000i 0.696971i
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) −20.0000 10.0000i −0.868744 0.434372i
\(531\) 0 0
\(532\) 8.00000i 0.346844i
\(533\) 6.00000i 0.259889i
\(534\) 0 0
\(535\) −8.00000 + 16.0000i −0.345870 + 0.691740i
\(536\) −4.00000 −0.172774
\(537\) 0 0
\(538\) 14.0000i 0.603583i
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 16.0000i 0.687259i
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) 24.0000 + 12.0000i 1.02805 + 0.514024i
\(546\) 0 0
\(547\) 44.0000i 1.88130i −0.339372 0.940652i \(-0.610215\pi\)
0.339372 0.940652i \(-0.389785\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) 0 0
\(550\) 8.00000 6.00000i 0.341121 0.255841i
\(551\) 4.00000 0.170406
\(552\) 0 0
\(553\) 32.0000i 1.36078i
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 16.0000 0.678551
\(557\) 14.0000i 0.593199i 0.955002 + 0.296600i \(0.0958526\pi\)
−0.955002 + 0.296600i \(0.904147\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) −4.00000 + 8.00000i −0.169031 + 0.338062i
\(561\) 0 0
\(562\) 18.0000i 0.759284i
\(563\) 16.0000i 0.674320i 0.941447 + 0.337160i \(0.109466\pi\)
−0.941447 + 0.337160i \(0.890534\pi\)
\(564\) 0 0
\(565\) 12.0000 24.0000i 0.504844 1.00969i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 8.00000i 0.335673i
\(569\) −42.0000 −1.76073 −0.880366 0.474295i \(-0.842703\pi\)
−0.880366 + 0.474295i \(0.842703\pi\)
\(570\) 0 0
\(571\) −36.0000 −1.50655 −0.753277 0.657704i \(-0.771528\pi\)
−0.753277 + 0.657704i \(0.771528\pi\)
\(572\) 2.00000i 0.0836242i
\(573\) 0 0
\(574\) 24.0000 1.00174
\(575\) −24.0000 + 18.0000i −1.00087 + 0.750652i
\(576\) 0 0
\(577\) 26.0000i 1.08239i −0.840896 0.541197i \(-0.817971\pi\)
0.840896 0.541197i \(-0.182029\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 0 0
\(580\) −4.00000 2.00000i −0.166091 0.0830455i
\(581\) −48.0000 −1.99138
\(582\) 0 0
\(583\) 20.0000i 0.828315i
\(584\) 10.0000 0.413803
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) 36.0000i 1.48588i 0.669359 + 0.742940i \(0.266569\pi\)
−0.669359 + 0.742940i \(0.733431\pi\)
\(588\) 0 0
\(589\) 8.00000 0.329634
\(590\) −14.0000 + 28.0000i −0.576371 + 1.15274i
\(591\) 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
\(596\) 0 0
\(597\) 0 0
\(598\) 6.00000i 0.245358i
\(599\) −16.0000 −0.653742 −0.326871 0.945069i \(-0.605994\pi\)
−0.326871 + 0.945069i \(0.605994\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 32.0000i 1.30422i
\(603\) 0 0
\(604\) −8.00000 −0.325515
\(605\) 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 \(-0.119033\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) 0 0
\(610\) 10.0000 20.0000i 0.404888 0.809776i
\(611\) −8.00000 −0.323645
\(612\) 0 0
\(613\) 26.0000i 1.05013i 0.851062 + 0.525065i \(0.175959\pi\)
−0.851062 + 0.525065i \(0.824041\pi\)
\(614\) 28.0000 1.12999
\(615\) 0 0
\(616\) 8.00000 0.322329
\(617\) 34.0000i 1.36879i −0.729112 0.684394i \(-0.760067\pi\)
0.729112 0.684394i \(-0.239933\pi\)
\(618\) 0 0
\(619\) −42.0000 −1.68812 −0.844061 0.536247i \(-0.819842\pi\)
−0.844061 + 0.536247i \(0.819842\pi\)
\(620\) −8.00000 4.00000i −0.321288 0.160644i
\(621\) 0 0
\(622\) 8.00000i 0.320771i
\(623\) 72.0000i 2.88462i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −8.00000 −0.319744
\(627\) 0 0
\(628\) 10.0000i 0.399043i
\(629\) −24.0000 −0.956943
\(630\) 0 0
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 8.00000i 0.318223i
\(633\) 0 0
\(634\) 30.0000 1.19145
\(635\) 18.0000 36.0000i 0.714308 1.42862i
\(636\) 0 0
\(637\) 9.00000i 0.356593i
\(638\) 4.00000i 0.158362i
\(639\) 0 0
\(640\) −1.00000 + 2.00000i −0.0395285 + 0.0790569i
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 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
\(649\) 28.0000 1.09910
\(650\) −3.00000 4.00000i −0.117670 0.156893i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) 26.0000i 1.01746i 0.860927 + 0.508729i \(0.169885\pi\)
−0.860927 + 0.508729i \(0.830115\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 32.0000i 1.24749i
\(659\) 40.0000 1.55818 0.779089 0.626913i \(-0.215682\pi\)
0.779089 + 0.626913i \(0.215682\pi\)
\(660\) 0 0
\(661\) 24.0000 0.933492 0.466746 0.884391i \(-0.345426\pi\)
0.466746 + 0.884391i \(0.345426\pi\)
\(662\) 18.0000i 0.699590i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 8.00000 16.0000i 0.310227 0.620453i
\(666\) 0 0
\(667\) 12.0000i 0.464642i
\(668\) 0 0
\(669\) 0 0
\(670\) −8.00000 4.00000i −0.309067 0.154533i
\(671\) −20.0000 −0.772091
\(672\) 0 0
\(673\) 12.0000i 0.462566i 0.972887 + 0.231283i \(0.0742923\pi\)
−0.972887 + 0.231283i \(0.925708\pi\)
\(674\) −32.0000 −1.23259
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 22.0000i 0.845529i 0.906240 + 0.422764i \(0.138940\pi\)
−0.906240 + 0.422764i \(0.861060\pi\)
\(678\) 0 0
\(679\) −24.0000 −0.921035
\(680\) −8.00000 4.00000i −0.306786 0.153393i
\(681\) 0 0
\(682\) 8.00000i 0.306336i
\(683\) 12.0000i 0.459167i −0.973289 0.229584i \(-0.926264\pi\)
0.973289 0.229584i \(-0.0737364\pi\)
\(684\) 0 0
\(685\) 2.00000 4.00000i 0.0764161 0.152832i
\(686\) −8.00000 −0.305441
\(687\) 0 0
\(688\) 8.00000i 0.304997i
\(689\) 10.0000 0.380970
\(690\) 0 0
\(691\) 2.00000 0.0760836 0.0380418 0.999276i \(-0.487888\pi\)
0.0380418 + 0.999276i \(0.487888\pi\)
\(692\) 10.0000i 0.380143i
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 32.0000 + 16.0000i 1.21383 + 0.606915i
\(696\) 0 0
\(697\) 24.0000i 0.909065i
\(698\) 28.0000i 1.05982i
\(699\) 0 0
\(700\) −16.0000 + 12.0000i −0.604743 + 0.453557i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 12.0000i 0.452589i
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) −26.0000 −0.978523
\(707\) 56.0000i 2.10610i
\(708\) 0 0
\(709\) 32.0000 1.20179 0.600893 0.799330i \(-0.294812\pi\)
0.600893 + 0.799330i \(0.294812\pi\)
\(710\) −8.00000 + 16.0000i −0.300235 + 0.600469i
\(711\) 0 0
\(712\) 18.0000i 0.674579i
\(713\) 24.0000i 0.898807i
\(714\) 0 0
\(715\) −2.00000 + 4.00000i −0.0747958 + 0.149592i
\(716\) 0 0
\(717\) 0 0
\(718\) 20.0000i 0.746393i
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 24.0000 0.893807
\(722\) 15.0000i 0.558242i
\(723\) 0 0
\(724\) −6.00000 −0.222988
\(725\) −6.00000 8.00000i −0.222834 0.297113i
\(726\) 0 0
\(727\) 14.0000i 0.519231i −0.965712 0.259616i \(-0.916404\pi\)
0.965712 0.259616i \(-0.0835959\pi\)
\(728\) 4.00000i 0.148250i
\(729\) 0 0
\(730\) 20.0000 + 10.0000i 0.740233 + 0.370117i
\(731\) −32.0000 −1.18356
\(732\) 0 0
\(733\) 2.00000i 0.0738717i −0.999318 0.0369358i \(-0.988240\pi\)
0.999318 0.0369358i \(-0.0117597\pi\)
\(734\) 22.0000 0.812035
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 8.00000i 0.294684i
\(738\) 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
\(742\) 40.0000i 1.46845i
\(743\) 4.00000i 0.146746i 0.997305 + 0.0733729i \(0.0233763\pi\)
−0.997305 + 0.0733729i \(0.976624\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 2.00000 0.0732252
\(747\) 0 0
\(748\) 8.00000i 0.292509i
\(749\) −32.0000 −1.16925
\(750\) 0 0
\(751\) 48.0000 1.75154 0.875772 0.482724i \(-0.160353\pi\)
0.875772 + 0.482724i \(0.160353\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 0 0
\(754\) 2.00000 0.0728357
\(755\) −16.0000 8.00000i −0.582300 0.291150i
\(756\) 0 0
\(757\) 22.0000i 0.799604i 0.916602 + 0.399802i \(0.130921\pi\)
−0.916602 + 0.399802i \(0.869079\pi\)
\(758\) 26.0000i 0.944363i
\(759\) 0 0
\(760\) 2.00000 4.00000i 0.0725476 0.145095i
\(761\) −14.0000 −0.507500 −0.253750 0.967270i \(-0.581664\pi\)
−0.253750 + 0.967270i \(0.581664\pi\)
\(762\) 0 0
\(763\) 48.0000i 1.73772i
\(764\) 0 0
\(765\) 0 0
\(766\) −12.0000 −0.433578
\(767\) 14.0000i 0.505511i
\(768\) 0 0
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 16.0000 + 8.00000i 0.576600 + 0.288300i
\(771\) 0 0
\(772\) 6.00000i 0.215945i
\(773\) 14.0000i 0.503545i −0.967786 0.251773i \(-0.918987\pi\)
0.967786 0.251773i \(-0.0810135\pi\)
\(774\) 0 0
\(775\) −12.0000 16.0000i −0.431053 0.574737i
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) 26.0000i 0.932145i
\(779\) −12.0000 −0.429945
\(780\) 0 0
\(781\) 16.0000 0.572525
\(782\) 24.0000i 0.858238i
\(783\) 0 0
\(784\) −9.00000 −0.321429
\(785\) 10.0000 20.0000i 0.356915 0.713831i
\(786\) 0 0
\(787\) 28.0000i 0.998092i 0.866575 + 0.499046i \(0.166316\pi\)
−0.866575 + 0.499046i \(0.833684\pi\)
\(788\) 26.0000i 0.926212i
\(789\) 0 0
\(790\) 8.00000 16.0000i 0.284627 0.569254i
\(791\) 48.0000 1.70668
\(792\) 0 0
\(793\) 10.0000i 0.355110i
\(794\) 6.00000 0.212932
\(795\) 0 0
\(796\)