Properties

Label 490.2.c.a.99.2
Level $490$
Weight $2$
Character 490.99
Analytic conductor $3.913$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.91266969904\)
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: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 99.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 490.99
Dual form 490.2.c.a.99.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000i q^{8} +3.00000 q^{9} +(1.00000 - 2.00000i) q^{10} +3.00000 q^{11} +5.00000i q^{13} +1.00000 q^{16} -2.00000i q^{17} +3.00000i q^{18} +5.00000 q^{19} +(2.00000 + 1.00000i) q^{20} +3.00000i q^{22} +7.00000i q^{23} +(3.00000 + 4.00000i) q^{25} -5.00000 q^{26} +4.00000 q^{29} -2.00000 q^{31} +1.00000i q^{32} +2.00000 q^{34} -3.00000 q^{36} +1.00000i q^{37} +5.00000i q^{38} +(-1.00000 + 2.00000i) q^{40} +3.00000 q^{41} -2.00000i q^{43} -3.00000 q^{44} +(-6.00000 - 3.00000i) q^{45} -7.00000 q^{46} -7.00000i q^{47} +(-4.00000 + 3.00000i) q^{50} -5.00000i q^{52} -9.00000i q^{53} +(-6.00000 - 3.00000i) q^{55} +4.00000i q^{58} +4.00000 q^{59} +6.00000 q^{61} -2.00000i q^{62} -1.00000 q^{64} +(5.00000 - 10.0000i) q^{65} +2.00000i q^{67} +2.00000i q^{68} -6.00000 q^{71} -3.00000i q^{72} +16.0000i q^{73} -1.00000 q^{74} -5.00000 q^{76} -14.0000 q^{79} +(-2.00000 - 1.00000i) q^{80} +9.00000 q^{81} +3.00000i q^{82} +6.00000i q^{83} +(-2.00000 + 4.00000i) q^{85} +2.00000 q^{86} -3.00000i q^{88} -2.00000 q^{89} +(3.00000 - 6.00000i) q^{90} -7.00000i q^{92} +7.00000 q^{94} +(-10.0000 - 5.00000i) q^{95} -12.0000i q^{97} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 4 q^{5} + 6 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{4} - 4 q^{5} + 6 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{16} + 10 q^{19} + 4 q^{20} + 6 q^{25} - 10 q^{26} + 8 q^{29} - 4 q^{31} + 4 q^{34} - 6 q^{36} - 2 q^{40} + 6 q^{41} - 6 q^{44} - 12 q^{45} - 14 q^{46} - 8 q^{50} - 12 q^{55} + 8 q^{59} + 12 q^{61} - 2 q^{64} + 10 q^{65} - 12 q^{71} - 2 q^{74} - 10 q^{76} - 28 q^{79} - 4 q^{80} + 18 q^{81} - 4 q^{85} + 4 q^{86} - 4 q^{89} + 6 q^{90} + 14 q^{94} - 20 q^{95} + 18 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.00000 1.00000i −0.894427 0.447214i
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 3.00000 1.00000
\(10\) 1.00000 2.00000i 0.316228 0.632456i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 5.00000i 1.38675i 0.720577 + 0.693375i \(0.243877\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i −0.970143 0.242536i \(-0.922021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 3.00000i 0.707107i
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 2.00000 + 1.00000i 0.447214 + 0.223607i
\(21\) 0 0
\(22\) 3.00000i 0.639602i
\(23\) 7.00000i 1.45960i 0.683660 + 0.729800i \(0.260387\pi\)
−0.683660 + 0.729800i \(0.739613\pi\)
\(24\) 0 0
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) −5.00000 −0.980581
\(27\) 0 0
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 1.00000i 0.164399i 0.996616 + 0.0821995i \(0.0261945\pi\)
−0.996616 + 0.0821995i \(0.973806\pi\)
\(38\) 5.00000i 0.811107i
\(39\) 0 0
\(40\) −1.00000 + 2.00000i −0.158114 + 0.316228i
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) −3.00000 −0.452267
\(45\) −6.00000 3.00000i −0.894427 0.447214i
\(46\) −7.00000 −1.03209
\(47\) 7.00000i 1.02105i −0.859861 0.510527i \(-0.829450\pi\)
0.859861 0.510527i \(-0.170550\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 5.00000i 0.693375i
\(53\) 9.00000i 1.23625i −0.786082 0.618123i \(-0.787894\pi\)
0.786082 0.618123i \(-0.212106\pi\)
\(54\) 0 0
\(55\) −6.00000 3.00000i −0.809040 0.404520i
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000i 0.525226i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 5.00000 10.0000i 0.620174 1.24035i
\(66\) 0 0
\(67\) 2.00000i 0.244339i 0.992509 + 0.122169i \(0.0389851\pi\)
−0.992509 + 0.122169i \(0.961015\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 16.0000i 1.87266i 0.351123 + 0.936329i \(0.385800\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) −5.00000 −0.573539
\(77\) 0 0
\(78\) 0 0
\(79\) −14.0000 −1.57512 −0.787562 0.616236i \(-0.788657\pi\)
−0.787562 + 0.616236i \(0.788657\pi\)
\(80\) −2.00000 1.00000i −0.223607 0.111803i
\(81\) 9.00000 1.00000
\(82\) 3.00000i 0.331295i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 0 0
\(85\) −2.00000 + 4.00000i −0.216930 + 0.433861i
\(86\) 2.00000 0.215666
\(87\) 0 0
\(88\) 3.00000i 0.319801i
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 3.00000 6.00000i 0.316228 0.632456i
\(91\) 0 0
\(92\) 7.00000i 0.729800i
\(93\) 0 0
\(94\) 7.00000 0.721995
\(95\) −10.0000 5.00000i −1.02598 0.512989i
\(96\) 0 0
\(97\) 12.0000i 1.21842i −0.793011 0.609208i \(-0.791488\pi\)
0.793011 0.609208i \(-0.208512\pi\)
\(98\) 0 0
\(99\) 9.00000 0.904534
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 8.00000i 0.788263i 0.919054 + 0.394132i \(0.128955\pi\)
−0.919054 + 0.394132i \(0.871045\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) 16.0000i 1.54678i −0.633932 0.773389i \(-0.718560\pi\)
0.633932 0.773389i \(-0.281440\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 3.00000 6.00000i 0.286039 0.572078i
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000i 1.31701i −0.752577 0.658505i \(-0.771189\pi\)
0.752577 0.658505i \(-0.228811\pi\)
\(114\) 0 0
\(115\) 7.00000 14.0000i 0.652753 1.30551i
\(116\) −4.00000 −0.371391
\(117\) 15.0000i 1.38675i
\(118\) 4.00000i 0.368230i
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 6.00000i 0.543214i
\(123\) 0 0
\(124\) 2.00000 0.179605
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 7.00000i 0.621150i 0.950549 + 0.310575i \(0.100522\pi\)
−0.950549 + 0.310575i \(0.899478\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 10.0000 + 5.00000i 0.877058 + 0.438529i
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −2.00000 −0.172774
\(135\) 0 0
\(136\) −2.00000 −0.171499
\(137\) 8.00000i 0.683486i −0.939793 0.341743i \(-0.888983\pi\)
0.939793 0.341743i \(-0.111017\pi\)
\(138\) 0 0
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000i 0.503509i
\(143\) 15.0000i 1.25436i
\(144\) 3.00000 0.250000
\(145\) −8.00000 4.00000i −0.664364 0.332182i
\(146\) −16.0000 −1.32417
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) −6.00000 −0.488273 −0.244137 0.969741i \(-0.578505\pi\)
−0.244137 + 0.969741i \(0.578505\pi\)
\(152\) 5.00000i 0.405554i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 4.00000 + 2.00000i 0.321288 + 0.160644i
\(156\) 0 0
\(157\) 9.00000i 0.718278i −0.933284 0.359139i \(-0.883070\pi\)
0.933284 0.359139i \(-0.116930\pi\)
\(158\) 14.0000i 1.11378i
\(159\) 0 0
\(160\) 1.00000 2.00000i 0.0790569 0.158114i
\(161\) 0 0
\(162\) 9.00000i 0.707107i
\(163\) 12.0000i 0.939913i 0.882690 + 0.469956i \(0.155730\pi\)
−0.882690 + 0.469956i \(0.844270\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) 15.0000i 1.16073i 0.814355 + 0.580367i \(0.197091\pi\)
−0.814355 + 0.580367i \(0.802909\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) −4.00000 2.00000i −0.306786 0.153393i
\(171\) 15.0000 1.14708
\(172\) 2.00000i 0.152499i
\(173\) 9.00000i 0.684257i −0.939653 0.342129i \(-0.888852\pi\)
0.939653 0.342129i \(-0.111148\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) 2.00000i 0.149906i
\(179\) −13.0000 −0.971666 −0.485833 0.874052i \(-0.661484\pi\)
−0.485833 + 0.874052i \(0.661484\pi\)
\(180\) 6.00000 + 3.00000i 0.447214 + 0.223607i
\(181\) 26.0000 1.93256 0.966282 0.257485i \(-0.0828937\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 7.00000 0.516047
\(185\) 1.00000 2.00000i 0.0735215 0.147043i
\(186\) 0 0
\(187\) 6.00000i 0.438763i
\(188\) 7.00000i 0.510527i
\(189\) 0 0
\(190\) 5.00000 10.0000i 0.362738 0.725476i
\(191\) −20.0000 −1.44715 −0.723575 0.690246i \(-0.757502\pi\)
−0.723575 + 0.690246i \(0.757502\pi\)
\(192\) 0 0
\(193\) 10.0000i 0.719816i 0.932988 + 0.359908i \(0.117192\pi\)
−0.932988 + 0.359908i \(0.882808\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) 0 0
\(197\) 5.00000i 0.356235i −0.984009 0.178118i \(-0.942999\pi\)
0.984009 0.178118i \(-0.0570008\pi\)
\(198\) 9.00000i 0.639602i
\(199\) −18.0000 −1.27599 −0.637993 0.770042i \(-0.720235\pi\)
−0.637993 + 0.770042i \(0.720235\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −6.00000 3.00000i −0.419058 0.209529i
\(206\) −8.00000 −0.557386
\(207\) 21.0000i 1.45960i
\(208\) 5.00000i 0.346688i
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) −9.00000 −0.619586 −0.309793 0.950804i \(-0.600260\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(212\) 9.00000i 0.618123i
\(213\) 0 0
\(214\) 16.0000 1.09374
\(215\) −2.00000 + 4.00000i −0.136399 + 0.272798i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) 6.00000 + 3.00000i 0.404520 + 0.202260i
\(221\) 10.0000 0.672673
\(222\) 0 0
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) 0 0
\(225\) 9.00000 + 12.0000i 0.600000 + 0.800000i
\(226\) 14.0000 0.931266
\(227\) 6.00000i 0.398234i −0.979976 0.199117i \(-0.936193\pi\)
0.979976 0.199117i \(-0.0638074\pi\)
\(228\) 0 0
\(229\) −16.0000 −1.05731 −0.528655 0.848837i \(-0.677303\pi\)
−0.528655 + 0.848837i \(0.677303\pi\)
\(230\) 14.0000 + 7.00000i 0.923133 + 0.461566i
\(231\) 0 0
\(232\) 4.00000i 0.262613i
\(233\) 8.00000i 0.524097i 0.965055 + 0.262049i \(0.0843981\pi\)
−0.965055 + 0.262049i \(0.915602\pi\)
\(234\) −15.0000 −0.980581
\(235\) −7.00000 + 14.0000i −0.456630 + 0.913259i
\(236\) −4.00000 −0.260378
\(237\) 0 0
\(238\) 0 0
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 0 0
\(241\) −9.00000 −0.579741 −0.289870 0.957066i \(-0.593612\pi\)
−0.289870 + 0.957066i \(0.593612\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) −6.00000 −0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 25.0000i 1.59071i
\(248\) 2.00000i 0.127000i
\(249\) 0 0
\(250\) 11.0000 2.00000i 0.695701 0.126491i
\(251\) 5.00000 0.315597 0.157799 0.987471i \(-0.449560\pi\)
0.157799 + 0.987471i \(0.449560\pi\)
\(252\) 0 0
\(253\) 21.0000i 1.32026i
\(254\) −7.00000 −0.439219
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000i 0.374270i −0.982334 0.187135i \(-0.940080\pi\)
0.982334 0.187135i \(-0.0599201\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −5.00000 + 10.0000i −0.310087 + 0.620174i
\(261\) 12.0000 0.742781
\(262\) 1.00000i 0.0617802i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) −9.00000 + 18.0000i −0.552866 + 1.10573i
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000i 0.122169i
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) 8.00000 0.483298
\(275\) 9.00000 + 12.0000i 0.542720 + 0.723627i
\(276\) 0 0
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) 16.0000i 0.959616i
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 0 0
\(283\) 14.0000i 0.832214i −0.909316 0.416107i \(-0.863394\pi\)
0.909316 0.416107i \(-0.136606\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) −15.0000 −0.886969
\(287\) 0 0
\(288\) 3.00000i 0.176777i
\(289\) 13.0000 0.764706
\(290\) 4.00000 8.00000i 0.234888 0.469776i
\(291\) 0 0
\(292\) 16.0000i 0.936329i
\(293\) 9.00000i 0.525786i 0.964825 + 0.262893i \(0.0846766\pi\)
−0.964825 + 0.262893i \(0.915323\pi\)
\(294\) 0 0
\(295\) −8.00000 4.00000i −0.465778 0.232889i
\(296\) 1.00000 0.0581238
\(297\) 0 0
\(298\) 18.0000i 1.04271i
\(299\) −35.0000 −2.02410
\(300\) 0 0
\(301\) 0 0
\(302\) 6.00000i 0.345261i
\(303\) 0 0
\(304\) 5.00000 0.286770
\(305\) −12.0000 6.00000i −0.687118 0.343559i
\(306\) 6.00000 0.342997
\(307\) 22.0000i 1.25561i −0.778372 0.627803i \(-0.783954\pi\)
0.778372 0.627803i \(-0.216046\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2.00000 + 4.00000i −0.113592 + 0.227185i
\(311\) 6.00000 0.340229 0.170114 0.985424i \(-0.445586\pi\)
0.170114 + 0.985424i \(0.445586\pi\)
\(312\) 0 0
\(313\) 22.0000i 1.24351i 0.783210 + 0.621757i \(0.213581\pi\)
−0.783210 + 0.621757i \(0.786419\pi\)
\(314\) 9.00000 0.507899
\(315\) 0 0
\(316\) 14.0000 0.787562
\(317\) 2.00000i 0.112331i −0.998421 0.0561656i \(-0.982113\pi\)
0.998421 0.0561656i \(-0.0178875\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 2.00000 + 1.00000i 0.111803 + 0.0559017i
\(321\) 0 0
\(322\) 0 0
\(323\) 10.0000i 0.556415i
\(324\) −9.00000 −0.500000
\(325\) −20.0000 + 15.0000i −1.10940 + 0.832050i
\(326\) −12.0000 −0.664619
\(327\) 0 0
\(328\) 3.00000i 0.165647i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 3.00000i 0.164399i
\(334\) −15.0000 −0.820763
\(335\) 2.00000 4.00000i 0.109272 0.218543i
\(336\) 0 0
\(337\) 10.0000i 0.544735i 0.962193 + 0.272367i \(0.0878066\pi\)
−0.962193 + 0.272367i \(0.912193\pi\)
\(338\) 12.0000i 0.652714i
\(339\) 0 0
\(340\) 2.00000 4.00000i 0.108465 0.216930i
\(341\) −6.00000 −0.324918
\(342\) 15.0000i 0.811107i
\(343\) 0 0
\(344\) −2.00000 −0.107833
\(345\) 0 0
\(346\) 9.00000 0.483843
\(347\) 12.0000i 0.644194i −0.946707 0.322097i \(-0.895612\pi\)
0.946707 0.322097i \(-0.104388\pi\)
\(348\) 0 0
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 3.00000i 0.159901i
\(353\) 24.0000i 1.27739i −0.769460 0.638696i \(-0.779474\pi\)
0.769460 0.638696i \(-0.220526\pi\)
\(354\) 0 0
\(355\) 12.0000 + 6.00000i 0.636894 + 0.318447i
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) 13.0000i 0.687071i
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) −3.00000 + 6.00000i −0.158114 + 0.316228i
\(361\) 6.00000 0.315789
\(362\) 26.0000i 1.36653i
\(363\) 0 0
\(364\) 0 0
\(365\) 16.0000 32.0000i 0.837478 1.67496i
\(366\) 0 0
\(367\) 13.0000i 0.678594i 0.940679 + 0.339297i \(0.110189\pi\)
−0.940679 + 0.339297i \(0.889811\pi\)
\(368\) 7.00000i 0.364900i
\(369\) 9.00000 0.468521
\(370\) 2.00000 + 1.00000i 0.103975 + 0.0519875i
\(371\) 0 0
\(372\) 0 0
\(373\) 26.0000i 1.34623i −0.739538 0.673114i \(-0.764956\pi\)
0.739538 0.673114i \(-0.235044\pi\)
\(374\) 6.00000 0.310253
\(375\) 0 0
\(376\) −7.00000 −0.360997
\(377\) 20.0000i 1.03005i
\(378\) 0 0
\(379\) 29.0000 1.48963 0.744815 0.667271i \(-0.232538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(380\) 10.0000 + 5.00000i 0.512989 + 0.256495i
\(381\) 0 0
\(382\) 20.0000i 1.02329i
\(383\) 21.0000i 1.07305i −0.843884 0.536525i \(-0.819737\pi\)
0.843884 0.536525i \(-0.180263\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 6.00000i 0.304997i
\(388\) 12.0000i 0.609208i
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 14.0000 0.708010
\(392\) 0 0
\(393\) 0 0
\(394\) 5.00000 0.251896
\(395\) 28.0000 + 14.0000i 1.40883 + 0.704416i
\(396\) −9.00000 −0.452267
\(397\) 14.0000i 0.702640i −0.936255 0.351320i \(-0.885733\pi\)
0.936255 0.351320i \(-0.114267\pi\)
\(398\) 18.0000i 0.902258i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −15.0000 −0.749064 −0.374532 0.927214i \(-0.622197\pi\)
−0.374532 + 0.927214i \(0.622197\pi\)
\(402\) 0 0
\(403\) 10.0000i 0.498135i
\(404\) 0 0
\(405\) −18.0000 9.00000i −0.894427 0.447214i
\(406\) 0 0
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 3.00000 6.00000i 0.148159 0.296319i
\(411\) 0 0
\(412\) 8.00000i 0.394132i
\(413\) 0 0
\(414\) −21.0000 −1.03209
\(415\) 6.00000 12.0000i 0.294528 0.589057i
\(416\) −5.00000 −0.245145
\(417\) 0 0
\(418\) 15.0000i 0.733674i
\(419\) −35.0000 −1.70986 −0.854931 0.518742i \(-0.826401\pi\)
−0.854931 + 0.518742i \(0.826401\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 9.00000i 0.438113i
\(423\) 21.0000i 1.02105i
\(424\) −9.00000 −0.437079
\(425\) 8.00000 6.00000i 0.388057 0.291043i
\(426\) 0 0
\(427\) 0 0
\(428\) 16.0000i 0.773389i
\(429\) 0 0
\(430\) −4.00000 2.00000i −0.192897 0.0964486i
\(431\) 2.00000 0.0963366 0.0481683 0.998839i \(-0.484662\pi\)
0.0481683 + 0.998839i \(0.484662\pi\)
\(432\) 0 0
\(433\) 28.0000i 1.34559i −0.739827 0.672797i \(-0.765093\pi\)
0.739827 0.672797i \(-0.234907\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 35.0000i 1.67428i
\(438\) 0 0
\(439\) 28.0000 1.33637 0.668184 0.743996i \(-0.267072\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) −3.00000 + 6.00000i −0.143019 + 0.286039i
\(441\) 0 0
\(442\) 10.0000i 0.475651i
\(443\) 30.0000i 1.42534i −0.701498 0.712672i \(-0.747485\pi\)
0.701498 0.712672i \(-0.252515\pi\)
\(444\) 0 0
\(445\) 4.00000 + 2.00000i 0.189618 + 0.0948091i
\(446\) −8.00000 −0.378811
\(447\) 0 0
\(448\) 0 0
\(449\) −5.00000 −0.235965 −0.117982 0.993016i \(-0.537643\pi\)
−0.117982 + 0.993016i \(0.537643\pi\)
\(450\) −12.0000 + 9.00000i −0.565685 + 0.424264i
\(451\) 9.00000 0.423793
\(452\) 14.0000i 0.658505i
\(453\) 0 0
\(454\) 6.00000 0.281594
\(455\) 0 0
\(456\) 0 0
\(457\) 10.0000i 0.467780i −0.972263 0.233890i \(-0.924854\pi\)
0.972263 0.233890i \(-0.0751456\pi\)
\(458\) 16.0000i 0.747631i
\(459\) 0 0
\(460\) −7.00000 + 14.0000i −0.326377 + 0.652753i
\(461\) −32.0000 −1.49039 −0.745194 0.666847i \(-0.767643\pi\)
−0.745194 + 0.666847i \(0.767643\pi\)
\(462\) 0 0
\(463\) 17.0000i 0.790057i 0.918669 + 0.395029i \(0.129265\pi\)
−0.918669 + 0.395029i \(0.870735\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) −8.00000 −0.370593
\(467\) 34.0000i 1.57333i 0.617379 + 0.786666i \(0.288195\pi\)
−0.617379 + 0.786666i \(0.711805\pi\)
\(468\) 15.0000i 0.693375i
\(469\) 0 0
\(470\) −14.0000 7.00000i −0.645772 0.322886i
\(471\) 0 0
\(472\) 4.00000i 0.184115i
\(473\) 6.00000i 0.275880i
\(474\) 0 0
\(475\) 15.0000 + 20.0000i 0.688247 + 0.917663i
\(476\) 0 0
\(477\) 27.0000i 1.23625i
\(478\) 20.0000i 0.914779i
\(479\) −36.0000 −1.64488 −0.822441 0.568850i \(-0.807388\pi\)
−0.822441 + 0.568850i \(0.807388\pi\)
\(480\) 0 0
\(481\) −5.00000 −0.227980
\(482\) 9.00000i 0.409939i
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) −12.0000 + 24.0000i −0.544892 + 1.08978i
\(486\) 0 0
\(487\) 32.0000i 1.45006i −0.688718 0.725029i \(-0.741826\pi\)
0.688718 0.725029i \(-0.258174\pi\)
\(488\) 6.00000i 0.271607i
\(489\) 0 0
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) 8.00000i 0.360302i
\(494\) −25.0000 −1.12480
\(495\) −18.0000 9.00000i −0.809040 0.404520i
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 2.00000 + 11.0000i 0.0894427 + 0.491935i
\(501\) 0 0
\(502\) 5.00000i 0.223161i
\(503\) 40.0000i 1.78351i −0.452517 0.891756i \(-0.649474\pi\)
0.452517 0.891756i \(-0.350526\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −21.0000 −0.933564
\(507\) 0 0
\(508\) 7.00000i 0.310575i
\(509\) 34.0000 1.50702 0.753512 0.657434i \(-0.228358\pi\)
0.753512 + 0.657434i \(0.228358\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) 8.00000 16.0000i 0.352522 0.705044i
\(516\) 0 0
\(517\) 21.0000i 0.923579i
\(518\) 0 0
\(519\) 0 0
\(520\) −10.0000 5.00000i −0.438529 0.219265i
\(521\) −27.0000 −1.18289 −0.591446 0.806345i \(-0.701443\pi\)
−0.591446 + 0.806345i \(0.701443\pi\)
\(522\) 12.0000i 0.525226i
\(523\) 16.0000i 0.699631i −0.936819 0.349816i \(-0.886244\pi\)
0.936819 0.349816i \(-0.113756\pi\)
\(524\) 1.00000 0.0436852
\(525\) 0 0
\(526\) 0 0
\(527\) 4.00000i 0.174243i
\(528\) 0 0
\(529\) −26.0000 −1.13043
\(530\) −18.0000 9.00000i −0.781870 0.390935i
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 15.0000i 0.649722i
\(534\) 0 0
\(535\) −16.0000 + 32.0000i −0.691740 + 1.38348i
\(536\) 2.00000 0.0863868
\(537\) 0 0
\(538\) 10.0000i 0.431131i
\(539\) 0 0
\(540\) 0 0
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 24.0000i 1.03089i
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) 4.00000 + 2.00000i 0.171341 + 0.0856706i
\(546\) 0 0
\(547\) 26.0000i 1.11168i −0.831289 0.555840i \(-0.812397\pi\)
0.831289 0.555840i \(-0.187603\pi\)
\(548\) 8.00000i 0.341743i
\(549\) 18.0000 0.768221
\(550\) −12.0000 + 9.00000i −0.511682 + 0.383761i
\(551\) 20.0000 0.852029
\(552\) 0 0
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 16.0000 0.678551
\(557\) 23.0000i 0.974541i 0.873251 + 0.487271i \(0.162007\pi\)
−0.873251 + 0.487271i \(0.837993\pi\)
\(558\) 6.00000i 0.254000i
\(559\) 10.0000 0.422955
\(560\) 0 0
\(561\) 0 0
\(562\) 9.00000i 0.379642i
\(563\) 2.00000i 0.0842900i −0.999112 0.0421450i \(-0.986581\pi\)
0.999112 0.0421450i \(-0.0134191\pi\)
\(564\) 0 0
\(565\) −14.0000 + 28.0000i −0.588984 + 1.17797i
\(566\) 14.0000 0.588464
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) 15.0000 0.628833 0.314416 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 15.0000i 0.627182i
\(573\) 0 0
\(574\) 0 0
\(575\) −28.0000 + 21.0000i −1.16768 + 0.875761i
\(576\) −3.00000 −0.125000
\(577\) 4.00000i 0.166522i −0.996528 0.0832611i \(-0.973466\pi\)
0.996528 0.0832611i \(-0.0265335\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 0 0
\(580\) 8.00000 + 4.00000i 0.332182 + 0.166091i
\(581\) 0 0
\(582\) 0 0
\(583\) 27.0000i 1.11823i
\(584\) 16.0000 0.662085
\(585\) 15.0000 30.0000i 0.620174 1.24035i
\(586\) −9.00000 −0.371787
\(587\) 34.0000i 1.40333i 0.712507 + 0.701665i \(0.247560\pi\)
−0.712507 + 0.701665i \(0.752440\pi\)
\(588\) 0 0
\(589\) −10.0000 −0.412043
\(590\) 4.00000 8.00000i 0.164677 0.329355i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 6.00000i 0.246390i 0.992382 + 0.123195i \(0.0393141\pi\)
−0.992382 + 0.123195i \(0.960686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) 35.0000i 1.43126i
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 6.00000i 0.244339i
\(604\) 6.00000 0.244137
\(605\) 4.00000 + 2.00000i 0.162623 + 0.0813116i
\(606\) 0 0
\(607\) 13.0000i 0.527654i −0.964570 0.263827i \(-0.915015\pi\)
0.964570 0.263827i \(-0.0849848\pi\)
\(608\) 5.00000i 0.202777i
\(609\) 0 0
\(610\) 6.00000 12.0000i 0.242933 0.485866i
\(611\) 35.0000 1.41595
\(612\) 6.00000i 0.242536i
\(613\) 15.0000i 0.605844i 0.953015 + 0.302922i \(0.0979622\pi\)
−0.953015 + 0.302922i \(0.902038\pi\)
\(614\) 22.0000 0.887848
\(615\) 0 0
\(616\) 0 0
\(617\) 14.0000i 0.563619i 0.959470 + 0.281809i \(0.0909346\pi\)
−0.959470 + 0.281809i \(0.909065\pi\)
\(618\) 0 0
\(619\) −19.0000 −0.763674 −0.381837 0.924230i \(-0.624709\pi\)
−0.381837 + 0.924230i \(0.624709\pi\)
\(620\) −4.00000 2.00000i −0.160644 0.0803219i
\(621\) 0 0
\(622\) 6.00000i 0.240578i
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −22.0000 −0.879297
\(627\) 0 0
\(628\) 9.00000i 0.359139i
\(629\) 2.00000 0.0797452
\(630\) 0 0
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) 14.0000i 0.556890i
\(633\) 0 0
\(634\) 2.00000 0.0794301
\(635\) 7.00000 14.0000i 0.277787 0.555573i
\(636\) 0 0
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) −18.0000 −0.712069
\(640\) −1.00000 + 2.00000i −0.0395285 + 0.0790569i
\(641\) −5.00000 −0.197488 −0.0987441 0.995113i \(-0.531483\pi\)
−0.0987441 + 0.995113i \(0.531483\pi\)
\(642\) 0 0
\(643\) 14.0000i 0.552106i 0.961142 + 0.276053i \(0.0890266\pi\)
−0.961142 + 0.276053i \(0.910973\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 10.0000 0.393445
\(647\) 27.0000i 1.06148i −0.847535 0.530740i \(-0.821914\pi\)
0.847535 0.530740i \(-0.178086\pi\)
\(648\) 9.00000i 0.353553i
\(649\) 12.0000 0.471041
\(650\) −15.0000 20.0000i −0.588348 0.784465i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) 3.00000i 0.117399i −0.998276 0.0586995i \(-0.981305\pi\)
0.998276 0.0586995i \(-0.0186954\pi\)
\(654\) 0 0
\(655\) 2.00000 + 1.00000i 0.0781465 + 0.0390732i
\(656\) 3.00000 0.117130
\(657\) 48.0000i 1.87266i
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) 16.0000 0.622328 0.311164 0.950356i \(-0.399281\pi\)
0.311164 + 0.950356i \(0.399281\pi\)
\(662\) 5.00000i 0.194331i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −3.00000 −0.116248
\(667\) 28.0000i 1.08416i
\(668\) 15.0000i 0.580367i
\(669\) 0 0
\(670\) 4.00000 + 2.00000i 0.154533 + 0.0772667i
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 32.0000i 1.23351i −0.787155 0.616755i \(-0.788447\pi\)
0.787155 0.616755i \(-0.211553\pi\)
\(674\) −10.0000 −0.385186
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 17.0000i 0.653363i −0.945134 0.326682i \(-0.894070\pi\)
0.945134 0.326682i \(-0.105930\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 4.00000 + 2.00000i 0.153393 + 0.0766965i
\(681\) 0 0
\(682\) 6.00000i 0.229752i
\(683\) 44.0000i 1.68361i 0.539779 + 0.841807i \(0.318508\pi\)
−0.539779 + 0.841807i \(0.681492\pi\)
\(684\) −15.0000 −0.573539
\(685\) −8.00000 + 16.0000i −0.305664 + 0.611329i
\(686\) 0 0
\(687\) 0 0
\(688\) 2.00000i 0.0762493i
\(689\) 45.0000 1.71436
\(690\) 0 0
\(691\) −44.0000 −1.67384 −0.836919 0.547326i \(-0.815646\pi\)
−0.836919 + 0.547326i \(0.815646\pi\)
\(692\) 9.00000i 0.342129i
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 32.0000 + 16.0000i 1.21383 + 0.606915i
\(696\) 0 0
\(697\) 6.00000i 0.227266i
\(698\) 12.0000i 0.454207i
\(699\) 0 0
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) 5.00000i 0.188579i
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) 0 0
\(709\) −12.0000 −0.450669 −0.225335 0.974281i \(-0.572348\pi\)
−0.225335 + 0.974281i \(0.572348\pi\)
\(710\) −6.00000 + 12.0000i −0.225176 + 0.450352i
\(711\) −42.0000 −1.57512
\(712\) 2.00000i 0.0749532i
\(713\) 14.0000i 0.524304i
\(714\) 0 0
\(715\) 15.0000 30.0000i 0.560968 1.12194i
\(716\) 13.0000 0.485833
\(717\) 0 0
\(718\) 16.0000i 0.597115i
\(719\) −26.0000 −0.969636 −0.484818 0.874615i \(-0.661114\pi\)
−0.484818 + 0.874615i \(0.661114\pi\)
\(720\) −6.00000 3.00000i −0.223607 0.111803i
\(721\) 0 0
\(722\) 6.00000i 0.223297i
\(723\) 0 0
\(724\) −26.0000 −0.966282
\(725\) 12.0000 + 16.0000i 0.445669 + 0.594225i
\(726\) 0 0
\(727\) 29.0000i 1.07555i −0.843088 0.537775i \(-0.819265\pi\)
0.843088 0.537775i \(-0.180735\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 32.0000 + 16.0000i 1.18437 + 0.592187i
\(731\) −4.00000 −0.147945
\(732\) 0 0
\(733\) 41.0000i 1.51437i −0.653201 0.757185i \(-0.726574\pi\)
0.653201 0.757185i \(-0.273426\pi\)
\(734\) −13.0000 −0.479839
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) 6.00000i 0.221013i
\(738\) 9.00000i 0.331295i
\(739\) 29.0000 1.06678 0.533391 0.845869i \(-0.320917\pi\)
0.533391 + 0.845869i \(0.320917\pi\)
\(740\) −1.00000 + 2.00000i −0.0367607 + 0.0735215i
\(741\) 0 0
\(742\) 0 0
\(743\) 21.0000i 0.770415i 0.922830 + 0.385208i \(0.125870\pi\)
−0.922830 + 0.385208i \(0.874130\pi\)
\(744\) 0 0
\(745\) −36.0000 18.0000i −1.31894 0.659469i
\(746\) 26.0000 0.951928
\(747\) 18.0000i 0.658586i
\(748\) 6.00000i 0.219382i
\(749\) 0 0
\(750\) 0 0
\(751\) 28.0000 1.02173 0.510867 0.859660i \(-0.329324\pi\)
0.510867 + 0.859660i \(0.329324\pi\)
\(752\) 7.00000i 0.255264i
\(753\) 0 0
\(754\) −20.0000 −0.728357
\(755\) 12.0000 + 6.00000i 0.436725 + 0.218362i
\(756\) 0 0
\(757\) 42.0000i 1.52652i 0.646094 + 0.763258i \(0.276401\pi\)
−0.646094 + 0.763258i \(0.723599\pi\)
\(758\) 29.0000i 1.05333i
\(759\) 0 0
\(760\) −5.00000 + 10.0000i −0.181369 + 0.362738i
\(761\) 1.00000 0.0362500 0.0181250 0.999836i \(-0.494230\pi\)
0.0181250 + 0.999836i \(0.494230\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 20.0000 0.723575
\(765\) −6.00000 + 12.0000i −0.216930 + 0.433861i
\(766\) 21.0000 0.758761
\(767\) 20.0000i 0.722158i
\(768\) 0 0
\(769\) 29.0000 1.04577 0.522883 0.852404i \(-0.324856\pi\)
0.522883 + 0.852404i \(0.324856\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.0000i 0.359908i
\(773\) 45.0000i 1.61854i −0.587439 0.809269i \(-0.699864\pi\)
0.587439 0.809269i \(-0.300136\pi\)
\(774\) 6.00000 0.215666
\(775\) −6.00000 8.00000i −0.215526 0.287368i
\(776\) −12.0000 −0.430775
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) 15.0000 0.537431
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 14.0000i 0.500639i
\(783\) 0 0
\(784\) 0 0
\(785\) −9.00000 + 18.0000i −0.321224 + 0.642448i
\(786\) 0 0
\(787\) 18.0000i 0.641631i 0.947142 + 0.320815i \(0.103957\pi\)
−0.947142 + 0.320815i \(0.896043\pi\)
\(788\) 5.00000i 0.178118i
\(789\) 0 0
\(790\) −14.0000 + 28.0000i −0.498098 + 0.996195i
\(791\) 0 0
\(792\) 9.00000i 0.319801i
\(793\) 30.0000i 1.06533i
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) 18.0000 0.637993
\(797\) 2.00000i 0.0708436i −0.999372 0.0354218i \(-0.