Properties

Label 819.2.et.c.136.2
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 136.2
Character \(\chi\) \(=\) 819.136
Dual form 819.2.et.c.271.2

$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.12005 + 1.12005i −0.791995 + 0.791995i −0.981818 0.189823i \(-0.939208\pi\)
0.189823 + 0.981818i \(0.439208\pi\)
\(3\) 0 0
\(4\) 0.509024i 0.254512i
\(5\) 0.973479 3.63307i 0.435353 1.62476i −0.304866 0.952395i \(-0.598612\pi\)
0.740219 0.672365i \(-0.234722\pi\)
\(6\) 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 0.700257 + 0.713891i \(0.253069\pi\)
−0.963386 + 0.268119i \(0.913598\pi\)
\(12\) 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 −0.173657 0.984806i \(-0.555559\pi\)
0.342011 + 0.939696i \(0.388892\pi\)
\(20\) −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 \(-0.878874\pi\)
0.928469 0.371411i \(-0.121126\pi\)
\(24\) 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 −0.703260 0.710933i \(-0.748273\pi\)
0.967316 + 0.253574i \(0.0816063\pi\)
\(30\) 0 0
\(31\) −8.90596 + 2.38635i −1.59956 + 0.428600i −0.944909 0.327332i \(-0.893850\pi\)
−0.654649 + 0.755933i \(0.727184\pi\)
\(32\) −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 −0.916177 0.400775i \(-0.868741\pi\)
−0.400775 0.916177i \(-0.631259\pi\)
\(38\) −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 −0.750013 0.661423i \(-0.769953\pi\)
−0.318819 + 0.947816i \(0.603286\pi\)
\(42\) 0 0
\(43\) 10.9295 6.31017i 1.66674 0.962291i 0.697358 0.716723i \(-0.254359\pi\)
0.969379 0.245568i \(-0.0789746\pi\)
\(44\) 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 0.160582 0.987023i \(-0.448663\pi\)
−0.354444 + 0.935077i \(0.615330\pi\)
\(48\) 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 −0.506450 0.862270i \(-0.669042\pi\)
0.999972 + 0.00746338i \(0.00237569\pi\)
\(54\) 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 −0.546803 0.837261i \(-0.684156\pi\)
0.837261 + 0.546803i \(0.184156\pi\)
\(60\) 0 0
\(61\) 0.902515 + 0.521067i 0.115555 + 0.0667158i 0.556664 0.830738i \(-0.312081\pi\)
−0.441108 + 0.897454i \(0.645415\pi\)
\(62\) 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 0.429113 0.903251i \(-0.358826\pi\)
−0.0800024 + 0.996795i \(0.525493\pi\)
\(68\) 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 0.649253 0.760573i \(-0.275082\pi\)
0.181983 + 0.983302i \(0.441748\pi\)
\(72\) 0 0
\(73\) 0.559835 + 2.08933i 0.0655238 + 0.244538i 0.990918 0.134468i \(-0.0429326\pi\)
−0.925394 + 0.379006i \(0.876266\pi\)
\(74\) 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 −0.988791 0.149309i \(-0.952295\pi\)
0.365090 0.930972i \(-0.381038\pi\)
\(80\) 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 0.785208 0.619233i \(-0.212556\pi\)
−0.619233 + 0.785208i \(0.712556\pi\)
\(84\) 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 −0.578494 0.815686i \(-0.696360\pi\)
0.815686 + 0.578494i \(0.196360\pi\)
\(90\) 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 0.583348 + 0.812222i \(0.301742\pi\)
−0.911305 + 0.411731i \(0.864924\pi\)
\(98\) 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 0.954358 0.298665i \(-0.0965415\pi\)
−0.735831 + 0.677165i \(0.763208\pi\)
\(102\) 0 0
\(103\) 6.67838 + 11.5673i 0.658040 + 1.13976i 0.981122 + 0.193389i \(0.0619478\pi\)
−0.323082 + 0.946371i \(0.604719\pi\)
\(104\) 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 0.871182 0.490960i \(-0.163354\pi\)
−0.999946 + 0.0104068i \(0.996687\pi\)
\(110\) −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 −0.762684 0.646771i \(-0.776119\pi\)
−0.178778 0.983889i \(-0.557215\pi\)
\(114\) 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 0.768476 0.639878i \(-0.221015\pi\)
−0.169913 + 0.985459i \(0.554349\pi\)
\(128\) −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 −0.820101 0.572219i \(-0.806083\pi\)
0.0855060 + 0.996338i \(0.472749\pi\)
\(132\) 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 0.926156 0.377140i \(-0.123092\pi\)
−0.377140 + 0.926156i \(0.623092\pi\)
\(138\) 0 0
\(139\) 8.85473 5.11228i 0.751048 0.433618i −0.0750244 0.997182i \(-0.523903\pi\)
0.826073 + 0.563564i \(0.190570\pi\)
\(140\) −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 −0.920630 0.390435i \(-0.872325\pi\)
0.602072 0.798442i \(-0.294342\pi\)
\(150\) 0 0
\(151\) −0.268230 + 0.0718719i −0.0218282 + 0.00584885i −0.269717 0.962940i \(-0.586930\pi\)
0.247888 + 0.968789i \(0.420263\pi\)
\(152\) −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 0.510827 0.859683i \(-0.329339\pi\)
−0.489094 + 0.872231i \(0.662672\pi\)
\(158\) 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 −0.294357 0.955696i \(-0.595105\pi\)
0.222927 + 0.974835i \(0.428439\pi\)
\(164\) 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 0.937435 0.348161i \(-0.113194\pi\)
−0.985923 + 0.167202i \(0.946527\pi\)
\(168\) 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 0.327314 + 0.944916i \(0.393857\pi\)
−0.981978 + 0.188996i \(0.939477\pi\)
\(174\) 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 −0.607260 0.794503i \(-0.707731\pi\)
0.384430 + 0.923154i \(0.374398\pi\)
\(180\) 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 −0.807005 0.590544i \(-0.798913\pi\)
0.914929 + 0.403615i \(0.132246\pi\)
\(192\) 0 0
\(193\) 0.676598 2.52510i 0.0487026 0.181761i −0.937290 0.348551i \(-0.886674\pi\)
0.985992 + 0.166791i \(0.0533404\pi\)
\(194\) −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 0.957896 0.287117i \(-0.0926968\pi\)
−0.973120 + 0.230297i \(0.926030\pi\)
\(198\) 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 −0.619574 0.784938i \(-0.712695\pi\)
0.989563 + 0.144098i \(0.0460280\pi\)
\(212\) −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 −0.0614354 0.998111i \(-0.519568\pi\)
0.445851 + 0.895107i \(0.352901\pi\)
\(224\) −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 0.999105 0.0422908i \(-0.0134656\pi\)
−0.0422908 + 0.999105i \(0.513466\pi\)
\(228\) 0 0
\(229\) −8.29019 2.22135i −0.547831 0.146791i −0.0257212 0.999669i \(-0.508188\pi\)
−0.522110 + 0.852878i \(0.674855\pi\)
\(230\) 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 −0.635814 0.771842i \(-0.719336\pi\)
0.350528 + 0.936552i \(0.386002\pi\)
\(234\) 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 −0.221208 0.975227i \(-0.571000\pi\)
0.975227 + 0.221208i \(0.0710001\pi\)
\(240\) 0 0
\(241\) 3.99187 3.99187i 0.257139 0.257139i −0.566751 0.823889i \(-0.691800\pi\)
0.823889 + 0.566751i \(0.191800\pi\)
\(242\) 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 0.986218 0.165451i \(-0.0529079\pi\)
−0.636394 + 0.771365i \(0.719575\pi\)
\(252\) 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 −0.915983 0.401218i \(-0.868587\pi\)
0.110527 0.993873i \(-0.464746\pi\)
\(264\) 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 \(0.298068\pi\)
−0.592684 + 0.805435i \(0.701932\pi\)
\(270\) 0 0
\(271\) −5.35562 + 5.35562i −0.325330 + 0.325330i −0.850808 0.525477i \(-0.823887\pi\)
0.525477 + 0.850808i \(0.323887\pi\)
\(272\) 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 \(0.236823\pi\)
−0.735764 + 0.677238i \(0.763177\pi\)
\(278\) −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 0.899120 0.437701i \(-0.144207\pi\)
−0.437701 + 0.899120i \(0.644207\pi\)
\(282\) 0 0
\(283\) 8.86524 + 15.3550i 0.526984 + 0.912763i 0.999506 + 0.0314437i \(0.0100105\pi\)
−0.472522 + 0.881319i \(0.656656\pi\)
\(284\) 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 0.603462 0.797392i \(-0.293788\pi\)
0.123917 + 0.992293i \(0.460454\pi\)
\(294\) 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 −0.853474 0.521135i \(-0.825509\pi\)
0.521135 + 0.853474i \(0.325509\pi\)
\(308\) 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 −0.171992 0.985098i \(-0.555020\pi\)
0.939116 0.343600i \(-0.111646\pi\)
\(312\) 0 0
\(313\) 11.8883 6.86374i 0.671969 0.387962i −0.124853 0.992175i \(-0.539846\pi\)
0.796822 + 0.604214i \(0.206513\pi\)
\(314\) −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 0.195419 0.980720i \(-0.437393\pi\)
−0.321122 + 0.947038i \(0.604060\pi\)
\(318\) 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 0.864002 + 0.503488i \(0.167950\pi\)
−0.496504 + 0.868035i \(0.665383\pi\)
\(332\) 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 \(0.344257\pi\)
−0.469990 + 0.882672i \(0.655743\pi\)
\(338\) −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 0.969628 0.244585i \(-0.0786517\pi\)
−0.962015 + 0.272997i \(0.911985\pi\)
\(350\) 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 0.826865 + 0.562401i \(0.190122\pi\)
−0.997286 + 0.0736213i \(0.976544\pi\)
\(354\) 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 −0.997659 0.0683856i \(-0.978215\pi\)
0.898191 + 0.439606i \(0.144882\pi\)
\(360\) 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 −0.399364 0.916792i \(-0.630769\pi\)
0.594283 + 0.804256i \(0.297436\pi\)
\(368\) 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 −0.553383 0.832927i \(-0.686663\pi\)
0.998027 + 0.0627799i \(0.0199966\pi\)
\(374\) −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 0.979679 0.200572i \(-0.0642801\pi\)
−0.948713 + 0.316139i \(0.897613\pi\)
\(380\) −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 0.496336 0.868130i \(-0.334678\pi\)
0.863905 + 0.503655i \(0.168012\pi\)
\(384\) 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 0.747318 0.664467i \(-0.231341\pi\)
−0.201787 + 0.979430i \(0.564675\pi\)
\(390\) 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 −0.775122 0.631812i \(-0.782312\pi\)
0.355369 0.934726i \(-0.384355\pi\)
\(398\) 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 0.910610 0.413267i \(-0.135612\pi\)
−0.413267 + 0.910610i \(0.635612\pi\)
\(402\) 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 −0.999525 0.0308137i \(-0.990190\pi\)
−0.0308137 0.999525i \(-0.509810\pi\)
\(410\) −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 0.736911 0.675990i \(-0.236284\pi\)
−0.216970 + 0.976178i \(0.569617\pi\)
\(420\) 0 0
\(421\) 6.08177 6.08177i 0.296407 0.296407i −0.543197 0.839605i \(-0.682787\pi\)
0.839605 + 0.543197i \(0.182787\pi\)
\(422\) 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 −0.646033 0.763309i \(-0.723573\pi\)
−0.941136 + 0.338029i \(0.890240\pi\)
\(432\) 0 0
\(433\) 14.7993 + 25.6331i 0.711209 + 1.23185i 0.964403 + 0.264435i \(0.0851855\pi\)
−0.253194 + 0.967415i \(0.581481\pi\)
\(434\) −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 0.926211 0.377005i \(-0.123046\pi\)
−0.789601 + 0.613620i \(0.789713\pi\)
\(444\) 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 0.734996 + 0.678072i \(0.237184\pi\)
−0.975561 + 0.219729i \(0.929483\pi\)
\(450\) 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 −0.653798 0.756669i \(-0.726825\pi\)
0.756669 + 0.653798i \(0.226825\pi\)
\(458\) 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 0.468533 + 0.883446i \(0.344783\pi\)
−0.847485 + 0.530820i \(0.821884\pi\)
\(462\) 0 0
\(463\) 10.2951 + 10.2951i 0.478455 + 0.478455i 0.904637 0.426182i \(-0.140142\pi\)
−0.426182 + 0.904637i \(0.640142\pi\)
\(464\) 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 0.973791 0.227443i \(-0.0730365\pi\)
−0.683867 + 0.729607i \(0.739703\pi\)
\(468\) 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 −0.235496 0.971875i \(-0.575671\pi\)
−0.689883 + 0.723921i \(0.742338\pi\)
\(480\) 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 −0.512858 0.858473i \(-0.671413\pi\)
0.858473 + 0.512858i \(0.171413\pi\)
\(488\) −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 −0.393940 0.919136i \(-0.628888\pi\)
−0.992965 + 0.118406i \(0.962222\pi\)
\(492\) 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 0.146088 0.989272i \(-0.453332\pi\)
−0.368120 + 0.929778i \(0.619999\pi\)
\(500\) 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 0.401690 0.915776i \(-0.368423\pi\)
0.993930 + 0.110015i \(0.0350897\pi\)
\(504\) 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 0.995710 0.0925266i \(-0.0294943\pi\)
−0.0925266 + 0.995710i \(0.529494\pi\)
\(510\) 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 0.115374 0.993322i \(-0.463193\pi\)
−0.802555 + 0.596578i \(0.796527\pi\)
\(522\) 0 0
\(523\) 1.70402i 0.0745115i −0.999306 0.0372557i \(-0.988138\pi\)
0.999306 0.0372557i \(-0.0118616\pi\)
\(524\) 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 −0.995946 0.0899476i \(-0.971330\pi\)
0.907489 + 0.420076i \(0.137997\pi\)
\(542\) 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 −0.862497 0.506063i \(-0.831100\pi\)
0.999975 0.00701474i \(-0.00223288\pi\)
\(558\) 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 \(0.146145\pi\)
−0.896439 + 0.443167i \(0.853855\pi\)
\(570\) 0 0
\(571\) −2.38493 1.37694i −0.0998064 0.0576232i 0.449266 0.893398i \(-0.351686\pi\)
−0.549072 + 0.835775i \(0.685019\pi\)
\(572\) −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 −0.382347 0.924019i \(-0.624884\pi\)
0.130888 + 0.991397i \(0.458217\pi\)
\(578\) 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 0.0832057 0.996532i \(-0.473484\pi\)
0.570324 + 0.821420i \(0.306817\pi\)
\(588\) 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 −0.0599148 0.998203i \(-0.519083\pi\)
−0.550989 + 0.834512i \(0.685750\pi\)
\(594\) 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 0.466651 + 0.884441i \(0.345460\pi\)
−0.999274 + 0.0380886i \(0.987873\pi\)
\(600\) 0 0
\(601\) −36.7529 21.2193i −1.49918 0.865554i −0.499183 0.866496i \(-0.666367\pi\)
−1.00000 0.000942846i \(0.999700\pi\)
\(602\) 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 0.375983 0.926627i \(-0.377305\pi\)
−0.614491 + 0.788924i \(0.710638\pi\)
\(608\) −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 0.851269 0.524730i \(-0.175834\pi\)
0.474855 + 0.880064i \(0.342501\pi\)
\(614\) 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 0.399640 0.916672i \(-0.369135\pi\)
−0.112238 + 0.993681i \(0.535802\pi\)
\(618\) 0 0
\(619\) 0.183786 + 0.685897i 0.00738697 + 0.0275685i 0.969521 0.245008i \(-0.0787907\pi\)
−0.962134 + 0.272577i \(0.912124\pi\)
\(620\) 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 −0.617019 0.786948i \(-0.711660\pi\)
0.927828 0.373008i \(-0.121674\pi\)
\(632\) −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 \(-0.907965\pi\)
0.958490 0.285126i \(-0.0920353\pi\)
\(642\) 0 0
\(643\) −4.71705 + 17.6043i −0.186022 + 0.694244i 0.808387 + 0.588651i \(0.200341\pi\)
−0.994409 + 0.105593i \(0.966326\pi\)
\(644\) −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 −0.951409 0.307929i \(-0.900364\pi\)
0.209031 0.977909i \(-0.432969\pi\)
\(648\) 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 0.818153 0.575001i \(-0.194998\pi\)
−0.907042 + 0.421041i \(0.861665\pi\)
\(660\) 0 0
\(661\) 40.6603 + 10.8949i 1.58150 + 0.423762i 0.939390 0.342850i \(-0.111392\pi\)
0.642111 + 0.766612i \(0.278059\pi\)
\(662\) −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 0.000233516 1.00000i \(-0.499926\pi\)
−0.865909 + 0.500202i \(0.833259\pi\)
\(674\) −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 −0.767217 0.641387i \(-0.778359\pi\)
0.171849 + 0.985123i \(0.445026\pi\)
\(678\) 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 0.991891 0.127092i \(-0.0405643\pi\)
−0.127092 + 0.991891i \(0.540564\pi\)
\(684\) 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 0.879601 0.475712i \(-0.157809\pi\)
−0.475712 + 0.879601i \(0.657809\pi\)
\(692\) 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 \(0.105953\pi\)
−0.945112 + 0.326747i \(0.894047\pi\)
\(702\) 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 −0.501963 0.864889i \(-0.667389\pi\)
−0.00226813 + 0.999997i \(0.500722\pi\)
\(710\) 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 −0.110862 + 0.993836i \(0.535361\pi\)
−0.805256 + 0.592927i \(0.797972\pi\)
\(720\) 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 −0.924223 0.381852i \(-0.875286\pi\)
0.991327 + 0.131418i \(0.0419529\pi\)
\(734\) −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 −0.465063 0.885278i \(-0.653968\pi\)
0.845395 0.534142i \(-0.179365\pi\)
\(740\) 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 0.888879 + 0.458141i \(0.151485\pi\)
−0.540721 + 0.841202i \(0.681849\pi\)
\(744\) 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 \(0.115477\pi\)
−0.934913 + 0.354877i \(0.884523\pi\)
\(752\) −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 −0.805701 0.592322i \(-0.798211\pi\)
0.915817 + 0.401597i \(0.131545\pi\)
\(758\) −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 0.950329 + 0.311247i \(0.100747\pi\)
−0.667385 + 0.744713i \(0.732587\pi\)
\(762\) 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 0.162924 0.986639i \(-0.447908\pi\)
0.634415 + 0.772992i \(0.281241\pi\)
\(770\) −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 0.489820 0.871824i \(-0.337063\pi\)
−0.871824 + 0.489820i \(0.837063\pi\)
\(774\) 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 −0.808902 0.587943i \(-0.799938\pi\)
0.587943 + 0.808902i \(0.299938\pi\)
\(788\) −0.405946 + 0.108773i −0.0144612 + 0.00387487i