Properties

Label 80.6.n.d.63.5
Level $80$
Weight $6$
Character 80.63
Analytic conductor $12.831$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + 133816049059481 x^{8} + 14779507781220031 x^{6} + 824105698447750789 x^{4} + 12044868290803250652 x^{2} + 579398322543528055824\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{65}\cdot 3^{4}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 63.5
Root \(-1.99079 + 10.4027i\) of defining polynomial
Character \(\chi\) \(=\) 80.63
Dual form 80.6.n.d.47.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.839817 + 0.839817i) q^{3} +(3.71634 - 55.7780i) q^{5} +(99.3589 + 99.3589i) q^{7} +241.589i q^{9} +O(q^{10})\) \(q+(-0.839817 + 0.839817i) q^{3} +(3.71634 - 55.7780i) q^{5} +(99.3589 + 99.3589i) q^{7} +241.589i q^{9} -637.781i q^{11} +(-640.389 - 640.389i) q^{13} +(43.7223 + 49.9644i) q^{15} +(648.760 - 648.760i) q^{17} +2506.12 q^{19} -166.887 q^{21} +(2801.60 - 2801.60i) q^{23} +(-3097.38 - 414.580i) q^{25} +(-406.966 - 406.966i) q^{27} -4955.21i q^{29} -1961.18i q^{31} +(535.619 + 535.619i) q^{33} +(5911.30 - 5172.79i) q^{35} +(-1897.88 + 1897.88i) q^{37} +1075.62 q^{39} -5828.95 q^{41} +(-10692.1 + 10692.1i) q^{43} +(13475.4 + 897.828i) q^{45} +(8309.52 + 8309.52i) q^{47} +2937.38i q^{49} +1089.68i q^{51} +(7437.17 + 7437.17i) q^{53} +(-35574.2 - 2370.21i) q^{55} +(-2104.68 + 2104.68i) q^{57} -16738.4 q^{59} +23742.5 q^{61} +(-24004.1 + 24004.1i) q^{63} +(-38099.5 + 33339.7i) q^{65} +(4154.05 + 4154.05i) q^{67} +4705.66i q^{69} +12276.0i q^{71} +(36092.8 + 36092.8i) q^{73} +(2949.40 - 2253.06i) q^{75} +(63369.2 - 63369.2i) q^{77} +64330.4 q^{79} -58022.7 q^{81} +(-62856.9 + 62856.9i) q^{83} +(-33775.5 - 38597.6i) q^{85} +(4161.47 + 4161.47i) q^{87} -24423.5i q^{89} -127257. i q^{91} +(1647.03 + 1647.03i) q^{93} +(9313.60 - 139787. i) q^{95} +(-89666.0 + 89666.0i) q^{97} +154081. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 44q^{5} + O(q^{10}) \) \( 20q - 44q^{5} + 804q^{13} - 2236q^{17} - 4520q^{21} + 948q^{25} - 11096q^{33} + 44260q^{37} - 6760q^{41} - 92816q^{45} + 182452q^{53} - 34288q^{57} - 41080q^{61} - 155772q^{65} + 264372q^{73} + 399304q^{77} - 520220q^{81} - 344796q^{85} + 713496q^{93} + 374772q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.839817 + 0.839817i −0.0538743 + 0.0538743i −0.733531 0.679656i \(-0.762129\pi\)
0.679656 + 0.733531i \(0.262129\pi\)
\(4\) 0 0
\(5\) 3.71634 55.7780i 0.0664799 0.997788i
\(6\) 0 0
\(7\) 99.3589 + 99.3589i 0.766411 + 0.766411i 0.977473 0.211062i \(-0.0676921\pi\)
−0.211062 + 0.977473i \(0.567692\pi\)
\(8\) 0 0
\(9\) 241.589i 0.994195i
\(10\) 0 0
\(11\) 637.781i 1.58924i −0.607107 0.794620i \(-0.707670\pi\)
0.607107 0.794620i \(-0.292330\pi\)
\(12\) 0 0
\(13\) −640.389 640.389i −1.05096 1.05096i −0.998630 0.0523281i \(-0.983336\pi\)
−0.0523281 0.998630i \(-0.516664\pi\)
\(14\) 0 0
\(15\) 43.7223 + 49.9644i 0.0501736 + 0.0573367i
\(16\) 0 0
\(17\) 648.760 648.760i 0.544455 0.544455i −0.380377 0.924832i \(-0.624206\pi\)
0.924832 + 0.380377i \(0.124206\pi\)
\(18\) 0 0
\(19\) 2506.12 1.59264 0.796321 0.604874i \(-0.206776\pi\)
0.796321 + 0.604874i \(0.206776\pi\)
\(20\) 0 0
\(21\) −166.887 −0.0825797
\(22\) 0 0
\(23\) 2801.60 2801.60i 1.10430 1.10430i 0.110413 0.993886i \(-0.464783\pi\)
0.993886 0.110413i \(-0.0352174\pi\)
\(24\) 0 0
\(25\) −3097.38 414.580i −0.991161 0.132666i
\(26\) 0 0
\(27\) −406.966 406.966i −0.107436 0.107436i
\(28\) 0 0
\(29\) 4955.21i 1.09413i −0.837091 0.547063i \(-0.815746\pi\)
0.837091 0.547063i \(-0.184254\pi\)
\(30\) 0 0
\(31\) 1961.18i 0.366533i −0.983063 0.183267i \(-0.941333\pi\)
0.983063 0.183267i \(-0.0586672\pi\)
\(32\) 0 0
\(33\) 535.619 + 535.619i 0.0856192 + 0.0856192i
\(34\) 0 0
\(35\) 5911.30 5172.79i 0.815666 0.713765i
\(36\) 0 0
\(37\) −1897.88 + 1897.88i −0.227911 + 0.227911i −0.811819 0.583909i \(-0.801523\pi\)
0.583909 + 0.811819i \(0.301523\pi\)
\(38\) 0 0
\(39\) 1075.62 0.113239
\(40\) 0 0
\(41\) −5828.95 −0.541540 −0.270770 0.962644i \(-0.587278\pi\)
−0.270770 + 0.962644i \(0.587278\pi\)
\(42\) 0 0
\(43\) −10692.1 + 10692.1i −0.881844 + 0.881844i −0.993722 0.111878i \(-0.964314\pi\)
0.111878 + 0.993722i \(0.464314\pi\)
\(44\) 0 0
\(45\) 13475.4 + 897.828i 0.991996 + 0.0660940i
\(46\) 0 0
\(47\) 8309.52 + 8309.52i 0.548695 + 0.548695i 0.926063 0.377368i \(-0.123171\pi\)
−0.377368 + 0.926063i \(0.623171\pi\)
\(48\) 0 0
\(49\) 2937.38i 0.174771i
\(50\) 0 0
\(51\) 1089.68i 0.0586642i
\(52\) 0 0
\(53\) 7437.17 + 7437.17i 0.363679 + 0.363679i 0.865165 0.501487i \(-0.167213\pi\)
−0.501487 + 0.865165i \(0.667213\pi\)
\(54\) 0 0
\(55\) −35574.2 2370.21i −1.58572 0.105653i
\(56\) 0 0
\(57\) −2104.68 + 2104.68i −0.0858025 + 0.0858025i
\(58\) 0 0
\(59\) −16738.4 −0.626014 −0.313007 0.949751i \(-0.601336\pi\)
−0.313007 + 0.949751i \(0.601336\pi\)
\(60\) 0 0
\(61\) 23742.5 0.816961 0.408481 0.912767i \(-0.366059\pi\)
0.408481 + 0.912767i \(0.366059\pi\)
\(62\) 0 0
\(63\) −24004.1 + 24004.1i −0.761962 + 0.761962i
\(64\) 0 0
\(65\) −38099.5 + 33339.7i −1.11850 + 0.978765i
\(66\) 0 0
\(67\) 4154.05 + 4154.05i 0.113054 + 0.113054i 0.761371 0.648317i \(-0.224527\pi\)
−0.648317 + 0.761371i \(0.724527\pi\)
\(68\) 0 0
\(69\) 4705.66i 0.118987i
\(70\) 0 0
\(71\) 12276.0i 0.289008i 0.989504 + 0.144504i \(0.0461587\pi\)
−0.989504 + 0.144504i \(0.953841\pi\)
\(72\) 0 0
\(73\) 36092.8 + 36092.8i 0.792709 + 0.792709i 0.981934 0.189225i \(-0.0605976\pi\)
−0.189225 + 0.981934i \(0.560598\pi\)
\(74\) 0 0
\(75\) 2949.40 2253.06i 0.0605454 0.0462508i
\(76\) 0 0
\(77\) 63369.2 63369.2i 1.21801 1.21801i
\(78\) 0 0
\(79\) 64330.4 1.15971 0.579854 0.814721i \(-0.303110\pi\)
0.579854 + 0.814721i \(0.303110\pi\)
\(80\) 0 0
\(81\) −58022.7 −0.982619
\(82\) 0 0
\(83\) −62856.9 + 62856.9i −1.00152 + 1.00152i −0.00151672 + 0.999999i \(0.500483\pi\)
−0.999999 + 0.00151672i \(0.999517\pi\)
\(84\) 0 0
\(85\) −33775.5 38597.6i −0.507055 0.579446i
\(86\) 0 0
\(87\) 4161.47 + 4161.47i 0.0589453 + 0.0589453i
\(88\) 0 0
\(89\) 24423.5i 0.326838i −0.986557 0.163419i \(-0.947748\pi\)
0.986557 0.163419i \(-0.0522523\pi\)
\(90\) 0 0
\(91\) 127257.i 1.61093i
\(92\) 0 0
\(93\) 1647.03 + 1647.03i 0.0197467 + 0.0197467i
\(94\) 0 0
\(95\) 9313.60 139787.i 0.105879 1.58912i
\(96\) 0 0
\(97\) −89666.0 + 89666.0i −0.967605 + 0.967605i −0.999492 0.0318862i \(-0.989849\pi\)
0.0318862 + 0.999492i \(0.489849\pi\)
\(98\) 0 0
\(99\) 154081. 1.58002
\(100\) 0 0
\(101\) 31536.0 0.307612 0.153806 0.988101i \(-0.450847\pi\)
0.153806 + 0.988101i \(0.450847\pi\)
\(102\) 0 0
\(103\) 4384.20 4384.20i 0.0407190 0.0407190i −0.686454 0.727173i \(-0.740834\pi\)
0.727173 + 0.686454i \(0.240834\pi\)
\(104\) 0 0
\(105\) −620.207 + 9308.61i −0.00548989 + 0.0823970i
\(106\) 0 0
\(107\) 150691. + 150691.i 1.27241 + 1.27241i 0.944820 + 0.327589i \(0.106236\pi\)
0.327589 + 0.944820i \(0.393764\pi\)
\(108\) 0 0
\(109\) 201206.i 1.62209i −0.584984 0.811045i \(-0.698899\pi\)
0.584984 0.811045i \(-0.301101\pi\)
\(110\) 0 0
\(111\) 3187.75i 0.0245571i
\(112\) 0 0
\(113\) −25930.0 25930.0i −0.191032 0.191032i 0.605110 0.796142i \(-0.293129\pi\)
−0.796142 + 0.605110i \(0.793129\pi\)
\(114\) 0 0
\(115\) −145856. 166679.i −1.02844 1.17527i
\(116\) 0 0
\(117\) 154711. 154711.i 1.04486 1.04486i
\(118\) 0 0
\(119\) 128920. 0.834552
\(120\) 0 0
\(121\) −245713. −1.52569
\(122\) 0 0
\(123\) 4895.25 4895.25i 0.0291751 0.0291751i
\(124\) 0 0
\(125\) −34635.4 + 171225.i −0.198264 + 0.980149i
\(126\) 0 0
\(127\) 46278.8 + 46278.8i 0.254609 + 0.254609i 0.822857 0.568248i \(-0.192379\pi\)
−0.568248 + 0.822857i \(0.692379\pi\)
\(128\) 0 0
\(129\) 17958.8i 0.0950175i
\(130\) 0 0
\(131\) 83739.0i 0.426333i −0.977016 0.213167i \(-0.931622\pi\)
0.977016 0.213167i \(-0.0683777\pi\)
\(132\) 0 0
\(133\) 249006. + 249006.i 1.22062 + 1.22062i
\(134\) 0 0
\(135\) −24212.2 + 21187.4i −0.114341 + 0.100056i
\(136\) 0 0
\(137\) 29275.6 29275.6i 0.133261 0.133261i −0.637330 0.770591i \(-0.719961\pi\)
0.770591 + 0.637330i \(0.219961\pi\)
\(138\) 0 0
\(139\) −56681.4 −0.248830 −0.124415 0.992230i \(-0.539705\pi\)
−0.124415 + 0.992230i \(0.539705\pi\)
\(140\) 0 0
\(141\) −13957.0 −0.0591211
\(142\) 0 0
\(143\) −408428. + 408428.i −1.67023 + 1.67023i
\(144\) 0 0
\(145\) −276392. 18415.3i −1.09171 0.0727374i
\(146\) 0 0
\(147\) −2466.86 2466.86i −0.00941568 0.00941568i
\(148\) 0 0
\(149\) 30050.0i 0.110886i −0.998462 0.0554432i \(-0.982343\pi\)
0.998462 0.0554432i \(-0.0176572\pi\)
\(150\) 0 0
\(151\) 255984.i 0.913631i −0.889561 0.456816i \(-0.848990\pi\)
0.889561 0.456816i \(-0.151010\pi\)
\(152\) 0 0
\(153\) 156734. + 156734.i 0.541294 + 0.541294i
\(154\) 0 0
\(155\) −109391. 7288.42i −0.365723 0.0243671i
\(156\) 0 0
\(157\) 30035.3 30035.3i 0.0972486 0.0972486i −0.656809 0.754057i \(-0.728094\pi\)
0.754057 + 0.656809i \(0.228094\pi\)
\(158\) 0 0
\(159\) −12491.7 −0.0391859
\(160\) 0 0
\(161\) 556728. 1.69269
\(162\) 0 0
\(163\) −397588. + 397588.i −1.17210 + 1.17210i −0.190391 + 0.981708i \(0.560976\pi\)
−0.981708 + 0.190391i \(0.939024\pi\)
\(164\) 0 0
\(165\) 31866.3 27885.2i 0.0911218 0.0797379i
\(166\) 0 0
\(167\) 162249. + 162249.i 0.450185 + 0.450185i 0.895416 0.445231i \(-0.146878\pi\)
−0.445231 + 0.895416i \(0.646878\pi\)
\(168\) 0 0
\(169\) 448903.i 1.20903i
\(170\) 0 0
\(171\) 605453.i 1.58340i
\(172\) 0 0
\(173\) −158564. 158564.i −0.402800 0.402800i 0.476419 0.879219i \(-0.341935\pi\)
−0.879219 + 0.476419i \(0.841935\pi\)
\(174\) 0 0
\(175\) −266560. 348944.i −0.657960 0.861313i
\(176\) 0 0
\(177\) 14057.2 14057.2i 0.0337261 0.0337261i
\(178\) 0 0
\(179\) 509602. 1.18877 0.594386 0.804180i \(-0.297395\pi\)
0.594386 + 0.804180i \(0.297395\pi\)
\(180\) 0 0
\(181\) −356971. −0.809910 −0.404955 0.914337i \(-0.632713\pi\)
−0.404955 + 0.914337i \(0.632713\pi\)
\(182\) 0 0
\(183\) −19939.3 + 19939.3i −0.0440132 + 0.0440132i
\(184\) 0 0
\(185\) 98807.0 + 112913.i 0.212255 + 0.242558i
\(186\) 0 0
\(187\) −413767. 413767.i −0.865270 0.865270i
\(188\) 0 0
\(189\) 80871.5i 0.164680i
\(190\) 0 0
\(191\) 296067.i 0.587227i −0.955924 0.293614i \(-0.905142\pi\)
0.955924 0.293614i \(-0.0948579\pi\)
\(192\) 0 0
\(193\) 10953.8 + 10953.8i 0.0211676 + 0.0211676i 0.717611 0.696444i \(-0.245235\pi\)
−0.696444 + 0.717611i \(0.745235\pi\)
\(194\) 0 0
\(195\) 3997.37 59995.9i 0.00752813 0.112989i
\(196\) 0 0
\(197\) −153834. + 153834.i −0.282415 + 0.282415i −0.834071 0.551656i \(-0.813996\pi\)
0.551656 + 0.834071i \(0.313996\pi\)
\(198\) 0 0
\(199\) −415211. −0.743252 −0.371626 0.928383i \(-0.621200\pi\)
−0.371626 + 0.928383i \(0.621200\pi\)
\(200\) 0 0
\(201\) −6977.28 −0.0121814
\(202\) 0 0
\(203\) 492345. 492345.i 0.838550 0.838550i
\(204\) 0 0
\(205\) −21662.4 + 325127.i −0.0360016 + 0.540342i
\(206\) 0 0
\(207\) 676837. + 676837.i 1.09789 + 1.09789i
\(208\) 0 0
\(209\) 1.59836e6i 2.53109i
\(210\) 0 0
\(211\) 673870.i 1.04200i −0.853555 0.521002i \(-0.825558\pi\)
0.853555 0.521002i \(-0.174442\pi\)
\(212\) 0 0
\(213\) −10309.6 10309.6i −0.0155701 0.0155701i
\(214\) 0 0
\(215\) 556649. + 636120.i 0.821269 + 0.938518i
\(216\) 0 0
\(217\) 194861. 194861.i 0.280915 0.280915i
\(218\) 0 0
\(219\) −60622.7 −0.0854132
\(220\) 0 0
\(221\) −830917. −1.14440
\(222\) 0 0
\(223\) 916244. 916244.i 1.23381 1.23381i 0.271323 0.962488i \(-0.412539\pi\)
0.962488 0.271323i \(-0.0874611\pi\)
\(224\) 0 0
\(225\) 100158. 748294.i 0.131896 0.985407i
\(226\) 0 0
\(227\) 317650. + 317650.i 0.409152 + 0.409152i 0.881443 0.472291i \(-0.156573\pi\)
−0.472291 + 0.881443i \(0.656573\pi\)
\(228\) 0 0
\(229\) 1.15003e6i 1.44917i 0.689183 + 0.724587i \(0.257970\pi\)
−0.689183 + 0.724587i \(0.742030\pi\)
\(230\) 0 0
\(231\) 106437.i 0.131239i
\(232\) 0 0
\(233\) 290928. + 290928.i 0.351071 + 0.351071i 0.860508 0.509437i \(-0.170146\pi\)
−0.509437 + 0.860508i \(0.670146\pi\)
\(234\) 0 0
\(235\) 494370. 432608.i 0.583959 0.511004i
\(236\) 0 0
\(237\) −54025.7 + 54025.7i −0.0624784 + 0.0624784i
\(238\) 0 0
\(239\) 152082. 0.172220 0.0861101 0.996286i \(-0.472556\pi\)
0.0861101 + 0.996286i \(0.472556\pi\)
\(240\) 0 0
\(241\) 43181.5 0.0478912 0.0239456 0.999713i \(-0.492377\pi\)
0.0239456 + 0.999713i \(0.492377\pi\)
\(242\) 0 0
\(243\) 147621. 147621.i 0.160374 0.160374i
\(244\) 0 0
\(245\) 163841. + 10916.3i 0.174385 + 0.0116188i
\(246\) 0 0
\(247\) −1.60489e6 1.60489e6i −1.67380 1.67380i
\(248\) 0 0
\(249\) 105577.i 0.107912i
\(250\) 0 0
\(251\) 547660.i 0.548689i 0.961631 + 0.274345i \(0.0884609\pi\)
−0.961631 + 0.274345i \(0.911539\pi\)
\(252\) 0 0
\(253\) −1.78681e6 1.78681e6i −1.75500 1.75500i
\(254\) 0 0
\(255\) 60780.2 + 4049.62i 0.0585344 + 0.00389999i
\(256\) 0 0
\(257\) −226438. + 226438.i −0.213853 + 0.213853i −0.805902 0.592049i \(-0.798319\pi\)
0.592049 + 0.805902i \(0.298319\pi\)
\(258\) 0 0
\(259\) −377143. −0.349347
\(260\) 0 0
\(261\) 1.19713e6 1.08778
\(262\) 0 0
\(263\) −21617.3 + 21617.3i −0.0192714 + 0.0192714i −0.716677 0.697405i \(-0.754338\pi\)
0.697405 + 0.716677i \(0.254338\pi\)
\(264\) 0 0
\(265\) 442470. 387191.i 0.387051 0.338697i
\(266\) 0 0
\(267\) 20511.3 + 20511.3i 0.0176082 + 0.0176082i
\(268\) 0 0
\(269\) 1.78124e6i 1.50087i 0.660947 + 0.750433i \(0.270155\pi\)
−0.660947 + 0.750433i \(0.729845\pi\)
\(270\) 0 0
\(271\) 1.45155e6i 1.20063i 0.799765 + 0.600314i \(0.204958\pi\)
−0.799765 + 0.600314i \(0.795042\pi\)
\(272\) 0 0
\(273\) 106872. + 106872.i 0.0867878 + 0.0867878i
\(274\) 0 0
\(275\) −264411. + 1.97545e6i −0.210838 + 1.57519i
\(276\) 0 0
\(277\) −831788. + 831788.i −0.651348 + 0.651348i −0.953318 0.301969i \(-0.902356\pi\)
0.301969 + 0.953318i \(0.402356\pi\)
\(278\) 0 0
\(279\) 473801. 0.364406
\(280\) 0 0
\(281\) 2.43146e6 1.83696 0.918482 0.395463i \(-0.129416\pi\)
0.918482 + 0.395463i \(0.129416\pi\)
\(282\) 0 0
\(283\) 141203. 141203.i 0.104804 0.104804i −0.652760 0.757565i \(-0.726389\pi\)
0.757565 + 0.652760i \(0.226389\pi\)
\(284\) 0 0
\(285\) 109573. + 125217.i 0.0799085 + 0.0913168i
\(286\) 0 0
\(287\) −579158. 579158.i −0.415042 0.415042i
\(288\) 0 0
\(289\) 578078.i 0.407138i
\(290\) 0 0
\(291\) 150606.i 0.104258i
\(292\) 0 0
\(293\) 540576. + 540576.i 0.367864 + 0.367864i 0.866698 0.498834i \(-0.166238\pi\)
−0.498834 + 0.866698i \(0.666238\pi\)
\(294\) 0 0
\(295\) −62205.6 + 933636.i −0.0416174 + 0.624629i
\(296\) 0 0
\(297\) −259555. + 259555.i −0.170741 + 0.170741i
\(298\) 0 0
\(299\) −3.58823e6 −2.32114
\(300\) 0 0
\(301\) −2.12471e6 −1.35171
\(302\) 0 0
\(303\) −26484.5 + 26484.5i −0.0165724 + 0.0165724i
\(304\) 0 0
\(305\) 88235.1 1.32431e6i 0.0543115 0.815154i
\(306\) 0 0
\(307\) −779170. 779170.i −0.471831 0.471831i 0.430676 0.902507i \(-0.358275\pi\)
−0.902507 + 0.430676i \(0.858275\pi\)
\(308\) 0 0
\(309\) 7363.86i 0.00438742i
\(310\) 0 0
\(311\) 1.56490e6i 0.917459i 0.888576 + 0.458730i \(0.151695\pi\)
−0.888576 + 0.458730i \(0.848305\pi\)
\(312\) 0 0
\(313\) 684828. + 684828.i 0.395112 + 0.395112i 0.876505 0.481393i \(-0.159869\pi\)
−0.481393 + 0.876505i \(0.659869\pi\)
\(314\) 0 0
\(315\) 1.24969e6 + 1.42811e6i 0.709621 + 0.810932i
\(316\) 0 0
\(317\) 1.90957e6 1.90957e6i 1.06730 1.06730i 0.0697372 0.997565i \(-0.477784\pi\)
0.997565 0.0697372i \(-0.0222161\pi\)
\(318\) 0 0
\(319\) −3.16034e6 −1.73883
\(320\) 0 0
\(321\) −253105. −0.137100
\(322\) 0 0
\(323\) 1.62587e6 1.62587e6i 0.867122 0.867122i
\(324\) 0 0
\(325\) 1.71803e6 + 2.24902e6i 0.902242 + 1.18109i
\(326\) 0 0
\(327\) 168976. + 168976.i 0.0873890 + 0.0873890i
\(328\) 0 0
\(329\) 1.65125e6i 0.841052i
\(330\) 0 0
\(331\) 740425.i 0.371459i −0.982601 0.185730i \(-0.940535\pi\)
0.982601 0.185730i \(-0.0594649\pi\)
\(332\) 0 0
\(333\) −458508. 458508.i −0.226588 0.226588i
\(334\) 0 0
\(335\) 247142. 216267.i 0.120319 0.105288i
\(336\) 0 0
\(337\) −2.17170e6 + 2.17170e6i −1.04166 + 1.04166i −0.0425641 + 0.999094i \(0.513553\pi\)
−0.999094 + 0.0425641i \(0.986447\pi\)
\(338\) 0 0
\(339\) 43553.0 0.0205835
\(340\) 0 0
\(341\) −1.25080e6 −0.582510
\(342\) 0 0
\(343\) 1.37807e6 1.37807e6i 0.632464 0.632464i
\(344\) 0 0
\(345\) 262473. + 17487.8i 0.118723 + 0.00791022i
\(346\) 0 0
\(347\) 706412. + 706412.i 0.314945 + 0.314945i 0.846822 0.531877i \(-0.178513\pi\)
−0.531877 + 0.846822i \(0.678513\pi\)
\(348\) 0 0
\(349\) 3.03307e6i 1.33297i −0.745520 0.666483i \(-0.767799\pi\)
0.745520 0.666483i \(-0.232201\pi\)
\(350\) 0 0
\(351\) 521234.i 0.225821i
\(352\) 0 0
\(353\) −2.72516e6 2.72516e6i −1.16401 1.16401i −0.983590 0.180418i \(-0.942255\pi\)
−0.180418 0.983590i \(-0.557745\pi\)
\(354\) 0 0
\(355\) 684730. + 45621.7i 0.288369 + 0.0192132i
\(356\) 0 0
\(357\) −108269. + 108269.i −0.0449609 + 0.0449609i
\(358\) 0 0
\(359\) 2.47478e6 1.01345 0.506723 0.862109i \(-0.330857\pi\)
0.506723 + 0.862109i \(0.330857\pi\)
\(360\) 0 0
\(361\) 3.80455e6 1.53651
\(362\) 0 0
\(363\) 206354. 206354.i 0.0821953 0.0821953i
\(364\) 0 0
\(365\) 2.14732e6 1.87905e6i 0.843654 0.738256i
\(366\) 0 0
\(367\) −405936. 405936.i −0.157323 0.157323i 0.624056 0.781379i \(-0.285484\pi\)
−0.781379 + 0.624056i \(0.785484\pi\)
\(368\) 0 0
\(369\) 1.40821e6i 0.538397i
\(370\) 0 0
\(371\) 1.47790e6i 0.557455i
\(372\) 0 0
\(373\) −378559. 378559.i −0.140884 0.140884i 0.633147 0.774031i \(-0.281763\pi\)
−0.774031 + 0.633147i \(0.781763\pi\)
\(374\) 0 0
\(375\) −114710. 172885.i −0.0421235 0.0634862i
\(376\) 0 0
\(377\) −3.17326e6 + 3.17326e6i −1.14988 + 1.14988i
\(378\) 0 0
\(379\) 3.91279e6 1.39923 0.699614 0.714521i \(-0.253355\pi\)
0.699614 + 0.714521i \(0.253355\pi\)
\(380\) 0 0
\(381\) −77731.5 −0.0274337
\(382\) 0 0
\(383\) 2.53247e6 2.53247e6i 0.882161 0.882161i −0.111593 0.993754i \(-0.535595\pi\)
0.993754 + 0.111593i \(0.0355952\pi\)
\(384\) 0 0
\(385\) −3.29911e6 3.77011e6i −1.13434 1.29629i
\(386\) 0 0
\(387\) −2.58310e6 2.58310e6i −0.876725 0.876725i
\(388\) 0 0
\(389\) 3.01392e6i 1.00985i 0.863163 + 0.504925i \(0.168480\pi\)
−0.863163 + 0.504925i \(0.831520\pi\)
\(390\) 0 0
\(391\) 3.63513e6i 1.20248i
\(392\) 0 0
\(393\) 70325.4 + 70325.4i 0.0229684 + 0.0229684i
\(394\) 0 0
\(395\) 239074. 3.58822e6i 0.0770972 1.15714i
\(396\) 0 0
\(397\) 3.43650e6 3.43650e6i 1.09431 1.09431i 0.0992459 0.995063i \(-0.468357\pi\)
0.995063 0.0992459i \(-0.0316430\pi\)
\(398\) 0 0
\(399\) −418238. −0.131520
\(400\) 0 0
\(401\) −4.30306e6 −1.33634 −0.668169 0.744009i \(-0.732922\pi\)
−0.668169 + 0.744009i \(0.732922\pi\)
\(402\) 0 0
\(403\) −1.25592e6 + 1.25592e6i −0.385211 + 0.385211i
\(404\) 0 0
\(405\) −215632. + 3.23639e6i −0.0653244 + 0.980445i
\(406\) 0 0
\(407\) 1.21043e6 + 1.21043e6i 0.362205 + 0.362205i
\(408\) 0 0
\(409\) 452926.i 0.133881i 0.997757 + 0.0669405i \(0.0213238\pi\)
−0.997757 + 0.0669405i \(0.978676\pi\)
\(410\) 0 0
\(411\) 49172.2i 0.0143587i
\(412\) 0 0
\(413\) −1.66311e6 1.66311e6i −0.479784 0.479784i
\(414\) 0 0
\(415\) 3.27244e6 + 3.73963e6i 0.932719 + 1.06588i
\(416\) 0 0
\(417\) 47602.0 47602.0i 0.0134056 0.0134056i
\(418\) 0 0
\(419\) −448753. −0.124874 −0.0624370 0.998049i \(-0.519887\pi\)
−0.0624370 + 0.998049i \(0.519887\pi\)
\(420\) 0 0
\(421\) 3.61031e6 0.992748 0.496374 0.868109i \(-0.334664\pi\)
0.496374 + 0.868109i \(0.334664\pi\)
\(422\) 0 0
\(423\) −2.00749e6 + 2.00749e6i −0.545510 + 0.545510i
\(424\) 0 0
\(425\) −2.27842e6 + 1.74049e6i −0.611873 + 0.467412i
\(426\) 0 0
\(427\) 2.35903e6 + 2.35903e6i 0.626128 + 0.626128i
\(428\) 0 0
\(429\) 686009.i 0.179964i
\(430\) 0 0
\(431\) 3.33480e6i 0.864722i −0.901701 0.432361i \(-0.857681\pi\)
0.901701 0.432361i \(-0.142319\pi\)
\(432\) 0 0
\(433\) 4.26797e6 + 4.26797e6i 1.09396 + 1.09396i 0.995101 + 0.0988602i \(0.0315197\pi\)
0.0988602 + 0.995101i \(0.468480\pi\)
\(434\) 0 0
\(435\) 247584. 216653.i 0.0627336 0.0548962i
\(436\) 0 0
\(437\) 7.02115e6 7.02115e6i 1.75875 1.75875i
\(438\) 0 0
\(439\) −985119. −0.243965 −0.121982 0.992532i \(-0.538925\pi\)
−0.121982 + 0.992532i \(0.538925\pi\)
\(440\) 0 0
\(441\) −709641. −0.173757
\(442\) 0 0
\(443\) −941343. + 941343.i −0.227897 + 0.227897i −0.811814 0.583917i \(-0.801519\pi\)
0.583917 + 0.811814i \(0.301519\pi\)
\(444\) 0 0
\(445\) −1.36229e6 90766.0i −0.326115 0.0217282i
\(446\) 0 0
\(447\) 25236.5 + 25236.5i 0.00597393 + 0.00597393i
\(448\) 0 0
\(449\) 2.05024e6i 0.479941i −0.970780 0.239971i \(-0.922862\pi\)
0.970780 0.239971i \(-0.0771378\pi\)
\(450\) 0 0
\(451\) 3.71759e6i 0.860638i
\(452\) 0 0
\(453\) 214980. + 214980.i 0.0492213 + 0.0492213i
\(454\) 0 0
\(455\) −7.09813e6 472929.i −1.60737 0.107095i
\(456\) 0 0
\(457\) −5.54554e6 + 5.54554e6i −1.24209 + 1.24209i −0.282958 + 0.959132i \(0.591316\pi\)
−0.959132 + 0.282958i \(0.908684\pi\)
\(458\) 0 0
\(459\) −528047. −0.116988
\(460\) 0 0
\(461\) −3.71258e6 −0.813624 −0.406812 0.913512i \(-0.633360\pi\)
−0.406812 + 0.913512i \(0.633360\pi\)
\(462\) 0 0
\(463\) −4.14889e6 + 4.14889e6i −0.899455 + 0.899455i −0.995388 0.0959328i \(-0.969417\pi\)
0.0959328 + 0.995388i \(0.469417\pi\)
\(464\) 0 0
\(465\) 97989.3 85747.4i 0.0210158 0.0183903i
\(466\) 0 0
\(467\) −599788. 599788.i −0.127264 0.127264i 0.640606 0.767870i \(-0.278683\pi\)
−0.767870 + 0.640606i \(0.778683\pi\)
\(468\) 0 0
\(469\) 825483.i 0.173291i
\(470\) 0 0
\(471\) 50448.4i 0.0104784i
\(472\) 0 0
\(473\) 6.81922e6 + 6.81922e6i 1.40146 + 1.40146i
\(474\) 0 0
\(475\) −7.76241e6 1.03899e6i −1.57857 0.211289i
\(476\) 0 0
\(477\) −1.79674e6 + 1.79674e6i −0.361568 + 0.361568i
\(478\) 0 0
\(479\) 130460. 0.0259799 0.0129900 0.999916i \(-0.495865\pi\)
0.0129900 + 0.999916i \(0.495865\pi\)
\(480\) 0 0
\(481\) 2.43077e6 0.479049
\(482\) 0 0
\(483\) −467550. + 467550.i −0.0911927 + 0.0911927i
\(484\) 0 0
\(485\) 4.66816e6 + 5.33462e6i 0.901138 + 1.02979i
\(486\) 0 0
\(487\) 5.53566e6 + 5.53566e6i 1.05766 + 1.05766i 0.998232 + 0.0594298i \(0.0189283\pi\)
0.0594298 + 0.998232i \(0.481072\pi\)
\(488\) 0 0
\(489\) 667803.i 0.126292i
\(490\) 0 0
\(491\) 2.06198e6i 0.385993i −0.981199 0.192997i \(-0.938179\pi\)
0.981199 0.192997i \(-0.0618206\pi\)
\(492\) 0 0
\(493\) −3.21474e6 3.21474e6i −0.595702 0.595702i
\(494\) 0 0
\(495\) 572618. 8.59434e6i 0.105039 1.57652i
\(496\) 0 0
\(497\) −1.21973e6 + 1.21973e6i −0.221499 + 0.221499i
\(498\) 0 0
\(499\) 3.96927e6 0.713608 0.356804 0.934179i \(-0.383866\pi\)
0.356804 + 0.934179i \(0.383866\pi\)
\(500\) 0 0
\(501\) −272519. −0.0485068
\(502\) 0 0
\(503\) −7.68593e6 + 7.68593e6i −1.35449 + 1.35449i −0.473928 + 0.880564i \(0.657164\pi\)
−0.880564 + 0.473928i \(0.842836\pi\)
\(504\) 0 0
\(505\) 117199. 1.75902e6i 0.0204500 0.306932i
\(506\) 0 0
\(507\) −376996. 376996.i −0.0651354 0.0651354i
\(508\) 0 0
\(509\) 149834.i 0.0256340i 0.999918 + 0.0128170i \(0.00407988\pi\)
−0.999918 + 0.0128170i \(0.995920\pi\)
\(510\) 0 0
\(511\) 7.17229e6i 1.21508i
\(512\) 0 0
\(513\) −1.01991e6 1.01991e6i −0.171107 0.171107i
\(514\) 0 0
\(515\) −228249. 260835.i −0.0379220 0.0433360i
\(516\) 0 0
\(517\) 5.29965e6 5.29965e6i 0.872009 0.872009i
\(518\) 0 0
\(519\) 266330. 0.0434011
\(520\) 0 0
\(521\) 1.13714e6 0.183536 0.0917678 0.995780i \(-0.470748\pi\)
0.0917678 + 0.995780i \(0.470748\pi\)
\(522\) 0 0
\(523\) −4.86949e6 + 4.86949e6i −0.778447 + 0.778447i −0.979567 0.201119i \(-0.935542\pi\)
0.201119 + 0.979567i \(0.435542\pi\)
\(524\) 0 0
\(525\) 516911. + 69187.9i 0.0818498 + 0.0109555i
\(526\) 0 0
\(527\) −1.27234e6 1.27234e6i −0.199561 0.199561i
\(528\) 0 0
\(529\) 9.26159e6i 1.43895i
\(530\) 0 0
\(531\) 4.04382e6i 0.622380i
\(532\) 0 0
\(533\) 3.73280e6 + 3.73280e6i 0.569136 + 0.569136i
\(534\) 0 0
\(535\) 8.96524e6 7.84521e6i 1.35418 1.18500i
\(536\) 0 0
\(537\) −427972. + 427972.i −0.0640442 + 0.0640442i
\(538\) 0 0
\(539\) 1.87341e6 0.277754
\(540\) 0 0
\(541\) −6.42771e6 −0.944198 −0.472099 0.881546i \(-0.656503\pi\)
−0.472099 + 0.881546i \(0.656503\pi\)
\(542\) 0 0
\(543\) 299790. 299790.i 0.0436333 0.0436333i
\(544\) 0 0
\(545\) −1.12229e7 747751.i −1.61850 0.107836i
\(546\) 0 0
\(547\) 6.88980e6 + 6.88980e6i 0.984551 + 0.984551i 0.999882 0.0153314i \(-0.00488033\pi\)
−0.0153314 + 0.999882i \(0.504880\pi\)
\(548\) 0 0
\(549\) 5.73593e6i 0.812219i
\(550\) 0 0
\(551\) 1.24184e7i 1.74255i
\(552\) 0 0
\(553\) 6.39179e6 + 6.39179e6i 0.888812 + 0.888812i
\(554\) 0 0
\(555\) −177806. 11846.8i −0.0245027 0.00163255i
\(556\) 0 0
\(557\) −626234. + 626234.i −0.0855261 + 0.0855261i −0.748576 0.663049i \(-0.769262\pi\)
0.663049 + 0.748576i \(0.269262\pi\)
\(558\) 0 0
\(559\) 1.36942e7 1.85356
\(560\) 0 0
\(561\) 694977. 0.0932316
\(562\) 0 0
\(563\) 3.78102e6 3.78102e6i 0.502733 0.502733i −0.409553 0.912286i \(-0.634315\pi\)
0.912286 + 0.409553i \(0.134315\pi\)
\(564\) 0 0
\(565\) −1.54269e6 + 1.34996e6i −0.203309 + 0.177910i
\(566\) 0 0
\(567\) −5.76507e6 5.76507e6i −0.753090 0.753090i
\(568\) 0 0
\(569\) 5.86991e6i 0.760065i −0.924973 0.380032i \(-0.875913\pi\)
0.924973 0.380032i \(-0.124087\pi\)
\(570\) 0 0
\(571\) 3.63228e6i 0.466218i −0.972451 0.233109i \(-0.925110\pi\)
0.972451 0.233109i \(-0.0748899\pi\)
\(572\) 0 0
\(573\) 248642. + 248642.i 0.0316365 + 0.0316365i
\(574\) 0 0
\(575\) −9.83910e6 + 7.51613e6i −1.24104 + 0.948035i
\(576\) 0 0
\(577\) 7.85335e6 7.85335e6i 0.982009 0.982009i −0.0178322 0.999841i \(-0.505676\pi\)
0.999841 + 0.0178322i \(0.00567647\pi\)
\(578\) 0 0
\(579\) −18398.4 −0.00228078
\(580\) 0 0
\(581\) −1.24908e7 −1.53514
\(582\) 0 0
\(583\) 4.74328e6 4.74328e6i 0.577973 0.577973i
\(584\) 0 0
\(585\) −8.05452e6 9.20444e6i −0.973084 1.11201i
\(586\) 0 0
\(587\) 4.62105e6 + 4.62105e6i 0.553535 + 0.553535i 0.927459 0.373924i \(-0.121988\pi\)
−0.373924 + 0.927459i \(0.621988\pi\)
\(588\) 0 0
\(589\) 4.91496e6i 0.583757i
\(590\) 0 0
\(591\) 258386.i 0.0304298i
\(592\) 0 0
\(593\) −6.65088e6 6.65088e6i −0.776681 0.776681i 0.202584 0.979265i \(-0.435066\pi\)
−0.979265 + 0.202584i \(0.935066\pi\)
\(594\) 0 0
\(595\) 479111. 7.19091e6i 0.0554809 0.832706i
\(596\) 0 0
\(597\) 348701. 348701.i 0.0400422 0.0400422i
\(598\) 0 0
\(599\) 4.31406e6 0.491269 0.245634 0.969363i \(-0.421004\pi\)
0.245634 + 0.969363i \(0.421004\pi\)
\(600\) 0 0
\(601\) 1.43695e7 1.62277 0.811384 0.584513i \(-0.198714\pi\)
0.811384 + 0.584513i \(0.198714\pi\)
\(602\) 0 0
\(603\) −1.00357e6 + 1.00357e6i −0.112397 + 0.112397i
\(604\) 0 0
\(605\) −913154. + 1.37054e7i −0.101427 + 1.52231i
\(606\) 0 0
\(607\) 997962. + 997962.i 0.109937 + 0.109937i 0.759935 0.649999i \(-0.225231\pi\)
−0.649999 + 0.759935i \(0.725231\pi\)
\(608\) 0 0
\(609\) 826959.i 0.0903526i
\(610\) 0 0
\(611\) 1.06426e7i 1.15331i
\(612\) 0 0
\(613\) −6.18198e6 6.18198e6i −0.664472 0.664472i 0.291959 0.956431i \(-0.405693\pi\)
−0.956431 + 0.291959i \(0.905693\pi\)
\(614\) 0 0
\(615\) −254855. 291240.i −0.0271710 0.0310501i
\(616\) 0 0
\(617\) −274155. + 274155.i −0.0289924 + 0.0289924i −0.721454 0.692462i \(-0.756526\pi\)
0.692462 + 0.721454i \(0.256526\pi\)
\(618\) 0 0
\(619\) 1.04395e7 1.09510 0.547549 0.836774i \(-0.315561\pi\)
0.547549 + 0.836774i \(0.315561\pi\)
\(620\) 0 0
\(621\) −2.28031e6 −0.237283
\(622\) 0 0
\(623\) 2.42669e6 2.42669e6i 0.250492 0.250492i
\(624\) 0 0
\(625\) 9.42187e6 + 2.56822e6i 0.964800 + 0.262986i
\(626\) 0 0
\(627\) 1.34233e6 + 1.34233e6i 0.136361 + 0.136361i
\(628\) 0 0
\(629\) 2.46254e6i 0.248174i
\(630\) 0 0
\(631\) 1.95332e7i 1.95299i 0.215544 + 0.976494i \(0.430848\pi\)
−0.215544 + 0.976494i \(0.569152\pi\)
\(632\) 0 0
\(633\) 565927. + 565927.i 0.0561373 + 0.0561373i
\(634\) 0 0
\(635\) 2.75333e6 2.40935e6i 0.270972 0.237119i
\(636\) 0 0
\(637\) 1.88107e6 1.88107e6i 0.183677 0.183677i
\(638\) 0 0
\(639\) −2.96574e6 −0.287330
\(640\) 0 0
\(641\) 1.16310e7 1.11808 0.559038 0.829142i \(-0.311171\pi\)
0.559038 + 0.829142i \(0.311171\pi\)
\(642\) 0 0
\(643\) −8.86995e6 + 8.86995e6i −0.846045 + 0.846045i −0.989637 0.143592i \(-0.954135\pi\)
0.143592 + 0.989637i \(0.454135\pi\)
\(644\) 0 0
\(645\) −1.00171e6 66741.1i −0.0948073 0.00631675i
\(646\) 0 0
\(647\) 7.82351e6 + 7.82351e6i 0.734752 + 0.734752i 0.971557 0.236805i \(-0.0761003\pi\)
−0.236805 + 0.971557i \(0.576100\pi\)
\(648\) 0 0
\(649\) 1.06754e7i 0.994887i
\(650\) 0 0
\(651\) 327295.i 0.0302682i
\(652\) 0 0
\(653\) −5.80259e6 5.80259e6i −0.532524 0.532524i 0.388799 0.921323i \(-0.372890\pi\)
−0.921323 + 0.388799i \(0.872890\pi\)
\(654\) 0 0
\(655\) −4.67079e6 311202.i −0.425390 0.0283426i
\(656\) 0 0
\(657\) −8.71964e6 + 8.71964e6i −0.788107 + 0.788107i
\(658\) 0 0
\(659\) −1.87531e7 −1.68213 −0.841065 0.540934i \(-0.818071\pi\)
−0.841065 + 0.540934i \(0.818071\pi\)
\(660\) 0 0
\(661\) −1.79645e7 −1.59923 −0.799615 0.600513i \(-0.794963\pi\)
−0.799615 + 0.600513i \(0.794963\pi\)
\(662\) 0 0
\(663\) 697819. 697819.i 0.0616536 0.0616536i
\(664\) 0 0
\(665\) 1.48144e7 1.29637e7i 1.29907 1.13677i
\(666\) 0 0
\(667\) −1.38825e7 1.38825e7i −1.20824 1.20824i
\(668\) 0 0
\(669\) 1.53895e6i 0.132941i
\(670\) 0 0
\(671\) 1.51425e7i 1.29835i
\(672\) 0 0
\(673\) 1.23479e7 + 1.23479e7i 1.05089 + 1.05089i 0.998634 + 0.0522545i \(0.0166407\pi\)
0.0522545 + 0.998634i \(0.483359\pi\)
\(674\) 0 0
\(675\) 1.09181e6 + 1.42925e6i 0.0922332 + 0.120739i
\(676\) 0 0
\(677\) −5.66444e6 + 5.66444e6i −0.474991 + 0.474991i −0.903525 0.428535i \(-0.859030\pi\)
0.428535 + 0.903525i \(0.359030\pi\)
\(678\) 0 0
\(679\) −1.78182e7 −1.48317
\(680\) 0 0
\(681\) −533536. −0.0440855
\(682\) 0 0
\(683\) −2.21820e6 + 2.21820e6i −0.181948 + 0.181948i −0.792204 0.610256i \(-0.791067\pi\)
0.610256 + 0.792204i \(0.291067\pi\)
\(684\) 0 0
\(685\) −1.52413e6 1.74173e6i −0.124107 0.141826i
\(686\) 0 0
\(687\) −965815. 965815.i −0.0780732 0.0780732i
\(688\) 0 0
\(689\) 9.52536e6i 0.764422i
\(690\) 0 0
\(691\) 1.63246e7i 1.30061i 0.759674 + 0.650304i \(0.225358\pi\)
−0.759674 + 0.650304i \(0.774642\pi\)
\(692\) 0 0
\(693\) 1.53093e7 + 1.53093e7i 1.21094 + 1.21094i
\(694\) 0 0
\(695\) −210647. + 3.16157e6i −0.0165422 + 0.248280i
\(696\) 0 0
\(697\) −3.78159e6 + 3.78159e6i −0.294844 + 0.294844i
\(698\) 0 0
\(699\) −488652. −0.0378274
\(700\) 0 0
\(701\) 1.64161e7 1.26175 0.630876 0.775884i \(-0.282696\pi\)
0.630876 + 0.775884i \(0.282696\pi\)
\(702\) 0 0
\(703\) −4.75633e6 + 4.75633e6i −0.362981 + 0.362981i
\(704\) 0 0
\(705\) −51868.8 + 778491.i −0.00393037 + 0.0589903i
\(706\) 0 0
\(707\) 3.13338e6 + 3.13338e6i 0.235757 + 0.235757i
\(708\) 0 0
\(709\) 2.37201e6i 0.177215i 0.996067 + 0.0886077i \(0.0282417\pi\)
−0.996067 + 0.0886077i \(0.971758\pi\)
\(710\) 0 0
\(711\) 1.55415e7i 1.15298i
\(712\) 0 0
\(713\) −5.49445e6 5.49445e6i −0.404762 0.404762i
\(714\) 0 0
\(715\) 2.12634e7 + 2.42991e7i 1.55549 + 1.77757i
\(716\) 0 0
\(717\) −127721. + 127721.i −0.00927824 + 0.00927824i
\(718\) 0 0
\(719\) −8.62894e6 −0.622494 −0.311247 0.950329i \(-0.600747\pi\)
−0.311247 + 0.950329i \(0.600747\pi\)
\(720\) 0 0
\(721\) 871219. 0.0624150
\(722\) 0 0
\(723\) −36264.6 + 36264.6i −0.00258010 + 0.00258010i
\(724\) 0 0
\(725\) −2.05433e6 + 1.53482e7i −0.145153 + 1.08446i
\(726\) 0 0
\(727\) −1.16170e7 1.16170e7i −0.815187 0.815187i 0.170219 0.985406i \(-0.445552\pi\)
−0.985406 + 0.170219i \(0.945552\pi\)
\(728\) 0 0
\(729\) 1.38516e7i 0.965339i
\(730\) 0 0
\(731\) 1.38732e7i 0.960249i
\(732\) 0 0
\(733\) −7.58933e6 7.58933e6i −0.521727 0.521727i 0.396366 0.918093i \(-0.370271\pi\)
−0.918093 + 0.396366i \(0.870271\pi\)
\(734\) 0 0
\(735\) −146765. + 128429.i −0.0100208 + 0.00876890i
\(736\) 0 0
\(737\) 2.64937e6 2.64937e6i 0.179669 0.179669i
\(738\) 0 0
\(739\) −1.89099e6 −0.127373 −0.0636867 0.997970i \(-0.520286\pi\)
−0.0636867 + 0.997970i \(0.520286\pi\)
\(740\) 0 0
\(741\) 2.69563e6 0.180350
\(742\) 0 0
\(743\) 1.86435e7 1.86435e7i 1.23895 1.23895i 0.278523 0.960430i \(-0.410155\pi\)
0.960430 0.278523i \(-0.0898447\pi\)
\(744\) 0 0
\(745\) −1.67613e6 111676.i −0.110641 0.00737172i
\(746\) 0 0
\(747\) −1.51856e7 1.51856e7i −0.995702 0.995702i
\(748\) 0 0
\(749\) 2.99449e7i 1.95038i
\(750\) 0 0
\(751\) 4.60302e6i 0.297813i −0.988851 0.148906i \(-0.952425\pi\)
0.988851 0.148906i \(-0.0475753\pi\)
\(752\) 0 0
\(753\) −459934. 459934.i −0.0295602 0.0295602i
\(754\) 0 0
\(755\) −1.42783e7 951325.i −0.911610 0.0607381i
\(756\) 0 0
\(757\) 6.60445e6 6.60445e6i 0.418887 0.418887i −0.465933 0.884820i \(-0.654281\pi\)
0.884820 + 0.465933i \(0.154281\pi\)
\(758\) 0 0
\(759\) 3.00118e6 0.189098
\(760\) 0 0
\(761\) −7.76470e6 −0.486030 −0.243015 0.970023i \(-0.578136\pi\)
−0.243015 + 0.970023i \(0.578136\pi\)
\(762\) 0 0
\(763\) 1.99916e7 1.99916e7i 1.24319 1.24319i
\(764\) 0 0
\(765\) 9.32476e6 8.15981e6i 0.576082 0.504112i
\(766\) 0 0
\(767\) 1.07191e7 + 1.07191e7i 0.657915 + 0.657915i
\(768\) 0 0
\(769\) 1.03998e7i 0.634172i 0.948397 + 0.317086i \(0.102704\pi\)
−0.948397 + 0.317086i \(0.897296\pi\)
\(770\) 0 0
\(771\) 380332.i 0.0230424i
\(772\) 0 0
\(773\) −2.28295e7 2.28295e7i −1.37419 1.37419i −0.854125 0.520068i \(-0.825907\pi\)
−0.520068 0.854125i \(-0.674093\pi\)
\(774\) 0 0
\(775\) −813067. + 6.07452e6i −0.0486264 + 0.363294i
\(776\) 0 0
\(777\) 316731. 316731.i 0.0188208 0.0188208i
\(778\) 0 0
\(779\) −1.46081e7 −0.862480
\(780\) 0 0
\(781\) 7.82938e6 0.459303
\(782\) 0 0
\(783\) −2.01661e6 + 2.01661e6i −0.117548 + 0.117548i
\(784\) 0 0
\(785\) −1.56369e6 1.78693e6i −0.0905683 0.103498i
\(786\) 0 0
\(787\) −5.72096e6 5.72096e6i −0.329255 0.329255i 0.523048 0.852303i \(-0.324795\pi\)
−0.852303 + 0.523048i \(0.824795\pi\)
\(788\) 0 0
\(789\) 36309.2i 0.00207646i
\(790\) 0 0