Properties

Label 108.6.h.a.35.4
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 35.4
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.12358 - 2.39768i) q^{2} +(20.5022 + 24.5695i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(-181.157 - 104.591i) q^{7} +(-46.1351 - 175.042i) q^{8} +O(q^{10})\) \(q+(-5.12358 - 2.39768i) q^{2} +(20.5022 + 24.5695i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(-181.157 - 104.591i) q^{7} +(-46.1351 - 175.042i) q^{8} +(397.087 - 34.1946i) q^{10} +(75.3585 - 130.525i) q^{11} +(-210.949 - 365.375i) q^{13} +(677.397 + 970.239i) q^{14} +(-183.317 + 1007.46i) q^{16} +662.619i q^{17} +624.161i q^{19} +(-2116.49 - 776.889i) q^{20} +(-699.063 + 488.069i) q^{22} +(1186.88 + 2055.74i) q^{23} +(919.485 - 1592.59i) q^{25} +(204.763 + 2377.82i) q^{26} +(-1144.38 - 6595.28i) q^{28} +(3944.46 + 2277.34i) q^{29} +(8615.25 - 4974.02i) q^{31} +(3354.81 - 4722.26i) q^{32} +(1588.75 - 3394.98i) q^{34} +14738.0 q^{35} -5944.72 q^{37} +(1496.54 - 3197.94i) q^{38} +(8981.30 + 9055.14i) q^{40} +(-10531.7 + 6080.46i) q^{41} +(15161.2 + 8753.33i) q^{43} +(4751.94 - 824.530i) q^{44} +(-1152.08 - 13378.5i) q^{46} +(9291.01 - 16092.5i) q^{47} +(13475.1 + 23339.5i) q^{49} +(-8529.60 + 5955.16i) q^{50} +(4652.14 - 12673.9i) q^{52} -32790.2i q^{53} +10618.8i q^{55} +(-9950.10 + 36535.3i) q^{56} +(-14749.5 - 21125.7i) q^{58} +(1808.33 + 3132.12i) q^{59} +(7916.16 - 13711.2i) q^{61} +(-56067.1 + 4828.15i) q^{62} +(-28511.1 + 16151.1i) q^{64} +(25742.7 + 14862.5i) q^{65} +(-41652.4 + 24048.0i) q^{67} +(-16280.2 + 13585.2i) q^{68} +(-75511.5 - 35337.1i) q^{70} +32192.2 q^{71} -34777.5 q^{73} +(30458.3 + 14253.6i) q^{74} +(-15335.3 + 12796.7i) q^{76} +(-27303.5 + 15763.7i) q^{77} +(73506.0 + 42438.7i) q^{79} +(-24305.1 - 67929.1i) q^{80} +(68538.9 - 5902.15i) q^{82} +(-7548.53 + 13074.4i) q^{83} +(-23342.6 - 40430.5i) q^{85} +(-56692.0 - 81200.2i) q^{86} +(-26323.9 - 7169.11i) q^{88} +40174.5i q^{89} +88253.7i q^{91} +(-26174.7 + 71308.4i) q^{92} +(-86188.0 + 60174.4i) q^{94} +(-21987.8 - 38083.9i) q^{95} +(4298.65 - 7445.49i) q^{97} +(-13079.9 - 151891. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.12358 2.39768i −0.905730 0.423855i
\(3\) 0 0
\(4\) 20.5022 + 24.5695i 0.640695 + 0.767796i
\(5\) −61.0162 + 35.2277i −1.09149 + 0.630173i −0.933973 0.357343i \(-0.883683\pi\)
−0.157518 + 0.987516i \(0.550349\pi\)
\(6\) 0 0
\(7\) −181.157 104.591i −1.39737 0.806770i −0.403250 0.915090i \(-0.632120\pi\)
−0.994116 + 0.108320i \(0.965453\pi\)
\(8\) −46.1351 175.042i −0.254863 0.966977i
\(9\) 0 0
\(10\) 397.087 34.1946i 1.25570 0.108133i
\(11\) 75.3585 130.525i 0.187781 0.325246i −0.756729 0.653728i \(-0.773204\pi\)
0.944510 + 0.328483i \(0.106537\pi\)
\(12\) 0 0
\(13\) −210.949 365.375i −0.346194 0.599626i 0.639376 0.768895i \(-0.279193\pi\)
−0.985570 + 0.169268i \(0.945860\pi\)
\(14\) 677.397 + 970.239i 0.923684 + 1.32300i
\(15\) 0 0
\(16\) −183.317 + 1007.46i −0.179021 + 0.983845i
\(17\) 662.619i 0.556086i 0.960569 + 0.278043i \(0.0896857\pi\)
−0.960569 + 0.278043i \(0.910314\pi\)
\(18\) 0 0
\(19\) 624.161i 0.396655i 0.980136 + 0.198327i \(0.0635509\pi\)
−0.980136 + 0.198327i \(0.936449\pi\)
\(20\) −2116.49 776.889i −1.18316 0.434294i
\(21\) 0 0
\(22\) −699.063 + 488.069i −0.307935 + 0.214993i
\(23\) 1186.88 + 2055.74i 0.467830 + 0.810306i 0.999324 0.0367563i \(-0.0117025\pi\)
−0.531494 + 0.847062i \(0.678369\pi\)
\(24\) 0 0
\(25\) 919.485 1592.59i 0.294235 0.509630i
\(26\) 204.763 + 2377.82i 0.0594044 + 0.689836i
\(27\) 0 0
\(28\) −1144.38 6595.28i −0.275850 1.58978i
\(29\) 3944.46 + 2277.34i 0.870950 + 0.502843i 0.867664 0.497152i \(-0.165621\pi\)
0.00328601 + 0.999995i \(0.498954\pi\)
\(30\) 0 0
\(31\) 8615.25 4974.02i 1.61014 0.929615i 0.620804 0.783966i \(-0.286806\pi\)
0.989336 0.145649i \(-0.0465270\pi\)
\(32\) 3354.81 4722.26i 0.579152 0.815220i
\(33\) 0 0
\(34\) 1588.75 3394.98i 0.235699 0.503663i
\(35\) 14738.0 2.03362
\(36\) 0 0
\(37\) −5944.72 −0.713883 −0.356941 0.934127i \(-0.616180\pi\)
−0.356941 + 0.934127i \(0.616180\pi\)
\(38\) 1496.54 3197.94i 0.168124 0.359262i
\(39\) 0 0
\(40\) 8981.30 + 9055.14i 0.887543 + 0.894840i
\(41\) −10531.7 + 6080.46i −0.978447 + 0.564907i −0.901801 0.432151i \(-0.857755\pi\)
−0.0766464 + 0.997058i \(0.524421\pi\)
\(42\) 0 0
\(43\) 15161.2 + 8753.33i 1.25044 + 0.721941i 0.971197 0.238279i \(-0.0765833\pi\)
0.279243 + 0.960221i \(0.409917\pi\)
\(44\) 4751.94 824.530i 0.370032 0.0642059i
\(45\) 0 0
\(46\) −1152.08 13378.5i −0.0802762 0.932210i
\(47\) 9291.01 16092.5i 0.613505 1.06262i −0.377139 0.926156i \(-0.623092\pi\)
0.990645 0.136466i \(-0.0435744\pi\)
\(48\) 0 0
\(49\) 13475.1 + 23339.5i 0.801755 + 1.38868i
\(50\) −8529.60 + 5955.16i −0.482507 + 0.336875i
\(51\) 0 0
\(52\) 4652.14 12673.9i 0.238586 0.649984i
\(53\) 32790.2i 1.60345i −0.597696 0.801723i \(-0.703917\pi\)
0.597696 0.801723i \(-0.296083\pi\)
\(54\) 0 0
\(55\) 10618.8i 0.473337i
\(56\) −9950.10 + 36535.3i −0.423992 + 1.55684i
\(57\) 0 0
\(58\) −14749.5 21125.7i −0.575713 0.824596i
\(59\) 1808.33 + 3132.12i 0.0676312 + 0.117141i 0.897858 0.440285i \(-0.145123\pi\)
−0.830227 + 0.557426i \(0.811789\pi\)
\(60\) 0 0
\(61\) 7916.16 13711.2i 0.272389 0.471792i −0.697084 0.716990i \(-0.745520\pi\)
0.969473 + 0.245198i \(0.0788528\pi\)
\(62\) −56067.1 + 4828.15i −1.85237 + 0.159515i
\(63\) 0 0
\(64\) −28511.1 + 16151.1i −0.870090 + 0.492893i
\(65\) 25742.7 + 14862.5i 0.755736 + 0.436324i
\(66\) 0 0
\(67\) −41652.4 + 24048.0i −1.13358 + 0.654474i −0.944833 0.327552i \(-0.893776\pi\)
−0.188749 + 0.982025i \(0.560443\pi\)
\(68\) −16280.2 + 13585.2i −0.426960 + 0.356281i
\(69\) 0 0
\(70\) −75511.5 35337.1i −1.84191 0.861958i
\(71\) 32192.2 0.757887 0.378944 0.925420i \(-0.376287\pi\)
0.378944 + 0.925420i \(0.376287\pi\)
\(72\) 0 0
\(73\) −34777.5 −0.763820 −0.381910 0.924200i \(-0.624734\pi\)
−0.381910 + 0.924200i \(0.624734\pi\)
\(74\) 30458.3 + 14253.6i 0.646585 + 0.302582i
\(75\) 0 0
\(76\) −15335.3 + 12796.7i −0.304550 + 0.254135i
\(77\) −27303.5 + 15763.7i −0.524797 + 0.302991i
\(78\) 0 0
\(79\) 73506.0 + 42438.7i 1.32512 + 0.765058i 0.984540 0.175158i \(-0.0560435\pi\)
0.340579 + 0.940216i \(0.389377\pi\)
\(80\) −24305.1 67929.1i −0.424593 1.18667i
\(81\) 0 0
\(82\) 68538.9 5902.15i 1.12565 0.0969338i
\(83\) −7548.53 + 13074.4i −0.120273 + 0.208318i −0.919875 0.392211i \(-0.871710\pi\)
0.799602 + 0.600530i \(0.205044\pi\)
\(84\) 0 0
\(85\) −23342.6 40430.5i −0.350430 0.606962i
\(86\) −56692.0 81200.2i −0.826563 1.18389i
\(87\) 0 0
\(88\) −26323.9 7169.11i −0.362363 0.0986866i
\(89\) 40174.5i 0.537620i 0.963193 + 0.268810i \(0.0866303\pi\)
−0.963193 + 0.268810i \(0.913370\pi\)
\(90\) 0 0
\(91\) 88253.7i 1.11720i
\(92\) −26174.7 + 71308.4i −0.322413 + 0.878357i
\(93\) 0 0
\(94\) −86188.0 + 60174.4i −1.00607 + 0.702412i
\(95\) −21987.8 38083.9i −0.249961 0.432945i
\(96\) 0 0
\(97\) 4298.65 7445.49i 0.0463877 0.0803459i −0.841899 0.539635i \(-0.818562\pi\)
0.888287 + 0.459289i \(0.151896\pi\)
\(98\) −13079.9 151891.i −0.137575 1.59760i
\(99\) 0 0
\(100\) 57980.7 10060.5i 0.579807 0.100605i
\(101\) 5537.77 + 3197.23i 0.0540171 + 0.0311868i 0.526765 0.850011i \(-0.323405\pi\)
−0.472748 + 0.881198i \(0.656738\pi\)
\(102\) 0 0
\(103\) 74198.4 42838.4i 0.689130 0.397869i −0.114156 0.993463i \(-0.536416\pi\)
0.803286 + 0.595593i \(0.203083\pi\)
\(104\) −54223.7 + 53781.5i −0.491593 + 0.487584i
\(105\) 0 0
\(106\) −78620.5 + 168003.i −0.679628 + 1.45229i
\(107\) −10199.1 −0.0861200 −0.0430600 0.999072i \(-0.513711\pi\)
−0.0430600 + 0.999072i \(0.513711\pi\)
\(108\) 0 0
\(109\) 30565.5 0.246414 0.123207 0.992381i \(-0.460682\pi\)
0.123207 + 0.992381i \(0.460682\pi\)
\(110\) 25460.6 54406.5i 0.200626 0.428715i
\(111\) 0 0
\(112\) 138580. 163335.i 1.04389 1.23036i
\(113\) 55820.3 32227.9i 0.411241 0.237430i −0.280082 0.959976i \(-0.590362\pi\)
0.691323 + 0.722546i \(0.257028\pi\)
\(114\) 0 0
\(115\) −144838. 83622.4i −1.02126 0.589628i
\(116\) 24917.3 + 143604.i 0.171932 + 0.990880i
\(117\) 0 0
\(118\) −1755.30 20383.5i −0.0116050 0.134764i
\(119\) 69304.0 120038.i 0.448633 0.777055i
\(120\) 0 0
\(121\) 69167.7 + 119802.i 0.429477 + 0.743876i
\(122\) −73434.2 + 51270.0i −0.446682 + 0.311863i
\(123\) 0 0
\(124\) 298841. + 109694.i 1.74536 + 0.640660i
\(125\) 90607.8i 0.518670i
\(126\) 0 0
\(127\) 142174.i 0.782189i −0.920350 0.391095i \(-0.872096\pi\)
0.920350 0.391095i \(-0.127904\pi\)
\(128\) 184804. 14390.9i 0.996982 0.0776362i
\(129\) 0 0
\(130\) −96259.1 137872.i −0.499555 0.715514i
\(131\) 44178.9 + 76520.1i 0.224925 + 0.389581i 0.956297 0.292398i \(-0.0944531\pi\)
−0.731372 + 0.681978i \(0.761120\pi\)
\(132\) 0 0
\(133\) 65281.7 113071.i 0.320009 0.554272i
\(134\) 271069. 23342.8i 1.30412 0.112303i
\(135\) 0 0
\(136\) 115986. 30570.0i 0.537722 0.141725i
\(137\) 88390.4 + 51032.2i 0.402350 + 0.232297i 0.687497 0.726187i \(-0.258709\pi\)
−0.285148 + 0.958484i \(0.592043\pi\)
\(138\) 0 0
\(139\) 78817.2 45505.1i 0.346006 0.199767i −0.316919 0.948453i \(-0.602648\pi\)
0.662925 + 0.748686i \(0.269315\pi\)
\(140\) 302162. + 362105.i 1.30293 + 1.56140i
\(141\) 0 0
\(142\) −164939. 77186.7i −0.686442 0.321234i
\(143\) −63587.4 −0.260034
\(144\) 0 0
\(145\) −320902. −1.26751
\(146\) 178185. + 83385.4i 0.691815 + 0.323749i
\(147\) 0 0
\(148\) −121880. 146059.i −0.457381 0.548116i
\(149\) −398601. + 230133.i −1.47087 + 0.849205i −0.999465 0.0327141i \(-0.989585\pi\)
−0.471401 + 0.881919i \(0.656252\pi\)
\(150\) 0 0
\(151\) −157479. 90920.8i −0.562059 0.324505i 0.191913 0.981412i \(-0.438531\pi\)
−0.753971 + 0.656907i \(0.771864\pi\)
\(152\) 109254. 28795.7i 0.383556 0.101092i
\(153\) 0 0
\(154\) 177688. 15301.4i 0.603748 0.0519911i
\(155\) −350447. + 606991.i −1.17164 + 2.02933i
\(156\) 0 0
\(157\) 181731. + 314767.i 0.588408 + 1.01915i 0.994441 + 0.105295i \(0.0335786\pi\)
−0.406033 + 0.913859i \(0.633088\pi\)
\(158\) −274860. 393682.i −0.875928 1.25459i
\(159\) 0 0
\(160\) −38343.3 + 406316.i −0.118410 + 1.25477i
\(161\) 496549.i 1.50972i
\(162\) 0 0
\(163\) 342002.i 1.00823i −0.863636 0.504115i \(-0.831819\pi\)
0.863636 0.504115i \(-0.168181\pi\)
\(164\) −365316. 134094.i −1.06062 0.389315i
\(165\) 0 0
\(166\) 70023.9 48889.0i 0.197231 0.137702i
\(167\) 8208.18 + 14217.0i 0.0227749 + 0.0394472i 0.877188 0.480147i \(-0.159417\pi\)
−0.854413 + 0.519594i \(0.826083\pi\)
\(168\) 0 0
\(169\) 96647.2 167398.i 0.260299 0.450851i
\(170\) 22658.0 + 263117.i 0.0601312 + 0.698276i
\(171\) 0 0
\(172\) 95773.9 + 551965.i 0.246846 + 1.42263i
\(173\) 60123.0 + 34712.1i 0.152730 + 0.0881790i 0.574418 0.818562i \(-0.305229\pi\)
−0.421687 + 0.906741i \(0.638562\pi\)
\(174\) 0 0
\(175\) −333142. + 192340.i −0.822308 + 0.474760i
\(176\) 117684. + 99848.0i 0.286375 + 0.242973i
\(177\) 0 0
\(178\) 96325.7 205837.i 0.227873 0.486938i
\(179\) −146989. −0.342888 −0.171444 0.985194i \(-0.554843\pi\)
−0.171444 + 0.985194i \(0.554843\pi\)
\(180\) 0 0
\(181\) 238346. 0.540768 0.270384 0.962752i \(-0.412849\pi\)
0.270384 + 0.962752i \(0.412849\pi\)
\(182\) 211605. 452175.i 0.473529 1.01188i
\(183\) 0 0
\(184\) 305083. 302596.i 0.664315 0.658898i
\(185\) 362724. 209419.i 0.779197 0.449869i
\(186\) 0 0
\(187\) 86488.2 + 49934.0i 0.180864 + 0.104422i
\(188\) 585871. 101657.i 1.20895 0.209770i
\(189\) 0 0
\(190\) 21343.0 + 247846.i 0.0428914 + 0.498079i
\(191\) 223937. 387870.i 0.444162 0.769312i −0.553831 0.832629i \(-0.686835\pi\)
0.997993 + 0.0633172i \(0.0201680\pi\)
\(192\) 0 0
\(193\) −29922.0 51826.4i −0.0578226 0.100152i 0.835665 0.549239i \(-0.185082\pi\)
−0.893488 + 0.449088i \(0.851749\pi\)
\(194\) −39876.4 + 27840.8i −0.0760698 + 0.0531101i
\(195\) 0 0
\(196\) −297171. + 809588.i −0.552543 + 1.50530i
\(197\) 834312.i 1.53166i 0.643042 + 0.765831i \(0.277672\pi\)
−0.643042 + 0.765831i \(0.722328\pi\)
\(198\) 0 0
\(199\) 413079.i 0.739435i −0.929144 0.369718i \(-0.879454\pi\)
0.929144 0.369718i \(-0.120546\pi\)
\(200\) −321191. 87473.6i −0.567790 0.154633i
\(201\) 0 0
\(202\) −20707.3 29659.1i −0.0357063 0.0511422i
\(203\) −476378. 825112.i −0.811357 1.40531i
\(204\) 0 0
\(205\) 428402. 742013.i 0.711978 1.23318i
\(206\) −482875. + 41582.2i −0.792805 + 0.0682714i
\(207\) 0 0
\(208\) 406771. 145543.i 0.651915 0.233256i
\(209\) 81468.5 + 47035.9i 0.129010 + 0.0744841i
\(210\) 0 0
\(211\) −416461. + 240444.i −0.643973 + 0.371798i −0.786143 0.618044i \(-0.787925\pi\)
0.142170 + 0.989842i \(0.454592\pi\)
\(212\) 805637. 672272.i 1.23112 1.02732i
\(213\) 0 0
\(214\) 52256.1 + 24454.3i 0.0780015 + 0.0365024i
\(215\) −1.23344e6 −1.81979
\(216\) 0 0
\(217\) −2.08095e6 −2.99994
\(218\) −156605. 73286.4i −0.223185 0.104444i
\(219\) 0 0
\(220\) −260899. + 217710.i −0.363426 + 0.303264i
\(221\) 242105. 139779.i 0.333443 0.192514i
\(222\) 0 0
\(223\) −202627. 116987.i −0.272858 0.157534i 0.357328 0.933979i \(-0.383688\pi\)
−0.630186 + 0.776445i \(0.717021\pi\)
\(224\) −1.10165e6 + 504587.i −1.46698 + 0.671918i
\(225\) 0 0
\(226\) −363272. + 31282.8i −0.473109 + 0.0407412i
\(227\) 60951.8 105572.i 0.0785094 0.135982i −0.824098 0.566448i \(-0.808317\pi\)
0.902607 + 0.430466i \(0.141651\pi\)
\(228\) 0 0
\(229\) 460471. + 797559.i 0.580248 + 1.00502i 0.995450 + 0.0952893i \(0.0303776\pi\)
−0.415202 + 0.909729i \(0.636289\pi\)
\(230\) 541591. + 775722.i 0.675074 + 0.966911i
\(231\) 0 0
\(232\) 216651. 795511.i 0.264265 0.970345i
\(233\) 564143.i 0.680768i 0.940287 + 0.340384i \(0.110557\pi\)
−0.940287 + 0.340384i \(0.889443\pi\)
\(234\) 0 0
\(235\) 1.30920e6i 1.54646i
\(236\) −39879.7 + 108645.i −0.0466092 + 0.126978i
\(237\) 0 0
\(238\) −642899. + 448856.i −0.735699 + 0.513647i
\(239\) 812725. + 1.40768e6i 0.920341 + 1.59408i 0.798887 + 0.601481i \(0.205422\pi\)
0.121454 + 0.992597i \(0.461244\pi\)
\(240\) 0 0
\(241\) 595736. 1.03184e6i 0.660710 1.14438i −0.319719 0.947512i \(-0.603589\pi\)
0.980429 0.196871i \(-0.0630781\pi\)
\(242\) −67139.3 779658.i −0.0736950 0.855787i
\(243\) 0 0
\(244\) 499175. 86614.1i 0.536758 0.0931352i
\(245\) −1.64440e6 949394.i −1.75022 1.01049i
\(246\) 0 0
\(247\) 228053. 131666.i 0.237845 0.137320i
\(248\) −1.26813e6 1.27855e6i −1.30928 1.32004i
\(249\) 0 0
\(250\) −217249. + 464237.i −0.219840 + 0.469775i
\(251\) 1.48383e6 1.48662 0.743311 0.668946i \(-0.233254\pi\)
0.743311 + 0.668946i \(0.233254\pi\)
\(252\) 0 0
\(253\) 357767. 0.351398
\(254\) −340889. + 728442.i −0.331535 + 0.708453i
\(255\) 0 0
\(256\) −981365. 369369.i −0.935903 0.352258i
\(257\) 1.18845e6 686154.i 1.12240 0.648020i 0.180390 0.983595i \(-0.442264\pi\)
0.942014 + 0.335575i \(0.108931\pi\)
\(258\) 0 0
\(259\) 1.07693e6 + 621764.i 0.997556 + 0.575939i
\(260\) 162617. + 937199.i 0.149188 + 0.859802i
\(261\) 0 0
\(262\) −42883.3 497984.i −0.0385954 0.448190i
\(263\) 85328.1 147793.i 0.0760681 0.131754i −0.825482 0.564428i \(-0.809097\pi\)
0.901550 + 0.432674i \(0.142430\pi\)
\(264\) 0 0
\(265\) 1.15512e6 + 2.00073e6i 1.01045 + 1.75015i
\(266\) −605585. + 422805.i −0.524773 + 0.366384i
\(267\) 0 0
\(268\) −1.44481e6 530339.i −1.22878 0.451042i
\(269\) 28534.0i 0.0240427i 0.999928 + 0.0120213i \(0.00382660\pi\)
−0.999928 + 0.0120213i \(0.996173\pi\)
\(270\) 0 0
\(271\) 485769.i 0.401797i 0.979612 + 0.200899i \(0.0643862\pi\)
−0.979612 + 0.200899i \(0.935614\pi\)
\(272\) −667561. 121470.i −0.547102 0.0995510i
\(273\) 0 0
\(274\) −330517. 473400.i −0.265960 0.380936i
\(275\) −138582. 240031.i −0.110503 0.191397i
\(276\) 0 0
\(277\) −696662. + 1.20665e6i −0.545535 + 0.944894i 0.453038 + 0.891491i \(0.350340\pi\)
−0.998573 + 0.0534030i \(0.982993\pi\)
\(278\) −512934. + 44170.7i −0.398061 + 0.0342785i
\(279\) 0 0
\(280\) −679940. 2.57977e6i −0.518293 1.96646i
\(281\) −691310. 399128.i −0.522285 0.301541i 0.215584 0.976485i \(-0.430834\pi\)
−0.737869 + 0.674944i \(0.764168\pi\)
\(282\) 0 0
\(283\) 1.50272e6 867593.i 1.11535 0.643947i 0.175139 0.984544i \(-0.443962\pi\)
0.940209 + 0.340597i \(0.110629\pi\)
\(284\) 660012. + 790945.i 0.485574 + 0.581903i
\(285\) 0 0
\(286\) 325795. + 152462.i 0.235521 + 0.110217i
\(287\) 2.54385e6 1.82300
\(288\) 0 0
\(289\) 980793. 0.690769
\(290\) 1.64417e6 + 769421.i 1.14802 + 0.537241i
\(291\) 0 0
\(292\) −713016. 854464.i −0.489375 0.586458i
\(293\) 376330. 217274.i 0.256094 0.147856i −0.366457 0.930435i \(-0.619429\pi\)
0.622551 + 0.782579i \(0.286096\pi\)
\(294\) 0 0
\(295\) −220675. 127407.i −0.147638 0.0852387i
\(296\) 274260. + 1.04057e6i 0.181942 + 0.690308i
\(297\) 0 0
\(298\) 2.59405e6 223384.i 1.69215 0.145717i
\(299\) 500745. 867315.i 0.323920 0.561047i
\(300\) 0 0
\(301\) −1.83104e6 3.17145e6i −1.16488 2.01763i
\(302\) 588860. + 843426.i 0.371531 + 0.532145i
\(303\) 0 0
\(304\) −628816. 114420.i −0.390247 0.0710095i
\(305\) 1.11547e6i 0.686609i
\(306\) 0 0
\(307\) 48971.1i 0.0296547i −0.999890 0.0148274i \(-0.995280\pi\)
0.999890 0.0148274i \(-0.00471987\pi\)
\(308\) −947087. 347641.i −0.568870 0.208812i
\(309\) 0 0
\(310\) 3.25092e6 2.26971e6i 1.92133 1.34142i
\(311\) −36344.9 62951.1i −0.0213080 0.0369065i 0.855175 0.518340i \(-0.173450\pi\)
−0.876483 + 0.481433i \(0.840116\pi\)
\(312\) 0 0
\(313\) −319768. + 553854.i −0.184490 + 0.319547i −0.943405 0.331644i \(-0.892397\pi\)
0.758914 + 0.651191i \(0.225730\pi\)
\(314\) −176401. 2.04847e6i −0.100967 1.17248i
\(315\) 0 0
\(316\) 464340. + 2.67609e6i 0.261588 + 1.50759i
\(317\) 2.43119e6 + 1.40365e6i 1.35885 + 0.784531i 0.989469 0.144748i \(-0.0462373\pi\)
0.369379 + 0.929279i \(0.379571\pi\)
\(318\) 0 0
\(319\) 594498. 343234.i 0.327095 0.188848i
\(320\) 1.17067e6 1.98986e6i 0.639088 1.08630i
\(321\) 0 0
\(322\) −1.19057e6 + 2.54411e6i −0.639904 + 1.36740i
\(323\) −413581. −0.220574
\(324\) 0 0
\(325\) −775859. −0.407450
\(326\) −820013. + 1.75228e6i −0.427343 + 0.913185i
\(327\) 0 0
\(328\) 1.55021e6 + 1.56296e6i 0.795622 + 0.802163i
\(329\) −3.36626e6 + 1.94351e6i −1.71458 + 0.989915i
\(330\) 0 0
\(331\) 2.68009e6 + 1.54735e6i 1.34456 + 0.776280i 0.987472 0.157793i \(-0.0504377\pi\)
0.357084 + 0.934072i \(0.383771\pi\)
\(332\) −475994. + 82591.7i −0.237004 + 0.0411236i
\(333\) 0 0
\(334\) −7967.47 92522.6i −0.00390800 0.0453818i
\(335\) 1.69431e6 2.93464e6i 0.824863 1.42870i
\(336\) 0 0
\(337\) 66234.5 + 114721.i 0.0317694 + 0.0550263i 0.881473 0.472234i \(-0.156552\pi\)
−0.849704 + 0.527261i \(0.823219\pi\)
\(338\) −896547. + 625947.i −0.426856 + 0.298020i
\(339\) 0 0
\(340\) 514781. 1.40243e6i 0.241505 0.657936i
\(341\) 1.49934e6i 0.698255i
\(342\) 0 0
\(343\) 2.12177e6i 0.973786i
\(344\) 832733. 3.05768e6i 0.379411 1.39314i
\(345\) 0 0
\(346\) −224817. 322006.i −0.100958 0.144602i
\(347\) 840739. + 1.45620e6i 0.374833 + 0.649229i 0.990302 0.138932i \(-0.0443668\pi\)
−0.615469 + 0.788161i \(0.711033\pi\)
\(348\) 0 0
\(349\) −8603.35 + 14901.4i −0.00378097 + 0.00654884i −0.867910 0.496722i \(-0.834537\pi\)
0.864129 + 0.503271i \(0.167870\pi\)
\(350\) 2.16805e6 186699.i 0.946019 0.0814653i
\(351\) 0 0
\(352\) −363558. 793748.i −0.156393 0.341449i
\(353\) 1.66268e6 + 959951.i 0.710187 + 0.410027i 0.811130 0.584865i \(-0.198853\pi\)
−0.100943 + 0.994892i \(0.532186\pi\)
\(354\) 0 0
\(355\) −1.96425e6 + 1.13406e6i −0.827227 + 0.477600i
\(356\) −987065. + 823666.i −0.412782 + 0.344450i
\(357\) 0 0
\(358\) 753111. + 352433.i 0.310564 + 0.145335i
\(359\) −207171. −0.0848386 −0.0424193 0.999100i \(-0.513507\pi\)
−0.0424193 + 0.999100i \(0.513507\pi\)
\(360\) 0 0
\(361\) 2.08652e6 0.842665
\(362\) −1.22119e6 571478.i −0.489790 0.229207i
\(363\) 0 0
\(364\) −2.16835e6 + 1.80940e6i −0.857779 + 0.715782i
\(365\) 2.12199e6 1.22513e6i 0.833703 0.481338i
\(366\) 0 0
\(367\) −1.53243e6 884750.i −0.593904 0.342891i 0.172736 0.984968i \(-0.444739\pi\)
−0.766640 + 0.642078i \(0.778073\pi\)
\(368\) −2.28865e6 + 818881.i −0.880967 + 0.315211i
\(369\) 0 0
\(370\) −2.36057e6 + 203277.i −0.896421 + 0.0771942i
\(371\) −3.42956e6 + 5.94017e6i −1.29361 + 2.24060i
\(372\) 0 0
\(373\) 171024. + 296222.i 0.0636481 + 0.110242i 0.896093 0.443865i \(-0.146393\pi\)
−0.832445 + 0.554107i \(0.813060\pi\)
\(374\) −323404. 463212.i −0.119555 0.171238i
\(375\) 0 0
\(376\) −3.24550e6 883884.i −1.18389 0.322423i
\(377\) 1.92161e6i 0.696326i
\(378\) 0 0
\(379\) 1.91370e6i 0.684345i 0.939637 + 0.342172i \(0.111163\pi\)
−0.939637 + 0.342172i \(0.888837\pi\)
\(380\) 484904. 1.32103e6i 0.172265 0.469305i
\(381\) 0 0
\(382\) −2.07735e6 + 1.45035e6i −0.728368 + 0.508529i
\(383\) −1.50852e6 2.61283e6i −0.525477 0.910153i −0.999560 0.0296726i \(-0.990554\pi\)
0.474083 0.880480i \(1.65722\pi\)
\(384\) 0 0
\(385\) 1.11064e6 1.92368e6i 0.381874 0.661425i
\(386\) 29044.5 + 337280.i 0.00992192 + 0.115219i
\(387\) 0 0
\(388\) 271064. 47033.4i 0.0914096 0.0158609i
\(389\) −2.16211e6 1.24829e6i −0.724442 0.418257i 0.0919434 0.995764i \(-0.470692\pi\)
−0.816385 + 0.577507i \(0.804025\pi\)
\(390\) 0 0
\(391\) −1.36217e6 + 786451.i −0.450599 + 0.260154i
\(392\) 3.46372e6 3.43547e6i 1.13848 1.12920i
\(393\) 0 0
\(394\) 2.00042e6 4.27467e6i 0.649202 1.38727i
\(395\) −5.98008e6 −1.92848
\(396\) 0 0
\(397\) −160060. −0.0509692 −0.0254846 0.999675i \(-0.508113\pi\)
−0.0254846 + 0.999675i \(0.508113\pi\)
\(398\) −990432. + 2.11644e6i −0.313413 + 0.669729i
\(399\) 0 0
\(400\) 1.43591e6 + 1.21829e6i 0.448723 + 0.380716i
\(401\) −2.51150e6 + 1.45002e6i −0.779960 + 0.450310i −0.836416 0.548095i \(-0.815353\pi\)
0.0564561 + 0.998405i \(0.482020\pi\)
\(402\) 0 0
\(403\) −3.63476e6 2.09853e6i −1.11484 0.643655i
\(404\) 34982.3 + 201610.i 0.0106634 + 0.0614553i
\(405\) 0 0
\(406\) 462408. + 5.36973e6i 0.139223 + 1.61673i
\(407\) −447985. + 775933.i −0.134053 + 0.232187i
\(408\) 0 0
\(409\) −565751. 979909.i −0.167231 0.289653i 0.770214 0.637785i \(-0.220149\pi\)
−0.937445 + 0.348133i \(0.886816\pi\)
\(410\) −3.97406e6 + 2.77460e6i −1.16755 + 0.815155i
\(411\) 0 0
\(412\) 2.57375e6 + 944731.i 0.747004 + 0.274198i
\(413\) 756540.i 0.218251i
\(414\) 0 0
\(415\) 1.06367e6i 0.303170i
\(416\) −2.43309e6 229606.i −0.689326 0.0650503i
\(417\) 0 0
\(418\) −304634. 436328.i −0.0852780 0.122144i
\(419\) −257000. 445137.i −0.0715152 0.123868i 0.828050 0.560654i \(-0.189450\pi\)
−0.899566 + 0.436786i \(0.856117\pi\)
\(420\) 0 0
\(421\) −3.24121e6 + 5.61394e6i −0.891255 + 1.54370i −0.0528829 + 0.998601i \(0.516841\pi\)
−0.838372 + 0.545098i \(0.816492\pi\)
\(422\) 2.71028e6 233392.i 0.740854 0.0637978i
\(423\) 0 0
\(424\) −5.73965e6 + 1.51278e6i −1.55050 + 0.408658i
\(425\) 1.05528e6 + 609268.i 0.283398 + 0.163620i
\(426\) 0 0
\(427\) −2.86814e6 + 1.65592e6i −0.761255 + 0.439511i
\(428\) −209105. 250587.i −0.0551766 0.0661226i
\(429\) 0 0
\(430\) 6.31963e6 + 2.95740e6i 1.64824 + 0.771327i
\(431\) 680530. 0.176463 0.0882316 0.996100i \(-0.471878\pi\)
0.0882316 + 0.996100i \(0.471878\pi\)
\(432\) 0 0
\(433\) −1.78685e6 −0.458003 −0.229002 0.973426i \(-0.573546\pi\)
−0.229002 + 0.973426i \(0.573546\pi\)
\(434\) 1.06619e7 + 4.98946e6i 2.71714 + 1.27154i
\(435\) 0 0
\(436\) 626661. + 750978.i 0.157876 + 0.189196i
\(437\) −1.28311e6 + 740806.i −0.321412 + 0.185567i
\(438\) 0 0
\(439\) −5.72585e6 3.30582e6i −1.41801 0.818687i −0.421884 0.906650i \(-0.638631\pi\)
−0.996124 + 0.0879624i \(0.971964\pi\)
\(440\) 1.85874e6 489901.i 0.457706 0.120636i
\(441\) 0 0
\(442\) −1.57559e6 + 135680.i −0.383608 + 0.0330339i
\(443\) −1.27077e6 + 2.20104e6i −0.307650 + 0.532866i −0.977848 0.209317i \(-0.932876\pi\)
0.670198 + 0.742183i \(0.266209\pi\)
\(444\) 0 0
\(445\) −1.41526e6 2.45129e6i −0.338793 0.586807i
\(446\) 757681. + 1.08523e6i 0.180364 + 0.258336i
\(447\) 0 0
\(448\) 6.85425e6 + 56120.1i 1.61349 + 0.0132106i
\(449\) 4.29742e6i 1.00599i −0.864290 0.502993i \(-0.832232\pi\)
0.864290 0.502993i \(-0.167768\pi\)
\(450\) 0 0
\(451\) 1.83286e6i 0.424314i
\(452\) 1.93626e6 + 710732.i 0.445777 + 0.163629i
\(453\) 0 0
\(454\) −565419. + 394762.i −0.128745 + 0.0898867i
\(455\) −3.10898e6 5.38491e6i −0.704027 1.21941i
\(456\) 0 0
\(457\) 795252. 1.37742e6i 0.178121 0.308514i −0.763116 0.646261i \(-0.776332\pi\)
0.941237 + 0.337747i \(0.109665\pi\)
\(458\) −446967. 5.19042e6i −0.0995662 1.15622i
\(459\) 0 0
\(460\) −914948. 5.27304e6i −0.201605 1.16189i
\(461\) 3.92509e6 + 2.26615e6i 0.860195 + 0.496634i 0.864078 0.503359i \(-0.167903\pi\)
−0.00388260 + 0.999992i \(0.501236\pi\)
\(462\) 0 0
\(463\) 6.33289e6 3.65630e6i 1.37293 0.792664i 0.381637 0.924312i \(-0.375360\pi\)
0.991296 + 0.131648i \(0.0420270\pi\)
\(464\) −3.01741e6 + 3.55641e6i −0.650638 + 0.766860i
\(465\) 0 0
\(466\) 1.35264e6 2.89043e6i 0.288547 0.616592i
\(467\) −5.59542e6 −1.18724 −0.593622 0.804744i \(-0.702303\pi\)
−0.593622 + 0.804744i \(0.702303\pi\)
\(468\) 0 0
\(469\) 1.00608e7 2.11204
\(470\) 3.13906e6 6.70782e6i 0.655473 1.40067i
\(471\) 0 0
\(472\) 464823. 461033.i 0.0960358 0.0952527i
\(473\) 2.28505e6 1.31928e6i 0.469617 0.271133i
\(474\) 0 0
\(475\) 994036. + 573907.i 0.202147 + 0.116710i
\(476\) 4.37016e6 758285.i 0.884056 0.153396i
\(477\) 0 0
\(478\) −788891. 9.16103e6i −0.157924 1.83390i
\(479\) 3.79751e6 6.57748e6i 0.756241 1.30985i −0.188515 0.982070i \(-0.560367\pi\)
0.944755 0.327777i \(-0.106299\pi\)
\(480\) 0 0
\(481\) 1.25403e6 + 2.17205e6i 0.247142 + 0.428063i
\(482\) −5.52634e6 + 3.85836e6i −1.08348 + 0.756458i
\(483\) 0 0
\(484\) −1.52538e6 + 4.15562e6i −0.295981 + 0.806348i
\(485\) 605727.i 0.116929i
\(486\) 0 0
\(487\) 9.63136e6i 1.84020i −0.391682 0.920101i \(-0.628107\pi\)
0.391682 0.920101i \(-0.371893\pi\)
\(488\) −2.76524e6 753090.i −0.525634 0.143152i
\(489\) 0 0
\(490\) 6.14887e6 + 8.80704e6i 1.15692 + 1.65707i
\(491\) 3.74298e6 + 6.48304e6i 0.700671 + 1.21360i 0.968231 + 0.250056i \(0.0804492\pi\)
−0.267560 + 0.963541i \(0.586218\pi\)
\(492\) 0 0
\(493\) −1.50901e6 + 2.61368e6i −0.279624 + 0.484323i
\(494\) −1.48414e6 + 127805.i −0.273627 + 0.0235630i
\(495\) 0 0
\(496\) 3.43179e6 + 9.59132e6i 0.626348 + 1.75055i
\(497\) −5.83184e6 3.36702e6i −1.05905 0.611441i
\(498\) 0 0
\(499\) 983698. 567938.i 0.176852 0.102106i −0.408961 0.912552i \(-0.634109\pi\)
0.585813 + 0.810446i \(0.300775\pi\)
\(500\) 2.22619e6 1.85766e6i 0.398232 0.332309i
\(501\) 0 0
\(502\) −7.60254e6 3.55776e6i −1.34648 0.630112i
\(503\) 9.15158e6 1.61278 0.806391 0.591382i \(-0.201417\pi\)
0.806391 + 0.591382i \(0.201417\pi\)
\(504\) 0 0
\(505\) −450525. −0.0786123
\(506\) −1.83305e6 857812.i −0.318272 0.148942i
\(507\) 0 0
\(508\) 3.49315e6 2.91489e6i 0.600562 0.501145i
\(509\) −659417. + 380714.i −0.112815 + 0.0651336i −0.555346 0.831620i \(-0.687414\pi\)
0.442531 + 0.896753i \(0.354081\pi\)
\(510\) 0 0
\(511\) 6.30019e6 + 3.63741e6i 1.06734 + 0.616227i
\(512\) 4.14248e6 + 4.24550e6i 0.698370 + 0.715737i
\(513\) 0 0
\(514\) −7.73432e6 + 666032.i −1.29126 + 0.111195i
\(515\) −3.01820e6 + 5.22768e6i −0.501453 + 0.868542i
\(516\) 0 0
\(517\) −1.40031e6 2.42541e6i −0.230409 0.399080i
\(518\) −4.02693e6 5.76779e6i −0.659402 0.944464i
\(519\) 0 0
\(520\) 1.41392e6 5.19172e6i 0.229307 0.841982i
\(521\) 8.50821e6i 1.37323i 0.727020 + 0.686616i \(0.240905\pi\)
−0.727020 + 0.686616i \(0.759095\pi\)
\(522\) 0 0
\(523\) 8.02433e6i 1.28279i 0.767212 + 0.641394i \(0.221644\pi\)
−0.767212 + 0.641394i \(0.778356\pi\)
\(524\) −974293. + 2.65429e6i −0.155011 + 0.422298i
\(525\) 0 0
\(526\) −791545. + 552638.i −0.124742 + 0.0870916i
\(527\) 3.29588e6 + 5.70863e6i 0.516945 + 0.895376i
\(528\) 0 0
\(529\) 400790. 694188.i 0.0622698 0.107854i
\(530\) −1.12125e6 1.30205e7i −0.173385 2.01344i
\(531\) 0 0
\(532\) 4.11652e6 714275.i 0.630596 0.109417i
\(533\) 4.44330e6 + 2.56534e6i 0.677466 + 0.391135i
\(534\) 0 0
\(535\) 622313. 359292.i 0.0939992 0.0542705i
\(536\) 6.13104e6 + 6.18144e6i 0.921769 + 0.929347i
\(537\) 0 0
\(538\) 68415.6 146197.i 0.0101906 0.0217762i
\(539\) 4.06185e6 0.602216
\(540\) 0 0
\(541\) −7.93678e6 −1.16587 −0.582937 0.812518i \(-0.698096\pi\)
−0.582937 + 0.812518i \(0.698096\pi\)
\(542\) 1.16472e6 2.48888e6i 0.170304 0.363920i
\(543\) 0 0
\(544\) 3.12906e6 + 2.22296e6i 0.453332 + 0.322058i
\(545\) −1.86499e6 + 1.07675e6i −0.268959 + 0.155283i
\(546\) 0 0
\(547\) 5.32459e6 + 3.07415e6i 0.760883 + 0.439296i 0.829613 0.558339i \(-0.188561\pi\)
−0.0687298 + 0.997635i \(0.521895\pi\)
\(548\) 558366. + 3.21798e6i 0.0794268 + 0.457754i
\(549\) 0 0
\(550\) 134518. + 1.56210e6i 0.0189615 + 0.220192i
\(551\) −1.42143e6 + 2.46198e6i −0.199455 + 0.345466i
\(552\) 0 0
\(553\) −8.87742e6 1.53761e7i −1.23445 2.13813i
\(554\) 6.46258e6 4.51202e6i 0.894605 0.624592i
\(555\) 0 0
\(556\) 2.73397e6 + 1.00354e6i 0.375065 + 0.137673i
\(557\) 6.19751e6i 0.846407i 0.906035 + 0.423203i \(0.139094\pi\)
−0.906035 + 0.423203i \(0.860906\pi\)
\(558\) 0 0
\(559\) 7.38604e6i 0.999728i
\(560\) −2.70174e6 + 1.48479e7i −0.364060 + 2.00076i
\(561\) 0 0
\(562\) 2.58500e6 + 3.70251e6i 0.345239 + 0.494488i
\(563\) −744431. 1.28939e6i −0.0989814 0.171441i 0.812282 0.583265i \(-0.198225\pi\)
−0.911263 + 0.411824i \(0.864892\pi\)
\(564\) 0 0
\(565\) −2.27063e6 + 3.93284e6i −0.299244 + 0.518305i
\(566\) −9.77950e6 + 842150.i −1.28315 + 0.110497i
\(567\) 0 0
\(568\) −1.48519e6 5.63497e6i −0.193157 0.732860i
\(569\) −149856. 86519.3i −0.0194041 0.0112029i 0.490267 0.871573i \(-0.336899\pi\)
−0.509671 + 0.860370i \(0.670233\pi\)
\(570\) 0 0
\(571\) −5.22869e6 + 3.01878e6i −0.671123 + 0.387473i −0.796502 0.604636i \(-0.793319\pi\)
0.125379 + 0.992109i \(0.459985\pi\)
\(572\) −1.30368e6 1.56231e6i −0.166603 0.199653i
\(573\) 0 0
\(574\) −1.30336e7 6.09934e6i −1.65115 0.772687i
\(575\) 4.36528e6 0.550608
\(576\) 0 0
\(577\) 1.58937e7 1.98740 0.993698 0.112090i \(-0.0357546\pi\)
0.993698 + 0.112090i \(0.0357546\pi\)
\(578\) −5.02518e6 2.35163e6i −0.625650 0.292786i
\(579\) 0 0
\(580\) −6.57920e6 7.88438e6i −0.812088 0.973190i
\(581\) 2.73494e6 1.57902e6i 0.336130 0.194065i
\(582\) 0 0
\(583\) −4.27993e6 2.47102e6i −0.521514 0.301096i
\(584\) 1.60446e6 + 6.08751e6i 0.194669 + 0.738597i
\(585\) 0 0
\(586\) −2.44911e6 + 210902.i −0.294622 + 0.0253710i
\(587\) 7.04599e6 1.22040e7i 0.844008 1.46186i −0.0424722 0.999098i \(-0.513523\pi\)
0.886480 0.462767i \(-0.153143\pi\)
\(588\) 0 0
\(589\) 3.10459e6 + 5.37730e6i 0.368736 + 0.638670i
\(590\) 825165. + 1.18189e6i 0.0975912 + 0.139780i
\(591\) 0 0
\(592\) 1.08977e6 5.98905e6i 0.127800 0.702350i
\(593\) 1.07696e7i 1.25766i −0.777544 0.628828i \(-0.783535\pi\)
0.777544 0.628828i \(-0.216465\pi\)
\(594\) 0 0
\(595\) 9.76569e6i 1.13086i
\(596\) −1.38264e7 5.07519e6i −1.59439 0.585244i
\(597\) 0 0
\(598\) −4.64515e6 + 3.24313e6i −0.531187 + 0.370862i
\(599\) −5.44302e6 9.42759e6i −0.619831 1.07358i −0.989516 0.144422i \(-0.953868\pi\)
0.369685 0.929157i \(1.62053\pi\)
\(600\) 0 0
\(601\) −6.66377e6 + 1.15420e7i −0.752548 + 1.30345i 0.194036 + 0.980994i \(0.437842\pi\)
−0.946584 + 0.322457i \(0.895491\pi\)
\(602\) 1.77734e6 + 2.06395e7i 0.199885 + 2.32117i
\(603\) 0 0
\(604\) −994804. 5.73327e6i −0.110955 0.639455i
\(605\) −8.44070e6 4.87324e6i −0.937540 0.541289i
\(606\) 0 0
\(607\) −1.90927e6 + 1.10232e6i −0.210327 + 0.121432i −0.601463 0.798900i \(-0.705415\pi\)
0.391136 + 0.920333i \(0.372082\pi\)
\(608\) 2.94745e6 + 2.09394e6i 0.323361 + 0.229723i
\(609\) 0 0
\(610\) 2.67455e6 5.71522e6i 0.291022 0.621882i
\(611\) −7.83973e6 −0.849568
\(612\) 0 0
\(613\) 2.50240e6 0.268971 0.134485 0.990916i \(-0.457062\pi\)
0.134485 + 0.990916i \(0.457062\pi\)
\(614\) −117417. + 250908.i −0.0125693 + 0.0268592i
\(615\) 0 0
\(616\) 4.01894e6 + 4.05198e6i 0.426737 + 0.430245i
\(617\) 6.29534e6 3.63461e6i 0.665742 0.384366i −0.128719 0.991681i \(-0.541087\pi\)
0.794461 + 0.607315i \(0.207753\pi\)
\(618\) 0 0
\(619\) 9.08516e6 + 5.24532e6i 0.953028 + 0.550231i 0.894020 0.448026i \(-0.147873\pi\)
0.0590081 + 0.998258i \(0.481206\pi\)
\(620\) −2.20984e7 + 3.83439e6i −2.30877 + 0.400605i
\(621\) 0 0
\(622\) 35279.0 + 409679.i 0.00365629 + 0.0424588i
\(623\) 4.20189e6 7.27789e6i 0.433735 0.751252i
\(624\) 0 0
\(625\) 6.06530e6 + 1.05054e7i 0.621087 + 1.07575i
\(626\) 2.96632e6 2.07102e6i 0.302540 0.211226i
\(627\) 0 0
\(628\) −4.00777e6 + 1.09184e7i −0.405512 + 1.10474i
\(629\) 3.93908e6i 0.396980i
\(630\) 0 0
\(631\) 1.25868e7i 1.25846i 0.777218 + 0.629231i \(0.216630\pi\)
−0.777218 + 0.629231i \(0.783370\pi\)
\(632\) 4.03733e6 1.48245e7i 0.402070 1.47635i
\(633\) 0 0
\(634\) −9.09090e6 1.30209e7i −0.898222 1.28653i
\(635\) 5.00848e6 + 8.67494e6i 0.492914 + 0.853753i
\(636\) 0 0
\(637\) 5.68513e6 9.84693e6i 0.555126 0.961506i
\(638\) −3.86893e6 + 333168.i −0.376304 + 0.0324050i
\(639\) 0 0
\(640\) −1.07691e7 + 7.38832e6i −1.03927 + 0.713010i
\(641\) 4.75044e6 + 2.74267e6i 0.456655 + 0.263650i 0.710637 0.703559i \(-0.248407\pi\)
−0.253981 + 0.967209i \(0.581740\pi\)
\(642\) 0 0
\(643\) 1.03225e7 5.95970e6i 0.984595 0.568456i 0.0809407 0.996719i \(-0.474208\pi\)
0.903654 + 0.428263i \(0.140874\pi\)
\(644\) 1.22000e7 1.01804e7i 1.15916 0.967273i
\(645\) 0 0
\(646\) 2.11902e6 + 991636.i 0.199781 + 0.0934913i
\(647\) 1.43126e7 1.34418 0.672092 0.740468i \(-0.265396\pi\)
0.672092 + 0.740468i \(0.265396\pi\)
\(648\) 0 0
\(649\) 545092. 0.0507993
\(650\) 3.97518e6 + 1.86027e6i 0.369040 + 0.172700i
\(651\) 0 0
\(652\) 8.40281e6 7.01181e6i 0.774115 0.645968i
\(653\) 3.09615e6 1.78757e6i 0.284145 0.164051i −0.351154 0.936318i \(-0.614211\pi\)
0.635298 + 0.772267i \(0.280877\pi\)
\(654\) 0 0
\(655\) −5.39126e6 3.11265e6i −0.491006 0.283483i
\(656\) −4.19517e6 1.17249e7i −0.380618 1.06377i
\(657\) 0 0
\(658\) 2.19073e7 1.88652e6i 1.97253 0.169862i
\(659\) −1.66026e6 + 2.87565e6i −0.148923 + 0.257942i −0.930830 0.365453i \(-0.880914\pi\)
0.781907 + 0.623396i \(0.214247\pi\)
\(660\) 0 0
\(661\) −4.26668e6 7.39011e6i −0.379828 0.657881i 0.611209 0.791469i \(-0.290683\pi\)
−0.991037 + 0.133588i \(0.957350\pi\)
\(662\) −1.00216e7 1.43540e7i −0.888775 1.27300i
\(663\) 0 0
\(664\) 2.63682e6 + 718116.i 0.232092 + 0.0632084i
\(665\) 9.19890e6i 0.806644i
\(666\) 0 0
\(667\) 1.08117e7i 0.940981i
\(668\) −181018. + 493151.i −0.0156957 + 0.0427601i
\(669\) 0 0
\(670\) −1.57173e7 + 1.09734e7i −1.35267 + 0.944399i
\(671\) −1.19310e6 2.06651e6i −0.102299 0.177187i
\(672\) 0 0
\(673\) −9.81452e6 + 1.69992e7i −0.835279 + 1.44675i 0.0585245 + 0.998286i \(0.481360\pi\)
−0.893803 + 0.448459i \(0.851973\pi\)
\(674\) −64292.1 746594.i −0.00545140 0.0633046i
\(675\) 0 0
\(676\) 6.09436e6 1.05746e6i 0.512934 0.0890013i
\(677\) −1.67817e7 9.68890e6i −1.40722 0.812461i −0.412104 0.911137i \(-0.635206\pi\)
−0.995120 + 0.0986755i \(0.968539\pi\)
\(678\) 0 0
\(679\) −1.55746e6 + 899202.i −0.129641 + 0.0748484i
\(680\) −6.00011e6 + 5.95118e6i −0.497607 + 0.493550i
\(681\) 0 0
\(682\) −3.59494e6 + 7.68199e6i −0.295958 + 0.632430i
\(683\) −1.79967e7 −1.47618 −0.738092 0.674700i \(-0.764273\pi\)
−0.738092 + 0.674700i \(0.764273\pi\)
\(684\) 0 0
\(685\) −7.19100e6 −0.585548
\(686\) −5.08734e6 + 1.08711e7i −0.412744 + 0.881988i
\(687\) 0 0
\(688\) −1.15979e7 + 1.36696e7i −0.934134 + 1.10100i
\(689\) −1.19807e7 + 6.91707e6i −0.961468 + 0.555104i
\(690\) 0 0
\(691\) 9.29000e6 + 5.36359e6i 0.740152 + 0.427327i 0.822124 0.569308i \(-0.192789\pi\)
−0.0819727 + 0.996635i \(0.526122\pi\)
\(692\) 379800. + 2.18887e6i 0.0301501 + 0.173762i
\(693\) 0 0
\(694\) −816083. 9.47680e6i −0.0643185 0.746901i
\(695\) −3.20608e6 + 5.55310e6i −0.251775 + 0.436088i
\(696\) 0 0
\(697\) −4.02903e6 6.97848e6i −0.314137 0.544100i
\(698\) 79808.9 55720.6i 0.00620030 0.00432890i
\(699\) 0 0
\(700\) −1.15558e7 4.24174e6i −0.891367 0.327189i
\(701\) 3.82293e6i 0.293834i 0.989149 + 0.146917i \(0.0469350\pi\)
−0.989149 + 0.146917i \(0.953065\pi\)
\(702\) 0 0
\(703\) 3.71046e6i 0.283165i
\(704\) −40434.9 + 4.93853e6i −0.00307485 + 0.375549i
\(705\) 0 0
\(706\) −6.21724e6 8.90498e6i −0.469446 0.672390i
\(707\) −668804. 1.15840e6i −0.0503211 0.0871587i
\(708\) 0 0
\(709\) 1.02820e7 1.78090e7i 0.768181 1.33053i −0.170368 0.985381i \(-0.554496\pi\)
0.938549 0.345147i \(-0.112171\pi\)
\(710\) 1.27831e7 1.10080e6i 0.951678 0.0819526i
\(711\) 0 0
\(712\) 7.03220e6 1.85345e6i 0.519866 0.137019i
\(713\) 2.04506e7 + 1.18072e7i 1.50654 + 0.869804i
\(714\) 0 0
\(715\) 3.87986e6 2.24004e6i 0.283825 0.163867i
\(716\) −3.01360e6 3.61144e6i −0.219687 0.263268i
\(717\) 0 0
\(718\) 1.06146e6 + 496731.i 0.0768409 + 0.0359592i
\(719\) −482918. −0.0348378 −0.0174189 0.999848i \(-0.505545\pi\)
−0.0174189 + 0.999848i \(0.505545\pi\)
\(720\) 0 0
\(721\) −1.79221e7 −1.28396
\(722\) −1.06905e7 5.00282e6i −0.763227 0.357167i
\(723\) 0 0
\(724\) 4.88662e6 + 5.85603e6i 0.346467 + 0.415200i
\(725\) 7.25375e6 4.18796e6i 0.512528 0.295908i
\(726\) 0 0
\(727\) −2.15466e7 1.24399e7i −1.51197 0.872935i −0.999902 0.0139889i \(-0.995547\pi\)
−0.512066 0.858946i \(1.32888\pi\)
\(728\) 1.54481e7 4.07159e6i 1.08030 0.284732i
\(729\) 0 0
\(730\) −1.38097e7 + 1.18920e6i −0.959127 + 0.0825941i
\(731\) −5.80012e6 + 1.00461e7i −0.401461 + 0.695351i
\(732\) 0 0
\(733\) 5.66177e6 + 9.80648e6i 0.389218 + 0.674145i 0.992344 0.123501i \(-0.0394121\pi\)
−0.603127 + 0.797645i \(0.706079\pi\)
\(734\) 5.73019e6 + 8.20738e6i 0.392581 + 0.562295i
\(735\) 0 0
\(736\) 1.36895e7 + 1.29185e6i 0.931522 + 0.0879058i
\(737\) 7.24889e6i 0.491590i
\(738\) 0 0
\(739\) 2.22042e7i 1.49563i −0.663909 0.747814i \(-0.731104\pi\)
0.663909 0.747814i \(-0.268896\pi\)
\(740\) 1.25820e7 + 4.61839e6i 0.844635 + 0.310035i
\(741\) 0 0
\(742\) 3.18143e7 2.22120e7i 2.12135 1.48108i
\(743\) 650311. + 1.12637e6i 0.0432165 + 0.0748531i 0.886825 0.462106i \(-0.152906\pi\)
−0.843608 + 0.536959i \(0.819573\pi\)
\(744\) 0 0
\(745\) 1.62141e7 2.80836e7i 1.07029 1.85380i
\(746\) −166009. 1.92778e6i −0.0109215 0.126827i
\(747\) 0 0
\(748\) 546349. + 3.14873e6i 0.0357040 + 0.205770i
\(749\) 1.84765e6 + 1.06674e6i 0.120341 + 0.0694790i
\(750\) 0 0
\(751\) −1.35125e7 + 7.80146e6i −0.874253 + 0.504750i −0.868759 0.495235i \(-0.835082\pi\)
−0.00549352 + 0.999985i \(0.501749\pi\)
\(752\) 1.45093e7 + 1.23103e7i 0.935626 + 0.793826i
\(753\) 0 0
\(754\) −4.60742e6 + 9.84554e6i −0.295141 + 0.630683i
\(755\) 1.28117e7 0.817976
\(756\) 0 0
\(757\) −1.06995e6 −0.0678613 −0.0339307 0.999424i \(-0.510803\pi\)
−0.0339307 + 0.999424i \(0.510803\pi\)
\(758\) 4.58844e6 9.80498e6i 0.290063 0.619832i
\(759\) 0 0
\(760\) −5.65187e6 + 5.60578e6i −0.354942 + 0.352048i
\(761\) 1.68821e7 9.74690e6i 1.05673 0.610105i 0.132207 0.991222i \(-0.457794\pi\)
0.924527 + 0.381117i \(0.124460\pi\)
\(762\) 0 0
\(763\) −5.53716e6 3.19688e6i −0.344331 0.198799i
\(764\) 1.41210e7 2.45019e6i 0.875247 0.151868i
\(765\) 0 0
\(766\) 1.46428e6 + 1.70040e7i 0.0901679 + 1.04708i
\(767\) 762932. 1.32144e6i 0.0468271 0.0811069i
\(768\) 0 0
\(769\) 6.92454e6 + 1.19937e7i 0.422255 + 0.731368i 0.996160 0.0875545i \(-0.0279052\pi\)
−0.573904 + 0.818922i \(0.694572\pi\)
\(770\) −1.03028e7 + 7.19317e6i −0.626223 + 0.437214i
\(771\) 0 0
\(772\) 659880. 1.79772e6i 0.0398494 0.108562i
\(773\) 1.41475e7i 0.851588i 0.904820 + 0.425794i \(0.140005\pi\)
−0.904820 + 0.425794i \(0.859995\pi\)
\(774\) 0 0