Properties

Label 54.9.d.a.17.1
Level 5454
Weight 99
Character 54.17
Analytic conductor 21.99821.998
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,9,Mod(17,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.17");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: N N == 54=233 54 = 2 \cdot 3^{3}
Weight: k k == 9 9
Character orbit: [χ][\chi] == 54.d (of order 66, 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: 21.998444943321.9984449433
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x164x15150208x141927740x13+8702363206x12+239206241152x11++81 ⁣ ⁣61 x^{16} - 4 x^{15} - 150208 x^{14} - 1927740 x^{13} + 8702363206 x^{12} + 239206241152 x^{11} + \cdots + 81\!\cdots\!61 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 228336 2^{28}\cdot 3^{36}
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 17.1
Root 220.333+0.866025i220.333 + 0.866025i of defining polynomial
Character χ\chi == 54.17
Dual form 54.9.d.a.35.1

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+(9.79796+5.65685i)q2+(64.0000110.851i)q4+(935.250539.967i)q5+(2056.093561.25i)q7+1448.15iq8+12218.1q10+(8419.53+4861.02i)q11+(4116.02+7129.16i)q13+(40291.0+23262.0i)q14+(8192.0014189.0i)q1687809.9iq17+123643.q19+(119712.+69115.7i)q20+(54996.195256.1i)q22+(92029.453133.2i)q23+(387816.+671717.i)q2593134.9iq26526359.q28+(430885.+248772.i)q29+(577977.+1.00109e6i)q31+(160530.+92681.9i)q32+(496728.+860358.i)q34+4.44088e6iq35+1.20145e6q37+(1.21145e6+699428.i)q38+(781955.1.35439e6i)q40+(1.53952e6888843.i)q41+(528726.915780.i)q43+1.24442e6iq44+1.20227e6q46+(3.80689e62.19791e6i)q47+(5.57261e6+9.65205e6i)q49+(7.59961e64.38763e6i)q50+(526851.+912532.i)q52+1.04810e6iq53+1.04991e7q55+(5.15724e62.97754e6i)q56+(2.81453e64.87491e6i)q58+(8.70048e6+5.02323e6i)q59+(4.15770e67.20135e6i)q611.30781e7iq622.09715e6q64+(7.69902e64.44503e6i)q65+(6.19183e61.07246e7i)q67+(9.73384e65.61983e6i)q68+(2.51214e74.35116e7i)q701.69579e7iq712.42736e7q73+(1.17718e7+6.79644e6i)q74+(7.91313e61.37059e7i)q76+(3.46226e7+1.99894e7i)q77+(6.39004e6+1.10679e7i)q79+1.76936e7iq80+2.01122e7q82+(2.79188e71.61189e7i)q83+(4.74144e7+8.21242e7i)q85+(1.03609e7+5.98185e6i)q86+(7.03950e61.21928e7i)q88+2.10088e7iq89+3.38516e7q91+(1.17798e7+6.80105e6i)q92+(2.48665e7+4.30700e7i)q94+(1.15637e86.67629e7i)q95+(4.46651e77.73622e7i)q971.26094e8iq98+O(q100)q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-935.250 - 539.967i) q^{5} +(-2056.09 - 3561.25i) q^{7} +1448.15i q^{8} +12218.1 q^{10} +(-8419.53 + 4861.02i) q^{11} +(-4116.02 + 7129.16i) q^{13} +(40291.0 + 23262.0i) q^{14} +(-8192.00 - 14189.0i) q^{16} -87809.9i q^{17} +123643. q^{19} +(-119712. + 69115.7i) q^{20} +(54996.1 - 95256.1i) q^{22} +(-92029.4 - 53133.2i) q^{23} +(387816. + 671717. i) q^{25} -93134.9i q^{26} -526359. q^{28} +(-430885. + 248772. i) q^{29} +(-577977. + 1.00109e6i) q^{31} +(160530. + 92681.9i) q^{32} +(496728. + 860358. i) q^{34} +4.44088e6i q^{35} +1.20145e6 q^{37} +(-1.21145e6 + 699428. i) q^{38} +(781955. - 1.35439e6i) q^{40} +(-1.53952e6 - 888843. i) q^{41} +(-528726. - 915780. i) q^{43} +1.24442e6i q^{44} +1.20227e6 q^{46} +(3.80689e6 - 2.19791e6i) q^{47} +(-5.57261e6 + 9.65205e6i) q^{49} +(-7.59961e6 - 4.38763e6i) q^{50} +(526851. + 912532. i) q^{52} +1.04810e6i q^{53} +1.04991e7 q^{55} +(5.15724e6 - 2.97754e6i) q^{56} +(2.81453e6 - 4.87491e6i) q^{58} +(8.70048e6 + 5.02323e6i) q^{59} +(-4.15770e6 - 7.20135e6i) q^{61} -1.30781e7i q^{62} -2.09715e6 q^{64} +(7.69902e6 - 4.44503e6i) q^{65} +(6.19183e6 - 1.07246e7i) q^{67} +(-9.73384e6 - 5.61983e6i) q^{68} +(-2.51214e7 - 4.35116e7i) q^{70} -1.69579e7i q^{71} -2.42736e7 q^{73} +(-1.17718e7 + 6.79644e6i) q^{74} +(7.91313e6 - 1.37059e7i) q^{76} +(3.46226e7 + 1.99894e7i) q^{77} +(6.39004e6 + 1.10679e7i) q^{79} +1.76936e7i q^{80} +2.01122e7 q^{82} +(2.79188e7 - 1.61189e7i) q^{83} +(-4.74144e7 + 8.21242e7i) q^{85} +(1.03609e7 + 5.98185e6i) q^{86} +(-7.03950e6 - 1.21928e7i) q^{88} +2.10088e7i q^{89} +3.38516e7 q^{91} +(-1.17798e7 + 6.80105e6i) q^{92} +(-2.48665e7 + 4.30700e7i) q^{94} +(-1.15637e8 - 6.67629e7i) q^{95} +(-4.46651e7 - 7.73622e7i) q^{97} -1.26094e8i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+1024q4+882q51846q745756q113370q13+94464q14131072q16+362180q19+112896q2061824q221311138q23+963394q25472576q28+2851290q29+89415484q97+O(q100) 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29}+ \cdots - 89415484 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/54Z)×\left(\mathbb{Z}/54\mathbb{Z}\right)^\times.

nn 2929
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\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 −9.79796 + 5.65685i −0.612372 + 0.353553i
33 0 0
44 64.0000 110.851i 0.250000 0.433013i
55 −935.250 539.967i −1.49640 0.863947i −0.496408 0.868089i 0.665348π-0.665348\pi
−0.999991 + 0.00414227i 0.998681π0.998681\pi
66 0 0
77 −2056.09 3561.25i −0.856347 1.48324i −0.875389 0.483419i 0.839395π-0.839395\pi
0.0190419 0.999819i 0.493938π-0.493938\pi
88 1448.15i 0.353553i
99 0 0
1010 12218.1 1.22181
1111 −8419.53 + 4861.02i −0.575065 + 0.332014i −0.759170 0.650893i 0.774395π-0.774395\pi
0.184105 + 0.982907i 0.441061π0.441061\pi
1212 0 0
1313 −4116.02 + 7129.16i −0.144113 + 0.249612i −0.929042 0.369975i 0.879366π-0.879366\pi
0.784928 + 0.619586i 0.212700π0.212700\pi
1414 40291.0 + 23262.0i 1.04881 + 0.605529i
1515 0 0
1616 −8192.00 14189.0i −0.125000 0.216506i
1717 87809.9i 1.05135i −0.850685 0.525676i 0.823813π-0.823813\pi
0.850685 0.525676i 0.176187π-0.176187\pi
1818 0 0
1919 123643. 0.948754 0.474377 0.880322i 0.342673π-0.342673\pi
0.474377 + 0.880322i 0.342673π0.342673\pi
2020 −119712. + 69115.7i −0.748200 + 0.431973i
2121 0 0
2222 54996.1 95256.1i 0.234769 0.406632i
2323 −92029.4 53133.2i −0.328863 0.189869i 0.326473 0.945206i 0.394140π-0.394140\pi
−0.655336 + 0.755337i 0.727473π0.727473\pi
2424 0 0
2525 387816. + 671717.i 0.992808 + 1.71959i
2626 93134.9i 0.203807i
2727 0 0
2828 −526359. −0.856347
2929 −430885. + 248772.i −0.609213 + 0.351729i −0.772657 0.634823i 0.781073π-0.781073\pi
0.163444 + 0.986553i 0.447740π0.447740\pi
3030 0 0
3131 −577977. + 1.00109e6i −0.625841 + 1.08399i 0.362536 + 0.931970i 0.381911π0.381911\pi
−0.988378 + 0.152019i 0.951422π0.951422\pi
3232 160530. + 92681.9i 0.153093 + 0.0883883i
3333 0 0
3434 496728. + 860358.i 0.371709 + 0.643819i
3535 4.44088e6i 2.95935i
3636 0 0
3737 1.20145e6 0.641061 0.320531 0.947238i 0.396139π-0.396139\pi
0.320531 + 0.947238i 0.396139π0.396139\pi
3838 −1.21145e6 + 699428.i −0.580991 + 0.335435i
3939 0 0
4040 781955. 1.35439e6i 0.305451 0.529057i
4141 −1.53952e6 888843.i −0.544816 0.314550i 0.202212 0.979342i 0.435187π-0.435187\pi
−0.747029 + 0.664792i 0.768520π0.768520\pi
4242 0 0
4343 −528726. 915780.i −0.154652 0.267866i 0.778280 0.627917i 0.216092π-0.216092\pi
−0.932932 + 0.360052i 0.882759π0.882759\pi
4444 1.24442e6i 0.332014i
4545 0 0
4646 1.20227e6 0.268516
4747 3.80689e6 2.19791e6i 0.780151 0.450420i −0.0563327 0.998412i 0.517941π-0.517941\pi
0.836484 + 0.547992i 0.184607π0.184607\pi
4848 0 0
4949 −5.57261e6 + 9.65205e6i −0.966662 + 1.67431i
5050 −7.59961e6 4.38763e6i −1.21594 0.702021i
5151 0 0
5252 526851. + 912532.i 0.0720567 + 0.124806i
5353 1.04810e6i 0.132831i 0.997792 + 0.0664157i 0.0211563π0.0211563\pi
−0.997792 + 0.0664157i 0.978844π0.978844\pi
5454 0 0
5555 1.04991e7 1.14737
5656 5.15724e6 2.97754e6i 0.524404 0.302765i
5757 0 0
5858 2.81453e6 4.87491e6i 0.248710 0.430779i
5959 8.70048e6 + 5.02323e6i 0.718018 + 0.414548i 0.814023 0.580833i 0.197273π-0.197273\pi
−0.0960047 + 0.995381i 0.530606π0.530606\pi
6060 0 0
6161 −4.15770e6 7.20135e6i −0.300285 0.520109i 0.675915 0.736979i 0.263749π-0.263749\pi
−0.976200 + 0.216870i 0.930415π0.930415\pi
6262 1.30781e7i 0.885073i
6363 0 0
6464 −2.09715e6 −0.125000
6565 7.69902e6 4.44503e6i 0.431302 0.249013i
6666 0 0
6767 6.19183e6 1.07246e7i 0.307270 0.532207i −0.670494 0.741915i 0.733918π-0.733918\pi
0.977764 + 0.209708i 0.0672513π0.0672513\pi
6868 −9.73384e6 5.61983e6i −0.455248 0.262838i
6969 0 0
7070 −2.51214e7 4.35116e7i −1.04629 1.81223i
7171 1.69579e7i 0.667328i −0.942692 0.333664i 0.891715π-0.891715\pi
0.942692 0.333664i 0.108285π-0.108285\pi
7272 0 0
7373 −2.42736e7 −0.854757 −0.427378 0.904073i 0.640563π-0.640563\pi
−0.427378 + 0.904073i 0.640563π0.640563\pi
7474 −1.17718e7 + 6.79644e6i −0.392568 + 0.226649i
7575 0 0
7676 7.91313e6 1.37059e7i 0.237189 0.410823i
7777 3.46226e7 + 1.99894e7i 0.984911 + 0.568639i
7878 0 0
7979 6.39004e6 + 1.10679e7i 0.164057 + 0.284155i 0.936320 0.351148i 0.114209π-0.114209\pi
−0.772263 + 0.635303i 0.780875π0.780875\pi
8080 1.76936e7i 0.431973i
8181 0 0
8282 2.01122e7 0.444841
8383 2.79188e7 1.61189e7i 0.588281 0.339644i −0.176136 0.984366i 0.556360π-0.556360\pi
0.764418 + 0.644722i 0.223027π0.223027\pi
8484 0 0
8585 −4.74144e7 + 8.21242e7i −0.908312 + 1.57324i
8686 1.03609e7 + 5.98185e6i 0.189410 + 0.109356i
8787 0 0
8888 −7.03950e6 1.21928e7i −0.117385 0.203316i
8989 2.10088e7i 0.334843i 0.985885 + 0.167422i 0.0535441π0.0535441\pi
−0.985885 + 0.167422i 0.946456π0.946456\pi
9090 0 0
9191 3.38516e7 0.493644
9292 −1.17798e7 + 6.80105e6i −0.164432 + 0.0949346i
9393 0 0
9494 −2.48665e7 + 4.30700e7i −0.318495 + 0.551650i
9595 −1.15637e8 6.67629e7i −1.41972 0.819673i
9696 0 0
9797 −4.46651e7 7.73622e7i −0.504523 0.873860i −0.999986 0.00523116i 0.998335π-0.998335\pi
0.495463 0.868629i 0.334998π-0.334998\pi
9898 1.26094e8i 1.36707i
9999 0 0
100100 9.92808e7 0.992808
101101 3.08430e7 1.78072e7i 0.296395 0.171124i −0.344427 0.938813i 0.611927π-0.611927\pi
0.640822 + 0.767689i 0.278594π0.278594\pi
102102 0 0
103103 −4.35300e6 + 7.53962e6i −0.0386759 + 0.0669886i −0.884715 0.466132i 0.845647π-0.845647\pi
0.846040 + 0.533120i 0.178981π0.178981\pi
104104 −1.03241e7 5.96064e6i −0.0882510 0.0509518i
105105 0 0
106106 −5.92897e6 1.02693e7i −0.0469630 0.0813422i
107107 2.34341e8i 1.78778i 0.448290 + 0.893888i 0.352033π0.352033\pi
−0.448290 + 0.893888i 0.647967π0.647967\pi
108108 0 0
109109 2.66492e8 1.88789 0.943947 0.330098i 0.107082π-0.107082\pi
0.943947 + 0.330098i 0.107082π0.107082\pi
110110 −1.02870e8 + 5.93921e7i −0.702617 + 0.405656i
111111 0 0
112112 −3.36870e7 + 5.83476e7i −0.214087 + 0.370809i
113113 2.47560e8 + 1.42929e8i 1.51833 + 0.876610i 0.999767 + 0.0215714i 0.00686693π0.00686693\pi
0.518565 + 0.855038i 0.326466π0.326466\pi
114114 0 0
115115 5.73803e7 + 9.93856e7i 0.328074 + 0.568241i
116116 6.36855e7i 0.351729i
117117 0 0
118118 −1.13663e8 −0.586259
119119 −3.12713e8 + 1.80545e8i −1.55940 + 0.900322i
120120 0 0
121121 −5.99205e7 + 1.03785e8i −0.279534 + 0.484166i
122122 8.14740e7 + 4.70390e7i 0.367773 + 0.212334i
123123 0 0
124124 7.39811e7 + 1.28139e8i 0.312921 + 0.541994i
125125 4.15781e8i 1.70304i
126126 0 0
127127 −8.18752e7 −0.314730 −0.157365 0.987541i 0.550300π-0.550300\pi
−0.157365 + 0.987541i 0.550300π0.550300\pi
128128 2.05478e7 1.18633e7i 0.0765466 0.0441942i
129129 0 0
130130 −5.02898e7 + 8.71044e7i −0.176078 + 0.304977i
131131 −3.27800e8 1.89256e8i −1.11308 0.642634i −0.173451 0.984843i 0.555492π-0.555492\pi
−0.939624 + 0.342208i 0.888825π0.888825\pi
132132 0 0
133133 −2.54220e8 4.40322e8i −0.812463 1.40723i
134134 1.40105e8i 0.434545i
135135 0 0
136136 1.27162e8 0.371709
137137 −8.36881e7 + 4.83174e7i −0.237565 + 0.137158i −0.614057 0.789262i 0.710463π-0.710463\pi
0.376492 + 0.926420i 0.377130π0.377130\pi
138138 0 0
139139 −2.13230e8 + 3.69325e8i −0.571200 + 0.989348i 0.425243 + 0.905079i 0.360189π0.360189\pi
−0.996443 + 0.0842686i 0.973145π0.973145\pi
140140 4.92277e8 + 2.84216e8i 1.28144 + 0.739839i
141141 0 0
142142 9.59286e7 + 1.66153e8i 0.235936 + 0.408653i
143143 8.00322e7i 0.191391i
144144 0 0
145145 5.37313e8 1.21550
146146 2.37832e8 1.37312e8i 0.523429 0.302202i
147147 0 0
148148 7.68929e7 1.33182e8i 0.160265 0.277588i
149149 −3.73436e8 2.15603e8i −0.757653 0.437431i 0.0707992 0.997491i 0.477445π-0.477445\pi
−0.828453 + 0.560059i 0.810778π0.810778\pi
150150 0 0
151151 −4.20280e8 7.27947e8i −0.808409 1.40021i −0.913965 0.405793i 0.866996π-0.866996\pi
0.105556 0.994413i 0.466338π-0.466338\pi
152152 1.79054e8i 0.335435i
153153 0 0
154154 −4.52308e8 −0.804176
155155 1.08111e9 6.24177e8i 1.87302 1.08139i
156156 0 0
157157 2.10919e8 3.65323e8i 0.347150 0.601282i −0.638592 0.769546i 0.720483π-0.720483\pi
0.985742 + 0.168264i 0.0538160π0.0538160\pi
158158 −1.25219e8 7.22951e7i −0.200928 0.116006i
159159 0 0
160160 −1.00090e8 1.73361e8i −0.152726 0.264529i
161161 4.36987e8i 0.650376i
162162 0 0
163163 −5.50818e8 −0.780293 −0.390146 0.920753i 0.627576π-0.627576\pi
−0.390146 + 0.920753i 0.627576π0.627576\pi
164164 −1.97059e8 + 1.13772e8i −0.272408 + 0.157275i
165165 0 0
166166 −1.82365e8 + 3.15866e8i −0.240165 + 0.415978i
167167 −5.25550e8 3.03427e8i −0.675691 0.390111i 0.122538 0.992464i 0.460897π-0.460897\pi
−0.798230 + 0.602353i 0.794230π0.794230\pi
168168 0 0
169169 3.73982e8 + 6.47756e8i 0.458463 + 0.794081i
170170 1.07287e9i 1.28455i
171171 0 0
172172 −1.35354e8 −0.154652
173173 8.26617e8 4.77248e8i 0.922826 0.532794i 0.0382907 0.999267i 0.487809π-0.487809\pi
0.884536 + 0.466473i 0.154475π0.154475\pi
174174 0 0
175175 1.59477e9 2.76222e9i 1.70038 2.94514i
176176 1.37946e8 + 7.96429e7i 0.143766 + 0.0830035i
177177 0 0
178178 −1.18844e8 2.05844e8i −0.118385 0.205049i
179179 9.44019e8i 0.919536i 0.888039 + 0.459768i 0.152067π0.152067\pi
−0.888039 + 0.459768i 0.847933π0.847933\pi
180180 0 0
181181 −8.68230e8 −0.808948 −0.404474 0.914550i 0.632545π-0.632545\pi
−0.404474 + 0.914550i 0.632545π0.632545\pi
182182 −3.31677e8 + 1.91494e8i −0.302294 + 0.174530i
183183 0 0
184184 7.69451e7 1.33273e8i 0.0671289 0.116271i
185185 −1.12366e9 6.48744e8i −0.959284 0.553843i
186186 0 0
187187 4.26845e8 + 7.39318e8i 0.349063 + 0.604595i
188188 5.62665e8i 0.450420i
189189 0 0
190190 1.51067e9 1.15919
191191 6.09956e7 3.52159e7i 0.0458316 0.0264609i −0.476909 0.878953i 0.658243π-0.658243\pi
0.522741 + 0.852492i 0.324910π0.324910\pi
192192 0 0
193193 −1.36871e9 + 2.37068e9i −0.986467 + 1.70861i −0.351242 + 0.936285i 0.614241π0.614241\pi
−0.635225 + 0.772327i 0.719093π0.719093\pi
194194 8.75254e8 + 5.05328e8i 0.617913 + 0.356752i
195195 0 0
196196 7.13294e8 + 1.23546e9i 0.483331 + 0.837154i
197197 5.47276e8i 0.363364i 0.983357 + 0.181682i 0.0581541π0.0581541\pi
−0.983357 + 0.181682i 0.941846π0.941846\pi
198198 0 0
199199 −2.66467e9 −1.69915 −0.849574 0.527469i 0.823141π-0.823141\pi
−0.849574 + 0.527469i 0.823141π0.823141\pi
200200 −9.72749e8 + 5.61617e8i −0.607968 + 0.351011i
201201 0 0
202202 −2.01465e8 + 3.48948e8i −0.121003 + 0.209583i
203203 1.77188e9 + 1.02299e9i 1.04340 + 0.602405i
204204 0 0
205205 9.59891e8 + 1.66258e9i 0.543509 + 0.941385i
206206 9.84972e7i 0.0546959i
207207 0 0
208208 1.34874e8 0.0720567
209209 −1.04101e9 + 6.01029e8i −0.545595 + 0.315000i
210210 0 0
211211 −9.39137e8 + 1.62663e9i −0.473804 + 0.820653i −0.999550 0.0299884i 0.990453π-0.990453\pi
0.525746 + 0.850642i 0.323786π0.323786\pi
212212 1.16184e8 + 6.70786e7i 0.0575176 + 0.0332078i
213213 0 0
214214 −1.32563e9 2.29606e9i −0.632074 1.09478i
215215 1.14198e9i 0.534446i
216216 0 0
217217 4.75349e9 2.14375
218218 −2.61107e9 + 1.50750e9i −1.15609 + 0.667471i
219219 0 0
220220 6.71945e8 1.16384e9i 0.286842 0.496826i
221221 6.26011e8 + 3.61427e8i 0.262430 + 0.151514i
222222 0 0
223223 1.45052e9 + 2.51237e9i 0.586548 + 1.01593i 0.994680 + 0.103009i 0.0328470π0.0328470\pi
−0.408132 + 0.912923i 0.633820π0.633820\pi
224224 7.62249e8i 0.302765i
225225 0 0
226226 −3.23411e9 −1.23971
227227 −3.60966e9 + 2.08404e9i −1.35945 + 0.784877i −0.989549 0.144195i 0.953941π-0.953941\pi
−0.369898 + 0.929072i 0.620607π0.620607\pi
228228 0 0
229229 1.80018e9 3.11801e9i 0.654599 1.13380i −0.327396 0.944887i 0.606171π-0.606171\pi
0.981994 0.188911i 0.0604957π-0.0604957\pi
230230 −1.12442e9 6.49184e8i −0.401807 0.231983i
231231 0 0
232232 −3.60260e8 6.23988e8i −0.124355 0.215389i
233233 2.86365e9i 0.971618i 0.874065 + 0.485809i 0.161475π0.161475\pi
−0.874065 + 0.485809i 0.838525π0.838525\pi
234234 0 0
235235 −4.74719e9 −1.55656
236236 1.11366e9 6.42973e8i 0.359009 0.207274i
237237 0 0
238238 2.04263e9 3.53795e9i 0.636624 1.10266i
239239 −1.21500e9 7.01479e8i −0.372378 0.214992i 0.302119 0.953270i 0.402306π-0.402306\pi
−0.674497 + 0.738278i 0.735639π0.735639\pi
240240 0 0
241241 2.21808e9 + 3.84182e9i 0.657519 + 1.13886i 0.981256 + 0.192709i 0.0617273π0.0617273\pi
−0.323737 + 0.946147i 0.604939π0.604939\pi
242242 1.35585e9i 0.395320i
243243 0 0
244244 −1.06437e9 −0.300285
245245 1.04236e10 6.01805e9i 2.89303 1.67029i
246246 0 0
247247 −5.08916e8 + 8.81468e8i −0.136728 + 0.236820i
248248 −1.44973e9 8.37001e8i −0.383248 0.221268i
249249 0 0
250250 2.35201e9 + 4.07381e9i 0.602116 + 1.04290i
251251 2.42084e9i 0.609916i −0.952366 0.304958i 0.901357π-0.901357\pi
0.952366 0.304958i 0.0986425π-0.0986425\pi
252252 0 0
253253 1.03313e9 0.252157
254254 8.02210e8 4.63156e8i 0.192732 0.111274i
255255 0 0
256256 −1.34218e8 + 2.32472e8i −0.0312500 + 0.0541266i
257257 2.08915e9 + 1.20617e9i 0.478891 + 0.276488i 0.719954 0.694022i 0.244163π-0.244163\pi
−0.241063 + 0.970509i 0.577496π0.577496\pi
258258 0 0
259259 −2.47029e9 4.27867e9i −0.548971 0.950846i
260260 1.13793e9i 0.249013i
261261 0 0
262262 4.28237e9 0.908822
263263 −5.65030e9 + 3.26220e9i −1.18100 + 0.681849i −0.956245 0.292567i 0.905490π-0.905490\pi
−0.224752 + 0.974416i 0.572157π0.572157\pi
264264 0 0
265265 5.65941e8 9.80238e8i 0.114759 0.198769i
266266 4.98168e9 + 2.87617e9i 0.995060 + 0.574498i
267267 0 0
268268 −7.92554e8 1.37274e9i −0.153635 0.266103i
269269 6.64127e9i 1.26836i −0.773186 0.634180i 0.781338π-0.781338\pi
0.773186 0.634180i 0.218662π-0.218662\pi
270270 0 0
271271 −2.72229e9 −0.504728 −0.252364 0.967632i 0.581208π-0.581208\pi
−0.252364 + 0.967632i 0.581208π0.581208\pi
272272 −1.24593e9 + 7.19339e8i −0.227624 + 0.131419i
273273 0 0
274274 5.46649e8 9.46823e8i 0.0969853 0.167983i
275275 −6.53045e9 3.77036e9i −1.14186 0.659252i
276276 0 0
277277 −5.00946e9 8.67663e9i −0.850886 1.47378i −0.880410 0.474214i 0.842732π-0.842732\pi
0.0295233 0.999564i 0.490601π-0.490601\pi
278278 4.82484e9i 0.807799i
279279 0 0
280280 −6.43108e9 −1.04629
281281 6.83019e9 3.94341e9i 1.09549 0.632480i 0.160456 0.987043i 0.448704π-0.448704\pi
0.935032 + 0.354563i 0.115370π0.115370\pi
282282 0 0
283283 4.86855e8 8.43258e8i 0.0759021 0.131466i −0.825576 0.564291i 0.809150π-0.809150\pi
0.901478 + 0.432824i 0.142483π0.142483\pi
284284 −1.87981e9 1.08531e9i −0.288962 0.166832i
285285 0 0
286286 4.52730e8 + 7.84152e8i 0.0676668 + 0.117202i
287287 7.31016e9i 1.07746i
288288 0 0
289289 −7.34822e8 −0.105339
290290 −5.26458e9 + 3.03950e9i −0.744340 + 0.429745i
291291 0 0
292292 −1.55351e9 + 2.69076e9i −0.213689 + 0.370121i
293293 4.59420e9 + 2.65246e9i 0.623361 + 0.359898i 0.778176 0.628046i 0.216145π-0.216145\pi
−0.154815 + 0.987943i 0.549478π0.549478\pi
294294 0 0
295295 −5.42475e9 9.39595e9i −0.716295 1.24066i
296296 1.73989e9i 0.226649i
297297 0 0
298298 4.87854e9 0.618621
299299 7.57590e8 4.37395e8i 0.0947871 0.0547254i
300300 0 0
301301 −2.17422e9 + 3.76585e9i −0.264872 + 0.458772i
302302 8.23578e9 + 4.75493e9i 0.990095 + 0.571632i
303303 0 0
304304 −1.01288e9 1.75436e9i −0.118594 0.205411i
305305 8.98008e9i 1.03772i
306306 0 0
307307 1.34241e10 1.51124 0.755618 0.655013i 0.227337π-0.227337\pi
0.755618 + 0.655013i 0.227337π0.227337\pi
308308 4.43169e9 2.55864e9i 0.492455 0.284319i
309309 0 0
310310 −7.06176e9 + 1.22313e10i −0.764656 + 1.32442i
311311 −1.98291e9 1.14483e9i −0.211964 0.122377i 0.390260 0.920705i 0.372385π-0.372385\pi
−0.602224 + 0.798327i 0.705718π0.705718\pi
312312 0 0
313313 8.94161e9 + 1.54873e10i 0.931619 + 1.61361i 0.780555 + 0.625088i 0.214937π0.214937\pi
0.151065 + 0.988524i 0.451730π0.451730\pi
314314 4.77256e9i 0.490945i
315315 0 0
316316 1.63585e9 0.164057
317317 −5.77404e9 + 3.33364e9i −0.571798 + 0.330128i −0.757867 0.652409i 0.773758π-0.773758\pi
0.186069 + 0.982537i 0.440425π0.440425\pi
318318 0 0
319319 2.41856e9 4.18908e9i 0.233558 0.404535i
320320 1.96136e9 + 1.13239e9i 0.187050 + 0.107993i
321321 0 0
322322 −2.47197e9 4.28158e9i −0.229943 0.398272i
323323 1.08570e10i 0.997474i
324324 0 0
325325 −6.38503e9 −0.572308
326326 5.39689e9 3.11590e9i 0.477830 0.275875i
327327 0 0
328328 1.28718e9 2.22946e9i 0.111210 0.192622i
329329 −1.56546e10 9.03820e9i −1.33616 0.771433i
330330 0 0
331331 −7.84292e9 1.35843e10i −0.653380 1.13169i −0.982297 0.187328i 0.940017π-0.940017\pi
0.328918 0.944359i 0.393316π-0.393316\pi
332332 4.12645e9i 0.339644i
333333 0 0
334334 6.86576e9 0.551700
335335 −1.15818e10 + 6.68676e9i −0.919597 + 0.530929i
336336 0 0
337337 −1.29188e9 + 2.23761e9i −0.100162 + 0.173486i −0.911751 0.410743i 0.865270π-0.865270\pi
0.811589 + 0.584229i 0.198603π0.198603\pi
338338 −7.32852e9 4.23112e9i −0.561500 0.324182i
339339 0 0
340340 6.06905e9 + 1.05119e10i 0.454156 + 0.786621i
341341 1.12382e10i 0.831152i
342342 0 0
343343 2.21253e10 1.59850
344344 1.32619e9 7.65677e8i 0.0947049 0.0546779i
345345 0 0
346346 −5.39944e9 + 9.35211e9i −0.376742 + 0.652537i
347347 −1.45626e10 8.40775e9i −1.00444 0.579912i −0.0948784 0.995489i 0.530246π-0.530246\pi
−0.909558 + 0.415577i 0.863580π0.863580\pi
348348 0 0
349349 1.22366e10 + 2.11945e10i 0.824822 + 1.42863i 0.902055 + 0.431620i 0.142058π0.142058\pi
−0.0772336 + 0.997013i 0.524609π0.524609\pi
350350 3.60855e10i 2.40470i
351351 0 0
352352 −1.80211e9 −0.117385
353353 9.05088e9 5.22553e9i 0.582897 0.336536i −0.179387 0.983779i 0.557411π-0.557411\pi
0.762284 + 0.647243i 0.224078π0.224078\pi
354354 0 0
355355 −9.15672e9 + 1.58599e10i −0.576536 + 0.998590i
356356 2.32885e9 + 1.34456e9i 0.144991 + 0.0837108i
357357 0 0
358358 −5.34018e9 9.24946e9i −0.325105 0.563098i
359359 2.37497e10i 1.42982i 0.699219 + 0.714908i 0.253531π0.253531\pi
−0.699219 + 0.714908i 0.746469π0.746469\pi
360360 0 0
361361 −1.69607e9 −0.0998656
362362 8.50688e9 4.91145e9i 0.495377 0.286006i
363363 0 0
364364 2.16651e9 3.75250e9i 0.123411 0.213754i
365365 2.27019e10 + 1.31069e10i 1.27906 + 0.738464i
366366 0 0
367367 −5.17433e9 8.96220e9i −0.285226 0.494027i 0.687438 0.726243i 0.258735π-0.258735\pi
−0.972664 + 0.232217i 0.925402π0.925402\pi
368368 1.74107e9i 0.0949346i
369369 0 0
370370 1.46794e10 0.783252
371371 3.73256e9 2.15499e9i 0.197020 0.113750i
372372 0 0
373373 4.02672e9 6.97448e9i 0.208025 0.360310i −0.743067 0.669217i 0.766630π-0.766630\pi
0.951092 + 0.308907i 0.0999631π0.0999631\pi
374374 −8.36443e9 4.82920e9i −0.427513 0.246825i
375375 0 0
376376 3.18291e9 + 5.51296e9i 0.159248 + 0.275825i
377377 4.09580e9i 0.202756i
378378 0 0
379379 −2.63218e10 −1.27573 −0.637864 0.770149i 0.720182π-0.720182\pi
−0.637864 + 0.770149i 0.720182π0.720182\pi
380380 −1.48015e10 + 8.54565e9i −0.709858 + 0.409837i
381381 0 0
382382 −3.98422e8 + 6.90087e8i −0.0187107 + 0.0324079i
383383 2.64941e10 + 1.52964e10i 1.23127 + 0.710876i 0.967295 0.253653i 0.0816321π-0.0816321\pi
0.263978 + 0.964529i 0.414965π0.414965\pi
384384 0 0
385385 −2.15872e10 3.73901e10i −0.982547 1.70182i
386386 3.09704e10i 1.39508i
387387 0 0
388388 −1.14343e10 −0.504523
389389 −3.76791e10 + 2.17540e10i −1.64552 + 0.950039i −0.666691 + 0.745334i 0.732290π0.732290\pi
−0.978824 + 0.204704i 0.934377π0.934377\pi
390390 0 0
391391 −4.66562e9 + 8.08109e9i −0.199619 + 0.345751i
392392 −1.39777e10 8.07001e9i −0.591957 0.341767i
393393 0 0
394394 −3.09586e9 5.36219e9i −0.128468 0.222514i
395395 1.38016e10i 0.566947i
396396 0 0
397397 4.31419e10 1.73675 0.868375 0.495908i 0.165165π-0.165165\pi
0.868375 + 0.495908i 0.165165π0.165165\pi
398398 2.61083e10 1.50737e10i 1.04051 0.600740i
399399 0 0
400400 6.35397e9 1.10054e10i 0.248202 0.429899i
401401 1.57455e10 + 9.09069e9i 0.608948 + 0.351576i 0.772554 0.634950i 0.218979π-0.218979\pi
−0.163606 + 0.986526i 0.552312π0.552312\pi
402402 0 0
403403 −4.75794e9 8.24099e9i −0.180384 0.312434i
404404 4.55864e9i 0.171124i
405405 0 0
406406 −2.31477e10 −0.851930
407407 −1.01157e10 + 5.84028e9i −0.368652 + 0.212841i
408408 0 0
409409 3.23724e9 5.60707e9i 0.115686 0.200374i −0.802368 0.596830i 0.796427π-0.796427\pi
0.918054 + 0.396456i 0.129760π0.129760\pi
410410 −1.88099e10 1.08599e10i −0.665659 0.384319i
411411 0 0
412412 5.57184e8 + 9.65071e8i 0.0193379 + 0.0334943i
413413 4.13128e10i 1.41999i
414414 0 0
415415 −3.48148e10 −1.17374
416416 −1.32149e9 + 7.62961e8i −0.0441255 + 0.0254759i
417417 0 0
418418 6.79986e9 1.17777e10i 0.222738 0.385794i
419419 3.28096e10 + 1.89427e10i 1.06450 + 0.614589i 0.926673 0.375868i 0.122655π-0.122655\pi
0.137826 + 0.990456i 0.455989π0.455989\pi
420420 0 0
421421 2.38781e10 + 4.13581e10i 0.760102 + 1.31654i 0.942798 + 0.333366i 0.108184π0.108184\pi
−0.182696 + 0.983170i 0.558482π0.558482\pi
422422 2.12502e10i 0.670061i
423423 0 0
424424 −1.51782e9 −0.0469630
425425 5.89834e10 3.40541e10i 1.80790 1.04379i
426426 0 0
427427 −1.70972e10 + 2.96133e10i −0.514297 + 0.890789i
428428 2.59770e10 + 1.49978e10i 0.774130 + 0.446944i
429429 0 0
430430 −6.46000e9 1.11890e10i −0.188955 0.327280i
431431 2.73395e10i 0.792285i −0.918189 0.396143i 0.870349π-0.870349\pi
0.918189 0.396143i 0.129651π-0.129651\pi
432432 0 0
433433 −6.96958e9 −0.198269 −0.0991345 0.995074i 0.531607π-0.531607\pi
−0.0991345 + 0.995074i 0.531607π0.531607\pi
434434 −4.65745e10 + 2.68898e10i −1.31277 + 0.757930i
435435 0 0
436436 1.70555e10 2.95409e10i 0.471973 0.817482i
437437 −1.13788e10 6.56953e9i −0.312010 0.180139i
438438 0 0
439439 4.26214e9 + 7.38223e9i 0.114754 + 0.198760i 0.917682 0.397317i 0.130059π-0.130059\pi
−0.802927 + 0.596077i 0.796725π0.796725\pi
440440 1.52044e10i 0.405656i
441441 0 0
442442 −8.17817e9 −0.214273
443443 1.77214e10 1.02315e10i 0.460134 0.265658i −0.251967 0.967736i 0.581077π-0.581077\pi
0.712101 + 0.702077i 0.247744π0.247744\pi
444444 0 0
445445 1.13441e10 1.96485e10i 0.289287 0.501060i
446446 −2.84242e10 1.64107e10i −0.718372 0.414752i
447447 0 0
448448 4.31193e9 + 7.46849e9i 0.107043 + 0.185405i
449449 1.52992e10i 0.376430i 0.982128 + 0.188215i 0.0602702π0.0602702\pi
−0.982128 + 0.188215i 0.939730π0.939730\pi
450450 0 0
451451 1.72827e10 0.417740
452452 3.16877e10 1.82949e10i 0.759166 0.438305i
453453 0 0
454454 2.35782e10 4.08386e10i 0.554992 0.961274i
455455 −3.16597e10 1.82788e10i −0.738689 0.426483i
456456 0 0
457457 −1.20106e10 2.08029e10i −0.275359 0.476935i 0.694867 0.719138i 0.255463π-0.255463\pi
−0.970226 + 0.242203i 0.922130π0.922130\pi
458458 4.07335e10i 0.925742i
459459 0 0
460460 1.46894e10 0.328074
461461 −4.96796e10 + 2.86825e10i −1.09995 + 0.635058i −0.936209 0.351445i 0.885690π-0.885690\pi
−0.163744 + 0.986503i 0.552357π0.552357\pi
462462 0 0
463463 3.03202e10 5.25162e10i 0.659795 1.14280i −0.320874 0.947122i 0.603977π-0.603977\pi
0.980669 0.195676i 0.0626900π-0.0626900\pi
464464 7.05962e9 + 4.07587e9i 0.152303 + 0.0879324i
465465 0 0
466466 −1.61992e10 2.80579e10i −0.343519 0.594992i
467467 1.01091e10i 0.212543i 0.994337 + 0.106271i 0.0338912π0.0338912\pi
−0.994337 + 0.106271i 0.966109π0.966109\pi
468468 0 0
469469 −5.09238e10 −1.05252
470470 4.65128e10 2.68542e10i 0.953193 0.550326i
471471 0 0
472472 −7.27441e9 + 1.25996e10i −0.146565 + 0.253858i
473473 8.90324e9 + 5.14029e9i 0.177870 + 0.102693i
474474 0 0
475475 4.79505e10 + 8.30528e10i 0.941931 + 1.63147i
476476 4.62195e10i 0.900322i
477477 0 0
478478 1.58727e10 0.304045
479479 −1.87971e10 + 1.08525e10i −0.357067 + 0.206153i −0.667793 0.744347i 0.732761π-0.732761\pi
0.310727 + 0.950499i 0.399428π0.399428\pi
480480 0 0
481481 −4.94520e9 + 8.56534e9i −0.0923855 + 0.160016i
482482 −4.34652e10 2.50947e10i −0.805293 0.464936i
483483 0 0
484484 7.66982e9 + 1.32845e10i 0.139767 + 0.242083i
485485 9.64707e10i 1.74353i
486486 0 0
487487 −5.82792e9 −0.103609 −0.0518045 0.998657i 0.516497π-0.516497\pi
−0.0518045 + 0.998657i 0.516497π0.516497\pi
488488 1.04287e10 6.02100e9i 0.183886 0.106167i
489489 0 0
490490 −6.80865e10 + 1.17929e11i −1.18107 + 2.04568i
491491 2.15718e10 + 1.24545e10i 0.371159 + 0.214288i 0.673964 0.738764i 0.264590π-0.264590\pi
−0.302806 + 0.953052i 0.597923π0.597923\pi
492492 0 0
493493 2.18446e10 + 3.78360e10i 0.369791 + 0.640497i
494494 1.15154e10i 0.193363i
495495 0 0
496496 1.89392e10 0.312921
497497 −6.03915e10 + 3.48670e10i −0.989806 + 0.571465i
498498 0 0
499499 −8.19755e9 + 1.41986e10i −0.132215 + 0.229004i −0.924530 0.381109i 0.875542π-0.875542\pi
0.792315 + 0.610112i 0.208876π0.208876\pi
500500 −4.60899e10 2.66100e10i −0.737438 0.425760i
501501 0 0
502502 1.36943e10 + 2.37192e10i 0.215638 + 0.373496i
503503 4.61285e10i 0.720606i −0.932835 0.360303i 0.882673π-0.882673\pi
0.932835 0.360303i 0.117327π-0.117327\pi
504504 0 0
505505 −3.84612e10 −0.591367
506506 −1.01225e10 + 5.84424e9i −0.154414 + 0.0891509i
507507 0 0
508508 −5.24001e9 + 9.07597e9i −0.0786824 + 0.136282i
509509 6.69443e9 + 3.86503e9i 0.0997339 + 0.0575814i 0.549037 0.835798i 0.314994π-0.314994\pi
−0.449303 + 0.893379i 0.648328π0.648328\pi
510510 0 0
511511 4.99087e10 + 8.64444e10i 0.731969 + 1.26781i
512512 3.03700e9i 0.0441942i
513513 0 0
514514 −2.72925e10 −0.391013
515515 8.14229e9 4.70095e9i 0.115749 0.0668278i
516516 0 0
517517 −2.13681e10 + 3.70107e10i −0.299092 + 0.518042i
518518 4.84077e10 + 2.79482e10i 0.672349 + 0.388181i
519519 0 0
520520 6.43709e9 + 1.11494e10i 0.0880392 + 0.152488i
521521 3.97902e10i 0.540039i 0.962855 + 0.270019i 0.0870301π0.0870301\pi
−0.962855 + 0.270019i 0.912970π0.912970\pi
522522 0 0
523523 −3.49978e10 −0.467772 −0.233886 0.972264i 0.575144π-0.575144\pi
−0.233886 + 0.972264i 0.575144π0.575144\pi
524524 −4.19585e10 + 2.42247e10i −0.556538 + 0.321317i
525525 0 0
526526 3.69076e10 6.39259e10i 0.482140 0.835091i
527527 8.79053e10 + 5.07521e10i 1.13965 + 0.657979i
528528 0 0
529529 −3.35092e10 5.80397e10i −0.427899 0.741143i
530530 1.28058e10i 0.162294i
531531 0 0
532532 −6.50804e10 −0.812463
533533 1.26734e10 7.31699e9i 0.157031 0.0906617i
534534 0 0
535535 1.26536e11 2.19167e11i 1.54454 2.67523i
536536 1.55308e10 + 8.96673e9i 0.188163 + 0.108636i
537537 0 0
538538 3.75687e10 + 6.50709e10i 0.448433 + 0.776708i
539539 1.08354e11i 1.28378i
540540 0 0
541541 2.34001e10 0.273168 0.136584 0.990629i 0.456388π-0.456388\pi
0.136584 + 0.990629i 0.456388π0.456388\pi
542542 2.66729e10 1.53996e10i 0.309081 0.178448i
543543 0 0
544544 8.13839e9 1.40961e10i 0.0929272 0.160955i
545545 −2.49236e11 1.43897e11i −2.82504 1.63104i
546546 0 0
547547 −1.16091e10 2.01075e10i −0.129673 0.224600i 0.793877 0.608078i 0.208059π-0.208059\pi
−0.923550 + 0.383478i 0.874726π0.874726\pi
548548 1.23692e10i 0.137158i
549549 0 0
550550 8.53134e10 0.932324
551551 −5.32757e10 + 3.07588e10i −0.577994 + 0.333705i
552552 0 0
553553 2.62770e10 4.55131e10i 0.280980 0.486671i
554554 9.81649e10 + 5.66755e10i 1.04212 + 0.601667i
555555 0 0
556556 2.72934e10 + 4.72735e10i 0.285600 + 0.494674i
557557 3.65617e10i 0.379844i −0.981799 0.189922i 0.939176π-0.939176\pi
0.981799 0.189922i 0.0608236π-0.0608236\pi
558558 0 0
559559 8.70499e9 0.0891499
560560 6.30115e10 3.63797e10i 0.640719 0.369919i
561561 0 0
562562 −4.46146e10 + 7.72748e10i −0.447231 + 0.774627i
563563 1.15433e11 + 6.66450e10i 1.14893 + 0.663337i 0.948627 0.316397i 0.102473π-0.102473\pi
0.200306 + 0.979733i 0.435806π0.435806\pi
564564 0 0
565565 −1.54354e11 2.67348e11i −1.51469 2.62352i
566566 1.10163e10i 0.107342i
567567 0 0
568568 2.45577e10 0.235936
569569 1.42643e11 8.23549e10i 1.36082 0.785670i 0.371087 0.928598i 0.378985π-0.378985\pi
0.989733 + 0.142928i 0.0456517π0.0456517\pi
570570 0 0
571571 −6.84597e10 + 1.18576e11i −0.644007 + 1.11545i 0.340523 + 0.940236i 0.389396π0.389396\pi
−0.984530 + 0.175216i 0.943937π0.943937\pi
572572 −8.87167e9 5.12206e9i −0.0828745 0.0478476i
573573 0 0
574574 −4.13525e10 7.16247e10i −0.380938 0.659804i
575575 8.24235e10i 0.754015i
576576 0 0
577577 −1.01555e11 −0.916218 −0.458109 0.888896i 0.651473π-0.651473\pi
−0.458109 + 0.888896i 0.651473π0.651473\pi
578578 7.19976e9 4.15678e9i 0.0645070 0.0372431i
579579 0 0
580580 3.43881e10 5.95619e10i 0.303876 0.526328i
581581 −1.14807e11 6.62840e10i −1.00755 0.581707i
582582 0 0
583583 −5.09485e9 8.82453e9i −0.0441018 0.0763866i
584584 3.51519e10i 0.302202i
585585 0 0
586586 −6.00184e10 −0.508972
587587 3.25669e10 1.88025e10i 0.274299 0.158367i −0.356541 0.934280i 0.616044π-0.616044\pi
0.630840 + 0.775913i 0.282711π0.282711\pi
588588 0 0
589589 −7.14626e10 + 1.23777e11i −0.593769 + 1.02844i
590590 1.06303e11 + 6.13741e10i 0.877278 + 0.506497i
591591 0 0
592592 −9.84229e9 1.70474e10i −0.0801326 0.138794i
593593 1.30215e11i 1.05304i 0.850163 + 0.526519i 0.176503π0.176503\pi
−0.850163 + 0.526519i 0.823497π0.823497\pi
594594 0 0
595595 3.89953e11 3.11132
596596 −4.77998e10 + 2.75972e10i −0.378827 + 0.218716i
597597 0 0
598598 −4.94856e9 + 8.57115e9i −0.0386967 + 0.0670246i
599599 −1.13848e11 6.57304e10i −0.884341 0.510575i −0.0122537 0.999925i 0.503901π-0.503901\pi
−0.872087 + 0.489350i 0.837234π0.837234\pi
600600 0 0
601601 2.15092e10 + 3.72550e10i 0.164864 + 0.285553i 0.936607 0.350382i 0.113948π-0.113948\pi
−0.771743 + 0.635935i 0.780615π0.780615\pi
602602 4.91969e10i 0.374586i
603603 0 0
604604 −1.07592e11 −0.808409
605605 1.12081e11 6.47102e10i 0.836588 0.483004i
606606 0 0
607607 −1.29606e10 + 2.24485e10i −0.0954710 + 0.165361i −0.909805 0.415036i 0.863769π-0.863769\pi
0.814334 + 0.580396i 0.197102π0.197102\pi
608608 1.98483e10 + 1.14594e10i 0.145248 + 0.0838588i
609609 0 0
610610 −5.07990e10 8.79865e10i −0.366890 0.635472i
611611 3.61866e10i 0.259646i
612612 0 0
613613 1.28485e11 0.909933 0.454967 0.890508i 0.349651π-0.349651\pi
0.454967 + 0.890508i 0.349651π0.349651\pi
614614 −1.31529e11 + 7.59383e10i −0.925439 + 0.534303i
615615 0 0
616616 −2.89477e10 + 5.01389e10i −0.201044 + 0.348219i
617617 1.02289e11 + 5.90563e10i 0.705808 + 0.407498i 0.809507 0.587110i 0.199735π-0.199735\pi
−0.103699 + 0.994609i 0.533068π0.533068\pi
618618 0 0
619619 −6.40218e10 1.10889e11i −0.436079 0.755312i 0.561304 0.827610i 0.310300π-0.310300\pi
−0.997383 + 0.0722982i 0.976967π0.976967\pi
620620 1.59789e11i 1.08139i
621621 0 0
622622 2.59046e10 0.173068
623623 7.48177e10 4.31960e10i 0.496652 0.286742i
624624 0 0
625625 −7.30176e10 + 1.26470e11i −0.478528 + 0.828835i
626626 −1.75219e11 1.01163e11i −1.14100 0.658754i
627627 0 0
628628 −2.69977e10 4.67613e10i −0.173575 0.300641i
629629 1.05499e11i 0.673980i
630630 0 0
631631 −2.40613e11 −1.51775 −0.758877 0.651233i 0.774252π-0.774252\pi
−0.758877 + 0.651233i 0.774252π0.774252\pi
632632 −1.60280e10 + 9.25377e9i −0.100464 + 0.0580030i
633633 0 0
634634 3.77159e10 6.53258e10i 0.233436 0.404322i
635635 7.65738e10 + 4.42099e10i 0.470961 + 0.271910i
636636 0 0
637637 −4.58740e10 7.94561e10i −0.278618 0.482580i
638638 5.47259e10i 0.330301i
639639 0 0
640640 −2.56231e10 −0.152726
641641 −1.87111e11 + 1.08029e11i −1.10833 + 0.639893i −0.938396 0.345563i 0.887688π-0.887688\pi
−0.169932 + 0.985456i 0.554355π0.554355\pi
642642 0 0
643643 −1.85669e10 + 3.21588e10i −0.108616 + 0.188129i −0.915210 0.402977i 0.867975π-0.867975\pi
0.806594 + 0.591106i 0.201309π0.201309\pi
644644 4.84405e10 + 2.79671e10i 0.281621 + 0.162594i
645645 0 0
646646 6.14167e10 + 1.06377e11i 0.352660 + 0.610825i
647647 5.88598e10i 0.335894i 0.985796 + 0.167947i 0.0537137π0.0537137\pi
−0.985796 + 0.167947i 0.946286π0.946286\pi
648648 0 0
649649 −9.76719e10 −0.550543
650650 6.25603e10 3.61192e10i 0.350465 0.202341i
651651 0 0
652652 −3.52523e10 + 6.10588e10i −0.195073 + 0.337877i
653653 1.48938e11 + 8.59893e10i 0.819129 + 0.472925i 0.850116 0.526595i 0.176532π-0.176532\pi
−0.0309867 + 0.999520i 0.509865π0.509865\pi
654654 0 0
655655 2.04384e11 + 3.54003e11i 1.11040 + 1.92328i
656656 2.91256e10i 0.157275i
657657 0 0
658658 2.04511e11 1.09097
659659 −2.34850e11 + 1.35591e11i −1.24523 + 0.718934i −0.970154 0.242489i 0.922036π-0.922036\pi
−0.275075 + 0.961423i 0.588703π0.588703\pi
660660 0 0
661661 1.21597e11 2.10613e11i 0.636968 1.10326i −0.349126 0.937076i 0.613522π-0.613522\pi
0.986095 0.166185i 0.0531451π-0.0531451\pi
662662 1.53689e11 + 8.87325e10i 0.800223 + 0.462009i
663663 0 0
664664 2.33427e10 + 4.04308e10i 0.120082 + 0.207989i
665665 5.49082e11i 2.80770i
666666 0 0
667667 5.28721e10 0.267130
668668 −6.72704e10 + 3.88386e10i −0.337846 + 0.195055i
669669 0 0
670670 7.56521e10 1.31033e11i 0.375424 0.650253i
671671 7.00118e10 + 4.04213e10i 0.345367 + 0.199398i
672672 0 0
673673 1.44609e10 + 2.50471e10i 0.0704914 + 0.122095i 0.899117 0.437709i 0.144210π-0.144210\pi
−0.828625 + 0.559804i 0.810877π0.810877\pi
674674 2.92320e10i 0.141651i
675675 0 0
676676 9.57394e10 0.458463
677677 −1.58076e11 + 9.12654e10i −0.752509 + 0.434462i −0.826600 0.562790i 0.809728π-0.809728\pi
0.0740905 + 0.997252i 0.476395π0.476395\pi
678678 0 0
679679 −1.83671e11 + 3.18127e11i −0.864095 + 1.49666i
680680 −1.18929e11 6.86634e10i −0.556225 0.321137i
681681 0 0
682682 6.35730e10 + 1.10112e11i 0.293857 + 0.508974i
683683 3.71514e11i 1.70723i −0.520903 0.853616i 0.674405π-0.674405\pi
0.520903 0.853616i 0.325595π-0.325595\pi
684684 0 0
685685 1.04359e11 0.473989
686686 −2.16783e11 + 1.25159e11i −0.978876 + 0.565155i
687687 0 0
688688 −8.66264e9 + 1.50041e10i −0.0386631 + 0.0669665i
689689 −7.47209e9 4.31401e9i −0.0331562 0.0191428i
690690 0 0
691691 −9.88238e10 1.71168e11i −0.433460 0.750775i 0.563708 0.825974i 0.309374π-0.309374\pi
−0.997169 + 0.0751987i 0.976041π0.976041\pi
692692 1.22175e11i 0.532794i
693693 0 0
694694 1.90246e11 0.820119
695695 3.98846e11 2.30274e11i 1.70949 0.986973i
696696 0 0
697697 −7.80492e10 + 1.35185e11i −0.330702 + 0.572793i
698698 −2.39788e11 1.38442e11i −1.01020 0.583237i
699699 0 0
700700 −2.04130e11 3.53564e11i −0.850189 1.47257i
701701 6.70096e10i 0.277501i −0.990327 0.138751i 0.955691π-0.955691\pi
0.990327 0.138751i 0.0443087π-0.0443087\pi
702702 0 0
703703 1.48551e11 0.608209
704704 1.76570e10 1.01943e10i 0.0718831 0.0415017i
705705 0 0
706706 −5.91201e10 + 1.02399e11i −0.237967 + 0.412170i
707707 −1.26832e11 7.32264e10i −0.507634 0.293083i
708708 0 0
709709 5.70291e10 + 9.87774e10i 0.225690 + 0.390906i 0.956526 0.291647i 0.0942031π-0.0942031\pi
−0.730836 + 0.682553i 0.760870π0.760870\pi
710710 2.07193e11i 0.815345i
711711 0 0
712712 −3.04240e10 −0.118385
713713 1.06382e11 6.14196e10i 0.411632 0.237656i
714714 0 0
715715 −4.32147e10 + 7.48501e10i −0.165351 + 0.286397i
716716 1.04646e11 + 6.04172e10i 0.398171 + 0.229884i
717717 0 0
718718 −1.34348e11 2.32698e11i −0.505516 0.875580i
719719 2.31072e11i 0.864633i 0.901722 + 0.432317i 0.142304π0.142304\pi
−0.901722 + 0.432317i 0.857696π0.857696\pi
720720 0 0
721721 3.58007e10 0.132480
722722 1.66181e10 9.59444e9i 0.0611549 0.0353078i
723723 0 0
724724 −5.55667e10 + 9.62444e10i −0.202237 + 0.350285i
725725 −3.34208e11 1.92955e11i −1.20966 0.698400i
726726 0 0
727727 1.70637e11 + 2.95551e11i 0.610850 + 1.05802i 0.991097 + 0.133138i 0.0425055π0.0425055\pi
−0.380248 + 0.924885i 0.624161π0.624161\pi
728728 4.90224e10i 0.174530i
729729 0 0
730730 −2.96576e11 −1.04435
731731 −8.04145e10 + 4.64274e10i −0.281621 + 0.162594i
732732 0 0
733733 2.07203e11 3.58887e11i 0.717763 1.24320i −0.244122 0.969745i 0.578500π-0.578500\pi
0.961884 0.273457i 0.0881670π-0.0881670\pi
734734 1.01396e11 + 5.85408e10i 0.349330 + 0.201685i
735735 0 0
736736 −9.84897e9 1.70589e10i −0.0335645 0.0581353i
737737 1.20394e11i 0.408071i
738738 0 0
739739 2.71838e11 0.911449 0.455725 0.890121i 0.349380π-0.349380\pi
0.455725 + 0.890121i 0.349380π0.349380\pi
740740 −1.43828e11 + 8.30392e10i −0.479642 + 0.276921i
741741 0 0
742742 −2.43810e10 + 4.22291e10i −0.0804332 + 0.139314i
743743 2.96676e11 + 1.71286e11i 0.973479 + 0.562039i 0.900295 0.435280i 0.143351π-0.143351\pi
0.0731842 + 0.997318i 0.476684π0.476684\pi
744744 0 0
745745 2.32837e11 + 4.03286e11i 0.755835 + 1.30914i
746746 9.11142e10i 0.294192i
747747 0 0
748748 1.09272e11 0.349063
749749 8.34547e11 4.81826e11i 2.65170 1.53096i
750750 0 0
751751 −5.25839e10 + 9.10780e10i −0.165308 + 0.286321i −0.936765 0.349960i 0.886195π-0.886195\pi
0.771457 + 0.636282i 0.219528π0.219528\pi
752752 −6.23721e10 3.60105e10i −0.195038 0.112605i
753753 0 0
754754 2.31693e10 + 4.01304e10i 0.0716849 + 0.124162i
755755 9.07750e11i 2.79369i
756756 0 0
757757 −4.23531e11 −1.28974 −0.644869 0.764293i 0.723088π-0.723088\pi
−0.644869 + 0.764293i 0.723088π0.723088\pi
758758 2.57900e11 1.48898e11i 0.781221 0.451038i
759759 0 0
760760 9.66830e10 1.67460e11i 0.289798 0.501945i
761761 −4.62418e11 2.66977e11i −1.37878 0.796041i −0.386770 0.922176i 0.626409π-0.626409\pi
−0.992013 + 0.126135i 0.959743π0.959743\pi
762762 0 0
763763 −5.47931e11 9.49044e11i −1.61669 2.80019i
764764 9.01526e9i 0.0264609i
765765 0 0
766766 −3.46118e11 −1.00533
767767 −7.16228e10 + 4.13514e10i −0.206952 + 0.119484i
768768 0 0
769769 −5.66789e10 + 9.81707e10i −0.162075 + 0.280722i −0.935613 0.353028i 0.885152π-0.885152\pi
0.773538 + 0.633750i 0.218485π0.218485\pi
770770 4.23021e11 + 2.44231e11i 1.20337 + 0.694766i
771771 0 0
772772 1.75195e11 + 3.03447e11i 0.493234 + 0.854306i
773773 2.83942e11i 0.795265i −0.917545 0.397632i 0.869832π-0.869832\pi
0.917545 0.397632i 0.130168π-0.130168\pi
774774 0 0
775775 −8.96595e11 −2.48536
776776 1.12032e11 6.46820e10i 0.308956 0.178376i
777777 0 0
778778 2.46119e11 4.26290e11i 0.671779 1.16355i
779779 −1.90350e11 1.09899e11i −0.516897 0.298430i
780780 0 0
781781 8.24328e10 + 1.42778e11i 0.221562 + 0.383757i
782782 1.05571e11i 0.282304i
783783 0 0
784784 1.82603e11 0.483331
785785 −3.94524e11 + 2.27779e11i −1.03895 + 0.599839i
786786 0 0
787787 3.25568e11 5.63900e11i 0.848678 1.46995i −0.0337110 0.999432i 0.510733π-0.510733\pi
0.882389 0.470521i 0.155934π-0.155934\pi
788788 6.06662e10 + 3.50257e10i 0.157341 + 0.0908409i
789789 0 0
790790 7.80739e10 + 1.35228e11i 0.200446 + 0.347183i
791791 1.17550e12i 3.00273i
792792 0 0
793793 6.84528e10 0.173100
794794 −4.22703e11 + 2.44047e11i −1.06354 + 0.614034i
795795 0 0
796796 −1.70539e11 + 2.95382e11i −0.424787 + 0.735753i
797797 −4.16469e11 2.40448e11i −1.03216 0.595921i −0.114561 0.993416i 0.536546π-0.536546\pi
−0.917604 + 0.397496i 0.869879π0.869879\pi
798798 0 0
799799 −1.92998e11 3.34283e11i −0.473550 0.820213i
800800 1.43774e11i 0.351011i
801801 0 0
802802 −2.05699e11 −0.497204
803803 2.04372e11 1.17994e11i 0.491541 0.283791i
804804 0 0
805805 2.35958e11 4.08692e11i 0.561890 0.973223i
806806 9.32361e10 + 5.38299e10i 0.220925 + 0.127551i
807807 0 0
808808 2.57876e10 + 4.46654e10i 0.0605013 + 0.104791i
809809 1.97505e11i 0.461089i 0.973062 + 0.230545i 0.0740508π0.0740508\pi
−0.973062 + 0.230545i 0.925949π0.925949\pi
810810 0 0
811811 −1.30697e11 −0.302121 −0.151061 0.988524i 0.548269π-0.548269\pi
−0.151061 + 0.988524i 0.548269π0.548269\pi
812812 2.26800e11 1.30943e11i 0.521698 0.301203i
813813 0 0
814814 6.60752e10 1.14446e11i 0.150501 0.260676i
815815 5.15152e11 + 2.97423e11i 1.16763 + 0.674131i
816816 0 0
817817 −6.53730e10 1.13229e11i −0.146727 0.254139i
818818 7.32504e10i 0.163605i
819819 0 0
820820 2.45732e11 0.543509
821821 −2.25465e10 + 1.30172e10i −0.0496256 + 0.0286514i −0.524608 0.851344i 0.675788π-0.675788\pi
0.474982 + 0.879996i 0.342455π0.342455\pi
822822 0 0
823823 1.02310e11 1.77206e11i 0.223007 0.386260i −0.732712 0.680539i 0.761746π-0.761746\pi
0.955720 + 0.294278i 0.0950792π0.0950792\pi
824824 −1.09185e10 6.30382e9i −0.0236840 0.0136740i
825825 0 0
826826 2.33701e11 + 4.04781e11i 0.502042 + 0.869562i
827827 2.31574e11i 0.495072i −0.968879 0.247536i 0.920379π-0.920379\pi
0.968879 0.247536i 0.0796208π-0.0796208\pi
828828 0 0
829829 7.98205e11 1.69004 0.845019 0.534736i 0.179589π-0.179589\pi
0.845019 + 0.534736i 0.179589π0.179589\pi
830830 3.41114e11 1.96942e11i 0.718765 0.414979i
831831 0 0
832832 8.63192e9 1.49509e10i 0.0180142 0.0312015i
833833 8.47545e11 + 4.89331e11i 1.76029 + 1.01630i
834834 0 0
835835 3.27681e11 + 5.67559e11i 0.674070 + 1.16752i
836836 1.53863e11i 0.315000i
837837 0 0
838838 −4.28623e11 −0.869160
839839 −5.56790e11 + 3.21463e11i −1.12368 + 0.648758i −0.942338 0.334662i 0.891378π-0.891378\pi
−0.181343 + 0.983420i 0.558045π0.558045\pi
840840 0 0
841841 −1.26349e11 + 2.18842e11i −0.252573 + 0.437469i
842842 −4.67914e11 2.70150e11i −0.930931 0.537473i
843843 0 0
844844 1.20210e11 + 2.08209e11i 0.236902 + 0.410327i
845845 8.07752e11i 1.58435i
846846 0 0
847847 4.92808e11 0.957511
848848 1.48715e10 8.58606e9i 0.0287588 0.0166039i
849849 0 0
850850 −3.85278e11 + 6.67321e11i −0.738071 + 1.27838i
851851 −1.10569e11 6.38370e10i −0.210821 0.121718i
852852 0 0
853853 9.75384e10 + 1.68942e11i 0.184238 + 0.319110i 0.943320 0.331886i 0.107685π-0.107685\pi
−0.759081 + 0.650996i 0.774352π0.774352\pi
854854 3.86866e11i 0.727326i
855855 0 0
856856 −3.39362e11 −0.632074
857857 3.84904e10 2.22224e10i 0.0713557 0.0411972i −0.463898 0.885889i 0.653549π-0.653549\pi
0.535253 + 0.844692i 0.320216π0.320216\pi
858858 0 0
859859 −1.25294e11 + 2.17015e11i −0.230122 + 0.398582i −0.957844 0.287290i 0.907246π-0.907246\pi
0.727722 + 0.685872i 0.240579π0.240579\pi
860860 1.26590e11 + 7.30866e10i 0.231422 + 0.133611i
861861 0 0
862862 1.54656e11 + 2.67871e11i 0.280115 + 0.485174i
863863 3.91558e11i 0.705915i 0.935639 + 0.352958i 0.114824π0.114824\pi
−0.935639 + 0.352958i 0.885176π0.885176\pi
864864 0 0
865865 −1.03079e12 −1.84122
866866 6.82876e10 3.94259e10i 0.121415 0.0700987i
867867 0 0
868868 3.04224e11 5.26931e11i 0.535937 0.928271i
869869 −1.07602e11 6.21242e10i −0.188687 0.108939i
870870 0 0
871871 5.09714e10 + 8.82851e10i 0.0885633 + 0.153396i
872872 3.85921e11i 0.667471i
873873 0 0
874874 1.48651e11 0.254755
875875 −1.48070e12 + 8.54884e11i −2.52601 + 1.45839i
876876 0 0
877877 3.99055e10 6.91184e10i 0.0674582 0.116841i −0.830324 0.557282i 0.811844π-0.811844\pi
0.897782 + 0.440441i 0.145178π0.145178\pi
878878 −8.35204e10 4.82206e10i −0.140545 0.0811436i
879879 0 0
880880 −8.60090e10 1.48972e11i −0.143421 0.248413i
881881 5.84453e11i 0.970166i 0.874468 + 0.485083i 0.161211π0.161211\pi
−0.874468 + 0.485083i 0.838789π0.838789\pi
882882 0 0
883883 7.52384e10 0.123765 0.0618823 0.998083i 0.480290π-0.480290\pi
0.0618823 + 0.998083i 0.480290π0.480290\pi
884884 8.01294e10 4.62627e10i 0.131215 0.0757569i
885885 0 0
886886 −1.15756e11 + 2.00495e11i −0.187849 + 0.325364i
887887 −6.05896e11 3.49814e11i −0.978822 0.565123i −0.0769076 0.997038i 0.524505π-0.524505\pi
−0.901914 + 0.431915i 0.857838π0.857838\pi
888888 0 0
889889 1.68343e11 + 2.91578e11i 0.269518 + 0.466819i
890890 2.56687e11i 0.409113i
891891 0 0
892892 3.71333e11 0.586548
893893 4.70694e11 2.71755e11i 0.740172 0.427338i
894894 0 0
895895 5.09739e11 8.82894e11i 0.794430 1.37599i
896896 −8.44963e10 4.87840e10i −0.131101 0.0756911i
897897 0 0
898898 −8.65455e10 1.49901e11i −0.133088 0.230515i
899899 5.75137e11i 0.880507i
900900 0 0
901901 9.20338e10 0.139652
902902 −1.69335e11 + 9.77658e10i −0.255812 + 0.147693i
903903 0 0
904904 −2.06983e11 + 3.58505e11i −0.309928 + 0.536812i
905905 8.12012e11 + 4.68815e11i 1.21051 + 0.698888i
906906 0 0
907907 −5.79947e10 1.00450e11i −0.0856958 0.148429i 0.819992 0.572375i 0.193978π-0.193978\pi
−0.905687 + 0.423946i 0.860645π0.860645\pi
908908 5.33513e11i 0.784877i
909909 0 0
910910 4.13601e11 0.603137
911911 −9.81176e11 + 5.66482e11i −1.42454 + 0.822456i −0.996682 0.0813913i 0.974064π-0.974064\pi
−0.427854 + 0.903848i 0.640730π0.640730\pi
912912 0 0
913913 −1.56709e11 + 2.71428e11i −0.225533 + 0.390635i
914914 2.35358e11 + 1.35884e11i 0.337244 + 0.194708i
915915 0 0
916916 −2.30424e11 3.99105e11i −0.327299 0.566899i
917917 1.55651e12i 2.20127i
918918 0 0
919919 −3.06256e11 −0.429361 −0.214680 0.976684i 0.568871π-0.568871\pi
−0.214680 + 0.976684i 0.568871π0.568871\pi
920920 −1.43926e11 + 8.30956e10i −0.200903 + 0.115992i
921921 0 0
922922 3.24506e11 5.62060e11i 0.449054 0.777784i
923923 1.20896e11 + 6.97992e10i 0.166573 + 0.0961709i
924924 0 0
925925 4.65942e11 + 8.07035e11i 0.636451 + 1.10237i
926926 6.86069e11i 0.933090i
927927 0 0
928928 −9.22265e10 −0.124355
929929 8.75115e11 5.05248e11i 1.17490 0.678331i 0.220074 0.975483i 0.429370π-0.429370\pi
0.954830 + 0.297152i 0.0960369π0.0960369\pi
930930 0 0
931931 −6.89012e11 + 1.19340e12i −0.917124 + 1.58851i
932932 3.17439e11 + 1.83273e11i 0.420723 + 0.242905i
933933 0 0
934934 −5.71858e10 9.90488e10i −0.0751452 0.130155i
935935 9.21929e11i 1.20629i
936936 0 0
937937 −3.80033e11 −0.493018 −0.246509 0.969141i 0.579283π-0.579283\pi
−0.246509 + 0.969141i 0.579283π0.579283\pi
938938 4.98950e11 2.88069e11i 0.644533 0.372121i
939939 0 0
940940 −3.03820e11 + 5.26232e11i −0.389139 + 0.674009i
941941 −4.20722e11 2.42904e11i −0.536583 0.309796i 0.207110 0.978318i 0.433594π-0.433594\pi
−0.743693 + 0.668521i 0.766928π0.766928\pi
942942 0 0
943943 9.44541e10 + 1.63599e11i 0.119447 + 0.206888i
944944 1.64601e11i 0.207274i
945945 0 0
946946 −1.16311e11 −0.145231
947947 −4.64773e9 + 2.68337e9i −0.00577885 + 0.00333642i −0.502887 0.864352i 0.667729π-0.667729\pi
0.497108 + 0.867689i 0.334395π0.334395\pi
948948 0 0
949949 9.99106e10 1.73050e11i 0.123182 0.213357i
950950 −9.39635e11 5.42498e11i −1.15363 0.666046i
951951 0 0
952952 −2.61457e11 4.52857e11i −0.318312 0.551332i
953953 2.87948e11i 0.349094i −0.984649 0.174547i 0.944154π-0.944154\pi
0.984649 0.174547i 0.0558462π-0.0558462\pi
954954 0 0
955955 −7.60616e10 −0.0914433
956956 −1.55520e11 + 8.97893e10i −0.186189 + 0.107496i
957957 0 0
958958 1.22782e11 2.12665e11i 0.145772 0.252484i
959959 3.44141e11 + 1.98690e11i 0.406876 + 0.234910i
960960 0 0
961961 −2.41670e11 4.18585e11i −0.283354 0.490784i
962962 1.11897e11i 0.130653i
963963 0 0
964964 5.67827e11 0.657519
965965 2.56017e12 1.47812e12i 2.95230 1.70451i
966966 0 0
967967 −4.51417e11 + 7.81877e11i −0.516264 + 0.894195i 0.483558 + 0.875312i 0.339344π0.339344\pi
−0.999822 + 0.0188827i 0.993989π0.993989\pi
968968 −1.50297e11 8.67741e10i −0.171179 0.0988300i
969969 0 0
970970 −5.45721e11 9.45216e11i −0.616429 1.06769i
971971 8.08040e11i 0.908983i −0.890751 0.454492i 0.849821π-0.849821\pi
0.890751 0.454492i 0.150179π-0.150179\pi
972972 0 0
973973 1.75368e12 1.95658
974974 5.71017e10 3.29677e10i 0.0634473 0.0366313i
975975 0 0
976976 −6.81198e10 + 1.17987e11i −0.0750713 + 0.130027i
977977 −1.39658e12 8.06317e11i −1.53281 0.884968i −0.999231 0.0392176i 0.987513π-0.987513\pi
−0.533579 0.845750i 0.679153π-0.679153\pi
978978 0 0
979979 −1.02124e11 1.76884e11i −0.111173 0.192557i
980980 1.54062e12i 1.67029i
981981 0 0
982982 −2.81812e11 −0.303050
983983 −1.24469e12 + 7.18625e11i −1.33306 + 0.769641i −0.985767 0.168117i 0.946231π-0.946231\pi
−0.347290 + 0.937758i 0.612898π0.612898\pi
984984 0 0
985985 2.95511e11 5.11840e11i 0.313927 0.543737i
986986 −4.28065e11 2.47143e11i −0.452900 0.261482i
987987 0 0
988988 6.51412e10 + 1.12828e11i 0.0683641 + 0.118410i
989989 1.12372e11i 0.117455i
990990 0 0
991991 −1.11953e12 −1.16075 −0.580377 0.814348i 0.697095π-0.697095\pi
−0.580377 + 0.814348i 0.697095π0.697095\pi
992992 −1.85565e11 + 1.07136e11i −0.191624 + 0.110634i
993993 0 0
994994 3.94476e11 6.83252e11i 0.404087 0.699899i
995995 2.49213e12 + 1.43883e12i 2.54261 + 1.46797i
996996 0 0
997997 −4.45668e11 7.71920e11i −0.451057 0.781253i 0.547395 0.836874i 0.315619π-0.315619\pi
−0.998452 + 0.0556212i 0.982286π0.982286\pi
998998 1.85489e11i 0.186981i
999999 0 0
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 54.9.d.a.17.1 16
3.2 odd 2 18.9.d.a.5.6 16
4.3 odd 2 432.9.q.c.17.1 16
9.2 odd 6 inner 54.9.d.a.35.1 16
9.4 even 3 162.9.b.c.161.8 16
9.5 odd 6 162.9.b.c.161.9 16
9.7 even 3 18.9.d.a.11.6 yes 16
12.11 even 2 144.9.q.b.113.5 16
36.7 odd 6 144.9.q.b.65.5 16
36.11 even 6 432.9.q.c.305.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.9.d.a.5.6 16 3.2 odd 2
18.9.d.a.11.6 yes 16 9.7 even 3
54.9.d.a.17.1 16 1.1 even 1 trivial
54.9.d.a.35.1 16 9.2 odd 6 inner
144.9.q.b.65.5 16 36.7 odd 6
144.9.q.b.113.5 16 12.11 even 2
162.9.b.c.161.8 16 9.4 even 3
162.9.b.c.161.9 16 9.5 odd 6
432.9.q.c.17.1 16 4.3 odd 2
432.9.q.c.305.1 16 36.11 even 6