Properties

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

Embedding invariants

Embedding label 649.3
Root \(-2.56155i\) of defining polynomial
Character \(\chi\) \(=\) 1950.649
Dual form 1950.2.f.o.649.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} -3.12311 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} -3.12311 q^{7} +1.00000 q^{8} -1.00000 q^{9} -5.12311i q^{11} +1.00000i q^{12} +(-0.561553 + 3.56155i) q^{13} -3.12311 q^{14} +1.00000 q^{16} -2.00000i q^{17} -1.00000 q^{18} -6.00000i q^{19} -3.12311i q^{21} -5.12311i q^{22} -5.12311i q^{23} +1.00000i q^{24} +(-0.561553 + 3.56155i) q^{26} -1.00000i q^{27} -3.12311 q^{28} -2.00000 q^{29} -3.12311i q^{31} +1.00000 q^{32} +5.12311 q^{33} -2.00000i q^{34} -1.00000 q^{36} +5.12311 q^{37} -6.00000i q^{38} +(-3.56155 - 0.561553i) q^{39} -0.876894i q^{41} -3.12311i q^{42} +6.24621i q^{43} -5.12311i q^{44} -5.12311i q^{46} +6.24621 q^{47} +1.00000i q^{48} +2.75379 q^{49} +2.00000 q^{51} +(-0.561553 + 3.56155i) q^{52} -13.3693i q^{53} -1.00000i q^{54} -3.12311 q^{56} +6.00000 q^{57} -2.00000 q^{58} -1.12311i q^{59} +10.0000 q^{61} -3.12311i q^{62} +3.12311 q^{63} +1.00000 q^{64} +5.12311 q^{66} -4.87689 q^{67} -2.00000i q^{68} +5.12311 q^{69} -10.2462i q^{71} -1.00000 q^{72} -13.1231 q^{73} +5.12311 q^{74} -6.00000i q^{76} +16.0000i q^{77} +(-3.56155 - 0.561553i) q^{78} -8.00000 q^{79} +1.00000 q^{81} -0.876894i q^{82} -6.24621 q^{83} -3.12311i q^{84} +6.24621i q^{86} -2.00000i q^{87} -5.12311i q^{88} +3.12311i q^{89} +(1.75379 - 11.1231i) q^{91} -5.12311i q^{92} +3.12311 q^{93} +6.24621 q^{94} +1.00000i q^{96} +13.1231 q^{97} +2.75379 q^{98} +5.12311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 4q^{4} + 4q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{2} + 4q^{4} + 4q^{7} + 4q^{8} - 4q^{9} + 6q^{13} + 4q^{14} + 4q^{16} - 4q^{18} + 6q^{26} + 4q^{28} - 8q^{29} + 4q^{32} + 4q^{33} - 4q^{36} + 4q^{37} - 6q^{39} - 8q^{47} + 44q^{49} + 8q^{51} + 6q^{52} + 4q^{56} + 24q^{57} - 8q^{58} + 40q^{61} - 4q^{63} + 4q^{64} + 4q^{66} - 36q^{67} + 4q^{69} - 4q^{72} - 36q^{73} + 4q^{74} - 6q^{78} - 32q^{79} + 4q^{81} + 8q^{83} + 40q^{91} - 4q^{93} - 8q^{94} + 36q^{97} + 44q^{98} + O(q^{100}) \)

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
\(7\) −3.12311 −1.18042 −0.590211 0.807249i \(-0.700956\pi\)
−0.590211 + 0.807249i \(0.700956\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 5.12311i 1.54467i −0.635213 0.772337i \(-0.719088\pi\)
0.635213 0.772337i \(-0.280912\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −0.561553 + 3.56155i −0.155747 + 0.987797i
\(14\) −3.12311 −0.834685
\(15\) 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
\(21\) 3.12311i 0.681518i
\(22\) 5.12311i 1.09225i
\(23\) 5.12311i 1.06824i −0.845408 0.534121i \(-0.820643\pi\)
0.845408 0.534121i \(-0.179357\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 0 0
\(26\) −0.561553 + 3.56155i −0.110130 + 0.698478i
\(27\) 1.00000i 0.192450i
\(28\) −3.12311 −0.590211
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 3.12311i 0.560926i −0.959865 0.280463i \(-0.909512\pi\)
0.959865 0.280463i \(-0.0904881\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.12311 0.891818
\(34\) 2.00000i 0.342997i
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 5.12311 0.842233 0.421117 0.907006i \(-0.361638\pi\)
0.421117 + 0.907006i \(0.361638\pi\)
\(38\) 6.00000i 0.973329i
\(39\) −3.56155 0.561553i −0.570305 0.0899204i
\(40\) 0 0
\(41\) 0.876894i 0.136948i −0.997653 0.0684739i \(-0.978187\pi\)
0.997653 0.0684739i \(-0.0218130\pi\)
\(42\) 3.12311i 0.481906i
\(43\) 6.24621i 0.952538i 0.879300 + 0.476269i \(0.158011\pi\)
−0.879300 + 0.476269i \(0.841989\pi\)
\(44\) 5.12311i 0.772337i
\(45\) 0 0
\(46\) 5.12311i 0.755361i
\(47\) 6.24621 0.911104 0.455552 0.890209i \(-0.349442\pi\)
0.455552 + 0.890209i \(0.349442\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 2.75379 0.393398
\(50\) 0 0
\(51\) 2.00000 0.280056
\(52\) −0.561553 + 3.56155i −0.0778734 + 0.493899i
\(53\) 13.3693i 1.83642i −0.396098 0.918208i \(-0.629636\pi\)
0.396098 0.918208i \(-0.370364\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0 0
\(56\) −3.12311 −0.417343
\(57\) 6.00000 0.794719
\(58\) −2.00000 −0.262613
\(59\) 1.12311i 0.146216i −0.997324 0.0731079i \(-0.976708\pi\)
0.997324 0.0731079i \(-0.0232918\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 3.12311i 0.396635i
\(63\) 3.12311 0.393474
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 5.12311 0.630611
\(67\) −4.87689 −0.595807 −0.297904 0.954596i \(-0.596287\pi\)
−0.297904 + 0.954596i \(0.596287\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 5.12311 0.616749
\(70\) 0 0
\(71\) 10.2462i 1.21600i −0.793936 0.608001i \(-0.791972\pi\)
0.793936 0.608001i \(-0.208028\pi\)
\(72\) −1.00000 −0.117851
\(73\) −13.1231 −1.53594 −0.767972 0.640484i \(-0.778734\pi\)
−0.767972 + 0.640484i \(0.778734\pi\)
\(74\) 5.12311 0.595549
\(75\) 0 0
\(76\) 6.00000i 0.688247i
\(77\) 16.0000i 1.82337i
\(78\) −3.56155 0.561553i −0.403266 0.0635833i
\(79\) −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
\(82\) 0.876894i 0.0968368i
\(83\) −6.24621 −0.685611 −0.342805 0.939406i \(-0.611377\pi\)
−0.342805 + 0.939406i \(0.611377\pi\)
\(84\) 3.12311i 0.340759i
\(85\) 0 0
\(86\) 6.24621i 0.673546i
\(87\) 2.00000i 0.214423i
\(88\) 5.12311i 0.546125i
\(89\) 3.12311i 0.331049i 0.986206 + 0.165524i \(0.0529316\pi\)
−0.986206 + 0.165524i \(0.947068\pi\)
\(90\) 0 0
\(91\) 1.75379 11.1231i 0.183847 1.16602i
\(92\) 5.12311i 0.534121i
\(93\) 3.12311 0.323851
\(94\) 6.24621 0.644247
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 13.1231 1.33245 0.666225 0.745751i \(-0.267909\pi\)
0.666225 + 0.745751i \(0.267909\pi\)
\(98\) 2.75379 0.278175
\(99\) 5.12311i 0.514891i
\(100\) 0 0
\(101\) −12.2462 −1.21854 −0.609272 0.792961i \(-0.708538\pi\)
−0.609272 + 0.792961i \(0.708538\pi\)
\(102\) 2.00000 0.198030
\(103\) 13.1231i 1.29306i −0.762889 0.646529i \(-0.776220\pi\)
0.762889 0.646529i \(-0.223780\pi\)
\(104\) −0.561553 + 3.56155i −0.0550648 + 0.349239i
\(105\) 0 0
\(106\) 13.3693i 1.29854i
\(107\) 8.00000i 0.773389i 0.922208 + 0.386695i \(0.126383\pi\)
−0.922208 + 0.386695i \(0.873617\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 2.87689i 0.275557i 0.990463 + 0.137778i \(0.0439961\pi\)
−0.990463 + 0.137778i \(0.956004\pi\)
\(110\) 0 0
\(111\) 5.12311i 0.486264i
\(112\) −3.12311 −0.295106
\(113\) 12.2462i 1.15203i 0.817440 + 0.576013i \(0.195392\pi\)
−0.817440 + 0.576013i \(0.804608\pi\)
\(114\) 6.00000 0.561951
\(115\) 0 0
\(116\) −2.00000 −0.185695
\(117\) 0.561553 3.56155i 0.0519156 0.329266i
\(118\) 1.12311i 0.103390i
\(119\) 6.24621i 0.572589i
\(120\) 0 0
\(121\) −15.2462 −1.38602
\(122\) 10.0000 0.905357
\(123\) 0.876894 0.0790669
\(124\) 3.12311i 0.280463i
\(125\) 0 0
\(126\) 3.12311 0.278228
\(127\) 13.1231i 1.16449i 0.813014 + 0.582244i \(0.197825\pi\)
−0.813014 + 0.582244i \(0.802175\pi\)
\(128\) 1.00000 0.0883883
\(129\) −6.24621 −0.549948
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 5.12311 0.445909
\(133\) 18.7386i 1.62485i
\(134\) −4.87689 −0.421300
\(135\) 0 0
\(136\) 2.00000i 0.171499i
\(137\) 10.4924 0.896428 0.448214 0.893926i \(-0.352060\pi\)
0.448214 + 0.893926i \(0.352060\pi\)
\(138\) 5.12311 0.436108
\(139\) 16.4924 1.39887 0.699435 0.714697i \(-0.253435\pi\)
0.699435 + 0.714697i \(0.253435\pi\)
\(140\) 0 0
\(141\) 6.24621i 0.526026i
\(142\) 10.2462i 0.859843i
\(143\) 18.2462 + 2.87689i 1.52582 + 0.240578i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −13.1231 −1.08608
\(147\) 2.75379i 0.227129i
\(148\) 5.12311 0.421117
\(149\) 14.0000i 1.14692i −0.819232 0.573462i \(-0.805600\pi\)
0.819232 0.573462i \(-0.194400\pi\)
\(150\) 0 0
\(151\) 13.3693i 1.08798i −0.839092 0.543990i \(-0.816913\pi\)
0.839092 0.543990i \(-0.183087\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 2.00000i 0.161690i
\(154\) 16.0000i 1.28932i
\(155\) 0 0
\(156\) −3.56155 0.561553i −0.285152 0.0449602i
\(157\) 21.3693i 1.70546i −0.522354 0.852729i \(-0.674946\pi\)
0.522354 0.852729i \(-0.325054\pi\)
\(158\) −8.00000 −0.636446
\(159\) 13.3693 1.06026
\(160\) 0 0
\(161\) 16.0000i 1.26098i
\(162\) 1.00000 0.0785674
\(163\) −7.12311 −0.557925 −0.278962 0.960302i \(-0.589990\pi\)
−0.278962 + 0.960302i \(0.589990\pi\)
\(164\) 0.876894i 0.0684739i
\(165\) 0 0
\(166\) −6.24621 −0.484800
\(167\) 22.2462 1.72146 0.860732 0.509059i \(-0.170006\pi\)
0.860732 + 0.509059i \(0.170006\pi\)
\(168\) 3.12311i 0.240953i
\(169\) −12.3693 4.00000i −0.951486 0.307692i
\(170\) 0 0
\(171\) 6.00000i 0.458831i
\(172\) 6.24621i 0.476269i
\(173\) 23.1231i 1.75802i 0.476806 + 0.879009i \(0.341794\pi\)
−0.476806 + 0.879009i \(0.658206\pi\)
\(174\) 2.00000i 0.151620i
\(175\) 0 0
\(176\) 5.12311i 0.386169i
\(177\) 1.12311 0.0844178
\(178\) 3.12311i 0.234087i
\(179\) −16.4924 −1.23270 −0.616351 0.787472i \(-0.711390\pi\)
−0.616351 + 0.787472i \(0.711390\pi\)
\(180\) 0 0
\(181\) −20.2462 −1.50489 −0.752445 0.658656i \(-0.771125\pi\)
−0.752445 + 0.658656i \(0.771125\pi\)
\(182\) 1.75379 11.1231i 0.129999 0.824499i
\(183\) 10.0000i 0.739221i
\(184\) 5.12311i 0.377680i
\(185\) 0 0
\(186\) 3.12311 0.228997
\(187\) −10.2462 −0.749277
\(188\) 6.24621 0.455552
\(189\) 3.12311i 0.227173i
\(190\) 0 0
\(191\) 16.4924 1.19335 0.596675 0.802483i \(-0.296488\pi\)
0.596675 + 0.802483i \(0.296488\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −25.1231 −1.80840 −0.904200 0.427109i \(-0.859532\pi\)
−0.904200 + 0.427109i \(0.859532\pi\)
\(194\) 13.1231 0.942184
\(195\) 0 0
\(196\) 2.75379 0.196699
\(197\) −16.2462 −1.15749 −0.578747 0.815507i \(-0.696458\pi\)
−0.578747 + 0.815507i \(0.696458\pi\)
\(198\) 5.12311i 0.364083i
\(199\) −18.2462 −1.29344 −0.646720 0.762728i \(-0.723860\pi\)
−0.646720 + 0.762728i \(0.723860\pi\)
\(200\) 0 0
\(201\) 4.87689i 0.343990i
\(202\) −12.2462 −0.861640
\(203\) 6.24621 0.438398
\(204\) 2.00000 0.140028
\(205\) 0 0
\(206\) 13.1231i 0.914330i
\(207\) 5.12311i 0.356080i
\(208\) −0.561553 + 3.56155i −0.0389367 + 0.246949i
\(209\) −30.7386 −2.12624
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 13.3693i 0.918208i
\(213\) 10.2462 0.702059
\(214\) 8.00000i 0.546869i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 9.75379i 0.662130i
\(218\) 2.87689i 0.194848i
\(219\) 13.1231i 0.886777i
\(220\) 0 0
\(221\) 7.12311 + 1.12311i 0.479152 + 0.0755483i
\(222\) 5.12311i 0.343840i
\(223\) 9.36932 0.627416 0.313708 0.949520i \(-0.398429\pi\)
0.313708 + 0.949520i \(0.398429\pi\)
\(224\) −3.12311 −0.208671
\(225\) 0 0
\(226\) 12.2462i 0.814606i
\(227\) −8.00000 −0.530979 −0.265489 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) 6.00000 0.397360
\(229\) 5.12311i 0.338544i −0.985569 0.169272i \(-0.945858\pi\)
0.985569 0.169272i \(-0.0541417\pi\)
\(230\) 0 0
\(231\) −16.0000 −1.05272
\(232\) −2.00000 −0.131306
\(233\) 7.75379i 0.507968i −0.967208 0.253984i \(-0.918259\pi\)
0.967208 0.253984i \(-0.0817410\pi\)
\(234\) 0.561553 3.56155i 0.0367099 0.232826i
\(235\) 0 0
\(236\) 1.12311i 0.0731079i
\(237\) 8.00000i 0.519656i
\(238\) 6.24621i 0.404882i
\(239\) 4.49242i 0.290591i 0.989388 + 0.145295i \(0.0464132\pi\)
−0.989388 + 0.145295i \(0.953587\pi\)
\(240\) 0 0
\(241\) 14.2462i 0.917679i 0.888519 + 0.458840i \(0.151735\pi\)
−0.888519 + 0.458840i \(0.848265\pi\)
\(242\) −15.2462 −0.980064
\(243\) 1.00000i 0.0641500i
\(244\) 10.0000 0.640184
\(245\) 0 0
\(246\) 0.876894 0.0559087
\(247\) 21.3693 + 3.36932i 1.35970 + 0.214384i
\(248\) 3.12311i 0.198317i
\(249\) 6.24621i 0.395838i
\(250\) 0 0
\(251\) 26.2462 1.65665 0.828323 0.560251i \(-0.189295\pi\)
0.828323 + 0.560251i \(0.189295\pi\)
\(252\) 3.12311 0.196737
\(253\) −26.2462 −1.65009
\(254\) 13.1231i 0.823417i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 12.2462i 0.763898i 0.924183 + 0.381949i \(0.124747\pi\)
−0.924183 + 0.381949i \(0.875253\pi\)
\(258\) −6.24621 −0.388872
\(259\) −16.0000 −0.994192
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) 4.00000 0.247121
\(263\) 27.3693i 1.68766i −0.536607 0.843832i \(-0.680294\pi\)
0.536607 0.843832i \(-0.319706\pi\)
\(264\) 5.12311 0.315305
\(265\) 0 0
\(266\) 18.7386i 1.14894i
\(267\) −3.12311 −0.191131
\(268\) −4.87689 −0.297904
\(269\) 16.2462 0.990549 0.495274 0.868737i \(-0.335067\pi\)
0.495274 + 0.868737i \(0.335067\pi\)
\(270\) 0 0
\(271\) 23.1231i 1.40463i −0.711867 0.702314i \(-0.752150\pi\)
0.711867 0.702314i \(-0.247850\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 11.1231 + 1.75379i 0.673201 + 0.106144i
\(274\) 10.4924 0.633870
\(275\) 0 0
\(276\) 5.12311 0.308375
\(277\) 29.8617i 1.79422i 0.441809 + 0.897109i \(0.354337\pi\)
−0.441809 + 0.897109i \(0.645663\pi\)
\(278\) 16.4924 0.989150
\(279\) 3.12311i 0.186975i
\(280\) 0 0
\(281\) 3.12311i 0.186309i 0.995652 + 0.0931544i \(0.0296950\pi\)
−0.995652 + 0.0931544i \(0.970305\pi\)
\(282\) 6.24621i 0.371956i
\(283\) 4.00000i 0.237775i −0.992908 0.118888i \(-0.962067\pi\)
0.992908 0.118888i \(-0.0379328\pi\)
\(284\) 10.2462i 0.608001i
\(285\) 0 0
\(286\) 18.2462 + 2.87689i 1.07892 + 0.170114i
\(287\) 2.73863i 0.161656i
\(288\) −1.00000 −0.0589256
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 13.1231i 0.769290i
\(292\) −13.1231 −0.767972
\(293\) 28.7386 1.67893 0.839464 0.543415i \(-0.182869\pi\)
0.839464 + 0.543415i \(0.182869\pi\)
\(294\) 2.75379i 0.160604i
\(295\) 0 0
\(296\) 5.12311 0.297774
\(297\) −5.12311 −0.297273
\(298\) 14.0000i 0.810998i
\(299\) 18.2462 + 2.87689i 1.05521 + 0.166375i
\(300\) 0 0
\(301\) 19.5076i 1.12440i
\(302\) 13.3693i 0.769318i
\(303\) 12.2462i 0.703526i
\(304\) 6.00000i 0.344124i
\(305\) 0 0
\(306\) 2.00000i 0.114332i
\(307\) −31.1231 −1.77629 −0.888145 0.459564i \(-0.848006\pi\)
−0.888145 + 0.459564i \(0.848006\pi\)
\(308\) 16.0000i 0.911685i
\(309\) 13.1231 0.746547
\(310\) 0 0
\(311\) 8.49242 0.481561 0.240781 0.970580i \(-0.422597\pi\)
0.240781 + 0.970580i \(0.422597\pi\)
\(312\) −3.56155 0.561553i −0.201633 0.0317917i
\(313\) 16.2462i 0.918290i 0.888361 + 0.459145i \(0.151844\pi\)
−0.888361 + 0.459145i \(0.848156\pi\)
\(314\) 21.3693i 1.20594i
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 13.3693 0.749714
\(319\) 10.2462i 0.573678i
\(320\) 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
\(326\) −7.12311 −0.394512
\(327\) −2.87689 −0.159093
\(328\) 0.876894i 0.0484184i
\(329\) −19.5076 −1.07549
\(330\) 0 0
\(331\) 7.75379i 0.426187i 0.977032 + 0.213093i \(0.0683539\pi\)
−0.977032 + 0.213093i \(0.931646\pi\)
\(332\) −6.24621 −0.342805
\(333\) −5.12311 −0.280744
\(334\) 22.2462 1.21726
\(335\) 0 0
\(336\) 3.12311i 0.170379i
\(337\) 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
\(339\) −12.2462 −0.665123
\(340\) 0 0
\(341\) −16.0000 −0.866449
\(342\) 6.00000i 0.324443i
\(343\) 13.2614 0.716046
\(344\) 6.24621i 0.336773i
\(345\) 0 0
\(346\) 23.1231i 1.24311i
\(347\) 14.2462i 0.764777i 0.924002 + 0.382388i \(0.124898\pi\)
−0.924002 + 0.382388i \(0.875102\pi\)
\(348\) 2.00000i 0.107211i
\(349\) 19.3693i 1.03682i 0.855133 + 0.518408i \(0.173475\pi\)
−0.855133 + 0.518408i \(0.826525\pi\)
\(350\) 0 0
\(351\) 3.56155 + 0.561553i 0.190102 + 0.0299735i
\(352\) 5.12311i 0.273062i
\(353\) −12.2462 −0.651800 −0.325900 0.945404i \(-0.605667\pi\)
−0.325900 + 0.945404i \(0.605667\pi\)
\(354\) 1.12311 0.0596924
\(355\) 0 0
\(356\) 3.12311i 0.165524i
\(357\) −6.24621 −0.330585
\(358\) −16.4924 −0.871652
\(359\) 17.7538i 0.937009i 0.883461 + 0.468505i \(0.155207\pi\)
−0.883461 + 0.468505i \(0.844793\pi\)
\(360\) 0 0
\(361\) −17.0000 −0.894737
\(362\) −20.2462 −1.06412
\(363\) 15.2462i 0.800219i
\(364\) 1.75379 11.1231i 0.0919235 0.583009i
\(365\) 0 0
\(366\) 10.0000i 0.522708i
\(367\) 8.63068i 0.450518i −0.974299 0.225259i \(-0.927677\pi\)
0.974299 0.225259i \(-0.0723228\pi\)
\(368\) 5.12311i 0.267060i
\(369\) 0.876894i 0.0456493i
\(370\) 0 0
\(371\) 41.7538i 2.16775i
\(372\) 3.12311 0.161925
\(373\) 7.12311i 0.368820i 0.982849 + 0.184410i \(0.0590375\pi\)
−0.982849 + 0.184410i \(0.940963\pi\)
\(374\) −10.2462 −0.529819
\(375\) 0 0
\(376\) 6.24621 0.322124
\(377\) 1.12311 7.12311i 0.0578429 0.366859i
\(378\) 3.12311i 0.160635i
\(379\) 6.00000i 0.308199i −0.988055 0.154100i \(-0.950752\pi\)
0.988055 0.154100i \(-0.0492477\pi\)
\(380\) 0 0
\(381\) −13.1231 −0.672317
\(382\) 16.4924 0.843826
\(383\) 1.75379 0.0896144 0.0448072 0.998996i \(-0.485733\pi\)
0.0448072 + 0.998996i \(0.485733\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) −25.1231 −1.27873
\(387\) 6.24621i 0.317513i
\(388\) 13.1231 0.666225
\(389\) 0.246211 0.0124834 0.00624170 0.999981i \(-0.498013\pi\)
0.00624170 + 0.999981i \(0.498013\pi\)
\(390\) 0 0
\(391\) −10.2462 −0.518173
\(392\) 2.75379 0.139087
\(393\) 4.00000i 0.201773i
\(394\) −16.2462 −0.818472
\(395\) 0 0
\(396\) 5.12311i 0.257446i
\(397\) 15.3693 0.771364 0.385682 0.922632i \(-0.373966\pi\)
0.385682 + 0.922632i \(0.373966\pi\)
\(398\) −18.2462 −0.914600
\(399\) −18.7386 −0.938105
\(400\) 0 0
\(401\) 1.36932i 0.0683804i 0.999415 + 0.0341902i \(0.0108852\pi\)
−0.999415 + 0.0341902i \(0.989115\pi\)
\(402\) 4.87689i 0.243237i
\(403\) 11.1231 + 1.75379i 0.554081 + 0.0873624i
\(404\) −12.2462 −0.609272
\(405\) 0 0
\(406\) 6.24621 0.309994
\(407\) 26.2462i 1.30098i
\(408\) 2.00000 0.0990148
\(409\) 8.49242i 0.419923i 0.977710 + 0.209962i \(0.0673339\pi\)
−0.977710 + 0.209962i \(0.932666\pi\)
\(410\) 0 0
\(411\) 10.4924i 0.517553i
\(412\) 13.1231i 0.646529i
\(413\) 3.50758i 0.172597i
\(414\) 5.12311i 0.251787i
\(415\) 0 0
\(416\) −0.561553 + 3.56155i −0.0275324 + 0.174619i
\(417\) 16.4924i 0.807637i
\(418\) −30.7386 −1.50348
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) 0.630683i 0.0307376i 0.999882 + 0.0153688i \(0.00489224\pi\)
−0.999882 + 0.0153688i \(0.995108\pi\)
\(422\) 4.00000 0.194717
\(423\) −6.24621 −0.303701
\(424\) 13.3693i 0.649271i
\(425\) 0 0
\(426\) 10.2462 0.496431
\(427\) −31.2311 −1.51138
\(428\) 8.00000i 0.386695i
\(429\) −2.87689 + 18.2462i −0.138898 + 0.880935i
\(430\) 0 0
\(431\) 32.4924i 1.56510i 0.622585 + 0.782552i \(0.286083\pi\)
−0.622585 + 0.782552i \(0.713917\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 18.0000i 0.865025i −0.901628 0.432512i \(-0.857627\pi\)
0.901628 0.432512i \(-0.142373\pi\)
\(434\) 9.75379i 0.468197i
\(435\) 0 0
\(436\) 2.87689i 0.137778i
\(437\) −30.7386 −1.47043
\(438\) 13.1231i 0.627046i
\(439\) 36.4924 1.74169 0.870844 0.491559i \(-0.163573\pi\)
0.870844 + 0.491559i \(0.163573\pi\)
\(440\) 0 0
\(441\) −2.75379 −0.131133
\(442\) 7.12311 + 1.12311i 0.338812 + 0.0534207i
\(443\) 3.50758i 0.166650i −0.996522 0.0833250i \(-0.973446\pi\)
0.996522 0.0833250i \(-0.0265540\pi\)
\(444\) 5.12311i 0.243132i
\(445\) 0 0
\(446\) 9.36932 0.443650
\(447\) 14.0000 0.662177
\(448\) −3.12311 −0.147553
\(449\) 28.8769i 1.36278i −0.731918 0.681392i \(-0.761375\pi\)
0.731918 0.681392i \(-0.238625\pi\)
\(450\) 0 0
\(451\) −4.49242 −0.211540
\(452\) 12.2462i 0.576013i
\(453\) 13.3693 0.628145
\(454\) −8.00000 −0.375459
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −31.3693 −1.46739 −0.733697 0.679476i \(-0.762207\pi\)
−0.733697 + 0.679476i \(0.762207\pi\)
\(458\) 5.12311i 0.239387i
\(459\) −2.00000 −0.0933520
\(460\) 0 0
\(461\) 18.4924i 0.861278i −0.902524 0.430639i \(-0.858288\pi\)
0.902524 0.430639i \(-0.141712\pi\)
\(462\) −16.0000 −0.744387
\(463\) −21.8617 −1.01600 −0.508001 0.861357i \(-0.669615\pi\)
−0.508001 + 0.861357i \(0.669615\pi\)
\(464\) −2.00000 −0.0928477
\(465\) 0 0
\(466\) 7.75379i 0.359187i
\(467\) 22.2462i 1.02943i 0.857361 + 0.514716i \(0.172103\pi\)
−0.857361 + 0.514716i \(0.827897\pi\)
\(468\) 0.561553 3.56155i 0.0259578 0.164633i
\(469\) 15.2311 0.703305
\(470\) 0 0
\(471\) 21.3693 0.984646
\(472\) 1.12311i 0.0516951i
\(473\) 32.0000 1.47136
\(474\) 8.00000i 0.367452i
\(475\) 0 0
\(476\) 6.24621i 0.286295i
\(477\) 13.3693i 0.612139i
\(478\) 4.49242i 0.205479i
\(479\) 12.4924i 0.570793i −0.958409 0.285397i \(-0.907875\pi\)
0.958409 0.285397i \(-0.0921253\pi\)
\(480\) 0 0
\(481\) −2.87689 + 18.2462i −0.131175 + 0.831956i
\(482\) 14.2462i 0.648897i
\(483\) −16.0000 −0.728025
\(484\) −15.2462 −0.693010
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −17.3693 −0.787079 −0.393539 0.919308i \(-0.628750\pi\)
−0.393539 + 0.919308i \(0.628750\pi\)
\(488\) 10.0000 0.452679
\(489\) 7.12311i 0.322118i
\(490\) 0 0
\(491\) 38.7386 1.74825 0.874125 0.485701i \(-0.161436\pi\)
0.874125 + 0.485701i \(0.161436\pi\)
\(492\) 0.876894 0.0395335
\(493\) 4.00000i 0.180151i
\(494\) 21.3693 + 3.36932i 0.961451 + 0.151593i
\(495\) 0 0
\(496\) 3.12311i 0.140232i
\(497\) 32.0000i 1.43540i
\(498\) 6.24621i 0.279899i
\(499\) 34.4924i 1.54409i 0.635566 + 0.772046i \(0.280767\pi\)
−0.635566 + 0.772046i \(0.719233\pi\)
\(500\) 0 0
\(501\) 22.2462i 0.993887i
\(502\) 26.2462 1.17143
\(503\) 35.3693i 1.57704i 0.615009 + 0.788520i \(0.289152\pi\)
−0.615009 + 0.788520i \(0.710848\pi\)
\(504\) 3.12311 0.139114
\(505\) 0 0
\(506\) −26.2462 −1.16679
\(507\) 4.00000 12.3693i 0.177646 0.549341i
\(508\) 13.1231i 0.582244i
\(509\) 32.2462i 1.42929i 0.699488 + 0.714644i \(0.253411\pi\)
−0.699488 + 0.714644i \(0.746589\pi\)
\(510\) 0 0
\(511\) 40.9848 1.81306
\(512\) 1.00000 0.0441942
\(513\) −6.00000 −0.264906
\(514\) 12.2462i 0.540157i
\(515\) 0 0
\(516\) −6.24621 −0.274974
\(517\) 32.0000i 1.40736i
\(518\) −16.0000 −0.703000
\(519\) −23.1231 −1.01499
\(520\) 0 0
\(521\) 0.246211 0.0107867 0.00539336 0.999985i \(-0.498283\pi\)
0.00539336 + 0.999985i \(0.498283\pi\)
\(522\) 2.00000 0.0875376
\(523\) 26.7386i 1.16920i −0.811322 0.584599i \(-0.801252\pi\)
0.811322 0.584599i \(-0.198748\pi\)
\(524\) 4.00000 0.174741
\(525\) 0 0
\(526\) 27.3693i 1.19336i
\(527\) −6.24621 −0.272089
\(528\) 5.12311 0.222955
\(529\) −3.24621 −0.141140
\(530\) 0 0
\(531\) 1.12311i 0.0487386i
\(532\) 18.7386i 0.812423i
\(533\) 3.12311 + 0.492423i 0.135277 + 0.0213292i
\(534\) −3.12311 −0.135150
\(535\) 0 0
\(536\) −4.87689 −0.210650
\(537\) 16.4924i 0.711701i
\(538\) 16.2462 0.700424
\(539\) 14.1080i 0.607672i
\(540\) 0 0
\(541\) 10.8769i 0.467634i −0.972281 0.233817i \(-0.924878\pi\)
0.972281 0.233817i \(-0.0751217\pi\)
\(542\) 23.1231i 0.993222i
\(543\) 20.2462i 0.868848i
\(544\) 2.00000i 0.0857493i
\(545\) 0 0
\(546\) 11.1231 + 1.75379i 0.476025 + 0.0750552i
\(547\) 20.9848i 0.897247i −0.893721 0.448624i \(-0.851914\pi\)
0.893721 0.448624i \(-0.148086\pi\)
\(548\) 10.4924 0.448214
\(549\) −10.0000 −0.426790
\(550\) 0 0
\(551\) 12.0000i 0.511217i
\(552\) 5.12311 0.218054
\(553\) 24.9848 1.06246
\(554\) 29.8617i 1.26870i
\(555\) 0 0
\(556\) 16.4924 0.699435
\(557\) −11.7538 −0.498024 −0.249012 0.968500i \(-0.580106\pi\)
−0.249012 + 0.968500i \(0.580106\pi\)
\(558\) 3.12311i 0.132212i
\(559\) −22.2462 3.50758i −0.940914 0.148355i
\(560\) 0 0
\(561\) 10.2462i 0.432595i
\(562\) 3.12311i 0.131740i
\(563\) 32.9848i 1.39015i −0.718939 0.695073i \(-0.755372\pi\)
0.718939 0.695073i \(-0.244628\pi\)
\(564\) 6.24621i 0.263013i
\(565\) 0 0
\(566\) 4.00000i 0.168133i
\(567\) −3.12311 −0.131158
\(568\) 10.2462i 0.429921i
\(569\) 12.7386 0.534031 0.267016 0.963692i \(-0.413962\pi\)
0.267016 + 0.963692i \(0.413962\pi\)
\(570\) 0 0
\(571\) −8.49242 −0.355397 −0.177698 0.984085i \(-0.556865\pi\)
−0.177698 + 0.984085i \(0.556865\pi\)
\(572\) 18.2462 + 2.87689i 0.762912 + 0.120289i
\(573\) 16.4924i 0.688981i
\(574\) 2.73863i 0.114308i
\(575\) 0 0
\(576\) −1.00000 −0.0416667
\(577\) −27.3693 −1.13940 −0.569700 0.821853i \(-0.692941\pi\)
−0.569700 + 0.821853i \(0.692941\pi\)
\(578\) 13.0000 0.540729
\(579\) 25.1231i 1.04408i
\(580\) 0 0
\(581\) 19.5076 0.809311
\(582\) 13.1231i 0.543970i
\(583\) −68.4924 −2.83667
\(584\) −13.1231 −0.543038
\(585\) 0 0
\(586\) 28.7386 1.18718
\(587\) 16.4924 0.680715 0.340358 0.940296i \(-0.389452\pi\)
0.340358 + 0.940296i \(0.389452\pi\)
\(588\) 2.75379i 0.113564i
\(589\) −18.7386 −0.772112
\(590\) 0 0
\(591\) 16.2462i 0.668280i
\(592\) 5.12311 0.210558
\(593\) −5.50758 −0.226169 −0.113085 0.993585i \(-0.536073\pi\)
−0.113085 + 0.993585i \(0.536073\pi\)
\(594\) −5.12311 −0.210204
\(595\) 0 0
\(596\) 14.0000i 0.573462i
\(597\) 18.2462i 0.746768i
\(598\) 18.2462 + 2.87689i 0.746143 + 0.117645i
\(599\) 36.4924 1.49104 0.745520 0.666483i \(-0.232201\pi\)
0.745520 + 0.666483i \(0.232201\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 19.5076i 0.795070i
\(603\) 4.87689 0.198602
\(604\) 13.3693i 0.543990i
\(605\) 0 0
\(606\) 12.2462i 0.497468i
\(607\) 15.3693i 0.623821i −0.950111 0.311911i \(-0.899031\pi\)
0.950111 0.311911i \(-0.100969\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 6.24621i 0.253109i
\(610\) 0 0
\(611\) −3.50758 + 22.2462i −0.141901 + 0.899985i
\(612\) 2.00000i 0.0808452i
\(613\) 39.3693 1.59011 0.795056 0.606536i \(-0.207441\pi\)
0.795056 + 0.606536i \(0.207441\pi\)
\(614\) −31.1231 −1.25603
\(615\) 0 0
\(616\) 16.0000i 0.644658i
\(617\) 40.7386 1.64008 0.820038 0.572309i \(-0.193952\pi\)
0.820038 + 0.572309i \(0.193952\pi\)
\(618\) 13.1231 0.527889
\(619\) 38.9848i 1.56693i 0.621434 + 0.783467i \(0.286550\pi\)
−0.621434 + 0.783467i \(0.713450\pi\)
\(620\) 0 0
\(621\) −5.12311 −0.205583
\(622\) 8.49242 0.340515
\(623\) 9.75379i 0.390777i
\(624\) −3.56155 0.561553i −0.142576 0.0224801i
\(625\) 0 0
\(626\) 16.2462i 0.649329i
\(627\) 30.7386i 1.22758i
\(628\) 21.3693i 0.852729i
\(629\) 10.2462i 0.408543i
\(630\) 0 0
\(631\) 35.6155i 1.41783i 0.705293 + 0.708916i \(0.250815\pi\)
−0.705293 + 0.708916i \(0.749185\pi\)
\(632\) −8.00000 −0.318223
\(633\) 4.00000i 0.158986i
\(634\) −6.00000 −0.238290
\(635\) 0 0
\(636\) 13.3693 0.530128
\(637\) −1.54640 + 9.80776i −0.0612705 + 0.388598i
\(638\) 10.2462i 0.405651i
\(639\) 10.2462i 0.405334i
\(640\) 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
\(643\) 17.3693 0.684979 0.342489 0.939522i \(-0.388730\pi\)
0.342489 + 0.939522i \(0.388730\pi\)
\(644\) 16.0000i 0.630488i
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) 29.6155i 1.16431i −0.813079 0.582153i \(-0.802210\pi\)
0.813079 0.582153i \(-0.197790\pi\)
\(648\) 1.00000 0.0392837
\(649\) −5.75379 −0.225856
\(650\) 0 0
\(651\) −9.75379 −0.382281
\(652\) −7.12311 −0.278962
\(653\) 13.8617i 0.542452i −0.962516 0.271226i \(-0.912571\pi\)
0.962516 0.271226i \(-0.0874290\pi\)
\(654\) −2.87689 −0.112495
\(655\) 0 0
\(656\) 0.876894i 0.0342370i
\(657\) 13.1231 0.511981
\(658\) −19.5076 −0.760485
\(659\) 21.7538 0.847407 0.423704 0.905801i \(-0.360730\pi\)
0.423704 + 0.905801i \(0.360730\pi\)
\(660\) 0 0
\(661\) 9.12311i 0.354848i −0.984135 0.177424i \(-0.943224\pi\)
0.984135 0.177424i \(-0.0567763\pi\)
\(662\) 7.75379i 0.301360i
\(663\) −1.12311 + 7.12311i −0.0436178 + 0.276638i
\(664\) −6.24621 −0.242400
\(665\) 0 0
\(666\) −5.12311 −0.198516
\(667\) 10.2462i 0.396735i
\(668\) 22.2462 0.860732
\(669\) 9.36932i 0.362239i
\(670\) 0 0
\(671\) 51.2311i 1.97775i
\(672\) 3.12311i 0.120476i
\(673\) 26.9848i 1.04019i 0.854109 + 0.520095i \(0.174103\pi\)
−0.854109 + 0.520095i \(0.825897\pi\)
\(674\) 6.00000i 0.231111i
\(675\) 0 0
\(676\) −12.3693 4.00000i −0.475743 0.153846i
\(677\) 12.8769i 0.494899i −0.968901 0.247450i \(-0.920408\pi\)
0.968901 0.247450i \(-0.0795925\pi\)
\(678\) −12.2462 −0.470313
\(679\) −40.9848 −1.57285
\(680\) 0 0
\(681\) 8.00000i 0.306561i
\(682\) −16.0000 −0.612672
\(683\) −16.9848 −0.649907 −0.324954 0.945730i \(-0.605349\pi\)
−0.324954 + 0.945730i \(0.605349\pi\)
\(684\) 6.00000i 0.229416i
\(685\) 0 0
\(686\) 13.2614 0.506321
\(687\) 5.12311 0.195459
\(688\) 6.24621i 0.238135i
\(689\) 47.6155 + 7.50758i 1.81401 + 0.286016i
\(690\) 0 0
\(691\) 28.7386i 1.09327i −0.837371 0.546635i \(-0.815909\pi\)
0.837371 0.546635i \(-0.184091\pi\)
\(692\) 23.1231i 0.879009i
\(693\) 16.0000i 0.607790i
\(694\) 14.2462i 0.540779i
\(695\) 0 0
\(696\) 2.00000i 0.0758098i
\(697\) −1.75379 −0.0664295
\(698\) 19.3693i 0.733139i
\(699\) 7.75379 0.293275
\(700\) 0 0
\(701\) −14.0000 −0.528773 −0.264386 0.964417i \(-0.585169\pi\)
−0.264386 + 0.964417i \(0.585169\pi\)
\(702\) 3.56155 + 0.561553i 0.134422 + 0.0211944i
\(703\) 30.7386i 1.15933i
\(704\) 5.12311i 0.193084i
\(705\) 0 0
\(706\) −12.2462 −0.460892
\(707\) 38.2462 1.43840
\(708\) 1.12311 0.0422089
\(709\) 1.61553i 0.0606724i −0.999540 0.0303362i \(-0.990342\pi\)
0.999540 0.0303362i \(-0.00965780\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 3.12311i 0.117043i
\(713\) −16.0000 −0.599205
\(714\) −6.24621 −0.233759
\(715\) 0 0
\(716\) −16.4924 −0.616351
\(717\) −4.49242 −0.167773
\(718\) 17.7538i 0.662566i
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 0 0
\(721\) 40.9848i 1.52636i
\(722\) −17.0000 −0.632674
\(723\) −14.2462 −0.529822
\(724\) −20.2462 −0.752445
\(725\) 0 0
\(726\) 15.2462i 0.565840i
\(727\) 19.8617i 0.736631i −0.929701 0.368316i \(-0.879935\pi\)
0.929701 0.368316i \(-0.120065\pi\)
\(728\) 1.75379 11.1231i 0.0649997 0.412250i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 12.4924 0.462049
\(732\) 10.0000i 0.369611i
\(733\) 35.3693 1.30640 0.653198 0.757187i \(-0.273427\pi\)
0.653198 + 0.757187i \(0.273427\pi\)
\(734\) 8.63068i 0.318564i
\(735\) 0 0
\(736\) 5.12311i 0.188840i
\(737\) 24.9848i 0.920329i
\(738\) 0.876894i 0.0322789i
\(739\) 37.2311i 1.36957i −0.728747 0.684783i \(-0.759897\pi\)
0.728747 0.684783i \(-0.240103\pi\)
\(740\) 0 0
\(741\) −3.36932 + 21.3693i −0.123775 + 0.785021i
\(742\) 41.7538i 1.53283i
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 3.12311 0.114499
\(745\) 0 0
\(746\) 7.12311i 0.260795i
\(747\) 6.24621 0.228537
\(748\) −10.2462 −0.374639
\(749\) 24.9848i 0.912926i
\(750\) 0 0
\(751\) −26.2462 −0.957738 −0.478869 0.877886i \(-0.658953\pi\)
−0.478869 + 0.877886i \(0.658953\pi\)
\(752\) 6.24621 0.227776
\(753\) 26.2462i 0.956465i
\(754\) 1.12311 7.12311i 0.0409011 0.259408i
\(755\) 0 0
\(756\) 3.12311i 0.113586i
\(757\) 3.12311i 0.113511i 0.998388 + 0.0567556i \(0.0180756\pi\)
−0.998388 + 0.0567556i \(0.981924\pi\)
\(758\) 6.00000i 0.217930i
\(759\) 26.2462i 0.952677i
\(760\) 0 0
\(761\) 3.12311i 0.113212i 0.998397 + 0.0566062i \(0.0180280\pi\)
−0.998397 + 0.0566062i \(0.981972\pi\)
\(762\) −13.1231 −0.475400
\(763\) 8.98485i 0.325273i
\(764\) 16.4924 0.596675
\(765\) 0 0
\(766\) 1.75379 0.0633670
\(767\) 4.00000 + 0.630683i 0.144432 + 0.0227726i
\(768\) 1.00000i 0.0360844i
\(769\) 32.9848i 1.18946i −0.803924 0.594732i \(-0.797258\pi\)
0.803924 0.594732i \(-0.202742\pi\)
\(770\) 0 0
\(771\) −12.2462 −0.441037
\(772\) −25.1231 −0.904200
\(773\) −16.2462 −0.584336 −0.292168 0.956367i \(-0.594377\pi\)
−0.292168 + 0.956367i \(0.594377\pi\)
\(774\) 6.24621i 0.224515i
\(775\) 0 0
\(776\) 13.1231 0.471092
\(777\) 16.0000i 0.573997i
\(778\) 0.246211 0.00882710
\(779\) −5.26137 −0.188508
\(780\) 0 0
\(781\) −52.4924 −1.87833
\(782\) −10.2462 −0.366404
\(783\) 2.00000i 0.0714742i
\(784\) 2.75379 0.0983496
\(785\) 0 0
\(786\) 4.00000i 0.142675i
\(787\) 12.3845 0.441459 0.220729 0.975335i \(-0.429156\pi\)
0.220729 + 0.975335i \(0.429156\pi\)
\(788\) −16.2462 −0.578747
\(789\) 27.3693 0.974373
\(790\) 0 0
\(791\) 38.2462i 1.35988i
\(792\) 5.12311i 0.182042i
\(793\) −5.61553 + 35.6155i −0.199413 + 1.26474i
\(794\) 15.3693 0.545437
\(795\) 0 0
\(796\) −18.2462 −0.646720