Properties

Label 124.5.b.a.63.6
Level $124$
Weight $5$
Character 124.63
Analytic conductor $12.818$
Analytic rank $0$
Dimension $60$
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] = [124,5,Mod(63,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.63");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 124.b (of order \(2\), degree \(1\), 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: \(12.8178754224\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 63.6
Character \(\chi\) \(=\) 124.63
Dual form 124.5.b.a.63.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.71949 + 1.47153i) q^{2} -6.32028i q^{3} +(11.6692 - 10.9467i) q^{4} -34.2840 q^{5} +(9.30050 + 23.5082i) q^{6} +45.8539i q^{7} +(-27.2950 + 57.8877i) q^{8} +41.0540 q^{9} +O(q^{10})\) \(q+(-3.71949 + 1.47153i) q^{2} -6.32028i q^{3} +(11.6692 - 10.9467i) q^{4} -34.2840 q^{5} +(9.30050 + 23.5082i) q^{6} +45.8539i q^{7} +(-27.2950 + 57.8877i) q^{8} +41.0540 q^{9} +(127.519 - 50.4501i) q^{10} +74.0573i q^{11} +(-69.1862 - 73.7525i) q^{12} +233.059 q^{13} +(-67.4756 - 170.553i) q^{14} +216.685i q^{15} +(16.3397 - 255.478i) q^{16} -427.011 q^{17} +(-152.700 + 60.4123i) q^{18} -535.858i q^{19} +(-400.067 + 375.297i) q^{20} +289.810 q^{21} +(-108.978 - 275.455i) q^{22} -625.741i q^{23} +(365.867 + 172.512i) q^{24} +550.396 q^{25} +(-866.860 + 342.954i) q^{26} -771.416i q^{27} +(501.949 + 535.078i) q^{28} +1347.30 q^{29} +(-318.859 - 805.957i) q^{30} +172.601i q^{31} +(315.169 + 974.292i) q^{32} +468.063 q^{33} +(1588.26 - 628.361i) q^{34} -1572.06i q^{35} +(479.067 - 449.406i) q^{36} +345.621 q^{37} +(788.533 + 1993.12i) q^{38} -1473.00i q^{39} +(935.782 - 1984.62i) q^{40} +686.886 q^{41} +(-1077.94 + 426.465i) q^{42} -973.443i q^{43} +(810.683 + 864.188i) q^{44} -1407.50 q^{45} +(920.798 + 2327.44i) q^{46} -2390.64i q^{47} +(-1614.69 - 103.271i) q^{48} +298.417 q^{49} +(-2047.19 + 809.926i) q^{50} +2698.83i q^{51} +(2719.61 - 2551.22i) q^{52} +611.221 q^{53} +(1135.16 + 2869.27i) q^{54} -2538.98i q^{55} +(-2654.38 - 1251.58i) q^{56} -3386.77 q^{57} +(-5011.27 + 1982.60i) q^{58} +4381.91i q^{59} +(2371.98 + 2528.54i) q^{60} +3155.99 q^{61} +(-253.988 - 641.986i) q^{62} +1882.49i q^{63} +(-2605.97 - 3160.09i) q^{64} -7990.20 q^{65} +(-1740.95 + 688.770i) q^{66} +4953.41i q^{67} +(-4982.87 + 4674.36i) q^{68} -3954.86 q^{69} +(2313.34 + 5847.25i) q^{70} -6469.57i q^{71} +(-1120.57 + 2376.52i) q^{72} +7051.59 q^{73} +(-1285.53 + 508.593i) q^{74} -3478.66i q^{75} +(-5865.87 - 6253.03i) q^{76} -3395.82 q^{77} +(2167.56 + 5478.80i) q^{78} -8207.15i q^{79} +(-560.190 + 8758.82i) q^{80} -1550.19 q^{81} +(-2554.86 + 1010.77i) q^{82} -4403.54i q^{83} +(3381.84 - 3172.46i) q^{84} +14639.7 q^{85} +(1432.45 + 3620.71i) q^{86} -8515.33i q^{87} +(-4287.01 - 2021.39i) q^{88} +10025.2 q^{89} +(5235.17 - 2071.18i) q^{90} +10686.7i q^{91} +(-6849.80 - 7301.89i) q^{92} +1090.89 q^{93} +(3517.90 + 8891.95i) q^{94} +18371.4i q^{95} +(6157.80 - 1991.96i) q^{96} -13502.1 q^{97} +(-1109.96 + 439.130i) q^{98} +3040.35i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9} + 53 q^{10} + 130 q^{12} + 120 q^{13} - 231 q^{14} - 590 q^{16} - 648 q^{17} + 230 q^{18} + 1113 q^{20} + 608 q^{21} + 1080 q^{22} - 1028 q^{24} + 8340 q^{25} - 1554 q^{26} - 165 q^{28} - 168 q^{29} - 2238 q^{30} - 1674 q^{32} - 1120 q^{33} + 1844 q^{34} + 1966 q^{36} - 2248 q^{37} - 5055 q^{38} - 1716 q^{40} + 6072 q^{41} + 5794 q^{42} - 120 q^{44} - 4040 q^{45} + 8850 q^{46} + 2276 q^{48} - 17604 q^{49} - 4539 q^{50} + 5896 q^{52} + 3480 q^{53} + 5148 q^{54} - 396 q^{56} - 10912 q^{57} - 7484 q^{58} + 22812 q^{60} + 2200 q^{61} - 19299 q^{64} - 9168 q^{65} - 468 q^{66} - 21930 q^{68} + 6496 q^{69} - 9615 q^{70} - 10079 q^{72} + 13752 q^{73} - 2106 q^{74} + 20099 q^{76} + 16608 q^{77} + 39460 q^{78} - 5787 q^{80} + 20732 q^{81} - 30525 q^{82} - 21760 q^{84} - 21200 q^{85} - 13398 q^{86} + 34690 q^{88} + 22296 q^{89} - 25419 q^{90} - 18852 q^{92} + 3196 q^{94} + 20790 q^{96} + 12120 q^{97} + 21921 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.71949 + 1.47153i −0.929872 + 0.367883i
\(3\) 6.32028i 0.702254i −0.936328 0.351127i \(-0.885799\pi\)
0.936328 0.351127i \(-0.114201\pi\)
\(4\) 11.6692 10.9467i 0.729324 0.684169i
\(5\) −34.2840 −1.37136 −0.685681 0.727902i \(-0.740495\pi\)
−0.685681 + 0.727902i \(0.740495\pi\)
\(6\) 9.30050 + 23.5082i 0.258347 + 0.653006i
\(7\) 45.8539i 0.935795i 0.883783 + 0.467897i \(0.154988\pi\)
−0.883783 + 0.467897i \(0.845012\pi\)
\(8\) −27.2950 + 57.8877i −0.426484 + 0.904495i
\(9\) 41.0540 0.506840
\(10\) 127.519 50.4501i 1.27519 0.504501i
\(11\) 74.0573i 0.612044i 0.952024 + 0.306022i \(0.0989981\pi\)
−0.952024 + 0.306022i \(0.901002\pi\)
\(12\) −69.1862 73.7525i −0.480460 0.512170i
\(13\) 233.059 1.37905 0.689523 0.724264i \(-0.257820\pi\)
0.689523 + 0.724264i \(0.257820\pi\)
\(14\) −67.4756 170.553i −0.344263 0.870169i
\(15\) 216.685i 0.963044i
\(16\) 16.3397 255.478i 0.0638269 0.997961i
\(17\) −427.011 −1.47755 −0.738774 0.673953i \(-0.764595\pi\)
−0.738774 + 0.673953i \(0.764595\pi\)
\(18\) −152.700 + 60.4123i −0.471296 + 0.186458i
\(19\) 535.858i 1.48437i −0.670194 0.742186i \(-0.733789\pi\)
0.670194 0.742186i \(-0.266211\pi\)
\(20\) −400.067 + 375.297i −1.00017 + 0.938243i
\(21\) 289.810 0.657165
\(22\) −108.978 275.455i −0.225161 0.569122i
\(23\) 625.741i 1.18288i −0.806351 0.591438i \(-0.798561\pi\)
0.806351 0.591438i \(-0.201439\pi\)
\(24\) 365.867 + 172.512i 0.635185 + 0.299500i
\(25\) 550.396 0.880634
\(26\) −866.860 + 342.954i −1.28234 + 0.507328i
\(27\) 771.416i 1.05818i
\(28\) 501.949 + 535.078i 0.640241 + 0.682497i
\(29\) 1347.30 1.60202 0.801012 0.598649i \(-0.204296\pi\)
0.801012 + 0.598649i \(0.204296\pi\)
\(30\) −318.859 805.957i −0.354288 0.895508i
\(31\) 172.601i 0.179605i
\(32\) 315.169 + 974.292i 0.307782 + 0.951457i
\(33\) 468.063 0.429810
\(34\) 1588.26 628.361i 1.37393 0.543565i
\(35\) 1572.06i 1.28331i
\(36\) 479.067 449.406i 0.369650 0.346764i
\(37\) 345.621 0.252463 0.126231 0.992001i \(-0.459712\pi\)
0.126231 + 0.992001i \(0.459712\pi\)
\(38\) 788.533 + 1993.12i 0.546075 + 1.38028i
\(39\) 1473.00i 0.968440i
\(40\) 935.782 1984.62i 0.584864 1.24039i
\(41\) 686.886 0.408617 0.204309 0.978907i \(-0.434505\pi\)
0.204309 + 0.978907i \(0.434505\pi\)
\(42\) −1077.94 + 426.465i −0.611079 + 0.241760i
\(43\) 973.443i 0.526470i −0.964732 0.263235i \(-0.915211\pi\)
0.964732 0.263235i \(-0.0847895\pi\)
\(44\) 810.683 + 864.188i 0.418741 + 0.446378i
\(45\) −1407.50 −0.695061
\(46\) 920.798 + 2327.44i 0.435160 + 1.09992i
\(47\) 2390.64i 1.08223i −0.840950 0.541113i \(-0.818003\pi\)
0.840950 0.541113i \(-0.181997\pi\)
\(48\) −1614.69 103.271i −0.700822 0.0448227i
\(49\) 298.417 0.124288
\(50\) −2047.19 + 809.926i −0.818876 + 0.323970i
\(51\) 2698.83i 1.03761i
\(52\) 2719.61 2551.22i 1.00577 0.943500i
\(53\) 611.221 0.217594 0.108797 0.994064i \(-0.465300\pi\)
0.108797 + 0.994064i \(0.465300\pi\)
\(54\) 1135.16 + 2869.27i 0.389288 + 0.983975i
\(55\) 2538.98i 0.839333i
\(56\) −2654.38 1251.58i −0.846422 0.399101i
\(57\) −3386.77 −1.04240
\(58\) −5011.27 + 1982.60i −1.48968 + 0.589357i
\(59\) 4381.91i 1.25881i 0.777078 + 0.629404i \(0.216701\pi\)
−0.777078 + 0.629404i \(0.783299\pi\)
\(60\) 2371.98 + 2528.54i 0.658884 + 0.702371i
\(61\) 3155.99 0.848156 0.424078 0.905626i \(-0.360598\pi\)
0.424078 + 0.905626i \(0.360598\pi\)
\(62\) −253.988 641.986i −0.0660738 0.167010i
\(63\) 1882.49i 0.474298i
\(64\) −2605.97 3160.09i −0.636223 0.771505i
\(65\) −7990.20 −1.89117
\(66\) −1740.95 + 688.770i −0.399668 + 0.158120i
\(67\) 4953.41i 1.10346i 0.834024 + 0.551728i \(0.186031\pi\)
−0.834024 + 0.551728i \(0.813969\pi\)
\(68\) −4982.87 + 4674.36i −1.07761 + 1.01089i
\(69\) −3954.86 −0.830679
\(70\) 2313.34 + 5847.25i 0.472109 + 1.19332i
\(71\) 6469.57i 1.28339i −0.766960 0.641695i \(-0.778231\pi\)
0.766960 0.641695i \(-0.221769\pi\)
\(72\) −1120.57 + 2376.52i −0.216159 + 0.458434i
\(73\) 7051.59 1.32325 0.661624 0.749836i \(-0.269868\pi\)
0.661624 + 0.749836i \(0.269868\pi\)
\(74\) −1285.53 + 508.593i −0.234758 + 0.0928768i
\(75\) 3478.66i 0.618428i
\(76\) −5865.87 6253.03i −1.01556 1.08259i
\(77\) −3395.82 −0.572747
\(78\) 2167.56 + 5478.80i 0.356273 + 0.900526i
\(79\) 8207.15i 1.31504i −0.753438 0.657519i \(-0.771606\pi\)
0.753438 0.657519i \(-0.228394\pi\)
\(80\) −560.190 + 8758.82i −0.0875297 + 1.36857i
\(81\) −1550.19 −0.236273
\(82\) −2554.86 + 1010.77i −0.379962 + 0.150323i
\(83\) 4403.54i 0.639213i −0.947550 0.319606i \(-0.896449\pi\)
0.947550 0.319606i \(-0.103551\pi\)
\(84\) 3381.84 3172.46i 0.479286 0.449612i
\(85\) 14639.7 2.02625
\(86\) 1432.45 + 3620.71i 0.193679 + 0.489550i
\(87\) 8515.33i 1.12503i
\(88\) −4287.01 2021.39i −0.553591 0.261027i
\(89\) 10025.2 1.26565 0.632824 0.774296i \(-0.281896\pi\)
0.632824 + 0.774296i \(0.281896\pi\)
\(90\) 5235.17 2071.18i 0.646318 0.255701i
\(91\) 10686.7i 1.29050i
\(92\) −6849.80 7301.89i −0.809286 0.862699i
\(93\) 1090.89 0.126128
\(94\) 3517.90 + 8891.95i 0.398133 + 1.00633i
\(95\) 18371.4i 2.03561i
\(96\) 6157.80 1991.96i 0.668164 0.216141i
\(97\) −13502.1 −1.43502 −0.717512 0.696546i \(-0.754719\pi\)
−0.717512 + 0.696546i \(0.754719\pi\)
\(98\) −1109.96 + 439.130i −0.115572 + 0.0457236i
\(99\) 3040.35i 0.310208i
\(100\) 6422.67 6025.02i 0.642267 0.602502i
\(101\) −12189.6 −1.19494 −0.597470 0.801892i \(-0.703827\pi\)
−0.597470 + 0.801892i \(0.703827\pi\)
\(102\) −3971.42 10038.3i −0.381720 0.964848i
\(103\) 13419.0i 1.26487i −0.774613 0.632436i \(-0.782055\pi\)
0.774613 0.632436i \(-0.217945\pi\)
\(104\) −6361.33 + 13491.2i −0.588141 + 1.24734i
\(105\) −9935.85 −0.901211
\(106\) −2273.43 + 899.431i −0.202334 + 0.0800491i
\(107\) 12335.1i 1.07740i 0.842498 + 0.538699i \(0.181084\pi\)
−0.842498 + 0.538699i \(0.818916\pi\)
\(108\) −8444.46 9001.79i −0.723976 0.771759i
\(109\) 11823.9 0.995193 0.497597 0.867409i \(-0.334216\pi\)
0.497597 + 0.867409i \(0.334216\pi\)
\(110\) 3736.20 + 9443.72i 0.308777 + 0.780473i
\(111\) 2184.43i 0.177293i
\(112\) 11714.7 + 749.239i 0.933887 + 0.0597288i
\(113\) 10630.5 0.832524 0.416262 0.909245i \(-0.363340\pi\)
0.416262 + 0.909245i \(0.363340\pi\)
\(114\) 12597.1 4983.75i 0.969303 0.383483i
\(115\) 21452.9i 1.62215i
\(116\) 15721.9 14748.5i 1.16839 1.09605i
\(117\) 9568.01 0.698956
\(118\) −6448.12 16298.5i −0.463094 1.17053i
\(119\) 19580.2i 1.38268i
\(120\) −12543.4 5914.41i −0.871068 0.410723i
\(121\) 9156.52 0.625403
\(122\) −11738.7 + 4644.14i −0.788676 + 0.312022i
\(123\) 4341.31i 0.286953i
\(124\) 1889.41 + 2014.11i 0.122880 + 0.130990i
\(125\) 2557.73 0.163695
\(126\) −2770.14 7001.90i −0.174486 0.441036i
\(127\) 15848.4i 0.982602i 0.870990 + 0.491301i \(0.163479\pi\)
−0.870990 + 0.491301i \(0.836521\pi\)
\(128\) 14343.0 + 7919.13i 0.875430 + 0.483345i
\(129\) −6152.43 −0.369715
\(130\) 29719.5 11757.8i 1.75855 0.695730i
\(131\) 32191.2i 1.87583i −0.346860 0.937917i \(-0.612752\pi\)
0.346860 0.937917i \(-0.387248\pi\)
\(132\) 5461.91 5123.74i 0.313471 0.294062i
\(133\) 24571.2 1.38907
\(134\) −7289.11 18424.2i −0.405943 1.02607i
\(135\) 26447.3i 1.45115i
\(136\) 11655.3 24718.7i 0.630150 1.33644i
\(137\) −20862.7 −1.11155 −0.555776 0.831332i \(-0.687579\pi\)
−0.555776 + 0.831332i \(0.687579\pi\)
\(138\) 14710.1 5819.71i 0.772425 0.305593i
\(139\) 224.364i 0.0116124i −0.999983 0.00580621i \(-0.998152\pi\)
0.999983 0.00580621i \(-0.00184819\pi\)
\(140\) −17208.8 18344.6i −0.878002 0.935951i
\(141\) −15109.5 −0.759997
\(142\) 9520.18 + 24063.5i 0.472138 + 1.19339i
\(143\) 17259.7i 0.844037i
\(144\) 670.810 10488.4i 0.0323500 0.505806i
\(145\) −46190.9 −2.19695
\(146\) −26228.3 + 10376.6i −1.23045 + 0.486801i
\(147\) 1886.08i 0.0872820i
\(148\) 4033.12 3783.41i 0.184127 0.172727i
\(149\) 3811.74 0.171692 0.0858462 0.996308i \(-0.472641\pi\)
0.0858462 + 0.996308i \(0.472641\pi\)
\(150\) 5118.96 + 12938.8i 0.227509 + 0.575059i
\(151\) 9236.23i 0.405080i −0.979274 0.202540i \(-0.935080\pi\)
0.979274 0.202540i \(-0.0649196\pi\)
\(152\) 31019.6 + 14626.2i 1.34261 + 0.633060i
\(153\) −17530.5 −0.748880
\(154\) 12630.7 4997.06i 0.532582 0.210704i
\(155\) 5917.45i 0.246304i
\(156\) −16124.5 17188.7i −0.662576 0.706307i
\(157\) −29667.1 −1.20358 −0.601790 0.798654i \(-0.705546\pi\)
−0.601790 + 0.798654i \(0.705546\pi\)
\(158\) 12077.1 + 30526.4i 0.483780 + 1.22282i
\(159\) 3863.09i 0.152806i
\(160\) −10805.3 33402.7i −0.422081 1.30479i
\(161\) 28692.7 1.10693
\(162\) 5765.91 2281.15i 0.219704 0.0869210i
\(163\) 20133.9i 0.757796i 0.925438 + 0.378898i \(0.123697\pi\)
−0.925438 + 0.378898i \(0.876303\pi\)
\(164\) 8015.39 7519.13i 0.298014 0.279563i
\(165\) −16047.1 −0.589425
\(166\) 6479.95 + 16378.9i 0.235156 + 0.594386i
\(167\) 7545.07i 0.270539i 0.990809 + 0.135270i \(0.0431901\pi\)
−0.990809 + 0.135270i \(0.956810\pi\)
\(168\) −7910.35 + 16776.4i −0.280270 + 0.594403i
\(169\) 25755.4 0.901769
\(170\) −54452.1 + 21542.8i −1.88416 + 0.745424i
\(171\) 21999.1i 0.752339i
\(172\) −10656.0 11359.3i −0.360194 0.383967i
\(173\) −6029.10 −0.201447 −0.100723 0.994914i \(-0.532116\pi\)
−0.100723 + 0.994914i \(0.532116\pi\)
\(174\) 12530.6 + 31672.7i 0.413878 + 1.04613i
\(175\) 25237.8i 0.824092i
\(176\) 18920.0 + 1210.07i 0.610796 + 0.0390648i
\(177\) 27694.9 0.884002
\(178\) −37288.6 + 14752.4i −1.17689 + 0.465610i
\(179\) 59397.2i 1.85379i 0.375325 + 0.926893i \(0.377531\pi\)
−0.375325 + 0.926893i \(0.622469\pi\)
\(180\) −16424.4 + 15407.5i −0.506925 + 0.475539i
\(181\) −3752.62 −0.114545 −0.0572727 0.998359i \(-0.518240\pi\)
−0.0572727 + 0.998359i \(0.518240\pi\)
\(182\) −15725.8 39748.9i −0.474755 1.20000i
\(183\) 19946.7i 0.595620i
\(184\) 36222.7 + 17079.6i 1.06991 + 0.504477i
\(185\) −11849.3 −0.346218
\(186\) −4057.53 + 1605.27i −0.117283 + 0.0464005i
\(187\) 31623.3i 0.904324i
\(188\) −26169.6 27896.8i −0.740425 0.789294i
\(189\) 35372.5 0.990243
\(190\) −27034.1 68332.1i −0.748867 1.89286i
\(191\) 8999.22i 0.246682i −0.992364 0.123341i \(-0.960639\pi\)
0.992364 0.123341i \(-0.0393610\pi\)
\(192\) −19972.6 + 16470.5i −0.541792 + 0.446790i
\(193\) −2072.92 −0.0556504 −0.0278252 0.999613i \(-0.508858\pi\)
−0.0278252 + 0.999613i \(0.508858\pi\)
\(194\) 50221.0 19868.8i 1.33439 0.527921i
\(195\) 50500.3i 1.32808i
\(196\) 3482.28 3266.68i 0.0906465 0.0850342i
\(197\) 31507.8 0.811869 0.405935 0.913902i \(-0.366946\pi\)
0.405935 + 0.913902i \(0.366946\pi\)
\(198\) −4473.97 11308.5i −0.114120 0.288454i
\(199\) 10209.6i 0.257811i −0.991657 0.128906i \(-0.958854\pi\)
0.991657 0.128906i \(-0.0411465\pi\)
\(200\) −15023.0 + 31861.2i −0.375576 + 0.796529i
\(201\) 31307.0 0.774906
\(202\) 45339.0 17937.4i 1.11114 0.439598i
\(203\) 61779.1i 1.49916i
\(204\) 29543.3 + 31493.2i 0.709902 + 0.756756i
\(205\) −23549.2 −0.560362
\(206\) 19746.5 + 49911.9i 0.465325 + 1.17617i
\(207\) 25689.2i 0.599528i
\(208\) 3808.11 59541.4i 0.0880202 1.37623i
\(209\) 39684.2 0.908500
\(210\) 36956.3 14620.9i 0.838011 0.331540i
\(211\) 46275.0i 1.03940i −0.854350 0.519698i \(-0.826044\pi\)
0.854350 0.519698i \(-0.173956\pi\)
\(212\) 7132.45 6690.85i 0.158696 0.148871i
\(213\) −40889.5 −0.901265
\(214\) −18151.5 45880.4i −0.396357 1.00184i
\(215\) 33373.6i 0.721981i
\(216\) 44655.5 + 21055.8i 0.957122 + 0.451298i
\(217\) −7914.42 −0.168074
\(218\) −43978.8 + 17399.2i −0.925403 + 0.366115i
\(219\) 44568.0i 0.929256i
\(220\) −27793.5 29627.9i −0.574246 0.612146i
\(221\) −99518.8 −2.03761
\(222\) 3214.45 + 8124.94i 0.0652231 + 0.164860i
\(223\) 34523.1i 0.694225i 0.937824 + 0.347112i \(0.112838\pi\)
−0.937824 + 0.347112i \(0.887162\pi\)
\(224\) −44675.1 + 14451.7i −0.890368 + 0.288021i
\(225\) 22596.0 0.446340
\(226\) −39540.0 + 15643.1i −0.774141 + 0.306272i
\(227\) 26009.3i 0.504751i 0.967629 + 0.252376i \(0.0812118\pi\)
−0.967629 + 0.252376i \(0.918788\pi\)
\(228\) −39520.9 + 37074.0i −0.760251 + 0.713181i
\(229\) 86590.4 1.65120 0.825598 0.564259i \(-0.190838\pi\)
0.825598 + 0.564259i \(0.190838\pi\)
\(230\) −31568.7 79794.0i −0.596762 1.50839i
\(231\) 21462.5i 0.402214i
\(232\) −36774.5 + 77992.2i −0.683237 + 1.44902i
\(233\) −27675.0 −0.509772 −0.254886 0.966971i \(-0.582038\pi\)
−0.254886 + 0.966971i \(0.582038\pi\)
\(234\) −35588.1 + 14079.6i −0.649939 + 0.257134i
\(235\) 81960.8i 1.48412i
\(236\) 47967.4 + 51133.3i 0.861236 + 0.918078i
\(237\) −51871.5 −0.923490
\(238\) 28812.8 + 72828.1i 0.508665 + 1.28572i
\(239\) 3547.80i 0.0621102i 0.999518 + 0.0310551i \(0.00988674\pi\)
−0.999518 + 0.0310551i \(0.990113\pi\)
\(240\) 55358.2 + 3540.56i 0.961080 + 0.0614681i
\(241\) −76033.0 −1.30909 −0.654543 0.756025i \(-0.727139\pi\)
−0.654543 + 0.756025i \(0.727139\pi\)
\(242\) −34057.6 + 13474.1i −0.581544 + 0.230075i
\(243\) 52687.1i 0.892260i
\(244\) 36827.8 34547.6i 0.618580 0.580281i
\(245\) −10230.9 −0.170444
\(246\) 6388.38 + 16147.5i 0.105565 + 0.266829i
\(247\) 124886.i 2.04702i
\(248\) −9991.46 4711.13i −0.162452 0.0765988i
\(249\) −27831.6 −0.448890
\(250\) −9513.44 + 3763.78i −0.152215 + 0.0602205i
\(251\) 61927.9i 0.982967i −0.870887 0.491484i \(-0.836455\pi\)
0.870887 0.491484i \(-0.163545\pi\)
\(252\) 20607.0 + 21967.1i 0.324500 + 0.345917i
\(253\) 46340.7 0.723971
\(254\) −23321.4 58947.9i −0.361483 0.913694i
\(255\) 92526.9i 1.42294i
\(256\) −65002.0 8348.86i −0.991852 0.127393i
\(257\) 4753.43 0.0719683 0.0359841 0.999352i \(-0.488543\pi\)
0.0359841 + 0.999352i \(0.488543\pi\)
\(258\) 22883.9 9053.51i 0.343788 0.136012i
\(259\) 15848.1i 0.236253i
\(260\) −93239.1 + 87466.3i −1.37928 + 1.29388i
\(261\) 55312.2 0.811969
\(262\) 47370.4 + 119735.i 0.690088 + 1.74429i
\(263\) 40642.1i 0.587578i −0.955870 0.293789i \(-0.905084\pi\)
0.955870 0.293789i \(-0.0949162\pi\)
\(264\) −12775.8 + 27095.1i −0.183307 + 0.388761i
\(265\) −20955.1 −0.298400
\(266\) −91392.3 + 36157.3i −1.29165 + 0.511014i
\(267\) 63362.0i 0.888805i
\(268\) 54223.5 + 57802.3i 0.754950 + 0.804777i
\(269\) −1417.58 −0.0195904 −0.00979520 0.999952i \(-0.503118\pi\)
−0.00979520 + 0.999952i \(0.503118\pi\)
\(270\) −38918.0 98370.3i −0.533855 1.34939i
\(271\) 8685.84i 0.118270i −0.998250 0.0591348i \(-0.981166\pi\)
0.998250 0.0591348i \(-0.0188342\pi\)
\(272\) −6977.23 + 109092.i −0.0943073 + 1.47454i
\(273\) 67542.7 0.906261
\(274\) 77598.7 30700.2i 1.03360 0.408922i
\(275\) 40760.8i 0.538986i
\(276\) −46150.0 + 43292.7i −0.605834 + 0.568324i
\(277\) 64381.4 0.839075 0.419538 0.907738i \(-0.362192\pi\)
0.419538 + 0.907738i \(0.362192\pi\)
\(278\) 330.159 + 834.518i 0.00427202 + 0.0107981i
\(279\) 7085.95i 0.0910311i
\(280\) 91002.8 + 42909.3i 1.16075 + 0.547312i
\(281\) −104740. −1.32647 −0.663237 0.748410i \(-0.730818\pi\)
−0.663237 + 0.748410i \(0.730818\pi\)
\(282\) 56199.6 22234.1i 0.706700 0.279590i
\(283\) 86277.0i 1.07726i −0.842541 0.538632i \(-0.818941\pi\)
0.842541 0.538632i \(-0.181059\pi\)
\(284\) −70820.4 75494.6i −0.878055 0.936007i
\(285\) 116112. 1.42951
\(286\) −25398.2 64197.3i −0.310507 0.784846i
\(287\) 31496.4i 0.382382i
\(288\) 12939.0 + 39998.6i 0.155996 + 0.482236i
\(289\) 98817.7 1.18315
\(290\) 171807. 67971.5i 2.04289 0.808222i
\(291\) 85337.3i 1.00775i
\(292\) 82286.3 77191.6i 0.965077 0.905325i
\(293\) 118.705 0.00138272 0.000691358 1.00000i \(-0.499780\pi\)
0.000691358 1.00000i \(0.499780\pi\)
\(294\) 2775.42 + 7015.24i 0.0321096 + 0.0811611i
\(295\) 150230.i 1.72628i
\(296\) −9433.73 + 20007.2i −0.107671 + 0.228351i
\(297\) 57129.0 0.647655
\(298\) −14177.7 + 5609.10i −0.159652 + 0.0631627i
\(299\) 145835.i 1.63124i
\(300\) −38079.8 40593.1i −0.423109 0.451034i
\(301\) 44636.2 0.492668
\(302\) 13591.4 + 34354.0i 0.149022 + 0.376673i
\(303\) 77041.6i 0.839150i
\(304\) −136900. 8755.75i −1.48134 0.0947428i
\(305\) −108200. −1.16313
\(306\) 65204.6 25796.8i 0.696363 0.275500i
\(307\) 56068.2i 0.594895i −0.954738 0.297447i \(-0.903865\pi\)
0.954738 0.297447i \(-0.0961353\pi\)
\(308\) −39626.4 + 37173.0i −0.417718 + 0.391856i
\(309\) −84812.0 −0.888260
\(310\) 8707.72 + 22009.9i 0.0906110 + 0.229031i
\(311\) 11136.2i 0.115137i −0.998342 0.0575686i \(-0.981665\pi\)
0.998342 0.0575686i \(-0.0183348\pi\)
\(312\) 85268.4 + 40205.4i 0.875950 + 0.413024i
\(313\) −125438. −1.28038 −0.640192 0.768215i \(-0.721145\pi\)
−0.640192 + 0.768215i \(0.721145\pi\)
\(314\) 110346. 43656.0i 1.11918 0.442777i
\(315\) 64539.3i 0.650434i
\(316\) −89841.2 95770.8i −0.899708 0.959089i
\(317\) 44565.5 0.443486 0.221743 0.975105i \(-0.428825\pi\)
0.221743 + 0.975105i \(0.428825\pi\)
\(318\) 5684.66 + 14368.7i 0.0562148 + 0.142090i
\(319\) 99777.5i 0.980508i
\(320\) 89343.2 + 108341.i 0.872492 + 1.05801i
\(321\) 77961.5 0.756607
\(322\) −106722. + 42222.2i −1.02930 + 0.407220i
\(323\) 228817.i 2.19323i
\(324\) −18089.4 + 16969.5i −0.172320 + 0.161651i
\(325\) 128275. 1.21443
\(326\) −29627.7 74887.7i −0.278780 0.704653i
\(327\) 74730.3i 0.698878i
\(328\) −18748.5 + 39762.2i −0.174269 + 0.369592i
\(329\) 109620. 1.01274
\(330\) 59687.0 23613.8i 0.548090 0.216839i
\(331\) 76858.6i 0.701514i 0.936466 + 0.350757i \(0.114076\pi\)
−0.936466 + 0.350757i \(0.885924\pi\)
\(332\) −48204.2 51385.7i −0.437329 0.466193i
\(333\) 14189.2 0.127958
\(334\) −11102.8 28063.8i −0.0995269 0.251567i
\(335\) 169823.i 1.51324i
\(336\) 4735.40 74040.0i 0.0419448 0.655825i
\(337\) −140790. −1.23968 −0.619842 0.784727i \(-0.712803\pi\)
−0.619842 + 0.784727i \(0.712803\pi\)
\(338\) −95797.0 + 37900.0i −0.838530 + 0.331746i
\(339\) 67187.8i 0.584643i
\(340\) 170833. 160256.i 1.47779 1.38630i
\(341\) −12782.3 −0.109926
\(342\) 32372.4 + 81825.5i 0.276773 + 0.699579i
\(343\) 123779.i 1.05210i
\(344\) 56350.4 + 26570.1i 0.476190 + 0.224531i
\(345\) 135589. 1.13916
\(346\) 22425.2 8872.02i 0.187320 0.0741089i
\(347\) 86322.6i 0.716911i 0.933547 + 0.358456i \(0.116697\pi\)
−0.933547 + 0.358456i \(0.883303\pi\)
\(348\) −93214.7 99366.9i −0.769708 0.820509i
\(349\) −89643.9 −0.735986 −0.367993 0.929828i \(-0.619955\pi\)
−0.367993 + 0.929828i \(0.619955\pi\)
\(350\) −37138.3 93871.8i −0.303170 0.766300i
\(351\) 179785.i 1.45928i
\(352\) −72153.4 + 23340.6i −0.582333 + 0.188376i
\(353\) 117441. 0.942478 0.471239 0.882006i \(-0.343807\pi\)
0.471239 + 0.882006i \(0.343807\pi\)
\(354\) −103011. + 40754.0i −0.822009 + 0.325209i
\(355\) 221803.i 1.75999i
\(356\) 116986. 109743.i 0.923067 0.865916i
\(357\) −123752. −0.970993
\(358\) −87404.9 220927.i −0.681977 1.72378i
\(359\) 208824.i 1.62029i −0.586233 0.810143i \(-0.699390\pi\)
0.586233 0.810143i \(-0.300610\pi\)
\(360\) 38417.6 81476.8i 0.296432 0.628679i
\(361\) −156823. −1.20336
\(362\) 13957.8 5522.11i 0.106513 0.0421393i
\(363\) 57871.8i 0.439191i
\(364\) 116984. + 124705.i 0.882922 + 0.941196i
\(365\) −241757. −1.81465
\(366\) 29352.3 + 74191.6i 0.219119 + 0.553851i
\(367\) 25998.4i 0.193025i 0.995332 + 0.0965127i \(0.0307688\pi\)
−0.995332 + 0.0965127i \(0.969231\pi\)
\(368\) −159863. 10224.4i −1.18046 0.0754992i
\(369\) 28199.4 0.207104
\(370\) 44073.3 17436.6i 0.321938 0.127368i
\(371\) 28026.9i 0.203623i
\(372\) 12729.7 11941.6i 0.0919885 0.0862931i
\(373\) 61928.2 0.445114 0.222557 0.974920i \(-0.428560\pi\)
0.222557 + 0.974920i \(0.428560\pi\)
\(374\) 46534.7 + 117623.i 0.332686 + 0.840906i
\(375\) 16165.6i 0.114955i
\(376\) 138389. + 65252.4i 0.978869 + 0.461552i
\(377\) 314001. 2.20926
\(378\) −131567. + 52051.7i −0.920799 + 0.364294i
\(379\) 215762.i 1.50210i 0.660248 + 0.751048i \(0.270451\pi\)
−0.660248 + 0.751048i \(0.729549\pi\)
\(380\) 201106. + 214379.i 1.39270 + 1.48462i
\(381\) 100166. 0.690036
\(382\) 13242.6 + 33472.5i 0.0907503 + 0.229383i
\(383\) 104151.i 0.710013i 0.934864 + 0.355006i \(0.115521\pi\)
−0.934864 + 0.355006i \(0.884479\pi\)
\(384\) 50051.1 90652.1i 0.339431 0.614774i
\(385\) 116422. 0.785444
\(386\) 7710.20 3050.37i 0.0517477 0.0204728i
\(387\) 39963.8i 0.266836i
\(388\) −157559. + 147804.i −1.04660 + 0.981798i
\(389\) 42415.3 0.280300 0.140150 0.990130i \(-0.455241\pi\)
0.140150 + 0.990130i \(0.455241\pi\)
\(390\) −74312.9 187835.i −0.488579 1.23495i
\(391\) 267199.i 1.74776i
\(392\) −8145.27 + 17274.6i −0.0530070 + 0.112418i
\(393\) −203457. −1.31731
\(394\) −117193. + 46364.8i −0.754934 + 0.298673i
\(395\) 281374.i 1.80339i
\(396\) 33281.8 + 35478.4i 0.212235 + 0.226242i
\(397\) −159398. −1.01135 −0.505674 0.862724i \(-0.668756\pi\)
−0.505674 + 0.862724i \(0.668756\pi\)
\(398\) 15023.7 + 37974.5i 0.0948445 + 0.239732i
\(399\) 155297.i 0.975477i
\(400\) 8993.29 140614.i 0.0562081 0.878838i
\(401\) −16058.4 −0.0998650 −0.0499325 0.998753i \(-0.515901\pi\)
−0.0499325 + 0.998753i \(0.515901\pi\)
\(402\) −116446. + 46069.2i −0.720563 + 0.285075i
\(403\) 40226.1i 0.247684i
\(404\) −142242. + 133436.i −0.871498 + 0.817540i
\(405\) 53146.8 0.324016
\(406\) −90909.9 229787.i −0.551517 1.39403i
\(407\) 25595.8i 0.154518i
\(408\) −156229. 73664.5i −0.938516 0.442525i
\(409\) 125083. 0.747741 0.373870 0.927481i \(-0.378030\pi\)
0.373870 + 0.927481i \(0.378030\pi\)
\(410\) 87591.0 34653.4i 0.521065 0.206148i
\(411\) 131858.i 0.780592i
\(412\) −146894. 156589.i −0.865385 0.922501i
\(413\) −200928. −1.17799
\(414\) 37802.5 + 95550.7i 0.220556 + 0.557485i
\(415\) 150971.i 0.876592i
\(416\) 73452.9 + 227067.i 0.424446 + 1.31210i
\(417\) −1418.04 −0.00815487
\(418\) −147605. + 58396.6i −0.844789 + 0.334222i
\(419\) 181403.i 1.03328i −0.856204 0.516638i \(-0.827183\pi\)
0.856204 0.516638i \(-0.172817\pi\)
\(420\) −115943. + 108765.i −0.657275 + 0.616580i
\(421\) −76021.6 −0.428916 −0.214458 0.976733i \(-0.568799\pi\)
−0.214458 + 0.976733i \(0.568799\pi\)
\(422\) 68095.2 + 172119.i 0.382377 + 0.966506i
\(423\) 98145.4i 0.548516i
\(424\) −16683.3 + 35382.2i −0.0928002 + 0.196813i
\(425\) −235025. −1.30118
\(426\) 152088. 60170.3i 0.838062 0.331560i
\(427\) 144714.i 0.793699i
\(428\) 135029. + 143941.i 0.737122 + 0.785772i
\(429\) 109086. 0.592728
\(430\) −49110.3 124133.i −0.265605 0.671350i
\(431\) 346086.i 1.86307i −0.363651 0.931535i \(-0.618470\pi\)
0.363651 0.931535i \(-0.381530\pi\)
\(432\) −197080. 12604.7i −1.05603 0.0675406i
\(433\) −236255. −1.26010 −0.630049 0.776555i \(-0.716965\pi\)
−0.630049 + 0.776555i \(0.716965\pi\)
\(434\) 29437.6 11646.3i 0.156287 0.0618315i
\(435\) 291940.i 1.54282i
\(436\) 137975. 129433.i 0.725818 0.680880i
\(437\) −335308. −1.75583
\(438\) 65583.3 + 165770.i 0.341858 + 0.864089i
\(439\) 281888.i 1.46268i 0.682015 + 0.731338i \(0.261104\pi\)
−0.682015 + 0.731338i \(0.738896\pi\)
\(440\) 146976. + 69301.5i 0.759173 + 0.357962i
\(441\) 12251.2 0.0629943
\(442\) 370159. 146445.i 1.89471 0.749601i
\(443\) 11327.7i 0.0577209i 0.999583 + 0.0288605i \(0.00918785\pi\)
−0.999583 + 0.0288605i \(0.990812\pi\)
\(444\) −23912.2 25490.5i −0.121298 0.129304i
\(445\) −343704. −1.73566
\(446\) −50801.9 128408.i −0.255394 0.645540i
\(447\) 24091.3i 0.120572i
\(448\) 144902. 119494.i 0.721970 0.595374i
\(449\) 49613.7 0.246098 0.123049 0.992401i \(-0.460733\pi\)
0.123049 + 0.992401i \(0.460733\pi\)
\(450\) −84045.5 + 33250.7i −0.415039 + 0.164201i
\(451\) 50868.9i 0.250092i
\(452\) 124049. 116369.i 0.607180 0.569587i
\(453\) −58375.6 −0.284469
\(454\) −38273.6 96741.4i −0.185689 0.469354i
\(455\) 366382.i 1.76975i
\(456\) 92441.9 196053.i 0.444569 0.942850i
\(457\) −96047.8 −0.459891 −0.229946 0.973203i \(-0.573855\pi\)
−0.229946 + 0.973203i \(0.573855\pi\)
\(458\) −322072. + 127421.i −1.53540 + 0.607447i
\(459\) 329403.i 1.56352i
\(460\) 234839. + 250338.i 1.10982 + 1.18307i
\(461\) 261473. 1.23034 0.615169 0.788395i \(-0.289088\pi\)
0.615169 + 0.788395i \(0.289088\pi\)
\(462\) −31582.8 79829.6i −0.147968 0.374007i
\(463\) 203922.i 0.951266i 0.879644 + 0.475633i \(0.157781\pi\)
−0.879644 + 0.475633i \(0.842219\pi\)
\(464\) 22014.5 344206.i 0.102252 1.59876i
\(465\) −37400.0 −0.172968
\(466\) 102937. 40724.7i 0.474023 0.187537i
\(467\) 318175.i 1.45892i 0.684021 + 0.729462i \(0.260230\pi\)
−0.684021 + 0.729462i \(0.739770\pi\)
\(468\) 111651. 104738.i 0.509765 0.478204i
\(469\) −227133. −1.03261
\(470\) −120608. 304852.i −0.545984 1.38005i
\(471\) 187504.i 0.845219i
\(472\) −253659. 119604.i −1.13859 0.536861i
\(473\) 72090.5 0.322223
\(474\) 192936. 76330.6i 0.858728 0.339737i
\(475\) 294934.i 1.30719i
\(476\) −214338. 228484.i −0.945987 1.00842i
\(477\) 25093.1 0.110285
\(478\) −5220.70 13196.0i −0.0228493 0.0577546i
\(479\) 326676.i 1.42379i −0.702286 0.711895i \(-0.747837\pi\)
0.702286 0.711895i \(-0.252163\pi\)
\(480\) −211114. + 68292.3i −0.916295 + 0.296408i
\(481\) 80550.1 0.348158
\(482\) 282804. 111885.i 1.21728 0.481591i
\(483\) 181346.i 0.777344i
\(484\) 106849. 100234.i 0.456121 0.427881i
\(485\) 462908. 1.96794
\(486\) 77530.7 + 195969.i 0.328247 + 0.829687i
\(487\) 312827.i 1.31901i −0.751702 0.659503i \(-0.770767\pi\)
0.751702 0.659503i \(-0.229233\pi\)
\(488\) −86142.6 + 182693.i −0.361725 + 0.767153i
\(489\) 127252. 0.532165
\(490\) 38053.8 15055.1i 0.158492 0.0627036i
\(491\) 178766.i 0.741517i 0.928729 + 0.370759i \(0.120902\pi\)
−0.928729 + 0.370759i \(0.879098\pi\)
\(492\) −47523.0 50659.6i −0.196324 0.209282i
\(493\) −575313. −2.36707
\(494\) 183774. + 464514.i 0.753063 + 1.90346i
\(495\) 104236.i 0.425408i
\(496\) 44095.7 + 2820.24i 0.179239 + 0.0114636i
\(497\) 296655. 1.20099
\(498\) 103519. 40955.1i 0.417410 0.165139i
\(499\) 122318.i 0.491236i −0.969367 0.245618i \(-0.921009\pi\)
0.969367 0.245618i \(-0.0789908\pi\)
\(500\) 29846.6 27998.7i 0.119386 0.111995i
\(501\) 47687.0 0.189987
\(502\) 91129.0 + 230340.i 0.361617 + 0.914034i
\(503\) 248135.i 0.980734i −0.871516 0.490367i \(-0.836863\pi\)
0.871516 0.490367i \(-0.163137\pi\)
\(504\) −108973. 51382.5i −0.429000 0.202280i
\(505\) 417908. 1.63869
\(506\) −172364. + 68191.8i −0.673201 + 0.266337i
\(507\) 162782.i 0.633271i
\(508\) 173487. + 184938.i 0.672265 + 0.716635i
\(509\) 334708. 1.29191 0.645953 0.763377i \(-0.276460\pi\)
0.645953 + 0.763377i \(0.276460\pi\)
\(510\) 136156. + 344153.i 0.523477 + 1.32316i
\(511\) 323343.i 1.23829i
\(512\) 254060. 64599.1i 0.969162 0.246426i
\(513\) −413369. −1.57074
\(514\) −17680.3 + 6994.83i −0.0669213 + 0.0264759i
\(515\) 460058.i 1.73460i
\(516\) −71793.9 + 67348.8i −0.269642 + 0.252948i
\(517\) 177044. 0.662370
\(518\) −23321.0 58946.8i −0.0869136 0.219685i
\(519\) 38105.6i 0.141467i
\(520\) 218092. 462534.i 0.806554 1.71056i
\(521\) 340339. 1.25382 0.626912 0.779090i \(-0.284318\pi\)
0.626912 + 0.779090i \(0.284318\pi\)
\(522\) −205733. + 81393.6i −0.755027 + 0.298710i
\(523\) 28259.2i 0.103313i 0.998665 + 0.0516567i \(0.0164502\pi\)
−0.998665 + 0.0516567i \(0.983550\pi\)
\(524\) −352387. 375645.i −1.28339 1.36809i
\(525\) 159510. 0.578722
\(526\) 59806.2 + 151168.i 0.216160 + 0.546372i
\(527\) 73702.5i 0.265375i
\(528\) 7648.00 119580.i 0.0274334 0.428933i
\(529\) −111711. −0.399194
\(530\) 77942.3 30836.2i 0.277474 0.109776i
\(531\) 179895.i 0.638014i
\(532\) 286726. 268973.i 1.01308 0.950356i
\(533\) 160085. 0.563502
\(534\) 93239.3 + 235674.i 0.326977 + 0.826475i
\(535\) 422898.i 1.47750i
\(536\) −286742. 135203.i −0.998070 0.470606i
\(537\) 375407. 1.30183
\(538\) 5272.68 2086.02i 0.0182166 0.00720698i
\(539\) 22099.9i 0.0760700i
\(540\) 289510. + 308618.i 0.992833 + 1.05836i
\(541\) 496161. 1.69523 0.847614 0.530614i \(-0.178039\pi\)
0.847614 + 0.530614i \(0.178039\pi\)
\(542\) 12781.5 + 32306.9i 0.0435094 + 0.109976i
\(543\) 23717.6i 0.0804400i
\(544\) −134581. 416034.i −0.454763 1.40582i
\(545\) −405371. −1.36477
\(546\) −251224. + 99391.4i −0.842707 + 0.333398i
\(547\) 122088.i 0.408034i 0.978967 + 0.204017i \(0.0653998\pi\)
−0.978967 + 0.204017i \(0.934600\pi\)
\(548\) −243451. + 228378.i −0.810682 + 0.760489i
\(549\) 129566. 0.429879
\(550\) −59980.9 151609.i −0.198284 0.501188i
\(551\) 721962.i 2.37800i
\(552\) 107948. 228938.i 0.354271 0.751345i
\(553\) 376330. 1.23061
\(554\) −239466. + 94739.4i −0.780233 + 0.308682i
\(555\) 74890.9i 0.243133i
\(556\) −2456.04 2618.14i −0.00794486 0.00846922i
\(557\) −324387. −1.04557 −0.522785 0.852464i \(-0.675107\pi\)
−0.522785 + 0.852464i \(0.675107\pi\)
\(558\) −10427.2 26356.1i −0.0334888 0.0846473i
\(559\) 226870.i 0.726027i
\(560\) −401626. 25686.9i −1.28070 0.0819099i
\(561\) −199868. −0.635065
\(562\) 389578. 154128.i 1.23345 0.487987i
\(563\) 180882.i 0.570662i −0.958429 0.285331i \(-0.907897\pi\)
0.958429 0.285331i \(-0.0921035\pi\)
\(564\) −176316. + 165399.i −0.554284 + 0.519966i
\(565\) −364457. −1.14169
\(566\) 126959. + 320906.i 0.396307 + 1.00172i
\(567\) 71082.3i 0.221103i
\(568\) 374509. + 176587.i 1.16082 + 0.547345i
\(569\) 345837. 1.06819 0.534093 0.845426i \(-0.320653\pi\)
0.534093 + 0.845426i \(0.320653\pi\)
\(570\) −431878. + 170863.i −1.32927 + 0.525894i
\(571\) 239120.i 0.733405i −0.930338 0.366703i \(-0.880487\pi\)
0.930338 0.366703i \(-0.119513\pi\)
\(572\) 188937. + 201407.i 0.577463 + 0.615576i
\(573\) −56877.6 −0.173234
\(574\) −46348.0 117151.i −0.140672 0.355566i
\(575\) 344405.i 1.04168i
\(576\) −106986. 129734.i −0.322463 0.391030i
\(577\) 78021.8 0.234350 0.117175 0.993111i \(-0.462616\pi\)
0.117175 + 0.993111i \(0.462616\pi\)
\(578\) −367551. + 145413.i −1.10018 + 0.435260i
\(579\) 13101.4i 0.0390807i
\(580\) −539011. + 505638.i −1.60229 + 1.50309i
\(581\) 201920. 0.598172
\(582\) −125577. 317411.i −0.370734 0.937079i
\(583\) 45265.4i 0.133177i
\(584\) −192473. + 408200.i −0.564344 + 1.19687i
\(585\) −328030. −0.958521
\(586\) −441.521 + 174.678i −0.00128575 + 0.000508678i
\(587\) 619048.i 1.79659i −0.439396 0.898293i \(-0.644808\pi\)
0.439396 0.898293i \(-0.355192\pi\)
\(588\) −20646.3 22009.0i −0.0597156 0.0636569i
\(589\) 92489.5 0.266601
\(590\) 221068. + 558777.i 0.635070 + 1.60522i
\(591\) 199138.i 0.570138i
\(592\) 5647.34 88298.7i 0.0161139 0.251948i
\(593\) −501794. −1.42697 −0.713486 0.700669i \(-0.752885\pi\)
−0.713486 + 0.700669i \(0.752885\pi\)
\(594\) −212491. + 84067.1i −0.602236 + 0.238261i
\(595\) 671287.i 1.89616i
\(596\) 44479.9 41726.0i 0.125219 0.117467i
\(597\) −64527.5 −0.181049
\(598\) 214600. + 542430.i 0.600106 + 1.51684i
\(599\) 290536.i 0.809742i 0.914374 + 0.404871i \(0.132684\pi\)
−0.914374 + 0.404871i \(0.867316\pi\)
\(600\) 201371. + 94949.9i 0.559365 + 0.263750i
\(601\) −126251. −0.349532 −0.174766 0.984610i \(-0.555917\pi\)
−0.174766 + 0.984610i \(0.555917\pi\)
\(602\) −166024. + 65683.6i −0.458118 + 0.181244i
\(603\) 203358.i 0.559275i
\(604\) −101106. 107779.i −0.277143 0.295435i
\(605\) −313923. −0.857653
\(606\) −113369. 286555.i −0.308709 0.780302i
\(607\) 392034.i 1.06401i −0.846741 0.532006i \(-0.821439\pi\)
0.846741 0.532006i \(-0.178561\pi\)
\(608\) 522082. 168886.i 1.41232 0.456863i
\(609\) 390461. 1.05279
\(610\) 402449. 159220.i 1.08156 0.427895i
\(611\) 557159.i 1.49244i
\(612\) −204567. + 191901.i −0.546176 + 0.512360i
\(613\) 186670. 0.496767 0.248384 0.968662i \(-0.420101\pi\)
0.248384 + 0.968662i \(0.420101\pi\)
\(614\) 82506.2 + 208545.i 0.218852 + 0.553176i
\(615\) 148838.i 0.393516i
\(616\) 92688.7 196576.i 0.244267 0.518047i
\(617\) 318253. 0.835992 0.417996 0.908449i \(-0.362733\pi\)
0.417996 + 0.908449i \(0.362733\pi\)
\(618\) 315457. 124804.i 0.825968 0.326776i
\(619\) 166643.i 0.434917i −0.976070 0.217458i \(-0.930223\pi\)
0.976070 0.217458i \(-0.0697766\pi\)
\(620\) −64776.5 69051.8i −0.168513 0.179635i
\(621\) −482707. −1.25170
\(622\) 16387.2 + 41420.9i 0.0423570 + 0.107063i
\(623\) 459695.i 1.18439i
\(624\) −376319. 24068.3i −0.966466 0.0618125i
\(625\) −431687. −1.10512
\(626\) 466565. 184586.i 1.19059 0.471032i
\(627\) 250815.i 0.637997i
\(628\) −346190. + 324756.i −0.877800 + 0.823452i
\(629\) −147584. −0.373026
\(630\) 94971.7 + 240053.i 0.239284 + 0.604821i
\(631\) 546542.i 1.37266i 0.727288 + 0.686332i \(0.240780\pi\)
−0.727288 + 0.686332i \(0.759220\pi\)
\(632\) 475093. + 224014.i 1.18945 + 0.560843i
\(633\) −292471. −0.729920
\(634\) −165761. + 65579.5i −0.412385 + 0.163151i
\(635\) 543347.i 1.34750i
\(636\) −42288.1 45079.1i −0.104545 0.111445i
\(637\) 69548.6 0.171400
\(638\) −146826. 371121.i −0.360712 0.911747i
\(639\) 265602.i 0.650473i
\(640\) −491738. 271500.i −1.20053 0.662841i
\(641\) −85487.5 −0.208059 −0.104030 0.994574i \(-0.533174\pi\)
−0.104030 + 0.994574i \(0.533174\pi\)
\(642\) −289977. + 114723.i −0.703547 + 0.278343i
\(643\) 662876.i 1.60328i 0.597805 + 0.801641i \(0.296040\pi\)
−0.597805 + 0.801641i \(0.703960\pi\)
\(644\) 334820. 314090.i 0.807309 0.757326i
\(645\) 210930. 0.507014
\(646\) −336712. 851084.i −0.806852 2.03942i
\(647\) 295935.i 0.706948i 0.935444 + 0.353474i \(0.115000\pi\)
−0.935444 + 0.353474i \(0.885000\pi\)
\(648\) 42312.4 89736.9i 0.100767 0.213708i
\(649\) −324512. −0.770445
\(650\) −477116. + 188760.i −1.12927 + 0.446770i
\(651\) 50021.4i 0.118030i
\(652\) 220399. + 234946.i 0.518460 + 0.552679i
\(653\) 623598. 1.46244 0.731221 0.682141i \(-0.238951\pi\)
0.731221 + 0.682141i \(0.238951\pi\)
\(654\) 109968. + 277959.i 0.257105 + 0.649867i
\(655\) 1.10364e6i 2.57245i
\(656\) 11223.5 175484.i 0.0260808 0.407784i
\(657\) 289496. 0.670675
\(658\) −407731. + 161310.i −0.941720 + 0.372571i
\(659\) 360136.i 0.829269i 0.909988 + 0.414635i \(0.136091\pi\)
−0.909988 + 0.414635i \(0.863909\pi\)
\(660\) −187256. + 175663.i −0.429882 + 0.403266i
\(661\) 605534. 1.38591 0.692955 0.720980i \(-0.256308\pi\)
0.692955 + 0.720980i \(0.256308\pi\)
\(662\) −113100. 285875.i −0.258075 0.652319i
\(663\) 628987.i 1.43092i
\(664\) 254911. + 120194.i 0.578165 + 0.272614i
\(665\) −842400. −1.90491
\(666\) −52776.4 + 20879.8i −0.118985 + 0.0470737i
\(667\) 843062.i 1.89499i
\(668\) 82593.6 + 88044.8i 0.185095 + 0.197311i
\(669\) 218196. 0.487522
\(670\) 249900. + 631655.i 0.556694 + 1.40712i
\(671\) 233724.i 0.519108i
\(672\) 91339.1 + 282359.i 0.202264 + 0.625264i
\(673\) −502267. −1.10893 −0.554465 0.832207i \(-0.687077\pi\)
−0.554465 + 0.832207i \(0.687077\pi\)
\(674\) 523665. 207177.i 1.15275 0.456059i
\(675\) 424584.i 0.931872i
\(676\) 300545. 281937.i 0.657682 0.616962i
\(677\) −544296. −1.18757 −0.593783 0.804625i \(-0.702366\pi\)
−0.593783 + 0.804625i \(0.702366\pi\)
\(678\) 98869.0 + 249904.i 0.215080 + 0.543643i
\(679\) 619126.i 1.34289i
\(680\) −399590. + 847457.i −0.864164 + 1.83274i
\(681\) 164386. 0.354463
\(682\) 47543.8 18809.6i 0.102217 0.0404400i
\(683\) 204667.i 0.438739i −0.975642 0.219370i \(-0.929600\pi\)
0.975642 0.219370i \(-0.0704001\pi\)
\(684\) −240818. 256712.i −0.514726 0.548699i
\(685\) 715259. 1.52434
\(686\) −182145. 460394.i −0.387051 0.978321i
\(687\) 547275.i 1.15956i
\(688\) −248693. 15905.7i −0.525396 0.0336029i
\(689\) 142450. 0.300072
\(690\) −504320. + 199523.i −1.05927 + 0.419078i
\(691\) 329946.i 0.691015i 0.938416 + 0.345507i \(0.112293\pi\)
−0.938416 + 0.345507i \(0.887707\pi\)
\(692\) −70354.7 + 65998.8i −0.146920 + 0.137824i
\(693\) −139412. −0.290291
\(694\) −127026. 321076.i −0.263740 0.666636i
\(695\) 7692.10i 0.0159248i
\(696\) 492933. + 232426.i 1.01758 + 0.479806i
\(697\) −293308. −0.603752
\(698\) 333429. 131914.i 0.684373 0.270757i
\(699\) 174914.i 0.357989i
\(700\) 276271. + 294505.i 0.563818 + 0.601030i
\(701\) 144602. 0.294264 0.147132 0.989117i \(-0.452996\pi\)
0.147132 + 0.989117i \(0.452996\pi\)
\(702\) 264560. + 668709.i 0.536846 + 1.35695i
\(703\) 185204.i 0.374748i
\(704\) 234027. 192991.i 0.472195 0.389396i
\(705\) 518015. 1.04223
\(706\) −436821. + 172819.i −0.876384 + 0.346722i
\(707\) 558940.i 1.11822i
\(708\) 323177. 303168.i 0.644724 0.604806i
\(709\) 15096.1 0.0300312 0.0150156 0.999887i \(-0.495220\pi\)
0.0150156 + 0.999887i \(0.495220\pi\)
\(710\) −326390. 824994.i −0.647472 1.63657i
\(711\) 336937.i 0.666514i
\(712\) −273637. + 580335.i −0.539778 + 1.14477i
\(713\) 108003. 0.212451
\(714\) 460294. 182105.i 0.902899 0.357212i
\(715\) 591733.i 1.15748i
\(716\) 650203. + 693117.i 1.26830 + 1.35201i
\(717\) 22423.1 0.0436171
\(718\) 307291. + 776718.i 0.596076 + 1.50666i
\(719\) 181074.i 0.350267i −0.984545 0.175133i \(-0.943964\pi\)
0.984545 0.175133i \(-0.0560356\pi\)
\(720\) −22998.1 + 359585.i −0.0443636 + 0.693644i
\(721\) 615315. 1.18366
\(722\) 583301. 230770.i 1.11897 0.442695i
\(723\) 480550.i 0.919310i
\(724\) −43790.1 + 41078.8i −0.0835407 + 0.0783684i
\(725\) 741549. 1.41080
\(726\) 85160.2 + 215253.i 0.161571 + 0.408392i
\(727\) 504679.i 0.954874i 0.878666 + 0.477437i \(0.158434\pi\)
−0.878666 + 0.477437i \(0.841566\pi\)
\(728\) −618626. 291692.i −1.16725 0.550379i
\(729\) −458562. −0.862866
\(730\) 899212. 355753.i 1.68739 0.667580i
\(731\) 415671.i 0.777885i
\(732\) −218351. 232762.i −0.407505 0.434400i
\(733\) 212915. 0.396276 0.198138 0.980174i \(-0.436511\pi\)
0.198138 + 0.980174i \(0.436511\pi\)
\(734\) −38257.5 96700.7i −0.0710108 0.179489i
\(735\) 64662.3i 0.119695i
\(736\) 609654. 197214.i 1.12545 0.364068i
\(737\) −366836. −0.675363
\(738\) −104887. + 41496.4i −0.192580 + 0.0761899i
\(739\) 61157.0i 0.111984i 0.998431 + 0.0559921i \(0.0178322\pi\)
−0.998431 + 0.0559921i \(0.982168\pi\)
\(740\) −138272. + 129711.i −0.252505 + 0.236871i
\(741\) −789318. −1.43752
\(742\) −41242.5 104246.i −0.0749095 0.189343i
\(743\) 56723.7i 0.102751i 0.998679 + 0.0513756i \(0.0163606\pi\)
−0.998679 + 0.0513756i \(0.983639\pi\)
\(744\) −29775.7 + 63148.8i −0.0537918 + 0.114083i
\(745\) −130682. −0.235452
\(746\) −230341. + 91129.4i −0.413899 + 0.163750i
\(747\) 180783.i 0.323979i
\(748\) −346171. 369018.i −0.618710 0.659545i
\(749\) −565614. −1.00822
\(750\) 23788.2 + 60127.6i 0.0422901 + 0.106894i
\(751\) 214929.i 0.381080i 0.981679 + 0.190540i \(0.0610238\pi\)
−0.981679 + 0.190540i \(0.938976\pi\)
\(752\) −610756. 39062.3i −1.08002 0.0690751i
\(753\) −391402. −0.690292
\(754\) −1.16792e6 + 462062.i −2.05433 + 0.812751i
\(755\) 316655.i 0.555511i
\(756\) 412768. 387212.i 0.722208 0.677493i
\(757\) −821257. −1.43314 −0.716568 0.697517i \(-0.754288\pi\)
−0.716568 + 0.697517i \(0.754288\pi\)
\(758\) −317502. 802526.i −0.552596 1.39676i
\(759\) 292886.i 0.508412i
\(760\) −1.06348e6 501446.i −1.84120 0.868155i
\(761\) −901445. −1.55657 −0.778287 0.627909i \(-0.783911\pi\)
−0.778287 + 0.627909i \(0.783911\pi\)
\(762\) −372567. + 147398.i −0.641645 + 0.253853i
\(763\) 542172.i 0.931297i
\(764\) −98511.7 105014.i −0.168772 0.179911i
\(765\) 601018. 1.02699
\(766\) −153262. 387389.i −0.261202 0.660221i
\(767\) 1.02124e6i 1.73595i
\(768\) −52767.1 + 410831.i −0.0894625 + 0.696532i
\(769\) −1.14370e6 −1.93402 −0.967009 0.254744i \(-0.918009\pi\)
−0.967009 + 0.254744i \(0.918009\pi\)
\(770\) −433032. + 171319.i −0.730362 + 0.288952i
\(771\) 30043.0i 0.0505400i
\(772\) −24189.3 + 22691.6i −0.0405871 + 0.0380742i
\(773\) 1.12591e6 1.88427 0.942136 0.335232i \(-0.108815\pi\)
0.942136 + 0.335232i \(0.108815\pi\)
\(774\) 58808.0 + 148645.i 0.0981645 + 0.248123i
\(775\) 94998.7i 0.158166i
\(776\) 368540. 781608.i 0.612014 1.29797i
\(777\) 100164. 0.165910
\(778\) −157763. + 62415.6i −0.260644 + 0.103118i
\(779\) 368073.i 0.606540i
\(780\) 552812. + 589298.i 0.908632 + 0.968602i
\(781\) 479119. 0.785491
\(782\) −393191. 993842.i −0.642970 1.62519i
\(783\) 1.03933e6i 1.69523i
\(784\) 4876.03 76238.9i 0.00793294 0.124035i
\(785\) 1.01711e6 1.65054
\(786\) 756757. 299394.i 1.22493 0.484616i
\(787\) 764877.i 1.23493i −0.786599 0.617465i \(-0.788160\pi\)
0.786599 0.617465i \(-0.211840\pi\)
\(788\) 367671. 344907.i 0.592116 0.555455i
\(789\) −256870. −0.412628
\(790\) −414052. 1.04657e6i −0.663438 1.67692i
\(791\) 487450.i 0.779072i
\(792\) −175999. 82986.3i −0.280582 0.132299i
\(793\) 735531. 1.16965
\(794\) 592878. 234559.i 0.940425 0.372058i
\(795\) 132442.i 0.209552i
\(796\) −111761. 119138.i −0.176386 0.188028i
\(797\) 2005.12 0.00315663 0.00157832 0.999999i \(-0.499498\pi\)
0.00157832 + 0.999999i \(0.499498\pi\)
\(798\) 228524. + 577625.i 0.358862 + 0.907069i
\(799\) 1.02083e6i 1.59904i
\(800\) 173468. + 536246.i 0.271043 + 0.837885i
\(801\) 411575. 0.641481
\(802\) 59729.0 23630.4i 0.0928617 0.0367387i
\(803\) 522222.i 0.809886i
\(804\) 365327. 342708.i 0.565157 0.530166i
\(805\) −983702. −1.51800
\(806\) −59194.1 149621.i −0.0911188 0.230314i
\(807\) 8959.51i 0.0137574i
\(808\) 332714. 705626.i 0.509622 1.08082i
\(809\) 1.07187e6 1.63775 0.818874 0.573974i \(-0.194599\pi\)
0.818874 + 0.573974i \(0.194599\pi\)
\(810\) −197679. + 78207.2i −0.301294 + 0.119200i
\(811\) 1.17100e6i 1.78039i 0.455576 + 0.890197i \(0.349433\pi\)
−0.455576 + 0.890197i \(0.650567\pi\)
\(812\) 676277. + 720911.i 1.02568 + 1.09338i
\(813\) −54897.0 −0.0830553
\(814\) −37665.0 95203.2i −0.0568446 0.143682i
\(815\) 690271.i 1.03921i
\(816\) 689492. + 44098.1i 1.03550 + 0.0662276i
\(817\) −521627. −0.781477
\(818\) −465244. + 184063.i −0.695303 + 0.275081i
\(819\) 438731.i 0.654079i
\(820\) −274800. + 257786.i −0.408686 + 0.383382i
\(821\) −429054. −0.636540 −0.318270 0.948000i \(-0.603102\pi\)
−0.318270 + 0.948000i \(0.603102\pi\)
\(822\) −194034. 490446.i −0.287167 0.725851i
\(823\) 141782.i 0.209326i 0.994508 + 0.104663i \(0.0333764\pi\)
−0.994508 + 0.104663i \(0.966624\pi\)
\(824\) 776796. + 366272.i 1.14407 + 0.539447i
\(825\) 257620. 0.378505
\(826\) 747348. 295672.i 1.09538 0.433361i
\(827\) 408769.i 0.597677i 0.954304 + 0.298838i \(0.0965992\pi\)
−0.954304 + 0.298838i \(0.903401\pi\)
\(828\) −281212. 299772.i −0.410179 0.437250i
\(829\) −735343. −1.06999 −0.534997 0.844854i \(-0.679687\pi\)
−0.534997 + 0.844854i \(0.679687\pi\)
\(830\) −222159. 561535.i −0.322484 0.815119i
\(831\) 406909.i 0.589244i
\(832\) −607344. 736486.i −0.877381 1.06394i
\(833\) −127427. −0.183642
\(834\) 5274.39 2086.70i 0.00758298 0.00300004i
\(835\) 258676.i 0.371007i
\(836\) 463082. 434411.i 0.662591 0.621567i
\(837\) 133147. 0.190055
\(838\) 266940. + 674726.i 0.380125 + 0.960815i
\(839\) 245759.i 0.349128i −0.984646 0.174564i \(-0.944148\pi\)
0.984646 0.174564i \(-0.0558517\pi\)
\(840\) 271199. 575164.i 0.384352 0.815141i
\(841\) 1.10794e6 1.56648
\(842\) 282761. 111868.i 0.398837 0.157791i
\(843\) 661984.i 0.931521i
\(844\) −506558. 539991.i −0.711123 0.758057i
\(845\) −883000. −1.23665
\(846\) 144424. + 365050.i 0.201790 + 0.510049i
\(847\) 419862.i 0.585248i
\(848\) 9987.15 156153.i 0.0138883 0.217150i
\(849\) −545295. −0.756513
\(850\) 874174. 345847.i 1.20993 0.478682i
\(851\) 216270.i 0.298632i
\(852\) −477147. + 447605.i −0.657315 + 0.616617i
\(853\) 528771. 0.726724 0.363362 0.931648i \(-0.381629\pi\)
0.363362 + 0.931648i \(0.381629\pi\)
\(854\) −212952. 538264.i −0.291989 0.738039i
\(855\) 754219.i 1.03173i
\(856\) −714052. 336687.i −0.974501 0.459493i
\(857\) 1.36027e6 1.85209 0.926045 0.377412i \(-0.123186\pi\)
0.926045 + 0.377412i \(0.123186\pi\)
\(858\) −405745. + 160524.i −0.551161 + 0.218055i
\(859\) 286244.i 0.387927i −0.981009 0.193964i \(-0.937866\pi\)
0.981009 0.193964i \(-0.0621344\pi\)
\(860\) 365330. + 389442.i 0.493957 + 0.526558i
\(861\) 199066. 0.268529
\(862\) 509277. + 1.28726e6i 0.685392 + 1.73242i
\(863\) 32079.7i 0.0430733i −0.999768 0.0215367i \(-0.993144\pi\)
0.999768 0.0215367i \(-0.00685586\pi\)
\(864\) 751584. 243126.i 1.00682 0.325690i
\(865\) 206702. 0.276257
\(866\) 878747. 347656.i 1.17173 0.463569i
\(867\) 624556.i 0.830870i
\(868\) −92354.8 + 86636.8i −0.122580 + 0.114991i
\(869\) 607800. 0.804861
\(870\) −429599. 1.08587e6i −0.567577 1.43462i
\(871\) 1.15444e6i 1.52172i
\(872\) −322733. + 684458.i −0.424434 + 0.900148i
\(873\) −554317. −0.727327
\(874\) 1.24718e6 493417.i 1.63269 0.645939i
\(875\) 117282.i 0.153185i
\(876\) −487873. 520073.i −0.635767 0.677728i
\(877\) 1.01706e6 1.32236 0.661179 0.750228i \(-0.270056\pi\)
0.661179 + 0.750228i \(0.270056\pi\)
\(878\) −414808. 1.04848e6i −0.538094 1.36010i
\(879\) 750.248i 0.000971017i
\(880\) −648654. 41486.2i −0.837622 0.0535720i
\(881\) 236693. 0.304954 0.152477 0.988307i \(-0.451275\pi\)
0.152477 + 0.988307i \(0.451275\pi\)
\(882\) −45568.2 + 18028.0i −0.0585767 + 0.0231746i
\(883\) 1.22889e6i 1.57613i −0.615590 0.788067i \(-0.711082\pi\)
0.615590 0.788067i \(-0.288918\pi\)
\(884\) −1.16130e6 + 1.08940e6i −1.48608 + 1.39407i
\(885\) −949493. −1.21229
\(886\) −16669.0 42133.2i −0.0212346 0.0536731i
\(887\) 715067.i 0.908865i 0.890781 + 0.454433i \(0.150158\pi\)
−0.890781 + 0.454433i \(0.849842\pi\)
\(888\) 126451. + 59623.8i 0.160361 + 0.0756125i
\(889\) −726711. −0.919514
\(890\) 1.27840e6 505772.i 1.61394 0.638520i
\(891\) 114803.i 0.144610i
\(892\) 377914. + 402856.i 0.474967 + 0.506315i
\(893\) −1.28104e6 −1.60643
\(894\) 35451.1 + 89607.3i 0.0443563 + 0.112116i
\(895\) 2.03638e6i 2.54221i
\(896\) −363123. + 657685.i −0.452312 + 0.819222i
\(897\) −921715. −1.14554
\(898\) −184537. + 73008.2i −0.228840 + 0.0905355i
\(899\) 232545.i 0.287732i
\(900\) 263677. 247351.i 0.325527 0.305372i
\(901\) −260998. −0.321505
\(902\) −74855.2 189206.i −0.0920045 0.232553i
\(903\) 282113.i 0.345978i
\(904\) −290159. + 615375.i −0.355058 + 0.753014i
\(905\) 128655. 0.157083
\(906\) 217127. 85901.6i 0.264520 0.104651i
\(907\) 739435.i 0.898846i 0.893319 + 0.449423i \(0.148370\pi\)
−0.893319 + 0.449423i \(0.851630\pi\)
\(908\) 284716. + 303508.i 0.345335 + 0.368127i
\(909\) −500431. −0.605643
\(910\) 539143. + 1.36275e6i 0.651061 + 1.64564i
\(911\) 1.43700e6i 1.73148i −0.500490 0.865742i \(-0.666847\pi\)
0.500490 0.865742i \(-0.333153\pi\)
\(912\) −55338.8 + 865246.i −0.0665335 + 1.04028i
\(913\) 326114. 0.391226
\(914\) 357249. 141337.i 0.427640 0.169186i
\(915\) 683855.i 0.816811i
\(916\) 1.01044e6 947878.i 1.20426 1.12970i
\(917\) 1.47609e6 1.75539
\(918\) −484728. 1.22521e6i −0.575192 1.45387i
\(919\) 1.53081e6i 1.81255i 0.422684 + 0.906277i \(0.361088\pi\)
−0.422684 + 0.906277i \(0.638912\pi\)
\(920\) −1.24186e6 585557.i −1.46723 0.691821i
\(921\) −354367. −0.417767
\(922\) −972545. + 384766.i −1.14406 + 0.452621i
\(923\) 1.50779e6i 1.76986i
\(924\) 234944. + 250450.i 0.275182 + 0.293344i
\(925\) 190229. 0.222327
\(926\) −300078. 758485.i −0.349955 0.884555i
\(927\) 550905.i 0.641087i
\(928\) 424628. + 1.31266e6i 0.493074 + 1.52426i
\(929\) −766377. −0.887997 −0.443998 0.896028i \(-0.646440\pi\)
−0.443998 + 0.896028i \(0.646440\pi\)
\(930\) 139109. 55035.3i 0.160838 0.0636319i
\(931\) 159909.i 0.184490i
\(932\) −322945. + 302950.i −0.371789 + 0.348770i
\(933\) −70383.8 −0.0808554
\(934\) −468205. 1.18345e6i −0.536714 1.35661i
\(935\) 1.08417e6i 1.24016i
\(936\) −261158. + 553870.i −0.298093 + 0.632202i
\(937\) −152632. −0.173847 −0.0869235 0.996215i \(-0.527704\pi\)
−0.0869235 + 0.996215i \(0.527704\pi\)
\(938\) 844820. 334234.i 0.960193 0.379879i
\(939\) 792803.i 0.899154i
\(940\) 897200. + 956415.i 1.01539 + 1.08241i
\(941\) −829824. −0.937145 −0.468573 0.883425i \(-0.655232\pi\)
−0.468573 + 0.883425i \(0.655232\pi\)
\(942\) −275918. 697420.i −0.310942 0.785945i
\(943\) 429813.i 0.483343i
\(944\) 1.11948e6 + 71599.0i 1.25624 + 0.0803457i
\(945\) −1.21271e6 −1.35798
\(946\) −268140. + 106084.i −0.299626 + 0.118540i
\(947\) 874022.i 0.974591i −0.873237 0.487296i \(-0.837983\pi\)
0.873237 0.487296i \(-0.162017\pi\)
\(948\) −605298. + 567822.i −0.673524 + 0.631823i
\(949\) 1.64344e6 1.82482
\(950\) 434005. + 1.09700e6i 0.480892 + 1.21552i
\(951\) 281666.i 0.311440i
\(952\) 1.13345e6 + 534440.i 1.25063 + 0.589691i
\(953\) −195337. −0.215079 −0.107540 0.994201i \(-0.534297\pi\)
−0.107540 + 0.994201i \(0.534297\pi\)
\(954\) −93333.4 + 36925.3i −0.102551 + 0.0405721i
\(955\) 308530.i 0.338291i
\(956\) 38836.7 + 41399.9i 0.0424939 + 0.0452985i
\(957\) 630622. 0.688565
\(958\) 480714. + 1.21507e6i 0.523788 + 1.32394i
\(959\) 956638.i 1.04019i
\(960\) 684743. 564674.i 0.742993 0.612711i
\(961\) −29791.0 −0.0322581
\(962\) −299605. + 118532.i −0.323742 + 0.128081i
\(963\) 506407.i 0.546068i
\(964\) −887243. + 832310.i −0.954748 + 0.895635i
\(965\) 71068.1 0.0763168
\(966\) 266856. + 674514.i 0.285972 + 0.722831i
\(967\) 323652.i 0.346119i −0.984911 0.173060i \(-0.944635\pi\)
0.984911 0.173060i \(-0.0553653\pi\)
\(968\) −249927. + 530050.i −0.266724 + 0.565674i
\(969\) 1.44619e6 1.54020
\(970\) −1.72178e6 + 681184.i −1.82993 + 0.723971i
\(971\) 655388.i 0.695120i 0.937658 + 0.347560i \(0.112990\pi\)
−0.937658 + 0.347560i \(0.887010\pi\)
\(972\) −576749. 614815.i −0.610456 0.650747i
\(973\) 10288.0 0.0108668
\(974\) 460336. + 1.16356e6i 0.485240 + 1.22651i
\(975\) 810732.i 0.852841i
\(976\) 51567.8 806285.i 0.0541351 0.846426i
\(977\) 477188. 0.499920 0.249960 0.968256i \(-0.419583\pi\)
0.249960 + 0.968256i \(0.419583\pi\)
\(978\) −473311. + 187255.i −0.494845 + 0.195774i
\(979\) 742439.i 0.774631i
\(980\) −119387. + 111995.i −0.124309 + 0.116613i
\(981\) 485418. 0.504404
\(982\) −263060. 664917.i −0.272792 0.689516i
\(983\) 1.23297e6i 1.27599i 0.770041 + 0.637995i \(0.220236\pi\)
−0.770041 + 0.637995i \(0.779764\pi\)
\(984\) 251308. + 118496.i 0.259548 + 0.122381i
\(985\) −1.08022e6 −1.11337
\(986\) 2.13987e6 846592.i 2.20107 0.870804i
\(987\) 692831.i 0.711202i
\(988\) −1.36709e6 1.45732e6i −1.40050 1.49294i
\(989\) −609123. −0.622748
\(990\) 153386. + 387703.i 0.156500 + 0.395575i
\(991\) 151177.i 0.153936i 0.997034 + 0.0769679i \(0.0245239\pi\)
−0.997034 + 0.0769679i \(0.975476\pi\)
\(992\) −168163. + 54398.4i −0.170887 + 0.0552793i
\(993\) 485768. 0.492641
\(994\) −1.10341e6 + 436538.i −1.11677 + 0.441824i
\(995\) 350026.i 0.353553i
\(996\) −324772. + 304664.i −0.327386 + 0.307116i
\(997\) 6029.29 0.00606563 0.00303282 0.999995i \(-0.499035\pi\)
0.00303282 + 0.999995i \(0.499035\pi\)
\(998\) 179995. + 454961.i 0.180717 + 0.456786i
\(999\) 266618.i 0.267152i
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 124.5.b.a.63.6 yes 60
4.3 odd 2 inner 124.5.b.a.63.5 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.5.b.a.63.5 60 4.3 odd 2 inner
124.5.b.a.63.6 yes 60 1.1 even 1 trivial