Properties

Label 90.6.c.b.19.1
Level $90$
Weight $6$
Character 90.19
Analytic conductor $14.435$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 90.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.4345437832\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 90.19
Dual form 90.6.c.b.19.2

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000i q^{2} -16.0000 q^{4} +(55.0000 - 10.0000i) q^{5} -4.00000i q^{7} +64.0000i q^{8} +O(q^{10})\) \(q-4.00000i q^{2} -16.0000 q^{4} +(55.0000 - 10.0000i) q^{5} -4.00000i q^{7} +64.0000i q^{8} +(-40.0000 - 220.000i) q^{10} +500.000 q^{11} +288.000i q^{13} -16.0000 q^{14} +256.000 q^{16} -1516.00i q^{17} +1344.00 q^{19} +(-880.000 + 160.000i) q^{20} -2000.00i q^{22} -4100.00i q^{23} +(2925.00 - 1100.00i) q^{25} +1152.00 q^{26} +64.0000i q^{28} -2646.00 q^{29} -5612.00 q^{31} -1024.00i q^{32} -6064.00 q^{34} +(-40.0000 - 220.000i) q^{35} -7288.00i q^{37} -5376.00i q^{38} +(640.000 + 3520.00i) q^{40} +18986.0 q^{41} +2404.00i q^{43} -8000.00 q^{44} -16400.0 q^{46} -8900.00i q^{47} +16791.0 q^{49} +(-4400.00 - 11700.0i) q^{50} -4608.00i q^{52} +39804.0i q^{53} +(27500.0 - 5000.00i) q^{55} +256.000 q^{56} +10584.0i q^{58} -28300.0 q^{59} +18290.0 q^{61} +22448.0i q^{62} -4096.00 q^{64} +(2880.00 + 15840.0i) q^{65} +65956.0i q^{67} +24256.0i q^{68} +(-880.000 + 160.000i) q^{70} +28800.0 q^{71} +30808.0i q^{73} -29152.0 q^{74} -21504.0 q^{76} -2000.00i q^{77} -60228.0 q^{79} +(14080.0 - 2560.00i) q^{80} -75944.0i q^{82} -2468.00i q^{83} +(-15160.0 - 83380.0i) q^{85} +9616.00 q^{86} +32000.0i q^{88} +22678.0 q^{89} +1152.00 q^{91} +65600.0i q^{92} -35600.0 q^{94} +(73920.0 - 13440.0i) q^{95} -36968.0i q^{97} -67164.0i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 32 q^{4} + 110 q^{5} + O(q^{10}) \) \( 2 q - 32 q^{4} + 110 q^{5} - 80 q^{10} + 1000 q^{11} - 32 q^{14} + 512 q^{16} + 2688 q^{19} - 1760 q^{20} + 5850 q^{25} + 2304 q^{26} - 5292 q^{29} - 11224 q^{31} - 12128 q^{34} - 80 q^{35} + 1280 q^{40} + 37972 q^{41} - 16000 q^{44} - 32800 q^{46} + 33582 q^{49} - 8800 q^{50} + 55000 q^{55} + 512 q^{56} - 56600 q^{59} + 36580 q^{61} - 8192 q^{64} + 5760 q^{65} - 1760 q^{70} + 57600 q^{71} - 58304 q^{74} - 43008 q^{76} - 120456 q^{79} + 28160 q^{80} - 30320 q^{85} + 19232 q^{86} + 45356 q^{89} + 2304 q^{91} - 71200 q^{94} + 147840 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) 0 0
\(4\) −16.0000 −0.500000
\(5\) 55.0000 10.0000i 0.983870 0.178885i
\(6\) 0 0
\(7\) 4.00000i 0.0308542i −0.999881 0.0154271i \(-0.995089\pi\)
0.999881 0.0154271i \(-0.00491080\pi\)
\(8\) 64.0000i 0.353553i
\(9\) 0 0
\(10\) −40.0000 220.000i −0.126491 0.695701i
\(11\) 500.000 1.24591 0.622957 0.782256i \(-0.285931\pi\)
0.622957 + 0.782256i \(0.285931\pi\)
\(12\) 0 0
\(13\) 288.000i 0.472644i 0.971675 + 0.236322i \(0.0759420\pi\)
−0.971675 + 0.236322i \(0.924058\pi\)
\(14\) −16.0000 −0.0218172
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) 1516.00i 1.27226i −0.771581 0.636132i \(-0.780534\pi\)
0.771581 0.636132i \(-0.219466\pi\)
\(18\) 0 0
\(19\) 1344.00 0.854113 0.427056 0.904225i \(-0.359551\pi\)
0.427056 + 0.904225i \(0.359551\pi\)
\(20\) −880.000 + 160.000i −0.491935 + 0.0894427i
\(21\) 0 0
\(22\) 2000.00i 0.880995i
\(23\) 4100.00i 1.61609i −0.589124 0.808043i \(-0.700527\pi\)
0.589124 0.808043i \(-0.299473\pi\)
\(24\) 0 0
\(25\) 2925.00 1100.00i 0.936000 0.352000i
\(26\) 1152.00 0.334210
\(27\) 0 0
\(28\) 64.0000i 0.0154271i
\(29\) −2646.00 −0.584245 −0.292122 0.956381i \(-0.594361\pi\)
−0.292122 + 0.956381i \(0.594361\pi\)
\(30\) 0 0
\(31\) −5612.00 −1.04885 −0.524425 0.851457i \(-0.675720\pi\)
−0.524425 + 0.851457i \(0.675720\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 0 0
\(34\) −6064.00 −0.899626
\(35\) −40.0000 220.000i −0.00551937 0.0303566i
\(36\) 0 0
\(37\) 7288.00i 0.875193i −0.899171 0.437597i \(-0.855830\pi\)
0.899171 0.437597i \(-0.144170\pi\)
\(38\) 5376.00i 0.603949i
\(39\) 0 0
\(40\) 640.000 + 3520.00i 0.0632456 + 0.347851i
\(41\) 18986.0 1.76390 0.881950 0.471343i \(-0.156231\pi\)
0.881950 + 0.471343i \(0.156231\pi\)
\(42\) 0 0
\(43\) 2404.00i 0.198273i 0.995074 + 0.0991364i \(0.0316080\pi\)
−0.995074 + 0.0991364i \(0.968392\pi\)
\(44\) −8000.00 −0.622957
\(45\) 0 0
\(46\) −16400.0 −1.14274
\(47\) 8900.00i 0.587686i −0.955854 0.293843i \(-0.905066\pi\)
0.955854 0.293843i \(-0.0949343\pi\)
\(48\) 0 0
\(49\) 16791.0 0.999048
\(50\) −4400.00 11700.0i −0.248902 0.661852i
\(51\) 0 0
\(52\) 4608.00i 0.236322i
\(53\) 39804.0i 1.94642i 0.229913 + 0.973211i \(0.426156\pi\)
−0.229913 + 0.973211i \(0.573844\pi\)
\(54\) 0 0
\(55\) 27500.0 5000.00i 1.22582 0.222876i
\(56\) 256.000 0.0109086
\(57\) 0 0
\(58\) 10584.0i 0.413123i
\(59\) −28300.0 −1.05842 −0.529208 0.848492i \(-0.677511\pi\)
−0.529208 + 0.848492i \(0.677511\pi\)
\(60\) 0 0
\(61\) 18290.0 0.629345 0.314673 0.949200i \(-0.398105\pi\)
0.314673 + 0.949200i \(0.398105\pi\)
\(62\) 22448.0i 0.741649i
\(63\) 0 0
\(64\) −4096.00 −0.125000
\(65\) 2880.00 + 15840.0i 0.0845491 + 0.465020i
\(66\) 0 0
\(67\) 65956.0i 1.79501i 0.441002 + 0.897506i \(0.354623\pi\)
−0.441002 + 0.897506i \(0.645377\pi\)
\(68\) 24256.0i 0.636132i
\(69\) 0 0
\(70\) −880.000 + 160.000i −0.0214653 + 0.00390279i
\(71\) 28800.0 0.678026 0.339013 0.940782i \(-0.389907\pi\)
0.339013 + 0.940782i \(0.389907\pi\)
\(72\) 0 0
\(73\) 30808.0i 0.676638i 0.941031 + 0.338319i \(0.109858\pi\)
−0.941031 + 0.338319i \(0.890142\pi\)
\(74\) −29152.0 −0.618855
\(75\) 0 0
\(76\) −21504.0 −0.427056
\(77\) 2000.00i 0.0384418i
\(78\) 0 0
\(79\) −60228.0 −1.08575 −0.542876 0.839813i \(-0.682665\pi\)
−0.542876 + 0.839813i \(0.682665\pi\)
\(80\) 14080.0 2560.00i 0.245967 0.0447214i
\(81\) 0 0
\(82\) 75944.0i 1.24727i
\(83\) 2468.00i 0.0393233i −0.999807 0.0196616i \(-0.993741\pi\)
0.999807 0.0196616i \(-0.00625890\pi\)
\(84\) 0 0
\(85\) −15160.0 83380.0i −0.227589 1.25174i
\(86\) 9616.00 0.140200
\(87\) 0 0
\(88\) 32000.0i 0.440497i
\(89\) 22678.0 0.303480 0.151740 0.988420i \(-0.451512\pi\)
0.151740 + 0.988420i \(0.451512\pi\)
\(90\) 0 0
\(91\) 1152.00 0.0145831
\(92\) 65600.0i 0.808043i
\(93\) 0 0
\(94\) −35600.0 −0.415557
\(95\) 73920.0 13440.0i 0.840336 0.152788i
\(96\) 0 0
\(97\) 36968.0i 0.398930i −0.979905 0.199465i \(-0.936080\pi\)
0.979905 0.199465i \(-0.0639204\pi\)
\(98\) 67164.0i 0.706434i
\(99\) 0 0
\(100\) −46800.0 + 17600.0i −0.468000 + 0.176000i
\(101\) −167918. −1.63792 −0.818962 0.573848i \(-0.805450\pi\)
−0.818962 + 0.573848i \(0.805450\pi\)
\(102\) 0 0
\(103\) 154364.i 1.43368i 0.697236 + 0.716841i \(0.254413\pi\)
−0.697236 + 0.716841i \(0.745587\pi\)
\(104\) −18432.0 −0.167105
\(105\) 0 0
\(106\) 159216. 1.37633
\(107\) 136788.i 1.15502i −0.816385 0.577509i \(-0.804025\pi\)
0.816385 0.577509i \(-0.195975\pi\)
\(108\) 0 0
\(109\) 53810.0 0.433807 0.216904 0.976193i \(-0.430404\pi\)
0.216904 + 0.976193i \(0.430404\pi\)
\(110\) −20000.0 110000.i −0.157597 0.866784i
\(111\) 0 0
\(112\) 1024.00i 0.00771356i
\(113\) 82692.0i 0.609211i 0.952479 + 0.304605i \(0.0985245\pi\)
−0.952479 + 0.304605i \(0.901475\pi\)
\(114\) 0 0
\(115\) −41000.0 225500.i −0.289094 1.59002i
\(116\) 42336.0 0.292122
\(117\) 0 0
\(118\) 113200.i 0.748413i
\(119\) −6064.00 −0.0392547
\(120\) 0 0
\(121\) 88949.0 0.552303
\(122\) 73160.0i 0.445014i
\(123\) 0 0
\(124\) 89792.0 0.524425
\(125\) 149875. 89750.0i 0.857935 0.513759i
\(126\) 0 0
\(127\) 211780.i 1.16513i −0.812783 0.582567i \(-0.802048\pi\)
0.812783 0.582567i \(-0.197952\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) 0 0
\(130\) 63360.0 11520.0i 0.328819 0.0597853i
\(131\) −169500. −0.862962 −0.431481 0.902122i \(-0.642009\pi\)
−0.431481 + 0.902122i \(0.642009\pi\)
\(132\) 0 0
\(133\) 5376.00i 0.0263530i
\(134\) 263824. 1.26927
\(135\) 0 0
\(136\) 97024.0 0.449813
\(137\) 252036.i 1.14726i −0.819115 0.573629i \(-0.805535\pi\)
0.819115 0.573629i \(-0.194465\pi\)
\(138\) 0 0
\(139\) −192016. −0.842947 −0.421474 0.906841i \(-0.638487\pi\)
−0.421474 + 0.906841i \(0.638487\pi\)
\(140\) 640.000 + 3520.00i 0.00275969 + 0.0151783i
\(141\) 0 0
\(142\) 115200.i 0.479437i
\(143\) 144000.i 0.588874i
\(144\) 0 0
\(145\) −145530. + 26460.0i −0.574821 + 0.104513i
\(146\) 123232. 0.478455
\(147\) 0 0
\(148\) 116608.i 0.437597i
\(149\) 235694. 0.869727 0.434863 0.900496i \(-0.356797\pi\)
0.434863 + 0.900496i \(0.356797\pi\)
\(150\) 0 0
\(151\) −371492. −1.32589 −0.662944 0.748669i \(-0.730693\pi\)
−0.662944 + 0.748669i \(0.730693\pi\)
\(152\) 86016.0i 0.301975i
\(153\) 0 0
\(154\) −8000.00 −0.0271824
\(155\) −308660. + 56120.0i −1.03193 + 0.187624i
\(156\) 0 0
\(157\) 264952.i 0.857863i 0.903337 + 0.428932i \(0.141110\pi\)
−0.903337 + 0.428932i \(0.858890\pi\)
\(158\) 240912.i 0.767743i
\(159\) 0 0
\(160\) −10240.0 56320.0i −0.0316228 0.173925i
\(161\) −16400.0 −0.0498631
\(162\) 0 0
\(163\) 403124.i 1.18842i 0.804310 + 0.594210i \(0.202535\pi\)
−0.804310 + 0.594210i \(0.797465\pi\)
\(164\) −303776. −0.881950
\(165\) 0 0
\(166\) −9872.00 −0.0278058
\(167\) 261900.i 0.726682i 0.931656 + 0.363341i \(0.118364\pi\)
−0.931656 + 0.363341i \(0.881636\pi\)
\(168\) 0 0
\(169\) 288349. 0.776608
\(170\) −333520. + 60640.0i −0.885115 + 0.160930i
\(171\) 0 0
\(172\) 38464.0i 0.0991364i
\(173\) 326228.i 0.828716i 0.910114 + 0.414358i \(0.135994\pi\)
−0.910114 + 0.414358i \(0.864006\pi\)
\(174\) 0 0
\(175\) −4400.00 11700.0i −0.0108607 0.0288796i
\(176\) 128000. 0.311479
\(177\) 0 0
\(178\) 90712.0i 0.214593i
\(179\) −109516. −0.255473 −0.127736 0.991808i \(-0.540771\pi\)
−0.127736 + 0.991808i \(0.540771\pi\)
\(180\) 0 0
\(181\) −53146.0 −0.120580 −0.0602898 0.998181i \(-0.519202\pi\)
−0.0602898 + 0.998181i \(0.519202\pi\)
\(182\) 4608.00i 0.0103118i
\(183\) 0 0
\(184\) 262400. 0.571372
\(185\) −72880.0 400840.i −0.156559 0.861076i
\(186\) 0 0
\(187\) 758000.i 1.58513i
\(188\) 142400.i 0.293843i
\(189\) 0 0
\(190\) −53760.0 295680.i −0.108038 0.594207i
\(191\) −232056. −0.460267 −0.230133 0.973159i \(-0.573916\pi\)
−0.230133 + 0.973159i \(0.573916\pi\)
\(192\) 0 0
\(193\) 1.03067e6i 1.99172i 0.0909274 + 0.995858i \(0.471017\pi\)
−0.0909274 + 0.995858i \(0.528983\pi\)
\(194\) −147872. −0.282086
\(195\) 0 0
\(196\) −268656. −0.499524
\(197\) 522796.i 0.959769i 0.877332 + 0.479884i \(0.159321\pi\)
−0.877332 + 0.479884i \(0.840679\pi\)
\(198\) 0 0
\(199\) 215292. 0.385385 0.192693 0.981259i \(-0.438278\pi\)
0.192693 + 0.981259i \(0.438278\pi\)
\(200\) 70400.0 + 187200.i 0.124451 + 0.330926i
\(201\) 0 0
\(202\) 671672.i 1.15819i
\(203\) 10584.0i 0.0180264i
\(204\) 0 0
\(205\) 1.04423e6 189860.i 1.73545 0.315536i
\(206\) 617456. 1.01377
\(207\) 0 0
\(208\) 73728.0i 0.118161i
\(209\) 672000. 1.06415
\(210\) 0 0
\(211\) −1.03008e6 −1.59281 −0.796407 0.604762i \(-0.793268\pi\)
−0.796407 + 0.604762i \(0.793268\pi\)
\(212\) 636864.i 0.973211i
\(213\) 0 0
\(214\) −547152. −0.816721
\(215\) 24040.0 + 132220.i 0.0354681 + 0.195075i
\(216\) 0 0
\(217\) 22448.0i 0.0323615i
\(218\) 215240.i 0.306748i
\(219\) 0 0
\(220\) −440000. + 80000.0i −0.612909 + 0.111438i
\(221\) 436608. 0.601327
\(222\) 0 0
\(223\) 456020.i 0.614075i −0.951697 0.307038i \(-0.900662\pi\)
0.951697 0.307038i \(-0.0993378\pi\)
\(224\) −4096.00 −0.00545431
\(225\) 0 0
\(226\) 330768. 0.430777
\(227\) 434252.i 0.559342i 0.960096 + 0.279671i \(0.0902253\pi\)
−0.960096 + 0.279671i \(0.909775\pi\)
\(228\) 0 0
\(229\) 722710. 0.910700 0.455350 0.890313i \(-0.349514\pi\)
0.455350 + 0.890313i \(0.349514\pi\)
\(230\) −902000. + 164000.i −1.12431 + 0.204420i
\(231\) 0 0
\(232\) 169344.i 0.206562i
\(233\) 565348.i 0.682223i −0.940023 0.341111i \(-0.889197\pi\)
0.940023 0.341111i \(-0.110803\pi\)
\(234\) 0 0
\(235\) −89000.0 489500.i −0.105128 0.578207i
\(236\) 452800. 0.529208
\(237\) 0 0
\(238\) 24256.0i 0.0277573i
\(239\) 324904. 0.367926 0.183963 0.982933i \(-0.441107\pi\)
0.183963 + 0.982933i \(0.441107\pi\)
\(240\) 0 0
\(241\) 915262. 1.01509 0.507543 0.861626i \(-0.330554\pi\)
0.507543 + 0.861626i \(0.330554\pi\)
\(242\) 355796.i 0.390537i
\(243\) 0 0
\(244\) −292640. −0.314673
\(245\) 923505. 167910.i 0.982933 0.178715i
\(246\) 0 0
\(247\) 387072.i 0.403691i
\(248\) 359168.i 0.370825i
\(249\) 0 0
\(250\) −359000. 599500.i −0.363282 0.606651i
\(251\) −1.36708e6 −1.36965 −0.684823 0.728709i \(-0.740121\pi\)
−0.684823 + 0.728709i \(0.740121\pi\)
\(252\) 0 0
\(253\) 2.05000e6i 2.01350i
\(254\) −847120. −0.823874
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) 892932.i 0.843307i −0.906757 0.421653i \(-0.861450\pi\)
0.906757 0.421653i \(-0.138550\pi\)
\(258\) 0 0
\(259\) −29152.0 −0.0270034
\(260\) −46080.0 253440.i −0.0422746 0.232510i
\(261\) 0 0
\(262\) 678000.i 0.610206i
\(263\) 1.86650e6i 1.66394i −0.554818 0.831972i \(-0.687212\pi\)
0.554818 0.831972i \(-0.312788\pi\)
\(264\) 0 0
\(265\) 398040. + 2.18922e6i 0.348187 + 1.91503i
\(266\) −21504.0 −0.0186344
\(267\) 0 0
\(268\) 1.05530e6i 0.897506i
\(269\) −1.37227e6 −1.15627 −0.578133 0.815943i \(-0.696218\pi\)
−0.578133 + 0.815943i \(0.696218\pi\)
\(270\) 0 0
\(271\) 458644. 0.379361 0.189680 0.981846i \(-0.439255\pi\)
0.189680 + 0.981846i \(0.439255\pi\)
\(272\) 388096.i 0.318066i
\(273\) 0 0
\(274\) −1.00814e6 −0.811234
\(275\) 1.46250e6 550000.i 1.16618 0.438562i
\(276\) 0 0
\(277\) 985408.i 0.771643i −0.922573 0.385822i \(-0.873918\pi\)
0.922573 0.385822i \(-0.126082\pi\)
\(278\) 768064.i 0.596054i
\(279\) 0 0
\(280\) 14080.0 2560.00i 0.0107327 0.00195139i
\(281\) −165798. −0.125260 −0.0626302 0.998037i \(-0.519949\pi\)
−0.0626302 + 0.998037i \(0.519949\pi\)
\(282\) 0 0
\(283\) 1.66471e6i 1.23558i 0.786342 + 0.617792i \(0.211972\pi\)
−0.786342 + 0.617792i \(0.788028\pi\)
\(284\) −460800. −0.339013
\(285\) 0 0
\(286\) 576000. 0.416397
\(287\) 75944.0i 0.0544238i
\(288\) 0 0
\(289\) −878399. −0.618653
\(290\) 105840. + 582120.i 0.0739018 + 0.406460i
\(291\) 0 0
\(292\) 492928.i 0.338319i
\(293\) 2.55104e6i 1.73600i 0.496567 + 0.867998i \(0.334594\pi\)
−0.496567 + 0.867998i \(0.665406\pi\)
\(294\) 0 0
\(295\) −1.55650e6 + 283000.i −1.04134 + 0.189335i
\(296\) 466432. 0.309428
\(297\) 0 0
\(298\) 942776.i 0.614990i
\(299\) 1.18080e6 0.763833
\(300\) 0 0
\(301\) 9616.00 0.00611756
\(302\) 1.48597e6i 0.937545i
\(303\) 0 0
\(304\) 344064. 0.213528
\(305\) 1.00595e6 182900.i 0.619194 0.112581i
\(306\) 0 0
\(307\) 736020.i 0.445701i 0.974853 + 0.222851i \(0.0715362\pi\)
−0.974853 + 0.222851i \(0.928464\pi\)
\(308\) 32000.0i 0.0192209i
\(309\) 0 0
\(310\) 224480. + 1.23464e6i 0.132670 + 0.729686i
\(311\) −1.71660e6 −1.00639 −0.503197 0.864172i \(-0.667843\pi\)
−0.503197 + 0.864172i \(0.667843\pi\)
\(312\) 0 0
\(313\) 2.83851e6i 1.63768i −0.574020 0.818842i \(-0.694617\pi\)
0.574020 0.818842i \(-0.305383\pi\)
\(314\) 1.05981e6 0.606601
\(315\) 0 0
\(316\) 963648. 0.542876
\(317\) 1.27605e6i 0.713215i 0.934254 + 0.356607i \(0.116067\pi\)
−0.934254 + 0.356607i \(0.883933\pi\)
\(318\) 0 0
\(319\) −1.32300e6 −0.727919
\(320\) −225280. + 40960.0i −0.122984 + 0.0223607i
\(321\) 0 0
\(322\) 65600.0i 0.0352585i
\(323\) 2.03750e6i 1.08666i
\(324\) 0 0
\(325\) 316800. + 842400.i 0.166371 + 0.442395i
\(326\) 1.61250e6 0.840339
\(327\) 0 0
\(328\) 1.21510e6i 0.623633i
\(329\) −35600.0 −0.0181326
\(330\) 0 0
\(331\) 443992. 0.222744 0.111372 0.993779i \(-0.464476\pi\)
0.111372 + 0.993779i \(0.464476\pi\)
\(332\) 39488.0i 0.0196616i
\(333\) 0 0
\(334\) 1.04760e6 0.513842
\(335\) 659560. + 3.62758e6i 0.321101 + 1.76606i
\(336\) 0 0
\(337\) 2.71326e6i 1.30142i 0.759328 + 0.650708i \(0.225528\pi\)
−0.759328 + 0.650708i \(0.774472\pi\)
\(338\) 1.15340e6i 0.549145i
\(339\) 0 0
\(340\) 242560. + 1.33408e6i 0.113795 + 0.625871i
\(341\) −2.80600e6 −1.30678
\(342\) 0 0
\(343\) 134392.i 0.0616791i
\(344\) −153856. −0.0701001
\(345\) 0 0
\(346\) 1.30491e6 0.585991
\(347\) 1.31051e6i 0.584273i 0.956377 + 0.292137i \(0.0943662\pi\)
−0.956377 + 0.292137i \(0.905634\pi\)
\(348\) 0 0
\(349\) 298910. 0.131364 0.0656821 0.997841i \(-0.479078\pi\)
0.0656821 + 0.997841i \(0.479078\pi\)
\(350\) −46800.0 + 17600.0i −0.0204209 + 0.00767967i
\(351\) 0 0
\(352\) 512000.i 0.220249i
\(353\) 737996.i 0.315223i 0.987501 + 0.157611i \(0.0503793\pi\)
−0.987501 + 0.157611i \(0.949621\pi\)
\(354\) 0 0
\(355\) 1.58400e6 288000.i 0.667090 0.121289i
\(356\) −362848. −0.151740
\(357\) 0 0
\(358\) 438064.i 0.180647i
\(359\) −2.34074e6 −0.958557 −0.479278 0.877663i \(-0.659102\pi\)
−0.479278 + 0.877663i \(0.659102\pi\)
\(360\) 0 0
\(361\) −669763. −0.270491
\(362\) 212584.i 0.0852627i
\(363\) 0 0
\(364\) −18432.0 −0.00729154
\(365\) 308080. + 1.69444e6i 0.121041 + 0.665724i
\(366\) 0 0
\(367\) 127292.i 0.0493328i 0.999696 + 0.0246664i \(0.00785236\pi\)
−0.999696 + 0.0246664i \(0.992148\pi\)
\(368\) 1.04960e6i 0.404021i
\(369\) 0 0
\(370\) −1.60336e6 + 291520.i −0.608873 + 0.110704i
\(371\) 159216. 0.0600554
\(372\) 0 0
\(373\) 4.03870e6i 1.50303i −0.659713 0.751517i \(-0.729322\pi\)
0.659713 0.751517i \(-0.270678\pi\)
\(374\) −3.03200e6 −1.12086
\(375\) 0 0
\(376\) 569600. 0.207778
\(377\) 762048.i 0.276140i
\(378\) 0 0
\(379\) −1.01214e6 −0.361944 −0.180972 0.983488i \(-0.557924\pi\)
−0.180972 + 0.983488i \(0.557924\pi\)
\(380\) −1.18272e6 + 215040.i −0.420168 + 0.0763942i
\(381\) 0 0
\(382\) 928224.i 0.325458i
\(383\) 2.37610e6i 0.827690i −0.910347 0.413845i \(-0.864186\pi\)
0.910347 0.413845i \(-0.135814\pi\)
\(384\) 0 0
\(385\) −20000.0 110000.i −0.00687667 0.0378217i
\(386\) 4.12269e6 1.40836
\(387\) 0 0
\(388\) 591488.i 0.199465i
\(389\) 1.42497e6 0.477456 0.238728 0.971087i \(-0.423270\pi\)
0.238728 + 0.971087i \(0.423270\pi\)
\(390\) 0 0
\(391\) −6.21560e6 −2.05609
\(392\) 1.07462e6i 0.353217i
\(393\) 0 0
\(394\) 2.09118e6 0.678659
\(395\) −3.31254e6 + 602280.i −1.06824 + 0.194225i
\(396\) 0 0
\(397\) 1.69345e6i 0.539257i 0.962964 + 0.269628i \(0.0869009\pi\)
−0.962964 + 0.269628i \(0.913099\pi\)
\(398\) 861168.i 0.272509i
\(399\) 0 0
\(400\) 748800. 281600.i 0.234000 0.0880000i
\(401\) 2.84501e6 0.883532 0.441766 0.897130i \(-0.354352\pi\)
0.441766 + 0.897130i \(0.354352\pi\)
\(402\) 0 0
\(403\) 1.61626e6i 0.495733i
\(404\) 2.68669e6 0.818962
\(405\) 0 0
\(406\) 42336.0 0.0127466
\(407\) 3.64400e6i 1.09042i
\(408\) 0 0
\(409\) 1.89069e6 0.558873 0.279436 0.960164i \(-0.409852\pi\)
0.279436 + 0.960164i \(0.409852\pi\)
\(410\) −759440. 4.17692e6i −0.223118 1.22715i
\(411\) 0 0
\(412\) 2.46982e6i 0.716841i
\(413\) 113200.i 0.0326566i
\(414\) 0 0
\(415\) −24680.0 135740.i −0.00703437 0.0386890i
\(416\) 294912. 0.0835524
\(417\) 0 0
\(418\) 2.68800e6i 0.752469i
\(419\) 4.60930e6 1.28263 0.641313 0.767280i \(-0.278390\pi\)
0.641313 + 0.767280i \(0.278390\pi\)
\(420\) 0 0
\(421\) −6.04151e6 −1.66127 −0.830635 0.556817i \(-0.812022\pi\)
−0.830635 + 0.556817i \(0.812022\pi\)
\(422\) 4.12032e6i 1.12629i
\(423\) 0 0
\(424\) −2.54746e6 −0.688164
\(425\) −1.66760e6 4.43430e6i −0.447837 1.19084i
\(426\) 0 0
\(427\) 73160.0i 0.0194180i
\(428\) 2.18861e6i 0.577509i
\(429\) 0 0
\(430\) 528880. 96160.0i 0.137939 0.0250798i
\(431\) 3800.00 0.000985350 0.000492675 1.00000i \(-0.499843\pi\)
0.000492675 1.00000i \(0.499843\pi\)
\(432\) 0 0
\(433\) 250736.i 0.0642683i −0.999484 0.0321342i \(-0.989770\pi\)
0.999484 0.0321342i \(-0.0102304\pi\)
\(434\) 89792.0 0.0228830
\(435\) 0 0
\(436\) −860960. −0.216904
\(437\) 5.51040e6i 1.38032i
\(438\) 0 0
\(439\) 3.58873e6 0.888750 0.444375 0.895841i \(-0.353426\pi\)
0.444375 + 0.895841i \(0.353426\pi\)
\(440\) 320000. + 1.76000e6i 0.0787986 + 0.433392i
\(441\) 0 0
\(442\) 1.74643e6i 0.425203i
\(443\) 1.41479e6i 0.342517i −0.985226 0.171258i \(-0.945217\pi\)
0.985226 0.171258i \(-0.0547833\pi\)
\(444\) 0 0
\(445\) 1.24729e6 226780.i 0.298585 0.0542881i
\(446\) −1.82408e6 −0.434217
\(447\) 0 0
\(448\) 16384.0i 0.00385678i
\(449\) −829806. −0.194250 −0.0971249 0.995272i \(-0.530965\pi\)
−0.0971249 + 0.995272i \(0.530965\pi\)
\(450\) 0 0
\(451\) 9.49300e6 2.19767
\(452\) 1.32307e6i 0.304605i
\(453\) 0 0
\(454\) 1.73701e6 0.395514
\(455\) 63360.0 11520.0i 0.0143478 0.00260870i
\(456\) 0 0
\(457\) 4.68198e6i 1.04867i 0.851512 + 0.524335i \(0.175686\pi\)
−0.851512 + 0.524335i \(0.824314\pi\)
\(458\) 2.89084e6i 0.643962i
\(459\) 0 0
\(460\) 656000. + 3.60800e6i 0.144547 + 0.795009i
\(461\) 141930. 0.0311044 0.0155522 0.999879i \(-0.495049\pi\)
0.0155522 + 0.999879i \(0.495049\pi\)
\(462\) 0 0
\(463\) 727476.i 0.157713i −0.996886 0.0788563i \(-0.974873\pi\)
0.996886 0.0788563i \(-0.0251268\pi\)
\(464\) −677376. −0.146061
\(465\) 0 0
\(466\) −2.26139e6 −0.482404
\(467\) 4.47640e6i 0.949809i 0.880037 + 0.474905i \(0.157517\pi\)
−0.880037 + 0.474905i \(0.842483\pi\)
\(468\) 0 0
\(469\) 263824. 0.0553837
\(470\) −1.95800e6 + 356000.i −0.408854 + 0.0743371i
\(471\) 0 0
\(472\) 1.81120e6i 0.374207i
\(473\) 1.20200e6i 0.247031i
\(474\) 0 0
\(475\) 3.93120e6 1.47840e6i 0.799450 0.300648i
\(476\) 97024.0 0.0196274
\(477\) 0 0
\(478\) 1.29962e6i 0.260163i
\(479\) −1.32718e6 −0.264297 −0.132149 0.991230i \(-0.542188\pi\)
−0.132149 + 0.991230i \(0.542188\pi\)
\(480\) 0 0
\(481\) 2.09894e6 0.413655
\(482\) 3.66105e6i 0.717774i
\(483\) 0 0
\(484\) −1.42318e6 −0.276152
\(485\) −369680. 2.03324e6i −0.0713628 0.392495i
\(486\) 0 0
\(487\) 4.11647e6i 0.786507i −0.919430 0.393253i \(-0.871350\pi\)
0.919430 0.393253i \(-0.128650\pi\)
\(488\) 1.17056e6i 0.222507i
\(489\) 0 0
\(490\) −671640. 3.69402e6i −0.126371 0.695039i
\(491\) 6.12316e6 1.14623 0.573115 0.819475i \(-0.305735\pi\)
0.573115 + 0.819475i \(0.305735\pi\)
\(492\) 0 0
\(493\) 4.01134e6i 0.743313i
\(494\) 1.54829e6 0.285453
\(495\) 0 0
\(496\) −1.43667e6 −0.262213
\(497\) 115200.i 0.0209200i
\(498\) 0 0
\(499\) 7.90490e6 1.42117 0.710584 0.703613i \(-0.248431\pi\)
0.710584 + 0.703613i \(0.248431\pi\)
\(500\) −2.39800e6 + 1.43600e6i −0.428967 + 0.256879i
\(501\) 0 0
\(502\) 5.46830e6i 0.968486i
\(503\) 3.97628e6i 0.700741i 0.936611 + 0.350370i \(0.113944\pi\)
−0.936611 + 0.350370i \(0.886056\pi\)
\(504\) 0 0
\(505\) −9.23549e6 + 1.67918e6i −1.61150 + 0.293001i
\(506\) −8.20000e6 −1.42376
\(507\) 0 0
\(508\) 3.38848e6i 0.582567i
\(509\) 781914. 0.133772 0.0668859 0.997761i \(-0.478694\pi\)
0.0668859 + 0.997761i \(0.478694\pi\)
\(510\) 0 0
\(511\) 123232. 0.0208772
\(512\) 262144.i 0.0441942i
\(513\) 0 0
\(514\) −3.57173e6 −0.596308
\(515\) 1.54364e6 + 8.49002e6i 0.256465 + 1.41056i
\(516\) 0 0
\(517\) 4.45000e6i 0.732207i
\(518\) 116608.i 0.0190943i
\(519\) 0 0
\(520\) −1.01376e6 + 184320.i −0.164409 + 0.0298926i
\(521\) −5.82694e6 −0.940472 −0.470236 0.882541i \(-0.655831\pi\)
−0.470236 + 0.882541i \(0.655831\pi\)
\(522\) 0 0
\(523\) 9.78938e6i 1.56495i 0.622681 + 0.782476i \(0.286043\pi\)
−0.622681 + 0.782476i \(0.713957\pi\)
\(524\) 2.71200e6 0.431481
\(525\) 0 0
\(526\) −7.46600e6 −1.17659
\(527\) 8.50779e6i 1.33441i
\(528\) 0 0
\(529\) −1.03737e7 −1.61173
\(530\) 8.75688e6 1.59216e6i 1.35413 0.246205i
\(531\) 0 0
\(532\) 86016.0i 0.0131765i
\(533\) 5.46797e6i 0.833696i
\(534\) 0 0
\(535\) −1.36788e6 7.52334e6i −0.206616 1.13639i
\(536\) −4.22118e6 −0.634633
\(537\) 0 0
\(538\) 5.48906e6i 0.817603i
\(539\) 8.39550e6 1.24473
\(540\) 0 0
\(541\) 4.76059e6 0.699307 0.349653 0.936879i \(-0.386299\pi\)
0.349653 + 0.936879i \(0.386299\pi\)
\(542\) 1.83458e6i 0.268249i
\(543\) 0 0
\(544\) −1.55238e6 −0.224906
\(545\) 2.95955e6 538100.i 0.426810 0.0776018i
\(546\) 0 0
\(547\) 1.16595e6i 0.166614i −0.996524 0.0833069i \(-0.973452\pi\)
0.996524 0.0833069i \(-0.0265482\pi\)
\(548\) 4.03258e6i 0.573629i
\(549\) 0 0
\(550\) −2.20000e6 5.85000e6i −0.310110 0.824611i
\(551\) −3.55622e6 −0.499011
\(552\) 0 0
\(553\) 240912.i 0.0335001i
\(554\) −3.94163e6 −0.545634
\(555\) 0 0
\(556\) 3.07226e6 0.421474
\(557\) 1.61293e6i 0.220282i 0.993916 + 0.110141i \(0.0351302\pi\)
−0.993916 + 0.110141i \(0.964870\pi\)
\(558\) 0 0
\(559\) −692352. −0.0937125
\(560\) −10240.0 56320.0i −0.00137984 0.00758914i
\(561\) 0 0
\(562\) 663192.i 0.0885724i
\(563\) 3.40603e6i 0.452874i 0.974026 + 0.226437i \(0.0727077\pi\)
−0.974026 + 0.226437i \(0.927292\pi\)
\(564\) 0 0
\(565\) 826920. + 4.54806e6i 0.108979 + 0.599384i
\(566\) 6.65883e6 0.873689
\(567\) 0 0
\(568\) 1.84320e6i 0.239719i
\(569\) −1.44009e7 −1.86470 −0.932350 0.361557i \(-0.882245\pi\)
−0.932350 + 0.361557i \(0.882245\pi\)
\(570\) 0 0
\(571\) 4.74772e6 0.609389 0.304695 0.952450i \(-0.401446\pi\)
0.304695 + 0.952450i \(0.401446\pi\)
\(572\) 2.30400e6i 0.294437i
\(573\) 0 0
\(574\) −303776. −0.0384834
\(575\) −4.51000e6 1.19925e7i −0.568862 1.51266i
\(576\) 0 0
\(577\) 1.09094e7i 1.36415i −0.731283 0.682074i \(-0.761078\pi\)
0.731283 0.682074i \(-0.238922\pi\)
\(578\) 3.51360e6i 0.437454i
\(579\) 0 0
\(580\) 2.32848e6 423360.i 0.287410 0.0522564i
\(581\) −9872.00 −0.00121329
\(582\) 0 0
\(583\) 1.99020e7i 2.42508i
\(584\) −1.97171e6 −0.239228
\(585\) 0 0
\(586\) 1.02042e7 1.22754
\(587\) 8.53223e6i 1.02204i −0.859569 0.511019i \(-0.829268\pi\)
0.859569 0.511019i \(-0.170732\pi\)
\(588\) 0 0
\(589\) −7.54253e6 −0.895836
\(590\) 1.13200e6 + 6.22600e6i 0.133880 + 0.736341i
\(591\) 0 0
\(592\) 1.86573e6i 0.218798i
\(593\) 4.63182e6i 0.540897i −0.962734 0.270449i \(-0.912828\pi\)
0.962734 0.270449i \(-0.0871721\pi\)
\(594\) 0 0
\(595\) −333520. + 60640.0i −0.0386215 + 0.00702210i
\(596\) −3.77110e6 −0.434863
\(597\) 0 0
\(598\) 4.72320e6i 0.540111i
\(599\) 6.27598e6 0.714684 0.357342 0.933974i \(-0.383683\pi\)
0.357342 + 0.933974i \(0.383683\pi\)
\(600\) 0 0
\(601\) 7.71988e6 0.871815 0.435907 0.899992i \(-0.356428\pi\)
0.435907 + 0.899992i \(0.356428\pi\)
\(602\) 38464.0i 0.00432577i
\(603\) 0 0
\(604\) 5.94387e6 0.662944
\(605\) 4.89220e6 889490.i 0.543395 0.0987990i
\(606\) 0 0
\(607\) 6.06160e6i 0.667753i −0.942617 0.333876i \(-0.891643\pi\)
0.942617 0.333876i \(-0.108357\pi\)
\(608\) 1.37626e6i 0.150987i
\(609\) 0 0
\(610\) −731600. 4.02380e6i −0.0796066 0.437836i
\(611\) 2.56320e6 0.277766
\(612\) 0 0
\(613\) 3.66489e6i 0.393921i 0.980411 + 0.196961i \(0.0631071\pi\)
−0.980411 + 0.196961i \(0.936893\pi\)
\(614\) 2.94408e6 0.315158
\(615\) 0 0
\(616\) 128000. 0.0135912
\(617\) 9.32522e6i 0.986157i 0.869985 + 0.493079i \(0.164129\pi\)
−0.869985 + 0.493079i \(0.835871\pi\)
\(618\) 0 0
\(619\) 7.40162e6 0.776426 0.388213 0.921570i \(-0.373093\pi\)
0.388213 + 0.921570i \(0.373093\pi\)
\(620\) 4.93856e6 897920.i 0.515966 0.0938120i
\(621\) 0 0
\(622\) 6.86640e6i 0.711628i
\(623\) 90712.0i 0.00936364i
\(624\) 0 0
\(625\) 7.34562e6 6.43500e6i 0.752192 0.658944i
\(626\) −1.13540e7 −1.15802
\(627\) 0 0
\(628\) 4.23923e6i 0.428932i
\(629\) −1.10486e7 −1.11348
\(630\) 0 0
\(631\) 160052. 0.0160025 0.00800125 0.999968i \(-0.497453\pi\)
0.00800125 + 0.999968i \(0.497453\pi\)
\(632\) 3.85459e6i 0.383871i
\(633\) 0 0
\(634\) 5.10421e6 0.504319
\(635\) −2.11780e6 1.16479e7i −0.208425 1.14634i
\(636\) 0 0
\(637\) 4.83581e6i 0.472194i
\(638\) 5.29200e6i 0.514717i
\(639\) 0 0
\(640\) 163840. + 901120.i 0.0158114 + 0.0869626i
\(641\) 1.69565e7 1.63002 0.815008 0.579450i \(-0.196732\pi\)
0.815008 + 0.579450i \(0.196732\pi\)
\(642\) 0 0
\(643\) 1.10128e7i 1.05044i −0.850967 0.525219i \(-0.823984\pi\)
0.850967 0.525219i \(-0.176016\pi\)
\(644\) 262400. 0.0249315
\(645\) 0 0
\(646\) −8.15002e6 −0.768382
\(647\) 3.33848e6i 0.313537i −0.987635 0.156768i \(-0.949892\pi\)
0.987635 0.156768i \(-0.0501076\pi\)
\(648\) 0 0
\(649\) −1.41500e7 −1.31870
\(650\) 3.36960e6 1.26720e6i 0.312820 0.117642i
\(651\) 0 0
\(652\) 6.44998e6i 0.594210i
\(653\) 4.76181e6i 0.437008i −0.975836 0.218504i \(-0.929882\pi\)
0.975836 0.218504i \(-0.0701177\pi\)
\(654\) 0 0
\(655\) −9.32250e6 + 1.69500e6i −0.849042 + 0.154371i
\(656\) 4.86042e6 0.440975
\(657\) 0 0
\(658\) 142400.i 0.0128217i
\(659\) 798188. 0.0715965 0.0357982 0.999359i \(-0.488603\pi\)
0.0357982 + 0.999359i \(0.488603\pi\)
\(660\) 0 0
\(661\) −1.54048e7 −1.37136 −0.685682 0.727901i \(-0.740496\pi\)
−0.685682 + 0.727901i \(0.740496\pi\)
\(662\) 1.77597e6i 0.157503i
\(663\) 0 0
\(664\) 157952. 0.0139029
\(665\) −53760.0 295680.i −0.00471417 0.0259279i
\(666\) 0 0
\(667\) 1.08486e7i 0.944189i
\(668\) 4.19040e6i 0.363341i
\(669\) 0 0
\(670\) 1.45103e7 2.63824e6i 1.24879 0.227053i
\(671\) 9.14500e6 0.784111
\(672\) 0 0
\(673\) 976704.i 0.0831238i 0.999136 + 0.0415619i \(0.0132334\pi\)
−0.999136 + 0.0415619i \(0.986767\pi\)
\(674\) 1.08530e7 0.920240
\(675\) 0 0
\(676\) −4.61358e6 −0.388304
\(677\) 1.93885e7i 1.62582i −0.582388 0.812911i \(-0.697881\pi\)
0.582388 0.812911i \(-0.302119\pi\)
\(678\) 0 0
\(679\) −147872. −0.0123087
\(680\) 5.33632e6 970240.i 0.442557 0.0804650i
\(681\) 0 0
\(682\) 1.12240e7i 0.924031i
\(683\) 5.25573e6i 0.431103i −0.976492 0.215552i \(-0.930845\pi\)
0.976492 0.215552i \(-0.0691550\pi\)
\(684\) 0 0
\(685\) −2.52036e6 1.38620e7i −0.205228 1.12875i
\(686\) −537568. −0.0436137
\(687\) 0 0
\(688\) 615424.i 0.0495682i
\(689\) −1.14636e7 −0.919965
\(690\) 0 0
\(691\) −5.45034e6 −0.434238 −0.217119 0.976145i \(-0.569666\pi\)
−0.217119 + 0.976145i \(0.569666\pi\)
\(692\) 5.21965e6i 0.414358i
\(693\) 0 0
\(694\) 5.24203e6 0.413144
\(695\) −1.05609e7 + 1.92016e6i −0.829350 + 0.150791i
\(696\) 0 0
\(697\) 2.87828e7i 2.24414i
\(698\) 1.19564e6i 0.0928885i
\(699\) 0 0
\(700\) 70400.0 + 187200.i 0.00543035 + 0.0144398i
\(701\) 4.43961e6 0.341232 0.170616 0.985338i \(-0.445424\pi\)
0.170616 + 0.985338i \(0.445424\pi\)
\(702\) 0 0
\(703\) 9.79507e6i 0.747514i
\(704\) −2.04800e6 −0.155739
\(705\) 0 0
\(706\) 2.95198e6 0.222896
\(707\) 671672.i 0.0505369i
\(708\) 0 0
\(709\) −4.55918e6 −0.340621 −0.170310 0.985390i \(-0.554477\pi\)
−0.170310 + 0.985390i \(0.554477\pi\)
\(710\) −1.15200e6 6.33600e6i −0.0857643 0.471704i
\(711\) 0 0
\(712\) 1.45139e6i 0.107296i
\(713\) 2.30092e7i 1.69503i
\(714\) 0 0
\(715\) 1.44000e6 + 7.92000e6i 0.105341 + 0.579375i
\(716\) 1.75226e6 0.127736
\(717\) 0 0
\(718\) 9.36298e6i 0.677802i
\(719\) −2.06630e7 −1.49063 −0.745317 0.666710i \(-0.767702\pi\)
−0.745317 + 0.666710i \(0.767702\pi\)
\(720\) 0 0
\(721\) 617456. 0.0442352
\(722\) 2.67905e6i 0.191266i
\(723\) 0 0
\(724\) 850336. 0.0602898
\(725\) −7.73955e6 + 2.91060e6i −0.546853 + 0.205654i
\(726\) 0 0
\(727\) 5.48161e6i 0.384656i 0.981331 + 0.192328i \(0.0616037\pi\)
−0.981331 + 0.192328i \(0.938396\pi\)
\(728\) 73728.0i 0.00515589i
\(729\) 0 0
\(730\) 6.77776e6 1.23232e6i 0.470738 0.0855887i
\(731\) 3.64446e6 0.252255
\(732\) 0 0
\(733\) 8.55579e6i 0.588166i 0.955780 + 0.294083i \(0.0950143\pi\)
−0.955780 + 0.294083i \(0.904986\pi\)
\(734\) 509168. 0.0348836
\(735\) 0 0
\(736\) −4.19840e6 −0.285686
\(737\) 3.29780e7i 2.23643i
\(738\) 0 0
\(739\) 5.29119e6 0.356404 0.178202 0.983994i \(-0.442972\pi\)
0.178202 + 0.983994i \(0.442972\pi\)
\(740\) 1.16608e6 + 6.41344e6i 0.0782797 + 0.430538i
\(741\) 0 0
\(742\) 636864.i 0.0424656i
\(743\) 2.36432e6i 0.157121i −0.996909 0.0785606i \(-0.974968\pi\)
0.996909 0.0785606i \(-0.0250324\pi\)
\(744\) 0 0
\(745\) 1.29632e7 2.35694e6i 0.855698 0.155581i
\(746\) −1.61548e7 −1.06281
\(747\) 0 0
\(748\) 1.21280e7i 0.792566i
\(749\) −547152. −0.0356372
\(750\) 0 0
\(751\) −8.79694e6 −0.569157 −0.284578 0.958653i \(-0.591854\pi\)
−0.284578 + 0.958653i \(0.591854\pi\)
\(752\) 2.27840e6i 0.146922i
\(753\) 0 0
\(754\) −3.04819e6 −0.195260
\(755\) −2.04321e7 + 3.71492e6i −1.30450 + 0.237182i
\(756\) 0 0
\(757\) 2.95808e7i 1.87616i 0.346421 + 0.938079i \(0.387397\pi\)
−0.346421 + 0.938079i \(0.612603\pi\)
\(758\) 4.04854e6i 0.255933i
\(759\) 0 0
\(760\) 860160. + 4.73088e6i 0.0540188 + 0.297104i
\(761\) 1.26296e7 0.790549 0.395274 0.918563i \(-0.370649\pi\)
0.395274 + 0.918563i \(0.370649\pi\)
\(762\) 0 0
\(763\) 215240.i 0.0133848i
\(764\) 3.71290e6 0.230133
\(765\) 0 0
\(766\) −9.50440e6 −0.585265
\(767\) 8.15040e6i 0.500254i
\(768\) 0 0
\(769\) 2.32186e7 1.41586 0.707929 0.706283i \(-0.249630\pi\)
0.707929 + 0.706283i \(0.249630\pi\)
\(770\) −440000. + 80000.0i −0.0267440 + 0.00486254i
\(771\) 0 0
\(772\) 1.64908e7i 0.995858i
\(773\) 1.73201e7i 1.04256i −0.853386 0.521280i \(-0.825455\pi\)
0.853386 0.521280i \(-0.174545\pi\)
\(774\) 0 0
\(775\) −1.64151e7 + 6.17320e6i −0.981724 + 0.369195i
\(776\) 2.36595e6 0.141043
\(777\) 0 0
\(778\) 5.69990e6i 0.337612i
\(779\) 2.55172e7 1.50657
\(780\) 0 0
\(781\) 1.44000e7 0.844763
\(782\) 2.48624e7i 1.45387i
\(783\) 0 0
\(784\) 4.29850e6 0.249762
\(785\) 2.64952e6 + 1.45724e7i 0.153459 + 0.844026i
\(786\) 0 0
\(787\) 556676.i 0.0320380i 0.999872 + 0.0160190i \(0.00509923\pi\)
−0.999872 + 0.0160190i \(0.994901\pi\)
\(788\) 8.36474e6i 0.479884i