Properties

Label 114.2.a.c.1.1
Level 114114
Weight 22
Character 114.1
Self dual yes
Analytic conductor 0.9100.910
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] = [114,2,Mod(1,114)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(114, 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("114.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 114=2319 114 = 2 \cdot 3 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 114.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 0.9102945830430.910294583043
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 114.1

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+1.00000q64.00000q7+1.00000q8+1.00000q9+1.00000q124.00000q134.00000q14+1.00000q16+6.00000q17+1.00000q18+1.00000q194.00000q216.00000q23+1.00000q245.00000q254.00000q26+1.00000q274.00000q28+6.00000q29+2.00000q31+1.00000q32+6.00000q34+1.00000q364.00000q37+1.00000q384.00000q39+6.00000q414.00000q424.00000q436.00000q46+6.00000q47+1.00000q48+9.00000q495.00000q50+6.00000q514.00000q52+6.00000q53+1.00000q544.00000q56+1.00000q57+6.00000q5812.0000q59+14.0000q61+2.00000q624.00000q63+1.00000q64+8.00000q67+6.00000q686.00000q69+1.00000q72+14.0000q734.00000q745.00000q75+1.00000q764.00000q7810.0000q79+1.00000q81+6.00000q8212.0000q834.00000q844.00000q86+6.00000q876.00000q89+16.0000q916.00000q92+2.00000q93+6.00000q94+1.00000q9610.0000q97+9.00000q98+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} +1.00000 q^{12} -4.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} +1.00000 q^{19} -4.00000 q^{21} -6.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} -4.00000 q^{28} +6.00000 q^{29} +2.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} +1.00000 q^{36} -4.00000 q^{37} +1.00000 q^{38} -4.00000 q^{39} +6.00000 q^{41} -4.00000 q^{42} -4.00000 q^{43} -6.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} +9.00000 q^{49} -5.00000 q^{50} +6.00000 q^{51} -4.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} -4.00000 q^{56} +1.00000 q^{57} +6.00000 q^{58} -12.0000 q^{59} +14.0000 q^{61} +2.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} +8.00000 q^{67} +6.00000 q^{68} -6.00000 q^{69} +1.00000 q^{72} +14.0000 q^{73} -4.00000 q^{74} -5.00000 q^{75} +1.00000 q^{76} -4.00000 q^{78} -10.0000 q^{79} +1.00000 q^{81} +6.00000 q^{82} -12.0000 q^{83} -4.00000 q^{84} -4.00000 q^{86} +6.00000 q^{87} -6.00000 q^{89} +16.0000 q^{91} -6.00000 q^{92} +2.00000 q^{93} +6.00000 q^{94} +1.00000 q^{96} -10.0000 q^{97} +9.00000 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 −4.00000 −1.51186 −0.755929 0.654654i 0.772814π-0.772814\pi
−0.755929 + 0.654654i 0.772814π0.772814\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 −4.00000 −1.10940 −0.554700 0.832050i 0.687167π-0.687167\pi
−0.554700 + 0.832050i 0.687167π0.687167\pi
1414 −4.00000 −1.06904
1515 0 0
1616 1.00000 0.250000
1717 6.00000 1.45521 0.727607 0.685994i 0.240633π-0.240633\pi
0.727607 + 0.685994i 0.240633π0.240633\pi
1818 1.00000 0.235702
1919 1.00000 0.229416
2020 0 0
2121 −4.00000 −0.872872
2222 0 0
2323 −6.00000 −1.25109 −0.625543 0.780189i 0.715123π-0.715123\pi
−0.625543 + 0.780189i 0.715123π0.715123\pi
2424 1.00000 0.204124
2525 −5.00000 −1.00000
2626 −4.00000 −0.784465
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 2.00000 0.359211 0.179605 0.983739i 0.442518π-0.442518\pi
0.179605 + 0.983739i 0.442518π0.442518\pi
3232 1.00000 0.176777
3333 0 0
3434 6.00000 1.02899
3535 0 0
3636 1.00000 0.166667
3737 −4.00000 −0.657596 −0.328798 0.944400i 0.606644π-0.606644\pi
−0.328798 + 0.944400i 0.606644π0.606644\pi
3838 1.00000 0.162221
3939 −4.00000 −0.640513
4040 0 0
4141 6.00000 0.937043 0.468521 0.883452i 0.344787π-0.344787\pi
0.468521 + 0.883452i 0.344787π0.344787\pi
4242 −4.00000 −0.617213
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 6.00000 0.875190 0.437595 0.899172i 0.355830π-0.355830\pi
0.437595 + 0.899172i 0.355830π0.355830\pi
4848 1.00000 0.144338
4949 9.00000 1.28571
5050 −5.00000 −0.707107
5151 6.00000 0.840168
5252 −4.00000 −0.554700
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 −4.00000 −0.534522
5757 1.00000 0.132453
5858 6.00000 0.787839
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 14.0000 1.79252 0.896258 0.443533i 0.146275π-0.146275\pi
0.896258 + 0.443533i 0.146275π0.146275\pi
6262 2.00000 0.254000
6363 −4.00000 −0.503953
6464 1.00000 0.125000
6565 0 0
6666 0 0
6767 8.00000 0.977356 0.488678 0.872464i 0.337479π-0.337479\pi
0.488678 + 0.872464i 0.337479π0.337479\pi
6868 6.00000 0.727607
6969 −6.00000 −0.722315
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 1.00000 0.117851
7373 14.0000 1.63858 0.819288 0.573382i 0.194369π-0.194369\pi
0.819288 + 0.573382i 0.194369π0.194369\pi
7474 −4.00000 −0.464991
7575 −5.00000 −0.577350
7676 1.00000 0.114708
7777 0 0
7878 −4.00000 −0.452911
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 6.00000 0.662589
8383 −12.0000 −1.31717 −0.658586 0.752506i 0.728845π-0.728845\pi
−0.658586 + 0.752506i 0.728845π0.728845\pi
8484 −4.00000 −0.436436
8585 0 0
8686 −4.00000 −0.431331
8787 6.00000 0.643268
8888 0 0
8989 −6.00000 −0.635999 −0.317999 0.948091i 0.603011π-0.603011\pi
−0.317999 + 0.948091i 0.603011π0.603011\pi
9090 0 0
9191 16.0000 1.67726
9292 −6.00000 −0.625543
9393 2.00000 0.207390
9494 6.00000 0.618853
9595 0 0
9696 1.00000 0.102062
9797 −10.0000 −1.01535 −0.507673 0.861550i 0.669494π-0.669494\pi
−0.507673 + 0.861550i 0.669494π0.669494\pi
9898 9.00000 0.909137
9999 0 0
100100 −5.00000 −0.500000
101101 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
102102 6.00000 0.594089
103103 −10.0000 −0.985329 −0.492665 0.870219i 0.663977π-0.663977\pi
−0.492665 + 0.870219i 0.663977π0.663977\pi
104104 −4.00000 −0.392232
105105 0 0
106106 6.00000 0.582772
107107 12.0000 1.16008 0.580042 0.814587i 0.303036π-0.303036\pi
0.580042 + 0.814587i 0.303036π0.303036\pi
108108 1.00000 0.0962250
109109 −16.0000 −1.53252 −0.766261 0.642529i 0.777885π-0.777885\pi
−0.766261 + 0.642529i 0.777885π0.777885\pi
110110 0 0
111111 −4.00000 −0.379663
112112 −4.00000 −0.377964
113113 −18.0000 −1.69330 −0.846649 0.532152i 0.821383π-0.821383\pi
−0.846649 + 0.532152i 0.821383π0.821383\pi
114114 1.00000 0.0936586
115115 0 0
116116 6.00000 0.557086
117117 −4.00000 −0.369800
118118 −12.0000 −1.10469
119119 −24.0000 −2.20008
120120 0 0
121121 −11.0000 −1.00000
122122 14.0000 1.26750
123123 6.00000 0.541002
124124 2.00000 0.179605
125125 0 0
126126 −4.00000 −0.356348
127127 2.00000 0.177471 0.0887357 0.996055i 0.471717π-0.471717\pi
0.0887357 + 0.996055i 0.471717π0.471717\pi
128128 1.00000 0.0883883
129129 −4.00000 −0.352180
130130 0 0
131131 12.0000 1.04844 0.524222 0.851581i 0.324356π-0.324356\pi
0.524222 + 0.851581i 0.324356π0.324356\pi
132132 0 0
133133 −4.00000 −0.346844
134134 8.00000 0.691095
135135 0 0
136136 6.00000 0.514496
137137 −18.0000 −1.53784 −0.768922 0.639343i 0.779207π-0.779207\pi
−0.768922 + 0.639343i 0.779207π0.779207\pi
138138 −6.00000 −0.510754
139139 20.0000 1.69638 0.848189 0.529694i 0.177693π-0.177693\pi
0.848189 + 0.529694i 0.177693π0.177693\pi
140140 0 0
141141 6.00000 0.505291
142142 0 0
143143 0 0
144144 1.00000 0.0833333
145145 0 0
146146 14.0000 1.15865
147147 9.00000 0.742307
148148 −4.00000 −0.328798
149149 12.0000 0.983078 0.491539 0.870855i 0.336434π-0.336434\pi
0.491539 + 0.870855i 0.336434π0.336434\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 1.00000 0.0811107
153153 6.00000 0.485071
154154 0 0
155155 0 0
156156 −4.00000 −0.320256
157157 2.00000 0.159617 0.0798087 0.996810i 0.474569π-0.474569\pi
0.0798087 + 0.996810i 0.474569π0.474569\pi
158158 −10.0000 −0.795557
159159 6.00000 0.475831
160160 0 0
161161 24.0000 1.89146
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 6.00000 0.468521
165165 0 0
166166 −12.0000 −0.931381
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 3.00000 0.230769
170170 0 0
171171 1.00000 0.0764719
172172 −4.00000 −0.304997
173173 18.0000 1.36851 0.684257 0.729241i 0.260127π-0.260127\pi
0.684257 + 0.729241i 0.260127π0.260127\pi
174174 6.00000 0.454859
175175 20.0000 1.51186
176176 0 0
177177 −12.0000 −0.901975
178178 −6.00000 −0.449719
179179 12.0000 0.896922 0.448461 0.893802i 0.351972π-0.351972\pi
0.448461 + 0.893802i 0.351972π0.351972\pi
180180 0 0
181181 −16.0000 −1.18927 −0.594635 0.803996i 0.702704π-0.702704\pi
−0.594635 + 0.803996i 0.702704π0.702704\pi
182182 16.0000 1.18600
183183 14.0000 1.03491
184184 −6.00000 −0.442326
185185 0 0
186186 2.00000 0.146647
187187 0 0
188188 6.00000 0.437595
189189 −4.00000 −0.290957
190190 0 0
191191 18.0000 1.30243 0.651217 0.758891i 0.274259π-0.274259\pi
0.651217 + 0.758891i 0.274259π0.274259\pi
192192 1.00000 0.0721688
193193 −10.0000 −0.719816 −0.359908 0.932988i 0.617192π-0.617192\pi
−0.359908 + 0.932988i 0.617192π0.617192\pi
194194 −10.0000 −0.717958
195195 0 0
196196 9.00000 0.642857
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 20.0000 1.41776 0.708881 0.705328i 0.249200π-0.249200\pi
0.708881 + 0.705328i 0.249200π0.249200\pi
200200 −5.00000 −0.353553
201201 8.00000 0.564276
202202 0 0
203203 −24.0000 −1.68447
204204 6.00000 0.420084
205205 0 0
206206 −10.0000 −0.696733
207207 −6.00000 −0.417029
208208 −4.00000 −0.277350
209209 0 0
210210 0 0
211211 −4.00000 −0.275371 −0.137686 0.990476i 0.543966π-0.543966\pi
−0.137686 + 0.990476i 0.543966π0.543966\pi
212212 6.00000 0.412082
213213 0 0
214214 12.0000 0.820303
215215 0 0
216216 1.00000 0.0680414
217217 −8.00000 −0.543075
218218 −16.0000 −1.08366
219219 14.0000 0.946032
220220 0 0
221221 −24.0000 −1.61441
222222 −4.00000 −0.268462
223223 −22.0000 −1.47323 −0.736614 0.676313i 0.763577π-0.763577\pi
−0.736614 + 0.676313i 0.763577π0.763577\pi
224224 −4.00000 −0.267261
225225 −5.00000 −0.333333
226226 −18.0000 −1.19734
227227 12.0000 0.796468 0.398234 0.917284i 0.369623π-0.369623\pi
0.398234 + 0.917284i 0.369623π0.369623\pi
228228 1.00000 0.0662266
229229 −10.0000 −0.660819 −0.330409 0.943838i 0.607187π-0.607187\pi
−0.330409 + 0.943838i 0.607187π0.607187\pi
230230 0 0
231231 0 0
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 −4.00000 −0.261488
235235 0 0
236236 −12.0000 −0.781133
237237 −10.0000 −0.649570
238238 −24.0000 −1.55569
239239 −18.0000 −1.16432 −0.582162 0.813073i 0.697793π-0.697793\pi
−0.582162 + 0.813073i 0.697793π0.697793\pi
240240 0 0
241241 14.0000 0.901819 0.450910 0.892570i 0.351100π-0.351100\pi
0.450910 + 0.892570i 0.351100π0.351100\pi
242242 −11.0000 −0.707107
243243 1.00000 0.0641500
244244 14.0000 0.896258
245245 0 0
246246 6.00000 0.382546
247247 −4.00000 −0.254514
248248 2.00000 0.127000
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 −4.00000 −0.251976
253253 0 0
254254 2.00000 0.125491
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 6.00000 0.371391
262262 12.0000 0.741362
263263 −18.0000 −1.10993 −0.554964 0.831875i 0.687268π-0.687268\pi
−0.554964 + 0.831875i 0.687268π0.687268\pi
264264 0 0
265265 0 0
266266 −4.00000 −0.245256
267267 −6.00000 −0.367194
268268 8.00000 0.488678
269269 −6.00000 −0.365826 −0.182913 0.983129i 0.558553π-0.558553\pi
−0.182913 + 0.983129i 0.558553π0.558553\pi
270270 0 0
271271 20.0000 1.21491 0.607457 0.794353i 0.292190π-0.292190\pi
0.607457 + 0.794353i 0.292190π0.292190\pi
272272 6.00000 0.363803
273273 16.0000 0.968364
274274 −18.0000 −1.08742
275275 0 0
276276 −6.00000 −0.361158
277277 −10.0000 −0.600842 −0.300421 0.953807i 0.597127π-0.597127\pi
−0.300421 + 0.953807i 0.597127π0.597127\pi
278278 20.0000 1.19952
279279 2.00000 0.119737
280280 0 0
281281 −18.0000 −1.07379 −0.536895 0.843649i 0.680403π-0.680403\pi
−0.536895 + 0.843649i 0.680403π0.680403\pi
282282 6.00000 0.357295
283283 −4.00000 −0.237775 −0.118888 0.992908i 0.537933π-0.537933\pi
−0.118888 + 0.992908i 0.537933π0.537933\pi
284284 0 0
285285 0 0
286286 0 0
287287 −24.0000 −1.41668
288288 1.00000 0.0589256
289289 19.0000 1.11765
290290 0 0
291291 −10.0000 −0.586210
292292 14.0000 0.819288
293293 −6.00000 −0.350524 −0.175262 0.984522i 0.556077π-0.556077\pi
−0.175262 + 0.984522i 0.556077π0.556077\pi
294294 9.00000 0.524891
295295 0 0
296296 −4.00000 −0.232495
297297 0 0
298298 12.0000 0.695141
299299 24.0000 1.38796
300300 −5.00000 −0.288675
301301 16.0000 0.922225
302302 −10.0000 −0.575435
303303 0 0
304304 1.00000 0.0573539
305305 0 0
306306 6.00000 0.342997
307307 −16.0000 −0.913168 −0.456584 0.889680i 0.650927π-0.650927\pi
−0.456584 + 0.889680i 0.650927π0.650927\pi
308308 0 0
309309 −10.0000 −0.568880
310310 0 0
311311 30.0000 1.70114 0.850572 0.525859i 0.176256π-0.176256\pi
0.850572 + 0.525859i 0.176256π0.176256\pi
312312 −4.00000 −0.226455
313313 −10.0000 −0.565233 −0.282617 0.959233i 0.591202π-0.591202\pi
−0.282617 + 0.959233i 0.591202π0.591202\pi
314314 2.00000 0.112867
315315 0 0
316316 −10.0000 −0.562544
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 0 0
320320 0 0
321321 12.0000 0.669775
322322 24.0000 1.33747
323323 6.00000 0.333849
324324 1.00000 0.0555556
325325 20.0000 1.10940
326326 −4.00000 −0.221540
327327 −16.0000 −0.884802
328328 6.00000 0.331295
329329 −24.0000 −1.32316
330330 0 0
331331 8.00000 0.439720 0.219860 0.975531i 0.429440π-0.429440\pi
0.219860 + 0.975531i 0.429440π0.429440\pi
332332 −12.0000 −0.658586
333333 −4.00000 −0.219199
334334 −12.0000 −0.656611
335335 0 0
336336 −4.00000 −0.218218
337337 2.00000 0.108947 0.0544735 0.998515i 0.482652π-0.482652\pi
0.0544735 + 0.998515i 0.482652π0.482652\pi
338338 3.00000 0.163178
339339 −18.0000 −0.977626
340340 0 0
341341 0 0
342342 1.00000 0.0540738
343343 −8.00000 −0.431959
344344 −4.00000 −0.215666
345345 0 0
346346 18.0000 0.967686
347347 24.0000 1.28839 0.644194 0.764862i 0.277193π-0.277193\pi
0.644194 + 0.764862i 0.277193π0.277193\pi
348348 6.00000 0.321634
349349 2.00000 0.107058 0.0535288 0.998566i 0.482953π-0.482953\pi
0.0535288 + 0.998566i 0.482953π0.482953\pi
350350 20.0000 1.06904
351351 −4.00000 −0.213504
352352 0 0
353353 −6.00000 −0.319348 −0.159674 0.987170i 0.551044π-0.551044\pi
−0.159674 + 0.987170i 0.551044π0.551044\pi
354354 −12.0000 −0.637793
355355 0 0
356356 −6.00000 −0.317999
357357 −24.0000 −1.27021
358358 12.0000 0.634220
359359 −6.00000 −0.316668 −0.158334 0.987386i 0.550612π-0.550612\pi
−0.158334 + 0.987386i 0.550612π0.550612\pi
360360 0 0
361361 1.00000 0.0526316
362362 −16.0000 −0.840941
363363 −11.0000 −0.577350
364364 16.0000 0.838628
365365 0 0
366366 14.0000 0.731792
367367 −4.00000 −0.208798 −0.104399 0.994535i 0.533292π-0.533292\pi
−0.104399 + 0.994535i 0.533292π0.533292\pi
368368 −6.00000 −0.312772
369369 6.00000 0.312348
370370 0 0
371371 −24.0000 −1.24602
372372 2.00000 0.103695
373373 −4.00000 −0.207112 −0.103556 0.994624i 0.533022π-0.533022\pi
−0.103556 + 0.994624i 0.533022π0.533022\pi
374374 0 0
375375 0 0
376376 6.00000 0.309426
377377 −24.0000 −1.23606
378378 −4.00000 −0.205738
379379 8.00000 0.410932 0.205466 0.978664i 0.434129π-0.434129\pi
0.205466 + 0.978664i 0.434129π0.434129\pi
380380 0 0
381381 2.00000 0.102463
382382 18.0000 0.920960
383383 24.0000 1.22634 0.613171 0.789950i 0.289894π-0.289894\pi
0.613171 + 0.789950i 0.289894π0.289894\pi
384384 1.00000 0.0510310
385385 0 0
386386 −10.0000 −0.508987
387387 −4.00000 −0.203331
388388 −10.0000 −0.507673
389389 24.0000 1.21685 0.608424 0.793612i 0.291802π-0.291802\pi
0.608424 + 0.793612i 0.291802π0.291802\pi
390390 0 0
391391 −36.0000 −1.82060
392392 9.00000 0.454569
393393 12.0000 0.605320
394394 12.0000 0.604551
395395 0 0
396396 0 0
397397 26.0000 1.30490 0.652451 0.757831i 0.273741π-0.273741\pi
0.652451 + 0.757831i 0.273741π0.273741\pi
398398 20.0000 1.00251
399399 −4.00000 −0.200250
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 8.00000 0.399004
403403 −8.00000 −0.398508
404404 0 0
405405 0 0
406406 −24.0000 −1.19110
407407 0 0
408408 6.00000 0.297044
409409 14.0000 0.692255 0.346128 0.938187i 0.387496π-0.387496\pi
0.346128 + 0.938187i 0.387496π0.387496\pi
410410 0 0
411411 −18.0000 −0.887875
412412 −10.0000 −0.492665
413413 48.0000 2.36193
414414 −6.00000 −0.294884
415415 0 0
416416 −4.00000 −0.196116
417417 20.0000 0.979404
418418 0 0
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 0 0
421421 −28.0000 −1.36464 −0.682318 0.731055i 0.739028π-0.739028\pi
−0.682318 + 0.731055i 0.739028π0.739028\pi
422422 −4.00000 −0.194717
423423 6.00000 0.291730
424424 6.00000 0.291386
425425 −30.0000 −1.45521
426426 0 0
427427 −56.0000 −2.71003
428428 12.0000 0.580042
429429 0 0
430430 0 0
431431 −12.0000 −0.578020 −0.289010 0.957326i 0.593326π-0.593326\pi
−0.289010 + 0.957326i 0.593326π0.593326\pi
432432 1.00000 0.0481125
433433 −10.0000 −0.480569 −0.240285 0.970702i 0.577241π-0.577241\pi
−0.240285 + 0.970702i 0.577241π0.577241\pi
434434 −8.00000 −0.384012
435435 0 0
436436 −16.0000 −0.766261
437437 −6.00000 −0.287019
438438 14.0000 0.668946
439439 26.0000 1.24091 0.620456 0.784241i 0.286947π-0.286947\pi
0.620456 + 0.784241i 0.286947π0.286947\pi
440440 0 0
441441 9.00000 0.428571
442442 −24.0000 −1.14156
443443 24.0000 1.14027 0.570137 0.821549i 0.306890π-0.306890\pi
0.570137 + 0.821549i 0.306890π0.306890\pi
444444 −4.00000 −0.189832
445445 0 0
446446 −22.0000 −1.04173
447447 12.0000 0.567581
448448 −4.00000 −0.188982
449449 −30.0000 −1.41579 −0.707894 0.706319i 0.750354π-0.750354\pi
−0.707894 + 0.706319i 0.750354π0.750354\pi
450450 −5.00000 −0.235702
451451 0 0
452452 −18.0000 −0.846649
453453 −10.0000 −0.469841
454454 12.0000 0.563188
455455 0 0
456456 1.00000 0.0468293
457457 2.00000 0.0935561 0.0467780 0.998905i 0.485105π-0.485105\pi
0.0467780 + 0.998905i 0.485105π0.485105\pi
458458 −10.0000 −0.467269
459459 6.00000 0.280056
460460 0 0
461461 12.0000 0.558896 0.279448 0.960161i 0.409849π-0.409849\pi
0.279448 + 0.960161i 0.409849π0.409849\pi
462462 0 0
463463 −4.00000 −0.185896 −0.0929479 0.995671i 0.529629π-0.529629\pi
−0.0929479 + 0.995671i 0.529629π0.529629\pi
464464 6.00000 0.278543
465465 0 0
466466 −6.00000 −0.277945
467467 −36.0000 −1.66588 −0.832941 0.553362i 0.813345π-0.813345\pi
−0.832941 + 0.553362i 0.813345π0.813345\pi
468468 −4.00000 −0.184900
469469 −32.0000 −1.47762
470470 0 0
471471 2.00000 0.0921551
472472 −12.0000 −0.552345
473473 0 0
474474 −10.0000 −0.459315
475475 −5.00000 −0.229416
476476 −24.0000 −1.10004
477477 6.00000 0.274721
478478 −18.0000 −0.823301
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 14.0000 0.637683
483483 24.0000 1.09204
484484 −11.0000 −0.500000
485485 0 0
486486 1.00000 0.0453609
487487 38.0000 1.72194 0.860972 0.508652i 0.169856π-0.169856\pi
0.860972 + 0.508652i 0.169856π0.169856\pi
488488 14.0000 0.633750
489489 −4.00000 −0.180886
490490 0 0
491491 36.0000 1.62466 0.812329 0.583200i 0.198200π-0.198200\pi
0.812329 + 0.583200i 0.198200π0.198200\pi
492492 6.00000 0.270501
493493 36.0000 1.62136
494494 −4.00000 −0.179969
495495 0 0
496496 2.00000 0.0898027
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 0 0
501501 −12.0000 −0.536120
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 −4.00000 −0.178174
505505 0 0
506506 0 0
507507 3.00000 0.133235
508508 2.00000 0.0887357
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 −56.0000 −2.47729
512512 1.00000 0.0441942
513513 1.00000 0.0441511
514514 18.0000 0.793946
515515 0 0
516516 −4.00000 −0.176090
517517 0 0
518518 16.0000 0.703000
519519 18.0000 0.790112
520520 0 0
521521 −30.0000 −1.31432 −0.657162 0.753749i 0.728243π-0.728243\pi
−0.657162 + 0.753749i 0.728243π0.728243\pi
522522 6.00000 0.262613
523523 8.00000 0.349816 0.174908 0.984585i 0.444037π-0.444037\pi
0.174908 + 0.984585i 0.444037π0.444037\pi
524524 12.0000 0.524222
525525 20.0000 0.872872
526526 −18.0000 −0.784837
527527 12.0000 0.522728
528528 0 0
529529 13.0000 0.565217
530530 0 0
531531 −12.0000 −0.520756
532532 −4.00000 −0.173422
533533 −24.0000 −1.03956
534534 −6.00000 −0.259645
535535 0 0
536536 8.00000 0.345547
537537 12.0000 0.517838
538538 −6.00000 −0.258678
539539 0 0
540540 0 0
541541 −22.0000 −0.945854 −0.472927 0.881102i 0.656803π-0.656803\pi
−0.472927 + 0.881102i 0.656803π0.656803\pi
542542 20.0000 0.859074
543543 −16.0000 −0.686626
544544 6.00000 0.257248
545545 0 0
546546 16.0000 0.684737
547547 32.0000 1.36822 0.684111 0.729378i 0.260191π-0.260191\pi
0.684111 + 0.729378i 0.260191π0.260191\pi
548548 −18.0000 −0.768922
549549 14.0000 0.597505
550550 0 0
551551 6.00000 0.255609
552552 −6.00000 −0.255377
553553 40.0000 1.70097
554554 −10.0000 −0.424859
555555 0 0
556556 20.0000 0.848189
557557 12.0000 0.508456 0.254228 0.967144i 0.418179π-0.418179\pi
0.254228 + 0.967144i 0.418179π0.418179\pi
558558 2.00000 0.0846668
559559 16.0000 0.676728
560560 0 0
561561 0 0
562562 −18.0000 −0.759284
563563 −36.0000 −1.51722 −0.758610 0.651546i 0.774121π-0.774121\pi
−0.758610 + 0.651546i 0.774121π0.774121\pi
564564 6.00000 0.252646
565565 0 0
566566 −4.00000 −0.168133
567567 −4.00000 −0.167984
568568 0 0
569569 42.0000 1.76073 0.880366 0.474295i 0.157297π-0.157297\pi
0.880366 + 0.474295i 0.157297π0.157297\pi
570570 0 0
571571 −28.0000 −1.17176 −0.585882 0.810397i 0.699252π-0.699252\pi
−0.585882 + 0.810397i 0.699252π0.699252\pi
572572 0 0
573573 18.0000 0.751961
574574 −24.0000 −1.00174
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 19.0000 0.790296
579579 −10.0000 −0.415586
580580 0 0
581581 48.0000 1.99138
582582 −10.0000 −0.414513
583583 0 0
584584 14.0000 0.579324
585585 0 0
586586 −6.00000 −0.247858
587587 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
588588 9.00000 0.371154
589589 2.00000 0.0824086
590590 0 0
591591 12.0000 0.493614
592592 −4.00000 −0.164399
593593 −6.00000 −0.246390 −0.123195 0.992382i 0.539314π-0.539314\pi
−0.123195 + 0.992382i 0.539314π0.539314\pi
594594 0 0
595595 0 0
596596 12.0000 0.491539
597597 20.0000 0.818546
598598 24.0000 0.981433
599599 −12.0000 −0.490307 −0.245153 0.969484i 0.578838π-0.578838\pi
−0.245153 + 0.969484i 0.578838π0.578838\pi
600600 −5.00000 −0.204124
601601 −22.0000 −0.897399 −0.448699 0.893683i 0.648113π-0.648113\pi
−0.448699 + 0.893683i 0.648113π0.648113\pi
602602 16.0000 0.652111
603603 8.00000 0.325785
604604 −10.0000 −0.406894
605605 0 0
606606 0 0
607607 −34.0000 −1.38002 −0.690009 0.723801i 0.742393π-0.742393\pi
−0.690009 + 0.723801i 0.742393π0.742393\pi
608608 1.00000 0.0405554
609609 −24.0000 −0.972529
610610 0 0
611611 −24.0000 −0.970936
612612 6.00000 0.242536
613613 2.00000 0.0807792 0.0403896 0.999184i 0.487140π-0.487140\pi
0.0403896 + 0.999184i 0.487140π0.487140\pi
614614 −16.0000 −0.645707
615615 0 0
616616 0 0
617617 −30.0000 −1.20775 −0.603877 0.797077i 0.706378π-0.706378\pi
−0.603877 + 0.797077i 0.706378π0.706378\pi
618618 −10.0000 −0.402259
619619 −4.00000 −0.160774 −0.0803868 0.996764i 0.525616π-0.525616\pi
−0.0803868 + 0.996764i 0.525616π0.525616\pi
620620 0 0
621621 −6.00000 −0.240772
622622 30.0000 1.20289
623623 24.0000 0.961540
624624 −4.00000 −0.160128
625625 25.0000 1.00000
626626 −10.0000 −0.399680
627627 0 0
628628 2.00000 0.0798087
629629 −24.0000 −0.956943
630630 0 0
631631 32.0000 1.27390 0.636950 0.770905i 0.280196π-0.280196\pi
0.636950 + 0.770905i 0.280196π0.280196\pi
632632 −10.0000 −0.397779
633633 −4.00000 −0.158986
634634 18.0000 0.714871
635635 0 0
636636 6.00000 0.237915
637637 −36.0000 −1.42637
638638 0 0
639639 0 0
640640 0 0
641641 −6.00000 −0.236986 −0.118493 0.992955i 0.537806π-0.537806\pi
−0.118493 + 0.992955i 0.537806π0.537806\pi
642642 12.0000 0.473602
643643 −4.00000 −0.157745 −0.0788723 0.996885i 0.525132π-0.525132\pi
−0.0788723 + 0.996885i 0.525132π0.525132\pi
644644 24.0000 0.945732
645645 0 0
646646 6.00000 0.236067
647647 −6.00000 −0.235884 −0.117942 0.993020i 0.537630π-0.537630\pi
−0.117942 + 0.993020i 0.537630π0.537630\pi
648648 1.00000 0.0392837
649649 0 0
650650 20.0000 0.784465
651651 −8.00000 −0.313545
652652 −4.00000 −0.156652
653653 36.0000 1.40879 0.704394 0.709809i 0.251219π-0.251219\pi
0.704394 + 0.709809i 0.251219π0.251219\pi
654654 −16.0000 −0.625650
655655 0 0
656656 6.00000 0.234261
657657 14.0000 0.546192
658658 −24.0000 −0.935617
659659 −12.0000 −0.467454 −0.233727 0.972302i 0.575092π-0.575092\pi
−0.233727 + 0.972302i 0.575092π0.575092\pi
660660 0 0
661661 −4.00000 −0.155582 −0.0777910 0.996970i 0.524787π-0.524787\pi
−0.0777910 + 0.996970i 0.524787π0.524787\pi
662662 8.00000 0.310929
663663 −24.0000 −0.932083
664664 −12.0000 −0.465690
665665 0 0
666666 −4.00000 −0.154997
667667 −36.0000 −1.39393
668668 −12.0000 −0.464294
669669 −22.0000 −0.850569
670670 0 0
671671 0 0
672672 −4.00000 −0.154303
673673 −10.0000 −0.385472 −0.192736 0.981251i 0.561736π-0.561736\pi
−0.192736 + 0.981251i 0.561736π0.561736\pi
674674 2.00000 0.0770371
675675 −5.00000 −0.192450
676676 3.00000 0.115385
677677 −18.0000 −0.691796 −0.345898 0.938272i 0.612426π-0.612426\pi
−0.345898 + 0.938272i 0.612426π0.612426\pi
678678 −18.0000 −0.691286
679679 40.0000 1.53506
680680 0 0
681681 12.0000 0.459841
682682 0 0
683683 −12.0000 −0.459167 −0.229584 0.973289i 0.573736π-0.573736\pi
−0.229584 + 0.973289i 0.573736π0.573736\pi
684684 1.00000 0.0382360
685685 0 0
686686 −8.00000 −0.305441
687687 −10.0000 −0.381524
688688 −4.00000 −0.152499
689689 −24.0000 −0.914327
690690 0 0
691691 −28.0000 −1.06517 −0.532585 0.846376i 0.678779π-0.678779\pi
−0.532585 + 0.846376i 0.678779π0.678779\pi
692692 18.0000 0.684257
693693 0 0
694694 24.0000 0.911028
695695 0 0
696696 6.00000 0.227429
697697 36.0000 1.36360
698698 2.00000 0.0757011
699699 −6.00000 −0.226941
700700 20.0000 0.755929
701701 −48.0000 −1.81293 −0.906467 0.422276i 0.861231π-0.861231\pi
−0.906467 + 0.422276i 0.861231π0.861231\pi
702702 −4.00000 −0.150970
703703 −4.00000 −0.150863
704704 0 0
705705 0 0
706706 −6.00000 −0.225813
707707 0 0
708708 −12.0000 −0.450988
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 −6.00000 −0.224860
713713 −12.0000 −0.449404
714714 −24.0000 −0.898177
715715 0 0
716716 12.0000 0.448461
717717 −18.0000 −0.672222
718718 −6.00000 −0.223918
719719 −18.0000 −0.671287 −0.335643 0.941989i 0.608954π-0.608954\pi
−0.335643 + 0.941989i 0.608954π0.608954\pi
720720 0 0
721721 40.0000 1.48968
722722 1.00000 0.0372161
723723 14.0000 0.520666
724724 −16.0000 −0.594635
725725 −30.0000 −1.11417
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 16.0000 0.592999
729729 1.00000 0.0370370
730730 0 0
731731 −24.0000 −0.887672
732732 14.0000 0.517455
733733 50.0000 1.84679 0.923396 0.383849i 0.125402π-0.125402\pi
0.923396 + 0.383849i 0.125402π0.125402\pi
734734 −4.00000 −0.147643
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 −4.00000 −0.146944
742742 −24.0000 −0.881068
743743 −12.0000 −0.440237 −0.220119 0.975473i 0.570644π-0.570644\pi
−0.220119 + 0.975473i 0.570644π0.570644\pi
744744 2.00000 0.0733236
745745 0 0
746746 −4.00000 −0.146450
747747 −12.0000 −0.439057
748748 0 0
749749 −48.0000 −1.75388
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 6.00000 0.218797
753753 12.0000 0.437304
754754 −24.0000 −0.874028
755755 0 0
756756 −4.00000 −0.145479
757757 −46.0000 −1.67190 −0.835949 0.548807i 0.815082π-0.815082\pi
−0.835949 + 0.548807i 0.815082π0.815082\pi
758758 8.00000 0.290573
759759 0 0
760760 0 0
761761 6.00000 0.217500 0.108750 0.994069i 0.465315π-0.465315\pi
0.108750 + 0.994069i 0.465315π0.465315\pi
762762 2.00000 0.0724524
763763 64.0000 2.31696
764764 18.0000 0.651217
765765 0 0
766766 24.0000 0.867155
767767 48.0000 1.73318
768768 1.00000 0.0360844
769769 14.0000 0.504853 0.252426 0.967616i 0.418771π-0.418771\pi
0.252426 + 0.967616i 0.418771π0.418771\pi
770770 0 0
771771 18.0000 0.648254
772772 −10.0000 −0.359908
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 −10.0000 −0.359211
776776 −10.0000 −0.358979
777777 16.0000 0.573997
778778 24.0000 0.860442
779779 6.00000 0.214972
780780 0 0
781781 0 0
782782 −36.0000 −1.28736
783783 6.00000 0.214423
784784 9.00000 0.321429
785785 0 0
786786 12.0000 0.428026
787787 20.0000 0.712923 0.356462 0.934310i 0.383983π-0.383983\pi
0.356462 + 0.934310i 0.383983π0.383983\pi
788788 12.0000 0.427482
789789 −18.0000 −0.640817
790790 0 0
791791 72.0000 2.56003
792792 0 0
793793 −56.0000 −1.98862
794794 26.0000 0.922705
795795 0 0
796796 20.0000 0.708881
797797 18.0000 0.637593 0.318796 0.947823i 0.396721π-0.396721\pi
0.318796 + 0.947823i 0.396721π0.396721\pi
798798 −4.00000 −0.141598
799799 36.0000 1.27359
800800 −5.00000 −0.176777
801801 −6.00000 −0.212000
802802 30.0000 1.05934
803803 0 0
804804 8.00000 0.282138
805805 0 0
806806 −8.00000 −0.281788
807807 −6.00000 −0.211210
808808 0 0
809809 −42.0000 −1.47664 −0.738321 0.674450i 0.764381π-0.764381\pi
−0.738321 + 0.674450i 0.764381π0.764381\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 20.0000 0.701431
814814 0 0
815815 0 0
816816 6.00000 0.210042
817817 −4.00000 −0.139942
818818 14.0000 0.489499
819819 16.0000 0.559085
820820 0 0
821821 −24.0000 −0.837606 −0.418803 0.908077i 0.637550π-0.637550\pi
−0.418803 + 0.908077i 0.637550π0.637550\pi
822822 −18.0000 −0.627822
823823 32.0000 1.11545 0.557725 0.830026i 0.311674π-0.311674\pi
0.557725 + 0.830026i 0.311674π0.311674\pi
824824 −10.0000 −0.348367
825825 0 0
826826 48.0000 1.67013
827827 −12.0000 −0.417281 −0.208640 0.977992i 0.566904π-0.566904\pi
−0.208640 + 0.977992i 0.566904π0.566904\pi
828828 −6.00000 −0.208514
829829 −16.0000 −0.555703 −0.277851 0.960624i 0.589622π-0.589622\pi
−0.277851 + 0.960624i 0.589622π0.589622\pi
830830 0 0
831831 −10.0000 −0.346896
832832 −4.00000 −0.138675
833833 54.0000 1.87099
834834 20.0000 0.692543
835835 0 0
836836 0 0
837837 2.00000 0.0691301
838838 0 0
839839 36.0000 1.24286 0.621429 0.783470i 0.286552π-0.286552\pi
0.621429 + 0.783470i 0.286552π0.286552\pi
840840 0 0
841841 7.00000 0.241379
842842 −28.0000 −0.964944
843843 −18.0000 −0.619953
844844 −4.00000 −0.137686
845845 0 0
846846 6.00000 0.206284
847847 44.0000 1.51186
848848 6.00000 0.206041
849849 −4.00000 −0.137280
850850 −30.0000 −1.02899
851851 24.0000 0.822709
852852 0 0
853853 38.0000 1.30110 0.650548 0.759465i 0.274539π-0.274539\pi
0.650548 + 0.759465i 0.274539π0.274539\pi
854854 −56.0000 −1.91628
855855 0 0
856856 12.0000 0.410152
857857 18.0000 0.614868 0.307434 0.951569i 0.400530π-0.400530\pi
0.307434 + 0.951569i 0.400530π0.400530\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 −24.0000 −0.817918
862862 −12.0000 −0.408722
863863 12.0000 0.408485 0.204242 0.978920i 0.434527π-0.434527\pi
0.204242 + 0.978920i 0.434527π0.434527\pi
864864 1.00000 0.0340207
865865 0 0
866866 −10.0000 −0.339814
867867 19.0000 0.645274
868868 −8.00000 −0.271538
869869 0 0
870870 0 0
871871 −32.0000 −1.08428
872872 −16.0000 −0.541828
873873 −10.0000 −0.338449
874874 −6.00000 −0.202953
875875 0 0
876876 14.0000 0.473016
877877 44.0000 1.48577 0.742887 0.669417i 0.233456π-0.233456\pi
0.742887 + 0.669417i 0.233456π0.233456\pi
878878 26.0000 0.877457
879879 −6.00000 −0.202375
880880 0 0
881881 −30.0000 −1.01073 −0.505363 0.862907i 0.668641π-0.668641\pi
−0.505363 + 0.862907i 0.668641π0.668641\pi
882882 9.00000 0.303046
883883 20.0000 0.673054 0.336527 0.941674i 0.390748π-0.390748\pi
0.336527 + 0.941674i 0.390748π0.390748\pi
884884 −24.0000 −0.807207
885885 0 0
886886 24.0000 0.806296
887887 12.0000 0.402921 0.201460 0.979497i 0.435431π-0.435431\pi
0.201460 + 0.979497i 0.435431π0.435431\pi
888888 −4.00000 −0.134231
889889 −8.00000 −0.268311
890890 0 0
891891 0 0
892892 −22.0000 −0.736614
893893 6.00000 0.200782
894894 12.0000 0.401340
895895 0 0
896896 −4.00000 −0.133631
897897 24.0000 0.801337
898898 −30.0000 −1.00111
899899 12.0000 0.400222
900900 −5.00000 −0.166667
901901 36.0000 1.19933
902902 0 0
903903 16.0000 0.532447
904904 −18.0000 −0.598671
905905 0 0
906906 −10.0000 −0.332228
907907 8.00000 0.265636 0.132818 0.991140i 0.457597π-0.457597\pi
0.132818 + 0.991140i 0.457597π0.457597\pi
908908 12.0000 0.398234
909909 0 0
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 1.00000 0.0331133
913913 0 0
914914 2.00000 0.0661541
915915 0 0
916916 −10.0000 −0.330409
917917 −48.0000 −1.58510
918918 6.00000 0.198030
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 −16.0000 −0.527218
922922 12.0000 0.395199
923923 0 0
924924 0 0
925925 20.0000 0.657596
926926 −4.00000 −0.131448
927927 −10.0000 −0.328443
928928 6.00000 0.196960
929929 6.00000 0.196854 0.0984268 0.995144i 0.468619π-0.468619\pi
0.0984268 + 0.995144i 0.468619π0.468619\pi
930930 0 0
931931 9.00000 0.294963
932932 −6.00000 −0.196537
933933 30.0000 0.982156
934934 −36.0000 −1.17796
935935 0 0
936936 −4.00000 −0.130744
937937 −58.0000 −1.89478 −0.947389 0.320085i 0.896288π-0.896288\pi
−0.947389 + 0.320085i 0.896288π0.896288\pi
938938 −32.0000 −1.04484
939939 −10.0000 −0.326338
940940 0 0
941941 18.0000 0.586783 0.293392 0.955992i 0.405216π-0.405216\pi
0.293392 + 0.955992i 0.405216π0.405216\pi
942942 2.00000 0.0651635
943943 −36.0000 −1.17232
944944 −12.0000 −0.390567
945945 0 0
946946 0 0
947947 −12.0000 −0.389948 −0.194974 0.980808i 0.562462π-0.562462\pi
−0.194974 + 0.980808i 0.562462π0.562462\pi
948948 −10.0000 −0.324785
949949 −56.0000 −1.81784
950950 −5.00000 −0.162221
951951 18.0000 0.583690
952952 −24.0000 −0.777844
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 −18.0000 −0.582162
957957 0 0
958958 −6.00000 −0.193851
959959 72.0000 2.32500
960960 0 0
961961 −27.0000 −0.870968
962962 16.0000 0.515861
963963 12.0000 0.386695
964964 14.0000 0.450910
965965 0 0
966966 24.0000 0.772187
967967 −28.0000 −0.900419 −0.450210 0.892923i 0.648651π-0.648651\pi
−0.450210 + 0.892923i 0.648651π0.648651\pi
968968 −11.0000 −0.353553
969969 6.00000 0.192748
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 −80.0000 −2.56468
974974 38.0000 1.21760
975975 20.0000 0.640513
976976 14.0000 0.448129
977977 −18.0000 −0.575871 −0.287936 0.957650i 0.592969π-0.592969\pi
−0.287936 + 0.957650i 0.592969π0.592969\pi
978978 −4.00000 −0.127906
979979 0 0
980980 0 0
981981 −16.0000 −0.510841
982982 36.0000 1.14881
983983 −48.0000 −1.53096 −0.765481 0.643458i 0.777499π-0.777499\pi
−0.765481 + 0.643458i 0.777499π0.777499\pi
984984 6.00000 0.191273
985985 0 0
986986 36.0000 1.14647
987987 −24.0000 −0.763928
988988 −4.00000 −0.127257
989989 24.0000 0.763156
990990 0 0
991991 26.0000 0.825917 0.412959 0.910750i 0.364495π-0.364495\pi
0.412959 + 0.910750i 0.364495π0.364495\pi
992992 2.00000 0.0635001
993993 8.00000 0.253872
994994 0 0
995995 0 0
996996 −12.0000 −0.380235
997997 26.0000 0.823428 0.411714 0.911313i 0.364930π-0.364930\pi
0.411714 + 0.911313i 0.364930π0.364930\pi
998998 −4.00000 −0.126618
999999 −4.00000 −0.126554
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 114.2.a.c.1.1 1
3.2 odd 2 342.2.a.c.1.1 1
4.3 odd 2 912.2.a.c.1.1 1
5.2 odd 4 2850.2.d.p.799.2 2
5.3 odd 4 2850.2.d.p.799.1 2
5.4 even 2 2850.2.a.g.1.1 1
7.6 odd 2 5586.2.a.u.1.1 1
8.3 odd 2 3648.2.a.bc.1.1 1
8.5 even 2 3648.2.a.i.1.1 1
12.11 even 2 2736.2.a.o.1.1 1
15.14 odd 2 8550.2.a.bj.1.1 1
19.18 odd 2 2166.2.a.a.1.1 1
57.56 even 2 6498.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.2.a.c.1.1 1 1.1 even 1 trivial
342.2.a.c.1.1 1 3.2 odd 2
912.2.a.c.1.1 1 4.3 odd 2
2166.2.a.a.1.1 1 19.18 odd 2
2736.2.a.o.1.1 1 12.11 even 2
2850.2.a.g.1.1 1 5.4 even 2
2850.2.d.p.799.1 2 5.3 odd 4
2850.2.d.p.799.2 2 5.2 odd 4
3648.2.a.i.1.1 1 8.5 even 2
3648.2.a.bc.1.1 1 8.3 odd 2
5586.2.a.u.1.1 1 7.6 odd 2
6498.2.a.t.1.1 1 57.56 even 2
8550.2.a.bj.1.1 1 15.14 odd 2