Properties

Label 43.6.c.a.6.12
Level $43$
Weight $6$
Character 43.6
Analytic conductor $6.897$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.12
Character \(\chi\) \(=\) 43.6
Dual form 43.6.c.a.36.12

$q$-expansion

\(f(q)\) \(=\) \(q+4.36550 q^{2} +(0.424863 - 0.735884i) q^{3} -12.9424 q^{4} +(-30.5339 + 52.8863i) q^{5} +(1.85474 - 3.21250i) q^{6} +(93.7016 + 162.296i) q^{7} -196.196 q^{8} +(121.139 + 209.819i) q^{9} +O(q^{10})\) \(q+4.36550 q^{2} +(0.424863 - 0.735884i) q^{3} -12.9424 q^{4} +(-30.5339 + 52.8863i) q^{5} +(1.85474 - 3.21250i) q^{6} +(93.7016 + 162.296i) q^{7} -196.196 q^{8} +(121.139 + 209.819i) q^{9} +(-133.296 + 230.875i) q^{10} +227.558 q^{11} +(-5.49874 + 9.52410i) q^{12} +(-266.361 - 461.350i) q^{13} +(409.055 + 708.503i) q^{14} +(25.9454 + 44.9388i) q^{15} -442.338 q^{16} +(-497.997 - 862.557i) q^{17} +(528.832 + 915.965i) q^{18} +(-1040.23 + 1801.72i) q^{19} +(395.182 - 684.475i) q^{20} +159.241 q^{21} +993.406 q^{22} +(574.238 - 994.609i) q^{23} +(-83.3564 + 144.378i) q^{24} +(-302.137 - 523.317i) q^{25} +(-1162.80 - 2014.02i) q^{26} +412.353 q^{27} +(-1212.72 - 2100.50i) q^{28} +(2126.57 + 3683.33i) q^{29} +(113.265 + 196.180i) q^{30} +(369.739 - 640.406i) q^{31} +4347.25 q^{32} +(96.6811 - 167.457i) q^{33} +(-2174.01 - 3765.49i) q^{34} -11444.3 q^{35} +(-1567.83 - 2715.56i) q^{36} +(8284.34 - 14348.9i) q^{37} +(-4541.11 + 7865.43i) q^{38} -452.667 q^{39} +(5990.63 - 10376.1i) q^{40} +8487.64 q^{41} +695.169 q^{42} +(9259.50 + 7827.52i) q^{43} -2945.15 q^{44} -14795.4 q^{45} +(2506.84 - 4341.97i) q^{46} +8271.90 q^{47} +(-187.933 + 325.509i) q^{48} +(-9156.50 + 15859.5i) q^{49} +(-1318.98 - 2284.54i) q^{50} -846.323 q^{51} +(3447.34 + 5970.97i) q^{52} +(-14039.9 + 24317.9i) q^{53} +1800.13 q^{54} +(-6948.24 + 12034.7i) q^{55} +(-18383.9 - 31841.8i) q^{56} +(883.906 + 1530.97i) q^{57} +(9283.54 + 16079.6i) q^{58} +8728.07 q^{59} +(-335.796 - 581.616i) q^{60} +(20730.1 + 35905.5i) q^{61} +(1614.09 - 2795.69i) q^{62} +(-22701.8 + 39320.7i) q^{63} +33132.7 q^{64} +32532.1 q^{65} +(422.061 - 731.032i) q^{66} +(-21098.2 + 36543.1i) q^{67} +(6445.28 + 11163.6i) q^{68} +(-487.945 - 845.145i) q^{69} -49960.1 q^{70} +(-7145.46 - 12376.3i) q^{71} +(-23767.0 - 41165.6i) q^{72} +(-39706.8 - 68774.1i) q^{73} +(36165.3 - 62640.2i) q^{74} -513.467 q^{75} +(13463.0 - 23318.6i) q^{76} +(21322.6 + 36931.8i) q^{77} -1976.12 q^{78} +(-25368.9 - 43940.3i) q^{79} +(13506.3 - 23393.6i) q^{80} +(-29261.6 + 50682.5i) q^{81} +37052.8 q^{82} +(36303.0 - 62878.6i) q^{83} -2060.97 q^{84} +60823.2 q^{85} +(40422.4 + 34171.0i) q^{86} +3614.00 q^{87} -44646.1 q^{88} +(22812.5 - 39512.3i) q^{89} -64589.2 q^{90} +(49916.8 - 86458.5i) q^{91} +(-7432.01 + 12872.6i) q^{92} +(-314.176 - 544.169i) q^{93} +36111.0 q^{94} +(-63524.3 - 110027. i) q^{95} +(1846.98 - 3199.07i) q^{96} -104823. q^{97} +(-39972.7 + 69234.7i) q^{98} +(27566.2 + 47746.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} + O(q^{10}) \) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} - 317q^{10} + 1326q^{11} - 648q^{12} + 1006q^{13} - 1272q^{14} + 683q^{15} + 3574q^{16} + 200q^{17} + 1861q^{18} + 3361q^{19} + 3825q^{20} - 1320q^{21} - 8768q^{22} + 560q^{23} - 7382q^{24} - 3232q^{25} - 3201q^{26} - 122q^{27} + 13934q^{28} + 8887q^{29} - 19449q^{30} - 6749q^{31} - 19086q^{32} + 7106q^{33} + 8423q^{34} + 31118q^{35} - 14112q^{36} - 4514q^{37} + 7072q^{38} - 5404q^{39} - 18519q^{40} - 28996q^{41} + 58118q^{42} - 14998q^{43} + 71050q^{44} - 92096q^{45} + 20052q^{46} - 10742q^{47} + 32927q^{48} + 7472q^{49} + 20362q^{50} + 20250q^{51} + 59532q^{52} - 50572q^{53} - 230084q^{54} + 38544q^{55} - 40355q^{56} - 18087q^{57} - 33436q^{58} + 112654q^{59} + 134093q^{60} - 20120q^{61} - 31491q^{62} + 188227q^{63} + 125164q^{64} - 36578q^{65} + 8803q^{66} - 73824q^{67} - 128456q^{68} + 8005q^{69} - 141610q^{70} + 142842q^{71} + 98466q^{72} - 91624q^{73} - 99720q^{74} + 298358q^{75} + 258288q^{76} + 68051q^{77} - 201116q^{78} + 99734q^{79} - 31261q^{80} - 28441q^{81} - 147772q^{82} - 47340q^{83} - 624232q^{84} - 71734q^{85} - 115526q^{86} - 215924q^{87} - 720684q^{88} + 60402q^{89} + 676108q^{90} + 164172q^{91} + 78997q^{92} - 40793q^{93} - 341874q^{94} + 123541q^{95} - 442140q^{96} + 318476q^{97} + 217473q^{98} - 134770q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.36550 0.771719 0.385859 0.922558i \(-0.373905\pi\)
0.385859 + 0.922558i \(0.373905\pi\)
\(3\) 0.424863 0.735884i 0.0272550 0.0472070i −0.852076 0.523418i \(-0.824657\pi\)
0.879331 + 0.476211i \(0.157990\pi\)
\(4\) −12.9424 −0.404450
\(5\) −30.5339 + 52.8863i −0.546207 + 0.946058i 0.452323 + 0.891854i \(0.350595\pi\)
−0.998530 + 0.0542039i \(0.982738\pi\)
\(6\) 1.85474 3.21250i 0.0210332 0.0364305i
\(7\) 93.7016 + 162.296i 0.722773 + 1.25188i 0.959884 + 0.280397i \(0.0904663\pi\)
−0.237111 + 0.971483i \(0.576200\pi\)
\(8\) −196.196 −1.08384
\(9\) 121.139 + 209.819i 0.498514 + 0.863452i
\(10\) −133.296 + 230.875i −0.421518 + 0.730091i
\(11\) 227.558 0.567037 0.283518 0.958967i \(-0.408498\pi\)
0.283518 + 0.958967i \(0.408498\pi\)
\(12\) −5.49874 + 9.52410i −0.0110233 + 0.0190929i
\(13\) −266.361 461.350i −0.437131 0.757133i 0.560336 0.828265i \(-0.310672\pi\)
−0.997467 + 0.0711325i \(0.977339\pi\)
\(14\) 409.055 + 708.503i 0.557778 + 0.966100i
\(15\) 25.9454 + 44.9388i 0.0297737 + 0.0515696i
\(16\) −442.338 −0.431970
\(17\) −497.997 862.557i −0.417931 0.723878i 0.577800 0.816178i \(-0.303911\pi\)
−0.995731 + 0.0923003i \(0.970578\pi\)
\(18\) 528.832 + 915.965i 0.384713 + 0.666342i
\(19\) −1040.23 + 1801.72i −0.661064 + 1.14500i 0.319273 + 0.947663i \(0.396561\pi\)
−0.980336 + 0.197333i \(0.936772\pi\)
\(20\) 395.182 684.475i 0.220913 0.382633i
\(21\) 159.241 0.0787966
\(22\) 993.406 0.437593
\(23\) 574.238 994.609i 0.226346 0.392042i −0.730377 0.683045i \(-0.760655\pi\)
0.956722 + 0.291002i \(0.0939888\pi\)
\(24\) −83.3564 + 144.378i −0.0295400 + 0.0511648i
\(25\) −302.137 523.317i −0.0966839 0.167461i
\(26\) −1162.80 2014.02i −0.337342 0.584294i
\(27\) 412.353 0.108858
\(28\) −1212.72 2100.50i −0.292326 0.506323i
\(29\) 2126.57 + 3683.33i 0.469553 + 0.813290i 0.999394 0.0348074i \(-0.0110818\pi\)
−0.529841 + 0.848097i \(0.677748\pi\)
\(30\) 113.265 + 196.180i 0.0229769 + 0.0397972i
\(31\) 369.739 640.406i 0.0691020 0.119688i −0.829404 0.558649i \(-0.811320\pi\)
0.898506 + 0.438961i \(0.144653\pi\)
\(32\) 4347.25 0.750481
\(33\) 96.6811 167.457i 0.0154546 0.0267681i
\(34\) −2174.01 3765.49i −0.322525 0.558630i
\(35\) −11444.3 −1.57914
\(36\) −1567.83 2715.56i −0.201624 0.349223i
\(37\) 8284.34 14348.9i 0.994841 1.72312i 0.409569 0.912279i \(-0.365679\pi\)
0.585272 0.810837i \(-0.300988\pi\)
\(38\) −4541.11 + 7865.43i −0.510156 + 0.883615i
\(39\) −452.667 −0.0476559
\(40\) 5990.63 10376.1i 0.592001 1.02538i
\(41\) 8487.64 0.788546 0.394273 0.918993i \(-0.370996\pi\)
0.394273 + 0.918993i \(0.370996\pi\)
\(42\) 695.169 0.0608089
\(43\) 9259.50 + 7827.52i 0.763689 + 0.645584i
\(44\) −2945.15 −0.229338
\(45\) −14795.4 −1.08917
\(46\) 2506.84 4341.97i 0.174675 0.302546i
\(47\) 8271.90 0.546211 0.273106 0.961984i \(-0.411949\pi\)
0.273106 + 0.961984i \(0.411949\pi\)
\(48\) −187.933 + 325.509i −0.0117733 + 0.0203920i
\(49\) −9156.50 + 15859.5i −0.544803 + 0.943626i
\(50\) −1318.98 2284.54i −0.0746128 0.129233i
\(51\) −846.323 −0.0455628
\(52\) 3447.34 + 5970.97i 0.176798 + 0.306222i
\(53\) −14039.9 + 24317.9i −0.686555 + 1.18915i 0.286391 + 0.958113i \(0.407544\pi\)
−0.972946 + 0.231035i \(0.925789\pi\)
\(54\) 1800.13 0.0840077
\(55\) −6948.24 + 12034.7i −0.309719 + 0.536450i
\(56\) −18383.9 31841.8i −0.783371 1.35684i
\(57\) 883.906 + 1530.97i 0.0360345 + 0.0624137i
\(58\) 9283.54 + 16079.6i 0.362363 + 0.627631i
\(59\) 8728.07 0.326429 0.163214 0.986591i \(-0.447814\pi\)
0.163214 + 0.986591i \(0.447814\pi\)
\(60\) −335.796 581.616i −0.0120420 0.0208573i
\(61\) 20730.1 + 35905.5i 0.713307 + 1.23548i 0.963609 + 0.267316i \(0.0861367\pi\)
−0.250302 + 0.968168i \(0.580530\pi\)
\(62\) 1614.09 2795.69i 0.0533273 0.0923656i
\(63\) −22701.8 + 39320.7i −0.720626 + 1.24816i
\(64\) 33132.7 1.01113
\(65\) 32532.1 0.955056
\(66\) 422.061 731.032i 0.0119266 0.0206574i
\(67\) −21098.2 + 36543.1i −0.574193 + 0.994531i 0.421936 + 0.906625i \(0.361351\pi\)
−0.996129 + 0.0879051i \(0.971983\pi\)
\(68\) 6445.28 + 11163.6i 0.169032 + 0.292772i
\(69\) −487.945 845.145i −0.0123381 0.0213702i
\(70\) −49960.1 −1.21865
\(71\) −7145.46 12376.3i −0.168223 0.291370i 0.769572 0.638559i \(-0.220469\pi\)
−0.937795 + 0.347190i \(0.887136\pi\)
\(72\) −23767.0 41165.6i −0.540310 0.935844i
\(73\) −39706.8 68774.1i −0.872082 1.51049i −0.859839 0.510565i \(-0.829436\pi\)
−0.0122429 0.999925i \(-0.503897\pi\)
\(74\) 36165.3 62640.2i 0.767738 1.32976i
\(75\) −513.467 −0.0105405
\(76\) 13463.0 23318.6i 0.267367 0.463094i
\(77\) 21322.6 + 36931.8i 0.409839 + 0.709862i
\(78\) −1976.12 −0.0367770
\(79\) −25368.9 43940.3i −0.457335 0.792128i 0.541484 0.840711i \(-0.317863\pi\)
−0.998819 + 0.0485832i \(0.984529\pi\)
\(80\) 13506.3 23393.6i 0.235945 0.408669i
\(81\) −29261.6 + 50682.5i −0.495547 + 0.858313i
\(82\) 37052.8 0.608536
\(83\) 36303.0 62878.6i 0.578425 1.00186i −0.417235 0.908799i \(-0.637001\pi\)
0.995660 0.0930634i \(-0.0296659\pi\)
\(84\) −2060.97 −0.0318693
\(85\) 60823.2 0.913108
\(86\) 40422.4 + 34171.0i 0.589353 + 0.498210i
\(87\) 3614.00 0.0511906
\(88\) −44646.1 −0.614577
\(89\) 22812.5 39512.3i 0.305279 0.528759i −0.672044 0.740511i \(-0.734584\pi\)
0.977323 + 0.211752i \(0.0679169\pi\)
\(90\) −64589.2 −0.840531
\(91\) 49916.8 86458.5i 0.631893 1.09447i
\(92\) −7432.01 + 12872.6i −0.0915455 + 0.158561i
\(93\) −314.176 544.169i −0.00376674 0.00652419i
\(94\) 36111.0 0.421521
\(95\) −63524.3 110027.i −0.722155 1.25081i
\(96\) 1846.98 3199.07i 0.0204543 0.0354279i
\(97\) −104823. −1.13116 −0.565582 0.824692i \(-0.691348\pi\)
−0.565582 + 0.824692i \(0.691348\pi\)
\(98\) −39972.7 + 69234.7i −0.420434 + 0.728214i
\(99\) 27566.2 + 47746.0i 0.282676 + 0.489609i
\(100\) 3910.38 + 6772.97i 0.0391038 + 0.0677297i
\(101\) 32216.9 + 55801.3i 0.314254 + 0.544303i 0.979279 0.202518i \(-0.0649124\pi\)
−0.665025 + 0.746821i \(0.731579\pi\)
\(102\) −3694.62 −0.0351617
\(103\) 2971.91 + 5147.50i 0.0276021 + 0.0478083i 0.879497 0.475905i \(-0.157880\pi\)
−0.851894 + 0.523714i \(0.824546\pi\)
\(104\) 52258.9 + 90515.1i 0.473780 + 0.820611i
\(105\) −4862.26 + 8421.68i −0.0430393 + 0.0745462i
\(106\) −61291.3 + 106160.i −0.529827 + 0.917688i
\(107\) 70544.3 0.595666 0.297833 0.954618i \(-0.403736\pi\)
0.297833 + 0.954618i \(0.403736\pi\)
\(108\) −5336.84 −0.0440276
\(109\) −80147.6 + 138820.i −0.646136 + 1.11914i 0.337901 + 0.941182i \(0.390283\pi\)
−0.984038 + 0.177960i \(0.943050\pi\)
\(110\) −30332.6 + 52537.5i −0.239016 + 0.413988i
\(111\) −7039.42 12192.6i −0.0542287 0.0939269i
\(112\) −41447.8 71789.6i −0.312217 0.540775i
\(113\) 115601. 0.851656 0.425828 0.904804i \(-0.359983\pi\)
0.425828 + 0.904804i \(0.359983\pi\)
\(114\) 3858.69 + 6683.45i 0.0278085 + 0.0481658i
\(115\) 35067.4 + 60738.6i 0.247263 + 0.428272i
\(116\) −27522.9 47671.1i −0.189911 0.328935i
\(117\) 64533.3 111775.i 0.435832 0.754883i
\(118\) 38102.4 0.251911
\(119\) 93326.4 161646.i 0.604139 1.04640i
\(120\) −5090.39 8816.82i −0.0322699 0.0558932i
\(121\) −109268. −0.678470
\(122\) 90497.2 + 156746.i 0.550472 + 0.953446i
\(123\) 3606.08 6245.92i 0.0214918 0.0372249i
\(124\) −4785.30 + 8288.39i −0.0279483 + 0.0484079i
\(125\) −153935. −0.881176
\(126\) −99104.9 + 171655.i −0.556121 + 0.963229i
\(127\) −171900. −0.945730 −0.472865 0.881135i \(-0.656780\pi\)
−0.472865 + 0.881135i \(0.656780\pi\)
\(128\) 5529.01 0.0298279
\(129\) 9694.17 3488.30i 0.0512904 0.0184561i
\(130\) 142019. 0.737034
\(131\) 213882. 1.08892 0.544459 0.838787i \(-0.316735\pi\)
0.544459 + 0.838787i \(0.316735\pi\)
\(132\) −1251.29 + 2167.29i −0.00625060 + 0.0108263i
\(133\) −389883. −1.91120
\(134\) −92104.0 + 159529.i −0.443115 + 0.767498i
\(135\) −12590.7 + 21807.8i −0.0594589 + 0.102986i
\(136\) 97705.2 + 169230.i 0.452971 + 0.784568i
\(137\) 339950. 1.54744 0.773720 0.633528i \(-0.218394\pi\)
0.773720 + 0.633528i \(0.218394\pi\)
\(138\) −2130.12 3689.48i −0.00952154 0.0164918i
\(139\) 144788. 250780.i 0.635617 1.10092i −0.350767 0.936463i \(-0.614079\pi\)
0.986384 0.164458i \(-0.0525876\pi\)
\(140\) 148117. 0.638681
\(141\) 3514.42 6087.16i 0.0148870 0.0257850i
\(142\) −31193.5 54028.7i −0.129820 0.224856i
\(143\) −60612.6 104984.i −0.247869 0.429322i
\(144\) −53584.3 92810.8i −0.215343 0.372986i
\(145\) −259730. −1.02589
\(146\) −173340. 300234.i −0.673002 1.16567i
\(147\) 7780.51 + 13476.2i 0.0296972 + 0.0514370i
\(148\) −107219. + 185709.i −0.402363 + 0.696914i
\(149\) 43963.9 76147.7i 0.162230 0.280990i −0.773438 0.633872i \(-0.781465\pi\)
0.935668 + 0.352881i \(0.114798\pi\)
\(150\) −2241.54 −0.00813428
\(151\) −58864.2 −0.210092 −0.105046 0.994467i \(-0.533499\pi\)
−0.105046 + 0.994467i \(0.533499\pi\)
\(152\) 204088. 353491.i 0.716488 1.24099i
\(153\) 120654. 208979.i 0.416689 0.721727i
\(154\) 93083.8 + 161226.i 0.316280 + 0.547814i
\(155\) 22579.1 + 39108.2i 0.0754880 + 0.130749i
\(156\) 5858.59 0.0192744
\(157\) 158855. + 275145.i 0.514342 + 0.890866i 0.999862 + 0.0166401i \(0.00529695\pi\)
−0.485520 + 0.874226i \(0.661370\pi\)
\(158\) −110748. 191821.i −0.352934 0.611300i
\(159\) 11930.1 + 20663.5i 0.0374240 + 0.0648204i
\(160\) −132738. + 229910.i −0.409918 + 0.709998i
\(161\) 215228. 0.654387
\(162\) −127741. + 221255.i −0.382423 + 0.662377i
\(163\) 102435. + 177423.i 0.301981 + 0.523047i 0.976585 0.215133i \(-0.0690186\pi\)
−0.674603 + 0.738180i \(0.735685\pi\)
\(164\) −109850. −0.318927
\(165\) 5904.10 + 10226.2i 0.0168828 + 0.0292418i
\(166\) 158481. 274497.i 0.446382 0.773156i
\(167\) 199629. 345767.i 0.553901 0.959384i −0.444087 0.895984i \(-0.646472\pi\)
0.997988 0.0634009i \(-0.0201947\pi\)
\(168\) −31242.5 −0.0854030
\(169\) 43750.7 75778.4i 0.117833 0.204093i
\(170\) 265524. 0.704662
\(171\) −504047. −1.31820
\(172\) −119840. 101307.i −0.308874 0.261107i
\(173\) −571301. −1.45127 −0.725637 0.688077i \(-0.758455\pi\)
−0.725637 + 0.688077i \(0.758455\pi\)
\(174\) 15776.9 0.0395048
\(175\) 56621.5 98071.3i 0.139761 0.242073i
\(176\) −100658. −0.244943
\(177\) 3708.23 6422.85i 0.00889680 0.0154097i
\(178\) 99587.8 172491.i 0.235590 0.408053i
\(179\) −103377. 179053.i −0.241151 0.417686i 0.719891 0.694087i \(-0.244192\pi\)
−0.961042 + 0.276401i \(0.910858\pi\)
\(180\) 191488. 0.440514
\(181\) 49747.6 + 86165.4i 0.112869 + 0.195495i 0.916926 0.399057i \(-0.130663\pi\)
−0.804057 + 0.594553i \(0.797329\pi\)
\(182\) 217912. 377435.i 0.487644 0.844624i
\(183\) 35229.8 0.0777646
\(184\) −112663. + 195138.i −0.245323 + 0.424911i
\(185\) 505907. + 876256.i 1.08678 + 1.88236i
\(186\) −1371.54 2375.57i −0.00290687 0.00503484i
\(187\) −113323. 196282.i −0.236982 0.410465i
\(188\) −107058. −0.220915
\(189\) 38638.2 + 66923.3i 0.0786796 + 0.136277i
\(190\) −277315. 480324.i −0.557301 0.965273i
\(191\) 230622. 399449.i 0.457422 0.792278i −0.541402 0.840764i \(-0.682106\pi\)
0.998824 + 0.0484856i \(0.0154395\pi\)
\(192\) 14076.9 24381.8i 0.0275583 0.0477324i
\(193\) 348735. 0.673910 0.336955 0.941521i \(-0.390603\pi\)
0.336955 + 0.941521i \(0.390603\pi\)
\(194\) −457603. −0.872941
\(195\) 13821.7 23939.8i 0.0260300 0.0450853i
\(196\) 118507. 205260.i 0.220345 0.381649i
\(197\) 351170. + 608245.i 0.644692 + 1.11664i 0.984373 + 0.176099i \(0.0563478\pi\)
−0.339680 + 0.940541i \(0.610319\pi\)
\(198\) 120340. + 208435.i 0.218146 + 0.377841i
\(199\) −405599. −0.726047 −0.363023 0.931780i \(-0.618255\pi\)
−0.363023 + 0.931780i \(0.618255\pi\)
\(200\) 59278.1 + 102673.i 0.104790 + 0.181501i
\(201\) 17927.6 + 31051.6i 0.0312992 + 0.0542118i
\(202\) 140643. + 243601.i 0.242516 + 0.420049i
\(203\) −398526. + 690267.i −0.678761 + 1.17565i
\(204\) 10953.4 0.0184279
\(205\) −259161. + 448879.i −0.430709 + 0.746011i
\(206\) 12973.9 + 22471.4i 0.0213011 + 0.0368946i
\(207\) 278250. 0.451346
\(208\) 117821. + 204072.i 0.188828 + 0.327059i
\(209\) −236712. + 409997.i −0.374847 + 0.649255i
\(210\) −21226.2 + 36764.9i −0.0332142 + 0.0575287i
\(211\) −289100. −0.447035 −0.223518 0.974700i \(-0.571754\pi\)
−0.223518 + 0.974700i \(0.571754\pi\)
\(212\) 181710. 314731.i 0.277677 0.480951i
\(213\) −12143.4 −0.0183396
\(214\) 307961. 0.459687
\(215\) −696697. + 250696.i −1.02789 + 0.369871i
\(216\) −80902.1 −0.117985
\(217\) 138580. 0.199780
\(218\) −349884. + 606018.i −0.498636 + 0.863662i
\(219\) −67479.7 −0.0950743
\(220\) 89926.9 155758.i 0.125266 0.216967i
\(221\) −265294. + 459502.i −0.365381 + 0.632859i
\(222\) −30730.6 53227.0i −0.0418493 0.0724852i
\(223\) −848271. −1.14228 −0.571140 0.820853i \(-0.693499\pi\)
−0.571140 + 0.820853i \(0.693499\pi\)
\(224\) 407344. + 705541.i 0.542428 + 0.939512i
\(225\) 73201.2 126788.i 0.0963966 0.166964i
\(226\) 504655. 0.657239
\(227\) 617857. 1.07016e6i 0.795835 1.37843i −0.126472 0.991970i \(-0.540365\pi\)
0.922307 0.386457i \(-0.126301\pi\)
\(228\) −11439.9 19814.4i −0.0145742 0.0252432i
\(229\) −3190.49 5526.09i −0.00402039 0.00696353i 0.864008 0.503478i \(-0.167946\pi\)
−0.868029 + 0.496514i \(0.834613\pi\)
\(230\) 153087. + 265154.i 0.190818 + 0.330506i
\(231\) 36236.7 0.0446806
\(232\) −417225. 722654.i −0.508921 0.881476i
\(233\) 716746. + 1.24144e6i 0.864919 + 1.49808i 0.867127 + 0.498087i \(0.165964\pi\)
−0.00220787 + 0.999998i \(0.500703\pi\)
\(234\) 281720. 487954.i 0.336340 0.582558i
\(235\) −252573. + 437470.i −0.298344 + 0.516747i
\(236\) −112962. −0.132024
\(237\) −43113.3 −0.0498586
\(238\) 407416. 705666.i 0.466226 0.807526i
\(239\) 831921. 1.44093e6i 0.942079 1.63173i 0.180584 0.983560i \(-0.442201\pi\)
0.761496 0.648170i \(-0.224465\pi\)
\(240\) −11476.6 19878.1i −0.0128614 0.0222765i
\(241\) 206523. + 357709.i 0.229048 + 0.396722i 0.957526 0.288346i \(-0.0931055\pi\)
−0.728478 + 0.685069i \(0.759772\pi\)
\(242\) −477010. −0.523588
\(243\) 74965.2 + 129844.i 0.0814412 + 0.141060i
\(244\) −268297. 464704.i −0.288497 0.499691i
\(245\) −559167. 968506.i −0.595150 1.03083i
\(246\) 15742.4 27266.6i 0.0165856 0.0287272i
\(247\) 1.10830e6 1.15589
\(248\) −72541.3 + 125645.i −0.0748955 + 0.129723i
\(249\) −30847.6 53429.6i −0.0315299 0.0546114i
\(250\) −672004. −0.680020
\(251\) −847355. 1.46766e6i −0.848948 1.47042i −0.882148 0.470972i \(-0.843903\pi\)
0.0332009 0.999449i \(-0.489430\pi\)
\(252\) 293816. 508905.i 0.291457 0.504818i
\(253\) 130673. 226332.i 0.128346 0.222302i
\(254\) −750431. −0.729838
\(255\) 25841.5 44758.8i 0.0248867 0.0431051i
\(256\) −1.03611e6 −0.988112
\(257\) −423541. −0.400003 −0.200001 0.979796i \(-0.564095\pi\)
−0.200001 + 0.979796i \(0.564095\pi\)
\(258\) 42319.9 15228.2i 0.0395818 0.0142429i
\(259\) 3.10503e6 2.87618
\(260\) −421043. −0.386272
\(261\) −515221. + 892389.i −0.468158 + 0.810873i
\(262\) 933700. 0.840339
\(263\) 245923. 425951.i 0.219235 0.379726i −0.735339 0.677699i \(-0.762977\pi\)
0.954574 + 0.297973i \(0.0963105\pi\)
\(264\) −18968.5 + 32854.3i −0.0167503 + 0.0290123i
\(265\) −857387. 1.48504e6i −0.750002 1.29904i
\(266\) −1.70204e6 −1.47491
\(267\) −19384.3 33574.7i −0.0166407 0.0288226i
\(268\) 273061. 472955.i 0.232232 0.402238i
\(269\) −1.50648e6 −1.26935 −0.634675 0.772779i \(-0.718866\pi\)
−0.634675 + 0.772779i \(0.718866\pi\)
\(270\) −54964.9 + 95202.0i −0.0458856 + 0.0794762i
\(271\) 841293. + 1.45716e6i 0.695864 + 1.20527i 0.969889 + 0.243549i \(0.0783116\pi\)
−0.274025 + 0.961723i \(0.588355\pi\)
\(272\) 220283. + 381541.i 0.180534 + 0.312694i
\(273\) −42415.6 73466.0i −0.0344444 0.0596595i
\(274\) 1.48405e6 1.19419
\(275\) −68753.8 119085.i −0.0548233 0.0949567i
\(276\) 6315.17 + 10938.2i 0.00499014 + 0.00864317i
\(277\) −273684. + 474035.i −0.214314 + 0.371203i −0.953060 0.302781i \(-0.902085\pi\)
0.738746 + 0.673984i \(0.235418\pi\)
\(278\) 632072. 1.09478e6i 0.490518 0.849602i
\(279\) 179159. 0.137793
\(280\) 2.24533e6 1.71153
\(281\) −15157.9 + 26254.3i −0.0114518 + 0.0198351i −0.871695 0.490050i \(-0.836979\pi\)
0.860243 + 0.509885i \(0.170312\pi\)
\(282\) 15342.2 26573.5i 0.0114886 0.0198988i
\(283\) −794499. 1.37611e6i −0.589695 1.02138i −0.994272 0.106877i \(-0.965915\pi\)
0.404578 0.914504i \(-0.367419\pi\)
\(284\) 92479.3 + 160179.i 0.0680376 + 0.117845i
\(285\) −107956. −0.0787293
\(286\) −264604. 458308.i −0.191285 0.331316i
\(287\) 795306. + 1.37751e6i 0.569940 + 0.987166i
\(288\) 526621. + 912135.i 0.374125 + 0.648004i
\(289\) 213926. 370530.i 0.150667 0.260963i
\(290\) −1.13385e6 −0.791700
\(291\) −44535.2 + 77137.3i −0.0308298 + 0.0533988i
\(292\) 513901. + 890102.i 0.352713 + 0.610918i
\(293\) −414223. −0.281881 −0.140940 0.990018i \(-0.545013\pi\)
−0.140940 + 0.990018i \(0.545013\pi\)
\(294\) 33965.8 + 58830.5i 0.0229179 + 0.0396949i
\(295\) −266502. + 461595.i −0.178298 + 0.308821i
\(296\) −1.62536e6 + 2.81520e6i −1.07825 + 1.86758i
\(297\) 93834.4 0.0617264
\(298\) 191924. 332423.i 0.125196 0.216845i
\(299\) −611817. −0.395771
\(300\) 6645.50 0.00426309
\(301\) −402745. + 2.23623e6i −0.256220 + 1.42266i
\(302\) −256972. −0.162132
\(303\) 54751.1 0.0342599
\(304\) 460131. 796970.i 0.285560 0.494605i
\(305\) −2.53188e6 −1.55845
\(306\) 526714. 912296.i 0.321567 0.556971i
\(307\) −1.00547e6 + 1.74152e6i −0.608867 + 1.05459i 0.382561 + 0.923930i \(0.375042\pi\)
−0.991427 + 0.130658i \(0.958291\pi\)
\(308\) −275965. 477986.i −0.165759 0.287104i
\(309\) 5050.62 0.00300918
\(310\) 98569.2 + 170727.i 0.0582555 + 0.100901i
\(311\) −901562. + 1.56155e6i −0.528561 + 0.915494i 0.470885 + 0.882195i \(0.343935\pi\)
−0.999445 + 0.0332991i \(0.989399\pi\)
\(312\) 88811.5 0.0516514
\(313\) 345410. 598267.i 0.199285 0.345171i −0.749012 0.662556i \(-0.769472\pi\)
0.948297 + 0.317385i \(0.102805\pi\)
\(314\) 693481. + 1.20115e6i 0.396927 + 0.687498i
\(315\) −1.38635e6 2.40123e6i −0.787221 1.36351i
\(316\) 328335. + 568693.i 0.184969 + 0.320376i
\(317\) 3.03303e6 1.69523 0.847614 0.530613i \(-0.178038\pi\)
0.847614 + 0.530613i \(0.178038\pi\)
\(318\) 52080.8 + 90206.6i 0.0288808 + 0.0500231i
\(319\) 483919. + 838172.i 0.266254 + 0.461165i
\(320\) −1.01167e6 + 1.75227e6i −0.552287 + 0.956588i
\(321\) 29971.7 51912.5i 0.0162349 0.0281196i
\(322\) 939579. 0.505002
\(323\) 2.07212e6 1.10512
\(324\) 378715. 655954.i 0.200424 0.347145i
\(325\) −160955. + 278782.i −0.0845270 + 0.146405i
\(326\) 447181. + 774540.i 0.233045 + 0.403645i
\(327\) 68103.5 + 117959.i 0.0352209 + 0.0610043i
\(328\) −1.66524e6 −0.854659
\(329\) 775090. + 1.34250e6i 0.394787 + 0.683791i
\(330\) 25774.4 + 44642.5i 0.0130288 + 0.0225665i
\(331\) −709993. 1.22974e6i −0.356192 0.616943i 0.631129 0.775678i \(-0.282592\pi\)
−0.987321 + 0.158735i \(0.949258\pi\)
\(332\) −469848. + 813800.i −0.233944 + 0.405203i
\(333\) 4.01423e6 1.98377
\(334\) 871480. 1.50945e6i 0.427456 0.740375i
\(335\) −1.28842e6 2.23160e6i −0.627256 1.08644i
\(336\) −70438.5 −0.0340378
\(337\) −906569. 1.57022e6i −0.434837 0.753159i 0.562446 0.826834i \(-0.309861\pi\)
−0.997282 + 0.0736750i \(0.976527\pi\)
\(338\) 190994. 330811.i 0.0909341 0.157503i
\(339\) 49114.4 85068.7i 0.0232119 0.0402041i
\(340\) −787198. −0.369306
\(341\) 84137.1 145730.i 0.0391834 0.0678676i
\(342\) −2.20042e6 −1.01728
\(343\) −282228. −0.129528
\(344\) −1.81668e6 1.53573e6i −0.827717 0.699711i
\(345\) 59595.4 0.0269566
\(346\) −2.49401e6 −1.11998
\(347\) 1.44905e6 2.50983e6i 0.646041 1.11898i −0.338019 0.941139i \(-0.609757\pi\)
0.984060 0.177837i \(-0.0569099\pi\)
\(348\) −46773.8 −0.0207040
\(349\) −870184. + 1.50720e6i −0.382426 + 0.662381i −0.991408 0.130802i \(-0.958245\pi\)
0.608982 + 0.793184i \(0.291578\pi\)
\(350\) 247181. 428130.i 0.107856 0.186813i
\(351\) −109835. 190239.i −0.0475851 0.0824199i
\(352\) 989253. 0.425550
\(353\) −2979.14 5160.02i −0.00127249 0.00220402i 0.865388 0.501102i \(-0.167072\pi\)
−0.866661 + 0.498898i \(0.833738\pi\)
\(354\) 16188.3 28039.0i 0.00686583 0.0118920i
\(355\) 872714. 0.367537
\(356\) −295248. + 511384.i −0.123470 + 0.213857i
\(357\) −79301.8 137355.i −0.0329316 0.0570392i
\(358\) −451290. 781658.i −0.186101 0.322336i
\(359\) 112246. + 194415.i 0.0459657 + 0.0796149i 0.888093 0.459664i \(-0.152030\pi\)
−0.842127 + 0.539279i \(0.818697\pi\)
\(360\) 2.90280e6 1.18048
\(361\) −926088. 1.60403e6i −0.374011 0.647806i
\(362\) 217173. + 376155.i 0.0871034 + 0.150868i
\(363\) −46424.0 + 80408.7i −0.0184917 + 0.0320285i
\(364\) −646043. + 1.11898e6i −0.255569 + 0.442659i
\(365\) 4.84961e6 1.90535
\(366\) 153796. 0.0600124
\(367\) 2.15113e6 3.72587e6i 0.833685 1.44398i −0.0614120 0.998113i \(-0.519560\pi\)
0.895097 0.445872i \(-0.147106\pi\)
\(368\) −254007. + 439953.i −0.0977746 + 0.169351i
\(369\) 1.02818e6 + 1.78087e6i 0.393102 + 0.680872i
\(370\) 2.20854e6 + 3.82530e6i 0.838687 + 1.45265i
\(371\) −5.26226e6 −1.98489
\(372\) 4066.19 + 7042.86i 0.00152346 + 0.00263871i
\(373\) −1.56011e6 2.70219e6i −0.580609 1.00564i −0.995407 0.0957304i \(-0.969481\pi\)
0.414799 0.909913i \(-0.363852\pi\)
\(374\) −494714. 856870.i −0.182884 0.316764i
\(375\) −65401.3 + 113278.i −0.0240164 + 0.0415977i
\(376\) −1.62291e6 −0.592006
\(377\) 1.13287e6 1.96219e6i 0.410512 0.711028i
\(378\) 168675. + 292154.i 0.0607185 + 0.105168i
\(379\) −4.12331e6 −1.47451 −0.737255 0.675614i \(-0.763878\pi\)
−0.737255 + 0.675614i \(0.763878\pi\)
\(380\) 822156. + 1.42402e6i 0.292076 + 0.505890i
\(381\) −73034.0 + 126499.i −0.0257758 + 0.0446451i
\(382\) 1.00678e6 1.74379e6i 0.353001 0.611416i
\(383\) −1.12528e6 −0.391979 −0.195990 0.980606i \(-0.562792\pi\)
−0.195990 + 0.980606i \(0.562792\pi\)
\(384\) 2349.07 4068.71i 0.000812958 0.00140808i
\(385\) −2.60425e6 −0.895427
\(386\) 1.52240e6 0.520069
\(387\) −520675. + 2.89104e6i −0.176721 + 0.981242i
\(388\) 1.35666e6 0.457499
\(389\) 1.57279e6 0.526983 0.263491 0.964662i \(-0.415126\pi\)
0.263491 + 0.964662i \(0.415126\pi\)
\(390\) 60338.6 104509.i 0.0200878 0.0347932i
\(391\) −1.14388e6 −0.378388
\(392\) 1.79647e6 3.11158e6i 0.590479 1.02274i
\(393\) 90870.3 157392.i 0.0296784 0.0514045i
\(394\) 1.53304e6 + 2.65529e6i 0.497521 + 0.861732i
\(395\) 3.09845e6 0.999199
\(396\) −356773. 617948.i −0.114328 0.198022i
\(397\) 696834. 1.20695e6i 0.221898 0.384338i −0.733486 0.679704i \(-0.762108\pi\)
0.955384 + 0.295366i \(0.0954415\pi\)
\(398\) −1.77064e6 −0.560304
\(399\) −165647. + 286909.i −0.0520896 + 0.0902219i
\(400\) 133647. + 231483.i 0.0417646 + 0.0723384i
\(401\) −356158. 616884.i −0.110607 0.191577i 0.805408 0.592720i \(-0.201946\pi\)
−0.916015 + 0.401144i \(0.868613\pi\)
\(402\) 78263.2 + 135556.i 0.0241542 + 0.0418363i
\(403\) −393935. −0.120826
\(404\) −416964. 722203.i −0.127100 0.220143i
\(405\) −1.78694e6 3.09507e6i −0.541343 0.937633i
\(406\) −1.73977e6 + 3.01336e6i −0.523812 + 0.907270i
\(407\) 1.88517e6 3.26521e6i 0.564111 0.977070i
\(408\) 166045. 0.0493828
\(409\) −617135. −0.182420 −0.0912100 0.995832i \(-0.529073\pi\)
−0.0912100 + 0.995832i \(0.529073\pi\)
\(410\) −1.13137e6 + 1.95958e6i −0.332387 + 0.575711i
\(411\) 144432. 250164.i 0.0421754 0.0730499i
\(412\) −38463.6 66621.0i −0.0111637 0.0193361i
\(413\) 817835. + 1.41653e6i 0.235934 + 0.408650i
\(414\) 1.21470e6 0.348312
\(415\) 2.21694e6 + 3.83986e6i 0.631880 + 1.09445i
\(416\) −1.15794e6 2.00560e6i −0.328058 0.568214i
\(417\) −123030. 213094.i −0.0346474 0.0600111i
\(418\) −1.03337e6 + 1.78984e6i −0.289277 + 0.501042i
\(419\) 1.98216e6 0.551575 0.275788 0.961219i \(-0.411061\pi\)
0.275788 + 0.961219i \(0.411061\pi\)
\(420\) 62929.3 108997.i 0.0174072 0.0301502i
\(421\) 271063. + 469495.i 0.0745359 + 0.129100i 0.900884 0.434059i \(-0.142919\pi\)
−0.826348 + 0.563159i \(0.809586\pi\)
\(422\) −1.26207e6 −0.344986
\(423\) 1.00205e6 + 1.73560e6i 0.272294 + 0.471627i
\(424\) 2.75458e6 4.77107e6i 0.744116 1.28885i
\(425\) −300927. + 521221.i −0.0808144 + 0.139975i
\(426\) −53011.8 −0.0141530
\(427\) −3.88488e6 + 6.72882e6i −1.03112 + 1.78595i
\(428\) −913013. −0.240917
\(429\) −103008. −0.0270227
\(430\) −3.04143e6 + 1.09441e6i −0.793244 + 0.285437i
\(431\) −4.50685e6 −1.16864 −0.584319 0.811524i \(-0.698638\pi\)
−0.584319 + 0.811524i \(0.698638\pi\)
\(432\) −182399. −0.0470234
\(433\) 2.71194e6 4.69722e6i 0.695121 1.20398i −0.275019 0.961439i \(-0.588684\pi\)
0.970140 0.242546i \(-0.0779824\pi\)
\(434\) 604973. 0.154174
\(435\) −110350. + 191131.i −0.0279607 + 0.0484293i
\(436\) 1.03730e6 1.79666e6i 0.261330 0.452636i
\(437\) 1.19467e6 + 2.06924e6i 0.299258 + 0.518330i
\(438\) −294583. −0.0733706
\(439\) −1.67647e6 2.90373e6i −0.415178 0.719110i 0.580269 0.814425i \(-0.302947\pi\)
−0.995447 + 0.0953151i \(0.969614\pi\)
\(440\) 1.36322e6 2.36116e6i 0.335686 0.581426i
\(441\) −4.43683e6 −1.08637
\(442\) −1.15814e6 + 2.00596e6i −0.281972 + 0.488389i
\(443\) 3.71963e6 + 6.44259e6i 0.900514 + 1.55974i 0.826829 + 0.562454i \(0.190143\pi\)
0.0736847 + 0.997282i \(0.476524\pi\)
\(444\) 91107.0 + 157802.i 0.0219328 + 0.0379887i
\(445\) 1.39311e6 + 2.41293e6i 0.333491 + 0.577624i
\(446\) −3.70313e6 −0.881519
\(447\) −37357.2 64704.6i −0.00884313 0.0153167i
\(448\) 3.10459e6 + 5.37731e6i 0.730818 + 1.26581i
\(449\) 2.18698e6 3.78796e6i 0.511952 0.886726i −0.487952 0.872870i \(-0.662256\pi\)
0.999904 0.0138560i \(-0.00441063\pi\)
\(450\) 319560. 553494.i 0.0743911 0.128849i
\(451\) 1.93143e6 0.447135
\(452\) −1.49615e6 −0.344452
\(453\) −25009.2 + 43317.2i −0.00572604 + 0.00991780i
\(454\) 2.69725e6 4.67178e6i 0.614161 1.06376i
\(455\) 3.04831e6 + 5.27983e6i 0.690289 + 1.19562i
\(456\) −173419. 300370.i −0.0390557 0.0676465i
\(457\) 3.86721e6 0.866177 0.433089 0.901351i \(-0.357424\pi\)
0.433089 + 0.901351i \(0.357424\pi\)
\(458\) −13928.1 24124.2i −0.00310261 0.00537388i
\(459\) −205351. 355678.i −0.0454951 0.0787999i
\(460\) −453857. 786103.i −0.100006 0.173215i
\(461\) −1.47161e6 + 2.54890e6i −0.322507 + 0.558599i −0.981005 0.193984i \(-0.937859\pi\)
0.658498 + 0.752583i \(0.271192\pi\)
\(462\) 158191. 0.0344809
\(463\) −3.22970e6 + 5.59400e6i −0.700180 + 1.21275i 0.268224 + 0.963357i \(0.413563\pi\)
−0.968403 + 0.249390i \(0.919770\pi\)
\(464\) −940662. 1.62927e6i −0.202833 0.351317i
\(465\) 38372.1 0.00822969
\(466\) 3.12896e6 + 5.41951e6i 0.667475 + 1.15610i
\(467\) 3.74977e6 6.49479e6i 0.795632 1.37807i −0.126806 0.991928i \(-0.540473\pi\)
0.922437 0.386147i \(-0.126194\pi\)
\(468\) −835215. + 1.44664e6i −0.176272 + 0.305312i
\(469\) −7.90773e6 −1.66004
\(470\) −1.10261e6 + 1.90977e6i −0.230238 + 0.398784i
\(471\) 269966. 0.0560734
\(472\) −1.71241e6 −0.353797
\(473\) 2.10708e6 + 1.78122e6i 0.433040 + 0.366070i
\(474\) −188211. −0.0384768
\(475\) 1.25716e6 0.255657
\(476\) −1.20787e6 + 2.09209e6i −0.244344 + 0.423216i
\(477\) −6.80313e6 −1.36903
\(478\) 3.63175e6 6.29038e6i 0.727021 1.25924i
\(479\) −2.23566e6 + 3.87228e6i −0.445213 + 0.771131i −0.998067 0.0621470i \(-0.980205\pi\)
0.552854 + 0.833278i \(0.313539\pi\)
\(480\) 112791. + 195360.i 0.0223446 + 0.0387020i
\(481\) −8.82649e6 −1.73950
\(482\) 901577. + 1.56158e6i 0.176761 + 0.306158i
\(483\) 91442.4 158383.i 0.0178353 0.0308916i
\(484\) 1.41419e6 0.274407
\(485\) 3.20064e6 5.54367e6i 0.617849 1.07015i
\(486\) 327261. + 566832.i 0.0628497 + 0.108859i
\(487\) 3.41494e6 + 5.91485e6i 0.652470 + 1.13011i 0.982522 + 0.186149i \(0.0596007\pi\)
−0.330051 + 0.943963i \(0.607066\pi\)
\(488\) −4.06716e6 7.04453e6i −0.773111 1.33907i
\(489\) 174084. 0.0329220
\(490\) −2.44104e6 4.22801e6i −0.459288 0.795511i
\(491\) 4.08976e6 + 7.08367e6i 0.765586 + 1.32603i 0.939936 + 0.341350i \(0.110884\pi\)
−0.174350 + 0.984684i \(0.555782\pi\)
\(492\) −46671.3 + 80837.1i −0.00869236 + 0.0150556i
\(493\) 2.11805e6 3.66857e6i 0.392482 0.679798i
\(494\) 4.83828e6 0.892019
\(495\) −3.36681e6 −0.617598
\(496\) −163549. + 283276.i −0.0298500 + 0.0517017i
\(497\) 1.33908e6 2.31936e6i 0.243173 0.421189i
\(498\) −134665. 233247.i −0.0243322 0.0421447i
\(499\) 1.84543e6 + 3.19637e6i 0.331777 + 0.574654i 0.982860 0.184352i \(-0.0590187\pi\)
−0.651084 + 0.759006i \(0.725685\pi\)
\(500\) 1.99229e6 0.356392
\(501\) −169630. 293807.i −0.0301931 0.0522960i
\(502\) −3.69913e6 6.40708e6i −0.655149 1.13475i
\(503\) −2.19122e6 3.79531e6i −0.386160 0.668848i 0.605770 0.795640i \(-0.292865\pi\)
−0.991929 + 0.126792i \(0.959532\pi\)
\(504\) 4.45401e6 7.71458e6i 0.781043 1.35281i
\(505\) −3.93483e6 −0.686590
\(506\) 570452. 988051.i 0.0990473 0.171555i
\(507\) −37176.1 64390.8i −0.00642308 0.0111251i
\(508\) 2.22480e6 0.382500
\(509\) 1.58121e6 + 2.73874e6i 0.270518 + 0.468551i 0.968995 0.247082i \(-0.0794718\pi\)
−0.698477 + 0.715633i \(0.746138\pi\)
\(510\) 112811. 195395.i 0.0192056 0.0332650i
\(511\) 7.44118e6 1.28885e7i 1.26064 2.18348i
\(512\) −4.70007e6 −0.792373
\(513\) −428940. + 742946.i −0.0719620 + 0.124642i
\(514\) −1.84897e6 −0.308690
\(515\) −362976. −0.0603059
\(516\) −125466. + 45146.9i −0.0207444 + 0.00746456i
\(517\) 1.88234e6 0.309722
\(518\) 1.35550e7 2.21960
\(519\) −242725. + 420411.i −0.0395544 + 0.0685103i
\(520\) −6.38267e6 −1.03513
\(521\) 1.59237e6 2.75806e6i 0.257010 0.445154i −0.708430 0.705781i \(-0.750596\pi\)
0.965439 + 0.260627i \(0.0839294\pi\)
\(522\) −2.24920e6 + 3.89572e6i −0.361286 + 0.625766i
\(523\) −21079.2 36510.2i −0.00336977 0.00583661i 0.864336 0.502915i \(-0.167739\pi\)
−0.867705 + 0.497079i \(0.834406\pi\)
\(524\) −2.76814e6 −0.440413
\(525\) −48112.7 83333.7i −0.00761837 0.0131954i
\(526\) 1.07358e6 1.85949e6i 0.169188 0.293042i
\(527\) −736515. −0.115520
\(528\) −42765.7 + 74072.4i −0.00667591 + 0.0115630i
\(529\) 2.55867e6 + 4.43175e6i 0.397535 + 0.688551i
\(530\) −3.74292e6 6.48294e6i −0.578791 1.00249i
\(531\) 1.05731e6 + 1.83131e6i 0.162729 + 0.281856i
\(532\) 5.04602e6 0.772984
\(533\) −2.26077e6 3.91577e6i −0.344698 0.597034i
\(534\) −84622.4 146570.i −0.0128420 0.0222430i
\(535\) −2.15399e6 + 3.73083e6i −0.325357 + 0.563535i
\(536\) 4.13938e6 7.16961e6i 0.622333 1.07791i
\(537\) −175683. −0.0262903
\(538\) −6.57652e6 −0.979582
\(539\) −2.08364e6 + 3.60897e6i −0.308923 + 0.535070i
\(540\) 162954. 282245.i 0.0240482 0.0416526i
\(541\) 3.67365e6 + 6.36296e6i 0.539641 + 0.934686i 0.998923 + 0.0463955i \(0.0147734\pi\)
−0.459282 + 0.888291i \(0.651893\pi\)
\(542\) 3.67267e6 + 6.36125e6i 0.537011 + 0.930131i
\(543\) 84543.7 0.0123050
\(544\) −2.16492e6 3.74975e6i −0.313649 0.543257i
\(545\) −4.89444e6 8.47741e6i −0.705848 1.22257i
\(546\) −185165. 320716.i −0.0265814 0.0460404i
\(547\) 1.09198e6 1.89136e6i 0.156044 0.270275i −0.777395 0.629013i \(-0.783459\pi\)
0.933439 + 0.358737i \(0.116793\pi\)
\(548\) −4.39977e6 −0.625862
\(549\) −5.02244e6 + 8.69912e6i −0.711187 + 1.23181i
\(550\) −300145. 519866.i −0.0423082 0.0732799i
\(551\) −8.84845e6 −1.24162
\(552\) 95732.8 + 165814.i 0.0133725 + 0.0231619i
\(553\) 4.75422e6 8.23456e6i 0.661099 1.14506i
\(554\) −1.19477e6 + 2.06940e6i −0.165390 + 0.286464i
\(555\) 859764. 0.118480
\(556\) −1.87390e6 + 3.24570e6i −0.257075 + 0.445267i
\(557\) 8.33597e6 1.13846 0.569230 0.822178i \(-0.307241\pi\)
0.569230 + 0.822178i \(0.307241\pi\)
\(558\) 782119. 0.106338
\(559\) 1.14486e6 6.35681e6i 0.154961 0.860419i
\(560\) 5.06225e6 0.682140
\(561\) −192588. −0.0258358
\(562\) −66171.9 + 114613.i −0.00883757 + 0.0153071i
\(563\) 9.33454e6 1.24114 0.620571 0.784150i \(-0.286901\pi\)
0.620571 + 0.784150i \(0.286901\pi\)
\(564\) −45485.0 + 78782.4i −0.00602103 + 0.0104287i
\(565\) −3.52974e6 + 6.11368e6i −0.465180 + 0.805716i
\(566\) −3.46839e6 6.00742e6i −0.455078 0.788219i
\(567\) −1.09674e7 −1.43267
\(568\) 1.40191e6 + 2.42818e6i 0.182326 + 0.315799i
\(569\) −1.91530e6 + 3.31740e6i −0.248002 + 0.429553i −0.962971 0.269603i \(-0.913107\pi\)
0.714969 + 0.699156i \(0.246441\pi\)
\(570\) −471284. −0.0607569
\(571\) −7.28871e6 + 1.26244e7i −0.935536 + 1.62040i −0.161860 + 0.986814i \(0.551749\pi\)
−0.773676 + 0.633582i \(0.781584\pi\)
\(572\) 784472. + 1.35874e6i 0.100251 + 0.173639i
\(573\) −195965. 339422.i −0.0249341 0.0431870i
\(574\) 3.47191e6 + 6.01352e6i 0.439834 + 0.761814i
\(575\) −693994. −0.0875359
\(576\) 4.01367e6 + 6.95187e6i 0.504063 + 0.873063i
\(577\) −4.73153e6 8.19524e6i −0.591646 1.02476i −0.994011 0.109281i \(-0.965145\pi\)
0.402365 0.915479i \(-0.368188\pi\)
\(578\) 933892. 1.61755e6i 0.116273 0.201390i
\(579\) 148164. 256628.i 0.0183674 0.0318133i
\(580\) 3.36153e6 0.414922
\(581\) 1.36066e7 1.67228
\(582\) −194419. + 336743.i −0.0237920 + 0.0412089i
\(583\) −3.19490e6 + 5.53373e6i −0.389302 + 0.674290i
\(584\) 7.79031e6 + 1.34932e7i 0.945198 + 1.63713i
\(585\) 3.94090e6 + 6.82585e6i 0.476109 + 0.824645i
\(586\) −1.80829e6 −0.217533
\(587\) 360633. + 624635.i 0.0431987 + 0.0748223i 0.886816 0.462122i \(-0.152912\pi\)
−0.843618 + 0.536944i \(0.819578\pi\)
\(588\) −100698. 174415.i −0.0120110 0.0208037i
\(589\) 769223. + 1.33233e6i 0.0913616 + 0.158243i
\(590\) −1.16342e6 + 2.01509e6i −0.137596 + 0.238323i
\(591\) 596797. 0.0702843
\(592\) −3.66448e6 + 6.34706e6i −0.429742 + 0.744335i
\(593\) −5.58315e6 9.67029e6i −0.651992 1.12928i −0.982639 0.185529i \(-0.940600\pi\)
0.330647 0.943755i \(-0.392733\pi\)
\(594\) 409634. 0.0476354
\(595\) 5.69923e6 + 9.87136e6i 0.659970 + 1.14310i
\(596\) −568998. + 985533.i −0.0656138 + 0.113646i
\(597\) −172324. + 298474.i −0.0197884 + 0.0342745i
\(598\) −2.67089e6 −0.305424
\(599\) −2.27539e6 + 3.94109e6i −0.259112 + 0.448796i −0.966004 0.258526i \(-0.916763\pi\)
0.706892 + 0.707322i \(0.250097\pi\)
\(600\) 100740. 0.0114242
\(601\) 8.68908e6 0.981268 0.490634 0.871366i \(-0.336765\pi\)
0.490634 + 0.871366i \(0.336765\pi\)
\(602\) −1.75818e6 + 9.76227e6i −0.197730 + 1.09789i
\(603\) −1.02232e7 −1.14497
\(604\) 761844. 0.0849716
\(605\) 3.33638e6 5.77879e6i 0.370585 0.641872i
\(606\) 239016. 0.0264390
\(607\) 7.75543e6 1.34328e7i 0.854347 1.47977i −0.0229025 0.999738i \(-0.507291\pi\)
0.877249 0.480035i \(-0.159376\pi\)
\(608\) −4.52212e6 + 7.83254e6i −0.496116 + 0.859298i
\(609\) 338638. + 586538.i 0.0369992 + 0.0640845i
\(610\) −1.10529e7 −1.20269
\(611\) −2.20331e6 3.81624e6i −0.238766 0.413554i
\(612\) −1.56155e6 + 2.70468e6i −0.168530 + 0.291902i
\(613\) −4.37654e6 −0.470414 −0.235207 0.971945i \(-0.575577\pi\)
−0.235207 + 0.971945i \(0.575577\pi\)
\(614\) −4.38937e6 + 7.60262e6i −0.469874 + 0.813846i
\(615\) 220215. + 381424.i 0.0234779 + 0.0406650i
\(616\) −4.18341e6 7.24588e6i −0.444200 0.769377i
\(617\) 315752. + 546899.i 0.0333913 + 0.0578355i 0.882238 0.470803i \(-0.156036\pi\)
−0.848847 + 0.528639i \(0.822703\pi\)
\(618\) 22048.5 0.00232224
\(619\) −6.46582e6 1.11991e7i −0.678261 1.17478i −0.975504 0.219981i \(-0.929401\pi\)
0.297243 0.954802i \(-0.403933\pi\)
\(620\) −292228. 506153.i −0.0305311 0.0528814i
\(621\) 236789. 410130.i 0.0246395 0.0426769i
\(622\) −3.93577e6 + 6.81696e6i −0.407900 + 0.706504i
\(623\) 8.55026e6 0.882591
\(624\) 200232. 0.0205860
\(625\) 5.64442e6 9.77642e6i 0.577988 1.00111i
\(626\) 1.50789e6 2.61174e6i 0.153792 0.266375i
\(627\) 201140. + 348385.i 0.0204329 + 0.0353908i
\(628\) −2.05596e6 3.56103e6i −0.208025 0.360310i
\(629\) −1.65023e7 −1.66310
\(630\) −6.05212e6 1.04826e7i −0.607514 1.05224i
\(631\) 526104. + 911240.i 0.0526016 + 0.0911086i 0.891127 0.453754i \(-0.149915\pi\)
−0.838526 + 0.544862i \(0.816582\pi\)
\(632\) 4.97729e6 + 8.62092e6i 0.495679 + 0.858540i
\(633\) −122828. + 212744.i −0.0121839 + 0.0211032i
\(634\) 1.32407e7 1.30824
\(635\) 5.24878e6 9.09116e6i 0.516564 0.894716i
\(636\) −154404. 267435.i −0.0151362 0.0262166i
\(637\) 9.75572e6 0.952600
\(638\) 2.11255e6 + 3.65904e6i 0.205473 + 0.355890i
\(639\) 1.73119e6 2.99850e6i 0.167723 0.290504i
\(640\) −168822. + 292409.i −0.0162922 + 0.0282189i
\(641\) 1.00920e7 0.970139 0.485069 0.874476i \(-0.338794\pi\)
0.485069 + 0.874476i \(0.338794\pi\)
\(642\) 130841. 226624.i 0.0125287 0.0217004i
\(643\) −1.49819e6 −0.142902 −0.0714510 0.997444i \(-0.522763\pi\)
−0.0714510 + 0.997444i \(0.522763\pi\)
\(644\) −2.78557e6 −0.264667
\(645\) −111518. + 619199.i −0.0105547 + 0.0586045i
\(646\) 9.04584e6 0.852840
\(647\) 65101.5 0.00611407 0.00305703 0.999995i \(-0.499027\pi\)
0.00305703 + 0.999995i \(0.499027\pi\)
\(648\) 5.74101e6 9.94372e6i 0.537094 0.930275i
\(649\) 1.98615e6 0.185097
\(650\) −702648. + 1.21702e6i −0.0652311 + 0.112984i
\(651\) 58877.7 101979.i 0.00544500 0.00943102i
\(652\) −1.32576e6 2.29628e6i −0.122136 0.211546i
\(653\) −1.02603e7 −0.941626 −0.470813 0.882233i \(-0.656039\pi\)
−0.470813 + 0.882233i \(0.656039\pi\)
\(654\) 297306. + 514949.i 0.0271806 + 0.0470782i
\(655\) −6.53064e6 + 1.13114e7i −0.594774 + 1.03018i
\(656\) −3.75440e6 −0.340629
\(657\) 9.62007e6 1.66625e7i 0.869491 1.50600i
\(658\) 3.38366e6 + 5.86067e6i 0.304664 + 0.527694i
\(659\) −1.08022e7 1.87100e7i −0.968948 1.67827i −0.698611 0.715502i \(-0.746198\pi\)
−0.270338 0.962766i \(-0.587135\pi\)
\(660\) −76413.2 132352.i −0.00682824 0.0118269i
\(661\) 8.27281e6 0.736461 0.368230 0.929735i \(-0.379964\pi\)
0.368230 + 0.929735i \(0.379964\pi\)
\(662\) −3.09948e6 5.36845e6i −0.274880 0.476106i
\(663\) 225427. + 390451.i 0.0199169 + 0.0344971i
\(664\) −7.12251e6 + 1.23365e7i −0.626921 + 1.08586i
\(665\) 1.19047e7 2.06195e7i 1.04391 1.80810i
\(666\) 1.75241e7 1.53091
\(667\) 4.88463e6 0.425125
\(668\) −2.58368e6 + 4.47506e6i −0.224025 + 0.388023i
\(669\) −360399. + 624229.i −0.0311328 + 0.0539236i
\(670\) −5.62459e6 9.74208e6i −0.484065 0.838425i
\(671\) 4.71730e6 + 8.17061e6i 0.404471 + 0.700564i
\(672\) 692262. 0.0591354
\(673\) −4.93783e6 8.55257e6i −0.420241 0.727879i 0.575722 0.817646i \(-0.304721\pi\)
−0.995963 + 0.0897669i \(0.971388\pi\)
\(674\) −3.95763e6 6.85482e6i −0.335572 0.581227i
\(675\) −124587. 215791.i −0.0105248 0.0182295i
\(676\) −566238. + 980753.i −0.0476576 + 0.0825454i
\(677\) −1.89768e7 −1.59130 −0.795649 0.605757i \(-0.792870\pi\)
−0.795649 + 0.605757i \(0.792870\pi\)
\(678\) 214409. 371367.i 0.0179130 0.0310263i
\(679\) −9.82205e6 1.70123e7i −0.817575 1.41608i
\(680\) −1.19333e7 −0.989663
\(681\) −525009. 909342.i −0.0433809 0.0751380i
\(682\) 367301. 636183.i 0.0302385 0.0523747i
\(683\) −8.19754e6 + 1.41986e7i −0.672407 + 1.16464i 0.304813 + 0.952412i \(0.401406\pi\)
−0.977220 + 0.212230i \(0.931927\pi\)
\(684\) 6.52358e6 0.533146
\(685\) −1.03800e7 + 1.79787e7i −0.845222 + 1.46397i
\(686\) −1.23207e6 −0.0999595
\(687\) −5422.08 −0.000438303
\(688\) −4.09583e6 3.46241e6i −0.329891 0.278873i
\(689\) 1.49587e7 1.20046
\(690\) 260164. 0.0208029
\(691\) 3.09629e6 5.36293e6i 0.246687 0.427274i −0.715918 0.698185i \(-0.753991\pi\)
0.962605 + 0.270910i \(0.0873247\pi\)
\(692\) 7.39400e6 0.586968
\(693\) −5.16599e6 + 8.94776e6i −0.408621 + 0.707753i
\(694\) 6.32584e6 1.09567e7i 0.498562 0.863535i
\(695\) 8.84188e6 + 1.53146e7i 0.694357 + 1.20266i
\(696\) −709053. −0.0554824
\(697\) −4.22682e6 7.32107e6i −0.329558 0.570811i
\(698\) −3.79879e6 + 6.57970e6i −0.295125 + 0.511172i
\(699\) 1.21808e6 0.0942934
\(700\) −732818. + 1.26928e6i −0.0565263 + 0.0979065i
\(701\) −7.45084e6 1.29052e7i −0.572677 0.991906i −0.996290 0.0860628i \(-0.972571\pi\)
0.423612 0.905844i \(-0.360762\pi\)
\(702\) −479483. 830489.i −0.0367224 0.0636050i
\(703\) 1.72352e7 + 2.98522e7i 1.31531 + 2.27818i
\(704\) 7.53963e6 0.573348
\(705\) 214618. + 371729.i 0.0162627 + 0.0281679i
\(706\) −13005.4 22526.1i −0.000982005 0.00170088i
\(707\) −6.03755e6 + 1.04574e7i −0.454268 + 0.786816i
\(708\) −47993.4 + 83127.1i −0.00359831 + 0.00623246i
\(709\) 1.80621e6 0.134943 0.0674717 0.997721i \(-0.478507\pi\)
0.0674717 + 0.997721i \(0.478507\pi\)
\(710\) 3.80984e6 0.283635
\(711\) 6.14634e6 1.06458e7i 0.455976 0.789774i
\(712\) −4.47572e6 + 7.75217e6i −0.330874 + 0.573090i
\(713\) −424636. 735491.i −0.0312819 0.0541818i
\(714\) −346192. 599622.i −0.0254139 0.0440182i
\(715\) 7.40295e6 0.541551
\(716\) 1.33794e6 + 2.31738e6i 0.0975336 + 0.168933i
\(717\) −706905. 1.22440e6i −0.0513527 0.0889455i
\(718\) 490009. + 848721.i 0.0354726 + 0.0614403i
\(719\) −4.91633e6 + 8.51534e6i −0.354666 + 0.614299i −0.987061 0.160347i \(-0.948739\pi\)
0.632395 + 0.774646i \(0.282072\pi\)
\(720\) 6.54455e6 0.470488
\(721\) −556946. + 964659.i −0.0399002 + 0.0691091i
\(722\) −4.04284e6 7.00240e6i −0.288631 0.499924i
\(723\) 350976. 0.0249708
\(724\) −643854. 1.11519e6i −0.0456500 0.0790681i
\(725\) 1.28503e6 2.22574e6i 0.0907964 0.157264i
\(726\) −202664. + 351024.i −0.0142704 + 0.0247170i
\(727\) −257638. −0.0180790 −0.00903950 0.999959i \(-0.502877\pi\)
−0.00903950 + 0.999959i \(0.502877\pi\)
\(728\) −9.79349e6 + 1.69628e7i −0.684871 + 1.18623i
\(729\) −1.40937e7 −0.982216
\(730\) 2.11710e7 1.47039
\(731\) 2.14047e6 1.18849e7i 0.148155 0.822628i
\(732\) −455958. −0.0314519
\(733\) −1.73566e7 −1.19317 −0.596587 0.802548i \(-0.703477\pi\)
−0.596587 + 0.802548i \(0.703477\pi\)
\(734\) 9.39077e6 1.62653e7i 0.643370 1.11435i
\(735\) −950277. −0.0648832
\(736\) 2.49636e6 4.32381e6i 0.169868 0.294220i
\(737\) −4.80106e6 + 8.31568e6i −0.325588 + 0.563935i
\(738\) 4.48854e6 + 7.77438e6i 0.303364 + 0.525442i
\(739\) −5.41470e6 −0.364723 −0.182361 0.983232i \(-0.558374\pi\)
−0.182361 + 0.983232i \(0.558374\pi\)
\(740\) −6.54764e6 1.13409e7i −0.439547 0.761318i
\(741\) 470875. 815580.i 0.0315036 0.0545659i
\(742\) −2.29724e7 −1.53178
\(743\) −42076.7 + 72879.0i −0.00279621 + 0.00484318i −0.867420 0.497576i \(-0.834223\pi\)
0.864624 + 0.502420i \(0.167557\pi\)
\(744\) 61640.2 + 106764.i 0.00408255 + 0.00707118i
\(745\) 2.68478e6 + 4.65017e6i 0.177222 + 0.306957i
\(746\) −6.81067e6 1.17964e7i −0.448067 0.776074i
\(747\) 1.75908e7 1.15341
\(748\) 1.46668e6 + 2.54036e6i 0.0958475 + 0.166013i
\(749\) 6.61012e6 + 1.14491e7i 0.430531 + 0.745702i
\(750\) −285510. + 494517.i −0.0185339 + 0.0321017i
\(751\) 1.47060e7 2.54715e7i 0.951469 1.64799i 0.209219 0.977869i \(-0.432908\pi\)
0.742250 0.670123i \(-0.233759\pi\)
\(752\) −3.65897e6 −0.235947
\(753\) −1.44004e6 −0.0925521
\(754\) 4.94554e6 8.56592e6i 0.316800 0.548714i
\(755\) 1.79735e6 3.11311e6i 0.114754 0.198759i
\(756\) −500071. 866148.i −0.0318219 0.0551172i
\(757\) 1.28831e7 + 2.23142e7i 0.817113 + 1.41528i 0.907801 + 0.419401i \(0.137760\pi\)
−0.0906882 + 0.995879i \(0.528907\pi\)
\(758\) −1.80003e7 −1.13791
\(759\) −111036. 192320.i −0.00699615 0.0121177i
\(760\) 1.24632e7 + 2.15869e7i 0.782701 + 1.35568i
\(761\) 9.62848e6 + 1.66770e7i 0.602693 + 1.04390i 0.992411 + 0.122961i \(0.0392390\pi\)
−0.389718 + 0.920934i \(0.627428\pi\)
\(762\) −318830. + 552230.i −0.0198917 + 0.0344534i
\(763\) −3.00398e7 −1.86804
\(764\) −2.98480e6 + 5.16983e6i −0.185004 + 0.320437i
\(765\) 7.36806e6 + 1.27619e7i 0.455197 + 0.788425i
\(766\) −4.91241e6 −0.302498
\(767\) −2.32481e6 4.02670e6i −0.142692 0.247150i
\(768\) −440205. + 762457.i −0.0269310 + 0.0466458i
\(769\) −7.79558e6 + 1.35023e7i −0.475371 + 0.823366i −0.999602 0.0282095i \(-0.991019\pi\)
0.524231 + 0.851576i \(0.324353\pi\)
\(770\) −1.13688e7 −0.691018
\(771\) −179947. + 311677.i −0.0109021 + 0.0188829i
\(772\) −4.51346e6 −0.272563