Properties

Label 108.6.h.a.35.10
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 35.10
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.66122 - 4.99179i) q^{2} +(-17.8359 + 26.5684i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(13.9322 + 8.04377i) q^{7} +(180.089 + 18.3284i) q^{8} +O(q^{10})\) \(q+(-2.66122 - 4.99179i) q^{2} +(-17.8359 + 26.5684i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(13.9322 + 8.04377i) q^{7} +(180.089 + 18.3284i) q^{8} +(20.4019 + 12.7174i) q^{10} +(43.3121 - 75.0187i) q^{11} +(162.502 + 281.462i) q^{13} +(3.07614 - 90.9529i) q^{14} +(-387.764 - 947.742i) q^{16} -1863.80i q^{17} -416.071i q^{19} +(9.18864 - 135.686i) q^{20} +(-489.740 - 16.5636i) q^{22} +(-1293.41 - 2240.24i) q^{23} +(-1553.47 + 2690.69i) q^{25} +(972.544 - 1560.21i) q^{26} +(-462.204 + 226.690i) q^{28} +(-4342.80 - 2507.32i) q^{29} +(6396.76 - 3693.17i) q^{31} +(-3699.00 + 4457.78i) q^{32} +(-9303.69 + 4959.98i) q^{34} -68.3704 q^{35} -10519.2 q^{37} +(-2076.94 + 1107.25i) q^{38} +(-701.768 + 315.222i) q^{40} +(-13207.4 + 7625.29i) q^{41} +(-6794.45 - 3922.78i) q^{43} +(1220.62 + 2488.76i) q^{44} +(-7740.79 + 12418.2i) q^{46} +(14244.6 - 24672.4i) q^{47} +(-8274.10 - 14331.2i) q^{49} +(17565.5 + 594.085i) q^{50} +(-10376.4 - 702.686i) q^{52} +5483.31i q^{53} +368.144i q^{55} +(2361.61 + 1703.95i) q^{56} +(-958.860 + 28350.9i) q^{58} +(-1901.12 - 3292.83i) q^{59} +(16590.1 - 28734.9i) q^{61} +(-35458.7 - 22102.9i) q^{62} +(32096.1 + 6601.49i) q^{64} +(-1196.18 - 690.617i) q^{65} +(57592.1 - 33250.8i) q^{67} +(49518.3 + 33242.5i) q^{68} +(181.948 + 341.290i) q^{70} -43573.3 q^{71} +22901.9 q^{73} +(27993.8 + 52509.6i) q^{74} +(11054.4 + 7420.98i) q^{76} +(1206.87 - 696.785i) q^{77} +(31941.7 + 18441.5i) q^{79} +(3441.08 + 2664.20i) q^{80} +(73211.6 + 45635.9i) q^{82} +(27504.3 - 47638.8i) q^{83} +(3960.48 + 6859.75i) q^{85} +(-1500.17 + 44355.8i) q^{86} +(9175.01 - 12716.2i) q^{88} -40969.8i q^{89} +5228.51i q^{91} +(82588.8 + 5592.90i) q^{92} +(-161068. - 5447.50i) q^{94} +(884.130 + 1531.36i) q^{95} +(23339.8 - 40425.7i) q^{97} +(-49518.9 + 79440.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66122 4.99179i −0.470441 0.882431i
\(3\) 0 0
\(4\) −17.8359 + 26.5684i −0.557371 + 0.830264i
\(5\) −3.68052 + 2.12495i −0.0658391 + 0.0380122i −0.532558 0.846393i \(-0.678769\pi\)
0.466719 + 0.884406i \(0.345436\pi\)
\(6\) 0 0
\(7\) 13.9322 + 8.04377i 0.107467 + 0.0620461i 0.552770 0.833334i \(-0.313571\pi\)
−0.445303 + 0.895380i \(0.646904\pi\)
\(8\) 180.089 + 18.3284i 0.994861 + 0.101251i
\(9\) 0 0
\(10\) 20.4019 + 12.7174i 0.0645166 + 0.0402160i
\(11\) 43.3121 75.0187i 0.107926 0.186934i −0.807004 0.590546i \(-0.798912\pi\)
0.914930 + 0.403613i \(0.132246\pi\)
\(12\) 0 0
\(13\) 162.502 + 281.462i 0.266686 + 0.461914i 0.968004 0.250935i \(-0.0807380\pi\)
−0.701318 + 0.712849i \(0.747405\pi\)
\(14\) 3.07614 90.9529i 0.00419455 0.124021i
\(15\) 0 0
\(16\) −387.764 947.742i −0.378676 0.925529i
\(17\) 1863.80i 1.56415i −0.623187 0.782073i \(-0.714163\pi\)
0.623187 0.782073i \(-0.285837\pi\)
\(18\) 0 0
\(19\) 416.071i 0.264413i −0.991222 0.132207i \(-0.957794\pi\)
0.991222 0.132207i \(-0.0422063\pi\)
\(20\) 9.18864 135.686i 0.00513660 0.0758508i
\(21\) 0 0
\(22\) −489.740 16.5636i −0.215729 0.00729623i
\(23\) −1293.41 2240.24i −0.509818 0.883030i −0.999935 0.0113741i \(-0.996379\pi\)
0.490117 0.871656i \(1.66305\pi\)
\(24\) 0 0
\(25\) −1553.47 + 2690.69i −0.497110 + 0.861020i
\(26\) 972.544 1560.21i 0.282147 0.452635i
\(27\) 0 0
\(28\) −462.204 + 226.690i −0.111414 + 0.0546433i
\(29\) −4342.80 2507.32i −0.958904 0.553623i −0.0630683 0.998009i \(-0.520089\pi\)
−0.895835 + 0.444386i \(0.853422\pi\)
\(30\) 0 0
\(31\) 6396.76 3693.17i 1.19552 0.690232i 0.235964 0.971762i \(-0.424175\pi\)
0.959553 + 0.281530i \(0.0908418\pi\)
\(32\) −3699.00 + 4457.78i −0.638571 + 0.769563i
\(33\) 0 0
\(34\) −9303.69 + 4959.98i −1.38025 + 0.735838i
\(35\) −68.3704 −0.00943405
\(36\) 0 0
\(37\) −10519.2 −1.26322 −0.631609 0.775287i \(-0.717605\pi\)
−0.631609 + 0.775287i \(0.717605\pi\)
\(38\) −2076.94 + 1107.25i −0.233327 + 0.124391i
\(39\) 0 0
\(40\) −701.768 + 315.222i −0.0693496 + 0.0311506i
\(41\) −13207.4 + 7625.29i −1.22704 + 0.708430i −0.966409 0.257009i \(-0.917263\pi\)
−0.260628 + 0.965439i \(0.583930\pi\)
\(42\) 0 0
\(43\) −6794.45 3922.78i −0.560381 0.323536i 0.192917 0.981215i \(-0.438205\pi\)
−0.753298 + 0.657679i \(0.771538\pi\)
\(44\) 1220.62 + 2488.76i 0.0950495 + 0.193799i
\(45\) 0 0
\(46\) −7740.79 + 12418.2i −0.539375 + 0.865293i
\(47\) 14244.6 24672.4i 0.940604 1.62917i 0.176280 0.984340i \(-0.443594\pi\)
0.764323 0.644833i \(-0.223073\pi\)
\(48\) 0 0
\(49\) −8274.10 14331.2i −0.492301 0.852690i
\(50\) 17565.5 + 594.085i 0.993652 + 0.0336065i
\(51\) 0 0
\(52\) −10376.4 702.686i −0.532153 0.0360373i
\(53\) 5483.31i 0.268135i 0.990972 + 0.134067i \(0.0428038\pi\)
−0.990972 + 0.134067i \(0.957196\pi\)
\(54\) 0 0
\(55\) 368.144i 0.0164101i
\(56\) 2361.61 + 1703.95i 0.100633 + 0.0726084i
\(57\) 0 0
\(58\) −958.860 + 28350.9i −0.0374270 + 1.10661i
\(59\) −1901.12 3292.83i −0.0711015 0.123151i 0.828283 0.560310i \(-0.189318\pi\)
−0.899384 + 0.437159i \(0.855985\pi\)
\(60\) 0 0
\(61\) 16590.1 28734.9i 0.570853 0.988747i −0.425625 0.904900i \(-0.639946\pi\)
0.996479 0.0838475i \(-0.0267209\pi\)
\(62\) −35458.7 22102.9i −1.17150 0.730248i
\(63\) 0 0
\(64\) 32096.1 + 6601.49i 0.979496 + 0.201462i
\(65\) −1196.18 690.617i −0.0351168 0.0202747i
\(66\) 0 0
\(67\) 57592.1 33250.8i 1.56738 0.904930i 0.570912 0.821011i \(-0.306590\pi\)
0.996473 0.0839192i \(-0.0267438\pi\)
\(68\) 49518.3 + 33242.5i 1.29865 + 0.871809i
\(69\) 0 0
\(70\) 181.948 + 341.290i 0.00443816 + 0.00832490i
\(71\) −43573.3 −1.02583 −0.512914 0.858440i \(-0.671434\pi\)
−0.512914 + 0.858440i \(0.671434\pi\)
\(72\) 0 0
\(73\) 22901.9 0.502996 0.251498 0.967858i \(-0.419077\pi\)
0.251498 + 0.967858i \(0.419077\pi\)
\(74\) 27993.8 + 52509.6i 0.594269 + 1.11470i
\(75\) 0 0
\(76\) 11054.4 + 7420.98i 0.219533 + 0.147376i
\(77\) 1206.87 696.785i 0.0231970 0.0133928i
\(78\) 0 0
\(79\) 31941.7 + 18441.5i 0.575824 + 0.332452i 0.759472 0.650540i \(-0.225457\pi\)
−0.183648 + 0.982992i \(0.558791\pi\)
\(80\) 3441.08 + 2664.20i 0.0601132 + 0.0465417i
\(81\) 0 0
\(82\) 73211.6 + 45635.9i 1.20239 + 0.749501i
\(83\) 27504.3 47638.8i 0.438233 0.759041i −0.559321 0.828951i \(-0.688938\pi\)
0.997553 + 0.0699102i \(0.0222713\pi\)
\(84\) 0 0
\(85\) 3960.48 + 6859.75i 0.0594567 + 0.102982i
\(86\) −1500.17 + 44355.8i −0.0218723 + 0.646702i
\(87\) 0 0
\(88\) 9175.01 12716.2i 0.126299 0.175046i
\(89\) 40969.8i 0.548263i −0.961692 0.274132i \(-0.911610\pi\)
0.961692 0.274132i \(-0.0883904\pi\)
\(90\) 0 0
\(91\) 5228.51i 0.0661873i
\(92\) 82588.8 + 5592.90i 1.01731 + 0.0688918i
\(93\) 0 0
\(94\) −161068. 5447.50i −1.88013 0.0635883i
\(95\) 884.130 + 1531.36i 0.0100509 + 0.0174087i
\(96\) 0 0
\(97\) 23339.8 40425.7i 0.251865 0.436243i −0.712174 0.702003i \(-0.752289\pi\)
0.964039 + 0.265760i \(0.0856227\pi\)
\(98\) −49518.9 + 79440.8i −0.520842 + 0.835562i
\(99\) 0 0
\(100\) −43779.9 89264.0i −0.437799 0.892640i
\(101\) 65827.1 + 38005.3i 0.642098 + 0.370716i 0.785422 0.618960i \(-0.212446\pi\)
−0.143324 + 0.989676i \(0.545779\pi\)
\(102\) 0 0
\(103\) −3270.29 + 1888.10i −0.0303734 + 0.0175361i −0.515110 0.857124i \(-0.672249\pi\)
0.484736 + 0.874660i \(0.338916\pi\)
\(104\) 24106.1 + 53666.6i 0.218546 + 0.486542i
\(105\) 0 0
\(106\) 27371.5 14592.3i 0.236610 0.126142i
\(107\) −57656.6 −0.486844 −0.243422 0.969920i \(-0.578270\pi\)
−0.243422 + 0.969920i \(0.578270\pi\)
\(108\) 0 0
\(109\) −176304. −1.42133 −0.710667 0.703529i \(-0.751607\pi\)
−0.710667 + 0.703529i \(0.751607\pi\)
\(110\) 1837.70 979.710i 0.0144808 0.00771998i
\(111\) 0 0
\(112\) 2221.00 16323.2i 0.0167303 0.122959i
\(113\) −111854. + 64579.2i −0.824057 + 0.475769i −0.851813 0.523845i \(-0.824497\pi\)
0.0277568 + 0.999615i \(0.491164\pi\)
\(114\) 0 0
\(115\) 9520.81 + 5496.84i 0.0671319 + 0.0387586i
\(116\) 144073. 70661.3i 0.994118 0.487570i
\(117\) 0 0
\(118\) −11377.8 + 18252.9i −0.0752236 + 0.120678i
\(119\) 14992.0 25966.9i 0.0970491 0.168094i
\(120\) 0 0
\(121\) 76773.6 + 132976.i 0.476704 + 0.825675i
\(122\) −187588. 6344.46i −1.14105 0.0385918i
\(123\) 0 0
\(124\) −15969.9 + 235823.i −0.0932712 + 1.37731i
\(125\) 26485.1i 0.151610i
\(126\) 0 0
\(127\) 43254.5i 0.237970i −0.992896 0.118985i \(-0.962036\pi\)
0.992896 0.118985i \(-0.0379640\pi\)
\(128\) −52461.5 177785.i −0.283019 0.959114i
\(129\) 0 0
\(130\) −264.109 + 7808.97i −0.00137064 + 0.0405262i
\(131\) 104818. + 181550.i 0.533650 + 0.924309i 0.999227 + 0.0393020i \(0.0125135\pi\)
−0.465577 + 0.885007i \(0.654153\pi\)
\(132\) 0 0
\(133\) 3346.78 5796.79i 0.0164058 0.0284157i
\(134\) −319246. 199000.i −1.53590 0.957394i
\(135\) 0 0
\(136\) 34160.5 335650.i 0.158372 1.55611i
\(137\) −99563.4 57483.0i −0.453209 0.261660i 0.255976 0.966683i \(-0.417603\pi\)
−0.709184 + 0.705023i \(0.750937\pi\)
\(138\) 0 0
\(139\) −186853. + 107880.i −0.820281 + 0.473590i −0.850514 0.525953i \(-0.823709\pi\)
0.0302321 + 0.999543i \(0.490375\pi\)
\(140\) 1219.44 1816.50i 0.00525826 0.00783275i
\(141\) 0 0
\(142\) 115958. + 217509.i 0.482592 + 0.905223i
\(143\) 28153.2 0.115130
\(144\) 0 0
\(145\) 21311.7 0.0841779
\(146\) −60946.9 114321.i −0.236630 0.443860i
\(147\) 0 0
\(148\) 187619. 279479.i 0.704080 1.04880i
\(149\) 192038. 110873.i 0.708633 0.409129i −0.101922 0.994792i \(-0.532499\pi\)
0.810555 + 0.585663i \(0.199166\pi\)
\(150\) 0 0
\(151\) −364405. 210389.i −1.30059 0.750898i −0.320088 0.947388i \(-0.603712\pi\)
−0.980506 + 0.196490i \(0.937046\pi\)
\(152\) 7625.92 74929.8i 0.0267722 0.263055i
\(153\) 0 0
\(154\) −6689.94 4170.13i −0.0227311 0.0141693i
\(155\) −15695.6 + 27185.6i −0.0524745 + 0.0908886i
\(156\) 0 0
\(157\) 110672. + 191690.i 0.358335 + 0.620654i 0.987683 0.156470i \(-0.0500113\pi\)
−0.629348 + 0.777124i \(0.716678\pi\)
\(158\) 7052.50 208523.i 0.0224750 0.664525i
\(159\) 0 0
\(160\) 4141.68 24267.1i 0.0127902 0.0749409i
\(161\) 41615.4i 0.126529i
\(162\) 0 0
\(163\) 324082.i 0.955402i 0.878522 + 0.477701i \(0.158530\pi\)
−0.878522 + 0.477701i \(0.841470\pi\)
\(164\) 32973.1 486904.i 0.0957303 1.41362i
\(165\) 0 0
\(166\) −310997. 10518.3i −0.875964 0.0296262i
\(167\) 125104. + 216686.i 0.347120 + 0.601229i 0.985737 0.168296i \(-0.0538263\pi\)
−0.638617 + 0.769525i \(0.720493\pi\)
\(168\) 0 0
\(169\) 132833. 230073.i 0.357757 0.619654i
\(170\) 23702.7 38025.2i 0.0629037 0.100913i
\(171\) 0 0
\(172\) 225407. 110552.i 0.580960 0.284935i
\(173\) 267332. + 154344.i 0.679102 + 0.392080i 0.799517 0.600644i \(-0.205089\pi\)
−0.120414 + 0.992724i \(0.538422\pi\)
\(174\) 0 0
\(175\) −43286.5 + 24991.5i −0.106846 + 0.0616875i
\(176\) −87893.3 11959.1i −0.213882 0.0291016i
\(177\) 0 0
\(178\) −204513. + 109030.i −0.483805 + 0.257926i
\(179\) −7856.73 −0.0183278 −0.00916388 0.999958i \(-0.502917\pi\)
−0.00916388 + 0.999958i \(0.502917\pi\)
\(180\) 0 0
\(181\) −449713. −1.02033 −0.510163 0.860078i \(-0.670415\pi\)
−0.510163 + 0.860078i \(0.670415\pi\)
\(182\) 26099.6 13914.2i 0.0584058 0.0311372i
\(183\) 0 0
\(184\) −191868. 427149.i −0.417790 0.930112i
\(185\) 38716.1 22352.7i 0.0831691 0.0480177i
\(186\) 0 0
\(187\) −139820. 80725.1i −0.292392 0.168812i
\(188\) 401443. + 818512.i 0.828379 + 1.68900i
\(189\) 0 0
\(190\) 5291.35 8488.66i 0.0106337 0.0170591i
\(191\) −255380. + 442331.i −0.506527 + 0.877331i 0.493444 + 0.869777i \(0.335738\pi\)
−0.999971 + 0.00755354i \(0.997596\pi\)
\(192\) 0 0
\(193\) 439991. + 762087.i 0.850257 + 1.47269i 0.880976 + 0.473161i \(0.156887\pi\)
−0.0307186 + 0.999528i \(0.509780\pi\)
\(194\) −263909. 8925.72i −0.503442 0.0170270i
\(195\) 0 0
\(196\) 528332. + 35778.6i 0.982351 + 0.0665247i
\(197\) 162799.i 0.298873i 0.988771 + 0.149437i \(0.0477460\pi\)
−0.988771 + 0.149437i \(0.952254\pi\)
\(198\) 0 0
\(199\) 786472.i 1.40783i 0.710283 + 0.703916i \(0.248567\pi\)
−0.710283 + 0.703916i \(0.751433\pi\)
\(200\) −329079. + 456091.i −0.581735 + 0.806262i
\(201\) 0 0
\(202\) 14534.2 429735.i 0.0250618 0.741007i
\(203\) −40336.6 69865.0i −0.0687004 0.118993i
\(204\) 0 0
\(205\) 32406.7 56130.1i 0.0538580 0.0932848i
\(206\) 18128.0 + 11299.9i 0.0297633 + 0.0185527i
\(207\) 0 0
\(208\) 203741. 263151.i 0.326527 0.421741i
\(209\) −31213.1 18020.9i −0.0494278 0.0285372i
\(210\) 0 0
\(211\) 879851. 507982.i 1.36051 0.785493i 0.370821 0.928704i \(-0.379076\pi\)
0.989692 + 0.143212i \(0.0457429\pi\)
\(212\) −145683. 97799.5i −0.222623 0.149450i
\(213\) 0 0
\(214\) 153437. + 287810.i 0.229031 + 0.429606i
\(215\) 33342.8 0.0491933
\(216\) 0 0
\(217\) 118828. 0.171305
\(218\) 469183. + 880072.i 0.668654 + 1.25423i
\(219\) 0 0
\(220\) −9781.01 6566.16i −0.0136247 0.00914650i
\(221\) 524588. 302871.i 0.722500 0.417136i
\(222\) 0 0
\(223\) −201948. 116595.i −0.271942 0.157006i 0.357828 0.933788i \(-0.383518\pi\)
−0.629770 + 0.776782i \(0.716851\pi\)
\(224\) −87392.7 + 32352.9i −0.116374 + 0.0430817i
\(225\) 0 0
\(226\) 620034. + 386494.i 0.807504 + 0.503352i
\(227\) −439493. + 761224.i −0.566092 + 0.980501i 0.430855 + 0.902421i \(0.358212\pi\)
−0.996947 + 0.0780796i \(0.975121\pi\)
\(228\) 0 0
\(229\) −191288. 331320.i −0.241045 0.417503i 0.719967 0.694008i \(-0.244157\pi\)
−0.961012 + 0.276506i \(0.910824\pi\)
\(230\) 2102.13 62154.1i 0.00262023 0.0774730i
\(231\) 0 0
\(232\) −736136. 531137.i −0.897921 0.647868i
\(233\) 224357.i 0.270738i 0.990795 + 0.135369i \(0.0432220\pi\)
−0.990795 + 0.135369i \(0.956778\pi\)
\(234\) 0 0
\(235\) 121076.i 0.143018i
\(236\) 121393. + 8220.75i 0.141878 + 0.00960797i
\(237\) 0 0
\(238\) −169518. 5733.30i −0.193987 0.00656089i
\(239\) −769108. 1.33213e6i −0.870949 1.50853i −0.861017 0.508577i \(-0.830172\pi\)
−0.00993200 0.999951i \(1.49684\pi\)
\(240\) 0 0
\(241\) 692903. 1.20014e6i 0.768475 1.33104i −0.169914 0.985459i \(-0.554349\pi\)
0.938390 0.345579i \(-0.112318\pi\)
\(242\) 459476. 737115.i 0.504341 0.809090i
\(243\) 0 0
\(244\) 467543. + 953285.i 0.502744 + 1.02506i
\(245\) 60905.9 + 35164.1i 0.0648253 + 0.0374269i
\(246\) 0 0
\(247\) 117108. 67612.4i 0.122136 0.0705154i
\(248\) 1.21968e6 547857.i 1.25926 0.565637i
\(249\) 0 0
\(250\) −132208. + 70482.6i −0.133785 + 0.0713234i
\(251\) 1.31402e6 1.31649 0.658246 0.752803i \(-0.271299\pi\)
0.658246 + 0.752803i \(0.271299\pi\)
\(252\) 0 0
\(253\) −224080. −0.220091
\(254\) −215917. + 115109.i −0.209992 + 0.111951i
\(255\) 0 0
\(256\) −747854. + 735001.i −0.713209 + 0.700952i
\(257\) −542479. + 313201.i −0.512331 + 0.295794i −0.733791 0.679375i \(-0.762251\pi\)
0.221461 + 0.975169i \(0.428918\pi\)
\(258\) 0 0
\(259\) −146556. 84614.0i −0.135754 0.0783777i
\(260\) 39683.6 19463.0i 0.0364064 0.0178557i
\(261\) 0 0
\(262\) 627315. 1.00637e6i 0.564589 0.905743i
\(263\) 750127. 1.29926e6i 0.668722 1.15826i −0.309540 0.950887i \(-0.600175\pi\)
0.978262 0.207374i \(-0.0664917\pi\)
\(264\) 0 0
\(265\) −11651.8 20181.4i −0.0101924 0.0176538i
\(266\) −37842.9 1279.89i −0.0327929 0.00110910i
\(267\) 0 0
\(268\) −143782. + 2.12319e6i −0.122283 + 1.80572i
\(269\) 264637.i 0.222982i 0.993765 + 0.111491i \(0.0355626\pi\)
−0.993765 + 0.111491i \(0.964437\pi\)
\(270\) 0 0
\(271\) 650898.i 0.538381i −0.963087 0.269190i \(-0.913244\pi\)
0.963087 0.269190i \(-0.0867561\pi\)
\(272\) −1.76640e6 + 722715.i −1.44766 + 0.592305i
\(273\) 0 0
\(274\) −21982.9 + 649974.i −0.0176892 + 0.523022i
\(275\) 134568. + 233079.i 0.107303 + 0.185853i
\(276\) 0 0
\(277\) 237366. 411129.i 0.185874 0.321943i −0.757997 0.652258i \(-0.773822\pi\)
0.943871 + 0.330315i \(0.107155\pi\)
\(278\) 1.03577e6 + 645639.i 0.803804 + 0.501046i
\(279\) 0 0
\(280\) −12312.8 1253.12i −0.00938557 0.000955208i
\(281\) −1.41561e6 817304.i −1.06949 0.617473i −0.141451 0.989945i \(-0.545177\pi\)
−0.928043 + 0.372472i \(0.878510\pi\)
\(282\) 0 0
\(283\) 1.06078e6 612441.i 0.787333 0.454567i −0.0516895 0.998663i \(-0.516461\pi\)
0.839023 + 0.544096i \(0.183127\pi\)
\(284\) 777167. 1.15767e6i 0.571766 0.851708i
\(285\) 0 0
\(286\) −74921.7 140535.i −0.0541618 0.101594i
\(287\) −245345. −0.175821
\(288\) 0 0
\(289\) −2.05390e6 −1.44655
\(290\) −56715.0 106383.i −0.0396007 0.0742812i
\(291\) 0 0
\(292\) −408475. + 608468.i −0.280355 + 0.417619i
\(293\) −963120. + 556058.i −0.655407 + 0.378400i −0.790525 0.612430i \(-0.790192\pi\)
0.135117 + 0.990830i \(0.456859\pi\)
\(294\) 0 0
\(295\) 13994.2 + 8079.55i 0.00936253 + 0.00540546i
\(296\) −1.89439e6 192800.i −1.25673 0.127902i
\(297\) 0 0
\(298\) −1.06451e6 663555.i −0.694399 0.432849i
\(299\) 420362. 728088.i 0.271923 0.470984i
\(300\) 0 0
\(301\) −63107.9 109306.i −0.0401483 0.0695389i
\(302\) −80458.0 + 2.37892e6i −0.0507635 + 1.50094i
\(303\) 0 0
\(304\) −394328. + 161338.i −0.244722 + 0.100127i
\(305\) 141013.i 0.0867977i
\(306\) 0 0
\(307\) 1.54327e6i 0.934537i −0.884115 0.467269i \(-0.845238\pi\)
0.884115 0.467269i \(-0.154762\pi\)
\(308\) −3013.02 + 44492.3i −0.00180978 + 0.0267244i
\(309\) 0 0
\(310\) 177474. + 6002.38i 0.104889 + 0.00354748i
\(311\) −1.17389e6 2.03323e6i −0.688218 1.19203i −0.972414 0.233262i \(-0.925060\pi\)
0.284196 0.958766i \(1.59173\pi\)
\(312\) 0 0
\(313\) −705005. + 1.22110e6i −0.406753 + 0.704517i −0.994524 0.104510i \(-0.966672\pi\)
0.587770 + 0.809028i \(0.300006\pi\)
\(314\) 662351. 1.06258e6i 0.379109 0.608187i
\(315\) 0 0
\(316\) −1.05967e6 + 519720.i −0.596971 + 0.292787i
\(317\) −1.72360e6 995122.i −0.963360 0.556196i −0.0661546 0.997809i \(-0.521073\pi\)
−0.897206 + 0.441613i \(0.854406\pi\)
\(318\) 0 0
\(319\) −376192. + 217194.i −0.206982 + 0.119501i
\(320\) −132158. + 43905.7i −0.0721472 + 0.0239688i
\(321\) 0 0
\(322\) −207735. + 110748.i −0.111653 + 0.0595244i
\(323\) −775473. −0.413581
\(324\) 0 0
\(325\) −1.00977e6 −0.530289
\(326\) 1.61775e6 862453.i 0.843077 0.449460i
\(327\) 0 0
\(328\) −2.51827e6 + 1.13116e6i −1.29246 + 0.580550i
\(329\) 396919. 229161.i 0.202168 0.116722i
\(330\) 0 0
\(331\) 2.45201e6 + 1.41567e6i 1.23013 + 0.710218i 0.967058 0.254557i \(-0.0819296\pi\)
0.263076 + 0.964775i \(0.415263\pi\)
\(332\) 775126. + 1.58042e6i 0.385946 + 0.786916i
\(333\) 0 0
\(334\) 748723. 1.20114e6i 0.367244 0.589152i
\(335\) −141312. + 244760.i −0.0687968 + 0.119160i
\(336\) 0 0
\(337\) −360837. 624988.i −0.173076 0.299776i 0.766418 0.642342i \(-0.222037\pi\)
−0.939494 + 0.342566i \(0.888704\pi\)
\(338\) −1.50197e6 50798.5i −0.715105 0.0241857i
\(339\) 0 0
\(340\) −252892. 17125.8i −0.118642 0.00803440i
\(341\) 639836.i 0.297977i
\(342\) 0 0
\(343\) 536603.i 0.246274i
\(344\) −1.15171e6 830981.i −0.524743 0.378613i
\(345\) 0 0
\(346\) 59024.9 1.74521e6i 0.0265061 0.783712i
\(347\) 751022. + 1.30081e6i 0.334833 + 0.579948i 0.983453 0.181165i \(-0.0579866\pi\)
−0.648619 + 0.761113i \(0.724653\pi\)
\(348\) 0 0
\(349\) −506792. + 877790.i −0.222724 + 0.385769i −0.955634 0.294556i \(-0.904828\pi\)
0.732910 + 0.680325i \(0.238161\pi\)
\(350\) 239947. + 149569.i 0.104700 + 0.0652638i
\(351\) 0 0
\(352\) 174206. + 470570.i 0.0749387 + 0.202427i
\(353\) 1.78252e6 + 1.02914e6i 0.761374 + 0.439579i 0.829789 0.558077i \(-0.188461\pi\)
−0.0684149 + 0.997657i \(0.521794\pi\)
\(354\) 0 0
\(355\) 160372. 92591.0i 0.0675396 0.0389940i
\(356\) 1.08850e6 + 730732.i 0.455203 + 0.305586i
\(357\) 0 0
\(358\) 20908.5 + 39219.1i 0.00862213 + 0.0161730i
\(359\) −301586. −0.123502 −0.0617512 0.998092i \(-0.519669\pi\)
−0.0617512 + 0.998092i \(0.519669\pi\)
\(360\) 0 0
\(361\) 2.30298e6 0.930086
\(362\) 1.19678e6 + 2.24487e6i 0.480003 + 0.900368i
\(363\) 0 0
\(364\) −138913. 93255.0i −0.0549529 0.0368909i
\(365\) −84290.9 + 48665.4i −0.0331168 + 0.0191200i
\(366\) 0 0
\(367\) −1.93072e6 1.11470e6i −0.748261 0.432009i 0.0768040 0.997046i \(-0.475528\pi\)
−0.825065 + 0.565037i \(0.808862\pi\)
\(368\) −1.62164e6 + 2.09450e6i −0.624215 + 0.806234i
\(369\) 0 0
\(370\) −214612. 133777.i −0.0814985 0.0508016i
\(371\) −44106.5 + 76394.7i −0.0166367 + 0.0288156i
\(372\) 0 0
\(373\) 898552. + 1.55634e6i 0.334404 + 0.579204i 0.983370 0.181613i \(-0.0581318\pi\)
−0.648966 + 0.760817i \(0.724798\pi\)
\(374\) −30871.3 + 912778.i −0.0114124 + 0.337432i
\(375\) 0 0
\(376\) 3.01751e6 4.18215e6i 1.10073 1.52556i
\(377\) 1.62978e6i 0.590574i
\(378\) 0 0
\(379\) 2.14708e6i 0.767804i 0.923374 + 0.383902i \(0.125420\pi\)
−0.923374 + 0.383902i \(0.874580\pi\)
\(380\) −56455.0 3823.13i −0.0200560 0.00135819i
\(381\) 0 0
\(382\) 2.88764e6 + 97663.5i 1.01248 + 0.0342431i
\(383\) 1.30237e6 + 2.25578e6i 0.453669 + 0.785777i 0.998611 0.0526965i \(-0.0167816\pi\)
−0.544942 + 0.838474i \(0.683448\pi\)
\(384\) 0 0
\(385\) −2961.27 + 5129.06i −0.00101818 + 0.00176354i
\(386\) 2.63326e6 4.22442e6i 0.899551 1.44311i
\(387\) 0 0
\(388\) 657764. + 1.34113e6i 0.221815 + 0.452264i
\(389\) 3.00548e6 + 1.73521e6i 1.00702 + 0.581405i 0.910319 0.413908i \(-0.135836\pi\)
0.0967049 + 0.995313i \(0.469170\pi\)
\(390\) 0 0
\(391\) −4.17537e6 + 2.41065e6i −1.38119 + 0.797429i
\(392\) −1.22741e6 2.73254e6i −0.403435 0.898154i
\(393\) 0 0
\(394\) 812660. 433244.i 0.263735 0.140602i
\(395\) −156749. −0.0505490
\(396\) 0 0
\(397\) 5.78885e6 1.84338 0.921692 0.387922i \(-0.126807\pi\)
0.921692 + 0.387922i \(0.126807\pi\)
\(398\) 3.92590e6 2.09297e6i 1.24231 0.662302i
\(399\) 0 0
\(400\) 3.15246e6 + 428935.i 0.985143 + 0.134042i
\(401\) 2.02846e6 1.17113e6i 0.629950 0.363702i −0.150782 0.988567i \(-0.548179\pi\)
0.780733 + 0.624865i \(0.214846\pi\)
\(402\) 0 0
\(403\) 2.07897e6 + 1.20029e6i 0.637655 + 0.368150i
\(404\) −2.18382e6 + 1.07107e6i −0.665678 + 0.326485i
\(405\) 0 0
\(406\) −241407. + 387278.i −0.0726833 + 0.116602i
\(407\) −455608. + 789137.i −0.136334 + 0.236138i
\(408\) 0 0
\(409\) −1.17070e6 2.02771e6i −0.346048 0.599373i 0.639495 0.768795i \(-0.279143\pi\)
−0.985544 + 0.169422i \(0.945810\pi\)
\(410\) −366431. 12393.1i −0.107655 0.00364101i
\(411\) 0 0
\(412\) 8164.48 120563.i 0.00236966 0.0349920i
\(413\) 61168.6i 0.0176463i
\(414\) 0 0
\(415\) 233781.i 0.0666328i
\(416\) −1.85579e6 316728.i −0.525770 0.0897333i
\(417\) 0 0
\(418\) −6891.64 + 203767.i −0.00192922 + 0.0570417i
\(419\) 2.33383e6 + 4.04232e6i 0.649434 + 1.12485i 0.983258 + 0.182217i \(0.0583274\pi\)
−0.333824 + 0.942635i \(0.608339\pi\)
\(420\) 0 0
\(421\) 2.03900e6 3.53165e6i 0.560676 0.971119i −0.436762 0.899577i \(-0.643875\pi\)
0.997438 0.0715416i \(-0.0227919\pi\)
\(422\) −4.87721e6 3.04018e6i −1.33318 0.831032i
\(423\) 0 0
\(424\) −100500. + 987484.i −0.0271489 + 0.266757i
\(425\) 5.01490e6 + 2.89536e6i 1.34676 + 0.777553i
\(426\) 0 0
\(427\) 462274. 266894.i 0.122696 0.0708385i
\(428\) 1.02836e6 1.53185e6i 0.271352 0.404209i
\(429\) 0 0
\(430\) −88732.4 166440.i −0.0231426 0.0434097i
\(431\) −4.54361e6 −1.17817 −0.589085 0.808071i \(-0.700512\pi\)
−0.589085 + 0.808071i \(0.700512\pi\)
\(432\) 0 0
\(433\) −6726.40 −0.00172410 −0.000862051 1.00000i \(-0.500274\pi\)
−0.000862051 1.00000i \(0.500274\pi\)
\(434\) −316227. 593164.i −0.0805888 0.151165i
\(435\) 0 0
\(436\) 3.14453e6 4.68413e6i 0.792210 1.18008i
\(437\) −932101. + 538148.i −0.233485 + 0.134803i
\(438\) 0 0
\(439\) −4.27223e6 2.46657e6i −1.05802 0.610847i −0.133134 0.991098i \(-0.542504\pi\)
−0.924883 + 0.380251i \(0.875838\pi\)
\(440\) −6747.49 + 66298.7i −0.00166154 + 0.0163258i
\(441\) 0 0
\(442\) −2.90791e6 1.81263e6i −0.707987 0.441319i
\(443\) −2.52747e6 + 4.37771e6i −0.611895 + 1.05983i 0.379025 + 0.925386i \(0.376259\pi\)
−0.990921 + 0.134448i \(0.957074\pi\)
\(444\) 0 0
\(445\) 87058.8 + 150790.i 0.0208407 + 0.0360972i
\(446\) −44588.7 + 1.31836e6i −0.0106142 + 0.313833i
\(447\) 0 0
\(448\) 394070. + 350147.i 0.0927637 + 0.0824244i
\(449\) 3.95256e6i 0.925257i 0.886552 + 0.462628i \(0.153094\pi\)
−0.886552 + 0.462628i \(0.846906\pi\)
\(450\) 0 0
\(451\) 1.32107e6i 0.305833i
\(452\) 279251. 4.12362e6i 0.0642908 0.949364i
\(453\) 0 0
\(454\) 4.96945e6 + 168073.i 1.13154 + 0.0382700i
\(455\) −11110.3 19243.6i −0.00251593 0.00435772i
\(456\) 0 0
\(457\) −3.74368e6 + 6.48424e6i −0.838509 + 1.45234i 0.0526320 + 0.998614i \(0.483239\pi\)
−0.891141 + 0.453726i \(0.850094\pi\)
\(458\) −1.14482e6 + 1.83658e6i −0.255020 + 0.409116i
\(459\) 0 0
\(460\) −315854. + 154912.i −0.0695973 + 0.0341343i
\(461\) −4.43539e6 2.56077e6i −0.972029 0.561201i −0.0721745 0.997392i \(-0.522994\pi\)
−0.899854 + 0.436191i \(0.856327\pi\)
\(462\) 0 0
\(463\) −3.47662e6 + 2.00723e6i −0.753711 + 0.435155i −0.827033 0.562153i \(-0.809973\pi\)
0.0733224 + 0.997308i \(0.476640\pi\)
\(464\) −692307. + 5.08810e6i −0.149281 + 1.09714i
\(465\) 0 0
\(466\) 1.11994e6 597062.i 0.238908 0.127366i
\(467\) 5.43636e6 1.15350 0.576748 0.816922i \(-0.304321\pi\)
0.576748 + 0.816922i \(0.304321\pi\)
\(468\) 0 0
\(469\) 1.06985e6 0.224590
\(470\) 604388. 322211.i 0.126203 0.0672814i
\(471\) 0 0
\(472\) −282018. 627847.i −0.0582669 0.129718i
\(473\) −588564. + 339807.i −0.120960 + 0.0698361i
\(474\) 0 0
\(475\) 1.11952e6 + 646353.i 0.227665 + 0.131443i
\(476\) 422505. + 861455.i 0.0854701 + 0.174267i
\(477\) 0 0
\(478\) −4.60297e6 + 7.38432e6i −0.921442 + 1.47823i
\(479\) 4.63944e6 8.03575e6i 0.923904 1.60025i 0.130589 0.991437i \(-0.458313\pi\)
0.793315 0.608812i \(-0.208354\pi\)
\(480\) 0 0
\(481\) −1.70939e6 2.96075e6i −0.336882 0.583497i
\(482\) −7.83482e6 264983.i −1.53607 0.0519518i
\(483\) 0 0
\(484\) −4.90228e6 331982.i −0.951229 0.0644171i
\(485\) 198384.i 0.0382958i
\(486\) 0 0
\(487\) 2.35999e6i 0.450908i 0.974254 + 0.225454i \(0.0723865\pi\)
−0.974254 + 0.225454i \(0.927614\pi\)
\(488\) 3.51436e6 4.87077e6i 0.668031 0.925866i
\(489\) 0 0
\(490\) 13447.6 397609.i 0.00253020 0.0748110i
\(491\) 4.26271e6 + 7.38323e6i 0.797961 + 1.38211i 0.920942 + 0.389701i \(0.127421\pi\)
−0.122980 + 0.992409i \(0.539245\pi\)
\(492\) 0 0
\(493\) −4.67314e6 + 8.09412e6i −0.865947 + 1.49986i
\(494\) −649156. 404647.i −0.119683 0.0746035i
\(495\) 0 0
\(496\) −5.98061e6 4.63040e6i −1.09154 0.845111i
\(497\) −607073. 350494.i −0.110243 0.0636486i
\(498\) 0 0
\(499\) −218746. + 126293.i −0.0393268 + 0.0227054i −0.519535 0.854449i \(-0.673895\pi\)
0.480208 + 0.877155i \(0.340561\pi\)
\(500\) 703668. + 472385.i 0.125876 + 0.0845027i
\(501\) 0 0
\(502\) −3.49689e6 6.55931e6i −0.619332 1.16171i
\(503\) −6.25307e6 −1.10198 −0.550989 0.834512i \(-0.685749\pi\)
−0.550989 + 0.834512i \(0.685749\pi\)
\(504\) 0 0
\(505\) −323037. −0.0563669
\(506\) 596326. + 1.11856e6i 0.103540 + 0.194215i
\(507\) 0 0
\(508\) 1.14920e6 + 771481.i 0.197578 + 0.132637i
\(509\) −431856. + 249332.i −0.0738830 + 0.0426564i −0.536486 0.843909i \(-0.680249\pi\)
0.462603 + 0.886565i \(0.346915\pi\)
\(510\) 0 0
\(511\) 319074. + 184218.i 0.0540555 + 0.0312090i
\(512\) 5.65917e6 + 1.77713e6i 0.954064 + 0.299601i
\(513\) 0 0
\(514\) 3.00708e6 + 1.87445e6i 0.502039 + 0.312943i
\(515\) 8024.25 13898.4i 0.00133317 0.00230912i
\(516\) 0 0
\(517\) −1.23393e6 2.13723e6i −0.203032 0.351661i
\(518\) −32358.5 + 956751.i −0.00529863 + 0.156666i
\(519\) 0 0
\(520\) −202762. 146297.i −0.0328835 0.0237261i
\(521\) 9.81352e6i 1.58391i −0.610579 0.791955i \(-0.709063\pi\)
0.610579 0.791955i \(-0.290937\pi\)
\(522\) 0 0
\(523\) 1.10853e7i 1.77211i −0.463576 0.886057i \(-0.653434\pi\)
0.463576 0.886057i \(-0.346566\pi\)
\(524\) −6.69301e6 453250.i −1.06486 0.0721123i
\(525\) 0 0
\(526\) −8.48187e6 286867.i −1.33668 0.0452081i
\(527\) −6.88333e6 1.19223e7i −1.07962 1.86996i
\(528\) 0 0
\(529\) −127624. + 221050.i −0.0198286 + 0.0343441i
\(530\) −69733.5 + 111870.i −0.0107833 + 0.0172991i
\(531\) 0 0
\(532\) 94319.1 + 192310.i 0.0144484 + 0.0294592i
\(533\) −4.29246e6 2.47825e6i −0.654467 0.377857i
\(534\) 0 0
\(535\) 212206. 122517.i 0.0320534 0.0185060i
\(536\) 1.09811e7 4.93253e6i 1.65096 0.741580i
\(537\) 0 0
\(538\) 1.32101e6 704257.i 0.196766 0.104900i
\(539\) −1.43347e6 −0.212529
\(540\) 0 0
\(541\) 2.27509e6 0.334200 0.167100 0.985940i \(-0.446560\pi\)
0.167100 + 0.985940i \(0.446560\pi\)
\(542\) −3.24914e6 + 1.73218e6i −0.475084 + 0.253276i
\(543\) 0 0
\(544\) 8.30842e6 + 6.89420e6i 1.20371 + 0.998818i
\(545\) 648891. 374637.i 0.0935794 0.0540281i
\(546\) 0 0
\(547\) 7.20659e6 + 4.16072e6i 1.02982 + 0.594567i 0.916933 0.399041i \(-0.130657\pi\)
0.112887 + 0.993608i \(0.463990\pi\)
\(548\) 3.30303e6 1.61999e6i 0.469852 0.230441i
\(549\) 0 0
\(550\) 805364. 1.29201e6i 0.113523 0.182120i
\(551\) −1.04322e6 + 1.80691e6i −0.146385 + 0.253547i
\(552\) 0 0
\(553\) 296679. + 513863.i 0.0412547 + 0.0714553i
\(554\) −2.68395e6 90774.4i −0.371535 0.0125658i
\(555\) 0 0
\(556\) 466489. 6.88852e6i 0.0639963 0.945015i
\(557\) 1.46783e6i 0.200465i −0.994964 0.100232i \(-0.968041\pi\)
0.994964 0.100232i \(-0.0319586\pi\)
\(558\) 0 0
\(559\) 2.54984e6i 0.345130i
\(560\) 26511.6 + 64797.5i 0.00357245 + 0.00873149i
\(561\) 0 0
\(562\) −312557. + 9.24146e6i −0.0417435 + 1.23424i
\(563\) −1.07987e6 1.87039e6i −0.143582 0.248691i 0.785261 0.619165i \(-0.212529\pi\)
−0.928843 + 0.370474i \(0.879195\pi\)
\(564\) 0 0
\(565\) 274455. 475370.i 0.0361701 0.0626485i
\(566\) −5.88014e6 3.66534e6i −0.771518 0.480921i
\(567\) 0 0
\(568\) −7.84707e6 798630.i −1.02056 0.103866i
\(569\) −2.42463e6 1.39986e6i −0.313954 0.181261i 0.334741 0.942310i \(-0.391351\pi\)
−0.648694 + 0.761049i \(0.724685\pi\)
\(570\) 0 0
\(571\) 9.90022e6 5.71589e6i 1.27073 0.733658i 0.295607 0.955310i \(-0.404478\pi\)
0.975126 + 0.221651i \(0.0711447\pi\)
\(572\) −502136. + 747987.i −0.0641699 + 0.0955881i
\(573\) 0 0
\(574\) 652915. + 1.22471e6i 0.0827136 + 0.155150i
\(575\) 8.03706e6 1.01374
\(576\) 0 0
\(577\) 669533. 0.0837206 0.0418603 0.999123i \(-0.486672\pi\)
0.0418603 + 0.999123i \(0.486672\pi\)
\(578\) 5.46586e6 + 1.02526e7i 0.680517 + 1.27648i
\(579\) 0 0
\(580\) −380112. + 566218.i −0.0469183 + 0.0698898i
\(581\) 766391. 442476.i 0.0941911 0.0543813i
\(582\) 0 0
\(583\) 411351. + 237494.i 0.0501235 + 0.0289388i
\(584\) 4.12438e6 + 419756.i 0.500411 + 0.0509289i
\(585\) 0 0
\(586\) 5.33879e6 + 3.32790e6i 0.642242 + 0.400337i
\(587\) −197174. + 341516.i −0.0236187 + 0.0409087i −0.877593 0.479406i \(-0.840852\pi\)
0.853974 + 0.520315i \(0.174185\pi\)
\(588\) 0 0
\(589\) −1.53662e6 2.66151e6i −0.182507 0.316111i
\(590\) 3089.82 91357.5i 0.000365429 0.0108047i
\(591\) 0 0
\(592\) 4.07897e6 + 9.96948e6i 0.478350 + 1.16914i
\(593\) 5.00148e6i 0.584066i 0.956408 + 0.292033i \(0.0943317\pi\)
−0.956408 + 0.292033i \(0.905668\pi\)
\(594\) 0 0
\(595\) 127429.i 0.0147562i
\(596\) −479434. + 7.07967e6i −0.0552858 + 0.816389i
\(597\) 0 0
\(598\) −4.75313e6 160757.i −0.543534 0.0183830i
\(599\) −5.30363e6 9.18615e6i −0.603957 1.04608i −0.992215 0.124533i \(-0.960257\pi\)
0.388259 0.921550i \(1.62692\pi\)
\(600\) 0 0
\(601\) 3.48253e6 6.03191e6i 0.393286 0.681191i −0.599595 0.800304i \(-0.704672\pi\)
0.992881 + 0.119113i \(0.0380050\pi\)
\(602\) −377689. + 605908.i −0.0424759 + 0.0681421i
\(603\) 0 0
\(604\) 1.20892e7 5.92919e6i 1.34836 0.661307i
\(605\) −565134. 326280.i −0.0627715 0.0362412i
\(606\) 0 0
\(607\) −1.36935e7 + 7.90597e6i −1.50850 + 0.870930i −0.508544 + 0.861036i \(0.669816\pi\)
−0.999951 + 0.00989422i \(0.996851\pi\)
\(608\) 1.85475e6 + 1.53905e6i 0.203483 + 0.168847i
\(609\) 0 0
\(610\) 703904. 375265.i 0.0765930 0.0408332i
\(611\) 9.25912e6 1.00338
\(612\) 0 0
\(613\) 133521. 0.0143515 0.00717575 0.999974i \(-0.497716\pi\)
0.00717575 + 0.999974i \(0.497716\pi\)
\(614\) −7.70369e6 + 4.10698e6i −0.824665 + 0.439645i
\(615\) 0 0
\(616\) 230115. 103363.i 0.0244339 0.0109753i
\(617\) −1.06772e7 + 6.16447e6i −1.12913 + 0.651902i −0.943715 0.330758i \(-0.892696\pi\)
−0.185413 + 0.982661i \(0.559362\pi\)
\(618\) 0 0
\(619\) 8.56059e6 + 4.94246e6i 0.898001 + 0.518461i 0.876551 0.481309i \(-0.159838\pi\)
0.0214502 + 0.999770i \(0.493172\pi\)
\(620\) −442334. 901886.i −0.0462137 0.0942263i
\(621\) 0 0
\(622\) −7.02550e6 + 1.12707e7i −0.728117 + 1.16808i
\(623\) 329552. 570801.i 0.0340176 0.0589202i
\(624\) 0 0
\(625\) −4.79831e6 8.31092e6i −0.491347 0.851038i
\(626\) 7.97166e6 + 269611.i 0.813042 + 0.0274981i
\(627\) 0 0
\(628\) −7.06683e6 478565.i −0.715032 0.0484219i
\(629\) 1.96057e7i 1.97586i
\(630\) 0 0
\(631\) 1.28910e7i 1.28888i −0.764653 0.644442i \(-0.777090\pi\)
0.764653 0.644442i \(-0.222910\pi\)
\(632\) 5.41434e6 + 3.90656e6i 0.539204 + 0.389047i
\(633\) 0 0
\(634\) −380559. + 1.12521e7i −0.0376010 + 1.11176i
\(635\) 91913.5 + 159199.i 0.00904576 + 0.0156677i
\(636\) 0 0
\(637\) 2.68911e6 4.65768e6i 0.262579 0.454801i
\(638\) 2.08532e6 + 1.29987e6i 0.202824 + 0.126429i
\(639\) 0 0
\(640\) 570870. + 542863.i 0.0550918 + 0.0523891i
\(641\) 7.67906e6 + 4.43351e6i 0.738181 + 0.426189i 0.821408 0.570342i \(-0.193189\pi\)
−0.0832264 + 0.996531i \(0.526522\pi\)
\(642\) 0 0
\(643\) 9.18917e6 5.30537e6i 0.876494 0.506044i 0.00699288 0.999976i \(-0.497774\pi\)
0.869501 + 0.493932i \(0.164441\pi\)
\(644\) 1.10566e6 + 742247.i 0.105052 + 0.0705235i
\(645\) 0 0
\(646\) 2.06370e6 + 3.87100e6i 0.194565 + 0.364957i
\(647\) −2.37142e6 −0.222714 −0.111357 0.993780i \(-0.535520\pi\)
−0.111357 + 0.993780i \(0.535520\pi\)
\(648\) 0 0
\(649\) −329365. −0.0306949
\(650\) 2.68721e6 + 5.04054e6i 0.249470 + 0.467944i
\(651\) 0 0
\(652\) −8.61036e6 5.78028e6i −0.793236 0.532513i
\(653\) 8.07136e6 4.66000e6i 0.740737 0.427665i −0.0816004 0.996665i \(-0.526003\pi\)
0.822337 + 0.569001i \(0.192670\pi\)
\(654\) 0 0
\(655\) −771568. 445465.i −0.0702701 0.0405705i
\(656\) 1.23482e7 + 9.56039e6i 1.12032 + 0.867393i
\(657\) 0 0
\(658\) −2.20021e6 1.37149e6i −0.198107 0.123489i
\(659\) −971185. + 1.68214e6i −0.0871141 + 0.150886i −0.906290 0.422656i \(-0.861098\pi\)
0.819176 + 0.573542i \(0.194431\pi\)
\(660\) 0 0
\(661\) −8.93142e6 1.54697e7i −0.795091 1.37714i −0.922781 0.385324i \(-0.874090\pi\)
0.127690 0.991814i \(-0.459244\pi\)
\(662\) 541387. 1.60073e7i 0.0480134 1.41962i
\(663\) 0 0
\(664\) 5.82636e6 8.07511e6i 0.512834 0.710769i
\(665\) 28446.9i 0.00249449i
\(666\) 0 0
\(667\) 1.29719e7i 1.12899i
\(668\) −7.98835e6 540970.i −0.692653 0.0469064i
\(669\) 0 0
\(670\) 1.59785e6 + 54041.4i 0.137515 + 0.00465093i
\(671\) −1.43710e6 2.48914e6i −0.123220 0.213424i
\(672\) 0 0
\(673\) 3.31863e6 5.74803e6i 0.282436 0.489194i −0.689548 0.724240i \(-0.742191\pi\)
0.971984 + 0.235046i \(0.0755241\pi\)
\(674\) −2.15954e6 + 3.46445e6i −0.183110 + 0.293754i
\(675\) 0 0
\(676\) 3.74350e6 + 7.63271e6i 0.315073 + 0.642409i
\(677\) 2.38918e6 + 1.37940e6i 0.200345 + 0.115669i 0.596816 0.802378i \(-0.296432\pi\)
−0.396472 + 0.918047i \(0.629765\pi\)
\(678\) 0 0
\(679\) 650351. 375480.i 0.0541344 0.0312545i
\(680\) 587511. + 1.30796e6i 0.0487241 + 0.108473i
\(681\) 0 0
\(682\) −3.19392e6 + 1.70274e6i −0.262944 + 0.140181i
\(683\) −462361. −0.0379253 −0.0189627 0.999820i \(-0.506036\pi\)
−0.0189627 + 0.999820i \(0.506036\pi\)
\(684\) 0 0
\(685\) 488594. 0.0397852
\(686\) −2.67861e6 + 1.42802e6i −0.217320 + 0.115857i
\(687\) 0 0
\(688\) −1.08314e6 + 7.96050e6i −0.0872392 + 0.641164i
\(689\) −1.54334e6 + 891048.i −0.123855 + 0.0715078i
\(690\) 0 0
\(691\) −4.14382e6 2.39243e6i −0.330146 0.190610i 0.325760 0.945452i \(-0.394380\pi\)
−0.655906 + 0.754843i \(0.727713\pi\)
\(692\) −8.86877e6 + 4.34973e6i −0.704041 + 0.345300i
\(693\) 0 0
\(694\) 4.49472e6 7.21067e6i 0.354245 0.568299i
\(695\) 458477. 794106.i 0.0360044 0.0623615i
\(696\) 0 0
\(697\) 1.42120e7 + 2.46160e7i 1.10809 + 1.91926i
\(698\) 5.73042e6 + 193810.i 0.445193 + 0.0150570i
\(699\) 0 0
\(700\) 108067. 1.59580e6i 0.00833585 0.123093i
\(701\) 1.31247e7i 1.00877i −0.863478 0.504387i \(-0.831719\pi\)
0.863478 0.504387i \(-0.168281\pi\)
\(702\) 0 0
\(703\) 4.37673e6i 0.334012i
\(704\) 1.88539e6 2.12189e6i 0.143373 0.161358i
\(705\) 0 0
\(706\) 393568. 1.16367e7i 0.0297172 0.878657i
\(707\) 611412. + 1.05900e6i 0.0460029 + 0.0796794i
\(708\) 0 0
\(709\) −3.98415e6 + 6.90074e6i −0.297659 + 0.515561i −0.975600 0.219555i \(-0.929539\pi\)
0.677941 + 0.735117i \(0.262873\pi\)
\(710\) −888980. 554140.i −0.0661830 0.0412547i
\(711\) 0 0
\(712\) 750912. 7.37822e6i 0.0555123 0.545446i
\(713\) −1.65472e7 9.55353e6i −1.21899 0.703785i
\(714\) 0 0
\(715\) −103618. + 59824.1i −0.00758004 + 0.00437634i
\(716\) 140132. 208741.i 0.0102154 0.0152169i
\(717\) 0 0
\(718\) 802586. + 1.50545e6i 0.0581006 + 0.108982i
\(719\) −5.58804e6 −0.403123 −0.201561 0.979476i \(-0.564602\pi\)
−0.201561 + 0.979476i \(0.564602\pi\)
\(720\) 0 0
\(721\) −60749.9 −0.00435219
\(722\) −6.12874e6 1.14960e7i −0.437550 0.820737i
\(723\) 0 0
\(724\) 8.02102e6 1.19482e7i 0.568700 0.847140i
\(725\) 1.34928e7 7.79008e6i 0.953362 0.550424i
\(726\) 0 0
\(727\) −2.72597e6 1.57384e6i −0.191287 0.110439i 0.401298 0.915948i \(-0.368559\pi\)
−0.592585 + 0.805508i \(0.701893\pi\)
\(728\) −95830.4 + 941598.i −0.00670154 + 0.0658472i
\(729\) 0 0
\(730\) 467244. + 291253.i 0.0324516 + 0.0202285i
\(731\) −7.31128e6 + 1.26635e7i −0.506057 + 0.876517i
\(732\) 0 0
\(733\) 1.20330e7 + 2.08418e7i 0.827209 + 1.43277i 0.900219 + 0.435438i \(0.143406\pi\)
−0.0730095 + 0.997331i \(0.523260\pi\)
\(734\) −426289. + 1.26042e7i −0.0292054 + 0.863524i
\(735\) 0 0
\(736\) 1.47708e7 + 2.52094e6i 1.00510 + 0.171541i
\(737\) 5.76065e6i 0.390663i
\(738\) 0 0
\(739\) 4.89450e6i 0.329683i −0.986320 0.164842i \(-0.947289\pi\)
0.986320 0.164842i \(-0.0527113\pi\)
\(740\) −96657.0 + 1.42731e6i −0.00648865 + 0.0958160i
\(741\) 0 0
\(742\) 498723. + 16867.4i 0.0332544 + 0.00112470i
\(743\) 2.80417e6 + 4.85696e6i 0.186351 + 0.322770i 0.944031 0.329857i \(-0.107000\pi\)
−0.757680 + 0.652626i \(0.773667\pi\)
\(744\) 0 0
\(745\) −471200. + 816142.i −0.0311039 + 0.0538735i
\(746\) 5.37766e6 8.62713e6i 0.353791 0.567570i
\(747\) 0 0
\(748\) 4.63855e6 2.27500e6i 0.303129 0.148671i
\(749\) −803285. 463777.i −0.0523197 0.0302068i
\(750\) 0 0
\(751\) 1.23051e7 7.10437e6i 0.796134 0.459648i −0.0459832 0.998942i \(-0.514642\pi\)
0.842118 + 0.539294i \(0.181309\pi\)
\(752\) −2.89067e7 3.93315e6i −1.86403 0.253627i
\(753\) 0 0
\(754\) −8.13550e6 + 4.33719e6i −0.521141 + 0.277830i
\(755\) 1.78826e6 0.114173
\(756\) 0 0
\(757\) −1.75241e7 −1.11147 −0.555733 0.831361i \(-0.687562\pi\)
−0.555733 + 0.831361i \(0.687562\pi\)
\(758\) 1.07178e7 5.71385e6i 0.677534 0.361206i
\(759\) 0 0
\(760\) 131155. + 291985.i 0.00823664 + 0.0183370i
\(761\) 9.78403e6 5.64882e6i 0.612430 0.353587i −0.161486 0.986875i \(-0.551629\pi\)
0.773916 + 0.633288i \(0.218295\pi\)
\(762\) 0 0
\(763\) −2.45631e6 1.41815e6i −0.152747 0.0881883i
\(764\) −7.19712e6 1.46744e7i −0.446093 0.909550i
\(765\) 0 0
\(766\) 7.79446e6 1.25043e7i 0.479970 0.769993i
\(767\) 617871. 1.07018e6i 0.0379236 0.0656855i
\(768\) 0 0
\(769\) −465579. 806407.i −0.0283908 0.0491743i 0.851481 0.524386i \(-0.175705\pi\)
−0.879872 + 0.475211i \(0.842372\pi\)
\(770\) 33483.7 + 1132.46i 0.00203520 + 6.88329e-5i
\(771\) 0 0
\(772\) −2.80951e7 1.90259e6i −1.69663 0.114896i
\(773\) 4.59758e6i 0.276745i 0.990380 + 0.138373i \(0.0441872\pi\)
−0.990380 + 0.138373i \(0.955813\pi\)
\(774\) 0 0