Properties

Label 43.5.f.a.2.6
Level $43$
Weight $5$
Character 43.2
Analytic conductor $4.445$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [43,5,Mod(2,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([9]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.2");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 43.f (of order \(14\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.44490841261\)
Analytic rank: \(0\)
Dimension: \(78\)
Relative dimension: \(13\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 2.6
Character \(\chi\) \(=\) 43.2
Dual form 43.5.f.a.22.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.495110 - 1.02811i) q^{2} +(6.66668 - 13.8435i) q^{3} +(9.16397 - 11.4913i) q^{4} +(-12.7517 - 2.91049i) q^{5} -17.5333 q^{6} +56.8875i q^{7} +(-34.1514 - 7.79484i) q^{8} +(-96.6955 - 121.252i) q^{9} +O(q^{10})\) \(q+(-0.495110 - 1.02811i) q^{2} +(6.66668 - 13.8435i) q^{3} +(9.16397 - 11.4913i) q^{4} +(-12.7517 - 2.91049i) q^{5} -17.5333 q^{6} +56.8875i q^{7} +(-34.1514 - 7.79484i) q^{8} +(-96.6955 - 121.252i) q^{9} +(3.32119 + 14.5511i) q^{10} +(117.846 + 147.774i) q^{11} +(-97.9860 - 203.470i) q^{12} +(54.4721 - 238.658i) q^{13} +(58.4865 - 28.1656i) q^{14} +(-125.303 + 157.125i) q^{15} +(-43.4345 - 190.299i) q^{16} +(-7.56301 - 33.1357i) q^{17} +(-76.7854 + 159.446i) q^{18} +(174.096 + 138.837i) q^{19} +(-150.301 + 119.861i) q^{20} +(787.523 + 379.251i) q^{21} +(93.5807 - 194.322i) q^{22} +(318.858 + 399.835i) q^{23} +(-335.585 + 420.810i) q^{24} +(-408.971 - 196.950i) q^{25} +(-272.335 + 62.1588i) q^{26} +(-1109.82 + 253.310i) q^{27} +(653.709 + 521.316i) q^{28} +(-75.2411 - 156.240i) q^{29} +(223.580 + 51.0306i) q^{30} +(1312.63 - 632.129i) q^{31} +(-612.340 + 488.325i) q^{32} +(2831.35 - 646.237i) q^{33} +(-30.3225 + 24.1814i) q^{34} +(165.571 - 725.412i) q^{35} -2279.45 q^{36} +2035.36i q^{37} +(56.5424 - 247.728i) q^{38} +(-2940.71 - 2345.14i) q^{39} +(412.802 + 198.795i) q^{40} +(-885.872 + 426.614i) q^{41} -997.429i q^{42} +(-63.1291 - 1847.92i) q^{43} +2778.04 q^{44} +(880.127 + 1827.60i) q^{45} +(253.204 - 525.783i) q^{46} +(-256.907 + 322.151i) q^{47} +(-2923.97 - 667.377i) q^{48} -835.193 q^{49} +517.978i q^{50} +(-509.135 - 116.207i) q^{51} +(-2243.30 - 2813.01i) q^{52} +(506.658 + 2219.81i) q^{53} +(809.914 + 1015.60i) q^{54} +(-1072.64 - 2227.35i) q^{55} +(443.430 - 1942.79i) q^{56} +(3082.63 - 1484.51i) q^{57} +(-123.378 + 154.712i) q^{58} +(1300.81 + 5699.21i) q^{59} +(657.289 + 2879.77i) q^{60} +(475.087 - 986.529i) q^{61} +(-1299.79 - 1036.55i) q^{62} +(6897.74 - 5500.77i) q^{63} +(-2008.58 - 967.281i) q^{64} +(-1389.22 + 2884.75i) q^{65} +(-2066.23 - 2590.97i) q^{66} +(-3578.65 + 4487.48i) q^{67} +(-450.078 - 216.746i) q^{68} +(7660.85 - 1748.54i) q^{69} +(-827.776 + 188.935i) q^{70} +(-587.312 - 468.366i) q^{71} +(2357.15 + 4894.67i) q^{72} +(469.645 + 107.193i) q^{73} +(2092.56 - 1007.73i) q^{74} +(-5452.96 + 4348.59i) q^{75} +(3190.81 - 728.282i) q^{76} +(-8406.49 + 6703.96i) q^{77} +(-955.078 + 4184.47i) q^{78} +3176.92 q^{79} +2553.05i q^{80} +(-1096.81 + 4805.46i) q^{81} +(877.209 + 699.550i) q^{82} +(-7134.64 - 3435.86i) q^{83} +(11574.9 - 5574.18i) q^{84} +444.548i q^{85} +(-1868.60 + 979.828i) q^{86} -2664.51 q^{87} +(-2872.73 - 5965.28i) q^{88} +(-5712.31 + 11861.7i) q^{89} +(1443.21 - 1809.73i) q^{90} +(13576.7 + 3098.78i) q^{91} +7516.61 q^{92} -22385.6i q^{93} +(458.403 + 104.628i) q^{94} +(-1815.93 - 2277.10i) q^{95} +(2677.85 + 11732.4i) q^{96} +(-7688.43 - 9640.99i) q^{97} +(413.512 + 858.667i) q^{98} +(6522.77 - 28578.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78 q - 7 q^{2} - 7 q^{3} + 69 q^{4} - 7 q^{5} - 140 q^{6} - 343 q^{8} + 486 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 78 q - 7 q^{2} - 7 q^{3} + 69 q^{4} - 7 q^{5} - 140 q^{6} - 343 q^{8} + 486 q^{9} - 189 q^{10} - 26 q^{11} - 119 q^{12} + 608 q^{13} + 45 q^{14} - 797 q^{15} + 593 q^{16} - 188 q^{17} - 574 q^{18} + 1421 q^{19} - 2107 q^{20} + 2952 q^{21} - 2359 q^{22} + 652 q^{23} - 253 q^{24} + 1264 q^{25} - 2023 q^{26} - 7 q^{27} + 1785 q^{28} - 2317 q^{29} - 252 q^{30} + 5714 q^{31} - 6517 q^{32} + 9023 q^{33} - 679 q^{34} + 1374 q^{35} - 8544 q^{36} + 95 q^{38} - 10339 q^{39} - 5901 q^{40} - 3611 q^{41} + 7001 q^{43} + 8148 q^{44} + 8862 q^{45} - 2660 q^{46} + 6268 q^{47} + 11081 q^{48} - 1074 q^{49} - 17353 q^{51} + 8277 q^{52} - 200 q^{53} - 8147 q^{54} + 9863 q^{55} + 15927 q^{56} - 25075 q^{57} + 13045 q^{58} + 1468 q^{59} - 357 q^{60} - 8239 q^{61} + 10073 q^{62} - 875 q^{63} + 1173 q^{64} - 19159 q^{65} - 24551 q^{66} + 42658 q^{67} + 3910 q^{68} - 903 q^{69} + 37870 q^{70} + 8960 q^{71} - 40586 q^{72} + 13342 q^{73} + 37116 q^{74} - 44996 q^{75} - 60438 q^{76} + 2625 q^{77} - 13562 q^{78} - 48318 q^{79} + 1048 q^{81} - 57211 q^{82} + 17014 q^{83} - 50382 q^{84} + 21461 q^{86} - 6174 q^{87} + 34909 q^{88} + 51590 q^{89} - 6494 q^{90} + 35840 q^{91} + 105420 q^{92} - 38115 q^{94} + 65915 q^{95} + 101606 q^{96} - 18427 q^{97} + 63455 q^{98} + 36377 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.495110 1.02811i −0.123778 0.257027i 0.829868 0.557961i \(-0.188416\pi\)
−0.953645 + 0.300934i \(0.902702\pi\)
\(3\) 6.66668 13.8435i 0.740743 1.53817i −0.0989417 0.995093i \(-0.531546\pi\)
0.839684 0.543075i \(-0.182740\pi\)
\(4\) 9.16397 11.4913i 0.572748 0.718203i
\(5\) −12.7517 2.91049i −0.510067 0.116420i −0.0402612 0.999189i \(-0.512819\pi\)
−0.469806 + 0.882770i \(0.655676\pi\)
\(6\) −17.5333 −0.487037
\(7\) 56.8875i 1.16097i 0.814271 + 0.580485i \(0.197137\pi\)
−0.814271 + 0.580485i \(0.802863\pi\)
\(8\) −34.1514 7.79484i −0.533616 0.121794i
\(9\) −96.6955 121.252i −1.19377 1.49694i
\(10\) 3.32119 + 14.5511i 0.0332119 + 0.145511i
\(11\) 117.846 + 147.774i 0.973932 + 1.22127i 0.975212 + 0.221273i \(0.0710211\pi\)
−0.00128019 + 0.999999i \(0.500407\pi\)
\(12\) −97.9860 203.470i −0.680458 1.41299i
\(13\) 54.4721 238.658i 0.322320 1.41218i −0.511093 0.859526i \(-0.670759\pi\)
0.833413 0.552651i \(-0.186384\pi\)
\(14\) 58.4865 28.1656i 0.298400 0.143702i
\(15\) −125.303 + 157.125i −0.556901 + 0.698332i
\(16\) −43.4345 190.299i −0.169666 0.743356i
\(17\) −7.56301 33.1357i −0.0261696 0.114656i 0.960156 0.279464i \(-0.0901568\pi\)
−0.986326 + 0.164808i \(0.947300\pi\)
\(18\) −76.7854 + 159.446i −0.236992 + 0.492119i
\(19\) 174.096 + 138.837i 0.482259 + 0.384589i 0.834225 0.551424i \(-0.185915\pi\)
−0.351966 + 0.936013i \(0.614487\pi\)
\(20\) −150.301 + 119.861i −0.375753 + 0.299653i
\(21\) 787.523 + 379.251i 1.78577 + 0.859980i
\(22\) 93.5807 194.322i 0.193349 0.401492i
\(23\) 318.858 + 399.835i 0.602756 + 0.755833i 0.985805 0.167896i \(-0.0536972\pi\)
−0.383048 + 0.923728i \(0.625126\pi\)
\(24\) −335.585 + 420.810i −0.582613 + 0.730573i
\(25\) −408.971 196.950i −0.654354 0.315120i
\(26\) −272.335 + 62.1588i −0.402863 + 0.0919509i
\(27\) −1109.82 + 253.310i −1.52239 + 0.347476i
\(28\) 653.709 + 521.316i 0.833813 + 0.664943i
\(29\) −75.2411 156.240i −0.0894662 0.185778i 0.851435 0.524461i \(-0.175733\pi\)
−0.940901 + 0.338682i \(0.890019\pi\)
\(30\) 223.580 + 51.0306i 0.248422 + 0.0567007i
\(31\) 1312.63 632.129i 1.36590 0.657783i 0.399956 0.916534i \(-0.369025\pi\)
0.965944 + 0.258751i \(0.0833111\pi\)
\(32\) −612.340 + 488.325i −0.597988 + 0.476880i
\(33\) 2831.35 646.237i 2.59995 0.593423i
\(34\) −30.3225 + 24.1814i −0.0262305 + 0.0209182i
\(35\) 165.571 725.412i 0.135160 0.592173i
\(36\) −2279.45 −1.75884
\(37\) 2035.36i 1.48675i 0.668877 + 0.743373i \(0.266775\pi\)
−0.668877 + 0.743373i \(0.733225\pi\)
\(38\) 56.5424 247.728i 0.0391568 0.171557i
\(39\) −2940.71 2345.14i −1.93341 1.54184i
\(40\) 412.802 + 198.795i 0.258001 + 0.124247i
\(41\) −885.872 + 426.614i −0.526991 + 0.253786i −0.678409 0.734684i \(-0.737330\pi\)
0.151418 + 0.988470i \(0.451616\pi\)
\(42\) 997.429i 0.565436i
\(43\) −63.1291 1847.92i −0.0341423 0.999417i
\(44\) 2778.04 1.43494
\(45\) 880.127 + 1827.60i 0.434630 + 0.902519i
\(46\) 253.204 525.783i 0.119661 0.248480i
\(47\) −256.907 + 322.151i −0.116300 + 0.145836i −0.836574 0.547854i \(-0.815445\pi\)
0.720274 + 0.693690i \(0.244016\pi\)
\(48\) −2923.97 667.377i −1.26908 0.289660i
\(49\) −835.193 −0.347852
\(50\) 517.978i 0.207191i
\(51\) −509.135 116.207i −0.195746 0.0446777i
\(52\) −2243.30 2813.01i −0.829622 1.04031i
\(53\) 506.658 + 2219.81i 0.180369 + 0.790250i 0.981454 + 0.191699i \(0.0613997\pi\)
−0.801084 + 0.598551i \(0.795743\pi\)
\(54\) 809.914 + 1015.60i 0.277748 + 0.348285i
\(55\) −1072.64 2227.35i −0.354591 0.736316i
\(56\) 443.430 1942.79i 0.141400 0.619513i
\(57\) 3082.63 1484.51i 0.948792 0.456914i
\(58\) −123.378 + 154.712i −0.0366761 + 0.0459904i
\(59\) 1300.81 + 5699.21i 0.373688 + 1.63723i 0.716326 + 0.697766i \(0.245822\pi\)
−0.342639 + 0.939467i \(0.611321\pi\)
\(60\) 657.289 + 2879.77i 0.182580 + 0.799937i
\(61\) 475.087 986.529i 0.127677 0.265125i −0.827325 0.561724i \(-0.810138\pi\)
0.955002 + 0.296599i \(0.0958526\pi\)
\(62\) −1299.79 1036.55i −0.338135 0.269654i
\(63\) 6897.74 5500.77i 1.73790 1.38593i
\(64\) −2008.58 967.281i −0.490376 0.236152i
\(65\) −1389.22 + 2884.75i −0.328810 + 0.682781i
\(66\) −2066.23 2590.97i −0.474341 0.594805i
\(67\) −3578.65 + 4487.48i −0.797204 + 0.999662i 0.202588 + 0.979264i \(0.435065\pi\)
−0.999792 + 0.0203982i \(0.993507\pi\)
\(68\) −450.078 216.746i −0.0973352 0.0468741i
\(69\) 7660.85 1748.54i 1.60908 0.367263i
\(70\) −827.776 + 188.935i −0.168934 + 0.0385581i
\(71\) −587.312 468.366i −0.116507 0.0929113i 0.563503 0.826114i \(-0.309453\pi\)
−0.680010 + 0.733203i \(0.738025\pi\)
\(72\) 2357.15 + 4894.67i 0.454697 + 0.944187i
\(73\) 469.645 + 107.193i 0.0881301 + 0.0201151i 0.266359 0.963874i \(-0.414179\pi\)
−0.178228 + 0.983989i \(0.557037\pi\)
\(74\) 2092.56 1007.73i 0.382134 0.184026i
\(75\) −5452.96 + 4348.59i −0.969415 + 0.773083i
\(76\) 3190.81 728.282i 0.552426 0.126088i
\(77\) −8406.49 + 6703.96i −1.41786 + 1.13071i
\(78\) −955.078 + 4184.47i −0.156982 + 0.687783i
\(79\) 3176.92 0.509041 0.254520 0.967067i \(-0.418082\pi\)
0.254520 + 0.967067i \(0.418082\pi\)
\(80\) 2553.05i 0.398914i
\(81\) −1096.81 + 4805.46i −0.167172 + 0.732428i
\(82\) 877.209 + 699.550i 0.130459 + 0.104038i
\(83\) −7134.64 3435.86i −1.03566 0.498746i −0.162767 0.986664i \(-0.552042\pi\)
−0.872889 + 0.487919i \(0.837756\pi\)
\(84\) 11574.9 5574.18i 1.64044 0.789992i
\(85\) 444.548i 0.0615291i
\(86\) −1868.60 + 979.828i −0.252651 + 0.132481i
\(87\) −2664.51 −0.352030
\(88\) −2872.73 5965.28i −0.370962 0.770310i
\(89\) −5712.31 + 11861.7i −0.721160 + 1.49750i 0.140535 + 0.990076i \(0.455118\pi\)
−0.861694 + 0.507428i \(0.830596\pi\)
\(90\) 1443.21 1809.73i 0.178174 0.223423i
\(91\) 13576.7 + 3098.78i 1.63950 + 0.374204i
\(92\) 7516.61 0.888069
\(93\) 22385.6i 2.58823i
\(94\) 458.403 + 104.628i 0.0518790 + 0.0118411i
\(95\) −1815.93 2277.10i −0.201211 0.252311i
\(96\) 2677.85 + 11732.4i 0.290566 + 1.27305i
\(97\) −7688.43 9640.99i −0.817136 1.02466i −0.999144 0.0413593i \(-0.986831\pi\)
0.182008 0.983297i \(-0.441740\pi\)
\(98\) 413.512 + 858.667i 0.0430563 + 0.0894073i
\(99\) 6522.77 28578.1i 0.665521 2.91584i
\(100\) −6011.00 + 2894.75i −0.601100 + 0.289475i
\(101\) 3609.28 4525.89i 0.353816 0.443671i −0.572792 0.819701i \(-0.694140\pi\)
0.926608 + 0.376030i \(0.122711\pi\)
\(102\) 132.605 + 580.980i 0.0127456 + 0.0558420i
\(103\) 200.488 + 878.395i 0.0188979 + 0.0827972i 0.983498 0.180922i \(-0.0579080\pi\)
−0.964600 + 0.263719i \(0.915051\pi\)
\(104\) −3720.60 + 7725.91i −0.343991 + 0.714304i
\(105\) −8938.44 7128.17i −0.810743 0.646546i
\(106\) 2031.35 1619.95i 0.180790 0.144175i
\(107\) −19033.7 9166.14i −1.66248 0.800606i −0.998607 0.0527564i \(-0.983199\pi\)
−0.663868 0.747850i \(-0.731086\pi\)
\(108\) −7259.54 + 15074.6i −0.622388 + 1.29240i
\(109\) −2215.89 2778.63i −0.186507 0.233872i 0.679784 0.733413i \(-0.262074\pi\)
−0.866290 + 0.499541i \(0.833502\pi\)
\(110\) −1758.88 + 2205.57i −0.145362 + 0.182279i
\(111\) 28176.5 + 13569.1i 2.28687 + 1.10130i
\(112\) 10825.6 2470.88i 0.863014 0.196977i
\(113\) −5905.80 + 1347.96i −0.462511 + 0.105565i −0.447426 0.894321i \(-0.647659\pi\)
−0.0150853 + 0.999886i \(0.504802\pi\)
\(114\) −3052.48 2434.27i −0.234878 0.187309i
\(115\) −2902.26 6026.61i −0.219453 0.455698i
\(116\) −2484.90 567.161i −0.184668 0.0421493i
\(117\) −34205.0 + 16472.3i −2.49872 + 1.20332i
\(118\) 5215.35 4159.10i 0.374558 0.298700i
\(119\) 1885.01 430.241i 0.133113 0.0303821i
\(120\) 5504.03 4389.32i 0.382225 0.304814i
\(121\) −4691.57 + 20555.1i −0.320441 + 1.40394i
\(122\) −1249.48 −0.0839477
\(123\) 15107.7i 0.998591i
\(124\) 4764.94 20876.6i 0.309895 1.35774i
\(125\) 11033.1 + 8798.63i 0.706121 + 0.563112i
\(126\) −9070.52 4368.13i −0.571335 0.275141i
\(127\) 15475.5 7452.59i 0.959481 0.462062i 0.112480 0.993654i \(-0.464120\pi\)
0.847000 + 0.531592i \(0.178406\pi\)
\(128\) 15075.3i 0.920126i
\(129\) −26002.6 11445.6i −1.56256 0.687794i
\(130\) 3653.65 0.216192
\(131\) 5991.97 + 12442.5i 0.349162 + 0.725043i 0.999398 0.0346896i \(-0.0110443\pi\)
−0.650236 + 0.759732i \(0.725330\pi\)
\(132\) 18520.3 38457.9i 1.06292 2.20718i
\(133\) −7898.07 + 9903.87i −0.446496 + 0.559889i
\(134\) 6385.44 + 1457.43i 0.355616 + 0.0811670i
\(135\) 14889.4 0.816975
\(136\) 1190.58i 0.0643698i
\(137\) 20387.4 + 4653.28i 1.08623 + 0.247924i 0.727907 0.685676i \(-0.240493\pi\)
0.358318 + 0.933600i \(0.383350\pi\)
\(138\) −5590.65 7010.45i −0.293565 0.368119i
\(139\) 197.492 + 865.270i 0.0102216 + 0.0447839i 0.979782 0.200070i \(-0.0641170\pi\)
−0.969560 + 0.244854i \(0.921260\pi\)
\(140\) −6818.61 8550.26i −0.347888 0.436238i
\(141\) 2746.99 + 5704.18i 0.138171 + 0.286916i
\(142\) −190.746 + 835.712i −0.00945972 + 0.0414458i
\(143\) 41686.7 20075.3i 2.03857 0.981723i
\(144\) −18874.3 + 23667.6i −0.910218 + 1.14138i
\(145\) 504.716 + 2211.31i 0.0240055 + 0.105175i
\(146\) −122.320 535.918i −0.00573840 0.0251416i
\(147\) −5567.97 + 11562.0i −0.257669 + 0.535055i
\(148\) 23388.8 + 18651.9i 1.06779 + 0.851531i
\(149\) 11529.4 9194.36i 0.519318 0.414142i −0.328441 0.944525i \(-0.606523\pi\)
0.847758 + 0.530383i \(0.177952\pi\)
\(150\) 7170.63 + 3453.19i 0.318695 + 0.153475i
\(151\) −10639.8 + 22093.9i −0.466639 + 0.968986i 0.526293 + 0.850303i \(0.323581\pi\)
−0.992932 + 0.118683i \(0.962133\pi\)
\(152\) −4863.41 6098.52i −0.210501 0.263959i
\(153\) −3286.47 + 4121.10i −0.140393 + 0.176048i
\(154\) 11054.5 + 5323.58i 0.466121 + 0.224472i
\(155\) −18578.0 + 4240.32i −0.773280 + 0.176496i
\(156\) −53897.2 + 12301.7i −2.21471 + 0.505494i
\(157\) 6996.97 + 5579.90i 0.283864 + 0.226374i 0.755062 0.655653i \(-0.227607\pi\)
−0.471198 + 0.882028i \(0.656178\pi\)
\(158\) −1572.93 3266.22i −0.0630078 0.130837i
\(159\) 34107.7 + 7784.87i 1.34914 + 0.307934i
\(160\) 9229.63 4444.76i 0.360532 0.173623i
\(161\) −22745.7 + 18139.1i −0.877499 + 0.699782i
\(162\) 5483.57 1251.59i 0.208946 0.0476905i
\(163\) −27957.1 + 22295.1i −1.05225 + 0.839138i −0.987319 0.158752i \(-0.949253\pi\)
−0.0649278 + 0.997890i \(0.520682\pi\)
\(164\) −3215.78 + 14089.3i −0.119564 + 0.523842i
\(165\) −37985.3 −1.39524
\(166\) 9036.30i 0.327925i
\(167\) 8037.08 35212.7i 0.288181 1.26260i −0.598838 0.800870i \(-0.704371\pi\)
0.887019 0.461733i \(-0.152772\pi\)
\(168\) −23938.9 19090.6i −0.848174 0.676396i
\(169\) −28257.8 13608.2i −0.989384 0.476462i
\(170\) 457.043 220.100i 0.0158146 0.00761592i
\(171\) 34534.4i 1.18103i
\(172\) −21813.5 16208.9i −0.737339 0.547893i
\(173\) 26418.4 0.882702 0.441351 0.897335i \(-0.354499\pi\)
0.441351 + 0.897335i \(0.354499\pi\)
\(174\) 1319.23 + 2739.40i 0.0435734 + 0.0904811i
\(175\) 11204.0 23265.4i 0.365845 0.759685i
\(176\) 23002.7 28844.4i 0.742596 0.931186i
\(177\) 87569.1 + 19987.1i 2.79515 + 0.637974i
\(178\) 15023.3 0.474162
\(179\) 22298.0i 0.695921i 0.937509 + 0.347961i \(0.113126\pi\)
−0.937509 + 0.347961i \(0.886874\pi\)
\(180\) 29066.9 + 6634.33i 0.897126 + 0.204763i
\(181\) −17325.5 21725.5i −0.528845 0.663150i 0.443616 0.896217i \(-0.353695\pi\)
−0.972461 + 0.233067i \(0.925124\pi\)
\(182\) −3536.06 15492.5i −0.106752 0.467712i
\(183\) −10489.8 13153.8i −0.313230 0.392778i
\(184\) −7772.81 16140.4i −0.229584 0.476737i
\(185\) 5923.88 25954.2i 0.173086 0.758341i
\(186\) −23014.8 + 11083.3i −0.665244 + 0.320365i
\(187\) 4005.32 5022.52i 0.114539 0.143628i
\(188\) 1347.63 + 5904.37i 0.0381291 + 0.167054i
\(189\) −14410.2 63135.1i −0.403409 1.76745i
\(190\) −1442.02 + 2994.39i −0.0399452 + 0.0829470i
\(191\) −31033.7 24748.5i −0.850680 0.678395i 0.0978089 0.995205i \(-0.468817\pi\)
−0.948489 + 0.316811i \(0.897388\pi\)
\(192\) −26781.1 + 21357.2i −0.726484 + 0.579352i
\(193\) −25793.9 12421.7i −0.692473 0.333477i 0.0543298 0.998523i \(-0.482698\pi\)
−0.746803 + 0.665046i \(0.768412\pi\)
\(194\) −6105.35 + 12677.9i −0.162221 + 0.336855i
\(195\) 30673.6 + 38463.4i 0.806668 + 1.01153i
\(196\) −7653.68 + 9597.41i −0.199232 + 0.249828i
\(197\) −56049.6 26992.1i −1.44424 0.695510i −0.462657 0.886537i \(-0.653104\pi\)
−0.981585 + 0.191027i \(0.938818\pi\)
\(198\) −32610.9 + 7443.21i −0.831825 + 0.189859i
\(199\) 51355.3 11721.5i 1.29682 0.295990i 0.482237 0.876041i \(-0.339824\pi\)
0.814581 + 0.580051i \(0.196967\pi\)
\(200\) 12431.8 + 9913.99i 0.310794 + 0.247850i
\(201\) 38264.8 + 79457.7i 0.947125 + 1.96673i
\(202\) −6440.09 1469.91i −0.157830 0.0360236i
\(203\) 8888.09 4280.28i 0.215683 0.103868i
\(204\) −6001.05 + 4785.68i −0.144201 + 0.114996i
\(205\) 12538.0 2861.72i 0.298347 0.0680957i
\(206\) 803.820 641.025i 0.0189419 0.0151057i
\(207\) 17648.8 77324.5i 0.411884 1.80458i
\(208\) −47782.3 −1.10444
\(209\) 42088.1i 0.963533i
\(210\) −2903.01 + 12718.9i −0.0658278 + 0.288410i
\(211\) 20195.7 + 16105.5i 0.453622 + 0.361751i 0.823488 0.567334i \(-0.192025\pi\)
−0.369866 + 0.929085i \(0.620596\pi\)
\(212\) 30151.4 + 14520.2i 0.670867 + 0.323072i
\(213\) −10399.3 + 5008.02i −0.229215 + 0.110384i
\(214\) 24106.9i 0.526398i
\(215\) −4573.35 + 23747.9i −0.0989368 + 0.513745i
\(216\) 39876.6 0.854693
\(217\) 35960.3 + 74672.3i 0.763666 + 1.58577i
\(218\) −1759.62 + 3653.89i −0.0370260 + 0.0768853i
\(219\) 4614.91 5786.92i 0.0962222 0.120659i
\(220\) −35424.7 8085.46i −0.731915 0.167055i
\(221\) −8320.07 −0.170350
\(222\) 35686.6i 0.724101i
\(223\) −61992.9 14149.5i −1.24661 0.284531i −0.452205 0.891914i \(-0.649362\pi\)
−0.794409 + 0.607383i \(0.792219\pi\)
\(224\) −27779.6 34834.5i −0.553643 0.694247i
\(225\) 15665.0 + 68632.9i 0.309432 + 1.35571i
\(226\) 4309.87 + 5404.41i 0.0843815 + 0.105811i
\(227\) −39846.9 82743.0i −0.773291 1.60576i −0.795463 0.606002i \(-0.792772\pi\)
0.0221720 0.999754i \(-0.492942\pi\)
\(228\) 11190.2 49027.3i 0.215262 0.943122i
\(229\) −22480.0 + 10825.8i −0.428671 + 0.206437i −0.635763 0.771884i \(-0.719314\pi\)
0.207092 + 0.978322i \(0.433600\pi\)
\(230\) −4759.06 + 5967.67i −0.0899633 + 0.112810i
\(231\) 36762.8 + 161069.i 0.688946 + 3.01847i
\(232\) 1351.73 + 5922.30i 0.0251138 + 0.110031i
\(233\) 21629.5 44914.2i 0.398415 0.827317i −0.601187 0.799108i \(-0.705305\pi\)
0.999602 0.0282085i \(-0.00898023\pi\)
\(234\) 33870.5 + 27010.8i 0.618571 + 0.493294i
\(235\) 4213.62 3360.25i 0.0762991 0.0608465i
\(236\) 77411.6 + 37279.5i 1.38989 + 0.669338i
\(237\) 21179.5 43979.8i 0.377068 0.782990i
\(238\) −1375.62 1724.97i −0.0242854 0.0304529i
\(239\) 44061.3 55251.2i 0.771368 0.967265i −0.228612 0.973518i \(-0.573419\pi\)
0.999980 + 0.00625234i \(0.00199020\pi\)
\(240\) 35343.2 + 17020.4i 0.613597 + 0.295493i
\(241\) 38199.9 8718.88i 0.657700 0.150116i 0.119370 0.992850i \(-0.461912\pi\)
0.538330 + 0.842734i \(0.319055\pi\)
\(242\) 23455.7 5353.61i 0.400514 0.0914147i
\(243\) −12878.4 10270.2i −0.218097 0.173927i
\(244\) −6982.77 14499.9i −0.117286 0.243548i
\(245\) 10650.1 + 2430.82i 0.177428 + 0.0404968i
\(246\) 15532.3 7479.96i 0.256664 0.123603i
\(247\) 42617.8 33986.6i 0.698549 0.557075i
\(248\) −49755.6 + 11356.4i −0.808981 + 0.184645i
\(249\) −95128.7 + 75862.6i −1.53431 + 1.22357i
\(250\) 3583.31 15699.5i 0.0573330 0.251192i
\(251\) −55273.8 −0.877347 −0.438674 0.898646i \(-0.644552\pi\)
−0.438674 + 0.898646i \(0.644552\pi\)
\(252\) 129673.i 2.04196i
\(253\) −21509.2 + 94237.8i −0.336033 + 1.47226i
\(254\) −15324.1 12220.6i −0.237524 0.189419i
\(255\) 6154.10 + 2963.66i 0.0946421 + 0.0455772i
\(256\) −16638.2 + 8012.54i −0.253879 + 0.122262i
\(257\) 32766.5i 0.496094i −0.968748 0.248047i \(-0.920211\pi\)
0.968748 0.248047i \(-0.0797887\pi\)
\(258\) 1106.86 + 32400.3i 0.0166286 + 0.486753i
\(259\) −115786. −1.72607
\(260\) 20418.6 + 42399.6i 0.302050 + 0.627214i
\(261\) −11668.9 + 24230.8i −0.171297 + 0.355703i
\(262\) 9825.49 12320.8i 0.143137 0.179488i
\(263\) −23381.9 5336.77i −0.338040 0.0771554i 0.0501313 0.998743i \(-0.484036\pi\)
−0.388171 + 0.921587i \(0.626893\pi\)
\(264\) −101732. −1.45965
\(265\) 29781.0i 0.424079i
\(266\) 14092.7 + 3216.56i 0.199173 + 0.0454598i
\(267\) 126126. + 158157.i 1.76922 + 2.21853i
\(268\) 18772.2 + 82246.3i 0.261364 + 1.14511i
\(269\) 57867.1 + 72563.0i 0.799700 + 1.00279i 0.999735 + 0.0230035i \(0.00732289\pi\)
−0.200035 + 0.979789i \(0.564106\pi\)
\(270\) −7371.88 15307.9i −0.101123 0.209984i
\(271\) −14981.1 + 65636.3i −0.203988 + 0.893728i 0.764492 + 0.644634i \(0.222990\pi\)
−0.968479 + 0.249094i \(0.919867\pi\)
\(272\) −5977.20 + 2878.47i −0.0807904 + 0.0389066i
\(273\) 133409. 167290.i 1.79003 2.24463i
\(274\) −5309.92 23264.3i −0.0707272 0.309876i
\(275\) −19091.4 83645.0i −0.252449 1.10605i
\(276\) 50110.9 104056.i 0.657830 1.36600i
\(277\) 10093.0 + 8048.93i 0.131541 + 0.104901i 0.687050 0.726610i \(-0.258905\pi\)
−0.555509 + 0.831510i \(0.687477\pi\)
\(278\) 791.810 631.447i 0.0102455 0.00817048i
\(279\) −203572. 98035.3i −2.61523 1.25943i
\(280\) −11308.9 + 23483.3i −0.144247 + 0.299531i
\(281\) −16056.0 20133.5i −0.203340 0.254981i 0.669697 0.742635i \(-0.266424\pi\)
−0.873037 + 0.487654i \(0.837853\pi\)
\(282\) 4504.44 5648.39i 0.0566425 0.0710275i
\(283\) 33665.3 + 16212.3i 0.420348 + 0.202429i 0.632087 0.774897i \(-0.282198\pi\)
−0.211739 + 0.977326i \(0.567913\pi\)
\(284\) −10764.2 + 2456.86i −0.133458 + 0.0304610i
\(285\) −43629.3 + 9958.11i −0.537142 + 0.122599i
\(286\) −41279.0 32918.9i −0.504658 0.402451i
\(287\) −24269.0 50395.1i −0.294638 0.611821i
\(288\) 118421. + 27028.8i 1.42772 + 0.325868i
\(289\) 74209.0 35737.2i 0.888508 0.427883i
\(290\) 2023.57 1613.74i 0.0240615 0.0191884i
\(291\) −184722. + 42161.5i −2.18138 + 0.497886i
\(292\) 5535.60 4414.50i 0.0649231 0.0517744i
\(293\) 141.537 620.116i 0.00164868 0.00722334i −0.974097 0.226131i \(-0.927392\pi\)
0.975746 + 0.218908i \(0.0702494\pi\)
\(294\) 14643.7 0.169417
\(295\) 76460.5i 0.878603i
\(296\) 15865.3 69510.3i 0.181077 0.793352i
\(297\) −168221. 134151.i −1.90707 1.52084i
\(298\) −15161.1 7301.20i −0.170725 0.0822170i
\(299\) 112793. 54318.1i 1.26165 0.607579i
\(300\) 102512.i 1.13902i
\(301\) 105124. 3591.26i 1.16029 0.0396382i
\(302\) 27982.7 0.306815
\(303\) −38592.3 80137.7i −0.420354 0.872874i
\(304\) 18858.7 39160.5i 0.204063 0.423742i
\(305\) −8929.44 + 11197.2i −0.0959897 + 0.120367i
\(306\) 5864.10 + 1338.44i 0.0626265 + 0.0142941i
\(307\) 61943.9 0.657237 0.328619 0.944463i \(-0.393417\pi\)
0.328619 + 0.944463i \(0.393417\pi\)
\(308\) 158036.i 1.66592i
\(309\) 13496.7 + 3080.53i 0.141354 + 0.0322632i
\(310\) 13557.7 + 17000.8i 0.141079 + 0.176907i
\(311\) 10419.5 + 45650.7i 0.107727 + 0.471983i 0.999798 + 0.0200880i \(0.00639464\pi\)
−0.892071 + 0.451895i \(0.850748\pi\)
\(312\) 82149.6 + 103012.i 0.843911 + 1.05823i
\(313\) 30952.8 + 64274.2i 0.315945 + 0.656067i 0.997102 0.0760704i \(-0.0242374\pi\)
−0.681157 + 0.732137i \(0.738523\pi\)
\(314\) 2272.46 9956.30i 0.0230482 0.100981i
\(315\) −103968. + 50068.2i −1.04780 + 0.504593i
\(316\) 29113.2 36506.8i 0.291552 0.365595i
\(317\) −39137.3 171472.i −0.389468 1.70637i −0.666494 0.745510i \(-0.732206\pi\)
0.277026 0.960862i \(-0.410651\pi\)
\(318\) −8883.41 38920.8i −0.0878467 0.384881i
\(319\) 14221.3 29530.8i 0.139752 0.290198i
\(320\) 22797.5 + 18180.4i 0.222632 + 0.177543i
\(321\) −253783. + 202385.i −2.46293 + 1.96412i
\(322\) 29910.5 + 14404.1i 0.288477 + 0.138923i
\(323\) 3283.76 6818.80i 0.0314751 0.0653586i
\(324\) 45169.6 + 56640.8i 0.430285 + 0.539560i
\(325\) −69281.2 + 86875.9i −0.655917 + 0.822494i
\(326\) 36763.6 + 17704.4i 0.345925 + 0.166589i
\(327\) −53238.6 + 12151.4i −0.497888 + 0.113640i
\(328\) 33579.2 7664.23i 0.312121 0.0712395i
\(329\) −18326.4 14614.8i −0.169311 0.135021i
\(330\) 18806.9 + 39053.0i 0.172699 + 0.358613i
\(331\) −20957.6 4783.44i −0.191287 0.0436601i 0.125804 0.992055i \(-0.459849\pi\)
−0.317091 + 0.948395i \(0.602706\pi\)
\(332\) −104864. + 50499.8i −0.951371 + 0.458156i
\(333\) 246792. 196810.i 2.22557 1.77484i
\(334\) −40181.7 + 9171.21i −0.360193 + 0.0822117i
\(335\) 58694.6 46807.4i 0.523008 0.417085i
\(336\) 37965.5 166338.i 0.336287 1.47337i
\(337\) −35182.6 −0.309790 −0.154895 0.987931i \(-0.549504\pi\)
−0.154895 + 0.987931i \(0.549504\pi\)
\(338\) 35789.6i 0.313273i
\(339\) −20711.6 + 90743.5i −0.180225 + 0.789616i
\(340\) 5108.41 + 4073.82i 0.0441904 + 0.0352407i
\(341\) 248100. + 119479.i 2.13363 + 1.02750i
\(342\) −35505.0 + 17098.3i −0.303555 + 0.146184i
\(343\) 89074.9i 0.757124i
\(344\) −12248.3 + 63601.3i −0.103505 + 0.537463i
\(345\) −102778. −0.863498
\(346\) −13080.0 27160.9i −0.109259 0.226878i
\(347\) −13809.1 + 28674.9i −0.114685 + 0.238146i −0.950408 0.311005i \(-0.899334\pi\)
0.835723 + 0.549151i \(0.185049\pi\)
\(348\) −24417.5 + 30618.6i −0.201624 + 0.252829i
\(349\) 30927.2 + 7058.94i 0.253916 + 0.0579547i 0.347584 0.937649i \(-0.387002\pi\)
−0.0936680 + 0.995603i \(0.529859\pi\)
\(350\) −29466.5 −0.240543
\(351\) 278666.i 2.26188i
\(352\) −144323. 32940.9i −1.16480 0.265858i
\(353\) −48610.0 60955.0i −0.390100 0.489170i 0.547539 0.836780i \(-0.315565\pi\)
−0.937639 + 0.347610i \(0.886993\pi\)
\(354\) −22807.5 99926.2i −0.182000 0.797394i
\(355\) 6126.05 + 7681.82i 0.0486098 + 0.0609547i
\(356\) 83958.7 + 174342.i 0.662469 + 1.37563i
\(357\) 6610.71 28963.4i 0.0518695 0.227255i
\(358\) 22924.7 11040.0i 0.178870 0.0861394i
\(359\) 45405.6 56936.9i 0.352307 0.441779i −0.573826 0.818978i \(-0.694541\pi\)
0.926132 + 0.377199i \(0.123113\pi\)
\(360\) −15811.7 69275.7i −0.122004 0.534535i
\(361\) −17965.5 78711.9i −0.137856 0.603985i
\(362\) −13758.1 + 28568.9i −0.104988 + 0.218010i
\(363\) 253278. + 201982.i 1.92214 + 1.53285i
\(364\) 160025. 127616.i 1.20777 0.963166i
\(365\) −5676.78 2733.79i −0.0426105 0.0205201i
\(366\) −8329.87 + 17297.2i −0.0621836 + 0.129126i
\(367\) 112796. + 141441.i 0.837453 + 1.05013i 0.998007 + 0.0631059i \(0.0201006\pi\)
−0.160554 + 0.987027i \(0.551328\pi\)
\(368\) 62238.9 78045.1i 0.459585 0.576302i
\(369\) 137388. + 66162.4i 1.00901 + 0.485913i
\(370\) −29616.7 + 6759.81i −0.216338 + 0.0493777i
\(371\) −126280. + 28822.5i −0.917457 + 0.209404i
\(372\) −257239. 205141.i −1.85888 1.48240i
\(373\) −74044.4 153755.i −0.532200 1.10512i −0.977732 0.209858i \(-0.932700\pi\)
0.445532 0.895266i \(-0.353015\pi\)
\(374\) −7146.76 1631.20i −0.0510935 0.0116618i
\(375\) 195358. 94079.6i 1.38921 0.669011i
\(376\) 11284.9 8999.38i 0.0798217 0.0636556i
\(377\) −41386.4 + 9446.17i −0.291189 + 0.0664619i
\(378\) −57775.0 + 46074.0i −0.404349 + 0.322458i
\(379\) 21230.2 93015.5i 0.147800 0.647555i −0.845694 0.533669i \(-0.820813\pi\)
0.993494 0.113886i \(-0.0363299\pi\)
\(380\) −42807.9 −0.296454
\(381\) 263919.i 1.81811i
\(382\) −10079.0 + 44159.1i −0.0690704 + 0.302617i
\(383\) −116913. 93235.2i −0.797014 0.635598i 0.137910 0.990445i \(-0.455962\pi\)
−0.934924 + 0.354847i \(0.884533\pi\)
\(384\) 208696. + 100503.i 1.41531 + 0.681576i
\(385\) 126709. 61019.7i 0.854840 0.411669i
\(386\) 32669.0i 0.219261i
\(387\) −217960. + 186340.i −1.45531 + 1.24418i
\(388\) −181244. −1.20392
\(389\) 73556.8 + 152742.i 0.486098 + 1.00939i 0.989391 + 0.145277i \(0.0464073\pi\)
−0.503293 + 0.864116i \(0.667878\pi\)
\(390\) 24357.7 50579.3i 0.160143 0.332540i
\(391\) 10837.3 13589.5i 0.0708872 0.0888897i
\(392\) 28523.0 + 6510.20i 0.185620 + 0.0423664i
\(393\) 212194. 1.37388
\(394\) 70989.0i 0.457297i
\(395\) −40511.1 9246.40i −0.259645 0.0592623i
\(396\) −268624. 336844.i −1.71299 2.14802i
\(397\) −2008.83 8801.25i −0.0127456 0.0558423i 0.968155 0.250351i \(-0.0805460\pi\)
−0.980901 + 0.194509i \(0.937689\pi\)
\(398\) −37477.5 46995.3i −0.236594 0.296680i
\(399\) 84450.4 + 175363.i 0.530464 + 1.10152i
\(400\) −19716.0 + 86381.3i −0.123225 + 0.539883i
\(401\) −107557. + 51796.8i −0.668884 + 0.322118i −0.737326 0.675537i \(-0.763912\pi\)
0.0684414 + 0.997655i \(0.478197\pi\)
\(402\) 62745.7 78680.6i 0.388268 0.486873i
\(403\) −79360.9 347703.i −0.488649 2.14091i
\(404\) −18932.8 82950.2i −0.115999 0.508223i
\(405\) 27972.5 58085.4i 0.170538 0.354125i
\(406\) −8801.17 7018.70i −0.0533935 0.0425799i
\(407\) −300773. + 239858.i −1.81572 + 1.44799i
\(408\) 16481.9 + 7937.25i 0.0990116 + 0.0476815i
\(409\) −63883.3 + 132655.i −0.381892 + 0.793007i 0.618084 + 0.786112i \(0.287909\pi\)
−0.999976 + 0.00689485i \(0.997805\pi\)
\(410\) −9149.85 11473.6i −0.0544310 0.0682543i
\(411\) 200334. 251211.i 1.18596 1.48715i
\(412\) 11931.1 + 5745.73i 0.0702890 + 0.0338494i
\(413\) −324214. + 73999.7i −1.90078 + 0.433840i
\(414\) −88236.0 + 20139.3i −0.514808 + 0.117502i
\(415\) 80978.6 + 64578.3i 0.470191 + 0.374965i
\(416\) 83187.1 + 172740.i 0.480695 + 0.998173i
\(417\) 13295.0 + 3034.50i 0.0764568 + 0.0174508i
\(418\) 43271.0 20838.2i 0.247654 0.119264i
\(419\) 75694.5 60364.3i 0.431158 0.343837i −0.383740 0.923441i \(-0.625364\pi\)
0.814898 + 0.579604i \(0.196793\pi\)
\(420\) −163823. + 37391.6i −0.928703 + 0.211970i
\(421\) −216534. + 172680.i −1.22169 + 0.974266i −1.00000 0.000850673i \(-0.999729\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(422\) 6559.11 28737.3i 0.0368316 0.161370i
\(423\) 63903.3 0.357143
\(424\) 79759.1i 0.443658i
\(425\) −3433.03 + 15041.1i −0.0190064 + 0.0832724i
\(426\) 10297.6 + 8212.02i 0.0567433 + 0.0452513i
\(427\) 56121.2 + 27026.6i 0.307802 + 0.148230i
\(428\) −279754. + 134723.i −1.52718 + 0.735450i
\(429\) 710926.i 3.86287i
\(430\) 26679.6 7055.91i 0.144292 0.0381607i
\(431\) 298979. 1.60948 0.804742 0.593625i \(-0.202304\pi\)
0.804742 + 0.593625i \(0.202304\pi\)
\(432\) 96409.3 + 200196.i 0.516596 + 1.07272i
\(433\) −28980.8 + 60179.2i −0.154573 + 0.320974i −0.963847 0.266458i \(-0.914147\pi\)
0.809273 + 0.587432i \(0.199861\pi\)
\(434\) 58966.8 73942.0i 0.313060 0.392565i
\(435\) 33977.0 + 7755.04i 0.179559 + 0.0409832i
\(436\) −52236.3 −0.274789
\(437\) 113879.i 0.596321i
\(438\) −8234.46 1879.46i −0.0429227 0.00979682i
\(439\) 175445. + 220001.i 0.910357 + 1.14155i 0.989478 + 0.144687i \(0.0462174\pi\)
−0.0791205 + 0.996865i \(0.525211\pi\)
\(440\) 19270.2 + 84428.4i 0.0995363 + 0.436097i
\(441\) 80759.4 + 101269.i 0.415256 + 0.520714i
\(442\) 4119.35 + 8553.92i 0.0210855 + 0.0437845i
\(443\) 8893.34 38964.3i 0.0453166 0.198545i −0.947202 0.320637i \(-0.896103\pi\)
0.992519 + 0.122092i \(0.0389602\pi\)
\(444\) 414134. 199436.i 2.10075 1.01167i
\(445\) 107365. 134631.i 0.542179 0.679870i
\(446\) 16146.1 + 70740.8i 0.0811706 + 0.355632i
\(447\) −50419.6 220903.i −0.252339 1.10557i
\(448\) 55026.2 114263.i 0.274166 0.569312i
\(449\) −255841. 204026.i −1.26905 1.01203i −0.998787 0.0492439i \(-0.984319\pi\)
−0.270260 0.962787i \(-0.587110\pi\)
\(450\) 62806.0 50086.1i 0.310153 0.247339i
\(451\) −167439. 80634.2i −0.823195 0.396430i
\(452\) −38630.8 + 80217.7i −0.189085 + 0.392639i
\(453\) 234924. + 294585.i 1.14480 + 1.43554i
\(454\) −65340.0 + 81933.8i −0.317006 + 0.397513i
\(455\) −164106. 79029.4i −0.792688 0.381739i
\(456\) −116848. + 26669.7i −0.561941 + 0.128259i
\(457\) 193301. 44119.6i 0.925552 0.211251i 0.266922 0.963718i \(-0.413993\pi\)
0.658630 + 0.752467i \(0.271136\pi\)
\(458\) 22260.1 + 17751.8i 0.106120 + 0.0846277i
\(459\) 16787.2 + 34859.0i 0.0796807 + 0.165459i
\(460\) −95849.5 21877.0i −0.452975 0.103389i
\(461\) 33869.0 16310.5i 0.159368 0.0767475i −0.352500 0.935812i \(-0.614668\pi\)
0.511867 + 0.859064i \(0.328954\pi\)
\(462\) 147394. 117543.i 0.690551 0.550696i
\(463\) 77250.4 17631.9i 0.360362 0.0822502i −0.0385068 0.999258i \(-0.512260\pi\)
0.398869 + 0.917008i \(0.369403\pi\)
\(464\) −26464.2 + 21104.5i −0.122920 + 0.0980255i
\(465\) −65153.1 + 285454.i −0.301321 + 1.32017i
\(466\) −56885.6 −0.261957
\(467\) 308210.i 1.41323i 0.707599 + 0.706614i \(0.249778\pi\)
−0.707599 + 0.706614i \(0.750222\pi\)
\(468\) −124167. + 544010.i −0.566909 + 2.48379i
\(469\) −255282. 203581.i −1.16058 0.925530i
\(470\) −5540.89 2668.35i −0.0250833 0.0120795i
\(471\) 123892. 59663.2i 0.558472 0.268946i
\(472\) 204776.i 0.919167i
\(473\) 265635. 227099.i 1.18731 1.01506i
\(474\) −55702.1 −0.247922
\(475\) −43856.2 91068.3i −0.194376 0.403627i
\(476\) 12330.1 25603.8i 0.0544195 0.113003i
\(477\) 220166. 276079.i 0.967639 1.21338i
\(478\) −78619.3 17944.3i −0.344091 0.0785365i
\(479\) −329421. −1.43575 −0.717877 0.696170i \(-0.754886\pi\)
−0.717877 + 0.696170i \(0.754886\pi\)
\(480\) 157402.i 0.683170i
\(481\) 485754. + 110870.i 2.09955 + 0.479208i
\(482\) −27877.1 34956.8i −0.119992 0.150466i
\(483\) 99470.1 + 435807.i 0.426382 + 1.86810i
\(484\) 193211. + 242279.i 0.824785 + 1.03425i
\(485\) 69980.5 + 145316.i 0.297504 + 0.617774i
\(486\) −4182.62 + 18325.3i −0.0177083 + 0.0775850i
\(487\) −266723. + 128447.i −1.12461 + 0.541585i −0.901315 0.433165i \(-0.857397\pi\)
−0.223298 + 0.974750i \(0.571682\pi\)
\(488\) −23914.8 + 29988.2i −0.100421 + 0.125924i
\(489\) 122261. + 535659.i 0.511292 + 2.24012i
\(490\) −2773.84 12153.0i −0.0115528 0.0506163i
\(491\) −17005.3 + 35311.8i −0.0705376 + 0.146473i −0.933256 0.359211i \(-0.883046\pi\)
0.862719 + 0.505684i \(0.168760\pi\)
\(492\) 173606. + 138446.i 0.717191 + 0.571941i
\(493\) −4608.06 + 3674.81i −0.0189594 + 0.0151196i
\(494\) −56042.3 26988.6i −0.229648 0.110593i
\(495\) −166353. + 345435.i −0.678921 + 1.40979i
\(496\) −177307. 222336.i −0.720714 0.903746i
\(497\) 26644.2 33410.8i 0.107867 0.135261i
\(498\) 125094. + 60242.1i 0.504403 + 0.242908i
\(499\) −73826.4 + 16850.4i −0.296490 + 0.0676720i −0.368179 0.929755i \(-0.620018\pi\)
0.0716882 + 0.997427i \(0.477161\pi\)
\(500\) 202215. 46154.2i 0.808858 0.184617i
\(501\) −433887. 346014.i −1.72863 1.37853i
\(502\) 27366.6 + 56827.3i 0.108596 + 0.225502i
\(503\) −45091.7 10291.9i −0.178222 0.0406779i 0.132479 0.991186i \(-0.457706\pi\)
−0.310700 + 0.950508i \(0.600564\pi\)
\(504\) −278446. + 134092.i −1.09617 + 0.527889i
\(505\) −59196.9 + 47207.9i −0.232122 + 0.185111i
\(506\) 107536. 24544.4i 0.420003 0.0958630i
\(507\) −376772. + 300465.i −1.46576 + 1.16890i
\(508\) 56177.1 246128.i 0.217687 0.953747i
\(509\) 156279. 0.603206 0.301603 0.953434i \(-0.402478\pi\)
0.301603 + 0.953434i \(0.402478\pi\)
\(510\) 7794.41i 0.0299670i
\(511\) −6097.97 + 26717.0i −0.0233531 + 0.102316i
\(512\) 205058. + 163528.i 0.782232 + 0.623809i
\(513\) −228384. 109984.i −0.867823 0.417921i
\(514\) −33687.4 + 16223.0i −0.127509 + 0.0614052i
\(515\) 11784.5i 0.0444322i
\(516\) −369811. + 193915.i −1.38893 + 0.728304i
\(517\) −77881.0 −0.291374
\(518\) 57327.0 + 119041.i 0.213649 + 0.443646i
\(519\) 176123. 365723.i 0.653855 1.35774i
\(520\) 69930.1 87689.6i 0.258617 0.324296i
\(521\) 205308. + 46860.3i 0.756365 + 0.172635i 0.583279 0.812272i \(-0.301769\pi\)
0.173085 + 0.984907i \(0.444626\pi\)
\(522\) 30689.3 0.112628
\(523\) 442638.i 1.61825i −0.587638 0.809124i \(-0.699942\pi\)
0.587638 0.809124i \(-0.300058\pi\)
\(524\) 197890. + 45167.0i 0.720710 + 0.164497i
\(525\) −247381. 310206.i −0.897526 1.12546i
\(526\) 6089.85 + 26681.4i 0.0220108 + 0.0964354i
\(527\) −30873.5 38714.1i −0.111164 0.139395i
\(528\) −245957. 510734.i −0.882248 1.83201i
\(529\) 4072.61 17843.3i 0.0145533 0.0637622i
\(530\) −30618.0 + 14744.9i −0.109000 + 0.0524915i
\(531\) 565260. 708813.i 2.00474 2.51387i
\(532\) 41430.2 + 181517.i 0.146384 + 0.641350i
\(533\) 53559.4 + 234659.i 0.188530 + 0.826005i
\(534\) 100156. 207976.i 0.351232 0.729340i
\(535\) 216034. + 172281.i 0.754768 + 0.601908i
\(536\) 157195. 125359.i 0.547154 0.436341i
\(537\) 308683. + 148654.i 1.07044 + 0.515498i
\(538\) 45952.0 95420.2i 0.158759 0.329667i
\(539\) −98423.9 123420.i −0.338784 0.424822i
\(540\) 136446. 171097.i 0.467921 0.586754i
\(541\) 71091.5 + 34235.8i 0.242897 + 0.116973i 0.551372 0.834259i \(-0.314104\pi\)
−0.308475 + 0.951232i \(0.599819\pi\)
\(542\) 74898.4 17095.1i 0.254961 0.0581932i
\(543\) −416260. + 95008.7i −1.41177 + 0.322228i
\(544\) 20812.1 + 16597.1i 0.0703264 + 0.0560834i
\(545\) 20169.1 + 41881.5i 0.0679037 + 0.141003i
\(546\) −238044. 54332.1i −0.798496 0.182251i
\(547\) 177676. 85564.1i 0.593818 0.285968i −0.112738 0.993625i \(-0.535962\pi\)
0.706556 + 0.707657i \(0.250248\pi\)
\(548\) 240301. 191634.i 0.800193 0.638133i
\(549\) −165558. + 37787.5i −0.549294 + 0.125373i
\(550\) −76543.6 + 61041.5i −0.253037 + 0.201790i
\(551\) 8592.65 37646.9i 0.0283024 0.124001i
\(552\) −275259. −0.903364
\(553\) 180727.i 0.590981i
\(554\) 3277.99 14361.8i 0.0106804 0.0467940i
\(555\) −319805. 255036.i −1.03824 0.827971i
\(556\) 11752.9 + 5659.88i 0.0380184 + 0.0183087i
\(557\) 222408. 107106.i 0.716869 0.345226i −0.0396359 0.999214i \(-0.512620\pi\)
0.756505 + 0.653988i \(0.226906\pi\)
\(558\) 257832.i 0.828074i
\(559\) −444460. 85593.9i −1.42236 0.273917i
\(560\) −145237. −0.463127
\(561\) −42827.0 88931.3i −0.136079 0.282572i
\(562\) −12750.0 + 26475.6i −0.0403679 + 0.0838248i
\(563\) −642.352 + 805.484i −0.00202655 + 0.00254121i −0.782844 0.622218i \(-0.786232\pi\)
0.780817 + 0.624760i \(0.214803\pi\)
\(564\) 90721.4 + 20706.6i 0.285201 + 0.0650954i
\(565\) 79232.2 0.248202
\(566\) 42638.4i 0.133097i
\(567\) −273371. 62395.1i −0.850327 0.194082i
\(568\) 16406.7 + 20573.4i 0.0508540 + 0.0637689i
\(569\) 129203. + 566074.i 0.399068 + 1.74843i 0.631080 + 0.775717i \(0.282612\pi\)
−0.232013 + 0.972713i \(0.574531\pi\)
\(570\) 31839.3 + 39925.2i 0.0979973 + 0.122885i
\(571\) −45418.3 94312.1i −0.139303 0.289265i 0.819633 0.572889i \(-0.194177\pi\)
−0.958935 + 0.283624i \(0.908463\pi\)
\(572\) 151326. 663002.i 0.462510 2.02639i
\(573\) −549498. + 264624.i −1.67362 + 0.805973i
\(574\) −39795.7 + 49902.2i −0.120785 + 0.151459i
\(575\) −51656.1 226320.i −0.156238 0.684522i
\(576\) 76935.5 + 337076.i 0.231890 + 1.01598i
\(577\) −205709. + 427160.i −0.617878 + 1.28304i 0.323674 + 0.946169i \(0.395082\pi\)
−0.941552 + 0.336868i \(0.890632\pi\)
\(578\) −73483.3 58601.0i −0.219955 0.175408i
\(579\) −343920. + 274267.i −1.02589 + 0.818119i
\(580\) 30035.9 + 14464.5i 0.0892862 + 0.0429980i
\(581\) 195458. 405872.i 0.579029 1.20237i
\(582\) 134804. + 169039.i 0.397976 + 0.499046i
\(583\) −268323. + 336466.i −0.789443 + 0.989930i
\(584\) −15203.5 7321.62i −0.0445778 0.0214675i
\(585\) 484114. 110496.i 1.41461 0.322875i
\(586\) −707.622 + 161.510i −0.00206066 + 0.000470332i
\(587\) 209105. + 166756.i 0.606861 + 0.483955i 0.878049 0.478571i \(-0.158845\pi\)
−0.271188 + 0.962526i \(0.587417\pi\)
\(588\) 81837.2 + 169937.i 0.236699 + 0.491510i
\(589\) 316286. + 72190.2i 0.911694 + 0.208088i
\(590\) −78609.5 + 37856.3i −0.225825 + 0.108751i
\(591\) −747330. + 595975.i −2.13962 + 1.70629i
\(592\) 387326. 88404.7i 1.10518 0.252251i
\(593\) −150358. + 119907.i −0.427580 + 0.340984i −0.813517 0.581541i \(-0.802450\pi\)
0.385936 + 0.922525i \(0.373878\pi\)
\(594\) −54634.3 + 239368.i −0.154843 + 0.678413i
\(595\) −25289.2 −0.0714335
\(596\) 216744.i 0.610175i
\(597\) 180103. 789081.i 0.505326 2.21398i
\(598\) −111690. 89069.5i −0.312328 0.249073i
\(599\) −451404. 217385.i −1.25809 0.605865i −0.318422 0.947949i \(-0.603153\pi\)
−0.939669 + 0.342084i \(0.888867\pi\)
\(600\) 220123. 106006.i 0.611453 0.294460i
\(601\) 171866.i 0.475819i 0.971287 + 0.237909i \(0.0764621\pi\)
−0.971287 + 0.237909i \(0.923538\pi\)
\(602\) −55740.0 106300.i −0.153806 0.293320i
\(603\) 890157. 2.44812
\(604\) 156383. + 324732.i 0.428662 + 0.890127i
\(605\) 119651. 248458.i 0.326893 0.678800i
\(606\) −63282.7 + 79354.0i −0.172322 + 0.216084i
\(607\) 474591. + 108322.i 1.28808 + 0.293995i 0.811093 0.584917i \(-0.198873\pi\)
0.476984 + 0.878912i \(0.341730\pi\)
\(608\) −174403. −0.471788
\(609\) 151578.i 0.408696i
\(610\) 15932.9 + 3636.59i 0.0428190 + 0.00977315i
\(611\) 62889.7 + 78861.2i 0.168460 + 0.211242i
\(612\) 17239.5 + 75531.3i 0.0460280 + 0.201662i
\(613\) −105723. 132572.i −0.281350 0.352802i 0.620996 0.783814i \(-0.286728\pi\)
−0.902346 + 0.431011i \(0.858157\pi\)
\(614\) −30669.1 63685.0i −0.0813512 0.168927i
\(615\) 43970.7 192648.i 0.116255 0.509349i
\(616\) 339350. 163422.i 0.894307 0.430676i
\(617\) −74768.4 + 93756.6i −0.196403 + 0.246281i −0.870275 0.492567i \(-0.836059\pi\)
0.673872 + 0.738848i \(0.264630\pi\)
\(618\) −3515.23 15401.2i −0.00920399 0.0403253i
\(619\) −63202.1 276907.i −0.164949 0.722690i −0.987966 0.154673i \(-0.950568\pi\)
0.823017 0.568017i \(-0.192289\pi\)
\(620\) −121522. + 252343.i −0.316134 + 0.656460i
\(621\) −455158. 362977.i −1.18026 0.941230i
\(622\) 41775.0 33314.4i 0.107978 0.0861096i
\(623\) −674784. 324959.i −1.73856 0.837245i
\(624\) −318550. + 661475.i −0.818103 + 1.69881i
\(625\) 61802.8 + 77498.2i 0.158215 + 0.198395i
\(626\) 50755.7 63645.6i 0.129520 0.162413i
\(627\) 582647. + 280588.i 1.48208 + 0.713730i
\(628\) 128240. 29270.0i 0.325165 0.0742169i
\(629\) 67442.9 15393.4i 0.170465 0.0389075i
\(630\) 102951. + 82100.7i 0.259388 + 0.206855i
\(631\) −31478.6 65365.9i −0.0790599 0.164170i 0.857692 0.514164i \(-0.171898\pi\)
−0.936752 + 0.349994i \(0.886183\pi\)
\(632\) −108496. 24763.6i −0.271632 0.0619983i
\(633\) 357595. 172209.i 0.892451 0.429782i
\(634\) −156914. + 125135.i −0.390376 + 0.311314i
\(635\) −219029. + 49991.9i −0.543193 + 0.123980i
\(636\) 402020. 320600.i 0.993879 0.792592i
\(637\) −45494.7 + 199325.i −0.112120 + 0.491229i
\(638\) −37402.0 −0.0918868
\(639\) 116502.i 0.285319i
\(640\) 43876.6 192236.i 0.107121 0.469326i
\(641\) 50504.8 + 40276.2i 0.122918 + 0.0980241i 0.683020 0.730400i \(-0.260666\pi\)
−0.560101 + 0.828424i \(0.689238\pi\)
\(642\) 333724. + 160713.i 0.809688 + 0.389925i
\(643\) 172994. 83309.3i 0.418416 0.201498i −0.212817 0.977092i \(-0.568264\pi\)
0.631232 + 0.775594i \(0.282549\pi\)
\(644\) 427602.i 1.03102i
\(645\) 298265. + 221631.i 0.716939 + 0.532734i
\(646\) −8636.28 −0.0206948
\(647\) −149887. 311244.i −0.358060 0.743520i 0.641664 0.766986i \(-0.278244\pi\)
−0.999725 + 0.0234658i \(0.992530\pi\)
\(648\) 74915.6 155564.i 0.178411 0.370475i
\(649\) −688900. + 863853.i −1.63556 + 2.05093i
\(650\) 123619. + 28215.3i 0.292591 + 0.0667819i
\(651\) 1.27346e6 3.00486
\(652\) 525574.i 1.23634i
\(653\) −238658. 54472.1i −0.559692 0.127746i −0.0666894 0.997774i \(-0.521244\pi\)
−0.493003 + 0.870028i \(0.664101\pi\)
\(654\) 38851.9 + 48718.7i 0.0908357 + 0.113904i
\(655\) −40194.1 176102.i −0.0936871 0.410470i
\(656\) 119662. + 150051.i 0.278066 + 0.348683i
\(657\) −32415.1 67310.7i −0.0750960 0.155938i
\(658\) −5952.00 + 26077.4i −0.0137471 + 0.0602300i
\(659\) 514617. 247826.i 1.18499 0.570659i 0.265626 0.964076i \(-0.414421\pi\)
0.919360 + 0.393417i \(0.128707\pi\)
\(660\) −348096. + 436499.i −0.799119 + 1.00206i
\(661\) 26060.2 + 114177.i 0.0596450 + 0.261322i 0.995955 0.0898525i \(-0.0286396\pi\)
−0.936310 + 0.351174i \(0.885782\pi\)
\(662\) 5458.45 + 23915.0i 0.0124553 + 0.0545701i
\(663\) −55467.3 + 115179.i −0.126186 + 0.262027i
\(664\) 216876. + 172953.i 0.491899 + 0.392276i
\(665\) 129539. 103304.i 0.292925 0.233600i
\(666\) −324530. 156286.i −0.731656 0.352347i
\(667\) 38478.9 79902.3i 0.0864911 0.179601i
\(668\) −330987. 415044.i −0.741751 0.930126i
\(669\) −609165. + 763869.i −1.36108 + 1.70674i
\(670\) −77183.2 37169.5i −0.171939 0.0828012i
\(671\) 201770. 46052.7i 0.448138 0.102285i
\(672\) −667430. + 152337.i −1.47798 + 0.337338i
\(673\) −569913. 454490.i −1.25828 1.00345i −0.999294 0.0375665i \(-0.988039\pi\)
−0.258989 0.965880i \(-0.583389\pi\)
\(674\) 17419.2 + 36171.4i 0.0383451 + 0.0796243i
\(675\) 503775. + 114983.i 1.10568 + 0.252364i
\(676\) −415329. + 200012.i −0.908865 + 0.437686i
\(677\) −385340. + 307298.i −0.840749 + 0.670475i −0.946070 0.323963i \(-0.894985\pi\)
0.105320 + 0.994438i \(0.466413\pi\)
\(678\) 103549. 23634.3i 0.225260 0.0514142i
\(679\) 548452. 437376.i 1.18960 0.948671i
\(680\) 3465.18 15182.0i 0.00749390 0.0328329i
\(681\) −1.41110e6 −3.04273
\(682\) 314228.i 0.675580i
\(683\) −79597.7 + 348740.i −0.170631 + 0.747585i 0.815108 + 0.579309i \(0.196677\pi\)
−0.985740 + 0.168277i \(0.946180\pi\)
\(684\) −396843. 316472.i −0.848216 0.676430i
\(685\) −246430. 118674.i −0.525185 0.252916i
\(686\) 91578.5 44101.9i 0.194601 0.0937150i
\(687\) 383374.i 0.812285i
\(688\) −348916. + 92277.0i −0.737130 + 0.194947i
\(689\) 557375. 1.17411
\(690\) 50886.4 + 105667.i 0.106882 + 0.221942i
\(691\) 34238.3 71096.5i 0.0717060 0.148899i −0.862035 0.506849i \(-0.830810\pi\)
0.933741 + 0.357950i \(0.116524\pi\)
\(692\) 242097. 303580.i 0.505566 0.633960i
\(693\) 1.62574e6 + 371064.i 3.38520 + 0.772650i
\(694\) 36317.9 0.0754052
\(695\) 11608.5i 0.0240328i
\(696\) 90997.0 + 20769.5i 0.187849 + 0.0428753i
\(697\) 20836.0 + 26127.5i 0.0428893 + 0.0537814i
\(698\) −8055.04 35291.5i −0.0165332 0.0724367i
\(699\) −477573. 598857.i −0.977429 1.22566i
\(700\) −164675. 341951.i −0.336071 0.697859i
\(701\) 154827. 678342.i 0.315073 1.38042i −0.531007 0.847367i \(-0.678186\pi\)
0.846080 0.533056i \(-0.178957\pi\)
\(702\) 286499. 137971.i 0.581365 0.279970i
\(703\) −282582. + 354347.i −0.571786 + 0.716997i
\(704\) −93763.7 410805.i −0.189186 0.828878i
\(705\) −18426.8 80732.9i −0.0370741 0.162432i
\(706\) −38600.9 + 80155.6i −0.0774441 + 0.160814i
\(707\) 257467. + 205323.i 0.515089 + 0.410770i
\(708\) 1.03216e6 823118.i 2.05911 1.64208i
\(709\) −97775.0 47086.0i −0.194507 0.0936697i 0.334095 0.942539i \(-0.391569\pi\)
−0.528602 + 0.848870i \(0.677284\pi\)
\(710\) 4864.66 10101.6i 0.00965019 0.0200388i
\(711\) −307194. 385209.i −0.607678 0.762004i
\(712\) 287544. 360568.i 0.567210 0.711259i
\(713\) 671290. + 323276.i 1.32048 + 0.635909i
\(714\) −33050.5 + 7543.56i −0.0648309 + 0.0147972i
\(715\) −590005. + 134665.i −1.15410 + 0.263416i
\(716\) 256232. + 204338.i 0.499813 + 0.398587i
\(717\) −471127. 978305.i −0.916431 1.90299i
\(718\) −81018.0 18491.8i −0.157157 0.0358700i
\(719\) −206375. + 99385.2i −0.399209 + 0.192249i −0.622706 0.782456i \(-0.713967\pi\)
0.223497 + 0.974705i \(0.428253\pi\)
\(720\) 309563. 246868.i 0.597151 0.476212i
\(721\) −49969.8 + 11405.3i −0.0961251 + 0.0219399i
\(722\) −72029.3 + 57441.5i −0.138177 + 0.110192i
\(723\) 133967. 586947.i 0.256283 1.12285i
\(724\) −408423. −0.779171
\(725\) 78716.2i 0.149757i
\(726\) 82259.0 360400.i 0.156067 0.683773i
\(727\) 632880. + 504705.i 1.19744 + 0.954925i 0.999679 0.0253262i \(-0.00806244\pi\)
0.197758 + 0.980251i \(0.436634\pi\)
\(728\) −439508. 211656.i −0.829285 0.399363i
\(729\) −587746. + 283044.i −1.10595 + 0.532596i
\(730\) 7189.87i 0.0134920i
\(731\) −60754.7 + 16067.7i −0.113696 + 0.0300689i
\(732\) −247281. −0.461497
\(733\) 404049. + 839015.i 0.752013 + 1.56157i 0.825582 + 0.564282i \(0.190847\pi\)
−0.0735690 + 0.997290i \(0.523439\pi\)
\(734\) 89570.5 185995.i 0.166254 0.345231i
\(735\) 104652. 131229.i 0.193719 0.242916i
\(736\) −390499. 89128.9i −0.720883 0.164537i
\(737\) −1.08486e6 −1.99728
\(738\) 174007.i 0.319487i
\(739\) 420928. + 96074.2i 0.770760 + 0.175921i 0.589778 0.807565i \(-0.299215\pi\)
0.180982 + 0.983486i \(0.442072\pi\)
\(740\) −243960. 305916.i −0.445508 0.558649i
\(741\) −186374. 816558.i −0.339429 1.48714i
\(742\) 92155.0 + 115559.i 0.167383 + 0.209891i
\(743\) 23074.3 + 47914.3i 0.0417976 + 0.0867935i 0.920822 0.389983i \(-0.127519\pi\)
−0.879024 + 0.476777i \(0.841805\pi\)
\(744\) −174492. + 764501.i −0.315232 + 1.38112i
\(745\) −173779. + 83687.5i −0.313101 + 0.150782i
\(746\) −121416. + 152251.i −0.218172 + 0.273579i
\(747\) 273281. + 1.19732e6i 0.489743 + 2.14571i
\(748\) −21010.3 92052.3i −0.0375517 0.164525i
\(749\) 521439. 1.08278e6i 0.929480 1.93008i
\(750\) −193448. 154269.i −0.343907 0.274257i
\(751\) 632528. 504424.i 1.12150 0.894368i 0.126279 0.991995i \(-0.459697\pi\)
0.995223 + 0.0976270i \(0.0311252\pi\)
\(752\) 72463.7 + 34896.7i 0.128140 + 0.0617090i
\(753\) −368493. + 765183.i −0.649889 + 1.34951i
\(754\) 30202.5 + 37872.7i 0.0531251 + 0.0666168i
\(755\) 199980. 250767.i 0.350826 0.439922i
\(756\) −857556. 412977.i −1.50044 0.722574i
\(757\) −550142. + 125566.i −0.960027 + 0.219120i −0.673694 0.739010i \(-0.735293\pi\)
−0.286333 + 0.958130i \(0.592436\pi\)
\(758\) −106141. + 24226.0i −0.184733 + 0.0421642i
\(759\) 1.16119e6 + 926016.i 2.01567 + 1.60744i
\(760\) 44266.9 + 91921.2i 0.0766394 + 0.159143i
\(761\) 31454.2 + 7179.22i 0.0543137 + 0.0123968i 0.249591 0.968351i \(-0.419704\pi\)
−0.195278 + 0.980748i \(0.562561\pi\)
\(762\) −271337. + 130669.i −0.467303 + 0.225041i
\(763\) 158070. 126056.i 0.271518 0.216529i
\(764\) −568783. + 129821.i −0.974450 + 0.222412i
\(765\) 53902.4 42985.8i 0.0921055 0.0734517i
\(766\) −37970.8 + 166361.i −0.0647131 + 0.283527i
\(767\) 1.43102e6 2.43251
\(768\) 283748.i 0.481073i
\(769\) 105464. 462067.i 0.178341 0.781361i −0.804056 0.594554i \(-0.797329\pi\)
0.982397 0.186808i \(-0.0598141\pi\)
\(770\) −125470. 100059.i −0.211620 0.168761i
\(771\) −453603. 218444.i −0.763075 0.367478i
\(772\) −379116. + 182572.i −0.636117 + 0.306338i
\(773\) 341880.i 0.572157i 0.958206 + 0.286078i \(0.0923518\pi\)
−0.958206 + 0.286078i \(0.907648\pi\)
\(774\) 299492. + 131828.i 0.499923 + 0.220052i
\(775\) −661326. −1.10106
\(776\) 187421. + 389184.i 0.311240 + 0.646296i
\(777\) −771911. + 1.60289e6i −1.27857 + 2.65498i
\(778\) 120617. 151249.i 0.199273 0.249880i
\(779\) −213456. 48719.9i −0.351750 0.0802845i
\(780\) 723084. 1.18850
\(781\) 141984.i 0.232776i
\(782\) −19337.2 4413.58i −0.0316213 0.00721734i
\(783\) 123081. + 154339.i 0.200756 + 0.251740i
\(784\) 36276.2 + 158936.i 0.0590187 + 0.258578i
\(785\) −72982.9 91517.7i −0.118436 0.148513i
\(786\) −105059. 218158.i −0.170055 0.353123i
\(787\) 176656. 773983.i 0.285220 1.24963i −0.605782 0.795631i \(-0.707139\pi\)
0.891002 0.454000i \(-0.150003\pi\)
\(788\) −823809. + 396725.i −1.32670 + 0.638907i
\(789\) −229759. + 288109.i −0.369079 + 0.462810i
\(790\) 10551.2 + 46227.7i 0.0169062 + 0.0740710i
\(791\) −76682.2 335967.i −0.122558 0.536962i
\(792\) −445524. + 925140.i −0.710266 + 1.47488i
\(793\) −209564. 167122.i −0.333250 0.265758i
\(794\) −8054.03 + 6422.87i −0.0127753 + 0.0101880i
\(795\) −412273. 198540.i −0.652305 0.314134i
\(796\) 335923. 697552.i 0.530169 1.10091i
\(797\) 143017. + 179338.i 0.225150 + 0.282329i 0.881557 0.472078i \(-0.156496\pi\)
−0.656407 + 0.754407i \(0.727925\pi\)
\(798\) 138480. 173648.i 0.217460 0.272687i
\(799\) 12617.7 + 6076.36i 0.0197645 + 0.00951810i
\(800\) 346605. 79110.3i 0.541570 0.123610i
\(801\) 1.99061e6 454345.i 3.10257 0.708142i
\(802\) 106505. + 84935.2i 0.165586 + 0.132050i
\(803\) 39505.3 + 82033.6i 0.0612667 + 0.127222i
\(804\) 1.26373e6 + 288437.i 1.95497 + 0.446210i
\(805\) 342839. 165103.i 0.529052 0.254778i
\(806\) −318183. + 253743.i −0.489787 + 0.390592i
\(807\) 1.39031e6 317329.i 2.13483 0.487262i
\(808\) −158541. + 126432.i −0.242839 + 0.193657i
\(809\) −133692. + 585742.i −0.204272 + 0.894972i 0.764028 + 0.645183i \(0.223219\pi\)
−0.968300 + 0.249790i \(0.919638\pi\)
\(810\) −73567.5 −0.112128
\(811\) 1.26190e6i 1.91859i 0.282400 + 0.959297i \(0.408869\pi\)
−0.282400 + 0.959297i \(0.591131\pi\)
\(812\) 32264.4 141360.i 0.0489341 0.214394i
\(813\) 808763. + 644967.i 1.22360 + 0.975790i
\(814\) 395515. + 190470.i 0.596918 + 0.287460i
\(815\) 421390. 202931.i 0.634409 0.305515i
\(816\) 101935.i 0.153089i
\(817\) 245569. 330480.i 0.367899 0.495109i
\(818\) 168013. 0.251093
\(819\) −937067. 1.94584e6i −1.39702 2.90094i
\(820\) 82013.2 170302.i 0.121971 0.253275i
\(821\) −27330.5 + 34271.3i −0.0405472 + 0.0508445i −0.801692 0.597738i \(-0.796066\pi\)
0.761144 + 0.648582i \(0.224638\pi\)
\(822\) −357459. 81587.6i −0.529032 0.120748i
\(823\) −162705. −0.240216 −0.120108 0.992761i \(-0.538324\pi\)
−0.120108 + 0.992761i \(0.538324\pi\)
\(824\) 31561.2i 0.0464836i
\(825\) −1.28522e6 293342.i −1.88829 0.430990i
\(826\) 236601. + 296688.i 0.346782 + 0.434851i
\(827\) 275858. + 1.20861e6i 0.403344 + 1.76716i 0.613700 + 0.789539i \(0.289680\pi\)
−0.210356 + 0.977625i \(0.567462\pi\)
\(828\) −726823. 911407.i −1.06015 1.32939i
\(829\) −276961. 575115.i −0.403004 0.836847i −0.999416 0.0341681i \(-0.989122\pi\)
0.596412 0.802678i \(-0.296592\pi\)
\(830\) 26300.0 115228.i 0.0381769 0.167264i
\(831\) 178712. 86063.4i 0.258793 0.124628i
\(832\) −340261. + 426673.i −0.491547 + 0.616381i
\(833\) 6316.57 + 27674.7i 0.00910314 + 0.0398835i
\(834\) −3462.70 15171.1i −0.00497832 0.0218115i
\(835\) −204973. + 425630.i −0.293983 + 0.610463i
\(836\) 483645. + 385694.i 0.692013 + 0.551862i
\(837\) −1.29666e6 + 1.03405e6i −1.85087 + 1.47602i
\(838\) −99538.0 47935.0i −0.141743 0.0682597i
\(839\) 307723. 638993.i 0.437155 0.907762i −0.559714 0.828686i \(-0.689089\pi\)
0.996869 0.0790756i \(-0.0251969\pi\)
\(840\) 249698. + 313111.i 0.353880 + 0.443751i
\(841\) 422233. 529463.i 0.596980 0.748590i
\(842\) 284741. + 137124.i 0.401630 + 0.193415i
\(843\) −385759. + 88047.0i −0.542826 + 0.123897i
\(844\) 370145. 84483.3i 0.519622 0.118600i
\(845\) 320728. + 255772.i 0.449183 + 0.358212i
\(846\) −31639.2 65699.4i −0.0442063 0.0917954i
\(847\) −1.16933e6 266892.i −1.62994 0.372022i
\(848\) 400422. 192833.i 0.556834 0.268157i
\(849\) 448872. 357963.i 0.622740 0.496618i
\(850\) 17163.6 3917.47i 0.0237558 0.00542210i
\(851\) −813807. + 648990.i −1.12373 + 0.896146i
\(852\) −37750.0 + 165394.i −0.0520042 + 0.227845i
\(853\) 464727. 0.638705 0.319352 0.947636i \(-0.396535\pi\)
0.319352 + 0.947636i \(0.396535\pi\)
\(854\) 71079.7i 0.0974608i
\(855\) −100512. + 440371.i −0.137494 + 0.602402i
\(856\) 578579. + 461401.i 0.789615 + 0.629697i
\(857\) −653636. 314774.i −0.889968 0.428586i −0.0677125 0.997705i \(-0.521570\pi\)
−0.822255 + 0.569119i \(0.807284\pi\)
\(858\) −730908. + 351987.i −0.992860 + 0.478136i
\(859\) 1.45027e6i 1.96545i −0.185073 0.982725i \(-0.559252\pi\)
0.185073 0.982725i \(-0.440748\pi\)
\(860\) 230982. + 270178.i 0.312307 + 0.365303i
\(861\) −859439. −1.15933
\(862\) −148028. 307382.i −0.199218 0.413680i
\(863\) 348155. 722952.i 0.467468 0.970707i −0.525329 0.850899i \(-0.676058\pi\)
0.992797 0.119808i \(-0.0382278\pi\)
\(864\) 555892. 697066.i 0.744668 0.933784i
\(865\) −336879. 76890.4i −0.450238 0.102764i
\(866\) 76219.3 0.101632
\(867\) 1.26556e6i 1.68362i
\(868\) 1.18762e6 + 271066.i 1.57629 + 0.359779i
\(869\) 374387. + 469466.i 0.495771 + 0.621677i
\(870\) −8849.37 38771.6i −0.0116916 0.0512242i
\(871\) 876037. + 1.09852e6i 1.15474 + 1.44800i
\(872\) 54016.7 + 112167.i 0.0710387 + 0.147513i
\(873\) −425555. + 1.86448e6i −0.558377 + 2.44641i
\(874\) 117080. 56382.5i 0.153270 0.0738111i
\(875\) −500532. + 627648.i −0.653757 + 0.819785i
\(876\) −24208.0 106062.i −0.0315465 0.138214i
\(877\) −91224.6 399681.i −0.118608 0.519654i −0.998971 0.0453542i \(-0.985558\pi\)
0.880363 0.474300i \(-0.157299\pi\)
\(878\) 139320. 289301.i 0.180727 0.375284i
\(879\) −7641.00 6093.49i −0.00988946 0.00788658i
\(880\) −377274. + 300866.i −0.487182 + 0.388515i
\(881\) 598573. + 288257.i 0.771196 + 0.371389i 0.777737 0.628590i \(-0.216368\pi\)
−0.00654043 + 0.999979i \(0.502082\pi\)
\(882\) 64130.6 133169.i 0.0824381 0.171185i
\(883\) −239651. 300513.i −0.307368 0.385427i 0.604024 0.796966i \(-0.293563\pi\)
−0.911392 + 0.411539i \(0.864992\pi\)
\(884\) −76244.8 + 95608.0i −0.0975677 + 0.122346i
\(885\) −1.05848e6 509738.i −1.35144 0.650819i
\(886\) −44462.6 + 10148.3i −0.0566406 + 0.0129278i
\(887\) 431550. 98498.5i 0.548509 0.125194i 0.0607196 0.998155i \(-0.480660\pi\)
0.487790 + 0.872961i \(0.337803\pi\)
\(888\) −856498. 683035.i −1.08618 0.866197i
\(889\) 423960. + 880361.i 0.536440 + 1.11393i
\(890\) −191573. 43725.2i −0.241854 0.0552017i
\(891\) −839376. + 404222.i −1.05731 + 0.509172i
\(892\) −730696. + 582710.i −0.918347 + 0.732357i
\(893\) −89452.8 + 20417.0i −0.112174 + 0.0256029i
\(894\) −202148. + 161208.i −0.252927 + 0.201703i
\(895\) 64898.1 284337.i 0.0810188 0.354967i
\(896\) −857599. −1.06824
\(897\) 1.92357e6i 2.39069i
\(898\) −83091.5 + 364048.i −0.103040 + 0.451446i
\(899\) −197527. 157523.i −0.244404 0.194905i
\(900\) 932231. + 448939.i 1.15090 + 0.554245i
\(901\) 69723.2 33576.9i 0.0858870 0.0413610i
\(902\) 212068.i 0.260652i
\(903\) 651111. 1.47922e6i 0.798509 1.81409i
\(904\) 212199. 0.259661
\(905\) 157697. + 327462.i 0.192543 + 0.399819i
\(906\) 186552. 387379.i 0.227271 0.471932i
\(907\) 266420. 334080.i 0.323856 0.406103i −0.593075 0.805147i \(-0.702086\pi\)
0.916932 + 0.399044i \(0.130658\pi\)
\(908\) −1.31598e6 300363.i −1.59616 0.364313i
\(909\) −897775. −1.08653
\(910\) 207847.i 0.250993i
\(911\) −443226. 101163.i −0.534058 0.121895i −0.0530174 0.998594i \(-0.516884\pi\)
−0.481041 + 0.876698i \(0.659741\pi\)
\(912\) −416394. 522142.i −0.500628 0.627767i
\(913\) −333056. 1.45921e6i −0.399554 1.75056i
\(914\) −141065. 176890.i −0.168860 0.211743i
\(915\) 95478.4 + 198263.i 0.114041 + 0.236810i
\(916\) −81603.9 + 357530.i −0.0972568 + 0.426110i
\(917\) −707821. + 340869.i −0.841753 + 0.405367i
\(918\) 27527.2 34518.1i 0.0326646 0.0409601i
\(919\) 63261.7 + 277167.i 0.0749048 + 0.328179i 0.998472 0.0552568i \(-0.0175978\pi\)
−0.923567 + 0.383436i \(0.874741\pi\)
\(920\) 52139.9 + 228440.i 0.0616020 + 0.269896i
\(921\) 412961. 857522.i 0.486843 1.01094i
\(922\) −33537.8 26745.5i −0.0394523 0.0314622i
\(923\) −143771. + 114654.i −0.168760 + 0.134581i
\(924\) 2.18777e6 + 1.05358e6i 2.56247 + 1.23402i
\(925\) 400864. 832402.i 0.468504 0.972858i
\(926\) −56374.9 70691.9i −0.0657452 0.0824418i
\(927\) 87121.2 109246.i 0.101383 0.127130i
\(928\) 122369. + 58929.7i 0.142094 + 0.0684287i
\(929\) 373829. 85324.1i 0.433154 0.0988645i −0.000384025 1.00000i \(-0.500122\pi\)
0.433538 + 0.901135i \(0.357265\pi\)
\(930\) 325735. 74347.0i 0.376616 0.0859602i
\(931\) −145403. 115955.i −0.167755 0.133780i
\(932\) −317908. 660143.i −0.365990 0.759987i
\(933\) 701429. + 160097.i 0.805787 + 0.183916i
\(934\) 316872. 152598.i 0.363237 0.174926i
\(935\) −65692.6 + 52388.1i −0.0751438 + 0.0599252i
\(936\) 1.29655e6 295929.i 1.47992 0.337781i
\(937\) 515138. 410809.i 0.586739 0.467909i −0.284562 0.958658i \(-0.591848\pi\)
0.871301 + 0.490749i \(0.163277\pi\)
\(938\) −82909.9 + 363252.i −0.0942325 + 0.412859i
\(939\) 1.09613e6 1.24317
\(940\) 79212.9i 0.0896479i
\(941\) −203162. + 890113.i −0.229437 + 1.00523i 0.720663 + 0.693286i \(0.243838\pi\)
−0.950100 + 0.311945i \(0.899019\pi\)
\(942\) −122680. 97834.3i −0.138253 0.110253i
\(943\) −453043. 218174.i −0.509467 0.245346i
\(944\) 1.02805e6 495085.i 1.15364 0.555566i
\(945\) 847020.i 0.948484i
\(946\) −365000. 160662.i −0.407860 0.179528i
\(947\) −725516. −0.808997 −0.404499 0.914539i \(-0.632554\pi\)
−0.404499 + 0.914539i \(0.632554\pi\)
\(948\) −311294. 646409.i −0.346381 0.719268i
\(949\) 51165.1 106246.i 0.0568122 0.117972i
\(950\) −71914.3 + 90177.7i −0.0796834 + 0.0999198i
\(951\) −2.63469e6 601350.i −2.91318 0.664915i
\(952\) −67729.4 −0.0747314
\(953\) 741988.i 0.816980i 0.912763 + 0.408490i \(0.133944\pi\)
−0.912763 + 0.408490i \(0.866056\pi\)
\(954\) −392845. 89664.4i −0.431643 0.0985197i
\(955\) 323701. + 405908.i 0.354926 + 0.445063i
\(956\) −231128. 1.01264e6i −0.252893 1.10800i
\(957\) −314002. 393746.i −0.342853 0.429924i
\(958\) 163099. + 338680.i 0.177714 + 0.369027i
\(959\) −264714. + 1.15979e6i −0.287832 + 1.26108i
\(960\) 403664. 194394.i 0.438004 0.210932i
\(961\) 747604. 937466.i 0.809515 1.01510i
\(962\) −126515. 554300.i −0.136708 0.598955i
\(963\) 729056. + 3.19420e6i 0.786155 + 3.44437i
\(964\) 249872. 518864.i 0.268883 0.558341i
\(965\) 292763. + 233470.i 0.314385 + 0.250713i
\(966\) 398807. 318038.i 0.427375 0.340820i
\(967\) 446319. + 214936.i 0.477301 + 0.229856i 0.657036 0.753859i \(-0.271810\pi\)
−0.179735 + 0.983715i \(0.557524\pi\)
\(968\) 320448. 665417.i 0.341985 0.710139i
\(969\) −72504.3 90917.6i −0.0772176 0.0968278i
\(970\) 114752. 143895.i 0.121960 0.152933i
\(971\) −313328. 150891.i −0.332323 0.160038i 0.260280 0.965533i \(-0.416185\pi\)
−0.592603 + 0.805495i \(0.701900\pi\)
\(972\) −236035. + 53873.4i −0.249830 + 0.0570220i
\(973\) −49223.1 + 11234.9i −0.0519928 + 0.0118670i
\(974\) 264115. + 210625.i 0.278404 + 0.222019i
\(975\) 740791. + 1.53827e6i 0.779268 + 1.61817i
\(976\) −208371. 47559.3i −0.218744 0.0499270i
\(977\) 171495. 82587.6i 0.179665 0.0865219i −0.341889 0.939740i \(-0.611067\pi\)
0.521554 + 0.853218i \(0.325353\pi\)
\(978\) 490182. 390907.i 0.512483 0.408692i
\(979\) −2.42602e6 + 553724.i −2.53122 + 0.577734i
\(980\) 125530. 100107.i 0.130706 0.104235i
\(981\) −122649. + 537362.i −0.127446 + 0.558379i
\(982\) 44723.8 0.0463784
\(983\) 1.58916e6i 1.64460i 0.569051 + 0.822302i \(0.307311\pi\)
−0.569051 + 0.822302i \(0.692689\pi\)
\(984\) 117762. 515949.i 0.121623 0.532864i
\(985\) 636166. + 507326.i 0.655689 + 0.522895i
\(986\) 6059.59 + 2918.15i 0.00623289 + 0.00300160i
\(987\) −324497. + 156269.i −0.333101 + 0.160413i
\(988\) 801184.i 0.820764i
\(989\) 718735. 614466.i 0.734812 0.628211i
\(990\) 437507. 0.446390
\(991\) −109074. 226495.i −0.111064 0.230628i 0.838027 0.545629i \(-0.183709\pi\)
−0.949091 + 0.315001i \(0.897995\pi\)
\(992\) −495092. + 1.02807e6i −0.503109 + 1.04472i
\(993\) −205938. + 258238.i −0.208851 + 0.261891i
\(994\) −47541.6 10851.1i −0.0481173 0.0109825i
\(995\) −688982. −0.695923
\(996\) 1.78835e6i 1.80274i
\(997\) −300388. 68561.7i −0.302199 0.0689749i 0.0687328 0.997635i \(-0.478104\pi\)
−0.370932 + 0.928660i \(0.620962\pi\)
\(998\) 53876.2 + 67558.6i 0.0540924 + 0.0678297i
\(999\) −515576. 2.25889e6i −0.516609 2.26341i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 43.5.f.a.2.6 78
43.22 odd 14 inner 43.5.f.a.22.6 yes 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.5.f.a.2.6 78 1.1 even 1 trivial
43.5.f.a.22.6 yes 78 43.22 odd 14 inner