Properties

Label 108.6.b.c.107.8
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
Analytic rank 0
Dimension 20
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.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{50}\cdot 3^{40} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.8
Root \(-1.93085 + 1.11477i\) of \(x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} - 4371873792 x^{6} + 17152147456 x^{4} - 32033996800 x^{2} + 41943040000\)
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.c.107.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.63934 + 4.33073i) q^{2} +(-5.51036 - 31.5220i) q^{4} -80.5384i q^{5} -216.819i q^{7} +(156.567 + 90.8555i) q^{8} +O(q^{10})\) \(q+(-3.63934 + 4.33073i) q^{2} +(-5.51036 - 31.5220i) q^{4} -80.5384i q^{5} -216.819i q^{7} +(156.567 + 90.8555i) q^{8} +(348.790 + 293.107i) q^{10} -153.345 q^{11} -945.747 q^{13} +(938.984 + 789.079i) q^{14} +(-963.272 + 347.395i) q^{16} +2184.11i q^{17} -719.706i q^{19} +(-2538.73 + 443.796i) q^{20} +(558.076 - 664.096i) q^{22} +2622.17 q^{23} -3361.43 q^{25} +(3441.90 - 4095.77i) q^{26} +(-6834.57 + 1194.75i) q^{28} +155.049i q^{29} +4909.55i q^{31} +(2001.20 - 5435.96i) q^{32} +(-9458.78 - 7948.73i) q^{34} -17462.3 q^{35} +114.620 q^{37} +(3116.85 + 2619.26i) q^{38} +(7317.35 - 12609.7i) q^{40} -3356.63i q^{41} -13109.4i q^{43} +(844.988 + 4833.74i) q^{44} +(-9542.96 + 11355.9i) q^{46} -9409.97 q^{47} -30203.6 q^{49} +(12233.4 - 14557.4i) q^{50} +(5211.41 + 29811.8i) q^{52} +19619.3i q^{53} +12350.2i q^{55} +(19699.2 - 33946.8i) q^{56} +(-671.476 - 564.277i) q^{58} -21595.2 q^{59} +33298.2 q^{61} +(-21261.9 - 17867.5i) q^{62} +(16258.6 + 28450.0i) q^{64} +76168.9i q^{65} -23493.1i q^{67} +(68847.5 - 12035.2i) q^{68} +(63551.2 - 75624.3i) q^{70} -2402.72 q^{71} +4867.76 q^{73} +(-417.141 + 496.388i) q^{74} +(-22686.6 + 3965.84i) q^{76} +33248.2i q^{77} -11925.5i q^{79} +(27978.7 + 77580.4i) q^{80} +(14536.6 + 12215.9i) q^{82} -83940.6 q^{83} +175905. q^{85} +(56773.1 + 47709.5i) q^{86} +(-24008.8 - 13932.2i) q^{88} -36800.9i q^{89} +205056. i q^{91} +(-14449.1 - 82655.9i) q^{92} +(34246.1 - 40752.0i) q^{94} -57963.9 q^{95} -28249.7 q^{97} +(109921. - 130803. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 20q^{4} + O(q^{10}) \) \( 20q + 20q^{4} + 184q^{10} - 116q^{13} - 4168q^{16} + 696q^{22} - 15228q^{25} - 4764q^{28} - 16520q^{34} - 6452q^{37} + 1504q^{40} - 9336q^{46} - 44464q^{49} + 8236q^{52} - 58736q^{58} + 84604q^{61} - 6496q^{64} + 138696q^{70} + 85420q^{73} + 89172q^{76} + 221200q^{82} + 180320q^{85} - 85824q^{88} - 60936q^{94} - 219908q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.63934 + 4.33073i −0.643351 + 0.765571i
\(3\) 0 0
\(4\) −5.51036 31.5220i −0.172199 0.985062i
\(5\) 80.5384i 1.44071i −0.693603 0.720357i \(-0.743978\pi\)
0.693603 0.720357i \(-0.256022\pi\)
\(6\) 0 0
\(7\) 216.819i 1.67245i −0.548388 0.836224i \(-0.684758\pi\)
0.548388 0.836224i \(-0.315242\pi\)
\(8\) 156.567 + 90.8555i 0.864920 + 0.501910i
\(9\) 0 0
\(10\) 348.790 + 293.107i 1.10297 + 0.926885i
\(11\) −153.345 −0.382110 −0.191055 0.981579i \(-0.561191\pi\)
−0.191055 + 0.981579i \(0.561191\pi\)
\(12\) 0 0
\(13\) −945.747 −1.55209 −0.776044 0.630679i \(-0.782777\pi\)
−0.776044 + 0.630679i \(0.782777\pi\)
\(14\) 938.984 + 789.079i 1.28038 + 1.07597i
\(15\) 0 0
\(16\) −963.272 + 347.395i −0.940695 + 0.339253i
\(17\) 2184.11i 1.83296i 0.400084 + 0.916478i \(0.368981\pi\)
−0.400084 + 0.916478i \(0.631019\pi\)
\(18\) 0 0
\(19\) 719.706i 0.457373i −0.973500 0.228687i \(-0.926557\pi\)
0.973500 0.228687i \(-0.0734431\pi\)
\(20\) −2538.73 + 443.796i −1.41919 + 0.248089i
\(21\) 0 0
\(22\) 558.076 664.096i 0.245831 0.292532i
\(23\) 2622.17 1.03357 0.516786 0.856115i \(-0.327128\pi\)
0.516786 + 0.856115i \(0.327128\pi\)
\(24\) 0 0
\(25\) −3361.43 −1.07566
\(26\) 3441.90 4095.77i 0.998538 1.18823i
\(27\) 0 0
\(28\) −6834.57 + 1194.75i −1.64747 + 0.287994i
\(29\) 155.049i 0.0342353i 0.999853 + 0.0171177i \(0.00544899\pi\)
−0.999853 + 0.0171177i \(0.994551\pi\)
\(30\) 0 0
\(31\) 4909.55i 0.917567i 0.888548 + 0.458783i \(0.151715\pi\)
−0.888548 + 0.458783i \(0.848285\pi\)
\(32\) 2001.20 5435.96i 0.345475 0.938428i
\(33\) 0 0
\(34\) −9458.78 7948.73i −1.40326 1.17923i
\(35\) −17462.3 −2.40952
\(36\) 0 0
\(37\) 114.620 0.0137644 0.00688218 0.999976i \(-0.497809\pi\)
0.00688218 + 0.999976i \(0.497809\pi\)
\(38\) 3116.85 + 2619.26i 0.350152 + 0.294252i
\(39\) 0 0
\(40\) 7317.35 12609.7i 0.723109 1.24610i
\(41\) 3356.63i 0.311849i −0.987769 0.155924i \(-0.950164\pi\)
0.987769 0.155924i \(-0.0498356\pi\)
\(42\) 0 0
\(43\) 13109.4i 1.08121i −0.841276 0.540606i \(-0.818195\pi\)
0.841276 0.540606i \(-0.181805\pi\)
\(44\) 844.988 + 4833.74i 0.0657989 + 0.376402i
\(45\) 0 0
\(46\) −9542.96 + 11355.9i −0.664949 + 0.791273i
\(47\) −9409.97 −0.621360 −0.310680 0.950515i \(-0.600557\pi\)
−0.310680 + 0.950515i \(0.600557\pi\)
\(48\) 0 0
\(49\) −30203.6 −1.79708
\(50\) 12233.4 14557.4i 0.692026 0.823493i
\(51\) 0 0
\(52\) 5211.41 + 29811.8i 0.267268 + 1.52890i
\(53\) 19619.3i 0.959388i 0.877436 + 0.479694i \(0.159252\pi\)
−0.877436 + 0.479694i \(0.840748\pi\)
\(54\) 0 0
\(55\) 12350.2i 0.550511i
\(56\) 19699.2 33946.8i 0.839419 1.44653i
\(57\) 0 0
\(58\) −671.476 564.277i −0.0262096 0.0220253i
\(59\) −21595.2 −0.807658 −0.403829 0.914835i \(-0.632321\pi\)
−0.403829 + 0.914835i \(0.632321\pi\)
\(60\) 0 0
\(61\) 33298.2 1.14577 0.572884 0.819637i \(-0.305825\pi\)
0.572884 + 0.819637i \(0.305825\pi\)
\(62\) −21261.9 17867.5i −0.702463 0.590317i
\(63\) 0 0
\(64\) 16258.6 + 28450.0i 0.496172 + 0.868224i
\(65\) 76168.9i 2.23612i
\(66\) 0 0
\(67\) 23493.1i 0.639371i −0.947524 0.319685i \(-0.896423\pi\)
0.947524 0.319685i \(-0.103577\pi\)
\(68\) 68847.5 12035.2i 1.80558 0.315633i
\(69\) 0 0
\(70\) 63551.2 75624.3i 1.55017 1.84466i
\(71\) −2402.72 −0.0565662 −0.0282831 0.999600i \(-0.509004\pi\)
−0.0282831 + 0.999600i \(0.509004\pi\)
\(72\) 0 0
\(73\) 4867.76 0.106911 0.0534555 0.998570i \(-0.482976\pi\)
0.0534555 + 0.998570i \(0.482976\pi\)
\(74\) −417.141 + 496.388i −0.00885531 + 0.0105376i
\(75\) 0 0
\(76\) −22686.6 + 3965.84i −0.450541 + 0.0787592i
\(77\) 33248.2i 0.639059i
\(78\) 0 0
\(79\) 11925.5i 0.214985i −0.994206 0.107492i \(-0.965718\pi\)
0.994206 0.107492i \(-0.0342821\pi\)
\(80\) 27978.7 + 77580.4i 0.488767 + 1.35527i
\(81\) 0 0
\(82\) 14536.6 + 12215.9i 0.238742 + 0.200628i
\(83\) −83940.6 −1.33745 −0.668724 0.743511i \(-0.733159\pi\)
−0.668724 + 0.743511i \(0.733159\pi\)
\(84\) 0 0
\(85\) 175905. 2.64077
\(86\) 56773.1 + 47709.5i 0.827745 + 0.695599i
\(87\) 0 0
\(88\) −24008.8 13932.2i −0.330494 0.191785i
\(89\) 36800.9i 0.492474i −0.969210 0.246237i \(-0.920806\pi\)
0.969210 0.246237i \(-0.0791941\pi\)
\(90\) 0 0
\(91\) 205056.i 2.59579i
\(92\) −14449.1 82655.9i −0.177980 1.01813i
\(93\) 0 0
\(94\) 34246.1 40752.0i 0.399753 0.475696i
\(95\) −57963.9 −0.658945
\(96\) 0 0
\(97\) −28249.7 −0.304849 −0.152424 0.988315i \(-0.548708\pi\)
−0.152424 + 0.988315i \(0.548708\pi\)
\(98\) 109921. 130803.i 1.15616 1.37579i
\(99\) 0 0
\(100\) 18522.7 + 105959.i 0.185227 + 1.05959i
\(101\) 4051.50i 0.0395196i −0.999805 0.0197598i \(-0.993710\pi\)
0.999805 0.0197598i \(-0.00629015\pi\)
\(102\) 0 0
\(103\) 108384.i 1.00663i −0.864103 0.503316i \(-0.832113\pi\)
0.864103 0.503316i \(-0.167887\pi\)
\(104\) −148073. 85926.3i −1.34243 0.779009i
\(105\) 0 0
\(106\) −84965.9 71401.4i −0.734480 0.617223i
\(107\) −94762.1 −0.800157 −0.400079 0.916481i \(-0.631017\pi\)
−0.400079 + 0.916481i \(0.631017\pi\)
\(108\) 0 0
\(109\) −105703. −0.852160 −0.426080 0.904685i \(-0.640106\pi\)
−0.426080 + 0.904685i \(0.640106\pi\)
\(110\) −53485.2 44946.5i −0.421456 0.354172i
\(111\) 0 0
\(112\) 75322.0 + 208856.i 0.567383 + 1.57326i
\(113\) 80853.1i 0.595663i −0.954618 0.297832i \(-0.903737\pi\)
0.954618 0.297832i \(-0.0962634\pi\)
\(114\) 0 0
\(115\) 211185.i 1.48908i
\(116\) 4887.46 854.378i 0.0337239 0.00589529i
\(117\) 0 0
\(118\) 78592.4 93522.9i 0.519607 0.618319i
\(119\) 473557. 3.06552
\(120\) 0 0
\(121\) −137536. −0.853992
\(122\) −121184. + 144205.i −0.737131 + 0.877166i
\(123\) 0 0
\(124\) 154759. 27053.4i 0.903860 0.158004i
\(125\) 19041.9i 0.109002i
\(126\) 0 0
\(127\) 47941.0i 0.263753i 0.991266 + 0.131877i \(0.0421003\pi\)
−0.991266 + 0.131877i \(0.957900\pi\)
\(128\) −182380. 33127.8i −0.983900 0.178718i
\(129\) 0 0
\(130\) −329867. 277205.i −1.71191 1.43861i
\(131\) −301162. −1.53328 −0.766640 0.642077i \(-0.778073\pi\)
−0.766640 + 0.642077i \(0.778073\pi\)
\(132\) 0 0
\(133\) −156046. −0.764933
\(134\) 101742. + 85499.4i 0.489484 + 0.411340i
\(135\) 0 0
\(136\) −198438. + 341960.i −0.919980 + 1.58536i
\(137\) 134846.i 0.613814i 0.951739 + 0.306907i \(0.0992941\pi\)
−0.951739 + 0.306907i \(0.900706\pi\)
\(138\) 0 0
\(139\) 88215.4i 0.387264i −0.981074 0.193632i \(-0.937973\pi\)
0.981074 0.193632i \(-0.0620268\pi\)
\(140\) 96223.5 + 550446.i 0.414917 + 2.37353i
\(141\) 0 0
\(142\) 8744.31 10405.5i 0.0363919 0.0433054i
\(143\) 145026. 0.593068
\(144\) 0 0
\(145\) 12487.4 0.0493233
\(146\) −17715.5 + 21080.9i −0.0687813 + 0.0818480i
\(147\) 0 0
\(148\) −631.598 3613.05i −0.00237021 0.0135587i
\(149\) 424905.i 1.56793i −0.620806 0.783965i \(-0.713194\pi\)
0.620806 0.783965i \(-0.286806\pi\)
\(150\) 0 0
\(151\) 188045.i 0.671150i 0.942014 + 0.335575i \(0.108931\pi\)
−0.942014 + 0.335575i \(0.891069\pi\)
\(152\) 65389.2 112682.i 0.229560 0.395591i
\(153\) 0 0
\(154\) −143989. 121002.i −0.489245 0.411139i
\(155\) 395407. 1.32195
\(156\) 0 0
\(157\) −348168. −1.12730 −0.563650 0.826014i \(-0.690603\pi\)
−0.563650 + 0.826014i \(0.690603\pi\)
\(158\) 51645.9 + 43400.9i 0.164586 + 0.138311i
\(159\) 0 0
\(160\) −437803. 161174.i −1.35201 0.497730i
\(161\) 568536.i 1.72859i
\(162\) 0 0
\(163\) 25262.9i 0.0744756i −0.999306 0.0372378i \(-0.988144\pi\)
0.999306 0.0372378i \(-0.0118559\pi\)
\(164\) −105808. + 18496.2i −0.307190 + 0.0537000i
\(165\) 0 0
\(166\) 305489. 363524.i 0.860448 1.02391i
\(167\) 385026. 1.06831 0.534157 0.845386i \(-0.320629\pi\)
0.534157 + 0.845386i \(0.320629\pi\)
\(168\) 0 0
\(169\) 523144. 1.40898
\(170\) −640178. + 761795.i −1.69894 + 2.02170i
\(171\) 0 0
\(172\) −413233. + 72237.4i −1.06506 + 0.186183i
\(173\) 547742.i 1.39143i 0.718318 + 0.695715i \(0.244912\pi\)
−0.718318 + 0.695715i \(0.755088\pi\)
\(174\) 0 0
\(175\) 728823.i 1.79898i
\(176\) 147713. 53271.4i 0.359449 0.129632i
\(177\) 0 0
\(178\) 159374. + 133931.i 0.377024 + 0.316834i
\(179\) 450824. 1.05166 0.525829 0.850590i \(-0.323755\pi\)
0.525829 + 0.850590i \(0.323755\pi\)
\(180\) 0 0
\(181\) 1585.85 0.00359805 0.00179902 0.999998i \(-0.499427\pi\)
0.00179902 + 0.999998i \(0.499427\pi\)
\(182\) −888041. 746269.i −1.98726 1.67000i
\(183\) 0 0
\(184\) 410545. + 238238.i 0.893956 + 0.518760i
\(185\) 9231.31i 0.0198305i
\(186\) 0 0
\(187\) 334923.i 0.700391i
\(188\) 51852.3 + 296621.i 0.106998 + 0.612078i
\(189\) 0 0
\(190\) 210951. 251026.i 0.423933 0.504469i
\(191\) −310556. −0.615966 −0.307983 0.951392i \(-0.599654\pi\)
−0.307983 + 0.951392i \(0.599654\pi\)
\(192\) 0 0
\(193\) 86770.6 0.167679 0.0838397 0.996479i \(-0.473282\pi\)
0.0838397 + 0.996479i \(0.473282\pi\)
\(194\) 102810. 122342.i 0.196125 0.233383i
\(195\) 0 0
\(196\) 166433. + 952077.i 0.309456 + 1.77024i
\(197\) 406767.i 0.746758i −0.927679 0.373379i \(-0.878199\pi\)
0.927679 0.373379i \(-0.121801\pi\)
\(198\) 0 0
\(199\) 1.07477e6i 1.92389i −0.273235 0.961947i \(-0.588094\pi\)
0.273235 0.961947i \(-0.411906\pi\)
\(200\) −526290. 305404.i −0.930358 0.539884i
\(201\) 0 0
\(202\) 17546.0 + 14744.8i 0.0302551 + 0.0254250i
\(203\) 33617.6 0.0572568
\(204\) 0 0
\(205\) −270338. −0.449285
\(206\) 469380. + 394445.i 0.770648 + 0.647618i
\(207\) 0 0
\(208\) 911011. 328548.i 1.46004 0.526551i
\(209\) 110363.i 0.174767i
\(210\) 0 0
\(211\) 629852.i 0.973941i −0.873419 0.486970i \(-0.838102\pi\)
0.873419 0.486970i \(-0.161898\pi\)
\(212\) 618440. 108110.i 0.945057 0.165206i
\(213\) 0 0
\(214\) 344872. 410389.i 0.514782 0.612577i
\(215\) −1.05581e6 −1.55772
\(216\) 0 0
\(217\) 1.06449e6 1.53458
\(218\) 384690. 457771.i 0.548238 0.652389i
\(219\) 0 0
\(220\) 389302. 68053.9i 0.542288 0.0947974i
\(221\) 2.06561e6i 2.84491i
\(222\) 0 0
\(223\) 1.27771e6i 1.72056i 0.509825 + 0.860278i \(0.329710\pi\)
−0.509825 + 0.860278i \(0.670290\pi\)
\(224\) −1.17862e6 433899.i −1.56947 0.577788i
\(225\) 0 0
\(226\) 350153. + 294252.i 0.456023 + 0.383221i
\(227\) 1.43061e6 1.84271 0.921354 0.388724i \(-0.127084\pi\)
0.921354 + 0.388724i \(0.127084\pi\)
\(228\) 0 0
\(229\) 618971. 0.779977 0.389988 0.920820i \(-0.372479\pi\)
0.389988 + 0.920820i \(0.372479\pi\)
\(230\) 914584. + 768575.i 1.14000 + 0.958002i
\(231\) 0 0
\(232\) −14087.1 + 24275.6i −0.0171831 + 0.0296108i
\(233\) 391086.i 0.471936i 0.971761 + 0.235968i \(0.0758260\pi\)
−0.971761 + 0.235968i \(0.924174\pi\)
\(234\) 0 0
\(235\) 757864.i 0.895203i
\(236\) 118997. + 680724.i 0.139078 + 0.795593i
\(237\) 0 0
\(238\) −1.72344e6 + 2.05085e6i −1.97221 + 2.34688i
\(239\) −1.39491e6 −1.57961 −0.789806 0.613356i \(-0.789819\pi\)
−0.789806 + 0.613356i \(0.789819\pi\)
\(240\) 0 0
\(241\) −745913. −0.827266 −0.413633 0.910444i \(-0.635740\pi\)
−0.413633 + 0.910444i \(0.635740\pi\)
\(242\) 500542. 595632.i 0.549417 0.653792i
\(243\) 0 0
\(244\) −183485. 1.04963e6i −0.197300 1.12865i
\(245\) 2.43255e6i 2.58908i
\(246\) 0 0
\(247\) 680659.i 0.709884i
\(248\) −446060. + 768675.i −0.460536 + 0.793621i
\(249\) 0 0
\(250\) −82465.1 69299.9i −0.0834488 0.0701266i
\(251\) −1.22222e6 −1.22452 −0.612260 0.790657i \(-0.709739\pi\)
−0.612260 + 0.790657i \(0.709739\pi\)
\(252\) 0 0
\(253\) −402096. −0.394938
\(254\) −207619. 174474.i −0.201922 0.169686i
\(255\) 0 0
\(256\) 807209. 669272.i 0.769815 0.638268i
\(257\) 1.79287e6i 1.69323i 0.532207 + 0.846614i \(0.321363\pi\)
−0.532207 + 0.846614i \(0.678637\pi\)
\(258\) 0 0
\(259\) 24851.8i 0.0230202i
\(260\) 2.40100e6 419718.i 2.20271 0.385057i
\(261\) 0 0
\(262\) 1.09603e6 1.30425e6i 0.986438 1.17384i
\(263\) 996371. 0.888243 0.444122 0.895967i \(-0.353516\pi\)
0.444122 + 0.895967i \(0.353516\pi\)
\(264\) 0 0
\(265\) 1.58011e6 1.38220
\(266\) 567905. 675793.i 0.492121 0.585611i
\(267\) 0 0
\(268\) −740549. + 129455.i −0.629820 + 0.110099i
\(269\) 2.16053e6i 1.82045i 0.414109 + 0.910227i \(0.364093\pi\)
−0.414109 + 0.910227i \(0.635907\pi\)
\(270\) 0 0
\(271\) 1.68130e6i 1.39066i −0.718688 0.695332i \(-0.755257\pi\)
0.718688 0.695332i \(-0.244743\pi\)
\(272\) −758749. 2.10389e6i −0.621836 1.72425i
\(273\) 0 0
\(274\) −583982. 490751.i −0.469919 0.394898i
\(275\) 515459. 0.411020
\(276\) 0 0
\(277\) 1.08867e6 0.852507 0.426254 0.904604i \(-0.359833\pi\)
0.426254 + 0.904604i \(0.359833\pi\)
\(278\) 382036. + 321046.i 0.296478 + 0.249147i
\(279\) 0 0
\(280\) −2.73402e6 1.58654e6i −2.08404 1.20936i
\(281\) 728495.i 0.550377i −0.961390 0.275189i \(-0.911260\pi\)
0.961390 0.275189i \(-0.0887403\pi\)
\(282\) 0 0
\(283\) 733677.i 0.544551i −0.962219 0.272276i \(-0.912224\pi\)
0.962219 0.272276i \(-0.0877762\pi\)
\(284\) 13239.8 + 75738.4i 0.00974063 + 0.0557212i
\(285\) 0 0
\(286\) −527798. + 628066.i −0.381551 + 0.454036i
\(287\) −727782. −0.521551
\(288\) 0 0
\(289\) −3.35048e6 −2.35973
\(290\) −45446.0 + 54079.6i −0.0317322 + 0.0377605i
\(291\) 0 0
\(292\) −26823.1 153442.i −0.0184099 0.105314i
\(293\) 400766.i 0.272723i −0.990659 0.136361i \(-0.956459\pi\)
0.990659 0.136361i \(-0.0435409\pi\)
\(294\) 0 0
\(295\) 1.73924e6i 1.16360i
\(296\) 17945.7 + 10413.9i 0.0119051 + 0.00690847i
\(297\) 0 0
\(298\) 1.84015e6 + 1.54638e6i 1.20036 + 1.00873i
\(299\) −2.47990e6 −1.60419
\(300\) 0 0
\(301\) −2.84236e6 −1.80827
\(302\) −814371. 684360.i −0.513813 0.431785i
\(303\) 0 0
\(304\) 250022. + 693272.i 0.155165 + 0.430249i
\(305\) 2.68178e6i 1.65072i
\(306\) 0 0
\(307\) 1.18446e6i 0.717258i −0.933480 0.358629i \(-0.883244\pi\)
0.933480 0.358629i \(-0.116756\pi\)
\(308\) 1.04805e6 183210.i 0.629513 0.110045i
\(309\) 0 0
\(310\) −1.43902e6 + 1.71240e6i −0.850479 + 1.01205i
\(311\) −2.98276e6 −1.74871 −0.874354 0.485289i \(-0.838714\pi\)
−0.874354 + 0.485289i \(0.838714\pi\)
\(312\) 0 0
\(313\) −2.44466e6 −1.41045 −0.705224 0.708984i \(-0.749154\pi\)
−0.705224 + 0.708984i \(0.749154\pi\)
\(314\) 1.26710e6 1.50782e6i 0.725249 0.863028i
\(315\) 0 0
\(316\) −375914. + 65713.6i −0.211773 + 0.0370201i
\(317\) 164872.i 0.0921508i −0.998938 0.0460754i \(-0.985329\pi\)
0.998938 0.0460754i \(-0.0146715\pi\)
\(318\) 0 0
\(319\) 23776.0i 0.0130817i
\(320\) 2.29131e6 1.30944e6i 1.25086 0.714842i
\(321\) 0 0
\(322\) 2.46217e6 + 2.06910e6i 1.32336 + 1.11209i
\(323\) 1.57192e6 0.838346
\(324\) 0 0
\(325\) 3.17906e6 1.66952
\(326\) 109407. + 91940.4i 0.0570164 + 0.0479140i
\(327\) 0 0
\(328\) 304968. 525538.i 0.156520 0.269724i
\(329\) 2.04026e6i 1.03919i
\(330\) 0 0
\(331\) 3.03272e6i 1.52147i −0.649065 0.760733i \(-0.724840\pi\)
0.649065 0.760733i \(-0.275160\pi\)
\(332\) 462543. + 2.64597e6i 0.230307 + 1.31747i
\(333\) 0 0
\(334\) −1.40124e6 + 1.66744e6i −0.687300 + 0.817870i
\(335\) −1.89209e6 −0.921151
\(336\) 0 0
\(337\) −2.77189e6 −1.32954 −0.664769 0.747049i \(-0.731470\pi\)
−0.664769 + 0.747049i \(0.731470\pi\)
\(338\) −1.90390e6 + 2.26559e6i −0.906468 + 1.07867i
\(339\) 0 0
\(340\) −969299. 5.54487e6i −0.454737 2.60132i
\(341\) 752856.i 0.350611i
\(342\) 0 0
\(343\) 2.90463e6i 1.33308i
\(344\) 1.19106e6 2.05250e6i 0.542671 0.935161i
\(345\) 0 0
\(346\) −2.37212e6 1.99342e6i −1.06524 0.895177i
\(347\) −1.11916e6 −0.498961 −0.249481 0.968380i \(-0.580260\pi\)
−0.249481 + 0.968380i \(0.580260\pi\)
\(348\) 0 0
\(349\) 2.08395e6 0.915849 0.457925 0.888991i \(-0.348593\pi\)
0.457925 + 0.888991i \(0.348593\pi\)
\(350\) −3.15633e6 2.65244e6i −1.37725 1.15738i
\(351\) 0 0
\(352\) −306875. + 833578.i −0.132009 + 0.358583i
\(353\) 2.22872e6i 0.951961i 0.879456 + 0.475980i \(0.157907\pi\)
−0.879456 + 0.475980i \(0.842093\pi\)
\(354\) 0 0
\(355\) 193511.i 0.0814957i
\(356\) −1.16004e6 + 202786.i −0.485117 + 0.0848034i
\(357\) 0 0
\(358\) −1.64070e6 + 1.95239e6i −0.676585 + 0.805119i
\(359\) 3.79795e6 1.55530 0.777649 0.628699i \(-0.216412\pi\)
0.777649 + 0.628699i \(0.216412\pi\)
\(360\) 0 0
\(361\) 1.95812e6 0.790810
\(362\) −5771.47 + 6867.90i −0.00231481 + 0.00275456i
\(363\) 0 0
\(364\) 6.46377e6 1.12993e6i 2.55701 0.446992i
\(365\) 392042.i 0.154028i
\(366\) 0 0
\(367\) 1.00563e6i 0.389737i 0.980829 + 0.194868i \(0.0624280\pi\)
−0.980829 + 0.194868i \(0.937572\pi\)
\(368\) −2.52586e6 + 910928.i −0.972276 + 0.350642i
\(369\) 0 0
\(370\) 39978.3 + 33595.9i 0.0151817 + 0.0127580i
\(371\) 4.25385e6 1.60453
\(372\) 0 0
\(373\) 3.13554e6 1.16692 0.583458 0.812143i \(-0.301699\pi\)
0.583458 + 0.812143i \(0.301699\pi\)
\(374\) 1.45046e6 + 1.21890e6i 0.536199 + 0.450597i
\(375\) 0 0
\(376\) −1.47329e6 854947.i −0.537427 0.311867i
\(377\) 146637.i 0.0531363i
\(378\) 0 0
\(379\) 1.35382e6i 0.484133i −0.970260 0.242066i \(-0.922175\pi\)
0.970260 0.242066i \(-0.0778251\pi\)
\(380\) 319402. + 1.82714e6i 0.113470 + 0.649101i
\(381\) 0 0
\(382\) 1.13022e6 1.34493e6i 0.396283 0.471566i
\(383\) 3.31845e6 1.15595 0.577974 0.816055i \(-0.303843\pi\)
0.577974 + 0.816055i \(0.303843\pi\)
\(384\) 0 0
\(385\) 2.67775e6 0.920702
\(386\) −315788. + 375780.i −0.107877 + 0.128370i
\(387\) 0 0
\(388\) 155666. + 890486.i 0.0524946 + 0.300295i
\(389\) 3.73290e6i 1.25076i −0.780322 0.625378i \(-0.784945\pi\)
0.780322 0.625378i \(-0.215055\pi\)
\(390\) 0 0
\(391\) 5.72710e6i 1.89449i
\(392\) −4.72889e6 2.74416e6i −1.55433 0.901974i
\(393\) 0 0
\(394\) 1.76160e6 + 1.48036e6i 0.571697 + 0.480428i
\(395\) −960458. −0.309732
\(396\) 0 0
\(397\) −908240. −0.289217 −0.144609 0.989489i \(-0.546192\pi\)
−0.144609 + 0.989489i \(0.546192\pi\)
\(398\) 4.65452e6 + 3.91144e6i 1.47288 + 1.23774i
\(399\) 0 0
\(400\) 3.23797e6 1.16775e6i 1.01187 0.364921i
\(401\) 128575.i 0.0399297i −0.999801 0.0199649i \(-0.993645\pi\)
0.999801 0.0199649i \(-0.00635544\pi\)
\(402\) 0 0
\(403\) 4.64319e6i 1.42414i
\(404\) −127711. + 22325.3i −0.0389293 + 0.00680524i
\(405\) 0 0
\(406\) −122346. + 145589.i −0.0368362 + 0.0438342i
\(407\) −17576.4 −0.00525950
\(408\) 0 0
\(409\) 4.22625e6 1.24924 0.624622 0.780927i \(-0.285253\pi\)
0.624622 + 0.780927i \(0.285253\pi\)
\(410\) 983851. 1.17076e6i 0.289048 0.343960i
\(411\) 0 0
\(412\) −3.41647e6 + 597233.i −0.991595 + 0.173341i
\(413\) 4.68225e6i 1.35077i
\(414\) 0 0
\(415\) 6.76044e6i 1.92688i
\(416\) −1.89263e6 + 5.14104e6i −0.536207 + 1.45652i
\(417\) 0 0
\(418\) −477954. 401650.i −0.133797 0.112437i
\(419\) 2.78414e6 0.774739 0.387370 0.921924i \(-0.373384\pi\)
0.387370 + 0.921924i \(0.373384\pi\)
\(420\) 0 0
\(421\) −2.45303e6 −0.674525 −0.337262 0.941411i \(-0.609501\pi\)
−0.337262 + 0.941411i \(0.609501\pi\)
\(422\) 2.72772e6 + 2.29225e6i 0.745621 + 0.626586i
\(423\) 0 0
\(424\) −1.78252e6 + 3.07174e6i −0.481527 + 0.829794i
\(425\) 7.34174e6i 1.97164i
\(426\) 0 0
\(427\) 7.21969e6i 1.91624i
\(428\) 522174. + 2.98709e6i 0.137786 + 0.788204i
\(429\) 0 0
\(430\) 3.84245e6 4.57241e6i 1.00216 1.19254i
\(431\) −1.70611e6 −0.442397 −0.221199 0.975229i \(-0.570997\pi\)
−0.221199 + 0.975229i \(0.570997\pi\)
\(432\) 0 0
\(433\) 194630. 0.0498872 0.0249436 0.999689i \(-0.492059\pi\)
0.0249436 + 0.999689i \(0.492059\pi\)
\(434\) −3.87403e6 + 4.60999e6i −0.987275 + 1.17483i
\(435\) 0 0
\(436\) 582462. + 3.33197e6i 0.146741 + 0.839431i
\(437\) 1.88719e6i 0.472728i
\(438\) 0 0
\(439\) 550852.i 0.136419i −0.997671 0.0682093i \(-0.978271\pi\)
0.997671 0.0682093i \(-0.0217286\pi\)
\(440\) −1.12208e6 + 1.93363e6i −0.276307 + 0.476148i
\(441\) 0 0
\(442\) 8.94561e6 + 7.51748e6i 2.17798 + 1.83028i
\(443\) −5.84486e6 −1.41503 −0.707514 0.706700i \(-0.750183\pi\)
−0.707514 + 0.706700i \(0.750183\pi\)
\(444\) 0 0
\(445\) −2.96388e6 −0.709514
\(446\) −5.53339e6 4.65001e6i −1.31721 1.10692i
\(447\) 0 0
\(448\) 6.16850e6 3.52517e6i 1.45206 0.829822i
\(449\) 3.10126e6i 0.725977i −0.931794 0.362989i \(-0.881756\pi\)
0.931794 0.362989i \(-0.118244\pi\)
\(450\) 0 0
\(451\) 514723.i 0.119160i
\(452\) −2.54865e6 + 445530.i −0.586765 + 0.102573i
\(453\) 0 0
\(454\) −5.20648e6 + 6.19558e6i −1.18551 + 1.41072i
\(455\) 1.65149e7 3.73979
\(456\) 0 0
\(457\) 917472. 0.205496 0.102748 0.994707i \(-0.467237\pi\)
0.102748 + 0.994707i \(0.467237\pi\)
\(458\) −2.25265e6 + 2.68059e6i −0.501799 + 0.597128i
\(459\) 0 0
\(460\) −6.65697e6 + 1.16371e6i −1.46684 + 0.256418i
\(461\) 7.26023e6i 1.59110i −0.605886 0.795552i \(-0.707181\pi\)
0.605886 0.795552i \(-0.292819\pi\)
\(462\) 0 0
\(463\) 7.02175e6i 1.52227i −0.648591 0.761137i \(-0.724641\pi\)
0.648591 0.761137i \(-0.275359\pi\)
\(464\) −53863.4 149355.i −0.0116144 0.0322050i
\(465\) 0 0
\(466\) −1.69369e6 1.42330e6i −0.361300 0.303620i
\(467\) −2.85330e6 −0.605417 −0.302709 0.953083i \(-0.597891\pi\)
−0.302709 + 0.953083i \(0.597891\pi\)
\(468\) 0 0
\(469\) −5.09375e6 −1.06931
\(470\) −3.28210e6 2.75813e6i −0.685342 0.575930i
\(471\) 0 0
\(472\) −3.38110e6 1.96204e6i −0.698559 0.405372i
\(473\) 2.01026e6i 0.413142i
\(474\) 0 0
\(475\) 2.41924e6i 0.491978i
\(476\) −2.60947e6 1.49275e7i −0.527880 3.01973i
\(477\) 0 0
\(478\) 5.07655e6 6.04096e6i 1.01625 1.20931i
\(479\) −919797. −0.183169 −0.0915847 0.995797i \(-0.529193\pi\)
−0.0915847 + 0.995797i \(0.529193\pi\)
\(480\) 0 0
\(481\) −108401. −0.0213635
\(482\) 2.71463e6 3.23034e6i 0.532223 0.633331i
\(483\) 0 0
\(484\) 757875. + 4.33542e6i 0.147056 + 0.841235i
\(485\) 2.27518e6i 0.439200i
\(486\) 0 0
\(487\) 5.70621e6i 1.09025i 0.838355 + 0.545124i \(0.183517\pi\)
−0.838355 + 0.545124i \(0.816483\pi\)
\(488\) 5.21341e6 + 3.02533e6i 0.990997 + 0.575072i
\(489\) 0 0
\(490\) −1.05347e7 8.85287e6i −1.98213 1.66569i
\(491\) −2.01852e6 −0.377859 −0.188930 0.981991i \(-0.560502\pi\)
−0.188930 + 0.981991i \(0.560502\pi\)
\(492\) 0 0
\(493\) −338645. −0.0627519
\(494\) −2.94775e6 2.47715e6i −0.543467 0.456705i
\(495\) 0 0
\(496\) −1.70556e6 4.72923e6i −0.311287 0.863150i
\(497\) 520955.i 0.0946040i
\(498\) 0 0
\(499\) 1.19282e6i 0.214448i 0.994235 + 0.107224i \(0.0341962\pi\)
−0.994235 + 0.107224i \(0.965804\pi\)
\(500\) 600238. 104928.i 0.107374 0.0187700i
\(501\) 0 0
\(502\) 4.44808e6 5.29310e6i 0.787796 0.937457i
\(503\) 9.18424e6 1.61854 0.809270 0.587437i \(-0.199863\pi\)
0.809270 + 0.587437i \(0.199863\pi\)
\(504\) 0 0
\(505\) −326302. −0.0569365
\(506\) 1.46337e6 1.74137e6i 0.254084 0.302353i
\(507\) 0 0
\(508\) 1.51120e6 264172.i 0.259813 0.0454180i
\(509\) 1.17272e6i 0.200632i −0.994956 0.100316i \(-0.968015\pi\)
0.994956 0.100316i \(-0.0319853\pi\)
\(510\) 0 0
\(511\) 1.05542e6i 0.178803i
\(512\) −39277.0 + 5.93151e6i −0.00662161 + 0.999978i
\(513\) 0 0
\(514\) −7.76442e6 6.52486e6i −1.29629 1.08934i
\(515\) −8.72904e6 −1.45027
\(516\) 0 0
\(517\) 1.44297e6 0.237428
\(518\) 107626. + 90444.3i 0.0176236 + 0.0148101i
\(519\) 0 0
\(520\) −6.92036e6 + 1.19256e7i −1.12233 + 1.93406i
\(521\) 6.12848e6i 0.989141i 0.869137 + 0.494571i \(0.164675\pi\)
−0.869137 + 0.494571i \(0.835325\pi\)
\(522\) 0 0
\(523\) 6.43682e6i 1.02900i −0.857489 0.514502i \(-0.827977\pi\)
0.857489 0.514502i \(-0.172023\pi\)
\(524\) 1.65951e6 + 9.49322e6i 0.264029 + 1.51038i
\(525\) 0 0
\(526\) −3.62614e6 + 4.31501e6i −0.571452 + 0.680013i
\(527\) −1.07230e7 −1.68186
\(528\) 0 0
\(529\) 439409. 0.0682700
\(530\) −5.75056e6 + 6.84302e6i −0.889242 + 1.05818i
\(531\) 0 0
\(532\) 859870. + 4.91888e6i 0.131721 + 0.753507i
\(533\) 3.17452e6i 0.484016i
\(534\) 0 0
\(535\) 7.63199e6i 1.15280i
\(536\) 2.13447e6 3.67825e6i 0.320907 0.553005i
\(537\) 0 0
\(538\) −9.35667e6 7.86291e6i −1.39369 1.17119i
\(539\) 4.63157e6 0.686683
\(540\) 0 0
\(541\) −1.06503e7 −1.56448 −0.782238 0.622980i \(-0.785922\pi\)
−0.782238 + 0.622980i \(0.785922\pi\)
\(542\) 7.28126e6 + 6.11883e6i 1.06465 + 0.894686i
\(543\) 0 0
\(544\) 1.18727e7 + 4.37085e6i 1.72010 + 0.633240i
\(545\) 8.51315e6i 1.22772i
\(546\) 0 0
\(547\) 1.81400e6i 0.259220i 0.991565 + 0.129610i \(0.0413725\pi\)
−0.991565 + 0.129610i \(0.958628\pi\)
\(548\) 4.25062e6 743051.i 0.604645 0.105698i
\(549\) 0 0
\(550\) −1.87593e6 + 2.23231e6i −0.264430 + 0.314665i
\(551\) 111590. 0.0156583
\(552\) 0 0
\(553\) −2.58567e6 −0.359551
\(554\) −3.96206e6 + 4.71475e6i −0.548462 + 0.652655i
\(555\) 0 0
\(556\) −2.78072e6 + 486099.i −0.381479 + 0.0666864i
\(557\) 6.09580e6i 0.832517i −0.909246 0.416258i \(-0.863341\pi\)
0.909246 0.416258i \(-0.136659\pi\)
\(558\) 0 0
\(559\) 1.23981e7i 1.67814i
\(560\) 1.68209e7 6.06631e6i 2.26662 0.817437i
\(561\) 0 0
\(562\) 3.15491e6 + 2.65124e6i 0.421353 + 0.354086i
\(563\) 2.10559e6 0.279964 0.139982 0.990154i \(-0.455296\pi\)
0.139982 + 0.990154i \(0.455296\pi\)
\(564\) 0 0
\(565\) −6.51178e6 −0.858181
\(566\) 3.17735e6 + 2.67010e6i 0.416893 + 0.350338i
\(567\) 0 0
\(568\) −376187. 218300.i −0.0489252 0.0283911i
\(569\) 8.26598e6i 1.07032i −0.844751 0.535160i \(-0.820251\pi\)
0.844751 0.535160i \(-0.179749\pi\)
\(570\) 0 0
\(571\) 6.32978e6i 0.812453i −0.913772 0.406227i \(-0.866844\pi\)
0.913772 0.406227i \(-0.133156\pi\)
\(572\) −799144. 4.57150e6i −0.102126 0.584209i
\(573\) 0 0
\(574\) 2.64865e6 3.15182e6i 0.335540 0.399284i
\(575\) −8.81423e6 −1.11177
\(576\) 0 0
\(577\) 1.46843e7 1.83617 0.918087 0.396380i \(-0.129734\pi\)
0.918087 + 0.396380i \(0.129734\pi\)
\(578\) 1.21935e7 1.45100e7i 1.51813 1.80654i
\(579\) 0 0
\(580\) −68810.2 393628.i −0.00849342 0.0485866i
\(581\) 1.81999e7i 2.23681i
\(582\) 0 0
\(583\) 3.00853e6i 0.366592i
\(584\) 762132. + 442263.i 0.0924694 + 0.0536597i
\(585\) 0 0
\(586\) 1.73561e6 + 1.45852e6i 0.208789 + 0.175457i
\(587\) −3.94562e6 −0.472628 −0.236314 0.971677i \(-0.575939\pi\)
−0.236314 + 0.971677i \(0.575939\pi\)
\(588\) 0 0
\(589\) 3.53343e6 0.419671
\(590\) −7.53218e6 6.32970e6i −0.890822 0.748606i
\(591\) 0 0
\(592\) −110410. + 39818.4i −0.0129481 + 0.00466960i
\(593\) 2.10090e6i 0.245341i 0.992447 + 0.122670i \(0.0391458\pi\)
−0.992447 + 0.122670i \(0.960854\pi\)
\(594\) 0 0
\(595\) 3.81395e7i 4.41655i
\(596\) −1.33939e7 + 2.34138e6i −1.54451 + 0.269996i
\(597\) 0 0
\(598\) 9.02522e6 1.07398e7i 1.03206 1.22813i
\(599\) −1.27405e7 −1.45084 −0.725420 0.688307i \(-0.758354\pi\)
−0.725420 + 0.688307i \(0.758354\pi\)
\(600\) 0 0
\(601\) −1.23040e7 −1.38951 −0.694755 0.719246i \(-0.744487\pi\)
−0.694755 + 0.719246i \(0.744487\pi\)
\(602\) 1.03443e7 1.23095e7i 1.16335 1.38436i
\(603\) 0 0
\(604\) 5.92755e6 1.03620e6i 0.661124 0.115571i
\(605\) 1.10769e7i 1.23036i
\(606\) 0 0
\(607\) 9.64207e6i 1.06218i 0.847315 + 0.531091i \(0.178218\pi\)
−0.847315 + 0.531091i \(0.821782\pi\)
\(608\) −3.91229e6 1.44028e6i −0.429212 0.158011i
\(609\) 0 0
\(610\) 1.16141e7 + 9.75993e6i 1.26375 + 1.06199i
\(611\) 8.89944e6 0.964406
\(612\) 0 0
\(613\) 9.91038e6 1.06522 0.532610 0.846361i \(-0.321211\pi\)
0.532610 + 0.846361i \(0.321211\pi\)
\(614\) 5.12958e6 + 4.31067e6i 0.549112 + 0.461449i
\(615\) 0 0
\(616\) −3.02078e6 + 5.20557e6i −0.320750 + 0.552735i
\(617\) 1.03111e6i 0.109041i 0.998513 + 0.0545207i \(0.0173631\pi\)
−0.998513 + 0.0545207i \(0.982637\pi\)
\(618\) 0 0
\(619\) 3.43026e6i 0.359833i 0.983682 + 0.179917i \(0.0575828\pi\)
−0.983682 + 0.179917i \(0.942417\pi\)
\(620\) −2.17884e6 1.24640e7i −0.227639 1.30220i
\(621\) 0 0
\(622\) 1.08553e7 1.29175e7i 1.12503 1.33876i
\(623\) −7.97914e6 −0.823637
\(624\) 0 0
\(625\) −8.97087e6 −0.918618
\(626\) 8.89695e6 1.05871e7i 0.907413 1.07980i
\(627\) 0 0
\(628\) 1.91853e6 + 1.09749e7i 0.194120 + 1.11046i
\(629\) 250343.i 0.0252295i
\(630\) 0 0
\(631\) 3.03674e6i 0.303623i 0.988409 + 0.151811i \(0.0485106\pi\)
−0.988409 + 0.151811i \(0.951489\pi\)
\(632\) 1.08349e6 1.86714e6i 0.107903 0.185944i
\(633\) 0 0
\(634\) 714016. + 600026.i 0.0705480 + 0.0592853i
\(635\) 3.86109e6 0.379993
\(636\) 0 0
\(637\) 2.85649e7 2.78923
\(638\) 102968. + 86529.2i 0.0100149 + 0.00841610i
\(639\) 0 0
\(640\) −2.66806e6 + 1.46886e7i −0.257481 + 1.41752i
\(641\) 2.28706e6i 0.219853i −0.993940 0.109927i \(-0.964938\pi\)
0.993940 0.109927i \(-0.0350616\pi\)
\(642\) 0 0
\(643\) 1.33547e7i 1.27382i 0.770940 + 0.636908i \(0.219787\pi\)
−0.770940 + 0.636908i \(0.780213\pi\)
\(644\) −1.79214e7 + 3.13284e6i −1.70277 + 0.297662i
\(645\) 0 0
\(646\) −5.72074e6 + 6.80754e6i −0.539351 + 0.641813i
\(647\) −1.21139e7 −1.13769 −0.568843 0.822446i \(-0.692609\pi\)
−0.568843 + 0.822446i \(0.692609\pi\)
\(648\) 0 0
\(649\) 3.31152e6 0.308614
\(650\) −1.15697e7 + 1.37676e7i −1.07409 + 1.27813i
\(651\) 0 0
\(652\) −796337. + 139208.i −0.0733631 + 0.0128246i
\(653\) 5.51376e6i 0.506017i −0.967464 0.253008i \(-0.918580\pi\)
0.967464 0.253008i \(-0.0814200\pi\)
\(654\) 0 0
\(655\) 2.42551e7i 2.20902i
\(656\) 1.16608e6 + 3.23335e6i 0.105796 + 0.293354i
\(657\) 0 0
\(658\) −8.83581e6 7.42521e6i −0.795576 0.668566i
\(659\) 7.16100e6 0.642333 0.321166 0.947023i \(-0.395925\pi\)
0.321166 + 0.947023i \(0.395925\pi\)
\(660\) 0 0
\(661\) −4.29525e6 −0.382371 −0.191186 0.981554i \(-0.561233\pi\)
−0.191186 + 0.981554i \(0.561233\pi\)
\(662\) 1.31339e7 + 1.10371e7i 1.16479 + 0.978836i
\(663\) 0 0
\(664\) −1.31423e7 7.62646e6i −1.15678 0.671279i
\(665\) 1.25677e7i 1.10205i
\(666\) 0 0
\(667\) 406565.i 0.0353847i
\(668\) −2.12163e6 1.21368e7i −0.183962 1.05235i
\(669\) 0 0
\(670\) 6.88598e6 8.19414e6i 0.592623 0.705207i
\(671\) −5.10612e6 −0.437809
\(672\) 0 0
\(673\) 8.72112e6 0.742224 0.371112 0.928588i \(-0.378977\pi\)
0.371112 + 0.928588i \(0.378977\pi\)
\(674\) 1.00878e7 1.20043e7i 0.855359 1.01786i
\(675\) 0 0
\(676\) −2.88271e6 1.64905e7i −0.242624 1.38793i
\(677\) 1.55598e7i 1.30476i −0.757890 0.652382i \(-0.773770\pi\)
0.757890 0.652382i \(-0.226230\pi\)
\(678\) 0 0
\(679\) 6.12507e6i 0.509843i
\(680\) 2.75409e7 + 1.59819e7i 2.28405 + 1.32543i
\(681\) 0 0
\(682\) 3.26041e6 + 2.73990e6i 0.268418 + 0.225566i
\(683\) −1.62106e7 −1.32968 −0.664840 0.746986i \(-0.731500\pi\)
−0.664840 + 0.746986i \(0.731500\pi\)
\(684\) 0 0
\(685\) 1.08603e7 0.884331
\(686\) −1.25792e7 1.05710e7i −1.02057 0.857638i
\(687\) 0 0
\(688\) 4.55413e6 + 1.26279e7i 0.366804 + 1.01709i
\(689\) 1.85549e7i 1.48905i
\(690\) 0 0
\(691\) 1.77172e7i 1.41156i −0.708429 0.705782i \(-0.750596\pi\)
0.708429 0.705782i \(-0.249404\pi\)
\(692\) 1.72659e7 3.01826e6i 1.37064 0.239603i
\(693\) 0 0
\(694\) 4.07299e6 4.84676e6i 0.321007 0.381990i
\(695\) −7.10472e6 −0.557937
\(696\) 0 0
\(697\) 7.33125e6 0.571605
\(698\) −7.58422e6 + 9.02502e6i −0.589213 + 0.701148i
\(699\) 0 0
\(700\) 2.29740e7 4.01608e6i 1.77211 0.309783i
\(701\) 1.38386e6i 0.106364i −0.998585 0.0531821i \(-0.983064\pi\)
0.998585 0.0531821i \(-0.0169364\pi\)
\(702\) 0 0
\(703\) 82492.7i 0.00629545i
\(704\) −2.49317e6 4.36267e6i −0.189592 0.331757i
\(705\) 0 0
\(706\) −9.65198e6 8.11108e6i −0.728794 0.612445i
\(707\) −878444. −0.0660945
\(708\) 0 0
\(709\) −3.82723e6 −0.285936 −0.142968 0.989727i \(-0.545665\pi\)
−0.142968 + 0.989727i \(0.545665\pi\)
\(710\) −838043. 704253.i −0.0623908 0.0524304i
\(711\) 0 0
\(712\) 3.34356e6 5.76181e6i 0.247178 0.425950i
\(713\) 1.28737e7i 0.948371i
\(714\) 0 0
\(715\) 1.16801e7i 0.854442i
\(716\) −2.48420e6 1.42109e7i −0.181094 1.03595i
\(717\) 0 0
\(718\) −1.38221e7 + 1.64479e7i −1.00060 + 1.19069i
\(719\) 1.09144e7 0.787365 0.393682 0.919247i \(-0.371201\pi\)
0.393682 + 0.919247i \(0.371201\pi\)
\(720\) 0 0
\(721\) −2.34997e7 −1.68354
\(722\) −7.12628e6 + 8.48009e6i −0.508768 + 0.605421i
\(723\) 0 0
\(724\) −8738.63 49989.3i −0.000619580 0.00354430i
\(725\) 521187.i 0.0368255i
\(726\) 0 0
\(727\) 3.42329e6i 0.240219i 0.992761 + 0.120110i \(0.0383246\pi\)
−0.992761 + 0.120110i \(0.961675\pi\)
\(728\) −1.86305e7 + 3.21050e7i −1.30285 + 2.24515i
\(729\) 0 0
\(730\) 1.69783e6 + 1.42677e6i 0.117920 + 0.0990942i
\(731\) 2.86323e7 1.98181
\(732\) 0 0
\(733\) 1.27970e6 0.0879724 0.0439862 0.999032i \(-0.485994\pi\)
0.0439862 + 0.999032i \(0.485994\pi\)
\(734\) −4.35509e6 3.65982e6i −0.298371 0.250737i
\(735\) 0 0
\(736\) 5.24749e6 1.42540e7i 0.357073 0.969932i
\(737\) 3.60255e6i 0.244310i
\(738\) 0 0
\(739\) 73084.4i 0.00492281i 0.999997 + 0.00246141i \(0.000783491\pi\)
−0.999997 + 0.00246141i \(0.999217\pi\)
\(740\) −290989. + 50867.9i −0.0195343 + 0.00341479i
\(741\) 0 0
\(742\) −1.54812e7 + 1.84222e7i −1.03227 + 1.22838i
\(743\) 2.23684e7 1.48649 0.743247 0.669017i \(-0.233285\pi\)
0.743247 + 0.669017i \(0.233285\pi\)
\(744\) 0 0
\(745\) −3.42212e7 −2.25894
\(746\) −1.14113e7 + 1.35792e7i −0.750737 + 0.893358i
\(747\) 0 0
\(748\) −1.05574e7 + 1.84555e6i −0.689929 + 0.120607i
\(749\) 2.05462e7i 1.33822i
\(750\) 0 0
\(751\) 1.91551e7i 1.23932i −0.784869 0.619662i \(-0.787270\pi\)
0.784869 0.619662i \(-0.212730\pi\)
\(752\) 9.06436e6 3.26898e6i 0.584511 0.210798i
\(753\) 0 0
\(754\) 635046. + 533663.i 0.0406796 + 0.0341853i
\(755\) 1.51448e7 0.966935
\(756\) 0 0
\(757\) −6.56784e6 −0.416565 −0.208283 0.978069i \(-0.566787\pi\)
−0.208283 + 0.978069i \(0.566787\pi\)
\(758\) 5.86304e6 + 4.92703e6i 0.370638 + 0.311467i
\(759\) 0 0
\(760\) −9.07525e6 5.26634e6i −0.569934 0.330731i
\(761\) 1.18923e7i 0.744397i −0.928153 0.372199i \(-0.878604\pi\)
0.928153 0.372199i \(-0.121396\pi\)
\(762\) 0 0
\(763\) 2.29185e7i 1.42519i
\(764\) 1.71128e6 + 9.78935e6i 0.106069 + 0.606765i
\(765\) 0 0
\(766\) −1.20770e7 + 1.43713e7i −0.743681 + 0.884961i
\(767\) 2.04236e7 1.25356
\(768\) 0 0
\(769\) 2.93438e7 1.78937 0.894686 0.446695i \(-0.147399\pi\)
0.894686 + 0.446695i \(0.147399\pi\)
\(770\) −9.74527e6 + 1.15966e7i −0.592334 + 0.704863i
\(771\) 0 0
\(772\) −478138. 2.73518e6i −0.0288742 0.165175i
\(773\) 2.17877e7i 1.31148i −0.754986 0.655741i \(-0.772356\pi\)
0.754986 0.655741i \(-0.227644\pi\)
\(774\) 0 0
\(775\) 1.65031e7i 0.986988i
\(776\) −4.42297e6 2.56664e6i −0.263670 0.153007i
\(777\) 0 0
\(778\) 1.61662e7 + 1.35853e7i 0.957542 + 0.804675i
\(779\) −2.41579e6 −0.142631
\(780\) 0 0
\(781\) 368445. 0.0216145
\(782\) −2.48025e7 2.08429e7i −1.45037 1.21882i
\(783\) 0 0
\(784\) 2.90942e7 1.04926e7i 1.69051 0.609666i
\(785\) 2.80409e7i 1.62412i
\(786\)