Properties

Label 108.6.h.a.35.5
Level 108
Weight 6
Character 108.35
Analytic conductor 17.321
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 35.5
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.87383 + 2.87155i) q^{2} +(15.5084 - 27.9909i) q^{4} +(-70.1957 + 40.5275i) q^{5} +(-89.9985 - 51.9607i) q^{7} +(4.79147 + 180.956i) q^{8} +O(q^{10})\) \(q+(-4.87383 + 2.87155i) q^{2} +(15.5084 - 27.9909i) q^{4} +(-70.1957 + 40.5275i) q^{5} +(-89.9985 - 51.9607i) q^{7} +(4.79147 + 180.956i) q^{8} +(225.745 - 399.094i) q^{10} +(-214.271 + 371.129i) q^{11} +(42.9574 + 74.4044i) q^{13} +(587.845 - 5.18738i) q^{14} +(-542.976 - 868.190i) q^{16} -1509.75i q^{17} +1224.53i q^{19} +(45.7731 + 2593.36i) q^{20} +(-21.3913 - 2424.11i) q^{22} +(-1530.14 - 2650.27i) q^{23} +(1722.45 - 2983.38i) q^{25} +(-423.023 - 239.280i) q^{26} +(-2850.16 + 1713.31i) q^{28} +(4347.44 + 2510.00i) q^{29} +(3400.78 - 1963.44i) q^{31} +(5139.42 + 2672.23i) q^{32} +(4335.30 + 7358.24i) q^{34} +8423.34 q^{35} +13035.3 q^{37} +(-3516.29 - 5968.14i) q^{38} +(-7670.03 - 12508.1i) q^{40} +(15071.6 - 8701.62i) q^{41} +(5754.33 + 3322.27i) q^{43} +(7065.19 + 11753.3i) q^{44} +(15068.0 + 8523.13i) q^{46} +(-10068.4 + 17438.9i) q^{47} +(-3003.68 - 5202.52i) q^{49} +(171.957 + 19486.6i) q^{50} +(2748.85 - 48.5176i) q^{52} -18043.0i q^{53} -34735.5i q^{55} +(8971.37 - 16534.7i) q^{56} +(-28396.3 + 250.580i) q^{58} +(-14736.4 - 25524.2i) q^{59} +(-11989.0 + 20765.6i) q^{61} +(-10936.7 + 19335.0i) q^{62} +(-32722.1 + 1734.09i) q^{64} +(-6030.85 - 3481.91i) q^{65} +(348.663 - 201.301i) q^{67} +(-42259.1 - 23413.8i) q^{68} +(-41054.0 + 24188.0i) q^{70} -36645.5 q^{71} +58635.9 q^{73} +(-63531.8 + 37431.5i) q^{74} +(34275.6 + 18990.5i) q^{76} +(38568.2 - 22267.4i) q^{77} +(-39354.5 - 22721.3i) q^{79} +(73300.1 + 38937.7i) q^{80} +(-48469.5 + 85689.1i) q^{82} +(27253.7 - 47204.9i) q^{83} +(61186.2 + 105978. i) q^{85} +(-37585.7 + 331.671i) q^{86} +(-68184.6 - 36995.4i) q^{88} +45338.5i q^{89} -8928.39i q^{91} +(-97913.4 + 1728.19i) q^{92} +(-1005.15 - 113906. i) q^{94} +(-49627.1 - 85956.6i) q^{95} +(41820.0 - 72434.3i) q^{97} +(29578.7 + 16731.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.87383 + 2.87155i −0.861580 + 0.507622i
\(3\) 0 0
\(4\) 15.5084 27.9909i 0.484639 0.874714i
\(5\) −70.1957 + 40.5275i −1.25570 + 0.724978i −0.972235 0.234005i \(-0.924817\pi\)
−0.283463 + 0.958983i \(0.591483\pi\)
\(6\) 0 0
\(7\) −89.9985 51.9607i −0.694209 0.400802i 0.110978 0.993823i \(-0.464602\pi\)
−0.805187 + 0.593021i \(0.797935\pi\)
\(8\) 4.79147 + 180.956i 0.0264694 + 0.999650i
\(9\) 0 0
\(10\) 225.745 399.094i 0.713869 1.26205i
\(11\) −214.271 + 371.129i −0.533927 + 0.924789i 0.465287 + 0.885160i \(0.345951\pi\)
−0.999214 + 0.0396293i \(0.987382\pi\)
\(12\) 0 0
\(13\) 42.9574 + 74.4044i 0.0704985 + 0.122107i 0.899120 0.437702i \(-0.144208\pi\)
−0.828621 + 0.559809i \(0.810874\pi\)
\(14\) 587.845 5.18738i 0.801573 0.00707339i
\(15\) 0 0
\(16\) −542.976 868.190i −0.530250 0.847841i
\(17\) 1509.75i 1.26701i −0.773737 0.633507i \(-0.781615\pi\)
0.773737 0.633507i \(-0.218385\pi\)
\(18\) 0 0
\(19\) 1224.53i 0.778189i 0.921198 + 0.389094i \(0.127212\pi\)
−0.921198 + 0.389094i \(0.872788\pi\)
\(20\) 45.7731 + 2593.36i 0.0255880 + 1.44973i
\(21\) 0 0
\(22\) −21.3913 2424.11i −0.00942280 1.06781i
\(23\) −1530.14 2650.27i −0.603129 1.04465i −0.992344 0.123503i \(-0.960587\pi\)
0.389215 0.921147i \(1.62725\pi\)
\(24\) 0 0
\(25\) 1722.45 2983.38i 0.551186 0.954681i
\(26\) −423.023 239.280i −0.122724 0.0694183i
\(27\) 0 0
\(28\) −2850.16 + 1713.31i −0.687028 + 0.412990i
\(29\) 4347.44 + 2510.00i 0.959929 + 0.554215i 0.896151 0.443749i \(-0.146352\pi\)
0.0637776 + 0.997964i \(0.479685\pi\)
\(30\) 0 0
\(31\) 3400.78 1963.44i 0.635587 0.366956i −0.147326 0.989088i \(-0.547067\pi\)
0.782913 + 0.622132i \(0.213733\pi\)
\(32\) 5139.42 + 2672.23i 0.887236 + 0.461316i
\(33\) 0 0
\(34\) 4335.30 + 7358.24i 0.643165 + 1.09163i
\(35\) 8423.34 1.16229
\(36\) 0 0
\(37\) 13035.3 1.56537 0.782684 0.622419i \(-0.213850\pi\)
0.782684 + 0.622419i \(0.213850\pi\)
\(38\) −3516.29 5968.14i −0.395026 0.670471i
\(39\) 0 0
\(40\) −7670.03 12508.1i −0.757961 1.23607i
\(41\) 15071.6 8701.62i 1.40024 0.808426i 0.405819 0.913954i \(-0.366986\pi\)
0.994416 + 0.105527i \(0.0336531\pi\)
\(42\) 0 0
\(43\) 5754.33 + 3322.27i 0.474596 + 0.274008i 0.718162 0.695876i \(-0.244984\pi\)
−0.243566 + 0.969884i \(0.578317\pi\)
\(44\) 7065.19 + 11753.3i 0.550164 + 0.915223i
\(45\) 0 0
\(46\) 15068.0 + 8523.13i 1.04993 + 0.593888i
\(47\) −10068.4 + 17438.9i −0.664836 + 1.15153i 0.314494 + 0.949260i \(0.398165\pi\)
−0.979330 + 0.202270i \(0.935168\pi\)
\(48\) 0 0
\(49\) −3003.68 5202.52i −0.178716 0.309545i
\(50\) 171.957 + 19486.6i 0.00972738 + 1.10233i
\(51\) 0 0
\(52\) 2748.85 48.5176i 0.140975 0.00248823i
\(53\) 18043.0i 0.882304i −0.897432 0.441152i \(-0.854570\pi\)
0.897432 0.441152i \(-0.145430\pi\)
\(54\) 0 0
\(55\) 34735.5i 1.54834i
\(56\) 8971.37 16534.7i 0.382286 0.704575i
\(57\) 0 0
\(58\) −28396.3 + 250.580i −1.10839 + 0.00978084i
\(59\) −14736.4 25524.2i −0.551140 0.954602i −0.998193 0.0600943i \(-0.980860\pi\)
0.447053 0.894507i \(1.64753\pi\)
\(60\) 0 0
\(61\) −11989.0 + 20765.6i −0.412533 + 0.714528i −0.995166 0.0982073i \(-0.968689\pi\)
0.582633 + 0.812735i \(0.302023\pi\)
\(62\) −10936.7 + 19335.0i −0.361334 + 0.638800i
\(63\) 0 0
\(64\) −32722.1 + 1734.09i −0.998599 + 0.0529203i
\(65\) −6030.85 3481.91i −0.177050 0.102220i
\(66\) 0 0
\(67\) 348.663 201.301i 0.00948897 0.00547846i −0.495248 0.868752i \(-0.664923\pi\)
0.504737 + 0.863273i \(0.331589\pi\)
\(68\) −42259.1 23413.8i −1.10828 0.614044i
\(69\) 0 0
\(70\) −41054.0 + 24188.0i −1.00141 + 0.590004i
\(71\) −36645.5 −0.862730 −0.431365 0.902178i \(-0.641968\pi\)
−0.431365 + 0.902178i \(0.641968\pi\)
\(72\) 0 0
\(73\) 58635.9 1.28782 0.643911 0.765100i \(-0.277311\pi\)
0.643911 + 0.765100i \(0.277311\pi\)
\(74\) −63531.8 + 37431.5i −1.34869 + 0.794616i
\(75\) 0 0
\(76\) 34275.6 + 18990.5i 0.680693 + 0.377141i
\(77\) 38568.2 22267.4i 0.741314 0.427998i
\(78\) 0 0
\(79\) −39354.5 22721.3i −0.709457 0.409605i 0.101403 0.994845i \(-0.467667\pi\)
−0.810860 + 0.585240i \(0.801000\pi\)
\(80\) 73300.1 + 38937.7i 1.28050 + 0.680213i
\(81\) 0 0
\(82\) −48469.5 + 85689.1i −0.796039 + 1.40731i
\(83\) 27253.7 47204.9i 0.434241 0.752128i −0.562992 0.826462i \(-0.690350\pi\)
0.997233 + 0.0743344i \(0.0236832\pi\)
\(84\) 0 0
\(85\) 61186.2 + 105978.i 0.918557 + 1.59099i
\(86\) −37585.7 + 331.671i −0.547995 + 0.00483572i
\(87\) 0 0
\(88\) −68184.6 36995.4i −0.938598 0.509261i
\(89\) 45338.5i 0.606726i 0.952875 + 0.303363i \(0.0981094\pi\)
−0.952875 + 0.303363i \(0.901891\pi\)
\(90\) 0 0
\(91\) 8928.39i 0.113024i
\(92\) −97913.4 + 1728.19i −1.20607 + 0.0212873i
\(93\) 0 0
\(94\) −1005.15 113906.i −0.0117331 1.32962i
\(95\) −49627.1 85956.6i −0.564169 0.977170i
\(96\) 0 0
\(97\) 41820.0 72434.3i 0.451289 0.781655i −0.547178 0.837016i \(-0.684298\pi\)
0.998466 + 0.0553615i \(0.0176311\pi\)
\(98\) 29578.7 + 16731.0i 0.311110 + 0.175977i
\(99\) 0 0
\(100\) −56794.7 94480.6i −0.567947 0.944806i
\(101\) −107672. 62164.7i −1.05027 0.606374i −0.127545 0.991833i \(-0.540710\pi\)
−0.922725 + 0.385459i \(0.874043\pi\)
\(102\) 0 0
\(103\) −57893.0 + 33424.5i −0.537691 + 0.310436i −0.744143 0.668021i \(-0.767142\pi\)
0.206452 + 0.978457i \(0.433808\pi\)
\(104\) −13258.1 + 8129.91i −0.120198 + 0.0737059i
\(105\) 0 0
\(106\) 51811.2 + 87938.4i 0.447877 + 0.760175i
\(107\) 144038. 1.21624 0.608119 0.793846i \(-0.291924\pi\)
0.608119 + 0.793846i \(0.291924\pi\)
\(108\) 0 0
\(109\) −137855. −1.11136 −0.555680 0.831396i \(-0.687542\pi\)
−0.555680 + 0.831396i \(0.687542\pi\)
\(110\) 99744.6 + 169295.i 0.785973 + 1.33402i
\(111\) 0 0
\(112\) 3755.33 + 106349.i 0.0282881 + 0.801104i
\(113\) 24697.0 14258.8i 0.181948 0.105048i −0.406259 0.913758i \(-0.633167\pi\)
0.588208 + 0.808710i \(0.299834\pi\)
\(114\) 0 0
\(115\) 214818. + 124025.i 1.51470 + 0.874511i
\(116\) 137679. 82762.5i 0.949999 0.571069i
\(117\) 0 0
\(118\) 145117. + 82084.4i 0.959428 + 0.542695i
\(119\) −78447.4 + 135875.i −0.507821 + 0.879573i
\(120\) 0 0
\(121\) −11298.8 19570.0i −0.0701565 0.121515i
\(122\) −1196.90 135635.i −0.00728042 0.825034i
\(123\) 0 0
\(124\) −2217.58 125641.i −0.0129517 0.733798i
\(125\) 25930.3i 0.148434i
\(126\) 0 0
\(127\) 74540.3i 0.410093i −0.978752 0.205046i \(-0.934266\pi\)
0.978752 0.205046i \(-0.0657345\pi\)
\(128\) 154502. 102415.i 0.833509 0.552506i
\(129\) 0 0
\(130\) 39391.8 347.609i 0.204431 0.00180398i
\(131\) 66965.9 + 115988.i 0.340938 + 0.590522i 0.984607 0.174782i \(-0.0559221\pi\)
−0.643669 + 0.765304i \(0.722589\pi\)
\(132\) 0 0
\(133\) 63627.3 110206.i 0.311899 0.540226i
\(134\) −1121.28 + 1982.31i −0.00539451 + 0.00953694i
\(135\) 0 0
\(136\) 273197. 7233.90i 1.26657 0.0335371i
\(137\) 143212. + 82683.3i 0.651894 + 0.376371i 0.789182 0.614160i \(-0.210505\pi\)
−0.137287 + 0.990531i \(0.543838\pi\)
\(138\) 0 0
\(139\) −105373. + 60837.0i −0.462585 + 0.267074i −0.713131 0.701031i \(-0.752723\pi\)
0.250546 + 0.968105i \(0.419390\pi\)
\(140\) 130633. 235777.i 0.563291 1.01667i
\(141\) 0 0
\(142\) 178604. 105229.i 0.743311 0.437941i
\(143\) −36818.2 −0.150564
\(144\) 0 0
\(145\) −406896. −1.60717
\(146\) −285781. + 168376.i −1.10956 + 0.653728i
\(147\) 0 0
\(148\) 202157. 364869.i 0.758639 1.36925i
\(149\) 60786.2 35094.9i 0.224305 0.129503i −0.383637 0.923484i \(-0.625329\pi\)
0.607942 + 0.793981i \(0.291995\pi\)
\(150\) 0 0
\(151\) −31118.1 17966.1i −0.111064 0.0641225i 0.443439 0.896304i \(-0.353758\pi\)
−0.554503 + 0.832182i \(0.687092\pi\)
\(152\) −221586. + 5867.29i −0.777916 + 0.0205982i
\(153\) 0 0
\(154\) −124033. + 219278.i −0.421440 + 0.745062i
\(155\) −159147. + 275651.i −0.532070 + 0.921573i
\(156\) 0 0
\(157\) −84404.3 146193.i −0.273285 0.473343i 0.696416 0.717638i \(-0.254777\pi\)
−0.969701 + 0.244295i \(0.921443\pi\)
\(158\) 257052. 2268.33i 0.819179 0.00722876i
\(159\) 0 0
\(160\) −469064. + 20708.9i −1.44854 + 0.0639525i
\(161\) 318028.i 0.966941i
\(162\) 0 0
\(163\) 325623.i 0.959943i −0.877284 0.479972i \(-0.840647\pi\)
0.877284 0.479972i \(-0.159353\pi\)
\(164\) −9827.91 556817.i −0.0285333 1.61660i
\(165\) 0 0
\(166\) 2720.82 + 308329.i 0.00766353 + 0.868449i
\(167\) 106712. + 184831.i 0.296090 + 0.512843i 0.975238 0.221158i \(-0.0709838\pi\)
−0.679148 + 0.734002i \(0.737650\pi\)
\(168\) 0 0
\(169\) 181956. 315157.i 0.490060 0.848809i
\(170\) −602531. 340818.i −1.59903 0.904482i
\(171\) 0 0
\(172\) 182234. 109546.i 0.469686 0.282341i
\(173\) 27550.4 + 15906.2i 0.0699862 + 0.0404066i 0.534585 0.845115i \(-0.320468\pi\)
−0.464599 + 0.885521i \(0.653801\pi\)
\(174\) 0 0
\(175\) −310037. + 179000.i −0.765276 + 0.441832i
\(176\) 438554. 15485.9i 1.06719 0.0376839i
\(177\) 0 0
\(178\) −130192. 220972.i −0.307988 0.522742i
\(179\) 475398. 1.10898 0.554491 0.832189i \(-0.312913\pi\)
0.554491 + 0.832189i \(0.312913\pi\)
\(180\) 0 0
\(181\) 4695.48 0.0106533 0.00532664 0.999986i \(-0.498304\pi\)
0.00532664 + 0.999986i \(0.498304\pi\)
\(182\) 25638.3 + 43515.5i 0.0573734 + 0.0973789i
\(183\) 0 0
\(184\) 472251. 289586.i 1.02832 0.630569i
\(185\) −915021. + 528288.i −1.96563 + 1.13486i
\(186\) 0 0
\(187\) 560310. + 323495.i 1.17172 + 0.676493i
\(188\) 331986. + 552273.i 0.685054 + 1.13962i
\(189\) 0 0
\(190\) 488702. + 276431.i 0.982110 + 0.555525i
\(191\) 302770. 524412.i 0.600522 1.04013i −0.392220 0.919871i \(-0.628293\pi\)
0.992742 0.120263i \(-0.0383738\pi\)
\(192\) 0 0
\(193\) 46694.6 + 80877.5i 0.0902347 + 0.156291i 0.907610 0.419815i \(-0.137905\pi\)
−0.817375 + 0.576106i \(0.804572\pi\)
\(194\) 4175.00 + 473121.i 0.00796439 + 0.902542i
\(195\) 0 0
\(196\) −192205. + 3392.45i −0.357376 + 0.00630774i
\(197\) 466419.i 0.856270i −0.903715 0.428135i \(-0.859171\pi\)
0.903715 0.428135i \(-0.140829\pi\)
\(198\) 0 0
\(199\) 625885.i 1.12037i 0.828367 + 0.560185i \(0.189270\pi\)
−0.828367 + 0.560185i \(0.810730\pi\)
\(200\) 548113. + 297394.i 0.968936 + 0.525723i
\(201\) 0 0
\(202\) 703286. 6206.07i 1.21270 0.0107013i
\(203\) −260842. 451792.i −0.444261 0.769482i
\(204\) 0 0
\(205\) −705309. + 1.22163e6i −1.17218 + 2.03028i
\(206\) 186181. 329148.i 0.305679 0.540409i
\(207\) 0 0
\(208\) 41272.3 77695.0i 0.0661455 0.124519i
\(209\) −454457. 262381.i −0.719660 0.415496i
\(210\) 0 0
\(211\) −756200. + 436592.i −1.16931 + 0.675103i −0.953518 0.301336i \(-0.902567\pi\)
−0.215794 + 0.976439i \(0.569234\pi\)
\(212\) −505038. 279818.i −0.771764 0.427599i
\(213\) 0 0
\(214\) −702018. + 413613.i −1.04789 + 0.617390i
\(215\) −538572. −0.794599
\(216\) 0 0
\(217\) −408088. −0.588307
\(218\) 671880. 395856.i 0.957525 0.564151i
\(219\) 0 0
\(220\) −972276. 538694.i −1.35436 0.750387i
\(221\) 112332. 64854.8i 0.154711 0.0893226i
\(222\) 0 0
\(223\) 419169. + 242007.i 0.564452 + 0.325886i 0.754930 0.655805i \(-0.227671\pi\)
−0.190479 + 0.981691i \(0.561004\pi\)
\(224\) −323689. 507544.i −0.431031 0.675856i
\(225\) 0 0
\(226\) −79424.2 + 140414.i −0.103438 + 0.182868i
\(227\) 117910. 204225.i 0.151874 0.263054i −0.780042 0.625727i \(-0.784802\pi\)
0.931917 + 0.362673i \(0.118136\pi\)
\(228\) 0 0
\(229\) 124091. + 214932.i 0.156369 + 0.270840i 0.933557 0.358429i \(-0.116688\pi\)
−0.777187 + 0.629269i \(0.783354\pi\)
\(230\) −1.40313e6 + 12381.8i −1.74895 + 0.0154334i
\(231\) 0 0
\(232\) −433368. + 798722.i −0.528612 + 0.974262i
\(233\) 340275.i 0.410620i 0.978697 + 0.205310i \(0.0658202\pi\)
−0.978697 + 0.205310i \(0.934180\pi\)
\(234\) 0 0
\(235\) 1.63218e6i 1.92797i
\(236\) −942983. + 16643.8i −1.10211 + 0.0194524i
\(237\) 0 0
\(238\) −7831.62 887496.i −0.00896208 1.01560i
\(239\) 303908. + 526384.i 0.344149 + 0.596084i 0.985199 0.171415i \(-0.0548340\pi\)
−0.641049 + 0.767500i \(0.721501\pi\)
\(240\) 0 0
\(241\) 756653. 1.31056e6i 0.839179 1.45350i −0.0514039 0.998678i \(-0.516370\pi\)
0.890582 0.454822i \(-0.150297\pi\)
\(242\) 111265. + 62936.1i 0.122129 + 0.0690815i
\(243\) 0 0
\(244\) 395315. + 657624.i 0.425078 + 0.707137i
\(245\) 421690. + 243463.i 0.448826 + 0.259130i
\(246\) 0 0
\(247\) −91110.3 + 52602.6i −0.0950223 + 0.0548611i
\(248\) 371592. + 605984.i 0.383651 + 0.625651i
\(249\) 0 0
\(250\) −74460.0 126380.i −0.0753482 0.127887i
\(251\) −1.13311e6 −1.13524 −0.567622 0.823289i \(-0.692136\pi\)
−0.567622 + 0.823289i \(0.692136\pi\)
\(252\) 0 0
\(253\) 1.31146e6 1.28811
\(254\) 214046. + 363297.i 0.208172 + 0.353327i
\(255\) 0 0
\(256\) −458930. + 942812.i −0.437670 + 0.899136i
\(257\) 928992. 536354.i 0.877362 0.506545i 0.00757446 0.999971i \(-0.497589\pi\)
0.869788 + 0.493426i \(0.164256\pi\)
\(258\) 0 0
\(259\) −1.17316e6 677323.i −1.08669 0.627403i
\(260\) −190991. + 114810.i −0.175218 + 0.105328i
\(261\) 0 0
\(262\) −659446. 373012.i −0.593507 0.335714i
\(263\) 341490. 591477.i 0.304430 0.527289i −0.672704 0.739912i \(-0.734867\pi\)
0.977134 + 0.212623i \(0.0682006\pi\)
\(264\) 0 0
\(265\) 731236. + 1.26654e6i 0.639651 + 1.10791i
\(266\) 6352.09 + 719833.i 0.00550443 + 0.623775i
\(267\) 0 0
\(268\) −227.356 12881.2i −0.000193361 0.0109552i
\(269\) 931829.i 0.785155i −0.919719 0.392577i \(-0.871583\pi\)
0.919719 0.392577i \(-0.128417\pi\)
\(270\) 0 0
\(271\) 1.76382e6i 1.45892i −0.684023 0.729460i \(-0.739771\pi\)
0.684023 0.729460i \(-0.260229\pi\)
\(272\) −1.31074e6 + 819755.i −1.07423 + 0.671834i
\(273\) 0 0
\(274\) −935419. + 8254.50i −0.752713 + 0.00664224i
\(275\) 738145. + 1.27850e6i 0.588586 + 1.01946i
\(276\) 0 0
\(277\) 309348. 535806.i 0.242241 0.419573i −0.719111 0.694895i \(-0.755451\pi\)
0.961352 + 0.275321i \(0.0887843\pi\)
\(278\) 338873. 599092.i 0.262981 0.464924i
\(279\) 0 0
\(280\) 40360.2 + 1.52425e6i 0.0307651 + 1.16188i
\(281\) 1.58185e6 + 913279.i 1.19508 + 0.689982i 0.959455 0.281861i \(-0.0909518\pi\)
0.235628 + 0.971843i \(0.424285\pi\)
\(282\) 0 0
\(283\) 1.63561e6 944320.i 1.21399 0.700895i 0.250361 0.968153i \(-0.419451\pi\)
0.963625 + 0.267258i \(0.0861174\pi\)
\(284\) −568315. + 1.02574e6i −0.418113 + 0.754642i
\(285\) 0 0
\(286\) 179445. 105725.i 0.129723 0.0764298i
\(287\) −1.80857e6 −1.29607
\(288\) 0 0
\(289\) −859473. −0.605324
\(290\) 1.98314e6 1.16842e6i 1.38471 0.815838i
\(291\) 0 0
\(292\) 909351. 1.64127e6i 0.624129 1.12648i
\(293\) 965146. 557227.i 0.656786 0.379196i −0.134265 0.990945i \(-0.542867\pi\)
0.791051 + 0.611750i \(0.209534\pi\)
\(294\) 0 0
\(295\) 2.06886e6 + 1.19446e6i 1.38413 + 0.799128i
\(296\) 62458.3 + 2.35881e6i 0.0414344 + 1.56482i
\(297\) 0 0
\(298\) −195485. + 345597.i −0.127518 + 0.225439i
\(299\) 131461. 227698.i 0.0850394 0.147293i
\(300\) 0 0
\(301\) −345254. 597998.i −0.219646 0.380438i
\(302\) 203255. 1793.60i 0.128240 0.00113164i
\(303\) 0 0
\(304\) 1.06312e6 664890.i 0.659780 0.412634i
\(305\) 1.94354e6i 1.19631i
\(306\) 0 0
\(307\) 1.64394e6i 0.995497i 0.867321 + 0.497749i \(0.165840\pi\)
−0.867321 + 0.497749i \(0.834160\pi\)
\(308\) −25149.5 1.42489e6i −0.0151061 0.855863i
\(309\) 0 0
\(310\) −15888.1 1.80047e6i −0.00939003 1.06410i
\(311\) −363235. 629141.i −0.212954 0.368848i 0.739683 0.672955i \(-0.234975\pi\)
−0.952638 + 0.304107i \(0.901642\pi\)
\(312\) 0 0
\(313\) 702457. 1.21669e6i 0.405284 0.701972i −0.589071 0.808081i \(-0.700506\pi\)
0.994354 + 0.106110i \(0.0338394\pi\)
\(314\) 831171. + 470147.i 0.475736 + 0.269097i
\(315\) 0 0
\(316\) −1.24632e6 + 749193.i −0.702118 + 0.422062i
\(317\) −1.21701e6 702639.i −0.680213 0.392721i 0.119722 0.992807i \(-0.461800\pi\)
−0.799935 + 0.600086i \(0.795133\pi\)
\(318\) 0 0
\(319\) −1.86306e6 + 1.07564e6i −1.02506 + 0.591821i
\(320\) 2.22667e6 1.44787e6i 1.21557 0.790414i
\(321\) 0 0
\(322\) −913231. 1.55001e6i −0.490841 0.833097i
\(323\) 1.84873e6 0.985976
\(324\) 0 0
\(325\) 295969. 0.155431
\(326\) 935040. + 1.58703e6i 0.487289 + 0.827068i
\(327\) 0 0
\(328\) 1.64682e6 + 2.68561e6i 0.845206 + 1.37835i
\(329\) 1.81228e6 1.04632e6i 0.923071 0.532935i
\(330\) 0 0
\(331\) 214028. + 123569.i 0.107374 + 0.0619926i 0.552725 0.833363i \(-0.313588\pi\)
−0.445351 + 0.895356i \(0.646921\pi\)
\(332\) −898642. 1.49493e6i −0.447447 0.744347i
\(333\) 0 0
\(334\) −1.05085e6 594407.i −0.515436 0.291553i
\(335\) −16316.4 + 28260.9i −0.00794352 + 0.0137586i
\(336\) 0 0
\(337\) 1.07901e6 + 1.86890e6i 0.517549 + 0.896421i 0.999792 + 0.0203835i \(0.00648871\pi\)
−0.482244 + 0.876037i \(0.660178\pi\)
\(338\) 18165.1 + 2.05851e6i 0.00864863 + 0.980082i
\(339\) 0 0
\(340\) 3.91531e6 69105.8i 1.83683 0.0324203i
\(341\) 1.68284e6i 0.783712i
\(342\) 0 0
\(343\) 2.37090e6i 1.08812i
\(344\) −573612. + 1.05720e6i −0.261350 + 0.481682i
\(345\) 0 0
\(346\) −179951. + 1587.96i −0.0808100 + 0.000713099i
\(347\) −804114. 1.39277e6i −0.358504 0.620947i 0.629207 0.777237i \(-0.283380\pi\)
−0.987711 + 0.156291i \(0.950046\pi\)
\(348\) 0 0
\(349\) 233867. 405070.i 0.102779 0.178019i −0.810049 0.586362i \(-0.800560\pi\)
0.912829 + 0.408343i \(0.133893\pi\)
\(350\) 997061. 1.76270e6i 0.435062 0.769145i
\(351\) 0 0
\(352\) −2.09297e6 + 1.33480e6i −0.900339 + 0.574197i
\(353\) −397710. 229618.i −0.169875 0.0980773i 0.412652 0.910889i \(-0.364603\pi\)
−0.582527 + 0.812811i \(0.697936\pi\)
\(354\) 0 0
\(355\) 2.57236e6 1.48515e6i 1.08333 0.625460i
\(356\) 1.26906e6 + 703130.i 0.530712 + 0.294043i
\(357\) 0 0
\(358\) −2.31701e6 + 1.36513e6i −0.955477 + 0.562945i
\(359\) 2.21493e6 0.907037 0.453518 0.891247i \(-0.350169\pi\)
0.453518 + 0.891247i \(0.350169\pi\)
\(360\) 0 0
\(361\) 976629. 0.394423
\(362\) −22885.0 + 13483.3i −0.00917864 + 0.00540784i
\(363\) 0 0
\(364\) −249913. 138465.i −0.0988635 0.0547757i
\(365\) −4.11598e6 + 2.37636e6i −1.61712 + 0.933643i
\(366\) 0 0
\(367\) −2.54558e6 1.46969e6i −0.986555 0.569588i −0.0823124 0.996607i \(-0.526231\pi\)
−0.904243 + 0.427019i \(0.859564\pi\)
\(368\) −1.47011e6 + 2.76748e6i −0.565889 + 1.06528i
\(369\) 0 0
\(370\) 2.94266e6 5.20231e6i 1.11747 1.97557i
\(371\) −937525. + 1.62384e6i −0.353629 + 0.612504i
\(372\) 0 0
\(373\) −830424. 1.43834e6i −0.309049 0.535289i 0.669105 0.743168i \(-0.266678\pi\)
−0.978155 + 0.207878i \(0.933344\pi\)
\(374\) −3.65978e6 + 32295.4i −1.35293 + 0.0119388i
\(375\) 0 0
\(376\) −3.20392e6 1.73837e6i −1.16872 0.634123i
\(377\) 431292.i 0.156285i
\(378\) 0 0
\(379\) 4.69152e6i 1.67770i −0.544360 0.838852i \(-0.683227\pi\)
0.544360 0.838852i \(-0.316773\pi\)
\(380\) −3.17564e6 + 56050.5i −1.12816 + 0.0199123i
\(381\) 0 0
\(382\) 30226.3 + 3.42531e6i 0.0105981 + 1.20100i
\(383\) −2.64821e6 4.58683e6i −0.922476 1.59777i −0.795571 0.605860i \(-0.792829\pi\)
−0.126904 0.991915i \(1.45950\pi\)
\(384\) 0 0
\(385\) −1.80488e6 + 3.12614e6i −0.620578 + 1.07487i
\(386\) −459825. 260097.i −0.157081 0.0888521i
\(387\) 0 0
\(388\) −1.37894e6 2.29392e6i −0.465013 0.773569i
\(389\) 1.59537e6 + 921088.i 0.534549 + 0.308622i 0.742867 0.669439i \(-0.233465\pi\)
−0.208318 + 0.978061i \(0.566799\pi\)
\(390\) 0 0
\(391\) −4.00124e6 + 2.31011e6i −1.32359 + 0.764173i
\(392\) 927034. 568461.i 0.304706 0.186847i
\(393\) 0 0
\(394\) 1.33934e6 + 2.27325e6i 0.434662 + 0.737744i
\(395\) 3.68335e6 1.18782
\(396\) 0 0
\(397\) 75711.5 0.0241094 0.0120547 0.999927i \(-0.496163\pi\)
0.0120547 + 0.999927i \(0.496163\pi\)
\(398\) −1.79726e6 3.05046e6i −0.568725 0.965288i
\(399\) 0 0
\(400\) −3.52539e6 + 124486.i −1.10168 + 0.0389019i
\(401\) −2.92456e6 + 1.68849e6i −0.908237 + 0.524371i −0.879863 0.475227i \(-0.842366\pi\)
−0.0283735 + 0.999597i \(0.509033\pi\)
\(402\) 0 0
\(403\) 292178. + 168689.i 0.0896158 + 0.0517397i
\(404\) −3.40988e6 + 2.04977e6i −1.03941 + 0.624814i
\(405\) 0 0
\(406\) 2.56864e6 + 1.45294e6i 0.773373 + 0.437454i
\(407\) −2.79309e6 + 4.83777e6i −0.835793 + 1.44764i
\(408\) 0 0
\(409\) −1.75008e6 3.03123e6i −0.517310 0.896007i −0.999798 0.0201041i \(-0.993600\pi\)
0.482488 0.875902i \(-0.339733\pi\)
\(410\) −70413.0 7.97935e6i −0.0206868 2.34427i
\(411\) 0 0
\(412\) 37750.8 + 2.13884e6i 0.0109568 + 0.620776i
\(413\) 3.06285e6i 0.883591i
\(414\) 0 0
\(415\) 4.41810e6i 1.25926i
\(416\) 21950.6 + 497188.i 0.00621888 + 0.140860i
\(417\) 0 0
\(418\) 2.96839e6 26194.2i 0.830960 0.00733271i
\(419\) 2.65830e6 + 4.60430e6i 0.739721 + 1.28123i 0.952621 + 0.304161i \(0.0983760\pi\)
−0.212899 + 0.977074i \(0.568291\pi\)
\(420\) 0 0
\(421\) −2.59023e6 + 4.48640e6i −0.712250 + 1.23365i 0.251761 + 0.967790i \(0.418990\pi\)
−0.964011 + 0.265864i \(0.914343\pi\)
\(422\) 2.43190e6 4.29934e6i 0.664758 1.17522i
\(423\) 0 0
\(424\) 3.26498e6 86452.4i 0.881995 0.0233541i
\(425\) −4.50414e6 2.60047e6i −1.20959 0.698360i
\(426\) 0 0
\(427\) 2.15799e6 1.24591e6i 0.572768 0.330688i
\(428\) 2.23381e6 4.03176e6i 0.589437 1.06386i
\(429\) 0 0
\(430\) 2.62491e6 1.54654e6i 0.684610 0.403356i
\(431\) −5.72244e6 −1.48384 −0.741922 0.670486i \(-0.766086\pi\)
−0.741922 + 0.670486i \(0.766086\pi\)
\(432\) 0 0
\(433\) −6.17405e6 −1.58252 −0.791262 0.611478i \(-0.790575\pi\)
−0.791262 + 0.611478i \(0.790575\pi\)
\(434\) 1.98895e6 1.17184e6i 0.506873 0.298638i
\(435\) 0 0
\(436\) −2.13791e6 + 3.85867e6i −0.538609 + 0.972123i
\(437\) 3.24533e6 1.87369e6i 0.812935 0.469348i
\(438\) 0 0
\(439\) −5.02340e6 2.90026e6i −1.24405 0.718251i −0.274131 0.961692i \(-0.588390\pi\)
−0.969915 + 0.243442i \(0.921723\pi\)
\(440\) 6.28559e6 166434.i 1.54780 0.0409837i
\(441\) 0 0
\(442\) −361252. + 638657.i −0.0879539 + 0.155493i
\(443\) 2.08981e6 3.61966e6i 0.505939 0.876312i −0.494037 0.869441i \(-0.664479\pi\)
0.999976 0.00687158i \(-0.00218731\pi\)
\(444\) 0 0
\(445\) −1.83746e6 3.18257e6i −0.439863 0.761864i
\(446\) −2.73789e6 + 24160.2i −0.651747 + 0.00575127i
\(447\) 0 0
\(448\) 3.03504e6 + 1.54420e6i 0.714447 + 0.363503i
\(449\) 970936.i 0.227287i 0.993522 + 0.113644i \(0.0362522\pi\)
−0.993522 + 0.113644i \(0.963748\pi\)
\(450\) 0 0
\(451\) 7.45802e6i 1.72656i
\(452\) −16104.4 912423.i −0.00370765 0.210063i
\(453\) 0 0
\(454\) 11771.2 + 1.33394e6i 0.00268029 + 0.303737i
\(455\) 361845. + 626734.i 0.0819397 + 0.141924i
\(456\) 0 0
\(457\) −1.03810e6 + 1.79803e6i −0.232513 + 0.402724i −0.958547 0.284935i \(-0.908028\pi\)
0.726034 + 0.687659i \(0.241361\pi\)
\(458\) −1.22199e6 691209.i −0.272209 0.153973i
\(459\) 0 0
\(460\) 6.80306e6 4.08950e6i 1.49903 0.901105i
\(461\) −2.52767e6 1.45935e6i −0.553947 0.319821i 0.196766 0.980451i \(-0.436956\pi\)
−0.750712 + 0.660629i \(0.770290\pi\)
\(462\) 0 0
\(463\) 5.02987e6 2.90400e6i 1.09045 0.629569i 0.156751 0.987638i \(-0.449898\pi\)
0.933695 + 0.358069i \(0.116565\pi\)
\(464\) −181404. 5.13727e6i −0.0391158 1.10774i
\(465\) 0 0
\(466\) −977114. 1.65844e6i −0.208440 0.353781i
\(467\) 8.31962e6 1.76527 0.882636 0.470058i \(-0.155767\pi\)
0.882636 + 0.470058i \(0.155767\pi\)
\(468\) 0 0
\(469\) −41838.9 −0.00878311
\(470\) 4.68689e6 + 7.95498e6i 0.978678 + 1.66110i
\(471\) 0 0
\(472\) 4.54815e6 2.78894e6i 0.939679 0.576214i
\(473\) −2.46598e6 + 1.42373e6i −0.506799 + 0.292601i
\(474\) 0 0
\(475\) 3.65323e6 + 2.10919e6i 0.742922 + 0.428926i
\(476\) 2.58666e6 + 4.30302e6i 0.523265 + 0.870474i
\(477\) 0 0
\(478\) −2.99273e6 1.69282e6i −0.599098 0.338876i
\(479\) −57304.6 + 99254.5i −0.0114117 + 0.0197657i −0.871675 0.490085i \(-0.836966\pi\)
0.860263 + 0.509850i \(0.170299\pi\)
\(480\) 0 0
\(481\) 559963. + 969884.i 0.110356 + 0.191142i
\(482\) 75538.8 + 8.56022e6i 0.0148099 + 1.67829i
\(483\) 0 0
\(484\) −723009. + 12761.2i −0.140291 + 0.00247616i
\(485\) 6.77943e6i 1.30870i
\(486\) 0 0
\(487\) 2.72517e6i 0.520681i 0.965517 + 0.260340i \(0.0838348\pi\)
−0.965517 + 0.260340i \(0.916165\pi\)
\(488\) −3.81510e6 2.06998e6i −0.725197 0.393475i
\(489\) 0 0
\(490\) −2.75436e6 + 24305.6i −0.518240 + 0.00457315i
\(491\) 2.94851e6 + 5.10696e6i 0.551948 + 0.956002i 0.998134 + 0.0610621i \(0.0194488\pi\)
−0.446186 + 0.894940i \(0.647218\pi\)
\(492\) 0 0
\(493\) 3.78946e6 6.56353e6i 0.702198 1.21624i
\(494\) 293006. 518004.i 0.0540205 0.0955027i
\(495\) 0 0
\(496\) −3.55119e6 1.88642e6i −0.648141 0.344298i
\(497\) 3.29804e6 + 1.90413e6i 0.598915 + 0.345784i
\(498\) 0 0
\(499\) 6.34312e6 3.66220e6i 1.14039 0.658402i 0.193860 0.981029i \(-0.437899\pi\)
0.946526 + 0.322627i \(0.104566\pi\)
\(500\) 725811. + 402138.i 0.129837 + 0.0719367i
\(501\) 0 0
\(502\) 5.52260e6 3.25379e6i 0.978103 0.576275i
\(503\) −5.80816e6 −1.02357 −0.511786 0.859113i \(-0.671016\pi\)
−0.511786 + 0.859113i \(0.671016\pi\)
\(504\) 0 0
\(505\) 1.00775e7 1.75843
\(506\) −6.39181e6 + 3.76591e6i −1.10981 + 0.653873i
\(507\) 0 0
\(508\) −2.08645e6 1.15600e6i −0.358714 0.198747i
\(509\) 3.70500e6 2.13908e6i 0.633861 0.365960i −0.148385 0.988930i \(-0.547407\pi\)
0.782246 + 0.622970i \(0.214074\pi\)
\(510\) 0 0
\(511\) −5.27714e6 3.04676e6i −0.894018 0.516162i
\(512\) −470581. 5.91295e6i −0.0793340 0.996848i
\(513\) 0 0
\(514\) −2.98758e6 + 5.28174e6i −0.498784 + 0.881798i
\(515\) 2.70922e6 4.69251e6i 0.450119 0.779628i
\(516\) 0 0
\(517\) −4.31472e6 7.47332e6i −0.709948 1.22967i
\(518\) 7.66274e6 67619.0i 1.25476 0.0110725i
\(519\) 0 0
\(520\) 601176. 1.10800e6i 0.0974975 0.179693i
\(521\) 6.07298e6i 0.980184i −0.871671 0.490092i \(-0.836963\pi\)
0.871671 0.490092i \(-0.163037\pi\)
\(522\) 0 0
\(523\) 525817.i 0.0840583i −0.999116 0.0420291i \(-0.986618\pi\)
0.999116 0.0420291i \(-0.0133822\pi\)
\(524\) 4.28515e6 75633.5i 0.681770 0.0120333i
\(525\) 0 0
\(526\) 34091.8 + 3.86336e6i 0.00537262 + 0.608837i
\(527\) −2.96430e6 5.13432e6i −0.464939 0.805297i
\(528\) 0 0
\(529\) −1.46446e6 + 2.53652e6i −0.227530 + 0.394093i
\(530\) −7.20085e6 4.07312e6i −1.11351 0.629850i
\(531\) 0 0
\(532\) −2.09799e6 3.49010e6i −0.321384 0.534637i
\(533\) 1.29488e6 + 747598.i 0.197429 + 0.113986i
\(534\) 0 0
\(535\) −1.01109e7 + 5.83751e6i −1.52723 + 0.881746i
\(536\) 38097.2 + 62128.1i 0.00572771 + 0.00934063i
\(537\) 0 0
\(538\) 2.67579e6 + 4.54158e6i 0.398562 + 0.676474i
\(539\) 2.57440e6 0.381685
\(540\) 0 0
\(541\) 1.11917e7 1.64400 0.822000 0.569488i \(-0.192858\pi\)
0.822000 + 0.569488i \(0.192858\pi\)
\(542\) 5.06490e6 + 8.59657e6i 0.740581 + 1.25698i
\(543\) 0 0
\(544\) 4.03438e6 7.75921e6i 0.584494 1.12414i
\(545\) 9.67679e6 5.58690e6i 1.39553 0.805711i
\(546\) 0 0
\(547\) −776917. 448553.i −0.111021 0.0640982i 0.443461 0.896294i \(-0.353750\pi\)
−0.554482 + 0.832195i \(0.687084\pi\)
\(548\) 4.53537e6 2.72633e6i 0.645151 0.387817i
\(549\) 0 0
\(550\) −7.26888e6 4.11160e6i −1.02461 0.579567i
\(551\) −3.07356e6 + 5.32357e6i −0.431284 + 0.747006i
\(552\) 0 0
\(553\) 2.36123e6 + 4.08977e6i 0.328341 + 0.568704i
\(554\) 30883.0 + 3.49973e6i 0.00427509 + 0.484463i
\(555\) 0 0
\(556\) 68711.4 + 3.89296e6i 0.00942631 + 0.534064i
\(557\) 2.91603e6i 0.398249i −0.979974 0.199124i \(-0.936190\pi\)
0.979974 0.199124i \(-0.0638098\pi\)
\(558\) 0 0
\(559\) 570864.i 0.0772686i
\(560\) −4.57367e6 7.31306e6i −0.616304 0.985437i
\(561\) 0 0
\(562\) −1.03322e7 + 91175.1i −1.37991 + 0.0121769i
\(563\) −1.88482e6 3.26460e6i −0.250610 0.434070i 0.713084 0.701079i \(-0.247298\pi\)
−0.963694 + 0.267009i \(0.913965\pi\)
\(564\) 0 0
\(565\) −1.15575e6 + 2.00182e6i −0.152315 + 0.263817i
\(566\) −5.26003e6 + 9.29918e6i −0.690156 + 1.22012i
\(567\) 0 0
\(568\) −175586. 6.63122e6i −0.0228359 0.862428i
\(569\) 578222. + 333836.i 0.0748710 + 0.0432268i 0.536968 0.843603i \(-0.319570\pi\)
−0.462097 + 0.886829i \(0.652903\pi\)
\(570\) 0 0
\(571\) 5.54218e6 3.19978e6i 0.711361 0.410704i −0.100204 0.994967i \(-0.531949\pi\)
0.811565 + 0.584262i \(0.198616\pi\)
\(572\) −570992. + 1.03057e6i −0.0729693 + 0.131701i
\(573\) 0 0
\(574\) 8.81465e6 5.19339e6i 1.11667 0.657917i
\(575\) −1.05424e7 −1.32974
\(576\) 0 0
\(577\) −8.64788e6 −1.08136 −0.540680 0.841229i \(-0.681833\pi\)
−0.540680 + 0.841229i \(0.681833\pi\)
\(578\) 4.18893e6 2.46802e6i 0.521535 0.307276i
\(579\) 0 0
\(580\) −6.31032e6 + 1.13894e7i −0.778899 + 1.40582i
\(581\) −4.90560e6 + 2.83225e6i −0.602908 + 0.348089i
\(582\) 0 0
\(583\) 6.69626e6 + 3.86609e6i 0.815945 + 0.471086i
\(584\) 280952. + 1.06105e7i 0.0340879 + 1.28737i
\(585\) 0 0
\(586\) −3.10385e6 + 5.48729e6i −0.373385 + 0.660107i
\(587\) −358200. + 620420.i −0.0429072 + 0.0743175i −0.886681 0.462381i \(-0.846995\pi\)
0.843774 + 0.536698i \(0.180329\pi\)
\(588\) 0 0
\(589\) 2.40429e6 + 4.16436e6i 0.285561 + 0.494606i
\(590\) −1.35132e7 + 119246.i −1.59819 + 0.0141031i
\(591\) 0 0
\(592\) −7.07785e6 1.13171e7i −0.830037 1.32718i
\(593\) 6.55369e6i 0.765331i −0.923887 0.382665i \(-0.875006\pi\)
0.923887 0.382665i \(-0.124994\pi\)
\(594\) 0 0
\(595\) 1.27171e7i 1.47264i
\(596\) −39637.4 2.24572e6i −0.00457077 0.258965i
\(597\) 0 0
\(598\) 13124.1 + 1.48726e6i 0.00150078 + 0.170072i
\(599\) −1.04139e6 1.80373e6i −0.118589 0.205402i 0.800620 0.599173i \(-0.204504\pi\)
−0.919209 + 0.393771i \(0.871170\pi\)
\(600\) 0 0
\(601\) 392578. 679965.i 0.0443343 0.0767893i −0.843007 0.537903i \(-0.819217\pi\)
0.887341 + 0.461114i \(0.152550\pi\)
\(602\) 3.39989e6 + 1.92313e6i 0.382361 + 0.216280i
\(603\) 0 0
\(604\) −985480. + 592398.i −0.109915 + 0.0660725i
\(605\) 1.58625e6 + 915822.i 0.176191 + 0.101724i
\(606\) 0 0
\(607\) 8.67650e6 5.00938e6i 0.955812 0.551838i 0.0609306 0.998142i \(-0.480593\pi\)
0.894882 + 0.446304i \(0.147260\pi\)
\(608\) −3.27222e6 + 6.29336e6i −0.358991 + 0.690437i
\(609\) 0 0
\(610\) 5.58096e6 + 9.47247e6i 0.607273 + 1.03072i
\(611\) −1.73005e6 −0.187480
\(612\) 0 0
\(613\) −4.81550e6 −0.517595 −0.258797 0.965932i \(-0.583326\pi\)
−0.258797 + 0.965932i \(0.583326\pi\)
\(614\) −4.72065e6 8.01229e6i −0.505337 0.857700i
\(615\) 0 0
\(616\) 4.21421e6 + 6.87245e6i 0.447470 + 0.729726i
\(617\) −8.76037e6 + 5.05780e6i −0.926423 + 0.534871i −0.885678 0.464299i \(-0.846306\pi\)
−0.0407445 + 0.999170i \(0.512973\pi\)
\(618\) 0 0
\(619\) −1.10769e7 6.39527e6i −1.16196 0.670860i −0.210190 0.977661i \(-0.567408\pi\)
−0.951774 + 0.306800i \(0.900742\pi\)
\(620\) 5.24757e6 + 8.72957e6i 0.548251 + 0.912040i
\(621\) 0 0
\(622\) 3.57695e6 + 2.02328e6i 0.370712 + 0.209691i
\(623\) 2.35582e6 4.08040e6i 0.243177 0.421195i
\(624\) 0 0
\(625\) 4.33178e6 + 7.50287e6i 0.443575 + 0.768294i
\(626\) 70128.2 + 7.94709e6i 0.00715248 + 0.810536i
\(627\) 0 0
\(628\) −5.40103e6 + 95329.1i −0.546484 + 0.00964554i
\(629\) 1.96800e7i 1.98334i
\(630\) 0 0
\(631\) 1.13313e7i 1.13294i 0.824082 + 0.566471i \(0.191692\pi\)
−0.824082 + 0.566471i \(0.808308\pi\)
\(632\) 3.92299e6 7.23029e6i 0.390683 0.720051i
\(633\) 0 0
\(634\) 7.94915e6 70146.4i 0.785412 0.00693078i
\(635\) 3.02093e6 + 5.23241e6i 0.297308 + 0.514953i
\(636\) 0 0
\(637\) 258060. 446974.i 0.0251984 0.0436449i
\(638\) 5.99151e6 1.05924e7i 0.582753 1.03025i
\(639\) 0 0
\(640\) −6.69479e6 + 1.34507e7i −0.646081 + 1.29806i
\(641\) 1.30074e7 + 7.50980e6i 1.25039 + 0.721910i 0.971186 0.238323i \(-0.0765976\pi\)
0.279200 + 0.960233i \(0.409931\pi\)
\(642\) 0 0
\(643\) 2.31540e6 1.33680e6i 0.220851 0.127508i −0.385493 0.922711i \(-0.625969\pi\)
0.606344 + 0.795202i \(0.292635\pi\)
\(644\) 8.90186e6 + 4.93211e6i 0.845797 + 0.468617i
\(645\) 0 0
\(646\) −9.01038e6 + 5.30870e6i −0.849497 + 0.500503i
\(647\) 1.55764e7 1.46288 0.731438 0.681908i \(-0.238850\pi\)
0.731438 + 0.681908i \(0.238850\pi\)
\(648\) 0 0
\(649\) 1.26303e7 1.17707
\(650\) −1.44250e6 + 849888.i −0.133916 + 0.0789003i
\(651\) 0 0
\(652\) −9.11446e6 5.04990e6i −0.839676 0.465226i
\(653\) −415132. + 239677.i −0.0380981 + 0.0219959i −0.518928 0.854818i \(-0.673669\pi\)
0.480830 + 0.876814i \(0.340335\pi\)
\(654\) 0 0
\(655\) −9.40143e6 5.42792e6i −0.856230 0.494345i
\(656\) −1.57382e7 8.36027e6i −1.42789 0.758509i
\(657\) 0 0
\(658\) −5.82818e6 + 1.03036e7i −0.524769 + 0.927737i
\(659\) 155358. 269087.i 0.0139354 0.0241368i −0.858974 0.512020i \(-0.828897\pi\)
0.872909 + 0.487883i \(0.162231\pi\)
\(660\) 0 0
\(661\) 1.04750e7 + 1.81433e7i 0.932505 + 1.61515i 0.779023 + 0.626995i \(0.215715\pi\)
0.153482 + 0.988151i \(0.450951\pi\)
\(662\) −1.39797e6 + 12336.2i −0.123980 + 0.00109405i
\(663\) 0 0
\(664\) 8.67259e6 + 4.70555e6i 0.763358 + 0.414181i
\(665\) 1.03146e7i 0.904481i
\(666\) 0 0
\(667\) 1.53625e7i 1.33705i
\(668\) 6.82853e6 120525.i 0.592088 0.0104505i
\(669\) 0 0
\(670\) −1628.91 184592.i −0.000140188 0.0158864i
\(671\) −5.13780e6 8.89893e6i −0.440525 0.763012i
\(672\) 0 0
\(673\) 6.73764e6 1.16699e7i 0.573417 0.993187i −0.422795 0.906225i \(-0.638951\pi\)
0.996212 0.0869616i \(-0.0277157\pi\)
\(674\) −1.06256e7 6.01028e6i −0.900953 0.509619i
\(675\) 0 0
\(676\) −5.99965e6 9.98069e6i −0.504963 0.840028i
\(677\) −3.38026e6 1.95159e6i −0.283451 0.163650i 0.351534 0.936175i \(-0.385660\pi\)
−0.634985 + 0.772525i \(0.718994\pi\)
\(678\) 0 0
\(679\) −7.52747e6 + 4.34599e6i −0.626577 + 0.361755i
\(680\) −1.88841e7 + 1.15798e7i −1.56612 + 0.960347i
\(681\) 0 0
\(682\) −4.83235e6 8.20187e6i −0.397830 0.675230i
\(683\) −1.55558e7 −1.27597 −0.637985 0.770048i \(-0.720232\pi\)
−0.637985 + 0.770048i \(0.720232\pi\)
\(684\) 0 0
\(685\) −1.34038e7 −1.09144
\(686\) −6.80814e6 1.15554e7i −0.552355 0.937504i
\(687\) 0 0
\(688\) −240109. 6.79976e6i −0.0193391 0.547675i
\(689\) 1.34248e6 775080.i 0.107736 0.0622011i
\(690\) 0 0
\(691\) 9.52435e6 + 5.49889e6i 0.758823 + 0.438107i 0.828873 0.559437i \(-0.188983\pi\)
−0.0700501 + 0.997543i \(0.522316\pi\)
\(692\) 872493. 524478.i 0.0692622 0.0416353i
\(693\) 0 0
\(694\) 7.91850e6 + 4.47905e6i 0.624086 + 0.353010i
\(695\) 4.93114e6 8.54099e6i 0.387245 0.670728i
\(696\) 0 0
\(697\) −1.31372e7 2.27543e7i −1.02429 1.77412i
\(698\) 23347.6 + 2.64580e6i 0.00181386 + 0.205551i
\(699\) 0 0
\(700\) 202169. + 1.14542e7i 0.0155944 + 0.883527i
\(701\) 1.51787e7i 1.16665i 0.812239 + 0.583324i \(0.198248\pi\)
−0.812239 + 0.583324i \(0.801752\pi\)
\(702\) 0 0
\(703\) 1.59621e7i 1.21815i
\(704\) 6.36783e6 1.25157e7i 0.484239 0.951749i
\(705\) 0 0
\(706\) 2.59773e6 22923.4i 0.196147 0.00173088i
\(707\) 6.46024e6 + 1.11895e7i 0.486071 + 0.841900i
\(708\) 0 0
\(709\) −6.34771e6 + 1.09946e7i −0.474244 + 0.821414i −0.999565 0.0294896i \(-0.990612\pi\)
0.525321 + 0.850904i \(0.323945\pi\)
\(710\) −8.27255e6 + 1.46250e7i −0.615876 + 1.08881i
\(711\) 0 0
\(712\) −8.20427e6 + 217238.i −0.606513 + 0.0160597i
\(713\) −1.04073e7 6.00867e6i −0.766682 0.442644i
\(714\) 0 0
\(715\) 2.58447e6 1.49215e6i 0.189063 0.109156i
\(716\) 7.37269e6 1.33068e7i 0.537456 0.970043i
\(717\) 0 0
\(718\) −1.07952e7 + 6.36029e6i −0.781484 + 0.460432i
\(719\) −1.30901e7 −0.944324 −0.472162 0.881512i \(-0.656526\pi\)
−0.472162 + 0.881512i \(0.656526\pi\)
\(720\) 0 0
\(721\) 6.94705e6 0.497693
\(722\) −4.75993e6 + 2.80444e6i −0.339826 + 0.200218i
\(723\) 0 0
\(724\) 72819.5 131430.i 0.00516299 0.00931857i
\(725\) 1.49766e7 8.64672e6i 1.05820 0.610951i
\(726\) 0 0
\(727\) 6.63075e6 + 3.82826e6i 0.465293 + 0.268637i 0.714267 0.699873i \(-0.246760\pi\)
−0.248974 + 0.968510i \(0.580093\pi\)
\(728\) 1.61564e6 42780.1i 0.112984 0.00299167i
\(729\) 0 0
\(730\) 1.32368e7 2.34012e7i 0.919337 1.62529i
\(731\) 5.01578e6 8.68758e6i 0.347172 0.601319i
\(732\) 0 0
\(733\) 9.24808e6 + 1.60181e7i 0.635757 + 1.10116i 0.986354 + 0.164638i \(0.0526455\pi\)
−0.350597 + 0.936527i \(0.614021\pi\)
\(734\) 1.66270e7 146723.i 1.13913 0.0100521i
\(735\) 0 0
\(736\) −781875. 1.77097e7i −0.0532038 1.20508i
\(737\) 172532.i 0.0117004i
\(738\) 0 0
\(739\) 3.75594e6i 0.252992i −0.991967 0.126496i \(-0.959627\pi\)
0.991967 0.126496i \(-0.0403732\pi\)
\(740\) 596666. + 3.38052e7i 0.0400546 + 2.26936i
\(741\) 0 0
\(742\) −93595.7 1.06065e7i −0.00624088 0.707231i
\(743\) 22492.7 + 38958.6i 0.00149476 + 0.00258899i 0.866772 0.498705i \(-0.166191\pi\)
−0.865277 + 0.501294i \(0.832858\pi\)
\(744\) 0 0
\(745\) −2.84462e6 + 4.92702e6i −0.187773 + 0.325232i
\(746\) 8.17760e6 + 4.62561e6i 0.537996 + 0.304314i
\(747\) 0 0
\(748\) 1.77444e7 1.06666e7i 1.15960 0.697066i
\(749\) −1.29632e7 7.48433e6i −0.844324 0.487471i
\(750\) 0 0
\(751\) −2.26479e7 + 1.30757e7i −1.46530 + 0.845993i −0.999248 0.0387633i \(-0.987658\pi\)
−0.466054 + 0.884756i \(0.654325\pi\)
\(752\) 2.06072e7 727667.i 1.32884 0.0469232i
\(753\) 0 0
\(754\) −1.23848e6 2.10204e6i −0.0793339 0.134652i
\(755\) 2.91248e6 0.185950
\(756\) 0 0
\(757\) −8.60555e6 −0.545807 −0.272903 0.962041i \(-0.587984\pi\)
−0.272903 + 0.962041i \(0.587984\pi\)
\(758\) 1.34719e7 + 2.28657e7i 0.851640 + 1.44548i
\(759\) 0 0
\(760\) 1.53166e7 9.39217e6i 0.961894 0.589837i
\(761\) −2.15910e7 + 1.24656e7i −1.35148 + 0.780280i −0.988458 0.151498i \(-0.951590\pi\)
−0.363027 + 0.931779i \(0.618257\pi\)
\(762\) 0 0
\(763\) 1.24067e7 + 7.16302e6i 0.771516 + 0.445435i
\(764\) −9.98326e6 1.66076e7i −0.618784 1.02937i
\(765\) 0 0
\(766\) 2.60782e7 + 1.47510e7i 1.60585 + 0.908341i
\(767\) 1.26608e6 2.19291e6i 0.0777090 0.134596i
\(768\) 0 0
\(769\) −1.62777e7 2.81939e7i −0.992610 1.71925i −0.601398 0.798950i \(-0.705389\pi\)
−0.391212 0.920300i \(-0.627944\pi\)
\(770\) −180186. 2.04191e7i −0.0109520 1.24111i
\(771\) 0 0
\(772\) 2.98799e6 52738.5i 0.180441 0.00318482i
\(773\) 1.64551e6i 0.0990493i −0.998773 0.0495246i \(-0.984229\pi\)
0.998773 0.0495246i \(-0.0157706\pi\)
\(774\) 0 0
\(775\) 1.35278e7i 0.809044i
\(776\)