Properties

Label 8624.2.a.ch.1.1
Level 86248624
Weight 22
Character 8624.1
Self dual yes
Analytic conductor 68.86368.863
Analytic rank 00
Dimension 33
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8624,2,Mod(1,8624)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8624, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("8624.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 8624=247211 8624 = 2^{4} \cdot 7^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 8624.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: 68.862986703268.8629867032
Analytic rank: 00
Dimension: 33
Coefficient field: Q(ζ18)+\Q(\zeta_{18})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x33x1 x^{3} - 3x - 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 77)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.879391.87939 of defining polynomial
Character χ\chi == 8624.1

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) == q2.87939q3+2.34730q5+5.29086q91.00000q110.184793q136.75877q153.92127q170.773318q198.35504q23+0.509800q256.59627q278.17024q292.65270q31+2.87939q336.82295q37+0.532089q39+0.426022q411.18479q43+12.4192q45+7.68004q47+11.2909q51+6.55438q532.34730q55+2.22668q570.204393q59+14.5817q610.433763q653.75877q67+24.0574q69+9.96585q71+0.120615q731.46791q750.327696q79+3.12061q813.35504q839.20439q85+23.5253q874.65270q89+7.63816q931.81521q95+13.1206q975.29086q99+O(q100)q-2.87939 q^{3} +2.34730 q^{5} +5.29086 q^{9} -1.00000 q^{11} -0.184793 q^{13} -6.75877 q^{15} -3.92127 q^{17} -0.773318 q^{19} -8.35504 q^{23} +0.509800 q^{25} -6.59627 q^{27} -8.17024 q^{29} -2.65270 q^{31} +2.87939 q^{33} -6.82295 q^{37} +0.532089 q^{39} +0.426022 q^{41} -1.18479 q^{43} +12.4192 q^{45} +7.68004 q^{47} +11.2909 q^{51} +6.55438 q^{53} -2.34730 q^{55} +2.22668 q^{57} -0.204393 q^{59} +14.5817 q^{61} -0.433763 q^{65} -3.75877 q^{67} +24.0574 q^{69} +9.96585 q^{71} +0.120615 q^{73} -1.46791 q^{75} -0.327696 q^{79} +3.12061 q^{81} -3.35504 q^{83} -9.20439 q^{85} +23.5253 q^{87} -4.65270 q^{89} +7.63816 q^{93} -1.81521 q^{95} +13.1206 q^{97} -5.29086 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q3q3+6q53q11+3q139q153q179q19+3q256q273q299q31+3q333q39+9q41+3q45+3q47+18q51+9q536q55++45q97+O(q100) 3 q - 3 q^{3} + 6 q^{5} - 3 q^{11} + 3 q^{13} - 9 q^{15} - 3 q^{17} - 9 q^{19} + 3 q^{25} - 6 q^{27} - 3 q^{29} - 9 q^{31} + 3 q^{33} - 3 q^{39} + 9 q^{41} + 3 q^{45} + 3 q^{47} + 18 q^{51} + 9 q^{53} - 6 q^{55}+ \cdots + 45 q^{97}+O(q^{100}) Copy content Toggle raw display

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 0 0
33 −2.87939 −1.66241 −0.831207 0.555963i 0.812350π-0.812350\pi
−0.831207 + 0.555963i 0.812350π0.812350\pi
44 0 0
55 2.34730 1.04974 0.524871 0.851182i 0.324113π-0.324113\pi
0.524871 + 0.851182i 0.324113π0.324113\pi
66 0 0
77 0 0
88 0 0
99 5.29086 1.76362
1010 0 0
1111 −1.00000 −0.301511
1212 0 0
1313 −0.184793 −0.0512522 −0.0256261 0.999672i 0.508158π-0.508158\pi
−0.0256261 + 0.999672i 0.508158π0.508158\pi
1414 0 0
1515 −6.75877 −1.74511
1616 0 0
1717 −3.92127 −0.951049 −0.475524 0.879703i 0.657742π-0.657742\pi
−0.475524 + 0.879703i 0.657742π0.657742\pi
1818 0 0
1919 −0.773318 −0.177411 −0.0887057 0.996058i 0.528273π-0.528273\pi
−0.0887057 + 0.996058i 0.528273π0.528273\pi
2020 0 0
2121 0 0
2222 0 0
2323 −8.35504 −1.74215 −0.871073 0.491154i 0.836575π-0.836575\pi
−0.871073 + 0.491154i 0.836575π0.836575\pi
2424 0 0
2525 0.509800 0.101960
2626 0 0
2727 −6.59627 −1.26945
2828 0 0
2929 −8.17024 −1.51718 −0.758588 0.651570i 0.774111π-0.774111\pi
−0.758588 + 0.651570i 0.774111π0.774111\pi
3030 0 0
3131 −2.65270 −0.476440 −0.238220 0.971211i 0.576564π-0.576564\pi
−0.238220 + 0.971211i 0.576564π0.576564\pi
3232 0 0
3333 2.87939 0.501237
3434 0 0
3535 0 0
3636 0 0
3737 −6.82295 −1.12169 −0.560843 0.827922i 0.689523π-0.689523\pi
−0.560843 + 0.827922i 0.689523π0.689523\pi
3838 0 0
3939 0.532089 0.0852024
4040 0 0
4141 0.426022 0.0665335 0.0332667 0.999447i 0.489409π-0.489409\pi
0.0332667 + 0.999447i 0.489409π0.489409\pi
4242 0 0
4343 −1.18479 −0.180679 −0.0903396 0.995911i 0.528795π-0.528795\pi
−0.0903396 + 0.995911i 0.528795π0.528795\pi
4444 0 0
4545 12.4192 1.85135
4646 0 0
4747 7.68004 1.12025 0.560125 0.828408i 0.310753π-0.310753\pi
0.560125 + 0.828408i 0.310753π0.310753\pi
4848 0 0
4949 0 0
5050 0 0
5151 11.2909 1.58104
5252 0 0
5353 6.55438 0.900313 0.450157 0.892950i 0.351368π-0.351368\pi
0.450157 + 0.892950i 0.351368π0.351368\pi
5454 0 0
5555 −2.34730 −0.316509
5656 0 0
5757 2.22668 0.294931
5858 0 0
5959 −0.204393 −0.0266097 −0.0133048 0.999911i 0.504235π-0.504235\pi
−0.0133048 + 0.999911i 0.504235π0.504235\pi
6060 0 0
6161 14.5817 1.86700 0.933499 0.358580i 0.116739π-0.116739\pi
0.933499 + 0.358580i 0.116739π0.116739\pi
6262 0 0
6363 0 0
6464 0 0
6565 −0.433763 −0.0538017
6666 0 0
6767 −3.75877 −0.459207 −0.229603 0.973284i 0.573743π-0.573743\pi
−0.229603 + 0.973284i 0.573743π0.573743\pi
6868 0 0
6969 24.0574 2.89617
7070 0 0
7171 9.96585 1.18273 0.591365 0.806404i 0.298589π-0.298589\pi
0.591365 + 0.806404i 0.298589π0.298589\pi
7272 0 0
7373 0.120615 0.0141169 0.00705844 0.999975i 0.497753π-0.497753\pi
0.00705844 + 0.999975i 0.497753π0.497753\pi
7474 0 0
7575 −1.46791 −0.169500
7676 0 0
7777 0 0
7878 0 0
7979 −0.327696 −0.0368687 −0.0184343 0.999830i 0.505868π-0.505868\pi
−0.0184343 + 0.999830i 0.505868π0.505868\pi
8080 0 0
8181 3.12061 0.346735
8282 0 0
8383 −3.35504 −0.368263 −0.184132 0.982902i 0.558947π-0.558947\pi
−0.184132 + 0.982902i 0.558947π0.558947\pi
8484 0 0
8585 −9.20439 −0.998357
8686 0 0
8787 23.5253 2.52217
8888 0 0
8989 −4.65270 −0.493186 −0.246593 0.969119i 0.579311π-0.579311\pi
−0.246593 + 0.969119i 0.579311π0.579311\pi
9090 0 0
9191 0 0
9292 0 0
9393 7.63816 0.792040
9494 0 0
9595 −1.81521 −0.186236
9696 0 0
9797 13.1206 1.33220 0.666098 0.745864i 0.267963π-0.267963\pi
0.666098 + 0.745864i 0.267963π0.267963\pi
9898 0 0
9999 −5.29086 −0.531751
100100 0 0
101101 −5.90167 −0.587239 −0.293619 0.955922i 0.594860π-0.594860\pi
−0.293619 + 0.955922i 0.594860π0.594860\pi
102102 0 0
103103 −0.921274 −0.0907759 −0.0453879 0.998969i 0.514452π-0.514452\pi
−0.0453879 + 0.998969i 0.514452π0.514452\pi
104104 0 0
105105 0 0
106106 0 0
107107 10.3473 1.00031 0.500155 0.865936i 0.333276π-0.333276\pi
0.500155 + 0.865936i 0.333276π0.333276\pi
108108 0 0
109109 0.475652 0.0455592 0.0227796 0.999741i 0.492748π-0.492748\pi
0.0227796 + 0.999741i 0.492748π0.492748\pi
110110 0 0
111111 19.6459 1.86471
112112 0 0
113113 −3.14290 −0.295659 −0.147830 0.989013i 0.547229π-0.547229\pi
−0.147830 + 0.989013i 0.547229π0.547229\pi
114114 0 0
115115 −19.6117 −1.82880
116116 0 0
117117 −0.977711 −0.0903894
118118 0 0
119119 0 0
120120 0 0
121121 1.00000 0.0909091
122122 0 0
123123 −1.22668 −0.110606
124124 0 0
125125 −10.5398 −0.942711
126126 0 0
127127 0.445622 0.0395426 0.0197713 0.999805i 0.493706π-0.493706\pi
0.0197713 + 0.999805i 0.493706π0.493706\pi
128128 0 0
129129 3.41147 0.300364
130130 0 0
131131 12.0865 1.05600 0.528000 0.849245i 0.322942π-0.322942\pi
0.528000 + 0.849245i 0.322942π0.322942\pi
132132 0 0
133133 0 0
134134 0 0
135135 −15.4834 −1.33260
136136 0 0
137137 −16.3482 −1.39672 −0.698362 0.715745i 0.746087π-0.746087\pi
−0.698362 + 0.715745i 0.746087π0.746087\pi
138138 0 0
139139 20.7297 1.75827 0.879134 0.476575i 0.158122π-0.158122\pi
0.879134 + 0.476575i 0.158122π0.158122\pi
140140 0 0
141141 −22.1138 −1.86232
142142 0 0
143143 0.184793 0.0154531
144144 0 0
145145 −19.1780 −1.59264
146146 0 0
147147 0 0
148148 0 0
149149 −0.714193 −0.0585090 −0.0292545 0.999572i 0.509313π-0.509313\pi
−0.0292545 + 0.999572i 0.509313π0.509313\pi
150150 0 0
151151 9.54488 0.776751 0.388376 0.921501i 0.373036π-0.373036\pi
0.388376 + 0.921501i 0.373036π0.373036\pi
152152 0 0
153153 −20.7469 −1.67729
154154 0 0
155155 −6.22668 −0.500139
156156 0 0
157157 9.24123 0.737530 0.368765 0.929523i 0.379781π-0.379781\pi
0.368765 + 0.929523i 0.379781π0.379781\pi
158158 0 0
159159 −18.8726 −1.49669
160160 0 0
161161 0 0
162162 0 0
163163 8.80335 0.689531 0.344766 0.938689i 0.387958π-0.387958\pi
0.344766 + 0.938689i 0.387958π0.387958\pi
164164 0 0
165165 6.75877 0.526170
166166 0 0
167167 −8.38238 −0.648648 −0.324324 0.945946i 0.605137π-0.605137\pi
−0.324324 + 0.945946i 0.605137π0.605137\pi
168168 0 0
169169 −12.9659 −0.997373
170170 0 0
171171 −4.09152 −0.312886
172172 0 0
173173 5.44562 0.414023 0.207012 0.978339i 0.433626π-0.433626\pi
0.207012 + 0.978339i 0.433626π0.433626\pi
174174 0 0
175175 0 0
176176 0 0
177177 0.588526 0.0442363
178178 0 0
179179 10.0915 0.754276 0.377138 0.926157i 0.376908π-0.376908\pi
0.377138 + 0.926157i 0.376908π0.376908\pi
180180 0 0
181181 19.8794 1.47762 0.738812 0.673912i 0.235387π-0.235387\pi
0.738812 + 0.673912i 0.235387π0.235387\pi
182182 0 0
183183 −41.9864 −3.10372
184184 0 0
185185 −16.0155 −1.17748
186186 0 0
187187 3.92127 0.286752
188188 0 0
189189 0 0
190190 0 0
191191 25.3851 1.83680 0.918399 0.395654i 0.129482π-0.129482\pi
0.918399 + 0.395654i 0.129482π0.129482\pi
192192 0 0
193193 −7.73143 −0.556520 −0.278260 0.960506i 0.589758π-0.589758\pi
−0.278260 + 0.960506i 0.589758π0.589758\pi
194194 0 0
195195 1.24897 0.0894406
196196 0 0
197197 −5.37464 −0.382927 −0.191464 0.981500i 0.561323π-0.561323\pi
−0.191464 + 0.981500i 0.561323π0.561323\pi
198198 0 0
199199 −8.78106 −0.622473 −0.311236 0.950333i 0.600743π-0.600743\pi
−0.311236 + 0.950333i 0.600743π0.600743\pi
200200 0 0
201201 10.8229 0.763392
202202 0 0
203203 0 0
204204 0 0
205205 1.00000 0.0698430
206206 0 0
207207 −44.2053 −3.07248
208208 0 0
209209 0.773318 0.0534916
210210 0 0
211211 −4.24123 −0.291978 −0.145989 0.989286i 0.546636π-0.546636\pi
−0.145989 + 0.989286i 0.546636π0.546636\pi
212212 0 0
213213 −28.6955 −1.96619
214214 0 0
215215 −2.78106 −0.189667
216216 0 0
217217 0 0
218218 0 0
219219 −0.347296 −0.0234681
220220 0 0
221221 0.724622 0.0487434
222222 0 0
223223 18.0351 1.20772 0.603859 0.797091i 0.293629π-0.293629\pi
0.603859 + 0.797091i 0.293629π0.293629\pi
224224 0 0
225225 2.69728 0.179819
226226 0 0
227227 −18.2053 −1.20833 −0.604165 0.796859i 0.706493π-0.706493\pi
−0.604165 + 0.796859i 0.706493π0.706493\pi
228228 0 0
229229 19.2412 1.27150 0.635748 0.771897i 0.280692π-0.280692\pi
0.635748 + 0.771897i 0.280692π0.280692\pi
230230 0 0
231231 0 0
232232 0 0
233233 9.32501 0.610902 0.305451 0.952208i 0.401193π-0.401193\pi
0.305451 + 0.952208i 0.401193π0.401193\pi
234234 0 0
235235 18.0273 1.17597
236236 0 0
237237 0.943563 0.0612910
238238 0 0
239239 −11.1898 −0.723811 −0.361905 0.932215i 0.617874π-0.617874\pi
−0.361905 + 0.932215i 0.617874π0.617874\pi
240240 0 0
241241 20.2044 1.30148 0.650740 0.759301i 0.274459π-0.274459\pi
0.650740 + 0.759301i 0.274459π0.274459\pi
242242 0 0
243243 10.8033 0.693035
244244 0 0
245245 0 0
246246 0 0
247247 0.142903 0.00909273
248248 0 0
249249 9.66044 0.612206
250250 0 0
251251 5.89218 0.371911 0.185956 0.982558i 0.440462π-0.440462\pi
0.185956 + 0.982558i 0.440462π0.440462\pi
252252 0 0
253253 8.35504 0.525277
254254 0 0
255255 26.5030 1.65968
256256 0 0
257257 −2.73648 −0.170697 −0.0853485 0.996351i 0.527200π-0.527200\pi
−0.0853485 + 0.996351i 0.527200π0.527200\pi
258258 0 0
259259 0 0
260260 0 0
261261 −43.2276 −2.67572
262262 0 0
263263 −6.19759 −0.382160 −0.191080 0.981575i 0.561199π-0.561199\pi
−0.191080 + 0.981575i 0.561199π0.561199\pi
264264 0 0
265265 15.3851 0.945097
266266 0 0
267267 13.3969 0.819879
268268 0 0
269269 −4.20945 −0.256654 −0.128327 0.991732i 0.540961π-0.540961\pi
−0.128327 + 0.991732i 0.540961π0.540961\pi
270270 0 0
271271 −25.5817 −1.55398 −0.776989 0.629514i 0.783254π-0.783254\pi
−0.776989 + 0.629514i 0.783254π0.783254\pi
272272 0 0
273273 0 0
274274 0 0
275275 −0.509800 −0.0307421
276276 0 0
277277 −15.3577 −0.922756 −0.461378 0.887204i 0.652645π-0.652645\pi
−0.461378 + 0.887204i 0.652645π0.652645\pi
278278 0 0
279279 −14.0351 −0.840258
280280 0 0
281281 19.2540 1.14860 0.574299 0.818645i 0.305275π-0.305275\pi
0.574299 + 0.818645i 0.305275π0.305275\pi
282282 0 0
283283 27.0651 1.60885 0.804427 0.594052i 0.202473π-0.202473\pi
0.804427 + 0.594052i 0.202473π0.202473\pi
284284 0 0
285285 5.22668 0.309602
286286 0 0
287287 0 0
288288 0 0
289289 −1.62361 −0.0955063
290290 0 0
291291 −37.7793 −2.21466
292292 0 0
293293 4.03508 0.235732 0.117866 0.993030i 0.462395π-0.462395\pi
0.117866 + 0.993030i 0.462395π0.462395\pi
294294 0 0
295295 −0.479771 −0.0279333
296296 0 0
297297 6.59627 0.382754
298298 0 0
299299 1.54395 0.0892888
300300 0 0
301301 0 0
302302 0 0
303303 16.9932 0.976233
304304 0 0
305305 34.2276 1.95987
306306 0 0
307307 −2.92902 −0.167168 −0.0835839 0.996501i 0.526637π-0.526637\pi
−0.0835839 + 0.996501i 0.526637π0.526637\pi
308308 0 0
309309 2.65270 0.150907
310310 0 0
311311 −15.6236 −0.885934 −0.442967 0.896538i 0.646074π-0.646074\pi
−0.442967 + 0.896538i 0.646074π0.646074\pi
312312 0 0
313313 −21.9760 −1.24215 −0.621077 0.783749i 0.713305π-0.713305\pi
−0.621077 + 0.783749i 0.713305π0.713305\pi
314314 0 0
315315 0 0
316316 0 0
317317 −3.01186 −0.169163 −0.0845814 0.996417i 0.526955π-0.526955\pi
−0.0845814 + 0.996417i 0.526955π0.526955\pi
318318 0 0
319319 8.17024 0.457446
320320 0 0
321321 −29.7939 −1.66293
322322 0 0
323323 3.03239 0.168727
324324 0 0
325325 −0.0942073 −0.00522568
326326 0 0
327327 −1.36959 −0.0757382
328328 0 0
329329 0 0
330330 0 0
331331 −27.4688 −1.50982 −0.754912 0.655826i 0.772321π-0.772321\pi
−0.754912 + 0.655826i 0.772321π0.772321\pi
332332 0 0
333333 −36.0993 −1.97823
334334 0 0
335335 −8.82295 −0.482049
336336 0 0
337337 17.2422 0.939240 0.469620 0.882869i 0.344391π-0.344391\pi
0.469620 + 0.882869i 0.344391π0.344391\pi
338338 0 0
339339 9.04963 0.491508
340340 0 0
341341 2.65270 0.143652
342342 0 0
343343 0 0
344344 0 0
345345 56.4698 3.04023
346346 0 0
347347 11.4311 0.613652 0.306826 0.951766i 0.400733π-0.400733\pi
0.306826 + 0.951766i 0.400733π0.400733\pi
348348 0 0
349349 28.3209 1.51598 0.757991 0.652265i 0.226181π-0.226181\pi
0.757991 + 0.652265i 0.226181π0.226181\pi
350350 0 0
351351 1.21894 0.0650622
352352 0 0
353353 16.4361 0.874807 0.437403 0.899265i 0.355898π-0.355898\pi
0.437403 + 0.899265i 0.355898π0.355898\pi
354354 0 0
355355 23.3928 1.24156
356356 0 0
357357 0 0
358358 0 0
359359 −24.8631 −1.31222 −0.656112 0.754664i 0.727800π-0.727800\pi
−0.656112 + 0.754664i 0.727800π0.727800\pi
360360 0 0
361361 −18.4020 −0.968525
362362 0 0
363363 −2.87939 −0.151129
364364 0 0
365365 0.283119 0.0148191
366366 0 0
367367 −4.29860 −0.224385 −0.112193 0.993686i 0.535787π-0.535787\pi
−0.112193 + 0.993686i 0.535787π0.535787\pi
368368 0 0
369369 2.25402 0.117340
370370 0 0
371371 0 0
372372 0 0
373373 −2.72967 −0.141337 −0.0706686 0.997500i 0.522513π-0.522513\pi
−0.0706686 + 0.997500i 0.522513π0.522513\pi
374374 0 0
375375 30.3482 1.56718
376376 0 0
377377 1.50980 0.0777587
378378 0 0
379379 16.4584 0.845412 0.422706 0.906267i 0.361080π-0.361080\pi
0.422706 + 0.906267i 0.361080π0.361080\pi
380380 0 0
381381 −1.28312 −0.0657362
382382 0 0
383383 7.85978 0.401616 0.200808 0.979631i 0.435643π-0.435643\pi
0.200808 + 0.979631i 0.435643π0.435643\pi
384384 0 0
385385 0 0
386386 0 0
387387 −6.26857 −0.318649
388388 0 0
389389 9.64321 0.488930 0.244465 0.969658i 0.421388π-0.421388\pi
0.244465 + 0.969658i 0.421388π0.421388\pi
390390 0 0
391391 32.7624 1.65687
392392 0 0
393393 −34.8016 −1.75551
394394 0 0
395395 −0.769200 −0.0387026
396396 0 0
397397 −9.43376 −0.473467 −0.236733 0.971575i 0.576077π-0.576077\pi
−0.236733 + 0.971575i 0.576077π0.576077\pi
398398 0 0
399399 0 0
400400 0 0
401401 −18.2199 −0.909857 −0.454929 0.890528i 0.650335π-0.650335\pi
−0.454929 + 0.890528i 0.650335π0.650335\pi
402402 0 0
403403 0.490200 0.0244186
404404 0 0
405405 7.32501 0.363983
406406 0 0
407407 6.82295 0.338201
408408 0 0
409409 6.41147 0.317027 0.158513 0.987357i 0.449330π-0.449330\pi
0.158513 + 0.987357i 0.449330π0.449330\pi
410410 0 0
411411 47.0729 2.32193
412412 0 0
413413 0 0
414414 0 0
415415 −7.87527 −0.386582
416416 0 0
417417 −59.6887 −2.92297
418418 0 0
419419 −1.62092 −0.0791871 −0.0395935 0.999216i 0.512606π-0.512606\pi
−0.0395935 + 0.999216i 0.512606π0.512606\pi
420420 0 0
421421 31.1489 1.51810 0.759052 0.651030i 0.225663π-0.225663\pi
0.759052 + 0.651030i 0.225663π0.225663\pi
422422 0 0
423423 40.6340 1.97569
424424 0 0
425425 −1.99907 −0.0969690
426426 0 0
427427 0 0
428428 0 0
429429 −0.532089 −0.0256895
430430 0 0
431431 −34.2080 −1.64774 −0.823871 0.566777i 0.808190π-0.808190\pi
−0.823871 + 0.566777i 0.808190π0.808190\pi
432432 0 0
433433 −20.4979 −0.985068 −0.492534 0.870293i 0.663929π-0.663929\pi
−0.492534 + 0.870293i 0.663929π0.663929\pi
434434 0 0
435435 55.2208 2.64764
436436 0 0
437437 6.46110 0.309077
438438 0 0
439439 −31.3218 −1.49491 −0.747455 0.664313i 0.768724π-0.768724\pi
−0.747455 + 0.664313i 0.768724π0.768724\pi
440440 0 0
441441 0 0
442442 0 0
443443 29.3979 1.39673 0.698367 0.715740i 0.253910π-0.253910\pi
0.698367 + 0.715740i 0.253910π0.253910\pi
444444 0 0
445445 −10.9213 −0.517718
446446 0 0
447447 2.05644 0.0972661
448448 0 0
449449 −6.90074 −0.325666 −0.162833 0.986654i 0.552063π-0.552063\pi
−0.162833 + 0.986654i 0.552063π0.552063\pi
450450 0 0
451451 −0.426022 −0.0200606
452452 0 0
453453 −27.4834 −1.29128
454454 0 0
455455 0 0
456456 0 0
457457 12.3746 0.578861 0.289431 0.957199i 0.406534π-0.406534\pi
0.289431 + 0.957199i 0.406534π0.406534\pi
458458 0 0
459459 25.8658 1.20731
460460 0 0
461461 20.0942 0.935881 0.467940 0.883760i 0.344996π-0.344996\pi
0.467940 + 0.883760i 0.344996π0.344996\pi
462462 0 0
463463 −8.69190 −0.403947 −0.201974 0.979391i 0.564735π-0.564735\pi
−0.201974 + 0.979391i 0.564735π0.564735\pi
464464 0 0
465465 17.9290 0.831438
466466 0 0
467467 −4.76920 −0.220692 −0.110346 0.993893i 0.535196π-0.535196\pi
−0.110346 + 0.993893i 0.535196π0.535196\pi
468468 0 0
469469 0 0
470470 0 0
471471 −26.6091 −1.22608
472472 0 0
473473 1.18479 0.0544768
474474 0 0
475475 −0.394238 −0.0180889
476476 0 0
477477 34.6783 1.58781
478478 0 0
479479 39.6141 1.81001 0.905007 0.425396i 0.139865π-0.139865\pi
0.905007 + 0.425396i 0.139865π0.139865\pi
480480 0 0
481481 1.26083 0.0574889
482482 0 0
483483 0 0
484484 0 0
485485 30.7980 1.39846
486486 0 0
487487 −5.15570 −0.233627 −0.116813 0.993154i 0.537268π-0.537268\pi
−0.116813 + 0.993154i 0.537268π0.537268\pi
488488 0 0
489489 −25.3482 −1.14629
490490 0 0
491491 −10.1925 −0.459983 −0.229991 0.973193i 0.573870π-0.573870\pi
−0.229991 + 0.973193i 0.573870π0.573870\pi
492492 0 0
493493 32.0378 1.44291
494494 0 0
495495 −12.4192 −0.558202
496496 0 0
497497 0 0
498498 0 0
499499 −5.88981 −0.263664 −0.131832 0.991272i 0.542086π-0.542086\pi
−0.131832 + 0.991272i 0.542086π0.542086\pi
500500 0 0
501501 24.1361 1.07832
502502 0 0
503503 12.8348 0.572276 0.286138 0.958188i 0.407628π-0.407628\pi
0.286138 + 0.958188i 0.407628π0.407628\pi
504504 0 0
505505 −13.8530 −0.616449
506506 0 0
507507 37.3337 1.65805
508508 0 0
509509 32.2131 1.42782 0.713910 0.700238i 0.246923π-0.246923\pi
0.713910 + 0.700238i 0.246923π0.246923\pi
510510 0 0
511511 0 0
512512 0 0
513513 5.10101 0.225215
514514 0 0
515515 −2.16250 −0.0952913
516516 0 0
517517 −7.68004 −0.337768
518518 0 0
519519 −15.6800 −0.688278
520520 0 0
521521 18.5280 0.811725 0.405863 0.913934i 0.366971π-0.366971\pi
0.405863 + 0.913934i 0.366971π0.366971\pi
522522 0 0
523523 37.2422 1.62849 0.814243 0.580524i 0.197152π-0.197152\pi
0.814243 + 0.580524i 0.197152π0.197152\pi
524524 0 0
525525 0 0
526526 0 0
527527 10.4020 0.453117
528528 0 0
529529 46.8066 2.03507
530530 0 0
531531 −1.08141 −0.0469294
532532 0 0
533533 −0.0787257 −0.00340999
534534 0 0
535535 24.2882 1.05007
536536 0 0
537537 −29.0574 −1.25392
538538 0 0
539539 0 0
540540 0 0
541541 36.1566 1.55449 0.777247 0.629195i 0.216615π-0.216615\pi
0.777247 + 0.629195i 0.216615π0.216615\pi
542542 0 0
543543 −57.2404 −2.45642
544544 0 0
545545 1.11650 0.0478254
546546 0 0
547547 −12.7980 −0.547202 −0.273601 0.961843i 0.588215π-0.588215\pi
−0.273601 + 0.961843i 0.588215π0.588215\pi
548548 0 0
549549 77.1498 3.29267
550550 0 0
551551 6.31820 0.269164
552552 0 0
553553 0 0
554554 0 0
555555 46.1147 1.95746
556556 0 0
557557 −30.6587 −1.29905 −0.649525 0.760340i 0.725032π-0.725032\pi
−0.649525 + 0.760340i 0.725032π0.725032\pi
558558 0 0
559559 0.218941 0.00926021
560560 0 0
561561 −11.2909 −0.476700
562562 0 0
563563 14.5047 0.611302 0.305651 0.952144i 0.401126π-0.401126\pi
0.305651 + 0.952144i 0.401126π0.401126\pi
564564 0 0
565565 −7.37733 −0.310366
566566 0 0
567567 0 0
568568 0 0
569569 19.0051 0.796733 0.398367 0.917226i 0.369577π-0.369577\pi
0.398367 + 0.917226i 0.369577π0.369577\pi
570570 0 0
571571 21.0009 0.878862 0.439431 0.898276i 0.355180π-0.355180\pi
0.439431 + 0.898276i 0.355180π0.355180\pi
572572 0 0
573573 −73.0934 −3.05352
574574 0 0
575575 −4.25940 −0.177629
576576 0 0
577577 −5.18748 −0.215958 −0.107979 0.994153i 0.534438π-0.534438\pi
−0.107979 + 0.994153i 0.534438π0.534438\pi
578578 0 0
579579 22.2618 0.925167
580580 0 0
581581 0 0
582582 0 0
583583 −6.55438 −0.271455
584584 0 0
585585 −2.29498 −0.0948857
586586 0 0
587587 −8.33813 −0.344151 −0.172076 0.985084i 0.555047π-0.555047\pi
−0.172076 + 0.985084i 0.555047π0.555047\pi
588588 0 0
589589 2.05138 0.0845258
590590 0 0
591591 15.4757 0.636583
592592 0 0
593593 6.10195 0.250577 0.125288 0.992120i 0.460014π-0.460014\pi
0.125288 + 0.992120i 0.460014π0.460014\pi
594594 0 0
595595 0 0
596596 0 0
597597 25.2841 1.03481
598598 0 0
599599 13.8503 0.565907 0.282954 0.959134i 0.408686π-0.408686\pi
0.282954 + 0.959134i 0.408686π0.408686\pi
600600 0 0
601601 31.2695 1.27551 0.637755 0.770239i 0.279863π-0.279863\pi
0.637755 + 0.770239i 0.279863π0.279863\pi
602602 0 0
603603 −19.8871 −0.809866
604604 0 0
605605 2.34730 0.0954312
606606 0 0
607607 −37.7962 −1.53410 −0.767051 0.641587i 0.778276π-0.778276\pi
−0.767051 + 0.641587i 0.778276π0.778276\pi
608608 0 0
609609 0 0
610610 0 0
611611 −1.41921 −0.0574153
612612 0 0
613613 21.1343 0.853608 0.426804 0.904344i 0.359639π-0.359639\pi
0.426804 + 0.904344i 0.359639π0.359639\pi
614614 0 0
615615 −2.87939 −0.116108
616616 0 0
617617 23.7743 0.957115 0.478558 0.878056i 0.341160π-0.341160\pi
0.478558 + 0.878056i 0.341160π0.341160\pi
618618 0 0
619619 −13.5021 −0.542694 −0.271347 0.962482i 0.587469π-0.587469\pi
−0.271347 + 0.962482i 0.587469π0.587469\pi
620620 0 0
621621 55.1121 2.21157
622622 0 0
623623 0 0
624624 0 0
625625 −27.2891 −1.09156
626626 0 0
627627 −2.22668 −0.0889251
628628 0 0
629629 26.7547 1.06678
630630 0 0
631631 38.2354 1.52213 0.761063 0.648678i 0.224678π-0.224678\pi
0.761063 + 0.648678i 0.224678π0.224678\pi
632632 0 0
633633 12.2121 0.485389
634634 0 0
635635 1.04601 0.0415096
636636 0 0
637637 0 0
638638 0 0
639639 52.7279 2.08588
640640 0 0
641641 38.5553 1.52284 0.761422 0.648257i 0.224502π-0.224502\pi
0.761422 + 0.648257i 0.224502π0.224502\pi
642642 0 0
643643 −19.2627 −0.759647 −0.379823 0.925059i 0.624015π-0.624015\pi
−0.379823 + 0.925059i 0.624015π0.624015\pi
644644 0 0
645645 8.00774 0.315304
646646 0 0
647647 −39.7844 −1.56408 −0.782042 0.623225i 0.785822π-0.785822\pi
−0.782042 + 0.623225i 0.785822π0.785822\pi
648648 0 0
649649 0.204393 0.00802312
650650 0 0
651651 0 0
652652 0 0
653653 4.76651 0.186528 0.0932640 0.995641i 0.470270π-0.470270\pi
0.0932640 + 0.995641i 0.470270π0.470270\pi
654654 0 0
655655 28.3705 1.10853
656656 0 0
657657 0.638156 0.0248968
658658 0 0
659659 38.3550 1.49410 0.747050 0.664768i 0.231470π-0.231470\pi
0.747050 + 0.664768i 0.231470π0.231470\pi
660660 0 0
661661 −10.3628 −0.403065 −0.201533 0.979482i 0.564592π-0.564592\pi
−0.201533 + 0.979482i 0.564592π0.564592\pi
662662 0 0
663663 −2.08647 −0.0810316
664664 0 0
665665 0 0
666666 0 0
667667 68.2627 2.64314
668668 0 0
669669 −51.9299 −2.00773
670670 0 0
671671 −14.5817 −0.562921
672672 0 0
673673 −25.6168 −0.987455 −0.493728 0.869617i 0.664366π-0.664366\pi
−0.493728 + 0.869617i 0.664366π0.664366\pi
674674 0 0
675675 −3.36278 −0.129433
676676 0 0
677677 41.8375 1.60795 0.803973 0.594666i 0.202716π-0.202716\pi
0.803973 + 0.594666i 0.202716π0.202716\pi
678678 0 0
679679 0 0
680680 0 0
681681 52.4201 2.00874
682682 0 0
683683 46.0428 1.76178 0.880890 0.473321i 0.156945π-0.156945\pi
0.880890 + 0.473321i 0.156945π0.156945\pi
684684 0 0
685685 −38.3741 −1.46620
686686 0 0
687687 −55.4029 −2.11375
688688 0 0
689689 −1.21120 −0.0461430
690690 0 0
691691 −8.00000 −0.304334 −0.152167 0.988355i 0.548625π-0.548625\pi
−0.152167 + 0.988355i 0.548625π0.548625\pi
692692 0 0
693693 0 0
694694 0 0
695695 48.6587 1.84573
696696 0 0
697697 −1.67055 −0.0632766
698698 0 0
699699 −26.8503 −1.01557
700700 0 0
701701 −32.8144 −1.23938 −0.619691 0.784846i 0.712742π-0.712742\pi
−0.619691 + 0.784846i 0.712742π0.712742\pi
702702 0 0
703703 5.27631 0.199000
704704 0 0
705705 −51.9077 −1.95496
706706 0 0
707707 0 0
708708 0 0
709709 7.40198 0.277987 0.138994 0.990293i 0.455613π-0.455613\pi
0.138994 + 0.990293i 0.455613π0.455613\pi
710710 0 0
711711 −1.73379 −0.0650223
712712 0 0
713713 22.1634 0.830027
714714 0 0
715715 0.433763 0.0162218
716716 0 0
717717 32.2199 1.20327
718718 0 0
719719 14.1370 0.527222 0.263611 0.964629i 0.415086π-0.415086\pi
0.263611 + 0.964629i 0.415086π0.415086\pi
720720 0 0
721721 0 0
722722 0 0
723723 −58.1762 −2.16360
724724 0 0
725725 −4.16519 −0.154691
726726 0 0
727727 −15.2790 −0.566667 −0.283333 0.959021i 0.591440π-0.591440\pi
−0.283333 + 0.959021i 0.591440π0.591440\pi
728728 0 0
729729 −40.4688 −1.49885
730730 0 0
731731 4.64590 0.171835
732732 0 0
733733 1.34493 0.0496762 0.0248381 0.999691i 0.492093π-0.492093\pi
0.0248381 + 0.999691i 0.492093π0.492093\pi
734734 0 0
735735 0 0
736736 0 0
737737 3.75877 0.138456
738738 0 0
739739 25.6536 0.943684 0.471842 0.881683i 0.343589π-0.343589\pi
0.471842 + 0.881683i 0.343589π0.343589\pi
740740 0 0
741741 −0.411474 −0.0151159
742742 0 0
743743 6.08109 0.223094 0.111547 0.993759i 0.464420π-0.464420\pi
0.111547 + 0.993759i 0.464420π0.464420\pi
744744 0 0
745745 −1.67642 −0.0614194
746746 0 0
747747 −17.7510 −0.649476
748748 0 0
749749 0 0
750750 0 0
751751 −20.8108 −0.759396 −0.379698 0.925111i 0.623972π-0.623972\pi
−0.379698 + 0.925111i 0.623972π0.623972\pi
752752 0 0
753753 −16.9659 −0.618270
754754 0 0
755755 22.4047 0.815389
756756 0 0
757757 −5.25402 −0.190961 −0.0954804 0.995431i 0.530439π-0.530439\pi
−0.0954804 + 0.995431i 0.530439π0.530439\pi
758758 0 0
759759 −24.0574 −0.873227
760760 0 0
761761 −40.9813 −1.48557 −0.742786 0.669529i 0.766496π-0.766496\pi
−0.742786 + 0.669529i 0.766496π0.766496\pi
762762 0 0
763763 0 0
764764 0 0
765765 −48.6991 −1.76072
766766 0 0
767767 0.0377703 0.00136381
768768 0 0
769769 47.5580 1.71499 0.857493 0.514496i 0.172021π-0.172021\pi
0.857493 + 0.514496i 0.172021π0.172021\pi
770770 0 0
771771 7.87939 0.283769
772772 0 0
773773 20.4929 0.737078 0.368539 0.929612i 0.379858π-0.379858\pi
0.368539 + 0.929612i 0.379858π0.379858\pi
774774 0 0
775775 −1.35235 −0.0485778
776776 0 0
777777 0 0
778778 0 0
779779 −0.329451 −0.0118038
780780 0 0
781781 −9.96585 −0.356606
782782 0 0
783783 53.8931 1.92598
784784 0 0
785785 21.6919 0.774217
786786 0 0
787787 19.1206 0.681576 0.340788 0.940140i 0.389306π-0.389306\pi
0.340788 + 0.940140i 0.389306π0.389306\pi
788788 0 0
789789 17.8452 0.635307
790790 0 0
791791 0 0
792792 0 0
793793 −2.69459 −0.0956878
794794 0 0
795795 −44.2995 −1.57114
796796 0 0
797797 −52.5144 −1.86015 −0.930077 0.367365i 0.880260π-0.880260\pi
−0.930077 + 0.367365i 0.880260π0.880260\pi
798798 0 0
799799 −30.1156 −1.06541
800800 0 0
801801 −24.6168 −0.869792
802802 0 0
803803 −0.120615 −0.00425640
804804 0 0
805805 0 0
806806 0 0
807807 12.1206 0.426666
808808 0 0
809809 40.6715 1.42993 0.714967 0.699159i 0.246442π-0.246442\pi
0.714967 + 0.699159i 0.246442π0.246442\pi
810810 0 0
811811 20.5648 0.722128 0.361064 0.932541i 0.382414π-0.382414\pi
0.361064 + 0.932541i 0.382414π0.382414\pi
812812 0 0
813813 73.6596 2.58336
814814 0 0
815815 20.6641 0.723831
816816 0 0
817817 0.916222 0.0320545
818818 0 0
819819 0 0
820820 0 0
821821 6.36278 0.222062 0.111031 0.993817i 0.464585π-0.464585\pi
0.111031 + 0.993817i 0.464585π0.464585\pi
822822 0 0
823823 2.50887 0.0874536 0.0437268 0.999044i 0.486077π-0.486077\pi
0.0437268 + 0.999044i 0.486077π0.486077\pi
824824 0 0
825825 1.46791 0.0511061
826826 0 0
827827 41.2645 1.43491 0.717453 0.696607i 0.245308π-0.245308\pi
0.717453 + 0.696607i 0.245308π0.245308\pi
828828 0 0
829829 −46.7779 −1.62466 −0.812331 0.583196i 0.801802π-0.801802\pi
−0.812331 + 0.583196i 0.801802π0.801802\pi
830830 0 0
831831 44.2208 1.53400
832832 0 0
833833 0 0
834834 0 0
835835 −19.6759 −0.680913
836836 0 0
837837 17.4979 0.604817
838838 0 0
839839 −16.5439 −0.571161 −0.285580 0.958355i 0.592186π-0.592186\pi
−0.285580 + 0.958355i 0.592186π0.592186\pi
840840 0 0
841841 37.7529 1.30182
842842 0 0
843843 −55.4397 −1.90945
844844 0 0
845845 −30.4347 −1.04699
846846 0 0
847847 0 0
848848 0 0
849849 −77.9309 −2.67458
850850 0 0
851851 57.0060 1.95414
852852 0 0
853853 13.2163 0.452516 0.226258 0.974067i 0.427351π-0.427351\pi
0.226258 + 0.974067i 0.427351π0.427351\pi
854854 0 0
855855 −9.60401 −0.328450
856856 0 0
857857 −50.7211 −1.73260 −0.866300 0.499524i 0.833508π-0.833508\pi
−0.866300 + 0.499524i 0.833508π0.833508\pi
858858 0 0
859859 −55.1124 −1.88041 −0.940205 0.340609i 0.889367π-0.889367\pi
−0.940205 + 0.340609i 0.889367π0.889367\pi
860860 0 0
861861 0 0
862862 0 0
863863 −10.5202 −0.358113 −0.179056 0.983839i 0.557304π-0.557304\pi
−0.179056 + 0.983839i 0.557304π0.557304\pi
864864 0 0
865865 12.7825 0.434618
866866 0 0
867867 4.67499 0.158771
868868 0 0
869869 0.327696 0.0111163
870870 0 0
871871 0.694593 0.0235354
872872 0 0
873873 69.4193 2.34949
874874 0 0
875875 0 0
876876 0 0
877877 −39.6536 −1.33901 −0.669504 0.742808i 0.733493π-0.733493\pi
−0.669504 + 0.742808i 0.733493π0.733493\pi
878878 0 0
879879 −11.6186 −0.391884
880880 0 0
881881 25.0077 0.842532 0.421266 0.906937i 0.361586π-0.361586\pi
0.421266 + 0.906937i 0.361586π0.361586\pi
882882 0 0
883883 −50.9341 −1.71407 −0.857034 0.515260i 0.827695π-0.827695\pi
−0.857034 + 0.515260i 0.827695π0.827695\pi
884884 0 0
885885 1.38144 0.0464368
886886 0 0
887887 −32.0360 −1.07566 −0.537832 0.843052i 0.680757π-0.680757\pi
−0.537832 + 0.843052i 0.680757π0.680757\pi
888888 0 0
889889 0 0
890890 0 0
891891 −3.12061 −0.104545
892892 0 0
893893 −5.93912 −0.198745
894894 0 0
895895 23.6878 0.791795
896896 0 0
897897 −4.44562 −0.148435
898898 0 0
899899 21.6732 0.722843
900900 0 0
901901 −25.7015 −0.856242
902902 0 0
903903 0 0
904904 0 0
905905 46.6628 1.55112
906906 0 0
907907 16.4730 0.546976 0.273488 0.961875i 0.411823π-0.411823\pi
0.273488 + 0.961875i 0.411823π0.411823\pi
908908 0 0
909909 −31.2249 −1.03567
910910 0 0
911911 45.3979 1.50410 0.752049 0.659107i 0.229066π-0.229066\pi
0.752049 + 0.659107i 0.229066π0.229066\pi
912912 0 0
913913 3.35504 0.111036
914914 0 0
915915 −98.5545 −3.25811
916916 0 0
917917 0 0
918918 0 0
919919 12.3209 0.406429 0.203214 0.979134i 0.434861π-0.434861\pi
0.203214 + 0.979134i 0.434861π0.434861\pi
920920 0 0
921921 8.43376 0.277902
922922 0 0
923923 −1.84161 −0.0606175
924924 0 0
925925 −3.47834 −0.114367
926926 0 0
927927 −4.87433 −0.160094
928928 0 0
929929 5.93313 0.194660 0.0973299 0.995252i 0.468970π-0.468970\pi
0.0973299 + 0.995252i 0.468970π0.468970\pi
930930 0 0
931931 0 0
932932 0 0
933933 44.9864 1.47279
934934 0 0
935935 9.20439 0.301016
936936 0 0
937937 −45.0242 −1.47088 −0.735438 0.677593i 0.763023π-0.763023\pi
−0.735438 + 0.677593i 0.763023π0.763023\pi
938938 0 0
939939 63.2772 2.06497
940940 0 0
941941 −6.06242 −0.197629 −0.0988147 0.995106i 0.531505π-0.531505\pi
−0.0988147 + 0.995106i 0.531505π0.531505\pi
942942 0 0
943943 −3.55943 −0.115911
944944 0 0
945945 0 0
946946 0 0
947947 18.9426 0.615553 0.307776 0.951459i 0.400415π-0.400415\pi
0.307776 + 0.951459i 0.400415π0.400415\pi
948948 0 0
949949 −0.0222887 −0.000723522 0
950950 0 0
951951 8.67230 0.281219
952952 0 0
953953 −12.4970 −0.404818 −0.202409 0.979301i 0.564877π-0.564877\pi
−0.202409 + 0.979301i 0.564877π0.564877\pi
954954 0 0
955955 59.5863 1.92817
956956 0 0
957957 −23.5253 −0.760464
958958 0 0
959959 0 0
960960 0 0
961961 −23.9632 −0.773005
962962 0 0
963963 54.7461 1.76417
964964 0 0
965965 −18.1480 −0.584203
966966 0 0
967967 18.5294 0.595865 0.297933 0.954587i 0.403703π-0.403703\pi
0.297933 + 0.954587i 0.403703π0.403703\pi
968968 0 0
969969 −8.73143 −0.280494
970970 0 0
971971 −41.4739 −1.33096 −0.665480 0.746415i 0.731773π-0.731773\pi
−0.665480 + 0.746415i 0.731773π0.731773\pi
972972 0 0
973973 0 0
974974 0 0
975975 0.271259 0.00868724
976976 0 0
977977 −22.2321 −0.711267 −0.355633 0.934626i 0.615735π-0.615735\pi
−0.355633 + 0.934626i 0.615735π0.615735\pi
978978 0 0
979979 4.65270 0.148701
980980 0 0
981981 2.51661 0.0803491
982982 0 0
983983 −35.4124 −1.12948 −0.564740 0.825269i 0.691024π-0.691024\pi
−0.564740 + 0.825269i 0.691024π0.691024\pi
984984 0 0
985985 −12.6159 −0.401975
986986 0 0
987987 0 0
988988 0 0
989989 9.89899 0.314769
990990 0 0
991991 −45.5725 −1.44766 −0.723830 0.689979i 0.757620π-0.757620\pi
−0.723830 + 0.689979i 0.757620π0.757620\pi
992992 0 0
993993 79.0934 2.50995
994994 0 0
995995 −20.6117 −0.653436
996996 0 0
997997 22.8367 0.723245 0.361622 0.932325i 0.382223π-0.382223\pi
0.361622 + 0.932325i 0.382223π0.382223\pi
998998 0 0
999999 45.0060 1.42393
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 8624.2.a.ch.1.1 3
4.3 odd 2 539.2.a.j.1.1 3
7.2 even 3 1232.2.q.m.529.3 6
7.4 even 3 1232.2.q.m.177.3 6
7.6 odd 2 8624.2.a.co.1.3 3
12.11 even 2 4851.2.a.bj.1.3 3
28.3 even 6 539.2.e.m.177.3 6
28.11 odd 6 77.2.e.a.23.3 6
28.19 even 6 539.2.e.m.67.3 6
28.23 odd 6 77.2.e.a.67.3 yes 6
28.27 even 2 539.2.a.g.1.1 3
44.43 even 2 5929.2.a.x.1.3 3
84.11 even 6 693.2.i.h.100.1 6
84.23 even 6 693.2.i.h.298.1 6
84.83 odd 2 4851.2.a.bk.1.3 3
308.39 even 30 847.2.n.f.366.1 24
308.51 even 30 847.2.n.f.753.3 24
308.79 even 30 847.2.n.f.81.1 24
308.95 even 30 847.2.n.f.632.1 24
308.107 even 30 847.2.n.f.130.1 24
308.123 even 30 847.2.n.f.807.3 24
308.135 odd 30 847.2.n.g.130.3 24
308.151 even 30 847.2.n.f.9.3 24
308.163 odd 30 847.2.n.g.81.3 24
308.179 odd 30 847.2.n.g.9.1 24
308.191 odd 30 847.2.n.g.753.1 24
308.207 odd 30 847.2.n.g.807.1 24
308.219 even 6 847.2.e.c.606.1 6
308.235 odd 30 847.2.n.g.632.3 24
308.247 odd 30 847.2.n.g.487.1 24
308.263 even 6 847.2.e.c.485.1 6
308.291 odd 30 847.2.n.g.366.3 24
308.303 even 30 847.2.n.f.487.3 24
308.307 odd 2 5929.2.a.u.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.e.a.23.3 6 28.11 odd 6
77.2.e.a.67.3 yes 6 28.23 odd 6
539.2.a.g.1.1 3 28.27 even 2
539.2.a.j.1.1 3 4.3 odd 2
539.2.e.m.67.3 6 28.19 even 6
539.2.e.m.177.3 6 28.3 even 6
693.2.i.h.100.1 6 84.11 even 6
693.2.i.h.298.1 6 84.23 even 6
847.2.e.c.485.1 6 308.263 even 6
847.2.e.c.606.1 6 308.219 even 6
847.2.n.f.9.3 24 308.151 even 30
847.2.n.f.81.1 24 308.79 even 30
847.2.n.f.130.1 24 308.107 even 30
847.2.n.f.366.1 24 308.39 even 30
847.2.n.f.487.3 24 308.303 even 30
847.2.n.f.632.1 24 308.95 even 30
847.2.n.f.753.3 24 308.51 even 30
847.2.n.f.807.3 24 308.123 even 30
847.2.n.g.9.1 24 308.179 odd 30
847.2.n.g.81.3 24 308.163 odd 30
847.2.n.g.130.3 24 308.135 odd 30
847.2.n.g.366.3 24 308.291 odd 30
847.2.n.g.487.1 24 308.247 odd 30
847.2.n.g.632.3 24 308.235 odd 30
847.2.n.g.753.1 24 308.191 odd 30
847.2.n.g.807.1 24 308.207 odd 30
1232.2.q.m.177.3 6 7.4 even 3
1232.2.q.m.529.3 6 7.2 even 3
4851.2.a.bj.1.3 3 12.11 even 2
4851.2.a.bk.1.3 3 84.83 odd 2
5929.2.a.u.1.3 3 308.307 odd 2
5929.2.a.x.1.3 3 44.43 even 2
8624.2.a.ch.1.1 3 1.1 even 1 trivial
8624.2.a.co.1.3 3 7.6 odd 2