Properties

Label 1521.4.a.h.1.1
Level 15211521
Weight 44
Character 1521.1
Self dual yes
Analytic conductor 89.74289.742
Analytic rank 11
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1521,4,Mod(1,1521)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1521.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 1521=32132 1521 = 3^{2} \cdot 13^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1521.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: 89.741905118789.7419051187
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 39)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 1521.1

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+1.00000q27.00000q47.00000q510.0000q715.0000q87.00000q10+22.0000q1110.0000q14+41.0000q1637.0000q17+30.0000q19+49.0000q20+22.0000q22+162.000q2376.0000q25+70.0000q28+113.000q29+196.000q31+161.000q3237.0000q34+70.0000q35+13.0000q37+30.0000q38+105.000q40285.000q41246.000q43154.000q44+162.000q46+462.000q47243.000q4976.0000q50+537.000q53154.000q55+150.000q56+113.000q58576.000q59635.000q61+196.000q62167.000q64+202.000q67+259.000q68+70.0000q70+1086.00q71805.000q73+13.0000q74210.000q76220.000q77+884.000q79287.000q80285.000q82518.000q83+259.000q85246.000q86330.000q88194.000q891134.00q92+462.000q94210.000q951202.00q97243.000q98+O(q100)q+1.00000 q^{2} -7.00000 q^{4} -7.00000 q^{5} -10.0000 q^{7} -15.0000 q^{8} -7.00000 q^{10} +22.0000 q^{11} -10.0000 q^{14} +41.0000 q^{16} -37.0000 q^{17} +30.0000 q^{19} +49.0000 q^{20} +22.0000 q^{22} +162.000 q^{23} -76.0000 q^{25} +70.0000 q^{28} +113.000 q^{29} +196.000 q^{31} +161.000 q^{32} -37.0000 q^{34} +70.0000 q^{35} +13.0000 q^{37} +30.0000 q^{38} +105.000 q^{40} -285.000 q^{41} -246.000 q^{43} -154.000 q^{44} +162.000 q^{46} +462.000 q^{47} -243.000 q^{49} -76.0000 q^{50} +537.000 q^{53} -154.000 q^{55} +150.000 q^{56} +113.000 q^{58} -576.000 q^{59} -635.000 q^{61} +196.000 q^{62} -167.000 q^{64} +202.000 q^{67} +259.000 q^{68} +70.0000 q^{70} +1086.00 q^{71} -805.000 q^{73} +13.0000 q^{74} -210.000 q^{76} -220.000 q^{77} +884.000 q^{79} -287.000 q^{80} -285.000 q^{82} -518.000 q^{83} +259.000 q^{85} -246.000 q^{86} -330.000 q^{88} -194.000 q^{89} -1134.00 q^{92} +462.000 q^{94} -210.000 q^{95} -1202.00 q^{97} -243.000 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 0.353553 0.176777 0.984251i 0.443433π-0.443433\pi
0.176777 + 0.984251i 0.443433π0.443433\pi
33 0 0
44 −7.00000 −0.875000
55 −7.00000 −0.626099 −0.313050 0.949737i 0.601351π-0.601351\pi
−0.313050 + 0.949737i 0.601351π0.601351\pi
66 0 0
77 −10.0000 −0.539949 −0.269975 0.962867i 0.587015π-0.587015\pi
−0.269975 + 0.962867i 0.587015π0.587015\pi
88 −15.0000 −0.662913
99 0 0
1010 −7.00000 −0.221359
1111 22.0000 0.603023 0.301511 0.953463i 0.402509π-0.402509\pi
0.301511 + 0.953463i 0.402509π0.402509\pi
1212 0 0
1313 0 0
1414 −10.0000 −0.190901
1515 0 0
1616 41.0000 0.640625
1717 −37.0000 −0.527872 −0.263936 0.964540i 0.585021π-0.585021\pi
−0.263936 + 0.964540i 0.585021π0.585021\pi
1818 0 0
1919 30.0000 0.362235 0.181118 0.983461i 0.442029π-0.442029\pi
0.181118 + 0.983461i 0.442029π0.442029\pi
2020 49.0000 0.547837
2121 0 0
2222 22.0000 0.213201
2323 162.000 1.46867 0.734333 0.678789i 0.237495π-0.237495\pi
0.734333 + 0.678789i 0.237495π0.237495\pi
2424 0 0
2525 −76.0000 −0.608000
2626 0 0
2727 0 0
2828 70.0000 0.472456
2929 113.000 0.723571 0.361786 0.932261i 0.382167π-0.382167\pi
0.361786 + 0.932261i 0.382167π0.382167\pi
3030 0 0
3131 196.000 1.13557 0.567785 0.823177i 0.307801π-0.307801\pi
0.567785 + 0.823177i 0.307801π0.307801\pi
3232 161.000 0.889408
3333 0 0
3434 −37.0000 −0.186631
3535 70.0000 0.338062
3636 0 0
3737 13.0000 0.0577618 0.0288809 0.999583i 0.490806π-0.490806\pi
0.0288809 + 0.999583i 0.490806π0.490806\pi
3838 30.0000 0.128070
3939 0 0
4040 105.000 0.415049
4141 −285.000 −1.08560 −0.542799 0.839863i 0.682635π-0.682635\pi
−0.542799 + 0.839863i 0.682635π0.682635\pi
4242 0 0
4343 −246.000 −0.872434 −0.436217 0.899842i 0.643682π-0.643682\pi
−0.436217 + 0.899842i 0.643682π0.643682\pi
4444 −154.000 −0.527645
4545 0 0
4646 162.000 0.519252
4747 462.000 1.43382 0.716911 0.697165i 0.245555π-0.245555\pi
0.716911 + 0.697165i 0.245555π0.245555\pi
4848 0 0
4949 −243.000 −0.708455
5050 −76.0000 −0.214960
5151 0 0
5252 0 0
5353 537.000 1.39175 0.695874 0.718164i 0.255017π-0.255017\pi
0.695874 + 0.718164i 0.255017π0.255017\pi
5454 0 0
5555 −154.000 −0.377552
5656 150.000 0.357939
5757 0 0
5858 113.000 0.255821
5959 −576.000 −1.27100 −0.635498 0.772102i 0.719205π-0.719205\pi
−0.635498 + 0.772102i 0.719205π0.719205\pi
6060 0 0
6161 −635.000 −1.33284 −0.666421 0.745575i 0.732175π-0.732175\pi
−0.666421 + 0.745575i 0.732175π0.732175\pi
6262 196.000 0.401484
6363 0 0
6464 −167.000 −0.326172
6565 0 0
6666 0 0
6767 202.000 0.368332 0.184166 0.982895i 0.441042π-0.441042\pi
0.184166 + 0.982895i 0.441042π0.441042\pi
6868 259.000 0.461888
6969 0 0
7070 70.0000 0.119523
7171 1086.00 1.81527 0.907637 0.419755i 0.137884π-0.137884\pi
0.907637 + 0.419755i 0.137884π0.137884\pi
7272 0 0
7373 −805.000 −1.29066 −0.645330 0.763904i 0.723280π-0.723280\pi
−0.645330 + 0.763904i 0.723280π0.723280\pi
7474 13.0000 0.0204219
7575 0 0
7676 −210.000 −0.316956
7777 −220.000 −0.325602
7878 0 0
7979 884.000 1.25896 0.629480 0.777017i 0.283268π-0.283268\pi
0.629480 + 0.777017i 0.283268π0.283268\pi
8080 −287.000 −0.401095
8181 0 0
8282 −285.000 −0.383817
8383 −518.000 −0.685035 −0.342517 0.939511i 0.611280π-0.611280\pi
−0.342517 + 0.939511i 0.611280π0.611280\pi
8484 0 0
8585 259.000 0.330500
8686 −246.000 −0.308452
8787 0 0
8888 −330.000 −0.399751
8989 −194.000 −0.231056 −0.115528 0.993304i 0.536856π-0.536856\pi
−0.115528 + 0.993304i 0.536856π0.536856\pi
9090 0 0
9191 0 0
9292 −1134.00 −1.28508
9393 0 0
9494 462.000 0.506933
9595 −210.000 −0.226795
9696 0 0
9797 −1202.00 −1.25819 −0.629096 0.777328i 0.716575π-0.716575\pi
−0.629096 + 0.777328i 0.716575π0.716575\pi
9898 −243.000 −0.250477
9999 0 0
100100 532.000 0.532000
101101 429.000 0.422645 0.211322 0.977416i 0.432223π-0.432223\pi
0.211322 + 0.977416i 0.432223π0.432223\pi
102102 0 0
103103 −1302.00 −1.24553 −0.622766 0.782408i 0.713991π-0.713991\pi
−0.622766 + 0.782408i 0.713991π0.713991\pi
104104 0 0
105105 0 0
106106 537.000 0.492057
107107 1338.00 1.20887 0.604436 0.796654i 0.293398π-0.293398\pi
0.604436 + 0.796654i 0.293398π0.293398\pi
108108 0 0
109109 −1034.00 −0.908617 −0.454308 0.890844i 0.650114π-0.650114\pi
−0.454308 + 0.890844i 0.650114π0.650114\pi
110110 −154.000 −0.133485
111111 0 0
112112 −410.000 −0.345905
113113 −1077.00 −0.896599 −0.448299 0.893884i 0.647970π-0.647970\pi
−0.448299 + 0.893884i 0.647970π0.647970\pi
114114 0 0
115115 −1134.00 −0.919531
116116 −791.000 −0.633125
117117 0 0
118118 −576.000 −0.449365
119119 370.000 0.285024
120120 0 0
121121 −847.000 −0.636364
122122 −635.000 −0.471231
123123 0 0
124124 −1372.00 −0.993623
125125 1407.00 1.00677
126126 0 0
127127 −988.000 −0.690321 −0.345161 0.938544i 0.612176π-0.612176\pi
−0.345161 + 0.938544i 0.612176π0.612176\pi
128128 −1455.00 −1.00473
129129 0 0
130130 0 0
131131 −560.000 −0.373492 −0.186746 0.982408i 0.559794π-0.559794\pi
−0.186746 + 0.982408i 0.559794π0.559794\pi
132132 0 0
133133 −300.000 −0.195589
134134 202.000 0.130225
135135 0 0
136136 555.000 0.349933
137137 519.000 0.323658 0.161829 0.986819i 0.448261π-0.448261\pi
0.161829 + 0.986819i 0.448261π0.448261\pi
138138 0 0
139139 −348.000 −0.212352 −0.106176 0.994347i 0.533861π-0.533861\pi
−0.106176 + 0.994347i 0.533861π0.533861\pi
140140 −490.000 −0.295804
141141 0 0
142142 1086.00 0.641796
143143 0 0
144144 0 0
145145 −791.000 −0.453027
146146 −805.000 −0.456317
147147 0 0
148148 −91.0000 −0.0505416
149149 645.000 0.354634 0.177317 0.984154i 0.443258π-0.443258\pi
0.177317 + 0.984154i 0.443258π0.443258\pi
150150 0 0
151151 2914.00 1.57045 0.785225 0.619211i 0.212547π-0.212547\pi
0.785225 + 0.619211i 0.212547π0.212547\pi
152152 −450.000 −0.240130
153153 0 0
154154 −220.000 −0.115118
155155 −1372.00 −0.710979
156156 0 0
157157 −2079.00 −1.05683 −0.528415 0.848986i 0.677213π-0.677213\pi
−0.528415 + 0.848986i 0.677213π0.677213\pi
158158 884.000 0.445109
159159 0 0
160160 −1127.00 −0.556857
161161 −1620.00 −0.793006
162162 0 0
163163 1700.00 0.816897 0.408449 0.912781i 0.366070π-0.366070\pi
0.408449 + 0.912781i 0.366070π0.366070\pi
164164 1995.00 0.949898
165165 0 0
166166 −518.000 −0.242196
167167 −3680.00 −1.70519 −0.852596 0.522571i 0.824973π-0.824973\pi
−0.852596 + 0.522571i 0.824973π0.824973\pi
168168 0 0
169169 0 0
170170 259.000 0.116849
171171 0 0
172172 1722.00 0.763379
173173 −4146.00 −1.82205 −0.911025 0.412352i 0.864707π-0.864707\pi
−0.911025 + 0.412352i 0.864707π0.864707\pi
174174 0 0
175175 760.000 0.328289
176176 902.000 0.386311
177177 0 0
178178 −194.000 −0.0816905
179179 −3674.00 −1.53412 −0.767060 0.641575i 0.778281π-0.778281\pi
−0.767060 + 0.641575i 0.778281π0.778281\pi
180180 0 0
181181 −3283.00 −1.34820 −0.674098 0.738642i 0.735467π-0.735467\pi
−0.674098 + 0.738642i 0.735467π0.735467\pi
182182 0 0
183183 0 0
184184 −2430.00 −0.973598
185185 −91.0000 −0.0361646
186186 0 0
187187 −814.000 −0.318319
188188 −3234.00 −1.25459
189189 0 0
190190 −210.000 −0.0801842
191191 596.000 0.225786 0.112893 0.993607i 0.463988π-0.463988\pi
0.112893 + 0.993607i 0.463988π0.463988\pi
192192 0 0
193193 −393.000 −0.146574 −0.0732869 0.997311i 0.523349π-0.523349\pi
−0.0732869 + 0.997311i 0.523349π0.523349\pi
194194 −1202.00 −0.444838
195195 0 0
196196 1701.00 0.619898
197197 3522.00 1.27377 0.636884 0.770960i 0.280223π-0.280223\pi
0.636884 + 0.770960i 0.280223π0.280223\pi
198198 0 0
199199 2018.00 0.718855 0.359428 0.933173i 0.382972π-0.382972\pi
0.359428 + 0.933173i 0.382972π0.382972\pi
200200 1140.00 0.403051
201201 0 0
202202 429.000 0.149427
203203 −1130.00 −0.390692
204204 0 0
205205 1995.00 0.679692
206206 −1302.00 −0.440362
207207 0 0
208208 0 0
209209 660.000 0.218436
210210 0 0
211211 160.000 0.0522031 0.0261016 0.999659i 0.491691π-0.491691\pi
0.0261016 + 0.999659i 0.491691π0.491691\pi
212212 −3759.00 −1.21778
213213 0 0
214214 1338.00 0.427401
215215 1722.00 0.546230
216216 0 0
217217 −1960.00 −0.613150
218218 −1034.00 −0.321245
219219 0 0
220220 1078.00 0.330358
221221 0 0
222222 0 0
223223 4072.00 1.22279 0.611393 0.791327i 0.290609π-0.290609\pi
0.611393 + 0.791327i 0.290609π0.290609\pi
224224 −1610.00 −0.480235
225225 0 0
226226 −1077.00 −0.316995
227227 5794.00 1.69410 0.847051 0.531511i 0.178376π-0.178376\pi
0.847051 + 0.531511i 0.178376π0.178376\pi
228228 0 0
229229 6482.00 1.87049 0.935246 0.353999i 0.115178π-0.115178\pi
0.935246 + 0.353999i 0.115178π0.115178\pi
230230 −1134.00 −0.325103
231231 0 0
232232 −1695.00 −0.479665
233233 −6890.00 −1.93725 −0.968624 0.248530i 0.920053π-0.920053\pi
−0.968624 + 0.248530i 0.920053π0.920053\pi
234234 0 0
235235 −3234.00 −0.897714
236236 4032.00 1.11212
237237 0 0
238238 370.000 0.100771
239239 −2466.00 −0.667415 −0.333708 0.942677i 0.608300π-0.608300\pi
−0.333708 + 0.942677i 0.608300π0.608300\pi
240240 0 0
241241 −3617.00 −0.966770 −0.483385 0.875408i 0.660593π-0.660593\pi
−0.483385 + 0.875408i 0.660593π0.660593\pi
242242 −847.000 −0.224989
243243 0 0
244244 4445.00 1.16624
245245 1701.00 0.443563
246246 0 0
247247 0 0
248248 −2940.00 −0.752783
249249 0 0
250250 1407.00 0.355946
251251 −4860.00 −1.22215 −0.611077 0.791571i 0.709263π-0.709263\pi
−0.611077 + 0.791571i 0.709263π0.709263\pi
252252 0 0
253253 3564.00 0.885639
254254 −988.000 −0.244065
255255 0 0
256256 −119.000 −0.0290527
257257 −565.000 −0.137135 −0.0685676 0.997646i 0.521843π-0.521843\pi
−0.0685676 + 0.997646i 0.521843π0.521843\pi
258258 0 0
259259 −130.000 −0.0311884
260260 0 0
261261 0 0
262262 −560.000 −0.132049
263263 498.000 0.116760 0.0583802 0.998294i 0.481406π-0.481406\pi
0.0583802 + 0.998294i 0.481406π0.481406\pi
264264 0 0
265265 −3759.00 −0.871372
266266 −300.000 −0.0691511
267267 0 0
268268 −1414.00 −0.322290
269269 −5546.00 −1.25705 −0.628523 0.777791i 0.716340π-0.716340\pi
−0.628523 + 0.777791i 0.716340π0.716340\pi
270270 0 0
271271 −2256.00 −0.505691 −0.252845 0.967507i 0.581366π-0.581366\pi
−0.252845 + 0.967507i 0.581366π0.581366\pi
272272 −1517.00 −0.338168
273273 0 0
274274 519.000 0.114430
275275 −1672.00 −0.366638
276276 0 0
277277 2309.00 0.500846 0.250423 0.968137i 0.419430π-0.419430\pi
0.250423 + 0.968137i 0.419430π0.419430\pi
278278 −348.000 −0.0750779
279279 0 0
280280 −1050.00 −0.224105
281281 −5833.00 −1.23832 −0.619159 0.785265i 0.712527π-0.712527\pi
−0.619159 + 0.785265i 0.712527π0.712527\pi
282282 0 0
283283 1650.00 0.346581 0.173290 0.984871i 0.444560π-0.444560\pi
0.173290 + 0.984871i 0.444560π0.444560\pi
284284 −7602.00 −1.58837
285285 0 0
286286 0 0
287287 2850.00 0.586168
288288 0 0
289289 −3544.00 −0.721352
290290 −791.000 −0.160169
291291 0 0
292292 5635.00 1.12933
293293 −2991.00 −0.596369 −0.298184 0.954508i 0.596381π-0.596381\pi
−0.298184 + 0.954508i 0.596381π0.596381\pi
294294 0 0
295295 4032.00 0.795770
296296 −195.000 −0.0382910
297297 0 0
298298 645.000 0.125382
299299 0 0
300300 0 0
301301 2460.00 0.471070
302302 2914.00 0.555238
303303 0 0
304304 1230.00 0.232057
305305 4445.00 0.834492
306306 0 0
307307 −2422.00 −0.450263 −0.225132 0.974328i 0.572281π-0.572281\pi
−0.225132 + 0.974328i 0.572281π0.572281\pi
308308 1540.00 0.284901
309309 0 0
310310 −1372.00 −0.251369
311311 3402.00 0.620288 0.310144 0.950690i 0.399623π-0.399623\pi
0.310144 + 0.950690i 0.399623π0.399623\pi
312312 0 0
313313 2310.00 0.417153 0.208577 0.978006i 0.433117π-0.433117\pi
0.208577 + 0.978006i 0.433117π0.433117\pi
314314 −2079.00 −0.373646
315315 0 0
316316 −6188.00 −1.10159
317317 257.000 0.0455349 0.0227674 0.999741i 0.492752π-0.492752\pi
0.0227674 + 0.999741i 0.492752π0.492752\pi
318318 0 0
319319 2486.00 0.436330
320320 1169.00 0.204216
321321 0 0
322322 −1620.00 −0.280370
323323 −1110.00 −0.191214
324324 0 0
325325 0 0
326326 1700.00 0.288817
327327 0 0
328328 4275.00 0.719657
329329 −4620.00 −0.774191
330330 0 0
331331 1028.00 0.170707 0.0853535 0.996351i 0.472798π-0.472798\pi
0.0853535 + 0.996351i 0.472798π0.472798\pi
332332 3626.00 0.599405
333333 0 0
334334 −3680.00 −0.602876
335335 −1414.00 −0.230612
336336 0 0
337337 2487.00 0.402005 0.201002 0.979591i 0.435580π-0.435580\pi
0.201002 + 0.979591i 0.435580π0.435580\pi
338338 0 0
339339 0 0
340340 −1813.00 −0.289187
341341 4312.00 0.684774
342342 0 0
343343 5860.00 0.922479
344344 3690.00 0.578347
345345 0 0
346346 −4146.00 −0.644192
347347 2850.00 0.440911 0.220455 0.975397i 0.429246π-0.429246\pi
0.220455 + 0.975397i 0.429246π0.429246\pi
348348 0 0
349349 −2018.00 −0.309516 −0.154758 0.987952i 0.549460π-0.549460\pi
−0.154758 + 0.987952i 0.549460π0.549460\pi
350350 760.000 0.116068
351351 0 0
352352 3542.00 0.536333
353353 5287.00 0.797163 0.398582 0.917133i 0.369503π-0.369503\pi
0.398582 + 0.917133i 0.369503π0.369503\pi
354354 0 0
355355 −7602.00 −1.13654
356356 1358.00 0.202174
357357 0 0
358358 −3674.00 −0.542394
359359 7278.00 1.06997 0.534983 0.844863i 0.320318π-0.320318\pi
0.534983 + 0.844863i 0.320318π0.320318\pi
360360 0 0
361361 −5959.00 −0.868786
362362 −3283.00 −0.476659
363363 0 0
364364 0 0
365365 5635.00 0.808080
366366 0 0
367367 −4202.00 −0.597664 −0.298832 0.954306i 0.596597π-0.596597\pi
−0.298832 + 0.954306i 0.596597π0.596597\pi
368368 6642.00 0.940865
369369 0 0
370370 −91.0000 −0.0127861
371371 −5370.00 −0.751473
372372 0 0
373373 −1583.00 −0.219744 −0.109872 0.993946i 0.535044π-0.535044\pi
−0.109872 + 0.993946i 0.535044π0.535044\pi
374374 −814.000 −0.112543
375375 0 0
376376 −6930.00 −0.950499
377377 0 0
378378 0 0
379379 −2052.00 −0.278111 −0.139056 0.990285i 0.544407π-0.544407\pi
−0.139056 + 0.990285i 0.544407π0.544407\pi
380380 1470.00 0.198446
381381 0 0
382382 596.000 0.0798273
383383 6872.00 0.916822 0.458411 0.888740i 0.348419π-0.348419\pi
0.458411 + 0.888740i 0.348419π0.348419\pi
384384 0 0
385385 1540.00 0.203859
386386 −393.000 −0.0518217
387387 0 0
388388 8414.00 1.10092
389389 11653.0 1.51884 0.759422 0.650598i 0.225482π-0.225482\pi
0.759422 + 0.650598i 0.225482π0.225482\pi
390390 0 0
391391 −5994.00 −0.775268
392392 3645.00 0.469644
393393 0 0
394394 3522.00 0.450345
395395 −6188.00 −0.788233
396396 0 0
397397 6134.00 0.775458 0.387729 0.921774i 0.373260π-0.373260\pi
0.387729 + 0.921774i 0.373260π0.373260\pi
398398 2018.00 0.254154
399399 0 0
400400 −3116.00 −0.389500
401401 10795.0 1.34433 0.672165 0.740401i 0.265364π-0.265364\pi
0.672165 + 0.740401i 0.265364π0.265364\pi
402402 0 0
403403 0 0
404404 −3003.00 −0.369814
405405 0 0
406406 −1130.00 −0.138130
407407 286.000 0.0348317
408408 0 0
409409 −8489.00 −1.02629 −0.513147 0.858301i 0.671520π-0.671520\pi
−0.513147 + 0.858301i 0.671520π0.671520\pi
410410 1995.00 0.240307
411411 0 0
412412 9114.00 1.08984
413413 5760.00 0.686274
414414 0 0
415415 3626.00 0.428900
416416 0 0
417417 0 0
418418 660.000 0.0772288
419419 −1496.00 −0.174426 −0.0872129 0.996190i 0.527796π-0.527796\pi
−0.0872129 + 0.996190i 0.527796π0.527796\pi
420420 0 0
421421 −11695.0 −1.35387 −0.676935 0.736043i 0.736692π-0.736692\pi
−0.676935 + 0.736043i 0.736692π0.736692\pi
422422 160.000 0.0184566
423423 0 0
424424 −8055.00 −0.922607
425425 2812.00 0.320946
426426 0 0
427427 6350.00 0.719668
428428 −9366.00 −1.05776
429429 0 0
430430 1722.00 0.193121
431431 −10590.0 −1.18353 −0.591766 0.806110i 0.701569π-0.701569\pi
−0.591766 + 0.806110i 0.701569π0.701569\pi
432432 0 0
433433 −13949.0 −1.54814 −0.774072 0.633098i 0.781783π-0.781783\pi
−0.774072 + 0.633098i 0.781783π0.781783\pi
434434 −1960.00 −0.216781
435435 0 0
436436 7238.00 0.795040
437437 4860.00 0.532003
438438 0 0
439439 −10726.0 −1.16611 −0.583057 0.812431i 0.698144π-0.698144\pi
−0.583057 + 0.812431i 0.698144π0.698144\pi
440440 2310.00 0.250284
441441 0 0
442442 0 0
443443 −16228.0 −1.74044 −0.870221 0.492662i 0.836024π-0.836024\pi
−0.870221 + 0.492662i 0.836024π0.836024\pi
444444 0 0
445445 1358.00 0.144664
446446 4072.00 0.432320
447447 0 0
448448 1670.00 0.176116
449449 −7538.00 −0.792294 −0.396147 0.918187i 0.629653π-0.629653\pi
−0.396147 + 0.918187i 0.629653π0.629653\pi
450450 0 0
451451 −6270.00 −0.654640
452452 7539.00 0.784524
453453 0 0
454454 5794.00 0.598956
455455 0 0
456456 0 0
457457 15539.0 1.59056 0.795278 0.606245i 0.207325π-0.207325\pi
0.795278 + 0.606245i 0.207325π0.207325\pi
458458 6482.00 0.661319
459459 0 0
460460 7938.00 0.804589
461461 −4811.00 −0.486053 −0.243027 0.970020i 0.578140π-0.578140\pi
−0.243027 + 0.970020i 0.578140π0.578140\pi
462462 0 0
463463 562.000 0.0564111 0.0282056 0.999602i 0.491021π-0.491021\pi
0.0282056 + 0.999602i 0.491021π0.491021\pi
464464 4633.00 0.463538
465465 0 0
466466 −6890.00 −0.684921
467467 −4914.00 −0.486922 −0.243461 0.969911i 0.578283π-0.578283\pi
−0.243461 + 0.969911i 0.578283π0.578283\pi
468468 0 0
469469 −2020.00 −0.198880
470470 −3234.00 −0.317390
471471 0 0
472472 8640.00 0.842560
473473 −5412.00 −0.526097
474474 0 0
475475 −2280.00 −0.220239
476476 −2590.00 −0.249396
477477 0 0
478478 −2466.00 −0.235967
479479 3600.00 0.343399 0.171700 0.985149i 0.445074π-0.445074\pi
0.171700 + 0.985149i 0.445074π0.445074\pi
480480 0 0
481481 0 0
482482 −3617.00 −0.341805
483483 0 0
484484 5929.00 0.556818
485485 8414.00 0.787753
486486 0 0
487487 −17130.0 −1.59391 −0.796955 0.604038i 0.793557π-0.793557\pi
−0.796955 + 0.604038i 0.793557π0.793557\pi
488488 9525.00 0.883558
489489 0 0
490490 1701.00 0.156823
491491 11838.0 1.08807 0.544034 0.839063i 0.316896π-0.316896\pi
0.544034 + 0.839063i 0.316896π0.316896\pi
492492 0 0
493493 −4181.00 −0.381953
494494 0 0
495495 0 0
496496 8036.00 0.727474
497497 −10860.0 −0.980156
498498 0 0
499499 8976.00 0.805252 0.402626 0.915364i 0.368097π-0.368097\pi
0.402626 + 0.915364i 0.368097π0.368097\pi
500500 −9849.00 −0.880921
501501 0 0
502502 −4860.00 −0.432096
503503 −1682.00 −0.149099 −0.0745494 0.997217i 0.523752π-0.523752\pi
−0.0745494 + 0.997217i 0.523752π0.523752\pi
504504 0 0
505505 −3003.00 −0.264617
506506 3564.00 0.313121
507507 0 0
508508 6916.00 0.604031
509509 −15167.0 −1.32076 −0.660379 0.750933i 0.729604π-0.729604\pi
−0.660379 + 0.750933i 0.729604π0.729604\pi
510510 0 0
511511 8050.00 0.696890
512512 11521.0 0.994455
513513 0 0
514514 −565.000 −0.0484846
515515 9114.00 0.779827
516516 0 0
517517 10164.0 0.864627
518518 −130.000 −0.0110268
519519 0 0
520520 0 0
521521 6783.00 0.570381 0.285191 0.958471i 0.407943π-0.407943\pi
0.285191 + 0.958471i 0.407943π0.407943\pi
522522 0 0
523523 −13918.0 −1.16366 −0.581828 0.813312i 0.697662π-0.697662\pi
−0.581828 + 0.813312i 0.697662π0.697662\pi
524524 3920.00 0.326805
525525 0 0
526526 498.000 0.0412810
527527 −7252.00 −0.599435
528528 0 0
529529 14077.0 1.15698
530530 −3759.00 −0.308076
531531 0 0
532532 2100.00 0.171140
533533 0 0
534534 0 0
535535 −9366.00 −0.756874
536536 −3030.00 −0.244172
537537 0 0
538538 −5546.00 −0.444433
539539 −5346.00 −0.427214
540540 0 0
541541 −1335.00 −0.106093 −0.0530463 0.998592i 0.516893π-0.516893\pi
−0.0530463 + 0.998592i 0.516893π0.516893\pi
542542 −2256.00 −0.178789
543543 0 0
544544 −5957.00 −0.469493
545545 7238.00 0.568884
546546 0 0
547547 −3806.00 −0.297501 −0.148750 0.988875i 0.547525π-0.547525\pi
−0.148750 + 0.988875i 0.547525π0.547525\pi
548548 −3633.00 −0.283201
549549 0 0
550550 −1672.00 −0.129626
551551 3390.00 0.262103
552552 0 0
553553 −8840.00 −0.679774
554554 2309.00 0.177076
555555 0 0
556556 2436.00 0.185808
557557 1905.00 0.144915 0.0724573 0.997372i 0.476916π-0.476916\pi
0.0724573 + 0.997372i 0.476916π0.476916\pi
558558 0 0
559559 0 0
560560 2870.00 0.216571
561561 0 0
562562 −5833.00 −0.437812
563563 4800.00 0.359318 0.179659 0.983729i 0.442501π-0.442501\pi
0.179659 + 0.983729i 0.442501π0.442501\pi
564564 0 0
565565 7539.00 0.561359
566566 1650.00 0.122535
567567 0 0
568568 −16290.0 −1.20337
569569 −14678.0 −1.08143 −0.540715 0.841206i 0.681846π-0.681846\pi
−0.540715 + 0.841206i 0.681846π0.681846\pi
570570 0 0
571571 −586.000 −0.0429481 −0.0214740 0.999769i 0.506836π-0.506836\pi
−0.0214740 + 0.999769i 0.506836π0.506836\pi
572572 0 0
573573 0 0
574574 2850.00 0.207242
575575 −12312.0 −0.892949
576576 0 0
577577 8939.00 0.644949 0.322474 0.946578i 0.395485π-0.395485\pi
0.322474 + 0.946578i 0.395485π0.395485\pi
578578 −3544.00 −0.255036
579579 0 0
580580 5537.00 0.396399
581581 5180.00 0.369884
582582 0 0
583583 11814.0 0.839255
584584 12075.0 0.855594
585585 0 0
586586 −2991.00 −0.210848
587587 13792.0 0.969773 0.484887 0.874577i 0.338861π-0.338861\pi
0.484887 + 0.874577i 0.338861π0.338861\pi
588588 0 0
589589 5880.00 0.411343
590590 4032.00 0.281347
591591 0 0
592592 533.000 0.0370037
593593 −9569.00 −0.662650 −0.331325 0.943517i 0.607496π-0.607496\pi
−0.331325 + 0.943517i 0.607496π0.607496\pi
594594 0 0
595595 −2590.00 −0.178453
596596 −4515.00 −0.310305
597597 0 0
598598 0 0
599599 5192.00 0.354156 0.177078 0.984197i 0.443336π-0.443336\pi
0.177078 + 0.984197i 0.443336π0.443336\pi
600600 0 0
601601 −3677.00 −0.249564 −0.124782 0.992184i 0.539823π-0.539823\pi
−0.124782 + 0.992184i 0.539823π0.539823\pi
602602 2460.00 0.166548
603603 0 0
604604 −20398.0 −1.37414
605605 5929.00 0.398427
606606 0 0
607607 −10960.0 −0.732871 −0.366435 0.930443i 0.619422π-0.619422\pi
−0.366435 + 0.930443i 0.619422π0.619422\pi
608608 4830.00 0.322175
609609 0 0
610610 4445.00 0.295037
611611 0 0
612612 0 0
613613 −26027.0 −1.71488 −0.857439 0.514585i 0.827946π-0.827946\pi
−0.857439 + 0.514585i 0.827946π0.827946\pi
614614 −2422.00 −0.159192
615615 0 0
616616 3300.00 0.215845
617617 −17681.0 −1.15366 −0.576832 0.816863i 0.695711π-0.695711\pi
−0.576832 + 0.816863i 0.695711π0.695711\pi
618618 0 0
619619 3192.00 0.207265 0.103633 0.994616i 0.466953π-0.466953\pi
0.103633 + 0.994616i 0.466953π0.466953\pi
620620 9604.00 0.622106
621621 0 0
622622 3402.00 0.219305
623623 1940.00 0.124758
624624 0 0
625625 −349.000 −0.0223360
626626 2310.00 0.147486
627627 0 0
628628 14553.0 0.924726
629629 −481.000 −0.0304908
630630 0 0
631631 7580.00 0.478217 0.239109 0.970993i 0.423145π-0.423145\pi
0.239109 + 0.970993i 0.423145π0.423145\pi
632632 −13260.0 −0.834580
633633 0 0
634634 257.000 0.0160990
635635 6916.00 0.432210
636636 0 0
637637 0 0
638638 2486.00 0.154266
639639 0 0
640640 10185.0 0.629059
641641 27707.0 1.70727 0.853635 0.520871i 0.174393π-0.174393\pi
0.853635 + 0.520871i 0.174393π0.174393\pi
642642 0 0
643643 11216.0 0.687894 0.343947 0.938989i 0.388236π-0.388236\pi
0.343947 + 0.938989i 0.388236π0.388236\pi
644644 11340.0 0.693880
645645 0 0
646646 −1110.00 −0.0676043
647647 2536.00 0.154097 0.0770483 0.997027i 0.475450π-0.475450\pi
0.0770483 + 0.997027i 0.475450π0.475450\pi
648648 0 0
649649 −12672.0 −0.766440
650650 0 0
651651 0 0
652652 −11900.0 −0.714785
653653 −17730.0 −1.06252 −0.531262 0.847207i 0.678282π-0.678282\pi
−0.531262 + 0.847207i 0.678282π0.678282\pi
654654 0 0
655655 3920.00 0.233843
656656 −11685.0 −0.695461
657657 0 0
658658 −4620.00 −0.273718
659659 −18920.0 −1.11839 −0.559195 0.829036i 0.688890π-0.688890\pi
−0.559195 + 0.829036i 0.688890π0.688890\pi
660660 0 0
661661 5241.00 0.308398 0.154199 0.988040i 0.450720π-0.450720\pi
0.154199 + 0.988040i 0.450720π0.450720\pi
662662 1028.00 0.0603540
663663 0 0
664664 7770.00 0.454118
665665 2100.00 0.122458
666666 0 0
667667 18306.0 1.06269
668668 25760.0 1.49204
669669 0 0
670670 −1414.00 −0.0815337
671671 −13970.0 −0.803735
672672 0 0
673673 20467.0 1.17228 0.586140 0.810210i 0.300647π-0.300647\pi
0.586140 + 0.810210i 0.300647π0.300647\pi
674674 2487.00 0.142130
675675 0 0
676676 0 0
677677 70.0000 0.00397388 0.00198694 0.999998i 0.499368π-0.499368\pi
0.00198694 + 0.999998i 0.499368π0.499368\pi
678678 0 0
679679 12020.0 0.679360
680680 −3885.00 −0.219093
681681 0 0
682682 4312.00 0.242104
683683 −6432.00 −0.360342 −0.180171 0.983635i 0.557665π-0.557665\pi
−0.180171 + 0.983635i 0.557665π0.557665\pi
684684 0 0
685685 −3633.00 −0.202642
686686 5860.00 0.326146
687687 0 0
688688 −10086.0 −0.558903
689689 0 0
690690 0 0
691691 −6666.00 −0.366985 −0.183492 0.983021i 0.558740π-0.558740\pi
−0.183492 + 0.983021i 0.558740π0.558740\pi
692692 29022.0 1.59429
693693 0 0
694694 2850.00 0.155885
695695 2436.00 0.132954
696696 0 0
697697 10545.0 0.573056
698698 −2018.00 −0.109430
699699 0 0
700700 −5320.00 −0.287253
701701 14054.0 0.757221 0.378611 0.925556i 0.376402π-0.376402\pi
0.378611 + 0.925556i 0.376402π0.376402\pi
702702 0 0
703703 390.000 0.0209234
704704 −3674.00 −0.196689
705705 0 0
706706 5287.00 0.281840
707707 −4290.00 −0.228207
708708 0 0
709709 −71.0000 −0.00376088 −0.00188044 0.999998i 0.500599π-0.500599\pi
−0.00188044 + 0.999998i 0.500599π0.500599\pi
710710 −7602.00 −0.401828
711711 0 0
712712 2910.00 0.153170
713713 31752.0 1.66777
714714 0 0
715715 0 0
716716 25718.0 1.34236
717717 0 0
718718 7278.00 0.378290
719719 −3936.00 −0.204156 −0.102078 0.994776i 0.532549π-0.532549\pi
−0.102078 + 0.994776i 0.532549π0.532549\pi
720720 0 0
721721 13020.0 0.672524
722722 −5959.00 −0.307162
723723 0 0
724724 22981.0 1.17967
725725 −8588.00 −0.439931
726726 0 0
727727 34202.0 1.74482 0.872409 0.488777i 0.162557π-0.162557\pi
0.872409 + 0.488777i 0.162557π0.162557\pi
728728 0 0
729729 0 0
730730 5635.00 0.285700
731731 9102.00 0.460533
732732 0 0
733733 −27363.0 −1.37882 −0.689410 0.724371i 0.742130π-0.742130\pi
−0.689410 + 0.724371i 0.742130π0.742130\pi
734734 −4202.00 −0.211306
735735 0 0
736736 26082.0 1.30624
737737 4444.00 0.222112
738738 0 0
739739 21776.0 1.08396 0.541978 0.840393i 0.317676π-0.317676\pi
0.541978 + 0.840393i 0.317676π0.317676\pi
740740 637.000 0.0316440
741741 0 0
742742 −5370.00 −0.265686
743743 −2484.00 −0.122650 −0.0613251 0.998118i 0.519533π-0.519533\pi
−0.0613251 + 0.998118i 0.519533π0.519533\pi
744744 0 0
745745 −4515.00 −0.222036
746746 −1583.00 −0.0776914
747747 0 0
748748 5698.00 0.278529
749749 −13380.0 −0.652730
750750 0 0
751751 32906.0 1.59888 0.799439 0.600748i 0.205130π-0.205130\pi
0.799439 + 0.600748i 0.205130π0.205130\pi
752752 18942.0 0.918542
753753 0 0
754754 0 0
755755 −20398.0 −0.983257
756756 0 0
757757 −3914.00 −0.187922 −0.0939609 0.995576i 0.529953π-0.529953\pi
−0.0939609 + 0.995576i 0.529953π0.529953\pi
758758 −2052.00 −0.0983272
759759 0 0
760760 3150.00 0.150345
761761 33038.0 1.57375 0.786877 0.617110i 0.211697π-0.211697\pi
0.786877 + 0.617110i 0.211697π0.211697\pi
762762 0 0
763763 10340.0 0.490607
764764 −4172.00 −0.197562
765765 0 0
766766 6872.00 0.324145
767767 0 0
768768 0 0
769769 −17586.0 −0.824665 −0.412332 0.911033i 0.635286π-0.635286\pi
−0.412332 + 0.911033i 0.635286π0.635286\pi
770770 1540.00 0.0720750
771771 0 0
772772 2751.00 0.128252
773773 −18314.0 −0.852146 −0.426073 0.904689i 0.640103π-0.640103\pi
−0.426073 + 0.904689i 0.640103π0.640103\pi
774774 0 0
775775 −14896.0 −0.690426
776776 18030.0 0.834071
777777 0 0
778778 11653.0 0.536993
779779 −8550.00 −0.393242
780780 0 0
781781 23892.0 1.09465
782782 −5994.00 −0.274098
783783 0 0
784784 −9963.00 −0.453854
785785 14553.0 0.661680
786786 0 0
787787 −42068.0 −1.90542 −0.952708 0.303888i 0.901715π-0.901715\pi
−0.952708 + 0.303888i 0.901715π0.901715\pi
788788 −24654.0 −1.11455
789789 0 0
790790 −6188.00 −0.278682
791791 10770.0 0.484118
792792 0 0
793793 0 0
794794 6134.00 0.274166
795795 0 0
796796 −14126.0 −0.628998
797797 4282.00 0.190309 0.0951545 0.995463i 0.469665π-0.469665\pi
0.0951545 + 0.995463i 0.469665π0.469665\pi
798798 0 0
799799 −17094.0 −0.756874
800800 −12236.0 −0.540760
801801 0 0
802802 10795.0 0.475293
803803 −17710.0 −0.778297
804804 0 0
805805 11340.0 0.496500
806806 0 0
807807 0 0
808808 −6435.00 −0.280176
809809 −40221.0 −1.74795 −0.873977 0.485967i 0.838468π-0.838468\pi
−0.873977 + 0.485967i 0.838468π0.838468\pi
810810 0 0
811811 −7084.00 −0.306724 −0.153362 0.988170i 0.549010π-0.549010\pi
−0.153362 + 0.988170i 0.549010π0.549010\pi
812812 7910.00 0.341855
813813 0 0
814814 286.000 0.0123149
815815 −11900.0 −0.511459
816816 0 0
817817 −7380.00 −0.316026
818818 −8489.00 −0.362850
819819 0 0
820820 −13965.0 −0.594730
821821 −17338.0 −0.737028 −0.368514 0.929622i 0.620133π-0.620133\pi
−0.368514 + 0.929622i 0.620133π0.620133\pi
822822 0 0
823823 35496.0 1.50342 0.751709 0.659495i 0.229230π-0.229230\pi
0.751709 + 0.659495i 0.229230π0.229230\pi
824824 19530.0 0.825679
825825 0 0
826826 5760.00 0.242634
827827 14992.0 0.630378 0.315189 0.949029i 0.397932π-0.397932\pi
0.315189 + 0.949029i 0.397932π0.397932\pi
828828 0 0
829829 −20659.0 −0.865521 −0.432760 0.901509i 0.642460π-0.642460\pi
−0.432760 + 0.901509i 0.642460π0.642460\pi
830830 3626.00 0.151639
831831 0 0
832832 0 0
833833 8991.00 0.373973
834834 0 0
835835 25760.0 1.06762
836836 −4620.00 −0.191132
837837 0 0
838838 −1496.00 −0.0616688
839839 −28716.0 −1.18163 −0.590814 0.806808i 0.701193π-0.701193\pi
−0.590814 + 0.806808i 0.701193π0.701193\pi
840840 0 0
841841 −11620.0 −0.476444
842842 −11695.0 −0.478665
843843 0 0
844844 −1120.00 −0.0456777
845845 0 0
846846 0 0
847847 8470.00 0.343604
848848 22017.0 0.891588
849849 0 0
850850 2812.00 0.113472
851851 2106.00 0.0848328
852852 0 0
853853 13377.0 0.536952 0.268476 0.963286i 0.413480π-0.413480\pi
0.268476 + 0.963286i 0.413480π0.413480\pi
854854 6350.00 0.254441
855855 0 0
856856 −20070.0 −0.801377
857857 27419.0 1.09290 0.546450 0.837492i 0.315979π-0.315979\pi
0.546450 + 0.837492i 0.315979π0.315979\pi
858858 0 0
859859 2422.00 0.0962021 0.0481010 0.998842i 0.484683π-0.484683\pi
0.0481010 + 0.998842i 0.484683π0.484683\pi
860860 −12054.0 −0.477951
861861 0 0
862862 −10590.0 −0.418442
863863 34522.0 1.36169 0.680847 0.732425i 0.261612π-0.261612\pi
0.680847 + 0.732425i 0.261612π0.261612\pi
864864 0 0
865865 29022.0 1.14078
866866 −13949.0 −0.547351
867867 0 0
868868 13720.0 0.536506
869869 19448.0 0.759181
870870 0 0
871871 0 0
872872 15510.0 0.602334
873873 0 0
874874 4860.00 0.188091
875875 −14070.0 −0.543603
876876 0 0
877877 13733.0 0.528769 0.264385 0.964417i 0.414831π-0.414831\pi
0.264385 + 0.964417i 0.414831π0.414831\pi
878878 −10726.0 −0.412284
879879 0 0
880880 −6314.00 −0.241869
881881 22759.0 0.870341 0.435170 0.900348i 0.356688π-0.356688\pi
0.435170 + 0.900348i 0.356688π0.356688\pi
882882 0 0
883883 −2168.00 −0.0826263 −0.0413131 0.999146i 0.513154π-0.513154\pi
−0.0413131 + 0.999146i 0.513154π0.513154\pi
884884 0 0
885885 0 0
886886 −16228.0 −0.615339
887887 −15888.0 −0.601428 −0.300714 0.953714i 0.597225π-0.597225\pi
−0.300714 + 0.953714i 0.597225π0.597225\pi
888888 0 0
889889 9880.00 0.372739
890890 1358.00 0.0511464
891891 0 0
892892 −28504.0 −1.06994
893893 13860.0 0.519381
894894 0 0
895895 25718.0 0.960512
896896 14550.0 0.542502
897897 0 0
898898 −7538.00 −0.280118
899899 22148.0 0.821665
900900 0 0
901901 −19869.0 −0.734664
902902 −6270.00 −0.231450
903903 0 0
904904 16155.0 0.594366
905905 22981.0 0.844104
906906 0 0
907907 −11628.0 −0.425691 −0.212845 0.977086i 0.568273π-0.568273\pi
−0.212845 + 0.977086i 0.568273π0.568273\pi
908908 −40558.0 −1.48234
909909 0 0
910910 0 0
911911 12584.0 0.457658 0.228829 0.973467i 0.426510π-0.426510\pi
0.228829 + 0.973467i 0.426510π0.426510\pi
912912 0 0
913913 −11396.0 −0.413092
914914 15539.0 0.562346
915915 0 0
916916 −45374.0 −1.63668
917917 5600.00 0.201667
918918 0 0
919919 17184.0 0.616809 0.308405 0.951255i 0.400205π-0.400205\pi
0.308405 + 0.951255i 0.400205π0.400205\pi
920920 17010.0 0.609569
921921 0 0
922922 −4811.00 −0.171846
923923 0 0
924924 0 0
925925 −988.000 −0.0351192
926926 562.000 0.0199443
927927 0 0
928928 18193.0 0.643550
929929 −12777.0 −0.451238 −0.225619 0.974216i 0.572440π-0.572440\pi
−0.225619 + 0.974216i 0.572440π0.572440\pi
930930 0 0
931931 −7290.00 −0.256627
932932 48230.0 1.69509
933933 0 0
934934 −4914.00 −0.172153
935935 5698.00 0.199299
936936 0 0
937937 9191.00 0.320445 0.160222 0.987081i 0.448779π-0.448779\pi
0.160222 + 0.987081i 0.448779π0.448779\pi
938938 −2020.00 −0.0703149
939939 0 0
940940 22638.0 0.785500
941941 −50498.0 −1.74940 −0.874701 0.484662i 0.838942π-0.838942\pi
−0.874701 + 0.484662i 0.838942π0.838942\pi
942942 0 0
943943 −46170.0 −1.59438
944944 −23616.0 −0.814232
945945 0 0
946946 −5412.00 −0.186003
947947 −1560.00 −0.0535303 −0.0267651 0.999642i 0.508521π-0.508521\pi
−0.0267651 + 0.999642i 0.508521π0.508521\pi
948948 0 0
949949 0 0
950950 −2280.00 −0.0778663
951951 0 0
952952 −5550.00 −0.188946
953953 21498.0 0.730733 0.365366 0.930864i 0.380944π-0.380944\pi
0.365366 + 0.930864i 0.380944π0.380944\pi
954954 0 0
955955 −4172.00 −0.141364
956956 17262.0 0.583988
957957 0 0
958958 3600.00 0.121410
959959 −5190.00 −0.174759
960960 0 0
961961 8625.00 0.289517
962962 0 0
963963 0 0
964964 25319.0 0.845923
965965 2751.00 0.0917698
966966 0 0
967967 −418.000 −0.0139007 −0.00695035 0.999976i 0.502212π-0.502212\pi
−0.00695035 + 0.999976i 0.502212π0.502212\pi
968968 12705.0 0.421853
969969 0 0
970970 8414.00 0.278513
971971 −18132.0 −0.599262 −0.299631 0.954055i 0.596864π-0.596864\pi
−0.299631 + 0.954055i 0.596864π0.596864\pi
972972 0 0
973973 3480.00 0.114659
974974 −17130.0 −0.563532
975975 0 0
976976 −26035.0 −0.853853
977977 −12501.0 −0.409358 −0.204679 0.978829i 0.565615π-0.565615\pi
−0.204679 + 0.978829i 0.565615π0.565615\pi
978978 0 0
979979 −4268.00 −0.139332
980980 −11907.0 −0.388118
981981 0 0
982982 11838.0 0.384690
983983 43708.0 1.41818 0.709089 0.705119i 0.249106π-0.249106\pi
0.709089 + 0.705119i 0.249106π0.249106\pi
984984 0 0
985985 −24654.0 −0.797504
986986 −4181.00 −0.135041
987987 0 0
988988 0 0
989989 −39852.0 −1.28131
990990 0 0
991991 −39614.0 −1.26981 −0.634904 0.772591i 0.718960π-0.718960\pi
−0.634904 + 0.772591i 0.718960π0.718960\pi
992992 31556.0 1.00998
993993 0 0
994994 −10860.0 −0.346538
995995 −14126.0 −0.450075
996996 0 0
997997 −36503.0 −1.15954 −0.579770 0.814780i 0.696858π-0.696858\pi
−0.579770 + 0.814780i 0.696858π0.696858\pi
998998 8976.00 0.284700
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 1521.4.a.h.1.1 1
3.2 odd 2 507.4.a.b.1.1 1
13.3 even 3 117.4.g.a.100.1 2
13.9 even 3 117.4.g.a.55.1 2
13.12 even 2 1521.4.a.e.1.1 1
39.5 even 4 507.4.b.d.337.2 2
39.8 even 4 507.4.b.d.337.1 2
39.29 odd 6 39.4.e.b.22.1 yes 2
39.35 odd 6 39.4.e.b.16.1 2
39.38 odd 2 507.4.a.d.1.1 1
156.35 even 6 624.4.q.c.289.1 2
156.107 even 6 624.4.q.c.529.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.e.b.16.1 2 39.35 odd 6
39.4.e.b.22.1 yes 2 39.29 odd 6
117.4.g.a.55.1 2 13.9 even 3
117.4.g.a.100.1 2 13.3 even 3
507.4.a.b.1.1 1 3.2 odd 2
507.4.a.d.1.1 1 39.38 odd 2
507.4.b.d.337.1 2 39.8 even 4
507.4.b.d.337.2 2 39.5 even 4
624.4.q.c.289.1 2 156.35 even 6
624.4.q.c.529.1 2 156.107 even 6
1521.4.a.e.1.1 1 13.12 even 2
1521.4.a.h.1.1 1 1.1 even 1 trivial