Properties

Label 108.6.h.a.35.3
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 35.3
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.3

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.48009 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 0.398314 0.917249i \(-0.369595\pi\)
0.993518 + 0.113675i \(0.0362621\pi\)
\(6\) 0 0
\(7\) −124.034 71.6112i −0.956745 0.552377i −0.0615753 0.998102i \(-0.519612\pi\)
−0.895170 + 0.445725i \(0.852946\pi\)
\(8\) −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 −0.277446 0.960741i \(-0.589488\pi\)
0.970749 0.240095i \(-0.0771787\pi\)
\(12\) 0 0
\(13\) 179.796 + 311.416i 0.295068 + 0.511072i 0.975001 0.222202i \(-0.0713245\pi\)
−0.679933 + 0.733274i \(0.737991\pi\)
\(14\) 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 \(0.149174\pi\)
−0.892181 + 0.451678i \(0.850826\pi\)
\(18\) 0 0
\(19\) 348.135i 0.221240i −0.993863 0.110620i \(-0.964716\pi\)
0.993863 0.110620i \(-0.0352837\pi\)
\(20\) 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 −0.995588 0.0938304i \(-0.970089\pi\)
0.416535 0.909120i \(1.63676\pi\)
\(24\) 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 0.0849079 0.996389i \(-0.472940\pi\)
−0.820444 + 0.571727i \(0.806274\pi\)
\(30\) 0 0
\(31\) −2346.41 + 1354.70i −0.438531 + 0.253186i −0.702974 0.711215i \(-0.748145\pi\)
0.264443 + 0.964401i \(0.414812\pi\)
\(32\) −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 0.277215 0.960808i \(-0.410589\pi\)
0.970692 + 0.240329i \(0.0772552\pi\)
\(42\) 0 0
\(43\) −12474.1 7201.91i −1.02882 0.593987i −0.112170 0.993689i \(-0.535780\pi\)
−0.916645 + 0.399702i \(0.869113\pi\)
\(44\) 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 −0.822443 0.568848i \(-0.807389\pi\)
0.903858 + 0.427832i \(0.140723\pi\)
\(48\) 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 \(-0.894044\pi\)
0.945108 0.326757i \(-0.105956\pi\)
\(54\) 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 −0.950909 0.309470i \(-0.899848\pi\)
0.207445 0.978247i \(1.56651\pi\)
\(60\) 0 0
\(61\) −211.489 + 366.310i −0.00727718 + 0.0126044i −0.869641 0.493685i \(-0.835650\pi\)
0.862364 + 0.506289i \(0.168983\pi\)
\(62\) 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 −0.296960 0.954890i \(-0.595973\pi\)
0.678479 + 0.734620i \(0.262639\pi\)
\(68\) −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 0.951147 0.308738i \(-0.0999065\pi\)
0.208199 + 0.978086i \(0.433240\pi\)
\(80\) 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 0.161670 + 0.986845i \(0.448312\pi\)
−0.935468 + 0.353412i \(0.885021\pi\)
\(84\) 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 \(-0.833989\pi\)
0.867054 0.498215i \(-0.166011\pi\)
\(90\) 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 −0.482262 0.876027i \(-0.660185\pi\)
0.999793 0.0203622i \(-0.00648193\pi\)
\(98\) −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 0.660417 0.750899i \(-0.270380\pi\)
−0.320089 + 0.947387i \(0.603713\pi\)
\(102\) 0 0
\(103\) 42984.3 24817.0i 0.399225 0.230492i −0.286925 0.957953i \(-0.592633\pi\)
0.686149 + 0.727461i \(0.259300\pi\)
\(104\) 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 −0.894246 0.447577i \(-0.852287\pi\)
−0.0595101 + 0.998228i \(0.518954\pi\)
\(114\) 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 \(0.250366\pi\)
−0.706293 + 0.707919i \(0.749634\pi\)
\(128\) 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 0.857864 0.513877i \(-0.171791\pi\)
−0.873962 + 0.485994i \(0.838458\pi\)
\(132\) 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 0.946456 0.322832i \(-0.104635\pi\)
0.193647 + 0.981071i \(0.437968\pi\)
\(138\) 0 0
\(139\) −86135.1 + 49730.1i −0.378132 + 0.218315i −0.677005 0.735978i \(-0.736723\pi\)
0.298873 + 0.954293i \(0.403389\pi\)
\(140\) −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 0.234182 0.972193i \(-0.424759\pi\)
0.959035 + 0.283289i \(0.0914255\pi\)
\(150\) 0 0
\(151\) 320356. + 184958.i 1.14338 + 0.660131i 0.947266 0.320450i \(-0.103834\pi\)
0.196115 + 0.980581i \(0.437167\pi\)
\(152\) −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 0.986147 + 0.165873i \(0.0530442\pi\)
−0.349423 + 0.936965i \(0.613622\pi\)
\(158\) −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 \(0.0732509\pi\)
−0.973638 + 0.228099i \(0.926749\pi\)
\(164\) 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 0.969643 0.244526i \(-0.0786325\pi\)
−0.696587 + 0.717472i \(0.745299\pi\)
\(168\) 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 −0.482426 0.875937i \(-0.660244\pi\)
−0.999796 + 0.0201751i \(0.993578\pi\)
\(174\) 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 −0.759504 0.650502i \(-0.774558\pi\)
0.943104 + 0.332499i \(0.107892\pi\)
\(192\) 0 0
\(193\) 145169. + 251439.i 0.280530 + 0.485892i 0.971515 0.236977i \(-0.0761565\pi\)
−0.690985 + 0.722869i \(0.742823\pi\)
\(194\) −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 \(0.0684875\pi\)
−0.976942 + 0.213504i \(0.931512\pi\)
\(198\) 0 0
\(199\) 524007.i 0.938004i −0.883197 0.469002i \(-0.844614\pi\)
0.883197 0.469002i \(-0.155386\pi\)
\(200\) −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 −0.167463 0.985878i \(-0.553558\pi\)
0.770064 + 0.637967i \(0.220224\pi\)
\(212\) 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 0.477315 0.878733i \(-0.341610\pi\)
−0.522347 + 0.852733i \(0.674944\pi\)
\(224\) −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 −0.419763 0.907634i \(-0.637887\pi\)
0.995915 0.0902911i \(-0.0287798\pi\)
\(228\) 0 0
\(229\) 714088. + 1.23684e6i 0.899836 + 1.55856i 0.827703 + 0.561166i \(0.189647\pi\)
0.0721321 + 0.997395i \(0.477020\pi\)
\(230\) 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 \(0.0736196\pi\)
−0.973373 + 0.229226i \(0.926380\pi\)
\(234\) 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 0.996817 0.0797266i \(-0.0254047\pi\)
−0.567454 + 0.823405i \(0.692071\pi\)
\(240\) 0 0
\(241\) −595565. + 1.03155e6i −0.660520 + 1.14405i 0.319959 + 0.947432i \(0.396331\pi\)
−0.980479 + 0.196623i \(0.937002\pi\)
\(242\) 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 0.128828 0.991667i \(-0.458878\pi\)
0.923223 + 0.384265i \(0.125545\pi\)
\(258\) 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 0.235087 + 0.971974i \(0.424463\pi\)
−0.959298 + 0.282396i \(0.908871\pi\)
\(264\) 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 \(-0.814397\pi\)
0.834766 0.550605i \(-0.185603\pi\)
\(270\) 0 0
\(271\) 109448.i 0.0905280i −0.998975 0.0452640i \(-0.985587\pi\)
0.998975 0.0452640i \(-0.0144129\pi\)
\(272\) −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 −0.679305 0.733856i \(-0.737719\pi\)
0.975190 + 0.221368i \(0.0710520\pi\)
\(278\) 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 0.549638 0.835403i \(-0.314766\pi\)
−0.448661 + 0.893702i \(0.648099\pi\)
\(282\) 0 0
\(283\) 921332. 531931.i 0.683833 0.394811i −0.117465 0.993077i \(-0.537477\pi\)
0.801298 + 0.598266i \(0.204143\pi\)
\(284\) 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 −0.312524 0.949910i \(-0.601175\pi\)
0.666384 + 0.745609i \(0.267841\pi\)
\(294\) 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 \(-0.681209\pi\)
0.539031 0.842286i \(-0.318791\pi\)
\(308\) −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 −0.977261 0.212039i \(-0.931990\pi\)
0.304999 0.952353i \(1.59866\pi\)
\(312\) 0 0
\(313\) 1.41302e6 2.44742e6i 0.815244 1.41204i −0.0939092 0.995581i \(-0.529936\pi\)
0.909153 0.416463i \(-0.136730\pi\)
\(314\) −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 0.550988 0.834513i \(-0.314251\pi\)
−0.447215 + 0.894426i \(0.647584\pi\)
\(318\) 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 0.585867 0.810407i \(-0.300754\pi\)
−0.408900 + 0.912579i \(0.634088\pi\)
\(332\) −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 −0.970302 0.241895i \(-0.922231\pi\)
0.275664 0.961254i \(-0.411102\pi\)
\(338\) −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 0.918777 + 0.394777i \(0.129178\pi\)
−0.117502 + 0.993073i \(0.537488\pi\)
\(348\) 0 0
\(349\) −956981. + 1.65754e6i −0.420571 + 0.728451i −0.995995 0.0894044i \(-0.971504\pi\)
0.575424 + 0.817855i \(0.304837\pi\)
\(350\) 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 −0.0529474 0.998597i \(-0.516862\pi\)
−0.891284 + 0.453445i \(0.850195\pi\)
\(354\) 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 0.999313 0.0370602i \(-0.0117993\pi\)
0.467561 + 0.883961i \(0.345133\pi\)
\(368\) 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 0.589917 0.807464i \(-0.299160\pi\)
−0.994243 + 0.107152i \(0.965827\pi\)
\(374\) −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 \(0.0498737\pi\)
−0.987750 + 0.156043i \(0.950126\pi\)
\(380\) −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 0.972533 0.232764i \(-0.0747771\pi\)
−0.687846 + 0.725856i \(0.741444\pi\)
\(384\) 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 0.514990 0.857196i \(-0.327796\pi\)
−0.484859 + 0.874592i \(0.661129\pi\)
\(390\) 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 −0.522218 0.852812i \(-0.674895\pi\)
0.477448 + 0.878660i \(0.341562\pi\)
\(402\) 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 0.943075 + 0.332580i \(0.107919\pi\)
−0.183515 + 0.983017i \(0.558748\pi\)
\(410\) −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 0.999018 0.0442975i \(-0.0141050\pi\)
−0.537872 + 0.843027i \(0.680772\pi\)
\(420\) 0 0
\(421\) 1.80550e6 3.12721e6i 0.496468 0.859908i −0.503524 0.863981i \(-0.667963\pi\)
0.999992 + 0.00407351i \(0.00129664\pi\)
\(422\) −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 0.610147 0.792289i \(-0.291111\pi\)
−0.381069 + 0.924547i \(0.624444\pi\)
\(440\) −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 −0.847369 0.531004i \(-0.821815\pi\)
0.883548 + 0.468342i \(0.155148\pi\)
\(444\) 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 \(-0.559561\pi\)
0.186028 0.982544i \(-0.440439\pi\)
\(450\) 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 −0.998048 0.0624588i \(-0.980106\pi\)
0.553115 + 0.833105i \(0.313439\pi\)
\(458\) −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 0.714037 0.700108i \(-0.246865\pi\)
−0.249293 + 0.968428i \(0.580198\pi\)
\(462\) 0 0
\(463\) −5.77486e6 + 3.33412e6i −1.25196 + 0.722817i −0.971498 0.237049i \(-0.923820\pi\)
−0.280459 + 0.959866i \(0.590487\pi\)
\(464\) −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 −0.999065 0.0432268i \(-0.986236\pi\)
0.536968 + 0.843603i \(0.319570\pi\)
\(480\) 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 \(0.155620\pi\)
−0.882853 + 0.469650i \(0.844380\pi\)
\(488\) 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 0.896642 0.442757i \(-0.145999\pi\)
−0.831759 + 0.555136i \(0.812666\pi\)
\(492\) 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 −0.463605 0.886042i \(-0.653444\pi\)
0.535532 + 0.844515i \(0.320111\pi\)
\(500\) 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 −0.481641 0.876369i \(-0.659959\pi\)
0.518137 + 0.855297i \(0.326626\pi\)
\(510\) 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 \(0.134911\pi\)
−0.911518 + 0.411259i \(0.865089\pi\)
\(522\) 0 0
\(523\) 5.13482e6i 0.820863i 0.911891 + 0.410432i \(0.134622\pi\)
−0.911891 + 0.410432i \(0.865378\pi\)
\(524\) −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 0.233690 0.972311i \(-0.424920\pi\)
−0.725201 + 0.688537i \(0.758253\pi\)
\(548\) 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 \(0.221402\pi\)
−0.767698 + 0.640812i \(0.778598\pi\)
\(558\) 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 0.645998 0.763339i \(-0.276441\pi\)
−0.984070 + 0.177781i \(0.943108\pi\)
\(564\) 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 −0.0798721 0.996805i \(-0.525451\pi\)
−0.903195 + 0.429231i \(0.858785\pi\)
\(570\) 0 0
\(571\) 1.07595e7 6.21203e6i 1.38103 0.797339i 0.388750 0.921343i \(-0.372907\pi\)
0.992282 + 0.124004i \(0.0395735\pi\)
\(572\) 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 −0.101390 0.994847i \(-0.532329\pi\)
0.912258 0.409617i \(-0.134338\pi\)
\(588\) 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 \(0.0328289\pi\)
−0.994686 + 0.102952i \(0.967171\pi\)
\(594\) 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 0.585026 0.811015i \(-0.301084\pi\)
−0.994872 + 0.101140i \(0.967751\pi\)
\(600\) 0 0
\(601\) 1.35517e6 2.34722e6i 0.153041 0.265075i −0.779303 0.626647i \(-0.784427\pi\)
0.932344 + 0.361573i \(0.117760\pi\)
\(602\) −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 −0.601675 0.798741i \(-0.705500\pi\)
0.390893 + 0.920436i \(0.372166\pi\)
\(608\) −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 −0.114350 0.993440i \(-0.536479\pi\)
0.803170 + 0.595750i \(0.203145\pi\)
\(618\) 0 0
\(619\) −3.79004e6 2.18818e6i −0.397573 0.229539i 0.287863 0.957671i \(-0.407055\pi\)
−0.685436 + 0.728133i \(0.740388\pi\)
\(620\) −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 \(-0.955362\pi\)
0.990183 0.139775i \(-0.0446378\pi\)
\(632\) −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 0.704191 0.710011i \(-0.251310\pi\)
−0.262792 + 0.964853i \(0.584643\pi\)
\(642\) 0 0
\(643\) 1.45248e7 8.38588e6i 1.38542 0.799873i 0.392626 0.919698i \(-0.371567\pi\)
0.992795 + 0.119825i \(0.0382334\pi\)
\(644\) −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 −0.471278 0.881985i \(-0.656207\pi\)
0.528183 + 0.849131i \(0.322874\pi\)
\(654\) 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 −0.866728 0.498781i \(-0.833781\pi\)
0.865321 + 0.501218i \(0.167115\pi\)
\(660\) 0 0
\(661\) 4.41600e6 + 7.64875e6i 0.393121 + 0.680905i 0.992859 0.119291i \(-0.0380621\pi\)
−0.599739 + 0.800196i \(0.704729\pi\)
\(662\) −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 −0.688242 0.725481i \(-0.741617\pi\)
0.972406 + 0.233295i \(0.0749508\pi\)
\(674\) 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 −0.132689 0.991158i \(-0.542361\pi\)
−0.924712 + 0.380667i \(0.875694\pi\)
\(678\) 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 0.813921 0.580975i \(-0.197329\pi\)
−0.0961788 + 0.995364i \(0.530662\pi\)
\(692\) −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 \(0.152126\pi\)
−0.887955 + 0.459931i \(0.847874\pi\)
\(702\) 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 −0.970999 0.239084i \(-0.923153\pi\)
0.692553 + 0.721367i \(0.256486\pi\)
\(710\) −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 0.737322 0.675542i \(-0.236090\pi\)
−0.216375 + 0.976310i \(0.569424\pi\)
\(728\) −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 −0.992148 0.125067i \(-0.960085\pi\)
0.387763 0.921759i \(-0.373248\pi\)
\(734\) −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 \(-0.997996\pi\)
0.999980 0.00629629i \(-0.00200418\pi\)
\(740\) −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 0.740202 0.672385i \(-0.234730\pi\)
−0.952403 + 0.304841i \(0.901397\pi\)
\(744\) 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 −0.677757 + 0.735286i \(0.737048\pi\)
−0.975655 + 0.219312i \(0.929619\pi\)
\(752\) 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 −0.809307 0.587386i \(-0.800157\pi\)
0.104038 + 0.994573i \(0.466824\pi\)
\(762\) 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 0.818200 0.574934i \(-0.194972\pi\)
−0.907007 + 0.421115i \(0.861639\pi\)
\(770\) 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 \(-0.933928\pi\)
0.978534 0.206084i \(-0.0660719\pi\)
\(774\) 0 0