Properties

Label 819.2.fm.e.496.2
Level $819$
Weight $2$
Character 819.496
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 496.2
Character \(\chi\) \(=\) 819.496
Dual form 819.2.fm.e.748.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.96303 - 0.525993i) q^{2} +(1.84478 + 1.06508i) q^{4} +(1.56698 + 1.56698i) q^{5} +(2.60496 + 0.462799i) q^{7} +(-0.187059 - 0.187059i) q^{8} +O(q^{10})\) \(q+(-1.96303 - 0.525993i) q^{2} +(1.84478 + 1.06508i) q^{4} +(1.56698 + 1.56698i) q^{5} +(2.60496 + 0.462799i) q^{7} +(-0.187059 - 0.187059i) q^{8} +(-2.25182 - 3.90026i) q^{10} +(1.16197 - 4.33653i) q^{11} +(3.51879 - 0.786201i) q^{13} +(-4.87020 - 2.27868i) q^{14} +(-1.86136 - 3.22397i) q^{16} +(1.31427 - 2.27639i) q^{17} +(-6.01372 + 1.61137i) q^{19} +(1.22177 + 4.55971i) q^{20} +(-4.56197 + 7.90156i) q^{22} +(4.58893 - 2.64942i) q^{23} -0.0891302i q^{25} +(-7.32104 - 0.307521i) q^{26} +(4.31266 + 3.62827i) q^{28} +(2.06391 + 3.57480i) q^{29} +(2.44135 + 2.44135i) q^{31} +(2.09506 + 7.81887i) q^{32} +(-3.77733 + 3.77733i) q^{34} +(3.35673 + 4.80713i) q^{35} +(0.0290943 - 0.108582i) q^{37} +12.6527 q^{38} -0.586237i q^{40} +(2.03234 - 7.58481i) q^{41} +(-5.47731 - 3.16233i) q^{43} +(6.76235 - 6.76235i) q^{44} +(-10.4018 + 2.78716i) q^{46} +(-5.82732 + 5.82732i) q^{47} +(6.57163 + 2.41114i) q^{49} +(-0.0468819 + 0.174966i) q^{50} +(7.32877 + 2.29744i) q^{52} -9.24486 q^{53} +(8.61605 - 4.97448i) q^{55} +(-0.400711 - 0.573853i) q^{56} +(-2.17121 - 8.10305i) q^{58} +(1.27986 + 4.77649i) q^{59} +(3.33568 + 1.92586i) q^{61} +(-3.50831 - 6.07658i) q^{62} -9.00526i q^{64} +(6.74585 + 4.28192i) q^{65} +(10.1688 + 2.72472i) q^{67} +(4.84909 - 2.79963i) q^{68} +(-4.06086 - 11.2022i) q^{70} +(-3.56722 - 13.3131i) q^{71} +(11.8088 - 11.8088i) q^{73} +(-0.114226 + 0.197846i) q^{74} +(-12.8102 - 3.43249i) q^{76} +(5.03382 - 10.7587i) q^{77} -13.3186 q^{79} +(2.13518 - 7.96862i) q^{80} +(-7.97912 + 13.8202i) q^{82} +(5.15552 + 5.15552i) q^{83} +(5.62651 - 1.50762i) q^{85} +(9.08878 + 9.08878i) q^{86} +(-1.02854 + 0.593831i) q^{88} +(7.93017 + 2.12488i) q^{89} +(9.53016 - 0.419530i) q^{91} +11.2874 q^{92} +(14.5044 - 8.37409i) q^{94} +(-11.9484 - 6.89840i) q^{95} +(1.93349 - 0.518076i) q^{97} +(-11.6321 - 8.18979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96303 0.525993i −1.38807 0.371933i −0.514027 0.857774i \(-0.671847\pi\)
−0.874047 + 0.485841i \(0.838514\pi\)
\(3\) 0 0
\(4\) 1.84478 + 1.06508i 0.922391 + 0.532542i
\(5\) 1.56698 + 1.56698i 0.700776 + 0.700776i 0.964577 0.263801i \(-0.0849763\pi\)
−0.263801 + 0.964577i \(0.584976\pi\)
\(6\) 0 0
\(7\) 2.60496 + 0.462799i 0.984582 + 0.174921i
\(8\) −0.187059 0.187059i −0.0661354 0.0661354i
\(9\) 0 0
\(10\) −2.25182 3.90026i −0.712087 1.23337i
\(11\) 1.16197 4.33653i 0.350347 1.30751i −0.535893 0.844286i \(-0.680025\pi\)
0.886240 0.463227i \(-0.153308\pi\)
\(12\) 0 0
\(13\) 3.51879 0.786201i 0.975937 0.218053i
\(14\) −4.87020 2.27868i −1.30161 0.609003i
\(15\) 0 0
\(16\) −1.86136 3.22397i −0.465340 0.805992i
\(17\) 1.31427 2.27639i 0.318758 0.552105i −0.661471 0.749971i \(-0.730068\pi\)
0.980229 + 0.197865i \(0.0634009\pi\)
\(18\) 0 0
\(19\) −6.01372 + 1.61137i −1.37964 + 0.369674i −0.870991 0.491299i \(-0.836522\pi\)
−0.508650 + 0.860973i \(0.669855\pi\)
\(20\) 1.22177 + 4.55971i 0.273196 + 1.01958i
\(21\) 0 0
\(22\) −4.56197 + 7.90156i −0.972615 + 1.68462i
\(23\) 4.58893 2.64942i 0.956859 0.552443i 0.0616538 0.998098i \(-0.480363\pi\)
0.895205 + 0.445655i \(0.147029\pi\)
\(24\) 0 0
\(25\) 0.0891302i 0.0178260i
\(26\) −7.32104 0.307521i −1.43577 0.0603099i
\(27\) 0 0
\(28\) 4.31266 + 3.62827i 0.815016 + 0.685678i
\(29\) 2.06391 + 3.57480i 0.383258 + 0.663823i 0.991526 0.129909i \(-0.0414685\pi\)
−0.608267 + 0.793732i \(0.708135\pi\)
\(30\) 0 0
\(31\) 2.44135 + 2.44135i 0.438479 + 0.438479i 0.891500 0.453021i \(-0.149654\pi\)
−0.453021 + 0.891500i \(0.649654\pi\)
\(32\) 2.09506 + 7.81887i 0.370358 + 1.38219i
\(33\) 0 0
\(34\) −3.77733 + 3.77733i −0.647807 + 0.647807i
\(35\) 3.35673 + 4.80713i 0.567391 + 0.812552i
\(36\) 0 0
\(37\) 0.0290943 0.108582i 0.00478308 0.0178507i −0.963493 0.267733i \(-0.913725\pi\)
0.968276 + 0.249883i \(0.0803920\pi\)
\(38\) 12.6527 2.05254
\(39\) 0 0
\(40\) 0.586237i 0.0926922i
\(41\) 2.03234 7.58481i 0.317399 1.18455i −0.604336 0.796729i \(-0.706562\pi\)
0.921735 0.387819i \(-0.126772\pi\)
\(42\) 0 0
\(43\) −5.47731 3.16233i −0.835282 0.482250i 0.0203758 0.999792i \(-0.493514\pi\)
−0.855658 + 0.517542i \(0.826847\pi\)
\(44\) 6.76235 6.76235i 1.01946 1.01946i
\(45\) 0 0
\(46\) −10.4018 + 2.78716i −1.53366 + 0.410944i
\(47\) −5.82732 + 5.82732i −0.850002 + 0.850002i −0.990133 0.140131i \(-0.955248\pi\)
0.140131 + 0.990133i \(0.455248\pi\)
\(48\) 0 0
\(49\) 6.57163 + 2.41114i 0.938805 + 0.344449i
\(50\) −0.0468819 + 0.174966i −0.00663010 + 0.0247439i
\(51\) 0 0
\(52\) 7.32877 + 2.29744i 1.01632 + 0.318598i
\(53\) −9.24486 −1.26988 −0.634940 0.772562i \(-0.718975\pi\)
−0.634940 + 0.772562i \(0.718975\pi\)
\(54\) 0 0
\(55\) 8.61605 4.97448i 1.16179 0.670759i
\(56\) −0.400711 0.573853i −0.0535473 0.0766843i
\(57\) 0 0
\(58\) −2.17121 8.10305i −0.285093 1.06398i
\(59\) 1.27986 + 4.77649i 0.166623 + 0.621846i 0.997828 + 0.0658791i \(0.0209852\pi\)
−0.831205 + 0.555967i \(0.812348\pi\)
\(60\) 0 0
\(61\) 3.33568 + 1.92586i 0.427090 + 0.246581i 0.698106 0.715994i \(-0.254026\pi\)
−0.271016 + 0.962575i \(0.587360\pi\)
\(62\) −3.50831 6.07658i −0.445556 0.771726i
\(63\) 0 0
\(64\) 9.00526i 1.12566i
\(65\) 6.74585 + 4.28192i 0.836719 + 0.531107i
\(66\) 0 0
\(67\) 10.1688 + 2.72472i 1.24232 + 0.332878i 0.819364 0.573273i \(-0.194327\pi\)
0.422954 + 0.906151i \(0.360993\pi\)
\(68\) 4.84909 2.79963i 0.588039 0.339505i
\(69\) 0 0
\(70\) −4.06086 11.2022i −0.485365 1.33891i
\(71\) −3.56722 13.3131i −0.423352 1.57997i −0.767496 0.641053i \(-0.778498\pi\)
0.344145 0.938917i \(-0.388169\pi\)
\(72\) 0 0
\(73\) 11.8088 11.8088i 1.38211 1.38211i 0.541259 0.840856i \(-0.317948\pi\)
0.840856 0.541259i \(-0.182052\pi\)
\(74\) −0.114226 + 0.197846i −0.0132785 + 0.0229991i
\(75\) 0 0
\(76\) −12.8102 3.43249i −1.46944 0.393734i
\(77\) 5.03382 10.7587i 0.573657 1.22607i
\(78\) 0 0
\(79\) −13.3186 −1.49846 −0.749229 0.662311i \(-0.769576\pi\)
−0.749229 + 0.662311i \(0.769576\pi\)
\(80\) 2.13518 7.96862i 0.238721 0.890918i
\(81\) 0 0
\(82\) −7.97912 + 13.8202i −0.881146 + 1.52619i
\(83\) 5.15552 + 5.15552i 0.565892 + 0.565892i 0.930975 0.365083i \(-0.118959\pi\)
−0.365083 + 0.930975i \(0.618959\pi\)
\(84\) 0 0
\(85\) 5.62651 1.50762i 0.610280 0.163524i
\(86\) 9.08878 + 9.08878i 0.980068 + 0.980068i
\(87\) 0 0
\(88\) −1.02854 + 0.593831i −0.109643 + 0.0633025i
\(89\) 7.93017 + 2.12488i 0.840596 + 0.225237i 0.653331 0.757072i \(-0.273371\pi\)
0.187265 + 0.982309i \(0.440038\pi\)
\(90\) 0 0
\(91\) 9.53016 0.419530i 0.999032 0.0439787i
\(92\) 11.2874 1.17680
\(93\) 0 0
\(94\) 14.5044 8.37409i 1.49601 0.863722i
\(95\) −11.9484 6.89840i −1.22588 0.707761i
\(96\) 0 0
\(97\) 1.93349 0.518076i 0.196316 0.0526027i −0.159321 0.987227i \(-0.550931\pi\)
0.355637 + 0.934624i \(0.384264\pi\)
\(98\) −11.6321 8.18979i −1.17502 0.827294i
\(99\) 0 0
\(100\) 0.0949312 0.164426i 0.00949312 0.0164426i
\(101\) 4.49537 + 7.78621i 0.447306 + 0.774757i 0.998210 0.0598118i \(-0.0190500\pi\)
−0.550903 + 0.834569i \(0.685717\pi\)
\(102\) 0 0
\(103\) −5.08145 −0.500690 −0.250345 0.968157i \(-0.580544\pi\)
−0.250345 + 0.968157i \(0.580544\pi\)
\(104\) −0.805288 0.511156i −0.0789650 0.0501230i
\(105\) 0 0
\(106\) 18.1480 + 4.86273i 1.76269 + 0.472310i
\(107\) −0.521017 0.902428i −0.0503686 0.0872410i 0.839742 0.542986i \(-0.182706\pi\)
−0.890110 + 0.455745i \(0.849373\pi\)
\(108\) 0 0
\(109\) 2.86707 2.86707i 0.274616 0.274616i −0.556339 0.830955i \(-0.687795\pi\)
0.830955 + 0.556339i \(0.187795\pi\)
\(110\) −19.5301 + 5.23309i −1.86213 + 0.498955i
\(111\) 0 0
\(112\) −3.35672 9.25974i −0.317180 0.874963i
\(113\) −4.39010 + 7.60388i −0.412986 + 0.715313i −0.995215 0.0977122i \(-0.968848\pi\)
0.582229 + 0.813025i \(0.302181\pi\)
\(114\) 0 0
\(115\) 11.3424 + 3.03918i 1.05768 + 0.283405i
\(116\) 8.79296i 0.816406i
\(117\) 0 0
\(118\) 10.0496i 0.925141i
\(119\) 4.47714 5.32166i 0.410419 0.487836i
\(120\) 0 0
\(121\) −7.92903 4.57783i −0.720821 0.416166i
\(122\) −5.53507 5.53507i −0.501121 0.501121i
\(123\) 0 0
\(124\) 1.90351 + 7.10399i 0.170940 + 0.637957i
\(125\) 7.97458 7.97458i 0.713268 0.713268i
\(126\) 0 0
\(127\) −6.20223 + 3.58086i −0.550359 + 0.317750i −0.749267 0.662268i \(-0.769594\pi\)
0.198908 + 0.980018i \(0.436261\pi\)
\(128\) −0.546587 + 2.03989i −0.0483119 + 0.180303i
\(129\) 0 0
\(130\) −10.9901 11.9538i −0.963892 1.04842i
\(131\) 8.06442i 0.704591i 0.935889 + 0.352296i \(0.114599\pi\)
−0.935889 + 0.352296i \(0.885401\pi\)
\(132\) 0 0
\(133\) −16.4112 + 1.41442i −1.42303 + 0.122645i
\(134\) −18.5285 10.6975i −1.60062 0.924119i
\(135\) 0 0
\(136\) −0.671666 + 0.179972i −0.0575949 + 0.0154325i
\(137\) 4.00328 1.07268i 0.342023 0.0916449i −0.0837188 0.996489i \(-0.526680\pi\)
0.425742 + 0.904845i \(0.360013\pi\)
\(138\) 0 0
\(139\) 14.1275 + 8.15651i 1.19828 + 0.691826i 0.960171 0.279413i \(-0.0901397\pi\)
0.238107 + 0.971239i \(0.423473\pi\)
\(140\) 1.07244 + 12.4433i 0.0906373 + 1.05165i
\(141\) 0 0
\(142\) 28.0103i 2.35057i
\(143\) 0.679344 16.1729i 0.0568096 1.35244i
\(144\) 0 0
\(145\) −2.36753 + 8.83576i −0.196613 + 0.733770i
\(146\) −29.3924 + 16.9697i −2.43253 + 1.40442i
\(147\) 0 0
\(148\) 0.169321 0.169321i 0.0139181 0.0139181i
\(149\) 1.57172 + 5.86575i 0.128761 + 0.480541i 0.999946 0.0104133i \(-0.00331473\pi\)
−0.871185 + 0.490955i \(0.836648\pi\)
\(150\) 0 0
\(151\) 13.6338 + 13.6338i 1.10950 + 1.10950i 0.993216 + 0.116285i \(0.0370987\pi\)
0.116285 + 0.993216i \(0.462901\pi\)
\(152\) 1.42634 + 0.823499i 0.115692 + 0.0667946i
\(153\) 0 0
\(154\) −15.5406 + 18.4720i −1.25230 + 1.48851i
\(155\) 7.65110i 0.614551i
\(156\) 0 0
\(157\) 8.31072i 0.663268i −0.943408 0.331634i \(-0.892400\pi\)
0.943408 0.331634i \(-0.107600\pi\)
\(158\) 26.1448 + 7.00549i 2.07997 + 0.557327i
\(159\) 0 0
\(160\) −8.96911 + 15.5350i −0.709071 + 1.22815i
\(161\) 13.1801 4.77789i 1.03874 0.376550i
\(162\) 0 0
\(163\) 0.385067 0.103178i 0.0301607 0.00808155i −0.243707 0.969849i \(-0.578364\pi\)
0.273868 + 0.961767i \(0.411697\pi\)
\(164\) 11.8277 11.8277i 0.923588 0.923588i
\(165\) 0 0
\(166\) −7.40869 12.8322i −0.575026 0.995974i
\(167\) −19.9784 5.35319i −1.54597 0.414243i −0.617784 0.786348i \(-0.711969\pi\)
−0.928191 + 0.372105i \(0.878636\pi\)
\(168\) 0 0
\(169\) 11.7638 5.53295i 0.904906 0.425612i
\(170\) −11.8380 −0.907934
\(171\) 0 0
\(172\) −6.73629 11.6676i −0.513637 0.889646i
\(173\) −9.58243 + 16.5973i −0.728539 + 1.26187i 0.228962 + 0.973435i \(0.426467\pi\)
−0.957501 + 0.288431i \(0.906867\pi\)
\(174\) 0 0
\(175\) 0.0412493 0.232181i 0.00311816 0.0175512i
\(176\) −16.1437 + 4.32568i −1.21687 + 0.326061i
\(177\) 0 0
\(178\) −14.4495 8.34243i −1.08304 0.625292i
\(179\) 5.86324 3.38514i 0.438239 0.253018i −0.264611 0.964355i \(-0.585244\pi\)
0.702850 + 0.711338i \(0.251910\pi\)
\(180\) 0 0
\(181\) −16.5594 −1.23085 −0.615424 0.788197i \(-0.711015\pi\)
−0.615424 + 0.788197i \(0.711015\pi\)
\(182\) −18.9287 4.18925i −1.40309 0.310528i
\(183\) 0 0
\(184\) −1.35400 0.362803i −0.0998183 0.0267462i
\(185\) 0.215736 0.124555i 0.0158612 0.00915747i
\(186\) 0 0
\(187\) −8.34448 8.34448i −0.610209 0.610209i
\(188\) −16.9567 + 4.54354i −1.23670 + 0.331372i
\(189\) 0 0
\(190\) 19.8266 + 19.8266i 1.43837 + 1.43837i
\(191\) −4.44834 + 7.70475i −0.321870 + 0.557496i −0.980874 0.194644i \(-0.937645\pi\)
0.659003 + 0.752140i \(0.270978\pi\)
\(192\) 0 0
\(193\) −1.15868 + 4.32426i −0.0834038 + 0.311267i −0.995007 0.0998038i \(-0.968178\pi\)
0.911603 + 0.411071i \(0.134845\pi\)
\(194\) −4.06800 −0.292066
\(195\) 0 0
\(196\) 9.55515 + 11.4474i 0.682511 + 0.817670i
\(197\) −1.57369 0.421669i −0.112121 0.0300427i 0.202322 0.979319i \(-0.435151\pi\)
−0.314443 + 0.949276i \(0.601818\pi\)
\(198\) 0 0
\(199\) −6.21777 + 10.7695i −0.440766 + 0.763429i −0.997746 0.0670965i \(-0.978626\pi\)
0.556981 + 0.830526i \(0.311960\pi\)
\(200\) −0.0166726 + 0.0166726i −0.00117893 + 0.00117893i
\(201\) 0 0
\(202\) −4.72907 17.6491i −0.332736 1.24179i
\(203\) 3.72199 + 10.2674i 0.261233 + 0.720629i
\(204\) 0 0
\(205\) 15.0699 8.70062i 1.05253 0.607678i
\(206\) 9.97506 + 2.67281i 0.694995 + 0.186223i
\(207\) 0 0
\(208\) −9.08442 9.88106i −0.629891 0.685128i
\(209\) 27.9510i 1.93341i
\(210\) 0 0
\(211\) 0.111585 + 0.193271i 0.00768182 + 0.0133053i 0.869841 0.493333i \(-0.164221\pi\)
−0.862159 + 0.506638i \(0.830888\pi\)
\(212\) −17.0547 9.84656i −1.17132 0.676264i
\(213\) 0 0
\(214\) 0.548103 + 2.04555i 0.0374676 + 0.139831i
\(215\) −3.62754 13.5382i −0.247396 0.923295i
\(216\) 0 0
\(217\) 5.22976 + 7.48946i 0.355019 + 0.508418i
\(218\) −7.13622 + 4.12010i −0.483326 + 0.279048i
\(219\) 0 0
\(220\) 21.1930 1.42883
\(221\) 2.83496 9.04342i 0.190700 0.608326i
\(222\) 0 0
\(223\) −1.45774 + 5.44036i −0.0976174 + 0.364313i −0.997403 0.0720186i \(-0.977056\pi\)
0.899786 + 0.436332i \(0.143723\pi\)
\(224\) 1.83898 + 21.3374i 0.122872 + 1.42567i
\(225\) 0 0
\(226\) 12.6175 12.6175i 0.839304 0.839304i
\(227\) −4.17248 + 1.11801i −0.276937 + 0.0742050i −0.394614 0.918847i \(-0.629122\pi\)
0.117677 + 0.993052i \(0.462455\pi\)
\(228\) 0 0
\(229\) −16.9969 + 16.9969i −1.12319 + 1.12319i −0.131929 + 0.991259i \(0.542117\pi\)
−0.991259 + 0.131929i \(0.957883\pi\)
\(230\) −20.6669 11.9320i −1.36273 0.786775i
\(231\) 0 0
\(232\) 0.282625 1.05477i 0.0185553 0.0692492i
\(233\) 13.6445i 0.893880i 0.894564 + 0.446940i \(0.147486\pi\)
−0.894564 + 0.446940i \(0.852514\pi\)
\(234\) 0 0
\(235\) −18.2626 −1.19132
\(236\) −2.72631 + 10.1747i −0.177468 + 0.662319i
\(237\) 0 0
\(238\) −11.5879 + 8.09165i −0.751134 + 0.524504i
\(239\) 4.70084 4.70084i 0.304072 0.304072i −0.538533 0.842605i \(-0.681021\pi\)
0.842605 + 0.538533i \(0.181021\pi\)
\(240\) 0 0
\(241\) 4.03655 + 15.0646i 0.260017 + 0.970397i 0.965230 + 0.261401i \(0.0841847\pi\)
−0.705213 + 0.708995i \(0.749149\pi\)
\(242\) 13.1570 + 13.1570i 0.845767 + 0.845767i
\(243\) 0 0
\(244\) 4.10240 + 7.10557i 0.262629 + 0.454887i
\(245\) 6.51942 + 14.0759i 0.416510 + 0.899274i
\(246\) 0 0
\(247\) −19.8941 + 10.3981i −1.26583 + 0.661613i
\(248\) 0.913353i 0.0579980i
\(249\) 0 0
\(250\) −19.8489 + 11.4598i −1.25536 + 0.724781i
\(251\) 2.67179 4.62768i 0.168642 0.292096i −0.769301 0.638887i \(-0.779395\pi\)
0.937943 + 0.346791i \(0.112729\pi\)
\(252\) 0 0
\(253\) −6.15709 22.9786i −0.387093 1.44465i
\(254\) 14.0587 3.76701i 0.882120 0.236363i
\(255\) 0 0
\(256\) −6.85933 + 11.8807i −0.428708 + 0.742544i
\(257\) −7.85983 13.6136i −0.490283 0.849195i 0.509655 0.860379i \(-0.329773\pi\)
−0.999937 + 0.0111844i \(0.996440\pi\)
\(258\) 0 0
\(259\) 0.126041 0.269386i 0.00783180 0.0167388i
\(260\) 7.88400 + 15.0841i 0.488945 + 0.935477i
\(261\) 0 0
\(262\) 4.24183 15.8307i 0.262061 0.978025i
\(263\) −3.44067 5.95942i −0.212161 0.367473i 0.740230 0.672354i \(-0.234717\pi\)
−0.952391 + 0.304881i \(0.901383\pi\)
\(264\) 0 0
\(265\) −14.4865 14.4865i −0.889901 0.889901i
\(266\) 32.9598 + 5.85565i 2.02089 + 0.359033i
\(267\) 0 0
\(268\) 15.8572 + 15.8572i 0.968631 + 0.968631i
\(269\) 18.7176 + 10.8066i 1.14123 + 0.658890i 0.946735 0.322013i \(-0.104360\pi\)
0.194496 + 0.980903i \(0.437693\pi\)
\(270\) 0 0
\(271\) −5.82362 1.56043i −0.353760 0.0947896i 0.0775628 0.996987i \(-0.475286\pi\)
−0.431322 + 0.902198i \(0.641953\pi\)
\(272\) −9.78534 −0.593323
\(273\) 0 0
\(274\) −8.42279 −0.508840
\(275\) −0.386516 0.103567i −0.0233078 0.00624530i
\(276\) 0 0
\(277\) −17.1918 9.92569i −1.03295 0.596377i −0.115125 0.993351i \(-0.536727\pi\)
−0.917830 + 0.396974i \(0.870060\pi\)
\(278\) −23.4425 23.4425i −1.40599 1.40599i
\(279\) 0 0
\(280\) 0.271310 1.52712i 0.0162139 0.0912631i
\(281\) 15.4156 + 15.4156i 0.919617 + 0.919617i 0.997001 0.0773842i \(-0.0246568\pi\)
−0.0773842 + 0.997001i \(0.524657\pi\)
\(282\) 0 0
\(283\) −14.1867 24.5721i −0.843314 1.46066i −0.887077 0.461621i \(-0.847268\pi\)
0.0437635 0.999042i \(-0.486065\pi\)
\(284\) 7.59879 28.3591i 0.450905 1.68280i
\(285\) 0 0
\(286\) −9.84040 + 31.3906i −0.581875 + 1.85616i
\(287\) 8.80442 18.8176i 0.519708 1.11077i
\(288\) 0 0
\(289\) 5.04537 + 8.73884i 0.296786 + 0.514049i
\(290\) 9.29510 16.0996i 0.545827 0.945400i
\(291\) 0 0
\(292\) 34.3620 9.20727i 2.01088 0.538815i
\(293\) −2.70937 10.1115i −0.158283 0.590720i −0.998802 0.0489378i \(-0.984416\pi\)
0.840519 0.541782i \(-0.182250\pi\)
\(294\) 0 0
\(295\) −5.47916 + 9.49019i −0.319009 + 0.552540i
\(296\) −0.0257535 + 0.0148688i −0.00149689 + 0.000864232i
\(297\) 0 0
\(298\) 12.3414i 0.714917i
\(299\) 14.0645 12.9306i 0.813372 0.747795i
\(300\) 0 0
\(301\) −12.8047 10.7726i −0.738048 0.620924i
\(302\) −19.5923 33.9348i −1.12741 1.95273i
\(303\) 0 0
\(304\) 16.3887 + 16.3887i 0.939956 + 0.939956i
\(305\) 2.20917 + 8.24474i 0.126497 + 0.472092i
\(306\) 0 0
\(307\) −6.15683 + 6.15683i −0.351389 + 0.351389i −0.860626 0.509237i \(-0.829928\pi\)
0.509237 + 0.860626i \(0.329928\pi\)
\(308\) 20.7453 14.4860i 1.18207 0.825419i
\(309\) 0 0
\(310\) 4.02442 15.0194i 0.228572 0.853042i
\(311\) 5.30855 0.301020 0.150510 0.988608i \(-0.451908\pi\)
0.150510 + 0.988608i \(0.451908\pi\)
\(312\) 0 0
\(313\) 18.4802i 1.04456i −0.852774 0.522280i \(-0.825082\pi\)
0.852774 0.522280i \(-0.174918\pi\)
\(314\) −4.37139 + 16.3142i −0.246692 + 0.920665i
\(315\) 0 0
\(316\) −24.5699 14.1854i −1.38216 0.797993i
\(317\) 14.8596 14.8596i 0.834598 0.834598i −0.153544 0.988142i \(-0.549069\pi\)
0.988142 + 0.153544i \(0.0490685\pi\)
\(318\) 0 0
\(319\) 17.9004 4.79640i 1.00223 0.268547i
\(320\) 14.1111 14.1111i 0.788834 0.788834i
\(321\) 0 0
\(322\) −28.3862 + 2.44649i −1.58190 + 0.136337i
\(323\) −4.23556 + 15.8073i −0.235673 + 0.879544i
\(324\) 0 0
\(325\) −0.0700742 0.313631i −0.00388702 0.0173971i
\(326\) −0.810170 −0.0448711
\(327\) 0 0
\(328\) −1.79898 + 1.03864i −0.0993319 + 0.0573493i
\(329\) −17.8768 + 12.4831i −0.985580 + 0.688213i
\(330\) 0 0
\(331\) −7.91671 29.5456i −0.435142 1.62397i −0.740727 0.671806i \(-0.765519\pi\)
0.305586 0.952165i \(-0.401148\pi\)
\(332\) 4.01974 + 15.0019i 0.220612 + 0.823335i
\(333\) 0 0
\(334\) 36.4025 + 21.0170i 1.99186 + 1.15000i
\(335\) 11.6648 + 20.2039i 0.637314 + 1.10386i
\(336\) 0 0
\(337\) 2.64409i 0.144033i −0.997403 0.0720163i \(-0.977057\pi\)
0.997403 0.0720163i \(-0.0229434\pi\)
\(338\) −26.0030 + 4.67370i −1.41438 + 0.254216i
\(339\) 0 0
\(340\) 11.9854 + 3.21148i 0.650000 + 0.174167i
\(341\) 13.4237 7.75020i 0.726936 0.419697i
\(342\) 0 0
\(343\) 16.0030 + 9.32228i 0.864079 + 0.503356i
\(344\) 0.433039 + 1.61612i 0.0233479 + 0.0871355i
\(345\) 0 0
\(346\) 27.5407 27.5407i 1.48060 1.48060i
\(347\) −1.58944 + 2.75299i −0.0853255 + 0.147788i −0.905530 0.424283i \(-0.860526\pi\)
0.820204 + 0.572071i \(0.193860\pi\)
\(348\) 0 0
\(349\) 20.2719 + 5.43184i 1.08513 + 0.290760i 0.756696 0.653767i \(-0.226812\pi\)
0.328434 + 0.944527i \(0.393479\pi\)
\(350\) −0.203099 + 0.434081i −0.0108561 + 0.0232026i
\(351\) 0 0
\(352\) 36.3412 1.93699
\(353\) 5.34444 19.9457i 0.284456 1.06160i −0.664780 0.747039i \(-0.731475\pi\)
0.949236 0.314565i \(-0.101859\pi\)
\(354\) 0 0
\(355\) 15.2716 26.4511i 0.810530 1.40388i
\(356\) 12.3662 + 12.3662i 0.655410 + 0.655410i
\(357\) 0 0
\(358\) −13.2903 + 3.56113i −0.702414 + 0.188211i
\(359\) −18.9082 18.9082i −0.997935 0.997935i 0.00206292 0.999998i \(-0.499343\pi\)
−0.999998 + 0.00206292i \(0.999343\pi\)
\(360\) 0 0
\(361\) 17.1138 9.88065i 0.900726 0.520034i
\(362\) 32.5066 + 8.71011i 1.70851 + 0.457793i
\(363\) 0 0
\(364\) 18.0279 + 9.37649i 0.944919 + 0.491462i
\(365\) 37.0084 1.93711
\(366\) 0 0
\(367\) −20.8759 + 12.0527i −1.08971 + 0.629146i −0.933500 0.358578i \(-0.883262\pi\)
−0.156212 + 0.987724i \(0.549928\pi\)
\(368\) −17.0833 9.86304i −0.890528 0.514147i
\(369\) 0 0
\(370\) −0.489012 + 0.131030i −0.0254225 + 0.00681194i
\(371\) −24.0825 4.27851i −1.25030 0.222129i
\(372\) 0 0
\(373\) −15.4025 + 26.6780i −0.797514 + 1.38133i 0.123717 + 0.992318i \(0.460518\pi\)
−0.921231 + 0.389017i \(0.872815\pi\)
\(374\) 11.9914 + 20.7696i 0.620058 + 1.07397i
\(375\) 0 0
\(376\) 2.18011 0.112430
\(377\) 10.0730 + 10.9563i 0.518785 + 0.564279i
\(378\) 0 0
\(379\) 16.9707 + 4.54729i 0.871728 + 0.233579i 0.666835 0.745206i \(-0.267649\pi\)
0.204893 + 0.978784i \(0.434315\pi\)
\(380\) −14.6948 25.4521i −0.753826 1.30566i
\(381\) 0 0
\(382\) 12.7849 12.7849i 0.654132 0.654132i
\(383\) 7.61566 2.04061i 0.389142 0.104270i −0.0589428 0.998261i \(-0.518773\pi\)
0.448085 + 0.893991i \(0.352106\pi\)
\(384\) 0 0
\(385\) 24.7467 8.97082i 1.26121 0.457195i
\(386\) 4.54907 7.87921i 0.231541 0.401041i
\(387\) 0 0
\(388\) 4.11866 + 1.10359i 0.209093 + 0.0560263i
\(389\) 4.32264i 0.219166i −0.993978 0.109583i \(-0.965048\pi\)
0.993978 0.109583i \(-0.0349516\pi\)
\(390\) 0 0
\(391\) 13.9283i 0.704382i
\(392\) −0.778258 1.68031i −0.0393080 0.0848686i
\(393\) 0 0
\(394\) 2.86741 + 1.65550i 0.144458 + 0.0834029i
\(395\) −20.8700 20.8700i −1.05008 1.05008i
\(396\) 0 0
\(397\) 8.67254 + 32.3664i 0.435262 + 1.62442i 0.740437 + 0.672125i \(0.234618\pi\)
−0.305175 + 0.952296i \(0.598715\pi\)
\(398\) 17.8704 17.8704i 0.895761 0.895761i
\(399\) 0 0
\(400\) −0.287353 + 0.165903i −0.0143676 + 0.00829516i
\(401\) −0.964760 + 3.60053i −0.0481778 + 0.179802i −0.985822 0.167795i \(-0.946335\pi\)
0.937644 + 0.347597i \(0.113002\pi\)
\(402\) 0 0
\(403\) 10.5100 + 6.67120i 0.523539 + 0.332316i
\(404\) 19.1518i 0.952838i
\(405\) 0 0
\(406\) −1.90582 22.1130i −0.0945844 1.09745i
\(407\) −0.437060 0.252337i −0.0216643 0.0125079i
\(408\) 0 0
\(409\) −16.1066 + 4.31575i −0.796421 + 0.213400i −0.634012 0.773323i \(-0.718593\pi\)
−0.162409 + 0.986724i \(0.551926\pi\)
\(410\) −34.1592 + 9.15294i −1.68700 + 0.452031i
\(411\) 0 0
\(412\) −9.37417 5.41218i −0.461832 0.266639i
\(413\) 1.12342 + 13.0349i 0.0552800 + 0.641404i
\(414\) 0 0
\(415\) 16.1572i 0.793127i
\(416\) 13.5193 + 25.8658i 0.662837 + 1.26818i
\(417\) 0 0
\(418\) 14.7020 54.8688i 0.719101 2.68372i
\(419\) −14.2653 + 8.23605i −0.696904 + 0.402357i −0.806193 0.591652i \(-0.798476\pi\)
0.109290 + 0.994010i \(0.465142\pi\)
\(420\) 0 0
\(421\) 2.29534 2.29534i 0.111868 0.111868i −0.648957 0.760825i \(-0.724795\pi\)
0.760825 + 0.648957i \(0.224795\pi\)
\(422\) −0.117386 0.438090i −0.00571425 0.0213259i
\(423\) 0 0
\(424\) 1.72934 + 1.72934i 0.0839840 + 0.0839840i
\(425\) −0.202895 0.117141i −0.00984185 0.00568220i
\(426\) 0 0
\(427\) 7.79803 + 6.56053i 0.377373 + 0.317486i
\(428\) 2.21971i 0.107294i
\(429\) 0 0
\(430\) 28.4839i 1.37362i
\(431\) −30.8568 8.26807i −1.48632 0.398259i −0.577828 0.816158i \(-0.696100\pi\)
−0.908493 + 0.417900i \(0.862766\pi\)
\(432\) 0 0
\(433\) −2.29443 + 3.97407i −0.110263 + 0.190982i −0.915876 0.401460i \(-0.868503\pi\)
0.805613 + 0.592442i \(0.201836\pi\)
\(434\) −6.32678 17.4529i −0.303695 0.837765i
\(435\) 0 0
\(436\) 8.34280 2.23545i 0.399548 0.107058i
\(437\) −23.3273 + 23.3273i −1.11590 + 1.11590i
\(438\) 0 0
\(439\) −8.62001 14.9303i −0.411411 0.712584i 0.583634 0.812017i \(-0.301630\pi\)
−0.995044 + 0.0994331i \(0.968297\pi\)
\(440\) −2.54223 0.681190i −0.121196 0.0324744i
\(441\) 0 0
\(442\) −10.3219 + 16.2614i −0.490962 + 0.773474i
\(443\) −10.7110 −0.508893 −0.254447 0.967087i \(-0.581893\pi\)
−0.254447 + 0.967087i \(0.581893\pi\)
\(444\) 0 0
\(445\) 9.09678 + 15.7561i 0.431229 + 0.746910i
\(446\) 5.72318 9.91284i 0.271000 0.469387i
\(447\) 0 0
\(448\) 4.16763 23.4584i 0.196902 1.10830i
\(449\) 4.72490 1.26603i 0.222982 0.0597478i −0.145598 0.989344i \(-0.546511\pi\)
0.368580 + 0.929596i \(0.379844\pi\)
\(450\) 0 0
\(451\) −30.5302 17.6266i −1.43761 0.830006i
\(452\) −16.1976 + 9.35166i −0.761869 + 0.439865i
\(453\) 0 0
\(454\) 8.77878 0.412008
\(455\) 15.5910 + 14.2762i 0.730917 + 0.669279i
\(456\) 0 0
\(457\) 5.77841 + 1.54832i 0.270303 + 0.0724274i 0.391424 0.920210i \(-0.371982\pi\)
−0.121122 + 0.992638i \(0.538649\pi\)
\(458\) 42.3058 24.4253i 1.97682 1.14132i
\(459\) 0 0
\(460\) 17.6872 + 17.6872i 0.824671 + 0.824671i
\(461\) −18.4425 + 4.94165i −0.858953 + 0.230156i −0.661305 0.750117i \(-0.729997\pi\)
−0.197648 + 0.980273i \(0.563330\pi\)
\(462\) 0 0
\(463\) −19.3096 19.3096i −0.897393 0.897393i 0.0978122 0.995205i \(-0.468816\pi\)
−0.995205 + 0.0978122i \(0.968816\pi\)
\(464\) 7.68335 13.3080i 0.356691 0.617806i
\(465\) 0 0
\(466\) 7.17691 26.7846i 0.332464 1.24077i
\(467\) 1.06678 0.0493647 0.0246824 0.999695i \(-0.492143\pi\)
0.0246824 + 0.999695i \(0.492143\pi\)
\(468\) 0 0
\(469\) 25.2283 + 11.8039i 1.16494 + 0.545054i
\(470\) 35.8501 + 9.60601i 1.65364 + 0.443092i
\(471\) 0 0
\(472\) 0.654077 1.13290i 0.0301063 0.0521457i
\(473\) −20.0780 + 20.0780i −0.923187 + 0.923187i
\(474\) 0 0
\(475\) 0.143622 + 0.536004i 0.00658982 + 0.0245935i
\(476\) 13.9274 5.04876i 0.638360 0.231410i
\(477\) 0 0
\(478\) −11.7005 + 6.75529i −0.535169 + 0.308980i
\(479\) −37.0845 9.93677i −1.69444 0.454023i −0.722907 0.690945i \(-0.757195\pi\)
−0.971529 + 0.236922i \(0.923861\pi\)
\(480\) 0 0
\(481\) 0.0170100 0.404950i 0.000775588 0.0184641i
\(482\) 31.6955i 1.44369i
\(483\) 0 0
\(484\) −9.75155 16.8902i −0.443252 0.767735i
\(485\) 3.84156 + 2.21792i 0.174436 + 0.100711i
\(486\) 0 0
\(487\) 6.88259 + 25.6862i 0.311880 + 1.16395i 0.926860 + 0.375408i \(0.122498\pi\)
−0.614980 + 0.788543i \(0.710836\pi\)
\(488\) −0.263721 0.984219i −0.0119381 0.0445535i
\(489\) 0 0
\(490\) −5.39402 31.0606i −0.243677 1.40317i
\(491\) 14.4502 8.34283i 0.652129 0.376507i −0.137142 0.990551i \(-0.543792\pi\)
0.789271 + 0.614044i \(0.210458\pi\)
\(492\) 0 0
\(493\) 10.8502 0.488667
\(494\) 44.5222 9.94756i 2.00315 0.447562i
\(495\) 0 0
\(496\) 3.32660 12.4150i 0.149369 0.557452i
\(497\) −3.13121 36.3309i −0.140454 1.62966i
\(498\) 0 0
\(499\) 24.5083 24.5083i 1.09714 1.09714i 0.102400 0.994743i \(-0.467348\pi\)
0.994743 0.102400i \(-0.0326523\pi\)
\(500\) 23.2050 6.21775i 1.03776 0.278066i
\(501\) 0 0
\(502\) −7.67894 + 7.67894i −0.342728 + 0.342728i
\(503\) −35.6704 20.5943i −1.59046 0.918254i −0.993227 0.116188i \(-0.962933\pi\)
−0.597235 0.802066i \(-0.703734\pi\)
\(504\) 0 0
\(505\) −5.15669 + 19.2450i −0.229470 + 0.856393i
\(506\) 48.3463i 2.14926i
\(507\) 0 0
\(508\) −15.2557 −0.676861
\(509\) −8.60918 + 32.1299i −0.381595 + 1.42413i 0.461869 + 0.886948i \(0.347179\pi\)
−0.843464 + 0.537185i \(0.819488\pi\)
\(510\) 0 0
\(511\) 36.2265 25.2963i 1.60257 1.11904i
\(512\) 22.7009 22.7009i 1.00325 1.00325i
\(513\) 0 0
\(514\) 8.26844 + 30.8582i 0.364705 + 1.36110i
\(515\) −7.96255 7.96255i −0.350872 0.350872i
\(516\) 0 0
\(517\) 18.4992 + 32.0415i 0.813592 + 1.40918i
\(518\) −0.389118 + 0.462517i −0.0170969 + 0.0203218i
\(519\) 0 0
\(520\) −0.460900 2.06285i −0.0202118 0.0904618i
\(521\) 7.74380i 0.339262i −0.985508 0.169631i \(-0.945742\pi\)
0.985508 0.169631i \(-0.0542576\pi\)
\(522\) 0 0
\(523\) −25.4357 + 14.6853i −1.11223 + 0.642144i −0.939405 0.342809i \(-0.888622\pi\)
−0.172821 + 0.984953i \(0.555288\pi\)
\(524\) −8.58929 + 14.8771i −0.375225 + 0.649908i
\(525\) 0 0
\(526\) 3.61954 + 13.5083i 0.157819 + 0.588990i
\(527\) 8.76605 2.34886i 0.381855 0.102318i
\(528\) 0 0
\(529\) 2.53887 4.39745i 0.110386 0.191194i
\(530\) 20.8177 + 36.0574i 0.904265 + 1.56623i
\(531\) 0 0
\(532\) −31.7816 14.8701i −1.37791 0.644699i
\(533\) 1.18821 28.2872i 0.0514670 1.22525i
\(534\) 0 0
\(535\) 0.597665 2.23051i 0.0258393 0.0964336i
\(536\) −1.39248 2.41185i −0.0601462 0.104176i
\(537\) 0 0
\(538\) −31.0590 31.0590i −1.33905 1.33905i
\(539\) 18.0920 25.6964i 0.779279 1.10682i
\(540\) 0 0
\(541\) −22.3031 22.3031i −0.958885 0.958885i 0.0403026 0.999188i \(-0.487168\pi\)
−0.999188 + 0.0403026i \(0.987168\pi\)
\(542\) 10.6112 + 6.12637i 0.455789 + 0.263150i
\(543\) 0 0
\(544\) 20.5523 + 5.50697i 0.881172 + 0.236109i
\(545\) 8.98531 0.384888
\(546\) 0 0
\(547\) −24.0410 −1.02792 −0.513959 0.857815i \(-0.671822\pi\)
−0.513959 + 0.857815i \(0.671822\pi\)
\(548\) 8.52767 + 2.28498i 0.364284 + 0.0976096i
\(549\) 0 0
\(550\) 0.704268 + 0.406609i 0.0300301 + 0.0173379i
\(551\) −18.1721 18.1721i −0.774157 0.774157i
\(552\) 0 0
\(553\) −34.6944 6.16383i −1.47536 0.262113i
\(554\) 28.5272 + 28.5272i 1.21201 + 1.21201i
\(555\) 0 0
\(556\) 17.3748 + 30.0940i 0.736854 + 1.27627i
\(557\) −6.46251 + 24.1184i −0.273825 + 1.02193i 0.682799 + 0.730606i \(0.260762\pi\)
−0.956624 + 0.291324i \(0.905904\pi\)
\(558\) 0 0
\(559\) −21.7597 6.82130i −0.920338 0.288510i
\(560\) 9.24994 19.7698i 0.390881 0.835425i
\(561\) 0 0
\(562\) −22.1528 38.3698i −0.934461 1.61853i
\(563\) −10.6879 + 18.5120i −0.450442 + 0.780189i −0.998413 0.0563081i \(-0.982067\pi\)
0.547971 + 0.836497i \(0.315400\pi\)
\(564\) 0 0
\(565\) −18.7944 + 5.03594i −0.790685 + 0.211863i
\(566\) 14.9243 + 55.6981i 0.627313 + 2.34116i
\(567\) 0 0
\(568\) −1.82305 + 3.15761i −0.0764934 + 0.132490i
\(569\) −6.81979 + 3.93741i −0.285901 + 0.165065i −0.636092 0.771614i \(-0.719450\pi\)
0.350191 + 0.936678i \(0.386117\pi\)
\(570\) 0 0
\(571\) 30.5555i 1.27871i 0.768912 + 0.639355i \(0.220798\pi\)
−0.768912 + 0.639355i \(0.779202\pi\)
\(572\) 18.4787 29.1119i 0.772634 1.21723i
\(573\) 0 0
\(574\) −27.1813 + 32.3085i −1.13452 + 1.34853i
\(575\) −0.236143 0.409012i −0.00984786 0.0170570i
\(576\) 0 0
\(577\) −10.2122 10.2122i −0.425140 0.425140i 0.461829 0.886969i \(-0.347193\pi\)
−0.886969 + 0.461829i \(0.847193\pi\)
\(578\) −5.30766 19.8085i −0.220770 0.823923i
\(579\) 0 0
\(580\) −13.7784 + 13.7784i −0.572117 + 0.572117i
\(581\) 11.0440 + 15.8159i 0.458180 + 0.656154i
\(582\) 0 0
\(583\) −10.7422 + 40.0906i −0.444898 + 1.66038i
\(584\) −4.41789 −0.182813
\(585\) 0 0
\(586\) 21.2743i 0.878834i
\(587\) 6.93252 25.8725i 0.286136 1.06787i −0.661870 0.749619i \(-0.730237\pi\)
0.948005 0.318254i \(-0.103097\pi\)
\(588\) 0 0
\(589\) −18.6155 10.7477i −0.767037 0.442849i
\(590\) 15.7476 15.7476i 0.648317 0.648317i
\(591\) 0 0
\(592\) −0.404218 + 0.108310i −0.0166133 + 0.00445151i
\(593\) 4.55865 4.55865i 0.187201 0.187201i −0.607284 0.794485i \(-0.707741\pi\)
0.794485 + 0.607284i \(0.207741\pi\)
\(594\) 0 0
\(595\) 15.3545 1.32334i 0.629475 0.0542518i
\(596\) −3.34804 + 12.4951i −0.137141 + 0.511817i
\(597\) 0 0
\(598\) −34.4105 + 17.9853i −1.40715 + 0.735475i
\(599\) 11.7896 0.481711 0.240855 0.970561i \(-0.422572\pi\)
0.240855 + 0.970561i \(0.422572\pi\)
\(600\) 0 0
\(601\) 12.6934 7.32853i 0.517774 0.298937i −0.218250 0.975893i \(-0.570035\pi\)
0.736023 + 0.676956i \(0.236701\pi\)
\(602\) 19.4696 + 27.8822i 0.793523 + 1.13639i
\(603\) 0 0
\(604\) 10.6302 + 39.6725i 0.432537 + 1.61425i
\(605\) −5.25127 19.5980i −0.213495 0.796773i
\(606\) 0 0
\(607\) 8.67196 + 5.00676i 0.351984 + 0.203218i 0.665559 0.746345i \(-0.268193\pi\)
−0.313575 + 0.949564i \(0.601527\pi\)
\(608\) −25.1982 43.6446i −1.02192 1.77002i
\(609\) 0 0
\(610\) 17.3467i 0.702348i
\(611\) −15.9237 + 25.0866i −0.644203 + 1.01489i
\(612\) 0 0
\(613\) 5.30907 + 1.42256i 0.214431 + 0.0574567i 0.364435 0.931229i \(-0.381262\pi\)
−0.150004 + 0.988685i \(0.547929\pi\)
\(614\) 15.3245 8.84762i 0.618447 0.357061i
\(615\) 0 0
\(616\) −2.95414 + 1.07090i −0.119026 + 0.0431476i
\(617\) −1.17910 4.40045i −0.0474687 0.177156i 0.938122 0.346306i \(-0.112564\pi\)
−0.985590 + 0.169151i \(0.945898\pi\)
\(618\) 0 0
\(619\) −24.3594 + 24.3594i −0.979088 + 0.979088i −0.999786 0.0206980i \(-0.993411\pi\)
0.0206980 + 0.999786i \(0.493411\pi\)
\(620\) −8.14907 + 14.1146i −0.327274 + 0.566856i
\(621\) 0 0
\(622\) −10.4209 2.79226i −0.417839 0.111960i
\(623\) 19.6744 + 9.20531i 0.788237 + 0.368803i
\(624\) 0 0
\(625\) 24.5464 0.981856
\(626\) −9.72044 + 36.2772i −0.388507 + 1.44993i
\(627\) 0 0
\(628\) 8.85163 15.3315i 0.353218 0.611792i
\(629\) −0.208936 0.208936i −0.00833082 0.00833082i
\(630\) 0 0
\(631\) −29.1395 + 7.80790i −1.16003 + 0.310828i −0.786976 0.616984i \(-0.788354\pi\)
−0.373049 + 0.927812i \(0.621688\pi\)
\(632\) 2.49136 + 2.49136i 0.0991012 + 0.0991012i
\(633\) 0 0
\(634\) −36.9859 + 21.3538i −1.46890 + 0.848070i
\(635\) −15.3299 4.10764i −0.608349 0.163007i
\(636\) 0 0
\(637\) 25.0199 + 3.31769i 0.991323 + 0.131452i
\(638\) −37.6620 −1.49105
\(639\) 0 0
\(640\) −4.05297 + 2.33998i −0.160208 + 0.0924959i
\(641\) 5.38559 + 3.10937i 0.212718 + 0.122813i 0.602574 0.798063i \(-0.294142\pi\)
−0.389856 + 0.920876i \(0.627475\pi\)
\(642\) 0 0
\(643\) 14.3667 3.84955i 0.566568 0.151811i 0.0358459 0.999357i \(-0.488587\pi\)
0.530722 + 0.847546i \(0.321921\pi\)
\(644\) 29.4033 + 5.22381i 1.15865 + 0.205847i
\(645\) 0 0
\(646\) 16.6291 28.8025i 0.654264 1.13322i
\(647\) −3.53916 6.13001i −0.139139 0.240995i 0.788032 0.615634i \(-0.211100\pi\)
−0.927171 + 0.374639i \(0.877767\pi\)
\(648\) 0 0
\(649\) 22.2005 0.871447
\(650\) −0.0274095 + 0.652526i −0.00107509 + 0.0255942i
\(651\) 0 0
\(652\) 0.820257 + 0.219787i 0.0321237 + 0.00860753i
\(653\) −21.2746 36.8487i −0.832539 1.44200i −0.896019 0.444017i \(-0.853553\pi\)
0.0634796 0.997983i \(-0.479780\pi\)
\(654\) 0 0
\(655\) −12.6368 + 12.6368i −0.493761 + 0.493761i
\(656\) −28.2361 + 7.56584i −1.10243 + 0.295396i
\(657\) 0 0
\(658\) 41.6588 15.1016i 1.62403 0.588721i
\(659\) −16.5688 + 28.6980i −0.645429 + 1.11791i 0.338774 + 0.940868i \(0.389988\pi\)
−0.984202 + 0.177047i \(0.943345\pi\)
\(660\) 0 0
\(661\) −24.7310 6.62666i −0.961925 0.257747i −0.256510 0.966542i \(-0.582573\pi\)
−0.705415 + 0.708794i \(0.749239\pi\)
\(662\) 62.1630i 2.41604i
\(663\) 0 0
\(664\) 1.92877i 0.0748510i
\(665\) −27.9325 23.4998i −1.08318 0.911281i
\(666\) 0 0
\(667\) 18.9423 + 10.9363i 0.733448 + 0.423457i
\(668\) −31.1542 31.1542i −1.20539 1.20539i
\(669\) 0 0
\(670\) −12.2712 45.7966i −0.474076 1.76928i
\(671\) 12.2275 12.2275i 0.472037 0.472037i
\(672\) 0 0
\(673\) 0.329696 0.190350i 0.0127088 0.00733746i −0.493632 0.869671i \(-0.664331\pi\)
0.506341 + 0.862333i \(0.330998\pi\)
\(674\) −1.39077 + 5.19043i −0.0535705 + 0.199928i
\(675\) 0 0
\(676\) 27.5947 + 2.32233i 1.06133 + 0.0893205i
\(677\) 30.7685i 1.18253i 0.806477 + 0.591265i \(0.201371\pi\)
−0.806477 + 0.591265i \(0.798629\pi\)
\(678\) 0 0
\(679\) 5.27642 0.454753i 0.202490 0.0174518i
\(680\) −1.33450 0.770476i −0.0511759 0.0295464i
\(681\) 0 0
\(682\) −30.4278 + 8.15310i −1.16514 + 0.312199i
\(683\) 38.2684 10.2540i 1.46430 0.392358i 0.563328 0.826234i \(-0.309521\pi\)
0.900973 + 0.433875i \(0.142854\pi\)
\(684\) 0 0
\(685\) 7.95393 + 4.59221i 0.303904 + 0.175459i
\(686\) −26.5109 26.7174i −1.01219 1.02008i
\(687\) 0 0
\(688\) 23.5449i 0.897640i
\(689\) −32.5307 + 7.26832i −1.23932 + 0.276901i
\(690\) 0 0
\(691\) 1.21810 4.54600i 0.0463386 0.172938i −0.938878 0.344249i \(-0.888134\pi\)
0.985217 + 0.171311i \(0.0548003\pi\)
\(692\) −35.3550 + 20.4122i −1.34399 + 0.775955i
\(693\) 0 0
\(694\) 4.56817 4.56817i 0.173405 0.173405i
\(695\) 9.35642 + 34.9187i 0.354909 + 1.32454i
\(696\) 0 0
\(697\) −14.5949 14.5949i −0.552822 0.552822i
\(698\) −36.9373 21.3258i −1.39810 0.807192i
\(699\) 0 0
\(700\) 0.323388 0.384388i 0.0122229 0.0145285i
\(701\) 19.5366i 0.737886i −0.929452 0.368943i \(-0.879720\pi\)
0.929452 0.368943i \(-0.120280\pi\)
\(702\) 0 0
\(703\) 0.699860i 0.0263957i
\(704\) −39.0516 10.4638i −1.47181 0.394371i
\(705\) 0 0
\(706\) −20.9826 + 36.3430i −0.789692 + 1.36779i
\(707\) 8.10682 + 22.3632i 0.304888 + 0.841056i
\(708\) 0 0
\(709\) 33.4014 8.94988i 1.25442 0.336120i 0.430375 0.902650i \(-0.358381\pi\)
0.824041 + 0.566530i \(0.191715\pi\)
\(710\) −43.8917 + 43.8917i −1.64723 + 1.64723i
\(711\) 0 0
\(712\) −1.08593 1.88089i −0.0406970 0.0704893i
\(713\) 17.6713 + 4.73502i 0.661797 + 0.177328i
\(714\) 0 0
\(715\) 26.4071 24.2781i 0.987571 0.907949i
\(716\) 14.4219 0.538970
\(717\) 0 0
\(718\) 27.1718 + 47.0629i 1.01404 + 1.75637i
\(719\) −8.27022 + 14.3244i −0.308427 + 0.534211i −0.978018 0.208518i \(-0.933136\pi\)
0.669591 + 0.742730i \(0.266469\pi\)
\(720\) 0 0
\(721\) −13.2370 2.35169i −0.492971 0.0875815i
\(722\) −38.7921 + 10.3943i −1.44369 + 0.386836i
\(723\) 0 0
\(724\) −30.5484 17.6371i −1.13532 0.655478i
\(725\) 0.318622 0.183957i 0.0118333 0.00683198i
\(726\) 0 0
\(727\) 21.0001 0.778851 0.389426 0.921058i \(-0.372674\pi\)
0.389426 + 0.921058i \(0.372674\pi\)
\(728\) −1.86118 1.70423i −0.0689800 0.0631629i
\(729\) 0 0
\(730\) −72.6486 19.4661i −2.68885 0.720474i
\(731\) −14.3974 + 8.31232i −0.532506 + 0.307442i
\(732\) 0 0
\(733\) −9.61770 9.61770i −0.355238 0.355238i 0.506816 0.862054i \(-0.330822\pi\)
−0.862054 + 0.506816i \(0.830822\pi\)
\(734\) 47.3197 12.6793i 1.74660 0.468001i
\(735\) 0 0
\(736\) 30.3296 + 30.3296i 1.11796 + 1.11796i
\(737\) 23.6317 40.9313i 0.870485 1.50772i
\(738\) 0 0
\(739\) 10.3610 38.6677i 0.381135 1.42241i −0.463036 0.886339i \(-0.653240\pi\)
0.844171 0.536074i \(-0.180093\pi\)
\(740\) 0.530647 0.0195070
\(741\) 0 0
\(742\) 45.0243 + 21.0661i 1.65289 + 0.773360i
\(743\) −12.1952 3.26770i −0.447399 0.119880i 0.0280832 0.999606i \(-0.491060\pi\)
−0.475482 + 0.879725i \(0.657726\pi\)
\(744\) 0 0
\(745\) −6.72867 + 11.6544i −0.246519 + 0.426984i
\(746\) 44.2682 44.2682i 1.62077 1.62077i
\(747\) 0 0
\(748\) −6.50616 24.2813i −0.237889 0.887813i
\(749\) −0.939586 2.59192i −0.0343317 0.0947065i
\(750\) 0 0
\(751\) 13.0628 7.54179i 0.476667 0.275204i −0.242359 0.970187i \(-0.577921\pi\)
0.719026 + 0.694983i \(0.244588\pi\)
\(752\) 29.6338 + 7.94035i 1.08063 + 0.289555i
\(753\) 0 0
\(754\) −14.0106 26.8059i −0.510237 0.976214i
\(755\) 42.7278i 1.55502i
\(756\) 0 0
\(757\) 6.07461 + 10.5215i 0.220786 + 0.382412i 0.955047 0.296455i \(-0.0958046\pi\)
−0.734261 + 0.678867i \(0.762471\pi\)
\(758\) −30.9223 17.8530i −1.12315 0.648450i
\(759\) 0 0
\(760\) 0.944645 + 3.52546i 0.0342659 + 0.127882i
\(761\) 6.05559 + 22.5998i 0.219515 + 0.819241i 0.984528 + 0.175226i \(0.0560657\pi\)
−0.765013 + 0.644014i \(0.777268\pi\)
\(762\) 0 0
\(763\) 8.79549 6.14173i 0.318418 0.222346i
\(764\) −16.4124 + 9.47572i −0.593781 + 0.342819i
\(765\) 0 0
\(766\) −16.0231 −0.578940
\(767\) 8.25883 + 15.8012i 0.298209 + 0.570550i
\(768\) 0 0
\(769\) −9.41454 + 35.1355i −0.339497 + 1.26702i 0.559414 + 0.828888i \(0.311026\pi\)
−0.898911 + 0.438131i \(0.855640\pi\)
\(770\) −53.2971 + 4.59345i −1.92069 + 0.165537i
\(771\) 0 0
\(772\) −6.74322 + 6.74322i −0.242694 + 0.242694i
\(773\) −34.2562 + 9.17892i −1.23211 + 0.330143i −0.815401 0.578897i \(-0.803483\pi\)
−0.416709 + 0.909040i \(0.636817\pi\)
\(774\) 0 0
\(775\) 0.217598 0.217598i 0.00781634 0.00781634i
\(776\) −0.458588 0.264766i −0.0164623 0.00950453i
\(777\) 0 0
\(778\) −2.27368 + 8.48548i −0.0815153 + 0.304219i
\(779\) 48.8878i 1.75159i
\(780\) 0 0
\(781\) −61.8775 −2.21415
\(782\) −7.32617 + 27.3416i −0.261983 + 0.977735i
\(783\) 0 0
\(784\) −4.45871 25.6747i −0.159240 0.916955i
\(785\) 13.0228 13.0228i 0.464802 0.464802i
\(786\) 0 0
\(787\) 7.98311 + 29.7934i 0.284567 + 1.06202i 0.949155 + 0.314809i \(0.101941\pi\)
−0.664588 + 0.747210i \(0.731393\pi\)
\(788\) −2.45400 2.45400i −0.0874201