Properties

Label 108.6.h.a.35.1
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 35.1
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.65362 + 0.191212i) q^{2} +(31.9269 - 2.16208i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(-13.9322 - 8.04377i) q^{7} +(-180.089 + 18.3284i) q^{8} +O(q^{10})\) \(q+(-5.65362 + 0.191212i) q^{2} +(31.9269 - 2.16208i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(-13.9322 - 8.04377i) q^{7} +(-180.089 + 18.3284i) q^{8} +(20.4019 - 12.7174i) q^{10} +(-43.3121 + 75.0187i) q^{11} +(162.502 + 281.462i) q^{13} +(80.3056 + 42.8124i) q^{14} +(1014.65 - 138.057i) q^{16} -1863.80i q^{17} +416.071i q^{19} +(-112.913 + 75.8006i) q^{20} +(230.526 - 432.409i) q^{22} +(1293.41 + 2240.24i) q^{23} +(-1553.47 + 2690.69i) q^{25} +(-972.544 - 1560.21i) q^{26} +(-462.204 - 226.690i) q^{28} +(-4342.80 - 2507.32i) q^{29} +(-6396.76 + 3693.17i) q^{31} +(-5710.05 + 974.537i) q^{32} +(356.382 + 10537.2i) q^{34} +68.3704 q^{35} -10519.2 q^{37} +(-79.5579 - 2352.31i) q^{38} +(623.874 - 450.138i) q^{40} +(-13207.4 + 7625.29i) q^{41} +(6794.45 + 3922.78i) q^{43} +(-1220.62 + 2488.76i) q^{44} +(-7740.79 - 12418.2i) q^{46} +(-14244.6 + 24672.4i) q^{47} +(-8274.10 - 14331.2i) q^{49} +(8268.23 - 15509.2i) q^{50} +(5796.72 + 8634.85i) q^{52} +5483.31i q^{53} -368.144i q^{55} +(2656.47 + 1193.24i) q^{56} +(25032.0 + 13345.0i) q^{58} +(1901.12 + 3292.83i) q^{59} +(16590.1 - 28734.9i) q^{61} +(35458.7 - 22102.9i) q^{62} +(32096.1 - 6601.49i) q^{64} +(-1196.18 - 690.617i) q^{65} +(-57592.1 + 33250.8i) q^{67} +(-4029.69 - 59505.3i) q^{68} +(-386.540 + 13.0733i) q^{70} +43573.3 q^{71} +22901.9 q^{73} +(59471.5 - 2011.40i) q^{74} +(899.581 + 13283.8i) q^{76} +(1206.87 - 696.785i) q^{77} +(-31941.7 - 18441.5i) q^{79} +(-3441.08 + 2664.20i) q^{80} +(73211.6 - 45635.9i) q^{82} +(-27504.3 + 47638.8i) q^{83} +(3960.48 + 6859.75i) q^{85} +(-39163.3 - 20878.7i) q^{86} +(6425.06 - 14303.9i) q^{88} -40969.8i q^{89} -5228.51i q^{91} +(46138.0 + 68727.5i) q^{92} +(75816.1 - 142212. i) q^{94} +(-884.130 - 1531.36i) q^{95} +(23339.8 - 40425.7i) q^{97} +(49518.9 + 79440.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.65362 + 0.191212i −0.999429 + 0.0338019i
\(3\) 0 0
\(4\) 31.9269 2.16208i 0.997715 0.0675651i
\(5\) −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 0.445303 0.895380i \(-0.353096\pi\)
−0.552770 + 0.833334i \(0.686429\pi\)
\(8\) −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 −0.914930 0.403613i \(-0.867754\pi\)
0.807004 + 0.590546i \(0.201088\pi\)
\(12\) 0 0
\(13\) 162.502 + 281.462i 0.266686 + 0.461914i 0.968004 0.250935i \(-0.0807380\pi\)
−0.701318 + 0.712849i \(0.747405\pi\)
\(14\) 80.3056 + 42.8124i 0.109503 + 0.0583781i
\(15\) 0 0
\(16\) 1014.65 138.057i 0.990870 0.134821i
\(17\) 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 \(0.0422063\pi\)
−0.991222 + 0.132207i \(0.957794\pi\)
\(20\) −112.913 + 75.8006i −0.0631204 + 0.0423738i
\(21\) 0 0
\(22\) 230.526 432.409i 0.101546 0.190475i
\(23\) 1293.41 + 2240.24i 0.509818 + 0.883030i 0.999935 + 0.0113741i \(0.00362056\pi\)
−0.490117 + 0.871656i \(0.663046\pi\)
\(24\) 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 −0.959553 0.281530i \(-0.909158\pi\)
−0.235964 + 0.971762i \(0.575825\pi\)
\(32\) −5710.05 + 974.537i −0.985746 + 0.168238i
\(33\) 0 0
\(34\) 356.382 + 10537.2i 0.0528711 + 1.56325i
\(35\) 68.3704 0.00943405
\(36\) 0 0
\(37\) −10519.2 −1.26322 −0.631609 0.775287i \(-0.717605\pi\)
−0.631609 + 0.775287i \(0.717605\pi\)
\(38\) −79.5579 2352.31i −0.00893767 0.264262i
\(39\) 0 0
\(40\) 623.874 450.138i 0.0616520 0.0444832i
\(41\) −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 0.753298 0.657679i \(-0.228462\pi\)
−0.192917 + 0.981215i \(0.561795\pi\)
\(44\) −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 \(0.556406\pi\)
−0.764323 + 0.644833i \(0.776927\pi\)
\(48\) 0 0
\(49\) −8274.10 14331.2i −0.492301 0.852690i
\(50\) 8268.23 15509.2i 0.467722 0.877331i
\(51\) 0 0
\(52\) 5796.72 + 8634.85i 0.297286 + 0.442840i
\(53\) 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
\(56\) 2656.47 + 1193.24i 0.113197 + 0.0508461i
\(57\) 0 0
\(58\) 25032.0 + 13345.0i 0.977069 + 0.520894i
\(59\) 1901.12 + 3292.83i 0.0711015 + 0.123151i 0.899384 0.437159i \(-0.144015\pi\)
−0.828283 + 0.560310i \(0.810682\pi\)
\(60\) 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 \(0.693410\pi\)
−0.996473 + 0.0839192i \(0.973256\pi\)
\(68\) −4029.69 59505.3i −0.105682 1.56057i
\(69\) 0 0
\(70\) −386.540 + 13.0733i −0.00942866 + 0.000318889i
\(71\) 43573.3 1.02583 0.512914 0.858440i \(-0.328566\pi\)
0.512914 + 0.858440i \(0.328566\pi\)
\(72\) 0 0
\(73\) 22901.9 0.502996 0.251498 0.967858i \(-0.419077\pi\)
0.251498 + 0.967858i \(0.419077\pi\)
\(74\) 59471.5 2011.40i 1.26250 0.0426991i
\(75\) 0 0
\(76\) 899.581 + 13283.8i 0.0178651 + 0.263809i
\(77\) 1206.87 696.785i 0.0231970 0.0133928i
\(78\) 0 0
\(79\) −31941.7 18441.5i −0.575824 0.332452i 0.183648 0.982992i \(-0.441209\pi\)
−0.759472 + 0.650540i \(0.774543\pi\)
\(80\) −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 −0.997553 0.0699102i \(-0.977729\pi\)
0.559321 + 0.828951i \(0.311062\pi\)
\(84\) 0 0
\(85\) 3960.48 + 6859.75i 0.0594567 + 0.102982i
\(86\) −39163.3 20878.7i −0.570997 0.304409i
\(87\) 0 0
\(88\) 6425.06 14303.9i 0.0884444 0.196901i
\(89\) 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
\(92\) 46138.0 + 68727.5i 0.568315 + 0.846567i
\(93\) 0 0
\(94\) 75816.1 142212.i 0.884997 1.66004i
\(95\) −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 −0.484736 0.874660i \(-0.661084\pi\)
0.515110 + 0.857124i \(0.327751\pi\)
\(104\) −34423.6 47709.8i −0.312085 0.432538i
\(105\) 0 0
\(106\) −1048.48 31000.6i −0.00906346 0.267981i
\(107\) 57656.6 0.486844 0.243422 0.969920i \(-0.421730\pi\)
0.243422 + 0.969920i \(0.421730\pi\)
\(108\) 0 0
\(109\) −176304. −1.42133 −0.710667 0.703529i \(-0.751607\pi\)
−0.710667 + 0.703529i \(0.751607\pi\)
\(110\) 70.3936 + 2081.35i 0.000554692 + 0.0164007i
\(111\) 0 0
\(112\) −15246.8 6238.18i −0.114851 0.0469908i
\(113\) −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
\(122\) −88299.7 + 165629.i −0.537106 + 1.00748i
\(123\) 0 0
\(124\) −196244. + 131742.i −1.14615 + 0.769430i
\(125\) 26485.1i 0.151610i
\(126\) 0 0
\(127\) 43254.5i 0.237970i 0.992896 + 0.118985i \(0.0379640\pi\)
−0.992896 + 0.118985i \(0.962036\pi\)
\(128\) −180197. + 43459.5i −0.972127 + 0.234455i
\(129\) 0 0
\(130\) 6894.82 + 3675.76i 0.0357820 + 0.0190761i
\(131\) −104818. 181550.i −0.533650 0.924309i −0.999227 0.0393020i \(-0.987487\pi\)
0.465577 0.885007i \(1.65415\pi\)
\(132\) 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 −0.0302321 0.999543i \(-0.509625\pi\)
0.850514 + 0.525953i \(0.176291\pi\)
\(140\) 2182.85 147.823i 0.00941249 0.000637413i
\(141\) 0 0
\(142\) −246347. + 8331.75i −1.02524 + 0.0346749i
\(143\) −28153.2 −0.115130
\(144\) 0 0
\(145\) 21311.7 0.0841779
\(146\) −129479. + 4379.13i −0.502709 + 0.0170022i
\(147\) 0 0
\(148\) −335845. + 22743.4i −1.26033 + 0.0853495i
\(149\) 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 0.980506 0.196490i \(-0.0629543\pi\)
0.320088 + 0.947388i \(0.396288\pi\)
\(152\) −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 \(0.716678\pi\)
\(158\) 184112. + 98153.8i 0.586733 + 0.312798i
\(159\) 0 0
\(160\) 18945.1 15720.4i 0.0585056 0.0485471i
\(161\) 41615.4i 0.126529i
\(162\) 0 0
\(163\) 324082.i 0.955402i −0.878522 0.477701i \(-0.841470\pi\)
0.878522 0.477701i \(-0.158530\pi\)
\(164\) −405184. + 272007.i −1.17637 + 0.789716i
\(165\) 0 0
\(166\) 146390. 274591.i 0.412325 0.773421i
\(167\) −125104. 216686.i −0.347120 0.601229i 0.638617 0.769525i \(-0.279507\pi\)
−0.985737 + 0.168296i \(0.946174\pi\)
\(168\) 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
\(176\) −33589.8 + 82097.4i −0.0817382 + 0.199778i
\(177\) 0 0
\(178\) 7833.94 + 231628.i 0.0185323 + 0.547950i
\(179\) 7856.73 0.0183278 0.00916388 0.999958i \(-0.497083\pi\)
0.00916388 + 0.999958i \(0.497083\pi\)
\(180\) 0 0
\(181\) −449713. −1.02033 −0.510163 0.860078i \(-0.670415\pi\)
−0.510163 + 0.860078i \(0.670415\pi\)
\(182\) 999.756 + 29560.0i 0.00223726 + 0.0661495i
\(183\) 0 0
\(184\) −273988. 379737.i −0.596606 0.826873i
\(185\) 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 \(-0.664262\pi\)
0.999971 0.00755354i \(-0.00240439\pi\)
\(192\) 0 0
\(193\) 439991. + 762087.i 0.850257 + 1.47269i 0.880976 + 0.473161i \(0.156887\pi\)
−0.0307186 + 0.999528i \(0.509780\pi\)
\(194\) −124225. + 233015.i −0.236975 + 0.444507i
\(195\) 0 0
\(196\) −295151. 439660.i −0.548788 0.817479i
\(197\) 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 \(-0.751433\pi\)
0.710283 0.703916i \(-0.248567\pi\)
\(200\) 230447. 513036.i 0.407376 0.906928i
\(201\) 0 0
\(202\) −379429. 202281.i −0.654262 0.348800i
\(203\) 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 −0.989692 0.143212i \(-0.954257\pi\)
−0.370821 + 0.928704i \(0.620924\pi\)
\(212\) 11855.4 + 175065.i 0.0181166 + 0.267522i
\(213\) 0 0
\(214\) −325969. + 11024.7i −0.486566 + 0.0164562i
\(215\) −33342.8 −0.0491933
\(216\) 0 0
\(217\) 118828. 0.171305
\(218\) 996757. 33711.5i 1.42052 0.0480438i
\(219\) 0 0
\(220\) −795.958 11753.7i −0.00110875 0.0163726i
\(221\) 524588. 302871.i 0.722500 0.417136i
\(222\) 0 0
\(223\) 201948. + 116595.i 0.271942 + 0.157006i 0.629770 0.776782i \(-0.283149\pi\)
−0.357828 + 0.933788i \(0.616482\pi\)
\(224\) 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 \(-0.641788\pi\)
0.996947 0.0780796i \(-0.0248788\pi\)
\(228\) 0 0
\(229\) −191288. 331320.i −0.241045 0.417503i 0.719967 0.694008i \(-0.244157\pi\)
−0.961012 + 0.276506i \(0.910824\pi\)
\(230\) 54878.1 + 29256.6i 0.0684037 + 0.0364673i
\(231\) 0 0
\(232\) 828046. + 371944.i 1.01003 + 0.453688i
\(233\) 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
\(236\) 67816.1 + 101019.i 0.0792598 + 0.118066i
\(237\) 0 0
\(238\) 79793.8 149674.i 0.0913118 0.171278i
\(239\) 769108. + 1.33213e6i 0.870949 + 1.50853i 0.861017 + 0.508577i \(0.169828\pi\)
0.00993200 + 0.999951i \(0.496838\pi\)
\(240\) 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
\(248\) 1.08430e6 782342.i 1.11949 0.807732i
\(249\) 0 0
\(250\) 5064.28 + 149737.i 0.00512469 + 0.151523i
\(251\) −1.31402e6 −1.31649 −0.658246 0.752803i \(-0.728701\pi\)
−0.658246 + 0.752803i \(0.728701\pi\)
\(252\) 0 0
\(253\) −224080. −0.220091
\(254\) −8270.79 244544.i −0.00804382 0.237834i
\(255\) 0 0
\(256\) 1.01046e6 280160.i 0.963646 0.267181i
\(257\) −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 \(0.399825\pi\)
−0.978262 + 0.207374i \(0.933508\pi\)
\(264\) 0 0
\(265\) −11651.8 20181.4i −0.0101924 0.0176538i
\(266\) −17813.0 + 33412.8i −0.0154359 + 0.0289540i
\(267\) 0 0
\(268\) −1.76684e6 + 1.18611e6i −1.50266 + 1.00876i
\(269\) 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 \(0.0867561\pi\)
−0.963087 + 0.269190i \(0.913244\pi\)
\(272\) −257311. 1.89111e6i −0.210880 1.54986i
\(273\) 0 0
\(274\) 573886. + 305949.i 0.461795 + 0.246191i
\(275\) −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 −0.839023 0.544096i \(-0.816873\pi\)
0.0516895 + 0.998663i \(0.483539\pi\)
\(284\) 1.39116e6 94209.1i 1.02348 0.0693102i
\(285\) 0 0
\(286\) 159168. 5383.24i 0.115064 0.00389160i
\(287\) 245345. 0.175821
\(288\) 0 0
\(289\) −2.05390e6 −1.44655
\(290\) −120488. + 4075.06i −0.0841298 + 0.00284537i
\(291\) 0 0
\(292\) 731186. 49515.9i 0.501847 0.0339850i
\(293\) −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
\(302\) −2.10044e6 1.11978e6i −1.32523 0.706506i
\(303\) 0 0
\(304\) 57441.6 + 422167.i 0.0356486 + 0.261999i
\(305\) 141013.i 0.0867977i
\(306\) 0 0
\(307\) 1.54327e6i 0.934537i 0.884115 + 0.467269i \(0.154762\pi\)
−0.884115 + 0.467269i \(0.845238\pi\)
\(308\) 37025.0 24855.5i 0.0222391 0.0149295i
\(309\) 0 0
\(310\) −83538.7 + 156698.i −0.0493723 + 0.0926104i
\(311\) 1.17389e6 + 2.03323e6i 0.688218 + 1.19203i 0.972414 + 0.233262i \(0.0749399\pi\)
−0.284196 + 0.958766i \(0.591727\pi\)
\(312\) 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
\(320\) −104103. + 92499.6i −0.0568312 + 0.0504969i
\(321\) 0 0
\(322\) 7957.38 + 235278.i 0.00427691 + 0.126457i
\(323\) 775473. 0.413581
\(324\) 0 0
\(325\) −1.00977e6 −0.530289
\(326\) 61968.5 + 1.83224e6i 0.0322944 + 0.954856i
\(327\) 0 0
\(328\) 2.23875e6 1.61530e6i 1.14900 0.829028i
\(329\) 396919. 229161.i 0.202168 0.116722i
\(330\) 0 0
\(331\) −2.45201e6 1.41567e6i −1.23013 0.710218i −0.263076 0.964775i \(-0.584737\pi\)
−0.967058 + 0.254557i \(0.918070\pi\)
\(332\) −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 \(0.888704\pi\)
\(338\) −706993. + 1.32615e6i −0.336607 + 0.631392i
\(339\) 0 0
\(340\) 141277. + 210448.i 0.0662788 + 0.0987295i
\(341\) 639836.i 0.297977i
\(342\) 0 0
\(343\) 536603.i 0.246274i
\(344\) −1.29550e6 581918.i −0.590259 0.265134i
\(345\) 0 0
\(346\) −1.54090e6 821486.i −0.691967 0.368901i
\(347\) −751022. 1.30081e6i −0.334833 0.579948i 0.648619 0.761113i \(-0.275347\pi\)
−0.983453 + 0.181165i \(0.942013\pi\)
\(348\) 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
\(356\) −88580.2 1.30804e6i −0.0370435 0.547010i
\(357\) 0 0
\(358\) −44419.0 + 1502.30i −0.0183173 + 0.000619513i
\(359\) 301586. 0.123502 0.0617512 0.998092i \(-0.480331\pi\)
0.0617512 + 0.998092i \(0.480331\pi\)
\(360\) 0 0
\(361\) 2.30298e6 0.930086
\(362\) 2.54251e6 85990.7i 1.01974 0.0344889i
\(363\) 0 0
\(364\) −11304.5 166930.i −0.00447196 0.0660361i
\(365\) −84290.9 + 48665.4i −0.0331168 + 0.0191200i
\(366\) 0 0
\(367\) 1.93072e6 + 1.11470e6i 0.748261 + 0.432009i 0.825065 0.565037i \(-0.191138\pi\)
−0.0768040 + 0.997046i \(0.524472\pi\)
\(368\) 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 \(0.724798\pi\)
\(374\) −805925. 429654.i −0.297931 0.158833i
\(375\) 0 0
\(376\) 2.11310e6 4.70432e6i 0.770814 1.71604i
\(377\) 1.62978e6i 0.590574i
\(378\) 0 0
\(379\) 2.14708e6i 0.767804i −0.923374 0.383902i \(-0.874580\pi\)
0.923374 0.383902i \(-0.125420\pi\)
\(380\) −31538.4 46979.9i −0.0112042 0.0166899i
\(381\) 0 0
\(382\) −1.35924e6 + 2.54960e6i −0.476582 + 0.893951i
\(383\) −1.30237e6 2.25578e6i −0.453669 0.785777i 0.544942 0.838474i \(-0.316552\pi\)
−0.998611 + 0.0526965i \(0.983218\pi\)
\(384\) 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
\(392\) 1.75274e6 + 2.42923e6i 0.576106 + 0.798462i
\(393\) 0 0
\(394\) −31129.2 920406.i −0.0101025 0.298703i
\(395\) 156749. 0.0505490
\(396\) 0 0
\(397\) 5.78885e6 1.84338 0.921692 0.387922i \(-0.126807\pi\)
0.921692 + 0.387922i \(0.126807\pi\)
\(398\) 150383. + 4.44642e6i 0.0475874 + 1.40703i
\(399\) 0 0
\(400\) −1.20476e6 + 2.94458e6i −0.376487 + 0.920180i
\(401\) 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 \(0.945810\pi\)
\(410\) −172483. + 323535.i −0.0506741 + 0.0950520i
\(411\) 0 0
\(412\) 100328. 67351.9i 0.0291192 0.0195482i
\(413\) 61168.6i 0.0176463i
\(414\) 0 0
\(415\) 233781.i 0.0666328i
\(416\) −1.20219e6 1.44880e6i −0.340596 0.410463i
\(417\) 0 0
\(418\) 179913. + 95915.0i 0.0503642 + 0.0268501i
\(419\) −2.33383e6 4.04232e6i −0.649434 1.12485i −0.983258 0.182217i \(-0.941673\pi\)
0.333824 0.942635i \(1.60834\pi\)
\(420\) 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
\(428\) 1.84080e6 124658.i 0.485731 0.0328937i
\(429\) 0 0
\(430\) 188508. 6375.56i 0.0491652 0.00166283i
\(431\) 4.54361e6 1.17817 0.589085 0.808071i \(-0.299488\pi\)
0.589085 + 0.808071i \(0.299488\pi\)
\(432\) 0 0
\(433\) −6726.40 −0.00172410 −0.000862051 1.00000i \(-0.500274\pi\)
−0.000862051 1.00000i \(0.500274\pi\)
\(434\) −671809. + 22721.4i −0.171207 + 0.00579043i
\(435\) 0 0
\(436\) −5.62884e6 + 381184.i −1.41809 + 0.0960326i
\(437\) −932101. + 538148.i −0.233485 + 0.134803i
\(438\) 0 0
\(439\) 4.27223e6 + 2.46657e6i 1.05802 + 0.610847i 0.924883 0.380251i \(-0.124162\pi\)
0.133134 + 0.991098i \(0.457496\pi\)
\(440\) 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 \(-0.623741\pi\)
0.990921 0.134448i \(-0.0429260\pi\)
\(444\) 0 0
\(445\) 87058.8 + 150790.i 0.0208407 + 0.0360972i
\(446\) −1.16403e6 620567.i −0.277094 0.147724i
\(447\) 0 0
\(448\) −500271. 166201.i −0.117763 0.0391235i
\(449\) 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
\(452\) −3.43154e6 + 2.30365e6i −0.790028 + 0.530360i
\(453\) 0 0
\(454\) −2.33917e6 + 4.38771e6i −0.532626 + 0.999076i
\(455\) 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 −0.0733224 0.997308i \(-0.523360\pi\)
0.827033 + 0.562153i \(0.190027\pi\)
\(464\) −4.75258e6 1.94450e6i −1.02479 0.419288i
\(465\) 0 0
\(466\) −42899.8 1.26843e6i −0.00915146 0.270583i
\(467\) −5.43636e6 −1.15350 −0.576748 0.816922i \(-0.695679\pi\)
−0.576748 + 0.816922i \(0.695679\pi\)
\(468\) 0 0
\(469\) 1.06985e6 0.224590
\(470\) 23151.3 + 684521.i 0.00483427 + 0.142936i
\(471\) 0 0
\(472\) −402723. 558159.i −0.0832054 0.115319i
\(473\) −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 \(0.541687\pi\)
−0.793315 + 0.608812i \(0.791646\pi\)
\(480\) 0 0
\(481\) −1.70939e6 2.96075e6i −0.336882 0.583497i
\(482\) −3.68793e6 + 6.91765e6i −0.723045 + 1.35625i
\(483\) 0 0
\(484\) 2.73865e6 + 4.07951e6i 0.531401 + 0.791580i
\(485\) 198384.i 0.0382958i
\(486\) 0 0
\(487\) 2.35999e6i 0.450908i −0.974254 0.225454i \(-0.927614\pi\)
0.974254 0.225454i \(-0.0723865\pi\)
\(488\) −2.46103e6 + 5.47891e6i −0.467808 + 1.04147i
\(489\) 0 0
\(490\) −351063. 187158.i −0.0660533 0.0352143i
\(491\) −4.26271e6 7.38323e6i −0.797961 1.38211i −0.920942 0.389701i \(-0.872579\pi\)
0.122980 0.992409i \(1.53925\pi\)
\(492\) 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 −0.480208 0.877155i \(-0.659439\pi\)
0.519535 + 0.854449i \(0.326105\pi\)
\(500\) −57263.0 845587.i −0.0102435 0.151263i
\(501\) 0 0
\(502\) 7.42898e6 251257.i 1.31574 0.0444999i
\(503\) 6.25307e6 1.10198 0.550989 0.834512i \(-0.314251\pi\)
0.550989 + 0.834512i \(0.314251\pi\)
\(504\) 0 0
\(505\) −323037. −0.0563669
\(506\) 1.26687e6 42846.9i 0.219965 0.00743949i
\(507\) 0 0
\(508\) 93519.8 + 1.38098e6i 0.0160785 + 0.237426i
\(509\) −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
\(518\) −844750. 450352.i −0.138326 0.0737442i
\(519\) 0 0
\(520\) 228077. + 102448.i 0.0369891 + 0.0166149i
\(521\) 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 \(0.346566\pi\)
−0.463576 + 0.886057i \(0.653434\pi\)
\(524\) −3.73903e6 5.56969e6i −0.594882 0.886141i
\(525\) 0 0
\(526\) 3.99250e6 7.48895e6i 0.629188 1.18020i
\(527\) 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
\(536\) 9.76227e6 7.04368e6i 1.46770 1.05898i
\(537\) 0 0
\(538\) −50601.9 1.49616e6i −0.00753722 0.222855i
\(539\) 1.43347e6 0.212529
\(540\) 0 0
\(541\) 2.27509e6 0.334200 0.167100 0.985940i \(-0.446560\pi\)
0.167100 + 0.985940i \(0.446560\pi\)
\(542\) −124460. 3.67993e6i −0.0181983 0.538073i
\(543\) 0 0
\(544\) 1.81634e6 + 1.06424e7i 0.263148 + 1.54185i
\(545\) 648891. 374637.i 0.0935794 0.0540281i
\(546\) 0 0
\(547\) −7.20659e6 4.16072e6i −1.02982 0.594567i −0.112887 0.993608i \(-0.536010\pi\)
−0.916933 + 0.399041i \(0.869343\pi\)
\(548\) −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
\(554\) −1.26336e6 + 2.36976e6i −0.174885 + 0.328042i
\(555\) 0 0
\(556\) 5.73239e6 3.84825e6i 0.786409 0.527930i
\(557\) 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
\(560\) 69372.1 9439.03i 0.00934791 0.00127191i
\(561\) 0 0
\(562\) 8.15962e6 + 4.35005e6i 1.08976 + 0.580969i
\(563\) 1.07987e6 + 1.87039e6i 0.143582 + 0.248691i 0.928843 0.370474i \(-0.120805\pi\)
−0.785261 + 0.619165i \(0.787471\pi\)
\(564\) 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 −0.975126 0.221651i \(-0.928855\pi\)
−0.295607 + 0.955310i \(0.595522\pi\)
\(572\) −898844. + 60869.6i −0.114867 + 0.00777876i
\(573\) 0 0
\(574\) −1.38709e6 + 46912.9i −0.175721 + 0.00594309i
\(575\) −8.03706e6 −1.01374
\(576\) 0 0
\(577\) 669533. 0.0837206 0.0418603 0.999123i \(-0.486672\pi\)
0.0418603 + 0.999123i \(0.486672\pi\)
\(578\) 1.16119e7 392730.i 1.44572 0.0488961i
\(579\) 0 0
\(580\) 680416. 46077.7i 0.0839855 0.00568749i
\(581\) 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 −0.853974 0.520315i \(-0.825815\pi\)
0.877593 + 0.479406i \(0.159148\pi\)
\(588\) 0 0
\(589\) −1.53662e6 2.66151e6i −0.182507 0.316111i
\(590\) 80662.8 + 43002.9i 0.00953989 + 0.00508590i
\(591\) 0 0
\(592\) −1.06733e7 + 1.45225e6i −1.25168 + 0.170309i
\(593\) 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
\(596\) 5.89145e6 3.95504e6i 0.679371 0.456073i
\(597\) 0 0
\(598\) 2.23735e6 4.19671e6i 0.255847 0.479906i
\(599\) 5.30363e6 + 9.18615e6i 0.603957 + 1.04608i 0.992215 + 0.124533i \(0.0397434\pi\)
−0.388259 + 0.921550i \(0.626923\pi\)
\(600\) 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 \(-0.330184\pi\)
0.999951 0.00989422i \(-0.00314948\pi\)
\(608\) −405477. 2.37579e6i −0.0444843 0.260645i
\(609\) 0 0
\(610\) −26963.3 797231.i −0.00293392 0.0867481i
\(611\) −9.25912e6 −1.00338
\(612\) 0 0
\(613\) 133521. 0.0143515 0.00717575 0.999974i \(-0.497716\pi\)
0.00717575 + 0.999974i \(0.497716\pi\)
\(614\) −295093. 8.72508e6i −0.0315891 0.934003i
\(615\) 0 0
\(616\) −204573. + 147603.i −0.0217218 + 0.0156727i
\(617\) −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 −0.0214502 0.999770i \(-0.506828\pi\)
−0.876551 + 0.481309i \(0.840162\pi\)
\(620\) 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
\(626\) 3.75234e6 7.03847e6i 0.382707 0.717864i
\(627\) 0 0
\(628\) 3.94786e6 + 5.88077e6i 0.399450 + 0.595025i
\(629\) 1.96057e7i 1.97586i
\(630\) 0 0
\(631\) 1.28910e7i 1.28888i 0.764653 + 0.644442i \(0.222910\pi\)
−0.764653 + 0.644442i \(0.777090\pi\)
\(632\) 6.09035e6 + 2.73568e6i 0.606526 + 0.272441i
\(633\) 0 0
\(634\) 9.93487e6 + 5.29647e6i 0.981610 + 0.523315i
\(635\) −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 −0.869501 0.493932i \(-0.835559\pi\)
−0.00699288 + 0.999976i \(0.502226\pi\)
\(644\) −89976.1 1.32865e6i −0.00854894 0.126240i
\(645\) 0 0
\(646\) −4.38423e6 + 148280.i −0.413345 + 0.0139798i
\(647\) 2.37142e6 0.222714 0.111357 0.993780i \(-0.464480\pi\)
0.111357 + 0.993780i \(0.464480\pi\)
\(648\) 0 0
\(649\) −329365. −0.0306949
\(650\) 5.70884e6 193080.i 0.529986 0.0179248i
\(651\) 0 0
\(652\) −700693. 1.03469e7i −0.0645519 0.953219i
\(653\) 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 −0.819176 0.573542i \(-0.805569\pi\)
0.906290 + 0.422656i \(0.138902\pi\)
\(660\) 0 0
\(661\) −8.93142e6 1.54697e7i −0.795091 1.37714i −0.922781 0.385324i \(-0.874090\pi\)
0.127690 0.991814i \(-0.459244\pi\)
\(662\) 1.41334e7 + 7.53480e6i 1.25344 + 0.668232i
\(663\) 0 0
\(664\) 4.08007e6 9.08333e6i 0.359127 0.799512i
\(665\) 28446.9i 0.00249449i
\(666\) 0 0
\(667\) 1.29719e7i 1.12899i
\(668\) −4.46267e6 6.64763e6i −0.386949 0.576402i
\(669\) 0 0
\(670\) −752126. + 1.41080e6i −0.0647297 + 0.121417i
\(671\) 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
\(680\) −838968. 1.16278e6i −0.0695782 0.0964327i
\(681\) 0 0
\(682\) 122344. + 3.61739e6i 0.0100722 + 0.297807i
\(683\) 462361. 0.0379253 0.0189627 0.999820i \(-0.493964\pi\)
0.0189627 + 0.999820i \(0.493964\pi\)
\(684\) 0 0
\(685\) 488594. 0.0397852
\(686\) −102605. 3.03375e6i −0.00832451 0.246133i
\(687\) 0 0
\(688\) 7.43556e6 + 3.04223e6i 0.598884 + 0.245031i
\(689\) −1.54334e6 + 891048.i −0.123855 + 0.0715078i
\(690\) 0 0
\(691\) 4.14382e6 + 2.39243e6i 0.330146 + 0.190610i 0.655906 0.754843i \(-0.272287\pi\)
−0.325760 + 0.945452i \(0.605620\pi\)
\(692\) 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
\(698\) 2.69737e6 5.05960e6i 0.209557 0.393077i
\(699\) 0 0
\(700\) 1.32797e6 891490.i 0.102434 0.0687656i
\(701\) 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
\(704\) −894915. + 2.69374e6i −0.0680534 + 0.204844i
\(705\) 0 0
\(706\) −1.02745e7 5.47752e6i −0.775797 0.413592i
\(707\) −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
\(716\) 250841. 16986.9i 0.0182859 0.00123832i
\(717\) 0 0
\(718\) −1.70505e6 + 57667.0i −0.123432 + 0.00417461i
\(719\) 5.58804e6 0.403123 0.201561 0.979476i \(-0.435398\pi\)
0.201561 + 0.979476i \(0.435398\pi\)
\(720\) 0 0
\(721\) −60749.9 −0.00435219
\(722\) −1.30202e7 + 440359.i −0.929554 + 0.0314386i
\(723\) 0 0
\(724\) −1.43579e7 + 972317.i −1.01799 + 0.0689385i
\(725\) 1.34928e7 7.79008e6i 0.953362 0.550424i
\(726\) 0 0
\(727\) 2.72597e6 + 1.57384e6i 0.191287 + 0.110439i 0.592585 0.805508i \(-0.298107\pi\)
−0.401298 + 0.915948i \(0.631441\pi\)
\(728\) 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 \(0.523260\pi\)
\(734\) −1.11287e7 5.93291e6i −0.762436 0.406469i
\(735\) 0 0
\(736\) −9.56861e6 1.15314e7i −0.651110 0.784674i
\(737\) 5.76065e6i 0.390663i
\(738\) 0 0
\(739\) 4.89450e6i 0.329683i 0.986320 + 0.164842i \(0.0527113\pi\)
−0.986320 + 0.164842i \(0.947289\pi\)
\(740\) 1.18776e6 797361.i 0.0797348 0.0535273i
\(741\) 0 0
\(742\) −234754. + 440340.i −0.0156532 + 0.0293615i
\(743\) −2.80417e6 4.85696e6i −0.186351 0.322770i 0.757680 0.652626i \(-0.226333\pi\)
−0.944031 + 0.329857i \(0.893000\pi\)
\(744\) 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 −0.842118 0.539294i \(-0.818691\pi\)
0.0459832 + 0.998942i \(0.485358\pi\)
\(752\) −1.10471e7 + 2.70005e7i −0.712368 + 1.74111i
\(753\) 0 0
\(754\) 311633. + 9.21414e6i 0.0199625 + 0.590237i
\(755\) −1.78826e6 −0.114173
\(756\) 0 0
\(757\) −1.75241e7 −1.11147 −0.555733 0.831361i \(-0.687562\pi\)
−0.555733 + 0.831361i \(0.687562\pi\)
\(758\) 410548. + 1.21388e7i 0.0259532 + 0.767365i
\(759\) 0 0
\(760\) 187289. + 259576.i 0.0117619 + 0.0163016i
\(761\) 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 \(0.842372\pi\)
\(770\) 15761.1 29564.0i 0.000957989 0.00179695i
\(771\) 0 0
\(772\) 1.56952e7 + 2.33797e7i 0.947817 + 1.41188i
\(773\) 4.59758e6i 0.276745i 0.990380 + 0.138373i \(0.0441872\pi\)
−0.990380 + 0.138373i \(0.955813\pi\)
\(774\) 0 0