Properties

Label 546.2.c.b.337.2
Level $546$
Weight $2$
Character 546.337
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 337.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 546.337
Dual form 546.2.c.b.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +2.00000i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +2.00000i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} -2.00000 q^{10} -1.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -1.00000 q^{14} +2.00000i q^{15} +1.00000 q^{16} -2.00000 q^{17} +1.00000i q^{18} +4.00000i q^{19} -2.00000i q^{20} +1.00000i q^{21} -6.00000 q^{23} -1.00000i q^{24} +1.00000 q^{25} +(-3.00000 + 2.00000i) q^{26} +1.00000 q^{27} -1.00000i q^{28} -2.00000 q^{30} +1.00000i q^{32} -2.00000i q^{34} -2.00000 q^{35} -1.00000 q^{36} -2.00000i q^{37} -4.00000 q^{38} +(2.00000 + 3.00000i) q^{39} +2.00000 q^{40} -1.00000 q^{42} +4.00000 q^{43} +2.00000i q^{45} -6.00000i q^{46} +8.00000i q^{47} +1.00000 q^{48} -1.00000 q^{49} +1.00000i q^{50} -2.00000 q^{51} +(-2.00000 - 3.00000i) q^{52} +4.00000 q^{53} +1.00000i q^{54} +1.00000 q^{56} +4.00000i q^{57} -6.00000i q^{59} -2.00000i q^{60} +12.0000 q^{61} +1.00000i q^{63} -1.00000 q^{64} +(-6.00000 + 4.00000i) q^{65} -2.00000i q^{67} +2.00000 q^{68} -6.00000 q^{69} -2.00000i q^{70} -1.00000i q^{72} -14.0000i q^{73} +2.00000 q^{74} +1.00000 q^{75} -4.00000i q^{76} +(-3.00000 + 2.00000i) q^{78} +2.00000i q^{80} +1.00000 q^{81} -14.0000i q^{83} -1.00000i q^{84} -4.00000i q^{85} +4.00000i q^{86} +4.00000i q^{89} -2.00000 q^{90} +(-3.00000 + 2.00000i) q^{91} +6.00000 q^{92} -8.00000 q^{94} -8.00000 q^{95} +1.00000i q^{96} -2.00000i q^{97} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} - 2q^{4} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{4} + 2q^{9} - 4q^{10} - 2q^{12} + 4q^{13} - 2q^{14} + 2q^{16} - 4q^{17} - 12q^{23} + 2q^{25} - 6q^{26} + 2q^{27} - 4q^{30} - 4q^{35} - 2q^{36} - 8q^{38} + 4q^{39} + 4q^{40} - 2q^{42} + 8q^{43} + 2q^{48} - 2q^{49} - 4q^{51} - 4q^{52} + 8q^{53} + 2q^{56} + 24q^{61} - 2q^{64} - 12q^{65} + 4q^{68} - 12q^{69} + 4q^{74} + 2q^{75} - 6q^{78} + 2q^{81} - 4q^{90} - 6q^{91} + 12q^{92} - 16q^{94} - 16q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000 0.577350
\(4\) −1.00000 −0.500000
\(5\) 2.00000i 0.894427i 0.894427 + 0.447214i \(0.147584\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 1.00000i 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) −2.00000 −0.632456
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.00000 + 3.00000i 0.554700 + 0.832050i
\(14\) −1.00000 −0.267261
\(15\) 2.00000i 0.516398i
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.00000i 0.917663i 0.888523 + 0.458831i \(0.151732\pi\)
−0.888523 + 0.458831i \(0.848268\pi\)
\(20\) 2.00000i 0.447214i
\(21\) 1.00000i 0.218218i
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 1.00000 0.200000
\(26\) −3.00000 + 2.00000i −0.588348 + 0.392232i
\(27\) 1.00000 0.192450
\(28\) 1.00000i 0.188982i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −2.00000 −0.365148
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 2.00000i 0.342997i
\(35\) −2.00000 −0.338062
\(36\) −1.00000 −0.166667
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) −4.00000 −0.648886
\(39\) 2.00000 + 3.00000i 0.320256 + 0.480384i
\(40\) 2.00000 0.316228
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −1.00000 −0.154303
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 2.00000i 0.298142i
\(46\) 6.00000i 0.884652i
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 1.00000 0.144338
\(49\) −1.00000 −0.142857
\(50\) 1.00000i 0.141421i
\(51\) −2.00000 −0.280056
\(52\) −2.00000 3.00000i −0.277350 0.416025i
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 4.00000i 0.529813i
\(58\) 0 0
\(59\) 6.00000i 0.781133i −0.920575 0.390567i \(-0.872279\pi\)
0.920575 0.390567i \(-0.127721\pi\)
\(60\) 2.00000i 0.258199i
\(61\) 12.0000 1.53644 0.768221 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 0 0
\(63\) 1.00000i 0.125988i
\(64\) −1.00000 −0.125000
\(65\) −6.00000 + 4.00000i −0.744208 + 0.496139i
\(66\) 0 0
\(67\) 2.00000i 0.244339i −0.992509 0.122169i \(-0.961015\pi\)
0.992509 0.122169i \(-0.0389851\pi\)
\(68\) 2.00000 0.242536
\(69\) −6.00000 −0.722315
\(70\) 2.00000i 0.239046i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 14.0000i 1.63858i −0.573382 0.819288i \(-0.694369\pi\)
0.573382 0.819288i \(-0.305631\pi\)
\(74\) 2.00000 0.232495
\(75\) 1.00000 0.115470
\(76\) 4.00000i 0.458831i
\(77\) 0 0
\(78\) −3.00000 + 2.00000i −0.339683 + 0.226455i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 2.00000i 0.223607i
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 14.0000i 1.53670i −0.640030 0.768350i \(-0.721078\pi\)
0.640030 0.768350i \(-0.278922\pi\)
\(84\) 1.00000i 0.109109i
\(85\) 4.00000i 0.433861i
\(86\) 4.00000i 0.431331i
\(87\) 0 0
\(88\) 0 0
\(89\) 4.00000i 0.423999i 0.977270 + 0.212000i \(0.0679975\pi\)
−0.977270 + 0.212000i \(0.932002\pi\)
\(90\) −2.00000 −0.210819
\(91\) −3.00000 + 2.00000i −0.314485 + 0.209657i
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) −8.00000 −0.820783
\(96\) 1.00000i 0.102062i
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 2.00000i 0.198030i
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 3.00000 2.00000i 0.294174 0.196116i
\(105\) −2.00000 −0.195180
\(106\) 4.00000i 0.388514i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 6.00000i 0.574696i −0.957826 0.287348i \(-0.907226\pi\)
0.957826 0.287348i \(-0.0927736\pi\)
\(110\) 0 0
\(111\) 2.00000i 0.189832i
\(112\) 1.00000i 0.0944911i
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) −4.00000 −0.374634
\(115\) 12.0000i 1.11901i
\(116\) 0 0
\(117\) 2.00000 + 3.00000i 0.184900 + 0.277350i
\(118\) 6.00000 0.552345
\(119\) 2.00000i 0.183340i
\(120\) 2.00000 0.182574
\(121\) 11.0000 1.00000
\(122\) 12.0000i 1.08643i
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000i 1.07331i
\(126\) −1.00000 −0.0890871
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.00000 0.352180
\(130\) −4.00000 6.00000i −0.350823 0.526235i
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −4.00000 −0.346844
\(134\) 2.00000 0.172774
\(135\) 2.00000i 0.172133i
\(136\) 2.00000i 0.171499i
\(137\) 2.00000i 0.170872i −0.996344 0.0854358i \(-0.972772\pi\)
0.996344 0.0854358i \(-0.0272282\pi\)
\(138\) 6.00000i 0.510754i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 2.00000 0.169031
\(141\) 8.00000i 0.673722i
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 14.0000 1.15865
\(147\) −1.00000 −0.0824786
\(148\) 2.00000i 0.164399i
\(149\) 6.00000i 0.491539i −0.969328 0.245770i \(-0.920959\pi\)
0.969328 0.245770i \(-0.0790407\pi\)
\(150\) 1.00000i 0.0816497i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 4.00000 0.324443
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) −2.00000 3.00000i −0.160128 0.240192i
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 0 0
\(159\) 4.00000 0.317221
\(160\) −2.00000 −0.158114
\(161\) 6.00000i 0.472866i
\(162\) 1.00000i 0.0785674i
\(163\) 14.0000i 1.09656i −0.836293 0.548282i \(-0.815282\pi\)
0.836293 0.548282i \(-0.184718\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 14.0000 1.08661
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 1.00000 0.0771517
\(169\) −5.00000 + 12.0000i −0.384615 + 0.923077i
\(170\) 4.00000 0.306786
\(171\) 4.00000i 0.305888i
\(172\) −4.00000 −0.304997
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) 1.00000i 0.0755929i
\(176\) 0 0
\(177\) 6.00000i 0.450988i
\(178\) −4.00000 −0.299813
\(179\) −20.0000 −1.49487 −0.747435 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 2.00000i 0.149071i
\(181\) 12.0000 0.891953 0.445976 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) −2.00000 3.00000i −0.148250 0.222375i
\(183\) 12.0000 0.887066
\(184\) 6.00000i 0.442326i
\(185\) 4.00000 0.294086
\(186\) 0 0
\(187\) 0 0
\(188\) 8.00000i 0.583460i
\(189\) 1.00000i 0.0727393i
\(190\) 8.00000i 0.580381i
\(191\) 2.00000 0.144715 0.0723575 0.997379i \(-0.476948\pi\)
0.0723575 + 0.997379i \(0.476948\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 4.00000i 0.287926i −0.989583 0.143963i \(-0.954015\pi\)
0.989583 0.143963i \(-0.0459847\pi\)
\(194\) 2.00000 0.143592
\(195\) −6.00000 + 4.00000i −0.429669 + 0.286446i
\(196\) 1.00000 0.0714286
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) 0 0
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 2.00000i 0.141069i
\(202\) 2.00000i 0.140720i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 0 0
\(206\) 14.0000i 0.975426i
\(207\) −6.00000 −0.417029
\(208\) 2.00000 + 3.00000i 0.138675 + 0.208013i
\(209\) 0 0
\(210\) 2.00000i 0.138013i
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) −4.00000 −0.274721
\(213\) 0 0
\(214\) 12.0000i 0.820303i
\(215\) 8.00000i 0.545595i
\(216\) 1.00000i 0.0680414i
\(217\) 0 0
\(218\) 6.00000 0.406371
\(219\) 14.0000i 0.946032i
\(220\) 0 0
\(221\) −4.00000 6.00000i −0.269069 0.403604i
\(222\) 2.00000 0.134231
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 1.00000 0.0666667
\(226\) 14.0000i 0.931266i
\(227\) 22.0000i 1.46019i −0.683345 0.730096i \(-0.739475\pi\)
0.683345 0.730096i \(-0.260525\pi\)
\(228\) 4.00000i 0.264906i
\(229\) 14.0000i 0.925146i 0.886581 + 0.462573i \(0.153074\pi\)
−0.886581 + 0.462573i \(0.846926\pi\)
\(230\) 12.0000 0.791257
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −3.00000 + 2.00000i −0.196116 + 0.130744i
\(235\) −16.0000 −1.04372
\(236\) 6.00000i 0.390567i
\(237\) 0 0
\(238\) 2.00000 0.129641
\(239\) 16.0000i 1.03495i −0.855697 0.517477i \(-0.826871\pi\)
0.855697 0.517477i \(-0.173129\pi\)
\(240\) 2.00000i 0.129099i
\(241\) 10.0000i 0.644157i 0.946713 + 0.322078i \(0.104381\pi\)
−0.946713 + 0.322078i \(0.895619\pi\)
\(242\) 11.0000i 0.707107i
\(243\) 1.00000 0.0641500
\(244\) −12.0000 −0.768221
\(245\) 2.00000i 0.127775i
\(246\) 0 0
\(247\) −12.0000 + 8.00000i −0.763542 + 0.509028i
\(248\) 0 0
\(249\) 14.0000i 0.887214i
\(250\) −12.0000 −0.758947
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 0 0
\(254\) 12.0000i 0.752947i
\(255\) 4.00000i 0.250490i
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 2.00000 0.124274
\(260\) 6.00000 4.00000i 0.372104 0.248069i
\(261\) 0 0
\(262\) 12.0000i 0.741362i
\(263\) −6.00000 −0.369976 −0.184988 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) 0 0
\(265\) 8.00000i 0.491436i
\(266\) 4.00000i 0.245256i
\(267\) 4.00000i 0.244796i
\(268\) 2.00000i 0.122169i
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) −2.00000 −0.121716
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −2.00000 −0.121268
\(273\) −3.00000 + 2.00000i −0.181568 + 0.121046i
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 20.0000i 1.19952i
\(279\) 0 0
\(280\) 2.00000i 0.119523i
\(281\) 30.0000i 1.78965i 0.446417 + 0.894825i \(0.352700\pi\)
−0.446417 + 0.894825i \(0.647300\pi\)
\(282\) −8.00000 −0.476393
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) 0 0
\(285\) −8.00000 −0.473879
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 2.00000i 0.117242i
\(292\) 14.0000i 0.819288i
\(293\) 6.00000i 0.350524i 0.984522 + 0.175262i \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 12.0000 0.698667
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −12.0000 18.0000i −0.693978 1.04097i
\(300\) −1.00000 −0.0577350
\(301\) 4.00000i 0.230556i
\(302\) 0 0
\(303\) 2.00000 0.114897
\(304\) 4.00000i 0.229416i
\(305\) 24.0000i 1.37424i
\(306\) 2.00000i 0.114332i
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) 0 0
\(309\) 14.0000 0.796432
\(310\) 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
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 8.00000i 0.451466i
\(315\) −2.00000 −0.112687
\(316\) 0 0
\(317\) 2.00000i 0.112331i −0.998421 0.0561656i \(-0.982113\pi\)
0.998421 0.0561656i \(-0.0178875\pi\)
\(318\) 4.00000i 0.224309i
\(319\) 0 0
\(320\) 2.00000i 0.111803i
\(321\) −12.0000 −0.669775
\(322\) 6.00000 0.334367
\(323\) 8.00000i 0.445132i
\(324\) −1.00000 −0.0555556
\(325\) 2.00000 + 3.00000i 0.110940 + 0.166410i
\(326\) 14.0000 0.775388
\(327\) 6.00000i 0.331801i
\(328\) 0 0
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) 10.0000i 0.549650i −0.961494 0.274825i \(-0.911380\pi\)
0.961494 0.274825i \(-0.0886199\pi\)
\(332\) 14.0000i 0.768350i
\(333\) 2.00000i 0.109599i
\(334\) 12.0000 0.656611
\(335\) 4.00000 0.218543
\(336\) 1.00000i 0.0545545i
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −12.0000 5.00000i −0.652714 0.271964i
\(339\) 14.0000 0.760376
\(340\) 4.00000i 0.216930i
\(341\) 0 0
\(342\) −4.00000 −0.216295
\(343\) 1.00000i 0.0539949i
\(344\) 4.00000i 0.215666i
\(345\) 12.0000i 0.646058i
\(346\) 6.00000i 0.322562i
\(347\) −32.0000 −1.71785 −0.858925 0.512101i \(-0.828867\pi\)
−0.858925 + 0.512101i \(0.828867\pi\)
\(348\) 0 0
\(349\) 14.0000i 0.749403i 0.927146 + 0.374701i \(0.122255\pi\)
−0.927146 + 0.374701i \(0.877745\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 2.00000 + 3.00000i 0.106752 + 0.160128i
\(352\) 0 0
\(353\) 24.0000i 1.27739i −0.769460 0.638696i \(-0.779474\pi\)
0.769460 0.638696i \(-0.220526\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) 4.00000i 0.212000i
\(357\) 2.00000i 0.105851i
\(358\) 20.0000i 1.05703i
\(359\) 24.0000i 1.26667i 0.773877 + 0.633336i \(0.218315\pi\)
−0.773877 + 0.633336i \(0.781685\pi\)
\(360\) 2.00000 0.105409
\(361\) 3.00000 0.157895
\(362\) 12.0000i 0.630706i
\(363\) 11.0000 0.577350
\(364\) 3.00000 2.00000i 0.157243 0.104828i
\(365\) 28.0000 1.46559
\(366\) 12.0000i 0.627250i
\(367\) −22.0000 −1.14839 −0.574195 0.818718i \(-0.694685\pi\)
−0.574195 + 0.818718i \(0.694685\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) 4.00000i 0.207950i
\(371\) 4.00000i 0.207670i
\(372\) 0 0
\(373\) 34.0000 1.76045 0.880227 0.474554i \(-0.157390\pi\)
0.880227 + 0.474554i \(0.157390\pi\)
\(374\) 0 0
\(375\) 12.0000i 0.619677i
\(376\) 8.00000 0.412568
\(377\) 0 0
\(378\) −1.00000 −0.0514344
\(379\) 26.0000i 1.33553i −0.744372 0.667765i \(-0.767251\pi\)
0.744372 0.667765i \(-0.232749\pi\)
\(380\) 8.00000 0.410391
\(381\) −12.0000 −0.614779
\(382\) 2.00000i 0.102329i
\(383\) 24.0000i 1.22634i −0.789950 0.613171i \(-0.789894\pi\)
0.789950 0.613171i \(-0.210106\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) 4.00000 0.203331
\(388\) 2.00000i 0.101535i
\(389\) 20.0000 1.01404 0.507020 0.861934i \(-0.330747\pi\)
0.507020 + 0.861934i \(0.330747\pi\)
\(390\) −4.00000 6.00000i −0.202548 0.303822i
\(391\) 12.0000 0.606866
\(392\) 1.00000i 0.0505076i
\(393\) 12.0000 0.605320
\(394\) −18.0000 −0.906827
\(395\) 0 0
\(396\) 0 0
\(397\) 18.0000i 0.903394i 0.892171 + 0.451697i \(0.149181\pi\)
−0.892171 + 0.451697i \(0.850819\pi\)
\(398\) 10.0000i 0.501255i
\(399\) −4.00000 −0.200250
\(400\) 1.00000 0.0500000
\(401\) 30.0000i 1.49813i −0.662497 0.749064i \(-0.730503\pi\)
0.662497 0.749064i \(-0.269497\pi\)
\(402\) 2.00000 0.0997509
\(403\) 0 0
\(404\) −2.00000 −0.0995037
\(405\) 2.00000i 0.0993808i
\(406\) 0 0
\(407\) 0 0
\(408\) 2.00000i 0.0990148i
\(409\) 14.0000i 0.692255i 0.938187 + 0.346128i \(0.112504\pi\)
−0.938187 + 0.346128i \(0.887496\pi\)
\(410\) 0 0
\(411\) 2.00000i 0.0986527i
\(412\) −14.0000 −0.689730
\(413\) 6.00000 0.295241
\(414\) 6.00000i 0.294884i
\(415\) 28.0000 1.37447
\(416\) −3.00000 + 2.00000i −0.147087 + 0.0980581i
\(417\) 20.0000 0.979404
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 2.00000 0.0975900
\(421\) 30.0000i 1.46211i −0.682318 0.731055i \(-0.739028\pi\)
0.682318 0.731055i \(-0.260972\pi\)
\(422\) 28.0000i 1.36302i
\(423\) 8.00000i 0.388973i
\(424\) 4.00000i 0.194257i
\(425\) −2.00000 −0.0970143
\(426\) 0 0
\(427\) 12.0000i 0.580721i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 1.00000 0.0481125
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 6.00000i 0.287348i
\(437\) 24.0000i 1.14808i
\(438\) 14.0000 0.668946
\(439\) 30.0000 1.43182 0.715911 0.698192i \(-0.246012\pi\)
0.715911 + 0.698192i \(0.246012\pi\)
\(440\) 0 0
\(441\) −1.00000 −0.0476190
\(442\) 6.00000 4.00000i 0.285391 0.190261i
\(443\) 4.00000 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) 2.00000i 0.0949158i
\(445\) −8.00000 −0.379236
\(446\) −16.0000 −0.757622
\(447\) 6.00000i 0.283790i
\(448\) 1.00000i 0.0472456i
\(449\) 14.0000i 0.660701i 0.943858 + 0.330350i \(0.107167\pi\)
−0.943858 + 0.330350i \(0.892833\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 0 0
\(452\) −14.0000 −0.658505
\(453\) 0 0
\(454\) 22.0000 1.03251
\(455\) −4.00000 6.00000i −0.187523 0.281284i
\(456\) 4.00000 0.187317
\(457\) 8.00000i 0.374224i 0.982339 + 0.187112i \(0.0599128\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) −14.0000 −0.654177
\(459\) −2.00000 −0.0933520
\(460\) 12.0000i 0.559503i
\(461\) 10.0000i 0.465746i 0.972507 + 0.232873i \(0.0748127\pi\)
−0.972507 + 0.232873i \(0.925187\pi\)
\(462\) 0 0
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 6.00000i 0.277945i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −2.00000 3.00000i −0.0924500 0.138675i
\(469\) 2.00000 0.0923514
\(470\) 16.0000i 0.738025i
\(471\) 8.00000 0.368621
\(472\) −6.00000 −0.276172
\(473\) 0 0
\(474\) 0 0
\(475\) 4.00000i 0.183533i
\(476\) 2.00000i 0.0916698i
\(477\) 4.00000 0.183147
\(478\) 16.0000 0.731823
\(479\) 16.0000i 0.731059i −0.930800 0.365529i \(-0.880888\pi\)
0.930800 0.365529i \(-0.119112\pi\)
\(480\) −2.00000 −0.0912871
\(481\) 6.00000 4.00000i 0.273576 0.182384i
\(482\) −10.0000 −0.455488
\(483\) 6.00000i 0.273009i
\(484\) −11.0000 −0.500000
\(485\) 4.00000 0.181631
\(486\) 1.00000i 0.0453609i
\(487\) 28.0000i 1.26880i 0.773004 + 0.634401i \(0.218753\pi\)
−0.773004 + 0.634401i \(0.781247\pi\)
\(488\) 12.0000i 0.543214i
\(489\) 14.0000i 0.633102i
\(490\) 2.00000 0.0903508
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −8.00000 12.0000i −0.359937 0.539906i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 14.0000 0.627355
\(499\) 14.0000i 0.626726i 0.949633 + 0.313363i \(0.101456\pi\)
−0.949633 + 0.313363i \(0.898544\pi\)
\(500\) 12.0000i 0.536656i
\(501\) 12.0000i 0.536120i
\(502\) 28.0000i 1.24970i
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 1.00000 0.0445435
\(505\) 4.00000i 0.177998i
\(506\) 0 0
\(507\) −5.00000 + 12.0000i −0.222058 + 0.532939i
\(508\) 12.0000 0.532414
\(509\) 26.0000i 1.15243i −0.817298 0.576215i \(-0.804529\pi\)
0.817298 0.576215i \(-0.195471\pi\)
\(510\) 4.00000 0.177123
\(511\) 14.0000 0.619324
\(512\) 1.00000i 0.0441942i
\(513\) 4.00000i 0.176604i
\(514\) 18.0000i 0.793946i
\(515\) 28.0000i 1.23383i
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) 2.00000i 0.0878750i
\(519\) −6.00000 −0.263371
\(520\) 4.00000 + 6.00000i 0.175412 + 0.263117i
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) −12.0000 −0.524222
\(525\) 1.00000i 0.0436436i
\(526\) 6.00000i 0.261612i
\(527\) 0 0
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) −8.00000 −0.347498
\(531\) 6.00000i 0.260378i
\(532\) 4.00000 0.173422
\(533\) 0 0
\(534\) −4.00000 −0.173097
\(535\) 24.0000i 1.03761i
\(536\) −2.00000 −0.0863868
\(537\) −20.0000 −0.863064
\(538\) 10.0000i 0.431131i
\(539\) 0 0
\(540\) 2.00000i 0.0860663i
\(541\) 30.0000i 1.28980i −0.764267 0.644900i \(-0.776899\pi\)
0.764267 0.644900i \(-0.223101\pi\)
\(542\) 0 0
\(543\) 12.0000 0.514969
\(544\) 2.00000i 0.0857493i
\(545\) 12.0000 0.514024
\(546\) −2.00000 3.00000i −0.0855921 0.128388i
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) 12.0000 0.512148
\(550\) 0 0
\(551\) 0 0
\(552\) 6.00000i 0.255377i
\(553\) 0 0
\(554\) 22.0000i 0.934690i
\(555\) 4.00000 0.169791
\(556\) −20.0000 −0.848189
\(557\) 18.0000i 0.762684i 0.924434 + 0.381342i \(0.124538\pi\)
−0.924434 + 0.381342i \(0.875462\pi\)
\(558\) 0 0
\(559\) 8.00000 + 12.0000i 0.338364 + 0.507546i
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) −30.0000 −1.26547
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) 8.00000i 0.336861i
\(565\) 28.0000i 1.17797i
\(566\) 16.0000i 0.672530i
\(567\) 1.00000i 0.0419961i
\(568\) 0 0
\(569\) 30.0000 1.25767 0.628833 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) 8.00000i 0.335083i
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 0 0
\(573\) 2.00000 0.0835512
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) −1.00000 −0.0416667
\(577\) 22.0000i 0.915872i −0.888985 0.457936i \(-0.848589\pi\)
0.888985 0.457936i \(-0.151411\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 4.00000i 0.166234i
\(580\) 0 0
\(581\) 14.0000 0.580818
\(582\) 2.00000 0.0829027
\(583\) 0 0
\(584\) −14.0000 −0.579324
\(585\) −6.00000 + 4.00000i −0.248069 + 0.165380i
\(586\) −6.00000 −0.247858
\(587\) 18.0000i 0.742940i 0.928445 + 0.371470i \(0.121146\pi\)
−0.928445 + 0.371470i \(0.878854\pi\)
\(588\) 1.00000 0.0412393
\(589\) 0 0
\(590\) 12.0000i 0.494032i
\(591\) 18.0000i 0.740421i
\(592\) 2.00000i 0.0821995i
\(593\) 24.0000i 0.985562i −0.870153 0.492781i \(-0.835980\pi\)
0.870153 0.492781i \(-0.164020\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) 6.00000i 0.245770i
\(597\) −10.0000 −0.409273
\(598\) 18.0000 12.0000i 0.736075 0.490716i
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) −18.0000 −0.734235 −0.367118 0.930175i \(-0.619655\pi\)
−0.367118 + 0.930175i \(0.619655\pi\)
\(602\) −4.00000 −0.163028
\(603\) 2.00000i 0.0814463i
\(604\) 0 0
\(605\) 22.0000i 0.894427i
\(606\) 2.00000i 0.0812444i
\(607\) 18.0000 0.730597 0.365299 0.930890i \(-0.380967\pi\)
0.365299 + 0.930890i \(0.380967\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −24.0000 −0.971732
\(611\) −24.0000 + 16.0000i −0.970936 + 0.647291i
\(612\) 2.00000 0.0808452
\(613\) 34.0000i 1.37325i −0.727013 0.686624i \(-0.759092\pi\)
0.727013 0.686624i \(-0.240908\pi\)
\(614\) −28.0000 −1.12999
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000i 0.724653i 0.932051 + 0.362326i \(0.118017\pi\)
−0.932051 + 0.362326i \(0.881983\pi\)
\(618\) 14.0000i 0.563163i
\(619\) 16.0000i 0.643094i −0.946894 0.321547i \(-0.895797\pi\)
0.946894 0.321547i \(-0.104203\pi\)
\(620\) 0 0
\(621\) −6.00000 −0.240772
\(622\) 12.0000i 0.481156i
\(623\) −4.00000 −0.160257
\(624\) 2.00000 + 3.00000i 0.0800641 + 0.120096i
\(625\) −19.0000 −0.760000
\(626\) 6.00000i 0.239808i
\(627\) 0 0
\(628\) −8.00000 −0.319235
\(629\) 4.00000i 0.159490i
\(630\) 2.00000i 0.0796819i
\(631\) 20.0000i 0.796187i −0.917345 0.398094i \(-0.869672\pi\)
0.917345 0.398094i \(-0.130328\pi\)
\(632\) 0 0
\(633\) −28.0000 −1.11290
\(634\) 2.00000 0.0794301
\(635\) 24.0000i 0.952411i
\(636\) −4.00000 −0.158610
\(637\) −2.00000 3.00000i −0.0792429 0.118864i
\(638\) 0 0
\(639\) 0 0
\(640\) 2.00000 0.0790569
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 44.0000i 1.73519i −0.497271 0.867595i \(-0.665665\pi\)
0.497271 0.867595i \(-0.334335\pi\)
\(644\) 6.00000i 0.236433i
\(645\) 8.00000i 0.315000i
\(646\) 8.00000 0.314756
\(647\) 28.0000 1.10079 0.550397 0.834903i \(-0.314476\pi\)
0.550397 + 0.834903i \(0.314476\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 0 0
\(650\) −3.00000 + 2.00000i −0.117670 + 0.0784465i
\(651\) 0 0
\(652\) 14.0000i 0.548282i
\(653\) 4.00000 0.156532 0.0782660 0.996933i \(-0.475062\pi\)
0.0782660 + 0.996933i \(0.475062\pi\)
\(654\) 6.00000 0.234619
\(655\) 24.0000i 0.937758i
\(656\) 0 0
\(657\) 14.0000i 0.546192i
\(658\) 8.00000i 0.311872i
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) 10.0000i 0.388955i 0.980907 + 0.194477i \(0.0623011\pi\)
−0.980907 + 0.194477i \(0.937699\pi\)
\(662\) 10.0000 0.388661
\(663\) −4.00000 6.00000i −0.155347 0.233021i
\(664\) −14.0000 −0.543305
\(665\) 8.00000i 0.310227i
\(666\) 2.00000 0.0774984
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 16.0000i 0.618596i
\(670\) 4.00000i 0.154533i
\(671\) 0 0
\(672\) −1.00000 −0.0385758
\(673\) −46.0000 −1.77317 −0.886585 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 22.0000i 0.847408i
\(675\) 1.00000 0.0384900
\(676\) 5.00000 12.0000i 0.192308 0.461538i
\(677\) −22.0000 −0.845529 −0.422764 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) 14.0000i 0.537667i
\(679\) 2.00000 0.0767530
\(680\) −4.00000 −0.153393
\(681\) 22.0000i 0.843042i
\(682\) 0 0
\(683\) 16.0000i 0.612223i 0.951996 + 0.306111i \(0.0990280\pi\)
−0.951996 + 0.306111i \(0.900972\pi\)
\(684\) 4.00000i 0.152944i
\(685\) 4.00000 0.152832
\(686\) 1.00000 0.0381802
\(687\) 14.0000i 0.534133i
\(688\) 4.00000 0.152499
\(689\) 8.00000 + 12.0000i 0.304776 + 0.457164i
\(690\) 12.0000 0.456832
\(691\) 40.0000i 1.52167i −0.648944 0.760836i \(-0.724789\pi\)
0.648944 0.760836i \(-0.275211\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 32.0000i 1.21470i
\(695\) 40.0000i 1.51729i
\(696\) 0 0
\(697\) 0 0
\(698\) −14.0000 −0.529908
\(699\) −6.00000 −0.226941
\(700\) 1.00000i 0.0377964i
\(701\) −48.0000 −1.81293 −0.906467 0.422276i \(-0.861231\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) −3.00000 + 2.00000i −0.113228 + 0.0754851i
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) −16.0000 −0.602595
\(706\) 24.0000 0.903252
\(707\) 2.00000i 0.0752177i
\(708\) 6.00000i 0.225494i
\(709\) 46.0000i 1.72757i −0.503864 0.863783i \(-0.668089\pi\)
0.503864 0.863783i \(-0.331911\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 4.00000 0.149906
\(713\) 0 0
\(714\) 2.00000 0.0748481
\(715\) 0 0
\(716\) 20.0000 0.747435
\(717\) 16.0000i 0.597531i
\(718\) −24.0000 −0.895672
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 2.00000i 0.0745356i
\(721\) 14.0000i 0.521387i
\(722\) 3.00000i 0.111648i
\(723\) 10.0000i 0.371904i
\(724\) −12.0000 −0.445976
\(725\) 0 0
\(726\) 11.0000i 0.408248i
\(727\) 38.0000 1.40934 0.704671 0.709534i \(-0.251095\pi\)
0.704671 + 0.709534i \(0.251095\pi\)
\(728\) 2.00000 + 3.00000i 0.0741249 + 0.111187i
\(729\) 1.00000 0.0370370
\(730\) 28.0000i 1.03633i
\(731\) −8.00000 −0.295891
\(732\) −12.0000 −0.443533
\(733\) 14.0000i 0.517102i −0.965998 0.258551i \(-0.916755\pi\)
0.965998 0.258551i \(-0.0832450\pi\)
\(734\) 22.0000i 0.812035i
\(735\) 2.00000i 0.0737711i
\(736\) 6.00000i 0.221163i
\(737\) 0 0
\(738\) 0 0
\(739\) 34.0000i 1.25071i 0.780340 + 0.625355i \(0.215046\pi\)
−0.780340 + 0.625355i \(0.784954\pi\)
\(740\) −4.00000 −0.147043
\(741\) −12.0000 + 8.00000i −0.440831 + 0.293887i
\(742\) −4.00000 −0.146845
\(743\) 16.0000i 0.586983i 0.955962 + 0.293492i \(0.0948173\pi\)
−0.955962 + 0.293492i \(0.905183\pi\)
\(744\) 0 0
\(745\) 12.0000 0.439646
\(746\) 34.0000i 1.24483i
\(747\) 14.0000i 0.512233i
\(748\) 0 0
\(749\) 12.0000i 0.438470i
\(750\) −12.0000 −0.438178
\(751\) 12.0000 0.437886 0.218943 0.975738i \(-0.429739\pi\)
0.218943 + 0.975738i \(0.429739\pi\)
\(752\) 8.00000i 0.291730i
\(753\) −28.0000 −1.02038
\(754\) 0 0
\(755\) 0 0
\(756\) 1.00000i 0.0363696i
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) 26.0000 0.944363
\(759\) 0 0
\(760\) 8.00000i 0.290191i
\(761\) 40.0000i 1.45000i 0.688749 + 0.724999i \(0.258160\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 12.0000i 0.434714i
\(763\) 6.00000 0.217215
\(764\) −2.00000 −0.0723575
\(765\) 4.00000i 0.144620i
\(766\) 24.0000 0.867155
\(767\) 18.0000 12.0000i 0.649942 0.433295i
\(768\) 1.00000 0.0360844
\(769\) 26.0000i 0.937584i −0.883309 0.468792i \(-0.844689\pi\)
0.883309 0.468792i \(-0.155311\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 4.00000i 0.143963i
\(773\) 26.0000i 0.935155i 0.883952 + 0.467578i \(0.154873\pi\)
−0.883952 + 0.467578i \(0.845127\pi\)
\(774\) 4.00000i 0.143777i
\(775\) 0 0
\(776\) −2.00000 −0.0717958
\(777\) 2.00000 0.0717496
\(778\) 20.0000i 0.717035i
\(779\) 0 0
\(780\) 6.00000 4.00000i 0.214834 0.143223i
\(781\) 0 0
\(782\) 12.0000i 0.429119i
\(783\) 0 0
\(784\) −1.00000 −0.0357143
\(785\) 16.0000i 0.571064i
\(786\) 12.0000i 0.428026i
\(787\) 48.0000i 1.71102i 0.517790 + 0.855508i \(0.326755\pi\)
−0.517790 + 0.855508i \(0.673245\pi\)
\(788\) 18.0000i 0.641223i
\(789\) −6.00000 −0.213606
\(790\) 0 0
\(791\) 14.0000i 0.497783i
\(792\) 0 0
\(793\) 24.0000 + 36.0000i 0.852265 + 1.27840i
\(794\) −18.0000 −0.638796
\(795\) 8.00000i 0.283731i
\(796\) 10.0000 0.354441
\(797\) −42.0000 −1.48772