Properties

Label 108.5.f.a.19.2
Level 108
Weight 5
Character 108.19
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 19.2
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.2

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 −0.931022 0.364962i \(-0.881082\pi\)
0.149444 0.988770i \(-0.452251\pi\)
\(6\) 0 0
\(7\) 10.5700 + 6.10260i 0.215715 + 0.124543i 0.603964 0.797011i \(-0.293587\pi\)
−0.388250 + 0.921554i \(0.626920\pi\)
\(8\) −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 0.841574 0.540142i \(-0.181630\pi\)
−0.0469902 + 0.998895i \(0.514963\pi\)
\(12\) 0 0
\(13\) −104.491 180.984i −0.618290 1.07091i −0.989798 0.142480i \(-0.954492\pi\)
0.371507 0.928430i \(-0.378841\pi\)
\(14\) −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 \(-0.988142\pi\)
0.999306 0.0372429i \(-0.0118575\pi\)
\(20\) −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 −0.997280 0.0737029i \(-0.976518\pi\)
−0.434812 + 0.900521i \(0.643185\pi\)
\(24\) 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 0.161587 + 0.986858i \(0.448339\pi\)
−0.935438 + 0.353491i \(0.884995\pi\)
\(30\) 0 0
\(31\) −593.492 + 342.653i −0.617577 + 0.356558i −0.775925 0.630825i \(-0.782717\pi\)
0.158348 + 0.987383i \(0.449383\pi\)
\(32\) −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 0.877405 0.479751i \(-0.159273\pi\)
−0.854179 + 0.519979i \(0.825940\pi\)
\(42\) 0 0
\(43\) 1405.46 + 811.442i 0.760118 + 0.438855i 0.829338 0.558747i \(-0.188718\pi\)
−0.0692198 + 0.997601i \(0.522051\pi\)
\(44\) 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 −0.0263007 0.999654i \(-0.508373\pi\)
−0.878876 + 0.477050i \(0.841706\pi\)
\(48\) 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 0.391540 0.920161i \(-0.371942\pi\)
0.992653 + 0.120997i \(0.0386091\pi\)
\(60\) 0 0
\(61\) −1090.13 + 1888.16i −0.292967 + 0.507433i −0.974510 0.224345i \(-0.927976\pi\)
0.681543 + 0.731778i \(0.261309\pi\)
\(62\) 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 −0.476079 0.879403i \(-0.657942\pi\)
0.523545 + 0.851998i \(0.324609\pi\)
\(68\) −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 \(0.151100\pi\)
−0.889432 + 0.457067i \(0.848900\pi\)
\(72\) 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 0.0954846 0.995431i \(-0.469560\pi\)
−0.814326 + 0.580408i \(0.802893\pi\)
\(80\) 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 0.377606 0.925966i \(-0.376747\pi\)
−0.613108 + 0.789999i \(0.710081\pi\)
\(84\) 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 −0.672275 0.740302i \(-0.734683\pi\)
0.977257 + 0.212056i \(0.0680160\pi\)
\(98\) 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 −0.176802 0.984246i \(-0.556575\pi\)
0.940783 0.339008i \(-0.110091\pi\)
\(102\) 0 0
\(103\) −9636.52 + 5563.65i −0.908334 + 0.524427i −0.879895 0.475168i \(-0.842387\pi\)
−0.0284395 + 0.999596i \(0.509054\pi\)
\(104\) −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 \(0.0624679\pi\)
−0.980805 + 0.194991i \(0.937532\pi\)
\(108\) 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 −0.961639 0.274317i \(-0.911548\pi\)
0.243254 0.969963i \(-0.421785\pi\)
\(114\) 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 \(0.0815003\pi\)
−0.967400 + 0.253252i \(0.918500\pi\)
\(128\) 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 −0.741863 0.670552i \(-0.766057\pi\)
0.209784 + 0.977748i \(0.432724\pi\)
\(132\) 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 −0.819856 0.572570i \(-0.805947\pi\)
0.905788 + 0.423731i \(0.139280\pi\)
\(138\) 0 0
\(139\) −16276.4 + 9397.17i −0.842419 + 0.486371i −0.858086 0.513506i \(-0.828346\pi\)
0.0156666 + 0.999877i \(0.495013\pi\)
\(140\) 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 0.766927 0.641735i \(-0.221785\pi\)
−0.939222 + 0.343311i \(0.888452\pi\)
\(150\) 0 0
\(151\) 974.974 + 562.901i 0.0427601 + 0.0246876i 0.521228 0.853418i \(-0.325474\pi\)
−0.478468 + 0.878105i \(0.658808\pi\)
\(152\) −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 0.899442 0.437041i \(-0.143973\pi\)
−0.828209 + 0.560419i \(0.810640\pi\)
\(158\) 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 \(-0.710385\pi\)
0.613861 0.789414i \(-0.289615\pi\)
\(164\) 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 −0.390469 0.920616i \(-0.627687\pi\)
0.602043 + 0.798464i \(0.294354\pi\)
\(168\) 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 −0.703968 0.710232i \(-0.748590\pi\)
0.967063 + 0.254539i \(0.0819236\pi\)
\(174\) 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 \(0.114184\pi\)
−0.936347 + 0.351075i \(0.885816\pi\)
\(180\) 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 0.705114 0.709094i \(-0.250896\pi\)
−0.261537 + 0.965194i \(0.584229\pi\)
\(192\) 0 0
\(193\) −23049.7 39923.2i −0.618800 1.07179i −0.989705 0.143123i \(-0.954286\pi\)
0.370905 0.928671i \(-0.379048\pi\)
\(194\) −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 \(-0.618974\pi\)
0.365124 0.930959i \(-0.381026\pi\)
\(200\) 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 −0.663189 0.748452i \(-0.730797\pi\)
0.316584 + 0.948564i \(0.397464\pi\)
\(212\) 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 0.954487 0.298253i \(-0.0964039\pi\)
0.218949 + 0.975736i \(0.429737\pi\)
\(224\) 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 −0.131212 0.991354i \(-0.541887\pi\)
−0.924144 + 0.382044i \(0.875220\pi\)
\(228\) 0 0
\(229\) 20463.2 + 35443.2i 0.390213 + 0.675868i 0.992477 0.122428i \(-0.0390681\pi\)
−0.602265 + 0.798297i \(0.705735\pi\)
\(230\) −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 −0.117209 0.993107i \(-0.537395\pi\)
0.801452 + 0.598059i \(0.204061\pi\)
\(240\) 0 0
\(241\) −37826.8 + 65517.9i −0.651276 + 1.12804i 0.331537 + 0.943442i \(0.392433\pi\)
−0.982814 + 0.184601i \(0.940901\pi\)
\(242\) 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 \(0.213350\pi\)
−0.783662 + 0.621188i \(0.786650\pi\)
\(252\) 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 0.765678 0.643224i \(-0.222403\pi\)
−0.939887 + 0.341485i \(0.889070\pi\)
\(258\) 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 −0.154765 0.987951i \(-0.549462\pi\)
−0.932973 + 0.359945i \(0.882795\pi\)
\(264\) 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 \(0.105870\pi\)
−0.945197 + 0.326502i \(0.894130\pi\)
\(272\) −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 −0.519332 0.854572i \(-0.673819\pi\)
0.999748 + 0.0224689i \(0.00715269\pi\)
\(278\) 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 −0.631795 0.775136i \(-0.717681\pi\)
0.987185 + 0.159582i \(0.0510147\pi\)
\(282\) 0 0
\(283\) 132300. 76383.2i 1.65191 0.953730i 0.675621 0.737249i \(-0.263876\pi\)
0.976287 0.216481i \(-0.0694578\pi\)
\(284\) −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 0.730470 0.682945i \(-0.239301\pi\)
−0.956683 + 0.291133i \(0.905968\pi\)
\(294\) 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 \(0.000772612\pi\)
−0.999997 + 0.00242723i \(0.999227\pi\)
\(308\) 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 −0.547234 0.836979i \(-0.684319\pi\)
0.451228 + 0.892409i \(0.350986\pi\)
\(312\) 0 0
\(313\) −8976.10 + 15547.1i −0.0916218 + 0.158694i −0.908194 0.418550i \(-0.862538\pi\)
0.816572 + 0.577244i \(0.195872\pi\)
\(314\) −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 −0.977343 0.211663i \(-0.932112\pi\)
0.671977 + 0.740572i \(0.265445\pi\)
\(318\) 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 0.999412 0.0342747i \(-0.0109121\pi\)
0.470023 + 0.882654i \(0.344245\pi\)
\(332\) −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 0.982741 + 0.184989i \(0.0592251\pi\)
−0.331165 + 0.943573i \(0.607442\pi\)
\(338\) 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 0.122138 0.992513i \(-0.461025\pi\)
0.920611 + 0.390482i \(0.127692\pi\)
\(348\) 0 0
\(349\) 89475.8 154977.i 0.734606 1.27238i −0.220290 0.975435i \(-0.570700\pi\)
0.954896 0.296941i \(-0.0959664\pi\)
\(350\) 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 −0.808198 0.588911i \(-0.799557\pi\)
0.914111 + 0.405465i \(0.132890\pi\)
\(354\) 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 \(-0.751571\pi\)
0.710587 0.703609i \(-0.248429\pi\)
\(360\) 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 −0.356467 0.934308i \(-0.616019\pi\)
−0.987368 + 0.158445i \(0.949352\pi\)
\(368\) −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 0.970203 0.242293i \(-0.0778996\pi\)
−0.694934 + 0.719074i \(0.744566\pi\)
\(374\) 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 \(0.299439\pi\)
−0.589211 + 0.807979i \(0.700561\pi\)
\(380\) −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 −0.225611 0.974217i \(-0.572438\pi\)
0.730891 + 0.682494i \(0.239105\pi\)
\(384\) 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 −0.591745 0.806125i \(-0.701561\pi\)
0.993997 + 0.109404i \(0.0348942\pi\)
\(390\) 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 0.700135 0.714010i \(-0.253123\pi\)
−0.968419 + 0.249330i \(0.919790\pi\)
\(402\) 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 −0.972212 0.234102i \(-0.924785\pi\)
0.283368 0.959011i \(-0.408548\pi\)
\(410\) −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 −0.356491 0.934299i \(-0.616027\pi\)
0.630881 + 0.775879i \(0.282693\pi\)
\(420\) 0 0
\(421\) −70485.7 + 122085.i −0.397683 + 0.688807i −0.993440 0.114358i \(-0.963519\pi\)
0.595757 + 0.803165i \(0.296852\pi\)
\(422\) 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 \(0.171889\pi\)
−0.857705 + 0.514142i \(0.828111\pi\)
\(432\) 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 −0.222670 0.974894i \(-0.571477\pi\)
−0.955618 + 0.294609i \(0.904811\pi\)
\(440\) −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 0.285632 0.958339i \(-0.407796\pi\)
−0.687130 + 0.726534i \(0.741130\pi\)
\(444\) 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 −0.999594 0.0285035i \(-0.990926\pi\)
0.524482 + 0.851422i \(0.324259\pi\)
\(458\) −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 −0.999946 0.0103639i \(-0.996701\pi\)
0.508949 + 0.860797i \(0.330034\pi\)
\(462\) 0 0
\(463\) 22687.9 13098.9i 0.105836 0.0611044i −0.446148 0.894959i \(-0.647204\pi\)
0.551984 + 0.833855i \(0.313871\pi\)
\(464\) −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 \(0.0710911\pi\)
−0.975163 + 0.221487i \(0.928909\pi\)
\(468\) 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 0.433960 0.900932i \(-0.357116\pi\)
−0.563250 + 0.826287i \(0.690449\pi\)
\(480\) 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 \(0.0468218\pi\)
−0.989201 + 0.146565i \(0.953178\pi\)
\(488\) 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 −0.815862 0.578247i \(-0.803737\pi\)
0.0928458 + 0.995681i \(0.470404\pi\)
\(492\) 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 −0.591119 0.806585i \(-0.701313\pi\)
0.402964 + 0.915216i \(0.367980\pi\)
\(500\) 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 \(-0.843027\pi\)
0.880849 0.473397i \(-0.156973\pi\)
\(504\) 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 0.955674 0.294426i \(-0.0951284\pi\)
−0.732817 + 0.680425i \(0.761795\pi\)
\(510\) 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 \(-0.976890\pi\)
0.997366 0.0725397i \(-0.0231104\pi\)
\(524\) −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 0.357335 0.933976i \(-0.383686\pi\)
−0.630180 + 0.776449i \(0.717019\pi\)
\(548\) 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 −0.786771 + 0.617245i \(0.788249\pi\)
−0.927935 + 0.372741i \(0.878418\pi\)
\(564\) 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 −0.919778 0.392439i \(-0.871631\pi\)
0.799751 + 0.600331i \(0.204965\pi\)
\(570\) 0 0
\(571\) 276094. 159403.i 0.846809 0.488905i −0.0127640 0.999919i \(-0.504063\pi\)
0.859573 + 0.511013i \(0.170730\pi\)
\(572\) 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 0.482641 0.875818i \(-0.339678\pi\)
−0.517161 + 0.855888i \(0.673011\pi\)
\(588\) 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 0.163204 0.986592i \(-0.447817\pi\)
0.936016 + 0.351958i \(0.114484\pi\)
\(600\) 0 0
\(601\) 118996. 206108.i 0.329446 0.570618i −0.652956 0.757396i \(-0.726471\pi\)
0.982402 + 0.186778i \(0.0598046\pi\)
\(602\) −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 −0.994480 0.104927i \(-0.966539\pi\)
−0.406371 + 0.913708i \(0.633206\pi\)
\(608\) −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 0.974814 + 0.223021i \(0.0715919\pi\)
−0.294265 + 0.955724i \(0.595075\pi\)
\(618\) 0 0
\(619\) −176869. 102115.i −0.461605 0.266508i 0.251114 0.967958i \(-0.419203\pi\)
−0.712719 + 0.701450i \(0.752537\pi\)
\(620\) 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 \(0.0713618\pi\)
−0.974975 + 0.222317i \(0.928638\pi\)
\(632\) 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 −0.701556 0.712614i \(-0.747511\pi\)
0.967920 + 0.251258i \(0.0808444\pi\)
\(642\) 0 0
\(643\) −298938. + 172592.i −0.723035 + 0.417445i −0.815869 0.578237i \(-0.803741\pi\)
0.0928336 + 0.995682i \(0.470408\pi\)
\(644\) −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 \(0.157799\pi\)
−0.879617 + 0.475683i \(0.842201\pi\)
\(648\) 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 0.592529 0.805549i \(-0.298129\pi\)
−0.993890 + 0.110371i \(0.964796\pi\)
\(654\) 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 −0.122175 0.992509i \(-0.538987\pi\)
−0.920625 + 0.390447i \(0.872320\pi\)
\(660\) 0 0
\(661\) −154294. 267245.i −0.353140 0.611656i 0.633658 0.773613i \(-0.281553\pi\)
−0.986798 + 0.161957i \(0.948219\pi\)
\(662\) −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 −0.695623 0.718407i \(-0.744871\pi\)
0.969970 + 0.243223i \(0.0782047\pi\)
\(674\) −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 −0.680731 0.732533i \(-0.738338\pi\)
0.974758 + 0.223264i \(0.0716711\pi\)
\(678\) 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 \(0.0425972\pi\)
−0.991059 + 0.133424i \(0.957403\pi\)
\(684\) 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 0.988048 + 0.154145i \(0.0492623\pi\)
0.627518 + 0.778602i \(0.284071\pi\)
\(692\) 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 −0.270913 0.962604i \(-0.587326\pi\)
0.969096 0.246684i \(-0.0793410\pi\)
\(710\) −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 \(0.266672\pi\)
−0.669117 + 0.743157i \(0.733328\pi\)
\(720\) 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 0.694681 0.719318i \(-0.255546\pi\)
−0.275607 + 0.961270i \(0.588879\pi\)
\(728\) −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 0.641169 0.767400i \(-0.278450\pi\)
−0.985172 + 0.171569i \(0.945116\pi\)
\(734\) 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 \(0.397012\pi\)
−0.317932 + 0.948114i \(0.602988\pi\)
\(740\) 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 0.00958322 0.999954i \(-0.496950\pi\)
0.870777 + 0.491678i \(0.163616\pi\)
\(744\) 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 −0.346639 0.937999i \(-0.612677\pi\)
0.639011 + 0.769197i \(0.279344\pi\)
\(752\) −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 0.788171 0.615456i \(-0.211028\pi\)
−0.927086 + 0.374848i \(0.877695\pi\)
\(762\) 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 0.999991 + 0.00415186i \(0.00132158\pi\)
−0.496400 + 0.868094i \(0.665345\pi\)
\(770\) −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
\(778\) −332401.