Properties

Label 324.3.o.a.65.9
Level $324$
Weight $3$
Character 324.65
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 65.9
Character \(\chi\) \(=\) 324.65
Dual form 324.3.o.a.5.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.463613 + 2.96396i) q^{3} +(-2.73041 - 2.03271i) q^{5} +(-1.12154 - 0.737649i) q^{7} +(-8.57013 - 2.74826i) q^{9} +O(q^{10})\) \(q+(-0.463613 + 2.96396i) q^{3} +(-2.73041 - 2.03271i) q^{5} +(-1.12154 - 0.737649i) q^{7} +(-8.57013 - 2.74826i) q^{9} +(-0.325590 - 2.78560i) q^{11} +(6.15219 - 20.5497i) q^{13} +(7.29073 - 7.15043i) q^{15} +(5.48948 - 0.967944i) q^{17} +(0.824658 - 4.67687i) q^{19} +(2.70633 - 2.98222i) q^{21} +(10.9269 + 16.6136i) q^{23} +(-3.84688 - 12.8495i) q^{25} +(12.1190 - 24.1274i) q^{27} +(-14.1673 - 13.3662i) q^{29} +(-0.486900 - 8.35975i) q^{31} +(8.40736 + 0.326405i) q^{33} +(1.56284 + 4.29386i) q^{35} +(34.4216 + 12.5284i) q^{37} +(58.0564 + 27.7620i) q^{39} +(-6.96530 - 29.3889i) q^{41} +(24.2316 - 56.1752i) q^{43} +(17.8135 + 24.9245i) q^{45} +(16.7341 + 0.974651i) q^{47} +(-18.6942 - 43.3380i) q^{49} +(0.323952 + 16.7194i) q^{51} +(-84.4954 + 48.7834i) q^{53} +(-4.77333 + 8.26766i) q^{55} +(13.4797 + 4.61251i) q^{57} +(4.20200 - 35.9504i) q^{59} +(0.599932 - 0.301297i) q^{61} +(7.58450 + 9.40404i) q^{63} +(-58.5697 + 43.6035i) q^{65} +(23.3316 + 24.7300i) q^{67} +(-54.3079 + 24.6847i) q^{69} +(-56.0789 - 66.8323i) q^{71} +(-70.3977 - 59.0707i) q^{73} +(39.8688 - 5.44482i) q^{75} +(-1.68963 + 3.36434i) q^{77} +(-31.3766 - 7.43638i) q^{79} +(65.8941 + 47.1059i) q^{81} +(-12.1078 + 51.0870i) q^{83} +(-16.9561 - 8.51566i) q^{85} +(46.1849 - 35.7946i) q^{87} +(-75.7179 + 90.2371i) q^{89} +(-22.0584 + 18.5092i) q^{91} +(25.0037 + 2.43254i) q^{93} +(-11.7584 + 11.0935i) q^{95} +(-34.4044 - 46.2131i) q^{97} +(-4.86521 + 24.7678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q+O(q^{10}) \) Copy content Toggle raw display \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{31}{54}\right)\)

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 0
\(3\) −0.463613 + 2.96396i −0.154538 + 0.987987i
\(4\) 0 0
\(5\) −2.73041 2.03271i −0.546081 0.406543i 0.288457 0.957493i \(-0.406858\pi\)
−0.834538 + 0.550950i \(0.814265\pi\)
\(6\) 0 0
\(7\) −1.12154 0.737649i −0.160220 0.105378i 0.466867 0.884328i \(-0.345383\pi\)
−0.627087 + 0.778949i \(0.715753\pi\)
\(8\) 0 0
\(9\) −8.57013 2.74826i −0.952236 0.305362i
\(10\) 0 0
\(11\) −0.325590 2.78560i −0.0295991 0.253237i −0.999934 0.0114725i \(-0.996348\pi\)
0.970335 0.241764i \(-0.0777260\pi\)
\(12\) 0 0
\(13\) 6.15219 20.5497i 0.473245 1.58075i −0.304721 0.952442i \(-0.598563\pi\)
0.777966 0.628307i \(-0.216252\pi\)
\(14\) 0 0
\(15\) 7.29073 7.15043i 0.486049 0.476695i
\(16\) 0 0
\(17\) 5.48948 0.967944i 0.322911 0.0569379i −0.00984318 0.999952i \(-0.503133\pi\)
0.332754 + 0.943014i \(0.392022\pi\)
\(18\) 0 0
\(19\) 0.824658 4.67687i 0.0434031 0.246151i −0.955385 0.295362i \(-0.904560\pi\)
0.998788 + 0.0492113i \(0.0156708\pi\)
\(20\) 0 0
\(21\) 2.70633 2.98222i 0.128873 0.142011i
\(22\) 0 0
\(23\) 10.9269 + 16.6136i 0.475084 + 0.722330i 0.990934 0.134349i \(-0.0428943\pi\)
−0.515850 + 0.856679i \(0.672524\pi\)
\(24\) 0 0
\(25\) −3.84688 12.8495i −0.153875 0.513979i
\(26\) 0 0
\(27\) 12.1190 24.1274i 0.448850 0.893607i
\(28\) 0 0
\(29\) −14.1673 13.3662i −0.488528 0.460902i 0.402126 0.915584i \(-0.368271\pi\)
−0.890654 + 0.454682i \(0.849753\pi\)
\(30\) 0 0
\(31\) −0.486900 8.35975i −0.0157064 0.269669i −0.997014 0.0772226i \(-0.975395\pi\)
0.981307 0.192447i \(-0.0616423\pi\)
\(32\) 0 0
\(33\) 8.40736 + 0.326405i 0.254769 + 0.00989106i
\(34\) 0 0
\(35\) 1.56284 + 4.29386i 0.0446524 + 0.122682i
\(36\) 0 0
\(37\) 34.4216 + 12.5284i 0.930313 + 0.338606i 0.762334 0.647184i \(-0.224054\pi\)
0.167979 + 0.985791i \(0.446276\pi\)
\(38\) 0 0
\(39\) 58.0564 + 27.7620i 1.48862 + 0.711845i
\(40\) 0 0
\(41\) −6.96530 29.3889i −0.169885 0.716803i −0.989578 0.143999i \(-0.954004\pi\)
0.819693 0.572804i \(-0.194144\pi\)
\(42\) 0 0
\(43\) 24.2316 56.1752i 0.563526 1.30640i −0.363567 0.931568i \(-0.618441\pi\)
0.927093 0.374832i \(-0.122300\pi\)
\(44\) 0 0
\(45\) 17.8135 + 24.9245i 0.395856 + 0.553877i
\(46\) 0 0
\(47\) 16.7341 + 0.974651i 0.356045 + 0.0207373i 0.235235 0.971938i \(-0.424414\pi\)
0.120810 + 0.992676i \(0.461451\pi\)
\(48\) 0 0
\(49\) −18.6942 43.3380i −0.381514 0.884449i
\(50\) 0 0
\(51\) 0.323952 + 16.7194i 0.00635200 + 0.327831i
\(52\) 0 0
\(53\) −84.4954 + 48.7834i −1.59425 + 0.920442i −0.601686 + 0.798733i \(0.705504\pi\)
−0.992566 + 0.121709i \(0.961162\pi\)
\(54\) 0 0
\(55\) −4.77333 + 8.26766i −0.0867879 + 0.150321i
\(56\) 0 0
\(57\) 13.4797 + 4.61251i 0.236486 + 0.0809212i
\(58\) 0 0
\(59\) 4.20200 35.9504i 0.0712204 0.609329i −0.909748 0.415161i \(-0.863725\pi\)
0.980968 0.194168i \(-0.0622007\pi\)
\(60\) 0 0
\(61\) 0.599932 0.301297i 0.00983495 0.00493930i −0.443875 0.896089i \(-0.646397\pi\)
0.453710 + 0.891149i \(0.350100\pi\)
\(62\) 0 0
\(63\) 7.58450 + 9.40404i 0.120389 + 0.149270i
\(64\) 0 0
\(65\) −58.5697 + 43.6035i −0.901072 + 0.670823i
\(66\) 0 0
\(67\) 23.3316 + 24.7300i 0.348233 + 0.369105i 0.877688 0.479233i \(-0.159085\pi\)
−0.529455 + 0.848338i \(0.677604\pi\)
\(68\) 0 0
\(69\) −54.3079 + 24.6847i −0.787071 + 0.357749i
\(70\) 0 0
\(71\) −56.0789 66.8323i −0.789844 0.941299i 0.209489 0.977811i \(-0.432820\pi\)
−0.999333 + 0.0365116i \(0.988375\pi\)
\(72\) 0 0
\(73\) −70.3977 59.0707i −0.964352 0.809187i 0.0173037 0.999850i \(-0.494492\pi\)
−0.981656 + 0.190663i \(0.938936\pi\)
\(74\) 0 0
\(75\) 39.8688 5.44482i 0.531584 0.0725975i
\(76\) 0 0
\(77\) −1.68963 + 3.36434i −0.0219433 + 0.0436927i
\(78\) 0 0
\(79\) −31.3766 7.43638i −0.397172 0.0941314i 0.0271762 0.999631i \(-0.491348\pi\)
−0.424348 + 0.905499i \(0.639497\pi\)
\(80\) 0 0
\(81\) 65.8941 + 47.1059i 0.813508 + 0.581554i
\(82\) 0 0
\(83\) −12.1078 + 51.0870i −0.145878 + 0.615506i 0.850156 + 0.526531i \(0.176507\pi\)
−0.996034 + 0.0889756i \(0.971641\pi\)
\(84\) 0 0
\(85\) −16.9561 8.51566i −0.199483 0.100184i
\(86\) 0 0
\(87\) 46.1849 35.7946i 0.530861 0.411432i
\(88\) 0 0
\(89\) −75.7179 + 90.2371i −0.850763 + 1.01390i 0.148923 + 0.988849i \(0.452419\pi\)
−0.999686 + 0.0250510i \(0.992025\pi\)
\(90\) 0 0
\(91\) −22.0584 + 18.5092i −0.242400 + 0.203398i
\(92\) 0 0
\(93\) 25.0037 + 2.43254i 0.268857 + 0.0261563i
\(94\) 0 0
\(95\) −11.7584 + 11.0935i −0.123772 + 0.116773i
\(96\) 0 0
\(97\) −34.4044 46.2131i −0.354685 0.476424i 0.588593 0.808430i \(-0.299682\pi\)
−0.943277 + 0.332006i \(0.892275\pi\)
\(98\) 0 0
\(99\) −4.86521 + 24.7678i −0.0491436 + 0.250179i
\(100\) 0 0
\(101\) 43.0589 + 85.7373i 0.426325 + 0.848884i 0.999565 + 0.0294959i \(0.00939018\pi\)
−0.573239 + 0.819388i \(0.694314\pi\)
\(102\) 0 0
\(103\) −4.90799 0.573662i −0.0476504 0.00556953i 0.0922343 0.995737i \(-0.470599\pi\)
−0.139885 + 0.990168i \(0.544673\pi\)
\(104\) 0 0
\(105\) −13.4514 + 2.64150i −0.128108 + 0.0251571i
\(106\) 0 0
\(107\) −14.0709 8.12382i −0.131503 0.0759235i 0.432805 0.901488i \(-0.357524\pi\)
−0.564309 + 0.825564i \(0.690857\pi\)
\(108\) 0 0
\(109\) 48.9682 + 84.8154i 0.449249 + 0.778123i 0.998337 0.0576419i \(-0.0183582\pi\)
−0.549088 + 0.835765i \(0.685025\pi\)
\(110\) 0 0
\(111\) −53.0921 + 96.2159i −0.478307 + 0.866809i
\(112\) 0 0
\(113\) −73.9777 + 31.9109i −0.654670 + 0.282397i −0.697392 0.716690i \(-0.745656\pi\)
0.0427221 + 0.999087i \(0.486397\pi\)
\(114\) 0 0
\(115\) 3.93569 67.5731i 0.0342234 0.587593i
\(116\) 0 0
\(117\) −109.201 + 159.206i −0.933342 + 1.36073i
\(118\) 0 0
\(119\) −6.87069 2.96373i −0.0577369 0.0249053i
\(120\) 0 0
\(121\) 110.085 26.0906i 0.909792 0.215625i
\(122\) 0 0
\(123\) 90.3368 7.01979i 0.734445 0.0570715i
\(124\) 0 0
\(125\) −44.7214 + 122.871i −0.357771 + 0.982969i
\(126\) 0 0
\(127\) 28.7457 10.4626i 0.226344 0.0823825i −0.226359 0.974044i \(-0.572682\pi\)
0.452703 + 0.891662i \(0.350460\pi\)
\(128\) 0 0
\(129\) 155.267 + 97.8651i 1.20362 + 0.758644i
\(130\) 0 0
\(131\) 90.8501 5.29142i 0.693512 0.0403925i 0.292231 0.956348i \(-0.405602\pi\)
0.401281 + 0.915955i \(0.368565\pi\)
\(132\) 0 0
\(133\) −4.37478 + 4.63699i −0.0328931 + 0.0348646i
\(134\) 0 0
\(135\) −82.1337 + 41.2432i −0.608398 + 0.305505i
\(136\) 0 0
\(137\) −29.1836 + 8.73699i −0.213019 + 0.0637737i −0.391535 0.920163i \(-0.628056\pi\)
0.178516 + 0.983937i \(0.442870\pi\)
\(138\) 0 0
\(139\) 114.683 75.4283i 0.825059 0.542650i −0.0653230 0.997864i \(-0.520808\pi\)
0.890382 + 0.455214i \(0.150437\pi\)
\(140\) 0 0
\(141\) −10.6470 + 49.1474i −0.0755105 + 0.348563i
\(142\) 0 0
\(143\) −59.2465 10.4467i −0.414311 0.0730542i
\(144\) 0 0
\(145\) 11.5129 + 65.2931i 0.0793995 + 0.450297i
\(146\) 0 0
\(147\) 137.119 35.3168i 0.932782 0.240250i
\(148\) 0 0
\(149\) −7.06730 2.11581i −0.0474315 0.0142001i 0.263000 0.964796i \(-0.415288\pi\)
−0.310431 + 0.950596i \(0.600473\pi\)
\(150\) 0 0
\(151\) −101.697 + 11.8866i −0.673488 + 0.0787195i −0.445961 0.895052i \(-0.647138\pi\)
−0.227527 + 0.973772i \(0.573064\pi\)
\(152\) 0 0
\(153\) −49.7057 6.79114i −0.324874 0.0443865i
\(154\) 0 0
\(155\) −15.6635 + 23.8152i −0.101055 + 0.153647i
\(156\) 0 0
\(157\) 119.595 160.644i 0.761753 1.02321i −0.236911 0.971531i \(-0.576135\pi\)
0.998664 0.0516804i \(-0.0164577\pi\)
\(158\) 0 0
\(159\) −105.419 273.058i −0.663012 1.71734i
\(160\) 0 0
\(161\) 26.6931i 0.165795i
\(162\) 0 0
\(163\) 6.31642 0.0387510 0.0193755 0.999812i \(-0.493832\pi\)
0.0193755 + 0.999812i \(0.493832\pi\)
\(164\) 0 0
\(165\) −22.2920 17.9810i −0.135103 0.108976i
\(166\) 0 0
\(167\) −100.555 74.8604i −0.602126 0.448266i 0.252438 0.967613i \(-0.418768\pi\)
−0.854563 + 0.519347i \(0.826175\pi\)
\(168\) 0 0
\(169\) −243.245 159.984i −1.43932 0.946654i
\(170\) 0 0
\(171\) −19.9207 + 37.8150i −0.116495 + 0.221140i
\(172\) 0 0
\(173\) −0.656602 5.61759i −0.00379539 0.0324716i 0.991208 0.132313i \(-0.0422405\pi\)
−0.995003 + 0.0998416i \(0.968166\pi\)
\(174\) 0 0
\(175\) −5.16397 + 17.2489i −0.0295084 + 0.0985649i
\(176\) 0 0
\(177\) 104.608 + 29.1216i 0.591003 + 0.164529i
\(178\) 0 0
\(179\) 225.032 39.6793i 1.25716 0.221672i 0.494907 0.868946i \(-0.335202\pi\)
0.762257 + 0.647274i \(0.224091\pi\)
\(180\) 0 0
\(181\) −29.2518 + 165.895i −0.161612 + 0.916549i 0.790876 + 0.611976i \(0.209625\pi\)
−0.952489 + 0.304574i \(0.901486\pi\)
\(182\) 0 0
\(183\) 0.614897 + 1.91786i 0.00336009 + 0.0104801i
\(184\) 0 0
\(185\) −68.5182 104.177i −0.370369 0.563118i
\(186\) 0 0
\(187\) −4.48363 14.9764i −0.0239766 0.0800875i
\(188\) 0 0
\(189\) −31.3895 + 18.1203i −0.166082 + 0.0958747i
\(190\) 0 0
\(191\) 273.406 + 257.945i 1.43144 + 1.35050i 0.838061 + 0.545577i \(0.183689\pi\)
0.593383 + 0.804921i \(0.297792\pi\)
\(192\) 0 0
\(193\) −12.1104 207.928i −0.0627482 1.07734i −0.871881 0.489719i \(-0.837100\pi\)
0.809132 0.587626i \(-0.199938\pi\)
\(194\) 0 0
\(195\) −102.085 193.813i −0.523515 0.993915i
\(196\) 0 0
\(197\) −76.7979 211.001i −0.389837 1.07107i −0.967075 0.254492i \(-0.918092\pi\)
0.577238 0.816576i \(-0.304131\pi\)
\(198\) 0 0
\(199\) −68.4585 24.9169i −0.344013 0.125210i 0.164235 0.986421i \(-0.447484\pi\)
−0.508248 + 0.861211i \(0.669707\pi\)
\(200\) 0 0
\(201\) −84.1157 + 57.6888i −0.418486 + 0.287009i
\(202\) 0 0
\(203\) 6.02968 + 25.4412i 0.0297028 + 0.125326i
\(204\) 0 0
\(205\) −40.7211 + 94.4021i −0.198640 + 0.460498i
\(206\) 0 0
\(207\) −47.9867 172.411i −0.231820 0.832901i
\(208\) 0 0
\(209\) −13.2964 0.774427i −0.0636191 0.00370539i
\(210\) 0 0
\(211\) 80.7991 + 187.313i 0.382934 + 0.887741i 0.995270 + 0.0971438i \(0.0309707\pi\)
−0.612336 + 0.790598i \(0.709770\pi\)
\(212\) 0 0
\(213\) 224.087 135.231i 1.05205 0.634889i
\(214\) 0 0
\(215\) −180.350 + 104.125i −0.838838 + 0.484303i
\(216\) 0 0
\(217\) −5.62049 + 9.73497i −0.0259009 + 0.0448616i
\(218\) 0 0
\(219\) 207.720 181.270i 0.948495 0.827717i
\(220\) 0 0
\(221\) 13.8813 118.762i 0.0628115 0.537386i
\(222\) 0 0
\(223\) −172.014 + 86.3886i −0.771363 + 0.387393i −0.790530 0.612423i \(-0.790195\pi\)
0.0191673 + 0.999816i \(0.493898\pi\)
\(224\) 0 0
\(225\) −2.34547 + 120.694i −0.0104243 + 0.536417i
\(226\) 0 0
\(227\) 275.719 205.265i 1.21462 0.904252i 0.217208 0.976125i \(-0.430305\pi\)
0.997414 + 0.0718729i \(0.0228976\pi\)
\(228\) 0 0
\(229\) 205.025 + 217.314i 0.895306 + 0.948969i 0.998958 0.0456449i \(-0.0145343\pi\)
−0.103652 + 0.994614i \(0.533053\pi\)
\(230\) 0 0
\(231\) −9.18843 6.56776i −0.0397768 0.0284319i
\(232\) 0 0
\(233\) −256.685 305.905i −1.10165 1.31290i −0.945667 0.325137i \(-0.894590\pi\)
−0.155984 0.987760i \(-0.549855\pi\)
\(234\) 0 0
\(235\) −43.7098 36.6768i −0.185999 0.156072i
\(236\) 0 0
\(237\) 36.5877 89.5513i 0.154379 0.377854i
\(238\) 0 0
\(239\) 199.116 396.473i 0.833123 1.65888i 0.0839882 0.996467i \(-0.473234\pi\)
0.749135 0.662418i \(-0.230470\pi\)
\(240\) 0 0
\(241\) 245.473 + 58.1781i 1.01856 + 0.241403i 0.705786 0.708425i \(-0.250594\pi\)
0.312773 + 0.949828i \(0.398742\pi\)
\(242\) 0 0
\(243\) −170.169 + 173.469i −0.700286 + 0.713863i
\(244\) 0 0
\(245\) −37.0509 + 156.330i −0.151228 + 0.638083i
\(246\) 0 0
\(247\) −91.0349 45.7195i −0.368562 0.185099i
\(248\) 0 0
\(249\) −145.807 59.5718i −0.585569 0.239244i
\(250\) 0 0
\(251\) −46.8842 + 55.8744i −0.186790 + 0.222607i −0.851310 0.524663i \(-0.824191\pi\)
0.664520 + 0.747270i \(0.268636\pi\)
\(252\) 0 0
\(253\) 42.7211 35.8473i 0.168858 0.141689i
\(254\) 0 0
\(255\) 33.1011 46.3092i 0.129808 0.181605i
\(256\) 0 0
\(257\) 349.927 330.139i 1.36158 1.28459i 0.439157 0.898410i \(-0.355277\pi\)
0.922425 0.386177i \(-0.126204\pi\)
\(258\) 0 0
\(259\) −29.3636 39.4422i −0.113373 0.152287i
\(260\) 0 0
\(261\) 84.6818 + 153.485i 0.324451 + 0.588065i
\(262\) 0 0
\(263\) 147.438 + 293.572i 0.560599 + 1.11625i 0.978210 + 0.207619i \(0.0665714\pi\)
−0.417610 + 0.908626i \(0.637132\pi\)
\(264\) 0 0
\(265\) 329.869 + 38.5562i 1.24479 + 0.145495i
\(266\) 0 0
\(267\) −232.355 266.260i −0.870245 0.997228i
\(268\) 0 0
\(269\) 17.5198 + 10.1151i 0.0651293 + 0.0376024i 0.532211 0.846612i \(-0.321361\pi\)
−0.467082 + 0.884214i \(0.654695\pi\)
\(270\) 0 0
\(271\) 200.845 + 347.873i 0.741124 + 1.28366i 0.951984 + 0.306148i \(0.0990404\pi\)
−0.210860 + 0.977516i \(0.567626\pi\)
\(272\) 0 0
\(273\) −44.6340 73.9614i −0.163495 0.270921i
\(274\) 0 0
\(275\) −34.5410 + 14.8995i −0.125604 + 0.0541801i
\(276\) 0 0
\(277\) 19.1583 328.935i 0.0691636 1.18749i −0.767967 0.640489i \(-0.778732\pi\)
0.837131 0.547003i \(-0.184231\pi\)
\(278\) 0 0
\(279\) −18.8020 + 72.9822i −0.0673906 + 0.261585i
\(280\) 0 0
\(281\) −2.06475 0.890644i −0.00734785 0.00316955i 0.392403 0.919794i \(-0.371644\pi\)
−0.399751 + 0.916624i \(0.630903\pi\)
\(282\) 0 0
\(283\) 41.7414 9.89290i 0.147496 0.0349572i −0.156204 0.987725i \(-0.549926\pi\)
0.303701 + 0.952768i \(0.401778\pi\)
\(284\) 0 0
\(285\) −27.4292 39.9945i −0.0962430 0.140331i
\(286\) 0 0
\(287\) −13.8668 + 38.0988i −0.0483165 + 0.132749i
\(288\) 0 0
\(289\) −242.374 + 88.2168i −0.838663 + 0.305248i
\(290\) 0 0
\(291\) 152.924 80.5483i 0.525513 0.276798i
\(292\) 0 0
\(293\) 287.173 16.7259i 0.980112 0.0570850i 0.439399 0.898292i \(-0.355192\pi\)
0.540713 + 0.841207i \(0.318154\pi\)
\(294\) 0 0
\(295\) −84.5500 + 89.6178i −0.286610 + 0.303789i
\(296\) 0 0
\(297\) −71.1551 25.9030i −0.239579 0.0872154i
\(298\) 0 0
\(299\) 408.629 122.336i 1.36665 0.409149i
\(300\) 0 0
\(301\) −68.6144 + 45.1284i −0.227955 + 0.149928i
\(302\) 0 0
\(303\) −274.085 + 87.8759i −0.904569 + 0.290019i
\(304\) 0 0
\(305\) −2.25051 0.396826i −0.00737872 0.00130107i
\(306\) 0 0
\(307\) 76.3210 + 432.838i 0.248603 + 1.40990i 0.811975 + 0.583692i \(0.198392\pi\)
−0.563373 + 0.826203i \(0.690496\pi\)
\(308\) 0 0
\(309\) 3.97572 14.2811i 0.0128664 0.0462173i
\(310\) 0 0
\(311\) 144.598 + 43.2899i 0.464946 + 0.139196i 0.510704 0.859757i \(-0.329385\pi\)
−0.0457573 + 0.998953i \(0.514570\pi\)
\(312\) 0 0
\(313\) −300.097 + 35.0763i −0.958775 + 0.112065i −0.581063 0.813858i \(-0.697363\pi\)
−0.377712 + 0.925923i \(0.623289\pi\)
\(314\) 0 0
\(315\) −1.59306 41.0940i −0.00505733 0.130457i
\(316\) 0 0
\(317\) −159.614 + 242.682i −0.503516 + 0.765558i −0.994402 0.105665i \(-0.966303\pi\)
0.490886 + 0.871224i \(0.336673\pi\)
\(318\) 0 0
\(319\) −32.6201 + 43.8163i −0.102257 + 0.137355i
\(320\) 0 0
\(321\) 30.6021 37.9392i 0.0953337 0.118191i
\(322\) 0 0
\(323\) 26.4718i 0.0819561i
\(324\) 0 0
\(325\) −287.720 −0.885292
\(326\) 0 0
\(327\) −274.092 + 105.818i −0.838201 + 0.323603i
\(328\) 0 0
\(329\) −18.0491 13.4370i −0.0548603 0.0408420i
\(330\) 0 0
\(331\) −22.9699 15.1076i −0.0693956 0.0456422i 0.514337 0.857588i \(-0.328038\pi\)
−0.583733 + 0.811946i \(0.698408\pi\)
\(332\) 0 0
\(333\) −260.566 201.970i −0.782480 0.606516i
\(334\) 0 0
\(335\) −13.4357 114.950i −0.0401065 0.343133i
\(336\) 0 0
\(337\) −0.144206 + 0.481683i −0.000427912 + 0.00142933i −0.958203 0.286088i \(-0.907645\pi\)
0.957775 + 0.287518i \(0.0928301\pi\)
\(338\) 0 0
\(339\) −60.2855 234.061i −0.177833 0.690446i
\(340\) 0 0
\(341\) −23.1284 + 4.07816i −0.0678252 + 0.0119594i
\(342\) 0 0
\(343\) −22.4239 + 127.172i −0.0653759 + 0.370765i
\(344\) 0 0
\(345\) 198.460 + 42.9930i 0.575245 + 0.124617i
\(346\) 0 0
\(347\) 62.1170 + 94.4443i 0.179011 + 0.272174i 0.913836 0.406084i \(-0.133106\pi\)
−0.734824 + 0.678257i \(0.762735\pi\)
\(348\) 0 0
\(349\) 13.2984 + 44.4199i 0.0381044 + 0.127278i 0.974926 0.222531i \(-0.0714318\pi\)
−0.936821 + 0.349809i \(0.886247\pi\)
\(350\) 0 0
\(351\) −421.253 397.478i −1.20015 1.13241i
\(352\) 0 0
\(353\) −17.3182 16.3388i −0.0490599 0.0462857i 0.661321 0.750103i \(-0.269996\pi\)
−0.710381 + 0.703817i \(0.751477\pi\)
\(354\) 0 0
\(355\) 17.2675 + 296.472i 0.0486409 + 0.835131i
\(356\) 0 0
\(357\) 11.9697 18.9904i 0.0335286 0.0531945i
\(358\) 0 0
\(359\) 191.030 + 524.850i 0.532117 + 1.46198i 0.856547 + 0.516069i \(0.172605\pi\)
−0.324431 + 0.945909i \(0.605173\pi\)
\(360\) 0 0
\(361\) 318.036 + 115.756i 0.880986 + 0.320653i
\(362\) 0 0
\(363\) 26.2947 + 338.383i 0.0724372 + 0.932185i
\(364\) 0 0
\(365\) 72.1406 + 304.385i 0.197646 + 0.833932i
\(366\) 0 0
\(367\) −159.410 + 369.555i −0.434361 + 1.00696i 0.550692 + 0.834708i \(0.314364\pi\)
−0.985053 + 0.172253i \(0.944895\pi\)
\(368\) 0 0
\(369\) −21.0749 + 271.009i −0.0571136 + 0.734442i
\(370\) 0 0
\(371\) 130.750 + 7.61533i 0.352426 + 0.0205265i
\(372\) 0 0
\(373\) −257.462 596.864i −0.690247 1.60017i −0.795660 0.605743i \(-0.792876\pi\)
0.105414 0.994428i \(-0.466383\pi\)
\(374\) 0 0
\(375\) −343.452 189.517i −0.915871 0.505379i
\(376\) 0 0
\(377\) −361.831 + 208.903i −0.959763 + 0.554120i
\(378\) 0 0
\(379\) −198.056 + 343.043i −0.522575 + 0.905126i 0.477080 + 0.878860i \(0.341695\pi\)
−0.999655 + 0.0262660i \(0.991638\pi\)
\(380\) 0 0
\(381\) 17.6838 + 90.0517i 0.0464141 + 0.236356i
\(382\) 0 0
\(383\) 71.1395 608.637i 0.185743 1.58913i −0.503105 0.864225i \(-0.667809\pi\)
0.688848 0.724906i \(-0.258117\pi\)
\(384\) 0 0
\(385\) 11.4521 5.75147i 0.0297458 0.0149389i
\(386\) 0 0
\(387\) −362.052 + 414.834i −0.935535 + 1.07192i
\(388\) 0 0
\(389\) −139.851 + 104.115i −0.359514 + 0.267648i −0.761727 0.647898i \(-0.775648\pi\)
0.402213 + 0.915546i \(0.368241\pi\)
\(390\) 0 0
\(391\) 76.0642 + 80.6233i 0.194538 + 0.206198i
\(392\) 0 0
\(393\) −26.4357 + 271.729i −0.0672665 + 0.691423i
\(394\) 0 0
\(395\) 70.5548 + 84.0839i 0.178620 + 0.212871i
\(396\) 0 0
\(397\) 118.408 + 99.3563i 0.298257 + 0.250268i 0.779619 0.626255i \(-0.215413\pi\)
−0.481361 + 0.876522i \(0.659857\pi\)
\(398\) 0 0
\(399\) −11.7157 15.1164i −0.0293626 0.0378858i
\(400\) 0 0
\(401\) 76.5653 152.454i 0.190936 0.380185i −0.777713 0.628620i \(-0.783620\pi\)
0.968648 + 0.248435i \(0.0799164\pi\)
\(402\) 0 0
\(403\) −174.786 41.4251i −0.433712 0.102792i
\(404\) 0 0
\(405\) −84.1650 262.562i −0.207815 0.648301i
\(406\) 0 0
\(407\) 23.6919 99.9639i 0.0582110 0.245612i
\(408\) 0 0
\(409\) 151.309 + 75.9904i 0.369949 + 0.185795i 0.624054 0.781381i \(-0.285485\pi\)
−0.254105 + 0.967177i \(0.581781\pi\)
\(410\) 0 0
\(411\) −12.3662 90.5496i −0.0300881 0.220315i
\(412\) 0 0
\(413\) −31.2315 + 37.2203i −0.0756211 + 0.0901217i
\(414\) 0 0
\(415\) 136.905 114.877i 0.329891 0.276811i
\(416\) 0 0
\(417\) 170.398 + 374.886i 0.408628 + 0.899007i
\(418\) 0 0
\(419\) −460.866 + 434.805i −1.09992 + 1.03772i −0.100836 + 0.994903i \(0.532152\pi\)
−0.999083 + 0.0428165i \(0.986367\pi\)
\(420\) 0 0
\(421\) −111.277 149.470i −0.264315 0.355036i 0.650076 0.759869i \(-0.274737\pi\)
−0.914391 + 0.404833i \(0.867330\pi\)
\(422\) 0 0
\(423\) −140.735 54.3426i −0.332707 0.128470i
\(424\) 0 0
\(425\) −33.5550 66.8134i −0.0789528 0.157208i
\(426\) 0 0
\(427\) −0.895101 0.104622i −0.00209625 0.000245017i
\(428\) 0 0
\(429\) 58.4312 170.761i 0.136203 0.398044i
\(430\) 0 0
\(431\) −414.846 239.512i −0.962520 0.555711i −0.0655726 0.997848i \(-0.520887\pi\)
−0.896948 + 0.442136i \(0.854221\pi\)
\(432\) 0 0
\(433\) 408.999 + 708.407i 0.944571 + 1.63604i 0.756608 + 0.653868i \(0.226855\pi\)
0.187962 + 0.982176i \(0.439812\pi\)
\(434\) 0 0
\(435\) −198.864 + 3.85315i −0.457158 + 0.00885783i
\(436\) 0 0
\(437\) 86.7105 37.4033i 0.198422 0.0855910i
\(438\) 0 0
\(439\) 3.17667 54.5413i 0.00723614 0.124240i −0.992756 0.120152i \(-0.961662\pi\)
0.999992 0.00408775i \(-0.00130117\pi\)
\(440\) 0 0
\(441\) 41.1074 + 422.788i 0.0932140 + 0.958704i
\(442\) 0 0
\(443\) −77.9496 33.6242i −0.175959 0.0759011i 0.306278 0.951942i \(-0.400916\pi\)
−0.482237 + 0.876041i \(0.660175\pi\)
\(444\) 0 0
\(445\) 390.167 92.4712i 0.876779 0.207800i
\(446\) 0 0
\(447\) 9.54767 19.9663i 0.0213594 0.0446673i
\(448\) 0 0
\(449\) 281.924 774.580i 0.627893 1.72512i −0.0588949 0.998264i \(-0.518758\pi\)
0.686788 0.726858i \(-0.259020\pi\)
\(450\) 0 0
\(451\) −79.5979 + 28.9713i −0.176492 + 0.0642379i
\(452\) 0 0
\(453\) 11.9164 306.936i 0.0263055 0.677563i
\(454\) 0 0
\(455\) 97.8524 5.69925i 0.215060 0.0125258i
\(456\) 0 0
\(457\) 85.6511 90.7849i 0.187420 0.198654i −0.626850 0.779140i \(-0.715656\pi\)
0.814270 + 0.580486i \(0.197137\pi\)
\(458\) 0 0
\(459\) 43.1729 144.177i 0.0940586 0.314112i
\(460\) 0 0
\(461\) 478.686 143.309i 1.03837 0.310866i 0.278150 0.960538i \(-0.410279\pi\)
0.760215 + 0.649671i \(0.225094\pi\)
\(462\) 0 0
\(463\) −550.479 + 362.056i −1.18894 + 0.781978i −0.980589 0.196076i \(-0.937180\pi\)
−0.208351 + 0.978054i \(0.566810\pi\)
\(464\) 0 0
\(465\) −63.3256 57.4672i −0.136184 0.123585i
\(466\) 0 0
\(467\) 590.932 + 104.197i 1.26538 + 0.223121i 0.765761 0.643125i \(-0.222363\pi\)
0.499618 + 0.866246i \(0.333474\pi\)
\(468\) 0 0
\(469\) −7.92525 44.9463i −0.0168982 0.0958344i
\(470\) 0 0
\(471\) 420.697 + 428.952i 0.893200 + 0.910727i
\(472\) 0 0
\(473\) −164.371 49.2095i −0.347508 0.104037i
\(474\) 0 0
\(475\) −63.2676 + 7.39493i −0.133195 + 0.0155683i
\(476\) 0 0
\(477\) 858.205 185.865i 1.79917 0.389653i
\(478\) 0 0
\(479\) −50.5194 + 76.8111i −0.105469 + 0.160357i −0.884366 0.466794i \(-0.845409\pi\)
0.778897 + 0.627151i \(0.215779\pi\)
\(480\) 0 0
\(481\) 469.224 630.277i 0.975517 1.31035i
\(482\) 0 0
\(483\) 79.1172 + 12.3753i 0.163804 + 0.0256216i
\(484\) 0 0
\(485\) 196.115i 0.404361i
\(486\) 0 0
\(487\) −779.390 −1.60039 −0.800196 0.599739i \(-0.795271\pi\)
−0.800196 + 0.599739i \(0.795271\pi\)
\(488\) 0 0
\(489\) −2.92837 + 18.7216i −0.00598850 + 0.0382855i
\(490\) 0 0
\(491\) 178.490 + 132.881i 0.363524 + 0.270633i 0.763387 0.645941i \(-0.223535\pi\)
−0.399863 + 0.916575i \(0.630942\pi\)
\(492\) 0 0
\(493\) −90.7088 59.6601i −0.183994 0.121015i
\(494\) 0 0
\(495\) 63.6298 57.7365i 0.128545 0.116639i
\(496\) 0 0
\(497\) 13.5961 + 116.322i 0.0273563 + 0.234048i
\(498\) 0 0
\(499\) −139.850 + 467.131i −0.280260 + 0.936134i 0.695727 + 0.718306i \(0.255082\pi\)
−0.975987 + 0.217828i \(0.930103\pi\)
\(500\) 0 0
\(501\) 268.502 263.335i 0.535932 0.525618i
\(502\) 0 0
\(503\) −587.794 + 103.644i −1.16858 + 0.206052i −0.724072 0.689724i \(-0.757732\pi\)
−0.444506 + 0.895776i \(0.646621\pi\)
\(504\) 0 0
\(505\) 56.7110 321.624i 0.112299 0.636879i
\(506\) 0 0
\(507\) 586.959 646.796i 1.15771 1.27573i
\(508\) 0 0
\(509\) 107.851 + 163.980i 0.211889 + 0.322161i 0.925757 0.378119i \(-0.123429\pi\)
−0.713868 + 0.700280i \(0.753058\pi\)
\(510\) 0 0
\(511\) 35.3805 + 118.179i 0.0692377 + 0.231270i
\(512\) 0 0
\(513\) −102.847 76.5756i −0.200481 0.149270i
\(514\) 0 0
\(515\) 12.2347 + 11.5429i 0.0237568 + 0.0224133i
\(516\) 0 0
\(517\) −2.73347 46.9319i −0.00528718 0.0907774i
\(518\) 0 0
\(519\) 16.9547 + 0.658245i 0.0326681 + 0.00126830i
\(520\) 0 0
\(521\) 195.289 + 536.553i 0.374836 + 1.02985i 0.973467 + 0.228828i \(0.0734893\pi\)
−0.598631 + 0.801025i \(0.704289\pi\)
\(522\) 0 0
\(523\) 169.881 + 61.8316i 0.324820 + 0.118225i 0.499283 0.866439i \(-0.333597\pi\)
−0.174463 + 0.984664i \(0.555819\pi\)
\(524\) 0 0
\(525\) −48.7309 23.3026i −0.0928207 0.0443859i
\(526\) 0 0
\(527\) −10.7646 45.4194i −0.0204262 0.0861849i
\(528\) 0 0
\(529\) 52.9128 122.666i 0.100024 0.231882i
\(530\) 0 0
\(531\) −134.813 + 296.551i −0.253885 + 0.558477i
\(532\) 0 0
\(533\) −646.786 37.6710i −1.21348 0.0706773i
\(534\) 0 0
\(535\) 21.9058 + 50.7834i 0.0409454 + 0.0949221i
\(536\) 0 0
\(537\) 13.2799 + 685.383i 0.0247298 + 1.27632i
\(538\) 0 0
\(539\) −114.636 + 66.1850i −0.212682 + 0.122792i
\(540\) 0 0
\(541\) 27.4106 47.4765i 0.0506665 0.0877570i −0.839580 0.543236i \(-0.817199\pi\)
0.890246 + 0.455479i \(0.150532\pi\)
\(542\) 0 0
\(543\) −478.146 163.613i −0.880564 0.301312i
\(544\) 0 0
\(545\) 38.7022 331.119i 0.0710133 0.607557i
\(546\) 0 0
\(547\) 800.139 401.845i 1.46278 0.734634i 0.473515 0.880786i \(-0.342985\pi\)
0.989262 + 0.146152i \(0.0466888\pi\)
\(548\) 0 0
\(549\) −5.96954 + 0.933385i −0.0108735 + 0.00170015i
\(550\) 0 0
\(551\) −74.1949 + 55.2361i −0.134655 + 0.100247i
\(552\) 0 0
\(553\) 29.7047 + 31.4851i 0.0537155 + 0.0569351i
\(554\) 0 0
\(555\) 340.542 154.788i 0.613589 0.278896i
\(556\) 0 0
\(557\) −119.963 142.967i −0.215374 0.256673i 0.647531 0.762039i \(-0.275802\pi\)
−0.862905 + 0.505367i \(0.831357\pi\)
\(558\) 0 0
\(559\) −1005.31 843.553i −1.79840 1.50904i
\(560\) 0 0
\(561\) 46.4680 6.34606i 0.0828307 0.0113121i
\(562\) 0 0
\(563\) 313.727 624.681i 0.557241 1.10956i −0.421951 0.906619i \(-0.638654\pi\)
0.979191 0.202939i \(-0.0650493\pi\)
\(564\) 0 0
\(565\) 266.855 + 63.2457i 0.472309 + 0.111939i
\(566\) 0 0
\(567\) −39.1553 101.438i −0.0690571 0.178903i
\(568\) 0 0
\(569\) 32.8207 138.482i 0.0576814 0.243377i −0.936565 0.350494i \(-0.886014\pi\)
0.994246 + 0.107117i \(0.0341619\pi\)
\(570\) 0 0
\(571\) −555.691 279.078i −0.973189 0.488754i −0.110163 0.993914i \(-0.535137\pi\)
−0.863026 + 0.505160i \(0.831434\pi\)
\(572\) 0 0
\(573\) −891.293 + 690.777i −1.55549 + 1.20554i
\(574\) 0 0
\(575\) 171.441 204.316i 0.298159 0.355332i
\(576\) 0 0
\(577\) 842.690 707.100i 1.46047 1.22548i 0.535999 0.844219i \(-0.319935\pi\)
0.924468 0.381259i \(-0.124509\pi\)
\(578\) 0 0
\(579\) 621.904 + 60.5032i 1.07410 + 0.104496i
\(580\) 0 0
\(581\) 51.2638 48.3649i 0.0882337 0.0832442i
\(582\) 0 0
\(583\) 163.402 + 219.487i 0.280278 + 0.376479i
\(584\) 0 0
\(585\) 621.783 212.723i 1.06288 0.363629i
\(586\) 0 0
\(587\) 115.940 + 230.856i 0.197513 + 0.393281i 0.970486 0.241158i \(-0.0775274\pi\)
−0.772973 + 0.634439i \(0.781231\pi\)
\(588\) 0 0
\(589\) −39.4990 4.61677i −0.0670611 0.00783831i
\(590\) 0 0
\(591\) 661.002 129.803i 1.11845 0.219633i
\(592\) 0 0
\(593\) −968.521 559.176i −1.63326 0.942961i −0.983080 0.183178i \(-0.941361\pi\)
−0.650177 0.759783i \(-0.725305\pi\)
\(594\) 0 0
\(595\) 12.7354 + 22.0583i 0.0214040 + 0.0370728i
\(596\) 0 0
\(597\) 105.591 191.357i 0.176869 0.320530i
\(598\) 0 0
\(599\) −894.950 + 386.044i −1.49407 + 0.644480i −0.977342 0.211667i \(-0.932111\pi\)
−0.516731 + 0.856148i \(0.672851\pi\)
\(600\) 0 0
\(601\) 29.7319 510.476i 0.0494706 0.849378i −0.878735 0.477310i \(-0.841612\pi\)
0.928206 0.372068i \(-0.121351\pi\)
\(602\) 0 0
\(603\) −131.990 276.061i −0.218889 0.457812i
\(604\) 0 0
\(605\) −353.611 152.533i −0.584481 0.252121i
\(606\) 0 0
\(607\) 110.564 26.2041i 0.182148 0.0431699i −0.138529 0.990358i \(-0.544238\pi\)
0.320678 + 0.947188i \(0.396089\pi\)
\(608\) 0 0
\(609\) −78.2022 + 6.07685i −0.128411 + 0.00997840i
\(610\) 0 0
\(611\) 122.980 337.885i 0.201277 0.553004i
\(612\) 0 0
\(613\) 449.826 163.723i 0.733810 0.267085i 0.0520333 0.998645i \(-0.483430\pi\)
0.681777 + 0.731560i \(0.261208\pi\)
\(614\) 0 0
\(615\) −260.925 164.462i −0.424269 0.267418i
\(616\) 0 0
\(617\) −382.002 + 22.2491i −0.619128 + 0.0360601i −0.364843 0.931069i \(-0.618877\pi\)
−0.254285 + 0.967129i \(0.581840\pi\)
\(618\) 0 0
\(619\) 650.364 689.346i 1.05067 1.11364i 0.0573371 0.998355i \(-0.481739\pi\)
0.993332 0.115289i \(-0.0367795\pi\)
\(620\) 0 0
\(621\) 533.265 62.2988i 0.858720 0.100320i
\(622\) 0 0
\(623\) 151.484 45.3514i 0.243153 0.0727951i
\(624\) 0 0
\(625\) 91.7104 60.3189i 0.146737 0.0965102i
\(626\) 0 0
\(627\) 8.45975 39.0509i 0.0134924 0.0622822i
\(628\) 0 0
\(629\) 201.084 + 35.4564i 0.319688 + 0.0563696i
\(630\) 0 0
\(631\) −147.927 838.935i −0.234432 1.32953i −0.843806 0.536649i \(-0.819690\pi\)
0.609373 0.792883i \(-0.291421\pi\)
\(632\) 0 0
\(633\) −592.649 + 152.644i −0.936255 + 0.241145i
\(634\) 0 0
\(635\) −99.7548 29.8646i −0.157094 0.0470309i
\(636\) 0 0
\(637\) −1005.59 + 117.537i −1.57864 + 0.184517i
\(638\) 0 0
\(639\) 296.931 + 726.880i 0.464681 + 1.13753i
\(640\) 0 0
\(641\) −426.418 + 648.336i −0.665238 + 1.01145i 0.332426 + 0.943129i \(0.392133\pi\)
−0.997664 + 0.0683157i \(0.978237\pi\)
\(642\) 0 0
\(643\) 404.817 543.763i 0.629575 0.845666i −0.366838 0.930285i \(-0.619560\pi\)
0.996413 + 0.0846188i \(0.0269672\pi\)
\(644\) 0 0
\(645\) −225.010 582.825i −0.348853 0.903604i
\(646\) 0 0
\(647\) 470.864i 0.727765i 0.931445 + 0.363883i \(0.118549\pi\)
−0.931445 + 0.363883i \(0.881451\pi\)
\(648\) 0 0
\(649\) −101.512 −0.156412
\(650\) 0 0
\(651\) −26.2483 21.1722i −0.0403200 0.0325225i
\(652\) 0 0
\(653\) −359.566 267.687i −0.550637 0.409934i 0.285562 0.958360i \(-0.407820\pi\)
−0.836199 + 0.548426i \(0.815227\pi\)
\(654\) 0 0
\(655\) −258.814 170.224i −0.395135 0.259885i
\(656\) 0 0
\(657\) 440.975 + 699.714i 0.671195 + 1.06501i
\(658\) 0 0
\(659\) −92.8169 794.099i −0.140845 1.20501i −0.860051 0.510209i \(-0.829568\pi\)
0.719206 0.694797i \(-0.244506\pi\)
\(660\) 0 0
\(661\) 50.9942 170.332i 0.0771470 0.257689i −0.910712 0.413042i \(-0.864466\pi\)
0.987859 + 0.155353i \(0.0496515\pi\)
\(662\) 0 0
\(663\) 345.571 + 96.2035i 0.521224 + 0.145103i
\(664\) 0 0
\(665\) 21.3706 3.76821i 0.0321362 0.00566649i
\(666\) 0 0
\(667\) 67.2547 381.421i 0.100832 0.571845i
\(668\) 0 0
\(669\) −176.305 549.893i −0.263534 0.821963i
\(670\) 0 0
\(671\) −1.03463 1.57307i −0.00154192 0.00234437i
\(672\) 0 0
\(673\) 42.0757 + 140.542i 0.0625195 + 0.208830i 0.983542 0.180680i \(-0.0578297\pi\)
−0.921022 + 0.389509i \(0.872645\pi\)
\(674\) 0 0
\(675\) −356.644 62.9071i −0.528362 0.0931957i
\(676\) 0 0
\(677\) 667.218 + 629.488i 0.985551 + 0.929820i 0.997539 0.0701086i \(-0.0223346\pi\)
−0.0119883 + 0.999928i \(0.503816\pi\)
\(678\) 0 0
\(679\) 4.49687 + 77.2083i 0.00662279 + 0.113709i
\(680\) 0 0
\(681\) 480.571 + 912.384i 0.705685 + 1.33977i
\(682\) 0 0
\(683\) 15.7714 + 43.3315i 0.0230913 + 0.0634430i 0.950703 0.310104i \(-0.100364\pi\)
−0.927611 + 0.373547i \(0.878142\pi\)
\(684\) 0 0
\(685\) 97.4429 + 35.4663i 0.142252 + 0.0517756i
\(686\) 0 0
\(687\) −739.162 + 506.937i −1.07593 + 0.737899i
\(688\) 0 0
\(689\) 482.655 + 2036.48i 0.700515 + 2.95571i
\(690\) 0 0
\(691\) −326.588 + 757.115i −0.472631 + 1.09568i 0.500564 + 0.865699i \(0.333126\pi\)
−0.973195 + 0.229981i \(0.926133\pi\)
\(692\) 0 0
\(693\) 23.7265 24.1893i 0.0342373 0.0349051i
\(694\) 0 0
\(695\) −466.456 27.1680i −0.671160 0.0390906i
\(696\) 0 0
\(697\) −66.6827 154.588i −0.0956710 0.221790i
\(698\) 0 0
\(699\) 1025.69 618.982i 1.46737 0.885525i
\(700\) 0 0
\(701\) 294.380 169.960i 0.419942 0.242454i −0.275110 0.961413i \(-0.588714\pi\)
0.695053 + 0.718959i \(0.255381\pi\)
\(702\) 0 0
\(703\) 86.9798 150.653i 0.123727 0.214301i
\(704\) 0 0
\(705\) 128.973 112.550i 0.182941 0.159646i
\(706\) 0 0
\(707\) 14.9517 127.920i 0.0211481 0.180934i
\(708\) 0 0
\(709\) −428.776 + 215.339i −0.604762 + 0.303723i −0.724706 0.689058i \(-0.758025\pi\)
0.119945 + 0.992781i \(0.461728\pi\)
\(710\) 0 0
\(711\) 248.464 + 149.962i 0.349457 + 0.210917i
\(712\) 0 0
\(713\) 133.565 99.4355i 0.187328 0.139461i
\(714\) 0 0
\(715\) 140.532 + 148.955i 0.196548 + 0.208329i
\(716\) 0 0
\(717\) 1082.82 + 773.983i 1.51021 + 1.07947i
\(718\) 0 0
\(719\) 803.447 + 957.511i 1.11745 + 1.33173i 0.937474 + 0.348054i \(0.113158\pi\)
0.179976 + 0.983671i \(0.442398\pi\)
\(720\) 0 0
\(721\) 5.08136 + 4.26376i 0.00704765 + 0.00591368i
\(722\) 0 0
\(723\) −286.242 + 700.600i −0.395909 + 0.969018i
\(724\) 0 0
\(725\) −117.248 + 233.460i −0.161722 + 0.322014i
\(726\) 0 0
\(727\) 1207.93 + 286.284i 1.66152 + 0.393788i 0.950829 0.309715i \(-0.100234\pi\)
0.710692 + 0.703503i \(0.248382\pi\)
\(728\) 0 0
\(729\) −435.262 584.798i −0.597067 0.802192i
\(730\) 0 0
\(731\) 78.6446 331.828i 0.107585 0.453937i
\(732\) 0 0
\(733\) −560.163 281.324i −0.764206 0.383799i 0.0236007 0.999721i \(-0.492487\pi\)
−0.787806 + 0.615923i \(0.788783\pi\)
\(734\) 0 0
\(735\) −446.179 182.294i −0.607047 0.248019i
\(736\) 0 0
\(737\) 61.2915 73.0444i 0.0831635 0.0991104i
\(738\) 0 0
\(739\) 559.999 469.895i 0.757780 0.635853i −0.179768 0.983709i \(-0.557535\pi\)
0.937548 + 0.347856i \(0.113090\pi\)
\(740\) 0 0
\(741\) 177.716 248.628i 0.239832 0.335530i
\(742\) 0 0
\(743\) −625.438 + 590.071i −0.841774 + 0.794173i −0.980574 0.196147i \(-0.937157\pi\)
0.138800 + 0.990320i \(0.455675\pi\)
\(744\) 0 0
\(745\) 14.9958 + 20.1428i 0.0201285 + 0.0270373i
\(746\) 0 0
\(747\) 244.166 404.547i 0.326862 0.541562i
\(748\) 0 0
\(749\) 9.78853 + 19.4906i 0.0130688 + 0.0260221i
\(750\) 0 0
\(751\) 600.914 + 70.2368i 0.800152 + 0.0935243i 0.506334 0.862337i \(-0.331000\pi\)
0.293817 + 0.955862i \(0.405074\pi\)
\(752\) 0 0
\(753\) −143.873 164.867i −0.191067 0.218947i
\(754\) 0 0
\(755\) 301.836 + 174.265i 0.399782 + 0.230814i
\(756\) 0 0
\(757\) −307.576 532.737i −0.406309 0.703748i 0.588164 0.808742i \(-0.299851\pi\)
−0.994473 + 0.104994i \(0.966518\pi\)
\(758\) 0 0
\(759\) 86.4439 + 143.243i 0.113892 + 0.188726i
\(760\) 0 0
\(761\) −1221.70 + 526.991i −1.60539 + 0.692498i −0.995025 0.0996221i \(-0.968237\pi\)
−0.610365 + 0.792120i \(0.708977\pi\)
\(762\) 0 0
\(763\) 7.64417 131.245i 0.0100186 0.172012i
\(764\) 0 0
\(765\) 121.912 + 119.580i 0.159363 + 0.156314i
\(766\) 0 0
\(767\) −712.920 307.524i −0.929491 0.400943i
\(768\) 0 0
\(769\) −908.671 + 215.359i −1.18163 + 0.280051i −0.774053 0.633121i \(-0.781773\pi\)
−0.407574 + 0.913172i \(0.633625\pi\)
\(770\) 0 0
\(771\) 816.288 + 1190.23i 1.05874 + 1.54374i
\(772\) 0 0
\(773\) 389.447 1070.00i 0.503813 1.38421i −0.383712 0.923453i \(-0.625354\pi\)
0.887524 0.460761i \(-0.152423\pi\)
\(774\) 0 0
\(775\) −105.545 + 38.4153i −0.136187 + 0.0495682i
\(776\) 0 0
\(777\) 130.519 68.7467i 0.167978 0.0884772i
\(778\) 0 0
\(779\) −143.192 + 8.33998i −0.183815 + 0.0107060i
\(780\) 0 0
\(781\) −167.909 + 177.973i −0.214993 + 0.227879i
\(782\) 0 0
\(783\) −494.183 + 179.836i −0.631141 + 0.229676i
\(784\) 0 0
\(785\) −653.087 + 195.522i −0.831958 + 0.249072i
\(786\) 0 0
\(787\) −384.701 + 253.022i −0.488819 + 0.321501i −0.769880 0.638188i \(-0.779684\pi\)
0.281061 + 0.959690i \(0.409314\pi\)
\(788\) 0 0
\(789\) −938.491 + 300.895i −1.18947 + 0.381363i
\(790\) 0 0
\(791\) 106.508 + 18.7802i 0.134650 + 0.0237424i
\(792\) 0 0
\(793\) −2.50068 14.1821i −0.00315345 0.0178841i
\(794\) 0 0