Properties

Label 819.2.et.c.271.2
Level $819$
Weight $2$
Character 819.271
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 271.2
Character \(\chi\) \(=\) 819.271
Dual form 819.2.et.c.136.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.12005 - 1.12005i) q^{2} +0.509024i q^{4} +(0.973479 + 3.63307i) q^{5} +(2.28455 + 1.33448i) q^{7} +(-1.66997 + 1.66997i) q^{8} +O(q^{10})\) \(q+(-1.12005 - 1.12005i) q^{2} +0.509024i q^{4} +(0.973479 + 3.63307i) q^{5} +(2.28455 + 1.33448i) q^{7} +(-1.66997 + 1.66997i) q^{8} +(2.97888 - 5.15957i) q^{10} +(-0.872699 - 3.25696i) q^{11} +(-3.03769 + 1.94228i) q^{13} +(-1.06413 - 4.05349i) q^{14} +4.75894 q^{16} +3.33792 q^{17} +(0.733837 + 0.196631i) q^{19} +(-1.84932 + 0.495525i) q^{20} +(-2.67049 + 4.62542i) q^{22} +3.56245i q^{23} +(-7.92144 + 4.57345i) q^{25} +(5.57781 + 1.22692i) q^{26} +(-0.679283 + 1.16289i) q^{28} +(1.42199 + 2.46295i) q^{29} +(-8.90596 - 2.38635i) q^{31} +(-1.99032 - 1.99032i) q^{32} +(-3.73864 - 3.73864i) q^{34} +(-2.62430 + 9.59903i) q^{35} +(-8.01070 + 8.01070i) q^{37} +(-0.601698 - 1.04217i) q^{38} +(-7.69280 - 4.44144i) q^{40} +(-6.84386 - 1.83381i) q^{41} +(10.9295 + 6.31017i) q^{43} +(1.65787 - 0.444225i) q^{44} +(3.99012 - 3.99012i) q^{46} +(-1.32905 + 0.356118i) q^{47} +(3.43833 + 6.09737i) q^{49} +(13.9949 + 3.74992i) q^{50} +(-0.988666 - 1.54626i) q^{52} +(3.59290 + 6.22308i) q^{53} +(10.9832 - 6.34116i) q^{55} +(-6.04366 + 1.58659i) q^{56} +(1.16593 - 4.35132i) q^{58} +(2.23105 + 2.23105i) q^{59} +(0.902515 - 0.521067i) q^{61} +(7.30230 + 12.6480i) q^{62} -5.05937i q^{64} +(-10.0136 - 9.14539i) q^{65} +(2.85760 - 0.765690i) q^{67} +1.69908i q^{68} +(13.6907 - 7.81204i) q^{70} +(7.00412 - 1.87675i) q^{71} +(0.559835 - 2.08933i) q^{73} +17.9448 q^{74} +(-0.100090 + 0.373541i) q^{76} +(2.35262 - 8.60528i) q^{77} +(-5.54357 + 9.60175i) q^{79} +(4.63273 + 17.2896i) q^{80} +(5.61151 + 9.71942i) q^{82} +(1.51210 - 1.51210i) q^{83} +(3.24940 + 12.1269i) q^{85} +(-5.17392 - 19.3093i) q^{86} +(6.89639 + 3.98163i) q^{88} +(2.23766 + 2.23766i) q^{89} +(-9.53168 + 0.383488i) q^{91} -1.81337 q^{92} +(1.88747 + 1.08973i) q^{94} +2.85750i q^{95} +(-3.23001 - 12.0545i) q^{97} +(2.97826 - 10.6805i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.12005 1.12005i −0.791995 0.791995i 0.189823 0.981818i \(-0.439208\pi\)
−0.981818 + 0.189823i \(0.939208\pi\)
\(3\) 0 0
\(4\) 0.509024i 0.254512i
\(5\) 0.973479 + 3.63307i 0.435353 + 1.62476i 0.740219 + 0.672365i \(0.234722\pi\)
−0.304866 + 0.952395i \(0.598612\pi\)
\(6\) 0 0
\(7\) 2.28455 + 1.33448i 0.863478 + 0.504386i
\(8\) −1.66997 + 1.66997i −0.590423 + 0.590423i
\(9\) 0 0
\(10\) 2.97888 5.15957i 0.942005 1.63160i
\(11\) −0.872699 3.25696i −0.263129 0.982010i −0.963386 0.268119i \(-0.913598\pi\)
0.700257 0.713891i \(-0.253069\pi\)
\(12\) 0 0
\(13\) −3.03769 + 1.94228i −0.842504 + 0.538690i
\(14\) −1.06413 4.05349i −0.284400 1.08334i
\(15\) 0 0
\(16\) 4.75894 1.18974
\(17\) 3.33792 0.809565 0.404782 0.914413i \(-0.367347\pi\)
0.404782 + 0.914413i \(0.367347\pi\)
\(18\) 0 0
\(19\) 0.733837 + 0.196631i 0.168354 + 0.0451103i 0.342011 0.939696i \(-0.388892\pi\)
−0.173657 + 0.984806i \(0.555559\pi\)
\(20\) −1.84932 + 0.495525i −0.413521 + 0.110803i
\(21\) 0 0
\(22\) −2.67049 + 4.62542i −0.569350 + 0.986143i
\(23\) 3.56245i 0.742822i 0.928469 + 0.371411i \(0.121126\pi\)
−0.928469 + 0.371411i \(0.878874\pi\)
\(24\) 0 0
\(25\) −7.92144 + 4.57345i −1.58429 + 0.914690i
\(26\) 5.57781 + 1.22692i 1.09390 + 0.240619i
\(27\) 0 0
\(28\) −0.679283 + 1.16289i −0.128372 + 0.219766i
\(29\) 1.42199 + 2.46295i 0.264056 + 0.457358i 0.967316 0.253574i \(-0.0816063\pi\)
−0.703260 + 0.710933i \(0.748273\pi\)
\(30\) 0 0
\(31\) −8.90596 2.38635i −1.59956 0.428600i −0.654649 0.755933i \(-0.727184\pi\)
−0.944909 + 0.327332i \(0.893850\pi\)
\(32\) −1.99032 1.99032i −0.351842 0.351842i
\(33\) 0 0
\(34\) −3.73864 3.73864i −0.641171 0.641171i
\(35\) −2.62430 + 9.59903i −0.443588 + 1.62253i
\(36\) 0 0
\(37\) −8.01070 + 8.01070i −1.31695 + 1.31695i −0.400775 + 0.916177i \(0.631259\pi\)
−0.916177 + 0.400775i \(0.868741\pi\)
\(38\) −0.601698 1.04217i −0.0976083 0.169063i
\(39\) 0 0
\(40\) −7.69280 4.44144i −1.21634 0.702253i
\(41\) −6.84386 1.83381i −1.06883 0.286393i −0.318819 0.947816i \(-0.603286\pi\)
−0.750013 + 0.661423i \(0.769953\pi\)
\(42\) 0 0
\(43\) 10.9295 + 6.31017i 1.66674 + 0.962291i 0.969379 + 0.245568i \(0.0789746\pi\)
0.697358 + 0.716723i \(0.254359\pi\)
\(44\) 1.65787 0.444225i 0.249933 0.0669695i
\(45\) 0 0
\(46\) 3.99012 3.99012i 0.588311 0.588311i
\(47\) −1.32905 + 0.356118i −0.193862 + 0.0519452i −0.354444 0.935077i \(-0.615330\pi\)
0.160582 + 0.987023i \(0.448663\pi\)
\(48\) 0 0
\(49\) 3.43833 + 6.09737i 0.491190 + 0.871052i
\(50\) 13.9949 + 3.74992i 1.97918 + 0.530319i
\(51\) 0 0
\(52\) −0.988666 1.54626i −0.137103 0.214427i
\(53\) 3.59290 + 6.22308i 0.493523 + 0.854806i 0.999972 0.00746338i \(-0.00237569\pi\)
−0.506450 + 0.862270i \(0.669042\pi\)
\(54\) 0 0
\(55\) 10.9832 6.34116i 1.48098 0.855042i
\(56\) −6.04366 + 1.58659i −0.807618 + 0.212016i
\(57\) 0 0
\(58\) 1.16593 4.35132i 0.153095 0.571357i
\(59\) 2.23105 + 2.23105i 0.290458 + 0.290458i 0.837261 0.546803i \(-0.184156\pi\)
−0.546803 + 0.837261i \(0.684156\pi\)
\(60\) 0 0
\(61\) 0.902515 0.521067i 0.115555 0.0667158i −0.441108 0.897454i \(-0.645415\pi\)
0.556664 + 0.830738i \(0.312081\pi\)
\(62\) 7.30230 + 12.6480i 0.927393 + 1.60629i
\(63\) 0 0
\(64\) 5.05937i 0.632421i
\(65\) −10.0136 9.14539i −1.24203 1.13435i
\(66\) 0 0
\(67\) 2.85760 0.765690i 0.349111 0.0935440i −0.0800024 0.996795i \(-0.525493\pi\)
0.429113 + 0.903251i \(0.358826\pi\)
\(68\) 1.69908i 0.206044i
\(69\) 0 0
\(70\) 13.6907 7.81204i 1.63636 0.933717i
\(71\) 7.00412 1.87675i 0.831236 0.222729i 0.181983 0.983302i \(-0.441748\pi\)
0.649253 + 0.760573i \(0.275082\pi\)
\(72\) 0 0
\(73\) 0.559835 2.08933i 0.0655238 0.244538i −0.925394 0.379006i \(-0.876266\pi\)
0.990918 + 0.134468i \(0.0429326\pi\)
\(74\) 17.9448 2.08604
\(75\) 0 0
\(76\) −0.100090 + 0.373541i −0.0114811 + 0.0428481i
\(77\) 2.35262 8.60528i 0.268106 0.980663i
\(78\) 0 0
\(79\) −5.54357 + 9.60175i −0.623700 + 1.08028i 0.365090 + 0.930972i \(0.381038\pi\)
−0.988791 + 0.149309i \(0.952295\pi\)
\(80\) 4.63273 + 17.2896i 0.517955 + 1.93304i
\(81\) 0 0
\(82\) 5.61151 + 9.71942i 0.619688 + 1.07333i
\(83\) 1.51210 1.51210i 0.165975 0.165975i −0.619233 0.785208i \(-0.712556\pi\)
0.785208 + 0.619233i \(0.212556\pi\)
\(84\) 0 0
\(85\) 3.24940 + 12.1269i 0.352447 + 1.31535i
\(86\) −5.17392 19.3093i −0.557918 2.08218i
\(87\) 0 0
\(88\) 6.89639 + 3.98163i 0.735158 + 0.424444i
\(89\) 2.23766 + 2.23766i 0.237192 + 0.237192i 0.815686 0.578494i \(-0.196360\pi\)
−0.578494 + 0.815686i \(0.696360\pi\)
\(90\) 0 0
\(91\) −9.53168 + 0.383488i −0.999192 + 0.0402005i
\(92\) −1.81337 −0.189057
\(93\) 0 0
\(94\) 1.88747 + 1.08973i 0.194678 + 0.112397i
\(95\) 2.85750i 0.293174i
\(96\) 0 0
\(97\) −3.23001 12.0545i −0.327957 1.22395i −0.911305 0.411731i \(-0.864924\pi\)
0.583348 0.812222i \(-0.301742\pi\)
\(98\) 2.97826 10.6805i 0.300849 1.07889i
\(99\) 0 0
\(100\) −2.32800 4.03221i −0.232800 0.403221i
\(101\) 2.19617 3.80388i 0.218527 0.378500i −0.735831 0.677165i \(-0.763208\pi\)
0.954358 + 0.298665i \(0.0965415\pi\)
\(102\) 0 0
\(103\) 6.67838 11.5673i 0.658040 1.13976i −0.323082 0.946371i \(-0.604719\pi\)
0.981122 0.193389i \(-0.0619478\pi\)
\(104\) 1.82931 8.31638i 0.179378 0.815488i
\(105\) 0 0
\(106\) 2.94594 10.9944i 0.286135 1.06787i
\(107\) −0.177558 −0.0171652 −0.00858260 0.999963i \(-0.502732\pi\)
−0.00858260 + 0.999963i \(0.502732\pi\)
\(108\) 0 0
\(109\) −1.34434 + 5.01713i −0.128764 + 0.480554i −0.999946 0.0104068i \(-0.996687\pi\)
0.871182 + 0.490960i \(0.163354\pi\)
\(110\) −19.4042 5.19933i −1.85012 0.495737i
\(111\) 0 0
\(112\) 10.8720 + 6.35071i 1.02731 + 0.600086i
\(113\) −10.0079 + 17.3342i −0.941462 + 1.63066i −0.178778 + 0.983889i \(0.557215\pi\)
−0.762684 + 0.646771i \(0.776119\pi\)
\(114\) 0 0
\(115\) −12.9426 + 3.46797i −1.20691 + 0.323390i
\(116\) −1.25370 + 0.723825i −0.116403 + 0.0672055i
\(117\) 0 0
\(118\) 4.99777i 0.460082i
\(119\) 7.62564 + 4.45439i 0.699042 + 0.408333i
\(120\) 0 0
\(121\) −0.319891 + 0.184689i −0.0290810 + 0.0167899i
\(122\) −1.59448 0.427240i −0.144358 0.0386805i
\(123\) 0 0
\(124\) 1.21471 4.53335i 0.109084 0.407107i
\(125\) −11.0291 11.0291i −0.986469 0.986469i
\(126\) 0 0
\(127\) 6.74547 3.89450i 0.598564 0.345581i −0.169913 0.985459i \(-0.554349\pi\)
0.768476 + 0.639878i \(0.221015\pi\)
\(128\) −9.64739 + 9.64739i −0.852717 + 0.852717i
\(129\) 0 0
\(130\) 0.972393 + 21.4590i 0.0852845 + 1.88208i
\(131\) −8.40782 4.85426i −0.734595 0.424118i 0.0855060 0.996338i \(-0.472749\pi\)
−0.820101 + 0.572219i \(0.806083\pi\)
\(132\) 0 0
\(133\) 1.41409 + 1.42850i 0.122617 + 0.123867i
\(134\) −4.05826 2.34304i −0.350580 0.202408i
\(135\) 0 0
\(136\) −5.57422 + 5.57422i −0.477985 + 0.477985i
\(137\) 6.42607 6.42607i 0.549017 0.549017i −0.377140 0.926156i \(-0.623092\pi\)
0.926156 + 0.377140i \(0.123092\pi\)
\(138\) 0 0
\(139\) 8.85473 + 5.11228i 0.751048 + 0.433618i 0.826073 0.563564i \(-0.190570\pi\)
−0.0750244 + 0.997182i \(0.523903\pi\)
\(140\) −4.88614 1.33583i −0.412954 0.112899i
\(141\) 0 0
\(142\) −9.94701 5.74291i −0.834735 0.481934i
\(143\) 8.97690 + 8.19861i 0.750686 + 0.685602i
\(144\) 0 0
\(145\) −7.56381 + 7.56381i −0.628140 + 0.628140i
\(146\) −2.96720 + 1.71311i −0.245567 + 0.141778i
\(147\) 0 0
\(148\) −4.07764 4.07764i −0.335180 0.335180i
\(149\) −3.88850 + 14.5121i −0.318559 + 1.18888i 0.602072 + 0.798442i \(0.294342\pi\)
−0.920630 + 0.390435i \(0.872325\pi\)
\(150\) 0 0
\(151\) −0.268230 0.0718719i −0.0218282 0.00584885i 0.247888 0.968789i \(-0.420263\pi\)
−0.269717 + 0.962940i \(0.586930\pi\)
\(152\) −1.55385 + 0.897117i −0.126034 + 0.0727658i
\(153\) 0 0
\(154\) −12.2734 + 7.00329i −0.989018 + 0.564341i
\(155\) 34.6791i 2.78549i
\(156\) 0 0
\(157\) 0.272321 0.157225i 0.0217336 0.0125479i −0.489094 0.872231i \(-0.662672\pi\)
0.510827 + 0.859683i \(0.329339\pi\)
\(158\) 16.9635 4.54536i 1.34954 0.361609i
\(159\) 0 0
\(160\) 5.29344 9.16852i 0.418484 0.724835i
\(161\) −4.75401 + 8.13859i −0.374669 + 0.641410i
\(162\) 0 0
\(163\) −0.911958 0.244358i −0.0714300 0.0191396i 0.222927 0.974835i \(-0.428439\pi\)
−0.294357 + 0.955696i \(0.595105\pi\)
\(164\) 0.933452 3.48369i 0.0728904 0.272031i
\(165\) 0 0
\(166\) −3.38726 −0.262903
\(167\) −0.626601 + 2.33851i −0.0484878 + 0.180959i −0.985923 0.167202i \(-0.946527\pi\)
0.937435 + 0.348161i \(0.113194\pi\)
\(168\) 0 0
\(169\) 5.45513 11.8001i 0.419626 0.907697i
\(170\) 9.94326 17.2222i 0.762614 1.32089i
\(171\) 0 0
\(172\) −3.21203 + 5.56340i −0.244915 + 0.424205i
\(173\) −8.61076 14.9143i −0.654664 1.13391i −0.981978 0.188996i \(-0.939477\pi\)
0.327314 0.944916i \(-0.393857\pi\)
\(174\) 0 0
\(175\) −24.2001 0.122737i −1.82936 0.00927805i
\(176\) −4.15313 15.4997i −0.313054 1.16833i
\(177\) 0 0
\(178\) 5.01259i 0.375710i
\(179\) −2.98125 1.72123i −0.222829 0.128651i 0.384430 0.923154i \(-0.374398\pi\)
−0.607260 + 0.794503i \(0.707731\pi\)
\(180\) 0 0
\(181\) 25.9767 1.93084 0.965418 0.260708i \(-0.0839561\pi\)
0.965418 + 0.260708i \(0.0839561\pi\)
\(182\) 11.1055 + 10.2464i 0.823193 + 0.759516i
\(183\) 0 0
\(184\) −5.94917 5.94917i −0.438579 0.438579i
\(185\) −36.9017 21.3052i −2.71307 1.56639i
\(186\) 0 0
\(187\) −2.91300 10.8715i −0.213020 0.795000i
\(188\) −0.181273 0.676520i −0.0132207 0.0493403i
\(189\) 0 0
\(190\) 3.20055 3.20055i 0.232192 0.232192i
\(191\) 1.49154 + 2.58342i 0.107924 + 0.186930i 0.914929 0.403615i \(-0.132246\pi\)
−0.807005 + 0.590544i \(0.798913\pi\)
\(192\) 0 0
\(193\) 0.676598 + 2.52510i 0.0487026 + 0.181761i 0.985992 0.166791i \(-0.0533404\pi\)
−0.937290 + 0.348551i \(0.886674\pi\)
\(194\) −9.88393 + 17.1195i −0.709624 + 1.22911i
\(195\) 0 0
\(196\) −3.10371 + 1.75019i −0.221693 + 0.125014i
\(197\) −0.213689 + 0.797498i −0.0152247 + 0.0568194i −0.973120 0.230297i \(-0.926030\pi\)
0.957896 + 0.287117i \(0.0926968\pi\)
\(198\) 0 0
\(199\) −8.20173 −0.581405 −0.290703 0.956813i \(-0.593889\pi\)
−0.290703 + 0.956813i \(0.593889\pi\)
\(200\) 5.59104 20.8661i 0.395347 1.47545i
\(201\) 0 0
\(202\) −6.72036 + 1.80071i −0.472843 + 0.126698i
\(203\) −0.0381616 + 7.52434i −0.00267842 + 0.528105i
\(204\) 0 0
\(205\) 26.6494i 1.86128i
\(206\) −20.4361 + 5.47583i −1.42385 + 0.381519i
\(207\) 0 0
\(208\) −14.4562 + 9.24318i −1.00236 + 0.640899i
\(209\) 2.56168i 0.177195i
\(210\) 0 0
\(211\) 5.37441 + 9.30875i 0.369989 + 0.640841i 0.989563 0.144098i \(-0.0460280\pi\)
−0.619574 + 0.784938i \(0.712695\pi\)
\(212\) −3.16770 + 1.82887i −0.217559 + 0.125608i
\(213\) 0 0
\(214\) 0.198874 + 0.198874i 0.0135947 + 0.0135947i
\(215\) −12.2856 + 45.8506i −0.837873 + 3.12699i
\(216\) 0 0
\(217\) −17.1616 17.3365i −1.16500 1.17688i
\(218\) 7.12516 4.11371i 0.482576 0.278616i
\(219\) 0 0
\(220\) 3.22781 + 5.59072i 0.217619 + 0.376927i
\(221\) −10.1396 + 6.48316i −0.682061 + 0.436105i
\(222\) 0 0
\(223\) 5.74055 + 1.53818i 0.384416 + 0.103004i 0.445851 0.895107i \(-0.352901\pi\)
−0.0614354 + 0.998111i \(0.519568\pi\)
\(224\) −1.89094 7.20302i −0.126344 0.481272i
\(225\) 0 0
\(226\) 30.6245 8.20580i 2.03711 0.545842i
\(227\) 14.4159 14.4159i 0.956815 0.956815i −0.0422908 0.999105i \(-0.513466\pi\)
0.999105 + 0.0422908i \(0.0134656\pi\)
\(228\) 0 0
\(229\) −8.29019 + 2.22135i −0.547831 + 0.146791i −0.522110 0.852878i \(-0.674855\pi\)
−0.0257212 + 0.999669i \(0.508188\pi\)
\(230\) 18.3807 + 10.6121i 1.21199 + 0.699741i
\(231\) 0 0
\(232\) −6.48772 1.73838i −0.425939 0.114130i
\(233\) −4.35471 2.51419i −0.285286 0.164710i 0.350528 0.936552i \(-0.386002\pi\)
−0.635814 + 0.771842i \(0.719336\pi\)
\(234\) 0 0
\(235\) −2.58761 4.48187i −0.168797 0.292365i
\(236\) −1.13566 + 1.13566i −0.0739250 + 0.0739250i
\(237\) 0 0
\(238\) −3.55197 13.5302i −0.230240 0.877035i
\(239\) 11.6568 + 11.6568i 0.754018 + 0.754018i 0.975227 0.221208i \(-0.0710001\pi\)
−0.221208 + 0.975227i \(0.571000\pi\)
\(240\) 0 0
\(241\) 3.99187 + 3.99187i 0.257139 + 0.257139i 0.823889 0.566751i \(-0.191800\pi\)
−0.566751 + 0.823889i \(0.691800\pi\)
\(242\) 0.565154 + 0.151433i 0.0363295 + 0.00973446i
\(243\) 0 0
\(244\) 0.265236 + 0.459402i 0.0169800 + 0.0294102i
\(245\) −18.8050 + 18.4274i −1.20141 + 1.17728i
\(246\) 0 0
\(247\) −2.61108 + 0.828010i −0.166139 + 0.0526850i
\(248\) 18.8578 10.8875i 1.19747 0.691360i
\(249\) 0 0
\(250\) 24.7062i 1.56256i
\(251\) 5.54226 9.59948i 0.349825 0.605914i −0.636394 0.771365i \(-0.719575\pi\)
0.986218 + 0.165451i \(0.0529079\pi\)
\(252\) 0 0
\(253\) 11.6027 3.10894i 0.729458 0.195458i
\(254\) −11.9173 3.19323i −0.747758 0.200361i
\(255\) 0 0
\(256\) 11.4924 0.718273
\(257\) 2.40321 0.149908 0.0749540 0.997187i \(-0.476119\pi\)
0.0749540 + 0.997187i \(0.476119\pi\)
\(258\) 0 0
\(259\) −28.9910 + 7.61073i −1.80141 + 0.472908i
\(260\) 4.65523 5.09715i 0.288705 0.316112i
\(261\) 0 0
\(262\) 3.98017 + 14.8542i 0.245896 + 0.917695i
\(263\) −13.0623 + 22.6246i −0.805456 + 1.39509i 0.110527 + 0.993873i \(0.464746\pi\)
−0.915983 + 0.401218i \(0.868587\pi\)
\(264\) 0 0
\(265\) −19.1113 + 19.1113i −1.17400 + 1.17400i
\(266\) 0.0161477 3.18385i 0.000990079 0.195214i
\(267\) 0 0
\(268\) 0.389755 + 1.45459i 0.0238081 + 0.0888530i
\(269\) 26.4202i 1.61087i −0.592684 0.805435i \(-0.701932\pi\)
0.592684 0.805435i \(-0.298068\pi\)
\(270\) 0 0
\(271\) −5.35562 5.35562i −0.325330 0.325330i 0.525477 0.850808i \(-0.323887\pi\)
−0.850808 + 0.525477i \(0.823887\pi\)
\(272\) 15.8850 0.963168
\(273\) 0 0
\(274\) −14.3950 −0.869637
\(275\) 21.8086 + 21.8086i 1.31511 + 1.31511i
\(276\) 0 0
\(277\) 22.5430i 1.35448i −0.735764 0.677238i \(-0.763177\pi\)
0.735764 0.677238i \(-0.236823\pi\)
\(278\) −4.19173 15.6437i −0.251403 0.938250i
\(279\) 0 0
\(280\) −11.6476 20.4126i −0.696075 1.21988i
\(281\) 7.73479 7.73479i 0.461419 0.461419i −0.437701 0.899120i \(-0.644207\pi\)
0.899120 + 0.437701i \(0.144207\pi\)
\(282\) 0 0
\(283\) 8.86524 15.3550i 0.526984 0.912763i −0.472522 0.881319i \(-0.656656\pi\)
0.999506 0.0314437i \(-0.0100105\pi\)
\(284\) 0.955310 + 3.56527i 0.0566872 + 0.211560i
\(285\) 0 0
\(286\) −0.871725 19.2374i −0.0515462 1.13753i
\(287\) −13.1880 13.3224i −0.778461 0.786397i
\(288\) 0 0
\(289\) −5.85829 −0.344605
\(290\) 16.9437 0.994968
\(291\) 0 0
\(292\) 1.06352 + 0.284970i 0.0622379 + 0.0166766i
\(293\) 12.4507 3.33616i 0.727379 0.194901i 0.123917 0.992293i \(-0.460454\pi\)
0.603462 + 0.797392i \(0.293788\pi\)
\(294\) 0 0
\(295\) −5.93368 + 10.2774i −0.345472 + 0.598376i
\(296\) 26.7552i 1.55512i
\(297\) 0 0
\(298\) 20.6096 11.8990i 1.19388 0.689288i
\(299\) −6.91925 10.8216i −0.400151 0.625830i
\(300\) 0 0
\(301\) 16.5483 + 29.0011i 0.953826 + 1.67160i
\(302\) 0.219930 + 0.380931i 0.0126556 + 0.0219201i
\(303\) 0 0
\(304\) 3.49229 + 0.935756i 0.200297 + 0.0536693i
\(305\) 2.77166 + 2.77166i 0.158705 + 0.158705i
\(306\) 0 0
\(307\) −5.82305 5.82305i −0.332339 0.332339i 0.521135 0.853474i \(-0.325509\pi\)
−0.853474 + 0.521135i \(0.825509\pi\)
\(308\) 4.38030 + 1.19754i 0.249591 + 0.0682362i
\(309\) 0 0
\(310\) −38.8423 + 38.8423i −2.20610 + 2.20610i
\(311\) 13.5284 + 23.4318i 0.767124 + 1.32870i 0.939116 + 0.343600i \(0.111646\pi\)
−0.171992 + 0.985098i \(0.555020\pi\)
\(312\) 0 0
\(313\) 11.8883 + 6.86374i 0.671969 + 0.387962i 0.796822 0.604214i \(-0.206513\pi\)
−0.124853 + 0.992175i \(0.539846\pi\)
\(314\) −0.481113 0.128914i −0.0271508 0.00727502i
\(315\) 0 0
\(316\) −4.88752 2.82181i −0.274945 0.158739i
\(317\) −2.23807 + 0.599689i −0.125702 + 0.0336819i −0.321122 0.947038i \(-0.604060\pi\)
0.195419 + 0.980720i \(0.437393\pi\)
\(318\) 0 0
\(319\) 6.78076 6.78076i 0.379650 0.379650i
\(320\) 18.3811 4.92519i 1.02753 0.275327i
\(321\) 0 0
\(322\) 14.4404 3.79089i 0.804730 0.211258i
\(323\) 2.44949 + 0.656339i 0.136293 + 0.0365197i
\(324\) 0 0
\(325\) 15.1800 29.2783i 0.842035 1.62407i
\(326\) 0.747745 + 1.29513i 0.0414138 + 0.0717307i
\(327\) 0 0
\(328\) 14.4914 8.36663i 0.800155 0.461970i
\(329\) −3.51152 0.960022i −0.193596 0.0529277i
\(330\) 0 0
\(331\) 6.68605 24.9527i 0.367498 1.37152i −0.496504 0.868035i \(-0.665383\pi\)
0.864002 0.503488i \(-0.167950\pi\)
\(332\) 0.769698 + 0.769698i 0.0422427 + 0.0422427i
\(333\) 0 0
\(334\) 3.32107 1.91742i 0.181721 0.104917i
\(335\) 5.56362 + 9.63647i 0.303973 + 0.526497i
\(336\) 0 0
\(337\) 32.4074i 1.76534i −0.469990 0.882672i \(-0.655743\pi\)
0.469990 0.882672i \(-0.344257\pi\)
\(338\) −19.3267 + 7.10664i −1.05123 + 0.386550i
\(339\) 0 0
\(340\) −6.17289 + 1.65402i −0.334772 + 0.0897019i
\(341\) 31.0889i 1.68356i
\(342\) 0 0
\(343\) −0.281778 + 18.5181i −0.0152146 + 0.999884i
\(344\) −28.7897 + 7.71418i −1.55224 + 0.415921i
\(345\) 0 0
\(346\) −7.06025 + 26.3492i −0.379562 + 1.41654i
\(347\) 31.0215 1.66532 0.832660 0.553784i \(-0.186817\pi\)
0.832660 + 0.553784i \(0.186817\pi\)
\(348\) 0 0
\(349\) 0.142223 0.530784i 0.00761303 0.0284122i −0.962015 0.272997i \(-0.911985\pi\)
0.969628 + 0.244585i \(0.0786517\pi\)
\(350\) 26.9679 + 27.2428i 1.44149 + 1.45619i
\(351\) 0 0
\(352\) −4.74544 + 8.21934i −0.252933 + 0.438092i
\(353\) −3.20193 11.9498i −0.170422 0.636022i −0.997286 0.0736213i \(-0.976544\pi\)
0.826865 0.562401i \(-0.190122\pi\)
\(354\) 0 0
\(355\) 13.6367 + 23.6195i 0.723762 + 1.25359i
\(356\) −1.13903 + 1.13903i −0.0603682 + 0.0603682i
\(357\) 0 0
\(358\) 1.41129 + 5.26701i 0.0745891 + 0.278370i
\(359\) −1.88465 7.03362i −0.0994682 0.371220i 0.898191 0.439606i \(-0.144882\pi\)
−0.997659 + 0.0683856i \(0.978215\pi\)
\(360\) 0 0
\(361\) −15.9546 9.21141i −0.839717 0.484811i
\(362\) −29.0952 29.0952i −1.52921 1.52921i
\(363\) 0 0
\(364\) −0.195205 4.85186i −0.0102315 0.254306i
\(365\) 8.13569 0.425842
\(366\) 0 0
\(367\) 3.73411 + 2.15589i 0.194919 + 0.112536i 0.594283 0.804256i \(-0.297436\pi\)
−0.399364 + 0.916792i \(0.630769\pi\)
\(368\) 16.9535i 0.883761i
\(369\) 0 0
\(370\) 17.4689 + 65.1947i 0.908163 + 3.38931i
\(371\) −0.0964222 + 19.0116i −0.00500599 + 0.987032i
\(372\) 0 0
\(373\) 8.58752 + 14.8740i 0.444645 + 0.770147i 0.998027 0.0627799i \(-0.0199966\pi\)
−0.553383 + 0.832927i \(0.686663\pi\)
\(374\) −8.91388 + 15.4393i −0.460926 + 0.798347i
\(375\) 0 0
\(376\) 1.62477 2.81418i 0.0837909 0.145130i
\(377\) −9.10328 4.71980i −0.468843 0.243082i
\(378\) 0 0
\(379\) 0.602843 2.24984i 0.0309659 0.115566i −0.948713 0.316139i \(-0.897613\pi\)
0.979679 + 0.200572i \(0.0642801\pi\)
\(380\) −1.45454 −0.0746163
\(381\) 0 0
\(382\) 1.22296 4.56415i 0.0625721 0.233522i
\(383\) 26.6204 + 7.13293i 1.36024 + 0.364476i 0.863905 0.503655i \(-0.168012\pi\)
0.496336 + 0.868130i \(0.334678\pi\)
\(384\) 0 0
\(385\) 33.5538 + 0.170177i 1.71006 + 0.00867302i
\(386\) 2.07041 3.58606i 0.105381 0.182526i
\(387\) 0 0
\(388\) 6.13606 1.64415i 0.311511 0.0834691i
\(389\) 10.7596 6.21203i 0.545531 0.314962i −0.201787 0.979430i \(-0.564675\pi\)
0.747318 + 0.664467i \(0.231341\pi\)
\(390\) 0 0
\(391\) 11.8912i 0.601362i
\(392\) −15.9243 4.44051i −0.804299 0.224279i
\(393\) 0 0
\(394\) 1.13258 0.653895i 0.0570585 0.0329428i
\(395\) −40.2804 10.7931i −2.02673 0.543060i
\(396\) 0 0
\(397\) −8.36351 + 31.2130i −0.419752 + 1.56654i 0.355369 + 0.934726i \(0.384355\pi\)
−0.775122 + 0.631812i \(0.782312\pi\)
\(398\) 9.18635 + 9.18635i 0.460470 + 0.460470i
\(399\) 0 0
\(400\) −37.6977 + 21.7648i −1.88488 + 1.08824i
\(401\) 9.95929 9.95929i 0.497343 0.497343i −0.413267 0.910610i \(-0.635612\pi\)
0.910610 + 0.413267i \(0.135612\pi\)
\(402\) 0 0
\(403\) 31.6885 10.0489i 1.57852 0.500569i
\(404\) 1.93627 + 1.11790i 0.0963329 + 0.0556178i
\(405\) 0 0
\(406\) 8.47038 8.38490i 0.420378 0.416135i
\(407\) 33.0815 + 19.0996i 1.63979 + 0.946731i
\(408\) 0 0
\(409\) −20.8373 + 20.8373i −1.03034 + 1.03034i −0.0308137 + 0.999525i \(0.509810\pi\)
−0.999525 + 0.0308137i \(0.990190\pi\)
\(410\) −29.8487 + 29.8487i −1.47412 + 1.47412i
\(411\) 0 0
\(412\) 5.88804 + 3.39946i 0.290083 + 0.167479i
\(413\) 2.11965 + 8.07422i 0.104301 + 0.397307i
\(414\) 0 0
\(415\) 6.96559 + 4.02159i 0.341927 + 0.197412i
\(416\) 9.91172 + 2.18023i 0.485962 + 0.106894i
\(417\) 0 0
\(418\) −2.86921 + 2.86921i −0.140338 + 0.140338i
\(419\) 10.6429 6.14470i 0.519941 0.300188i −0.216970 0.976178i \(-0.569617\pi\)
0.736911 + 0.675990i \(0.236284\pi\)
\(420\) 0 0
\(421\) 6.08177 + 6.08177i 0.296407 + 0.296407i 0.839605 0.543197i \(-0.182787\pi\)
−0.543197 + 0.839605i \(0.682787\pi\)
\(422\) 4.40666 16.4459i 0.214513 0.800572i
\(423\) 0 0
\(424\) −16.3924 4.39232i −0.796084 0.213310i
\(425\) −26.4411 + 15.2658i −1.28258 + 0.740500i
\(426\) 0 0
\(427\) 2.75719 + 0.0139838i 0.133430 + 0.000676724i
\(428\) 0.0903814i 0.00436875i
\(429\) 0 0
\(430\) 65.1155 37.5945i 3.14015 1.81297i
\(431\) −32.9505 + 8.82906i −1.58717 + 0.425281i −0.941136 0.338029i \(-0.890240\pi\)
−0.646033 + 0.763309i \(0.723573\pi\)
\(432\) 0 0
\(433\) 14.7993 25.6331i 0.711209 1.23185i −0.253194 0.967415i \(-0.581481\pi\)
0.964403 0.264435i \(-0.0851855\pi\)
\(434\) −0.195971 + 38.6396i −0.00940690 + 1.85476i
\(435\) 0 0
\(436\) −2.55384 0.684299i −0.122307 0.0327720i
\(437\) −0.700488 + 2.61426i −0.0335089 + 0.125057i
\(438\) 0 0
\(439\) 18.4285 0.879545 0.439772 0.898109i \(-0.355059\pi\)
0.439772 + 0.898109i \(0.355059\pi\)
\(440\) −7.75208 + 28.9311i −0.369566 + 1.37924i
\(441\) 0 0
\(442\) 18.6183 + 4.09536i 0.885582 + 0.194796i
\(443\) 2.87530 4.98017i 0.136610 0.236615i −0.789601 0.613620i \(-0.789713\pi\)
0.926211 + 0.377005i \(0.123046\pi\)
\(444\) 0 0
\(445\) −5.95128 + 10.3079i −0.282118 + 0.488642i
\(446\) −4.70687 8.15254i −0.222877 0.386034i
\(447\) 0 0
\(448\) 6.75163 11.5584i 0.318984 0.546082i
\(449\) −5.09748 19.0241i −0.240565 0.897801i −0.975561 0.219729i \(-0.929483\pi\)
0.734996 0.678072i \(-0.237184\pi\)
\(450\) 0 0
\(451\) 23.8905i 1.12496i
\(452\) −8.82351 5.09426i −0.415023 0.239614i
\(453\) 0 0
\(454\) −32.2930 −1.51558
\(455\) −10.6721 34.2560i −0.500317 1.60595i
\(456\) 0 0
\(457\) 2.19914 + 2.19914i 0.102871 + 0.102871i 0.756669 0.653798i \(-0.226825\pi\)
−0.653798 + 0.756669i \(0.726825\pi\)
\(458\) 11.7734 + 6.79740i 0.550137 + 0.317622i
\(459\) 0 0
\(460\) −1.76528 6.58812i −0.0823066 0.307173i
\(461\) −8.13643 30.3656i −0.378951 1.41427i −0.847485 0.530820i \(-0.821884\pi\)
0.468533 0.883446i \(-0.344783\pi\)
\(462\) 0 0
\(463\) 10.2951 10.2951i 0.478455 0.478455i −0.426182 0.904637i \(-0.640142\pi\)
0.904637 + 0.426182i \(0.140142\pi\)
\(464\) 6.76715 + 11.7210i 0.314157 + 0.544136i
\(465\) 0 0
\(466\) 2.06147 + 7.69351i 0.0954958 + 0.356395i
\(467\) 6.26532 10.8518i 0.289924 0.502164i −0.683867 0.729607i \(-0.739703\pi\)
0.973791 + 0.227443i \(0.0730365\pi\)
\(468\) 0 0
\(469\) 7.55012 + 2.06414i 0.348632 + 0.0953133i
\(470\) −2.12167 + 7.91817i −0.0978652 + 0.365238i
\(471\) 0 0
\(472\) −7.45155 −0.342985
\(473\) 11.0138 41.1039i 0.506413 1.88996i
\(474\) 0 0
\(475\) −6.71233 + 1.79856i −0.307983 + 0.0825238i
\(476\) −2.26739 + 3.88164i −0.103926 + 0.177915i
\(477\) 0 0
\(478\) 26.1125i 1.19436i
\(479\) −20.2529 + 5.42675i −0.925379 + 0.247954i −0.689883 0.723921i \(-0.742338\pi\)
−0.235496 + 0.971875i \(0.575671\pi\)
\(480\) 0 0
\(481\) 8.77505 39.8930i 0.400108 1.81897i
\(482\) 8.94218i 0.407305i
\(483\) 0 0
\(484\) −0.0940112 0.162832i −0.00427324 0.00740146i
\(485\) 40.6507 23.4697i 1.84585 1.06570i
\(486\) 0 0
\(487\) 7.62705 + 7.62705i 0.345615 + 0.345615i 0.858473 0.512858i \(-0.171413\pi\)
−0.512858 + 0.858473i \(0.671413\pi\)
\(488\) −0.637005 + 2.37734i −0.0288359 + 0.107617i
\(489\) 0 0
\(490\) 41.7022 + 0.423018i 1.88391 + 0.0191100i
\(491\) −30.7318 + 17.7430i −1.38691 + 0.800730i −0.992965 0.118406i \(-0.962222\pi\)
−0.393940 + 0.919136i \(0.628888\pi\)
\(492\) 0 0
\(493\) 4.74647 + 8.22113i 0.213770 + 0.370261i
\(494\) 3.85196 + 1.99713i 0.173308 + 0.0898552i
\(495\) 0 0
\(496\) −42.3830 11.3565i −1.90305 0.509921i
\(497\) 18.5057 + 5.05933i 0.830096 + 0.226942i
\(498\) 0 0
\(499\) −4.95983 + 1.32898i −0.222033 + 0.0594935i −0.368120 0.929778i \(-0.619999\pi\)
0.146088 + 0.989272i \(0.453332\pi\)
\(500\) 5.61406 5.61406i 0.251069 0.251069i
\(501\) 0 0
\(502\) −16.9595 + 4.54429i −0.756940 + 0.202821i
\(503\) 31.3005 + 18.0713i 1.39562 + 0.805761i 0.993930 0.110015i \(-0.0350897\pi\)
0.401690 + 0.915776i \(0.368423\pi\)
\(504\) 0 0
\(505\) 15.9577 + 4.27585i 0.710108 + 0.190273i
\(506\) −16.4778 9.51348i −0.732529 0.422926i
\(507\) 0 0
\(508\) 1.98239 + 3.43361i 0.0879546 + 0.152342i
\(509\) 20.3768 20.3768i 0.903184 0.903184i −0.0925266 0.995710i \(-0.529494\pi\)
0.995710 + 0.0925266i \(0.0294943\pi\)
\(510\) 0 0
\(511\) 4.06714 4.02610i 0.179920 0.178104i
\(512\) 6.42274 + 6.42274i 0.283848 + 0.283848i
\(513\) 0 0
\(514\) −2.69171 2.69171i −0.118726 0.118726i
\(515\) 48.5261 + 13.0025i 2.13832 + 0.572960i
\(516\) 0 0
\(517\) 2.31972 + 4.01788i 0.102021 + 0.176706i
\(518\) 40.9957 + 23.9469i 1.80125 + 1.05217i
\(519\) 0 0
\(520\) 31.9948 1.44981i 1.40307 0.0635785i
\(521\) −15.6852 + 9.05586i −0.687182 + 0.396745i −0.802555 0.596578i \(-0.796527\pi\)
0.115374 + 0.993322i \(0.463193\pi\)
\(522\) 0 0
\(523\) 1.70402i 0.0745115i 0.999306 + 0.0372557i \(0.0118616\pi\)
−0.999306 + 0.0372557i \(0.988138\pi\)
\(524\) 2.47094 4.27979i 0.107943 0.186963i
\(525\) 0 0
\(526\) 39.9711 10.7102i 1.74282 0.466988i
\(527\) −29.7274 7.96543i −1.29495 0.346980i
\(528\) 0 0
\(529\) 10.3090 0.448216
\(530\) 42.8113 1.85960
\(531\) 0 0
\(532\) −0.727144 + 0.719805i −0.0315257 + 0.0312075i
\(533\) 24.3513 7.72212i 1.05477 0.334482i
\(534\) 0 0
\(535\) −0.172849 0.645082i −0.00747292 0.0278893i
\(536\) −3.49341 + 6.05077i −0.150892 + 0.261353i
\(537\) 0 0
\(538\) −29.5920 + 29.5920i −1.27580 + 1.27580i
\(539\) 16.8582 16.5197i 0.726136 0.711552i
\(540\) 0 0
\(541\) −2.05747 7.67860i −0.0884577 0.330129i 0.907489 0.420076i \(-0.137997\pi\)
−0.995946 + 0.0899476i \(0.971330\pi\)
\(542\) 11.9971i 0.515320i
\(543\) 0 0
\(544\) −6.64353 6.64353i −0.284839 0.284839i
\(545\) −19.5363 −0.836842
\(546\) 0 0
\(547\) −45.6503 −1.95187 −0.975933 0.218072i \(-0.930023\pi\)
−0.975933 + 0.218072i \(0.930023\pi\)
\(548\) 3.27103 + 3.27103i 0.139731 + 0.139731i
\(549\) 0 0
\(550\) 48.8534i 2.08311i
\(551\) 0.559213 + 2.08701i 0.0238233 + 0.0889097i
\(552\) 0 0
\(553\) −25.4779 + 14.5379i −1.08343 + 0.618214i
\(554\) −25.2493 + 25.2493i −1.07274 + 1.07274i
\(555\) 0 0
\(556\) −2.60227 + 4.50727i −0.110361 + 0.191151i
\(557\) 3.24461 + 12.1091i 0.137479 + 0.513077i 0.999975 + 0.00701474i \(0.00223288\pi\)
−0.862497 + 0.506063i \(0.831100\pi\)
\(558\) 0 0
\(559\) −45.4566 + 2.05982i −1.92261 + 0.0871211i
\(560\) −12.4889 + 45.6812i −0.527752 + 1.93038i
\(561\) 0 0
\(562\) −17.3267 −0.730883
\(563\) 14.7021 0.619621 0.309810 0.950798i \(-0.399734\pi\)
0.309810 + 0.950798i \(0.399734\pi\)
\(564\) 0 0
\(565\) −72.7188 19.4849i −3.05930 0.819737i
\(566\) −27.1279 + 7.26891i −1.14027 + 0.305535i
\(567\) 0 0
\(568\) −8.56254 + 14.8308i −0.359276 + 0.622285i
\(569\) 21.1424i 0.886335i −0.896439 0.443167i \(-0.853855\pi\)
0.896439 0.443167i \(-0.146145\pi\)
\(570\) 0 0
\(571\) −2.38493 + 1.37694i −0.0998064 + 0.0576232i −0.549072 0.835775i \(-0.685019\pi\)
0.449266 + 0.893398i \(0.351686\pi\)
\(572\) −4.17329 + 4.56946i −0.174494 + 0.191059i
\(573\) 0 0
\(574\) −0.150595 + 29.6929i −0.00628573 + 1.23936i
\(575\) −16.2927 28.2197i −0.679451 1.17684i
\(576\) 0 0
\(577\) −6.04026 1.61848i −0.251459 0.0673783i 0.130888 0.991397i \(-0.458217\pi\)
−0.382347 + 0.924019i \(0.624884\pi\)
\(578\) 6.56158 + 6.56158i 0.272926 + 0.272926i
\(579\) 0 0
\(580\) −3.85016 3.85016i −0.159869 0.159869i
\(581\) 5.47235 1.43660i 0.227031 0.0596004i
\(582\) 0 0
\(583\) 17.1328 17.1328i 0.709568 0.709568i
\(584\) 2.55421 + 4.42403i 0.105694 + 0.183067i
\(585\) 0 0
\(586\) −17.6821 10.2088i −0.730441 0.421720i
\(587\) 15.8338 + 4.24265i 0.653530 + 0.175113i 0.570324 0.821420i \(-0.306817\pi\)
0.0832057 + 0.996532i \(0.473484\pi\)
\(588\) 0 0
\(589\) −6.06630 3.50238i −0.249958 0.144313i
\(590\) 18.1573 4.86523i 0.747523 0.200298i
\(591\) 0 0
\(592\) −38.1225 + 38.1225i −1.56682 + 1.56682i
\(593\) −14.8765 + 3.98614i −0.610904 + 0.163691i −0.550989 0.834512i \(-0.685750\pi\)
−0.0599148 + 0.998203i \(0.519083\pi\)
\(594\) 0 0
\(595\) −8.75971 + 32.0408i −0.359113 + 1.31354i
\(596\) −7.38701 1.97934i −0.302584 0.0810770i
\(597\) 0 0
\(598\) −4.37084 + 19.8707i −0.178737 + 0.812572i
\(599\) −13.0357 22.5784i −0.532623 0.922530i −0.999274 0.0380886i \(-0.987873\pi\)
0.466651 0.884441i \(-0.345460\pi\)
\(600\) 0 0
\(601\) −36.7529 + 21.2193i −1.49918 + 0.865554i −1.00000 0.000942846i \(-0.999700\pi\)
−0.499183 + 0.866496i \(0.666367\pi\)
\(602\) 13.9478 51.0176i 0.568471 2.07932i
\(603\) 0 0
\(604\) 0.0365845 0.136535i 0.00148860 0.00555555i
\(605\) −0.982396 0.982396i −0.0399401 0.0399401i
\(606\) 0 0
\(607\) −5.87620 + 3.39263i −0.238508 + 0.137702i −0.614491 0.788924i \(-0.710638\pi\)
0.375983 + 0.926627i \(0.377305\pi\)
\(608\) −1.06921 1.85193i −0.0433623 0.0751057i
\(609\) 0 0
\(610\) 6.20879i 0.251386i
\(611\) 3.34557 3.66316i 0.135347 0.148196i
\(612\) 0 0
\(613\) 32.8333 8.79765i 1.32612 0.355334i 0.474855 0.880064i \(-0.342501\pi\)
0.851269 + 0.524730i \(0.175834\pi\)
\(614\) 13.0442i 0.526422i
\(615\) 0 0
\(616\) 10.4417 + 18.2993i 0.420710 + 0.737301i
\(617\) 7.13892 1.91287i 0.287402 0.0770091i −0.112238 0.993681i \(-0.535802\pi\)
0.399640 + 0.916672i \(0.369135\pi\)
\(618\) 0 0
\(619\) 0.183786 0.685897i 0.00738697 0.0275685i −0.962134 0.272577i \(-0.912124\pi\)
0.969521 + 0.245008i \(0.0787907\pi\)
\(620\) 17.6525 0.708942
\(621\) 0 0
\(622\) 11.0924 41.3973i 0.444764 1.65988i
\(623\) 2.12594 + 8.09817i 0.0851739 + 0.324446i
\(624\) 0 0
\(625\) 6.46561 11.1988i 0.258624 0.447951i
\(626\) −5.62781 21.0033i −0.224933 0.839460i
\(627\) 0 0
\(628\) 0.0800312 + 0.138618i 0.00319359 + 0.00553146i
\(629\) −26.7391 + 26.7391i −1.06616 + 1.06616i
\(630\) 0 0
\(631\) 7.80744 + 29.1378i 0.310809 + 1.15996i 0.927828 + 0.373008i \(0.121674\pi\)
−0.617019 + 0.786948i \(0.711660\pi\)
\(632\) −6.77702 25.2922i −0.269575 1.00607i
\(633\) 0 0
\(634\) 3.17843 + 1.83507i 0.126232 + 0.0728798i
\(635\) 20.7156 + 20.7156i 0.822073 + 0.822073i
\(636\) 0 0
\(637\) −22.2874 11.8437i −0.883057 0.469266i
\(638\) −15.1896 −0.601361
\(639\) 0 0
\(640\) −44.4412 25.6581i −1.75669 1.01423i
\(641\) 14.4376i 0.570251i 0.958490 + 0.285126i \(0.0920353\pi\)
−0.958490 + 0.285126i \(0.907965\pi\)
\(642\) 0 0
\(643\) −4.71705 17.6043i −0.186022 0.694244i −0.994409 0.105593i \(-0.966326\pi\)
0.808387 0.588651i \(-0.200341\pi\)
\(644\) −4.14274 2.41991i −0.163247 0.0953577i
\(645\) 0 0
\(646\) −2.00842 3.47868i −0.0790202 0.136867i
\(647\) −18.8833 + 32.7068i −0.742379 + 1.28584i 0.209031 + 0.977909i \(0.432969\pi\)
−0.951409 + 0.307929i \(0.900364\pi\)
\(648\) 0 0
\(649\) 5.31939 9.21346i 0.208804 0.361660i
\(650\) −49.7956 + 15.7909i −1.95314 + 0.619368i
\(651\) 0 0
\(652\) 0.124384 0.464209i 0.00487127 0.0181798i
\(653\) 26.5542 1.03915 0.519573 0.854426i \(-0.326091\pi\)
0.519573 + 0.854426i \(0.326091\pi\)
\(654\) 0 0
\(655\) 9.45104 35.2718i 0.369283 1.37818i
\(656\) −32.5695 8.72698i −1.27163 0.340731i
\(657\) 0 0
\(658\) 2.85780 + 5.00835i 0.111409 + 0.195246i
\(659\) −2.28186 + 3.95230i −0.0888888 + 0.153960i −0.907042 0.421041i \(-0.861665\pi\)
0.818153 + 0.575001i \(0.194998\pi\)
\(660\) 0 0
\(661\) 40.6603 10.8949i 1.58150 0.423762i 0.642111 0.766612i \(-0.278059\pi\)
0.939390 + 0.342850i \(0.111392\pi\)
\(662\) −35.4369 + 20.4595i −1.37730 + 0.795182i
\(663\) 0 0
\(664\) 5.05033i 0.195991i
\(665\) −3.81328 + 6.52811i −0.147873 + 0.253149i
\(666\) 0 0
\(667\) −8.77413 + 5.06575i −0.339736 + 0.196146i
\(668\) −1.19036 0.318955i −0.0460563 0.0123407i
\(669\) 0 0
\(670\) 4.56180 17.0249i 0.176238 0.657728i
\(671\) −2.48472 2.48472i −0.0959215 0.0959215i
\(672\) 0 0
\(673\) −22.4576 + 12.9659i −0.865675 + 0.499798i −0.865909 0.500202i \(-0.833259\pi\)
0.000233516 1.00000i \(0.499926\pi\)
\(674\) −36.2979 + 36.2979i −1.39814 + 1.39814i
\(675\) 0 0
\(676\) 6.00652 + 2.77679i 0.231020 + 0.106800i
\(677\) −15.4910 8.94374i −0.595368 0.343736i 0.171849 0.985123i \(-0.445026\pi\)
−0.767217 + 0.641387i \(0.778359\pi\)
\(678\) 0 0
\(679\) 8.70743 31.8496i 0.334161 1.22227i
\(680\) −25.6779 14.8252i −0.984704 0.568519i
\(681\) 0 0
\(682\) 34.8211 34.8211i 1.33337 1.33337i
\(683\) 22.6009 22.6009i 0.864799 0.864799i −0.127092 0.991891i \(-0.540564\pi\)
0.991891 + 0.127092i \(0.0405643\pi\)
\(684\) 0 0
\(685\) 29.6021 + 17.0908i 1.13104 + 0.653004i
\(686\) 21.0568 20.4256i 0.803953 0.779853i
\(687\) 0 0
\(688\) 52.0130 + 30.0297i 1.98298 + 1.14487i
\(689\) −23.0011 11.9254i −0.876271 0.454322i
\(690\) 0 0
\(691\) 10.6170 10.6170i 0.403889 0.403889i −0.475712 0.879601i \(-0.657809\pi\)
0.879601 + 0.475712i \(0.157809\pi\)
\(692\) 7.59173 4.38309i 0.288594 0.166620i
\(693\) 0 0
\(694\) −34.7456 34.7456i −1.31893 1.31893i
\(695\) −9.95340 + 37.1466i −0.377554 + 1.40905i
\(696\) 0 0
\(697\) −22.8443 6.12110i −0.865288 0.231853i
\(698\) −0.753802 + 0.435208i −0.0285318 + 0.0164729i
\(699\) 0 0
\(700\) 0.0624761 12.3184i 0.00236138 0.465593i
\(701\) 17.3022i 0.653495i −0.945112 0.326747i \(-0.894047\pi\)
0.945112 0.326747i \(-0.105953\pi\)
\(702\) 0 0
\(703\) −7.45371 + 4.30340i −0.281122 + 0.162306i
\(704\) −16.4782 + 4.41531i −0.621044 + 0.166408i
\(705\) 0 0
\(706\) −9.79802 + 16.9707i −0.368753 + 0.638700i
\(707\) 10.0935 5.75940i 0.379604 0.216605i
\(708\) 0 0
\(709\) −13.4262 3.59754i −0.504231 0.135108i −0.00226813 0.999997i \(-0.500722\pi\)
−0.501963 + 0.864889i \(0.667389\pi\)
\(710\) 11.1812 41.7289i 0.419623 1.56606i
\(711\) 0 0
\(712\) −7.47365 −0.280087
\(713\) 8.50123 31.7270i 0.318374 1.18819i
\(714\) 0 0
\(715\) −21.0473 + 40.5949i −0.787126 + 1.51816i
\(716\) 0.876146 1.51753i 0.0327431 0.0567128i
\(717\) 0 0
\(718\) −5.76710 + 9.98891i −0.215226 + 0.372783i
\(719\) −24.5650 42.5477i −0.916118 1.58676i −0.805256 0.592927i \(-0.797972\pi\)
−0.110862 0.993836i \(-0.535361\pi\)
\(720\) 0 0
\(721\) 30.6934 17.5139i 1.14308 0.652252i
\(722\) 7.55274 + 28.1872i 0.281084 + 1.04902i
\(723\) 0 0
\(724\) 13.2228i 0.491421i
\(725\) −22.5283 13.0067i −0.836682 0.483059i
\(726\) 0 0
\(727\) 19.4676 0.722014 0.361007 0.932563i \(-0.382433\pi\)
0.361007 + 0.932563i \(0.382433\pi\)
\(728\) 15.2772 16.5580i 0.566210 0.613681i
\(729\) 0 0
\(730\) −9.11238 9.11238i −0.337264 0.337264i
\(731\) 36.4819 + 21.0628i 1.34933 + 0.779037i
\(732\) 0 0
\(733\) 1.81677 + 6.78026i 0.0671038 + 0.250435i 0.991327 0.131418i \(-0.0419529\pi\)
−0.924223 + 0.381852i \(0.875286\pi\)
\(734\) −1.76768 6.59709i −0.0652464 0.243503i
\(735\) 0 0
\(736\) 7.09041 7.09041i 0.261356 0.261356i
\(737\) −4.98764 8.63885i −0.183722 0.318216i
\(738\) 0 0
\(739\) 10.3392 + 38.5863i 0.380332 + 1.41942i 0.845395 + 0.534142i \(0.179365\pi\)
−0.465063 + 0.885278i \(0.653968\pi\)
\(740\) 10.8449 18.7839i 0.398666 0.690509i
\(741\) 0 0
\(742\) 21.4019 21.1859i 0.785690 0.777760i
\(743\) 9.49010 35.4175i 0.348158 1.29934i −0.540721 0.841202i \(-0.681849\pi\)
0.888879 0.458141i \(-0.151485\pi\)
\(744\) 0 0
\(745\) −56.5089 −2.07033
\(746\) 7.04119 26.2781i 0.257796 0.962109i
\(747\) 0 0
\(748\) 5.53384 1.48279i 0.202337 0.0542161i
\(749\) −0.405640 0.236948i −0.0148218 0.00865788i
\(750\) 0 0
\(751\) 19.4504i 0.709755i −0.934913 0.354877i \(-0.884523\pi\)
0.934913 0.354877i \(-0.115477\pi\)
\(752\) −6.32488 + 1.69475i −0.230645 + 0.0618010i
\(753\) 0 0
\(754\) 4.90972 + 15.4825i 0.178802 + 0.563841i
\(755\) 1.04446i 0.0380119i
\(756\) 0 0
\(757\) 3.02968 + 5.24756i 0.110116 + 0.190726i 0.915817 0.401597i \(-0.131545\pi\)
−0.805701 + 0.592322i \(0.798211\pi\)
\(758\) −3.19515 + 1.84472i −0.116053 + 0.0670032i
\(759\) 0 0
\(760\) −4.77194 4.77194i −0.173096 0.173096i
\(761\) 7.80535 29.1300i 0.282944 1.05596i −0.667385 0.744713i \(-0.732587\pi\)
0.950329 0.311247i \(-0.100747\pi\)
\(762\) 0 0
\(763\) −9.76645 + 9.66789i −0.353569 + 0.350001i
\(764\) −1.31502 + 0.759229i −0.0475759 + 0.0274679i
\(765\) 0 0
\(766\) −21.8270 37.8055i −0.788641 1.36597i
\(767\) −11.1105 2.44392i −0.401178 0.0882450i
\(768\) 0 0
\(769\) 22.1109 + 5.92460i 0.797339 + 0.213646i 0.634415 0.772992i \(-0.281241\pi\)
0.162924 + 0.986639i \(0.447908\pi\)
\(770\) −37.3914 37.7726i −1.34749 1.36123i
\(771\) 0 0
\(772\) −1.28534 + 0.344405i −0.0462603 + 0.0123954i
\(773\) −10.6208 + 10.6208i −0.382004 + 0.382004i −0.871824 0.489820i \(-0.837063\pi\)
0.489820 + 0.871824i \(0.337063\pi\)
\(774\) 0 0
\(775\) 81.4619 21.8277i 2.92620 0.784073i
\(776\) 25.5247 + 14.7367i 0.916283 + 0.529016i
\(777\) 0 0
\(778\) −19.0090 5.09345i −0.681506 0.182609i
\(779\) −4.66170 2.69143i −0.167023 0.0964306i
\(780\) 0 0
\(781\) −12.2250 21.1743i −0.437444 0.757675i
\(782\) 13.3187 13.3187i 0.476276 0.476276i
\(783\) 0 0
\(784\) 16.3628 + 29.0170i 0.584386 + 1.03632i
\(785\) 0.836308 + 0.836308i 0.0298491 + 0.0298491i
\(786\) 0 0
\(787\) −6.19869 6.19869i −0.220959 0.220959i 0.587943 0.808902i \(-0.299938\pi\)
−0.808902 + 0.587943i \(0.799938\pi\)
\(788\) −0.405946 0.108773i −0.0144612 0.00387487i