Properties

Label 804.2.y.b.49.2
Level 804
Weight 2
Character 804.49
Analytic conductor 6.420
Analytic rank 0
Dimension 120
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 49.2
Character \(\chi\) = 804.49
Dual form 804.2.y.b.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.841254 - 0.540641i) q^{3} +(-0.355125 - 2.46995i) q^{5} +(1.47905 + 0.141233i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\) \(q+(-0.841254 - 0.540641i) q^{3} +(-0.355125 - 2.46995i) q^{5} +(1.47905 + 0.141233i) q^{7} +(0.415415 + 0.909632i) q^{9} +(-5.48535 - 2.19600i) q^{11} +(-2.97924 - 2.84070i) q^{13} +(-1.03661 + 2.26985i) q^{15} +(-2.20441 + 6.36922i) q^{17} +(3.49676 - 0.333900i) q^{19} +(-1.16790 - 0.918450i) q^{21} +(0.152650 - 3.20453i) q^{23} +(-1.17707 + 0.345620i) q^{25} +(0.142315 - 0.989821i) q^{27} +(-3.60506 + 6.24415i) q^{29} +(1.09094 - 1.04021i) q^{31} +(3.42732 + 4.81300i) q^{33} +(-0.176412 - 3.70335i) q^{35} +(3.11904 + 5.40233i) q^{37} +(0.970499 + 4.00045i) q^{39} +(-4.79453 + 0.924070i) q^{41} +(-8.41053 - 9.70626i) q^{43} +(2.09922 - 1.34909i) q^{45} +(-9.68103 + 4.99092i) q^{47} +(-4.70585 - 0.906977i) q^{49} +(5.29793 - 4.16634i) q^{51} +(5.19018 - 5.98979i) q^{53} +(-3.47603 + 14.3284i) q^{55} +(-3.12218 - 1.60960i) q^{57} +(-11.5248 - 3.38399i) q^{59} +(0.979919 - 0.392300i) q^{61} +(0.485952 + 1.40407i) q^{63} +(-5.95839 + 8.36739i) q^{65} +(-6.24891 + 5.28688i) q^{67} +(-1.86092 + 2.61329i) q^{69} +(0.204053 + 0.589573i) q^{71} +(-6.65132 + 2.66279i) q^{73} +(1.17707 + 0.345620i) q^{75} +(-7.80299 - 4.02272i) q^{77} +(-0.340589 + 1.40392i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(12.0626 - 9.48612i) q^{83} +(16.5145 + 3.18291i) q^{85} +(6.40862 - 3.30387i) q^{87} +(14.0357 - 9.02019i) q^{89} +(-4.00526 - 4.62232i) q^{91} +(-1.48014 + 0.285273i) q^{93} +(-2.06651 - 8.51825i) q^{95} +(2.46726 + 4.27341i) q^{97} +(-0.281142 - 5.90191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{33}\right)\) \(1\)

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 0
\(3\) −0.841254 0.540641i −0.485698 0.312139i
\(4\) 0 0
\(5\) −0.355125 2.46995i −0.158817 1.10460i −0.900818 0.434197i \(-0.857032\pi\)
0.742001 0.670398i \(-0.233877\pi\)
\(6\) 0 0
\(7\) 1.47905 + 0.141233i 0.559030 + 0.0533809i 0.370747 0.928734i \(-0.379102\pi\)
0.188283 + 0.982115i \(0.439708\pi\)
\(8\) 0 0
\(9\) 0.415415 + 0.909632i 0.138472 + 0.303211i
\(10\) 0 0
\(11\) −5.48535 2.19600i −1.65390 0.662120i −0.658033 0.752989i \(-0.728611\pi\)
−0.995863 + 0.0908687i \(0.971036\pi\)
\(12\) 0 0
\(13\) −2.97924 2.84070i −0.826293 0.787869i 0.153444 0.988157i \(-0.450964\pi\)
−0.979737 + 0.200288i \(0.935812\pi\)
\(14\) 0 0
\(15\) −1.03661 + 2.26985i −0.267650 + 0.586073i
\(16\) 0 0
\(17\) −2.20441 + 6.36922i −0.534648 + 1.54476i 0.277151 + 0.960826i \(0.410610\pi\)
−0.811799 + 0.583937i \(0.801512\pi\)
\(18\) 0 0
\(19\) 3.49676 0.333900i 0.802212 0.0766020i 0.314108 0.949387i \(-0.398295\pi\)
0.488104 + 0.872785i \(0.337689\pi\)
\(20\) 0 0
\(21\) −1.16790 0.918450i −0.254857 0.200422i
\(22\) 0 0
\(23\) 0.152650 3.20453i 0.0318298 0.668190i −0.925423 0.378937i \(-0.876290\pi\)
0.957252 0.289254i \(-0.0934071\pi\)
\(24\) 0 0
\(25\) −1.17707 + 0.345620i −0.235415 + 0.0691240i
\(26\) 0 0
\(27\) 0.142315 0.989821i 0.0273885 0.190491i
\(28\) 0 0
\(29\) −3.60506 + 6.24415i −0.669443 + 1.15951i 0.308616 + 0.951187i \(0.400134\pi\)
−0.978060 + 0.208324i \(0.933199\pi\)
\(30\) 0 0
\(31\) 1.09094 1.04021i 0.195939 0.186827i −0.585758 0.810486i \(-0.699203\pi\)
0.781697 + 0.623659i \(0.214355\pi\)
\(32\) 0 0
\(33\) 3.42732 + 4.81300i 0.596620 + 0.837836i
\(34\) 0 0
\(35\) −0.176412 3.70335i −0.0298191 0.625980i
\(36\) 0 0
\(37\) 3.11904 + 5.40233i 0.512767 + 0.888138i 0.999890 + 0.0148049i \(0.00471271\pi\)
−0.487124 + 0.873333i \(0.661954\pi\)
\(38\) 0 0
\(39\) 0.970499 + 4.00045i 0.155404 + 0.640585i
\(40\) 0 0
\(41\) −4.79453 + 0.924070i −0.748780 + 0.144315i −0.549345 0.835596i \(-0.685123\pi\)
−0.199435 + 0.979911i \(0.563911\pi\)
\(42\) 0 0
\(43\) −8.41053 9.70626i −1.28259 1.48019i −0.794319 0.607501i \(-0.792172\pi\)
−0.488274 0.872690i \(-0.662373\pi\)
\(44\) 0 0
\(45\) 2.09922 1.34909i 0.312933 0.201110i
\(46\) 0 0
\(47\) −9.68103 + 4.99092i −1.41212 + 0.728000i −0.984406 0.175913i \(-0.943712\pi\)
−0.427717 + 0.903913i \(0.640682\pi\)
\(48\) 0 0
\(49\) −4.70585 0.906977i −0.672264 0.129568i
\(50\) 0 0
\(51\) 5.29793 4.16634i 0.741858 0.583404i
\(52\) 0 0
\(53\) 5.19018 5.98979i 0.712927 0.822761i −0.277511 0.960722i \(-0.589510\pi\)
0.990438 + 0.137961i \(0.0440550\pi\)
\(54\) 0 0
\(55\) −3.47603 + 14.3284i −0.468708 + 1.93204i
\(56\) 0 0
\(57\) −3.12218 1.60960i −0.413543 0.213196i
\(58\) 0 0
\(59\) −11.5248 3.38399i −1.50040 0.440557i −0.574557 0.818464i \(-0.694826\pi\)
−0.925844 + 0.377907i \(0.876644\pi\)
\(60\) 0 0
\(61\) 0.979919 0.392300i 0.125466 0.0502289i −0.308080 0.951360i \(-0.599686\pi\)
0.433546 + 0.901132i \(0.357262\pi\)
\(62\) 0 0
\(63\) 0.485952 + 1.40407i 0.0612242 + 0.176896i
\(64\) 0 0
\(65\) −5.95839 + 8.36739i −0.739047 + 1.03785i
\(66\) 0 0
\(67\) −6.24891 + 5.28688i −0.763426 + 0.645895i
\(68\) 0 0
\(69\) −1.86092 + 2.61329i −0.224028 + 0.314603i
\(70\) 0 0
\(71\) 0.204053 + 0.589573i 0.0242167 + 0.0699695i 0.956461 0.291859i \(-0.0942738\pi\)
−0.932245 + 0.361828i \(0.882153\pi\)
\(72\) 0 0
\(73\) −6.65132 + 2.66279i −0.778478 + 0.311656i −0.726657 0.687001i \(-0.758927\pi\)
−0.0518216 + 0.998656i \(0.516503\pi\)
\(74\) 0 0
\(75\) 1.17707 + 0.345620i 0.135917 + 0.0399088i
\(76\) 0 0
\(77\) −7.80299 4.02272i −0.889233 0.458432i
\(78\) 0 0
\(79\) −0.340589 + 1.40392i −0.0383192 + 0.157954i −0.987757 0.156002i \(-0.950139\pi\)
0.949438 + 0.313956i \(0.101654\pi\)
\(80\) 0 0
\(81\) −0.654861 + 0.755750i −0.0727623 + 0.0839722i
\(82\) 0 0
\(83\) 12.0626 9.48612i 1.32404 1.04124i 0.328739 0.944421i \(-0.393376\pi\)
0.995302 0.0968166i \(-0.0308660\pi\)
\(84\) 0 0
\(85\) 16.5145 + 3.18291i 1.79125 + 0.345235i
\(86\) 0 0
\(87\) 6.40862 3.30387i 0.687076 0.354212i
\(88\) 0 0
\(89\) 14.0357 9.02019i 1.48778 0.956138i 0.491417 0.870924i \(-0.336479\pi\)
0.996363 0.0852136i \(-0.0271573\pi\)
\(90\) 0 0
\(91\) −4.00526 4.62232i −0.419866 0.484551i
\(92\) 0 0
\(93\) −1.48014 + 0.285273i −0.153483 + 0.0295815i
\(94\) 0 0
\(95\) −2.06651 8.51825i −0.212019 0.873954i
\(96\) 0 0
\(97\) 2.46726 + 4.27341i 0.250512 + 0.433899i 0.963667 0.267107i \(-0.0860677\pi\)
−0.713155 + 0.701006i \(0.752734\pi\)
\(98\) 0 0
\(99\) −0.281142 5.90191i −0.0282559 0.593164i
\(100\) 0 0
\(101\) −5.56064 7.80883i −0.553304 0.777007i 0.439308 0.898336i \(-0.355224\pi\)
−0.992612 + 0.121329i \(0.961284\pi\)
\(102\) 0 0
\(103\) 11.0138 10.5017i 1.08523 1.03476i 0.0859664 0.996298i \(-0.472602\pi\)
0.999260 0.0384633i \(-0.0122463\pi\)
\(104\) 0 0
\(105\) −1.85377 + 3.21083i −0.180910 + 0.313345i
\(106\) 0 0
\(107\) 0.307691 2.14004i 0.0297456 0.206885i −0.969529 0.244978i \(-0.921219\pi\)
0.999274 + 0.0380928i \(0.0121283\pi\)
\(108\) 0 0
\(109\) 13.8306 4.06102i 1.32473 0.388975i 0.458532 0.888678i \(-0.348376\pi\)
0.866197 + 0.499703i \(0.166557\pi\)
\(110\) 0 0
\(111\) 0.296820 6.23101i 0.0281729 0.591421i
\(112\) 0 0
\(113\) −0.263627 0.207318i −0.0247999 0.0195029i 0.605682 0.795707i \(-0.292900\pi\)
−0.630482 + 0.776204i \(0.717143\pi\)
\(114\) 0 0
\(115\) −7.96923 + 0.760970i −0.743135 + 0.0709608i
\(116\) 0 0
\(117\) 1.34637 3.89009i 0.124472 0.359639i
\(118\) 0 0
\(119\) −4.15998 + 9.10909i −0.381345 + 0.835029i
\(120\) 0 0
\(121\) 17.3056 + 16.5008i 1.57324 + 1.50008i
\(122\) 0 0
\(123\) 4.53300 + 1.81474i 0.408727 + 0.163630i
\(124\) 0 0
\(125\) −3.91135 8.56467i −0.349842 0.766047i
\(126\) 0 0
\(127\) −8.37607 0.799818i −0.743256 0.0709724i −0.283444 0.958989i \(-0.591477\pi\)
−0.459812 + 0.888016i \(0.652083\pi\)
\(128\) 0 0
\(129\) 1.82778 + 12.7125i 0.160927 + 1.11927i
\(130\) 0 0
\(131\) 1.98265 + 1.27417i 0.173225 + 0.111325i 0.624380 0.781120i \(-0.285352\pi\)
−0.451155 + 0.892446i \(0.648988\pi\)
\(132\) 0 0
\(133\) 5.21906 0.452550
\(134\) 0 0
\(135\) −2.49535 −0.214765
\(136\) 0 0
\(137\) 2.51013 + 1.61316i 0.214455 + 0.137822i 0.643458 0.765481i \(-0.277499\pi\)
−0.429004 + 0.903303i \(0.641135\pi\)
\(138\) 0 0
\(139\) −1.32971 9.24835i −0.112785 0.784434i −0.965189 0.261552i \(-0.915766\pi\)
0.852405 0.522883i \(-0.175143\pi\)
\(140\) 0 0
\(141\) 10.8425 + 1.03533i 0.913102 + 0.0871907i
\(142\) 0 0
\(143\) 10.1040 + 22.1247i 0.844939 + 1.85016i
\(144\) 0 0
\(145\) 16.7030 + 6.68687i 1.38711 + 0.555314i
\(146\) 0 0
\(147\) 3.46846 + 3.30717i 0.286074 + 0.272771i
\(148\) 0 0
\(149\) −6.36841 + 13.9449i −0.521720 + 1.14241i 0.447064 + 0.894502i \(0.352470\pi\)
−0.968784 + 0.247906i \(0.920258\pi\)
\(150\) 0 0
\(151\) 4.53268 13.0963i 0.368865 1.06576i −0.595993 0.802990i \(-0.703241\pi\)
0.964857 0.262774i \(-0.0846375\pi\)
\(152\) 0 0
\(153\) −6.70939 + 0.640669i −0.542422 + 0.0517950i
\(154\) 0 0
\(155\) −2.95669 2.32517i −0.237487 0.186762i
\(156\) 0 0
\(157\) −0.889333 + 18.6694i −0.0709765 + 1.48998i 0.629888 + 0.776686i \(0.283101\pi\)
−0.700864 + 0.713294i \(0.747202\pi\)
\(158\) 0 0
\(159\) −7.60459 + 2.23291i −0.603083 + 0.177081i
\(160\) 0 0
\(161\) 0.678362 4.71811i 0.0534624 0.371839i
\(162\) 0 0
\(163\) −7.00651 + 12.1356i −0.548793 + 0.950537i 0.449565 + 0.893248i \(0.351579\pi\)
−0.998358 + 0.0572890i \(0.981754\pi\)
\(164\) 0 0
\(165\) 10.6707 10.1745i 0.830716 0.792086i
\(166\) 0 0
\(167\) −11.5995 16.2892i −0.897593 1.26049i −0.964862 0.262759i \(-0.915368\pi\)
0.0672681 0.997735i \(-0.478572\pi\)
\(168\) 0 0
\(169\) 0.187734 + 3.94101i 0.0144410 + 0.303155i
\(170\) 0 0
\(171\) 1.75633 + 3.04206i 0.134310 + 0.232632i
\(172\) 0 0
\(173\) −3.46917 14.3001i −0.263756 1.08722i −0.937426 0.348185i \(-0.886798\pi\)
0.673670 0.739032i \(-0.264717\pi\)
\(174\) 0 0
\(175\) −1.78977 + 0.344950i −0.135294 + 0.0260758i
\(176\) 0 0
\(177\) 7.86575 + 9.07756i 0.591226 + 0.682312i
\(178\) 0 0
\(179\) 1.75728 1.12934i 0.131345 0.0844105i −0.473318 0.880891i \(-0.656944\pi\)
0.604664 + 0.796481i \(0.293308\pi\)
\(180\) 0 0
\(181\) −0.862051 + 0.444418i −0.0640757 + 0.0330333i −0.489967 0.871741i \(-0.662991\pi\)
0.425891 + 0.904775i \(0.359961\pi\)
\(182\) 0 0
\(183\) −1.03645 0.199760i −0.0766169 0.0147667i
\(184\) 0 0
\(185\) 12.2358 9.62237i 0.899597 0.707451i
\(186\) 0 0
\(187\) 26.0788 30.0965i 1.90707 2.20088i
\(188\) 0 0
\(189\) 0.350286 1.44390i 0.0254796 0.105028i
\(190\) 0 0
\(191\) −0.385144 0.198556i −0.0278680 0.0143670i 0.444236 0.895910i \(-0.353475\pi\)
−0.472104 + 0.881543i \(0.656505\pi\)
\(192\) 0 0
\(193\) −12.1857 3.57804i −0.877146 0.257553i −0.187994 0.982170i \(-0.560199\pi\)
−0.689152 + 0.724617i \(0.742017\pi\)
\(194\) 0 0
\(195\) 9.53627 3.81775i 0.682906 0.273394i
\(196\) 0 0
\(197\) 2.24805 + 6.49531i 0.160167 + 0.462772i 0.996319 0.0857261i \(-0.0273210\pi\)
−0.836152 + 0.548498i \(0.815200\pi\)
\(198\) 0 0
\(199\) 15.4553 21.7039i 1.09560 1.53855i 0.279939 0.960018i \(-0.409686\pi\)
0.815659 0.578534i \(-0.196375\pi\)
\(200\) 0 0
\(201\) 8.11522 1.06919i 0.572404 0.0754149i
\(202\) 0 0
\(203\) −6.21396 + 8.72629i −0.436135 + 0.612466i
\(204\) 0 0
\(205\) 3.98506 + 11.5141i 0.278329 + 0.804179i
\(206\) 0 0
\(207\) 2.97835 1.19235i 0.207010 0.0828743i
\(208\) 0 0
\(209\) −19.9142 5.84734i −1.37750 0.404469i
\(210\) 0 0
\(211\) −3.60383 1.85791i −0.248098 0.127904i 0.329693 0.944088i \(-0.393055\pi\)
−0.577791 + 0.816185i \(0.696085\pi\)
\(212\) 0 0
\(213\) 0.147087 0.606300i 0.0100782 0.0415430i
\(214\) 0 0
\(215\) −20.9872 + 24.2205i −1.43131 + 1.65183i
\(216\) 0 0
\(217\) 1.76047 1.38445i 0.119509 0.0939827i
\(218\) 0 0
\(219\) 7.03506 + 1.35590i 0.475385 + 0.0916230i
\(220\) 0 0
\(221\) 24.6605 12.7134i 1.65885 0.855195i
\(222\) 0 0
\(223\) −15.4018 + 9.89816i −1.03138 + 0.662830i −0.942841 0.333242i \(-0.891857\pi\)
−0.0885426 + 0.996072i \(0.528221\pi\)
\(224\) 0 0
\(225\) −0.803361 0.927128i −0.0535574 0.0618086i
\(226\) 0 0
\(227\) 21.4002 4.12455i 1.42038 0.273756i 0.579498 0.814974i \(-0.303249\pi\)
0.840883 + 0.541218i \(0.182036\pi\)
\(228\) 0 0
\(229\) −0.204044 0.841082i −0.0134836 0.0555802i 0.964672 0.263453i \(-0.0848613\pi\)
−0.978156 + 0.207872i \(0.933346\pi\)
\(230\) 0 0
\(231\) 4.38944 + 7.60274i 0.288804 + 0.500224i
\(232\) 0 0
\(233\) −0.695598 14.6024i −0.0455702 0.956635i −0.899682 0.436546i \(-0.856202\pi\)
0.854112 0.520089i \(-0.174101\pi\)
\(234\) 0 0
\(235\) 15.7653 + 22.1393i 1.02841 + 1.44421i
\(236\) 0 0
\(237\) 1.04554 0.996921i 0.0679151 0.0647570i
\(238\) 0 0
\(239\) 3.23505 5.60327i 0.209258 0.362445i −0.742223 0.670153i \(-0.766229\pi\)
0.951481 + 0.307708i \(0.0995619\pi\)
\(240\) 0 0
\(241\) 2.93940 20.4440i 0.189343 1.31691i −0.644369 0.764714i \(-0.722880\pi\)
0.833713 0.552198i \(-0.186211\pi\)
\(242\) 0 0
\(243\) 0.959493 0.281733i 0.0615515 0.0180732i
\(244\) 0 0
\(245\) −0.569024 + 11.9453i −0.0363536 + 0.763157i
\(246\) 0 0
\(247\) −11.3662 8.93849i −0.723215 0.568743i
\(248\) 0 0
\(249\) −15.2763 + 1.45871i −0.968095 + 0.0924419i
\(250\) 0 0
\(251\) 2.76248 7.98165i 0.174366 0.503797i −0.823626 0.567133i \(-0.808053\pi\)
0.997992 + 0.0633354i \(0.0201738\pi\)
\(252\) 0 0
\(253\) −7.87450 + 17.2427i −0.495065 + 1.08404i
\(254\) 0 0
\(255\) −12.1721 11.6060i −0.762245 0.726799i
\(256\) 0 0
\(257\) 24.1495 + 9.66800i 1.50640 + 0.603073i 0.970478 0.241191i \(-0.0775380\pi\)
0.535927 + 0.844264i \(0.319962\pi\)
\(258\) 0 0
\(259\) 3.85024 + 8.43085i 0.239242 + 0.523868i
\(260\) 0 0
\(261\) −7.17748 0.685366i −0.444275 0.0424231i
\(262\) 0 0
\(263\) 0.0507775 + 0.353166i 0.00313108 + 0.0217771i 0.991327 0.131418i \(-0.0419529\pi\)
−0.988196 + 0.153195i \(0.951044\pi\)
\(264\) 0 0
\(265\) −16.6377 10.6924i −1.02204 0.656827i
\(266\) 0 0
\(267\) −16.6843 −1.02106
\(268\) 0 0
\(269\) −3.27549 −0.199710 −0.0998551 0.995002i \(-0.531838\pi\)
−0.0998551 + 0.995002i \(0.531838\pi\)
\(270\) 0 0
\(271\) 9.69447 + 6.23026i 0.588897 + 0.378461i 0.800891 0.598810i \(-0.204359\pi\)
−0.211994 + 0.977271i \(0.567996\pi\)
\(272\) 0 0
\(273\) 0.870427 + 6.05395i 0.0526806 + 0.366402i
\(274\) 0 0
\(275\) 7.21565 + 0.689011i 0.435120 + 0.0415489i
\(276\) 0 0
\(277\) 3.43127 + 7.51344i 0.206165 + 0.451439i 0.984264 0.176703i \(-0.0565431\pi\)
−0.778099 + 0.628142i \(0.783816\pi\)
\(278\) 0 0
\(279\) 1.39940 + 0.560236i 0.0837800 + 0.0335405i
\(280\) 0 0
\(281\) −1.46621 1.39803i −0.0874666 0.0833993i 0.645085 0.764111i \(-0.276822\pi\)
−0.732551 + 0.680712i \(0.761671\pi\)
\(282\) 0 0
\(283\) 7.66627 16.7868i 0.455712 0.997871i −0.532732 0.846284i \(-0.678835\pi\)
0.988444 0.151586i \(-0.0484382\pi\)
\(284\) 0 0
\(285\) −2.86686 + 8.28325i −0.169818 + 0.490657i
\(286\) 0 0
\(287\) −7.22188 + 0.689606i −0.426294 + 0.0407061i
\(288\) 0 0
\(289\) −22.3447 17.5720i −1.31439 1.03365i
\(290\) 0 0
\(291\) 0.234794 4.92892i 0.0137638 0.288939i
\(292\) 0 0
\(293\) −3.39791 + 0.997717i −0.198508 + 0.0582873i −0.379475 0.925202i \(-0.623895\pi\)
0.180967 + 0.983489i \(0.442077\pi\)
\(294\) 0 0
\(295\) −4.26553 + 29.6674i −0.248349 + 1.72730i
\(296\) 0 0
\(297\) −2.95430 + 5.11700i −0.171426 + 0.296918i
\(298\) 0 0
\(299\) −9.55789 + 9.11343i −0.552747 + 0.527043i
\(300\) 0 0
\(301\) −11.0688 15.5439i −0.637994 0.895937i
\(302\) 0 0
\(303\) 0.456138 + 9.57551i 0.0262044 + 0.550099i
\(304\) 0 0
\(305\) −1.31696 2.28103i −0.0754087 0.130612i
\(306\) 0 0
\(307\) −3.22405 13.2897i −0.184006 0.758484i −0.986762 0.162176i \(-0.948149\pi\)
0.802756 0.596308i \(-0.203366\pi\)
\(308\) 0 0
\(309\) −14.9431 + 2.88004i −0.850082 + 0.163840i
\(310\) 0 0
\(311\) 17.3083 + 19.9749i 0.981465 + 1.13267i 0.991154 + 0.132718i \(0.0423706\pi\)
−0.00968834 + 0.999953i \(0.503084\pi\)
\(312\) 0 0
\(313\) 7.91102 5.08410i 0.447157 0.287371i −0.297619 0.954685i \(-0.596193\pi\)
0.744776 + 0.667314i \(0.232556\pi\)
\(314\) 0 0
\(315\) 3.29540 1.69890i 0.185675 0.0957219i
\(316\) 0 0
\(317\) −25.7843 4.96952i −1.44819 0.279116i −0.596269 0.802785i \(-0.703351\pi\)
−0.851922 + 0.523669i \(0.824563\pi\)
\(318\) 0 0
\(319\) 33.4872 26.3346i 1.87492 1.47446i
\(320\) 0 0
\(321\) −1.41584 + 1.63397i −0.0790244 + 0.0911991i
\(322\) 0 0
\(323\) −5.58161 + 23.0077i −0.310569 + 1.28018i
\(324\) 0 0
\(325\) 4.48859 + 2.31403i 0.248982 + 0.128359i
\(326\) 0 0
\(327\) −13.8306 4.06102i −0.764832 0.224575i
\(328\) 0 0
\(329\) −15.0236 + 6.01456i −0.828280 + 0.331593i
\(330\) 0 0
\(331\) −5.76571 16.6589i −0.316912 0.915658i −0.985148 0.171708i \(-0.945071\pi\)
0.668236 0.743950i \(-0.267050\pi\)
\(332\) 0 0
\(333\) −3.61844 + 5.08139i −0.198289 + 0.278458i
\(334\) 0 0
\(335\) 15.2775 + 13.5570i 0.834698 + 0.740698i
\(336\) 0 0
\(337\) 0.749932 1.05313i 0.0408514 0.0573678i −0.793645 0.608381i \(-0.791819\pi\)
0.834496 + 0.551013i \(0.185759\pi\)
\(338\) 0 0
\(339\) 0.109692 + 0.316935i 0.00595766 + 0.0172135i
\(340\) 0 0
\(341\) −8.26850 + 3.31021i −0.447765 + 0.179258i
\(342\) 0 0
\(343\) −16.8113 4.93624i −0.907724 0.266532i
\(344\) 0 0
\(345\) 7.11556 + 3.66832i 0.383089 + 0.197496i
\(346\) 0 0
\(347\) −0.957910 + 3.94856i −0.0514233 + 0.211970i −0.991727 0.128368i \(-0.959026\pi\)
0.940303 + 0.340338i \(0.110541\pi\)
\(348\) 0 0
\(349\) 1.84876 2.13359i 0.0989621 0.114208i −0.704108 0.710093i \(-0.748653\pi\)
0.803070 + 0.595885i \(0.203198\pi\)
\(350\) 0 0
\(351\) −3.23578 + 2.54464i −0.172713 + 0.135823i
\(352\) 0 0
\(353\) 2.02391 + 0.390077i 0.107722 + 0.0207617i 0.242827 0.970070i \(-0.421925\pi\)
−0.135105 + 0.990831i \(0.543137\pi\)
\(354\) 0 0
\(355\) 1.38375 0.713374i 0.0734419 0.0378620i
\(356\) 0 0
\(357\) 8.42435 5.41400i 0.445864 0.286539i
\(358\) 0 0
\(359\) −3.53098 4.07497i −0.186358 0.215068i 0.654881 0.755732i \(-0.272719\pi\)
−0.841239 + 0.540663i \(0.818173\pi\)
\(360\) 0 0
\(361\) −6.54078 + 1.26063i −0.344252 + 0.0663491i
\(362\) 0 0
\(363\) −5.63736 23.2375i −0.295885 1.21965i
\(364\) 0 0
\(365\) 8.93900 + 15.4828i 0.467889 + 0.810407i
\(366\) 0 0
\(367\) 0.727177 + 15.2653i 0.0379583 + 0.796843i 0.934947 + 0.354789i \(0.115447\pi\)
−0.896988 + 0.442054i \(0.854250\pi\)
\(368\) 0 0
\(369\) −2.83228 3.97738i −0.147443 0.207054i
\(370\) 0 0
\(371\) 8.52252 8.12621i 0.442467 0.421892i
\(372\) 0 0
\(373\) −16.4002 + 28.4059i −0.849169 + 1.47080i 0.0327821 + 0.999463i \(0.489563\pi\)
−0.881951 + 0.471341i \(0.843770\pi\)
\(374\) 0 0
\(375\) −1.33997 + 9.31970i −0.0691958 + 0.481267i
\(376\) 0 0
\(377\) 28.4781 8.36194i 1.46670 0.430662i
\(378\) 0 0
\(379\) −0.958498 + 20.1213i −0.0492347 + 1.03356i 0.830176 + 0.557501i \(0.188240\pi\)
−0.879411 + 0.476063i \(0.842063\pi\)
\(380\) 0 0
\(381\) 6.61399 + 5.20130i 0.338845 + 0.266471i
\(382\) 0 0
\(383\) −4.20668 + 0.401689i −0.214951 + 0.0205254i −0.201976 0.979390i \(-0.564736\pi\)
−0.0129753 + 0.999916i \(0.504130\pi\)
\(384\) 0 0
\(385\) −7.16488 + 20.7016i −0.365156 + 1.05505i
\(386\) 0 0
\(387\) 5.33527 11.6826i 0.271207 0.593860i
\(388\) 0 0
\(389\) −18.5594 17.6963i −0.940996 0.897238i 0.0538584 0.998549i \(-0.482848\pi\)
−0.994855 + 0.101310i \(0.967697\pi\)
\(390\) 0 0
\(391\) 20.0738 + 8.03636i 1.01518 + 0.406416i
\(392\) 0 0
\(393\) −0.979043 2.14381i −0.0493862 0.108141i
\(394\) 0 0
\(395\) 3.58858 + 0.342667i 0.180561 + 0.0172415i
\(396\) 0 0
\(397\) 4.00435 + 27.8509i 0.200973 + 1.39780i 0.801406 + 0.598121i \(0.204086\pi\)
−0.600433 + 0.799675i \(0.705005\pi\)
\(398\) 0 0
\(399\) −4.39055 2.82164i −0.219803 0.141259i
\(400\) 0 0
\(401\) 14.5750 0.727843 0.363922 0.931430i \(-0.381438\pi\)
0.363922 + 0.931430i \(0.381438\pi\)
\(402\) 0 0
\(403\) −6.20511 −0.309098
\(404\) 0 0
\(405\) 2.09922 + 1.34909i 0.104311 + 0.0670367i
\(406\) 0 0
\(407\) −5.24548 36.4831i −0.260009 1.80840i
\(408\) 0 0
\(409\) −15.6492 1.49432i −0.773802 0.0738891i −0.299318 0.954153i \(-0.596759\pi\)
−0.474484 + 0.880264i \(0.657365\pi\)
\(410\) 0 0
\(411\) −1.23951 2.71416i −0.0611407 0.133879i
\(412\) 0 0
\(413\) −16.5679 6.63278i −0.815252 0.326378i
\(414\) 0 0
\(415\) −27.7140 26.4252i −1.36043 1.29716i
\(416\) 0 0
\(417\) −3.88141 + 8.49910i −0.190073 + 0.416203i
\(418\) 0 0
\(419\) −0.327445 + 0.946089i −0.0159967 + 0.0462195i −0.952717 0.303860i \(-0.901724\pi\)
0.936720 + 0.350080i \(0.113846\pi\)
\(420\) 0 0
\(421\) −17.7600 + 1.69588i −0.865570 + 0.0826520i −0.518388 0.855146i \(-0.673468\pi\)
−0.347183 + 0.937798i \(0.612862\pi\)
\(422\) 0 0
\(423\) −8.56154 6.73287i −0.416276 0.327363i
\(424\) 0 0
\(425\) 0.393421 8.25893i 0.0190837 0.400617i
\(426\) 0 0
\(427\) 1.50476 0.441837i 0.0728204 0.0213820i
\(428\) 0 0
\(429\) 3.46148 24.0751i 0.167122 1.16236i
\(430\) 0 0
\(431\) −6.12638 + 10.6112i −0.295097 + 0.511123i −0.975007 0.222172i \(-0.928685\pi\)
0.679910 + 0.733295i \(0.262019\pi\)
\(432\) 0 0
\(433\) −22.9641 + 21.8962i −1.10359 + 1.05227i −0.105258 + 0.994445i \(0.533567\pi\)
−0.998327 + 0.0578216i \(0.981585\pi\)
\(434\) 0 0
\(435\) −10.4363 14.6557i −0.500380 0.702686i
\(436\) 0 0
\(437\) −0.536211 11.2564i −0.0256504 0.538469i
\(438\) 0 0
\(439\) 10.8042 + 18.7135i 0.515657 + 0.893145i 0.999835 + 0.0181751i \(0.00578562\pi\)
−0.484177 + 0.874970i \(0.660881\pi\)
\(440\) 0 0
\(441\) −1.12986 4.65736i −0.0538030 0.221779i
\(442\) 0 0
\(443\) −19.9873 + 3.85223i −0.949625 + 0.183025i −0.640467 0.767986i \(-0.721259\pi\)
−0.309158 + 0.951011i \(0.600047\pi\)
\(444\) 0 0
\(445\) −27.2638 31.4641i −1.29243 1.49154i
\(446\) 0 0
\(447\) 12.8966 8.28815i 0.609989 0.392016i
\(448\) 0 0
\(449\) 31.3987 16.1872i 1.48180 0.763919i 0.487761 0.872977i \(-0.337814\pi\)
0.994035 + 0.109058i \(0.0347834\pi\)
\(450\) 0 0
\(451\) 28.3289 + 5.45996i 1.33396 + 0.257099i
\(452\) 0 0
\(453\) −10.8935 + 8.56678i −0.511824 + 0.402502i
\(454\) 0 0
\(455\) −9.99453 + 11.5343i −0.468551 + 0.540736i
\(456\) 0 0
\(457\) 4.61069 19.0055i 0.215679 0.889041i −0.756348 0.654170i \(-0.773018\pi\)
0.972027 0.234871i \(-0.0754667\pi\)
\(458\) 0 0
\(459\) 5.99067 + 3.08841i 0.279621 + 0.144154i
\(460\) 0 0
\(461\) 11.0086 + 3.23243i 0.512723 + 0.150549i 0.527852 0.849336i \(-0.322998\pi\)
−0.0151287 + 0.999886i \(0.504816\pi\)
\(462\) 0 0
\(463\) −39.0083 + 15.6166i −1.81287 + 0.725764i −0.826126 + 0.563485i \(0.809460\pi\)
−0.986745 + 0.162279i \(0.948116\pi\)
\(464\) 0 0
\(465\) 1.23024 + 3.55456i 0.0570512 + 0.164839i
\(466\) 0 0
\(467\) −3.73990 + 5.25196i −0.173062 + 0.243032i −0.891992 0.452051i \(-0.850693\pi\)
0.718930 + 0.695082i \(0.244632\pi\)
\(468\) 0 0
\(469\) −9.98916 + 6.93703i −0.461257 + 0.320322i
\(470\) 0 0
\(471\) 10.8416 15.2249i 0.499554 0.701526i
\(472\) 0 0
\(473\) 24.8197 + 71.7118i 1.14121 + 3.29731i
\(474\) 0 0
\(475\) −4.00055 + 1.60158i −0.183558 + 0.0734854i
\(476\) 0 0
\(477\) 7.60459 + 2.23291i 0.348190 + 0.102238i
\(478\) 0 0
\(479\) 17.2982 + 8.91783i 0.790374 + 0.407466i 0.805631 0.592418i \(-0.201826\pi\)
−0.0152572 + 0.999884i \(0.504857\pi\)
\(480\) 0 0
\(481\) 6.05405 24.9551i 0.276041 1.13786i
\(482\) 0 0
\(483\) −3.12148 + 3.60238i −0.142032 + 0.163914i
\(484\) 0 0
\(485\) 9.67893 7.61160i 0.439498 0.345625i
\(486\) 0 0
\(487\) −37.1105 7.15246i −1.68164 0.324109i −0.743072 0.669211i \(-0.766632\pi\)
−0.938565 + 0.345102i \(0.887844\pi\)
\(488\) 0 0
\(489\) 12.4553 6.42114i 0.563247 0.290374i
\(490\) 0 0
\(491\) 10.8557 6.97656i 0.489913 0.314848i −0.272258 0.962224i \(-0.587770\pi\)
0.762170 + 0.647377i \(0.224134\pi\)
\(492\) 0 0
\(493\) −31.8234 36.7261i −1.43325 1.65406i
\(494\) 0 0
\(495\) −14.4776 + 2.79032i −0.650718 + 0.125416i
\(496\) 0 0
\(497\) 0.218539 + 0.900830i 0.00980281 + 0.0404078i
\(498\) 0 0
\(499\) −13.2811 23.0036i −0.594544 1.02978i −0.993611 0.112859i \(-0.963999\pi\)
0.399067 0.916922i \(-0.369334\pi\)
\(500\) 0 0
\(501\) 0.951501 + 19.9745i 0.0425099 + 0.892393i
\(502\) 0 0
\(503\) 0.260265 + 0.365491i 0.0116046 + 0.0162964i 0.820338 0.571880i \(-0.193786\pi\)
−0.808733 + 0.588176i \(0.799846\pi\)
\(504\) 0 0
\(505\) −17.3127 + 16.5076i −0.770404 + 0.734579i
\(506\) 0 0
\(507\) 1.97274 3.41689i 0.0876125 0.151749i
\(508\) 0 0
\(509\) 0.909677 6.32695i 0.0403207 0.280437i −0.959679 0.281098i \(-0.909301\pi\)
1.00000 0.000661179i \(0.000210460\pi\)
\(510\) 0 0
\(511\) −10.2137 + 2.99902i −0.451829 + 0.132669i
\(512\) 0 0
\(513\) 0.167139 3.50869i 0.00737939 0.154912i
\(514\) 0 0
\(515\) −29.8499 23.4742i −1.31534 1.03440i
\(516\) 0 0
\(517\) 64.0639 6.11736i 2.81753 0.269041i
\(518\) 0 0
\(519\) −4.81277 + 13.9056i −0.211257 + 0.610388i
\(520\) 0 0
\(521\) 14.3913 31.5125i 0.630493 1.38059i −0.277142 0.960829i \(-0.589387\pi\)
0.907636 0.419759i \(-0.137885\pi\)
\(522\) 0 0
\(523\) 13.2435 + 12.6277i 0.579098 + 0.552169i 0.921994 0.387205i \(-0.126559\pi\)
−0.342896 + 0.939373i \(0.611408\pi\)
\(524\) 0 0
\(525\) 1.69214 + 0.677432i 0.0738512 + 0.0295656i
\(526\) 0 0
\(527\) 4.22045 + 9.24149i 0.183846 + 0.402566i
\(528\) 0 0
\(529\) 12.6502 + 1.20794i 0.550007 + 0.0525193i
\(530\) 0 0
\(531\) −1.70939 11.8891i −0.0741813 0.515942i
\(532\) 0 0
\(533\) 16.9091 + 10.8668i 0.732413 + 0.470693i
\(534\) 0 0
\(535\) −5.39506 −0.233249
\(536\) 0 0
\(537\) −2.08888 −0.0901420
\(538\) 0 0
\(539\) 23.8215 + 15.3091i 1.02606 + 0.659412i
\(540\) 0 0
\(541\) −4.30171 29.9191i −0.184945 1.28632i −0.844863 0.534983i \(-0.820318\pi\)
0.659918 0.751338i \(-0.270591\pi\)
\(542\) 0 0
\(543\) 0.965474 + 0.0921915i 0.0414324 + 0.00395632i
\(544\) 0 0
\(545\) −14.9421 32.7187i −0.640050 1.40151i
\(546\) 0 0
\(547\) 1.56434 + 0.626266i 0.0668862 + 0.0267772i 0.404864 0.914377i \(-0.367319\pi\)
−0.337978 + 0.941154i \(0.609743\pi\)
\(548\) 0 0
\(549\) 0.763922 + 0.728398i 0.0326034 + 0.0310873i
\(550\) 0 0
\(551\) −10.5211 + 23.0381i −0.448215 + 0.981454i
\(552\) 0 0
\(553\) −0.702029 + 2.02838i −0.0298533 + 0.0862555i
\(554\) 0 0
\(555\) −15.4957 + 1.47966i −0.657755 + 0.0628080i
\(556\) 0 0
\(557\) 18.6575 + 14.6724i 0.790545 + 0.621692i 0.929590 0.368594i \(-0.120161\pi\)
−0.139045 + 0.990286i \(0.544403\pi\)
\(558\) 0 0
\(559\) −2.51561 + 52.8091i −0.106399 + 2.23359i
\(560\) 0 0
\(561\) −38.2103 + 11.2196i −1.61324 + 0.473690i
\(562\) 0 0
\(563\) −0.235424 + 1.63741i −0.00992194 + 0.0690086i −0.994181 0.107724i \(-0.965644\pi\)
0.984259 + 0.176733i \(0.0565528\pi\)
\(564\) 0 0
\(565\) −0.418445 + 0.724769i −0.0176041 + 0.0304912i
\(566\) 0 0
\(567\) −1.07531 + 1.02531i −0.0451588 + 0.0430589i
\(568\) 0 0
\(569\) 18.1493 + 25.4871i 0.760858 + 1.06847i 0.995347 + 0.0963563i \(0.0307188\pi\)
−0.234489 + 0.972119i \(0.575342\pi\)
\(570\) 0 0
\(571\) −0.225113 4.72571i −0.00942070 0.197765i −0.998671 0.0515342i \(-0.983589\pi\)
0.989251 0.146231i \(-0.0467141\pi\)
\(572\) 0 0
\(573\) 0.216657 + 0.375260i 0.00905096 + 0.0156767i
\(574\) 0 0
\(575\) 0.927868 + 3.82473i 0.0386948 + 0.159502i
\(576\) 0 0
\(577\) −18.7120 + 3.60645i −0.778993 + 0.150139i −0.563222 0.826306i \(-0.690438\pi\)
−0.215771 + 0.976444i \(0.569226\pi\)
\(578\) 0 0
\(579\) 8.31682 + 9.59813i 0.345635 + 0.398885i
\(580\) 0 0
\(581\) 19.1810 12.3269i 0.795761 0.511405i
\(582\) 0 0
\(583\) −41.6236 + 21.4585i −1.72387 + 0.888718i
\(584\) 0 0
\(585\) −10.0864 1.94400i −0.417023 0.0803746i
\(586\) 0 0
\(587\) −31.1811 + 24.5211i −1.28698 + 1.01209i −0.288473 + 0.957488i \(0.593148\pi\)
−0.998508 + 0.0546052i \(0.982610\pi\)
\(588\) 0 0
\(589\) 3.46744 4.00163i 0.142873 0.164884i
\(590\) 0 0
\(591\) 1.62045 6.67959i 0.0666565 0.274762i
\(592\) 0 0
\(593\) −40.8279 21.0483i −1.67660 0.864348i −0.990607 0.136742i \(-0.956337\pi\)
−0.685995 0.727606i \(-0.740633\pi\)
\(594\) 0 0
\(595\) 23.9763 + 7.04008i 0.982933 + 0.288615i
\(596\) 0 0
\(597\) −24.7359 + 9.90275i −1.01237 + 0.405292i
\(598\) 0 0
\(599\) 0.854355 + 2.46850i 0.0349080 + 0.100860i 0.961108 0.276172i \(-0.0890659\pi\)
−0.926200 + 0.377032i \(0.876945\pi\)
\(600\) 0 0
\(601\) 17.8996 25.1365i 0.730141 1.02534i −0.267941 0.963435i \(-0.586343\pi\)
0.998082 0.0619039i \(-0.0197172\pi\)
\(602\) 0 0
\(603\) −7.40501 3.48796i −0.301555 0.142041i
\(604\) 0 0
\(605\) 34.6106 48.6038i 1.40712 1.97603i
\(606\) 0 0
\(607\) −12.5606 36.2914i −0.509818 1.47302i −0.847005 0.531585i \(-0.821597\pi\)
0.337187 0.941438i \(-0.390524\pi\)
\(608\) 0 0
\(609\) 9.94531 3.98150i 0.403004 0.161339i
\(610\) 0 0
\(611\) 43.0198 + 12.6318i 1.74040 + 0.511027i
\(612\) 0 0
\(613\) −2.89578 1.49288i −0.116959 0.0602968i 0.398754 0.917058i \(-0.369443\pi\)
−0.515713 + 0.856761i \(0.672473\pi\)
\(614\) 0 0
\(615\) 2.87254 11.8408i 0.115832 0.477465i
\(616\) 0 0
\(617\) −22.8331 + 26.3508i −0.919226 + 1.06084i 0.0787274 + 0.996896i \(0.474914\pi\)
−0.997953 + 0.0639470i \(0.979631\pi\)
\(618\) 0 0
\(619\) 27.5173 21.6399i 1.10601 0.869779i 0.113699 0.993515i \(-0.463730\pi\)
0.992315 + 0.123736i \(0.0394876\pi\)
\(620\) 0 0
\(621\) −3.15019 0.607149i −0.126413 0.0243640i
\(622\) 0 0
\(623\) 22.0335 11.3591i 0.882753 0.455091i
\(624\) 0 0
\(625\) −24.9254 + 16.0186i −0.997016 + 0.640743i
\(626\) 0 0
\(627\) 13.5916 + 15.6855i 0.542796 + 0.626420i
\(628\) 0 0
\(629\) −41.2843 + 7.95689i −1.64611 + 0.317262i
\(630\) 0 0
\(631\) 6.34760 + 26.1652i 0.252694 + 1.04162i 0.946820 + 0.321765i \(0.104276\pi\)
−0.694126 + 0.719854i \(0.744209\pi\)
\(632\) 0 0
\(633\) 2.02728 + 3.51135i 0.0805771 + 0.139564i
\(634\) 0 0
\(635\) 0.999044 + 20.9725i 0.0396459 + 0.832269i
\(636\) 0 0
\(637\) 11.4434 + 16.0700i 0.453404 + 0.636717i
\(638\) 0 0
\(639\) −0.451528 + 0.430531i −0.0178622 + 0.0170315i
\(640\) 0 0
\(641\) −13.8172 + 23.9322i −0.545748 + 0.945264i 0.452811 + 0.891606i \(0.350421\pi\)
−0.998559 + 0.0536573i \(0.982912\pi\)
\(642\) 0 0
\(643\) 0.825602 5.74219i 0.0325586 0.226450i −0.967045 0.254606i \(-0.918054\pi\)
0.999604 + 0.0281558i \(0.00896347\pi\)
\(644\) 0 0
\(645\) 30.7502 9.02906i 1.21079 0.355519i
\(646\) 0 0
\(647\) −1.14692 + 24.0768i −0.0450901 + 0.946557i 0.857082 + 0.515180i \(0.172275\pi\)
−0.902172 + 0.431377i \(0.858028\pi\)
\(648\) 0 0
\(649\) 55.7863 + 43.8709i 2.18980 + 1.72208i
\(650\) 0 0
\(651\) −2.22949 + 0.212891i −0.0873808 + 0.00834385i
\(652\) 0 0
\(653\) 5.17802 14.9609i 0.202631 0.585465i −0.797202 0.603713i \(-0.793687\pi\)
0.999834 + 0.0182474i \(0.00580866\pi\)
\(654\) 0 0
\(655\) 2.44305 5.34954i 0.0954580 0.209024i
\(656\) 0 0
\(657\) −5.18522 4.94409i −0.202295 0.192887i
\(658\) 0 0
\(659\) 30.9378 + 12.3856i 1.20516 + 0.482475i 0.885314 0.464993i \(-0.153943\pi\)
0.319850 + 0.947468i \(0.396367\pi\)
\(660\) 0 0
\(661\) −5.95544 13.0406i −0.231640 0.507220i 0.757743 0.652553i \(-0.226302\pi\)
−0.989383 + 0.145333i \(0.953575\pi\)
\(662\) 0 0
\(663\) −27.6191 2.63731i −1.07264 0.102425i
\(664\) 0 0
\(665\) −1.85342 12.8908i −0.0718725 0.499884i
\(666\) 0 0
\(667\) 19.4592 + 12.5057i 0.753465 + 0.484223i
\(668\) 0 0
\(669\) 18.3082 0.707836
\(670\) 0 0
\(671\) −6.23669 −0.240765
\(672\) 0 0
\(673\) 9.63727 + 6.19350i 0.371490 + 0.238742i 0.713043 0.701121i \(-0.247317\pi\)
−0.341553 + 0.939862i \(0.610953\pi\)
\(674\) 0 0
\(675\) 0.174587 + 1.21428i 0.00671986 + 0.0467377i
\(676\) 0 0
\(677\) 3.27965 + 0.313169i 0.126047 + 0.0120361i 0.157889 0.987457i \(-0.449531\pi\)
−0.0318417 + 0.999493i \(0.510137\pi\)
\(678\) 0 0
\(679\) 3.04566 + 6.66907i 0.116882 + 0.255935i
\(680\) 0 0
\(681\) −20.2329 8.10003i −0.775326 0.310394i
\(682\) 0 0
\(683\) 21.4827 + 20.4837i 0.822013 + 0.783788i 0.979010 0.203811i \(-0.0653328\pi\)
−0.156997 + 0.987599i \(0.550181\pi\)
\(684\) 0 0
\(685\) 3.09302 6.77277i 0.118178 0.258774i
\(686\) 0 0
\(687\) −0.283070 + 0.817878i −0.0107998 + 0.0312040i
\(688\) 0 0
\(689\) −32.4780 + 3.10128i −1.23731 + 0.118149i
\(690\) 0 0
\(691\) −1.72884 1.35957i −0.0657681 0.0517206i 0.584734 0.811225i \(-0.301199\pi\)
−0.650502 + 0.759505i \(0.725441\pi\)
\(692\) 0 0
\(693\) 0.417716 8.76895i 0.0158677 0.333105i
\(694\) 0 0
\(695\) −22.3707 + 6.56864i −0.848570 + 0.249163i
\(696\) 0 0
\(697\) 4.68350 32.5744i 0.177400 1.23384i
\(698\) 0 0
\(699\) −7.30948 + 12.6604i −0.276470 + 0.478860i
\(700\) 0 0
\(701\) 1.28010 1.22057i 0.0483488 0.0461005i −0.665520 0.746380i \(-0.731790\pi\)
0.713868 + 0.700280i \(0.246941\pi\)
\(702\) 0 0
\(703\) 12.7104 + 17.8492i 0.479381 + 0.673196i
\(704\) 0 0
\(705\) −1.29322 27.1481i −0.0487056 1.02246i
\(706\) 0 0
\(707\) −7.12163 12.3350i −0.267836 0.463906i
\(708\) 0 0
\(709\) 5.73098 + 23.6234i 0.215232 + 0.887196i 0.972277 + 0.233834i \(0.0751272\pi\)
−0.757045 + 0.653363i \(0.773358\pi\)
\(710\) 0 0
\(711\) −1.41854 + 0.273401i −0.0531994 + 0.0102533i
\(712\) 0 0
\(713\) −3.16685 3.65474i −0.118599 0.136871i
\(714\) 0 0
\(715\) 51.0587 32.8134i 1.90949 1.22715i
\(716\) 0 0
\(717\) −5.75085 + 2.96477i −0.214769 + 0.110721i
\(718\) 0 0
\(719\) 28.7183 + 5.53499i 1.07101 + 0.206420i 0.694136 0.719844i \(-0.255787\pi\)
0.376875 + 0.926264i \(0.376999\pi\)
\(720\) 0 0
\(721\) 17.7733 13.9770i 0.661911 0.520532i
\(722\) 0 0
\(723\) −13.5256 + 15.6094i −0.503024 + 0.580520i
\(724\) 0 0
\(725\) 2.08532 8.59581i 0.0774469 0.319240i
\(726\) 0 0
\(727\) −30.1238 15.5299i −1.11723 0.575972i −0.202194 0.979345i \(-0.564807\pi\)
−0.915036 + 0.403373i \(0.867838\pi\)
\(728\) 0 0
\(729\) −0.959493 0.281733i −0.0355368 0.0104345i
\(730\) 0 0
\(731\) 80.3616 32.1719i 2.97228 1.18992i
\(732\) 0 0
\(733\) −13.6465 39.4289i −0.504044 1.45634i −0.854348 0.519702i \(-0.826043\pi\)
0.350304 0.936636i \(-0.386078\pi\)
\(734\) 0 0
\(735\) 6.93681 9.74138i 0.255868 0.359316i
\(736\) 0 0
\(737\) 45.8875 15.2778i 1.69029 0.562764i
\(738\) 0 0
\(739\) 13.7855 19.3590i 0.507106 0.712131i −0.479080 0.877771i \(-0.659030\pi\)
0.986186 + 0.165640i \(0.0529691\pi\)
\(740\) 0 0
\(741\) 4.72936 + 13.6646i 0.173737 + 0.501981i
\(742\) 0 0
\(743\) −12.7618 + 5.10907i −0.468187 + 0.187434i −0.593746 0.804652i \(-0.702352\pi\)
0.125560 + 0.992086i \(0.459927\pi\)
\(744\) 0 0
\(745\) 36.7047 + 10.7775i 1.34476 + 0.394856i
\(746\) 0 0
\(747\) 13.6399 + 7.03184i 0.499056 + 0.257281i
\(748\) 0 0
\(749\) 0.757335 3.12178i 0.0276724 0.114067i
\(750\) 0 0
\(751\) 16.0055 18.4713i 0.584048 0.674027i −0.384422 0.923157i \(-0.625599\pi\)
0.968470 + 0.249130i \(0.0801447\pi\)
\(752\) 0 0
\(753\) −6.63915 + 5.22109i −0.241944 + 0.190267i
\(754\) 0 0
\(755\) −33.9570 6.54467i −1.23582 0.238185i
\(756\) 0 0
\(757\) −28.1436 + 14.5090i −1.02290 + 0.527339i −0.886214 0.463276i \(-0.846674\pi\)
−0.136681 + 0.990615i \(0.543644\pi\)
\(758\) 0 0
\(759\) 15.9466 10.2482i 0.578824 0.371988i
\(760\) 0 0
\(761\) −4.12239 4.75749i −0.149437 0.172459i 0.676096 0.736814i \(-0.263670\pi\)
−0.825532 + 0.564355i \(0.809125\pi\)
\(762\) 0 0
\(763\) 21.0297 4.05315i 0.761327 0.146734i
\(764\) 0 0
\(765\) 3.96510 + 16.3443i 0.143358 + 0.590931i
\(766\) 0 0
\(767\) 24.7223 + 42.8202i 0.892670 + 1.54615i
\(768\) 0 0
\(769\) −0.368907 7.74431i −0.0133031 0.279267i −0.995711 0.0925187i \(-0.970508\pi\)
0.982408 0.186748i \(-0.0597948\pi\)
\(770\) 0 0
\(771\) −15.0889 21.1895i −0.543415 0.763119i
\(772\) 0 0
\(773\) −1.34077 + 1.27842i −0.0482240 + 0.0459815i −0.713808 0.700342i \(-0.753031\pi\)
0.665584 + 0.746323i \(0.268183\pi\)
\(774\) 0 0
\(775\) −0.924601 + 1.60146i −0.0332126 + 0.0575260i
\(776\) 0 0
\(777\) 1.31903 9.17408i 0.0473201 0.329118i
\(778\) 0