Properties

Label 315.3.ca.b.37.3
Level 315
Weight 3
Character 315.37
Analytic conductor 8.583
Analytic rank 0
Dimension 64
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.3
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.88660 + 0.773463i) q^{2} +(4.27013 - 2.46536i) q^{4} +(-0.160937 + 4.99741i) q^{5} +(5.19830 - 4.68804i) q^{7} +(-1.96674 + 1.96674i) q^{8} +O(q^{10})\) \(q+(-2.88660 + 0.773463i) q^{2} +(4.27013 - 2.46536i) q^{4} +(-0.160937 + 4.99741i) q^{5} +(5.19830 - 4.68804i) q^{7} +(-1.96674 + 1.96674i) q^{8} +(-3.40075 - 14.5500i) q^{10} +(-6.71313 - 11.6275i) q^{11} +(-3.94411 + 3.94411i) q^{13} +(-11.3794 + 17.5532i) q^{14} +(-5.70544 + 9.88212i) q^{16} +(2.53643 - 9.46609i) q^{17} +(-4.57992 - 2.64422i) q^{19} +(11.6332 + 21.7363i) q^{20} +(28.3716 + 28.3716i) q^{22} +(1.98091 + 7.39285i) q^{23} +(-24.9482 - 1.60854i) q^{25} +(8.33445 - 14.4357i) q^{26} +(10.6397 - 32.8342i) q^{28} -36.7188i q^{29} +(-9.71723 - 16.8307i) q^{31} +(11.7054 - 43.6852i) q^{32} +29.2867i q^{34} +(22.5914 + 26.7325i) q^{35} +(43.7832 - 11.7317i) q^{37} +(15.2656 + 4.09041i) q^{38} +(-9.51208 - 10.1451i) q^{40} -57.9301 q^{41} +(46.3359 - 46.3359i) q^{43} +(-57.3319 - 33.1006i) q^{44} +(-11.4362 - 19.8080i) q^{46} +(61.3721 - 16.4446i) q^{47} +(5.04463 - 48.7396i) q^{49} +(73.2597 - 14.6533i) q^{50} +(-7.11820 + 26.5655i) q^{52} +(38.8830 + 10.4187i) q^{53} +(59.1877 - 31.6770i) q^{55} +(-1.00355 + 19.4438i) q^{56} +(28.4006 + 105.992i) q^{58} +(60.4517 - 34.9018i) q^{59} +(-39.4523 + 68.3334i) q^{61} +(41.0677 + 41.0677i) q^{62} +89.5118i q^{64} +(-19.0756 - 20.3451i) q^{65} +(28.7353 - 107.241i) q^{67} +(-12.5064 - 46.6746i) q^{68} +(-85.8891 - 59.6925i) q^{70} +121.479 q^{71} +(4.70119 + 1.25968i) q^{73} +(-117.311 + 67.7293i) q^{74} -26.0758 q^{76} +(-89.4070 - 28.9718i) q^{77} +(-116.005 - 66.9753i) q^{79} +(-48.4668 - 30.1028i) q^{80} +(167.221 - 44.8068i) q^{82} +(-99.6896 + 99.6896i) q^{83} +(46.8977 + 14.1990i) q^{85} +(-97.9142 + 169.592i) q^{86} +(36.0712 + 9.66526i) q^{88} +(20.5641 + 11.8727i) q^{89} +(-2.01253 + 38.9928i) q^{91} +(26.6847 + 26.6847i) q^{92} +(-164.438 + 94.9381i) q^{94} +(13.9513 - 22.4622i) q^{95} +(-40.9086 - 40.9086i) q^{97} +(23.1364 + 144.594i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.88660 + 0.773463i −1.44330 + 0.386731i −0.893688 0.448688i \(-0.851891\pi\)
−0.549613 + 0.835419i \(0.685225\pi\)
\(3\) 0 0
\(4\) 4.27013 2.46536i 1.06753 0.616340i
\(5\) −0.160937 + 4.99741i −0.0321874 + 0.999482i
\(6\) 0 0
\(7\) 5.19830 4.68804i 0.742614 0.669719i
\(8\) −1.96674 + 1.96674i −0.245842 + 0.245842i
\(9\) 0 0
\(10\) −3.40075 14.5500i −0.340075 1.45500i
\(11\) −6.71313 11.6275i −0.610285 1.05704i −0.991192 0.132431i \(-0.957722\pi\)
0.380907 0.924613i \(-0.375612\pi\)
\(12\) 0 0
\(13\) −3.94411 + 3.94411i −0.303393 + 0.303393i −0.842340 0.538947i \(-0.818822\pi\)
0.538947 + 0.842340i \(0.318822\pi\)
\(14\) −11.3794 + 17.5532i −0.812814 + 1.25380i
\(15\) 0 0
\(16\) −5.70544 + 9.88212i −0.356590 + 0.617632i
\(17\) 2.53643 9.46609i 0.149202 0.556829i −0.850330 0.526249i \(-0.823598\pi\)
0.999532 0.0305799i \(-0.00973539\pi\)
\(18\) 0 0
\(19\) −4.57992 2.64422i −0.241049 0.139169i 0.374610 0.927182i \(-0.377777\pi\)
−0.615659 + 0.788013i \(0.711110\pi\)
\(20\) 11.6332 + 21.7363i 0.581659 + 1.08682i
\(21\) 0 0
\(22\) 28.3716 + 28.3716i 1.28962 + 1.28962i
\(23\) 1.98091 + 7.39285i 0.0861264 + 0.321428i 0.995525 0.0944974i \(-0.0301244\pi\)
−0.909399 + 0.415925i \(0.863458\pi\)
\(24\) 0 0
\(25\) −24.9482 1.60854i −0.997928 0.0643415i
\(26\) 8.33445 14.4357i 0.320556 0.555219i
\(27\) 0 0
\(28\) 10.6397 32.8342i 0.379990 1.17265i
\(29\) 36.7188i 1.26616i −0.774085 0.633082i \(-0.781789\pi\)
0.774085 0.633082i \(-0.218211\pi\)
\(30\) 0 0
\(31\) −9.71723 16.8307i −0.313459 0.542927i 0.665650 0.746264i \(-0.268155\pi\)
−0.979109 + 0.203337i \(0.934821\pi\)
\(32\) 11.7054 43.6852i 0.365794 1.36516i
\(33\) 0 0
\(34\) 29.2867i 0.861373i
\(35\) 22.5914 + 26.7325i 0.645470 + 0.763786i
\(36\) 0 0
\(37\) 43.7832 11.7317i 1.18333 0.317072i 0.387083 0.922045i \(-0.373483\pi\)
0.796246 + 0.604973i \(0.206816\pi\)
\(38\) 15.2656 + 4.09041i 0.401727 + 0.107642i
\(39\) 0 0
\(40\) −9.51208 10.1451i −0.237802 0.253628i
\(41\) −57.9301 −1.41293 −0.706464 0.707749i \(-0.749711\pi\)
−0.706464 + 0.707749i \(0.749711\pi\)
\(42\) 0 0
\(43\) 46.3359 46.3359i 1.07758 1.07758i 0.0808525 0.996726i \(-0.474236\pi\)
0.996726 0.0808525i \(-0.0257643\pi\)
\(44\) −57.3319 33.1006i −1.30300 0.752286i
\(45\) 0 0
\(46\) −11.4362 19.8080i −0.248613 0.430610i
\(47\) 61.3721 16.4446i 1.30579 0.349885i 0.462153 0.886800i \(-0.347077\pi\)
0.843636 + 0.536915i \(0.180410\pi\)
\(48\) 0 0
\(49\) 5.04463 48.7396i 0.102952 0.994686i
\(50\) 73.2597 14.6533i 1.46519 0.293066i
\(51\) 0 0
\(52\) −7.11820 + 26.5655i −0.136889 + 0.510875i
\(53\) 38.8830 + 10.4187i 0.733641 + 0.196578i 0.606250 0.795274i \(-0.292673\pi\)
0.127391 + 0.991853i \(0.459340\pi\)
\(54\) 0 0
\(55\) 59.1877 31.6770i 1.07614 0.575945i
\(56\) −1.00355 + 19.4438i −0.0179206 + 0.347212i
\(57\) 0 0
\(58\) 28.4006 + 105.992i 0.489666 + 1.82746i
\(59\) 60.4517 34.9018i 1.02461 0.591556i 0.109171 0.994023i \(-0.465181\pi\)
0.915434 + 0.402467i \(0.131847\pi\)
\(60\) 0 0
\(61\) −39.4523 + 68.3334i −0.646759 + 1.12022i 0.337133 + 0.941457i \(0.390543\pi\)
−0.983892 + 0.178763i \(0.942790\pi\)
\(62\) 41.0677 + 41.0677i 0.662383 + 0.662383i
\(63\) 0 0
\(64\) 89.5118i 1.39862i
\(65\) −19.0756 20.3451i −0.293470 0.313001i
\(66\) 0 0
\(67\) 28.7353 107.241i 0.428885 1.60062i −0.326407 0.945229i \(-0.605838\pi\)
0.755291 0.655389i \(-0.227495\pi\)
\(68\) −12.5064 46.6746i −0.183918 0.686392i
\(69\) 0 0
\(70\) −85.8891 59.6925i −1.22699 0.852750i
\(71\) 121.479 1.71097 0.855486 0.517826i \(-0.173259\pi\)
0.855486 + 0.517826i \(0.173259\pi\)
\(72\) 0 0
\(73\) 4.70119 + 1.25968i 0.0643998 + 0.0172559i 0.290875 0.956761i \(-0.406054\pi\)
−0.226475 + 0.974017i \(0.572720\pi\)
\(74\) −117.311 + 67.7293i −1.58528 + 0.915261i
\(75\) 0 0
\(76\) −26.0758 −0.343103
\(77\) −89.4070 28.9718i −1.16113 0.376257i
\(78\) 0 0
\(79\) −116.005 66.9753i −1.46841 0.847788i −0.469039 0.883177i \(-0.655400\pi\)
−0.999374 + 0.0353889i \(0.988733\pi\)
\(80\) −48.4668 30.1028i −0.605835 0.376285i
\(81\) 0 0
\(82\) 167.221 44.8068i 2.03928 0.546424i
\(83\) −99.6896 + 99.6896i −1.20108 + 1.20108i −0.227242 + 0.973838i \(0.572971\pi\)
−0.973838 + 0.227242i \(0.927029\pi\)
\(84\) 0 0
\(85\) 46.8977 + 14.1990i 0.551738 + 0.167047i
\(86\) −97.9142 + 169.592i −1.13854 + 1.97200i
\(87\) 0 0
\(88\) 36.0712 + 9.66526i 0.409900 + 0.109832i
\(89\) 20.5641 + 11.8727i 0.231058 + 0.133401i 0.611060 0.791584i \(-0.290743\pi\)
−0.380002 + 0.924986i \(0.624077\pi\)
\(90\) 0 0
\(91\) −2.01253 + 38.9928i −0.0221158 + 0.428492i
\(92\) 26.6847 + 26.6847i 0.290052 + 0.290052i
\(93\) 0 0
\(94\) −164.438 + 94.9381i −1.74934 + 1.00998i
\(95\) 13.9513 22.4622i 0.146856 0.236444i
\(96\) 0 0
\(97\) −40.9086 40.9086i −0.421738 0.421738i 0.464064 0.885802i \(-0.346391\pi\)
−0.885802 + 0.464064i \(0.846391\pi\)
\(98\) 23.1364 + 144.594i 0.236086 + 1.47545i
\(99\) 0 0
\(100\) −110.498 + 54.6376i −1.10498 + 0.546376i
\(101\) −34.1609 59.1683i −0.338226 0.585825i 0.645873 0.763445i \(-0.276494\pi\)
−0.984099 + 0.177620i \(0.943160\pi\)
\(102\) 0 0
\(103\) 32.8404 + 122.562i 0.318839 + 1.18992i 0.920362 + 0.391067i \(0.127894\pi\)
−0.601524 + 0.798855i \(0.705439\pi\)
\(104\) 15.5141i 0.149174i
\(105\) 0 0
\(106\) −120.298 −1.13489
\(107\) −58.6252 + 15.7086i −0.547899 + 0.146809i −0.522141 0.852859i \(-0.674867\pi\)
−0.0257581 + 0.999668i \(0.508200\pi\)
\(108\) 0 0
\(109\) 18.6575 10.7719i 0.171170 0.0988251i −0.411967 0.911199i \(-0.635158\pi\)
0.583137 + 0.812374i \(0.301825\pi\)
\(110\) −146.350 + 137.218i −1.33046 + 1.24744i
\(111\) 0 0
\(112\) 16.6691 + 78.1175i 0.148831 + 0.697478i
\(113\) −12.3946 + 12.3946i −0.109686 + 0.109686i −0.759820 0.650134i \(-0.774713\pi\)
0.650134 + 0.759820i \(0.274713\pi\)
\(114\) 0 0
\(115\) −37.2639 + 8.70962i −0.324034 + 0.0757358i
\(116\) −90.5250 156.794i −0.780388 1.35167i
\(117\) 0 0
\(118\) −147.505 + 147.505i −1.25004 + 1.25004i
\(119\) −31.1923 61.0985i −0.262120 0.513432i
\(120\) 0 0
\(121\) −29.6323 + 51.3247i −0.244895 + 0.424171i
\(122\) 61.0298 227.766i 0.500244 1.86694i
\(123\) 0 0
\(124\) −82.9877 47.9129i −0.669255 0.386395i
\(125\) 12.0536 124.417i 0.0964288 0.995340i
\(126\) 0 0
\(127\) −21.0785 21.0785i −0.165973 0.165973i 0.619234 0.785207i \(-0.287443\pi\)
−0.785207 + 0.619234i \(0.787443\pi\)
\(128\) −22.4125 83.6445i −0.175097 0.653472i
\(129\) 0 0
\(130\) 70.7998 + 43.9739i 0.544614 + 0.338261i
\(131\) 62.6091 108.442i 0.477932 0.827803i −0.521748 0.853100i \(-0.674720\pi\)
0.999680 + 0.0252971i \(0.00805318\pi\)
\(132\) 0 0
\(133\) −36.2040 + 7.72540i −0.272211 + 0.0580857i
\(134\) 331.789i 2.47604i
\(135\) 0 0
\(136\) 13.6288 + 23.6058i 0.100212 + 0.173572i
\(137\) 9.48345 35.3927i 0.0692222 0.258341i −0.922639 0.385665i \(-0.873972\pi\)
0.991861 + 0.127324i \(0.0406388\pi\)
\(138\) 0 0
\(139\) 84.6491i 0.608986i −0.952515 0.304493i \(-0.901513\pi\)
0.952515 0.304493i \(-0.0984870\pi\)
\(140\) 162.374 + 58.4552i 1.15981 + 0.417537i
\(141\) 0 0
\(142\) −350.662 + 93.9595i −2.46945 + 0.661687i
\(143\) 72.3374 + 19.3828i 0.505856 + 0.135544i
\(144\) 0 0
\(145\) 183.499 + 5.90941i 1.26551 + 0.0407546i
\(146\) −14.5448 −0.0996217
\(147\) 0 0
\(148\) 158.037 158.037i 1.06782 1.06782i
\(149\) −28.2589 16.3153i −0.189657 0.109499i 0.402165 0.915567i \(-0.368258\pi\)
−0.591822 + 0.806069i \(0.701591\pi\)
\(150\) 0 0
\(151\) 78.0454 + 135.179i 0.516857 + 0.895223i 0.999808 + 0.0195756i \(0.00623149\pi\)
−0.482951 + 0.875647i \(0.660435\pi\)
\(152\) 14.2080 3.80702i 0.0934737 0.0250462i
\(153\) 0 0
\(154\) 280.491 + 14.4770i 1.82137 + 0.0940063i
\(155\) 85.6740 45.8523i 0.552735 0.295821i
\(156\) 0 0
\(157\) 17.2166 64.2534i 0.109660 0.409257i −0.889172 0.457573i \(-0.848719\pi\)
0.998832 + 0.0483159i \(0.0153854\pi\)
\(158\) 386.662 + 103.606i 2.44723 + 0.655733i
\(159\) 0 0
\(160\) 216.429 + 65.5272i 1.35268 + 0.409545i
\(161\) 44.9553 + 29.1437i 0.279225 + 0.181017i
\(162\) 0 0
\(163\) −15.1289 56.4617i −0.0928152 0.346391i 0.903864 0.427820i \(-0.140718\pi\)
−0.996679 + 0.0814289i \(0.974052\pi\)
\(164\) −247.369 + 142.818i −1.50835 + 0.870844i
\(165\) 0 0
\(166\) 210.658 364.871i 1.26902 2.19802i
\(167\) 93.0212 + 93.0212i 0.557013 + 0.557013i 0.928456 0.371443i \(-0.121137\pi\)
−0.371443 + 0.928456i \(0.621137\pi\)
\(168\) 0 0
\(169\) 137.888i 0.815905i
\(170\) −146.358 4.71331i −0.860927 0.0277254i
\(171\) 0 0
\(172\) 83.6255 312.095i 0.486195 1.81450i
\(173\) −62.6748 233.906i −0.362282 1.35206i −0.871068 0.491162i \(-0.836572\pi\)
0.508786 0.860893i \(-0.330094\pi\)
\(174\) 0 0
\(175\) −137.229 + 108.596i −0.784166 + 0.620551i
\(176\) 153.206 0.870486
\(177\) 0 0
\(178\) −68.5435 18.3662i −0.385076 0.103181i
\(179\) −228.989 + 132.207i −1.27927 + 0.738585i −0.976713 0.214548i \(-0.931172\pi\)
−0.302553 + 0.953133i \(0.597839\pi\)
\(180\) 0 0
\(181\) 286.020 1.58022 0.790110 0.612965i \(-0.210023\pi\)
0.790110 + 0.612965i \(0.210023\pi\)
\(182\) −24.3501 114.113i −0.133792 0.626996i
\(183\) 0 0
\(184\) −18.4357 10.6439i −0.100194 0.0578471i
\(185\) 51.5816 + 220.690i 0.278819 + 1.19292i
\(186\) 0 0
\(187\) −127.094 + 34.0548i −0.679649 + 0.182111i
\(188\) 221.525 221.525i 1.17832 1.17832i
\(189\) 0 0
\(190\) −22.8983 + 75.6303i −0.120517 + 0.398054i
\(191\) −38.1037 + 65.9976i −0.199496 + 0.345537i −0.948365 0.317181i \(-0.897264\pi\)
0.748869 + 0.662718i \(0.230597\pi\)
\(192\) 0 0
\(193\) −236.585 63.3927i −1.22583 0.328459i −0.412874 0.910788i \(-0.635475\pi\)
−0.812953 + 0.582329i \(0.802142\pi\)
\(194\) 149.728 + 86.4456i 0.771795 + 0.445596i
\(195\) 0 0
\(196\) −98.6195 220.561i −0.503161 1.12531i
\(197\) −136.078 136.078i −0.690750 0.690750i 0.271647 0.962397i \(-0.412432\pi\)
−0.962397 + 0.271647i \(0.912432\pi\)
\(198\) 0 0
\(199\) 107.888 62.2892i 0.542151 0.313011i −0.203799 0.979013i \(-0.565329\pi\)
0.745950 + 0.666002i \(0.231996\pi\)
\(200\) 52.2302 45.9030i 0.261151 0.229515i
\(201\) 0 0
\(202\) 144.373 + 144.373i 0.714720 + 0.714720i
\(203\) −172.139 190.875i −0.847975 0.940272i
\(204\) 0 0
\(205\) 9.32309 289.500i 0.0454785 1.41220i
\(206\) −189.594 328.387i −0.920360 1.59411i
\(207\) 0 0
\(208\) −16.4733 61.4790i −0.0791984 0.295572i
\(209\) 71.0040i 0.339732i
\(210\) 0 0
\(211\) −25.5567 −0.121122 −0.0605610 0.998164i \(-0.519289\pi\)
−0.0605610 + 0.998164i \(0.519289\pi\)
\(212\) 191.721 51.3715i 0.904344 0.242318i
\(213\) 0 0
\(214\) 157.078 90.6889i 0.734008 0.423780i
\(215\) 224.102 + 239.017i 1.04234 + 1.11170i
\(216\) 0 0
\(217\) −129.416 41.9365i −0.596388 0.193256i
\(218\) −45.5252 + 45.5252i −0.208831 + 0.208831i
\(219\) 0 0
\(220\) 174.644 281.184i 0.793836 1.27811i
\(221\) 27.3313 + 47.3393i 0.123671 + 0.214205i
\(222\) 0 0
\(223\) −58.9789 + 58.9789i −0.264479 + 0.264479i −0.826871 0.562392i \(-0.809881\pi\)
0.562392 + 0.826871i \(0.309881\pi\)
\(224\) −143.949 281.964i −0.642631 1.25877i
\(225\) 0 0
\(226\) 26.1914 45.3649i 0.115891 0.200730i
\(227\) −106.629 + 397.945i −0.469732 + 1.75306i 0.170972 + 0.985276i \(0.445309\pi\)
−0.640704 + 0.767788i \(0.721358\pi\)
\(228\) 0 0
\(229\) −325.569 187.967i −1.42170 0.820818i −0.425255 0.905074i \(-0.639816\pi\)
−0.996444 + 0.0842553i \(0.973149\pi\)
\(230\) 100.829 53.9634i 0.438389 0.234624i
\(231\) 0 0
\(232\) 72.2163 + 72.2163i 0.311277 + 0.311277i
\(233\) −6.28523 23.4568i −0.0269752 0.100673i 0.951126 0.308804i \(-0.0999287\pi\)
−0.978101 + 0.208131i \(0.933262\pi\)
\(234\) 0 0
\(235\) 72.3034 + 309.348i 0.307674 + 1.31638i
\(236\) 172.091 298.070i 0.729199 1.26301i
\(237\) 0 0
\(238\) 137.297 + 152.241i 0.576878 + 0.639668i
\(239\) 50.6675i 0.211998i −0.994366 0.105999i \(-0.966196\pi\)
0.994366 0.105999i \(-0.0338040\pi\)
\(240\) 0 0
\(241\) 58.3080 + 100.992i 0.241942 + 0.419055i 0.961267 0.275618i \(-0.0888824\pi\)
−0.719326 + 0.694673i \(0.755549\pi\)
\(242\) 45.8390 171.074i 0.189417 0.706916i
\(243\) 0 0
\(244\) 389.057i 1.59449i
\(245\) 242.760 + 33.0541i 0.990857 + 0.134915i
\(246\) 0 0
\(247\) 28.4928 7.63463i 0.115356 0.0309094i
\(248\) 52.2129 + 13.9904i 0.210536 + 0.0564130i
\(249\) 0 0
\(250\) 61.4383 + 368.467i 0.245753 + 1.47387i
\(251\) −320.629 −1.27741 −0.638704 0.769452i \(-0.720529\pi\)
−0.638704 + 0.769452i \(0.720529\pi\)
\(252\) 0 0
\(253\) 72.6621 72.6621i 0.287202 0.287202i
\(254\) 77.1488 + 44.5419i 0.303736 + 0.175362i
\(255\) 0 0
\(256\) −49.6319 85.9650i −0.193875 0.335801i
\(257\) 191.876 51.4131i 0.746600 0.200051i 0.134591 0.990901i \(-0.457028\pi\)
0.612009 + 0.790850i \(0.290361\pi\)
\(258\) 0 0
\(259\) 172.600 266.242i 0.666407 1.02796i
\(260\) −131.613 39.8480i −0.506204 0.153261i
\(261\) 0 0
\(262\) −96.8516 + 361.455i −0.369663 + 1.37960i
\(263\) 15.3255 + 4.10646i 0.0582720 + 0.0156139i 0.287837 0.957679i \(-0.407064\pi\)
−0.229565 + 0.973293i \(0.573730\pi\)
\(264\) 0 0
\(265\) −58.3240 + 192.637i −0.220091 + 0.726933i
\(266\) 98.5313 50.3026i 0.370418 0.189108i
\(267\) 0 0
\(268\) −141.686 528.778i −0.528677 1.97305i
\(269\) 89.8942 51.9004i 0.334179 0.192938i −0.323516 0.946223i \(-0.604865\pi\)
0.657695 + 0.753284i \(0.271532\pi\)
\(270\) 0 0
\(271\) 78.5571 136.065i 0.289878 0.502084i −0.683902 0.729574i \(-0.739718\pi\)
0.973781 + 0.227490i \(0.0730518\pi\)
\(272\) 79.0736 + 79.0736i 0.290712 + 0.290712i
\(273\) 0 0
\(274\) 109.500i 0.399634i
\(275\) 148.777 + 300.883i 0.541009 + 1.09412i
\(276\) 0 0
\(277\) 54.1211 201.983i 0.195383 0.729179i −0.796784 0.604264i \(-0.793467\pi\)
0.992167 0.124916i \(-0.0398660\pi\)
\(278\) 65.4729 + 244.348i 0.235514 + 0.878950i
\(279\) 0 0
\(280\) −97.0073 8.14441i −0.346455 0.0290872i
\(281\) −454.909 −1.61889 −0.809446 0.587194i \(-0.800232\pi\)
−0.809446 + 0.587194i \(0.800232\pi\)
\(282\) 0 0
\(283\) 99.1636 + 26.5708i 0.350401 + 0.0938898i 0.429727 0.902959i \(-0.358610\pi\)
−0.0793253 + 0.996849i \(0.525277\pi\)
\(284\) 518.731 299.489i 1.82652 1.05454i
\(285\) 0 0
\(286\) −223.801 −0.782522
\(287\) −301.138 + 271.578i −1.04926 + 0.946266i
\(288\) 0 0
\(289\) 167.108 + 96.4798i 0.578228 + 0.333840i
\(290\) −534.259 + 124.871i −1.84227 + 0.430591i
\(291\) 0 0
\(292\) 23.1802 6.21112i 0.0793843 0.0212710i
\(293\) −102.346 + 102.346i −0.349302 + 0.349302i −0.859850 0.510547i \(-0.829443\pi\)
0.510547 + 0.859850i \(0.329443\pi\)
\(294\) 0 0
\(295\) 164.690 + 307.719i 0.558270 + 1.04311i
\(296\) −63.0369 + 109.183i −0.212963 + 0.368862i
\(297\) 0 0
\(298\) 94.1914 + 25.2385i 0.316079 + 0.0846930i
\(299\) −36.9711 21.3453i −0.123649 0.0713889i
\(300\) 0 0
\(301\) 23.6435 458.092i 0.0785498 1.52190i
\(302\) −329.842 329.842i −1.09219 1.09219i
\(303\) 0 0
\(304\) 52.2610 30.1729i 0.171911 0.0992529i
\(305\) −335.141 208.157i −1.09882 0.682481i
\(306\) 0 0
\(307\) 29.1999 + 29.1999i 0.0951137 + 0.0951137i 0.753063 0.657949i \(-0.228576\pi\)
−0.657949 + 0.753063i \(0.728576\pi\)
\(308\) −453.205 + 96.7072i −1.47144 + 0.313985i
\(309\) 0 0
\(310\) −211.842 + 198.623i −0.683360 + 0.640719i
\(311\) 201.089 + 348.297i 0.646589 + 1.11992i 0.983932 + 0.178543i \(0.0571384\pi\)
−0.337343 + 0.941382i \(0.609528\pi\)
\(312\) 0 0
\(313\) 74.2751 + 277.198i 0.237301 + 0.885618i 0.977098 + 0.212788i \(0.0682545\pi\)
−0.739798 + 0.672829i \(0.765079\pi\)
\(314\) 198.790i 0.633091i
\(315\) 0 0
\(316\) −660.473 −2.09010
\(317\) 335.924 90.0106i 1.05970 0.283945i 0.313444 0.949607i \(-0.398517\pi\)
0.746254 + 0.665662i \(0.231851\pi\)
\(318\) 0 0
\(319\) −426.947 + 246.498i −1.33839 + 0.772721i
\(320\) −447.327 14.4058i −1.39790 0.0450180i
\(321\) 0 0
\(322\) −152.310 49.3549i −0.473011 0.153276i
\(323\) −36.6471 + 36.6471i −0.113458 + 0.113458i
\(324\) 0 0
\(325\) 104.743 92.0542i 0.322285 0.283244i
\(326\) 87.3421 + 151.281i 0.267921 + 0.464052i
\(327\) 0 0
\(328\) 113.933 113.933i 0.347358 0.347358i
\(329\) 241.938 373.199i 0.735373 1.13434i
\(330\) 0 0
\(331\) −36.2176 + 62.7307i −0.109419 + 0.189519i −0.915535 0.402239i \(-0.868232\pi\)
0.806116 + 0.591757i \(0.201566\pi\)
\(332\) −179.917 + 671.458i −0.541918 + 2.02246i
\(333\) 0 0
\(334\) −340.464 196.567i −1.01935 0.588523i
\(335\) 531.305 + 160.861i 1.58598 + 0.480182i
\(336\) 0 0
\(337\) −255.737 255.737i −0.758865 0.758865i 0.217251 0.976116i \(-0.430291\pi\)
−0.976116 + 0.217251i \(0.930291\pi\)
\(338\) −106.651 398.028i −0.315536 1.17760i
\(339\) 0 0
\(340\) 235.265 54.9881i 0.691956 0.161730i
\(341\) −130.466 + 225.974i −0.382599 + 0.662680i
\(342\) 0 0
\(343\) −202.270 277.013i −0.589707 0.807617i
\(344\) 182.261i 0.529829i
\(345\) 0 0
\(346\) 361.835 + 626.716i 1.04576 + 1.81132i
\(347\) 74.6974 278.775i 0.215266 0.803385i −0.770806 0.637070i \(-0.780146\pi\)
0.986073 0.166315i \(-0.0531869\pi\)
\(348\) 0 0
\(349\) 480.492i 1.37677i 0.725347 + 0.688384i \(0.241680\pi\)
−0.725347 + 0.688384i \(0.758320\pi\)
\(350\) 312.131 419.616i 0.891802 1.19890i
\(351\) 0 0
\(352\) −586.529 + 157.160i −1.66627 + 0.446477i
\(353\) 93.2268 + 24.9800i 0.264098 + 0.0707650i 0.388438 0.921475i \(-0.373015\pi\)
−0.124340 + 0.992240i \(0.539681\pi\)
\(354\) 0 0
\(355\) −19.5505 + 607.080i −0.0550718 + 1.71009i
\(356\) 117.082 0.328882
\(357\) 0 0
\(358\) 558.742 558.742i 1.56073 1.56073i
\(359\) −280.865 162.157i −0.782353 0.451692i 0.0549104 0.998491i \(-0.482513\pi\)
−0.837264 + 0.546799i \(0.815846\pi\)
\(360\) 0 0
\(361\) −166.516 288.415i −0.461264 0.798932i
\(362\) −825.626 + 221.226i −2.28073 + 0.611121i
\(363\) 0 0
\(364\) 87.5375 + 171.466i 0.240488 + 0.471060i
\(365\) −7.05173 + 23.2910i −0.0193198 + 0.0638110i
\(366\) 0 0
\(367\) −66.7783 + 249.220i −0.181957 + 0.679074i 0.813304 + 0.581839i \(0.197667\pi\)
−0.995261 + 0.0972351i \(0.969000\pi\)
\(368\) −84.3589 22.6039i −0.229236 0.0614237i
\(369\) 0 0
\(370\) −319.591 597.149i −0.863760 1.61392i
\(371\) 250.968 128.125i 0.676464 0.345352i
\(372\) 0 0
\(373\) 127.015 + 474.026i 0.340523 + 1.27085i 0.897756 + 0.440492i \(0.145196\pi\)
−0.557234 + 0.830356i \(0.688137\pi\)
\(374\) 340.531 196.605i 0.910510 0.525683i
\(375\) 0 0
\(376\) −88.3607 + 153.045i −0.235002 + 0.407035i
\(377\) 144.823 + 144.823i 0.384145 + 0.384145i
\(378\) 0 0
\(379\) 177.802i 0.469134i −0.972100 0.234567i \(-0.924633\pi\)
0.972100 0.234567i \(-0.0753672\pi\)
\(380\) 4.19656 130.312i 0.0110436 0.342925i
\(381\) 0 0
\(382\) 58.9436 219.981i 0.154303 0.575866i
\(383\) 119.288 + 445.189i 0.311457 + 1.16237i 0.927243 + 0.374460i \(0.122172\pi\)
−0.615786 + 0.787913i \(0.711162\pi\)
\(384\) 0 0
\(385\) 159.173 442.141i 0.413435 1.14842i
\(386\) 731.958 1.89626
\(387\) 0 0
\(388\) −275.540 73.8306i −0.710153 0.190285i
\(389\) −258.574 + 149.288i −0.664714 + 0.383773i −0.794071 0.607825i \(-0.792042\pi\)
0.129357 + 0.991598i \(0.458709\pi\)
\(390\) 0 0
\(391\) 75.0058 0.191831
\(392\) 85.9367 + 105.780i 0.219226 + 0.269846i
\(393\) 0 0
\(394\) 498.053 + 287.551i 1.26409 + 0.729825i
\(395\) 353.372 568.944i 0.894614 1.44036i
\(396\) 0 0
\(397\) 86.8147 23.2619i 0.218677 0.0585943i −0.147817 0.989015i \(-0.547225\pi\)
0.366494 + 0.930420i \(0.380558\pi\)
\(398\) −263.252 + 263.252i −0.661436 + 0.661436i
\(399\) 0 0
\(400\) 158.236 237.364i 0.395591 0.593409i
\(401\) 48.6620 84.2851i 0.121352 0.210187i −0.798949 0.601398i \(-0.794610\pi\)
0.920301 + 0.391211i \(0.127944\pi\)
\(402\) 0 0
\(403\) 104.708 + 28.0565i 0.259822 + 0.0696190i
\(404\) −291.743 168.438i −0.722135 0.416925i
\(405\) 0 0
\(406\) 644.532 + 417.838i 1.58752 + 1.02916i
\(407\) −430.332 430.332i −1.05733 1.05733i
\(408\) 0 0
\(409\) 232.510 134.240i 0.568485 0.328215i −0.188059 0.982158i \(-0.560220\pi\)
0.756544 + 0.653943i \(0.226886\pi\)
\(410\) 197.006 + 842.883i 0.480502 + 2.05581i
\(411\) 0 0
\(412\) 442.392 + 442.392i 1.07377 + 1.07377i
\(413\) 150.625 464.830i 0.364710 1.12550i
\(414\) 0 0
\(415\) −482.146 514.234i −1.16180 1.23912i
\(416\) 126.132 + 218.466i 0.303201 + 0.525160i
\(417\) 0 0
\(418\) −54.9190 204.960i −0.131385 0.490336i
\(419\) 515.863i 1.23118i −0.788068 0.615588i \(-0.788919\pi\)
0.788068 0.615588i \(-0.211081\pi\)
\(420\) 0 0
\(421\) −470.236 −1.11695 −0.558475 0.829521i \(-0.688613\pi\)
−0.558475 + 0.829521i \(0.688613\pi\)
\(422\) 73.7721 19.7672i 0.174815 0.0468417i
\(423\) 0 0
\(424\) −96.9634 + 55.9819i −0.228687 + 0.132033i
\(425\) −78.5060 + 232.082i −0.184720 + 0.546075i
\(426\) 0 0
\(427\) 115.265 + 540.172i 0.269941 + 1.26504i
\(428\) −211.610 + 211.610i −0.494416 + 0.494416i
\(429\) 0 0
\(430\) −831.764 516.611i −1.93434 1.20142i
\(431\) 135.577 + 234.827i 0.314564 + 0.544841i 0.979345 0.202198i \(-0.0648083\pi\)
−0.664781 + 0.747039i \(0.731475\pi\)
\(432\) 0 0
\(433\) −135.694 + 135.694i −0.313381 + 0.313381i −0.846218 0.532837i \(-0.821126\pi\)
0.532837 + 0.846218i \(0.321126\pi\)
\(434\) 406.009 + 20.9554i 0.935506 + 0.0482842i
\(435\) 0 0
\(436\) 53.1134 91.9950i 0.121820 0.210998i
\(437\) 10.4759 39.0966i 0.0239723 0.0894660i
\(438\) 0 0
\(439\) 406.331 + 234.596i 0.925584 + 0.534386i 0.885412 0.464806i \(-0.153876\pi\)
0.0401720 + 0.999193i \(0.487209\pi\)
\(440\) −54.1064 + 178.707i −0.122969 + 0.406153i
\(441\) 0 0
\(442\) −115.510 115.510i −0.261335 0.261335i
\(443\) −79.5993 297.069i −0.179682 0.670584i −0.995707 0.0925661i \(-0.970493\pi\)
0.816024 0.578018i \(-0.196174\pi\)
\(444\) 0 0
\(445\) −62.6423 + 100.857i −0.140769 + 0.226644i
\(446\) 124.631 215.867i 0.279441 0.484006i
\(447\) 0 0
\(448\) 419.635 + 465.309i 0.936685 + 1.03864i
\(449\) 556.174i 1.23870i 0.785117 + 0.619348i \(0.212603\pi\)
−0.785117 + 0.619348i \(0.787397\pi\)
\(450\) 0 0
\(451\) 388.892 + 673.581i 0.862289 + 1.49353i
\(452\) −22.3693 + 83.4834i −0.0494896 + 0.184698i
\(453\) 0 0
\(454\) 1231.18i 2.71186i
\(455\) −194.539 16.3328i −0.427558 0.0358964i
\(456\) 0 0
\(457\) 496.047 132.915i 1.08544 0.290843i 0.328618 0.944463i \(-0.393417\pi\)
0.756823 + 0.653620i \(0.226750\pi\)
\(458\) 1085.17 + 290.772i 2.36938 + 0.634872i
\(459\) 0 0
\(460\) −137.649 + 129.060i −0.299237 + 0.280565i
\(461\) 140.261 0.304254 0.152127 0.988361i \(-0.451388\pi\)
0.152127 + 0.988361i \(0.451388\pi\)
\(462\) 0 0
\(463\) −440.572 + 440.572i −0.951560 + 0.951560i −0.998880 0.0473198i \(-0.984932\pi\)
0.0473198 + 0.998880i \(0.484932\pi\)
\(464\) 362.859 + 209.497i 0.782024 + 0.451502i
\(465\) 0 0
\(466\) 36.2859 + 62.8490i 0.0778667 + 0.134869i
\(467\) 428.655 114.858i 0.917892 0.245948i 0.231208 0.972904i \(-0.425732\pi\)
0.686684 + 0.726956i \(0.259066\pi\)
\(468\) 0 0
\(469\) −353.377 692.185i −0.753470 1.47587i
\(470\) −447.980 837.041i −0.953150 1.78094i
\(471\) 0 0
\(472\) −50.2500 + 187.535i −0.106462 + 0.397321i
\(473\) −849.829 227.711i −1.79668 0.481419i
\(474\) 0 0
\(475\) 110.008 + 73.3355i 0.231595 + 0.154391i
\(476\) −283.825 183.998i −0.596270 0.386551i
\(477\) 0 0
\(478\) 39.1894 + 146.257i 0.0819862 + 0.305977i
\(479\) 190.500 109.985i 0.397703 0.229614i −0.287789 0.957694i \(-0.592920\pi\)
0.685492 + 0.728080i \(0.259587\pi\)
\(480\) 0 0
\(481\) −126.415 + 218.957i −0.262816 + 0.455211i
\(482\) −246.426 246.426i −0.511257 0.511257i
\(483\) 0 0
\(484\) 292.217i 0.603755i
\(485\) 211.021 197.853i 0.435095 0.407945i
\(486\) 0 0
\(487\) −100.187 + 373.904i −0.205723 + 0.767770i 0.783504 + 0.621386i \(0.213430\pi\)
−0.989228 + 0.146384i \(0.953237\pi\)
\(488\) −56.8016 211.987i −0.116397 0.434399i
\(489\) 0 0
\(490\) −726.318 + 92.3518i −1.48228 + 0.188473i
\(491\) −285.045 −0.580539 −0.290269 0.956945i \(-0.593745\pi\)
−0.290269 + 0.956945i \(0.593745\pi\)
\(492\) 0 0
\(493\) −347.583 93.1347i −0.705037 0.188914i
\(494\) −76.3423 + 44.0763i −0.154539 + 0.0892232i
\(495\) 0 0
\(496\) 221.764 0.447106
\(497\) 631.484 569.498i 1.27059 1.14587i
\(498\) 0 0
\(499\) 439.080 + 253.503i 0.879920 + 0.508022i 0.870632 0.491935i \(-0.163710\pi\)
0.00928793 + 0.999957i \(0.497044\pi\)
\(500\) −255.263 560.995i −0.510527 1.12199i
\(501\) 0 0
\(502\) 925.530 247.995i 1.84368 0.494014i
\(503\) −261.451 + 261.451i −0.519784 + 0.519784i −0.917506 0.397722i \(-0.869801\pi\)
0.397722 + 0.917506i \(0.369801\pi\)
\(504\) 0 0
\(505\) 301.186 161.193i 0.596408 0.319195i
\(506\) −153.545 + 265.948i −0.303449 + 0.525589i
\(507\) 0 0
\(508\) −141.974 38.0419i −0.279477 0.0748856i
\(509\) −9.46947 5.46720i −0.0186041 0.0107411i 0.490669 0.871346i \(-0.336752\pi\)
−0.509273 + 0.860605i \(0.670086\pi\)
\(510\) 0 0
\(511\) 30.3436 15.4911i 0.0593808 0.0303153i
\(512\) 454.686 + 454.686i 0.888059 + 0.888059i
\(513\) 0 0
\(514\) −514.104 + 296.818i −1.00020 + 0.577467i
\(515\) −617.777 + 144.392i −1.19957 + 0.280373i
\(516\) 0 0
\(517\) −603.209 603.209i −1.16675 1.16675i
\(518\) −292.298 + 902.033i −0.564282 + 1.74138i
\(519\) 0 0
\(520\) 77.5302 + 2.49679i 0.149096 + 0.00480152i
\(521\) −71.2494 123.408i −0.136755 0.236867i 0.789511 0.613736i \(-0.210334\pi\)
−0.926267 + 0.376869i \(0.877001\pi\)
\(522\) 0 0
\(523\) 8.25954 + 30.8250i 0.0157926 + 0.0589389i 0.973372 0.229229i \(-0.0736205\pi\)
−0.957580 + 0.288168i \(0.906954\pi\)
\(524\) 617.416i 1.17827i
\(525\) 0 0
\(526\) −47.4149 −0.0901424
\(527\) −183.968 + 49.2942i −0.349086 + 0.0935374i
\(528\) 0 0
\(529\) 407.397 235.211i 0.770127 0.444633i
\(530\) 19.3604 601.179i 0.0365291 1.13430i
\(531\) 0 0
\(532\) −135.550 + 122.244i −0.254793 + 0.229783i
\(533\) 228.483 228.483i 0.428673 0.428673i
\(534\) 0 0
\(535\) −69.0672 295.502i −0.129098 0.552341i
\(536\) 154.401 + 267.431i 0.288062 + 0.498938i
\(537\) 0 0
\(538\) −219.346 + 219.346i −0.407706 + 0.407706i
\(539\) −600.585 + 268.539i −1.11426 + 0.498218i
\(540\) 0 0
\(541\) −86.8285 + 150.391i −0.160496 + 0.277988i −0.935047 0.354524i \(-0.884643\pi\)
0.774551 + 0.632512i \(0.217976\pi\)
\(542\) −121.522 + 453.526i −0.224210 + 0.836764i
\(543\) 0 0
\(544\) −383.838 221.609i −0.705584 0.407369i
\(545\) 50.8291 + 94.9729i 0.0932643 + 0.174262i
\(546\) 0 0
\(547\) 95.8716 + 95.8716i 0.175268 + 0.175268i 0.789289 0.614021i \(-0.210449\pi\)
−0.614021 + 0.789289i \(0.710449\pi\)
\(548\) −46.7602 174.511i −0.0853289 0.318452i
\(549\) 0 0
\(550\) −662.183 753.457i −1.20397 1.36992i
\(551\) −97.0925 + 168.169i −0.176211 + 0.305207i
\(552\) 0 0
\(553\) −917.009 + 195.676i −1.65824 + 0.353845i
\(554\) 624.904i 1.12799i
\(555\) 0 0
\(556\) −208.690 361.462i −0.375342 0.650112i
\(557\) −12.5270 + 46.7512i −0.0224900 + 0.0839340i −0.976259 0.216608i \(-0.930501\pi\)
0.953769 + 0.300542i \(0.0971674\pi\)
\(558\) 0 0
\(559\) 365.508i 0.653860i
\(560\) −393.068 + 70.7304i −0.701907 + 0.126304i
\(561\) 0 0
\(562\) 1313.14 351.855i 2.33655 0.626076i
\(563\) −272.294 72.9609i −0.483648 0.129593i 0.00875281 0.999962i \(-0.497214\pi\)
−0.492401 + 0.870369i \(0.663881\pi\)
\(564\) 0 0
\(565\) −59.9460 63.9355i −0.106099 0.113160i
\(566\) −306.797 −0.542045
\(567\) 0 0
\(568\) −238.918 + 238.918i −0.420629 + 0.420629i
\(569\) 466.721 + 269.461i 0.820247 + 0.473570i 0.850502 0.525972i \(-0.176298\pi\)
−0.0302544 + 0.999542i \(0.509632\pi\)
\(570\) 0 0
\(571\) 150.339 + 260.394i 0.263290 + 0.456032i 0.967114 0.254342i \(-0.0818590\pi\)
−0.703824 + 0.710374i \(0.748526\pi\)
\(572\) 356.676 95.5709i 0.623559 0.167082i
\(573\) 0 0
\(574\) 659.210 1016.86i 1.14845 1.77153i
\(575\) −37.5284 187.625i −0.0652668 0.326304i
\(576\) 0 0
\(577\) 72.3090 269.861i 0.125319 0.467697i −0.874532 0.484968i \(-0.838831\pi\)
0.999851 + 0.0172714i \(0.00549794\pi\)
\(578\) −556.998 149.247i −0.963664 0.258213i
\(579\) 0 0
\(580\) 798.132 427.156i 1.37609 0.736477i
\(581\) −50.8680 + 985.565i −0.0875524 + 1.69633i
\(582\) 0 0
\(583\) −139.884 522.053i −0.239938 0.895460i
\(584\) −11.7235 + 6.76855i −0.0200744 + 0.0115900i
\(585\) 0 0
\(586\) 216.271 374.592i 0.369062 0.639235i
\(587\) 210.055 + 210.055i 0.357845 + 0.357845i 0.863018 0.505173i \(-0.168571\pi\)
−0.505173 + 0.863018i \(0.668571\pi\)
\(588\) 0 0
\(589\) 102.778i 0.174496i
\(590\) −713.403 760.881i −1.20916 1.28963i
\(591\) 0 0
\(592\) −133.869 + 499.605i −0.226129 + 0.843927i
\(593\) 271.762 + 1014.23i 0.458284 + 1.71034i 0.678250 + 0.734831i \(0.262739\pi\)
−0.219966 + 0.975508i \(0.570595\pi\)
\(594\) 0 0
\(595\) 310.354 146.047i 0.521603 0.245458i
\(596\) −160.892 −0.269953
\(597\) 0 0
\(598\) 123.231 + 33.0196i 0.206071 + 0.0552167i
\(599\) 516.500 298.201i 0.862270 0.497832i −0.00250190 0.999997i \(-0.500796\pi\)
0.864772 + 0.502165i \(0.167463\pi\)
\(600\) 0 0
\(601\) −480.552 −0.799588 −0.399794 0.916605i \(-0.630918\pi\)
−0.399794 + 0.916605i \(0.630918\pi\)
\(602\) 286.068 + 1340.62i 0.475196 + 2.22694i
\(603\) 0 0
\(604\) 666.528 + 384.820i 1.10352 + 0.637119i
\(605\) −251.722 156.345i −0.416069 0.258421i
\(606\) 0 0
\(607\) 822.130 220.289i 1.35441 0.362914i 0.492652 0.870226i \(-0.336028\pi\)
0.861762 + 0.507312i \(0.169361\pi\)
\(608\) −169.123 + 169.123i −0.278163 + 0.278163i
\(609\) 0 0
\(610\) 1128.42 + 341.647i 1.84987 + 0.560077i
\(611\) −177.199 + 306.918i −0.290015 + 0.502320i
\(612\) 0 0
\(613\) 1030.27 + 276.060i 1.68070 + 0.450343i 0.967964 0.251089i \(-0.0807885\pi\)
0.712737 + 0.701431i \(0.247455\pi\)
\(614\) −106.874 61.7035i −0.174061 0.100494i
\(615\) 0 0
\(616\) 232.820 118.860i 0.377955 0.192955i
\(617\) 270.729 + 270.729i 0.438783 + 0.438783i 0.891602 0.452819i \(-0.149582\pi\)
−0.452819 + 0.891602i \(0.649582\pi\)
\(618\) 0 0
\(619\) 136.247 78.6625i 0.220109 0.127080i −0.385892 0.922544i \(-0.626106\pi\)
0.606001 + 0.795464i \(0.292773\pi\)
\(620\) 252.796 407.012i 0.407736 0.656471i
\(621\) 0 0
\(622\) −849.859 849.859i −1.36633 1.36633i
\(623\) 162.558 34.6875i 0.260928 0.0556782i
\(624\) 0 0
\(625\) 619.825 + 80.2602i 0.991720 + 0.128416i
\(626\) −428.805 742.712i −0.684992 1.18644i
\(627\) 0 0
\(628\) −84.8905 316.816i −0.135176 0.504483i
\(629\) 444.212i 0.706219i
\(630\) 0 0
\(631\) −131.406 −0.208250 −0.104125 0.994564i \(-0.533204\pi\)
−0.104125 + 0.994564i \(0.533204\pi\)
\(632\) 359.874 96.4279i 0.569421 0.152576i
\(633\) 0 0
\(634\) −900.060 + 519.650i −1.41965 + 0.819637i
\(635\) 108.730 101.946i 0.171229 0.160545i
\(636\) 0 0
\(637\) 172.338 + 212.131i 0.270546 + 0.333016i
\(638\) 1041.77 1041.77i 1.63287 1.63287i
\(639\) 0 0
\(640\) 421.613 98.5428i 0.658770 0.153973i
\(641\) 128.958 + 223.362i 0.201182 + 0.348458i 0.948910 0.315548i \(-0.102188\pi\)
−0.747727 + 0.664006i \(0.768855\pi\)
\(642\) 0 0
\(643\) 778.940 778.940i 1.21142 1.21142i 0.240854 0.970561i \(-0.422573\pi\)
0.970561 0.240854i \(-0.0774274\pi\)
\(644\) 263.814 + 13.6162i 0.409650 + 0.0211432i
\(645\) 0 0
\(646\) 77.4404 134.131i 0.119877 0.207633i
\(647\) −98.6974 + 368.344i −0.152546 + 0.569310i 0.846757 + 0.531980i \(0.178552\pi\)
−0.999303 + 0.0373301i \(0.988115\pi\)
\(648\) 0 0
\(649\) −811.641 468.601i −1.25060 0.722035i
\(650\) −231.150 + 346.738i −0.355615 + 0.533444i
\(651\) 0 0
\(652\) −203.801 203.801i −0.312578 0.312578i
\(653\) −291.908 1089.41i −0.447026 1.66832i −0.710532 0.703665i \(-0.751546\pi\)
0.263506 0.964658i \(-0.415121\pi\)
\(654\) 0 0
\(655\) 531.854 + 330.336i 0.811990 + 0.504329i
\(656\) 330.517 572.472i 0.503836 0.872670i
\(657\) 0 0
\(658\) −409.723 + 1264.41i −0.622679 + 1.92159i
\(659\) 737.560i 1.11921i −0.828759 0.559605i \(-0.810953\pi\)
0.828759 0.559605i \(-0.189047\pi\)
\(660\) 0 0
\(661\) −166.939 289.147i −0.252555 0.437439i 0.711673 0.702511i \(-0.247938\pi\)
−0.964229 + 0.265072i \(0.914604\pi\)
\(662\) 56.0259 209.092i 0.0846313 0.315848i
\(663\) 0 0
\(664\) 392.127i 0.590553i
\(665\) −32.7804 182.170i −0.0492939 0.273939i
\(666\) 0 0
\(667\) 271.456 72.7365i 0.406981 0.109050i
\(668\) 626.543 + 167.882i 0.937939 + 0.251320i
\(669\) 0 0
\(670\) −1658.09 53.3972i −2.47476 0.0796973i
\(671\) 1059.40 1.57883
\(672\) 0 0
\(673\) −183.139 + 183.139i −0.272123 + 0.272123i −0.829954 0.557831i \(-0.811634\pi\)
0.557831 + 0.829954i \(0.311634\pi\)
\(674\) 936.016 + 540.409i 1.38875 + 0.801794i
\(675\) 0 0
\(676\) 339.943 + 588.799i 0.502875 + 0.871005i
\(677\) 806.946 216.220i 1.19194 0.319380i 0.392290 0.919842i \(-0.371683\pi\)
0.799654 + 0.600461i \(0.205016\pi\)
\(678\) 0 0
\(679\) −404.436 20.8742i −0.595635 0.0307425i
\(680\) −120.161 + 64.3098i −0.176708 + 0.0945733i
\(681\) 0 0
\(682\) 201.821 753.208i 0.295926 1.10441i
\(683\) 909.178 + 243.613i 1.33115 + 0.356681i 0.853145 0.521674i \(-0.174692\pi\)
0.478008 + 0.878355i \(0.341359\pi\)
\(684\) 0 0
\(685\) 175.346 + 53.0887i 0.255979 + 0.0775017i
\(686\) 798.131 + 643.177i 1.16346 + 0.937576i
\(687\) 0 0
\(688\) 193.530 + 722.263i 0.281293 + 1.04980i
\(689\) −194.451 + 112.266i −0.282222 + 0.162941i
\(690\) 0 0
\(691\) −409.191 + 708.740i −0.592172 + 1.02567i 0.401767 + 0.915742i \(0.368396\pi\)
−0.993939 + 0.109931i \(0.964937\pi\)
\(692\) −844.291 844.291i −1.22007 1.22007i
\(693\) 0 0
\(694\) 862.487i 1.24278i
\(695\) 423.026 + 13.6232i 0.608670 + 0.0196017i
\(696\) 0 0
\(697\) −146.936 + 548.371i −0.210812 + 0.786760i
\(698\) −371.643 1386.99i −0.532439 1.98709i
\(699\) 0 0
\(700\) −318.257 + 802.040i −0.454652 + 1.14577i
\(701\) −480.047 −0.684803 −0.342402 0.939554i \(-0.611240\pi\)
−0.342402 + 0.939554i \(0.611240\pi\)
\(702\) 0 0
\(703\) −231.545 62.0422i −0.329366 0.0882535i
\(704\) 1040.80 600.905i 1.47841 0.853558i
\(705\) 0 0
\(706\) −288.430 −0.408541
\(707\) −454.962 147.427i −0.643510 0.208525i
\(708\) 0 0
\(709\) −1211.17 699.271i −1.70828 0.986278i −0.936688 0.350166i \(-0.886125\pi\)
−0.771597 0.636112i \(-0.780542\pi\)
\(710\) −413.120 1767.52i −0.581859 2.48947i
\(711\) 0 0
\(712\) −63.7948 + 17.0938i −0.0895994 + 0.0240081i
\(713\) 105.178 105.178i 0.147515 0.147515i
\(714\) 0 0
\(715\) −108.505 + 358.380i −0.151756 + 0.501231i
\(716\) −651.874 + 1129.08i −0.910438 + 1.57693i
\(717\) 0 0
\(718\) 936.168 + 250.845i 1.30385 + 0.349367i
\(719\) −742.957 428.946i −1.03332 0.596587i −0.115386 0.993321i \(-0.536810\pi\)
−0.917934 + 0.396734i \(0.870144\pi\)
\(720\) 0 0
\(721\) 745.289 + 483.157i 1.03369 + 0.670120i
\(722\) 703.744 + 703.744i 0.974715 + 0.974715i
\(723\) 0 0
\(724\) 1221.34 705.142i 1.68694 0.973953i
\(725\) −59.0635 + 916.067i −0.0814669 + 1.26354i
\(726\) 0 0
\(727\) 8.47406 + 8.47406i 0.0116562 + 0.0116562i 0.712911 0.701255i \(-0.247376\pi\)
−0.701255 + 0.712911i \(0.747376\pi\)
\(728\) −72.7305 80.6468i −0.0999046 0.110779i
\(729\) 0 0
\(730\) 2.34079 72.6862i 0.00320656 0.0995701i
\(731\) −321.092 556.147i −0.439250 0.760804i
\(732\) 0 0
\(733\) −288.580 1076.99i −0.393697 1.46930i −0.823989 0.566606i \(-0.808256\pi\)
0.430292 0.902690i \(-0.358411\pi\)
\(734\) 771.050i 1.05048i
\(735\) 0 0
\(736\) 346.145 0.470306
\(737\) −1439.85 + 385.807i −1.95367 + 0.523483i
\(738\) 0 0
\(739\) −635.156 + 366.708i −0.859481 + 0.496221i −0.863838 0.503769i \(-0.831946\pi\)
0.00435760 + 0.999991i \(0.498613\pi\)
\(740\) 764.341 + 815.209i 1.03289 + 1.10163i
\(741\) 0 0
\(742\) −625.345 + 563.962i −0.842784 + 0.760056i
\(743\) 342.256 342.256i 0.460641 0.460641i −0.438225 0.898865i \(-0.644393\pi\)
0.898865 + 0.438225i \(0.144393\pi\)
\(744\) 0 0
\(745\) 86.0820 138.595i 0.115546 0.186034i
\(746\) −733.284 1270.08i −0.982954 1.70253i
\(747\) 0 0
\(748\) −458.752 + 458.752i −0.613304 + 0.613304i
\(749\) −231.109 + 356.495i −0.308557 + 0.475961i
\(750\) 0 0
\(751\) −217.704 + 377.075i −0.289886 + 0.502097i −0.973782 0.227482i \(-0.926951\pi\)
0.683897 + 0.729579i \(0.260284\pi\)
\(752\) −187.648 + 700.310i −0.249531 + 0.931264i
\(753\) 0 0
\(754\) −530.061 306.031i −0.702999 0.405877i
\(755\) −688.103 + 368.270i −0.911395 + 0.487774i
\(756\) 0 0
\(757\) 136.675 + 136.675i 0.180548 + 0.180548i 0.791595 0.611047i \(-0.209251\pi\)
−0.611047 + 0.791595i \(0.709251\pi\)
\(758\) 137.523 + 513.243i 0.181429 + 0.677101i
\(759\) 0 0
\(760\) 16.7387 + 71.6159i 0.0220246 + 0.0942315i
\(761\) −191.516 + 331.716i −0.251664 + 0.435895i −0.963984 0.265960i \(-0.914311\pi\)
0.712320 + 0.701855i \(0.247644\pi\)
\(762\) 0 0
\(763\) 46.4882 143.463i 0.0609282 0.188025i
\(764\) 375.758i 0.491829i
\(765\) 0 0
\(766\) −688.674 1192.82i −0.899052 1.55720i
\(767\) −100.772 + 376.085i −0.131384 + 0.490332i
\(768\) 0 0
\(769\) 210.497i 0.273729i 0.990590 + 0.136864i \(0.0437024\pi\)
−0.990590 + 0.136864i \(0.956298\pi\)
\(770\) −117.489 + 1399.40i −0.152583 + 1.81740i
\(771\) 0 0
\(772\) −1166.53 + 312.571i −1.51105 + 0.404885i
\(773\) 415.715 + 111.390i 0.537794 + 0.144101i 0.517485 0.855692i \(-0.326868\pi\)
0.0203089 + 0.999794i \(0.493535\pi\)
\(774\) 0 0
\(775\) 215.355 + 435.527i 0.277877 + 0.561971i