Properties

Label 819.2.fm.e.496.5
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 496.5
Character \(\chi\) \(=\) 819.496
Dual form 819.2.fm.e.748.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.61214 + 2.09786i) q^{7} +(-2.17732 - 2.17732i) q^{8} +O(q^{10})\) \(q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.61214 + 2.09786i) q^{7} +(-2.17732 - 2.17732i) q^{8} +(-0.448776 - 0.777302i) q^{10} +(0.824353 - 3.07653i) q^{11} +(2.63686 - 2.45905i) q^{13} +(1.17177 + 2.82317i) q^{14} +(-1.11349 - 1.92862i) q^{16} +(-1.74975 + 3.03065i) q^{17} +(6.06267 - 1.62449i) q^{19} +(0.133761 + 0.499204i) q^{20} +(1.83988 - 3.18676i) q^{22} +(4.89067 - 2.82363i) q^{23} -4.39645i q^{25} +(3.67792 - 1.95572i) q^{26} +(-0.230987 - 1.74483i) q^{28} +(-4.54654 - 7.87483i) q^{29} +(-0.888029 - 0.888029i) q^{31} +(0.928002 + 3.46335i) q^{32} +(-2.85886 + 2.85886i) q^{34} +(0.266825 - 2.03806i) q^{35} +(0.151142 - 0.564068i) q^{37} +7.25141 q^{38} +2.39219i q^{40} +(-0.704976 + 2.63101i) q^{41} +(6.60921 + 3.81583i) q^{43} +(-1.49823 + 1.49823i) q^{44} +(6.30208 - 1.68864i) q^{46} +(-0.267009 + 0.267009i) q^{47} +(-1.80201 + 6.76408i) q^{49} +(1.31462 - 4.90623i) q^{50} +(-2.33706 + 0.539622i) q^{52} +11.6025 q^{53} +(-2.14292 + 1.23721i) q^{55} +(1.05756 - 8.07786i) q^{56} +(-2.71900 - 10.1474i) q^{58} +(-0.635122 - 2.37031i) q^{59} +(-6.70242 - 3.86964i) q^{61} +(-0.725461 - 1.25654i) q^{62} +8.59639i q^{64} +(-2.79940 - 0.0976783i) q^{65} +(-6.90457 - 1.85007i) q^{67} +(2.01610 - 1.16400i) q^{68} +(0.907181 - 2.19459i) q^{70} +(2.51079 + 9.37039i) q^{71} +(-7.71628 + 7.71628i) q^{73} +(0.337334 - 0.584279i) q^{74} +(-4.03312 - 1.08067i) q^{76} +(7.78309 - 3.23042i) q^{77} -10.8188 q^{79} +(-0.447786 + 1.67116i) q^{80} +(-1.57344 + 2.72528i) q^{82} +(-10.3355 - 10.3355i) q^{83} +(2.62607 - 0.703654i) q^{85} +(6.23456 + 6.23456i) q^{86} +(-8.49348 + 4.90371i) q^{88} +(7.02589 + 1.88258i) q^{89} +(9.40974 + 1.56743i) q^{91} -3.75677 q^{92} +(-0.377810 + 0.218129i) q^{94} +(-4.22288 - 2.43808i) q^{95} +(-0.704543 + 0.188782i) q^{97} +(-4.03355 + 7.00956i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.11595 + 0.299019i 0.789098 + 0.211438i 0.630792 0.775952i \(-0.282730\pi\)
0.158306 + 0.987390i \(0.449397\pi\)
\(3\) 0 0
\(4\) −0.576113 0.332619i −0.288056 0.166309i
\(5\) −0.549341 0.549341i −0.245673 0.245673i 0.573519 0.819192i \(-0.305578\pi\)
−0.819192 + 0.573519i \(0.805578\pi\)
\(6\) 0 0
\(7\) 1.61214 + 2.09786i 0.609331 + 0.792916i
\(8\) −2.17732 2.17732i −0.769800 0.769800i
\(9\) 0 0
\(10\) −0.448776 0.777302i −0.141915 0.245805i
\(11\) 0.824353 3.07653i 0.248552 0.927608i −0.723013 0.690834i \(-0.757243\pi\)
0.971565 0.236774i \(-0.0760899\pi\)
\(12\) 0 0
\(13\) 2.63686 2.45905i 0.731335 0.682019i
\(14\) 1.17177 + 2.82317i 0.313170 + 0.754524i
\(15\) 0 0
\(16\) −1.11349 1.92862i −0.278373 0.482156i
\(17\) −1.74975 + 3.03065i −0.424376 + 0.735041i −0.996362 0.0852225i \(-0.972840\pi\)
0.571986 + 0.820263i \(0.306173\pi\)
\(18\) 0 0
\(19\) 6.06267 1.62449i 1.39087 0.372683i 0.515814 0.856701i \(-0.327490\pi\)
0.875058 + 0.484017i \(0.160823\pi\)
\(20\) 0.133761 + 0.499204i 0.0299099 + 0.111625i
\(21\) 0 0
\(22\) 1.83988 3.18676i 0.392263 0.679420i
\(23\) 4.89067 2.82363i 1.01978 0.588768i 0.105737 0.994394i \(-0.466280\pi\)
0.914039 + 0.405626i \(0.132947\pi\)
\(24\) 0 0
\(25\) 4.39645i 0.879290i
\(26\) 3.67792 1.95572i 0.721299 0.383548i
\(27\) 0 0
\(28\) −0.230987 1.74483i −0.0436525 0.329742i
\(29\) −4.54654 7.87483i −0.844271 1.46232i −0.886253 0.463202i \(-0.846701\pi\)
0.0419819 0.999118i \(-0.486633\pi\)
\(30\) 0 0
\(31\) −0.888029 0.888029i −0.159495 0.159495i 0.622848 0.782343i \(-0.285975\pi\)
−0.782343 + 0.622848i \(0.785975\pi\)
\(32\) 0.928002 + 3.46335i 0.164049 + 0.612239i
\(33\) 0 0
\(34\) −2.85886 + 2.85886i −0.490290 + 0.490290i
\(35\) 0.266825 2.03806i 0.0451017 0.344494i
\(36\) 0 0
\(37\) 0.151142 0.564068i 0.0248475 0.0927322i −0.952389 0.304887i \(-0.901381\pi\)
0.977236 + 0.212155i \(0.0680480\pi\)
\(38\) 7.25141 1.17633
\(39\) 0 0
\(40\) 2.39219i 0.378238i
\(41\) −0.704976 + 2.63101i −0.110099 + 0.410894i −0.998874 0.0474499i \(-0.984891\pi\)
0.888775 + 0.458344i \(0.151557\pi\)
\(42\) 0 0
\(43\) 6.60921 + 3.81583i 1.00790 + 0.581909i 0.910575 0.413344i \(-0.135639\pi\)
0.0973205 + 0.995253i \(0.468973\pi\)
\(44\) −1.49823 + 1.49823i −0.225867 + 0.225867i
\(45\) 0 0
\(46\) 6.30208 1.68864i 0.929191 0.248976i
\(47\) −0.267009 + 0.267009i −0.0389472 + 0.0389472i −0.726312 0.687365i \(-0.758767\pi\)
0.687365 + 0.726312i \(0.258767\pi\)
\(48\) 0 0
\(49\) −1.80201 + 6.76408i −0.257430 + 0.966297i
\(50\) 1.31462 4.90623i 0.185915 0.693845i
\(51\) 0 0
\(52\) −2.33706 + 0.539622i −0.324092 + 0.0748321i
\(53\) 11.6025 1.59372 0.796862 0.604161i \(-0.206492\pi\)
0.796862 + 0.604161i \(0.206492\pi\)
\(54\) 0 0
\(55\) −2.14292 + 1.23721i −0.288951 + 0.166826i
\(56\) 1.05756 8.07786i 0.141323 1.07945i
\(57\) 0 0
\(58\) −2.71900 10.1474i −0.357022 1.33242i
\(59\) −0.635122 2.37031i −0.0826858 0.308588i 0.912180 0.409790i \(-0.134398\pi\)
−0.994866 + 0.101202i \(0.967731\pi\)
\(60\) 0 0
\(61\) −6.70242 3.86964i −0.858157 0.495457i 0.00523788 0.999986i \(-0.498333\pi\)
−0.863395 + 0.504529i \(0.831666\pi\)
\(62\) −0.725461 1.25654i −0.0921337 0.159580i
\(63\) 0 0
\(64\) 8.59639i 1.07455i
\(65\) −2.79940 0.0976783i −0.347223 0.0121155i
\(66\) 0 0
\(67\) −6.90457 1.85007i −0.843528 0.226023i −0.188921 0.981992i \(-0.560499\pi\)
−0.654607 + 0.755970i \(0.727166\pi\)
\(68\) 2.01610 1.16400i 0.244488 0.141155i
\(69\) 0 0
\(70\) 0.907181 2.19459i 0.108429 0.262303i
\(71\) 2.51079 + 9.37039i 0.297976 + 1.11206i 0.938825 + 0.344394i \(0.111916\pi\)
−0.640849 + 0.767667i \(0.721418\pi\)
\(72\) 0 0
\(73\) −7.71628 + 7.71628i −0.903122 + 0.903122i −0.995705 0.0925826i \(-0.970488\pi\)
0.0925826 + 0.995705i \(0.470488\pi\)
\(74\) 0.337334 0.584279i 0.0392142 0.0679210i
\(75\) 0 0
\(76\) −4.03312 1.08067i −0.462630 0.123961i
\(77\) 7.78309 3.23042i 0.886965 0.368140i
\(78\) 0 0
\(79\) −10.8188 −1.21721 −0.608607 0.793472i \(-0.708271\pi\)
−0.608607 + 0.793472i \(0.708271\pi\)
\(80\) −0.447786 + 1.67116i −0.0500640 + 0.186841i
\(81\) 0 0
\(82\) −1.57344 + 2.72528i −0.173757 + 0.300956i
\(83\) −10.3355 10.3355i −1.13447 1.13447i −0.989426 0.145040i \(-0.953669\pi\)
−0.145040 0.989426i \(-0.546331\pi\)
\(84\) 0 0
\(85\) 2.62607 0.703654i 0.284837 0.0763220i
\(86\) 6.23456 + 6.23456i 0.672290 + 0.672290i
\(87\) 0 0
\(88\) −8.49348 + 4.90371i −0.905408 + 0.522737i
\(89\) 7.02589 + 1.88258i 0.744743 + 0.199553i 0.611185 0.791488i \(-0.290693\pi\)
0.133558 + 0.991041i \(0.457360\pi\)
\(90\) 0 0
\(91\) 9.40974 + 1.56743i 0.986409 + 0.164311i
\(92\) −3.75677 −0.391670
\(93\) 0 0
\(94\) −0.377810 + 0.218129i −0.0389681 + 0.0224983i
\(95\) −4.22288 2.43808i −0.433258 0.250142i
\(96\) 0 0
\(97\) −0.704543 + 0.188782i −0.0715355 + 0.0191679i −0.294409 0.955679i \(-0.595123\pi\)
0.222874 + 0.974847i \(0.428456\pi\)
\(98\) −4.03355 + 7.00956i −0.407450 + 0.708072i
\(99\) 0 0
\(100\) −1.46234 + 2.53285i −0.146234 + 0.253285i
\(101\) 5.71320 + 9.89554i 0.568484 + 0.984643i 0.996716 + 0.0809746i \(0.0258033\pi\)
−0.428232 + 0.903669i \(0.640863\pi\)
\(102\) 0 0
\(103\) 19.3170 1.90336 0.951679 0.307094i \(-0.0993568\pi\)
0.951679 + 0.307094i \(0.0993568\pi\)
\(104\) −11.0955 0.387150i −1.08800 0.0379631i
\(105\) 0 0
\(106\) 12.9478 + 3.46936i 1.25760 + 0.336974i
\(107\) 4.59094 + 7.95175i 0.443823 + 0.768724i 0.997969 0.0636951i \(-0.0202885\pi\)
−0.554146 + 0.832419i \(0.686955\pi\)
\(108\) 0 0
\(109\) 1.79167 1.79167i 0.171610 0.171610i −0.616076 0.787687i \(-0.711279\pi\)
0.787687 + 0.616076i \(0.211279\pi\)
\(110\) −2.76134 + 0.739899i −0.263284 + 0.0705466i
\(111\) 0 0
\(112\) 2.25088 5.44516i 0.212688 0.514519i
\(113\) −1.25451 + 2.17288i −0.118015 + 0.204407i −0.918981 0.394302i \(-0.870986\pi\)
0.800966 + 0.598710i \(0.204320\pi\)
\(114\) 0 0
\(115\) −4.23779 1.13551i −0.395176 0.105887i
\(116\) 6.04906i 0.561641i
\(117\) 0 0
\(118\) 2.83506i 0.260989i
\(119\) −9.17871 + 1.21511i −0.841411 + 0.111389i
\(120\) 0 0
\(121\) 0.740817 + 0.427711i 0.0673470 + 0.0388828i
\(122\) −6.32249 6.32249i −0.572411 0.572411i
\(123\) 0 0
\(124\) 0.216230 + 0.806980i 0.0194180 + 0.0724689i
\(125\) −5.16186 + 5.16186i −0.461691 + 0.461691i
\(126\) 0 0
\(127\) −14.6248 + 8.44360i −1.29774 + 0.749249i −0.980013 0.198934i \(-0.936252\pi\)
−0.317724 + 0.948183i \(0.602919\pi\)
\(128\) −0.714478 + 2.66647i −0.0631515 + 0.235685i
\(129\) 0 0
\(130\) −3.09479 0.946077i −0.271431 0.0829764i
\(131\) 9.18546i 0.802537i 0.915960 + 0.401269i \(0.131431\pi\)
−0.915960 + 0.401269i \(0.868569\pi\)
\(132\) 0 0
\(133\) 13.1818 + 10.0997i 1.14301 + 0.875757i
\(134\) −7.15197 4.12919i −0.617836 0.356708i
\(135\) 0 0
\(136\) 10.4085 2.78894i 0.892519 0.239150i
\(137\) −6.08217 + 1.62971i −0.519635 + 0.139236i −0.509098 0.860709i \(-0.670021\pi\)
−0.0105372 + 0.999944i \(0.503354\pi\)
\(138\) 0 0
\(139\) −16.6243 9.59802i −1.41005 0.814093i −0.414658 0.909977i \(-0.636099\pi\)
−0.995393 + 0.0958840i \(0.969432\pi\)
\(140\) −0.831617 + 1.08540i −0.0702844 + 0.0917329i
\(141\) 0 0
\(142\) 11.2077i 0.940528i
\(143\) −5.39164 10.1395i −0.450872 0.847909i
\(144\) 0 0
\(145\) −1.82837 + 6.82358i −0.151838 + 0.566667i
\(146\) −10.9183 + 6.30369i −0.903606 + 0.521697i
\(147\) 0 0
\(148\) −0.274694 + 0.274694i −0.0225797 + 0.0225797i
\(149\) 2.99088 + 11.1621i 0.245022 + 0.914435i 0.973372 + 0.229230i \(0.0736207\pi\)
−0.728350 + 0.685205i \(0.759713\pi\)
\(150\) 0 0
\(151\) 8.90574 + 8.90574i 0.724738 + 0.724738i 0.969567 0.244828i \(-0.0787315\pi\)
−0.244828 + 0.969567i \(0.578732\pi\)
\(152\) −16.7374 9.66336i −1.35759 0.783802i
\(153\) 0 0
\(154\) 9.65151 1.27770i 0.777741 0.102960i
\(155\) 0.975662i 0.0783671i
\(156\) 0 0
\(157\) 5.49387i 0.438459i −0.975673 0.219229i \(-0.929646\pi\)
0.975673 0.219229i \(-0.0703543\pi\)
\(158\) −12.0733 3.23503i −0.960501 0.257365i
\(159\) 0 0
\(160\) 1.39277 2.41235i 0.110108 0.190713i
\(161\) 13.8080 + 5.70785i 1.08822 + 0.449841i
\(162\) 0 0
\(163\) 10.2964 2.75892i 0.806480 0.216096i 0.168053 0.985778i \(-0.446252\pi\)
0.638427 + 0.769682i \(0.279585\pi\)
\(164\) 1.28127 1.28127i 0.100050 0.100050i
\(165\) 0 0
\(166\) −8.44340 14.6244i −0.655335 1.13507i
\(167\) −12.5089 3.35175i −0.967967 0.259366i −0.259998 0.965609i \(-0.583722\pi\)
−0.707969 + 0.706243i \(0.750389\pi\)
\(168\) 0 0
\(169\) 0.906105 12.9684i 0.0697004 0.997568i
\(170\) 3.14098 0.240902
\(171\) 0 0
\(172\) −2.53843 4.39670i −0.193554 0.335245i
\(173\) −0.498608 + 0.863615i −0.0379085 + 0.0656594i −0.884357 0.466811i \(-0.845403\pi\)
0.846449 + 0.532470i \(0.178736\pi\)
\(174\) 0 0
\(175\) 9.22312 7.08769i 0.697202 0.535779i
\(176\) −6.85138 + 1.83582i −0.516442 + 0.138380i
\(177\) 0 0
\(178\) 7.27763 + 4.20174i 0.545482 + 0.314934i
\(179\) 4.88304 2.81922i 0.364975 0.210719i −0.306286 0.951940i \(-0.599086\pi\)
0.671261 + 0.741221i \(0.265753\pi\)
\(180\) 0 0
\(181\) −21.5094 −1.59878 −0.799390 0.600813i \(-0.794844\pi\)
−0.799390 + 0.600813i \(0.794844\pi\)
\(182\) 10.0321 + 4.56286i 0.743631 + 0.338222i
\(183\) 0 0
\(184\) −16.7965 4.50062i −1.23826 0.331790i
\(185\) −0.392894 + 0.226838i −0.0288862 + 0.0166774i
\(186\) 0 0
\(187\) 7.88147 + 7.88147i 0.576350 + 0.576350i
\(188\) 0.242639 0.0650150i 0.0176963 0.00474171i
\(189\) 0 0
\(190\) −3.98350 3.98350i −0.288993 0.288993i
\(191\) 4.39198 7.60714i 0.317793 0.550433i −0.662234 0.749297i \(-0.730392\pi\)
0.980027 + 0.198863i \(0.0637250\pi\)
\(192\) 0 0
\(193\) 0.249296 0.930384i 0.0179447 0.0669705i −0.956373 0.292149i \(-0.905630\pi\)
0.974318 + 0.225178i \(0.0722964\pi\)
\(194\) −0.842685 −0.0605013
\(195\) 0 0
\(196\) 3.28802 3.29749i 0.234859 0.235535i
\(197\) 16.6329 + 4.45678i 1.18505 + 0.317532i 0.796926 0.604076i \(-0.206458\pi\)
0.388120 + 0.921609i \(0.373124\pi\)
\(198\) 0 0
\(199\) −1.12555 + 1.94951i −0.0797883 + 0.138197i −0.903159 0.429307i \(-0.858758\pi\)
0.823370 + 0.567505i \(0.192091\pi\)
\(200\) −9.57249 + 9.57249i −0.676877 + 0.676877i
\(201\) 0 0
\(202\) 3.41670 + 12.7513i 0.240398 + 0.897179i
\(203\) 9.19063 22.2333i 0.645056 1.56047i
\(204\) 0 0
\(205\) 1.83259 1.05805i 0.127994 0.0738973i
\(206\) 21.5568 + 5.77613i 1.50194 + 0.402442i
\(207\) 0 0
\(208\) −7.67872 2.34738i −0.532423 0.162762i
\(209\) 19.9911i 1.38282i
\(210\) 0 0
\(211\) −10.3549 17.9352i −0.712859 1.23471i −0.963780 0.266700i \(-0.914067\pi\)
0.250921 0.968008i \(-0.419267\pi\)
\(212\) −6.68434 3.85920i −0.459082 0.265051i
\(213\) 0 0
\(214\) 2.74555 + 10.2465i 0.187682 + 0.700440i
\(215\) −1.53452 5.72691i −0.104653 0.390572i
\(216\) 0 0
\(217\) 0.431332 3.29459i 0.0292807 0.223651i
\(218\) 2.53516 1.46367i 0.171702 0.0991325i
\(219\) 0 0
\(220\) 1.64608 0.110979
\(221\) 2.83869 + 12.2941i 0.190951 + 0.826993i
\(222\) 0 0
\(223\) −5.92307 + 22.1052i −0.396638 + 1.48027i 0.422333 + 0.906441i \(0.361211\pi\)
−0.818972 + 0.573834i \(0.805455\pi\)
\(224\) −5.76954 + 7.53022i −0.385494 + 0.503134i
\(225\) 0 0
\(226\) −2.04971 + 2.04971i −0.136345 + 0.136345i
\(227\) 15.1087 4.04837i 1.00280 0.268699i 0.280182 0.959947i \(-0.409605\pi\)
0.722618 + 0.691248i \(0.242939\pi\)
\(228\) 0 0
\(229\) 3.61172 3.61172i 0.238669 0.238669i −0.577630 0.816299i \(-0.696022\pi\)
0.816299 + 0.577630i \(0.196022\pi\)
\(230\) −4.38963 2.53435i −0.289444 0.167110i
\(231\) 0 0
\(232\) −7.24678 + 27.0453i −0.475774 + 1.77561i
\(233\) 3.18656i 0.208758i 0.994538 + 0.104379i \(0.0332855\pi\)
−0.994538 + 0.104379i \(0.966714\pi\)
\(234\) 0 0
\(235\) 0.293358 0.0191366
\(236\) −0.422507 + 1.57682i −0.0275029 + 0.102642i
\(237\) 0 0
\(238\) −10.6063 1.38860i −0.687508 0.0900094i
\(239\) 1.61918 1.61918i 0.104736 0.104736i −0.652797 0.757533i \(-0.726404\pi\)
0.757533 + 0.652797i \(0.226404\pi\)
\(240\) 0 0
\(241\) −1.64242 6.12960i −0.105798 0.394842i 0.892637 0.450777i \(-0.148853\pi\)
−0.998434 + 0.0559344i \(0.982186\pi\)
\(242\) 0.698823 + 0.698823i 0.0449221 + 0.0449221i
\(243\) 0 0
\(244\) 2.57423 + 4.45870i 0.164798 + 0.285439i
\(245\) 4.70571 2.72587i 0.300637 0.174149i
\(246\) 0 0
\(247\) 11.9917 19.1920i 0.763016 1.22116i
\(248\) 3.86705i 0.245558i
\(249\) 0 0
\(250\) −7.30388 + 4.21690i −0.461938 + 0.266700i
\(251\) −10.7306 + 18.5859i −0.677308 + 1.17313i 0.298481 + 0.954416i \(0.403520\pi\)
−0.975789 + 0.218716i \(0.929813\pi\)
\(252\) 0 0
\(253\) −4.65534 17.3740i −0.292679 1.09229i
\(254\) −18.8453 + 5.04959i −1.18246 + 0.316839i
\(255\) 0 0
\(256\) 7.00174 12.1274i 0.437609 0.757961i
\(257\) 14.1914 + 24.5801i 0.885232 + 1.53327i 0.845447 + 0.534059i \(0.179334\pi\)
0.0397853 + 0.999208i \(0.487333\pi\)
\(258\) 0 0
\(259\) 1.42700 0.592283i 0.0886692 0.0368027i
\(260\) 1.58028 + 0.987406i 0.0980048 + 0.0612364i
\(261\) 0 0
\(262\) −2.74662 + 10.2505i −0.169687 + 0.633280i
\(263\) −6.33755 10.9770i −0.390790 0.676868i 0.601764 0.798674i \(-0.294465\pi\)
−0.992554 + 0.121806i \(0.961131\pi\)
\(264\) 0 0
\(265\) −6.37373 6.37373i −0.391535 0.391535i
\(266\) 11.6903 + 15.2124i 0.716777 + 0.932733i
\(267\) 0 0
\(268\) 3.36244 + 3.36244i 0.205394 + 0.205394i
\(269\) −5.62758 3.24908i −0.343120 0.198100i 0.318531 0.947912i \(-0.396810\pi\)
−0.661651 + 0.749812i \(0.730144\pi\)
\(270\) 0 0
\(271\) −6.14616 1.64686i −0.373353 0.100040i 0.0672633 0.997735i \(-0.478573\pi\)
−0.440616 + 0.897696i \(0.645240\pi\)
\(272\) 7.79332 0.472539
\(273\) 0 0
\(274\) −7.27473 −0.439482
\(275\) −13.5258 3.62423i −0.815636 0.218549i
\(276\) 0 0
\(277\) 15.6622 + 9.04260i 0.941053 + 0.543317i 0.890290 0.455394i \(-0.150501\pi\)
0.0507626 + 0.998711i \(0.483835\pi\)
\(278\) −15.6819 15.6819i −0.940538 0.940538i
\(279\) 0 0
\(280\) −5.01847 + 3.85654i −0.299911 + 0.230472i
\(281\) 6.43538 + 6.43538i 0.383903 + 0.383903i 0.872506 0.488603i \(-0.162493\pi\)
−0.488603 + 0.872506i \(0.662493\pi\)
\(282\) 0 0
\(283\) 7.33715 + 12.7083i 0.436148 + 0.755431i 0.997389 0.0722219i \(-0.0230090\pi\)
−0.561240 + 0.827653i \(0.689676\pi\)
\(284\) 1.67027 6.23354i 0.0991124 0.369892i
\(285\) 0 0
\(286\) −2.98491 12.9274i −0.176502 0.764414i
\(287\) −6.65599 + 2.76261i −0.392891 + 0.163072i
\(288\) 0 0
\(289\) 2.37677 + 4.11668i 0.139810 + 0.242158i
\(290\) −4.08075 + 7.06807i −0.239630 + 0.415051i
\(291\) 0 0
\(292\) 7.01203 1.87887i 0.410348 0.109952i
\(293\) −1.69762 6.33562i −0.0991763 0.370131i 0.898443 0.439090i \(-0.144699\pi\)
−0.997620 + 0.0689587i \(0.978032\pi\)
\(294\) 0 0
\(295\) −0.953209 + 1.65101i −0.0554980 + 0.0961253i
\(296\) −1.55724 + 0.899074i −0.0905129 + 0.0522576i
\(297\) 0 0
\(298\) 13.3507i 0.773385i
\(299\) 5.95258 19.4720i 0.344246 1.12609i
\(300\) 0 0
\(301\) 2.64990 + 20.0168i 0.152738 + 1.15375i
\(302\) 7.27540 + 12.6014i 0.418652 + 0.725127i
\(303\) 0 0
\(304\) −9.88377 9.88377i −0.566873 0.566873i
\(305\) 1.55616 + 5.80767i 0.0891055 + 0.332546i
\(306\) 0 0
\(307\) 23.5768 23.5768i 1.34560 1.34560i 0.455225 0.890377i \(-0.349559\pi\)
0.890377 0.455225i \(-0.150441\pi\)
\(308\) −5.55843 0.727718i −0.316721 0.0414656i
\(309\) 0 0
\(310\) −0.291741 + 1.08879i −0.0165698 + 0.0618393i
\(311\) 2.90579 0.164772 0.0823861 0.996600i \(-0.473746\pi\)
0.0823861 + 0.996600i \(0.473746\pi\)
\(312\) 0 0
\(313\) 0.960626i 0.0542978i −0.999631 0.0271489i \(-0.991357\pi\)
0.999631 0.0271489i \(-0.00864282\pi\)
\(314\) 1.64277 6.13090i 0.0927069 0.345987i
\(315\) 0 0
\(316\) 6.23287 + 3.59855i 0.350626 + 0.202434i
\(317\) 23.7216 23.7216i 1.33234 1.33234i 0.429064 0.903274i \(-0.358844\pi\)
0.903274 0.429064i \(-0.141156\pi\)
\(318\) 0 0
\(319\) −27.9751 + 7.49590i −1.56630 + 0.419690i
\(320\) 4.72235 4.72235i 0.263988 0.263988i
\(321\) 0 0
\(322\) 13.7023 + 10.4985i 0.763602 + 0.585061i
\(323\) −5.68489 + 21.2163i −0.316316 + 1.18051i
\(324\) 0 0
\(325\) −10.8111 11.5928i −0.599692 0.643055i
\(326\) 12.3153 0.682082
\(327\) 0 0
\(328\) 7.26351 4.19359i 0.401060 0.231552i
\(329\) −0.990602 0.129691i −0.0546137 0.00715010i
\(330\) 0 0
\(331\) 3.27417 + 12.2194i 0.179965 + 0.671637i 0.995653 + 0.0931447i \(0.0296919\pi\)
−0.815688 + 0.578492i \(0.803641\pi\)
\(332\) 2.51662 + 9.39217i 0.138118 + 0.515462i
\(333\) 0 0
\(334\) −12.9571 7.48078i −0.708981 0.409330i
\(335\) 2.77665 + 4.80929i 0.151704 + 0.262760i
\(336\) 0 0
\(337\) 12.8172i 0.698196i −0.937086 0.349098i \(-0.886488\pi\)
0.937086 0.349098i \(-0.113512\pi\)
\(338\) 4.88896 14.2012i 0.265924 0.772441i
\(339\) 0 0
\(340\) −1.74696 0.468097i −0.0947423 0.0253861i
\(341\) −3.46410 + 2.00000i −0.187591 + 0.108306i
\(342\) 0 0
\(343\) −17.0952 + 7.12427i −0.923052 + 0.384675i
\(344\) −6.08209 22.6987i −0.327925 1.22383i
\(345\) 0 0
\(346\) −0.814660 + 0.814660i −0.0437964 + 0.0437964i
\(347\) 9.29372 16.0972i 0.498913 0.864143i −0.501086 0.865397i \(-0.667066\pi\)
0.999999 + 0.00125445i \(0.000399304\pi\)
\(348\) 0 0
\(349\) −4.62637 1.23963i −0.247644 0.0663560i 0.132862 0.991135i \(-0.457583\pi\)
−0.380506 + 0.924779i \(0.624250\pi\)
\(350\) 12.4119 5.15164i 0.663445 0.275367i
\(351\) 0 0
\(352\) 11.4201 0.608693
\(353\) −3.19876 + 11.9379i −0.170253 + 0.635392i 0.827059 + 0.562116i \(0.190012\pi\)
−0.997312 + 0.0732769i \(0.976654\pi\)
\(354\) 0 0
\(355\) 3.76826 6.52683i 0.199999 0.346408i
\(356\) −3.42152 3.42152i −0.181340 0.181340i
\(357\) 0 0
\(358\) 6.29224 1.68600i 0.332555 0.0891079i
\(359\) −4.20137 4.20137i −0.221740 0.221740i 0.587491 0.809231i \(-0.300116\pi\)
−0.809231 + 0.587491i \(0.800116\pi\)
\(360\) 0 0
\(361\) 17.6626 10.1975i 0.929608 0.536710i
\(362\) −24.0035 6.43171i −1.26159 0.338043i
\(363\) 0 0
\(364\) −4.89971 4.03287i −0.256815 0.211380i
\(365\) 8.47775 0.443746
\(366\) 0 0
\(367\) −5.05707 + 2.91970i −0.263977 + 0.152407i −0.626147 0.779705i \(-0.715369\pi\)
0.362170 + 0.932112i \(0.382036\pi\)
\(368\) −10.8914 6.28818i −0.567756 0.327794i
\(369\) 0 0
\(370\) −0.506280 + 0.135657i −0.0263202 + 0.00705249i
\(371\) 18.7048 + 24.3404i 0.971106 + 1.26369i
\(372\) 0 0
\(373\) −5.17801 + 8.96858i −0.268107 + 0.464375i −0.968373 0.249507i \(-0.919731\pi\)
0.700266 + 0.713882i \(0.253065\pi\)
\(374\) 6.43864 + 11.1521i 0.332934 + 0.576659i
\(375\) 0 0
\(376\) 1.16273 0.0599632
\(377\) −31.3532 9.58469i −1.61477 0.493636i
\(378\) 0 0
\(379\) 6.76845 + 1.81360i 0.347672 + 0.0931584i 0.428429 0.903575i \(-0.359067\pi\)
−0.0807572 + 0.996734i \(0.525734\pi\)
\(380\) 1.62190 + 2.80922i 0.0832018 + 0.144110i
\(381\) 0 0
\(382\) 7.17592 7.17592i 0.367152 0.367152i
\(383\) −7.14098 + 1.91342i −0.364887 + 0.0977711i −0.436604 0.899654i \(-0.643819\pi\)
0.0717170 + 0.997425i \(0.477152\pi\)
\(384\) 0 0
\(385\) −6.05017 2.50097i −0.308345 0.127461i
\(386\) 0.556404 0.963720i 0.0283202 0.0490521i
\(387\) 0 0
\(388\) 0.468688 + 0.125585i 0.0237940 + 0.00637559i
\(389\) 10.2280i 0.518581i 0.965799 + 0.259290i \(0.0834886\pi\)
−0.965799 + 0.259290i \(0.916511\pi\)
\(390\) 0 0
\(391\) 19.7626i 0.999436i
\(392\) 18.6511 10.8040i 0.942025 0.545686i
\(393\) 0 0
\(394\) 17.2289 + 9.94711i 0.867979 + 0.501128i
\(395\) 5.94323 + 5.94323i 0.299037 + 0.299037i
\(396\) 0 0
\(397\) 7.30250 + 27.2533i 0.366502 + 1.36780i 0.865373 + 0.501128i \(0.167081\pi\)
−0.498872 + 0.866676i \(0.666252\pi\)
\(398\) −1.83900 + 1.83900i −0.0921810 + 0.0921810i
\(399\) 0 0
\(400\) −8.47910 + 4.89541i −0.423955 + 0.244770i
\(401\) 1.82731 6.81960i 0.0912514 0.340555i −0.905173 0.425043i \(-0.860259\pi\)
0.996424 + 0.0844884i \(0.0269256\pi\)
\(402\) 0 0
\(403\) −4.52532 0.157900i −0.225422 0.00786558i
\(404\) 7.60126i 0.378177i
\(405\) 0 0
\(406\) 16.9045 22.0632i 0.838955 1.09498i
\(407\) −1.61078 0.929982i −0.0798432 0.0460975i
\(408\) 0 0
\(409\) 30.3999 8.14562i 1.50318 0.402775i 0.589014 0.808123i \(-0.299516\pi\)
0.914163 + 0.405348i \(0.132850\pi\)
\(410\) 2.36146 0.632752i 0.116624 0.0312494i
\(411\) 0 0
\(412\) −11.1288 6.42519i −0.548274 0.316546i
\(413\) 3.94866 5.15366i 0.194301 0.253595i
\(414\) 0 0
\(415\) 11.3554i 0.557415i
\(416\) 10.9636 + 6.85037i 0.537534 + 0.335867i
\(417\) 0 0
\(418\) 5.97772 22.3092i 0.292380 1.09118i
\(419\) −20.4187 + 11.7887i −0.997519 + 0.575918i −0.907513 0.420023i \(-0.862022\pi\)
−0.0900058 + 0.995941i \(0.528689\pi\)
\(420\) 0 0
\(421\) 4.63273 4.63273i 0.225785 0.225785i −0.585144 0.810929i \(-0.698962\pi\)
0.810929 + 0.585144i \(0.198962\pi\)
\(422\) −6.19260 23.1111i −0.301451 1.12503i
\(423\) 0 0
\(424\) −25.2624 25.2624i −1.22685 1.22685i
\(425\) 13.3241 + 7.69267i 0.646314 + 0.373149i
\(426\) 0 0
\(427\) −2.68727 20.2991i −0.130046 0.982343i
\(428\) 6.10813i 0.295248i
\(429\) 0 0
\(430\) 6.84981i 0.330327i
\(431\) −27.8082 7.45118i −1.33947 0.358911i −0.483234 0.875491i \(-0.660538\pi\)
−0.856239 + 0.516580i \(0.827205\pi\)
\(432\) 0 0
\(433\) −1.92063 + 3.32663i −0.0922998 + 0.159868i −0.908478 0.417932i \(-0.862755\pi\)
0.816179 + 0.577800i \(0.196088\pi\)
\(434\) 1.46649 3.54763i 0.0703937 0.170291i
\(435\) 0 0
\(436\) −1.62814 + 0.436260i −0.0779739 + 0.0208930i
\(437\) 25.0636 25.0636i 1.19895 1.19895i
\(438\) 0 0
\(439\) 7.29107 + 12.6285i 0.347984 + 0.602726i 0.985891 0.167388i \(-0.0535331\pi\)
−0.637907 + 0.770113i \(0.720200\pi\)
\(440\) 7.35963 + 1.97201i 0.350857 + 0.0940118i
\(441\) 0 0
\(442\) −0.508333 + 14.5685i −0.0241789 + 0.692953i
\(443\) −32.2060 −1.53015 −0.765076 0.643940i \(-0.777299\pi\)
−0.765076 + 0.643940i \(0.777299\pi\)
\(444\) 0 0
\(445\) −2.82543 4.89379i −0.133938 0.231988i
\(446\) −13.2197 + 22.8973i −0.625973 + 1.08422i
\(447\) 0 0
\(448\) −18.0340 + 13.8586i −0.852027 + 0.654756i
\(449\) 19.3546 5.18606i 0.913402 0.244745i 0.228639 0.973511i \(-0.426572\pi\)
0.684763 + 0.728766i \(0.259906\pi\)
\(450\) 0 0
\(451\) 7.51321 + 4.33776i 0.353783 + 0.204257i
\(452\) 1.44548 0.834549i 0.0679897 0.0392539i
\(453\) 0 0
\(454\) 18.0711 0.848120
\(455\) −4.30811 6.03021i −0.201967 0.282701i
\(456\) 0 0
\(457\) 14.5061 + 3.88690i 0.678567 + 0.181822i 0.581611 0.813467i \(-0.302423\pi\)
0.0969563 + 0.995289i \(0.469089\pi\)
\(458\) 5.11049 2.95054i 0.238797 0.137870i
\(459\) 0 0
\(460\) 2.06375 + 2.06375i 0.0962228 + 0.0962228i
\(461\) 29.9515 8.02549i 1.39498 0.373784i 0.518441 0.855113i \(-0.326512\pi\)
0.876540 + 0.481329i \(0.159846\pi\)
\(462\) 0 0
\(463\) 3.61564 + 3.61564i 0.168033 + 0.168033i 0.786114 0.618081i \(-0.212090\pi\)
−0.618081 + 0.786114i \(0.712090\pi\)
\(464\) −10.1251 + 17.5371i −0.470044 + 0.814141i
\(465\) 0 0
\(466\) −0.952840 + 3.55605i −0.0441395 + 0.164731i
\(467\) 17.6775 0.818017 0.409009 0.912530i \(-0.365875\pi\)
0.409009 + 0.912530i \(0.365875\pi\)
\(468\) 0 0
\(469\) −7.24994 17.4674i −0.334771 0.806569i
\(470\) 0.327374 + 0.0877195i 0.0151006 + 0.00404620i
\(471\) 0 0
\(472\) −3.77806 + 6.54379i −0.173899 + 0.301202i
\(473\) 17.1878 17.1878i 0.790297 0.790297i
\(474\) 0 0
\(475\) −7.14198 26.6542i −0.327696 1.22298i
\(476\) 5.69214 + 2.35297i 0.260899 + 0.107848i
\(477\) 0 0
\(478\) 2.29110 1.32276i 0.104792 0.0605018i
\(479\) −19.1281 5.12537i −0.873987 0.234184i −0.206176 0.978515i \(-0.566102\pi\)
−0.667811 + 0.744331i \(0.732769\pi\)
\(480\) 0 0
\(481\) −0.988534 1.85904i −0.0450733 0.0847647i
\(482\) 7.33146i 0.333939i
\(483\) 0 0
\(484\) −0.284529 0.492819i −0.0129332 0.0224009i
\(485\) 0.490740 + 0.283329i 0.0222834 + 0.0128653i
\(486\) 0 0
\(487\) 10.1291 + 37.8022i 0.458992 + 1.71298i 0.676080 + 0.736828i \(0.263677\pi\)
−0.217089 + 0.976152i \(0.569656\pi\)
\(488\) 6.16787 + 23.0188i 0.279206 + 1.04201i
\(489\) 0 0
\(490\) 6.06643 1.63485i 0.274054 0.0738548i
\(491\) −16.0715 + 9.27889i −0.725297 + 0.418750i −0.816699 0.577064i \(-0.804198\pi\)
0.0914021 + 0.995814i \(0.470865\pi\)
\(492\) 0 0
\(493\) 31.8212 1.43315
\(494\) 19.1210 17.8316i 0.860293 0.802282i
\(495\) 0 0
\(496\) −0.723862 + 2.70149i −0.0325023 + 0.121300i
\(497\) −15.6100 + 20.3737i −0.700204 + 0.913883i
\(498\) 0 0
\(499\) 3.54363 3.54363i 0.158635 0.158635i −0.623327 0.781962i \(-0.714219\pi\)
0.781962 + 0.623327i \(0.214219\pi\)
\(500\) 4.69074 1.25688i 0.209776 0.0562094i
\(501\) 0 0
\(502\) −17.5323 + 17.5323i −0.782507 + 0.782507i
\(503\) 2.98438 + 1.72303i 0.133067 + 0.0768262i 0.565056 0.825053i \(-0.308855\pi\)
−0.431989 + 0.901879i \(0.642188\pi\)
\(504\) 0 0
\(505\) 2.29754 8.57453i 0.102239 0.381561i
\(506\) 20.7805i 0.923808i
\(507\) 0 0
\(508\) 11.2340 0.498428
\(509\) −7.93556 + 29.6159i −0.351737 + 1.31270i 0.532803 + 0.846239i \(0.321138\pi\)
−0.884541 + 0.466463i \(0.845528\pi\)
\(510\) 0 0
\(511\) −28.6274 3.74794i −1.26640 0.165799i
\(512\) 15.3439 15.3439i 0.678111 0.678111i
\(513\) 0 0
\(514\) 8.48696 + 31.6738i 0.374344 + 1.39707i
\(515\) −10.6116 10.6116i −0.467604 0.467604i
\(516\) 0 0
\(517\) 0.601351 + 1.04157i 0.0264474 + 0.0458082i
\(518\) 1.76956 0.234261i 0.0777501 0.0102929i
\(519\) 0 0
\(520\) 5.88252 + 6.30787i 0.257966 + 0.276619i
\(521\) 13.0906i 0.573510i 0.958004 + 0.286755i \(0.0925766\pi\)
−0.958004 + 0.286755i \(0.907423\pi\)
\(522\) 0 0
\(523\) −29.9435 + 17.2879i −1.30934 + 0.755946i −0.981985 0.188957i \(-0.939489\pi\)
−0.327351 + 0.944903i \(0.606156\pi\)
\(524\) 3.05526 5.29186i 0.133469 0.231176i
\(525\) 0 0
\(526\) −3.79009 14.1448i −0.165256 0.616743i
\(527\) 4.24513 1.13748i 0.184921 0.0495494i
\(528\) 0 0
\(529\) 4.44578 7.70032i 0.193295 0.334797i
\(530\) −5.20691 9.01864i −0.226174 0.391745i
\(531\) 0 0
\(532\) −4.23486 10.2031i −0.183604 0.442360i
\(533\) 4.61086 + 8.67118i 0.199719 + 0.375590i
\(534\) 0 0
\(535\) 1.84623 6.89022i 0.0798194 0.297890i
\(536\) 11.0053 + 19.0617i 0.475355 + 0.823340i
\(537\) 0 0
\(538\) −5.30857 5.30857i −0.228869 0.228869i
\(539\) 19.3244 + 11.1199i 0.832360 + 0.478969i
\(540\) 0 0
\(541\) 23.6775 + 23.6775i 1.01797 + 1.01797i 0.999835 + 0.0181382i \(0.00577388\pi\)
0.0181382 + 0.999835i \(0.494226\pi\)
\(542\) −6.36638 3.67563i −0.273460 0.157882i
\(543\) 0 0
\(544\) −12.1200 3.24754i −0.519640 0.139237i
\(545\) −1.96847 −0.0843201
\(546\) 0 0
\(547\) −9.25725 −0.395811 −0.197906 0.980221i \(-0.563414\pi\)
−0.197906 + 0.980221i \(0.563414\pi\)
\(548\) 4.04609 + 1.08415i 0.172840 + 0.0463124i
\(549\) 0 0
\(550\) −14.0104 8.08893i −0.597407 0.344913i
\(551\) −40.3567 40.3567i −1.71926 1.71926i
\(552\) 0 0
\(553\) −17.4415 22.6964i −0.741687 0.965148i
\(554\) 14.7744 + 14.7744i 0.627705 + 0.627705i
\(555\) 0 0
\(556\) 6.38496 + 11.0591i 0.270783 + 0.469009i
\(557\) −2.46966 + 9.21689i −0.104643 + 0.390532i −0.998304 0.0582092i \(-0.981461\pi\)
0.893662 + 0.448742i \(0.148128\pi\)
\(558\) 0 0
\(559\) 26.8109 6.19058i 1.13398 0.261834i
\(560\) −4.22775 + 1.75475i −0.178655 + 0.0741518i
\(561\) 0 0
\(562\) 5.25728 + 9.10588i 0.221765 + 0.384108i
\(563\) 1.08829 1.88498i 0.0458661 0.0794424i −0.842181 0.539195i \(-0.818729\pi\)
0.888047 + 0.459753i \(0.152062\pi\)
\(564\) 0 0
\(565\) 1.88281 0.504497i 0.0792104 0.0212244i
\(566\) 4.38789 + 16.3758i 0.184437 + 0.688327i
\(567\) 0 0
\(568\) 14.9356 25.8692i 0.626683 1.08545i
\(569\) −20.3648 + 11.7576i −0.853738 + 0.492906i −0.861910 0.507061i \(-0.830732\pi\)
0.00817222 + 0.999967i \(0.497399\pi\)
\(570\) 0 0
\(571\) 13.2414i 0.554134i −0.960851 0.277067i \(-0.910638\pi\)
0.960851 0.277067i \(-0.0893624\pi\)
\(572\) −0.266400 + 7.63486i −0.0111388 + 0.319230i
\(573\) 0 0
\(574\) −8.25385 + 1.09268i −0.344509 + 0.0456074i
\(575\) −12.4139 21.5016i −0.517697 0.896678i
\(576\) 0 0
\(577\) 1.10520 + 1.10520i 0.0460102 + 0.0460102i 0.729738 0.683727i \(-0.239642\pi\)
−0.683727 + 0.729738i \(0.739642\pi\)
\(578\) 1.42140 + 5.30472i 0.0591223 + 0.220647i
\(579\) 0 0
\(580\) 3.32300 3.32300i 0.137980 0.137980i
\(581\) 5.02013 38.3446i 0.208270 1.59080i
\(582\) 0 0
\(583\) 9.56454 35.6954i 0.396123 1.47835i
\(584\) 33.6017 1.39045
\(585\) 0 0
\(586\) 7.57788i 0.313039i
\(587\) 6.57121 24.5241i 0.271223 1.01222i −0.687108 0.726556i \(-0.741120\pi\)
0.958331 0.285662i \(-0.0922133\pi\)
\(588\) 0 0
\(589\) −6.82642 3.94124i −0.281278 0.162396i
\(590\) −1.55742 + 1.55742i −0.0641179 + 0.0641179i
\(591\) 0 0
\(592\) −1.25617 + 0.336590i −0.0516283 + 0.0138338i
\(593\) 13.5799 13.5799i 0.557660 0.557660i −0.370981 0.928641i \(-0.620978\pi\)
0.928641 + 0.370981i \(0.120978\pi\)
\(594\) 0 0
\(595\) 5.70976 + 4.37474i 0.234077 + 0.179347i
\(596\) 1.98964 7.42545i 0.0814989 0.304158i
\(597\) 0 0
\(598\) 12.4653 19.9499i 0.509743 0.815810i
\(599\) 6.33246 0.258737 0.129369 0.991597i \(-0.458705\pi\)
0.129369 + 0.991597i \(0.458705\pi\)
\(600\) 0 0
\(601\) −20.1592 + 11.6389i −0.822309 + 0.474760i −0.851212 0.524822i \(-0.824132\pi\)
0.0289030 + 0.999582i \(0.490799\pi\)
\(602\) −3.02824 + 23.1302i −0.123422 + 0.942717i
\(603\) 0 0
\(604\) −2.16849 8.09292i −0.0882347 0.329296i
\(605\) −0.172002 0.641921i −0.00699288 0.0260978i
\(606\) 0 0
\(607\) −9.09221 5.24939i −0.369041 0.213066i 0.303998 0.952673i \(-0.401678\pi\)
−0.673040 + 0.739607i \(0.735012\pi\)
\(608\) 11.2523 + 19.4896i 0.456343 + 0.790409i
\(609\) 0 0
\(610\) 6.94641i 0.281252i
\(611\) −0.0474768 + 1.36066i −0.00192071 + 0.0550462i
\(612\) 0 0
\(613\) −8.40441 2.25196i −0.339451 0.0909556i 0.0850667 0.996375i \(-0.472890\pi\)
−0.424518 + 0.905420i \(0.639556\pi\)
\(614\) 33.3606 19.2607i 1.34632 0.777300i
\(615\) 0 0
\(616\) −23.9800 9.91264i −0.966180 0.399392i
\(617\) −7.98973 29.8181i −0.321654 1.20043i −0.917633 0.397430i \(-0.869902\pi\)
0.595978 0.803000i \(-0.296764\pi\)
\(618\) 0 0
\(619\) −2.31233 + 2.31233i −0.0929403 + 0.0929403i −0.752048 0.659108i \(-0.770934\pi\)
0.659108 + 0.752048i \(0.270934\pi\)
\(620\) 0.324524 0.562091i 0.0130332 0.0225741i
\(621\) 0 0
\(622\) 3.24272 + 0.868885i 0.130021 + 0.0348391i
\(623\) 7.37733 + 17.7743i 0.295566 + 0.712112i
\(624\) 0 0
\(625\) −16.3110 −0.652440
\(626\) 0.287245 1.07201i 0.0114806 0.0428462i
\(627\) 0 0
\(628\) −1.82737 + 3.16509i −0.0729198 + 0.126301i
\(629\) 1.44503 + 1.44503i 0.0576173 + 0.0576173i
\(630\) 0 0
\(631\) 5.07213 1.35907i 0.201918 0.0541039i −0.156442 0.987687i \(-0.550003\pi\)
0.358361 + 0.933583i \(0.383336\pi\)
\(632\) 23.5561 + 23.5561i 0.937011 + 0.937011i
\(633\) 0 0
\(634\) 33.5654 19.3790i 1.33305 0.769638i
\(635\) 12.6724 + 3.39556i 0.502889 + 0.134749i
\(636\) 0 0
\(637\) 11.8816 + 22.2672i 0.470765 + 0.882259i
\(638\) −33.4603 −1.32471
\(639\) 0 0
\(640\) 1.85729 1.07231i 0.0734160 0.0423867i
\(641\) 28.4420 + 16.4210i 1.12339 + 0.648589i 0.942264 0.334871i \(-0.108693\pi\)
0.181126 + 0.983460i \(0.442026\pi\)
\(642\) 0 0
\(643\) −35.7163 + 9.57017i −1.40852 + 0.377411i −0.881395 0.472380i \(-0.843395\pi\)
−0.527120 + 0.849791i \(0.676728\pi\)
\(644\) −6.05644 7.88117i −0.238657 0.310562i
\(645\) 0 0
\(646\) −12.6881 + 21.9765i −0.499208 + 0.864653i
\(647\) −24.0363 41.6322i −0.944966 1.63673i −0.755819 0.654780i \(-0.772761\pi\)
−0.189147 0.981949i \(-0.560572\pi\)
\(648\) 0 0
\(649\) −7.81588 −0.306800
\(650\) −8.59821 16.1698i −0.337249 0.634231i
\(651\) 0 0
\(652\) −6.84958 1.83534i −0.268250 0.0718775i
\(653\) −17.6801 30.6228i −0.691876 1.19836i −0.971223 0.238174i \(-0.923451\pi\)
0.279347 0.960190i \(-0.409882\pi\)
\(654\) 0 0
\(655\) 5.04595 5.04595i 0.197162 0.197162i
\(656\) 5.85921 1.56997i 0.228764 0.0612970i
\(657\) 0 0
\(658\) −1.06669 0.440938i −0.0415837 0.0171895i
\(659\) −14.6210 + 25.3243i −0.569554 + 0.986496i 0.427056 + 0.904225i \(0.359551\pi\)
−0.996610 + 0.0822711i \(0.973783\pi\)
\(660\) 0 0
\(661\) 21.1225 + 5.65976i 0.821570 + 0.220139i 0.645033 0.764155i \(-0.276844\pi\)
0.176537 + 0.984294i \(0.443510\pi\)
\(662\) 14.6153i 0.568038i
\(663\) 0 0
\(664\) 45.0073i 1.74662i
\(665\) −1.69312 12.7895i −0.0656565 0.495956i
\(666\) 0 0
\(667\) −44.4713 25.6755i −1.72193 0.994159i
\(668\) 6.09168 + 6.09168i 0.235694 + 0.235694i
\(669\) 0 0
\(670\) 1.66054 + 6.19721i 0.0641521 + 0.239419i
\(671\) −17.4302 + 17.4302i −0.672886 + 0.672886i
\(672\) 0 0
\(673\) −6.52213 + 3.76555i −0.251409 + 0.145151i −0.620409 0.784278i \(-0.713034\pi\)
0.369000 + 0.929429i \(0.379700\pi\)
\(674\) 3.83258 14.3034i 0.147625 0.550945i
\(675\) 0 0
\(676\) −4.83555 + 7.16986i −0.185983 + 0.275764i
\(677\) 30.7509i 1.18185i 0.806726 + 0.590926i \(0.201237\pi\)
−0.806726 + 0.590926i \(0.798763\pi\)
\(678\) 0 0
\(679\) −1.53186 1.17369i −0.0587873 0.0450420i
\(680\) −7.24989 4.18573i −0.278021 0.160515i
\(681\) 0 0
\(682\) −4.46380 + 1.19607i −0.170928 + 0.0458000i
\(683\) −14.8258 + 3.97256i −0.567293 + 0.152006i −0.531055 0.847338i \(-0.678204\pi\)
−0.0362380 + 0.999343i \(0.511537\pi\)
\(684\) 0 0
\(685\) 4.23646 + 2.44592i 0.161867 + 0.0934538i
\(686\) −21.2077 + 2.83858i −0.809713 + 0.108377i
\(687\) 0 0
\(688\) 16.9956i 0.647951i
\(689\) 30.5942 28.5311i 1.16555 1.08695i
\(690\) 0 0
\(691\) 12.7049 47.4152i 0.483316 1.80376i −0.104212 0.994555i \(-0.533232\pi\)
0.587528 0.809204i \(-0.300101\pi\)
\(692\) 0.574509 0.331693i 0.0218396 0.0126091i
\(693\) 0 0
\(694\) 15.1847 15.1847i 0.576404 0.576404i
\(695\) 3.85980 + 14.4050i 0.146411 + 0.546412i
\(696\) 0 0
\(697\) −6.74013 6.74013i −0.255301 0.255301i
\(698\) −4.79214 2.76674i −0.181385 0.104723i
\(699\) 0 0
\(700\) −7.67105 + 1.01552i −0.289939 + 0.0383832i
\(701\) 40.9218i 1.54559i 0.634653 + 0.772797i \(0.281143\pi\)
−0.634653 + 0.772797i \(0.718857\pi\)
\(702\) 0 0
\(703\) 3.66529i 0.138239i
\(704\) 26.4470 + 7.08646i 0.996760 + 0.267081i
\(705\) 0 0
\(706\) −7.13933 + 12.3657i −0.268692 + 0.465389i
\(707\) −11.5490 + 27.9385i −0.434344 + 1.05073i
\(708\) 0 0
\(709\) −20.0521 + 5.37294i −0.753071 + 0.201785i −0.614880 0.788621i \(-0.710796\pi\)
−0.138191 + 0.990406i \(0.544129\pi\)
\(710\) 6.15685 6.15685i 0.231062 0.231062i
\(711\) 0 0
\(712\) −11.1986 19.3966i −0.419687 0.726919i
\(713\) −6.85053 1.83559i −0.256554 0.0687435i
\(714\) 0 0
\(715\) −2.60820 + 8.53191i −0.0975413 + 0.319075i
\(716\) −3.75090 −0.140178
\(717\) 0 0
\(718\) −3.43224 5.94482i −0.128090 0.221859i
\(719\) −6.50138 + 11.2607i −0.242461 + 0.419954i −0.961415 0.275103i \(-0.911288\pi\)
0.718954 + 0.695058i \(0.244621\pi\)
\(720\) 0 0
\(721\) 31.1417 + 40.5243i 1.15978 + 1.50920i
\(722\) 22.7598 6.09847i 0.847033 0.226962i
\(723\) 0 0
\(724\) 12.3918 + 7.15442i 0.460539 + 0.265892i
\(725\) −34.6213 + 19.9886i −1.28580 + 0.742359i
\(726\) 0 0
\(727\) 9.09604 0.337353 0.168677 0.985671i \(-0.446051\pi\)
0.168677 + 0.985671i \(0.446051\pi\)
\(728\) −17.0752 23.9008i −0.632851 0.885824i
\(729\) 0 0
\(730\) 9.46076 + 2.53500i 0.350159 + 0.0938247i
\(731\) −23.1289 + 13.3535i −0.855453 + 0.493896i
\(732\) 0 0
\(733\) 24.5299 + 24.5299i 0.906033 + 0.906033i 0.995949 0.0899161i \(-0.0286599\pi\)
−0.0899161 + 0.995949i \(0.528660\pi\)
\(734\) −6.51649 + 1.74609i −0.240528 + 0.0644493i
\(735\) 0 0
\(736\) 14.3178 + 14.3178i 0.527760 + 0.527760i
\(737\) −11.3836 + 19.7170i −0.419321 + 0.726285i
\(738\) 0 0
\(739\) −12.5301 + 46.7628i −0.460926 + 1.72020i 0.209130 + 0.977888i \(0.432937\pi\)
−0.670056 + 0.742311i \(0.733730\pi\)
\(740\) 0.301802 0.0110945
\(741\) 0 0
\(742\) 13.5955 + 32.7558i 0.499106 + 1.20250i
\(743\) 11.2679 + 3.01923i 0.413379 + 0.110765i 0.459514 0.888171i \(-0.348024\pi\)
−0.0461346 + 0.998935i \(0.514690\pi\)
\(744\) 0 0
\(745\) 4.48879 7.77482i 0.164457 0.284847i
\(746\) −8.46019 + 8.46019i −0.309749 + 0.309749i
\(747\) 0 0
\(748\) −1.91909 7.16214i −0.0701689 0.261874i
\(749\) −9.28039 + 22.4505i −0.339098 + 0.820322i
\(750\) 0 0
\(751\) −12.9544 + 7.47922i −0.472712 + 0.272921i −0.717374 0.696688i \(-0.754656\pi\)
0.244662 + 0.969608i \(0.421323\pi\)
\(752\) 0.812272 + 0.217648i 0.0296205 + 0.00793679i
\(753\) 0 0
\(754\) −32.1227 20.0713i −1.16984 0.730952i
\(755\) 9.78458i 0.356097i
\(756\) 0 0
\(757\) 13.2377 + 22.9284i 0.481134 + 0.833348i 0.999766 0.0216496i \(-0.00689182\pi\)
−0.518632 + 0.854998i \(0.673558\pi\)
\(758\) 7.01097 + 4.04778i 0.254650 + 0.147022i
\(759\) 0 0
\(760\) 3.88608 + 14.5031i 0.140963 + 0.526081i
\(761\) −10.6129 39.6079i −0.384718 1.43579i −0.838611 0.544731i \(-0.816632\pi\)
0.453893 0.891056i \(-0.350035\pi\)
\(762\) 0 0
\(763\) 6.64708 + 0.870244i 0.240640 + 0.0315050i
\(764\) −5.06055 + 2.92171i −0.183084 + 0.105704i
\(765\) 0 0
\(766\) −8.54114 −0.308604
\(767\) −7.50344 4.68838i −0.270934 0.169288i
\(768\) 0 0
\(769\) −0.837092 + 3.12407i −0.0301863 + 0.112657i −0.979375 0.202050i \(-0.935240\pi\)
0.949189 + 0.314707i \(0.101906\pi\)
\(770\) −6.00387 4.60008i −0.216365 0.165775i
\(771\) 0 0
\(772\) −0.453085 + 0.453085i −0.0163069 + 0.0163069i
\(773\) −20.3857 + 5.46232i −0.733221 + 0.196466i −0.606063 0.795417i \(-0.707252\pi\)
−0.127158 + 0.991882i \(0.540585\pi\)
\(774\) 0 0
\(775\) −3.90417 + 3.90417i −0.140242 + 0.140242i
\(776\) 1.94506 + 1.12298i 0.0698234 + 0.0403126i
\(777\) 0 0
\(778\) −3.05836 + 11.4140i −0.109648 + 0.409211i
\(779\) 17.0962i 0.612533i
\(780\) 0 0
\(781\) 30.8980 1.10562
\(782\) −5.90937 + 22.0541i −0.211319 + 0.788652i
\(783\) 0 0
\(784\) 15.0519 4.05634i 0.537568 0.144869i
\(785\) −3.01801 + 3.01801i −0.107718 + 0.107718i
\(786\) 0 0
\(787\) −12.5317 46.7690i −0.446707 1.66713i −0.711389 0.702798i \(-0.751934\pi\)
0.264682 0.964336i \(-0.414733\pi\)
\(788\) −8.10003 8.10003i −0.288552