Properties

Label 819.2.et.c.136.6
Level $819$
Weight $2$
Character 819.136
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
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.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 136.6
Character \(\chi\) \(=\) 819.136
Dual form 819.2.et.c.271.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.411775 - 0.411775i) q^{2} +1.66088i q^{4} +(0.180309 - 0.672922i) q^{5} +(2.60113 + 0.483875i) q^{7} +(1.50746 + 1.50746i) q^{8} +O(q^{10})\) \(q+(0.411775 - 0.411775i) q^{2} +1.66088i q^{4} +(0.180309 - 0.672922i) q^{5} +(2.60113 + 0.483875i) q^{7} +(1.50746 + 1.50746i) q^{8} +(-0.202846 - 0.351339i) q^{10} +(0.230214 - 0.859171i) q^{11} +(0.659853 + 3.54466i) q^{13} +(1.27033 - 0.871831i) q^{14} -2.08030 q^{16} +0.0460661 q^{17} +(-0.843398 + 0.225988i) q^{19} +(1.11765 + 0.299472i) q^{20} +(-0.258989 - 0.448581i) q^{22} -3.19116i q^{23} +(3.90981 + 2.25733i) q^{25} +(1.73131 + 1.18789i) q^{26} +(-0.803659 + 4.32017i) q^{28} +(-4.08244 + 7.07099i) q^{29} +(3.90039 - 1.04511i) q^{31} +(-3.87153 + 3.87153i) q^{32} +(0.0189689 - 0.0189689i) q^{34} +(0.794617 - 1.66311i) q^{35} +(-4.97904 - 4.97904i) q^{37} +(-0.254234 + 0.440346i) q^{38} +(1.28621 - 0.742594i) q^{40} +(8.56284 - 2.29441i) q^{41} +(1.29226 - 0.746085i) q^{43} +(1.42698 + 0.382359i) q^{44} +(-1.31404 - 1.31404i) q^{46} +(12.1286 + 3.24985i) q^{47} +(6.53173 + 2.51724i) q^{49} +(2.53947 - 0.680450i) q^{50} +(-5.88726 + 1.09594i) q^{52} +(-4.89224 + 8.47362i) q^{53} +(-0.536646 - 0.309833i) q^{55} +(3.19167 + 4.65051i) q^{56} +(1.23061 + 4.59270i) q^{58} +(-6.25586 + 6.25586i) q^{59} +(0.877507 + 0.506629i) q^{61} +(1.17573 - 2.03643i) q^{62} -0.972206i q^{64} +(2.50426 + 0.195103i) q^{65} +(2.42048 + 0.648566i) q^{67} +0.0765105i q^{68} +(-0.357623 - 1.01203i) q^{70} +(0.798336 + 0.213913i) q^{71} +(-4.09226 - 15.2725i) q^{73} -4.10048 q^{74} +(-0.375340 - 1.40079i) q^{76} +(1.01455 - 2.12342i) q^{77} +(-4.73655 - 8.20394i) q^{79} +(-0.375097 + 1.39988i) q^{80} +(2.58118 - 4.47074i) q^{82} +(3.50364 + 3.50364i) q^{83} +(0.00830614 - 0.0309989i) q^{85} +(0.224900 - 0.839337i) q^{86} +(1.64220 - 0.948127i) q^{88} +(3.69759 - 3.69759i) q^{89} +(0.00119323 + 9.53939i) q^{91} +5.30014 q^{92} +(6.33246 - 3.65605i) q^{94} +0.608289i q^{95} +(-0.288642 + 1.07723i) q^{97} +(3.72614 - 1.65306i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.411775 0.411775i 0.291169 0.291169i −0.546373 0.837542i \(-0.683992\pi\)
0.837542 + 0.546373i \(0.183992\pi\)
\(3\) 0 0
\(4\) 1.66088i 0.830442i
\(5\) 0.180309 0.672922i 0.0806367 0.300940i −0.913816 0.406129i \(-0.866878\pi\)
0.994452 + 0.105189i \(0.0335449\pi\)
\(6\) 0 0
\(7\) 2.60113 + 0.483875i 0.983134 + 0.182887i
\(8\) 1.50746 + 1.50746i 0.532967 + 0.532967i
\(9\) 0 0
\(10\) −0.202846 0.351339i −0.0641454 0.111103i
\(11\) 0.230214 0.859171i 0.0694122 0.259050i −0.922496 0.386007i \(-0.873854\pi\)
0.991908 + 0.126957i \(0.0405209\pi\)
\(12\) 0 0
\(13\) 0.659853 + 3.54466i 0.183010 + 0.983111i
\(14\) 1.27033 0.871831i 0.339509 0.233007i
\(15\) 0 0
\(16\) −2.08030 −0.520075
\(17\) 0.0460661 0.0111727 0.00558634 0.999984i \(-0.498222\pi\)
0.00558634 + 0.999984i \(0.498222\pi\)
\(18\) 0 0
\(19\) −0.843398 + 0.225988i −0.193489 + 0.0518452i −0.354262 0.935146i \(-0.615268\pi\)
0.160773 + 0.986991i \(0.448601\pi\)
\(20\) 1.11765 + 0.299472i 0.249913 + 0.0669640i
\(21\) 0 0
\(22\) −0.258989 0.448581i −0.0552165 0.0956379i
\(23\) 3.19116i 0.665403i −0.943032 0.332701i \(-0.892040\pi\)
0.943032 0.332701i \(-0.107960\pi\)
\(24\) 0 0
\(25\) 3.90981 + 2.25733i 0.781963 + 0.451466i
\(26\) 1.73131 + 1.18789i 0.339538 + 0.232964i
\(27\) 0 0
\(28\) −0.803659 + 4.32017i −0.151877 + 0.816435i
\(29\) −4.08244 + 7.07099i −0.758090 + 1.31305i 0.185734 + 0.982600i \(0.440534\pi\)
−0.943824 + 0.330450i \(0.892800\pi\)
\(30\) 0 0
\(31\) 3.90039 1.04511i 0.700531 0.187707i 0.109063 0.994035i \(-0.465215\pi\)
0.591468 + 0.806328i \(0.298548\pi\)
\(32\) −3.87153 + 3.87153i −0.684397 + 0.684397i
\(33\) 0 0
\(34\) 0.0189689 0.0189689i 0.00325313 0.00325313i
\(35\) 0.794617 1.66311i 0.134315 0.281117i
\(36\) 0 0
\(37\) −4.97904 4.97904i −0.818549 0.818549i 0.167349 0.985898i \(-0.446479\pi\)
−0.985898 + 0.167349i \(0.946479\pi\)
\(38\) −0.254234 + 0.440346i −0.0412422 + 0.0714335i
\(39\) 0 0
\(40\) 1.28621 0.742594i 0.203368 0.117414i
\(41\) 8.56284 2.29441i 1.33729 0.358326i 0.481863 0.876247i \(-0.339960\pi\)
0.855429 + 0.517921i \(0.173294\pi\)
\(42\) 0 0
\(43\) 1.29226 0.746085i 0.197067 0.113777i −0.398219 0.917290i \(-0.630372\pi\)
0.595287 + 0.803513i \(0.297038\pi\)
\(44\) 1.42698 + 0.382359i 0.215126 + 0.0576428i
\(45\) 0 0
\(46\) −1.31404 1.31404i −0.193744 0.193744i
\(47\) 12.1286 + 3.24985i 1.76914 + 0.474039i 0.988536 0.150987i \(-0.0482451\pi\)
0.780604 + 0.625026i \(0.214912\pi\)
\(48\) 0 0
\(49\) 6.53173 + 2.51724i 0.933104 + 0.359606i
\(50\) 2.53947 0.680450i 0.359136 0.0962301i
\(51\) 0 0
\(52\) −5.88726 + 1.09594i −0.816416 + 0.151979i
\(53\) −4.89224 + 8.47362i −0.672001 + 1.16394i 0.305334 + 0.952245i \(0.401232\pi\)
−0.977336 + 0.211695i \(0.932102\pi\)
\(54\) 0 0
\(55\) −0.536646 0.309833i −0.0723613 0.0417778i
\(56\) 3.19167 + 4.65051i 0.426505 + 0.621451i
\(57\) 0 0
\(58\) 1.23061 + 4.59270i 0.161587 + 0.603051i
\(59\) −6.25586 + 6.25586i −0.814444 + 0.814444i −0.985297 0.170853i \(-0.945348\pi\)
0.170853 + 0.985297i \(0.445348\pi\)
\(60\) 0 0
\(61\) 0.877507 + 0.506629i 0.112353 + 0.0648672i 0.555124 0.831768i \(-0.312671\pi\)
−0.442770 + 0.896635i \(0.646004\pi\)
\(62\) 1.17573 2.03643i 0.149318 0.258627i
\(63\) 0 0
\(64\) 0.972206i 0.121526i
\(65\) 2.50426 + 0.195103i 0.310615 + 0.0241996i
\(66\) 0 0
\(67\) 2.42048 + 0.648566i 0.295709 + 0.0792350i 0.403623 0.914925i \(-0.367751\pi\)
−0.107915 + 0.994160i \(0.534417\pi\)
\(68\) 0.0765105i 0.00927826i
\(69\) 0 0
\(70\) −0.357623 1.01203i −0.0427442 0.120961i
\(71\) 0.798336 + 0.213913i 0.0947450 + 0.0253869i 0.305880 0.952070i \(-0.401049\pi\)
−0.211135 + 0.977457i \(0.567716\pi\)
\(72\) 0 0
\(73\) −4.09226 15.2725i −0.478963 1.78751i −0.605830 0.795594i \(-0.707159\pi\)
0.126867 0.991920i \(-0.459508\pi\)
\(74\) −4.10048 −0.476672
\(75\) 0 0
\(76\) −0.375340 1.40079i −0.0430544 0.160681i
\(77\) 1.01455 2.12342i 0.115618 0.241986i
\(78\) 0 0
\(79\) −4.73655 8.20394i −0.532903 0.923016i −0.999262 0.0384199i \(-0.987768\pi\)
0.466358 0.884596i \(-0.345566\pi\)
\(80\) −0.375097 + 1.39988i −0.0419371 + 0.156511i
\(81\) 0 0
\(82\) 2.58118 4.47074i 0.285044 0.493711i
\(83\) 3.50364 + 3.50364i 0.384574 + 0.384574i 0.872747 0.488173i \(-0.162336\pi\)
−0.488173 + 0.872747i \(0.662336\pi\)
\(84\) 0 0
\(85\) 0.00830614 0.0309989i 0.000900927 0.00336231i
\(86\) 0.224900 0.839337i 0.0242516 0.0905081i
\(87\) 0 0
\(88\) 1.64220 0.948127i 0.175060 0.101071i
\(89\) 3.69759 3.69759i 0.391944 0.391944i −0.483436 0.875380i \(-0.660611\pi\)
0.875380 + 0.483436i \(0.160611\pi\)
\(90\) 0 0
\(91\) 0.00119323 + 9.53939i 0.000125084 + 1.00000i
\(92\) 5.30014 0.552578
\(93\) 0 0
\(94\) 6.33246 3.65605i 0.653143 0.377092i
\(95\) 0.608289i 0.0624092i
\(96\) 0 0
\(97\) −0.288642 + 1.07723i −0.0293071 + 0.109376i −0.979030 0.203716i \(-0.934698\pi\)
0.949723 + 0.313092i \(0.101365\pi\)
\(98\) 3.72614 1.65306i 0.376396 0.166985i
\(99\) 0 0
\(100\) −3.74917 + 6.49375i −0.374917 + 0.649375i
\(101\) −7.30376 12.6505i −0.726752 1.25877i −0.958249 0.285935i \(-0.907696\pi\)
0.231497 0.972836i \(-0.425638\pi\)
\(102\) 0 0
\(103\) −6.34652 10.9925i −0.625342 1.08312i −0.988475 0.151386i \(-0.951626\pi\)
0.363133 0.931737i \(-0.381707\pi\)
\(104\) −4.34872 + 6.33812i −0.426427 + 0.621504i
\(105\) 0 0
\(106\) 1.47472 + 5.50372i 0.143237 + 0.534569i
\(107\) −11.7922 −1.14000 −0.569999 0.821645i \(-0.693056\pi\)
−0.569999 + 0.821645i \(0.693056\pi\)
\(108\) 0 0
\(109\) 0.888593 + 3.31627i 0.0851118 + 0.317641i 0.995335 0.0964758i \(-0.0307570\pi\)
−0.910224 + 0.414117i \(0.864090\pi\)
\(110\) −0.348558 + 0.0933959i −0.0332337 + 0.00890495i
\(111\) 0 0
\(112\) −5.41113 1.00661i −0.511304 0.0951152i
\(113\) −7.53468 13.0504i −0.708803 1.22768i −0.965301 0.261138i \(-0.915902\pi\)
0.256498 0.966545i \(-0.417431\pi\)
\(114\) 0 0
\(115\) −2.14740 0.575395i −0.200246 0.0536559i
\(116\) −11.7441 6.78045i −1.09041 0.629549i
\(117\) 0 0
\(118\) 5.15201i 0.474281i
\(119\) 0.119824 + 0.0222902i 0.0109842 + 0.00204334i
\(120\) 0 0
\(121\) 8.84110 + 5.10441i 0.803737 + 0.464038i
\(122\) 0.569952 0.152718i 0.0516010 0.0138265i
\(123\) 0 0
\(124\) 1.73580 + 6.47810i 0.155879 + 0.581750i
\(125\) 4.68705 4.68705i 0.419223 0.419223i
\(126\) 0 0
\(127\) −6.17582 3.56561i −0.548016 0.316397i 0.200306 0.979733i \(-0.435806\pi\)
−0.748321 + 0.663337i \(0.769140\pi\)
\(128\) −8.14339 8.14339i −0.719781 0.719781i
\(129\) 0 0
\(130\) 1.11153 0.950851i 0.0974874 0.0833951i
\(131\) 11.8790 6.85837i 1.03788 0.599219i 0.118646 0.992937i \(-0.462145\pi\)
0.919231 + 0.393718i \(0.128811\pi\)
\(132\) 0 0
\(133\) −2.30314 + 0.179724i −0.199707 + 0.0155841i
\(134\) 1.26376 0.729630i 0.109172 0.0630304i
\(135\) 0 0
\(136\) 0.0694428 + 0.0694428i 0.00595467 + 0.00595467i
\(137\) −8.25603 8.25603i −0.705361 0.705361i 0.260195 0.965556i \(-0.416213\pi\)
−0.965556 + 0.260195i \(0.916213\pi\)
\(138\) 0 0
\(139\) −0.834941 + 0.482054i −0.0708188 + 0.0408873i −0.534991 0.844858i \(-0.679685\pi\)
0.464172 + 0.885745i \(0.346352\pi\)
\(140\) 2.76223 + 1.31977i 0.233451 + 0.111541i
\(141\) 0 0
\(142\) 0.416818 0.240650i 0.0349786 0.0201949i
\(143\) 3.19738 + 0.249103i 0.267378 + 0.0208311i
\(144\) 0 0
\(145\) 4.02213 + 4.02213i 0.334019 + 0.334019i
\(146\) −7.97393 4.60375i −0.659927 0.381009i
\(147\) 0 0
\(148\) 8.26961 8.26961i 0.679757 0.679757i
\(149\) −0.600793 2.24219i −0.0492189 0.183687i 0.936940 0.349490i \(-0.113645\pi\)
−0.986159 + 0.165803i \(0.946979\pi\)
\(150\) 0 0
\(151\) −13.1629 + 3.52700i −1.07118 + 0.287023i −0.750980 0.660325i \(-0.770418\pi\)
−0.320205 + 0.947348i \(0.603752\pi\)
\(152\) −1.61206 0.930720i −0.130755 0.0754914i
\(153\) 0 0
\(154\) −0.456605 1.29214i −0.0367943 0.104123i
\(155\) 2.81310i 0.225954i
\(156\) 0 0
\(157\) 3.81144 + 2.20054i 0.304186 + 0.175622i 0.644322 0.764754i \(-0.277140\pi\)
−0.340136 + 0.940376i \(0.610473\pi\)
\(158\) −5.32857 1.42778i −0.423918 0.113588i
\(159\) 0 0
\(160\) 1.90717 + 3.30331i 0.150775 + 0.261150i
\(161\) 1.54412 8.30061i 0.121694 0.654180i
\(162\) 0 0
\(163\) −0.294730 + 0.0789727i −0.0230850 + 0.00618562i −0.270343 0.962764i \(-0.587137\pi\)
0.247258 + 0.968950i \(0.420470\pi\)
\(164\) 3.81074 + 14.2219i 0.297569 + 1.11054i
\(165\) 0 0
\(166\) 2.88542 0.223952
\(167\) −0.106108 0.396000i −0.00821087 0.0306434i 0.961699 0.274108i \(-0.0883826\pi\)
−0.969910 + 0.243465i \(0.921716\pi\)
\(168\) 0 0
\(169\) −12.1292 + 4.67791i −0.933014 + 0.359839i
\(170\) −0.00934431 0.0161848i −0.000716676 0.00124132i
\(171\) 0 0
\(172\) 1.23916 + 2.14629i 0.0944851 + 0.163653i
\(173\) 1.03796 1.79781i 0.0789149 0.136685i −0.823867 0.566783i \(-0.808188\pi\)
0.902782 + 0.430098i \(0.141521\pi\)
\(174\) 0 0
\(175\) 9.07766 + 7.76347i 0.686207 + 0.586863i
\(176\) −0.478915 + 1.78734i −0.0360996 + 0.134725i
\(177\) 0 0
\(178\) 3.04514i 0.228243i
\(179\) −11.6148 + 6.70581i −0.868131 + 0.501216i −0.866727 0.498783i \(-0.833780\pi\)
−0.00140439 + 0.999999i \(0.500447\pi\)
\(180\) 0 0
\(181\) −2.32661 −0.172935 −0.0864677 0.996255i \(-0.527558\pi\)
−0.0864677 + 0.996255i \(0.527558\pi\)
\(182\) 3.92857 + 3.92759i 0.291205 + 0.291132i
\(183\) 0 0
\(184\) 4.81054 4.81054i 0.354638 0.354638i
\(185\) −4.24827 + 2.45274i −0.312339 + 0.180329i
\(186\) 0 0
\(187\) 0.0106051 0.0395787i 0.000775520 0.00289428i
\(188\) −5.39762 + 20.1442i −0.393662 + 1.46917i
\(189\) 0 0
\(190\) 0.250478 + 0.250478i 0.0181716 + 0.0181716i
\(191\) 11.4976 19.9143i 0.831934 1.44095i −0.0645691 0.997913i \(-0.520567\pi\)
0.896503 0.443038i \(-0.146099\pi\)
\(192\) 0 0
\(193\) 1.74638 6.51759i 0.125707 0.469146i −0.874157 0.485644i \(-0.838585\pi\)
0.999864 + 0.0164980i \(0.00525171\pi\)
\(194\) 0.324719 + 0.562430i 0.0233135 + 0.0403801i
\(195\) 0 0
\(196\) −4.18084 + 10.8484i −0.298632 + 0.774889i
\(197\) −3.30495 12.3342i −0.235468 0.878778i −0.977937 0.208898i \(-0.933012\pi\)
0.742470 0.669880i \(-0.233654\pi\)
\(198\) 0 0
\(199\) 0.830455 0.0588694 0.0294347 0.999567i \(-0.490629\pi\)
0.0294347 + 0.999567i \(0.490629\pi\)
\(200\) 2.49105 + 9.29672i 0.176144 + 0.657377i
\(201\) 0 0
\(202\) −8.21665 2.20165i −0.578122 0.154907i
\(203\) −14.0404 + 16.4172i −0.985444 + 1.15226i
\(204\) 0 0
\(205\) 6.17583i 0.431339i
\(206\) −7.13977 1.91310i −0.497451 0.133292i
\(207\) 0 0
\(208\) −1.37269 7.37395i −0.0951792 0.511292i
\(209\) 0.776649i 0.0537220i
\(210\) 0 0
\(211\) 11.5683 20.0368i 0.796392 1.37939i −0.125560 0.992086i \(-0.540073\pi\)
0.921952 0.387305i \(-0.126594\pi\)
\(212\) −14.0737 8.12545i −0.966585 0.558058i
\(213\) 0 0
\(214\) −4.85574 + 4.85574i −0.331931 + 0.331931i
\(215\) −0.269052 1.00411i −0.0183492 0.0684801i
\(216\) 0 0
\(217\) 10.6511 0.831155i 0.723045 0.0564225i
\(218\) 1.73146 + 0.999657i 0.117269 + 0.0677053i
\(219\) 0 0
\(220\) 0.514596 0.891307i 0.0346941 0.0600919i
\(221\) 0.0303969 + 0.163289i 0.00204472 + 0.0109840i
\(222\) 0 0
\(223\) −13.8755 + 3.71792i −0.929171 + 0.248971i −0.691501 0.722375i \(-0.743050\pi\)
−0.237670 + 0.971346i \(0.576384\pi\)
\(224\) −11.9437 + 8.19701i −0.798021 + 0.547686i
\(225\) 0 0
\(226\) −8.47643 2.27125i −0.563844 0.151081i
\(227\) 14.5357 + 14.5357i 0.964765 + 0.964765i 0.999400 0.0346350i \(-0.0110269\pi\)
−0.0346350 + 0.999400i \(0.511027\pi\)
\(228\) 0 0
\(229\) 3.99397 + 1.07018i 0.263929 + 0.0707196i 0.388357 0.921509i \(-0.373043\pi\)
−0.124428 + 0.992229i \(0.539709\pi\)
\(230\) −1.12118 + 0.647313i −0.0739283 + 0.0426826i
\(231\) 0 0
\(232\) −16.8133 + 4.50512i −1.10385 + 0.295775i
\(233\) 1.72269 0.994594i 0.112857 0.0651580i −0.442509 0.896764i \(-0.645912\pi\)
0.555366 + 0.831606i \(0.312578\pi\)
\(234\) 0 0
\(235\) 4.37380 7.57564i 0.285315 0.494180i
\(236\) −10.3903 10.3903i −0.676348 0.676348i
\(237\) 0 0
\(238\) 0.0585190 0.0401619i 0.00379322 0.00260331i
\(239\) −10.1339 + 10.1339i −0.655510 + 0.655510i −0.954314 0.298805i \(-0.903412\pi\)
0.298805 + 0.954314i \(0.403412\pi\)
\(240\) 0 0
\(241\) −19.5579 + 19.5579i −1.25984 + 1.25984i −0.308664 + 0.951171i \(0.599882\pi\)
−0.951171 + 0.308664i \(0.900118\pi\)
\(242\) 5.74241 1.53867i 0.369136 0.0989097i
\(243\) 0 0
\(244\) −0.841452 + 1.45744i −0.0538684 + 0.0933029i
\(245\) 2.87164 3.94147i 0.183462 0.251811i
\(246\) 0 0
\(247\) −1.35757 2.84044i −0.0863800 0.180733i
\(248\) 7.45513 + 4.30422i 0.473401 + 0.273318i
\(249\) 0 0
\(250\) 3.86002i 0.244129i
\(251\) 3.92297 + 6.79478i 0.247616 + 0.428883i 0.962864 0.269988i \(-0.0870197\pi\)
−0.715248 + 0.698871i \(0.753686\pi\)
\(252\) 0 0
\(253\) −2.74175 0.734651i −0.172373 0.0461871i
\(254\) −4.01127 + 1.07482i −0.251690 + 0.0674401i
\(255\) 0 0
\(256\) −4.76207 −0.297629
\(257\) 0.363807 0.0226936 0.0113468 0.999936i \(-0.496388\pi\)
0.0113468 + 0.999936i \(0.496388\pi\)
\(258\) 0 0
\(259\) −10.5419 15.3604i −0.655041 0.954446i
\(260\) −0.324044 + 4.15928i −0.0200964 + 0.257948i
\(261\) 0 0
\(262\) 2.06739 7.71559i 0.127724 0.476671i
\(263\) 11.1731 + 19.3524i 0.688963 + 1.19332i 0.972174 + 0.234261i \(0.0752671\pi\)
−0.283211 + 0.959058i \(0.591400\pi\)
\(264\) 0 0
\(265\) 4.81997 + 4.81997i 0.296088 + 0.296088i
\(266\) −0.874367 + 1.02238i −0.0536109 + 0.0626861i
\(267\) 0 0
\(268\) −1.07719 + 4.02014i −0.0658000 + 0.245569i
\(269\) 26.2941i 1.60318i −0.597874 0.801590i \(-0.703988\pi\)
0.597874 0.801590i \(-0.296012\pi\)
\(270\) 0 0
\(271\) 0.167050 0.167050i 0.0101476 0.0101476i −0.702015 0.712162i \(-0.747716\pi\)
0.712162 + 0.702015i \(0.247716\pi\)
\(272\) −0.0958314 −0.00581063
\(273\) 0 0
\(274\) −6.79925 −0.410758
\(275\) 2.83953 2.83953i 0.171230 0.171230i
\(276\) 0 0
\(277\) 1.88689i 0.113372i 0.998392 + 0.0566860i \(0.0180534\pi\)
−0.998392 + 0.0566860i \(0.981947\pi\)
\(278\) −0.145310 + 0.542305i −0.00871513 + 0.0325253i
\(279\) 0 0
\(280\) 3.70492 1.30922i 0.221411 0.0782407i
\(281\) −14.2823 14.2823i −0.852011 0.852011i 0.138370 0.990381i \(-0.455814\pi\)
−0.990381 + 0.138370i \(0.955814\pi\)
\(282\) 0 0
\(283\) 8.56272 + 14.8311i 0.509001 + 0.881615i 0.999946 + 0.0104246i \(0.00331831\pi\)
−0.490945 + 0.871191i \(0.663348\pi\)
\(284\) −0.355285 + 1.32594i −0.0210823 + 0.0786802i
\(285\) 0 0
\(286\) 1.41917 1.21402i 0.0839174 0.0717867i
\(287\) 23.3833 1.82470i 1.38027 0.107709i
\(288\) 0 0
\(289\) −16.9979 −0.999875
\(290\) 3.31242 0.194512
\(291\) 0 0
\(292\) 25.3659 6.79677i 1.48443 0.397751i
\(293\) 0.0551536 + 0.0147783i 0.00322210 + 0.000863360i 0.260430 0.965493i \(-0.416136\pi\)
−0.257208 + 0.966356i \(0.582802\pi\)
\(294\) 0 0
\(295\) 3.08172 + 5.33770i 0.179425 + 0.310773i
\(296\) 15.0114i 0.872519i
\(297\) 0 0
\(298\) −1.17067 0.675886i −0.0678150 0.0391530i
\(299\) 11.3116 2.10570i 0.654165 0.121776i
\(300\) 0 0
\(301\) 3.72234 1.31537i 0.214552 0.0758168i
\(302\) −3.96783 + 6.87249i −0.228323 + 0.395467i
\(303\) 0 0
\(304\) 1.75452 0.470123i 0.100629 0.0269634i
\(305\) 0.499145 0.499145i 0.0285809 0.0285809i
\(306\) 0 0
\(307\) 17.7169 17.7169i 1.01116 1.01116i 0.0112203 0.999937i \(-0.496428\pi\)
0.999937 0.0112203i \(-0.00357162\pi\)
\(308\) 3.52675 + 1.68505i 0.200955 + 0.0960144i
\(309\) 0 0
\(310\) −1.15836 1.15836i −0.0657907 0.0657907i
\(311\) 9.52232 16.4931i 0.539961 0.935240i −0.458944 0.888465i \(-0.651772\pi\)
0.998905 0.0467749i \(-0.0148944\pi\)
\(312\) 0 0
\(313\) −2.59097 + 1.49590i −0.146450 + 0.0845530i −0.571435 0.820648i \(-0.693613\pi\)
0.424984 + 0.905201i \(0.360280\pi\)
\(314\) 2.47558 0.663329i 0.139705 0.0374338i
\(315\) 0 0
\(316\) 13.6258 7.86686i 0.766511 0.442545i
\(317\) −0.683930 0.183258i −0.0384133 0.0102928i 0.239561 0.970881i \(-0.422996\pi\)
−0.277975 + 0.960588i \(0.589663\pi\)
\(318\) 0 0
\(319\) 5.13536 + 5.13536i 0.287525 + 0.287525i
\(320\) −0.654219 0.175298i −0.0365720 0.00979943i
\(321\) 0 0
\(322\) −2.78215 4.05381i −0.155043 0.225910i
\(323\) −0.0388521 + 0.0104104i −0.00216179 + 0.000579249i
\(324\) 0 0
\(325\) −5.42156 + 15.3485i −0.300734 + 0.851379i
\(326\) −0.0888434 + 0.153881i −0.00492058 + 0.00852269i
\(327\) 0 0
\(328\) 16.3669 + 9.44941i 0.903708 + 0.521756i
\(329\) 29.9755 + 14.3220i 1.65261 + 0.789598i
\(330\) 0 0
\(331\) −2.45661 9.16821i −0.135028 0.503930i −0.999998 0.00210683i \(-0.999329\pi\)
0.864970 0.501823i \(-0.167337\pi\)
\(332\) −5.81913 + 5.81913i −0.319366 + 0.319366i
\(333\) 0 0
\(334\) −0.206755 0.119370i −0.0113131 0.00653164i
\(335\) 0.872869 1.51185i 0.0476899 0.0826014i
\(336\) 0 0
\(337\) 28.3561i 1.54465i −0.635226 0.772327i \(-0.719093\pi\)
0.635226 0.772327i \(-0.280907\pi\)
\(338\) −3.06825 + 6.92073i −0.166891 + 0.376438i
\(339\) 0 0
\(340\) 0.0514856 + 0.0137955i 0.00279220 + 0.000748167i
\(341\) 3.59170i 0.194502i
\(342\) 0 0
\(343\) 15.7718 + 9.70820i 0.851599 + 0.524194i
\(344\) 3.07272 + 0.823332i 0.165670 + 0.0443911i
\(345\) 0 0
\(346\) −0.312884 1.16770i −0.0168207 0.0627758i
\(347\) 22.3797 1.20140 0.600702 0.799473i \(-0.294888\pi\)
0.600702 + 0.799473i \(0.294888\pi\)
\(348\) 0 0
\(349\) −2.36174 8.81412i −0.126421 0.471809i 0.873465 0.486886i \(-0.161867\pi\)
−0.999886 + 0.0150770i \(0.995201\pi\)
\(350\) 6.93475 0.541150i 0.370678 0.0289257i
\(351\) 0 0
\(352\) 2.43503 + 4.21759i 0.129787 + 0.224798i
\(353\) −0.743912 + 2.77632i −0.0395945 + 0.147769i −0.982893 0.184177i \(-0.941038\pi\)
0.943299 + 0.331945i \(0.107705\pi\)
\(354\) 0 0
\(355\) 0.287894 0.498648i 0.0152798 0.0264655i
\(356\) 6.14126 + 6.14126i 0.325486 + 0.325486i
\(357\) 0 0
\(358\) −2.02140 + 7.54396i −0.106834 + 0.398711i
\(359\) −2.08854 + 7.79454i −0.110229 + 0.411380i −0.998886 0.0471928i \(-0.984972\pi\)
0.888657 + 0.458573i \(0.151639\pi\)
\(360\) 0 0
\(361\) −15.7942 + 9.11880i −0.831275 + 0.479937i
\(362\) −0.958038 + 0.958038i −0.0503534 + 0.0503534i
\(363\) 0 0
\(364\) −15.8438 + 0.00198181i −0.830442 + 0.000103875i
\(365\) −11.0151 −0.576557
\(366\) 0 0
\(367\) −1.45417 + 0.839564i −0.0759069 + 0.0438249i −0.537473 0.843281i \(-0.680621\pi\)
0.461566 + 0.887106i \(0.347288\pi\)
\(368\) 6.63857i 0.346060i
\(369\) 0 0
\(370\) −0.739354 + 2.75931i −0.0384372 + 0.143450i
\(371\) −16.8255 + 19.6737i −0.873537 + 1.02141i
\(372\) 0 0
\(373\) 16.1379 27.9516i 0.835587 1.44728i −0.0579649 0.998319i \(-0.518461\pi\)
0.893552 0.448960i \(-0.148206\pi\)
\(374\) −0.0119306 0.0206644i −0.000616916 0.00106853i
\(375\) 0 0
\(376\) 13.3844 + 23.1824i 0.690246 + 1.19554i
\(377\) −27.7580 9.80502i −1.42961 0.504984i
\(378\) 0 0
\(379\) 5.38351 + 20.0915i 0.276532 + 1.03203i 0.954808 + 0.297224i \(0.0960609\pi\)
−0.678276 + 0.734808i \(0.737272\pi\)
\(380\) −1.01030 −0.0518272
\(381\) 0 0
\(382\) −3.46582 12.9346i −0.177327 0.661793i
\(383\) 27.1672 7.27943i 1.38818 0.371962i 0.514094 0.857734i \(-0.328128\pi\)
0.874086 + 0.485772i \(0.161461\pi\)
\(384\) 0 0
\(385\) −1.24596 1.06558i −0.0635002 0.0543072i
\(386\) −1.96466 3.40289i −0.0999986 0.173203i
\(387\) 0 0
\(388\) −1.78915 0.479401i −0.0908302 0.0243379i
\(389\) 9.23904 + 5.33416i 0.468438 + 0.270453i 0.715586 0.698525i \(-0.246160\pi\)
−0.247148 + 0.968978i \(0.579493\pi\)
\(390\) 0 0
\(391\) 0.147004i 0.00743433i
\(392\) 6.05168 + 13.6409i 0.305656 + 0.688972i
\(393\) 0 0
\(394\) −6.43981 3.71803i −0.324433 0.187312i
\(395\) −6.37466 + 1.70809i −0.320744 + 0.0859431i
\(396\) 0 0
\(397\) −0.614054 2.29168i −0.0308185 0.115016i 0.948803 0.315868i \(-0.102296\pi\)
−0.979622 + 0.200852i \(0.935629\pi\)
\(398\) 0.341960 0.341960i 0.0171409 0.0171409i
\(399\) 0 0
\(400\) −8.13359 4.69593i −0.406679 0.234797i
\(401\) −22.0398 22.0398i −1.10061 1.10061i −0.994336 0.106278i \(-0.966107\pi\)
−0.106278 0.994336i \(-0.533893\pi\)
\(402\) 0 0
\(403\) 6.27823 + 13.1359i 0.312741 + 0.654347i
\(404\) 21.0110 12.1307i 1.04534 0.603525i
\(405\) 0 0
\(406\) 0.978682 + 12.5416i 0.0485712 + 0.622432i
\(407\) −5.42410 + 3.13160i −0.268862 + 0.155228i
\(408\) 0 0
\(409\) 16.2736 + 16.2736i 0.804679 + 0.804679i 0.983823 0.179144i \(-0.0573328\pi\)
−0.179144 + 0.983823i \(0.557333\pi\)
\(410\) −2.54305 2.54305i −0.125592 0.125592i
\(411\) 0 0
\(412\) 18.2573 10.5408i 0.899471 0.519310i
\(413\) −19.2994 + 13.2452i −0.949659 + 0.651756i
\(414\) 0 0
\(415\) 2.98941 1.72594i 0.146745 0.0847230i
\(416\) −16.2779 11.1686i −0.798090 0.547586i
\(417\) 0 0
\(418\) 0.319804 + 0.319804i 0.0156421 + 0.0156421i
\(419\) −15.0030 8.66198i −0.732944 0.423166i 0.0865540 0.996247i \(-0.472414\pi\)
−0.819498 + 0.573082i \(0.805748\pi\)
\(420\) 0 0
\(421\) −28.4825 + 28.4825i −1.38815 + 1.38815i −0.558947 + 0.829203i \(0.688794\pi\)
−0.829203 + 0.558947i \(0.811206\pi\)
\(422\) −3.48714 13.0142i −0.169751 0.633520i
\(423\) 0 0
\(424\) −20.1485 + 5.39877i −0.978497 + 0.262187i
\(425\) 0.180110 + 0.103987i 0.00873662 + 0.00504409i
\(426\) 0 0
\(427\) 2.03736 + 1.74241i 0.0985949 + 0.0843211i
\(428\) 19.5855i 0.946702i
\(429\) 0 0
\(430\) −0.524258 0.302680i −0.0252819 0.0145965i
\(431\) 32.7297 + 8.76990i 1.57653 + 0.422431i 0.937851 0.347039i \(-0.112813\pi\)
0.638683 + 0.769470i \(0.279479\pi\)
\(432\) 0 0
\(433\) 15.2303 + 26.3796i 0.731921 + 1.26772i 0.956061 + 0.293167i \(0.0947091\pi\)
−0.224141 + 0.974557i \(0.571958\pi\)
\(434\) 4.04361 4.72811i 0.194099 0.226956i
\(435\) 0 0
\(436\) −5.50794 + 1.47585i −0.263783 + 0.0706804i
\(437\) 0.721163 + 2.69142i 0.0344979 + 0.128748i
\(438\) 0 0
\(439\) −2.72571 −0.130091 −0.0650455 0.997882i \(-0.520719\pi\)
−0.0650455 + 0.997882i \(0.520719\pi\)
\(440\) −0.341912 1.27603i −0.0163000 0.0608324i
\(441\) 0 0
\(442\) 0.0797547 + 0.0547214i 0.00379355 + 0.00260283i
\(443\) 17.3901 + 30.1206i 0.826229 + 1.43107i 0.900976 + 0.433869i \(0.142852\pi\)
−0.0747467 + 0.997203i \(0.523815\pi\)
\(444\) 0 0
\(445\) −1.82148 3.15490i −0.0863465 0.149557i
\(446\) −4.18262 + 7.24452i −0.198053 + 0.343038i
\(447\) 0 0
\(448\) 0.470426 2.52883i 0.0222255 0.119476i
\(449\) −9.41298 + 35.1297i −0.444226 + 1.65787i 0.273746 + 0.961802i \(0.411737\pi\)
−0.717972 + 0.696072i \(0.754930\pi\)
\(450\) 0 0
\(451\) 7.88516i 0.371298i
\(452\) 21.6753 12.5142i 1.01952 0.588620i
\(453\) 0 0
\(454\) 11.9708 0.561818
\(455\) 6.41949 + 1.71924i 0.300950 + 0.0805990i
\(456\) 0 0
\(457\) 22.5125 22.5125i 1.05309 1.05309i 0.0545801 0.998509i \(-0.482618\pi\)
0.998509 0.0545801i \(-0.0173820\pi\)
\(458\) 2.08529 1.20394i 0.0974392 0.0562566i
\(459\) 0 0
\(460\) 0.955664 3.56659i 0.0445581 0.166293i
\(461\) 4.67038 17.4301i 0.217521 0.811800i −0.767743 0.640758i \(-0.778620\pi\)
0.985264 0.171042i \(-0.0547133\pi\)
\(462\) 0 0
\(463\) 16.2446 + 16.2446i 0.754951 + 0.754951i 0.975399 0.220448i \(-0.0707518\pi\)
−0.220448 + 0.975399i \(0.570752\pi\)
\(464\) 8.49270 14.7098i 0.394264 0.682885i
\(465\) 0 0
\(466\) 0.299810 1.11891i 0.0138884 0.0518323i
\(467\) 18.7401 + 32.4588i 0.867188 + 1.50201i 0.864859 + 0.502016i \(0.167408\pi\)
0.00232895 + 0.999997i \(0.499259\pi\)
\(468\) 0 0
\(469\) 5.98216 + 2.85821i 0.276230 + 0.131980i
\(470\) −1.31844 4.92047i −0.0608149 0.226964i
\(471\) 0 0
\(472\) −18.8609 −0.868144
\(473\) −0.343519 1.28203i −0.0157950 0.0589478i
\(474\) 0 0
\(475\) −3.80766 1.02026i −0.174707 0.0468127i
\(476\) −0.0370215 + 0.199013i −0.00169688 + 0.00912177i
\(477\) 0 0
\(478\) 8.34579i 0.381728i
\(479\) −25.8166 6.91755i −1.17959 0.316071i −0.384828 0.922988i \(-0.625739\pi\)
−0.794765 + 0.606918i \(0.792406\pi\)
\(480\) 0 0
\(481\) 14.3636 20.9344i 0.654922 0.954528i
\(482\) 16.1069i 0.733649i
\(483\) 0 0
\(484\) −8.47784 + 14.6840i −0.385356 + 0.667456i
\(485\) 0.672845 + 0.388467i 0.0305523 + 0.0176394i
\(486\) 0 0
\(487\) −17.5241 + 17.5241i −0.794093 + 0.794093i −0.982157 0.188064i \(-0.939779\pi\)
0.188064 + 0.982157i \(0.439779\pi\)
\(488\) 0.559083 + 2.08653i 0.0253085 + 0.0944527i
\(489\) 0 0
\(490\) −0.440529 2.80546i −0.0199011 0.126738i
\(491\) −9.62086 5.55460i −0.434183 0.250676i 0.266944 0.963712i \(-0.413986\pi\)
−0.701127 + 0.713036i \(0.747319\pi\)
\(492\) 0 0
\(493\) −0.188062 + 0.325733i −0.00846989 + 0.0146703i
\(494\) −1.72863 0.610608i −0.0777748 0.0274726i
\(495\) 0 0
\(496\) −8.11399 + 2.17414i −0.364329 + 0.0976216i
\(497\) 1.97307 + 0.942711i 0.0885041 + 0.0422863i
\(498\) 0 0
\(499\) −0.179598 0.0481231i −0.00803990 0.00215428i 0.254797 0.966995i \(-0.417991\pi\)
−0.262837 + 0.964840i \(0.584658\pi\)
\(500\) 7.78465 + 7.78465i 0.348140 + 0.348140i
\(501\) 0 0
\(502\) 4.41330 + 1.18254i 0.196975 + 0.0527793i
\(503\) −0.488766 + 0.282189i −0.0217930 + 0.0125822i −0.510857 0.859666i \(-0.670672\pi\)
0.489064 + 0.872248i \(0.337338\pi\)
\(504\) 0 0
\(505\) −9.82973 + 2.63387i −0.437417 + 0.117206i
\(506\) −1.43149 + 0.826474i −0.0636377 + 0.0367412i
\(507\) 0 0
\(508\) 5.92207 10.2573i 0.262749 0.455095i
\(509\) −16.1364 16.1364i −0.715235 0.715235i 0.252390 0.967625i \(-0.418783\pi\)
−0.967625 + 0.252390i \(0.918783\pi\)
\(510\) 0 0
\(511\) −3.25450 41.7059i −0.143971 1.84496i
\(512\) 14.3259 14.3259i 0.633121 0.633121i
\(513\) 0 0
\(514\) 0.149806 0.149806i 0.00660767 0.00660767i
\(515\) −8.54144 + 2.28867i −0.376381 + 0.100851i
\(516\) 0 0
\(517\) 5.58436 9.67239i 0.245600 0.425391i
\(518\) −10.6659 1.98412i −0.468632 0.0871772i
\(519\) 0 0
\(520\) 3.48095 + 4.06917i 0.152650 + 0.178445i
\(521\) −20.6918 11.9464i −0.906523 0.523381i −0.0272119 0.999630i \(-0.508663\pi\)
−0.879311 + 0.476249i \(0.841996\pi\)
\(522\) 0 0
\(523\) 32.7387i 1.43156i 0.698324 + 0.715782i \(0.253929\pi\)
−0.698324 + 0.715782i \(0.746071\pi\)
\(524\) 11.3910 + 19.7297i 0.497616 + 0.861897i
\(525\) 0 0
\(526\) 12.5696 + 3.36802i 0.548061 + 0.146853i
\(527\) 0.179676 0.0481440i 0.00782680 0.00209719i
\(528\) 0 0
\(529\) 12.8165 0.557239
\(530\) 3.96948 0.172423
\(531\) 0 0
\(532\) −0.298501 3.82524i −0.0129417 0.165845i
\(533\) 13.7831 + 28.8384i 0.597013 + 1.24913i
\(534\) 0 0
\(535\) −2.12625 + 7.93526i −0.0919256 + 0.343071i
\(536\) 2.67109 + 4.62646i 0.115373 + 0.199833i
\(537\) 0 0
\(538\) −10.8272 10.8272i −0.466796 0.466796i
\(539\) 3.66644 5.03237i 0.157925 0.216760i
\(540\) 0 0
\(541\) −4.57076 + 17.0583i −0.196512 + 0.733394i 0.795358 + 0.606140i \(0.207283\pi\)
−0.991870 + 0.127254i \(0.959384\pi\)
\(542\) 0.137574i 0.00590931i
\(543\) 0 0
\(544\) −0.178346 + 0.178346i −0.00764654 + 0.00764654i
\(545\) 2.39182 0.102454
\(546\) 0 0
\(547\) 24.8672 1.06324 0.531621 0.846982i \(-0.321583\pi\)
0.531621 + 0.846982i \(0.321583\pi\)
\(548\) 13.7123 13.7123i 0.585761 0.585761i
\(549\) 0 0
\(550\) 2.33849i 0.0997136i
\(551\) 1.84516 6.88624i 0.0786066 0.293364i
\(552\) 0 0
\(553\) −8.35069 23.6314i −0.355107 1.00491i
\(554\) 0.776972 + 0.776972i 0.0330104 + 0.0330104i
\(555\) 0 0
\(556\) −0.800635 1.38674i −0.0339545 0.0588109i
\(557\) −9.42880 + 35.1888i −0.399511 + 1.49100i 0.414448 + 0.910073i \(0.363975\pi\)
−0.813959 + 0.580922i \(0.802692\pi\)
\(558\) 0 0
\(559\) 3.49732 + 4.08830i 0.147921 + 0.172917i
\(560\) −1.65304 + 3.45977i −0.0698538 + 0.146202i
\(561\) 0 0
\(562\) −11.7622 −0.496157
\(563\) 39.9539 1.68386 0.841928 0.539590i \(-0.181421\pi\)
0.841928 + 0.539590i \(0.181421\pi\)
\(564\) 0 0
\(565\) −10.1405 + 2.71714i −0.426614 + 0.114311i
\(566\) 9.63296 + 2.58114i 0.404904 + 0.108494i
\(567\) 0 0
\(568\) 0.880992 + 1.52592i 0.0369656 + 0.0640263i
\(569\) 26.1438i 1.09600i 0.836477 + 0.548002i \(0.184611\pi\)
−0.836477 + 0.548002i \(0.815389\pi\)
\(570\) 0 0
\(571\) 20.3089 + 11.7254i 0.849902 + 0.490691i 0.860618 0.509251i \(-0.170078\pi\)
−0.0107157 + 0.999943i \(0.503411\pi\)
\(572\) −0.413732 + 5.31047i −0.0172990 + 0.222042i
\(573\) 0 0
\(574\) 8.87726 10.3800i 0.370530 0.433253i
\(575\) 7.20351 12.4768i 0.300407 0.520320i
\(576\) 0 0
\(577\) 15.6987 4.20645i 0.653544 0.175117i 0.0832134 0.996532i \(-0.473482\pi\)
0.570331 + 0.821415i \(0.306815\pi\)
\(578\) −6.99929 + 6.99929i −0.291132 + 0.291132i
\(579\) 0 0
\(580\) −6.68028 + 6.68028i −0.277384 + 0.277384i
\(581\) 7.41809 + 10.8087i 0.307754 + 0.448422i
\(582\) 0 0
\(583\) 6.15402 + 6.15402i 0.254874 + 0.254874i
\(584\) 16.8538 29.1916i 0.697415 1.20796i
\(585\) 0 0
\(586\) 0.0287962 0.0166255i 0.00118956 0.000686792i
\(587\) −25.3256 + 6.78596i −1.04530 + 0.280087i −0.740307 0.672269i \(-0.765320\pi\)
−0.304991 + 0.952355i \(0.598653\pi\)
\(588\) 0 0
\(589\) −3.05340 + 1.76288i −0.125813 + 0.0726383i
\(590\) 3.46690 + 0.928954i 0.142730 + 0.0382444i
\(591\) 0 0
\(592\) 10.3579 + 10.3579i 0.425707 + 0.425707i
\(593\) −9.92038 2.65816i −0.407381 0.109157i 0.0493084 0.998784i \(-0.484298\pi\)
−0.456690 + 0.889626i \(0.650965\pi\)
\(594\) 0 0
\(595\) 0.0366049 0.0766130i 0.00150066 0.00314083i
\(596\) 3.72402 0.997848i 0.152542 0.0408734i
\(597\) 0 0
\(598\) 3.79074 5.52489i 0.155015 0.225929i
\(599\) −9.56265 + 16.5630i −0.390719 + 0.676746i −0.992545 0.121882i \(-0.961107\pi\)
0.601825 + 0.798628i \(0.294440\pi\)
\(600\) 0 0
\(601\) −38.9868 22.5091i −1.59031 0.918164i −0.993254 0.115961i \(-0.963005\pi\)
−0.597052 0.802202i \(-0.703661\pi\)
\(602\) 0.991127 2.07440i 0.0403953 0.0845463i
\(603\) 0 0
\(604\) −5.85793 21.8621i −0.238356 0.889556i
\(605\) 5.02900 5.02900i 0.204458 0.204458i
\(606\) 0 0
\(607\) −41.0361 23.6922i −1.66561 0.961638i −0.969964 0.243248i \(-0.921787\pi\)
−0.695641 0.718389i \(-0.744880\pi\)
\(608\) 2.39032 4.14016i 0.0969404 0.167906i
\(609\) 0 0
\(610\) 0.411070i 0.0166437i
\(611\) −3.51650 + 45.1362i −0.142262 + 1.82601i
\(612\) 0 0
\(613\) −38.9499 10.4366i −1.57317 0.421531i −0.636369 0.771385i \(-0.719564\pi\)
−0.936804 + 0.349854i \(0.886231\pi\)
\(614\) 14.5907i 0.588834i
\(615\) 0 0
\(616\) 4.73036 1.67158i 0.190591 0.0673498i
\(617\) 12.1180 + 3.24702i 0.487854 + 0.130720i 0.494357 0.869259i \(-0.335404\pi\)
−0.00650361 + 0.999979i \(0.502070\pi\)
\(618\) 0 0
\(619\) −2.16855 8.09314i −0.0871614 0.325291i 0.908553 0.417769i \(-0.137188\pi\)
−0.995715 + 0.0924781i \(0.970521\pi\)
\(620\) 4.67224 0.187642
\(621\) 0 0
\(622\) −2.87041 10.7125i −0.115093 0.429532i
\(623\) 11.4071 7.82873i 0.457014 0.313651i
\(624\) 0 0
\(625\) 8.97776 + 15.5499i 0.359110 + 0.621997i
\(626\) −0.450922 + 1.68287i −0.0180225 + 0.0672608i
\(627\) 0 0
\(628\) −3.65484 + 6.33036i −0.145844 + 0.252609i
\(629\) −0.229365 0.229365i −0.00914538 0.00914538i
\(630\) 0 0
\(631\) 3.60680 13.4608i 0.143584 0.535864i −0.856230 0.516595i \(-0.827199\pi\)
0.999814 0.0192694i \(-0.00613403\pi\)
\(632\) 5.22695 19.5073i 0.207917 0.775957i
\(633\) 0 0
\(634\) −0.357086 + 0.206164i −0.0141817 + 0.00818781i
\(635\) −3.51294 + 3.51294i −0.139407 + 0.139407i
\(636\) 0 0
\(637\) −4.61277 + 24.8138i −0.182764 + 0.983157i
\(638\) 4.22922 0.167436
\(639\) 0 0
\(640\) −6.94820 + 4.01155i −0.274652 + 0.158570i
\(641\) 48.2934i 1.90747i −0.300644 0.953736i \(-0.597202\pi\)
0.300644 0.953736i \(-0.402798\pi\)
\(642\) 0 0
\(643\) 4.25643 15.8852i 0.167857 0.626451i −0.829801 0.558059i \(-0.811546\pi\)
0.997658 0.0683924i \(-0.0217870\pi\)
\(644\) 13.7864 + 2.56461i 0.543258 + 0.101060i
\(645\) 0 0
\(646\) −0.0117116 + 0.0202850i −0.000460785 + 0.000798104i
\(647\) 7.10098 + 12.2993i 0.279168 + 0.483533i 0.971178 0.238354i \(-0.0766080\pi\)
−0.692010 + 0.721888i \(0.743275\pi\)
\(648\) 0 0
\(649\) 3.93467 + 6.81505i 0.154449 + 0.267514i
\(650\) 4.08764 + 8.55256i 0.160330 + 0.335459i
\(651\) 0 0
\(652\) −0.131164 0.489512i −0.00513680 0.0191708i
\(653\) 9.98626 0.390793 0.195396 0.980724i \(-0.437401\pi\)
0.195396 + 0.980724i \(0.437401\pi\)
\(654\) 0 0
\(655\) −2.47325 9.23031i −0.0966380 0.360658i
\(656\) −17.8133 + 4.77306i −0.695492 + 0.186357i
\(657\) 0 0
\(658\) 18.2406 6.44573i 0.711093 0.251281i
\(659\) −12.1444 21.0347i −0.473079 0.819397i 0.526446 0.850208i \(-0.323524\pi\)
−0.999525 + 0.0308117i \(0.990191\pi\)
\(660\) 0 0
\(661\) 23.2228 + 6.22253i 0.903262 + 0.242028i 0.680416 0.732826i \(-0.261799\pi\)
0.222845 + 0.974854i \(0.428466\pi\)
\(662\) −4.78681 2.76366i −0.186044 0.107413i
\(663\) 0 0
\(664\) 10.5632i 0.409931i
\(665\) −0.294336 + 1.58224i −0.0114139 + 0.0613566i
\(666\) 0 0
\(667\) 22.5647 + 13.0277i 0.873707 + 0.504435i
\(668\) 0.657709 0.176233i 0.0254475 0.00681865i
\(669\) 0 0
\(670\) −0.263118 0.981968i −0.0101651 0.0379367i
\(671\) 0.637296 0.637296i 0.0246025 0.0246025i
\(672\) 0 0
\(673\) −18.1748 10.4933i −0.700589 0.404485i 0.106978 0.994261i \(-0.465883\pi\)
−0.807567 + 0.589776i \(0.799216\pi\)
\(674\) −11.6763 11.6763i −0.449754 0.449754i
\(675\) 0 0
\(676\) −7.76946 20.1452i −0.298825 0.774814i
\(677\) −42.3269 + 24.4375i −1.62676 + 0.939208i −0.641705 + 0.766952i \(0.721772\pi\)
−0.985052 + 0.172256i \(0.944894\pi\)
\(678\) 0 0
\(679\) −1.27204 + 2.66234i −0.0488163 + 0.102171i
\(680\) 0.0592508 0.0342084i 0.00227216 0.00131183i
\(681\) 0 0
\(682\) −1.47897 1.47897i −0.0566328 0.0566328i
\(683\) −28.8168 28.8168i −1.10264 1.10264i −0.994091 0.108553i \(-0.965378\pi\)
−0.108553 0.994091i \(-0.534622\pi\)
\(684\) 0 0
\(685\) −7.04431 + 4.06703i −0.269149 + 0.155393i
\(686\) 10.4920 2.49685i 0.400588 0.0953302i
\(687\) 0 0
\(688\) −2.68828 + 1.55208i −0.102490 + 0.0591726i
\(689\) −33.2642 11.7500i −1.26727 0.447639i
\(690\) 0 0
\(691\) 2.28413 + 2.28413i 0.0868923 + 0.0868923i 0.749217 0.662325i \(-0.230430\pi\)
−0.662325 + 0.749217i \(0.730430\pi\)
\(692\) 2.98595 + 1.72394i 0.113509 + 0.0655342i
\(693\) 0 0
\(694\) 9.21538 9.21538i 0.349811 0.349811i
\(695\) 0.173837 + 0.648769i 0.00659402 + 0.0246092i
\(696\) 0 0
\(697\) 0.394457 0.105694i 0.0149411 0.00400346i
\(698\) −4.60193 2.65693i −0.174186 0.100566i
\(699\) 0 0
\(700\) −12.8942 + 15.0769i −0.487356 + 0.569855i
\(701\) 8.12097i 0.306725i 0.988170 + 0.153362i \(0.0490102\pi\)
−0.988170 + 0.153362i \(0.950990\pi\)
\(702\) 0 0
\(703\) 5.32452 + 3.07411i 0.200818 + 0.115942i
\(704\) −0.835292 0.223816i −0.0314812 0.00843537i
\(705\) 0 0
\(706\) 0.836893 + 1.44954i 0.0314969 + 0.0545542i
\(707\) −12.8768 36.4396i −0.484281 1.37045i
\(708\) 0 0
\(709\) 13.1733 3.52976i 0.494732 0.132563i −0.00282213 0.999996i \(-0.500898\pi\)
0.497554 + 0.867433i \(0.334232\pi\)
\(710\) −0.0867828 0.323878i −0.00325690 0.0121549i
\(711\) 0 0
\(712\) 11.1479 0.417786
\(713\) −3.33510 12.4468i −0.124901 0.466135i
\(714\) 0 0
\(715\) 0.744143 2.10667i 0.0278294 0.0787850i
\(716\) −11.1376 19.2908i −0.416230 0.720932i
\(717\) 0 0
\(718\) 2.34958 + 4.06960i 0.0876857 + 0.151876i
\(719\) 14.0292 24.2993i 0.523200 0.906210i −0.476435 0.879210i \(-0.658071\pi\)
0.999635 0.0270000i \(-0.00859542\pi\)
\(720\) 0 0
\(721\) −11.1891 31.6638i −0.416705 1.17922i
\(722\) −2.74877 + 10.2586i −0.102299 + 0.381784i
\(723\) 0 0
\(724\) 3.86423i 0.143613i
\(725\) −31.9231 + 18.4308i −1.18560 + 0.684504i
\(726\) 0 0
\(727\) −21.2410 −0.787785 −0.393893 0.919156i \(-0.628872\pi\)
−0.393893 + 0.919156i \(0.628872\pi\)
\(728\) −14.3784 + 14.3820i −0.532900 + 0.533034i
\(729\) 0 0
\(730\) −4.53574 + 4.53574i −0.167875 + 0.167875i
\(731\) 0.0595293 0.0343692i 0.00220177 0.00127119i
\(732\) 0 0
\(733\) −2.19607 + 8.19585i −0.0811138 + 0.302721i −0.994550 0.104261i \(-0.966752\pi\)
0.913436 + 0.406982i \(0.133419\pi\)
\(734\) −0.253078 + 0.944500i −0.00934128 + 0.0348621i
\(735\) 0 0
\(736\) 12.3547 + 12.3547i 0.455399 + 0.455399i
\(737\) 1.11446 1.93030i 0.0410516 0.0711035i
\(738\) 0 0
\(739\) 5.71616 21.3330i 0.210272 0.784747i −0.777505 0.628877i \(-0.783515\pi\)
0.987777 0.155871i \(-0.0498183\pi\)
\(740\) −4.07372 7.05589i −0.149753 0.259380i
\(741\) 0 0
\(742\) 1.17282 + 15.0295i 0.0430555 + 0.551749i
\(743\) 7.10193 + 26.5048i 0.260544 + 0.972365i 0.964921 + 0.262539i \(0.0845598\pi\)
−0.704377 + 0.709826i \(0.748774\pi\)
\(744\) 0 0
\(745\) −1.61715 −0.0592478
\(746\) −4.86459 18.1549i −0.178105 0.664699i
\(747\) 0 0
\(748\) 0.0657356 + 0.0176138i 0.00240353 + 0.000644024i
\(749\) −30.6731 5.70596i −1.12077 0.208491i
\(750\) 0 0
\(751\) 8.08325i 0.294962i −0.989065 0.147481i \(-0.952883\pi\)
0.989065 0.147481i \(-0.0471165\pi\)
\(752\) −25.2312 6.76067i −0.920086 0.246536i
\(753\) 0 0
\(754\) −15.4675 + 7.39259i −0.563294 + 0.269222i
\(755\) 9.49358i 0.345507i
\(756\) 0 0
\(757\) −15.2508 + 26.4151i −0.554299 + 0.960074i 0.443659 + 0.896196i \(0.353680\pi\)
−0.997958 + 0.0638779i \(0.979653\pi\)
\(758\) 10.4900 + 6.05638i 0.381013 + 0.219978i
\(759\) 0 0
\(760\) −0.916971 + 0.916971i −0.0332620 + 0.0332620i
\(761\) 3.64361 + 13.5982i 0.132081 + 0.492933i 0.999993 0.00378550i \(-0.00120496\pi\)
−0.867912 + 0.496718i \(0.834538\pi\)
\(762\) 0 0
\(763\) 0.706683 + 9.05602i 0.0255836 + 0.327850i
\(764\) 33.0754 + 19.0961i 1.19663 + 0.690872i
\(765\) 0 0
\(766\) 8.18928 14.1843i 0.295891 0.512498i
\(767\) −26.3028 18.0469i −0.949741 0.651637i
\(768\) 0 0
\(769\) −3.42800 + 0.918529i −0.123617 + 0.0331230i −0.320097 0.947385i \(-0.603715\pi\)
0.196480 + 0.980508i \(0.437049\pi\)
\(770\) −0.951837 + 0.0742762i −0.0343018 + 0.00267673i
\(771\) 0 0
\(772\) 10.8250 + 2.90054i 0.389599 + 0.104393i
\(773\) 34.6723 + 34.6723i 1.24708 + 1.24708i 0.957005 + 0.290072i \(0.0936793\pi\)
0.290072 + 0.957005i \(0.406321\pi\)
\(774\) 0 0
\(775\) 17.6090 + 4.71831i 0.632532 + 0.169487i
\(776\) −2.05899 + 1.18876i −0.0739134 + 0.0426739i
\(777\) 0 0
\(778\) 6.00087 1.60793i 0.215142 0.0576471i
\(779\) −6.70338 + 3.87020i −0.240173 + 0.138664i
\(780\) 0 0
\(781\) 0.367577 0.636661i 0.0131529 0.0227815i
\(782\) −0.0605326 0.0605326i −0.00216464 0.00216464i
\(783\) 0 0
\(784\) −13.5880 5.23662i −0.485285 0.187022i
\(785\) 2.16803 2.16803i 0.0773802 0.0773802i
\(786\) 0 0
\(787\) −21.7018 + 21.7018i −0.773585 + 0.773585i −0.978731 0.205146i \(-0.934233\pi\)
0.205146 + 0.978731i \(0.434233\pi\)
\(788\) 20.4857