Properties

Label 196.6.e.g.177.1
Level $196$
Weight $6$
Character 196.177
Analytic conductor $31.435$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 196.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.4352286833\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 4)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 196.177
Dual form 196.6.e.g.165.1

$q$-expansion

\(f(q)\) \(=\) \(q+(6.00000 + 10.3923i) q^{3} +(-27.0000 + 46.7654i) q^{5} +(49.5000 - 85.7365i) q^{9} +O(q^{10})\) \(q+(6.00000 + 10.3923i) q^{3} +(-27.0000 + 46.7654i) q^{5} +(49.5000 - 85.7365i) q^{9} +(-270.000 - 467.654i) q^{11} -418.000 q^{13} -648.000 q^{15} +(-297.000 - 514.419i) q^{17} +(-418.000 + 723.997i) q^{19} +(2052.00 - 3554.17i) q^{23} +(104.500 + 180.999i) q^{25} +4104.00 q^{27} -594.000 q^{29} +(-2128.00 - 3685.80i) q^{31} +(3240.00 - 5611.84i) q^{33} +(149.000 - 258.076i) q^{37} +(-2508.00 - 4343.98i) q^{39} +17226.0 q^{41} -12100.0 q^{43} +(2673.00 + 4629.77i) q^{45} +(648.000 - 1122.37i) q^{47} +(3564.00 - 6173.03i) q^{51} +(-9747.00 - 16882.3i) q^{53} +29160.0 q^{55} -10032.0 q^{57} +(3834.00 + 6640.68i) q^{59} +(17369.0 - 30084.0i) q^{61} +(11286.0 - 19547.9i) q^{65} +(-10906.0 - 18889.7i) q^{67} +49248.0 q^{69} -46872.0 q^{71} +(-33781.0 - 58510.4i) q^{73} +(-1254.00 + 2171.99i) q^{75} +(38456.0 - 66607.7i) q^{79} +(12595.5 + 21816.0i) q^{81} +67716.0 q^{83} +32076.0 q^{85} +(-3564.00 - 6173.03i) q^{87} +(-14877.0 + 25767.7i) q^{89} +(25536.0 - 44229.6i) q^{93} +(-22572.0 - 39095.9i) q^{95} -122398. q^{97} -53460.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 12 q^{3} - 54 q^{5} + 99 q^{9} + O(q^{10}) \) \( 2 q + 12 q^{3} - 54 q^{5} + 99 q^{9} - 540 q^{11} - 836 q^{13} - 1296 q^{15} - 594 q^{17} - 836 q^{19} + 4104 q^{23} + 209 q^{25} + 8208 q^{27} - 1188 q^{29} - 4256 q^{31} + 6480 q^{33} + 298 q^{37} - 5016 q^{39} + 34452 q^{41} - 24200 q^{43} + 5346 q^{45} + 1296 q^{47} + 7128 q^{51} - 19494 q^{53} + 58320 q^{55} - 20064 q^{57} + 7668 q^{59} + 34738 q^{61} + 22572 q^{65} - 21812 q^{67} + 98496 q^{69} - 93744 q^{71} - 67562 q^{73} - 2508 q^{75} + 76912 q^{79} + 25191 q^{81} + 135432 q^{83} + 64152 q^{85} - 7128 q^{87} - 29754 q^{89} + 51072 q^{93} - 45144 q^{95} - 244796 q^{97} - 106920 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).

\(n\) \(99\) \(101\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 6.00000 + 10.3923i 0.384900 + 0.666667i 0.991755 0.128146i \(-0.0409025\pi\)
−0.606855 + 0.794812i \(0.707569\pi\)
\(4\) 0 0
\(5\) −27.0000 + 46.7654i −0.482991 + 0.836564i −0.999809 0.0195305i \(-0.993783\pi\)
0.516819 + 0.856095i \(0.327116\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 49.5000 85.7365i 0.203704 0.352825i
\(10\) 0 0
\(11\) −270.000 467.654i −0.672794 1.16531i −0.977108 0.212742i \(-0.931761\pi\)
0.304315 0.952572i \(-0.401573\pi\)
\(12\) 0 0
\(13\) −418.000 −0.685990 −0.342995 0.939337i \(-0.611441\pi\)
−0.342995 + 0.939337i \(0.611441\pi\)
\(14\) 0 0
\(15\) −648.000 −0.743613
\(16\) 0 0
\(17\) −297.000 514.419i −0.249249 0.431713i 0.714068 0.700076i \(-0.246851\pi\)
−0.963318 + 0.268363i \(0.913517\pi\)
\(18\) 0 0
\(19\) −418.000 + 723.997i −0.265639 + 0.460101i −0.967731 0.251986i \(-0.918916\pi\)
0.702092 + 0.712087i \(0.252250\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2052.00 3554.17i 0.808831 1.40094i −0.104843 0.994489i \(-0.533434\pi\)
0.913674 0.406448i \(-0.133233\pi\)
\(24\) 0 0
\(25\) 104.500 + 180.999i 0.0334400 + 0.0579198i
\(26\) 0 0
\(27\) 4104.00 1.08342
\(28\) 0 0
\(29\) −594.000 −0.131157 −0.0655785 0.997847i \(-0.520889\pi\)
−0.0655785 + 0.997847i \(0.520889\pi\)
\(30\) 0 0
\(31\) −2128.00 3685.80i −0.397711 0.688855i 0.595732 0.803183i \(-0.296862\pi\)
−0.993443 + 0.114328i \(0.963529\pi\)
\(32\) 0 0
\(33\) 3240.00 5611.84i 0.517917 0.897059i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 149.000 258.076i 0.0178930 0.0309915i −0.856940 0.515416i \(-0.827638\pi\)
0.874833 + 0.484424i \(0.160971\pi\)
\(38\) 0 0
\(39\) −2508.00 4343.98i −0.264038 0.457327i
\(40\) 0 0
\(41\) 17226.0 1.60039 0.800193 0.599742i \(-0.204730\pi\)
0.800193 + 0.599742i \(0.204730\pi\)
\(42\) 0 0
\(43\) −12100.0 −0.997963 −0.498981 0.866613i \(-0.666292\pi\)
−0.498981 + 0.866613i \(0.666292\pi\)
\(44\) 0 0
\(45\) 2673.00 + 4629.77i 0.196774 + 0.340823i
\(46\) 0 0
\(47\) 648.000 1122.37i 0.0427888 0.0741124i −0.843838 0.536598i \(-0.819709\pi\)
0.886627 + 0.462486i \(0.153042\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 3564.00 6173.03i 0.191872 0.332333i
\(52\) 0 0
\(53\) −9747.00 16882.3i −0.476630 0.825547i 0.523011 0.852326i \(-0.324808\pi\)
−0.999641 + 0.0267784i \(0.991475\pi\)
\(54\) 0 0
\(55\) 29160.0 1.29981
\(56\) 0 0
\(57\) −10032.0 −0.408978
\(58\) 0 0
\(59\) 3834.00 + 6640.68i 0.143391 + 0.248361i 0.928772 0.370653i \(-0.120866\pi\)
−0.785380 + 0.619013i \(0.787533\pi\)
\(60\) 0 0
\(61\) 17369.0 30084.0i 0.597655 1.03517i −0.395512 0.918461i \(-0.629433\pi\)
0.993166 0.116707i \(-0.0372339\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 11286.0 19547.9i 0.331327 0.573875i
\(66\) 0 0
\(67\) −10906.0 18889.7i −0.296810 0.514090i 0.678594 0.734513i \(-0.262589\pi\)
−0.975404 + 0.220423i \(0.929256\pi\)
\(68\) 0 0
\(69\) 49248.0 1.24528
\(70\) 0 0
\(71\) −46872.0 −1.10349 −0.551744 0.834014i \(-0.686037\pi\)
−0.551744 + 0.834014i \(0.686037\pi\)
\(72\) 0 0
\(73\) −33781.0 58510.4i −0.741934 1.28507i −0.951614 0.307297i \(-0.900575\pi\)
0.209679 0.977770i \(-0.432758\pi\)
\(74\) 0 0
\(75\) −1254.00 + 2171.99i −0.0257421 + 0.0445867i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 38456.0 66607.7i 0.693260 1.20076i −0.277503 0.960725i \(-0.589507\pi\)
0.970764 0.240037i \(-0.0771597\pi\)
\(80\) 0 0
\(81\) 12595.5 + 21816.0i 0.213306 + 0.369457i
\(82\) 0 0
\(83\) 67716.0 1.07894 0.539468 0.842006i \(-0.318625\pi\)
0.539468 + 0.842006i \(0.318625\pi\)
\(84\) 0 0
\(85\) 32076.0 0.481541
\(86\) 0 0
\(87\) −3564.00 6173.03i −0.0504824 0.0874380i
\(88\) 0 0
\(89\) −14877.0 + 25767.7i −0.199086 + 0.344827i −0.948232 0.317578i \(-0.897131\pi\)
0.749146 + 0.662404i \(0.230464\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 25536.0 44229.6i 0.306158 0.530281i
\(94\) 0 0
\(95\) −22572.0 39095.9i −0.256603 0.444449i
\(96\) 0 0
\(97\) −122398. −1.32082 −0.660412 0.750903i \(-0.729618\pi\)
−0.660412 + 0.750903i \(0.729618\pi\)
\(98\) 0 0
\(99\) −53460.0 −0.548202
\(100\) 0 0
\(101\) −5643.00 9773.96i −0.0550436 0.0953383i 0.837191 0.546911i \(-0.184196\pi\)
−0.892234 + 0.451573i \(0.850863\pi\)
\(102\) 0 0
\(103\) 13628.0 23604.4i 0.126572 0.219230i −0.795774 0.605594i \(-0.792936\pi\)
0.922346 + 0.386364i \(0.126269\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −61182.0 + 105970.i −0.516612 + 0.894798i 0.483202 + 0.875509i \(0.339474\pi\)
−0.999814 + 0.0192889i \(0.993860\pi\)
\(108\) 0 0
\(109\) −49951.0 86517.7i −0.402697 0.697491i 0.591354 0.806412i \(-0.298594\pi\)
−0.994050 + 0.108921i \(0.965260\pi\)
\(110\) 0 0
\(111\) 3576.00 0.0275480
\(112\) 0 0
\(113\) −29646.0 −0.218409 −0.109204 0.994019i \(-0.534830\pi\)
−0.109204 + 0.994019i \(0.534830\pi\)
\(114\) 0 0
\(115\) 110808. + 191925.i 0.781316 + 1.35328i
\(116\) 0 0
\(117\) −20691.0 + 35837.9i −0.139739 + 0.242035i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −65274.5 + 113059.i −0.405303 + 0.702006i
\(122\) 0 0
\(123\) 103356. + 179018.i 0.615989 + 1.06692i
\(124\) 0 0
\(125\) −180036. −1.03059
\(126\) 0 0
\(127\) 336512. 1.85136 0.925681 0.378305i \(-0.123493\pi\)
0.925681 + 0.378305i \(0.123493\pi\)
\(128\) 0 0
\(129\) −72600.0 125747.i −0.384116 0.665308i
\(130\) 0 0
\(131\) −50490.0 + 87451.2i −0.257056 + 0.445233i −0.965452 0.260582i \(-0.916086\pi\)
0.708396 + 0.705815i \(0.249419\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −110808. + 191925.i −0.523283 + 0.906353i
\(136\) 0 0
\(137\) 158571. + 274653.i 0.721809 + 1.25021i 0.960274 + 0.279059i \(0.0900225\pi\)
−0.238465 + 0.971151i \(0.576644\pi\)
\(138\) 0 0
\(139\) −148324. −0.651140 −0.325570 0.945518i \(-0.605556\pi\)
−0.325570 + 0.945518i \(0.605556\pi\)
\(140\) 0 0
\(141\) 15552.0 0.0658777
\(142\) 0 0
\(143\) 112860. + 195479.i 0.461530 + 0.799393i
\(144\) 0 0
\(145\) 16038.0 27778.6i 0.0633476 0.109721i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −98307.0 + 170273.i −0.362759 + 0.628318i −0.988414 0.151782i \(-0.951499\pi\)
0.625654 + 0.780100i \(0.284832\pi\)
\(150\) 0 0
\(151\) −37180.0 64397.6i −0.132699 0.229841i 0.792017 0.610499i \(-0.209031\pi\)
−0.924716 + 0.380658i \(0.875698\pi\)
\(152\) 0 0
\(153\) −58806.0 −0.203092
\(154\) 0 0
\(155\) 229824. 0.768362
\(156\) 0 0
\(157\) −60439.0 104683.i −0.195690 0.338945i 0.751437 0.659805i \(-0.229361\pi\)
−0.947126 + 0.320861i \(0.896028\pi\)
\(158\) 0 0
\(159\) 116964. 202588.i 0.366910 0.635507i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 55670.0 96423.3i 0.164116 0.284258i −0.772225 0.635350i \(-0.780856\pi\)
0.936341 + 0.351091i \(0.114189\pi\)
\(164\) 0 0
\(165\) 174960. + 303040.i 0.500298 + 0.866542i
\(166\) 0 0
\(167\) −491832. −1.36466 −0.682332 0.731043i \(-0.739034\pi\)
−0.682332 + 0.731043i \(0.739034\pi\)
\(168\) 0 0
\(169\) −196569. −0.529417
\(170\) 0 0
\(171\) 41382.0 + 71675.7i 0.108223 + 0.187448i
\(172\) 0 0
\(173\) −353727. + 612673.i −0.898572 + 1.55637i −0.0692518 + 0.997599i \(0.522061\pi\)
−0.829320 + 0.558773i \(0.811272\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −46008.0 + 79688.2i −0.110382 + 0.191188i
\(178\) 0 0
\(179\) −246834. 427529.i −0.575801 0.997317i −0.995954 0.0898633i \(-0.971357\pi\)
0.420153 0.907453i \(-0.361976\pi\)
\(180\) 0 0
\(181\) −559450. −1.26930 −0.634651 0.772799i \(-0.718856\pi\)
−0.634651 + 0.772799i \(0.718856\pi\)
\(182\) 0 0
\(183\) 416856. 0.920149
\(184\) 0 0
\(185\) 8046.00 + 13936.1i 0.0172843 + 0.0299372i
\(186\) 0 0
\(187\) −160380. + 277786.i −0.335387 + 0.580907i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 362016. 627030.i 0.718033 1.24367i −0.243745 0.969839i \(-0.578376\pi\)
0.961778 0.273830i \(-0.0882906\pi\)
\(192\) 0 0
\(193\) −3553.00 6153.98i −0.00686597 0.0118922i 0.862572 0.505934i \(-0.168852\pi\)
−0.869438 + 0.494042i \(0.835519\pi\)
\(194\) 0 0
\(195\) 270864. 0.510111
\(196\) 0 0
\(197\) −530442. −0.973806 −0.486903 0.873456i \(-0.661873\pi\)
−0.486903 + 0.873456i \(0.661873\pi\)
\(198\) 0 0
\(199\) −28084.0 48642.9i −0.0502720 0.0870737i 0.839794 0.542905i \(-0.182675\pi\)
−0.890066 + 0.455831i \(0.849342\pi\)
\(200\) 0 0
\(201\) 130872. 226677.i 0.228484 0.395747i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −465102. + 805580.i −0.772972 + 1.33883i
\(206\) 0 0
\(207\) −203148. 351863.i −0.329524 0.570752i
\(208\) 0 0
\(209\) 451440. 0.714882
\(210\) 0 0
\(211\) −339196. −0.524499 −0.262249 0.965000i \(-0.584464\pi\)
−0.262249 + 0.965000i \(0.584464\pi\)
\(212\) 0 0
\(213\) −281232. 487108.i −0.424733 0.735659i
\(214\) 0 0
\(215\) 326700. 565861.i 0.482007 0.834860i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 405372. 702125.i 0.571141 0.989246i
\(220\) 0 0
\(221\) 124146. + 215027.i 0.170983 + 0.296151i
\(222\) 0 0
\(223\) 779360. 1.04948 0.524742 0.851261i \(-0.324162\pi\)
0.524742 + 0.851261i \(0.324162\pi\)
\(224\) 0 0
\(225\) 20691.0 0.0272474
\(226\) 0 0
\(227\) 372438. + 645082.i 0.479722 + 0.830902i 0.999729 0.0232592i \(-0.00740430\pi\)
−0.520008 + 0.854162i \(0.674071\pi\)
\(228\) 0 0
\(229\) 136373. 236205.i 0.171846 0.297646i −0.767219 0.641385i \(-0.778360\pi\)
0.939065 + 0.343739i \(0.111693\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 76923.0 133235.i 0.0928253 0.160778i −0.815874 0.578230i \(-0.803744\pi\)
0.908699 + 0.417452i \(0.137077\pi\)
\(234\) 0 0
\(235\) 34992.0 + 60607.9i 0.0413332 + 0.0715912i
\(236\) 0 0
\(237\) 922944. 1.06734
\(238\) 0 0
\(239\) 1.15474e6 1.30764 0.653820 0.756650i \(-0.273166\pi\)
0.653820 + 0.756650i \(0.273166\pi\)
\(240\) 0 0
\(241\) −328537. 569043.i −0.364369 0.631106i 0.624306 0.781180i \(-0.285382\pi\)
−0.988675 + 0.150074i \(0.952049\pi\)
\(242\) 0 0
\(243\) 347490. 601870.i 0.377508 0.653864i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 174724. 302631.i 0.182226 0.315625i
\(248\) 0 0
\(249\) 406296. + 703725.i 0.415283 + 0.719291i
\(250\) 0 0
\(251\) 1.34190e6 1.34442 0.672211 0.740359i \(-0.265345\pi\)
0.672211 + 0.740359i \(0.265345\pi\)
\(252\) 0 0
\(253\) −2.21616e6 −2.17671
\(254\) 0 0
\(255\) 192456. + 333344.i 0.185345 + 0.321027i
\(256\) 0 0
\(257\) −66177.0 + 114622.i −0.0624992 + 0.108252i −0.895582 0.444897i \(-0.853240\pi\)
0.833083 + 0.553148i \(0.186574\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −29403.0 + 50927.5i −0.0267172 + 0.0462755i
\(262\) 0 0
\(263\) −471636. 816898.i −0.420453 0.728246i 0.575531 0.817780i \(-0.304796\pi\)
−0.995984 + 0.0895341i \(0.971462\pi\)
\(264\) 0 0
\(265\) 1.05268e6 0.920831
\(266\) 0 0
\(267\) −357048. −0.306513
\(268\) 0 0
\(269\) −483759. 837895.i −0.407613 0.706007i 0.587008 0.809581i \(-0.300306\pi\)
−0.994622 + 0.103574i \(0.966972\pi\)
\(270\) 0 0
\(271\) 259160. 448878.i 0.214360 0.371283i −0.738714 0.674019i \(-0.764567\pi\)
0.953075 + 0.302736i \(0.0978999\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 56430.0 97739.6i 0.0449965 0.0779361i
\(276\) 0 0
\(277\) −1.11136e6 1.92494e6i −0.870275 1.50736i −0.861712 0.507397i \(-0.830608\pi\)
−0.00856270 0.999963i \(-0.502726\pi\)
\(278\) 0 0
\(279\) −421344. −0.324061
\(280\) 0 0
\(281\) −196614. −0.148542 −0.0742709 0.997238i \(-0.523663\pi\)
−0.0742709 + 0.997238i \(0.523663\pi\)
\(282\) 0 0
\(283\) 776138. + 1.34431e6i 0.576067 + 0.997777i 0.995925 + 0.0901872i \(0.0287465\pi\)
−0.419858 + 0.907590i \(0.637920\pi\)
\(284\) 0 0
\(285\) 270864. 469150.i 0.197533 0.342137i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 533510. 924067.i 0.375749 0.650817i
\(290\) 0 0
\(291\) −734388. 1.27200e6i −0.508385 0.880549i
\(292\) 0 0
\(293\) −1.07217e6 −0.729616 −0.364808 0.931083i \(-0.618865\pi\)
−0.364808 + 0.931083i \(0.618865\pi\)
\(294\) 0 0
\(295\) −414072. −0.277026
\(296\) 0 0
\(297\) −1.10808e6 1.91925e6i −0.728920 1.26253i
\(298\) 0 0
\(299\) −857736. + 1.48564e6i −0.554850 + 0.961029i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 67716.0 117288.i 0.0423726 0.0733914i
\(304\) 0 0
\(305\) 937926. + 1.62454e6i 0.577323 + 0.999953i
\(306\) 0 0
\(307\) 1.58589e6 0.960346 0.480173 0.877174i \(-0.340574\pi\)
0.480173 + 0.877174i \(0.340574\pi\)
\(308\) 0 0
\(309\) 327072. 0.194871
\(310\) 0 0
\(311\) 365364. + 632829.i 0.214203 + 0.371010i 0.953026 0.302890i \(-0.0979514\pi\)
−0.738823 + 0.673900i \(0.764618\pi\)
\(312\) 0 0
\(313\) −292429. + 506502.i −0.168717 + 0.292227i −0.937969 0.346719i \(-0.887296\pi\)
0.769252 + 0.638946i \(0.220629\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.24143e6 2.15023e6i 0.693865 1.20181i −0.276696 0.960957i \(-0.589240\pi\)
0.970562 0.240852i \(-0.0774270\pi\)
\(318\) 0 0
\(319\) 160380. + 277786.i 0.0882416 + 0.152839i
\(320\) 0 0
\(321\) −1.46837e6 −0.795376
\(322\) 0 0
\(323\) 496584. 0.264842
\(324\) 0 0
\(325\) −43681.0 75657.7i −0.0229395 0.0397324i
\(326\) 0 0
\(327\) 599412. 1.03821e6i 0.309996 0.536929i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −188974. + 327313.i −0.0948052 + 0.164207i −0.909527 0.415644i \(-0.863556\pi\)
0.814722 + 0.579852i \(0.196889\pi\)
\(332\) 0 0
\(333\) −14751.0 25549.5i −0.00728972 0.0126262i
\(334\) 0 0
\(335\) 1.17785e6 0.573426
\(336\) 0 0
\(337\) 639122. 0.306555 0.153278 0.988183i \(-0.451017\pi\)
0.153278 + 0.988183i \(0.451017\pi\)
\(338\) 0 0
\(339\) −177876. 308090.i −0.0840656 0.145606i
\(340\) 0 0
\(341\) −1.14912e6 + 1.99033e6i −0.535155 + 0.926915i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −1.32970e6 + 2.30310e6i −0.601457 + 1.04175i
\(346\) 0 0
\(347\) 1.45233e6 + 2.51551e6i 0.647503 + 1.12151i 0.983717 + 0.179722i \(0.0575199\pi\)
−0.336215 + 0.941785i \(0.609147\pi\)
\(348\) 0 0
\(349\) −3.99157e6 −1.75420 −0.877102 0.480304i \(-0.840526\pi\)
−0.877102 + 0.480304i \(0.840526\pi\)
\(350\) 0 0
\(351\) −1.71547e6 −0.743217
\(352\) 0 0
\(353\) −714609. 1.23774e6i −0.305233 0.528679i 0.672080 0.740478i \(-0.265401\pi\)
−0.977313 + 0.211799i \(0.932068\pi\)
\(354\) 0 0
\(355\) 1.26554e6 2.19199e6i 0.532974 0.923139i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −580932. + 1.00620e6i −0.237897 + 0.412050i −0.960111 0.279620i \(-0.909791\pi\)
0.722214 + 0.691670i \(0.243125\pi\)
\(360\) 0 0
\(361\) 888602. + 1.53910e6i 0.358872 + 0.621584i
\(362\) 0 0
\(363\) −1.56659e6 −0.624005
\(364\) 0 0
\(365\) 3.64835e6 1.43339
\(366\) 0 0
\(367\) 544616. + 943303.i 0.211069 + 0.365583i 0.952049 0.305944i \(-0.0989721\pi\)
−0.740980 + 0.671527i \(0.765639\pi\)
\(368\) 0 0
\(369\) 852687. 1.47690e6i 0.326005 0.564657i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.75288e6 + 3.03608e6i −0.652350 + 1.12990i 0.330201 + 0.943911i \(0.392884\pi\)
−0.982551 + 0.185993i \(0.940450\pi\)
\(374\) 0 0
\(375\) −1.08022e6 1.87099e6i −0.396673 0.687057i
\(376\) 0 0
\(377\) 248292. 0.0899724
\(378\) 0 0
\(379\) 4.04385e6 1.44610 0.723048 0.690798i \(-0.242740\pi\)
0.723048 + 0.690798i \(0.242740\pi\)
\(380\) 0 0
\(381\) 2.01907e6 + 3.49714e6i 0.712589 + 1.23424i
\(382\) 0 0
\(383\) −2.59373e6 + 4.49247e6i −0.903499 + 1.56491i −0.0805786 + 0.996748i \(0.525677\pi\)
−0.822920 + 0.568157i \(0.807657\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −598950. + 1.03741e6i −0.203289 + 0.352106i
\(388\) 0 0
\(389\) 475173. + 823024.i 0.159213 + 0.275765i 0.934585 0.355740i \(-0.115771\pi\)
−0.775372 + 0.631504i \(0.782438\pi\)
\(390\) 0 0
\(391\) −2.43778e6 −0.806403
\(392\) 0 0
\(393\) −1.21176e6 −0.395763
\(394\) 0 0
\(395\) 2.07662e6 + 3.59682e6i 0.669677 + 1.15991i
\(396\) 0 0
\(397\) 260369. 450972.i 0.0829112 0.143606i −0.821588 0.570082i \(-0.806912\pi\)
0.904499 + 0.426475i \(0.140245\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −382185. + 661964.i −0.118690 + 0.205576i −0.919249 0.393677i \(-0.871203\pi\)
0.800559 + 0.599254i \(0.204536\pi\)
\(402\) 0 0
\(403\) 889504. + 1.54067e6i 0.272826 + 0.472548i
\(404\) 0 0
\(405\) −1.36031e6 −0.412099
\(406\) 0 0
\(407\) −160920. −0.0481531
\(408\) 0 0
\(409\) −1.32025e6 2.28675e6i −0.390255 0.675942i 0.602228 0.798324i \(-0.294280\pi\)
−0.992483 + 0.122382i \(0.960947\pi\)
\(410\) 0 0
\(411\) −1.90285e6 + 3.29584e6i −0.555649 + 0.962412i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.82833e6 + 3.16676e6i −0.521116 + 0.902600i
\(416\) 0 0
\(417\) −889944. 1.54143e6i −0.250624 0.434093i
\(418\) 0 0
\(419\) −4.98020e6 −1.38584 −0.692918 0.721016i \(-0.743675\pi\)
−0.692918 + 0.721016i \(0.743675\pi\)
\(420\) 0 0
\(421\) −237994. −0.0654426 −0.0327213 0.999465i \(-0.510417\pi\)
−0.0327213 + 0.999465i \(0.510417\pi\)
\(422\) 0 0
\(423\) −64152.0 111115.i −0.0174325 0.0301939i
\(424\) 0 0
\(425\) 62073.0 107514.i 0.0166698 0.0288729i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.35432e6 + 2.34575e6i −0.355286 + 0.615373i
\(430\) 0 0
\(431\) 1.94119e6 + 3.36224e6i 0.503356 + 0.871838i 0.999992 + 0.00387961i \(0.00123492\pi\)
−0.496636 + 0.867959i \(0.665432\pi\)
\(432\) 0 0
\(433\) −66958.0 −0.0171626 −0.00858129 0.999963i \(-0.502732\pi\)
−0.00858129 + 0.999963i \(0.502732\pi\)
\(434\) 0 0
\(435\) 384912. 0.0975300
\(436\) 0 0
\(437\) 1.71547e6 + 2.97128e6i 0.429715 + 0.744287i
\(438\) 0 0
\(439\) 3.25068e6 5.63034e6i 0.805031 1.39435i −0.111240 0.993794i \(-0.535482\pi\)
0.916270 0.400560i \(-0.131184\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.30380e6 3.99030e6i 0.557745 0.966043i −0.439939 0.898028i \(-0.645000\pi\)
0.997684 0.0680154i \(-0.0216667\pi\)
\(444\) 0 0
\(445\) −803358. 1.39146e6i −0.192313 0.333096i
\(446\) 0 0
\(447\) −2.35937e6 −0.558505
\(448\) 0 0
\(449\) 3.77671e6 0.884092 0.442046 0.896992i \(-0.354253\pi\)
0.442046 + 0.896992i \(0.354253\pi\)
\(450\) 0 0
\(451\) −4.65102e6 8.05580e6i −1.07673 1.86495i
\(452\) 0 0
\(453\) 446160. 772772.i 0.102152 0.176932i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.59035e6 2.75456e6i 0.356206 0.616967i −0.631117 0.775687i \(-0.717403\pi\)
0.987324 + 0.158720i \(0.0507368\pi\)
\(458\) 0 0
\(459\) −1.21889e6 2.11118e6i −0.270042 0.467727i
\(460\) 0 0
\(461\) 6.68547e6 1.46514 0.732571 0.680691i \(-0.238320\pi\)
0.732571 + 0.680691i \(0.238320\pi\)
\(462\) 0 0
\(463\) −4.35122e6 −0.943318 −0.471659 0.881781i \(-0.656345\pi\)
−0.471659 + 0.881781i \(0.656345\pi\)
\(464\) 0 0
\(465\) 1.37894e6 + 2.38840e6i 0.295743 + 0.512242i
\(466\) 0 0
\(467\) −3.53997e6 + 6.13141e6i −0.751117 + 1.30097i 0.196165 + 0.980571i \(0.437151\pi\)
−0.947282 + 0.320401i \(0.896182\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 725268. 1.25620e6i 0.150642 0.260920i
\(472\) 0 0
\(473\) 3.26700e6 + 5.65861e6i 0.671423 + 1.16294i
\(474\) 0 0
\(475\) −174724. −0.0355319
\(476\) 0 0
\(477\) −1.92991e6 −0.388365
\(478\) 0 0
\(479\) −1.61093e6 2.79021e6i −0.320802 0.555646i 0.659852 0.751396i \(-0.270619\pi\)
−0.980654 + 0.195750i \(0.937286\pi\)
\(480\) 0 0
\(481\) −62282.0 + 107876.i −0.0122744 + 0.0212599i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.30475e6 5.72399e6i 0.637946 1.10495i
\(486\) 0 0
\(487\) −1.14855e6 1.98934e6i −0.219446 0.380091i 0.735193 0.677858i \(-0.237091\pi\)
−0.954639 + 0.297767i \(0.903758\pi\)
\(488\) 0 0
\(489\) 1.33608e6 0.252674
\(490\) 0 0
\(491\) 2.82150e6 0.528173 0.264087 0.964499i \(-0.414930\pi\)
0.264087 + 0.964499i \(0.414930\pi\)
\(492\) 0 0
\(493\) 176418. + 305565.i 0.0326908 + 0.0566221i
\(494\) 0 0
\(495\) 1.44342e6 2.50008e6i 0.264777 0.458607i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 2.06814e6 3.58213e6i 0.371817 0.644006i −0.618028 0.786156i \(-0.712068\pi\)
0.989845 + 0.142150i \(0.0454016\pi\)
\(500\) 0 0
\(501\) −2.95099e6 5.11127e6i −0.525259 0.909776i
\(502\) 0 0
\(503\) 8.33263e6 1.46846 0.734230 0.678901i \(-0.237543\pi\)
0.734230 + 0.678901i \(0.237543\pi\)
\(504\) 0 0
\(505\) 609444. 0.106342
\(506\) 0 0
\(507\) −1.17941e6 2.04280e6i −0.203773 0.352945i
\(508\) 0 0
\(509\) −2.17050e6 + 3.75942e6i −0.371335 + 0.643171i −0.989771 0.142664i \(-0.954433\pi\)
0.618436 + 0.785835i \(0.287767\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1.71547e6 + 2.97128e6i −0.287800 + 0.498484i
\(514\) 0 0
\(515\) 735912. + 1.27464e6i 0.122267 + 0.211772i
\(516\) 0 0
\(517\) −699840. −0.115152
\(518\) 0 0
\(519\) −8.48945e6 −1.38344
\(520\) 0 0
\(521\) 3.37092e6 + 5.83861e6i 0.544070 + 0.942356i 0.998665 + 0.0516581i \(0.0164506\pi\)
−0.454595 + 0.890698i \(0.650216\pi\)
\(522\) 0 0
\(523\) 3.86098e6 6.68741e6i 0.617224 1.06906i −0.372765 0.927926i \(-0.621590\pi\)
0.989990 0.141138i \(-0.0450763\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.26403e6 + 2.18937e6i −0.198258 + 0.343394i
\(528\) 0 0
\(529\) −5.20324e6 9.01227e6i −0.808415 1.40022i
\(530\) 0 0
\(531\) 759132. 0.116837
\(532\) 0 0
\(533\) −7.20047e6 −1.09785
\(534\) 0 0
\(535\) −3.30383e6 5.72240e6i −0.499037 0.864358i
\(536\) 0 0
\(537\) 2.96201e6 5.13035e6i 0.443252 0.767735i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 341033. 590686.i 0.0500960 0.0867689i −0.839890 0.542757i \(-0.817381\pi\)
0.889986 + 0.455988i \(0.150714\pi\)
\(542\) 0 0
\(543\) −3.35670e6 5.81397e6i −0.488554 0.846201i
\(544\) 0 0
\(545\) 5.39471e6 0.777995
\(546\) 0 0
\(547\) 2.15772e6 0.308337 0.154169 0.988045i \(-0.450730\pi\)
0.154169 + 0.988045i \(0.450730\pi\)
\(548\) 0 0
\(549\) −1.71953e6 2.97832e6i −0.243489 0.421735i
\(550\) 0 0
\(551\) 248292. 430054.i 0.0348404 0.0603454i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −96552.0 + 167233.i −0.0133054 + 0.0230457i
\(556\) 0 0
\(557\) 1.33798e6 + 2.31746e6i 0.182731 + 0.316500i 0.942810 0.333331i \(-0.108173\pi\)
−0.760078 + 0.649831i \(0.774839\pi\)
\(558\) 0 0
\(559\) 5.05780e6 0.684592
\(560\) 0 0
\(561\) −3.84912e6 −0.516362
\(562\) 0 0
\(563\) 1.77665e6 + 3.07725e6i 0.236228 + 0.409159i 0.959629 0.281269i \(-0.0907554\pi\)
−0.723401 + 0.690428i \(0.757422\pi\)
\(564\) 0 0
\(565\) 800442. 1.38641e6i 0.105489 0.182713i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.46123e6 1.11912e7i 0.836633 1.44909i −0.0560613 0.998427i \(-0.517854\pi\)
0.892694 0.450663i \(-0.148812\pi\)
\(570\) 0 0
\(571\) 3.04179e6 + 5.26853e6i 0.390426 + 0.676237i 0.992506 0.122199i \(-0.0389945\pi\)
−0.602080 + 0.798436i \(0.705661\pi\)
\(572\) 0 0
\(573\) 8.68838e6 1.10548
\(574\) 0 0
\(575\) 857736. 0.108189
\(576\) 0 0
\(577\) 7.91203e6 + 1.37040e7i 0.989347 + 1.71360i 0.620749 + 0.784010i \(0.286829\pi\)
0.368598 + 0.929589i \(0.379838\pi\)
\(578\) 0 0
\(579\) 42636.0 73847.7i 0.00528543 0.00915463i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −5.26338e6 + 9.11644e6i −0.641347 + 1.11085i
\(584\) 0 0
\(585\) −1.11731e6 1.93524e6i −0.134985 0.233801i
\(586\) 0 0
\(587\) 4.60220e6 0.551278 0.275639 0.961261i \(-0.411111\pi\)
0.275639 + 0.961261i \(0.411111\pi\)
\(588\) 0 0
\(589\) 3.55802e6 0.422590
\(590\) 0 0
\(591\) −3.18265e6 5.51251e6i −0.374818 0.649204i
\(592\) 0 0
\(593\) −4.30561e6 + 7.45753e6i −0.502803 + 0.870880i 0.497192 + 0.867641i \(0.334365\pi\)
−0.999995 + 0.00323965i \(0.998969\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 337008. 583715.i 0.0386994 0.0670294i
\(598\) 0 0
\(599\) 3.99114e6 + 6.91286e6i 0.454496 + 0.787210i 0.998659 0.0517695i \(-0.0164861\pi\)
−0.544163 + 0.838979i \(0.683153\pi\)
\(600\) 0 0
\(601\) 1.01740e7 1.14896 0.574481 0.818518i \(-0.305204\pi\)
0.574481 + 0.818518i \(0.305204\pi\)
\(602\) 0 0
\(603\) −2.15939e6 −0.241845
\(604\) 0 0
\(605\) −3.52482e6 6.10517e6i −0.391515 0.678125i
\(606\) 0 0
\(607\) 4.97922e6 8.62426e6i 0.548516 0.950057i −0.449861 0.893099i \(-0.648526\pi\)
0.998377 0.0569587i \(-0.0181403\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −270864. + 469150.i −0.0293527 + 0.0508404i
\(612\) 0 0
\(613\) −2.09793e6 3.63372e6i −0.225497 0.390572i 0.730972 0.682408i \(-0.239067\pi\)
−0.956468 + 0.291836i \(0.905734\pi\)
\(614\) 0 0
\(615\) −1.11624e7 −1.19007
\(616\) 0 0
\(617\) 9.12551e6 0.965038 0.482519 0.875885i \(-0.339722\pi\)
0.482519 + 0.875885i \(0.339722\pi\)
\(618\) 0 0
\(619\) −3.22867e6 5.59222e6i −0.338686 0.586621i 0.645500 0.763760i \(-0.276649\pi\)
−0.984186 + 0.177139i \(0.943316\pi\)
\(620\) 0 0
\(621\) 8.42141e6 1.45863e7i 0.876306 1.51781i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 4.53441e6 7.85383e6i 0.464324 0.804232i
\(626\) 0 0
\(627\) 2.70864e6 + 4.69150e6i 0.275158 + 0.476588i
\(628\) 0 0
\(629\) −177012. −0.0178392
\(630\) 0 0
\(631\) −1.40514e7 −1.40490 −0.702450 0.711733i \(-0.747910\pi\)
−0.702450 + 0.711733i \(0.747910\pi\)
\(632\) 0 0
\(633\) −2.03518e6 3.52503e6i −0.201880 0.349666i
\(634\) 0 0
\(635\) −9.08582e6 + 1.57371e7i −0.894190 + 1.54878i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −2.32016e6 + 4.01864e6i −0.224785 + 0.389338i
\(640\) 0 0
\(641\) −4.23584e6 7.33669e6i −0.407188 0.705270i 0.587386 0.809307i \(-0.300157\pi\)
−0.994573 + 0.104037i \(0.966824\pi\)
\(642\) 0 0
\(643\) 488564. 0.0466009 0.0233004 0.999729i \(-0.492583\pi\)
0.0233004 + 0.999729i \(0.492583\pi\)
\(644\) 0 0
\(645\) 7.84080e6 0.742098
\(646\) 0 0
\(647\) −1.24060e6 2.14878e6i −0.116512 0.201804i 0.801871 0.597497i \(-0.203838\pi\)
−0.918383 + 0.395693i \(0.870505\pi\)
\(648\) 0 0
\(649\) 2.07036e6 3.58597e6i 0.192945 0.334191i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.64565e6 4.58240e6i 0.242800 0.420543i −0.718711 0.695309i \(-0.755267\pi\)
0.961511 + 0.274767i \(0.0886007\pi\)
\(654\) 0 0
\(655\) −2.72646e6 4.72237e6i −0.248311 0.430087i
\(656\) 0 0
\(657\) −6.68864e6 −0.604539
\(658\) 0 0
\(659\) 4.72468e6 0.423798 0.211899 0.977292i \(-0.432035\pi\)
0.211899 + 0.977292i \(0.432035\pi\)
\(660\) 0 0
\(661\) 3.08710e6 + 5.34702e6i 0.274819 + 0.476001i 0.970090 0.242747i \(-0.0780486\pi\)
−0.695270 + 0.718748i \(0.744715\pi\)
\(662\) 0 0
\(663\) −1.48975e6 + 2.58033e6i −0.131623 + 0.227977i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.21889e6 + 2.11118e6i −0.106084 + 0.183743i
\(668\) 0 0
\(669\) 4.67616e6 + 8.09935e6i 0.403947 + 0.699656i
\(670\) 0 0
\(671\) −1.87585e7 −1.60839
\(672\) 0 0
\(673\) −9.40925e6 −0.800787 −0.400394 0.916343i \(-0.631127\pi\)
−0.400394 + 0.916343i \(0.631127\pi\)
\(674\) 0 0
\(675\) 428868. + 742821.i 0.0362297 + 0.0627516i
\(676\) 0 0
\(677\) −7.50430e6 + 1.29978e7i −0.629272 + 1.08993i 0.358426 + 0.933558i \(0.383314\pi\)
−0.987698 + 0.156373i \(0.950020\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −4.46926e6 + 7.74098e6i −0.369290 + 0.639629i
\(682\) 0 0
\(683\) 6.48535e6 + 1.12329e7i 0.531963 + 0.921387i 0.999304 + 0.0373096i \(0.0118788\pi\)
−0.467341 + 0.884077i \(0.654788\pi\)
\(684\) 0 0
\(685\) −1.71257e7 −1.39451
\(686\) 0 0
\(687\) 3.27295e6 0.264574
\(688\) 0 0
\(689\) 4.07425e6 + 7.05680e6i 0.326963 + 0.566317i
\(690\) 0 0
\(691\) −1.13278e7 + 1.96203e7i −0.902506 + 1.56319i −0.0782761 + 0.996932i \(0.524942\pi\)
−0.824230 + 0.566255i \(0.808392\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.00475e6 6.93643e6i 0.314495 0.544721i
\(696\) 0 0
\(697\) −5.11612e6 8.86138e6i −0.398895 0.690907i
\(698\) 0 0
\(699\) 1.84615e6 0.142914
\(700\) 0 0
\(701\) 1.90169e7 1.46166 0.730828 0.682562i \(-0.239134\pi\)
0.730828 + 0.682562i \(0.239134\pi\)
\(702\) 0 0
\(703\) 124564. + 215751.i 0.00950614 + 0.0164651i
\(704\) 0 0
\(705\) −419904. + 727295.i −0.0318183 + 0.0551109i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −7.56556e6 + 1.31039e7i −0.565231 + 0.979008i 0.431798 + 0.901971i \(0.357879\pi\)
−0.997028 + 0.0770376i \(0.975454\pi\)
\(710\) 0 0
\(711\) −3.80714e6 6.59417e6i −0.282439 0.489199i
\(712\) 0 0
\(713\) −1.74666e7 −1.28672
\(714\) 0 0
\(715\) −1.21889e7 −0.891659
\(716\) 0 0
\(717\) 6.92842e6 + 1.20004e7i 0.503311 + 0.871760i
\(718\) 0 0
\(719\) 7.51615e6 1.30184e7i 0.542217 0.939148i −0.456559 0.889693i \(-0.650918\pi\)
0.998776 0.0494547i \(-0.0157484\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 3.94244e6 6.82851e6i 0.280492 0.485826i
\(724\) 0 0
\(725\) −62073.0 107514.i −0.00438589 0.00759658i
\(726\) 0 0
\(727\) −7.41230e6 −0.520136 −0.260068 0.965590i \(-0.583745\pi\)
−0.260068 + 0.965590i \(0.583745\pi\)
\(728\) 0 0
\(729\) 1.44612e7 1.00782
\(730\) 0 0
\(731\) 3.59370e6 + 6.22447e6i 0.248742 + 0.430833i
\(732\) 0 0
\(733\) 1.38964e6 2.40693e6i 0.0955306 0.165464i −0.814299 0.580445i \(-0.802879\pi\)
0.909830 + 0.414981i \(0.136212\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.88924e6 + 1.02005e7i −0.399384 + 0.691753i
\(738\) 0 0
\(739\) 6.05231e6 + 1.04829e7i 0.407671 + 0.706107i 0.994628 0.103511i \(-0.0330076\pi\)
−0.586957 + 0.809618i \(0.699674\pi\)
\(740\) 0 0
\(741\) 4.19338e6 0.280555
\(742\) 0 0
\(743\) 4.46926e6 0.297005 0.148502 0.988912i \(-0.452555\pi\)
0.148502 + 0.988912i \(0.452555\pi\)
\(744\) 0 0
\(745\) −5.30858e6 9.19473e6i −0.350419 0.606943i
\(746\) 0 0
\(747\) 3.35194e6 5.80573e6i 0.219783 0.380676i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.44231e7 + 2.49816e7i −0.933168 + 1.61629i −0.155298 + 0.987868i \(0.549634\pi\)
−0.777869 + 0.628426i \(0.783700\pi\)
\(752\) 0 0
\(753\) 8.05140e6 + 1.39454e7i 0.517469 + 0.896282i
\(754\) 0 0
\(755\) 4.01544e6 0.256369
\(756\) 0 0
\(757\) 9.60868e6 0.609430 0.304715 0.952444i \(-0.401439\pi\)
0.304715 + 0.952444i \(0.401439\pi\)
\(758\) 0 0
\(759\) −1.32970e7 2.30310e7i −0.837815 1.45114i
\(760\) 0 0
\(761\) −2.27294e6 + 3.93685e6i −0.142274 + 0.246426i −0.928353 0.371700i \(-0.878775\pi\)
0.786078 + 0.618127i \(0.212108\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 1.58776e6 2.75008e6i 0.0980916 0.169900i
\(766\) 0 0
\(767\) −1.60261e6 2.77581e6i −0.0983649 0.170373i
\(768\) 0 0
\(769\) −2.15923e7 −1.31669 −0.658345 0.752716i \(-0.728743\pi\)
−0.658345 + 0.752716i \(0.728743\pi\)
\(770\) 0 0
\(771\) −1.58825e6 −0.0962238
\(772\) 0 0
\(773\) 7.42000e6 + 1.28518e7i 0.446638 + 0.773599i 0.998165 0.0605578i \(-0.0192879\pi\)
−0.551527 + 0.834157i \(0.685955\pi\)
\(774\) 0 0
\(775\) 444752. 770333.i 0.0265989 0.0460706i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.20047e6 + 1.24716e7i −0.425125 + 0.736339i
\(780\) 0 0
\(781\) 1.26554e7 + 2.19199e7i 0.742420 + 1.28591i
\(782\) 0 0
\(783\) −2.43778e6 −0.142098
\(784\) 0 0
\(785\) 6.52741e6 0.378065
\(786\) 0 0
\(787\) 1.24393e7 + 2.15454e7i 0.715909 + 1.23999i 0.962608 + 0.270898i \(0.0873208\pi\)
−0.246699 + 0.969092i \(0.579346\pi\)
\(788\) 0 0
\(789\) 5.65963e6 9.80277e6i 0.323665 0.560604i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0