Properties

Label 1950.2.f.p.649.3
Level $1950$
Weight $2$
Character 1950.649
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{17})\)
Defining polynomial: \(x^{4} + 9 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 649.3
Root \(-1.56155i\) of defining polynomial
Character \(\chi\) \(=\) 1950.649
Dual form 1950.2.f.p.649.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +0.438447 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +0.438447 q^{7} +1.00000 q^{8} -1.00000 q^{9} -1.56155i q^{11} +1.00000i q^{12} +(0.561553 - 3.56155i) q^{13} +0.438447 q^{14} +1.00000 q^{16} -6.68466i q^{17} -1.00000 q^{18} -7.68466i q^{19} +0.438447i q^{21} -1.56155i q^{22} +3.12311i q^{23} +1.00000i q^{24} +(0.561553 - 3.56155i) q^{26} -1.00000i q^{27} +0.438447 q^{28} +1.00000 q^{29} -5.56155i q^{31} +1.00000 q^{32} +1.56155 q^{33} -6.68466i q^{34} -1.00000 q^{36} +4.56155 q^{37} -7.68466i q^{38} +(3.56155 + 0.561553i) q^{39} +4.56155i q^{41} +0.438447i q^{42} +11.1231i q^{43} -1.56155i q^{44} +3.12311i q^{46} +8.12311 q^{47} +1.00000i q^{48} -6.80776 q^{49} +6.68466 q^{51} +(0.561553 - 3.56155i) q^{52} +5.00000i q^{53} -1.00000i q^{54} +0.438447 q^{56} +7.68466 q^{57} +1.00000 q^{58} -9.56155i q^{59} -0.684658 q^{61} -5.56155i q^{62} -0.438447 q^{63} +1.00000 q^{64} +1.56155 q^{66} -4.12311 q^{67} -6.68466i q^{68} -3.12311 q^{69} +13.9309i q^{71} -1.00000 q^{72} +7.12311 q^{73} +4.56155 q^{74} -7.68466i q^{76} -0.684658i q^{77} +(3.56155 + 0.561553i) q^{78} +2.31534 q^{79} +1.00000 q^{81} +4.56155i q^{82} +14.9309 q^{83} +0.438447i q^{84} +11.1231i q^{86} +1.00000i q^{87} -1.56155i q^{88} -5.12311i q^{89} +(0.246211 - 1.56155i) q^{91} +3.12311i q^{92} +5.56155 q^{93} +8.12311 q^{94} +1.00000i q^{96} -13.1231 q^{97} -6.80776 q^{98} +1.56155i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 4q^{4} + 10q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{2} + 4q^{4} + 10q^{7} + 4q^{8} - 4q^{9} - 6q^{13} + 10q^{14} + 4q^{16} - 4q^{18} - 6q^{26} + 10q^{28} + 4q^{29} + 4q^{32} - 2q^{33} - 4q^{36} + 10q^{37} + 6q^{39} + 16q^{47} + 14q^{49} + 2q^{51} - 6q^{52} + 10q^{56} + 6q^{57} + 4q^{58} + 22q^{61} - 10q^{63} + 4q^{64} - 2q^{66} + 4q^{69} - 4q^{72} + 12q^{73} + 10q^{74} + 6q^{78} + 34q^{79} + 4q^{81} + 2q^{83} - 32q^{91} + 14q^{93} + 16q^{94} - 36q^{97} + 14q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 0.438447 0.165717 0.0828587 0.996561i \(-0.473595\pi\)
0.0828587 + 0.996561i \(0.473595\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 1.56155i 0.470826i −0.971895 0.235413i \(-0.924356\pi\)
0.971895 0.235413i \(-0.0756443\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 0.561553 3.56155i 0.155747 0.987797i
\(14\) 0.438447 0.117180
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.68466i 1.62127i −0.585553 0.810634i \(-0.699123\pi\)
0.585553 0.810634i \(-0.300877\pi\)
\(18\) −1.00000 −0.235702
\(19\) 7.68466i 1.76298i −0.472201 0.881491i \(-0.656540\pi\)
0.472201 0.881491i \(-0.343460\pi\)
\(20\) 0 0
\(21\) 0.438447i 0.0956770i
\(22\) 1.56155i 0.332924i
\(23\) 3.12311i 0.651213i 0.945505 + 0.325606i \(0.105568\pi\)
−0.945505 + 0.325606i \(0.894432\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 0 0
\(26\) 0.561553 3.56155i 0.110130 0.698478i
\(27\) 1.00000i 0.192450i
\(28\) 0.438447 0.0828587
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) 5.56155i 0.998884i −0.866347 0.499442i \(-0.833538\pi\)
0.866347 0.499442i \(-0.166462\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.56155 0.271831
\(34\) 6.68466i 1.14641i
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 4.56155 0.749915 0.374957 0.927042i \(-0.377657\pi\)
0.374957 + 0.927042i \(0.377657\pi\)
\(38\) 7.68466i 1.24662i
\(39\) 3.56155 + 0.561553i 0.570305 + 0.0899204i
\(40\) 0 0
\(41\) 4.56155i 0.712395i 0.934411 + 0.356197i \(0.115927\pi\)
−0.934411 + 0.356197i \(0.884073\pi\)
\(42\) 0.438447i 0.0676539i
\(43\) 11.1231i 1.69626i 0.529790 + 0.848129i \(0.322271\pi\)
−0.529790 + 0.848129i \(0.677729\pi\)
\(44\) 1.56155i 0.235413i
\(45\) 0 0
\(46\) 3.12311i 0.460477i
\(47\) 8.12311 1.18488 0.592438 0.805616i \(-0.298165\pi\)
0.592438 + 0.805616i \(0.298165\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −6.80776 −0.972538
\(50\) 0 0
\(51\) 6.68466 0.936039
\(52\) 0.561553 3.56155i 0.0778734 0.493899i
\(53\) 5.00000i 0.686803i 0.939189 + 0.343401i \(0.111579\pi\)
−0.939189 + 0.343401i \(0.888421\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0 0
\(56\) 0.438447 0.0585900
\(57\) 7.68466 1.01786
\(58\) 1.00000 0.131306
\(59\) 9.56155i 1.24481i −0.782696 0.622404i \(-0.786156\pi\)
0.782696 0.622404i \(-0.213844\pi\)
\(60\) 0 0
\(61\) −0.684658 −0.0876615 −0.0438308 0.999039i \(-0.513956\pi\)
−0.0438308 + 0.999039i \(0.513956\pi\)
\(62\) 5.56155i 0.706318i
\(63\) −0.438447 −0.0552392
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.56155 0.192214
\(67\) −4.12311 −0.503718 −0.251859 0.967764i \(-0.581042\pi\)
−0.251859 + 0.967764i \(0.581042\pi\)
\(68\) 6.68466i 0.810634i
\(69\) −3.12311 −0.375978
\(70\) 0 0
\(71\) 13.9309i 1.65329i 0.562724 + 0.826645i \(0.309753\pi\)
−0.562724 + 0.826645i \(0.690247\pi\)
\(72\) −1.00000 −0.117851
\(73\) 7.12311 0.833696 0.416848 0.908976i \(-0.363135\pi\)
0.416848 + 0.908976i \(0.363135\pi\)
\(74\) 4.56155 0.530270
\(75\) 0 0
\(76\) 7.68466i 0.881491i
\(77\) 0.684658i 0.0780241i
\(78\) 3.56155 + 0.561553i 0.403266 + 0.0635833i
\(79\) 2.31534 0.260496 0.130248 0.991481i \(-0.458423\pi\)
0.130248 + 0.991481i \(0.458423\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 4.56155i 0.503739i
\(83\) 14.9309 1.63888 0.819438 0.573168i \(-0.194286\pi\)
0.819438 + 0.573168i \(0.194286\pi\)
\(84\) 0.438447i 0.0478385i
\(85\) 0 0
\(86\) 11.1231i 1.19944i
\(87\) 1.00000i 0.107211i
\(88\) 1.56155i 0.166462i
\(89\) 5.12311i 0.543048i −0.962432 0.271524i \(-0.912472\pi\)
0.962432 0.271524i \(-0.0875277\pi\)
\(90\) 0 0
\(91\) 0.246211 1.56155i 0.0258100 0.163695i
\(92\) 3.12311i 0.325606i
\(93\) 5.56155 0.576706
\(94\) 8.12311 0.837834
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −13.1231 −1.33245 −0.666225 0.745751i \(-0.732091\pi\)
−0.666225 + 0.745751i \(0.732091\pi\)
\(98\) −6.80776 −0.687688
\(99\) 1.56155i 0.156942i
\(100\) 0 0
\(101\) −12.4384 −1.23767 −0.618836 0.785520i \(-0.712395\pi\)
−0.618836 + 0.785520i \(0.712395\pi\)
\(102\) 6.68466 0.661880
\(103\) 7.12311i 0.701860i 0.936402 + 0.350930i \(0.114135\pi\)
−0.936402 + 0.350930i \(0.885865\pi\)
\(104\) 0.561553 3.56155i 0.0550648 0.349239i
\(105\) 0 0
\(106\) 5.00000i 0.485643i
\(107\) 0.315342i 0.0304852i 0.999884 + 0.0152426i \(0.00485206\pi\)
−0.999884 + 0.0152426i \(0.995148\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 20.5616i 1.96944i −0.174146 0.984720i \(-0.555717\pi\)
0.174146 0.984720i \(-0.444283\pi\)
\(110\) 0 0
\(111\) 4.56155i 0.432963i
\(112\) 0.438447 0.0414294
\(113\) 4.24621i 0.399450i −0.979852 0.199725i \(-0.935995\pi\)
0.979852 0.199725i \(-0.0640049\pi\)
\(114\) 7.68466 0.719734
\(115\) 0 0
\(116\) 1.00000 0.0928477
\(117\) −0.561553 + 3.56155i −0.0519156 + 0.329266i
\(118\) 9.56155i 0.880212i
\(119\) 2.93087i 0.268672i
\(120\) 0 0
\(121\) 8.56155 0.778323
\(122\) −0.684658 −0.0619861
\(123\) −4.56155 −0.411301
\(124\) 5.56155i 0.499442i
\(125\) 0 0
\(126\) −0.438447 −0.0390600
\(127\) 11.4384i 1.01500i −0.861652 0.507499i \(-0.830570\pi\)
0.861652 0.507499i \(-0.169430\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.1231 −0.979335
\(130\) 0 0
\(131\) −6.31534 −0.551774 −0.275887 0.961190i \(-0.588972\pi\)
−0.275887 + 0.961190i \(0.588972\pi\)
\(132\) 1.56155 0.135916
\(133\) 3.36932i 0.292157i
\(134\) −4.12311 −0.356182
\(135\) 0 0
\(136\) 6.68466i 0.573205i
\(137\) 6.56155 0.560591 0.280296 0.959914i \(-0.409567\pi\)
0.280296 + 0.959914i \(0.409567\pi\)
\(138\) −3.12311 −0.265856
\(139\) −16.4924 −1.39887 −0.699435 0.714697i \(-0.746565\pi\)
−0.699435 + 0.714697i \(0.746565\pi\)
\(140\) 0 0
\(141\) 8.12311i 0.684089i
\(142\) 13.9309i 1.16905i
\(143\) −5.56155 0.876894i −0.465080 0.0733296i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 7.12311 0.589512
\(147\) 6.80776i 0.561495i
\(148\) 4.56155 0.374957
\(149\) 19.3693i 1.58680i 0.608703 + 0.793398i \(0.291690\pi\)
−0.608703 + 0.793398i \(0.708310\pi\)
\(150\) 0 0
\(151\) 3.31534i 0.269799i 0.990859 + 0.134899i \(0.0430711\pi\)
−0.990859 + 0.134899i \(0.956929\pi\)
\(152\) 7.68466i 0.623308i
\(153\) 6.68466i 0.540423i
\(154\) 0.684658i 0.0551713i
\(155\) 0 0
\(156\) 3.56155 + 0.561553i 0.285152 + 0.0449602i
\(157\) 10.6847i 0.852729i 0.904552 + 0.426364i \(0.140206\pi\)
−0.904552 + 0.426364i \(0.859794\pi\)
\(158\) 2.31534 0.184199
\(159\) −5.00000 −0.396526
\(160\) 0 0
\(161\) 1.36932i 0.107917i
\(162\) 1.00000 0.0785674
\(163\) 16.4924 1.29179 0.645893 0.763428i \(-0.276485\pi\)
0.645893 + 0.763428i \(0.276485\pi\)
\(164\) 4.56155i 0.356197i
\(165\) 0 0
\(166\) 14.9309 1.15886
\(167\) 13.4384 1.03990 0.519949 0.854197i \(-0.325951\pi\)
0.519949 + 0.854197i \(0.325951\pi\)
\(168\) 0.438447i 0.0338269i
\(169\) −12.3693 4.00000i −0.951486 0.307692i
\(170\) 0 0
\(171\) 7.68466i 0.587661i
\(172\) 11.1231i 0.848129i
\(173\) 0.123106i 0.00935955i −0.999989 0.00467977i \(-0.998510\pi\)
0.999989 0.00467977i \(-0.00148962\pi\)
\(174\) 1.00000i 0.0758098i
\(175\) 0 0
\(176\) 1.56155i 0.117706i
\(177\) 9.56155 0.718690
\(178\) 5.12311i 0.383993i
\(179\) 19.1231 1.42933 0.714664 0.699468i \(-0.246580\pi\)
0.714664 + 0.699468i \(0.246580\pi\)
\(180\) 0 0
\(181\) 0.192236 0.0142888 0.00714439 0.999974i \(-0.497726\pi\)
0.00714439 + 0.999974i \(0.497726\pi\)
\(182\) 0.246211 1.56155i 0.0182504 0.115750i
\(183\) 0.684658i 0.0506114i
\(184\) 3.12311i 0.230238i
\(185\) 0 0
\(186\) 5.56155 0.407793
\(187\) −10.4384 −0.763335
\(188\) 8.12311 0.592438
\(189\) 0.438447i 0.0318923i
\(190\) 0 0
\(191\) −16.4924 −1.19335 −0.596675 0.802483i \(-0.703512\pi\)
−0.596675 + 0.802483i \(0.703512\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −4.87689 −0.351047 −0.175523 0.984475i \(-0.556162\pi\)
−0.175523 + 0.984475i \(0.556162\pi\)
\(194\) −13.1231 −0.942184
\(195\) 0 0
\(196\) −6.80776 −0.486269
\(197\) 12.2462 0.872506 0.436253 0.899824i \(-0.356305\pi\)
0.436253 + 0.899824i \(0.356305\pi\)
\(198\) 1.56155i 0.110975i
\(199\) 5.93087 0.420428 0.210214 0.977655i \(-0.432584\pi\)
0.210214 + 0.977655i \(0.432584\pi\)
\(200\) 0 0
\(201\) 4.12311i 0.290821i
\(202\) −12.4384 −0.875166
\(203\) 0.438447 0.0307730
\(204\) 6.68466 0.468020
\(205\) 0 0
\(206\) 7.12311i 0.496290i
\(207\) 3.12311i 0.217071i
\(208\) 0.561553 3.56155i 0.0389367 0.246949i
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) −17.3693 −1.19575 −0.597877 0.801588i \(-0.703989\pi\)
−0.597877 + 0.801588i \(0.703989\pi\)
\(212\) 5.00000i 0.343401i
\(213\) −13.9309 −0.954527
\(214\) 0.315342i 0.0215563i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 2.43845i 0.165533i
\(218\) 20.5616i 1.39260i
\(219\) 7.12311i 0.481335i
\(220\) 0 0
\(221\) −23.8078 3.75379i −1.60148 0.252507i
\(222\) 4.56155i 0.306151i
\(223\) 15.3693 1.02921 0.514603 0.857429i \(-0.327939\pi\)
0.514603 + 0.857429i \(0.327939\pi\)
\(224\) 0.438447 0.0292950
\(225\) 0 0
\(226\) 4.24621i 0.282454i
\(227\) −3.31534 −0.220047 −0.110023 0.993929i \(-0.535093\pi\)
−0.110023 + 0.993929i \(0.535093\pi\)
\(228\) 7.68466 0.508929
\(229\) 7.19224i 0.475276i −0.971354 0.237638i \(-0.923627\pi\)
0.971354 0.237638i \(-0.0763732\pi\)
\(230\) 0 0
\(231\) 0.684658 0.0450472
\(232\) 1.00000 0.0656532
\(233\) 3.12311i 0.204601i 0.994754 + 0.102301i \(0.0326204\pi\)
−0.994754 + 0.102301i \(0.967380\pi\)
\(234\) −0.561553 + 3.56155i −0.0367099 + 0.232826i
\(235\) 0 0
\(236\) 9.56155i 0.622404i
\(237\) 2.31534i 0.150398i
\(238\) 2.93087i 0.189980i
\(239\) 6.93087i 0.448321i 0.974552 + 0.224160i \(0.0719639\pi\)
−0.974552 + 0.224160i \(0.928036\pi\)
\(240\) 0 0
\(241\) 20.2462i 1.30417i −0.758145 0.652087i \(-0.773894\pi\)
0.758145 0.652087i \(-0.226106\pi\)
\(242\) 8.56155 0.550357
\(243\) 1.00000i 0.0641500i
\(244\) −0.684658 −0.0438308
\(245\) 0 0
\(246\) −4.56155 −0.290834
\(247\) −27.3693 4.31534i −1.74147 0.274579i
\(248\) 5.56155i 0.353159i
\(249\) 14.9309i 0.946205i
\(250\) 0 0
\(251\) 11.4384 0.721988 0.360994 0.932568i \(-0.382437\pi\)
0.360994 + 0.932568i \(0.382437\pi\)
\(252\) −0.438447 −0.0276196
\(253\) 4.87689 0.306608
\(254\) 11.4384i 0.717712i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 15.8078i 0.986061i 0.870012 + 0.493031i \(0.164111\pi\)
−0.870012 + 0.493031i \(0.835889\pi\)
\(258\) −11.1231 −0.692494
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) −6.31534 −0.390163
\(263\) 24.7386i 1.52545i 0.646723 + 0.762725i \(0.276139\pi\)
−0.646723 + 0.762725i \(0.723861\pi\)
\(264\) 1.56155 0.0961069
\(265\) 0 0
\(266\) 3.36932i 0.206586i
\(267\) 5.12311 0.313529
\(268\) −4.12311 −0.251859
\(269\) 9.49242 0.578763 0.289382 0.957214i \(-0.406550\pi\)
0.289382 + 0.957214i \(0.406550\pi\)
\(270\) 0 0
\(271\) 4.19224i 0.254660i −0.991860 0.127330i \(-0.959359\pi\)
0.991860 0.127330i \(-0.0406408\pi\)
\(272\) 6.68466i 0.405317i
\(273\) 1.56155 + 0.246211i 0.0945095 + 0.0149014i
\(274\) 6.56155 0.396398
\(275\) 0 0
\(276\) −3.12311 −0.187989
\(277\) 15.6155i 0.938246i 0.883133 + 0.469123i \(0.155430\pi\)
−0.883133 + 0.469123i \(0.844570\pi\)
\(278\) −16.4924 −0.989150
\(279\) 5.56155i 0.332961i
\(280\) 0 0
\(281\) 5.93087i 0.353806i 0.984228 + 0.176903i \(0.0566079\pi\)
−0.984228 + 0.176903i \(0.943392\pi\)
\(282\) 8.12311i 0.483724i
\(283\) 7.36932i 0.438060i −0.975718 0.219030i \(-0.929711\pi\)
0.975718 0.219030i \(-0.0702893\pi\)
\(284\) 13.9309i 0.826645i
\(285\) 0 0
\(286\) −5.56155 0.876894i −0.328862 0.0518519i
\(287\) 2.00000i 0.118056i
\(288\) −1.00000 −0.0589256
\(289\) −27.6847 −1.62851
\(290\) 0 0
\(291\) 13.1231i 0.769290i
\(292\) 7.12311 0.416848
\(293\) 0.630683 0.0368449 0.0184225 0.999830i \(-0.494136\pi\)
0.0184225 + 0.999830i \(0.494136\pi\)
\(294\) 6.80776i 0.397037i
\(295\) 0 0
\(296\) 4.56155 0.265135
\(297\) −1.56155 −0.0906105
\(298\) 19.3693i 1.12203i
\(299\) 11.1231 + 1.75379i 0.643266 + 0.101424i
\(300\) 0 0
\(301\) 4.87689i 0.281100i
\(302\) 3.31534i 0.190776i
\(303\) 12.4384i 0.714570i
\(304\) 7.68466i 0.440745i
\(305\) 0 0
\(306\) 6.68466i 0.382136i
\(307\) 2.06913 0.118092 0.0590458 0.998255i \(-0.481194\pi\)
0.0590458 + 0.998255i \(0.481194\pi\)
\(308\) 0.684658i 0.0390120i
\(309\) −7.12311 −0.405219
\(310\) 0 0
\(311\) 14.8769 0.843591 0.421796 0.906691i \(-0.361400\pi\)
0.421796 + 0.906691i \(0.361400\pi\)
\(312\) 3.56155 + 0.561553i 0.201633 + 0.0317917i
\(313\) 24.8617i 1.40527i 0.711551 + 0.702634i \(0.247993\pi\)
−0.711551 + 0.702634i \(0.752007\pi\)
\(314\) 10.6847i 0.602970i
\(315\) 0 0
\(316\) 2.31534 0.130248
\(317\) −30.0000 −1.68497 −0.842484 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) −5.00000 −0.280386
\(319\) 1.56155i 0.0874302i
\(320\) 0 0
\(321\) −0.315342 −0.0176006
\(322\) 1.36932i 0.0763090i
\(323\) −51.3693 −2.85827
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 16.4924 0.913431
\(327\) 20.5616 1.13706
\(328\) 4.56155i 0.251870i
\(329\) 3.56155 0.196355
\(330\) 0 0
\(331\) 24.4924i 1.34623i −0.739540 0.673113i \(-0.764957\pi\)
0.739540 0.673113i \(-0.235043\pi\)
\(332\) 14.9309 0.819438
\(333\) −4.56155 −0.249972
\(334\) 13.4384 0.735319
\(335\) 0 0
\(336\) 0.438447i 0.0239193i
\(337\) 10.6847i 0.582030i 0.956718 + 0.291015i \(0.0939930\pi\)
−0.956718 + 0.291015i \(0.906007\pi\)
\(338\) −12.3693 4.00000i −0.672802 0.217571i
\(339\) 4.24621 0.230623
\(340\) 0 0
\(341\) −8.68466 −0.470301
\(342\) 7.68466i 0.415539i
\(343\) −6.05398 −0.326884
\(344\) 11.1231i 0.599718i
\(345\) 0 0
\(346\) 0.123106i 0.00661820i
\(347\) 18.5616i 0.996436i −0.867052 0.498218i \(-0.833988\pi\)
0.867052 0.498218i \(-0.166012\pi\)
\(348\) 1.00000i 0.0536056i
\(349\) 22.0000i 1.17763i 0.808267 + 0.588817i \(0.200406\pi\)
−0.808267 + 0.588817i \(0.799594\pi\)
\(350\) 0 0
\(351\) −3.56155 0.561553i −0.190102 0.0299735i
\(352\) 1.56155i 0.0832310i
\(353\) −15.4384 −0.821706 −0.410853 0.911702i \(-0.634769\pi\)
−0.410853 + 0.911702i \(0.634769\pi\)
\(354\) 9.56155 0.508191
\(355\) 0 0
\(356\) 5.12311i 0.271524i
\(357\) 2.93087 0.155118
\(358\) 19.1231 1.01069
\(359\) 3.87689i 0.204615i 0.994753 + 0.102307i \(0.0326225\pi\)
−0.994753 + 0.102307i \(0.967377\pi\)
\(360\) 0 0
\(361\) −40.0540 −2.10810
\(362\) 0.192236 0.0101037
\(363\) 8.56155i 0.449365i
\(364\) 0.246211 1.56155i 0.0129050 0.0818476i
\(365\) 0 0
\(366\) 0.684658i 0.0357877i
\(367\) 19.6847i 1.02753i −0.857931 0.513765i \(-0.828250\pi\)
0.857931 0.513765i \(-0.171750\pi\)
\(368\) 3.12311i 0.162803i
\(369\) 4.56155i 0.237465i
\(370\) 0 0
\(371\) 2.19224i 0.113815i
\(372\) 5.56155 0.288353
\(373\) 32.4384i 1.67960i −0.542897 0.839800i \(-0.682672\pi\)
0.542897 0.839800i \(-0.317328\pi\)
\(374\) −10.4384 −0.539759
\(375\) 0 0
\(376\) 8.12311 0.418917
\(377\) 0.561553 3.56155i 0.0289214 0.183429i
\(378\) 0.438447i 0.0225513i
\(379\) 7.31534i 0.375764i 0.982192 + 0.187882i \(0.0601622\pi\)
−0.982192 + 0.187882i \(0.939838\pi\)
\(380\) 0 0
\(381\) 11.4384 0.586009
\(382\) −16.4924 −0.843826
\(383\) 13.9309 0.711834 0.355917 0.934518i \(-0.384169\pi\)
0.355917 + 0.934518i \(0.384169\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) −4.87689 −0.248227
\(387\) 11.1231i 0.565419i
\(388\) −13.1231 −0.666225
\(389\) 6.80776 0.345167 0.172584 0.984995i \(-0.444788\pi\)
0.172584 + 0.984995i \(0.444788\pi\)
\(390\) 0 0
\(391\) 20.8769 1.05579
\(392\) −6.80776 −0.343844
\(393\) 6.31534i 0.318567i
\(394\) 12.2462 0.616955
\(395\) 0 0
\(396\) 1.56155i 0.0784710i
\(397\) −35.0540 −1.75931 −0.879654 0.475614i \(-0.842226\pi\)
−0.879654 + 0.475614i \(0.842226\pi\)
\(398\) 5.93087 0.297288
\(399\) 3.36932 0.168677
\(400\) 0 0
\(401\) 22.0000i 1.09863i 0.835616 + 0.549314i \(0.185111\pi\)
−0.835616 + 0.549314i \(0.814889\pi\)
\(402\) 4.12311i 0.205642i
\(403\) −19.8078 3.12311i −0.986695 0.155573i
\(404\) −12.4384 −0.618836
\(405\) 0 0
\(406\) 0.438447 0.0217598
\(407\) 7.12311i 0.353079i
\(408\) 6.68466 0.330940
\(409\) 27.6155i 1.36550i 0.730652 + 0.682750i \(0.239216\pi\)
−0.730652 + 0.682750i \(0.760784\pi\)
\(410\) 0 0
\(411\) 6.56155i 0.323658i
\(412\) 7.12311i 0.350930i
\(413\) 4.19224i 0.206286i
\(414\) 3.12311i 0.153492i
\(415\) 0 0
\(416\) 0.561553 3.56155i 0.0275324 0.174619i
\(417\) 16.4924i 0.807637i
\(418\) −12.0000 −0.586939
\(419\) 5.68466 0.277714 0.138857 0.990312i \(-0.455657\pi\)
0.138857 + 0.990312i \(0.455657\pi\)
\(420\) 0 0
\(421\) 4.63068i 0.225686i −0.993613 0.112843i \(-0.964004\pi\)
0.993613 0.112843i \(-0.0359957\pi\)
\(422\) −17.3693 −0.845525
\(423\) −8.12311 −0.394959
\(424\) 5.00000i 0.242821i
\(425\) 0 0
\(426\) −13.9309 −0.674953
\(427\) −0.300187 −0.0145270
\(428\) 0.315342i 0.0152426i
\(429\) 0.876894 5.56155i 0.0423369 0.268514i
\(430\) 0 0
\(431\) 8.17708i 0.393876i −0.980416 0.196938i \(-0.936900\pi\)
0.980416 0.196938i \(-0.0630998\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 5.05398i 0.242879i −0.992599 0.121439i \(-0.961249\pi\)
0.992599 0.121439i \(-0.0387510\pi\)
\(434\) 2.43845i 0.117049i
\(435\) 0 0
\(436\) 20.5616i 0.984720i
\(437\) 24.0000 1.14808
\(438\) 7.12311i 0.340355i
\(439\) 27.3002 1.30297 0.651483 0.758663i \(-0.274147\pi\)
0.651483 + 0.758663i \(0.274147\pi\)
\(440\) 0 0
\(441\) 6.80776 0.324179
\(442\) −23.8078 3.75379i −1.13242 0.178550i
\(443\) 28.5616i 1.35700i 0.734600 + 0.678500i \(0.237370\pi\)
−0.734600 + 0.678500i \(0.762630\pi\)
\(444\) 4.56155i 0.216482i
\(445\) 0 0
\(446\) 15.3693 0.727758
\(447\) −19.3693 −0.916137
\(448\) 0.438447 0.0207147
\(449\) 5.43845i 0.256656i −0.991732 0.128328i \(-0.959039\pi\)
0.991732 0.128328i \(-0.0409611\pi\)
\(450\) 0 0
\(451\) 7.12311 0.335414
\(452\) 4.24621i 0.199725i
\(453\) −3.31534 −0.155768
\(454\) −3.31534 −0.155597
\(455\) 0 0
\(456\) 7.68466 0.359867
\(457\) −28.7386 −1.34434 −0.672168 0.740398i \(-0.734637\pi\)
−0.672168 + 0.740398i \(0.734637\pi\)
\(458\) 7.19224i 0.336071i
\(459\) −6.68466 −0.312013
\(460\) 0 0
\(461\) 22.2462i 1.03611i −0.855348 0.518055i \(-0.826656\pi\)
0.855348 0.518055i \(-0.173344\pi\)
\(462\) 0.684658 0.0318532
\(463\) −11.5616 −0.537311 −0.268655 0.963236i \(-0.586579\pi\)
−0.268655 + 0.963236i \(0.586579\pi\)
\(464\) 1.00000 0.0464238
\(465\) 0 0
\(466\) 3.12311i 0.144675i
\(467\) 40.8078i 1.88836i 0.329433 + 0.944179i \(0.393143\pi\)
−0.329433 + 0.944179i \(0.606857\pi\)
\(468\) −0.561553 + 3.56155i −0.0259578 + 0.164633i
\(469\) −1.80776 −0.0834748
\(470\) 0 0
\(471\) −10.6847 −0.492323
\(472\) 9.56155i 0.440106i
\(473\) 17.3693 0.798642
\(474\) 2.31534i 0.106347i
\(475\) 0 0
\(476\) 2.93087i 0.134336i
\(477\) 5.00000i 0.228934i
\(478\) 6.93087i 0.317011i
\(479\) 32.1231i 1.46774i 0.679289 + 0.733871i \(0.262288\pi\)
−0.679289 + 0.733871i \(0.737712\pi\)
\(480\) 0 0
\(481\) 2.56155 16.2462i 0.116797 0.740763i
\(482\) 20.2462i 0.922190i
\(483\) −1.36932 −0.0623061
\(484\) 8.56155 0.389161
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −6.68466 −0.302911 −0.151455 0.988464i \(-0.548396\pi\)
−0.151455 + 0.988464i \(0.548396\pi\)
\(488\) −0.684658 −0.0309930
\(489\) 16.4924i 0.745813i
\(490\) 0 0
\(491\) 38.7386 1.74825 0.874125 0.485701i \(-0.161436\pi\)
0.874125 + 0.485701i \(0.161436\pi\)
\(492\) −4.56155 −0.205651
\(493\) 6.68466i 0.301062i
\(494\) −27.3693 4.31534i −1.23140 0.194156i
\(495\) 0 0
\(496\) 5.56155i 0.249721i
\(497\) 6.10795i 0.273979i
\(498\) 14.9309i 0.669068i
\(499\) 28.1231i 1.25896i −0.777015 0.629482i \(-0.783267\pi\)
0.777015 0.629482i \(-0.216733\pi\)
\(500\) 0 0
\(501\) 13.4384i 0.600386i
\(502\) 11.4384 0.510523
\(503\) 8.73863i 0.389636i 0.980839 + 0.194818i \(0.0624117\pi\)
−0.980839 + 0.194818i \(0.937588\pi\)
\(504\) −0.438447 −0.0195300
\(505\) 0 0
\(506\) 4.87689 0.216804
\(507\) 4.00000 12.3693i 0.177646 0.549341i
\(508\) 11.4384i 0.507499i
\(509\) 22.4924i 0.996959i 0.866901 + 0.498480i \(0.166108\pi\)
−0.866901 + 0.498480i \(0.833892\pi\)
\(510\) 0 0
\(511\) 3.12311 0.138158
\(512\) 1.00000 0.0441942
\(513\) −7.68466 −0.339286
\(514\) 15.8078i 0.697251i
\(515\) 0 0
\(516\) −11.1231 −0.489667
\(517\) 12.6847i 0.557871i
\(518\) 2.00000 0.0878750
\(519\) 0.123106 0.00540374
\(520\) 0 0
\(521\) −16.2462 −0.711759 −0.355880 0.934532i \(-0.615819\pi\)
−0.355880 + 0.934532i \(0.615819\pi\)
\(522\) −1.00000 −0.0437688
\(523\) 0.630683i 0.0275778i 0.999905 + 0.0137889i \(0.00438929\pi\)
−0.999905 + 0.0137889i \(0.995611\pi\)
\(524\) −6.31534 −0.275887
\(525\) 0 0
\(526\) 24.7386i 1.07866i
\(527\) −37.1771 −1.61946
\(528\) 1.56155 0.0679579
\(529\) 13.2462 0.575922
\(530\) 0 0
\(531\) 9.56155i 0.414936i
\(532\) 3.36932i 0.146078i
\(533\) 16.2462 + 2.56155i 0.703702 + 0.110953i
\(534\) 5.12311 0.221698
\(535\) 0 0
\(536\) −4.12311 −0.178091
\(537\) 19.1231i 0.825223i
\(538\) 9.49242 0.409247
\(539\) 10.6307i 0.457896i
\(540\) 0 0
\(541\) 32.2462i 1.38637i 0.720758 + 0.693186i \(0.243794\pi\)
−0.720758 + 0.693186i \(0.756206\pi\)
\(542\) 4.19224i 0.180072i
\(543\) 0.192236i 0.00824963i
\(544\) 6.68466i 0.286602i
\(545\) 0 0
\(546\) 1.56155 + 0.246211i 0.0668283 + 0.0105369i
\(547\) 7.12311i 0.304562i −0.988337 0.152281i \(-0.951338\pi\)
0.988337 0.152281i \(-0.0486619\pi\)
\(548\) 6.56155 0.280296
\(549\) 0.684658 0.0292205
\(550\) 0 0
\(551\) 7.68466i 0.327377i
\(552\) −3.12311 −0.132928
\(553\) 1.01515 0.0431688
\(554\) 15.6155i 0.663440i
\(555\) 0 0
\(556\) −16.4924 −0.699435
\(557\) 41.8617 1.77374 0.886869 0.462020i \(-0.152875\pi\)
0.886869 + 0.462020i \(0.152875\pi\)
\(558\) 5.56155i 0.235439i
\(559\) 39.6155 + 6.24621i 1.67556 + 0.264187i
\(560\) 0 0
\(561\) 10.4384i 0.440712i
\(562\) 5.93087i 0.250179i
\(563\) 43.3002i 1.82489i 0.409205 + 0.912443i \(0.365806\pi\)
−0.409205 + 0.912443i \(0.634194\pi\)
\(564\) 8.12311i 0.342044i
\(565\) 0 0
\(566\) 7.36932i 0.309755i
\(567\) 0.438447 0.0184131
\(568\) 13.9309i 0.584526i
\(569\) 7.31534 0.306675 0.153338 0.988174i \(-0.450998\pi\)
0.153338 + 0.988174i \(0.450998\pi\)
\(570\) 0 0
\(571\) 27.1231 1.13507 0.567533 0.823350i \(-0.307898\pi\)
0.567533 + 0.823350i \(0.307898\pi\)
\(572\) −5.56155 0.876894i −0.232540 0.0366648i
\(573\) 16.4924i 0.688981i
\(574\) 2.00000i 0.0834784i
\(575\) 0 0
\(576\) −1.00000 −0.0416667
\(577\) −8.63068 −0.359300 −0.179650 0.983731i \(-0.557497\pi\)
−0.179650 + 0.983731i \(0.557497\pi\)
\(578\) −27.6847 −1.15153
\(579\) 4.87689i 0.202677i
\(580\) 0 0
\(581\) 6.54640 0.271590
\(582\) 13.1231i 0.543970i
\(583\) 7.80776 0.323365
\(584\) 7.12311 0.294756
\(585\) 0 0
\(586\) 0.630683 0.0260533
\(587\) 18.9309 0.781361 0.390680 0.920526i \(-0.372240\pi\)
0.390680 + 0.920526i \(0.372240\pi\)
\(588\) 6.80776i 0.280747i
\(589\) −42.7386 −1.76101
\(590\) 0 0
\(591\) 12.2462i 0.503742i
\(592\) 4.56155 0.187479
\(593\) −24.8078 −1.01873 −0.509366 0.860550i \(-0.670120\pi\)
−0.509366 + 0.860550i \(0.670120\pi\)
\(594\) −1.56155 −0.0640713
\(595\) 0 0
\(596\) 19.3693i 0.793398i
\(597\) 5.93087i 0.242734i
\(598\) 11.1231 + 1.75379i 0.454858 + 0.0717178i
\(599\) 22.9848 0.939135 0.469568 0.882896i \(-0.344410\pi\)
0.469568 + 0.882896i \(0.344410\pi\)
\(600\) 0 0
\(601\) 11.7386 0.478829 0.239414 0.970917i \(-0.423045\pi\)
0.239414 + 0.970917i \(0.423045\pi\)
\(602\) 4.87689i 0.198767i
\(603\) 4.12311 0.167906
\(604\) 3.31534i 0.134899i
\(605\) 0 0
\(606\) 12.4384i 0.505277i
\(607\) 47.0540i 1.90986i −0.296828 0.954931i \(-0.595929\pi\)
0.296828 0.954931i \(-0.404071\pi\)
\(608\) 7.68466i 0.311654i
\(609\) 0.438447i 0.0177668i
\(610\) 0 0
\(611\) 4.56155 28.9309i 0.184541 1.17042i
\(612\) 6.68466i 0.270211i
\(613\) −39.3693 −1.59011 −0.795056 0.606536i \(-0.792559\pi\)
−0.795056 + 0.606536i \(0.792559\pi\)
\(614\) 2.06913 0.0835033
\(615\) 0 0
\(616\) 0.684658i 0.0275857i
\(617\) −27.6847 −1.11454 −0.557271 0.830331i \(-0.688152\pi\)
−0.557271 + 0.830331i \(0.688152\pi\)
\(618\) −7.12311 −0.286533
\(619\) 2.24621i 0.0902829i −0.998981 0.0451414i \(-0.985626\pi\)
0.998981 0.0451414i \(-0.0143738\pi\)
\(620\) 0 0
\(621\) 3.12311 0.125326
\(622\) 14.8769 0.596509
\(623\) 2.24621i 0.0899926i
\(624\) 3.56155 + 0.561553i 0.142576 + 0.0224801i
\(625\) 0 0
\(626\) 24.8617i 0.993675i
\(627\) 12.0000i 0.479234i
\(628\) 10.6847i 0.426364i
\(629\) 30.4924i 1.21581i
\(630\) 0 0
\(631\) 22.8769i 0.910715i −0.890309 0.455357i \(-0.849511\pi\)
0.890309 0.455357i \(-0.150489\pi\)
\(632\) 2.31534 0.0920993
\(633\) 17.3693i 0.690368i
\(634\) −30.0000 −1.19145
\(635\) 0 0
\(636\) −5.00000 −0.198263
\(637\) −3.82292 + 24.2462i −0.151470 + 0.960670i
\(638\) 1.56155i 0.0618225i
\(639\) 13.9309i 0.551097i
\(640\) 0 0
\(641\) −19.4233 −0.767174 −0.383587 0.923505i \(-0.625311\pi\)
−0.383587 + 0.923505i \(0.625311\pi\)
\(642\) −0.315342 −0.0124455
\(643\) 15.6847 0.618543 0.309271 0.950974i \(-0.399915\pi\)
0.309271 + 0.950974i \(0.399915\pi\)
\(644\) 1.36932i 0.0539586i
\(645\) 0 0
\(646\) −51.3693 −2.02110
\(647\) 10.8769i 0.427615i 0.976876 + 0.213807i \(0.0685865\pi\)
−0.976876 + 0.213807i \(0.931413\pi\)
\(648\) 1.00000 0.0392837
\(649\) −14.9309 −0.586088
\(650\) 0 0
\(651\) 2.43845 0.0955703
\(652\) 16.4924 0.645893
\(653\) 46.3002i 1.81187i −0.423421 0.905933i \(-0.639171\pi\)
0.423421 0.905933i \(-0.360829\pi\)
\(654\) 20.5616 0.804020
\(655\) 0 0
\(656\) 4.56155i 0.178099i
\(657\) −7.12311 −0.277899
\(658\) 3.56155 0.138844
\(659\) 12.5616 0.489329 0.244664 0.969608i \(-0.421322\pi\)
0.244664 + 0.969608i \(0.421322\pi\)
\(660\) 0 0
\(661\) 15.3002i 0.595108i −0.954705 0.297554i \(-0.903829\pi\)
0.954705 0.297554i \(-0.0961709\pi\)
\(662\) 24.4924i 0.951925i
\(663\) 3.75379 23.8078i 0.145785 0.924617i
\(664\) 14.9309 0.579430
\(665\) 0 0
\(666\) −4.56155 −0.176757
\(667\) 3.12311i 0.120927i
\(668\) 13.4384 0.519949
\(669\) 15.3693i 0.594212i
\(670\) 0 0
\(671\) 1.06913i 0.0412733i
\(672\) 0.438447i 0.0169135i
\(673\) 22.1231i 0.852783i 0.904539 + 0.426392i \(0.140215\pi\)
−0.904539 + 0.426392i \(0.859785\pi\)
\(674\) 10.6847i 0.411558i
\(675\) 0 0
\(676\) −12.3693 4.00000i −0.475743 0.153846i
\(677\) 36.2462i 1.39306i 0.717530 + 0.696528i \(0.245273\pi\)
−0.717530 + 0.696528i \(0.754727\pi\)
\(678\) 4.24621 0.163075
\(679\) −5.75379 −0.220810
\(680\) 0 0
\(681\) 3.31534i 0.127044i
\(682\) −8.68466 −0.332553
\(683\) 35.6695 1.36486 0.682428 0.730953i \(-0.260924\pi\)
0.682428 + 0.730953i \(0.260924\pi\)
\(684\) 7.68466i 0.293830i
\(685\) 0 0
\(686\) −6.05398 −0.231142
\(687\) 7.19224 0.274401
\(688\) 11.1231i 0.424064i
\(689\) 17.8078 + 2.80776i 0.678422 + 0.106967i
\(690\) 0 0
\(691\) 35.0000i 1.33146i 0.746191 + 0.665731i \(0.231880\pi\)
−0.746191 + 0.665731i \(0.768120\pi\)
\(692\) 0.123106i 0.00467977i
\(693\) 0.684658i 0.0260080i
\(694\) 18.5616i 0.704587i
\(695\) 0 0
\(696\) 1.00000i 0.0379049i
\(697\) 30.4924 1.15498
\(698\) 22.0000i 0.832712i
\(699\) −3.12311 −0.118127
\(700\) 0 0
\(701\) 26.6847 1.00787 0.503933 0.863743i \(-0.331886\pi\)
0.503933 + 0.863743i \(0.331886\pi\)
\(702\) −3.56155 0.561553i −0.134422 0.0211944i
\(703\) 35.0540i 1.32209i
\(704\) 1.56155i 0.0588532i
\(705\) 0 0
\(706\) −15.4384 −0.581034
\(707\) −5.45360 −0.205104
\(708\) 9.56155 0.359345
\(709\) 6.49242i 0.243828i −0.992541 0.121914i \(-0.961097\pi\)
0.992541 0.121914i \(-0.0389032\pi\)
\(710\) 0 0
\(711\) −2.31534 −0.0868321
\(712\) 5.12311i 0.191997i
\(713\) 17.3693 0.650486
\(714\) 2.93087 0.109685
\(715\) 0 0
\(716\) 19.1231 0.714664
\(717\) −6.93087 −0.258838
\(718\) 3.87689i 0.144684i
\(719\) −25.3693 −0.946116 −0.473058 0.881031i \(-0.656850\pi\)
−0.473058 + 0.881031i \(0.656850\pi\)
\(720\) 0 0
\(721\) 3.12311i 0.116311i
\(722\) −40.0540 −1.49065
\(723\) 20.2462 0.752965
\(724\) 0.192236 0.00714439
\(725\) 0 0
\(726\) 8.56155i 0.317749i
\(727\) 0.384472i 0.0142593i 0.999975 + 0.00712964i \(0.00226945\pi\)
−0.999975 + 0.00712964i \(0.997731\pi\)
\(728\) 0.246211 1.56155i 0.00912520 0.0578750i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 74.3542 2.75009
\(732\) 0.684658i 0.0253057i
\(733\) 39.6847 1.46579 0.732893 0.680344i \(-0.238170\pi\)
0.732893 + 0.680344i \(0.238170\pi\)
\(734\) 19.6847i 0.726574i
\(735\) 0 0
\(736\) 3.12311i 0.115119i
\(737\) 6.43845i 0.237163i
\(738\) 4.56155i 0.167913i
\(739\) 47.4924i 1.74704i 0.486791 + 0.873519i \(0.338167\pi\)
−0.486791 + 0.873519i \(0.661833\pi\)
\(740\) 0 0
\(741\) 4.31534 27.3693i 0.158528 1.00544i
\(742\) 2.19224i 0.0804795i
\(743\) 26.3693 0.967396 0.483698 0.875235i \(-0.339293\pi\)
0.483698 + 0.875235i \(0.339293\pi\)
\(744\) 5.56155 0.203896
\(745\) 0 0
\(746\) 32.4384i 1.18766i
\(747\) −14.9309 −0.546292
\(748\) −10.4384 −0.381667
\(749\) 0.138261i 0.00505193i
\(750\) 0 0
\(751\) −14.8078 −0.540343 −0.270171 0.962812i \(-0.587080\pi\)
−0.270171 + 0.962812i \(0.587080\pi\)
\(752\) 8.12311 0.296219
\(753\) 11.4384i 0.416840i
\(754\) 0.561553 3.56155i 0.0204505 0.129704i
\(755\) 0 0
\(756\) 0.438447i 0.0159462i
\(757\) 2.93087i 0.106524i 0.998581 + 0.0532621i \(0.0169619\pi\)
−0.998581 + 0.0532621i \(0.983038\pi\)
\(758\) 7.31534i 0.265705i
\(759\) 4.87689i 0.177020i
\(760\) 0 0
\(761\) 42.6695i 1.54677i 0.633938 + 0.773384i \(0.281438\pi\)
−0.633938 + 0.773384i \(0.718562\pi\)
\(762\) 11.4384 0.414371
\(763\) 9.01515i 0.326371i
\(764\) −16.4924 −0.596675
\(765\) 0 0
\(766\) 13.9309 0.503343
\(767\) −34.0540 5.36932i −1.22962 0.193875i
\(768\) 1.00000i 0.0360844i
\(769\) 2.24621i 0.0810004i 0.999180 + 0.0405002i \(0.0128951\pi\)
−0.999180 + 0.0405002i \(0.987105\pi\)
\(770\) 0 0
\(771\) −15.8078 −0.569303
\(772\) −4.87689 −0.175523
\(773\) −31.2311 −1.12330 −0.561652 0.827374i \(-0.689834\pi\)
−0.561652 + 0.827374i \(0.689834\pi\)
\(774\) 11.1231i 0.399812i
\(775\) 0 0
\(776\) −13.1231 −0.471092
\(777\) 2.00000i 0.0717496i
\(778\) 6.80776 0.244070
\(779\) 35.0540 1.25594
\(780\) 0 0
\(781\) 21.7538 0.778412
\(782\) 20.8769 0.746556
\(783\) 1.00000i 0.0357371i
\(784\) −6.80776 −0.243134
\(785\) 0 0
\(786\) 6.31534i 0.225261i
\(787\) 30.9309 1.10257 0.551283 0.834318i \(-0.314138\pi\)
0.551283 + 0.834318i \(0.314138\pi\)
\(788\) 12.2462 0.436253
\(789\) −24.7386 −0.880719
\(790\) 0 0
\(791\) 1.86174i 0.0661958i
\(792\) 1.56155i 0.0554874i
\(793\) −0.384472 + 2.43845i −0.0136530 + 0.0865918i
\(794\) −35.0540 −1.24402
\(795\) 0 0
\(796\) 5.93087