Properties

Label 324.3.o.a.5.9
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

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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 5.9
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.9

$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

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 −0.834538 0.550950i \(-0.814265\pi\)
0.288457 + 0.957493i \(0.406858\pi\)
\(6\) 0 0
\(7\) −1.12154 + 0.737649i −0.160220 + 0.105378i −0.627087 0.778949i \(-0.715753\pi\)
0.466867 + 0.884328i \(0.345383\pi\)
\(8\) 0 0
\(9\) −8.57013 + 2.74826i −0.952236 + 0.305362i
\(10\) 0 0
\(11\) −0.325590 + 2.78560i −0.0295991 + 0.253237i 0.970335 + 0.241764i \(0.0777260\pi\)
−0.999934 + 0.0114725i \(0.996348\pi\)
\(12\) 0 0
\(13\) 6.15219 + 20.5497i 0.473245 + 1.58075i 0.777966 + 0.628307i \(0.216252\pi\)
−0.304721 + 0.952442i \(0.598563\pi\)
\(14\) 0 0
\(15\) 7.29073 + 7.15043i 0.486049 + 0.476695i
\(16\) 0 0
\(17\) 5.48948 + 0.967944i 0.322911 + 0.0569379i 0.332754 0.943014i \(-0.392022\pi\)
−0.00984318 + 0.999952i \(0.503133\pi\)
\(18\) 0 0
\(19\) 0.824658 + 4.67687i 0.0434031 + 0.246151i 0.998788 0.0492113i \(-0.0156708\pi\)
−0.955385 + 0.295362i \(0.904560\pi\)
\(20\) 0 0
\(21\) 2.70633 + 2.98222i 0.128873 + 0.142011i
\(22\) 0 0
\(23\) 10.9269 16.6136i 0.475084 0.722330i −0.515850 0.856679i \(-0.672524\pi\)
0.990934 + 0.134349i \(0.0428943\pi\)
\(24\) 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 −0.890654 0.454682i \(-0.849753\pi\)
0.402126 + 0.915584i \(0.368271\pi\)
\(30\) 0 0
\(31\) −0.486900 + 8.35975i −0.0157064 + 0.269669i 0.981307 + 0.192447i \(0.0616423\pi\)
−0.997014 + 0.0772226i \(0.975395\pi\)
\(32\) 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 0.167979 0.985791i \(-0.446276\pi\)
0.762334 + 0.647184i \(0.224054\pi\)
\(38\) 0 0
\(39\) 58.0564 27.7620i 1.48862 0.711845i
\(40\) 0 0
\(41\) −6.96530 + 29.3889i −0.169885 + 0.716803i 0.819693 + 0.572804i \(0.194144\pi\)
−0.989578 + 0.143999i \(0.954004\pi\)
\(42\) 0 0
\(43\) 24.2316 + 56.1752i 0.563526 + 1.30640i 0.927093 + 0.374832i \(0.122300\pi\)
−0.363567 + 0.931568i \(0.618441\pi\)
\(44\) 0 0
\(45\) 17.8135 24.9245i 0.395856 0.553877i
\(46\) 0 0
\(47\) 16.7341 0.974651i 0.356045 0.0207373i 0.120810 0.992676i \(-0.461451\pi\)
0.235235 + 0.971938i \(0.424414\pi\)
\(48\) 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 −0.992566 0.121709i \(-0.961162\pi\)
−0.601686 0.798733i \(-0.705504\pi\)
\(54\) 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 0.980968 + 0.194168i \(0.0622007\pi\)
−0.909748 + 0.415161i \(0.863725\pi\)
\(60\) 0 0
\(61\) 0.599932 + 0.301297i 0.00983495 + 0.00493930i 0.453710 0.891149i \(-0.350100\pi\)
−0.443875 + 0.896089i \(0.646397\pi\)
\(62\) 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 −0.529455 0.848338i \(-0.677604\pi\)
0.877688 + 0.479233i \(0.159085\pi\)
\(68\) 0 0
\(69\) −54.3079 24.6847i −0.787071 0.357749i
\(70\) 0 0
\(71\) −56.0789 + 66.8323i −0.789844 + 0.941299i −0.999333 0.0365116i \(-0.988375\pi\)
0.209489 + 0.977811i \(0.432820\pi\)
\(72\) 0 0
\(73\) −70.3977 + 59.0707i −0.964352 + 0.809187i −0.981656 0.190663i \(-0.938936\pi\)
0.0173037 + 0.999850i \(0.494492\pi\)
\(74\) 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 −0.424348 0.905499i \(-0.639497\pi\)
0.0271762 + 0.999631i \(0.491348\pi\)
\(80\) 0 0
\(81\) 65.8941 47.1059i 0.813508 0.581554i
\(82\) 0 0
\(83\) −12.1078 51.0870i −0.145878 0.615506i −0.996034 0.0889756i \(-0.971641\pi\)
0.850156 0.526531i \(-0.176507\pi\)
\(84\) 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 −0.999686 0.0250510i \(-0.992025\pi\)
0.148923 0.988849i \(-0.452419\pi\)
\(90\) 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 −0.943277 0.332006i \(-0.892275\pi\)
0.588593 + 0.808430i \(0.299682\pi\)
\(98\) 0 0
\(99\) −4.86521 24.7678i −0.0491436 0.250179i
\(100\) 0 0
\(101\) 43.0589 85.7373i 0.426325 0.848884i −0.573239 0.819388i \(-0.694314\pi\)
0.999565 0.0294959i \(-0.00939018\pi\)
\(102\) 0 0
\(103\) −4.90799 + 0.573662i −0.0476504 + 0.00556953i −0.139885 0.990168i \(-0.544673\pi\)
0.0922343 + 0.995737i \(0.470599\pi\)
\(104\) 0 0
\(105\) −13.4514 2.64150i −0.128108 0.0251571i
\(106\) 0 0
\(107\) −14.0709 + 8.12382i −0.131503 + 0.0759235i −0.564309 0.825564i \(-0.690857\pi\)
0.432805 + 0.901488i \(0.357524\pi\)
\(108\) 0 0
\(109\) 48.9682 84.8154i 0.449249 0.778123i −0.549088 0.835765i \(-0.685025\pi\)
0.998337 + 0.0576419i \(0.0183582\pi\)
\(110\) 0 0
\(111\) −53.0921 96.2159i −0.478307 0.866809i
\(112\) 0 0
\(113\) −73.9777 31.9109i −0.654670 0.282397i 0.0427221 0.999087i \(-0.486397\pi\)
−0.697392 + 0.716690i \(0.745656\pi\)
\(114\) 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 0.452703 0.891662i \(-0.350460\pi\)
−0.226359 + 0.974044i \(0.572682\pi\)
\(128\) 0 0
\(129\) 155.267 97.8651i 1.20362 0.758644i
\(130\) 0 0
\(131\) 90.8501 + 5.29142i 0.693512 + 0.0403925i 0.401281 0.915955i \(-0.368565\pi\)
0.292231 + 0.956348i \(0.405602\pi\)
\(132\) 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 0.178516 0.983937i \(-0.442870\pi\)
−0.391535 + 0.920163i \(0.628056\pi\)
\(138\) 0 0
\(139\) 114.683 + 75.4283i 0.825059 + 0.542650i 0.890382 0.455214i \(-0.150437\pi\)
−0.0653230 + 0.997864i \(0.520808\pi\)
\(140\) 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 −0.310431 0.950596i \(-0.600473\pi\)
0.263000 + 0.964796i \(0.415288\pi\)
\(150\) 0 0
\(151\) −101.697 11.8866i −0.673488 0.0787195i −0.227527 0.973772i \(-0.573064\pi\)
−0.445961 + 0.895052i \(0.647138\pi\)
\(152\) 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 0.998664 + 0.0516804i \(0.0164577\pi\)
−0.236911 + 0.971531i \(0.576135\pi\)
\(158\) 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 −0.854563 0.519347i \(-0.826175\pi\)
0.252438 + 0.967613i \(0.418768\pi\)
\(168\) 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 −0.995003 0.0998416i \(-0.968166\pi\)
0.991208 + 0.132313i \(0.0422405\pi\)
\(174\) 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 0.762257 0.647274i \(-0.224091\pi\)
0.494907 + 0.868946i \(0.335202\pi\)
\(180\) 0 0
\(181\) −29.2518 165.895i −0.161612 0.916549i −0.952489 0.304574i \(-0.901486\pi\)
0.790876 0.611976i \(-0.209625\pi\)
\(182\) 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 0.593383 0.804921i \(-0.297792\pi\)
0.838061 0.545577i \(-0.183689\pi\)
\(192\) 0 0
\(193\) −12.1104 + 207.928i −0.0627482 + 1.07734i 0.809132 + 0.587626i \(0.199938\pi\)
−0.871881 + 0.489719i \(0.837100\pi\)
\(194\) 0 0
\(195\) −102.085 + 193.813i −0.523515 + 0.993915i
\(196\) 0 0
\(197\) −76.7979 + 211.001i −0.389837 + 1.07107i 0.577238 + 0.816576i \(0.304131\pi\)
−0.967075 + 0.254492i \(0.918092\pi\)
\(198\) 0 0
\(199\) −68.4585 + 24.9169i −0.344013 + 0.125210i −0.508248 0.861211i \(-0.669707\pi\)
0.164235 + 0.986421i \(0.447484\pi\)
\(200\) 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 −0.612336 0.790598i \(-0.709770\pi\)
0.995270 0.0971438i \(-0.0309707\pi\)
\(212\) 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 0.0191673 0.999816i \(-0.493898\pi\)
−0.790530 + 0.612423i \(0.790195\pi\)
\(224\) 0 0
\(225\) −2.34547 120.694i −0.0104243 0.536417i
\(226\) 0 0
\(227\) 275.719 + 205.265i 1.21462 + 0.904252i 0.997414 0.0718729i \(-0.0228976\pi\)
0.217208 + 0.976125i \(0.430305\pi\)
\(228\) 0 0
\(229\) 205.025 217.314i 0.895306 0.948969i −0.103652 0.994614i \(-0.533053\pi\)
0.998958 + 0.0456449i \(0.0145343\pi\)
\(230\) 0 0
\(231\) −9.18843 + 6.56776i −0.0397768 + 0.0284319i
\(232\) 0 0
\(233\) −256.685 + 305.905i −1.10165 + 1.31290i −0.155984 + 0.987760i \(0.549855\pi\)
−0.945667 + 0.325137i \(0.894590\pi\)
\(234\) 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 0.749135 + 0.662418i \(0.230470\pi\)
0.0839882 + 0.996467i \(0.473234\pi\)
\(240\) 0 0
\(241\) 245.473 58.1781i 1.01856 0.241403i 0.312773 0.949828i \(-0.398742\pi\)
0.705786 + 0.708425i \(0.250594\pi\)
\(242\) 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 0.664520 0.747270i \(-0.268636\pi\)
−0.851310 + 0.524663i \(0.824191\pi\)
\(252\) 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 0.922425 + 0.386177i \(0.126204\pi\)
0.439157 + 0.898410i \(0.355277\pi\)
\(258\) 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 −0.417610 0.908626i \(-0.637132\pi\)
0.978210 0.207619i \(-0.0665714\pi\)
\(264\) 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 −0.467082 0.884214i \(-0.654695\pi\)
0.532211 + 0.846612i \(0.321361\pi\)
\(270\) 0 0
\(271\) 200.845 347.873i 0.741124 1.28366i −0.210860 0.977516i \(-0.567626\pi\)
0.951984 0.306148i \(-0.0990404\pi\)
\(272\) 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 0.837131 + 0.547003i \(0.184231\pi\)
−0.767967 + 0.640489i \(0.778732\pi\)
\(278\) 0 0
\(279\) −18.8020 72.9822i −0.0673906 0.261585i
\(280\) 0 0
\(281\) −2.06475 + 0.890644i −0.00734785 + 0.00316955i −0.399751 0.916624i \(-0.630903\pi\)
0.392403 + 0.919794i \(0.371644\pi\)
\(282\) 0 0
\(283\) 41.7414 + 9.89290i 0.147496 + 0.0349572i 0.303701 0.952768i \(-0.401778\pi\)
−0.156204 + 0.987725i \(0.549926\pi\)
\(284\) 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 0.540713 0.841207i \(-0.318154\pi\)
0.439399 + 0.898292i \(0.355192\pi\)
\(294\) 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 −0.563373 0.826203i \(-0.690496\pi\)
0.811975 0.583692i \(-0.198392\pi\)
\(308\) 0 0
\(309\) 3.97572 + 14.2811i 0.0128664 + 0.0462173i
\(310\) 0 0
\(311\) 144.598 43.2899i 0.464946 0.139196i −0.0457573 0.998953i \(-0.514570\pi\)
0.510704 + 0.859757i \(0.329385\pi\)
\(312\) 0 0
\(313\) −300.097 35.0763i −0.958775 0.112065i −0.377712 0.925923i \(-0.623289\pi\)
−0.581063 + 0.813858i \(0.697363\pi\)
\(314\) 0 0
\(315\) −1.59306 + 41.0940i −0.00505733 + 0.130457i
\(316\) 0 0
\(317\) −159.614 242.682i −0.503516 0.765558i 0.490886 0.871224i \(-0.336673\pi\)
−0.994402 + 0.105665i \(0.966303\pi\)
\(318\) 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 −0.583733 0.811946i \(-0.698408\pi\)
0.514337 + 0.857588i \(0.328038\pi\)
\(332\) 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 0.957775 0.287518i \(-0.0928301\pi\)
−0.958203 + 0.286088i \(0.907645\pi\)
\(338\) 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 −0.734824 0.678257i \(-0.762735\pi\)
0.913836 + 0.406084i \(0.133106\pi\)
\(348\) 0 0
\(349\) 13.2984 44.4199i 0.0381044 0.127278i −0.936821 0.349809i \(-0.886247\pi\)
0.974926 + 0.222531i \(0.0714318\pi\)
\(350\) 0 0
\(351\) −421.253 + 397.478i −1.20015 + 1.13241i
\(352\) 0 0
\(353\) −17.3182 + 16.3388i −0.0490599 + 0.0462857i −0.710381 0.703817i \(-0.751477\pi\)
0.661321 + 0.750103i \(0.269996\pi\)
\(354\) 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 −0.324431 0.945909i \(-0.605173\pi\)
0.856547 0.516069i \(-0.172605\pi\)
\(360\) 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 −0.985053 0.172253i \(-0.944895\pi\)
0.550692 0.834708i \(-0.314364\pi\)
\(368\) 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 0.105414 + 0.994428i \(0.466383\pi\)
−0.795660 + 0.605743i \(0.792876\pi\)
\(374\) 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 −0.999655 0.0262660i \(-0.991638\pi\)
0.477080 0.878860i \(-0.341695\pi\)
\(380\) 0 0
\(381\) 17.6838 90.0517i 0.0464141 0.236356i
\(382\) 0 0
\(383\) 71.1395 + 608.637i 0.185743 + 1.58913i 0.688848 + 0.724906i \(0.258117\pi\)
−0.503105 + 0.864225i \(0.667809\pi\)
\(384\) 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 0.402213 0.915546i \(-0.368241\pi\)
−0.761727 + 0.647898i \(0.775648\pi\)
\(390\) 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 −0.481361 0.876522i \(-0.659857\pi\)
0.779619 + 0.626255i \(0.215413\pi\)
\(398\) 0 0
\(399\) −11.7157 + 15.1164i −0.0293626 + 0.0378858i
\(400\) 0 0
\(401\) 76.5653 + 152.454i 0.190936 + 0.380185i 0.968648 0.248435i \(-0.0799164\pi\)
−0.777713 + 0.628620i \(0.783620\pi\)
\(402\) 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 −0.254105 0.967177i \(-0.581781\pi\)
0.624054 + 0.781381i \(0.285485\pi\)
\(410\) 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 −0.999083 0.0428165i \(-0.986367\pi\)
−0.100836 0.994903i \(-0.532152\pi\)
\(420\) 0 0
\(421\) −111.277 + 149.470i −0.264315 + 0.355036i −0.914391 0.404833i \(-0.867330\pi\)
0.650076 + 0.759869i \(0.274737\pi\)
\(422\) 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 −0.896948 0.442136i \(-0.854221\pi\)
−0.0655726 + 0.997848i \(0.520887\pi\)
\(432\) 0 0
\(433\) 408.999 708.407i 0.944571 1.63604i 0.187962 0.982176i \(-0.439812\pi\)
0.756608 0.653868i \(-0.226855\pi\)
\(434\) 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 0.999992 + 0.00408775i \(0.00130117\pi\)
−0.992756 + 0.120152i \(0.961662\pi\)
\(440\) 0 0
\(441\) 41.1074 422.788i 0.0932140 0.958704i
\(442\) 0 0
\(443\) −77.9496 + 33.6242i −0.175959 + 0.0759011i −0.482237 0.876041i \(-0.660175\pi\)
0.306278 + 0.951942i \(0.400916\pi\)
\(444\) 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 0.686788 + 0.726858i \(0.259020\pi\)
−0.0588949 + 0.998264i \(0.518758\pi\)
\(450\) 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 0.814270 0.580486i \(-0.197137\pi\)
−0.626850 + 0.779140i \(0.715656\pi\)
\(458\) 0 0
\(459\) 43.1729 + 144.177i 0.0940586 + 0.314112i
\(460\) 0 0
\(461\) 478.686 + 143.309i 1.03837 + 0.310866i 0.760215 0.649671i \(-0.225094\pi\)
0.278150 + 0.960538i \(0.410279\pi\)
\(462\) 0 0
\(463\) −550.479 362.056i −1.18894 0.781978i −0.208351 0.978054i \(-0.566810\pi\)
−0.980589 + 0.196076i \(0.937180\pi\)
\(464\) 0 0
\(465\) −63.3256 + 57.4672i −0.136184 + 0.123585i
\(466\) 0 0
\(467\) 590.932 104.197i 1.26538 0.223121i 0.499618 0.866246i \(-0.333474\pi\)
0.765761 + 0.643125i \(0.222363\pi\)
\(468\) 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 0.778897 0.627151i \(-0.215779\pi\)
−0.884366 + 0.466794i \(0.845409\pi\)
\(480\) 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 −0.399863 0.916575i \(-0.630942\pi\)
0.763387 + 0.645941i \(0.223535\pi\)
\(492\) 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 −0.975987 0.217828i \(-0.930103\pi\)
0.695727 0.718306i \(-0.255082\pi\)
\(500\) 0 0
\(501\) 268.502 + 263.335i 0.535932 + 0.525618i
\(502\) 0 0
\(503\) −587.794 103.644i −1.16858 0.206052i −0.444506 0.895776i \(-0.646621\pi\)
−0.724072 + 0.689724i \(0.757732\pi\)
\(504\) 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 −0.713868 0.700280i \(-0.753058\pi\)
0.925757 + 0.378119i \(0.123429\pi\)
\(510\) 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 −0.598631 0.801025i \(-0.704289\pi\)
0.973467 0.228828i \(-0.0734893\pi\)
\(522\) 0 0
\(523\) 169.881 61.8316i 0.324820 0.118225i −0.174463 0.984664i \(-0.555819\pi\)
0.499283 + 0.866439i \(0.333597\pi\)
\(524\) 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 0.890246 0.455479i \(-0.150532\pi\)
−0.839580 + 0.543236i \(0.817199\pi\)
\(542\) 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 0.989262 0.146152i \(-0.0466888\pi\)
0.473515 + 0.880786i \(0.342985\pi\)
\(548\) 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 −0.862905 0.505367i \(-0.831357\pi\)
0.647531 + 0.762039i \(0.275802\pi\)
\(558\) 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 0.979191 + 0.202939i \(0.0650493\pi\)
−0.421951 + 0.906619i \(0.638654\pi\)
\(564\) 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 0.994246 0.107117i \(-0.0341619\pi\)
−0.936565 + 0.350494i \(0.886014\pi\)
\(570\) 0 0
\(571\) −555.691 + 279.078i −0.973189 + 0.488754i −0.863026 0.505160i \(-0.831434\pi\)
−0.110163 + 0.993914i \(0.535137\pi\)
\(572\) 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 0.924468 + 0.381259i \(0.124509\pi\)
0.535999 + 0.844219i \(0.319935\pi\)
\(578\) 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 −0.772973 0.634439i \(-0.781231\pi\)
0.970486 + 0.241158i \(0.0775274\pi\)
\(588\) 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 −0.650177 + 0.759783i \(0.725305\pi\)
−0.983080 + 0.183178i \(0.941361\pi\)
\(594\) 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 −0.516731 0.856148i \(-0.672851\pi\)
−0.977342 + 0.211667i \(0.932111\pi\)
\(600\) 0 0
\(601\) 29.7319 + 510.476i 0.0494706 + 0.849378i 0.928206 + 0.372068i \(0.121351\pi\)
−0.878735 + 0.477310i \(0.841612\pi\)
\(602\) 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 0.320678 0.947188i \(-0.396089\pi\)
−0.138529 + 0.990358i \(0.544238\pi\)
\(608\) 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 0.681777 0.731560i \(-0.261208\pi\)
0.0520333 + 0.998645i \(0.483430\pi\)
\(614\) 0 0
\(615\) −260.925 + 164.462i −0.424269 + 0.267418i
\(616\) 0 0
\(617\) −382.002 22.2491i −0.619128 0.0360601i −0.254285 0.967129i \(-0.581840\pi\)
−0.364843 + 0.931069i \(0.618877\pi\)
\(618\) 0 0
\(619\) 650.364 + 689.346i 1.05067 + 1.11364i 0.993332 + 0.115289i \(0.0367795\pi\)
0.0573371 + 0.998355i \(0.481739\pi\)
\(620\) 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 0.609373 + 0.792883i \(0.291421\pi\)
−0.843806 + 0.536649i \(0.819690\pi\)
\(632\) 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 −0.997664 0.0683157i \(-0.978237\pi\)
0.332426 0.943129i \(-0.392133\pi\)
\(642\) 0 0
\(643\) 404.817 + 543.763i 0.629575 + 0.845666i 0.996413 0.0846188i \(-0.0269672\pi\)
−0.366838 + 0.930285i \(0.619560\pi\)
\(644\) 0 0
\(645\) −225.010 + 582.825i −0.348853 + 0.903604i
\(646\) 0 0
\(647\) 470.864i 0.727765i −0.931445 0.363883i \(-0.881451\pi\)
0.931445 0.363883i \(-0.118549\pi\)
\(648\) 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 −0.836199 0.548426i \(-0.815227\pi\)
0.285562 + 0.958360i \(0.407820\pi\)
\(654\) 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 0.719206 + 0.694797i \(0.244506\pi\)
−0.860051 + 0.510209i \(0.829568\pi\)
\(660\) 0 0
\(661\) 50.9942 + 170.332i 0.0771470 + 0.257689i 0.987859 0.155353i \(-0.0496515\pi\)
−0.910712 + 0.413042i \(0.864466\pi\)
\(662\) 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 −0.921022 0.389509i \(-0.872645\pi\)
0.983542 + 0.180680i \(0.0578297\pi\)
\(674\) 0 0
\(675\) −356.644 + 62.9071i −0.528362 + 0.0931957i
\(676\) 0 0
\(677\) 667.218 629.488i 0.985551 0.929820i −0.0119883 0.999928i \(-0.503816\pi\)
0.997539 + 0.0701086i \(0.0223346\pi\)
\(678\) 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 −0.927611 0.373547i \(-0.878142\pi\)
0.950703 + 0.310104i \(0.100364\pi\)
\(684\) 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 −0.973195 0.229981i \(-0.926133\pi\)
0.500564 0.865699i \(-0.333126\pi\)
\(692\) 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 0.695053 0.718959i \(-0.255381\pi\)
−0.275110 + 0.961413i \(0.588714\pi\)
\(702\) 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 0.119945 0.992781i \(-0.461728\pi\)
−0.724706 + 0.689058i \(0.758025\pi\)
\(710\) 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 0.179976 0.983671i \(-0.442398\pi\)
0.937474 0.348054i \(-0.113158\pi\)
\(720\) 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 0.710692 0.703503i \(-0.248382\pi\)
0.950829 + 0.309715i \(0.100234\pi\)
\(728\) 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 −0.787806 0.615923i \(-0.788783\pi\)
0.0236007 + 0.999721i \(0.492487\pi\)
\(734\) 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 0.937548 0.347856i \(-0.113090\pi\)
−0.179768 + 0.983709i \(0.557535\pi\)
\(740\) 0 0
\(741\) 177.716 + 248.628i 0.239832 + 0.335530i
\(742\) 0 0
\(743\) −625.438 590.071i −0.841774 0.794173i 0.138800 0.990320i \(-0.455675\pi\)
−0.980574 + 0.196147i \(0.937157\pi\)
\(744\) 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 0.293817 0.955862i \(-0.405074\pi\)
0.506334 + 0.862337i \(0.331000\pi\)
\(752\) 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 −0.994473 0.104994i \(-0.966518\pi\)
0.588164 + 0.808742i \(0.299851\pi\)
\(758\) 0 0
\(759\) 86.4439 143.243i 0.113892 0.188726i
\(760\) 0 0
\(761\) −1221.70 526.991i −1.60539 0.692498i −0.610365 0.792120i \(-0.708977\pi\)
−0.995025 + 0.0996221i \(0.968237\pi\)
\(762\) 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 −0.407574 0.913172i \(-0.633625\pi\)
−0.774053 + 0.633121i \(0.781773\pi\)
\(770\) 0 0
\(771\) 816.288 1190.23i 1.05874 1.54374i
\(772\) 0 0
\(773\) 389.447 + 1070.00i 0.503813 + 1.38421i 0.887524 + 0.460761i \(0.152423\pi\)
−0.383712 + 0.923453i \(0.625354\pi\)
\(774\) 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 0.281061 0.959690i \(-0.409314\pi\)
−0.769880 + 0.638188i \(0.779684\pi\)
\(788\) 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
\(795\