Properties

Label 108.6.h.a.71.3
Level 108
Weight 6
Character 108.71
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 71.3
Character \(\chi\) \(=\) 108.71
Dual form 108.6.h.a.35.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.48009 + 1.40307i) q^{2} +(28.0628 - 15.3779i) q^{4} +(77.8058 + 44.9212i) q^{5} +(-124.034 + 71.6112i) q^{7} +(-132.210 + 123.647i) q^{8} +O(q^{10})\) \(q+(-5.48009 + 1.40307i) q^{2} +(28.0628 - 15.3779i) q^{4} +(77.8058 + 44.9212i) q^{5} +(-124.034 + 71.6112i) q^{7} +(-132.210 + 123.647i) q^{8} +(-489.410 - 137.005i) q^{10} +(278.231 + 481.910i) q^{11} +(179.796 - 311.416i) q^{13} +(579.243 - 566.465i) q^{14} +(551.037 - 863.095i) q^{16} -1076.42i q^{17} +348.135i q^{19} +(2874.24 + 64.1196i) q^{20} +(-2200.88 - 2250.53i) q^{22} +(-1469.06 + 2544.48i) q^{23} +(2473.33 + 4283.93i) q^{25} +(-548.358 + 1958.85i) q^{26} +(-2379.51 + 3917.00i) q^{28} +(-3331.19 + 1923.26i) q^{29} +(-2346.41 - 1354.70i) q^{31} +(-1808.75 + 5502.99i) q^{32} +(1510.30 + 5898.87i) q^{34} -12867.4 q^{35} -1992.90 q^{37} +(-488.460 - 1907.81i) q^{38} +(-15841.1 + 3681.39i) q^{40} +(13432.0 + 7754.99i) q^{41} +(-12474.1 + 7201.91i) q^{43} +(15218.7 + 9245.10i) q^{44} +(4480.46 - 16005.2i) q^{46} +(1232.97 + 2135.56i) q^{47} +(1852.82 - 3209.17i) q^{49} +(-19564.7 - 20006.0i) q^{50} +(256.637 - 11504.1i) q^{52} +13364.2i q^{53} +49993.8i q^{55} +(7544.08 - 24804.1i) q^{56} +(15556.7 - 15213.6i) q^{58} +(-19878.8 + 34431.1i) q^{59} +(-211.489 - 366.310i) q^{61} +(14759.3 + 4131.70i) q^{62} +(2191.00 - 32694.7i) q^{64} +(27978.3 - 16153.3i) q^{65} +(14018.6 + 8093.63i) q^{67} +(-16553.1 - 30207.3i) q^{68} +(70514.7 - 18054.0i) q^{70} +6902.73 q^{71} -11089.5 q^{73} +(10921.3 - 2796.19i) q^{74} +(5353.60 + 9769.63i) q^{76} +(-69020.2 - 39848.8i) q^{77} +(64310.3 - 37129.6i) q^{79} +(81645.2 - 42400.5i) q^{80} +(-84489.6 - 23651.9i) q^{82} +(-48564.9 - 84116.9i) q^{83} +(48354.0 - 83751.6i) q^{85} +(58254.2 - 56969.2i) q^{86} +(-96371.4 - 29311.0i) q^{88} +74459.8i q^{89} +51501.6i q^{91} +(-2096.90 + 93996.2i) q^{92} +(-9753.11 - 9973.11i) q^{94} +(-15638.6 + 27086.9i) q^{95} +(47958.5 + 83066.5i) q^{97} +(-5650.89 + 20186.2i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.48009 + 1.40307i −0.968752 + 0.248031i
\(3\) 0 0
\(4\) 28.0628 15.3779i 0.876961 0.480561i
\(5\) 77.8058 + 44.9212i 1.39183 + 0.803575i 0.993518 0.113675i \(-0.0362621\pi\)
0.398314 + 0.917249i \(0.369595\pi\)
\(6\) 0 0
\(7\) −124.034 + 71.6112i −0.956745 + 0.552377i −0.895170 0.445725i \(-0.852946\pi\)
−0.0615753 + 0.998102i \(0.519612\pi\)
\(8\) −132.210 + 123.647i −0.730364 + 0.683058i
\(9\) 0 0
\(10\) −489.410 137.005i −1.54765 0.433247i
\(11\) 278.231 + 481.910i 0.693303 + 1.20084i 0.970749 + 0.240095i \(0.0771787\pi\)
−0.277446 + 0.960741i \(0.589488\pi\)
\(12\) 0 0
\(13\) 179.796 311.416i 0.295068 0.511072i −0.679933 0.733274i \(-0.737991\pi\)
0.975001 + 0.222202i \(0.0713245\pi\)
\(14\) 579.243 566.465i 0.789842 0.772419i
\(15\) 0 0
\(16\) 551.037 863.095i 0.538123 0.842867i
\(17\) 1076.42i 0.903356i −0.892181 0.451678i \(-0.850826\pi\)
0.892181 0.451678i \(-0.149174\pi\)
\(18\) 0 0
\(19\) 348.135i 0.221240i 0.993863 + 0.110620i \(0.0352837\pi\)
−0.993863 + 0.110620i \(0.964716\pi\)
\(20\) 2874.24 + 64.1196i 1.60675 + 0.0358439i
\(21\) 0 0
\(22\) −2200.88 2250.53i −0.969484 0.991352i
\(23\) −1469.06 + 2544.48i −0.579054 + 1.00295i 0.416535 + 0.909120i \(0.363244\pi\)
−0.995588 + 0.0938304i \(0.970089\pi\)
\(24\) 0 0
\(25\) 2473.33 + 4283.93i 0.791464 + 1.37086i
\(26\) −548.358 + 1958.85i −0.159086 + 0.568288i
\(27\) 0 0
\(28\) −2379.51 + 3917.00i −0.573578 + 0.944188i
\(29\) −3331.19 + 1923.26i −0.735536 + 0.424662i −0.820444 0.571727i \(-0.806274\pi\)
0.0849079 + 0.996389i \(0.472940\pi\)
\(30\) 0 0
\(31\) −2346.41 1354.70i −0.438531 0.253186i 0.264443 0.964401i \(-0.414812\pi\)
−0.702974 + 0.711215i \(0.748145\pi\)
\(32\) −1808.75 + 5502.99i −0.312250 + 0.950000i
\(33\) 0 0
\(34\) 1510.30 + 5898.87i 0.224060 + 0.875128i
\(35\) −12867.4 −1.77550
\(36\) 0 0
\(37\) −1992.90 −0.239321 −0.119661 0.992815i \(-0.538181\pi\)
−0.119661 + 0.992815i \(0.538181\pi\)
\(38\) −488.460 1907.81i −0.0548744 0.214327i
\(39\) 0 0
\(40\) −15841.1 + 3681.39i −1.56543 + 0.363800i
\(41\) 13432.0 + 7754.99i 1.24791 + 0.720479i 0.970692 0.240329i \(-0.0772552\pi\)
0.277215 + 0.960808i \(0.410589\pi\)
\(42\) 0 0
\(43\) −12474.1 + 7201.91i −1.02882 + 0.593987i −0.916645 0.399702i \(-0.869113\pi\)
−0.112170 + 0.993689i \(0.535780\pi\)
\(44\) 15218.7 + 9245.10i 1.18508 + 0.719913i
\(45\) 0 0
\(46\) 4480.46 16005.2i 0.312197 1.11523i
\(47\) 1232.97 + 2135.56i 0.0814153 + 0.141015i 0.903858 0.427832i \(-0.140723\pi\)
−0.822443 + 0.568848i \(0.807389\pi\)
\(48\) 0 0
\(49\) 1852.82 3209.17i 0.110241 0.190943i
\(50\) −19564.7 20006.0i −1.10675 1.13171i
\(51\) 0 0
\(52\) 256.637 11504.1i 0.0131617 0.589988i
\(53\) 13364.2i 0.653514i 0.945108 + 0.326757i \(0.105956\pi\)
−0.945108 + 0.326757i \(0.894044\pi\)
\(54\) 0 0
\(55\) 49993.8i 2.22848i
\(56\) 7544.08 24804.1i 0.321467 1.05695i
\(57\) 0 0
\(58\) 15556.7 15213.6i 0.607223 0.593828i
\(59\) −19878.8 + 34431.1i −0.743464 + 1.28772i 0.207445 + 0.978247i \(0.433485\pi\)
−0.950909 + 0.309470i \(0.899848\pi\)
\(60\) 0 0
\(61\) −211.489 366.310i −0.00727718 0.0126044i 0.862364 0.506289i \(-0.168983\pi\)
−0.869641 + 0.493685i \(0.835650\pi\)
\(62\) 14759.3 + 4131.70i 0.487626 + 0.136505i
\(63\) 0 0
\(64\) 2191.00 32694.7i 0.0668640 0.997762i
\(65\) 27978.3 16153.3i 0.821369 0.474218i
\(66\) 0 0
\(67\) 14018.6 + 8093.63i 0.381520 + 0.220271i 0.678479 0.734620i \(-0.262639\pi\)
−0.296960 + 0.954890i \(0.595973\pi\)
\(68\) −16553.1 30207.3i −0.434118 0.792209i
\(69\) 0 0
\(70\) 70514.7 18054.0i 1.72002 0.440380i
\(71\) 6902.73 0.162508 0.0812541 0.996693i \(-0.474107\pi\)
0.0812541 + 0.996693i \(0.474107\pi\)
\(72\) 0 0
\(73\) −11089.5 −0.243558 −0.121779 0.992557i \(-0.538860\pi\)
−0.121779 + 0.992557i \(0.538860\pi\)
\(74\) 10921.3 2796.19i 0.231843 0.0593590i
\(75\) 0 0
\(76\) 5353.60 + 9769.63i 0.106319 + 0.194019i
\(77\) −69020.2 39848.8i −1.32663 0.765930i
\(78\) 0 0
\(79\) 64310.3 37129.6i 1.15935 0.669349i 0.208199 0.978086i \(-0.433240\pi\)
0.951147 + 0.308738i \(0.0999065\pi\)
\(80\) 81645.2 42400.5i 1.42628 0.740707i
\(81\) 0 0
\(82\) −84489.6 23651.9i −1.38761 0.388446i
\(83\) −48564.9 84116.9i −0.773798 1.34026i −0.935468 0.353412i \(-0.885021\pi\)
0.161670 0.986845i \(1.55169\pi\)
\(84\) 0 0
\(85\) 48354.0 83751.6i 0.725914 1.25732i
\(86\) 58254.2 56969.2i 0.849340 0.830604i
\(87\) 0 0
\(88\) −96371.4 29311.0i −1.32660 0.403482i
\(89\) 74459.8i 0.996430i 0.867054 + 0.498215i \(0.166011\pi\)
−0.867054 + 0.498215i \(0.833989\pi\)
\(90\) 0 0
\(91\) 51501.6i 0.651954i
\(92\) −2096.90 + 93996.2i −0.0258290 + 1.15782i
\(93\) 0 0
\(94\) −9753.11 9973.11i −0.113847 0.116416i
\(95\) −15638.6 + 27086.9i −0.177783 + 0.307929i
\(96\) 0 0
\(97\) 47958.5 + 83066.5i 0.517530 + 0.896389i 0.999793 + 0.0203622i \(0.00648193\pi\)
−0.482262 + 0.876027i \(0.660185\pi\)
\(98\) −5650.89 + 20186.2i −0.0594363 + 0.212319i
\(99\) 0 0
\(100\) 135286. + 82184.1i 1.35286 + 0.821841i
\(101\) 34890.0 20143.7i 0.340328 0.196488i −0.320089 0.947387i \(-0.603713\pi\)
0.660417 + 0.750899i \(0.270380\pi\)
\(102\) 0 0
\(103\) 42984.3 + 24817.0i 0.399225 + 0.230492i 0.686149 0.727461i \(-0.259300\pi\)
−0.286925 + 0.957953i \(0.592633\pi\)
\(104\) 14734.7 + 63403.5i 0.133585 + 0.574817i
\(105\) 0 0
\(106\) −18751.0 73237.2i −0.162092 0.633093i
\(107\) −14176.4 −0.119703 −0.0598517 0.998207i \(-0.519063\pi\)
−0.0598517 + 0.998207i \(0.519063\pi\)
\(108\) 0 0
\(109\) 21788.2 0.175653 0.0878264 0.996136i \(-0.472008\pi\)
0.0878264 + 0.996136i \(0.472008\pi\)
\(110\) −70145.0 273971.i −0.552733 2.15885i
\(111\) 0 0
\(112\) −6540.21 + 146514.i −0.0492659 + 1.10365i
\(113\) −129459. 74743.4i −0.953756 0.550651i −0.0595101 0.998228i \(-0.518954\pi\)
−0.894246 + 0.447577i \(0.852287\pi\)
\(114\) 0 0
\(115\) −228602. + 131983.i −1.61189 + 0.930625i
\(116\) −63906.5 + 105199.i −0.440961 + 0.725882i
\(117\) 0 0
\(118\) 60628.2 216577.i 0.400839 1.43188i
\(119\) 77083.6 + 133513.i 0.498993 + 0.864282i
\(120\) 0 0
\(121\) −74299.1 + 128690.i −0.461339 + 0.799062i
\(122\) 1672.94 + 1710.68i 0.0101761 + 0.0104056i
\(123\) 0 0
\(124\) −86679.4 1933.67i −0.506246 0.0112935i
\(125\) 163661.i 0.936853i
\(126\) 0 0
\(127\) 257349.i 1.41584i −0.706293 0.707919i \(-0.749634\pi\)
0.706293 0.707919i \(-0.250366\pi\)
\(128\) 33866.2 + 182244.i 0.182701 + 0.983168i
\(129\) 0 0
\(130\) −130659. + 127777.i −0.678082 + 0.663124i
\(131\) −3161.94 + 5476.65i −0.0160982 + 0.0278828i −0.873962 0.485994i \(-0.838458\pi\)
0.857864 + 0.513877i \(0.171791\pi\)
\(132\) 0 0
\(133\) −24930.4 43180.7i −0.122208 0.211670i
\(134\) −88179.0 24684.7i −0.424232 0.118759i
\(135\) 0 0
\(136\) 133096. + 142313.i 0.617045 + 0.659779i
\(137\) 250464. 144606.i 1.14010 0.658239i 0.193647 0.981071i \(-0.437968\pi\)
0.946456 + 0.322832i \(0.104635\pi\)
\(138\) 0 0
\(139\) −86135.1 49730.1i −0.378132 0.218315i 0.298873 0.954293i \(-0.403389\pi\)
−0.677005 + 0.735978i \(0.736723\pi\)
\(140\) −361096. + 197875.i −1.55705 + 0.853238i
\(141\) 0 0
\(142\) −37827.6 + 9685.05i −0.157430 + 0.0403070i
\(143\) 200099. 0.818285
\(144\) 0 0
\(145\) −345581. −1.36499
\(146\) 60771.2 15559.3i 0.235948 0.0604100i
\(147\) 0 0
\(148\) −55926.3 + 30646.7i −0.209875 + 0.115008i
\(149\) 323359. + 186691.i 1.19322 + 0.688904i 0.959035 0.283289i \(-0.0914255\pi\)
0.234182 + 0.972193i \(0.424759\pi\)
\(150\) 0 0
\(151\) 320356. 184958.i 1.14338 0.660131i 0.196115 0.980581i \(-0.437167\pi\)
0.947266 + 0.320450i \(0.103834\pi\)
\(152\) −43045.8 46027.0i −0.151120 0.161586i
\(153\) 0 0
\(154\) 434148. + 121535.i 1.47515 + 0.412951i
\(155\) −121710. 210807.i −0.406908 0.704785i
\(156\) 0 0
\(157\) 196653. 340613.i 0.636724 1.10284i −0.349423 0.936965i \(-0.613622\pi\)
0.986147 0.165873i \(-0.0530442\pi\)
\(158\) −300331. + 293706.i −0.957100 + 0.935987i
\(159\) 0 0
\(160\) −387932. + 346913.i −1.19800 + 1.07132i
\(161\) 420803.i 1.27942i
\(162\) 0 0
\(163\) 154747.i 0.456198i −0.973638 0.228099i \(-0.926749\pi\)
0.973638 0.228099i \(-0.0732509\pi\)
\(164\) 496196. + 11069.3i 1.44060 + 0.0321374i
\(165\) 0 0
\(166\) 384163. + 392828.i 1.08204 + 1.10645i
\(167\) 98410.6 170452.i 0.273055 0.472946i −0.696587 0.717472i \(-0.745299\pi\)
0.969643 + 0.244526i \(0.0786325\pi\)
\(168\) 0 0
\(169\) 120993. + 209567.i 0.325870 + 0.564424i
\(170\) −147475. + 526811.i −0.391377 + 1.39808i
\(171\) 0 0
\(172\) −239306. + 393931.i −0.616784 + 1.01531i
\(173\) −583484. + 336874.i −1.48222 + 0.855762i −0.999796 0.0201751i \(-0.993578\pi\)
−0.482426 + 0.875937i \(0.660244\pi\)
\(174\) 0 0
\(175\) −613554. 354235.i −1.51446 0.874373i
\(176\) 569249. + 25410.7i 1.38523 + 0.0618350i
\(177\) 0 0
\(178\) −104473. 408046.i −0.247145 0.965293i
\(179\) 583842. 1.36196 0.680978 0.732304i \(-0.261555\pi\)
0.680978 + 0.732304i \(0.261555\pi\)
\(180\) 0 0
\(181\) −623067. −1.41364 −0.706819 0.707395i \(-0.749870\pi\)
−0.706819 + 0.707395i \(0.749870\pi\)
\(182\) −72260.5 282233.i −0.161705 0.631582i
\(183\) 0 0
\(184\) −120392. 518050.i −0.262153 1.12805i
\(185\) −155059. 89523.4i −0.333095 0.192312i
\(186\) 0 0
\(187\) 518737. 299493.i 1.08478 0.626300i
\(188\) 67440.9 + 40969.2i 0.139165 + 0.0845401i
\(189\) 0 0
\(190\) 47696.2 170381.i 0.0958517 0.342403i
\(191\) 92566.8 + 160330.i 0.183600 + 0.318004i 0.943104 0.332499i \(-0.107892\pi\)
−0.759504 + 0.650502i \(0.774558\pi\)
\(192\) 0 0
\(193\) 145169. 251439.i 0.280530 0.485892i −0.690985 0.722869i \(-0.742823\pi\)
0.971515 + 0.236977i \(0.0761565\pi\)
\(194\) −379365. 387923.i −0.723691 0.740015i
\(195\) 0 0
\(196\) 2644.67 118551.i 0.00491735 0.220427i
\(197\) 232595.i 0.427007i −0.976942 0.213504i \(-0.931512\pi\)
0.976942 0.213504i \(-0.0684875\pi\)
\(198\) 0 0
\(199\) 524007.i 0.938004i 0.883197 + 0.469002i \(0.155386\pi\)
−0.883197 + 0.469002i \(0.844614\pi\)
\(200\) −856692. 260560.i −1.51443 0.460609i
\(201\) 0 0
\(202\) −162937. + 159343.i −0.280958 + 0.274760i
\(203\) 275454. 477100.i 0.469147 0.812587i
\(204\) 0 0
\(205\) 696727. + 1.20677e6i 1.15792 + 2.00557i
\(206\) −270378. 75689.3i −0.443919 0.124270i
\(207\) 0 0
\(208\) −169707. 326783.i −0.271983 0.523722i
\(209\) −167770. + 96861.9i −0.265673 + 0.153386i
\(210\) 0 0
\(211\) 389705. + 224996.i 0.602601 + 0.347912i 0.770064 0.637967i \(-0.220224\pi\)
−0.167463 + 0.985878i \(0.553558\pi\)
\(212\) 205515. + 375038.i 0.314053 + 0.573106i
\(213\) 0 0
\(214\) 77688.0 19890.5i 0.115963 0.0296901i
\(215\) −1.29407e6 −1.90925
\(216\) 0 0
\(217\) 388047. 0.559416
\(218\) −119401. + 30570.4i −0.170164 + 0.0435673i
\(219\) 0 0
\(220\) 768802. + 1.40296e6i 1.07092 + 1.95429i
\(221\) −335214. 193536.i −0.461680 0.266551i
\(222\) 0 0
\(223\) −33442.0 + 19307.7i −0.0450329 + 0.0259998i −0.522347 0.852733i \(-0.674944\pi\)
0.477315 + 0.878733i \(0.341610\pi\)
\(224\) −169729. 812085.i −0.226014 1.08139i
\(225\) 0 0
\(226\) 814319. + 227959.i 1.06053 + 0.296884i
\(227\) 447303. + 774752.i 0.576152 + 0.997925i 0.995915 + 0.0902911i \(0.0287798\pi\)
−0.419763 + 0.907634i \(0.637887\pi\)
\(228\) 0 0
\(229\) 714088. 1.23684e6i 0.899836 1.55856i 0.0721321 0.997395i \(-0.477020\pi\)
0.827703 0.561166i \(-0.189647\pi\)
\(230\) 1.06758e6 1.04403e6i 1.33070 1.30134i
\(231\) 0 0
\(232\) 202612. 666165.i 0.247141 0.812572i
\(233\) 379913.i 0.458453i −0.973373 0.229226i \(-0.926380\pi\)
0.973373 0.229226i \(-0.0736196\pi\)
\(234\) 0 0
\(235\) 221545.i 0.261693i
\(236\) −28374.6 + 1.27193e6i −0.0331626 + 1.48656i
\(237\) 0 0
\(238\) −609753. 623508.i −0.697769 0.713509i
\(239\) 379157. 656720.i 0.429363 0.743679i −0.567454 0.823405i \(-0.692071\pi\)
0.996817 + 0.0797266i \(0.0254047\pi\)
\(240\) 0 0
\(241\) −595565. 1.03155e6i −0.660520 1.14405i −0.980479 0.196623i \(-0.937002\pi\)
0.319959 0.947432i \(-0.396331\pi\)
\(242\) 226604. 809479.i 0.248731 0.888520i
\(243\) 0 0
\(244\) −11568.1 7027.40i −0.0124390 0.00755649i
\(245\) 288320. 166461.i 0.306873 0.177173i
\(246\) 0 0
\(247\) 108415. + 62593.3i 0.113070 + 0.0652808i
\(248\) 477724. 111021.i 0.493228 0.114624i
\(249\) 0 0
\(250\) −229629. 896880.i −0.232368 0.907578i
\(251\) 705353. 0.706679 0.353340 0.935495i \(-0.385046\pi\)
0.353340 + 0.935495i \(0.385046\pi\)
\(252\) 0 0
\(253\) −1.63495e6 −1.60584
\(254\) 361080. + 1.41030e6i 0.351172 + 1.37160i
\(255\) 0 0
\(256\) −441291. 951196.i −0.420848 0.907131i
\(257\) 1.11396e6 + 643145.i 1.05205 + 0.607402i 0.923223 0.384265i \(-0.125545\pi\)
0.128828 + 0.991667i \(0.458878\pi\)
\(258\) 0 0
\(259\) 247188. 142714.i 0.228969 0.132196i
\(260\) 536745. 883555.i 0.492418 0.810588i
\(261\) 0 0
\(262\) 9643.59 34449.0i 0.00867932 0.0310044i
\(263\) −812371. 1.40707e6i −0.724211 1.25437i −0.959298 0.282396i \(-0.908871\pi\)
0.235087 0.971974i \(1.57554\pi\)
\(264\) 0 0
\(265\) −600338. + 1.03982e6i −0.525147 + 0.909581i
\(266\) 197206. + 201655.i 0.170890 + 0.174745i
\(267\) 0 0
\(268\) 517863. + 11552.7i 0.440431 + 0.00982530i
\(269\) 1.30693e6i 1.10121i 0.834766 + 0.550605i \(0.185603\pi\)
−0.834766 + 0.550605i \(0.814397\pi\)
\(270\) 0 0
\(271\) 109448.i 0.0905280i 0.998975 + 0.0452640i \(0.0144129\pi\)
−0.998975 + 0.0452640i \(0.985587\pi\)
\(272\) −929052. 593147.i −0.761409 0.486116i
\(273\) 0 0
\(274\) −1.16967e6 + 1.14387e6i −0.941214 + 0.920451i
\(275\) −1.37631e6 + 2.38384e6i −1.09745 + 1.90084i
\(276\) 0 0
\(277\) 377853. + 654461.i 0.295885 + 0.512488i 0.975190 0.221368i \(-0.0710520\pi\)
−0.679305 + 0.733856i \(0.737719\pi\)
\(278\) 541803. + 151672.i 0.420465 + 0.117704i
\(279\) 0 0
\(280\) 1.70120e6 1.59102e6i 1.29677 1.21277i
\(281\) 133655. 77165.9i 0.100977 0.0582988i −0.448661 0.893702i \(-0.648099\pi\)
0.549638 + 0.835403i \(0.314766\pi\)
\(282\) 0 0
\(283\) 921332. + 531931.i 0.683833 + 0.394811i 0.801298 0.598266i \(-0.204143\pi\)
−0.117465 + 0.993077i \(0.537477\pi\)
\(284\) 193710. 106150.i 0.142513 0.0780951i
\(285\) 0 0
\(286\) −1.09656e6 + 280754.i −0.792716 + 0.202960i
\(287\) −2.22137e6 −1.59190
\(288\) 0 0
\(289\) 261179. 0.183947
\(290\) 1.89381e6 484876.i 1.32234 0.338560i
\(291\) 0 0
\(292\) −311201. + 170533.i −0.213591 + 0.117045i
\(293\) 519996. + 300220.i 0.353860 + 0.204301i 0.666384 0.745609i \(-0.267841\pi\)
−0.312524 + 0.949910i \(0.601175\pi\)
\(294\) 0 0
\(295\) −3.09337e6 + 1.78596e6i −2.06955 + 1.19486i
\(296\) 263481. 246415.i 0.174792 0.163470i
\(297\) 0 0
\(298\) −2.03398e6 569389.i −1.32680 0.371423i
\(299\) 528261. + 914974.i 0.341720 + 0.591876i
\(300\) 0 0
\(301\) 1.03147e6 1.78657e6i 0.656209 1.13659i
\(302\) −1.49607e6 + 1.46307e6i −0.943920 + 0.923097i
\(303\) 0 0
\(304\) 300474. + 191836.i 0.186476 + 0.119054i
\(305\) 38001.3i 0.0233910i
\(306\) 0 0
\(307\) 2.78186e6i 1.68457i 0.539031 + 0.842286i \(0.318791\pi\)
−0.539031 + 0.842286i \(0.681209\pi\)
\(308\) −2.54969e6 56879.4i −1.53148 0.0341647i
\(309\) 0 0
\(310\) 962758. + 984475.i 0.569001 + 0.581836i
\(311\) −1.14667e6 + 1.98609e6i −0.672262 + 1.16439i 0.304999 + 0.952353i \(0.401344\pi\)
−0.977261 + 0.212039i \(0.931990\pi\)
\(312\) 0 0
\(313\) 1.41302e6 + 2.44742e6i 0.815244 + 1.41204i 0.909153 + 0.416463i \(0.136730\pi\)
−0.0939092 + 0.995581i \(0.529936\pi\)
\(314\) −599770. + 2.14251e6i −0.343290 + 1.22630i
\(315\) 0 0
\(316\) 1.23375e6 2.03092e6i 0.695039 1.14413i
\(317\) 185665. 107194.i 0.103773 0.0599132i −0.447215 0.894426i \(-0.647584\pi\)
0.550988 + 0.834513i \(0.314251\pi\)
\(318\) 0 0
\(319\) −1.85368e6 1.07022e6i −1.01990 0.588839i
\(320\) 1.63916e6 2.44541e6i 0.894840 1.33499i
\(321\) 0 0
\(322\) 590418. + 2.30604e6i 0.317337 + 1.23944i
\(323\) 374739. 0.199859
\(324\) 0 0
\(325\) 1.77878e6 0.934142
\(326\) 217121. + 848027.i 0.113151 + 0.441943i
\(327\) 0 0
\(328\) −2.73473e6 + 635539.i −1.40356 + 0.326180i
\(329\) −305860. 176588.i −0.155787 0.0899439i
\(330\) 0 0
\(331\) 352745. 203658.i 0.176967 0.102172i −0.408900 0.912579i \(-0.634088\pi\)
0.585867 + 0.810407i \(0.300754\pi\)
\(332\) −2.65641e6 1.61372e6i −1.32267 0.803497i
\(333\) 0 0
\(334\) −300142. + 1.07217e6i −0.147218 + 0.525893i
\(335\) 727151. + 1.25946e6i 0.354008 + 0.613159i
\(336\) 0 0
\(337\) −1.44822e6 + 2.50838e6i −0.694638 + 1.20315i 0.275664 + 0.961254i \(0.411102\pi\)
−0.970302 + 0.241895i \(0.922231\pi\)
\(338\) −957092. 978681.i −0.455682 0.465961i
\(339\) 0 0
\(340\) 69019.5 3.09389e6i 0.0323798 1.45147i
\(341\) 1.50768e6i 0.702139i
\(342\) 0 0
\(343\) 1.87641e6i 0.861176i
\(344\) 758706. 2.49454e6i 0.345683 1.13657i
\(345\) 0 0
\(346\) 2.72488e6 2.66477e6i 1.22365 1.19666i
\(347\) 1.79724e6 3.11291e6i 0.801275 1.38785i −0.117502 0.993073i \(-0.537488\pi\)
0.918777 0.394777i \(-0.129178\pi\)
\(348\) 0 0
\(349\) −956981. 1.65754e6i −0.420571 0.728451i 0.575424 0.817855i \(-0.304837\pi\)
−0.995995 + 0.0894044i \(0.971504\pi\)
\(350\) 3.85935e6 + 1.08038e6i 1.68401 + 0.471418i
\(351\) 0 0
\(352\) −3.15519e6 + 659447.i −1.35728 + 0.283676i
\(353\) −2.21063e6 + 1.27631e6i −0.944232 + 0.545152i −0.891284 0.453445i \(-0.850195\pi\)
−0.0529474 + 0.998597i \(0.516862\pi\)
\(354\) 0 0
\(355\) 537073. + 310079.i 0.226184 + 0.130587i
\(356\) 1.14504e6 + 2.08955e6i 0.478845 + 0.873830i
\(357\) 0 0
\(358\) −3.19951e6 + 819174.i −1.31940 + 0.337807i
\(359\) −2.70497e6 −1.10771 −0.553856 0.832612i \(-0.686844\pi\)
−0.553856 + 0.832612i \(0.686844\pi\)
\(360\) 0 0
\(361\) 2.35490e6 0.951053
\(362\) 3.41446e6 874209.i 1.36946 0.350626i
\(363\) 0 0
\(364\) 791989. + 1.44528e6i 0.313304 + 0.571739i
\(365\) −862824. 498151.i −0.338992 0.195717i
\(366\) 0 0
\(367\) 3.78493e6 2.18523e6i 1.46687 0.846900i 0.467561 0.883961i \(-0.345133\pi\)
0.999313 + 0.0370602i \(0.0117993\pi\)
\(368\) 1.38662e6 + 2.67004e6i 0.533751 + 1.02778i
\(369\) 0 0
\(370\) 975346. + 273037.i 0.370386 + 0.103685i
\(371\) −957029. 1.65762e6i −0.360986 0.625246i
\(372\) 0 0
\(373\) −1.08643e6 + 1.88176e6i −0.404325 + 0.700312i −0.994243 0.107152i \(-0.965827\pi\)
0.589917 + 0.807464i \(0.299160\pi\)
\(374\) −2.42251e6 + 2.36907e6i −0.895544 + 0.875789i
\(375\) 0 0
\(376\) −427065. 129890.i −0.155785 0.0473813i
\(377\) 1.38318e6i 0.501216i
\(378\) 0 0
\(379\) 872712.i 0.312085i −0.987750 0.156043i \(-0.950126\pi\)
0.987750 0.156043i \(-0.0498737\pi\)
\(380\) −22322.3 + 1.00062e6i −0.00793011 + 0.355477i
\(381\) 0 0
\(382\) −732230. 748747.i −0.256737 0.262529i
\(383\) 817267. 1.41555e6i 0.284687 0.493092i −0.687846 0.725856i \(-0.741444\pi\)
0.972533 + 0.232764i \(0.0747771\pi\)
\(384\) 0 0
\(385\) −3.58011e6 6.20094e6i −1.23096 2.13209i
\(386\) −442748. + 1.58159e6i −0.151248 + 0.540289i
\(387\) 0 0
\(388\) 2.62324e6 + 1.59357e6i 0.884624 + 0.537394i
\(389\) 89924.7 51918.0i 0.0301304 0.0173958i −0.484859 0.874592i \(-0.661129\pi\)
0.514990 + 0.857196i \(0.327796\pi\)
\(390\) 0 0
\(391\) 2.73893e6 + 1.58132e6i 0.906021 + 0.523092i
\(392\) 151842. + 653379.i 0.0499089 + 0.214758i
\(393\) 0 0
\(394\) 326348. + 1.27464e6i 0.105911 + 0.413664i
\(395\) 6.67162e6 2.15149
\(396\) 0 0
\(397\) −3.33523e6 −1.06206 −0.531031 0.847352i \(-0.678195\pi\)
−0.531031 + 0.847352i \(0.678195\pi\)
\(398\) −735221. 2.87161e6i −0.232654 0.908693i
\(399\) 0 0
\(400\) 5.06033e6 + 225888.i 1.58135 + 0.0705899i
\(401\) −144161. 83231.6i −0.0447701 0.0258480i 0.477448 0.878660i \(-0.341562\pi\)
−0.522218 + 0.852812i \(0.674895\pi\)
\(402\) 0 0
\(403\) −843751. + 487140.i −0.258793 + 0.149414i
\(404\) 669340. 1.10183e6i 0.204030 0.335861i
\(405\) 0 0
\(406\) −840105. + 3.00104e6i −0.252941 + 0.903558i
\(407\) −554486. 960398.i −0.165922 0.287386i
\(408\) 0 0
\(409\) 2.56963e6 4.45073e6i 0.759560 1.31560i −0.183515 0.983017i \(-0.558748\pi\)
0.943075 0.332580i \(-0.107919\pi\)
\(410\) −5.51131e6 5.63563e6i −1.61918 1.65570i
\(411\) 0 0
\(412\) 1.58789e6 + 35423.3i 0.460870 + 0.0102812i
\(413\) 5.69417e6i 1.64269i
\(414\) 0 0
\(415\) 8.72638e6i 2.48722i
\(416\) 1.38851e6 + 1.55269e6i 0.393383 + 0.439897i
\(417\) 0 0
\(418\) 783488. 766205.i 0.219327 0.214489i
\(419\) 1.65720e6 2.87035e6i 0.461146 0.798729i −0.537872 0.843027i \(-0.680772\pi\)
0.999018 + 0.0442975i \(0.0141050\pi\)
\(420\) 0 0
\(421\) 1.80550e6 + 3.12721e6i 0.496468 + 0.859908i 0.999992 0.00407351i \(-0.00129664\pi\)
−0.503524 + 0.863981i \(0.667963\pi\)
\(422\) −2.45130e6 686214.i −0.670064 0.187577i
\(423\) 0 0
\(424\) −1.65244e6 1.76689e6i −0.446388 0.477303i
\(425\) 4.61130e6 2.66234e6i 1.23837 0.714974i
\(426\) 0 0
\(427\) 52463.7 + 30289.9i 0.0139248 + 0.00803950i
\(428\) −397829. + 218004.i −0.104975 + 0.0575248i
\(429\) 0 0
\(430\) 7.09164e6 1.81568e6i 1.84959 0.473553i
\(431\) 7.53077e6 1.95275 0.976374 0.216090i \(-0.0693303\pi\)
0.976374 + 0.216090i \(0.0693303\pi\)
\(432\) 0 0
\(433\) 2.24585e6 0.575653 0.287827 0.957683i \(-0.407067\pi\)
0.287827 + 0.957683i \(0.407067\pi\)
\(434\) −2.12653e6 + 544459.i −0.541936 + 0.138753i
\(435\) 0 0
\(436\) 611437. 335058.i 0.154041 0.0844118i
\(437\) −885823. 511430.i −0.221893 0.128110i
\(438\) 0 0
\(439\) 925006. 534052.i 0.229078 0.132258i −0.381069 0.924547i \(-0.624444\pi\)
0.610147 + 0.792289i \(0.291111\pi\)
\(440\) −6.18157e6 6.60968e6i −1.52218 1.62760i
\(441\) 0 0
\(442\) 2.10855e6 + 590263.i 0.513367 + 0.143711i
\(443\) 149436. + 258831.i 0.0361781 + 0.0626623i 0.883548 0.468342i \(-0.155148\pi\)
−0.847369 + 0.531004i \(0.821815\pi\)
\(444\) 0 0
\(445\) −3.34482e6 + 5.79340e6i −0.800705 + 1.38686i
\(446\) 156175. 152730.i 0.0371770 0.0363569i
\(447\) 0 0
\(448\) 2.06954e6 + 4.21216e6i 0.487169 + 0.991538i
\(449\) 8.39456e6i 1.96509i 0.186028 + 0.982544i \(0.440439\pi\)
−0.186028 + 0.982544i \(0.559561\pi\)
\(450\) 0 0
\(451\) 8.63070e6i 1.99804i
\(452\) −4.78239e6 106687.i −1.10103 0.0245621i
\(453\) 0 0
\(454\) −3.53829e6 3.61811e6i −0.805665 0.823838i
\(455\) −2.31351e6 + 4.00712e6i −0.523894 + 0.907411i
\(456\) 0 0
\(457\) −1.98648e6 3.44069e6i −0.444933 0.770646i 0.553115 0.833105i \(-0.313439\pi\)
−0.998048 + 0.0624588i \(0.980106\pi\)
\(458\) −2.17789e6 + 7.77990e6i −0.485146 + 1.73305i
\(459\) 0 0
\(460\) −4.38557e6 + 7.21925e6i −0.966344 + 1.59073i
\(461\) 2.12064e6 1.22435e6i 0.464744 0.268320i −0.249293 0.968428i \(-0.580198\pi\)
0.714037 + 0.700108i \(0.246865\pi\)
\(462\) 0 0
\(463\) −5.77486e6 3.33412e6i −1.25196 0.722817i −0.280459 0.959866i \(-0.590487\pi\)
−0.971498 + 0.237049i \(0.923820\pi\)
\(464\) −175651. + 3.93492e6i −0.0378752 + 0.848479i
\(465\) 0 0
\(466\) 533047. + 2.08196e6i 0.113710 + 0.444127i
\(467\) −3.34371e6 −0.709474 −0.354737 0.934966i \(-0.615430\pi\)
−0.354737 + 0.934966i \(0.615430\pi\)
\(468\) 0 0
\(469\) −2.31838e6 −0.486689
\(470\) −310844. 1.21409e6i −0.0649080 0.253516i
\(471\) 0 0
\(472\) −1.62911e6 7.01008e6i −0.336586 1.44833i
\(473\) −6.94134e6 4.00759e6i −1.42656 0.823626i
\(474\) 0 0
\(475\) −1.49139e6 + 861052.i −0.303288 + 0.175104i
\(476\) 4.21633e6 + 2.56135e6i 0.852938 + 0.518145i
\(477\) 0 0
\(478\) −1.15639e6 + 4.13087e6i −0.231491 + 0.826936i
\(479\) −2.32045e6 4.01914e6i −0.462097 0.800376i 0.536968 0.843603i \(-0.319570\pi\)
−0.999065 + 0.0432268i \(0.986236\pi\)
\(480\) 0 0
\(481\) −358315. + 620620.i −0.0706159 + 0.122310i
\(482\) 4.71109e6 + 4.81735e6i 0.923642 + 0.944476i
\(483\) 0 0
\(484\) −106053. + 4.75396e6i −0.0205783 + 0.922448i
\(485\) 8.61740e6i 1.66350i
\(486\) 0 0
\(487\) 4.91616e6i 0.939299i −0.882853 0.469650i \(-0.844380\pi\)
0.882853 0.469650i \(-0.155620\pi\)
\(488\) 73253.9 + 22279.9i 0.0139246 + 0.00423510i
\(489\) 0 0
\(490\) −1.34646e6 + 1.31676e6i −0.253340 + 0.247751i
\(491\) 346602. 600332.i 0.0648824 0.112380i −0.831759 0.555136i \(-0.812666\pi\)
0.896642 + 0.442757i \(0.145999\pi\)
\(492\) 0 0
\(493\) 2.07024e6 + 3.58575e6i 0.383621 + 0.664451i
\(494\) −681946. 190903.i −0.125728 0.0351961i
\(495\) 0 0
\(496\) −2.46220e6 + 1.27869e6i −0.449385 + 0.233378i
\(497\) −856175. + 494313.i −0.155479 + 0.0897658i
\(498\) 0 0
\(499\) 400079. + 230986.i 0.0719274 + 0.0415273i 0.535532 0.844515i \(-0.320111\pi\)
−0.463605 + 0.886042i \(0.653444\pi\)
\(500\) 2.51678e6 + 4.59279e6i 0.450215 + 0.821584i
\(501\) 0 0
\(502\) −3.86540e6 + 989663.i −0.684597 + 0.175278i
\(503\) −3.22518e6 −0.568373 −0.284187 0.958769i \(-0.591724\pi\)
−0.284187 + 0.958769i \(0.591724\pi\)
\(504\) 0 0
\(505\) 3.61952e6 0.631572
\(506\) 8.95965e6 2.29395e6i 1.55566 0.398298i
\(507\) 0 0
\(508\) −3.95750e6 7.22193e6i −0.680396 1.24164i
\(509\) 213328. + 123165.i 0.0364967 + 0.0210714i 0.518137 0.855297i \(-0.326626\pi\)
−0.481641 + 0.876369i \(0.659959\pi\)
\(510\) 0 0
\(511\) 1.37547e6 794129.i 0.233023 0.134536i
\(512\) 3.75291e6 + 4.59347e6i 0.632694 + 0.774402i
\(513\) 0 0
\(514\) −7.00698e6 1.96152e6i −1.16983 0.327481i
\(515\) 2.22962e6 + 3.86181e6i 0.370436 + 0.641613i
\(516\) 0 0
\(517\) −686097. + 1.18836e6i −0.112891 + 0.195533i
\(518\) −1.15437e6 + 1.12891e6i −0.189026 + 0.184856i
\(519\) 0 0
\(520\) −1.70171e6 + 5.59505e6i −0.275981 + 0.907394i
\(521\) 5.09612e6i 0.822519i −0.911518 0.411259i \(-0.865089\pi\)
0.911518 0.411259i \(-0.134911\pi\)
\(522\) 0 0
\(523\) 5.13482e6i 0.820863i −0.911891 0.410432i \(-0.865378\pi\)
0.911891 0.410432i \(-0.134622\pi\)
\(524\) −4513.29 + 202314.i −0.000718068 + 0.0321883i
\(525\) 0 0
\(526\) 6.42609e6 + 6.57104e6i 1.01270 + 1.03555i
\(527\) −1.45823e6 + 2.52572e6i −0.228717 + 0.396150i
\(528\) 0 0
\(529\) −1.09808e6 1.90193e6i −0.170606 0.295498i
\(530\) 1.83097e6 6.54060e6i 0.283133 1.01141i
\(531\) 0 0
\(532\) −1.36364e6 828391.i −0.208892 0.126898i
\(533\) 4.83005e6 2.78863e6i 0.736434 0.425180i
\(534\) 0 0
\(535\) −1.10301e6 636821.i −0.166607 0.0961906i
\(536\) −2.85415e6 + 663291.i −0.429106 + 0.0997223i
\(537\) 0 0
\(538\) −1.83372e6 7.16207e6i −0.273134 1.06680i
\(539\) 2.06204e6 0.305721
\(540\) 0 0
\(541\) 1.10092e7 1.61720 0.808601 0.588357i \(-0.200225\pi\)
0.808601 + 0.588357i \(0.200225\pi\)
\(542\) −153563. 599783.i −0.0224537 0.0876992i
\(543\) 0 0
\(544\) 5.92352e6 + 1.94697e6i 0.858188 + 0.282073i
\(545\) 1.69525e6 + 978751.i 0.244479 + 0.141150i
\(546\) 0 0
\(547\) −3.43955e6 + 1.98583e6i −0.491511 + 0.283774i −0.725201 0.688537i \(-0.758253\pi\)
0.233690 + 0.972311i \(0.424920\pi\)
\(548\) 4.80498e6 7.90966e6i 0.683503 1.12514i
\(549\) 0 0
\(550\) 4.19760e6 1.49947e7i 0.591690 2.11364i
\(551\) −669555. 1.15970e6i −0.0939523 0.162730i
\(552\) 0 0
\(553\) −5.31779e6 + 9.21068e6i −0.739466 + 1.28079i
\(554\) −2.98893e6 3.05635e6i −0.413752 0.423086i
\(555\) 0 0
\(556\) −3.18194e6 70983.8i −0.436521 0.00973805i
\(557\) 9.38422e6i 1.28162i −0.767698 0.640812i \(-0.778598\pi\)
0.767698 0.640812i \(-0.221402\pi\)
\(558\) 0 0
\(559\) 5.17950e6i 0.701065i
\(560\) −7.09044e6 + 1.11058e7i −0.955439 + 1.49651i
\(561\) 0 0
\(562\) −624174. + 610405.i −0.0833613 + 0.0815224i
\(563\) −2.54261e6 + 4.40393e6i −0.338072 + 0.585558i −0.984070 0.177781i \(-0.943108\pi\)
0.645998 + 0.763339i \(0.276441\pi\)
\(564\) 0 0
\(565\) −6.71512e6 1.16309e7i −0.884978 1.53283i
\(566\) −5.79532e6 1.62233e6i −0.760390 0.212863i
\(567\) 0 0
\(568\) −912611. + 853500.i −0.118690 + 0.111002i
\(569\) −7.59213e6 + 4.38332e6i −0.983067 + 0.567574i −0.903195 0.429231i \(-0.858785\pi\)
−0.0798721 + 0.996805i \(0.525451\pi\)
\(570\) 0 0
\(571\) 1.07595e7 + 6.21203e6i 1.38103 + 0.797339i 0.992282 0.124004i \(-0.0395735\pi\)
0.388750 + 0.921343i \(0.372907\pi\)
\(572\) 5.61533e6 3.07711e6i 0.717605 0.393236i
\(573\) 0 0
\(574\) 1.21733e7 3.11675e6i 1.54216 0.394842i
\(575\) −1.45338e7 −1.83320
\(576\) 0 0
\(577\) 9.43597e6 1.17990 0.589952 0.807438i \(-0.299146\pi\)
0.589952 + 0.807438i \(0.299146\pi\)
\(578\) −1.43128e6 + 366453.i −0.178199 + 0.0456246i
\(579\) 0 0
\(580\) −9.69795e6 + 5.31432e6i −1.19704 + 0.655961i
\(581\) 1.20474e7 + 6.95558e6i 1.48065 + 0.854856i
\(582\) 0 0
\(583\) −6.44036e6 + 3.71834e6i −0.784763 + 0.453083i
\(584\) 1.46614e6 1.37117e6i 0.177886 0.166364i
\(585\) 0 0
\(586\) −3.27086e6 915639.i −0.393475 0.110149i
\(587\) 6.76932e6 + 1.17248e7i 0.810868 + 1.40446i 0.912258 + 0.409617i \(0.134338\pi\)
−0.101390 + 0.994847i \(0.532329\pi\)
\(588\) 0 0
\(589\) 471619. 816869.i 0.0560149 0.0970206i
\(590\) 1.44461e7 1.41274e7i 1.70852 1.67083i
\(591\) 0 0
\(592\) −1.09816e6 + 1.72006e6i −0.128784 + 0.201716i
\(593\) 1.76321e6i 0.205905i −0.994686 0.102952i \(-0.967171\pi\)
0.994686 0.102952i \(-0.0328289\pi\)
\(594\) 0 0
\(595\) 1.38508e7i 1.60391i
\(596\) 1.19453e7 + 266479.i 1.37746 + 0.0307290i
\(597\) 0 0
\(598\) −4.17869e6 4.27295e6i −0.477845 0.488624i
\(599\) −3.59905e6 + 6.23374e6i −0.409846 + 0.709875i −0.994872 0.101140i \(-0.967751\pi\)
0.585026 + 0.811015i \(0.301084\pi\)
\(600\) 0 0
\(601\) 1.35517e6 + 2.34722e6i 0.153041 + 0.265075i 0.932344 0.361573i \(-0.117760\pi\)
−0.779303 + 0.626647i \(0.784427\pi\)
\(602\) −3.14589e6 + 1.12378e7i −0.353795 + 1.26383i
\(603\) 0 0
\(604\) 6.14581e6 1.01168e7i 0.685467 1.12837i
\(605\) −1.15618e7 + 6.67521e6i −1.28421 + 0.741440i
\(606\) 0 0
\(607\) −1.91340e6 1.10470e6i −0.210782 0.121695i 0.390893 0.920436i \(-0.372166\pi\)
−0.601675 + 0.798741i \(0.705500\pi\)
\(608\) −1.91578e6 629689.i −0.210178 0.0690823i
\(609\) 0 0
\(610\) 53318.7 + 208251.i 0.00580170 + 0.0226601i
\(611\) 886728. 0.0960921
\(612\) 0 0
\(613\) −4.95842e6 −0.532957 −0.266478 0.963841i \(-0.585860\pi\)
−0.266478 + 0.963841i \(0.585860\pi\)
\(614\) −3.90316e6 1.52449e7i −0.417826 1.63193i
\(615\) 0 0
\(616\) 1.40523e7 3.26570e6i 1.49210 0.346757i
\(617\) 6.51356e6 + 3.76060e6i 0.688819 + 0.397690i 0.803170 0.595750i \(-0.203145\pi\)
−0.114350 + 0.993440i \(0.536479\pi\)
\(618\) 0 0
\(619\) −3.79004e6 + 2.18818e6i −0.397573 + 0.229539i −0.685436 0.728133i \(-0.740388\pi\)
0.287863 + 0.957671i \(0.407055\pi\)
\(620\) −6.65729e6 4.04419e6i −0.695534 0.422525i
\(621\) 0 0
\(622\) 3.49723e6 1.24928e7i 0.362450 1.29475i
\(623\) −5.33215e6 9.23555e6i −0.550405 0.953329i
\(624\) 0 0
\(625\) 377275. 653459.i 0.0386329 0.0669142i
\(626\) −1.11774e7 1.14295e7i −1.14000 1.16571i
\(627\) 0 0
\(628\) 280698. 1.25827e7i 0.0284014 1.27313i
\(629\) 2.14520e6i 0.216192i
\(630\) 0 0
\(631\) 2.79597e6i 0.279549i 0.990183 + 0.139775i \(0.0446378\pi\)
−0.990183 + 0.139775i \(0.955362\pi\)
\(632\) −3.91152e6 + 1.28607e7i −0.389541 + 1.28077i
\(633\) 0 0
\(634\) −867062. + 847935.i −0.0856697 + 0.0837798i
\(635\) 1.15604e7 2.00233e7i 1.13773 1.97061i
\(636\) 0 0
\(637\) −666257. 1.15399e6i −0.0650569 0.112682i
\(638\) 1.16599e7 + 3.26406e6i 1.13408 + 0.317473i
\(639\) 0 0
\(640\) −5.55163e6 + 1.57009e7i −0.535760 + 1.51522i
\(641\) 4.59173e6 2.65104e6i 0.441399 0.254842i −0.262792 0.964853i \(-0.584643\pi\)
0.704191 + 0.710011i \(0.251310\pi\)
\(642\) 0 0
\(643\) 1.45248e7 + 8.38588e6i 1.38542 + 0.799873i 0.992795 0.119825i \(-0.0382334\pi\)
0.392626 + 0.919698i \(0.371567\pi\)
\(644\) −6.47109e6 1.18089e7i −0.614841 1.12201i
\(645\) 0 0
\(646\) −2.05361e6 + 525787.i −0.193614 + 0.0495711i
\(647\) −8.06422e6 −0.757359 −0.378679 0.925528i \(-0.623622\pi\)
−0.378679 + 0.925528i \(0.623622\pi\)
\(648\) 0 0
\(649\) −2.21235e7 −2.06178
\(650\) −9.74785e6 + 2.49575e6i −0.904952 + 0.231696i
\(651\) 0 0
\(652\) −2.37969e6 4.34263e6i −0.219231 0.400068i
\(653\) 620058. + 357991.i 0.0569049 + 0.0328540i 0.528183 0.849131i \(-0.322874\pi\)
−0.471278 + 0.881985i \(0.656207\pi\)
\(654\) 0 0
\(655\) −492035. + 284077.i −0.0448118 + 0.0258721i
\(656\) 1.40948e7 7.31984e6i 1.27879 0.664113i
\(657\) 0 0
\(658\) 1.92390e6 + 538575.i 0.173228 + 0.0484933i
\(659\) −15687.4 27171.4i −0.00140714 0.00243724i 0.865321 0.501218i \(-0.167115\pi\)
−0.866728 + 0.498781i \(0.833781\pi\)
\(660\) 0 0
\(661\) 4.41600e6 7.64875e6i 0.393121 0.680905i −0.599739 0.800196i \(-0.704729\pi\)
0.992859 + 0.119291i \(0.0380621\pi\)
\(662\) −1.64733e6 + 1.61099e6i −0.146095 + 0.142872i
\(663\) 0 0
\(664\) 1.68216e7 + 5.11621e6i 1.48063 + 0.450327i
\(665\) 4.47961e6i 0.392813i
\(666\) 0 0
\(667\) 1.13015e7i 0.983608i
\(668\) 140469. 6.29671e6i 0.0121798 0.545975i
\(669\) 0 0
\(670\) −5.75197e6 5.88172e6i −0.495028 0.506194i
\(671\) 117685. 203837.i 0.0100906 0.0174774i
\(672\) 0 0
\(673\) 3.33892e6 + 5.78318e6i 0.284163 + 0.492186i 0.972406 0.233295i \(-0.0749508\pi\)
−0.688242 + 0.725481i \(0.741617\pi\)
\(674\) 4.41691e6 1.57781e7i 0.374514 1.33784i
\(675\) 0 0
\(676\) 6.61811e6 + 4.02039e6i 0.557016 + 0.338377i
\(677\) −1.26099e7 + 7.28033e6i −1.05740 + 0.610491i −0.924712 0.380667i \(-0.875694\pi\)
−0.132689 + 0.991158i \(0.542361\pi\)
\(678\) 0 0
\(679\) −1.18970e7 6.86872e6i −0.990289 0.571744i
\(680\) 3.96272e6 + 1.70516e7i 0.328641 + 1.41414i
\(681\) 0 0
\(682\) 2.11539e6 + 8.26221e6i 0.174152 + 0.680198i
\(683\) 5.63380e6 0.462114 0.231057 0.972940i \(-0.425782\pi\)
0.231057 + 0.972940i \(0.425782\pi\)
\(684\) 0 0
\(685\) 2.59834e7 2.11578
\(686\) 2.63274e6 + 1.02829e7i 0.213598 + 0.834266i
\(687\) 0 0
\(688\) −657747. + 1.47348e7i −0.0529771 + 1.18679i
\(689\) 4.16183e6 + 2.40284e6i 0.333993 + 0.192831i
\(690\) 0 0
\(691\) 9.00873e6 5.20119e6i 0.717742 0.414389i −0.0961788 0.995364i \(-0.530662\pi\)
0.813921 + 0.580975i \(0.197329\pi\)
\(692\) −1.11937e7 + 1.84264e7i −0.888606 + 1.46277i
\(693\) 0 0
\(694\) −5.48138e6 + 1.95807e7i −0.432008 + 1.54322i
\(695\) −4.46787e6 7.73858e6i −0.350864 0.607714i
\(696\) 0 0
\(697\) 8.34762e6 1.44585e7i 0.650850 1.12730i
\(698\) 7.56999e6 + 7.74075e6i 0.588108 + 0.601374i
\(699\) 0 0
\(700\) −2.26654e7 505628.i −1.74831 0.0390019i
\(701\) 1.19679e7i 0.919862i −0.887955 0.459931i \(-0.847874\pi\)
0.887955 0.459931i \(-0.152126\pi\)
\(702\) 0 0
\(703\) 693798.i 0.0529474i
\(704\) 1.63655e7 8.04079e6i 1.24451 0.611459i
\(705\) 0 0
\(706\) 1.03237e7 1.00959e7i 0.779512 0.762316i
\(707\) −2.88503e6 + 4.99702e6i −0.217071 + 0.375978i
\(708\) 0 0
\(709\) −3.72698e6 6.45531e6i −0.278446 0.482283i 0.692553 0.721367i \(-0.256486\pi\)
−0.970999 + 0.239084i \(0.923153\pi\)
\(710\) −3.37827e6 945708.i −0.251506 0.0704062i
\(711\) 0 0
\(712\) −9.20670e6 9.84433e6i −0.680619 0.727757i
\(713\) 6.89402e6 3.98027e6i 0.507866 0.293216i
\(714\) 0 0
\(715\) 1.55689e7 + 8.98868e6i 1.13892 + 0.657553i
\(716\) 1.63842e7 8.97830e6i 1.19438 0.654503i
\(717\) 0 0
\(718\) 1.48235e7 3.79528e6i 1.07310 0.274747i
\(719\) −1.53936e7 −1.11050 −0.555248 0.831685i \(-0.687377\pi\)
−0.555248 + 0.831685i \(0.687377\pi\)
\(720\) 0 0
\(721\) −7.10870e6 −0.509275
\(722\) −1.29051e7 + 3.30410e6i −0.921334 + 0.235890i
\(723\) 0 0
\(724\) −1.74850e7 + 9.58149e6i −1.23971 + 0.679339i
\(725\) −1.64782e7 9.51371e6i −1.16430 0.672210i
\(726\) 0 0
\(727\) 7.42385e6 4.28616e6i 0.520946 0.300768i −0.216375 0.976310i \(-0.569424\pi\)
0.737322 + 0.675542i \(0.236090\pi\)
\(728\) −6.36800e6 6.80903e6i −0.445322 0.476164i
\(729\) 0 0
\(730\) 5.42729e6 + 1.51931e6i 0.376943 + 0.105521i
\(731\) 7.75228e6 + 1.34273e7i 0.536582 + 0.929387i
\(732\) 0 0
\(733\) −8.79172e6 + 1.52277e7i −0.604386 + 1.04683i 0.387763 + 0.921759i \(0.373248\pi\)
−0.992148 + 0.125067i \(0.960085\pi\)
\(734\) −1.76757e7 + 1.72858e7i −1.21098 + 1.18427i
\(735\) 0 0
\(736\) −1.13451e7 1.26865e7i −0.771993 0.863272i
\(737\) 9.00758e6i 0.610857i
\(738\) 0 0
\(739\) 186950.i 0.0125926i 0.999980 + 0.00629629i \(0.00200418\pi\)
−0.999980 + 0.00629629i \(0.997996\pi\)
\(740\) −5.72807e6 127784.i −0.384529 0.00857821i
\(741\) 0 0
\(742\) 7.57037e6 + 7.74114e6i 0.504786 + 0.516173i
\(743\) −3.19316e6 + 5.53072e6i −0.212202 + 0.367544i −0.952403 0.304841i \(-0.901397\pi\)
0.740202 + 0.672385i \(0.234730\pi\)
\(744\) 0 0
\(745\) 1.67728e7 + 2.90513e7i 1.10717 + 1.91768i
\(746\) 3.31351e6 1.18365e7i 0.217992 0.778714i
\(747\) 0 0
\(748\) 9.95160e6 1.63817e7i 0.650338 1.07055i
\(749\) 1.75836e6 1.01519e6i 0.114526 0.0661214i
\(750\) 0 0
\(751\) −2.55553e7 1.47544e7i −1.65341 0.954598i −0.975655 0.219312i \(-0.929619\pi\)
−0.677757 0.735286i \(1.26295\pi\)
\(752\) 2.52260e6 + 112606.i 0.162669 + 0.00726135i
\(753\) 0 0
\(754\) −1.94070e6 7.57994e6i −0.124317 0.485554i
\(755\) 3.32341e7 2.12186
\(756\) 0 0
\(757\) −2.98899e7 −1.89576 −0.947882 0.318621i \(-0.896780\pi\)
−0.947882 + 0.318621i \(0.896780\pi\)
\(758\) 1.22448e6 + 4.78254e6i 0.0774067 + 0.302333i
\(759\) 0 0
\(760\) −1.28162e6 5.51483e6i −0.0804871 0.346336i
\(761\) −1.12672e7 6.50513e6i −0.705269 0.407187i 0.104038 0.994573i \(-0.466824\pi\)
−0.809307 + 0.587386i \(0.800157\pi\)
\(762\) 0 0
\(763\) −2.70248e6 + 1.56028e6i −0.168055 + 0.0970265i
\(764\) 5.06323e6 + 3.07583e6i 0.313830 + 0.190646i
\(765\) 0 0
\(766\) −2.49258e6 + 8.90402e6i −0.153489 + 0.548295i
\(767\) 7.14825e6 + 1.23811e7i 0.438744 + 0.759927i
\(768\) 0 0
\(769\) −1.45635e6 + 2.52248e6i −0.0888077 + 0.153819i −0.907007 0.421115i \(-0.861639\pi\)
0.818200 + 0.574934i \(0.194972\pi\)
\(770\) 2.83197e7 + 2.89585e7i 1.72132 + 1.76015i
\(771\) 0 0
\(772\) 207210. 9.28847e6i 0.0125132 0.560920i
\(773\) 6.84734e6i 0.412167i 0.978534 + 0.206084i \(0.0660719\pi\)
−0.978534 + 0.206084i \(0.933928\pi\)
\(774\) 0 0
\(775\) 1.34025e7i 0.801551i
\(776\)