Properties

Label 90.6.c.a.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 10)
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.a.19.2

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -158.000i q^{7} +64.0000i q^{8} +O(q^{10})\) \(q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -158.000i q^{7} +64.0000i q^{8} +(-40.0000 + 220.000i) q^{10} +148.000 q^{11} +684.000i q^{13} -632.000 q^{14} +256.000 q^{16} +2048.00i q^{17} -2220.00 q^{19} +(880.000 + 160.000i) q^{20} -592.000i q^{22} +1246.00i q^{23} +(2925.00 + 1100.00i) q^{25} +2736.00 q^{26} +2528.00i q^{28} -270.000 q^{29} -2048.00 q^{31} -1024.00i q^{32} +8192.00 q^{34} +(-1580.00 + 8690.00i) q^{35} +4372.00i q^{37} +8880.00i q^{38} +(640.000 - 3520.00i) q^{40} +2398.00 q^{41} +2294.00i q^{43} -2368.00 q^{44} +4984.00 q^{46} -10682.0i q^{47} -8157.00 q^{49} +(4400.00 - 11700.0i) q^{50} -10944.0i q^{52} -2964.00i q^{53} +(-8140.00 - 1480.00i) q^{55} +10112.0 q^{56} +1080.00i q^{58} -39740.0 q^{59} -42298.0 q^{61} +8192.00i q^{62} -4096.00 q^{64} +(6840.00 - 37620.0i) q^{65} -32098.0i q^{67} -32768.0i q^{68} +(34760.0 + 6320.00i) q^{70} +4248.00 q^{71} +30104.0i q^{73} +17488.0 q^{74} +35520.0 q^{76} -23384.0i q^{77} -35280.0 q^{79} +(-14080.0 - 2560.00i) q^{80} -9592.00i q^{82} +27826.0i q^{83} +(20480.0 - 112640. i) q^{85} +9176.00 q^{86} +9472.00i q^{88} -85210.0 q^{89} +108072. q^{91} -19936.0i q^{92} -42728.0 q^{94} +(122100. + 22200.0i) q^{95} +97232.0i q^{97} +32628.0i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 32q^{4} - 110q^{5} + O(q^{10}) \) \( 2q - 32q^{4} - 110q^{5} - 80q^{10} + 296q^{11} - 1264q^{14} + 512q^{16} - 4440q^{19} + 1760q^{20} + 5850q^{25} + 5472q^{26} - 540q^{29} - 4096q^{31} + 16384q^{34} - 3160q^{35} + 1280q^{40} + 4796q^{41} - 4736q^{44} + 9968q^{46} - 16314q^{49} + 8800q^{50} - 16280q^{55} + 20224q^{56} - 79480q^{59} - 84596q^{61} - 8192q^{64} + 13680q^{65} + 69520q^{70} + 8496q^{71} + 34976q^{74} + 71040q^{76} - 70560q^{79} - 28160q^{80} + 40960q^{85} + 18352q^{86} - 170420q^{89} + 216144q^{91} - 85456q^{94} + 244200q^{95} + O(q^{100}) \)

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
\(7\) 158.000i 1.21874i −0.792885 0.609371i \(-0.791422\pi\)
0.792885 0.609371i \(-0.208578\pi\)
\(8\) 64.0000i 0.353553i
\(9\) 0 0
\(10\) −40.0000 + 220.000i −0.126491 + 0.695701i
\(11\) 148.000 0.368791 0.184395 0.982852i \(-0.440967\pi\)
0.184395 + 0.982852i \(0.440967\pi\)
\(12\) 0 0
\(13\) 684.000i 1.12253i 0.827636 + 0.561265i \(0.189685\pi\)
−0.827636 + 0.561265i \(0.810315\pi\)
\(14\) −632.000 −0.861781
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) 2048.00i 1.71873i 0.511363 + 0.859365i \(0.329141\pi\)
−0.511363 + 0.859365i \(0.670859\pi\)
\(18\) 0 0
\(19\) −2220.00 −1.41081 −0.705406 0.708804i \(-0.749235\pi\)
−0.705406 + 0.708804i \(0.749235\pi\)
\(20\) 880.000 + 160.000i 0.491935 + 0.0894427i
\(21\) 0 0
\(22\) 592.000i 0.260774i
\(23\) 1246.00i 0.491132i 0.969380 + 0.245566i \(0.0789738\pi\)
−0.969380 + 0.245566i \(0.921026\pi\)
\(24\) 0 0
\(25\) 2925.00 + 1100.00i 0.936000 + 0.352000i
\(26\) 2736.00 0.793748
\(27\) 0 0
\(28\) 2528.00i 0.609371i
\(29\) −270.000 −0.0596168 −0.0298084 0.999556i \(-0.509490\pi\)
−0.0298084 + 0.999556i \(0.509490\pi\)
\(30\) 0 0
\(31\) −2048.00 −0.382759 −0.191380 0.981516i \(-0.561296\pi\)
−0.191380 + 0.981516i \(0.561296\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 0 0
\(34\) 8192.00 1.21533
\(35\) −1580.00 + 8690.00i −0.218015 + 1.19908i
\(36\) 0 0
\(37\) 4372.00i 0.525020i 0.964929 + 0.262510i \(0.0845503\pi\)
−0.964929 + 0.262510i \(0.915450\pi\)
\(38\) 8880.00i 0.997594i
\(39\) 0 0
\(40\) 640.000 3520.00i 0.0632456 0.347851i
\(41\) 2398.00 0.222787 0.111393 0.993776i \(-0.464469\pi\)
0.111393 + 0.993776i \(0.464469\pi\)
\(42\) 0 0
\(43\) 2294.00i 0.189200i 0.995515 + 0.0946002i \(0.0301573\pi\)
−0.995515 + 0.0946002i \(0.969843\pi\)
\(44\) −2368.00 −0.184395
\(45\) 0 0
\(46\) 4984.00 0.347283
\(47\) 10682.0i 0.705355i −0.935745 0.352678i \(-0.885271\pi\)
0.935745 0.352678i \(-0.114729\pi\)
\(48\) 0 0
\(49\) −8157.00 −0.485333
\(50\) 4400.00 11700.0i 0.248902 0.661852i
\(51\) 0 0
\(52\) 10944.0i 0.561265i
\(53\) 2964.00i 0.144940i −0.997371 0.0724700i \(-0.976912\pi\)
0.997371 0.0724700i \(-0.0230882\pi\)
\(54\) 0 0
\(55\) −8140.00 1480.00i −0.362842 0.0659713i
\(56\) 10112.0 0.430891
\(57\) 0 0
\(58\) 1080.00i 0.0421555i
\(59\) −39740.0 −1.48627 −0.743135 0.669141i \(-0.766662\pi\)
−0.743135 + 0.669141i \(0.766662\pi\)
\(60\) 0 0
\(61\) −42298.0 −1.45544 −0.727722 0.685873i \(-0.759421\pi\)
−0.727722 + 0.685873i \(0.759421\pi\)
\(62\) 8192.00i 0.270652i
\(63\) 0 0
\(64\) −4096.00 −0.125000
\(65\) 6840.00 37620.0i 0.200804 1.10442i
\(66\) 0 0
\(67\) 32098.0i 0.873556i −0.899569 0.436778i \(-0.856119\pi\)
0.899569 0.436778i \(-0.143881\pi\)
\(68\) 32768.0i 0.859365i
\(69\) 0 0
\(70\) 34760.0 + 6320.00i 0.847881 + 0.154160i
\(71\) 4248.00 0.100009 0.0500044 0.998749i \(-0.484076\pi\)
0.0500044 + 0.998749i \(0.484076\pi\)
\(72\) 0 0
\(73\) 30104.0i 0.661176i 0.943775 + 0.330588i \(0.107247\pi\)
−0.943775 + 0.330588i \(0.892753\pi\)
\(74\) 17488.0 0.371245
\(75\) 0 0
\(76\) 35520.0 0.705406
\(77\) 23384.0i 0.449461i
\(78\) 0 0
\(79\) −35280.0 −0.636005 −0.318003 0.948090i \(-0.603012\pi\)
−0.318003 + 0.948090i \(0.603012\pi\)
\(80\) −14080.0 2560.00i −0.245967 0.0447214i
\(81\) 0 0
\(82\) 9592.00i 0.157534i
\(83\) 27826.0i 0.443359i 0.975120 + 0.221680i \(0.0711539\pi\)
−0.975120 + 0.221680i \(0.928846\pi\)
\(84\) 0 0
\(85\) 20480.0 112640.i 0.307456 1.69101i
\(86\) 9176.00 0.133785
\(87\) 0 0
\(88\) 9472.00i 0.130387i
\(89\) −85210.0 −1.14029 −0.570145 0.821544i \(-0.693113\pi\)
−0.570145 + 0.821544i \(0.693113\pi\)
\(90\) 0 0
\(91\) 108072. 1.36807
\(92\) 19936.0i 0.245566i
\(93\) 0 0
\(94\) −42728.0 −0.498762
\(95\) 122100. + 22200.0i 1.38805 + 0.252374i
\(96\) 0 0
\(97\) 97232.0i 1.04925i 0.851333 + 0.524626i \(0.175795\pi\)
−0.851333 + 0.524626i \(0.824205\pi\)
\(98\) 32628.0i 0.343183i
\(99\) 0 0
\(100\) −46800.0 17600.0i −0.468000 0.176000i
\(101\) 4298.00 0.0419240 0.0209620 0.999780i \(-0.493327\pi\)
0.0209620 + 0.999780i \(0.493327\pi\)
\(102\) 0 0
\(103\) 124114.i 1.15273i 0.817192 + 0.576365i \(0.195529\pi\)
−0.817192 + 0.576365i \(0.804471\pi\)
\(104\) −43776.0 −0.396874
\(105\) 0 0
\(106\) −11856.0 −0.102488
\(107\) 42342.0i 0.357530i −0.983892 0.178765i \(-0.942790\pi\)
0.983892 0.178765i \(-0.0572101\pi\)
\(108\) 0 0
\(109\) 35990.0 0.290145 0.145073 0.989421i \(-0.453658\pi\)
0.145073 + 0.989421i \(0.453658\pi\)
\(110\) −5920.00 + 32560.0i −0.0466487 + 0.256568i
\(111\) 0 0
\(112\) 40448.0i 0.304686i
\(113\) 228816.i 1.68574i 0.538118 + 0.842869i \(0.319135\pi\)
−0.538118 + 0.842869i \(0.680865\pi\)
\(114\) 0 0
\(115\) 12460.0 68530.0i 0.0878564 0.483210i
\(116\) 4320.00 0.0298084
\(117\) 0 0
\(118\) 158960.i 1.05095i
\(119\) 323584. 2.09469
\(120\) 0 0
\(121\) −139147. −0.863993
\(122\) 169192.i 1.02915i
\(123\) 0 0
\(124\) 32768.0 0.191380
\(125\) −149875. 89750.0i −0.857935 0.513759i
\(126\) 0 0
\(127\) 175238.i 0.964093i −0.876146 0.482047i \(-0.839894\pi\)
0.876146 0.482047i \(-0.160106\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) 0 0
\(130\) −150480. 27360.0i −0.780945 0.141990i
\(131\) −299652. −1.52559 −0.762797 0.646638i \(-0.776174\pi\)
−0.762797 + 0.646638i \(0.776174\pi\)
\(132\) 0 0
\(133\) 350760.i 1.71942i
\(134\) −128392. −0.617698
\(135\) 0 0
\(136\) −131072. −0.607663
\(137\) 107928.i 0.491284i 0.969361 + 0.245642i \(0.0789988\pi\)
−0.969361 + 0.245642i \(0.921001\pi\)
\(138\) 0 0
\(139\) 196460. 0.862456 0.431228 0.902243i \(-0.358080\pi\)
0.431228 + 0.902243i \(0.358080\pi\)
\(140\) 25280.0 139040.i 0.109008 0.599542i
\(141\) 0 0
\(142\) 16992.0i 0.0707170i
\(143\) 101232.i 0.413978i
\(144\) 0 0
\(145\) 14850.0 + 2700.00i 0.0586552 + 0.0106646i
\(146\) 120416. 0.467522
\(147\) 0 0
\(148\) 69952.0i 0.262510i
\(149\) 138850. 0.512366 0.256183 0.966628i \(-0.417535\pi\)
0.256183 + 0.966628i \(0.417535\pi\)
\(150\) 0 0
\(151\) 416152. 1.48528 0.742642 0.669688i \(-0.233572\pi\)
0.742642 + 0.669688i \(0.233572\pi\)
\(152\) 142080.i 0.498797i
\(153\) 0 0
\(154\) −93536.0 −0.317817
\(155\) 112640. + 20480.0i 0.376585 + 0.0684701i
\(156\) 0 0
\(157\) 433108.i 1.40232i −0.713004 0.701160i \(-0.752666\pi\)
0.713004 0.701160i \(-0.247334\pi\)
\(158\) 141120.i 0.449724i
\(159\) 0 0
\(160\) −10240.0 + 56320.0i −0.0316228 + 0.173925i
\(161\) 196868. 0.598564
\(162\) 0 0
\(163\) 149134.i 0.439651i 0.975539 + 0.219825i \(0.0705487\pi\)
−0.975539 + 0.219825i \(0.929451\pi\)
\(164\) −38368.0 −0.111393
\(165\) 0 0
\(166\) 111304. 0.313502
\(167\) 559602.i 1.55270i −0.630301 0.776351i \(-0.717068\pi\)
0.630301 0.776351i \(-0.282932\pi\)
\(168\) 0 0
\(169\) −96563.0 −0.260072
\(170\) −450560. 81920.0i −1.19572 0.217404i
\(171\) 0 0
\(172\) 36704.0i 0.0946002i
\(173\) 343804.i 0.873365i −0.899616 0.436682i \(-0.856153\pi\)
0.899616 0.436682i \(-0.143847\pi\)
\(174\) 0 0
\(175\) 173800. 462150.i 0.428997 1.14074i
\(176\) 37888.0 0.0921977
\(177\) 0 0
\(178\) 340840.i 0.806307i
\(179\) 23980.0 0.0559392 0.0279696 0.999609i \(-0.491096\pi\)
0.0279696 + 0.999609i \(0.491096\pi\)
\(180\) 0 0
\(181\) −651898. −1.47905 −0.739526 0.673128i \(-0.764950\pi\)
−0.739526 + 0.673128i \(0.764950\pi\)
\(182\) 432288.i 0.967375i
\(183\) 0 0
\(184\) −79744.0 −0.173641
\(185\) 43720.0 240460.i 0.0939184 0.516551i
\(186\) 0 0
\(187\) 303104.i 0.633852i
\(188\) 170912.i 0.352678i
\(189\) 0 0
\(190\) 88800.0 488400.i 0.178455 0.981503i
\(191\) −202752. −0.402144 −0.201072 0.979576i \(-0.564443\pi\)
−0.201072 + 0.979576i \(0.564443\pi\)
\(192\) 0 0
\(193\) 452656.i 0.874732i −0.899284 0.437366i \(-0.855911\pi\)
0.899284 0.437366i \(-0.144089\pi\)
\(194\) 388928. 0.741933
\(195\) 0 0
\(196\) 130512. 0.242667
\(197\) 337468.i 0.619537i 0.950812 + 0.309768i \(0.100252\pi\)
−0.950812 + 0.309768i \(0.899748\pi\)
\(198\) 0 0
\(199\) 561000. 1.00422 0.502112 0.864803i \(-0.332557\pi\)
0.502112 + 0.864803i \(0.332557\pi\)
\(200\) −70400.0 + 187200.i −0.124451 + 0.330926i
\(201\) 0 0
\(202\) 17192.0i 0.0296448i
\(203\) 42660.0i 0.0726576i
\(204\) 0 0
\(205\) −131890. 23980.0i −0.219193 0.0398533i
\(206\) 496456. 0.815103
\(207\) 0 0
\(208\) 175104.i 0.280632i
\(209\) −328560. −0.520294
\(210\) 0 0
\(211\) −805548. −1.24562 −0.622810 0.782373i \(-0.714009\pi\)
−0.622810 + 0.782373i \(0.714009\pi\)
\(212\) 47424.0i 0.0724700i
\(213\) 0 0
\(214\) −169368. −0.252812
\(215\) 22940.0 126170.i 0.0338452 0.186149i
\(216\) 0 0
\(217\) 323584.i 0.466485i
\(218\) 143960.i 0.205164i
\(219\) 0 0
\(220\) 130240. + 23680.0i 0.181421 + 0.0329856i
\(221\) −1.40083e6 −1.92932
\(222\) 0 0
\(223\) 1.21855e6i 1.64090i 0.571717 + 0.820451i \(0.306278\pi\)
−0.571717 + 0.820451i \(0.693722\pi\)
\(224\) −161792. −0.215445
\(225\) 0 0
\(226\) 915264. 1.19200
\(227\) 564338.i 0.726900i 0.931614 + 0.363450i \(0.118401\pi\)
−0.931614 + 0.363450i \(0.881599\pi\)
\(228\) 0 0
\(229\) −560330. −0.706082 −0.353041 0.935608i \(-0.614852\pi\)
−0.353041 + 0.935608i \(0.614852\pi\)
\(230\) −274120. 49840.0i −0.341681 0.0621239i
\(231\) 0 0
\(232\) 17280.0i 0.0210777i
\(233\) 293576.i 0.354267i 0.984187 + 0.177134i \(0.0566824\pi\)
−0.984187 + 0.177134i \(0.943318\pi\)
\(234\) 0 0
\(235\) −106820. + 587510.i −0.126178 + 0.693978i
\(236\) 635840. 0.743135
\(237\) 0 0
\(238\) 1.29434e6i 1.48117i
\(239\) 584240. 0.661602 0.330801 0.943701i \(-0.392681\pi\)
0.330801 + 0.943701i \(0.392681\pi\)
\(240\) 0 0
\(241\) −563798. −0.625289 −0.312645 0.949870i \(-0.601215\pi\)
−0.312645 + 0.949870i \(0.601215\pi\)
\(242\) 556588.i 0.610936i
\(243\) 0 0
\(244\) 676768. 0.727722
\(245\) 448635. + 81570.0i 0.477505 + 0.0868191i
\(246\) 0 0
\(247\) 1.51848e6i 1.58368i
\(248\) 131072.i 0.135326i
\(249\) 0 0
\(250\) −359000. + 599500.i −0.363282 + 0.606651i
\(251\) 1.01975e6 1.02167 0.510833 0.859680i \(-0.329337\pi\)
0.510833 + 0.859680i \(0.329337\pi\)
\(252\) 0 0
\(253\) 184408.i 0.181125i
\(254\) −700952. −0.681717
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) 657408.i 0.620872i 0.950594 + 0.310436i \(0.100475\pi\)
−0.950594 + 0.310436i \(0.899525\pi\)
\(258\) 0 0
\(259\) 690776. 0.639864
\(260\) −109440. + 601920.i −0.100402 + 0.552211i
\(261\) 0 0
\(262\) 1.19861e6i 1.07876i
\(263\) 562366.i 0.501337i 0.968073 + 0.250668i \(0.0806504\pi\)
−0.968073 + 0.250668i \(0.919350\pi\)
\(264\) 0 0
\(265\) −29640.0 + 163020.i −0.0259277 + 0.142602i
\(266\) 1.40304e6 1.21581
\(267\) 0 0
\(268\) 513568.i 0.436778i
\(269\) 366570. 0.308870 0.154435 0.988003i \(-0.450644\pi\)
0.154435 + 0.988003i \(0.450644\pi\)
\(270\) 0 0
\(271\) 1.16075e6 0.960099 0.480050 0.877241i \(-0.340619\pi\)
0.480050 + 0.877241i \(0.340619\pi\)
\(272\) 524288.i 0.429682i
\(273\) 0 0
\(274\) 431712. 0.347390
\(275\) 432900. + 162800.i 0.345188 + 0.129814i
\(276\) 0 0
\(277\) 2.51501e6i 1.96943i 0.174172 + 0.984715i \(0.444275\pi\)
−0.174172 + 0.984715i \(0.555725\pi\)
\(278\) 785840.i 0.609849i
\(279\) 0 0
\(280\) −556160. 101120.i −0.423940 0.0770800i
\(281\) −2.08600e6 −1.57597 −0.787987 0.615692i \(-0.788876\pi\)
−0.787987 + 0.615692i \(0.788876\pi\)
\(282\) 0 0
\(283\) 2.23803e6i 1.66111i −0.556935 0.830556i \(-0.688023\pi\)
0.556935 0.830556i \(-0.311977\pi\)
\(284\) −67968.0 −0.0500044
\(285\) 0 0
\(286\) 404928. 0.292727
\(287\) 378884.i 0.271520i
\(288\) 0 0
\(289\) −2.77445e6 −1.95403
\(290\) 10800.0 59400.0i 0.00754100 0.0414755i
\(291\) 0 0
\(292\) 481664.i 0.330588i
\(293\) 975756.i 0.664006i 0.943278 + 0.332003i \(0.107724\pi\)
−0.943278 + 0.332003i \(0.892276\pi\)
\(294\) 0 0
\(295\) 2.18570e6 + 397400.i 1.46230 + 0.265872i
\(296\) −279808. −0.185623
\(297\) 0 0
\(298\) 555400.i 0.362297i
\(299\) −852264. −0.551310
\(300\) 0 0
\(301\) 362452. 0.230587
\(302\) 1.66461e6i 1.05025i
\(303\) 0 0
\(304\) −568320. −0.352703
\(305\) 2.32639e6 + 422980.i 1.43197 + 0.260358i
\(306\) 0 0
\(307\) 87858.0i 0.0532029i −0.999646 0.0266015i \(-0.991531\pi\)
0.999646 0.0266015i \(-0.00846850\pi\)
\(308\) 374144.i 0.224730i
\(309\) 0 0
\(310\) 81920.0 450560.i 0.0484156 0.266286i
\(311\) −599352. −0.351383 −0.175692 0.984445i \(-0.556216\pi\)
−0.175692 + 0.984445i \(0.556216\pi\)
\(312\) 0 0
\(313\) 2.09342e6i 1.20780i −0.797060 0.603900i \(-0.793613\pi\)
0.797060 0.603900i \(-0.206387\pi\)
\(314\) −1.73243e6 −0.991590
\(315\) 0 0
\(316\) 564480. 0.318003
\(317\) 2.41625e6i 1.35050i −0.737590 0.675249i \(-0.764036\pi\)
0.737590 0.675249i \(-0.235964\pi\)
\(318\) 0 0
\(319\) −39960.0 −0.0219861
\(320\) 225280. + 40960.0i 0.122984 + 0.0223607i
\(321\) 0 0
\(322\) 787472.i 0.423249i
\(323\) 4.54656e6i 2.42480i
\(324\) 0 0
\(325\) −752400. + 2.00070e6i −0.395130 + 1.05069i
\(326\) 596536. 0.310880
\(327\) 0 0
\(328\) 153472.i 0.0787670i
\(329\) −1.68776e6 −0.859647
\(330\) 0 0
\(331\) −1.64095e6 −0.823237 −0.411618 0.911356i \(-0.635036\pi\)
−0.411618 + 0.911356i \(0.635036\pi\)
\(332\) 445216.i 0.221680i
\(333\) 0 0
\(334\) −2.23841e6 −1.09793
\(335\) −320980. + 1.76539e6i −0.156267 + 0.859466i
\(336\) 0 0
\(337\) 2.18773e6i 1.04935i −0.851304 0.524673i \(-0.824188\pi\)
0.851304 0.524673i \(-0.175812\pi\)
\(338\) 386252.i 0.183899i
\(339\) 0 0
\(340\) −327680. + 1.80224e6i −0.153728 + 0.845503i
\(341\) −303104. −0.141158
\(342\) 0 0
\(343\) 1.36670e6i 0.627246i
\(344\) −146816. −0.0668925
\(345\) 0 0
\(346\) −1.37522e6 −0.617562
\(347\) 2.74502e6i 1.22383i 0.790923 + 0.611916i \(0.209601\pi\)
−0.790923 + 0.611916i \(0.790399\pi\)
\(348\) 0 0
\(349\) 2.65115e6 1.16512 0.582560 0.812788i \(-0.302051\pi\)
0.582560 + 0.812788i \(0.302051\pi\)
\(350\) −1.84860e6 695200.i −0.806627 0.303347i
\(351\) 0 0
\(352\) 151552.i 0.0651936i
\(353\) 3.05766e6i 1.30603i −0.757345 0.653015i \(-0.773504\pi\)
0.757345 0.653015i \(-0.226496\pi\)
\(354\) 0 0
\(355\) −233640. 42480.0i −0.0983957 0.0178901i
\(356\) 1.36336e6 0.570145
\(357\) 0 0
\(358\) 95920.0i 0.0395550i
\(359\) 3.79356e6 1.55350 0.776749 0.629810i \(-0.216867\pi\)
0.776749 + 0.629810i \(0.216867\pi\)
\(360\) 0 0
\(361\) 2.45230e6 0.990389
\(362\) 2.60759e6i 1.04585i
\(363\) 0 0
\(364\) −1.72915e6 −0.684037
\(365\) 301040. 1.65572e6i 0.118275 0.650511i
\(366\) 0 0
\(367\) 3.11060e6i 1.20553i 0.797917 + 0.602767i \(0.205935\pi\)
−0.797917 + 0.602767i \(0.794065\pi\)
\(368\) 318976.i 0.122783i
\(369\) 0 0
\(370\) −961840. 174880.i −0.365257 0.0664104i
\(371\) −468312. −0.176645
\(372\) 0 0
\(373\) 1.41520e6i 0.526677i −0.964703 0.263339i \(-0.915176\pi\)
0.964703 0.263339i \(-0.0848236\pi\)
\(374\) 1.21242e6 0.448201
\(375\) 0 0
\(376\) 683648. 0.249381
\(377\) 184680.i 0.0669216i
\(378\) 0 0
\(379\) 3.90262e6 1.39559 0.697796 0.716297i \(-0.254164\pi\)
0.697796 + 0.716297i \(0.254164\pi\)
\(380\) −1.95360e6 355200.i −0.694027 0.126187i
\(381\) 0 0
\(382\) 811008.i 0.284359i
\(383\) 695674.i 0.242331i −0.992632 0.121165i \(-0.961337\pi\)
0.992632 0.121165i \(-0.0386632\pi\)
\(384\) 0 0
\(385\) −233840. + 1.28612e6i −0.0804020 + 0.442211i
\(386\) −1.81062e6 −0.618529
\(387\) 0 0
\(388\) 1.55571e6i 0.524626i
\(389\) 498290. 0.166958 0.0834792 0.996510i \(-0.473397\pi\)
0.0834792 + 0.996510i \(0.473397\pi\)
\(390\) 0 0
\(391\) −2.55181e6 −0.844124
\(392\) 522048.i 0.171591i
\(393\) 0 0
\(394\) 1.34987e6 0.438079
\(395\) 1.94040e6 + 352800.i 0.625747 + 0.113772i
\(396\) 0 0
\(397\) 1.09567e6i 0.348901i −0.984666 0.174451i \(-0.944185\pi\)
0.984666 0.174451i \(-0.0558150\pi\)
\(398\) 2.24400e6i 0.710093i
\(399\) 0 0
\(400\) 748800. + 281600.i 0.234000 + 0.0880000i
\(401\) 2.49160e6 0.773779 0.386890 0.922126i \(-0.373549\pi\)
0.386890 + 0.922126i \(0.373549\pi\)
\(402\) 0 0
\(403\) 1.40083e6i 0.429659i
\(404\) −68768.0 −0.0209620
\(405\) 0 0
\(406\) 170640. 0.0513766
\(407\) 647056.i 0.193623i
\(408\) 0 0
\(409\) 3.63349e6 1.07403 0.537014 0.843573i \(-0.319552\pi\)
0.537014 + 0.843573i \(0.319552\pi\)
\(410\) −95920.0 + 527560.i −0.0281806 + 0.154993i
\(411\) 0 0
\(412\) 1.98582e6i 0.576365i
\(413\) 6.27892e6i 1.81138i
\(414\) 0 0
\(415\) 278260. 1.53043e6i 0.0793105 0.436208i
\(416\) 700416. 0.198437
\(417\) 0 0
\(418\) 1.31424e6i 0.367904i
\(419\) −3.64378e6 −1.01395 −0.506976 0.861960i \(-0.669237\pi\)
−0.506976 + 0.861960i \(0.669237\pi\)
\(420\) 0 0
\(421\) −1.82530e6 −0.501913 −0.250957 0.967998i \(-0.580745\pi\)
−0.250957 + 0.967998i \(0.580745\pi\)
\(422\) 3.22219e6i 0.880786i
\(423\) 0 0
\(424\) 189696. 0.0512441
\(425\) −2.25280e6 + 5.99040e6i −0.604993 + 1.60873i
\(426\) 0 0
\(427\) 6.68308e6i 1.77381i
\(428\) 677472.i 0.178765i
\(429\) 0 0
\(430\) −504680. 91760.0i −0.131627 0.0239322i
\(431\) −2.85435e6 −0.740141 −0.370070 0.929004i \(-0.620666\pi\)
−0.370070 + 0.929004i \(0.620666\pi\)
\(432\) 0 0
\(433\) 587776.i 0.150658i −0.997159 0.0753290i \(-0.975999\pi\)
0.997159 0.0753290i \(-0.0240007\pi\)
\(434\) 1.29434e6 0.329855
\(435\) 0 0
\(436\) −575840. −0.145073
\(437\) 2.76612e6i 0.692895i
\(438\) 0 0
\(439\) −6.11604e6 −1.51464 −0.757319 0.653045i \(-0.773491\pi\)
−0.757319 + 0.653045i \(0.773491\pi\)
\(440\) 94720.0 520960.i 0.0233244 0.128284i
\(441\) 0 0
\(442\) 5.60333e6i 1.36424i
\(443\) 2.35771e6i 0.570795i 0.958409 + 0.285398i \(0.0921257\pi\)
−0.958409 + 0.285398i \(0.907874\pi\)
\(444\) 0 0
\(445\) 4.68655e6 + 852100.i 1.12190 + 0.203981i
\(446\) 4.87422e6 1.16029
\(447\) 0 0
\(448\) 647168.i 0.152343i
\(449\) 5.49735e6 1.28688 0.643439 0.765497i \(-0.277507\pi\)
0.643439 + 0.765497i \(0.277507\pi\)
\(450\) 0 0
\(451\) 354904. 0.0821617
\(452\) 3.66106e6i 0.842869i
\(453\) 0 0
\(454\) 2.25735e6 0.513996
\(455\) −5.94396e6 1.08072e6i −1.34601 0.244729i
\(456\) 0 0
\(457\) 1.16039e6i 0.259905i 0.991520 + 0.129952i \(0.0414824\pi\)
−0.991520 + 0.129952i \(0.958518\pi\)
\(458\) 2.24132e6i 0.499275i
\(459\) 0 0
\(460\) −199360. + 1.09648e6i −0.0439282 + 0.241605i
\(461\) 2.30330e6 0.504775 0.252387 0.967626i \(-0.418784\pi\)
0.252387 + 0.967626i \(0.418784\pi\)
\(462\) 0 0
\(463\) 2.71343e6i 0.588257i 0.955766 + 0.294128i \(0.0950293\pi\)
−0.955766 + 0.294128i \(0.904971\pi\)
\(464\) −69120.0 −0.0149042
\(465\) 0 0
\(466\) 1.17430e6 0.250505
\(467\) 4.05050e6i 0.859441i 0.902962 + 0.429721i \(0.141388\pi\)
−0.902962 + 0.429721i \(0.858612\pi\)
\(468\) 0 0
\(469\) −5.07148e6 −1.06464
\(470\) 2.35004e6 + 427280.i 0.490716 + 0.0892212i
\(471\) 0 0
\(472\) 2.54336e6i 0.525476i
\(473\) 339512.i 0.0697754i
\(474\) 0 0
\(475\) −6.49350e6 2.44200e6i −1.32052 0.496606i
\(476\) −5.17734e6 −1.04734
\(477\) 0 0
\(478\) 2.33696e6i 0.467823i
\(479\) 5.60528e6 1.11624 0.558121 0.829759i \(-0.311522\pi\)
0.558121 + 0.829759i \(0.311522\pi\)
\(480\) 0 0
\(481\) −2.99045e6 −0.589350
\(482\) 2.25519e6i 0.442146i
\(483\) 0 0
\(484\) 2.22635e6 0.431997
\(485\) 972320. 5.34776e6i 0.187696 1.03233i
\(486\) 0 0
\(487\) 7.13168e6i 1.36260i −0.732003 0.681301i \(-0.761414\pi\)
0.732003 0.681301i \(-0.238586\pi\)
\(488\) 2.70707e6i 0.514577i
\(489\) 0 0
\(490\) 326280. 1.79454e6i 0.0613904 0.337647i
\(491\) −5.88145e6 −1.10098 −0.550492 0.834841i \(-0.685560\pi\)
−0.550492 + 0.834841i \(0.685560\pi\)
\(492\) 0 0
\(493\) 552960.i 0.102465i
\(494\) −6.07392e6 −1.11983
\(495\) 0 0
\(496\) −524288. −0.0956898
\(497\) 671184.i 0.121885i
\(498\) 0 0
\(499\) −1.75710e6 −0.315897 −0.157948 0.987447i \(-0.550488\pi\)
−0.157948 + 0.987447i \(0.550488\pi\)
\(500\) 2.39800e6 + 1.43600e6i 0.428967 + 0.256879i
\(501\) 0 0
\(502\) 4.07899e6i 0.722426i
\(503\) 4.91411e6i 0.866015i −0.901390 0.433007i \(-0.857452\pi\)
0.901390 0.433007i \(-0.142548\pi\)
\(504\) 0 0
\(505\) −236390. 42980.0i −0.0412478 0.00749960i
\(506\) 737632. 0.128075
\(507\) 0 0
\(508\) 2.80381e6i 0.482047i
\(509\) −5.75499e6 −0.984578 −0.492289 0.870432i \(-0.663840\pi\)
−0.492289 + 0.870432i \(0.663840\pi\)
\(510\) 0 0
\(511\) 4.75643e6 0.805803
\(512\) 262144.i 0.0441942i
\(513\) 0 0
\(514\) 2.62963e6 0.439023
\(515\) 1.24114e6 6.82627e6i 0.206207 1.13414i
\(516\) 0 0
\(517\) 1.58094e6i 0.260128i
\(518\) 2.76310e6i 0.452452i
\(519\) 0 0
\(520\) 2.40768e6 + 437760.i 0.390472 + 0.0709950i
\(521\) 1.61980e6 0.261437 0.130718 0.991420i \(-0.458272\pi\)
0.130718 + 0.991420i \(0.458272\pi\)
\(522\) 0 0
\(523\) 1.19117e7i 1.90422i 0.305751 + 0.952112i \(0.401093\pi\)
−0.305751 + 0.952112i \(0.598907\pi\)
\(524\) 4.79443e6 0.762797
\(525\) 0 0
\(526\) 2.24946e6 0.354499
\(527\) 4.19430e6i 0.657860i
\(528\) 0 0
\(529\) 4.88383e6 0.758789
\(530\) 652080. + 118560.i 0.100835 + 0.0183336i
\(531\) 0 0
\(532\) 5.61216e6i 0.859708i
\(533\) 1.64023e6i 0.250085i
\(534\) 0 0
\(535\) −423420. + 2.32881e6i −0.0639568 + 0.351763i
\(536\) 2.05427e6 0.308849
\(537\) 0 0
\(538\) 1.46628e6i 0.218404i
\(539\) −1.20724e6 −0.178986
\(540\) 0 0
\(541\) 4.07630e6 0.598788 0.299394 0.954130i \(-0.403215\pi\)
0.299394 + 0.954130i \(0.403215\pi\)
\(542\) 4.64301e6i 0.678893i
\(543\) 0 0
\(544\) 2.09715e6 0.303831
\(545\) −1.97945e6 359900.i −0.285465 0.0519028i
\(546\) 0 0
\(547\) 1.23680e7i 1.76739i −0.468065 0.883694i \(-0.655049\pi\)
0.468065 0.883694i \(-0.344951\pi\)
\(548\) 1.72685e6i 0.245642i
\(549\) 0 0
\(550\) 651200. 1.73160e6i 0.0917926 0.244085i
\(551\) 599400. 0.0841081
\(552\) 0 0
\(553\) 5.57424e6i 0.775127i
\(554\) 1.00600e7 1.39260
\(555\) 0 0
\(556\) −3.14336e6 −0.431228
\(557\) 130308.i 0.0177964i 0.999960 + 0.00889822i \(0.00283243\pi\)
−0.999960 + 0.00889822i \(0.997168\pi\)
\(558\) 0 0
\(559\) −1.56910e6 −0.212383
\(560\) −404480. + 2.22464e6i −0.0545038 + 0.299771i
\(561\) 0 0
\(562\) 8.34401e6i 1.11438i
\(563\) 5.91687e6i 0.786721i 0.919384 + 0.393361i \(0.128688\pi\)
−0.919384 + 0.393361i \(0.871312\pi\)
\(564\) 0 0
\(565\) 2.28816e6 1.25849e7i 0.301554 1.65855i
\(566\) −8.95210e6 −1.17458
\(567\) 0 0
\(568\) 271872.i 0.0353585i
\(569\) −9.03013e6 −1.16927 −0.584633 0.811298i \(-0.698761\pi\)
−0.584633 + 0.811298i \(0.698761\pi\)
\(570\) 0 0
\(571\) −1.07093e7 −1.37459 −0.687294 0.726379i \(-0.741202\pi\)
−0.687294 + 0.726379i \(0.741202\pi\)
\(572\) 1.61971e6i 0.206989i
\(573\) 0 0
\(574\) −1.51554e6 −0.191994
\(575\) −1.37060e6 + 3.64455e6i −0.172879 + 0.459700i
\(576\) 0 0
\(577\) 1.22051e6i 0.152617i 0.997084 + 0.0763084i \(0.0243134\pi\)
−0.997084 + 0.0763084i \(0.975687\pi\)
\(578\) 1.10978e7i 1.38171i
\(579\) 0 0
\(580\) −237600. 43200.0i −0.0293276 0.00533229i
\(581\) 4.39651e6 0.540341
\(582\) 0 0
\(583\) 438672.i 0.0534526i
\(584\) −1.92666e6 −0.233761
\(585\) 0 0
\(586\) 3.90302e6 0.469523
\(587\) 1.47104e7i 1.76210i −0.473026 0.881049i \(-0.656838\pi\)
0.473026 0.881049i \(-0.343162\pi\)
\(588\) 0 0
\(589\) 4.54656e6 0.540001
\(590\) 1.58960e6 8.74280e6i 0.188000 1.03400i
\(591\) 0 0
\(592\) 1.11923e6i 0.131255i
\(593\) 8.52014e6i 0.994970i −0.867472 0.497485i \(-0.834257\pi\)
0.867472 0.497485i \(-0.165743\pi\)
\(594\) 0 0
\(595\) −1.77971e7 3.23584e6i −2.06090 0.374709i
\(596\) −2.22160e6 −0.256183
\(597\) 0 0
\(598\) 3.40906e6i 0.389835i
\(599\) 2.90100e6 0.330355 0.165177 0.986264i \(-0.447180\pi\)
0.165177 + 0.986264i \(0.447180\pi\)
\(600\) 0 0
\(601\) 5.72760e6 0.646825 0.323412 0.946258i \(-0.395170\pi\)
0.323412 + 0.946258i \(0.395170\pi\)
\(602\) 1.44981e6i 0.163049i
\(603\) 0 0
\(604\) −6.65843e6 −0.742642
\(605\) 7.65308e6 + 1.39147e6i 0.850057 + 0.154556i
\(606\) 0 0
\(607\) 8.79924e6i 0.969334i 0.874699 + 0.484667i \(0.161059\pi\)
−0.874699 + 0.484667i \(0.838941\pi\)
\(608\) 2.27328e6i 0.249399i
\(609\) 0 0
\(610\) 1.69192e6 9.30556e6i 0.184101 1.01255i
\(611\) 7.30649e6 0.791782
\(612\) 0 0
\(613\) 1.03408e6i 0.111149i 0.998455 + 0.0555744i \(0.0176990\pi\)
−0.998455 + 0.0555744i \(0.982301\pi\)
\(614\) −351432. −0.0376201
\(615\) 0 0
\(616\) 1.49658e6 0.158908
\(617\) 1.29854e7i 1.37323i 0.727020 + 0.686616i \(0.240905\pi\)
−0.727020 + 0.686616i \(0.759095\pi\)
\(618\) 0 0
\(619\) −7.92002e6 −0.830806 −0.415403 0.909637i \(-0.636359\pi\)
−0.415403 + 0.909637i \(0.636359\pi\)
\(620\) −1.80224e6 327680.i −0.188293 0.0342350i
\(621\) 0 0
\(622\) 2.39741e6i 0.248465i
\(623\) 1.34632e7i 1.38972i
\(624\) 0 0
\(625\) 7.34562e6 + 6.43500e6i 0.752192 + 0.658944i
\(626\) −8.37366e6 −0.854043
\(627\) 0 0
\(628\) 6.92973e6i 0.701160i
\(629\) −8.95386e6 −0.902368
\(630\) 0 0
\(631\) 1.68218e7 1.68189 0.840945 0.541120i \(-0.181999\pi\)
0.840945 + 0.541120i \(0.181999\pi\)
\(632\) 2.25792e6i 0.224862i
\(633\) 0 0
\(634\) −9.66501e6 −0.954947
\(635\) −1.75238e6 + 9.63809e6i −0.172462 + 0.948542i
\(636\) 0 0
\(637\) 5.57939e6i 0.544801i
\(638\) 159840.i 0.0155465i
\(639\) 0 0
\(640\) 163840. 901120.i 0.0158114 0.0869626i
\(641\) 1.55154e7 1.49148 0.745741 0.666236i \(-0.232096\pi\)
0.745741 + 0.666236i \(0.232096\pi\)
\(642\) 0 0
\(643\) 1.05801e7i 1.00916i 0.863364 + 0.504582i \(0.168354\pi\)
−0.863364 + 0.504582i \(0.831646\pi\)
\(644\) −3.14989e6 −0.299282
\(645\) 0 0
\(646\) −1.81862e7 −1.71460
\(647\) 1.37883e7i 1.29494i 0.762090 + 0.647471i \(0.224173\pi\)
−0.762090 + 0.647471i \(0.775827\pi\)
\(648\) 0 0
\(649\) −5.88152e6 −0.548123
\(650\) 8.00280e6 + 3.00960e6i 0.742948 + 0.279399i
\(651\) 0 0
\(652\) 2.38614e6i 0.219825i
\(653\) 1.58924e6i 0.145850i 0.997337 + 0.0729248i \(0.0232333\pi\)
−0.997337 + 0.0729248i \(0.976767\pi\)
\(654\) 0 0
\(655\) 1.64809e7 + 2.99652e6i 1.50099 + 0.272907i
\(656\) 613888. 0.0556967
\(657\) 0 0
\(658\) 6.75102e6i 0.607862i
\(659\) −9.12434e6 −0.818442 −0.409221 0.912435i \(-0.634199\pi\)
−0.409221 + 0.912435i \(0.634199\pi\)
\(660\) 0 0
\(661\) 6.50310e6 0.578918 0.289459 0.957190i \(-0.406525\pi\)
0.289459 + 0.957190i \(0.406525\pi\)
\(662\) 6.56379e6i 0.582116i
\(663\) 0 0
\(664\) −1.78086e6 −0.156751
\(665\) 3.50760e6 1.92918e7i 0.307578 1.69168i
\(666\) 0 0
\(667\) 336420.i 0.0292797i
\(668\) 8.95363e6i 0.776351i
\(669\) 0 0
\(670\) 7.06156e6 + 1.28392e6i 0.607734 + 0.110497i
\(671\) −6.26010e6 −0.536754
\(672\) 0 0
\(673\) 2.17810e6i 0.185370i −0.995695 0.0926850i \(-0.970455\pi\)
0.995695 0.0926850i \(-0.0295449\pi\)
\(674\) −8.75091e6 −0.741999
\(675\) 0 0
\(676\) 1.54501e6 0.130036
\(677\) 3.98419e6i 0.334094i 0.985949 + 0.167047i \(0.0534231\pi\)
−0.985949 + 0.167047i \(0.946577\pi\)
\(678\) 0 0
\(679\) 1.53627e7 1.27877
\(680\) 7.20896e6 + 1.31072e6i 0.597861 + 0.108702i
\(681\) 0 0
\(682\) 1.21242e6i 0.0998138i
\(683\) 5.91563e6i 0.485231i 0.970122 + 0.242616i \(0.0780054\pi\)
−0.970122 + 0.242616i \(0.921995\pi\)
\(684\) 0 0
\(685\) 1.07928e6 5.93604e6i 0.0878836 0.483360i
\(686\) −5.46680e6 −0.443530
\(687\) 0 0
\(688\) 587264.i 0.0473001i
\(689\) 2.02738e6 0.162700
\(690\) 0 0
\(691\) −1.55471e7 −1.23867 −0.619335 0.785127i \(-0.712598\pi\)
−0.619335 + 0.785127i \(0.712598\pi\)
\(692\) 5.50086e6i 0.436682i
\(693\) 0 0
\(694\) 1.09801e7 0.865379
\(695\) −1.08053e7 1.96460e6i −0.848545 0.154281i
\(696\) 0 0
\(697\) 4.91110e6i 0.382910i
\(698\) 1.06046e7i 0.823864i
\(699\) 0 0
\(700\) −2.78080e6 + 7.39440e6i −0.214499 + 0.570372i
\(701\) 2.27103e7 1.74553 0.872766 0.488139i \(-0.162324\pi\)
0.872766 + 0.488139i \(0.162324\pi\)
\(702\) 0 0
\(703\) 9.70584e6i 0.740704i
\(704\) −606208. −0.0460988
\(705\) 0 0
\(706\) −1.22307e7 −0.923502
\(707\) 679084.i 0.0510946i
\(708\) 0 0
\(709\) −6.29841e6 −0.470560 −0.235280 0.971928i \(-0.575601\pi\)
−0.235280 + 0.971928i \(0.575601\pi\)
\(710\) −169920. + 934560.i −0.0126502 + 0.0695763i
\(711\) 0 0
\(712\) 5.45344e6i 0.403154i
\(713\) 2.55181e6i 0.187985i
\(714\) 0 0
\(715\) 1.01232e6 5.56776e6i 0.0740547 0.407301i
\(716\) −383680. −0.0279696
\(717\) 0 0
\(718\) 1.51742e7i 1.09849i
\(719\) 2.11911e7 1.52873 0.764367 0.644782i \(-0.223052\pi\)
0.764367 + 0.644782i \(0.223052\pi\)
\(720\) 0 0
\(721\) 1.96100e7 1.40488
\(722\) 9.80920e6i 0.700311i
\(723\) 0 0
\(724\) 1.04304e7 0.739526
\(725\) −789750. 297000.i −0.0558013 0.0209851i
\(726\) 0 0
\(727\) 1.35610e7i 0.951605i −0.879552 0.475803i \(-0.842158\pi\)
0.879552 0.475803i \(-0.157842\pi\)
\(728\) 6.91661e6i 0.483687i
\(729\) 0 0
\(730\) −6.62288e6 1.20416e6i −0.459981 0.0836329i
\(731\) −4.69811e6 −0.325185
\(732\) 0 0
\(733\) 2.69413e7i 1.85208i 0.377429 + 0.926038i \(0.376808\pi\)
−0.377429 + 0.926038i \(0.623192\pi\)
\(734\) 1.24424e7 0.852441
\(735\) 0 0
\(736\) 1.27590e6 0.0868207
\(737\) 4.75050e6i 0.322160i
\(738\) 0 0
\(739\) −2.77414e6 −0.186860 −0.0934302 0.995626i \(-0.529783\pi\)
−0.0934302 + 0.995626i \(0.529783\pi\)
\(740\) −699520. + 3.84736e6i −0.0469592 + 0.258276i
\(741\) 0 0
\(742\) 1.87325e6i 0.124907i
\(743\) 1.85538e7i 1.23299i −0.787358 0.616497i \(-0.788551\pi\)
0.787358 0.616497i \(-0.211449\pi\)
\(744\) 0 0
\(745\) −7.63675e6 1.38850e6i −0.504101 0.0916548i
\(746\) −5.66078e6 −0.372417
\(747\) 0 0
\(748\) 4.84966e6i 0.316926i
\(749\) −6.69004e6 −0.435736
\(750\) 0 0
\(751\) −2.19285e6 −0.141876 −0.0709380 0.997481i \(-0.522599\pi\)
−0.0709380 + 0.997481i \(0.522599\pi\)
\(752\) 2.73459e6i 0.176339i
\(753\) 0 0
\(754\) −738720. −0.0473207
\(755\) −2.28884e7 4.16152e6i −1.46133 0.265696i
\(756\) 0 0
\(757\) 9.48749e6i 0.601744i 0.953665 + 0.300872i \(0.0972777\pi\)
−0.953665 + 0.300872i \(0.902722\pi\)
\(758\) 1.56105e7i 0.986832i
\(759\) 0 0
\(760\) −1.42080e6 + 7.81440e6i −0.0892275 + 0.490752i
\(761\) −9.69580e6 −0.606907 −0.303453 0.952846i \(-0.598140\pi\)
−0.303453 + 0.952846i \(0.598140\pi\)
\(762\) 0 0
\(763\) 5.68642e6i 0.353612i
\(764\) 3.24403e6 0.201072
\(765\) 0 0
\(766\) −2.78270e6 −0.171354
\(767\) 2.71822e7i 1.66838i
\(768\) 0 0
\(769\) −9.32787e6 −0.568809 −0.284405 0.958704i \(-0.591796\pi\)
−0.284405 + 0.958704i \(0.591796\pi\)
\(770\) 5.14448e6 + 935360.i 0.312690 + 0.0568528i
\(771\) 0 0
\(772\) 7.24250e6i 0.437366i
\(773\) 9.68080e6i 0.582723i 0.956613 + 0.291362i \(0.0941083\pi\)
−0.956613 + 0.291362i \(0.905892\pi\)
\(774\) 0 0
\(775\) −5.99040e6 2.25280e6i −0.358263 0.134731i
\(776\) −6.22285e6 −0.370967
\(777\) 0 0
\(778\) 1.99316e6i 0.118057i
\(779\) −5.32356e6 −0.314310
\(780\) 0 0
\(781\) 628704. 0.0368824
\(782\) 1.02072e7i 0.596886i
\(783\) 0 0
\(784\) −2.08819e6 −0.121333
\(785\) −4.33108e6 + 2.38209e7i −0.250855 + 1.37970i
\(786\) 0 0
\(787\) 5.52302e6i 0.317863i 0.987290 + 0.158931i \(0.0508049\pi\)
−0.987290 + 0.158931i \(0.949195\pi\)
\(788\) 5.39949e6i 0.309768i
\(789\) 0 0
\(790\) 1.41120e6 7.76160e6i 0.0804490 0.442470i
\(791\) 3.61529e7 2.05448
\(792\) 0 0
\(793\) 2.89318e7i 1.63378i
\(794\) −4.38267e6 −0.246711
\(795\) 0 0
\(796\) −8.97600e6 −0.502112
\(797\) 1.71119e7i 0.954230i −0.878841 0.477115i \(-0.841682\pi\)
0.878841 0.477115i \(-0.158318\pi\)
\(798\) 0 0
\(799\) 2.18767e7 1.21232
\(800\) 1.12640e6 2.99520e6i 0.0622254 0.165463i
\(801\) 0 0
\(802\) 9.96639e6i 0.547145i
\(803\) 4.45539e6i 0.243836i
\(804\) 0