Properties

Label 3150.2.a.j.1.1
Level 31503150
Weight 22
Character 3150.1
Self dual yes
Analytic conductor 25.15325.153
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] = [3150,2,Mod(1,3150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("3150.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3150=232527 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3150.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: 25.152876636725.1528766367
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 350)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 3150.1

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) == q1.00000q2+1.00000q41.00000q71.00000q8+5.00000q116.00000q13+1.00000q14+1.00000q16+1.00000q173.00000q195.00000q22+6.00000q261.00000q28+6.00000q294.00000q311.00000q321.00000q34+8.00000q37+3.00000q3811.0000q418.00000q43+5.00000q442.00000q47+1.00000q496.00000q524.00000q53+1.00000q566.00000q584.00000q592.00000q61+4.00000q62+1.00000q64+9.00000q67+1.00000q68+10.0000q717.00000q738.00000q743.00000q765.00000q772.00000q79+11.0000q8211.0000q83+8.00000q865.00000q88+11.0000q89+6.00000q91+2.00000q9410.0000q971.00000q98+O(q100)q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{11} -6.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} -3.00000 q^{19} -5.00000 q^{22} +6.00000 q^{26} -1.00000 q^{28} +6.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} -1.00000 q^{34} +8.00000 q^{37} +3.00000 q^{38} -11.0000 q^{41} -8.00000 q^{43} +5.00000 q^{44} -2.00000 q^{47} +1.00000 q^{49} -6.00000 q^{52} -4.00000 q^{53} +1.00000 q^{56} -6.00000 q^{58} -4.00000 q^{59} -2.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +9.00000 q^{67} +1.00000 q^{68} +10.0000 q^{71} -7.00000 q^{73} -8.00000 q^{74} -3.00000 q^{76} -5.00000 q^{77} -2.00000 q^{79} +11.0000 q^{82} -11.0000 q^{83} +8.00000 q^{86} -5.00000 q^{88} +11.0000 q^{89} +6.00000 q^{91} +2.00000 q^{94} -10.0000 q^{97} -1.00000 q^{98} +O(q^{100})

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.00000 −0.707107
33 0 0
44 1.00000 0.500000
55 0 0
66 0 0
77 −1.00000 −0.377964
88 −1.00000 −0.353553
99 0 0
1010 0 0
1111 5.00000 1.50756 0.753778 0.657129i 0.228229π-0.228229\pi
0.753778 + 0.657129i 0.228229π0.228229\pi
1212 0 0
1313 −6.00000 −1.66410 −0.832050 0.554700i 0.812833π-0.812833\pi
−0.832050 + 0.554700i 0.812833π0.812833\pi
1414 1.00000 0.267261
1515 0 0
1616 1.00000 0.250000
1717 1.00000 0.242536 0.121268 0.992620i 0.461304π-0.461304\pi
0.121268 + 0.992620i 0.461304π0.461304\pi
1818 0 0
1919 −3.00000 −0.688247 −0.344124 0.938924i 0.611824π-0.611824\pi
−0.344124 + 0.938924i 0.611824π0.611824\pi
2020 0 0
2121 0 0
2222 −5.00000 −1.06600
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 0 0
2525 0 0
2626 6.00000 1.17670
2727 0 0
2828 −1.00000 −0.188982
2929 6.00000 1.11417 0.557086 0.830455i 0.311919π-0.311919\pi
0.557086 + 0.830455i 0.311919π0.311919\pi
3030 0 0
3131 −4.00000 −0.718421 −0.359211 0.933257i 0.616954π-0.616954\pi
−0.359211 + 0.933257i 0.616954π0.616954\pi
3232 −1.00000 −0.176777
3333 0 0
3434 −1.00000 −0.171499
3535 0 0
3636 0 0
3737 8.00000 1.31519 0.657596 0.753371i 0.271573π-0.271573\pi
0.657596 + 0.753371i 0.271573π0.271573\pi
3838 3.00000 0.486664
3939 0 0
4040 0 0
4141 −11.0000 −1.71791 −0.858956 0.512050i 0.828886π-0.828886\pi
−0.858956 + 0.512050i 0.828886π0.828886\pi
4242 0 0
4343 −8.00000 −1.21999 −0.609994 0.792406i 0.708828π-0.708828\pi
−0.609994 + 0.792406i 0.708828π0.708828\pi
4444 5.00000 0.753778
4545 0 0
4646 0 0
4747 −2.00000 −0.291730 −0.145865 0.989305i 0.546597π-0.546597\pi
−0.145865 + 0.989305i 0.546597π0.546597\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 0 0
5252 −6.00000 −0.832050
5353 −4.00000 −0.549442 −0.274721 0.961524i 0.588586π-0.588586\pi
−0.274721 + 0.961524i 0.588586π0.588586\pi
5454 0 0
5555 0 0
5656 1.00000 0.133631
5757 0 0
5858 −6.00000 −0.787839
5959 −4.00000 −0.520756 −0.260378 0.965507i 0.583847π-0.583847\pi
−0.260378 + 0.965507i 0.583847π0.583847\pi
6060 0 0
6161 −2.00000 −0.256074 −0.128037 0.991769i 0.540868π-0.540868\pi
−0.128037 + 0.991769i 0.540868π0.540868\pi
6262 4.00000 0.508001
6363 0 0
6464 1.00000 0.125000
6565 0 0
6666 0 0
6767 9.00000 1.09952 0.549762 0.835321i 0.314718π-0.314718\pi
0.549762 + 0.835321i 0.314718π0.314718\pi
6868 1.00000 0.121268
6969 0 0
7070 0 0
7171 10.0000 1.18678 0.593391 0.804914i 0.297789π-0.297789\pi
0.593391 + 0.804914i 0.297789π0.297789\pi
7272 0 0
7373 −7.00000 −0.819288 −0.409644 0.912245i 0.634347π-0.634347\pi
−0.409644 + 0.912245i 0.634347π0.634347\pi
7474 −8.00000 −0.929981
7575 0 0
7676 −3.00000 −0.344124
7777 −5.00000 −0.569803
7878 0 0
7979 −2.00000 −0.225018 −0.112509 0.993651i 0.535889π-0.535889\pi
−0.112509 + 0.993651i 0.535889π0.535889\pi
8080 0 0
8181 0 0
8282 11.0000 1.21475
8383 −11.0000 −1.20741 −0.603703 0.797209i 0.706309π-0.706309\pi
−0.603703 + 0.797209i 0.706309π0.706309\pi
8484 0 0
8585 0 0
8686 8.00000 0.862662
8787 0 0
8888 −5.00000 −0.533002
8989 11.0000 1.16600 0.582999 0.812473i 0.301879π-0.301879\pi
0.582999 + 0.812473i 0.301879π0.301879\pi
9090 0 0
9191 6.00000 0.628971
9292 0 0
9393 0 0
9494 2.00000 0.206284
9595 0 0
9696 0 0
9797 −10.0000 −1.01535 −0.507673 0.861550i 0.669494π-0.669494\pi
−0.507673 + 0.861550i 0.669494π0.669494\pi
9898 −1.00000 −0.101015
9999 0 0
100100 0 0
101101 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
102102 0 0
103103 4.00000 0.394132 0.197066 0.980390i 0.436859π-0.436859\pi
0.197066 + 0.980390i 0.436859π0.436859\pi
104104 6.00000 0.588348
105105 0 0
106106 4.00000 0.388514
107107 −3.00000 −0.290021 −0.145010 0.989430i 0.546322π-0.546322\pi
−0.145010 + 0.989430i 0.546322π0.546322\pi
108108 0 0
109109 −18.0000 −1.72409 −0.862044 0.506834i 0.830816π-0.830816\pi
−0.862044 + 0.506834i 0.830816π0.830816\pi
110110 0 0
111111 0 0
112112 −1.00000 −0.0944911
113113 1.00000 0.0940721 0.0470360 0.998893i 0.485022π-0.485022\pi
0.0470360 + 0.998893i 0.485022π0.485022\pi
114114 0 0
115115 0 0
116116 6.00000 0.557086
117117 0 0
118118 4.00000 0.368230
119119 −1.00000 −0.0916698
120120 0 0
121121 14.0000 1.27273
122122 2.00000 0.181071
123123 0 0
124124 −4.00000 −0.359211
125125 0 0
126126 0 0
127127 −14.0000 −1.24230 −0.621150 0.783692i 0.713334π-0.713334\pi
−0.621150 + 0.783692i 0.713334π0.713334\pi
128128 −1.00000 −0.0883883
129129 0 0
130130 0 0
131131 −8.00000 −0.698963 −0.349482 0.936943i 0.613642π-0.613642\pi
−0.349482 + 0.936943i 0.613642π0.613642\pi
132132 0 0
133133 3.00000 0.260133
134134 −9.00000 −0.777482
135135 0 0
136136 −1.00000 −0.0857493
137137 3.00000 0.256307 0.128154 0.991754i 0.459095π-0.459095\pi
0.128154 + 0.991754i 0.459095π0.459095\pi
138138 0 0
139139 −11.0000 −0.933008 −0.466504 0.884519i 0.654487π-0.654487\pi
−0.466504 + 0.884519i 0.654487π0.654487\pi
140140 0 0
141141 0 0
142142 −10.0000 −0.839181
143143 −30.0000 −2.50873
144144 0 0
145145 0 0
146146 7.00000 0.579324
147147 0 0
148148 8.00000 0.657596
149149 −12.0000 −0.983078 −0.491539 0.870855i 0.663566π-0.663566\pi
−0.491539 + 0.870855i 0.663566π0.663566\pi
150150 0 0
151151 8.00000 0.651031 0.325515 0.945537i 0.394462π-0.394462\pi
0.325515 + 0.945537i 0.394462π0.394462\pi
152152 3.00000 0.243332
153153 0 0
154154 5.00000 0.402911
155155 0 0
156156 0 0
157157 4.00000 0.319235 0.159617 0.987179i 0.448974π-0.448974\pi
0.159617 + 0.987179i 0.448974π0.448974\pi
158158 2.00000 0.159111
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 −19.0000 −1.48819 −0.744097 0.668071i 0.767120π-0.767120\pi
−0.744097 + 0.668071i 0.767120π0.767120\pi
164164 −11.0000 −0.858956
165165 0 0
166166 11.0000 0.853766
167167 −12.0000 −0.928588 −0.464294 0.885681i 0.653692π-0.653692\pi
−0.464294 + 0.885681i 0.653692π0.653692\pi
168168 0 0
169169 23.0000 1.76923
170170 0 0
171171 0 0
172172 −8.00000 −0.609994
173173 −2.00000 −0.152057 −0.0760286 0.997106i 0.524224π-0.524224\pi
−0.0760286 + 0.997106i 0.524224π0.524224\pi
174174 0 0
175175 0 0
176176 5.00000 0.376889
177177 0 0
178178 −11.0000 −0.824485
179179 −3.00000 −0.224231 −0.112115 0.993695i 0.535763π-0.535763\pi
−0.112115 + 0.993695i 0.535763π0.535763\pi
180180 0 0
181181 10.0000 0.743294 0.371647 0.928374i 0.378793π-0.378793\pi
0.371647 + 0.928374i 0.378793π0.378793\pi
182182 −6.00000 −0.444750
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 5.00000 0.365636
188188 −2.00000 −0.145865
189189 0 0
190190 0 0
191191 6.00000 0.434145 0.217072 0.976156i 0.430349π-0.430349\pi
0.217072 + 0.976156i 0.430349π0.430349\pi
192192 0 0
193193 −19.0000 −1.36765 −0.683825 0.729646i 0.739685π-0.739685\pi
−0.683825 + 0.729646i 0.739685π0.739685\pi
194194 10.0000 0.717958
195195 0 0
196196 1.00000 0.0714286
197197 22.0000 1.56744 0.783718 0.621117i 0.213321π-0.213321\pi
0.783718 + 0.621117i 0.213321π0.213321\pi
198198 0 0
199199 −10.0000 −0.708881 −0.354441 0.935079i 0.615329π-0.615329\pi
−0.354441 + 0.935079i 0.615329π0.615329\pi
200200 0 0
201201 0 0
202202 0 0
203203 −6.00000 −0.421117
204204 0 0
205205 0 0
206206 −4.00000 −0.278693
207207 0 0
208208 −6.00000 −0.416025
209209 −15.0000 −1.03757
210210 0 0
211211 1.00000 0.0688428 0.0344214 0.999407i 0.489041π-0.489041\pi
0.0344214 + 0.999407i 0.489041π0.489041\pi
212212 −4.00000 −0.274721
213213 0 0
214214 3.00000 0.205076
215215 0 0
216216 0 0
217217 4.00000 0.271538
218218 18.0000 1.21911
219219 0 0
220220 0 0
221221 −6.00000 −0.403604
222222 0 0
223223 22.0000 1.47323 0.736614 0.676313i 0.236423π-0.236423\pi
0.736614 + 0.676313i 0.236423π0.236423\pi
224224 1.00000 0.0668153
225225 0 0
226226 −1.00000 −0.0665190
227227 28.0000 1.85843 0.929213 0.369546i 0.120487π-0.120487\pi
0.929213 + 0.369546i 0.120487π0.120487\pi
228228 0 0
229229 −14.0000 −0.925146 −0.462573 0.886581i 0.653074π-0.653074\pi
−0.462573 + 0.886581i 0.653074π0.653074\pi
230230 0 0
231231 0 0
232232 −6.00000 −0.393919
233233 −6.00000 −0.393073 −0.196537 0.980497i 0.562969π-0.562969\pi
−0.196537 + 0.980497i 0.562969π0.562969\pi
234234 0 0
235235 0 0
236236 −4.00000 −0.260378
237237 0 0
238238 1.00000 0.0648204
239239 −4.00000 −0.258738 −0.129369 0.991596i 0.541295π-0.541295\pi
−0.129369 + 0.991596i 0.541295π0.541295\pi
240240 0 0
241241 −5.00000 −0.322078 −0.161039 0.986948i 0.551485π-0.551485\pi
−0.161039 + 0.986948i 0.551485π0.551485\pi
242242 −14.0000 −0.899954
243243 0 0
244244 −2.00000 −0.128037
245245 0 0
246246 0 0
247247 18.0000 1.14531
248248 4.00000 0.254000
249249 0 0
250250 0 0
251251 −27.0000 −1.70422 −0.852112 0.523359i 0.824679π-0.824679\pi
−0.852112 + 0.523359i 0.824679π0.824679\pi
252252 0 0
253253 0 0
254254 14.0000 0.878438
255255 0 0
256256 1.00000 0.0625000
257257 −2.00000 −0.124757 −0.0623783 0.998053i 0.519869π-0.519869\pi
−0.0623783 + 0.998053i 0.519869π0.519869\pi
258258 0 0
259259 −8.00000 −0.497096
260260 0 0
261261 0 0
262262 8.00000 0.494242
263263 10.0000 0.616626 0.308313 0.951285i 0.400236π-0.400236\pi
0.308313 + 0.951285i 0.400236π0.400236\pi
264264 0 0
265265 0 0
266266 −3.00000 −0.183942
267267 0 0
268268 9.00000 0.549762
269269 −18.0000 −1.09748 −0.548740 0.835993i 0.684892π-0.684892\pi
−0.548740 + 0.835993i 0.684892π0.684892\pi
270270 0 0
271271 −6.00000 −0.364474 −0.182237 0.983255i 0.558334π-0.558334\pi
−0.182237 + 0.983255i 0.558334π0.558334\pi
272272 1.00000 0.0606339
273273 0 0
274274 −3.00000 −0.181237
275275 0 0
276276 0 0
277277 −30.0000 −1.80253 −0.901263 0.433273i 0.857359π-0.857359\pi
−0.901263 + 0.433273i 0.857359π0.857359\pi
278278 11.0000 0.659736
279279 0 0
280280 0 0
281281 −14.0000 −0.835170 −0.417585 0.908638i 0.637123π-0.637123\pi
−0.417585 + 0.908638i 0.637123π0.637123\pi
282282 0 0
283283 −13.0000 −0.772770 −0.386385 0.922338i 0.626276π-0.626276\pi
−0.386385 + 0.922338i 0.626276π0.626276\pi
284284 10.0000 0.593391
285285 0 0
286286 30.0000 1.77394
287287 11.0000 0.649309
288288 0 0
289289 −16.0000 −0.941176
290290 0 0
291291 0 0
292292 −7.00000 −0.409644
293293 14.0000 0.817889 0.408944 0.912559i 0.365897π-0.365897\pi
0.408944 + 0.912559i 0.365897π0.365897\pi
294294 0 0
295295 0 0
296296 −8.00000 −0.464991
297297 0 0
298298 12.0000 0.695141
299299 0 0
300300 0 0
301301 8.00000 0.461112
302302 −8.00000 −0.460348
303303 0 0
304304 −3.00000 −0.172062
305305 0 0
306306 0 0
307307 13.0000 0.741949 0.370975 0.928643i 0.379024π-0.379024\pi
0.370975 + 0.928643i 0.379024π0.379024\pi
308308 −5.00000 −0.284901
309309 0 0
310310 0 0
311311 −6.00000 −0.340229 −0.170114 0.985424i 0.554414π-0.554414\pi
−0.170114 + 0.985424i 0.554414π0.554414\pi
312312 0 0
313313 −10.0000 −0.565233 −0.282617 0.959233i 0.591202π-0.591202\pi
−0.282617 + 0.959233i 0.591202π0.591202\pi
314314 −4.00000 −0.225733
315315 0 0
316316 −2.00000 −0.112509
317317 −4.00000 −0.224662 −0.112331 0.993671i 0.535832π-0.535832\pi
−0.112331 + 0.993671i 0.535832π0.535832\pi
318318 0 0
319319 30.0000 1.67968
320320 0 0
321321 0 0
322322 0 0
323323 −3.00000 −0.166924
324324 0 0
325325 0 0
326326 19.0000 1.05231
327327 0 0
328328 11.0000 0.607373
329329 2.00000 0.110264
330330 0 0
331331 −17.0000 −0.934405 −0.467202 0.884150i 0.654738π-0.654738\pi
−0.467202 + 0.884150i 0.654738π0.654738\pi
332332 −11.0000 −0.603703
333333 0 0
334334 12.0000 0.656611
335335 0 0
336336 0 0
337337 −29.0000 −1.57973 −0.789865 0.613280i 0.789850π-0.789850\pi
−0.789865 + 0.613280i 0.789850π0.789850\pi
338338 −23.0000 −1.25104
339339 0 0
340340 0 0
341341 −20.0000 −1.08306
342342 0 0
343343 −1.00000 −0.0539949
344344 8.00000 0.431331
345345 0 0
346346 2.00000 0.107521
347347 −19.0000 −1.01997 −0.509987 0.860182i 0.670350π-0.670350\pi
−0.509987 + 0.860182i 0.670350π0.670350\pi
348348 0 0
349349 −8.00000 −0.428230 −0.214115 0.976808i 0.568687π-0.568687\pi
−0.214115 + 0.976808i 0.568687π0.568687\pi
350350 0 0
351351 0 0
352352 −5.00000 −0.266501
353353 18.0000 0.958043 0.479022 0.877803i 0.340992π-0.340992\pi
0.479022 + 0.877803i 0.340992π0.340992\pi
354354 0 0
355355 0 0
356356 11.0000 0.582999
357357 0 0
358358 3.00000 0.158555
359359 −26.0000 −1.37223 −0.686114 0.727494i 0.740685π-0.740685\pi
−0.686114 + 0.727494i 0.740685π0.740685\pi
360360 0 0
361361 −10.0000 −0.526316
362362 −10.0000 −0.525588
363363 0 0
364364 6.00000 0.314485
365365 0 0
366366 0 0
367367 −8.00000 −0.417597 −0.208798 0.977959i 0.566955π-0.566955\pi
−0.208798 + 0.977959i 0.566955π0.566955\pi
368368 0 0
369369 0 0
370370 0 0
371371 4.00000 0.207670
372372 0 0
373373 −4.00000 −0.207112 −0.103556 0.994624i 0.533022π-0.533022\pi
−0.103556 + 0.994624i 0.533022π0.533022\pi
374374 −5.00000 −0.258544
375375 0 0
376376 2.00000 0.103142
377377 −36.0000 −1.85409
378378 0 0
379379 9.00000 0.462299 0.231149 0.972918i 0.425751π-0.425751\pi
0.231149 + 0.972918i 0.425751π0.425751\pi
380380 0 0
381381 0 0
382382 −6.00000 −0.306987
383383 6.00000 0.306586 0.153293 0.988181i 0.451012π-0.451012\pi
0.153293 + 0.988181i 0.451012π0.451012\pi
384384 0 0
385385 0 0
386386 19.0000 0.967075
387387 0 0
388388 −10.0000 −0.507673
389389 −8.00000 −0.405616 −0.202808 0.979219i 0.565007π-0.565007\pi
−0.202808 + 0.979219i 0.565007π0.565007\pi
390390 0 0
391391 0 0
392392 −1.00000 −0.0505076
393393 0 0
394394 −22.0000 −1.10834
395395 0 0
396396 0 0
397397 10.0000 0.501886 0.250943 0.968002i 0.419259π-0.419259\pi
0.250943 + 0.968002i 0.419259π0.419259\pi
398398 10.0000 0.501255
399399 0 0
400400 0 0
401401 −37.0000 −1.84769 −0.923846 0.382765i 0.874972π-0.874972\pi
−0.923846 + 0.382765i 0.874972π0.874972\pi
402402 0 0
403403 24.0000 1.19553
404404 0 0
405405 0 0
406406 6.00000 0.297775
407407 40.0000 1.98273
408408 0 0
409409 −21.0000 −1.03838 −0.519192 0.854658i 0.673767π-0.673767\pi
−0.519192 + 0.854658i 0.673767π0.673767\pi
410410 0 0
411411 0 0
412412 4.00000 0.197066
413413 4.00000 0.196827
414414 0 0
415415 0 0
416416 6.00000 0.294174
417417 0 0
418418 15.0000 0.733674
419419 39.0000 1.90527 0.952637 0.304109i 0.0983586π-0.0983586\pi
0.952637 + 0.304109i 0.0983586π0.0983586\pi
420420 0 0
421421 20.0000 0.974740 0.487370 0.873195i 0.337956π-0.337956\pi
0.487370 + 0.873195i 0.337956π0.337956\pi
422422 −1.00000 −0.0486792
423423 0 0
424424 4.00000 0.194257
425425 0 0
426426 0 0
427427 2.00000 0.0967868
428428 −3.00000 −0.145010
429429 0 0
430430 0 0
431431 36.0000 1.73406 0.867029 0.498257i 0.166026π-0.166026\pi
0.867029 + 0.498257i 0.166026π0.166026\pi
432432 0 0
433433 −1.00000 −0.0480569 −0.0240285 0.999711i 0.507649π-0.507649\pi
−0.0240285 + 0.999711i 0.507649π0.507649\pi
434434 −4.00000 −0.192006
435435 0 0
436436 −18.0000 −0.862044
437437 0 0
438438 0 0
439439 28.0000 1.33637 0.668184 0.743996i 0.267072π-0.267072\pi
0.668184 + 0.743996i 0.267072π0.267072\pi
440440 0 0
441441 0 0
442442 6.00000 0.285391
443443 −37.0000 −1.75792 −0.878962 0.476893i 0.841763π-0.841763\pi
−0.878962 + 0.476893i 0.841763π0.841763\pi
444444 0 0
445445 0 0
446446 −22.0000 −1.04173
447447 0 0
448448 −1.00000 −0.0472456
449449 −33.0000 −1.55737 −0.778683 0.627417i 0.784112π-0.784112\pi
−0.778683 + 0.627417i 0.784112π0.784112\pi
450450 0 0
451451 −55.0000 −2.58985
452452 1.00000 0.0470360
453453 0 0
454454 −28.0000 −1.31411
455455 0 0
456456 0 0
457457 25.0000 1.16945 0.584725 0.811231i 0.301202π-0.301202\pi
0.584725 + 0.811231i 0.301202π0.301202\pi
458458 14.0000 0.654177
459459 0 0
460460 0 0
461461 38.0000 1.76984 0.884918 0.465746i 0.154214π-0.154214\pi
0.884918 + 0.465746i 0.154214π0.154214\pi
462462 0 0
463463 8.00000 0.371792 0.185896 0.982569i 0.440481π-0.440481\pi
0.185896 + 0.982569i 0.440481π0.440481\pi
464464 6.00000 0.278543
465465 0 0
466466 6.00000 0.277945
467467 4.00000 0.185098 0.0925490 0.995708i 0.470499π-0.470499\pi
0.0925490 + 0.995708i 0.470499π0.470499\pi
468468 0 0
469469 −9.00000 −0.415581
470470 0 0
471471 0 0
472472 4.00000 0.184115
473473 −40.0000 −1.83920
474474 0 0
475475 0 0
476476 −1.00000 −0.0458349
477477 0 0
478478 4.00000 0.182956
479479 6.00000 0.274147 0.137073 0.990561i 0.456230π-0.456230\pi
0.137073 + 0.990561i 0.456230π0.456230\pi
480480 0 0
481481 −48.0000 −2.18861
482482 5.00000 0.227744
483483 0 0
484484 14.0000 0.636364
485485 0 0
486486 0 0
487487 −34.0000 −1.54069 −0.770344 0.637629i 0.779915π-0.779915\pi
−0.770344 + 0.637629i 0.779915π0.779915\pi
488488 2.00000 0.0905357
489489 0 0
490490 0 0
491491 12.0000 0.541552 0.270776 0.962642i 0.412720π-0.412720\pi
0.270776 + 0.962642i 0.412720π0.412720\pi
492492 0 0
493493 6.00000 0.270226
494494 −18.0000 −0.809858
495495 0 0
496496 −4.00000 −0.179605
497497 −10.0000 −0.448561
498498 0 0
499499 36.0000 1.61158 0.805791 0.592200i 0.201741π-0.201741\pi
0.805791 + 0.592200i 0.201741π0.201741\pi
500500 0 0
501501 0 0
502502 27.0000 1.20507
503503 30.0000 1.33763 0.668817 0.743427i 0.266801π-0.266801\pi
0.668817 + 0.743427i 0.266801π0.266801\pi
504504 0 0
505505 0 0
506506 0 0
507507 0 0
508508 −14.0000 −0.621150
509509 14.0000 0.620539 0.310270 0.950649i 0.399581π-0.399581\pi
0.310270 + 0.950649i 0.399581π0.399581\pi
510510 0 0
511511 7.00000 0.309662
512512 −1.00000 −0.0441942
513513 0 0
514514 2.00000 0.0882162
515515 0 0
516516 0 0
517517 −10.0000 −0.439799
518518 8.00000 0.351500
519519 0 0
520520 0 0
521521 −11.0000 −0.481919 −0.240959 0.970535i 0.577462π-0.577462\pi
−0.240959 + 0.970535i 0.577462π0.577462\pi
522522 0 0
523523 13.0000 0.568450 0.284225 0.958758i 0.408264π-0.408264\pi
0.284225 + 0.958758i 0.408264π0.408264\pi
524524 −8.00000 −0.349482
525525 0 0
526526 −10.0000 −0.436021
527527 −4.00000 −0.174243
528528 0 0
529529 −23.0000 −1.00000
530530 0 0
531531 0 0
532532 3.00000 0.130066
533533 66.0000 2.85878
534534 0 0
535535 0 0
536536 −9.00000 −0.388741
537537 0 0
538538 18.0000 0.776035
539539 5.00000 0.215365
540540 0 0
541541 −42.0000 −1.80572 −0.902861 0.429934i 0.858537π-0.858537\pi
−0.902861 + 0.429934i 0.858537π0.858537\pi
542542 6.00000 0.257722
543543 0 0
544544 −1.00000 −0.0428746
545545 0 0
546546 0 0
547547 27.0000 1.15444 0.577218 0.816590i 0.304138π-0.304138\pi
0.577218 + 0.816590i 0.304138π0.304138\pi
548548 3.00000 0.128154
549549 0 0
550550 0 0
551551 −18.0000 −0.766826
552552 0 0
553553 2.00000 0.0850487
554554 30.0000 1.27458
555555 0 0
556556 −11.0000 −0.466504
557557 −4.00000 −0.169485 −0.0847427 0.996403i 0.527007π-0.527007\pi
−0.0847427 + 0.996403i 0.527007π0.527007\pi
558558 0 0
559559 48.0000 2.03018
560560 0 0
561561 0 0
562562 14.0000 0.590554
563563 −20.0000 −0.842900 −0.421450 0.906852i 0.638479π-0.638479\pi
−0.421450 + 0.906852i 0.638479π0.638479\pi
564564 0 0
565565 0 0
566566 13.0000 0.546431
567567 0 0
568568 −10.0000 −0.419591
569569 −21.0000 −0.880366 −0.440183 0.897908i 0.645086π-0.645086\pi
−0.440183 + 0.897908i 0.645086π0.645086\pi
570570 0 0
571571 12.0000 0.502184 0.251092 0.967963i 0.419210π-0.419210\pi
0.251092 + 0.967963i 0.419210π0.419210\pi
572572 −30.0000 −1.25436
573573 0 0
574574 −11.0000 −0.459131
575575 0 0
576576 0 0
577577 13.0000 0.541197 0.270599 0.962692i 0.412778π-0.412778\pi
0.270599 + 0.962692i 0.412778π0.412778\pi
578578 16.0000 0.665512
579579 0 0
580580 0 0
581581 11.0000 0.456357
582582 0 0
583583 −20.0000 −0.828315
584584 7.00000 0.289662
585585 0 0
586586 −14.0000 −0.578335
587587 13.0000 0.536567 0.268284 0.963340i 0.413544π-0.413544\pi
0.268284 + 0.963340i 0.413544π0.413544\pi
588588 0 0
589589 12.0000 0.494451
590590 0 0
591591 0 0
592592 8.00000 0.328798
593593 39.0000 1.60154 0.800769 0.598973i 0.204424π-0.204424\pi
0.800769 + 0.598973i 0.204424π0.204424\pi
594594 0 0
595595 0 0
596596 −12.0000 −0.491539
597597 0 0
598598 0 0
599599 24.0000 0.980613 0.490307 0.871550i 0.336885π-0.336885\pi
0.490307 + 0.871550i 0.336885π0.336885\pi
600600 0 0
601601 21.0000 0.856608 0.428304 0.903635i 0.359111π-0.359111\pi
0.428304 + 0.903635i 0.359111π0.359111\pi
602602 −8.00000 −0.326056
603603 0 0
604604 8.00000 0.325515
605605 0 0
606606 0 0
607607 28.0000 1.13648 0.568242 0.822861i 0.307624π-0.307624\pi
0.568242 + 0.822861i 0.307624π0.307624\pi
608608 3.00000 0.121666
609609 0 0
610610 0 0
611611 12.0000 0.485468
612612 0 0
613613 18.0000 0.727013 0.363507 0.931592i 0.381579π-0.381579\pi
0.363507 + 0.931592i 0.381579π0.381579\pi
614614 −13.0000 −0.524637
615615 0 0
616616 5.00000 0.201456
617617 −14.0000 −0.563619 −0.281809 0.959470i 0.590935π-0.590935\pi
−0.281809 + 0.959470i 0.590935π0.590935\pi
618618 0 0
619619 −4.00000 −0.160774 −0.0803868 0.996764i 0.525616π-0.525616\pi
−0.0803868 + 0.996764i 0.525616π0.525616\pi
620620 0 0
621621 0 0
622622 6.00000 0.240578
623623 −11.0000 −0.440706
624624 0 0
625625 0 0
626626 10.0000 0.399680
627627 0 0
628628 4.00000 0.159617
629629 8.00000 0.318981
630630 0 0
631631 −16.0000 −0.636950 −0.318475 0.947931i 0.603171π-0.603171\pi
−0.318475 + 0.947931i 0.603171π0.603171\pi
632632 2.00000 0.0795557
633633 0 0
634634 4.00000 0.158860
635635 0 0
636636 0 0
637637 −6.00000 −0.237729
638638 −30.0000 −1.18771
639639 0 0
640640 0 0
641641 −2.00000 −0.0789953 −0.0394976 0.999220i 0.512576π-0.512576\pi
−0.0394976 + 0.999220i 0.512576π0.512576\pi
642642 0 0
643643 16.0000 0.630978 0.315489 0.948929i 0.397831π-0.397831\pi
0.315489 + 0.948929i 0.397831π0.397831\pi
644644 0 0
645645 0 0
646646 3.00000 0.118033
647647 8.00000 0.314512 0.157256 0.987558i 0.449735π-0.449735\pi
0.157256 + 0.987558i 0.449735π0.449735\pi
648648 0 0
649649 −20.0000 −0.785069
650650 0 0
651651 0 0
652652 −19.0000 −0.744097
653653 28.0000 1.09572 0.547862 0.836569i 0.315442π-0.315442\pi
0.547862 + 0.836569i 0.315442π0.315442\pi
654654 0 0
655655 0 0
656656 −11.0000 −0.429478
657657 0 0
658658 −2.00000 −0.0779681
659659 −1.00000 −0.0389545 −0.0194772 0.999810i 0.506200π-0.506200\pi
−0.0194772 + 0.999810i 0.506200π0.506200\pi
660660 0 0
661661 −50.0000 −1.94477 −0.972387 0.233373i 0.925024π-0.925024\pi
−0.972387 + 0.233373i 0.925024π0.925024\pi
662662 17.0000 0.660724
663663 0 0
664664 11.0000 0.426883
665665 0 0
666666 0 0
667667 0 0
668668 −12.0000 −0.464294
669669 0 0
670670 0 0
671671 −10.0000 −0.386046
672672 0 0
673673 34.0000 1.31060 0.655302 0.755367i 0.272541π-0.272541\pi
0.655302 + 0.755367i 0.272541π0.272541\pi
674674 29.0000 1.11704
675675 0 0
676676 23.0000 0.884615
677677 48.0000 1.84479 0.922395 0.386248i 0.126229π-0.126229\pi
0.922395 + 0.386248i 0.126229π0.126229\pi
678678 0 0
679679 10.0000 0.383765
680680 0 0
681681 0 0
682682 20.0000 0.765840
683683 13.0000 0.497431 0.248716 0.968577i 0.419992π-0.419992\pi
0.248716 + 0.968577i 0.419992π0.419992\pi
684684 0 0
685685 0 0
686686 1.00000 0.0381802
687687 0 0
688688 −8.00000 −0.304997
689689 24.0000 0.914327
690690 0 0
691691 49.0000 1.86405 0.932024 0.362397i 0.118041π-0.118041\pi
0.932024 + 0.362397i 0.118041π0.118041\pi
692692 −2.00000 −0.0760286
693693 0 0
694694 19.0000 0.721230
695695 0 0
696696 0 0
697697 −11.0000 −0.416655
698698 8.00000 0.302804
699699 0 0
700700 0 0
701701 32.0000 1.20862 0.604312 0.796748i 0.293448π-0.293448\pi
0.604312 + 0.796748i 0.293448π0.293448\pi
702702 0 0
703703 −24.0000 −0.905177
704704 5.00000 0.188445
705705 0 0
706706 −18.0000 −0.677439
707707 0 0
708708 0 0
709709 4.00000 0.150223 0.0751116 0.997175i 0.476069π-0.476069\pi
0.0751116 + 0.997175i 0.476069π0.476069\pi
710710 0 0
711711 0 0
712712 −11.0000 −0.412242
713713 0 0
714714 0 0
715715 0 0
716716 −3.00000 −0.112115
717717 0 0
718718 26.0000 0.970311
719719 48.0000 1.79010 0.895049 0.445968i 0.147140π-0.147140\pi
0.895049 + 0.445968i 0.147140π0.147140\pi
720720 0 0
721721 −4.00000 −0.148968
722722 10.0000 0.372161
723723 0 0
724724 10.0000 0.371647
725725 0 0
726726 0 0
727727 6.00000 0.222528 0.111264 0.993791i 0.464510π-0.464510\pi
0.111264 + 0.993791i 0.464510π0.464510\pi
728728 −6.00000 −0.222375
729729 0 0
730730 0 0
731731 −8.00000 −0.295891
732732 0 0
733733 40.0000 1.47743 0.738717 0.674016i 0.235432π-0.235432\pi
0.738717 + 0.674016i 0.235432π0.235432\pi
734734 8.00000 0.295285
735735 0 0
736736 0 0
737737 45.0000 1.65760
738738 0 0
739739 4.00000 0.147142 0.0735712 0.997290i 0.476560π-0.476560\pi
0.0735712 + 0.997290i 0.476560π0.476560\pi
740740 0 0
741741 0 0
742742 −4.00000 −0.146845
743743 24.0000 0.880475 0.440237 0.897881i 0.354894π-0.354894\pi
0.440237 + 0.897881i 0.354894π0.354894\pi
744744 0 0
745745 0 0
746746 4.00000 0.146450
747747 0 0
748748 5.00000 0.182818
749749 3.00000 0.109618
750750 0 0
751751 50.0000 1.82453 0.912263 0.409605i 0.134333π-0.134333\pi
0.912263 + 0.409605i 0.134333π0.134333\pi
752752 −2.00000 −0.0729325
753753 0 0
754754 36.0000 1.31104
755755 0 0
756756 0 0
757757 −2.00000 −0.0726912 −0.0363456 0.999339i 0.511572π-0.511572\pi
−0.0363456 + 0.999339i 0.511572π0.511572\pi
758758 −9.00000 −0.326895
759759 0 0
760760 0 0
761761 −27.0000 −0.978749 −0.489375 0.872074i 0.662775π-0.662775\pi
−0.489375 + 0.872074i 0.662775π0.662775\pi
762762 0 0
763763 18.0000 0.651644
764764 6.00000 0.217072
765765 0 0
766766 −6.00000 −0.216789
767767 24.0000 0.866590
768768 0 0
769769 19.0000 0.685158 0.342579 0.939489i 0.388700π-0.388700\pi
0.342579 + 0.939489i 0.388700π0.388700\pi
770770 0 0
771771 0 0
772772 −19.0000 −0.683825
773773 −36.0000 −1.29483 −0.647415 0.762138i 0.724150π-0.724150\pi
−0.647415 + 0.762138i 0.724150π0.724150\pi
774774 0 0
775775 0 0
776776 10.0000 0.358979
777777 0 0
778778 8.00000 0.286814
779779 33.0000 1.18235
780780 0 0
781781 50.0000 1.78914
782782 0 0
783783 0 0
784784 1.00000 0.0357143
785785 0 0
786786 0 0
787787 52.0000 1.85360 0.926800 0.375555i 0.122548π-0.122548\pi
0.926800 + 0.375555i 0.122548π0.122548\pi
788788 22.0000 0.783718
789789 0 0
790790 0 0
791791 −1.00000 −0.0355559
792792 0 0
793793 12.0000 0.426132
794794 −10.0000 −0.354887
795795 0 0
796796 −10.0000 −0.354441
797797 −42.0000 −1.48772 −0.743858 0.668338i 0.767006π-0.767006\pi
−0.743858 + 0.668338i 0.767006π0.767006\pi
798798 0 0
799799 −2.00000 −0.0707549
800800 0 0
801801 0 0
802802 37.0000 1.30652
803803 −35.0000 −1.23512
804804 0 0
805805 0 0
806806 −24.0000 −0.845364
807807 0 0
808808 0 0
809809 −6.00000 −0.210949 −0.105474 0.994422i 0.533636π-0.533636\pi
−0.105474 + 0.994422i 0.533636π0.533636\pi
810810 0 0
811811 −28.0000 −0.983213 −0.491606 0.870817i 0.663590π-0.663590\pi
−0.491606 + 0.870817i 0.663590π0.663590\pi
812812 −6.00000 −0.210559
813813 0 0
814814 −40.0000 −1.40200
815815 0 0
816816 0 0
817817 24.0000 0.839654
818818 21.0000 0.734248
819819 0 0
820820 0 0
821821 24.0000 0.837606 0.418803 0.908077i 0.362450π-0.362450\pi
0.418803 + 0.908077i 0.362450π0.362450\pi
822822 0 0
823823 10.0000 0.348578 0.174289 0.984695i 0.444237π-0.444237\pi
0.174289 + 0.984695i 0.444237π0.444237\pi
824824 −4.00000 −0.139347
825825 0 0
826826 −4.00000 −0.139178
827827 −41.0000 −1.42571 −0.712855 0.701312i 0.752598π-0.752598\pi
−0.712855 + 0.701312i 0.752598π0.752598\pi
828828 0 0
829829 −4.00000 −0.138926 −0.0694629 0.997585i 0.522129π-0.522129\pi
−0.0694629 + 0.997585i 0.522129π0.522129\pi
830830 0 0
831831 0 0
832832 −6.00000 −0.208013
833833 1.00000 0.0346479
834834 0 0
835835 0 0
836836 −15.0000 −0.518786
837837 0 0
838838 −39.0000 −1.34723
839839 −2.00000 −0.0690477 −0.0345238 0.999404i 0.510991π-0.510991\pi
−0.0345238 + 0.999404i 0.510991π0.510991\pi
840840 0 0
841841 7.00000 0.241379
842842 −20.0000 −0.689246
843843 0 0
844844 1.00000 0.0344214
845845 0 0
846846 0 0
847847 −14.0000 −0.481046
848848 −4.00000 −0.137361
849849 0 0
850850 0 0
851851 0 0
852852 0 0
853853 −34.0000 −1.16414 −0.582069 0.813139i 0.697757π-0.697757\pi
−0.582069 + 0.813139i 0.697757π0.697757\pi
854854 −2.00000 −0.0684386
855855 0 0
856856 3.00000 0.102538
857857 −3.00000 −0.102478 −0.0512390 0.998686i 0.516317π-0.516317\pi
−0.0512390 + 0.998686i 0.516317π0.516317\pi
858858 0 0
859859 −51.0000 −1.74010 −0.870049 0.492966i 0.835913π-0.835913\pi
−0.870049 + 0.492966i 0.835913π0.835913\pi
860860 0 0
861861 0 0
862862 −36.0000 −1.22616
863863 −4.00000 −0.136162 −0.0680808 0.997680i 0.521688π-0.521688\pi
−0.0680808 + 0.997680i 0.521688π0.521688\pi
864864 0 0
865865 0 0
866866 1.00000 0.0339814
867867 0 0
868868 4.00000 0.135769
869869 −10.0000 −0.339227
870870 0 0
871871 −54.0000 −1.82972
872872 18.0000 0.609557
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 32.0000 1.08056 0.540282 0.841484i 0.318318π-0.318318\pi
0.540282 + 0.841484i 0.318318π0.318318\pi
878878 −28.0000 −0.944954
879879 0 0
880880 0 0
881881 −26.0000 −0.875962 −0.437981 0.898984i 0.644306π-0.644306\pi
−0.437981 + 0.898984i 0.644306π0.644306\pi
882882 0 0
883883 15.0000 0.504790 0.252395 0.967624i 0.418782π-0.418782\pi
0.252395 + 0.967624i 0.418782π0.418782\pi
884884 −6.00000 −0.201802
885885 0 0
886886 37.0000 1.24304
887887 34.0000 1.14161 0.570804 0.821086i 0.306632π-0.306632\pi
0.570804 + 0.821086i 0.306632π0.306632\pi
888888 0 0
889889 14.0000 0.469545
890890 0 0
891891 0 0
892892 22.0000 0.736614
893893 6.00000 0.200782
894894 0 0
895895 0 0
896896 1.00000 0.0334077
897897 0 0
898898 33.0000 1.10122
899899 −24.0000 −0.800445
900900 0 0
901901 −4.00000 −0.133259
902902 55.0000 1.83130
903903 0 0
904904 −1.00000 −0.0332595
905905 0 0
906906 0 0
907907 −4.00000 −0.132818 −0.0664089 0.997792i 0.521154π-0.521154\pi
−0.0664089 + 0.997792i 0.521154π0.521154\pi
908908 28.0000 0.929213
909909 0 0
910910 0 0
911911 12.0000 0.397578 0.198789 0.980042i 0.436299π-0.436299\pi
0.198789 + 0.980042i 0.436299π0.436299\pi
912912 0 0
913913 −55.0000 −1.82023
914914 −25.0000 −0.826927
915915 0 0
916916 −14.0000 −0.462573
917917 8.00000 0.264183
918918 0 0
919919 −34.0000 −1.12156 −0.560778 0.827966i 0.689498π-0.689498\pi
−0.560778 + 0.827966i 0.689498π0.689498\pi
920920 0 0
921921 0 0
922922 −38.0000 −1.25146
923923 −60.0000 −1.97492
924924 0 0
925925 0 0
926926 −8.00000 −0.262896
927927 0 0
928928 −6.00000 −0.196960
929929 −46.0000 −1.50921 −0.754606 0.656179i 0.772172π-0.772172\pi
−0.754606 + 0.656179i 0.772172π0.772172\pi
930930 0 0
931931 −3.00000 −0.0983210
932932 −6.00000 −0.196537
933933 0 0
934934 −4.00000 −0.130884
935935 0 0
936936 0 0
937937 −7.00000 −0.228680 −0.114340 0.993442i 0.536475π-0.536475\pi
−0.114340 + 0.993442i 0.536475π0.536475\pi
938938 9.00000 0.293860
939939 0 0
940940 0 0
941941 −56.0000 −1.82555 −0.912774 0.408465i 0.866064π-0.866064\pi
−0.912774 + 0.408465i 0.866064π0.866064\pi
942942 0 0
943943 0 0
944944 −4.00000 −0.130189
945945 0 0
946946 40.0000 1.30051
947947 4.00000 0.129983 0.0649913 0.997886i 0.479298π-0.479298\pi
0.0649913 + 0.997886i 0.479298π0.479298\pi
948948 0 0
949949 42.0000 1.36338
950950 0 0
951951 0 0
952952 1.00000 0.0324102
953953 −9.00000 −0.291539 −0.145769 0.989319i 0.546566π-0.546566\pi
−0.145769 + 0.989319i 0.546566π0.546566\pi
954954 0 0
955955 0 0
956956 −4.00000 −0.129369
957957 0 0
958958 −6.00000 −0.193851
959959 −3.00000 −0.0968751
960960 0 0
961961 −15.0000 −0.483871
962962 48.0000 1.54758
963963 0 0
964964 −5.00000 −0.161039
965965 0 0
966966 0 0
967967 −2.00000 −0.0643157 −0.0321578 0.999483i 0.510238π-0.510238\pi
−0.0321578 + 0.999483i 0.510238π0.510238\pi
968968 −14.0000 −0.449977
969969 0 0
970970 0 0
971971 51.0000 1.63667 0.818334 0.574743i 0.194898π-0.194898\pi
0.818334 + 0.574743i 0.194898π0.194898\pi
972972 0 0
973973 11.0000 0.352644
974974 34.0000 1.08943
975975 0 0
976976 −2.00000 −0.0640184
977977 −21.0000 −0.671850 −0.335925 0.941889i 0.609049π-0.609049\pi
−0.335925 + 0.941889i 0.609049π0.609049\pi
978978 0 0
979979 55.0000 1.75781
980980 0 0
981981 0 0
982982 −12.0000 −0.382935
983983 4.00000 0.127580 0.0637901 0.997963i 0.479681π-0.479681\pi
0.0637901 + 0.997963i 0.479681π0.479681\pi
984984 0 0
985985 0 0
986986 −6.00000 −0.191079
987987 0 0
988988 18.0000 0.572656
989989 0 0
990990 0 0
991991 4.00000 0.127064 0.0635321 0.997980i 0.479763π-0.479763\pi
0.0635321 + 0.997980i 0.479763π0.479763\pi
992992 4.00000 0.127000
993993 0 0
994994 10.0000 0.317181
995995 0 0
996996 0 0
997997 −58.0000 −1.83688 −0.918439 0.395562i 0.870550π-0.870550\pi
−0.918439 + 0.395562i 0.870550π0.870550\pi
998998 −36.0000 −1.13956
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 3150.2.a.j.1.1 1
3.2 odd 2 350.2.a.d.1.1 yes 1
5.2 odd 4 3150.2.g.v.2899.1 2
5.3 odd 4 3150.2.g.v.2899.2 2
5.4 even 2 3150.2.a.bq.1.1 1
12.11 even 2 2800.2.a.bg.1.1 1
15.2 even 4 350.2.c.a.99.2 2
15.8 even 4 350.2.c.a.99.1 2
15.14 odd 2 350.2.a.c.1.1 1
21.20 even 2 2450.2.a.bg.1.1 1
60.23 odd 4 2800.2.g.a.449.2 2
60.47 odd 4 2800.2.g.a.449.1 2
60.59 even 2 2800.2.a.b.1.1 1
105.62 odd 4 2450.2.c.r.99.2 2
105.83 odd 4 2450.2.c.r.99.1 2
105.104 even 2 2450.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.a.c.1.1 1 15.14 odd 2
350.2.a.d.1.1 yes 1 3.2 odd 2
350.2.c.a.99.1 2 15.8 even 4
350.2.c.a.99.2 2 15.2 even 4
2450.2.a.a.1.1 1 105.104 even 2
2450.2.a.bg.1.1 1 21.20 even 2
2450.2.c.r.99.1 2 105.83 odd 4
2450.2.c.r.99.2 2 105.62 odd 4
2800.2.a.b.1.1 1 60.59 even 2
2800.2.a.bg.1.1 1 12.11 even 2
2800.2.g.a.449.1 2 60.47 odd 4
2800.2.g.a.449.2 2 60.23 odd 4
3150.2.a.j.1.1 1 1.1 even 1 trivial
3150.2.a.bq.1.1 1 5.4 even 2
3150.2.g.v.2899.1 2 5.2 odd 4
3150.2.g.v.2899.2 2 5.3 odd 4