Properties

Label 315.3.ca.b.37.13
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 37.13
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.13

$q$-expansion

\(f(q)\) \(=\) \(q+(2.38023 - 0.637781i) q^{2} +(1.79464 - 1.03614i) q^{4} +(-2.91424 + 4.06291i) q^{5} +(-4.25379 + 5.55925i) q^{7} +(-3.35897 + 3.35897i) q^{8} +O(q^{10})\) \(q+(2.38023 - 0.637781i) q^{2} +(1.79464 - 1.03614i) q^{4} +(-2.91424 + 4.06291i) q^{5} +(-4.25379 + 5.55925i) q^{7} +(-3.35897 + 3.35897i) q^{8} +(-4.34532 + 11.5293i) q^{10} +(-4.95365 - 8.57997i) q^{11} +(-14.1612 + 14.1612i) q^{13} +(-6.57942 + 15.9453i) q^{14} +(-9.99739 + 17.3160i) q^{16} +(4.22139 - 15.7544i) q^{17} +(23.3583 + 13.4859i) q^{19} +(-1.02028 + 10.3110i) q^{20} +(-17.2630 - 17.2630i) q^{22} +(-1.79608 - 6.70305i) q^{23} +(-8.01443 - 23.6806i) q^{25} +(-24.6752 + 42.7387i) q^{26} +(-1.87388 + 14.3844i) q^{28} +18.5702i q^{29} +(19.6183 + 33.9798i) q^{31} +(-7.83442 + 29.2385i) q^{32} -40.1915i q^{34} +(-10.1902 - 33.4837i) q^{35} +(42.8463 - 11.4806i) q^{37} +(64.1994 + 17.2022i) q^{38} +(-3.85835 - 23.4360i) q^{40} +55.1266 q^{41} +(-36.0471 + 36.0471i) q^{43} +(-17.7800 - 10.2653i) q^{44} +(-8.55017 - 14.8093i) q^{46} +(-24.5013 + 6.56509i) q^{47} +(-12.8106 - 47.2958i) q^{49} +(-34.1792 - 51.2538i) q^{50} +(-10.7413 + 40.0872i) q^{52} +(-15.4837 - 4.14884i) q^{53} +(49.2957 + 4.87786i) q^{55} +(-4.38501 - 32.9617i) q^{56} +(11.8437 + 44.2013i) q^{58} +(36.0497 - 20.8133i) q^{59} +(-51.6108 + 89.3925i) q^{61} +(68.3677 + 68.3677i) q^{62} -5.38813i q^{64} +(-16.2665 - 98.8047i) q^{65} +(1.98123 - 7.39406i) q^{67} +(-8.74787 - 32.6475i) q^{68} +(-45.6103 - 73.2000i) q^{70} -58.5591 q^{71} +(-19.6506 - 5.26536i) q^{73} +(94.6621 - 54.6532i) q^{74} +55.8931 q^{76} +(68.7699 + 8.95880i) q^{77} +(-47.2373 - 27.2725i) q^{79} +(-41.2185 - 91.0814i) q^{80} +(131.214 - 35.1587i) q^{82} +(-40.8378 + 40.8378i) q^{83} +(51.7067 + 63.0633i) q^{85} +(-62.8103 + 108.791i) q^{86} +(45.4590 + 12.1807i) q^{88} +(49.6991 + 28.6938i) q^{89} +(-18.4869 - 138.964i) q^{91} +(-10.1686 - 10.1686i) q^{92} +(-54.1316 + 31.2529i) q^{94} +(-122.864 + 55.6015i) q^{95} +(37.4558 + 37.4558i) q^{97} +(-60.6565 - 104.405i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.38023 0.637781i 1.19012 0.318891i 0.391184 0.920312i \(-0.372065\pi\)
0.798932 + 0.601422i \(0.205399\pi\)
\(3\) 0 0
\(4\) 1.79464 1.03614i 0.448660 0.259034i
\(5\) −2.91424 + 4.06291i −0.582848 + 0.812581i
\(6\) 0 0
\(7\) −4.25379 + 5.55925i −0.607684 + 0.794179i
\(8\) −3.35897 + 3.35897i −0.419871 + 0.419871i
\(9\) 0 0
\(10\) −4.34532 + 11.5293i −0.434532 + 1.15293i
\(11\) −4.95365 8.57997i −0.450331 0.779997i 0.548075 0.836429i \(-0.315361\pi\)
−0.998406 + 0.0564323i \(0.982027\pi\)
\(12\) 0 0
\(13\) −14.1612 + 14.1612i −1.08932 + 1.08932i −0.0937246 + 0.995598i \(0.529877\pi\)
−0.995598 + 0.0937246i \(0.970123\pi\)
\(14\) −6.57942 + 15.9453i −0.469959 + 1.13895i
\(15\) 0 0
\(16\) −9.99739 + 17.3160i −0.624837 + 1.08225i
\(17\) 4.22139 15.7544i 0.248317 0.926731i −0.723370 0.690460i \(-0.757408\pi\)
0.971687 0.236271i \(-0.0759253\pi\)
\(18\) 0 0
\(19\) 23.3583 + 13.4859i 1.22939 + 0.709787i 0.966902 0.255150i \(-0.0821247\pi\)
0.262485 + 0.964936i \(0.415458\pi\)
\(20\) −1.02028 + 10.3110i −0.0510142 + 0.515550i
\(21\) 0 0
\(22\) −17.2630 17.2630i −0.784680 0.784680i
\(23\) −1.79608 6.70305i −0.0780903 0.291437i 0.915826 0.401575i \(-0.131537\pi\)
−0.993916 + 0.110138i \(0.964871\pi\)
\(24\) 0 0
\(25\) −8.01443 23.6806i −0.320577 0.947222i
\(26\) −24.6752 + 42.7387i −0.949046 + 1.64380i
\(27\) 0 0
\(28\) −1.87388 + 14.3844i −0.0669243 + 0.513727i
\(29\) 18.5702i 0.640350i 0.947358 + 0.320175i \(0.103742\pi\)
−0.947358 + 0.320175i \(0.896258\pi\)
\(30\) 0 0
\(31\) 19.6183 + 33.9798i 0.632847 + 1.09612i 0.986967 + 0.160923i \(0.0514470\pi\)
−0.354120 + 0.935200i \(0.615220\pi\)
\(32\) −7.83442 + 29.2385i −0.244826 + 0.913702i
\(33\) 0 0
\(34\) 40.1915i 1.18210i
\(35\) −10.1902 33.4837i −0.291148 0.956678i
\(36\) 0 0
\(37\) 42.8463 11.4806i 1.15801 0.310288i 0.371839 0.928297i \(-0.378727\pi\)
0.786170 + 0.618010i \(0.212061\pi\)
\(38\) 64.1994 + 17.2022i 1.68946 + 0.452689i
\(39\) 0 0
\(40\) −3.85835 23.4360i −0.0964587 0.585901i
\(41\) 55.1266 1.34455 0.672275 0.740301i \(-0.265317\pi\)
0.672275 + 0.740301i \(0.265317\pi\)
\(42\) 0 0
\(43\) −36.0471 + 36.0471i −0.838304 + 0.838304i −0.988636 0.150331i \(-0.951966\pi\)
0.150331 + 0.988636i \(0.451966\pi\)
\(44\) −17.7800 10.2653i −0.404091 0.233302i
\(45\) 0 0
\(46\) −8.55017 14.8093i −0.185873 0.321942i
\(47\) −24.5013 + 6.56509i −0.521303 + 0.139683i −0.509869 0.860252i \(-0.670306\pi\)
−0.0114339 + 0.999935i \(0.503640\pi\)
\(48\) 0 0
\(49\) −12.8106 47.2958i −0.261440 0.965220i
\(50\) −34.1792 51.2538i −0.683585 1.02508i
\(51\) 0 0
\(52\) −10.7413 + 40.0872i −0.206564 + 0.770907i
\(53\) −15.4837 4.14884i −0.292145 0.0782800i 0.109770 0.993957i \(-0.464989\pi\)
−0.401915 + 0.915677i \(0.631655\pi\)
\(54\) 0 0
\(55\) 49.2957 + 4.87786i 0.896286 + 0.0886884i
\(56\) −4.38501 32.9617i −0.0783038 0.588602i
\(57\) 0 0
\(58\) 11.8437 + 44.2013i 0.204202 + 0.762091i
\(59\) 36.0497 20.8133i 0.611011 0.352767i −0.162350 0.986733i \(-0.551907\pi\)
0.773361 + 0.633966i \(0.218574\pi\)
\(60\) 0 0
\(61\) −51.6108 + 89.3925i −0.846078 + 1.46545i 0.0386035 + 0.999255i \(0.487709\pi\)
−0.884682 + 0.466196i \(0.845624\pi\)
\(62\) 68.3677 + 68.3677i 1.10270 + 1.10270i
\(63\) 0 0
\(64\) 5.38813i 0.0841895i
\(65\) −16.2665 98.8047i −0.250254 1.52007i
\(66\) 0 0
\(67\) 1.98123 7.39406i 0.0295706 0.110359i −0.949563 0.313576i \(-0.898473\pi\)
0.979134 + 0.203217i \(0.0651396\pi\)
\(68\) −8.74787 32.6475i −0.128645 0.480110i
\(69\) 0 0
\(70\) −45.6103 73.2000i −0.651575 1.04571i
\(71\) −58.5591 −0.824776 −0.412388 0.911008i \(-0.635305\pi\)
−0.412388 + 0.911008i \(0.635305\pi\)
\(72\) 0 0
\(73\) −19.6506 5.26536i −0.269186 0.0721282i 0.121701 0.992567i \(-0.461165\pi\)
−0.390887 + 0.920439i \(0.627832\pi\)
\(74\) 94.6621 54.6532i 1.27922 0.738557i
\(75\) 0 0
\(76\) 55.8931 0.735435
\(77\) 68.7699 + 8.95880i 0.893116 + 0.116348i
\(78\) 0 0
\(79\) −47.2373 27.2725i −0.597940 0.345221i 0.170291 0.985394i \(-0.445529\pi\)
−0.768231 + 0.640173i \(0.778863\pi\)
\(80\) −41.2185 91.0814i −0.515231 1.13852i
\(81\) 0 0
\(82\) 131.214 35.1587i 1.60017 0.428765i
\(83\) −40.8378 + 40.8378i −0.492022 + 0.492022i −0.908943 0.416921i \(-0.863109\pi\)
0.416921 + 0.908943i \(0.363109\pi\)
\(84\) 0 0
\(85\) 51.7067 + 63.0633i 0.608314 + 0.741921i
\(86\) −62.8103 + 108.791i −0.730352 + 1.26501i
\(87\) 0 0
\(88\) 45.4590 + 12.1807i 0.516580 + 0.138417i
\(89\) 49.6991 + 28.6938i 0.558416 + 0.322402i 0.752510 0.658581i \(-0.228843\pi\)
−0.194093 + 0.980983i \(0.562176\pi\)
\(90\) 0 0
\(91\) −18.4869 138.964i −0.203153 1.52708i
\(92\) −10.1686 10.1686i −0.110528 0.110528i
\(93\) 0 0
\(94\) −54.1316 + 31.2529i −0.575868 + 0.332478i
\(95\) −122.864 + 55.6015i −1.29330 + 0.585279i
\(96\) 0 0
\(97\) 37.4558 + 37.4558i 0.386142 + 0.386142i 0.873309 0.487167i \(-0.161970\pi\)
−0.487167 + 0.873309i \(0.661970\pi\)
\(98\) −60.6565 104.405i −0.618944 1.06535i
\(99\) 0 0
\(100\) −38.9193 34.1940i −0.389193 0.341940i
\(101\) 63.1499 + 109.379i 0.625247 + 1.08296i 0.988493 + 0.151266i \(0.0483350\pi\)
−0.363246 + 0.931693i \(0.618332\pi\)
\(102\) 0 0
\(103\) −27.2007 101.514i −0.264085 0.985578i −0.962808 0.270186i \(-0.912915\pi\)
0.698724 0.715392i \(-0.253752\pi\)
\(104\) 95.1341i 0.914751i
\(105\) 0 0
\(106\) −39.5008 −0.372649
\(107\) −32.6136 + 8.73879i −0.304800 + 0.0816709i −0.407977 0.912992i \(-0.633766\pi\)
0.103177 + 0.994663i \(0.467099\pi\)
\(108\) 0 0
\(109\) 35.1577 20.2983i 0.322548 0.186223i −0.329980 0.943988i \(-0.607042\pi\)
0.652528 + 0.757765i \(0.273709\pi\)
\(110\) 120.446 19.8294i 1.09497 0.180268i
\(111\) 0 0
\(112\) −53.7371 129.237i −0.479796 1.15390i
\(113\) −106.341 + 106.341i −0.941068 + 0.941068i −0.998358 0.0572893i \(-0.981754\pi\)
0.0572893 + 0.998358i \(0.481754\pi\)
\(114\) 0 0
\(115\) 32.4681 + 12.2370i 0.282331 + 0.106409i
\(116\) 19.2412 + 33.3268i 0.165873 + 0.287300i
\(117\) 0 0
\(118\) 72.5323 72.5323i 0.614680 0.614680i
\(119\) 69.6260 + 90.4838i 0.585092 + 0.760368i
\(120\) 0 0
\(121\) 11.4228 19.7849i 0.0944033 0.163511i
\(122\) −65.8328 + 245.691i −0.539613 + 2.01386i
\(123\) 0 0
\(124\) 70.4154 + 40.6544i 0.567866 + 0.327858i
\(125\) 119.568 + 36.4489i 0.956543 + 0.291591i
\(126\) 0 0
\(127\) 128.619 + 128.619i 1.01275 + 1.01275i 0.999918 + 0.0128332i \(0.00408505\pi\)
0.0128332 + 0.999918i \(0.495915\pi\)
\(128\) −34.7741 129.779i −0.271673 1.01390i
\(129\) 0 0
\(130\) −101.734 224.804i −0.782569 1.72926i
\(131\) 59.4366 102.947i 0.453715 0.785857i −0.544899 0.838502i \(-0.683432\pi\)
0.998613 + 0.0526451i \(0.0167652\pi\)
\(132\) 0 0
\(133\) −174.333 + 72.4885i −1.31078 + 0.545027i
\(134\) 18.8632i 0.140770i
\(135\) 0 0
\(136\) 38.7392 + 67.0982i 0.284847 + 0.493369i
\(137\) 30.9311 115.436i 0.225774 0.842600i −0.756319 0.654203i \(-0.773004\pi\)
0.982093 0.188397i \(-0.0603292\pi\)
\(138\) 0 0
\(139\) 141.309i 1.01661i 0.861176 + 0.508307i \(0.169729\pi\)
−0.861176 + 0.508307i \(0.830271\pi\)
\(140\) −52.9814 49.5329i −0.378439 0.353806i
\(141\) 0 0
\(142\) −139.384 + 37.3479i −0.981580 + 0.263013i
\(143\) 191.652 + 51.3530i 1.34022 + 0.359112i
\(144\) 0 0
\(145\) −75.4488 54.1179i −0.520337 0.373227i
\(146\) −50.1311 −0.343364
\(147\) 0 0
\(148\) 64.9983 64.9983i 0.439177 0.439177i
\(149\) −138.446 79.9316i −0.929165 0.536453i −0.0426173 0.999091i \(-0.513570\pi\)
−0.886547 + 0.462638i \(0.846903\pi\)
\(150\) 0 0
\(151\) 36.6513 + 63.4819i 0.242724 + 0.420410i 0.961489 0.274843i \(-0.0886258\pi\)
−0.718765 + 0.695253i \(0.755292\pi\)
\(152\) −123.759 + 33.1611i −0.814203 + 0.218165i
\(153\) 0 0
\(154\) 169.402 22.5362i 1.10001 0.146339i
\(155\) −195.229 19.3181i −1.25954 0.124633i
\(156\) 0 0
\(157\) −21.2192 + 79.1910i −0.135154 + 0.504401i 0.864843 + 0.502042i \(0.167418\pi\)
−0.999997 + 0.00235945i \(0.999249\pi\)
\(158\) −129.830 34.7877i −0.821706 0.220175i
\(159\) 0 0
\(160\) −95.9618 117.038i −0.599761 0.731490i
\(161\) 44.9041 + 18.5285i 0.278907 + 0.115084i
\(162\) 0 0
\(163\) −11.9897 44.7462i −0.0735564 0.274516i 0.919346 0.393451i \(-0.128719\pi\)
−0.992902 + 0.118934i \(0.962052\pi\)
\(164\) 98.9324 57.1187i 0.603246 0.348284i
\(165\) 0 0
\(166\) −71.1579 + 123.249i −0.428662 + 0.742464i
\(167\) −60.5283 60.5283i −0.362445 0.362445i 0.502267 0.864712i \(-0.332499\pi\)
−0.864712 + 0.502267i \(0.832499\pi\)
\(168\) 0 0
\(169\) 232.079i 1.37325i
\(170\) 163.295 + 117.128i 0.960556 + 0.688987i
\(171\) 0 0
\(172\) −27.3419 + 102.041i −0.158964 + 0.593263i
\(173\) 28.2921 + 105.588i 0.163538 + 0.610333i 0.998222 + 0.0596036i \(0.0189837\pi\)
−0.834684 + 0.550729i \(0.814350\pi\)
\(174\) 0 0
\(175\) 165.738 + 56.1778i 0.947074 + 0.321016i
\(176\) 198.094 1.12553
\(177\) 0 0
\(178\) 136.596 + 36.6007i 0.767391 + 0.205622i
\(179\) 218.631 126.227i 1.22140 0.705177i 0.256185 0.966628i \(-0.417534\pi\)
0.965217 + 0.261451i \(0.0842010\pi\)
\(180\) 0 0
\(181\) 119.101 0.658017 0.329008 0.944327i \(-0.393286\pi\)
0.329008 + 0.944327i \(0.393286\pi\)
\(182\) −132.632 318.977i −0.728748 1.75262i
\(183\) 0 0
\(184\) 28.5483 + 16.4824i 0.155154 + 0.0895782i
\(185\) −78.2196 + 207.538i −0.422809 + 1.12183i
\(186\) 0 0
\(187\) −156.084 + 41.8225i −0.834673 + 0.223650i
\(188\) −37.1686 + 37.1686i −0.197705 + 0.197705i
\(189\) 0 0
\(190\) −256.983 + 210.705i −1.35254 + 1.10897i
\(191\) −26.3773 + 45.6869i −0.138101 + 0.239198i −0.926778 0.375610i \(-0.877433\pi\)
0.788677 + 0.614808i \(0.210767\pi\)
\(192\) 0 0
\(193\) 177.369 + 47.5259i 0.919010 + 0.246248i 0.687162 0.726504i \(-0.258856\pi\)
0.231848 + 0.972752i \(0.425523\pi\)
\(194\) 113.042 + 65.2649i 0.582692 + 0.336417i
\(195\) 0 0
\(196\) −71.9952 71.6054i −0.367322 0.365334i
\(197\) 121.992 + 121.992i 0.619251 + 0.619251i 0.945339 0.326088i \(-0.105731\pi\)
−0.326088 + 0.945339i \(0.605731\pi\)
\(198\) 0 0
\(199\) 80.9671 46.7464i 0.406870 0.234906i −0.282574 0.959245i \(-0.591188\pi\)
0.689444 + 0.724339i \(0.257855\pi\)
\(200\) 106.463 + 52.6221i 0.532313 + 0.263110i
\(201\) 0 0
\(202\) 220.071 + 220.071i 1.08946 + 1.08946i
\(203\) −103.236 78.9935i −0.508553 0.389131i
\(204\) 0 0
\(205\) −160.652 + 223.974i −0.783668 + 1.09256i
\(206\) −129.488 224.280i −0.628583 1.08874i
\(207\) 0 0
\(208\) −103.640 386.790i −0.498270 1.85957i
\(209\) 267.218i 1.27856i
\(210\) 0 0
\(211\) 21.8880 0.103735 0.0518674 0.998654i \(-0.483483\pi\)
0.0518674 + 0.998654i \(0.483483\pi\)
\(212\) −32.0864 + 8.59753i −0.151351 + 0.0405544i
\(213\) 0 0
\(214\) −72.0545 + 41.6007i −0.336703 + 0.194396i
\(215\) −41.4062 251.506i −0.192587 1.16979i
\(216\) 0 0
\(217\) −272.354 35.4801i −1.25509 0.163503i
\(218\) 70.7377 70.7377i 0.324485 0.324485i
\(219\) 0 0
\(220\) 93.5222 42.3231i 0.425101 0.192378i
\(221\) 163.322 + 282.882i 0.739012 + 1.28001i
\(222\) 0 0
\(223\) −88.4889 + 88.4889i −0.396811 + 0.396811i −0.877107 0.480295i \(-0.840529\pi\)
0.480295 + 0.877107i \(0.340529\pi\)
\(224\) −129.218 167.928i −0.576866 0.749677i
\(225\) 0 0
\(226\) −185.294 + 320.938i −0.819883 + 1.42008i
\(227\) −4.21650 + 15.7362i −0.0185749 + 0.0693225i −0.974591 0.223991i \(-0.928091\pi\)
0.956016 + 0.293314i \(0.0947580\pi\)
\(228\) 0 0
\(229\) 345.781 + 199.637i 1.50996 + 0.871776i 0.999933 + 0.0116184i \(0.00369834\pi\)
0.510028 + 0.860158i \(0.329635\pi\)
\(230\) 85.0861 + 8.41936i 0.369940 + 0.0366059i
\(231\) 0 0
\(232\) −62.3766 62.3766i −0.268865 0.268865i
\(233\) 46.2513 + 172.612i 0.198503 + 0.740825i 0.991332 + 0.131380i \(0.0419408\pi\)
−0.792829 + 0.609445i \(0.791393\pi\)
\(234\) 0 0
\(235\) 44.7291 118.679i 0.190337 0.505015i
\(236\) 43.1308 74.7047i 0.182758 0.316545i
\(237\) 0 0
\(238\) 223.435 + 170.966i 0.938802 + 0.718346i
\(239\) 372.693i 1.55938i 0.626164 + 0.779692i \(0.284624\pi\)
−0.626164 + 0.779692i \(0.715376\pi\)
\(240\) 0 0
\(241\) 0.499495 + 0.865151i 0.00207259 + 0.00358984i 0.867060 0.498204i \(-0.166007\pi\)
−0.864987 + 0.501794i \(0.832674\pi\)
\(242\) 14.5705 54.3778i 0.0602087 0.224702i
\(243\) 0 0
\(244\) 213.903i 0.876652i
\(245\) 229.491 + 85.7830i 0.936699 + 0.350135i
\(246\) 0 0
\(247\) −521.759 + 139.805i −2.11239 + 0.566012i
\(248\) −180.034 48.2401i −0.725945 0.194516i
\(249\) 0 0
\(250\) 307.846 + 10.4987i 1.23138 + 0.0419946i
\(251\) 40.4760 0.161259 0.0806296 0.996744i \(-0.474307\pi\)
0.0806296 + 0.996744i \(0.474307\pi\)
\(252\) 0 0
\(253\) −48.6148 + 48.6148i −0.192153 + 0.192153i
\(254\) 388.175 + 224.113i 1.52825 + 0.882334i
\(255\) 0 0
\(256\) −154.765 268.060i −0.604550 1.04711i
\(257\) −485.965 + 130.214i −1.89091 + 0.506669i −0.892457 + 0.451133i \(0.851020\pi\)
−0.998457 + 0.0555353i \(0.982313\pi\)
\(258\) 0 0
\(259\) −118.435 + 287.030i −0.457280 + 1.10822i
\(260\) −131.568 160.465i −0.506030 0.617172i
\(261\) 0 0
\(262\) 75.8151 282.946i 0.289371 1.07995i
\(263\) −302.228 80.9818i −1.14916 0.307916i −0.366530 0.930406i \(-0.619454\pi\)
−0.782627 + 0.622491i \(0.786121\pi\)
\(264\) 0 0
\(265\) 61.9795 50.8180i 0.233885 0.191766i
\(266\) −368.722 + 283.726i −1.38617 + 1.06664i
\(267\) 0 0
\(268\) −4.10565 15.3225i −0.0153196 0.0571735i
\(269\) −274.266 + 158.348i −1.01958 + 0.588653i −0.913981 0.405756i \(-0.867008\pi\)
−0.105596 + 0.994409i \(0.533675\pi\)
\(270\) 0 0
\(271\) 83.6427 144.873i 0.308645 0.534588i −0.669421 0.742883i \(-0.733458\pi\)
0.978066 + 0.208295i \(0.0667913\pi\)
\(272\) 230.601 + 230.601i 0.847797 + 0.847797i
\(273\) 0 0
\(274\) 294.492i 1.07479i
\(275\) −163.478 + 186.069i −0.594464 + 0.676613i
\(276\) 0 0
\(277\) 67.5940 252.264i 0.244022 0.910701i −0.729851 0.683606i \(-0.760411\pi\)
0.973873 0.227095i \(-0.0729227\pi\)
\(278\) 90.1245 + 336.349i 0.324189 + 1.20989i
\(279\) 0 0
\(280\) 146.699 + 78.2424i 0.523926 + 0.279437i
\(281\) 288.113 1.02531 0.512657 0.858594i \(-0.328661\pi\)
0.512657 + 0.858594i \(0.328661\pi\)
\(282\) 0 0
\(283\) −311.860 83.5625i −1.10198 0.295274i −0.338408 0.941000i \(-0.609888\pi\)
−0.763570 + 0.645726i \(0.776555\pi\)
\(284\) −105.093 + 60.6752i −0.370044 + 0.213645i
\(285\) 0 0
\(286\) 488.929 1.70954
\(287\) −234.497 + 306.463i −0.817062 + 1.06781i
\(288\) 0 0
\(289\) 19.8992 + 11.4888i 0.0688555 + 0.0397538i
\(290\) −214.101 80.6932i −0.738280 0.278253i
\(291\) 0 0
\(292\) −40.7214 + 10.9113i −0.139457 + 0.0373673i
\(293\) −98.1765 + 98.1765i −0.335074 + 0.335074i −0.854509 0.519436i \(-0.826142\pi\)
0.519436 + 0.854509i \(0.326142\pi\)
\(294\) 0 0
\(295\) −20.4949 + 207.121i −0.0694741 + 0.702106i
\(296\) −105.356 + 182.483i −0.355934 + 0.616496i
\(297\) 0 0
\(298\) −380.511 101.958i −1.27688 0.342140i
\(299\) 120.358 + 69.4886i 0.402535 + 0.232403i
\(300\) 0 0
\(301\) −47.0581 353.731i −0.156339 1.17519i
\(302\) 127.726 + 127.726i 0.422934 + 0.422934i
\(303\) 0 0
\(304\) −467.045 + 269.648i −1.53633 + 0.887001i
\(305\) −212.787 470.201i −0.697663 1.54164i
\(306\) 0 0
\(307\) −38.0161 38.0161i −0.123831 0.123831i 0.642475 0.766306i \(-0.277907\pi\)
−0.766306 + 0.642475i \(0.777907\pi\)
\(308\) 132.700 55.1772i 0.430844 0.179147i
\(309\) 0 0
\(310\) −477.011 + 78.5319i −1.53875 + 0.253329i
\(311\) −182.194 315.569i −0.585832 1.01469i −0.994771 0.102129i \(-0.967434\pi\)
0.408939 0.912562i \(-0.365899\pi\)
\(312\) 0 0
\(313\) 61.0959 + 228.013i 0.195195 + 0.728476i 0.992216 + 0.124526i \(0.0397409\pi\)
−0.797022 + 0.603951i \(0.793592\pi\)
\(314\) 202.026i 0.643396i
\(315\) 0 0
\(316\) −113.032 −0.357696
\(317\) 306.481 82.1214i 0.966818 0.259058i 0.259334 0.965788i \(-0.416497\pi\)
0.707484 + 0.706730i \(0.249830\pi\)
\(318\) 0 0
\(319\) 159.331 91.9900i 0.499471 0.288370i
\(320\) 21.8915 + 15.7023i 0.0684108 + 0.0490696i
\(321\) 0 0
\(322\) 118.699 + 15.4632i 0.368632 + 0.0480224i
\(323\) 311.068 311.068i 0.963059 0.963059i
\(324\) 0 0
\(325\) 448.839 + 221.851i 1.38104 + 0.682619i
\(326\) −57.0765 98.8595i −0.175081 0.303250i
\(327\) 0 0
\(328\) −185.169 + 185.169i −0.564539 + 0.564539i
\(329\) 67.7262 164.135i 0.205855 0.498891i
\(330\) 0 0
\(331\) 258.974 448.556i 0.782399 1.35515i −0.148142 0.988966i \(-0.547329\pi\)
0.930541 0.366189i \(-0.119338\pi\)
\(332\) −30.9756 + 115.603i −0.0933001 + 0.348201i
\(333\) 0 0
\(334\) −182.675 105.468i −0.546932 0.315771i
\(335\) 24.2676 + 29.5976i 0.0724406 + 0.0883511i
\(336\) 0 0
\(337\) 153.115 + 153.115i 0.454348 + 0.454348i 0.896795 0.442447i \(-0.145889\pi\)
−0.442447 + 0.896795i \(0.645889\pi\)
\(338\) −148.016 552.402i −0.437916 1.63432i
\(339\) 0 0
\(340\) 158.137 + 59.6008i 0.465109 + 0.175296i
\(341\) 194.364 336.648i 0.569982 0.987237i
\(342\) 0 0
\(343\) 317.422 + 129.969i 0.925430 + 0.378919i
\(344\) 242.162i 0.703960i
\(345\) 0 0
\(346\) 134.684 + 233.279i 0.389259 + 0.674216i
\(347\) 106.451 397.282i 0.306777 1.14491i −0.624629 0.780922i \(-0.714750\pi\)
0.931405 0.363984i \(-0.118584\pi\)
\(348\) 0 0
\(349\) 338.935i 0.971160i −0.874192 0.485580i \(-0.838609\pi\)
0.874192 0.485580i \(-0.161391\pi\)
\(350\) 430.324 + 28.0118i 1.22950 + 0.0800337i
\(351\) 0 0
\(352\) 289.674 77.6179i 0.822937 0.220505i
\(353\) 452.404 + 121.221i 1.28160 + 0.343403i 0.834464 0.551063i \(-0.185778\pi\)
0.447135 + 0.894466i \(0.352444\pi\)
\(354\) 0 0
\(355\) 170.655 237.920i 0.480719 0.670198i
\(356\) 118.923 0.334052
\(357\) 0 0
\(358\) 439.887 439.887i 1.22874 1.22874i
\(359\) −303.691 175.336i −0.845935 0.488401i 0.0133422 0.999911i \(-0.495753\pi\)
−0.859277 + 0.511510i \(0.829086\pi\)
\(360\) 0 0
\(361\) 183.241 + 317.383i 0.507594 + 0.879178i
\(362\) 283.488 75.9604i 0.783116 0.209835i
\(363\) 0 0
\(364\) −177.163 230.236i −0.486713 0.632517i
\(365\) 78.6591 64.4940i 0.215504 0.176696i
\(366\) 0 0
\(367\) 104.910 391.530i 0.285859 1.06684i −0.662351 0.749194i \(-0.730441\pi\)
0.948210 0.317645i \(-0.102892\pi\)
\(368\) 134.026 + 35.9122i 0.364201 + 0.0975874i
\(369\) 0 0
\(370\) −53.8170 + 543.876i −0.145451 + 1.46993i
\(371\) 88.9287 68.4294i 0.239700 0.184446i
\(372\) 0 0
\(373\) 19.7292 + 73.6304i 0.0528933 + 0.197401i 0.987317 0.158764i \(-0.0507509\pi\)
−0.934423 + 0.356165i \(0.884084\pi\)
\(374\) −344.842 + 199.095i −0.922038 + 0.532339i
\(375\) 0 0
\(376\) 60.2471 104.351i 0.160232 0.277529i
\(377\) −262.976 262.976i −0.697548 0.697548i
\(378\) 0 0
\(379\) 503.251i 1.32784i −0.747804 0.663919i \(-0.768892\pi\)
0.747804 0.663919i \(-0.231108\pi\)
\(380\) −162.886 + 227.088i −0.428647 + 0.597601i
\(381\) 0 0
\(382\) −33.6459 + 125.568i −0.0880784 + 0.328713i
\(383\) −193.815 723.327i −0.506044 1.88858i −0.456311 0.889820i \(-0.650830\pi\)
−0.0497332 0.998763i \(-0.515837\pi\)
\(384\) 0 0
\(385\) −236.811 + 253.298i −0.615093 + 0.657917i
\(386\) 452.490 1.17226
\(387\) 0 0
\(388\) 106.029 + 28.4104i 0.273271 + 0.0732227i
\(389\) 385.145 222.364i 0.990091 0.571629i 0.0847892 0.996399i \(-0.472978\pi\)
0.905301 + 0.424770i \(0.139645\pi\)
\(390\) 0 0
\(391\) −113.185 −0.289475
\(392\) 201.895 + 115.835i 0.515039 + 0.295497i
\(393\) 0 0
\(394\) 368.175 + 212.566i 0.934454 + 0.539507i
\(395\) 248.466 112.442i 0.629028 0.284664i
\(396\) 0 0
\(397\) −652.508 + 174.839i −1.64360 + 0.440400i −0.957810 0.287403i \(-0.907208\pi\)
−0.685786 + 0.727803i \(0.740542\pi\)
\(398\) 162.906 162.906i 0.409313 0.409313i
\(399\) 0 0
\(400\) 490.176 + 97.9659i 1.22544 + 0.244915i
\(401\) −195.581 + 338.757i −0.487734 + 0.844780i −0.999901 0.0141063i \(-0.995510\pi\)
0.512167 + 0.858886i \(0.328843\pi\)
\(402\) 0 0
\(403\) −759.013 203.377i −1.88341 0.504657i
\(404\) 226.663 + 130.864i 0.561047 + 0.323920i
\(405\) 0 0
\(406\) −296.107 122.181i −0.729327 0.300938i
\(407\) −310.749 310.749i −0.763511 0.763511i
\(408\) 0 0
\(409\) −150.958 + 87.1558i −0.369091 + 0.213095i −0.673061 0.739587i \(-0.735021\pi\)
0.303970 + 0.952682i \(0.401688\pi\)
\(410\) −239.543 + 635.572i −0.584250 + 1.55017i
\(411\) 0 0
\(412\) −153.998 153.998i −0.373782 0.373782i
\(413\) −37.6414 + 288.944i −0.0911414 + 0.699623i
\(414\) 0 0
\(415\) −46.9091 284.931i −0.113034 0.686581i
\(416\) −303.107 524.996i −0.728622 1.26201i
\(417\) 0 0
\(418\) −170.427 636.042i −0.407720 1.52163i
\(419\) 190.392i 0.454396i 0.973849 + 0.227198i \(0.0729564\pi\)
−0.973849 + 0.227198i \(0.927044\pi\)
\(420\) 0 0
\(421\) 581.913 1.38222 0.691108 0.722751i \(-0.257123\pi\)
0.691108 + 0.722751i \(0.257123\pi\)
\(422\) 52.0986 13.9598i 0.123456 0.0330800i
\(423\) 0 0
\(424\) 65.9451 38.0734i 0.155531 0.0897958i
\(425\) −406.906 + 26.2980i −0.957426 + 0.0618777i
\(426\) 0 0
\(427\) −277.414 667.174i −0.649681 1.56247i
\(428\) −49.4751 + 49.4751i −0.115596 + 0.115596i
\(429\) 0 0
\(430\) −258.962 572.234i −0.602237 1.33078i
\(431\) −286.895 496.916i −0.665649 1.15294i −0.979109 0.203336i \(-0.934822\pi\)
0.313460 0.949601i \(-0.398512\pi\)
\(432\) 0 0
\(433\) 267.818 267.818i 0.618518 0.618518i −0.326633 0.945151i \(-0.605914\pi\)
0.945151 + 0.326633i \(0.105914\pi\)
\(434\) −670.895 + 89.2515i −1.54584 + 0.205649i
\(435\) 0 0
\(436\) 42.0637 72.8564i 0.0964763 0.167102i
\(437\) 48.4436 180.794i 0.110855 0.413716i
\(438\) 0 0
\(439\) 334.556 + 193.156i 0.762086 + 0.439991i 0.830044 0.557698i \(-0.188315\pi\)
−0.0679581 + 0.997688i \(0.521648\pi\)
\(440\) −181.967 + 149.198i −0.413562 + 0.339087i
\(441\) 0 0
\(442\) 569.160 + 569.160i 1.28769 + 1.28769i
\(443\) 125.217 + 467.317i 0.282657 + 1.05489i 0.950534 + 0.310619i \(0.100536\pi\)
−0.667877 + 0.744271i \(0.732797\pi\)
\(444\) 0 0
\(445\) −261.415 + 118.302i −0.587449 + 0.265848i
\(446\) −154.188 + 267.061i −0.345712 + 0.598791i
\(447\) 0 0
\(448\) 29.9540 + 22.9200i 0.0668615 + 0.0511606i
\(449\) 213.080i 0.474566i 0.971441 + 0.237283i \(0.0762569\pi\)
−0.971441 + 0.237283i \(0.923743\pi\)
\(450\) 0 0
\(451\) −273.078 472.984i −0.605494 1.04875i
\(452\) −80.6599 + 301.027i −0.178451 + 0.665989i
\(453\) 0 0
\(454\) 40.1450i 0.0884252i
\(455\) 618.475 + 329.865i 1.35929 + 0.724977i
\(456\) 0 0
\(457\) 740.545 198.429i 1.62045 0.434198i 0.669316 0.742978i \(-0.266587\pi\)
0.951134 + 0.308780i \(0.0999206\pi\)
\(458\) 950.364 + 254.649i 2.07503 + 0.556003i
\(459\) 0 0
\(460\) 70.9477 11.6803i 0.154234 0.0253921i
\(461\) −332.527 −0.721317 −0.360659 0.932698i \(-0.617448\pi\)
−0.360659 + 0.932698i \(0.617448\pi\)
\(462\) 0 0
\(463\) −394.630 + 394.630i −0.852332 + 0.852332i −0.990420 0.138088i \(-0.955904\pi\)
0.138088 + 0.990420i \(0.455904\pi\)
\(464\) −321.561 185.653i −0.693018 0.400114i
\(465\) 0 0
\(466\) 220.178 + 381.359i 0.472484 + 0.818367i
\(467\) 594.918 159.408i 1.27392 0.341345i 0.442386 0.896825i \(-0.354132\pi\)
0.831530 + 0.555480i \(0.187466\pi\)
\(468\) 0 0
\(469\) 32.6777 + 42.4670i 0.0696753 + 0.0905479i
\(470\) 30.7747 311.010i 0.0654782 0.661723i
\(471\) 0 0
\(472\) −51.1786 + 191.001i −0.108429 + 0.404663i
\(473\) 487.847 + 130.718i 1.03139 + 0.276360i
\(474\) 0 0
\(475\) 132.151 661.221i 0.278212 1.39204i
\(476\) 218.707 + 90.2439i 0.459469 + 0.189588i
\(477\) 0 0
\(478\) 237.696 + 887.095i 0.497273 + 1.85585i
\(479\) −219.614 + 126.794i −0.458484 + 0.264706i −0.711407 0.702781i \(-0.751942\pi\)
0.252923 + 0.967487i \(0.418608\pi\)
\(480\) 0 0
\(481\) −444.176 + 769.335i −0.923442 + 1.59945i
\(482\) 1.74069 + 1.74069i 0.00361139 + 0.00361139i
\(483\) 0 0
\(484\) 47.3423i 0.0978147i
\(485\) −261.335 + 43.0244i −0.538834 + 0.0887100i
\(486\) 0 0
\(487\) 107.670 401.832i 0.221089 0.825116i −0.762845 0.646582i \(-0.776198\pi\)
0.983934 0.178534i \(-0.0571355\pi\)
\(488\) −126.908 473.626i −0.260057 0.970545i
\(489\) 0 0
\(490\) 600.954 + 57.8182i 1.22644 + 0.117996i
\(491\) 283.991 0.578392 0.289196 0.957270i \(-0.406612\pi\)
0.289196 + 0.957270i \(0.406612\pi\)
\(492\) 0 0
\(493\) 292.562 + 78.3918i 0.593433 + 0.159010i
\(494\) −1152.74 + 665.537i −2.33349 + 1.34724i
\(495\) 0 0
\(496\) −784.525 −1.58170
\(497\) 249.098 325.545i 0.501203 0.655020i
\(498\) 0 0
\(499\) −716.123 413.454i −1.43512 0.828565i −0.437612 0.899164i \(-0.644176\pi\)
−0.997505 + 0.0705988i \(0.977509\pi\)
\(500\) 252.347 58.4760i 0.504695 0.116952i
\(501\) 0 0
\(502\) 96.3424 25.8149i 0.191917 0.0514240i
\(503\) −118.670 + 118.670i −0.235924 + 0.235924i −0.815160 0.579236i \(-0.803351\pi\)
0.579236 + 0.815160i \(0.303351\pi\)
\(504\) 0 0
\(505\) −628.430 62.1838i −1.24442 0.123136i
\(506\) −84.7090 + 146.720i −0.167409 + 0.289961i
\(507\) 0 0
\(508\) 364.093 + 97.5583i 0.716718 + 0.192044i
\(509\) 154.005 + 88.9151i 0.302565 + 0.174686i 0.643594 0.765367i \(-0.277442\pi\)
−0.341030 + 0.940052i \(0.610776\pi\)
\(510\) 0 0
\(511\) 112.861 86.8448i 0.220863 0.169951i
\(512\) −159.321 159.321i −0.311175 0.311175i
\(513\) 0 0
\(514\) −1073.66 + 619.879i −2.08883 + 1.20599i
\(515\) 491.713 + 185.323i 0.954783 + 0.359851i
\(516\) 0 0
\(517\) 177.699 + 177.699i 0.343711 + 0.343711i
\(518\) −98.8418 + 758.734i −0.190814 + 1.46474i
\(519\) 0 0
\(520\) 386.521 + 277.243i 0.743310 + 0.533160i
\(521\) −376.277 651.731i −0.722221 1.25092i −0.960108 0.279631i \(-0.909788\pi\)
0.237887 0.971293i \(-0.423545\pi\)
\(522\) 0 0
\(523\) 141.063 + 526.453i 0.269718 + 1.00660i 0.959299 + 0.282393i \(0.0911284\pi\)
−0.689580 + 0.724209i \(0.742205\pi\)
\(524\) 246.338i 0.470110i
\(525\) 0 0
\(526\) −771.022 −1.46582
\(527\) 618.149 165.633i 1.17296 0.314293i
\(528\) 0 0
\(529\) 416.422 240.422i 0.787188 0.454483i
\(530\) 115.115 160.488i 0.217198 0.302808i
\(531\) 0 0
\(532\) −237.757 + 310.724i −0.446912 + 0.584067i
\(533\) −780.658 + 780.658i −1.46465 + 1.46465i
\(534\) 0 0
\(535\) 59.5389 157.973i 0.111288 0.295277i
\(536\) 18.1815 + 31.4913i 0.0339208 + 0.0587525i
\(537\) 0 0
\(538\) −551.826 + 551.826i −1.02570 + 1.02570i
\(539\) −342.337 + 344.201i −0.635134 + 0.638591i
\(540\) 0 0
\(541\) −30.4507 + 52.7421i −0.0562859 + 0.0974901i −0.892795 0.450462i \(-0.851259\pi\)
0.836510 + 0.547952i \(0.184593\pi\)
\(542\) 106.692 398.178i 0.196848 0.734646i
\(543\) 0 0
\(544\) 427.563 + 246.854i 0.785962 + 0.453775i
\(545\) −19.9878 + 201.997i −0.0366748 + 0.370636i
\(546\) 0 0
\(547\) 219.616 + 219.616i 0.401492 + 0.401492i 0.878759 0.477266i \(-0.158372\pi\)
−0.477266 + 0.878759i \(0.658372\pi\)
\(548\) −64.0976 239.215i −0.116966 0.436524i
\(549\) 0 0
\(550\) −270.444 + 547.150i −0.491716 + 0.994818i
\(551\) −250.436 + 433.768i −0.454512 + 0.787238i
\(552\) 0 0
\(553\) 352.552 146.593i 0.637526 0.265086i
\(554\) 643.557i 1.16166i
\(555\) 0 0
\(556\) 146.416 + 253.600i 0.263338 + 0.456115i
\(557\) −257.028 + 959.243i −0.461451 + 1.72216i 0.206943 + 0.978353i \(0.433648\pi\)
−0.668395 + 0.743807i \(0.733018\pi\)
\(558\) 0 0
\(559\) 1020.94i 1.82637i
\(560\) 681.679 + 158.297i 1.21728 + 0.282673i
\(561\) 0 0
\(562\) 685.776 183.753i 1.22024 0.326963i
\(563\) −275.338 73.7765i −0.489055 0.131042i 0.00586099 0.999983i \(-0.498134\pi\)
−0.494916 + 0.868941i \(0.664801\pi\)
\(564\) 0 0
\(565\) −122.150 741.955i −0.216195 1.31319i
\(566\) −795.593 −1.40564
\(567\) 0 0
\(568\) 196.698 196.698i 0.346300 0.346300i
\(569\) −231.224 133.497i −0.406368 0.234617i 0.282860 0.959161i \(-0.408717\pi\)
−0.689228 + 0.724544i \(0.742050\pi\)
\(570\) 0 0
\(571\) 104.149 + 180.391i 0.182397 + 0.315921i 0.942696 0.333652i \(-0.108281\pi\)
−0.760299 + 0.649573i \(0.774948\pi\)
\(572\) 397.155 106.417i 0.694328 0.186045i
\(573\) 0 0
\(574\) −362.701 + 879.010i −0.631883 + 1.53138i
\(575\) −144.338 + 96.2533i −0.251022 + 0.167397i
\(576\) 0 0
\(577\) −41.0956 + 153.371i −0.0712228 + 0.265807i −0.992350 0.123454i \(-0.960603\pi\)
0.921128 + 0.389261i \(0.127270\pi\)
\(578\) 54.6922 + 14.6547i 0.0946232 + 0.0253542i
\(579\) 0 0
\(580\) −191.477 18.9468i −0.330133 0.0326670i
\(581\) −53.3122 400.743i −0.0917594 0.689747i
\(582\) 0 0
\(583\) 41.1038 + 153.401i 0.0705039 + 0.263124i
\(584\) 83.6919 48.3196i 0.143308 0.0827390i
\(585\) 0 0
\(586\) −171.068 + 296.298i −0.291925 + 0.505628i
\(587\) −20.2654 20.2654i −0.0345236 0.0345236i 0.689634 0.724158i \(-0.257771\pi\)
−0.724158 + 0.689634i \(0.757771\pi\)
\(588\) 0 0
\(589\) 1058.28i 1.79674i
\(590\) 83.3156 + 506.068i 0.141213 + 0.857743i
\(591\) 0 0
\(592\) −229.553 + 856.703i −0.387758 + 1.44713i
\(593\) 189.157 + 705.944i 0.318983 + 1.19046i 0.920223 + 0.391393i \(0.128007\pi\)
−0.601240 + 0.799068i \(0.705327\pi\)
\(594\) 0 0
\(595\) −570.534 + 19.1926i −0.958881 + 0.0322564i
\(596\) −331.280 −0.555839
\(597\) 0 0
\(598\) 330.798 + 88.6371i 0.553174 + 0.148223i
\(599\) 728.928 420.847i 1.21691 0.702583i 0.252653 0.967557i \(-0.418697\pi\)
0.964256 + 0.264974i \(0.0853634\pi\)
\(600\) 0 0
\(601\) −374.471 −0.623079 −0.311540 0.950233i \(-0.600845\pi\)
−0.311540 + 0.950233i \(0.600845\pi\)
\(602\) −337.613 811.950i −0.560818 1.34875i
\(603\) 0 0
\(604\) 131.552 + 75.9515i 0.217801 + 0.125747i
\(605\) 47.0953 + 104.068i 0.0778435 + 0.172013i
\(606\) 0 0
\(607\) 488.562 130.910i 0.804880 0.215667i 0.167155 0.985931i \(-0.446542\pi\)
0.637725 + 0.770264i \(0.279875\pi\)
\(608\) −577.307 + 577.307i −0.949519 + 0.949519i
\(609\) 0 0
\(610\) −806.368 983.475i −1.32192 1.61225i
\(611\) 253.997 439.937i 0.415708 0.720027i
\(612\) 0 0
\(613\) 660.473 + 176.973i 1.07744 + 0.288700i 0.753548 0.657393i \(-0.228341\pi\)
0.323896 + 0.946093i \(0.395007\pi\)
\(614\) −114.733 66.2412i −0.186862 0.107885i
\(615\) 0 0
\(616\) −261.089 + 200.904i −0.423845 + 0.326143i
\(617\) −5.21905 5.21905i −0.00845875 0.00845875i 0.702865 0.711324i \(-0.251904\pi\)
−0.711324 + 0.702865i \(0.751904\pi\)
\(618\) 0 0
\(619\) −803.223 + 463.741i −1.29761 + 0.749178i −0.979991 0.199040i \(-0.936218\pi\)
−0.317622 + 0.948217i \(0.602884\pi\)
\(620\) −370.382 + 167.615i −0.597391 + 0.270347i
\(621\) 0 0
\(622\) −634.928 634.928i −1.02078 1.02078i
\(623\) −370.925 + 154.232i −0.595386 + 0.247564i
\(624\) 0 0
\(625\) −496.538 + 379.573i −0.794460 + 0.607316i
\(626\) 290.845 + 503.758i 0.464609 + 0.804726i
\(627\) 0 0
\(628\) 43.9719 + 164.105i 0.0700189 + 0.261314i
\(629\) 723.484i 1.15021i
\(630\) 0 0
\(631\) −659.617 −1.04535 −0.522676 0.852531i \(-0.675066\pi\)
−0.522676 + 0.852531i \(0.675066\pi\)
\(632\) 250.276 67.0613i 0.396006 0.106110i
\(633\) 0 0
\(634\) 677.121 390.936i 1.06801 0.616619i
\(635\) −897.396 + 147.741i −1.41322 + 0.232663i
\(636\) 0 0
\(637\) 851.177 + 488.352i 1.33623 + 0.766643i
\(638\) 320.576 320.576i 0.502470 0.502470i
\(639\) 0 0
\(640\) 628.619 + 236.922i 0.982218 + 0.370191i
\(641\) 115.909 + 200.760i 0.180825 + 0.313198i 0.942162 0.335159i \(-0.108790\pi\)
−0.761337 + 0.648357i \(0.775457\pi\)
\(642\) 0 0
\(643\) −207.642 + 207.642i −0.322927 + 0.322927i −0.849889 0.526962i \(-0.823331\pi\)
0.526962 + 0.849889i \(0.323331\pi\)
\(644\) 99.7848 13.2747i 0.154945 0.0206129i
\(645\) 0 0
\(646\) 542.021 938.808i 0.839042 1.45326i
\(647\) −119.193 + 444.834i −0.184224 + 0.687534i 0.810571 + 0.585640i \(0.199157\pi\)
−0.994795 + 0.101894i \(0.967510\pi\)
\(648\) 0 0
\(649\) −357.154 206.203i −0.550315 0.317725i
\(650\) 1209.83 + 241.796i 1.86128 + 0.371994i
\(651\) 0 0
\(652\) −67.8803 67.8803i −0.104111 0.104111i
\(653\) −211.888 790.779i −0.324485 1.21099i −0.914829 0.403842i \(-0.867675\pi\)
0.590344 0.807152i \(-0.298992\pi\)
\(654\) 0 0
\(655\) 245.053 + 541.498i 0.374126 + 0.826715i
\(656\) −551.122 + 954.571i −0.840125 + 1.45514i
\(657\) 0 0
\(658\) 56.5217 433.874i 0.0858992 0.659383i
\(659\) 472.040i 0.716297i 0.933665 + 0.358149i \(0.116592\pi\)
−0.933665 + 0.358149i \(0.883408\pi\)
\(660\) 0 0
\(661\) 20.0334 + 34.6989i 0.0303078 + 0.0524946i 0.880781 0.473523i \(-0.157018\pi\)
−0.850474 + 0.526018i \(0.823685\pi\)
\(662\) 330.338 1232.84i 0.499000 1.86229i
\(663\) 0 0
\(664\) 274.346i 0.413172i
\(665\) 213.534 919.549i 0.321104 1.38278i
\(666\) 0 0
\(667\) 124.477 33.3534i 0.186622 0.0500052i
\(668\) −171.342 45.9110i −0.256500 0.0687291i
\(669\) 0 0
\(670\) 76.6394 + 54.9718i 0.114387 + 0.0820475i
\(671\) 1022.65 1.52406
\(672\) 0 0
\(673\) −170.430 + 170.430i −0.253239 + 0.253239i −0.822297 0.569059i \(-0.807308\pi\)
0.569059 + 0.822297i \(0.307308\pi\)
\(674\) 462.104 + 266.796i 0.685614 + 0.395839i
\(675\) 0 0
\(676\) −240.465 416.498i −0.355718 0.616122i
\(677\) −873.260 + 233.989i −1.28990 + 0.345627i −0.837621 0.546251i \(-0.816054\pi\)
−0.452276 + 0.891878i \(0.649388\pi\)
\(678\) 0 0
\(679\) −367.555 + 48.8972i −0.541319 + 0.0720135i
\(680\) −385.509 38.1465i −0.566925 0.0560978i
\(681\) 0 0
\(682\) 247.923 925.262i 0.363524 1.35669i
\(683\) 370.963 + 99.3993i 0.543138 + 0.145533i 0.519948 0.854198i \(-0.325951\pi\)
0.0231896 + 0.999731i \(0.492618\pi\)
\(684\) 0 0
\(685\) 378.866 + 462.079i 0.553090 + 0.674568i
\(686\) 838.431 + 106.911i 1.22220 + 0.155846i
\(687\) 0 0
\(688\) −263.814 984.567i −0.383451 1.43106i
\(689\) 278.020 160.515i 0.403512 0.232968i
\(690\) 0 0
\(691\) −143.113 + 247.880i −0.207111 + 0.358726i −0.950803 0.309796i \(-0.899739\pi\)
0.743693 + 0.668522i \(0.233073\pi\)
\(692\) 160.177 + 160.177i 0.231470 + 0.231470i
\(693\) 0 0
\(694\) 1013.52i 1.46040i
\(695\) −574.127 411.809i −0.826082 0.592531i
\(696\) 0 0
\(697\) 232.711 868.488i 0.333875 1.24604i
\(698\) −216.166 806.743i −0.309694 1.15579i
\(699\) 0 0
\(700\) 355.648 70.9080i 0.508068 0.101297i
\(701\) 737.080 1.05147 0.525735 0.850648i \(-0.323790\pi\)
0.525735 + 0.850648i \(0.323790\pi\)
\(702\) 0 0
\(703\) 1155.65 + 309.655i 1.64388 + 0.440476i
\(704\) −46.2299 + 26.6909i −0.0656675 + 0.0379132i
\(705\) 0 0
\(706\) 1154.14 1.63476
\(707\) −876.691 114.208i −1.24002 0.161539i
\(708\) 0 0
\(709\) 777.250 + 448.745i 1.09626 + 0.632927i 0.935237 0.354023i \(-0.115187\pi\)
0.161025 + 0.986950i \(0.448520\pi\)
\(710\) 254.458 675.146i 0.358391 0.950910i
\(711\) 0 0
\(712\) −263.319 + 70.5562i −0.369830 + 0.0990958i
\(713\) 192.533 192.533i 0.270032 0.270032i
\(714\) 0 0
\(715\) −767.162 + 629.010i −1.07295 + 0.879734i
\(716\) 261.576 453.063i 0.365330 0.632769i
\(717\) 0 0
\(718\) −834.680 223.652i −1.16251 0.311493i
\(719\) −86.3910 49.8778i −0.120154 0.0693711i 0.438718 0.898625i \(-0.355433\pi\)
−0.558873 + 0.829254i \(0.688766\pi\)
\(720\) 0 0
\(721\) 680.051 + 280.606i 0.943205 + 0.389189i
\(722\) 638.578 + 638.578i 0.884457 + 0.884457i
\(723\) 0 0
\(724\) 213.744 123.405i 0.295226 0.170449i
\(725\) 439.752 148.829i 0.606554 0.205282i
\(726\) 0 0
\(727\) −794.241 794.241i −1.09249 1.09249i −0.995262 0.0972298i \(-0.969002\pi\)
−0.0972298 0.995262i \(-0.530998\pi\)
\(728\) 528.874 + 404.680i 0.726476 + 0.555880i
\(729\) 0 0
\(730\) 146.094 203.678i 0.200129 0.279011i
\(731\) 415.733 + 720.070i 0.568718 + 0.985048i
\(732\) 0 0
\(733\) −100.435 374.828i −0.137019 0.511362i −0.999981 0.00609363i \(-0.998060\pi\)
0.862963 0.505268i \(-0.168606\pi\)
\(734\) 998.842i 1.36082i
\(735\) 0 0
\(736\) 210.058 0.285405
\(737\) −73.2551 + 19.6287i −0.0993964 + 0.0266332i
\(738\) 0 0
\(739\) −994.736 + 574.311i −1.34606 + 0.777147i −0.987689 0.156433i \(-0.950000\pi\)
−0.358369 + 0.933580i \(0.616667\pi\)
\(740\) 74.6615 + 453.502i 0.100894 + 0.612841i
\(741\) 0 0
\(742\) 168.028 219.595i 0.226453 0.295950i
\(743\) −720.519 + 720.519i −0.969743 + 0.969743i −0.999556 0.0298125i \(-0.990509\pi\)
0.0298125 + 0.999556i \(0.490509\pi\)
\(744\) 0 0
\(745\) 728.218 329.552i 0.977473 0.442351i
\(746\) 93.9202 + 162.675i 0.125898 + 0.218062i
\(747\) 0 0
\(748\) −236.780 + 236.780i −0.316551 + 0.316551i
\(749\) 90.1503 218.480i 0.120361 0.291696i
\(750\) 0 0
\(751\) 301.457 522.139i 0.401407 0.695258i −0.592489 0.805579i \(-0.701854\pi\)
0.993896 + 0.110321i \(0.0351878\pi\)
\(752\) 131.268 489.897i 0.174558 0.651459i
\(753\) 0 0
\(754\) −793.664 458.222i −1.05260 0.607722i
\(755\) −364.732 36.0906i −0.483088 0.0478021i
\(756\) 0 0
\(757\) 590.863 + 590.863i 0.780532 + 0.780532i 0.979921 0.199389i \(-0.0638956\pi\)
−0.199389 + 0.979921i \(0.563896\pi\)
\(758\) −320.964 1197.85i −0.423435 1.58028i
\(759\) 0 0
\(760\) 225.932 599.460i 0.297280 0.788764i
\(761\) 104.936 181.755i 0.137892 0.238837i −0.788806 0.614642i \(-0.789301\pi\)
0.926699 + 0.375805i \(0.122634\pi\)
\(762\) 0 0
\(763\) −36.7101 + 281.796i −0.0481128 + 0.369326i
\(764\) 109.322i 0.143092i
\(765\) 0 0
\(766\) −922.649 1598.08i −1.20450 2.08626i
\(767\) −215.765 + 805.247i −0.281311 + 1.04987i
\(768\) 0 0
\(769\) 864.088i 1.12365i 0.827256 + 0.561826i \(0.189901\pi\)
−0.827256 + 0.561826i \(0.810099\pi\)
\(770\) −402.116 + 753.941i −0.522229 + 0.979145i
\(771\) 0 0
\(772\) 367.557 98.4865i 0.476110 0.127573i
\(773\) 1017.55 + 272.652i 1.31637 + 0.352719i 0.847615 0.530612i \(-0.178038\pi\)
0.468750 + 0.883331i \(0.344704\pi\)
\(774\) 0 0
\(775\) 647.432 736.900i 0.835396 0.950839i