Properties

Label 108.6.h.a.35.15
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 35.15
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0499164 - 5.65663i) q^{2} +(-31.9950 - 0.564717i) q^{4} +(-70.1957 + 40.5275i) q^{5} +(89.9985 + 51.9607i) q^{7} +(-4.79147 + 180.956i) q^{8} +O(q^{10})\) \(q+(0.0499164 - 5.65663i) q^{2} +(-31.9950 - 0.564717i) q^{4} +(-70.1957 + 40.5275i) q^{5} +(89.9985 + 51.9607i) q^{7} +(-4.79147 + 180.956i) q^{8} +(225.745 + 399.094i) q^{10} +(214.271 - 371.129i) q^{11} +(42.9574 + 74.4044i) q^{13} +(298.415 - 506.495i) q^{14} +(1023.36 + 36.1363i) q^{16} -1509.75i q^{17} -1224.53i q^{19} +(2268.80 - 1257.04i) q^{20} +(-2088.64 - 1230.58i) q^{22} +(1530.14 + 2650.27i) q^{23} +(1722.45 - 2983.38i) q^{25} +(423.023 - 239.280i) q^{26} +(-2850.16 - 1713.31i) q^{28} +(4347.44 + 2510.00i) q^{29} +(-3400.78 + 1963.44i) q^{31} +(255.492 - 5786.98i) q^{32} +(-8540.08 - 75.3610i) q^{34} -8423.34 q^{35} +13035.3 q^{37} +(-6926.71 - 61.1240i) q^{38} +(-6997.35 - 12896.5i) q^{40} +(15071.6 - 8701.62i) q^{41} +(-5754.33 - 3322.27i) q^{43} +(-7065.19 + 11753.3i) q^{44} +(15068.0 - 8523.13i) q^{46} +(10068.4 - 17438.9i) q^{47} +(-3003.68 - 5202.52i) q^{49} +(-16789.9 - 9892.22i) q^{50} +(-1332.41 - 2404.83i) q^{52} -18043.0i q^{53} +34735.5i q^{55} +(-9833.82 + 16036.8i) q^{56} +(14415.1 - 24466.6i) q^{58} +(14736.4 + 25524.2i) q^{59} +(-11989.0 + 20765.6i) q^{61} +(10936.7 + 19335.0i) q^{62} +(-32722.1 - 1734.09i) q^{64} +(-6030.85 - 3481.91i) q^{65} +(-348.663 + 201.301i) q^{67} +(-852.579 + 48304.3i) q^{68} +(-420.463 + 47647.8i) q^{70} +36645.5 q^{71} +58635.9 q^{73} +(650.675 - 73735.9i) q^{74} +(-691.512 + 39178.8i) q^{76} +(38568.2 - 22267.4i) q^{77} +(39354.5 + 22721.3i) q^{79} +(-73300.1 + 38937.7i) q^{80} +(-48469.5 - 85689.1i) q^{82} +(-27253.7 + 47204.9i) q^{83} +(61186.2 + 105978. i) q^{85} +(-19080.1 + 32384.3i) q^{86} +(66131.2 + 40551.9i) q^{88} +45338.5i q^{89} +8928.39i q^{91} +(-47460.1 - 85659.6i) q^{92} +(-98143.1 - 57823.6i) q^{94} +(49627.1 + 85956.6i) q^{95} +(41820.0 - 72434.3i) q^{97} +(-29578.7 + 16731.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0499164 5.65663i 0.00882405 0.999961i
\(3\) 0 0
\(4\) −31.9950 0.564717i −0.999844 0.0176474i
\(5\) −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 0.805187 0.593021i \(-0.202065\pi\)
−0.110978 + 0.993823i \(0.535398\pi\)
\(8\) −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 \(-0.654049\pi\)
0.999214 0.0396293i \(-0.0126177\pi\)
\(12\) 0 0
\(13\) 42.9574 + 74.4044i 0.0704985 + 0.122107i 0.899120 0.437702i \(-0.144208\pi\)
−0.828621 + 0.559809i \(0.810874\pi\)
\(14\) 298.415 506.495i 0.406912 0.690645i
\(15\) 0 0
\(16\) 1023.36 + 36.1363i 0.999377 + 0.0352893i
\(17\) 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 \(-0.872788\pi\)
0.921198 0.389094i \(-0.127212\pi\)
\(20\) 2268.80 1257.04i 1.26830 0.702705i
\(21\) 0 0
\(22\) −2088.64 1230.58i −0.920042 0.542067i
\(23\) 1530.14 + 2650.27i 0.603129 + 1.04465i 0.992344 + 0.123503i \(0.0394130\pi\)
−0.389215 + 0.921147i \(0.627254\pi\)
\(24\) 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 −0.782913 0.622132i \(-0.786267\pi\)
0.147326 + 0.989088i \(0.452933\pi\)
\(32\) 255.492 5786.98i 0.0441065 0.999027i
\(33\) 0 0
\(34\) −8540.08 75.3610i −1.26696 0.0111802i
\(35\) −8423.34 −1.16229
\(36\) 0 0
\(37\) 13035.3 1.56537 0.782684 0.622419i \(-0.213850\pi\)
0.782684 + 0.622419i \(0.213850\pi\)
\(38\) −6926.71 61.1240i −0.778158 0.00686677i
\(39\) 0 0
\(40\) −6997.35 12896.5i −0.691486 1.27445i
\(41\) 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 0.243566 0.969884i \(-0.421683\pi\)
−0.718162 + 0.695876i \(0.755016\pi\)
\(44\) −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 \(-0.601835\pi\)
0.979330 0.202270i \(-0.0648319\pi\)
\(48\) 0 0
\(49\) −3003.68 5202.52i −0.178716 0.309545i
\(50\) −16789.9 9892.22i −0.949781 0.559588i
\(51\) 0 0
\(52\) −1332.41 2404.83i −0.0683326 0.123332i
\(53\) 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
\(56\) −9833.82 + 16036.8i −0.419037 + 0.683357i
\(57\) 0 0
\(58\) 14415.1 24466.6i 0.562664 0.955001i
\(59\) 14736.4 + 25524.2i 0.551140 + 0.954602i 0.998193 + 0.0600943i \(0.0191401\pi\)
−0.447053 + 0.894507i \(0.647527\pi\)
\(60\) 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 −0.504737 0.863273i \(-0.668411\pi\)
0.495248 + 0.868752i \(0.335077\pi\)
\(68\) −852.579 + 48304.3i −0.0223595 + 1.26682i
\(69\) 0 0
\(70\) −420.463 + 47647.8i −0.0102561 + 1.16224i
\(71\) 36645.5 0.862730 0.431365 0.902178i \(-0.358032\pi\)
0.431365 + 0.902178i \(0.358032\pi\)
\(72\) 0 0
\(73\) 58635.9 1.28782 0.643911 0.765100i \(-0.277311\pi\)
0.643911 + 0.765100i \(0.277311\pi\)
\(74\) 650.675 73735.9i 0.0138129 1.56531i
\(75\) 0 0
\(76\) −691.512 + 39178.8i −0.0137330 + 0.778067i
\(77\) 38568.2 22267.4i 0.741314 0.427998i
\(78\) 0 0
\(79\) 39354.5 + 22721.3i 0.709457 + 0.409605i 0.810860 0.585240i \(-0.199000\pi\)
−0.101403 + 0.994845i \(0.532333\pi\)
\(80\) −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 −0.997233 0.0743344i \(-0.976317\pi\)
0.562992 + 0.826462i \(0.309650\pi\)
\(84\) 0 0
\(85\) 61186.2 + 105978.i 0.918557 + 1.59099i
\(86\) −19080.1 + 32384.3i −0.278185 + 0.472160i
\(87\) 0 0
\(88\) 66131.2 + 40551.9i 0.910332 + 0.558219i
\(89\) 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
\(92\) −47460.1 85659.6i −0.584600 1.05513i
\(93\) 0 0
\(94\) −98143.1 57823.6i −1.14562 0.674971i
\(95\) 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 −0.206452 0.978457i \(-0.566192\pi\)
0.744143 + 0.668021i \(0.232858\pi\)
\(104\) −13669.8 + 7416.89i −0.123930 + 0.0672417i
\(105\) 0 0
\(106\) −102062. 900.639i −0.882270 0.00778550i
\(107\) −144038. −1.21624 −0.608119 0.793846i \(-0.708076\pi\)
−0.608119 + 0.793846i \(0.708076\pi\)
\(108\) 0 0
\(109\) −137855. −1.11136 −0.555680 0.831396i \(-0.687542\pi\)
−0.555680 + 0.831396i \(0.687542\pi\)
\(110\) 196486. + 1733.87i 1.54828 + 0.0136626i
\(111\) 0 0
\(112\) 90223.4 + 56426.8i 0.679633 + 0.425050i
\(113\) 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
\(122\) 116865. + 68854.0i 0.710860 + 0.418822i
\(123\) 0 0
\(124\) 109917. 60899.9i 0.641964 0.355683i
\(125\) 25930.3i 0.148434i
\(126\) 0 0
\(127\) 74540.3i 0.410093i 0.978752 + 0.205046i \(0.0657345\pi\)
−0.978752 + 0.205046i \(0.934266\pi\)
\(128\) −11442.5 + 185010.i −0.0617299 + 0.998093i
\(129\) 0 0
\(130\) −19996.9 + 33940.5i −0.103778 + 0.176141i
\(131\) −66965.9 115988.i −0.340938 0.590522i 0.643669 0.765304i \(-0.277411\pi\)
−0.984607 + 0.174782i \(0.944078\pi\)
\(132\) 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 −0.250546 0.968105i \(-0.580610\pi\)
0.713131 + 0.701031i \(0.247277\pi\)
\(140\) 269505. + 4756.81i 1.16211 + 0.0205114i
\(141\) 0 0
\(142\) 1829.21 207290.i 0.00761277 0.862696i
\(143\) 36818.2 0.150564
\(144\) 0 0
\(145\) −406896. −1.60717
\(146\) 2926.89 331682.i 0.0113638 1.28777i
\(147\) 0 0
\(148\) −417065. 7361.26i −1.56512 0.0276247i
\(149\) 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 0.554503 0.832182i \(-0.312908\pi\)
−0.443439 + 0.896304i \(0.646242\pi\)
\(152\) 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 \(0.921443\pi\)
\(158\) 130491. 221480.i 0.415850 0.705815i
\(159\) 0 0
\(160\) 216597. + 416576.i 0.668888 + 1.28645i
\(161\) 318028.i 0.966941i
\(162\) 0 0
\(163\) 325623.i 0.959943i 0.877284 + 0.479972i \(0.159353\pi\)
−0.877284 + 0.479972i \(0.840647\pi\)
\(164\) −487131. + 269897.i −1.41428 + 0.783590i
\(165\) 0 0
\(166\) 265660. + 156521.i 0.748267 + 0.440861i
\(167\) −106712. 184831.i −0.296090 0.512843i 0.679148 0.734002i \(-0.262350\pi\)
−0.975238 + 0.221158i \(0.929016\pi\)
\(168\) 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
\(176\) 232688. 372056.i 0.566230 0.905371i
\(177\) 0 0
\(178\) 256463. + 2263.13i 0.606702 + 0.00535378i
\(179\) −475398. −1.10898 −0.554491 0.832189i \(-0.687087\pi\)
−0.554491 + 0.832189i \(0.687087\pi\)
\(180\) 0 0
\(181\) 4695.48 0.0106533 0.00532664 0.999986i \(-0.498304\pi\)
0.00532664 + 0.999986i \(0.498304\pi\)
\(182\) 50504.6 + 445.673i 0.113019 + 0.000997327i
\(183\) 0 0
\(184\) −486914. + 264188.i −1.06025 + 0.575267i
\(185\) −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 \(0.371707\pi\)
−0.992742 + 0.120263i \(0.961626\pi\)
\(192\) 0 0
\(193\) 46694.6 + 80877.5i 0.0902347 + 0.156291i 0.907610 0.419815i \(-0.137905\pi\)
−0.817375 + 0.576106i \(0.804572\pi\)
\(194\) −407647. 240176.i −0.777642 0.458168i
\(195\) 0 0
\(196\) 93164.7 + 168151.i 0.173225 + 0.312650i
\(197\) 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 \(-0.810730\pi\)
0.828367 0.560185i \(-0.189270\pi\)
\(200\) 531607. + 325983.i 0.939757 + 0.576262i
\(201\) 0 0
\(202\) −357018. + 605960.i −0.615618 + 1.04488i
\(203\) 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 0.215794 0.976439i \(-0.430766\pi\)
0.953518 + 0.301336i \(0.0974326\pi\)
\(212\) −10189.2 + 577285.i −0.0155704 + 0.882167i
\(213\) 0 0
\(214\) −7189.87 + 814772.i −0.0107321 + 1.21619i
\(215\) 538572. 0.794599
\(216\) 0 0
\(217\) −408088. −0.588307
\(218\) −6881.20 + 779793.i −0.00980670 + 1.11132i
\(219\) 0 0
\(220\) 19615.7 1.11136e6i 0.0273242 1.54810i
\(221\) 112332. 64854.8i 0.154711 0.0893226i
\(222\) 0 0
\(223\) −419169. 242007.i −0.564452 0.325886i 0.190479 0.981691i \(-0.438996\pi\)
−0.754930 + 0.655805i \(0.772329\pi\)
\(224\) 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 −0.931917 0.362673i \(-0.881864\pi\)
0.780042 + 0.625727i \(0.215198\pi\)
\(228\) 0 0
\(229\) 124091. + 214932.i 0.156369 + 0.270840i 0.933557 0.358429i \(-0.116688\pi\)
−0.777187 + 0.629269i \(0.783354\pi\)
\(230\) −712288. + 1.20895e6i −0.887842 + 1.50692i
\(231\) 0 0
\(232\) −475030. + 774669.i −0.579430 + 0.944923i
\(233\) 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
\(236\) −457078. 824969.i −0.534207 0.964179i
\(237\) 0 0
\(238\) −764679. 450531.i −0.875057 0.515563i
\(239\) −303908. 526384.i −0.344149 0.596084i 0.641049 0.767500i \(-0.278499\pi\)
−0.985199 + 0.171415i \(0.945166\pi\)
\(240\) 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
\(248\) −339002. 624800.i −0.350004 0.645077i
\(249\) 0 0
\(250\) 146678. + 1294.34i 0.148428 + 0.00130978i
\(251\) 1.13311e6 1.13524 0.567622 0.823289i \(-0.307864\pi\)
0.567622 + 0.823289i \(0.307864\pi\)
\(252\) 0 0
\(253\) 1.31146e6 1.28811
\(254\) 421647. + 3720.78i 0.410077 + 0.00361868i
\(255\) 0 0
\(256\) 1.04596e6 + 73961.0i 0.997509 + 0.0705347i
\(257\) 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 −0.977134 0.212623i \(-0.931799\pi\)
0.672704 + 0.739912i \(0.265133\pi\)
\(264\) 0 0
\(265\) 731236. + 1.26654e6i 0.639651 + 1.10791i
\(266\) −620218. 365418.i −0.537452 0.316654i
\(267\) 0 0
\(268\) 11269.2 6243.72i 0.00958417 0.00531015i
\(269\) 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 \(0.260229\pi\)
−0.684023 + 0.729460i \(0.739771\pi\)
\(272\) 54556.6 1.54502e6i 0.0447121 1.26622i
\(273\) 0 0
\(274\) 474858. 805969.i 0.382109 0.648548i
\(275\) −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 −0.963625 0.267258i \(-0.913883\pi\)
−0.250361 + 0.968153i \(0.580549\pi\)
\(284\) −1.17247e6 20694.3i −0.862596 0.0152249i
\(285\) 0 0
\(286\) 1837.83 208267.i 0.00132859 0.150558i
\(287\) 1.80857e6 1.29607
\(288\) 0 0
\(289\) −859473. −0.605324
\(290\) −20310.7 + 2.30166e6i −0.0141818 + 1.60711i
\(291\) 0 0
\(292\) −1.87606e6 33112.7i −1.28762 0.0227267i
\(293\) 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
\(302\) 103181. 175127.i 0.0651001 0.110493i
\(303\) 0 0
\(304\) 44249.9 1.25314e6i 0.0274618 0.777704i
\(305\) 1.94354e6i 1.19631i
\(306\) 0 0
\(307\) 1.64394e6i 0.995497i −0.867321 0.497749i \(-0.834160\pi\)
0.867321 0.497749i \(-0.165840\pi\)
\(308\) −1.24656e6 + 690664.i −0.748752 + 0.414849i
\(309\) 0 0
\(310\) −1.55131e6 913995.i −0.916842 0.540182i
\(311\) 363235. + 629141.i 0.212954 + 0.368848i 0.952638 0.304107i \(-0.0983581\pi\)
−0.739683 + 0.672955i \(0.765025\pi\)
\(312\) 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
\(320\) 2.36723e6 1.20442e6i 1.29230 0.657510i
\(321\) 0 0
\(322\) 1.79897e6 + 15874.8i 0.966904 + 0.00853234i
\(323\) −1.84873e6 −0.985976
\(324\) 0 0
\(325\) 295969. 0.155431
\(326\) 1.84193e6 + 16253.9i 0.959906 + 0.00847059i
\(327\) 0 0
\(328\) 1.50239e6 + 2.76900e6i 0.771080 + 1.42114i
\(329\) 1.81228e6 1.04632e6i 0.923071 0.532935i
\(330\) 0 0
\(331\) −214028. 123569.i −0.107374 0.0619926i 0.445351 0.895356i \(-0.353079\pi\)
−0.552725 + 0.833363i \(0.686412\pi\)
\(332\) 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 \(0.660178\pi\)
\(338\) −1.77364e6 1.04499e6i −0.844451 0.497531i
\(339\) 0 0
\(340\) −1.89781e6 3.42531e6i −0.890337 1.60695i
\(341\) 1.68284e6i 0.783712i
\(342\) 0 0
\(343\) 2.37090e6i 1.08812i
\(344\) 628755. 1.02536e6i 0.286474 0.467177i
\(345\) 0 0
\(346\) 91350.9 155048.i 0.0410225 0.0696269i
\(347\) 804114. + 1.39277e6i 0.358504 + 0.620947i 0.987711 0.156291i \(-0.0499537\pi\)
−0.629207 + 0.777237i \(0.716620\pi\)
\(348\) 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
\(356\) 25603.4 1.45061e6i 0.0107071 0.606631i
\(357\) 0 0
\(358\) −23730.1 + 2.68915e6i −0.00978572 + 1.10894i
\(359\) −2.21493e6 −0.907037 −0.453518 0.891247i \(-0.649831\pi\)
−0.453518 + 0.891247i \(0.649831\pi\)
\(360\) 0 0
\(361\) 976629. 0.394423
\(362\) 234.381 26560.6i 9.40050e−5 0.0106529i
\(363\) 0 0
\(364\) 5042.01 285664.i 0.00199458 0.113006i
\(365\) −4.11598e6 + 2.37636e6i −1.61712 + 0.933643i
\(366\) 0 0
\(367\) 2.54558e6 + 1.46969e6i 0.986555 + 0.569588i 0.904243 0.427019i \(-0.140436\pi\)
0.0823124 + 0.996607i \(0.473769\pi\)
\(368\) 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 \(0.933344\pi\)
\(374\) −1.85786e6 + 3.15332e6i −0.686806 + 1.16571i
\(375\) 0 0
\(376\) 3.10744e6 + 1.90549e6i 1.13353 + 0.695083i
\(377\) 431292.i 0.156285i
\(378\) 0 0
\(379\) 4.69152e6i 1.67770i 0.544360 + 0.838852i \(0.316773\pi\)
−0.544360 + 0.838852i \(0.683227\pi\)
\(380\) −1.53928e6 2.77821e6i −0.546837 0.986974i
\(381\) 0 0
\(382\) 2.95129e6 + 1.73883e6i 1.03479 + 0.609677i
\(383\) 2.64821e6 + 4.58683e6i 0.922476 + 1.59777i 0.795571 + 0.605860i \(0.207171\pi\)
0.126904 + 0.991915i \(0.459496\pi\)
\(384\) 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
\(392\) 955818. 518605.i 0.314167 0.170460i
\(393\) 0 0
\(394\) −2.63836e6 23281.9i −0.856236 0.00755576i
\(395\) −3.68335e6 −1.18782
\(396\) 0 0
\(397\) 75711.5 0.0241094 0.0120547 0.999927i \(-0.496163\pi\)
0.0120547 + 0.999927i \(0.496163\pi\)
\(398\) −3.54040e6 31241.9i −1.12033 0.00988620i
\(399\) 0 0
\(400\) 1.87050e6 2.99083e6i 0.584532 0.934636i
\(401\) −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 \(-0.339733\pi\)
\(410\) 6.87512e6 + 4.05066e6i 2.01986 + 1.19005i
\(411\) 0 0
\(412\) −1.87116e6 + 1.03673e6i −0.543086 + 0.300899i
\(413\) 3.06285e6i 0.883591i
\(414\) 0 0
\(415\) 4.41810e6i 1.25926i
\(416\) 441552. 229584.i 0.125098 0.0650442i
\(417\) 0 0
\(418\) −1.50688e6 + 2.55760e6i −0.421830 + 0.715966i
\(419\) −2.65830e6 4.60430e6i −0.739721 1.28123i −0.952621 0.304161i \(-0.901624\pi\)
0.212899 0.977074i \(1.56829\pi\)
\(420\) 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
\(428\) 4.60851e6 + 81340.9i 1.21605 + 0.0214635i
\(429\) 0 0
\(430\) 26883.6 3.04651e6i 0.00701158 0.794568i
\(431\) 5.72244e6 1.48384 0.741922 0.670486i \(-0.233914\pi\)
0.741922 + 0.670486i \(0.233914\pi\)
\(432\) 0 0
\(433\) −6.17405e6 −1.58252 −0.791262 0.611478i \(-0.790575\pi\)
−0.791262 + 0.611478i \(0.790575\pi\)
\(434\) −20370.2 + 2.30840e6i −0.00519125 + 0.588284i
\(435\) 0 0
\(436\) 4.41066e6 + 77848.8i 1.11119 + 0.0196126i
\(437\) 3.24533e6 1.87369e6i 0.812935 0.469348i
\(438\) 0 0
\(439\) 5.02340e6 + 2.90026e6i 1.24405 + 0.718251i 0.969915 0.243442i \(-0.0782765\pi\)
0.274131 + 0.961692i \(0.411610\pi\)
\(440\) −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 \(0.335521\pi\)
−0.999976 + 0.00687158i \(0.997813\pi\)
\(444\) 0 0
\(445\) −1.83746e6 3.18257e6i −0.439863 0.761864i
\(446\) −1.38987e6 + 2.35900e6i −0.330854 + 0.561554i
\(447\) 0 0
\(448\) −2.85484e6 1.85633e6i −0.672026 0.436978i
\(449\) 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
\(452\) −798233. + 442265.i −0.183774 + 0.101821i
\(453\) 0 0
\(454\) 1.14934e6 + 677166.i 0.261704 + 0.154190i
\(455\) −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 −0.933695 0.358069i \(-0.883435\pi\)
−0.156751 + 0.987638i \(0.550102\pi\)
\(464\) 4.35831e6 + 2.72574e6i 0.939773 + 0.587745i
\(465\) 0 0
\(466\) 1.92481e6 + 16985.3i 0.410604 + 0.00362333i
\(467\) −8.31962e6 −1.76527 −0.882636 0.470058i \(-0.844233\pi\)
−0.882636 + 0.470058i \(0.844233\pi\)
\(468\) 0 0
\(469\) −41838.9 −0.00878311
\(470\) 9.23266e6 + 81472.6i 1.92789 + 0.0170125i
\(471\) 0 0
\(472\) −4.68936e6 + 2.54434e6i −0.968856 + 0.525679i
\(473\) −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 −0.860263 0.509850i \(-0.829701\pi\)
0.871675 + 0.490085i \(0.163034\pi\)
\(480\) 0 0
\(481\) 559963. + 969884.i 0.110356 + 0.191142i
\(482\) −7.37560e6 4.34553e6i −1.44604 0.851972i
\(483\) 0 0
\(484\) 350453. + 632524.i 0.0680011 + 0.122734i
\(485\) 6.77943e6i 1.30870i
\(486\) 0 0
\(487\) 2.72517e6i 0.520681i −0.965517 0.260340i \(-0.916165\pi\)
0.965517 0.260340i \(-0.0838348\pi\)
\(488\) −3.70021e6 2.26898e6i −0.703358 0.431302i
\(489\) 0 0
\(490\) 1.39823e6 2.37319e6i 0.263080 0.446522i
\(491\) −2.94851e6 5.10696e6i −0.551948 0.956002i −0.998134 0.0610621i \(-0.980551\pi\)
0.446186 0.894940i \(1.64722\pi\)
\(492\) 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 −0.946526 0.322627i \(-0.895434\pi\)
−0.193860 + 0.981029i \(0.562101\pi\)
\(500\) 14643.3 829640.i 0.00261947 0.148410i
\(501\) 0 0
\(502\) 56560.9 6.40961e6i 0.0100174 1.13520i
\(503\) 5.80816e6 1.02357 0.511786 0.859113i \(-0.328984\pi\)
0.511786 + 0.859113i \(0.328984\pi\)
\(504\) 0 0
\(505\) 1.00775e7 1.75843
\(506\) 65463.1 7.41843e6i 0.0113663 1.28806i
\(507\) 0 0
\(508\) 42094.2 2.38492e6i 0.00723707 0.410029i
\(509\) 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
\(518\) 3.88993e6 6.60231e6i 0.636967 1.08111i
\(519\) 0 0
\(520\) 658969. 1.07463e6i 0.106870 0.174282i
\(521\) 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 \(0.0133822\pi\)
−0.999116 + 0.0420291i \(0.986618\pi\)
\(524\) 2.07707e6 + 3.74886e6i 0.330464 + 0.596446i
\(525\) 0 0
\(526\) 3.32872e6 + 1.96121e6i 0.524582 + 0.309071i
\(527\) 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
\(536\) −34756.0 64057.2i −0.00522537 0.00963066i
\(537\) 0 0
\(538\) −5.27101e6 46513.5i −0.785124 0.00692825i
\(539\) −2.57440e6 −0.381685
\(540\) 0 0
\(541\) 1.11917e7 1.64400 0.822000 0.569488i \(-0.192858\pi\)
0.822000 + 0.569488i \(0.192858\pi\)
\(542\) 9.97730e6 + 88043.6i 1.45886 + 0.0128736i
\(543\) 0 0
\(544\) −8.73687e6 385728.i −1.26578 0.0558836i
\(545\) 9.67679e6 5.58690e6i 1.39553 0.805711i
\(546\) 0 0
\(547\) 776917. + 448553.i 0.111021 + 0.0640982i 0.554482 0.832195i \(-0.312916\pi\)
−0.443461 + 0.896294i \(0.646250\pi\)
\(548\) −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
\(554\) −3.01542e6 1.77661e6i −0.417420 0.245934i
\(555\) 0 0
\(556\) −3.40576e6 + 1.88698e6i −0.467226 + 0.258869i
\(557\) 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
\(560\) −8.62013e6 304388.i −1.16157 0.0410164i
\(561\) 0 0
\(562\) 5.24504e6 8.90233e6i 0.700500 1.18895i
\(563\) 1.88482e6 + 3.26460e6i 0.250610 + 0.434070i 0.963694 0.267009i \(-0.0860354\pi\)
−0.713084 + 0.701079i \(0.752702\pi\)
\(564\) 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 −0.811565 0.584262i \(-0.801384\pi\)
0.100204 + 0.994967i \(0.468051\pi\)
\(572\) −1.17800e6 20791.8i −0.150541 0.00265707i
\(573\) 0 0
\(574\) 90277.1 1.02304e7i 0.0114366 1.29602i
\(575\) 1.05424e7 1.32974
\(576\) 0 0
\(577\) −8.64788e6 −1.08136 −0.540680 0.841229i \(-0.681833\pi\)
−0.540680 + 0.841229i \(0.681833\pi\)
\(578\) −42901.8 + 4.86173e6i −0.00534141 + 0.605300i
\(579\) 0 0
\(580\) 1.30186e7 + 229781.i 1.60692 + 0.0283625i
\(581\) −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 −0.843774 0.536698i \(-0.819671\pi\)
0.886681 + 0.462381i \(0.153005\pi\)
\(588\) 0 0
\(589\) 2.40429e6 + 4.16436e6i 0.285561 + 0.494606i
\(590\) −6.85989e6 + 1.16432e7i −0.811310 + 1.37702i
\(591\) 0 0
\(592\) 1.33398e7 + 471047.i 1.56439 + 0.0552408i
\(593\) 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
\(596\) −1.96467e6 + 1.08854e6i −0.226556 + 0.125524i
\(597\) 0 0
\(598\) 1.28144e6 + 754995.i 0.146536 + 0.0863358i
\(599\) 1.04139e6 + 1.80373e6i 0.118589 + 0.205402i 0.919209 0.393771i \(-0.128830\pi\)
−0.800620 + 0.599173i \(0.795496\pi\)
\(600\) 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 −0.894882 0.446304i \(-0.852740\pi\)
−0.0609306 + 0.998142i \(0.519407\pi\)
\(608\) −7.08632e6 312857.i −0.777431 0.0343232i
\(609\) 0 0
\(610\) −1.09939e7 97014.3i −1.19626 0.0105563i
\(611\) 1.73005e6 0.187480
\(612\) 0 0
\(613\) −4.81550e6 −0.517595 −0.258797 0.965932i \(-0.583326\pi\)
−0.258797 + 0.965932i \(0.583326\pi\)
\(614\) −9.29917e6 82059.5i −0.995458 0.00878432i
\(615\) 0 0
\(616\) 3.84461e6 + 7.08583e6i 0.408226 + 0.752383i
\(617\) −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 0.951774 0.306800i \(-0.0992584\pi\)
0.210190 + 0.977661i \(0.432592\pi\)
\(620\) −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
\(626\) −6.84731e6 4.03428e6i −0.698368 0.411462i
\(627\) 0 0
\(628\) 2.61796e6 + 4.72510e6i 0.264889 + 0.478092i
\(629\) 1.96800e7i 1.98334i
\(630\) 0 0
\(631\) 1.13313e7i 1.13294i −0.824082 0.566471i \(-0.808308\pi\)
0.824082 0.566471i \(-0.191692\pi\)
\(632\) −4.30012e6 + 7.01256e6i −0.428241 + 0.698367i
\(633\) 0 0
\(634\) −4.03532e6 + 6.84909e6i −0.398708 + 0.676721i
\(635\) −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 −0.606344 0.795202i \(-0.707365\pi\)
0.385493 + 0.922711i \(0.374031\pi\)
\(644\) 179596. 1.01753e7i 0.0170640 0.966791i
\(645\) 0 0
\(646\) −92281.7 + 1.04576e7i −0.00870030 + 0.985937i
\(647\) −1.55764e7 −1.46288 −0.731438 0.681908i \(-0.761150\pi\)
−0.731438 + 0.681908i \(0.761150\pi\)
\(648\) 0 0
\(649\) 1.26303e7 1.17707
\(650\) 14773.7 1.67419e6i 0.00137153 0.155425i
\(651\) 0 0
\(652\) 183885. 1.04183e7i 0.0169405 0.959794i
\(653\) −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 −0.872909 0.487883i \(-0.837769\pi\)
0.858974 + 0.512020i \(0.171103\pi\)
\(660\) 0 0
\(661\) 1.04750e7 + 1.81433e7i 0.932505 + 1.61515i 0.779023 + 0.626995i \(0.215715\pi\)
0.153482 + 0.988151i \(0.450951\pi\)
\(662\) −709668. + 1.20451e6i −0.0629376 + 0.106823i
\(663\) 0 0
\(664\) −8.41142e6 5.15791e6i −0.740370 0.453997i
\(665\) 1.03146e7i 0.904481i
\(666\) 0 0
\(667\) 1.53625e7i 1.33705i
\(668\) 3.30989e6 + 5.97395e6i 0.286994 + 0.517989i
\(669\) 0 0
\(670\) −159047. 93706.7i −0.0136880 0.00806462i
\(671\) 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
\(680\) −1.94704e7 + 1.05642e7i −1.61474 + 0.876123i
\(681\) 0 0
\(682\) 9.51920e6 + 84001.1i 0.783681 + 0.00691551i
\(683\) 1.55558e7 1.27597 0.637985 0.770048i \(-0.279768\pi\)
0.637985 + 0.770048i \(0.279768\pi\)
\(684\) 0 0
\(685\) −1.34038e7 −1.09144
\(686\) −1.34113e7 118347.i −1.08808 0.00960164i
\(687\) 0 0
\(688\) −5.76871e6 3.60782e6i −0.464631 0.290586i
\(689\) 1.34248e6 775080.i 0.107736 0.0622011i
\(690\) 0 0
\(691\) −9.52435e6 5.49889e6i −0.758823 0.438107i 0.0700501 0.997543i \(-0.477684\pi\)
−0.828873 + 0.559437i \(0.811017\pi\)
\(692\) −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
\(698\) −2.27966e6 1.34312e6i −0.177105 0.104346i
\(699\) 0 0
\(700\) −1.00207e7 + 5.55202e6i −0.772954 + 0.428258i
\(701\) 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
\(704\) −7.65497e6 + 1.17725e7i −0.582119 + 0.895238i
\(705\) 0 0
\(706\) −1.31872e6 + 2.23824e6i −0.0995725 + 0.169003i
\(707\) −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
\(716\) 1.52104e7 + 268465.i 1.10881 + 0.0195707i
\(717\) 0 0
\(718\) −110561. + 1.25291e7i −0.00800374 + 0.907001i
\(719\) 1.30901e7 0.944324 0.472162 0.881512i \(-0.343474\pi\)
0.472162 + 0.881512i \(0.343474\pi\)
\(720\) 0 0
\(721\) 6.94705e6 0.497693
\(722\) 48749.8 5.52443e6i 0.00348040 0.394407i
\(723\) 0 0
\(724\) −150232. 2651.62i −0.0106516 0.000188003i
\(725\) 1.49766e7 8.64672e6i 1.05820 0.610951i
\(726\) 0 0
\(727\) −6.63075e6 3.82826e6i −0.465293 0.268637i 0.248974 0.968510i \(-0.419907\pi\)
−0.714267 + 0.699873i \(0.753240\pi\)
\(728\) −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 \(0.614021\pi\)
\(734\) 8.44057e6 1.43260e7i 0.578271 0.981491i
\(735\) 0 0
\(736\) 1.57280e7 8.17774e6i 1.07024 0.556466i
\(737\) 172532.i 0.0117004i
\(738\) 0 0
\(739\) 3.75594e6i 0.252992i 0.991967 + 0.126496i \(0.0403732\pi\)
−0.991967 + 0.126496i \(0.959627\pi\)
\(740\) 2.95745e7 1.63859e7i 1.98535 1.09999i
\(741\) 0 0
\(742\) −9.13868e6 5.38429e6i −0.609359 0.359020i
\(743\) −22492.7 38958.6i −0.00149476 0.00258899i 0.865277 0.501294i \(-0.167142\pi\)
−0.866772 + 0.498705i \(0.833809\pi\)
\(744\) 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 0.466054 0.884756i \(-0.345675\pi\)
0.999248 + 0.0387633i \(0.0123418\pi\)
\(752\) 1.09338e7 1.74825e7i 0.705059 1.12735i
\(753\) 0 0
\(754\) 2.43966e6 + 21528.5i 0.156279 + 0.00137907i
\(755\) −2.91248e6 −0.185950
\(756\) 0 0
\(757\) −8.60555e6 −0.545807 −0.272903 0.962041i \(-0.587984\pi\)
−0.272903 + 0.962041i \(0.587984\pi\)
\(758\) 2.65382e7 + 234183.i 1.67764 + 0.0148041i
\(759\) 0 0
\(760\) −1.57921e7 + 8.56845e6i −0.991761 + 0.538107i
\(761\) −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 \(-0.627944\pi\)
\(770\) 1.75934e7 + 1.03656e7i 1.06935 + 0.630039i
\(771\) 0 0
\(772\) −1.44832e6 2.61405e6i −0.0874625 0.157859i
\(773\) 1.64551e6i 0.0990493i −0.998773 0.0495246i \(-0.984229\pi\)
0.998773 0.0495246i \(-0.0157706\pi\)
\(774\) 0 0