Properties

Label 297.2.a.d.1.1
Level 297297
Weight 22
Character 297.1
Self dual yes
Analytic conductor 2.3722.372
Analytic rank 00
Dimension 11
CM no
Inner twists 11

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [297,2,Mod(1,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 297=3311 297 = 3^{3} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 297.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 2.371556940032.37155694003
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 == 297.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+2.00000q2+2.00000q4+2.00000q5+1.00000q7+4.00000q101.00000q115.00000q13+2.00000q144.00000q16+2.00000q17+3.00000q19+4.00000q202.00000q22+4.00000q231.00000q2510.0000q26+2.00000q28+6.00000q298.00000q318.00000q32+4.00000q34+2.00000q359.00000q37+6.00000q384.00000q412.00000q44+8.00000q46+10.0000q476.00000q492.00000q5010.0000q526.00000q532.00000q55+12.0000q5814.0000q59+9.00000q6116.0000q628.00000q6410.0000q65+5.00000q67+4.00000q68+4.00000q70+12.0000q71+7.00000q7318.0000q74+6.00000q761.00000q77+11.0000q798.00000q808.00000q82+12.0000q83+4.00000q85+6.00000q895.00000q91+8.00000q92+20.0000q94+6.00000q957.00000q9712.0000q98+O(q100)q+2.00000 q^{2} +2.00000 q^{4} +2.00000 q^{5} +1.00000 q^{7} +4.00000 q^{10} -1.00000 q^{11} -5.00000 q^{13} +2.00000 q^{14} -4.00000 q^{16} +2.00000 q^{17} +3.00000 q^{19} +4.00000 q^{20} -2.00000 q^{22} +4.00000 q^{23} -1.00000 q^{25} -10.0000 q^{26} +2.00000 q^{28} +6.00000 q^{29} -8.00000 q^{31} -8.00000 q^{32} +4.00000 q^{34} +2.00000 q^{35} -9.00000 q^{37} +6.00000 q^{38} -4.00000 q^{41} -2.00000 q^{44} +8.00000 q^{46} +10.0000 q^{47} -6.00000 q^{49} -2.00000 q^{50} -10.0000 q^{52} -6.00000 q^{53} -2.00000 q^{55} +12.0000 q^{58} -14.0000 q^{59} +9.00000 q^{61} -16.0000 q^{62} -8.00000 q^{64} -10.0000 q^{65} +5.00000 q^{67} +4.00000 q^{68} +4.00000 q^{70} +12.0000 q^{71} +7.00000 q^{73} -18.0000 q^{74} +6.00000 q^{76} -1.00000 q^{77} +11.0000 q^{79} -8.00000 q^{80} -8.00000 q^{82} +12.0000 q^{83} +4.00000 q^{85} +6.00000 q^{89} -5.00000 q^{91} +8.00000 q^{92} +20.0000 q^{94} +6.00000 q^{95} -7.00000 q^{97} -12.0000 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 2.00000 1.41421 0.707107 0.707107i 0.250000π-0.250000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
33 0 0
44 2.00000 1.00000
55 2.00000 0.894427 0.447214 0.894427i 0.352416π-0.352416\pi
0.447214 + 0.894427i 0.352416π0.352416\pi
66 0 0
77 1.00000 0.377964 0.188982 0.981981i 0.439481π-0.439481\pi
0.188982 + 0.981981i 0.439481π0.439481\pi
88 0 0
99 0 0
1010 4.00000 1.26491
1111 −1.00000 −0.301511
1212 0 0
1313 −5.00000 −1.38675 −0.693375 0.720577i 0.743877π-0.743877\pi
−0.693375 + 0.720577i 0.743877π0.743877\pi
1414 2.00000 0.534522
1515 0 0
1616 −4.00000 −1.00000
1717 2.00000 0.485071 0.242536 0.970143i 0.422021π-0.422021\pi
0.242536 + 0.970143i 0.422021π0.422021\pi
1818 0 0
1919 3.00000 0.688247 0.344124 0.938924i 0.388176π-0.388176\pi
0.344124 + 0.938924i 0.388176π0.388176\pi
2020 4.00000 0.894427
2121 0 0
2222 −2.00000 −0.426401
2323 4.00000 0.834058 0.417029 0.908893i 0.363071π-0.363071\pi
0.417029 + 0.908893i 0.363071π0.363071\pi
2424 0 0
2525 −1.00000 −0.200000
2626 −10.0000 −1.96116
2727 0 0
2828 2.00000 0.377964
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 −8.00000 −1.43684 −0.718421 0.695608i 0.755135π-0.755135\pi
−0.718421 + 0.695608i 0.755135π0.755135\pi
3232 −8.00000 −1.41421
3333 0 0
3434 4.00000 0.685994
3535 2.00000 0.338062
3636 0 0
3737 −9.00000 −1.47959 −0.739795 0.672832i 0.765078π-0.765078\pi
−0.739795 + 0.672832i 0.765078π0.765078\pi
3838 6.00000 0.973329
3939 0 0
4040 0 0
4141 −4.00000 −0.624695 −0.312348 0.949968i 0.601115π-0.601115\pi
−0.312348 + 0.949968i 0.601115π0.601115\pi
4242 0 0
4343 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4444 −2.00000 −0.301511
4545 0 0
4646 8.00000 1.17954
4747 10.0000 1.45865 0.729325 0.684167i 0.239834π-0.239834\pi
0.729325 + 0.684167i 0.239834π0.239834\pi
4848 0 0
4949 −6.00000 −0.857143
5050 −2.00000 −0.282843
5151 0 0
5252 −10.0000 −1.38675
5353 −6.00000 −0.824163 −0.412082 0.911147i 0.635198π-0.635198\pi
−0.412082 + 0.911147i 0.635198π0.635198\pi
5454 0 0
5555 −2.00000 −0.269680
5656 0 0
5757 0 0
5858 12.0000 1.57568
5959 −14.0000 −1.82264 −0.911322 0.411693i 0.864937π-0.864937\pi
−0.911322 + 0.411693i 0.864937π0.864937\pi
6060 0 0
6161 9.00000 1.15233 0.576166 0.817333i 0.304548π-0.304548\pi
0.576166 + 0.817333i 0.304548π0.304548\pi
6262 −16.0000 −2.03200
6363 0 0
6464 −8.00000 −1.00000
6565 −10.0000 −1.24035
6666 0 0
6767 5.00000 0.610847 0.305424 0.952217i 0.401202π-0.401202\pi
0.305424 + 0.952217i 0.401202π0.401202\pi
6868 4.00000 0.485071
6969 0 0
7070 4.00000 0.478091
7171 12.0000 1.42414 0.712069 0.702109i 0.247758π-0.247758\pi
0.712069 + 0.702109i 0.247758π0.247758\pi
7272 0 0
7373 7.00000 0.819288 0.409644 0.912245i 0.365653π-0.365653\pi
0.409644 + 0.912245i 0.365653π0.365653\pi
7474 −18.0000 −2.09246
7575 0 0
7676 6.00000 0.688247
7777 −1.00000 −0.113961
7878 0 0
7979 11.0000 1.23760 0.618798 0.785550i 0.287620π-0.287620\pi
0.618798 + 0.785550i 0.287620π0.287620\pi
8080 −8.00000 −0.894427
8181 0 0
8282 −8.00000 −0.883452
8383 12.0000 1.31717 0.658586 0.752506i 0.271155π-0.271155\pi
0.658586 + 0.752506i 0.271155π0.271155\pi
8484 0 0
8585 4.00000 0.433861
8686 0 0
8787 0 0
8888 0 0
8989 6.00000 0.635999 0.317999 0.948091i 0.396989π-0.396989\pi
0.317999 + 0.948091i 0.396989π0.396989\pi
9090 0 0
9191 −5.00000 −0.524142
9292 8.00000 0.834058
9393 0 0
9494 20.0000 2.06284
9595 6.00000 0.615587
9696 0 0
9797 −7.00000 −0.710742 −0.355371 0.934725i 0.615646π-0.615646\pi
−0.355371 + 0.934725i 0.615646π0.615646\pi
9898 −12.0000 −1.21218
9999 0 0
100100 −2.00000 −0.200000
101101 −14.0000 −1.39305 −0.696526 0.717532i 0.745272π-0.745272\pi
−0.696526 + 0.717532i 0.745272π0.745272\pi
102102 0 0
103103 11.0000 1.08386 0.541931 0.840423i 0.317693π-0.317693\pi
0.541931 + 0.840423i 0.317693π0.317693\pi
104104 0 0
105105 0 0
106106 −12.0000 −1.16554
107107 18.0000 1.74013 0.870063 0.492941i 0.164078π-0.164078\pi
0.870063 + 0.492941i 0.164078π0.164078\pi
108108 0 0
109109 10.0000 0.957826 0.478913 0.877862i 0.341031π-0.341031\pi
0.478913 + 0.877862i 0.341031π0.341031\pi
110110 −4.00000 −0.381385
111111 0 0
112112 −4.00000 −0.377964
113113 6.00000 0.564433 0.282216 0.959351i 0.408930π-0.408930\pi
0.282216 + 0.959351i 0.408930π0.408930\pi
114114 0 0
115115 8.00000 0.746004
116116 12.0000 1.11417
117117 0 0
118118 −28.0000 −2.57761
119119 2.00000 0.183340
120120 0 0
121121 1.00000 0.0909091
122122 18.0000 1.62964
123123 0 0
124124 −16.0000 −1.43684
125125 −12.0000 −1.07331
126126 0 0
127127 −16.0000 −1.41977 −0.709885 0.704317i 0.751253π-0.751253\pi
−0.709885 + 0.704317i 0.751253π0.751253\pi
128128 0 0
129129 0 0
130130 −20.0000 −1.75412
131131 −6.00000 −0.524222 −0.262111 0.965038i 0.584419π-0.584419\pi
−0.262111 + 0.965038i 0.584419π0.584419\pi
132132 0 0
133133 3.00000 0.260133
134134 10.0000 0.863868
135135 0 0
136136 0 0
137137 4.00000 0.341743 0.170872 0.985293i 0.445342π-0.445342\pi
0.170872 + 0.985293i 0.445342π0.445342\pi
138138 0 0
139139 1.00000 0.0848189 0.0424094 0.999100i 0.486497π-0.486497\pi
0.0424094 + 0.999100i 0.486497π0.486497\pi
140140 4.00000 0.338062
141141 0 0
142142 24.0000 2.01404
143143 5.00000 0.418121
144144 0 0
145145 12.0000 0.996546
146146 14.0000 1.15865
147147 0 0
148148 −18.0000 −1.47959
149149 4.00000 0.327693 0.163846 0.986486i 0.447610π-0.447610\pi
0.163846 + 0.986486i 0.447610π0.447610\pi
150150 0 0
151151 −13.0000 −1.05792 −0.528962 0.848645i 0.677419π-0.677419\pi
−0.528962 + 0.848645i 0.677419π0.677419\pi
152152 0 0
153153 0 0
154154 −2.00000 −0.161165
155155 −16.0000 −1.28515
156156 0 0
157157 −22.0000 −1.75579 −0.877896 0.478852i 0.841053π-0.841053\pi
−0.877896 + 0.478852i 0.841053π0.841053\pi
158158 22.0000 1.75023
159159 0 0
160160 −16.0000 −1.26491
161161 4.00000 0.315244
162162 0 0
163163 7.00000 0.548282 0.274141 0.961689i 0.411606π-0.411606\pi
0.274141 + 0.961689i 0.411606π0.411606\pi
164164 −8.00000 −0.624695
165165 0 0
166166 24.0000 1.86276
167167 −6.00000 −0.464294 −0.232147 0.972681i 0.574575π-0.574575\pi
−0.232147 + 0.972681i 0.574575π0.574575\pi
168168 0 0
169169 12.0000 0.923077
170170 8.00000 0.613572
171171 0 0
172172 0 0
173173 −24.0000 −1.82469 −0.912343 0.409426i 0.865729π-0.865729\pi
−0.912343 + 0.409426i 0.865729π0.865729\pi
174174 0 0
175175 −1.00000 −0.0755929
176176 4.00000 0.301511
177177 0 0
178178 12.0000 0.899438
179179 −6.00000 −0.448461 −0.224231 0.974536i 0.571987π-0.571987\pi
−0.224231 + 0.974536i 0.571987π0.571987\pi
180180 0 0
181181 13.0000 0.966282 0.483141 0.875542i 0.339496π-0.339496\pi
0.483141 + 0.875542i 0.339496π0.339496\pi
182182 −10.0000 −0.741249
183183 0 0
184184 0 0
185185 −18.0000 −1.32339
186186 0 0
187187 −2.00000 −0.146254
188188 20.0000 1.45865
189189 0 0
190190 12.0000 0.870572
191191 16.0000 1.15772 0.578860 0.815427i 0.303498π-0.303498\pi
0.578860 + 0.815427i 0.303498π0.303498\pi
192192 0 0
193193 13.0000 0.935760 0.467880 0.883792i 0.345018π-0.345018\pi
0.467880 + 0.883792i 0.345018π0.345018\pi
194194 −14.0000 −1.00514
195195 0 0
196196 −12.0000 −0.857143
197197 26.0000 1.85242 0.926212 0.377004i 0.123046π-0.123046\pi
0.926212 + 0.377004i 0.123046π0.123046\pi
198198 0 0
199199 3.00000 0.212664 0.106332 0.994331i 0.466089π-0.466089\pi
0.106332 + 0.994331i 0.466089π0.466089\pi
200200 0 0
201201 0 0
202202 −28.0000 −1.97007
203203 6.00000 0.421117
204204 0 0
205205 −8.00000 −0.558744
206206 22.0000 1.53281
207207 0 0
208208 20.0000 1.38675
209209 −3.00000 −0.207514
210210 0 0
211211 −3.00000 −0.206529 −0.103264 0.994654i 0.532929π-0.532929\pi
−0.103264 + 0.994654i 0.532929π0.532929\pi
212212 −12.0000 −0.824163
213213 0 0
214214 36.0000 2.46091
215215 0 0
216216 0 0
217217 −8.00000 −0.543075
218218 20.0000 1.35457
219219 0 0
220220 −4.00000 −0.269680
221221 −10.0000 −0.672673
222222 0 0
223223 4.00000 0.267860 0.133930 0.990991i 0.457240π-0.457240\pi
0.133930 + 0.990991i 0.457240π0.457240\pi
224224 −8.00000 −0.534522
225225 0 0
226226 12.0000 0.798228
227227 18.0000 1.19470 0.597351 0.801980i 0.296220π-0.296220\pi
0.597351 + 0.801980i 0.296220π0.296220\pi
228228 0 0
229229 6.00000 0.396491 0.198246 0.980152i 0.436476π-0.436476\pi
0.198246 + 0.980152i 0.436476π0.436476\pi
230230 16.0000 1.05501
231231 0 0
232232 0 0
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 20.0000 1.30466
236236 −28.0000 −1.82264
237237 0 0
238238 4.00000 0.259281
239239 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
240240 0 0
241241 −17.0000 −1.09507 −0.547533 0.836784i 0.684433π-0.684433\pi
−0.547533 + 0.836784i 0.684433π0.684433\pi
242242 2.00000 0.128565
243243 0 0
244244 18.0000 1.15233
245245 −12.0000 −0.766652
246246 0 0
247247 −15.0000 −0.954427
248248 0 0
249249 0 0
250250 −24.0000 −1.51789
251251 −10.0000 −0.631194 −0.315597 0.948893i 0.602205π-0.602205\pi
−0.315597 + 0.948893i 0.602205π0.602205\pi
252252 0 0
253253 −4.00000 −0.251478
254254 −32.0000 −2.00786
255255 0 0
256256 16.0000 1.00000
257257 −22.0000 −1.37232 −0.686161 0.727450i 0.740706π-0.740706\pi
−0.686161 + 0.727450i 0.740706π0.740706\pi
258258 0 0
259259 −9.00000 −0.559233
260260 −20.0000 −1.24035
261261 0 0
262262 −12.0000 −0.741362
263263 10.0000 0.616626 0.308313 0.951285i 0.400236π-0.400236\pi
0.308313 + 0.951285i 0.400236π0.400236\pi
264264 0 0
265265 −12.0000 −0.737154
266266 6.00000 0.367884
267267 0 0
268268 10.0000 0.610847
269269 −28.0000 −1.70719 −0.853595 0.520937i 0.825583π-0.825583\pi
−0.853595 + 0.520937i 0.825583π0.825583\pi
270270 0 0
271271 −1.00000 −0.0607457 −0.0303728 0.999539i 0.509669π-0.509669\pi
−0.0303728 + 0.999539i 0.509669π0.509669\pi
272272 −8.00000 −0.485071
273273 0 0
274274 8.00000 0.483298
275275 1.00000 0.0603023
276276 0 0
277277 22.0000 1.32185 0.660926 0.750451i 0.270164π-0.270164\pi
0.660926 + 0.750451i 0.270164π0.270164\pi
278278 2.00000 0.119952
279279 0 0
280280 0 0
281281 −12.0000 −0.715860 −0.357930 0.933748i 0.616517π-0.616517\pi
−0.357930 + 0.933748i 0.616517π0.616517\pi
282282 0 0
283283 4.00000 0.237775 0.118888 0.992908i 0.462067π-0.462067\pi
0.118888 + 0.992908i 0.462067π0.462067\pi
284284 24.0000 1.42414
285285 0 0
286286 10.0000 0.591312
287287 −4.00000 −0.236113
288288 0 0
289289 −13.0000 −0.764706
290290 24.0000 1.40933
291291 0 0
292292 14.0000 0.819288
293293 6.00000 0.350524 0.175262 0.984522i 0.443923π-0.443923\pi
0.175262 + 0.984522i 0.443923π0.443923\pi
294294 0 0
295295 −28.0000 −1.63022
296296 0 0
297297 0 0
298298 8.00000 0.463428
299299 −20.0000 −1.15663
300300 0 0
301301 0 0
302302 −26.0000 −1.49613
303303 0 0
304304 −12.0000 −0.688247
305305 18.0000 1.03068
306306 0 0
307307 −28.0000 −1.59804 −0.799022 0.601302i 0.794649π-0.794649\pi
−0.799022 + 0.601302i 0.794649π0.794649\pi
308308 −2.00000 −0.113961
309309 0 0
310310 −32.0000 −1.81748
311311 −6.00000 −0.340229 −0.170114 0.985424i 0.554414π-0.554414\pi
−0.170114 + 0.985424i 0.554414π0.554414\pi
312312 0 0
313313 −13.0000 −0.734803 −0.367402 0.930062i 0.619753π-0.619753\pi
−0.367402 + 0.930062i 0.619753π0.619753\pi
314314 −44.0000 −2.48306
315315 0 0
316316 22.0000 1.23760
317317 −22.0000 −1.23564 −0.617822 0.786318i 0.711985π-0.711985\pi
−0.617822 + 0.786318i 0.711985π0.711985\pi
318318 0 0
319319 −6.00000 −0.335936
320320 −16.0000 −0.894427
321321 0 0
322322 8.00000 0.445823
323323 6.00000 0.333849
324324 0 0
325325 5.00000 0.277350
326326 14.0000 0.775388
327327 0 0
328328 0 0
329329 10.0000 0.551318
330330 0 0
331331 −5.00000 −0.274825 −0.137412 0.990514i 0.543879π-0.543879\pi
−0.137412 + 0.990514i 0.543879π0.543879\pi
332332 24.0000 1.31717
333333 0 0
334334 −12.0000 −0.656611
335335 10.0000 0.546358
336336 0 0
337337 23.0000 1.25289 0.626445 0.779466i 0.284509π-0.284509\pi
0.626445 + 0.779466i 0.284509π0.284509\pi
338338 24.0000 1.30543
339339 0 0
340340 8.00000 0.433861
341341 8.00000 0.433224
342342 0 0
343343 −13.0000 −0.701934
344344 0 0
345345 0 0
346346 −48.0000 −2.58050
347347 −22.0000 −1.18102 −0.590511 0.807030i 0.701074π-0.701074\pi
−0.590511 + 0.807030i 0.701074π0.701074\pi
348348 0 0
349349 −3.00000 −0.160586 −0.0802932 0.996771i 0.525586π-0.525586\pi
−0.0802932 + 0.996771i 0.525586π0.525586\pi
350350 −2.00000 −0.106904
351351 0 0
352352 8.00000 0.426401
353353 −18.0000 −0.958043 −0.479022 0.877803i 0.659008π-0.659008\pi
−0.479022 + 0.877803i 0.659008π0.659008\pi
354354 0 0
355355 24.0000 1.27379
356356 12.0000 0.635999
357357 0 0
358358 −12.0000 −0.634220
359359 20.0000 1.05556 0.527780 0.849381i 0.323025π-0.323025\pi
0.527780 + 0.849381i 0.323025π0.323025\pi
360360 0 0
361361 −10.0000 −0.526316
362362 26.0000 1.36653
363363 0 0
364364 −10.0000 −0.524142
365365 14.0000 0.732793
366366 0 0
367367 −5.00000 −0.260998 −0.130499 0.991448i 0.541658π-0.541658\pi
−0.130499 + 0.991448i 0.541658π0.541658\pi
368368 −16.0000 −0.834058
369369 0 0
370370 −36.0000 −1.87155
371371 −6.00000 −0.311504
372372 0 0
373373 1.00000 0.0517780 0.0258890 0.999665i 0.491758π-0.491758\pi
0.0258890 + 0.999665i 0.491758π0.491758\pi
374374 −4.00000 −0.206835
375375 0 0
376376 0 0
377377 −30.0000 −1.54508
378378 0 0
379379 −11.0000 −0.565032 −0.282516 0.959263i 0.591169π-0.591169\pi
−0.282516 + 0.959263i 0.591169π0.591169\pi
380380 12.0000 0.615587
381381 0 0
382382 32.0000 1.63726
383383 10.0000 0.510976 0.255488 0.966812i 0.417764π-0.417764\pi
0.255488 + 0.966812i 0.417764π0.417764\pi
384384 0 0
385385 −2.00000 −0.101929
386386 26.0000 1.32337
387387 0 0
388388 −14.0000 −0.710742
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 8.00000 0.404577
392392 0 0
393393 0 0
394394 52.0000 2.61972
395395 22.0000 1.10694
396396 0 0
397397 −14.0000 −0.702640 −0.351320 0.936255i 0.614267π-0.614267\pi
−0.351320 + 0.936255i 0.614267π0.614267\pi
398398 6.00000 0.300753
399399 0 0
400400 4.00000 0.200000
401401 16.0000 0.799002 0.399501 0.916733i 0.369183π-0.369183\pi
0.399501 + 0.916733i 0.369183π0.369183\pi
402402 0 0
403403 40.0000 1.99254
404404 −28.0000 −1.39305
405405 0 0
406406 12.0000 0.595550
407407 9.00000 0.446113
408408 0 0
409409 3.00000 0.148340 0.0741702 0.997246i 0.476369π-0.476369\pi
0.0741702 + 0.997246i 0.476369π0.476369\pi
410410 −16.0000 −0.790184
411411 0 0
412412 22.0000 1.08386
413413 −14.0000 −0.688895
414414 0 0
415415 24.0000 1.17811
416416 40.0000 1.96116
417417 0 0
418418 −6.00000 −0.293470
419419 −20.0000 −0.977064 −0.488532 0.872546i 0.662467π-0.662467\pi
−0.488532 + 0.872546i 0.662467π0.662467\pi
420420 0 0
421421 −35.0000 −1.70580 −0.852898 0.522078i 0.825157π-0.825157\pi
−0.852898 + 0.522078i 0.825157π0.825157\pi
422422 −6.00000 −0.292075
423423 0 0
424424 0 0
425425 −2.00000 −0.0970143
426426 0 0
427427 9.00000 0.435541
428428 36.0000 1.74013
429429 0 0
430430 0 0
431431 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
432432 0 0
433433 −2.00000 −0.0961139 −0.0480569 0.998845i 0.515303π-0.515303\pi
−0.0480569 + 0.998845i 0.515303π0.515303\pi
434434 −16.0000 −0.768025
435435 0 0
436436 20.0000 0.957826
437437 12.0000 0.574038
438438 0 0
439439 16.0000 0.763638 0.381819 0.924237i 0.375298π-0.375298\pi
0.381819 + 0.924237i 0.375298π0.375298\pi
440440 0 0
441441 0 0
442442 −20.0000 −0.951303
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 12.0000 0.568855
446446 8.00000 0.378811
447447 0 0
448448 −8.00000 −0.377964
449449 −20.0000 −0.943858 −0.471929 0.881636i 0.656442π-0.656442\pi
−0.471929 + 0.881636i 0.656442π0.656442\pi
450450 0 0
451451 4.00000 0.188353
452452 12.0000 0.564433
453453 0 0
454454 36.0000 1.68956
455455 −10.0000 −0.468807
456456 0 0
457457 6.00000 0.280668 0.140334 0.990104i 0.455182π-0.455182\pi
0.140334 + 0.990104i 0.455182π0.455182\pi
458458 12.0000 0.560723
459459 0 0
460460 16.0000 0.746004
461461 18.0000 0.838344 0.419172 0.907907i 0.362320π-0.362320\pi
0.419172 + 0.907907i 0.362320π0.362320\pi
462462 0 0
463463 7.00000 0.325318 0.162659 0.986682i 0.447993π-0.447993\pi
0.162659 + 0.986682i 0.447993π0.447993\pi
464464 −24.0000 −1.11417
465465 0 0
466466 −12.0000 −0.555889
467467 −12.0000 −0.555294 −0.277647 0.960683i 0.589555π-0.589555\pi
−0.277647 + 0.960683i 0.589555π0.589555\pi
468468 0 0
469469 5.00000 0.230879
470470 40.0000 1.84506
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 −3.00000 −0.137649
476476 4.00000 0.183340
477477 0 0
478478 0 0
479479 10.0000 0.456912 0.228456 0.973554i 0.426632π-0.426632\pi
0.228456 + 0.973554i 0.426632π0.426632\pi
480480 0 0
481481 45.0000 2.05182
482482 −34.0000 −1.54866
483483 0 0
484484 2.00000 0.0909091
485485 −14.0000 −0.635707
486486 0 0
487487 −1.00000 −0.0453143 −0.0226572 0.999743i 0.507213π-0.507213\pi
−0.0226572 + 0.999743i 0.507213π0.507213\pi
488488 0 0
489489 0 0
490490 −24.0000 −1.08421
491491 2.00000 0.0902587 0.0451294 0.998981i 0.485630π-0.485630\pi
0.0451294 + 0.998981i 0.485630π0.485630\pi
492492 0 0
493493 12.0000 0.540453
494494 −30.0000 −1.34976
495495 0 0
496496 32.0000 1.43684
497497 12.0000 0.538274
498498 0 0
499499 −28.0000 −1.25345 −0.626726 0.779240i 0.715605π-0.715605\pi
−0.626726 + 0.779240i 0.715605π0.715605\pi
500500 −24.0000 −1.07331
501501 0 0
502502 −20.0000 −0.892644
503503 8.00000 0.356702 0.178351 0.983967i 0.442924π-0.442924\pi
0.178351 + 0.983967i 0.442924π0.442924\pi
504504 0 0
505505 −28.0000 −1.24598
506506 −8.00000 −0.355643
507507 0 0
508508 −32.0000 −1.41977
509509 18.0000 0.797836 0.398918 0.916987i 0.369386π-0.369386\pi
0.398918 + 0.916987i 0.369386π0.369386\pi
510510 0 0
511511 7.00000 0.309662
512512 32.0000 1.41421
513513 0 0
514514 −44.0000 −1.94076
515515 22.0000 0.969436
516516 0 0
517517 −10.0000 −0.439799
518518 −18.0000 −0.790875
519519 0 0
520520 0 0
521521 24.0000 1.05146 0.525730 0.850652i 0.323792π-0.323792\pi
0.525730 + 0.850652i 0.323792π0.323792\pi
522522 0 0
523523 11.0000 0.480996 0.240498 0.970650i 0.422689π-0.422689\pi
0.240498 + 0.970650i 0.422689π0.422689\pi
524524 −12.0000 −0.524222
525525 0 0
526526 20.0000 0.872041
527527 −16.0000 −0.696971
528528 0 0
529529 −7.00000 −0.304348
530530 −24.0000 −1.04249
531531 0 0
532532 6.00000 0.260133
533533 20.0000 0.866296
534534 0 0
535535 36.0000 1.55642
536536 0 0
537537 0 0
538538 −56.0000 −2.41433
539539 6.00000 0.258438
540540 0 0
541541 −41.0000 −1.76273 −0.881364 0.472438i 0.843374π-0.843374\pi
−0.881364 + 0.472438i 0.843374π0.843374\pi
542542 −2.00000 −0.0859074
543543 0 0
544544 −16.0000 −0.685994
545545 20.0000 0.856706
546546 0 0
547547 −7.00000 −0.299298 −0.149649 0.988739i 0.547814π-0.547814\pi
−0.149649 + 0.988739i 0.547814π0.547814\pi
548548 8.00000 0.341743
549549 0 0
550550 2.00000 0.0852803
551551 18.0000 0.766826
552552 0 0
553553 11.0000 0.467768
554554 44.0000 1.86938
555555 0 0
556556 2.00000 0.0848189
557557 −10.0000 −0.423714 −0.211857 0.977301i 0.567951π-0.567951\pi
−0.211857 + 0.977301i 0.567951π0.567951\pi
558558 0 0
559559 0 0
560560 −8.00000 −0.338062
561561 0 0
562562 −24.0000 −1.01238
563563 −4.00000 −0.168580 −0.0842900 0.996441i 0.526862π-0.526862\pi
−0.0842900 + 0.996441i 0.526862π0.526862\pi
564564 0 0
565565 12.0000 0.504844
566566 8.00000 0.336265
567567 0 0
568568 0 0
569569 −24.0000 −1.00613 −0.503066 0.864248i 0.667795π-0.667795\pi
−0.503066 + 0.864248i 0.667795π0.667795\pi
570570 0 0
571571 −37.0000 −1.54840 −0.774201 0.632940i 0.781848π-0.781848\pi
−0.774201 + 0.632940i 0.781848π0.781848\pi
572572 10.0000 0.418121
573573 0 0
574574 −8.00000 −0.333914
575575 −4.00000 −0.166812
576576 0 0
577577 27.0000 1.12402 0.562012 0.827129i 0.310027π-0.310027\pi
0.562012 + 0.827129i 0.310027π0.310027\pi
578578 −26.0000 −1.08146
579579 0 0
580580 24.0000 0.996546
581581 12.0000 0.497844
582582 0 0
583583 6.00000 0.248495
584584 0 0
585585 0 0
586586 12.0000 0.495715
587587 −22.0000 −0.908037 −0.454019 0.890992i 0.650010π-0.650010\pi
−0.454019 + 0.890992i 0.650010π0.650010\pi
588588 0 0
589589 −24.0000 −0.988903
590590 −56.0000 −2.30548
591591 0 0
592592 36.0000 1.47959
593593 4.00000 0.164260 0.0821302 0.996622i 0.473828π-0.473828\pi
0.0821302 + 0.996622i 0.473828π0.473828\pi
594594 0 0
595595 4.00000 0.163984
596596 8.00000 0.327693
597597 0 0
598598 −40.0000 −1.63572
599599 32.0000 1.30748 0.653742 0.756717i 0.273198π-0.273198\pi
0.653742 + 0.756717i 0.273198π0.273198\pi
600600 0 0
601601 −46.0000 −1.87638 −0.938190 0.346122i 0.887498π-0.887498\pi
−0.938190 + 0.346122i 0.887498π0.887498\pi
602602 0 0
603603 0 0
604604 −26.0000 −1.05792
605605 2.00000 0.0813116
606606 0 0
607607 17.0000 0.690009 0.345004 0.938601i 0.387877π-0.387877\pi
0.345004 + 0.938601i 0.387877π0.387877\pi
608608 −24.0000 −0.973329
609609 0 0
610610 36.0000 1.45760
611611 −50.0000 −2.02278
612612 0 0
613613 41.0000 1.65597 0.827987 0.560747i 0.189486π-0.189486\pi
0.827987 + 0.560747i 0.189486π0.189486\pi
614614 −56.0000 −2.25998
615615 0 0
616616 0 0
617617 48.0000 1.93241 0.966204 0.257780i 0.0829910π-0.0829910\pi
0.966204 + 0.257780i 0.0829910π0.0829910\pi
618618 0 0
619619 −43.0000 −1.72832 −0.864158 0.503221i 0.832148π-0.832148\pi
−0.864158 + 0.503221i 0.832148π0.832148\pi
620620 −32.0000 −1.28515
621621 0 0
622622 −12.0000 −0.481156
623623 6.00000 0.240385
624624 0 0
625625 −19.0000 −0.760000
626626 −26.0000 −1.03917
627627 0 0
628628 −44.0000 −1.75579
629629 −18.0000 −0.717707
630630 0 0
631631 49.0000 1.95066 0.975330 0.220754i 0.0708517π-0.0708517\pi
0.975330 + 0.220754i 0.0708517π0.0708517\pi
632632 0 0
633633 0 0
634634 −44.0000 −1.74746
635635 −32.0000 −1.26988
636636 0 0
637637 30.0000 1.18864
638638 −12.0000 −0.475085
639639 0 0
640640 0 0
641641 −18.0000 −0.710957 −0.355479 0.934684i 0.615682π-0.615682\pi
−0.355479 + 0.934684i 0.615682π0.615682\pi
642642 0 0
643643 −4.00000 −0.157745 −0.0788723 0.996885i 0.525132π-0.525132\pi
−0.0788723 + 0.996885i 0.525132π0.525132\pi
644644 8.00000 0.315244
645645 0 0
646646 12.0000 0.472134
647647 16.0000 0.629025 0.314512 0.949253i 0.398159π-0.398159\pi
0.314512 + 0.949253i 0.398159π0.398159\pi
648648 0 0
649649 14.0000 0.549548
650650 10.0000 0.392232
651651 0 0
652652 14.0000 0.548282
653653 −4.00000 −0.156532 −0.0782660 0.996933i 0.524938π-0.524938\pi
−0.0782660 + 0.996933i 0.524938π0.524938\pi
654654 0 0
655655 −12.0000 −0.468879
656656 16.0000 0.624695
657657 0 0
658658 20.0000 0.779681
659659 −34.0000 −1.32445 −0.662226 0.749304i 0.730388π-0.730388\pi
−0.662226 + 0.749304i 0.730388π0.730388\pi
660660 0 0
661661 −5.00000 −0.194477 −0.0972387 0.995261i 0.531001π-0.531001\pi
−0.0972387 + 0.995261i 0.531001π0.531001\pi
662662 −10.0000 −0.388661
663663 0 0
664664 0 0
665665 6.00000 0.232670
666666 0 0
667667 24.0000 0.929284
668668 −12.0000 −0.464294
669669 0 0
670670 20.0000 0.772667
671671 −9.00000 −0.347441
672672 0 0
673673 41.0000 1.58043 0.790217 0.612827i 0.209968π-0.209968\pi
0.790217 + 0.612827i 0.209968π0.209968\pi
674674 46.0000 1.77185
675675 0 0
676676 24.0000 0.923077
677677 36.0000 1.38359 0.691796 0.722093i 0.256820π-0.256820\pi
0.691796 + 0.722093i 0.256820π0.256820\pi
678678 0 0
679679 −7.00000 −0.268635
680680 0 0
681681 0 0
682682 16.0000 0.612672
683683 −14.0000 −0.535695 −0.267848 0.963461i 0.586312π-0.586312\pi
−0.267848 + 0.963461i 0.586312π0.586312\pi
684684 0 0
685685 8.00000 0.305664
686686 −26.0000 −0.992685
687687 0 0
688688 0 0
689689 30.0000 1.14291
690690 0 0
691691 −16.0000 −0.608669 −0.304334 0.952565i 0.598434π-0.598434\pi
−0.304334 + 0.952565i 0.598434π0.598434\pi
692692 −48.0000 −1.82469
693693 0 0
694694 −44.0000 −1.67022
695695 2.00000 0.0758643
696696 0 0
697697 −8.00000 −0.303022
698698 −6.00000 −0.227103
699699 0 0
700700 −2.00000 −0.0755929
701701 −38.0000 −1.43524 −0.717620 0.696435i 0.754769π-0.754769\pi
−0.717620 + 0.696435i 0.754769π0.754769\pi
702702 0 0
703703 −27.0000 −1.01832
704704 8.00000 0.301511
705705 0 0
706706 −36.0000 −1.35488
707707 −14.0000 −0.526524
708708 0 0
709709 17.0000 0.638448 0.319224 0.947679i 0.396578π-0.396578\pi
0.319224 + 0.947679i 0.396578π0.396578\pi
710710 48.0000 1.80141
711711 0 0
712712 0 0
713713 −32.0000 −1.19841
714714 0 0
715715 10.0000 0.373979
716716 −12.0000 −0.448461
717717 0 0
718718 40.0000 1.49279
719719 42.0000 1.56634 0.783168 0.621810i 0.213603π-0.213603\pi
0.783168 + 0.621810i 0.213603π0.213603\pi
720720 0 0
721721 11.0000 0.409661
722722 −20.0000 −0.744323
723723 0 0
724724 26.0000 0.966282
725725 −6.00000 −0.222834
726726 0 0
727727 24.0000 0.890111 0.445055 0.895503i 0.353184π-0.353184\pi
0.445055 + 0.895503i 0.353184π0.353184\pi
728728 0 0
729729 0 0
730730 28.0000 1.03633
731731 0 0
732732 0 0
733733 −6.00000 −0.221615 −0.110808 0.993842i 0.535344π-0.535344\pi
−0.110808 + 0.993842i 0.535344π0.535344\pi
734734 −10.0000 −0.369107
735735 0 0
736736 −32.0000 −1.17954
737737 −5.00000 −0.184177
738738 0 0
739739 44.0000 1.61857 0.809283 0.587419i 0.199856π-0.199856\pi
0.809283 + 0.587419i 0.199856π0.199856\pi
740740 −36.0000 −1.32339
741741 0 0
742742 −12.0000 −0.440534
743743 38.0000 1.39408 0.697042 0.717030i 0.254499π-0.254499\pi
0.697042 + 0.717030i 0.254499π0.254499\pi
744744 0 0
745745 8.00000 0.293097
746746 2.00000 0.0732252
747747 0 0
748748 −4.00000 −0.146254
749749 18.0000 0.657706
750750 0 0
751751 −35.0000 −1.27717 −0.638584 0.769552i 0.720480π-0.720480\pi
−0.638584 + 0.769552i 0.720480π0.720480\pi
752752 −40.0000 −1.45865
753753 0 0
754754 −60.0000 −2.18507
755755 −26.0000 −0.946237
756756 0 0
757757 17.0000 0.617876 0.308938 0.951082i 0.400027π-0.400027\pi
0.308938 + 0.951082i 0.400027π0.400027\pi
758758 −22.0000 −0.799076
759759 0 0
760760 0 0
761761 36.0000 1.30500 0.652499 0.757789i 0.273720π-0.273720\pi
0.652499 + 0.757789i 0.273720π0.273720\pi
762762 0 0
763763 10.0000 0.362024
764764 32.0000 1.15772
765765 0 0
766766 20.0000 0.722629
767767 70.0000 2.52755
768768 0 0
769769 −7.00000 −0.252426 −0.126213 0.992003i 0.540282π-0.540282\pi
−0.126213 + 0.992003i 0.540282π0.540282\pi
770770 −4.00000 −0.144150
771771 0 0
772772 26.0000 0.935760
773773 42.0000 1.51064 0.755318 0.655359i 0.227483π-0.227483\pi
0.755318 + 0.655359i 0.227483π0.227483\pi
774774 0 0
775775 8.00000 0.287368
776776 0 0
777777 0 0
778778 48.0000 1.72088
779779 −12.0000 −0.429945
780780 0 0
781781 −12.0000 −0.429394
782782 16.0000 0.572159
783783 0 0
784784 24.0000 0.857143
785785 −44.0000 −1.57043
786786 0 0
787787 −29.0000 −1.03374 −0.516869 0.856064i 0.672903π-0.672903\pi
−0.516869 + 0.856064i 0.672903π0.672903\pi
788788 52.0000 1.85242
789789 0 0
790790 44.0000 1.56545
791791 6.00000 0.213335
792792 0 0
793793 −45.0000 −1.59800
794794 −28.0000 −0.993683
795795 0 0
796796 6.00000 0.212664
797797 28.0000 0.991811 0.495905 0.868377i 0.334836π-0.334836\pi
0.495905 + 0.868377i 0.334836π0.334836\pi
798798 0 0
799799 20.0000 0.707549
800800 8.00000 0.282843
801801 0 0
802802 32.0000 1.12996
803803 −7.00000 −0.247025
804804 0 0
805805 8.00000 0.281963
806806 80.0000 2.81788
807807 0 0
808808 0 0
809809 42.0000 1.47664 0.738321 0.674450i 0.235619π-0.235619\pi
0.738321 + 0.674450i 0.235619π0.235619\pi
810810 0 0
811811 −20.0000 −0.702295 −0.351147 0.936320i 0.614208π-0.614208\pi
−0.351147 + 0.936320i 0.614208π0.614208\pi
812812 12.0000 0.421117
813813 0 0
814814 18.0000 0.630900
815815 14.0000 0.490399
816816 0 0
817817 0 0
818818 6.00000 0.209785
819819 0 0
820820 −16.0000 −0.558744
821821 −40.0000 −1.39601 −0.698005 0.716093i 0.745929π-0.745929\pi
−0.698005 + 0.716093i 0.745929π0.745929\pi
822822 0 0
823823 21.0000 0.732014 0.366007 0.930612i 0.380725π-0.380725\pi
0.366007 + 0.930612i 0.380725π0.380725\pi
824824 0 0
825825 0 0
826826 −28.0000 −0.974245
827827 10.0000 0.347734 0.173867 0.984769i 0.444374π-0.444374\pi
0.173867 + 0.984769i 0.444374π0.444374\pi
828828 0 0
829829 −11.0000 −0.382046 −0.191023 0.981586i 0.561180π-0.561180\pi
−0.191023 + 0.981586i 0.561180π0.561180\pi
830830 48.0000 1.66610
831831 0 0
832832 40.0000 1.38675
833833 −12.0000 −0.415775
834834 0 0
835835 −12.0000 −0.415277
836836 −6.00000 −0.207514
837837 0 0
838838 −40.0000 −1.38178
839839 −4.00000 −0.138095 −0.0690477 0.997613i 0.521996π-0.521996\pi
−0.0690477 + 0.997613i 0.521996π0.521996\pi
840840 0 0
841841 7.00000 0.241379
842842 −70.0000 −2.41236
843843 0 0
844844 −6.00000 −0.206529
845845 24.0000 0.825625
846846 0 0
847847 1.00000 0.0343604
848848 24.0000 0.824163
849849 0 0
850850 −4.00000 −0.137199
851851 −36.0000 −1.23406
852852 0 0
853853 −19.0000 −0.650548 −0.325274 0.945620i 0.605456π-0.605456\pi
−0.325274 + 0.945620i 0.605456π0.605456\pi
854854 18.0000 0.615947
855855 0 0
856856 0 0
857857 −14.0000 −0.478231 −0.239115 0.970991i 0.576857π-0.576857\pi
−0.239115 + 0.970991i 0.576857π0.576857\pi
858858 0 0
859859 3.00000 0.102359 0.0511793 0.998689i 0.483702π-0.483702\pi
0.0511793 + 0.998689i 0.483702π0.483702\pi
860860 0 0
861861 0 0
862862 0 0
863863 6.00000 0.204242 0.102121 0.994772i 0.467437π-0.467437\pi
0.102121 + 0.994772i 0.467437π0.467437\pi
864864 0 0
865865 −48.0000 −1.63205
866866 −4.00000 −0.135926
867867 0 0
868868 −16.0000 −0.543075
869869 −11.0000 −0.373149
870870 0 0
871871 −25.0000 −0.847093
872872 0 0
873873 0 0
874874 24.0000 0.811812
875875 −12.0000 −0.405674
876876 0 0
877877 −3.00000 −0.101303 −0.0506514 0.998716i 0.516130π-0.516130\pi
−0.0506514 + 0.998716i 0.516130π0.516130\pi
878878 32.0000 1.07995
879879 0 0
880880 8.00000 0.269680
881881 −32.0000 −1.07811 −0.539054 0.842271i 0.681218π-0.681218\pi
−0.539054 + 0.842271i 0.681218π0.681218\pi
882882 0 0
883883 −53.0000 −1.78359 −0.891796 0.452438i 0.850554π-0.850554\pi
−0.891796 + 0.452438i 0.850554π0.850554\pi
884884 −20.0000 −0.672673
885885 0 0
886886 52.0000 1.74697
887887 −26.0000 −0.872995 −0.436497 0.899706i 0.643781π-0.643781\pi
−0.436497 + 0.899706i 0.643781π0.643781\pi
888888 0 0
889889 −16.0000 −0.536623
890890 24.0000 0.804482
891891 0 0
892892 8.00000 0.267860
893893 30.0000 1.00391
894894 0 0
895895 −12.0000 −0.401116
896896 0 0
897897 0 0
898898 −40.0000 −1.33482
899899 −48.0000 −1.60089
900900 0 0
901901 −12.0000 −0.399778
902902 8.00000 0.266371
903903 0 0
904904 0 0
905905 26.0000 0.864269
906906 0 0
907907 9.00000 0.298840 0.149420 0.988774i 0.452259π-0.452259\pi
0.149420 + 0.988774i 0.452259π0.452259\pi
908908 36.0000 1.19470
909909 0 0
910910 −20.0000 −0.662994
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 12.0000 0.396925
915915 0 0
916916 12.0000 0.396491
917917 −6.00000 −0.198137
918918 0 0
919919 −56.0000 −1.84727 −0.923635 0.383274i 0.874797π-0.874797\pi
−0.923635 + 0.383274i 0.874797π0.874797\pi
920920 0 0
921921 0 0
922922 36.0000 1.18560
923923 −60.0000 −1.97492
924924 0 0
925925 9.00000 0.295918
926926 14.0000 0.460069
927927 0 0
928928 −48.0000 −1.57568
929929 −6.00000 −0.196854 −0.0984268 0.995144i 0.531381π-0.531381\pi
−0.0984268 + 0.995144i 0.531381π0.531381\pi
930930 0 0
931931 −18.0000 −0.589926
932932 −12.0000 −0.393073
933933 0 0
934934 −24.0000 −0.785304
935935 −4.00000 −0.130814
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 10.0000 0.326512
939939 0 0
940940 40.0000 1.30466
941941 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
942942 0 0
943943 −16.0000 −0.521032
944944 56.0000 1.82264
945945 0 0
946946 0 0
947947 54.0000 1.75476 0.877382 0.479792i 0.159288π-0.159288\pi
0.877382 + 0.479792i 0.159288π0.159288\pi
948948 0 0
949949 −35.0000 −1.13615
950950 −6.00000 −0.194666
951951 0 0
952952 0 0
953953 32.0000 1.03658 0.518291 0.855204i 0.326568π-0.326568\pi
0.518291 + 0.855204i 0.326568π0.326568\pi
954954 0 0
955955 32.0000 1.03550
956956 0 0
957957 0 0
958958 20.0000 0.646171
959959 4.00000 0.129167
960960 0 0
961961 33.0000 1.06452
962962 90.0000 2.90172
963963 0 0
964964 −34.0000 −1.09507
965965 26.0000 0.836970
966966 0 0
967967 −41.0000 −1.31847 −0.659236 0.751936i 0.729120π-0.729120\pi
−0.659236 + 0.751936i 0.729120π0.729120\pi
968968 0 0
969969 0 0
970970 −28.0000 −0.899026
971971 −50.0000 −1.60458 −0.802288 0.596937i 0.796384π-0.796384\pi
−0.802288 + 0.596937i 0.796384π0.796384\pi
972972 0 0
973973 1.00000 0.0320585
974974 −2.00000 −0.0640841
975975 0 0
976976 −36.0000 −1.15233
977977 30.0000 0.959785 0.479893 0.877327i 0.340676π-0.340676\pi
0.479893 + 0.877327i 0.340676π0.340676\pi
978978 0 0
979979 −6.00000 −0.191761
980980 −24.0000 −0.766652
981981 0 0
982982 4.00000 0.127645
983983 −42.0000 −1.33959 −0.669796 0.742545i 0.733618π-0.733618\pi
−0.669796 + 0.742545i 0.733618π0.733618\pi
984984 0 0
985985 52.0000 1.65686
986986 24.0000 0.764316
987987 0 0
988988 −30.0000 −0.954427
989989 0 0
990990 0 0
991991 7.00000 0.222362 0.111181 0.993800i 0.464537π-0.464537\pi
0.111181 + 0.993800i 0.464537π0.464537\pi
992992 64.0000 2.03200
993993 0 0
994994 24.0000 0.761234
995995 6.00000 0.190213
996996 0 0
997997 38.0000 1.20347 0.601736 0.798695i 0.294476π-0.294476\pi
0.601736 + 0.798695i 0.294476π0.294476\pi
998998 −56.0000 −1.77265
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 297.2.a.d.1.1 yes 1
3.2 odd 2 297.2.a.a.1.1 1
4.3 odd 2 4752.2.a.o.1.1 1
5.4 even 2 7425.2.a.b.1.1 1
9.2 odd 6 891.2.e.l.595.1 2
9.4 even 3 891.2.e.a.298.1 2
9.5 odd 6 891.2.e.l.298.1 2
9.7 even 3 891.2.e.a.595.1 2
11.10 odd 2 3267.2.a.a.1.1 1
12.11 even 2 4752.2.a.c.1.1 1
15.14 odd 2 7425.2.a.u.1.1 1
33.32 even 2 3267.2.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
297.2.a.a.1.1 1 3.2 odd 2
297.2.a.d.1.1 yes 1 1.1 even 1 trivial
891.2.e.a.298.1 2 9.4 even 3
891.2.e.a.595.1 2 9.7 even 3
891.2.e.l.298.1 2 9.5 odd 6
891.2.e.l.595.1 2 9.2 odd 6
3267.2.a.a.1.1 1 11.10 odd 2
3267.2.a.k.1.1 1 33.32 even 2
4752.2.a.c.1.1 1 12.11 even 2
4752.2.a.o.1.1 1 4.3 odd 2
7425.2.a.b.1.1 1 5.4 even 2
7425.2.a.u.1.1 1 15.14 odd 2