Properties

Label 3549.2.a.c.1.1
Level 35493549
Weight 22
Character 3549.1
Self dual yes
Analytic conductor 28.33928.339
Analytic rank 11
Dimension 11
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3549,2,Mod(1,3549)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3549, 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("3549.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3549=37132 3549 = 3 \cdot 7 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3549.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: 28.338907677428.3389076774
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 21)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 3549.1

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+1.00000q2+1.00000q31.00000q4+2.00000q5+1.00000q6+1.00000q73.00000q8+1.00000q9+2.00000q104.00000q111.00000q12+1.00000q14+2.00000q151.00000q166.00000q17+1.00000q184.00000q192.00000q20+1.00000q214.00000q223.00000q241.00000q25+1.00000q271.00000q282.00000q29+2.00000q30+5.00000q324.00000q336.00000q34+2.00000q351.00000q366.00000q374.00000q386.00000q402.00000q41+1.00000q424.00000q43+4.00000q44+2.00000q451.00000q48+1.00000q491.00000q506.00000q51+6.00000q53+1.00000q548.00000q553.00000q564.00000q572.00000q5812.0000q592.00000q602.00000q61+1.00000q63+7.00000q644.00000q664.00000q67+6.00000q68+2.00000q703.00000q72+6.00000q736.00000q741.00000q75+4.00000q764.00000q7716.0000q792.00000q80+1.00000q812.00000q82+12.0000q831.00000q8412.0000q854.00000q862.00000q87+12.0000q88+14.0000q89+2.00000q908.00000q95+5.00000q9618.0000q97+1.00000q984.00000q99+O(q100)q+1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} +1.00000 q^{14} +2.00000 q^{15} -1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -2.00000 q^{20} +1.00000 q^{21} -4.00000 q^{22} -3.00000 q^{24} -1.00000 q^{25} +1.00000 q^{27} -1.00000 q^{28} -2.00000 q^{29} +2.00000 q^{30} +5.00000 q^{32} -4.00000 q^{33} -6.00000 q^{34} +2.00000 q^{35} -1.00000 q^{36} -6.00000 q^{37} -4.00000 q^{38} -6.00000 q^{40} -2.00000 q^{41} +1.00000 q^{42} -4.00000 q^{43} +4.00000 q^{44} +2.00000 q^{45} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -6.00000 q^{51} +6.00000 q^{53} +1.00000 q^{54} -8.00000 q^{55} -3.00000 q^{56} -4.00000 q^{57} -2.00000 q^{58} -12.0000 q^{59} -2.00000 q^{60} -2.00000 q^{61} +1.00000 q^{63} +7.00000 q^{64} -4.00000 q^{66} -4.00000 q^{67} +6.00000 q^{68} +2.00000 q^{70} -3.00000 q^{72} +6.00000 q^{73} -6.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} -4.00000 q^{77} -16.0000 q^{79} -2.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +12.0000 q^{83} -1.00000 q^{84} -12.0000 q^{85} -4.00000 q^{86} -2.00000 q^{87} +12.0000 q^{88} +14.0000 q^{89} +2.00000 q^{90} -8.00000 q^{95} +5.00000 q^{96} -18.0000 q^{97} +1.00000 q^{98} -4.00000 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 1.00000 0.707107 0.353553 0.935414i 0.384973π-0.384973\pi
0.353553 + 0.935414i 0.384973π0.384973\pi
33 1.00000 0.577350
44 −1.00000 −0.500000
55 2.00000 0.894427 0.447214 0.894427i 0.352416π-0.352416\pi
0.447214 + 0.894427i 0.352416π0.352416\pi
66 1.00000 0.408248
77 1.00000 0.377964
88 −3.00000 −1.06066
99 1.00000 0.333333
1010 2.00000 0.632456
1111 −4.00000 −1.20605 −0.603023 0.797724i 0.706037π-0.706037\pi
−0.603023 + 0.797724i 0.706037π0.706037\pi
1212 −1.00000 −0.288675
1313 0 0
1414 1.00000 0.267261
1515 2.00000 0.516398
1616 −1.00000 −0.250000
1717 −6.00000 −1.45521 −0.727607 0.685994i 0.759367π-0.759367\pi
−0.727607 + 0.685994i 0.759367π0.759367\pi
1818 1.00000 0.235702
1919 −4.00000 −0.917663 −0.458831 0.888523i 0.651732π-0.651732\pi
−0.458831 + 0.888523i 0.651732π0.651732\pi
2020 −2.00000 −0.447214
2121 1.00000 0.218218
2222 −4.00000 −0.852803
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 −3.00000 −0.612372
2525 −1.00000 −0.200000
2626 0 0
2727 1.00000 0.192450
2828 −1.00000 −0.188982
2929 −2.00000 −0.371391 −0.185695 0.982607i 0.559454π-0.559454\pi
−0.185695 + 0.982607i 0.559454π0.559454\pi
3030 2.00000 0.365148
3131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3232 5.00000 0.883883
3333 −4.00000 −0.696311
3434 −6.00000 −1.02899
3535 2.00000 0.338062
3636 −1.00000 −0.166667
3737 −6.00000 −0.986394 −0.493197 0.869918i 0.664172π-0.664172\pi
−0.493197 + 0.869918i 0.664172π0.664172\pi
3838 −4.00000 −0.648886
3939 0 0
4040 −6.00000 −0.948683
4141 −2.00000 −0.312348 −0.156174 0.987730i 0.549916π-0.549916\pi
−0.156174 + 0.987730i 0.549916π0.549916\pi
4242 1.00000 0.154303
4343 −4.00000 −0.609994 −0.304997 0.952353i 0.598656π-0.598656\pi
−0.304997 + 0.952353i 0.598656π0.598656\pi
4444 4.00000 0.603023
4545 2.00000 0.298142
4646 0 0
4747 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4848 −1.00000 −0.144338
4949 1.00000 0.142857
5050 −1.00000 −0.141421
5151 −6.00000 −0.840168
5252 0 0
5353 6.00000 0.824163 0.412082 0.911147i 0.364802π-0.364802\pi
0.412082 + 0.911147i 0.364802π0.364802\pi
5454 1.00000 0.136083
5555 −8.00000 −1.07872
5656 −3.00000 −0.400892
5757 −4.00000 −0.529813
5858 −2.00000 −0.262613
5959 −12.0000 −1.56227 −0.781133 0.624364i 0.785358π-0.785358\pi
−0.781133 + 0.624364i 0.785358π0.785358\pi
6060 −2.00000 −0.258199
6161 −2.00000 −0.256074 −0.128037 0.991769i 0.540868π-0.540868\pi
−0.128037 + 0.991769i 0.540868π0.540868\pi
6262 0 0
6363 1.00000 0.125988
6464 7.00000 0.875000
6565 0 0
6666 −4.00000 −0.492366
6767 −4.00000 −0.488678 −0.244339 0.969690i 0.578571π-0.578571\pi
−0.244339 + 0.969690i 0.578571π0.578571\pi
6868 6.00000 0.727607
6969 0 0
7070 2.00000 0.239046
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 −3.00000 −0.353553
7373 6.00000 0.702247 0.351123 0.936329i 0.385800π-0.385800\pi
0.351123 + 0.936329i 0.385800π0.385800\pi
7474 −6.00000 −0.697486
7575 −1.00000 −0.115470
7676 4.00000 0.458831
7777 −4.00000 −0.455842
7878 0 0
7979 −16.0000 −1.80014 −0.900070 0.435745i 0.856485π-0.856485\pi
−0.900070 + 0.435745i 0.856485π0.856485\pi
8080 −2.00000 −0.223607
8181 1.00000 0.111111
8282 −2.00000 −0.220863
8383 12.0000 1.31717 0.658586 0.752506i 0.271155π-0.271155\pi
0.658586 + 0.752506i 0.271155π0.271155\pi
8484 −1.00000 −0.109109
8585 −12.0000 −1.30158
8686 −4.00000 −0.431331
8787 −2.00000 −0.214423
8888 12.0000 1.27920
8989 14.0000 1.48400 0.741999 0.670402i 0.233878π-0.233878\pi
0.741999 + 0.670402i 0.233878π0.233878\pi
9090 2.00000 0.210819
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 −8.00000 −0.820783
9696 5.00000 0.510310
9797 −18.0000 −1.82762 −0.913812 0.406138i 0.866875π-0.866875\pi
−0.913812 + 0.406138i 0.866875π0.866875\pi
9898 1.00000 0.101015
9999 −4.00000 −0.402015
100100 1.00000 0.100000
101101 14.0000 1.39305 0.696526 0.717532i 0.254728π-0.254728\pi
0.696526 + 0.717532i 0.254728π0.254728\pi
102102 −6.00000 −0.594089
103103 8.00000 0.788263 0.394132 0.919054i 0.371045π-0.371045\pi
0.394132 + 0.919054i 0.371045π0.371045\pi
104104 0 0
105105 2.00000 0.195180
106106 6.00000 0.582772
107107 4.00000 0.386695 0.193347 0.981130i 0.438066π-0.438066\pi
0.193347 + 0.981130i 0.438066π0.438066\pi
108108 −1.00000 −0.0962250
109109 18.0000 1.72409 0.862044 0.506834i 0.169184π-0.169184\pi
0.862044 + 0.506834i 0.169184π0.169184\pi
110110 −8.00000 −0.762770
111111 −6.00000 −0.569495
112112 −1.00000 −0.0944911
113113 −14.0000 −1.31701 −0.658505 0.752577i 0.728811π-0.728811\pi
−0.658505 + 0.752577i 0.728811π0.728811\pi
114114 −4.00000 −0.374634
115115 0 0
116116 2.00000 0.185695
117117 0 0
118118 −12.0000 −1.10469
119119 −6.00000 −0.550019
120120 −6.00000 −0.547723
121121 5.00000 0.454545
122122 −2.00000 −0.181071
123123 −2.00000 −0.180334
124124 0 0
125125 −12.0000 −1.07331
126126 1.00000 0.0890871
127127 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
128128 −3.00000 −0.265165
129129 −4.00000 −0.352180
130130 0 0
131131 4.00000 0.349482 0.174741 0.984614i 0.444091π-0.444091\pi
0.174741 + 0.984614i 0.444091π0.444091\pi
132132 4.00000 0.348155
133133 −4.00000 −0.346844
134134 −4.00000 −0.345547
135135 2.00000 0.172133
136136 18.0000 1.54349
137137 6.00000 0.512615 0.256307 0.966595i 0.417494π-0.417494\pi
0.256307 + 0.966595i 0.417494π0.417494\pi
138138 0 0
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 0 0
142142 0 0
143143 0 0
144144 −1.00000 −0.0833333
145145 −4.00000 −0.332182
146146 6.00000 0.496564
147147 1.00000 0.0824786
148148 6.00000 0.493197
149149 −6.00000 −0.491539 −0.245770 0.969328i 0.579041π-0.579041\pi
−0.245770 + 0.969328i 0.579041π0.579041\pi
150150 −1.00000 −0.0816497
151151 −8.00000 −0.651031 −0.325515 0.945537i 0.605538π-0.605538\pi
−0.325515 + 0.945537i 0.605538π0.605538\pi
152152 12.0000 0.973329
153153 −6.00000 −0.485071
154154 −4.00000 −0.322329
155155 0 0
156156 0 0
157157 −2.00000 −0.159617 −0.0798087 0.996810i 0.525431π-0.525431\pi
−0.0798087 + 0.996810i 0.525431π0.525431\pi
158158 −16.0000 −1.27289
159159 6.00000 0.475831
160160 10.0000 0.790569
161161 0 0
162162 1.00000 0.0785674
163163 −4.00000 −0.313304 −0.156652 0.987654i 0.550070π-0.550070\pi
−0.156652 + 0.987654i 0.550070π0.550070\pi
164164 2.00000 0.156174
165165 −8.00000 −0.622799
166166 12.0000 0.931381
167167 8.00000 0.619059 0.309529 0.950890i 0.399829π-0.399829\pi
0.309529 + 0.950890i 0.399829π0.399829\pi
168168 −3.00000 −0.231455
169169 0 0
170170 −12.0000 −0.920358
171171 −4.00000 −0.305888
172172 4.00000 0.304997
173173 −10.0000 −0.760286 −0.380143 0.924928i 0.624125π-0.624125\pi
−0.380143 + 0.924928i 0.624125π0.624125\pi
174174 −2.00000 −0.151620
175175 −1.00000 −0.0755929
176176 4.00000 0.301511
177177 −12.0000 −0.901975
178178 14.0000 1.04934
179179 −4.00000 −0.298974 −0.149487 0.988764i 0.547762π-0.547762\pi
−0.149487 + 0.988764i 0.547762π0.547762\pi
180180 −2.00000 −0.149071
181181 −26.0000 −1.93256 −0.966282 0.257485i 0.917106π-0.917106\pi
−0.966282 + 0.257485i 0.917106π0.917106\pi
182182 0 0
183183 −2.00000 −0.147844
184184 0 0
185185 −12.0000 −0.882258
186186 0 0
187187 24.0000 1.75505
188188 0 0
189189 1.00000 0.0727393
190190 −8.00000 −0.580381
191191 −8.00000 −0.578860 −0.289430 0.957199i 0.593466π-0.593466\pi
−0.289430 + 0.957199i 0.593466π0.593466\pi
192192 7.00000 0.505181
193193 −2.00000 −0.143963 −0.0719816 0.997406i 0.522932π-0.522932\pi
−0.0719816 + 0.997406i 0.522932π0.522932\pi
194194 −18.0000 −1.29232
195195 0 0
196196 −1.00000 −0.0714286
197197 −22.0000 −1.56744 −0.783718 0.621117i 0.786679π-0.786679\pi
−0.783718 + 0.621117i 0.786679π0.786679\pi
198198 −4.00000 −0.284268
199199 24.0000 1.70131 0.850657 0.525720i 0.176204π-0.176204\pi
0.850657 + 0.525720i 0.176204π0.176204\pi
200200 3.00000 0.212132
201201 −4.00000 −0.282138
202202 14.0000 0.985037
203203 −2.00000 −0.140372
204204 6.00000 0.420084
205205 −4.00000 −0.279372
206206 8.00000 0.557386
207207 0 0
208208 0 0
209209 16.0000 1.10674
210210 2.00000 0.138013
211211 4.00000 0.275371 0.137686 0.990476i 0.456034π-0.456034\pi
0.137686 + 0.990476i 0.456034π0.456034\pi
212212 −6.00000 −0.412082
213213 0 0
214214 4.00000 0.273434
215215 −8.00000 −0.545595
216216 −3.00000 −0.204124
217217 0 0
218218 18.0000 1.21911
219219 6.00000 0.405442
220220 8.00000 0.539360
221221 0 0
222222 −6.00000 −0.402694
223223 −16.0000 −1.07144 −0.535720 0.844396i 0.679960π-0.679960\pi
−0.535720 + 0.844396i 0.679960π0.679960\pi
224224 5.00000 0.334077
225225 −1.00000 −0.0666667
226226 −14.0000 −0.931266
227227 12.0000 0.796468 0.398234 0.917284i 0.369623π-0.369623\pi
0.398234 + 0.917284i 0.369623π0.369623\pi
228228 4.00000 0.264906
229229 10.0000 0.660819 0.330409 0.943838i 0.392813π-0.392813\pi
0.330409 + 0.943838i 0.392813π0.392813\pi
230230 0 0
231231 −4.00000 −0.263181
232232 6.00000 0.393919
233233 −6.00000 −0.393073 −0.196537 0.980497i 0.562969π-0.562969\pi
−0.196537 + 0.980497i 0.562969π0.562969\pi
234234 0 0
235235 0 0
236236 12.0000 0.781133
237237 −16.0000 −1.03931
238238 −6.00000 −0.388922
239239 −24.0000 −1.55243 −0.776215 0.630468i 0.782863π-0.782863\pi
−0.776215 + 0.630468i 0.782863π0.782863\pi
240240 −2.00000 −0.129099
241241 −2.00000 −0.128831 −0.0644157 0.997923i 0.520518π-0.520518\pi
−0.0644157 + 0.997923i 0.520518π0.520518\pi
242242 5.00000 0.321412
243243 1.00000 0.0641500
244244 2.00000 0.128037
245245 2.00000 0.127775
246246 −2.00000 −0.127515
247247 0 0
248248 0 0
249249 12.0000 0.760469
250250 −12.0000 −0.758947
251251 −20.0000 −1.26239 −0.631194 0.775625i 0.717435π-0.717435\pi
−0.631194 + 0.775625i 0.717435π0.717435\pi
252252 −1.00000 −0.0629941
253253 0 0
254254 0 0
255255 −12.0000 −0.751469
256256 −17.0000 −1.06250
257257 26.0000 1.62184 0.810918 0.585160i 0.198968π-0.198968\pi
0.810918 + 0.585160i 0.198968π0.198968\pi
258258 −4.00000 −0.249029
259259 −6.00000 −0.372822
260260 0 0
261261 −2.00000 −0.123797
262262 4.00000 0.247121
263263 16.0000 0.986602 0.493301 0.869859i 0.335790π-0.335790\pi
0.493301 + 0.869859i 0.335790π0.335790\pi
264264 12.0000 0.738549
265265 12.0000 0.737154
266266 −4.00000 −0.245256
267267 14.0000 0.856786
268268 4.00000 0.244339
269269 6.00000 0.365826 0.182913 0.983129i 0.441447π-0.441447\pi
0.182913 + 0.983129i 0.441447π0.441447\pi
270270 2.00000 0.121716
271271 −16.0000 −0.971931 −0.485965 0.873978i 0.661532π-0.661532\pi
−0.485965 + 0.873978i 0.661532π0.661532\pi
272272 6.00000 0.363803
273273 0 0
274274 6.00000 0.362473
275275 4.00000 0.241209
276276 0 0
277277 22.0000 1.32185 0.660926 0.750451i 0.270164π-0.270164\pi
0.660926 + 0.750451i 0.270164π0.270164\pi
278278 12.0000 0.719712
279279 0 0
280280 −6.00000 −0.358569
281281 22.0000 1.31241 0.656205 0.754583i 0.272161π-0.272161\pi
0.656205 + 0.754583i 0.272161π0.272161\pi
282282 0 0
283283 −20.0000 −1.18888 −0.594438 0.804141i 0.702626π-0.702626\pi
−0.594438 + 0.804141i 0.702626π0.702626\pi
284284 0 0
285285 −8.00000 −0.473879
286286 0 0
287287 −2.00000 −0.118056
288288 5.00000 0.294628
289289 19.0000 1.11765
290290 −4.00000 −0.234888
291291 −18.0000 −1.05518
292292 −6.00000 −0.351123
293293 −14.0000 −0.817889 −0.408944 0.912559i 0.634103π-0.634103\pi
−0.408944 + 0.912559i 0.634103π0.634103\pi
294294 1.00000 0.0583212
295295 −24.0000 −1.39733
296296 18.0000 1.04623
297297 −4.00000 −0.232104
298298 −6.00000 −0.347571
299299 0 0
300300 1.00000 0.0577350
301301 −4.00000 −0.230556
302302 −8.00000 −0.460348
303303 14.0000 0.804279
304304 4.00000 0.229416
305305 −4.00000 −0.229039
306306 −6.00000 −0.342997
307307 −4.00000 −0.228292 −0.114146 0.993464i 0.536413π-0.536413\pi
−0.114146 + 0.993464i 0.536413π0.536413\pi
308308 4.00000 0.227921
309309 8.00000 0.455104
310310 0 0
311311 −24.0000 −1.36092 −0.680458 0.732787i 0.738219π-0.738219\pi
−0.680458 + 0.732787i 0.738219π0.738219\pi
312312 0 0
313313 26.0000 1.46961 0.734803 0.678280i 0.237274π-0.237274\pi
0.734803 + 0.678280i 0.237274π0.237274\pi
314314 −2.00000 −0.112867
315315 2.00000 0.112687
316316 16.0000 0.900070
317317 18.0000 1.01098 0.505490 0.862832i 0.331312π-0.331312\pi
0.505490 + 0.862832i 0.331312π0.331312\pi
318318 6.00000 0.336463
319319 8.00000 0.447914
320320 14.0000 0.782624
321321 4.00000 0.223258
322322 0 0
323323 24.0000 1.33540
324324 −1.00000 −0.0555556
325325 0 0
326326 −4.00000 −0.221540
327327 18.0000 0.995402
328328 6.00000 0.331295
329329 0 0
330330 −8.00000 −0.440386
331331 4.00000 0.219860 0.109930 0.993939i 0.464937π-0.464937\pi
0.109930 + 0.993939i 0.464937π0.464937\pi
332332 −12.0000 −0.658586
333333 −6.00000 −0.328798
334334 8.00000 0.437741
335335 −8.00000 −0.437087
336336 −1.00000 −0.0545545
337337 −14.0000 −0.762629 −0.381314 0.924445i 0.624528π-0.624528\pi
−0.381314 + 0.924445i 0.624528π0.624528\pi
338338 0 0
339339 −14.0000 −0.760376
340340 12.0000 0.650791
341341 0 0
342342 −4.00000 −0.216295
343343 1.00000 0.0539949
344344 12.0000 0.646997
345345 0 0
346346 −10.0000 −0.537603
347347 −28.0000 −1.50312 −0.751559 0.659665i 0.770698π-0.770698\pi
−0.751559 + 0.659665i 0.770698π0.770698\pi
348348 2.00000 0.107211
349349 2.00000 0.107058 0.0535288 0.998566i 0.482953π-0.482953\pi
0.0535288 + 0.998566i 0.482953π0.482953\pi
350350 −1.00000 −0.0534522
351351 0 0
352352 −20.0000 −1.06600
353353 −10.0000 −0.532246 −0.266123 0.963939i 0.585743π-0.585743\pi
−0.266123 + 0.963939i 0.585743π0.585743\pi
354354 −12.0000 −0.637793
355355 0 0
356356 −14.0000 −0.741999
357357 −6.00000 −0.317554
358358 −4.00000 −0.211407
359359 −32.0000 −1.68890 −0.844448 0.535638i 0.820071π-0.820071\pi
−0.844448 + 0.535638i 0.820071π0.820071\pi
360360 −6.00000 −0.316228
361361 −3.00000 −0.157895
362362 −26.0000 −1.36653
363363 5.00000 0.262432
364364 0 0
365365 12.0000 0.628109
366366 −2.00000 −0.104542
367367 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
368368 0 0
369369 −2.00000 −0.104116
370370 −12.0000 −0.623850
371371 6.00000 0.311504
372372 0 0
373373 −10.0000 −0.517780 −0.258890 0.965907i 0.583357π-0.583357\pi
−0.258890 + 0.965907i 0.583357π0.583357\pi
374374 24.0000 1.24101
375375 −12.0000 −0.619677
376376 0 0
377377 0 0
378378 1.00000 0.0514344
379379 −12.0000 −0.616399 −0.308199 0.951322i 0.599726π-0.599726\pi
−0.308199 + 0.951322i 0.599726π0.599726\pi
380380 8.00000 0.410391
381381 0 0
382382 −8.00000 −0.409316
383383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
384384 −3.00000 −0.153093
385385 −8.00000 −0.407718
386386 −2.00000 −0.101797
387387 −4.00000 −0.203331
388388 18.0000 0.913812
389389 6.00000 0.304212 0.152106 0.988364i 0.451394π-0.451394\pi
0.152106 + 0.988364i 0.451394π0.451394\pi
390390 0 0
391391 0 0
392392 −3.00000 −0.151523
393393 4.00000 0.201773
394394 −22.0000 −1.10834
395395 −32.0000 −1.61009
396396 4.00000 0.201008
397397 18.0000 0.903394 0.451697 0.892171i 0.350819π-0.350819\pi
0.451697 + 0.892171i 0.350819π0.350819\pi
398398 24.0000 1.20301
399399 −4.00000 −0.200250
400400 1.00000 0.0500000
401401 30.0000 1.49813 0.749064 0.662497i 0.230503π-0.230503\pi
0.749064 + 0.662497i 0.230503π0.230503\pi
402402 −4.00000 −0.199502
403403 0 0
404404 −14.0000 −0.696526
405405 2.00000 0.0993808
406406 −2.00000 −0.0992583
407407 24.0000 1.18964
408408 18.0000 0.891133
409409 22.0000 1.08783 0.543915 0.839140i 0.316941π-0.316941\pi
0.543915 + 0.839140i 0.316941π0.316941\pi
410410 −4.00000 −0.197546
411411 6.00000 0.295958
412412 −8.00000 −0.394132
413413 −12.0000 −0.590481
414414 0 0
415415 24.0000 1.17811
416416 0 0
417417 12.0000 0.587643
418418 16.0000 0.782586
419419 −12.0000 −0.586238 −0.293119 0.956076i 0.594693π-0.594693\pi
−0.293119 + 0.956076i 0.594693π0.594693\pi
420420 −2.00000 −0.0975900
421421 −38.0000 −1.85201 −0.926003 0.377515i 0.876779π-0.876779\pi
−0.926003 + 0.377515i 0.876779π0.876779\pi
422422 4.00000 0.194717
423423 0 0
424424 −18.0000 −0.874157
425425 6.00000 0.291043
426426 0 0
427427 −2.00000 −0.0967868
428428 −4.00000 −0.193347
429429 0 0
430430 −8.00000 −0.385794
431431 24.0000 1.15604 0.578020 0.816023i 0.303826π-0.303826\pi
0.578020 + 0.816023i 0.303826π0.303826\pi
432432 −1.00000 −0.0481125
433433 −14.0000 −0.672797 −0.336399 0.941720i 0.609209π-0.609209\pi
−0.336399 + 0.941720i 0.609209π0.609209\pi
434434 0 0
435435 −4.00000 −0.191785
436436 −18.0000 −0.862044
437437 0 0
438438 6.00000 0.286691
439439 −24.0000 −1.14546 −0.572729 0.819745i 0.694115π-0.694115\pi
−0.572729 + 0.819745i 0.694115π0.694115\pi
440440 24.0000 1.14416
441441 1.00000 0.0476190
442442 0 0
443443 36.0000 1.71041 0.855206 0.518289i 0.173431π-0.173431\pi
0.855206 + 0.518289i 0.173431π0.173431\pi
444444 6.00000 0.284747
445445 28.0000 1.32733
446446 −16.0000 −0.757622
447447 −6.00000 −0.283790
448448 7.00000 0.330719
449449 30.0000 1.41579 0.707894 0.706319i 0.249646π-0.249646\pi
0.707894 + 0.706319i 0.249646π0.249646\pi
450450 −1.00000 −0.0471405
451451 8.00000 0.376705
452452 14.0000 0.658505
453453 −8.00000 −0.375873
454454 12.0000 0.563188
455455 0 0
456456 12.0000 0.561951
457457 −10.0000 −0.467780 −0.233890 0.972263i 0.575146π-0.575146\pi
−0.233890 + 0.972263i 0.575146π0.575146\pi
458458 10.0000 0.467269
459459 −6.00000 −0.280056
460460 0 0
461461 10.0000 0.465746 0.232873 0.972507i 0.425187π-0.425187\pi
0.232873 + 0.972507i 0.425187π0.425187\pi
462462 −4.00000 −0.186097
463463 −16.0000 −0.743583 −0.371792 0.928316i 0.621256π-0.621256\pi
−0.371792 + 0.928316i 0.621256π0.621256\pi
464464 2.00000 0.0928477
465465 0 0
466466 −6.00000 −0.277945
467467 36.0000 1.66588 0.832941 0.553362i 0.186655π-0.186655\pi
0.832941 + 0.553362i 0.186655π0.186655\pi
468468 0 0
469469 −4.00000 −0.184703
470470 0 0
471471 −2.00000 −0.0921551
472472 36.0000 1.65703
473473 16.0000 0.735681
474474 −16.0000 −0.734904
475475 4.00000 0.183533
476476 6.00000 0.275010
477477 6.00000 0.274721
478478 −24.0000 −1.09773
479479 16.0000 0.731059 0.365529 0.930800i 0.380888π-0.380888\pi
0.365529 + 0.930800i 0.380888π0.380888\pi
480480 10.0000 0.456435
481481 0 0
482482 −2.00000 −0.0910975
483483 0 0
484484 −5.00000 −0.227273
485485 −36.0000 −1.63468
486486 1.00000 0.0453609
487487 8.00000 0.362515 0.181257 0.983436i 0.441983π-0.441983\pi
0.181257 + 0.983436i 0.441983π0.441983\pi
488488 6.00000 0.271607
489489 −4.00000 −0.180886
490490 2.00000 0.0903508
491491 20.0000 0.902587 0.451294 0.892375i 0.350963π-0.350963\pi
0.451294 + 0.892375i 0.350963π0.350963\pi
492492 2.00000 0.0901670
493493 12.0000 0.540453
494494 0 0
495495 −8.00000 −0.359573
496496 0 0
497497 0 0
498498 12.0000 0.537733
499499 −4.00000 −0.179065 −0.0895323 0.995984i 0.528537π-0.528537\pi
−0.0895323 + 0.995984i 0.528537π0.528537\pi
500500 12.0000 0.536656
501501 8.00000 0.357414
502502 −20.0000 −0.892644
503503 24.0000 1.07011 0.535054 0.844818i 0.320291π-0.320291\pi
0.535054 + 0.844818i 0.320291π0.320291\pi
504504 −3.00000 −0.133631
505505 28.0000 1.24598
506506 0 0
507507 0 0
508508 0 0
509509 10.0000 0.443242 0.221621 0.975133i 0.428865π-0.428865\pi
0.221621 + 0.975133i 0.428865π0.428865\pi
510510 −12.0000 −0.531369
511511 6.00000 0.265424
512512 −11.0000 −0.486136
513513 −4.00000 −0.176604
514514 26.0000 1.14681
515515 16.0000 0.705044
516516 4.00000 0.176090
517517 0 0
518518 −6.00000 −0.263625
519519 −10.0000 −0.438951
520520 0 0
521521 18.0000 0.788594 0.394297 0.918983i 0.370988π-0.370988\pi
0.394297 + 0.918983i 0.370988π0.370988\pi
522522 −2.00000 −0.0875376
523523 −20.0000 −0.874539 −0.437269 0.899331i 0.644054π-0.644054\pi
−0.437269 + 0.899331i 0.644054π0.644054\pi
524524 −4.00000 −0.174741
525525 −1.00000 −0.0436436
526526 16.0000 0.697633
527527 0 0
528528 4.00000 0.174078
529529 −23.0000 −1.00000
530530 12.0000 0.521247
531531 −12.0000 −0.520756
532532 4.00000 0.173422
533533 0 0
534534 14.0000 0.605839
535535 8.00000 0.345870
536536 12.0000 0.518321
537537 −4.00000 −0.172613
538538 6.00000 0.258678
539539 −4.00000 −0.172292
540540 −2.00000 −0.0860663
541541 34.0000 1.46177 0.730887 0.682498i 0.239107π-0.239107\pi
0.730887 + 0.682498i 0.239107π0.239107\pi
542542 −16.0000 −0.687259
543543 −26.0000 −1.11577
544544 −30.0000 −1.28624
545545 36.0000 1.54207
546546 0 0
547547 4.00000 0.171028 0.0855138 0.996337i 0.472747π-0.472747\pi
0.0855138 + 0.996337i 0.472747π0.472747\pi
548548 −6.00000 −0.256307
549549 −2.00000 −0.0853579
550550 4.00000 0.170561
551551 8.00000 0.340811
552552 0 0
553553 −16.0000 −0.680389
554554 22.0000 0.934690
555555 −12.0000 −0.509372
556556 −12.0000 −0.508913
557557 2.00000 0.0847427 0.0423714 0.999102i 0.486509π-0.486509\pi
0.0423714 + 0.999102i 0.486509π0.486509\pi
558558 0 0
559559 0 0
560560 −2.00000 −0.0845154
561561 24.0000 1.01328
562562 22.0000 0.928014
563563 4.00000 0.168580 0.0842900 0.996441i 0.473138π-0.473138\pi
0.0842900 + 0.996441i 0.473138π0.473138\pi
564564 0 0
565565 −28.0000 −1.17797
566566 −20.0000 −0.840663
567567 1.00000 0.0419961
568568 0 0
569569 10.0000 0.419222 0.209611 0.977785i 0.432780π-0.432780\pi
0.209611 + 0.977785i 0.432780π0.432780\pi
570570 −8.00000 −0.335083
571571 −4.00000 −0.167395 −0.0836974 0.996491i 0.526673π-0.526673\pi
−0.0836974 + 0.996491i 0.526673π0.526673\pi
572572 0 0
573573 −8.00000 −0.334205
574574 −2.00000 −0.0834784
575575 0 0
576576 7.00000 0.291667
577577 −34.0000 −1.41544 −0.707719 0.706494i 0.750276π-0.750276\pi
−0.707719 + 0.706494i 0.750276π0.750276\pi
578578 19.0000 0.790296
579579 −2.00000 −0.0831172
580580 4.00000 0.166091
581581 12.0000 0.497844
582582 −18.0000 −0.746124
583583 −24.0000 −0.993978
584584 −18.0000 −0.744845
585585 0 0
586586 −14.0000 −0.578335
587587 −28.0000 −1.15568 −0.577842 0.816149i 0.696105π-0.696105\pi
−0.577842 + 0.816149i 0.696105π0.696105\pi
588588 −1.00000 −0.0412393
589589 0 0
590590 −24.0000 −0.988064
591591 −22.0000 −0.904959
592592 6.00000 0.246598
593593 6.00000 0.246390 0.123195 0.992382i 0.460686π-0.460686\pi
0.123195 + 0.992382i 0.460686π0.460686\pi
594594 −4.00000 −0.164122
595595 −12.0000 −0.491952
596596 6.00000 0.245770
597597 24.0000 0.982255
598598 0 0
599599 48.0000 1.96123 0.980613 0.195952i 0.0627798π-0.0627798\pi
0.980613 + 0.195952i 0.0627798π0.0627798\pi
600600 3.00000 0.122474
601601 −6.00000 −0.244745 −0.122373 0.992484i 0.539050π-0.539050\pi
−0.122373 + 0.992484i 0.539050π0.539050\pi
602602 −4.00000 −0.163028
603603 −4.00000 −0.162893
604604 8.00000 0.325515
605605 10.0000 0.406558
606606 14.0000 0.568711
607607 −16.0000 −0.649420 −0.324710 0.945814i 0.605267π-0.605267\pi
−0.324710 + 0.945814i 0.605267π0.605267\pi
608608 −20.0000 −0.811107
609609 −2.00000 −0.0810441
610610 −4.00000 −0.161955
611611 0 0
612612 6.00000 0.242536
613613 26.0000 1.05013 0.525065 0.851062i 0.324041π-0.324041\pi
0.525065 + 0.851062i 0.324041π0.324041\pi
614614 −4.00000 −0.161427
615615 −4.00000 −0.161296
616616 12.0000 0.483494
617617 6.00000 0.241551 0.120775 0.992680i 0.461462π-0.461462\pi
0.120775 + 0.992680i 0.461462π0.461462\pi
618618 8.00000 0.321807
619619 20.0000 0.803868 0.401934 0.915669i 0.368338π-0.368338\pi
0.401934 + 0.915669i 0.368338π0.368338\pi
620620 0 0
621621 0 0
622622 −24.0000 −0.962312
623623 14.0000 0.560898
624624 0 0
625625 −19.0000 −0.760000
626626 26.0000 1.03917
627627 16.0000 0.638978
628628 2.00000 0.0798087
629629 36.0000 1.43541
630630 2.00000 0.0796819
631631 40.0000 1.59237 0.796187 0.605050i 0.206847π-0.206847\pi
0.796187 + 0.605050i 0.206847π0.206847\pi
632632 48.0000 1.90934
633633 4.00000 0.158986
634634 18.0000 0.714871
635635 0 0
636636 −6.00000 −0.237915
637637 0 0
638638 8.00000 0.316723
639639 0 0
640640 −6.00000 −0.237171
641641 18.0000 0.710957 0.355479 0.934684i 0.384318π-0.384318\pi
0.355479 + 0.934684i 0.384318π0.384318\pi
642642 4.00000 0.157867
643643 −20.0000 −0.788723 −0.394362 0.918955i 0.629034π-0.629034\pi
−0.394362 + 0.918955i 0.629034π0.629034\pi
644644 0 0
645645 −8.00000 −0.315000
646646 24.0000 0.944267
647647 −40.0000 −1.57256 −0.786281 0.617869i 0.787996π-0.787996\pi
−0.786281 + 0.617869i 0.787996π0.787996\pi
648648 −3.00000 −0.117851
649649 48.0000 1.88416
650650 0 0
651651 0 0
652652 4.00000 0.156652
653653 −18.0000 −0.704394 −0.352197 0.935926i 0.614565π-0.614565\pi
−0.352197 + 0.935926i 0.614565π0.614565\pi
654654 18.0000 0.703856
655655 8.00000 0.312586
656656 2.00000 0.0780869
657657 6.00000 0.234082
658658 0 0
659659 12.0000 0.467454 0.233727 0.972302i 0.424908π-0.424908\pi
0.233727 + 0.972302i 0.424908π0.424908\pi
660660 8.00000 0.311400
661661 −22.0000 −0.855701 −0.427850 0.903850i 0.640729π-0.640729\pi
−0.427850 + 0.903850i 0.640729π0.640729\pi
662662 4.00000 0.155464
663663 0 0
664664 −36.0000 −1.39707
665665 −8.00000 −0.310227
666666 −6.00000 −0.232495
667667 0 0
668668 −8.00000 −0.309529
669669 −16.0000 −0.618596
670670 −8.00000 −0.309067
671671 8.00000 0.308837
672672 5.00000 0.192879
673673 34.0000 1.31060 0.655302 0.755367i 0.272541π-0.272541\pi
0.655302 + 0.755367i 0.272541π0.272541\pi
674674 −14.0000 −0.539260
675675 −1.00000 −0.0384900
676676 0 0
677677 −18.0000 −0.691796 −0.345898 0.938272i 0.612426π-0.612426\pi
−0.345898 + 0.938272i 0.612426π0.612426\pi
678678 −14.0000 −0.537667
679679 −18.0000 −0.690777
680680 36.0000 1.38054
681681 12.0000 0.459841
682682 0 0
683683 12.0000 0.459167 0.229584 0.973289i 0.426264π-0.426264\pi
0.229584 + 0.973289i 0.426264π0.426264\pi
684684 4.00000 0.152944
685685 12.0000 0.458496
686686 1.00000 0.0381802
687687 10.0000 0.381524
688688 4.00000 0.152499
689689 0 0
690690 0 0
691691 −20.0000 −0.760836 −0.380418 0.924815i 0.624220π-0.624220\pi
−0.380418 + 0.924815i 0.624220π0.624220\pi
692692 10.0000 0.380143
693693 −4.00000 −0.151947
694694 −28.0000 −1.06287
695695 24.0000 0.910372
696696 6.00000 0.227429
697697 12.0000 0.454532
698698 2.00000 0.0757011
699699 −6.00000 −0.226941
700700 1.00000 0.0377964
701701 30.0000 1.13308 0.566542 0.824033i 0.308281π-0.308281\pi
0.566542 + 0.824033i 0.308281π0.308281\pi
702702 0 0
703703 24.0000 0.905177
704704 −28.0000 −1.05529
705705 0 0
706706 −10.0000 −0.376355
707707 14.0000 0.526524
708708 12.0000 0.450988
709709 −6.00000 −0.225335 −0.112667 0.993633i 0.535939π-0.535939\pi
−0.112667 + 0.993633i 0.535939π0.535939\pi
710710 0 0
711711 −16.0000 −0.600047
712712 −42.0000 −1.57402
713713 0 0
714714 −6.00000 −0.224544
715715 0 0
716716 4.00000 0.149487
717717 −24.0000 −0.896296
718718 −32.0000 −1.19423
719719 −48.0000 −1.79010 −0.895049 0.445968i 0.852860π-0.852860\pi
−0.895049 + 0.445968i 0.852860π0.852860\pi
720720 −2.00000 −0.0745356
721721 8.00000 0.297936
722722 −3.00000 −0.111648
723723 −2.00000 −0.0743808
724724 26.0000 0.966282
725725 2.00000 0.0742781
726726 5.00000 0.185567
727727 −40.0000 −1.48352 −0.741759 0.670667i 0.766008π-0.766008\pi
−0.741759 + 0.670667i 0.766008π0.766008\pi
728728 0 0
729729 1.00000 0.0370370
730730 12.0000 0.444140
731731 24.0000 0.887672
732732 2.00000 0.0739221
733733 18.0000 0.664845 0.332423 0.943131i 0.392134π-0.392134\pi
0.332423 + 0.943131i 0.392134π0.392134\pi
734734 0 0
735735 2.00000 0.0737711
736736 0 0
737737 16.0000 0.589368
738738 −2.00000 −0.0736210
739739 −36.0000 −1.32428 −0.662141 0.749380i 0.730352π-0.730352\pi
−0.662141 + 0.749380i 0.730352π0.730352\pi
740740 12.0000 0.441129
741741 0 0
742742 6.00000 0.220267
743743 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
744744 0 0
745745 −12.0000 −0.439646
746746 −10.0000 −0.366126
747747 12.0000 0.439057
748748 −24.0000 −0.877527
749749 4.00000 0.146157
750750 −12.0000 −0.438178
751751 −32.0000 −1.16770 −0.583848 0.811863i 0.698454π-0.698454\pi
−0.583848 + 0.811863i 0.698454π0.698454\pi
752752 0 0
753753 −20.0000 −0.728841
754754 0 0
755755 −16.0000 −0.582300
756756 −1.00000 −0.0363696
757757 −10.0000 −0.363456 −0.181728 0.983349i 0.558169π-0.558169\pi
−0.181728 + 0.983349i 0.558169π0.558169\pi
758758 −12.0000 −0.435860
759759 0 0
760760 24.0000 0.870572
761761 −18.0000 −0.652499 −0.326250 0.945284i 0.605785π-0.605785\pi
−0.326250 + 0.945284i 0.605785π0.605785\pi
762762 0 0
763763 18.0000 0.651644
764764 8.00000 0.289430
765765 −12.0000 −0.433861
766766 0 0
767767 0 0
768768 −17.0000 −0.613435
769769 −2.00000 −0.0721218 −0.0360609 0.999350i 0.511481π-0.511481\pi
−0.0360609 + 0.999350i 0.511481π0.511481\pi
770770 −8.00000 −0.288300
771771 26.0000 0.936367
772772 2.00000 0.0719816
773773 −14.0000 −0.503545 −0.251773 0.967786i 0.581013π-0.581013\pi
−0.251773 + 0.967786i 0.581013π0.581013\pi
774774 −4.00000 −0.143777
775775 0 0
776776 54.0000 1.93849
777777 −6.00000 −0.215249
778778 6.00000 0.215110
779779 8.00000 0.286630
780780 0 0
781781 0 0
782782 0 0
783783 −2.00000 −0.0714742
784784 −1.00000 −0.0357143
785785 −4.00000 −0.142766
786786 4.00000 0.142675
787787 44.0000 1.56843 0.784215 0.620489i 0.213066π-0.213066\pi
0.784215 + 0.620489i 0.213066π0.213066\pi
788788 22.0000 0.783718
789789 16.0000 0.569615
790790 −32.0000 −1.13851
791791 −14.0000 −0.497783
792792 12.0000 0.426401
793793 0 0
794794 18.0000 0.638796
795795 12.0000 0.425596
796796 −24.0000 −0.850657
797797 −26.0000 −0.920967 −0.460484 0.887668i 0.652324π-0.652324\pi
−0.460484 + 0.887668i 0.652324π0.652324\pi
798798 −4.00000 −0.141598
799799 0 0
800800 −5.00000 −0.176777
801801 14.0000 0.494666
802802 30.0000 1.05934
803803 −24.0000 −0.846942
804804 4.00000 0.141069
805805 0 0
806806 0 0
807807 6.00000 0.211210
808808 −42.0000 −1.47755
809809 42.0000 1.47664 0.738321 0.674450i 0.235619π-0.235619\pi
0.738321 + 0.674450i 0.235619π0.235619\pi
810810 2.00000 0.0702728
811811 −44.0000 −1.54505 −0.772524 0.634985i 0.781006π-0.781006\pi
−0.772524 + 0.634985i 0.781006π0.781006\pi
812812 2.00000 0.0701862
813813 −16.0000 −0.561144
814814 24.0000 0.841200
815815 −8.00000 −0.280228
816816 6.00000 0.210042
817817 16.0000 0.559769
818818 22.0000 0.769212
819819 0 0
820820 4.00000 0.139686
821821 −38.0000 −1.32621 −0.663105 0.748527i 0.730762π-0.730762\pi
−0.663105 + 0.748527i 0.730762π0.730762\pi
822822 6.00000 0.209274
823823 24.0000 0.836587 0.418294 0.908312i 0.362628π-0.362628\pi
0.418294 + 0.908312i 0.362628π0.362628\pi
824824 −24.0000 −0.836080
825825 4.00000 0.139262
826826 −12.0000 −0.417533
827827 12.0000 0.417281 0.208640 0.977992i 0.433096π-0.433096\pi
0.208640 + 0.977992i 0.433096π0.433096\pi
828828 0 0
829829 14.0000 0.486240 0.243120 0.969996i 0.421829π-0.421829\pi
0.243120 + 0.969996i 0.421829π0.421829\pi
830830 24.0000 0.833052
831831 22.0000 0.763172
832832 0 0
833833 −6.00000 −0.207888
834834 12.0000 0.415526
835835 16.0000 0.553703
836836 −16.0000 −0.553372
837837 0 0
838838 −12.0000 −0.414533
839839 8.00000 0.276191 0.138095 0.990419i 0.455902π-0.455902\pi
0.138095 + 0.990419i 0.455902π0.455902\pi
840840 −6.00000 −0.207020
841841 −25.0000 −0.862069
842842 −38.0000 −1.30957
843843 22.0000 0.757720
844844 −4.00000 −0.137686
845845 0 0
846846 0 0
847847 5.00000 0.171802
848848 −6.00000 −0.206041
849849 −20.0000 −0.686398
850850 6.00000 0.205798
851851 0 0
852852 0 0
853853 10.0000 0.342393 0.171197 0.985237i 0.445237π-0.445237\pi
0.171197 + 0.985237i 0.445237π0.445237\pi
854854 −2.00000 −0.0684386
855855 −8.00000 −0.273594
856856 −12.0000 −0.410152
857857 −14.0000 −0.478231 −0.239115 0.970991i 0.576857π-0.576857\pi
−0.239115 + 0.970991i 0.576857π0.576857\pi
858858 0 0
859859 44.0000 1.50126 0.750630 0.660722i 0.229750π-0.229750\pi
0.750630 + 0.660722i 0.229750π0.229750\pi
860860 8.00000 0.272798
861861 −2.00000 −0.0681598
862862 24.0000 0.817443
863863 24.0000 0.816970 0.408485 0.912765i 0.366057π-0.366057\pi
0.408485 + 0.912765i 0.366057π0.366057\pi
864864 5.00000 0.170103
865865 −20.0000 −0.680020
866866 −14.0000 −0.475739
867867 19.0000 0.645274
868868 0 0
869869 64.0000 2.17105
870870 −4.00000 −0.135613
871871 0 0
872872 −54.0000 −1.82867
873873 −18.0000 −0.609208
874874 0 0
875875 −12.0000 −0.405674
876876 −6.00000 −0.202721
877877 −46.0000 −1.55331 −0.776655 0.629926i 0.783085π-0.783085\pi
−0.776655 + 0.629926i 0.783085π0.783085\pi
878878 −24.0000 −0.809961
879879 −14.0000 −0.472208
880880 8.00000 0.269680
881881 −6.00000 −0.202145 −0.101073 0.994879i 0.532227π-0.532227\pi
−0.101073 + 0.994879i 0.532227π0.532227\pi
882882 1.00000 0.0336718
883883 −28.0000 −0.942275 −0.471138 0.882060i 0.656156π-0.656156\pi
−0.471138 + 0.882060i 0.656156π0.656156\pi
884884 0 0
885885 −24.0000 −0.806751
886886 36.0000 1.20944
887887 8.00000 0.268614 0.134307 0.990940i 0.457119π-0.457119\pi
0.134307 + 0.990940i 0.457119π0.457119\pi
888888 18.0000 0.604040
889889 0 0
890890 28.0000 0.938562
891891 −4.00000 −0.134005
892892 16.0000 0.535720
893893 0 0
894894 −6.00000 −0.200670
895895 −8.00000 −0.267411
896896 −3.00000 −0.100223
897897 0 0
898898 30.0000 1.00111
899899 0 0
900900 1.00000 0.0333333
901901 −36.0000 −1.19933
902902 8.00000 0.266371
903903 −4.00000 −0.133112
904904 42.0000 1.39690
905905 −52.0000 −1.72854
906906 −8.00000 −0.265782
907907 −4.00000 −0.132818 −0.0664089 0.997792i 0.521154π-0.521154\pi
−0.0664089 + 0.997792i 0.521154π0.521154\pi
908908 −12.0000 −0.398234
909909 14.0000 0.464351
910910 0 0
911911 −24.0000 −0.795155 −0.397578 0.917568i 0.630149π-0.630149\pi
−0.397578 + 0.917568i 0.630149π0.630149\pi
912912 4.00000 0.132453
913913 −48.0000 −1.58857
914914 −10.0000 −0.330771
915915 −4.00000 −0.132236
916916 −10.0000 −0.330409
917917 4.00000 0.132092
918918 −6.00000 −0.198030
919919 8.00000 0.263896 0.131948 0.991257i 0.457877π-0.457877\pi
0.131948 + 0.991257i 0.457877π0.457877\pi
920920 0 0
921921 −4.00000 −0.131804
922922 10.0000 0.329332
923923 0 0
924924 4.00000 0.131590
925925 6.00000 0.197279
926926 −16.0000 −0.525793
927927 8.00000 0.262754
928928 −10.0000 −0.328266
929929 −26.0000 −0.853032 −0.426516 0.904480i 0.640259π-0.640259\pi
−0.426516 + 0.904480i 0.640259π0.640259\pi
930930 0 0
931931 −4.00000 −0.131095
932932 6.00000 0.196537
933933 −24.0000 −0.785725
934934 36.0000 1.17796
935935 48.0000 1.56977
936936 0 0
937937 42.0000 1.37208 0.686040 0.727564i 0.259347π-0.259347\pi
0.686040 + 0.727564i 0.259347π0.259347\pi
938938 −4.00000 −0.130605
939939 26.0000 0.848478
940940 0 0
941941 −38.0000 −1.23876 −0.619382 0.785090i 0.712617π-0.712617\pi
−0.619382 + 0.785090i 0.712617π0.712617\pi
942942 −2.00000 −0.0651635
943943 0 0
944944 12.0000 0.390567
945945 2.00000 0.0650600
946946 16.0000 0.520205
947947 −44.0000 −1.42981 −0.714904 0.699223i 0.753530π-0.753530\pi
−0.714904 + 0.699223i 0.753530π0.753530\pi
948948 16.0000 0.519656
949949 0 0
950950 4.00000 0.129777
951951 18.0000 0.583690
952952 18.0000 0.583383
953953 26.0000 0.842223 0.421111 0.907009i 0.361640π-0.361640\pi
0.421111 + 0.907009i 0.361640π0.361640\pi
954954 6.00000 0.194257
955955 −16.0000 −0.517748
956956 24.0000 0.776215
957957 8.00000 0.258603
958958 16.0000 0.516937
959959 6.00000 0.193750
960960 14.0000 0.451848
961961 −31.0000 −1.00000
962962 0 0
963963 4.00000 0.128898
964964 2.00000 0.0644157
965965 −4.00000 −0.128765
966966 0 0
967967 −40.0000 −1.28631 −0.643157 0.765735i 0.722376π-0.722376\pi
−0.643157 + 0.765735i 0.722376π0.722376\pi
968968 −15.0000 −0.482118
969969 24.0000 0.770991
970970 −36.0000 −1.15589
971971 12.0000 0.385098 0.192549 0.981287i 0.438325π-0.438325\pi
0.192549 + 0.981287i 0.438325π0.438325\pi
972972 −1.00000 −0.0320750
973973 12.0000 0.384702
974974 8.00000 0.256337
975975 0 0
976976 2.00000 0.0640184
977977 30.0000 0.959785 0.479893 0.877327i 0.340676π-0.340676\pi
0.479893 + 0.877327i 0.340676π0.340676\pi
978978 −4.00000 −0.127906
979979 −56.0000 −1.78977
980980 −2.00000 −0.0638877
981981 18.0000 0.574696
982982 20.0000 0.638226
983983 −24.0000 −0.765481 −0.382741 0.923856i 0.625020π-0.625020\pi
−0.382741 + 0.923856i 0.625020π0.625020\pi
984984 6.00000 0.191273
985985 −44.0000 −1.40196
986986 12.0000 0.382158
987987 0 0
988988 0 0
989989 0 0
990990 −8.00000 −0.254257
991991 −16.0000 −0.508257 −0.254128 0.967170i 0.581789π-0.581789\pi
−0.254128 + 0.967170i 0.581789π0.581789\pi
992992 0 0
993993 4.00000 0.126936
994994 0 0
995995 48.0000 1.52170
996996 −12.0000 −0.380235
997997 −26.0000 −0.823428 −0.411714 0.911313i 0.635070π-0.635070\pi
−0.411714 + 0.911313i 0.635070π0.635070\pi
998998 −4.00000 −0.126618
999999 −6.00000 −0.189832
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 3549.2.a.c.1.1 1
13.12 even 2 21.2.a.a.1.1 1
39.38 odd 2 63.2.a.a.1.1 1
52.51 odd 2 336.2.a.a.1.1 1
65.12 odd 4 525.2.d.a.274.1 2
65.38 odd 4 525.2.d.a.274.2 2
65.64 even 2 525.2.a.d.1.1 1
91.12 odd 6 147.2.e.c.67.1 2
91.25 even 6 147.2.e.b.79.1 2
91.38 odd 6 147.2.e.c.79.1 2
91.51 even 6 147.2.e.b.67.1 2
91.90 odd 2 147.2.a.a.1.1 1
104.51 odd 2 1344.2.a.s.1.1 1
104.77 even 2 1344.2.a.g.1.1 1
117.25 even 6 567.2.f.g.190.1 2
117.38 odd 6 567.2.f.b.190.1 2
117.77 odd 6 567.2.f.b.379.1 2
117.103 even 6 567.2.f.g.379.1 2
143.142 odd 2 2541.2.a.j.1.1 1
156.155 even 2 1008.2.a.l.1.1 1
195.38 even 4 1575.2.d.a.1324.1 2
195.77 even 4 1575.2.d.a.1324.2 2
195.194 odd 2 1575.2.a.c.1.1 1
208.51 odd 4 5376.2.c.l.2689.1 2
208.77 even 4 5376.2.c.r.2689.2 2
208.155 odd 4 5376.2.c.l.2689.2 2
208.181 even 4 5376.2.c.r.2689.1 2
221.220 even 2 6069.2.a.b.1.1 1
247.246 odd 2 7581.2.a.d.1.1 1
260.259 odd 2 8400.2.a.bn.1.1 1
273.38 even 6 441.2.e.b.226.1 2
273.116 odd 6 441.2.e.a.226.1 2
273.194 even 6 441.2.e.b.361.1 2
273.233 odd 6 441.2.e.a.361.1 2
273.272 even 2 441.2.a.f.1.1 1
312.77 odd 2 4032.2.a.h.1.1 1
312.155 even 2 4032.2.a.k.1.1 1
364.51 odd 6 2352.2.q.x.1537.1 2
364.103 even 6 2352.2.q.e.1537.1 2
364.207 odd 6 2352.2.q.x.961.1 2
364.311 even 6 2352.2.q.e.961.1 2
364.363 even 2 2352.2.a.v.1.1 1
429.428 even 2 7623.2.a.g.1.1 1
455.454 odd 2 3675.2.a.n.1.1 1
728.181 odd 2 9408.2.a.bv.1.1 1
728.363 even 2 9408.2.a.m.1.1 1
1092.1091 odd 2 7056.2.a.p.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.2.a.a.1.1 1 13.12 even 2
63.2.a.a.1.1 1 39.38 odd 2
147.2.a.a.1.1 1 91.90 odd 2
147.2.e.b.67.1 2 91.51 even 6
147.2.e.b.79.1 2 91.25 even 6
147.2.e.c.67.1 2 91.12 odd 6
147.2.e.c.79.1 2 91.38 odd 6
336.2.a.a.1.1 1 52.51 odd 2
441.2.a.f.1.1 1 273.272 even 2
441.2.e.a.226.1 2 273.116 odd 6
441.2.e.a.361.1 2 273.233 odd 6
441.2.e.b.226.1 2 273.38 even 6
441.2.e.b.361.1 2 273.194 even 6
525.2.a.d.1.1 1 65.64 even 2
525.2.d.a.274.1 2 65.12 odd 4
525.2.d.a.274.2 2 65.38 odd 4
567.2.f.b.190.1 2 117.38 odd 6
567.2.f.b.379.1 2 117.77 odd 6
567.2.f.g.190.1 2 117.25 even 6
567.2.f.g.379.1 2 117.103 even 6
1008.2.a.l.1.1 1 156.155 even 2
1344.2.a.g.1.1 1 104.77 even 2
1344.2.a.s.1.1 1 104.51 odd 2
1575.2.a.c.1.1 1 195.194 odd 2
1575.2.d.a.1324.1 2 195.38 even 4
1575.2.d.a.1324.2 2 195.77 even 4
2352.2.a.v.1.1 1 364.363 even 2
2352.2.q.e.961.1 2 364.311 even 6
2352.2.q.e.1537.1 2 364.103 even 6
2352.2.q.x.961.1 2 364.207 odd 6
2352.2.q.x.1537.1 2 364.51 odd 6
2541.2.a.j.1.1 1 143.142 odd 2
3549.2.a.c.1.1 1 1.1 even 1 trivial
3675.2.a.n.1.1 1 455.454 odd 2
4032.2.a.h.1.1 1 312.77 odd 2
4032.2.a.k.1.1 1 312.155 even 2
5376.2.c.l.2689.1 2 208.51 odd 4
5376.2.c.l.2689.2 2 208.155 odd 4
5376.2.c.r.2689.1 2 208.181 even 4
5376.2.c.r.2689.2 2 208.77 even 4
6069.2.a.b.1.1 1 221.220 even 2
7056.2.a.p.1.1 1 1092.1091 odd 2
7581.2.a.d.1.1 1 247.246 odd 2
7623.2.a.g.1.1 1 429.428 even 2
8400.2.a.bn.1.1 1 260.259 odd 2
9408.2.a.m.1.1 1 728.363 even 2
9408.2.a.bv.1.1 1 728.181 odd 2