Properties

Label 1200.3.bg.f.1057.2
Level $1200$
Weight $3$
Character 1200.1057
Analytic conductor $32.698$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.bg (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.6976317232\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 600)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1057.2
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1200.1057
Dual form 1200.3.bg.f.193.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 1.22474i) q^{3} +(-3.22474 - 3.22474i) q^{7} -3.00000i q^{9} +O(q^{10})\) \(q+(1.22474 - 1.22474i) q^{3} +(-3.22474 - 3.22474i) q^{7} -3.00000i q^{9} +6.89898 q^{11} +(18.1237 - 18.1237i) q^{13} +(-0.449490 - 0.449490i) q^{17} -9.89898i q^{19} -7.89898 q^{21} +(-10.6515 + 10.6515i) q^{23} +(-3.67423 - 3.67423i) q^{27} +36.2929i q^{29} -25.6969 q^{31} +(8.44949 - 8.44949i) q^{33} +(13.3031 + 13.3031i) q^{37} -44.3939i q^{39} -3.10102 q^{41} +(-2.72985 + 2.72985i) q^{43} +(-37.1464 - 37.1464i) q^{47} -28.2020i q^{49} -1.10102 q^{51} +(65.1918 - 65.1918i) q^{53} +(-12.1237 - 12.1237i) q^{57} -80.3837i q^{59} +13.7878 q^{61} +(-9.67423 + 9.67423i) q^{63} +(-84.3712 - 84.3712i) q^{67} +26.0908i q^{69} -98.2929 q^{71} +(52.4949 - 52.4949i) q^{73} +(-22.2474 - 22.2474i) q^{77} -68.2020i q^{79} -9.00000 q^{81} +(89.7321 - 89.7321i) q^{83} +(44.4495 + 44.4495i) q^{87} +40.5857i q^{89} -116.889 q^{91} +(-31.4722 + 31.4722i) q^{93} +(105.720 + 105.720i) q^{97} -20.6969i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{7} + O(q^{10}) \) \( 4 q - 8 q^{7} + 8 q^{11} + 48 q^{13} + 8 q^{17} - 12 q^{21} - 72 q^{23} - 44 q^{31} + 24 q^{33} + 112 q^{37} - 32 q^{41} - 104 q^{43} - 80 q^{47} - 24 q^{51} + 104 q^{53} - 24 q^{57} - 180 q^{61} - 24 q^{63} - 264 q^{67} - 256 q^{71} + 112 q^{73} - 40 q^{77} - 36 q^{81} + 16 q^{83} + 168 q^{87} - 252 q^{91} - 72 q^{93} + 320 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).

\(n\) \(401\) \(577\) \(751\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.22474 3.22474i −0.460678 0.460678i 0.438200 0.898878i \(-0.355616\pi\)
−0.898878 + 0.438200i \(0.855616\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 6.89898 0.627180 0.313590 0.949558i \(-0.398468\pi\)
0.313590 + 0.949558i \(0.398468\pi\)
\(12\) 0 0
\(13\) 18.1237 18.1237i 1.39413 1.39413i 0.578329 0.815804i \(-0.303705\pi\)
0.815804 0.578329i \(-0.196295\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.449490 0.449490i −0.0264406 0.0264406i 0.693763 0.720203i \(-0.255952\pi\)
−0.720203 + 0.693763i \(0.755952\pi\)
\(18\) 0 0
\(19\) 9.89898i 0.520999i −0.965474 0.260499i \(-0.916113\pi\)
0.965474 0.260499i \(-0.0838872\pi\)
\(20\) 0 0
\(21\) −7.89898 −0.376142
\(22\) 0 0
\(23\) −10.6515 + 10.6515i −0.463110 + 0.463110i −0.899673 0.436563i \(-0.856195\pi\)
0.436563 + 0.899673i \(0.356195\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 0 0
\(29\) 36.2929i 1.25148i 0.780033 + 0.625739i \(0.215202\pi\)
−0.780033 + 0.625739i \(0.784798\pi\)
\(30\) 0 0
\(31\) −25.6969 −0.828933 −0.414467 0.910064i \(-0.636032\pi\)
−0.414467 + 0.910064i \(0.636032\pi\)
\(32\) 0 0
\(33\) 8.44949 8.44949i 0.256045 0.256045i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 13.3031 + 13.3031i 0.359542 + 0.359542i 0.863644 0.504102i \(-0.168176\pi\)
−0.504102 + 0.863644i \(0.668176\pi\)
\(38\) 0 0
\(39\) 44.3939i 1.13830i
\(40\) 0 0
\(41\) −3.10102 −0.0756346 −0.0378173 0.999285i \(-0.512040\pi\)
−0.0378173 + 0.999285i \(0.512040\pi\)
\(42\) 0 0
\(43\) −2.72985 + 2.72985i −0.0634848 + 0.0634848i −0.738136 0.674652i \(-0.764294\pi\)
0.674652 + 0.738136i \(0.264294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −37.1464 37.1464i −0.790350 0.790350i 0.191201 0.981551i \(-0.438762\pi\)
−0.981551 + 0.191201i \(0.938762\pi\)
\(48\) 0 0
\(49\) 28.2020i 0.575552i
\(50\) 0 0
\(51\) −1.10102 −0.0215886
\(52\) 0 0
\(53\) 65.1918 65.1918i 1.23003 1.23003i 0.266085 0.963950i \(-0.414270\pi\)
0.963950 0.266085i \(-0.0857302\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −12.1237 12.1237i −0.212697 0.212697i
\(58\) 0 0
\(59\) 80.3837i 1.36244i −0.732081 0.681218i \(-0.761451\pi\)
0.732081 0.681218i \(-0.238549\pi\)
\(60\) 0 0
\(61\) 13.7878 0.226029 0.113014 0.993593i \(-0.463949\pi\)
0.113014 + 0.993593i \(0.463949\pi\)
\(62\) 0 0
\(63\) −9.67423 + 9.67423i −0.153559 + 0.153559i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −84.3712 84.3712i −1.25927 1.25927i −0.951441 0.307830i \(-0.900397\pi\)
−0.307830 0.951441i \(-0.599603\pi\)
\(68\) 0 0
\(69\) 26.0908i 0.378128i
\(70\) 0 0
\(71\) −98.2929 −1.38441 −0.692203 0.721703i \(-0.743360\pi\)
−0.692203 + 0.721703i \(0.743360\pi\)
\(72\) 0 0
\(73\) 52.4949 52.4949i 0.719108 0.719108i −0.249314 0.968423i \(-0.580205\pi\)
0.968423 + 0.249314i \(0.0802053\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −22.2474 22.2474i −0.288928 0.288928i
\(78\) 0 0
\(79\) 68.2020i 0.863317i −0.902037 0.431658i \(-0.857929\pi\)
0.902037 0.431658i \(-0.142071\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 89.7321 89.7321i 1.08111 1.08111i 0.0847040 0.996406i \(-0.473006\pi\)
0.996406 0.0847040i \(-0.0269945\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 44.4495 + 44.4495i 0.510914 + 0.510914i
\(88\) 0 0
\(89\) 40.5857i 0.456019i 0.973659 + 0.228010i \(0.0732218\pi\)
−0.973659 + 0.228010i \(0.926778\pi\)
\(90\) 0 0
\(91\) −116.889 −1.28449
\(92\) 0 0
\(93\) −31.4722 + 31.4722i −0.338411 + 0.338411i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 105.720 + 105.720i 1.08989 + 1.08989i 0.995539 + 0.0943546i \(0.0300787\pi\)
0.0943546 + 0.995539i \(0.469921\pi\)
\(98\) 0 0
\(99\) 20.6969i 0.209060i
\(100\) 0 0
\(101\) −197.485 −1.95529 −0.977647 0.210253i \(-0.932571\pi\)
−0.977647 + 0.210253i \(0.932571\pi\)
\(102\) 0 0
\(103\) −45.7980 + 45.7980i −0.444640 + 0.444640i −0.893568 0.448928i \(-0.851806\pi\)
0.448928 + 0.893568i \(0.351806\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 139.485 + 139.485i 1.30360 + 1.30360i 0.925951 + 0.377645i \(0.123266\pi\)
0.377645 + 0.925951i \(0.376734\pi\)
\(108\) 0 0
\(109\) 140.576i 1.28968i −0.764316 0.644842i \(-0.776923\pi\)
0.764316 0.644842i \(-0.223077\pi\)
\(110\) 0 0
\(111\) 32.5857 0.293565
\(112\) 0 0
\(113\) 105.980 105.980i 0.937872 0.937872i −0.0603074 0.998180i \(-0.519208\pi\)
0.998180 + 0.0603074i \(0.0192081\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −54.3712 54.3712i −0.464711 0.464711i
\(118\) 0 0
\(119\) 2.89898i 0.0243612i
\(120\) 0 0
\(121\) −73.4041 −0.606645
\(122\) 0 0
\(123\) −3.79796 + 3.79796i −0.0308777 + 0.0308777i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −66.6969 66.6969i −0.525173 0.525173i 0.393956 0.919129i \(-0.371106\pi\)
−0.919129 + 0.393956i \(0.871106\pi\)
\(128\) 0 0
\(129\) 6.68673i 0.0518351i
\(130\) 0 0
\(131\) 32.6765 0.249439 0.124720 0.992192i \(-0.460197\pi\)
0.124720 + 0.992192i \(0.460197\pi\)
\(132\) 0 0
\(133\) −31.9217 + 31.9217i −0.240013 + 0.240013i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 45.3281 + 45.3281i 0.330862 + 0.330862i 0.852914 0.522052i \(-0.174833\pi\)
−0.522052 + 0.852914i \(0.674833\pi\)
\(138\) 0 0
\(139\) 252.747i 1.81832i 0.416443 + 0.909162i \(0.363276\pi\)
−0.416443 + 0.909162i \(0.636724\pi\)
\(140\) 0 0
\(141\) −90.9898 −0.645318
\(142\) 0 0
\(143\) 125.035 125.035i 0.874372 0.874372i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −34.5403 34.5403i −0.234968 0.234968i
\(148\) 0 0
\(149\) 75.2122i 0.504780i 0.967626 + 0.252390i \(0.0812166\pi\)
−0.967626 + 0.252390i \(0.918783\pi\)
\(150\) 0 0
\(151\) −187.091 −1.23901 −0.619506 0.784992i \(-0.712667\pi\)
−0.619506 + 0.784992i \(0.712667\pi\)
\(152\) 0 0
\(153\) −1.34847 + 1.34847i −0.00881352 + 0.00881352i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −119.452 119.452i −0.760839 0.760839i 0.215635 0.976474i \(-0.430818\pi\)
−0.976474 + 0.215635i \(0.930818\pi\)
\(158\) 0 0
\(159\) 159.687i 1.00432i
\(160\) 0 0
\(161\) 68.6969 0.426689
\(162\) 0 0
\(163\) 104.866 104.866i 0.643350 0.643350i −0.308027 0.951377i \(-0.599669\pi\)
0.951377 + 0.308027i \(0.0996688\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 67.3031 + 67.3031i 0.403012 + 0.403012i 0.879293 0.476281i \(-0.158015\pi\)
−0.476281 + 0.879293i \(0.658015\pi\)
\(168\) 0 0
\(169\) 487.939i 2.88721i
\(170\) 0 0
\(171\) −29.6969 −0.173666
\(172\) 0 0
\(173\) −47.8638 + 47.8638i −0.276669 + 0.276669i −0.831778 0.555109i \(-0.812677\pi\)
0.555109 + 0.831778i \(0.312677\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −98.4495 98.4495i −0.556212 0.556212i
\(178\) 0 0
\(179\) 134.000i 0.748603i 0.927307 + 0.374302i \(0.122118\pi\)
−0.927307 + 0.374302i \(0.877882\pi\)
\(180\) 0 0
\(181\) −34.4143 −0.190134 −0.0950671 0.995471i \(-0.530307\pi\)
−0.0950671 + 0.995471i \(0.530307\pi\)
\(182\) 0 0
\(183\) 16.8865 16.8865i 0.0922759 0.0922759i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −3.10102 3.10102i −0.0165830 0.0165830i
\(188\) 0 0
\(189\) 23.6969i 0.125381i
\(190\) 0 0
\(191\) 238.272 1.24750 0.623750 0.781624i \(-0.285608\pi\)
0.623750 + 0.781624i \(0.285608\pi\)
\(192\) 0 0
\(193\) −61.8763 + 61.8763i −0.320602 + 0.320602i −0.848998 0.528396i \(-0.822794\pi\)
0.528396 + 0.848998i \(0.322794\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −72.2474 72.2474i −0.366738 0.366738i 0.499548 0.866286i \(-0.333499\pi\)
−0.866286 + 0.499548i \(0.833499\pi\)
\(198\) 0 0
\(199\) 85.4541i 0.429417i 0.976678 + 0.214709i \(0.0688802\pi\)
−0.976678 + 0.214709i \(0.931120\pi\)
\(200\) 0 0
\(201\) −206.666 −1.02819
\(202\) 0 0
\(203\) 117.035 117.035i 0.576528 0.576528i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 31.9546 + 31.9546i 0.154370 + 0.154370i
\(208\) 0 0
\(209\) 68.2929i 0.326760i
\(210\) 0 0
\(211\) −99.4745 −0.471443 −0.235722 0.971821i \(-0.575745\pi\)
−0.235722 + 0.971821i \(0.575745\pi\)
\(212\) 0 0
\(213\) −120.384 + 120.384i −0.565182 + 0.565182i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 82.8661 + 82.8661i 0.381871 + 0.381871i
\(218\) 0 0
\(219\) 128.586i 0.587149i
\(220\) 0 0
\(221\) −16.2929 −0.0737233
\(222\) 0 0
\(223\) −2.35076 + 2.35076i −0.0105415 + 0.0105415i −0.712358 0.701816i \(-0.752373\pi\)
0.701816 + 0.712358i \(0.252373\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 204.474 + 204.474i 0.900769 + 0.900769i 0.995503 0.0947340i \(-0.0302000\pi\)
−0.0947340 + 0.995503i \(0.530200\pi\)
\(228\) 0 0
\(229\) 131.808i 0.575582i 0.957693 + 0.287791i \(0.0929208\pi\)
−0.957693 + 0.287791i \(0.907079\pi\)
\(230\) 0 0
\(231\) −54.4949 −0.235909
\(232\) 0 0
\(233\) −139.616 + 139.616i −0.599212 + 0.599212i −0.940103 0.340891i \(-0.889271\pi\)
0.340891 + 0.940103i \(0.389271\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −83.5301 83.5301i −0.352448 0.352448i
\(238\) 0 0
\(239\) 118.697i 0.496640i 0.968678 + 0.248320i \(0.0798784\pi\)
−0.968678 + 0.248320i \(0.920122\pi\)
\(240\) 0 0
\(241\) 277.384 1.15097 0.575485 0.817812i \(-0.304813\pi\)
0.575485 + 0.817812i \(0.304813\pi\)
\(242\) 0 0
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −179.406 179.406i −0.726342 0.726342i
\(248\) 0 0
\(249\) 219.798i 0.882723i
\(250\) 0 0
\(251\) −37.5755 −0.149703 −0.0748516 0.997195i \(-0.523848\pi\)
−0.0748516 + 0.997195i \(0.523848\pi\)
\(252\) 0 0
\(253\) −73.4847 + 73.4847i −0.290453 + 0.290453i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 79.8684 + 79.8684i 0.310772 + 0.310772i 0.845209 0.534437i \(-0.179476\pi\)
−0.534437 + 0.845209i \(0.679476\pi\)
\(258\) 0 0
\(259\) 85.7980i 0.331266i
\(260\) 0 0
\(261\) 108.879 0.417159
\(262\) 0 0
\(263\) 222.767 222.767i 0.847024 0.847024i −0.142737 0.989761i \(-0.545590\pi\)
0.989761 + 0.142737i \(0.0455902\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 49.7071 + 49.7071i 0.186169 + 0.186169i
\(268\) 0 0
\(269\) 450.091i 1.67320i 0.547814 + 0.836600i \(0.315460\pi\)
−0.547814 + 0.836600i \(0.684540\pi\)
\(270\) 0 0
\(271\) 99.2122 0.366097 0.183048 0.983104i \(-0.441403\pi\)
0.183048 + 0.983104i \(0.441403\pi\)
\(272\) 0 0
\(273\) −143.159 + 143.159i −0.524392 + 0.524392i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 26.5936 + 26.5936i 0.0960059 + 0.0960059i 0.753478 0.657473i \(-0.228374\pi\)
−0.657473 + 0.753478i \(0.728374\pi\)
\(278\) 0 0
\(279\) 77.0908i 0.276311i
\(280\) 0 0
\(281\) 325.101 1.15694 0.578472 0.815703i \(-0.303649\pi\)
0.578472 + 0.815703i \(0.303649\pi\)
\(282\) 0 0
\(283\) −158.351 + 158.351i −0.559543 + 0.559543i −0.929177 0.369634i \(-0.879483\pi\)
0.369634 + 0.929177i \(0.379483\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.0000 + 10.0000i 0.0348432 + 0.0348432i
\(288\) 0 0
\(289\) 288.596i 0.998602i
\(290\) 0 0
\(291\) 258.959 0.889894
\(292\) 0 0
\(293\) 347.126 347.126i 1.18473 1.18473i 0.206226 0.978504i \(-0.433882\pi\)
0.978504 0.206226i \(-0.0661182\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −25.3485 25.3485i −0.0853484 0.0853484i
\(298\) 0 0
\(299\) 386.091i 1.29127i
\(300\) 0 0
\(301\) 17.6061 0.0584921
\(302\) 0 0
\(303\) −241.868 + 241.868i −0.798245 + 0.798245i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −107.250 107.250i −0.349348 0.349348i 0.510519 0.859867i \(-0.329453\pi\)
−0.859867 + 0.510519i \(0.829453\pi\)
\(308\) 0 0
\(309\) 112.182i 0.363047i
\(310\) 0 0
\(311\) 356.788 1.14723 0.573614 0.819126i \(-0.305541\pi\)
0.573614 + 0.819126i \(0.305541\pi\)
\(312\) 0 0
\(313\) −103.386 + 103.386i −0.330307 + 0.330307i −0.852703 0.522396i \(-0.825038\pi\)
0.522396 + 0.852703i \(0.325038\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −207.060 207.060i −0.653187 0.653187i 0.300572 0.953759i \(-0.402822\pi\)
−0.953759 + 0.300572i \(0.902822\pi\)
\(318\) 0 0
\(319\) 250.384i 0.784902i
\(320\) 0 0
\(321\) 341.666 1.06438
\(322\) 0 0
\(323\) −4.44949 + 4.44949i −0.0137755 + 0.0137755i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −172.169 172.169i −0.526511 0.526511i
\(328\) 0 0
\(329\) 239.576i 0.728193i
\(330\) 0 0
\(331\) 565.555 1.70863 0.854313 0.519759i \(-0.173978\pi\)
0.854313 + 0.519759i \(0.173978\pi\)
\(332\) 0 0
\(333\) 39.9092 39.9092i 0.119847 0.119847i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 65.6538 + 65.6538i 0.194818 + 0.194818i 0.797774 0.602956i \(-0.206011\pi\)
−0.602956 + 0.797774i \(0.706011\pi\)
\(338\) 0 0
\(339\) 259.596i 0.765770i
\(340\) 0 0
\(341\) −177.283 −0.519890
\(342\) 0 0
\(343\) −248.957 + 248.957i −0.725822 + 0.725822i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −106.177 106.177i −0.305986 0.305986i 0.537364 0.843350i \(-0.319420\pi\)
−0.843350 + 0.537364i \(0.819420\pi\)
\(348\) 0 0
\(349\) 335.980i 0.962692i 0.876531 + 0.481346i \(0.159852\pi\)
−0.876531 + 0.481346i \(0.840148\pi\)
\(350\) 0 0
\(351\) −133.182 −0.379435
\(352\) 0 0
\(353\) 419.328 419.328i 1.18790 1.18790i 0.210251 0.977648i \(-0.432572\pi\)
0.977648 0.210251i \(-0.0674280\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 3.55051 + 3.55051i 0.00994541 + 0.00994541i
\(358\) 0 0
\(359\) 191.019i 0.532087i −0.963961 0.266044i \(-0.914283\pi\)
0.963961 0.266044i \(-0.0857166\pi\)
\(360\) 0 0
\(361\) 263.010 0.728560
\(362\) 0 0
\(363\) −89.9013 + 89.9013i −0.247662 + 0.247662i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 207.341 + 207.341i 0.564961 + 0.564961i 0.930712 0.365752i \(-0.119188\pi\)
−0.365752 + 0.930712i \(0.619188\pi\)
\(368\) 0 0
\(369\) 9.30306i 0.0252115i
\(370\) 0 0
\(371\) −420.454 −1.13330
\(372\) 0 0
\(373\) −353.052 + 353.052i −0.946521 + 0.946521i −0.998641 0.0521200i \(-0.983402\pi\)
0.0521200 + 0.998641i \(0.483402\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 657.762 + 657.762i 1.74473 + 1.74473i
\(378\) 0 0
\(379\) 607.393i 1.60262i −0.598250 0.801310i \(-0.704137\pi\)
0.598250 0.801310i \(-0.295863\pi\)
\(380\) 0 0
\(381\) −163.373 −0.428802
\(382\) 0 0
\(383\) −207.414 + 207.414i −0.541552 + 0.541552i −0.923984 0.382432i \(-0.875087\pi\)
0.382432 + 0.923984i \(0.375087\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 8.18954 + 8.18954i 0.0211616 + 0.0211616i
\(388\) 0 0
\(389\) 593.889i 1.52671i 0.645981 + 0.763353i \(0.276448\pi\)
−0.645981 + 0.763353i \(0.723552\pi\)
\(390\) 0 0
\(391\) 9.57551 0.0244898
\(392\) 0 0
\(393\) 40.0204 40.0204i 0.101833 0.101833i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −288.062 288.062i −0.725598 0.725598i 0.244141 0.969740i \(-0.421494\pi\)
−0.969740 + 0.244141i \(0.921494\pi\)
\(398\) 0 0
\(399\) 78.1918i 0.195970i
\(400\) 0 0
\(401\) 129.748 0.323561 0.161781 0.986827i \(-0.448276\pi\)
0.161781 + 0.986827i \(0.448276\pi\)
\(402\) 0 0
\(403\) −465.724 + 465.724i −1.15564 + 1.15564i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 91.7775 + 91.7775i 0.225498 + 0.225498i
\(408\) 0 0
\(409\) 262.696i 0.642288i 0.947030 + 0.321144i \(0.104067\pi\)
−0.947030 + 0.321144i \(0.895933\pi\)
\(410\) 0 0
\(411\) 111.031 0.270147
\(412\) 0 0
\(413\) −259.217 + 259.217i −0.627644 + 0.627644i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 309.551 + 309.551i 0.742327 + 0.742327i
\(418\) 0 0
\(419\) 638.030i 1.52274i 0.648315 + 0.761372i \(0.275474\pi\)
−0.648315 + 0.761372i \(0.724526\pi\)
\(420\) 0 0
\(421\) −272.606 −0.647520 −0.323760 0.946139i \(-0.604947\pi\)
−0.323760 + 0.946139i \(0.604947\pi\)
\(422\) 0 0
\(423\) −111.439 + 111.439i −0.263450 + 0.263450i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −44.4620 44.4620i −0.104126 0.104126i
\(428\) 0 0
\(429\) 306.272i 0.713922i
\(430\) 0 0
\(431\) 264.960 0.614757 0.307378 0.951587i \(-0.400548\pi\)
0.307378 + 0.951587i \(0.400548\pi\)
\(432\) 0 0
\(433\) 210.619 210.619i 0.486417 0.486417i −0.420756 0.907174i \(-0.638235\pi\)
0.907174 + 0.420756i \(0.138235\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 105.439 + 105.439i 0.241280 + 0.241280i
\(438\) 0 0
\(439\) 423.999i 0.965829i −0.875667 0.482915i \(-0.839578\pi\)
0.875667 0.482915i \(-0.160422\pi\)
\(440\) 0 0
\(441\) −84.6061 −0.191851
\(442\) 0 0
\(443\) −533.040 + 533.040i −1.20325 + 1.20325i −0.230078 + 0.973172i \(0.573898\pi\)
−0.973172 + 0.230078i \(0.926102\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 92.1158 + 92.1158i 0.206076 + 0.206076i
\(448\) 0 0
\(449\) 7.23266i 0.0161084i −0.999968 0.00805418i \(-0.997436\pi\)
0.999968 0.00805418i \(-0.00256375\pi\)
\(450\) 0 0
\(451\) −21.3939 −0.0474365
\(452\) 0 0
\(453\) −229.139 + 229.139i −0.505825 + 0.505825i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 183.918 + 183.918i 0.402447 + 0.402447i 0.879095 0.476647i \(-0.158148\pi\)
−0.476647 + 0.879095i \(0.658148\pi\)
\(458\) 0 0
\(459\) 3.30306i 0.00719621i
\(460\) 0 0
\(461\) 632.595 1.37222 0.686112 0.727496i \(-0.259316\pi\)
0.686112 + 0.727496i \(0.259316\pi\)
\(462\) 0 0
\(463\) −382.838 + 382.838i −0.826863 + 0.826863i −0.987082 0.160218i \(-0.948780\pi\)
0.160218 + 0.987082i \(0.448780\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −164.581 164.581i −0.352422 0.352422i 0.508588 0.861010i \(-0.330168\pi\)
−0.861010 + 0.508588i \(0.830168\pi\)
\(468\) 0 0
\(469\) 544.151i 1.16024i
\(470\) 0 0
\(471\) −292.596 −0.621223
\(472\) 0 0
\(473\) −18.8332 + 18.8332i −0.0398164 + 0.0398164i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −195.576 195.576i −0.410012 0.410012i
\(478\) 0 0
\(479\) 356.606i 0.744480i 0.928136 + 0.372240i \(0.121410\pi\)
−0.928136 + 0.372240i \(0.878590\pi\)
\(480\) 0 0
\(481\) 482.202 1.00250
\(482\) 0 0
\(483\) 84.1362 84.1362i 0.174195 0.174195i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 170.103 + 170.103i 0.349288 + 0.349288i 0.859844 0.510556i \(-0.170560\pi\)
−0.510556 + 0.859844i \(0.670560\pi\)
\(488\) 0 0
\(489\) 256.868i 0.525293i
\(490\) 0 0
\(491\) 439.514 0.895141 0.447571 0.894249i \(-0.352289\pi\)
0.447571 + 0.894249i \(0.352289\pi\)
\(492\) 0 0
\(493\) 16.3133 16.3133i 0.0330898 0.0330898i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 316.969 + 316.969i 0.637765 + 0.637765i
\(498\) 0 0
\(499\) 751.413i 1.50584i −0.658113 0.752919i \(-0.728645\pi\)
0.658113 0.752919i \(-0.271355\pi\)
\(500\) 0 0
\(501\) 164.858 0.329058
\(502\) 0 0
\(503\) 543.626 543.626i 1.08077 1.08077i 0.0843284 0.996438i \(-0.473126\pi\)
0.996438 0.0843284i \(-0.0268745\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −597.601 597.601i −1.17870 1.17870i
\(508\) 0 0
\(509\) 471.798i 0.926912i 0.886120 + 0.463456i \(0.153391\pi\)
−0.886120 + 0.463456i \(0.846609\pi\)
\(510\) 0 0
\(511\) −338.565 −0.662554
\(512\) 0 0
\(513\) −36.3712 + 36.3712i −0.0708990 + 0.0708990i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −256.272 256.272i −0.495691 0.495691i
\(518\) 0 0
\(519\) 117.242i 0.225899i
\(520\) 0 0
\(521\) 881.928 1.69276 0.846380 0.532580i \(-0.178777\pi\)
0.846380 + 0.532580i \(0.178777\pi\)
\(522\) 0 0
\(523\) 305.493 305.493i 0.584116 0.584116i −0.351916 0.936032i \(-0.614470\pi\)
0.936032 + 0.351916i \(0.114470\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 11.5505 + 11.5505i 0.0219175 + 0.0219175i
\(528\) 0 0
\(529\) 302.090i 0.571058i
\(530\) 0 0
\(531\) −241.151 −0.454145
\(532\) 0 0
\(533\) −56.2020 + 56.2020i −0.105445 + 0.105445i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 164.116 + 164.116i 0.305616 + 0.305616i
\(538\) 0 0
\(539\) 194.565i 0.360975i
\(540\) 0 0
\(541\) −761.867 −1.40826 −0.704129 0.710072i \(-0.748662\pi\)
−0.704129 + 0.710072i \(0.748662\pi\)
\(542\) 0 0
\(543\) −42.1487 + 42.1487i −0.0776220 + 0.0776220i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 178.020 + 178.020i 0.325449 + 0.325449i 0.850853 0.525404i \(-0.176086\pi\)
−0.525404 + 0.850853i \(0.676086\pi\)
\(548\) 0 0
\(549\) 41.3633i 0.0753429i
\(550\) 0 0
\(551\) 359.262 0.652019
\(552\) 0 0
\(553\) −219.934 + 219.934i −0.397711 + 0.397711i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 82.9852 + 82.9852i 0.148986 + 0.148986i 0.777665 0.628679i \(-0.216404\pi\)
−0.628679 + 0.777665i \(0.716404\pi\)
\(558\) 0 0
\(559\) 98.9500i 0.177013i
\(560\) 0 0
\(561\) −7.59592 −0.0135400
\(562\) 0 0
\(563\) −228.227 + 228.227i −0.405377 + 0.405377i −0.880123 0.474746i \(-0.842540\pi\)
0.474746 + 0.880123i \(0.342540\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 29.0227 + 29.0227i 0.0511864 + 0.0511864i
\(568\) 0 0
\(569\) 613.787i 1.07871i −0.842078 0.539356i \(-0.818668\pi\)
0.842078 0.539356i \(-0.181332\pi\)
\(570\) 0 0
\(571\) 541.656 0.948610 0.474305 0.880361i \(-0.342699\pi\)
0.474305 + 0.880361i \(0.342699\pi\)
\(572\) 0 0
\(573\) 291.823 291.823i 0.509290 0.509290i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −341.967 341.967i −0.592664 0.592664i 0.345686 0.938350i \(-0.387646\pi\)
−0.938350 + 0.345686i \(0.887646\pi\)
\(578\) 0 0
\(579\) 151.565i 0.261771i
\(580\) 0 0
\(581\) −578.727 −0.996087
\(582\) 0 0
\(583\) 449.757 449.757i 0.771453 0.771453i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 454.141 + 454.141i 0.773664 + 0.773664i 0.978745 0.205081i \(-0.0657458\pi\)
−0.205081 + 0.978745i \(0.565746\pi\)
\(588\) 0 0
\(589\) 254.373i 0.431873i
\(590\) 0 0
\(591\) −176.969 −0.299441
\(592\) 0 0
\(593\) 50.6357 50.6357i 0.0853891 0.0853891i −0.663122 0.748511i \(-0.730769\pi\)
0.748511 + 0.663122i \(0.230769\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 104.659 + 104.659i 0.175309 + 0.175309i
\(598\) 0 0
\(599\) 506.443i 0.845481i 0.906251 + 0.422740i \(0.138932\pi\)
−0.906251 + 0.422740i \(0.861068\pi\)
\(600\) 0 0
\(601\) −785.120 −1.30636 −0.653178 0.757204i \(-0.726565\pi\)
−0.653178 + 0.757204i \(0.726565\pi\)
\(602\) 0 0
\(603\) −253.114 + 253.114i −0.419757 + 0.419757i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 766.252 + 766.252i 1.26236 + 1.26236i 0.949946 + 0.312413i \(0.101137\pi\)
0.312413 + 0.949946i \(0.398863\pi\)
\(608\) 0 0
\(609\) 286.677i 0.470733i
\(610\) 0 0
\(611\) −1346.46 −2.20370
\(612\) 0 0
\(613\) −182.697 + 182.697i −0.298037 + 0.298037i −0.840245 0.542207i \(-0.817589\pi\)
0.542207 + 0.840245i \(0.317589\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −71.1214 71.1214i −0.115270 0.115270i 0.647119 0.762389i \(-0.275974\pi\)
−0.762389 + 0.647119i \(0.775974\pi\)
\(618\) 0 0
\(619\) 1031.35i 1.66616i 0.553154 + 0.833079i \(0.313424\pi\)
−0.553154 + 0.833079i \(0.686576\pi\)
\(620\) 0 0
\(621\) 78.2724 0.126043
\(622\) 0 0
\(623\) 130.879 130.879i 0.210078 0.210078i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −83.6413 83.6413i −0.133399 0.133399i
\(628\) 0 0
\(629\) 11.9592i 0.0190130i
\(630\) 0 0
\(631\) 374.201 0.593029 0.296514 0.955028i \(-0.404176\pi\)
0.296514 + 0.955028i \(0.404176\pi\)
\(632\) 0 0
\(633\) −121.831 + 121.831i −0.192466 + 0.192466i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −511.126 511.126i −0.802396 0.802396i
\(638\) 0 0
\(639\) 294.879i 0.461469i
\(640\) 0 0
\(641\) −884.827 −1.38038 −0.690192 0.723626i \(-0.742474\pi\)
−0.690192 + 0.723626i \(0.742474\pi\)
\(642\) 0 0
\(643\) 683.787 683.787i 1.06343 1.06343i 0.0655849 0.997847i \(-0.479109\pi\)
0.997847 0.0655849i \(-0.0208913\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −597.898 597.898i −0.924108 0.924108i 0.0732085 0.997317i \(-0.476676\pi\)
−0.997317 + 0.0732085i \(0.976676\pi\)
\(648\) 0 0
\(649\) 554.565i 0.854492i
\(650\) 0 0
\(651\) 202.980 0.311797
\(652\) 0 0
\(653\) 282.136 282.136i 0.432062 0.432062i −0.457268 0.889329i \(-0.651172\pi\)
0.889329 + 0.457268i \(0.151172\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −157.485 157.485i −0.239703 0.239703i
\(658\) 0 0
\(659\) 503.505i 0.764044i −0.924153 0.382022i \(-0.875228\pi\)
0.924153 0.382022i \(-0.124772\pi\)
\(660\) 0 0
\(661\) 38.7673 0.0586495 0.0293248 0.999570i \(-0.490664\pi\)
0.0293248 + 0.999570i \(0.490664\pi\)
\(662\) 0 0
\(663\) −19.9546 + 19.9546i −0.0300974 + 0.0300974i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −386.574 386.574i −0.579572 0.579572i
\(668\) 0 0
\(669\) 5.75817i 0.00860713i
\(670\) 0 0
\(671\) 95.1214 0.141761
\(672\) 0 0
\(673\) −359.728 + 359.728i −0.534513 + 0.534513i −0.921912 0.387399i \(-0.873374\pi\)
0.387399 + 0.921912i \(0.373374\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 40.0454 + 40.0454i 0.0591513 + 0.0591513i 0.736064 0.676912i \(-0.236682\pi\)
−0.676912 + 0.736064i \(0.736682\pi\)
\(678\) 0 0
\(679\) 681.838i 1.00418i
\(680\) 0 0
\(681\) 500.858 0.735475
\(682\) 0 0
\(683\) 502.243 502.243i 0.735348 0.735348i −0.236326 0.971674i \(-0.575943\pi\)
0.971674 + 0.236326i \(0.0759432\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 161.431 + 161.431i 0.234980 + 0.234980i
\(688\) 0 0
\(689\) 2363.04i 3.42966i
\(690\) 0 0
\(691\) 242.241 0.350566 0.175283 0.984518i \(-0.443916\pi\)
0.175283 + 0.984518i \(0.443916\pi\)
\(692\) 0 0
\(693\) −66.7423 + 66.7423i −0.0963093 + 0.0963093i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.39388 + 1.39388i 0.00199982 + 0.00199982i
\(698\) 0 0
\(699\) 341.989i 0.489254i
\(700\) 0 0
\(701\) 619.181 0.883282 0.441641 0.897192i \(-0.354397\pi\)
0.441641 + 0.897192i \(0.354397\pi\)
\(702\) 0 0
\(703\) 131.687 131.687i 0.187321 0.187321i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 636.838 + 636.838i 0.900761 + 0.900761i
\(708\) 0 0
\(709\) 618.514i 0.872376i 0.899856 + 0.436188i \(0.143672\pi\)
−0.899856 + 0.436188i \(0.856328\pi\)
\(710\) 0 0
\(711\) −204.606 −0.287772
\(712\) 0 0
\(713\) 273.712 273.712i 0.383887 0.383887i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 145.373 + 145.373i 0.202752 + 0.202752i
\(718\) 0 0
\(719\) 555.989i 0.773281i 0.922231 + 0.386640i \(0.126365\pi\)
−0.922231 + 0.386640i \(0.873635\pi\)
\(720\) 0 0
\(721\) 295.373 0.409672
\(722\) 0 0
\(723\) 339.724 339.724i 0.469881 0.469881i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 103.992 + 103.992i 0.143043 + 0.143043i 0.775002 0.631959i \(-0.217749\pi\)
−0.631959 + 0.775002i \(0.717749\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 2.45408 0.00335715
\(732\) 0 0
\(733\) 462.979 462.979i 0.631621 0.631621i −0.316853 0.948475i \(-0.602626\pi\)
0.948475 + 0.316853i \(0.102626\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −582.075 582.075i −0.789790 0.789790i
\(738\) 0 0
\(739\) 701.414i 0.949140i −0.880218 0.474570i \(-0.842604\pi\)
0.880218 0.474570i \(-0.157396\pi\)
\(740\) 0 0
\(741\) −439.454 −0.593055
\(742\) 0 0
\(743\) 634.534 634.534i 0.854016 0.854016i −0.136609 0.990625i \(-0.543620\pi\)
0.990625 + 0.136609i \(0.0436205\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −269.196 269.196i −0.360370 0.360370i
\(748\) 0 0
\(749\) 899.605i 1.20107i
\(750\) 0 0
\(751\) 934.241 1.24400 0.621998 0.783019i \(-0.286321\pi\)
0.621998 + 0.783019i \(0.286321\pi\)
\(752\) 0 0
\(753\) −46.0204 + 46.0204i −0.0611161 + 0.0611161i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −656.598 656.598i −0.867369 0.867369i 0.124812 0.992180i \(-0.460167\pi\)
−0.992180 + 0.124812i \(0.960167\pi\)
\(758\) 0 0
\(759\) 180.000i 0.237154i
\(760\) 0 0
\(761\) −911.292 −1.19749 −0.598746 0.800939i \(-0.704334\pi\)
−0.598746 + 0.800939i \(0.704334\pi\)
\(762\) 0 0
\(763\) −453.320 + 453.320i −0.594129 + 0.594129i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1456.85 1456.85i −1.89942 1.89942i
\(768\) 0 0
\(769\) 769.847i 1.00110i −0.865707 0.500551i \(-0.833131\pi\)
0.865707 0.500551i \(-0.166869\pi\)
\(770\) 0 0
\(771\) 195.637 0.253744
\(772\) 0 0
\(773\) −480.515 + 480.515i −0.621624 + 0.621624i −0.945947 0.324323i \(-0.894864\pi\)
0.324323 + 0.945947i \(0.394864\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −105.081 105.081i −0.135239 0.135239i
\(778\) 0 0
\(779\) 30.6969i 0.0394056i
\(780\) 0 0
\(781\) −678.120 −0.868272
\(782\) 0 0
\(783\) 133.348 133.348i 0.170305 0.170305i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 48.0079 + 48.0079i 0.0610012 + 0.0610012i 0.736949 0.675948i \(-0.236266\pi\)
−0.675948 + 0.736949i \(0.736266\pi\)
\(788\) 0 0
\(789\) 545.666i 0.691592i
\(790\) 0 0
\(791\) −683.514 −0.864114
\(792\) 0 0
\(793\) 249.885 249.885i 0.315114 0.315114i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −650.080 650.080i −0.815658 0.815658i 0.169817 0.985476i \(-0.445682\pi\)
−0.985476 + 0.169817i \(0.945682\pi\)
\(798\) 0 0
\(799\) 33.3939i 0.0417946i