Properties

Label 294.8.e.j.67.1
Level 294294
Weight 88
Character 294.67
Analytic conductor 91.84191.841
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,8,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, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: N N == 294=2372 294 = 2 \cdot 3 \cdot 7^{2}
Weight: k k == 8 8
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: 91.841197492391.8411974923
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
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 67.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 294.67
Dual form 294.8.e.j.79.1

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+(4.00000+6.92820i)q2+(13.5000+23.3827i)q3+(32.0000+55.4256i)q4+(61.0000+105.655i)q5216.000q6512.000q8+(364.500631.333i)q9+(488.000+845.241i)q10+(506.000876.418i)q11+(864.0001496.49i)q12+3126.00q133294.00q15+(2048.003547.24i)q16+(14147.024503.3i)q17+(2916.005050.66i)q18+(11114.0+19250.0i)q197808.00q20+8096.00q22+(54320.0+94085.0i)q23+(6912.0011971.9i)q24+(31620.554768.3i)q25+(12504.0+21657.6i)q26+19683.0q2741354.0q29+(13176.022821.5i)q30+(23328.0+40405.3i)q31+(16384.028377.9i)q32+(13662.0+23663.3i)q33+226352.q34+46656.0q36+(42857.0+74230.5i)q37+(88912.0+154000.i)q38+(42201.0+73094.3i)q39+(31232.054095.4i)q40155694.q41+926804.q43+(32384.0+56090.7i)q44+(44469.077022.6i)q45+(434560.+752680.i)q46+(264576.+458259.i)q47+110592.q48+505928.q50+(381969.+661590.i)q51+(100032.+173261.i)q52+(147033.254669.i)q53+(78732.0+136368.i)q54+123464.q55600156.q57+(165416.286509.i)q58+(333646.577892.i)q59+(105408.182572.i)q60+(416715.721772.i)q61373248.q62+262144.q64+(190686.+330278.i)q65+(109296.+189306.i)q66+(576998.+999390.i)q67+(905408.+1.56821e6i)q682.93328e6q69+3.84234e6q71+(186624.+323242.i)q72+(741845.+1.28491e6i)q73+(342856.+593844.i)q74+(853754.+1.47874e6i)q751.42259e6q76675216.q78+(1.88191e6+3.25957e6i)q79+(249856.432763.i)q80+(265720.+460241.i)q81+(622776.1.07868e6i)q825.39309e6q83+3.45187e6q85+(3.70722e6+6.42109e6i)q86+(558279.966968.i)q87+(259072.+448726.i)q88+(1.25134e62.16739e6i)q89+711504.q906.95296e6q92+(629856.1.09094e6i)q93+(2.11661e6+3.66607e6i)q94+(1.35591e6+2.34850e6i)q95+(442368.+766204.i)q964.59755e6q97737748.q99+O(q100)q+(4.00000 + 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(61.0000 + 105.655i) q^{5} -216.000 q^{6} -512.000 q^{8} +(-364.500 - 631.333i) q^{9} +(-488.000 + 845.241i) q^{10} +(506.000 - 876.418i) q^{11} +(-864.000 - 1496.49i) q^{12} +3126.00 q^{13} -3294.00 q^{15} +(-2048.00 - 3547.24i) q^{16} +(14147.0 - 24503.3i) q^{17} +(2916.00 - 5050.66i) q^{18} +(11114.0 + 19250.0i) q^{19} -7808.00 q^{20} +8096.00 q^{22} +(54320.0 + 94085.0i) q^{23} +(6912.00 - 11971.9i) q^{24} +(31620.5 - 54768.3i) q^{25} +(12504.0 + 21657.6i) q^{26} +19683.0 q^{27} -41354.0 q^{29} +(-13176.0 - 22821.5i) q^{30} +(-23328.0 + 40405.3i) q^{31} +(16384.0 - 28377.9i) q^{32} +(13662.0 + 23663.3i) q^{33} +226352. q^{34} +46656.0 q^{36} +(42857.0 + 74230.5i) q^{37} +(-88912.0 + 154000. i) q^{38} +(-42201.0 + 73094.3i) q^{39} +(-31232.0 - 54095.4i) q^{40} -155694. q^{41} +926804. q^{43} +(32384.0 + 56090.7i) q^{44} +(44469.0 - 77022.6i) q^{45} +(-434560. + 752680. i) q^{46} +(264576. + 458259. i) q^{47} +110592. q^{48} +505928. q^{50} +(381969. + 661590. i) q^{51} +(-100032. + 173261. i) q^{52} +(147033. - 254669. i) q^{53} +(78732.0 + 136368. i) q^{54} +123464. q^{55} -600156. q^{57} +(-165416. - 286509. i) q^{58} +(333646. - 577892. i) q^{59} +(105408. - 182572. i) q^{60} +(-416715. - 721772. i) q^{61} -373248. q^{62} +262144. q^{64} +(190686. + 330278. i) q^{65} +(-109296. + 189306. i) q^{66} +(-576998. + 999390. i) q^{67} +(905408. + 1.56821e6i) q^{68} -2.93328e6 q^{69} +3.84234e6 q^{71} +(186624. + 323242. i) q^{72} +(-741845. + 1.28491e6i) q^{73} +(-342856. + 593844. i) q^{74} +(853754. + 1.47874e6i) q^{75} -1.42259e6 q^{76} -675216. q^{78} +(1.88191e6 + 3.25957e6i) q^{79} +(249856. - 432763. i) q^{80} +(-265720. + 460241. i) q^{81} +(-622776. - 1.07868e6i) q^{82} -5.39309e6 q^{83} +3.45187e6 q^{85} +(3.70722e6 + 6.42109e6i) q^{86} +(558279. - 966968. i) q^{87} +(-259072. + 448726. i) q^{88} +(-1.25134e6 - 2.16739e6i) q^{89} +711504. q^{90} -6.95296e6 q^{92} +(-629856. - 1.09094e6i) q^{93} +(-2.11661e6 + 3.66607e6i) q^{94} +(-1.35591e6 + 2.34850e6i) q^{95} +(442368. + 766204. i) q^{96} -4.59755e6 q^{97} -737748. q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+8q227q364q4+122q5432q61024q8729q9976q10+1012q111728q12+6252q136588q154096q16+28294q17+5832q18+22228q19+1475496q99+O(q100) 2 q + 8 q^{2} - 27 q^{3} - 64 q^{4} + 122 q^{5} - 432 q^{6} - 1024 q^{8} - 729 q^{9} - 976 q^{10} + 1012 q^{11} - 1728 q^{12} + 6252 q^{13} - 6588 q^{15} - 4096 q^{16} + 28294 q^{17} + 5832 q^{18} + 22228 q^{19}+ \cdots - 1475496 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 4.00000 + 6.92820i 0.353553 + 0.612372i
33 −13.5000 + 23.3827i −0.288675 + 0.500000i
44 −32.0000 + 55.4256i −0.250000 + 0.433013i
55 61.0000 + 105.655i 0.218240 + 0.378003i 0.954270 0.298946i 0.0966350π-0.0966350\pi
−0.736030 + 0.676949i 0.763302π0.763302\pi
66 −216.000 −0.408248
77 0 0
88 −512.000 −0.353553
99 −364.500 631.333i −0.166667 0.288675i
1010 −488.000 + 845.241i −0.154319 + 0.267289i
1111 506.000 876.418i 0.114624 0.198535i −0.803005 0.595972i 0.796767π-0.796767\pi
0.917629 + 0.397437i 0.130100π0.130100\pi
1212 −864.000 1496.49i −0.144338 0.250000i
1313 3126.00 0.394627 0.197314 0.980340i 0.436778π-0.436778\pi
0.197314 + 0.980340i 0.436778π0.436778\pi
1414 0 0
1515 −3294.00 −0.252002
1616 −2048.00 3547.24i −0.125000 0.216506i
1717 14147.0 24503.3i 0.698382 1.20963i −0.270645 0.962679i 0.587237π-0.587237\pi
0.969027 0.246954i 0.0794297π-0.0794297\pi
1818 2916.00 5050.66i 0.117851 0.204124i
1919 11114.0 + 19250.0i 0.371734 + 0.643863i 0.989832 0.142238i 0.0454299π-0.0454299\pi
−0.618098 + 0.786101i 0.712097π0.712097\pi
2020 −7808.00 −0.218240
2121 0 0
2222 8096.00 0.162103
2323 54320.0 + 94085.0i 0.930920 + 1.61240i 0.781753 + 0.623589i 0.214326π0.214326\pi
0.149167 + 0.988812i 0.452341π0.452341\pi
2424 6912.00 11971.9i 0.102062 0.176777i
2525 31620.5 54768.3i 0.404742 0.701034i
2626 12504.0 + 21657.6i 0.139522 + 0.241659i
2727 19683.0 0.192450
2828 0 0
2929 −41354.0 −0.314865 −0.157433 0.987530i 0.550322π-0.550322\pi
−0.157433 + 0.987530i 0.550322π0.550322\pi
3030 −13176.0 22821.5i −0.0890962 0.154319i
3131 −23328.0 + 40405.3i −0.140641 + 0.243597i −0.927738 0.373232i 0.878250π-0.878250\pi
0.787097 + 0.616829i 0.211583π0.211583\pi
3232 16384.0 28377.9i 0.0883883 0.153093i
3333 13662.0 + 23663.3i 0.0661783 + 0.114624i
3434 226352. 0.987662
3535 0 0
3636 46656.0 0.166667
3737 42857.0 + 74230.5i 0.139096 + 0.240922i 0.927155 0.374678i 0.122247π-0.122247\pi
−0.788058 + 0.615600i 0.788914π0.788914\pi
3838 −88912.0 + 154000.i −0.262856 + 0.455280i
3939 −42201.0 + 73094.3i −0.113919 + 0.197314i
4040 −31232.0 54095.4i −0.0771596 0.133644i
4141 −155694. −0.352800 −0.176400 0.984319i 0.556445π-0.556445\pi
−0.176400 + 0.984319i 0.556445π0.556445\pi
4242 0 0
4343 926804. 1.77766 0.888829 0.458239i 0.151519π-0.151519\pi
0.888829 + 0.458239i 0.151519π0.151519\pi
4444 32384.0 + 56090.7i 0.0573121 + 0.0992674i
4545 44469.0 77022.6i 0.0727467 0.126001i
4646 −434560. + 752680.i −0.658260 + 1.14014i
4747 264576. + 458259.i 0.371713 + 0.643826i 0.989829 0.142261i 0.0454372π-0.0454372\pi
−0.618116 + 0.786087i 0.712104π0.712104\pi
4848 110592. 0.144338
4949 0 0
5050 505928. 0.572392
5151 381969. + 661590.i 0.403211 + 0.698382i
5252 −100032. + 173261.i −0.0986569 + 0.170879i
5353 147033. 254669.i 0.135659 0.234969i −0.790190 0.612862i 0.790018π-0.790018\pi
0.925849 + 0.377893i 0.123351π0.123351\pi
5454 78732.0 + 136368.i 0.0680414 + 0.117851i
5555 123464. 0.100062
5656 0 0
5757 −600156. −0.429242
5858 −165416. 286509.i −0.111322 0.192815i
5959 333646. 577892.i 0.211497 0.366323i −0.740686 0.671851i 0.765500π-0.765500\pi
0.952183 + 0.305528i 0.0988329π0.0988329\pi
6060 105408. 182572.i 0.0630005 0.109120i
6161 −416715. 721772.i −0.235063 0.407141i 0.724228 0.689561i 0.242196π-0.242196\pi
−0.959291 + 0.282419i 0.908863π0.908863\pi
6262 −373248. −0.198896
6363 0 0
6464 262144. 0.125000
6565 190686. + 330278.i 0.0861236 + 0.149170i
6666 −109296. + 189306.i −0.0467951 + 0.0810515i
6767 −576998. + 999390.i −0.234376 + 0.405951i −0.959091 0.283098i 0.908638π-0.908638\pi
0.724715 + 0.689048i 0.241971π0.241971\pi
6868 905408. + 1.56821e6i 0.349191 + 0.604817i
6969 −2.93328e6 −1.07493
7070 0 0
7171 3.84234e6 1.27406 0.637032 0.770838i 0.280162π-0.280162\pi
0.637032 + 0.770838i 0.280162π0.280162\pi
7272 186624. + 323242.i 0.0589256 + 0.102062i
7373 −741845. + 1.28491e6i −0.223194 + 0.386584i −0.955776 0.294095i 0.904982π-0.904982\pi
0.732582 + 0.680679i 0.238315π0.238315\pi
7474 −342856. + 593844.i −0.0983560 + 0.170358i
7575 853754. + 1.47874e6i 0.233678 + 0.404742i
7676 −1.42259e6 −0.371734
7777 0 0
7878 −675216. −0.161106
7979 1.88191e6 + 3.25957e6i 0.429442 + 0.743815i 0.996824 0.0796396i 0.0253769π-0.0253769\pi
−0.567382 + 0.823455i 0.692044π0.692044\pi
8080 249856. 432763.i 0.0545601 0.0945008i
8181 −265720. + 460241.i −0.0555556 + 0.0962250i
8282 −622776. 1.07868e6i −0.124734 0.216045i
8383 −5.39309e6 −1.03530 −0.517648 0.855594i 0.673192π-0.673192\pi
−0.517648 + 0.855594i 0.673192π0.673192\pi
8484 0 0
8585 3.45187e6 0.609660
8686 3.70722e6 + 6.42109e6i 0.628497 + 1.08859i
8787 558279. 966968.i 0.0908937 0.157433i
8888 −259072. + 448726.i −0.0405258 + 0.0701927i
8989 −1.25134e6 2.16739e6i −0.188153 0.325891i 0.756481 0.654015i 0.226917π-0.226917\pi
−0.944635 + 0.328124i 0.893584π0.893584\pi
9090 711504. 0.102879
9191 0 0
9292 −6.95296e6 −0.930920
9393 −629856. 1.09094e6i −0.0811991 0.140641i
9494 −2.11661e6 + 3.66607e6i −0.262841 + 0.455254i
9595 −1.35591e6 + 2.34850e6i −0.162255 + 0.281034i
9696 442368. + 766204.i 0.0510310 + 0.0883883i
9797 −4.59755e6 −0.511476 −0.255738 0.966746i 0.582318π-0.582318\pi
−0.255738 + 0.966746i 0.582318π0.582318\pi
9898 0 0
9999 −737748. −0.0764161
100100 2.02371e6 + 3.50517e6i 0.202371 + 0.350517i
101101 −1.02642e7 + 1.77782e7i −0.991292 + 1.71697i −0.381609 + 0.924324i 0.624630π0.624630\pi
−0.609684 + 0.792645i 0.708703π0.708703\pi
102102 −3.05575e6 + 5.29272e6i −0.285113 + 0.493831i
103103 −7.11670e6 1.23265e7i −0.641724 1.11150i −0.985048 0.172282i 0.944886π-0.944886\pi
0.343324 0.939217i 0.388447π-0.388447\pi
104104 −1.60051e6 −0.139522
105105 0 0
106106 2.35253e6 0.191851
107107 4.66012e6 + 8.07157e6i 0.367751 + 0.636964i 0.989214 0.146480i 0.0467945π-0.0467945\pi
−0.621462 + 0.783444i 0.713461π0.713461\pi
108108 −629856. + 1.09094e6i −0.0481125 + 0.0833333i
109109 −2.15312e6 + 3.72932e6i −0.159249 + 0.275827i −0.934598 0.355706i 0.884241π-0.884241\pi
0.775349 + 0.631533i 0.217574π0.217574\pi
110110 493856. + 855384.i 0.0353774 + 0.0612755i
111111 −2.31428e6 −0.160615
112112 0 0
113113 6.93570e6 0.452184 0.226092 0.974106i 0.427405π-0.427405\pi
0.226092 + 0.974106i 0.427405π0.427405\pi
114114 −2.40062e6 4.15800e6i −0.151760 0.262856i
115115 −6.62704e6 + 1.14784e7i −0.406328 + 0.703781i
116116 1.32333e6 2.29207e6i 0.0787163 0.136341i
117117 −1.13943e6 1.97355e6i −0.0657712 0.113919i
118118 5.33834e6 0.299102
119119 0 0
120120 1.68653e6 0.0890962
121121 9.23151e6 + 1.59895e7i 0.473723 + 0.820512i
122122 3.33372e6 5.77417e6i 0.166215 0.287892i
123123 2.10187e6 3.64054e6i 0.101845 0.176400i
124124 −1.49299e6 2.58594e6i −0.0703204 0.121799i
125125 1.72467e7 0.789805
126126 0 0
127127 −3.14502e7 −1.36242 −0.681209 0.732089i 0.738545π-0.738545\pi
−0.681209 + 0.732089i 0.738545π0.738545\pi
128128 1.04858e6 + 1.81619e6i 0.0441942 + 0.0765466i
129129 −1.25119e7 + 2.16712e7i −0.513166 + 0.888829i
130130 −1.52549e6 + 2.64222e6i −0.0608986 + 0.105479i
131131 2.24401e6 + 3.88674e6i 0.0872118 + 0.151055i 0.906332 0.422567i 0.138871π-0.138871\pi
−0.819120 + 0.573623i 0.805538π0.805538\pi
132132 −1.74874e6 −0.0661783
133133 0 0
134134 −9.23197e6 −0.331457
135135 1.20066e6 + 2.07961e6i 0.0420004 + 0.0727467i
136136 −7.24326e6 + 1.25457e7i −0.246915 + 0.427670i
137137 −7.81282e6 + 1.35322e7i −0.259589 + 0.449621i −0.966132 0.258049i 0.916920π-0.916920\pi
0.706543 + 0.707670i 0.250254π0.250254\pi
138138 −1.17331e7 2.03224e7i −0.380046 0.658260i
139139 −5.42435e7 −1.71315 −0.856577 0.516020i 0.827413π-0.827413\pi
−0.856577 + 0.516020i 0.827413π0.827413\pi
140140 0 0
141141 −1.42871e7 −0.429217
142142 1.53693e7 + 2.66205e7i 0.450450 + 0.780201i
143143 1.58176e6 2.73968e6i 0.0452338 0.0783473i
144144 −1.49299e6 + 2.58594e6i −0.0416667 + 0.0721688i
145145 −2.52259e6 4.36926e6i −0.0687162 0.119020i
146146 −1.18695e7 −0.315644
147147 0 0
148148 −5.48570e6 −0.139096
149149 1.62475e7 + 2.81415e7i 0.402378 + 0.696939i 0.994012 0.109267i 0.0348505π-0.0348505\pi
−0.591635 + 0.806206i 0.701517π0.701517\pi
150150 −6.83003e6 + 1.18300e7i −0.165235 + 0.286196i
151151 3.81669e7 6.61070e7i 0.902127 1.56253i 0.0773993 0.997000i 0.475338π-0.475338\pi
0.824728 0.565530i 0.191328π-0.191328\pi
152152 −5.69037e6 9.85601e6i −0.131428 0.227640i
153153 −2.06263e7 −0.465588
154154 0 0
155155 −5.69203e6 −0.122774
156156 −2.70086e6 4.67803e6i −0.0569596 0.0986569i
157157 1.46210e7 2.53244e7i 0.301529 0.522264i −0.674953 0.737861i 0.735836π-0.735836\pi
0.976483 + 0.215596i 0.0691695π0.0691695\pi
158158 −1.50553e7 + 2.60765e7i −0.303661 + 0.525957i
159159 3.96989e6 + 6.87605e6i 0.0783229 + 0.135659i
160160 3.99770e6 0.0771596
161161 0 0
162162 −4.25153e6 −0.0785674
163163 4.75449e7 + 8.23502e7i 0.859899 + 1.48939i 0.872025 + 0.489462i 0.162807π0.162807\pi
−0.0121263 + 0.999926i 0.503860π0.503860\pi
164164 4.98221e6 8.62944e6i 0.0882000 0.152767i
165165 −1.66676e6 + 2.88692e6i −0.0288855 + 0.0500312i
166166 −2.15724e7 3.73644e7i −0.366032 0.633987i
167167 −2.29949e7 −0.382054 −0.191027 0.981585i 0.561182π-0.561182\pi
−0.191027 + 0.981585i 0.561182π0.561182\pi
168168 0 0
169169 −5.29766e7 −0.844269
170170 1.38075e7 + 2.39152e7i 0.215547 + 0.373339i
171171 8.10211e6 1.40333e7i 0.123911 0.214621i
172172 −2.96577e7 + 5.13687e7i −0.444415 + 0.769749i
173173 −5.97430e7 1.03478e8i −0.877255 1.51945i −0.854341 0.519713i 0.826039π-0.826039\pi
−0.0229141 0.999737i 0.507294π-0.507294\pi
174174 8.93246e6 0.128543
175175 0 0
176176 −4.14515e6 −0.0573121
177177 9.00844e6 + 1.56031e7i 0.122108 + 0.211497i
178178 1.00108e7 1.73391e7i 0.133045 0.230440i
179179 −4.69127e7 + 8.12553e7i −0.611372 + 1.05893i 0.379638 + 0.925135i 0.376049π0.376049\pi
−0.991010 + 0.133791i 0.957285π0.957285\pi
180180 2.84602e6 + 4.92944e6i 0.0363734 + 0.0630005i
181181 1.48834e8 1.86564 0.932819 0.360346i 0.117341π-0.117341\pi
0.932819 + 0.360346i 0.117341π0.117341\pi
182182 0 0
183183 2.25026e7 0.271428
184184 −2.78118e7 4.81715e7i −0.329130 0.570070i
185185 −5.22855e6 + 9.05612e6i −0.0607128 + 0.105158i
186186 5.03885e6 8.72754e6i 0.0574164 0.0994481i
187187 −1.43168e7 2.47974e7i −0.160103 0.277306i
188188 −3.38657e7 −0.371713
189189 0 0
190190 −2.16945e7 −0.229463
191191 5.07030e7 + 8.78202e7i 0.526522 + 0.911963i 0.999522 + 0.0309010i 0.00983767π0.00983767\pi
−0.473000 + 0.881062i 0.656829π0.656829\pi
192192 −3.53894e6 + 6.12963e6i −0.0360844 + 0.0625000i
193193 −3.52948e7 + 6.11324e7i −0.353395 + 0.612097i −0.986842 0.161688i 0.948306π-0.948306\pi
0.633447 + 0.773786i 0.281639π0.281639\pi
194194 −1.83902e7 3.18528e7i −0.180834 0.313214i
195195 −1.02970e7 −0.0994469
196196 0 0
197197 5.02307e7 0.468099 0.234049 0.972225i 0.424802π-0.424802\pi
0.234049 + 0.972225i 0.424802π0.424802\pi
198198 −2.95099e6 5.11127e6i −0.0270172 0.0467951i
199199 −1.04449e8 + 1.80910e8i −0.939544 + 1.62734i −0.173220 + 0.984883i 0.555417π0.555417\pi
−0.766324 + 0.642454i 0.777916π0.777916\pi
200200 −1.61897e7 + 2.80414e7i −0.143098 + 0.247853i
201201 −1.55789e7 2.69835e7i −0.135317 0.234376i
202202 −1.64228e8 −1.40190
203203 0 0
204204 −4.88920e7 −0.403211
205205 −9.49733e6 1.64499e7i −0.0769951 0.133359i
206206 5.69336e7 9.86119e7i 0.453767 0.785948i
207207 3.95993e7 6.85880e7i 0.310307 0.537467i
208208 −6.40205e6 1.10887e7i −0.0493284 0.0854393i
209209 2.24947e7 0.170439
210210 0 0
211211 −8.44931e7 −0.619202 −0.309601 0.950866i 0.600196π-0.600196\pi
−0.309601 + 0.950866i 0.600196π0.600196\pi
212212 9.41011e6 + 1.62988e7i 0.0678296 + 0.117484i
213213 −5.18715e7 + 8.98441e7i −0.367790 + 0.637032i
214214 −3.72810e7 + 6.45725e7i −0.260039 + 0.450401i
215215 5.65350e7 + 9.79216e7i 0.387957 + 0.671961i
216216 −1.00777e7 −0.0680414
217217 0 0
218218 −3.44500e7 −0.225212
219219 −2.00298e7 3.46927e7i −0.128861 0.223194i
220220 −3.95085e6 + 6.84307e6i −0.0250156 + 0.0433283i
221221 4.42235e7 7.65974e7i 0.275601 0.477354i
222222 −9.25711e6 1.60338e7i −0.0567858 0.0983560i
223223 1.50175e8 0.906837 0.453418 0.891298i 0.350204π-0.350204\pi
0.453418 + 0.891298i 0.350204π0.350204\pi
224224 0 0
225225 −4.61027e7 −0.269828
226226 2.77428e7 + 4.80519e7i 0.159871 + 0.276905i
227227 1.51437e8 2.62296e8i 0.859293 1.48834i −0.0133116 0.999911i 0.504237π-0.504237\pi
0.872604 0.488428i 0.162429π-0.162429\pi
228228 1.92050e7 3.32640e7i 0.107310 0.185867i
229229 2.65687e7 + 4.60183e7i 0.146199 + 0.253225i 0.929820 0.368015i 0.119963π-0.119963\pi
−0.783620 + 0.621240i 0.786629π0.786629\pi
230230 −1.06033e8 −0.574635
231231 0 0
232232 2.11732e7 0.111322
233233 6.81754e7 + 1.18083e8i 0.353087 + 0.611565i 0.986789 0.162013i 0.0517986π-0.0517986\pi
−0.633702 + 0.773578i 0.718465π0.718465\pi
234234 9.11542e6 1.57884e7i 0.0465073 0.0805530i
235235 −3.22783e7 + 5.59076e7i −0.162246 + 0.281018i
236236 2.13533e7 + 3.69851e7i 0.105748 + 0.183162i
237237 −1.01623e8 −0.495877
238238 0 0
239239 2.26802e8 1.07462 0.537309 0.843385i 0.319441π-0.319441\pi
0.537309 + 0.843385i 0.319441π0.319441\pi
240240 6.74611e6 + 1.16846e7i 0.0315003 + 0.0545601i
241241 −2.02527e8 + 3.50786e8i −0.932014 + 1.61430i −0.152139 + 0.988359i 0.548616π0.548616\pi
−0.779874 + 0.625936i 0.784717π0.784717\pi
242242 −7.38521e7 + 1.27916e8i −0.334972 + 0.580189i
243243 −7.17445e6 1.24265e7i −0.0320750 0.0555556i
244244 5.33395e7 0.235063
245245 0 0
246246 3.36299e7 0.144030
247247 3.47424e7 + 6.01755e7i 0.146697 + 0.254086i
248248 1.19439e7 2.06875e7i 0.0497241 0.0861246i
249249 7.28067e7 1.26105e8i 0.298864 0.517648i
250250 6.89866e7 + 1.19488e8i 0.279238 + 0.483655i
251251 −3.08065e7 −0.122966 −0.0614828 0.998108i 0.519583π-0.519583\pi
−0.0614828 + 0.998108i 0.519583π0.519583\pi
252252 0 0
253253 1.09944e8 0.426824
254254 −1.25801e8 2.17893e8i −0.481687 0.834307i
255255 −4.66002e7 + 8.07139e7i −0.175994 + 0.304830i
256256 −8.38861e6 + 1.45295e7i −0.0312500 + 0.0541266i
257257 1.37566e8 + 2.38271e8i 0.505527 + 0.875599i 0.999980 + 0.00639407i 0.00203531π0.00203531\pi
−0.494452 + 0.869205i 0.664631π0.664631\pi
258258 −2.00190e8 −0.725726
259259 0 0
260260 −2.44078e7 −0.0861236
261261 1.50735e7 + 2.61081e7i 0.0524775 + 0.0908937i
262262 −1.79521e7 + 3.10939e7i −0.0616681 + 0.106812i
263263 2.41998e8 4.19153e8i 0.820288 1.42078i −0.0851790 0.996366i 0.527146π-0.527146\pi
0.905467 0.424416i 0.139520π-0.139520\pi
264264 −6.99494e6 1.21156e7i −0.0233976 0.0405258i
265265 3.58761e7 0.118425
266266 0 0
267267 6.75726e7 0.217261
268268 −3.69279e7 6.39610e7i −0.117188 0.202975i
269269 −1.23687e8 + 2.14233e8i −0.387429 + 0.671047i −0.992103 0.125427i 0.959970π-0.959970\pi
0.604674 + 0.796473i 0.293303π0.293303\pi
270270 −9.60530e6 + 1.66369e7i −0.0296987 + 0.0514397i
271271 1.14143e8 + 1.97702e8i 0.348384 + 0.603418i 0.985963 0.166967i 0.0533973π-0.0533973\pi
−0.637579 + 0.770385i 0.720064π0.720064\pi
272272 −1.15892e8 −0.349191
273273 0 0
274274 −1.25005e8 −0.367114
275275 −3.19999e7 5.54255e7i −0.0927865 0.160711i
276276 9.38650e7 1.62579e8i 0.268733 0.465460i
277277 1.77558e8 3.07539e8i 0.501950 0.869403i −0.498047 0.867150i 0.665949π-0.665949\pi
0.999997 0.00225351i 0.000717315π-0.000717315\pi
278278 −2.16974e8 3.75810e8i −0.605691 1.04909i
279279 3.40122e7 0.0937606
280280 0 0
281281 2.28167e8 0.613453 0.306726 0.951798i 0.400766π-0.400766\pi
0.306726 + 0.951798i 0.400766π0.400766\pi
282282 −5.71484e7 9.89840e7i −0.151751 0.262841i
283283 1.06896e8 1.85149e8i 0.280354 0.485588i −0.691118 0.722742i 0.742881π-0.742881\pi
0.971472 + 0.237154i 0.0762147π0.0762147\pi
284284 −1.22955e8 + 2.12964e8i −0.318516 + 0.551686i
285285 −3.66095e7 6.34095e7i −0.0936779 0.162255i
286286 2.53081e7 0.0639703
287287 0 0
288288 −2.38879e7 −0.0589256
289289 −1.95106e8 3.37933e8i −0.475475 0.823547i
290290 2.01808e7 3.49541e7i 0.0485897 0.0841599i
291291 6.20669e7 1.07503e8i 0.147650 0.255738i
292292 −4.74781e7 8.22344e7i −0.111597 0.193292i
293293 3.78816e8 0.879816 0.439908 0.898043i 0.355011π-0.355011\pi
0.439908 + 0.898043i 0.355011π0.355011\pi
294294 0 0
295295 8.14096e7 0.184628
296296 −2.19428e7 3.80060e7i −0.0491780 0.0851788i
297297 9.95960e6 1.72505e7i 0.0220594 0.0382080i
298298 −1.29980e8 + 2.25132e8i −0.284524 + 0.492810i
299299 1.69804e8 + 2.94110e8i 0.367367 + 0.636297i
300300 −1.09280e8 −0.233678
301301 0 0
302302 6.10671e8 1.27580
303303 −2.77134e8 4.80011e8i −0.572323 0.991292i
304304 4.55229e7 7.88481e7i 0.0929336 0.160966i
305305 5.08392e7 8.80561e7i 0.102601 0.177709i
306306 −8.25053e7 1.42903e8i −0.164610 0.285113i
307307 6.33814e8 1.25019 0.625097 0.780547i 0.285059π-0.285059\pi
0.625097 + 0.780547i 0.285059π0.285059\pi
308308 0 0
309309 3.84302e8 0.740999
310310 −2.27681e7 3.94356e7i −0.0434072 0.0751834i
311311 1.95098e8 3.37919e8i 0.367782 0.637018i −0.621436 0.783465i 0.713451π-0.713451\pi
0.989218 + 0.146447i 0.0467838π0.0467838\pi
312312 2.16069e7 3.74243e7i 0.0402765 0.0697609i
313313 5.02221e8 + 8.69872e8i 0.925741 + 1.60343i 0.790365 + 0.612636i 0.209891π0.209891\pi
0.135376 + 0.990794i 0.456776π0.456776\pi
314314 2.33937e8 0.426427
315315 0 0
316316 −2.40885e8 −0.429442
317317 −1.21487e8 2.10422e8i −0.214202 0.371009i 0.738823 0.673899i 0.235382π-0.235382\pi
−0.953025 + 0.302890i 0.902048π0.902048\pi
318318 −3.17591e7 + 5.50084e7i −0.0553826 + 0.0959255i
319319 −2.09251e7 + 3.62434e7i −0.0360911 + 0.0625117i
320320 1.59908e7 + 2.76969e7i 0.0272800 + 0.0472504i
321321 −2.51647e8 −0.424642
322322 0 0
323323 6.28919e8 1.03845
324324 −1.70061e7 2.94555e7i −0.0277778 0.0481125i
325325 9.88457e7 1.71206e8i 0.159722 0.276647i
326326 −3.80359e8 + 6.58801e8i −0.608040 + 1.05316i
327327 −5.81343e7 1.00692e8i −0.0919423 0.159249i
328328 7.97153e7 0.124734
329329 0 0
330330 −2.66682e7 −0.0408503
331331 1.41758e7 + 2.45533e7i 0.0214858 + 0.0372144i 0.876568 0.481277i 0.159827π-0.159827\pi
−0.855083 + 0.518492i 0.826494π0.826494\pi
332332 1.72579e8 2.98915e8i 0.258824 0.448296i
333333 3.12428e7 5.41140e7i 0.0463654 0.0803073i
334334 −9.19797e7 1.59314e8i −0.135076 0.233959i
335335 −1.40788e8 −0.204601
336336 0 0
337337 −1.01675e9 −1.44714 −0.723572 0.690249i 0.757501π-0.757501\pi
−0.723572 + 0.690249i 0.757501π0.757501\pi
338338 −2.11907e8 3.67033e8i −0.298494 0.517007i
339339 −9.36319e7 + 1.62175e8i −0.130534 + 0.226092i
340340 −1.10460e8 + 1.91322e8i −0.152415 + 0.263991i
341341 2.36079e7 + 4.08901e7i 0.0322417 + 0.0558442i
342342 1.29634e8 0.175237
343343 0 0
344344 −4.74524e8 −0.628497
345345 −1.78930e8 3.09916e8i −0.234594 0.406328i
346346 4.77944e8 8.27824e8i 0.620313 1.07441i
347347 4.85247e8 8.40472e8i 0.623461 1.07987i −0.365375 0.930860i 0.619059π-0.619059\pi
0.988836 0.149006i 0.0476075π-0.0476075\pi
348348 3.57299e7 + 6.18859e7i 0.0454469 + 0.0787163i
349349 8.84145e8 1.11336 0.556678 0.830728i 0.312076π-0.312076\pi
0.556678 + 0.830728i 0.312076π0.312076\pi
350350 0 0
351351 6.15291e7 0.0759461
352352 −1.65806e7 2.87185e7i −0.0202629 0.0350963i
353353 5.45231e8 9.44367e8i 0.659734 1.14269i −0.320951 0.947096i 0.604002π-0.604002\pi
0.980684 0.195597i 0.0626643π-0.0626643\pi
354354 −7.20675e7 + 1.24825e8i −0.0863432 + 0.149551i
355355 2.34382e8 + 4.05962e8i 0.278052 + 0.481600i
356356 1.60172e8 0.188153
357357 0 0
358358 −7.50604e8 −0.864610
359359 −5.16865e8 8.95236e8i −0.589585 1.02119i −0.994287 0.106742i 0.965958π-0.965958\pi
0.404702 0.914449i 0.367375π-0.367375\pi
360360 −2.27681e7 + 3.94356e7i −0.0257199 + 0.0445481i
361361 1.99894e8 3.46226e8i 0.223627 0.387333i
362362 5.95336e8 + 1.03115e9i 0.659603 + 1.14247i
363363 −4.98502e8 −0.547008
364364 0 0
365365 −1.81010e8 −0.194840
366366 9.00104e7 + 1.55903e8i 0.0959642 + 0.166215i
367367 1.21092e8 2.09737e8i 0.127874 0.221484i −0.794979 0.606637i 0.792518π-0.792518\pi
0.922853 + 0.385153i 0.125851π0.125851\pi
368368 2.22495e8 3.85372e8i 0.232730 0.403100i
369369 5.67505e7 + 9.82947e7i 0.0588000 + 0.101845i
370370 −8.36569e7 −0.0858609
371371 0 0
372372 8.06216e7 0.0811991
373373 7.18844e8 + 1.24507e9i 0.717222 + 1.24226i 0.962096 + 0.272710i 0.0879199π0.0879199\pi
−0.244874 + 0.969555i 0.578747π0.578747\pi
374374 1.14534e8 1.98379e8i 0.113210 0.196085i
375375 −2.32830e8 + 4.03273e8i −0.227997 + 0.394902i
376376 −1.35463e8 2.34629e8i −0.131420 0.227627i
377377 −1.29273e8 −0.124254
378378 0 0
379379 1.20169e9 1.13385 0.566924 0.823770i 0.308133π-0.308133\pi
0.566924 + 0.823770i 0.308133π0.308133\pi
380380 −8.67781e7 1.50304e8i −0.0811274 0.140517i
381381 4.24577e8 7.35390e8i 0.393296 0.681209i
382382 −4.05624e8 + 7.02561e8i −0.372307 + 0.644855i
383383 −3.15429e8 5.46340e8i −0.286884 0.496898i 0.686180 0.727431i 0.259286π-0.259286\pi
−0.973064 + 0.230534i 0.925953π0.925953\pi
384384 −5.66231e7 −0.0510310
385385 0 0
386386 −5.64717e8 −0.499775
387387 −3.37820e8 5.85122e8i −0.296276 0.513166i
388388 1.47122e8 2.54822e8i 0.127869 0.221476i
389389 7.10929e8 1.23137e9i 0.612354 1.06063i −0.378488 0.925606i 0.623556π-0.623556\pi
0.990843 0.135022i 0.0431106π-0.0431106\pi
390390 −4.11882e7 7.13400e7i −0.0351598 0.0608986i
391391 3.07386e9 2.60055
392392 0 0
393393 −1.21177e8 −0.100704
394394 2.00923e8 + 3.48009e8i 0.165498 + 0.286651i
395395 −2.29593e8 + 3.97667e8i −0.187443 + 0.324661i
396396 2.36079e7 4.08901e7i 0.0191040 0.0330891i
397397 −3.52485e7 6.10521e7i −0.0282731 0.0489704i 0.851543 0.524285i 0.175667π-0.175667\pi
−0.879816 + 0.475315i 0.842334π0.842334\pi
398398 −1.67118e9 −1.32872
399399 0 0
400400 −2.59035e8 −0.202371
401401 −1.01161e9 1.75216e9i −0.783444 1.35697i −0.929924 0.367752i 0.880128π-0.880128\pi
0.146480 0.989214i 0.453206π-0.453206\pi
402402 1.24632e8 2.15868e8i 0.0956835 0.165729i
403403 −7.29233e7 + 1.26307e8i −0.0555007 + 0.0961301i
404404 −6.56911e8 1.13780e9i −0.495646 0.858484i
405405 −6.48358e7 −0.0484978
406406 0 0
407407 8.67426e7 0.0637752
408408 −1.95568e8 3.38734e8i −0.142557 0.246915i
409409 −7.18632e8 + 1.24471e9i −0.519368 + 0.899571i 0.480379 + 0.877061i 0.340499π0.340499\pi
−0.999747 + 0.0225102i 0.992834π0.992834\pi
410410 7.59787e7 1.31599e8i 0.0544438 0.0942994i
411411 −2.10946e8 3.65369e8i −0.149874 0.259589i
412412 9.10938e8 0.641724
413413 0 0
414414 6.33588e8 0.438840
415415 −3.28979e8 5.69808e8i −0.225943 0.391345i
416416 5.12164e7 8.87094e7i 0.0348805 0.0604147i
417417 7.32288e8 1.26836e9i 0.494545 0.856577i
418418 8.99789e7 + 1.55848e8i 0.0602593 + 0.104372i
419419 8.62098e7 0.0572542 0.0286271 0.999590i 0.490886π-0.490886\pi
0.0286271 + 0.999590i 0.490886π0.490886\pi
420420 0 0
421421 −1.18254e9 −0.772378 −0.386189 0.922420i 0.626209π-0.626209\pi
−0.386189 + 0.922420i 0.626209π0.626209\pi
422422 −3.37972e8 5.85385e8i −0.218921 0.379183i
423423 1.92876e8 3.34071e8i 0.123904 0.214609i
424424 −7.52809e7 + 1.30390e8i −0.0479628 + 0.0830740i
425425 −8.94670e8 1.54961e9i −0.565330 0.979180i
426426 −8.29945e8 −0.520134
427427 0 0
428428 −5.96496e8 −0.367751
429429 4.27074e7 + 7.39714e7i 0.0261158 + 0.0452338i
430430 −4.52280e8 + 7.83373e8i −0.274327 + 0.475148i
431431 −3.02329e8 + 5.23649e8i −0.181890 + 0.315043i −0.942524 0.334138i 0.891555π-0.891555\pi
0.760634 + 0.649181i 0.224888π0.224888\pi
432432 −4.03108e7 6.98203e7i −0.0240563 0.0416667i
433433 7.16394e7 0.0424076 0.0212038 0.999775i 0.493250π-0.493250\pi
0.0212038 + 0.999775i 0.493250π0.493250\pi
434434 0 0
435435 1.36220e8 0.0793467
436436 −1.37800e8 2.38676e8i −0.0796244 0.137913i
437437 −1.20742e9 + 2.09132e9i −0.692110 + 1.19877i
438438 1.60239e8 2.77541e8i 0.0911187 0.157822i
439439 −9.74587e7 1.68803e8i −0.0549788 0.0952260i 0.837226 0.546857i 0.184176π-0.184176\pi
−0.892205 + 0.451631i 0.850842π0.850842\pi
440440 −6.32136e7 −0.0353774
441441 0 0
442442 7.07576e8 0.389758
443443 1.04009e9 + 1.80149e9i 0.568405 + 0.984507i 0.996724 + 0.0808791i 0.0257728π0.0257728\pi
−0.428319 + 0.903628i 0.640894π0.640894\pi
444444 7.40569e7 1.28270e8i 0.0401537 0.0695482i
445445 1.52664e8 2.64422e8i 0.0821253 0.142245i
446446 6.00698e8 + 1.04044e9i 0.320615 + 0.555322i
447447 −8.77364e8 −0.464626
448448 0 0
449449 1.78606e9 0.931180 0.465590 0.885000i 0.345842π-0.345842\pi
0.465590 + 0.885000i 0.345842π0.345842\pi
450450 −1.84411e8 3.19409e8i −0.0953987 0.165235i
451451 −7.87812e7 + 1.36453e8i −0.0404394 + 0.0700431i
452452 −2.21942e8 + 3.84415e8i −0.113046 + 0.195802i
453453 1.03051e9 + 1.78489e9i 0.520843 + 0.902127i
454454 2.42299e9 1.21522
455455 0 0
456456 3.07280e8 0.151760
457457 1.12154e9 + 1.94256e9i 0.549678 + 0.952069i 0.998296 + 0.0583463i 0.0185827π0.0185827\pi
−0.448619 + 0.893723i 0.648084π0.648084\pi
458458 −2.12549e8 + 3.68146e8i −0.103379 + 0.179057i
459459 2.78455e8 4.82299e8i 0.134404 0.232794i
460460 −4.24131e8 7.34616e8i −0.203164 0.351891i
461461 −2.60254e9 −1.23721 −0.618607 0.785701i 0.712303π-0.712303\pi
−0.618607 + 0.785701i 0.712303π0.712303\pi
462462 0 0
463463 −7.12557e8 −0.333646 −0.166823 0.985987i 0.553351π-0.553351\pi
−0.166823 + 0.985987i 0.553351π0.553351\pi
464464 8.46930e7 + 1.46693e8i 0.0393581 + 0.0681703i
465465 7.68424e7 1.33095e8i 0.0354418 0.0613870i
466466 −5.45403e8 + 9.44666e8i −0.249670 + 0.432442i
467467 3.16734e8 + 5.48600e8i 0.143908 + 0.249257i 0.928965 0.370167i 0.120700π-0.120700\pi
−0.785057 + 0.619424i 0.787366π0.787366\pi
468468 1.45847e8 0.0657712
469469 0 0
470470 −5.16452e8 −0.229450
471471 3.94768e8 + 6.83759e8i 0.174088 + 0.301529i
472472 −1.70827e8 + 2.95881e8i −0.0747754 + 0.129515i
473473 4.68963e8 8.12267e8i 0.203763 0.352927i
474474 −4.06493e8 7.04067e8i −0.175319 0.303661i
475475 1.40572e9 0.601827
476476 0 0
477477 −2.14374e8 −0.0904395
478478 9.07208e8 + 1.57133e9i 0.379935 + 0.658067i
479479 1.10276e8 1.91004e8i 0.0458466 0.0794086i −0.842191 0.539179i 0.818735π-0.818735\pi
0.888038 + 0.459770i 0.152068π0.152068\pi
480480 −5.39689e7 + 9.34769e7i −0.0222741 + 0.0385798i
481481 1.33971e8 + 2.32045e8i 0.0548912 + 0.0950744i
482482 −3.24042e9 −1.31807
483483 0 0
484484 −1.18163e9 −0.473723
485485 −2.80451e8 4.85755e8i −0.111625 0.193340i
486486 5.73956e7 9.94121e7i 0.0226805 0.0392837i
487487 −1.96466e9 + 3.40289e9i −0.770791 + 1.33505i 0.166339 + 0.986069i 0.446805π0.446805\pi
−0.937130 + 0.348980i 0.886528π0.886528\pi
488488 2.13358e8 + 3.69547e8i 0.0831074 + 0.143946i
489489 −2.56742e9 −0.992925
490490 0 0
491491 −3.28904e9 −1.25396 −0.626980 0.779036i 0.715709π-0.715709\pi
−0.626980 + 0.779036i 0.715709π0.715709\pi
492492 1.34520e8 + 2.32995e8i 0.0509223 + 0.0882000i
493493 −5.85035e8 + 1.01331e9i −0.219896 + 0.380871i
494494 −2.77939e8 + 4.81404e8i −0.103730 + 0.179666i
495495 −4.50026e7 7.79468e7i −0.0166771 0.0288855i
496496 1.91103e8 0.0703204
497497 0 0
498498 1.16491e9 0.422658
499499 2.15315e9 + 3.72937e9i 0.775752 + 1.34364i 0.934371 + 0.356302i 0.115962π0.115962\pi
−0.158619 + 0.987340i 0.550704π0.550704\pi
500500 −5.51893e8 + 9.55906e8i −0.197451 + 0.341995i
501501 3.10432e8 5.37683e8i 0.110289 0.191027i
502502 −1.23226e8 2.13433e8i −0.0434749 0.0753008i
503503 −2.56392e9 −0.898291 −0.449145 0.893459i 0.648271π-0.648271\pi
−0.449145 + 0.893459i 0.648271π0.648271\pi
504504 0 0
505505 −2.50447e9 −0.865360
506506 4.39775e8 + 7.61712e8i 0.150905 + 0.261375i
507507 7.15185e8 1.23874e9i 0.243720 0.422135i
508508 1.00641e9 1.74315e9i 0.340604 0.589944i
509509 −2.10193e9 3.64065e9i −0.706490 1.22368i −0.966151 0.257977i 0.916944π-0.916944\pi
0.259661 0.965700i 0.416389π-0.416389\pi
510510 −7.45603e8 −0.248893
511511 0 0
512512 −1.34218e8 −0.0441942
513513 2.18757e8 + 3.78898e8i 0.0715403 + 0.123911i
514514 −1.10053e9 + 1.90617e9i −0.357462 + 0.619142i
515515 8.68237e8 1.50383e9i 0.280100 0.485148i
516516 −8.00759e8 1.38695e9i −0.256583 0.444415i
517517 5.35502e8 0.170429
518518 0 0
519519 3.22612e9 1.01297
520520 −9.76312e7 1.69102e8i −0.0304493 0.0527397i
521521 −2.25385e9 + 3.90378e9i −0.698220 + 1.20935i 0.270862 + 0.962618i 0.412691π0.412691\pi
−0.969083 + 0.246735i 0.920642π0.920642\pi
522522 −1.20588e8 + 2.08865e8i −0.0371072 + 0.0642716i
523523 2.73176e9 + 4.73154e9i 0.835000 + 1.44626i 0.894031 + 0.448006i 0.147866π0.147866\pi
−0.0590308 + 0.998256i 0.518801π0.518801\pi
524524 −2.87233e8 −0.0872118
525525 0 0
526526 3.87197e9 1.16006
527527 6.60042e8 + 1.14323e9i 0.196442 + 0.340248i
528528 5.59596e7 9.69248e7i 0.0165446 0.0286560i
529529 −4.19891e9 + 7.27273e9i −1.23322 + 2.13601i
530530 1.43504e8 + 2.48557e8i 0.0418696 + 0.0725203i
531531 −4.86456e8 −0.140998
532532 0 0
533533 −4.86699e8 −0.139224
534534 2.70291e8 + 4.68157e8i 0.0768133 + 0.133045i
535535 −5.68535e8 + 9.84731e8i −0.160516 + 0.278022i
536536 2.95423e8 5.11688e8i 0.0828643 0.143525i
537537 −1.26664e9 2.19389e9i −0.352976 0.611372i
538538 −1.97900e9 −0.547907
539539 0 0
540540 −1.53685e8 −0.0420004
541541 3.29315e9 + 5.70390e9i 0.894171 + 1.54875i 0.834827 + 0.550512i 0.185568π0.185568\pi
0.0593443 + 0.998238i 0.481099π0.481099\pi
542542 −9.13146e8 + 1.58162e9i −0.246345 + 0.426681i
543543 −2.00926e9 + 3.48014e9i −0.538563 + 0.932819i
544544 −4.63569e8 8.02925e8i −0.123458 0.213835i
545545 −5.25362e8 −0.139018
546546 0 0
547547 −1.71749e9 −0.448681 −0.224340 0.974511i 0.572023π-0.572023\pi
−0.224340 + 0.974511i 0.572023π0.572023\pi
548548 −5.00021e8 8.66061e8i −0.129794 0.224810i
549549 −3.03785e8 + 5.26171e8i −0.0783544 + 0.135714i
550550 2.56000e8 4.43404e8i 0.0656100 0.113640i
551551 −4.59608e8 7.96065e8i −0.117046 0.202730i
552552 1.50184e9 0.380046
553553 0 0
554554 2.84093e9 0.709865
555555 −1.41171e8 2.44515e8i −0.0350526 0.0607128i
556556 1.73579e9 3.00648e9i 0.428288 0.741817i
557557 −2.47132e9 + 4.28045e9i −0.605949 + 1.04953i 0.385952 + 0.922519i 0.373873π0.373873\pi
−0.991901 + 0.127015i 0.959460π0.959460\pi
558558 1.36049e8 + 2.35644e8i 0.0331494 + 0.0574164i
559559 2.89719e9 0.701513
560560 0 0
561561 7.73105e8 0.184871
562562 9.12669e8 + 1.58079e9i 0.216888 + 0.375661i
563563 1.69154e9 2.92983e9i 0.399487 0.691932i −0.594176 0.804335i 0.702522π-0.702522\pi
0.993663 + 0.112404i 0.0358549π0.0358549\pi
564564 4.57187e8 7.91872e8i 0.107304 0.185857i
565565 4.23078e8 + 7.32792e8i 0.0986848 + 0.170927i
566566 1.71033e9 0.396481
567567 0 0
568568 −1.96728e9 −0.450450
569569 1.12318e9 + 1.94540e9i 0.255596 + 0.442706i 0.965057 0.262039i 0.0843949π-0.0843949\pi
−0.709461 + 0.704745i 0.751062π0.751062\pi
570570 2.92876e8 5.07276e8i 0.0662403 0.114731i
571571 3.40547e8 5.89845e8i 0.0765509 0.132590i −0.825209 0.564828i 0.808943π-0.808943\pi
0.901760 + 0.432238i 0.142276π0.142276\pi
572572 1.01232e8 + 1.75340e8i 0.0226169 + 0.0391736i
573573 −2.73796e9 −0.607976
574574 0 0
575575 6.87050e9 1.50713
576576 −9.55515e7 1.65500e8i −0.0208333 0.0360844i
577577 3.74148e8 6.48043e8i 0.0810827 0.140439i −0.822633 0.568573i 0.807496π-0.807496\pi
0.903715 + 0.428134i 0.140829π0.140829\pi
578578 1.56085e9 2.70347e9i 0.336212 0.582336i
579579 −9.52959e8 1.65057e9i −0.204032 0.353395i
580580 3.22892e8 0.0687162
581581 0 0
582582 9.93071e8 0.208809
583583 −1.48797e8 2.57725e8i −0.0310996 0.0538662i
584584 3.79825e8 6.57876e8i 0.0789111 0.136678i
585585 1.39010e8 2.40773e8i 0.0287079 0.0497235i
586586 1.51527e9 + 2.62452e9i 0.311062 + 0.538775i
587587 −6.17294e9 −1.25968 −0.629838 0.776727i 0.716879π-0.716879\pi
−0.629838 + 0.776727i 0.716879π0.716879\pi
588588 0 0
589589 −1.03707e9 −0.209124
590590 3.25638e8 + 5.64022e8i 0.0652760 + 0.113061i
591591 −6.78115e8 + 1.17453e9i −0.135129 + 0.234049i
592592 1.75542e8 3.04048e8i 0.0347741 0.0602305i
593593 −5.02125e9 8.69705e9i −0.988826 1.71270i −0.623513 0.781813i 0.714295π-0.714295\pi
−0.365314 0.930885i 0.619038π-0.619038\pi
594594 1.59354e8 0.0311967
595595 0 0
596596 −2.07968e9 −0.402378
597597 −2.82011e9 4.88458e9i −0.542446 0.939544i
598598 −1.35843e9 + 2.35288e9i −0.259767 + 0.449930i
599599 6.61221e8 1.14527e9i 0.125705 0.217728i −0.796303 0.604898i 0.793214π-0.793214\pi
0.922008 + 0.387170i 0.126547π0.126547\pi
600600 −4.37122e8 7.57117e8i −0.0826177 0.143098i
601601 −4.48600e8 −0.0842944 −0.0421472 0.999111i 0.513420π-0.513420\pi
−0.0421472 + 0.999111i 0.513420π0.513420\pi
602602 0 0
603603 8.41263e8 0.156250
604604 2.44268e9 + 4.23085e9i 0.451064 + 0.781265i
605605 −1.12624e9 + 1.95071e9i −0.206771 + 0.358137i
606606 2.21707e9 3.84009e9i 0.404693 0.700950i
607607 −4.45750e8 7.72061e8i −0.0808967 0.140117i 0.822739 0.568420i 0.192445π-0.192445\pi
−0.903635 + 0.428303i 0.859112π0.859112\pi
608608 7.28367e8 0.131428
609609 0 0
610610 8.13428e8 0.145099
611611 8.27065e8 + 1.43252e9i 0.146688 + 0.254071i
612612 6.60042e8 1.14323e9i 0.116397 0.201606i
613613 −1.75709e9 + 3.04336e9i −0.308092 + 0.533632i −0.977945 0.208862i 0.933024π-0.933024\pi
0.669853 + 0.742494i 0.266357π0.266357\pi
614614 2.53525e9 + 4.39119e9i 0.442010 + 0.765584i
615615 5.12856e8 0.0889063
616616 0 0
617617 3.78067e9 0.647993 0.323996 0.946058i 0.394973π-0.394973\pi
0.323996 + 0.946058i 0.394973π0.394973\pi
618618 1.53721e9 + 2.66252e9i 0.261983 + 0.453767i
619619 −1.34483e9 + 2.32932e9i −0.227903 + 0.394740i −0.957187 0.289472i 0.906520π-0.906520\pi
0.729283 + 0.684212i 0.239854π0.239854\pi
620620 1.82145e8 3.15484e8i 0.0306935 0.0531627i
621621 1.06918e9 + 1.85188e9i 0.179156 + 0.310307i
622622 3.12156e9 0.520123
623623 0 0
624624 3.45711e8 0.0569596
625625 −1.41831e9 2.45658e9i −0.232375 0.402486i
626626 −4.01777e9 + 6.95898e9i −0.654598 + 1.13380i
627627 −3.03679e8 + 5.25987e8i −0.0492015 + 0.0852195i
628628 9.35747e8 + 1.62076e9i 0.150765 + 0.261132i
629629 2.42519e9 0.388570
630630 0 0
631631 −6.91824e9 −1.09621 −0.548104 0.836410i 0.684650π-0.684650\pi
−0.548104 + 0.836410i 0.684650π0.684650\pi
632632 −9.63539e8 1.66890e9i −0.151831 0.262978i
633633 1.14066e9 1.97568e9i 0.178748 0.309601i
634634 9.71898e8 1.68338e9i 0.151464 0.262343i
635635 −1.91846e9 3.32287e9i −0.297334 0.514998i
636636 −5.08146e8 −0.0783229
637637 0 0
638638 −3.34802e8 −0.0510406
639639 −1.40053e9 2.42579e9i −0.212344 0.367790i
640640 −1.27926e8 + 2.21575e8i −0.0192899 + 0.0334111i
641641 2.74979e9 4.76278e9i 0.412379 0.714262i −0.582770 0.812637i 0.698031π-0.698031\pi
0.995149 + 0.0983750i 0.0313645π0.0313645\pi
642642 −1.00659e9 1.74346e9i −0.150134 0.260039i
643643 −1.35931e9 −0.201641 −0.100821 0.994905i 0.532147π-0.532147\pi
−0.100821 + 0.994905i 0.532147π0.532147\pi
644644 0 0
645645 −3.05289e9 −0.447974
646646 2.51568e9 + 4.35728e9i 0.367148 + 0.635919i
647647 3.64592e9 6.31492e9i 0.529228 0.916649i −0.470191 0.882565i 0.655815π-0.655815\pi
0.999419 0.0340847i 0.0108516π-0.0108516\pi
648648 1.36049e8 2.35644e8i 0.0196419 0.0340207i
649649 −3.37650e8 5.84827e8i −0.0484853 0.0839790i
650650 1.58153e9 0.225882
651651 0 0
652652 −6.08575e9 −0.859899
653653 4.98442e8 + 8.63327e8i 0.0700517 + 0.121333i 0.898924 0.438105i 0.144350π-0.144350\pi
−0.828872 + 0.559438i 0.811017π0.811017\pi
654654 4.65075e8 8.05533e8i 0.0650130 0.112606i
655655 −2.73769e8 + 4.74182e8i −0.0380662 + 0.0659327i
656656 3.18861e8 + 5.52284e8i 0.0441000 + 0.0763834i
657657 1.08161e9 0.148796
658658 0 0
659659 −1.35118e10 −1.83914 −0.919568 0.392932i 0.871461π-0.871461\pi
−0.919568 + 0.392932i 0.871461π0.871461\pi
660660 −1.06673e8 1.84763e8i −0.0144428 0.0250156i
661661 3.89968e9 6.75444e9i 0.525199 0.909671i −0.474370 0.880325i 0.657324π-0.657324\pi
0.999569 0.0293460i 0.00934245π-0.00934245\pi
662662 −1.13407e8 + 1.96426e8i −0.0151927 + 0.0263146i
663663 1.19404e9 + 2.06813e9i 0.159118 + 0.275601i
664664 2.76126e9 0.366032
665665 0 0
666666 4.99884e8 0.0655706
667667 −2.24635e9 3.89079e9i −0.293114 0.507689i
668668 7.35838e8 1.27451e9i 0.0955135 0.165434i
669669 −2.02736e9 + 3.51148e9i −0.261781 + 0.453418i
670670 −5.63150e8 9.75404e8i −0.0723373 0.125292i
671671 −8.43431e8 −0.107776
672672 0 0
673673 −6.85231e9 −0.866531 −0.433265 0.901266i 0.642639π-0.642639\pi
−0.433265 + 0.901266i 0.642639π0.642639\pi
674674 −4.06702e9 7.04428e9i −0.511642 0.886191i
675675 6.22386e8 1.07800e9i 0.0778927 0.134914i
676676 1.69525e9 2.93626e9i 0.211067 0.365579i
677677 3.82852e9 + 6.63119e9i 0.474210 + 0.821355i 0.999564 0.0295283i 0.00940051π-0.00940051\pi
−0.525354 + 0.850884i 0.676067π0.676067\pi
678678 −1.49811e9 −0.184604
679679 0 0
680680 −1.76736e9 −0.215547
681681 4.08880e9 + 7.08200e9i 0.496113 + 0.859293i
682682 −1.88863e8 + 3.27121e8i −0.0227983 + 0.0394878i
683683 2.76338e9 4.78631e9i 0.331870 0.574815i −0.651009 0.759070i 0.725654π-0.725654\pi
0.982878 + 0.184255i 0.0589873π0.0589873\pi
684684 5.18535e8 + 8.98129e8i 0.0619557 + 0.107310i
685685 −1.90633e9 −0.226611
686686 0 0
687687 −1.43471e9 −0.168817
688688 −1.89809e9 3.28760e9i −0.222207 0.384874i
689689 4.59625e8 7.96094e8i 0.0535348 0.0927251i
690690 1.43144e9 2.47933e9i 0.165883 0.287318i
691691 −7.59635e8 1.31573e9i −0.0875854 0.151702i 0.818905 0.573930i 0.194582π-0.194582\pi
−0.906490 + 0.422227i 0.861248π0.861248\pi
692692 7.64711e9 0.877255
693693 0 0
694694 7.76395e9 0.881708
695695 −3.30886e9 5.73111e9i −0.373879 0.647577i
696696 −2.85839e8 + 4.95087e8i −0.0321358 + 0.0556608i
697697 −2.20260e9 + 3.81502e9i −0.246389 + 0.426758i
698698 3.53658e9 + 6.12553e9i 0.393631 + 0.681789i
699699 −3.68147e9 −0.407710
700700 0 0
701701 6.81967e9 0.747739 0.373869 0.927481i 0.378031π-0.378031\pi
0.373869 + 0.927481i 0.378031π0.378031\pi
702702 2.46116e8 + 4.26286e8i 0.0268510 + 0.0465073i
703703 −9.52625e8 + 1.65000e9i −0.103414 + 0.179118i
704704 1.32645e8 2.29748e8i 0.0143280 0.0248169i
705705 −8.71513e8 1.50951e9i −0.0936725 0.162246i
706706 8.72369e9 0.933005
707707 0 0
708708 −1.15308e9 −0.122108
709709 −6.08497e9 1.05395e10i −0.641205 1.11060i −0.985164 0.171615i 0.945102π-0.945102\pi
0.343959 0.938984i 0.388232π-0.388232\pi
710710 −1.87506e9 + 3.24770e9i −0.196612 + 0.340543i
711711 1.37191e9 2.37622e9i 0.143147 0.247938i
712712 6.40689e8 + 1.10971e9i 0.0665223 + 0.115220i
713713 −5.06871e9 −0.523702
714714 0 0
715715 3.85948e8 0.0394874
716716 −3.00242e9 5.20034e9i −0.305686 0.529463i
717717 −3.06183e9 + 5.30324e9i −0.310216 + 0.537309i
718718 4.13492e9 7.16189e9i 0.416899 0.722091i
719719 −1.00013e9 1.73227e9i −0.100347 0.173806i 0.811481 0.584379i 0.198662π-0.198662\pi
−0.911828 + 0.410573i 0.865329π0.865329\pi
720720 −3.64290e8 −0.0363734
721721 0 0
722722 3.19830e9 0.316256
723723 −5.46822e9 9.47123e9i −0.538098 0.932014i
724724 −4.76269e9 + 8.24922e9i −0.466409 + 0.807845i
725725 −1.30763e9 + 2.26489e9i −0.127439 + 0.220731i
726726 −1.99401e9 3.45372e9i −0.193396 0.334972i
727727 1.21193e10 1.16979 0.584895 0.811109i 0.301136π-0.301136\pi
0.584895 + 0.811109i 0.301136π0.301136\pi
728728 0 0
729729 3.87420e8 0.0370370
730730 −7.24041e8 1.25408e9i −0.0688863 0.119315i
731731 1.31115e10 2.27098e10i 1.24148 2.15031i
732732 −7.20084e8 + 1.24722e9i −0.0678569 + 0.117532i
733733 −6.52266e9 1.12976e10i −0.611732 1.05955i −0.990948 0.134243i 0.957140π-0.957140\pi
0.379217 0.925308i 0.376193π-0.376193\pi
734734 1.93746e9 0.180841
735735 0 0
736736 3.55992e9 0.329130
737737 5.83922e8 + 1.01138e9i 0.0537302 + 0.0930635i
738738 −4.54004e8 + 7.86357e8i −0.0415779 + 0.0720150i
739739 −1.13794e9 + 1.97096e9i −0.103720 + 0.179648i −0.913214 0.407479i 0.866408π-0.866408\pi
0.809495 + 0.587127i 0.199741π0.199741\pi
740740 −3.34627e8 5.79592e8i −0.0303564 0.0525789i
741741 −1.87609e9 −0.169391
742742 0 0
743743 2.13411e9 0.190878 0.0954390 0.995435i 0.469575π-0.469575\pi
0.0954390 + 0.995435i 0.469575π0.469575\pi
744744 3.22486e8 + 5.58563e8i 0.0287082 + 0.0497241i
745745 −1.98219e9 + 3.43326e9i −0.175630 + 0.304200i
746746 −5.75075e9 + 9.96059e9i −0.507152 + 0.878414i
747747 1.96578e9 + 3.40483e9i 0.172549 + 0.298864i
748748 1.83255e9 0.160103
749749 0 0
750750 −3.72528e9 −0.322436
751751 −1.02089e10 1.76823e10i −0.879503 1.52334i −0.851887 0.523725i 0.824542π-0.824542\pi
−0.0276155 0.999619i 0.508791π-0.508791\pi
752752 1.08370e9 1.87703e9i 0.0929283 0.160957i
753753 4.15887e8 7.20338e8i 0.0354971 0.0614828i
754754 −5.17090e8 8.95627e8i −0.0439306 0.0760900i
755755 9.31273e9 0.787522
756756 0 0
757757 8.04759e9 0.674265 0.337132 0.941457i 0.390543π-0.390543\pi
0.337132 + 0.941457i 0.390543π0.390543\pi
758758 4.80676e9 + 8.32555e9i 0.400876 + 0.694337i
759759 −1.48424e9 + 2.57078e9i −0.123213 + 0.213412i
760760 6.94225e8 1.20243e9i 0.0573657 0.0993604i
761761 −2.80867e9 4.86476e9i −0.231023 0.400143i 0.727087 0.686546i 0.240874π-0.240874\pi
−0.958109 + 0.286403i 0.907541π0.907541\pi
762762 6.79324e9 0.556204
763763 0 0
764764 −6.48998e9 −0.526522
765765 −1.25821e9 2.17928e9i −0.101610 0.175994i
766766 2.52343e9 4.37072e9i 0.202858 0.351360i
767767 1.04298e9 1.80649e9i 0.0834624 0.144561i
768768 −2.26492e8 3.92296e8i −0.0180422 0.0312500i
769769 −8.92653e9 −0.707849 −0.353924 0.935274i 0.615153π-0.615153\pi
−0.353924 + 0.935274i 0.615153π0.615153\pi
770770 0 0
771771 −7.42855e9 −0.583733
772772 −2.25887e9 3.91247e9i −0.176697 0.306049i
773773 8.99328e9 1.55768e10i 0.700310 1.21297i −0.268048 0.963406i 0.586379π-0.586379\pi
0.968358 0.249566i 0.0802880π-0.0802880\pi
774774 2.70256e9 4.68097e9i 0.209499 0.362863i
775775 1.47529e9 + 2.55527e9i 0.113847 + 0.197188i
776776 2.35395e9 0.180834
777777 0 0
778778 1.13749e10 0.866000
779779 −1.73038e9 2.99711e9i −0.131148 0.227155i
780780 3.29505e8 5.70720e8i 0.0248617 0.0430618i
781781 1.94422e9 3.36749e9i 0.146038 0.252946i
782782 1.22954e10 + 2.12963e10i 0.919434 + 1.59251i
783783 −8.13971e8 −0.0605958
784784 0 0
785785 3.56753e9 0.263223
786786 −4.84706e8 8.39536e8i −0.0356041 0.0616681i
787787 6.57941e9 1.13959e10i 0.481144 0.833366i −0.518622 0.855004i 0.673555π-0.673555\pi
0.999766 + 0.0216375i 0.00688797π0.00688797\pi
788788 −1.60738e9 + 2.78407e9i −0.117025 + 0.202693i
789789 6.53395e9 + 1.13171e10i 0.473594 + 0.820288i
790790 −3.67349e9 −0.265084
791791 0 0
792792 3.77727e8 0.0270172
793793 −1.30265e9 2.25626e9i −0.0927624 0.160669i
794794 2.81988e8 4.88417e8i 0.0199921 0.0346273i
795795 −4.84327e8 + 8.38878e8i −0.0341864 + 0.0592126i
796796 −6.68471e9 1.15783e10i −0.469772 0.813669i
797797 2.50099e9 0.174988 0.0874939 0.996165i 0.472114π-0.472114\pi
0.0874939 + 0.996165i 0.472114π0.472114\pi
798798 0 0
799799 1.49718e10 1.03839
800800 −1.03614e9 1.79465e9i −0.0715490 0.123927i
801801 −9.12231e8 + 1.58003e9i −0.0627178 + 0.108630i
802802 8.09289e9 1.40173e10i 0.553979 0.959519i
803803 7.50747e8 + 1.30033e9i 0.0511669 + 0.0886237i
804804 1.99411e9 0.135317
805805 0 0
806806 −1.16677e9 −0.0784899
807807 −3.33956e9 5.78428e9i −0.223682 0.387429i
808808 5.25529e9 9.10243e9i 0.350475 0.607040i
809809 −5.60593e9 + 9.70975e9i −0.372244 + 0.644746i −0.989910 0.141695i 0.954745π-0.954745\pi
0.617666 + 0.786440i 0.288078π0.288078\pi
810810 −2.59343e8 4.49196e8i −0.0171466 0.0296987i
811811 −2.38194e10 −1.56804 −0.784020 0.620736i 0.786834π-0.786834\pi
−0.784020 + 0.620736i 0.786834π0.786834\pi
812812 0 0
813813 −6.16374e9 −0.402279
814814 3.46970e8 + 6.00970e8i 0.0225479 + 0.0390542i
815815 −5.80048e9 + 1.00467e10i −0.375329 + 0.650089i
816816 1.56455e9 2.70987e9i 0.100803 0.174596i
817817 1.03005e10 + 1.78410e10i 0.660817 + 1.14457i
818818 −1.14981e10 −0.734497
819819 0 0
820820 1.21566e9 0.0769951
821821 1.01461e10 + 1.75735e10i 0.639877 + 1.10830i 0.985459 + 0.169912i 0.0543483π0.0543483\pi
−0.345582 + 0.938389i 0.612318π0.612318\pi
822822 1.68757e9 2.92296e9i 0.105977 0.183557i
823823 2.77965e9 4.81449e9i 0.173816 0.301059i −0.765935 0.642918i 0.777723π-0.777723\pi
0.939751 + 0.341860i 0.111057π0.111057\pi
824824 3.64375e9 + 6.31116e9i 0.226884 + 0.392974i
825825 1.72800e9 0.107141
826826 0 0
827827 2.02195e10 1.24308 0.621542 0.783381i 0.286507π-0.286507\pi
0.621542 + 0.783381i 0.286507π0.286507\pi
828828 2.53435e9 + 4.38963e9i 0.155153 + 0.268733i
829829 −1.87400e9 + 3.24586e9i −0.114243 + 0.197874i −0.917477 0.397789i 0.869777π-0.869777\pi
0.803234 + 0.595663i 0.203111π0.203111\pi
830830 2.63183e9 4.55846e9i 0.159766 0.276723i
831831 4.79406e9 + 8.30356e9i 0.289801 + 0.501950i
832832 8.19462e8 0.0493284
833833 0 0
834834 1.17166e10 0.699392
835835 −1.40269e9 2.42953e9i −0.0833795 0.144418i
836836 −7.19832e8 + 1.24678e9i −0.0426097 + 0.0738022i
837837 −4.59165e8 + 7.95297e8i −0.0270664 + 0.0468803i
838838 3.44839e8 + 5.97279e8i 0.0202424 + 0.0350609i
839839 2.03224e10 1.18798 0.593988 0.804474i 0.297553π-0.297553\pi
0.593988 + 0.804474i 0.297553π0.297553\pi
840840 0 0
841841 −1.55397e10 −0.900860
842842 −4.73017e9 8.19290e9i −0.273077 0.472983i
843843 −3.08026e9 + 5.33516e9i −0.177089 + 0.306726i
844844 2.70378e9 4.68308e9i 0.154801 0.268123i
845845 −3.23158e9 5.59725e9i −0.184254 0.319136i
846846 3.08601e9 0.175227
847847 0 0
848848 −1.20449e9 −0.0678296
849849 2.88618e9 + 4.99901e9i 0.161863 + 0.280354i
850850 7.15736e9 1.23969e10i 0.399748 0.692385i
851851 −4.65598e9 + 8.06440e9i −0.258975 + 0.448558i
852852 −3.31978e9 5.75002e9i −0.183895 0.318516i
853853 3.86410e8 0.0213170 0.0106585 0.999943i 0.496607π-0.496607\pi
0.0106585 + 0.999943i 0.496607π0.496607\pi
854854 0 0
855855 1.97691e9 0.108170
856856 −2.38598e9 4.13264e9i −0.130020 0.225201i
857857 2.32122e9 4.02047e9i 0.125975 0.218195i −0.796139 0.605114i 0.793127π-0.793127\pi
0.922114 + 0.386919i 0.126461π0.126461\pi
858858 −3.41659e8 + 5.91771e8i −0.0184666 + 0.0319851i
859859 1.36654e10 + 2.36691e10i 0.735606 + 1.27411i 0.954457 + 0.298349i 0.0964358π0.0964358\pi
−0.218851 + 0.975758i 0.570231π0.570231\pi
860860 −7.23649e9 −0.387957
861861 0 0
862862 −4.83726e9 −0.257231
863863 −9.21669e9 1.59638e10i −0.488132 0.845469i 0.511775 0.859120i 0.328988π-0.328988\pi
−0.999907 + 0.0136503i 0.995655π0.995655\pi
864864 3.22486e8 5.58563e8i 0.0170103 0.0294628i
865865 7.28865e9 1.26243e10i 0.382905 0.663210i
866866 2.86558e8 + 4.96332e8i 0.0149934 + 0.0259693i
867867 1.05357e10 0.549032
868868 0 0
869869 3.80899e9 0.196898
870870 5.44880e8 + 9.43760e8i 0.0280533 + 0.0485897i
871871 −1.80370e9 + 3.12409e9i −0.0924911 + 0.160199i
872872 1.10240e9 1.90941e9i 0.0563029 0.0975196i
873873 1.67581e9 + 2.90258e9i 0.0852460 + 0.147650i
874874 −1.93188e10 −0.978791
875875 0 0
876876 2.56382e9 0.128861
877877 6.51437e9 + 1.12832e10i 0.326117 + 0.564852i 0.981738 0.190239i 0.0609262π-0.0609262\pi
−0.655620 + 0.755091i 0.727593π0.727593\pi
878878 7.79670e8 1.35043e9i 0.0388759 0.0673350i
879879 −5.11402e9 + 8.85774e9i −0.253981 + 0.439908i
880880 −2.52854e8 4.37956e8i −0.0125078 0.0216641i
881881 3.46348e10 1.70646 0.853232 0.521531i 0.174639π-0.174639\pi
0.853232 + 0.521531i 0.174639π0.174639\pi
882882 0 0
883883 3.40346e10 1.66363 0.831817 0.555049i 0.187301π-0.187301\pi
0.831817 + 0.555049i 0.187301π0.187301\pi
884884 2.83031e9 + 4.90223e9i 0.137800 + 0.238677i
885885 −1.09903e9 + 1.90358e9i −0.0532977 + 0.0923142i
886886 −8.32073e9 + 1.44119e10i −0.401923 + 0.696152i
887887 2.39074e9 + 4.14089e9i 0.115027 + 0.199233i 0.917791 0.397065i 0.129971π-0.129971\pi
−0.802764 + 0.596298i 0.796638π0.796638\pi
888888 1.18491e9 0.0567858
889889 0 0
890890 2.44263e9 0.116143
891891 2.68909e8 + 4.65764e8i 0.0127360 + 0.0220594i
892892 −4.80558e9 + 8.32352e9i −0.226709 + 0.392672i
893893 −5.88100e9 + 1.01862e10i −0.276357 + 0.478665i
894894 −3.50946e9 6.07856e9i −0.164270 0.284524i
895895 −1.14467e10 −0.533704
896896 0 0
897897 −9.16943e9 −0.424198
898898 7.14424e9 + 1.23742e10i 0.329222 + 0.570229i
899899 9.64706e8 1.67092e9i 0.0442829 0.0767002i
900900 1.47529e9 2.55527e9i 0.0674571 0.116839i
901901 −4.16015e9 7.20559e9i −0.189484 0.328196i
902902 −1.26050e9 −0.0571899
903903 0 0
904904 −3.55108e9 −0.159871
905905 9.07888e9 + 1.57251e10i 0.407157 + 0.705217i
906906 −8.24405e9 + 1.42791e10i −0.368292 + 0.637900i
907907 1.39320e10 2.41309e10i 0.619993 1.07386i −0.369494 0.929233i 0.620469π-0.620469\pi
0.989486 0.144626i 0.0461978π-0.0461978\pi
908908 9.69196e9 + 1.67870e10i 0.429646 + 0.744169i
909909 1.49653e10 0.660862
910910 0 0
911911 3.21050e10 1.40689 0.703443 0.710752i 0.251645π-0.251645\pi
0.703443 + 0.710752i 0.251645π0.251645\pi
912912 1.22912e9 + 2.12890e9i 0.0536552 + 0.0929336i
913913 −2.72890e9 + 4.72660e9i −0.118670 + 0.205542i
914914 −8.97232e9 + 1.55405e10i −0.388681 + 0.673215i
915915 1.37266e9 + 2.37752e9i 0.0592364 + 0.102601i
916916 −3.40079e9 −0.146199
917917 0 0
918918 4.45529e9 0.190076
919919 −1.41227e10 2.44612e10i −0.600224 1.03962i −0.992787 0.119893i 0.961745π-0.961745\pi
0.392563 0.919725i 0.371588π-0.371588\pi
920920 3.39304e9 5.87693e9i 0.143659 0.248824i
921921 −8.55648e9 + 1.48203e10i −0.360900 + 0.625097i
922922 −1.04102e10 1.80309e10i −0.437421 0.757636i
923923 1.20111e10 0.502780
924924 0 0
925925 5.42064e9 0.225193
926926 −2.85023e9 4.93674e9i −0.117962 0.204316i
927927 −5.18807e9 + 8.98601e9i −0.213908 + 0.370500i
928928 −6.77544e8 + 1.17354e9i −0.0278304 + 0.0482037i
929929 −5.14871e9 8.91783e9i −0.210690 0.364925i 0.741241 0.671239i 0.234238π-0.234238\pi
−0.951931 + 0.306314i 0.900904π0.900904\pi
930930 1.22948e9 0.0501223
931931 0 0
932932 −8.72645e9 −0.353087
933933 5.26764e9 + 9.12382e9i 0.212339 + 0.367782i
934934 −2.53388e9 + 4.38880e9i −0.101759 + 0.176251i
935935 1.74665e9 3.02528e9i 0.0698818 0.121039i
936936 5.83387e8 + 1.01046e9i 0.0232536 + 0.0402765i
937937 −3.96648e10 −1.57513 −0.787565 0.616231i 0.788659π-0.788659\pi
−0.787565 + 0.616231i 0.788659π0.788659\pi
938938 0 0
939939 −2.71199e10 −1.06895
940940 −2.06581e9 3.57809e9i −0.0811228 0.140509i
941941 −1.43147e9 + 2.47938e9i −0.0560040 + 0.0970017i −0.892668 0.450714i 0.851169π-0.851169\pi
0.836664 + 0.547716i 0.184503π0.184503\pi
942942 −3.15815e9 + 5.47007e9i −0.123099 + 0.213213i
943943 −8.45730e9 1.46485e10i −0.328428 0.568855i
944944 −2.73323e9 −0.105748
945945 0 0
946946 7.50341e9 0.288164
947947 −3.42124e9 5.92575e9i −0.130906 0.226735i 0.793120 0.609065i 0.208455π-0.208455\pi
−0.924026 + 0.382330i 0.875122π0.875122\pi
948948 3.25194e9 5.63253e9i 0.123969 0.214721i
949949 −2.31901e9 + 4.01664e9i −0.0880786 + 0.152557i
950950 5.62288e9 + 9.73912e9i 0.212778 + 0.368542i
951951 6.56031e9 0.247339
952952 0 0
953953 −2.50283e10 −0.936711 −0.468356 0.883540i 0.655153π-0.655153\pi
−0.468356 + 0.883540i 0.655153π0.655153\pi
954954 −8.57496e8 1.48523e9i −0.0319752 0.0553826i
955955 −6.18576e9 + 1.07141e10i −0.229817 + 0.398054i
956956 −7.25766e9 + 1.25706e10i −0.268655 + 0.465323i
957957 −5.64978e8 9.78571e8i −0.0208372 0.0360911i
958958 1.76442e9 0.0648368
959959 0 0
960960 −8.63502e8 −0.0315003
961961 1.26679e10 + 2.19415e10i 0.460440 + 0.797506i
962962 −1.07177e9 + 1.85636e9i −0.0388140 + 0.0672278i
963963 3.39723e9 5.88417e9i 0.122584 0.212321i
964964 −1.29617e10 2.24503e10i −0.466007 0.807148i
965965 −8.61193e9 −0.308500
966966 0 0
967967 −5.13292e10 −1.82546 −0.912730 0.408564i 0.866030π-0.866030\pi
−0.912730 + 0.408564i 0.866030π0.866030\pi
968968 −4.72653e9 8.18660e9i −0.167486 0.290095i
969969 −8.49041e9 + 1.47058e10i −0.299775 + 0.519225i
970970 2.24360e9 3.88604e9i 0.0789306 0.136712i
971971 −1.81266e10 3.13962e10i −0.635403 1.10055i −0.986430 0.164184i 0.947501π-0.947501\pi
0.351027 0.936365i 0.385833π-0.385833\pi
972972 9.18330e8 0.0320750
973973 0 0
974974 −3.14346e10 −1.09006
975975 2.66883e9 + 4.62256e9i 0.0922158 + 0.159722i
976976 −1.70686e9 + 2.95638e9i −0.0587658 + 0.101785i
977977 1.78987e10 3.10014e10i 0.614031 1.06353i −0.376523 0.926407i 0.622880π-0.622880\pi
0.990554 0.137125i 0.0437863π-0.0437863\pi
978978 −1.02697e10 1.77876e10i −0.351052 0.608040i
979979 −2.53272e9 −0.0862677
980980 0 0
981981 3.13925e9 0.106166
982982 −1.31561e10 2.27871e10i −0.443342 0.767890i
983983 −2.44510e10 + 4.23504e10i −0.821030 + 1.42207i 0.0838854 + 0.996475i 0.473267π0.473267\pi
−0.904916 + 0.425591i 0.860066π0.860066\pi
984984 −1.07616e9 + 1.86396e9i −0.0360075 + 0.0623668i
985985 3.06407e9 + 5.30713e9i 0.102158 + 0.176943i
986986 −9.36056e9 −0.310980
987987 0 0
988988 −4.44702e9 −0.146697
989989 5.03440e10 + 8.71984e10i 1.65486 + 2.86630i
990990 3.60021e8 6.23575e8i 0.0117925 0.0204252i
991991 3.44941e9 5.97455e9i 0.112587 0.195006i −0.804226 0.594324i 0.797420π-0.797420\pi
0.916812 + 0.399318i 0.130753π0.130753\pi
992992 7.64412e8 + 1.32400e9i 0.0248620 + 0.0430623i
993993 −7.65495e8 −0.0248096
994994 0 0
995995 −2.54855e10 −0.820185
996996 4.65963e9 + 8.07072e9i 0.149432 + 0.258824i
997997 2.76515e9 4.78939e9i 0.0883662 0.153055i −0.818454 0.574571i 0.805169π-0.805169\pi
0.906821 + 0.421517i 0.138502π0.138502\pi
998998 −1.72252e10 + 2.98349e10i −0.548539 + 0.950098i
999999 8.43554e8 + 1.46108e9i 0.0267691 + 0.0463654i
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 294.8.e.j.67.1 2
7.2 even 3 inner 294.8.e.j.79.1 2
7.3 odd 6 294.8.a.c.1.1 1
7.4 even 3 42.8.a.c.1.1 1
7.5 odd 6 294.8.e.n.79.1 2
7.6 odd 2 294.8.e.n.67.1 2
21.11 odd 6 126.8.a.g.1.1 1
28.11 odd 6 336.8.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.8.a.c.1.1 1 7.4 even 3
126.8.a.g.1.1 1 21.11 odd 6
294.8.a.c.1.1 1 7.3 odd 6
294.8.e.j.67.1 2 1.1 even 1 trivial
294.8.e.j.79.1 2 7.2 even 3 inner
294.8.e.n.67.1 2 7.6 odd 2
294.8.e.n.79.1 2 7.5 odd 6
336.8.a.d.1.1 1 28.11 odd 6