Properties

Label 882.4.a.f.1.1
Level 882882
Weight 44
Character 882.1
Self dual yes
Analytic conductor 52.04052.040
Analytic rank 11
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] = [882,4,Mod(1,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, 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("882.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 882=23272 882 = 2 \cdot 3^{2} \cdot 7^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 882.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: 52.039684625152.0396846251
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 14)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 882.1

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) == q2.00000q2+4.00000q4+9.00000q58.00000q818.0000q10+57.0000q1170.0000q13+16.0000q1651.0000q17+5.00000q19+36.0000q20114.000q2269.0000q2344.0000q25+140.000q26114.000q29+23.0000q3132.0000q32+102.000q34253.000q3710.0000q3872.0000q40+42.0000q41124.000q43+228.000q44+138.000q46201.000q47+88.0000q50280.000q52+393.000q53+513.000q55+228.000q58219.000q59709.000q6146.0000q62+64.0000q64630.000q65+419.000q67204.000q68+96.0000q71313.000q73+506.000q74+20.0000q76+461.000q79+144.000q8084.0000q82+588.000q83459.000q85+248.000q86456.000q88+1017.00q89276.000q92+402.000q94+45.0000q951834.00q97+O(q100)q-2.00000 q^{2} +4.00000 q^{4} +9.00000 q^{5} -8.00000 q^{8} -18.0000 q^{10} +57.0000 q^{11} -70.0000 q^{13} +16.0000 q^{16} -51.0000 q^{17} +5.00000 q^{19} +36.0000 q^{20} -114.000 q^{22} -69.0000 q^{23} -44.0000 q^{25} +140.000 q^{26} -114.000 q^{29} +23.0000 q^{31} -32.0000 q^{32} +102.000 q^{34} -253.000 q^{37} -10.0000 q^{38} -72.0000 q^{40} +42.0000 q^{41} -124.000 q^{43} +228.000 q^{44} +138.000 q^{46} -201.000 q^{47} +88.0000 q^{50} -280.000 q^{52} +393.000 q^{53} +513.000 q^{55} +228.000 q^{58} -219.000 q^{59} -709.000 q^{61} -46.0000 q^{62} +64.0000 q^{64} -630.000 q^{65} +419.000 q^{67} -204.000 q^{68} +96.0000 q^{71} -313.000 q^{73} +506.000 q^{74} +20.0000 q^{76} +461.000 q^{79} +144.000 q^{80} -84.0000 q^{82} +588.000 q^{83} -459.000 q^{85} +248.000 q^{86} -456.000 q^{88} +1017.00 q^{89} -276.000 q^{92} +402.000 q^{94} +45.0000 q^{95} -1834.00 q^{97} +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 −0.707107
33 0 0
44 4.00000 0.500000
55 9.00000 0.804984 0.402492 0.915423i 0.368144π-0.368144\pi
0.402492 + 0.915423i 0.368144π0.368144\pi
66 0 0
77 0 0
88 −8.00000 −0.353553
99 0 0
1010 −18.0000 −0.569210
1111 57.0000 1.56238 0.781188 0.624295i 0.214614π-0.214614\pi
0.781188 + 0.624295i 0.214614π0.214614\pi
1212 0 0
1313 −70.0000 −1.49342 −0.746712 0.665148i 0.768369π-0.768369\pi
−0.746712 + 0.665148i 0.768369π0.768369\pi
1414 0 0
1515 0 0
1616 16.0000 0.250000
1717 −51.0000 −0.727607 −0.363803 0.931476i 0.618522π-0.618522\pi
−0.363803 + 0.931476i 0.618522π0.618522\pi
1818 0 0
1919 5.00000 0.0603726 0.0301863 0.999544i 0.490390π-0.490390\pi
0.0301863 + 0.999544i 0.490390π0.490390\pi
2020 36.0000 0.402492
2121 0 0
2222 −114.000 −1.10477
2323 −69.0000 −0.625543 −0.312772 0.949828i 0.601257π-0.601257\pi
−0.312772 + 0.949828i 0.601257π0.601257\pi
2424 0 0
2525 −44.0000 −0.352000
2626 140.000 1.05601
2727 0 0
2828 0 0
2929 −114.000 −0.729975 −0.364987 0.931012i 0.618927π-0.618927\pi
−0.364987 + 0.931012i 0.618927π0.618927\pi
3030 0 0
3131 23.0000 0.133256 0.0666278 0.997778i 0.478776π-0.478776\pi
0.0666278 + 0.997778i 0.478776π0.478776\pi
3232 −32.0000 −0.176777
3333 0 0
3434 102.000 0.514496
3535 0 0
3636 0 0
3737 −253.000 −1.12413 −0.562067 0.827092i 0.689994π-0.689994\pi
−0.562067 + 0.827092i 0.689994π0.689994\pi
3838 −10.0000 −0.0426898
3939 0 0
4040 −72.0000 −0.284605
4141 42.0000 0.159983 0.0799914 0.996796i 0.474511π-0.474511\pi
0.0799914 + 0.996796i 0.474511π0.474511\pi
4242 0 0
4343 −124.000 −0.439763 −0.219882 0.975527i 0.570567π-0.570567\pi
−0.219882 + 0.975527i 0.570567π0.570567\pi
4444 228.000 0.781188
4545 0 0
4646 138.000 0.442326
4747 −201.000 −0.623806 −0.311903 0.950114i 0.600966π-0.600966\pi
−0.311903 + 0.950114i 0.600966π0.600966\pi
4848 0 0
4949 0 0
5050 88.0000 0.248902
5151 0 0
5252 −280.000 −0.746712
5353 393.000 1.01854 0.509271 0.860606i 0.329915π-0.329915\pi
0.509271 + 0.860606i 0.329915π0.329915\pi
5454 0 0
5555 513.000 1.25769
5656 0 0
5757 0 0
5858 228.000 0.516170
5959 −219.000 −0.483244 −0.241622 0.970371i 0.577679π-0.577679\pi
−0.241622 + 0.970371i 0.577679π0.577679\pi
6060 0 0
6161 −709.000 −1.48817 −0.744083 0.668087i 0.767113π-0.767113\pi
−0.744083 + 0.668087i 0.767113π0.767113\pi
6262 −46.0000 −0.0942259
6363 0 0
6464 64.0000 0.125000
6565 −630.000 −1.20218
6666 0 0
6767 419.000 0.764015 0.382007 0.924159i 0.375233π-0.375233\pi
0.382007 + 0.924159i 0.375233π0.375233\pi
6868 −204.000 −0.363803
6969 0 0
7070 0 0
7171 96.0000 0.160466 0.0802331 0.996776i 0.474434π-0.474434\pi
0.0802331 + 0.996776i 0.474434π0.474434\pi
7272 0 0
7373 −313.000 −0.501834 −0.250917 0.968009i 0.580732π-0.580732\pi
−0.250917 + 0.968009i 0.580732π0.580732\pi
7474 506.000 0.794883
7575 0 0
7676 20.0000 0.0301863
7777 0 0
7878 0 0
7979 461.000 0.656539 0.328269 0.944584i 0.393535π-0.393535\pi
0.328269 + 0.944584i 0.393535π0.393535\pi
8080 144.000 0.201246
8181 0 0
8282 −84.0000 −0.113125
8383 588.000 0.777607 0.388804 0.921321i 0.372888π-0.372888\pi
0.388804 + 0.921321i 0.372888π0.372888\pi
8484 0 0
8585 −459.000 −0.585712
8686 248.000 0.310960
8787 0 0
8888 −456.000 −0.552384
8989 1017.00 1.21126 0.605628 0.795748i 0.292922π-0.292922\pi
0.605628 + 0.795748i 0.292922π0.292922\pi
9090 0 0
9191 0 0
9292 −276.000 −0.312772
9393 0 0
9494 402.000 0.441097
9595 45.0000 0.0485990
9696 0 0
9797 −1834.00 −1.91974 −0.959868 0.280451i 0.909516π-0.909516\pi
−0.959868 + 0.280451i 0.909516π0.909516\pi
9898 0 0
9999 0 0
100100 −176.000 −0.176000
101101 285.000 0.280778 0.140389 0.990096i 0.455165π-0.455165\pi
0.140389 + 0.990096i 0.455165π0.455165\pi
102102 0 0
103103 −499.000 −0.477359 −0.238679 0.971098i 0.576714π-0.576714\pi
−0.238679 + 0.971098i 0.576714π0.576714\pi
104104 560.000 0.528005
105105 0 0
106106 −786.000 −0.720218
107107 1107.00 1.00017 0.500083 0.865978i 0.333303π-0.333303\pi
0.500083 + 0.865978i 0.333303π0.333303\pi
108108 0 0
109109 923.000 0.811077 0.405538 0.914078i 0.367084π-0.367084\pi
0.405538 + 0.914078i 0.367084π0.367084\pi
110110 −1026.00 −0.889321
111111 0 0
112112 0 0
113113 −1542.00 −1.28371 −0.641855 0.766826i 0.721835π-0.721835\pi
−0.641855 + 0.766826i 0.721835π0.721835\pi
114114 0 0
115115 −621.000 −0.503553
116116 −456.000 −0.364987
117117 0 0
118118 438.000 0.341705
119119 0 0
120120 0 0
121121 1918.00 1.44102
122122 1418.00 1.05229
123123 0 0
124124 92.0000 0.0666278
125125 −1521.00 −1.08834
126126 0 0
127127 −2056.00 −1.43654 −0.718270 0.695765i 0.755066π-0.755066\pi
−0.718270 + 0.695765i 0.755066π0.755066\pi
128128 −128.000 −0.0883883
129129 0 0
130130 1260.00 0.850072
131131 −2049.00 −1.36658 −0.683290 0.730147i 0.739451π-0.739451\pi
−0.683290 + 0.730147i 0.739451π0.739451\pi
132132 0 0
133133 0 0
134134 −838.000 −0.540240
135135 0 0
136136 408.000 0.257248
137137 141.000 0.0879302 0.0439651 0.999033i 0.486001π-0.486001\pi
0.0439651 + 0.999033i 0.486001π0.486001\pi
138138 0 0
139139 1484.00 0.905548 0.452774 0.891625i 0.350434π-0.350434\pi
0.452774 + 0.891625i 0.350434π0.350434\pi
140140 0 0
141141 0 0
142142 −192.000 −0.113467
143143 −3990.00 −2.33329
144144 0 0
145145 −1026.00 −0.587618
146146 626.000 0.354850
147147 0 0
148148 −1012.00 −0.562067
149149 57.0000 0.0313397 0.0156699 0.999877i 0.495012π-0.495012\pi
0.0156699 + 0.999877i 0.495012π0.495012\pi
150150 0 0
151151 839.000 0.452165 0.226082 0.974108i 0.427408π-0.427408\pi
0.226082 + 0.974108i 0.427408π0.427408\pi
152152 −40.0000 −0.0213449
153153 0 0
154154 0 0
155155 207.000 0.107269
156156 0 0
157157 −2833.00 −1.44011 −0.720057 0.693915i 0.755885π-0.755885\pi
−0.720057 + 0.693915i 0.755885π0.755885\pi
158158 −922.000 −0.464243
159159 0 0
160160 −288.000 −0.142302
161161 0 0
162162 0 0
163163 −2311.00 −1.11050 −0.555250 0.831684i 0.687377π-0.687377\pi
−0.555250 + 0.831684i 0.687377π0.687377\pi
164164 168.000 0.0799914
165165 0 0
166166 −1176.00 −0.549851
167167 −1260.00 −0.583843 −0.291921 0.956442i 0.594295π-0.594295\pi
−0.291921 + 0.956442i 0.594295π0.594295\pi
168168 0 0
169169 2703.00 1.23031
170170 918.000 0.414161
171171 0 0
172172 −496.000 −0.219882
173173 −3267.00 −1.43575 −0.717877 0.696170i 0.754886π-0.754886\pi
−0.717877 + 0.696170i 0.754886π0.754886\pi
174174 0 0
175175 0 0
176176 912.000 0.390594
177177 0 0
178178 −2034.00 −0.856487
179179 −1287.00 −0.537402 −0.268701 0.963224i 0.586594π-0.586594\pi
−0.268701 + 0.963224i 0.586594π0.586594\pi
180180 0 0
181181 −2674.00 −1.09810 −0.549052 0.835788i 0.685011π-0.685011\pi
−0.549052 + 0.835788i 0.685011π0.685011\pi
182182 0 0
183183 0 0
184184 552.000 0.221163
185185 −2277.00 −0.904910
186186 0 0
187187 −2907.00 −1.13680
188188 −804.000 −0.311903
189189 0 0
190190 −90.0000 −0.0343647
191191 −4185.00 −1.58542 −0.792712 0.609596i 0.791332π-0.791332\pi
−0.792712 + 0.609596i 0.791332π0.791332\pi
192192 0 0
193193 −85.0000 −0.0317017 −0.0158509 0.999874i 0.505046π-0.505046\pi
−0.0158509 + 0.999874i 0.505046π0.505046\pi
194194 3668.00 1.35746
195195 0 0
196196 0 0
197197 390.000 0.141047 0.0705237 0.997510i 0.477533π-0.477533\pi
0.0705237 + 0.997510i 0.477533π0.477533\pi
198198 0 0
199199 −2833.00 −1.00918 −0.504588 0.863360i 0.668356π-0.668356\pi
−0.504588 + 0.863360i 0.668356π0.668356\pi
200200 352.000 0.124451
201201 0 0
202202 −570.000 −0.198540
203203 0 0
204204 0 0
205205 378.000 0.128784
206206 998.000 0.337543
207207 0 0
208208 −1120.00 −0.373356
209209 285.000 0.0943247
210210 0 0
211211 −124.000 −0.0404574 −0.0202287 0.999795i 0.506439π-0.506439\pi
−0.0202287 + 0.999795i 0.506439π0.506439\pi
212212 1572.00 0.509271
213213 0 0
214214 −2214.00 −0.707224
215215 −1116.00 −0.354003
216216 0 0
217217 0 0
218218 −1846.00 −0.573518
219219 0 0
220220 2052.00 0.628845
221221 3570.00 1.08663
222222 0 0
223223 56.0000 0.0168163 0.00840816 0.999965i 0.497324π-0.497324\pi
0.00840816 + 0.999965i 0.497324π0.497324\pi
224224 0 0
225225 0 0
226226 3084.00 0.907720
227227 3057.00 0.893834 0.446917 0.894576i 0.352522π-0.352522\pi
0.446917 + 0.894576i 0.352522π0.352522\pi
228228 0 0
229229 −961.000 −0.277313 −0.138656 0.990341i 0.544278π-0.544278\pi
−0.138656 + 0.990341i 0.544278π0.544278\pi
230230 1242.00 0.356065
231231 0 0
232232 912.000 0.258085
233233 2829.00 0.795425 0.397712 0.917510i 0.369804π-0.369804\pi
0.397712 + 0.917510i 0.369804π0.369804\pi
234234 0 0
235235 −1809.00 −0.502154
236236 −876.000 −0.241622
237237 0 0
238238 0 0
239239 3540.00 0.958090 0.479045 0.877790i 0.340983π-0.340983\pi
0.479045 + 0.877790i 0.340983π0.340983\pi
240240 0 0
241241 5231.00 1.39817 0.699084 0.715040i 0.253591π-0.253591\pi
0.699084 + 0.715040i 0.253591π0.253591\pi
242242 −3836.00 −1.01896
243243 0 0
244244 −2836.00 −0.744083
245245 0 0
246246 0 0
247247 −350.000 −0.0901618
248248 −184.000 −0.0471130
249249 0 0
250250 3042.00 0.769572
251251 −5040.00 −1.26742 −0.633709 0.773571i 0.718468π-0.718468\pi
−0.633709 + 0.773571i 0.718468π0.718468\pi
252252 0 0
253253 −3933.00 −0.977334
254254 4112.00 1.01579
255255 0 0
256256 256.000 0.0625000
257257 1437.00 0.348784 0.174392 0.984676i 0.444204π-0.444204\pi
0.174392 + 0.984676i 0.444204π0.444204\pi
258258 0 0
259259 0 0
260260 −2520.00 −0.601091
261261 0 0
262262 4098.00 0.966318
263263 2325.00 0.545117 0.272558 0.962139i 0.412130π-0.412130\pi
0.272558 + 0.962139i 0.412130π0.412130\pi
264264 0 0
265265 3537.00 0.819910
266266 0 0
267267 0 0
268268 1676.00 0.382007
269269 2385.00 0.540580 0.270290 0.962779i 0.412880π-0.412880\pi
0.270290 + 0.962779i 0.412880π0.412880\pi
270270 0 0
271271 −331.000 −0.0741949 −0.0370975 0.999312i 0.511811π-0.511811\pi
−0.0370975 + 0.999312i 0.511811π0.511811\pi
272272 −816.000 −0.181902
273273 0 0
274274 −282.000 −0.0621761
275275 −2508.00 −0.549957
276276 0 0
277277 4871.00 1.05657 0.528285 0.849067i 0.322835π-0.322835\pi
0.528285 + 0.849067i 0.322835π0.322835\pi
278278 −2968.00 −0.640319
279279 0 0
280280 0 0
281281 7026.00 1.49159 0.745794 0.666177i 0.232070π-0.232070\pi
0.745794 + 0.666177i 0.232070π0.232070\pi
282282 0 0
283283 −5353.00 −1.12439 −0.562196 0.827004i 0.690043π-0.690043\pi
−0.562196 + 0.827004i 0.690043π0.690043\pi
284284 384.000 0.0802331
285285 0 0
286286 7980.00 1.64989
287287 0 0
288288 0 0
289289 −2312.00 −0.470588
290290 2052.00 0.415509
291291 0 0
292292 −1252.00 −0.250917
293293 −4158.00 −0.829054 −0.414527 0.910037i 0.636053π-0.636053\pi
−0.414527 + 0.910037i 0.636053π0.636053\pi
294294 0 0
295295 −1971.00 −0.389004
296296 2024.00 0.397441
297297 0 0
298298 −114.000 −0.0221605
299299 4830.00 0.934201
300300 0 0
301301 0 0
302302 −1678.00 −0.319729
303303 0 0
304304 80.0000 0.0150931
305305 −6381.00 −1.19795
306306 0 0
307307 −9604.00 −1.78544 −0.892719 0.450615i 0.851205π-0.851205\pi
−0.892719 + 0.450615i 0.851205π0.851205\pi
308308 0 0
309309 0 0
310310 −414.000 −0.0758504
311311 −10131.0 −1.84719 −0.923595 0.383369i 0.874764π-0.874764\pi
−0.923595 + 0.383369i 0.874764π0.874764\pi
312312 0 0
313313 10799.0 1.95015 0.975073 0.221885i 0.0712210π-0.0712210\pi
0.975073 + 0.221885i 0.0712210π0.0712210\pi
314314 5666.00 1.01831
315315 0 0
316316 1844.00 0.328269
317317 −531.000 −0.0940818 −0.0470409 0.998893i 0.514979π-0.514979\pi
−0.0470409 + 0.998893i 0.514979π0.514979\pi
318318 0 0
319319 −6498.00 −1.14050
320320 576.000 0.100623
321321 0 0
322322 0 0
323323 −255.000 −0.0439275
324324 0 0
325325 3080.00 0.525685
326326 4622.00 0.785242
327327 0 0
328328 −336.000 −0.0565625
329329 0 0
330330 0 0
331331 −7015.00 −1.16489 −0.582446 0.812869i 0.697904π-0.697904\pi
−0.582446 + 0.812869i 0.697904π0.697904\pi
332332 2352.00 0.388804
333333 0 0
334334 2520.00 0.412839
335335 3771.00 0.615020
336336 0 0
337337 8990.00 1.45316 0.726582 0.687079i 0.241108π-0.241108\pi
0.726582 + 0.687079i 0.241108π0.241108\pi
338338 −5406.00 −0.869963
339339 0 0
340340 −1836.00 −0.292856
341341 1311.00 0.208195
342342 0 0
343343 0 0
344344 992.000 0.155480
345345 0 0
346346 6534.00 1.01523
347347 8709.00 1.34733 0.673665 0.739037i 0.264719π-0.264719\pi
0.673665 + 0.739037i 0.264719π0.264719\pi
348348 0 0
349349 6482.00 0.994193 0.497097 0.867695i 0.334399π-0.334399\pi
0.497097 + 0.867695i 0.334399π0.334399\pi
350350 0 0
351351 0 0
352352 −1824.00 −0.276192
353353 2133.00 0.321609 0.160805 0.986986i 0.448591π-0.448591\pi
0.160805 + 0.986986i 0.448591π0.448591\pi
354354 0 0
355355 864.000 0.129173
356356 4068.00 0.605628
357357 0 0
358358 2574.00 0.380000
359359 −3849.00 −0.565856 −0.282928 0.959141i 0.591306π-0.591306\pi
−0.282928 + 0.959141i 0.591306π0.591306\pi
360360 0 0
361361 −6834.00 −0.996355
362362 5348.00 0.776477
363363 0 0
364364 0 0
365365 −2817.00 −0.403969
366366 0 0
367367 6491.00 0.923236 0.461618 0.887079i 0.347269π-0.347269\pi
0.461618 + 0.887079i 0.347269π0.347269\pi
368368 −1104.00 −0.156386
369369 0 0
370370 4554.00 0.639868
371371 0 0
372372 0 0
373373 923.000 0.128126 0.0640632 0.997946i 0.479594π-0.479594\pi
0.0640632 + 0.997946i 0.479594π0.479594\pi
374374 5814.00 0.803836
375375 0 0
376376 1608.00 0.220549
377377 7980.00 1.09016
378378 0 0
379379 6344.00 0.859814 0.429907 0.902873i 0.358546π-0.358546\pi
0.429907 + 0.902873i 0.358546π0.358546\pi
380380 180.000 0.0242995
381381 0 0
382382 8370.00 1.12106
383383 5007.00 0.668005 0.334002 0.942572i 0.391601π-0.391601\pi
0.334002 + 0.942572i 0.391601π0.391601\pi
384384 0 0
385385 0 0
386386 170.000 0.0224165
387387 0 0
388388 −7336.00 −0.959868
389389 −12291.0 −1.60200 −0.801001 0.598664i 0.795699π-0.795699\pi
−0.801001 + 0.598664i 0.795699π0.795699\pi
390390 0 0
391391 3519.00 0.455150
392392 0 0
393393 0 0
394394 −780.000 −0.0997356
395395 4149.00 0.528503
396396 0 0
397397 887.000 0.112134 0.0560671 0.998427i 0.482144π-0.482144\pi
0.0560671 + 0.998427i 0.482144π0.482144\pi
398398 5666.00 0.713595
399399 0 0
400400 −704.000 −0.0880000
401401 −11955.0 −1.48879 −0.744394 0.667740i 0.767262π-0.767262\pi
−0.744394 + 0.667740i 0.767262π0.767262\pi
402402 0 0
403403 −1610.00 −0.199007
404404 1140.00 0.140389
405405 0 0
406406 0 0
407407 −14421.0 −1.75632
408408 0 0
409409 −3421.00 −0.413588 −0.206794 0.978384i 0.566303π-0.566303\pi
−0.206794 + 0.978384i 0.566303π0.566303\pi
410410 −756.000 −0.0910639
411411 0 0
412412 −1996.00 −0.238679
413413 0 0
414414 0 0
415415 5292.00 0.625962
416416 2240.00 0.264002
417417 0 0
418418 −570.000 −0.0666976
419419 5460.00 0.636607 0.318304 0.947989i 0.396887π-0.396887\pi
0.318304 + 0.947989i 0.396887π0.396887\pi
420420 0 0
421421 7730.00 0.894863 0.447431 0.894318i 0.352339π-0.352339\pi
0.447431 + 0.894318i 0.352339π0.352339\pi
422422 248.000 0.0286077
423423 0 0
424424 −3144.00 −0.360109
425425 2244.00 0.256118
426426 0 0
427427 0 0
428428 4428.00 0.500083
429429 0 0
430430 2232.00 0.250318
431431 11313.0 1.26433 0.632167 0.774832i 0.282166π-0.282166\pi
0.632167 + 0.774832i 0.282166π0.282166\pi
432432 0 0
433433 4214.00 0.467695 0.233847 0.972273i 0.424868π-0.424868\pi
0.233847 + 0.972273i 0.424868π0.424868\pi
434434 0 0
435435 0 0
436436 3692.00 0.405538
437437 −345.000 −0.0377656
438438 0 0
439439 16553.0 1.79962 0.899808 0.436286i 0.143706π-0.143706\pi
0.899808 + 0.436286i 0.143706π0.143706\pi
440440 −4104.00 −0.444660
441441 0 0
442442 −7140.00 −0.768360
443443 16395.0 1.75835 0.879176 0.476497i 0.158094π-0.158094\pi
0.879176 + 0.476497i 0.158094π0.158094\pi
444444 0 0
445445 9153.00 0.975042
446446 −112.000 −0.0118909
447447 0 0
448448 0 0
449449 15090.0 1.58606 0.793030 0.609182i 0.208502π-0.208502\pi
0.793030 + 0.609182i 0.208502π0.208502\pi
450450 0 0
451451 2394.00 0.249954
452452 −6168.00 −0.641855
453453 0 0
454454 −6114.00 −0.632036
455455 0 0
456456 0 0
457457 −14785.0 −1.51338 −0.756688 0.653776i 0.773184π-0.773184\pi
−0.756688 + 0.653776i 0.773184π0.773184\pi
458458 1922.00 0.196090
459459 0 0
460460 −2484.00 −0.251776
461461 −2898.00 −0.292784 −0.146392 0.989227i 0.546766π-0.546766\pi
−0.146392 + 0.989227i 0.546766π0.546766\pi
462462 0 0
463463 464.000 0.0465743 0.0232872 0.999729i 0.492587π-0.492587\pi
0.0232872 + 0.999729i 0.492587π0.492587\pi
464464 −1824.00 −0.182494
465465 0 0
466466 −5658.00 −0.562450
467467 −4233.00 −0.419443 −0.209721 0.977761i 0.567256π-0.567256\pi
−0.209721 + 0.977761i 0.567256π0.567256\pi
468468 0 0
469469 0 0
470470 3618.00 0.355076
471471 0 0
472472 1752.00 0.170852
473473 −7068.00 −0.687076
474474 0 0
475475 −220.000 −0.0212511
476476 0 0
477477 0 0
478478 −7080.00 −0.677472
479479 −2739.00 −0.261270 −0.130635 0.991431i 0.541702π-0.541702\pi
−0.130635 + 0.991431i 0.541702π0.541702\pi
480480 0 0
481481 17710.0 1.67881
482482 −10462.0 −0.988654
483483 0 0
484484 7672.00 0.720511
485485 −16506.0 −1.54536
486486 0 0
487487 17051.0 1.58656 0.793280 0.608857i 0.208372π-0.208372\pi
0.793280 + 0.608857i 0.208372π0.208372\pi
488488 5672.00 0.526146
489489 0 0
490490 0 0
491491 4296.00 0.394859 0.197429 0.980317i 0.436741π-0.436741\pi
0.197429 + 0.980317i 0.436741π0.436741\pi
492492 0 0
493493 5814.00 0.531135
494494 700.000 0.0637540
495495 0 0
496496 368.000 0.0333139
497497 0 0
498498 0 0
499499 3401.00 0.305110 0.152555 0.988295i 0.451250π-0.451250\pi
0.152555 + 0.988295i 0.451250π0.451250\pi
500500 −6084.00 −0.544170
501501 0 0
502502 10080.0 0.896200
503503 −16800.0 −1.48921 −0.744607 0.667503i 0.767363π-0.767363\pi
−0.744607 + 0.667503i 0.767363π0.767363\pi
504504 0 0
505505 2565.00 0.226022
506506 7866.00 0.691080
507507 0 0
508508 −8224.00 −0.718270
509509 −1839.00 −0.160142 −0.0800710 0.996789i 0.525515π-0.525515\pi
−0.0800710 + 0.996789i 0.525515π0.525515\pi
510510 0 0
511511 0 0
512512 −512.000 −0.0441942
513513 0 0
514514 −2874.00 −0.246628
515515 −4491.00 −0.384266
516516 0 0
517517 −11457.0 −0.974620
518518 0 0
519519 0 0
520520 5040.00 0.425036
521521 −303.000 −0.0254792 −0.0127396 0.999919i 0.504055π-0.504055\pi
−0.0127396 + 0.999919i 0.504055π0.504055\pi
522522 0 0
523523 −21667.0 −1.81153 −0.905767 0.423777i 0.860704π-0.860704\pi
−0.905767 + 0.423777i 0.860704π0.860704\pi
524524 −8196.00 −0.683290
525525 0 0
526526 −4650.00 −0.385456
527527 −1173.00 −0.0969577
528528 0 0
529529 −7406.00 −0.608696
530530 −7074.00 −0.579764
531531 0 0
532532 0 0
533533 −2940.00 −0.238922
534534 0 0
535535 9963.00 0.805118
536536 −3352.00 −0.270120
537537 0 0
538538 −4770.00 −0.382248
539539 0 0
540540 0 0
541541 5039.00 0.400450 0.200225 0.979750i 0.435833π-0.435833\pi
0.200225 + 0.979750i 0.435833π0.435833\pi
542542 662.000 0.0524637
543543 0 0
544544 1632.00 0.128624
545545 8307.00 0.652904
546546 0 0
547547 −2392.00 −0.186974 −0.0934868 0.995621i 0.529801π-0.529801\pi
−0.0934868 + 0.995621i 0.529801π0.529801\pi
548548 564.000 0.0439651
549549 0 0
550550 5016.00 0.388878
551551 −570.000 −0.0440704
552552 0 0
553553 0 0
554554 −9742.00 −0.747108
555555 0 0
556556 5936.00 0.452774
557557 22149.0 1.68489 0.842445 0.538783i 0.181116π-0.181116\pi
0.842445 + 0.538783i 0.181116π0.181116\pi
558558 0 0
559559 8680.00 0.656753
560560 0 0
561561 0 0
562562 −14052.0 −1.05471
563563 8349.00 0.624988 0.312494 0.949920i 0.398836π-0.398836\pi
0.312494 + 0.949920i 0.398836π0.398836\pi
564564 0 0
565565 −13878.0 −1.03337
566566 10706.0 0.795065
567567 0 0
568568 −768.000 −0.0567334
569569 15345.0 1.13057 0.565286 0.824895i 0.308766π-0.308766\pi
0.565286 + 0.824895i 0.308766π0.308766\pi
570570 0 0
571571 −11593.0 −0.849653 −0.424827 0.905275i 0.639665π-0.639665\pi
−0.424827 + 0.905275i 0.639665π0.639665\pi
572572 −15960.0 −1.16665
573573 0 0
574574 0 0
575575 3036.00 0.220191
576576 0 0
577577 −14593.0 −1.05288 −0.526442 0.850211i 0.676474π-0.676474\pi
−0.526442 + 0.850211i 0.676474π0.676474\pi
578578 4624.00 0.332756
579579 0 0
580580 −4104.00 −0.293809
581581 0 0
582582 0 0
583583 22401.0 1.59135
584584 2504.00 0.177425
585585 0 0
586586 8316.00 0.586230
587587 15372.0 1.08087 0.540435 0.841386i 0.318260π-0.318260\pi
0.540435 + 0.841386i 0.318260π0.318260\pi
588588 0 0
589589 115.000 0.00804498
590590 3942.00 0.275067
591591 0 0
592592 −4048.00 −0.281033
593593 14373.0 0.995326 0.497663 0.867370i 0.334192π-0.334192\pi
0.497663 + 0.867370i 0.334192π0.334192\pi
594594 0 0
595595 0 0
596596 228.000 0.0156699
597597 0 0
598598 −9660.00 −0.660580
599599 −2547.00 −0.173736 −0.0868678 0.996220i 0.527686π-0.527686\pi
−0.0868678 + 0.996220i 0.527686π0.527686\pi
600600 0 0
601601 −7042.00 −0.477952 −0.238976 0.971025i 0.576812π-0.576812\pi
−0.238976 + 0.971025i 0.576812π0.576812\pi
602602 0 0
603603 0 0
604604 3356.00 0.226082
605605 17262.0 1.16000
606606 0 0
607607 −22591.0 −1.51061 −0.755305 0.655373i 0.772511π-0.772511\pi
−0.755305 + 0.655373i 0.772511π0.772511\pi
608608 −160.000 −0.0106725
609609 0 0
610610 12762.0 0.847079
611611 14070.0 0.931606
612612 0 0
613613 −8485.00 −0.559063 −0.279532 0.960136i 0.590179π-0.590179\pi
−0.279532 + 0.960136i 0.590179π0.590179\pi
614614 19208.0 1.26249
615615 0 0
616616 0 0
617617 18282.0 1.19288 0.596439 0.802658i 0.296582π-0.296582\pi
0.596439 + 0.802658i 0.296582π0.296582\pi
618618 0 0
619619 2291.00 0.148761 0.0743805 0.997230i 0.476302π-0.476302\pi
0.0743805 + 0.997230i 0.476302π0.476302\pi
620620 828.000 0.0536343
621621 0 0
622622 20262.0 1.30616
623623 0 0
624624 0 0
625625 −8189.00 −0.524096
626626 −21598.0 −1.37896
627627 0 0
628628 −11332.0 −0.720057
629629 12903.0 0.817927
630630 0 0
631631 −6928.00 −0.437083 −0.218541 0.975828i 0.570130π-0.570130\pi
−0.218541 + 0.975828i 0.570130π0.570130\pi
632632 −3688.00 −0.232121
633633 0 0
634634 1062.00 0.0665259
635635 −18504.0 −1.15639
636636 0 0
637637 0 0
638638 12996.0 0.806452
639639 0 0
640640 −1152.00 −0.0711512
641641 −24975.0 −1.53893 −0.769464 0.638690i 0.779477π-0.779477\pi
−0.769464 + 0.638690i 0.779477π0.779477\pi
642642 0 0
643643 9548.00 0.585593 0.292797 0.956175i 0.405414π-0.405414\pi
0.292797 + 0.956175i 0.405414π0.405414\pi
644644 0 0
645645 0 0
646646 510.000 0.0310614
647647 −10131.0 −0.615596 −0.307798 0.951452i 0.599592π-0.599592\pi
−0.307798 + 0.951452i 0.599592π0.599592\pi
648648 0 0
649649 −12483.0 −0.755009
650650 −6160.00 −0.371716
651651 0 0
652652 −9244.00 −0.555250
653653 −16659.0 −0.998342 −0.499171 0.866504i 0.666362π-0.666362\pi
−0.499171 + 0.866504i 0.666362π0.666362\pi
654654 0 0
655655 −18441.0 −1.10008
656656 672.000 0.0399957
657657 0 0
658658 0 0
659659 −29556.0 −1.74710 −0.873550 0.486735i 0.838188π-0.838188\pi
−0.873550 + 0.486735i 0.838188π0.838188\pi
660660 0 0
661661 191.000 0.0112391 0.00561955 0.999984i 0.498211π-0.498211\pi
0.00561955 + 0.999984i 0.498211π0.498211\pi
662662 14030.0 0.823703
663663 0 0
664664 −4704.00 −0.274926
665665 0 0
666666 0 0
667667 7866.00 0.456631
668668 −5040.00 −0.291921
669669 0 0
670670 −7542.00 −0.434885
671671 −40413.0 −2.32508
672672 0 0
673673 2606.00 0.149263 0.0746314 0.997211i 0.476222π-0.476222\pi
0.0746314 + 0.997211i 0.476222π0.476222\pi
674674 −17980.0 −1.02754
675675 0 0
676676 10812.0 0.615157
677677 4209.00 0.238944 0.119472 0.992838i 0.461880π-0.461880\pi
0.119472 + 0.992838i 0.461880π0.461880\pi
678678 0 0
679679 0 0
680680 3672.00 0.207081
681681 0 0
682682 −2622.00 −0.147216
683683 −24303.0 −1.36154 −0.680768 0.732500i 0.738354π-0.738354\pi
−0.680768 + 0.732500i 0.738354π0.738354\pi
684684 0 0
685685 1269.00 0.0707825
686686 0 0
687687 0 0
688688 −1984.00 −0.109941
689689 −27510.0 −1.52111
690690 0 0
691691 15041.0 0.828056 0.414028 0.910264i 0.364122π-0.364122\pi
0.414028 + 0.910264i 0.364122π0.364122\pi
692692 −13068.0 −0.717877
693693 0 0
694694 −17418.0 −0.952706
695695 13356.0 0.728952
696696 0 0
697697 −2142.00 −0.116405
698698 −12964.0 −0.703001
699699 0 0
700700 0 0
701701 −24726.0 −1.33222 −0.666111 0.745852i 0.732042π-0.732042\pi
−0.666111 + 0.745852i 0.732042π0.732042\pi
702702 0 0
703703 −1265.00 −0.0678668
704704 3648.00 0.195297
705705 0 0
706706 −4266.00 −0.227412
707707 0 0
708708 0 0
709709 −4957.00 −0.262573 −0.131286 0.991344i 0.541911π-0.541911\pi
−0.131286 + 0.991344i 0.541911π0.541911\pi
710710 −1728.00 −0.0913390
711711 0 0
712712 −8136.00 −0.428244
713713 −1587.00 −0.0833571
714714 0 0
715715 −35910.0 −1.87826
716716 −5148.00 −0.268701
717717 0 0
718718 7698.00 0.400121
719719 −27669.0 −1.43516 −0.717580 0.696476i 0.754750π-0.754750\pi
−0.717580 + 0.696476i 0.754750π0.754750\pi
720720 0 0
721721 0 0
722722 13668.0 0.704529
723723 0 0
724724 −10696.0 −0.549052
725725 5016.00 0.256951
726726 0 0
727727 −13888.0 −0.708497 −0.354249 0.935151i 0.615263π-0.615263\pi
−0.354249 + 0.935151i 0.615263π0.615263\pi
728728 0 0
729729 0 0
730730 5634.00 0.285649
731731 6324.00 0.319975
732732 0 0
733733 14243.0 0.717704 0.358852 0.933394i 0.383168π-0.383168\pi
0.358852 + 0.933394i 0.383168π0.383168\pi
734734 −12982.0 −0.652826
735735 0 0
736736 2208.00 0.110581
737737 23883.0 1.19368
738738 0 0
739739 36959.0 1.83973 0.919864 0.392238i 0.128299π-0.128299\pi
0.919864 + 0.392238i 0.128299π0.128299\pi
740740 −9108.00 −0.452455
741741 0 0
742742 0 0
743743 12528.0 0.618584 0.309292 0.950967i 0.399908π-0.399908\pi
0.309292 + 0.950967i 0.399908π0.399908\pi
744744 0 0
745745 513.000 0.0252280
746746 −1846.00 −0.0905990
747747 0 0
748748 −11628.0 −0.568398
749749 0 0
750750 0 0
751751 −17767.0 −0.863285 −0.431643 0.902045i 0.642066π-0.642066\pi
−0.431643 + 0.902045i 0.642066π0.642066\pi
752752 −3216.00 −0.155951
753753 0 0
754754 −15960.0 −0.770861
755755 7551.00 0.363985
756756 0 0
757757 −28726.0 −1.37921 −0.689606 0.724184i 0.742216π-0.742216\pi
−0.689606 + 0.724184i 0.742216π0.742216\pi
758758 −12688.0 −0.607980
759759 0 0
760760 −360.000 −0.0171823
761761 26469.0 1.26084 0.630421 0.776254i 0.282882π-0.282882\pi
0.630421 + 0.776254i 0.282882π0.282882\pi
762762 0 0
763763 0 0
764764 −16740.0 −0.792712
765765 0 0
766766 −10014.0 −0.472351
767767 15330.0 0.721687
768768 0 0
769769 5054.00 0.236999 0.118499 0.992954i 0.462192π-0.462192\pi
0.118499 + 0.992954i 0.462192π0.462192\pi
770770 0 0
771771 0 0
772772 −340.000 −0.0158509
773773 35565.0 1.65483 0.827415 0.561590i 0.189810π-0.189810\pi
0.827415 + 0.561590i 0.189810π0.189810\pi
774774 0 0
775775 −1012.00 −0.0469060
776776 14672.0 0.678730
777777 0 0
778778 24582.0 1.13279
779779 210.000 0.00965858
780780 0 0
781781 5472.00 0.250709
782782 −7038.00 −0.321839
783783 0 0
784784 0 0
785785 −25497.0 −1.15927
786786 0 0
787787 −8629.00 −0.390839 −0.195420 0.980720i 0.562607π-0.562607\pi
−0.195420 + 0.980720i 0.562607π0.562607\pi
788788 1560.00 0.0705237
789789 0 0
790790 −8298.00 −0.373708
791791 0 0
792792 0 0
793793 49630.0 2.22246
794794 −1774.00 −0.0792908
795795 0 0
796796 −11332.0 −0.504588
797797 −20706.0 −0.920256 −0.460128 0.887853i 0.652197π-0.652197\pi
−0.460128 + 0.887853i 0.652197π0.652197\pi
798798 0 0
799799 10251.0 0.453885
800800 1408.00 0.0622254
801801 0 0
802802 23910.0 1.05273
803803 −17841.0 −0.784054
804804 0 0
805805 0 0
806806 3220.00 0.140719
807807 0 0
808808 −2280.00 −0.0992700
809809 16185.0 0.703380 0.351690 0.936117i 0.385607π-0.385607\pi
0.351690 + 0.936117i 0.385607π0.385607\pi
810810 0 0
811811 −11788.0 −0.510398 −0.255199 0.966889i 0.582141π-0.582141\pi
−0.255199 + 0.966889i 0.582141π0.582141\pi
812812 0 0
813813 0 0
814814 28842.0 1.24191
815815 −20799.0 −0.893935
816816 0 0
817817 −620.000 −0.0265496
818818 6842.00 0.292451
819819 0 0
820820 1512.00 0.0643919
821821 29793.0 1.26648 0.633242 0.773954i 0.281724π-0.281724\pi
0.633242 + 0.773954i 0.281724π0.281724\pi
822822 0 0
823823 30323.0 1.28432 0.642159 0.766572i 0.278039π-0.278039\pi
0.642159 + 0.766572i 0.278039π0.278039\pi
824824 3992.00 0.168772
825825 0 0
826826 0 0
827827 −21156.0 −0.889560 −0.444780 0.895640i 0.646718π-0.646718\pi
−0.444780 + 0.895640i 0.646718π0.646718\pi
828828 0 0
829829 −5269.00 −0.220748 −0.110374 0.993890i 0.535205π-0.535205\pi
−0.110374 + 0.993890i 0.535205π0.535205\pi
830830 −10584.0 −0.442622
831831 0 0
832832 −4480.00 −0.186678
833833 0 0
834834 0 0
835835 −11340.0 −0.469984
836836 1140.00 0.0471623
837837 0 0
838838 −10920.0 −0.450149
839839 39816.0 1.63838 0.819190 0.573522i 0.194423π-0.194423\pi
0.819190 + 0.573522i 0.194423π0.194423\pi
840840 0 0
841841 −11393.0 −0.467137
842842 −15460.0 −0.632763
843843 0 0
844844 −496.000 −0.0202287
845845 24327.0 0.990384
846846 0 0
847847 0 0
848848 6288.00 0.254635
849849 0 0
850850 −4488.00 −0.181103
851851 17457.0 0.703194
852852 0 0
853853 14546.0 0.583875 0.291938 0.956437i 0.405700π-0.405700\pi
0.291938 + 0.956437i 0.405700π0.405700\pi
854854 0 0
855855 0 0
856856 −8856.00 −0.353612
857857 31449.0 1.25353 0.626766 0.779207i 0.284378π-0.284378\pi
0.626766 + 0.779207i 0.284378π0.284378\pi
858858 0 0
859859 −24523.0 −0.974056 −0.487028 0.873386i 0.661919π-0.661919\pi
−0.487028 + 0.873386i 0.661919π0.661919\pi
860860 −4464.00 −0.177001
861861 0 0
862862 −22626.0 −0.894019
863863 8163.00 0.321983 0.160992 0.986956i 0.448531π-0.448531\pi
0.160992 + 0.986956i 0.448531π0.448531\pi
864864 0 0
865865 −29403.0 −1.15576
866866 −8428.00 −0.330710
867867 0 0
868868 0 0
869869 26277.0 1.02576
870870 0 0
871871 −29330.0 −1.14100
872872 −7384.00 −0.286759
873873 0 0
874874 690.000 0.0267043
875875 0 0
876876 0 0
877877 4367.00 0.168145 0.0840725 0.996460i 0.473207π-0.473207\pi
0.0840725 + 0.996460i 0.473207π0.473207\pi
878878 −33106.0 −1.27252
879879 0 0
880880 8208.00 0.314422
881881 50190.0 1.91935 0.959673 0.281118i 0.0907053π-0.0907053\pi
0.959673 + 0.281118i 0.0907053π0.0907053\pi
882882 0 0
883883 12308.0 0.469079 0.234540 0.972107i 0.424642π-0.424642\pi
0.234540 + 0.972107i 0.424642π0.424642\pi
884884 14280.0 0.543313
885885 0 0
886886 −32790.0 −1.24334
887887 −31617.0 −1.19684 −0.598419 0.801183i 0.704204π-0.704204\pi
−0.598419 + 0.801183i 0.704204π0.704204\pi
888888 0 0
889889 0 0
890890 −18306.0 −0.689459
891891 0 0
892892 224.000 0.00840816
893893 −1005.00 −0.0376607
894894 0 0
895895 −11583.0 −0.432600
896896 0 0
897897 0 0
898898 −30180.0 −1.12151
899899 −2622.00 −0.0972732
900900 0 0
901901 −20043.0 −0.741098
902902 −4788.00 −0.176744
903903 0 0
904904 12336.0 0.453860
905905 −24066.0 −0.883957
906906 0 0
907907 −13525.0 −0.495138 −0.247569 0.968870i 0.579632π-0.579632\pi
−0.247569 + 0.968870i 0.579632π0.579632\pi
908908 12228.0 0.446917
909909 0 0
910910 0 0
911911 19248.0 0.700016 0.350008 0.936747i 0.386179π-0.386179\pi
0.350008 + 0.936747i 0.386179π0.386179\pi
912912 0 0
913913 33516.0 1.21492
914914 29570.0 1.07012
915915 0 0
916916 −3844.00 −0.138656
917917 0 0
918918 0 0
919919 −8695.00 −0.312102 −0.156051 0.987749i 0.549876π-0.549876\pi
−0.156051 + 0.987749i 0.549876π0.549876\pi
920920 4968.00 0.178033
921921 0 0
922922 5796.00 0.207029
923923 −6720.00 −0.239644
924924 0 0
925925 11132.0 0.395695
926926 −928.000 −0.0329330
927927 0 0
928928 3648.00 0.129043
929929 −19479.0 −0.687928 −0.343964 0.938983i 0.611770π-0.611770\pi
−0.343964 + 0.938983i 0.611770π0.611770\pi
930930 0 0
931931 0 0
932932 11316.0 0.397712
933933 0 0
934934 8466.00 0.296591
935935 −26163.0 −0.915103
936936 0 0
937937 −12502.0 −0.435883 −0.217942 0.975962i 0.569934π-0.569934\pi
−0.217942 + 0.975962i 0.569934π0.569934\pi
938938 0 0
939939 0 0
940940 −7236.00 −0.251077
941941 15993.0 0.554046 0.277023 0.960863i 0.410652π-0.410652\pi
0.277023 + 0.960863i 0.410652π0.410652\pi
942942 0 0
943943 −2898.00 −0.100076
944944 −3504.00 −0.120811
945945 0 0
946946 14136.0 0.485836
947947 −44001.0 −1.50986 −0.754932 0.655804i 0.772330π-0.772330\pi
−0.754932 + 0.655804i 0.772330π0.772330\pi
948948 0 0
949949 21910.0 0.749451
950950 440.000 0.0150268
951951 0 0
952952 0 0
953953 4002.00 0.136031 0.0680155 0.997684i 0.478333π-0.478333\pi
0.0680155 + 0.997684i 0.478333π0.478333\pi
954954 0 0
955955 −37665.0 −1.27624
956956 14160.0 0.479045
957957 0 0
958958 5478.00 0.184745
959959 0 0
960960 0 0
961961 −29262.0 −0.982243
962962 −35420.0 −1.18710
963963 0 0
964964 20924.0 0.699084
965965 −765.000 −0.0255194
966966 0 0
967967 10544.0 0.350643 0.175322 0.984511i 0.443903π-0.443903\pi
0.175322 + 0.984511i 0.443903π0.443903\pi
968968 −15344.0 −0.509478
969969 0 0
970970 33012.0 1.09273
971971 6183.00 0.204348 0.102174 0.994767i 0.467420π-0.467420\pi
0.102174 + 0.994767i 0.467420π0.467420\pi
972972 0 0
973973 0 0
974974 −34102.0 −1.12187
975975 0 0
976976 −11344.0 −0.372042
977977 −3723.00 −0.121913 −0.0609567 0.998140i 0.519415π-0.519415\pi
−0.0609567 + 0.998140i 0.519415π0.519415\pi
978978 0 0
979979 57969.0 1.89244
980980 0 0
981981 0 0
982982 −8592.00 −0.279207
983983 45897.0 1.48920 0.744602 0.667509i 0.232639π-0.232639\pi
0.744602 + 0.667509i 0.232639π0.232639\pi
984984 0 0
985985 3510.00 0.113541
986986 −11628.0 −0.375569
987987 0 0
988988 −1400.00 −0.0450809
989989 8556.00 0.275091
990990 0 0
991991 6467.00 0.207297 0.103648 0.994614i 0.466948π-0.466948\pi
0.103648 + 0.994614i 0.466948π0.466948\pi
992992 −736.000 −0.0235565
993993 0 0
994994 0 0
995995 −25497.0 −0.812371
996996 0 0
997997 23039.0 0.731848 0.365924 0.930645i 0.380753π-0.380753\pi
0.365924 + 0.930645i 0.380753π0.380753\pi
998998 −6802.00 −0.215745
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 882.4.a.f.1.1 1
3.2 odd 2 98.4.a.d.1.1 1
7.2 even 3 126.4.g.d.109.1 2
7.3 odd 6 882.4.g.u.667.1 2
7.4 even 3 126.4.g.d.37.1 2
7.5 odd 6 882.4.g.u.361.1 2
7.6 odd 2 882.4.a.c.1.1 1
12.11 even 2 784.4.a.p.1.1 1
15.14 odd 2 2450.4.a.q.1.1 1
21.2 odd 6 14.4.c.a.11.1 yes 2
21.5 even 6 98.4.c.a.67.1 2
21.11 odd 6 14.4.c.a.9.1 2
21.17 even 6 98.4.c.a.79.1 2
21.20 even 2 98.4.a.f.1.1 1
84.11 even 6 112.4.i.a.65.1 2
84.23 even 6 112.4.i.a.81.1 2
84.83 odd 2 784.4.a.c.1.1 1
105.2 even 12 350.4.j.b.249.2 4
105.23 even 12 350.4.j.b.249.1 4
105.32 even 12 350.4.j.b.149.1 4
105.44 odd 6 350.4.e.e.151.1 2
105.53 even 12 350.4.j.b.149.2 4
105.74 odd 6 350.4.e.e.51.1 2
105.104 even 2 2450.4.a.d.1.1 1
168.11 even 6 448.4.i.e.65.1 2
168.53 odd 6 448.4.i.b.65.1 2
168.107 even 6 448.4.i.e.193.1 2
168.149 odd 6 448.4.i.b.193.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.c.a.9.1 2 21.11 odd 6
14.4.c.a.11.1 yes 2 21.2 odd 6
98.4.a.d.1.1 1 3.2 odd 2
98.4.a.f.1.1 1 21.20 even 2
98.4.c.a.67.1 2 21.5 even 6
98.4.c.a.79.1 2 21.17 even 6
112.4.i.a.65.1 2 84.11 even 6
112.4.i.a.81.1 2 84.23 even 6
126.4.g.d.37.1 2 7.4 even 3
126.4.g.d.109.1 2 7.2 even 3
350.4.e.e.51.1 2 105.74 odd 6
350.4.e.e.151.1 2 105.44 odd 6
350.4.j.b.149.1 4 105.32 even 12
350.4.j.b.149.2 4 105.53 even 12
350.4.j.b.249.1 4 105.23 even 12
350.4.j.b.249.2 4 105.2 even 12
448.4.i.b.65.1 2 168.53 odd 6
448.4.i.b.193.1 2 168.149 odd 6
448.4.i.e.65.1 2 168.11 even 6
448.4.i.e.193.1 2 168.107 even 6
784.4.a.c.1.1 1 84.83 odd 2
784.4.a.p.1.1 1 12.11 even 2
882.4.a.c.1.1 1 7.6 odd 2
882.4.a.f.1.1 1 1.1 even 1 trivial
882.4.g.u.361.1 2 7.5 odd 6
882.4.g.u.667.1 2 7.3 odd 6
2450.4.a.d.1.1 1 105.104 even 2
2450.4.a.q.1.1 1 15.14 odd 2