Properties

Label 819.2.et.c.136.8
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 136.8
Character \(\chi\) \(=\) 819.136
Dual form 819.2.et.c.271.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.48267 - 1.48267i) q^{2} -2.39661i q^{4} +(-0.507149 + 1.89270i) q^{5} +(-0.313052 + 2.62717i) q^{7} +(-0.588043 - 0.588043i) q^{8} +O(q^{10})\) \(q+(1.48267 - 1.48267i) q^{2} -2.39661i q^{4} +(-0.507149 + 1.89270i) q^{5} +(-0.313052 + 2.62717i) q^{7} +(-0.588043 - 0.588043i) q^{8} +(2.05432 + 3.55819i) q^{10} +(-0.648767 + 2.42123i) q^{11} +(3.33753 + 1.36415i) q^{13} +(3.43106 + 4.35937i) q^{14} +3.04948 q^{16} -7.32088 q^{17} +(0.930935 - 0.249443i) q^{19} +(4.53608 + 1.21544i) q^{20} +(2.62798 + 4.55179i) q^{22} +6.63818i q^{23} +(1.00500 + 0.580235i) q^{25} +(6.97103 - 2.92587i) q^{26} +(6.29629 + 0.750265i) q^{28} +(5.21743 - 9.03685i) q^{29} +(-2.92062 + 0.782577i) q^{31} +(5.69745 - 5.69745i) q^{32} +(-10.8544 + 10.8544i) q^{34} +(-4.81368 - 1.92488i) q^{35} +(-0.974084 - 0.974084i) q^{37} +(1.01043 - 1.75011i) q^{38} +(1.41122 - 0.814767i) q^{40} +(-0.710011 + 0.190247i) q^{41} +(10.1261 - 5.84633i) q^{43} +(5.80275 + 1.55484i) q^{44} +(9.84223 + 9.84223i) q^{46} +(3.62699 + 0.971849i) q^{47} +(-6.80400 - 1.64488i) q^{49} +(2.35037 - 0.629781i) q^{50} +(3.26933 - 7.99876i) q^{52} +(1.15862 - 2.00679i) q^{53} +(-4.25365 - 2.45585i) q^{55} +(1.72898 - 1.36080i) q^{56} +(-5.66294 - 21.1344i) q^{58} +(3.35900 - 3.35900i) q^{59} +(-8.18748 - 4.72704i) q^{61} +(-3.17000 + 5.49061i) q^{62} -10.7959i q^{64} +(-4.27455 + 5.62513i) q^{65} +(-6.06032 - 1.62386i) q^{67} +17.5453i q^{68} +(-9.99105 + 4.28314i) q^{70} +(-8.32895 - 2.23174i) q^{71} +(2.01139 + 7.50661i) q^{73} -2.88849 q^{74} +(-0.597819 - 2.23109i) q^{76} +(-6.15788 - 2.46239i) q^{77} +(-2.31642 - 4.01217i) q^{79} +(-1.54654 + 5.77176i) q^{80} +(-0.770638 + 1.33478i) q^{82} +(10.1090 + 10.1090i) q^{83} +(3.71277 - 13.8563i) q^{85} +(6.34554 - 23.6819i) q^{86} +(1.80529 - 1.04229i) q^{88} +(2.89859 - 2.89859i) q^{89} +(-4.62866 + 8.34119i) q^{91} +15.9091 q^{92} +(6.81855 - 3.93669i) q^{94} +1.88849i q^{95} +(-2.63968 + 9.85141i) q^{97} +(-12.5269 + 7.64926i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48267 1.48267i 1.04840 1.04840i 0.0496376 0.998767i \(-0.484193\pi\)
0.998767 0.0496376i \(-0.0158066\pi\)
\(3\) 0 0
\(4\) 2.39661i 1.19831i
\(5\) −0.507149 + 1.89270i −0.226804 + 0.846443i 0.754870 + 0.655874i \(0.227700\pi\)
−0.981674 + 0.190569i \(0.938967\pi\)
\(6\) 0 0
\(7\) −0.313052 + 2.62717i −0.118323 + 0.992975i
\(8\) −0.588043 0.588043i −0.207905 0.207905i
\(9\) 0 0
\(10\) 2.05432 + 3.55819i 0.649633 + 1.12520i
\(11\) −0.648767 + 2.42123i −0.195611 + 0.730029i 0.796497 + 0.604642i \(0.206684\pi\)
−0.992108 + 0.125387i \(0.959983\pi\)
\(12\) 0 0
\(13\) 3.33753 + 1.36415i 0.925664 + 0.378347i
\(14\) 3.43106 + 4.35937i 0.916990 + 1.16509i
\(15\) 0 0
\(16\) 3.04948 0.762369
\(17\) −7.32088 −1.77557 −0.887787 0.460254i \(-0.847758\pi\)
−0.887787 + 0.460254i \(0.847758\pi\)
\(18\) 0 0
\(19\) 0.930935 0.249443i 0.213571 0.0572262i −0.150447 0.988618i \(-0.548071\pi\)
0.364018 + 0.931392i \(0.381405\pi\)
\(20\) 4.53608 + 1.21544i 1.01430 + 0.271780i
\(21\) 0 0
\(22\) 2.62798 + 4.55179i 0.560287 + 0.970445i
\(23\) 6.63818i 1.38416i 0.721822 + 0.692079i \(0.243305\pi\)
−0.721822 + 0.692079i \(0.756695\pi\)
\(24\) 0 0
\(25\) 1.00500 + 0.580235i 0.200999 + 0.116047i
\(26\) 6.97103 2.92587i 1.36713 0.573810i
\(27\) 0 0
\(28\) 6.29629 + 0.750265i 1.18989 + 0.141787i
\(29\) 5.21743 9.03685i 0.968852 1.67810i 0.269965 0.962870i \(-0.412988\pi\)
0.698888 0.715232i \(-0.253679\pi\)
\(30\) 0 0
\(31\) −2.92062 + 0.782577i −0.524558 + 0.140555i −0.511374 0.859358i \(-0.670863\pi\)
−0.0131839 + 0.999913i \(0.504197\pi\)
\(32\) 5.69745 5.69745i 1.00718 1.00718i
\(33\) 0 0
\(34\) −10.8544 + 10.8544i −1.86152 + 1.86152i
\(35\) −4.81368 1.92488i −0.813661 0.325364i
\(36\) 0 0
\(37\) −0.974084 0.974084i −0.160138 0.160138i 0.622490 0.782628i \(-0.286121\pi\)
−0.782628 + 0.622490i \(0.786121\pi\)
\(38\) 1.01043 1.75011i 0.163913 0.283905i
\(39\) 0 0
\(40\) 1.41122 0.814767i 0.223133 0.128826i
\(41\) −0.710011 + 0.190247i −0.110885 + 0.0297116i −0.313835 0.949478i \(-0.601614\pi\)
0.202950 + 0.979189i \(0.434947\pi\)
\(42\) 0 0
\(43\) 10.1261 5.84633i 1.54422 0.891556i 0.545656 0.838009i \(-0.316281\pi\)
0.998565 0.0535470i \(-0.0170527\pi\)
\(44\) 5.80275 + 1.55484i 0.874798 + 0.234401i
\(45\) 0 0
\(46\) 9.84223 + 9.84223i 1.45116 + 1.45116i
\(47\) 3.62699 + 0.971849i 0.529051 + 0.141759i 0.513450 0.858120i \(-0.328367\pi\)
0.0156008 + 0.999878i \(0.495034\pi\)
\(48\) 0 0
\(49\) −6.80400 1.64488i −0.972000 0.234983i
\(50\) 2.35037 0.629781i 0.332393 0.0890645i
\(51\) 0 0
\(52\) 3.26933 7.99876i 0.453375 1.10923i
\(53\) 1.15862 2.00679i 0.159149 0.275654i −0.775413 0.631454i \(-0.782458\pi\)
0.934562 + 0.355800i \(0.115792\pi\)
\(54\) 0 0
\(55\) −4.25365 2.45585i −0.573563 0.331147i
\(56\) 1.72898 1.36080i 0.231044 0.181844i
\(57\) 0 0
\(58\) −5.66294 21.1344i −0.743580 2.77508i
\(59\) 3.35900 3.35900i 0.437305 0.437305i −0.453799 0.891104i \(-0.649932\pi\)
0.891104 + 0.453799i \(0.149932\pi\)
\(60\) 0 0
\(61\) −8.18748 4.72704i −1.04830 0.605236i −0.126126 0.992014i \(-0.540254\pi\)
−0.922173 + 0.386778i \(0.873588\pi\)
\(62\) −3.17000 + 5.49061i −0.402591 + 0.697308i
\(63\) 0 0
\(64\) 10.7959i 1.34949i
\(65\) −4.27455 + 5.62513i −0.530193 + 0.697711i
\(66\) 0 0
\(67\) −6.06032 1.62386i −0.740386 0.198386i −0.131136 0.991364i \(-0.541863\pi\)
−0.609249 + 0.792979i \(0.708529\pi\)
\(68\) 17.5453i 2.12768i
\(69\) 0 0
\(70\) −9.99105 + 4.28314i −1.19416 + 0.511933i
\(71\) −8.32895 2.23174i −0.988465 0.264858i −0.271859 0.962337i \(-0.587639\pi\)
−0.716606 + 0.697479i \(0.754305\pi\)
\(72\) 0 0
\(73\) 2.01139 + 7.50661i 0.235415 + 0.878583i 0.977961 + 0.208787i \(0.0669516\pi\)
−0.742546 + 0.669795i \(0.766382\pi\)
\(74\) −2.88849 −0.335780
\(75\) 0 0
\(76\) −0.597819 2.23109i −0.0685745 0.255923i
\(77\) −6.15788 2.46239i −0.701755 0.280615i
\(78\) 0 0
\(79\) −2.31642 4.01217i −0.260618 0.451404i 0.705788 0.708423i \(-0.250593\pi\)
−0.966406 + 0.257019i \(0.917260\pi\)
\(80\) −1.54654 + 5.77176i −0.172908 + 0.645302i
\(81\) 0 0
\(82\) −0.770638 + 1.33478i −0.0851028 + 0.147402i
\(83\) 10.1090 + 10.1090i 1.10961 + 1.10961i 0.993202 + 0.116405i \(0.0371372\pi\)
0.116405 + 0.993202i \(0.462863\pi\)
\(84\) 0 0
\(85\) 3.71277 13.8563i 0.402707 1.50292i
\(86\) 6.34554 23.6819i 0.684257 2.55368i
\(87\) 0 0
\(88\) 1.80529 1.04229i 0.192445 0.111108i
\(89\) 2.89859 2.89859i 0.307250 0.307250i −0.536592 0.843842i \(-0.680289\pi\)
0.843842 + 0.536592i \(0.180289\pi\)
\(90\) 0 0
\(91\) −4.62866 + 8.34119i −0.485216 + 0.874394i
\(92\) 15.9091 1.65864
\(93\) 0 0
\(94\) 6.81855 3.93669i 0.703280 0.406039i
\(95\) 1.88849i 0.193755i
\(96\) 0 0
\(97\) −2.63968 + 9.85141i −0.268019 + 1.00026i 0.692358 + 0.721554i \(0.256572\pi\)
−0.960377 + 0.278705i \(0.910095\pi\)
\(98\) −12.5269 + 7.64926i −1.26541 + 0.772692i
\(99\) 0 0
\(100\) 1.39060 2.40859i 0.139060 0.240859i
\(101\) 1.90282 + 3.29578i 0.189337 + 0.327942i 0.945030 0.326985i \(-0.106033\pi\)
−0.755692 + 0.654927i \(0.772699\pi\)
\(102\) 0 0
\(103\) −4.75097 8.22892i −0.468127 0.810819i 0.531210 0.847240i \(-0.321738\pi\)
−0.999337 + 0.0364211i \(0.988404\pi\)
\(104\) −1.16043 2.76479i −0.113790 0.271110i
\(105\) 0 0
\(106\) −1.25755 4.69325i −0.122144 0.455849i
\(107\) 9.75503 0.943055 0.471527 0.881851i \(-0.343703\pi\)
0.471527 + 0.881851i \(0.343703\pi\)
\(108\) 0 0
\(109\) 1.54206 + 5.75506i 0.147703 + 0.551235i 0.999620 + 0.0275585i \(0.00877324\pi\)
−0.851917 + 0.523676i \(0.824560\pi\)
\(110\) −9.94797 + 2.66555i −0.948501 + 0.254150i
\(111\) 0 0
\(112\) −0.954645 + 8.01148i −0.0902055 + 0.757014i
\(113\) −5.65861 9.80099i −0.532317 0.922000i −0.999288 0.0377273i \(-0.987988\pi\)
0.466971 0.884273i \(-0.345345\pi\)
\(114\) 0 0
\(115\) −12.5641 3.36655i −1.17161 0.313932i
\(116\) −21.6578 12.5042i −2.01088 1.16098i
\(117\) 0 0
\(118\) 9.96057i 0.916945i
\(119\) 2.29182 19.2332i 0.210091 1.76310i
\(120\) 0 0
\(121\) 4.08482 + 2.35837i 0.371347 + 0.214397i
\(122\) −19.1479 + 5.13068i −1.73357 + 0.464510i
\(123\) 0 0
\(124\) 1.87553 + 6.99958i 0.168428 + 0.628581i
\(125\) −8.53568 + 8.53568i −0.763454 + 0.763454i
\(126\) 0 0
\(127\) 9.81199 + 5.66496i 0.870673 + 0.502684i 0.867572 0.497312i \(-0.165679\pi\)
0.00310144 + 0.999995i \(0.499013\pi\)
\(128\) −4.61185 4.61185i −0.407634 0.407634i
\(129\) 0 0
\(130\) 2.00246 + 14.6779i 0.175627 + 1.28734i
\(131\) 12.3925 7.15480i 1.08274 0.625118i 0.151102 0.988518i \(-0.451718\pi\)
0.931633 + 0.363401i \(0.118384\pi\)
\(132\) 0 0
\(133\) 0.363897 + 2.52381i 0.0315539 + 0.218842i
\(134\) −11.3931 + 6.57780i −0.984213 + 0.568235i
\(135\) 0 0
\(136\) 4.30500 + 4.30500i 0.369150 + 0.369150i
\(137\) 4.02745 + 4.02745i 0.344089 + 0.344089i 0.857902 0.513813i \(-0.171768\pi\)
−0.513813 + 0.857902i \(0.671768\pi\)
\(138\) 0 0
\(139\) 9.38055 5.41586i 0.795648 0.459368i −0.0462992 0.998928i \(-0.514743\pi\)
0.841947 + 0.539560i \(0.181409\pi\)
\(140\) −4.61319 + 11.5365i −0.389885 + 0.975015i
\(141\) 0 0
\(142\) −15.6580 + 9.04015i −1.31399 + 0.758633i
\(143\) −5.46820 + 7.19592i −0.457274 + 0.601753i
\(144\) 0 0
\(145\) 14.4581 + 14.4581i 1.20068 + 1.20068i
\(146\) 14.1120 + 8.14759i 1.16792 + 0.674300i
\(147\) 0 0
\(148\) −2.33450 + 2.33450i −0.191895 + 0.191895i
\(149\) −2.30894 8.61708i −0.189156 0.705939i −0.993703 0.112050i \(-0.964258\pi\)
0.804547 0.593889i \(-0.202408\pi\)
\(150\) 0 0
\(151\) −12.4233 + 3.32882i −1.01100 + 0.270896i −0.726046 0.687647i \(-0.758644\pi\)
−0.284951 + 0.958542i \(0.591977\pi\)
\(152\) −0.694113 0.400747i −0.0563000 0.0325048i
\(153\) 0 0
\(154\) −12.7810 + 5.47918i −1.02992 + 0.441525i
\(155\) 5.92474i 0.475887i
\(156\) 0 0
\(157\) −3.95550 2.28371i −0.315683 0.182260i 0.333784 0.942650i \(-0.391675\pi\)
−0.649467 + 0.760390i \(0.725008\pi\)
\(158\) −9.38320 2.51422i −0.746487 0.200021i
\(159\) 0 0
\(160\) 7.89413 + 13.6730i 0.624086 + 1.08095i
\(161\) −17.4396 2.07810i −1.37443 0.163777i
\(162\) 0 0
\(163\) 2.47798 0.663973i 0.194091 0.0520064i −0.160464 0.987042i \(-0.551299\pi\)
0.354555 + 0.935035i \(0.384632\pi\)
\(164\) 0.455948 + 1.70162i 0.0356036 + 0.132874i
\(165\) 0 0
\(166\) 29.9766 2.32664
\(167\) −1.90396 7.10569i −0.147333 0.549855i −0.999640 0.0268134i \(-0.991464\pi\)
0.852307 0.523041i \(-0.175203\pi\)
\(168\) 0 0
\(169\) 9.27820 + 9.10577i 0.713708 + 0.700444i
\(170\) −15.0394 26.0491i −1.15347 1.99787i
\(171\) 0 0
\(172\) −14.0114 24.2684i −1.06836 1.85045i
\(173\) 9.17077 15.8842i 0.697241 1.20766i −0.272178 0.962247i \(-0.587744\pi\)
0.969419 0.245410i \(-0.0789225\pi\)
\(174\) 0 0
\(175\) −1.83899 + 2.45865i −0.139015 + 0.185856i
\(176\) −1.97840 + 7.38349i −0.149127 + 0.556551i
\(177\) 0 0
\(178\) 8.59529i 0.644244i
\(179\) 1.65369 0.954758i 0.123603 0.0713620i −0.436924 0.899498i \(-0.643932\pi\)
0.560527 + 0.828136i \(0.310599\pi\)
\(180\) 0 0
\(181\) −18.9344 −1.40738 −0.703691 0.710506i \(-0.748466\pi\)
−0.703691 + 0.710506i \(0.748466\pi\)
\(182\) 5.50445 + 19.2300i 0.408017 + 1.42542i
\(183\) 0 0
\(184\) 3.90354 3.90354i 0.287773 0.287773i
\(185\) 2.33766 1.34965i 0.171868 0.0992281i
\(186\) 0 0
\(187\) 4.74955 17.7255i 0.347321 1.29622i
\(188\) 2.32914 8.69248i 0.169870 0.633965i
\(189\) 0 0
\(190\) 2.80000 + 2.80000i 0.203134 + 0.203134i
\(191\) 5.39449 9.34352i 0.390331 0.676074i −0.602162 0.798374i \(-0.705694\pi\)
0.992493 + 0.122300i \(0.0390271\pi\)
\(192\) 0 0
\(193\) 5.08690 18.9846i 0.366163 1.36654i −0.499674 0.866213i \(-0.666547\pi\)
0.865837 0.500326i \(-0.166786\pi\)
\(194\) 10.6926 + 18.5201i 0.767685 + 1.32967i
\(195\) 0 0
\(196\) −3.94214 + 16.3065i −0.281581 + 1.16475i
\(197\) 2.96842 + 11.0783i 0.211491 + 0.789295i 0.987372 + 0.158417i \(0.0506389\pi\)
−0.775881 + 0.630879i \(0.782694\pi\)
\(198\) 0 0
\(199\) −5.55472 −0.393764 −0.196882 0.980427i \(-0.563082\pi\)
−0.196882 + 0.980427i \(0.563082\pi\)
\(200\) −0.249778 0.932185i −0.0176620 0.0659155i
\(201\) 0 0
\(202\) 7.70779 + 2.06530i 0.542318 + 0.145314i
\(203\) 22.1080 + 16.5361i 1.55168 + 1.16060i
\(204\) 0 0
\(205\) 1.44032i 0.100597i
\(206\) −19.2449 5.15665i −1.34085 0.359281i
\(207\) 0 0
\(208\) 10.1777 + 4.15994i 0.705698 + 0.288440i
\(209\) 2.41584i 0.167107i
\(210\) 0 0
\(211\) −8.06339 + 13.9662i −0.555106 + 0.961473i 0.442789 + 0.896626i \(0.353989\pi\)
−0.997895 + 0.0648467i \(0.979344\pi\)
\(212\) −4.80949 2.77676i −0.330317 0.190709i
\(213\) 0 0
\(214\) 14.4635 14.4635i 0.988703 0.988703i
\(215\) 5.92991 + 22.1307i 0.404417 + 1.50930i
\(216\) 0 0
\(217\) −1.14165 7.91793i −0.0775004 0.537504i
\(218\) 10.8192 + 6.24648i 0.732770 + 0.423065i
\(219\) 0 0
\(220\) −5.88571 + 10.1944i −0.396815 + 0.687303i
\(221\) −24.4337 9.98677i −1.64359 0.671783i
\(222\) 0 0
\(223\) 25.6580 6.87505i 1.71819 0.460387i 0.740781 0.671747i \(-0.234456\pi\)
0.977408 + 0.211359i \(0.0677890\pi\)
\(224\) 13.1845 + 16.7517i 0.880929 + 1.11927i
\(225\) 0 0
\(226\) −22.9215 6.14179i −1.52471 0.408546i
\(227\) −1.25693 1.25693i −0.0834252 0.0834252i 0.664163 0.747588i \(-0.268788\pi\)
−0.747588 + 0.664163i \(0.768788\pi\)
\(228\) 0 0
\(229\) −8.68390 2.32685i −0.573849 0.153762i −0.0397875 0.999208i \(-0.512668\pi\)
−0.534061 + 0.845446i \(0.679335\pi\)
\(230\) −23.6199 + 13.6370i −1.55745 + 0.899194i
\(231\) 0 0
\(232\) −8.38214 + 2.24599i −0.550314 + 0.147456i
\(233\) −0.891738 + 0.514845i −0.0584197 + 0.0337286i −0.528925 0.848668i \(-0.677405\pi\)
0.470506 + 0.882397i \(0.344072\pi\)
\(234\) 0 0
\(235\) −3.67884 + 6.37195i −0.239981 + 0.415660i
\(236\) −8.05022 8.05022i −0.524025 0.524025i
\(237\) 0 0
\(238\) −25.1184 31.9144i −1.62818 2.06870i
\(239\) 13.2347 13.2347i 0.856079 0.856079i −0.134795 0.990874i \(-0.543038\pi\)
0.990874 + 0.134795i \(0.0430376\pi\)
\(240\) 0 0
\(241\) 2.07666 2.07666i 0.133769 0.133769i −0.637052 0.770821i \(-0.719846\pi\)
0.770821 + 0.637052i \(0.219846\pi\)
\(242\) 9.55311 2.55975i 0.614097 0.164547i
\(243\) 0 0
\(244\) −11.3289 + 19.6222i −0.725257 + 1.25618i
\(245\) 6.56391 12.0438i 0.419353 0.769447i
\(246\) 0 0
\(247\) 3.44730 + 0.437409i 0.219346 + 0.0278317i
\(248\) 2.17764 + 1.25726i 0.138280 + 0.0798361i
\(249\) 0 0
\(250\) 25.3112i 1.60082i
\(251\) −0.244838 0.424072i −0.0154540 0.0267672i 0.858195 0.513324i \(-0.171586\pi\)
−0.873649 + 0.486557i \(0.838253\pi\)
\(252\) 0 0
\(253\) −16.0726 4.30664i −1.01047 0.270756i
\(254\) 22.9472 6.14868i 1.43983 0.385802i
\(255\) 0 0
\(256\) 7.91613 0.494758
\(257\) −18.7117 −1.16720 −0.583602 0.812040i \(-0.698357\pi\)
−0.583602 + 0.812040i \(0.698357\pi\)
\(258\) 0 0
\(259\) 2.86402 2.25414i 0.177961 0.140065i
\(260\) 13.4812 + 10.2444i 0.836072 + 0.635333i
\(261\) 0 0
\(262\) 7.76574 28.9821i 0.479769 1.79052i
\(263\) −1.72119 2.98119i −0.106133 0.183828i 0.808067 0.589090i \(-0.200514\pi\)
−0.914201 + 0.405262i \(0.867180\pi\)
\(264\) 0 0
\(265\) 3.21067 + 3.21067i 0.197230 + 0.197230i
\(266\) 4.28151 + 3.20243i 0.262516 + 0.196354i
\(267\) 0 0
\(268\) −3.89176 + 14.5242i −0.237727 + 0.887208i
\(269\) 9.04672i 0.551588i 0.961217 + 0.275794i \(0.0889408\pi\)
−0.961217 + 0.275794i \(0.911059\pi\)
\(270\) 0 0
\(271\) −5.53295 + 5.53295i −0.336103 + 0.336103i −0.854898 0.518796i \(-0.826381\pi\)
0.518796 + 0.854898i \(0.326381\pi\)
\(272\) −22.3249 −1.35364
\(273\) 0 0
\(274\) 11.9428 0.721488
\(275\) −2.05689 + 2.05689i −0.124035 + 0.124035i
\(276\) 0 0
\(277\) 1.54911i 0.0930772i −0.998916 0.0465386i \(-0.985181\pi\)
0.998916 0.0465386i \(-0.0148190\pi\)
\(278\) 5.87832 21.9382i 0.352558 1.31576i
\(279\) 0 0
\(280\) 1.69874 + 3.96257i 0.101519 + 0.236809i
\(281\) −4.20181 4.20181i −0.250659 0.250659i 0.570582 0.821241i \(-0.306718\pi\)
−0.821241 + 0.570582i \(0.806718\pi\)
\(282\) 0 0
\(283\) −2.32807 4.03233i −0.138389 0.239697i 0.788498 0.615038i \(-0.210859\pi\)
−0.926887 + 0.375340i \(0.877526\pi\)
\(284\) −5.34860 + 19.9613i −0.317381 + 1.18448i
\(285\) 0 0
\(286\) 2.56163 + 18.7767i 0.151473 + 1.11029i
\(287\) −0.277540 1.92487i −0.0163826 0.113622i
\(288\) 0 0
\(289\) 36.5953 2.15266
\(290\) 42.8731 2.51759
\(291\) 0 0
\(292\) 17.9904 4.82052i 1.05281 0.282100i
\(293\) −10.8009 2.89410i −0.630997 0.169075i −0.0708751 0.997485i \(-0.522579\pi\)
−0.560122 + 0.828410i \(0.689246\pi\)
\(294\) 0 0
\(295\) 4.65408 + 8.06111i 0.270971 + 0.469336i
\(296\) 1.14561i 0.0665871i
\(297\) 0 0
\(298\) −16.1997 9.35289i −0.938422 0.541798i
\(299\) −9.05547 + 22.1551i −0.523691 + 1.28126i
\(300\) 0 0
\(301\) 12.1893 + 28.4332i 0.702577 + 1.63886i
\(302\) −13.4841 + 23.3552i −0.775925 + 1.34394i
\(303\) 0 0
\(304\) 2.83886 0.760671i 0.162820 0.0436275i
\(305\) 13.0992 13.0992i 0.750056 0.750056i
\(306\) 0 0
\(307\) 2.63969 2.63969i 0.150655 0.150655i −0.627756 0.778411i \(-0.716026\pi\)
0.778411 + 0.627756i \(0.216026\pi\)
\(308\) −5.90139 + 14.7580i −0.336263 + 0.840917i
\(309\) 0 0
\(310\) −8.78443 8.78443i −0.498922 0.498922i
\(311\) 16.2833 28.2035i 0.923341 1.59927i 0.129133 0.991627i \(-0.458780\pi\)
0.794208 0.607646i \(-0.207886\pi\)
\(312\) 0 0
\(313\) −12.7123 + 7.33945i −0.718541 + 0.414850i −0.814216 0.580563i \(-0.802833\pi\)
0.0956743 + 0.995413i \(0.469499\pi\)
\(314\) −9.25067 + 2.47871i −0.522046 + 0.139882i
\(315\) 0 0
\(316\) −9.61560 + 5.55157i −0.540920 + 0.312300i
\(317\) −9.92063 2.65822i −0.557198 0.149301i −0.0307793 0.999526i \(-0.509799\pi\)
−0.526419 + 0.850225i \(0.676466\pi\)
\(318\) 0 0
\(319\) 18.4954 + 18.4954i 1.03554 + 1.03554i
\(320\) 20.4335 + 5.47513i 1.14226 + 0.306069i
\(321\) 0 0
\(322\) −28.9383 + 22.7760i −1.61267 + 1.26926i
\(323\) −6.81526 + 1.82614i −0.379211 + 0.101609i
\(324\) 0 0
\(325\) 2.56268 + 3.30752i 0.142152 + 0.183468i
\(326\) 2.68957 4.65848i 0.148962 0.258009i
\(327\) 0 0
\(328\) 0.529391 + 0.305644i 0.0292307 + 0.0168764i
\(329\) −3.68864 + 9.22446i −0.203362 + 0.508561i
\(330\) 0 0
\(331\) −6.55085 24.4481i −0.360068 1.34379i −0.873986 0.485951i \(-0.838473\pi\)
0.513918 0.857839i \(-0.328193\pi\)
\(332\) 24.2274 24.2274i 1.32965 1.32965i
\(333\) 0 0
\(334\) −13.3583 7.71243i −0.730935 0.422006i
\(335\) 6.14696 10.6469i 0.335845 0.581700i
\(336\) 0 0
\(337\) 0.741618i 0.0403985i −0.999796 0.0201993i \(-0.993570\pi\)
0.999796 0.0201993i \(-0.00643006\pi\)
\(338\) 27.2573 0.255654i 1.48260 0.0139058i
\(339\) 0 0
\(340\) −33.2081 8.89808i −1.80096 0.482566i
\(341\) 7.57920i 0.410436i
\(342\) 0 0
\(343\) 6.45138 17.3603i 0.348342 0.937368i
\(344\) −9.39250 2.51671i −0.506410 0.135692i
\(345\) 0 0
\(346\) −9.95385 37.1483i −0.535122 1.99710i
\(347\) −34.1772 −1.83473 −0.917364 0.398048i \(-0.869688\pi\)
−0.917364 + 0.398048i \(0.869688\pi\)
\(348\) 0 0
\(349\) 7.26033 + 27.0959i 0.388636 + 1.45041i 0.832354 + 0.554244i \(0.186993\pi\)
−0.443718 + 0.896167i \(0.646341\pi\)
\(350\) 0.918749 + 6.37198i 0.0491092 + 0.340596i
\(351\) 0 0
\(352\) 10.0985 + 17.4912i 0.538253 + 0.932282i
\(353\) 2.49904 9.32655i 0.133011 0.496402i −0.866988 0.498330i \(-0.833947\pi\)
0.999998 + 0.00192769i \(0.000613602\pi\)
\(354\) 0 0
\(355\) 8.44803 14.6324i 0.448375 0.776608i
\(356\) −6.94679 6.94679i −0.368179 0.368179i
\(357\) 0 0
\(358\) 1.03628 3.86746i 0.0547693 0.204402i
\(359\) −8.84959 + 33.0271i −0.467064 + 1.74311i 0.182891 + 0.983133i \(0.441454\pi\)
−0.649955 + 0.759973i \(0.725212\pi\)
\(360\) 0 0
\(361\) −15.6501 + 9.03557i −0.823688 + 0.475556i
\(362\) −28.0734 + 28.0734i −1.47551 + 1.47551i
\(363\) 0 0
\(364\) 19.9906 + 11.0931i 1.04779 + 0.581437i
\(365\) −15.2279 −0.797063
\(366\) 0 0
\(367\) −23.1967 + 13.3926i −1.21086 + 0.699090i −0.962947 0.269692i \(-0.913078\pi\)
−0.247913 + 0.968782i \(0.579745\pi\)
\(368\) 20.2430i 1.05524i
\(369\) 0 0
\(370\) 1.46489 5.46705i 0.0761561 0.284218i
\(371\) 4.90946 + 3.67212i 0.254886 + 0.190647i
\(372\) 0 0
\(373\) −1.83233 + 3.17370i −0.0948747 + 0.164328i −0.909556 0.415581i \(-0.863578\pi\)
0.814682 + 0.579908i \(0.196912\pi\)
\(374\) −19.2391 33.3231i −0.994831 1.72310i
\(375\) 0 0
\(376\) −1.56134 2.70432i −0.0805198 0.139464i
\(377\) 29.7409 23.0434i 1.53174 1.18680i
\(378\) 0 0
\(379\) −6.16351 23.0025i −0.316598 1.18156i −0.922492 0.386016i \(-0.873851\pi\)
0.605894 0.795545i \(-0.292816\pi\)
\(380\) 4.52597 0.232178
\(381\) 0 0
\(382\) −5.85511 21.8516i −0.299574 1.11802i
\(383\) 29.5578 7.91998i 1.51033 0.404692i 0.593786 0.804623i \(-0.297632\pi\)
0.916545 + 0.399931i \(0.130966\pi\)
\(384\) 0 0
\(385\) 7.78354 10.4062i 0.396686 0.530351i
\(386\) −20.6056 35.6900i −1.04880 1.81657i
\(387\) 0 0
\(388\) 23.6100 + 6.32628i 1.19862 + 0.321168i
\(389\) 1.02102 + 0.589484i 0.0517676 + 0.0298880i 0.525660 0.850694i \(-0.323818\pi\)
−0.473893 + 0.880583i \(0.657152\pi\)
\(390\) 0 0
\(391\) 48.5974i 2.45767i
\(392\) 3.03378 + 4.96831i 0.153229 + 0.250937i
\(393\) 0 0
\(394\) 20.8266 + 12.0242i 1.04923 + 0.605773i
\(395\) 8.76861 2.34954i 0.441197 0.118218i
\(396\) 0 0
\(397\) −3.14500 11.7373i −0.157843 0.589078i −0.998845 0.0480464i \(-0.984700\pi\)
0.841002 0.541032i \(-0.181966\pi\)
\(398\) −8.23581 + 8.23581i −0.412824 + 0.412824i
\(399\) 0 0
\(400\) 3.06471 + 1.76941i 0.153236 + 0.0884707i
\(401\) 1.52505 + 1.52505i 0.0761573 + 0.0761573i 0.744159 0.668002i \(-0.232850\pi\)
−0.668002 + 0.744159i \(0.732850\pi\)
\(402\) 0 0
\(403\) −10.8152 1.37228i −0.538743 0.0683582i
\(404\) 7.89869 4.56031i 0.392975 0.226884i
\(405\) 0 0
\(406\) 57.2963 8.26131i 2.84357 0.410002i
\(407\) 2.99044 1.72653i 0.148230 0.0855809i
\(408\) 0 0
\(409\) −3.39607 3.39607i −0.167925 0.167925i 0.618142 0.786067i \(-0.287886\pi\)
−0.786067 + 0.618142i \(0.787886\pi\)
\(410\) −2.13552 2.13552i −0.105466 0.105466i
\(411\) 0 0
\(412\) −19.7215 + 11.3862i −0.971609 + 0.560959i
\(413\) 7.77311 + 9.87620i 0.382490 + 0.485976i
\(414\) 0 0
\(415\) −24.2601 + 14.0066i −1.19088 + 0.687556i
\(416\) 26.7876 11.2432i 1.31337 0.551245i
\(417\) 0 0
\(418\) 3.58189 + 3.58189i 0.175196 + 0.175196i
\(419\) 18.2738 + 10.5504i 0.892733 + 0.515420i 0.874836 0.484420i \(-0.160969\pi\)
0.0178978 + 0.999840i \(0.494303\pi\)
\(420\) 0 0
\(421\) 24.4128 24.4128i 1.18981 1.18981i 0.212688 0.977120i \(-0.431778\pi\)
0.977120 0.212688i \(-0.0682218\pi\)
\(422\) 8.75191 + 32.6626i 0.426036 + 1.58999i
\(423\) 0 0
\(424\) −1.86140 + 0.498760i −0.0903975 + 0.0242219i
\(425\) −7.35746 4.24783i −0.356889 0.206050i
\(426\) 0 0
\(427\) 14.9818 20.0300i 0.725022 0.969322i
\(428\) 23.3790i 1.13007i
\(429\) 0 0
\(430\) 41.6046 + 24.0204i 2.00635 + 1.15837i
\(431\) 7.96117 + 2.13319i 0.383476 + 0.102752i 0.445407 0.895328i \(-0.353059\pi\)
−0.0619308 + 0.998080i \(0.519726\pi\)
\(432\) 0 0
\(433\) −13.2942 23.0262i −0.638878 1.10657i −0.985679 0.168631i \(-0.946065\pi\)
0.346801 0.937939i \(-0.387268\pi\)
\(434\) −13.4324 10.0470i −0.644774 0.482270i
\(435\) 0 0
\(436\) 13.7926 3.69573i 0.660548 0.176993i
\(437\) 1.65585 + 6.17972i 0.0792101 + 0.295616i
\(438\) 0 0
\(439\) −17.8799 −0.853362 −0.426681 0.904402i \(-0.640317\pi\)
−0.426681 + 0.904402i \(0.640317\pi\)
\(440\) 1.05719 + 3.94548i 0.0503994 + 0.188093i
\(441\) 0 0
\(442\) −51.0341 + 21.4199i −2.42744 + 1.01884i
\(443\) −10.8928 18.8669i −0.517532 0.896392i −0.999793 0.0203640i \(-0.993517\pi\)
0.482261 0.876028i \(-0.339816\pi\)
\(444\) 0 0
\(445\) 4.01615 + 6.95618i 0.190384 + 0.329755i
\(446\) 27.8489 48.2358i 1.31869 2.28403i
\(447\) 0 0
\(448\) 28.3626 + 3.37968i 1.34001 + 0.159675i
\(449\) 0.850694 3.17483i 0.0401467 0.149830i −0.942943 0.332954i \(-0.891955\pi\)
0.983090 + 0.183125i \(0.0586212\pi\)
\(450\) 0 0
\(451\) 1.84253i 0.0867612i
\(452\) −23.4892 + 13.5615i −1.10484 + 0.637878i
\(453\) 0 0
\(454\) −3.72721 −0.174927
\(455\) −13.4400 12.9909i −0.630076 0.609024i
\(456\) 0 0
\(457\) 25.5511 25.5511i 1.19523 1.19523i 0.219653 0.975578i \(-0.429507\pi\)
0.975578 0.219653i \(-0.0704925\pi\)
\(458\) −16.3253 + 9.42541i −0.762831 + 0.440421i
\(459\) 0 0
\(460\) −8.06830 + 30.1113i −0.376187 + 1.40395i
\(461\) −3.32485 + 12.4085i −0.154854 + 0.577922i 0.844264 + 0.535927i \(0.180038\pi\)
−0.999118 + 0.0419948i \(0.986629\pi\)
\(462\) 0 0
\(463\) 22.2200 + 22.2200i 1.03265 + 1.03265i 0.999449 + 0.0332014i \(0.0105703\pi\)
0.0332014 + 0.999449i \(0.489430\pi\)
\(464\) 15.9104 27.5577i 0.738623 1.27933i
\(465\) 0 0
\(466\) −0.558807 + 2.08550i −0.0258862 + 0.0966087i
\(467\) 17.1486 + 29.7023i 0.793543 + 1.37446i 0.923760 + 0.382972i \(0.125099\pi\)
−0.130217 + 0.991486i \(0.541567\pi\)
\(468\) 0 0
\(469\) 6.16334 15.4131i 0.284597 0.711711i
\(470\) 3.99298 + 14.9020i 0.184182 + 0.687378i
\(471\) 0 0
\(472\) −3.95048 −0.181835
\(473\) 7.58581 + 28.3106i 0.348796 + 1.30172i
\(474\) 0 0
\(475\) 1.08032 + 0.289472i 0.0495686 + 0.0132819i
\(476\) −46.0944 5.49260i −2.11273 0.251753i
\(477\) 0 0
\(478\) 39.2452i 1.79503i
\(479\) −2.30910 0.618722i −0.105505 0.0282701i 0.205680 0.978619i \(-0.434059\pi\)
−0.311186 + 0.950349i \(0.600726\pi\)
\(480\) 0 0
\(481\) −1.92224 4.57983i −0.0876465 0.208822i
\(482\) 6.15798i 0.280489i
\(483\) 0 0
\(484\) 5.65210 9.78972i 0.256913 0.444987i
\(485\) −17.3071 9.99226i −0.785875 0.453725i
\(486\) 0 0
\(487\) −5.93438 + 5.93438i −0.268912 + 0.268912i −0.828662 0.559749i \(-0.810897\pi\)
0.559749 + 0.828662i \(0.310897\pi\)
\(488\) 2.03489 + 7.59430i 0.0921149 + 0.343778i
\(489\) 0 0
\(490\) −8.12479 27.5890i −0.367041 1.24634i
\(491\) 5.46870 + 3.15735i 0.246799 + 0.142489i 0.618298 0.785944i \(-0.287823\pi\)
−0.371499 + 0.928433i \(0.621156\pi\)
\(492\) 0 0
\(493\) −38.1962 + 66.1577i −1.72027 + 2.97959i
\(494\) 5.75974 4.46267i 0.259143 0.200785i
\(495\) 0 0
\(496\) −8.90635 + 2.38645i −0.399907 + 0.107155i
\(497\) 8.47054 21.1829i 0.379956 0.950182i
\(498\) 0 0
\(499\) 33.9532 + 9.09774i 1.51996 + 0.407271i 0.919727 0.392558i \(-0.128410\pi\)
0.600228 + 0.799829i \(0.295077\pi\)
\(500\) 20.4567 + 20.4567i 0.914851 + 0.914851i
\(501\) 0 0
\(502\) −0.991772 0.265744i −0.0442649 0.0118608i
\(503\) 8.32980 4.80921i 0.371408 0.214432i −0.302666 0.953097i \(-0.597877\pi\)
0.674073 + 0.738665i \(0.264543\pi\)
\(504\) 0 0
\(505\) −7.20294 + 1.93002i −0.320527 + 0.0858849i
\(506\) −30.2156 + 17.4450i −1.34325 + 0.775525i
\(507\) 0 0
\(508\) 13.5767 23.5155i 0.602369 1.04333i
\(509\) 9.11455 + 9.11455i 0.403995 + 0.403995i 0.879638 0.475643i \(-0.157785\pi\)
−0.475643 + 0.879638i \(0.657785\pi\)
\(510\) 0 0
\(511\) −20.3508 + 2.93429i −0.900266 + 0.129806i
\(512\) 20.9607 20.9607i 0.926340 0.926340i
\(513\) 0 0
\(514\) −27.7432 + 27.7432i −1.22370 + 1.22370i
\(515\) 17.9844 4.81889i 0.792485 0.212346i
\(516\) 0 0
\(517\) −4.70614 + 8.15128i −0.206976 + 0.358493i
\(518\) 0.904247 7.58853i 0.0397303 0.333421i
\(519\) 0 0
\(520\) 5.82144 0.794198i 0.255287 0.0348279i
\(521\) 9.09809 + 5.25278i 0.398594 + 0.230129i 0.685877 0.727717i \(-0.259419\pi\)
−0.287283 + 0.957846i \(0.592752\pi\)
\(522\) 0 0
\(523\) 0.571212i 0.0249773i 0.999922 + 0.0124887i \(0.00397537\pi\)
−0.999922 + 0.0124887i \(0.996025\pi\)
\(524\) −17.1473 29.6999i −0.749082 1.29745i
\(525\) 0 0
\(526\) −6.97208 1.86816i −0.303997 0.0814558i
\(527\) 21.3815 5.72915i 0.931392 0.249566i
\(528\) 0 0
\(529\) −21.0655 −0.915891
\(530\) 9.52071 0.413553
\(531\) 0 0
\(532\) 6.04859 0.872121i 0.262240 0.0378112i
\(533\) −2.62921 0.333606i −0.113884 0.0144501i
\(534\) 0 0
\(535\) −4.94725 + 18.4634i −0.213888 + 0.798242i
\(536\) 2.60883 + 4.51863i 0.112684 + 0.195175i
\(537\) 0 0
\(538\) 13.4133 + 13.4133i 0.578288 + 0.578288i
\(539\) 8.39684 15.4069i 0.361678 0.663622i
\(540\) 0 0
\(541\) −3.18970 + 11.9041i −0.137136 + 0.511798i 0.862844 + 0.505470i \(0.168681\pi\)
−0.999980 + 0.00632795i \(0.997986\pi\)
\(542\) 16.4070i 0.704743i
\(543\) 0 0
\(544\) −41.7103 + 41.7103i −1.78832 + 1.78832i
\(545\) −11.6747 −0.500089
\(546\) 0 0
\(547\) −16.2110 −0.693132 −0.346566 0.938026i \(-0.612652\pi\)
−0.346566 + 0.938026i \(0.612652\pi\)
\(548\) 9.65224 9.65224i 0.412323 0.412323i
\(549\) 0 0
\(550\) 6.09938i 0.260078i
\(551\) 2.60291 9.71418i 0.110887 0.413838i
\(552\) 0 0
\(553\) 11.2658 4.82961i 0.479070 0.205376i
\(554\) −2.29682 2.29682i −0.0975826 0.0975826i
\(555\) 0 0
\(556\) −12.9797 22.4815i −0.550463 0.953429i
\(557\) −8.66766 + 32.3481i −0.367260 + 1.37063i 0.497070 + 0.867710i \(0.334409\pi\)
−0.864330 + 0.502924i \(0.832257\pi\)
\(558\) 0 0
\(559\) 41.7715 5.69873i 1.76675 0.241031i
\(560\) −14.6792 5.86987i −0.620310 0.248047i
\(561\) 0 0
\(562\) −12.4598 −0.525584
\(563\) 0.157014 0.00661736 0.00330868 0.999995i \(-0.498947\pi\)
0.00330868 + 0.999995i \(0.498947\pi\)
\(564\) 0 0
\(565\) 21.4201 5.73951i 0.901152 0.241463i
\(566\) −9.43036 2.52686i −0.396388 0.106212i
\(567\) 0 0
\(568\) 3.58543 + 6.21014i 0.150441 + 0.260572i
\(569\) 42.2556i 1.77145i 0.464213 + 0.885724i \(0.346337\pi\)
−0.464213 + 0.885724i \(0.653663\pi\)
\(570\) 0 0
\(571\) 28.4747 + 16.4399i 1.19163 + 0.687987i 0.958676 0.284502i \(-0.0918281\pi\)
0.232952 + 0.972488i \(0.425161\pi\)
\(572\) 17.2458 + 13.1051i 0.721084 + 0.547954i
\(573\) 0 0
\(574\) −3.26545 2.44245i −0.136297 0.101946i
\(575\) −3.85171 + 6.67136i −0.160627 + 0.278215i
\(576\) 0 0
\(577\) 41.6112 11.1497i 1.73230 0.464167i 0.751586 0.659635i \(-0.229289\pi\)
0.980710 + 0.195467i \(0.0626223\pi\)
\(578\) 54.2587 54.2587i 2.25686 2.25686i
\(579\) 0 0
\(580\) 34.6504 34.6504i 1.43878 1.43878i
\(581\) −29.7227 + 23.3934i −1.23310 + 0.970521i
\(582\) 0 0
\(583\) 4.10723 + 4.10723i 0.170104 + 0.170104i
\(584\) 3.23143 5.59700i 0.133717 0.231605i
\(585\) 0 0
\(586\) −20.3052 + 11.7232i −0.838800 + 0.484281i
\(587\) 15.3441 4.11144i 0.633318 0.169697i 0.0721432 0.997394i \(-0.477016\pi\)
0.561175 + 0.827697i \(0.310349\pi\)
\(588\) 0 0
\(589\) −2.52369 + 1.45706i −0.103987 + 0.0600369i
\(590\) 18.8524 + 5.05149i 0.776142 + 0.207967i
\(591\) 0 0
\(592\) −2.97045 2.97045i −0.122085 0.122085i
\(593\) −18.7597 5.02665i −0.770369 0.206420i −0.147834 0.989012i \(-0.547230\pi\)
−0.622534 + 0.782592i \(0.713897\pi\)
\(594\) 0 0
\(595\) 35.2404 + 14.0918i 1.44472 + 0.577708i
\(596\) −20.6518 + 5.53363i −0.845931 + 0.226666i
\(597\) 0 0
\(598\) 19.4225 + 46.2750i 0.794243 + 1.89232i
\(599\) −22.3885 + 38.7780i −0.914770 + 1.58443i −0.107531 + 0.994202i \(0.534295\pi\)
−0.807238 + 0.590226i \(0.799039\pi\)
\(600\) 0 0
\(601\) −33.7722 19.4984i −1.37760 0.795355i −0.385726 0.922613i \(-0.626049\pi\)
−0.991870 + 0.127258i \(0.959382\pi\)
\(602\) 60.2297 + 24.0844i 2.45478 + 0.981608i
\(603\) 0 0
\(604\) 7.97789 + 29.7739i 0.324616 + 1.21148i
\(605\) −6.53531 + 6.53531i −0.265698 + 0.265698i
\(606\) 0 0
\(607\) 27.6946 + 15.9895i 1.12409 + 0.648992i 0.942441 0.334372i \(-0.108524\pi\)
0.181646 + 0.983364i \(0.441857\pi\)
\(608\) 3.88276 6.72514i 0.157467 0.272741i
\(609\) 0 0
\(610\) 38.8434i 1.57272i
\(611\) 10.7794 + 8.19132i 0.436089 + 0.331386i
\(612\) 0 0
\(613\) −21.4241 5.74057i −0.865311 0.231859i −0.201252 0.979540i \(-0.564501\pi\)
−0.664059 + 0.747680i \(0.731168\pi\)
\(614\) 7.82757i 0.315895i
\(615\) 0 0
\(616\) 2.17311 + 5.06909i 0.0875570 + 0.204239i
\(617\) −19.7363 5.28833i −0.794554 0.212900i −0.161363 0.986895i \(-0.551589\pi\)
−0.633192 + 0.773995i \(0.718256\pi\)
\(618\) 0 0
\(619\) −7.46806 27.8712i −0.300167 1.12024i −0.937027 0.349258i \(-0.886434\pi\)
0.636860 0.770980i \(-0.280233\pi\)
\(620\) −14.1993 −0.570258
\(621\) 0 0
\(622\) −17.6737 65.9592i −0.708651 2.64472i
\(623\) 6.70766 + 8.52248i 0.268737 + 0.341446i
\(624\) 0 0
\(625\) −8.92548 15.4594i −0.357019 0.618375i
\(626\) −7.96615 + 29.7301i −0.318391 + 1.18825i
\(627\) 0 0
\(628\) −5.47316 + 9.47979i −0.218403 + 0.378285i
\(629\) 7.13115 + 7.13115i 0.284338 + 0.284338i
\(630\) 0 0
\(631\) −0.897330 + 3.34888i −0.0357221 + 0.133317i −0.981484 0.191544i \(-0.938651\pi\)
0.945762 + 0.324860i \(0.105317\pi\)
\(632\) −0.997169 + 3.72148i −0.0396652 + 0.148033i
\(633\) 0 0
\(634\) −18.6503 + 10.7677i −0.740697 + 0.427641i
\(635\) −15.6982 + 15.6982i −0.622965 + 0.622965i
\(636\) 0 0
\(637\) −20.4647 14.7715i −0.810840 0.585268i
\(638\) 54.8451 2.17134
\(639\) 0 0
\(640\) 11.0678 6.38997i 0.437491 0.252586i
\(641\) 6.69397i 0.264396i 0.991223 + 0.132198i \(0.0422035\pi\)
−0.991223 + 0.132198i \(0.957797\pi\)
\(642\) 0 0
\(643\) −11.3176 + 42.2380i −0.446324 + 1.66570i 0.266092 + 0.963948i \(0.414268\pi\)
−0.712416 + 0.701757i \(0.752399\pi\)
\(644\) −4.98040 + 41.7960i −0.196255 + 1.64699i
\(645\) 0 0
\(646\) −7.39721 + 12.8123i −0.291039 + 0.504095i
\(647\) −1.21242 2.09997i −0.0476652 0.0825585i 0.841208 0.540711i \(-0.181845\pi\)
−0.888874 + 0.458152i \(0.848511\pi\)
\(648\) 0 0
\(649\) 5.95371 + 10.3121i 0.233704 + 0.404787i
\(650\) 8.70356 + 1.10435i 0.341382 + 0.0433161i
\(651\) 0 0
\(652\) −1.59129 5.93876i −0.0623196 0.232580i
\(653\) −18.9747 −0.742539 −0.371269 0.928525i \(-0.621077\pi\)
−0.371269 + 0.928525i \(0.621077\pi\)
\(654\) 0 0
\(655\) 7.25709 + 27.0838i 0.283558 + 1.05825i
\(656\) −2.16516 + 0.580154i −0.0845354 + 0.0226512i
\(657\) 0 0
\(658\) 8.20778 + 19.1459i 0.319973 + 0.746383i
\(659\) 1.16446 + 2.01691i 0.0453610 + 0.0785676i 0.887814 0.460202i \(-0.152223\pi\)
−0.842453 + 0.538769i \(0.818890\pi\)
\(660\) 0 0
\(661\) −24.8482 6.65805i −0.966482 0.258968i −0.259140 0.965840i \(-0.583439\pi\)
−0.707342 + 0.706872i \(0.750106\pi\)
\(662\) −45.9612 26.5357i −1.78633 1.03134i
\(663\) 0 0
\(664\) 11.8891i 0.461385i
\(665\) −4.96137 0.591196i −0.192394 0.0229256i
\(666\) 0 0
\(667\) 59.9883 + 34.6343i 2.32276 + 1.34104i
\(668\) −17.0296 + 4.56306i −0.658894 + 0.176550i
\(669\) 0 0
\(670\) −6.67184 24.8997i −0.257756 0.961958i
\(671\) 16.7570 16.7570i 0.646898 0.646898i
\(672\) 0 0
\(673\) −24.9952 14.4310i −0.963493 0.556273i −0.0662467 0.997803i \(-0.521102\pi\)
−0.897246 + 0.441530i \(0.854436\pi\)
\(674\) −1.09957 1.09957i −0.0423540 0.0423540i
\(675\) 0 0
\(676\) 21.8230 22.2362i 0.839346 0.855240i
\(677\) −13.4814 + 7.78352i −0.518134 + 0.299145i −0.736171 0.676796i \(-0.763368\pi\)
0.218037 + 0.975941i \(0.430035\pi\)
\(678\) 0 0
\(679\) −25.0549 10.0189i −0.961520 0.384489i
\(680\) −10.3314 + 5.96481i −0.396189 + 0.228740i
\(681\) 0 0
\(682\) −11.2374 11.2374i −0.430304 0.430304i
\(683\) 29.7469 + 29.7469i 1.13823 + 1.13823i 0.988767 + 0.149467i \(0.0477557\pi\)
0.149467 + 0.988767i \(0.452244\pi\)
\(684\) 0 0
\(685\) −9.66529 + 5.58026i −0.369292 + 0.213211i
\(686\) −16.1743 35.3048i −0.617538 1.34794i
\(687\) 0 0
\(688\) 30.8794 17.8282i 1.17727 0.679695i
\(689\) 6.60449 5.11719i 0.251611 0.194949i
\(690\) 0 0
\(691\) 15.4899 + 15.4899i 0.589263 + 0.589263i 0.937432 0.348169i \(-0.113197\pi\)
−0.348169 + 0.937432i \(0.613197\pi\)
\(692\) −38.0684 21.9788i −1.44714 0.835508i
\(693\) 0 0
\(694\) −50.6735 + 50.6735i −1.92354 + 1.92354i
\(695\) 5.49329 + 20.5013i 0.208373 + 0.777657i
\(696\) 0 0
\(697\) 5.19791 1.39278i 0.196885 0.0527551i
\(698\) 50.9389 + 29.4096i 1.92807 + 1.11317i
\(699\) 0 0
\(700\) 5.89243 + 4.40735i 0.222713 + 0.166582i
\(701\) 15.8478i 0.598564i 0.954165 + 0.299282i \(0.0967471\pi\)
−0.954165 + 0.299282i \(0.903253\pi\)
\(702\) 0 0
\(703\) −1.14979 0.663830i −0.0433650 0.0250368i
\(704\) 26.1394 + 7.00403i 0.985165 + 0.263974i
\(705\) 0 0
\(706\) −10.1229 17.5334i −0.380981 0.659879i
\(707\) −9.25423 + 3.96727i −0.348041 + 0.149204i
\(708\) 0 0
\(709\) −46.6694 + 12.5050i −1.75271 + 0.469637i −0.985201 0.171404i \(-0.945170\pi\)
−0.767507 + 0.641041i \(0.778503\pi\)
\(710\) −9.16940 34.2207i −0.344121 1.28428i
\(711\) 0 0
\(712\) −3.40899 −0.127757
\(713\) −5.19489 19.3876i −0.194550 0.726071i
\(714\) 0 0
\(715\) −10.8466 13.9991i −0.405638 0.523536i
\(716\) −2.28818 3.96325i −0.0855134 0.148114i
\(717\) 0 0
\(718\) 35.8473 + 62.0893i 1.33781 + 2.31715i
\(719\) −5.32163 + 9.21734i −0.198463 + 0.343749i −0.948030 0.318180i \(-0.896928\pi\)
0.749567 + 0.661928i \(0.230262\pi\)
\(720\) 0 0
\(721\) 23.1060 9.90549i 0.860513 0.368900i
\(722\) −9.80710 + 36.6006i −0.364983 + 1.36213i
\(723\) 0 0
\(724\) 45.3784i 1.68647i
\(725\) 10.4870 6.05467i 0.389478 0.224865i
\(726\) 0 0
\(727\) 5.89296 0.218558 0.109279 0.994011i \(-0.465146\pi\)
0.109279 + 0.994011i \(0.465146\pi\)
\(728\) 7.62684 2.18313i 0.282669 0.0809120i
\(729\) 0 0
\(730\) −22.5779 + 22.5779i −0.835645 + 0.835645i
\(731\) −74.1322 + 42.8003i −2.74188 + 1.58302i
\(732\) 0 0
\(733\) 9.93532 37.0791i 0.366970 1.36955i −0.497762 0.867314i \(-0.665845\pi\)
0.864731 0.502235i \(-0.167489\pi\)
\(734\) −14.5362 + 54.2499i −0.536542 + 2.00240i
\(735\) 0 0
\(736\) 37.8207 + 37.8207i 1.39409 + 1.39409i
\(737\) 7.86347 13.6199i 0.289655 0.501696i
\(738\) 0 0
\(739\) −5.34503 + 19.9479i −0.196620 + 0.733796i 0.795221 + 0.606319i \(0.207355\pi\)
−0.991842 + 0.127477i \(0.959312\pi\)
\(740\) −3.23458 5.60246i −0.118906 0.205950i
\(741\) 0 0
\(742\) 12.7236 1.83457i 0.467099 0.0673491i
\(743\) −8.72671 32.5685i −0.320152 1.19482i −0.919097 0.394033i \(-0.871080\pi\)
0.598945 0.800790i \(-0.295587\pi\)
\(744\) 0 0
\(745\) 17.4806 0.640439
\(746\) 1.98879 + 7.42228i 0.0728150 + 0.271749i
\(747\) 0 0
\(748\) −42.4812 11.3828i −1.55327 0.416197i
\(749\) −3.05384 + 25.6281i −0.111585 + 0.936430i
\(750\) 0 0
\(751\) 31.7749i 1.15948i 0.814801 + 0.579741i \(0.196846\pi\)
−0.814801 + 0.579741i \(0.803154\pi\)
\(752\) 11.0604 + 2.96363i 0.403332 + 0.108072i
\(753\) 0 0
\(754\) 9.93020 78.2617i 0.361637 2.85012i
\(755\) 25.2019i 0.917191i
\(756\) 0 0
\(757\) −13.6215 + 23.5930i −0.495080 + 0.857504i −0.999984 0.00567171i \(-0.998195\pi\)
0.504904 + 0.863176i \(0.331528\pi\)
\(758\) −43.2436 24.9667i −1.57068 0.906831i
\(759\) 0 0
\(760\) 1.11051 1.11051i 0.0402826 0.0402826i
\(761\) −7.38152 27.5482i −0.267580 0.998622i −0.960652 0.277754i \(-0.910410\pi\)
0.693072 0.720868i \(-0.256257\pi\)
\(762\) 0 0
\(763\) −15.6022 + 2.24962i −0.564839 + 0.0814418i
\(764\) −22.3928 12.9285i −0.810143 0.467736i
\(765\) 0 0
\(766\) 32.0817 55.5671i 1.15916 2.00772i
\(767\) 15.7929 6.62859i 0.570250 0.239344i
\(768\) 0 0
\(769\) −27.2629 + 7.30506i −0.983124 + 0.263427i −0.714360 0.699779i \(-0.753282\pi\)
−0.268764 + 0.963206i \(0.586615\pi\)
\(770\) −3.88861 26.9694i −0.140136 0.971910i
\(771\) 0 0
\(772\) −45.4986 12.1913i −1.63753 0.438775i
\(773\) −8.57861 8.57861i −0.308551 0.308551i 0.535796 0.844347i \(-0.320011\pi\)
−0.844347 + 0.535796i \(0.820011\pi\)
\(774\) 0 0
\(775\) −3.38929 0.908157i −0.121747 0.0326220i
\(776\) 7.34530 4.24081i 0.263681 0.152236i
\(777\) 0 0
\(778\) 2.38784 0.639819i 0.0856082 0.0229386i
\(779\) −0.613518 + 0.354215i −0.0219816 + 0.0126911i
\(780\) 0 0
\(781\) 10.8071 18.7184i 0.386708 0.669799i
\(782\) −72.0538 72.0538i −2.57664 2.57664i
\(783\) 0 0
\(784\) −20.7486 5.01602i −0.741022 0.179144i
\(785\) 6.32841 6.32841i 0.225871 0.225871i
\(786\) 0 0
\(787\) 13.1589 13.1589i 0.469063 0.469063i −0.432548 0.901611i \(-0.642385\pi\)
0.901611 + 0.432548i \(0.142385\pi\)
\(788\) 26.5504 7.11415i 0.945817 0.253431i