Properties

Label 819.2.et.c.145.6
Level $819$
Weight $2$
Character 819.145
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 145.6
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.c.514.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.745928 - 0.745928i) q^{2} +0.887184i q^{4} +(-3.80456 + 1.01943i) q^{5} +(0.148943 - 2.64156i) q^{7} +(2.15363 + 2.15363i) q^{8} +O(q^{10})\) \(q+(0.745928 - 0.745928i) q^{2} +0.887184i q^{4} +(-3.80456 + 1.01943i) q^{5} +(0.148943 - 2.64156i) q^{7} +(2.15363 + 2.15363i) q^{8} +(-2.07751 + 3.59835i) q^{10} +(0.913987 - 0.244902i) q^{11} +(-0.783899 - 3.51930i) q^{13} +(-1.85931 - 2.08151i) q^{14} +1.43854 q^{16} -7.96173 q^{17} +(0.451695 - 1.68575i) q^{19} +(-0.904422 - 3.37535i) q^{20} +(0.499089 - 0.864448i) q^{22} -6.93477i q^{23} +(9.10535 - 5.25697i) q^{25} +(-3.20988 - 2.04041i) q^{26} +(2.34355 + 0.132140i) q^{28} +(-1.71573 - 2.97173i) q^{29} +(-1.17258 + 4.37613i) q^{31} +(-3.23422 + 3.23422i) q^{32} +(-5.93888 + 5.93888i) q^{34} +(2.12622 + 10.2018i) q^{35} +(-6.88481 - 6.88481i) q^{37} +(-0.920514 - 1.59438i) q^{38} +(-10.3891 - 5.99815i) q^{40} +(0.117207 - 0.437421i) q^{41} +(0.0936549 + 0.0540717i) q^{43} +(0.217273 + 0.810875i) q^{44} +(-5.17284 - 5.17284i) q^{46} +(-1.19435 - 4.45738i) q^{47} +(-6.95563 - 0.786882i) q^{49} +(2.87061 - 10.7132i) q^{50} +(3.12227 - 0.695463i) q^{52} +(-0.747827 - 1.29527i) q^{53} +(-3.22766 + 1.86349i) q^{55} +(6.00970 - 5.36817i) q^{56} +(-3.49650 - 0.936885i) q^{58} +(3.42925 - 3.42925i) q^{59} +(-5.73215 + 3.30946i) q^{61} +(2.38961 + 4.13893i) q^{62} +7.70205i q^{64} +(6.57008 + 12.5903i) q^{65} +(1.17090 + 4.36986i) q^{67} -7.06353i q^{68} +(9.19581 + 6.02380i) q^{70} +(2.68009 + 10.0022i) q^{71} +(3.95501 + 1.05974i) q^{73} -10.2711 q^{74} +(1.49557 + 0.400736i) q^{76} +(-0.510791 - 2.45082i) q^{77} +(0.473848 - 0.820728i) q^{79} +(-5.47300 + 1.46649i) q^{80} +(-0.238857 - 0.413712i) q^{82} +(8.26062 + 8.26062i) q^{83} +(30.2909 - 8.11643i) q^{85} +(0.110193 - 0.0295262i) q^{86} +(2.49582 + 1.44096i) q^{88} +(-3.79135 + 3.79135i) q^{89} +(-9.41319 + 1.54654i) q^{91} +6.15242 q^{92} +(-4.21578 - 2.43398i) q^{94} +6.87400i q^{95} +(-11.5503 + 3.09490i) q^{97} +(-5.77535 + 4.60144i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.745928 0.745928i 0.527450 0.527450i −0.392361 0.919811i \(-0.628342\pi\)
0.919811 + 0.392361i \(0.128342\pi\)
\(3\) 0 0
\(4\) 0.887184i 0.443592i
\(5\) −3.80456 + 1.01943i −1.70145 + 0.455903i −0.973305 0.229517i \(-0.926285\pi\)
−0.728148 + 0.685420i \(0.759619\pi\)
\(6\) 0 0
\(7\) 0.148943 2.64156i 0.0562951 0.998414i
\(8\) 2.15363 + 2.15363i 0.761423 + 0.761423i
\(9\) 0 0
\(10\) −2.07751 + 3.59835i −0.656966 + 1.13790i
\(11\) 0.913987 0.244902i 0.275578 0.0738408i −0.118383 0.992968i \(-0.537771\pi\)
0.393961 + 0.919127i \(0.371105\pi\)
\(12\) 0 0
\(13\) −0.783899 3.51930i −0.217414 0.976079i
\(14\) −1.85931 2.08151i −0.496921 0.556307i
\(15\) 0 0
\(16\) 1.43854 0.359634
\(17\) −7.96173 −1.93100 −0.965502 0.260395i \(-0.916147\pi\)
−0.965502 + 0.260395i \(0.916147\pi\)
\(18\) 0 0
\(19\) 0.451695 1.68575i 0.103626 0.386737i −0.894560 0.446948i \(-0.852511\pi\)
0.998186 + 0.0602114i \(0.0191775\pi\)
\(20\) −0.904422 3.37535i −0.202235 0.754751i
\(21\) 0 0
\(22\) 0.499089 0.864448i 0.106406 0.184301i
\(23\) 6.93477i 1.44600i −0.690848 0.723000i \(-0.742763\pi\)
0.690848 0.723000i \(-0.257237\pi\)
\(24\) 0 0
\(25\) 9.10535 5.25697i 1.82107 1.05139i
\(26\) −3.20988 2.04041i −0.629509 0.400158i
\(27\) 0 0
\(28\) 2.34355 + 0.132140i 0.442889 + 0.0249721i
\(29\) −1.71573 2.97173i −0.318603 0.551836i 0.661594 0.749862i \(-0.269880\pi\)
−0.980197 + 0.198026i \(0.936547\pi\)
\(30\) 0 0
\(31\) −1.17258 + 4.37613i −0.210602 + 0.785976i 0.777067 + 0.629418i \(0.216707\pi\)
−0.987669 + 0.156558i \(0.949960\pi\)
\(32\) −3.23422 + 3.23422i −0.571734 + 0.571734i
\(33\) 0 0
\(34\) −5.93888 + 5.93888i −1.01851 + 1.01851i
\(35\) 2.12622 + 10.2018i 0.359396 + 1.72442i
\(36\) 0 0
\(37\) −6.88481 6.88481i −1.13186 1.13186i −0.989868 0.141988i \(-0.954651\pi\)
−0.141988 0.989868i \(-0.545349\pi\)
\(38\) −0.920514 1.59438i −0.149327 0.258642i
\(39\) 0 0
\(40\) −10.3891 5.99815i −1.64266 0.948391i
\(41\) 0.117207 0.437421i 0.0183046 0.0683137i −0.956169 0.292814i \(-0.905408\pi\)
0.974474 + 0.224500i \(0.0720750\pi\)
\(42\) 0 0
\(43\) 0.0936549 + 0.0540717i 0.0142822 + 0.00824585i 0.507124 0.861873i \(-0.330709\pi\)
−0.492842 + 0.870119i \(0.664042\pi\)
\(44\) 0.217273 + 0.810875i 0.0327552 + 0.122244i
\(45\) 0 0
\(46\) −5.17284 5.17284i −0.762693 0.762693i
\(47\) −1.19435 4.45738i −0.174214 0.650175i −0.996684 0.0813671i \(-0.974071\pi\)
0.822470 0.568808i \(-0.192595\pi\)
\(48\) 0 0
\(49\) −6.95563 0.786882i −0.993662 0.112412i
\(50\) 2.87061 10.7132i 0.405965 1.51508i
\(51\) 0 0
\(52\) 3.12227 0.695463i 0.432981 0.0964433i
\(53\) −0.747827 1.29527i −0.102722 0.177920i 0.810083 0.586315i \(-0.199422\pi\)
−0.912805 + 0.408395i \(0.866089\pi\)
\(54\) 0 0
\(55\) −3.22766 + 1.86349i −0.435218 + 0.251273i
\(56\) 6.00970 5.36817i 0.803080 0.717351i
\(57\) 0 0
\(58\) −3.49650 0.936885i −0.459113 0.123019i
\(59\) 3.42925 3.42925i 0.446451 0.446451i −0.447722 0.894173i \(-0.647765\pi\)
0.894173 + 0.447722i \(0.147765\pi\)
\(60\) 0 0
\(61\) −5.73215 + 3.30946i −0.733926 + 0.423733i −0.819857 0.572568i \(-0.805947\pi\)
0.0859304 + 0.996301i \(0.472614\pi\)
\(62\) 2.38961 + 4.13893i 0.303481 + 0.525645i
\(63\) 0 0
\(64\) 7.70205i 0.962757i
\(65\) 6.57008 + 12.5903i 0.814918 + 1.56163i
\(66\) 0 0
\(67\) 1.17090 + 4.36986i 0.143048 + 0.533863i 0.999835 + 0.0181915i \(0.00579086\pi\)
−0.856786 + 0.515672i \(0.827542\pi\)
\(68\) 7.06353i 0.856578i
\(69\) 0 0
\(70\) 9.19581 + 6.02380i 1.09911 + 0.719982i
\(71\) 2.68009 + 10.0022i 0.318068 + 1.18705i 0.921099 + 0.389329i \(0.127293\pi\)
−0.603030 + 0.797718i \(0.706040\pi\)
\(72\) 0 0
\(73\) 3.95501 + 1.05974i 0.462899 + 0.124033i 0.482729 0.875770i \(-0.339646\pi\)
−0.0198296 + 0.999803i \(0.506312\pi\)
\(74\) −10.2711 −1.19400
\(75\) 0 0
\(76\) 1.49557 + 0.400736i 0.171553 + 0.0459676i
\(77\) −0.510791 2.45082i −0.0582100 0.279297i
\(78\) 0 0
\(79\) 0.473848 0.820728i 0.0533120 0.0923391i −0.838138 0.545459i \(-0.816356\pi\)
0.891450 + 0.453119i \(0.149689\pi\)
\(80\) −5.47300 + 1.46649i −0.611900 + 0.163958i
\(81\) 0 0
\(82\) −0.238857 0.413712i −0.0263773 0.0456869i
\(83\) 8.26062 + 8.26062i 0.906721 + 0.906721i 0.996006 0.0892850i \(-0.0284582\pi\)
−0.0892850 + 0.996006i \(0.528458\pi\)
\(84\) 0 0
\(85\) 30.2909 8.11643i 3.28551 0.880351i
\(86\) 0.110193 0.0295262i 0.0118824 0.00318389i
\(87\) 0 0
\(88\) 2.49582 + 1.44096i 0.266055 + 0.153607i
\(89\) −3.79135 + 3.79135i −0.401882 + 0.401882i −0.878896 0.477014i \(-0.841719\pi\)
0.477014 + 0.878896i \(0.341719\pi\)
\(90\) 0 0
\(91\) −9.41319 + 1.54654i −0.986771 + 0.162121i
\(92\) 6.15242 0.641434
\(93\) 0 0
\(94\) −4.21578 2.43398i −0.434824 0.251046i
\(95\) 6.87400i 0.705258i
\(96\) 0 0
\(97\) −11.5503 + 3.09490i −1.17276 + 0.314240i −0.792050 0.610456i \(-0.790986\pi\)
−0.380708 + 0.924695i \(0.624320\pi\)
\(98\) −5.77535 + 4.60144i −0.583399 + 0.464816i
\(99\) 0 0
\(100\) 4.66390 + 8.07812i 0.466390 + 0.807812i
\(101\) 9.35838 16.2092i 0.931194 1.61287i 0.149909 0.988700i \(-0.452102\pi\)
0.781284 0.624175i \(-0.214565\pi\)
\(102\) 0 0
\(103\) 3.28825 5.69542i 0.324001 0.561186i −0.657309 0.753621i \(-0.728305\pi\)
0.981310 + 0.192435i \(0.0616386\pi\)
\(104\) 5.89105 9.26751i 0.577665 0.908754i
\(105\) 0 0
\(106\) −1.52400 0.408356i −0.148024 0.0396630i
\(107\) −5.19352 −0.502077 −0.251038 0.967977i \(-0.580772\pi\)
−0.251038 + 0.967977i \(0.580772\pi\)
\(108\) 0 0
\(109\) 11.0247 + 2.95407i 1.05598 + 0.282949i 0.744720 0.667377i \(-0.232583\pi\)
0.311259 + 0.950325i \(0.399249\pi\)
\(110\) −1.01757 + 3.79763i −0.0970218 + 0.362090i
\(111\) 0 0
\(112\) 0.214260 3.79997i 0.0202456 0.359064i
\(113\) 1.34429 2.32838i 0.126460 0.219036i −0.795842 0.605504i \(-0.792972\pi\)
0.922303 + 0.386468i \(0.126305\pi\)
\(114\) 0 0
\(115\) 7.06951 + 26.3838i 0.659236 + 2.46030i
\(116\) 2.63647 1.52217i 0.244790 0.141330i
\(117\) 0 0
\(118\) 5.11595i 0.470961i
\(119\) −1.18584 + 21.0314i −0.108706 + 1.92794i
\(120\) 0 0
\(121\) −8.75088 + 5.05232i −0.795535 + 0.459302i
\(122\) −1.80715 + 6.74438i −0.163612 + 0.610608i
\(123\) 0 0
\(124\) −3.88243 1.04029i −0.348653 0.0934212i
\(125\) −15.3571 + 15.3571i −1.37358 + 1.37358i
\(126\) 0 0
\(127\) −7.89995 + 4.56104i −0.701007 + 0.404727i −0.807722 0.589563i \(-0.799300\pi\)
0.106715 + 0.994290i \(0.465967\pi\)
\(128\) −0.723260 0.723260i −0.0639277 0.0639277i
\(129\) 0 0
\(130\) 14.2922 + 4.49064i 1.25351 + 0.393855i
\(131\) 6.79059 + 3.92055i 0.593297 + 0.342540i 0.766400 0.642364i \(-0.222046\pi\)
−0.173103 + 0.984904i \(0.555379\pi\)
\(132\) 0 0
\(133\) −4.38572 1.44426i −0.380290 0.125233i
\(134\) 4.13300 + 2.38619i 0.357037 + 0.206135i
\(135\) 0 0
\(136\) −17.1466 17.1466i −1.47031 1.47031i
\(137\) −5.38162 5.38162i −0.459783 0.459783i 0.438801 0.898584i \(-0.355403\pi\)
−0.898584 + 0.438801i \(0.855403\pi\)
\(138\) 0 0
\(139\) 3.86004 + 2.22859i 0.327404 + 0.189027i 0.654688 0.755899i \(-0.272800\pi\)
−0.327284 + 0.944926i \(0.606133\pi\)
\(140\) −9.05088 + 1.88635i −0.764939 + 0.159425i
\(141\) 0 0
\(142\) 9.46010 + 5.46179i 0.793874 + 0.458343i
\(143\) −1.57836 3.02462i −0.131989 0.252932i
\(144\) 0 0
\(145\) 9.55706 + 9.55706i 0.793671 + 0.793671i
\(146\) 3.74064 2.15966i 0.309578 0.178735i
\(147\) 0 0
\(148\) 6.10810 6.10810i 0.502082 0.502082i
\(149\) 0.726851 + 0.194759i 0.0595459 + 0.0159553i 0.288469 0.957489i \(-0.406854\pi\)
−0.228923 + 0.973445i \(0.573520\pi\)
\(150\) 0 0
\(151\) −0.0169291 + 0.0631804i −0.00137767 + 0.00514154i −0.966611 0.256247i \(-0.917514\pi\)
0.965234 + 0.261389i \(0.0841805\pi\)
\(152\) 4.60326 2.65769i 0.373374 0.215567i
\(153\) 0 0
\(154\) −2.20915 1.44712i −0.178018 0.116613i
\(155\) 17.8446i 1.43331i
\(156\) 0 0
\(157\) 6.41355 3.70286i 0.511857 0.295521i −0.221740 0.975106i \(-0.571174\pi\)
0.733597 + 0.679585i \(0.237840\pi\)
\(158\) −0.258748 0.965660i −0.0205849 0.0768238i
\(159\) 0 0
\(160\) 9.00773 15.6018i 0.712124 1.23343i
\(161\) −18.3186 1.03289i −1.44371 0.0814028i
\(162\) 0 0
\(163\) −1.19910 + 4.47509i −0.0939206 + 0.350516i −0.996854 0.0792649i \(-0.974743\pi\)
0.902933 + 0.429781i \(0.141409\pi\)
\(164\) 0.388073 + 0.103984i 0.0303034 + 0.00811978i
\(165\) 0 0
\(166\) 12.3237 0.956501
\(167\) −12.2105 3.27179i −0.944874 0.253178i −0.246688 0.969095i \(-0.579342\pi\)
−0.698186 + 0.715916i \(0.746009\pi\)
\(168\) 0 0
\(169\) −11.7710 + 5.51756i −0.905462 + 0.424427i
\(170\) 16.5406 28.6491i 1.26860 2.19729i
\(171\) 0 0
\(172\) −0.0479715 + 0.0830891i −0.00365779 + 0.00633549i
\(173\) −9.15937 15.8645i −0.696374 1.20616i −0.969715 0.244238i \(-0.921462\pi\)
0.273341 0.961917i \(-0.411871\pi\)
\(174\) 0 0
\(175\) −12.5304 24.8353i −0.947210 1.87737i
\(176\) 1.31480 0.352301i 0.0991070 0.0265557i
\(177\) 0 0
\(178\) 5.65615i 0.423946i
\(179\) 15.5371 + 8.97032i 1.16129 + 0.670473i 0.951614 0.307297i \(-0.0994244\pi\)
0.209680 + 0.977770i \(0.432758\pi\)
\(180\) 0 0
\(181\) −11.3348 −0.842512 −0.421256 0.906942i \(-0.638411\pi\)
−0.421256 + 0.906942i \(0.638411\pi\)
\(182\) −5.86796 + 8.17516i −0.434962 + 0.605984i
\(183\) 0 0
\(184\) 14.9349 14.9349i 1.10102 1.10102i
\(185\) 33.2123 + 19.1751i 2.44182 + 1.40978i
\(186\) 0 0
\(187\) −7.27693 + 1.94985i −0.532141 + 0.142587i
\(188\) 3.95451 1.05961i 0.288413 0.0772799i
\(189\) 0 0
\(190\) 5.12751 + 5.12751i 0.371989 + 0.371989i
\(191\) −7.33438 12.7035i −0.530697 0.919194i −0.999358 0.0358162i \(-0.988597\pi\)
0.468661 0.883378i \(-0.344736\pi\)
\(192\) 0 0
\(193\) −11.3200 + 3.03319i −0.814834 + 0.218334i −0.642087 0.766632i \(-0.721931\pi\)
−0.172747 + 0.984966i \(0.555264\pi\)
\(194\) −6.30714 + 10.9243i −0.452826 + 0.784318i
\(195\) 0 0
\(196\) 0.698110 6.17093i 0.0498650 0.440781i
\(197\) 10.2849 + 2.75584i 0.732772 + 0.196346i 0.605863 0.795569i \(-0.292828\pi\)
0.126909 + 0.991914i \(0.459495\pi\)
\(198\) 0 0
\(199\) 21.2553 1.50674 0.753372 0.657594i \(-0.228426\pi\)
0.753372 + 0.657594i \(0.228426\pi\)
\(200\) 30.9311 + 8.28797i 2.18716 + 0.586048i
\(201\) 0 0
\(202\) −5.11021 19.0716i −0.359553 1.34187i
\(203\) −8.10553 + 4.08957i −0.568897 + 0.287032i
\(204\) 0 0
\(205\) 1.78368i 0.124578i
\(206\) −1.79557 6.70117i −0.125103 0.466892i
\(207\) 0 0
\(208\) −1.12767 5.06264i −0.0781896 0.351031i
\(209\) 1.65137i 0.114228i
\(210\) 0 0
\(211\) −11.7558 20.3617i −0.809305 1.40176i −0.913346 0.407184i \(-0.866511\pi\)
0.104041 0.994573i \(-0.466823\pi\)
\(212\) 1.14915 0.663460i 0.0789237 0.0455666i
\(213\) 0 0
\(214\) −3.87399 + 3.87399i −0.264820 + 0.264820i
\(215\) −0.411438 0.110245i −0.0280599 0.00751862i
\(216\) 0 0
\(217\) 11.3851 + 3.74923i 0.772874 + 0.254514i
\(218\) 10.4272 6.02014i 0.706218 0.407735i
\(219\) 0 0
\(220\) −1.65326 2.86353i −0.111463 0.193059i
\(221\) 6.24119 + 28.0198i 0.419828 + 1.88481i
\(222\) 0 0
\(223\) −1.56806 + 5.85209i −0.105005 + 0.391885i −0.998346 0.0574955i \(-0.981689\pi\)
0.893341 + 0.449380i \(0.148355\pi\)
\(224\) 8.06165 + 9.02508i 0.538642 + 0.603013i
\(225\) 0 0
\(226\) −0.734061 2.73955i −0.0488290 0.182232i
\(227\) −14.7585 14.7585i −0.979553 0.979553i 0.0202417 0.999795i \(-0.493556\pi\)
−0.999795 + 0.0202417i \(0.993556\pi\)
\(228\) 0 0
\(229\) 5.67737 + 21.1882i 0.375171 + 1.40016i 0.853094 + 0.521756i \(0.174723\pi\)
−0.477923 + 0.878402i \(0.658610\pi\)
\(230\) 24.9537 + 14.4070i 1.64540 + 0.949973i
\(231\) 0 0
\(232\) 2.70496 10.0950i 0.177589 0.662772i
\(233\) −9.92317 5.72914i −0.650088 0.375329i 0.138402 0.990376i \(-0.455803\pi\)
−0.788490 + 0.615048i \(0.789137\pi\)
\(234\) 0 0
\(235\) 9.08797 + 15.7408i 0.592833 + 1.02682i
\(236\) 3.04238 + 3.04238i 0.198042 + 0.198042i
\(237\) 0 0
\(238\) 14.8033 + 16.5724i 0.959557 + 1.07423i
\(239\) −4.89413 + 4.89413i −0.316575 + 0.316575i −0.847450 0.530875i \(-0.821863\pi\)
0.530875 + 0.847450i \(0.321863\pi\)
\(240\) 0 0
\(241\) −5.87042 + 5.87042i −0.378147 + 0.378147i −0.870433 0.492286i \(-0.836161\pi\)
0.492286 + 0.870433i \(0.336161\pi\)
\(242\) −2.75886 + 10.2962i −0.177346 + 0.661864i
\(243\) 0 0
\(244\) −2.93610 5.08547i −0.187964 0.325564i
\(245\) 27.2653 4.09704i 1.74192 0.261750i
\(246\) 0 0
\(247\) −6.28674 0.268196i −0.400016 0.0170649i
\(248\) −11.9499 + 6.89926i −0.758817 + 0.438103i
\(249\) 0 0
\(250\) 22.9105i 1.44899i
\(251\) 7.81291 13.5324i 0.493146 0.854155i −0.506822 0.862050i \(-0.669180\pi\)
0.999969 + 0.00789592i \(0.00251338\pi\)
\(252\) 0 0
\(253\) −1.69834 6.33829i −0.106774 0.398485i
\(254\) −2.49059 + 9.29499i −0.156273 + 0.583220i
\(255\) 0 0
\(256\) −16.4831 −1.03019
\(257\) −0.563873 −0.0351734 −0.0175867 0.999845i \(-0.505598\pi\)
−0.0175867 + 0.999845i \(0.505598\pi\)
\(258\) 0 0
\(259\) −19.2121 + 17.1612i −1.19378 + 1.06634i
\(260\) −11.1699 + 5.82887i −0.692728 + 0.361491i
\(261\) 0 0
\(262\) 7.98974 2.14084i 0.493608 0.132262i
\(263\) 0.904321 1.56633i 0.0557628 0.0965840i −0.836796 0.547514i \(-0.815574\pi\)
0.892559 + 0.450930i \(0.148908\pi\)
\(264\) 0 0
\(265\) 4.16560 + 4.16560i 0.255891 + 0.255891i
\(266\) −4.34874 + 2.19412i −0.266638 + 0.134530i
\(267\) 0 0
\(268\) −3.87687 + 1.03880i −0.236817 + 0.0634550i
\(269\) 4.60590i 0.280827i 0.990093 + 0.140413i \(0.0448431\pi\)
−0.990093 + 0.140413i \(0.955157\pi\)
\(270\) 0 0
\(271\) 2.86878 2.86878i 0.174266 0.174266i −0.614585 0.788851i \(-0.710676\pi\)
0.788851 + 0.614585i \(0.210676\pi\)
\(272\) −11.4532 −0.694455
\(273\) 0 0
\(274\) −8.02860 −0.485026
\(275\) 7.03473 7.03473i 0.424210 0.424210i
\(276\) 0 0
\(277\) 12.2090i 0.733571i −0.930306 0.366785i \(-0.880458\pi\)
0.930306 0.366785i \(-0.119542\pi\)
\(278\) 4.54168 1.21694i 0.272392 0.0729871i
\(279\) 0 0
\(280\) −17.3918 + 26.5500i −1.03936 + 1.58667i
\(281\) −0.757979 0.757979i −0.0452172 0.0452172i 0.684137 0.729354i \(-0.260179\pi\)
−0.729354 + 0.684137i \(0.760179\pi\)
\(282\) 0 0
\(283\) 10.3386 17.9070i 0.614568 1.06446i −0.375893 0.926663i \(-0.622664\pi\)
0.990460 0.137799i \(-0.0440028\pi\)
\(284\) −8.87383 + 2.37774i −0.526565 + 0.141093i
\(285\) 0 0
\(286\) −3.43349 1.07881i −0.203026 0.0637912i
\(287\) −1.13802 0.374759i −0.0671749 0.0221213i
\(288\) 0 0
\(289\) 46.3892 2.72878
\(290\) 14.2578 0.837244
\(291\) 0 0
\(292\) −0.940186 + 3.50882i −0.0550203 + 0.205338i
\(293\) 0.652210 + 2.43408i 0.0381025 + 0.142201i 0.982357 0.187017i \(-0.0598818\pi\)
−0.944254 + 0.329217i \(0.893215\pi\)
\(294\) 0 0
\(295\) −9.55094 + 16.5427i −0.556077 + 0.963154i
\(296\) 29.6547i 1.72364i
\(297\) 0 0
\(298\) 0.687454 0.396902i 0.0398232 0.0229919i
\(299\) −24.4056 + 5.43616i −1.41141 + 0.314381i
\(300\) 0 0
\(301\) 0.156783 0.239341i 0.00903679 0.0137954i
\(302\) 0.0345001 + 0.0597559i 0.00198526 + 0.00343856i
\(303\) 0 0
\(304\) 0.649779 2.42501i 0.0372674 0.139084i
\(305\) 18.4346 18.4346i 1.05556 1.05556i
\(306\) 0 0
\(307\) 14.0560 14.0560i 0.802217 0.802217i −0.181225 0.983442i \(-0.558006\pi\)
0.983442 + 0.181225i \(0.0580061\pi\)
\(308\) 2.17433 0.453165i 0.123894 0.0258215i
\(309\) 0 0
\(310\) −13.3108 13.3108i −0.756003 0.756003i
\(311\) −5.07374 8.78798i −0.287706 0.498321i 0.685556 0.728020i \(-0.259559\pi\)
−0.973262 + 0.229699i \(0.926226\pi\)
\(312\) 0 0
\(313\) −23.2110 13.4009i −1.31196 0.757461i −0.329540 0.944141i \(-0.606894\pi\)
−0.982421 + 0.186680i \(0.940227\pi\)
\(314\) 2.02197 7.54611i 0.114107 0.425852i
\(315\) 0 0
\(316\) 0.728137 + 0.420390i 0.0409609 + 0.0236488i
\(317\) 3.31452 + 12.3700i 0.186162 + 0.694767i 0.994379 + 0.105881i \(0.0337664\pi\)
−0.808217 + 0.588885i \(0.799567\pi\)
\(318\) 0 0
\(319\) −2.29594 2.29594i −0.128548 0.128548i
\(320\) −7.85171 29.3030i −0.438924 1.63809i
\(321\) 0 0
\(322\) −14.4348 + 12.8939i −0.804420 + 0.718548i
\(323\) −3.59627 + 13.4215i −0.200102 + 0.746791i
\(324\) 0 0
\(325\) −25.6386 27.9235i −1.42217 1.54892i
\(326\) 2.44366 + 4.23254i 0.135342 + 0.234419i
\(327\) 0 0
\(328\) 1.19446 0.689624i 0.0659532 0.0380781i
\(329\) −11.9523 + 2.49105i −0.658951 + 0.137336i
\(330\) 0 0
\(331\) 0.730127 + 0.195637i 0.0401314 + 0.0107532i 0.278829 0.960341i \(-0.410054\pi\)
−0.238697 + 0.971094i \(0.576720\pi\)
\(332\) −7.32869 + 7.32869i −0.402214 + 0.402214i
\(333\) 0 0
\(334\) −11.5486 + 6.66761i −0.631913 + 0.364835i
\(335\) −8.90953 15.4318i −0.486779 0.843127i
\(336\) 0 0
\(337\) 12.9685i 0.706440i −0.935540 0.353220i \(-0.885087\pi\)
0.935540 0.353220i \(-0.114913\pi\)
\(338\) −4.66462 + 12.8960i −0.253722 + 0.701451i
\(339\) 0 0
\(340\) 7.20077 + 26.8736i 0.390517 + 1.45743i
\(341\) 4.28689i 0.232148i
\(342\) 0 0
\(343\) −3.11459 + 18.2565i −0.168172 + 0.985758i
\(344\) 0.0852476 + 0.318148i 0.00459624 + 0.0171534i
\(345\) 0 0
\(346\) −18.6660 5.00154i −1.00349 0.268884i
\(347\) 14.3863 0.772298 0.386149 0.922436i \(-0.373805\pi\)
0.386149 + 0.922436i \(0.373805\pi\)
\(348\) 0 0
\(349\) 32.9693 + 8.83410i 1.76481 + 0.472879i 0.987683 0.156468i \(-0.0500108\pi\)
0.777125 + 0.629347i \(0.216677\pi\)
\(350\) −27.8721 9.17853i −1.48983 0.490613i
\(351\) 0 0
\(352\) −2.16397 + 3.74810i −0.115340 + 0.199774i
\(353\) 5.35753 1.43555i 0.285152 0.0764064i −0.113408 0.993549i \(-0.536177\pi\)
0.398560 + 0.917142i \(0.369510\pi\)
\(354\) 0 0
\(355\) −20.3932 35.3220i −1.08236 1.87470i
\(356\) −3.36363 3.36363i −0.178272 0.178272i
\(357\) 0 0
\(358\) 18.2807 4.89831i 0.966166 0.258883i
\(359\) 6.42126 1.72057i 0.338901 0.0908083i −0.0853548 0.996351i \(-0.527202\pi\)
0.424256 + 0.905542i \(0.360536\pi\)
\(360\) 0 0
\(361\) 13.8168 + 7.97711i 0.727198 + 0.419848i
\(362\) −8.45497 + 8.45497i −0.444383 + 0.444383i
\(363\) 0 0
\(364\) −1.37206 8.35124i −0.0719156 0.437724i
\(365\) −16.1274 −0.844148
\(366\) 0 0
\(367\) −6.19248 3.57523i −0.323245 0.186626i 0.329593 0.944123i \(-0.393088\pi\)
−0.652838 + 0.757498i \(0.726422\pi\)
\(368\) 9.97592i 0.520031i
\(369\) 0 0
\(370\) 39.0772 10.4707i 2.03153 0.544346i
\(371\) −3.53292 + 1.78250i −0.183420 + 0.0925430i
\(372\) 0 0
\(373\) −7.66980 13.2845i −0.397127 0.687844i 0.596243 0.802804i \(-0.296659\pi\)
−0.993370 + 0.114960i \(0.963326\pi\)
\(374\) −3.97361 + 6.88250i −0.205471 + 0.355886i
\(375\) 0 0
\(376\) 7.02735 12.1717i 0.362408 0.627709i
\(377\) −9.11346 + 8.36770i −0.469367 + 0.430958i
\(378\) 0 0
\(379\) −22.8646 6.12656i −1.17448 0.314700i −0.381743 0.924268i \(-0.624676\pi\)
−0.792734 + 0.609568i \(0.791343\pi\)
\(380\) −6.09851 −0.312847
\(381\) 0 0
\(382\) −14.9468 4.00499i −0.764746 0.204913i
\(383\) −0.160303 + 0.598259i −0.00819110 + 0.0305696i −0.969900 0.243502i \(-0.921704\pi\)
0.961709 + 0.274071i \(0.0883705\pi\)
\(384\) 0 0
\(385\) 4.44178 + 8.80361i 0.226374 + 0.448673i
\(386\) −6.18138 + 10.7065i −0.314624 + 0.544945i
\(387\) 0 0
\(388\) −2.74575 10.2473i −0.139394 0.520226i
\(389\) 8.18610 4.72624i 0.415052 0.239630i −0.277906 0.960608i \(-0.589640\pi\)
0.692958 + 0.720978i \(0.256307\pi\)
\(390\) 0 0
\(391\) 55.2128i 2.79223i
\(392\) −13.2852 16.6745i −0.671004 0.842190i
\(393\) 0 0
\(394\) 9.72748 5.61616i 0.490063 0.282938i
\(395\) −0.966109 + 3.60557i −0.0486102 + 0.181416i
\(396\) 0 0
\(397\) 8.63653 + 2.31415i 0.433455 + 0.116144i 0.468948 0.883226i \(-0.344633\pi\)
−0.0354925 + 0.999370i \(0.511300\pi\)
\(398\) 15.8549 15.8549i 0.794733 0.794733i
\(399\) 0 0
\(400\) 13.0984 7.56234i 0.654918 0.378117i
\(401\) 4.68942 + 4.68942i 0.234178 + 0.234178i 0.814434 0.580256i \(-0.197047\pi\)
−0.580256 + 0.814434i \(0.697047\pi\)
\(402\) 0 0
\(403\) 16.3201 + 0.696225i 0.812963 + 0.0346814i
\(404\) 14.3805 + 8.30261i 0.715459 + 0.413070i
\(405\) 0 0
\(406\) −2.99561 + 9.09666i −0.148670 + 0.451460i
\(407\) −7.97874 4.60653i −0.395491 0.228337i
\(408\) 0 0
\(409\) 11.5748 + 11.5748i 0.572336 + 0.572336i 0.932781 0.360444i \(-0.117375\pi\)
−0.360444 + 0.932781i \(0.617375\pi\)
\(410\) 1.33050 + 1.33050i 0.0657086 + 0.0657086i
\(411\) 0 0
\(412\) 5.05288 + 2.91728i 0.248938 + 0.143724i
\(413\) −8.54780 9.56933i −0.420610 0.470876i
\(414\) 0 0
\(415\) −39.8492 23.0069i −1.95612 1.12937i
\(416\) 13.9175 + 8.84690i 0.682361 + 0.433755i
\(417\) 0 0
\(418\) −1.23180 1.23180i −0.0602495 0.0602495i
\(419\) −19.8994 + 11.4889i −0.972150 + 0.561271i −0.899891 0.436115i \(-0.856354\pi\)
−0.0722588 + 0.997386i \(0.523021\pi\)
\(420\) 0 0
\(421\) −3.33707 + 3.33707i −0.162639 + 0.162639i −0.783735 0.621096i \(-0.786688\pi\)
0.621096 + 0.783735i \(0.286688\pi\)
\(422\) −23.9574 6.41935i −1.16623 0.312489i
\(423\) 0 0
\(424\) 1.17900 4.40008i 0.0572572 0.213687i
\(425\) −72.4944 + 41.8546i −3.51649 + 2.03025i
\(426\) 0 0
\(427\) 7.88835 + 15.6347i 0.381744 + 0.756617i
\(428\) 4.60761i 0.222717i
\(429\) 0 0
\(430\) −0.389138 + 0.224669i −0.0187659 + 0.0108345i
\(431\) −7.29082 27.2097i −0.351186 1.31065i −0.885216 0.465180i \(-0.845990\pi\)
0.534030 0.845466i \(-0.320677\pi\)
\(432\) 0 0
\(433\) −9.88975 + 17.1295i −0.475271 + 0.823193i −0.999599 0.0283231i \(-0.990983\pi\)
0.524328 + 0.851516i \(0.324317\pi\)
\(434\) 11.2891 5.69584i 0.541896 0.273409i
\(435\) 0 0
\(436\) −2.62081 + 9.78098i −0.125514 + 0.468424i
\(437\) −11.6903 3.13240i −0.559221 0.149843i
\(438\) 0 0
\(439\) 21.9076 1.04559 0.522797 0.852457i \(-0.324889\pi\)
0.522797 + 0.852457i \(0.324889\pi\)
\(440\) −10.9645 2.93792i −0.522710 0.140060i
\(441\) 0 0
\(442\) 25.5562 + 16.2452i 1.21558 + 0.772707i
\(443\) −9.87688 + 17.1073i −0.469265 + 0.812791i −0.999383 0.0351334i \(-0.988814\pi\)
0.530118 + 0.847924i \(0.322148\pi\)
\(444\) 0 0
\(445\) 10.5594 18.2895i 0.500565 0.867003i
\(446\) 3.19557 + 5.53489i 0.151315 + 0.262085i
\(447\) 0 0
\(448\) 20.3454 + 1.14717i 0.961230 + 0.0541985i
\(449\) 31.7673 8.51202i 1.49919 0.401707i 0.586362 0.810049i \(-0.300560\pi\)
0.912829 + 0.408342i \(0.133893\pi\)
\(450\) 0 0
\(451\) 0.428502i 0.0201774i
\(452\) 2.06571 + 1.19264i 0.0971626 + 0.0560969i
\(453\) 0 0
\(454\) −22.0175 −1.03333
\(455\) 34.2365 15.4800i 1.60503 0.725713i
\(456\) 0 0
\(457\) 11.0934 11.0934i 0.518926 0.518926i −0.398320 0.917246i \(-0.630407\pi\)
0.917246 + 0.398320i \(0.130407\pi\)
\(458\) 20.0398 + 11.5700i 0.936398 + 0.540630i
\(459\) 0 0
\(460\) −23.4073 + 6.27196i −1.09137 + 0.292432i
\(461\) 1.60974 0.431329i 0.0749731 0.0200890i −0.221138 0.975243i \(-0.570977\pi\)
0.296111 + 0.955154i \(0.404310\pi\)
\(462\) 0 0
\(463\) −18.8646 18.8646i −0.876713 0.876713i 0.116480 0.993193i \(-0.462839\pi\)
−0.993193 + 0.116480i \(0.962839\pi\)
\(464\) −2.46814 4.27494i −0.114580 0.198459i
\(465\) 0 0
\(466\) −11.6755 + 3.12844i −0.540857 + 0.144922i
\(467\) 11.4518 19.8351i 0.529926 0.917859i −0.469465 0.882951i \(-0.655553\pi\)
0.999391 0.0349075i \(-0.0111136\pi\)
\(468\) 0 0
\(469\) 11.7176 2.44214i 0.541069 0.112767i
\(470\) 18.5205 + 4.96255i 0.854286 + 0.228905i
\(471\) 0 0
\(472\) 14.7707 0.679876
\(473\) 0.0988416 + 0.0264845i 0.00454474 + 0.00121776i
\(474\) 0 0
\(475\) −4.74909 17.7239i −0.217903 0.813226i
\(476\) −18.6587 1.05206i −0.855220 0.0482212i
\(477\) 0 0
\(478\) 7.30134i 0.333956i
\(479\) −0.198528 0.740918i −0.00907099 0.0338534i 0.961242 0.275706i \(-0.0889116\pi\)
−0.970313 + 0.241853i \(0.922245\pi\)
\(480\) 0 0
\(481\) −18.8328 + 29.6267i −0.858700 + 1.35086i
\(482\) 8.75782i 0.398908i
\(483\) 0 0
\(484\) −4.48234 7.76365i −0.203743 0.352893i
\(485\) 40.7889 23.5495i 1.85213 1.06933i
\(486\) 0 0
\(487\) −5.22200 + 5.22200i −0.236631 + 0.236631i −0.815454 0.578822i \(-0.803512\pi\)
0.578822 + 0.815454i \(0.303512\pi\)
\(488\) −19.4723 5.21758i −0.881469 0.236189i
\(489\) 0 0
\(490\) 17.2819 23.3940i 0.780715 1.05684i
\(491\) −6.17910 + 3.56750i −0.278859 + 0.160999i −0.632907 0.774228i \(-0.718138\pi\)
0.354048 + 0.935227i \(0.384805\pi\)
\(492\) 0 0
\(493\) 13.6602 + 23.6601i 0.615223 + 1.06560i
\(494\) −4.88951 + 4.48940i −0.219989 + 0.201988i
\(495\) 0 0
\(496\) −1.68680 + 6.29522i −0.0757395 + 0.282664i
\(497\) 26.8206 5.58985i 1.20307 0.250739i
\(498\) 0 0
\(499\) −5.54585 20.6974i −0.248266 0.926542i −0.971714 0.236163i \(-0.924110\pi\)
0.723447 0.690380i \(-0.242556\pi\)
\(500\) −13.6246 13.6246i −0.609309 0.609309i
\(501\) 0 0
\(502\) −4.26629 15.9220i −0.190414 0.710634i
\(503\) 20.5890 + 11.8871i 0.918020 + 0.530019i 0.883003 0.469367i \(-0.155518\pi\)
0.0350174 + 0.999387i \(0.488851\pi\)
\(504\) 0 0
\(505\) −19.0804 + 71.2091i −0.849068 + 3.16876i
\(506\) −5.99475 3.46107i −0.266499 0.153863i
\(507\) 0 0
\(508\) −4.04648 7.00871i −0.179534 0.310961i
\(509\) −21.9137 21.9137i −0.971309 0.971309i 0.0282911 0.999600i \(-0.490993\pi\)
−0.999600 + 0.0282911i \(0.990993\pi\)
\(510\) 0 0
\(511\) 3.38844 10.2895i 0.149896 0.455182i
\(512\) −10.8487 + 10.8487i −0.479449 + 0.479449i
\(513\) 0 0
\(514\) −0.420608 + 0.420608i −0.0185522 + 0.0185522i
\(515\) −6.70428 + 25.0207i −0.295426 + 1.10254i
\(516\) 0 0
\(517\) −2.18324 3.78149i −0.0960189 0.166310i
\(518\) −1.52981 + 27.1318i −0.0672162 + 1.19210i
\(519\) 0 0
\(520\) −12.9653 + 41.2643i −0.568567 + 1.80956i
\(521\) −23.5185 + 13.5784i −1.03036 + 0.594881i −0.917089 0.398683i \(-0.869467\pi\)
−0.113275 + 0.993564i \(0.536134\pi\)
\(522\) 0 0
\(523\) 42.2101i 1.84572i −0.385137 0.922859i \(-0.625846\pi\)
0.385137 0.922859i \(-0.374154\pi\)
\(524\) −3.47825 + 6.02451i −0.151948 + 0.263182i
\(525\) 0 0
\(526\) −0.493811 1.84293i −0.0215312 0.0803554i
\(527\) 9.33577 34.8416i 0.406673 1.51772i
\(528\) 0 0
\(529\) −25.0911 −1.09092
\(530\) 6.21447 0.269939
\(531\) 0 0
\(532\) 1.28132 3.89094i 0.0555523 0.168694i
\(533\) −1.63130 0.0695920i −0.0706593 0.00301436i
\(534\) 0 0
\(535\) 19.7591 5.29443i 0.854260 0.228898i
\(536\) −6.88937 + 11.9327i −0.297576 + 0.515416i
\(537\) 0 0
\(538\) 3.43567 + 3.43567i 0.148122 + 0.148122i
\(539\) −6.55007 + 0.984249i −0.282131 + 0.0423946i
\(540\) 0 0
\(541\) 6.69743 1.79457i 0.287945 0.0771547i −0.111955 0.993713i \(-0.535711\pi\)
0.399900 + 0.916559i \(0.369045\pi\)
\(542\) 4.27980i 0.183833i
\(543\) 0 0
\(544\) 25.7500 25.7500i 1.10402 1.10402i
\(545\) −44.9558 −1.92570
\(546\) 0 0
\(547\) 32.4507 1.38749 0.693747 0.720219i \(-0.255959\pi\)
0.693747 + 0.720219i \(0.255959\pi\)
\(548\) 4.77449 4.77449i 0.203956 0.203956i
\(549\) 0 0
\(550\) 10.4948i 0.447499i
\(551\) −5.78456 + 1.54997i −0.246431 + 0.0660309i
\(552\) 0 0
\(553\) −2.09742 1.37394i −0.0891915 0.0584257i
\(554\) −9.10707 9.10707i −0.386922 0.386922i
\(555\) 0 0
\(556\) −1.97717 + 3.42456i −0.0838508 + 0.145234i
\(557\) −5.55001 + 1.48712i −0.235161 + 0.0630113i −0.374475 0.927237i \(-0.622177\pi\)
0.139314 + 0.990248i \(0.455510\pi\)
\(558\) 0 0
\(559\) 0.116879 0.371987i 0.00494344 0.0157334i
\(560\) 3.05864 + 14.6757i 0.129251 + 0.620160i
\(561\) 0 0
\(562\) −1.13079 −0.0476997
\(563\) 43.6474 1.83952 0.919760 0.392482i \(-0.128383\pi\)
0.919760 + 0.392482i \(0.128383\pi\)
\(564\) 0 0
\(565\) −2.74083 + 10.2289i −0.115307 + 0.430333i
\(566\) −5.64548 21.0692i −0.237297 0.885605i
\(567\) 0 0
\(568\) −15.7692 + 27.3130i −0.661661 + 1.14603i
\(569\) 3.16172i 0.132546i −0.997802 0.0662730i \(-0.978889\pi\)
0.997802 0.0662730i \(-0.0211108\pi\)
\(570\) 0 0
\(571\) −31.3887 + 18.1222i −1.31357 + 0.758393i −0.982686 0.185277i \(-0.940682\pi\)
−0.330888 + 0.943670i \(0.607348\pi\)
\(572\) 2.68340 1.40030i 0.112198 0.0585493i
\(573\) 0 0
\(574\) −1.12842 + 0.569334i −0.0470993 + 0.0237635i
\(575\) −36.4559 63.1435i −1.52032 2.63327i
\(576\) 0 0
\(577\) 1.35035 5.03959i 0.0562160 0.209801i −0.932105 0.362189i \(-0.882030\pi\)
0.988321 + 0.152388i \(0.0486963\pi\)
\(578\) 34.6030 34.6030i 1.43930 1.43930i
\(579\) 0 0
\(580\) −8.47888 + 8.47888i −0.352066 + 0.352066i
\(581\) 23.0513 20.5905i 0.956327 0.854239i
\(582\) 0 0
\(583\) −1.00072 1.00072i −0.0414456 0.0414456i
\(584\) 6.23534 + 10.7999i 0.258020 + 0.446904i
\(585\) 0 0
\(586\) 2.30215 + 1.32915i 0.0951010 + 0.0549066i
\(587\) −9.40982 + 35.1179i −0.388385 + 1.44947i 0.444377 + 0.895840i \(0.353425\pi\)
−0.832762 + 0.553632i \(0.813242\pi\)
\(588\) 0 0
\(589\) 6.84740 + 3.95335i 0.282142 + 0.162895i
\(590\) 5.21535 + 19.4640i 0.214713 + 0.801319i
\(591\) 0 0
\(592\) −9.90405 9.90405i −0.407054 0.407054i
\(593\) 10.9522 + 40.8740i 0.449751 + 1.67849i 0.703078 + 0.711113i \(0.251809\pi\)
−0.253327 + 0.967381i \(0.581525\pi\)
\(594\) 0 0
\(595\) −16.9284 81.2241i −0.693996 3.32986i
\(596\) −0.172787 + 0.644851i −0.00707764 + 0.0264141i
\(597\) 0 0
\(598\) −14.1498 + 22.2598i −0.578629 + 0.910270i
\(599\) −16.9264 29.3174i −0.691594 1.19788i −0.971315 0.237795i \(-0.923575\pi\)
0.279721 0.960081i \(-0.409758\pi\)
\(600\) 0 0
\(601\) −21.1918 + 12.2351i −0.864431 + 0.499080i −0.865494 0.500920i \(-0.832995\pi\)
0.00106241 + 0.999999i \(0.499662\pi\)
\(602\) −0.0615826 0.295479i −0.00250992 0.0120428i
\(603\) 0 0
\(604\) −0.0560526 0.0150193i −0.00228075 0.000611125i
\(605\) 28.1428 28.1428i 1.14417 1.14417i
\(606\) 0 0
\(607\) 19.8343 11.4513i 0.805048 0.464795i −0.0401853 0.999192i \(-0.512795\pi\)
0.845233 + 0.534398i \(0.179461\pi\)
\(608\) 3.99119 + 6.91295i 0.161864 + 0.280357i
\(609\) 0 0
\(610\) 27.5017i 1.11351i
\(611\) −14.7506 + 7.69741i −0.596746 + 0.311404i
\(612\) 0 0
\(613\) −9.00681 33.6139i −0.363782 1.35765i −0.869065 0.494698i \(-0.835279\pi\)
0.505283 0.862954i \(-0.331388\pi\)
\(614\) 20.9695i 0.846260i
\(615\) 0 0
\(616\) 4.17812 6.37822i 0.168341 0.256986i
\(617\) 8.38788 + 31.3040i 0.337684 + 1.26025i 0.900930 + 0.433963i \(0.142885\pi\)
−0.563247 + 0.826289i \(0.690448\pi\)
\(618\) 0 0
\(619\) −38.0001 10.1821i −1.52735 0.409253i −0.605200 0.796074i \(-0.706907\pi\)
−0.922155 + 0.386820i \(0.873573\pi\)
\(620\) 15.8315 0.635807
\(621\) 0 0
\(622\) −10.3398 2.77055i −0.414590 0.111089i
\(623\) 9.45037 + 10.5798i 0.378621 + 0.423869i
\(624\) 0 0
\(625\) 16.4867 28.5558i 0.659467 1.14223i
\(626\) −27.3098 + 7.31763i −1.09152 + 0.292471i
\(627\) 0 0
\(628\) 3.28512 + 5.69000i 0.131091 + 0.227056i
\(629\) 54.8150 + 54.8150i 2.18562 + 2.18562i
\(630\) 0 0
\(631\) 15.0028 4.01998i 0.597251 0.160033i 0.0524858 0.998622i \(-0.483286\pi\)
0.544765 + 0.838589i \(0.316619\pi\)
\(632\) 2.78804 0.747052i 0.110902 0.0297161i
\(633\) 0 0
\(634\) 11.6995 + 6.75471i 0.464646 + 0.268264i
\(635\) 25.4062 25.4062i 1.00821 1.00821i
\(636\) 0 0
\(637\) 2.68323 + 25.0958i 0.106314 + 0.994333i
\(638\) −3.42520 −0.135605
\(639\) 0 0
\(640\) 3.48900 + 2.01438i 0.137915 + 0.0796252i
\(641\) 13.5078i 0.533526i −0.963762 0.266763i \(-0.914046\pi\)
0.963762 0.266763i \(-0.0859541\pi\)
\(642\) 0 0
\(643\) 25.1020 6.72606i 0.989926 0.265250i 0.272706 0.962097i \(-0.412081\pi\)
0.717219 + 0.696848i \(0.245415\pi\)
\(644\) 0.916360 16.2520i 0.0361096 0.640417i
\(645\) 0 0
\(646\) 7.32889 + 12.6940i 0.288351 + 0.499439i
\(647\) −11.5556 + 20.0149i −0.454298 + 0.786868i −0.998648 0.0519911i \(-0.983443\pi\)
0.544349 + 0.838859i \(0.316777\pi\)
\(648\) 0 0
\(649\) 2.29446 3.97413i 0.0900656 0.155998i
\(650\) −39.9535 1.70444i −1.56710 0.0668535i
\(651\) 0 0
\(652\) −3.97023 1.06382i −0.155486 0.0416624i
\(653\) 33.5022 1.31104 0.655522 0.755176i \(-0.272449\pi\)
0.655522 + 0.755176i \(0.272449\pi\)
\(654\) 0 0
\(655\) −29.8320 7.99345i −1.16563 0.312330i
\(656\) 0.168606 0.629246i 0.00658296 0.0245679i
\(657\) 0 0
\(658\) −7.05741 + 10.7737i −0.275126 + 0.420002i
\(659\) −0.940246 + 1.62855i −0.0366268 + 0.0634395i −0.883758 0.467945i \(-0.844995\pi\)
0.847131 + 0.531384i \(0.178328\pi\)
\(660\) 0 0
\(661\) −12.6624 47.2568i −0.492511 1.83807i −0.543548 0.839378i \(-0.682920\pi\)
0.0510377 0.998697i \(-0.483747\pi\)
\(662\) 0.690553 0.398691i 0.0268391 0.0154956i
\(663\) 0 0
\(664\) 35.5807i 1.38080i
\(665\) 18.1581 + 1.02383i 0.704139 + 0.0397026i
\(666\) 0 0
\(667\) −20.6082 + 11.8982i −0.797955 + 0.460699i
\(668\) 2.90268 10.8329i 0.112308 0.419139i
\(669\) 0 0
\(670\) −18.1568 4.86511i −0.701460 0.187956i
\(671\) −4.42862 + 4.42862i −0.170965 + 0.170965i
\(672\) 0 0
\(673\) −16.4185 + 9.47923i −0.632887 + 0.365397i −0.781869 0.623442i \(-0.785734\pi\)
0.148982 + 0.988840i \(0.452400\pi\)
\(674\) −9.67357 9.67357i −0.372612 0.372612i
\(675\) 0 0
\(676\) −4.89509 10.4431i −0.188273 0.401656i
\(677\) 7.78358 + 4.49385i 0.299147 + 0.172713i 0.642060 0.766655i \(-0.278080\pi\)
−0.342913 + 0.939367i \(0.611413\pi\)
\(678\) 0 0
\(679\) 6.45501 + 30.9718i 0.247721 + 1.18859i
\(680\) 82.7153 + 47.7557i 3.17199 + 1.83135i
\(681\) 0 0
\(682\) 3.19771 + 3.19771i 0.122447 + 0.122447i
\(683\) 20.5680 + 20.5680i 0.787011 + 0.787011i 0.981003 0.193992i \(-0.0621437\pi\)
−0.193992 + 0.981003i \(0.562144\pi\)
\(684\) 0 0
\(685\) 25.9609 + 14.9885i 0.991916 + 0.572683i
\(686\) 11.2948 + 15.9413i 0.431236 + 0.608641i
\(687\) 0 0
\(688\) 0.134726 + 0.0777840i 0.00513638 + 0.00296549i
\(689\) −3.97224 + 3.64719i −0.151330 + 0.138947i
\(690\) 0 0
\(691\) −14.2144 14.2144i −0.540741 0.540741i 0.383005 0.923746i \(-0.374889\pi\)
−0.923746 + 0.383005i \(0.874889\pi\)
\(692\) 14.0747 8.12605i 0.535041 0.308906i
\(693\) 0 0
\(694\) 10.7311 10.7311i 0.407349 0.407349i
\(695\) −16.9577 4.54379i −0.643240 0.172356i
\(696\) 0 0
\(697\) −0.933168 + 3.48263i −0.0353463 + 0.131914i
\(698\) 31.1823 18.0031i 1.18027 0.681428i
\(699\) 0 0
\(700\) 22.0335 11.1168i 0.832786 0.420175i
\(701\) 26.4403i 0.998636i 0.866419 + 0.499318i \(0.166416\pi\)
−0.866419 + 0.499318i \(0.833584\pi\)
\(702\) 0 0
\(703\) −14.7159 + 8.49622i −0.555020 + 0.320441i
\(704\) 1.88625 + 7.03958i 0.0710907 + 0.265314i
\(705\) 0 0
\(706\) 2.92551 5.06714i 0.110103 0.190704i
\(707\) −41.4236 27.1349i −1.55790 1.02051i
\(708\) 0 0
\(709\) 0.263276 0.982560i 0.00988755 0.0369008i −0.960806 0.277222i \(-0.910586\pi\)
0.970693 + 0.240321i \(0.0772528\pi\)
\(710\) −41.5595 11.1358i −1.55970 0.417920i
\(711\) 0 0
\(712\) −16.3303 −0.612005
\(713\) 30.3475 + 8.13158i 1.13652 + 0.304530i
\(714\) 0 0
\(715\) 9.08836 + 9.89834i 0.339885 + 0.370177i
\(716\) −7.95833 + 13.7842i −0.297417 + 0.515141i
\(717\) 0 0
\(718\) 3.50637 6.07322i 0.130857 0.226650i
\(719\) −16.1333 27.9438i −0.601672 1.04213i −0.992568 0.121691i \(-0.961168\pi\)
0.390896 0.920435i \(-0.372165\pi\)
\(720\) 0 0
\(721\) −14.5550 9.53439i −0.542057 0.355079i
\(722\) 16.2567 4.35596i 0.605010 0.162112i
\(723\) 0 0
\(724\) 10.0561i 0.373732i
\(725\) −31.2446 18.0391i −1.16039 0.669954i
\(726\) 0 0
\(727\) −14.6393 −0.542941 −0.271471 0.962447i \(-0.587510\pi\)
−0.271471 + 0.962447i \(0.587510\pi\)
\(728\) −23.6032 16.9419i −0.874793 0.627908i
\(729\) 0 0
\(730\) −12.0299 + 12.0299i −0.445246 + 0.445246i
\(731\) −0.745655 0.430504i −0.0275791 0.0159228i
\(732\) 0 0
\(733\) 48.6040 13.0234i 1.79523 0.481031i 0.802014 0.597305i \(-0.203762\pi\)
0.993217 + 0.116275i \(0.0370952\pi\)
\(734\) −7.28601 + 1.95228i −0.268931 + 0.0720599i
\(735\) 0 0
\(736\) 22.4286 + 22.4286i 0.826728 + 0.826728i
\(737\) 2.14038 + 3.70724i 0.0788417 + 0.136558i
\(738\) 0 0
\(739\) 20.1849 5.40853i 0.742514 0.198956i 0.132319 0.991207i \(-0.457758\pi\)
0.610195 + 0.792251i \(0.291091\pi\)
\(740\) −17.0119 + 29.4654i −0.625369 + 1.08317i
\(741\) 0 0
\(742\) −1.30568 + 3.96492i −0.0479332 + 0.145557i
\(743\) −25.4705 6.82479i −0.934421 0.250377i −0.240682 0.970604i \(-0.577371\pi\)
−0.693739 + 0.720227i \(0.744038\pi\)
\(744\) 0 0
\(745\) −2.96389 −0.108589
\(746\) −15.6304 4.18815i −0.572269 0.153339i
\(747\) 0 0
\(748\) −1.72987 6.45597i −0.0632504 0.236054i
\(749\) −0.773538 + 13.7190i −0.0282645 + 0.501280i
\(750\) 0 0
\(751\) 15.3030i 0.558416i −0.960231 0.279208i \(-0.909928\pi\)
0.960231 0.279208i \(-0.0900719\pi\)
\(752\) −1.71812 6.41209i −0.0626532 0.233825i
\(753\) 0 0
\(754\) −0.556280 + 13.0397i −0.0202585 + 0.474877i
\(755\) 0.257632i 0.00937618i
\(756\) 0 0
\(757\) 9.00227 + 15.5924i 0.327193 + 0.566715i 0.981954 0.189121i \(-0.0605640\pi\)
−0.654761 + 0.755836i \(0.727231\pi\)
\(758\) −21.6253 + 12.4854i −0.785467 + 0.453490i
\(759\) 0 0
\(760\) −14.8041 + 14.8041i −0.537000 + 0.537000i
\(761\) 40.8513 + 10.9461i 1.48086 + 0.396795i 0.906639 0.421907i \(-0.138639\pi\)
0.574219 + 0.818701i \(0.305306\pi\)
\(762\) 0 0
\(763\) 9.44540 28.6825i 0.341947 1.03838i
\(764\) 11.2704 6.50694i 0.407747 0.235413i
\(765\) 0 0
\(766\) 0.326683 + 0.565832i 0.0118035 + 0.0204443i
\(767\) −14.7568 9.38040i −0.532836 0.338707i
\(768\) 0 0
\(769\) 2.44052 9.10816i 0.0880075 0.328449i −0.907859 0.419275i \(-0.862284\pi\)
0.995867 + 0.0908266i \(0.0289509\pi\)
\(770\) 9.88010 + 3.25361i 0.356054 + 0.117252i
\(771\) 0 0
\(772\) −2.69100 10.0430i −0.0968513 0.361454i
\(773\) 17.2254 + 17.2254i 0.619556 + 0.619556i 0.945418 0.325861i \(-0.105654\pi\)
−0.325861 + 0.945418i \(0.605654\pi\)
\(774\) 0 0
\(775\) 12.3284 + 46.0104i 0.442851 + 1.65274i
\(776\) −31.5404 18.2099i −1.13223 0.653696i
\(777\) 0 0
\(778\) 2.58080 9.63167i 0.0925261 0.345312i
\(779\) −0.684440 0.395162i −0.0245226 0.0141581i
\(780\) 0 0
\(781\) 4.89914 + 8.48556i 0.175305 + 0.303637i
\(782\) 41.1848 + 41.1848i 1.47276 + 1.47276i
\(783\) 0 0
\(784\) −10.0059 1.13196i −0.357354 0.0404271i
\(785\) −20.6259 + 20.6259i −0.736171 + 0.736171i
\(786\) 0 0
\(787\) −11.7876 + 11.7876i −0.420182 + 0.420182i −0.885266 0.465085i \(-0.846024\pi\)
0.465085 + 0.885266i \(0.346024\pi\)
\(788\) −2.44494