Properties

Label 4020.2.g.c.1609.20
Level 4020
Weight 2
Character 4020.1609
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(38\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1609.20
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000i q^{3}\) \(+(-2.23543 - 0.0533841i) q^{5}\) \(+4.50874i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000i q^{3}\) \(+(-2.23543 - 0.0533841i) q^{5}\) \(+4.50874i q^{7}\) \(-1.00000 q^{9}\) \(+0.971195 q^{11}\) \(-1.87337i q^{13}\) \(+(0.0533841 - 2.23543i) q^{15}\) \(+5.03013i q^{17}\) \(+1.77783 q^{19}\) \(-4.50874 q^{21}\) \(+5.44812i q^{23}\) \(+(4.99430 + 0.238673i) q^{25}\) \(-1.00000i q^{27}\) \(+3.85056 q^{29}\) \(+5.05491 q^{31}\) \(+0.971195i q^{33}\) \(+(0.240695 - 10.0790i) q^{35}\) \(+10.1759i q^{37}\) \(+1.87337 q^{39}\) \(+5.79630 q^{41}\) \(+8.65164i q^{43}\) \(+(2.23543 + 0.0533841i) q^{45}\) \(-1.27397i q^{47}\) \(-13.3288 q^{49}\) \(-5.03013 q^{51}\) \(-4.85441i q^{53}\) \(+(-2.17104 - 0.0518463i) q^{55}\) \(+1.77783i q^{57}\) \(+0.801017 q^{59}\) \(-9.97361 q^{61}\) \(-4.50874i q^{63}\) \(+(-0.100008 + 4.18779i) q^{65}\) \(+1.00000i q^{67}\) \(-5.44812 q^{69}\) \(-12.3349 q^{71}\) \(+9.73950i q^{73}\) \(+(-0.238673 + 4.99430i) q^{75}\) \(+4.37887i q^{77}\) \(+5.68322 q^{79}\) \(+1.00000 q^{81}\) \(-16.8058i q^{83}\) \(+(0.268529 - 11.2445i) q^{85}\) \(+3.85056i q^{87}\) \(-16.4007 q^{89}\) \(+8.44655 q^{91}\) \(+5.05491i q^{93}\) \(+(-3.97422 - 0.0949080i) q^{95}\) \(+11.3278i q^{97}\) \(-0.971195 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) −2.23543 0.0533841i −0.999715 0.0238741i
\(6\) 0 0
\(7\) 4.50874i 1.70414i 0.523424 + 0.852072i \(0.324654\pi\)
−0.523424 + 0.852072i \(0.675346\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 0.971195 0.292826 0.146413 0.989224i \(-0.453227\pi\)
0.146413 + 0.989224i \(0.453227\pi\)
\(12\) 0 0
\(13\) 1.87337i 0.519580i −0.965665 0.259790i \(-0.916347\pi\)
0.965665 0.259790i \(-0.0836533\pi\)
\(14\) 0 0
\(15\) 0.0533841 2.23543i 0.0137837 0.577186i
\(16\) 0 0
\(17\) 5.03013i 1.21999i 0.792407 + 0.609993i \(0.208828\pi\)
−0.792407 + 0.609993i \(0.791172\pi\)
\(18\) 0 0
\(19\) 1.77783 0.407863 0.203932 0.978985i \(-0.434628\pi\)
0.203932 + 0.978985i \(0.434628\pi\)
\(20\) 0 0
\(21\) −4.50874 −0.983888
\(22\) 0 0
\(23\) 5.44812i 1.13601i 0.823024 + 0.568006i \(0.192285\pi\)
−0.823024 + 0.568006i \(0.807715\pi\)
\(24\) 0 0
\(25\) 4.99430 + 0.238673i 0.998860 + 0.0477345i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 3.85056 0.715031 0.357515 0.933907i \(-0.383624\pi\)
0.357515 + 0.933907i \(0.383624\pi\)
\(30\) 0 0
\(31\) 5.05491 0.907889 0.453945 0.891030i \(-0.350016\pi\)
0.453945 + 0.891030i \(0.350016\pi\)
\(32\) 0 0
\(33\) 0.971195i 0.169063i
\(34\) 0 0
\(35\) 0.240695 10.0790i 0.0406849 1.70366i
\(36\) 0 0
\(37\) 10.1759i 1.67291i 0.548036 + 0.836455i \(0.315376\pi\)
−0.548036 + 0.836455i \(0.684624\pi\)
\(38\) 0 0
\(39\) 1.87337 0.299980
\(40\) 0 0
\(41\) 5.79630 0.905230 0.452615 0.891706i \(-0.350491\pi\)
0.452615 + 0.891706i \(0.350491\pi\)
\(42\) 0 0
\(43\) 8.65164i 1.31936i 0.751546 + 0.659681i \(0.229309\pi\)
−0.751546 + 0.659681i \(0.770691\pi\)
\(44\) 0 0
\(45\) 2.23543 + 0.0533841i 0.333238 + 0.00795803i
\(46\) 0 0
\(47\) 1.27397i 0.185827i −0.995674 0.0929137i \(-0.970382\pi\)
0.995674 0.0929137i \(-0.0296181\pi\)
\(48\) 0 0
\(49\) −13.3288 −1.90411
\(50\) 0 0
\(51\) −5.03013 −0.704359
\(52\) 0 0
\(53\) 4.85441i 0.666805i −0.942785 0.333402i \(-0.891803\pi\)
0.942785 0.333402i \(-0.108197\pi\)
\(54\) 0 0
\(55\) −2.17104 0.0518463i −0.292743 0.00699096i
\(56\) 0 0
\(57\) 1.77783i 0.235480i
\(58\) 0 0
\(59\) 0.801017 0.104283 0.0521417 0.998640i \(-0.483395\pi\)
0.0521417 + 0.998640i \(0.483395\pi\)
\(60\) 0 0
\(61\) −9.97361 −1.27699 −0.638495 0.769626i \(-0.720443\pi\)
−0.638495 + 0.769626i \(0.720443\pi\)
\(62\) 0 0
\(63\) 4.50874i 0.568048i
\(64\) 0 0
\(65\) −0.100008 + 4.18779i −0.0124045 + 0.519432i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −5.44812 −0.655877
\(70\) 0 0
\(71\) −12.3349 −1.46388 −0.731941 0.681368i \(-0.761385\pi\)
−0.731941 + 0.681368i \(0.761385\pi\)
\(72\) 0 0
\(73\) 9.73950i 1.13992i 0.821672 + 0.569961i \(0.193042\pi\)
−0.821672 + 0.569961i \(0.806958\pi\)
\(74\) 0 0
\(75\) −0.238673 + 4.99430i −0.0275596 + 0.576692i
\(76\) 0 0
\(77\) 4.37887i 0.499018i
\(78\) 0 0
\(79\) 5.68322 0.639413 0.319706 0.947517i \(-0.396416\pi\)
0.319706 + 0.947517i \(0.396416\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 16.8058i 1.84467i −0.386388 0.922336i \(-0.626277\pi\)
0.386388 0.922336i \(-0.373723\pi\)
\(84\) 0 0
\(85\) 0.268529 11.2445i 0.0291260 1.21964i
\(86\) 0 0
\(87\) 3.85056i 0.412823i
\(88\) 0 0
\(89\) −16.4007 −1.73847 −0.869235 0.494399i \(-0.835388\pi\)
−0.869235 + 0.494399i \(0.835388\pi\)
\(90\) 0 0
\(91\) 8.44655 0.885439
\(92\) 0 0
\(93\) 5.05491i 0.524170i
\(94\) 0 0
\(95\) −3.97422 0.0949080i −0.407747 0.00973736i
\(96\) 0 0
\(97\) 11.3278i 1.15017i 0.818095 + 0.575083i \(0.195030\pi\)
−0.818095 + 0.575083i \(0.804970\pi\)
\(98\) 0 0
\(99\) −0.971195 −0.0976087
\(100\) 0 0
\(101\) 8.75522 0.871177 0.435589 0.900146i \(-0.356540\pi\)
0.435589 + 0.900146i \(0.356540\pi\)
\(102\) 0 0
\(103\) 2.99346i 0.294954i −0.989065 0.147477i \(-0.952885\pi\)
0.989065 0.147477i \(-0.0471153\pi\)
\(104\) 0 0
\(105\) 10.0790 + 0.240695i 0.983608 + 0.0234894i
\(106\) 0 0
\(107\) 1.83928i 0.177810i 0.996040 + 0.0889052i \(0.0283368\pi\)
−0.996040 + 0.0889052i \(0.971663\pi\)
\(108\) 0 0
\(109\) 11.2793 1.08036 0.540179 0.841550i \(-0.318356\pi\)
0.540179 + 0.841550i \(0.318356\pi\)
\(110\) 0 0
\(111\) −10.1759 −0.965855
\(112\) 0 0
\(113\) 12.1469i 1.14269i −0.820711 0.571344i \(-0.806422\pi\)
0.820711 0.571344i \(-0.193578\pi\)
\(114\) 0 0
\(115\) 0.290843 12.1789i 0.0271212 1.13569i
\(116\) 0 0
\(117\) 1.87337i 0.173193i
\(118\) 0 0
\(119\) −22.6796 −2.07903
\(120\) 0 0
\(121\) −10.0568 −0.914253
\(122\) 0 0
\(123\) 5.79630i 0.522635i
\(124\) 0 0
\(125\) −11.1517 0.800152i −0.997436 0.0715678i
\(126\) 0 0
\(127\) 21.5167i 1.90930i −0.297730 0.954650i \(-0.596229\pi\)
0.297730 0.954650i \(-0.403771\pi\)
\(128\) 0 0
\(129\) −8.65164 −0.761734
\(130\) 0 0
\(131\) 19.7230 1.72321 0.861603 0.507582i \(-0.169461\pi\)
0.861603 + 0.507582i \(0.169461\pi\)
\(132\) 0 0
\(133\) 8.01580i 0.695058i
\(134\) 0 0
\(135\) −0.0533841 + 2.23543i −0.00459457 + 0.192395i
\(136\) 0 0
\(137\) 17.0580i 1.45737i 0.684851 + 0.728683i \(0.259867\pi\)
−0.684851 + 0.728683i \(0.740133\pi\)
\(138\) 0 0
\(139\) 6.94806 0.589327 0.294663 0.955601i \(-0.404792\pi\)
0.294663 + 0.955601i \(0.404792\pi\)
\(140\) 0 0
\(141\) 1.27397 0.107287
\(142\) 0 0
\(143\) 1.81941i 0.152147i
\(144\) 0 0
\(145\) −8.60766 0.205558i −0.714827 0.0170707i
\(146\) 0 0
\(147\) 13.3288i 1.09934i
\(148\) 0 0
\(149\) −17.4588 −1.43028 −0.715142 0.698979i \(-0.753638\pi\)
−0.715142 + 0.698979i \(0.753638\pi\)
\(150\) 0 0
\(151\) −6.90694 −0.562079 −0.281040 0.959696i \(-0.590679\pi\)
−0.281040 + 0.959696i \(0.590679\pi\)
\(152\) 0 0
\(153\) 5.03013i 0.406662i
\(154\) 0 0
\(155\) −11.2999 0.269852i −0.907630 0.0216750i
\(156\) 0 0
\(157\) 9.22557i 0.736281i 0.929770 + 0.368141i \(0.120005\pi\)
−0.929770 + 0.368141i \(0.879995\pi\)
\(158\) 0 0
\(159\) 4.85441 0.384980
\(160\) 0 0
\(161\) −24.5642 −1.93593
\(162\) 0 0
\(163\) 25.2659i 1.97897i −0.144620 0.989487i \(-0.546196\pi\)
0.144620 0.989487i \(-0.453804\pi\)
\(164\) 0 0
\(165\) 0.0518463 2.17104i 0.00403623 0.169015i
\(166\) 0 0
\(167\) 0.666796i 0.0515982i −0.999667 0.0257991i \(-0.991787\pi\)
0.999667 0.0257991i \(-0.00821302\pi\)
\(168\) 0 0
\(169\) 9.49048 0.730037
\(170\) 0 0
\(171\) −1.77783 −0.135954
\(172\) 0 0
\(173\) 16.8775i 1.28317i −0.767052 0.641585i \(-0.778277\pi\)
0.767052 0.641585i \(-0.221723\pi\)
\(174\) 0 0
\(175\) −1.07611 + 22.5180i −0.0813466 + 1.70220i
\(176\) 0 0
\(177\) 0.801017i 0.0602081i
\(178\) 0 0
\(179\) −25.1781 −1.88190 −0.940949 0.338549i \(-0.890064\pi\)
−0.940949 + 0.338549i \(0.890064\pi\)
\(180\) 0 0
\(181\) 4.21845 0.313555 0.156777 0.987634i \(-0.449890\pi\)
0.156777 + 0.987634i \(0.449890\pi\)
\(182\) 0 0
\(183\) 9.97361i 0.737271i
\(184\) 0 0
\(185\) 0.543232 22.7475i 0.0399392 1.67243i
\(186\) 0 0
\(187\) 4.88524i 0.357244i
\(188\) 0 0
\(189\) 4.50874 0.327963
\(190\) 0 0
\(191\) −19.3167 −1.39771 −0.698854 0.715264i \(-0.746306\pi\)
−0.698854 + 0.715264i \(0.746306\pi\)
\(192\) 0 0
\(193\) 22.0344i 1.58607i 0.609174 + 0.793036i \(0.291501\pi\)
−0.609174 + 0.793036i \(0.708499\pi\)
\(194\) 0 0
\(195\) −4.18779 0.100008i −0.299894 0.00716174i
\(196\) 0 0
\(197\) 23.8537i 1.69951i −0.527179 0.849754i \(-0.676750\pi\)
0.527179 0.849754i \(-0.323250\pi\)
\(198\) 0 0
\(199\) −5.29391 −0.375276 −0.187638 0.982238i \(-0.560083\pi\)
−0.187638 + 0.982238i \(0.560083\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 17.3612i 1.21852i
\(204\) 0 0
\(205\) −12.9572 0.309430i −0.904972 0.0216115i
\(206\) 0 0
\(207\) 5.44812i 0.378671i
\(208\) 0 0
\(209\) 1.72662 0.119433
\(210\) 0 0
\(211\) 4.36599 0.300567 0.150283 0.988643i \(-0.451981\pi\)
0.150283 + 0.988643i \(0.451981\pi\)
\(212\) 0 0
\(213\) 12.3349i 0.845172i
\(214\) 0 0
\(215\) 0.461859 19.3401i 0.0314986 1.31899i
\(216\) 0 0
\(217\) 22.7913i 1.54717i
\(218\) 0 0
\(219\) −9.73950 −0.658134
\(220\) 0 0
\(221\) 9.42330 0.633880
\(222\) 0 0
\(223\) 5.00754i 0.335329i 0.985844 + 0.167665i \(0.0536226\pi\)
−0.985844 + 0.167665i \(0.946377\pi\)
\(224\) 0 0
\(225\) −4.99430 0.238673i −0.332953 0.0159115i
\(226\) 0 0
\(227\) 18.3845i 1.22022i −0.792316 0.610111i \(-0.791125\pi\)
0.792316 0.610111i \(-0.208875\pi\)
\(228\) 0 0
\(229\) −24.6317 −1.62771 −0.813855 0.581068i \(-0.802635\pi\)
−0.813855 + 0.581068i \(0.802635\pi\)
\(230\) 0 0
\(231\) −4.37887 −0.288108
\(232\) 0 0
\(233\) 8.36272i 0.547860i 0.961750 + 0.273930i \(0.0883237\pi\)
−0.961750 + 0.273930i \(0.911676\pi\)
\(234\) 0 0
\(235\) −0.0680096 + 2.84787i −0.00443646 + 0.185774i
\(236\) 0 0
\(237\) 5.68322i 0.369165i
\(238\) 0 0
\(239\) −22.6245 −1.46346 −0.731730 0.681595i \(-0.761287\pi\)
−0.731730 + 0.681595i \(0.761287\pi\)
\(240\) 0 0
\(241\) 16.5883 1.06854 0.534272 0.845313i \(-0.320586\pi\)
0.534272 + 0.845313i \(0.320586\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 29.7955 + 0.711543i 1.90357 + 0.0454588i
\(246\) 0 0
\(247\) 3.33054i 0.211917i
\(248\) 0 0
\(249\) 16.8058 1.06502
\(250\) 0 0
\(251\) 30.0957 1.89963 0.949813 0.312819i \(-0.101273\pi\)
0.949813 + 0.312819i \(0.101273\pi\)
\(252\) 0 0
\(253\) 5.29119i 0.332654i
\(254\) 0 0
\(255\) 11.2445 + 0.268529i 0.704158 + 0.0168159i
\(256\) 0 0
\(257\) 11.4033i 0.711319i −0.934616 0.355659i \(-0.884256\pi\)
0.934616 0.355659i \(-0.115744\pi\)
\(258\) 0 0
\(259\) −45.8806 −2.85088
\(260\) 0 0
\(261\) −3.85056 −0.238344
\(262\) 0 0
\(263\) 20.9006i 1.28879i 0.764695 + 0.644393i \(0.222890\pi\)
−0.764695 + 0.644393i \(0.777110\pi\)
\(264\) 0 0
\(265\) −0.259148 + 10.8517i −0.0159194 + 0.666615i
\(266\) 0 0
\(267\) 16.4007i 1.00371i
\(268\) 0 0
\(269\) −6.93394 −0.422770 −0.211385 0.977403i \(-0.567797\pi\)
−0.211385 + 0.977403i \(0.567797\pi\)
\(270\) 0 0
\(271\) −2.74661 −0.166845 −0.0834223 0.996514i \(-0.526585\pi\)
−0.0834223 + 0.996514i \(0.526585\pi\)
\(272\) 0 0
\(273\) 8.44655i 0.511209i
\(274\) 0 0
\(275\) 4.85044 + 0.231798i 0.292492 + 0.0139779i
\(276\) 0 0
\(277\) 25.9747i 1.56067i 0.625362 + 0.780334i \(0.284951\pi\)
−0.625362 + 0.780334i \(0.715049\pi\)
\(278\) 0 0
\(279\) −5.05491 −0.302630
\(280\) 0 0
\(281\) 26.2101 1.56356 0.781782 0.623552i \(-0.214311\pi\)
0.781782 + 0.623552i \(0.214311\pi\)
\(282\) 0 0
\(283\) 23.3253i 1.38654i 0.720677 + 0.693271i \(0.243831\pi\)
−0.720677 + 0.693271i \(0.756169\pi\)
\(284\) 0 0
\(285\) 0.0949080 3.97422i 0.00562186 0.235413i
\(286\) 0 0
\(287\) 26.1340i 1.54264i
\(288\) 0 0
\(289\) −8.30221 −0.488365
\(290\) 0 0
\(291\) −11.3278 −0.664049
\(292\) 0 0
\(293\) 17.1915i 1.00434i 0.864770 + 0.502168i \(0.167464\pi\)
−0.864770 + 0.502168i \(0.832536\pi\)
\(294\) 0 0
\(295\) −1.79062 0.0427615i −0.104254 0.00248967i
\(296\) 0 0
\(297\) 0.971195i 0.0563544i
\(298\) 0 0
\(299\) 10.2064 0.590249
\(300\) 0 0
\(301\) −39.0080 −2.24838
\(302\) 0 0
\(303\) 8.75522i 0.502974i
\(304\) 0 0
\(305\) 22.2953 + 0.532432i 1.27663 + 0.0304870i
\(306\) 0 0
\(307\) 20.2599i 1.15629i 0.815934 + 0.578145i \(0.196223\pi\)
−0.815934 + 0.578145i \(0.803777\pi\)
\(308\) 0 0
\(309\) 2.99346 0.170292
\(310\) 0 0
\(311\) −11.1037 −0.629632 −0.314816 0.949153i \(-0.601943\pi\)
−0.314816 + 0.949153i \(0.601943\pi\)
\(312\) 0 0
\(313\) 1.11630i 0.0630967i −0.999502 0.0315484i \(-0.989956\pi\)
0.999502 0.0315484i \(-0.0100438\pi\)
\(314\) 0 0
\(315\) −0.240695 + 10.0790i −0.0135616 + 0.567886i
\(316\) 0 0
\(317\) 2.89619i 0.162666i −0.996687 0.0813331i \(-0.974082\pi\)
0.996687 0.0813331i \(-0.0259178\pi\)
\(318\) 0 0
\(319\) 3.73964 0.209380
\(320\) 0 0
\(321\) −1.83928 −0.102659
\(322\) 0 0
\(323\) 8.94274i 0.497587i
\(324\) 0 0
\(325\) 0.447123 9.35618i 0.0248019 0.518988i
\(326\) 0 0
\(327\) 11.2793i 0.623745i
\(328\) 0 0
\(329\) 5.74399 0.316677
\(330\) 0 0
\(331\) 15.0647 0.828028 0.414014 0.910270i \(-0.364126\pi\)
0.414014 + 0.910270i \(0.364126\pi\)
\(332\) 0 0
\(333\) 10.1759i 0.557637i
\(334\) 0 0
\(335\) 0.0533841 2.23543i 0.00291668 0.122135i
\(336\) 0 0
\(337\) 17.1955i 0.936697i −0.883544 0.468348i \(-0.844849\pi\)
0.883544 0.468348i \(-0.155151\pi\)
\(338\) 0 0
\(339\) 12.1469 0.659731
\(340\) 0 0
\(341\) 4.90930 0.265854
\(342\) 0 0
\(343\) 28.5348i 1.54073i
\(344\) 0 0
\(345\) 12.1789 + 0.290843i 0.655690 + 0.0156585i
\(346\) 0 0
\(347\) 4.96587i 0.266582i −0.991077 0.133291i \(-0.957446\pi\)
0.991077 0.133291i \(-0.0425544\pi\)
\(348\) 0 0
\(349\) −14.5284 −0.777689 −0.388844 0.921304i \(-0.627126\pi\)
−0.388844 + 0.921304i \(0.627126\pi\)
\(350\) 0 0
\(351\) −1.87337 −0.0999932
\(352\) 0 0
\(353\) 11.2401i 0.598251i −0.954214 0.299125i \(-0.903305\pi\)
0.954214 0.299125i \(-0.0966948\pi\)
\(354\) 0 0
\(355\) 27.5738 + 0.658486i 1.46346 + 0.0349488i
\(356\) 0 0
\(357\) 22.6796i 1.20033i
\(358\) 0 0
\(359\) 6.47309 0.341636 0.170818 0.985303i \(-0.445359\pi\)
0.170818 + 0.985303i \(0.445359\pi\)
\(360\) 0 0
\(361\) −15.8393 −0.833648
\(362\) 0 0
\(363\) 10.0568i 0.527844i
\(364\) 0 0
\(365\) 0.519934 21.7720i 0.0272146 1.13960i
\(366\) 0 0
\(367\) 4.66944i 0.243743i 0.992546 + 0.121871i \(0.0388896\pi\)
−0.992546 + 0.121871i \(0.961110\pi\)
\(368\) 0 0
\(369\) −5.79630 −0.301743
\(370\) 0 0
\(371\) 21.8873 1.13633
\(372\) 0 0
\(373\) 33.8473i 1.75255i 0.481815 + 0.876273i \(0.339978\pi\)
−0.481815 + 0.876273i \(0.660022\pi\)
\(374\) 0 0
\(375\) 0.800152 11.1517i 0.0413197 0.575870i
\(376\) 0 0
\(377\) 7.21353i 0.371516i
\(378\) 0 0
\(379\) −26.6749 −1.37020 −0.685098 0.728450i \(-0.740241\pi\)
−0.685098 + 0.728450i \(0.740241\pi\)
\(380\) 0 0
\(381\) 21.5167 1.10234
\(382\) 0 0
\(383\) 4.72526i 0.241449i −0.992686 0.120725i \(-0.961478\pi\)
0.992686 0.120725i \(-0.0385218\pi\)
\(384\) 0 0
\(385\) 0.233762 9.78865i 0.0119136 0.498876i
\(386\) 0 0
\(387\) 8.65164i 0.439787i
\(388\) 0 0
\(389\) 15.8613 0.804198 0.402099 0.915596i \(-0.368281\pi\)
0.402099 + 0.915596i \(0.368281\pi\)
\(390\) 0 0
\(391\) −27.4048 −1.38592
\(392\) 0 0
\(393\) 19.7230i 0.994894i
\(394\) 0 0
\(395\) −12.7044 0.303393i −0.639230 0.0152654i
\(396\) 0 0
\(397\) 17.9367i 0.900218i −0.892974 0.450109i \(-0.851385\pi\)
0.892974 0.450109i \(-0.148615\pi\)
\(398\) 0 0
\(399\) −8.01580 −0.401292
\(400\) 0 0
\(401\) 7.83427 0.391225 0.195612 0.980681i \(-0.437331\pi\)
0.195612 + 0.980681i \(0.437331\pi\)
\(402\) 0 0
\(403\) 9.46973i 0.471721i
\(404\) 0 0
\(405\) −2.23543 0.0533841i −0.111079 0.00265268i
\(406\) 0 0
\(407\) 9.88279i 0.489872i
\(408\) 0 0
\(409\) 24.7241 1.22253 0.611265 0.791426i \(-0.290661\pi\)
0.611265 + 0.791426i \(0.290661\pi\)
\(410\) 0 0
\(411\) −17.0580 −0.841411
\(412\) 0 0
\(413\) 3.61158i 0.177714i
\(414\) 0 0
\(415\) −0.897160 + 37.5681i −0.0440399 + 1.84415i
\(416\) 0 0
\(417\) 6.94806i 0.340248i
\(418\) 0 0
\(419\) −13.4506 −0.657105 −0.328553 0.944486i \(-0.606561\pi\)
−0.328553 + 0.944486i \(0.606561\pi\)
\(420\) 0 0
\(421\) −10.7666 −0.524732 −0.262366 0.964968i \(-0.584503\pi\)
−0.262366 + 0.964968i \(0.584503\pi\)
\(422\) 0 0
\(423\) 1.27397i 0.0619424i
\(424\) 0 0
\(425\) −1.20055 + 25.1220i −0.0582355 + 1.21859i
\(426\) 0 0
\(427\) 44.9685i 2.17618i
\(428\) 0 0
\(429\) 1.81941 0.0878419
\(430\) 0 0
\(431\) −11.6621 −0.561746 −0.280873 0.959745i \(-0.590624\pi\)
−0.280873 + 0.959745i \(0.590624\pi\)
\(432\) 0 0
\(433\) 5.61780i 0.269974i 0.990847 + 0.134987i \(0.0430993\pi\)
−0.990847 + 0.134987i \(0.956901\pi\)
\(434\) 0 0
\(435\) 0.205558 8.60766i 0.00985578 0.412706i
\(436\) 0 0
\(437\) 9.68586i 0.463338i
\(438\) 0 0
\(439\) 4.31288 0.205842 0.102921 0.994690i \(-0.467181\pi\)
0.102921 + 0.994690i \(0.467181\pi\)
\(440\) 0 0
\(441\) 13.3288 0.634703
\(442\) 0 0
\(443\) 5.40726i 0.256907i −0.991716 0.128453i \(-0.958999\pi\)
0.991716 0.128453i \(-0.0410012\pi\)
\(444\) 0 0
\(445\) 36.6626 + 0.875535i 1.73797 + 0.0415044i
\(446\) 0 0
\(447\) 17.4588i 0.825775i
\(448\) 0 0
\(449\) −0.546480 −0.0257900 −0.0128950 0.999917i \(-0.504105\pi\)
−0.0128950 + 0.999917i \(0.504105\pi\)
\(450\) 0 0
\(451\) 5.62933 0.265075
\(452\) 0 0
\(453\) 6.90694i 0.324517i
\(454\) 0 0
\(455\) −18.8817 0.450911i −0.885187 0.0211390i
\(456\) 0 0
\(457\) 16.7141i 0.781852i −0.920422 0.390926i \(-0.872155\pi\)
0.920422 0.390926i \(-0.127845\pi\)
\(458\) 0 0
\(459\) 5.03013 0.234786
\(460\) 0 0
\(461\) 21.0447 0.980151 0.490075 0.871680i \(-0.336969\pi\)
0.490075 + 0.871680i \(0.336969\pi\)
\(462\) 0 0
\(463\) 30.1870i 1.40291i 0.712714 + 0.701455i \(0.247466\pi\)
−0.712714 + 0.701455i \(0.752534\pi\)
\(464\) 0 0
\(465\) 0.269852 11.2999i 0.0125141 0.524021i
\(466\) 0 0
\(467\) 8.97008i 0.415086i −0.978226 0.207543i \(-0.933453\pi\)
0.978226 0.207543i \(-0.0665467\pi\)
\(468\) 0 0
\(469\) −4.50874 −0.208194
\(470\) 0 0
\(471\) −9.22557 −0.425092
\(472\) 0 0
\(473\) 8.40242i 0.386344i
\(474\) 0 0
\(475\) 8.87904 + 0.424321i 0.407398 + 0.0194692i
\(476\) 0 0
\(477\) 4.85441i 0.222268i
\(478\) 0 0
\(479\) 21.7966 0.995910 0.497955 0.867203i \(-0.334084\pi\)
0.497955 + 0.867203i \(0.334084\pi\)
\(480\) 0 0
\(481\) 19.0633 0.869210
\(482\) 0 0
\(483\) 24.5642i 1.11771i
\(484\) 0 0
\(485\) 0.604725 25.3226i 0.0274591 1.14984i
\(486\) 0 0
\(487\) 15.5188i 0.703222i −0.936146 0.351611i \(-0.885634\pi\)
0.936146 0.351611i \(-0.114366\pi\)
\(488\) 0 0
\(489\) 25.2659 1.14256
\(490\) 0 0
\(491\) −13.9191 −0.628160 −0.314080 0.949397i \(-0.601696\pi\)
−0.314080 + 0.949397i \(0.601696\pi\)
\(492\) 0 0
\(493\) 19.3688i 0.872327i
\(494\) 0 0
\(495\) 2.17104 + 0.0518463i 0.0975809 + 0.00233032i
\(496\) 0 0
\(497\) 55.6148i 2.49467i
\(498\) 0 0
\(499\) 10.0156 0.448359 0.224179 0.974548i \(-0.428030\pi\)
0.224179 + 0.974548i \(0.428030\pi\)
\(500\) 0 0
\(501\) 0.666796 0.0297902
\(502\) 0 0
\(503\) 1.95986i 0.0873860i 0.999045 + 0.0436930i \(0.0139123\pi\)
−0.999045 + 0.0436930i \(0.986088\pi\)
\(504\) 0 0
\(505\) −19.5717 0.467389i −0.870929 0.0207986i
\(506\) 0 0
\(507\) 9.49048i 0.421487i
\(508\) 0 0
\(509\) −14.3393 −0.635579 −0.317790 0.948161i \(-0.602941\pi\)
−0.317790 + 0.948161i \(0.602941\pi\)
\(510\) 0 0
\(511\) −43.9129 −1.94259
\(512\) 0 0
\(513\) 1.77783i 0.0784933i
\(514\) 0 0
\(515\) −0.159803 + 6.69167i −0.00704176 + 0.294870i
\(516\) 0 0
\(517\) 1.23727i 0.0544151i
\(518\) 0 0
\(519\) 16.8775 0.740839
\(520\) 0 0
\(521\) −22.8190 −0.999717 −0.499858 0.866107i \(-0.666615\pi\)
−0.499858 + 0.866107i \(0.666615\pi\)
\(522\) 0 0
\(523\) 2.43411i 0.106436i 0.998583 + 0.0532182i \(0.0169479\pi\)
−0.998583 + 0.0532182i \(0.983052\pi\)
\(524\) 0 0
\(525\) −22.5180 1.07611i −0.982767 0.0469655i
\(526\) 0 0
\(527\) 25.4269i 1.10761i
\(528\) 0 0
\(529\) −6.68206 −0.290524
\(530\) 0 0
\(531\) −0.801017 −0.0347612
\(532\) 0 0
\(533\) 10.8586i 0.470339i
\(534\) 0 0
\(535\) 0.0981885 4.11159i 0.00424506 0.177760i
\(536\) 0 0
\(537\) 25.1781i 1.08651i
\(538\) 0 0
\(539\) −12.9448 −0.557573
\(540\) 0 0
\(541\) 11.0605 0.475528 0.237764 0.971323i \(-0.423585\pi\)
0.237764 + 0.971323i \(0.423585\pi\)
\(542\) 0 0
\(543\) 4.21845i 0.181031i
\(544\) 0 0
\(545\) −25.2140 0.602133i −1.08005 0.0257926i
\(546\) 0 0
\(547\) 6.45735i 0.276096i 0.990426 + 0.138048i \(0.0440829\pi\)
−0.990426 + 0.138048i \(0.955917\pi\)
\(548\) 0 0
\(549\) 9.97361 0.425663
\(550\) 0 0
\(551\) 6.84566 0.291635
\(552\) 0 0
\(553\) 25.6242i 1.08965i
\(554\) 0 0
\(555\) 22.7475 + 0.543232i 0.965580 + 0.0230589i
\(556\) 0 0
\(557\) 6.22074i 0.263581i −0.991278 0.131791i \(-0.957927\pi\)
0.991278 0.131791i \(-0.0420727\pi\)
\(558\) 0 0
\(559\) 16.2077 0.685514
\(560\) 0 0
\(561\) −4.88524 −0.206255
\(562\) 0 0
\(563\) 0.338641i 0.0142720i 0.999975 + 0.00713601i \(0.00227148\pi\)
−0.999975 + 0.00713601i \(0.997729\pi\)
\(564\) 0 0
\(565\) −0.648453 + 27.1536i −0.0272806 + 1.14236i
\(566\) 0 0
\(567\) 4.50874i 0.189349i
\(568\) 0 0
\(569\) 19.4703 0.816238 0.408119 0.912929i \(-0.366185\pi\)
0.408119 + 0.912929i \(0.366185\pi\)
\(570\) 0 0
\(571\) 42.0804 1.76101 0.880506 0.474036i \(-0.157203\pi\)
0.880506 + 0.474036i \(0.157203\pi\)
\(572\) 0 0
\(573\) 19.3167i 0.806967i
\(574\) 0 0
\(575\) −1.30032 + 27.2096i −0.0542270 + 1.13472i
\(576\) 0 0
\(577\) 39.7519i 1.65489i −0.561545 0.827446i \(-0.689793\pi\)
0.561545 0.827446i \(-0.310207\pi\)
\(578\) 0 0
\(579\) −22.0344 −0.915720
\(580\) 0 0
\(581\) 75.7729 3.14359
\(582\) 0 0
\(583\) 4.71458i 0.195258i
\(584\) 0 0
\(585\) 0.100008 4.18779i 0.00413483 0.173144i
\(586\) 0 0
\(587\) 35.0378i 1.44616i 0.690762 + 0.723082i \(0.257275\pi\)
−0.690762 + 0.723082i \(0.742725\pi\)
\(588\) 0 0
\(589\) 8.98680 0.370295
\(590\) 0 0
\(591\) 23.8537 0.981212
\(592\) 0 0
\(593\) 6.07946i 0.249653i 0.992179 + 0.124827i \(0.0398375\pi\)
−0.992179 + 0.124827i \(0.960163\pi\)
\(594\) 0 0
\(595\) 50.6986 + 1.21073i 2.07844 + 0.0496350i
\(596\) 0 0
\(597\) 5.29391i 0.216665i
\(598\) 0 0
\(599\) 29.3951 1.20105 0.600526 0.799605i \(-0.294958\pi\)
0.600526 + 0.799605i \(0.294958\pi\)
\(600\) 0 0
\(601\) 36.7322 1.49834 0.749168 0.662380i \(-0.230453\pi\)
0.749168 + 0.662380i \(0.230453\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) 22.4812 + 0.536872i 0.913992 + 0.0218269i
\(606\) 0 0
\(607\) 19.9776i 0.810868i 0.914124 + 0.405434i \(0.132880\pi\)
−0.914124 + 0.405434i \(0.867120\pi\)
\(608\) 0 0
\(609\) −17.3612 −0.703511
\(610\) 0 0
\(611\) −2.38662 −0.0965521
\(612\) 0 0
\(613\) 42.8707i 1.73153i −0.500449 0.865766i \(-0.666832\pi\)
0.500449 0.865766i \(-0.333168\pi\)
\(614\) 0 0
\(615\) 0.309430 12.9572i 0.0124774 0.522486i
\(616\) 0 0
\(617\) 22.0503i 0.887713i −0.896098 0.443856i \(-0.853610\pi\)
0.896098 0.443856i \(-0.146390\pi\)
\(618\) 0 0
\(619\) −25.2362 −1.01433 −0.507164 0.861850i \(-0.669306\pi\)
−0.507164 + 0.861850i \(0.669306\pi\)
\(620\) 0 0
\(621\) 5.44812 0.218626
\(622\) 0 0
\(623\) 73.9465i 2.96260i
\(624\) 0 0
\(625\) 24.8861 + 2.38401i 0.995443 + 0.0953603i
\(626\) 0 0
\(627\) 1.72662i 0.0689547i
\(628\) 0 0
\(629\) −51.1862 −2.04093
\(630\) 0 0
\(631\) −45.3673 −1.80604 −0.903021 0.429596i \(-0.858656\pi\)
−0.903021 + 0.429596i \(0.858656\pi\)
\(632\) 0 0
\(633\) 4.36599i 0.173532i
\(634\) 0 0
\(635\) −1.14865 + 48.0991i −0.0455828 + 1.90876i
\(636\) 0 0
\(637\) 24.9697i 0.989337i
\(638\) 0 0
\(639\) 12.3349 0.487960
\(640\) 0 0
\(641\) 2.22317 0.0878099 0.0439050 0.999036i \(-0.486020\pi\)
0.0439050 + 0.999036i \(0.486020\pi\)
\(642\) 0 0
\(643\) 11.2031i 0.441806i 0.975296 + 0.220903i \(0.0709005\pi\)
−0.975296 + 0.220903i \(0.929100\pi\)
\(644\) 0 0
\(645\) 19.3401 + 0.461859i 0.761517 + 0.0181857i
\(646\) 0 0
\(647\) 10.0190i 0.393889i 0.980415 + 0.196944i \(0.0631019\pi\)
−0.980415 + 0.196944i \(0.936898\pi\)
\(648\) 0 0
\(649\) 0.777943 0.0305369
\(650\) 0 0
\(651\) −22.7913 −0.893262
\(652\) 0 0
\(653\) 36.4424i 1.42610i 0.701112 + 0.713051i \(0.252687\pi\)
−0.701112 + 0.713051i \(0.747313\pi\)
\(654\) 0 0
\(655\) −44.0894 1.05289i −1.72272 0.0411400i
\(656\) 0 0
\(657\) 9.73950i 0.379974i
\(658\) 0 0
\(659\) 8.19584 0.319264 0.159632 0.987177i \(-0.448969\pi\)
0.159632 + 0.987177i \(0.448969\pi\)
\(660\) 0 0
\(661\) 20.5546 0.799480 0.399740 0.916629i \(-0.369100\pi\)
0.399740 + 0.916629i \(0.369100\pi\)
\(662\) 0 0
\(663\) 9.42330i 0.365971i
\(664\) 0 0
\(665\) 0.427916 17.9188i 0.0165939 0.694860i
\(666\) 0 0
\(667\) 20.9783i 0.812284i
\(668\) 0 0
\(669\) −5.00754 −0.193603
\(670\) 0 0
\(671\) −9.68632 −0.373936
\(672\) 0 0
\(673\) 0.667917i 0.0257463i −0.999917 0.0128731i \(-0.995902\pi\)
0.999917 0.0128731i \(-0.00409776\pi\)
\(674\) 0 0
\(675\) 0.238673 4.99430i 0.00918652 0.192231i
\(676\) 0 0
\(677\) 11.6730i 0.448628i −0.974517 0.224314i \(-0.927986\pi\)
0.974517 0.224314i \(-0.0720141\pi\)
\(678\) 0 0
\(679\) −51.0742 −1.96005
\(680\) 0 0
\(681\) 18.3845 0.704496
\(682\) 0 0
\(683\) 4.30766i 0.164828i 0.996598 + 0.0824141i \(0.0262630\pi\)
−0.996598 + 0.0824141i \(0.973737\pi\)
\(684\) 0 0
\(685\) 0.910627 38.1321i 0.0347933 1.45695i
\(686\) 0 0
\(687\) 24.6317i 0.939759i
\(688\) 0 0
\(689\) −9.09412 −0.346458
\(690\) 0 0
\(691\) 3.59363 0.136708 0.0683541 0.997661i \(-0.478225\pi\)
0.0683541 + 0.997661i \(0.478225\pi\)
\(692\) 0 0
\(693\) 4.37887i 0.166339i
\(694\) 0 0
\(695\) −15.5319 0.370916i −0.589159 0.0140696i
\(696\) 0 0
\(697\) 29.1561i 1.10437i
\(698\) 0 0
\(699\) −8.36272 −0.316307
\(700\) 0 0
\(701\) 3.93948 0.148792 0.0743961 0.997229i \(-0.476297\pi\)
0.0743961 + 0.997229i \(0.476297\pi\)
\(702\) 0 0
\(703\) 18.0911i 0.682318i
\(704\) 0 0
\(705\) −2.84787 0.0680096i −0.107257 0.00256139i
\(706\) 0 0
\(707\) 39.4750i 1.48461i
\(708\) 0 0
\(709\) 12.7293 0.478057 0.239029 0.971013i \(-0.423171\pi\)
0.239029 + 0.971013i \(0.423171\pi\)
\(710\) 0 0
\(711\) −5.68322 −0.213138
\(712\) 0 0
\(713\) 27.5398i 1.03137i
\(714\) 0 0
\(715\) −0.0971274 + 4.06716i −0.00363236 + 0.152103i
\(716\) 0 0
\(717\) 22.6245i 0.844929i
\(718\) 0 0
\(719\) −42.9125 −1.60037 −0.800184 0.599755i \(-0.795265\pi\)
−0.800184 + 0.599755i \(0.795265\pi\)
\(720\) 0 0
\(721\) 13.4967 0.502645
\(722\) 0 0
\(723\) 16.5883i 0.616924i
\(724\) 0 0
\(725\) 19.2308 + 0.919023i 0.714216 + 0.0341317i
\(726\) 0 0
\(727\) 21.4563i 0.795769i 0.917435 + 0.397885i \(0.130256\pi\)
−0.917435 + 0.397885i \(0.869744\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −43.5189 −1.60960
\(732\) 0 0
\(733\) 28.7221i 1.06087i 0.847724 + 0.530437i \(0.177972\pi\)
−0.847724 + 0.530437i \(0.822028\pi\)
\(734\) 0 0
\(735\) −0.711543 + 29.7955i −0.0262457 + 1.09902i
\(736\) 0 0
\(737\) 0.971195i 0.0357744i
\(738\) 0 0
\(739\) −9.08106 −0.334052 −0.167026 0.985952i \(-0.553416\pi\)
−0.167026 + 0.985952i \(0.553416\pi\)
\(740\) 0 0
\(741\) 3.33054 0.122351
\(742\) 0 0
\(743\) 31.5678i 1.15811i −0.815288 0.579055i \(-0.803421\pi\)
0.815288 0.579055i \(-0.196579\pi\)
\(744\) 0 0
\(745\) 39.0280 + 0.932024i 1.42988 + 0.0341467i
\(746\) 0 0
\(747\) 16.8058i 0.614891i
\(748\) 0 0
\(749\) −8.29286 −0.303014
\(750\) 0 0
\(751\) 0.509836 0.0186042 0.00930208 0.999957i \(-0.497039\pi\)
0.00930208 + 0.999957i \(0.497039\pi\)
\(752\) 0 0
\(753\) 30.0957i 1.09675i
\(754\) 0 0
\(755\) 15.4400 + 0.368721i 0.561919 + 0.0134191i
\(756\) 0 0
\(757\) 28.3209i 1.02934i 0.857388 + 0.514671i \(0.172086\pi\)
−0.857388 + 0.514671i \(0.827914\pi\)
\(758\) 0 0
\(759\) −5.29119 −0.192058
\(760\) 0 0
\(761\) 49.7335 1.80284 0.901419 0.432947i \(-0.142526\pi\)
0.901419 + 0.432947i \(0.142526\pi\)
\(762\) 0 0
\(763\) 50.8553i 1.84109i
\(764\) 0 0
\(765\) −0.268529 + 11.2445i −0.00970868 + 0.406546i
\(766\) 0 0
\(767\) 1.50060i 0.0541836i
\(768\) 0 0
\(769\) −35.9613 −1.29680 −0.648398 0.761301i \(-0.724561\pi\)
−0.648398 + 0.761301i \(0.724561\pi\)
\(770\) 0 0
\(771\) 11.4033 0.410680
\(772\) 0 0
\(773\) 17.5692i 0.631919i 0.948773 + 0.315960i \(0.102326\pi\)
−0.948773 + 0.315960i \(0.897674\pi\)
\(774\) 0 0
\(775\) 25.2458 + 1.20647i 0.906854 + 0.0433377i
\(776\) 0 0
\(777\) 45.8806i 1.64596i
\(778\) 0 0
\(779\) 10.3049 0.369210
\(780\) 0 0
\(781\) −11.9796 −0.428663
\(782\) 0 0
\(783\) 3.85056i 0.137608i
\(784\) 0 0
\(785\) 0.492499 20.6231i 0.0175780 0.736071i
\(786\) 0 0
\(787\) 0.129874i 0.00462949i 0.999997 + 0.00231475i \(0.000736808\pi\)
−0.999997 + 0.00231475i \(0.999263\pi\)
\(788\) 0 0
\(789\) −20.9006 −0.744080
\(790\) 0 0
\(791\) 54.7674 1.94731
\(792\) 0 0