Properties

Label 819.2.et.c.136.3
Level $819$
Weight $2$
Character 819.136
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 136.3
Character \(\chi\) \(=\) 819.136
Dual form 819.2.et.c.271.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.09987 + 1.09987i) q^{2} -0.419447i q^{4} +(-0.745735 + 2.78312i) q^{5} +(-1.80794 + 1.93167i) q^{7} +(-1.73841 - 1.73841i) q^{8} +O(q^{10})\) \(q+(-1.09987 + 1.09987i) q^{2} -0.419447i q^{4} +(-0.745735 + 2.78312i) q^{5} +(-1.80794 + 1.93167i) q^{7} +(-1.73841 - 1.73841i) q^{8} +(-2.24087 - 3.88130i) q^{10} +(-1.41711 + 5.28871i) q^{11} +(-0.662549 + 3.54415i) q^{13} +(-0.136094 - 4.11310i) q^{14} +4.66296 q^{16} +4.36465 q^{17} +(-1.39486 + 0.373751i) q^{19} +(1.16737 + 0.312796i) q^{20} +(-4.25828 - 7.37555i) q^{22} -8.37225i q^{23} +(-2.85951 - 1.65094i) q^{25} +(-3.16940 - 4.62684i) q^{26} +(0.810234 + 0.758334i) q^{28} +(-0.882488 + 1.52851i) q^{29} +(0.770818 - 0.206540i) q^{31} +(-1.65185 + 1.65185i) q^{32} +(-4.80057 + 4.80057i) q^{34} +(-4.02784 - 6.47222i) q^{35} +(3.86358 + 3.86358i) q^{37} +(1.12309 - 1.94525i) q^{38} +(6.13459 - 3.54181i) q^{40} +(-3.88124 + 1.03997i) q^{41} +(-5.58033 + 3.22180i) q^{43} +(2.21833 + 0.594400i) q^{44} +(9.20842 + 9.20842i) q^{46} +(8.52304 + 2.28374i) q^{47} +(-0.462723 - 6.98469i) q^{49} +(4.96092 - 1.32927i) q^{50} +(1.48658 + 0.277904i) q^{52} +(-0.139208 + 0.241116i) q^{53} +(-13.6623 - 7.88795i) q^{55} +(6.50098 - 0.215103i) q^{56} +(-0.710548 - 2.65180i) q^{58} +(5.16369 - 5.16369i) q^{59} +(4.10703 + 2.37119i) q^{61} +(-0.620634 + 1.07497i) q^{62} +5.69226i q^{64} +(-9.36972 - 4.48695i) q^{65} +(1.87565 + 0.502580i) q^{67} -1.83074i q^{68} +(11.5487 + 2.68852i) q^{70} +(-11.3490 - 3.04095i) q^{71} +(-3.72736 - 13.9107i) q^{73} -8.49891 q^{74} +(0.156769 + 0.585069i) q^{76} +(-7.65402 - 12.2990i) q^{77} +(-0.431242 - 0.746933i) q^{79} +(-3.47733 + 12.9776i) q^{80} +(3.12503 - 5.41271i) q^{82} +(-4.29551 - 4.29551i) q^{83} +(-3.25487 + 12.1473i) q^{85} +(2.59408 - 9.68124i) q^{86} +(11.6575 - 6.73043i) q^{88} +(-4.21484 + 4.21484i) q^{89} +(-5.64830 - 7.68744i) q^{91} -3.51171 q^{92} +(-11.8861 + 6.86245i) q^{94} -4.16078i q^{95} +(-0.575652 + 2.14836i) q^{97} +(8.19122 + 7.17334i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09987 + 1.09987i −0.777729 + 0.777729i −0.979444 0.201716i \(-0.935348\pi\)
0.201716 + 0.979444i \(0.435348\pi\)
\(3\) 0 0
\(4\) 0.419447i 0.209723i
\(5\) −0.745735 + 2.78312i −0.333503 + 1.24465i 0.571981 + 0.820267i \(0.306175\pi\)
−0.905483 + 0.424382i \(0.860491\pi\)
\(6\) 0 0
\(7\) −1.80794 + 1.93167i −0.683336 + 0.730104i
\(8\) −1.73841 1.73841i −0.614621 0.614621i
\(9\) 0 0
\(10\) −2.24087 3.88130i −0.708624 1.22737i
\(11\) −1.41711 + 5.28871i −0.427273 + 1.59461i 0.331635 + 0.943408i \(0.392400\pi\)
−0.758908 + 0.651198i \(0.774267\pi\)
\(12\) 0 0
\(13\) −0.662549 + 3.54415i −0.183758 + 0.982972i
\(14\) −0.136094 4.11310i −0.0363725 1.09927i
\(15\) 0 0
\(16\) 4.66296 1.16574
\(17\) 4.36465 1.05858 0.529292 0.848440i \(-0.322458\pi\)
0.529292 + 0.848440i \(0.322458\pi\)
\(18\) 0 0
\(19\) −1.39486 + 0.373751i −0.320003 + 0.0857444i −0.415245 0.909710i \(-0.636304\pi\)
0.0952423 + 0.995454i \(0.469637\pi\)
\(20\) 1.16737 + 0.312796i 0.261032 + 0.0699433i
\(21\) 0 0
\(22\) −4.25828 7.37555i −0.907868 1.57247i
\(23\) 8.37225i 1.74573i −0.487958 0.872867i \(-0.662258\pi\)
0.487958 0.872867i \(-0.337742\pi\)
\(24\) 0 0
\(25\) −2.85951 1.65094i −0.571901 0.330187i
\(26\) −3.16940 4.62684i −0.621571 0.907399i
\(27\) 0 0
\(28\) 0.810234 + 0.758334i 0.153120 + 0.143312i
\(29\) −0.882488 + 1.52851i −0.163874 + 0.283838i −0.936255 0.351322i \(-0.885732\pi\)
0.772381 + 0.635160i \(0.219066\pi\)
\(30\) 0 0
\(31\) 0.770818 0.206540i 0.138443 0.0370957i −0.188932 0.981990i \(-0.560503\pi\)
0.327375 + 0.944894i \(0.393836\pi\)
\(32\) −1.65185 + 1.65185i −0.292008 + 0.292008i
\(33\) 0 0
\(34\) −4.80057 + 4.80057i −0.823290 + 0.823290i
\(35\) −4.02784 6.47222i −0.680829 1.09401i
\(36\) 0 0
\(37\) 3.86358 + 3.86358i 0.635169 + 0.635169i 0.949360 0.314191i \(-0.101733\pi\)
−0.314191 + 0.949360i \(0.601733\pi\)
\(38\) 1.12309 1.94525i 0.182189 0.315561i
\(39\) 0 0
\(40\) 6.13459 3.54181i 0.969965 0.560009i
\(41\) −3.88124 + 1.03997i −0.606147 + 0.162417i −0.548823 0.835939i \(-0.684924\pi\)
−0.0573248 + 0.998356i \(0.518257\pi\)
\(42\) 0 0
\(43\) −5.58033 + 3.22180i −0.850992 + 0.491320i −0.860985 0.508630i \(-0.830152\pi\)
0.00999354 + 0.999950i \(0.496819\pi\)
\(44\) 2.21833 + 0.594400i 0.334426 + 0.0896092i
\(45\) 0 0
\(46\) 9.20842 + 9.20842i 1.35771 + 1.35771i
\(47\) 8.52304 + 2.28374i 1.24321 + 0.333118i 0.819711 0.572777i \(-0.194134\pi\)
0.423502 + 0.905895i \(0.360800\pi\)
\(48\) 0 0
\(49\) −0.462723 6.98469i −0.0661033 0.997813i
\(50\) 4.96092 1.32927i 0.701580 0.187988i
\(51\) 0 0
\(52\) 1.48658 + 0.277904i 0.206152 + 0.0385384i
\(53\) −0.139208 + 0.241116i −0.0191217 + 0.0331198i −0.875428 0.483349i \(-0.839420\pi\)
0.856306 + 0.516468i \(0.172754\pi\)
\(54\) 0 0
\(55\) −13.6623 7.88795i −1.84223 1.06361i
\(56\) 6.50098 0.215103i 0.868729 0.0287444i
\(57\) 0 0
\(58\) −0.710548 2.65180i −0.0932995 0.348198i
\(59\) 5.16369 5.16369i 0.672255 0.672255i −0.285980 0.958235i \(-0.592319\pi\)
0.958235 + 0.285980i \(0.0923192\pi\)
\(60\) 0 0
\(61\) 4.10703 + 2.37119i 0.525851 + 0.303600i 0.739325 0.673348i \(-0.235145\pi\)
−0.213474 + 0.976949i \(0.568478\pi\)
\(62\) −0.620634 + 1.07497i −0.0788207 + 0.136521i
\(63\) 0 0
\(64\) 5.69226i 0.711533i
\(65\) −9.36972 4.48695i −1.16217 0.556538i
\(66\) 0 0
\(67\) 1.87565 + 0.502580i 0.229148 + 0.0613999i 0.371566 0.928407i \(-0.378821\pi\)
−0.142418 + 0.989807i \(0.545488\pi\)
\(68\) 1.83074i 0.222010i
\(69\) 0 0
\(70\) 11.5487 + 2.68852i 1.38034 + 0.321339i
\(71\) −11.3490 3.04095i −1.34688 0.360894i −0.487895 0.872902i \(-0.662235\pi\)
−0.858981 + 0.512008i \(0.828902\pi\)
\(72\) 0 0
\(73\) −3.72736 13.9107i −0.436254 1.62812i −0.738047 0.674749i \(-0.764252\pi\)
0.301793 0.953373i \(-0.402415\pi\)
\(74\) −8.49891 −0.987978
\(75\) 0 0
\(76\) 0.156769 + 0.585069i 0.0179826 + 0.0671121i
\(77\) −7.65402 12.2990i −0.872256 1.40161i
\(78\) 0 0
\(79\) −0.431242 0.746933i −0.0485185 0.0840365i 0.840746 0.541429i \(-0.182117\pi\)
−0.889265 + 0.457393i \(0.848783\pi\)
\(80\) −3.47733 + 12.9776i −0.388777 + 1.45094i
\(81\) 0 0
\(82\) 3.12503 5.41271i 0.345102 0.597734i
\(83\) −4.29551 4.29551i −0.471494 0.471494i 0.430904 0.902398i \(-0.358195\pi\)
−0.902398 + 0.430904i \(0.858195\pi\)
\(84\) 0 0
\(85\) −3.25487 + 12.1473i −0.353040 + 1.31756i
\(86\) 2.59408 9.68124i 0.279727 1.04395i
\(87\) 0 0
\(88\) 11.6575 6.73043i 1.24269 0.717467i
\(89\) −4.21484 + 4.21484i −0.446772 + 0.446772i −0.894280 0.447508i \(-0.852312\pi\)
0.447508 + 0.894280i \(0.352312\pi\)
\(90\) 0 0
\(91\) −5.64830 7.68744i −0.592103 0.805862i
\(92\) −3.51171 −0.366121
\(93\) 0 0
\(94\) −11.8861 + 6.86245i −1.22596 + 0.707807i
\(95\) 4.16078i 0.426887i
\(96\) 0 0
\(97\) −0.575652 + 2.14836i −0.0584486 + 0.218133i −0.988973 0.148097i \(-0.952685\pi\)
0.930524 + 0.366230i \(0.119352\pi\)
\(98\) 8.19122 + 7.17334i 0.827438 + 0.724617i
\(99\) 0 0
\(100\) −0.692481 + 1.19941i −0.0692481 + 0.119941i
\(101\) 7.92218 + 13.7216i 0.788287 + 1.36535i 0.927016 + 0.375023i \(0.122365\pi\)
−0.138729 + 0.990330i \(0.544302\pi\)
\(102\) 0 0
\(103\) −5.32654 9.22583i −0.524839 0.909048i −0.999582 0.0289234i \(-0.990792\pi\)
0.474742 0.880125i \(-0.342541\pi\)
\(104\) 7.31297 5.00941i 0.717096 0.491213i
\(105\) 0 0
\(106\) −0.112085 0.418309i −0.0108867 0.0406297i
\(107\) 14.5513 1.40672 0.703361 0.710833i \(-0.251682\pi\)
0.703361 + 0.710833i \(0.251682\pi\)
\(108\) 0 0
\(109\) −2.22729 8.31237i −0.213336 0.796181i −0.986746 0.162274i \(-0.948117\pi\)
0.773410 0.633906i \(-0.218550\pi\)
\(110\) 23.7026 6.35109i 2.25995 0.605553i
\(111\) 0 0
\(112\) −8.43034 + 9.00731i −0.796592 + 0.851111i
\(113\) 6.81406 + 11.8023i 0.641013 + 1.11027i 0.985207 + 0.171368i \(0.0548187\pi\)
−0.344195 + 0.938898i \(0.611848\pi\)
\(114\) 0 0
\(115\) 23.3010 + 6.24347i 2.17283 + 0.582207i
\(116\) 0.641131 + 0.370157i 0.0595275 + 0.0343682i
\(117\) 0 0
\(118\) 11.3588i 1.04566i
\(119\) −7.89102 + 8.43108i −0.723368 + 0.772876i
\(120\) 0 0
\(121\) −16.4360 9.48931i −1.49418 0.862665i
\(122\) −7.12523 + 1.90920i −0.645088 + 0.172851i
\(123\) 0 0
\(124\) −0.0866325 0.323317i −0.00777983 0.0290347i
\(125\) −3.45974 + 3.45974i −0.309448 + 0.309448i
\(126\) 0 0
\(127\) 3.01715 + 1.74195i 0.267728 + 0.154573i 0.627855 0.778330i \(-0.283933\pi\)
−0.360126 + 0.932904i \(0.617266\pi\)
\(128\) −9.56447 9.56447i −0.845388 0.845388i
\(129\) 0 0
\(130\) 15.2406 5.37043i 1.33669 0.471018i
\(131\) 5.01539 2.89564i 0.438197 0.252993i −0.264636 0.964348i \(-0.585252\pi\)
0.702832 + 0.711356i \(0.251918\pi\)
\(132\) 0 0
\(133\) 1.79985 3.37013i 0.156067 0.292227i
\(134\) −2.61576 + 1.51021i −0.225967 + 0.130462i
\(135\) 0 0
\(136\) −7.58755 7.58755i −0.650627 0.650627i
\(137\) 2.42365 + 2.42365i 0.207067 + 0.207067i 0.803019 0.595953i \(-0.203226\pi\)
−0.595953 + 0.803019i \(0.703226\pi\)
\(138\) 0 0
\(139\) −16.1580 + 9.32882i −1.37050 + 0.791260i −0.990991 0.133927i \(-0.957241\pi\)
−0.379512 + 0.925187i \(0.623908\pi\)
\(140\) −2.71475 + 1.68946i −0.229439 + 0.142786i
\(141\) 0 0
\(142\) 15.8271 9.13779i 1.32818 0.766826i
\(143\) −17.8051 8.52647i −1.48894 0.713019i
\(144\) 0 0
\(145\) −3.59594 3.59594i −0.298626 0.298626i
\(146\) 19.3996 + 11.2004i 1.60552 + 0.926950i
\(147\) 0 0
\(148\) 1.62057 1.62057i 0.133210 0.133210i
\(149\) 3.69990 + 13.8082i 0.303108 + 1.13121i 0.934562 + 0.355801i \(0.115792\pi\)
−0.631454 + 0.775413i \(0.717542\pi\)
\(150\) 0 0
\(151\) −0.0198676 + 0.00532352i −0.00161681 + 0.000433222i −0.259627 0.965709i \(-0.583600\pi\)
0.258011 + 0.966142i \(0.416933\pi\)
\(152\) 3.07457 + 1.77510i 0.249381 + 0.143980i
\(153\) 0 0
\(154\) 21.9459 + 5.10894i 1.76845 + 0.411690i
\(155\) 2.29930i 0.184684i
\(156\) 0 0
\(157\) 5.26575 + 3.04018i 0.420253 + 0.242633i 0.695185 0.718830i \(-0.255322\pi\)
−0.274933 + 0.961463i \(0.588656\pi\)
\(158\) 1.29584 + 0.347220i 0.103092 + 0.0276234i
\(159\) 0 0
\(160\) −3.36545 5.82913i −0.266062 0.460833i
\(161\) 16.1724 + 15.1365i 1.27457 + 1.19292i
\(162\) 0 0
\(163\) 13.7573 3.68627i 1.07756 0.288731i 0.323963 0.946070i \(-0.394985\pi\)
0.753595 + 0.657339i \(0.228318\pi\)
\(164\) 0.436214 + 1.62797i 0.0340626 + 0.127123i
\(165\) 0 0
\(166\) 9.44905 0.733388
\(167\) 0.579671 + 2.16336i 0.0448563 + 0.167406i 0.984720 0.174142i \(-0.0557153\pi\)
−0.939864 + 0.341548i \(0.889049\pi\)
\(168\) 0 0
\(169\) −12.1221 4.69635i −0.932466 0.361258i
\(170\) −9.78060 16.9405i −0.750138 1.29928i
\(171\) 0 0
\(172\) 1.35138 + 2.34065i 0.103041 + 0.178473i
\(173\) 1.62494 2.81448i 0.123542 0.213981i −0.797620 0.603160i \(-0.793908\pi\)
0.921162 + 0.389179i \(0.127241\pi\)
\(174\) 0 0
\(175\) 8.35888 2.53884i 0.631872 0.191918i
\(176\) −6.60790 + 24.6610i −0.498089 + 1.85889i
\(177\) 0 0
\(178\) 9.27158i 0.694934i
\(179\) −18.3339 + 10.5851i −1.37034 + 0.791165i −0.990970 0.134081i \(-0.957192\pi\)
−0.379367 + 0.925246i \(0.623858\pi\)
\(180\) 0 0
\(181\) 18.5217 1.37671 0.688353 0.725376i \(-0.258334\pi\)
0.688353 + 0.725376i \(0.258334\pi\)
\(182\) 14.6676 + 2.24279i 1.08724 + 0.166247i
\(183\) 0 0
\(184\) −14.5544 + 14.5544i −1.07296 + 1.07296i
\(185\) −13.6340 + 7.87160i −1.00239 + 0.578732i
\(186\) 0 0
\(187\) −6.18517 + 23.0834i −0.452304 + 1.68802i
\(188\) 0.957909 3.57496i 0.0698627 0.260731i
\(189\) 0 0
\(190\) 4.57633 + 4.57633i 0.332002 + 0.332002i
\(191\) −13.7090 + 23.7447i −0.991948 + 1.71810i −0.386292 + 0.922376i \(0.626244\pi\)
−0.605655 + 0.795727i \(0.707089\pi\)
\(192\) 0 0
\(193\) −4.93597 + 18.4213i −0.355299 + 1.32599i 0.524809 + 0.851220i \(0.324137\pi\)
−0.880108 + 0.474774i \(0.842530\pi\)
\(194\) −1.72978 2.99607i −0.124191 0.215105i
\(195\) 0 0
\(196\) −2.92971 + 0.194088i −0.209265 + 0.0138634i
\(197\) −1.20155 4.48424i −0.0856068 0.319489i 0.909822 0.415000i \(-0.136218\pi\)
−0.995428 + 0.0955106i \(0.969552\pi\)
\(198\) 0 0
\(199\) −0.447121 −0.0316956 −0.0158478 0.999874i \(-0.505045\pi\)
−0.0158478 + 0.999874i \(0.505045\pi\)
\(200\) 2.10099 + 7.84100i 0.148562 + 0.554442i
\(201\) 0 0
\(202\) −23.8055 6.37866i −1.67495 0.448801i
\(203\) −1.35711 4.46814i −0.0952502 0.313602i
\(204\) 0 0
\(205\) 11.5775i 0.808607i
\(206\) 16.0058 + 4.28873i 1.11518 + 0.298810i
\(207\) 0 0
\(208\) −3.08944 + 16.5262i −0.214214 + 1.14589i
\(209\) 7.90665i 0.546914i
\(210\) 0 0
\(211\) −14.3795 + 24.9060i −0.989924 + 1.71460i −0.372331 + 0.928100i \(0.621442\pi\)
−0.617592 + 0.786498i \(0.711892\pi\)
\(212\) 0.101135 + 0.0583905i 0.00694600 + 0.00401028i
\(213\) 0 0
\(214\) −16.0045 + 16.0045i −1.09405 + 1.09405i
\(215\) −4.80522 17.9333i −0.327713 1.22304i
\(216\) 0 0
\(217\) −0.994622 + 1.86238i −0.0675194 + 0.126427i
\(218\) 11.5923 + 6.69282i 0.785130 + 0.453295i
\(219\) 0 0
\(220\) −3.30857 + 5.73062i −0.223064 + 0.386358i
\(221\) −2.89179 + 15.4690i −0.194523 + 1.04056i
\(222\) 0 0
\(223\) 14.0758 3.77160i 0.942586 0.252565i 0.245372 0.969429i \(-0.421090\pi\)
0.697213 + 0.716864i \(0.254423\pi\)
\(224\) −0.204392 6.17727i −0.0136565 0.412736i
\(225\) 0 0
\(226\) −20.4756 5.48643i −1.36202 0.364952i
\(227\) −12.6759 12.6759i −0.841326 0.841326i 0.147705 0.989031i \(-0.452811\pi\)
−0.989031 + 0.147705i \(0.952811\pi\)
\(228\) 0 0
\(229\) −6.61427 1.77229i −0.437083 0.117116i 0.0335661 0.999437i \(-0.489314\pi\)
−0.470649 + 0.882320i \(0.655980\pi\)
\(230\) −32.4952 + 18.7611i −2.14267 + 1.23707i
\(231\) 0 0
\(232\) 4.19131 1.12306i 0.275173 0.0737324i
\(233\) −6.74247 + 3.89276i −0.441714 + 0.255023i −0.704324 0.709878i \(-0.748750\pi\)
0.262611 + 0.964902i \(0.415417\pi\)
\(234\) 0 0
\(235\) −12.7119 + 22.0176i −0.829230 + 1.43627i
\(236\) −2.16589 2.16589i −0.140988 0.140988i
\(237\) 0 0
\(238\) −0.594001 17.9523i −0.0385034 1.16367i
\(239\) 2.22428 2.22428i 0.143877 0.143877i −0.631499 0.775376i \(-0.717560\pi\)
0.775376 + 0.631499i \(0.217560\pi\)
\(240\) 0 0
\(241\) 6.34946 6.34946i 0.409005 0.409005i −0.472387 0.881391i \(-0.656607\pi\)
0.881391 + 0.472387i \(0.156607\pi\)
\(242\) 28.5146 7.64045i 1.83298 0.491147i
\(243\) 0 0
\(244\) 0.994590 1.72268i 0.0636721 0.110283i
\(245\) 19.7843 + 3.92091i 1.26397 + 0.250498i
\(246\) 0 0
\(247\) −0.400470 5.19122i −0.0254813 0.330310i
\(248\) −1.69905 0.980946i −0.107890 0.0622901i
\(249\) 0 0
\(250\) 7.61055i 0.481333i
\(251\) −12.3486 21.3883i −0.779434 1.35002i −0.932269 0.361767i \(-0.882174\pi\)
0.152835 0.988252i \(-0.451160\pi\)
\(252\) 0 0
\(253\) 44.2784 + 11.8644i 2.78376 + 0.745905i
\(254\) −5.23441 + 1.40256i −0.328436 + 0.0880042i
\(255\) 0 0
\(256\) 9.65491 0.603432
\(257\) 6.15108 0.383694 0.191847 0.981425i \(-0.438552\pi\)
0.191847 + 0.981425i \(0.438552\pi\)
\(258\) 0 0
\(259\) −14.4483 + 0.478063i −0.897773 + 0.0297054i
\(260\) −1.88204 + 3.93010i −0.116719 + 0.243734i
\(261\) 0 0
\(262\) −2.33146 + 8.70113i −0.144038 + 0.537558i
\(263\) 8.57461 + 14.8517i 0.528733 + 0.915792i 0.999439 + 0.0335020i \(0.0106660\pi\)
−0.470706 + 0.882290i \(0.656001\pi\)
\(264\) 0 0
\(265\) −0.567242 0.567242i −0.0348454 0.0348454i
\(266\) 1.72711 + 5.68633i 0.105896 + 0.348651i
\(267\) 0 0
\(268\) 0.210806 0.786737i 0.0128770 0.0480576i
\(269\) 2.31154i 0.140937i −0.997514 0.0704685i \(-0.977551\pi\)
0.997514 0.0704685i \(-0.0224494\pi\)
\(270\) 0 0
\(271\) −4.58217 + 4.58217i −0.278347 + 0.278347i −0.832449 0.554102i \(-0.813062\pi\)
0.554102 + 0.832449i \(0.313062\pi\)
\(272\) 20.3522 1.23403
\(273\) 0 0
\(274\) −5.33142 −0.322083
\(275\) 12.7835 12.7835i 0.770877 0.770877i
\(276\) 0 0
\(277\) 24.1768i 1.45265i 0.687354 + 0.726323i \(0.258772\pi\)
−0.687354 + 0.726323i \(0.741228\pi\)
\(278\) 7.51123 28.0323i 0.450494 1.68127i
\(279\) 0 0
\(280\) −4.24934 + 18.2534i −0.253947 + 1.09085i
\(281\) −18.6196 18.6196i −1.11075 1.11075i −0.993049 0.117703i \(-0.962447\pi\)
−0.117703 0.993049i \(-0.537553\pi\)
\(282\) 0 0
\(283\) −6.25230 10.8293i −0.371661 0.643736i 0.618160 0.786052i \(-0.287878\pi\)
−0.989821 + 0.142317i \(0.954545\pi\)
\(284\) −1.27552 + 4.76029i −0.0756880 + 0.282472i
\(285\) 0 0
\(286\) 28.9614 10.2053i 1.71252 0.603454i
\(287\) 5.00814 9.37749i 0.295621 0.553536i
\(288\) 0 0
\(289\) 2.05017 0.120598
\(290\) 7.91016 0.464500
\(291\) 0 0
\(292\) −5.83479 + 1.56343i −0.341455 + 0.0914927i
\(293\) 0.0851383 + 0.0228127i 0.00497383 + 0.00133274i 0.261305 0.965256i \(-0.415847\pi\)
−0.256331 + 0.966589i \(0.582514\pi\)
\(294\) 0 0
\(295\) 10.5204 + 18.2219i 0.612523 + 1.06092i
\(296\) 13.4330i 0.780776i
\(297\) 0 0
\(298\) −19.2567 11.1179i −1.11551 0.644042i
\(299\) 29.6725 + 5.54702i 1.71601 + 0.320793i
\(300\) 0 0
\(301\) 3.86541 16.6042i 0.222799 0.957049i
\(302\) 0.0159967 0.0277071i 0.000920507 0.00159436i
\(303\) 0 0
\(304\) −6.50417 + 1.74279i −0.373040 + 0.0999557i
\(305\) −9.66207 + 9.66207i −0.553248 + 0.553248i
\(306\) 0 0
\(307\) −7.58728 + 7.58728i −0.433029 + 0.433029i −0.889658 0.456628i \(-0.849057\pi\)
0.456628 + 0.889658i \(0.349057\pi\)
\(308\) −5.15879 + 3.21045i −0.293950 + 0.182933i
\(309\) 0 0
\(310\) −2.52894 2.52894i −0.143634 0.143634i
\(311\) 15.1148 26.1796i 0.857082 1.48451i −0.0176172 0.999845i \(-0.505608\pi\)
0.874700 0.484665i \(-0.161059\pi\)
\(312\) 0 0
\(313\) 24.9891 14.4275i 1.41247 0.815489i 0.416849 0.908976i \(-0.363135\pi\)
0.995621 + 0.0934866i \(0.0298012\pi\)
\(314\) −9.13548 + 2.44784i −0.515545 + 0.138140i
\(315\) 0 0
\(316\) −0.313299 + 0.180883i −0.0176244 + 0.0101755i
\(317\) −16.2082 4.34297i −0.910343 0.243926i −0.226890 0.973920i \(-0.572856\pi\)
−0.683453 + 0.729995i \(0.739523\pi\)
\(318\) 0 0
\(319\) −6.83329 6.83329i −0.382591 0.382591i
\(320\) −15.8423 4.24492i −0.885609 0.237298i
\(321\) 0 0
\(322\) −34.4359 + 1.13941i −1.91904 + 0.0634968i
\(323\) −6.08807 + 1.63129i −0.338749 + 0.0907676i
\(324\) 0 0
\(325\) 7.74574 9.04071i 0.429656 0.501488i
\(326\) −11.0769 + 19.1858i −0.613493 + 1.06260i
\(327\) 0 0
\(328\) 8.55508 + 4.93928i 0.472375 + 0.272726i
\(329\) −19.8206 + 12.3349i −1.09274 + 0.680044i
\(330\) 0 0
\(331\) 1.62870 + 6.07840i 0.0895215 + 0.334099i 0.996132 0.0878697i \(-0.0280059\pi\)
−0.906610 + 0.421969i \(0.861339\pi\)
\(332\) −1.80174 + 1.80174i −0.0988833 + 0.0988833i
\(333\) 0 0
\(334\) −3.01699 1.74186i −0.165083 0.0953104i
\(335\) −2.79748 + 4.84538i −0.152843 + 0.264731i
\(336\) 0 0
\(337\) 17.1415i 0.933758i −0.884321 0.466879i \(-0.845378\pi\)
0.884321 0.466879i \(-0.154622\pi\)
\(338\) 18.4981 8.16734i 1.00617 0.444245i
\(339\) 0 0
\(340\) 5.09517 + 1.36525i 0.276324 + 0.0740408i
\(341\) 4.36932i 0.236612i
\(342\) 0 0
\(343\) 14.3287 + 11.7341i 0.773678 + 0.633579i
\(344\) 15.3017 + 4.10008i 0.825013 + 0.221062i
\(345\) 0 0
\(346\) 1.30834 + 4.88281i 0.0703370 + 0.262501i
\(347\) −4.22975 −0.227065 −0.113532 0.993534i \(-0.536217\pi\)
−0.113532 + 0.993534i \(0.536217\pi\)
\(348\) 0 0
\(349\) 4.82352 + 18.0016i 0.258197 + 0.963605i 0.966284 + 0.257479i \(0.0828919\pi\)
−0.708087 + 0.706125i \(0.750441\pi\)
\(350\) −6.40131 + 11.9861i −0.342165 + 0.640685i
\(351\) 0 0
\(352\) −6.39530 11.0770i −0.340871 0.590405i
\(353\) 1.15293 4.30278i 0.0613641 0.229014i −0.928433 0.371501i \(-0.878843\pi\)
0.989797 + 0.142487i \(0.0455099\pi\)
\(354\) 0 0
\(355\) 16.9267 29.3178i 0.898373 1.55603i
\(356\) 1.76790 + 1.76790i 0.0936985 + 0.0936985i
\(357\) 0 0
\(358\) 8.52271 31.8072i 0.450439 1.68106i
\(359\) 4.24764 15.8524i 0.224182 0.836657i −0.758549 0.651616i \(-0.774091\pi\)
0.982731 0.185041i \(-0.0592420\pi\)
\(360\) 0 0
\(361\) −14.6485 + 8.45734i −0.770976 + 0.445123i
\(362\) −20.3715 + 20.3715i −1.07070 + 1.07070i
\(363\) 0 0
\(364\) −3.22447 + 2.36916i −0.169008 + 0.124178i
\(365\) 41.4947 2.17193
\(366\) 0 0
\(367\) −24.1880 + 13.9650i −1.26260 + 0.728964i −0.973578 0.228357i \(-0.926665\pi\)
−0.289026 + 0.957321i \(0.593331\pi\)
\(368\) 39.0394i 2.03507i
\(369\) 0 0
\(370\) 6.33793 23.6535i 0.329493 1.22969i
\(371\) −0.214077 0.704827i −0.0111143 0.0365928i
\(372\) 0 0
\(373\) 2.92406 5.06463i 0.151402 0.262237i −0.780341 0.625354i \(-0.784954\pi\)
0.931743 + 0.363118i \(0.118288\pi\)
\(374\) −18.5859 32.1917i −0.961054 1.66459i
\(375\) 0 0
\(376\) −10.8465 18.7866i −0.559364 0.968846i
\(377\) −4.83260 4.14039i −0.248892 0.213241i
\(378\) 0 0
\(379\) −0.411597 1.53610i −0.0211423 0.0789043i 0.954549 0.298055i \(-0.0963380\pi\)
−0.975691 + 0.219151i \(0.929671\pi\)
\(380\) −1.74523 −0.0895282
\(381\) 0 0
\(382\) −11.0380 41.1943i −0.564752 2.10768i
\(383\) 13.6049 3.64543i 0.695179 0.186273i 0.106109 0.994355i \(-0.466161\pi\)
0.589070 + 0.808082i \(0.299494\pi\)
\(384\) 0 0
\(385\) 39.9376 12.1302i 2.03541 0.618214i
\(386\) −14.8322 25.6901i −0.754937 1.30759i
\(387\) 0 0
\(388\) 0.901124 + 0.241455i 0.0457476 + 0.0122580i
\(389\) −0.216783 0.125160i −0.0109913 0.00634584i 0.494494 0.869181i \(-0.335353\pi\)
−0.505486 + 0.862835i \(0.668687\pi\)
\(390\) 0 0
\(391\) 36.5419i 1.84800i
\(392\) −11.3378 + 12.9467i −0.572648 + 0.653905i
\(393\) 0 0
\(394\) 6.25365 + 3.61055i 0.315055 + 0.181897i
\(395\) 2.40040 0.643184i 0.120777 0.0323621i
\(396\) 0 0
\(397\) 1.74276 + 6.50408i 0.0874668 + 0.326430i 0.995770 0.0918822i \(-0.0292883\pi\)
−0.908303 + 0.418313i \(0.862622\pi\)
\(398\) 0.491777 0.491777i 0.0246505 0.0246505i
\(399\) 0 0
\(400\) −13.3338 7.69825i −0.666688 0.384913i
\(401\) 20.3892 + 20.3892i 1.01819 + 1.01819i 0.999831 + 0.0183568i \(0.00584349\pi\)
0.0183568 + 0.999831i \(0.494157\pi\)
\(402\) 0 0
\(403\) 0.221305 + 2.86874i 0.0110240 + 0.142902i
\(404\) 5.75549 3.32294i 0.286347 0.165322i
\(405\) 0 0
\(406\) 6.40704 + 3.42174i 0.317976 + 0.169818i
\(407\) −25.9085 + 14.9583i −1.28423 + 0.741453i
\(408\) 0 0
\(409\) 19.0625 + 19.0625i 0.942582 + 0.942582i 0.998439 0.0558573i \(-0.0177892\pi\)
−0.0558573 + 0.998439i \(0.517789\pi\)
\(410\) 12.7338 + 12.7338i 0.628877 + 0.628877i
\(411\) 0 0
\(412\) −3.86975 + 2.23420i −0.190649 + 0.110071i
\(413\) 0.638932 + 19.3102i 0.0314398 + 0.950192i
\(414\) 0 0
\(415\) 15.1582 8.75161i 0.744089 0.429600i
\(416\) −4.75998 6.94884i −0.233377 0.340695i
\(417\) 0 0
\(418\) 8.69632 + 8.69632i 0.425351 + 0.425351i
\(419\) −12.0707 6.96900i −0.589691 0.340458i 0.175284 0.984518i \(-0.443916\pi\)
−0.764975 + 0.644060i \(0.777249\pi\)
\(420\) 0 0
\(421\) 15.9864 15.9864i 0.779131 0.779131i −0.200552 0.979683i \(-0.564274\pi\)
0.979683 + 0.200552i \(0.0642735\pi\)
\(422\) −11.5778 43.2091i −0.563600 2.10338i
\(423\) 0 0
\(424\) 0.661159 0.177157i 0.0321087 0.00860351i
\(425\) −12.4807 7.20576i −0.605405 0.349531i
\(426\) 0 0
\(427\) −12.0056 + 3.64647i −0.580993 + 0.176465i
\(428\) 6.10348i 0.295023i
\(429\) 0 0
\(430\) 25.0095 + 14.4393i 1.20607 + 0.696323i
\(431\) −3.10956 0.833204i −0.149782 0.0401340i 0.183149 0.983085i \(-0.441371\pi\)
−0.332931 + 0.942951i \(0.608038\pi\)
\(432\) 0 0
\(433\) −5.34137 9.25152i −0.256690 0.444600i 0.708663 0.705547i \(-0.249299\pi\)
−0.965353 + 0.260947i \(0.915965\pi\)
\(434\) −0.954423 3.14234i −0.0458138 0.150837i
\(435\) 0 0
\(436\) −3.48660 + 0.934231i −0.166978 + 0.0447416i
\(437\) 3.12914 + 11.6781i 0.149687 + 0.558639i
\(438\) 0 0
\(439\) 14.5610 0.694961 0.347480 0.937687i \(-0.387037\pi\)
0.347480 + 0.937687i \(0.387037\pi\)
\(440\) 10.0382 + 37.4632i 0.478554 + 1.78599i
\(441\) 0 0
\(442\) −13.8333 20.1946i −0.657985 0.960557i
\(443\) 2.49941 + 4.32911i 0.118751 + 0.205682i 0.919273 0.393621i \(-0.128778\pi\)
−0.800522 + 0.599303i \(0.795444\pi\)
\(444\) 0 0
\(445\) −8.58724 14.8735i −0.407074 0.705073i
\(446\) −11.3333 + 19.6299i −0.536649 + 0.929503i
\(447\) 0 0
\(448\) −10.9956 10.2913i −0.519493 0.486216i
\(449\) −6.89362 + 25.7273i −0.325330 + 1.21415i 0.588650 + 0.808388i \(0.299660\pi\)
−0.913980 + 0.405760i \(0.867007\pi\)
\(450\) 0 0
\(451\) 22.0005i 1.03596i
\(452\) 4.95044 2.85814i 0.232849 0.134435i
\(453\) 0 0
\(454\) 27.8837 1.30865
\(455\) 25.6072 9.98711i 1.20048 0.468203i
\(456\) 0 0
\(457\) −8.85252 + 8.85252i −0.414103 + 0.414103i −0.883165 0.469062i \(-0.844592\pi\)
0.469062 + 0.883165i \(0.344592\pi\)
\(458\) 9.22416 5.32557i 0.431017 0.248848i
\(459\) 0 0
\(460\) 2.61881 9.77352i 0.122102 0.455693i
\(461\) −2.58295 + 9.63971i −0.120300 + 0.448966i −0.999629 0.0272495i \(-0.991325\pi\)
0.879329 + 0.476216i \(0.157992\pi\)
\(462\) 0 0
\(463\) −8.87215 8.87215i −0.412324 0.412324i 0.470224 0.882547i \(-0.344173\pi\)
−0.882547 + 0.470224i \(0.844173\pi\)
\(464\) −4.11501 + 7.12740i −0.191034 + 0.330881i
\(465\) 0 0
\(466\) 3.13431 11.6974i 0.145194 0.541872i
\(467\) −7.33629 12.7068i −0.339483 0.588002i 0.644853 0.764307i \(-0.276919\pi\)
−0.984336 + 0.176305i \(0.943585\pi\)
\(468\) 0 0
\(469\) −4.36188 + 2.71452i −0.201413 + 0.125345i
\(470\) −10.2351 38.1980i −0.472111 1.76194i
\(471\) 0 0
\(472\) −17.9532 −0.826364
\(473\) −9.13127 34.0784i −0.419856 1.56692i
\(474\) 0 0
\(475\) 4.60565 + 1.23408i 0.211322 + 0.0566235i
\(476\) 3.53639 + 3.30986i 0.162090 + 0.151707i
\(477\) 0 0
\(478\) 4.89286i 0.223794i
\(479\) −13.3439 3.57549i −0.609699 0.163368i −0.0592583 0.998243i \(-0.518874\pi\)
−0.550441 + 0.834874i \(0.685540\pi\)
\(480\) 0 0
\(481\) −16.2529 + 11.1333i −0.741070 + 0.507636i
\(482\) 13.9672i 0.636189i
\(483\) 0 0
\(484\) −3.98026 + 6.89402i −0.180921 + 0.313364i
\(485\) −5.54986 3.20421i −0.252006 0.145496i
\(486\) 0 0
\(487\) 21.2572 21.2572i 0.963257 0.963257i −0.0360915 0.999348i \(-0.511491\pi\)
0.999348 + 0.0360915i \(0.0114908\pi\)
\(488\) −3.01759 11.2618i −0.136600 0.509798i
\(489\) 0 0
\(490\) −26.0727 + 17.4477i −1.17785 + 0.788208i
\(491\) −27.2827 15.7517i −1.23125 0.710863i −0.263961 0.964533i \(-0.585029\pi\)
−0.967291 + 0.253670i \(0.918362\pi\)
\(492\) 0 0
\(493\) −3.85175 + 6.67143i −0.173474 + 0.300466i
\(494\) 6.15016 + 5.26923i 0.276709 + 0.237074i
\(495\) 0 0
\(496\) 3.59429 0.963087i 0.161388 0.0432439i
\(497\) 26.3924 16.4247i 1.18386 0.736747i
\(498\) 0 0
\(499\) −22.5875 6.05231i −1.01116 0.270938i −0.285044 0.958515i \(-0.592008\pi\)
−0.726112 + 0.687576i \(0.758675\pi\)
\(500\) 1.45118 + 1.45118i 0.0648985 + 0.0648985i
\(501\) 0 0
\(502\) 37.1063 + 9.94261i 1.65614 + 0.443760i
\(503\) 7.16456 4.13646i 0.319452 0.184436i −0.331696 0.943386i \(-0.607621\pi\)
0.651148 + 0.758951i \(0.274288\pi\)
\(504\) 0 0
\(505\) −44.0968 + 11.8157i −1.96228 + 0.525792i
\(506\) −61.7499 + 35.6513i −2.74512 + 1.58490i
\(507\) 0 0
\(508\) 0.730656 1.26553i 0.0324176 0.0561489i
\(509\) 6.51433 + 6.51433i 0.288742 + 0.288742i 0.836583 0.547840i \(-0.184550\pi\)
−0.547840 + 0.836583i \(0.684550\pi\)
\(510\) 0 0
\(511\) 33.6097 + 17.9496i 1.48681 + 0.794044i
\(512\) 8.50976 8.50976i 0.376082 0.376082i
\(513\) 0 0
\(514\) −6.76541 + 6.76541i −0.298409 + 0.298409i
\(515\) 29.6488 7.94436i 1.30648 0.350071i
\(516\) 0 0
\(517\) −24.1561 + 41.8396i −1.06238 + 1.84010i
\(518\) 15.3655 16.4171i 0.675121 0.721326i
\(519\) 0 0
\(520\) 8.48825 + 24.0886i 0.372234 + 1.05635i
\(521\) −5.78613 3.34062i −0.253495 0.146355i 0.367869 0.929878i \(-0.380088\pi\)
−0.621364 + 0.783522i \(0.713421\pi\)
\(522\) 0 0
\(523\) 32.1180i 1.40442i −0.711969 0.702211i \(-0.752196\pi\)
0.711969 0.702211i \(-0.247804\pi\)
\(524\) −1.21457 2.10369i −0.0530586 0.0919001i
\(525\) 0 0
\(526\) −25.7659 6.90396i −1.12345 0.301027i
\(527\) 3.36435 0.901475i 0.146553 0.0392689i
\(528\) 0 0
\(529\) −47.0945 −2.04759
\(530\) 1.24779 0.0542005
\(531\) 0 0
\(532\) −1.41359 0.754943i −0.0612869 0.0327309i
\(533\) −1.11432 14.4447i −0.0482665 0.625671i
\(534\) 0 0
\(535\) −10.8514 + 40.4979i −0.469146 + 1.75088i
\(536\) −2.38696 4.13434i −0.103101 0.178576i
\(537\) 0 0
\(538\) 2.54240 + 2.54240i 0.109611 + 0.109611i
\(539\) 37.5957 + 7.45083i 1.61936 + 0.320930i
\(540\) 0 0
\(541\) −1.62221 + 6.05418i −0.0697443 + 0.260289i −0.991990 0.126314i \(-0.959685\pi\)
0.922246 + 0.386604i \(0.126352\pi\)
\(542\) 10.0796i 0.432957i
\(543\) 0 0
\(544\) −7.20974 + 7.20974i −0.309115 + 0.309115i
\(545\) 24.7953 1.06211
\(546\) 0 0
\(547\) −17.9848 −0.768973 −0.384487 0.923131i \(-0.625622\pi\)
−0.384487 + 0.923131i \(0.625622\pi\)
\(548\) 1.01659 1.01659i 0.0434267 0.0434267i
\(549\) 0 0
\(550\) 28.1206i 1.19907i
\(551\) 0.659662 2.46189i 0.0281026 0.104880i
\(552\) 0 0
\(553\) 2.22249 + 0.517390i 0.0945099 + 0.0220017i
\(554\) −26.5915 26.5915i −1.12976 1.12976i
\(555\) 0 0
\(556\) 3.91295 + 6.77742i 0.165946 + 0.287427i
\(557\) −9.77773 + 36.4910i −0.414296 + 1.54617i 0.371946 + 0.928254i \(0.378691\pi\)
−0.786242 + 0.617919i \(0.787976\pi\)
\(558\) 0 0
\(559\) −7.72133 21.9121i −0.326577 0.926785i
\(560\) −18.7816 30.1797i −0.793669 1.27533i
\(561\) 0 0
\(562\) 40.9584 1.72773
\(563\) 6.37316 0.268596 0.134298 0.990941i \(-0.457122\pi\)
0.134298 + 0.990941i \(0.457122\pi\)
\(564\) 0 0
\(565\) −37.9287 + 10.1630i −1.59567 + 0.427559i
\(566\) 18.7876 + 5.03413i 0.789703 + 0.211600i
\(567\) 0 0
\(568\) 14.4428 + 25.0156i 0.606005 + 1.04963i
\(569\) 4.40653i 0.184731i 0.995725 + 0.0923657i \(0.0294429\pi\)
−0.995725 + 0.0923657i \(0.970557\pi\)
\(570\) 0 0
\(571\) 12.2682 + 7.08302i 0.513406 + 0.296415i 0.734233 0.678898i \(-0.237542\pi\)
−0.220826 + 0.975313i \(0.570875\pi\)
\(572\) −3.57640 + 7.46829i −0.149537 + 0.312265i
\(573\) 0 0
\(574\) 4.80573 + 15.8224i 0.200587 + 0.660414i
\(575\) −13.8221 + 23.9405i −0.576419 + 0.998388i
\(576\) 0 0
\(577\) 8.98371 2.40718i 0.373997 0.100212i −0.0669241 0.997758i \(-0.521319\pi\)
0.440921 + 0.897546i \(0.354652\pi\)
\(578\) −2.25493 + 2.25493i −0.0937929 + 0.0937929i
\(579\) 0 0
\(580\) −1.50830 + 1.50830i −0.0626289 + 0.0626289i
\(581\) 16.0635 0.531508i 0.666428 0.0220507i
\(582\) 0 0
\(583\) −1.07792 1.07792i −0.0446428 0.0446428i
\(584\) −17.7028 + 30.6621i −0.732547 + 1.26881i
\(585\) 0 0
\(586\) −0.118733 + 0.0685503i −0.00490480 + 0.00283179i
\(587\) 10.0172 2.68411i 0.413455 0.110785i −0.0460944 0.998937i \(-0.514678\pi\)
0.459550 + 0.888152i \(0.348011\pi\)
\(588\) 0 0
\(589\) −0.997987 + 0.576188i −0.0411213 + 0.0237414i
\(590\) −31.6130 8.47066i −1.30148 0.348732i
\(591\) 0 0
\(592\) 18.0157 + 18.0157i 0.740441 + 0.740441i
\(593\) −11.6126 3.11158i −0.476871 0.127777i 0.0123741 0.999923i \(-0.496061\pi\)
−0.489245 + 0.872146i \(0.662728\pi\)
\(594\) 0 0
\(595\) −17.5801 28.2490i −0.720714 1.15810i
\(596\) 5.79182 1.55191i 0.237242 0.0635688i
\(597\) 0 0
\(598\) −38.7371 + 26.5350i −1.58408 + 1.08510i
\(599\) 9.16962 15.8822i 0.374660 0.648931i −0.615616 0.788046i \(-0.711093\pi\)
0.990276 + 0.139116i \(0.0444260\pi\)
\(600\) 0 0
\(601\) 29.4396 + 16.9969i 1.20086 + 0.693319i 0.960747 0.277424i \(-0.0894808\pi\)
0.240117 + 0.970744i \(0.422814\pi\)
\(602\) 14.0111 + 22.5140i 0.571048 + 0.917602i
\(603\) 0 0
\(604\) 0.00223293 + 0.00833342i 9.08568e−5 + 0.000339082i
\(605\) 38.6668 38.6668i 1.57203 1.57203i
\(606\) 0 0
\(607\) 35.5453 + 20.5221i 1.44274 + 0.832965i 0.998032 0.0627107i \(-0.0199745\pi\)
0.444707 + 0.895676i \(0.353308\pi\)
\(608\) 1.68672 2.92148i 0.0684053 0.118482i
\(609\) 0 0
\(610\) 21.2541i 0.860554i
\(611\) −13.7409 + 28.6939i −0.555896 + 1.16083i
\(612\) 0 0
\(613\) −25.8999 6.93987i −1.04609 0.280299i −0.305454 0.952207i \(-0.598808\pi\)
−0.740635 + 0.671908i \(0.765475\pi\)
\(614\) 16.6901i 0.673558i
\(615\) 0 0
\(616\) −8.07495 + 34.6866i −0.325349 + 1.39756i
\(617\) 10.2681 + 2.75133i 0.413378 + 0.110764i 0.459513 0.888171i \(-0.348024\pi\)
−0.0461351 + 0.998935i \(0.514690\pi\)
\(618\) 0 0
\(619\) −7.23874 27.0153i −0.290949 1.08584i −0.944381 0.328853i \(-0.893338\pi\)
0.653432 0.756985i \(-0.273329\pi\)
\(620\) 0.964435 0.0387326
\(621\) 0 0
\(622\) 12.1699 + 45.4187i 0.487969 + 1.82112i
\(623\) −0.521525 15.7618i −0.0208945 0.631485i
\(624\) 0 0
\(625\) −15.3035 26.5064i −0.612140 1.06026i
\(626\) −11.6165 + 43.3533i −0.464288 + 1.73275i
\(627\) 0 0
\(628\) 1.27520 2.20870i 0.0508858 0.0881368i
\(629\) 16.8632 + 16.8632i 0.672379 + 0.672379i
\(630\) 0 0
\(631\) −0.748324 + 2.79278i −0.0297903 + 0.111179i −0.979220 0.202801i \(-0.934996\pi\)
0.949430 + 0.313980i \(0.101662\pi\)
\(632\) −0.548800 + 2.04815i −0.0218301 + 0.0814711i
\(633\) 0 0
\(634\) 22.6037 13.0503i 0.897708 0.518292i
\(635\) −7.09805 + 7.09805i −0.281677 + 0.281677i
\(636\) 0 0
\(637\) 25.0614 + 2.98774i 0.992969 + 0.118378i
\(638\) 15.0315 0.595103
\(639\) 0 0
\(640\) 33.7516 19.4865i 1.33415 0.770272i
\(641\) 15.0751i 0.595431i −0.954655 0.297715i \(-0.903775\pi\)
0.954655 0.297715i \(-0.0962246\pi\)
\(642\) 0 0
\(643\) 10.7996 40.3048i 0.425896 1.58946i −0.336063 0.941839i \(-0.609096\pi\)
0.761959 0.647625i \(-0.224238\pi\)
\(644\) 6.34896 6.78348i 0.250184 0.267307i
\(645\) 0 0
\(646\) 4.90190 8.49033i 0.192863 0.334048i
\(647\) 0.214109 + 0.370847i 0.00841747 + 0.0145795i 0.870203 0.492693i \(-0.163987\pi\)
−0.861786 + 0.507272i \(0.830654\pi\)
\(648\) 0 0
\(649\) 19.9918 + 34.6267i 0.784745 + 1.35922i
\(650\) 1.42430 + 18.4630i 0.0558657 + 0.724178i
\(651\) 0 0
\(652\) −1.54619 5.77047i −0.0605536 0.225989i
\(653\) 16.3850 0.641195 0.320597 0.947216i \(-0.396116\pi\)
0.320597 + 0.947216i \(0.396116\pi\)
\(654\) 0 0
\(655\) 4.31875 + 16.1178i 0.168748 + 0.629775i
\(656\) −18.0980 + 4.84936i −0.706610 + 0.189336i
\(657\) 0 0
\(658\) 8.23334 35.3670i 0.320969 1.37875i
\(659\) 13.2020 + 22.8666i 0.514278 + 0.890755i 0.999863 + 0.0165659i \(0.00527333\pi\)
−0.485585 + 0.874190i \(0.661393\pi\)
\(660\) 0 0
\(661\) 26.7452 + 7.16635i 1.04027 + 0.278739i 0.738224 0.674555i \(-0.235665\pi\)
0.302043 + 0.953294i \(0.402331\pi\)
\(662\) −8.47684 4.89411i −0.329462 0.190215i
\(663\) 0 0
\(664\) 14.9347i 0.579580i
\(665\) 8.03726 + 7.52243i 0.311672 + 0.291707i
\(666\) 0 0
\(667\) 12.7971 + 7.38841i 0.495506 + 0.286080i
\(668\) 0.907416 0.243141i 0.0351090 0.00940742i
\(669\) 0 0
\(670\) −2.25243 8.40618i −0.0870189 0.324759i
\(671\) −18.3606 + 18.3606i −0.708805 + 0.708805i
\(672\) 0 0
\(673\) −16.8918 9.75249i −0.651131 0.375931i 0.137758 0.990466i \(-0.456010\pi\)
−0.788889 + 0.614535i \(0.789344\pi\)
\(674\) 18.8535 + 18.8535i 0.726210 + 0.726210i
\(675\) 0 0
\(676\) −1.96987 + 5.08456i −0.0757642 + 0.195560i
\(677\) 1.91182 1.10379i 0.0734772 0.0424221i −0.462811 0.886457i \(-0.653159\pi\)
0.536288 + 0.844035i \(0.319826\pi\)
\(678\) 0 0
\(679\) −3.10919 4.99607i −0.119320 0.191732i
\(680\) 26.7754 15.4588i 1.02679 0.592816i
\(681\) 0 0
\(682\) −4.80570 4.80570i −0.184020 0.184020i
\(683\) 9.24232 + 9.24232i 0.353647 + 0.353647i 0.861465 0.507817i \(-0.169548\pi\)
−0.507817 + 0.861465i \(0.669548\pi\)
\(684\) 0 0
\(685\) −8.55271 + 4.93791i −0.326782 + 0.188668i
\(686\) −28.6658 + 2.85380i −1.09446 + 0.108959i
\(687\) 0 0
\(688\) −26.0208 + 15.0231i −0.992035 + 0.572752i
\(689\) −0.762319 0.653127i −0.0290421 0.0248821i
\(690\) 0 0
\(691\) −35.9312 35.9312i −1.36689 1.36689i −0.864842 0.502045i \(-0.832581\pi\)
−0.502045 0.864842i \(-0.667419\pi\)
\(692\) −1.18053 0.681577i −0.0448768 0.0259097i
\(693\) 0 0
\(694\) 4.65219 4.65219i 0.176595 0.176595i
\(695\) −13.9137 51.9265i −0.527775 1.96968i
\(696\) 0 0
\(697\) −16.9402 + 4.53912i −0.641657 + 0.171932i
\(698\) −25.1048 14.4943i −0.950230 0.548616i
\(699\) 0 0
\(700\) −1.06491 3.50611i −0.0402498 0.132518i
\(701\) 12.9407i 0.488765i 0.969679 + 0.244383i \(0.0785853\pi\)
−0.969679 + 0.244383i \(0.921415\pi\)
\(702\) 0 0
\(703\) −6.83317 3.94513i −0.257718 0.148793i
\(704\) −30.1047 8.06654i −1.13461 0.304019i
\(705\) 0 0
\(706\) 3.46444 + 6.00059i 0.130386 + 0.225835i
\(707\) −40.8285 9.50477i −1.53551 0.357464i
\(708\) 0 0
\(709\) −23.8425 + 6.38859i −0.895426 + 0.239929i −0.677051 0.735936i \(-0.736742\pi\)
−0.218375 + 0.975865i \(0.570076\pi\)
\(710\) 13.6287 + 50.8631i 0.511477 + 1.90886i
\(711\) 0 0
\(712\) 14.6542 0.549190
\(713\) −1.72920 6.45347i −0.0647592 0.241684i
\(714\) 0 0
\(715\) 37.0081 43.1952i 1.38402 1.61541i
\(716\) 4.43987 + 7.69008i 0.165926 + 0.287392i
\(717\) 0 0
\(718\) 12.7638 + 22.1075i 0.476340 + 0.825045i
\(719\) 7.46614 12.9317i 0.278440 0.482273i −0.692557 0.721363i \(-0.743516\pi\)
0.970997 + 0.239091i \(0.0768493\pi\)
\(720\) 0 0
\(721\) 27.4513 + 6.39060i 1.02234 + 0.237998i
\(722\) 6.80954 25.4136i 0.253425 0.945795i
\(723\) 0 0
\(724\) 7.76886i 0.288727i
\(725\) 5.04696 2.91387i 0.187439 0.108218i
\(726\) 0 0
\(727\) 8.06701 0.299189 0.149595 0.988747i \(-0.452203\pi\)
0.149595 + 0.988747i \(0.452203\pi\)
\(728\) −3.54486 + 23.1830i −0.131381 + 0.859218i
\(729\) 0 0
\(730\) −45.6390 + 45.6390i −1.68917 + 1.68917i
\(731\) −24.3562 + 14.0620i −0.900846 + 0.520104i
\(732\) 0 0
\(733\) 0.991378 3.69987i 0.0366174 0.136658i −0.945197 0.326500i \(-0.894131\pi\)
0.981815 + 0.189842i \(0.0607975\pi\)
\(734\) 11.2441 41.9635i 0.415026 1.54890i
\(735\) 0 0
\(736\) 13.8297 + 13.8297i 0.509769 + 0.509769i
\(737\) −5.31600 + 9.20757i −0.195817 + 0.339165i
\(738\) 0 0
\(739\) 4.96535 18.5309i 0.182653 0.681671i −0.812467 0.583007i \(-0.801876\pi\)
0.995121 0.0986647i \(-0.0314571\pi\)
\(740\) 3.30172 + 5.71875i 0.121374 + 0.210225i
\(741\) 0 0
\(742\) 1.01068 + 0.539764i 0.0371032 + 0.0198153i
\(743\) −2.24541 8.37997i −0.0823759 0.307431i 0.912428 0.409236i \(-0.134205\pi\)
−0.994804 + 0.101805i \(0.967538\pi\)
\(744\) 0 0
\(745\) −41.1891 −1.50905
\(746\) 2.35435 + 8.78656i 0.0861989 + 0.321699i
\(747\) 0 0
\(748\) 9.68225 + 2.59435i 0.354018 + 0.0948588i
\(749\) −26.3078 + 28.1083i −0.961264 + 1.02705i
\(750\) 0 0
\(751\) 30.1279i 1.09938i 0.835367 + 0.549692i \(0.185255\pi\)
−0.835367 + 0.549692i \(0.814745\pi\)
\(752\) 39.7426 + 10.6490i 1.44926 + 0.388329i
\(753\) 0 0
\(754\) 9.86916 0.761343i 0.359414 0.0277265i
\(755\) 0.0592640i 0.00215684i
\(756\) 0 0
\(757\) −0.444897 + 0.770584i −0.0161700 + 0.0280073i −0.873997 0.485931i \(-0.838481\pi\)
0.857827 + 0.513938i \(0.171814\pi\)
\(758\) 2.14223 + 1.23681i 0.0778091 + 0.0449231i
\(759\) 0 0
\(760\) −7.23314 + 7.23314i −0.262373 + 0.262373i
\(761\) 12.4145 + 46.3316i 0.450026 + 1.67952i 0.702314 + 0.711867i \(0.252150\pi\)
−0.252288 + 0.967652i \(0.581183\pi\)
\(762\) 0 0
\(763\) 20.0836 + 10.7258i 0.727075 + 0.388302i
\(764\) 9.95963 + 5.75019i 0.360327 + 0.208035i
\(765\) 0 0
\(766\) −10.9542 + 18.9732i −0.395791 + 0.685530i
\(767\) 14.8797 + 21.7221i 0.537275 + 0.784340i
\(768\) 0 0
\(769\) 4.85396 1.30061i 0.175038 0.0469013i −0.170235 0.985403i \(-0.554453\pi\)
0.345274 + 0.938502i \(0.387786\pi\)
\(770\) −30.5846 + 57.2680i −1.10219 + 2.06380i
\(771\) 0 0
\(772\) 7.72676 + 2.07038i 0.278092 + 0.0745146i
\(773\) −9.15642 9.15642i −0.329333 0.329333i 0.523000 0.852333i \(-0.324813\pi\)
−0.852333 + 0.523000i \(0.824813\pi\)
\(774\) 0 0
\(775\) −2.54514 0.681969i −0.0914242 0.0244970i
\(776\) 4.73545 2.73401i 0.169993 0.0981454i
\(777\) 0 0
\(778\) 0.376093 0.100774i 0.0134836 0.00361292i
\(779\) 5.02509 2.90123i 0.180042 0.103948i
\(780\) 0 0
\(781\) 32.1654 55.7121i 1.15097 1.99354i
\(782\) 40.1915 + 40.1915i 1.43725 + 1.43725i
\(783\) 0 0
\(784\) −2.15766 32.5693i −0.0770592 1.16319i
\(785\) −12.3880 + 12.3880i −0.442148 + 0.442148i
\(786\) 0 0
\(787\) 1.63546 1.63546i 0.0582978 0.0582978i −0.677357 0.735655i \(-0.736875\pi\)
0.735655 + 0.677357i \(0.236875\pi\)
\(788\) −1.88090 + 0.503986i −0.0670043 + 0.0179538<