Properties

Label 1950.2.f.g.649.1
Level $1950$
Weight $2$
Character 1950.649
Analytic conductor $15.571$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 649.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.649
Dual form 1950.2.f.g.649.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} -2.00000 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} -2.00000 q^{7} +1.00000 q^{8} -1.00000 q^{9} -1.00000i q^{12} +(2.00000 + 3.00000i) q^{13} -2.00000 q^{14} +1.00000 q^{16} -2.00000i q^{17} -1.00000 q^{18} -6.00000i q^{19} +2.00000i q^{21} -4.00000i q^{23} -1.00000i q^{24} +(2.00000 + 3.00000i) q^{26} +1.00000i q^{27} -2.00000 q^{28} +10.0000 q^{29} -10.0000i q^{31} +1.00000 q^{32} -2.00000i q^{34} -1.00000 q^{36} +8.00000 q^{37} -6.00000i q^{38} +(3.00000 - 2.00000i) q^{39} -10.0000i q^{41} +2.00000i q^{42} -4.00000i q^{43} -4.00000i q^{46} -12.0000 q^{47} -1.00000i q^{48} -3.00000 q^{49} -2.00000 q^{51} +(2.00000 + 3.00000i) q^{52} +6.00000i q^{53} +1.00000i q^{54} -2.00000 q^{56} -6.00000 q^{57} +10.0000 q^{58} +4.00000i q^{59} +2.00000 q^{61} -10.0000i q^{62} +2.00000 q^{63} +1.00000 q^{64} -2.00000 q^{67} -2.00000i q^{68} -4.00000 q^{69} -1.00000 q^{72} +4.00000 q^{73} +8.00000 q^{74} -6.00000i q^{76} +(3.00000 - 2.00000i) q^{78} +1.00000 q^{81} -10.0000i q^{82} +4.00000 q^{83} +2.00000i q^{84} -4.00000i q^{86} -10.0000i q^{87} -6.00000i q^{89} +(-4.00000 - 6.00000i) q^{91} -4.00000i q^{92} -10.0000 q^{93} -12.0000 q^{94} -1.00000i q^{96} -12.0000 q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{4} - 4q^{7} + 2q^{8} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{4} - 4q^{7} + 2q^{8} - 2q^{9} + 4q^{13} - 4q^{14} + 2q^{16} - 2q^{18} + 4q^{26} - 4q^{28} + 20q^{29} + 2q^{32} - 2q^{36} + 16q^{37} + 6q^{39} - 24q^{47} - 6q^{49} - 4q^{51} + 4q^{52} - 4q^{56} - 12q^{57} + 20q^{58} + 4q^{61} + 4q^{63} + 2q^{64} - 4q^{67} - 8q^{69} - 2q^{72} + 8q^{73} + 16q^{74} + 6q^{78} + 2q^{81} + 8q^{83} - 8q^{91} - 20q^{93} - 24q^{94} - 24q^{97} - 6q^{98} + O(q^{100}) \)

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
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.00000 + 3.00000i 0.554700 + 0.832050i
\(14\) −2.00000 −0.534522
\(15\) 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
\(21\) 2.00000i 0.436436i
\(22\) 0 0
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 0 0
\(26\) 2.00000 + 3.00000i 0.392232 + 0.588348i
\(27\) 1.00000i 0.192450i
\(28\) −2.00000 −0.377964
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) 10.0000i 1.79605i −0.439941 0.898027i \(-0.645001\pi\)
0.439941 0.898027i \(-0.354999\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 2.00000i 0.342997i
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 3.00000 2.00000i 0.480384 0.320256i
\(40\) 0 0
\(41\) 10.0000i 1.56174i −0.624695 0.780869i \(-0.714777\pi\)
0.624695 0.780869i \(-0.285223\pi\)
\(42\) 2.00000i 0.308607i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 4.00000i 0.589768i
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −2.00000 −0.280056
\(52\) 2.00000 + 3.00000i 0.277350 + 0.416025i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) −6.00000 −0.794719
\(58\) 10.0000 1.31306
\(59\) 4.00000i 0.520756i 0.965507 + 0.260378i \(0.0838471\pi\)
−0.965507 + 0.260378i \(0.916153\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 10.0000i 1.27000i
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) 2.00000i 0.242536i
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −1.00000 −0.117851
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 8.00000 0.929981
\(75\) 0 0
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) 3.00000 2.00000i 0.339683 0.226455i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 10.0000i 1.10432i
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 2.00000i 0.218218i
\(85\) 0 0
\(86\) 4.00000i 0.431331i
\(87\) 10.0000i 1.07211i
\(88\) 0 0
\(89\) 6.00000i 0.635999i −0.948091 0.317999i \(-0.896989\pi\)
0.948091 0.317999i \(-0.103011\pi\)
\(90\) 0 0
\(91\) −4.00000 6.00000i −0.419314 0.628971i
\(92\) 4.00000i 0.417029i
\(93\) −10.0000 −1.03695
\(94\) −12.0000 −1.23771
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −12.0000 −1.21842 −0.609208 0.793011i \(-0.708512\pi\)
−0.609208 + 0.793011i \(0.708512\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) 0 0
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) −2.00000 −0.198030
\(103\) 16.0000i 1.57653i 0.615338 + 0.788263i \(0.289020\pi\)
−0.615338 + 0.788263i \(0.710980\pi\)
\(104\) 2.00000 + 3.00000i 0.196116 + 0.294174i
\(105\) 0 0
\(106\) 6.00000i 0.582772i
\(107\) 8.00000i 0.773389i 0.922208 + 0.386695i \(0.126383\pi\)
−0.922208 + 0.386695i \(0.873617\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 4.00000i 0.383131i 0.981480 + 0.191565i \(0.0613564\pi\)
−0.981480 + 0.191565i \(0.938644\pi\)
\(110\) 0 0
\(111\) 8.00000i 0.759326i
\(112\) −2.00000 −0.188982
\(113\) 14.0000i 1.31701i −0.752577 0.658505i \(-0.771189\pi\)
0.752577 0.658505i \(-0.228811\pi\)
\(114\) −6.00000 −0.561951
\(115\) 0 0
\(116\) 10.0000 0.928477
\(117\) −2.00000 3.00000i −0.184900 0.277350i
\(118\) 4.00000i 0.368230i
\(119\) 4.00000i 0.366679i
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 2.00000 0.181071
\(123\) −10.0000 −0.901670
\(124\) 10.0000i 0.898027i
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) 12.0000i 1.04053i
\(134\) −2.00000 −0.172774
\(135\) 0 0
\(136\) 2.00000i 0.171499i
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) −4.00000 −0.340503
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 12.0000i 1.01058i
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 3.00000i 0.247436i
\(148\) 8.00000 0.657596
\(149\) 14.0000i 1.14692i 0.819232 + 0.573462i \(0.194400\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) 10.0000i 0.813788i −0.913475 0.406894i \(-0.866612\pi\)
0.913475 0.406894i \(-0.133388\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 0 0
\(156\) 3.00000 2.00000i 0.240192 0.160128i
\(157\) 2.00000i 0.159617i −0.996810 0.0798087i \(-0.974569\pi\)
0.996810 0.0798087i \(-0.0254309\pi\)
\(158\) 0 0
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) 8.00000i 0.630488i
\(162\) 1.00000 0.0785674
\(163\) 14.0000 1.09656 0.548282 0.836293i \(-0.315282\pi\)
0.548282 + 0.836293i \(0.315282\pi\)
\(164\) 10.0000i 0.780869i
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 2.00000i 0.154303i
\(169\) −5.00000 + 12.0000i −0.384615 + 0.923077i
\(170\) 0 0
\(171\) 6.00000i 0.458831i
\(172\) 4.00000i 0.304997i
\(173\) 6.00000i 0.456172i 0.973641 + 0.228086i \(0.0732467\pi\)
−0.973641 + 0.228086i \(0.926753\pi\)
\(174\) 10.0000i 0.758098i
\(175\) 0 0
\(176\) 0 0
\(177\) 4.00000 0.300658
\(178\) 6.00000i 0.449719i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) −4.00000 6.00000i −0.296500 0.444750i
\(183\) 2.00000i 0.147844i
\(184\) 4.00000i 0.294884i
\(185\) 0 0
\(186\) −10.0000 −0.733236
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) 2.00000i 0.145479i
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −16.0000 −1.15171 −0.575853 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −22.0000 −1.56744 −0.783718 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 2.00000i 0.141069i
\(202\) 2.00000 0.140720
\(203\) −20.0000 −1.40372
\(204\) −2.00000 −0.140028
\(205\) 0 0
\(206\) 16.0000i 1.11477i
\(207\) 4.00000i 0.278019i
\(208\) 2.00000 + 3.00000i 0.138675 + 0.208013i
\(209\) 0 0
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) 8.00000i 0.546869i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 20.0000i 1.35769i
\(218\) 4.00000i 0.270914i
\(219\) 4.00000i 0.270295i
\(220\) 0 0
\(221\) 6.00000 4.00000i 0.403604 0.269069i
\(222\) 8.00000i 0.536925i
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) −2.00000 −0.133631
\(225\) 0 0
\(226\) 14.0000i 0.931266i
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) −6.00000 −0.397360
\(229\) 4.00000i 0.264327i 0.991228 + 0.132164i \(0.0421925\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 10.0000 0.656532
\(233\) 6.00000i 0.393073i 0.980497 + 0.196537i \(0.0629694\pi\)
−0.980497 + 0.196537i \(0.937031\pi\)
\(234\) −2.00000 3.00000i −0.130744 0.196116i
\(235\) 0 0
\(236\) 4.00000i 0.260378i
\(237\) 0 0
\(238\) 4.00000i 0.259281i
\(239\) 16.0000i 1.03495i −0.855697 0.517477i \(-0.826871\pi\)
0.855697 0.517477i \(-0.173129\pi\)
\(240\) 0 0
\(241\) 20.0000i 1.28831i −0.764894 0.644157i \(-0.777208\pi\)
0.764894 0.644157i \(-0.222792\pi\)
\(242\) 11.0000 0.707107
\(243\) 1.00000i 0.0641500i
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) −10.0000 −0.637577
\(247\) 18.0000 12.0000i 1.14531 0.763542i
\(248\) 10.0000i 0.635001i
\(249\) 4.00000i 0.253490i
\(250\) 0 0
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 8.00000i 0.501965i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i 0.827541 + 0.561405i \(0.189739\pi\)
−0.827541 + 0.561405i \(0.810261\pi\)
\(258\) −4.00000 −0.249029
\(259\) −16.0000 −0.994192
\(260\) 0 0
\(261\) −10.0000 −0.618984
\(262\) −8.00000 −0.494242
\(263\) 24.0000i 1.47990i −0.672660 0.739952i \(-0.734848\pi\)
0.672660 0.739952i \(-0.265152\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 12.0000i 0.735767i
\(267\) −6.00000 −0.367194
\(268\) −2.00000 −0.122169
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) 10.0000i 0.607457i 0.952759 + 0.303728i \(0.0982315\pi\)
−0.952759 + 0.303728i \(0.901768\pi\)
\(272\) 2.00000i 0.121268i
\(273\) −6.00000 + 4.00000i −0.363137 + 0.242091i
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) −4.00000 −0.240772
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) 20.0000 1.19952
\(279\) 10.0000i 0.598684i
\(280\) 0 0
\(281\) 10.0000i 0.596550i 0.954480 + 0.298275i \(0.0964112\pi\)
−0.954480 + 0.298275i \(0.903589\pi\)
\(282\) 12.0000i 0.714590i
\(283\) 4.00000i 0.237775i −0.992908 0.118888i \(-0.962067\pi\)
0.992908 0.118888i \(-0.0379328\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 20.0000i 1.18056i
\(288\) −1.00000 −0.0589256
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 12.0000i 0.703452i
\(292\) 4.00000 0.234082
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 3.00000i 0.174964i
\(295\) 0 0
\(296\) 8.00000 0.464991
\(297\) 0 0
\(298\) 14.0000i 0.810998i
\(299\) 12.0000 8.00000i 0.693978 0.462652i
\(300\) 0 0
\(301\) 8.00000i 0.461112i
\(302\) 10.0000i 0.575435i
\(303\) 2.00000i 0.114897i
\(304\) 6.00000i 0.344124i
\(305\) 0 0
\(306\) 2.00000i 0.114332i
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) −28.0000 −1.58773 −0.793867 0.608091i \(-0.791935\pi\)
−0.793867 + 0.608091i \(0.791935\pi\)
\(312\) 3.00000 2.00000i 0.169842 0.113228i
\(313\) 26.0000i 1.46961i 0.678280 + 0.734803i \(0.262726\pi\)
−0.678280 + 0.734803i \(0.737274\pi\)
\(314\) 2.00000i 0.112867i
\(315\) 0 0
\(316\) 0 0
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) 0 0
\(321\) 8.00000 0.446516
\(322\) 8.00000i 0.445823i
\(323\) −12.0000 −0.667698
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 14.0000 0.775388
\(327\) 4.00000 0.221201
\(328\) 10.0000i 0.552158i
\(329\) 24.0000 1.32316
\(330\) 0 0
\(331\) 10.0000i 0.549650i 0.961494 + 0.274825i \(0.0886199\pi\)
−0.961494 + 0.274825i \(0.911380\pi\)
\(332\) 4.00000 0.219529
\(333\) −8.00000 −0.438397
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 2.00000i 0.109109i
\(337\) 2.00000i 0.108947i −0.998515 0.0544735i \(-0.982652\pi\)
0.998515 0.0544735i \(-0.0173480\pi\)
\(338\) −5.00000 + 12.0000i −0.271964 + 0.652714i
\(339\) −14.0000 −0.760376
\(340\) 0 0
\(341\) 0 0
\(342\) 6.00000i 0.324443i
\(343\) 20.0000 1.07990
\(344\) 4.00000i 0.215666i
\(345\) 0 0
\(346\) 6.00000i 0.322562i
\(347\) 12.0000i 0.644194i −0.946707 0.322097i \(-0.895612\pi\)
0.946707 0.322097i \(-0.104388\pi\)
\(348\) 10.0000i 0.536056i
\(349\) 16.0000i 0.856460i −0.903670 0.428230i \(-0.859137\pi\)
0.903670 0.428230i \(-0.140863\pi\)
\(350\) 0 0
\(351\) −3.00000 + 2.00000i −0.160128 + 0.106752i
\(352\) 0 0
\(353\) −26.0000 −1.38384 −0.691920 0.721974i \(-0.743235\pi\)
−0.691920 + 0.721974i \(0.743235\pi\)
\(354\) 4.00000 0.212598
\(355\) 0 0
\(356\) 6.00000i 0.317999i
\(357\) 4.00000 0.211702
\(358\) 0 0
\(359\) 4.00000i 0.211112i 0.994413 + 0.105556i \(0.0336622\pi\)
−0.994413 + 0.105556i \(0.966338\pi\)
\(360\) 0 0
\(361\) −17.0000 −0.894737
\(362\) 22.0000 1.15629
\(363\) 11.0000i 0.577350i
\(364\) −4.00000 6.00000i −0.209657 0.314485i
\(365\) 0 0
\(366\) 2.00000i 0.104542i
\(367\) 8.00000i 0.417597i 0.977959 + 0.208798i \(0.0669552\pi\)
−0.977959 + 0.208798i \(0.933045\pi\)
\(368\) 4.00000i 0.208514i
\(369\) 10.0000i 0.520579i
\(370\) 0 0
\(371\) 12.0000i 0.623009i
\(372\) −10.0000 −0.518476
\(373\) 6.00000i 0.310668i 0.987862 + 0.155334i \(0.0496454\pi\)
−0.987862 + 0.155334i \(0.950355\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −12.0000 −0.618853
\(377\) 20.0000 + 30.0000i 1.03005 + 1.54508i
\(378\) 2.00000i 0.102869i
\(379\) 34.0000i 1.74646i 0.487306 + 0.873231i \(0.337980\pi\)
−0.487306 + 0.873231i \(0.662020\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) 12.0000 0.613973
\(383\) 4.00000 0.204390 0.102195 0.994764i \(-0.467413\pi\)
0.102195 + 0.994764i \(0.467413\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) −16.0000 −0.814379
\(387\) 4.00000i 0.203331i
\(388\) −12.0000 −0.609208
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) −3.00000 −0.151523
\(393\) 8.00000i 0.403547i
\(394\) −22.0000 −1.10834
\(395\) 0 0
\(396\) 0 0
\(397\) 8.00000 0.401508 0.200754 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) 0 0
\(399\) 12.0000 0.600751
\(400\) 0 0
\(401\) 30.0000i 1.49813i 0.662497 + 0.749064i \(0.269497\pi\)
−0.662497 + 0.749064i \(0.730503\pi\)
\(402\) 2.00000i 0.0997509i
\(403\) 30.0000 20.0000i 1.49441 0.996271i
\(404\) 2.00000 0.0995037
\(405\) 0 0
\(406\) −20.0000 −0.992583
\(407\) 0 0
\(408\) −2.00000 −0.0990148
\(409\) 4.00000i 0.197787i 0.995098 + 0.0988936i \(0.0315304\pi\)
−0.995098 + 0.0988936i \(0.968470\pi\)
\(410\) 0 0
\(411\) 2.00000i 0.0986527i
\(412\) 16.0000i 0.788263i
\(413\) 8.00000i 0.393654i
\(414\) 4.00000i 0.196589i
\(415\) 0 0
\(416\) 2.00000 + 3.00000i 0.0980581 + 0.147087i
\(417\) 20.0000i 0.979404i
\(418\) 0 0
\(419\) −40.0000 −1.95413 −0.977064 0.212946i \(-0.931694\pi\)
−0.977064 + 0.212946i \(0.931694\pi\)
\(420\) 0 0
\(421\) 20.0000i 0.974740i −0.873195 0.487370i \(-0.837956\pi\)
0.873195 0.487370i \(-0.162044\pi\)
\(422\) 12.0000 0.584151
\(423\) 12.0000 0.583460
\(424\) 6.00000i 0.291386i
\(425\) 0 0
\(426\) 0 0
\(427\) −4.00000 −0.193574
\(428\) 8.00000i 0.386695i
\(429\) 0 0
\(430\) 0 0
\(431\) 20.0000i 0.963366i 0.876346 + 0.481683i \(0.159974\pi\)
−0.876346 + 0.481683i \(0.840026\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 26.0000i 1.24948i 0.780833 + 0.624740i \(0.214795\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(434\) 20.0000i 0.960031i
\(435\) 0 0
\(436\) 4.00000i 0.191565i
\(437\) −24.0000 −1.14808
\(438\) 4.00000i 0.191127i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 6.00000 4.00000i 0.285391 0.190261i
\(443\) 16.0000i 0.760183i 0.924949 + 0.380091i \(0.124107\pi\)
−0.924949 + 0.380091i \(0.875893\pi\)
\(444\) 8.00000i 0.379663i
\(445\) 0 0
\(446\) 14.0000 0.662919
\(447\) 14.0000 0.662177
\(448\) −2.00000 −0.0944911
\(449\) 6.00000i 0.283158i −0.989927 0.141579i \(-0.954782\pi\)
0.989927 0.141579i \(-0.0452178\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 14.0000i 0.658505i
\(453\) −10.0000 −0.469841
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) 28.0000 1.30978 0.654892 0.755722i \(-0.272714\pi\)
0.654892 + 0.755722i \(0.272714\pi\)
\(458\) 4.00000i 0.186908i
\(459\) 2.00000 0.0933520
\(460\) 0 0
\(461\) 30.0000i 1.39724i 0.715493 + 0.698620i \(0.246202\pi\)
−0.715493 + 0.698620i \(0.753798\pi\)
\(462\) 0 0
\(463\) −6.00000 −0.278844 −0.139422 0.990233i \(-0.544524\pi\)
−0.139422 + 0.990233i \(0.544524\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) 6.00000i 0.277945i
\(467\) 12.0000i 0.555294i −0.960683 0.277647i \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) −2.00000 3.00000i −0.0924500 0.138675i
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) −2.00000 −0.0921551
\(472\) 4.00000i 0.184115i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 4.00000i 0.183340i
\(477\) 6.00000i 0.274721i
\(478\) 16.0000i 0.731823i
\(479\) 24.0000i 1.09659i 0.836286 + 0.548294i \(0.184723\pi\)
−0.836286 + 0.548294i \(0.815277\pi\)
\(480\) 0 0
\(481\) 16.0000 + 24.0000i 0.729537 + 1.09431i
\(482\) 20.0000i 0.910975i
\(483\) 8.00000 0.364013
\(484\) 11.0000 0.500000
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 18.0000 0.815658 0.407829 0.913058i \(-0.366286\pi\)
0.407829 + 0.913058i \(0.366286\pi\)
\(488\) 2.00000 0.0905357
\(489\) 14.0000i 0.633102i
\(490\) 0 0
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) −10.0000 −0.450835
\(493\) 20.0000i 0.900755i
\(494\) 18.0000 12.0000i 0.809858 0.539906i
\(495\) 0 0
\(496\) 10.0000i 0.449013i
\(497\) 0 0
\(498\) 4.00000i 0.179244i
\(499\) 14.0000i 0.626726i 0.949633 + 0.313363i \(0.101456\pi\)
−0.949633 + 0.313363i \(0.898544\pi\)
\(500\) 0 0
\(501\) 12.0000i 0.536120i
\(502\) −28.0000 −1.24970
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) 2.00000 0.0890871
\(505\) 0 0
\(506\) 0 0
\(507\) 12.0000 + 5.00000i 0.532939 + 0.222058i
\(508\) 8.00000i 0.354943i
\(509\) 6.00000i 0.265945i −0.991120 0.132973i \(-0.957548\pi\)
0.991120 0.132973i \(-0.0424523\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) 1.00000 0.0441942
\(513\) 6.00000 0.264906
\(514\) 18.0000i 0.793946i
\(515\) 0 0
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) −16.0000 −0.703000
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −10.0000 −0.437688
\(523\) 4.00000i 0.174908i −0.996169 0.0874539i \(-0.972127\pi\)
0.996169 0.0874539i \(-0.0278730\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) 24.0000i 1.04645i
\(527\) −20.0000 −0.871214
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 4.00000i 0.173585i
\(532\) 12.0000i 0.520266i
\(533\) 30.0000 20.0000i 1.29944 0.866296i
\(534\) −6.00000 −0.259645
\(535\) 0 0
\(536\) −2.00000 −0.0863868
\(537\) 0 0
\(538\) 10.0000 0.431131
\(539\) 0 0
\(540\) 0 0
\(541\) 20.0000i 0.859867i 0.902861 + 0.429934i \(0.141463\pi\)
−0.902861 + 0.429934i \(0.858537\pi\)
\(542\) 10.0000i 0.429537i
\(543\) 22.0000i 0.944110i
\(544\) 2.00000i 0.0857493i
\(545\) 0 0
\(546\) −6.00000 + 4.00000i −0.256776 + 0.171184i
\(547\) 28.0000i 1.19719i 0.801050 + 0.598597i \(0.204275\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(548\) −2.00000 −0.0854358
\(549\) −2.00000 −0.0853579
\(550\) 0 0
\(551\) 60.0000i 2.55609i
\(552\) −4.00000 −0.170251
\(553\) 0 0
\(554\) 2.00000i 0.0849719i
\(555\) 0 0
\(556\) 20.0000 0.848189
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 10.0000i 0.423334i
\(559\) 12.0000 8.00000i 0.507546 0.338364i
\(560\) 0 0
\(561\) 0 0
\(562\) 10.0000i 0.421825i
\(563\) 16.0000i 0.674320i 0.941447 + 0.337160i \(0.109466\pi\)
−0.941447 + 0.337160i \(0.890534\pi\)
\(564\) 12.0000i 0.505291i
\(565\) 0 0
\(566\) 4.00000i 0.168133i
\(567\) −2.00000 −0.0839921
\(568\) 0 0
\(569\) −10.0000 −0.419222 −0.209611 0.977785i \(-0.567220\pi\)
−0.209611 + 0.977785i \(0.567220\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 0 0
\(573\) 12.0000i 0.501307i
\(574\) 20.0000i 0.834784i
\(575\) 0 0
\(576\) −1.00000 −0.0416667
\(577\) 8.00000 0.333044 0.166522 0.986038i \(-0.446746\pi\)
0.166522 + 0.986038i \(0.446746\pi\)
\(578\) 13.0000 0.540729
\(579\) 16.0000i 0.664937i
\(580\) 0 0
\(581\) −8.00000 −0.331896
\(582\) 12.0000i 0.497416i
\(583\) 0 0
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) 28.0000 1.15568 0.577842 0.816149i \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) 3.00000i 0.123718i
\(589\) −60.0000 −2.47226
\(590\) 0 0
\(591\) 22.0000i 0.904959i
\(592\) 8.00000 0.328798
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 14.0000i 0.573462i
\(597\) 0 0
\(598\) 12.0000 8.00000i 0.490716 0.327144i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 2.00000 0.0814463
\(604\) 10.0000i 0.406894i
\(605\) 0 0
\(606\) 2.00000i 0.0812444i
\(607\) 32.0000i 1.29884i −0.760430 0.649420i \(-0.775012\pi\)
0.760430 0.649420i \(-0.224988\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 20.0000i 0.810441i
\(610\) 0 0
\(611\) −24.0000 36.0000i −0.970936 1.45640i
\(612\) 2.00000i 0.0808452i
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) −2.00000 −0.0807134
\(615\) 0 0
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 16.0000 0.643614
\(619\) 26.0000i 1.04503i −0.852631 0.522514i \(-0.824994\pi\)
0.852631 0.522514i \(-0.175006\pi\)
\(620\) 0 0
\(621\) 4.00000 0.160514
\(622\) −28.0000 −1.12270
\(623\) 12.0000i 0.480770i
\(624\) 3.00000 2.00000i 0.120096 0.0800641i
\(625\) 0 0
\(626\) 26.0000i 1.03917i
\(627\) 0 0
\(628\) 2.00000i 0.0798087i
\(629\) 16.0000i 0.637962i
\(630\) 0 0
\(631\) 10.0000i 0.398094i −0.979990 0.199047i \(-0.936215\pi\)
0.979990 0.199047i \(-0.0637846\pi\)
\(632\) 0 0
\(633\) 12.0000i 0.476957i
\(634\) 18.0000 0.714871
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) −6.00000 9.00000i −0.237729 0.356593i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 8.00000 0.315735
\(643\) −6.00000 −0.236617 −0.118308 0.992977i \(-0.537747\pi\)
−0.118308 + 0.992977i \(0.537747\pi\)
\(644\) 8.00000i 0.315244i
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) 32.0000i 1.25805i −0.777385 0.629025i \(-0.783454\pi\)
0.777385 0.629025i \(-0.216546\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 20.0000 0.783862
\(652\) 14.0000 0.548282
\(653\) 26.0000i 1.01746i 0.860927 + 0.508729i \(0.169885\pi\)
−0.860927 + 0.508729i \(0.830115\pi\)
\(654\) 4.00000 0.156412
\(655\) 0 0
\(656\) 10.0000i 0.390434i
\(657\) −4.00000 −0.156055
\(658\) 24.0000 0.935617
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 0 0
\(661\) 40.0000i 1.55582i 0.628376 + 0.777910i \(0.283720\pi\)
−0.628376 + 0.777910i \(0.716280\pi\)
\(662\) 10.0000i 0.388661i
\(663\) −4.00000 6.00000i −0.155347 0.233021i
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) 40.0000i 1.54881i
\(668\) −12.0000 −0.464294
\(669\) 14.0000i 0.541271i
\(670\) 0 0
\(671\) 0 0
\(672\) 2.00000i 0.0771517i
\(673\) 6.00000i 0.231283i 0.993291 + 0.115642i \(0.0368924\pi\)
−0.993291 + 0.115642i \(0.963108\pi\)
\(674\) 2.00000i 0.0770371i
\(675\) 0 0
\(676\) −5.00000 + 12.0000i −0.192308 + 0.461538i
\(677\) 18.0000i 0.691796i 0.938272 + 0.345898i \(0.112426\pi\)
−0.938272 + 0.345898i \(0.887574\pi\)
\(678\) −14.0000 −0.537667
\(679\) 24.0000 0.921035
\(680\) 0 0
\(681\) 8.00000i 0.306561i
\(682\) 0 0
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 6.00000i 0.229416i
\(685\) 0 0
\(686\) 20.0000 0.763604
\(687\) 4.00000 0.152610
\(688\) 4.00000i 0.152499i
\(689\) −18.0000 + 12.0000i −0.685745 + 0.457164i
\(690\) 0 0
\(691\) 10.0000i 0.380418i 0.981744 + 0.190209i \(0.0609166\pi\)
−0.981744 + 0.190209i \(0.939083\pi\)
\(692\) 6.00000i 0.228086i
\(693\) 0 0
\(694\) 12.0000i 0.455514i
\(695\) 0 0
\(696\) 10.0000i 0.379049i
\(697\) −20.0000 −0.757554
\(698\) 16.0000i 0.605609i
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) −3.00000 + 2.00000i −0.113228 + 0.0754851i
\(703\) 48.0000i 1.81035i
\(704\) 0 0
\(705\) 0 0
\(706\) −26.0000 −0.978523
\(707\) −4.00000 −0.150435
\(708\) 4.00000 0.150329
\(709\) 36.0000i 1.35201i −0.736898 0.676004i \(-0.763710\pi\)
0.736898 0.676004i \(-0.236290\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.00000i 0.224860i
\(713\) −40.0000 −1.49801
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) 0 0
\(717\) −16.0000 −0.597531
\(718\) 4.00000i 0.149279i
\(719\) −20.0000 −0.745874 −0.372937 0.927857i \(-0.621649\pi\)
−0.372937 + 0.927857i \(0.621649\pi\)
\(720\) 0 0
\(721\) 32.0000i 1.19174i
\(722\) −17.0000 −0.632674
\(723\) −20.0000 −0.743808
\(724\) 22.0000 0.817624
\(725\) 0 0
\(726\) 11.0000i 0.408248i
\(727\) 8.00000i 0.296704i 0.988935 + 0.148352i \(0.0473968\pi\)
−0.988935 + 0.148352i \(0.952603\pi\)
\(728\) −4.00000 6.00000i −0.148250 0.222375i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 2.00000i 0.0739221i
\(733\) 44.0000 1.62518 0.812589 0.582838i \(-0.198058\pi\)
0.812589 + 0.582838i \(0.198058\pi\)
\(734\) 8.00000i 0.295285i
\(735\) 0 0
\(736\) 4.00000i 0.147442i
\(737\) 0 0
\(738\) 10.0000i 0.368105i
\(739\) 26.0000i 0.956425i −0.878244 0.478213i \(-0.841285\pi\)
0.878244 0.478213i \(-0.158715\pi\)
\(740\) 0 0
\(741\) −12.0000 18.0000i −0.440831 0.661247i
\(742\) 12.0000i 0.440534i
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) −10.0000 −0.366618
\(745\) 0 0
\(746\) 6.00000i 0.219676i
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) 16.0000i 0.584627i
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) −12.0000 −0.437595
\(753\) 28.0000i 1.02038i
\(754\) 20.0000 + 30.0000i 0.728357 + 1.09254i
\(755\) 0 0
\(756\) 2.00000i 0.0727393i
\(757\) 22.0000i 0.799604i −0.916602 0.399802i \(-0.869079\pi\)
0.916602 0.399802i \(-0.130921\pi\)
\(758\) 34.0000i 1.23494i
\(759\) 0 0
\(760\) 0 0
\(761\) 30.0000i 1.08750i −0.839248 0.543750i \(-0.817004\pi\)
0.839248 0.543750i \(-0.182996\pi\)
\(762\) 8.00000 0.289809
\(763\) 8.00000i 0.289619i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) 4.00000 0.144526
\(767\) −12.0000 + 8.00000i −0.433295 + 0.288863i
\(768\) 1.00000i 0.0360844i
\(769\) 24.0000i 0.865462i 0.901523 + 0.432731i \(0.142450\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) −16.0000 −0.575853
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 4.00000i 0.143777i
\(775\) 0 0
\(776\) −12.0000 −0.430775
\(777\) 16.0000i 0.573997i
\(778\) −30.0000 −1.07555
\(779\) −60.0000 −2.14972
\(780\) 0 0
\(781\) 0 0
\(782\) −8.00000 −0.286079
\(783\) 10.0000i 0.357371i
\(784\) −3.00000 −0.107143
\(785\) 0 0
\(786\) 8.00000i 0.285351i
\(787\) 38.0000 1.35455 0.677277 0.735728i \(-0.263160\pi\)
0.677277 + 0.735728i \(0.263160\pi\)
\(788\) −22.0000 −0.783718
\(789\) −24.0000 −0.854423
\(790\) 0 0
\(791\) 28.0000i 0.995565i
\(792\) 0 0
\(793\) 4.00000 + 6.00000i 0.142044 + 0.213066i
\(794\) 8.00000 0.283909
\(795\) 0 0
\(796\) 0 0
\(797\) 2.00000i 0.0708436i −0.999372 0.0354218i \(-0.988723\pi\)
0.999372 0.0354218i \(-0.0112775\pi\)
\(798\) 12.0000