Properties

Label 665.2.a.b.1.1
Level 665665
Weight 22
Character 665.1
Self dual yes
Analytic conductor 5.3105.310
Analytic rank 00
Dimension 11
CM no
Inner twists 11

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [665,2,Mod(1,665)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(665, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("665.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 665=5719 665 = 5 \cdot 7 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 665.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: 5.310051734425.31005173442
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 665.1

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) == q2.00000q2+3.00000q3+2.00000q4+1.00000q56.00000q6+1.00000q7+6.00000q92.00000q103.00000q11+6.00000q12+3.00000q132.00000q14+3.00000q154.00000q16+3.00000q1712.0000q18+1.00000q19+2.00000q20+3.00000q21+6.00000q224.00000q23+1.00000q256.00000q26+9.00000q27+2.00000q28+1.00000q296.00000q30+8.00000q31+8.00000q329.00000q336.00000q34+1.00000q35+12.0000q364.00000q372.00000q38+9.00000q398.00000q416.00000q424.00000q436.00000q44+6.00000q45+8.00000q46+1.00000q4712.0000q48+1.00000q492.00000q50+9.00000q51+6.00000q5212.0000q5318.0000q543.00000q55+3.00000q572.00000q58+6.00000q59+6.00000q606.00000q6116.0000q62+6.00000q638.00000q64+3.00000q65+18.0000q66+4.00000q67+6.00000q6812.0000q692.00000q70+10.0000q73+8.00000q74+3.00000q75+2.00000q763.00000q7718.0000q78+13.0000q794.00000q80+9.00000q81+16.0000q82+4.00000q83+6.00000q84+3.00000q85+8.00000q86+3.00000q876.00000q8912.0000q90+3.00000q918.00000q92+24.0000q932.00000q94+1.00000q95+24.0000q96+5.00000q972.00000q9818.0000q99+O(q100)q-2.00000 q^{2} +3.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} -6.00000 q^{6} +1.00000 q^{7} +6.00000 q^{9} -2.00000 q^{10} -3.00000 q^{11} +6.00000 q^{12} +3.00000 q^{13} -2.00000 q^{14} +3.00000 q^{15} -4.00000 q^{16} +3.00000 q^{17} -12.0000 q^{18} +1.00000 q^{19} +2.00000 q^{20} +3.00000 q^{21} +6.00000 q^{22} -4.00000 q^{23} +1.00000 q^{25} -6.00000 q^{26} +9.00000 q^{27} +2.00000 q^{28} +1.00000 q^{29} -6.00000 q^{30} +8.00000 q^{31} +8.00000 q^{32} -9.00000 q^{33} -6.00000 q^{34} +1.00000 q^{35} +12.0000 q^{36} -4.00000 q^{37} -2.00000 q^{38} +9.00000 q^{39} -8.00000 q^{41} -6.00000 q^{42} -4.00000 q^{43} -6.00000 q^{44} +6.00000 q^{45} +8.00000 q^{46} +1.00000 q^{47} -12.0000 q^{48} +1.00000 q^{49} -2.00000 q^{50} +9.00000 q^{51} +6.00000 q^{52} -12.0000 q^{53} -18.0000 q^{54} -3.00000 q^{55} +3.00000 q^{57} -2.00000 q^{58} +6.00000 q^{59} +6.00000 q^{60} -6.00000 q^{61} -16.0000 q^{62} +6.00000 q^{63} -8.00000 q^{64} +3.00000 q^{65} +18.0000 q^{66} +4.00000 q^{67} +6.00000 q^{68} -12.0000 q^{69} -2.00000 q^{70} +10.0000 q^{73} +8.00000 q^{74} +3.00000 q^{75} +2.00000 q^{76} -3.00000 q^{77} -18.0000 q^{78} +13.0000 q^{79} -4.00000 q^{80} +9.00000 q^{81} +16.0000 q^{82} +4.00000 q^{83} +6.00000 q^{84} +3.00000 q^{85} +8.00000 q^{86} +3.00000 q^{87} -6.00000 q^{89} -12.0000 q^{90} +3.00000 q^{91} -8.00000 q^{92} +24.0000 q^{93} -2.00000 q^{94} +1.00000 q^{95} +24.0000 q^{96} +5.00000 q^{97} -2.00000 q^{98} -18.0000 q^{99} +O(q^{100})

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −2.00000 −1.41421 −0.707107 0.707107i 0.750000π-0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
33 3.00000 1.73205 0.866025 0.500000i 0.166667π-0.166667\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
44 2.00000 1.00000
55 1.00000 0.447214
66 −6.00000 −2.44949
77 1.00000 0.377964
88 0 0
99 6.00000 2.00000
1010 −2.00000 −0.632456
1111 −3.00000 −0.904534 −0.452267 0.891883i 0.649385π-0.649385\pi
−0.452267 + 0.891883i 0.649385π0.649385\pi
1212 6.00000 1.73205
1313 3.00000 0.832050 0.416025 0.909353i 0.363423π-0.363423\pi
0.416025 + 0.909353i 0.363423π0.363423\pi
1414 −2.00000 −0.534522
1515 3.00000 0.774597
1616 −4.00000 −1.00000
1717 3.00000 0.727607 0.363803 0.931476i 0.381478π-0.381478\pi
0.363803 + 0.931476i 0.381478π0.381478\pi
1818 −12.0000 −2.82843
1919 1.00000 0.229416
2020 2.00000 0.447214
2121 3.00000 0.654654
2222 6.00000 1.27920
2323 −4.00000 −0.834058 −0.417029 0.908893i 0.636929π-0.636929\pi
−0.417029 + 0.908893i 0.636929π0.636929\pi
2424 0 0
2525 1.00000 0.200000
2626 −6.00000 −1.17670
2727 9.00000 1.73205
2828 2.00000 0.377964
2929 1.00000 0.185695 0.0928477 0.995680i 0.470403π-0.470403\pi
0.0928477 + 0.995680i 0.470403π0.470403\pi
3030 −6.00000 −1.09545
3131 8.00000 1.43684 0.718421 0.695608i 0.244865π-0.244865\pi
0.718421 + 0.695608i 0.244865π0.244865\pi
3232 8.00000 1.41421
3333 −9.00000 −1.56670
3434 −6.00000 −1.02899
3535 1.00000 0.169031
3636 12.0000 2.00000
3737 −4.00000 −0.657596 −0.328798 0.944400i 0.606644π-0.606644\pi
−0.328798 + 0.944400i 0.606644π0.606644\pi
3838 −2.00000 −0.324443
3939 9.00000 1.44115
4040 0 0
4141 −8.00000 −1.24939 −0.624695 0.780869i 0.714777π-0.714777\pi
−0.624695 + 0.780869i 0.714777π0.714777\pi
4242 −6.00000 −0.925820
4343 −4.00000 −0.609994 −0.304997 0.952353i 0.598656π-0.598656\pi
−0.304997 + 0.952353i 0.598656π0.598656\pi
4444 −6.00000 −0.904534
4545 6.00000 0.894427
4646 8.00000 1.17954
4747 1.00000 0.145865 0.0729325 0.997337i 0.476764π-0.476764\pi
0.0729325 + 0.997337i 0.476764π0.476764\pi
4848 −12.0000 −1.73205
4949 1.00000 0.142857
5050 −2.00000 −0.282843
5151 9.00000 1.26025
5252 6.00000 0.832050
5353 −12.0000 −1.64833 −0.824163 0.566352i 0.808354π-0.808354\pi
−0.824163 + 0.566352i 0.808354π0.808354\pi
5454 −18.0000 −2.44949
5555 −3.00000 −0.404520
5656 0 0
5757 3.00000 0.397360
5858 −2.00000 −0.262613
5959 6.00000 0.781133 0.390567 0.920575i 0.372279π-0.372279\pi
0.390567 + 0.920575i 0.372279π0.372279\pi
6060 6.00000 0.774597
6161 −6.00000 −0.768221 −0.384111 0.923287i 0.625492π-0.625492\pi
−0.384111 + 0.923287i 0.625492π0.625492\pi
6262 −16.0000 −2.03200
6363 6.00000 0.755929
6464 −8.00000 −1.00000
6565 3.00000 0.372104
6666 18.0000 2.21565
6767 4.00000 0.488678 0.244339 0.969690i 0.421429π-0.421429\pi
0.244339 + 0.969690i 0.421429π0.421429\pi
6868 6.00000 0.727607
6969 −12.0000 −1.44463
7070 −2.00000 −0.239046
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 10.0000 1.17041 0.585206 0.810885i 0.301014π-0.301014\pi
0.585206 + 0.810885i 0.301014π0.301014\pi
7474 8.00000 0.929981
7575 3.00000 0.346410
7676 2.00000 0.229416
7777 −3.00000 −0.341882
7878 −18.0000 −2.03810
7979 13.0000 1.46261 0.731307 0.682048i 0.238911π-0.238911\pi
0.731307 + 0.682048i 0.238911π0.238911\pi
8080 −4.00000 −0.447214
8181 9.00000 1.00000
8282 16.0000 1.76690
8383 4.00000 0.439057 0.219529 0.975606i 0.429548π-0.429548\pi
0.219529 + 0.975606i 0.429548π0.429548\pi
8484 6.00000 0.654654
8585 3.00000 0.325396
8686 8.00000 0.862662
8787 3.00000 0.321634
8888 0 0
8989 −6.00000 −0.635999 −0.317999 0.948091i 0.603011π-0.603011\pi
−0.317999 + 0.948091i 0.603011π0.603011\pi
9090 −12.0000 −1.26491
9191 3.00000 0.314485
9292 −8.00000 −0.834058
9393 24.0000 2.48868
9494 −2.00000 −0.206284
9595 1.00000 0.102598
9696 24.0000 2.44949
9797 5.00000 0.507673 0.253837 0.967247i 0.418307π-0.418307\pi
0.253837 + 0.967247i 0.418307π0.418307\pi
9898 −2.00000 −0.202031
9999 −18.0000 −1.80907
100100 2.00000 0.200000
101101 18.0000 1.79107 0.895533 0.444994i 0.146794π-0.146794\pi
0.895533 + 0.444994i 0.146794π0.146794\pi
102102 −18.0000 −1.78227
103103 3.00000 0.295599 0.147799 0.989017i 0.452781π-0.452781\pi
0.147799 + 0.989017i 0.452781π0.452781\pi
104104 0 0
105105 3.00000 0.292770
106106 24.0000 2.33109
107107 −20.0000 −1.93347 −0.966736 0.255774i 0.917670π-0.917670\pi
−0.966736 + 0.255774i 0.917670π0.917670\pi
108108 18.0000 1.73205
109109 7.00000 0.670478 0.335239 0.942133i 0.391183π-0.391183\pi
0.335239 + 0.942133i 0.391183π0.391183\pi
110110 6.00000 0.572078
111111 −12.0000 −1.13899
112112 −4.00000 −0.377964
113113 −20.0000 −1.88144 −0.940721 0.339182i 0.889850π-0.889850\pi
−0.940721 + 0.339182i 0.889850π0.889850\pi
114114 −6.00000 −0.561951
115115 −4.00000 −0.373002
116116 2.00000 0.185695
117117 18.0000 1.66410
118118 −12.0000 −1.10469
119119 3.00000 0.275010
120120 0 0
121121 −2.00000 −0.181818
122122 12.0000 1.08643
123123 −24.0000 −2.16401
124124 16.0000 1.43684
125125 1.00000 0.0894427
126126 −12.0000 −1.06904
127127 −8.00000 −0.709885 −0.354943 0.934888i 0.615500π-0.615500\pi
−0.354943 + 0.934888i 0.615500π0.615500\pi
128128 0 0
129129 −12.0000 −1.05654
130130 −6.00000 −0.526235
131131 14.0000 1.22319 0.611593 0.791173i 0.290529π-0.290529\pi
0.611593 + 0.791173i 0.290529π0.290529\pi
132132 −18.0000 −1.56670
133133 1.00000 0.0867110
134134 −8.00000 −0.691095
135135 9.00000 0.774597
136136 0 0
137137 −12.0000 −1.02523 −0.512615 0.858619i 0.671323π-0.671323\pi
−0.512615 + 0.858619i 0.671323π0.671323\pi
138138 24.0000 2.04302
139139 12.0000 1.01783 0.508913 0.860818i 0.330047π-0.330047\pi
0.508913 + 0.860818i 0.330047π0.330047\pi
140140 2.00000 0.169031
141141 3.00000 0.252646
142142 0 0
143143 −9.00000 −0.752618
144144 −24.0000 −2.00000
145145 1.00000 0.0830455
146146 −20.0000 −1.65521
147147 3.00000 0.247436
148148 −8.00000 −0.657596
149149 −6.00000 −0.491539 −0.245770 0.969328i 0.579041π-0.579041\pi
−0.245770 + 0.969328i 0.579041π0.579041\pi
150150 −6.00000 −0.489898
151151 13.0000 1.05792 0.528962 0.848645i 0.322581π-0.322581\pi
0.528962 + 0.848645i 0.322581π0.322581\pi
152152 0 0
153153 18.0000 1.45521
154154 6.00000 0.483494
155155 8.00000 0.642575
156156 18.0000 1.44115
157157 −18.0000 −1.43656 −0.718278 0.695756i 0.755069π-0.755069\pi
−0.718278 + 0.695756i 0.755069π0.755069\pi
158158 −26.0000 −2.06845
159159 −36.0000 −2.85499
160160 8.00000 0.632456
161161 −4.00000 −0.315244
162162 −18.0000 −1.41421
163163 −22.0000 −1.72317 −0.861586 0.507611i 0.830529π-0.830529\pi
−0.861586 + 0.507611i 0.830529π0.830529\pi
164164 −16.0000 −1.24939
165165 −9.00000 −0.700649
166166 −8.00000 −0.620920
167167 3.00000 0.232147 0.116073 0.993241i 0.462969π-0.462969\pi
0.116073 + 0.993241i 0.462969π0.462969\pi
168168 0 0
169169 −4.00000 −0.307692
170170 −6.00000 −0.460179
171171 6.00000 0.458831
172172 −8.00000 −0.609994
173173 −11.0000 −0.836315 −0.418157 0.908375i 0.637324π-0.637324\pi
−0.418157 + 0.908375i 0.637324π0.637324\pi
174174 −6.00000 −0.454859
175175 1.00000 0.0755929
176176 12.0000 0.904534
177177 18.0000 1.35296
178178 12.0000 0.899438
179179 −20.0000 −1.49487 −0.747435 0.664335i 0.768715π-0.768715\pi
−0.747435 + 0.664335i 0.768715π0.768715\pi
180180 12.0000 0.894427
181181 −20.0000 −1.48659 −0.743294 0.668965i 0.766738π-0.766738\pi
−0.743294 + 0.668965i 0.766738π0.766738\pi
182182 −6.00000 −0.444750
183183 −18.0000 −1.33060
184184 0 0
185185 −4.00000 −0.294086
186186 −48.0000 −3.51953
187187 −9.00000 −0.658145
188188 2.00000 0.145865
189189 9.00000 0.654654
190190 −2.00000 −0.145095
191191 −27.0000 −1.95365 −0.976826 0.214036i 0.931339π-0.931339\pi
−0.976826 + 0.214036i 0.931339π0.931339\pi
192192 −24.0000 −1.73205
193193 20.0000 1.43963 0.719816 0.694165i 0.244226π-0.244226\pi
0.719816 + 0.694165i 0.244226π0.244226\pi
194194 −10.0000 −0.717958
195195 9.00000 0.644503
196196 2.00000 0.142857
197197 −6.00000 −0.427482 −0.213741 0.976890i 0.568565π-0.568565\pi
−0.213741 + 0.976890i 0.568565π0.568565\pi
198198 36.0000 2.55841
199199 18.0000 1.27599 0.637993 0.770042i 0.279765π-0.279765\pi
0.637993 + 0.770042i 0.279765π0.279765\pi
200200 0 0
201201 12.0000 0.846415
202202 −36.0000 −2.53295
203203 1.00000 0.0701862
204204 18.0000 1.26025
205205 −8.00000 −0.558744
206206 −6.00000 −0.418040
207207 −24.0000 −1.66812
208208 −12.0000 −0.832050
209209 −3.00000 −0.207514
210210 −6.00000 −0.414039
211211 −27.0000 −1.85876 −0.929378 0.369129i 0.879656π-0.879656\pi
−0.929378 + 0.369129i 0.879656π0.879656\pi
212212 −24.0000 −1.64833
213213 0 0
214214 40.0000 2.73434
215215 −4.00000 −0.272798
216216 0 0
217217 8.00000 0.543075
218218 −14.0000 −0.948200
219219 30.0000 2.02721
220220 −6.00000 −0.404520
221221 9.00000 0.605406
222222 24.0000 1.61077
223223 −1.00000 −0.0669650 −0.0334825 0.999439i 0.510660π-0.510660\pi
−0.0334825 + 0.999439i 0.510660π0.510660\pi
224224 8.00000 0.534522
225225 6.00000 0.400000
226226 40.0000 2.66076
227227 7.00000 0.464606 0.232303 0.972643i 0.425374π-0.425374\pi
0.232303 + 0.972643i 0.425374π0.425374\pi
228228 6.00000 0.397360
229229 16.0000 1.05731 0.528655 0.848837i 0.322697π-0.322697\pi
0.528655 + 0.848837i 0.322697π0.322697\pi
230230 8.00000 0.527504
231231 −9.00000 −0.592157
232232 0 0
233233 6.00000 0.393073 0.196537 0.980497i 0.437031π-0.437031\pi
0.196537 + 0.980497i 0.437031π0.437031\pi
234234 −36.0000 −2.35339
235235 1.00000 0.0652328
236236 12.0000 0.781133
237237 39.0000 2.53332
238238 −6.00000 −0.388922
239239 23.0000 1.48775 0.743873 0.668321i 0.232987π-0.232987\pi
0.743873 + 0.668321i 0.232987π0.232987\pi
240240 −12.0000 −0.774597
241241 −18.0000 −1.15948 −0.579741 0.814801i 0.696846π-0.696846\pi
−0.579741 + 0.814801i 0.696846π0.696846\pi
242242 4.00000 0.257130
243243 0 0
244244 −12.0000 −0.768221
245245 1.00000 0.0638877
246246 48.0000 3.06037
247247 3.00000 0.190885
248248 0 0
249249 12.0000 0.760469
250250 −2.00000 −0.126491
251251 18.0000 1.13615 0.568075 0.822977i 0.307688π-0.307688\pi
0.568075 + 0.822977i 0.307688π0.307688\pi
252252 12.0000 0.755929
253253 12.0000 0.754434
254254 16.0000 1.00393
255255 9.00000 0.563602
256256 16.0000 1.00000
257257 26.0000 1.62184 0.810918 0.585160i 0.198968π-0.198968\pi
0.810918 + 0.585160i 0.198968π0.198968\pi
258258 24.0000 1.49417
259259 −4.00000 −0.248548
260260 6.00000 0.372104
261261 6.00000 0.371391
262262 −28.0000 −1.72985
263263 12.0000 0.739952 0.369976 0.929041i 0.379366π-0.379366\pi
0.369976 + 0.929041i 0.379366π0.379366\pi
264264 0 0
265265 −12.0000 −0.737154
266266 −2.00000 −0.122628
267267 −18.0000 −1.10158
268268 8.00000 0.488678
269269 −10.0000 −0.609711 −0.304855 0.952399i 0.598608π-0.598608\pi
−0.304855 + 0.952399i 0.598608π0.598608\pi
270270 −18.0000 −1.09545
271271 −20.0000 −1.21491 −0.607457 0.794353i 0.707810π-0.707810\pi
−0.607457 + 0.794353i 0.707810π0.707810\pi
272272 −12.0000 −0.727607
273273 9.00000 0.544705
274274 24.0000 1.44989
275275 −3.00000 −0.180907
276276 −24.0000 −1.44463
277277 −16.0000 −0.961347 −0.480673 0.876900i 0.659608π-0.659608\pi
−0.480673 + 0.876900i 0.659608π0.659608\pi
278278 −24.0000 −1.43942
279279 48.0000 2.87368
280280 0 0
281281 −27.0000 −1.61068 −0.805342 0.592810i 0.798019π-0.798019\pi
−0.805342 + 0.592810i 0.798019π0.798019\pi
282282 −6.00000 −0.357295
283283 −17.0000 −1.01055 −0.505273 0.862960i 0.668608π-0.668608\pi
−0.505273 + 0.862960i 0.668608π0.668608\pi
284284 0 0
285285 3.00000 0.177705
286286 18.0000 1.06436
287287 −8.00000 −0.472225
288288 48.0000 2.82843
289289 −8.00000 −0.470588
290290 −2.00000 −0.117444
291291 15.0000 0.879316
292292 20.0000 1.17041
293293 −23.0000 −1.34367 −0.671837 0.740699i 0.734495π-0.734495\pi
−0.671837 + 0.740699i 0.734495π0.734495\pi
294294 −6.00000 −0.349927
295295 6.00000 0.349334
296296 0 0
297297 −27.0000 −1.56670
298298 12.0000 0.695141
299299 −12.0000 −0.693978
300300 6.00000 0.346410
301301 −4.00000 −0.230556
302302 −26.0000 −1.49613
303303 54.0000 3.10222
304304 −4.00000 −0.229416
305305 −6.00000 −0.343559
306306 −36.0000 −2.05798
307307 −3.00000 −0.171219 −0.0856095 0.996329i 0.527284π-0.527284\pi
−0.0856095 + 0.996329i 0.527284π0.527284\pi
308308 −6.00000 −0.341882
309309 9.00000 0.511992
310310 −16.0000 −0.908739
311311 14.0000 0.793867 0.396934 0.917847i 0.370074π-0.370074\pi
0.396934 + 0.917847i 0.370074π0.370074\pi
312312 0 0
313313 9.00000 0.508710 0.254355 0.967111i 0.418137π-0.418137\pi
0.254355 + 0.967111i 0.418137π0.418137\pi
314314 36.0000 2.03160
315315 6.00000 0.338062
316316 26.0000 1.46261
317317 10.0000 0.561656 0.280828 0.959758i 0.409391π-0.409391\pi
0.280828 + 0.959758i 0.409391π0.409391\pi
318318 72.0000 4.03756
319319 −3.00000 −0.167968
320320 −8.00000 −0.447214
321321 −60.0000 −3.34887
322322 8.00000 0.445823
323323 3.00000 0.166924
324324 18.0000 1.00000
325325 3.00000 0.166410
326326 44.0000 2.43693
327327 21.0000 1.16130
328328 0 0
329329 1.00000 0.0551318
330330 18.0000 0.990867
331331 −24.0000 −1.31916 −0.659580 0.751635i 0.729266π-0.729266\pi
−0.659580 + 0.751635i 0.729266π0.729266\pi
332332 8.00000 0.439057
333333 −24.0000 −1.31519
334334 −6.00000 −0.328305
335335 4.00000 0.218543
336336 −12.0000 −0.654654
337337 32.0000 1.74315 0.871576 0.490261i 0.163099π-0.163099\pi
0.871576 + 0.490261i 0.163099π0.163099\pi
338338 8.00000 0.435143
339339 −60.0000 −3.25875
340340 6.00000 0.325396
341341 −24.0000 −1.29967
342342 −12.0000 −0.648886
343343 1.00000 0.0539949
344344 0 0
345345 −12.0000 −0.646058
346346 22.0000 1.18273
347347 −20.0000 −1.07366 −0.536828 0.843692i 0.680378π-0.680378\pi
−0.536828 + 0.843692i 0.680378π0.680378\pi
348348 6.00000 0.321634
349349 20.0000 1.07058 0.535288 0.844670i 0.320203π-0.320203\pi
0.535288 + 0.844670i 0.320203π0.320203\pi
350350 −2.00000 −0.106904
351351 27.0000 1.44115
352352 −24.0000 −1.27920
353353 −21.0000 −1.11772 −0.558859 0.829263i 0.688761π-0.688761\pi
−0.558859 + 0.829263i 0.688761π0.688761\pi
354354 −36.0000 −1.91338
355355 0 0
356356 −12.0000 −0.635999
357357 9.00000 0.476331
358358 40.0000 2.11407
359359 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
360360 0 0
361361 1.00000 0.0526316
362362 40.0000 2.10235
363363 −6.00000 −0.314918
364364 6.00000 0.314485
365365 10.0000 0.523424
366366 36.0000 1.88175
367367 13.0000 0.678594 0.339297 0.940679i 0.389811π-0.389811\pi
0.339297 + 0.940679i 0.389811π0.389811\pi
368368 16.0000 0.834058
369369 −48.0000 −2.49878
370370 8.00000 0.415900
371371 −12.0000 −0.623009
372372 48.0000 2.48868
373373 4.00000 0.207112 0.103556 0.994624i 0.466978π-0.466978\pi
0.103556 + 0.994624i 0.466978π0.466978\pi
374374 18.0000 0.930758
375375 3.00000 0.154919
376376 0 0
377377 3.00000 0.154508
378378 −18.0000 −0.925820
379379 −4.00000 −0.205466 −0.102733 0.994709i 0.532759π-0.532759\pi
−0.102733 + 0.994709i 0.532759π0.532759\pi
380380 2.00000 0.102598
381381 −24.0000 −1.22956
382382 54.0000 2.76288
383383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
384384 0 0
385385 −3.00000 −0.152894
386386 −40.0000 −2.03595
387387 −24.0000 −1.21999
388388 10.0000 0.507673
389389 9.00000 0.456318 0.228159 0.973624i 0.426729π-0.426729\pi
0.228159 + 0.973624i 0.426729π0.426729\pi
390390 −18.0000 −0.911465
391391 −12.0000 −0.606866
392392 0 0
393393 42.0000 2.11862
394394 12.0000 0.604551
395395 13.0000 0.654101
396396 −36.0000 −1.80907
397397 31.0000 1.55585 0.777923 0.628360i 0.216273π-0.216273\pi
0.777923 + 0.628360i 0.216273π0.216273\pi
398398 −36.0000 −1.80452
399399 3.00000 0.150188
400400 −4.00000 −0.200000
401401 −5.00000 −0.249688 −0.124844 0.992176i 0.539843π-0.539843\pi
−0.124844 + 0.992176i 0.539843π0.539843\pi
402402 −24.0000 −1.19701
403403 24.0000 1.19553
404404 36.0000 1.79107
405405 9.00000 0.447214
406406 −2.00000 −0.0992583
407407 12.0000 0.594818
408408 0 0
409409 −28.0000 −1.38451 −0.692255 0.721653i 0.743383π-0.743383\pi
−0.692255 + 0.721653i 0.743383π0.743383\pi
410410 16.0000 0.790184
411411 −36.0000 −1.77575
412412 6.00000 0.295599
413413 6.00000 0.295241
414414 48.0000 2.35907
415415 4.00000 0.196352
416416 24.0000 1.17670
417417 36.0000 1.76293
418418 6.00000 0.293470
419419 −6.00000 −0.293119 −0.146560 0.989202i 0.546820π-0.546820\pi
−0.146560 + 0.989202i 0.546820π0.546820\pi
420420 6.00000 0.292770
421421 −13.0000 −0.633581 −0.316791 0.948495i 0.602605π-0.602605\pi
−0.316791 + 0.948495i 0.602605π0.602605\pi
422422 54.0000 2.62868
423423 6.00000 0.291730
424424 0 0
425425 3.00000 0.145521
426426 0 0
427427 −6.00000 −0.290360
428428 −40.0000 −1.93347
429429 −27.0000 −1.30357
430430 8.00000 0.385794
431431 19.0000 0.915198 0.457599 0.889159i 0.348710π-0.348710\pi
0.457599 + 0.889159i 0.348710π0.348710\pi
432432 −36.0000 −1.73205
433433 −34.0000 −1.63394 −0.816968 0.576683i 0.804347π-0.804347\pi
−0.816968 + 0.576683i 0.804347π0.804347\pi
434434 −16.0000 −0.768025
435435 3.00000 0.143839
436436 14.0000 0.670478
437437 −4.00000 −0.191346
438438 −60.0000 −2.86691
439439 28.0000 1.33637 0.668184 0.743996i 0.267072π-0.267072\pi
0.668184 + 0.743996i 0.267072π0.267072\pi
440440 0 0
441441 6.00000 0.285714
442442 −18.0000 −0.856173
443443 24.0000 1.14027 0.570137 0.821549i 0.306890π-0.306890\pi
0.570137 + 0.821549i 0.306890π0.306890\pi
444444 −24.0000 −1.13899
445445 −6.00000 −0.284427
446446 2.00000 0.0947027
447447 −18.0000 −0.851371
448448 −8.00000 −0.377964
449449 13.0000 0.613508 0.306754 0.951789i 0.400757π-0.400757\pi
0.306754 + 0.951789i 0.400757π0.400757\pi
450450 −12.0000 −0.565685
451451 24.0000 1.13012
452452 −40.0000 −1.88144
453453 39.0000 1.83238
454454 −14.0000 −0.657053
455455 3.00000 0.140642
456456 0 0
457457 −24.0000 −1.12267 −0.561336 0.827588i 0.689713π-0.689713\pi
−0.561336 + 0.827588i 0.689713π0.689713\pi
458458 −32.0000 −1.49526
459459 27.0000 1.26025
460460 −8.00000 −0.373002
461461 34.0000 1.58354 0.791769 0.610821i 0.209160π-0.209160\pi
0.791769 + 0.610821i 0.209160π0.209160\pi
462462 18.0000 0.837436
463463 6.00000 0.278844 0.139422 0.990233i 0.455476π-0.455476\pi
0.139422 + 0.990233i 0.455476π0.455476\pi
464464 −4.00000 −0.185695
465465 24.0000 1.11297
466466 −12.0000 −0.555889
467467 3.00000 0.138823 0.0694117 0.997588i 0.477888π-0.477888\pi
0.0694117 + 0.997588i 0.477888π0.477888\pi
468468 36.0000 1.66410
469469 4.00000 0.184703
470470 −2.00000 −0.0922531
471471 −54.0000 −2.48819
472472 0 0
473473 12.0000 0.551761
474474 −78.0000 −3.58266
475475 1.00000 0.0458831
476476 6.00000 0.275010
477477 −72.0000 −3.29665
478478 −46.0000 −2.10399
479479 40.0000 1.82765 0.913823 0.406112i 0.133116π-0.133116\pi
0.913823 + 0.406112i 0.133116π0.133116\pi
480480 24.0000 1.09545
481481 −12.0000 −0.547153
482482 36.0000 1.63976
483483 −12.0000 −0.546019
484484 −4.00000 −0.181818
485485 5.00000 0.227038
486486 0 0
487487 −20.0000 −0.906287 −0.453143 0.891438i 0.649697π-0.649697\pi
−0.453143 + 0.891438i 0.649697π0.649697\pi
488488 0 0
489489 −66.0000 −2.98462
490490 −2.00000 −0.0903508
491491 27.0000 1.21849 0.609246 0.792981i 0.291472π-0.291472\pi
0.609246 + 0.792981i 0.291472π0.291472\pi
492492 −48.0000 −2.16401
493493 3.00000 0.135113
494494 −6.00000 −0.269953
495495 −18.0000 −0.809040
496496 −32.0000 −1.43684
497497 0 0
498498 −24.0000 −1.07547
499499 25.0000 1.11915 0.559577 0.828778i 0.310964π-0.310964\pi
0.559577 + 0.828778i 0.310964π0.310964\pi
500500 2.00000 0.0894427
501501 9.00000 0.402090
502502 −36.0000 −1.60676
503503 11.0000 0.490466 0.245233 0.969464i 0.421136π-0.421136\pi
0.245233 + 0.969464i 0.421136π0.421136\pi
504504 0 0
505505 18.0000 0.800989
506506 −24.0000 −1.06693
507507 −12.0000 −0.532939
508508 −16.0000 −0.709885
509509 24.0000 1.06378 0.531891 0.846813i 0.321482π-0.321482\pi
0.531891 + 0.846813i 0.321482π0.321482\pi
510510 −18.0000 −0.797053
511511 10.0000 0.442374
512512 −32.0000 −1.41421
513513 9.00000 0.397360
514514 −52.0000 −2.29362
515515 3.00000 0.132196
516516 −24.0000 −1.05654
517517 −3.00000 −0.131940
518518 8.00000 0.351500
519519 −33.0000 −1.44854
520520 0 0
521521 −2.00000 −0.0876216 −0.0438108 0.999040i 0.513950π-0.513950\pi
−0.0438108 + 0.999040i 0.513950π0.513950\pi
522522 −12.0000 −0.525226
523523 −20.0000 −0.874539 −0.437269 0.899331i 0.644054π-0.644054\pi
−0.437269 + 0.899331i 0.644054π0.644054\pi
524524 28.0000 1.22319
525525 3.00000 0.130931
526526 −24.0000 −1.04645
527527 24.0000 1.04546
528528 36.0000 1.56670
529529 −7.00000 −0.304348
530530 24.0000 1.04249
531531 36.0000 1.56227
532532 2.00000 0.0867110
533533 −24.0000 −1.03956
534534 36.0000 1.55787
535535 −20.0000 −0.864675
536536 0 0
537537 −60.0000 −2.58919
538538 20.0000 0.862261
539539 −3.00000 −0.129219
540540 18.0000 0.774597
541541 19.0000 0.816874 0.408437 0.912787i 0.366074π-0.366074\pi
0.408437 + 0.912787i 0.366074π0.366074\pi
542542 40.0000 1.71815
543543 −60.0000 −2.57485
544544 24.0000 1.02899
545545 7.00000 0.299847
546546 −18.0000 −0.770329
547547 26.0000 1.11168 0.555840 0.831289i 0.312397π-0.312397\pi
0.555840 + 0.831289i 0.312397π0.312397\pi
548548 −24.0000 −1.02523
549549 −36.0000 −1.53644
550550 6.00000 0.255841
551551 1.00000 0.0426014
552552 0 0
553553 13.0000 0.552816
554554 32.0000 1.35955
555555 −12.0000 −0.509372
556556 24.0000 1.01783
557557 40.0000 1.69485 0.847427 0.530912i 0.178150π-0.178150\pi
0.847427 + 0.530912i 0.178150π0.178150\pi
558558 −96.0000 −4.06400
559559 −12.0000 −0.507546
560560 −4.00000 −0.169031
561561 −27.0000 −1.13994
562562 54.0000 2.27785
563563 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
564564 6.00000 0.252646
565565 −20.0000 −0.841406
566566 34.0000 1.42913
567567 9.00000 0.377964
568568 0 0
569569 −38.0000 −1.59304 −0.796521 0.604610i 0.793329π-0.793329\pi
−0.796521 + 0.604610i 0.793329π0.793329\pi
570570 −6.00000 −0.251312
571571 28.0000 1.17176 0.585882 0.810397i 0.300748π-0.300748\pi
0.585882 + 0.810397i 0.300748π0.300748\pi
572572 −18.0000 −0.752618
573573 −81.0000 −3.38382
574574 16.0000 0.667827
575575 −4.00000 −0.166812
576576 −48.0000 −2.00000
577577 −7.00000 −0.291414 −0.145707 0.989328i 0.546546π-0.546546\pi
−0.145707 + 0.989328i 0.546546π0.546546\pi
578578 16.0000 0.665512
579579 60.0000 2.49351
580580 2.00000 0.0830455
581581 4.00000 0.165948
582582 −30.0000 −1.24354
583583 36.0000 1.49097
584584 0 0
585585 18.0000 0.744208
586586 46.0000 1.90024
587587 32.0000 1.32078 0.660391 0.750922i 0.270391π-0.270391\pi
0.660391 + 0.750922i 0.270391π0.270391\pi
588588 6.00000 0.247436
589589 8.00000 0.329634
590590 −12.0000 −0.494032
591591 −18.0000 −0.740421
592592 16.0000 0.657596
593593 13.0000 0.533846 0.266923 0.963718i 0.413993π-0.413993\pi
0.266923 + 0.963718i 0.413993π0.413993\pi
594594 54.0000 2.21565
595595 3.00000 0.122988
596596 −12.0000 −0.491539
597597 54.0000 2.21007
598598 24.0000 0.981433
599599 3.00000 0.122577 0.0612883 0.998120i 0.480479π-0.480479\pi
0.0612883 + 0.998120i 0.480479π0.480479\pi
600600 0 0
601601 20.0000 0.815817 0.407909 0.913023i 0.366258π-0.366258\pi
0.407909 + 0.913023i 0.366258π0.366258\pi
602602 8.00000 0.326056
603603 24.0000 0.977356
604604 26.0000 1.05792
605605 −2.00000 −0.0813116
606606 −108.000 −4.38720
607607 −43.0000 −1.74532 −0.872658 0.488332i 0.837606π-0.837606\pi
−0.872658 + 0.488332i 0.837606π0.837606\pi
608608 8.00000 0.324443
609609 3.00000 0.121566
610610 12.0000 0.485866
611611 3.00000 0.121367
612612 36.0000 1.45521
613613 −12.0000 −0.484675 −0.242338 0.970192i 0.577914π-0.577914\pi
−0.242338 + 0.970192i 0.577914π0.577914\pi
614614 6.00000 0.242140
615615 −24.0000 −0.967773
616616 0 0
617617 2.00000 0.0805170 0.0402585 0.999189i 0.487182π-0.487182\pi
0.0402585 + 0.999189i 0.487182π0.487182\pi
618618 −18.0000 −0.724066
619619 −26.0000 −1.04503 −0.522514 0.852631i 0.675006π-0.675006\pi
−0.522514 + 0.852631i 0.675006π0.675006\pi
620620 16.0000 0.642575
621621 −36.0000 −1.44463
622622 −28.0000 −1.12270
623623 −6.00000 −0.240385
624624 −36.0000 −1.44115
625625 1.00000 0.0400000
626626 −18.0000 −0.719425
627627 −9.00000 −0.359425
628628 −36.0000 −1.43656
629629 −12.0000 −0.478471
630630 −12.0000 −0.478091
631631 −11.0000 −0.437903 −0.218952 0.975736i 0.570264π-0.570264\pi
−0.218952 + 0.975736i 0.570264π0.570264\pi
632632 0 0
633633 −81.0000 −3.21946
634634 −20.0000 −0.794301
635635 −8.00000 −0.317470
636636 −72.0000 −2.85499
637637 3.00000 0.118864
638638 6.00000 0.237542
639639 0 0
640640 0 0
641641 30.0000 1.18493 0.592464 0.805597i 0.298155π-0.298155\pi
0.592464 + 0.805597i 0.298155π0.298155\pi
642642 120.000 4.73602
643643 41.0000 1.61688 0.808441 0.588577i 0.200312π-0.200312\pi
0.808441 + 0.588577i 0.200312π0.200312\pi
644644 −8.00000 −0.315244
645645 −12.0000 −0.472500
646646 −6.00000 −0.236067
647647 −24.0000 −0.943537 −0.471769 0.881722i 0.656384π-0.656384\pi
−0.471769 + 0.881722i 0.656384π0.656384\pi
648648 0 0
649649 −18.0000 −0.706562
650650 −6.00000 −0.235339
651651 24.0000 0.940634
652652 −44.0000 −1.72317
653653 −26.0000 −1.01746 −0.508729 0.860927i 0.669885π-0.669885\pi
−0.508729 + 0.860927i 0.669885π0.669885\pi
654654 −42.0000 −1.64233
655655 14.0000 0.547025
656656 32.0000 1.24939
657657 60.0000 2.34082
658658 −2.00000 −0.0779681
659659 3.00000 0.116863 0.0584317 0.998291i 0.481390π-0.481390\pi
0.0584317 + 0.998291i 0.481390π0.481390\pi
660660 −18.0000 −0.700649
661661 −14.0000 −0.544537 −0.272268 0.962221i 0.587774π-0.587774\pi
−0.272268 + 0.962221i 0.587774π0.587774\pi
662662 48.0000 1.86557
663663 27.0000 1.04859
664664 0 0
665665 1.00000 0.0387783
666666 48.0000 1.85996
667667 −4.00000 −0.154881
668668 6.00000 0.232147
669669 −3.00000 −0.115987
670670 −8.00000 −0.309067
671671 18.0000 0.694882
672672 24.0000 0.925820
673673 −26.0000 −1.00223 −0.501113 0.865382i 0.667076π-0.667076\pi
−0.501113 + 0.865382i 0.667076π0.667076\pi
674674 −64.0000 −2.46519
675675 9.00000 0.346410
676676 −8.00000 −0.307692
677677 3.00000 0.115299 0.0576497 0.998337i 0.481639π-0.481639\pi
0.0576497 + 0.998337i 0.481639π0.481639\pi
678678 120.000 4.60857
679679 5.00000 0.191882
680680 0 0
681681 21.0000 0.804722
682682 48.0000 1.83801
683683 12.0000 0.459167 0.229584 0.973289i 0.426264π-0.426264\pi
0.229584 + 0.973289i 0.426264π0.426264\pi
684684 12.0000 0.458831
685685 −12.0000 −0.458496
686686 −2.00000 −0.0763604
687687 48.0000 1.83131
688688 16.0000 0.609994
689689 −36.0000 −1.37149
690690 24.0000 0.913664
691691 8.00000 0.304334 0.152167 0.988355i 0.451375π-0.451375\pi
0.152167 + 0.988355i 0.451375π0.451375\pi
692692 −22.0000 −0.836315
693693 −18.0000 −0.683763
694694 40.0000 1.51838
695695 12.0000 0.455186
696696 0 0
697697 −24.0000 −0.909065
698698 −40.0000 −1.51402
699699 18.0000 0.680823
700700 2.00000 0.0755929
701701 15.0000 0.566542 0.283271 0.959040i 0.408580π-0.408580\pi
0.283271 + 0.959040i 0.408580π0.408580\pi
702702 −54.0000 −2.03810
703703 −4.00000 −0.150863
704704 24.0000 0.904534
705705 3.00000 0.112987
706706 42.0000 1.58069
707707 18.0000 0.676960
708708 36.0000 1.35296
709709 19.0000 0.713560 0.356780 0.934188i 0.383875π-0.383875\pi
0.356780 + 0.934188i 0.383875π0.383875\pi
710710 0 0
711711 78.0000 2.92523
712712 0 0
713713 −32.0000 −1.19841
714714 −18.0000 −0.673633
715715 −9.00000 −0.336581
716716 −40.0000 −1.49487
717717 69.0000 2.57685
718718 0 0
719719 30.0000 1.11881 0.559406 0.828894i 0.311029π-0.311029\pi
0.559406 + 0.828894i 0.311029π0.311029\pi
720720 −24.0000 −0.894427
721721 3.00000 0.111726
722722 −2.00000 −0.0744323
723723 −54.0000 −2.00828
724724 −40.0000 −1.48659
725725 1.00000 0.0371391
726726 12.0000 0.445362
727727 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
728728 0 0
729729 −27.0000 −1.00000
730730 −20.0000 −0.740233
731731 −12.0000 −0.443836
732732 −36.0000 −1.33060
733733 13.0000 0.480166 0.240083 0.970752i 0.422825π-0.422825\pi
0.240083 + 0.970752i 0.422825π0.422825\pi
734734 −26.0000 −0.959678
735735 3.00000 0.110657
736736 −32.0000 −1.17954
737737 −12.0000 −0.442026
738738 96.0000 3.53381
739739 29.0000 1.06678 0.533391 0.845869i 0.320917π-0.320917\pi
0.533391 + 0.845869i 0.320917π0.320917\pi
740740 −8.00000 −0.294086
741741 9.00000 0.330623
742742 24.0000 0.881068
743743 26.0000 0.953847 0.476924 0.878945i 0.341752π-0.341752\pi
0.476924 + 0.878945i 0.341752π0.341752\pi
744744 0 0
745745 −6.00000 −0.219823
746746 −8.00000 −0.292901
747747 24.0000 0.878114
748748 −18.0000 −0.658145
749749 −20.0000 −0.730784
750750 −6.00000 −0.219089
751751 21.0000 0.766301 0.383150 0.923686i 0.374839π-0.374839\pi
0.383150 + 0.923686i 0.374839π0.374839\pi
752752 −4.00000 −0.145865
753753 54.0000 1.96787
754754 −6.00000 −0.218507
755755 13.0000 0.473118
756756 18.0000 0.654654
757757 −42.0000 −1.52652 −0.763258 0.646094i 0.776401π-0.776401\pi
−0.763258 + 0.646094i 0.776401π0.776401\pi
758758 8.00000 0.290573
759759 36.0000 1.30672
760760 0 0
761761 −20.0000 −0.724999 −0.362500 0.931984i 0.618077π-0.618077\pi
−0.362500 + 0.931984i 0.618077π0.618077\pi
762762 48.0000 1.73886
763763 7.00000 0.253417
764764 −54.0000 −1.95365
765765 18.0000 0.650791
766766 0 0
767767 18.0000 0.649942
768768 48.0000 1.73205
769769 16.0000 0.576975 0.288487 0.957484i 0.406848π-0.406848\pi
0.288487 + 0.957484i 0.406848π0.406848\pi
770770 6.00000 0.216225
771771 78.0000 2.80910
772772 40.0000 1.43963
773773 7.00000 0.251773 0.125886 0.992045i 0.459823π-0.459823\pi
0.125886 + 0.992045i 0.459823π0.459823\pi
774774 48.0000 1.72532
775775 8.00000 0.287368
776776 0 0
777777 −12.0000 −0.430498
778778 −18.0000 −0.645331
779779 −8.00000 −0.286630
780780 18.0000 0.644503
781781 0 0
782782 24.0000 0.858238
783783 9.00000 0.321634
784784 −4.00000 −0.142857
785785 −18.0000 −0.642448
786786 −84.0000 −2.99618
787787 −5.00000 −0.178231 −0.0891154 0.996021i 0.528404π-0.528404\pi
−0.0891154 + 0.996021i 0.528404π0.528404\pi
788788 −12.0000 −0.427482
789789 36.0000 1.28163
790790 −26.0000 −0.925038
791791 −20.0000 −0.711118
792792 0 0
793793 −18.0000 −0.639199
794794 −62.0000 −2.20030
795795 −36.0000 −1.27679
796796 36.0000 1.27599
797797 37.0000 1.31061 0.655304 0.755366i 0.272541π-0.272541\pi
0.655304 + 0.755366i 0.272541π0.272541\pi
798798 −6.00000 −0.212398
799799 3.00000 0.106132
800800 8.00000 0.282843
801801 −36.0000 −1.27200
802802 10.0000 0.353112
803803 −30.0000 −1.05868
804804 24.0000 0.846415
805805 −4.00000 −0.140981
806806 −48.0000 −1.69073
807807 −30.0000 −1.05605
808808 0 0
809809 9.00000 0.316423 0.158212 0.987405i 0.449427π-0.449427\pi
0.158212 + 0.987405i 0.449427π0.449427\pi
810810 −18.0000 −0.632456
811811 −22.0000 −0.772524 −0.386262 0.922389i 0.626234π-0.626234\pi
−0.386262 + 0.922389i 0.626234π0.626234\pi
812812 2.00000 0.0701862
813813 −60.0000 −2.10429
814814 −24.0000 −0.841200
815815 −22.0000 −0.770626
816816 −36.0000 −1.26025
817817 −4.00000 −0.139942
818818 56.0000 1.95799
819819 18.0000 0.628971
820820 −16.0000 −0.558744
821821 25.0000 0.872506 0.436253 0.899824i 0.356305π-0.356305\pi
0.436253 + 0.899824i 0.356305π0.356305\pi
822822 72.0000 2.51129
823823 10.0000 0.348578 0.174289 0.984695i 0.444237π-0.444237\pi
0.174289 + 0.984695i 0.444237π0.444237\pi
824824 0 0
825825 −9.00000 −0.313340
826826 −12.0000 −0.417533
827827 −52.0000 −1.80822 −0.904109 0.427303i 0.859464π-0.859464\pi
−0.904109 + 0.427303i 0.859464π0.859464\pi
828828 −48.0000 −1.66812
829829 −14.0000 −0.486240 −0.243120 0.969996i 0.578171π-0.578171\pi
−0.243120 + 0.969996i 0.578171π0.578171\pi
830830 −8.00000 −0.277684
831831 −48.0000 −1.66510
832832 −24.0000 −0.832050
833833 3.00000 0.103944
834834 −72.0000 −2.49316
835835 3.00000 0.103819
836836 −6.00000 −0.207514
837837 72.0000 2.48868
838838 12.0000 0.414533
839839 42.0000 1.45000 0.725001 0.688748i 0.241839π-0.241839\pi
0.725001 + 0.688748i 0.241839π0.241839\pi
840840 0 0
841841 −28.0000 −0.965517
842842 26.0000 0.896019
843843 −81.0000 −2.78979
844844 −54.0000 −1.85876
845845 −4.00000 −0.137604
846846 −12.0000 −0.412568
847847 −2.00000 −0.0687208
848848 48.0000 1.64833
849849 −51.0000 −1.75032
850850 −6.00000 −0.205798
851851 16.0000 0.548473
852852 0 0
853853 −26.0000 −0.890223 −0.445112 0.895475i 0.646836π-0.646836\pi
−0.445112 + 0.895475i 0.646836π0.646836\pi
854854 12.0000 0.410632
855855 6.00000 0.205196
856856 0 0
857857 6.00000 0.204956 0.102478 0.994735i 0.467323π-0.467323\pi
0.102478 + 0.994735i 0.467323π0.467323\pi
858858 54.0000 1.84353
859859 2.00000 0.0682391 0.0341196 0.999418i 0.489137π-0.489137\pi
0.0341196 + 0.999418i 0.489137π0.489137\pi
860860 −8.00000 −0.272798
861861 −24.0000 −0.817918
862862 −38.0000 −1.29429
863863 6.00000 0.204242 0.102121 0.994772i 0.467437π-0.467437\pi
0.102121 + 0.994772i 0.467437π0.467437\pi
864864 72.0000 2.44949
865865 −11.0000 −0.374011
866866 68.0000 2.31073
867867 −24.0000 −0.815083
868868 16.0000 0.543075
869869 −39.0000 −1.32298
870870 −6.00000 −0.203419
871871 12.0000 0.406604
872872 0 0
873873 30.0000 1.01535
874874 8.00000 0.270604
875875 1.00000 0.0338062
876876 60.0000 2.02721
877877 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
878878 −56.0000 −1.88991
879879 −69.0000 −2.32731
880880 12.0000 0.404520
881881 −58.0000 −1.95407 −0.977035 0.213080i 0.931651π-0.931651\pi
−0.977035 + 0.213080i 0.931651π0.931651\pi
882882 −12.0000 −0.404061
883883 26.0000 0.874970 0.437485 0.899226i 0.355869π-0.355869\pi
0.437485 + 0.899226i 0.355869π0.355869\pi
884884 18.0000 0.605406
885885 18.0000 0.605063
886886 −48.0000 −1.61259
887887 −24.0000 −0.805841 −0.402921 0.915235i 0.632005π-0.632005\pi
−0.402921 + 0.915235i 0.632005π0.632005\pi
888888 0 0
889889 −8.00000 −0.268311
890890 12.0000 0.402241
891891 −27.0000 −0.904534
892892 −2.00000 −0.0669650
893893 1.00000 0.0334637
894894 36.0000 1.20402
895895 −20.0000 −0.668526
896896 0 0
897897 −36.0000 −1.20201
898898 −26.0000 −0.867631
899899 8.00000 0.266815
900900 12.0000 0.400000
901901 −36.0000 −1.19933
902902 −48.0000 −1.59823
903903 −12.0000 −0.399335
904904 0 0
905905 −20.0000 −0.664822
906906 −78.0000 −2.59138
907907 22.0000 0.730498 0.365249 0.930910i 0.380984π-0.380984\pi
0.365249 + 0.930910i 0.380984π0.380984\pi
908908 14.0000 0.464606
909909 108.000 3.58213
910910 −6.00000 −0.198898
911911 −8.00000 −0.265052 −0.132526 0.991180i 0.542309π-0.542309\pi
−0.132526 + 0.991180i 0.542309π0.542309\pi
912912 −12.0000 −0.397360
913913 −12.0000 −0.397142
914914 48.0000 1.58770
915915 −18.0000 −0.595062
916916 32.0000 1.05731
917917 14.0000 0.462321
918918 −54.0000 −1.78227
919919 35.0000 1.15454 0.577272 0.816552i 0.304117π-0.304117\pi
0.577272 + 0.816552i 0.304117π0.304117\pi
920920 0 0
921921 −9.00000 −0.296560
922922 −68.0000 −2.23946
923923 0 0
924924 −18.0000 −0.592157
925925 −4.00000 −0.131519
926926 −12.0000 −0.394344
927927 18.0000 0.591198
928928 8.00000 0.262613
929929 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
930930 −48.0000 −1.57398
931931 1.00000 0.0327737
932932 12.0000 0.393073
933933 42.0000 1.37502
934934 −6.00000 −0.196326
935935 −9.00000 −0.294331
936936 0 0
937937 −37.0000 −1.20874 −0.604369 0.796705i 0.706575π-0.706575\pi
−0.604369 + 0.796705i 0.706575π0.706575\pi
938938 −8.00000 −0.261209
939939 27.0000 0.881112
940940 2.00000 0.0652328
941941 38.0000 1.23876 0.619382 0.785090i 0.287383π-0.287383\pi
0.619382 + 0.785090i 0.287383π0.287383\pi
942942 108.000 3.51883
943943 32.0000 1.04206
944944 −24.0000 −0.781133
945945 9.00000 0.292770
946946 −24.0000 −0.780307
947947 −48.0000 −1.55979 −0.779895 0.625910i 0.784728π-0.784728\pi
−0.779895 + 0.625910i 0.784728π0.784728\pi
948948 78.0000 2.53332
949949 30.0000 0.973841
950950 −2.00000 −0.0648886
951951 30.0000 0.972817
952952 0 0
953953 22.0000 0.712650 0.356325 0.934362i 0.384030π-0.384030\pi
0.356325 + 0.934362i 0.384030π0.384030\pi
954954 144.000 4.66217
955955 −27.0000 −0.873699
956956 46.0000 1.48775
957957 −9.00000 −0.290929
958958 −80.0000 −2.58468
959959 −12.0000 −0.387500
960960 −24.0000 −0.774597
961961 33.0000 1.06452
962962 24.0000 0.773791
963963 −120.000 −3.86695
964964 −36.0000 −1.15948
965965 20.0000 0.643823
966966 24.0000 0.772187
967967 24.0000 0.771788 0.385894 0.922543i 0.373893π-0.373893\pi
0.385894 + 0.922543i 0.373893π0.373893\pi
968968 0 0
969969 9.00000 0.289122
970970 −10.0000 −0.321081
971971 −6.00000 −0.192549 −0.0962746 0.995355i 0.530693π-0.530693\pi
−0.0962746 + 0.995355i 0.530693π0.530693\pi
972972 0 0
973973 12.0000 0.384702
974974 40.0000 1.28168
975975 9.00000 0.288231
976976 24.0000 0.768221
977977 56.0000 1.79160 0.895799 0.444459i 0.146604π-0.146604\pi
0.895799 + 0.444459i 0.146604π0.146604\pi
978978 132.000 4.22089
979979 18.0000 0.575282
980980 2.00000 0.0638877
981981 42.0000 1.34096
982982 −54.0000 −1.72321
983983 9.00000 0.287055 0.143528 0.989646i 0.454155π-0.454155\pi
0.143528 + 0.989646i 0.454155π0.454155\pi
984984 0 0
985985 −6.00000 −0.191176
986986 −6.00000 −0.191079
987987 3.00000 0.0954911
988988 6.00000 0.190885
989989 16.0000 0.508770
990990 36.0000 1.14416
991991 −16.0000 −0.508257 −0.254128 0.967170i 0.581789π-0.581789\pi
−0.254128 + 0.967170i 0.581789π0.581789\pi
992992 64.0000 2.03200
993993 −72.0000 −2.28485
994994 0 0
995995 18.0000 0.570638
996996 24.0000 0.760469
997997 43.0000 1.36182 0.680912 0.732365i 0.261584π-0.261584\pi
0.680912 + 0.732365i 0.261584π0.261584\pi
998998 −50.0000 −1.58272
999999 −36.0000 −1.13899
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 665.2.a.b.1.1 1
3.2 odd 2 5985.2.a.r.1.1 1
5.4 even 2 3325.2.a.i.1.1 1
7.6 odd 2 4655.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
665.2.a.b.1.1 1 1.1 even 1 trivial
3325.2.a.i.1.1 1 5.4 even 2
4655.2.a.a.1.1 1 7.6 odd 2
5985.2.a.r.1.1 1 3.2 odd 2