Properties

Label 1734.2.a.b.1.1
Level 17341734
Weight 22
Character 1734.1
Self dual yes
Analytic conductor 13.84613.846
Analytic rank 11
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1734,2,Mod(1,1734)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1734, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1734.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1734=23172 1734 = 2 \cdot 3 \cdot 17^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1734.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,0,1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 13.846059710513.8460597105
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 102)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 1734.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q1.00000q21.00000q3+1.00000q4+1.00000q62.00000q71.00000q8+1.00000q91.00000q12+2.00000q13+2.00000q14+1.00000q161.00000q184.00000q19+2.00000q21+6.00000q23+1.00000q245.00000q252.00000q261.00000q272.00000q28+10.0000q311.00000q32+1.00000q368.00000q37+4.00000q382.00000q396.00000q412.00000q424.00000q436.00000q46+12.0000q471.00000q483.00000q49+5.00000q50+2.00000q52+6.00000q53+1.00000q54+2.00000q56+4.00000q5712.0000q598.00000q6110.0000q622.00000q63+1.00000q644.00000q676.00000q696.00000q711.00000q722.00000q73+8.00000q74+5.00000q754.00000q76+2.00000q78+10.0000q79+1.00000q81+6.00000q82+12.0000q83+2.00000q84+4.00000q8618.0000q894.00000q91+6.00000q9210.0000q9312.0000q94+1.00000q9614.0000q97+3.00000q98+O(q100)q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} +2.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} -1.00000 q^{18} -4.00000 q^{19} +2.00000 q^{21} +6.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} +10.0000 q^{31} -1.00000 q^{32} +1.00000 q^{36} -8.00000 q^{37} +4.00000 q^{38} -2.00000 q^{39} -6.00000 q^{41} -2.00000 q^{42} -4.00000 q^{43} -6.00000 q^{46} +12.0000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +5.00000 q^{50} +2.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} +2.00000 q^{56} +4.00000 q^{57} -12.0000 q^{59} -8.00000 q^{61} -10.0000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{67} -6.00000 q^{69} -6.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} +8.00000 q^{74} +5.00000 q^{75} -4.00000 q^{76} +2.00000 q^{78} +10.0000 q^{79} +1.00000 q^{81} +6.00000 q^{82} +12.0000 q^{83} +2.00000 q^{84} +4.00000 q^{86} -18.0000 q^{89} -4.00000 q^{91} +6.00000 q^{92} -10.0000 q^{93} -12.0000 q^{94} +1.00000 q^{96} -14.0000 q^{97} +3.00000 q^{98} +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
33 −1.00000 −0.577350
44 1.00000 0.500000
55 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
66 1.00000 0.408248
77 −2.00000 −0.755929 −0.377964 0.925820i 0.623376π-0.623376\pi
−0.377964 + 0.925820i 0.623376π0.623376\pi
88 −1.00000 −0.353553
99 1.00000 0.333333
1010 0 0
1111 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1212 −1.00000 −0.288675
1313 2.00000 0.554700 0.277350 0.960769i 0.410544π-0.410544\pi
0.277350 + 0.960769i 0.410544π0.410544\pi
1414 2.00000 0.534522
1515 0 0
1616 1.00000 0.250000
1717 0 0
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 0 0
2121 2.00000 0.436436
2222 0 0
2323 6.00000 1.25109 0.625543 0.780189i 0.284877π-0.284877\pi
0.625543 + 0.780189i 0.284877π0.284877\pi
2424 1.00000 0.204124
2525 −5.00000 −1.00000
2626 −2.00000 −0.392232
2727 −1.00000 −0.192450
2828 −2.00000 −0.377964
2929 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3030 0 0
3131 10.0000 1.79605 0.898027 0.439941i 0.145001π-0.145001\pi
0.898027 + 0.439941i 0.145001π0.145001\pi
3232 −1.00000 −0.176777
3333 0 0
3434 0 0
3535 0 0
3636 1.00000 0.166667
3737 −8.00000 −1.31519 −0.657596 0.753371i 0.728427π-0.728427\pi
−0.657596 + 0.753371i 0.728427π0.728427\pi
3838 4.00000 0.648886
3939 −2.00000 −0.320256
4040 0 0
4141 −6.00000 −0.937043 −0.468521 0.883452i 0.655213π-0.655213\pi
−0.468521 + 0.883452i 0.655213π0.655213\pi
4242 −2.00000 −0.308607
4343 −4.00000 −0.609994 −0.304997 0.952353i 0.598656π-0.598656\pi
−0.304997 + 0.952353i 0.598656π0.598656\pi
4444 0 0
4545 0 0
4646 −6.00000 −0.884652
4747 12.0000 1.75038 0.875190 0.483779i 0.160736π-0.160736\pi
0.875190 + 0.483779i 0.160736π0.160736\pi
4848 −1.00000 −0.144338
4949 −3.00000 −0.428571
5050 5.00000 0.707107
5151 0 0
5252 2.00000 0.277350
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 0 0
5656 2.00000 0.267261
5757 4.00000 0.529813
5858 0 0
5959 −12.0000 −1.56227 −0.781133 0.624364i 0.785358π-0.785358\pi
−0.781133 + 0.624364i 0.785358π0.785358\pi
6060 0 0
6161 −8.00000 −1.02430 −0.512148 0.858898i 0.671150π-0.671150\pi
−0.512148 + 0.858898i 0.671150π0.671150\pi
6262 −10.0000 −1.27000
6363 −2.00000 −0.251976
6464 1.00000 0.125000
6565 0 0
6666 0 0
6767 −4.00000 −0.488678 −0.244339 0.969690i 0.578571π-0.578571\pi
−0.244339 + 0.969690i 0.578571π0.578571\pi
6868 0 0
6969 −6.00000 −0.722315
7070 0 0
7171 −6.00000 −0.712069 −0.356034 0.934473i 0.615871π-0.615871\pi
−0.356034 + 0.934473i 0.615871π0.615871\pi
7272 −1.00000 −0.117851
7373 −2.00000 −0.234082 −0.117041 0.993127i 0.537341π-0.537341\pi
−0.117041 + 0.993127i 0.537341π0.537341\pi
7474 8.00000 0.929981
7575 5.00000 0.577350
7676 −4.00000 −0.458831
7777 0 0
7878 2.00000 0.226455
7979 10.0000 1.12509 0.562544 0.826767i 0.309823π-0.309823\pi
0.562544 + 0.826767i 0.309823π0.309823\pi
8080 0 0
8181 1.00000 0.111111
8282 6.00000 0.662589
8383 12.0000 1.31717 0.658586 0.752506i 0.271155π-0.271155\pi
0.658586 + 0.752506i 0.271155π0.271155\pi
8484 2.00000 0.218218
8585 0 0
8686 4.00000 0.431331
8787 0 0
8888 0 0
8989 −18.0000 −1.90800 −0.953998 0.299813i 0.903076π-0.903076\pi
−0.953998 + 0.299813i 0.903076π0.903076\pi
9090 0 0
9191 −4.00000 −0.419314
9292 6.00000 0.625543
9393 −10.0000 −1.03695
9494 −12.0000 −1.23771
9595 0 0
9696 1.00000 0.102062
9797 −14.0000 −1.42148 −0.710742 0.703452i 0.751641π-0.751641\pi
−0.710742 + 0.703452i 0.751641π0.751641\pi
9898 3.00000 0.303046
9999 0 0
100100 −5.00000 −0.500000
101101 6.00000 0.597022 0.298511 0.954406i 0.403510π-0.403510\pi
0.298511 + 0.954406i 0.403510π0.403510\pi
102102 0 0
103103 −4.00000 −0.394132 −0.197066 0.980390i 0.563141π-0.563141\pi
−0.197066 + 0.980390i 0.563141π0.563141\pi
104104 −2.00000 −0.196116
105105 0 0
106106 −6.00000 −0.582772
107107 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
108108 −1.00000 −0.0962250
109109 −20.0000 −1.91565 −0.957826 0.287348i 0.907226π-0.907226\pi
−0.957826 + 0.287348i 0.907226π0.907226\pi
110110 0 0
111111 8.00000 0.759326
112112 −2.00000 −0.188982
113113 6.00000 0.564433 0.282216 0.959351i 0.408930π-0.408930\pi
0.282216 + 0.959351i 0.408930π0.408930\pi
114114 −4.00000 −0.374634
115115 0 0
116116 0 0
117117 2.00000 0.184900
118118 12.0000 1.10469
119119 0 0
120120 0 0
121121 −11.0000 −1.00000
122122 8.00000 0.724286
123123 6.00000 0.541002
124124 10.0000 0.898027
125125 0 0
126126 2.00000 0.178174
127127 8.00000 0.709885 0.354943 0.934888i 0.384500π-0.384500\pi
0.354943 + 0.934888i 0.384500π0.384500\pi
128128 −1.00000 −0.0883883
129129 4.00000 0.352180
130130 0 0
131131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
132132 0 0
133133 8.00000 0.693688
134134 4.00000 0.345547
135135 0 0
136136 0 0
137137 −6.00000 −0.512615 −0.256307 0.966595i 0.582506π-0.582506\pi
−0.256307 + 0.966595i 0.582506π0.582506\pi
138138 6.00000 0.510754
139139 −8.00000 −0.678551 −0.339276 0.940687i 0.610182π-0.610182\pi
−0.339276 + 0.940687i 0.610182π0.610182\pi
140140 0 0
141141 −12.0000 −1.01058
142142 6.00000 0.503509
143143 0 0
144144 1.00000 0.0833333
145145 0 0
146146 2.00000 0.165521
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 −5.00000 −0.408248
151151 8.00000 0.651031 0.325515 0.945537i 0.394462π-0.394462\pi
0.325515 + 0.945537i 0.394462π0.394462\pi
152152 4.00000 0.324443
153153 0 0
154154 0 0
155155 0 0
156156 −2.00000 −0.160128
157157 −10.0000 −0.798087 −0.399043 0.916932i 0.630658π-0.630658\pi
−0.399043 + 0.916932i 0.630658π0.630658\pi
158158 −10.0000 −0.795557
159159 −6.00000 −0.475831
160160 0 0
161161 −12.0000 −0.945732
162162 −1.00000 −0.0785674
163163 −20.0000 −1.56652 −0.783260 0.621694i 0.786445π-0.786445\pi
−0.783260 + 0.621694i 0.786445π0.786445\pi
164164 −6.00000 −0.468521
165165 0 0
166166 −12.0000 −0.931381
167167 −18.0000 −1.39288 −0.696441 0.717614i 0.745234π-0.745234\pi
−0.696441 + 0.717614i 0.745234π0.745234\pi
168168 −2.00000 −0.154303
169169 −9.00000 −0.692308
170170 0 0
171171 −4.00000 −0.305888
172172 −4.00000 −0.304997
173173 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
174174 0 0
175175 10.0000 0.755929
176176 0 0
177177 12.0000 0.901975
178178 18.0000 1.34916
179179 −12.0000 −0.896922 −0.448461 0.893802i 0.648028π-0.648028\pi
−0.448461 + 0.893802i 0.648028π0.648028\pi
180180 0 0
181181 −8.00000 −0.594635 −0.297318 0.954779i 0.596092π-0.596092\pi
−0.297318 + 0.954779i 0.596092π0.596092\pi
182182 4.00000 0.296500
183183 8.00000 0.591377
184184 −6.00000 −0.442326
185185 0 0
186186 10.0000 0.733236
187187 0 0
188188 12.0000 0.875190
189189 2.00000 0.145479
190190 0 0
191191 −12.0000 −0.868290 −0.434145 0.900843i 0.642949π-0.642949\pi
−0.434145 + 0.900843i 0.642949π0.642949\pi
192192 −1.00000 −0.0721688
193193 −14.0000 −1.00774 −0.503871 0.863779i 0.668091π-0.668091\pi
−0.503871 + 0.863779i 0.668091π0.668091\pi
194194 14.0000 1.00514
195195 0 0
196196 −3.00000 −0.214286
197197 12.0000 0.854965 0.427482 0.904024i 0.359401π-0.359401\pi
0.427482 + 0.904024i 0.359401π0.359401\pi
198198 0 0
199199 −2.00000 −0.141776 −0.0708881 0.997484i 0.522583π-0.522583\pi
−0.0708881 + 0.997484i 0.522583π0.522583\pi
200200 5.00000 0.353553
201201 4.00000 0.282138
202202 −6.00000 −0.422159
203203 0 0
204204 0 0
205205 0 0
206206 4.00000 0.278693
207207 6.00000 0.417029
208208 2.00000 0.138675
209209 0 0
210210 0 0
211211 −8.00000 −0.550743 −0.275371 0.961338i 0.588801π-0.588801\pi
−0.275371 + 0.961338i 0.588801π0.588801\pi
212212 6.00000 0.412082
213213 6.00000 0.411113
214214 0 0
215215 0 0
216216 1.00000 0.0680414
217217 −20.0000 −1.35769
218218 20.0000 1.35457
219219 2.00000 0.135147
220220 0 0
221221 0 0
222222 −8.00000 −0.536925
223223 −28.0000 −1.87502 −0.937509 0.347960i 0.886874π-0.886874\pi
−0.937509 + 0.347960i 0.886874π0.886874\pi
224224 2.00000 0.133631
225225 −5.00000 −0.333333
226226 −6.00000 −0.399114
227227 −12.0000 −0.796468 −0.398234 0.917284i 0.630377π-0.630377\pi
−0.398234 + 0.917284i 0.630377π0.630377\pi
228228 4.00000 0.264906
229229 14.0000 0.925146 0.462573 0.886581i 0.346926π-0.346926\pi
0.462573 + 0.886581i 0.346926π0.346926\pi
230230 0 0
231231 0 0
232232 0 0
233233 30.0000 1.96537 0.982683 0.185296i 0.0593245π-0.0593245\pi
0.982683 + 0.185296i 0.0593245π0.0593245\pi
234234 −2.00000 −0.130744
235235 0 0
236236 −12.0000 −0.781133
237237 −10.0000 −0.649570
238238 0 0
239239 −12.0000 −0.776215 −0.388108 0.921614i 0.626871π-0.626871\pi
−0.388108 + 0.921614i 0.626871π0.626871\pi
240240 0 0
241241 10.0000 0.644157 0.322078 0.946713i 0.395619π-0.395619\pi
0.322078 + 0.946713i 0.395619π0.395619\pi
242242 11.0000 0.707107
243243 −1.00000 −0.0641500
244244 −8.00000 −0.512148
245245 0 0
246246 −6.00000 −0.382546
247247 −8.00000 −0.509028
248248 −10.0000 −0.635001
249249 −12.0000 −0.760469
250250 0 0
251251 12.0000 0.757433 0.378717 0.925513i 0.376365π-0.376365\pi
0.378717 + 0.925513i 0.376365π0.376365\pi
252252 −2.00000 −0.125988
253253 0 0
254254 −8.00000 −0.501965
255255 0 0
256256 1.00000 0.0625000
257257 18.0000 1.12281 0.561405 0.827541i 0.310261π-0.310261\pi
0.561405 + 0.827541i 0.310261π0.310261\pi
258258 −4.00000 −0.249029
259259 16.0000 0.994192
260260 0 0
261261 0 0
262262 0 0
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 0 0
266266 −8.00000 −0.490511
267267 18.0000 1.10158
268268 −4.00000 −0.244339
269269 −24.0000 −1.46331 −0.731653 0.681677i 0.761251π-0.761251\pi
−0.731653 + 0.681677i 0.761251π0.761251\pi
270270 0 0
271271 −16.0000 −0.971931 −0.485965 0.873978i 0.661532π-0.661532\pi
−0.485965 + 0.873978i 0.661532π0.661532\pi
272272 0 0
273273 4.00000 0.242091
274274 6.00000 0.362473
275275 0 0
276276 −6.00000 −0.361158
277277 4.00000 0.240337 0.120168 0.992754i 0.461657π-0.461657\pi
0.120168 + 0.992754i 0.461657π0.461657\pi
278278 8.00000 0.479808
279279 10.0000 0.598684
280280 0 0
281281 30.0000 1.78965 0.894825 0.446417i 0.147300π-0.147300\pi
0.894825 + 0.446417i 0.147300π0.147300\pi
282282 12.0000 0.714590
283283 16.0000 0.951101 0.475551 0.879688i 0.342249π-0.342249\pi
0.475551 + 0.879688i 0.342249π0.342249\pi
284284 −6.00000 −0.356034
285285 0 0
286286 0 0
287287 12.0000 0.708338
288288 −1.00000 −0.0589256
289289 0 0
290290 0 0
291291 14.0000 0.820695
292292 −2.00000 −0.117041
293293 18.0000 1.05157 0.525786 0.850617i 0.323771π-0.323771\pi
0.525786 + 0.850617i 0.323771π0.323771\pi
294294 −3.00000 −0.174964
295295 0 0
296296 8.00000 0.464991
297297 0 0
298298 6.00000 0.347571
299299 12.0000 0.693978
300300 5.00000 0.288675
301301 8.00000 0.461112
302302 −8.00000 −0.460348
303303 −6.00000 −0.344691
304304 −4.00000 −0.229416
305305 0 0
306306 0 0
307307 20.0000 1.14146 0.570730 0.821138i 0.306660π-0.306660\pi
0.570730 + 0.821138i 0.306660π0.306660\pi
308308 0 0
309309 4.00000 0.227552
310310 0 0
311311 −18.0000 −1.02069 −0.510343 0.859971i 0.670482π-0.670482\pi
−0.510343 + 0.859971i 0.670482π0.670482\pi
312312 2.00000 0.113228
313313 −14.0000 −0.791327 −0.395663 0.918396i 0.629485π-0.629485\pi
−0.395663 + 0.918396i 0.629485π0.629485\pi
314314 10.0000 0.564333
315315 0 0
316316 10.0000 0.562544
317317 −12.0000 −0.673987 −0.336994 0.941507i 0.609410π-0.609410\pi
−0.336994 + 0.941507i 0.609410π0.609410\pi
318318 6.00000 0.336463
319319 0 0
320320 0 0
321321 0 0
322322 12.0000 0.668734
323323 0 0
324324 1.00000 0.0555556
325325 −10.0000 −0.554700
326326 20.0000 1.10770
327327 20.0000 1.10600
328328 6.00000 0.331295
329329 −24.0000 −1.32316
330330 0 0
331331 20.0000 1.09930 0.549650 0.835395i 0.314761π-0.314761\pi
0.549650 + 0.835395i 0.314761π0.314761\pi
332332 12.0000 0.658586
333333 −8.00000 −0.438397
334334 18.0000 0.984916
335335 0 0
336336 2.00000 0.109109
337337 22.0000 1.19842 0.599208 0.800593i 0.295482π-0.295482\pi
0.599208 + 0.800593i 0.295482π0.295482\pi
338338 9.00000 0.489535
339339 −6.00000 −0.325875
340340 0 0
341341 0 0
342342 4.00000 0.216295
343343 20.0000 1.07990
344344 4.00000 0.215666
345345 0 0
346346 0 0
347347 12.0000 0.644194 0.322097 0.946707i 0.395612π-0.395612\pi
0.322097 + 0.946707i 0.395612π0.395612\pi
348348 0 0
349349 26.0000 1.39175 0.695874 0.718164i 0.255017π-0.255017\pi
0.695874 + 0.718164i 0.255017π0.255017\pi
350350 −10.0000 −0.534522
351351 −2.00000 −0.106752
352352 0 0
353353 −18.0000 −0.958043 −0.479022 0.877803i 0.659008π-0.659008\pi
−0.479022 + 0.877803i 0.659008π0.659008\pi
354354 −12.0000 −0.637793
355355 0 0
356356 −18.0000 −0.953998
357357 0 0
358358 12.0000 0.634220
359359 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
360360 0 0
361361 −3.00000 −0.157895
362362 8.00000 0.420471
363363 11.0000 0.577350
364364 −4.00000 −0.209657
365365 0 0
366366 −8.00000 −0.418167
367367 10.0000 0.521996 0.260998 0.965339i 0.415948π-0.415948\pi
0.260998 + 0.965339i 0.415948π0.415948\pi
368368 6.00000 0.312772
369369 −6.00000 −0.312348
370370 0 0
371371 −12.0000 −0.623009
372372 −10.0000 −0.518476
373373 −22.0000 −1.13912 −0.569558 0.821951i 0.692886π-0.692886\pi
−0.569558 + 0.821951i 0.692886π0.692886\pi
374374 0 0
375375 0 0
376376 −12.0000 −0.618853
377377 0 0
378378 −2.00000 −0.102869
379379 28.0000 1.43826 0.719132 0.694874i 0.244540π-0.244540\pi
0.719132 + 0.694874i 0.244540π0.244540\pi
380380 0 0
381381 −8.00000 −0.409852
382382 12.0000 0.613973
383383 −12.0000 −0.613171 −0.306586 0.951843i 0.599187π-0.599187\pi
−0.306586 + 0.951843i 0.599187π0.599187\pi
384384 1.00000 0.0510310
385385 0 0
386386 14.0000 0.712581
387387 −4.00000 −0.203331
388388 −14.0000 −0.710742
389389 −30.0000 −1.52106 −0.760530 0.649303i 0.775061π-0.775061\pi
−0.760530 + 0.649303i 0.775061π0.775061\pi
390390 0 0
391391 0 0
392392 3.00000 0.151523
393393 0 0
394394 −12.0000 −0.604551
395395 0 0
396396 0 0
397397 16.0000 0.803017 0.401508 0.915855i 0.368486π-0.368486\pi
0.401508 + 0.915855i 0.368486π0.368486\pi
398398 2.00000 0.100251
399399 −8.00000 −0.400501
400400 −5.00000 −0.250000
401401 18.0000 0.898877 0.449439 0.893311i 0.351624π-0.351624\pi
0.449439 + 0.893311i 0.351624π0.351624\pi
402402 −4.00000 −0.199502
403403 20.0000 0.996271
404404 6.00000 0.298511
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 38.0000 1.87898 0.939490 0.342578i 0.111300π-0.111300\pi
0.939490 + 0.342578i 0.111300π0.111300\pi
410410 0 0
411411 6.00000 0.295958
412412 −4.00000 −0.197066
413413 24.0000 1.18096
414414 −6.00000 −0.294884
415415 0 0
416416 −2.00000 −0.0980581
417417 8.00000 0.391762
418418 0 0
419419 36.0000 1.75872 0.879358 0.476162i 0.157972π-0.157972\pi
0.879358 + 0.476162i 0.157972π0.157972\pi
420420 0 0
421421 −22.0000 −1.07221 −0.536107 0.844150i 0.680106π-0.680106\pi
−0.536107 + 0.844150i 0.680106π0.680106\pi
422422 8.00000 0.389434
423423 12.0000 0.583460
424424 −6.00000 −0.291386
425425 0 0
426426 −6.00000 −0.290701
427427 16.0000 0.774294
428428 0 0
429429 0 0
430430 0 0
431431 30.0000 1.44505 0.722525 0.691345i 0.242982π-0.242982\pi
0.722525 + 0.691345i 0.242982π0.242982\pi
432432 −1.00000 −0.0481125
433433 14.0000 0.672797 0.336399 0.941720i 0.390791π-0.390791\pi
0.336399 + 0.941720i 0.390791π0.390791\pi
434434 20.0000 0.960031
435435 0 0
436436 −20.0000 −0.957826
437437 −24.0000 −1.14808
438438 −2.00000 −0.0955637
439439 −26.0000 −1.24091 −0.620456 0.784241i 0.713053π-0.713053\pi
−0.620456 + 0.784241i 0.713053π0.713053\pi
440440 0 0
441441 −3.00000 −0.142857
442442 0 0
443443 −36.0000 −1.71041 −0.855206 0.518289i 0.826569π-0.826569\pi
−0.855206 + 0.518289i 0.826569π0.826569\pi
444444 8.00000 0.379663
445445 0 0
446446 28.0000 1.32584
447447 6.00000 0.283790
448448 −2.00000 −0.0944911
449449 −6.00000 −0.283158 −0.141579 0.989927i 0.545218π-0.545218\pi
−0.141579 + 0.989927i 0.545218π0.545218\pi
450450 5.00000 0.235702
451451 0 0
452452 6.00000 0.282216
453453 −8.00000 −0.375873
454454 12.0000 0.563188
455455 0 0
456456 −4.00000 −0.187317
457457 −10.0000 −0.467780 −0.233890 0.972263i 0.575146π-0.575146\pi
−0.233890 + 0.972263i 0.575146π0.575146\pi
458458 −14.0000 −0.654177
459459 0 0
460460 0 0
461461 30.0000 1.39724 0.698620 0.715493i 0.253798π-0.253798\pi
0.698620 + 0.715493i 0.253798π0.253798\pi
462462 0 0
463463 20.0000 0.929479 0.464739 0.885448i 0.346148π-0.346148\pi
0.464739 + 0.885448i 0.346148π0.346148\pi
464464 0 0
465465 0 0
466466 −30.0000 −1.38972
467467 12.0000 0.555294 0.277647 0.960683i 0.410445π-0.410445\pi
0.277647 + 0.960683i 0.410445π0.410445\pi
468468 2.00000 0.0924500
469469 8.00000 0.369406
470470 0 0
471471 10.0000 0.460776
472472 12.0000 0.552345
473473 0 0
474474 10.0000 0.459315
475475 20.0000 0.917663
476476 0 0
477477 6.00000 0.274721
478478 12.0000 0.548867
479479 −6.00000 −0.274147 −0.137073 0.990561i 0.543770π-0.543770\pi
−0.137073 + 0.990561i 0.543770π0.543770\pi
480480 0 0
481481 −16.0000 −0.729537
482482 −10.0000 −0.455488
483483 12.0000 0.546019
484484 −11.0000 −0.500000
485485 0 0
486486 1.00000 0.0453609
487487 10.0000 0.453143 0.226572 0.973995i 0.427248π-0.427248\pi
0.226572 + 0.973995i 0.427248π0.427248\pi
488488 8.00000 0.362143
489489 20.0000 0.904431
490490 0 0
491491 −36.0000 −1.62466 −0.812329 0.583200i 0.801800π-0.801800\pi
−0.812329 + 0.583200i 0.801800π0.801800\pi
492492 6.00000 0.270501
493493 0 0
494494 8.00000 0.359937
495495 0 0
496496 10.0000 0.449013
497497 12.0000 0.538274
498498 12.0000 0.537733
499499 −32.0000 −1.43252 −0.716258 0.697835i 0.754147π-0.754147\pi
−0.716258 + 0.697835i 0.754147π0.754147\pi
500500 0 0
501501 18.0000 0.804181
502502 −12.0000 −0.535586
503503 6.00000 0.267527 0.133763 0.991013i 0.457294π-0.457294\pi
0.133763 + 0.991013i 0.457294π0.457294\pi
504504 2.00000 0.0890871
505505 0 0
506506 0 0
507507 9.00000 0.399704
508508 8.00000 0.354943
509509 −6.00000 −0.265945 −0.132973 0.991120i 0.542452π-0.542452\pi
−0.132973 + 0.991120i 0.542452π0.542452\pi
510510 0 0
511511 4.00000 0.176950
512512 −1.00000 −0.0441942
513513 4.00000 0.176604
514514 −18.0000 −0.793946
515515 0 0
516516 4.00000 0.176090
517517 0 0
518518 −16.0000 −0.703000
519519 0 0
520520 0 0
521521 −6.00000 −0.262865 −0.131432 0.991325i 0.541958π-0.541958\pi
−0.131432 + 0.991325i 0.541958π0.541958\pi
522522 0 0
523523 20.0000 0.874539 0.437269 0.899331i 0.355946π-0.355946\pi
0.437269 + 0.899331i 0.355946π0.355946\pi
524524 0 0
525525 −10.0000 −0.436436
526526 −12.0000 −0.523225
527527 0 0
528528 0 0
529529 13.0000 0.565217
530530 0 0
531531 −12.0000 −0.520756
532532 8.00000 0.346844
533533 −12.0000 −0.519778
534534 −18.0000 −0.778936
535535 0 0
536536 4.00000 0.172774
537537 12.0000 0.517838
538538 24.0000 1.03471
539539 0 0
540540 0 0
541541 16.0000 0.687894 0.343947 0.938989i 0.388236π-0.388236\pi
0.343947 + 0.938989i 0.388236π0.388236\pi
542542 16.0000 0.687259
543543 8.00000 0.343313
544544 0 0
545545 0 0
546546 −4.00000 −0.171184
547547 −8.00000 −0.342055 −0.171028 0.985266i 0.554709π-0.554709\pi
−0.171028 + 0.985266i 0.554709π0.554709\pi
548548 −6.00000 −0.256307
549549 −8.00000 −0.341432
550550 0 0
551551 0 0
552552 6.00000 0.255377
553553 −20.0000 −0.850487
554554 −4.00000 −0.169944
555555 0 0
556556 −8.00000 −0.339276
557557 −42.0000 −1.77960 −0.889799 0.456354i 0.849155π-0.849155\pi
−0.889799 + 0.456354i 0.849155π0.849155\pi
558558 −10.0000 −0.423334
559559 −8.00000 −0.338364
560560 0 0
561561 0 0
562562 −30.0000 −1.26547
563563 −12.0000 −0.505740 −0.252870 0.967500i 0.581374π-0.581374\pi
−0.252870 + 0.967500i 0.581374π0.581374\pi
564564 −12.0000 −0.505291
565565 0 0
566566 −16.0000 −0.672530
567567 −2.00000 −0.0839921
568568 6.00000 0.251754
569569 −6.00000 −0.251533 −0.125767 0.992060i 0.540139π-0.540139\pi
−0.125767 + 0.992060i 0.540139π0.540139\pi
570570 0 0
571571 −20.0000 −0.836974 −0.418487 0.908223i 0.637439π-0.637439\pi
−0.418487 + 0.908223i 0.637439π0.637439\pi
572572 0 0
573573 12.0000 0.501307
574574 −12.0000 −0.500870
575575 −30.0000 −1.25109
576576 1.00000 0.0416667
577577 2.00000 0.0832611 0.0416305 0.999133i 0.486745π-0.486745\pi
0.0416305 + 0.999133i 0.486745π0.486745\pi
578578 0 0
579579 14.0000 0.581820
580580 0 0
581581 −24.0000 −0.995688
582582 −14.0000 −0.580319
583583 0 0
584584 2.00000 0.0827606
585585 0 0
586586 −18.0000 −0.743573
587587 −12.0000 −0.495293 −0.247647 0.968850i 0.579657π-0.579657\pi
−0.247647 + 0.968850i 0.579657π0.579657\pi
588588 3.00000 0.123718
589589 −40.0000 −1.64817
590590 0 0
591591 −12.0000 −0.493614
592592 −8.00000 −0.328798
593593 18.0000 0.739171 0.369586 0.929197i 0.379500π-0.379500\pi
0.369586 + 0.929197i 0.379500π0.379500\pi
594594 0 0
595595 0 0
596596 −6.00000 −0.245770
597597 2.00000 0.0818546
598598 −12.0000 −0.490716
599599 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
600600 −5.00000 −0.204124
601601 22.0000 0.897399 0.448699 0.893683i 0.351887π-0.351887\pi
0.448699 + 0.893683i 0.351887π0.351887\pi
602602 −8.00000 −0.326056
603603 −4.00000 −0.162893
604604 8.00000 0.325515
605605 0 0
606606 6.00000 0.243733
607607 10.0000 0.405887 0.202944 0.979190i 0.434949π-0.434949\pi
0.202944 + 0.979190i 0.434949π0.434949\pi
608608 4.00000 0.162221
609609 0 0
610610 0 0
611611 24.0000 0.970936
612612 0 0
613613 −34.0000 −1.37325 −0.686624 0.727013i 0.740908π-0.740908\pi
−0.686624 + 0.727013i 0.740908π0.740908\pi
614614 −20.0000 −0.807134
615615 0 0
616616 0 0
617617 −18.0000 −0.724653 −0.362326 0.932051i 0.618017π-0.618017\pi
−0.362326 + 0.932051i 0.618017π0.618017\pi
618618 −4.00000 −0.160904
619619 28.0000 1.12542 0.562708 0.826656i 0.309760π-0.309760\pi
0.562708 + 0.826656i 0.309760π0.309760\pi
620620 0 0
621621 −6.00000 −0.240772
622622 18.0000 0.721734
623623 36.0000 1.44231
624624 −2.00000 −0.0800641
625625 25.0000 1.00000
626626 14.0000 0.559553
627627 0 0
628628 −10.0000 −0.399043
629629 0 0
630630 0 0
631631 −4.00000 −0.159237 −0.0796187 0.996825i 0.525370π-0.525370\pi
−0.0796187 + 0.996825i 0.525370π0.525370\pi
632632 −10.0000 −0.397779
633633 8.00000 0.317971
634634 12.0000 0.476581
635635 0 0
636636 −6.00000 −0.237915
637637 −6.00000 −0.237729
638638 0 0
639639 −6.00000 −0.237356
640640 0 0
641641 −30.0000 −1.18493 −0.592464 0.805597i 0.701845π-0.701845\pi
−0.592464 + 0.805597i 0.701845π0.701845\pi
642642 0 0
643643 4.00000 0.157745 0.0788723 0.996885i 0.474868π-0.474868\pi
0.0788723 + 0.996885i 0.474868π0.474868\pi
644644 −12.0000 −0.472866
645645 0 0
646646 0 0
647647 36.0000 1.41531 0.707653 0.706560i 0.249754π-0.249754\pi
0.707653 + 0.706560i 0.249754π0.249754\pi
648648 −1.00000 −0.0392837
649649 0 0
650650 10.0000 0.392232
651651 20.0000 0.783862
652652 −20.0000 −0.783260
653653 24.0000 0.939193 0.469596 0.882881i 0.344399π-0.344399\pi
0.469596 + 0.882881i 0.344399π0.344399\pi
654654 −20.0000 −0.782062
655655 0 0
656656 −6.00000 −0.234261
657657 −2.00000 −0.0780274
658658 24.0000 0.935617
659659 36.0000 1.40236 0.701180 0.712984i 0.252657π-0.252657\pi
0.701180 + 0.712984i 0.252657π0.252657\pi
660660 0 0
661661 −22.0000 −0.855701 −0.427850 0.903850i 0.640729π-0.640729\pi
−0.427850 + 0.903850i 0.640729π0.640729\pi
662662 −20.0000 −0.777322
663663 0 0
664664 −12.0000 −0.465690
665665 0 0
666666 8.00000 0.309994
667667 0 0
668668 −18.0000 −0.696441
669669 28.0000 1.08254
670670 0 0
671671 0 0
672672 −2.00000 −0.0771517
673673 34.0000 1.31060 0.655302 0.755367i 0.272541π-0.272541\pi
0.655302 + 0.755367i 0.272541π0.272541\pi
674674 −22.0000 −0.847408
675675 5.00000 0.192450
676676 −9.00000 −0.346154
677677 12.0000 0.461197 0.230599 0.973049i 0.425932π-0.425932\pi
0.230599 + 0.973049i 0.425932π0.425932\pi
678678 6.00000 0.230429
679679 28.0000 1.07454
680680 0 0
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 0 0
686686 −20.0000 −0.763604
687687 −14.0000 −0.534133
688688 −4.00000 −0.152499
689689 12.0000 0.457164
690690 0 0
691691 −32.0000 −1.21734 −0.608669 0.793424i 0.708296π-0.708296\pi
−0.608669 + 0.793424i 0.708296π0.708296\pi
692692 0 0
693693 0 0
694694 −12.0000 −0.455514
695695 0 0
696696 0 0
697697 0 0
698698 −26.0000 −0.984115
699699 −30.0000 −1.13470
700700 10.0000 0.377964
701701 −42.0000 −1.58632 −0.793159 0.609015i 0.791565π-0.791565\pi
−0.793159 + 0.609015i 0.791565π0.791565\pi
702702 2.00000 0.0754851
703703 32.0000 1.20690
704704 0 0
705705 0 0
706706 18.0000 0.677439
707707 −12.0000 −0.451306
708708 12.0000 0.450988
709709 −20.0000 −0.751116 −0.375558 0.926799i 0.622549π-0.622549\pi
−0.375558 + 0.926799i 0.622549π0.622549\pi
710710 0 0
711711 10.0000 0.375029
712712 18.0000 0.674579
713713 60.0000 2.24702
714714 0 0
715715 0 0
716716 −12.0000 −0.448461
717717 12.0000 0.448148
718718 0 0
719719 −6.00000 −0.223762 −0.111881 0.993722i 0.535688π-0.535688\pi
−0.111881 + 0.993722i 0.535688π0.535688\pi
720720 0 0
721721 8.00000 0.297936
722722 3.00000 0.111648
723723 −10.0000 −0.371904
724724 −8.00000 −0.297318
725725 0 0
726726 −11.0000 −0.408248
727727 8.00000 0.296704 0.148352 0.988935i 0.452603π-0.452603\pi
0.148352 + 0.988935i 0.452603π0.452603\pi
728728 4.00000 0.148250
729729 1.00000 0.0370370
730730 0 0
731731 0 0
732732 8.00000 0.295689
733733 26.0000 0.960332 0.480166 0.877178i 0.340576π-0.340576\pi
0.480166 + 0.877178i 0.340576π0.340576\pi
734734 −10.0000 −0.369107
735735 0 0
736736 −6.00000 −0.221163
737737 0 0
738738 6.00000 0.220863
739739 −4.00000 −0.147142 −0.0735712 0.997290i 0.523440π-0.523440\pi
−0.0735712 + 0.997290i 0.523440π0.523440\pi
740740 0 0
741741 8.00000 0.293887
742742 12.0000 0.440534
743743 −42.0000 −1.54083 −0.770415 0.637542i 0.779951π-0.779951\pi
−0.770415 + 0.637542i 0.779951π0.779951\pi
744744 10.0000 0.366618
745745 0 0
746746 22.0000 0.805477
747747 12.0000 0.439057
748748 0 0
749749 0 0
750750 0 0
751751 −2.00000 −0.0729810 −0.0364905 0.999334i 0.511618π-0.511618\pi
−0.0364905 + 0.999334i 0.511618π0.511618\pi
752752 12.0000 0.437595
753753 −12.0000 −0.437304
754754 0 0
755755 0 0
756756 2.00000 0.0727393
757757 −34.0000 −1.23575 −0.617876 0.786276i 0.712006π-0.712006\pi
−0.617876 + 0.786276i 0.712006π0.712006\pi
758758 −28.0000 −1.01701
759759 0 0
760760 0 0
761761 −54.0000 −1.95750 −0.978749 0.205061i 0.934261π-0.934261\pi
−0.978749 + 0.205061i 0.934261π0.934261\pi
762762 8.00000 0.289809
763763 40.0000 1.44810
764764 −12.0000 −0.434145
765765 0 0
766766 12.0000 0.433578
767767 −24.0000 −0.866590
768768 −1.00000 −0.0360844
769769 −22.0000 −0.793340 −0.396670 0.917961i 0.629834π-0.629834\pi
−0.396670 + 0.917961i 0.629834π0.629834\pi
770770 0 0
771771 −18.0000 −0.648254
772772 −14.0000 −0.503871
773773 −6.00000 −0.215805 −0.107903 0.994161i 0.534413π-0.534413\pi
−0.107903 + 0.994161i 0.534413π0.534413\pi
774774 4.00000 0.143777
775775 −50.0000 −1.79605
776776 14.0000 0.502571
777777 −16.0000 −0.573997
778778 30.0000 1.07555
779779 24.0000 0.859889
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −3.00000 −0.107143
785785 0 0
786786 0 0
787787 −32.0000 −1.14068 −0.570338 0.821410i 0.693188π-0.693188\pi
−0.570338 + 0.821410i 0.693188π0.693188\pi
788788 12.0000 0.427482
789789 −12.0000 −0.427211
790790 0 0
791791 −12.0000 −0.426671
792792 0 0
793793 −16.0000 −0.568177
794794 −16.0000 −0.567819
795795 0 0
796796 −2.00000 −0.0708881
797797 6.00000 0.212531 0.106265 0.994338i 0.466111π-0.466111\pi
0.106265 + 0.994338i 0.466111π0.466111\pi
798798 8.00000 0.283197
799799 0 0
800800 5.00000 0.176777
801801 −18.0000 −0.635999
802802 −18.0000 −0.635602
803803 0 0
804804 4.00000 0.141069
805805 0 0
806806 −20.0000 −0.704470
807807 24.0000 0.844840
808808 −6.00000 −0.211079
809809 −6.00000 −0.210949 −0.105474 0.994422i 0.533636π-0.533636\pi
−0.105474 + 0.994422i 0.533636π0.533636\pi
810810 0 0
811811 4.00000 0.140459 0.0702295 0.997531i 0.477627π-0.477627\pi
0.0702295 + 0.997531i 0.477627π0.477627\pi
812812 0 0
813813 16.0000 0.561144
814814 0 0
815815 0 0
816816 0 0
817817 16.0000 0.559769
818818 −38.0000 −1.32864
819819 −4.00000 −0.139771
820820 0 0
821821 36.0000 1.25641 0.628204 0.778048i 0.283790π-0.283790\pi
0.628204 + 0.778048i 0.283790π0.283790\pi
822822 −6.00000 −0.209274
823823 34.0000 1.18517 0.592583 0.805510i 0.298108π-0.298108\pi
0.592583 + 0.805510i 0.298108π0.298108\pi
824824 4.00000 0.139347
825825 0 0
826826 −24.0000 −0.835067
827827 −48.0000 −1.66912 −0.834562 0.550914i 0.814279π-0.814279\pi
−0.834562 + 0.550914i 0.814279π0.814279\pi
828828 6.00000 0.208514
829829 −10.0000 −0.347314 −0.173657 0.984806i 0.555558π-0.555558\pi
−0.173657 + 0.984806i 0.555558π0.555558\pi
830830 0 0
831831 −4.00000 −0.138758
832832 2.00000 0.0693375
833833 0 0
834834 −8.00000 −0.277017
835835 0 0
836836 0 0
837837 −10.0000 −0.345651
838838 −36.0000 −1.24360
839839 18.0000 0.621429 0.310715 0.950503i 0.399432π-0.399432\pi
0.310715 + 0.950503i 0.399432π0.399432\pi
840840 0 0
841841 −29.0000 −1.00000
842842 22.0000 0.758170
843843 −30.0000 −1.03325
844844 −8.00000 −0.275371
845845 0 0
846846 −12.0000 −0.412568
847847 22.0000 0.755929
848848 6.00000 0.206041
849849 −16.0000 −0.549119
850850 0 0
851851 −48.0000 −1.64542
852852 6.00000 0.205557
853853 28.0000 0.958702 0.479351 0.877623i 0.340872π-0.340872\pi
0.479351 + 0.877623i 0.340872π0.340872\pi
854854 −16.0000 −0.547509
855855 0 0
856856 0 0
857857 −6.00000 −0.204956 −0.102478 0.994735i 0.532677π-0.532677\pi
−0.102478 + 0.994735i 0.532677π0.532677\pi
858858 0 0
859859 −28.0000 −0.955348 −0.477674 0.878537i 0.658520π-0.658520\pi
−0.477674 + 0.878537i 0.658520π0.658520\pi
860860 0 0
861861 −12.0000 −0.408959
862862 −30.0000 −1.02180
863863 48.0000 1.63394 0.816970 0.576681i 0.195652π-0.195652\pi
0.816970 + 0.576681i 0.195652π0.195652\pi
864864 1.00000 0.0340207
865865 0 0
866866 −14.0000 −0.475739
867867 0 0
868868 −20.0000 −0.678844
869869 0 0
870870 0 0
871871 −8.00000 −0.271070
872872 20.0000 0.677285
873873 −14.0000 −0.473828
874874 24.0000 0.811812
875875 0 0
876876 2.00000 0.0675737
877877 4.00000 0.135070 0.0675352 0.997717i 0.478487π-0.478487\pi
0.0675352 + 0.997717i 0.478487π0.478487\pi
878878 26.0000 0.877457
879879 −18.0000 −0.607125
880880 0 0
881881 54.0000 1.81931 0.909653 0.415369i 0.136347π-0.136347\pi
0.909653 + 0.415369i 0.136347π0.136347\pi
882882 3.00000 0.101015
883883 20.0000 0.673054 0.336527 0.941674i 0.390748π-0.390748\pi
0.336527 + 0.941674i 0.390748π0.390748\pi
884884 0 0
885885 0 0
886886 36.0000 1.20944
887887 18.0000 0.604381 0.302190 0.953248i 0.402282π-0.402282\pi
0.302190 + 0.953248i 0.402282π0.402282\pi
888888 −8.00000 −0.268462
889889 −16.0000 −0.536623
890890 0 0
891891 0 0
892892 −28.0000 −0.937509
893893 −48.0000 −1.60626
894894 −6.00000 −0.200670
895895 0 0
896896 2.00000 0.0668153
897897 −12.0000 −0.400668
898898 6.00000 0.200223
899899 0 0
900900 −5.00000 −0.166667
901901 0 0
902902 0 0
903903 −8.00000 −0.266223
904904 −6.00000 −0.199557
905905 0 0
906906 8.00000 0.265782
907907 40.0000 1.32818 0.664089 0.747653i 0.268820π-0.268820\pi
0.664089 + 0.747653i 0.268820π0.268820\pi
908908 −12.0000 −0.398234
909909 6.00000 0.199007
910910 0 0
911911 −6.00000 −0.198789 −0.0993944 0.995048i 0.531691π-0.531691\pi
−0.0993944 + 0.995048i 0.531691π0.531691\pi
912912 4.00000 0.132453
913913 0 0
914914 10.0000 0.330771
915915 0 0
916916 14.0000 0.462573
917917 0 0
918918 0 0
919919 −16.0000 −0.527791 −0.263896 0.964551i 0.585007π-0.585007\pi
−0.263896 + 0.964551i 0.585007π0.585007\pi
920920 0 0
921921 −20.0000 −0.659022
922922 −30.0000 −0.987997
923923 −12.0000 −0.394985
924924 0 0
925925 40.0000 1.31519
926926 −20.0000 −0.657241
927927 −4.00000 −0.131377
928928 0 0
929929 18.0000 0.590561 0.295280 0.955411i 0.404587π-0.404587\pi
0.295280 + 0.955411i 0.404587π0.404587\pi
930930 0 0
931931 12.0000 0.393284
932932 30.0000 0.982683
933933 18.0000 0.589294
934934 −12.0000 −0.392652
935935 0 0
936936 −2.00000 −0.0653720
937937 −10.0000 −0.326686 −0.163343 0.986569i 0.552228π-0.552228\pi
−0.163343 + 0.986569i 0.552228π0.552228\pi
938938 −8.00000 −0.261209
939939 14.0000 0.456873
940940 0 0
941941 −12.0000 −0.391189 −0.195594 0.980685i 0.562664π-0.562664\pi
−0.195594 + 0.980685i 0.562664π0.562664\pi
942942 −10.0000 −0.325818
943943 −36.0000 −1.17232
944944 −12.0000 −0.390567
945945 0 0
946946 0 0
947947 −24.0000 −0.779895 −0.389948 0.920837i 0.627507π-0.627507\pi
−0.389948 + 0.920837i 0.627507π0.627507\pi
948948 −10.0000 −0.324785
949949 −4.00000 −0.129845
950950 −20.0000 −0.648886
951951 12.0000 0.389127
952952 0 0
953953 54.0000 1.74923 0.874616 0.484817i 0.161114π-0.161114\pi
0.874616 + 0.484817i 0.161114π0.161114\pi
954954 −6.00000 −0.194257
955955 0 0
956956 −12.0000 −0.388108
957957 0 0
958958 6.00000 0.193851
959959 12.0000 0.387500
960960 0 0
961961 69.0000 2.22581
962962 16.0000 0.515861
963963 0 0
964964 10.0000 0.322078
965965 0 0
966966 −12.0000 −0.386094
967967 −4.00000 −0.128631 −0.0643157 0.997930i 0.520486π-0.520486\pi
−0.0643157 + 0.997930i 0.520486π0.520486\pi
968968 11.0000 0.353553
969969 0 0
970970 0 0
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 16.0000 0.512936
974974 −10.0000 −0.320421
975975 10.0000 0.320256
976976 −8.00000 −0.256074
977977 −30.0000 −0.959785 −0.479893 0.877327i 0.659324π-0.659324\pi
−0.479893 + 0.877327i 0.659324π0.659324\pi
978978 −20.0000 −0.639529
979979 0 0
980980 0 0
981981 −20.0000 −0.638551
982982 36.0000 1.14881
983983 −6.00000 −0.191370 −0.0956851 0.995412i 0.530504π-0.530504\pi
−0.0956851 + 0.995412i 0.530504π0.530504\pi
984984 −6.00000 −0.191273
985985 0 0
986986 0 0
987987 24.0000 0.763928
988988 −8.00000 −0.254514
989989 −24.0000 −0.763156
990990 0 0
991991 −2.00000 −0.0635321 −0.0317660 0.999495i 0.510113π-0.510113\pi
−0.0317660 + 0.999495i 0.510113π0.510113\pi
992992 −10.0000 −0.317500
993993 −20.0000 −0.634681
994994 −12.0000 −0.380617
995995 0 0
996996 −12.0000 −0.380235
997997 −8.00000 −0.253363 −0.126681 0.991943i 0.540433π-0.540433\pi
−0.126681 + 0.991943i 0.540433π0.540433\pi
998998 32.0000 1.01294
999999 8.00000 0.253109
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 1734.2.a.b.1.1 1
3.2 odd 2 5202.2.a.j.1.1 1
17.2 even 8 1734.2.f.b.1483.1 4
17.4 even 4 1734.2.b.f.577.2 2
17.8 even 8 1734.2.f.b.829.2 4
17.9 even 8 1734.2.f.b.829.1 4
17.13 even 4 1734.2.b.f.577.1 2
17.15 even 8 1734.2.f.b.1483.2 4
17.16 even 2 102.2.a.b.1.1 1
51.50 odd 2 306.2.a.c.1.1 1
68.67 odd 2 816.2.a.d.1.1 1
85.33 odd 4 2550.2.d.g.2449.2 2
85.67 odd 4 2550.2.d.g.2449.1 2
85.84 even 2 2550.2.a.u.1.1 1
119.118 odd 2 4998.2.a.d.1.1 1
136.67 odd 2 3264.2.a.w.1.1 1
136.101 even 2 3264.2.a.i.1.1 1
204.203 even 2 2448.2.a.i.1.1 1
255.254 odd 2 7650.2.a.j.1.1 1
408.101 odd 2 9792.2.a.bg.1.1 1
408.203 even 2 9792.2.a.ba.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
102.2.a.b.1.1 1 17.16 even 2
306.2.a.c.1.1 1 51.50 odd 2
816.2.a.d.1.1 1 68.67 odd 2
1734.2.a.b.1.1 1 1.1 even 1 trivial
1734.2.b.f.577.1 2 17.13 even 4
1734.2.b.f.577.2 2 17.4 even 4
1734.2.f.b.829.1 4 17.9 even 8
1734.2.f.b.829.2 4 17.8 even 8
1734.2.f.b.1483.1 4 17.2 even 8
1734.2.f.b.1483.2 4 17.15 even 8
2448.2.a.i.1.1 1 204.203 even 2
2550.2.a.u.1.1 1 85.84 even 2
2550.2.d.g.2449.1 2 85.67 odd 4
2550.2.d.g.2449.2 2 85.33 odd 4
3264.2.a.i.1.1 1 136.101 even 2
3264.2.a.w.1.1 1 136.67 odd 2
4998.2.a.d.1.1 1 119.118 odd 2
5202.2.a.j.1.1 1 3.2 odd 2
7650.2.a.j.1.1 1 255.254 odd 2
9792.2.a.ba.1.1 1 408.203 even 2
9792.2.a.bg.1.1 1 408.101 odd 2