Properties

Label 1900.2.l.b.1557.1
Level $1900$
Weight $2$
Character 1900.1557
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 4 x^{11} + 28 x^{10} - 64 x^{9} + 236 x^{8} - 420 x^{7} + 946 x^{6} - 1216 x^{5} + 1896 x^{4} - 1564 x^{3} + 2284 x^{2} - 1088 x + 1370\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1557.1
Root \(1.24060 + 1.01288i\) of defining polynomial
Character \(\chi\) \(=\) 1900.1557
Dual form 1900.2.l.b.493.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.25348 - 2.25348i) q^{3} +(1.48119 + 1.48119i) q^{7} +7.15633i q^{9} +O(q^{10})\) \(q+(-2.25348 - 2.25348i) q^{3} +(1.48119 + 1.48119i) q^{7} +7.15633i q^{9} +0.806063 q^{11} +(0.437032 + 0.437032i) q^{13} +(-3.15633 - 3.15633i) q^{17} +(1.81645 + 3.96239i) q^{19} -6.67568i q^{21} +(-1.86907 + 1.86907i) q^{23} +(9.36619 - 9.36619i) q^{27} -4.50696 q^{29} -6.67568i q^{31} +(-1.81645 - 1.81645i) q^{33} +(-5.29626 + 5.29626i) q^{37} -1.96968i q^{39} -11.1826i q^{41} +(3.86907 - 3.86907i) q^{43} +(-6.83146 - 6.83146i) q^{47} -2.61213i q^{49} +14.2254i q^{51} +(-8.92916 - 8.92916i) q^{53} +(4.83583 - 13.0225i) q^{57} +12.9308 q^{59} -2.15633 q^{61} +(-10.5999 + 10.5999i) q^{63} +(-4.94399 + 4.94399i) q^{67} +8.42380 q^{69} +3.04278i q^{71} +(6.19394 - 6.19394i) q^{73} +(1.19394 + 1.19394i) q^{77} -1.46417 q^{79} -20.7440 q^{81} +(-5.32487 + 5.32487i) q^{83} +(10.1563 + 10.1563i) q^{87} -14.2254 q^{89} +1.29466i q^{91} +(-15.0435 + 15.0435i) q^{93} +(-7.46498 + 7.46498i) q^{97} +5.76845i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{7} + O(q^{10}) \) \( 12q - 4q^{7} + 8q^{11} + 4q^{17} - 4q^{23} + 28q^{43} - 20q^{47} - 24q^{57} + 16q^{61} - 20q^{63} + 76q^{73} + 16q^{77} + 4q^{81} - 84q^{83} + 80q^{87} - 8q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.25348 2.25348i −1.30105 1.30105i −0.927687 0.373359i \(-0.878206\pi\)
−0.373359 0.927687i \(-0.621794\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.48119 + 1.48119i 0.559839 + 0.559839i 0.929261 0.369423i \(-0.120445\pi\)
−0.369423 + 0.929261i \(0.620445\pi\)
\(8\) 0 0
\(9\) 7.15633i 2.38544i
\(10\) 0 0
\(11\) 0.806063 0.243037 0.121519 0.992589i \(-0.461224\pi\)
0.121519 + 0.992589i \(0.461224\pi\)
\(12\) 0 0
\(13\) 0.437032 + 0.437032i 0.121211 + 0.121211i 0.765110 0.643899i \(-0.222684\pi\)
−0.643899 + 0.765110i \(0.722684\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.15633 3.15633i −0.765521 0.765521i 0.211793 0.977315i \(-0.432070\pi\)
−0.977315 + 0.211793i \(0.932070\pi\)
\(18\) 0 0
\(19\) 1.81645 + 3.96239i 0.416721 + 0.909034i
\(20\) 0 0
\(21\) 6.67568i 1.45675i
\(22\) 0 0
\(23\) −1.86907 + 1.86907i −0.389728 + 0.389728i −0.874590 0.484863i \(-0.838870\pi\)
0.484863 + 0.874590i \(0.338870\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 9.36619 9.36619i 1.80252 1.80252i
\(28\) 0 0
\(29\) −4.50696 −0.836921 −0.418460 0.908235i \(-0.637430\pi\)
−0.418460 + 0.908235i \(0.637430\pi\)
\(30\) 0 0
\(31\) 6.67568i 1.19899i −0.800380 0.599494i \(-0.795369\pi\)
0.800380 0.599494i \(-0.204631\pi\)
\(32\) 0 0
\(33\) −1.81645 1.81645i −0.316203 0.316203i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.29626 + 5.29626i −0.870700 + 0.870700i −0.992549 0.121848i \(-0.961118\pi\)
0.121848 + 0.992549i \(0.461118\pi\)
\(38\) 0 0
\(39\) 1.96968i 0.315402i
\(40\) 0 0
\(41\) 11.1826i 1.74643i −0.487332 0.873217i \(-0.662030\pi\)
0.487332 0.873217i \(-0.337970\pi\)
\(42\) 0 0
\(43\) 3.86907 3.86907i 0.590027 0.590027i −0.347611 0.937639i \(-0.613007\pi\)
0.937639 + 0.347611i \(0.113007\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.83146 6.83146i −0.996470 0.996470i 0.00352351 0.999994i \(-0.498878\pi\)
−0.999994 + 0.00352351i \(0.998878\pi\)
\(48\) 0 0
\(49\) 2.61213i 0.373161i
\(50\) 0 0
\(51\) 14.2254i 1.99196i
\(52\) 0 0
\(53\) −8.92916 8.92916i −1.22651 1.22651i −0.965274 0.261240i \(-0.915869\pi\)
−0.261240 0.965274i \(-0.584131\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.83583 13.0225i 0.640522 1.72487i
\(58\) 0 0
\(59\) 12.9308 1.68344 0.841721 0.539913i \(-0.181543\pi\)
0.841721 + 0.539913i \(0.181543\pi\)
\(60\) 0 0
\(61\) −2.15633 −0.276089 −0.138045 0.990426i \(-0.544082\pi\)
−0.138045 + 0.990426i \(0.544082\pi\)
\(62\) 0 0
\(63\) −10.5999 + 10.5999i −1.33546 + 1.33546i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.94399 + 4.94399i −0.604004 + 0.604004i −0.941373 0.337368i \(-0.890463\pi\)
0.337368 + 0.941373i \(0.390463\pi\)
\(68\) 0 0
\(69\) 8.42380 1.01411
\(70\) 0 0
\(71\) 3.04278i 0.361112i 0.983565 + 0.180556i \(0.0577897\pi\)
−0.983565 + 0.180556i \(0.942210\pi\)
\(72\) 0 0
\(73\) 6.19394 6.19394i 0.724945 0.724945i −0.244663 0.969608i \(-0.578677\pi\)
0.969608 + 0.244663i \(0.0786773\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.19394 + 1.19394i 0.136062 + 0.136062i
\(78\) 0 0
\(79\) −1.46417 −0.164732 −0.0823660 0.996602i \(-0.526248\pi\)
−0.0823660 + 0.996602i \(0.526248\pi\)
\(80\) 0 0
\(81\) −20.7440 −2.30489
\(82\) 0 0
\(83\) −5.32487 + 5.32487i −0.584480 + 0.584480i −0.936131 0.351651i \(-0.885620\pi\)
0.351651 + 0.936131i \(0.385620\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 10.1563 + 10.1563i 1.08887 + 1.08887i
\(88\) 0 0
\(89\) −14.2254 −1.50789 −0.753946 0.656937i \(-0.771852\pi\)
−0.753946 + 0.656937i \(0.771852\pi\)
\(90\) 0 0
\(91\) 1.29466i 0.135717i
\(92\) 0 0
\(93\) −15.0435 + 15.0435i −1.55994 + 1.55994i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −7.46498 + 7.46498i −0.757954 + 0.757954i −0.975950 0.217995i \(-0.930048\pi\)
0.217995 + 0.975950i \(0.430048\pi\)
\(98\) 0 0
\(99\) 5.76845i 0.579751i
\(100\) 0 0
\(101\) 4.08110 0.406085 0.203042 0.979170i \(-0.434917\pi\)
0.203042 + 0.979170i \(0.434917\pi\)
\(102\) 0 0
\(103\) 1.31110 + 1.31110i 0.129186 + 0.129186i 0.768743 0.639557i \(-0.220882\pi\)
−0.639557 + 0.768743i \(0.720882\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.11271 + 7.11271i −0.687612 + 0.687612i −0.961703 0.274092i \(-0.911623\pi\)
0.274092 + 0.961703i \(0.411623\pi\)
\(108\) 0 0
\(109\) −19.3225 −1.85076 −0.925379 0.379043i \(-0.876253\pi\)
−0.925379 + 0.379043i \(0.876253\pi\)
\(110\) 0 0
\(111\) 23.8700 2.26564
\(112\) 0 0
\(113\) 6.23865 + 6.23865i 0.586882 + 0.586882i 0.936786 0.349903i \(-0.113786\pi\)
−0.349903 + 0.936786i \(0.613786\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.12754 + 3.12754i −0.289141 + 0.289141i
\(118\) 0 0
\(119\) 9.35026i 0.857137i
\(120\) 0 0
\(121\) −10.3503 −0.940933
\(122\) 0 0
\(123\) −25.1998 + 25.1998i −2.27219 + 2.27219i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 9.80322 9.80322i 0.869895 0.869895i −0.122565 0.992460i \(-0.539112\pi\)
0.992460 + 0.122565i \(0.0391121\pi\)
\(128\) 0 0
\(129\) −17.4377 −1.53531
\(130\) 0 0
\(131\) −9.14903 −0.799355 −0.399677 0.916656i \(-0.630878\pi\)
−0.399677 + 0.916656i \(0.630878\pi\)
\(132\) 0 0
\(133\) −3.17856 + 8.55958i −0.275616 + 0.742209i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.18664 3.18664i −0.272253 0.272253i 0.557753 0.830007i \(-0.311663\pi\)
−0.830007 + 0.557753i \(0.811663\pi\)
\(138\) 0 0
\(139\) 15.2447i 1.29304i 0.762897 + 0.646520i \(0.223776\pi\)
−0.762897 + 0.646520i \(0.776224\pi\)
\(140\) 0 0
\(141\) 30.7891i 2.59291i
\(142\) 0 0
\(143\) 0.352275 + 0.352275i 0.0294587 + 0.0294587i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −5.88637 + 5.88637i −0.485500 + 0.485500i
\(148\) 0 0
\(149\) 15.3806i 1.26003i −0.776585 0.630013i \(-0.783050\pi\)
0.776585 0.630013i \(-0.216950\pi\)
\(150\) 0 0
\(151\) 5.21151i 0.424106i −0.977258 0.212053i \(-0.931985\pi\)
0.977258 0.212053i \(-0.0680150\pi\)
\(152\) 0 0
\(153\) 22.5877 22.5877i 1.82611 1.82611i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 10.2447 + 10.2447i 0.817618 + 0.817618i 0.985762 0.168145i \(-0.0537775\pi\)
−0.168145 + 0.985762i \(0.553778\pi\)
\(158\) 0 0
\(159\) 40.2433i 3.19150i
\(160\) 0 0
\(161\) −5.53690 −0.436369
\(162\) 0 0
\(163\) 10.4133 10.4133i 0.815630 0.815630i −0.169841 0.985471i \(-0.554326\pi\)
0.985471 + 0.169841i \(0.0543256\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.42220 4.42220i 0.342200 0.342200i −0.514994 0.857194i \(-0.672206\pi\)
0.857194 + 0.514994i \(0.172206\pi\)
\(168\) 0 0
\(169\) 12.6180i 0.970616i
\(170\) 0 0
\(171\) −28.3561 + 12.9991i −2.16845 + 0.994064i
\(172\) 0 0
\(173\) 4.06992 + 4.06992i 0.309431 + 0.309431i 0.844689 0.535258i \(-0.179786\pi\)
−0.535258 + 0.844689i \(0.679786\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −29.1392 29.1392i −2.19024 2.19024i
\(178\) 0 0
\(179\) −2.87327 −0.214758 −0.107379 0.994218i \(-0.534246\pi\)
−0.107379 + 0.994218i \(0.534246\pi\)
\(180\) 0 0
\(181\) 18.0278i 1.34000i −0.742362 0.669999i \(-0.766295\pi\)
0.742362 0.669999i \(-0.233705\pi\)
\(182\) 0 0
\(183\) 4.85923 + 4.85923i 0.359205 + 0.359205i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.54420 2.54420i −0.186050 0.186050i
\(188\) 0 0
\(189\) 27.7463 2.01825
\(190\) 0 0
\(191\) −4.43866 −0.321170 −0.160585 0.987022i \(-0.551338\pi\)
−0.160585 + 0.987022i \(0.551338\pi\)
\(192\) 0 0
\(193\) 4.42220 + 4.42220i 0.318317 + 0.318317i 0.848120 0.529804i \(-0.177734\pi\)
−0.529804 + 0.848120i \(0.677734\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.3806 10.3806i −0.739586 0.739586i 0.232912 0.972498i \(-0.425175\pi\)
−0.972498 + 0.232912i \(0.925175\pi\)
\(198\) 0 0
\(199\) 8.23743i 0.583936i −0.956428 0.291968i \(-0.905690\pi\)
0.956428 0.291968i \(-0.0943100\pi\)
\(200\) 0 0
\(201\) 22.2823 1.57167
\(202\) 0 0
\(203\) −6.67568 6.67568i −0.468541 0.468541i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −13.3757 13.3757i −0.929672 0.929672i
\(208\) 0 0
\(209\) 1.46417 + 3.19394i 0.101279 + 0.220929i
\(210\) 0 0
\(211\) 22.5348i 1.55136i 0.631128 + 0.775679i \(0.282592\pi\)
−0.631128 + 0.775679i \(0.717408\pi\)
\(212\) 0 0
\(213\) 6.85685 6.85685i 0.469824 0.469824i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 9.88798 9.88798i 0.671239 0.671239i
\(218\) 0 0
\(219\) −27.9158 −1.88637
\(220\) 0 0
\(221\) 2.75883i 0.185579i
\(222\) 0 0
\(223\) −13.4361 13.4361i −0.899749 0.899749i 0.0956650 0.995414i \(-0.469502\pi\)
−0.995414 + 0.0956650i \(0.969502\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.06992 4.06992i 0.270130 0.270130i −0.559022 0.829153i \(-0.688823\pi\)
0.829153 + 0.559022i \(0.188823\pi\)
\(228\) 0 0
\(229\) 4.46898i 0.295318i 0.989038 + 0.147659i \(0.0471738\pi\)
−0.989038 + 0.147659i \(0.952826\pi\)
\(230\) 0 0
\(231\) 5.38102i 0.354045i
\(232\) 0 0
\(233\) 11.1114 11.1114i 0.727933 0.727933i −0.242274 0.970208i \(-0.577893\pi\)
0.970208 + 0.242274i \(0.0778934\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 3.29948 + 3.29948i 0.214324 + 0.214324i
\(238\) 0 0
\(239\) 10.4387i 0.675221i −0.941286 0.337610i \(-0.890381\pi\)
0.941286 0.337610i \(-0.109619\pi\)
\(240\) 0 0
\(241\) 13.6353i 0.878328i −0.898407 0.439164i \(-0.855275\pi\)
0.898407 0.439164i \(-0.144725\pi\)
\(242\) 0 0
\(243\) 18.6476 + 18.6476i 1.19625 + 1.19625i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −0.937845 + 2.52553i −0.0596737 + 0.160696i
\(248\) 0 0
\(249\) 23.9989 1.52087
\(250\) 0 0
\(251\) 8.96239 0.565701 0.282850 0.959164i \(-0.408720\pi\)
0.282850 + 0.959164i \(0.408720\pi\)
\(252\) 0 0
\(253\) −1.50659 + 1.50659i −0.0947183 + 0.0947183i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.76043 + 6.76043i −0.421704 + 0.421704i −0.885790 0.464086i \(-0.846383\pi\)
0.464086 + 0.885790i \(0.346383\pi\)
\(258\) 0 0
\(259\) −15.6896 −0.974904
\(260\) 0 0
\(261\) 32.2532i 1.99643i
\(262\) 0 0
\(263\) 4.36248 4.36248i 0.269002 0.269002i −0.559696 0.828698i \(-0.689082\pi\)
0.828698 + 0.559696i \(0.189082\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 32.0567 + 32.0567i 1.96184 + 1.96184i
\(268\) 0 0
\(269\) −17.4377 −1.06320 −0.531598 0.846997i \(-0.678408\pi\)
−0.531598 + 0.846997i \(0.678408\pi\)
\(270\) 0 0
\(271\) −8.28233 −0.503116 −0.251558 0.967842i \(-0.580943\pi\)
−0.251558 + 0.967842i \(0.580943\pi\)
\(272\) 0 0
\(273\) 2.91748 2.91748i 0.176574 0.176574i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 9.80606 + 9.80606i 0.589189 + 0.589189i 0.937412 0.348223i \(-0.113215\pi\)
−0.348223 + 0.937412i \(0.613215\pi\)
\(278\) 0 0
\(279\) 47.7733 2.86011
\(280\) 0 0
\(281\) 5.66498i 0.337944i 0.985621 + 0.168972i \(0.0540448\pi\)
−0.985621 + 0.168972i \(0.945955\pi\)
\(282\) 0 0
\(283\) −4.18172 + 4.18172i −0.248577 + 0.248577i −0.820387 0.571809i \(-0.806242\pi\)
0.571809 + 0.820387i \(0.306242\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 16.5637 16.5637i 0.977721 0.977721i
\(288\) 0 0
\(289\) 2.92478i 0.172046i
\(290\) 0 0
\(291\) 33.6444 1.97227
\(292\) 0 0
\(293\) 7.35054 + 7.35054i 0.429423 + 0.429423i 0.888432 0.459009i \(-0.151795\pi\)
−0.459009 + 0.888432i \(0.651795\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 7.54974 7.54974i 0.438080 0.438080i
\(298\) 0 0
\(299\) −1.63368 −0.0944784
\(300\) 0 0
\(301\) 11.4617 0.660640
\(302\) 0 0
\(303\) −9.19667 9.19667i −0.528335 0.528335i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −23.3924 + 23.3924i −1.33508 + 1.33508i −0.434313 + 0.900762i \(0.643009\pi\)
−0.900762 + 0.434313i \(0.856991\pi\)
\(308\) 0 0
\(309\) 5.90905i 0.336154i
\(310\) 0 0
\(311\) 11.2546 0.638188 0.319094 0.947723i \(-0.396621\pi\)
0.319094 + 0.947723i \(0.396621\pi\)
\(312\) 0 0
\(313\) −14.5369 + 14.5369i −0.821674 + 0.821674i −0.986348 0.164674i \(-0.947343\pi\)
0.164674 + 0.986348i \(0.447343\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.87154 9.87154i 0.554441 0.554441i −0.373279 0.927719i \(-0.621766\pi\)
0.927719 + 0.373279i \(0.121766\pi\)
\(318\) 0 0
\(319\) −3.63289 −0.203403
\(320\) 0 0
\(321\) 32.0567 1.78923
\(322\) 0 0
\(323\) 6.77329 18.2399i 0.376876 1.01489i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 43.5428 + 43.5428i 2.40792 + 2.40792i
\(328\) 0 0
\(329\) 20.2374i 1.11573i
\(330\) 0 0
\(331\) 20.3110i 1.11639i −0.829709 0.558196i \(-0.811494\pi\)
0.829709 0.558196i \(-0.188506\pi\)
\(332\) 0 0
\(333\) −37.9018 37.9018i −2.07700 2.07700i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11.7892 + 11.7892i −0.642197 + 0.642197i −0.951095 0.308898i \(-0.900040\pi\)
0.308898 + 0.951095i \(0.400040\pi\)
\(338\) 0 0
\(339\) 28.1173i 1.52712i
\(340\) 0 0
\(341\) 5.38102i 0.291399i
\(342\) 0 0
\(343\) 14.2374 14.2374i 0.768749 0.768749i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.6302 18.6302i −1.00012 1.00012i −1.00000 0.000122901i \(-0.999961\pi\)
−0.000122901 1.00000i \(-0.500039\pi\)
\(348\) 0 0
\(349\) 21.0640i 1.12753i −0.825936 0.563764i \(-0.809353\pi\)
0.825936 0.563764i \(-0.190647\pi\)
\(350\) 0 0
\(351\) 8.18664 0.436971
\(352\) 0 0
\(353\) 1.99271 1.99271i 0.106061 0.106061i −0.652085 0.758146i \(-0.726105\pi\)
0.758146 + 0.652085i \(0.226105\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −21.0706 + 21.0706i −1.11517 + 1.11517i
\(358\) 0 0
\(359\) 28.6458i 1.51187i 0.654649 + 0.755933i \(0.272816\pi\)
−0.654649 + 0.755933i \(0.727184\pi\)
\(360\) 0 0
\(361\) −12.4010 + 14.3949i −0.652687 + 0.757628i
\(362\) 0 0
\(363\) 23.3241 + 23.3241i 1.22420 + 1.22420i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 12.1368 + 12.1368i 0.633536 + 0.633536i 0.948953 0.315417i \(-0.102144\pi\)
−0.315417 + 0.948953i \(0.602144\pi\)
\(368\) 0 0
\(369\) 80.0266 4.16602
\(370\) 0 0
\(371\) 26.4516i 1.37330i
\(372\) 0 0
\(373\) −16.4789 16.4789i −0.853245 0.853245i 0.137286 0.990531i \(-0.456162\pi\)
−0.990531 + 0.137286i \(0.956162\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.96968 1.96968i −0.101444 0.101444i
\(378\) 0 0
\(379\) 2.92834 0.150419 0.0752094 0.997168i \(-0.476037\pi\)
0.0752094 + 0.997168i \(0.476037\pi\)
\(380\) 0 0
\(381\) −44.1827 −2.26355
\(382\) 0 0
\(383\) −21.3381 21.3381i −1.09033 1.09033i −0.995493 0.0948343i \(-0.969768\pi\)
−0.0948343 0.995493i \(-0.530232\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 27.6883 + 27.6883i 1.40748 + 1.40748i
\(388\) 0 0
\(389\) 24.5647i 1.24548i 0.782430 + 0.622739i \(0.213980\pi\)
−0.782430 + 0.622739i \(0.786020\pi\)
\(390\) 0 0
\(391\) 11.7988 0.596689
\(392\) 0 0
\(393\) 20.6171 + 20.6171i 1.04000 + 1.04000i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5.23155 + 5.23155i 0.262564 + 0.262564i 0.826095 0.563531i \(-0.190557\pi\)
−0.563531 + 0.826095i \(0.690557\pi\)
\(398\) 0 0
\(399\) 26.4516 12.1260i 1.32424 0.607060i
\(400\) 0 0
\(401\) 18.7324i 0.935450i 0.883874 + 0.467725i \(0.154926\pi\)
−0.883874 + 0.467725i \(0.845074\pi\)
\(402\) 0 0
\(403\) 2.91748 2.91748i 0.145330 0.145330i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.26912 + 4.26912i −0.211613 + 0.211613i
\(408\) 0 0
\(409\) −14.9850 −0.740962 −0.370481 0.928840i \(-0.620807\pi\)
−0.370481 + 0.928840i \(0.620807\pi\)
\(410\) 0 0
\(411\) 14.3621i 0.708428i
\(412\) 0 0
\(413\) 19.1530 + 19.1530i 0.942456 + 0.942456i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 34.3536 34.3536i 1.68231 1.68231i
\(418\) 0 0
\(419\) 34.2882i 1.67509i −0.546369 0.837544i \(-0.683990\pi\)
0.546369 0.837544i \(-0.316010\pi\)
\(420\) 0 0
\(421\) 21.6056i 1.05299i 0.850177 + 0.526497i \(0.176495\pi\)
−0.850177 + 0.526497i \(0.823505\pi\)
\(422\) 0 0
\(423\) 48.8881 48.8881i 2.37702 2.37702i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.19394 3.19394i −0.154565 0.154565i
\(428\) 0 0
\(429\) 1.58769i 0.0766544i
\(430\) 0 0
\(431\) 19.7431i 0.950990i −0.879718 0.475495i \(-0.842269\pi\)
0.879718 0.475495i \(-0.157731\pi\)
\(432\) 0 0
\(433\) −11.0296 11.0296i −0.530047 0.530047i 0.390539 0.920586i \(-0.372288\pi\)
−0.920586 + 0.390539i \(0.872288\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −10.8010 4.01091i −0.516683 0.191868i
\(438\) 0 0
\(439\) 12.3628 0.590047 0.295023 0.955490i \(-0.404673\pi\)
0.295023 + 0.955490i \(0.404673\pi\)
\(440\) 0 0
\(441\) 18.6932 0.890154
\(442\) 0 0
\(443\) −11.1744 + 11.1744i −0.530913 + 0.530913i −0.920844 0.389931i \(-0.872499\pi\)
0.389931 + 0.920844i \(0.372499\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −34.6598 + 34.6598i −1.63935 + 1.63935i
\(448\) 0 0
\(449\) −2.90615 −0.137150 −0.0685748 0.997646i \(-0.521845\pi\)
−0.0685748 + 0.997646i \(0.521845\pi\)
\(450\) 0 0
\(451\) 9.01391i 0.424449i
\(452\) 0 0
\(453\) −11.7440 + 11.7440i −0.551782 + 0.551782i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −14.1490 14.1490i −0.661864 0.661864i 0.293955 0.955819i \(-0.405028\pi\)
−0.955819 + 0.293955i \(0.905028\pi\)
\(458\) 0 0
\(459\) −59.1255 −2.75974
\(460\) 0 0
\(461\) −18.6859 −0.870291 −0.435145 0.900360i \(-0.643303\pi\)
−0.435145 + 0.900360i \(0.643303\pi\)
\(462\) 0 0
\(463\) −0.906679 + 0.906679i −0.0421369 + 0.0421369i −0.727861 0.685724i \(-0.759486\pi\)
0.685724 + 0.727861i \(0.259486\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.49437 8.49437i −0.393072 0.393072i 0.482709 0.875781i \(-0.339653\pi\)
−0.875781 + 0.482709i \(0.839653\pi\)
\(468\) 0 0
\(469\) −14.6460 −0.676290
\(470\) 0 0
\(471\) 46.1725i 2.12752i
\(472\) 0 0
\(473\) 3.11871 3.11871i 0.143399 0.143399i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 63.8999 63.8999i 2.92578 2.92578i
\(478\) 0 0
\(479\) 15.9307i 0.727890i −0.931420 0.363945i \(-0.881430\pi\)
0.931420 0.363945i \(-0.118570\pi\)
\(480\) 0 0
\(481\) −4.62927 −0.211077
\(482\) 0 0
\(483\) 12.4773 + 12.4773i 0.567736 + 0.567736i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.02714 + 1.02714i −0.0465441 + 0.0465441i −0.729996 0.683452i \(-0.760478\pi\)
0.683452 + 0.729996i \(0.260478\pi\)
\(488\) 0 0
\(489\) −46.9321 −2.12234
\(490\) 0 0
\(491\) −16.1866 −0.730493 −0.365246 0.930911i \(-0.619015\pi\)
−0.365246 + 0.930911i \(0.619015\pi\)
\(492\) 0 0
\(493\) 14.2254 + 14.2254i 0.640681 + 0.640681i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.50696 + 4.50696i −0.202165 + 0.202165i
\(498\) 0 0
\(499\) 15.0943i 0.675713i 0.941198 + 0.337856i \(0.109702\pi\)
−0.941198 + 0.337856i \(0.890298\pi\)
\(500\) 0 0
\(501\) −19.9307 −0.890436
\(502\) 0 0
\(503\) 26.9429 26.9429i 1.20132 1.20132i 0.227559 0.973764i \(-0.426925\pi\)
0.973764 0.227559i \(-0.0730745\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −28.4344 + 28.4344i −1.26282 + 1.26282i
\(508\) 0 0
\(509\) 24.6484 1.09252 0.546261 0.837615i \(-0.316051\pi\)
0.546261 + 0.837615i \(0.316051\pi\)
\(510\) 0 0
\(511\) 18.3488 0.811705
\(512\) 0 0
\(513\) 54.1256 + 20.0993i 2.38971 + 0.887406i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −5.50659 5.50659i −0.242179 0.242179i
\(518\) 0 0
\(519\) 18.3430i 0.805167i
\(520\) 0 0
\(521\) 7.60481i 0.333173i 0.986027 + 0.166586i \(0.0532745\pi\)
−0.986027 + 0.166586i \(0.946726\pi\)
\(522\) 0 0
\(523\) 22.5645 + 22.5645i 0.986675 + 0.986675i 0.999912 0.0132372i \(-0.00421365\pi\)
−0.0132372 + 0.999912i \(0.504214\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.0706 + 21.0706i −0.917850 + 0.917850i
\(528\) 0 0
\(529\) 16.0132i 0.696225i
\(530\) 0 0
\(531\) 92.5367i 4.01575i
\(532\) 0 0
\(533\) 4.88717 4.88717i 0.211687 0.211687i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 6.47486 + 6.47486i 0.279411 + 0.279411i
\(538\) 0 0
\(539\) 2.10554i 0.0906920i
\(540\) 0 0
\(541\) 36.3331 1.56208 0.781041 0.624479i \(-0.214689\pi\)
0.781041 + 0.624479i \(0.214689\pi\)
\(542\) 0 0
\(543\) −40.6253 + 40.6253i −1.74340 + 1.74340i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −7.18103 + 7.18103i −0.307039 + 0.307039i −0.843760 0.536721i \(-0.819663\pi\)
0.536721 + 0.843760i \(0.319663\pi\)
\(548\) 0 0
\(549\) 15.4314i 0.658595i
\(550\) 0 0
\(551\) −8.18664 17.8583i −0.348763 0.760790i
\(552\) 0 0
\(553\) −2.16872 2.16872i −0.0922234 0.0922234i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −24.3054 24.3054i −1.02985 1.02985i −0.999541 0.0303105i \(-0.990350\pi\)
−0.0303105 0.999541i \(-0.509650\pi\)
\(558\) 0 0
\(559\) 3.38181 0.143035
\(560\) 0 0
\(561\) 11.4666i 0.484120i
\(562\) 0 0
\(563\) 15.7743 + 15.7743i 0.664809 + 0.664809i 0.956510 0.291700i \(-0.0942210\pi\)
−0.291700 + 0.956510i \(0.594221\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −30.7259 30.7259i −1.29037 1.29037i
\(568\) 0 0
\(569\) −4.45189 −0.186633 −0.0933164 0.995637i \(-0.529747\pi\)
−0.0933164 + 0.995637i \(0.529747\pi\)
\(570\) 0 0
\(571\) 29.6834 1.24221 0.621105 0.783727i \(-0.286684\pi\)
0.621105 + 0.783727i \(0.286684\pi\)
\(572\) 0 0
\(573\) 10.0024 + 10.0024i 0.417857 + 0.417857i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 12.7235 + 12.7235i 0.529688 + 0.529688i 0.920479 0.390791i \(-0.127799\pi\)
−0.390791 + 0.920479i \(0.627799\pi\)
\(578\) 0 0
\(579\) 19.9307i 0.828290i
\(580\) 0 0
\(581\) −15.7743 −0.654430
\(582\) 0 0
\(583\) −7.19747 7.19747i −0.298089 0.298089i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.48849 2.48849i −0.102711 0.102711i 0.653884 0.756595i \(-0.273138\pi\)
−0.756595 + 0.653884i \(0.773138\pi\)
\(588\) 0 0
\(589\) 26.4516 12.1260i 1.08992 0.499643i
\(590\) 0 0
\(591\) 46.7848i 1.92447i
\(592\) 0 0
\(593\) 2.78892 2.78892i 0.114527 0.114527i −0.647521 0.762048i \(-0.724194\pi\)
0.762048 + 0.647521i \(0.224194\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −18.5629 + 18.5629i −0.759727 + 0.759727i
\(598\) 0 0
\(599\) −46.1947 −1.88746 −0.943732 0.330711i \(-0.892712\pi\)
−0.943732 + 0.330711i \(0.892712\pi\)
\(600\) 0 0
\(601\) 28.8714i 1.17769i 0.808246 + 0.588845i \(0.200417\pi\)
−0.808246 + 0.588845i \(0.799583\pi\)
\(602\) 0 0
\(603\) −35.3808 35.3808i −1.44082 1.44082i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 15.5365 15.5365i 0.630608 0.630608i −0.317613 0.948220i \(-0.602881\pi\)
0.948220 + 0.317613i \(0.102881\pi\)
\(608\) 0 0
\(609\) 30.0870i 1.21919i
\(610\) 0 0
\(611\) 5.97113i 0.241566i
\(612\) 0 0
\(613\) −23.4241 + 23.4241i −0.946089 + 0.946089i −0.998619 0.0525301i \(-0.983271\pi\)
0.0525301 + 0.998619i \(0.483271\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16.4558 + 16.4558i 0.662486 + 0.662486i 0.955965 0.293480i \(-0.0948133\pi\)
−0.293480 + 0.955965i \(0.594813\pi\)
\(618\) 0 0
\(619\) 41.2711i 1.65882i 0.558637 + 0.829412i \(0.311324\pi\)
−0.558637 + 0.829412i \(0.688676\pi\)
\(620\) 0 0
\(621\) 35.0121i 1.40499i
\(622\) 0 0
\(623\) −21.0706 21.0706i −0.844176 0.844176i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3.89799 10.4969i 0.155671 0.419207i
\(628\) 0 0
\(629\) 33.4335 1.33308
\(630\) 0 0
\(631\) 27.1939 1.08257 0.541287 0.840838i \(-0.317937\pi\)
0.541287 + 0.840838i \(0.317937\pi\)
\(632\) 0 0
\(633\) 50.7816 50.7816i 2.01839 2.01839i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.14158 1.14158i 0.0452311 0.0452311i
\(638\) 0 0
\(639\) −21.7752 −0.861412
\(640\) 0 0
\(641\) 4.96042i 0.195925i −0.995190 0.0979625i \(-0.968767\pi\)
0.995190 0.0979625i \(-0.0312325\pi\)
\(642\) 0 0
\(643\) −20.3176 + 20.3176i −0.801247 + 0.801247i −0.983290 0.182044i \(-0.941729\pi\)
0.182044 + 0.983290i \(0.441729\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.16125 8.16125i −0.320852 0.320852i 0.528242 0.849094i \(-0.322851\pi\)
−0.849094 + 0.528242i \(0.822851\pi\)
\(648\) 0 0
\(649\) 10.4230 0.409139
\(650\) 0 0
\(651\) −44.5647 −1.74663
\(652\) 0 0
\(653\) 23.4387 23.4387i 0.917226 0.917226i −0.0796012 0.996827i \(-0.525365\pi\)
0.996827 + 0.0796012i \(0.0253647\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 44.3258 + 44.3258i 1.72932 + 1.72932i
\(658\) 0 0
\(659\) 6.84519 0.266651 0.133325 0.991072i \(-0.457434\pi\)
0.133325 + 0.991072i \(0.457434\pi\)
\(660\) 0 0
\(661\) 13.0674i 0.508263i −0.967170 0.254131i \(-0.918210\pi\)
0.967170 0.254131i \(-0.0817896\pi\)
\(662\) 0 0
\(663\) −6.21696 + 6.21696i −0.241447 + 0.241447i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.42380 8.42380i 0.326171 0.326171i
\(668\) 0 0
\(669\) 60.5560i 2.34123i
\(670\) 0 0
\(671\) −1.73813 −0.0671000
\(672\) 0 0
\(673\) 9.16699 + 9.16699i 0.353361 + 0.353361i 0.861359 0.507997i \(-0.169614\pi\)
−0.507997 + 0.861359i \(0.669614\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.13824 4.13824i 0.159046 0.159046i −0.623098 0.782144i \(-0.714126\pi\)
0.782144 + 0.623098i \(0.214126\pi\)
\(678\) 0 0
\(679\) −22.1142 −0.848665
\(680\) 0 0
\(681\) −18.3430 −0.702904
\(682\) 0 0
\(683\) 34.7907 + 34.7907i 1.33123 + 1.33123i 0.904273 + 0.426956i \(0.140414\pi\)
0.426956 + 0.904273i \(0.359586\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 10.0707 10.0707i 0.384223 0.384223i
\(688\) 0 0
\(689\) 7.80465i 0.297333i
\(690\) 0 0
\(691\) 11.1939 0.425837 0.212919 0.977070i \(-0.431703\pi\)
0.212919 + 0.977070i \(0.431703\pi\)
\(692\) 0 0
\(693\) −8.54420 + 8.54420i −0.324567 + 0.324567i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −35.2960 + 35.2960i −1.33693 + 1.33693i
\(698\) 0 0
\(699\) −50.0787 −1.89415
\(700\) 0 0
\(701\) −1.75386 −0.0662425 −0.0331213 0.999451i \(-0.510545\pi\)
−0.0331213 + 0.999451i \(0.510545\pi\)
\(702\) 0 0
\(703\) −30.6062 11.3655i −1.15434 0.428657i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.04491 + 6.04491i 0.227342 + 0.227342i
\(708\) 0 0
\(709\) 27.4109i 1.02944i −0.857359 0.514719i \(-0.827896\pi\)
0.857359 0.514719i \(-0.172104\pi\)
\(710\) 0 0
\(711\) 10.4781i 0.392959i
\(712\) 0 0
\(713\) 12.4773 + 12.4773i 0.467278 + 0.467278i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −23.5233 + 23.5233i −0.878493 + 0.878493i
\(718\) 0 0
\(719\) 18.2170i 0.679378i 0.940538 + 0.339689i \(0.110322\pi\)
−0.940538 + 0.339689i \(0.889678\pi\)
\(720\) 0 0
\(721\) 3.88397i 0.144647i
\(722\) 0 0
\(723\) −30.7269 + 30.7269i −1.14274 + 1.14274i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.28726 2.28726i −0.0848297 0.0848297i 0.663419 0.748248i \(-0.269105\pi\)
−0.748248 + 0.663419i \(0.769105\pi\)
\(728\) 0 0
\(729\) 21.8119i 0.807850i
\(730\) 0 0
\(731\) −24.4241 −0.903357
\(732\) 0 0
\(733\) −25.8872 + 25.8872i −0.956164 + 0.956164i −0.999079 0.0429145i \(-0.986336\pi\)
0.0429145 + 0.999079i \(0.486336\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.98517 + 3.98517i −0.146796 + 0.146796i
\(738\) 0 0
\(739\) 48.8021i 1.79521i −0.440797 0.897607i \(-0.645304\pi\)
0.440797 0.897607i \(-0.354696\pi\)
\(740\) 0 0
\(741\) 7.80465 3.57782i 0.286711 0.131435i
\(742\) 0 0
\(743\) 0.674864 + 0.674864i 0.0247583 + 0.0247583i 0.719378 0.694619i \(-0.244427\pi\)
−0.694619 + 0.719378i \(0.744427\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −38.1065 38.1065i −1.39424 1.39424i
\(748\) 0 0
\(749\) −21.0706 −0.769903
\(750\) 0 0
\(751\) 11.7727i 0.429593i −0.976659 0.214797i \(-0.931091\pi\)
0.976659 0.214797i \(-0.0689089\pi\)
\(752\) 0 0
\(753\) −20.1965 20.1965i −0.736003 0.736003i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −36.0943 36.0943i −1.31187 1.31187i −0.920037 0.391832i \(-0.871841\pi\)
−0.391832 0.920037i \(-0.628159\pi\)
\(758\) 0 0
\(759\) 6.79012 0.246466
\(760\) 0 0
\(761\) −18.6194 −0.674953 −0.337477 0.941334i \(-0.609573\pi\)
−0.337477 + 0.941334i \(0.609573\pi\)
\(762\) 0 0
\(763\) −28.6203 28.6203i −1.03613 1.03613i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.65115 + 5.65115i 0.204051 + 0.204051i
\(768\) 0 0
\(769\) 23.5720i 0.850027i −0.905187 0.425013i \(-0.860269\pi\)
0.905187 0.425013i \(-0.139731\pi\)
\(770\) 0 0
\(771\) 30.4690 1.09731
\(772\) 0 0
\(773\) 27.7627 + 27.7627i 0.998556 + 0.998556i 0.999999 0.00144323i \(-0.000459394\pi\)
−0.00144323 + 0.999999i \(0.500459\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 35.3561 + 35.3561i 1.26839 + 1.26839i
\(778\) 0 0
\(779\) 44.3099 20.3127i 1.58757 0.727776i
\(780\) 0 0
\(781\) 2.45268i 0.0877637i
\(782\) 0 0
\(783\) −42.2130 + 42.2130i −1.50857 + 1.50857i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 20.7019 20.7019i 0.737943 0.737943i −0.234237 0.972180i \(-0.575259\pi\)
0.972180 + 0.234237i \(0.0752591\pi\)
\(788\) 0 0
\(789\) −19.6615 −0.699968
\(790\) 0 0
\(791\) 18.4813i 0.657119i
\(792\) 0 0
\(793\) −0.942383 0.942383i −0.0334650 0.0334650i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.81471 8.81471i 0.312233 0.312233i −0.533541 0.845774i \(-0.679139\pi\)
0.845774 + 0.533541i \(0.179139\pi\)
\(798\) 0 0
\(799\) 43.1246i 1.52564i
\(800\) 0 0
\(801\) 101.802i 3.59699i
\(802\) 0 0
\(803\) 4.99271