Properties

Label 1950.2.f.o.649.4
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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 649.4
Root \(1.56155i\) of defining polynomial
Character \(\chi\) \(=\) 1950.649
Dual form 1950.2.f.o.649.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +5.12311 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +5.12311 q^{7} +1.00000 q^{8} -1.00000 q^{9} +3.12311i q^{11} +1.00000i q^{12} +(3.56155 - 0.561553i) q^{13} +5.12311 q^{14} +1.00000 q^{16} -2.00000i q^{17} -1.00000 q^{18} -6.00000i q^{19} +5.12311i q^{21} +3.12311i q^{22} +3.12311i q^{23} +1.00000i q^{24} +(3.56155 - 0.561553i) q^{26} -1.00000i q^{27} +5.12311 q^{28} -2.00000 q^{29} +5.12311i q^{31} +1.00000 q^{32} -3.12311 q^{33} -2.00000i q^{34} -1.00000 q^{36} -3.12311 q^{37} -6.00000i q^{38} +(0.561553 + 3.56155i) q^{39} -9.12311i q^{41} +5.12311i q^{42} -10.2462i q^{43} +3.12311i q^{44} +3.12311i q^{46} -10.2462 q^{47} +1.00000i q^{48} +19.2462 q^{49} +2.00000 q^{51} +(3.56155 - 0.561553i) q^{52} +11.3693i q^{53} -1.00000i q^{54} +5.12311 q^{56} +6.00000 q^{57} -2.00000 q^{58} +7.12311i q^{59} +10.0000 q^{61} +5.12311i q^{62} -5.12311 q^{63} +1.00000 q^{64} -3.12311 q^{66} -13.1231 q^{67} -2.00000i q^{68} -3.12311 q^{69} +6.24621i q^{71} -1.00000 q^{72} -4.87689 q^{73} -3.12311 q^{74} -6.00000i q^{76} +16.0000i q^{77} +(0.561553 + 3.56155i) q^{78} -8.00000 q^{79} +1.00000 q^{81} -9.12311i q^{82} +10.2462 q^{83} +5.12311i q^{84} -10.2462i q^{86} -2.00000i q^{87} +3.12311i q^{88} -5.12311i q^{89} +(18.2462 - 2.87689i) q^{91} +3.12311i q^{92} -5.12311 q^{93} -10.2462 q^{94} +1.00000i q^{96} +4.87689 q^{97} +19.2462 q^{98} -3.12311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 4q^{4} + 4q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{2} + 4q^{4} + 4q^{7} + 4q^{8} - 4q^{9} + 6q^{13} + 4q^{14} + 4q^{16} - 4q^{18} + 6q^{26} + 4q^{28} - 8q^{29} + 4q^{32} + 4q^{33} - 4q^{36} + 4q^{37} - 6q^{39} - 8q^{47} + 44q^{49} + 8q^{51} + 6q^{52} + 4q^{56} + 24q^{57} - 8q^{58} + 40q^{61} - 4q^{63} + 4q^{64} + 4q^{66} - 36q^{67} + 4q^{69} - 4q^{72} - 36q^{73} + 4q^{74} - 6q^{78} - 32q^{79} + 4q^{81} + 8q^{83} + 40q^{91} - 4q^{93} - 8q^{94} + 36q^{97} + 44q^{98} + O(q^{100}) \)

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
\(7\) 5.12311 1.93635 0.968176 0.250270i \(-0.0805195\pi\)
0.968176 + 0.250270i \(0.0805195\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.12311i 0.941652i 0.882226 + 0.470826i \(0.156044\pi\)
−0.882226 + 0.470826i \(0.843956\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.56155 0.561553i 0.987797 0.155747i
\(14\) 5.12311 1.36921
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i −0.970143 0.242536i \(-0.922021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) −1.00000 −0.235702
\(19\) 6.00000i 1.37649i −0.725476 0.688247i \(-0.758380\pi\)
0.725476 0.688247i \(-0.241620\pi\)
\(20\) 0 0
\(21\) 5.12311i 1.11795i
\(22\) 3.12311i 0.665848i
\(23\) 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
\(26\) 3.56155 0.561553i 0.698478 0.110130i
\(27\) 1.00000i 0.192450i
\(28\) 5.12311 0.968176
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 5.12311i 0.920137i 0.887883 + 0.460068i \(0.152175\pi\)
−0.887883 + 0.460068i \(0.847825\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.12311 −0.543663
\(34\) 2.00000i 0.342997i
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −3.12311 −0.513435 −0.256718 0.966486i \(-0.582641\pi\)
−0.256718 + 0.966486i \(0.582641\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0.561553 + 3.56155i 0.0899204 + 0.570305i
\(40\) 0 0
\(41\) 9.12311i 1.42479i −0.701779 0.712395i \(-0.747611\pi\)
0.701779 0.712395i \(-0.252389\pi\)
\(42\) 5.12311i 0.790512i
\(43\) 10.2462i 1.56253i −0.624198 0.781266i \(-0.714574\pi\)
0.624198 0.781266i \(-0.285426\pi\)
\(44\) 3.12311i 0.470826i
\(45\) 0 0
\(46\) 3.12311i 0.460477i
\(47\) −10.2462 −1.49456 −0.747282 0.664507i \(-0.768641\pi\)
−0.747282 + 0.664507i \(0.768641\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 19.2462 2.74946
\(50\) 0 0
\(51\) 2.00000 0.280056
\(52\) 3.56155 0.561553i 0.493899 0.0778734i
\(53\) 11.3693i 1.56170i 0.624721 + 0.780848i \(0.285213\pi\)
−0.624721 + 0.780848i \(0.714787\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0 0
\(56\) 5.12311 0.684604
\(57\) 6.00000 0.794719
\(58\) −2.00000 −0.262613
\(59\) 7.12311i 0.927349i 0.886006 + 0.463675i \(0.153469\pi\)
−0.886006 + 0.463675i \(0.846531\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 5.12311i 0.650635i
\(63\) −5.12311 −0.645451
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.12311 −0.384428
\(67\) −13.1231 −1.60324 −0.801621 0.597832i \(-0.796029\pi\)
−0.801621 + 0.597832i \(0.796029\pi\)
\(68\) 2.00000i 0.242536i
\(69\) −3.12311 −0.375978
\(70\) 0 0
\(71\) 6.24621i 0.741289i 0.928775 + 0.370644i \(0.120863\pi\)
−0.928775 + 0.370644i \(0.879137\pi\)
\(72\) −1.00000 −0.117851
\(73\) −4.87689 −0.570797 −0.285399 0.958409i \(-0.592126\pi\)
−0.285399 + 0.958409i \(0.592126\pi\)
\(74\) −3.12311 −0.363054
\(75\) 0 0
\(76\) 6.00000i 0.688247i
\(77\) 16.0000i 1.82337i
\(78\) 0.561553 + 3.56155i 0.0635833 + 0.403266i
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 9.12311i 1.00748i
\(83\) 10.2462 1.12467 0.562334 0.826910i \(-0.309904\pi\)
0.562334 + 0.826910i \(0.309904\pi\)
\(84\) 5.12311i 0.558977i
\(85\) 0 0
\(86\) 10.2462i 1.10488i
\(87\) 2.00000i 0.214423i
\(88\) 3.12311i 0.332924i
\(89\) 5.12311i 0.543048i −0.962432 0.271524i \(-0.912472\pi\)
0.962432 0.271524i \(-0.0875277\pi\)
\(90\) 0 0
\(91\) 18.2462 2.87689i 1.91272 0.301580i
\(92\) 3.12311i 0.325606i
\(93\) −5.12311 −0.531241
\(94\) −10.2462 −1.05682
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 4.87689 0.495174 0.247587 0.968866i \(-0.420362\pi\)
0.247587 + 0.968866i \(0.420362\pi\)
\(98\) 19.2462 1.94416
\(99\) 3.12311i 0.313884i
\(100\) 0 0
\(101\) 4.24621 0.422514 0.211257 0.977431i \(-0.432244\pi\)
0.211257 + 0.977431i \(0.432244\pi\)
\(102\) 2.00000 0.198030
\(103\) 4.87689i 0.480535i −0.970707 0.240267i \(-0.922765\pi\)
0.970707 0.240267i \(-0.0772351\pi\)
\(104\) 3.56155 0.561553i 0.349239 0.0550648i
\(105\) 0 0
\(106\) 11.3693i 1.10429i
\(107\) 8.00000i 0.773389i 0.922208 + 0.386695i \(0.126383\pi\)
−0.922208 + 0.386695i \(0.873617\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 11.1231i 1.06540i 0.846304 + 0.532700i \(0.178823\pi\)
−0.846304 + 0.532700i \(0.821177\pi\)
\(110\) 0 0
\(111\) 3.12311i 0.296432i
\(112\) 5.12311 0.484088
\(113\) 4.24621i 0.399450i −0.979852 0.199725i \(-0.935995\pi\)
0.979852 0.199725i \(-0.0640049\pi\)
\(114\) 6.00000 0.561951
\(115\) 0 0
\(116\) −2.00000 −0.185695
\(117\) −3.56155 + 0.561553i −0.329266 + 0.0519156i
\(118\) 7.12311i 0.655735i
\(119\) 10.2462i 0.939269i
\(120\) 0 0
\(121\) 1.24621 0.113292
\(122\) 10.0000 0.905357
\(123\) 9.12311 0.822603
\(124\) 5.12311i 0.460068i
\(125\) 0 0
\(126\) −5.12311 −0.456403
\(127\) 4.87689i 0.432754i 0.976310 + 0.216377i \(0.0694241\pi\)
−0.976310 + 0.216377i \(0.930576\pi\)
\(128\) 1.00000 0.0883883
\(129\) 10.2462 0.902129
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) −3.12311 −0.271831
\(133\) 30.7386i 2.66538i
\(134\) −13.1231 −1.13366
\(135\) 0 0
\(136\) 2.00000i 0.171499i
\(137\) −22.4924 −1.92166 −0.960829 0.277143i \(-0.910612\pi\)
−0.960829 + 0.277143i \(0.910612\pi\)
\(138\) −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
\(141\) 10.2462i 0.862887i
\(142\) 6.24621i 0.524170i
\(143\) 1.75379 + 11.1231i 0.146659 + 0.930161i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −4.87689 −0.403615
\(147\) 19.2462i 1.58740i
\(148\) −3.12311 −0.256718
\(149\) 14.0000i 1.14692i −0.819232 0.573462i \(-0.805600\pi\)
0.819232 0.573462i \(-0.194400\pi\)
\(150\) 0 0
\(151\) 11.3693i 0.925222i 0.886561 + 0.462611i \(0.153087\pi\)
−0.886561 + 0.462611i \(0.846913\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 2.00000i 0.161690i
\(154\) 16.0000i 1.28932i
\(155\) 0 0
\(156\) 0.561553 + 3.56155i 0.0449602 + 0.285152i
\(157\) 3.36932i 0.268901i 0.990920 + 0.134450i \(0.0429269\pi\)
−0.990920 + 0.134450i \(0.957073\pi\)
\(158\) −8.00000 −0.636446
\(159\) −11.3693 −0.901645
\(160\) 0 0
\(161\) 16.0000i 1.26098i
\(162\) 1.00000 0.0785674
\(163\) 1.12311 0.0879684 0.0439842 0.999032i \(-0.485995\pi\)
0.0439842 + 0.999032i \(0.485995\pi\)
\(164\) 9.12311i 0.712395i
\(165\) 0 0
\(166\) 10.2462 0.795260
\(167\) 5.75379 0.445242 0.222621 0.974905i \(-0.428539\pi\)
0.222621 + 0.974905i \(0.428539\pi\)
\(168\) 5.12311i 0.395256i
\(169\) 12.3693 4.00000i 0.951486 0.307692i
\(170\) 0 0
\(171\) 6.00000i 0.458831i
\(172\) 10.2462i 0.781266i
\(173\) 14.8769i 1.13107i 0.824725 + 0.565535i \(0.191330\pi\)
−0.824725 + 0.565535i \(0.808670\pi\)
\(174\) 2.00000i 0.151620i
\(175\) 0 0
\(176\) 3.12311i 0.235413i
\(177\) −7.12311 −0.535405
\(178\) 5.12311i 0.383993i
\(179\) 16.4924 1.23270 0.616351 0.787472i \(-0.288610\pi\)
0.616351 + 0.787472i \(0.288610\pi\)
\(180\) 0 0
\(181\) −3.75379 −0.279017 −0.139508 0.990221i \(-0.544552\pi\)
−0.139508 + 0.990221i \(0.544552\pi\)
\(182\) 18.2462 2.87689i 1.35250 0.213250i
\(183\) 10.0000i 0.739221i
\(184\) 3.12311i 0.230238i
\(185\) 0 0
\(186\) −5.12311 −0.375644
\(187\) 6.24621 0.456768
\(188\) −10.2462 −0.747282
\(189\) 5.12311i 0.372651i
\(190\) 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
\(193\) −16.8769 −1.21483 −0.607413 0.794386i \(-0.707793\pi\)
−0.607413 + 0.794386i \(0.707793\pi\)
\(194\) 4.87689 0.350141
\(195\) 0 0
\(196\) 19.2462 1.37473
\(197\) 0.246211 0.0175418 0.00877091 0.999962i \(-0.497208\pi\)
0.00877091 + 0.999962i \(0.497208\pi\)
\(198\) 3.12311i 0.221949i
\(199\) −1.75379 −0.124323 −0.0621614 0.998066i \(-0.519799\pi\)
−0.0621614 + 0.998066i \(0.519799\pi\)
\(200\) 0 0
\(201\) 13.1231i 0.925633i
\(202\) 4.24621 0.298762
\(203\) −10.2462 −0.719143
\(204\) 2.00000 0.140028
\(205\) 0 0
\(206\) 4.87689i 0.339789i
\(207\) 3.12311i 0.217071i
\(208\) 3.56155 0.561553i 0.246949 0.0389367i
\(209\) 18.7386 1.29618
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 11.3693i 0.780848i
\(213\) −6.24621 −0.427983
\(214\) 8.00000i 0.546869i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 26.2462i 1.78171i
\(218\) 11.1231i 0.753352i
\(219\) 4.87689i 0.329550i
\(220\) 0 0
\(221\) −1.12311 7.12311i −0.0755483 0.479152i
\(222\) 3.12311i 0.209609i
\(223\) −15.3693 −1.02921 −0.514603 0.857429i \(-0.672061\pi\)
−0.514603 + 0.857429i \(0.672061\pi\)
\(224\) 5.12311 0.342302
\(225\) 0 0
\(226\) 4.24621i 0.282454i
\(227\) −8.00000 −0.530979 −0.265489 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) 6.00000 0.397360
\(229\) 3.12311i 0.206381i 0.994662 + 0.103190i \(0.0329051\pi\)
−0.994662 + 0.103190i \(0.967095\pi\)
\(230\) 0 0
\(231\) −16.0000 −1.05272
\(232\) −2.00000 −0.131306
\(233\) 24.2462i 1.58842i −0.607642 0.794211i \(-0.707884\pi\)
0.607642 0.794211i \(-0.292116\pi\)
\(234\) −3.56155 + 0.561553i −0.232826 + 0.0367099i
\(235\) 0 0
\(236\) 7.12311i 0.463675i
\(237\) 8.00000i 0.519656i
\(238\) 10.2462i 0.664163i
\(239\) 28.4924i 1.84302i −0.388353 0.921511i \(-0.626956\pi\)
0.388353 0.921511i \(-0.373044\pi\)
\(240\) 0 0
\(241\) 2.24621i 0.144691i −0.997380 0.0723456i \(-0.976952\pi\)
0.997380 0.0723456i \(-0.0230485\pi\)
\(242\) 1.24621 0.0801095
\(243\) 1.00000i 0.0641500i
\(244\) 10.0000 0.640184
\(245\) 0 0
\(246\) 9.12311 0.581668
\(247\) −3.36932 21.3693i −0.214384 1.35970i
\(248\) 5.12311i 0.325318i
\(249\) 10.2462i 0.649327i
\(250\) 0 0
\(251\) 9.75379 0.615654 0.307827 0.951442i \(-0.400398\pi\)
0.307827 + 0.951442i \(0.400398\pi\)
\(252\) −5.12311 −0.322725
\(253\) −9.75379 −0.613215
\(254\) 4.87689i 0.306004i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 4.24621i 0.264871i −0.991192 0.132436i \(-0.957720\pi\)
0.991192 0.132436i \(-0.0422798\pi\)
\(258\) 10.2462 0.637901
\(259\) −16.0000 −0.994192
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) 4.00000 0.247121
\(263\) 2.63068i 0.162215i −0.996705 0.0811074i \(-0.974154\pi\)
0.996705 0.0811074i \(-0.0258457\pi\)
\(264\) −3.12311 −0.192214
\(265\) 0 0
\(266\) 30.7386i 1.88471i
\(267\) 5.12311 0.313529
\(268\) −13.1231 −0.801621
\(269\) −0.246211 −0.0150118 −0.00750588 0.999972i \(-0.502389\pi\)
−0.00750588 + 0.999972i \(0.502389\pi\)
\(270\) 0 0
\(271\) 14.8769i 0.903707i −0.892092 0.451853i \(-0.850763\pi\)
0.892092 0.451853i \(-0.149237\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 2.87689 + 18.2462i 0.174118 + 1.10431i
\(274\) −22.4924 −1.35882
\(275\) 0 0
\(276\) −3.12311 −0.187989
\(277\) 27.8617i 1.67405i −0.547165 0.837025i \(-0.684293\pi\)
0.547165 0.837025i \(-0.315707\pi\)
\(278\) −16.4924 −0.989150
\(279\) 5.12311i 0.306712i
\(280\) 0 0
\(281\) 5.12311i 0.305619i −0.988256 0.152809i \(-0.951168\pi\)
0.988256 0.152809i \(-0.0488321\pi\)
\(282\) 10.2462i 0.610153i
\(283\) 4.00000i 0.237775i −0.992908 0.118888i \(-0.962067\pi\)
0.992908 0.118888i \(-0.0379328\pi\)
\(284\) 6.24621i 0.370644i
\(285\) 0 0
\(286\) 1.75379 + 11.1231i 0.103704 + 0.657723i
\(287\) 46.7386i 2.75889i
\(288\) −1.00000 −0.0589256
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 4.87689i 0.285889i
\(292\) −4.87689 −0.285399
\(293\) −20.7386 −1.21156 −0.605782 0.795631i \(-0.707140\pi\)
−0.605782 + 0.795631i \(0.707140\pi\)
\(294\) 19.2462i 1.12246i
\(295\) 0 0
\(296\) −3.12311 −0.181527
\(297\) 3.12311 0.181221
\(298\) 14.0000i 0.810998i
\(299\) 1.75379 + 11.1231i 0.101424 + 0.643266i
\(300\) 0 0
\(301\) 52.4924i 3.02561i
\(302\) 11.3693i 0.654231i
\(303\) 4.24621i 0.243938i
\(304\) 6.00000i 0.344124i
\(305\) 0 0
\(306\) 2.00000i 0.114332i
\(307\) −22.8769 −1.30565 −0.652827 0.757507i \(-0.726417\pi\)
−0.652827 + 0.757507i \(0.726417\pi\)
\(308\) 16.0000i 0.911685i
\(309\) 4.87689 0.277437
\(310\) 0 0
\(311\) −24.4924 −1.38884 −0.694419 0.719571i \(-0.744339\pi\)
−0.694419 + 0.719571i \(0.744339\pi\)
\(312\) 0.561553 + 3.56155i 0.0317917 + 0.201633i
\(313\) 0.246211i 0.0139167i −0.999976 0.00695834i \(-0.997785\pi\)
0.999976 0.00695834i \(-0.00221493\pi\)
\(314\) 3.36932i 0.190142i
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) −11.3693 −0.637560
\(319\) 6.24621i 0.349721i
\(320\) 0 0
\(321\) −8.00000 −0.446516
\(322\) 16.0000i 0.891645i
\(323\) −12.0000 −0.667698
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 1.12311 0.0622031
\(327\) −11.1231 −0.615109
\(328\) 9.12311i 0.503739i
\(329\) −52.4924 −2.89400
\(330\) 0 0
\(331\) 24.2462i 1.33269i 0.745643 + 0.666346i \(0.232143\pi\)
−0.745643 + 0.666346i \(0.767857\pi\)
\(332\) 10.2462 0.562334
\(333\) 3.12311 0.171145
\(334\) 5.75379 0.314833
\(335\) 0 0
\(336\) 5.12311i 0.279488i
\(337\) 6.00000i 0.326841i −0.986557 0.163420i \(-0.947747\pi\)
0.986557 0.163420i \(-0.0522527\pi\)
\(338\) 12.3693 4.00000i 0.672802 0.217571i
\(339\) 4.24621 0.230623
\(340\) 0 0
\(341\) −16.0000 −0.866449
\(342\) 6.00000i 0.324443i
\(343\) 62.7386 3.38757
\(344\) 10.2462i 0.552439i
\(345\) 0 0
\(346\) 14.8769i 0.799787i
\(347\) 2.24621i 0.120583i −0.998181 0.0602915i \(-0.980797\pi\)
0.998181 0.0602915i \(-0.0192030\pi\)
\(348\) 2.00000i 0.107211i
\(349\) 5.36932i 0.287413i −0.989620 0.143706i \(-0.954098\pi\)
0.989620 0.143706i \(-0.0459021\pi\)
\(350\) 0 0
\(351\) −0.561553 3.56155i −0.0299735 0.190102i
\(352\) 3.12311i 0.166462i
\(353\) 4.24621 0.226003 0.113002 0.993595i \(-0.463954\pi\)
0.113002 + 0.993595i \(0.463954\pi\)
\(354\) −7.12311 −0.378589
\(355\) 0 0
\(356\) 5.12311i 0.271524i
\(357\) 10.2462 0.542287
\(358\) 16.4924 0.871652
\(359\) 34.2462i 1.80745i 0.428118 + 0.903723i \(0.359177\pi\)
−0.428118 + 0.903723i \(0.640823\pi\)
\(360\) 0 0
\(361\) −17.0000 −0.894737
\(362\) −3.75379 −0.197295
\(363\) 1.24621i 0.0654091i
\(364\) 18.2462 2.87689i 0.956361 0.150790i
\(365\) 0 0
\(366\) 10.0000i 0.522708i
\(367\) 33.3693i 1.74186i −0.491403 0.870932i \(-0.663516\pi\)
0.491403 0.870932i \(-0.336484\pi\)
\(368\) 3.12311i 0.162803i
\(369\) 9.12311i 0.474930i
\(370\) 0 0
\(371\) 58.2462i 3.02399i
\(372\) −5.12311 −0.265621
\(373\) 1.12311i 0.0581522i −0.999577 0.0290761i \(-0.990743\pi\)
0.999577 0.0290761i \(-0.00925652\pi\)
\(374\) 6.24621 0.322984
\(375\) 0 0
\(376\) −10.2462 −0.528408
\(377\) −7.12311 + 1.12311i −0.366859 + 0.0578429i
\(378\) 5.12311i 0.263504i
\(379\) 6.00000i 0.308199i −0.988055 0.154100i \(-0.950752\pi\)
0.988055 0.154100i \(-0.0492477\pi\)
\(380\) 0 0
\(381\) −4.87689 −0.249851
\(382\) −16.4924 −0.843826
\(383\) 18.2462 0.932338 0.466169 0.884696i \(-0.345634\pi\)
0.466169 + 0.884696i \(0.345634\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) −16.8769 −0.859011
\(387\) 10.2462i 0.520844i
\(388\) 4.87689 0.247587
\(389\) −16.2462 −0.823716 −0.411858 0.911248i \(-0.635120\pi\)
−0.411858 + 0.911248i \(0.635120\pi\)
\(390\) 0 0
\(391\) 6.24621 0.315884
\(392\) 19.2462 0.972080
\(393\) 4.00000i 0.201773i
\(394\) 0.246211 0.0124039
\(395\) 0 0
\(396\) 3.12311i 0.156942i
\(397\) −9.36932 −0.470233 −0.235116 0.971967i \(-0.575547\pi\)
−0.235116 + 0.971967i \(0.575547\pi\)
\(398\) −1.75379 −0.0879095
\(399\) 30.7386 1.53886
\(400\) 0 0
\(401\) 23.3693i 1.16701i −0.812110 0.583504i \(-0.801681\pi\)
0.812110 0.583504i \(-0.198319\pi\)
\(402\) 13.1231i 0.654521i
\(403\) 2.87689 + 18.2462i 0.143308 + 0.908909i
\(404\) 4.24621 0.211257
\(405\) 0 0
\(406\) −10.2462 −0.508511
\(407\) 9.75379i 0.483477i
\(408\) 2.00000 0.0990148
\(409\) 24.4924i 1.21107i −0.795818 0.605536i \(-0.792959\pi\)
0.795818 0.605536i \(-0.207041\pi\)
\(410\) 0 0
\(411\) 22.4924i 1.10947i
\(412\) 4.87689i 0.240267i
\(413\) 36.4924i 1.79567i
\(414\) 3.12311i 0.153492i
\(415\) 0 0
\(416\) 3.56155 0.561553i 0.174619 0.0275324i
\(417\) 16.4924i 0.807637i
\(418\) 18.7386 0.916537
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) 25.3693i 1.23642i 0.786011 + 0.618212i \(0.212143\pi\)
−0.786011 + 0.618212i \(0.787857\pi\)
\(422\) 4.00000 0.194717
\(423\) 10.2462 0.498188
\(424\) 11.3693i 0.552143i
\(425\) 0 0
\(426\) −6.24621 −0.302630
\(427\) 51.2311 2.47924
\(428\) 8.00000i 0.386695i
\(429\) −11.1231 + 1.75379i −0.537029 + 0.0846737i
\(430\) 0 0
\(431\) 0.492423i 0.0237192i −0.999930 0.0118596i \(-0.996225\pi\)
0.999930 0.0118596i \(-0.00377511\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 18.0000i 0.865025i −0.901628 0.432512i \(-0.857627\pi\)
0.901628 0.432512i \(-0.142373\pi\)
\(434\) 26.2462i 1.25986i
\(435\) 0 0
\(436\) 11.1231i 0.532700i
\(437\) 18.7386 0.896390
\(438\) 4.87689i 0.233027i
\(439\) 3.50758 0.167408 0.0837038 0.996491i \(-0.473325\pi\)
0.0837038 + 0.996491i \(0.473325\pi\)
\(440\) 0 0
\(441\) −19.2462 −0.916486
\(442\) −1.12311 7.12311i −0.0534207 0.338812i
\(443\) 36.4924i 1.73381i −0.498476 0.866904i \(-0.666107\pi\)
0.498476 0.866904i \(-0.333893\pi\)
\(444\) 3.12311i 0.148216i
\(445\) 0 0
\(446\) −15.3693 −0.727758
\(447\) 14.0000 0.662177
\(448\) 5.12311 0.242044
\(449\) 37.1231i 1.75195i −0.482359 0.875974i \(-0.660220\pi\)
0.482359 0.875974i \(-0.339780\pi\)
\(450\) 0 0
\(451\) 28.4924 1.34166
\(452\) 4.24621i 0.199725i
\(453\) −11.3693 −0.534177
\(454\) −8.00000 −0.375459
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −6.63068 −0.310170 −0.155085 0.987901i \(-0.549565\pi\)
−0.155085 + 0.987901i \(0.549565\pi\)
\(458\) 3.12311i 0.145933i
\(459\) −2.00000 −0.0933520
\(460\) 0 0
\(461\) 14.4924i 0.674979i 0.941329 + 0.337490i \(0.109578\pi\)
−0.941329 + 0.337490i \(0.890422\pi\)
\(462\) −16.0000 −0.744387
\(463\) 35.8617 1.66664 0.833318 0.552794i \(-0.186438\pi\)
0.833318 + 0.552794i \(0.186438\pi\)
\(464\) −2.00000 −0.0928477
\(465\) 0 0
\(466\) 24.2462i 1.12318i
\(467\) 5.75379i 0.266254i 0.991099 + 0.133127i \(0.0425018\pi\)
−0.991099 + 0.133127i \(0.957498\pi\)
\(468\) −3.56155 + 0.561553i −0.164633 + 0.0259578i
\(469\) −67.2311 −3.10444
\(470\) 0 0
\(471\) −3.36932 −0.155250
\(472\) 7.12311i 0.327868i
\(473\) 32.0000 1.47136
\(474\) 8.00000i 0.367452i
\(475\) 0 0
\(476\) 10.2462i 0.469634i
\(477\) 11.3693i 0.520565i
\(478\) 28.4924i 1.30321i
\(479\) 20.4924i 0.936323i 0.883643 + 0.468161i \(0.155083\pi\)
−0.883643 + 0.468161i \(0.844917\pi\)
\(480\) 0 0
\(481\) −11.1231 + 1.75379i −0.507170 + 0.0799659i
\(482\) 2.24621i 0.102312i
\(483\) −16.0000 −0.728025
\(484\) 1.24621 0.0566460
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 7.36932 0.333936 0.166968 0.985962i \(-0.446602\pi\)
0.166968 + 0.985962i \(0.446602\pi\)
\(488\) 10.0000 0.452679
\(489\) 1.12311i 0.0507886i
\(490\) 0 0
\(491\) −10.7386 −0.484628 −0.242314 0.970198i \(-0.577906\pi\)
−0.242314 + 0.970198i \(0.577906\pi\)
\(492\) 9.12311 0.411301
\(493\) 4.00000i 0.180151i
\(494\) −3.36932 21.3693i −0.151593 0.961451i
\(495\) 0 0
\(496\) 5.12311i 0.230034i
\(497\) 32.0000i 1.43540i
\(498\) 10.2462i 0.459144i
\(499\) 1.50758i 0.0674884i 0.999431 + 0.0337442i \(0.0107432\pi\)
−0.999431 + 0.0337442i \(0.989257\pi\)
\(500\) 0 0
\(501\) 5.75379i 0.257060i
\(502\) 9.75379 0.435333
\(503\) 10.6307i 0.473999i 0.971510 + 0.236999i \(0.0761639\pi\)
−0.971510 + 0.236999i \(0.923836\pi\)
\(504\) −5.12311 −0.228201
\(505\) 0 0
\(506\) −9.75379 −0.433609
\(507\) 4.00000 + 12.3693i 0.177646 + 0.549341i
\(508\) 4.87689i 0.216377i
\(509\) 15.7538i 0.698274i 0.937072 + 0.349137i \(0.113525\pi\)
−0.937072 + 0.349137i \(0.886475\pi\)
\(510\) 0 0
\(511\) −24.9848 −1.10526
\(512\) 1.00000 0.0441942
\(513\) −6.00000 −0.264906
\(514\) 4.24621i 0.187292i
\(515\) 0 0
\(516\) 10.2462 0.451064
\(517\) 32.0000i 1.40736i
\(518\) −16.0000 −0.703000
\(519\) −14.8769 −0.653023
\(520\) 0 0
\(521\) −16.2462 −0.711759 −0.355880 0.934532i \(-0.615819\pi\)
−0.355880 + 0.934532i \(0.615819\pi\)
\(522\) 2.00000 0.0875376
\(523\) 22.7386i 0.994291i 0.867667 + 0.497146i \(0.165618\pi\)
−0.867667 + 0.497146i \(0.834382\pi\)
\(524\) 4.00000 0.174741
\(525\) 0 0
\(526\) 2.63068i 0.114703i
\(527\) 10.2462 0.446332
\(528\) −3.12311 −0.135916
\(529\) 13.2462 0.575922
\(530\) 0 0
\(531\) 7.12311i 0.309116i
\(532\) 30.7386i 1.33269i
\(533\) −5.12311 32.4924i −0.221906 1.40740i
\(534\) 5.12311 0.221698
\(535\) 0 0
\(536\) −13.1231 −0.566832
\(537\) 16.4924i 0.711701i
\(538\) −0.246211 −0.0106149
\(539\) 60.1080i 2.58903i
\(540\) 0 0
\(541\) 19.1231i 0.822167i −0.911598 0.411083i \(-0.865151\pi\)
0.911598 0.411083i \(-0.134849\pi\)
\(542\) 14.8769i 0.639017i
\(543\) 3.75379i 0.161090i
\(544\) 2.00000i 0.0857493i
\(545\) 0 0
\(546\) 2.87689 + 18.2462i 0.123120 + 0.780866i
\(547\) 44.9848i 1.92341i 0.274081 + 0.961707i \(0.411626\pi\)
−0.274081 + 0.961707i \(0.588374\pi\)
\(548\) −22.4924 −0.960829
\(549\) −10.0000 −0.426790
\(550\) 0 0
\(551\) 12.0000i 0.511217i
\(552\) −3.12311 −0.132928
\(553\) −40.9848 −1.74285
\(554\) 27.8617i 1.18373i
\(555\) 0 0
\(556\) −16.4924 −0.699435
\(557\) −28.2462 −1.19683 −0.598415 0.801186i \(-0.704203\pi\)
−0.598415 + 0.801186i \(0.704203\pi\)
\(558\) 5.12311i 0.216878i
\(559\) −5.75379 36.4924i −0.243359 1.54347i
\(560\) 0 0
\(561\) 6.24621i 0.263715i
\(562\) 5.12311i 0.216105i
\(563\) 32.9848i 1.39015i 0.718939 + 0.695073i \(0.244628\pi\)
−0.718939 + 0.695073i \(0.755372\pi\)
\(564\) 10.2462i 0.431443i
\(565\) 0 0
\(566\) 4.00000i 0.168133i
\(567\) 5.12311 0.215150
\(568\) 6.24621i 0.262085i
\(569\) −36.7386 −1.54016 −0.770082 0.637945i \(-0.779785\pi\)
−0.770082 + 0.637945i \(0.779785\pi\)
\(570\) 0 0
\(571\) 24.4924 1.02498 0.512488 0.858694i \(-0.328724\pi\)
0.512488 + 0.858694i \(0.328724\pi\)
\(572\) 1.75379 + 11.1231i 0.0733296 + 0.465080i
\(573\) 16.4924i 0.688981i
\(574\) 46.7386i 1.95083i
\(575\) 0 0
\(576\) −1.00000 −0.0416667
\(577\) −2.63068 −0.109517 −0.0547584 0.998500i \(-0.517439\pi\)
−0.0547584 + 0.998500i \(0.517439\pi\)
\(578\) 13.0000 0.540729
\(579\) 16.8769i 0.701380i
\(580\) 0 0
\(581\) 52.4924 2.17775
\(582\) 4.87689i 0.202154i
\(583\) −35.5076 −1.47057
\(584\) −4.87689 −0.201807
\(585\) 0 0
\(586\) −20.7386 −0.856705
\(587\) −16.4924 −0.680715 −0.340358 0.940296i \(-0.610548\pi\)
−0.340358 + 0.940296i \(0.610548\pi\)
\(588\) 19.2462i 0.793700i
\(589\) 30.7386 1.26656
\(590\) 0 0
\(591\) 0.246211i 0.0101278i
\(592\) −3.12311 −0.128359
\(593\) −38.4924 −1.58069 −0.790347 0.612659i \(-0.790100\pi\)
−0.790347 + 0.612659i \(0.790100\pi\)
\(594\) 3.12311 0.128143
\(595\) 0 0
\(596\) 14.0000i 0.573462i
\(597\) 1.75379i 0.0717778i
\(598\) 1.75379 + 11.1231i 0.0717178 + 0.454858i
\(599\) 3.50758 0.143316 0.0716579 0.997429i \(-0.477171\pi\)
0.0716579 + 0.997429i \(0.477171\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 52.4924i 2.13943i
\(603\) 13.1231 0.534414
\(604\) 11.3693i 0.462611i
\(605\) 0 0
\(606\) 4.24621i 0.172491i
\(607\) 9.36932i 0.380289i 0.981756 + 0.190144i \(0.0608956\pi\)
−0.981756 + 0.190144i \(0.939104\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 10.2462i 0.415197i
\(610\) 0 0
\(611\) −36.4924 + 5.75379i −1.47633 + 0.232773i
\(612\) 2.00000i 0.0808452i
\(613\) 14.6307 0.590928 0.295464 0.955354i \(-0.404526\pi\)
0.295464 + 0.955354i \(0.404526\pi\)
\(614\) −22.8769 −0.923236
\(615\) 0 0
\(616\) 16.0000i 0.644658i
\(617\) −8.73863 −0.351804 −0.175902 0.984408i \(-0.556284\pi\)
−0.175902 + 0.984408i \(0.556284\pi\)
\(618\) 4.87689 0.196177
\(619\) 26.9848i 1.08461i −0.840181 0.542306i \(-0.817551\pi\)
0.840181 0.542306i \(-0.182449\pi\)
\(620\) 0 0
\(621\) 3.12311 0.125326
\(622\) −24.4924 −0.982057
\(623\) 26.2462i 1.05153i
\(624\) 0.561553 + 3.56155i 0.0224801 + 0.142576i
\(625\) 0 0
\(626\) 0.246211i 0.00984058i
\(627\) 18.7386i 0.748349i
\(628\) 3.36932i 0.134450i
\(629\) 6.24621i 0.249053i
\(630\) 0 0
\(631\) 5.61553i 0.223551i −0.993734 0.111775i \(-0.964346\pi\)
0.993734 0.111775i \(-0.0356537\pi\)
\(632\) −8.00000 −0.318223
\(633\) 4.00000i 0.158986i
\(634\) −6.00000 −0.238290
\(635\) 0 0
\(636\) −11.3693 −0.450823
\(637\) 68.5464 10.8078i 2.71591 0.428219i
\(638\) 6.24621i 0.247290i
\(639\) 6.24621i 0.247096i
\(640\) 0 0
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) −8.00000 −0.315735
\(643\) −7.36932 −0.290617 −0.145309 0.989386i \(-0.546418\pi\)
−0.145309 + 0.989386i \(0.546418\pi\)
\(644\) 16.0000i 0.630488i
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) 11.6155i 0.456654i 0.973585 + 0.228327i \(0.0733255\pi\)
−0.973585 + 0.228327i \(0.926675\pi\)
\(648\) 1.00000 0.0392837
\(649\) −22.2462 −0.873240
\(650\) 0 0
\(651\) −26.2462 −1.02867
\(652\) 1.12311 0.0439842
\(653\) 43.8617i 1.71644i 0.513280 + 0.858221i \(0.328430\pi\)
−0.513280 + 0.858221i \(0.671570\pi\)
\(654\) −11.1231 −0.434948
\(655\) 0 0
\(656\) 9.12311i 0.356197i
\(657\) 4.87689 0.190266
\(658\) −52.4924 −2.04637
\(659\) 38.2462 1.48986 0.744930 0.667142i \(-0.232483\pi\)
0.744930 + 0.667142i \(0.232483\pi\)
\(660\) 0 0
\(661\) 0.876894i 0.0341072i −0.999855 0.0170536i \(-0.994571\pi\)
0.999855 0.0170536i \(-0.00542860\pi\)
\(662\) 24.2462i 0.942356i
\(663\) 7.12311 1.12311i 0.276638 0.0436178i
\(664\) 10.2462 0.397630
\(665\) 0 0
\(666\) 3.12311 0.121018
\(667\) 6.24621i 0.241854i
\(668\) 5.75379 0.222621
\(669\) 15.3693i 0.594212i
\(670\) 0 0
\(671\) 31.2311i 1.20566i
\(672\) 5.12311i 0.197628i
\(673\) 38.9848i 1.50276i −0.659872 0.751378i \(-0.729390\pi\)
0.659872 0.751378i \(-0.270610\pi\)
\(674\) 6.00000i 0.231111i
\(675\) 0 0
\(676\) 12.3693 4.00000i 0.475743 0.153846i
\(677\) 21.1231i 0.811827i −0.913912 0.405913i \(-0.866953\pi\)
0.913912 0.405913i \(-0.133047\pi\)
\(678\) 4.24621 0.163075
\(679\) 24.9848 0.958830
\(680\) 0 0
\(681\) 8.00000i 0.306561i
\(682\) −16.0000 −0.612672
\(683\) 48.9848 1.87435 0.937177 0.348856i \(-0.113430\pi\)
0.937177 + 0.348856i \(0.113430\pi\)
\(684\) 6.00000i 0.229416i
\(685\) 0 0
\(686\) 62.7386 2.39537
\(687\) −3.12311 −0.119154
\(688\) 10.2462i 0.390633i
\(689\) 6.38447 + 40.4924i 0.243229 + 1.54264i
\(690\) 0 0
\(691\) 20.7386i 0.788935i 0.918910 + 0.394467i \(0.129071\pi\)
−0.918910 + 0.394467i \(0.870929\pi\)
\(692\) 14.8769i 0.565535i
\(693\) 16.0000i 0.607790i
\(694\) 2.24621i 0.0852650i
\(695\) 0 0
\(696\) 2.00000i 0.0758098i
\(697\) −18.2462 −0.691125
\(698\) 5.36932i 0.203232i
\(699\) 24.2462 0.917076
\(700\) 0 0
\(701\) −14.0000 −0.528773 −0.264386 0.964417i \(-0.585169\pi\)
−0.264386 + 0.964417i \(0.585169\pi\)
\(702\) −0.561553 3.56155i −0.0211944 0.134422i
\(703\) 18.7386i 0.706741i
\(704\) 3.12311i 0.117706i
\(705\) 0 0
\(706\) 4.24621 0.159808
\(707\) 21.7538 0.818135
\(708\) −7.12311 −0.267703
\(709\) 39.6155i 1.48779i 0.668295 + 0.743896i \(0.267024\pi\)
−0.668295 + 0.743896i \(0.732976\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 5.12311i 0.191997i
\(713\) −16.0000 −0.599205
\(714\) 10.2462 0.383455
\(715\) 0 0
\(716\) 16.4924 0.616351
\(717\) 28.4924 1.06407
\(718\) 34.2462i 1.27806i
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 0 0
\(721\) 24.9848i 0.930484i
\(722\) −17.0000 −0.632674
\(723\) 2.24621 0.0835375
\(724\) −3.75379 −0.139508
\(725\) 0 0
\(726\) 1.24621i 0.0462512i
\(727\) 37.8617i 1.40421i 0.712071 + 0.702107i \(0.247757\pi\)
−0.712071 + 0.702107i \(0.752243\pi\)
\(728\) 18.2462 2.87689i 0.676250 0.106625i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −20.4924 −0.757940
\(732\) 10.0000i 0.369611i
\(733\) 10.6307 0.392653 0.196327 0.980539i \(-0.437099\pi\)
0.196327 + 0.980539i \(0.437099\pi\)
\(734\) 33.3693i 1.23168i
\(735\) 0 0
\(736\) 3.12311i 0.115119i
\(737\) 40.9848i 1.50970i
\(738\) 9.12311i 0.335826i
\(739\) 45.2311i 1.66385i 0.554887 + 0.831926i \(0.312761\pi\)
−0.554887 + 0.831926i \(0.687239\pi\)
\(740\) 0 0
\(741\) 21.3693 3.36932i 0.785021 0.123775i
\(742\) 58.2462i 2.13829i
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) −5.12311 −0.187822
\(745\) 0 0
\(746\) 1.12311i 0.0411198i
\(747\) −10.2462 −0.374889
\(748\) 6.24621 0.228384
\(749\) 40.9848i 1.49755i
\(750\) 0 0
\(751\) −9.75379 −0.355921 −0.177960 0.984038i \(-0.556950\pi\)
−0.177960 + 0.984038i \(0.556950\pi\)
\(752\) −10.2462 −0.373641
\(753\) 9.75379i 0.355448i
\(754\) −7.12311 + 1.12311i −0.259408 + 0.0409011i
\(755\) 0 0
\(756\) 5.12311i 0.186326i
\(757\) 5.12311i 0.186202i −0.995657 0.0931012i \(-0.970322\pi\)
0.995657 0.0931012i \(-0.0296780\pi\)
\(758\) 6.00000i 0.217930i
\(759\) 9.75379i 0.354040i
\(760\) 0 0
\(761\) 5.12311i 0.185712i −0.995680 0.0928562i \(-0.970400\pi\)
0.995680 0.0928562i \(-0.0295997\pi\)
\(762\) −4.87689 −0.176671
\(763\) 56.9848i 2.06299i
\(764\) −16.4924 −0.596675
\(765\) 0 0
\(766\) 18.2462 0.659262
\(767\) 4.00000 + 25.3693i 0.144432 + 0.916033i
\(768\) 1.00000i 0.0360844i
\(769\) 32.9848i 1.18946i 0.803924 + 0.594732i \(0.202742\pi\)
−0.803924 + 0.594732i \(0.797258\pi\)
\(770\) 0 0
\(771\) 4.24621 0.152924
\(772\) −16.8769 −0.607413
\(773\) 0.246211 0.00885560 0.00442780 0.999990i \(-0.498591\pi\)
0.00442780 + 0.999990i \(0.498591\pi\)
\(774\) 10.2462i 0.368292i
\(775\) 0 0
\(776\) 4.87689 0.175070
\(777\) 16.0000i 0.573997i
\(778\) −16.2462 −0.582455
\(779\) −54.7386 −1.96122
\(780\) 0 0
\(781\) −19.5076 −0.698036
\(782\) 6.24621 0.223364
\(783\) 2.00000i 0.0714742i
\(784\) 19.2462 0.687365
\(785\) 0 0
\(786\) 4.00000i 0.142675i
\(787\) 53.6155 1.91119 0.955594 0.294688i \(-0.0952157\pi\)
0.955594 + 0.294688i \(0.0952157\pi\)
\(788\) 0.246211 0.00877091
\(789\) 2.63068 0.0936548
\(790\) 0 0
\(791\) 21.7538i 0.773476i
\(792\) 3.12311i 0.110975i
\(793\) 35.6155 5.61553i 1.26474 0.199413i
\(794\) −9.36932 −0.332505
\(795\) 0 0
\(796\) −1.75379 −0.0621614