Properties

Label 2166.2.a.i.1.1
Level 21662166
Weight 22
Character 2166.1
Self dual yes
Analytic conductor 17.29617.296
Analytic rank 00
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] = [2166,2,Mod(1,2166)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2166, 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("2166.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2166=23192 2166 = 2 \cdot 3 \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2166.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,1,1,0,1,4] 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: 17.295597077817.2955970778
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 114)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 2166.1

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) == q+1.00000q2+1.00000q3+1.00000q4+1.00000q6+4.00000q7+1.00000q8+1.00000q9+4.00000q11+1.00000q12+4.00000q14+1.00000q162.00000q17+1.00000q18+4.00000q21+4.00000q222.00000q23+1.00000q245.00000q25+1.00000q27+4.00000q28+6.00000q296.00000q31+1.00000q32+4.00000q332.00000q34+1.00000q36+8.00000q3710.0000q41+4.00000q4212.0000q43+4.00000q442.00000q46+10.0000q47+1.00000q48+9.00000q495.00000q502.00000q512.00000q53+1.00000q54+4.00000q56+6.00000q584.00000q5910.0000q616.00000q62+4.00000q63+1.00000q64+4.00000q662.00000q682.00000q69+16.0000q71+1.00000q722.00000q73+8.00000q745.00000q75+16.0000q7710.0000q79+1.00000q8110.0000q8216.0000q83+4.00000q8412.0000q86+6.00000q87+4.00000q88+2.00000q892.00000q926.00000q93+10.0000q94+1.00000q96+10.0000q97+9.00000q98+4.00000q99+O(q100)q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{11} +1.00000 q^{12} +4.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} +4.00000 q^{21} +4.00000 q^{22} -2.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} +1.00000 q^{27} +4.00000 q^{28} +6.00000 q^{29} -6.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} +8.00000 q^{37} -10.0000 q^{41} +4.00000 q^{42} -12.0000 q^{43} +4.00000 q^{44} -2.00000 q^{46} +10.0000 q^{47} +1.00000 q^{48} +9.00000 q^{49} -5.00000 q^{50} -2.00000 q^{51} -2.00000 q^{53} +1.00000 q^{54} +4.00000 q^{56} +6.00000 q^{58} -4.00000 q^{59} -10.0000 q^{61} -6.00000 q^{62} +4.00000 q^{63} +1.00000 q^{64} +4.00000 q^{66} -2.00000 q^{68} -2.00000 q^{69} +16.0000 q^{71} +1.00000 q^{72} -2.00000 q^{73} +8.00000 q^{74} -5.00000 q^{75} +16.0000 q^{77} -10.0000 q^{79} +1.00000 q^{81} -10.0000 q^{82} -16.0000 q^{83} +4.00000 q^{84} -12.0000 q^{86} +6.00000 q^{87} +4.00000 q^{88} +2.00000 q^{89} -2.00000 q^{92} -6.00000 q^{93} +10.0000 q^{94} +1.00000 q^{96} +10.0000 q^{97} +9.00000 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
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 4.00000 1.51186 0.755929 0.654654i 0.227186π-0.227186\pi
0.755929 + 0.654654i 0.227186π0.227186\pi
88 1.00000 0.353553
99 1.00000 0.333333
1010 0 0
1111 4.00000 1.20605 0.603023 0.797724i 0.293963π-0.293963\pi
0.603023 + 0.797724i 0.293963π0.293963\pi
1212 1.00000 0.288675
1313 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1414 4.00000 1.06904
1515 0 0
1616 1.00000 0.250000
1717 −2.00000 −0.485071 −0.242536 0.970143i 0.577979π-0.577979\pi
−0.242536 + 0.970143i 0.577979π0.577979\pi
1818 1.00000 0.235702
1919 0 0
2020 0 0
2121 4.00000 0.872872
2222 4.00000 0.852803
2323 −2.00000 −0.417029 −0.208514 0.978019i 0.566863π-0.566863\pi
−0.208514 + 0.978019i 0.566863π0.566863\pi
2424 1.00000 0.204124
2525 −5.00000 −1.00000
2626 0 0
2727 1.00000 0.192450
2828 4.00000 0.755929
2929 6.00000 1.11417 0.557086 0.830455i 0.311919π-0.311919\pi
0.557086 + 0.830455i 0.311919π0.311919\pi
3030 0 0
3131 −6.00000 −1.07763 −0.538816 0.842424i 0.681128π-0.681128\pi
−0.538816 + 0.842424i 0.681128π0.681128\pi
3232 1.00000 0.176777
3333 4.00000 0.696311
3434 −2.00000 −0.342997
3535 0 0
3636 1.00000 0.166667
3737 8.00000 1.31519 0.657596 0.753371i 0.271573π-0.271573\pi
0.657596 + 0.753371i 0.271573π0.271573\pi
3838 0 0
3939 0 0
4040 0 0
4141 −10.0000 −1.56174 −0.780869 0.624695i 0.785223π-0.785223\pi
−0.780869 + 0.624695i 0.785223π0.785223\pi
4242 4.00000 0.617213
4343 −12.0000 −1.82998 −0.914991 0.403473i 0.867803π-0.867803\pi
−0.914991 + 0.403473i 0.867803π0.867803\pi
4444 4.00000 0.603023
4545 0 0
4646 −2.00000 −0.294884
4747 10.0000 1.45865 0.729325 0.684167i 0.239834π-0.239834\pi
0.729325 + 0.684167i 0.239834π0.239834\pi
4848 1.00000 0.144338
4949 9.00000 1.28571
5050 −5.00000 −0.707107
5151 −2.00000 −0.280056
5252 0 0
5353 −2.00000 −0.274721 −0.137361 0.990521i 0.543862π-0.543862\pi
−0.137361 + 0.990521i 0.543862π0.543862\pi
5454 1.00000 0.136083
5555 0 0
5656 4.00000 0.534522
5757 0 0
5858 6.00000 0.787839
5959 −4.00000 −0.520756 −0.260378 0.965507i 0.583847π-0.583847\pi
−0.260378 + 0.965507i 0.583847π0.583847\pi
6060 0 0
6161 −10.0000 −1.28037 −0.640184 0.768221i 0.721142π-0.721142\pi
−0.640184 + 0.768221i 0.721142π0.721142\pi
6262 −6.00000 −0.762001
6363 4.00000 0.503953
6464 1.00000 0.125000
6565 0 0
6666 4.00000 0.492366
6767 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6868 −2.00000 −0.242536
6969 −2.00000 −0.240772
7070 0 0
7171 16.0000 1.89885 0.949425 0.313993i 0.101667π-0.101667\pi
0.949425 + 0.313993i 0.101667π0.101667\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 0 0
7777 16.0000 1.82337
7878 0 0
7979 −10.0000 −1.12509 −0.562544 0.826767i 0.690177π-0.690177\pi
−0.562544 + 0.826767i 0.690177π0.690177\pi
8080 0 0
8181 1.00000 0.111111
8282 −10.0000 −1.10432
8383 −16.0000 −1.75623 −0.878114 0.478451i 0.841198π-0.841198\pi
−0.878114 + 0.478451i 0.841198π0.841198\pi
8484 4.00000 0.436436
8585 0 0
8686 −12.0000 −1.29399
8787 6.00000 0.643268
8888 4.00000 0.426401
8989 2.00000 0.212000 0.106000 0.994366i 0.466196π-0.466196\pi
0.106000 + 0.994366i 0.466196π0.466196\pi
9090 0 0
9191 0 0
9292 −2.00000 −0.208514
9393 −6.00000 −0.622171
9494 10.0000 1.03142
9595 0 0
9696 1.00000 0.102062
9797 10.0000 1.01535 0.507673 0.861550i 0.330506π-0.330506\pi
0.507673 + 0.861550i 0.330506π0.330506\pi
9898 9.00000 0.909137
9999 4.00000 0.402015
100100 −5.00000 −0.500000
101101 8.00000 0.796030 0.398015 0.917379i 0.369699π-0.369699\pi
0.398015 + 0.917379i 0.369699π0.369699\pi
102102 −2.00000 −0.198030
103103 6.00000 0.591198 0.295599 0.955312i 0.404481π-0.404481\pi
0.295599 + 0.955312i 0.404481π0.404481\pi
104104 0 0
105105 0 0
106106 −2.00000 −0.194257
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 4.00000 0.383131 0.191565 0.981480i 0.438644π-0.438644\pi
0.191565 + 0.981480i 0.438644π0.438644\pi
110110 0 0
111111 8.00000 0.759326
112112 4.00000 0.377964
113113 14.0000 1.31701 0.658505 0.752577i 0.271189π-0.271189\pi
0.658505 + 0.752577i 0.271189π0.271189\pi
114114 0 0
115115 0 0
116116 6.00000 0.557086
117117 0 0
118118 −4.00000 −0.368230
119119 −8.00000 −0.733359
120120 0 0
121121 5.00000 0.454545
122122 −10.0000 −0.905357
123123 −10.0000 −0.901670
124124 −6.00000 −0.538816
125125 0 0
126126 4.00000 0.356348
127127 −22.0000 −1.95218 −0.976092 0.217357i 0.930256π-0.930256\pi
−0.976092 + 0.217357i 0.930256π0.930256\pi
128128 1.00000 0.0883883
129129 −12.0000 −1.05654
130130 0 0
131131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
132132 4.00000 0.348155
133133 0 0
134134 0 0
135135 0 0
136136 −2.00000 −0.171499
137137 6.00000 0.512615 0.256307 0.966595i 0.417494π-0.417494\pi
0.256307 + 0.966595i 0.417494π0.417494\pi
138138 −2.00000 −0.170251
139139 −4.00000 −0.339276 −0.169638 0.985506i 0.554260π-0.554260\pi
−0.169638 + 0.985506i 0.554260π0.554260\pi
140140 0 0
141141 10.0000 0.842152
142142 16.0000 1.34269
143143 0 0
144144 1.00000 0.0833333
145145 0 0
146146 −2.00000 −0.165521
147147 9.00000 0.742307
148148 8.00000 0.657596
149149 20.0000 1.63846 0.819232 0.573462i 0.194400π-0.194400\pi
0.819232 + 0.573462i 0.194400π0.194400\pi
150150 −5.00000 −0.408248
151151 −10.0000 −0.813788 −0.406894 0.913475i 0.633388π-0.633388\pi
−0.406894 + 0.913475i 0.633388π0.633388\pi
152152 0 0
153153 −2.00000 −0.161690
154154 16.0000 1.28932
155155 0 0
156156 0 0
157157 18.0000 1.43656 0.718278 0.695756i 0.244931π-0.244931\pi
0.718278 + 0.695756i 0.244931π0.244931\pi
158158 −10.0000 −0.795557
159159 −2.00000 −0.158610
160160 0 0
161161 −8.00000 −0.630488
162162 1.00000 0.0785674
163163 20.0000 1.56652 0.783260 0.621694i 0.213555π-0.213555\pi
0.783260 + 0.621694i 0.213555π0.213555\pi
164164 −10.0000 −0.780869
165165 0 0
166166 −16.0000 −1.24184
167167 −12.0000 −0.928588 −0.464294 0.885681i 0.653692π-0.653692\pi
−0.464294 + 0.885681i 0.653692π0.653692\pi
168168 4.00000 0.308607
169169 −13.0000 −1.00000
170170 0 0
171171 0 0
172172 −12.0000 −0.914991
173173 −6.00000 −0.456172 −0.228086 0.973641i 0.573247π-0.573247\pi
−0.228086 + 0.973641i 0.573247π0.573247\pi
174174 6.00000 0.454859
175175 −20.0000 −1.51186
176176 4.00000 0.301511
177177 −4.00000 −0.300658
178178 2.00000 0.149906
179179 20.0000 1.49487 0.747435 0.664335i 0.231285π-0.231285\pi
0.747435 + 0.664335i 0.231285π0.231285\pi
180180 0 0
181181 −12.0000 −0.891953 −0.445976 0.895045i 0.647144π-0.647144\pi
−0.445976 + 0.895045i 0.647144π0.647144\pi
182182 0 0
183183 −10.0000 −0.739221
184184 −2.00000 −0.147442
185185 0 0
186186 −6.00000 −0.439941
187187 −8.00000 −0.585018
188188 10.0000 0.729325
189189 4.00000 0.290957
190190 0 0
191191 −2.00000 −0.144715 −0.0723575 0.997379i 0.523052π-0.523052\pi
−0.0723575 + 0.997379i 0.523052π0.523052\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 10.0000 0.717958
195195 0 0
196196 9.00000 0.642857
197197 −20.0000 −1.42494 −0.712470 0.701702i 0.752424π-0.752424\pi
−0.712470 + 0.701702i 0.752424π0.752424\pi
198198 4.00000 0.284268
199199 −4.00000 −0.283552 −0.141776 0.989899i 0.545281π-0.545281\pi
−0.141776 + 0.989899i 0.545281π0.545281\pi
200200 −5.00000 −0.353553
201201 0 0
202202 8.00000 0.562878
203203 24.0000 1.68447
204204 −2.00000 −0.140028
205205 0 0
206206 6.00000 0.418040
207207 −2.00000 −0.139010
208208 0 0
209209 0 0
210210 0 0
211211 20.0000 1.37686 0.688428 0.725304i 0.258301π-0.258301\pi
0.688428 + 0.725304i 0.258301π0.258301\pi
212212 −2.00000 −0.137361
213213 16.0000 1.09630
214214 4.00000 0.273434
215215 0 0
216216 1.00000 0.0680414
217217 −24.0000 −1.62923
218218 4.00000 0.270914
219219 −2.00000 −0.135147
220220 0 0
221221 0 0
222222 8.00000 0.536925
223223 −6.00000 −0.401790 −0.200895 0.979613i 0.564385π-0.564385\pi
−0.200895 + 0.979613i 0.564385π0.564385\pi
224224 4.00000 0.267261
225225 −5.00000 −0.333333
226226 14.0000 0.931266
227227 −20.0000 −1.32745 −0.663723 0.747978i 0.731025π-0.731025\pi
−0.663723 + 0.747978i 0.731025π0.731025\pi
228228 0 0
229229 −2.00000 −0.132164 −0.0660819 0.997814i 0.521050π-0.521050\pi
−0.0660819 + 0.997814i 0.521050π0.521050\pi
230230 0 0
231231 16.0000 1.05272
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 −4.00000 −0.260378
237237 −10.0000 −0.649570
238238 −8.00000 −0.518563
239239 −6.00000 −0.388108 −0.194054 0.980991i 0.562164π-0.562164\pi
−0.194054 + 0.980991i 0.562164π0.562164\pi
240240 0 0
241241 2.00000 0.128831 0.0644157 0.997923i 0.479482π-0.479482\pi
0.0644157 + 0.997923i 0.479482π0.479482\pi
242242 5.00000 0.321412
243243 1.00000 0.0641500
244244 −10.0000 −0.640184
245245 0 0
246246 −10.0000 −0.637577
247247 0 0
248248 −6.00000 −0.381000
249249 −16.0000 −1.01396
250250 0 0
251251 −24.0000 −1.51487 −0.757433 0.652913i 0.773547π-0.773547\pi
−0.757433 + 0.652913i 0.773547π0.773547\pi
252252 4.00000 0.251976
253253 −8.00000 −0.502956
254254 −22.0000 −1.38040
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 −12.0000 −0.747087
259259 32.0000 1.98838
260260 0 0
261261 6.00000 0.371391
262262 0 0
263263 −6.00000 −0.369976 −0.184988 0.982741i 0.559225π-0.559225\pi
−0.184988 + 0.982741i 0.559225π0.559225\pi
264264 4.00000 0.246183
265265 0 0
266266 0 0
267267 2.00000 0.122398
268268 0 0
269269 −14.0000 −0.853595 −0.426798 0.904347i 0.640358π-0.640358\pi
−0.426798 + 0.904347i 0.640358π0.640358\pi
270270 0 0
271271 −4.00000 −0.242983 −0.121491 0.992592i 0.538768π-0.538768\pi
−0.121491 + 0.992592i 0.538768π0.538768\pi
272272 −2.00000 −0.121268
273273 0 0
274274 6.00000 0.362473
275275 −20.0000 −1.20605
276276 −2.00000 −0.120386
277277 −2.00000 −0.120168 −0.0600842 0.998193i 0.519137π-0.519137\pi
−0.0600842 + 0.998193i 0.519137π0.519137\pi
278278 −4.00000 −0.239904
279279 −6.00000 −0.359211
280280 0 0
281281 −10.0000 −0.596550 −0.298275 0.954480i 0.596411π-0.596411\pi
−0.298275 + 0.954480i 0.596411π0.596411\pi
282282 10.0000 0.595491
283283 28.0000 1.66443 0.832214 0.554455i 0.187073π-0.187073\pi
0.832214 + 0.554455i 0.187073π0.187073\pi
284284 16.0000 0.949425
285285 0 0
286286 0 0
287287 −40.0000 −2.36113
288288 1.00000 0.0589256
289289 −13.0000 −0.764706
290290 0 0
291291 10.0000 0.586210
292292 −2.00000 −0.117041
293293 −14.0000 −0.817889 −0.408944 0.912559i 0.634103π-0.634103\pi
−0.408944 + 0.912559i 0.634103π0.634103\pi
294294 9.00000 0.524891
295295 0 0
296296 8.00000 0.464991
297297 4.00000 0.232104
298298 20.0000 1.15857
299299 0 0
300300 −5.00000 −0.288675
301301 −48.0000 −2.76667
302302 −10.0000 −0.575435
303303 8.00000 0.459588
304304 0 0
305305 0 0
306306 −2.00000 −0.114332
307307 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
308308 16.0000 0.911685
309309 6.00000 0.341328
310310 0 0
311311 34.0000 1.92796 0.963982 0.265969i 0.0856919π-0.0856919\pi
0.963982 + 0.265969i 0.0856919π0.0856919\pi
312312 0 0
313313 6.00000 0.339140 0.169570 0.985518i 0.445762π-0.445762\pi
0.169570 + 0.985518i 0.445762π0.445762\pi
314314 18.0000 1.01580
315315 0 0
316316 −10.0000 −0.562544
317317 −6.00000 −0.336994 −0.168497 0.985702i 0.553891π-0.553891\pi
−0.168497 + 0.985702i 0.553891π0.553891\pi
318318 −2.00000 −0.112154
319319 24.0000 1.34374
320320 0 0
321321 4.00000 0.223258
322322 −8.00000 −0.445823
323323 0 0
324324 1.00000 0.0555556
325325 0 0
326326 20.0000 1.10770
327327 4.00000 0.221201
328328 −10.0000 −0.552158
329329 40.0000 2.20527
330330 0 0
331331 −24.0000 −1.31916 −0.659580 0.751635i 0.729266π-0.729266\pi
−0.659580 + 0.751635i 0.729266π0.729266\pi
332332 −16.0000 −0.878114
333333 8.00000 0.438397
334334 −12.0000 −0.656611
335335 0 0
336336 4.00000 0.218218
337337 −26.0000 −1.41631 −0.708155 0.706057i 0.750472π-0.750472\pi
−0.708155 + 0.706057i 0.750472π0.750472\pi
338338 −13.0000 −0.707107
339339 14.0000 0.760376
340340 0 0
341341 −24.0000 −1.29967
342342 0 0
343343 8.00000 0.431959
344344 −12.0000 −0.646997
345345 0 0
346346 −6.00000 −0.322562
347347 28.0000 1.50312 0.751559 0.659665i 0.229302π-0.229302\pi
0.751559 + 0.659665i 0.229302π0.229302\pi
348348 6.00000 0.321634
349349 10.0000 0.535288 0.267644 0.963518i 0.413755π-0.413755\pi
0.267644 + 0.963518i 0.413755π0.413755\pi
350350 −20.0000 −1.06904
351351 0 0
352352 4.00000 0.213201
353353 −30.0000 −1.59674 −0.798369 0.602168i 0.794304π-0.794304\pi
−0.798369 + 0.602168i 0.794304π0.794304\pi
354354 −4.00000 −0.212598
355355 0 0
356356 2.00000 0.106000
357357 −8.00000 −0.423405
358358 20.0000 1.05703
359359 6.00000 0.316668 0.158334 0.987386i 0.449388π-0.449388\pi
0.158334 + 0.987386i 0.449388π0.449388\pi
360360 0 0
361361 0 0
362362 −12.0000 −0.630706
363363 5.00000 0.262432
364364 0 0
365365 0 0
366366 −10.0000 −0.522708
367367 −28.0000 −1.46159 −0.730794 0.682598i 0.760850π-0.760850\pi
−0.730794 + 0.682598i 0.760850π0.760850\pi
368368 −2.00000 −0.104257
369369 −10.0000 −0.520579
370370 0 0
371371 −8.00000 −0.415339
372372 −6.00000 −0.311086
373373 −8.00000 −0.414224 −0.207112 0.978317i 0.566407π-0.566407\pi
−0.207112 + 0.978317i 0.566407π0.566407\pi
374374 −8.00000 −0.413670
375375 0 0
376376 10.0000 0.515711
377377 0 0
378378 4.00000 0.205738
379379 −8.00000 −0.410932 −0.205466 0.978664i 0.565871π-0.565871\pi
−0.205466 + 0.978664i 0.565871π0.565871\pi
380380 0 0
381381 −22.0000 −1.12709
382382 −2.00000 −0.102329
383383 −8.00000 −0.408781 −0.204390 0.978889i 0.565521π-0.565521\pi
−0.204390 + 0.978889i 0.565521π0.565521\pi
384384 1.00000 0.0510310
385385 0 0
386386 −14.0000 −0.712581
387387 −12.0000 −0.609994
388388 10.0000 0.507673
389389 8.00000 0.405616 0.202808 0.979219i 0.434993π-0.434993\pi
0.202808 + 0.979219i 0.434993π0.434993\pi
390390 0 0
391391 4.00000 0.202289
392392 9.00000 0.454569
393393 0 0
394394 −20.0000 −1.00759
395395 0 0
396396 4.00000 0.201008
397397 −30.0000 −1.50566 −0.752828 0.658217i 0.771311π-0.771311\pi
−0.752828 + 0.658217i 0.771311π0.771311\pi
398398 −4.00000 −0.200502
399399 0 0
400400 −5.00000 −0.250000
401401 30.0000 1.49813 0.749064 0.662497i 0.230503π-0.230503\pi
0.749064 + 0.662497i 0.230503π0.230503\pi
402402 0 0
403403 0 0
404404 8.00000 0.398015
405405 0 0
406406 24.0000 1.19110
407407 32.0000 1.58618
408408 −2.00000 −0.0990148
409409 18.0000 0.890043 0.445021 0.895520i 0.353196π-0.353196\pi
0.445021 + 0.895520i 0.353196π0.353196\pi
410410 0 0
411411 6.00000 0.295958
412412 6.00000 0.295599
413413 −16.0000 −0.787309
414414 −2.00000 −0.0982946
415415 0 0
416416 0 0
417417 −4.00000 −0.195881
418418 0 0
419419 −12.0000 −0.586238 −0.293119 0.956076i 0.594693π-0.594693\pi
−0.293119 + 0.956076i 0.594693π0.594693\pi
420420 0 0
421421 8.00000 0.389896 0.194948 0.980814i 0.437546π-0.437546\pi
0.194948 + 0.980814i 0.437546π0.437546\pi
422422 20.0000 0.973585
423423 10.0000 0.486217
424424 −2.00000 −0.0971286
425425 10.0000 0.485071
426426 16.0000 0.775203
427427 −40.0000 −1.93574
428428 4.00000 0.193347
429429 0 0
430430 0 0
431431 4.00000 0.192673 0.0963366 0.995349i 0.469287π-0.469287\pi
0.0963366 + 0.995349i 0.469287π0.469287\pi
432432 1.00000 0.0481125
433433 18.0000 0.865025 0.432512 0.901628i 0.357627π-0.357627\pi
0.432512 + 0.901628i 0.357627π0.357627\pi
434434 −24.0000 −1.15204
435435 0 0
436436 4.00000 0.191565
437437 0 0
438438 −2.00000 −0.0955637
439439 −22.0000 −1.05000 −0.525001 0.851101i 0.675935π-0.675935\pi
−0.525001 + 0.851101i 0.675935π0.675935\pi
440440 0 0
441441 9.00000 0.428571
442442 0 0
443443 12.0000 0.570137 0.285069 0.958507i 0.407984π-0.407984\pi
0.285069 + 0.958507i 0.407984π0.407984\pi
444444 8.00000 0.379663
445445 0 0
446446 −6.00000 −0.284108
447447 20.0000 0.945968
448448 4.00000 0.188982
449449 18.0000 0.849473 0.424736 0.905317i 0.360367π-0.360367\pi
0.424736 + 0.905317i 0.360367π0.360367\pi
450450 −5.00000 −0.235702
451451 −40.0000 −1.88353
452452 14.0000 0.658505
453453 −10.0000 −0.469841
454454 −20.0000 −0.938647
455455 0 0
456456 0 0
457457 2.00000 0.0935561 0.0467780 0.998905i 0.485105π-0.485105\pi
0.0467780 + 0.998905i 0.485105π0.485105\pi
458458 −2.00000 −0.0934539
459459 −2.00000 −0.0933520
460460 0 0
461461 −12.0000 −0.558896 −0.279448 0.960161i 0.590151π-0.590151\pi
−0.279448 + 0.960161i 0.590151π0.590151\pi
462462 16.0000 0.744387
463463 36.0000 1.67306 0.836531 0.547920i 0.184580π-0.184580\pi
0.836531 + 0.547920i 0.184580π0.184580\pi
464464 6.00000 0.278543
465465 0 0
466466 −6.00000 −0.277945
467467 8.00000 0.370196 0.185098 0.982720i 0.440740π-0.440740\pi
0.185098 + 0.982720i 0.440740π0.440740\pi
468468 0 0
469469 0 0
470470 0 0
471471 18.0000 0.829396
472472 −4.00000 −0.184115
473473 −48.0000 −2.20704
474474 −10.0000 −0.459315
475475 0 0
476476 −8.00000 −0.366679
477477 −2.00000 −0.0915737
478478 −6.00000 −0.274434
479479 6.00000 0.274147 0.137073 0.990561i 0.456230π-0.456230\pi
0.137073 + 0.990561i 0.456230π0.456230\pi
480480 0 0
481481 0 0
482482 2.00000 0.0910975
483483 −8.00000 −0.364013
484484 5.00000 0.227273
485485 0 0
486486 1.00000 0.0453609
487487 −2.00000 −0.0906287 −0.0453143 0.998973i 0.514429π-0.514429\pi
−0.0453143 + 0.998973i 0.514429π0.514429\pi
488488 −10.0000 −0.452679
489489 20.0000 0.904431
490490 0 0
491491 24.0000 1.08310 0.541552 0.840667i 0.317837π-0.317837\pi
0.541552 + 0.840667i 0.317837π0.317837\pi
492492 −10.0000 −0.450835
493493 −12.0000 −0.540453
494494 0 0
495495 0 0
496496 −6.00000 −0.269408
497497 64.0000 2.87079
498498 −16.0000 −0.716977
499499 −4.00000 −0.179065 −0.0895323 0.995984i 0.528537π-0.528537\pi
−0.0895323 + 0.995984i 0.528537π0.528537\pi
500500 0 0
501501 −12.0000 −0.536120
502502 −24.0000 −1.07117
503503 34.0000 1.51599 0.757993 0.652263i 0.226180π-0.226180\pi
0.757993 + 0.652263i 0.226180π0.226180\pi
504504 4.00000 0.178174
505505 0 0
506506 −8.00000 −0.355643
507507 −13.0000 −0.577350
508508 −22.0000 −0.976092
509509 10.0000 0.443242 0.221621 0.975133i 0.428865π-0.428865\pi
0.221621 + 0.975133i 0.428865π0.428865\pi
510510 0 0
511511 −8.00000 −0.353899
512512 1.00000 0.0441942
513513 0 0
514514 18.0000 0.793946
515515 0 0
516516 −12.0000 −0.528271
517517 40.0000 1.75920
518518 32.0000 1.40600
519519 −6.00000 −0.263371
520520 0 0
521521 26.0000 1.13908 0.569540 0.821963i 0.307121π-0.307121\pi
0.569540 + 0.821963i 0.307121π0.307121\pi
522522 6.00000 0.262613
523523 −16.0000 −0.699631 −0.349816 0.936819i 0.613756π-0.613756\pi
−0.349816 + 0.936819i 0.613756π0.613756\pi
524524 0 0
525525 −20.0000 −0.872872
526526 −6.00000 −0.261612
527527 12.0000 0.522728
528528 4.00000 0.174078
529529 −19.0000 −0.826087
530530 0 0
531531 −4.00000 −0.173585
532532 0 0
533533 0 0
534534 2.00000 0.0865485
535535 0 0
536536 0 0
537537 20.0000 0.863064
538538 −14.0000 −0.603583
539539 36.0000 1.55063
540540 0 0
541541 2.00000 0.0859867 0.0429934 0.999075i 0.486311π-0.486311\pi
0.0429934 + 0.999075i 0.486311π0.486311\pi
542542 −4.00000 −0.171815
543543 −12.0000 −0.514969
544544 −2.00000 −0.0857493
545545 0 0
546546 0 0
547547 16.0000 0.684111 0.342055 0.939680i 0.388877π-0.388877\pi
0.342055 + 0.939680i 0.388877π0.388877\pi
548548 6.00000 0.256307
549549 −10.0000 −0.426790
550550 −20.0000 −0.852803
551551 0 0
552552 −2.00000 −0.0851257
553553 −40.0000 −1.70097
554554 −2.00000 −0.0849719
555555 0 0
556556 −4.00000 −0.169638
557557 4.00000 0.169485 0.0847427 0.996403i 0.472993π-0.472993\pi
0.0847427 + 0.996403i 0.472993π0.472993\pi
558558 −6.00000 −0.254000
559559 0 0
560560 0 0
561561 −8.00000 −0.337760
562562 −10.0000 −0.421825
563563 12.0000 0.505740 0.252870 0.967500i 0.418626π-0.418626\pi
0.252870 + 0.967500i 0.418626π0.418626\pi
564564 10.0000 0.421076
565565 0 0
566566 28.0000 1.17693
567567 4.00000 0.167984
568568 16.0000 0.671345
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 −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 −2.00000 −0.0835512
574574 −40.0000 −1.66957
575575 10.0000 0.417029
576576 1.00000 0.0416667
577577 −14.0000 −0.582828 −0.291414 0.956597i 0.594126π-0.594126\pi
−0.291414 + 0.956597i 0.594126π0.594126\pi
578578 −13.0000 −0.540729
579579 −14.0000 −0.581820
580580 0 0
581581 −64.0000 −2.65517
582582 10.0000 0.414513
583583 −8.00000 −0.331326
584584 −2.00000 −0.0827606
585585 0 0
586586 −14.0000 −0.578335
587587 28.0000 1.15568 0.577842 0.816149i 0.303895π-0.303895\pi
0.577842 + 0.816149i 0.303895π0.303895\pi
588588 9.00000 0.371154
589589 0 0
590590 0 0
591591 −20.0000 −0.822690
592592 8.00000 0.328798
593593 10.0000 0.410651 0.205325 0.978694i 0.434175π-0.434175\pi
0.205325 + 0.978694i 0.434175π0.434175\pi
594594 4.00000 0.164122
595595 0 0
596596 20.0000 0.819232
597597 −4.00000 −0.163709
598598 0 0
599599 4.00000 0.163436 0.0817178 0.996656i 0.473959π-0.473959\pi
0.0817178 + 0.996656i 0.473959π0.473959\pi
600600 −5.00000 −0.204124
601601 −42.0000 −1.71322 −0.856608 0.515968i 0.827432π-0.827432\pi
−0.856608 + 0.515968i 0.827432π0.827432\pi
602602 −48.0000 −1.95633
603603 0 0
604604 −10.0000 −0.406894
605605 0 0
606606 8.00000 0.324978
607607 22.0000 0.892952 0.446476 0.894795i 0.352679π-0.352679\pi
0.446476 + 0.894795i 0.352679π0.352679\pi
608608 0 0
609609 24.0000 0.972529
610610 0 0
611611 0 0
612612 −2.00000 −0.0808452
613613 2.00000 0.0807792 0.0403896 0.999184i 0.487140π-0.487140\pi
0.0403896 + 0.999184i 0.487140π0.487140\pi
614614 0 0
615615 0 0
616616 16.0000 0.644658
617617 −6.00000 −0.241551 −0.120775 0.992680i 0.538538π-0.538538\pi
−0.120775 + 0.992680i 0.538538π0.538538\pi
618618 6.00000 0.241355
619619 −20.0000 −0.803868 −0.401934 0.915669i 0.631662π-0.631662\pi
−0.401934 + 0.915669i 0.631662π0.631662\pi
620620 0 0
621621 −2.00000 −0.0802572
622622 34.0000 1.36328
623623 8.00000 0.320513
624624 0 0
625625 25.0000 1.00000
626626 6.00000 0.239808
627627 0 0
628628 18.0000 0.718278
629629 −16.0000 −0.637962
630630 0 0
631631 −16.0000 −0.636950 −0.318475 0.947931i 0.603171π-0.603171\pi
−0.318475 + 0.947931i 0.603171π0.603171\pi
632632 −10.0000 −0.397779
633633 20.0000 0.794929
634634 −6.00000 −0.238290
635635 0 0
636636 −2.00000 −0.0793052
637637 0 0
638638 24.0000 0.950169
639639 16.0000 0.632950
640640 0 0
641641 −46.0000 −1.81689 −0.908445 0.418004i 0.862730π-0.862730\pi
−0.908445 + 0.418004i 0.862730π0.862730\pi
642642 4.00000 0.157867
643643 28.0000 1.10421 0.552106 0.833774i 0.313824π-0.313824\pi
0.552106 + 0.833774i 0.313824π0.313824\pi
644644 −8.00000 −0.315244
645645 0 0
646646 0 0
647647 −18.0000 −0.707653 −0.353827 0.935311i 0.615120π-0.615120\pi
−0.353827 + 0.935311i 0.615120π0.615120\pi
648648 1.00000 0.0392837
649649 −16.0000 −0.628055
650650 0 0
651651 −24.0000 −0.940634
652652 20.0000 0.783260
653653 −36.0000 −1.40879 −0.704394 0.709809i 0.748781π-0.748781\pi
−0.704394 + 0.709809i 0.748781π0.748781\pi
654654 4.00000 0.156412
655655 0 0
656656 −10.0000 −0.390434
657657 −2.00000 −0.0780274
658658 40.0000 1.55936
659659 20.0000 0.779089 0.389545 0.921008i 0.372632π-0.372632\pi
0.389545 + 0.921008i 0.372632π0.372632\pi
660660 0 0
661661 8.00000 0.311164 0.155582 0.987823i 0.450275π-0.450275\pi
0.155582 + 0.987823i 0.450275π0.450275\pi
662662 −24.0000 −0.932786
663663 0 0
664664 −16.0000 −0.620920
665665 0 0
666666 8.00000 0.309994
667667 −12.0000 −0.464642
668668 −12.0000 −0.464294
669669 −6.00000 −0.231973
670670 0 0
671671 −40.0000 −1.54418
672672 4.00000 0.154303
673673 −14.0000 −0.539660 −0.269830 0.962908i 0.586968π-0.586968\pi
−0.269830 + 0.962908i 0.586968π0.586968\pi
674674 −26.0000 −1.00148
675675 −5.00000 −0.192450
676676 −13.0000 −0.500000
677677 −42.0000 −1.61419 −0.807096 0.590421i 0.798962π-0.798962\pi
−0.807096 + 0.590421i 0.798962π0.798962\pi
678678 14.0000 0.537667
679679 40.0000 1.53506
680680 0 0
681681 −20.0000 −0.766402
682682 −24.0000 −0.919007
683683 −36.0000 −1.37750 −0.688751 0.724998i 0.741841π-0.741841\pi
−0.688751 + 0.724998i 0.741841π0.741841\pi
684684 0 0
685685 0 0
686686 8.00000 0.305441
687687 −2.00000 −0.0763048
688688 −12.0000 −0.457496
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 −6.00000 −0.228086
693693 16.0000 0.607790
694694 28.0000 1.06287
695695 0 0
696696 6.00000 0.227429
697697 20.0000 0.757554
698698 10.0000 0.378506
699699 −6.00000 −0.226941
700700 −20.0000 −0.755929
701701 −8.00000 −0.302156 −0.151078 0.988522i 0.548274π-0.548274\pi
−0.151078 + 0.988522i 0.548274π0.548274\pi
702702 0 0
703703 0 0
704704 4.00000 0.150756
705705 0 0
706706 −30.0000 −1.12906
707707 32.0000 1.20348
708708 −4.00000 −0.150329
709709 −10.0000 −0.375558 −0.187779 0.982211i 0.560129π-0.560129\pi
−0.187779 + 0.982211i 0.560129π0.560129\pi
710710 0 0
711711 −10.0000 −0.375029
712712 2.00000 0.0749532
713713 12.0000 0.449404
714714 −8.00000 −0.299392
715715 0 0
716716 20.0000 0.747435
717717 −6.00000 −0.224074
718718 6.00000 0.223918
719719 34.0000 1.26799 0.633993 0.773339i 0.281415π-0.281415\pi
0.633993 + 0.773339i 0.281415π0.281415\pi
720720 0 0
721721 24.0000 0.893807
722722 0 0
723723 2.00000 0.0743808
724724 −12.0000 −0.445976
725725 −30.0000 −1.11417
726726 5.00000 0.185567
727727 8.00000 0.296704 0.148352 0.988935i 0.452603π-0.452603\pi
0.148352 + 0.988935i 0.452603π0.452603\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 24.0000 0.887672
732732 −10.0000 −0.369611
733733 −38.0000 −1.40356 −0.701781 0.712393i 0.747612π-0.747612\pi
−0.701781 + 0.712393i 0.747612π0.747612\pi
734734 −28.0000 −1.03350
735735 0 0
736736 −2.00000 −0.0737210
737737 0 0
738738 −10.0000 −0.368105
739739 4.00000 0.147142 0.0735712 0.997290i 0.476560π-0.476560\pi
0.0735712 + 0.997290i 0.476560π0.476560\pi
740740 0 0
741741 0 0
742742 −8.00000 −0.293689
743743 36.0000 1.32071 0.660356 0.750953i 0.270405π-0.270405\pi
0.660356 + 0.750953i 0.270405π0.270405\pi
744744 −6.00000 −0.219971
745745 0 0
746746 −8.00000 −0.292901
747747 −16.0000 −0.585409
748748 −8.00000 −0.292509
749749 16.0000 0.584627
750750 0 0
751751 −10.0000 −0.364905 −0.182453 0.983215i 0.558404π-0.558404\pi
−0.182453 + 0.983215i 0.558404π0.558404\pi
752752 10.0000 0.364662
753753 −24.0000 −0.874609
754754 0 0
755755 0 0
756756 4.00000 0.145479
757757 2.00000 0.0726912 0.0363456 0.999339i 0.488428π-0.488428\pi
0.0363456 + 0.999339i 0.488428π0.488428\pi
758758 −8.00000 −0.290573
759759 −8.00000 −0.290382
760760 0 0
761761 14.0000 0.507500 0.253750 0.967270i 0.418336π-0.418336\pi
0.253750 + 0.967270i 0.418336π0.418336\pi
762762 −22.0000 −0.796976
763763 16.0000 0.579239
764764 −2.00000 −0.0723575
765765 0 0
766766 −8.00000 −0.289052
767767 0 0
768768 1.00000 0.0360844
769769 30.0000 1.08183 0.540914 0.841078i 0.318079π-0.318079\pi
0.540914 + 0.841078i 0.318079π0.318079\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 −12.0000 −0.431331
775775 30.0000 1.07763
776776 10.0000 0.358979
777777 32.0000 1.14799
778778 8.00000 0.286814
779779 0 0
780780 0 0
781781 64.0000 2.29010
782782 4.00000 0.143040
783783 6.00000 0.214423
784784 9.00000 0.321429
785785 0 0
786786 0 0
787787 −4.00000 −0.142585 −0.0712923 0.997455i 0.522712π-0.522712\pi
−0.0712923 + 0.997455i 0.522712π0.522712\pi
788788 −20.0000 −0.712470
789789 −6.00000 −0.213606
790790 0 0
791791 56.0000 1.99113
792792 4.00000 0.142134
793793 0 0
794794 −30.0000 −1.06466
795795 0 0
796796 −4.00000 −0.141776
797797 34.0000 1.20434 0.602171 0.798367i 0.294303π-0.294303\pi
0.602171 + 0.798367i 0.294303π0.294303\pi
798798 0 0
799799 −20.0000 −0.707549
800800 −5.00000 −0.176777
801801 2.00000 0.0706665
802802 30.0000 1.05934
803803 −8.00000 −0.282314
804804 0 0
805805 0 0
806806 0 0
807807 −14.0000 −0.492823
808808 8.00000 0.281439
809809 54.0000 1.89854 0.949269 0.314464i 0.101825π-0.101825\pi
0.949269 + 0.314464i 0.101825π0.101825\pi
810810 0 0
811811 −16.0000 −0.561836 −0.280918 0.959732i 0.590639π-0.590639\pi
−0.280918 + 0.959732i 0.590639π0.590639\pi
812812 24.0000 0.842235
813813 −4.00000 −0.140286
814814 32.0000 1.12160
815815 0 0
816816 −2.00000 −0.0700140
817817 0 0
818818 18.0000 0.629355
819819 0 0
820820 0 0
821821 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
822822 6.00000 0.209274
823823 16.0000 0.557725 0.278862 0.960331i 0.410043π-0.410043\pi
0.278862 + 0.960331i 0.410043π0.410043\pi
824824 6.00000 0.209020
825825 −20.0000 −0.696311
826826 −16.0000 −0.556711
827827 12.0000 0.417281 0.208640 0.977992i 0.433096π-0.433096\pi
0.208640 + 0.977992i 0.433096π0.433096\pi
828828 −2.00000 −0.0695048
829829 4.00000 0.138926 0.0694629 0.997585i 0.477871π-0.477871\pi
0.0694629 + 0.997585i 0.477871π0.477871\pi
830830 0 0
831831 −2.00000 −0.0693792
832832 0 0
833833 −18.0000 −0.623663
834834 −4.00000 −0.138509
835835 0 0
836836 0 0
837837 −6.00000 −0.207390
838838 −12.0000 −0.414533
839839 −12.0000 −0.414286 −0.207143 0.978311i 0.566417π-0.566417\pi
−0.207143 + 0.978311i 0.566417π0.566417\pi
840840 0 0
841841 7.00000 0.241379
842842 8.00000 0.275698
843843 −10.0000 −0.344418
844844 20.0000 0.688428
845845 0 0
846846 10.0000 0.343807
847847 20.0000 0.687208
848848 −2.00000 −0.0686803
849849 28.0000 0.960958
850850 10.0000 0.342997
851851 −16.0000 −0.548473
852852 16.0000 0.548151
853853 54.0000 1.84892 0.924462 0.381273i 0.124514π-0.124514\pi
0.924462 + 0.381273i 0.124514π0.124514\pi
854854 −40.0000 −1.36877
855855 0 0
856856 4.00000 0.136717
857857 42.0000 1.43469 0.717346 0.696717i 0.245357π-0.245357\pi
0.717346 + 0.696717i 0.245357π0.245357\pi
858858 0 0
859859 4.00000 0.136478 0.0682391 0.997669i 0.478262π-0.478262\pi
0.0682391 + 0.997669i 0.478262π0.478262\pi
860860 0 0
861861 −40.0000 −1.36320
862862 4.00000 0.136241
863863 28.0000 0.953131 0.476566 0.879139i 0.341881π-0.341881\pi
0.476566 + 0.879139i 0.341881π0.341881\pi
864864 1.00000 0.0340207
865865 0 0
866866 18.0000 0.611665
867867 −13.0000 −0.441503
868868 −24.0000 −0.814613
869869 −40.0000 −1.35691
870870 0 0
871871 0 0
872872 4.00000 0.135457
873873 10.0000 0.338449
874874 0 0
875875 0 0
876876 −2.00000 −0.0675737
877877 −8.00000 −0.270141 −0.135070 0.990836i 0.543126π-0.543126\pi
−0.135070 + 0.990836i 0.543126π0.543126\pi
878878 −22.0000 −0.742464
879879 −14.0000 −0.472208
880880 0 0
881881 42.0000 1.41502 0.707508 0.706705i 0.249819π-0.249819\pi
0.707508 + 0.706705i 0.249819π0.249819\pi
882882 9.00000 0.303046
883883 36.0000 1.21150 0.605748 0.795656i 0.292874π-0.292874\pi
0.605748 + 0.795656i 0.292874π0.292874\pi
884884 0 0
885885 0 0
886886 12.0000 0.403148
887887 12.0000 0.402921 0.201460 0.979497i 0.435431π-0.435431\pi
0.201460 + 0.979497i 0.435431π0.435431\pi
888888 8.00000 0.268462
889889 −88.0000 −2.95143
890890 0 0
891891 4.00000 0.134005
892892 −6.00000 −0.200895
893893 0 0
894894 20.0000 0.668900
895895 0 0
896896 4.00000 0.133631
897897 0 0
898898 18.0000 0.600668
899899 −36.0000 −1.20067
900900 −5.00000 −0.166667
901901 4.00000 0.133259
902902 −40.0000 −1.33185
903903 −48.0000 −1.59734
904904 14.0000 0.465633
905905 0 0
906906 −10.0000 −0.332228
907907 32.0000 1.06254 0.531271 0.847202i 0.321714π-0.321714\pi
0.531271 + 0.847202i 0.321714π0.321714\pi
908908 −20.0000 −0.663723
909909 8.00000 0.265343
910910 0 0
911911 12.0000 0.397578 0.198789 0.980042i 0.436299π-0.436299\pi
0.198789 + 0.980042i 0.436299π0.436299\pi
912912 0 0
913913 −64.0000 −2.11809
914914 2.00000 0.0661541
915915 0 0
916916 −2.00000 −0.0660819
917917 0 0
918918 −2.00000 −0.0660098
919919 −32.0000 −1.05558 −0.527791 0.849374i 0.676980π-0.676980\pi
−0.527791 + 0.849374i 0.676980π0.676980\pi
920920 0 0
921921 0 0
922922 −12.0000 −0.395199
923923 0 0
924924 16.0000 0.526361
925925 −40.0000 −1.31519
926926 36.0000 1.18303
927927 6.00000 0.197066
928928 6.00000 0.196960
929929 −42.0000 −1.37798 −0.688988 0.724773i 0.741945π-0.741945\pi
−0.688988 + 0.724773i 0.741945π0.741945\pi
930930 0 0
931931 0 0
932932 −6.00000 −0.196537
933933 34.0000 1.11311
934934 8.00000 0.261768
935935 0 0
936936 0 0
937937 38.0000 1.24141 0.620703 0.784046i 0.286847π-0.286847\pi
0.620703 + 0.784046i 0.286847π0.286847\pi
938938 0 0
939939 6.00000 0.195803
940940 0 0
941941 −46.0000 −1.49956 −0.749779 0.661689i 0.769840π-0.769840\pi
−0.749779 + 0.661689i 0.769840π0.769840\pi
942942 18.0000 0.586472
943943 20.0000 0.651290
944944 −4.00000 −0.130189
945945 0 0
946946 −48.0000 −1.56061
947947 −8.00000 −0.259965 −0.129983 0.991516i 0.541492π-0.541492\pi
−0.129983 + 0.991516i 0.541492π0.541492\pi
948948 −10.0000 −0.324785
949949 0 0
950950 0 0
951951 −6.00000 −0.194563
952952 −8.00000 −0.259281
953953 30.0000 0.971795 0.485898 0.874016i 0.338493π-0.338493\pi
0.485898 + 0.874016i 0.338493π0.338493\pi
954954 −2.00000 −0.0647524
955955 0 0
956956 −6.00000 −0.194054
957957 24.0000 0.775810
958958 6.00000 0.193851
959959 24.0000 0.775000
960960 0 0
961961 5.00000 0.161290
962962 0 0
963963 4.00000 0.128898
964964 2.00000 0.0644157
965965 0 0
966966 −8.00000 −0.257396
967967 12.0000 0.385894 0.192947 0.981209i 0.438195π-0.438195\pi
0.192947 + 0.981209i 0.438195π0.438195\pi
968968 5.00000 0.160706
969969 0 0
970970 0 0
971971 −12.0000 −0.385098 −0.192549 0.981287i 0.561675π-0.561675\pi
−0.192549 + 0.981287i 0.561675π0.561675\pi
972972 1.00000 0.0320750
973973 −16.0000 −0.512936
974974 −2.00000 −0.0640841
975975 0 0
976976 −10.0000 −0.320092
977977 −18.0000 −0.575871 −0.287936 0.957650i 0.592969π-0.592969\pi
−0.287936 + 0.957650i 0.592969π0.592969\pi
978978 20.0000 0.639529
979979 8.00000 0.255681
980980 0 0
981981 4.00000 0.127710
982982 24.0000 0.765871
983983 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
984984 −10.0000 −0.318788
985985 0 0
986986 −12.0000 −0.382158
987987 40.0000 1.27321
988988 0 0
989989 24.0000 0.763156
990990 0 0
991991 50.0000 1.58830 0.794151 0.607720i 0.207916π-0.207916\pi
0.794151 + 0.607720i 0.207916π0.207916\pi
992992 −6.00000 −0.190500
993993 −24.0000 −0.761617
994994 64.0000 2.02996
995995 0 0
996996 −16.0000 −0.506979
997997 −22.0000 −0.696747 −0.348373 0.937356i 0.613266π-0.613266\pi
−0.348373 + 0.937356i 0.613266π0.613266\pi
998998 −4.00000 −0.126618
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 2166.2.a.i.1.1 1
3.2 odd 2 6498.2.a.h.1.1 1
19.18 odd 2 114.2.a.a.1.1 1
57.56 even 2 342.2.a.f.1.1 1
76.75 even 2 912.2.a.h.1.1 1
95.18 even 4 2850.2.d.s.799.2 2
95.37 even 4 2850.2.d.s.799.1 2
95.94 odd 2 2850.2.a.x.1.1 1
133.132 even 2 5586.2.a.p.1.1 1
152.37 odd 2 3648.2.a.bb.1.1 1
152.75 even 2 3648.2.a.j.1.1 1
228.227 odd 2 2736.2.a.j.1.1 1
285.284 even 2 8550.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.2.a.a.1.1 1 19.18 odd 2
342.2.a.f.1.1 1 57.56 even 2
912.2.a.h.1.1 1 76.75 even 2
2166.2.a.i.1.1 1 1.1 even 1 trivial
2736.2.a.j.1.1 1 228.227 odd 2
2850.2.a.x.1.1 1 95.94 odd 2
2850.2.d.s.799.1 2 95.37 even 4
2850.2.d.s.799.2 2 95.18 even 4
3648.2.a.j.1.1 1 152.75 even 2
3648.2.a.bb.1.1 1 152.37 odd 2
5586.2.a.p.1.1 1 133.132 even 2
6498.2.a.h.1.1 1 3.2 odd 2
8550.2.a.a.1.1 1 285.284 even 2