Properties

Label 294.6.e.s.67.2
Level 294294
Weight 66
Character 294.67
Analytic conductor 47.15347.153
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,6,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 294=2372 294 = 2 \cdot 3 \cdot 7^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 294.e (of order 33, degree 22, not 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: 47.152843025047.1528430250
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(3,9601)\Q(\sqrt{-3}, \sqrt{9601})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x3+2401x2+2400x+5760000 x^{4} - x^{3} + 2401x^{2} + 2400x + 5760000 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 67.2
Root 24.246241.9956i-24.2462 - 41.9956i of defining polynomial
Character χ\chi == 294.67
Dual form 294.6.e.s.79.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(2.000003.46410i)q2+(4.50000+7.79423i)q3+(8.00000+13.8564i)q4+(11.2462+19.4789i)q5+36.0000q6+64.0000q8+(40.500070.1481i)q9+(44.984777.9158i)q10+(170.231+294.849i)q11+(72.0000124.708i)q12+728.416q13202.431q15+(128.000221.703i)q16+(404.923701.348i)q17+(162.000+280.592i)q18+(513.101+888.717i)q19359.878q20+1361.85q22+(711.0151231.51i)q23+(288.000+498.831i)q24+(1309.552268.20i)q25+(1456.832523.31i)q26+729.000q27+5218.03q29+(404.862+701.242i)q30+(3518.87+6094.87i)q31+(512.000+886.810i)q32+(1532.082653.64i)q333239.39q34+1296.00q36+(6396.0511078.3i)q37+(2052.403554.87i)q38+(3277.87+5677.44i)q39+(719.755+1246.65i)q401173.51q41+3664.17q43+(2723.694717.58i)q44+(910.9401577.79i)q45+(2844.06+4926.06i)q46+(4656.60+8065.46i)q47+2304.00q4810476.4q50+(3644.31+6312.13i)q51+(5827.33+10093.2i)q52+(17821.4+30867.6i)q53+(1458.002525.33i)q547657.78q559235.81q57+(10436.118075.8i)q58+(15188.1+26306.5i)q59+(1619.452804.97i)q60+(16093.1+27874.1i)q61+28151.0q62+4096.00q64+(8191.89+14188.8i)q65+(6128.31+10614.5i)q66+(10675.5+18490.6i)q67+(6478.78+11221.6i)q68+12798.3q69+61153.7q71+(2592.004489.48i)q72+(20633.935739.0i)q73+(25584.2+44313.2i)q74+(11785.9+20413.8i)q7516419.2q76+26223.0q78+(17500.2+30311.3i)q79+(2879.024986.61i)q80+(3280.50+5681.99i)q81+(2347.01+4065.14i)q8286193.0q83+18215.4q85+(7328.3312693.0i)q86+(23481.1+40670.5i)q87+(10894.8+18870.3i)q88+(38996.3+67543.6i)q897287.52q90+22752.5q92+(31669.954853.8i)q93+(18626.432261.9i)q94+(11540.8+19989.3i)q95+(4608.007981.29i)q96+161765.q97+27577.4q99+O(q100)q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(11.2462 + 19.4789i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(44.9847 - 77.9158i) q^{10} +(-170.231 + 294.849i) q^{11} +(-72.0000 - 124.708i) q^{12} +728.416 q^{13} -202.431 q^{15} +(-128.000 - 221.703i) q^{16} +(404.923 - 701.348i) q^{17} +(-162.000 + 280.592i) q^{18} +(513.101 + 888.717i) q^{19} -359.878 q^{20} +1361.85 q^{22} +(-711.015 - 1231.51i) q^{23} +(-288.000 + 498.831i) q^{24} +(1309.55 - 2268.20i) q^{25} +(-1456.83 - 2523.31i) q^{26} +729.000 q^{27} +5218.03 q^{29} +(404.862 + 701.242i) q^{30} +(-3518.87 + 6094.87i) q^{31} +(-512.000 + 886.810i) q^{32} +(-1532.08 - 2653.64i) q^{33} -3239.39 q^{34} +1296.00 q^{36} +(-6396.05 - 11078.3i) q^{37} +(2052.40 - 3554.87i) q^{38} +(-3277.87 + 5677.44i) q^{39} +(719.755 + 1246.65i) q^{40} -1173.51 q^{41} +3664.17 q^{43} +(-2723.69 - 4717.58i) q^{44} +(910.940 - 1577.79i) q^{45} +(-2844.06 + 4926.06i) q^{46} +(4656.60 + 8065.46i) q^{47} +2304.00 q^{48} -10476.4 q^{50} +(3644.31 + 6312.13i) q^{51} +(-5827.33 + 10093.2i) q^{52} +(-17821.4 + 30867.6i) q^{53} +(-1458.00 - 2525.33i) q^{54} -7657.78 q^{55} -9235.81 q^{57} +(-10436.1 - 18075.8i) q^{58} +(-15188.1 + 26306.5i) q^{59} +(1619.45 - 2804.97i) q^{60} +(16093.1 + 27874.1i) q^{61} +28151.0 q^{62} +4096.00 q^{64} +(8191.89 + 14188.8i) q^{65} +(-6128.31 + 10614.5i) q^{66} +(-10675.5 + 18490.6i) q^{67} +(6478.78 + 11221.6i) q^{68} +12798.3 q^{69} +61153.7 q^{71} +(-2592.00 - 4489.48i) q^{72} +(20633.9 - 35739.0i) q^{73} +(-25584.2 + 44313.2i) q^{74} +(11785.9 + 20413.8i) q^{75} -16419.2 q^{76} +26223.0 q^{78} +(17500.2 + 30311.3i) q^{79} +(2879.02 - 4986.61i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(2347.01 + 4065.14i) q^{82} -86193.0 q^{83} +18215.4 q^{85} +(-7328.33 - 12693.0i) q^{86} +(-23481.1 + 40670.5i) q^{87} +(-10894.8 + 18870.3i) q^{88} +(38996.3 + 67543.6i) q^{89} -7287.52 q^{90} +22752.5 q^{92} +(-31669.9 - 54853.8i) q^{93} +(18626.4 - 32261.9i) q^{94} +(-11540.8 + 19989.3i) q^{95} +(-4608.00 - 7981.29i) q^{96} +161765. q^{97} +27577.4 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q8q218q332q453q5+144q6+256q8162q9212q10191q11288q12+758q13+954q15512q16340q17648q181769q19+1696q20++30942q99+O(q100) 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} - 53 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} - 212 q^{10} - 191 q^{11} - 288 q^{12} + 758 q^{13} + 954 q^{15} - 512 q^{16} - 340 q^{17} - 648 q^{18} - 1769 q^{19} + 1696 q^{20}+ \cdots + 30942 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/294Z)×\left(\mathbb{Z}/294\mathbb{Z}\right)^\times.

nn 197197 199199
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −2.00000 3.46410i −0.353553 0.612372i
33 −4.50000 + 7.79423i −0.288675 + 0.500000i
44 −8.00000 + 13.8564i −0.250000 + 0.433013i
55 11.2462 + 19.4789i 0.201178 + 0.348450i 0.948908 0.315552i 0.102190π-0.102190\pi
−0.747730 + 0.664002i 0.768856π0.768856\pi
66 36.0000 0.408248
77 0 0
88 64.0000 0.353553
99 −40.5000 70.1481i −0.166667 0.288675i
1010 44.9847 77.9158i 0.142254 0.246391i
1111 −170.231 + 294.849i −0.424186 + 0.734712i −0.996344 0.0854314i 0.972773π-0.972773\pi
0.572158 + 0.820144i 0.306106π0.306106\pi
1212 −72.0000 124.708i −0.144338 0.250000i
1313 728.416 1.19542 0.597711 0.801712i 0.296077π-0.296077\pi
0.597711 + 0.801712i 0.296077π0.296077\pi
1414 0 0
1515 −202.431 −0.232300
1616 −128.000 221.703i −0.125000 0.216506i
1717 404.923 701.348i 0.339821 0.588588i −0.644578 0.764539i 0.722967π-0.722967\pi
0.984399 + 0.175951i 0.0563001π0.0563001\pi
1818 −162.000 + 280.592i −0.117851 + 0.204124i
1919 513.101 + 888.717i 0.326076 + 0.564780i 0.981730 0.190282i 0.0609402π-0.0609402\pi
−0.655654 + 0.755062i 0.727607π0.727607\pi
2020 −359.878 −0.201178
2121 0 0
2222 1361.85 0.599890
2323 −711.015 1231.51i −0.280259 0.485423i 0.691190 0.722674i 0.257087π-0.257087\pi
−0.971448 + 0.237251i 0.923754π0.923754\pi
2424 −288.000 + 498.831i −0.102062 + 0.176777i
2525 1309.55 2268.20i 0.419055 0.725825i
2626 −1456.83 2523.31i −0.422645 0.732043i
2727 729.000 0.192450
2828 0 0
2929 5218.03 1.15216 0.576079 0.817394i 0.304582π-0.304582\pi
0.576079 + 0.817394i 0.304582π0.304582\pi
3030 404.862 + 701.242i 0.0821304 + 0.142254i
3131 −3518.87 + 6094.87i −0.657657 + 1.13909i 0.323564 + 0.946206i 0.395119π0.395119\pi
−0.981221 + 0.192889i 0.938214π0.938214\pi
3232 −512.000 + 886.810i −0.0883883 + 0.153093i
3333 −1532.08 2653.64i −0.244904 0.424186i
3434 −3239.39 −0.480580
3535 0 0
3636 1296.00 0.166667
3737 −6396.05 11078.3i −0.768082 1.33036i −0.938601 0.345004i 0.887878π-0.887878\pi
0.170519 0.985354i 0.445456π-0.445456\pi
3838 2052.40 3554.87i 0.230570 0.399360i
3939 −3277.87 + 5677.44i −0.345088 + 0.597711i
4040 719.755 + 1246.65i 0.0711270 + 0.123196i
4141 −1173.51 −0.109025 −0.0545124 0.998513i 0.517360π-0.517360\pi
−0.0545124 + 0.998513i 0.517360π0.517360\pi
4242 0 0
4343 3664.17 0.302207 0.151103 0.988518i 0.451717π-0.451717\pi
0.151103 + 0.988518i 0.451717π0.451717\pi
4444 −2723.69 4717.58i −0.212093 0.367356i
4545 910.940 1577.79i 0.0670592 0.116150i
4646 −2844.06 + 4926.06i −0.198173 + 0.343246i
4747 4656.60 + 8065.46i 0.307485 + 0.532580i 0.977812 0.209487i 0.0671793π-0.0671793\pi
−0.670326 + 0.742066i 0.733846π0.733846\pi
4848 2304.00 0.144338
4949 0 0
5050 −10476.4 −0.592633
5151 3644.31 + 6312.13i 0.196196 + 0.339821i
5252 −5827.33 + 10093.2i −0.298855 + 0.517633i
5353 −17821.4 + 30867.6i −0.871469 + 1.50943i −0.0109916 + 0.999940i 0.503499π0.503499\pi
−0.860477 + 0.509489i 0.829835π0.829835\pi
5454 −1458.00 2525.33i −0.0680414 0.117851i
5555 −7657.78 −0.341347
5656 0 0
5757 −9235.81 −0.376520
5858 −10436.1 18075.8i −0.407349 0.705549i
5959 −15188.1 + 26306.5i −0.568033 + 0.983861i 0.428728 + 0.903434i 0.358962π0.358962\pi
−0.996760 + 0.0804276i 0.974371π0.974371\pi
6060 1619.45 2804.97i 0.0580750 0.100589i
6161 16093.1 + 27874.1i 0.553753 + 0.959128i 0.997999 + 0.0632231i 0.0201380π0.0201380\pi
−0.444247 + 0.895904i 0.646529π0.646529\pi
6262 28151.0 0.930067
6363 0 0
6464 4096.00 0.125000
6565 8191.89 + 14188.8i 0.240492 + 0.416544i
6666 −6128.31 + 10614.5i −0.173173 + 0.299945i
6767 −10675.5 + 18490.6i −0.290538 + 0.503226i −0.973937 0.226819i 0.927168π-0.927168\pi
0.683399 + 0.730045i 0.260501π0.260501\pi
6868 6478.78 + 11221.6i 0.169911 + 0.294294i
6969 12798.3 0.323615
7070 0 0
7171 61153.7 1.43972 0.719859 0.694121i 0.244207π-0.244207\pi
0.719859 + 0.694121i 0.244207π0.244207\pi
7272 −2592.00 4489.48i −0.0589256 0.102062i
7373 20633.9 35739.0i 0.453184 0.784937i −0.545398 0.838177i 0.683622π-0.683622\pi
0.998582 + 0.0532401i 0.0169549π0.0169549\pi
7474 −25584.2 + 44313.2i −0.543116 + 0.940705i
7575 11785.9 + 20413.8i 0.241942 + 0.419055i
7676 −16419.2 −0.326076
7777 0 0
7878 26223.0 0.488029
7979 17500.2 + 30311.3i 0.315483 + 0.546433i 0.979540 0.201249i 0.0645001π-0.0645001\pi
−0.664057 + 0.747682i 0.731167π0.731167\pi
8080 2879.02 4986.61i 0.0502944 0.0871125i
8181 −3280.50 + 5681.99i −0.0555556 + 0.0962250i
8282 2347.01 + 4065.14i 0.0385461 + 0.0667638i
8383 −86193.0 −1.37334 −0.686668 0.726972i 0.740927π-0.740927\pi
−0.686668 + 0.726972i 0.740927π0.740927\pi
8484 0 0
8585 18215.4 0.273458
8686 −7328.33 12693.0i −0.106846 0.185063i
8787 −23481.1 + 40670.5i −0.332599 + 0.576079i
8888 −10894.8 + 18870.3i −0.149972 + 0.259760i
8989 38996.3 + 67543.6i 0.521853 + 0.903876i 0.999677 + 0.0254206i 0.00809249π0.00809249\pi
−0.477824 + 0.878456i 0.658574π0.658574\pi
9090 −7287.52 −0.0948361
9191 0 0
9292 22752.5 0.280259
9393 −31669.9 54853.8i −0.379698 0.657657i
9494 18626.4 32261.9i 0.217425 0.376591i
9595 −11540.8 + 19989.3i −0.131198 + 0.227242i
9696 −4608.00 7981.29i −0.0510310 0.0883883i
9797 161765. 1.74565 0.872823 0.488037i 0.162287π-0.162287\pi
0.872823 + 0.488037i 0.162287π0.162287\pi
9898 0 0
9999 27577.4 0.282791
100100 20952.8 + 36291.2i 0.209528 + 0.362912i
101101 −32927.2 + 57031.6i −0.321182 + 0.556304i −0.980732 0.195357i 0.937414π-0.937414\pi
0.659550 + 0.751661i 0.270747π0.270747\pi
102102 14577.2 25248.5i 0.138731 0.240290i
103103 65099.0 + 112755.i 0.604619 + 1.04723i 0.992112 + 0.125358i 0.0400078π0.0400078\pi
−0.387493 + 0.921873i 0.626659π0.626659\pi
104104 46618.6 0.422645
105105 0 0
106106 142571. 1.23244
107107 −1295.48 2243.83i −0.0109388 0.0189466i 0.860504 0.509443i 0.170149π-0.170149\pi
−0.871443 + 0.490497i 0.836815π0.836815\pi
108108 −5832.00 + 10101.3i −0.0481125 + 0.0833333i
109109 −55326.9 + 95828.9i −0.446036 + 0.772557i −0.998124 0.0612291i 0.980498π-0.980498\pi
0.552088 + 0.833786i 0.313831π0.313831\pi
110110 15315.6 + 26527.3i 0.120684 + 0.209032i
111111 115129. 0.886905
112112 0 0
113113 −193910. −1.42858 −0.714291 0.699849i 0.753251π-0.753251\pi
−0.714291 + 0.699849i 0.753251π0.753251\pi
114114 18471.6 + 31993.8i 0.133120 + 0.230570i
115115 15992.4 27699.7i 0.112764 0.195312i
116116 −41744.3 + 72303.2i −0.288039 + 0.498899i
117117 −29500.8 51097.0i −0.199237 0.345088i
118118 121505. 0.803319
119119 0 0
120120 −12955.6 −0.0821304
121121 22568.4 + 39089.6i 0.140132 + 0.242716i
122122 64372.5 111496.i 0.391562 0.678206i
123123 5280.77 9146.57i 0.0314728 0.0545124i
124124 −56302.0 97517.9i −0.328828 0.569547i
125125 129198. 0.739573
126126 0 0
127127 27429.2 0.150905 0.0754526 0.997149i 0.475960π-0.475960\pi
0.0754526 + 0.997149i 0.475960π0.475960\pi
128128 −8192.00 14189.0i −0.0441942 0.0765466i
129129 −16488.7 + 28559.3i −0.0872395 + 0.151103i
130130 32767.6 56755.1i 0.170054 0.294541i
131131 75188.0 + 130229.i 0.382798 + 0.663026i 0.991461 0.130403i 0.0416271π-0.0416271\pi
−0.608663 + 0.793429i 0.708294π0.708294\pi
132132 49026.5 0.244904
133133 0 0
134134 85404.3 0.410883
135135 8198.46 + 14200.1i 0.0387167 + 0.0670592i
136136 25915.1 44886.3i 0.120145 0.208097i
137137 −48051.0 + 83226.8i −0.218726 + 0.378845i −0.954419 0.298471i 0.903524π-0.903524\pi
0.735693 + 0.677316i 0.236857π0.236857\pi
138138 −25596.6 44334.5i −0.114415 0.198173i
139139 −100854. −0.442749 −0.221375 0.975189i 0.571054π-0.571054\pi
−0.221375 + 0.975189i 0.571054π0.571054\pi
140140 0 0
141141 −83818.7 −0.355053
142142 −122307. 211843.i −0.509017 0.881643i
143143 −123999. + 214772.i −0.507081 + 0.878291i
144144 −10368.0 + 17957.9i −0.0416667 + 0.0721688i
145145 58682.9 + 101642.i 0.231788 + 0.401469i
146146 −165071. −0.640898
147147 0 0
148148 204674. 0.768082
149149 180472. + 312587.i 0.665954 + 1.15347i 0.979026 + 0.203737i 0.0653087π0.0653087\pi
−0.313071 + 0.949730i 0.601358π0.601358\pi
150150 47143.7 81655.3i 0.171079 0.296317i
151151 217028. 375903.i 0.774592 1.34163i −0.160431 0.987047i 0.551288π-0.551288\pi
0.935023 0.354586i 0.115378π-0.115378\pi
152152 32838.4 + 56877.9i 0.115285 + 0.199680i
153153 −65597.6 −0.226548
154154 0 0
155155 −158295. −0.529223
156156 −52445.9 90839.0i −0.172544 0.298855i
157157 −255798. + 443055.i −0.828225 + 1.43453i 0.0712046 + 0.997462i 0.477316π0.477316\pi
−0.899430 + 0.437066i 0.856018π0.856018\pi
158158 70000.9 121245.i 0.223080 0.386386i
159159 −160393. 277808.i −0.503143 0.871469i
160160 −23032.2 −0.0711270
161161 0 0
162162 26244.0 0.0785674
163163 125635. + 217606.i 0.370374 + 0.641507i 0.989623 0.143688i 0.0458962π-0.0458962\pi
−0.619249 + 0.785195i 0.712563π0.712563\pi
164164 9388.04 16260.6i 0.0272562 0.0472091i
165165 34460.0 59686.5i 0.0985384 0.170674i
166166 172386. + 298581.i 0.485547 + 0.840993i
167167 −419277. −1.16335 −0.581674 0.813422i 0.697602π-0.697602\pi
−0.581674 + 0.813422i 0.697602π0.697602\pi
168168 0 0
169169 159297. 0.429032
170170 −36430.7 63099.8i −0.0966819 0.167458i
171171 41561.2 71986.0i 0.108692 0.188260i
172172 −29313.3 + 50772.2i −0.0755517 + 0.130859i
173173 −230688. 399564.i −0.586017 1.01501i −0.994748 0.102356i 0.967362π-0.967362\pi
0.408731 0.912655i 0.365971π-0.365971\pi
174174 187849. 0.470366
175175 0 0
176176 87158.2 0.212093
177177 −136693. 236759.i −0.327954 0.568033i
178178 155985. 270174.i 0.369006 0.639137i
179179 −370853. + 642336.i −0.865105 + 1.49841i 0.00183697 + 0.999998i 0.499415π0.499415\pi
−0.866942 + 0.498408i 0.833918π0.833918\pi
180180 14575.0 + 25244.7i 0.0335296 + 0.0580750i
181181 −301371. −0.683762 −0.341881 0.939743i 0.611064π-0.611064\pi
−0.341881 + 0.939743i 0.611064π0.611064\pi
182182 0 0
183183 −289676. −0.639418
184184 −45505.0 78816.9i −0.0990865 0.171623i
185185 143862. 249177.i 0.309042 0.535277i
186186 −126679. + 219415.i −0.268487 + 0.465034i
187187 137861. + 238782.i 0.288295 + 0.499342i
188188 −149011. −0.307485
189189 0 0
190190 92326.7 0.185542
191191 −131591. 227923.i −0.261002 0.452069i 0.705507 0.708703i 0.250720π-0.250720\pi
−0.966508 + 0.256635i 0.917386π0.917386\pi
192192 −18432.0 + 31925.2i −0.0360844 + 0.0625000i
193193 415563. 719777.i 0.803053 1.39093i −0.114545 0.993418i 0.536541π-0.536541\pi
0.917598 0.397510i 0.130126π-0.130126\pi
194194 −323531. 560372.i −0.617179 1.06899i
195195 −147454. −0.277696
196196 0 0
197197 −1.05421e6 −1.93536 −0.967681 0.252178i 0.918853π-0.918853\pi
−0.967681 + 0.252178i 0.918853π0.918853\pi
198198 −55154.8 95530.9i −0.0999817 0.173173i
199199 349284. 604977.i 0.625239 1.08295i −0.363256 0.931689i 0.618335π-0.618335\pi
0.988495 0.151256i 0.0483317π-0.0483317\pi
200200 83811.0 145165.i 0.148158 0.256618i
201201 −96079.9 166415.i −0.167742 0.290538i
202202 263418. 0.454220
203203 0 0
204204 −116618. −0.196196
205205 −13197.4 22858.6i −0.0219334 0.0379897i
206206 260396. 451019.i 0.427530 0.740504i
207207 −57592.2 + 99752.7i −0.0934196 + 0.161808i
208208 −93237.2 161492.i −0.149428 0.258816i
209209 −349382. −0.553268
210210 0 0
211211 −99693.6 −0.154156 −0.0770781 0.997025i 0.524559π-0.524559\pi
−0.0770781 + 0.997025i 0.524559π0.524559\pi
212212 −285142. 493881.i −0.435734 0.754714i
213213 −275192. + 476646.i −0.415611 + 0.719859i
214214 −5181.90 + 8975.32i −0.00773490 + 0.0133972i
215215 41207.8 + 71374.1i 0.0607972 + 0.105304i
216216 46656.0 0.0680414
217217 0 0
218218 442615. 0.630790
219219 185705. + 321651.i 0.261646 + 0.453184i
220220 61262.3 106109.i 0.0853368 0.147808i
221221 294953. 510873.i 0.406230 0.703610i
222222 −230258. 398819.i −0.313568 0.543116i
223223 −526194. −0.708572 −0.354286 0.935137i 0.615276π-0.615276\pi
−0.354286 + 0.935137i 0.615276π0.615276\pi
224224 0 0
225225 −212147. −0.279370
226226 387821. + 671725.i 0.505080 + 0.874824i
227227 −490802. + 850095.i −0.632182 + 1.09497i 0.354923 + 0.934896i 0.384507π0.384507\pi
−0.987105 + 0.160076i 0.948826π0.948826\pi
228228 73886.5 127975.i 0.0941300 0.163038i
229229 −42540.5 73682.3i −0.0536061 0.0928484i 0.837977 0.545705i 0.183738π-0.183738\pi
−0.891583 + 0.452857i 0.850405π0.850405\pi
230230 −127939. −0.159472
231231 0 0
232232 333954. 0.407349
233233 −56561.4 97967.3i −0.0682544 0.118220i 0.829879 0.557944i 0.188410π-0.188410\pi
−0.898133 + 0.439724i 0.855076π0.855076\pi
234234 −118003. + 204388.i −0.140882 + 0.244014i
235235 −104738. + 181411.i −0.123718 + 0.214286i
236236 −243009. 420905.i −0.284016 0.491931i
237237 −315004. −0.364288
238238 0 0
239239 −895100. −1.01362 −0.506812 0.862057i 0.669176π-0.669176\pi
−0.506812 + 0.862057i 0.669176π0.669176\pi
240240 25911.2 + 44879.5i 0.0290375 + 0.0502944i
241241 263857. 457014.i 0.292635 0.506859i −0.681797 0.731542i 0.738801π-0.738801\pi
0.974432 + 0.224683i 0.0721345π0.0721345\pi
242242 90273.6 156358.i 0.0990883 0.171626i
243243 −29524.5 51137.9i −0.0320750 0.0555556i
244244 −514980. −0.553753
245245 0 0
246246 −42246.2 −0.0445092
247247 373751. + 647355.i 0.389798 + 0.675150i
248248 −225208. + 390071.i −0.232517 + 0.402731i
249249 387868. 671808.i 0.396448 0.686668i
250250 −258396. 447556.i −0.261479 0.452894i
251251 1.19293e6 1.19517 0.597584 0.801806i 0.296127π-0.296127\pi
0.597584 + 0.801806i 0.296127π0.296127\pi
252252 0 0
253253 484147. 0.475528
254254 −54858.5 95017.7i −0.0533531 0.0924102i
255255 −81969.1 + 141975.i −0.0789405 + 0.136729i
256256 −32768.0 + 56755.8i −0.0312500 + 0.0541266i
257257 −597462. 1.03483e6i −0.564257 0.977322i −0.997118 0.0758617i 0.975829π-0.975829\pi
0.432861 0.901461i 0.357504π-0.357504\pi
258258 131910. 0.123375
259259 0 0
260260 −262140. −0.240492
261261 −211330. 366035.i −0.192026 0.332599i
262262 300752. 520917.i 0.270679 0.468830i
263263 1.06115e6 1.83797e6i 0.945993 1.63851i 0.192244 0.981347i 0.438424π-0.438424\pi
0.753750 0.657161i 0.228243π-0.228243\pi
264264 −98053.0 169833.i −0.0865867 0.149972i
265265 −801690. −0.701280
266266 0 0
267267 −701933. −0.602584
268268 −170809. 295849.i −0.145269 0.251613i
269269 77488.3 134214.i 0.0652913 0.113088i −0.831532 0.555477i 0.812536π-0.812536\pi
0.896823 + 0.442389i 0.145869π0.145869\pi
270270 32793.8 56800.6i 0.0273768 0.0474180i
271271 979439. + 1.69644e6i 0.810129 + 1.40318i 0.912773 + 0.408466i 0.133936π0.133936\pi
−0.102645 + 0.994718i 0.532730π0.532730\pi
272272 −207321. −0.169911
273273 0 0
274274 384408. 0.309326
275275 445851. + 772236.i 0.355515 + 0.615770i
276276 −102386. + 177338.i −0.0809038 + 0.140129i
277277 874763. 1.51513e6i 0.685001 1.18646i −0.288436 0.957499i 0.593135π-0.593135\pi
0.973437 0.228957i 0.0735315π-0.0735315\pi
278278 201709. + 349370.i 0.156536 + 0.271128i
279279 570057. 0.438438
280280 0 0
281281 1.40665e6 1.06272 0.531361 0.847145i 0.321681π-0.321681\pi
0.531361 + 0.847145i 0.321681π0.321681\pi
282282 167637. + 290357.i 0.125530 + 0.217425i
283283 978536. 1.69487e6i 0.726291 1.25797i −0.232150 0.972680i 0.574576π-0.574576\pi
0.958441 0.285292i 0.0920907π-0.0920907\pi
284284 −489230. + 847371.i −0.359929 + 0.623416i
285285 −103868. 179904.i −0.0757474 0.131198i
286286 991991. 0.717121
287287 0 0
288288 82944.0 0.0589256
289289 382002. + 661648.i 0.269043 + 0.465996i
290290 234732. 406567.i 0.163899 0.283882i
291291 −727944. + 1.26084e6i −0.503925 + 0.872823i
292292 330142. + 571823.i 0.226592 + 0.392469i
293293 1.26998e6 0.864229 0.432114 0.901819i 0.357768π-0.357768\pi
0.432114 + 0.901819i 0.357768π0.357768\pi
294294 0 0
295295 −683232. −0.457102
296296 −409348. 709011.i −0.271558 0.470353i
297297 −124098. + 214945.i −0.0816347 + 0.141395i
298298 721888. 1.25035e6i 0.470901 0.815624i
299299 −517915. 897055.i −0.335027 0.580285i
300300 −377150. −0.241942
301301 0 0
302302 −1.73622e6 −1.09544
303303 −296345. 513284.i −0.185435 0.321182i
304304 131354. 227511.i 0.0815190 0.141195i
305305 −361972. + 626954.i −0.222805 + 0.385910i
306306 131195. + 227237.i 0.0800967 + 0.138731i
307307 41854.4 0.0253451 0.0126726 0.999920i 0.495966π-0.495966\pi
0.0126726 + 0.999920i 0.495966π0.495966\pi
308308 0 0
309309 −1.17178e6 −0.698154
310310 316591. + 548351.i 0.187109 + 0.324082i
311311 −1.14595e6 + 1.98484e6i −0.671837 + 1.16366i 0.305546 + 0.952177i 0.401161π0.401161\pi
−0.977383 + 0.211478i 0.932172π0.932172\pi
312312 −209784. + 363356.i −0.122007 + 0.211323i
313313 1.13575e6 + 1.96717e6i 0.655271 + 1.13496i 0.981826 + 0.189785i 0.0607790π0.0607790\pi
−0.326555 + 0.945178i 0.605888π0.605888\pi
314314 2.04639e6 1.17129
315315 0 0
316316 −560007. −0.315483
317317 992372. + 1.71884e6i 0.554659 + 0.960698i 0.997930 + 0.0643100i 0.0204847π0.0204847\pi
−0.443271 + 0.896388i 0.646182π0.646182\pi
318318 −641570. + 1.11123e6i −0.355776 + 0.616222i
319319 −888270. + 1.53853e6i −0.488729 + 0.846504i
320320 46064.3 + 79785.8i 0.0251472 + 0.0435562i
321321 23318.6 0.0126310
322322 0 0
323323 831066. 0.443230
324324 −52488.0 90911.9i −0.0277778 0.0481125i
325325 953895. 1.65219e6i 0.500947 0.867666i
326326 502539. 870423.i 0.261894 0.453614i
327327 −497942. 862460.i −0.257519 0.446036i
328328 −75104.3 −0.0385461
329329 0 0
330330 −275680. −0.139354
331331 −319230. 552923.i −0.160153 0.277393i 0.774771 0.632242i 0.217865π-0.217865\pi
−0.934923 + 0.354850i 0.884532π0.884532\pi
332332 689544. 1.19432e6i 0.343334 0.594672i
333333 −518080. + 897342.i −0.256027 + 0.443453i
334334 838553. + 1.45242e6i 0.411305 + 0.712402i
335335 −480236. −0.233799
336336 0 0
337337 2.72026e6 1.30478 0.652388 0.757886i 0.273767π-0.273767\pi
0.652388 + 0.757886i 0.273767π0.273767\pi
338338 −318593. 551820.i −0.151686 0.262727i
339339 872597. 1.51138e6i 0.412396 0.714291i
340340 −145723. + 252399.i −0.0683645 + 0.118411i
341341 −1.19804e6 2.07507e6i −0.557938 0.966377i
342342 −332489. −0.153714
343343 0 0
344344 234507. 0.106846
345345 143932. + 249297.i 0.0651041 + 0.112764i
346346 −922753. + 1.59825e6i −0.414376 + 0.717721i
347347 −1.31038e6 + 2.26965e6i −0.584217 + 1.01189i 0.410755 + 0.911746i 0.365265π0.365265\pi
−0.994973 + 0.100148i 0.968068π0.968068\pi
348348 −375698. 650729.i −0.166300 0.288039i
349349 −575592. −0.252960 −0.126480 0.991969i 0.540368π-0.540368\pi
−0.126480 + 0.991969i 0.540368π0.540368\pi
350350 0 0
351351 531015. 0.230059
352352 −174316. 301925.i −0.0749862 0.129880i
353353 −1.29486e6 + 2.24276e6i −0.553077 + 0.957957i 0.444974 + 0.895544i 0.353213π0.353213\pi
−0.998050 + 0.0624135i 0.980120π0.980120\pi
354354 −546771. + 947036.i −0.231898 + 0.401660i
355355 687746. + 1.19121e6i 0.289639 + 0.501669i
356356 −1.24788e6 −0.521853
357357 0 0
358358 2.96682e6 1.22344
359359 −1.43389e6 2.48358e6i −0.587193 1.01705i −0.994598 0.103801i 0.966900π-0.966900\pi
0.407405 0.913248i 0.366434π-0.366434\pi
360360 58300.2 100979.i 0.0237090 0.0410652i
361361 711505. 1.23236e6i 0.287349 0.497703i
362362 602742. + 1.04398e6i 0.241746 + 0.418717i
363363 −406231. −0.161811
364364 0 0
365365 928210. 0.364682
366366 579352. + 1.00347e6i 0.226069 + 0.391562i
367367 −977255. + 1.69265e6i −0.378741 + 0.655999i −0.990879 0.134752i 0.956976π-0.956976\pi
0.612138 + 0.790751i 0.290310π0.290310\pi
368368 −182020. + 315268.i −0.0700647 + 0.121356i
369369 47527.0 + 82319.1i 0.0181708 + 0.0314728i
370370 −1.15090e6 −0.437052
371371 0 0
372372 1.01344e6 0.379698
373373 −1.10555e6 1.91486e6i −0.411439 0.712633i 0.583608 0.812035i 0.301640π-0.301640\pi
−0.995047 + 0.0994020i 0.968307π0.968307\pi
374374 551444. 955129.i 0.203855 0.353088i
375375 −581392. + 1.00700e6i −0.213496 + 0.369787i
376376 298022. + 516190.i 0.108712 + 0.188295i
377377 3.80090e6 1.37731
378378 0 0
379379 3.81232e6 1.36330 0.681649 0.731679i 0.261263π-0.261263\pi
0.681649 + 0.731679i 0.261263π0.261263\pi
380380 −184653. 319829.i −0.0655992 0.113621i
381381 −123432. + 213790.i −0.0435626 + 0.0754526i
382382 −526365. + 911691.i −0.184556 + 0.319661i
383383 1.90303e6 + 3.29614e6i 0.662901 + 1.14818i 0.979850 + 0.199735i 0.0640082π0.0640082\pi
−0.316949 + 0.948442i 0.602658π0.602658\pi
384384 147456. 0.0510310
385385 0 0
386386 −3.32451e6 −1.13569
387387 −148399. 257034.i −0.0503678 0.0872395i
388388 −1.29412e6 + 2.24149e6i −0.436411 + 0.755887i
389389 −1.53762e6 + 2.66324e6i −0.515200 + 0.892352i 0.484645 + 0.874711i 0.338949π0.338949\pi
−0.999844 + 0.0176410i 0.994384π0.994384\pi
390390 294908. + 510796.i 0.0981805 + 0.170054i
391391 −1.15163e6 −0.380952
392392 0 0
393393 −1.35338e6 −0.442017
394394 2.10842e6 + 3.65190e6i 0.684254 + 1.18516i
395395 −393621. + 681772.i −0.126936 + 0.219860i
396396 −220619. + 382124.i −0.0706977 + 0.122452i
397397 1.09566e6 + 1.89774e6i 0.348900 + 0.604312i 0.986054 0.166424i 0.0532220π-0.0532220\pi
−0.637154 + 0.770736i 0.719889π0.719889\pi
398398 −2.79427e6 −0.884221
399399 0 0
400400 −670488. −0.209528
401401 −888340. 1.53865e6i −0.275879 0.477836i 0.694478 0.719514i 0.255635π-0.255635\pi
−0.970356 + 0.241678i 0.922302π0.922302\pi
402402 −384319. + 665661.i −0.118612 + 0.205441i
403403 −2.56320e6 + 4.43960e6i −0.786177 + 1.36170i
404404 −526835. 912505.i −0.160591 0.278152i
405405 −147572. −0.0447061
406406 0 0
407407 4.35522e6 1.30324
408408 233236. + 403976.i 0.0693657 + 0.120145i
409409 1.18059e6 2.04484e6i 0.348973 0.604438i −0.637095 0.770786i 0.719864π-0.719864\pi
0.986067 + 0.166347i 0.0531973π0.0531973\pi
410410 −52789.8 + 91434.6i −0.0155092 + 0.0268628i
411411 −432459. 749041.i −0.126282 0.218726i
412412 −2.08317e6 −0.604619
413413 0 0
414414 460738. 0.132115
415415 −969341. 1.67895e6i −0.276284 0.478539i
416416 −372949. + 645966.i −0.105661 + 0.183011i
417417 453845. 786082.i 0.127811 0.221375i
418418 698765. + 1.21030e6i 0.195610 + 0.338806i
419419 3.23493e6 0.900181 0.450090 0.892983i 0.351392π-0.351392\pi
0.450090 + 0.892983i 0.351392π0.351392\pi
420420 0 0
421421 −2.85759e6 −0.785769 −0.392884 0.919588i 0.628523π-0.628523\pi
−0.392884 + 0.919588i 0.628523π0.628523\pi
422422 199387. + 345349.i 0.0545025 + 0.0944010i
423423 377184. 653302.i 0.102495 0.177527i
424424 −1.14057e6 + 1.97552e6i −0.308111 + 0.533664i
425425 −1.06053e6 1.83690e6i −0.284808 0.493301i
426426 2.20153e6 0.587762
427427 0 0
428428 41455.2 0.0109388
429429 −1.11599e6 1.93295e6i −0.292764 0.507081i
430430 164831. 285496.i 0.0429901 0.0744611i
431431 44193.1 76544.7i 0.0114594 0.0198482i −0.860239 0.509891i 0.829686π-0.829686\pi
0.871698 + 0.490043i 0.163019π0.163019\pi
432432 −93312.0 161621.i −0.0240563 0.0416667i
433433 3.09418e6 0.793097 0.396549 0.918014i 0.370208π-0.370208\pi
0.396549 + 0.918014i 0.370208π0.370208\pi
434434 0 0
435435 −1.05629e6 −0.267646
436436 −885230. 1.53326e6i −0.223018 0.386278i
437437 729645. 1.26378e6i 0.182771 0.316569i
438438 742820. 1.28660e6i 0.185011 0.320449i
439439 242589. + 420177.i 0.0600773 + 0.104057i 0.894500 0.447068i 0.147532π-0.147532\pi
−0.834422 + 0.551125i 0.814199π0.814199\pi
440440 −490098. −0.120684
441441 0 0
442442 −2.35962e6 −0.574495
443443 −637598. 1.10435e6i −0.154361 0.267361i 0.778465 0.627688i 0.215999π-0.215999\pi
−0.932826 + 0.360327i 0.882665π0.882665\pi
444444 −921032. + 1.59527e6i −0.221726 + 0.384041i
445445 −877118. + 1.51921e6i −0.209970 + 0.363679i
446446 1.05239e6 + 1.82279e6i 0.250518 + 0.433910i
447447 −3.24850e6 −0.768978
448448 0 0
449449 −3.79144e6 −0.887541 −0.443770 0.896141i 0.646359π-0.646359\pi
−0.443770 + 0.896141i 0.646359π0.646359\pi
450450 424293. + 734898.i 0.0987722 + 0.171079i
451451 199767. 346006.i 0.0462468 0.0801019i
452452 1.55128e6 2.68690e6i 0.357145 0.618594i
453453 1.95325e6 + 3.38313e6i 0.447211 + 0.774592i
454454 3.92642e6 0.894040
455455 0 0
456456 −591092. −0.133120
457457 −851404. 1.47467e6i −0.190698 0.330298i 0.754784 0.655973i 0.227742π-0.227742\pi
−0.945482 + 0.325675i 0.894408π0.894408\pi
458458 −170162. + 294729.i −0.0379052 + 0.0656537i
459459 295189. 511283.i 0.0653986 0.113274i
460460 255878. + 443194.i 0.0563818 + 0.0976562i
461461 −4.55537e6 −0.998323 −0.499161 0.866509i 0.666358π-0.666358\pi
−0.499161 + 0.866509i 0.666358π0.666358\pi
462462 0 0
463463 5.82647e6 1.26314 0.631572 0.775317i 0.282410π-0.282410\pi
0.631572 + 0.775317i 0.282410π0.282410\pi
464464 −667908. 1.15685e6i −0.144020 0.249449i
465465 712329. 1.23379e6i 0.152774 0.264612i
466466 −226246. + 391869.i −0.0482631 + 0.0835942i
467467 −1.77131e6 3.06799e6i −0.375839 0.650972i 0.614614 0.788828i 0.289312π-0.289312\pi
−0.990452 + 0.137857i 0.955979π0.955979\pi
468468 944027. 0.199237
469469 0 0
470470 837902. 0.174964
471471 −2.30218e6 3.98750e6i −0.478176 0.828225i
472472 −972038. + 1.68362e6i −0.200830 + 0.347847i
473473 −623754. + 1.08037e6i −0.128192 + 0.222035i
474474 630008. + 1.09121e6i 0.128795 + 0.223080i
475475 2.68772e6 0.546575
476476 0 0
477477 2.88707e6 0.580979
478478 1.79020e6 + 3.10072e6i 0.358370 + 0.620715i
479479 −2.11771e6 + 3.66798e6i −0.421723 + 0.730446i −0.996108 0.0881390i 0.971908π-0.971908\pi
0.574385 + 0.818585i 0.305241π0.305241\pi
480480 103645. 179518.i 0.0205326 0.0355635i
481481 −4.65899e6 8.06960e6i −0.918182 1.59034i
482482 −2.11086e6 −0.413849
483483 0 0
484484 −722189. −0.140132
485485 1.81924e6 + 3.15102e6i 0.351185 + 0.608270i
486486 −118098. + 204552.i −0.0226805 + 0.0392837i
487487 2.82740e6 4.89719e6i 0.540212 0.935675i −0.458679 0.888602i 0.651677π-0.651677\pi
0.998891 0.0470729i 0.0149893π-0.0149893\pi
488488 1.02996e6 + 1.78394e6i 0.195781 + 0.339103i
489489 −2.26142e6 −0.427671
490490 0 0
491491 8.33183e6 1.55968 0.779842 0.625976i 0.215299π-0.215299\pi
0.779842 + 0.625976i 0.215299π0.215299\pi
492492 84492.4 + 146345.i 0.0157364 + 0.0272562i
493493 2.11290e6 3.65966e6i 0.391528 0.678146i
494494 1.49500e6 2.58942e6i 0.275629 0.477403i
495495 310140. + 537179.i 0.0568912 + 0.0985384i
496496 1.80166e6 0.328828
497497 0 0
498498 −3.10295e6 −0.560662
499499 3.61884e6 + 6.26802e6i 0.650607 + 1.12688i 0.982976 + 0.183734i 0.0588187π0.0588187\pi
−0.332369 + 0.943149i 0.607848π0.607848\pi
500500 −1.03359e6 + 1.79022e6i −0.184893 + 0.320245i
501501 1.88674e6 3.26794e6i 0.335829 0.581674i
502502 −2.38585e6 4.13242e6i −0.422556 0.731888i
503503 6.16761e6 1.08692 0.543459 0.839436i 0.317114π-0.317114\pi
0.543459 + 0.839436i 0.317114π0.317114\pi
504504 0 0
505505 −1.48122e6 −0.258459
506506 −968294. 1.67713e6i −0.168124 0.291200i
507507 −716835. + 1.24159e6i −0.123851 + 0.214516i
508508 −219434. + 380071.i −0.0377263 + 0.0653439i
509509 917439. + 1.58905e6i 0.156958 + 0.271859i 0.933770 0.357873i 0.116498π-0.116498\pi
−0.776812 + 0.629732i 0.783165π0.783165\pi
510510 655753. 0.111639
511511 0 0
512512 262144. 0.0441942
513513 374050. + 647874.i 0.0627533 + 0.108692i
514514 −2.38985e6 + 4.13934e6i −0.398990 + 0.691071i
515515 −1.46423e6 + 2.53612e6i −0.243272 + 0.421359i
516516 −263820. 456950.i −0.0436198 0.0755517i
517517 −3.17079e6 −0.521724
518518 0 0
519519 4.15239e6 0.676674
520520 524281. + 908081.i 0.0850268 + 0.147271i
521521 2.65520e6 4.59894e6i 0.428551 0.742273i −0.568193 0.822895i 0.692357π-0.692357\pi
0.996745 + 0.0806224i 0.0256908π0.0256908\pi
522522 −845321. + 1.46414e6i −0.135783 + 0.235183i
523523 −1.49418e6 2.58799e6i −0.238862 0.413722i 0.721526 0.692388i 0.243441π-0.243441\pi
−0.960388 + 0.278666i 0.910108π0.910108\pi
524524 −2.40601e6 −0.382798
525525 0 0
526526 −8.48921e6 −1.33784
527527 2.84975e6 + 4.93591e6i 0.446972 + 0.774178i
528528 −392212. + 679331.i −0.0612260 + 0.106047i
529529 2.20709e6 3.82279e6i 0.342910 0.593937i
530530 1.60338e6 + 2.77713e6i 0.247940 + 0.429445i
531531 2.46047e6 0.378688
532532 0 0
533533 −854800. −0.130331
534534 1.40387e6 + 2.43157e6i 0.213046 + 0.369006i
535535 29138.3 50469.0i 0.00440128 0.00762325i
536536 −683235. + 1.18340e6i −0.102721 + 0.177917i
537537 −3.33768e6 5.78102e6i −0.499469 0.865105i
538538 −619907. −0.0923359
539539 0 0
540540 −262351. −0.0387167
541541 −1.08416e6 1.87782e6i −0.159258 0.275843i 0.775343 0.631540i 0.217577π-0.217577\pi
−0.934601 + 0.355697i 0.884243π0.884243\pi
542542 3.91775e6 6.78575e6i 0.572848 0.992201i
543543 1.35617e6 2.34895e6i 0.197385 0.341881i
544544 414642. + 718180.i 0.0600725 + 0.104049i
545545 −2.48886e6 −0.358930
546546 0 0
547547 −9.13272e6 −1.30506 −0.652532 0.757761i 0.726293π-0.726293\pi
−0.652532 + 0.757761i 0.726293π0.726293\pi
548548 −768816. 1.33163e6i −0.109363 0.189423i
549549 1.30354e6 2.25780e6i 0.184584 0.319709i
550550 1.78340e6 3.08894e6i 0.251387 0.435415i
551551 2.67738e6 + 4.63735e6i 0.375691 + 0.650715i
552552 819090. 0.114415
553553 0 0
554554 −6.99810e6 −0.968737
555555 1.29476e6 + 2.24259e6i 0.178426 + 0.309042i
556556 806835. 1.39748e6i 0.110687 0.191716i
557557 4.61014e6 7.98500e6i 0.629617 1.09053i −0.358012 0.933717i 0.616545π-0.616545\pi
0.987629 0.156811i 0.0501214π-0.0501214\pi
558558 −1.14011e6 1.97474e6i −0.155011 0.268487i
559559 2.66904e6 0.361264
560560 0 0
561561 −2.48150e6 −0.332894
562562 −2.81330e6 4.87277e6i −0.375729 0.650782i
563563 4.24638e6 7.35495e6i 0.564610 0.977933i −0.432476 0.901645i 0.642360π-0.642360\pi
0.997086 0.0762872i 0.0243066π-0.0243066\pi
564564 670550. 1.16143e6i 0.0887633 0.153743i
565565 −2.18075e6 3.77717e6i −0.287399 0.497789i
566566 −7.82828e6 −1.02713
567567 0 0
568568 3.91384e6 0.509017
569569 2.35456e6 + 4.07822e6i 0.304880 + 0.528068i 0.977235 0.212162i 0.0680503π-0.0680503\pi
−0.672355 + 0.740229i 0.734717π0.734717\pi
570570 −415470. + 719616.i −0.0535615 + 0.0927712i
571571 864035. 1.49655e6i 0.110902 0.192089i −0.805232 0.592960i 0.797959π-0.797959\pi
0.916134 + 0.400871i 0.131293π0.131293\pi
572572 −1.98398e6 3.43636e6i −0.253541 0.439145i
573573 2.36864e6 0.301379
574574 0 0
575575 −3.72443e6 −0.469776
576576 −165888. 287326.i −0.0208333 0.0360844i
577577 1.19249e6 2.06546e6i 0.149113 0.258272i −0.781787 0.623546i 0.785691π-0.785691\pi
0.930900 + 0.365274i 0.119025π0.119025\pi
578578 1.52801e6 2.64659e6i 0.190242 0.329509i
579579 3.74007e6 + 6.47799e6i 0.463643 + 0.803053i
580580 −1.87785e6 −0.231788
581581 0 0
582582 5.82355e6 0.712657
583583 −6.06750e6 1.05092e7i −0.739330 1.28056i
584584 1.32057e6 2.28729e6i 0.160225 0.277517i
585585 663543. 1.14929e6i 0.0801640 0.138848i
586586 −2.53997e6 4.39935e6i −0.305551 0.529230i
587587 3.44904e6 0.413145 0.206573 0.978431i 0.433769π-0.433769\pi
0.206573 + 0.978431i 0.433769π0.433769\pi
588588 0 0
589589 −7.22214e6 −0.857784
590590 1.36646e6 + 2.36678e6i 0.161610 + 0.279917i
591591 4.74395e6 8.21676e6i 0.558691 0.967681i
592592 −1.63739e6 + 2.83604e6i −0.192021 + 0.332589i
593593 567341. + 982664.i 0.0662533 + 0.114754i 0.897249 0.441524i 0.145562π-0.145562\pi
−0.830996 + 0.556278i 0.812229π0.812229\pi
594594 992786. 0.115449
595595 0 0
596596 −5.77511e6 −0.665954
597597 3.14355e6 + 5.44480e6i 0.360982 + 0.625239i
598598 −2.07166e6 + 3.58822e6i −0.236900 + 0.410323i
599599 −3.80933e6 + 6.59795e6i −0.433792 + 0.751349i −0.997196 0.0748320i 0.976158π-0.976158\pi
0.563404 + 0.826181i 0.309491π0.309491\pi
600600 754299. + 1.30648e6i 0.0855393 + 0.148158i
601601 −9.78414e6 −1.10493 −0.552467 0.833535i 0.686314π-0.686314\pi
−0.552467 + 0.833535i 0.686314π0.686314\pi
602602 0 0
603603 1.72944e6 0.193692
604604 3.47245e6 + 6.01445e6i 0.387296 + 0.670817i
605605 −507616. + 879217.i −0.0563829 + 0.0976580i
606606 −1.18538e6 + 2.05314e6i −0.131122 + 0.227110i
607607 926673. + 1.60504e6i 0.102083 + 0.176813i 0.912543 0.408981i 0.134116π-0.134116\pi
−0.810460 + 0.585795i 0.800783π0.800783\pi
608608 −1.05083e6 −0.115285
609609 0 0
610610 2.89578e6 0.315094
611611 3.39194e6 + 5.87501e6i 0.367574 + 0.636657i
612612 524781. 908947.i 0.0566369 0.0980980i
613613 3.56048e6 6.16694e6i 0.382699 0.662855i −0.608748 0.793364i 0.708328π-0.708328\pi
0.991447 + 0.130509i 0.0416612π0.0416612\pi
614614 −83708.7 144988.i −0.00896086 0.0155207i
615615 237554. 0.0253265
616616 0 0
617617 −2.75212e6 −0.291041 −0.145521 0.989355i 0.546486π-0.546486\pi
−0.145521 + 0.989355i 0.546486π0.546486\pi
618618 2.34357e6 + 4.05917e6i 0.246835 + 0.427530i
619619 −6.51660e6 + 1.12871e7i −0.683588 + 1.18401i 0.290291 + 0.956939i 0.406248π0.406248\pi
−0.973878 + 0.227070i 0.927085π0.927085\pi
620620 1.26636e6 2.19341e6i 0.132306 0.229160i
621621 −518330. 897774.i −0.0539358 0.0934196i
622622 9.16758e6 0.950120
623623 0 0
624624 1.67827e6 0.172544
625625 −2.63935e6 4.57149e6i −0.270269 0.468120i
626626 4.54299e6 7.86869e6i 0.463347 0.802540i
627627 1.57222e6 2.72317e6i 0.159715 0.276634i
628628 −4.09277e6 7.08889e6i −0.414112 0.717264i
629629 −1.03597e7 −1.04404
630630 0 0
631631 −4.40820e6 −0.440745 −0.220373 0.975416i 0.570727π-0.570727\pi
−0.220373 + 0.975416i 0.570727π0.570727\pi
632632 1.12001e6 + 1.93992e6i 0.111540 + 0.193193i
633633 448621. 777035.i 0.0445011 0.0770781i
634634 3.96949e6 6.87535e6i 0.392203 0.679316i
635635 308474. + 534293.i 0.0303588 + 0.0525829i
636636 5.13256e6 0.503143
637637 0 0
638638 7.10616e6 0.691168
639639 −2.47673e6 4.28982e6i −0.239953 0.415611i
640640 184257. 319143.i 0.0177818 0.0307989i
641641 3.99195e6 6.91426e6i 0.383742 0.664661i −0.607851 0.794051i 0.707968π-0.707968\pi
0.991594 + 0.129389i 0.0413017π0.0413017\pi
642642 −46637.1 80777.8i −0.00446575 0.00773490i
643643 −1.52102e6 −0.145080 −0.0725398 0.997366i 0.523110π-0.523110\pi
−0.0725398 + 0.997366i 0.523110π0.523110\pi
644644 0 0
645645 −741741. −0.0702026
646646 −1.66213e6 2.87890e6i −0.156706 0.271422i
647647 −6.26247e6 + 1.08469e7i −0.588146 + 1.01870i 0.406329 + 0.913727i 0.366809π0.366809\pi
−0.994475 + 0.104972i 0.966525π0.966525\pi
648648 −209952. + 363648.i −0.0196419 + 0.0340207i
649649 −5.17096e6 8.95637e6i −0.481903 0.834681i
650650 −7.63116e6 −0.708447
651651 0 0
652652 −4.02031e6 −0.370374
653653 8.53702e6 + 1.47865e7i 0.783471 + 1.35701i 0.929908 + 0.367792i 0.119886π0.119886\pi
−0.146436 + 0.989220i 0.546780π0.546780\pi
654654 −1.99177e6 + 3.44984e6i −0.182093 + 0.315395i
655655 −1.69115e6 + 2.92916e6i −0.154021 + 0.266772i
656656 150209. + 260169.i 0.0136281 + 0.0236046i
657657 −3.34269e6 −0.302122
658658 0 0
659659 −2.12585e6 −0.190686 −0.0953432 0.995444i 0.530395π-0.530395\pi
−0.0953432 + 0.995444i 0.530395π0.530395\pi
660660 551360. + 954984.i 0.0492692 + 0.0853368i
661661 −1.30005e6 + 2.25176e6i −0.115733 + 0.200456i −0.918073 0.396412i 0.870255π-0.870255\pi
0.802339 + 0.596868i 0.203588π0.203588\pi
662662 −1.27692e6 + 2.21169e6i −0.113245 + 0.196146i
663663 2.65457e6 + 4.59786e6i 0.234537 + 0.406230i
664664 −5.51635e6 −0.485547
665665 0 0
666666 4.14464e6 0.362078
667667 −3.71010e6 6.42608e6i −0.322902 0.559283i
668668 3.35421e6 5.80967e6i 0.290837 0.503744i
669669 2.36787e6 4.10128e6i 0.204547 0.354286i
670670 960472. + 1.66359e6i 0.0826604 + 0.143172i
671671 −1.09582e7 −0.939577
672672 0 0
673673 −1.44746e7 −1.23188 −0.615942 0.787792i 0.711224π-0.711224\pi
−0.615942 + 0.787792i 0.711224π0.711224\pi
674674 −5.44052e6 9.42326e6i −0.461308 0.799008i
675675 954660. 1.65352e6i 0.0806472 0.139685i
676676 −1.27437e6 + 2.20728e6i −0.107258 + 0.185776i
677677 −1.64423e6 2.84788e6i −0.137876 0.238809i 0.788816 0.614629i 0.210694π-0.210694\pi
−0.926693 + 0.375820i 0.877361π0.877361\pi
678678 −6.98077e6 −0.583216
679679 0 0
680680 1.16578e6 0.0966819
681681 −4.41722e6 7.65085e6i −0.364990 0.632182i
682682 −4.79217e6 + 8.30027e6i −0.394522 + 0.683332i
683683 −4.40943e6 + 7.63736e6i −0.361685 + 0.626458i −0.988238 0.152921i 0.951132π-0.951132\pi
0.626553 + 0.779379i 0.284465π0.284465\pi
684684 664979. + 1.15178e6i 0.0543460 + 0.0941300i
685685 −2.16156e6 −0.176011
686686 0 0
687687 765729. 0.0618989
688688 −469013. 812355.i −0.0377758 0.0654297i
689689 −1.29814e7 + 2.24844e7i −1.04177 + 1.80440i
690690 575726. 997188.i 0.0460356 0.0797359i
691691 −4.29808e6 7.44450e6i −0.342436 0.593117i 0.642448 0.766329i 0.277919π-0.277919\pi
−0.984885 + 0.173212i 0.944585π0.944585\pi
692692 7.38202e6 0.586017
693693 0 0
694694 1.04831e7 0.826208
695695 −1.13423e6 1.96454e6i −0.0890713 0.154276i
696696 −1.50279e6 + 2.60291e6i −0.117592 + 0.203675i
697697 −475180. + 823035.i −0.0370490 + 0.0641707i
698698 1.15118e6 + 1.99391e6i 0.0894348 + 0.154906i
699699 1.01811e6 0.0788134
700700 0 0
701701 2.06437e7 1.58669 0.793347 0.608770i 0.208337π-0.208337\pi
0.793347 + 0.608770i 0.208337π0.208337\pi
702702 −1.06203e6 1.83949e6i −0.0813381 0.140882i
703703 6.56364e6 1.13686e7i 0.500906 0.867595i
704704 −697266. + 1.20770e6i −0.0530233 + 0.0918390i
705705 −942640. 1.63270e6i −0.0714288 0.123718i
706706 1.03589e7 0.782169
707707 0 0
708708 4.37417e6 0.327954
709709 213441. + 369691.i 0.0159464 + 0.0276200i 0.873888 0.486126i 0.161591π-0.161591\pi
−0.857942 + 0.513746i 0.828257π0.828257\pi
710710 2.75098e6 4.76484e6i 0.204806 0.354734i
711711 1.41752e6 2.45521e6i 0.105161 0.182144i
712712 2.49576e6 + 4.32279e6i 0.184503 + 0.319569i
713713 1.00079e7 0.737257
714714 0 0
715715 −5.57805e6 −0.408054
716716 −5.93365e6 1.02774e7i −0.432553 0.749203i
717717 4.02795e6 6.97662e6i 0.292608 0.506812i
718718 −5.73558e6 + 9.93431e6i −0.415208 + 0.719162i
719719 1.90362e6 + 3.29716e6i 0.137328 + 0.237858i 0.926484 0.376334i 0.122815π-0.122815\pi
−0.789157 + 0.614192i 0.789482π0.789482\pi
720720 −466401. −0.0335296
721721 0 0
722722 −5.69204e6 −0.406373
723723 2.37472e6 + 4.11313e6i 0.168953 + 0.292635i
724724 2.41097e6 4.17592e6i 0.170940 0.296077i
725725 6.83326e6 1.18356e7i 0.482817 0.836264i
726726 812463. + 1.40723e6i 0.0572087 + 0.0990883i
727727 2.22044e7 1.55813 0.779065 0.626943i 0.215694π-0.215694\pi
0.779065 + 0.626943i 0.215694π0.215694\pi
728728 0 0
729729 531441. 0.0370370
730730 −1.85642e6 3.21541e6i −0.128934 0.223321i
731731 1.48371e6 2.56986e6i 0.102696 0.177875i
732732 2.31741e6 4.01387e6i 0.159855 0.276876i
733733 −1.45286e7 2.51643e7i −0.998766 1.72991i −0.542401 0.840120i 0.682485π-0.682485\pi
−0.456365 0.889793i 0.650849π-0.650849\pi
734734 7.81804e6 0.535621
735735 0 0
736736 1.45616e6 0.0990865
737737 −3.63461e6 6.29533e6i −0.246484 0.426923i
738738 190108. 329276.i 0.0128487 0.0222546i
739739 −1.06761e7 + 1.84916e7i −0.719122 + 1.24556i 0.242226 + 0.970220i 0.422123π0.422123\pi
−0.961348 + 0.275337i 0.911211π0.911211\pi
740740 2.30180e6 + 3.98683e6i 0.154521 + 0.267638i
741741 −6.72751e6 −0.450100
742742 0 0
743743 3.91874e6 0.260420 0.130210 0.991486i 0.458435π-0.458435\pi
0.130210 + 0.991486i 0.458435π0.458435\pi
744744 −2.02687e6 3.51064e6i −0.134244 0.232517i
745745 −4.05924e6 + 7.03081e6i −0.267950 + 0.464103i
746746 −4.42219e6 + 7.65946e6i −0.290931 + 0.503908i
747747 3.49081e6 + 6.04627e6i 0.228889 + 0.396448i
748748 −4.41155e6 −0.288295
749749 0 0
750750 4.65113e6 0.301930
751751 −2.83456e6 4.90960e6i −0.183394 0.317648i 0.759640 0.650344i 0.225375π-0.225375\pi
−0.943034 + 0.332696i 0.892042π0.892042\pi
752752 1.19209e6 2.06476e6i 0.0768713 0.133145i
753753 −5.36817e6 + 9.29794e6i −0.345015 + 0.597584i
754754 −7.60180e6 1.31667e7i −0.486954 0.843429i
755755 9.76293e6 0.623323
756756 0 0
757757 −1.91706e7 −1.21590 −0.607949 0.793976i 0.708007π-0.708007\pi
−0.607949 + 0.793976i 0.708007π0.708007\pi
758758 −7.62463e6 1.32063e7i −0.481999 0.834846i
759759 −2.17866e6 + 3.77355e6i −0.137273 + 0.237764i
760760 −738614. + 1.27932e6i −0.0463856 + 0.0803423i
761761 7.31680e6 + 1.26731e7i 0.457993 + 0.793268i 0.998855 0.0478438i 0.0152350π-0.0152350\pi
−0.540861 + 0.841112i 0.681902π0.681902\pi
762762 987453. 0.0616068
763763 0 0
764764 4.21092e6 0.261002
765765 −737722. 1.27777e6i −0.0455763 0.0789405i
766766 7.61212e6 1.31846e7i 0.468742 0.811884i
767767 −1.10632e7 + 1.91621e7i −0.679038 + 1.17613i
768768 −294912. 510803.i −0.0180422 0.0312500i
769769 −1.57337e7 −0.959432 −0.479716 0.877424i 0.659260π-0.659260\pi
−0.479716 + 0.877424i 0.659260π0.659260\pi
770770 0 0
771771 1.07543e7 0.651548
772772 6.64902e6 + 1.15164e7i 0.401526 + 0.695464i
773773 2.02452e6 3.50658e6i 0.121864 0.211074i −0.798639 0.601810i 0.794446π-0.794446\pi
0.920503 + 0.390736i 0.127780π0.127780\pi
774774 −593595. + 1.02814e6i −0.0356154 + 0.0616877i
775775 9.21626e6 + 1.59630e7i 0.551189 + 0.954687i
776776 1.03530e7 0.617179
777777 0 0
778778 1.23010e7 0.728602
779779 −602126. 1.04291e6i −0.0355504 0.0615750i
780780 1.17963e6 2.04318e6i 0.0694241 0.120246i
781781 −1.04103e7 + 1.80311e7i −0.610708 + 1.05778i
782782 2.30325e6 + 3.98935e6i 0.134687 + 0.233284i
783783 3.80395e6 0.221733
784784 0 0
785785 −1.15070e7 −0.666481
786786 2.70677e6 + 4.68826e6i 0.156277 + 0.270679i
787787 −1.08056e7 + 1.87158e7i −0.621886 + 1.07714i 0.367248 + 0.930123i 0.380300π0.380300\pi
−0.989134 + 0.147015i 0.953033π0.953033\pi
788788 8.43369e6 1.46076e7i 0.483840 0.838036i
789789 9.55037e6 + 1.65417e7i 0.546170 + 0.945993i
790790 3.14897e6 0.179515
791791 0 0
792792 1.76495e6 0.0999817
793793 1.17225e7 + 2.03039e7i 0.661968 + 1.14656i
794794 4.38265e6 7.59098e6i 0.246709 0.427313i
795795 3.60760e6 6.24855e6i 0.202442 0.350640i
796796 5.58854e6 + 9.67964e6i 0.312619 + 0.541473i
797797 −1.38162e7 −0.770445 −0.385222 0.922824i 0.625875π-0.625875\pi
−0.385222 + 0.922824i 0.625875π0.625875\pi
798798 0 0
799799 7.54226e6 0.417960
800800 1.34098e6 + 2.32264e6i 0.0740792 + 0.128309i
801801 3.15870e6 5.47103e6i 0.173951 0.301292i
802802 −3.55336e6 + 6.15460e6i −0.195076 + 0.337881i
803803 7.02505e6 + 1.21678e7i 0.384469 + 0.665919i
804804 3.07456e6 0.167742
805805 0 0
806806 2.05056e7 1.11182
807807 697395. + 1.20792e6i 0.0376960 + 0.0652913i
808808 −2.10734e6 + 3.65002e6i −0.113555 + 0.196683i
809809 1.75378e7 3.03764e7i 0.942116 1.63179i 0.180691 0.983540i 0.442167π-0.442167\pi
0.761425 0.648253i 0.224500π-0.224500\pi
810810 295145. + 511205.i 0.0158060 + 0.0273768i
811811 −6.56287e6 −0.350382 −0.175191 0.984534i 0.556054π-0.556054\pi
−0.175191 + 0.984534i 0.556054π0.556054\pi
812812 0 0
813813 −1.76299e7 −0.935456
814814 −8.71045e6 1.50869e7i −0.460765 0.798068i
815815 −2.82582e6 + 4.89446e6i −0.149022 + 0.258114i
816816 932944. 1.61591e6i 0.0490490 0.0849553i
817817 1.88009e6 + 3.25640e6i 0.0985423 + 0.170680i
818818 −9.44473e6 −0.493522
819819 0 0
820820 422318. 0.0219334
821821 889470. + 1.54061e6i 0.0460547 + 0.0797690i 0.888134 0.459585i 0.152002π-0.152002\pi
−0.842079 + 0.539354i 0.818668π0.818668\pi
822822 −1.72984e6 + 2.99616e6i −0.0892947 + 0.154663i
823823 −9.47928e6 + 1.64186e7i −0.487838 + 0.844960i −0.999902 0.0139869i 0.995548π-0.995548\pi
0.512064 + 0.858947i 0.328881π0.328881\pi
824824 4.16634e6 + 7.21631e6i 0.213765 + 0.370252i
825825 −8.02531e6 −0.410513
826826 0 0
827827 2.82110e7 1.43435 0.717174 0.696894i 0.245435π-0.245435\pi
0.717174 + 0.696894i 0.245435π0.245435\pi
828828 −921476. 1.59604e6i −0.0467098 0.0809038i
829829 −1.12010e7 + 1.94008e7i −0.566072 + 0.980466i 0.430877 + 0.902411i 0.358204π0.358204\pi
−0.996949 + 0.0780553i 0.975129π0.975129\pi
830830 −3.87736e6 + 6.71579e6i −0.195363 + 0.338378i
831831 7.87287e6 + 1.36362e7i 0.395485 + 0.685001i
832832 2.98359e6 0.149428
833833 0 0
834834 −3.63076e6 −0.180752
835835 −4.71526e6 8.16707e6i −0.234040 0.405368i
836836 2.79506e6 4.84118e6i 0.138317 0.239572i
837837 −2.56526e6 + 4.44316e6i −0.126566 + 0.219219i
838838 −6.46986e6 1.12061e7i −0.318262 0.551246i
839839 1.50303e7 0.737162 0.368581 0.929596i 0.379844π-0.379844\pi
0.368581 + 0.929596i 0.379844π0.379844\pi
840840 0 0
841841 6.71672e6 0.327467
842842 5.71518e6 + 9.89898e6i 0.277811 + 0.481183i
843843 −6.32992e6 + 1.09637e7i −0.306782 + 0.531361i
844844 797549. 1.38139e6i 0.0385391 0.0667516i
845845 1.79148e6 + 3.10293e6i 0.0863117 + 0.149496i
846846 −3.01747e6 −0.144950
847847 0 0
848848 9.12455e6 0.435734
849849 8.80682e6 + 1.52539e7i 0.419324 + 0.726291i
850850 −4.24213e6 + 7.34759e6i −0.201389 + 0.348817i
851851 −9.09539e6 + 1.57537e7i −0.430524 + 0.745689i
852852 −4.40307e6 7.62634e6i −0.207805 0.359929i
853853 3.18297e7 1.49782 0.748911 0.662670i 0.230577π-0.230577\pi
0.748911 + 0.662670i 0.230577π0.230577\pi
854854 0 0
855855 1.86962e6 0.0874656
856856 −82910.4 143605.i −0.00386745 0.00669862i
857857 1.08911e7 1.88640e7i 0.506549 0.877369i −0.493422 0.869790i 0.664254π-0.664254\pi
0.999971 0.00757884i 0.00241244π-0.00241244\pi
858858 −4.46396e6 + 7.73180e6i −0.207015 + 0.358561i
859859 1.86674e7 + 3.23329e7i 0.863181 + 1.49507i 0.868842 + 0.495089i 0.164864π0.164864\pi
−0.00566184 + 0.999984i 0.501802π0.501802\pi
860860 −1.31865e6 −0.0607972
861861 0 0
862862 −353545. −0.0162060
863863 7.73066e6 + 1.33899e7i 0.353338 + 0.611999i 0.986832 0.161749i 0.0517134π-0.0517134\pi
−0.633494 + 0.773747i 0.718380π0.718380\pi
864864 −373248. + 646484.i −0.0170103 + 0.0294628i
865865 5.18872e6 8.98712e6i 0.235787 0.408395i
866866 −6.18837e6 1.07186e7i −0.280402 0.485671i
867867 −6.87604e6 −0.310664
868868 0 0
869869 −1.19163e7 −0.535294
870870 2.11258e6 + 3.65910e6i 0.0946272 + 0.163899i
871871 −7.77623e6 + 1.34688e7i −0.347315 + 0.601568i
872872 −3.54092e6 + 6.13305e6i −0.157698 + 0.273140i
873873 −6.55150e6 1.13475e7i −0.290941 0.503925i
874874 −5.83716e6 −0.258478
875875 0 0
876876 −5.94256e6 −0.261646
877877 3.40881e6 + 5.90423e6i 0.149659 + 0.259218i 0.931102 0.364760i 0.118849π-0.118849\pi
−0.781442 + 0.623978i 0.785516π0.785516\pi
878878 970357. 1.68071e6i 0.0424810 0.0735793i
879879 −5.71492e6 + 9.89853e6i −0.249481 + 0.432114i
880880 980196. + 1.69775e6i 0.0426684 + 0.0739038i
881881 1.20903e7 0.524805 0.262402 0.964959i 0.415485π-0.415485\pi
0.262402 + 0.964959i 0.415485π0.415485\pi
882882 0 0
883883 1.63966e7 0.707706 0.353853 0.935301i 0.384871π-0.384871\pi
0.353853 + 0.935301i 0.384871π0.384871\pi
884884 4.71924e6 + 8.17397e6i 0.203115 + 0.351805i
885885 3.07454e6 5.32526e6i 0.131954 0.228551i
886886 −2.55039e6 + 4.41741e6i −0.109150 + 0.189053i
887887 −1.28503e7 2.22574e7i −0.548409 0.949872i −0.998384 0.0568310i 0.981900π-0.981900\pi
0.449975 0.893041i 0.351433π-0.351433\pi
888888 7.36826e6 0.313568
889889 0 0
890890 7.01695e6 0.296943
891891 −1.11688e6 1.93450e6i −0.0471318 0.0816347i
892892 4.20955e6 7.29116e6i 0.177143 0.306821i
893893 −4.77861e6 + 8.27679e6i −0.200527 + 0.347323i
894894 6.49700e6 + 1.12531e7i 0.271875 + 0.470901i
895895 −1.66827e7 −0.696160
896896 0 0
897897 9.32247e6 0.386856
898898 7.58288e6 + 1.31339e7i 0.313793 + 0.543505i
899899 −1.83616e7 + 3.18032e7i −0.757724 + 1.31242i
900900 1.69717e6 2.93959e6i 0.0698425 0.120971i
901901 1.44326e7 + 2.49980e7i 0.592287 + 1.02587i
902902 −1.59813e6 −0.0654029
903903 0 0
904904 −1.24103e7 −0.505080
905905 −3.38927e6 5.87039e6i −0.137558 0.238257i
906906 7.81300e6 1.35325e7i 0.316226 0.547719i
907907 1.17241e7 2.03067e7i 0.473217 0.819636i −0.526313 0.850291i 0.676426π-0.676426\pi
0.999530 + 0.0306552i 0.00975938π0.00975938\pi
908908 −7.85284e6 1.36015e7i −0.316091 0.547486i
909909 5.33421e6 0.214121
910910 0 0
911911 −3.29134e7 −1.31395 −0.656973 0.753914i 0.728163π-0.728163\pi
−0.656973 + 0.753914i 0.728163π0.728163\pi
912912 1.18218e6 + 2.04760e6i 0.0470650 + 0.0815190i
913913 1.46727e7 2.54139e7i 0.582550 1.00901i
914914 −3.40562e6 + 5.89870e6i −0.134844 + 0.233556i
915915 −3.25775e6 5.64259e6i −0.128637 0.222805i
916916 1.36130e6 0.0536061
917917 0 0
918918 −2.36151e6 −0.0924877
919919 1.26132e7 + 2.18467e7i 0.492647 + 0.853290i 0.999964 0.00846958i 0.00269598π-0.00269598\pi
−0.507317 + 0.861760i 0.669363π0.669363\pi
920920 1.02351e6 1.77278e6i 0.0398680 0.0690533i
921921 −188345. + 326222.i −0.00731651 + 0.0126726i
922922 9.11073e6 + 1.57802e7i 0.352960 + 0.611345i
923923 4.45454e7 1.72107
924924 0 0
925925 −3.35037e7 −1.28748
926926 −1.16529e7 2.01835e7i −0.446589 0.773515i
927927 5.27302e6 9.13314e6i 0.201540 0.349077i
928928 −2.67163e6 + 4.62740e6i −0.101837 + 0.176387i
929929 1.25582e7 + 2.17514e7i 0.477406 + 0.826891i 0.999665 0.0258958i 0.00824382π-0.00824382\pi
−0.522259 + 0.852787i 0.674910π0.674910\pi
930930 −5.69863e6 −0.216055
931931 0 0
932932 1.80997e6 0.0682544
933933 −1.03135e7 1.78635e7i −0.387885 0.671837i
934934 −7.08522e6 + 1.22720e7i −0.265758 + 0.460306i
935935 −3.10082e6 + 5.37077e6i −0.115997 + 0.200913i
936936 −1.88805e6 3.27021e6i −0.0704409 0.122007i
937937 −8.25845e6 −0.307291 −0.153645 0.988126i 0.549101π-0.549101\pi
−0.153645 + 0.988126i 0.549101π0.549101\pi
938938 0 0
939939 −2.04435e7 −0.756642
940940 −1.67580e6 2.90258e6i −0.0618591 0.107143i
941941 6.35439e6 1.10061e7i 0.233938 0.405192i −0.725026 0.688722i 0.758172π-0.758172\pi
0.958963 + 0.283530i 0.0915055π0.0915055\pi
942942 −9.20873e6 + 1.59500e7i −0.338121 + 0.585643i
943943 834380. + 1.44519e6i 0.0305552 + 0.0529231i
944944 7.77630e6 0.284016
945945 0 0
946946 4.99003e6 0.181291
947947 −5.31391e6 9.20397e6i −0.192548 0.333503i 0.753546 0.657395i 0.228342π-0.228342\pi
−0.946094 + 0.323892i 0.895009π0.895009\pi
948948 2.52003e6 4.36482e6i 0.0910721 0.157741i
949949 1.50301e7 2.60328e7i 0.541745 0.938330i
950950 −5.37544e6 9.31053e6i −0.193243 0.334707i
951951 −1.78627e7 −0.640465
952952 0 0
953953 749727. 0.0267406 0.0133703 0.999911i 0.495744π-0.495744\pi
0.0133703 + 0.999911i 0.495744π0.495744\pi
954954 −5.77413e6 1.00011e7i −0.205407 0.355776i
955955 2.95980e6 5.12652e6i 0.105016 0.181892i
956956 7.16080e6 1.24029e7i 0.253406 0.438912i
957957 −7.99443e6 1.38468e7i −0.282168 0.488729i
958958 1.69417e7 0.596407
959959 0 0
960960 −829158. −0.0290375
961961 −1.04504e7 1.81005e7i −0.365025 0.632242i
962962 −1.86359e7 + 3.22784e7i −0.649253 + 1.12454i
963963 −104934. + 181750.i −0.00364627 + 0.00631552i
964964 4.22172e6 + 7.31223e6i 0.146318 + 0.253430i
965965 1.86940e7 0.646225
966966 0 0
967967 2.97713e7 1.02384 0.511920 0.859033i 0.328934π-0.328934\pi
0.511920 + 0.859033i 0.328934π0.328934\pi
968968 1.44438e6 + 2.50174e6i 0.0495442 + 0.0858130i
969969 −3.73980e6 + 6.47752e6i −0.127950 + 0.221615i
970970 7.27696e6 1.26041e7i 0.248325 0.430112i
971971 −7.56052e6 1.30952e7i −0.257338 0.445722i 0.708190 0.706022i 0.249512π-0.249512\pi
−0.965528 + 0.260300i 0.916179π0.916179\pi
972972 944784. 0.0320750
973973 0 0
974974 −2.26192e7 −0.763975
975975 8.58505e6 + 1.48697e7i 0.289222 + 0.500947i
976976 4.11984e6 7.13577e6i 0.138438 0.239782i
977977 −965535. + 1.67236e6i −0.0323617 + 0.0560522i −0.881753 0.471712i 0.843636π-0.843636\pi
0.849391 + 0.527764i 0.176970π0.176970\pi
978978 4.52285e6 + 7.83380e6i 0.151205 + 0.261894i
979979 −2.65535e7 −0.885452
980980 0 0
981981 8.96295e6 0.297357
982982 −1.66637e7 2.88623e7i −0.551432 0.955108i
983983 2.11172e7 3.65760e7i 0.697030 1.20729i −0.272461 0.962167i 0.587838π-0.587838\pi
0.969491 0.245125i 0.0788291π-0.0788291\pi
984984 337969. 585380.i 0.0111273 0.0192730i
985985 −1.18558e7 2.05349e7i −0.389352 0.674377i
986986 −1.69032e7 −0.553704
987987 0 0
988988 −1.19600e7 −0.389798
989989 −2.60528e6 4.51247e6i −0.0846961 0.146698i
990990 1.24056e6 2.14871e6i 0.0402282 0.0696772i
991991 −2.91740e6 + 5.05308e6i −0.0943651 + 0.163445i −0.909343 0.416046i 0.863415π-0.863415\pi
0.814978 + 0.579491i 0.196749π0.196749\pi
992992 −3.60333e6 6.24114e6i −0.116258 0.201365i
993993 5.74615e6 0.184928
994994 0 0
995995 1.57124e7 0.503136
996996 6.20589e6 + 1.07489e7i 0.198224 + 0.343334i
997997 6.17303e6 1.06920e7i 0.196680 0.340660i −0.750770 0.660564i 0.770317π-0.770317\pi
0.947450 + 0.319904i 0.103651π0.103651\pi
998998 1.44754e7 2.50721e7i 0.460048 0.796827i
999999 −4.66272e6 8.07607e6i −0.147818 0.256027i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 294.6.e.s.67.2 4
7.2 even 3 inner 294.6.e.s.79.2 4
7.3 odd 6 294.6.a.r.1.2 2
7.4 even 3 294.6.a.w.1.1 2
7.5 odd 6 42.6.e.c.37.1 yes 4
7.6 odd 2 42.6.e.c.25.1 4
21.5 even 6 126.6.g.h.37.2 4
21.11 odd 6 882.6.a.bb.1.2 2
21.17 even 6 882.6.a.bh.1.1 2
21.20 even 2 126.6.g.h.109.2 4
28.19 even 6 336.6.q.f.289.1 4
28.27 even 2 336.6.q.f.193.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.e.c.25.1 4 7.6 odd 2
42.6.e.c.37.1 yes 4 7.5 odd 6
126.6.g.h.37.2 4 21.5 even 6
126.6.g.h.109.2 4 21.20 even 2
294.6.a.r.1.2 2 7.3 odd 6
294.6.a.w.1.1 2 7.4 even 3
294.6.e.s.67.2 4 1.1 even 1 trivial
294.6.e.s.79.2 4 7.2 even 3 inner
336.6.q.f.193.1 4 28.27 even 2
336.6.q.f.289.1 4 28.19 even 6
882.6.a.bb.1.2 2 21.11 odd 6
882.6.a.bh.1.1 2 21.17 even 6