Properties

Label 91.2.a.d.1.3
Level 9191
Weight 22
Character 91.1
Self dual yes
Analytic conductor 0.7270.727
Analytic rank 00
Dimension 33
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] = [91,2,Mod(1,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 91=713 91 = 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 91.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: 0.7266386583940.726638658394
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.316.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x24x+2 x^{3} - x^{2} - 4x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 2.342922.34292 of defining polynomial
Character χ\chi == 91.1

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+2.34292q21.14637q3+3.48929q41.34292q52.68585q61.00000q7+3.48929q81.68585q93.14637q10+1.14637q114.00000q12+1.00000q132.34292q14+1.53948q15+1.19656q16+5.83221q173.94981q183.34292q194.68585q20+1.14637q21+2.68585q223.17513q234.00000q243.19656q25+2.34292q26+5.37169q273.48929q28+10.4893q29+3.60688q30+1.63565q314.17513q321.31415q33+13.6644q34+1.34292q355.88240q36+8.51806q377.83221q381.14637q394.68585q400.292731q41+2.68585q428.15371q43+4.00000q44+2.26396q457.43910q4610.6142q471.37169q48+1.00000q497.48929q506.68585q51+3.48929q520.782020q53+12.5855q541.53948q553.48929q56+3.83221q57+24.5756q58+12.6430q59+5.37169q602.00000q61+3.83221q62+1.68585q6312.1751q641.34292q653.07896q666.10038q67+20.3503q68+3.63986q69+3.14637q70+1.53948q715.88240q7215.3001q73+19.9572q74+3.66442q7511.6644q761.14637q772.68585q78+0.882404q791.60688q801.10038q810.685846q8212.1292q83+4.00000q847.83221q8519.1035q8612.0246q87+4.00000q88+5.73604q89+5.30429q901.00000q9111.0790q921.87506q9324.8683q94+4.48929q95+4.78623q965.34292q97+2.34292q981.93260q99+O(q100)q+2.34292 q^{2} -1.14637 q^{3} +3.48929 q^{4} -1.34292 q^{5} -2.68585 q^{6} -1.00000 q^{7} +3.48929 q^{8} -1.68585 q^{9} -3.14637 q^{10} +1.14637 q^{11} -4.00000 q^{12} +1.00000 q^{13} -2.34292 q^{14} +1.53948 q^{15} +1.19656 q^{16} +5.83221 q^{17} -3.94981 q^{18} -3.34292 q^{19} -4.68585 q^{20} +1.14637 q^{21} +2.68585 q^{22} -3.17513 q^{23} -4.00000 q^{24} -3.19656 q^{25} +2.34292 q^{26} +5.37169 q^{27} -3.48929 q^{28} +10.4893 q^{29} +3.60688 q^{30} +1.63565 q^{31} -4.17513 q^{32} -1.31415 q^{33} +13.6644 q^{34} +1.34292 q^{35} -5.88240 q^{36} +8.51806 q^{37} -7.83221 q^{38} -1.14637 q^{39} -4.68585 q^{40} -0.292731 q^{41} +2.68585 q^{42} -8.15371 q^{43} +4.00000 q^{44} +2.26396 q^{45} -7.43910 q^{46} -10.6142 q^{47} -1.37169 q^{48} +1.00000 q^{49} -7.48929 q^{50} -6.68585 q^{51} +3.48929 q^{52} -0.782020 q^{53} +12.5855 q^{54} -1.53948 q^{55} -3.48929 q^{56} +3.83221 q^{57} +24.5756 q^{58} +12.6430 q^{59} +5.37169 q^{60} -2.00000 q^{61} +3.83221 q^{62} +1.68585 q^{63} -12.1751 q^{64} -1.34292 q^{65} -3.07896 q^{66} -6.10038 q^{67} +20.3503 q^{68} +3.63986 q^{69} +3.14637 q^{70} +1.53948 q^{71} -5.88240 q^{72} -15.3001 q^{73} +19.9572 q^{74} +3.66442 q^{75} -11.6644 q^{76} -1.14637 q^{77} -2.68585 q^{78} +0.882404 q^{79} -1.60688 q^{80} -1.10038 q^{81} -0.685846 q^{82} -12.1292 q^{83} +4.00000 q^{84} -7.83221 q^{85} -19.1035 q^{86} -12.0246 q^{87} +4.00000 q^{88} +5.73604 q^{89} +5.30429 q^{90} -1.00000 q^{91} -11.0790 q^{92} -1.87506 q^{93} -24.8683 q^{94} +4.48929 q^{95} +4.78623 q^{96} -5.34292 q^{97} +2.34292 q^{98} -1.93260 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+q22q3+3q4+2q5+4q63q7+3q8+7q98q10+2q1112q12+3q13q146q15q16+4q1715q184q192q20++14q99+O(q100) 3 q + q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} - 8 q^{10} + 2 q^{11} - 12 q^{12} + 3 q^{13} - q^{14} - 6 q^{15} - q^{16} + 4 q^{17} - 15 q^{18} - 4 q^{19} - 2 q^{20}+ \cdots + 14 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 2.34292 1.65670 0.828348 0.560213i 0.189281π-0.189281\pi
0.828348 + 0.560213i 0.189281π0.189281\pi
33 −1.14637 −0.661854 −0.330927 0.943656i 0.607361π-0.607361\pi
−0.330927 + 0.943656i 0.607361π0.607361\pi
44 3.48929 1.74464
55 −1.34292 −0.600573 −0.300287 0.953849i 0.597082π-0.597082\pi
−0.300287 + 0.953849i 0.597082π0.597082\pi
66 −2.68585 −1.09649
77 −1.00000 −0.377964
88 3.48929 1.23365
99 −1.68585 −0.561949
1010 −3.14637 −0.994968
1111 1.14637 0.345642 0.172821 0.984953i 0.444712π-0.444712\pi
0.172821 + 0.984953i 0.444712π0.444712\pi
1212 −4.00000 −1.15470
1313 1.00000 0.277350
1414 −2.34292 −0.626173
1515 1.53948 0.397492
1616 1.19656 0.299139
1717 5.83221 1.41452 0.707260 0.706954i 0.249931π-0.249931\pi
0.707260 + 0.706954i 0.249931π0.249931\pi
1818 −3.94981 −0.930979
1919 −3.34292 −0.766919 −0.383460 0.923558i 0.625267π-0.625267\pi
−0.383460 + 0.923558i 0.625267π0.625267\pi
2020 −4.68585 −1.04779
2121 1.14637 0.250157
2222 2.68585 0.572624
2323 −3.17513 −0.662061 −0.331031 0.943620i 0.607396π-0.607396\pi
−0.331031 + 0.943620i 0.607396π0.607396\pi
2424 −4.00000 −0.816497
2525 −3.19656 −0.639312
2626 2.34292 0.459485
2727 5.37169 1.03378
2828 −3.48929 −0.659414
2929 10.4893 1.94781 0.973906 0.226952i 0.0728760π-0.0728760\pi
0.973906 + 0.226952i 0.0728760π0.0728760\pi
3030 3.60688 0.658524
3131 1.63565 0.293772 0.146886 0.989153i 0.453075π-0.453075\pi
0.146886 + 0.989153i 0.453075π0.453075\pi
3232 −4.17513 −0.738067
3333 −1.31415 −0.228765
3434 13.6644 2.34343
3535 1.34292 0.226995
3636 −5.88240 −0.980401
3737 8.51806 1.40036 0.700180 0.713966i 0.253103π-0.253103\pi
0.700180 + 0.713966i 0.253103π0.253103\pi
3838 −7.83221 −1.27055
3939 −1.14637 −0.183565
4040 −4.68585 −0.740897
4141 −0.292731 −0.0457169 −0.0228584 0.999739i 0.507277π-0.507277\pi
−0.0228584 + 0.999739i 0.507277π0.507277\pi
4242 2.68585 0.414435
4343 −8.15371 −1.24343 −0.621715 0.783244i 0.713564π-0.713564\pi
−0.621715 + 0.783244i 0.713564π0.713564\pi
4444 4.00000 0.603023
4545 2.26396 0.337491
4646 −7.43910 −1.09683
4747 −10.6142 −1.54824 −0.774122 0.633036i 0.781809π-0.781809\pi
−0.774122 + 0.633036i 0.781809π0.781809\pi
4848 −1.37169 −0.197987
4949 1.00000 0.142857
5050 −7.48929 −1.05915
5151 −6.68585 −0.936206
5252 3.48929 0.483877
5353 −0.782020 −0.107419 −0.0537093 0.998557i 0.517104π-0.517104\pi
−0.0537093 + 0.998557i 0.517104π0.517104\pi
5454 12.5855 1.71266
5555 −1.53948 −0.207584
5656 −3.48929 −0.466276
5757 3.83221 0.507589
5858 24.5756 3.22693
5959 12.6430 1.64598 0.822989 0.568057i 0.192305π-0.192305\pi
0.822989 + 0.568057i 0.192305π0.192305\pi
6060 5.37169 0.693482
6161 −2.00000 −0.256074 −0.128037 0.991769i 0.540868π-0.540868\pi
−0.128037 + 0.991769i 0.540868π0.540868\pi
6262 3.83221 0.486691
6363 1.68585 0.212397
6464 −12.1751 −1.52189
6565 −1.34292 −0.166569
6666 −3.07896 −0.378994
6767 −6.10038 −0.745281 −0.372640 0.927976i 0.621547π-0.621547\pi
−0.372640 + 0.927976i 0.621547π0.621547\pi
6868 20.3503 2.46783
6969 3.63986 0.438188
7070 3.14637 0.376063
7171 1.53948 0.182703 0.0913514 0.995819i 0.470881π-0.470881\pi
0.0913514 + 0.995819i 0.470881π0.470881\pi
7272 −5.88240 −0.693248
7373 −15.3001 −1.79074 −0.895369 0.445324i 0.853088π-0.853088\pi
−0.895369 + 0.445324i 0.853088π0.853088\pi
7474 19.9572 2.31997
7575 3.66442 0.423131
7676 −11.6644 −1.33800
7777 −1.14637 −0.130640
7878 −2.68585 −0.304112
7979 0.882404 0.0992782 0.0496391 0.998767i 0.484193π-0.484193\pi
0.0496391 + 0.998767i 0.484193π0.484193\pi
8080 −1.60688 −0.179655
8181 −1.10038 −0.122265
8282 −0.685846 −0.0757390
8383 −12.1292 −1.33135 −0.665674 0.746243i 0.731856π-0.731856\pi
−0.665674 + 0.746243i 0.731856π0.731856\pi
8484 4.00000 0.436436
8585 −7.83221 −0.849523
8686 −19.1035 −2.05999
8787 −12.0246 −1.28917
8888 4.00000 0.426401
8989 5.73604 0.608019 0.304009 0.952669i 0.401675π-0.401675\pi
0.304009 + 0.952669i 0.401675π0.401675\pi
9090 5.30429 0.559121
9191 −1.00000 −0.104828
9292 −11.0790 −1.15506
9393 −1.87506 −0.194434
9494 −24.8683 −2.56497
9595 4.48929 0.460591
9696 4.78623 0.488493
9797 −5.34292 −0.542492 −0.271246 0.962510i 0.587436π-0.587436\pi
−0.271246 + 0.962510i 0.587436π0.587436\pi
9898 2.34292 0.236671
9999 −1.93260 −0.194233
100100 −11.1537 −1.11537
101101 11.1464 1.10910 0.554552 0.832149i 0.312889π-0.312889\pi
0.554552 + 0.832149i 0.312889π0.312889\pi
102102 −15.6644 −1.55101
103103 −3.41454 −0.336444 −0.168222 0.985749i 0.553803π-0.553803\pi
−0.168222 + 0.985749i 0.553803π0.553803\pi
104104 3.48929 0.342153
105105 −1.53948 −0.150238
106106 −1.83221 −0.177960
107107 4.97858 0.481297 0.240649 0.970612i 0.422640π-0.422640\pi
0.240649 + 0.970612i 0.422640π0.422640\pi
108108 18.7434 1.80358
109109 −13.4966 −1.29274 −0.646372 0.763023i 0.723714π-0.723714\pi
−0.646372 + 0.763023i 0.723714π0.723714\pi
110110 −3.60688 −0.343903
111111 −9.76481 −0.926835
112112 −1.19656 −0.113064
113113 16.4464 1.54715 0.773576 0.633704i 0.218466π-0.218466\pi
0.773576 + 0.633704i 0.218466π0.218466\pi
114114 8.97858 0.840921
115115 4.26396 0.397616
116116 36.6002 3.39824
117117 −1.68585 −0.155857
118118 29.6216 2.72689
119119 −5.83221 −0.534638
120120 5.37169 0.490366
121121 −9.68585 −0.880531
122122 −4.68585 −0.424237
123123 0.335577 0.0302579
124124 5.70727 0.512528
125125 11.0073 0.984527
126126 3.94981 0.351877
127127 12.0575 1.06993 0.534967 0.844873i 0.320324π-0.320324\pi
0.534967 + 0.844873i 0.320324π0.320324\pi
128128 −20.1751 −1.78325
129129 9.34713 0.822969
130130 −3.14637 −0.275955
131131 −3.66442 −0.320162 −0.160081 0.987104i 0.551176π-0.551176\pi
−0.160081 + 0.987104i 0.551176π0.551176\pi
132132 −4.58546 −0.399113
133133 3.34292 0.289868
134134 −14.2927 −1.23470
135135 −7.21377 −0.620862
136136 20.3503 1.74502
137137 −13.1035 −1.11951 −0.559755 0.828658i 0.689105π-0.689105\pi
−0.559755 + 0.828658i 0.689105π0.689105\pi
138138 8.52792 0.725945
139139 7.49663 0.635856 0.317928 0.948115i 0.397013π-0.397013\pi
0.317928 + 0.948115i 0.397013π0.397013\pi
140140 4.68585 0.396026
141141 12.1678 1.02471
142142 3.60688 0.302683
143143 1.14637 0.0958639
144144 −2.01721 −0.168101
145145 −14.0863 −1.16980
146146 −35.8469 −2.96671
147147 −1.14637 −0.0945506
148148 29.7220 2.44313
149149 2.16779 0.177592 0.0887961 0.996050i 0.471698π-0.471698\pi
0.0887961 + 0.996050i 0.471698π0.471698\pi
150150 8.58546 0.701000
151151 14.9112 1.21345 0.606727 0.794910i 0.292482π-0.292482\pi
0.606727 + 0.794910i 0.292482π0.292482\pi
152152 −11.6644 −0.946110
153153 −9.83221 −0.794887
154154 −2.68585 −0.216432
155155 −2.19656 −0.176432
156156 −4.00000 −0.320256
157157 22.8683 1.82509 0.912546 0.408975i 0.134114π-0.134114\pi
0.912546 + 0.408975i 0.134114π0.134114\pi
158158 2.06740 0.164474
159159 0.896480 0.0710955
160160 5.60688 0.443263
161161 3.17513 0.250236
162162 −2.57812 −0.202556
163163 7.07896 0.554467 0.277234 0.960803i 0.410582π-0.410582\pi
0.277234 + 0.960803i 0.410582π0.410582\pi
164164 −1.02142 −0.0797597
165165 1.76481 0.137390
166166 −28.4177 −2.20564
167167 2.61423 0.202295 0.101148 0.994871i 0.467749π-0.467749\pi
0.101148 + 0.994871i 0.467749π0.467749\pi
168168 4.00000 0.308607
169169 1.00000 0.0769231
170170 −18.3503 −1.40740
171171 5.63565 0.430969
172172 −28.4507 −2.16934
173173 11.0031 0.836553 0.418276 0.908320i 0.362634π-0.362634\pi
0.418276 + 0.908320i 0.362634π0.362634\pi
174174 −28.1726 −2.13576
175175 3.19656 0.241637
176176 1.37169 0.103395
177177 −14.4935 −1.08940
178178 13.4391 1.00730
179179 23.9614 1.79096 0.895478 0.445105i 0.146834π-0.146834\pi
0.895478 + 0.445105i 0.146834π0.146834\pi
180180 7.89962 0.588803
181181 6.56090 0.487668 0.243834 0.969817i 0.421595π-0.421595\pi
0.243834 + 0.969817i 0.421595π0.421595\pi
182182 −2.34292 −0.173669
183183 2.29273 0.169484
184184 −11.0790 −0.816752
185185 −11.4391 −0.841019
186186 −4.39312 −0.322119
187187 6.68585 0.488917
188188 −37.0361 −2.70114
189189 −5.37169 −0.390733
190190 10.5181 0.763060
191191 −4.39312 −0.317875 −0.158937 0.987289i 0.550807π-0.550807\pi
−0.158937 + 0.987289i 0.550807π0.550807\pi
192192 13.9572 1.00727
193193 −8.29273 −0.596924 −0.298462 0.954422i 0.596474π-0.596474\pi
−0.298462 + 0.954422i 0.596474π0.596474\pi
194194 −12.5181 −0.898744
195195 1.53948 0.110245
196196 3.48929 0.249235
197197 −3.17092 −0.225919 −0.112959 0.993600i 0.536033π-0.536033\pi
−0.112959 + 0.993600i 0.536033π0.536033\pi
198198 −4.52792 −0.321786
199199 −13.5970 −0.963867 −0.481934 0.876208i 0.660065π-0.660065\pi
−0.481934 + 0.876208i 0.660065π0.660065\pi
200200 −11.1537 −0.788687
201201 6.99327 0.493267
202202 26.1151 1.83745
203203 −10.4893 −0.736204
204204 −23.3288 −1.63335
205205 0.393115 0.0274564
206206 −8.00000 −0.557386
207207 5.35279 0.372045
208208 1.19656 0.0829663
209209 −3.83221 −0.265080
210210 −3.60688 −0.248899
211211 9.27552 0.638553 0.319277 0.947662i 0.396560π-0.396560\pi
0.319277 + 0.947662i 0.396560π0.396560\pi
212212 −2.72869 −0.187407
213213 −1.76481 −0.120923
214214 11.6644 0.797364
215215 10.9498 0.746771
216216 18.7434 1.27533
217217 −1.63565 −0.111035
218218 −31.6216 −2.14168
219219 17.5395 1.18521
220220 −5.37169 −0.362159
221221 5.83221 0.392317
222222 −22.8782 −1.53548
223223 −19.5928 −1.31203 −0.656016 0.754747i 0.727760π-0.727760\pi
−0.656016 + 0.754747i 0.727760π0.727760\pi
224224 4.17513 0.278963
225225 5.38890 0.359260
226226 38.5328 2.56316
227227 −19.6644 −1.30517 −0.652587 0.757714i 0.726316π-0.726316\pi
−0.652587 + 0.757714i 0.726316π0.726316\pi
228228 13.3717 0.885562
229229 7.76481 0.513113 0.256556 0.966529i 0.417412π-0.417412\pi
0.256556 + 0.966529i 0.417412π0.417412\pi
230230 9.99013 0.658730
231231 1.31415 0.0864650
232232 36.6002 2.40292
233233 12.1966 0.799023 0.399512 0.916728i 0.369180π-0.369180\pi
0.399512 + 0.916728i 0.369180π0.369180\pi
234234 −3.94981 −0.258207
235235 14.2541 0.929835
236236 44.1151 2.87165
237237 −1.01156 −0.0657077
238238 −13.6644 −0.885733
239239 −10.2927 −0.665781 −0.332891 0.942965i 0.608024π-0.608024\pi
−0.332891 + 0.942965i 0.608024π0.608024\pi
240240 1.84208 0.118906
241241 −4.02877 −0.259516 −0.129758 0.991546i 0.541420π-0.541420\pi
−0.129758 + 0.991546i 0.541420π0.541420\pi
242242 −22.6932 −1.45877
243243 −14.8536 −0.952861
244244 −6.97858 −0.446758
245245 −1.34292 −0.0857962
246246 0.786230 0.0501282
247247 −3.34292 −0.212705
248248 5.70727 0.362412
249249 13.9044 0.881158
250250 25.7894 1.63106
251251 2.91117 0.183752 0.0918758 0.995770i 0.470714π-0.470714\pi
0.0918758 + 0.995770i 0.470714π0.470714\pi
252252 5.88240 0.370557
253253 −3.63986 −0.228836
254254 28.2499 1.77256
255255 8.97858 0.562260
256256 −22.9185 −1.43241
257257 −19.5970 −1.22243 −0.611214 0.791465i 0.709319π-0.709319\pi
−0.611214 + 0.791465i 0.709319π0.709319\pi
258258 21.8996 1.36341
259259 −8.51806 −0.529286
260260 −4.68585 −0.290604
261261 −17.6833 −1.09457
262262 −8.58546 −0.530412
263263 7.56825 0.466678 0.233339 0.972395i 0.425035π-0.425035\pi
0.233339 + 0.972395i 0.425035π0.425035\pi
264264 −4.58546 −0.282216
265265 1.05019 0.0645128
266266 7.83221 0.480224
267267 −6.57560 −0.402420
268268 −21.2860 −1.30025
269269 −9.47208 −0.577523 −0.288761 0.957401i 0.593243π-0.593243\pi
−0.288761 + 0.957401i 0.593243π0.593243\pi
270270 −16.9013 −1.02858
271271 29.3717 1.78420 0.892102 0.451835i 0.149230π-0.149230\pi
0.892102 + 0.451835i 0.149230π0.149230\pi
272272 6.97858 0.423138
273273 1.14637 0.0693812
274274 −30.7005 −1.85469
275275 −3.66442 −0.220973
276276 12.7005 0.764483
277277 −1.90383 −0.114390 −0.0571949 0.998363i 0.518216π-0.518216\pi
−0.0571949 + 0.998363i 0.518216π0.518216\pi
278278 17.5640 1.05342
279279 −2.75746 −0.165085
280280 4.68585 0.280033
281281 −20.5756 −1.22744 −0.613719 0.789525i 0.710327π-0.710327\pi
−0.613719 + 0.789525i 0.710327π0.710327\pi
282282 28.5082 1.69764
283283 −26.9933 −1.60458 −0.802292 0.596932i 0.796386π-0.796386\pi
−0.802292 + 0.596932i 0.796386π0.796386\pi
284284 5.37169 0.318751
285285 −5.14637 −0.304844
286286 2.68585 0.158817
287287 0.292731 0.0172794
288288 7.03863 0.414756
289289 17.0147 1.00086
290290 −33.0031 −1.93801
291291 6.12494 0.359050
292292 −53.3864 −3.12420
293293 −14.9070 −0.870874 −0.435437 0.900219i 0.643406π-0.643406\pi
−0.435437 + 0.900219i 0.643406π0.643406\pi
294294 −2.68585 −0.156642
295295 −16.9786 −0.988531
296296 29.7220 1.72755
297297 6.15792 0.357319
298298 5.07896 0.294216
299299 −3.17513 −0.183623
300300 12.7862 0.738213
301301 8.15371 0.469972
302302 34.9357 2.01033
303303 −12.7778 −0.734066
304304 −4.00000 −0.229416
305305 2.68585 0.153791
306306 −23.0361 −1.31689
307307 26.0288 1.48554 0.742770 0.669546i 0.233512π-0.233512\pi
0.742770 + 0.669546i 0.233512π0.233512\pi
308308 −4.00000 −0.227921
309309 3.91431 0.222677
310310 −5.14637 −0.292294
311311 19.4966 1.10555 0.552776 0.833330i 0.313568π-0.313568\pi
0.552776 + 0.833330i 0.313568π0.313568\pi
312312 −4.00000 −0.226455
313313 −3.48194 −0.196811 −0.0984055 0.995146i 0.531374π-0.531374\pi
−0.0984055 + 0.995146i 0.531374π0.531374\pi
314314 53.5787 3.02362
315315 −2.26396 −0.127560
316316 3.07896 0.173205
317317 5.02142 0.282031 0.141016 0.990007i 0.454963π-0.454963\pi
0.141016 + 0.990007i 0.454963π0.454963\pi
318318 2.10038 0.117784
319319 12.0246 0.673246
320320 16.3503 0.914008
321321 −5.70727 −0.318549
322322 7.43910 0.414565
323323 −19.4966 −1.08482
324324 −3.83956 −0.213309
325325 −3.19656 −0.177313
326326 16.5855 0.918584
327327 15.4721 0.855608
328328 −1.02142 −0.0563986
329329 10.6142 0.585182
330330 4.13481 0.227614
331331 −6.14950 −0.338007 −0.169004 0.985615i 0.554055π-0.554055\pi
−0.169004 + 0.985615i 0.554055π0.554055\pi
332332 −42.3221 −2.32273
333333 −14.3601 −0.786931
334334 6.12494 0.335142
335335 8.19235 0.447596
336336 1.37169 0.0748320
337337 −25.6258 −1.39593 −0.697963 0.716134i 0.745910π-0.745910\pi
−0.697963 + 0.716134i 0.745910π0.745910\pi
338338 2.34292 0.127438
339339 −18.8536 −1.02399
340340 −27.3288 −1.48211
341341 1.87506 0.101540
342342 13.2039 0.713985
343343 −1.00000 −0.0539949
344344 −28.4507 −1.53396
345345 −4.88806 −0.263164
346346 25.7795 1.38591
347347 −16.7005 −0.896532 −0.448266 0.893900i 0.647958π-0.647958\pi
−0.448266 + 0.893900i 0.647958π0.647958\pi
348348 −41.9572 −2.24914
349349 −23.5500 −1.26060 −0.630300 0.776351i 0.717068π-0.717068\pi
−0.630300 + 0.776351i 0.717068π0.717068\pi
350350 7.48929 0.400319
351351 5.37169 0.286720
352352 −4.78623 −0.255107
353353 −7.64973 −0.407154 −0.203577 0.979059i 0.565257π-0.565257\pi
−0.203577 + 0.979059i 0.565257π0.565257\pi
354354 −33.9572 −1.80480
355355 −2.06740 −0.109726
356356 20.0147 1.06078
357357 6.68585 0.353853
358358 56.1396 2.96707
359359 18.3748 0.969786 0.484893 0.874573i 0.338858π-0.338858\pi
0.484893 + 0.874573i 0.338858π0.338858\pi
360360 7.89962 0.416346
361361 −7.82487 −0.411835
362362 15.3717 0.807918
363363 11.1035 0.582784
364364 −3.48929 −0.182888
365365 20.5468 1.07547
366366 5.37169 0.280783
367367 5.33871 0.278679 0.139339 0.990245i 0.455502π-0.455502\pi
0.139339 + 0.990245i 0.455502π0.455502\pi
368368 −3.79923 −0.198049
369369 0.493499 0.0256906
370370 −26.8009 −1.39331
371371 0.782020 0.0406004
372372 −6.54262 −0.339219
373373 21.5212 1.11433 0.557163 0.830403i 0.311890π-0.311890\pi
0.557163 + 0.830403i 0.311890π0.311890\pi
374374 15.6644 0.809988
375375 −12.6184 −0.651614
376376 −37.0361 −1.90999
377377 10.4893 0.540226
378378 −12.5855 −0.647326
379379 4.61002 0.236801 0.118400 0.992966i 0.462223π-0.462223\pi
0.118400 + 0.992966i 0.462223π0.462223\pi
380380 15.6644 0.803568
381381 −13.8223 −0.708140
382382 −10.2927 −0.526622
383383 −8.33558 −0.425928 −0.212964 0.977060i 0.568312π-0.568312\pi
−0.212964 + 0.977060i 0.568312π0.568312\pi
384384 23.1281 1.18025
385385 1.53948 0.0784592
386386 −19.4292 −0.988922
387387 13.7459 0.698744
388388 −18.6430 −0.946455
389389 −6.44223 −0.326634 −0.163317 0.986574i 0.552219π-0.552219\pi
−0.163317 + 0.986574i 0.552219π0.552219\pi
390390 3.60688 0.182642
391391 −18.5181 −0.936498
392392 3.48929 0.176236
393393 4.20077 0.211901
394394 −7.42923 −0.374279
395395 −1.18500 −0.0596238
396396 −6.74338 −0.338868
397397 1.40046 0.0702872 0.0351436 0.999382i 0.488811π-0.488811\pi
0.0351436 + 0.999382i 0.488811π0.488811\pi
398398 −31.8568 −1.59684
399399 −3.83221 −0.191851
400400 −3.82487 −0.191243
401401 −6.97858 −0.348494 −0.174247 0.984702i 0.555749π-0.555749\pi
−0.174247 + 0.984702i 0.555749π0.555749\pi
402402 16.3847 0.817194
403403 1.63565 0.0814777
404404 38.8929 1.93499
405405 1.47773 0.0734291
406406 −24.5756 −1.21967
407407 9.76481 0.484024
408408 −23.3288 −1.15495
409409 −18.3790 −0.908785 −0.454392 0.890802i 0.650144π-0.650144\pi
−0.454392 + 0.890802i 0.650144π0.650144\pi
410410 0.921039 0.0454869
411411 15.0214 0.740952
412412 −11.9143 −0.586976
413413 −12.6430 −0.622121
414414 12.5412 0.616365
415415 16.2885 0.799572
416416 −4.17513 −0.204703
417417 −8.59388 −0.420844
418418 −8.97858 −0.439157
419419 −30.0393 −1.46751 −0.733757 0.679412i 0.762235π-0.762235\pi
−0.733757 + 0.679412i 0.762235π0.762235\pi
420420 −5.37169 −0.262112
421421 −8.31729 −0.405360 −0.202680 0.979245i 0.564965π-0.564965\pi
−0.202680 + 0.979245i 0.564965π0.564965\pi
422422 21.7318 1.05789
423423 17.8940 0.870034
424424 −2.72869 −0.132517
425425 −18.6430 −0.904318
426426 −4.13481 −0.200332
427427 2.00000 0.0967868
428428 17.3717 0.839692
429429 −1.31415 −0.0634479
430430 25.6546 1.23717
431431 9.64973 0.464811 0.232406 0.972619i 0.425340π-0.425340\pi
0.232406 + 0.972619i 0.425340π0.425340\pi
432432 6.42754 0.309245
433433 26.3074 1.26425 0.632127 0.774865i 0.282182π-0.282182\pi
0.632127 + 0.774865i 0.282182π0.282182\pi
434434 −3.83221 −0.183952
435435 16.1481 0.774240
436436 −47.0937 −2.25538
437437 10.6142 0.507748
438438 41.0937 1.96353
439439 33.8139 1.61385 0.806925 0.590654i 0.201130π-0.201130\pi
0.806925 + 0.590654i 0.201130π0.201130\pi
440440 −5.37169 −0.256085
441441 −1.68585 −0.0802784
442442 13.6644 0.649950
443443 26.4464 1.25651 0.628254 0.778008i 0.283770π-0.283770\pi
0.628254 + 0.778008i 0.283770π0.283770\pi
444444 −34.0722 −1.61700
445445 −7.70306 −0.365160
446446 −45.9044 −2.17364
447447 −2.48508 −0.117540
448448 12.1751 0.575221
449449 2.64300 0.124731 0.0623655 0.998053i 0.480136π-0.480136\pi
0.0623655 + 0.998053i 0.480136π0.480136\pi
450450 12.6258 0.595185
451451 −0.335577 −0.0158017
452452 57.3864 2.69923
453453 −17.0937 −0.803130
454454 −46.0722 −2.16228
455455 1.34292 0.0629572
456456 13.3717 0.626187
457457 −33.6890 −1.57590 −0.787952 0.615737i 0.788859π-0.788859\pi
−0.787952 + 0.615737i 0.788859π0.788859\pi
458458 18.1923 0.850073
459459 31.3288 1.46231
460460 14.8782 0.693699
461461 33.0790 1.54064 0.770320 0.637657i 0.220096π-0.220096\pi
0.770320 + 0.637657i 0.220096π0.220096\pi
462462 3.07896 0.143246
463463 −2.51806 −0.117024 −0.0585120 0.998287i 0.518636π-0.518636\pi
−0.0585120 + 0.998287i 0.518636π0.518636\pi
464464 12.5510 0.582667
465465 2.51806 0.116772
466466 28.5756 1.32374
467467 2.57560 0.119184 0.0595922 0.998223i 0.481020π-0.481020\pi
0.0595922 + 0.998223i 0.481020π0.481020\pi
468468 −5.88240 −0.271914
469469 6.10038 0.281690
470470 33.3963 1.54045
471471 −26.2155 −1.20794
472472 44.1151 2.03056
473473 −9.34713 −0.429782
474474 −2.37000 −0.108858
475475 10.6858 0.490300
476476 −20.3503 −0.932753
477477 1.31836 0.0603638
478478 −24.1151 −1.10300
479479 0.513847 0.0234783 0.0117391 0.999931i 0.496263π-0.496263\pi
0.0117391 + 0.999931i 0.496263π0.496263\pi
480480 −6.42754 −0.293376
481481 8.51806 0.388390
482482 −9.43910 −0.429939
483483 −3.63986 −0.165620
484484 −33.7967 −1.53621
485485 7.17513 0.325806
486486 −34.8009 −1.57860
487487 36.0575 1.63392 0.816962 0.576692i 0.195657π-0.195657\pi
0.816962 + 0.576692i 0.195657π0.195657\pi
488488 −6.97858 −0.315905
489489 −8.11508 −0.366976
490490 −3.14637 −0.142138
491491 −9.22846 −0.416475 −0.208237 0.978078i 0.566773π-0.566773\pi
−0.208237 + 0.978078i 0.566773π0.566773\pi
492492 1.17092 0.0527893
493493 61.1758 2.75522
494494 −7.83221 −0.352388
495495 2.59533 0.116651
496496 1.95715 0.0878788
497497 −1.53948 −0.0690551
498498 32.5770 1.45981
499499 1.00314 0.0449065 0.0224533 0.999748i 0.492852π-0.492852\pi
0.0224533 + 0.999748i 0.492852π0.492852\pi
500500 38.4078 1.71765
501501 −2.99686 −0.133890
502502 6.82065 0.304421
503503 −30.3503 −1.35325 −0.676626 0.736327i 0.736559π-0.736559\pi
−0.676626 + 0.736327i 0.736559π0.736559\pi
504504 5.88240 0.262023
505505 −14.9687 −0.666099
506506 −8.52792 −0.379112
507507 −1.14637 −0.0509119
508508 42.0722 1.86665
509509 10.5995 0.469816 0.234908 0.972018i 0.424521π-0.424521\pi
0.234908 + 0.972018i 0.424521π0.424521\pi
510510 21.0361 0.931495
511511 15.3001 0.676836
512512 −13.3461 −0.589818
513513 −17.9572 −0.792828
514514 −45.9143 −2.02519
515515 4.58546 0.202060
516516 32.6148 1.43579
517517 −12.1678 −0.535139
518518 −19.9572 −0.876867
519519 −12.6136 −0.553676
520520 −4.68585 −0.205488
521521 −16.2646 −0.712564 −0.356282 0.934378i 0.615956π-0.615956\pi
−0.356282 + 0.934378i 0.615956π0.615956\pi
522522 −41.4307 −1.81337
523523 7.22219 0.315804 0.157902 0.987455i 0.449527π-0.449527\pi
0.157902 + 0.987455i 0.449527π0.449527\pi
524524 −12.7862 −0.558569
525525 −3.66442 −0.159929
526526 17.7318 0.773144
527527 9.53948 0.415546
528528 −1.57246 −0.0684326
529529 −12.9185 −0.561675
530530 2.46052 0.106878
531531 −21.3142 −0.924955
532532 11.6644 0.505717
533533 −0.292731 −0.0126796
534534 −15.4061 −0.666688
535535 −6.68585 −0.289054
536536 −21.2860 −0.919415
537537 −27.4685 −1.18535
538538 −22.1923 −0.956780
539539 1.14637 0.0493775
540540 −25.1709 −1.08318
541541 17.3534 0.746081 0.373041 0.927815i 0.378315π-0.378315\pi
0.373041 + 0.927815i 0.378315π0.378315\pi
542542 68.8156 2.95588
543543 −7.52119 −0.322765
544544 −24.3503 −1.04401
545545 18.1249 0.776387
546546 2.68585 0.114944
547547 −34.1109 −1.45848 −0.729238 0.684261i 0.760125π-0.760125\pi
−0.729238 + 0.684261i 0.760125π0.760125\pi
548548 −45.7220 −1.95315
549549 3.37169 0.143900
550550 −8.58546 −0.366085
551551 −35.0649 −1.49381
552552 12.7005 0.540571
553553 −0.882404 −0.0375236
554554 −4.46052 −0.189509
555555 13.1134 0.556632
556556 26.1579 1.10934
557557 −13.2222 −0.560242 −0.280121 0.959965i 0.590375π-0.590375\pi
−0.280121 + 0.959965i 0.590375π0.590375\pi
558558 −6.46052 −0.273496
559559 −8.15371 −0.344865
560560 1.60688 0.0679033
561561 −7.66442 −0.323592
562562 −48.2070 −2.03349
563563 −41.3717 −1.74361 −0.871804 0.489854i 0.837050π-0.837050\pi
−0.871804 + 0.489854i 0.837050π0.837050\pi
564564 42.4569 1.78776
565565 −22.0863 −0.929178
566566 −63.2432 −2.65831
567567 1.10038 0.0462118
568568 5.37169 0.225391
569569 −2.68164 −0.112420 −0.0562100 0.998419i 0.517902π-0.517902\pi
−0.0562100 + 0.998419i 0.517902π0.517902\pi
570570 −12.0575 −0.505035
571571 −28.9315 −1.21075 −0.605373 0.795942i 0.706976π-0.706976\pi
−0.605373 + 0.795942i 0.706976π0.706976\pi
572572 4.00000 0.167248
573573 5.03612 0.210387
574574 0.685846 0.0286267
575575 10.1495 0.423263
576576 20.5254 0.855225
577577 37.5296 1.56238 0.781189 0.624294i 0.214613π-0.214613\pi
0.781189 + 0.624294i 0.214613π0.214613\pi
578578 39.8641 1.65813
579579 9.50650 0.395077
580580 −49.1512 −2.04089
581581 12.1292 0.503202
582582 14.3503 0.594838
583583 −0.896480 −0.0371284
584584 −53.3864 −2.20914
585585 2.26396 0.0936033
586586 −34.9259 −1.44277
587587 23.0649 0.951990 0.475995 0.879448i 0.342088π-0.342088\pi
0.475995 + 0.879448i 0.342088π0.342088\pi
588588 −4.00000 −0.164957
589589 −5.46787 −0.225299
590590 −39.7795 −1.63770
591591 3.63504 0.149525
592592 10.1923 0.418903
593593 −11.0502 −0.453777 −0.226889 0.973921i 0.572855π-0.572855\pi
−0.226889 + 0.973921i 0.572855π0.572855\pi
594594 14.4275 0.591969
595595 7.83221 0.321089
596596 7.56404 0.309835
597597 15.5872 0.637940
598598 −7.43910 −0.304207
599599 −44.6044 −1.82248 −0.911242 0.411870i 0.864876π-0.864876\pi
−0.911242 + 0.411870i 0.864876π0.864876\pi
600600 12.7862 0.521996
601601 47.8715 1.95272 0.976359 0.216156i 0.0693520π-0.0693520\pi
0.976359 + 0.216156i 0.0693520π0.0693520\pi
602602 19.1035 0.778601
603603 10.2843 0.418809
604604 52.0294 2.11705
605605 13.0073 0.528824
606606 −29.9374 −1.21612
607607 45.0691 1.82930 0.914649 0.404249i 0.132467π-0.132467\pi
0.914649 + 0.404249i 0.132467π0.132467\pi
608608 13.9572 0.566037
609609 12.0246 0.487260
610610 6.29273 0.254785
611611 −10.6142 −0.429406
612612 −34.3074 −1.38680
613613 −25.5212 −1.03079 −0.515396 0.856952i 0.672355π-0.672355\pi
−0.515396 + 0.856952i 0.672355π0.672355\pi
614614 60.9834 2.46109
615615 −0.450654 −0.0181721
616616 −4.00000 −0.161165
617617 29.2432 1.17729 0.588643 0.808393i 0.299663π-0.299663\pi
0.588643 + 0.808393i 0.299663π0.299663\pi
618618 9.17092 0.368909
619619 4.78623 0.192375 0.0961874 0.995363i 0.469335π-0.469335\pi
0.0961874 + 0.995363i 0.469335π0.469335\pi
620620 −7.66442 −0.307811
621621 −17.0558 −0.684428
622622 45.6791 1.83157
623623 −5.73604 −0.229810
624624 −1.37169 −0.0549116
625625 1.20077 0.0480307
626626 −8.15792 −0.326056
627627 4.39312 0.175444
628628 79.7942 3.18413
629629 49.6791 1.98084
630630 −5.30429 −0.211328
631631 −28.3931 −1.13031 −0.565156 0.824984i 0.691184π-0.691184\pi
−0.565156 + 0.824984i 0.691184π0.691184\pi
632632 3.07896 0.122475
633633 −10.6331 −0.422629
634634 11.7648 0.467240
635635 −16.1923 −0.642574
636636 3.12808 0.124036
637637 1.00000 0.0396214
638638 28.1726 1.11536
639639 −2.59533 −0.102670
640640 27.0937 1.07097
641641 5.96137 0.235460 0.117730 0.993046i 0.462438π-0.462438\pi
0.117730 + 0.993046i 0.462438π0.462438\pi
642642 −13.3717 −0.527739
643643 31.1940 1.23017 0.615086 0.788460i 0.289121π-0.289121\pi
0.615086 + 0.788460i 0.289121π0.289121\pi
644644 11.0790 0.436572
645645 −12.5525 −0.494253
646646 −45.6791 −1.79722
647647 14.9112 0.586219 0.293109 0.956079i 0.405310π-0.405310\pi
0.293109 + 0.956079i 0.405310π0.405310\pi
648648 −3.83956 −0.150832
649649 14.4935 0.568920
650650 −7.48929 −0.293754
651651 1.87506 0.0734893
652652 24.7005 0.967348
653653 −3.57246 −0.139801 −0.0699006 0.997554i 0.522268π-0.522268\pi
−0.0699006 + 0.997554i 0.522268π0.522268\pi
654654 36.2499 1.41748
655655 4.92104 0.192281
656656 −0.350269 −0.0136757
657657 25.7936 1.00630
658658 24.8683 0.969468
659659 −3.90383 −0.152071 −0.0760357 0.997105i 0.524226π-0.524226\pi
−0.0760357 + 0.997105i 0.524226π0.524226\pi
660660 6.15792 0.239697
661661 13.7936 0.536508 0.268254 0.963348i 0.413553π-0.413553\pi
0.268254 + 0.963348i 0.413553π0.413553\pi
662662 −14.4078 −0.559975
663663 −6.68585 −0.259657
664664 −42.3221 −1.64242
665665 −4.48929 −0.174087
666666 −33.6447 −1.30371
667667 −33.3049 −1.28957
668668 9.12181 0.352933
669669 22.4605 0.868374
670670 19.1940 0.741530
671671 −2.29273 −0.0885099
672672 −4.78623 −0.184633
673673 5.70306 0.219837 0.109918 0.993941i 0.464941π-0.464941\pi
0.109918 + 0.993941i 0.464941π0.464941\pi
674674 −60.0393 −2.31263
675675 −17.1709 −0.660909
676676 3.48929 0.134203
677677 35.2614 1.35521 0.677604 0.735427i 0.263019π-0.263019\pi
0.677604 + 0.735427i 0.263019π0.263019\pi
678678 −44.1726 −1.69644
679679 5.34292 0.205043
680680 −27.3288 −1.04801
681681 22.5426 0.863835
682682 4.39312 0.168221
683683 1.03612 0.0396459 0.0198229 0.999804i 0.493690π-0.493690\pi
0.0198229 + 0.999804i 0.493690π0.493690\pi
684684 19.6644 0.751888
685685 17.5970 0.672348
686686 −2.34292 −0.0894532
687687 −8.90131 −0.339606
688688 −9.75639 −0.371959
689689 −0.782020 −0.0297926
690690 −11.4523 −0.435983
691691 3.67850 0.139937 0.0699684 0.997549i 0.477710π-0.477710\pi
0.0699684 + 0.997549i 0.477710π0.477710\pi
692692 38.3931 1.45949
693693 1.93260 0.0734132
694694 −39.1281 −1.48528
695695 −10.0674 −0.381878
696696 −41.9572 −1.59038
697697 −1.70727 −0.0646674
698698 −55.1758 −2.08843
699699 −13.9817 −0.528837
700700 11.1537 0.421571
701701 −0.0617493 −0.00233224 −0.00116612 0.999999i 0.500371π-0.500371\pi
−0.00116612 + 0.999999i 0.500371π0.500371\pi
702702 12.5855 0.475008
703703 −28.4752 −1.07396
704704 −13.9572 −0.526030
705705 −16.3404 −0.615415
706706 −17.9227 −0.674531
707707 −11.1464 −0.419202
708708 −50.5720 −1.90061
709709 −42.9834 −1.61428 −0.807138 0.590363i 0.798985π-0.798985\pi
−0.807138 + 0.590363i 0.798985π0.798985\pi
710710 −4.84377 −0.181783
711711 −1.48760 −0.0557892
712712 20.0147 0.750082
713713 −5.19342 −0.194495
714714 15.6644 0.586226
715715 −1.53948 −0.0575733
716716 83.6081 3.12458
717717 11.7992 0.440650
718718 43.0508 1.60664
719719 17.6546 0.658404 0.329202 0.944260i 0.393220π-0.393220\pi
0.329202 + 0.944260i 0.393220π0.393220\pi
720720 2.70896 0.100957
721721 3.41454 0.127164
722722 −18.3331 −0.682286
723723 4.61844 0.171762
724724 22.8929 0.850807
725725 −33.5296 −1.24526
726726 26.0147 0.965496
727727 −23.8077 −0.882977 −0.441488 0.897267i 0.645549π-0.645549\pi
−0.441488 + 0.897267i 0.645549π0.645549\pi
728728 −3.48929 −0.129322
729729 20.3288 0.752920
730730 48.1396 1.78173
731731 −47.5542 −1.75885
732732 8.00000 0.295689
733733 31.3492 1.15791 0.578954 0.815360i 0.303461π-0.303461\pi
0.578954 + 0.815360i 0.303461π0.303461\pi
734734 12.5082 0.461686
735735 1.53948 0.0567846
736736 13.2566 0.488645
737737 −6.99327 −0.257600
738738 1.15623 0.0425615
739739 −24.8108 −0.912680 −0.456340 0.889806i 0.650840π-0.650840\pi
−0.456340 + 0.889806i 0.650840π0.650840\pi
740740 −39.9143 −1.46728
741741 3.83221 0.140780
742742 1.83221 0.0672626
743743 21.3717 0.784051 0.392026 0.919954i 0.371774π-0.371774\pi
0.392026 + 0.919954i 0.371774π0.371774\pi
744744 −6.54262 −0.239864
745745 −2.91117 −0.106657
746746 50.4225 1.84610
747747 20.4479 0.748149
748748 23.3288 0.852987
749749 −4.97858 −0.181913
750750 −29.5640 −1.07953
751751 19.2243 0.701503 0.350751 0.936469i 0.385926π-0.385926\pi
0.350751 + 0.936469i 0.385926π0.385926\pi
752752 −12.7005 −0.463141
753753 −3.33727 −0.121617
754754 24.5756 0.894990
755755 −20.0246 −0.728768
756756 −18.7434 −0.681690
757757 −19.8610 −0.721860 −0.360930 0.932593i 0.617541π-0.617541\pi
−0.360930 + 0.932593i 0.617541π0.617541\pi
758758 10.8009 0.392307
759759 4.17262 0.151456
760760 15.6644 0.568208
761761 6.12073 0.221876 0.110938 0.993827i 0.464614π-0.464614\pi
0.110938 + 0.993827i 0.464614π0.464614\pi
762762 −32.3847 −1.17317
763763 13.4966 0.488611
764764 −15.3288 −0.554578
765765 13.2039 0.477388
766766 −19.5296 −0.705634
767767 12.6430 0.456512
768768 26.2730 0.948045
769769 3.82800 0.138041 0.0690206 0.997615i 0.478013π-0.478013\pi
0.0690206 + 0.997615i 0.478013π0.478013\pi
770770 3.60688 0.129983
771771 22.4653 0.809070
772772 −28.9357 −1.04142
773773 −6.53635 −0.235096 −0.117548 0.993067i 0.537503π-0.537503\pi
−0.117548 + 0.993067i 0.537503π0.537503\pi
774774 32.2056 1.15761
775775 −5.22846 −0.187812
776776 −18.6430 −0.669245
777777 9.76481 0.350311
778778 −15.0937 −0.541134
779779 0.978577 0.0350612
780780 5.37169 0.192337
781781 1.76481 0.0631498
782782 −43.3864 −1.55149
783783 56.3452 2.01361
784784 1.19656 0.0427342
785785 −30.7104 −1.09610
786786 9.84208 0.351055
787787 30.8066 1.09814 0.549068 0.835778i 0.314983π-0.314983\pi
0.549068 + 0.835778i 0.314983π0.314983\pi
788788 −11.0643 −0.394148
789789 −8.67598 −0.308873
790790 −2.77636 −0.0987786
791791 −16.4464 −0.584768
792792 −6.74338 −0.239616
793793 −2.00000 −0.0710221
794794 3.28117 0.116444
795795 −1.20390 −0.0426981
796796 −47.4439 −1.68161
797797 −38.8156 −1.37492 −0.687460 0.726222i 0.741274π-0.741274\pi
−0.687460 + 0.726222i 0.741274π0.741274\pi
798798 −8.97858 −0.317838
799799 −61.9044 −2.19002
800800 13.3461 0.471854
801801 −9.67008 −0.341675
802802 −16.3503 −0.577348
803803 −17.5395 −0.618955
804804 24.4015 0.860576
805805 −4.26396 −0.150285
806806 3.83221 0.134984
807807 10.8585 0.382236
808808 38.8929 1.36825
809809 1.04033 0.0365759 0.0182880 0.999833i 0.494178π-0.494178\pi
0.0182880 + 0.999833i 0.494178π0.494178\pi
810810 3.46221 0.121650
811811 12.6712 0.444944 0.222472 0.974939i 0.428587π-0.428587\pi
0.222472 + 0.974939i 0.428587π0.428587\pi
812812 −36.6002 −1.28441
813813 −33.6707 −1.18088
814814 22.8782 0.801880
815815 −9.50650 −0.332998
816816 −8.00000 −0.280056
817817 27.2572 0.953610
818818 −43.0607 −1.50558
819819 1.68585 0.0589082
820820 1.37169 0.0479016
821821 27.0361 0.943567 0.471783 0.881714i 0.343610π-0.343610\pi
0.471783 + 0.881714i 0.343610π0.343610\pi
822822 35.1940 1.22753
823823 −31.6363 −1.10277 −0.551386 0.834251i 0.685901π-0.685901\pi
−0.551386 + 0.834251i 0.685901π0.685901\pi
824824 −11.9143 −0.415055
825825 4.20077 0.146252
826826 −29.6216 −1.03067
827827 56.4800 1.96400 0.982002 0.188872i 0.0604832π-0.0604832\pi
0.982002 + 0.188872i 0.0604832π0.0604832\pi
828828 18.6774 0.649085
829829 −42.6760 −1.48220 −0.741099 0.671396i 0.765695π-0.765695\pi
−0.741099 + 0.671396i 0.765695π0.765695\pi
830830 38.1627 1.32465
831831 2.18248 0.0757094
832832 −12.1751 −0.422097
833833 5.83221 0.202074
834834 −20.1348 −0.697211
835835 −3.51071 −0.121493
836836 −13.3717 −0.462470
837837 8.78623 0.303697
838838 −70.3797 −2.43122
839839 −40.1642 −1.38662 −0.693311 0.720639i 0.743849π-0.743849\pi
−0.693311 + 0.720639i 0.743849π0.743849\pi
840840 −5.37169 −0.185341
841841 81.0252 2.79397
842842 −19.4868 −0.671558
843843 23.5872 0.812385
844844 32.3650 1.11405
845845 −1.34292 −0.0461980
846846 41.9242 1.44138
847847 9.68585 0.332810
848848 −0.935731 −0.0321331
849849 30.9442 1.06200
850850 −43.6791 −1.49818
851851 −27.0460 −0.927124
852852 −6.15792 −0.210967
853853 19.6932 0.674282 0.337141 0.941454i 0.390540π-0.390540\pi
0.337141 + 0.941454i 0.390540π0.390540\pi
854854 4.68585 0.160346
855855 −7.56825 −0.258829
856856 17.3717 0.593752
857857 1.66442 0.0568556 0.0284278 0.999596i 0.490950π-0.490950\pi
0.0284278 + 0.999596i 0.490950π0.490950\pi
858858 −3.07896 −0.105114
859859 −41.2944 −1.40895 −0.704474 0.709730i 0.748817π-0.748817\pi
−0.704474 + 0.709730i 0.748817π0.748817\pi
860860 38.2070 1.30285
861861 −0.335577 −0.0114364
862862 22.6086 0.770051
863863 −31.3288 −1.06645 −0.533223 0.845975i 0.679019π-0.679019\pi
−0.533223 + 0.845975i 0.679019π0.679019\pi
864864 −22.4275 −0.763000
865865 −14.7764 −0.502411
866866 61.6363 2.09449
867867 −19.5051 −0.662426
868868 −5.70727 −0.193717
869869 1.01156 0.0343147
870870 37.8337 1.28268
871871 −6.10038 −0.206704
872872 −47.0937 −1.59479
873873 9.00735 0.304852
874874 24.8683 0.841184
875875 −11.0073 −0.372116
876876 61.2003 2.06777
877877 −53.8041 −1.81683 −0.908417 0.418065i 0.862708π-0.862708\pi
−0.908417 + 0.418065i 0.862708π0.862708\pi
878878 79.2234 2.67366
879879 17.0888 0.576392
880880 −1.84208 −0.0620964
881881 8.09196 0.272625 0.136313 0.990666i 0.456475π-0.456475\pi
0.136313 + 0.990666i 0.456475π0.456475\pi
882882 −3.94981 −0.132997
883883 −27.0705 −0.910996 −0.455498 0.890237i 0.650539π-0.650539\pi
−0.455498 + 0.890237i 0.650539π0.650539\pi
884884 20.3503 0.684454
885885 19.4637 0.654264
886886 61.9620 2.08165
887887 −38.4935 −1.29249 −0.646243 0.763132i 0.723661π-0.723661\pi
−0.646243 + 0.763132i 0.723661π0.723661\pi
888888 −34.0722 −1.14339
889889 −12.0575 −0.404397
890890 −18.0477 −0.604959
891891 −1.26144 −0.0422599
892892 −68.3650 −2.28903
893893 35.4826 1.18738
894894 −5.82235 −0.194728
895895 −32.1783 −1.07560
896896 20.1751 0.674004
897897 3.63986 0.121532
898898 6.19235 0.206641
899899 17.1568 0.572213
900900 18.8034 0.626781
901901 −4.56090 −0.151946
902902 −0.786230 −0.0261786
903903 −9.34713 −0.311053
904904 57.3864 1.90864
905905 −8.81079 −0.292881
906906 −40.0491 −1.33054
907907 15.7031 0.521411 0.260706 0.965418i 0.416045π-0.416045\pi
0.260706 + 0.965418i 0.416045π0.416045\pi
908908 −68.6148 −2.27706
909909 −18.7911 −0.623260
910910 3.14637 0.104301
911911 44.9399 1.48893 0.744463 0.667663i 0.232705π-0.232705\pi
0.744463 + 0.667663i 0.232705π0.232705\pi
912912 4.58546 0.151840
913913 −13.9044 −0.460170
914914 −78.9307 −2.61080
915915 −3.07896 −0.101787
916916 27.0937 0.895200
917917 3.66442 0.121010
918918 73.4011 2.42260
919919 −27.2432 −0.898669 −0.449334 0.893364i 0.648339π-0.648339\pi
−0.449334 + 0.893364i 0.648339π0.648339\pi
920920 14.8782 0.490519
921921 −29.8385 −0.983211
922922 77.5015 2.55237
923923 1.53948 0.0506726
924924 4.58546 0.150851
925925 −27.2285 −0.895266
926926 −5.89962 −0.193873
927927 5.75639 0.189065
928928 −43.7942 −1.43761
929929 −17.1422 −0.562416 −0.281208 0.959647i 0.590735π-0.590735\pi
−0.281208 + 0.959647i 0.590735π0.590735\pi
930930 5.89962 0.193456
931931 −3.34292 −0.109560
932932 42.5573 1.39401
933933 −22.3503 −0.731715
934934 6.03442 0.197452
935935 −8.97858 −0.293631
936936 −5.88240 −0.192272
937937 −51.5197 −1.68308 −0.841538 0.540197i 0.818350π-0.818350\pi
−0.841538 + 0.540197i 0.818350π0.818350\pi
938938 14.2927 0.466674
939939 3.99158 0.130260
940940 49.7367 1.62223
941941 32.7575 1.06786 0.533931 0.845528i 0.320714π-0.320714\pi
0.533931 + 0.845528i 0.320714π0.320714\pi
942942 −61.4208 −2.00120
943943 0.929460 0.0302674
944944 15.1281 0.492377
945945 7.21377 0.234664
946946 −21.8996 −0.712018
947947 20.9295 0.680116 0.340058 0.940404i 0.389553π-0.389553\pi
0.340058 + 0.940404i 0.389553π0.389553\pi
948948 −3.52962 −0.114637
949949 −15.3001 −0.496662
950950 25.0361 0.812279
951951 −5.75639 −0.186664
952952 −20.3503 −0.659556
953953 46.4120 1.50343 0.751716 0.659487i 0.229226π-0.229226\pi
0.751716 + 0.659487i 0.229226π0.229226\pi
954954 3.08883 0.100004
955955 5.89962 0.190907
956956 −35.9143 −1.16155
957957 −13.7845 −0.445591
958958 1.20390 0.0388964
959959 13.1035 0.423135
960960 −18.7434 −0.604940
961961 −28.3246 −0.913698
962962 19.9572 0.643444
963963 −8.39312 −0.270464
964964 −14.0575 −0.452763
965965 11.1365 0.358497
966966 −8.52792 −0.274381
967967 −23.2186 −0.746660 −0.373330 0.927699i 0.621784π-0.621784\pi
−0.373330 + 0.927699i 0.621784π0.621784\pi
968968 −33.7967 −1.08627
969969 22.3503 0.717994
970970 16.8108 0.539762
971971 −14.1004 −0.452503 −0.226251 0.974069i 0.572647π-0.572647\pi
−0.226251 + 0.974069i 0.572647π0.572647\pi
972972 −51.8286 −1.66240
973973 −7.49663 −0.240331
974974 84.4800 2.70692
975975 3.66442 0.117355
976976 −2.39312 −0.0766018
977977 −2.95402 −0.0945074 −0.0472537 0.998883i 0.515047π-0.515047\pi
−0.0472537 + 0.998883i 0.515047π0.515047\pi
978978 −19.0130 −0.607969
979979 6.57560 0.210157
980980 −4.68585 −0.149684
981981 22.7533 0.726455
982982 −21.6216 −0.689972
983983 −35.0367 −1.11750 −0.558749 0.829337i 0.688719π-0.688719\pi
−0.558749 + 0.829337i 0.688719π0.688719\pi
984984 1.17092 0.0373277
985985 4.25831 0.135681
986986 143.330 4.56456
987987 −12.1678 −0.387305
988988 −11.6644 −0.371095
989989 25.8891 0.823227
990990 6.08065 0.193256
991991 47.9718 1.52388 0.761938 0.647650i 0.224248π-0.224248\pi
0.761938 + 0.647650i 0.224248π0.224248\pi
992992 −6.82908 −0.216823
993993 7.04958 0.223712
994994 −3.60688 −0.114403
995995 18.2598 0.578873
996996 48.5166 1.53731
997997 −38.4422 −1.21748 −0.608739 0.793371i 0.708324π-0.708324\pi
−0.608739 + 0.793371i 0.708324π0.708324\pi
998998 2.35027 0.0743965
999999 45.7564 1.44767
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 91.2.a.d.1.3 3
3.2 odd 2 819.2.a.i.1.1 3
4.3 odd 2 1456.2.a.t.1.2 3
5.4 even 2 2275.2.a.m.1.1 3
7.2 even 3 637.2.e.j.508.1 6
7.3 odd 6 637.2.e.i.79.1 6
7.4 even 3 637.2.e.j.79.1 6
7.5 odd 6 637.2.e.i.508.1 6
7.6 odd 2 637.2.a.j.1.3 3
8.3 odd 2 5824.2.a.bs.1.2 3
8.5 even 2 5824.2.a.by.1.2 3
13.5 odd 4 1183.2.c.f.337.1 6
13.8 odd 4 1183.2.c.f.337.6 6
13.12 even 2 1183.2.a.i.1.1 3
21.20 even 2 5733.2.a.x.1.1 3
91.90 odd 2 8281.2.a.bg.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.a.d.1.3 3 1.1 even 1 trivial
637.2.a.j.1.3 3 7.6 odd 2
637.2.e.i.79.1 6 7.3 odd 6
637.2.e.i.508.1 6 7.5 odd 6
637.2.e.j.79.1 6 7.4 even 3
637.2.e.j.508.1 6 7.2 even 3
819.2.a.i.1.1 3 3.2 odd 2
1183.2.a.i.1.1 3 13.12 even 2
1183.2.c.f.337.1 6 13.5 odd 4
1183.2.c.f.337.6 6 13.8 odd 4
1456.2.a.t.1.2 3 4.3 odd 2
2275.2.a.m.1.1 3 5.4 even 2
5733.2.a.x.1.1 3 21.20 even 2
5824.2.a.bs.1.2 3 8.3 odd 2
5824.2.a.by.1.2 3 8.5 even 2
8281.2.a.bg.1.1 3 91.90 odd 2