Properties

Label 650.2.c.d.649.1
Level $650$
Weight $2$
Character 650.649
Analytic conductor $5.190$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 650.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.19027613138\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 649.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 650.649
Dual form 650.2.c.d.649.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +3.00000 q^{7} +1.00000 q^{8} +2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +3.00000 q^{7} +1.00000 q^{8} +2.00000 q^{9} -1.00000i q^{12} +(-3.00000 + 2.00000i) q^{13} +3.00000 q^{14} +1.00000 q^{16} -3.00000i q^{17} +2.00000 q^{18} +6.00000i q^{19} -3.00000i q^{21} -6.00000i q^{23} -1.00000i q^{24} +(-3.00000 + 2.00000i) q^{26} -5.00000i q^{27} +3.00000 q^{28} +1.00000 q^{32} -3.00000i q^{34} +2.00000 q^{36} +3.00000 q^{37} +6.00000i q^{38} +(2.00000 + 3.00000i) q^{39} -3.00000i q^{42} -1.00000i q^{43} -6.00000i q^{46} +3.00000 q^{47} -1.00000i q^{48} +2.00000 q^{49} -3.00000 q^{51} +(-3.00000 + 2.00000i) q^{52} -6.00000i q^{53} -5.00000i q^{54} +3.00000 q^{56} +6.00000 q^{57} +6.00000i q^{59} -8.00000 q^{61} +6.00000 q^{63} +1.00000 q^{64} -12.0000 q^{67} -3.00000i q^{68} -6.00000 q^{69} +15.0000i q^{71} +2.00000 q^{72} -6.00000 q^{73} +3.00000 q^{74} +6.00000i q^{76} +(2.00000 + 3.00000i) q^{78} -10.0000 q^{79} +1.00000 q^{81} -6.00000 q^{83} -3.00000i q^{84} -1.00000i q^{86} +6.00000i q^{89} +(-9.00000 + 6.00000i) q^{91} -6.00000i q^{92} +3.00000 q^{94} -1.00000i q^{96} -12.0000 q^{97} +2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 2 q^{4} + 6 q^{7} + 2 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 2 q^{4} + 6 q^{7} + 2 q^{8} + 4 q^{9} - 6 q^{13} + 6 q^{14} + 2 q^{16} + 4 q^{18} - 6 q^{26} + 6 q^{28} + 2 q^{32} + 4 q^{36} + 6 q^{37} + 4 q^{39} + 6 q^{47} + 4 q^{49} - 6 q^{51} - 6 q^{52} + 6 q^{56} + 12 q^{57} - 16 q^{61} + 12 q^{63} + 2 q^{64} - 24 q^{67} - 12 q^{69} + 4 q^{72} - 12 q^{73} + 6 q^{74} + 4 q^{78} - 20 q^{79} + 2 q^{81} - 12 q^{83} - 18 q^{91} + 6 q^{94} - 24 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(-1\) \(-1\)

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 −0.957427 0.288675i \(-0.906785\pi\)
0.957427 0.288675i \(-0.0932147\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.00000 0.666667
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −3.00000 + 2.00000i −0.832050 + 0.554700i
\(14\) 3.00000 0.801784
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.00000i 0.727607i −0.931476 0.363803i \(-0.881478\pi\)
0.931476 0.363803i \(-0.118522\pi\)
\(18\) 2.00000 0.471405
\(19\) 6.00000i 1.37649i 0.725476 + 0.688247i \(0.241620\pi\)
−0.725476 + 0.688247i \(0.758380\pi\)
\(20\) 0 0
\(21\) 3.00000i 0.654654i
\(22\) 0 0
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 0 0
\(26\) −3.00000 + 2.00000i −0.588348 + 0.392232i
\(27\) 5.00000i 0.962250i
\(28\) 3.00000 0.566947
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 3.00000i 0.514496i
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 2.00000 + 3.00000i 0.320256 + 0.480384i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 3.00000i 0.462910i
\(43\) 1.00000i 0.152499i −0.997089 0.0762493i \(-0.975706\pi\)
0.997089 0.0762493i \(-0.0242945\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 6.00000i 0.884652i
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) −3.00000 + 2.00000i −0.416025 + 0.277350i
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) 5.00000i 0.680414i
\(55\) 0 0
\(56\) 3.00000 0.400892
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) 6.00000i 0.781133i 0.920575 + 0.390567i \(0.127721\pi\)
−0.920575 + 0.390567i \(0.872279\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) 6.00000 0.755929
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 3.00000i 0.363803i
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 15.0000i 1.78017i 0.455792 + 0.890086i \(0.349356\pi\)
−0.455792 + 0.890086i \(0.650644\pi\)
\(72\) 2.00000 0.235702
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 3.00000 0.348743
\(75\) 0 0
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) 2.00000 + 3.00000i 0.226455 + 0.339683i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 3.00000i 0.327327i
\(85\) 0 0
\(86\) 1.00000i 0.107833i
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000i 0.635999i 0.948091 + 0.317999i \(0.103011\pi\)
−0.948091 + 0.317999i \(0.896989\pi\)
\(90\) 0 0
\(91\) −9.00000 + 6.00000i −0.943456 + 0.628971i
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) 3.00000 0.309426
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −12.0000 −1.21842 −0.609208 0.793011i \(-0.708512\pi\)
−0.609208 + 0.793011i \(0.708512\pi\)
\(98\) 2.00000 0.202031
\(99\) 0 0
\(100\) 0 0
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) −3.00000 −0.297044
\(103\) 14.0000i 1.37946i 0.724066 + 0.689730i \(0.242271\pi\)
−0.724066 + 0.689730i \(0.757729\pi\)
\(104\) −3.00000 + 2.00000i −0.294174 + 0.196116i
\(105\) 0 0
\(106\) 6.00000i 0.582772i
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) 5.00000i 0.481125i
\(109\) 9.00000i 0.862044i −0.902342 0.431022i \(-0.858153\pi\)
0.902342 0.431022i \(-0.141847\pi\)
\(110\) 0 0
\(111\) 3.00000i 0.284747i
\(112\) 3.00000 0.283473
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 6.00000 0.561951
\(115\) 0 0
\(116\) 0 0
\(117\) −6.00000 + 4.00000i −0.554700 + 0.369800i
\(118\) 6.00000i 0.552345i
\(119\) 9.00000i 0.825029i
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) −8.00000 −0.724286
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 6.00000 0.534522
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) −3.00000 −0.262111 −0.131056 0.991375i \(-0.541837\pi\)
−0.131056 + 0.991375i \(0.541837\pi\)
\(132\) 0 0
\(133\) 18.0000i 1.56080i
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 3.00000i 0.257248i
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) −6.00000 −0.510754
\(139\) −5.00000 −0.424094 −0.212047 0.977259i \(-0.568013\pi\)
−0.212047 + 0.977259i \(0.568013\pi\)
\(140\) 0 0
\(141\) 3.00000i 0.252646i
\(142\) 15.0000i 1.25877i
\(143\) 0 0
\(144\) 2.00000 0.166667
\(145\) 0 0
\(146\) −6.00000 −0.496564
\(147\) 2.00000i 0.164957i
\(148\) 3.00000 0.246598
\(149\) 6.00000i 0.491539i 0.969328 + 0.245770i \(0.0790407\pi\)
−0.969328 + 0.245770i \(0.920959\pi\)
\(150\) 0 0
\(151\) 15.0000i 1.22068i −0.792139 0.610341i \(-0.791032\pi\)
0.792139 0.610341i \(-0.208968\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 0 0
\(156\) 2.00000 + 3.00000i 0.160128 + 0.240192i
\(157\) 22.0000i 1.75579i 0.478852 + 0.877896i \(0.341053\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) −10.0000 −0.795557
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) 18.0000i 1.41860i
\(162\) 1.00000 0.0785674
\(163\) −6.00000 −0.469956 −0.234978 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 5.00000 12.0000i 0.384615 0.923077i
\(170\) 0 0
\(171\) 12.0000i 0.917663i
\(172\) 1.00000i 0.0762493i
\(173\) 6.00000i 0.456172i −0.973641 0.228086i \(-0.926753\pi\)
0.973641 0.228086i \(-0.0732467\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) 6.00000i 0.449719i
\(179\) −15.0000 −1.12115 −0.560576 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −9.00000 + 6.00000i −0.667124 + 0.444750i
\(183\) 8.00000i 0.591377i
\(184\) 6.00000i 0.442326i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) 15.0000i 1.09109i
\(190\) 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
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 0 0
\(201\) 12.0000i 0.846415i
\(202\) 12.0000 0.844317
\(203\) 0 0
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) 14.0000i 0.975426i
\(207\) 12.0000i 0.834058i
\(208\) −3.00000 + 2.00000i −0.208013 + 0.138675i
\(209\) 0 0
\(210\) 0 0
\(211\) −23.0000 −1.58339 −0.791693 0.610920i \(-0.790800\pi\)
−0.791693 + 0.610920i \(0.790800\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 15.0000 1.02778
\(214\) 12.0000i 0.820303i
\(215\) 0 0
\(216\) 5.00000i 0.340207i
\(217\) 0 0
\(218\) 9.00000i 0.609557i
\(219\) 6.00000i 0.405442i
\(220\) 0 0
\(221\) 6.00000 + 9.00000i 0.403604 + 0.605406i
\(222\) 3.00000i 0.201347i
\(223\) 9.00000 0.602685 0.301342 0.953516i \(-0.402565\pi\)
0.301342 + 0.953516i \(0.402565\pi\)
\(224\) 3.00000 0.200446
\(225\) 0 0
\(226\) 6.00000i 0.399114i
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 6.00000 0.397360
\(229\) 9.00000i 0.594737i −0.954763 0.297368i \(-0.903891\pi\)
0.954763 0.297368i \(-0.0961089\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 21.0000i 1.37576i −0.725826 0.687878i \(-0.758542\pi\)
0.725826 0.687878i \(-0.241458\pi\)
\(234\) −6.00000 + 4.00000i −0.392232 + 0.261488i
\(235\) 0 0
\(236\) 6.00000i 0.390567i
\(237\) 10.0000i 0.649570i
\(238\) 9.00000i 0.583383i
\(239\) 9.00000i 0.582162i −0.956698 0.291081i \(-0.905985\pi\)
0.956698 0.291081i \(-0.0940149\pi\)
\(240\) 0 0
\(241\) 30.0000i 1.93247i −0.257663 0.966235i \(-0.582952\pi\)
0.257663 0.966235i \(-0.417048\pi\)
\(242\) 11.0000 0.707107
\(243\) 16.0000i 1.02640i
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 0 0
\(247\) −12.0000 18.0000i −0.763542 1.14531i
\(248\) 0 0
\(249\) 6.00000i 0.380235i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 6.00000 0.377964
\(253\) 0 0
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.00000i 0.187135i −0.995613 0.0935674i \(-0.970173\pi\)
0.995613 0.0935674i \(-0.0298271\pi\)
\(258\) −1.00000 −0.0622573
\(259\) 9.00000 0.559233
\(260\) 0 0
\(261\) 0 0
\(262\) −3.00000 −0.185341
\(263\) 24.0000i 1.47990i 0.672660 + 0.739952i \(0.265152\pi\)
−0.672660 + 0.739952i \(0.734848\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 18.0000i 1.10365i
\(267\) 6.00000 0.367194
\(268\) −12.0000 −0.733017
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 15.0000i 0.911185i 0.890188 + 0.455593i \(0.150573\pi\)
−0.890188 + 0.455593i \(0.849427\pi\)
\(272\) 3.00000i 0.181902i
\(273\) 6.00000 + 9.00000i 0.363137 + 0.544705i
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) −6.00000 −0.361158
\(277\) 8.00000i 0.480673i −0.970690 0.240337i \(-0.922742\pi\)
0.970690 0.240337i \(-0.0772579\pi\)
\(278\) −5.00000 −0.299880
\(279\) 0 0
\(280\) 0 0
\(281\) 30.0000i 1.78965i −0.446417 0.894825i \(-0.647300\pi\)
0.446417 0.894825i \(-0.352700\pi\)
\(282\) 3.00000i 0.178647i
\(283\) 4.00000i 0.237775i 0.992908 + 0.118888i \(0.0379328\pi\)
−0.992908 + 0.118888i \(0.962067\pi\)
\(284\) 15.0000i 0.890086i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 2.00000 0.117851
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) 12.0000i 0.703452i
\(292\) −6.00000 −0.351123
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 2.00000i 0.116642i
\(295\) 0 0
\(296\) 3.00000 0.174371
\(297\) 0 0
\(298\) 6.00000i 0.347571i
\(299\) 12.0000 + 18.0000i 0.693978 + 1.04097i
\(300\) 0 0
\(301\) 3.00000i 0.172917i
\(302\) 15.0000i 0.863153i
\(303\) 12.0000i 0.689382i
\(304\) 6.00000i 0.344124i
\(305\) 0 0
\(306\) 6.00000i 0.342997i
\(307\) 18.0000 1.02731 0.513657 0.857996i \(-0.328290\pi\)
0.513657 + 0.857996i \(0.328290\pi\)
\(308\) 0 0
\(309\) 14.0000 0.796432
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 2.00000 + 3.00000i 0.113228 + 0.169842i
\(313\) 19.0000i 1.07394i 0.843600 + 0.536972i \(0.180432\pi\)
−0.843600 + 0.536972i \(0.819568\pi\)
\(314\) 22.0000i 1.24153i
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 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
\(321\) 12.0000 0.669775
\(322\) 18.0000i 1.00310i
\(323\) 18.0000 1.00155
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.00000 −0.332309
\(327\) −9.00000 −0.497701
\(328\) 0 0
\(329\) 9.00000 0.496186
\(330\) 0 0
\(331\) 30.0000i 1.64895i 0.565899 + 0.824475i \(0.308529\pi\)
−0.565899 + 0.824475i \(0.691471\pi\)
\(332\) −6.00000 −0.329293
\(333\) 6.00000 0.328798
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 3.00000i 0.163663i
\(337\) 13.0000i 0.708155i −0.935216 0.354078i \(-0.884795\pi\)
0.935216 0.354078i \(-0.115205\pi\)
\(338\) 5.00000 12.0000i 0.271964 0.652714i
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) 0 0
\(342\) 12.0000i 0.648886i
\(343\) −15.0000 −0.809924
\(344\) 1.00000i 0.0539164i
\(345\) 0 0
\(346\) 6.00000i 0.322562i
\(347\) 33.0000i 1.77153i −0.464131 0.885766i \(-0.653633\pi\)
0.464131 0.885766i \(-0.346367\pi\)
\(348\) 0 0
\(349\) 21.0000i 1.12410i 0.827102 + 0.562052i \(0.189988\pi\)
−0.827102 + 0.562052i \(0.810012\pi\)
\(350\) 0 0
\(351\) 10.0000 + 15.0000i 0.533761 + 0.800641i
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) 6.00000i 0.317999i
\(357\) −9.00000 −0.476331
\(358\) −15.0000 −0.792775
\(359\) 24.0000i 1.26667i −0.773877 0.633336i \(-0.781685\pi\)
0.773877 0.633336i \(-0.218315\pi\)
\(360\) 0 0
\(361\) −17.0000 −0.894737
\(362\) 2.00000 0.105118
\(363\) 11.0000i 0.577350i
\(364\) −9.00000 + 6.00000i −0.471728 + 0.314485i
\(365\) 0 0
\(366\) 8.00000i 0.418167i
\(367\) 8.00000i 0.417597i −0.977959 0.208798i \(-0.933045\pi\)
0.977959 0.208798i \(-0.0669552\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 0 0
\(370\) 0 0
\(371\) 18.0000i 0.934513i
\(372\) 0 0
\(373\) 4.00000i 0.207112i 0.994624 + 0.103556i \(0.0330221\pi\)
−0.994624 + 0.103556i \(0.966978\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) 0 0
\(378\) 15.0000i 0.771517i
\(379\) 6.00000i 0.308199i 0.988055 + 0.154100i \(0.0492477\pi\)
−0.988055 + 0.154100i \(0.950752\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 12.0000 0.613973
\(383\) 9.00000 0.459879 0.229939 0.973205i \(-0.426147\pi\)
0.229939 + 0.973205i \(0.426147\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) −6.00000 −0.305392
\(387\) 2.00000i 0.101666i
\(388\) −12.0000 −0.609208
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 2.00000 0.101015
\(393\) 3.00000i 0.151330i
\(394\) 3.00000 0.151138
\(395\) 0 0
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 20.0000 1.00251
\(399\) 18.0000 0.901127
\(400\) 0 0
\(401\) 30.0000i 1.49813i 0.662497 + 0.749064i \(0.269497\pi\)
−0.662497 + 0.749064i \(0.730503\pi\)
\(402\) 12.0000i 0.598506i
\(403\) 0 0
\(404\) 12.0000 0.597022
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −3.00000 −0.148522
\(409\) 6.00000i 0.296681i 0.988936 + 0.148340i \(0.0473931\pi\)
−0.988936 + 0.148340i \(0.952607\pi\)
\(410\) 0 0
\(411\) 18.0000i 0.887875i
\(412\) 14.0000i 0.689730i
\(413\) 18.0000i 0.885722i
\(414\) 12.0000i 0.589768i
\(415\) 0 0
\(416\) −3.00000 + 2.00000i −0.147087 + 0.0980581i
\(417\) 5.00000i 0.244851i
\(418\) 0 0
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) 0 0
\(421\) 15.0000i 0.731055i −0.930800 0.365528i \(-0.880889\pi\)
0.930800 0.365528i \(-0.119111\pi\)
\(422\) −23.0000 −1.11962
\(423\) 6.00000 0.291730
\(424\) 6.00000i 0.291386i
\(425\) 0 0
\(426\) 15.0000 0.726752
\(427\) −24.0000 −1.16144
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) 0 0
\(431\) 15.0000i 0.722525i −0.932464 0.361262i \(-0.882346\pi\)
0.932464 0.361262i \(-0.117654\pi\)
\(432\) 5.00000i 0.240563i
\(433\) 11.0000i 0.528626i −0.964437 0.264313i \(-0.914855\pi\)
0.964437 0.264313i \(-0.0851452\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 9.00000i 0.431022i
\(437\) 36.0000 1.72211
\(438\) 6.00000i 0.286691i
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) 4.00000 0.190476
\(442\) 6.00000 + 9.00000i 0.285391 + 0.428086i
\(443\) 21.0000i 0.997740i −0.866677 0.498870i \(-0.833748\pi\)
0.866677 0.498870i \(-0.166252\pi\)
\(444\) 3.00000i 0.142374i
\(445\) 0 0
\(446\) 9.00000 0.426162
\(447\) 6.00000 0.283790
\(448\) 3.00000 0.141737
\(449\) 24.0000i 1.13263i −0.824189 0.566315i \(-0.808369\pi\)
0.824189 0.566315i \(-0.191631\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.00000i 0.282216i
\(453\) −15.0000 −0.704761
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) 18.0000 0.842004 0.421002 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) 9.00000i 0.420542i
\(459\) −15.0000 −0.700140
\(460\) 0 0
\(461\) 15.0000i 0.698620i −0.937007 0.349310i \(-0.886416\pi\)
0.937007 0.349310i \(-0.113584\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 21.0000i 0.972806i
\(467\) 12.0000i 0.555294i 0.960683 + 0.277647i \(0.0895545\pi\)
−0.960683 + 0.277647i \(0.910445\pi\)
\(468\) −6.00000 + 4.00000i −0.277350 + 0.184900i
\(469\) −36.0000 −1.66233
\(470\) 0 0
\(471\) 22.0000 1.01371
\(472\) 6.00000i 0.276172i
\(473\) 0 0
\(474\) 10.0000i 0.459315i
\(475\) 0 0
\(476\) 9.00000i 0.412514i
\(477\) 12.0000i 0.549442i
\(478\) 9.00000i 0.411650i
\(479\) 39.0000i 1.78196i −0.454047 0.890978i \(-0.650020\pi\)
0.454047 0.890978i \(-0.349980\pi\)
\(480\) 0 0
\(481\) −9.00000 + 6.00000i −0.410365 + 0.273576i
\(482\) 30.0000i 1.36646i
\(483\) −18.0000 −0.819028
\(484\) 11.0000 0.500000
\(485\) 0 0
\(486\) 16.0000i 0.725775i
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) −8.00000 −0.362143
\(489\) 6.00000i 0.271329i
\(490\) 0 0
\(491\) 27.0000 1.21849 0.609246 0.792981i \(-0.291472\pi\)
0.609246 + 0.792981i \(0.291472\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −12.0000 18.0000i −0.539906 0.809858i
\(495\) 0 0
\(496\) 0 0
\(497\) 45.0000i 2.01853i
\(498\) 6.00000i 0.268866i
\(499\) 36.0000i 1.61158i 0.592200 + 0.805791i \(0.298259\pi\)
−0.592200 + 0.805791i \(0.701741\pi\)
\(500\) 0 0
\(501\) 12.0000i 0.536120i
\(502\) 12.0000 0.535586
\(503\) 6.00000i 0.267527i −0.991013 0.133763i \(-0.957294\pi\)
0.991013 0.133763i \(-0.0427062\pi\)
\(504\) 6.00000 0.267261
\(505\) 0 0
\(506\) 0 0
\(507\) −12.0000 5.00000i −0.532939 0.222058i
\(508\) 2.00000i 0.0887357i
\(509\) 6.00000i 0.265945i 0.991120 + 0.132973i \(0.0424523\pi\)
−0.991120 + 0.132973i \(0.957548\pi\)
\(510\) 0 0
\(511\) −18.0000 −0.796273
\(512\) 1.00000 0.0441942
\(513\) 30.0000 1.32453
\(514\) 3.00000i 0.132324i
\(515\) 0 0
\(516\) −1.00000 −0.0440225
\(517\) 0 0
\(518\) 9.00000 0.395437
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 27.0000 1.18289 0.591446 0.806345i \(-0.298557\pi\)
0.591446 + 0.806345i \(0.298557\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i −0.936819 0.349816i \(-0.886244\pi\)
0.936819 0.349816i \(-0.113756\pi\)
\(524\) −3.00000 −0.131056
\(525\) 0 0
\(526\) 24.0000i 1.04645i
\(527\) 0 0
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) 0 0
\(531\) 12.0000i 0.520756i
\(532\) 18.0000i 0.780399i
\(533\) 0 0
\(534\) 6.00000 0.259645
\(535\) 0 0
\(536\) −12.0000 −0.518321
\(537\) 15.0000i 0.647298i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 15.0000i 0.644900i −0.946586 0.322450i \(-0.895494\pi\)
0.946586 0.322450i \(-0.104506\pi\)
\(542\) 15.0000i 0.644305i
\(543\) 2.00000i 0.0858282i
\(544\) 3.00000i 0.128624i
\(545\) 0 0
\(546\) 6.00000 + 9.00000i 0.256776 + 0.385164i
\(547\) 37.0000i 1.58201i 0.611812 + 0.791003i \(0.290441\pi\)
−0.611812 + 0.791003i \(0.709559\pi\)
\(548\) 18.0000 0.768922
\(549\) −16.0000 −0.682863
\(550\) 0 0
\(551\) 0 0
\(552\) −6.00000 −0.255377
\(553\) −30.0000 −1.27573
\(554\) 8.00000i 0.339887i
\(555\) 0 0
\(556\) −5.00000 −0.212047
\(557\) −27.0000 −1.14403 −0.572013 0.820244i \(-0.693837\pi\)
−0.572013 + 0.820244i \(0.693837\pi\)
\(558\) 0 0
\(559\) 2.00000 + 3.00000i 0.0845910 + 0.126886i
\(560\) 0 0
\(561\) 0 0
\(562\) 30.0000i 1.26547i
\(563\) 39.0000i 1.64365i 0.569737 + 0.821827i \(0.307045\pi\)
−0.569737 + 0.821827i \(0.692955\pi\)
\(564\) 3.00000i 0.126323i
\(565\) 0 0
\(566\) 4.00000i 0.168133i
\(567\) 3.00000 0.125988
\(568\) 15.0000i 0.629386i
\(569\) −45.0000 −1.88650 −0.943249 0.332086i \(-0.892248\pi\)
−0.943249 + 0.332086i \(0.892248\pi\)
\(570\) 0 0
\(571\) −23.0000 −0.962520 −0.481260 0.876578i \(-0.659821\pi\)
−0.481260 + 0.876578i \(0.659821\pi\)
\(572\) 0 0
\(573\) 12.0000i 0.501307i
\(574\) 0 0
\(575\) 0 0
\(576\) 2.00000 0.0833333
\(577\) −42.0000 −1.74848 −0.874241 0.485491i \(-0.838641\pi\)
−0.874241 + 0.485491i \(0.838641\pi\)
\(578\) 8.00000 0.332756
\(579\) 6.00000i 0.249351i
\(580\) 0 0
\(581\) −18.0000 −0.746766
\(582\) 12.0000i 0.497416i
\(583\) 0 0
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) 9.00000 0.371787
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 2.00000i 0.0824786i
\(589\) 0 0
\(590\) 0 0
\(591\) 3.00000i 0.123404i
\(592\) 3.00000 0.123299
\(593\) −36.0000 −1.47834 −0.739171 0.673517i \(-0.764783\pi\)
−0.739171 + 0.673517i \(0.764783\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000i 0.245770i
\(597\) 20.0000i 0.818546i
\(598\) 12.0000 + 18.0000i 0.490716 + 0.736075i
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) 37.0000 1.50926 0.754631 0.656150i \(-0.227816\pi\)
0.754631 + 0.656150i \(0.227816\pi\)
\(602\) 3.00000i 0.122271i
\(603\) −24.0000 −0.977356
\(604\) 15.0000i 0.610341i
\(605\) 0 0
\(606\) 12.0000i 0.487467i
\(607\) 22.0000i 0.892952i 0.894795 + 0.446476i \(0.147321\pi\)
−0.894795 + 0.446476i \(0.852679\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 0 0
\(610\) 0 0
\(611\) −9.00000 + 6.00000i −0.364101 + 0.242734i
\(612\) 6.00000i 0.242536i
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 18.0000 0.726421
\(615\) 0 0
\(616\) 0 0
\(617\) −12.0000 −0.483102 −0.241551 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 14.0000 0.563163
\(619\) 24.0000i 0.964641i −0.875995 0.482321i \(-0.839794\pi\)
0.875995 0.482321i \(-0.160206\pi\)
\(620\) 0 0
\(621\) −30.0000 −1.20386
\(622\) −18.0000 −0.721734
\(623\) 18.0000i 0.721155i
\(624\) 2.00000 + 3.00000i 0.0800641 + 0.120096i
\(625\) 0 0
\(626\) 19.0000i 0.759393i
\(627\) 0 0
\(628\) 22.0000i 0.877896i
\(629\) 9.00000i 0.358854i
\(630\) 0 0
\(631\) 15.0000i 0.597141i −0.954388 0.298570i \(-0.903490\pi\)
0.954388 0.298570i \(-0.0965097\pi\)
\(632\) −10.0000 −0.397779
\(633\) 23.0000i 0.914168i
\(634\) 18.0000 0.714871
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) −6.00000 + 4.00000i −0.237729 + 0.158486i
\(638\) 0 0
\(639\) 30.0000i 1.18678i
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 12.0000 0.473602
\(643\) −36.0000 −1.41970 −0.709851 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) 18.0000i 0.709299i
\(645\) 0 0
\(646\) 18.0000 0.708201
\(647\) 42.0000i 1.65119i 0.564263 + 0.825595i \(0.309160\pi\)
−0.564263 + 0.825595i \(0.690840\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −6.00000 −0.234978
\(653\) 36.0000i 1.40879i −0.709809 0.704394i \(-0.751219\pi\)
0.709809 0.704394i \(-0.248781\pi\)
\(654\) −9.00000 −0.351928
\(655\) 0 0
\(656\) 0 0
\(657\) −12.0000 −0.468165
\(658\) 9.00000 0.350857
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 30.0000i 1.16686i 0.812162 + 0.583432i \(0.198291\pi\)
−0.812162 + 0.583432i \(0.801709\pi\)
\(662\) 30.0000i 1.16598i
\(663\) 9.00000 6.00000i 0.349531 0.233021i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 0 0
\(668\) −12.0000 −0.464294
\(669\) 9.00000i 0.347960i
\(670\) 0 0
\(671\) 0 0
\(672\) 3.00000i 0.115728i
\(673\) 1.00000i 0.0385472i −0.999814 0.0192736i \(-0.993865\pi\)
0.999814 0.0192736i \(-0.00613535\pi\)
\(674\) 13.0000i 0.500741i
\(675\) 0 0
\(676\) 5.00000 12.0000i 0.192308 0.461538i
\(677\) 18.0000i 0.691796i −0.938272 0.345898i \(-0.887574\pi\)
0.938272 0.345898i \(-0.112426\pi\)
\(678\) −6.00000 −0.230429
\(679\) −36.0000 −1.38155
\(680\) 0 0
\(681\) 12.0000i 0.459841i
\(682\) 0 0
\(683\) −6.00000 −0.229584 −0.114792 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(684\) 12.0000i 0.458831i
\(685\) 0 0
\(686\) −15.0000 −0.572703
\(687\) −9.00000 −0.343371
\(688\) 1.00000i 0.0381246i
\(689\) 12.0000 + 18.0000i 0.457164 + 0.685745i
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 6.00000i 0.228086i
\(693\) 0 0
\(694\) 33.0000i 1.25266i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 21.0000i 0.794862i
\(699\) −21.0000 −0.794293
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 10.0000 + 15.0000i 0.377426 + 0.566139i
\(703\) 18.0000i 0.678883i
\(704\) 0 0
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 36.0000 1.35392
\(708\) 6.00000 0.225494
\(709\) 6.00000i 0.225335i 0.993633 + 0.112667i \(0.0359394\pi\)
−0.993633 + 0.112667i \(0.964061\pi\)
\(710\) 0 0
\(711\) −20.0000 −0.750059
\(712\) 6.00000i 0.224860i
\(713\) 0 0
\(714\) −9.00000 −0.336817
\(715\) 0 0
\(716\) −15.0000 −0.560576
\(717\) −9.00000 −0.336111
\(718\) 24.0000i 0.895672i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 42.0000i 1.56416i
\(722\) −17.0000 −0.632674
\(723\) −30.0000 −1.11571
\(724\) 2.00000 0.0743294
\(725\) 0 0
\(726\) 11.0000i 0.408248i
\(727\) 28.0000i 1.03846i −0.854634 0.519231i \(-0.826218\pi\)
0.854634 0.519231i \(-0.173782\pi\)
\(728\) −9.00000 + 6.00000i −0.333562 + 0.222375i
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) −3.00000 −0.110959
\(732\) 8.00000i 0.295689i
\(733\) 9.00000 0.332423 0.166211 0.986090i \(-0.446847\pi\)
0.166211 + 0.986090i \(0.446847\pi\)
\(734\) 8.00000i 0.295285i
\(735\) 0 0
\(736\) 6.00000i 0.221163i
\(737\) 0 0
\(738\) 0 0
\(739\) 36.0000i 1.32428i 0.749380 + 0.662141i \(0.230352\pi\)
−0.749380 + 0.662141i \(0.769648\pi\)
\(740\) 0 0
\(741\) −18.0000 + 12.0000i −0.661247 + 0.440831i
\(742\) 18.0000i 0.660801i
\(743\) 39.0000 1.43077 0.715386 0.698730i \(-0.246251\pi\)
0.715386 + 0.698730i \(0.246251\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 4.00000i 0.146450i
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 36.0000i 1.31541i
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 3.00000 0.109399
\(753\) 12.0000i 0.437304i
\(754\) 0 0
\(755\) 0 0
\(756\) 15.0000i 0.545545i
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 6.00000i 0.217930i
\(759\) 0 0
\(760\) 0 0
\(761\) 30.0000i 1.08750i −0.839248 0.543750i \(-0.817004\pi\)
0.839248 0.543750i \(-0.182996\pi\)
\(762\) 2.00000 0.0724524
\(763\) 27.0000i 0.977466i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) 9.00000 0.325183
\(767\) −12.0000 18.0000i −0.433295 0.649942i
\(768\) 1.00000i 0.0360844i
\(769\) 24.0000i 0.865462i −0.901523 0.432731i \(-0.857550\pi\)
0.901523 0.432731i \(-0.142450\pi\)
\(770\) 0 0
\(771\) −3.00000 −0.108042
\(772\) −6.00000 −0.215945
\(773\) −21.0000 −0.755318 −0.377659 0.925945i \(-0.623271\pi\)
−0.377659 + 0.925945i \(0.623271\pi\)
\(774\) 2.00000i 0.0718885i
\(775\) 0 0
\(776\) −12.0000 −0.430775
\(777\) 9.00000i 0.322873i
\(778\) 30.0000 1.07555
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −18.0000 −0.643679
\(783\) 0 0
\(784\) 2.00000 0.0714286
\(785\) 0 0
\(786\) 3.00000i 0.107006i
\(787\) −12.0000 −0.427754 −0.213877 0.976861i \(-0.568609\pi\)
−0.213877 + 0.976861i \(0.568609\pi\)
\(788\) 3.00000 0.106871
\(789\) 24.0000 0.854423
\(790\) 0 0
\(791\) 18.0000i 0.640006i
\(792\) 0 0
\(793\) 24.0000 16.0000i 0.852265 0.568177i
\(794\) 18.0000 0.638796
\(795\) 0 0
\(796\) 20.0000 0.708881
\(797\) 18.0000i