Properties

Label 320.2.s.b.303.6
Level $320$
Weight $2$
Character 320.303
Analytic conductor $2.555$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.s (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Defining polynomial: \(x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 303.6
Root \(-1.08900 - 0.902261i\) of defining polynomial
Character \(\chi\) \(=\) 320.303
Dual form 320.2.s.b.207.6

$q$-expansion

\(f(q)\) \(=\) \(q+0.496487 q^{3} +(-2.00635 + 0.987189i) q^{5} +(-1.55426 + 1.55426i) q^{7} -2.75350 q^{9} +O(q^{10})\) \(q+0.496487 q^{3} +(-2.00635 + 0.987189i) q^{5} +(-1.55426 + 1.55426i) q^{7} -2.75350 q^{9} +(4.19607 + 4.19607i) q^{11} +5.09530i q^{13} +(-0.996130 + 0.490127i) q^{15} +(0.213542 - 0.213542i) q^{17} +(-0.844754 - 0.844754i) q^{19} +(-0.771668 + 0.771668i) q^{21} +(-1.70744 - 1.70744i) q^{23} +(3.05092 - 3.96130i) q^{25} -2.85654 q^{27} +(2.24750 - 2.24750i) q^{29} +0.818209i q^{31} +(2.08329 + 2.08329i) q^{33} +(1.58404 - 4.65273i) q^{35} +5.12639i q^{37} +2.52975i q^{39} -3.34727i q^{41} +4.49131i q^{43} +(5.52450 - 2.71822i) q^{45} +(-4.29355 - 4.29355i) q^{47} +2.16858i q^{49} +(0.106021 - 0.106021i) q^{51} -1.00653 q^{53} +(-12.5611 - 4.27649i) q^{55} +(-0.419410 - 0.419410i) q^{57} +(7.65005 - 7.65005i) q^{59} +(-1.90291 - 1.90291i) q^{61} +(4.27964 - 4.27964i) q^{63} +(-5.03002 - 10.2230i) q^{65} +11.0221i q^{67} +(-0.847724 - 0.847724i) q^{69} +10.5331 q^{71} +(2.70854 - 2.70854i) q^{73} +(1.51474 - 1.96674i) q^{75} -13.0435 q^{77} +8.32010 q^{79} +6.84226 q^{81} +9.17237 q^{83} +(-0.217635 + 0.639248i) q^{85} +(1.11585 - 1.11585i) q^{87} -4.25101 q^{89} +(-7.91940 - 7.91940i) q^{91} +0.406230i q^{93} +(2.52881 + 0.860944i) q^{95} +(-7.16000 + 7.16000i) q^{97} +(-11.5539 - 11.5539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 2q^{5} - 2q^{7} + 10q^{9} + O(q^{10}) \) \( 18q + 2q^{5} - 2q^{7} + 10q^{9} + 2q^{11} + 20q^{15} - 6q^{17} + 2q^{19} - 16q^{21} + 2q^{23} - 6q^{25} + 24q^{27} + 14q^{29} - 8q^{33} - 2q^{35} - 14q^{45} - 38q^{47} - 8q^{51} + 12q^{53} + 6q^{55} - 24q^{57} - 10q^{59} + 14q^{61} + 6q^{63} - 32q^{69} - 24q^{71} - 14q^{73} - 16q^{75} - 44q^{77} + 16q^{79} + 2q^{81} - 40q^{83} + 14q^{85} - 24q^{87} + 12q^{89} - 34q^{95} + 18q^{97} - 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 0.496487 0.286647 0.143324 0.989676i \(-0.454221\pi\)
0.143324 + 0.989676i \(0.454221\pi\)
\(4\) 0 0
\(5\) −2.00635 + 0.987189i −0.897269 + 0.441484i
\(6\) 0 0
\(7\) −1.55426 + 1.55426i −0.587453 + 0.587453i −0.936941 0.349488i \(-0.886356\pi\)
0.349488 + 0.936941i \(0.386356\pi\)
\(8\) 0 0
\(9\) −2.75350 −0.917833
\(10\) 0 0
\(11\) 4.19607 + 4.19607i 1.26516 + 1.26516i 0.948558 + 0.316604i \(0.102543\pi\)
0.316604 + 0.948558i \(0.397457\pi\)
\(12\) 0 0
\(13\) 5.09530i 1.41318i 0.707622 + 0.706591i \(0.249768\pi\)
−0.707622 + 0.706591i \(0.750232\pi\)
\(14\) 0 0
\(15\) −0.996130 + 0.490127i −0.257200 + 0.126550i
\(16\) 0 0
\(17\) 0.213542 0.213542i 0.0517916 0.0517916i −0.680737 0.732528i \(-0.738340\pi\)
0.732528 + 0.680737i \(0.238340\pi\)
\(18\) 0 0
\(19\) −0.844754 0.844754i −0.193800 0.193800i 0.603536 0.797336i \(-0.293758\pi\)
−0.797336 + 0.603536i \(0.793758\pi\)
\(20\) 0 0
\(21\) −0.771668 + 0.771668i −0.168392 + 0.168392i
\(22\) 0 0
\(23\) −1.70744 1.70744i −0.356027 0.356027i 0.506319 0.862346i \(-0.331006\pi\)
−0.862346 + 0.506319i \(0.831006\pi\)
\(24\) 0 0
\(25\) 3.05092 3.96130i 0.610183 0.792260i
\(26\) 0 0
\(27\) −2.85654 −0.549741
\(28\) 0 0
\(29\) 2.24750 2.24750i 0.417350 0.417350i −0.466939 0.884289i \(-0.654643\pi\)
0.884289 + 0.466939i \(0.154643\pi\)
\(30\) 0 0
\(31\) 0.818209i 0.146955i 0.997297 + 0.0734773i \(0.0234097\pi\)
−0.997297 + 0.0734773i \(0.976590\pi\)
\(32\) 0 0
\(33\) 2.08329 + 2.08329i 0.362655 + 0.362655i
\(34\) 0 0
\(35\) 1.58404 4.65273i 0.267752 0.786455i
\(36\) 0 0
\(37\) 5.12639i 0.842774i 0.906881 + 0.421387i \(0.138457\pi\)
−0.906881 + 0.421387i \(0.861543\pi\)
\(38\) 0 0
\(39\) 2.52975i 0.405084i
\(40\) 0 0
\(41\) 3.34727i 0.522756i −0.965237 0.261378i \(-0.915823\pi\)
0.965237 0.261378i \(-0.0841769\pi\)
\(42\) 0 0
\(43\) 4.49131i 0.684919i 0.939533 + 0.342460i \(0.111260\pi\)
−0.939533 + 0.342460i \(0.888740\pi\)
\(44\) 0 0
\(45\) 5.52450 2.71822i 0.823543 0.405209i
\(46\) 0 0
\(47\) −4.29355 4.29355i −0.626278 0.626278i 0.320851 0.947130i \(-0.396031\pi\)
−0.947130 + 0.320851i \(0.896031\pi\)
\(48\) 0 0
\(49\) 2.16858i 0.309797i
\(50\) 0 0
\(51\) 0.106021 0.106021i 0.0148459 0.0148459i
\(52\) 0 0
\(53\) −1.00653 −0.138258 −0.0691291 0.997608i \(-0.522022\pi\)
−0.0691291 + 0.997608i \(0.522022\pi\)
\(54\) 0 0
\(55\) −12.5611 4.27649i −1.69374 0.576642i
\(56\) 0 0
\(57\) −0.419410 0.419410i −0.0555521 0.0555521i
\(58\) 0 0
\(59\) 7.65005 7.65005i 0.995952 0.995952i −0.00404030 0.999992i \(-0.501286\pi\)
0.999992 + 0.00404030i \(0.00128607\pi\)
\(60\) 0 0
\(61\) −1.90291 1.90291i −0.243643 0.243643i 0.574712 0.818355i \(-0.305114\pi\)
−0.818355 + 0.574712i \(0.805114\pi\)
\(62\) 0 0
\(63\) 4.27964 4.27964i 0.539184 0.539184i
\(64\) 0 0
\(65\) −5.03002 10.2230i −0.623897 1.26800i
\(66\) 0 0
\(67\) 11.0221i 1.34656i 0.739387 + 0.673280i \(0.235115\pi\)
−0.739387 + 0.673280i \(0.764885\pi\)
\(68\) 0 0
\(69\) −0.847724 0.847724i −0.102054 0.102054i
\(70\) 0 0
\(71\) 10.5331 1.25005 0.625027 0.780604i \(-0.285088\pi\)
0.625027 + 0.780604i \(0.285088\pi\)
\(72\) 0 0
\(73\) 2.70854 2.70854i 0.317010 0.317010i −0.530607 0.847618i \(-0.678036\pi\)
0.847618 + 0.530607i \(0.178036\pi\)
\(74\) 0 0
\(75\) 1.51474 1.96674i 0.174907 0.227099i
\(76\) 0 0
\(77\) −13.0435 −1.48645
\(78\) 0 0
\(79\) 8.32010 0.936085 0.468042 0.883706i \(-0.344959\pi\)
0.468042 + 0.883706i \(0.344959\pi\)
\(80\) 0 0
\(81\) 6.84226 0.760252
\(82\) 0 0
\(83\) 9.17237 1.00680 0.503399 0.864054i \(-0.332083\pi\)
0.503399 + 0.864054i \(0.332083\pi\)
\(84\) 0 0
\(85\) −0.217635 + 0.639248i −0.0236058 + 0.0693362i
\(86\) 0 0
\(87\) 1.11585 1.11585i 0.119632 0.119632i
\(88\) 0 0
\(89\) −4.25101 −0.450606 −0.225303 0.974289i \(-0.572337\pi\)
−0.225303 + 0.974289i \(0.572337\pi\)
\(90\) 0 0
\(91\) −7.91940 7.91940i −0.830178 0.830178i
\(92\) 0 0
\(93\) 0.406230i 0.0421241i
\(94\) 0 0
\(95\) 2.52881 + 0.860944i 0.259450 + 0.0883310i
\(96\) 0 0
\(97\) −7.16000 + 7.16000i −0.726987 + 0.726987i −0.970019 0.243031i \(-0.921858\pi\)
0.243031 + 0.970019i \(0.421858\pi\)
\(98\) 0 0
\(99\) −11.5539 11.5539i −1.16121 1.16121i
\(100\) 0 0
\(101\) 8.38846 8.38846i 0.834683 0.834683i −0.153470 0.988153i \(-0.549045\pi\)
0.988153 + 0.153470i \(0.0490448\pi\)
\(102\) 0 0
\(103\) 5.16478 + 5.16478i 0.508901 + 0.508901i 0.914189 0.405288i \(-0.132829\pi\)
−0.405288 + 0.914189i \(0.632829\pi\)
\(104\) 0 0
\(105\) 0.786458 2.31002i 0.0767504 0.225435i
\(106\) 0 0
\(107\) −8.97973 −0.868103 −0.434052 0.900888i \(-0.642916\pi\)
−0.434052 + 0.900888i \(0.642916\pi\)
\(108\) 0 0
\(109\) 10.9081 10.9081i 1.04481 1.04481i 0.0458592 0.998948i \(-0.485397\pi\)
0.998948 0.0458592i \(-0.0146025\pi\)
\(110\) 0 0
\(111\) 2.54519i 0.241579i
\(112\) 0 0
\(113\) −4.29684 4.29684i −0.404212 0.404212i 0.475502 0.879715i \(-0.342266\pi\)
−0.879715 + 0.475502i \(0.842266\pi\)
\(114\) 0 0
\(115\) 5.11131 + 1.74017i 0.476632 + 0.162271i
\(116\) 0 0
\(117\) 14.0299i 1.29707i
\(118\) 0 0
\(119\) 0.663798i 0.0608503i
\(120\) 0 0
\(121\) 24.2140i 2.20127i
\(122\) 0 0
\(123\) 1.66188i 0.149846i
\(124\) 0 0
\(125\) −2.21067 + 10.9596i −0.197728 + 0.980257i
\(126\) 0 0
\(127\) −0.759686 0.759686i −0.0674112 0.0674112i 0.672597 0.740009i \(-0.265179\pi\)
−0.740009 + 0.672597i \(0.765179\pi\)
\(128\) 0 0
\(129\) 2.22988i 0.196330i
\(130\) 0 0
\(131\) −7.59995 + 7.59995i −0.664010 + 0.664010i −0.956323 0.292312i \(-0.905575\pi\)
0.292312 + 0.956323i \(0.405575\pi\)
\(132\) 0 0
\(133\) 2.62593 0.227697
\(134\) 0 0
\(135\) 5.73123 2.81994i 0.493266 0.242702i
\(136\) 0 0
\(137\) 12.7789 + 12.7789i 1.09178 + 1.09178i 0.995339 + 0.0964376i \(0.0307448\pi\)
0.0964376 + 0.995339i \(0.469255\pi\)
\(138\) 0 0
\(139\) −7.74227 + 7.74227i −0.656691 + 0.656691i −0.954596 0.297905i \(-0.903712\pi\)
0.297905 + 0.954596i \(0.403712\pi\)
\(140\) 0 0
\(141\) −2.13169 2.13169i −0.179521 0.179521i
\(142\) 0 0
\(143\) −21.3802 + 21.3802i −1.78790 + 1.78790i
\(144\) 0 0
\(145\) −2.29057 + 6.72798i −0.190222 + 0.558728i
\(146\) 0 0
\(147\) 1.07667i 0.0888024i
\(148\) 0 0
\(149\) 9.57165 + 9.57165i 0.784140 + 0.784140i 0.980527 0.196386i \(-0.0629207\pi\)
−0.196386 + 0.980527i \(0.562921\pi\)
\(150\) 0 0
\(151\) 9.68791 0.788391 0.394195 0.919027i \(-0.371023\pi\)
0.394195 + 0.919027i \(0.371023\pi\)
\(152\) 0 0
\(153\) −0.587989 + 0.587989i −0.0475361 + 0.0475361i
\(154\) 0 0
\(155\) −0.807726 1.64162i −0.0648781 0.131858i
\(156\) 0 0
\(157\) −9.97637 −0.796201 −0.398101 0.917342i \(-0.630331\pi\)
−0.398101 + 0.917342i \(0.630331\pi\)
\(158\) 0 0
\(159\) −0.499732 −0.0396313
\(160\) 0 0
\(161\) 5.30761 0.418298
\(162\) 0 0
\(163\) −9.48267 −0.742740 −0.371370 0.928485i \(-0.621112\pi\)
−0.371370 + 0.928485i \(0.621112\pi\)
\(164\) 0 0
\(165\) −6.23643 2.12322i −0.485506 0.165293i
\(166\) 0 0
\(167\) 9.43528 9.43528i 0.730124 0.730124i −0.240520 0.970644i \(-0.577318\pi\)
0.970644 + 0.240520i \(0.0773180\pi\)
\(168\) 0 0
\(169\) −12.9621 −0.997082
\(170\) 0 0
\(171\) 2.32603 + 2.32603i 0.177876 + 0.177876i
\(172\) 0 0
\(173\) 8.94716i 0.680240i 0.940382 + 0.340120i \(0.110468\pi\)
−0.940382 + 0.340120i \(0.889532\pi\)
\(174\) 0 0
\(175\) 1.41497 + 10.8988i 0.106962 + 0.823870i
\(176\) 0 0
\(177\) 3.79815 3.79815i 0.285487 0.285487i
\(178\) 0 0
\(179\) 3.02430 + 3.02430i 0.226047 + 0.226047i 0.811039 0.584992i \(-0.198902\pi\)
−0.584992 + 0.811039i \(0.698902\pi\)
\(180\) 0 0
\(181\) −1.54845 + 1.54845i −0.115095 + 0.115095i −0.762309 0.647213i \(-0.775934\pi\)
0.647213 + 0.762309i \(0.275934\pi\)
\(182\) 0 0
\(183\) −0.944773 0.944773i −0.0698396 0.0698396i
\(184\) 0 0
\(185\) −5.06072 10.2854i −0.372071 0.756195i
\(186\) 0 0
\(187\) 1.79208 0.131050
\(188\) 0 0
\(189\) 4.43979 4.43979i 0.322947 0.322947i
\(190\) 0 0
\(191\) 20.1005i 1.45442i −0.686415 0.727210i \(-0.740817\pi\)
0.686415 0.727210i \(-0.259183\pi\)
\(192\) 0 0
\(193\) 3.82483 + 3.82483i 0.275317 + 0.275317i 0.831236 0.555919i \(-0.187634\pi\)
−0.555919 + 0.831236i \(0.687634\pi\)
\(194\) 0 0
\(195\) −2.49734 5.07558i −0.178838 0.363470i
\(196\) 0 0
\(197\) 1.11758i 0.0796246i 0.999207 + 0.0398123i \(0.0126760\pi\)
−0.999207 + 0.0398123i \(0.987324\pi\)
\(198\) 0 0
\(199\) 25.5830i 1.81353i 0.421635 + 0.906766i \(0.361456\pi\)
−0.421635 + 0.906766i \(0.638544\pi\)
\(200\) 0 0
\(201\) 5.47232i 0.385988i
\(202\) 0 0
\(203\) 6.98637i 0.490347i
\(204\) 0 0
\(205\) 3.30439 + 6.71581i 0.230788 + 0.469053i
\(206\) 0 0
\(207\) 4.70145 + 4.70145i 0.326773 + 0.326773i
\(208\) 0 0
\(209\) 7.08929i 0.490376i
\(210\) 0 0
\(211\) −0.411613 + 0.411613i −0.0283366 + 0.0283366i −0.721133 0.692797i \(-0.756378\pi\)
0.692797 + 0.721133i \(0.256378\pi\)
\(212\) 0 0
\(213\) 5.22957 0.358324
\(214\) 0 0
\(215\) −4.43378 9.01117i −0.302381 0.614557i
\(216\) 0 0
\(217\) −1.27171 1.27171i −0.0863290 0.0863290i
\(218\) 0 0
\(219\) 1.34475 1.34475i 0.0908701 0.0908701i
\(220\) 0 0
\(221\) 1.08806 + 1.08806i 0.0731909 + 0.0731909i
\(222\) 0 0
\(223\) 16.7466 16.7466i 1.12143 1.12143i 0.129908 0.991526i \(-0.458532\pi\)
0.991526 0.129908i \(-0.0414682\pi\)
\(224\) 0 0
\(225\) −8.40070 + 10.9074i −0.560047 + 0.727163i
\(226\) 0 0
\(227\) 13.7807i 0.914659i 0.889297 + 0.457330i \(0.151194\pi\)
−0.889297 + 0.457330i \(0.848806\pi\)
\(228\) 0 0
\(229\) −7.90971 7.90971i −0.522688 0.522688i 0.395694 0.918382i \(-0.370504\pi\)
−0.918382 + 0.395694i \(0.870504\pi\)
\(230\) 0 0
\(231\) −6.47594 −0.426086
\(232\) 0 0
\(233\) −1.67997 + 1.67997i −0.110058 + 0.110058i −0.759991 0.649933i \(-0.774797\pi\)
0.649933 + 0.759991i \(0.274797\pi\)
\(234\) 0 0
\(235\) 12.8529 + 4.37583i 0.838432 + 0.285448i
\(236\) 0 0
\(237\) 4.13083 0.268326
\(238\) 0 0
\(239\) −11.7685 −0.761241 −0.380620 0.924731i \(-0.624290\pi\)
−0.380620 + 0.924731i \(0.624290\pi\)
\(240\) 0 0
\(241\) −13.2730 −0.854991 −0.427495 0.904018i \(-0.640604\pi\)
−0.427495 + 0.904018i \(0.640604\pi\)
\(242\) 0 0
\(243\) 11.9667 0.767665
\(244\) 0 0
\(245\) −2.14080 4.35094i −0.136770 0.277971i
\(246\) 0 0
\(247\) 4.30427 4.30427i 0.273874 0.273874i
\(248\) 0 0
\(249\) 4.55396 0.288596
\(250\) 0 0
\(251\) −10.3795 10.3795i −0.655149 0.655149i 0.299079 0.954228i \(-0.403321\pi\)
−0.954228 + 0.299079i \(0.903321\pi\)
\(252\) 0 0
\(253\) 14.3291i 0.900863i
\(254\) 0 0
\(255\) −0.108053 + 0.317378i −0.00676654 + 0.0198750i
\(256\) 0 0
\(257\) 20.4353 20.4353i 1.27472 1.27472i 0.331140 0.943582i \(-0.392567\pi\)
0.943582 0.331140i \(-0.107433\pi\)
\(258\) 0 0
\(259\) −7.96772 7.96772i −0.495090 0.495090i
\(260\) 0 0
\(261\) −6.18848 + 6.18848i −0.383058 + 0.383058i
\(262\) 0 0
\(263\) −14.0611 14.0611i −0.867047 0.867047i 0.125098 0.992144i \(-0.460076\pi\)
−0.992144 + 0.125098i \(0.960076\pi\)
\(264\) 0 0
\(265\) 2.01946 0.993639i 0.124055 0.0610388i
\(266\) 0 0
\(267\) −2.11057 −0.129165
\(268\) 0 0
\(269\) −6.61443 + 6.61443i −0.403289 + 0.403289i −0.879390 0.476101i \(-0.842050\pi\)
0.476101 + 0.879390i \(0.342050\pi\)
\(270\) 0 0
\(271\) 10.6219i 0.645237i 0.946529 + 0.322619i \(0.104563\pi\)
−0.946529 + 0.322619i \(0.895437\pi\)
\(272\) 0 0
\(273\) −3.93188 3.93188i −0.237968 0.237968i
\(274\) 0 0
\(275\) 29.4237 3.82004i 1.77432 0.230357i
\(276\) 0 0
\(277\) 8.28511i 0.497804i 0.968529 + 0.248902i \(0.0800697\pi\)
−0.968529 + 0.248902i \(0.919930\pi\)
\(278\) 0 0
\(279\) 2.25294i 0.134880i
\(280\) 0 0
\(281\) 21.0176i 1.25380i −0.779098 0.626902i \(-0.784323\pi\)
0.779098 0.626902i \(-0.215677\pi\)
\(282\) 0 0
\(283\) 14.4748i 0.860436i −0.902725 0.430218i \(-0.858437\pi\)
0.902725 0.430218i \(-0.141563\pi\)
\(284\) 0 0
\(285\) 1.25552 + 0.427448i 0.0743706 + 0.0253198i
\(286\) 0 0
\(287\) 5.20251 + 5.20251i 0.307095 + 0.307095i
\(288\) 0 0
\(289\) 16.9088i 0.994635i
\(290\) 0 0
\(291\) −3.55485 + 3.55485i −0.208389 + 0.208389i
\(292\) 0 0
\(293\) −11.9165 −0.696171 −0.348086 0.937463i \(-0.613168\pi\)
−0.348086 + 0.937463i \(0.613168\pi\)
\(294\) 0 0
\(295\) −7.79667 + 22.9008i −0.453940 + 1.33333i
\(296\) 0 0
\(297\) −11.9862 11.9862i −0.695512 0.695512i
\(298\) 0 0
\(299\) 8.69993 8.69993i 0.503130 0.503130i
\(300\) 0 0
\(301\) −6.98065 6.98065i −0.402358 0.402358i
\(302\) 0 0
\(303\) 4.16477 4.16477i 0.239260 0.239260i
\(304\) 0 0
\(305\) 5.69645 + 1.93938i 0.326178 + 0.111049i
\(306\) 0 0
\(307\) 25.4511i 1.45257i −0.687392 0.726287i \(-0.741245\pi\)
0.687392 0.726287i \(-0.258755\pi\)
\(308\) 0 0
\(309\) 2.56425 + 2.56425i 0.145875 + 0.145875i
\(310\) 0 0
\(311\) −21.4775 −1.21788 −0.608939 0.793217i \(-0.708404\pi\)
−0.608939 + 0.793217i \(0.708404\pi\)
\(312\) 0 0
\(313\) 18.7965 18.7965i 1.06244 1.06244i 0.0645277 0.997916i \(-0.479446\pi\)
0.997916 0.0645277i \(-0.0205541\pi\)
\(314\) 0 0
\(315\) −4.36167 + 12.8113i −0.245752 + 0.721835i
\(316\) 0 0
\(317\) 16.2531 0.912864 0.456432 0.889758i \(-0.349127\pi\)
0.456432 + 0.889758i \(0.349127\pi\)
\(318\) 0 0
\(319\) 18.8613 1.05603
\(320\) 0 0
\(321\) −4.45832 −0.248839
\(322\) 0 0
\(323\) −0.360781 −0.0200744
\(324\) 0 0
\(325\) 20.1840 + 15.5453i 1.11961 + 0.862300i
\(326\) 0 0
\(327\) 5.41574 5.41574i 0.299491 0.299491i
\(328\) 0 0
\(329\) 13.3465 0.735818
\(330\) 0 0
\(331\) 8.71558 + 8.71558i 0.479052 + 0.479052i 0.904828 0.425777i \(-0.139999\pi\)
−0.425777 + 0.904828i \(0.639999\pi\)
\(332\) 0 0
\(333\) 14.1155i 0.773526i
\(334\) 0 0
\(335\) −10.8809 22.1142i −0.594485 1.20823i
\(336\) 0 0
\(337\) 0.0406874 0.0406874i 0.00221638 0.00221638i −0.705998 0.708214i \(-0.749501\pi\)
0.708214 + 0.705998i \(0.249501\pi\)
\(338\) 0 0
\(339\) −2.13333 2.13333i −0.115866 0.115866i
\(340\) 0 0
\(341\) −3.43326 + 3.43326i −0.185921 + 0.185921i
\(342\) 0 0
\(343\) −14.2503 14.2503i −0.769445 0.769445i
\(344\) 0 0
\(345\) 2.53770 + 0.863971i 0.136625 + 0.0465146i
\(346\) 0 0
\(347\) 35.7094 1.91698 0.958491 0.285124i \(-0.0920348\pi\)
0.958491 + 0.285124i \(0.0920348\pi\)
\(348\) 0 0
\(349\) −0.274452 + 0.274452i −0.0146911 + 0.0146911i −0.714414 0.699723i \(-0.753307\pi\)
0.699723 + 0.714414i \(0.253307\pi\)
\(350\) 0 0
\(351\) 14.5549i 0.776884i
\(352\) 0 0
\(353\) −15.6215 15.6215i −0.831446 0.831446i 0.156268 0.987715i \(-0.450054\pi\)
−0.987715 + 0.156268i \(0.950054\pi\)
\(354\) 0 0
\(355\) −21.1332 + 10.3982i −1.12163 + 0.551879i
\(356\) 0 0
\(357\) 0.329567i 0.0174426i
\(358\) 0 0
\(359\) 0.768787i 0.0405750i −0.999794 0.0202875i \(-0.993542\pi\)
0.999794 0.0202875i \(-0.00645816\pi\)
\(360\) 0 0
\(361\) 17.5728i 0.924883i
\(362\) 0 0
\(363\) 12.0219i 0.630988i
\(364\) 0 0
\(365\) −2.76045 + 8.10812i −0.144488 + 0.424399i
\(366\) 0 0
\(367\) −13.7849 13.7849i −0.719568 0.719568i 0.248949 0.968517i \(-0.419915\pi\)
−0.968517 + 0.248949i \(0.919915\pi\)
\(368\) 0 0
\(369\) 9.21671i 0.479803i
\(370\) 0 0
\(371\) 1.56441 1.56441i 0.0812202 0.0812202i
\(372\) 0 0
\(373\) −21.4003 −1.10806 −0.554031 0.832496i \(-0.686911\pi\)
−0.554031 + 0.832496i \(0.686911\pi\)
\(374\) 0 0
\(375\) −1.09757 + 5.44131i −0.0566782 + 0.280988i
\(376\) 0 0
\(377\) 11.4517 + 11.4517i 0.589791 + 0.589791i
\(378\) 0 0
\(379\) −11.3922 + 11.3922i −0.585180 + 0.585180i −0.936322 0.351142i \(-0.885793\pi\)
0.351142 + 0.936322i \(0.385793\pi\)
\(380\) 0 0
\(381\) −0.377174 0.377174i −0.0193232 0.0193232i
\(382\) 0 0
\(383\) −4.42635 + 4.42635i −0.226176 + 0.226176i −0.811093 0.584917i \(-0.801127\pi\)
0.584917 + 0.811093i \(0.301127\pi\)
\(384\) 0 0
\(385\) 26.1699 12.8764i 1.33374 0.656243i
\(386\) 0 0
\(387\) 12.3668i 0.628642i
\(388\) 0 0
\(389\) 12.3502 + 12.3502i 0.626180 + 0.626180i 0.947105 0.320924i \(-0.103994\pi\)
−0.320924 + 0.947105i \(0.603994\pi\)
\(390\) 0 0
\(391\) −0.729222 −0.0368784
\(392\) 0 0
\(393\) −3.77328 + 3.77328i −0.190337 + 0.190337i
\(394\) 0 0
\(395\) −16.6931 + 8.21351i −0.839920 + 0.413267i
\(396\) 0 0
\(397\) 17.9832 0.902551 0.451275 0.892385i \(-0.350969\pi\)
0.451275 + 0.892385i \(0.350969\pi\)
\(398\) 0 0
\(399\) 1.30374 0.0652686
\(400\) 0 0
\(401\) 9.06570 0.452720 0.226360 0.974044i \(-0.427317\pi\)
0.226360 + 0.974044i \(0.427317\pi\)
\(402\) 0 0
\(403\) −4.16902 −0.207674
\(404\) 0 0
\(405\) −13.7280 + 6.75461i −0.682150 + 0.335639i
\(406\) 0 0
\(407\) −21.5107 + 21.5107i −1.06625 + 1.06625i
\(408\) 0 0
\(409\) −30.0616 −1.48645 −0.743226 0.669040i \(-0.766705\pi\)
−0.743226 + 0.669040i \(0.766705\pi\)
\(410\) 0 0
\(411\) 6.34457 + 6.34457i 0.312955 + 0.312955i
\(412\) 0 0
\(413\) 23.7803i 1.17015i
\(414\) 0 0
\(415\) −18.4030 + 9.05486i −0.903369 + 0.444485i
\(416\) 0 0
\(417\) −3.84394 + 3.84394i −0.188239 + 0.188239i
\(418\) 0 0
\(419\) 15.3986 + 15.3986i 0.752271 + 0.752271i 0.974903 0.222631i \(-0.0714646\pi\)
−0.222631 + 0.974903i \(0.571465\pi\)
\(420\) 0 0
\(421\) −3.86468 + 3.86468i −0.188353 + 0.188353i −0.794984 0.606631i \(-0.792521\pi\)
0.606631 + 0.794984i \(0.292521\pi\)
\(422\) 0 0
\(423\) 11.8223 + 11.8223i 0.574819 + 0.574819i
\(424\) 0 0
\(425\) −0.194406 1.49740i −0.00943006 0.0726348i
\(426\) 0 0
\(427\) 5.91523 0.286258
\(428\) 0 0
\(429\) −10.6150 + 10.6150i −0.512497 + 0.512497i
\(430\) 0 0
\(431\) 27.2692i 1.31351i 0.754103 + 0.656756i \(0.228072\pi\)
−0.754103 + 0.656756i \(0.771928\pi\)
\(432\) 0 0
\(433\) 19.1435 + 19.1435i 0.919978 + 0.919978i 0.997027 0.0770497i \(-0.0245500\pi\)
−0.0770497 + 0.997027i \(0.524550\pi\)
\(434\) 0 0
\(435\) −1.13724 + 3.34036i −0.0545265 + 0.160158i
\(436\) 0 0
\(437\) 2.88474i 0.137996i
\(438\) 0 0
\(439\) 30.1995i 1.44134i −0.693276 0.720672i \(-0.743833\pi\)
0.693276 0.720672i \(-0.256167\pi\)
\(440\) 0 0
\(441\) 5.97118i 0.284342i
\(442\) 0 0
\(443\) 27.7051i 1.31631i −0.752884 0.658153i \(-0.771338\pi\)
0.752884 0.658153i \(-0.228662\pi\)
\(444\) 0 0
\(445\) 8.52903 4.19655i 0.404315 0.198935i
\(446\) 0 0
\(447\) 4.75220 + 4.75220i 0.224772 + 0.224772i
\(448\) 0 0
\(449\) 9.78315i 0.461695i −0.972990 0.230848i \(-0.925850\pi\)
0.972990 0.230848i \(-0.0741499\pi\)
\(450\) 0 0
\(451\) 14.0454 14.0454i 0.661371 0.661371i
\(452\) 0 0
\(453\) 4.80992 0.225990
\(454\) 0 0
\(455\) 23.7071 + 8.07118i 1.11140 + 0.378383i
\(456\) 0 0
\(457\) −0.557108 0.557108i −0.0260604 0.0260604i 0.693957 0.720017i \(-0.255866\pi\)
−0.720017 + 0.693957i \(0.755866\pi\)
\(458\) 0 0
\(459\) −0.609992 + 0.609992i −0.0284720 + 0.0284720i
\(460\) 0 0
\(461\) −12.5791 12.5791i −0.585865 0.585865i 0.350644 0.936509i \(-0.385963\pi\)
−0.936509 + 0.350644i \(0.885963\pi\)
\(462\) 0 0
\(463\) 3.29549 3.29549i 0.153154 0.153154i −0.626371 0.779525i \(-0.715460\pi\)
0.779525 + 0.626371i \(0.215460\pi\)
\(464\) 0 0
\(465\) −0.401026 0.815042i −0.0185971 0.0377967i
\(466\) 0 0
\(467\) 10.1995i 0.471979i 0.971756 + 0.235989i \(0.0758331\pi\)
−0.971756 + 0.235989i \(0.924167\pi\)
\(468\) 0 0
\(469\) −17.1311 17.1311i −0.791042 0.791042i
\(470\) 0 0
\(471\) −4.95314 −0.228229
\(472\) 0 0
\(473\) −18.8459 + 18.8459i −0.866534 + 0.866534i
\(474\) 0 0
\(475\) −5.92360 + 0.769051i −0.271793 + 0.0352865i
\(476\) 0 0
\(477\) 2.77149 0.126898
\(478\) 0 0
\(479\) −5.65795 −0.258518 −0.129259 0.991611i \(-0.541260\pi\)
−0.129259 + 0.991611i \(0.541260\pi\)
\(480\) 0 0
\(481\) −26.1205 −1.19099
\(482\) 0 0
\(483\) 2.63516 0.119904
\(484\) 0 0
\(485\) 7.29722 21.4338i 0.331350 0.973257i
\(486\) 0 0
\(487\) 19.7470 19.7470i 0.894823 0.894823i −0.100149 0.994972i \(-0.531932\pi\)
0.994972 + 0.100149i \(0.0319321\pi\)
\(488\) 0 0
\(489\) −4.70802 −0.212904
\(490\) 0 0
\(491\) 4.21405 + 4.21405i 0.190177 + 0.190177i 0.795773 0.605595i \(-0.207065\pi\)
−0.605595 + 0.795773i \(0.707065\pi\)
\(492\) 0 0
\(493\) 0.959871i 0.0432304i
\(494\) 0 0
\(495\) 34.5870 + 11.7753i 1.55457 + 0.529261i
\(496\) 0 0
\(497\) −16.3712 + 16.3712i −0.734348 + 0.734348i
\(498\) 0 0
\(499\) 16.8862 + 16.8862i 0.755928 + 0.755928i 0.975579 0.219650i \(-0.0704917\pi\)
−0.219650 + 0.975579i \(0.570492\pi\)
\(500\) 0 0
\(501\) 4.68450 4.68450i 0.209288 0.209288i
\(502\) 0 0
\(503\) 20.3714 + 20.3714i 0.908317 + 0.908317i 0.996136 0.0878190i \(-0.0279897\pi\)
−0.0878190 + 0.996136i \(0.527990\pi\)
\(504\) 0 0
\(505\) −8.54923 + 25.1112i −0.380436 + 1.11744i
\(506\) 0 0
\(507\) −6.43550 −0.285811
\(508\) 0 0
\(509\) −20.6309 + 20.6309i −0.914448 + 0.914448i −0.996618 0.0821701i \(-0.973815\pi\)
0.0821701 + 0.996618i \(0.473815\pi\)
\(510\) 0 0
\(511\) 8.41952i 0.372458i
\(512\) 0 0
\(513\) 2.41307 + 2.41307i 0.106540 + 0.106540i
\(514\) 0 0
\(515\) −15.4610 5.26376i −0.681293 0.231949i
\(516\) 0 0
\(517\) 36.0320i 1.58469i
\(518\) 0 0
\(519\) 4.44215i 0.194989i
\(520\) 0 0
\(521\) 19.0433i 0.834300i 0.908838 + 0.417150i \(0.136971\pi\)
−0.908838 + 0.417150i \(0.863029\pi\)
\(522\) 0 0
\(523\) 19.1782i 0.838603i 0.907847 + 0.419301i \(0.137725\pi\)
−0.907847 + 0.419301i \(0.862275\pi\)
\(524\) 0 0
\(525\) 0.702515 + 5.41111i 0.0306603 + 0.236160i
\(526\) 0 0
\(527\) 0.174722 + 0.174722i 0.00761101 + 0.00761101i
\(528\) 0 0
\(529\) 17.1693i 0.746490i
\(530\) 0 0
\(531\) −21.0644 + 21.0644i −0.914118 + 0.914118i
\(532\) 0 0
\(533\) 17.0553 0.738749
\(534\) 0 0
\(535\) 18.0165 8.86469i 0.778922 0.383254i
\(536\) 0 0
\(537\) 1.50153 + 1.50153i 0.0647957 + 0.0647957i
\(538\) 0 0
\(539\) −9.09950 + 9.09950i −0.391943 + 0.391943i
\(540\) 0 0
\(541\) 14.5231 + 14.5231i 0.624398 + 0.624398i 0.946653 0.322255i \(-0.104441\pi\)
−0.322255 + 0.946653i \(0.604441\pi\)
\(542\) 0 0
\(543\) −0.768787 + 0.768787i −0.0329918 + 0.0329918i
\(544\) 0 0
\(545\) −11.1172 + 32.6539i −0.476207 + 1.39874i
\(546\) 0 0
\(547\) 9.97058i 0.426311i −0.977018 0.213156i \(-0.931626\pi\)
0.977018 0.213156i \(-0.0683742\pi\)
\(548\) 0 0
\(549\) 5.23967 + 5.23967i 0.223624 + 0.223624i
\(550\) 0 0
\(551\) −3.79716 −0.161765
\(552\) 0 0
\(553\) −12.9316 + 12.9316i −0.549906 + 0.549906i
\(554\) 0 0
\(555\) −2.51258 5.10655i −0.106653 0.216761i
\(556\) 0 0
\(557\) 11.4424 0.484831 0.242416 0.970173i \(-0.422060\pi\)
0.242416 + 0.970173i \(0.422060\pi\)
\(558\) 0 0
\(559\) −22.8846 −0.967915
\(560\) 0 0
\(561\) 0.889743 0.0375650
\(562\) 0 0
\(563\) −47.0585 −1.98328 −0.991640 0.129034i \(-0.958812\pi\)
−0.991640 + 0.129034i \(0.958812\pi\)
\(564\) 0 0
\(565\) 12.8628 + 4.37919i 0.541141 + 0.184234i
\(566\) 0 0
\(567\) −10.6346 + 10.6346i −0.446612 + 0.446612i
\(568\) 0 0
\(569\) 41.4684 1.73845 0.869224 0.494419i \(-0.164619\pi\)
0.869224 + 0.494419i \(0.164619\pi\)
\(570\) 0 0
\(571\) −16.1745 16.1745i −0.676881 0.676881i 0.282412 0.959293i \(-0.408865\pi\)
−0.959293 + 0.282412i \(0.908865\pi\)
\(572\) 0 0
\(573\) 9.97963i 0.416905i
\(574\) 0 0
\(575\) −11.9730 + 1.55443i −0.499307 + 0.0648242i
\(576\) 0 0
\(577\) 20.0316 20.0316i 0.833926 0.833926i −0.154125 0.988051i \(-0.549256\pi\)
0.988051 + 0.154125i \(0.0492560\pi\)
\(578\) 0 0
\(579\) 1.89898 + 1.89898i 0.0789189 + 0.0789189i
\(580\) 0 0
\(581\) −14.2562 + 14.2562i −0.591447 + 0.591447i
\(582\) 0 0
\(583\) −4.22349 4.22349i −0.174919 0.174919i
\(584\) 0 0
\(585\) 13.8502 + 28.1490i 0.572634 + 1.16382i
\(586\) 0 0
\(587\) −29.1190 −1.20187 −0.600935 0.799298i \(-0.705205\pi\)
−0.600935 + 0.799298i \(0.705205\pi\)
\(588\) 0 0
\(589\) 0.691185 0.691185i 0.0284798 0.0284798i
\(590\) 0 0
\(591\) 0.554866i 0.0228242i
\(592\) 0 0
\(593\) −10.3431 10.3431i −0.424740 0.424740i 0.462092 0.886832i \(-0.347099\pi\)
−0.886832 + 0.462092i \(0.847099\pi\)
\(594\) 0 0
\(595\) −0.655294 1.33181i −0.0268644 0.0545991i
\(596\) 0 0
\(597\) 12.7016i 0.519843i
\(598\) 0 0
\(599\) 2.59479i 0.106020i −0.998594 0.0530101i \(-0.983118\pi\)
0.998594 0.0530101i \(-0.0168816\pi\)
\(600\) 0 0
\(601\) 14.4092i 0.587765i −0.955842 0.293882i \(-0.905053\pi\)
0.955842 0.293882i \(-0.0949474\pi\)
\(602\) 0 0
\(603\) 30.3493i 1.23592i
\(604\) 0 0
\(605\) −23.9038 48.5818i −0.971826 1.97513i
\(606\) 0 0
\(607\) 11.8502 + 11.8502i 0.480985 + 0.480985i 0.905446 0.424461i \(-0.139536\pi\)
−0.424461 + 0.905446i \(0.639536\pi\)
\(608\) 0 0
\(609\) 3.46864i 0.140557i
\(610\) 0 0
\(611\) 21.8769 21.8769i 0.885045 0.885045i
\(612\) 0 0
\(613\) 16.8256 0.679579 0.339789 0.940502i \(-0.389644\pi\)
0.339789 + 0.940502i \(0.389644\pi\)
\(614\) 0 0
\(615\) 1.64059 + 3.33431i 0.0661548 + 0.134453i
\(616\) 0 0
\(617\) −22.4849 22.4849i −0.905209 0.905209i 0.0906720 0.995881i \(-0.471098\pi\)
−0.995881 + 0.0906720i \(0.971098\pi\)
\(618\) 0 0
\(619\) 14.1269 14.1269i 0.567809 0.567809i −0.363705 0.931514i \(-0.618488\pi\)
0.931514 + 0.363705i \(0.118488\pi\)
\(620\) 0 0
\(621\) 4.87738 + 4.87738i 0.195723 + 0.195723i
\(622\) 0 0
\(623\) 6.60715 6.60715i 0.264710 0.264710i
\(624\) 0 0
\(625\) −6.38382 24.1712i −0.255353 0.966848i
\(626\) 0 0
\(627\) 3.51974i 0.140565i
\(628\) 0 0
\(629\) 1.09470 + 1.09470i 0.0436486 + 0.0436486i
\(630\) 0 0
\(631\) 33.9235 1.35047 0.675236 0.737601i \(-0.264042\pi\)
0.675236 + 0.737601i \(0.264042\pi\)
\(632\) 0 0
\(633\) −0.204361 + 0.204361i −0.00812261 + 0.00812261i
\(634\) 0 0
\(635\) 2.27415 + 0.774246i 0.0902470 + 0.0307250i
\(636\) 0 0
\(637\) −11.0496 −0.437799
\(638\) 0 0
\(639\) −29.0030 −1.14734
\(640\) 0 0
\(641\) 18.8495 0.744509 0.372254 0.928131i \(-0.378585\pi\)
0.372254 + 0.928131i \(0.378585\pi\)
\(642\) 0 0
\(643\) 16.4916 0.650364 0.325182 0.945652i \(-0.394574\pi\)
0.325182 + 0.945652i \(0.394574\pi\)
\(644\) 0 0
\(645\) −2.20131 4.47393i −0.0866766 0.176161i
\(646\) 0 0
\(647\) 0.316870 0.316870i 0.0124574 0.0124574i −0.700851 0.713308i \(-0.747196\pi\)
0.713308 + 0.700851i \(0.247196\pi\)
\(648\) 0 0
\(649\) 64.2002 2.52008
\(650\) 0 0
\(651\) −0.631386 0.631386i −0.0247460 0.0247460i
\(652\) 0 0
\(653\) 17.0751i 0.668200i −0.942538 0.334100i \(-0.891568\pi\)
0.942538 0.334100i \(-0.108432\pi\)
\(654\) 0 0
\(655\) 7.74560 22.7508i 0.302646 0.888946i
\(656\) 0 0
\(657\) −7.45796 + 7.45796i −0.290963 + 0.290963i
\(658\) 0 0
\(659\) 7.42245 + 7.42245i 0.289138 + 0.289138i 0.836739 0.547601i \(-0.184459\pi\)
−0.547601 + 0.836739i \(0.684459\pi\)
\(660\) 0 0
\(661\) 31.7614 31.7614i 1.23538 1.23538i 0.273507 0.961870i \(-0.411816\pi\)
0.961870 0.273507i \(-0.0881837\pi\)
\(662\) 0 0
\(663\) 0.540209 + 0.540209i 0.0209800 + 0.0209800i
\(664\) 0 0
\(665\) −5.26854 + 2.59229i −0.204305 + 0.100525i
\(666\) 0 0
\(667\) −7.67495 −0.297175
\(668\) 0 0
\(669\) 8.31446 8.31446i 0.321456 0.321456i
\(670\) 0 0
\(671\) 15.9695i 0.616496i
\(672\) 0 0
\(673\) 4.14672 + 4.14672i 0.159844 + 0.159844i 0.782498 0.622653i \(-0.213945\pi\)
−0.622653 + 0.782498i \(0.713945\pi\)
\(674\) 0 0
\(675\) −8.71507 + 11.3156i −0.335443 + 0.435538i
\(676\) 0 0
\(677\) 25.2618i 0.970890i 0.874267 + 0.485445i \(0.161342\pi\)
−0.874267 + 0.485445i \(0.838658\pi\)
\(678\) 0 0
\(679\) 22.2569i 0.854143i
\(680\) 0 0
\(681\) 6.84196i 0.262184i
\(682\) 0 0
\(683\) 8.20306i 0.313881i 0.987608 + 0.156941i \(0.0501631\pi\)
−0.987608 + 0.156941i \(0.949837\pi\)
\(684\) 0 0
\(685\) −38.2542 13.0238i −1.46162 0.497615i
\(686\) 0 0
\(687\) −3.92707 3.92707i −0.149827 0.149827i
\(688\) 0 0
\(689\) 5.12859i 0.195384i
\(690\) 0 0
\(691\) 7.89158 7.89158i 0.300210 0.300210i −0.540886 0.841096i \(-0.681911\pi\)
0.841096 + 0.540886i \(0.181911\pi\)
\(692\) 0 0
\(693\) 35.9153 1.36431
\(694\) 0 0
\(695\) 7.89066 23.1768i 0.299310 0.879147i
\(696\) 0 0
\(697\) −0.714783 0.714783i −0.0270744 0.0270744i
\(698\) 0 0
\(699\) −0.834083 + 0.834083i −0.0315479 + 0.0315479i
\(700\) 0 0
\(701\) 1.50228 + 1.50228i 0.0567405 + 0.0567405i 0.734908 0.678167i \(-0.237225\pi\)
−0.678167 + 0.734908i \(0.737225\pi\)
\(702\) 0 0
\(703\) 4.33054 4.33054i 0.163329 0.163329i
\(704\) 0 0
\(705\) 6.38131 + 2.17255i 0.240334 + 0.0818228i
\(706\) 0 0
\(707\) 26.0756i 0.980675i
\(708\) 0 0
\(709\) −36.0738 36.0738i −1.35478 1.35478i −0.880228 0.474551i \(-0.842610\pi\)
−0.474551 0.880228i \(-0.657390\pi\)
\(710\) 0 0
\(711\) −22.9094 −0.859170
\(712\) 0 0
\(713\) 1.39704 1.39704i 0.0523197 0.0523197i
\(714\) 0 0
\(715\) 21.7900 64.0026i 0.814899 2.39356i
\(716\) 0 0
\(717\) −5.84291 −0.218207
\(718\) 0 0
\(719\) 35.0340 1.30655 0.653274 0.757121i \(-0.273395\pi\)
0.653274 + 0.757121i \(0.273395\pi\)
\(720\) 0 0
\(721\) −16.0548 −0.597911
\(722\) 0 0
\(723\) −6.58989 −0.245081
\(724\) 0 0
\(725\) −2.04609 15.7599i −0.0759898 0.585310i
\(726\) 0 0
\(727\) −25.4241 + 25.4241i −0.942928 + 0.942928i −0.998457 0.0555295i \(-0.982315\pi\)
0.0555295 + 0.998457i \(0.482315\pi\)
\(728\) 0 0
\(729\) −14.5855 −0.540203
\(730\) 0 0
\(731\) 0.959085 + 0.959085i 0.0354731 + 0.0354731i
\(732\) 0 0
\(733\) 7.37554i 0.272422i −0.990680 0.136211i \(-0.956508\pi\)
0.990680 0.136211i \(-0.0434925\pi\)
\(734\) 0 0
\(735\) −1.06288 2.16019i −0.0392049 0.0796797i
\(736\) 0 0
\(737\) −46.2494 + 46.2494i −1.70362 + 1.70362i
\(738\) 0 0
\(739\) −5.55025 5.55025i −0.204169 0.204169i 0.597614 0.801784i \(-0.296115\pi\)
−0.801784 + 0.597614i \(0.796115\pi\)
\(740\) 0 0
\(741\) 2.13702 2.13702i 0.0785053 0.0785053i
\(742\) 0 0
\(743\) 6.78835 + 6.78835i 0.249040 + 0.249040i 0.820577 0.571536i \(-0.193652\pi\)
−0.571536 + 0.820577i \(0.693652\pi\)
\(744\) 0 0
\(745\) −28.6532 9.75510i −1.04977 0.357399i
\(746\) 0 0
\(747\) −25.2561 −0.924073
\(748\) 0 0
\(749\) 13.9568 13.9568i 0.509970 0.509970i
\(750\) 0 0
\(751\) 3.93385i 0.143548i 0.997421 + 0.0717742i \(0.0228661\pi\)
−0.997421 + 0.0717742i \(0.977134\pi\)
\(752\) 0 0
\(753\) −5.15330 5.15330i −0.187797 0.187797i
\(754\) 0 0
\(755\) −19.4374 + 9.56379i −0.707398 + 0.348062i
\(756\) 0 0
\(757\) 21.8327i 0.793525i 0.917921 + 0.396762i \(0.129866\pi\)
−0.917921 + 0.396762i \(0.870134\pi\)
\(758\) 0 0
\(759\) 7.11421i 0.258230i
\(760\) 0 0
\(761\) 4.27291i 0.154893i 0.996997 + 0.0774464i \(0.0246767\pi\)
−0.996997 + 0.0774464i \(0.975323\pi\)
\(762\) 0 0
\(763\) 33.9080i 1.22755i
\(764\) 0 0
\(765\) 0.599258 1.76017i 0.0216662 0.0636391i
\(766\) 0 0
\(767\) 38.9793 + 38.9793i 1.40746 + 1.40746i
\(768\) 0 0
\(769\) 26.1800i 0.944074i −0.881579 0.472037i \(-0.843519\pi\)
0.881579 0.472037i \(-0.156481\pi\)
\(770\) 0 0
\(771\) 10.1459 10.1459i 0.365395 0.365395i
\(772\) 0 0
\(773\) −15.0077 −0.539791 −0.269895 0.962890i \(-0.586989\pi\)
−0.269895 + 0.962890i \(0.586989\pi\)
\(774\) 0 0
\(775\) 3.24117 + 2.49629i 0.116426 + 0.0896693i
\(776\) 0 0
\(777\) −3.95587 3.95587i −0.141916 0.141916i
\(778\) 0 0
\(779\) −2.82762 + 2.82762i −0.101310 + 0.101310i
\(780\) 0 0
\(781\) 44.1977 + 44.1977i 1.58152 + 1.58152i
\(782\) 0 0
\(783\) −6.42007 + 6.42007i −0.229434 + 0.229434i
\(784\) 0 0
\(785\) 20.0161 9.84856i 0.714407 0.351510i
\(786\) 0 0
\(787\) 42.9223i 1.53001i −0.644022 0.765007i \(-0.722736\pi\)
0.644022 0.765007i \(-0.277264\pi\)
\(788\) 0 0
\(789\) −6.98118 6.98118i −0.248536 0.248536i
\(790\) 0 0
\(791\) 13.3568 0.474912
\(792\) 0 0
\(793\) 9.69591 9.69591i 0.344312 0.344312i
\(794\) 0 0
\(795\) 1.00264 0.493329i 0.0355599 0.0174966i
\(796\) 0 0
\(797\) 0.280831 0.00994753 0.00497377 0.999988i \(-0.498417\pi\)
0.00497377 + 0.999988i \(0.498417\pi\)