Properties

Label 108.6.h.a.35.7
Level 108
Weight 6
Character 108.35
Analytic conductor 17.321
Analytic rank 0
Dimension 56
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 35.7
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.95514 - 4.04436i) q^{2} +(-0.713689 + 31.9920i) q^{4} +(77.8058 - 44.9212i) q^{5} +(124.034 + 71.6112i) q^{7} +(132.210 - 123.647i) q^{8} +O(q^{10})\) \(q+(-3.95514 - 4.04436i) q^{2} +(-0.713689 + 31.9920i) q^{4} +(77.8058 - 44.9212i) q^{5} +(124.034 + 71.6112i) q^{7} +(132.210 - 123.647i) q^{8} +(-489.410 - 137.005i) q^{10} +(-278.231 + 481.910i) q^{11} +(179.796 + 311.416i) q^{13} +(-200.952 - 784.871i) q^{14} +(-1022.98 - 45.6648i) q^{16} +1076.42i q^{17} +348.135i q^{19} +(1381.59 + 2521.23i) q^{20} +(3049.46 - 780.757i) q^{22} +(1469.06 + 2544.48i) q^{23} +(2473.33 - 4283.93i) q^{25} +(548.358 - 1958.85i) q^{26} +(-2379.51 + 3917.00i) q^{28} +(-3331.19 - 1923.26i) q^{29} +(2346.41 - 1354.70i) q^{31} +(3861.35 + 4317.91i) q^{32} +(4353.43 - 4257.39i) q^{34} +12867.4 q^{35} -1992.90 q^{37} +(1407.98 - 1376.92i) q^{38} +(4732.35 - 15559.5i) q^{40} +(13432.0 - 7754.99i) q^{41} +(12474.1 + 7201.91i) q^{43} +(-15218.7 - 9245.10i) q^{44} +(4480.46 - 16005.2i) q^{46} +(-1232.97 + 2135.56i) q^{47} +(1852.82 + 3209.17i) q^{49} +(-27108.1 + 6940.52i) q^{50} +(-10091.1 + 5529.78i) q^{52} -13364.2i q^{53} +49993.8i q^{55} +(25253.0 - 5868.70i) q^{56} +(5396.96 + 21079.3i) q^{58} +(19878.8 + 34431.1i) q^{59} +(-211.489 + 366.310i) q^{61} +(-14759.3 - 4131.70i) q^{62} +(2191.00 - 32694.7i) q^{64} +(27978.3 + 16153.3i) q^{65} +(-14018.6 + 8093.63i) q^{67} +(-34436.8 - 768.229i) q^{68} +(-50892.5 - 52040.5i) q^{70} -6902.73 q^{71} -11089.5 q^{73} +(7882.20 + 8060.00i) q^{74} +(-11137.6 - 248.460i) q^{76} +(-69020.2 + 39848.8i) q^{77} +(-64310.3 - 37129.6i) q^{79} +(-81645.2 + 42400.5i) q^{80} +(-84489.6 - 23651.9i) q^{82} +(48564.9 - 84116.9i) q^{83} +(48354.0 + 83751.6i) q^{85} +(-20209.6 - 78934.2i) q^{86} +(22801.6 + 98115.6i) q^{88} -74459.8i q^{89} +51501.6i q^{91} +(-82451.5 + 45182.1i) q^{92} +(13513.5 - 3459.88i) q^{94} +(15638.6 + 27086.9i) q^{95} +(47958.5 - 83066.5i) q^{97} +(5650.89 - 20186.2i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.95514 4.04436i −0.699177 0.714949i
\(3\) 0 0
\(4\) −0.713689 + 31.9920i −0.0223028 + 0.999751i
\(5\) 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 0.895170 0.445725i \(-0.147054\pi\)
0.0615753 + 0.998102i \(0.480388\pi\)
\(8\) 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 \(0.410512\pi\)
−0.970749 + 0.240095i \(0.922821\pi\)
\(12\) 0 0
\(13\) 179.796 + 311.416i 0.295068 + 0.511072i 0.975001 0.222202i \(-0.0713245\pi\)
−0.679933 + 0.733274i \(0.737991\pi\)
\(14\) −200.952 784.871i −0.274013 1.07023i
\(15\) 0 0
\(16\) −1022.98 45.6648i −0.999005 0.0445945i
\(17\) 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 \(0.0352837\pi\)
−0.993863 + 0.110620i \(0.964716\pi\)
\(20\) 1381.59 + 2521.23i 0.772333 + 1.40941i
\(21\) 0 0
\(22\) 3049.46 780.757i 1.34328 0.343921i
\(23\) 1469.06 + 2544.48i 0.579054 + 1.00295i 0.995588 + 0.0938304i \(0.0299111\pi\)
−0.416535 + 0.909120i \(0.636756\pi\)
\(24\) 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 −0.264443 0.964401i \(-0.585188\pi\)
0.702974 + 0.711215i \(0.251855\pi\)
\(32\) 3861.35 + 4317.91i 0.666599 + 0.745417i
\(33\) 0 0
\(34\) 4353.43 4257.39i 0.645853 0.631606i
\(35\) 12867.4 1.77550
\(36\) 0 0
\(37\) −1992.90 −0.239321 −0.119661 0.992815i \(-0.538181\pi\)
−0.119661 + 0.992815i \(0.538181\pi\)
\(38\) 1407.98 1376.92i 0.158175 0.154686i
\(39\) 0 0
\(40\) 4732.35 15559.5i 0.467657 1.53760i
\(41\) 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 0.916645 0.399702i \(-0.130887\pi\)
0.112170 + 0.993689i \(0.464220\pi\)
\(44\) −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 \(-0.859277\pi\)
0.822443 + 0.568848i \(0.192611\pi\)
\(48\) 0 0
\(49\) 1852.82 + 3209.17i 0.110241 + 0.190943i
\(50\) −27108.1 + 6940.52i −1.53347 + 0.392615i
\(51\) 0 0
\(52\) −10091.1 + 5529.78i −0.517526 + 0.283596i
\(53\) 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
\(56\) 25253.0 5868.70i 1.07608 0.250076i
\(57\) 0 0
\(58\) 5396.96 + 21079.3i 0.210659 + 0.822785i
\(59\) 19878.8 + 34431.1i 0.743464 + 1.28772i 0.950909 + 0.309470i \(0.100152\pi\)
−0.207445 + 0.978247i \(0.566515\pi\)
\(60\) 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 −0.678479 0.734620i \(-0.737361\pi\)
0.296960 + 0.954890i \(0.404027\pi\)
\(68\) −34436.8 768.229i −0.903132 0.0201474i
\(69\) 0 0
\(70\) −50892.5 52040.5i −1.24139 1.26939i
\(71\) −6902.73 −0.162508 −0.0812541 0.996693i \(-0.525893\pi\)
−0.0812541 + 0.996693i \(0.525893\pi\)
\(72\) 0 0
\(73\) −11089.5 −0.243558 −0.121779 0.992557i \(-0.538860\pi\)
−0.121779 + 0.992557i \(0.538860\pi\)
\(74\) 7882.20 + 8060.00i 0.167328 + 0.171102i
\(75\) 0 0
\(76\) −11137.6 248.460i −0.221185 0.00493427i
\(77\) −69020.2 + 39848.8i −1.32663 + 0.765930i
\(78\) 0 0
\(79\) −64310.3 37129.6i −1.15935 0.669349i −0.208199 0.978086i \(-0.566760\pi\)
−0.951147 + 0.308738i \(0.900093\pi\)
\(80\) −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 \(-0.551688\pi\)
0.935468 0.353412i \(-0.114979\pi\)
\(84\) 0 0
\(85\) 48354.0 + 83751.6i 0.725914 + 1.25732i
\(86\) −20209.6 78934.2i −0.294654 1.15085i
\(87\) 0 0
\(88\) 22801.6 + 98115.6i 0.313877 + 1.35061i
\(89\) 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
\(92\) −82451.5 + 45182.1i −1.01562 + 0.556541i
\(93\) 0 0
\(94\) 13513.5 3459.88i 0.157743 0.0403870i
\(95\) 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 −0.686149 0.727461i \(-0.740700\pi\)
0.286925 + 0.957953i \(0.407367\pi\)
\(104\) 62276.3 + 18941.1i 0.564599 + 0.171721i
\(105\) 0 0
\(106\) −54049.8 + 52857.5i −0.467229 + 0.456922i
\(107\) 14176.4 0.119703 0.0598517 0.998207i \(-0.480937\pi\)
0.0598517 + 0.998207i \(0.480937\pi\)
\(108\) 0 0
\(109\) 21788.2 0.175653 0.0878264 0.996136i \(-0.472008\pi\)
0.0878264 + 0.996136i \(0.472008\pi\)
\(110\) 202193. 197733.i 1.59325 1.55810i
\(111\) 0 0
\(112\) −123615. 78920.9i −0.931160 0.594493i
\(113\) −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
\(122\) 2317.96 593.470i 0.0140996 0.00360993i
\(123\) 0 0
\(124\) 41665.1 + 76033.4i 0.243343 + 0.444069i
\(125\) 163661.i 0.936853i
\(126\) 0 0
\(127\) 257349.i 1.41584i −0.706293 0.707919i \(-0.749634\pi\)
0.706293 0.707919i \(-0.250366\pi\)
\(128\) −140895. + 120451.i −0.760098 + 0.649808i
\(129\) 0 0
\(130\) −45328.5 177043.i −0.235241 0.918799i
\(131\) 3161.94 + 5476.65i 0.0160982 + 0.0278828i 0.873962 0.485994i \(-0.161542\pi\)
−0.857864 + 0.513877i \(0.828209\pi\)
\(132\) 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 −0.298873 0.954293i \(-0.596611\pi\)
0.677005 + 0.735978i \(0.263277\pi\)
\(140\) −9183.35 + 411655.i −0.0395987 + 1.77506i
\(141\) 0 0
\(142\) 27301.3 + 27917.1i 0.113622 + 0.116185i
\(143\) −200099. −0.818285
\(144\) 0 0
\(145\) −345581. −1.36499
\(146\) 43860.4 + 44849.7i 0.170290 + 0.174132i
\(147\) 0 0
\(148\) 1422.31 63756.9i 0.00533753 0.239262i
\(149\) 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 −0.196115 0.980581i \(-0.562833\pi\)
−0.947266 + 0.320450i \(0.896166\pi\)
\(152\) 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 \(0.613622\pi\)
\(158\) 104191. + 406947.i 0.332038 + 1.29687i
\(159\) 0 0
\(160\) 494401. + 162502.i 1.52679 + 0.501833i
\(161\) 420803.i 1.27942i
\(162\) 0 0
\(163\) 154747.i 0.456198i −0.973638 0.228099i \(-0.926749\pi\)
0.973638 0.228099i \(-0.0732509\pi\)
\(164\) 238512. + 435253.i 0.692468 + 1.26367i
\(165\) 0 0
\(166\) −532280. + 136280.i −1.49924 + 0.383852i
\(167\) −98410.6 170452.i −0.273055 0.472946i 0.696587 0.717472i \(-0.254701\pi\)
−0.969643 + 0.244526i \(0.921368\pi\)
\(168\) 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
\(176\) 306631. 480279.i 0.746164 1.16872i
\(177\) 0 0
\(178\) −301142. + 294499.i −0.712396 + 0.696681i
\(179\) −583842. −1.36196 −0.680978 0.732304i \(-0.738445\pi\)
−0.680978 + 0.732304i \(0.738445\pi\)
\(180\) 0 0
\(181\) −623067. −1.41364 −0.706819 0.707395i \(-0.749870\pi\)
−0.706819 + 0.707395i \(0.749870\pi\)
\(182\) 208291. 203696.i 0.466114 0.455831i
\(183\) 0 0
\(184\) 508840. + 154762.i 1.10799 + 0.336992i
\(185\) −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 \(-0.892108\pi\)
0.759504 + 0.650502i \(0.225442\pi\)
\(192\) 0 0
\(193\) 145169. + 251439.i 0.280530 + 0.485892i 0.971515 0.236977i \(-0.0761565\pi\)
−0.690985 + 0.722869i \(0.742823\pi\)
\(194\) −525633. + 134579.i −1.00272 + 0.256727i
\(195\) 0 0
\(196\) −103990. + 56985.0i −0.193354 + 0.105955i
\(197\) 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 \(0.155386\pi\)
−0.883197 + 0.469002i \(0.844614\pi\)
\(200\) −202695. 872197.i −0.358317 1.54184i
\(201\) 0 0
\(202\) −56526.3 220779.i −0.0974703 0.380697i
\(203\) −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 \(-0.779776\pi\)
0.167463 + 0.985878i \(0.446442\pi\)
\(212\) 427549. + 9537.92i 0.653351 + 0.0145752i
\(213\) 0 0
\(214\) −56069.7 57334.5i −0.0836939 0.0855818i
\(215\) 1.29407e6 1.90925
\(216\) 0 0
\(217\) 388047. 0.559416
\(218\) −86175.4 88119.3i −0.122812 0.125583i
\(219\) 0 0
\(220\) −1.59940e6 35680.0i −2.22793 0.0497014i
\(221\) −335214. + 193536.i −0.461680 + 0.266551i
\(222\) 0 0
\(223\) 33442.0 + 19307.7i 0.0450329 + 0.0259998i 0.522347 0.852733i \(-0.325056\pi\)
−0.477315 + 0.878733i \(0.658390\pi\)
\(224\) 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 \(0.362113\pi\)
−0.995915 + 0.0902911i \(0.971220\pi\)
\(228\) 0 0
\(229\) 714088. + 1.23684e6i 0.899836 + 1.55856i 0.827703 + 0.561166i \(0.189647\pi\)
0.0721321 + 0.997395i \(0.477020\pi\)
\(230\) −370365. 1.44656e6i −0.461648 1.80309i
\(231\) 0 0
\(232\) −678221. + 157616.i −0.827278 + 0.192256i
\(233\) 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
\(236\) −1.11571e6 + 611390.i −1.30398 + 0.714559i
\(237\) 0 0
\(238\) 844850. 216308.i 0.966802 0.247531i
\(239\) −379157. 656720.i −0.429363 0.743679i 0.567454 0.823405i \(-0.307929\pi\)
−0.996817 + 0.0797266i \(0.974595\pi\)
\(240\) 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
\(248\) 142715. 469231.i 0.147347 0.484460i
\(249\) 0 0
\(250\) −661906. + 647305.i −0.669802 + 0.655026i
\(251\) −705353. −0.706679 −0.353340 0.935495i \(-0.614954\pi\)
−0.353340 + 0.935495i \(0.614954\pi\)
\(252\) 0 0
\(253\) −1.63495e6 −1.60584
\(254\) −1.04081e6 + 1.01785e6i −1.01225 + 0.989922i
\(255\) 0 0
\(256\) 1.04441e6 + 93428.4i 0.996023 + 0.0891003i
\(257\) 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 \(-0.575537\pi\)
0.959298 0.282396i \(-0.0911292\pi\)
\(264\) 0 0
\(265\) −600338. 1.03982e6i −0.525147 0.909581i
\(266\) 273241. 69958.3i 0.236778 0.0606227i
\(267\) 0 0
\(268\) −248927. 454259.i −0.211707 0.386337i
\(269\) 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 \(0.0144129\pi\)
−0.998975 + 0.0452640i \(0.985587\pi\)
\(272\) 49154.4 1.10116e6i 0.0402847 0.902458i
\(273\) 0 0
\(274\) −405785. 1.58490e6i −0.326527 1.27534i
\(275\) 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 −0.801298 0.598266i \(-0.795857\pi\)
0.117465 + 0.993077i \(0.462523\pi\)
\(284\) 4926.41 220833.i 0.00362439 0.162468i
\(285\) 0 0
\(286\) 791420. + 809272.i 0.572126 + 0.585032i
\(287\) 2.22137e6 1.59190
\(288\) 0 0
\(289\) 261179. 0.183947
\(290\) 1.36682e6 + 1.39765e6i 0.954370 + 0.975898i
\(291\) 0 0
\(292\) 7914.43 354774.i 0.00543203 0.243498i
\(293\) 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
\(302\) 519019. + 2.02717e6i 0.327466 + 1.27901i
\(303\) 0 0
\(304\) 15897.5 356136.i 0.00986609 0.221020i
\(305\) 38001.3i 0.0233910i
\(306\) 0 0
\(307\) 2.78186e6i 1.68457i 0.539031 + 0.842286i \(0.318791\pi\)
−0.539031 + 0.842286i \(0.681209\pi\)
\(308\) −1.22559e6 2.23654e6i −0.736152 1.34338i
\(309\) 0 0
\(310\) −1.33396e6 + 341535.i −0.788385 + 0.201851i
\(311\) 1.14667e6 + 1.98609e6i 0.672262 + 1.16439i 0.977261 + 0.212039i \(0.0680104\pi\)
−0.304999 + 0.952353i \(0.598656\pi\)
\(312\) 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
\(320\) −1.29821e6 2.64226e6i −0.708713 1.44245i
\(321\) 0 0
\(322\) 1.70188e6 1.66434e6i 0.914722 0.894544i
\(323\) −374739. −0.199859
\(324\) 0 0
\(325\) 1.77878e6 0.934142
\(326\) −625852. + 612046.i −0.326158 + 0.318963i
\(327\) 0 0
\(328\) 816971. 2.68611e6i 0.419298 1.37860i
\(329\) −305860. + 176588.i −0.155787 + 0.0899439i
\(330\) 0 0
\(331\) −352745. 203658.i −0.176967 0.102172i 0.408900 0.912579i \(-0.365912\pi\)
−0.585867 + 0.810407i \(0.699246\pi\)
\(332\) 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 \(-0.411102\pi\)
\(338\) −1.32611e6 + 339525.i −0.631375 + 0.161652i
\(339\) 0 0
\(340\) −2.71390e6 + 1.48717e6i −1.27320 + 0.697692i
\(341\) 1.50768e6i 0.702139i
\(342\) 0 0
\(343\) 1.87641e6i 0.861176i
\(344\) 2.53969e6 590213.i 1.15714 0.268914i
\(345\) 0 0
\(346\) 945320. + 3.69220e6i 0.424511 + 1.65804i
\(347\) −1.79724e6 3.11291e6i −0.801275 1.38785i −0.918777 0.394777i \(-0.870822\pi\)
0.117502 0.993073i \(1.53749\pi\)
\(348\) 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
\(356\) 2.38212e6 + 53141.1i 0.996182 + 0.0222232i
\(357\) 0 0
\(358\) 2.30918e6 + 2.36127e6i 0.952248 + 0.973728i
\(359\) 2.70497e6 1.10771 0.553856 0.832612i \(-0.313156\pi\)
0.553856 + 0.832612i \(0.313156\pi\)
\(360\) 0 0
\(361\) 2.35490e6 0.951053
\(362\) 2.46432e6 + 2.51991e6i 0.988383 + 1.01068i
\(363\) 0 0
\(364\) −1.64764e6 36756.1i −0.651792 0.0145404i
\(365\) −862824. + 498151.i −0.338992 + 0.195717i
\(366\) 0 0
\(367\) −3.78493e6 2.18523e6i −1.46687 0.846900i −0.467561 0.883961i \(-0.654867\pi\)
−0.999313 + 0.0370602i \(0.988201\pi\)
\(368\) −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 \(0.965827\pi\)
\(374\) 840421. + 3.28249e6i 0.310683 + 1.21346i
\(375\) 0 0
\(376\) 101044. + 434794.i 0.0368589 + 0.158604i
\(377\) 1.38318e6i 0.501216i
\(378\) 0 0
\(379\) 872712.i 0.312085i −0.987750 0.156043i \(-0.950126\pi\)
0.987750 0.156043i \(-0.0498737\pi\)
\(380\) −877727. + 480980.i −0.311818 + 0.170871i
\(381\) 0 0
\(382\) 1.01455e6 259756.i 0.355725 0.0910767i
\(383\) −817267. 1.41555e6i −0.284687 0.493092i 0.687846 0.725856i \(-0.258556\pi\)
−0.972533 + 0.232764i \(0.925223\pi\)
\(384\) 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
\(392\) 641764. + 195190.i 0.210941 + 0.0641568i
\(393\) 0 0
\(394\) 940699. 919948.i 0.305288 0.298554i
\(395\) −6.67162e6 −2.15149
\(396\) 0 0
\(397\) −3.33523e6 −1.06206 −0.531031 0.847352i \(-0.678195\pi\)
−0.531031 + 0.847352i \(0.678195\pi\)
\(398\) 2.11927e6 2.07252e6i 0.670625 0.655831i
\(399\) 0 0
\(400\) −2.72579e6 + 4.26943e6i −0.851810 + 1.33420i
\(401\) −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 \(0.558748\pi\)
\(410\) −7.63625e6 + 1.95512e6i −2.24347 + 0.574399i
\(411\) 0 0
\(412\) −763270. 1.39287e6i −0.221531 0.404266i
\(413\) 5.69417e6i 1.64269i
\(414\) 0 0
\(415\) 8.72638e6i 2.48722i
\(416\) −650411. + 1.97883e6i −0.184270 + 0.560628i
\(417\) 0 0
\(418\) 271809. + 1.06162e6i 0.0760892 + 0.297187i
\(419\) −1.65720e6 2.87035e6i −0.461146 0.798729i 0.537872 0.843027i \(-0.319228\pi\)
−0.999018 + 0.0442975i \(0.985895\pi\)
\(420\) 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
\(428\) −10117.5 + 453532.i −0.00266972 + 0.119674i
\(429\) 0 0
\(430\) −5.11825e6 5.23370e6i −1.33490 1.36502i
\(431\) −7.53077e6 −1.95275 −0.976374 0.216090i \(-0.930670\pi\)
−0.976374 + 0.216090i \(0.930670\pi\)
\(432\) 0 0
\(433\) 2.24585e6 0.575653 0.287827 0.957683i \(-0.407067\pi\)
0.287827 + 0.957683i \(0.407067\pi\)
\(434\) −1.53478e6 1.56940e6i −0.391131 0.399954i
\(435\) 0 0
\(436\) −15550.0 + 697049.i −0.00391755 + 0.175609i
\(437\) −885823. + 511430.i −0.221893 + 0.128110i
\(438\) 0 0
\(439\) −925006. 534052.i −0.229078 0.132258i 0.381069 0.924547i \(-0.375556\pi\)
−0.610147 + 0.792289i \(0.708889\pi\)
\(440\) 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 \(-0.844852\pi\)
0.847369 + 0.531004i \(0.178185\pi\)
\(444\) 0 0
\(445\) −3.34482e6 5.79340e6i −0.800705 1.38686i
\(446\) −54180.4 211616.i −0.0128975 0.0503747i
\(447\) 0 0
\(448\) 2.61306e6 3.89836e6i 0.615113 0.917670i
\(449\) 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
\(452\) −2.29880e6 4.19501e6i −0.529243 0.965800i
\(453\) 0 0
\(454\) 4.90252e6 1.25520e6i 1.11630 0.285807i
\(455\) 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 0.280459 0.959866i \(-0.409513\pi\)
0.971498 + 0.237049i \(0.0761801\pi\)
\(464\) 3.31992e6 + 2.11958e6i 0.715867 + 0.457040i
\(465\) 0 0
\(466\) 1.53651e6 1.50261e6i 0.327770 0.320540i
\(467\) 3.34371e6 0.709474 0.354737 0.934966i \(-0.384570\pi\)
0.354737 + 0.934966i \(0.384570\pi\)
\(468\) 0 0
\(469\) −2.31838e6 −0.486689
\(470\) 896008. 876242.i 0.187097 0.182970i
\(471\) 0 0
\(472\) 6.88546e6 + 2.09419e6i 1.42258 + 0.432674i
\(473\) −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 \(-0.680430\pi\)
0.999065 + 0.0432268i \(0.0137638\pi\)
\(480\) 0 0
\(481\) −358315. 620620.i −0.0706159 0.122310i
\(482\) 6.52749e6 1.67124e6i 1.27976 0.327659i
\(483\) 0 0
\(484\) 4.17008e6 2.28513e6i 0.809153 0.443403i
\(485\) 8.61740e6i 1.66350i
\(486\) 0 0
\(487\) 4.91616e6i 0.939299i −0.882853 0.469650i \(-0.844380\pi\)
0.882853 0.469650i \(-0.155620\pi\)
\(488\) 17332.0 + 74579.7i 0.00329457 + 0.0141766i
\(489\) 0 0
\(490\) −467115. 1.82445e6i −0.0878889 0.343274i
\(491\) −346602. 600332.i −0.0648824 0.112380i 0.831759 0.555136i \(-0.187334\pi\)
−0.896642 + 0.442757i \(0.854001\pi\)
\(492\) 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 \(-0.679889\pi\)
0.463605 + 0.886042i \(0.346556\pi\)
\(500\) 5.23587e6 + 116803.i 0.936620 + 0.0208944i
\(501\) 0 0
\(502\) 2.78977e6 + 2.85270e6i 0.494094 + 0.505239i
\(503\) 3.22518e6 0.568373 0.284187 0.958769i \(-0.408276\pi\)
0.284187 + 0.958769i \(0.408276\pi\)
\(504\) 0 0
\(505\) 3.61952e6 0.631572
\(506\) 6.46644e6 + 6.61231e6i 1.12277 + 1.14809i
\(507\) 0 0
\(508\) 8.23313e6 + 183667.i 1.41549 + 0.0315772i
\(509\) 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
\(518\) 400476. + 1.56417e6i 0.0655771 + 0.256129i
\(519\) 0 0
\(520\) 5.69632e6 1.32380e6i 0.923817 0.214691i
\(521\) 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 \(-0.865378\pi\)
0.911891 0.410432i \(-0.134622\pi\)
\(524\) −177466. + 97248.4i −0.0282349 + 0.0154723i
\(525\) 0 0
\(526\) −8.90373e6 + 2.27963e6i −1.40316 + 0.359253i
\(527\) 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
\(536\) −852647. + 2.80341e6i −0.128191 + 0.421478i
\(537\) 0 0
\(538\) −5.28568e6 + 5.16908e6i −0.787309 + 0.769941i
\(539\) −2.06204e6 −0.305721
\(540\) 0 0
\(541\) 1.10092e7 1.61720 0.808601 0.588357i \(-0.200225\pi\)
0.808601 + 0.588357i \(0.200225\pi\)
\(542\) 442645. 432881.i 0.0647229 0.0632951i
\(543\) 0 0
\(544\) −4.64789e6 + 4.15643e6i −0.673377 + 0.602176i
\(545\) 1.69525e6 978751.i 0.244479 0.141150i
\(546\) 0 0
\(547\) 3.43955e6 + 1.98583e6i 0.491511 + 0.283774i 0.725201 0.688537i \(-0.241747\pi\)
−0.233690 + 0.972311i \(0.575080\pi\)
\(548\) −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
\(554\) −4.14134e6 + 1.06031e6i −0.573279 + 0.146777i
\(555\) 0 0
\(556\) 1.52949e6 + 2.79113e6i 0.209827 + 0.382907i
\(557\) 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
\(560\) −1.31631e7 587588.i −1.77374 0.0791777i
\(561\) 0 0
\(562\) −216539. 845753.i −0.0289198 0.112954i
\(563\) 2.54261e6 + 4.40393e6i 0.338072 + 0.585558i 0.984070 0.177781i \(-0.0568919\pi\)
−0.645998 + 0.763339i \(0.723559\pi\)
\(564\) 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 −0.992282 0.124004i \(-0.960426\pi\)
−0.388750 + 0.921343i \(0.627093\pi\)
\(572\) 142809. 6.40157e6i 0.0182500 0.818082i
\(573\) 0 0
\(574\) −8.78585e6 8.98404e6i −1.11302 1.13813i
\(575\) 1.45338e7 1.83320
\(576\) 0 0
\(577\) 9.43597e6 1.17990 0.589952 0.807438i \(-0.299146\pi\)
0.589952 + 0.807438i \(0.299146\pi\)
\(578\) −1.03300e6 1.05630e6i −0.128612 0.131513i
\(579\) 0 0
\(580\) 246637. 1.10558e7i 0.0304431 1.36465i
\(581\) 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 \(0.467671\pi\)
−0.912258 + 0.409617i \(0.865662\pi\)
\(588\) 0 0
\(589\) 471619. + 816869.i 0.0560149 + 0.0970206i
\(590\) −5.01166e6 1.95744e7i −0.592723 2.31504i
\(591\) 0 0
\(592\) 2.03870e6 + 91005.3i 0.239083 + 0.0106724i
\(593\) 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
\(596\) 5.74186e6 + 1.04782e7i 0.662120 + 1.20828i
\(597\) 0 0
\(598\) 5.78983e6 1.48238e6i 0.662084 0.169514i
\(599\) 3.59905e6 + 6.23374e6i 0.409846 + 0.709875i 0.994872 0.101140i \(-0.0322489\pi\)
−0.585026 + 0.811015i \(0.698916\pi\)
\(600\) 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 −0.390893 0.920436i \(-0.627834\pi\)
0.601675 + 0.798741i \(0.294500\pi\)
\(608\) −1.50322e6 + 1.34427e6i −0.164916 + 0.147478i
\(609\) 0 0
\(610\) 153691. 150301.i 0.0167234 0.0163545i
\(611\) −886728. −0.0960921
\(612\) 0 0
\(613\) −4.95842e6 −0.532957 −0.266478 0.963841i \(-0.585860\pi\)
−0.266478 + 0.963841i \(0.585860\pi\)
\(614\) 1.12508e7 1.10027e7i 1.20438 1.17781i
\(615\) 0 0
\(616\) −4.19799e6 + 1.38025e7i −0.445748 + 1.46557i
\(617\) 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 0.685436 0.728133i \(-0.259612\pi\)
−0.287863 + 0.957671i \(0.592945\pi\)
\(620\) 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
\(626\) −1.54870e7 + 3.96514e6i −1.57954 + 0.404411i
\(627\) 0 0
\(628\) −1.10372e7 + 6.04824e6i −1.11676 + 0.611969i
\(629\) 2.14520e6i 0.216192i
\(630\) 0 0
\(631\) 2.79597e6i 0.279549i 0.990183 + 0.139775i \(0.0446378\pi\)
−0.990183 + 0.139775i \(0.955362\pi\)
\(632\) −1.30934e7 + 3.04285e6i −1.30395 + 0.303032i
\(633\) 0 0
\(634\) −300802. 1.17487e6i −0.0297206 0.116082i
\(635\) −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 −0.992795 0.119825i \(-0.961767\pi\)
−0.392626 + 0.919698i \(0.628433\pi\)
\(644\) −1.34624e7 300323.i −1.27911 0.0285347i
\(645\) 0 0
\(646\) 1.48215e6 + 1.51558e6i 0.139737 + 0.142889i
\(647\) 8.06422e6 0.757359 0.378679 0.925528i \(-0.376378\pi\)
0.378679 + 0.925528i \(0.376378\pi\)
\(648\) 0 0
\(649\) −2.21235e7 −2.06178
\(650\) −7.03531e6 7.19401e6i −0.653130 0.667863i
\(651\) 0 0
\(652\) 4.95067e6 + 110441.i 0.456084 + 0.0101745i
\(653\) 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 −0.865321 0.501218i \(-0.832885\pi\)
0.866728 + 0.498781i \(0.166219\pi\)
\(660\) 0 0
\(661\) 4.41600e6 + 7.64875e6i 0.393121 + 0.680905i 0.992859 0.119291i \(-0.0380621\pi\)
−0.599739 + 0.800196i \(0.704729\pi\)
\(662\) 571493. + 2.23212e6i 0.0506834 + 0.197958i
\(663\) 0 0
\(664\) −3.98001e6 1.71260e7i −0.350319 1.50742i
\(665\) 4.47961e6i 0.392813i
\(666\) 0 0
\(667\) 1.13015e7i 0.983608i
\(668\) 5.52335e6 3.02671e6i 0.478918 0.262439i
\(669\) 0 0
\(670\) 7.96970e6 2.04049e6i 0.685891 0.175610i
\(671\) −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
\(680\) 1.67485e7 + 5.09399e6i 1.38900 + 0.422460i
\(681\) 0 0
\(682\) 6.09760e6 5.96308e6i 0.501993 0.490919i
\(683\) −5.63380e6 −0.462114 −0.231057 0.972940i \(-0.574218\pi\)
−0.231057 + 0.972940i \(0.574218\pi\)
\(684\) 0 0
\(685\) 2.59834e7 2.11578
\(686\) −7.58887e6 + 7.42146e6i −0.615697 + 0.602115i
\(687\) 0 0
\(688\) −1.24319e7 7.93705e6i −1.00130 0.639275i
\(689\) 4.16183e6 2.40284e6i 0.333993 0.192831i
\(690\) 0 0
\(691\) −9.00873e6 5.20119e6i −0.717742 0.414389i 0.0961788 0.995364i \(-0.469338\pi\)
−0.813921 + 0.580975i \(0.802671\pi\)
\(692\) 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
\(698\) 1.04887e7 2.68543e6i 0.814859 0.208629i
\(699\) 0 0
\(700\) 1.08948e7 + 1.98817e7i 0.840379 + 1.53358i
\(701\) 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
\(704\) 1.51463e7 + 1.01525e7i 1.15179 + 0.772044i
\(705\) 0 0
\(706\) 3.58150e6 + 1.39885e7i 0.270429 + 1.05624i
\(707\) 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
\(716\) 416682. 1.86783e7i 0.0303754 1.36162i
\(717\) 0 0
\(718\) −1.06986e7 1.09399e7i −0.774487 0.791957i
\(719\) 1.53936e7 1.11050 0.555248 0.831685i \(-0.312623\pi\)
0.555248 + 0.831685i \(0.312623\pi\)
\(720\) 0 0
\(721\) −7.10870e6 −0.509275
\(722\) −9.31397e6 9.52407e6i −0.664954 0.679954i
\(723\) 0 0
\(724\) 444676. 1.99332e7i 0.0315281 1.41329i
\(725\) −1.64782e7 + 9.51371e6i −1.16430 + 0.672210i
\(726\) 0 0
\(727\) −7.42385e6 4.28616e6i −0.520946 0.300768i 0.216375 0.976310i \(-0.430576\pi\)
−0.737322 + 0.675542i \(0.763910\pi\)
\(728\) 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 \(-0.373248\pi\)
\(734\) 6.13209e6 + 2.39505e7i 0.420115 + 1.64087i
\(735\) 0 0
\(736\) −5.31430e6 + 1.61684e7i −0.361619 + 1.10020i
\(737\) 9.00758e6i 0.610857i
\(738\) 0 0
\(739\) 186950.i 0.0125926i 0.999980 + 0.00629629i \(0.00200418\pi\)
−0.999980 + 0.00629629i \(0.997996\pi\)
\(740\) −2.75337e6 5.02455e6i −0.184836 0.337301i
\(741\) 0 0
\(742\) −1.04892e7 + 2.68557e6i −0.699412 + 0.179071i
\(743\) 3.19316e6 + 5.53072e6i 0.212202 + 0.367544i 0.952403 0.304841i \(-0.0986033\pi\)
−0.740202 + 0.672385i \(0.765270\pi\)
\(744\) 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 \(-0.262952\pi\)
0.975655 0.219312i \(-0.0703814\pi\)
\(752\) 1.35882e6 2.12833e6i 0.0876228 0.137245i
\(753\) 0 0
\(754\) −5.59407e6 + 5.47067e6i −0.358344 + 0.350439i
\(755\) −3.32341e7 −2.12186
\(756\) 0 0
\(757\) −2.98899e7 −1.89576 −0.947882 0.318621i \(-0.896780\pi\)
−0.947882 + 0.318621i \(0.896780\pi\)
\(758\) −3.52956e6 + 3.45170e6i −0.223125 + 0.218203i
\(759\) 0 0
\(760\) 5.41679e6 + 1.64750e6i 0.340180 + 0.103464i
\(761\) −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 \(0.861639\pi\)
\(770\) 3.92387e7 1.00463e7i 2.38500 0.610634i
\(771\) 0 0
\(772\) −8.14766e6 + 4.46479e6i −0.492028 + 0.269623i
\(773\) 6.84734e6i 0.412167i −0.978534 0.206084i \(-0.933928\pi\)
0.978534 0.206084i \(-0.0660719\pi\)
\(774\) 0 0