Properties

Label 108.5.f.a.91.2
Level 108
Weight 5
Character 108.91
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 91.2
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.89672 + 0.903087i) q^{2} +(14.3689 - 7.03816i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(10.5700 - 6.10260i) q^{7} +(-49.6354 + 40.4021i) q^{8} +O(q^{10})\) \(q+(-3.89672 + 0.903087i) q^{2} +(14.3689 - 7.03816i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(10.5700 - 6.10260i) q^{7} +(-49.6354 + 40.4021i) q^{8} +(45.5763 - 149.524i) q^{10} +(96.1446 - 55.5091i) q^{11} +(-104.491 + 180.984i) q^{13} +(-35.6772 + 33.3258i) q^{14} +(156.929 - 202.261i) q^{16} -93.3790 q^{17} +26.8894i q^{19} +(-42.5651 + 623.812i) q^{20} +(-324.519 + 303.130i) q^{22} +(-757.577 - 437.387i) q^{23} +(-451.080 - 781.293i) q^{25} +(243.728 - 799.608i) q^{26} +(108.928 - 162.081i) q^{28} +(-650.809 - 1127.23i) q^{29} +(-593.492 - 342.653i) q^{31} +(-428.848 + 929.874i) q^{32} +(363.872 - 84.3293i) q^{34} +476.966i q^{35} -1760.25 q^{37} +(-24.2835 - 104.780i) q^{38} +(-397.492 - 2469.26i) q^{40} +(39.0421 - 67.6229i) q^{41} +(1405.46 - 811.442i) q^{43} +(990.807 - 1474.28i) q^{44} +(3347.06 + 1020.22i) q^{46} +(-1999.54 + 1154.43i) q^{47} +(-1126.02 + 1950.32i) q^{49} +(2463.31 + 2637.12i) q^{50} +(-227.626 + 3335.96i) q^{52} +1313.48 q^{53} +4338.47i q^{55} +(-278.089 + 729.956i) q^{56} +(3554.01 + 3804.78i) q^{58} +(4818.38 + 2781.89i) q^{59} +(-1090.13 - 1888.16i) q^{61} +(2622.12 + 799.247i) q^{62} +(831.345 - 4010.75i) q^{64} +(-4083.39 - 7072.65i) q^{65} +(213.077 + 123.020i) q^{67} +(-1341.75 + 657.216i) q^{68} +(-430.742 - 1858.60i) q^{70} -4608.15i q^{71} +2564.79 q^{73} +(6859.21 - 1589.66i) q^{74} +(189.252 + 386.370i) q^{76} +(677.500 - 1173.46i) q^{77} +(-4486.29 + 2590.16i) q^{79} +(3778.87 + 9263.05i) q^{80} +(-91.0669 + 298.766i) q^{82} +(-1622.37 + 936.677i) q^{83} +(1824.57 - 3160.25i) q^{85} +(-4743.88 + 4431.22i) q^{86} +(-2529.49 + 6639.66i) q^{88} +1167.17 q^{89} +2550.67i q^{91} +(-13963.9 - 952.813i) q^{92} +(6749.08 - 6304.26i) q^{94} +(-910.026 - 525.404i) q^{95} +(2869.58 + 4970.26i) q^{97} +(2626.47 - 8616.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.89672 + 0.903087i −0.974180 + 0.225772i
\(3\) 0 0
\(4\) 14.3689 7.03816i 0.898054 0.439885i
\(5\) −19.5394 + 33.8433i −0.781578 + 1.35373i 0.149444 + 0.988770i \(0.452251\pi\)
−0.931022 + 0.364962i \(0.881082\pi\)
\(6\) 0 0
\(7\) 10.5700 6.10260i 0.215715 0.124543i −0.388250 0.921554i \(-0.626920\pi\)
0.603964 + 0.797011i \(0.293587\pi\)
\(8\) −49.6354 + 40.4021i −0.775553 + 0.631282i
\(9\) 0 0
\(10\) 45.5763 149.524i 0.455763 1.49524i
\(11\) 96.1446 55.5091i 0.794583 0.458753i −0.0469902 0.998895i \(-0.514963\pi\)
0.841574 + 0.540142i \(0.181630\pi\)
\(12\) 0 0
\(13\) −104.491 + 180.984i −0.618290 + 1.07091i 0.371507 + 0.928430i \(0.378841\pi\)
−0.989798 + 0.142480i \(0.954492\pi\)
\(14\) −35.6772 + 33.3258i −0.182027 + 0.170030i
\(15\) 0 0
\(16\) 156.929 202.261i 0.613003 0.790081i
\(17\) −93.3790 −0.323111 −0.161555 0.986864i \(-0.551651\pi\)
−0.161555 + 0.986864i \(0.551651\pi\)
\(18\) 0 0
\(19\) 26.8894i 0.0744859i 0.999306 + 0.0372429i \(0.0118575\pi\)
−0.999306 + 0.0372429i \(0.988142\pi\)
\(20\) −42.5651 + 623.812i −0.106413 + 1.55953i
\(21\) 0 0
\(22\) −324.519 + 303.130i −0.670494 + 0.626303i
\(23\) −757.577 437.387i −1.43209 0.826819i −0.434812 0.900521i \(-0.643185\pi\)
−0.997280 + 0.0737029i \(0.976518\pi\)
\(24\) 0 0
\(25\) −451.080 781.293i −0.721728 1.25007i
\(26\) 243.728 799.608i 0.360545 1.18285i
\(27\) 0 0
\(28\) 108.928 162.081i 0.138939 0.206736i
\(29\) −650.809 1127.23i −0.773851 1.34035i −0.935438 0.353491i \(-0.884995\pi\)
0.161587 0.986858i \(-0.448339\pi\)
\(30\) 0 0
\(31\) −593.492 342.653i −0.617577 0.356558i 0.158348 0.987383i \(-0.449383\pi\)
−0.775925 + 0.630825i \(0.782717\pi\)
\(32\) −428.848 + 929.874i −0.418797 + 0.908080i
\(33\) 0 0
\(34\) 363.872 84.3293i 0.314768 0.0729493i
\(35\) 476.966i 0.389360i
\(36\) 0 0
\(37\) −1760.25 −1.28579 −0.642897 0.765953i \(-0.722268\pi\)
−0.642897 + 0.765953i \(0.722268\pi\)
\(38\) −24.2835 104.780i −0.0168168 0.0725626i
\(39\) 0 0
\(40\) −397.492 2469.26i −0.248432 1.54329i
\(41\) 39.0421 67.6229i 0.0232255 0.0402278i −0.854179 0.519979i \(-0.825940\pi\)
0.877405 + 0.479751i \(0.159273\pi\)
\(42\) 0 0
\(43\) 1405.46 811.442i 0.760118 0.438855i −0.0692198 0.997601i \(-0.522051\pi\)
0.829338 + 0.558747i \(0.188718\pi\)
\(44\) 990.807 1474.28i 0.511780 0.761510i
\(45\) 0 0
\(46\) 3347.06 + 1020.22i 1.58179 + 0.482144i
\(47\) −1999.54 + 1154.43i −0.905177 + 0.522604i −0.878876 0.477050i \(-0.841706\pi\)
−0.0263007 + 0.999654i \(0.508373\pi\)
\(48\) 0 0
\(49\) −1126.02 + 1950.32i −0.468978 + 0.812294i
\(50\) 2463.31 + 2637.12i 0.985323 + 1.05485i
\(51\) 0 0
\(52\) −227.626 + 3335.96i −0.0841811 + 1.23371i
\(53\) 1313.48 0.467598 0.233799 0.972285i \(-0.424884\pi\)
0.233799 + 0.972285i \(0.424884\pi\)
\(54\) 0 0
\(55\) 4338.47i 1.43420i
\(56\) −278.089 + 729.956i −0.0886764 + 0.232767i
\(57\) 0 0
\(58\) 3554.01 + 3804.78i 1.05648 + 1.13103i
\(59\) 4818.38 + 2781.89i 1.38419 + 0.799164i 0.992653 0.120997i \(-0.0386091\pi\)
0.391540 + 0.920161i \(0.371942\pi\)
\(60\) 0 0
\(61\) −1090.13 1888.16i −0.292967 0.507433i 0.681543 0.731778i \(-0.261309\pi\)
−0.974510 + 0.224345i \(0.927976\pi\)
\(62\) 2622.12 + 799.247i 0.682132 + 0.207921i
\(63\) 0 0
\(64\) 831.345 4010.75i 0.202965 0.979186i
\(65\) −4083.39 7072.65i −0.966484 1.67400i
\(66\) 0 0
\(67\) 213.077 + 123.020i 0.0474665 + 0.0274048i 0.523545 0.851998i \(-0.324609\pi\)
−0.476079 + 0.879403i \(0.657942\pi\)
\(68\) −1341.75 + 657.216i −0.290171 + 0.142131i
\(69\) 0 0
\(70\) −430.742 1858.60i −0.0879065 0.379307i
\(71\) 4608.15i 0.914134i −0.889432 0.457067i \(-0.848900\pi\)
0.889432 0.457067i \(-0.151100\pi\)
\(72\) 0 0
\(73\) 2564.79 0.481290 0.240645 0.970613i \(-0.422641\pi\)
0.240645 + 0.970613i \(0.422641\pi\)
\(74\) 6859.21 1589.66i 1.25259 0.290296i
\(75\) 0 0
\(76\) 189.252 + 386.370i 0.0327652 + 0.0668923i
\(77\) 677.500 1173.46i 0.114269 0.197919i
\(78\) 0 0
\(79\) −4486.29 + 2590.16i −0.718842 + 0.415023i −0.814326 0.580408i \(-0.802893\pi\)
0.0954846 + 0.995431i \(0.469560\pi\)
\(80\) 3778.87 + 9263.05i 0.590449 + 1.44735i
\(81\) 0 0
\(82\) −91.0669 + 298.766i −0.0135436 + 0.0444328i
\(83\) −1622.37 + 936.677i −0.235502 + 0.135967i −0.613108 0.789999i \(-0.710081\pi\)
0.377606 + 0.925966i \(0.376747\pi\)
\(84\) 0 0
\(85\) 1824.57 3160.25i 0.252536 0.437405i
\(86\) −4743.88 + 4431.22i −0.641411 + 0.599137i
\(87\) 0 0
\(88\) −2529.49 + 6639.66i −0.326639 + 0.857394i
\(89\) 1167.17 0.147352 0.0736759 0.997282i \(-0.476527\pi\)
0.0736759 + 0.997282i \(0.476527\pi\)
\(90\) 0 0
\(91\) 2550.67i 0.308015i
\(92\) −13963.9 952.813i −1.64980 0.112572i
\(93\) 0 0
\(94\) 6749.08 6304.26i 0.763816 0.713474i
\(95\) −910.026 525.404i −0.100834 0.0582165i
\(96\) 0 0
\(97\) 2869.58 + 4970.26i 0.304983 + 0.528245i 0.977257 0.212056i \(-0.0680160\pi\)
−0.672275 + 0.740302i \(0.734683\pi\)
\(98\) 2626.47 8616.73i 0.273476 0.897203i
\(99\) 0 0
\(100\) −11980.4 8051.53i −1.19804 0.805153i
\(101\) 7793.37 + 13498.5i 0.763981 + 1.32325i 0.940783 + 0.339008i \(0.110091\pi\)
−0.176802 + 0.984246i \(0.556575\pi\)
\(102\) 0 0
\(103\) −9636.52 5563.65i −0.908334 0.524427i −0.0284395 0.999596i \(-0.509054\pi\)
−0.879895 + 0.475168i \(0.842387\pi\)
\(104\) −2125.67 13204.9i −0.196530 1.22086i
\(105\) 0 0
\(106\) −5118.28 + 1186.19i −0.455525 + 0.105570i
\(107\) 4464.91i 0.389983i −0.980805 0.194991i \(-0.937532\pi\)
0.980805 0.194991i \(-0.0624679\pi\)
\(108\) 0 0
\(109\) −4736.05 −0.398624 −0.199312 0.979936i \(-0.563871\pi\)
−0.199312 + 0.979936i \(0.563871\pi\)
\(110\) −3918.02 16905.8i −0.323803 1.39717i
\(111\) 0 0
\(112\) 424.422 3095.57i 0.0338347 0.246777i
\(113\) −9173.06 + 15888.2i −0.718385 + 1.24428i 0.243254 + 0.969963i \(0.421785\pi\)
−0.961639 + 0.274317i \(0.911548\pi\)
\(114\) 0 0
\(115\) 29605.3 17092.6i 2.23858 1.29245i
\(116\) −17285.0 11616.6i −1.28456 0.863301i
\(117\) 0 0
\(118\) −21288.2 6488.84i −1.52888 0.466018i
\(119\) −987.017 + 569.855i −0.0696997 + 0.0402411i
\(120\) 0 0
\(121\) −1157.98 + 2005.68i −0.0790915 + 0.136990i
\(122\) 5953.10 + 6373.14i 0.399966 + 0.428188i
\(123\) 0 0
\(124\) −10939.4 746.442i −0.711462 0.0485459i
\(125\) 10831.1 0.693190
\(126\) 0 0
\(127\) 8169.42i 0.506505i −0.967400 0.253252i \(-0.918500\pi\)
0.967400 0.253252i \(-0.0815003\pi\)
\(128\) 382.534 + 16379.5i 0.0233480 + 0.999727i
\(129\) 0 0
\(130\) 22299.1 + 23872.5i 1.31947 + 1.41257i
\(131\) −9131.01 5271.79i −0.532079 0.307196i 0.209784 0.977748i \(-0.432724\pi\)
−0.741863 + 0.670552i \(0.766057\pi\)
\(132\) 0 0
\(133\) 164.095 + 284.221i 0.00927669 + 0.0160677i
\(134\) −941.399 286.948i −0.0524281 0.0159806i
\(135\) 0 0
\(136\) 4634.90 3772.70i 0.250589 0.203974i
\(137\) 1612.85 + 2793.54i 0.0859318 + 0.148838i 0.905788 0.423731i \(-0.139280\pi\)
−0.819856 + 0.572570i \(0.805947\pi\)
\(138\) 0 0
\(139\) −16276.4 9397.17i −0.842419 0.486371i 0.0156666 0.999877i \(-0.495013\pi\)
−0.858086 + 0.513506i \(0.828346\pi\)
\(140\) 3356.96 + 6853.46i 0.171274 + 0.349666i
\(141\) 0 0
\(142\) 4161.56 + 17956.7i 0.206386 + 0.890531i
\(143\) 23200.8i 1.13457i
\(144\) 0 0
\(145\) 50865.8 2.41930
\(146\) −9994.28 + 2316.23i −0.468863 + 0.108662i
\(147\) 0 0
\(148\) −25292.8 + 12388.9i −1.15471 + 0.565601i
\(149\) −3825.13 + 6625.31i −0.172295 + 0.298424i −0.939222 0.343311i \(-0.888452\pi\)
0.766927 + 0.641735i \(0.221785\pi\)
\(150\) 0 0
\(151\) 974.974 562.901i 0.0427601 0.0246876i −0.478468 0.878105i \(-0.658808\pi\)
0.521228 + 0.853418i \(0.325474\pi\)
\(152\) −1086.39 1334.67i −0.0470216 0.0577677i
\(153\) 0 0
\(154\) −1580.29 + 5184.51i −0.0666338 + 0.218608i
\(155\) 23193.0 13390.5i 0.965369 0.557356i
\(156\) 0 0
\(157\) 1755.81 3041.15i 0.0712326 0.123378i −0.828209 0.560419i \(-0.810640\pi\)
0.899442 + 0.437041i \(0.143973\pi\)
\(158\) 15142.7 14144.6i 0.606581 0.566602i
\(159\) 0 0
\(160\) −23090.6 32682.9i −0.901975 1.27667i
\(161\) −10676.8 −0.411898
\(162\) 0 0
\(163\) 41947.9i 1.57883i 0.613861 + 0.789414i \(0.289615\pi\)
−0.613861 + 0.789414i \(0.710385\pi\)
\(164\) 85.0502 1246.45i 0.00316219 0.0463433i
\(165\) 0 0
\(166\) 5476.03 5115.11i 0.198724 0.185626i
\(167\) 5900.58 + 3406.70i 0.211574 + 0.122152i 0.602043 0.798464i \(-0.294354\pi\)
−0.390469 + 0.920616i \(0.627687\pi\)
\(168\) 0 0
\(169\) −7556.26 13087.8i −0.264566 0.458241i
\(170\) −4255.87 + 13962.4i −0.147262 + 0.483127i
\(171\) 0 0
\(172\) 14483.8 21551.3i 0.489582 0.728480i
\(173\) 7874.16 + 13638.4i 0.263095 + 0.455693i 0.967063 0.254539i \(-0.0819236\pi\)
−0.703968 + 0.710232i \(0.748590\pi\)
\(174\) 0 0
\(175\) −9535.85 5505.52i −0.311375 0.179772i
\(176\) 3860.53 28157.2i 0.124630 0.909002i
\(177\) 0 0
\(178\) −4548.15 + 1054.06i −0.143547 + 0.0332679i
\(179\) 22497.6i 0.702151i −0.936347 0.351075i \(-0.885816\pi\)
0.936347 0.351075i \(-0.114184\pi\)
\(180\) 0 0
\(181\) −21847.2 −0.666867 −0.333434 0.942774i \(-0.608207\pi\)
−0.333434 + 0.942774i \(0.608207\pi\)
\(182\) −2303.48 9939.25i −0.0695410 0.300062i
\(183\) 0 0
\(184\) 55274.0 8897.79i 1.63262 0.262813i
\(185\) 34394.3 59572.7i 1.00495 1.74062i
\(186\) 0 0
\(187\) −8977.88 + 5183.38i −0.256738 + 0.148228i
\(188\) −20606.0 + 30660.9i −0.583012 + 0.867500i
\(189\) 0 0
\(190\) 4020.60 + 1225.52i 0.111374 + 0.0339479i
\(191\) 16182.1 9342.76i 0.443577 0.256099i −0.261537 0.965194i \(-0.584229\pi\)
0.705114 + 0.709094i \(0.250896\pi\)
\(192\) 0 0
\(193\) −23049.7 + 39923.2i −0.618800 + 1.07179i 0.370905 + 0.928671i \(0.379048\pi\)
−0.989705 + 0.143123i \(0.954286\pi\)
\(194\) −15670.5 16776.2i −0.416371 0.445750i
\(195\) 0 0
\(196\) −2452.94 + 35948.9i −0.0638520 + 0.935780i
\(197\) −15934.7 −0.410592 −0.205296 0.978700i \(-0.565816\pi\)
−0.205296 + 0.978700i \(0.565816\pi\)
\(198\) 0 0
\(199\) 73733.8i 1.86192i 0.365124 + 0.930959i \(0.381026\pi\)
−0.365124 + 0.930959i \(0.618974\pi\)
\(200\) 53955.4 + 20555.2i 1.34888 + 0.513881i
\(201\) 0 0
\(202\) −42558.9 45561.9i −1.04301 1.11660i
\(203\) −13758.1 7943.25i −0.333862 0.192755i
\(204\) 0 0
\(205\) 1525.72 + 2642.63i 0.0363051 + 0.0628823i
\(206\) 42575.3 + 12977.4i 1.00328 + 0.305810i
\(207\) 0 0
\(208\) 20208.3 + 49536.0i 0.467092 + 1.14497i
\(209\) 1492.61 + 2585.27i 0.0341706 + 0.0591852i
\(210\) 0 0
\(211\) −15431.2 8909.20i −0.346605 0.200112i 0.316584 0.948564i \(-0.397464\pi\)
−0.663189 + 0.748452i \(0.730797\pi\)
\(212\) 18873.3 9244.50i 0.419929 0.205689i
\(213\) 0 0
\(214\) 4032.20 + 17398.5i 0.0880471 + 0.379913i
\(215\) 63420.5i 1.37200i
\(216\) 0 0
\(217\) −8364.29 −0.177627
\(218\) 18455.1 4277.07i 0.388332 0.0899980i
\(219\) 0 0
\(220\) 30534.8 + 62338.9i 0.630885 + 1.28799i
\(221\) 9757.27 16900.1i 0.199776 0.346022i
\(222\) 0 0
\(223\) 58353.8 33690.6i 1.17344 0.677483i 0.218949 0.975736i \(-0.429737\pi\)
0.954487 + 0.298253i \(0.0964039\pi\)
\(224\) 1141.72 + 12445.9i 0.0227542 + 0.248044i
\(225\) 0 0
\(226\) 21396.4 70196.0i 0.418914 1.37434i
\(227\) −54381.5 + 31397.2i −1.05536 + 0.609310i −0.924144 0.382044i \(-0.875220\pi\)
−0.131212 + 0.991354i \(0.541887\pi\)
\(228\) 0 0
\(229\) 20463.2 35443.2i 0.390213 0.675868i −0.602265 0.798297i \(-0.705735\pi\)
0.992477 + 0.122428i \(0.0390681\pi\)
\(230\) −99927.3 + 93341.2i −1.88898 + 1.76448i
\(231\) 0 0
\(232\) 77845.7 + 29656.7i 1.44630 + 0.550993i
\(233\) −79254.5 −1.45986 −0.729932 0.683520i \(-0.760448\pi\)
−0.729932 + 0.683520i \(0.760448\pi\)
\(234\) 0 0
\(235\) 90227.9i 1.63382i
\(236\) 88814.0 + 6060.13i 1.59462 + 0.108807i
\(237\) 0 0
\(238\) 3331.50 3111.93i 0.0588148 0.0549383i
\(239\) 39084.7 + 22565.5i 0.684243 + 0.395048i 0.801452 0.598059i \(-0.204061\pi\)
−0.117209 + 0.993107i \(0.537395\pi\)
\(240\) 0 0
\(241\) −37826.8 65517.9i −0.651276 1.12804i −0.982814 0.184601i \(-0.940901\pi\)
0.331537 0.943442i \(-0.392433\pi\)
\(242\) 2701.02 8861.32i 0.0461208 0.151310i
\(243\) 0 0
\(244\) −28953.1 19458.2i −0.486312 0.326831i
\(245\) −44003.5 76216.3i −0.733086 1.26974i
\(246\) 0 0
\(247\) −4866.55 2809.70i −0.0797677 0.0460539i
\(248\) 43302.1 6970.60i 0.704053 0.113336i
\(249\) 0 0
\(250\) −42205.8 + 9781.43i −0.675292 + 0.156503i
\(251\) 78270.9i 1.24238i −0.783662 0.621188i \(-0.786650\pi\)
0.783662 0.621188i \(-0.213350\pi\)
\(252\) 0 0
\(253\) −97115.9 −1.51722
\(254\) 7377.70 + 31833.9i 0.114355 + 0.493427i
\(255\) 0 0
\(256\) −16282.8 63481.0i −0.248455 0.968643i
\(257\) −11506.3 + 19929.5i −0.174209 + 0.301739i −0.939887 0.341485i \(-0.889070\pi\)
0.765678 + 0.643224i \(0.222403\pi\)
\(258\) 0 0
\(259\) −18605.9 + 10742.1i −0.277365 + 0.160136i
\(260\) −108452. 72886.4i −1.60432 1.07820i
\(261\) 0 0
\(262\) 40341.9 + 12296.6i 0.587697 + 0.179136i
\(263\) −75237.8 + 43438.5i −1.08774 + 0.628006i −0.932973 0.359945i \(-0.882795\pi\)
−0.154765 + 0.987951i \(0.549462\pi\)
\(264\) 0 0
\(265\) −25664.7 + 44452.6i −0.365464 + 0.633003i
\(266\) −896.110 959.339i −0.0126648 0.0135584i
\(267\) 0 0
\(268\) 3927.51 + 267.990i 0.0546824 + 0.00373120i
\(269\) 54083.3 0.747409 0.373705 0.927548i \(-0.378087\pi\)
0.373705 + 0.927548i \(0.378087\pi\)
\(270\) 0 0
\(271\) 47957.3i 0.653004i −0.945197 0.326502i \(-0.894130\pi\)
0.945197 0.326502i \(-0.105870\pi\)
\(272\) −14653.8 + 18886.9i −0.198068 + 0.255284i
\(273\) 0 0
\(274\) −8807.65 9429.11i −0.117316 0.125594i
\(275\) −86737.8 50078.1i −1.14695 0.662190i
\(276\) 0 0
\(277\) 36861.8 + 63846.5i 0.480415 + 0.832103i 0.999748 0.0224689i \(-0.00715269\pi\)
−0.519332 + 0.854572i \(0.673819\pi\)
\(278\) 71911.0 + 21919.2i 0.930477 + 0.283618i
\(279\) 0 0
\(280\) −19270.4 23674.4i −0.245796 0.301969i
\(281\) 28062.0 + 48604.7i 0.355390 + 0.615554i 0.987185 0.159582i \(-0.0510147\pi\)
−0.631795 + 0.775136i \(0.717681\pi\)
\(282\) 0 0
\(283\) 132300. + 76383.2i 1.65191 + 0.953730i 0.976287 + 0.216481i \(0.0694578\pi\)
0.675621 + 0.737249i \(0.263876\pi\)
\(284\) −32432.9 66213.9i −0.402114 0.820942i
\(285\) 0 0
\(286\) −20952.4 90407.1i −0.256154 1.10528i
\(287\) 953.034i 0.0115703i
\(288\) 0 0
\(289\) −74801.4 −0.895600
\(290\) −198210. + 45936.2i −2.35683 + 0.546210i
\(291\) 0 0
\(292\) 36853.2 18051.4i 0.432224 0.211712i
\(293\) −19420.1 + 33636.7i −0.226213 + 0.391812i −0.956683 0.291133i \(-0.905968\pi\)
0.730470 + 0.682945i \(0.239301\pi\)
\(294\) 0 0
\(295\) −188297. + 108713.i −2.16371 + 1.24922i
\(296\) 87370.8 71117.8i 0.997201 0.811699i
\(297\) 0 0
\(298\) 8922.21 29271.4i 0.100471 0.329618i
\(299\) 158320. 91406.1i 1.77090 1.02243i
\(300\) 0 0
\(301\) 9903.82 17153.9i 0.109312 0.189335i
\(302\) −3290.85 + 3073.96i −0.0360823 + 0.0337042i
\(303\) 0 0
\(304\) 5438.67 + 4219.72i 0.0588498 + 0.0456600i
\(305\) 85202.0 0.915905
\(306\) 0 0
\(307\) 457.528i 0.00485446i −0.999997 0.00242723i \(-0.999227\pi\)
0.999997 0.00242723i \(-0.000772612\pi\)
\(308\) 1475.88 21629.7i 0.0155579 0.228008i
\(309\) 0 0
\(310\) −78283.9 + 73124.3i −0.814608 + 0.760919i
\(311\) −9285.82 5361.17i −0.0960062 0.0554292i 0.451228 0.892409i \(-0.350986\pi\)
−0.547234 + 0.836979i \(0.684319\pi\)
\(312\) 0 0
\(313\) −8976.10 15547.1i −0.0916218 0.158694i 0.816572 0.577244i \(-0.195872\pi\)
−0.908194 + 0.418550i \(0.862538\pi\)
\(314\) −4095.48 + 13436.2i −0.0415380 + 0.136275i
\(315\) 0 0
\(316\) −46232.9 + 68792.9i −0.462996 + 0.688921i
\(317\) −30685.9 53149.6i −0.305366 0.528909i 0.671977 0.740572i \(-0.265445\pi\)
−0.977343 + 0.211663i \(0.932112\pi\)
\(318\) 0 0
\(319\) −125143. 72251.6i −1.22978 0.710013i
\(320\) 119493. + 106503.i 1.16692 + 1.04007i
\(321\) 0 0
\(322\) 41604.5 9642.08i 0.401262 0.0929949i
\(323\) 2510.90i 0.0240672i
\(324\) 0 0
\(325\) 188535. 1.78495
\(326\) −37882.6 163459.i −0.356455 1.53806i
\(327\) 0 0
\(328\) 794.236 + 4933.87i 0.00738247 + 0.0458607i
\(329\) −14090.1 + 24404.7i −0.130173 + 0.225467i
\(330\) 0 0
\(331\) 160993. 92949.3i 1.46944 0.848379i 0.470023 0.882654i \(-0.344245\pi\)
0.999412 + 0.0342747i \(0.0109121\pi\)
\(332\) −16719.2 + 24877.5i −0.151684 + 0.225700i
\(333\) 0 0
\(334\) −26069.4 7946.22i −0.233689 0.0712308i
\(335\) −8326.81 + 4807.49i −0.0741975 + 0.0428379i
\(336\) 0 0
\(337\) 73998.8 128170.i 0.651576 1.12856i −0.331165 0.943573i \(-0.607442\pi\)
0.982741 0.184989i \(-0.0592251\pi\)
\(338\) 41264.1 + 44175.7i 0.361193 + 0.386678i
\(339\) 0 0
\(340\) 3974.69 58250.9i 0.0343831 0.503901i
\(341\) −76081.3 −0.654289
\(342\) 0 0
\(343\) 56791.2i 0.482717i
\(344\) −36976.6 + 97059.7i −0.312471 + 0.820204i
\(345\) 0 0
\(346\) −43000.1 46034.1i −0.359184 0.384528i
\(347\) 125556. + 72490.0i 1.04275 + 0.602031i 0.920611 0.390482i \(-0.127692\pi\)
0.122138 + 0.992513i \(0.461025\pi\)
\(348\) 0 0
\(349\) 89475.8 + 154977.i 0.734606 + 1.27238i 0.954896 + 0.296941i \(0.0959664\pi\)
−0.220290 + 0.975435i \(0.570700\pi\)
\(350\) 42130.5 + 12841.8i 0.343922 + 0.104831i
\(351\) 0 0
\(352\) 10385.0 + 113207.i 0.0838150 + 0.913670i
\(353\) 13197.7 + 22859.1i 0.105913 + 0.183446i 0.914111 0.405465i \(-0.132890\pi\)
−0.808198 + 0.588911i \(0.799557\pi\)
\(354\) 0 0
\(355\) 155955. + 90040.7i 1.23749 + 0.714467i
\(356\) 16771.0 8214.76i 0.132330 0.0648179i
\(357\) 0 0
\(358\) 20317.3 + 87666.9i 0.158526 + 0.684022i
\(359\) 181364.i 1.40722i 0.710587 + 0.703609i \(0.248429\pi\)
−0.710587 + 0.703609i \(0.751571\pi\)
\(360\) 0 0
\(361\) 129598. 0.994452
\(362\) 85132.6 19730.0i 0.649649 0.150560i
\(363\) 0 0
\(364\) 17952.0 + 36650.2i 0.135491 + 0.276614i
\(365\) −50114.6 + 86801.1i −0.376165 + 0.651537i
\(366\) 0 0
\(367\) −181000. + 104500.i −1.34383 + 0.775863i −0.987368 0.158445i \(-0.949352\pi\)
−0.356467 + 0.934308i \(0.616019\pi\)
\(368\) −207352. + 84589.4i −1.53113 + 0.624626i
\(369\) 0 0
\(370\) −80225.8 + 263199.i −0.586017 + 1.92257i
\(371\) 13883.5 8015.67i 0.100868 0.0582360i
\(372\) 0 0
\(373\) 38298.0 66334.0i 0.275269 0.476781i −0.694934 0.719074i \(-0.744566\pi\)
0.970203 + 0.242293i \(0.0778996\pi\)
\(374\) 30303.3 28306.0i 0.216644 0.202365i
\(375\) 0 0
\(376\) 52606.3 138086.i 0.372102 0.976729i
\(377\) 272015. 1.91386
\(378\) 0 0
\(379\) 232118.i 1.61596i −0.589211 0.807979i \(-0.700561\pi\)
0.589211 0.807979i \(-0.299439\pi\)
\(380\) −16773.9 1144.55i −0.116163 0.00792625i
\(381\) 0 0
\(382\) −54620.0 + 51020.0i −0.374304 + 0.349634i
\(383\) 74119.1 + 42792.7i 0.505280 + 0.291724i 0.730891 0.682494i \(-0.239105\pi\)
−0.225611 + 0.974217i \(0.572438\pi\)
\(384\) 0 0
\(385\) 26476.0 + 45857.7i 0.178620 + 0.309379i
\(386\) 53764.1 176386.i 0.360842 1.18383i
\(387\) 0 0
\(388\) 76214.1 + 51220.4i 0.506258 + 0.340236i
\(389\) 60869.2 + 105429.i 0.402252 + 0.696721i 0.993997 0.109404i \(-0.0348942\pi\)
−0.591745 + 0.806125i \(0.701561\pi\)
\(390\) 0 0
\(391\) 70741.7 + 40842.8i 0.462724 + 0.267154i
\(392\) −22906.6 142298.i −0.149069 0.926035i
\(393\) 0 0
\(394\) 62092.9 14390.4i 0.399990 0.0927001i
\(395\) 202441.i 1.29749i
\(396\) 0 0
\(397\) −71690.8 −0.454865 −0.227432 0.973794i \(-0.573033\pi\)
−0.227432 + 0.973794i \(0.573033\pi\)
\(398\) −66588.0 287320.i −0.420368 1.81384i
\(399\) 0 0
\(400\) −228812. 31371.6i −1.43008 0.196073i
\(401\) −43140.3 + 74721.1i −0.268283 + 0.464681i −0.968419 0.249330i \(-0.919790\pi\)
0.700135 + 0.714010i \(0.253123\pi\)
\(402\) 0 0
\(403\) 124029. 71608.3i 0.763684 0.440913i
\(404\) 206987. + 139107.i 1.26818 + 0.852291i
\(405\) 0 0
\(406\) 60785.0 + 18527.9i 0.368761 + 0.112402i
\(407\) −169239. + 97710.0i −1.02167 + 0.589862i
\(408\) 0 0
\(409\) −115231. + 199585.i −0.688844 + 1.19311i 0.283368 + 0.959011i \(0.408548\pi\)
−0.972212 + 0.234102i \(0.924785\pi\)
\(410\) −8331.84 8919.73i −0.0495648 0.0530620i
\(411\) 0 0
\(412\) −177624. 12120.0i −1.04642 0.0714015i
\(413\) 67907.1 0.398121
\(414\) 0 0
\(415\) 73208.6i 0.425075i
\(416\) −123481. 174778.i −0.713534 1.00995i
\(417\) 0 0
\(418\) −8150.99 8726.12i −0.0466507 0.0499423i
\(419\) 48172.3 + 27812.3i 0.274391 + 0.158420i 0.630881 0.775879i \(-0.282693\pi\)
−0.356491 + 0.934299i \(0.616027\pi\)
\(420\) 0 0
\(421\) −70485.7 122085.i −0.397683 0.688807i 0.595757 0.803165i \(-0.296852\pi\)
−0.993440 + 0.114358i \(0.963519\pi\)
\(422\) 68176.8 + 20781.0i 0.382835 + 0.116692i
\(423\) 0 0
\(424\) −65195.3 + 53067.4i −0.362647 + 0.295186i
\(425\) 42121.4 + 72956.4i 0.233198 + 0.403911i
\(426\) 0 0
\(427\) −23045.4 13305.2i −0.126394 0.0729738i
\(428\) −31424.7 64155.7i −0.171547 0.350225i
\(429\) 0 0
\(430\) −57274.3 247132.i −0.309758 1.33657i
\(431\) 191015.i 1.02828i −0.857705 0.514142i \(-0.828111\pi\)
0.857705 0.514142i \(-0.171889\pi\)
\(432\) 0 0
\(433\) 48243.4 0.257313 0.128657 0.991689i \(-0.458933\pi\)
0.128657 + 0.991689i \(0.458933\pi\)
\(434\) 32593.3 7553.68i 0.173041 0.0401032i
\(435\) 0 0
\(436\) −68051.7 + 33333.1i −0.357986 + 0.175349i
\(437\) 11761.1 20370.8i 0.0615863 0.106671i
\(438\) 0 0
\(439\) −227081. + 131105.i −1.17829 + 0.680285i −0.955618 0.294609i \(-0.904811\pi\)
−0.222670 + 0.974894i \(0.571477\pi\)
\(440\) −175283. 215342.i −0.905388 1.11230i
\(441\) 0 0
\(442\) −22759.1 + 74666.6i −0.116496 + 0.382192i
\(443\) −78793.6 + 45491.5i −0.401498 + 0.231805i −0.687130 0.726534i \(-0.741130\pi\)
0.285632 + 0.958339i \(0.407796\pi\)
\(444\) 0 0
\(445\) −22805.9 + 39501.0i −0.115167 + 0.199475i
\(446\) −196963. + 183981.i −0.990181 + 0.924920i
\(447\) 0 0
\(448\) −15688.7 47467.0i −0.0781681 0.236503i
\(449\) −283350. −1.40550 −0.702748 0.711438i \(-0.748044\pi\)
−0.702748 + 0.711438i \(0.748044\pi\)
\(450\) 0 0
\(451\) 8668.77i 0.0426191i
\(452\) −19982.8 + 292857.i −0.0978091 + 1.43344i
\(453\) 0 0
\(454\) 183555. 171457.i 0.890542 0.831848i
\(455\) −86323.1 49838.7i −0.416970 0.240737i
\(456\) 0 0
\(457\) −99226.7 171866.i −0.475112 0.822918i 0.524482 0.851422i \(-0.324259\pi\)
−0.999594 + 0.0285035i \(0.990926\pi\)
\(458\) −47730.9 + 156592.i −0.227546 + 0.746517i
\(459\) 0 0
\(460\) 305094. 453968.i 1.44184 2.14541i
\(461\) −104347. 180735.i −0.490998 0.850433i 0.508949 0.860797i \(-0.330034\pi\)
−0.999946 + 0.0103639i \(0.996701\pi\)
\(462\) 0 0
\(463\) 22687.9 + 13098.9i 0.105836 + 0.0611044i 0.551984 0.833855i \(-0.313871\pi\)
−0.446148 + 0.894959i \(0.647204\pi\)
\(464\) −330126. 45262.3i −1.53336 0.210233i
\(465\) 0 0
\(466\) 308833. 71573.7i 1.42217 0.329596i
\(467\) 96607.8i 0.442974i −0.975163 0.221487i \(-0.928909\pi\)
0.975163 0.221487i \(-0.0710911\pi\)
\(468\) 0 0
\(469\) 3002.97 0.0136523
\(470\) 81483.6 + 351593.i 0.368871 + 1.59164i
\(471\) 0 0
\(472\) −351556. + 56592.1i −1.57801 + 0.254022i
\(473\) 90084.9 156032.i 0.402652 0.697413i
\(474\) 0 0
\(475\) 21008.5 12129.3i 0.0931125 0.0537585i
\(476\) −10171.6 + 15135.0i −0.0448926 + 0.0667986i
\(477\) 0 0
\(478\) −172681. 52634.7i −0.755767 0.230365i
\(479\) −29664.3 + 17126.7i −0.129289 + 0.0746453i −0.563250 0.826287i \(-0.690449\pi\)
0.433960 + 0.900932i \(0.357116\pi\)
\(480\) 0 0
\(481\) 183931. 318577.i 0.794994 1.37697i
\(482\) 206569. + 221144.i 0.889141 + 0.951878i
\(483\) 0 0
\(484\) −2522.57 + 36969.4i −0.0107684 + 0.157816i
\(485\) −224280. −0.953470
\(486\) 0 0
\(487\) 69521.4i 0.293130i −0.989201 0.146565i \(-0.953178\pi\)
0.989201 0.146565i \(-0.0468218\pi\)
\(488\) 130394. + 49676.0i 0.547545 + 0.208597i
\(489\) 0 0
\(490\) 240299. + 257255.i 1.00083 + 1.07145i
\(491\) −174305. 100635.i −0.723016 0.417433i 0.0928458 0.995681i \(-0.470404\pi\)
−0.815862 + 0.578247i \(0.803737\pi\)
\(492\) 0 0
\(493\) 60771.9 + 105260.i 0.250040 + 0.433081i
\(494\) 21501.0 + 6553.71i 0.0881057 + 0.0268555i
\(495\) 0 0
\(496\) −162441. + 66268.0i −0.660286 + 0.269365i
\(497\) −28121.7 48708.2i −0.113849 0.197192i
\(498\) 0 0
\(499\) −46850.8 27049.3i −0.188155 0.108631i 0.402964 0.915216i \(-0.367980\pi\)
−0.591119 + 0.806585i \(0.701313\pi\)
\(500\) 155631. 76231.0i 0.622522 0.304924i
\(501\) 0 0
\(502\) 70685.5 + 305000.i 0.280493 + 1.21030i
\(503\) 239548.i 0.946795i 0.880849 + 0.473397i \(0.156973\pi\)
−0.880849 + 0.473397i \(0.843027\pi\)
\(504\) 0 0
\(505\) −609113. −2.38844
\(506\) 378433. 87704.1i 1.47805 0.342546i
\(507\) 0 0
\(508\) −57497.6 117385.i −0.222804 0.454869i
\(509\) 57738.0 100005.i 0.222857 0.386000i −0.732817 0.680425i \(-0.761795\pi\)
0.955674 + 0.294426i \(0.0951284\pi\)
\(510\) 0 0
\(511\) 27109.9 15651.9i 0.103821 0.0599412i
\(512\) 120778. + 232663.i 0.460733 + 0.887539i
\(513\) 0 0
\(514\) 26838.8 88051.1i 0.101587 0.333279i
\(515\) 376584. 217421.i 1.41987 0.819761i
\(516\) 0 0
\(517\) −128163. + 221985.i −0.479492 + 0.830505i
\(518\) 62800.9 58661.8i 0.234049 0.218623i
\(519\) 0 0
\(520\) 488431. + 186076.i 1.80633 + 0.688151i
\(521\) −217267. −0.800420 −0.400210 0.916424i \(-0.631063\pi\)
−0.400210 + 0.916424i \(0.631063\pi\)
\(522\) 0 0
\(523\) 39683.4i 0.145079i 0.997366 + 0.0725397i \(0.0231104\pi\)
−0.997366 + 0.0725397i \(0.976890\pi\)
\(524\) −168306. 11484.2i −0.612967 0.0418251i
\(525\) 0 0
\(526\) 253952. 237214.i 0.917867 0.857372i
\(527\) 55419.6 + 31996.5i 0.199546 + 0.115208i
\(528\) 0 0
\(529\) 242694. + 420359.i 0.867258 + 1.50213i
\(530\) 59863.7 196397.i 0.213114 0.699170i
\(531\) 0 0
\(532\) 4358.26 + 2929.01i 0.0153989 + 0.0103490i
\(533\) 8159.11 + 14132.0i 0.0287202 + 0.0497449i
\(534\) 0 0
\(535\) 151107. + 87241.9i 0.527932 + 0.304802i
\(536\) −15546.4 + 2502.60i −0.0541129 + 0.00871089i
\(537\) 0 0
\(538\) −210747. + 48841.9i −0.728111 + 0.168744i
\(539\) 250017.i 0.860580i
\(540\) 0 0
\(541\) −194992. −0.666228 −0.333114 0.942887i \(-0.608099\pi\)
−0.333114 + 0.942887i \(0.608099\pi\)
\(542\) 43309.6 + 186876.i 0.147430 + 0.636143i
\(543\) 0 0
\(544\) 40045.4 86830.7i 0.135318 0.293410i
\(545\) 92539.8 160284.i 0.311556 0.539630i
\(546\) 0 0
\(547\) −81637.9 + 47133.6i −0.272846 + 0.157527i −0.630180 0.776449i \(-0.717019\pi\)
0.357335 + 0.933976i \(0.383686\pi\)
\(548\) 42836.3 + 28788.5i 0.142643 + 0.0958647i
\(549\) 0 0
\(550\) 383218. + 116809.i 1.26684 + 0.386144i
\(551\) 30310.6 17499.9i 0.0998371 0.0576410i
\(552\) 0 0
\(553\) −31613.4 + 54756.1i −0.103376 + 0.179053i
\(554\) −201299. 215502.i −0.655876 0.702154i
\(555\) 0 0
\(556\) −300012. 20471.0i −0.970485 0.0662201i
\(557\) 563587. 1.81656 0.908282 0.418358i \(-0.137394\pi\)
0.908282 + 0.418358i \(0.137394\pi\)
\(558\) 0 0
\(559\) 339154.i 1.08536i
\(560\) 96471.5 + 74849.6i 0.307626 + 0.238679i
\(561\) 0 0
\(562\) −153244. 164057.i −0.485189 0.519423i
\(563\) −543509. 313795.i −1.71471 0.989986i −0.927935 0.372741i \(-0.878418\pi\)
−0.786771 0.617245i \(1.21175\pi\)
\(564\) 0 0
\(565\) −358473. 620894.i −1.12295 1.94500i
\(566\) −584516. 178166.i −1.82458 0.556150i
\(567\) 0 0
\(568\) 186179. + 228727.i 0.577077 + 0.708959i
\(569\) −38859.9 67307.3i −0.120026 0.207892i 0.799751 0.600331i \(-0.204965\pi\)
−0.919778 + 0.392439i \(0.871631\pi\)
\(570\) 0 0
\(571\) 276094. + 159403.i 0.846809 + 0.488905i 0.859573 0.511013i \(-0.170730\pi\)
−0.0127640 + 0.999919i \(0.504063\pi\)
\(572\) 163291. + 333370.i 0.499080 + 1.01891i
\(573\) 0 0
\(574\) 860.673 + 3713.71i 0.00261225 + 0.0112716i
\(575\) 789186.i 2.38695i
\(576\) 0 0
\(577\) 40053.7 0.120307 0.0601534 0.998189i \(-0.480841\pi\)
0.0601534 + 0.998189i \(0.480841\pi\)
\(578\) 291480. 67552.2i 0.872475 0.202201i
\(579\) 0 0
\(580\) 730883. 358001.i 2.17266 1.06421i
\(581\) −11432.3 + 19801.4i −0.0338675 + 0.0586602i
\(582\) 0 0
\(583\) 126284. 72910.3i 0.371546 0.214512i
\(584\) −127304. + 103623.i −0.373266 + 0.303830i
\(585\) 0 0
\(586\) 45298.0 148611.i 0.131912 0.432768i
\(587\) −11894.5 + 6867.28i −0.0345199 + 0.0199301i −0.517161 0.855888i \(-0.673011\pi\)
0.482641 + 0.875818i \(0.339678\pi\)
\(588\) 0 0
\(589\) 9213.72 15958.6i 0.0265586 0.0460008i
\(590\) 635563. 593673.i 1.82580 1.70547i
\(591\) 0 0
\(592\) −276234. + 356030.i −0.788195 + 1.01588i
\(593\) −537582. −1.52875 −0.764373 0.644775i \(-0.776951\pi\)
−0.764373 + 0.644775i \(0.776951\pi\)
\(594\) 0 0
\(595\) 44538.6i 0.125806i
\(596\) −8332.74 + 122120.i −0.0234582 + 0.343791i
\(597\) 0 0
\(598\) −534381. + 499161.i −1.49434 + 1.39585i
\(599\) 394401. + 227708.i 1.09922 + 0.634635i 0.936016 0.351958i \(-0.114484\pi\)
0.163204 + 0.986592i \(0.447817\pi\)
\(600\) 0 0
\(601\) 118996. + 206108.i 0.329446 + 0.570618i 0.982402 0.186778i \(-0.0598046\pi\)
−0.652956 + 0.757396i \(0.726471\pi\)
\(602\) −23100.9 + 75788.0i −0.0637436 + 0.209126i
\(603\) 0 0
\(604\) 10047.5 14950.3i 0.0275412 0.0409803i
\(605\) −45252.5 78379.7i −0.123632 0.214137i
\(606\) 0 0
\(607\) −516142. 297995.i −1.40085 0.808781i −0.406371 0.913708i \(-0.633206\pi\)
−0.994480 + 0.104927i \(0.966539\pi\)
\(608\) −25003.7 11531.5i −0.0676391 0.0311945i
\(609\) 0 0
\(610\) −332008. + 76944.8i −0.892256 + 0.206785i
\(611\) 482511.i 1.29248i
\(612\) 0 0
\(613\) 547275. 1.45641 0.728206 0.685358i \(-0.240354\pi\)
0.728206 + 0.685358i \(0.240354\pi\)
\(614\) 413.188 + 1782.86i 0.00109600 + 0.00472912i
\(615\) 0 0
\(616\) 13782.4 + 85617.8i 0.0363215 + 0.225633i
\(617\) 259077. 448735.i 0.680549 1.17874i −0.294265 0.955724i \(-0.595075\pi\)
0.974814 0.223021i \(-0.0715919\pi\)
\(618\) 0 0
\(619\) −176869. + 102115.i −0.461605 + 0.266508i −0.712719 0.701450i \(-0.752537\pi\)
0.251114 + 0.967958i \(0.419203\pi\)
\(620\) 239013. 355642.i 0.621781 0.925187i
\(621\) 0 0
\(622\) 41025.8 + 12505.1i 0.106042 + 0.0323226i
\(623\) 12337.1 7122.80i 0.0317860 0.0183516i
\(624\) 0 0
\(625\) 70291.3 121748.i 0.179946 0.311675i
\(626\) 49017.7 + 52476.4i 0.125085 + 0.133911i
\(627\) 0 0
\(628\) 3824.90 56055.6i 0.00969841 0.142135i
\(629\) 164370. 0.415454
\(630\) 0 0
\(631\) 177036.i 0.444633i −0.974975 0.222317i \(-0.928638\pi\)
0.974975 0.222317i \(-0.0713618\pi\)
\(632\) 118031. 309819.i 0.295503 0.775665i
\(633\) 0 0
\(634\) 167573. + 179397.i 0.416894 + 0.446310i
\(635\) 276480. + 159626.i 0.685672 + 0.395873i
\(636\) 0 0
\(637\) −235317. 407582.i −0.579929 1.00447i
\(638\) 552899. + 168529.i 1.35833 + 0.414031i
\(639\) 0 0
\(640\) −561812. 307101.i −1.37161 0.749758i
\(641\) 109444. + 189562.i 0.266364 + 0.461356i 0.967920 0.251258i \(-0.0808444\pi\)
−0.701556 + 0.712614i \(0.747511\pi\)
\(642\) 0 0
\(643\) −298938. 172592.i −0.723035 0.417445i 0.0928336 0.995682i \(-0.470408\pi\)
−0.815869 + 0.578237i \(0.803741\pi\)
\(644\) −153413. + 75145.0i −0.369906 + 0.181187i
\(645\) 0 0
\(646\) 2267.56 + 9784.29i 0.00543369 + 0.0234458i
\(647\) 398251.i 0.951366i −0.879617 0.475683i \(-0.842201\pi\)
0.879617 0.475683i \(-0.157799\pi\)
\(648\) 0 0
\(649\) 617681. 1.46648
\(650\) −734669. + 170264.i −1.73886 + 0.402991i
\(651\) 0 0
\(652\) 295236. + 602744.i 0.694502 + 1.41787i
\(653\) −171144. + 296430.i −0.401361 + 0.695178i −0.993890 0.110371i \(-0.964796\pi\)
0.592529 + 0.805549i \(0.298129\pi\)
\(654\) 0 0
\(655\) 356830. 206016.i 0.831722 0.480195i
\(656\) −7550.63 18508.7i −0.0175459 0.0430098i
\(657\) 0 0
\(658\) 32865.5 107823.i 0.0759082 0.249035i
\(659\) −452868. + 261464.i −1.04280 + 0.602061i −0.920625 0.390447i \(-0.872320\pi\)
−0.122175 + 0.992509i \(0.538987\pi\)
\(660\) 0 0
\(661\) −154294. + 267245.i −0.353140 + 0.611656i −0.986798 0.161957i \(-0.948219\pi\)
0.633658 + 0.773613i \(0.281553\pi\)
\(662\) −543403. + 507588.i −1.23996 + 1.15823i
\(663\) 0 0
\(664\) 42683.4 112040.i 0.0968106 0.254118i
\(665\) −12825.3 −0.0290018
\(666\) 0 0
\(667\) 1.13862e6i 2.55934i
\(668\) 108761. + 7421.23i 0.243737 + 0.0166312i
\(669\) 0 0
\(670\) 28105.7 26253.3i 0.0626101 0.0584836i
\(671\) −209620. 121024.i −0.465573 0.268798i
\(672\) 0 0
\(673\) 124260. + 215225.i 0.274348 + 0.475184i 0.969970 0.243223i \(-0.0782047\pi\)
−0.695623 + 0.718407i \(0.744871\pi\)
\(674\) −172604. + 566269.i −0.379955 + 1.24653i
\(675\) 0 0
\(676\) −200689. 134875.i −0.439168 0.295147i
\(677\) 134761. + 233413.i 0.294027 + 0.509270i 0.974758 0.223264i \(-0.0716711\pi\)
−0.680731 + 0.732533i \(0.738338\pi\)
\(678\) 0 0
\(679\) 60663.0 + 35023.8i 0.131578 + 0.0759668i
\(680\) 37117.4 + 230577.i 0.0802712 + 0.498653i
\(681\) 0 0
\(682\) 296468. 68708.1i 0.637395 0.147720i
\(683\) 124482.i 0.266848i −0.991059 0.133424i \(-0.957403\pi\)
0.991059 0.133424i \(-0.0425972\pi\)
\(684\) 0 0
\(685\) −126057. −0.268649
\(686\) −51287.4 221300.i −0.108984 0.470254i
\(687\) 0 0
\(688\) 56434.0 411608.i 0.119224 0.869574i
\(689\) −137247. + 237719.i −0.289111 + 0.500756i
\(690\) 0 0
\(691\) 771402. 445369.i 1.61557 0.932747i 0.627518 0.778602i \(-0.284071\pi\)
0.988048 0.154145i \(-0.0492623\pi\)
\(692\) 209132. + 140549.i 0.436726 + 0.293506i
\(693\) 0 0
\(694\) −554723. 169085.i −1.15175 0.351064i
\(695\) 636063. 367231.i 1.31683 0.760274i
\(696\) 0 0
\(697\) −3645.71 + 6314.56i −0.00750442 + 0.0129980i
\(698\) −488619. 523096.i −1.00291 1.07367i
\(699\) 0 0
\(700\) −175768. 11993.3i −0.358710 0.0244762i
\(701\) 170934. 0.347851 0.173925 0.984759i \(-0.444355\pi\)
0.173925 + 0.984759i \(0.444355\pi\)
\(702\) 0 0
\(703\) 47332.1i 0.0957734i
\(704\) −142704. 431759.i −0.287932 0.871156i
\(705\) 0 0
\(706\) −72071.4 77156.7i −0.144595 0.154798i
\(707\) 164752. + 95119.7i 0.329604 + 0.190297i
\(708\) 0 0
\(709\) 350963. + 607886.i 0.698183 + 1.20929i 0.969096 + 0.246684i \(0.0793410\pi\)
−0.270913 + 0.962604i \(0.587326\pi\)
\(710\) −689028. 210022.i −1.36685 0.416628i
\(711\) 0 0
\(712\) −57933.2 + 47156.3i −0.114279 + 0.0930206i
\(713\) 299744. + 519171.i 0.589618 + 1.02125i
\(714\) 0 0
\(715\) −785193. 453331.i −1.53590 0.886755i
\(716\) −158342. 323265.i −0.308866 0.630570i
\(717\) 0 0
\(718\) −163787. 706724.i −0.317710 1.37088i
\(719\) 768366.i 1.48631i −0.669117 0.743157i \(-0.733328\pi\)
0.669117 0.743157i \(-0.266672\pi\)
\(720\) 0 0
\(721\) −135811. −0.261255
\(722\) −505007. + 117038.i −0.968775 + 0.224519i
\(723\) 0 0
\(724\) −313920. + 153764.i −0.598883 + 0.293345i
\(725\) −587133. + 1.01695e6i −1.11702 + 1.93473i
\(726\) 0 0
\(727\) 221493. 127879.i 0.419074 0.241952i −0.275607 0.961270i \(-0.588879\pi\)
0.694681 + 0.719318i \(0.255546\pi\)
\(728\) −103052. 126604.i −0.194444 0.238882i
\(729\) 0 0
\(730\) 116894. 383497.i 0.219354 0.719642i
\(731\) −131240. + 75771.6i −0.245602 + 0.141799i
\(732\) 0 0
\(733\) −184829. + 320133.i −0.344003 + 0.595831i −0.985172 0.171569i \(-0.945116\pi\)
0.641169 + 0.767400i \(0.278450\pi\)
\(734\) 610932. 570667.i 1.13397 1.05923i
\(735\) 0 0
\(736\) 731600. 516878.i 1.35057 0.954184i
\(737\) 27314.9 0.0502881
\(738\) 0 0
\(739\) 1.03557e6i 1.89623i −0.317932 0.948114i \(-0.602988\pi\)
0.317932 0.948114i \(-0.397012\pi\)
\(740\) 74925.4 1.09807e6i 0.136825 2.00523i
\(741\) 0 0
\(742\) −46861.4 + 43772.9i −0.0851153 + 0.0795055i
\(743\) 486002. + 280593.i 0.880360 + 0.508276i 0.870777 0.491678i \(-0.163616\pi\)
0.00958322 + 0.999954i \(0.496950\pi\)
\(744\) 0 0
\(745\) −149482. 258910.i −0.269324 0.466483i
\(746\) −89331.1 + 293072.i −0.160518 + 0.526618i
\(747\) 0 0
\(748\) −92520.5 + 137667.i −0.165362 + 0.246052i
\(749\) −27247.6 47194.2i −0.0485696 0.0841250i
\(750\) 0 0
\(751\) 164898. + 95204.1i 0.292372 + 0.168801i 0.639011 0.769197i \(-0.279344\pi\)
−0.346639 + 0.937999i \(0.612677\pi\)
\(752\) −80288.2 + 585591.i −0.141976 + 1.03552i
\(753\) 0 0
\(754\) −1.05997e6 + 245653.i −1.86444 + 0.432095i
\(755\) 43995.1i 0.0771810i
\(756\) 0 0
\(757\) 523077. 0.912797 0.456398 0.889776i \(-0.349139\pi\)
0.456398 + 0.889776i \(0.349139\pi\)
\(758\) 209623. + 904499.i 0.364838 + 1.57424i
\(759\) 0 0
\(760\) 66396.9 10688.3i 0.114953 0.0185047i
\(761\) −80448.7 + 139341.i −0.138915 + 0.240608i −0.927086 0.374848i \(-0.877695\pi\)
0.788171 + 0.615456i \(0.211028\pi\)
\(762\) 0 0
\(763\) −50060.1 + 28902.2i −0.0859890 + 0.0496458i
\(764\) 166763. 248137.i 0.285702 0.425114i
\(765\) 0 0
\(766\) −327467. 99815.1i −0.558097 0.170113i
\(767\) −1.00695e6 + 581365.i −1.71167 + 0.988231i
\(768\) 0 0
\(769\) 297804. 515812.i 0.503591 0.872246i −0.496400 0.868094i \(-0.665345\pi\)
0.999991 0.00415186i \(-0.00132158\pi\)
\(770\) −144583. 154785.i −0.243857 0.261063i
\(771\) 0 0
\(772\) −50212.0 + 735879.i −0.0842505 + 1.23473i
\(773\) 583394. 0.976345 0.488172 0.872747i \(-0.337664\pi\)
0.488172 + 0.872747i \(0.337664\pi\)
\(774\) 0 0
\(775\) 618255.i 1.02935i
\(776\) −343242. 130764.i −0.570002 0.217152i
\(777\) 0 0
\(778\)