Properties

Label 35.10.a.e.1.6
Level 3535
Weight 1010
Character 35.1
Self dual yes
Analytic conductor 18.02618.026
Analytic rank 00
Dimension 66
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,10,Mod(1,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: N N == 35=57 35 = 5 \cdot 7
Weight: k k == 10 10
Character orbit: [χ][\chi] == 35.a (trivial)

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: yes
Analytic conductor: 18.026254265718.0262542657
Analytic rank: 00
Dimension: 66
Coefficient field: Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x63x53018x4+3368x3+2066979x26329061x14714266 x^{6} - 3x^{5} - 3018x^{4} + 3368x^{3} + 2066979x^{2} - 6329061x - 14714266 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 23325 2^{3}\cdot 3^{2}\cdot 5
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.6
Root 39.7818-39.7818 of defining polynomial
Character χ\chi == 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+42.7818q2260.219q3+1318.28q4+625.000q511132.6q62401.00q7+34494.1q8+48030.7q9+26738.6q10+41568.7q11343041.q12+103859.q13102719.q14162637.q15+800760.q16+355256.q17+2.05484e6q18349126.q19+823925.q20+624785.q21+1.77838e6q22+228204.q238.97601e6q24+390625.q25+4.44327e6q267.37660e6q273.16519e6q28+4.02216e6q296.95788e6q303.29476e6q31+1.65969e7q321.08169e7q33+1.51985e7q341.50062e6q35+6.33179e7q362.13083e7q371.49362e7q382.70260e7q39+2.15588e7q40+1.05289e7q41+2.67294e7q42+3.89712e6q43+5.47991e7q44+3.00192e7q45+9.76296e6q463.31846e7q472.08373e8q48+5.76480e6q49+1.67116e7q509.24443e7q51+1.36915e8q526.31880e7q533.15584e8q54+2.59804e7q558.28203e7q56+9.08490e7q57+1.72075e8q58+5.86733e7q592.14401e8q60+1.37845e8q611.40956e8q621.15322e8q63+3.00057e8q64+6.49118e7q654.62768e8q66+8.36796e7q67+4.68327e8q685.93829e7q696.41994e7q70+1.50169e8q71+1.65678e9q722.74817e8q739.11609e8q741.01648e8q754.60246e8q769.98063e7q771.15622e9q782.75964e8q79+5.00475e8q80+9.74140e8q81+4.50444e8q82+2.32312e8q83+8.23642e8q84+2.22035e8q85+1.66726e8q861.04664e9q87+1.43387e9q88+2.71482e8q89+1.28427e9q902.49365e8q91+3.00837e8q92+8.57358e8q931.41969e9q942.18204e8q954.31883e9q969.76607e8q97+2.46628e8q98+1.99657e9q99+O(q100)q+42.7818 q^{2} -260.219 q^{3} +1318.28 q^{4} +625.000 q^{5} -11132.6 q^{6} -2401.00 q^{7} +34494.1 q^{8} +48030.7 q^{9} +26738.6 q^{10} +41568.7 q^{11} -343041. q^{12} +103859. q^{13} -102719. q^{14} -162637. q^{15} +800760. q^{16} +355256. q^{17} +2.05484e6 q^{18} -349126. q^{19} +823925. q^{20} +624785. q^{21} +1.77838e6 q^{22} +228204. q^{23} -8.97601e6 q^{24} +390625. q^{25} +4.44327e6 q^{26} -7.37660e6 q^{27} -3.16519e6 q^{28} +4.02216e6 q^{29} -6.95788e6 q^{30} -3.29476e6 q^{31} +1.65969e7 q^{32} -1.08169e7 q^{33} +1.51985e7 q^{34} -1.50062e6 q^{35} +6.33179e7 q^{36} -2.13083e7 q^{37} -1.49362e7 q^{38} -2.70260e7 q^{39} +2.15588e7 q^{40} +1.05289e7 q^{41} +2.67294e7 q^{42} +3.89712e6 q^{43} +5.47991e7 q^{44} +3.00192e7 q^{45} +9.76296e6 q^{46} -3.31846e7 q^{47} -2.08373e8 q^{48} +5.76480e6 q^{49} +1.67116e7 q^{50} -9.24443e7 q^{51} +1.36915e8 q^{52} -6.31880e7 q^{53} -3.15584e8 q^{54} +2.59804e7 q^{55} -8.28203e7 q^{56} +9.08490e7 q^{57} +1.72075e8 q^{58} +5.86733e7 q^{59} -2.14401e8 q^{60} +1.37845e8 q^{61} -1.40956e8 q^{62} -1.15322e8 q^{63} +3.00057e8 q^{64} +6.49118e7 q^{65} -4.62768e8 q^{66} +8.36796e7 q^{67} +4.68327e8 q^{68} -5.93829e7 q^{69} -6.41994e7 q^{70} +1.50169e8 q^{71} +1.65678e9 q^{72} -2.74817e8 q^{73} -9.11609e8 q^{74} -1.01648e8 q^{75} -4.60246e8 q^{76} -9.98063e7 q^{77} -1.15622e9 q^{78} -2.75964e8 q^{79} +5.00475e8 q^{80} +9.74140e8 q^{81} +4.50444e8 q^{82} +2.32312e8 q^{83} +8.23642e8 q^{84} +2.22035e8 q^{85} +1.66726e8 q^{86} -1.04664e9 q^{87} +1.43387e9 q^{88} +2.71482e8 q^{89} +1.28427e9 q^{90} -2.49365e8 q^{91} +3.00837e8 q^{92} +8.57358e8 q^{93} -1.41969e9 q^{94} -2.18204e8 q^{95} -4.31883e9 q^{96} -9.76607e8 q^{97} +2.46628e8 q^{98} +1.99657e9 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+15q2124q3+3009q4+3750q5+4888q614406q7+22041q8+111090q9+9375q1047796q11541656q12+102168q1336015q1477500q15+2371065q16++3571968784q99+O(q100) 6 q + 15 q^{2} - 124 q^{3} + 3009 q^{4} + 3750 q^{5} + 4888 q^{6} - 14406 q^{7} + 22041 q^{8} + 111090 q^{9} + 9375 q^{10} - 47796 q^{11} - 541656 q^{12} + 102168 q^{13} - 36015 q^{14} - 77500 q^{15} + 2371065 q^{16}+ \cdots + 3571968784 q^{99}+O(q^{100}) Copy content Toggle raw display

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 42.7818 1.89071 0.945353 0.326050i 0.105718π-0.105718\pi
0.945353 + 0.326050i 0.105718π0.105718\pi
33 −260.219 −1.85478 −0.927391 0.374095i 0.877954π-0.877954\pi
−0.927391 + 0.374095i 0.877954π0.877954\pi
44 1318.28 2.57477
55 625.000 0.447214
66 −11132.6 −3.50684
77 −2401.00 −0.377964
88 34494.1 2.97742
99 48030.7 2.44021
1010 26738.6 0.845549
1111 41568.7 0.856050 0.428025 0.903767i 0.359210π-0.359210\pi
0.428025 + 0.903767i 0.359210π0.359210\pi
1212 −343041. −4.77563
1313 103859. 1.00855 0.504277 0.863542i 0.331759π-0.331759\pi
0.504277 + 0.863542i 0.331759π0.331759\pi
1414 −102719. −0.714619
1515 −162637. −0.829483
1616 800760. 3.05466
1717 355256. 1.03162 0.515812 0.856702i 0.327490π-0.327490\pi
0.515812 + 0.856702i 0.327490π0.327490\pi
1818 2.05484e6 4.61372
1919 −349126. −0.614597 −0.307299 0.951613i 0.599425π-0.599425\pi
−0.307299 + 0.951613i 0.599425π0.599425\pi
2020 823925. 1.15147
2121 624785. 0.701041
2222 1.77838e6 1.61854
2323 228204. 0.170039 0.0850193 0.996379i 0.472905π-0.472905\pi
0.0850193 + 0.996379i 0.472905π0.472905\pi
2424 −8.97601e6 −5.52246
2525 390625. 0.200000
2626 4.44327e6 1.90688
2727 −7.37660e6 −2.67128
2828 −3.16519e6 −0.973170
2929 4.02216e6 1.05601 0.528005 0.849241i 0.322940π-0.322940\pi
0.528005 + 0.849241i 0.322940π0.322940\pi
3030 −6.95788e6 −1.56831
3131 −3.29476e6 −0.640761 −0.320381 0.947289i 0.603811π-0.603811\pi
−0.320381 + 0.947289i 0.603811π0.603811\pi
3232 1.65969e7 2.79803
3333 −1.08169e7 −1.58778
3434 1.51985e7 1.95050
3535 −1.50062e6 −0.169031
3636 6.33179e7 6.28298
3737 −2.13083e7 −1.86914 −0.934570 0.355778i 0.884216π-0.884216\pi
−0.934570 + 0.355778i 0.884216π0.884216\pi
3838 −1.49362e7 −1.16202
3939 −2.70260e7 −1.87065
4040 2.15588e7 1.33154
4141 1.05289e7 0.581909 0.290954 0.956737i 0.406027π-0.406027\pi
0.290954 + 0.956737i 0.406027π0.406027\pi
4242 2.67294e7 1.32546
4343 3.89712e6 0.173835 0.0869173 0.996216i 0.472298π-0.472298\pi
0.0869173 + 0.996216i 0.472298π0.472298\pi
4444 5.47991e7 2.20413
4545 3.00192e7 1.09130
4646 9.76296e6 0.321493
4747 −3.31846e7 −0.991964 −0.495982 0.868333i 0.665192π-0.665192\pi
−0.495982 + 0.868333i 0.665192π0.665192\pi
4848 −2.08373e8 −5.66572
4949 5.76480e6 0.142857
5050 1.67116e7 0.378141
5151 −9.24443e7 −1.91344
5252 1.36915e8 2.59679
5353 −6.31880e7 −1.10000 −0.550001 0.835164i 0.685373π-0.685373\pi
−0.550001 + 0.835164i 0.685373π0.685373\pi
5454 −3.15584e8 −5.05060
5555 2.59804e7 0.382837
5656 −8.28203e7 −1.12536
5757 9.08490e7 1.13994
5858 1.72075e8 1.99660
5959 5.86733e7 0.630386 0.315193 0.949028i 0.397931π-0.397931\pi
0.315193 + 0.949028i 0.397931π0.397931\pi
6060 −2.14401e8 −2.13573
6161 1.37845e8 1.27470 0.637348 0.770576i 0.280032π-0.280032\pi
0.637348 + 0.770576i 0.280032π0.280032\pi
6262 −1.40956e8 −1.21149
6363 −1.15322e8 −0.922314
6464 3.00057e8 2.23560
6565 6.49118e7 0.451039
6666 −4.62768e8 −3.00203
6767 8.36796e7 0.507321 0.253660 0.967293i 0.418365π-0.418365\pi
0.253660 + 0.967293i 0.418365π0.418365\pi
6868 4.68327e8 2.65619
6969 −5.93829e7 −0.315384
7070 −6.41994e7 −0.319588
7171 1.50169e8 0.701322 0.350661 0.936503i 0.385957π-0.385957\pi
0.350661 + 0.936503i 0.385957π0.385957\pi
7272 1.65678e9 7.26554
7373 −2.74817e8 −1.13264 −0.566318 0.824187i 0.691633π-0.691633\pi
−0.566318 + 0.824187i 0.691633π0.691633\pi
7474 −9.11609e8 −3.53399
7575 −1.01648e8 −0.370956
7676 −4.60246e8 −1.58244
7777 −9.98063e7 −0.323556
7878 −1.15622e9 −3.53684
7979 −2.75964e8 −0.797133 −0.398566 0.917139i 0.630492π-0.630492\pi
−0.398566 + 0.917139i 0.630492π0.630492\pi
8080 5.00475e8 1.36608
8181 9.74140e8 2.51443
8282 4.50444e8 1.10022
8383 2.32312e8 0.537304 0.268652 0.963237i 0.413422π-0.413422\pi
0.268652 + 0.963237i 0.413422π0.413422\pi
8484 8.23642e8 1.80502
8585 2.22035e8 0.461356
8686 1.66726e8 0.328670
8787 −1.04664e9 −1.95867
8888 1.43387e9 2.54882
8989 2.71482e8 0.458654 0.229327 0.973349i 0.426347π-0.426347\pi
0.229327 + 0.973349i 0.426347π0.426347\pi
9090 1.28427e9 2.06332
9191 −2.49365e8 −0.381197
9292 3.00837e8 0.437810
9393 8.57358e8 1.18847
9494 −1.41969e9 −1.87551
9595 −2.18204e8 −0.274856
9696 −4.31883e9 −5.18974
9797 −9.76607e8 −1.12007 −0.560037 0.828467i 0.689213π-0.689213\pi
−0.560037 + 0.828467i 0.689213π0.689213\pi
9898 2.46628e8 0.270101
9999 1.99657e9 2.08894
100100 5.14953e8 0.514953
101101 1.11904e9 1.07004 0.535019 0.844840i 0.320304π-0.320304\pi
0.535019 + 0.844840i 0.320304π0.320304\pi
102102 −3.95493e9 −3.61775
103103 1.01154e9 0.885559 0.442779 0.896631i 0.353993π-0.353993\pi
0.442779 + 0.896631i 0.353993π0.353993\pi
104104 3.58252e9 3.00289
105105 3.90490e8 0.313515
106106 −2.70329e9 −2.07978
107107 −1.47411e9 −1.08719 −0.543593 0.839349i 0.682936π-0.682936\pi
−0.543593 + 0.839349i 0.682936π0.682936\pi
108108 −9.72443e9 −6.87792
109109 −1.79852e9 −1.22038 −0.610190 0.792255i 0.708907π-0.708907\pi
−0.610190 + 0.792255i 0.708907π0.708907\pi
110110 1.11149e9 0.723832
111111 5.54483e9 3.46685
112112 −1.92262e9 −1.15455
113113 1.09680e9 0.632812 0.316406 0.948624i 0.397524π-0.397524\pi
0.316406 + 0.948624i 0.397524π0.397524\pi
114114 3.88668e9 2.15530
115115 1.42627e8 0.0760436
116116 5.30233e9 2.71898
117117 4.98842e9 2.46108
118118 2.51015e9 1.19187
119119 −8.52970e8 −0.389917
120120 −5.61000e9 −2.46972
121121 −6.29995e8 −0.267179
122122 5.89725e9 2.41007
123123 −2.73981e9 −1.07931
124124 −4.34342e9 −1.64981
125125 2.44141e8 0.0894427
126126 −4.93367e9 −1.74382
127127 −3.23678e8 −0.110407 −0.0552035 0.998475i 0.517581π-0.517581\pi
−0.0552035 + 0.998475i 0.517581π0.517581\pi
128128 4.33936e9 1.42883
129129 −1.01410e9 −0.322425
130130 2.77704e9 0.852781
131131 −4.60246e9 −1.36543 −0.682714 0.730686i 0.739200π-0.739200\pi
−0.682714 + 0.730686i 0.739200π0.739200\pi
132132 −1.42598e10 −4.08817
133133 8.38251e8 0.232296
134134 3.57996e9 0.959194
135135 −4.61037e9 −1.19463
136136 1.22542e10 3.07158
137137 −3.07931e9 −0.746812 −0.373406 0.927668i 0.621810π-0.621810\pi
−0.373406 + 0.927668i 0.621810π0.621810\pi
138138 −2.54050e9 −0.596299
139139 −6.80655e9 −1.54654 −0.773268 0.634079i 0.781379π-0.781379\pi
−0.773268 + 0.634079i 0.781379π0.781379\pi
140140 −1.97824e9 −0.435215
141141 8.63524e9 1.83988
142142 6.42449e9 1.32599
143143 4.31728e9 0.863371
144144 3.84610e10 7.45401
145145 2.51385e9 0.472262
146146 −1.17572e10 −2.14148
147147 −1.50011e9 −0.264969
148148 −2.80904e10 −4.81260
149149 1.11783e10 1.85796 0.928981 0.370127i 0.120686π-0.120686\pi
0.928981 + 0.370127i 0.120686π0.120686\pi
150150 −4.34868e9 −0.701369
151151 −4.87685e9 −0.763384 −0.381692 0.924290i 0.624658π-0.624658\pi
−0.381692 + 0.924290i 0.624658π0.624658\pi
152152 −1.20428e10 −1.82991
153153 1.70632e10 2.51738
154154 −4.26989e9 −0.611750
155155 −2.05923e9 −0.286557
156156 −3.56279e10 −4.81647
157157 −5.01169e9 −0.658318 −0.329159 0.944274i 0.606765π-0.606765\pi
−0.329159 + 0.944274i 0.606765π0.606765\pi
158158 −1.18062e10 −1.50714
159159 1.64427e10 2.04026
160160 1.03731e10 1.25132
161161 −5.47917e8 −0.0642686
162162 4.16754e10 4.75404
163163 −1.45416e10 −1.61349 −0.806746 0.590899i 0.798773π-0.798773\pi
−0.806746 + 0.590899i 0.798773π0.798773\pi
164164 1.38800e10 1.49828
165165 −6.76058e9 −0.710079
166166 9.93872e9 1.01588
167167 −4.62247e8 −0.0459886 −0.0229943 0.999736i 0.507320π-0.507320\pi
−0.0229943 + 0.999736i 0.507320π0.507320\pi
168168 2.15514e10 2.08729
169169 1.82180e8 0.0171795
170170 9.49906e9 0.872289
171171 −1.67688e10 −1.49975
172172 5.13750e9 0.447583
173173 1.02318e9 0.0868449 0.0434224 0.999057i 0.486174π-0.486174\pi
0.0434224 + 0.999057i 0.486174π0.486174\pi
174174 −4.47771e10 −3.70326
175175 −9.37891e8 −0.0755929
176176 3.32865e10 2.61494
177177 −1.52679e10 −1.16923
178178 1.16145e10 0.867180
179179 1.42460e10 1.03718 0.518590 0.855023i 0.326457π-0.326457\pi
0.518590 + 0.855023i 0.326457π0.326457\pi
180180 3.95737e10 2.80983
181181 1.83877e10 1.27343 0.636714 0.771100i 0.280293π-0.280293\pi
0.636714 + 0.771100i 0.280293π0.280293\pi
182182 −1.06683e10 −0.720732
183183 −3.58698e10 −2.36428
184184 7.87168e9 0.506276
185185 −1.33177e10 −0.835905
186186 3.66793e10 2.24705
187187 1.47675e10 0.883121
188188 −4.37466e10 −2.55408
189189 1.77112e10 1.00965
190190 −9.33514e9 −0.519672
191191 −2.65507e10 −1.44353 −0.721766 0.692137i 0.756669π-0.756669\pi
−0.721766 + 0.692137i 0.756669π0.756669\pi
192192 −7.80805e10 −4.14655
193193 5.84127e9 0.303040 0.151520 0.988454i 0.451583π-0.451583\pi
0.151520 + 0.988454i 0.451583π0.451583\pi
194194 −4.17810e10 −2.11773
195195 −1.68913e10 −0.836578
196196 7.59962e9 0.367824
197197 −2.06491e10 −0.976793 −0.488397 0.872622i 0.662418π-0.662418\pi
−0.488397 + 0.872622i 0.662418π0.662418\pi
198198 8.54169e10 3.94958
199199 −2.66301e10 −1.20374 −0.601871 0.798593i 0.705578π-0.705578\pi
−0.601871 + 0.798593i 0.705578π0.705578\pi
200200 1.34743e10 0.595484
201201 −2.17750e10 −0.940969
202202 4.78745e10 2.02313
203203 −9.65720e9 −0.399134
204204 −1.21867e11 −4.92665
205205 6.58055e9 0.260238
206206 4.32756e10 1.67433
207207 1.09608e10 0.414930
208208 8.31660e10 3.08078
209209 −1.45127e10 −0.526126
210210 1.67059e10 0.592765
211211 1.35165e10 0.469454 0.234727 0.972061i 0.424580π-0.424580\pi
0.234727 + 0.972061i 0.424580π0.424580\pi
212212 −8.32995e10 −2.83225
213213 −3.90767e10 −1.30080
214214 −6.30652e10 −2.05555
215215 2.43570e9 0.0777412
216216 −2.54449e11 −7.95352
217217 7.91072e9 0.242185
218218 −7.69437e10 −2.30738
219219 7.15125e10 2.10079
220220 3.42495e10 0.985716
221221 3.68965e10 1.04045
222222 2.37218e11 6.55479
223223 4.47296e10 1.21122 0.605610 0.795762i 0.292929π-0.292929\pi
0.605610 + 0.795762i 0.292929π0.292929\pi
224224 −3.98492e10 −1.05756
225225 1.87620e10 0.488043
226226 4.69231e10 1.19646
227227 2.46775e10 0.616858 0.308429 0.951247i 0.400197π-0.400197\pi
0.308429 + 0.951247i 0.400197π0.400197\pi
228228 1.19764e11 2.93509
229229 −5.44437e10 −1.30824 −0.654121 0.756390i 0.726961π-0.726961\pi
−0.654121 + 0.756390i 0.726961π0.726961\pi
230230 6.10185e9 0.143776
231231 2.59715e10 0.600126
232232 1.38741e11 3.14418
233233 −5.82731e10 −1.29529 −0.647644 0.761943i 0.724246π-0.724246\pi
−0.647644 + 0.761943i 0.724246π0.724246\pi
234234 2.13413e11 4.65318
235235 −2.07404e10 −0.443620
236236 7.73478e10 1.62310
237237 7.18110e10 1.47851
238238 −3.64916e10 −0.737219
239239 5.53754e10 1.09781 0.548904 0.835885i 0.315045π-0.315045\pi
0.548904 + 0.835885i 0.315045π0.315045\pi
240240 −1.30233e11 −2.53379
241241 6.01280e10 1.14815 0.574077 0.818802i 0.305361π-0.305361\pi
0.574077 + 0.818802i 0.305361π0.305361\pi
242242 −2.69523e10 −0.505157
243243 −1.08296e11 −1.99243
244244 1.81718e11 3.28204
245245 3.60300e9 0.0638877
246246 −1.17214e11 −2.04066
247247 −3.62598e10 −0.619854
248248 −1.13650e11 −1.90781
249249 −6.04519e10 −0.996582
250250 1.04448e10 0.169110
251251 1.01611e9 0.0161588 0.00807938 0.999967i 0.497428π-0.497428\pi
0.00807938 + 0.999967i 0.497428π0.497428\pi
252252 −1.52026e11 −2.37474
253253 9.48612e9 0.145561
254254 −1.38475e10 −0.208747
255255 −5.77777e10 −0.855715
256256 3.20161e10 0.465895
257257 −1.10965e11 −1.58667 −0.793334 0.608787i 0.791657π-0.791657\pi
−0.793334 + 0.608787i 0.791657π0.791657\pi
258258 −4.33852e10 −0.609611
259259 5.11613e10 0.706469
260260 8.55720e10 1.16132
261261 1.93187e11 2.57689
262262 −1.96901e11 −2.58162
263263 1.21172e11 1.56171 0.780856 0.624711i 0.214783π-0.214783\pi
0.780856 + 0.624711i 0.214783π0.214783\pi
264264 −3.73121e11 −4.72750
265265 −3.94925e10 −0.491936
266266 3.58619e10 0.439203
267267 −7.06446e10 −0.850704
268268 1.10313e11 1.30623
269269 5.16654e10 0.601609 0.300805 0.953686i 0.402745π-0.402745\pi
0.300805 + 0.953686i 0.402745π0.402745\pi
270270 −1.97240e11 −2.25870
271271 −2.49166e10 −0.280626 −0.140313 0.990107i 0.544811π-0.544811\pi
−0.140313 + 0.990107i 0.544811π0.544811\pi
272272 2.84475e11 3.15126
273273 6.48895e10 0.707037
274274 −1.31738e11 −1.41200
275275 1.62378e10 0.171210
276276 −7.82833e10 −0.812041
277277 −2.22882e10 −0.227466 −0.113733 0.993511i 0.536281π-0.536281\pi
−0.113733 + 0.993511i 0.536281π0.536281\pi
278278 −2.91196e11 −2.92404
279279 −1.58250e11 −1.56359
280280 −5.17627e10 −0.503276
281281 9.03151e10 0.864135 0.432068 0.901841i 0.357784π-0.357784\pi
0.432068 + 0.901841i 0.357784π0.357784\pi
282282 3.69431e11 3.47866
283283 −9.63268e10 −0.892706 −0.446353 0.894857i 0.647277π-0.647277\pi
−0.446353 + 0.894857i 0.647277π0.647277\pi
284284 1.97965e11 1.80574
285285 5.67806e10 0.509798
286286 1.84701e11 1.63238
287287 −2.52798e10 −0.219941
288288 7.97162e11 6.82780
289289 7.61912e9 0.0642487
290290 1.07547e11 0.892908
291291 2.54131e11 2.07749
292292 −3.62286e11 −2.91627
293293 −4.21047e10 −0.333754 −0.166877 0.985978i 0.553368π-0.553368\pi
−0.166877 + 0.985978i 0.553368π0.553368\pi
294294 −6.41773e10 −0.500978
295295 3.66708e10 0.281917
296296 −7.35012e11 −5.56521
297297 −3.06635e11 −2.28675
298298 4.78227e11 3.51286
299299 2.37010e10 0.171493
300300 −1.34000e11 −0.955126
301301 −9.35700e9 −0.0657033
302302 −2.08640e11 −1.44333
303303 −2.91195e11 −1.98469
304304 −2.79566e11 −1.87738
305305 8.61531e10 0.570061
306306 7.29994e11 4.75963
307307 9.28980e10 0.596875 0.298438 0.954429i 0.403534π-0.403534\pi
0.298438 + 0.954429i 0.403534π0.403534\pi
308308 −1.31573e11 −0.833082
309309 −2.63223e11 −1.64252
310310 −8.80973e10 −0.541795
311311 −1.56495e11 −0.948588 −0.474294 0.880366i 0.657297π-0.657297\pi
−0.474294 + 0.880366i 0.657297π0.657297\pi
312312 −9.32239e11 −5.56969
313313 8.88488e10 0.523242 0.261621 0.965171i 0.415743π-0.415743\pi
0.261621 + 0.965171i 0.415743π0.415743\pi
314314 −2.14409e11 −1.24469
315315 −7.20761e10 −0.412471
316316 −3.63798e11 −2.05243
317317 6.19880e10 0.344779 0.172389 0.985029i 0.444851π-0.444851\pi
0.172389 + 0.985029i 0.444851π0.444851\pi
318318 7.03448e11 3.85753
319319 1.67196e11 0.903997
320320 1.87536e11 0.999791
321321 3.83591e11 2.01649
322322 −2.34409e10 −0.121513
323323 −1.24029e11 −0.634034
324324 1.28419e12 6.47406
325325 4.05699e10 0.201711
326326 −6.22114e11 −3.05064
327327 4.68007e11 2.26354
328328 3.63184e11 1.73259
329329 7.96762e10 0.374927
330330 −2.89230e11 −1.34255
331331 3.65322e11 1.67282 0.836410 0.548104i 0.184650π-0.184650\pi
0.836410 + 0.548104i 0.184650π0.184650\pi
332332 3.06252e11 1.38343
333333 −1.02345e12 −4.56110
334334 −1.97757e10 −0.0869508
335335 5.22997e10 0.226881
336336 5.00302e11 2.14144
337337 1.45738e11 0.615514 0.307757 0.951465i 0.400422π-0.400422\pi
0.307757 + 0.951465i 0.400422π0.400422\pi
338338 7.79400e9 0.0324815
339339 −2.85408e11 −1.17373
340340 2.92705e11 1.18788
341341 −1.36959e11 −0.548523
342342 −7.17397e11 −2.83558
343343 −1.38413e10 −0.0539949
344344 1.34428e11 0.517578
345345 −3.71143e10 −0.141044
346346 4.37734e10 0.164198
347347 2.96112e11 1.09641 0.548206 0.836343i 0.315311π-0.315311\pi
0.548206 + 0.836343i 0.315311π0.315311\pi
348348 −1.37976e12 −5.04311
349349 3.01854e11 1.08914 0.544569 0.838716i 0.316693π-0.316693\pi
0.544569 + 0.838716i 0.316693π0.316693\pi
350350 −4.01246e10 −0.142924
351351 −7.66126e11 −2.69413
352352 6.89912e11 2.39526
353353 −1.99229e11 −0.682916 −0.341458 0.939897i 0.610921π-0.610921\pi
−0.341458 + 0.939897i 0.610921π0.610921\pi
354354 −6.53187e11 −2.21066
355355 9.38555e10 0.313641
356356 3.57889e11 1.18093
357357 2.21959e11 0.723211
358358 6.09469e11 1.96100
359359 −6.48945e10 −0.206197 −0.103099 0.994671i 0.532876π-0.532876\pi
−0.103099 + 0.994671i 0.532876π0.532876\pi
360360 1.03549e12 3.24925
361361 −2.00799e11 −0.622270
362362 7.86660e11 2.40768
363363 1.63936e11 0.495559
364364 −3.28733e11 −0.981494
365365 −1.71761e11 −0.506530
366366 −1.53457e12 −4.47016
367367 −4.27450e10 −0.122995 −0.0614976 0.998107i 0.519588π-0.519588\pi
−0.0614976 + 0.998107i 0.519588π0.519588\pi
368368 1.82736e11 0.519409
369369 5.05710e11 1.41998
370370 −5.69756e11 −1.58045
371371 1.51714e11 0.415761
372372 1.13024e12 3.06004
373373 5.72742e11 1.53204 0.766018 0.642819i 0.222235π-0.222235\pi
0.766018 + 0.642819i 0.222235π0.222235\pi
374374 6.31781e11 1.66972
375375 −6.35299e10 −0.165897
376376 −1.14467e12 −2.95349
377377 4.17737e11 1.06504
378378 7.57717e11 1.90895
379379 −2.28088e11 −0.567840 −0.283920 0.958848i 0.591635π-0.591635\pi
−0.283920 + 0.958848i 0.591635π0.591635\pi
380380 −2.87654e11 −0.707691
381381 8.42271e10 0.204781
382382 −1.13589e12 −2.72929
383383 8.33542e11 1.97940 0.989699 0.143162i 0.0457271π-0.0457271\pi
0.989699 + 0.143162i 0.0457271π0.0457271\pi
384384 −1.12918e12 −2.65017
385385 −6.23790e10 −0.144699
386386 2.49900e11 0.572959
387387 1.87182e11 0.424193
388388 −1.28744e12 −2.88393
389389 −3.47070e11 −0.768501 −0.384251 0.923229i 0.625540π-0.625540\pi
−0.384251 + 0.923229i 0.625540π0.625540\pi
390390 −7.22638e11 −1.58172
391391 8.10708e10 0.175416
392392 1.98852e11 0.425346
393393 1.19764e12 2.53257
394394 −8.83404e11 −1.84683
395395 −1.72478e11 −0.356489
396396 2.63204e12 5.37854
397397 5.31999e11 1.07486 0.537432 0.843307i 0.319394π-0.319394\pi
0.537432 + 0.843307i 0.319394π0.319394\pi
398398 −1.13928e12 −2.27592
399399 −2.18129e11 −0.430858
400400 3.12797e11 0.610931
401401 −1.10007e11 −0.212456 −0.106228 0.994342i 0.533877π-0.533877\pi
−0.106228 + 0.994342i 0.533877π0.533877\pi
402402 −9.31572e11 −1.77910
403403 −3.42190e11 −0.646242
404404 1.47521e12 2.75510
405405 6.08837e11 1.12449
406406 −4.13152e11 −0.754645
407407 −8.85759e11 −1.60008
408408 −3.18878e12 −5.69710
409409 5.36319e11 0.947694 0.473847 0.880607i 0.342865π-0.342865\pi
0.473847 + 0.880607i 0.342865π0.342865\pi
410410 2.81528e11 0.492032
411411 8.01294e11 1.38517
412412 1.33350e12 2.28011
413413 −1.40875e11 −0.238263
414414 4.68922e11 0.784511
415415 1.45195e11 0.240290
416416 1.72374e12 2.82197
417417 1.77119e12 2.86849
418418 −6.20879e11 −0.994749
419419 2.77847e11 0.440395 0.220198 0.975455i 0.429330π-0.429330\pi
0.220198 + 0.975455i 0.429330π0.429330\pi
420420 5.14776e11 0.807228
421421 5.42301e11 0.841339 0.420670 0.907214i 0.361795π-0.361795\pi
0.420670 + 0.907214i 0.361795π0.361795\pi
422422 5.78260e11 0.887599
423423 −1.59388e12 −2.42060
424424 −2.17961e12 −3.27516
425425 1.38772e11 0.206325
426426 −1.67177e12 −2.45943
427427 −3.30966e11 −0.481790
428428 −1.94329e12 −2.79925
429429 −1.12344e12 −1.60137
430430 1.04204e11 0.146986
431431 −5.57666e11 −0.778442 −0.389221 0.921144i 0.627256π-0.627256\pi
−0.389221 + 0.921144i 0.627256π0.627256\pi
432432 −5.90688e12 −8.15984
433433 2.13337e11 0.291656 0.145828 0.989310i 0.453415π-0.453415\pi
0.145828 + 0.989310i 0.453415π0.453415\pi
434434 3.38435e11 0.457900
435435 −6.54150e11 −0.875942
436436 −2.37095e12 −3.14219
437437 −7.96718e10 −0.104505
438438 3.05943e12 3.97198
439439 −1.05316e12 −1.35334 −0.676668 0.736289i 0.736577π-0.736577\pi
−0.676668 + 0.736289i 0.736577π0.736577\pi
440440 8.96171e11 1.13987
441441 2.76887e11 0.348602
442442 1.57850e12 1.96718
443443 −7.98551e11 −0.985113 −0.492556 0.870281i 0.663937π-0.663937\pi
−0.492556 + 0.870281i 0.663937π0.663937\pi
444444 7.30964e12 8.92632
445445 1.69676e11 0.205117
446446 1.91361e12 2.29006
447447 −2.90880e12 −3.44611
448448 −7.20438e11 −0.844978
449449 −9.80369e11 −1.13836 −0.569182 0.822211i 0.692740π-0.692740\pi
−0.569182 + 0.822211i 0.692740π0.692740\pi
450450 8.02671e11 0.922745
451451 4.37671e11 0.498143
452452 1.44589e12 1.62934
453453 1.26905e12 1.41591
454454 1.05575e12 1.16630
455455 −1.55853e11 −0.170477
456456 3.13376e12 3.39409
457457 7.38737e11 0.792259 0.396130 0.918195i 0.370353π-0.370353\pi
0.396130 + 0.918195i 0.370353π0.370353\pi
458458 −2.32920e12 −2.47350
459459 −2.62058e12 −2.75576
460460 1.88023e11 0.195794
461461 −8.57026e11 −0.883771 −0.441885 0.897072i 0.645690π-0.645690\pi
−0.441885 + 0.897072i 0.645690π0.645690\pi
462462 1.11111e12 1.13466
463463 −8.66003e11 −0.875800 −0.437900 0.899024i 0.644278π-0.644278\pi
−0.437900 + 0.899024i 0.644278π0.644278\pi
464464 3.22078e12 3.22575
465465 5.35849e11 0.531501
466466 −2.49303e12 −2.44901
467467 −1.74446e12 −1.69721 −0.848606 0.529025i 0.822558π-0.822558\pi
−0.848606 + 0.529025i 0.822558π0.822558\pi
468468 6.57613e12 6.33672
469469 −2.00915e11 −0.191749
470470 −8.87309e11 −0.838754
471471 1.30414e12 1.22104
472472 2.02388e12 1.87692
473473 1.61998e11 0.148811
474474 3.07220e12 2.79542
475475 −1.36377e11 −0.122919
476476 −1.12445e12 −1.00395
477477 −3.03496e12 −2.68424
478478 2.36906e12 2.07563
479479 −6.51076e11 −0.565096 −0.282548 0.959253i 0.591180π-0.591180\pi
−0.282548 + 0.959253i 0.591180π0.591180\pi
480480 −2.69927e12 −2.32092
481481 −2.21306e12 −1.88513
482482 2.57238e12 2.17082
483483 1.42578e11 0.119204
484484 −8.30510e11 −0.687924
485485 −6.10379e11 −0.500913
486486 −4.63308e12 −3.76710
487487 9.91101e8 0.000798432 0 0.000399216 1.00000i 0.499873π-0.499873\pi
0.000399216 1.00000i 0.499873π0.499873\pi
488488 4.75484e12 3.79530
489489 3.78398e12 2.99267
490490 1.54143e11 0.120793
491491 8.38408e11 0.651012 0.325506 0.945540i 0.394465π-0.394465\pi
0.325506 + 0.945540i 0.394465π0.394465\pi
492492 −3.61184e12 −2.77898
493493 1.42890e12 1.08941
494494 −1.55126e12 −1.17196
495495 1.24786e12 0.934204
496496 −2.63831e12 −1.95730
497497 −3.60555e11 −0.265075
498498 −2.58624e12 −1.88424
499499 2.48735e12 1.79591 0.897955 0.440088i 0.145053π-0.145053\pi
0.897955 + 0.440088i 0.145053π0.145053\pi
500500 3.21846e11 0.230294
501501 1.20285e11 0.0852987
502502 4.34709e10 0.0305515
503503 −1.40863e12 −0.981163 −0.490582 0.871395i 0.663216π-0.663216\pi
−0.490582 + 0.871395i 0.663216π0.663216\pi
504504 −3.97792e12 −2.74611
505505 6.99400e11 0.478536
506506 4.05833e11 0.275214
507507 −4.74067e10 −0.0318643
508508 −4.26699e11 −0.284272
509509 −8.28720e11 −0.547240 −0.273620 0.961838i 0.588221π-0.588221\pi
−0.273620 + 0.961838i 0.588221π0.588221\pi
510510 −2.47183e12 −1.61791
511511 6.59835e11 0.428096
512512 −8.52047e11 −0.547960
513513 2.57536e12 1.64176
514514 −4.74727e12 −2.99992
515515 6.32215e11 0.396034
516516 −1.33687e12 −0.830169
517517 −1.37944e12 −0.849170
518518 2.18877e12 1.33572
519519 −2.66250e11 −0.161078
520520 2.23908e12 1.34293
521521 −8.58369e11 −0.510393 −0.255196 0.966889i 0.582140π-0.582140\pi
−0.255196 + 0.966889i 0.582140π0.582140\pi
522522 8.26488e12 4.87214
523523 1.43567e12 0.839069 0.419534 0.907739i 0.362193π-0.362193\pi
0.419534 + 0.907739i 0.362193π0.362193\pi
524524 −6.06733e12 −3.51566
525525 2.44057e11 0.140208
526526 5.18395e12 2.95274
527527 −1.17048e12 −0.661025
528528 −8.66176e12 −4.85013
529529 −1.74908e12 −0.971087
530530 −1.68956e12 −0.930105
531531 2.81812e12 1.53827
532532 1.10505e12 0.598108
533533 1.09352e12 0.586886
534534 −3.02230e12 −1.60843
535535 −9.21320e11 −0.486204
536536 2.88645e12 1.51051
537537 −3.70707e12 −1.92374
538538 2.21034e12 1.13747
539539 2.39635e11 0.122293
540540 −6.07777e12 −3.07590
541541 3.25599e12 1.63416 0.817081 0.576523i 0.195591π-0.195591\pi
0.817081 + 0.576523i 0.195591π0.195591\pi
542542 −1.06598e12 −0.530581
543543 −4.78483e12 −2.36193
544544 5.89616e12 2.88652
545545 −1.12407e12 −0.545770
546546 2.77609e12 1.33680
547547 −1.31051e12 −0.625887 −0.312944 0.949772i 0.601315π-0.601315\pi
−0.312944 + 0.949772i 0.601315π0.601315\pi
548548 −4.05940e12 −1.92287
549549 6.62079e12 3.11053
550550 6.94680e11 0.323707
551551 −1.40424e12 −0.649021
552552 −2.04836e12 −0.939031
553553 6.62590e11 0.301288
554554 −9.53528e11 −0.430070
555555 3.46552e12 1.55042
556556 −8.97294e12 −3.98197
557557 6.12448e11 0.269600 0.134800 0.990873i 0.456961π-0.456961\pi
0.134800 + 0.990873i 0.456961π0.456961\pi
558558 −6.77020e12 −2.95630
559559 4.04751e11 0.175321
560560 −1.20164e12 −0.516331
561561 −3.84278e12 −1.63800
562562 3.86384e12 1.63383
563563 2.74733e12 1.15245 0.576227 0.817290i 0.304524π-0.304524\pi
0.576227 + 0.817290i 0.304524π0.304524\pi
564564 1.13837e13 4.73725
565565 6.85500e11 0.283002
566566 −4.12103e12 −1.68784
567567 −2.33891e12 −0.950363
568568 5.17994e12 2.08813
569569 −7.10003e11 −0.283958 −0.141979 0.989870i 0.545347π-0.545347\pi
−0.141979 + 0.989870i 0.545347π0.545347\pi
570570 2.42918e12 0.963878
571571 2.87190e12 1.13060 0.565298 0.824887i 0.308761π-0.308761\pi
0.565298 + 0.824887i 0.308761π0.308761\pi
572572 5.69138e12 2.22298
573573 6.90899e12 2.67744
574574 −1.08152e12 −0.415843
575575 8.91421e10 0.0340077
576576 1.44120e13 5.45534
577577 −5.13479e12 −1.92855 −0.964277 0.264897i 0.914662π-0.914662\pi
−0.964277 + 0.264897i 0.914662π0.914662\pi
578578 3.25959e11 0.121475
579579 −1.52001e12 −0.562072
580580 3.31396e12 1.21596
581581 −5.57781e11 −0.203082
582582 1.08722e13 3.92793
583583 −2.62664e12 −0.941656
584584 −9.47956e12 −3.37233
585585 3.11776e12 1.10063
586586 −1.80131e12 −0.631030
587587 2.46529e12 0.857031 0.428515 0.903535i 0.359037π-0.359037\pi
0.428515 + 0.903535i 0.359037π0.359037\pi
588588 −1.97756e12 −0.682233
589589 1.15029e12 0.393810
590590 1.56884e12 0.533022
591591 5.37327e12 1.81174
592592 −1.70629e13 −5.70958
593593 −1.51279e12 −0.502379 −0.251189 0.967938i 0.580822π-0.580822\pi
−0.251189 + 0.967938i 0.580822π0.580822\pi
594594 −1.31184e13 −4.32356
595595 −5.33106e11 −0.174376
596596 1.47361e13 4.78382
597597 6.92964e12 2.23268
598598 1.01397e12 0.324243
599599 −5.89069e12 −1.86959 −0.934794 0.355191i 0.884416π-0.884416\pi
−0.934794 + 0.355191i 0.884416π0.884416\pi
600600 −3.50625e12 −1.10449
601601 −3.78551e12 −1.18356 −0.591779 0.806101i 0.701574π-0.701574\pi
−0.591779 + 0.806101i 0.701574π0.701574\pi
602602 −4.00309e11 −0.124226
603603 4.01919e12 1.23797
604604 −6.42905e12 −1.96553
605605 −3.93747e11 −0.119486
606606 −1.24578e13 −3.75246
607607 4.65336e12 1.39129 0.695645 0.718386i 0.255119π-0.255119\pi
0.695645 + 0.718386i 0.255119π0.255119\pi
608608 −5.79442e12 −1.71966
609609 2.51298e12 0.740306
610610 3.68578e12 1.07782
611611 −3.44651e12 −1.00045
612612 2.24941e13 6.48167
613613 5.65330e12 1.61707 0.808537 0.588445i 0.200260π-0.200260\pi
0.808537 + 0.588445i 0.200260π0.200260\pi
614614 3.97434e12 1.12852
615615 −1.71238e12 −0.482684
616616 −3.44273e12 −0.963363
617617 −4.91335e12 −1.36488 −0.682441 0.730941i 0.739081π-0.739081\pi
−0.682441 + 0.730941i 0.739081π0.739081\pi
618618 −1.12611e13 −3.10552
619619 1.31898e12 0.361101 0.180551 0.983566i 0.442212π-0.442212\pi
0.180551 + 0.983566i 0.442212π0.442212\pi
620620 −2.71464e12 −0.737818
621621 −1.68337e12 −0.454221
622622 −6.69512e12 −1.79350
623623 −6.51828e11 −0.173355
624624 −2.16413e13 −5.71418
625625 1.52588e11 0.0400000
626626 3.80111e12 0.989296
627627 3.77647e12 0.975848
628628 −6.60681e12 −1.69502
629629 −7.56992e12 −1.92825
630630 −3.08354e12 −0.779862
631631 −1.26560e12 −0.317808 −0.158904 0.987294i 0.550796π-0.550796\pi
−0.158904 + 0.987294i 0.550796π0.550796\pi
632632 −9.51913e12 −2.37340
633633 −3.51724e12 −0.870735
634634 2.65196e12 0.651875
635635 −2.02299e11 −0.0493755
636636 2.16761e13 5.25320
637637 5.98726e11 0.144079
638638 7.15293e12 1.70919
639639 7.21271e12 1.71137
640640 2.71210e12 0.638992
641641 7.10592e12 1.66249 0.831246 0.555905i 0.187628π-0.187628\pi
0.831246 + 0.555905i 0.187628π0.187628\pi
642642 1.64107e13 3.81259
643643 4.17010e12 0.962049 0.481024 0.876707i 0.340265π-0.340265\pi
0.481024 + 0.876707i 0.340265π0.340265\pi
644644 −7.22309e11 −0.165477
645645 −6.33815e11 −0.144193
646646 −5.30619e12 −1.19877
647647 −5.36916e12 −1.20458 −0.602292 0.798276i 0.705746π-0.705746\pi
−0.602292 + 0.798276i 0.705746π0.705746\pi
648648 3.36021e13 7.48650
649649 2.43897e12 0.539641
650650 1.73565e12 0.381375
651651 −2.05852e12 −0.449200
652652 −1.91699e13 −4.15436
653653 2.71691e12 0.584744 0.292372 0.956305i 0.405555π-0.405555\pi
0.292372 + 0.956305i 0.405555π0.405555\pi
654654 2.00222e13 4.27968
655655 −2.87653e12 −0.610638
656656 8.43110e12 1.77753
657657 −1.31996e13 −2.76387
658658 3.40869e12 0.708877
659659 6.36955e12 1.31560 0.657801 0.753192i 0.271487π-0.271487\pi
0.657801 + 0.753192i 0.271487π0.271487\pi
660660 −8.91235e12 −1.82829
661661 −5.58167e12 −1.13725 −0.568627 0.822596i 0.692525π-0.692525\pi
−0.568627 + 0.822596i 0.692525π0.692525\pi
662662 1.56291e13 3.16281
663663 −9.60116e12 −1.92980
664664 8.01340e12 1.59978
665665 5.23907e11 0.103886
666666 −4.37852e13 −8.62370
667667 9.17871e11 0.179562
668668 −6.09371e11 −0.118410
669669 −1.16395e13 −2.24655
670670 2.23748e12 0.428965
671671 5.73003e12 1.09120
672672 1.03695e13 1.96154
673673 4.49826e12 0.845234 0.422617 0.906308i 0.361112π-0.361112\pi
0.422617 + 0.906308i 0.361112π0.361112\pi
674674 6.23492e12 1.16376
675675 −2.88148e12 −0.534256
676676 2.40165e11 0.0442333
677677 5.35625e12 0.979969 0.489984 0.871731i 0.337002π-0.337002\pi
0.489984 + 0.871731i 0.337002π0.337002\pi
678678 −1.22103e13 −2.21917
679679 2.34483e12 0.423349
680680 7.65890e12 1.37365
681681 −6.42155e12 −1.14414
682682 −5.85934e12 −1.03710
683683 −2.20240e12 −0.387261 −0.193630 0.981075i 0.562026π-0.562026\pi
−0.193630 + 0.981075i 0.562026π0.562026\pi
684684 −2.21059e13 −3.86150
685685 −1.92457e12 −0.333984
686686 −5.92155e11 −0.102088
687687 1.41673e13 2.42650
688688 3.12066e12 0.531005
689689 −6.56264e12 −1.10941
690690 −1.58782e12 −0.266673
691691 4.30201e12 0.717827 0.358913 0.933371i 0.383147π-0.383147\pi
0.358913 + 0.933371i 0.383147π0.383147\pi
692692 1.34884e12 0.223605
693693 −4.79377e12 −0.789546
694694 1.26682e13 2.07299
695695 −4.25409e12 −0.691632
696696 −3.61029e13 −5.83177
697697 3.74045e12 0.600311
698698 1.29139e13 2.05924
699699 1.51637e13 2.40248
700700 −1.23640e12 −0.194634
701701 9.24701e12 1.44634 0.723170 0.690670i 0.242684π-0.242684\pi
0.723170 + 0.690670i 0.242684π0.242684\pi
702702 −3.27762e13 −5.09380
703703 7.43929e12 1.14877
704704 1.24730e13 1.91379
705705 5.39703e12 0.822817
706706 −8.52339e12 −1.29119
707707 −2.68681e12 −0.404436
708708 −2.01273e13 −3.01049
709709 −1.08956e13 −1.61936 −0.809680 0.586872i 0.800359π-0.800359\pi
−0.809680 + 0.586872i 0.800359π0.800359\pi
710710 4.01531e12 0.593002
711711 −1.32548e13 −1.94517
712712 9.36452e12 1.36561
713713 −7.51877e11 −0.108954
714714 9.49579e12 1.36738
715715 2.69830e12 0.386111
716716 1.87802e13 2.67050
717717 −1.44097e13 −2.03619
718718 −2.77630e12 −0.389858
719719 −6.34998e12 −0.886120 −0.443060 0.896492i 0.646107π-0.646107\pi
−0.443060 + 0.896492i 0.646107π0.646107\pi
720720 2.40382e13 3.33353
721721 −2.42872e12 −0.334710
722722 −8.59053e12 −1.17653
723723 −1.56464e13 −2.12957
724724 2.42402e13 3.27878
725725 1.57115e12 0.211202
726726 7.01349e12 0.936956
727727 4.81017e12 0.638639 0.319319 0.947647i 0.396546π-0.396546\pi
0.319319 + 0.947647i 0.396546π0.396546\pi
728728 −8.60163e12 −1.13498
729729 9.00655e12 1.18109
730730 −7.34822e12 −0.957700
731731 1.38448e12 0.179332
732732 −4.72865e13 −6.08747
733733 −1.10839e13 −1.41816 −0.709082 0.705126i 0.750890π-0.750890\pi
−0.709082 + 0.705126i 0.750890π0.750890\pi
734734 −1.82871e12 −0.232548
735735 −9.37568e11 −0.118498
736736 3.78748e12 0.475774
737737 3.47845e12 0.434292
738738 2.16352e13 2.68477
739739 −1.33603e13 −1.64784 −0.823922 0.566704i 0.808218π-0.808218\pi
−0.823922 + 0.566704i 0.808218π0.808218\pi
740740 −1.75565e13 −2.15226
741741 9.43548e12 1.14969
742742 6.49061e12 0.786082
743743 2.12151e12 0.255384 0.127692 0.991814i 0.459243π-0.459243\pi
0.127692 + 0.991814i 0.459243π0.459243\pi
744744 2.95738e13 3.53858
745745 6.98643e12 0.830906
746746 2.45029e13 2.89663
747747 1.11581e13 1.31114
748748 1.94677e13 2.27383
749749 3.53934e12 0.410918
750750 −2.71792e12 −0.313662
751751 2.36099e12 0.270841 0.135420 0.990788i 0.456762π-0.456762\pi
0.135420 + 0.990788i 0.456762π0.456762\pi
752752 −2.65729e13 −3.03011
753753 −2.64410e11 −0.0299710
754754 1.78715e13 2.01368
755755 −3.04803e12 −0.341396
756756 2.33483e13 2.59961
757757 6.53431e12 0.723217 0.361608 0.932330i 0.382228π-0.382228\pi
0.361608 + 0.932330i 0.382228π0.382228\pi
758758 −9.75801e12 −1.07362
759759 −2.46847e12 −0.269985
760760 −7.52674e12 −0.818363
761761 −7.47260e12 −0.807682 −0.403841 0.914829i 0.632325π-0.632325\pi
−0.403841 + 0.914829i 0.632325π0.632325\pi
762762 3.60339e12 0.387180
763763 4.31824e12 0.461260
764764 −3.50013e13 −3.71676
765765 1.06645e13 1.12581
766766 3.56604e13 3.74246
767767 6.09374e12 0.635777
768768 −8.33117e12 −0.864133
769769 3.53111e12 0.364119 0.182059 0.983288i 0.441724π-0.441724\pi
0.182059 + 0.983288i 0.441724π0.441724\pi
770770 −2.66868e12 −0.273583
771771 2.88751e13 2.94292
772772 7.70043e12 0.780256
773773 4.38854e12 0.442092 0.221046 0.975263i 0.429053π-0.429053\pi
0.221046 + 0.975263i 0.429053π0.429053\pi
774774 8.00796e12 0.802025
775775 −1.28702e12 −0.128152
776776 −3.36872e13 −3.33493
777777 −1.33131e13 −1.31034
778778 −1.48483e13 −1.45301
779779 −3.67591e12 −0.357640
780780 −2.22674e13 −2.15399
781781 6.24232e12 0.600366
782782 3.46835e12 0.331660
783783 −2.96698e13 −2.82090
784784 4.61622e12 0.436379
785785 −3.13231e12 −0.294409
786786 5.12374e13 4.78834
787787 −8.78357e12 −0.816178 −0.408089 0.912942i 0.633805π-0.633805\pi
−0.408089 + 0.912942i 0.633805π0.633805\pi
788788 −2.72213e13 −2.51501
789789 −3.15312e13 −2.89663
790790 −7.37890e12 −0.674015
791791 −2.63342e12 −0.239180
792792 6.88700e13 6.21966
793793 1.43164e13 1.28560
794794 2.27599e13 2.03225
795795 1.02767e13 0.912433
796796 −3.51059e13 −3.09935
797797 −3.11376e12 −0.273352 −0.136676 0.990616i 0.543642π-0.543642\pi
−0.136676 + 0.990616i 0.543642π0.543642\pi
798798 −9.33193e12 −0.814626
799799 −1.17890e13 −1.02333
800800 6.48318e12 0.559607
801801 1.30395e13 1.11921
802802 −4.70628e12 −0.401692
803803 −1.14238e13 −0.969593
804804 −2.87055e13 −2.42278
805805 −3.42448e11 −0.0287418
806806 −1.46395e13 −1.22185
807807 −1.34443e13 −1.11585
808808 3.86003e13 3.18595
809809 2.27913e13 1.87068 0.935341 0.353747i 0.115093π-0.115093\pi
0.935341 + 0.353747i 0.115093π0.115093\pi
810810 2.60471e13 2.12607
811811 6.23133e12 0.505810 0.252905 0.967491i 0.418614π-0.418614\pi
0.252905 + 0.967491i 0.418614π0.418614\pi
812812 −1.27309e13 −1.02768
813813 6.48377e12 0.520499
814814 −3.78944e13 −3.02527
815815 −9.08847e12 −0.721575
816816 −7.40256e13 −5.84489
817817 −1.36059e12 −0.106838
818818 2.29447e13 1.79181
819819 −1.19772e13 −0.930202
820820 8.67501e12 0.670051
821821 −6.34294e12 −0.487244 −0.243622 0.969870i 0.578336π-0.578336\pi
−0.243622 + 0.969870i 0.578336π0.578336\pi
822822 3.42808e13 2.61895
823823 −1.01100e13 −0.768158 −0.384079 0.923300i 0.625481π-0.625481\pi
−0.384079 + 0.923300i 0.625481π0.625481\pi
824824 3.48923e13 2.63668
825825 −4.22537e12 −0.317557
826826 −6.02686e12 −0.450486
827827 −2.09841e11 −0.0155997 −0.00779984 0.999970i 0.502483π-0.502483\pi
−0.00779984 + 0.999970i 0.502483π0.502483\pi
828828 1.44494e13 1.06835
829829 −1.42099e13 −1.04495 −0.522474 0.852655i 0.674991π-0.674991\pi
−0.522474 + 0.852655i 0.674991π0.674991\pi
830830 6.21170e12 0.454317
831831 5.79980e12 0.421899
832832 3.11636e13 2.25472
833833 2.04798e12 0.147375
834834 7.57746e13 5.42346
835835 −2.88904e11 −0.0205667
836836 −1.91318e13 −1.35465
837837 2.43041e13 1.71165
838838 1.18868e13 0.832658
839839 6.20295e12 0.432185 0.216092 0.976373i 0.430669π-0.430669\pi
0.216092 + 0.976373i 0.430669π0.430669\pi
840840 1.34696e13 0.933466
841841 1.67059e12 0.115157
842842 2.32006e13 1.59072
843843 −2.35017e13 −1.60278
844844 1.78185e13 1.20873
845845 1.13863e11 0.00768292
846846 −6.81890e13 −4.57665
847847 1.51262e12 0.100984
848848 −5.05984e13 −3.36012
849849 2.50660e13 1.65577
850850 5.93691e12 0.390099
851851 −4.86265e12 −0.317826
852852 −5.15141e13 −3.34925
853853 −3.60370e12 −0.233066 −0.116533 0.993187i 0.537178π-0.537178\pi
−0.116533 + 0.993187i 0.537178π0.537178\pi
854854 −1.41593e13 −0.910922
855855 −1.04805e13 −0.670708
856856 −5.08482e13 −3.23701
857857 −4.01270e12 −0.254110 −0.127055 0.991896i 0.540553π-0.540553\pi
−0.127055 + 0.991896i 0.540553π0.540553\pi
858858 −4.80626e13 −3.02771
859859 2.02534e13 1.26919 0.634597 0.772843i 0.281166π-0.281166\pi
0.634597 + 0.772843i 0.281166π0.281166\pi
860860 3.21094e12 0.200165
861861 6.57829e12 0.407942
862862 −2.38579e13 −1.47180
863863 1.57831e13 0.968598 0.484299 0.874903i 0.339075π-0.339075\pi
0.484299 + 0.874903i 0.339075π0.339075\pi
864864 −1.22429e14 −7.47433
865865 6.39487e11 0.0388382
866866 9.12694e12 0.551435
867867 −1.98264e12 −0.119167
868868 1.04285e13 0.623570
869869 −1.14715e13 −0.682385
870870 −2.79857e13 −1.65615
871871 8.69087e12 0.511660
872872 −6.20382e13 −3.63358
873873 −4.69071e13 −2.73322
874874 −3.40850e12 −0.197589
875875 −5.86182e11 −0.0338062
876876 9.42735e13 5.40905
877877 −8.86665e12 −0.506129 −0.253065 0.967449i 0.581439π-0.581439\pi
−0.253065 + 0.967449i 0.581439π0.581439\pi
878878 −4.50562e13 −2.55876
879879 1.09564e13 0.619040
880880 2.08041e13 1.16943
881881 −1.22614e13 −0.685720 −0.342860 0.939387i 0.611396π-0.611396\pi
−0.342860 + 0.939387i 0.611396π0.611396\pi
882882 1.18457e13 0.659103
883883 1.90484e13 1.05447 0.527236 0.849719i 0.323228π-0.323228\pi
0.527236 + 0.849719i 0.323228π0.323228\pi
884884 4.86400e13 2.67891
885885 −9.54242e12 −0.522894
886886 −3.41634e13 −1.86256
887887 2.67439e13 1.45067 0.725335 0.688396i 0.241685π-0.241685\pi
0.725335 + 0.688396i 0.241685π0.241685\pi
888888 1.91264e14 10.3223
889889 7.77152e11 0.0417300
890890 7.25904e12 0.387815
891891 4.04937e13 2.15247
892892 5.89661e13 3.11861
893893 1.15856e13 0.609659
894894 −1.24443e14 −6.51558
895895 8.90375e12 0.463841
896896 −1.04188e13 −0.540047
897897 −6.16744e12 −0.318082
898898 −4.19419e13 −2.15231
899899 −1.32520e13 −0.676650
900900 2.47336e13 1.25660
901901 −2.24479e13 −1.13479
902902 1.87244e13 0.941841
903903 2.43486e12 0.121865
904904 3.78332e13 1.88415
905905 1.14923e13 0.569495
906906 5.42920e13 2.67707
907907 3.03949e13 1.49131 0.745655 0.666332i 0.232137π-0.232137\pi
0.745655 + 0.666332i 0.232137π0.232137\pi
908908 3.25319e13 1.58827
909909 5.37483e13 2.61112
910910 −6.66768e12 −0.322321
911911 1.77272e13 0.852721 0.426361 0.904553i 0.359795π-0.359795\pi
0.426361 + 0.904553i 0.359795π0.359795\pi
912912 7.27482e13 3.48214
913913 9.65690e12 0.459959
914914 3.16045e13 1.49793
915915 −2.24186e13 −1.05734
916916 −7.17721e13 −3.36842
917917 1.10505e13 0.516083
918918 −1.12113e14 −5.21032
919919 −3.30500e13 −1.52845 −0.764226 0.644948i 0.776879π-0.776879\pi
−0.764226 + 0.644948i 0.776879π0.776879\pi
920920 4.91980e12 0.226414
921921 −2.41738e13 −1.10707
922922 −3.66651e13 −1.67095
923923 1.55964e13 0.707320
924924 3.42377e13 1.54518
925925 −8.32357e12 −0.373828
926926 −3.70491e13 −1.65588
927927 4.85852e13 2.16095
928928 6.67555e13 2.95475
929929 −3.62767e13 −1.59793 −0.798963 0.601380i 0.794618π-0.794618\pi
−0.798963 + 0.601380i 0.794618π0.794618\pi
930930 2.29246e13 1.00491
931931 −2.01264e12 −0.0877996
932932 −7.68203e13 −3.33506
933933 4.07228e13 1.75942
934934 −7.46313e13 −3.20893
935935 9.22970e12 0.394944
936936 1.72071e14 7.32768
937937 8.07643e11 0.0342288 0.0171144 0.999854i 0.494552π-0.494552\pi
0.0171144 + 0.999854i 0.494552π0.494552\pi
938938 −8.59548e12 −0.362541
939939 −2.31201e13 −0.970499
940940 −2.73416e13 −1.14222
941941 −2.62828e13 −1.09274 −0.546371 0.837543i 0.683991π-0.683991\pi
−0.546371 + 0.837543i 0.683991π0.683991\pi
942942 5.57932e13 2.30862
943943 2.40273e12 0.0989470
944944 4.69832e13 1.92561
945945 1.10695e13 0.451529
946946 6.93057e12 0.281358
947947 1.64435e13 0.664384 0.332192 0.943212i 0.392212π-0.392212\pi
0.332192 + 0.943212i 0.392212π0.392212\pi
948948 9.46670e13 3.80681
949949 −2.85422e13 −1.14232
950950 −5.83446e12 −0.232405
951951 −1.61304e13 −0.639489
952952 −2.94224e13 −1.16095
953953 −1.18588e13 −0.465717 −0.232859 0.972511i 0.574808π-0.574808\pi
−0.232859 + 0.972511i 0.574808π0.574808\pi
954954 −1.29841e14 −5.07510
955955 −1.65942e13 −0.645567
956956 7.30003e13 2.82660
957957 −4.35074e13 −1.67672
958958 −2.78542e13 −1.06843
959959 7.39343e12 0.282268
960960 −4.88003e13 −1.85439
961961 −1.55842e13 −0.589425
962962 −9.46787e13 −3.56422
963963 −7.08027e13 −2.65296
964964 7.92655e13 2.95623
965965 3.65079e12 0.135523
966966 6.09975e12 0.225380
967967 1.14207e13 0.420023 0.210011 0.977699i 0.432650π-0.432650\pi
0.210011 + 0.977699i 0.432650π0.432650\pi
968968 −2.17311e13 −0.795505
969969 3.22747e13 1.17599
970970 −2.61131e13 −0.947078
971971 8.26707e12 0.298446 0.149223 0.988804i 0.452323π-0.452323\pi
0.149223 + 0.988804i 0.452323π0.452323\pi
972972 −1.42764e14 −5.13004
973973 1.63425e13 0.584536
974974 4.24011e10 0.00150960
975975 −1.05570e13 −0.374129
976976 1.10381e14 3.89375
977977 −5.06889e13 −1.77987 −0.889934 0.456090i 0.849250π-0.849250\pi
−0.889934 + 0.456090i 0.849250π0.849250\pi
978978 1.61886e14 5.65826
979979 1.12851e13 0.392631
980980 4.74976e12 0.164496
981981 −8.63840e13 −2.97799
982982 3.58686e13 1.23087
983983 1.12786e13 0.385268 0.192634 0.981271i 0.438297π-0.438297\pi
0.192634 + 0.981271i 0.438297π0.438297\pi
984984 −9.45073e13 −3.21357
985985 −1.29057e13 −0.436835
986986 6.11307e13 2.05974
987987 −2.07332e13 −0.695408
988988 −4.78006e13 −1.59598
989989 8.89338e11 0.0295586
990990 5.33856e13 1.76630
991991 5.17189e13 1.70340 0.851702 0.524027i 0.175571π-0.175571\pi
0.851702 + 0.524027i 0.175571π0.175571\pi
992992 −5.46829e13 −1.79287
993993 −9.50635e13 −3.10272
994994 −1.54252e13 −0.501178
995995 −1.66438e13 −0.538330
996996 −7.96926e13 −2.56597
997997 1.92951e13 0.618471 0.309235 0.950986i 0.399927π-0.399927\pi
0.309235 + 0.950986i 0.399927π0.399927\pi
998998 1.06413e14 3.39554
999999 1.57183e14 4.99300
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 35.10.a.e.1.6 6
3.2 odd 2 315.10.a.l.1.1 6
5.2 odd 4 175.10.b.g.99.11 12
5.3 odd 4 175.10.b.g.99.2 12
5.4 even 2 175.10.a.g.1.1 6
7.6 odd 2 245.10.a.g.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.10.a.e.1.6 6 1.1 even 1 trivial
175.10.a.g.1.1 6 5.4 even 2
175.10.b.g.99.2 12 5.3 odd 4
175.10.b.g.99.11 12 5.2 odd 4
245.10.a.g.1.6 6 7.6 odd 2
315.10.a.l.1.1 6 3.2 odd 2