Properties

Label 1950.2.f.i.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 390)
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.i.649.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +1.00000 q^{8} -1.00000 q^{9} -4.00000i q^{11} -1.00000i q^{12} +(2.00000 - 3.00000i) q^{13} +1.00000 q^{16} -4.00000i q^{17} -1.00000 q^{18} +4.00000i q^{19} -4.00000i q^{22} +6.00000i q^{23} -1.00000i q^{24} +(2.00000 - 3.00000i) q^{26} +1.00000i q^{27} -4.00000 q^{29} -10.0000i q^{31} +1.00000 q^{32} -4.00000 q^{33} -4.00000i q^{34} -1.00000 q^{36} +4.00000 q^{37} +4.00000i q^{38} +(-3.00000 - 2.00000i) q^{39} +2.00000i q^{41} -12.0000i q^{43} -4.00000i q^{44} +6.00000i q^{46} -1.00000i q^{48} -7.00000 q^{49} -4.00000 q^{51} +(2.00000 - 3.00000i) q^{52} -2.00000i q^{53} +1.00000i q^{54} +4.00000 q^{57} -4.00000 q^{58} +4.00000i q^{59} -10.0000 q^{61} -10.0000i q^{62} +1.00000 q^{64} -4.00000 q^{66} +10.0000 q^{67} -4.00000i q^{68} +6.00000 q^{69} -12.0000i q^{71} -1.00000 q^{72} +6.00000 q^{73} +4.00000 q^{74} +4.00000i q^{76} +(-3.00000 - 2.00000i) q^{78} +8.00000 q^{79} +1.00000 q^{81} +2.00000i q^{82} -12.0000i q^{86} +4.00000i q^{87} -4.00000i q^{88} -10.0000i q^{89} +6.00000i q^{92} -10.0000 q^{93} -1.00000i q^{96} +14.0000 q^{97} -7.00000 q^{98} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{4} + 2q^{8} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{4} + 2q^{8} - 2q^{9} + 4q^{13} + 2q^{16} - 2q^{18} + 4q^{26} - 8q^{29} + 2q^{32} - 8q^{33} - 2q^{36} + 8q^{37} - 6q^{39} - 14q^{49} - 8q^{51} + 4q^{52} + 8q^{57} - 8q^{58} - 20q^{61} + 2q^{64} - 8q^{66} + 20q^{67} + 12q^{69} - 2q^{72} + 12q^{73} + 8q^{74} - 6q^{78} + 16q^{79} + 2q^{81} - 20q^{93} + 28q^{97} - 14q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 4.00000i 1.20605i −0.797724 0.603023i \(-0.793963\pi\)
0.797724 0.603023i \(-0.206037\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.00000 3.00000i 0.554700 0.832050i
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000i 0.970143i −0.874475 0.485071i \(-0.838794\pi\)
0.874475 0.485071i \(-0.161206\pi\)
\(18\) −1.00000 −0.235702
\(19\) 4.00000i 0.917663i 0.888523 + 0.458831i \(0.151732\pi\)
−0.888523 + 0.458831i \(0.848268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 4.00000i 0.852803i
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 0 0
\(26\) 2.00000 3.00000i 0.392232 0.588348i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 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
\(33\) −4.00000 −0.696311
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 4.00000i 0.648886i
\(39\) −3.00000 2.00000i −0.480384 0.320256i
\(40\) 0 0
\(41\) 2.00000i 0.312348i 0.987730 + 0.156174i \(0.0499160\pi\)
−0.987730 + 0.156174i \(0.950084\pi\)
\(42\) 0 0
\(43\) 12.0000i 1.82998i −0.403473 0.914991i \(-0.632197\pi\)
0.403473 0.914991i \(-0.367803\pi\)
\(44\) 4.00000i 0.603023i
\(45\) 0 0
\(46\) 6.00000i 0.884652i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 2.00000 3.00000i 0.277350 0.416025i
\(53\) 2.00000i 0.274721i −0.990521 0.137361i \(-0.956138\pi\)
0.990521 0.137361i \(-0.0438619\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0 0
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) −4.00000 −0.525226
\(59\) 4.00000i 0.520756i 0.965507 + 0.260378i \(0.0838471\pi\)
−0.965507 + 0.260378i \(0.916153\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 10.0000i 1.27000i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.00000 −0.492366
\(67\) 10.0000 1.22169 0.610847 0.791748i \(-0.290829\pi\)
0.610847 + 0.791748i \(0.290829\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 12.0000i 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) −1.00000 −0.117851
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) 4.00000i 0.458831i
\(77\) 0 0
\(78\) −3.00000 2.00000i −0.339683 0.226455i
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 12.0000i 1.29399i
\(87\) 4.00000i 0.428845i
\(88\) 4.00000i 0.426401i
\(89\) 10.0000i 1.06000i −0.847998 0.529999i \(-0.822192\pi\)
0.847998 0.529999i \(-0.177808\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) −10.0000 −1.03695
\(94\) 0 0
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −7.00000 −0.707107
\(99\) 4.00000i 0.402015i
\(100\) 0 0
\(101\) 8.00000 0.796030 0.398015 0.917379i \(-0.369699\pi\)
0.398015 + 0.917379i \(0.369699\pi\)
\(102\) −4.00000 −0.396059
\(103\) 4.00000i 0.394132i 0.980390 + 0.197066i \(0.0631413\pi\)
−0.980390 + 0.197066i \(0.936859\pi\)
\(104\) 2.00000 3.00000i 0.196116 0.294174i
\(105\) 0 0
\(106\) 2.00000i 0.194257i
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 6.00000i 0.574696i 0.957826 + 0.287348i \(0.0927736\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) 4.00000i 0.379663i
\(112\) 0 0
\(113\) 12.0000i 1.12887i 0.825479 + 0.564433i \(0.190905\pi\)
−0.825479 + 0.564433i \(0.809095\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) −4.00000 −0.371391
\(117\) −2.00000 + 3.00000i −0.184900 + 0.277350i
\(118\) 4.00000i 0.368230i
\(119\) 0 0
\(120\) 0 0
\(121\) −5.00000 −0.454545
\(122\) −10.0000 −0.905357
\(123\) 2.00000 0.180334
\(124\) 10.0000i 0.898027i
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000i 0.709885i −0.934888 0.354943i \(-0.884500\pi\)
0.934888 0.354943i \(-0.115500\pi\)
\(128\) 1.00000 0.0883883
\(129\) −12.0000 −1.05654
\(130\) 0 0
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) −4.00000 −0.348155
\(133\) 0 0
\(134\) 10.0000 0.863868
\(135\) 0 0
\(136\) 4.00000i 0.342997i
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 6.00000 0.510754
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 12.0000i 1.00702i
\(143\) −12.0000 8.00000i −1.00349 0.668994i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 6.00000 0.496564
\(147\) 7.00000i 0.577350i
\(148\) 4.00000 0.328798
\(149\) 2.00000i 0.163846i −0.996639 0.0819232i \(-0.973894\pi\)
0.996639 0.0819232i \(-0.0261062\pi\)
\(150\) 0 0
\(151\) 22.0000i 1.79033i 0.445730 + 0.895167i \(0.352944\pi\)
−0.445730 + 0.895167i \(0.647056\pi\)
\(152\) 4.00000i 0.324443i
\(153\) 4.00000i 0.323381i
\(154\) 0 0
\(155\) 0 0
\(156\) −3.00000 2.00000i −0.240192 0.160128i
\(157\) 14.0000i 1.11732i 0.829396 + 0.558661i \(0.188685\pi\)
−0.829396 + 0.558661i \(0.811315\pi\)
\(158\) 8.00000 0.636446
\(159\) −2.00000 −0.158610
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −2.00000 −0.156652 −0.0783260 0.996928i \(-0.524958\pi\)
−0.0783260 + 0.996928i \(0.524958\pi\)
\(164\) 2.00000i 0.156174i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) 0 0
\(171\) 4.00000i 0.305888i
\(172\) 12.0000i 0.914991i
\(173\) 22.0000i 1.67263i 0.548250 + 0.836315i \(0.315294\pi\)
−0.548250 + 0.836315i \(0.684706\pi\)
\(174\) 4.00000i 0.303239i
\(175\) 0 0
\(176\) 4.00000i 0.301511i
\(177\) 4.00000 0.300658
\(178\) 10.0000i 0.749532i
\(179\) −22.0000 −1.64436 −0.822179 0.569230i \(-0.807242\pi\)
−0.822179 + 0.569230i \(0.807242\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 10.0000i 0.739221i
\(184\) 6.00000i 0.442326i
\(185\) 0 0
\(186\) −10.0000 −0.733236
\(187\) −16.0000 −1.17004
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 14.0000 1.00514
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) 26.0000 1.85242 0.926212 0.377004i \(-0.123046\pi\)
0.926212 + 0.377004i \(0.123046\pi\)
\(198\) 4.00000i 0.284268i
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 10.0000i 0.705346i
\(202\) 8.00000 0.562878
\(203\) 0 0
\(204\) −4.00000 −0.280056
\(205\) 0 0
\(206\) 4.00000i 0.278693i
\(207\) 6.00000i 0.417029i
\(208\) 2.00000 3.00000i 0.138675 0.208013i
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 24.0000 1.65223 0.826114 0.563503i \(-0.190547\pi\)
0.826114 + 0.563503i \(0.190547\pi\)
\(212\) 2.00000i 0.137361i
\(213\) −12.0000 −0.822226
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 0 0
\(218\) 6.00000i 0.406371i
\(219\) 6.00000i 0.405442i
\(220\) 0 0
\(221\) −12.0000 8.00000i −0.807207 0.538138i
\(222\) 4.00000i 0.268462i
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.0000i 0.798228i
\(227\) −16.0000 −1.06196 −0.530979 0.847385i \(-0.678176\pi\)
−0.530979 + 0.847385i \(0.678176\pi\)
\(228\) 4.00000 0.264906
\(229\) 2.00000i 0.132164i 0.997814 + 0.0660819i \(0.0210498\pi\)
−0.997814 + 0.0660819i \(0.978950\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.00000 −0.262613
\(233\) 24.0000i 1.57229i 0.618041 + 0.786146i \(0.287927\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(234\) −2.00000 + 3.00000i −0.130744 + 0.196116i
\(235\) 0 0
\(236\) 4.00000i 0.260378i
\(237\) 8.00000i 0.519656i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 4.00000i 0.257663i −0.991667 0.128831i \(-0.958877\pi\)
0.991667 0.128831i \(-0.0411226\pi\)
\(242\) −5.00000 −0.321412
\(243\) 1.00000i 0.0641500i
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) 12.0000 + 8.00000i 0.763542 + 0.509028i
\(248\) 10.0000i 0.635001i
\(249\) 0 0
\(250\) 0 0
\(251\) 2.00000 0.126239 0.0631194 0.998006i \(-0.479895\pi\)
0.0631194 + 0.998006i \(0.479895\pi\)
\(252\) 0 0
\(253\) 24.0000 1.50887
\(254\) 8.00000i 0.501965i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 12.0000i 0.748539i 0.927320 + 0.374270i \(0.122107\pi\)
−0.927320 + 0.374270i \(0.877893\pi\)
\(258\) −12.0000 −0.747087
\(259\) 0 0
\(260\) 0 0
\(261\) 4.00000 0.247594
\(262\) −18.0000 −1.11204
\(263\) 14.0000i 0.863277i −0.902047 0.431638i \(-0.857936\pi\)
0.902047 0.431638i \(-0.142064\pi\)
\(264\) −4.00000 −0.246183
\(265\) 0 0
\(266\) 0 0
\(267\) −10.0000 −0.611990
\(268\) 10.0000 0.610847
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 2.00000i 0.121491i 0.998153 + 0.0607457i \(0.0193479\pi\)
−0.998153 + 0.0607457i \(0.980652\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) 22.0000i 1.32185i 0.750451 + 0.660926i \(0.229836\pi\)
−0.750451 + 0.660926i \(0.770164\pi\)
\(278\) −16.0000 −0.959616
\(279\) 10.0000i 0.598684i
\(280\) 0 0
\(281\) 30.0000i 1.78965i 0.446417 + 0.894825i \(0.352700\pi\)
−0.446417 + 0.894825i \(0.647300\pi\)
\(282\) 0 0
\(283\) 4.00000i 0.237775i 0.992908 + 0.118888i \(0.0379328\pi\)
−0.992908 + 0.118888i \(0.962067\pi\)
\(284\) 12.0000i 0.712069i
\(285\) 0 0
\(286\) −12.0000 8.00000i −0.709575 0.473050i
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 14.0000i 0.820695i
\(292\) 6.00000 0.351123
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 7.00000i 0.408248i
\(295\) 0 0
\(296\) 4.00000 0.232495
\(297\) 4.00000 0.232104
\(298\) 2.00000i 0.115857i
\(299\) 18.0000 + 12.0000i 1.04097 + 0.693978i
\(300\) 0 0
\(301\) 0 0
\(302\) 22.0000i 1.26596i
\(303\) 8.00000i 0.459588i
\(304\) 4.00000i 0.229416i
\(305\) 0 0
\(306\) 4.00000i 0.228665i
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) −3.00000 2.00000i −0.169842 0.113228i
\(313\) 10.0000i 0.565233i −0.959233 0.282617i \(-0.908798\pi\)
0.959233 0.282617i \(-0.0912024\pi\)
\(314\) 14.0000i 0.790066i
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) −2.00000 −0.112154
\(319\) 16.0000i 0.895828i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 16.0000 0.890264
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −2.00000 −0.110770
\(327\) 6.00000 0.331801
\(328\) 2.00000i 0.110432i
\(329\) 0 0
\(330\) 0 0
\(331\) 32.0000i 1.75888i 0.476011 + 0.879440i \(0.342082\pi\)
−0.476011 + 0.879440i \(0.657918\pi\)
\(332\) 0 0
\(333\) −4.00000 −0.219199
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 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
\(339\) 12.0000 0.651751
\(340\) 0 0
\(341\) −40.0000 −2.16612
\(342\) 4.00000i 0.216295i
\(343\) 0 0
\(344\) 12.0000i 0.646997i
\(345\) 0 0
\(346\) 22.0000i 1.18273i
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 4.00000i 0.214423i
\(349\) 14.0000i 0.749403i 0.927146 + 0.374701i \(0.122255\pi\)
−0.927146 + 0.374701i \(0.877745\pi\)
\(350\) 0 0
\(351\) 3.00000 + 2.00000i 0.160128 + 0.106752i
\(352\) 4.00000i 0.213201i
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 4.00000 0.212598
\(355\) 0 0
\(356\) 10.0000i 0.529999i
\(357\) 0 0
\(358\) −22.0000 −1.16274
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) 22.0000 1.15629
\(363\) 5.00000i 0.262432i
\(364\) 0 0
\(365\) 0 0
\(366\) 10.0000i 0.522708i
\(367\) 16.0000i 0.835193i −0.908633 0.417597i \(-0.862873\pi\)
0.908633 0.417597i \(-0.137127\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 2.00000i 0.104116i
\(370\) 0 0
\(371\) 0 0
\(372\) −10.0000 −0.518476
\(373\) 26.0000i 1.34623i −0.739538 0.673114i \(-0.764956\pi\)
0.739538 0.673114i \(-0.235044\pi\)
\(374\) −16.0000 −0.827340
\(375\) 0 0
\(376\) 0 0
\(377\) −8.00000 + 12.0000i −0.412021 + 0.618031i
\(378\) 0 0
\(379\) 16.0000i 0.821865i −0.911666 0.410932i \(-0.865203\pi\)
0.911666 0.410932i \(-0.134797\pi\)
\(380\) 0 0
\(381\) −8.00000 −0.409852
\(382\) −12.0000 −0.613973
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 12.0000i 0.609994i
\(388\) 14.0000 0.710742
\(389\) 20.0000 1.01404 0.507020 0.861934i \(-0.330747\pi\)
0.507020 + 0.861934i \(0.330747\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) −7.00000 −0.353553
\(393\) 18.0000i 0.907980i
\(394\) 26.0000 1.30986
\(395\) 0 0
\(396\) 4.00000i 0.201008i
\(397\) −28.0000 −1.40528 −0.702640 0.711546i \(-0.747995\pi\)
−0.702640 + 0.711546i \(0.747995\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 26.0000i 1.29838i 0.760627 + 0.649189i \(0.224892\pi\)
−0.760627 + 0.649189i \(0.775108\pi\)
\(402\) 10.0000i 0.498755i
\(403\) −30.0000 20.0000i −1.49441 0.996271i
\(404\) 8.00000 0.398015
\(405\) 0 0
\(406\) 0 0
\(407\) 16.0000i 0.793091i
\(408\) −4.00000 −0.198030
\(409\) 8.00000i 0.395575i −0.980245 0.197787i \(-0.936624\pi\)
0.980245 0.197787i \(-0.0633755\pi\)
\(410\) 0 0
\(411\) 2.00000i 0.0986527i
\(412\) 4.00000i 0.197066i
\(413\) 0 0
\(414\) 6.00000i 0.294884i
\(415\) 0 0
\(416\) 2.00000 3.00000i 0.0980581 0.147087i
\(417\) 16.0000i 0.783523i
\(418\) 16.0000 0.782586
\(419\) −14.0000 −0.683945 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(420\) 0 0
\(421\) 14.0000i 0.682318i 0.940006 + 0.341159i \(0.110819\pi\)
−0.940006 + 0.341159i \(0.889181\pi\)
\(422\) 24.0000 1.16830
\(423\) 0 0
\(424\) 2.00000i 0.0971286i
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) 0 0
\(429\) −8.00000 + 12.0000i −0.386244 + 0.579365i
\(430\) 0 0
\(431\) 12.0000i 0.578020i 0.957326 + 0.289010i \(0.0933260\pi\)
−0.957326 + 0.289010i \(0.906674\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 18.0000i 0.865025i 0.901628 + 0.432512i \(0.142373\pi\)
−0.901628 + 0.432512i \(0.857627\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 6.00000i 0.287348i
\(437\) −24.0000 −1.14808
\(438\) 6.00000i 0.286691i
\(439\) 32.0000 1.52728 0.763638 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) 0 0
\(441\) 7.00000 0.333333
\(442\) −12.0000 8.00000i −0.570782 0.380521i
\(443\) 36.0000i 1.71041i −0.518289 0.855206i \(-0.673431\pi\)
0.518289 0.855206i \(-0.326569\pi\)
\(444\) 4.00000i 0.189832i
\(445\) 0 0
\(446\) 20.0000 0.947027
\(447\) −2.00000 −0.0945968
\(448\) 0 0
\(449\) 30.0000i 1.41579i 0.706319 + 0.707894i \(0.250354\pi\)
−0.706319 + 0.707894i \(0.749646\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) 12.0000i 0.564433i
\(453\) 22.0000 1.03365
\(454\) −16.0000 −0.750917
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 14.0000 0.654892 0.327446 0.944870i \(-0.393812\pi\)
0.327446 + 0.944870i \(0.393812\pi\)
\(458\) 2.00000i 0.0934539i
\(459\) 4.00000 0.186704
\(460\) 0 0
\(461\) 26.0000i 1.21094i −0.795868 0.605470i \(-0.792985\pi\)
0.795868 0.605470i \(-0.207015\pi\)
\(462\) 0 0
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) −4.00000 −0.185695
\(465\) 0 0
\(466\) 24.0000i 1.11178i
\(467\) 4.00000i 0.185098i 0.995708 + 0.0925490i \(0.0295015\pi\)
−0.995708 + 0.0925490i \(0.970499\pi\)
\(468\) −2.00000 + 3.00000i −0.0924500 + 0.138675i
\(469\) 0 0
\(470\) 0 0
\(471\) 14.0000 0.645086
\(472\) 4.00000i 0.184115i
\(473\) −48.0000 −2.20704
\(474\) 8.00000i 0.367452i
\(475\) 0 0
\(476\) 0 0
\(477\) 2.00000i 0.0915737i
\(478\) 0 0
\(479\) 16.0000i 0.731059i 0.930800 + 0.365529i \(0.119112\pi\)
−0.930800 + 0.365529i \(0.880888\pi\)
\(480\) 0 0
\(481\) 8.00000 12.0000i 0.364769 0.547153i
\(482\) 4.00000i 0.182195i
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 24.0000 1.08754 0.543772 0.839233i \(-0.316996\pi\)
0.543772 + 0.839233i \(0.316996\pi\)
\(488\) −10.0000 −0.452679
\(489\) 2.00000i 0.0904431i
\(490\) 0 0
\(491\) 22.0000 0.992846 0.496423 0.868081i \(-0.334646\pi\)
0.496423 + 0.868081i \(0.334646\pi\)
\(492\) 2.00000 0.0901670
\(493\) 16.0000i 0.720604i
\(494\) 12.0000 + 8.00000i 0.539906 + 0.359937i
\(495\) 0 0
\(496\) 10.0000i 0.449013i
\(497\) 0 0
\(498\) 0 0
\(499\) 4.00000i 0.179065i −0.995984 0.0895323i \(-0.971463\pi\)
0.995984 0.0895323i \(-0.0285372\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 2.00000 0.0892644
\(503\) 22.0000i 0.980932i −0.871460 0.490466i \(-0.836827\pi\)
0.871460 0.490466i \(-0.163173\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 24.0000 1.06693
\(507\) −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
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −4.00000 −0.176604
\(514\) 12.0000i 0.529297i
\(515\) 0 0
\(516\) −12.0000 −0.528271
\(517\) 0 0
\(518\) 0 0
\(519\) 22.0000 0.965693
\(520\) 0 0
\(521\) 34.0000 1.48957 0.744784 0.667306i \(-0.232553\pi\)
0.744784 + 0.667306i \(0.232553\pi\)
\(522\) 4.00000 0.175075
\(523\) 4.00000i 0.174908i 0.996169 + 0.0874539i \(0.0278730\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) 14.0000i 0.610429i
\(527\) −40.0000 −1.74243
\(528\) −4.00000 −0.174078
\(529\) −13.0000 −0.565217
\(530\) 0 0
\(531\) 4.00000i 0.173585i
\(532\) 0 0
\(533\) 6.00000 + 4.00000i 0.259889 + 0.173259i
\(534\) −10.0000 −0.432742
\(535\) 0 0
\(536\) 10.0000 0.431934
\(537\) 22.0000i 0.949370i
\(538\) 0 0
\(539\) 28.0000i 1.20605i
\(540\) 0 0
\(541\) 18.0000i 0.773880i 0.922105 + 0.386940i \(0.126468\pi\)
−0.922105 + 0.386940i \(0.873532\pi\)
\(542\) 2.00000i 0.0859074i
\(543\) 22.0000i 0.944110i
\(544\) 4.00000i 0.171499i
\(545\) 0 0
\(546\) 0 0
\(547\) 12.0000i 0.513083i −0.966533 0.256541i \(-0.917417\pi\)
0.966533 0.256541i \(-0.0825830\pi\)
\(548\) 2.00000 0.0854358
\(549\) 10.0000 0.426790
\(550\) 0 0
\(551\) 16.0000i 0.681623i
\(552\) 6.00000 0.255377
\(553\) 0 0
\(554\) 22.0000i 0.934690i
\(555\) 0 0
\(556\) −16.0000 −0.678551
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 10.0000i 0.423334i
\(559\) −36.0000 24.0000i −1.52264 1.01509i
\(560\) 0 0
\(561\) 16.0000i 0.675521i
\(562\) 30.0000i 1.26547i
\(563\) 20.0000i 0.842900i 0.906852 + 0.421450i \(0.138479\pi\)
−0.906852 + 0.421450i \(0.861521\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 4.00000i 0.168133i
\(567\) 0 0
\(568\) 12.0000i 0.503509i
\(569\) −46.0000 −1.92842 −0.964210 0.265139i \(-0.914582\pi\)
−0.964210 + 0.265139i \(0.914582\pi\)
\(570\) 0 0
\(571\) 24.0000 1.00437 0.502184 0.864761i \(-0.332530\pi\)
0.502184 + 0.864761i \(0.332530\pi\)
\(572\) −12.0000 8.00000i −0.501745 0.334497i
\(573\) 12.0000i 0.501307i
\(574\) 0 0
\(575\) 0 0
\(576\) −1.00000 −0.0416667
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 1.00000 0.0415945
\(579\) 14.0000i 0.581820i
\(580\) 0 0
\(581\) 0 0
\(582\) 14.0000i 0.580319i
\(583\) −8.00000 −0.331326
\(584\) 6.00000 0.248282
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) −44.0000 −1.81607 −0.908037 0.418890i \(-0.862419\pi\)
−0.908037 + 0.418890i \(0.862419\pi\)
\(588\) 7.00000i 0.288675i
\(589\) 40.0000 1.64817
\(590\) 0 0
\(591\) 26.0000i 1.06950i
\(592\) 4.00000 0.164399
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) 2.00000i 0.0819232i
\(597\) 0 0
\(598\) 18.0000 + 12.0000i 0.736075 + 0.490716i
\(599\) −16.0000 −0.653742 −0.326871 0.945069i \(-0.605994\pi\)
−0.326871 + 0.945069i \(0.605994\pi\)
\(600\) 0 0
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) −10.0000 −0.407231
\(604\) 22.0000i 0.895167i
\(605\) 0 0
\(606\) 8.00000i 0.324978i
\(607\) 16.0000i 0.649420i 0.945814 + 0.324710i \(0.105267\pi\)
−0.945814 + 0.324710i \(0.894733\pi\)
\(608\) 4.00000i 0.162221i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 4.00000i 0.161690i
\(613\) 36.0000 1.45403 0.727013 0.686624i \(-0.240908\pi\)
0.727013 + 0.686624i \(0.240908\pi\)
\(614\) 2.00000 0.0807134
\(615\) 0 0
\(616\) 0 0
\(617\) 26.0000 1.04672 0.523360 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) 4.00000 0.160904
\(619\) 40.0000i 1.60774i −0.594808 0.803868i \(-0.702772\pi\)
0.594808 0.803868i \(-0.297228\pi\)
\(620\) 0 0
\(621\) −6.00000 −0.240772
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) −3.00000 2.00000i −0.120096 0.0800641i
\(625\) 0 0
\(626\) 10.0000i 0.399680i
\(627\) 16.0000i 0.638978i
\(628\) 14.0000i 0.558661i
\(629\) 16.0000i 0.637962i
\(630\) 0 0
\(631\) 22.0000i 0.875806i −0.899022 0.437903i \(-0.855721\pi\)
0.899022 0.437903i \(-0.144279\pi\)
\(632\) 8.00000 0.318223
\(633\) 24.0000i 0.953914i
\(634\) −6.00000 −0.238290
\(635\) 0 0
\(636\) −2.00000 −0.0793052
\(637\) −14.0000 + 21.0000i −0.554700 + 0.832050i
\(638\) 16.0000i 0.633446i
\(639\) 12.0000i 0.474713i
\(640\) 0 0
\(641\) −10.0000 −0.394976 −0.197488 0.980305i \(-0.563278\pi\)
−0.197488 + 0.980305i \(0.563278\pi\)
\(642\) 0 0
\(643\) −50.0000 −1.97181 −0.985904 0.167313i \(-0.946491\pi\)
−0.985904 + 0.167313i \(0.946491\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 16.0000 0.629512
\(647\) 38.0000i 1.49393i −0.664861 0.746967i \(-0.731509\pi\)
0.664861 0.746967i \(-0.268491\pi\)
\(648\) 1.00000 0.0392837
\(649\) 16.0000 0.628055
\(650\) 0 0
\(651\) 0 0
\(652\) −2.00000 −0.0783260
\(653\) 10.0000i 0.391330i −0.980671 0.195665i \(-0.937313\pi\)
0.980671 0.195665i \(-0.0626866\pi\)
\(654\) 6.00000 0.234619
\(655\) 0 0
\(656\) 2.00000i 0.0780869i
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −42.0000 −1.63609 −0.818044 0.575156i \(-0.804941\pi\)
−0.818044 + 0.575156i \(0.804941\pi\)
\(660\) 0 0
\(661\) 22.0000i 0.855701i 0.903850 + 0.427850i \(0.140729\pi\)
−0.903850 + 0.427850i \(0.859271\pi\)
\(662\) 32.0000i 1.24372i
\(663\) −8.00000 + 12.0000i −0.310694 + 0.466041i
\(664\) 0 0
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) 24.0000i 0.929284i
\(668\) 0 0
\(669\) 20.0000i 0.773245i
\(670\) 0 0
\(671\) 40.0000i 1.54418i
\(672\) 0 0
\(673\) 26.0000i 1.00223i −0.865382 0.501113i \(-0.832924\pi\)
0.865382 0.501113i \(-0.167076\pi\)
\(674\) 2.00000i 0.0770371i
\(675\) 0 0
\(676\) −5.00000 12.0000i −0.192308 0.461538i
\(677\) 34.0000i 1.30673i −0.757045 0.653363i \(-0.773358\pi\)
0.757045 0.653363i \(-0.226642\pi\)
\(678\) 12.0000 0.460857
\(679\) 0 0
\(680\) 0 0
\(681\) 16.0000i 0.613121i
\(682\) −40.0000 −1.53168
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 4.00000i 0.152944i
\(685\) 0 0
\(686\) 0 0
\(687\) 2.00000 0.0763048
\(688\) 12.0000i 0.457496i
\(689\) −6.00000 4.00000i −0.228582 0.152388i
\(690\) 0 0
\(691\) 8.00000i 0.304334i 0.988355 + 0.152167i \(0.0486252\pi\)
−0.988355 + 0.152167i \(0.951375\pi\)
\(692\) 22.0000i 0.836315i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 4.00000i 0.151620i
\(697\) 8.00000 0.303022
\(698\) 14.0000i 0.529908i
\(699\) 24.0000 0.907763
\(700\) 0 0
\(701\) −36.0000 −1.35970 −0.679851 0.733351i \(-0.737955\pi\)
−0.679851 + 0.733351i \(0.737955\pi\)
\(702\) 3.00000 + 2.00000i 0.113228 + 0.0754851i
\(703\) 16.0000i 0.603451i
\(704\) 4.00000i 0.150756i
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 0 0
\(708\) 4.00000 0.150329
\(709\) 50.0000i 1.87779i 0.344204 + 0.938895i \(0.388149\pi\)
−0.344204 + 0.938895i \(0.611851\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) 10.0000i 0.374766i
\(713\) 60.0000 2.24702
\(714\) 0 0
\(715\) 0 0
\(716\) −22.0000 −0.822179
\(717\) 0 0
\(718\) 0 0
\(719\) 8.00000 0.298350 0.149175 0.988811i \(-0.452338\pi\)
0.149175 + 0.988811i \(0.452338\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) −4.00000 −0.148762
\(724\) 22.0000 0.817624
\(725\) 0 0
\(726\) 5.00000i 0.185567i
\(727\) 4.00000i 0.148352i −0.997245 0.0741759i \(-0.976367\pi\)
0.997245 0.0741759i \(-0.0236326\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −48.0000 −1.77534
\(732\) 10.0000i 0.369611i
\(733\) −40.0000 −1.47743 −0.738717 0.674016i \(-0.764568\pi\)
−0.738717 + 0.674016i \(0.764568\pi\)
\(734\) 16.0000i 0.590571i
\(735\) 0 0
\(736\) 6.00000i 0.221163i
\(737\) 40.0000i 1.47342i
\(738\) 2.00000i 0.0736210i
\(739\) 8.00000i 0.294285i −0.989115 0.147142i \(-0.952992\pi\)
0.989115 0.147142i \(-0.0470076\pi\)
\(740\) 0 0
\(741\) 8.00000 12.0000i 0.293887 0.440831i
\(742\) 0 0
\(743\) −32.0000 −1.17397 −0.586983 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) −10.0000 −0.366618
\(745\) 0 0
\(746\) 26.0000i 0.951928i
\(747\) 0 0
\(748\) −16.0000 −0.585018
\(749\) 0 0
\(750\) 0 0
\(751\) 16.0000 0.583848 0.291924 0.956441i \(-0.405705\pi\)
0.291924 + 0.956441i \(0.405705\pi\)
\(752\) 0 0
\(753\) 2.00000i 0.0728841i
\(754\) −8.00000 + 12.0000i −0.291343 + 0.437014i
\(755\) 0 0
\(756\) 0 0
\(757\) 26.0000i 0.944986i −0.881334 0.472493i \(-0.843354\pi\)
0.881334 0.472493i \(-0.156646\pi\)
\(758\) 16.0000i 0.581146i
\(759\) 24.0000i 0.871145i
\(760\) 0 0
\(761\) 18.0000i 0.652499i −0.945284 0.326250i \(-0.894215\pi\)
0.945284 0.326250i \(-0.105785\pi\)
\(762\) −8.00000 −0.289809
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) 12.0000 + 8.00000i 0.433295 + 0.288863i
\(768\) 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
\(771\) 12.0000 0.432169
\(772\) 14.0000 0.503871
\(773\) 26.0000 0.935155 0.467578 0.883952i \(-0.345127\pi\)
0.467578 + 0.883952i \(0.345127\pi\)
\(774\) 12.0000i 0.431331i
\(775\) 0 0
\(776\) 14.0000 0.502571
\(777\) 0 0
\(778\) 20.0000 0.717035
\(779\) −8.00000 −0.286630
\(780\) 0 0
\(781\) −48.0000 −1.71758
\(782\) 24.0000 0.858238
\(783\) 4.00000i 0.142948i
\(784\) −7.00000 −0.250000
\(785\) 0 0
\(786\) 18.0000i 0.642039i
\(787\) 38.0000 1.35455 0.677277 0.735728i \(-0.263160\pi\)
0.677277 + 0.735728i \(0.263160\pi\)
\(788\) 26.0000 0.926212
\(789\) −14.0000 −0.498413
\(790\) 0 0
\(791\) 0 0
\(792\) 4.00000i 0.142134i
\(793\) −20.0000 + 30.0000i −0.710221 + 1.06533i
\(794\) −28.0000 −0.993683
\(795\) 0 0
\(796\) 0 0
\(797\) 42.0000i 1.48772i −0.668338 0.743858i \(-0.732994\pi\)
0.668338 0.743858i \(-0.267006\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0