Properties

Label 342.2.a.d.1.1
Level 342342
Weight 22
Character 342.1
Self dual yes
Analytic conductor 2.7312.731
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] = [342,2,Mod(1,342)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(342, 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("342.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 342=23219 342 = 2 \cdot 3^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 342.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,4,0,3,-1,0,-4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 2.730883749132.73088374913
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 38)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 342.1

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) == q1.00000q2+1.00000q4+4.00000q5+3.00000q71.00000q84.00000q102.00000q111.00000q133.00000q14+1.00000q163.00000q171.00000q19+4.00000q20+2.00000q22+1.00000q23+11.0000q25+1.00000q26+3.00000q28+5.00000q298.00000q311.00000q32+3.00000q34+12.0000q352.00000q37+1.00000q384.00000q40+8.00000q41+4.00000q432.00000q441.00000q468.00000q47+2.00000q4911.0000q501.00000q52+1.00000q538.00000q553.00000q565.00000q5815.0000q59+2.00000q61+8.00000q62+1.00000q644.00000q65+3.00000q673.00000q6812.0000q702.00000q71+9.00000q73+2.00000q741.00000q766.00000q7710.0000q79+4.00000q808.00000q82+6.00000q8312.0000q854.00000q86+2.00000q883.00000q91+1.00000q92+8.00000q944.00000q952.00000q972.00000q98+O(q100)q-1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} +3.00000 q^{7} -1.00000 q^{8} -4.00000 q^{10} -2.00000 q^{11} -1.00000 q^{13} -3.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} -1.00000 q^{19} +4.00000 q^{20} +2.00000 q^{22} +1.00000 q^{23} +11.0000 q^{25} +1.00000 q^{26} +3.00000 q^{28} +5.00000 q^{29} -8.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} +12.0000 q^{35} -2.00000 q^{37} +1.00000 q^{38} -4.00000 q^{40} +8.00000 q^{41} +4.00000 q^{43} -2.00000 q^{44} -1.00000 q^{46} -8.00000 q^{47} +2.00000 q^{49} -11.0000 q^{50} -1.00000 q^{52} +1.00000 q^{53} -8.00000 q^{55} -3.00000 q^{56} -5.00000 q^{58} -15.0000 q^{59} +2.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} +3.00000 q^{67} -3.00000 q^{68} -12.0000 q^{70} -2.00000 q^{71} +9.00000 q^{73} +2.00000 q^{74} -1.00000 q^{76} -6.00000 q^{77} -10.0000 q^{79} +4.00000 q^{80} -8.00000 q^{82} +6.00000 q^{83} -12.0000 q^{85} -4.00000 q^{86} +2.00000 q^{88} -3.00000 q^{91} +1.00000 q^{92} +8.00000 q^{94} -4.00000 q^{95} -2.00000 q^{97} -2.00000 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 0 0
44 1.00000 0.500000
55 4.00000 1.78885 0.894427 0.447214i 0.147584π-0.147584\pi
0.894427 + 0.447214i 0.147584π0.147584\pi
66 0 0
77 3.00000 1.13389 0.566947 0.823754i 0.308125π-0.308125\pi
0.566947 + 0.823754i 0.308125π0.308125\pi
88 −1.00000 −0.353553
99 0 0
1010 −4.00000 −1.26491
1111 −2.00000 −0.603023 −0.301511 0.953463i 0.597491π-0.597491\pi
−0.301511 + 0.953463i 0.597491π0.597491\pi
1212 0 0
1313 −1.00000 −0.277350 −0.138675 0.990338i 0.544284π-0.544284\pi
−0.138675 + 0.990338i 0.544284π0.544284\pi
1414 −3.00000 −0.801784
1515 0 0
1616 1.00000 0.250000
1717 −3.00000 −0.727607 −0.363803 0.931476i 0.618522π-0.618522\pi
−0.363803 + 0.931476i 0.618522π0.618522\pi
1818 0 0
1919 −1.00000 −0.229416
2020 4.00000 0.894427
2121 0 0
2222 2.00000 0.426401
2323 1.00000 0.208514 0.104257 0.994550i 0.466753π-0.466753\pi
0.104257 + 0.994550i 0.466753π0.466753\pi
2424 0 0
2525 11.0000 2.20000
2626 1.00000 0.196116
2727 0 0
2828 3.00000 0.566947
2929 5.00000 0.928477 0.464238 0.885710i 0.346328π-0.346328\pi
0.464238 + 0.885710i 0.346328π0.346328\pi
3030 0 0
3131 −8.00000 −1.43684 −0.718421 0.695608i 0.755135π-0.755135\pi
−0.718421 + 0.695608i 0.755135π0.755135\pi
3232 −1.00000 −0.176777
3333 0 0
3434 3.00000 0.514496
3535 12.0000 2.02837
3636 0 0
3737 −2.00000 −0.328798 −0.164399 0.986394i 0.552568π-0.552568\pi
−0.164399 + 0.986394i 0.552568π0.552568\pi
3838 1.00000 0.162221
3939 0 0
4040 −4.00000 −0.632456
4141 8.00000 1.24939 0.624695 0.780869i 0.285223π-0.285223\pi
0.624695 + 0.780869i 0.285223π0.285223\pi
4242 0 0
4343 4.00000 0.609994 0.304997 0.952353i 0.401344π-0.401344\pi
0.304997 + 0.952353i 0.401344π0.401344\pi
4444 −2.00000 −0.301511
4545 0 0
4646 −1.00000 −0.147442
4747 −8.00000 −1.16692 −0.583460 0.812142i 0.698301π-0.698301\pi
−0.583460 + 0.812142i 0.698301π0.698301\pi
4848 0 0
4949 2.00000 0.285714
5050 −11.0000 −1.55563
5151 0 0
5252 −1.00000 −0.138675
5353 1.00000 0.137361 0.0686803 0.997639i 0.478121π-0.478121\pi
0.0686803 + 0.997639i 0.478121π0.478121\pi
5454 0 0
5555 −8.00000 −1.07872
5656 −3.00000 −0.400892
5757 0 0
5858 −5.00000 −0.656532
5959 −15.0000 −1.95283 −0.976417 0.215894i 0.930733π-0.930733\pi
−0.976417 + 0.215894i 0.930733π0.930733\pi
6060 0 0
6161 2.00000 0.256074 0.128037 0.991769i 0.459132π-0.459132\pi
0.128037 + 0.991769i 0.459132π0.459132\pi
6262 8.00000 1.01600
6363 0 0
6464 1.00000 0.125000
6565 −4.00000 −0.496139
6666 0 0
6767 3.00000 0.366508 0.183254 0.983066i 0.441337π-0.441337\pi
0.183254 + 0.983066i 0.441337π0.441337\pi
6868 −3.00000 −0.363803
6969 0 0
7070 −12.0000 −1.43427
7171 −2.00000 −0.237356 −0.118678 0.992933i 0.537866π-0.537866\pi
−0.118678 + 0.992933i 0.537866π0.537866\pi
7272 0 0
7373 9.00000 1.05337 0.526685 0.850060i 0.323435π-0.323435\pi
0.526685 + 0.850060i 0.323435π0.323435\pi
7474 2.00000 0.232495
7575 0 0
7676 −1.00000 −0.114708
7777 −6.00000 −0.683763
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 4.00000 0.447214
8181 0 0
8282 −8.00000 −0.883452
8383 6.00000 0.658586 0.329293 0.944228i 0.393190π-0.393190\pi
0.329293 + 0.944228i 0.393190π0.393190\pi
8484 0 0
8585 −12.0000 −1.30158
8686 −4.00000 −0.431331
8787 0 0
8888 2.00000 0.213201
8989 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
9090 0 0
9191 −3.00000 −0.314485
9292 1.00000 0.104257
9393 0 0
9494 8.00000 0.825137
9595 −4.00000 −0.410391
9696 0 0
9797 −2.00000 −0.203069 −0.101535 0.994832i 0.532375π-0.532375\pi
−0.101535 + 0.994832i 0.532375π0.532375\pi
9898 −2.00000 −0.202031
9999 0 0
100100 11.0000 1.10000
101101 −2.00000 −0.199007 −0.0995037 0.995037i 0.531726π-0.531726\pi
−0.0995037 + 0.995037i 0.531726π0.531726\pi
102102 0 0
103103 −6.00000 −0.591198 −0.295599 0.955312i 0.595519π-0.595519\pi
−0.295599 + 0.955312i 0.595519π0.595519\pi
104104 1.00000 0.0980581
105105 0 0
106106 −1.00000 −0.0971286
107107 7.00000 0.676716 0.338358 0.941018i 0.390129π-0.390129\pi
0.338358 + 0.941018i 0.390129π0.390129\pi
108108 0 0
109109 −15.0000 −1.43674 −0.718370 0.695662i 0.755111π-0.755111\pi
−0.718370 + 0.695662i 0.755111π0.755111\pi
110110 8.00000 0.762770
111111 0 0
112112 3.00000 0.283473
113113 −14.0000 −1.31701 −0.658505 0.752577i 0.728811π-0.728811\pi
−0.658505 + 0.752577i 0.728811π0.728811\pi
114114 0 0
115115 4.00000 0.373002
116116 5.00000 0.464238
117117 0 0
118118 15.0000 1.38086
119119 −9.00000 −0.825029
120120 0 0
121121 −7.00000 −0.636364
122122 −2.00000 −0.181071
123123 0 0
124124 −8.00000 −0.718421
125125 24.0000 2.14663
126126 0 0
127127 18.0000 1.59724 0.798621 0.601834i 0.205563π-0.205563\pi
0.798621 + 0.601834i 0.205563π0.205563\pi
128128 −1.00000 −0.0883883
129129 0 0
130130 4.00000 0.350823
131131 −12.0000 −1.04844 −0.524222 0.851581i 0.675644π-0.675644\pi
−0.524222 + 0.851581i 0.675644π0.675644\pi
132132 0 0
133133 −3.00000 −0.260133
134134 −3.00000 −0.259161
135135 0 0
136136 3.00000 0.257248
137137 17.0000 1.45241 0.726204 0.687479i 0.241283π-0.241283\pi
0.726204 + 0.687479i 0.241283π0.241283\pi
138138 0 0
139139 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
140140 12.0000 1.01419
141141 0 0
142142 2.00000 0.167836
143143 2.00000 0.167248
144144 0 0
145145 20.0000 1.66091
146146 −9.00000 −0.744845
147147 0 0
148148 −2.00000 −0.164399
149149 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
150150 0 0
151151 2.00000 0.162758 0.0813788 0.996683i 0.474068π-0.474068\pi
0.0813788 + 0.996683i 0.474068π0.474068\pi
152152 1.00000 0.0811107
153153 0 0
154154 6.00000 0.483494
155155 −32.0000 −2.57030
156156 0 0
157157 −2.00000 −0.159617 −0.0798087 0.996810i 0.525431π-0.525431\pi
−0.0798087 + 0.996810i 0.525431π0.525431\pi
158158 10.0000 0.795557
159159 0 0
160160 −4.00000 −0.316228
161161 3.00000 0.236433
162162 0 0
163163 −16.0000 −1.25322 −0.626608 0.779334i 0.715557π-0.715557\pi
−0.626608 + 0.779334i 0.715557π0.715557\pi
164164 8.00000 0.624695
165165 0 0
166166 −6.00000 −0.465690
167167 12.0000 0.928588 0.464294 0.885681i 0.346308π-0.346308\pi
0.464294 + 0.885681i 0.346308π0.346308\pi
168168 0 0
169169 −12.0000 −0.923077
170170 12.0000 0.920358
171171 0 0
172172 4.00000 0.304997
173173 6.00000 0.456172 0.228086 0.973641i 0.426753π-0.426753\pi
0.228086 + 0.973641i 0.426753π0.426753\pi
174174 0 0
175175 33.0000 2.49457
176176 −2.00000 −0.150756
177177 0 0
178178 0 0
179179 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
180180 0 0
181181 22.0000 1.63525 0.817624 0.575753i 0.195291π-0.195291\pi
0.817624 + 0.575753i 0.195291π0.195291\pi
182182 3.00000 0.222375
183183 0 0
184184 −1.00000 −0.0737210
185185 −8.00000 −0.588172
186186 0 0
187187 6.00000 0.438763
188188 −8.00000 −0.583460
189189 0 0
190190 4.00000 0.290191
191191 −7.00000 −0.506502 −0.253251 0.967401i 0.581500π-0.581500\pi
−0.253251 + 0.967401i 0.581500π0.581500\pi
192192 0 0
193193 −6.00000 −0.431889 −0.215945 0.976406i 0.569283π-0.569283\pi
−0.215945 + 0.976406i 0.569283π0.569283\pi
194194 2.00000 0.143592
195195 0 0
196196 2.00000 0.142857
197197 −8.00000 −0.569976 −0.284988 0.958531i 0.591990π-0.591990\pi
−0.284988 + 0.958531i 0.591990π0.591990\pi
198198 0 0
199199 −25.0000 −1.77220 −0.886102 0.463491i 0.846597π-0.846597\pi
−0.886102 + 0.463491i 0.846597π0.846597\pi
200200 −11.0000 −0.777817
201201 0 0
202202 2.00000 0.140720
203203 15.0000 1.05279
204204 0 0
205205 32.0000 2.23498
206206 6.00000 0.418040
207207 0 0
208208 −1.00000 −0.0693375
209209 2.00000 0.138343
210210 0 0
211211 27.0000 1.85876 0.929378 0.369129i 0.120344π-0.120344\pi
0.929378 + 0.369129i 0.120344π0.120344\pi
212212 1.00000 0.0686803
213213 0 0
214214 −7.00000 −0.478510
215215 16.0000 1.09119
216216 0 0
217217 −24.0000 −1.62923
218218 15.0000 1.01593
219219 0 0
220220 −8.00000 −0.539360
221221 3.00000 0.201802
222222 0 0
223223 14.0000 0.937509 0.468755 0.883328i 0.344703π-0.344703\pi
0.468755 + 0.883328i 0.344703π0.344703\pi
224224 −3.00000 −0.200446
225225 0 0
226226 14.0000 0.931266
227227 17.0000 1.12833 0.564165 0.825662i 0.309198π-0.309198\pi
0.564165 + 0.825662i 0.309198π0.309198\pi
228228 0 0
229229 −10.0000 −0.660819 −0.330409 0.943838i 0.607187π-0.607187\pi
−0.330409 + 0.943838i 0.607187π0.607187\pi
230230 −4.00000 −0.263752
231231 0 0
232232 −5.00000 −0.328266
233233 6.00000 0.393073 0.196537 0.980497i 0.437031π-0.437031\pi
0.196537 + 0.980497i 0.437031π0.437031\pi
234234 0 0
235235 −32.0000 −2.08745
236236 −15.0000 −0.976417
237237 0 0
238238 9.00000 0.583383
239239 −15.0000 −0.970269 −0.485135 0.874439i 0.661229π-0.661229\pi
−0.485135 + 0.874439i 0.661229π0.661229\pi
240240 0 0
241241 −8.00000 −0.515325 −0.257663 0.966235i 0.582952π-0.582952\pi
−0.257663 + 0.966235i 0.582952π0.582952\pi
242242 7.00000 0.449977
243243 0 0
244244 2.00000 0.128037
245245 8.00000 0.511101
246246 0 0
247247 1.00000 0.0636285
248248 8.00000 0.508001
249249 0 0
250250 −24.0000 −1.51789
251251 −2.00000 −0.126239 −0.0631194 0.998006i 0.520105π-0.520105\pi
−0.0631194 + 0.998006i 0.520105π0.520105\pi
252252 0 0
253253 −2.00000 −0.125739
254254 −18.0000 −1.12942
255255 0 0
256256 1.00000 0.0625000
257257 −8.00000 −0.499026 −0.249513 0.968371i 0.580271π-0.580271\pi
−0.249513 + 0.968371i 0.580271π0.580271\pi
258258 0 0
259259 −6.00000 −0.372822
260260 −4.00000 −0.248069
261261 0 0
262262 12.0000 0.741362
263263 −24.0000 −1.47990 −0.739952 0.672660i 0.765152π-0.765152\pi
−0.739952 + 0.672660i 0.765152π0.765152\pi
264264 0 0
265265 4.00000 0.245718
266266 3.00000 0.183942
267267 0 0
268268 3.00000 0.183254
269269 −30.0000 −1.82913 −0.914566 0.404436i 0.867468π-0.867468\pi
−0.914566 + 0.404436i 0.867468π0.867468\pi
270270 0 0
271271 7.00000 0.425220 0.212610 0.977137i 0.431804π-0.431804\pi
0.212610 + 0.977137i 0.431804π0.431804\pi
272272 −3.00000 −0.181902
273273 0 0
274274 −17.0000 −1.02701
275275 −22.0000 −1.32665
276276 0 0
277277 28.0000 1.68236 0.841178 0.540758i 0.181862π-0.181862\pi
0.841178 + 0.540758i 0.181862π0.181862\pi
278278 0 0
279279 0 0
280280 −12.0000 −0.717137
281281 8.00000 0.477240 0.238620 0.971113i 0.423305π-0.423305\pi
0.238620 + 0.971113i 0.423305π0.423305\pi
282282 0 0
283283 −6.00000 −0.356663 −0.178331 0.983970i 0.557070π-0.557070\pi
−0.178331 + 0.983970i 0.557070π0.557070\pi
284284 −2.00000 −0.118678
285285 0 0
286286 −2.00000 −0.118262
287287 24.0000 1.41668
288288 0 0
289289 −8.00000 −0.470588
290290 −20.0000 −1.17444
291291 0 0
292292 9.00000 0.526685
293293 −9.00000 −0.525786 −0.262893 0.964825i 0.584677π-0.584677\pi
−0.262893 + 0.964825i 0.584677π0.584677\pi
294294 0 0
295295 −60.0000 −3.49334
296296 2.00000 0.116248
297297 0 0
298298 0 0
299299 −1.00000 −0.0578315
300300 0 0
301301 12.0000 0.691669
302302 −2.00000 −0.115087
303303 0 0
304304 −1.00000 −0.0573539
305305 8.00000 0.458079
306306 0 0
307307 −12.0000 −0.684876 −0.342438 0.939540i 0.611253π-0.611253\pi
−0.342438 + 0.939540i 0.611253π0.611253\pi
308308 −6.00000 −0.341882
309309 0 0
310310 32.0000 1.81748
311311 −7.00000 −0.396934 −0.198467 0.980108i 0.563596π-0.563596\pi
−0.198467 + 0.980108i 0.563596π0.563596\pi
312312 0 0
313313 29.0000 1.63918 0.819588 0.572953i 0.194202π-0.194202\pi
0.819588 + 0.572953i 0.194202π0.194202\pi
314314 2.00000 0.112867
315315 0 0
316316 −10.0000 −0.562544
317317 27.0000 1.51647 0.758236 0.651981i 0.226062π-0.226062\pi
0.758236 + 0.651981i 0.226062π0.226062\pi
318318 0 0
319319 −10.0000 −0.559893
320320 4.00000 0.223607
321321 0 0
322322 −3.00000 −0.167183
323323 3.00000 0.166924
324324 0 0
325325 −11.0000 −0.610170
326326 16.0000 0.886158
327327 0 0
328328 −8.00000 −0.441726
329329 −24.0000 −1.32316
330330 0 0
331331 17.0000 0.934405 0.467202 0.884150i 0.345262π-0.345262\pi
0.467202 + 0.884150i 0.345262π0.345262\pi
332332 6.00000 0.329293
333333 0 0
334334 −12.0000 −0.656611
335335 12.0000 0.655630
336336 0 0
337337 −32.0000 −1.74315 −0.871576 0.490261i 0.836901π-0.836901\pi
−0.871576 + 0.490261i 0.836901π0.836901\pi
338338 12.0000 0.652714
339339 0 0
340340 −12.0000 −0.650791
341341 16.0000 0.866449
342342 0 0
343343 −15.0000 −0.809924
344344 −4.00000 −0.215666
345345 0 0
346346 −6.00000 −0.322562
347347 2.00000 0.107366 0.0536828 0.998558i 0.482904π-0.482904\pi
0.0536828 + 0.998558i 0.482904π0.482904\pi
348348 0 0
349349 10.0000 0.535288 0.267644 0.963518i 0.413755π-0.413755\pi
0.267644 + 0.963518i 0.413755π0.413755\pi
350350 −33.0000 −1.76392
351351 0 0
352352 2.00000 0.106600
353353 −9.00000 −0.479022 −0.239511 0.970894i 0.576987π-0.576987\pi
−0.239511 + 0.970894i 0.576987π0.576987\pi
354354 0 0
355355 −8.00000 −0.424596
356356 0 0
357357 0 0
358358 0 0
359359 15.0000 0.791670 0.395835 0.918322i 0.370455π-0.370455\pi
0.395835 + 0.918322i 0.370455π0.370455\pi
360360 0 0
361361 1.00000 0.0526316
362362 −22.0000 −1.15629
363363 0 0
364364 −3.00000 −0.157243
365365 36.0000 1.88433
366366 0 0
367367 28.0000 1.46159 0.730794 0.682598i 0.239150π-0.239150\pi
0.730794 + 0.682598i 0.239150π0.239150\pi
368368 1.00000 0.0521286
369369 0 0
370370 8.00000 0.415900
371371 3.00000 0.155752
372372 0 0
373373 29.0000 1.50156 0.750782 0.660551i 0.229677π-0.229677\pi
0.750782 + 0.660551i 0.229677π0.229677\pi
374374 −6.00000 −0.310253
375375 0 0
376376 8.00000 0.412568
377377 −5.00000 −0.257513
378378 0 0
379379 15.0000 0.770498 0.385249 0.922813i 0.374116π-0.374116\pi
0.385249 + 0.922813i 0.374116π0.374116\pi
380380 −4.00000 −0.205196
381381 0 0
382382 7.00000 0.358151
383383 26.0000 1.32854 0.664269 0.747494i 0.268743π-0.268743\pi
0.664269 + 0.747494i 0.268743π0.268743\pi
384384 0 0
385385 −24.0000 −1.22315
386386 6.00000 0.305392
387387 0 0
388388 −2.00000 −0.101535
389389 30.0000 1.52106 0.760530 0.649303i 0.224939π-0.224939\pi
0.760530 + 0.649303i 0.224939π0.224939\pi
390390 0 0
391391 −3.00000 −0.151717
392392 −2.00000 −0.101015
393393 0 0
394394 8.00000 0.403034
395395 −40.0000 −2.01262
396396 0 0
397397 8.00000 0.401508 0.200754 0.979642i 0.435661π-0.435661\pi
0.200754 + 0.979642i 0.435661π0.435661\pi
398398 25.0000 1.25314
399399 0 0
400400 11.0000 0.550000
401401 8.00000 0.399501 0.199750 0.979847i 0.435987π-0.435987\pi
0.199750 + 0.979847i 0.435987π0.435987\pi
402402 0 0
403403 8.00000 0.398508
404404 −2.00000 −0.0995037
405405 0 0
406406 −15.0000 −0.744438
407407 4.00000 0.198273
408408 0 0
409409 −20.0000 −0.988936 −0.494468 0.869196i 0.664637π-0.664637\pi
−0.494468 + 0.869196i 0.664637π0.664637\pi
410410 −32.0000 −1.58037
411411 0 0
412412 −6.00000 −0.295599
413413 −45.0000 −2.21431
414414 0 0
415415 24.0000 1.17811
416416 1.00000 0.0490290
417417 0 0
418418 −2.00000 −0.0978232
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 0 0
421421 −13.0000 −0.633581 −0.316791 0.948495i 0.602605π-0.602605\pi
−0.316791 + 0.948495i 0.602605π0.602605\pi
422422 −27.0000 −1.31434
423423 0 0
424424 −1.00000 −0.0485643
425425 −33.0000 −1.60074
426426 0 0
427427 6.00000 0.290360
428428 7.00000 0.338358
429429 0 0
430430 −16.0000 −0.771589
431431 18.0000 0.867029 0.433515 0.901146i 0.357273π-0.357273\pi
0.433515 + 0.901146i 0.357273π0.357273\pi
432432 0 0
433433 14.0000 0.672797 0.336399 0.941720i 0.390791π-0.390791\pi
0.336399 + 0.941720i 0.390791π0.390791\pi
434434 24.0000 1.15204
435435 0 0
436436 −15.0000 −0.718370
437437 −1.00000 −0.0478365
438438 0 0
439439 20.0000 0.954548 0.477274 0.878755i 0.341625π-0.341625\pi
0.477274 + 0.878755i 0.341625π0.341625\pi
440440 8.00000 0.381385
441441 0 0
442442 −3.00000 −0.142695
443443 26.0000 1.23530 0.617649 0.786454i 0.288085π-0.288085\pi
0.617649 + 0.786454i 0.288085π0.288085\pi
444444 0 0
445445 0 0
446446 −14.0000 −0.662919
447447 0 0
448448 3.00000 0.141737
449449 −10.0000 −0.471929 −0.235965 0.971762i 0.575825π-0.575825\pi
−0.235965 + 0.971762i 0.575825π0.575825\pi
450450 0 0
451451 −16.0000 −0.753411
452452 −14.0000 −0.658505
453453 0 0
454454 −17.0000 −0.797850
455455 −12.0000 −0.562569
456456 0 0
457457 −7.00000 −0.327446 −0.163723 0.986506i 0.552350π-0.552350\pi
−0.163723 + 0.986506i 0.552350π0.552350\pi
458458 10.0000 0.467269
459459 0 0
460460 4.00000 0.186501
461461 28.0000 1.30409 0.652045 0.758180i 0.273911π-0.273911\pi
0.652045 + 0.758180i 0.273911π0.273911\pi
462462 0 0
463463 4.00000 0.185896 0.0929479 0.995671i 0.470371π-0.470371\pi
0.0929479 + 0.995671i 0.470371π0.470371\pi
464464 5.00000 0.232119
465465 0 0
466466 −6.00000 −0.277945
467467 2.00000 0.0925490 0.0462745 0.998929i 0.485265π-0.485265\pi
0.0462745 + 0.998929i 0.485265π0.485265\pi
468468 0 0
469469 9.00000 0.415581
470470 32.0000 1.47605
471471 0 0
472472 15.0000 0.690431
473473 −8.00000 −0.367840
474474 0 0
475475 −11.0000 −0.504715
476476 −9.00000 −0.412514
477477 0 0
478478 15.0000 0.686084
479479 20.0000 0.913823 0.456912 0.889512i 0.348956π-0.348956\pi
0.456912 + 0.889512i 0.348956π0.348956\pi
480480 0 0
481481 2.00000 0.0911922
482482 8.00000 0.364390
483483 0 0
484484 −7.00000 −0.318182
485485 −8.00000 −0.363261
486486 0 0
487487 −2.00000 −0.0906287 −0.0453143 0.998973i 0.514429π-0.514429\pi
−0.0453143 + 0.998973i 0.514429π0.514429\pi
488488 −2.00000 −0.0905357
489489 0 0
490490 −8.00000 −0.361403
491491 28.0000 1.26362 0.631811 0.775122i 0.282312π-0.282312\pi
0.631811 + 0.775122i 0.282312π0.282312\pi
492492 0 0
493493 −15.0000 −0.675566
494494 −1.00000 −0.0449921
495495 0 0
496496 −8.00000 −0.359211
497497 −6.00000 −0.269137
498498 0 0
499499 40.0000 1.79065 0.895323 0.445418i 0.146945π-0.146945\pi
0.895323 + 0.445418i 0.146945π0.146945\pi
500500 24.0000 1.07331
501501 0 0
502502 2.00000 0.0892644
503503 −39.0000 −1.73892 −0.869462 0.494000i 0.835534π-0.835534\pi
−0.869462 + 0.494000i 0.835534π0.835534\pi
504504 0 0
505505 −8.00000 −0.355995
506506 2.00000 0.0889108
507507 0 0
508508 18.0000 0.798621
509509 30.0000 1.32973 0.664863 0.746965i 0.268490π-0.268490\pi
0.664863 + 0.746965i 0.268490π0.268490\pi
510510 0 0
511511 27.0000 1.19441
512512 −1.00000 −0.0441942
513513 0 0
514514 8.00000 0.352865
515515 −24.0000 −1.05757
516516 0 0
517517 16.0000 0.703679
518518 6.00000 0.263625
519519 0 0
520520 4.00000 0.175412
521521 28.0000 1.22670 0.613351 0.789810i 0.289821π-0.289821\pi
0.613351 + 0.789810i 0.289821π0.289821\pi
522522 0 0
523523 29.0000 1.26808 0.634041 0.773300i 0.281395π-0.281395\pi
0.634041 + 0.773300i 0.281395π0.281395\pi
524524 −12.0000 −0.524222
525525 0 0
526526 24.0000 1.04645
527527 24.0000 1.04546
528528 0 0
529529 −22.0000 −0.956522
530530 −4.00000 −0.173749
531531 0 0
532532 −3.00000 −0.130066
533533 −8.00000 −0.346518
534534 0 0
535535 28.0000 1.21055
536536 −3.00000 −0.129580
537537 0 0
538538 30.0000 1.29339
539539 −4.00000 −0.172292
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 −7.00000 −0.300676
543543 0 0
544544 3.00000 0.128624
545545 −60.0000 −2.57012
546546 0 0
547547 28.0000 1.19719 0.598597 0.801050i 0.295725π-0.295725\pi
0.598597 + 0.801050i 0.295725π0.295725\pi
548548 17.0000 0.726204
549549 0 0
550550 22.0000 0.938083
551551 −5.00000 −0.213007
552552 0 0
553553 −30.0000 −1.27573
554554 −28.0000 −1.18961
555555 0 0
556556 0 0
557557 −28.0000 −1.18640 −0.593199 0.805056i 0.702135π-0.702135\pi
−0.593199 + 0.805056i 0.702135π0.702135\pi
558558 0 0
559559 −4.00000 −0.169182
560560 12.0000 0.507093
561561 0 0
562562 −8.00000 −0.337460
563563 36.0000 1.51722 0.758610 0.651546i 0.225879π-0.225879\pi
0.758610 + 0.651546i 0.225879π0.225879\pi
564564 0 0
565565 −56.0000 −2.35594
566566 6.00000 0.252199
567567 0 0
568568 2.00000 0.0839181
569569 −40.0000 −1.67689 −0.838444 0.544988i 0.816534π-0.816534\pi
−0.838444 + 0.544988i 0.816534π0.816534\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 2.00000 0.0836242
573573 0 0
574574 −24.0000 −1.00174
575575 11.0000 0.458732
576576 0 0
577577 −37.0000 −1.54033 −0.770165 0.637845i 0.779826π-0.779826\pi
−0.770165 + 0.637845i 0.779826π0.779826\pi
578578 8.00000 0.332756
579579 0 0
580580 20.0000 0.830455
581581 18.0000 0.746766
582582 0 0
583583 −2.00000 −0.0828315
584584 −9.00000 −0.372423
585585 0 0
586586 9.00000 0.371787
587587 12.0000 0.495293 0.247647 0.968850i 0.420343π-0.420343\pi
0.247647 + 0.968850i 0.420343π0.420343\pi
588588 0 0
589589 8.00000 0.329634
590590 60.0000 2.47016
591591 0 0
592592 −2.00000 −0.0821995
593593 −34.0000 −1.39621 −0.698106 0.715994i 0.745974π-0.745974\pi
−0.698106 + 0.715994i 0.745974π0.745974\pi
594594 0 0
595595 −36.0000 −1.47586
596596 0 0
597597 0 0
598598 1.00000 0.0408930
599599 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
600600 0 0
601601 −8.00000 −0.326327 −0.163163 0.986599i 0.552170π-0.552170\pi
−0.163163 + 0.986599i 0.552170π0.552170\pi
602602 −12.0000 −0.489083
603603 0 0
604604 2.00000 0.0813788
605605 −28.0000 −1.13836
606606 0 0
607607 −22.0000 −0.892952 −0.446476 0.894795i 0.647321π-0.647321\pi
−0.446476 + 0.894795i 0.647321π0.647321\pi
608608 1.00000 0.0405554
609609 0 0
610610 −8.00000 −0.323911
611611 8.00000 0.323645
612612 0 0
613613 34.0000 1.37325 0.686624 0.727013i 0.259092π-0.259092\pi
0.686624 + 0.727013i 0.259092π0.259092\pi
614614 12.0000 0.484281
615615 0 0
616616 6.00000 0.241747
617617 −18.0000 −0.724653 −0.362326 0.932051i 0.618017π-0.618017\pi
−0.362326 + 0.932051i 0.618017π0.618017\pi
618618 0 0
619619 10.0000 0.401934 0.200967 0.979598i 0.435592π-0.435592\pi
0.200967 + 0.979598i 0.435592π0.435592\pi
620620 −32.0000 −1.28515
621621 0 0
622622 7.00000 0.280674
623623 0 0
624624 0 0
625625 41.0000 1.64000
626626 −29.0000 −1.15907
627627 0 0
628628 −2.00000 −0.0798087
629629 6.00000 0.239236
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 0 0
634634 −27.0000 −1.07231
635635 72.0000 2.85723
636636 0 0
637637 −2.00000 −0.0792429
638638 10.0000 0.395904
639639 0 0
640640 −4.00000 −0.158114
641641 −42.0000 −1.65890 −0.829450 0.558581i 0.811346π-0.811346\pi
−0.829450 + 0.558581i 0.811346π0.811346\pi
642642 0 0
643643 −26.0000 −1.02534 −0.512670 0.858586i 0.671344π-0.671344\pi
−0.512670 + 0.858586i 0.671344π0.671344\pi
644644 3.00000 0.118217
645645 0 0
646646 −3.00000 −0.118033
647647 −23.0000 −0.904223 −0.452112 0.891961i 0.649329π-0.649329\pi
−0.452112 + 0.891961i 0.649329π0.649329\pi
648648 0 0
649649 30.0000 1.17760
650650 11.0000 0.431455
651651 0 0
652652 −16.0000 −0.626608
653653 36.0000 1.40879 0.704394 0.709809i 0.251219π-0.251219\pi
0.704394 + 0.709809i 0.251219π0.251219\pi
654654 0 0
655655 −48.0000 −1.87552
656656 8.00000 0.312348
657657 0 0
658658 24.0000 0.935617
659659 −5.00000 −0.194772 −0.0973862 0.995247i 0.531048π-0.531048\pi
−0.0973862 + 0.995247i 0.531048π0.531048\pi
660660 0 0
661661 −23.0000 −0.894596 −0.447298 0.894385i 0.647614π-0.647614\pi
−0.447298 + 0.894385i 0.647614π0.647614\pi
662662 −17.0000 −0.660724
663663 0 0
664664 −6.00000 −0.232845
665665 −12.0000 −0.465340
666666 0 0
667667 5.00000 0.193601
668668 12.0000 0.464294
669669 0 0
670670 −12.0000 −0.463600
671671 −4.00000 −0.154418
672672 0 0
673673 44.0000 1.69608 0.848038 0.529936i 0.177784π-0.177784\pi
0.848038 + 0.529936i 0.177784π0.177784\pi
674674 32.0000 1.23259
675675 0 0
676676 −12.0000 −0.461538
677677 −13.0000 −0.499631 −0.249815 0.968294i 0.580370π-0.580370\pi
−0.249815 + 0.968294i 0.580370π0.580370\pi
678678 0 0
679679 −6.00000 −0.230259
680680 12.0000 0.460179
681681 0 0
682682 −16.0000 −0.612672
683683 −4.00000 −0.153056 −0.0765279 0.997067i 0.524383π-0.524383\pi
−0.0765279 + 0.997067i 0.524383π0.524383\pi
684684 0 0
685685 68.0000 2.59815
686686 15.0000 0.572703
687687 0 0
688688 4.00000 0.152499
689689 −1.00000 −0.0380970
690690 0 0
691691 42.0000 1.59776 0.798878 0.601494i 0.205427π-0.205427\pi
0.798878 + 0.601494i 0.205427π0.205427\pi
692692 6.00000 0.228086
693693 0 0
694694 −2.00000 −0.0759190
695695 0 0
696696 0 0
697697 −24.0000 −0.909065
698698 −10.0000 −0.378506
699699 0 0
700700 33.0000 1.24728
701701 28.0000 1.05755 0.528773 0.848763i 0.322652π-0.322652\pi
0.528773 + 0.848763i 0.322652π0.322652\pi
702702 0 0
703703 2.00000 0.0754314
704704 −2.00000 −0.0753778
705705 0 0
706706 9.00000 0.338719
707707 −6.00000 −0.225653
708708 0 0
709709 −30.0000 −1.12667 −0.563337 0.826227i 0.690483π-0.690483\pi
−0.563337 + 0.826227i 0.690483π0.690483\pi
710710 8.00000 0.300235
711711 0 0
712712 0 0
713713 −8.00000 −0.299602
714714 0 0
715715 8.00000 0.299183
716716 0 0
717717 0 0
718718 −15.0000 −0.559795
719719 5.00000 0.186469 0.0932343 0.995644i 0.470279π-0.470279\pi
0.0932343 + 0.995644i 0.470279π0.470279\pi
720720 0 0
721721 −18.0000 −0.670355
722722 −1.00000 −0.0372161
723723 0 0
724724 22.0000 0.817624
725725 55.0000 2.04265
726726 0 0
727727 −17.0000 −0.630495 −0.315248 0.949009i 0.602088π-0.602088\pi
−0.315248 + 0.949009i 0.602088π0.602088\pi
728728 3.00000 0.111187
729729 0 0
730730 −36.0000 −1.33242
731731 −12.0000 −0.443836
732732 0 0
733733 −36.0000 −1.32969 −0.664845 0.746981i 0.731502π-0.731502\pi
−0.664845 + 0.746981i 0.731502π0.731502\pi
734734 −28.0000 −1.03350
735735 0 0
736736 −1.00000 −0.0368605
737737 −6.00000 −0.221013
738738 0 0
739739 −40.0000 −1.47142 −0.735712 0.677295i 0.763152π-0.763152\pi
−0.735712 + 0.677295i 0.763152π0.763152\pi
740740 −8.00000 −0.294086
741741 0 0
742742 −3.00000 −0.110133
743743 16.0000 0.586983 0.293492 0.955962i 0.405183π-0.405183\pi
0.293492 + 0.955962i 0.405183π0.405183\pi
744744 0 0
745745 0 0
746746 −29.0000 −1.06177
747747 0 0
748748 6.00000 0.219382
749749 21.0000 0.767323
750750 0 0
751751 32.0000 1.16770 0.583848 0.811863i 0.301546π-0.301546\pi
0.583848 + 0.811863i 0.301546π0.301546\pi
752752 −8.00000 −0.291730
753753 0 0
754754 5.00000 0.182089
755755 8.00000 0.291150
756756 0 0
757757 −2.00000 −0.0726912 −0.0363456 0.999339i 0.511572π-0.511572\pi
−0.0363456 + 0.999339i 0.511572π0.511572\pi
758758 −15.0000 −0.544825
759759 0 0
760760 4.00000 0.145095
761761 −27.0000 −0.978749 −0.489375 0.872074i 0.662775π-0.662775\pi
−0.489375 + 0.872074i 0.662775π0.662775\pi
762762 0 0
763763 −45.0000 −1.62911
764764 −7.00000 −0.253251
765765 0 0
766766 −26.0000 −0.939418
767767 15.0000 0.541619
768768 0 0
769769 −35.0000 −1.26213 −0.631066 0.775729i 0.717382π-0.717382\pi
−0.631066 + 0.775729i 0.717382π0.717382\pi
770770 24.0000 0.864900
771771 0 0
772772 −6.00000 −0.215945
773773 −9.00000 −0.323708 −0.161854 0.986815i 0.551747π-0.551747\pi
−0.161854 + 0.986815i 0.551747π0.551747\pi
774774 0 0
775775 −88.0000 −3.16105
776776 2.00000 0.0717958
777777 0 0
778778 −30.0000 −1.07555
779779 −8.00000 −0.286630
780780 0 0
781781 4.00000 0.143131
782782 3.00000 0.107280
783783 0 0
784784 2.00000 0.0714286
785785 −8.00000 −0.285532
786786 0 0
787787 −17.0000 −0.605985 −0.302992 0.952993i 0.597986π-0.597986\pi
−0.302992 + 0.952993i 0.597986π0.597986\pi
788788 −8.00000 −0.284988
789789 0 0
790790 40.0000 1.42314
791791 −42.0000 −1.49335
792792 0 0
793793 −2.00000 −0.0710221
794794 −8.00000 −0.283909
795795 0 0
796796 −25.0000 −0.886102
797797 −3.00000 −0.106265 −0.0531327 0.998587i 0.516921π-0.516921\pi
−0.0531327 + 0.998587i 0.516921π0.516921\pi
798798 0 0
799799 24.0000 0.849059
800800 −11.0000 −0.388909
801801 0 0
802802 −8.00000 −0.282490
803803 −18.0000 −0.635206
804804 0 0
805805 12.0000 0.422944
806806 −8.00000 −0.281788
807807 0 0
808808 2.00000 0.0703598
809809 15.0000 0.527372 0.263686 0.964609i 0.415062π-0.415062\pi
0.263686 + 0.964609i 0.415062π0.415062\pi
810810 0 0
811811 −3.00000 −0.105344 −0.0526721 0.998612i 0.516774π-0.516774\pi
−0.0526721 + 0.998612i 0.516774π0.516774\pi
812812 15.0000 0.526397
813813 0 0
814814 −4.00000 −0.140200
815815 −64.0000 −2.24182
816816 0 0
817817 −4.00000 −0.139942
818818 20.0000 0.699284
819819 0 0
820820 32.0000 1.11749
821821 −12.0000 −0.418803 −0.209401 0.977830i 0.567152π-0.567152\pi
−0.209401 + 0.977830i 0.567152π0.567152\pi
822822 0 0
823823 29.0000 1.01088 0.505438 0.862863i 0.331331π-0.331331\pi
0.505438 + 0.862863i 0.331331π0.331331\pi
824824 6.00000 0.209020
825825 0 0
826826 45.0000 1.56575
827827 −23.0000 −0.799788 −0.399894 0.916561i 0.630953π-0.630953\pi
−0.399894 + 0.916561i 0.630953π0.630953\pi
828828 0 0
829829 −15.0000 −0.520972 −0.260486 0.965478i 0.583883π-0.583883\pi
−0.260486 + 0.965478i 0.583883π0.583883\pi
830830 −24.0000 −0.833052
831831 0 0
832832 −1.00000 −0.0346688
833833 −6.00000 −0.207888
834834 0 0
835835 48.0000 1.66111
836836 2.00000 0.0691714
837837 0 0
838838 0 0
839839 −20.0000 −0.690477 −0.345238 0.938515i 0.612202π-0.612202\pi
−0.345238 + 0.938515i 0.612202π0.612202\pi
840840 0 0
841841 −4.00000 −0.137931
842842 13.0000 0.448010
843843 0 0
844844 27.0000 0.929378
845845 −48.0000 −1.65125
846846 0 0
847847 −21.0000 −0.721569
848848 1.00000 0.0343401
849849 0 0
850850 33.0000 1.13189
851851 −2.00000 −0.0685591
852852 0 0
853853 −6.00000 −0.205436 −0.102718 0.994711i 0.532754π-0.532754\pi
−0.102718 + 0.994711i 0.532754π0.532754\pi
854854 −6.00000 −0.205316
855855 0 0
856856 −7.00000 −0.239255
857857 12.0000 0.409912 0.204956 0.978771i 0.434295π-0.434295\pi
0.204956 + 0.978771i 0.434295π0.434295\pi
858858 0 0
859859 −50.0000 −1.70598 −0.852989 0.521929i 0.825213π-0.825213\pi
−0.852989 + 0.521929i 0.825213π0.825213\pi
860860 16.0000 0.545595
861861 0 0
862862 −18.0000 −0.613082
863863 −54.0000 −1.83818 −0.919091 0.394046i 0.871075π-0.871075\pi
−0.919091 + 0.394046i 0.871075π0.871075\pi
864864 0 0
865865 24.0000 0.816024
866866 −14.0000 −0.475739
867867 0 0
868868 −24.0000 −0.814613
869869 20.0000 0.678454
870870 0 0
871871 −3.00000 −0.101651
872872 15.0000 0.507964
873873 0 0
874874 1.00000 0.0338255
875875 72.0000 2.43404
876876 0 0
877877 13.0000 0.438979 0.219489 0.975615i 0.429561π-0.429561\pi
0.219489 + 0.975615i 0.429561π0.429561\pi
878878 −20.0000 −0.674967
879879 0 0
880880 −8.00000 −0.269680
881881 18.0000 0.606435 0.303218 0.952921i 0.401939π-0.401939\pi
0.303218 + 0.952921i 0.401939π0.401939\pi
882882 0 0
883883 34.0000 1.14419 0.572096 0.820187i 0.306131π-0.306131\pi
0.572096 + 0.820187i 0.306131π0.306131\pi
884884 3.00000 0.100901
885885 0 0
886886 −26.0000 −0.873487
887887 2.00000 0.0671534 0.0335767 0.999436i 0.489310π-0.489310\pi
0.0335767 + 0.999436i 0.489310π0.489310\pi
888888 0 0
889889 54.0000 1.81110
890890 0 0
891891 0 0
892892 14.0000 0.468755
893893 8.00000 0.267710
894894 0 0
895895 0 0
896896 −3.00000 −0.100223
897897 0 0
898898 10.0000 0.333704
899899 −40.0000 −1.33407
900900 0 0
901901 −3.00000 −0.0999445
902902 16.0000 0.532742
903903 0 0
904904 14.0000 0.465633
905905 88.0000 2.92522
906906 0 0
907907 53.0000 1.75984 0.879918 0.475125i 0.157597π-0.157597\pi
0.879918 + 0.475125i 0.157597π0.157597\pi
908908 17.0000 0.564165
909909 0 0
910910 12.0000 0.397796
911911 −12.0000 −0.397578 −0.198789 0.980042i 0.563701π-0.563701\pi
−0.198789 + 0.980042i 0.563701π0.563701\pi
912912 0 0
913913 −12.0000 −0.397142
914914 7.00000 0.231539
915915 0 0
916916 −10.0000 −0.330409
917917 −36.0000 −1.18882
918918 0 0
919919 5.00000 0.164935 0.0824674 0.996594i 0.473720π-0.473720\pi
0.0824674 + 0.996594i 0.473720π0.473720\pi
920920 −4.00000 −0.131876
921921 0 0
922922 −28.0000 −0.922131
923923 2.00000 0.0658308
924924 0 0
925925 −22.0000 −0.723356
926926 −4.00000 −0.131448
927927 0 0
928928 −5.00000 −0.164133
929929 55.0000 1.80449 0.902246 0.431222i 0.141918π-0.141918\pi
0.902246 + 0.431222i 0.141918π0.141918\pi
930930 0 0
931931 −2.00000 −0.0655474
932932 6.00000 0.196537
933933 0 0
934934 −2.00000 −0.0654420
935935 24.0000 0.784884
936936 0 0
937937 −7.00000 −0.228680 −0.114340 0.993442i 0.536475π-0.536475\pi
−0.114340 + 0.993442i 0.536475π0.536475\pi
938938 −9.00000 −0.293860
939939 0 0
940940 −32.0000 −1.04372
941941 −7.00000 −0.228193 −0.114097 0.993470i 0.536397π-0.536397\pi
−0.114097 + 0.993470i 0.536397π0.536397\pi
942942 0 0
943943 8.00000 0.260516
944944 −15.0000 −0.488208
945945 0 0
946946 8.00000 0.260102
947947 12.0000 0.389948 0.194974 0.980808i 0.437538π-0.437538\pi
0.194974 + 0.980808i 0.437538π0.437538\pi
948948 0 0
949949 −9.00000 −0.292152
950950 11.0000 0.356887
951951 0 0
952952 9.00000 0.291692
953953 46.0000 1.49009 0.745043 0.667016i 0.232429π-0.232429\pi
0.745043 + 0.667016i 0.232429π0.232429\pi
954954 0 0
955955 −28.0000 −0.906059
956956 −15.0000 −0.485135
957957 0 0
958958 −20.0000 −0.646171
959959 51.0000 1.64688
960960 0 0
961961 33.0000 1.06452
962962 −2.00000 −0.0644826
963963 0 0
964964 −8.00000 −0.257663
965965 −24.0000 −0.772587
966966 0 0
967967 48.0000 1.54358 0.771788 0.635880i 0.219363π-0.219363\pi
0.771788 + 0.635880i 0.219363π0.219363\pi
968968 7.00000 0.224989
969969 0 0
970970 8.00000 0.256865
971971 28.0000 0.898563 0.449281 0.893390i 0.351680π-0.351680\pi
0.449281 + 0.893390i 0.351680π0.351680\pi
972972 0 0
973973 0 0
974974 2.00000 0.0640841
975975 0 0
976976 2.00000 0.0640184
977977 −8.00000 −0.255943 −0.127971 0.991778i 0.540847π-0.540847\pi
−0.127971 + 0.991778i 0.540847π0.540847\pi
978978 0 0
979979 0 0
980980 8.00000 0.255551
981981 0 0
982982 −28.0000 −0.893516
983983 6.00000 0.191370 0.0956851 0.995412i 0.469496π-0.469496\pi
0.0956851 + 0.995412i 0.469496π0.469496\pi
984984 0 0
985985 −32.0000 −1.01960
986986 15.0000 0.477697
987987 0 0
988988 1.00000 0.0318142
989989 4.00000 0.127193
990990 0 0
991991 −8.00000 −0.254128 −0.127064 0.991894i 0.540555π-0.540555\pi
−0.127064 + 0.991894i 0.540555π0.540555\pi
992992 8.00000 0.254000
993993 0 0
994994 6.00000 0.190308
995995 −100.000 −3.17021
996996 0 0
997997 28.0000 0.886769 0.443384 0.896332i 0.353778π-0.353778\pi
0.443384 + 0.896332i 0.353778π0.353778\pi
998998 −40.0000 −1.26618
999999 0 0
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 342.2.a.d.1.1 1
3.2 odd 2 38.2.a.b.1.1 1
4.3 odd 2 2736.2.a.w.1.1 1
5.4 even 2 8550.2.a.u.1.1 1
12.11 even 2 304.2.a.d.1.1 1
15.2 even 4 950.2.b.c.799.2 2
15.8 even 4 950.2.b.c.799.1 2
15.14 odd 2 950.2.a.b.1.1 1
19.18 odd 2 6498.2.a.y.1.1 1
21.20 even 2 1862.2.a.f.1.1 1
24.5 odd 2 1216.2.a.n.1.1 1
24.11 even 2 1216.2.a.g.1.1 1
33.32 even 2 4598.2.a.a.1.1 1
39.38 odd 2 6422.2.a.b.1.1 1
57.2 even 18 722.2.e.d.99.1 6
57.5 odd 18 722.2.e.c.595.1 6
57.8 even 6 722.2.c.f.653.1 2
57.11 odd 6 722.2.c.d.653.1 2
57.14 even 18 722.2.e.d.595.1 6
57.17 odd 18 722.2.e.c.99.1 6
57.23 odd 18 722.2.e.c.415.1 6
57.26 odd 6 722.2.c.d.429.1 2
57.29 even 18 722.2.e.d.423.1 6
57.32 even 18 722.2.e.d.245.1 6
57.35 odd 18 722.2.e.c.389.1 6
57.41 even 18 722.2.e.d.389.1 6
57.44 odd 18 722.2.e.c.245.1 6
57.47 odd 18 722.2.e.c.423.1 6
57.50 even 6 722.2.c.f.429.1 2
57.53 even 18 722.2.e.d.415.1 6
57.56 even 2 722.2.a.b.1.1 1
60.59 even 2 7600.2.a.h.1.1 1
228.227 odd 2 5776.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.a.b.1.1 1 3.2 odd 2
304.2.a.d.1.1 1 12.11 even 2
342.2.a.d.1.1 1 1.1 even 1 trivial
722.2.a.b.1.1 1 57.56 even 2
722.2.c.d.429.1 2 57.26 odd 6
722.2.c.d.653.1 2 57.11 odd 6
722.2.c.f.429.1 2 57.50 even 6
722.2.c.f.653.1 2 57.8 even 6
722.2.e.c.99.1 6 57.17 odd 18
722.2.e.c.245.1 6 57.44 odd 18
722.2.e.c.389.1 6 57.35 odd 18
722.2.e.c.415.1 6 57.23 odd 18
722.2.e.c.423.1 6 57.47 odd 18
722.2.e.c.595.1 6 57.5 odd 18
722.2.e.d.99.1 6 57.2 even 18
722.2.e.d.245.1 6 57.32 even 18
722.2.e.d.389.1 6 57.41 even 18
722.2.e.d.415.1 6 57.53 even 18
722.2.e.d.423.1 6 57.29 even 18
722.2.e.d.595.1 6 57.14 even 18
950.2.a.b.1.1 1 15.14 odd 2
950.2.b.c.799.1 2 15.8 even 4
950.2.b.c.799.2 2 15.2 even 4
1216.2.a.g.1.1 1 24.11 even 2
1216.2.a.n.1.1 1 24.5 odd 2
1862.2.a.f.1.1 1 21.20 even 2
2736.2.a.w.1.1 1 4.3 odd 2
4598.2.a.a.1.1 1 33.32 even 2
5776.2.a.d.1.1 1 228.227 odd 2
6422.2.a.b.1.1 1 39.38 odd 2
6498.2.a.y.1.1 1 19.18 odd 2
7600.2.a.h.1.1 1 60.59 even 2
8550.2.a.u.1.1 1 5.4 even 2