Properties

Label 1216.2.a.o.1.1
Level 12161216
Weight 22
Character 1216.1
Self dual yes
Analytic conductor 9.7109.710
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] = [1216,2,Mod(1,1216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1216, 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("1216.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1216=2619 1216 = 2^{6} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1216.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: 9.709808885799.70980888579
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 19)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 1216.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+2.00000q33.00000q51.00000q7+1.00000q93.00000q11+4.00000q136.00000q153.00000q171.00000q192.00000q21+4.00000q254.00000q276.00000q294.00000q316.00000q33+3.00000q352.00000q37+8.00000q396.00000q41+1.00000q433.00000q453.00000q476.00000q496.00000q5112.0000q53+9.00000q552.00000q57+6.00000q59+1.00000q611.00000q6312.0000q65+4.00000q67+6.00000q717.00000q73+8.00000q75+3.00000q77+8.00000q7911.0000q8112.0000q83+9.00000q8512.0000q87+12.0000q894.00000q918.00000q93+3.00000q95+8.00000q973.00000q99+O(q100)q+2.00000 q^{3} -3.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} -3.00000 q^{11} +4.00000 q^{13} -6.00000 q^{15} -3.00000 q^{17} -1.00000 q^{19} -2.00000 q^{21} +4.00000 q^{25} -4.00000 q^{27} -6.00000 q^{29} -4.00000 q^{31} -6.00000 q^{33} +3.00000 q^{35} -2.00000 q^{37} +8.00000 q^{39} -6.00000 q^{41} +1.00000 q^{43} -3.00000 q^{45} -3.00000 q^{47} -6.00000 q^{49} -6.00000 q^{51} -12.0000 q^{53} +9.00000 q^{55} -2.00000 q^{57} +6.00000 q^{59} +1.00000 q^{61} -1.00000 q^{63} -12.0000 q^{65} +4.00000 q^{67} +6.00000 q^{71} -7.00000 q^{73} +8.00000 q^{75} +3.00000 q^{77} +8.00000 q^{79} -11.0000 q^{81} -12.0000 q^{83} +9.00000 q^{85} -12.0000 q^{87} +12.0000 q^{89} -4.00000 q^{91} -8.00000 q^{93} +3.00000 q^{95} +8.00000 q^{97} -3.00000 q^{99} +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 0 0
33 2.00000 1.15470 0.577350 0.816497i 0.304087π-0.304087\pi
0.577350 + 0.816497i 0.304087π0.304087\pi
44 0 0
55 −3.00000 −1.34164 −0.670820 0.741620i 0.734058π-0.734058\pi
−0.670820 + 0.741620i 0.734058π0.734058\pi
66 0 0
77 −1.00000 −0.377964 −0.188982 0.981981i 0.560519π-0.560519\pi
−0.188982 + 0.981981i 0.560519π0.560519\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 −3.00000 −0.904534 −0.452267 0.891883i 0.649385π-0.649385\pi
−0.452267 + 0.891883i 0.649385π0.649385\pi
1212 0 0
1313 4.00000 1.10940 0.554700 0.832050i 0.312833π-0.312833\pi
0.554700 + 0.832050i 0.312833π0.312833\pi
1414 0 0
1515 −6.00000 −1.54919
1616 0 0
1717 −3.00000 −0.727607 −0.363803 0.931476i 0.618522π-0.618522\pi
−0.363803 + 0.931476i 0.618522π0.618522\pi
1818 0 0
1919 −1.00000 −0.229416
2020 0 0
2121 −2.00000 −0.436436
2222 0 0
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 0 0
2525 4.00000 0.800000
2626 0 0
2727 −4.00000 −0.769800
2828 0 0
2929 −6.00000 −1.11417 −0.557086 0.830455i 0.688081π-0.688081\pi
−0.557086 + 0.830455i 0.688081π0.688081\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 0 0
3333 −6.00000 −1.04447
3434 0 0
3535 3.00000 0.507093
3636 0 0
3737 −2.00000 −0.328798 −0.164399 0.986394i 0.552568π-0.552568\pi
−0.164399 + 0.986394i 0.552568π0.552568\pi
3838 0 0
3939 8.00000 1.28103
4040 0 0
4141 −6.00000 −0.937043 −0.468521 0.883452i 0.655213π-0.655213\pi
−0.468521 + 0.883452i 0.655213π0.655213\pi
4242 0 0
4343 1.00000 0.152499 0.0762493 0.997089i 0.475706π-0.475706\pi
0.0762493 + 0.997089i 0.475706π0.475706\pi
4444 0 0
4545 −3.00000 −0.447214
4646 0 0
4747 −3.00000 −0.437595 −0.218797 0.975770i 0.570213π-0.570213\pi
−0.218797 + 0.975770i 0.570213π0.570213\pi
4848 0 0
4949 −6.00000 −0.857143
5050 0 0
5151 −6.00000 −0.840168
5252 0 0
5353 −12.0000 −1.64833 −0.824163 0.566352i 0.808354π-0.808354\pi
−0.824163 + 0.566352i 0.808354π0.808354\pi
5454 0 0
5555 9.00000 1.21356
5656 0 0
5757 −2.00000 −0.264906
5858 0 0
5959 6.00000 0.781133 0.390567 0.920575i 0.372279π-0.372279\pi
0.390567 + 0.920575i 0.372279π0.372279\pi
6060 0 0
6161 1.00000 0.128037 0.0640184 0.997949i 0.479608π-0.479608\pi
0.0640184 + 0.997949i 0.479608π0.479608\pi
6262 0 0
6363 −1.00000 −0.125988
6464 0 0
6565 −12.0000 −1.48842
6666 0 0
6767 4.00000 0.488678 0.244339 0.969690i 0.421429π-0.421429\pi
0.244339 + 0.969690i 0.421429π0.421429\pi
6868 0 0
6969 0 0
7070 0 0
7171 6.00000 0.712069 0.356034 0.934473i 0.384129π-0.384129\pi
0.356034 + 0.934473i 0.384129π0.384129\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 0 0
7575 8.00000 0.923760
7676 0 0
7777 3.00000 0.341882
7878 0 0
7979 8.00000 0.900070 0.450035 0.893011i 0.351411π-0.351411\pi
0.450035 + 0.893011i 0.351411π0.351411\pi
8080 0 0
8181 −11.0000 −1.22222
8282 0 0
8383 −12.0000 −1.31717 −0.658586 0.752506i 0.728845π-0.728845\pi
−0.658586 + 0.752506i 0.728845π0.728845\pi
8484 0 0
8585 9.00000 0.976187
8686 0 0
8787 −12.0000 −1.28654
8888 0 0
8989 12.0000 1.27200 0.635999 0.771690i 0.280588π-0.280588\pi
0.635999 + 0.771690i 0.280588π0.280588\pi
9090 0 0
9191 −4.00000 −0.419314
9292 0 0
9393 −8.00000 −0.829561
9494 0 0
9595 3.00000 0.307794
9696 0 0
9797 8.00000 0.812277 0.406138 0.913812i 0.366875π-0.366875\pi
0.406138 + 0.913812i 0.366875π0.366875\pi
9898 0 0
9999 −3.00000 −0.301511
100100 0 0
101101 −6.00000 −0.597022 −0.298511 0.954406i 0.596490π-0.596490\pi
−0.298511 + 0.954406i 0.596490π0.596490\pi
102102 0 0
103103 14.0000 1.37946 0.689730 0.724066i 0.257729π-0.257729\pi
0.689730 + 0.724066i 0.257729π0.257729\pi
104104 0 0
105105 6.00000 0.585540
106106 0 0
107107 18.0000 1.74013 0.870063 0.492941i 0.164078π-0.164078\pi
0.870063 + 0.492941i 0.164078π0.164078\pi
108108 0 0
109109 16.0000 1.53252 0.766261 0.642529i 0.222115π-0.222115\pi
0.766261 + 0.642529i 0.222115π0.222115\pi
110110 0 0
111111 −4.00000 −0.379663
112112 0 0
113113 6.00000 0.564433 0.282216 0.959351i 0.408930π-0.408930\pi
0.282216 + 0.959351i 0.408930π0.408930\pi
114114 0 0
115115 0 0
116116 0 0
117117 4.00000 0.369800
118118 0 0
119119 3.00000 0.275010
120120 0 0
121121 −2.00000 −0.181818
122122 0 0
123123 −12.0000 −1.08200
124124 0 0
125125 3.00000 0.268328
126126 0 0
127127 2.00000 0.177471 0.0887357 0.996055i 0.471717π-0.471717\pi
0.0887357 + 0.996055i 0.471717π0.471717\pi
128128 0 0
129129 2.00000 0.176090
130130 0 0
131131 15.0000 1.31056 0.655278 0.755388i 0.272551π-0.272551\pi
0.655278 + 0.755388i 0.272551π0.272551\pi
132132 0 0
133133 1.00000 0.0867110
134134 0 0
135135 12.0000 1.03280
136136 0 0
137137 −3.00000 −0.256307 −0.128154 0.991754i 0.540905π-0.540905\pi
−0.128154 + 0.991754i 0.540905π0.540905\pi
138138 0 0
139139 13.0000 1.10265 0.551323 0.834292i 0.314123π-0.314123\pi
0.551323 + 0.834292i 0.314123π0.314123\pi
140140 0 0
141141 −6.00000 −0.505291
142142 0 0
143143 −12.0000 −1.00349
144144 0 0
145145 18.0000 1.49482
146146 0 0
147147 −12.0000 −0.989743
148148 0 0
149149 −21.0000 −1.72039 −0.860194 0.509968i 0.829657π-0.829657\pi
−0.860194 + 0.509968i 0.829657π0.829657\pi
150150 0 0
151151 −10.0000 −0.813788 −0.406894 0.913475i 0.633388π-0.633388\pi
−0.406894 + 0.913475i 0.633388π0.633388\pi
152152 0 0
153153 −3.00000 −0.242536
154154 0 0
155155 12.0000 0.963863
156156 0 0
157157 −14.0000 −1.11732 −0.558661 0.829396i 0.688685π-0.688685\pi
−0.558661 + 0.829396i 0.688685π0.688685\pi
158158 0 0
159159 −24.0000 −1.90332
160160 0 0
161161 0 0
162162 0 0
163163 −20.0000 −1.56652 −0.783260 0.621694i 0.786445π-0.786445\pi
−0.783260 + 0.621694i 0.786445π0.786445\pi
164164 0 0
165165 18.0000 1.40130
166166 0 0
167167 −18.0000 −1.39288 −0.696441 0.717614i 0.745234π-0.745234\pi
−0.696441 + 0.717614i 0.745234π0.745234\pi
168168 0 0
169169 3.00000 0.230769
170170 0 0
171171 −1.00000 −0.0764719
172172 0 0
173173 18.0000 1.36851 0.684257 0.729241i 0.260127π-0.260127\pi
0.684257 + 0.729241i 0.260127π0.260127\pi
174174 0 0
175175 −4.00000 −0.302372
176176 0 0
177177 12.0000 0.901975
178178 0 0
179179 18.0000 1.34538 0.672692 0.739923i 0.265138π-0.265138\pi
0.672692 + 0.739923i 0.265138π0.265138\pi
180180 0 0
181181 −2.00000 −0.148659 −0.0743294 0.997234i 0.523682π-0.523682\pi
−0.0743294 + 0.997234i 0.523682π0.523682\pi
182182 0 0
183183 2.00000 0.147844
184184 0 0
185185 6.00000 0.441129
186186 0 0
187187 9.00000 0.658145
188188 0 0
189189 4.00000 0.290957
190190 0 0
191191 3.00000 0.217072 0.108536 0.994092i 0.465384π-0.465384\pi
0.108536 + 0.994092i 0.465384π0.465384\pi
192192 0 0
193193 −4.00000 −0.287926 −0.143963 0.989583i 0.545985π-0.545985\pi
−0.143963 + 0.989583i 0.545985π0.545985\pi
194194 0 0
195195 −24.0000 −1.71868
196196 0 0
197197 −18.0000 −1.28245 −0.641223 0.767354i 0.721573π-0.721573\pi
−0.641223 + 0.767354i 0.721573π0.721573\pi
198198 0 0
199199 11.0000 0.779769 0.389885 0.920864i 0.372515π-0.372515\pi
0.389885 + 0.920864i 0.372515π0.372515\pi
200200 0 0
201201 8.00000 0.564276
202202 0 0
203203 6.00000 0.421117
204204 0 0
205205 18.0000 1.25717
206206 0 0
207207 0 0
208208 0 0
209209 3.00000 0.207514
210210 0 0
211211 −14.0000 −0.963800 −0.481900 0.876226i 0.660053π-0.660053\pi
−0.481900 + 0.876226i 0.660053π0.660053\pi
212212 0 0
213213 12.0000 0.822226
214214 0 0
215215 −3.00000 −0.204598
216216 0 0
217217 4.00000 0.271538
218218 0 0
219219 −14.0000 −0.946032
220220 0 0
221221 −12.0000 −0.807207
222222 0 0
223223 −10.0000 −0.669650 −0.334825 0.942280i 0.608677π-0.608677\pi
−0.334825 + 0.942280i 0.608677π0.608677\pi
224224 0 0
225225 4.00000 0.266667
226226 0 0
227227 −12.0000 −0.796468 −0.398234 0.917284i 0.630377π-0.630377\pi
−0.398234 + 0.917284i 0.630377π0.630377\pi
228228 0 0
229229 −5.00000 −0.330409 −0.165205 0.986259i 0.552828π-0.552828\pi
−0.165205 + 0.986259i 0.552828π0.552828\pi
230230 0 0
231231 6.00000 0.394771
232232 0 0
233233 −21.0000 −1.37576 −0.687878 0.725826i 0.741458π-0.741458\pi
−0.687878 + 0.725826i 0.741458π0.741458\pi
234234 0 0
235235 9.00000 0.587095
236236 0 0
237237 16.0000 1.03931
238238 0 0
239239 15.0000 0.970269 0.485135 0.874439i 0.338771π-0.338771\pi
0.485135 + 0.874439i 0.338771π0.338771\pi
240240 0 0
241241 −10.0000 −0.644157 −0.322078 0.946713i 0.604381π-0.604381\pi
−0.322078 + 0.946713i 0.604381π0.604381\pi
242242 0 0
243243 −10.0000 −0.641500
244244 0 0
245245 18.0000 1.14998
246246 0 0
247247 −4.00000 −0.254514
248248 0 0
249249 −24.0000 −1.52094
250250 0 0
251251 −21.0000 −1.32551 −0.662754 0.748837i 0.730613π-0.730613\pi
−0.662754 + 0.748837i 0.730613π0.730613\pi
252252 0 0
253253 0 0
254254 0 0
255255 18.0000 1.12720
256256 0 0
257257 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
258258 0 0
259259 2.00000 0.124274
260260 0 0
261261 −6.00000 −0.371391
262262 0 0
263263 9.00000 0.554964 0.277482 0.960731i 0.410500π-0.410500\pi
0.277482 + 0.960731i 0.410500π0.410500\pi
264264 0 0
265265 36.0000 2.21146
266266 0 0
267267 24.0000 1.46878
268268 0 0
269269 −24.0000 −1.46331 −0.731653 0.681677i 0.761251π-0.761251\pi
−0.731653 + 0.681677i 0.761251π0.761251\pi
270270 0 0
271271 −16.0000 −0.971931 −0.485965 0.873978i 0.661532π-0.661532\pi
−0.485965 + 0.873978i 0.661532π0.661532\pi
272272 0 0
273273 −8.00000 −0.484182
274274 0 0
275275 −12.0000 −0.723627
276276 0 0
277277 19.0000 1.14160 0.570800 0.821089i 0.306633π-0.306633\pi
0.570800 + 0.821089i 0.306633π0.306633\pi
278278 0 0
279279 −4.00000 −0.239474
280280 0 0
281281 6.00000 0.357930 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
282282 0 0
283283 13.0000 0.772770 0.386385 0.922338i 0.373724π-0.373724\pi
0.386385 + 0.922338i 0.373724π0.373724\pi
284284 0 0
285285 6.00000 0.355409
286286 0 0
287287 6.00000 0.354169
288288 0 0
289289 −8.00000 −0.470588
290290 0 0
291291 16.0000 0.937937
292292 0 0
293293 12.0000 0.701047 0.350524 0.936554i 0.386004π-0.386004\pi
0.350524 + 0.936554i 0.386004π0.386004\pi
294294 0 0
295295 −18.0000 −1.04800
296296 0 0
297297 12.0000 0.696311
298298 0 0
299299 0 0
300300 0 0
301301 −1.00000 −0.0576390
302302 0 0
303303 −12.0000 −0.689382
304304 0 0
305305 −3.00000 −0.171780
306306 0 0
307307 −20.0000 −1.14146 −0.570730 0.821138i 0.693340π-0.693340\pi
−0.570730 + 0.821138i 0.693340π0.693340\pi
308308 0 0
309309 28.0000 1.59286
310310 0 0
311311 −3.00000 −0.170114 −0.0850572 0.996376i 0.527107π-0.527107\pi
−0.0850572 + 0.996376i 0.527107π0.527107\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 0 0
315315 3.00000 0.169031
316316 0 0
317317 −6.00000 −0.336994 −0.168497 0.985702i 0.553891π-0.553891\pi
−0.168497 + 0.985702i 0.553891π0.553891\pi
318318 0 0
319319 18.0000 1.00781
320320 0 0
321321 36.0000 2.00932
322322 0 0
323323 3.00000 0.166924
324324 0 0
325325 16.0000 0.887520
326326 0 0
327327 32.0000 1.76960
328328 0 0
329329 3.00000 0.165395
330330 0 0
331331 28.0000 1.53902 0.769510 0.638635i 0.220501π-0.220501\pi
0.769510 + 0.638635i 0.220501π0.220501\pi
332332 0 0
333333 −2.00000 −0.109599
334334 0 0
335335 −12.0000 −0.655630
336336 0 0
337337 32.0000 1.74315 0.871576 0.490261i 0.163099π-0.163099\pi
0.871576 + 0.490261i 0.163099π0.163099\pi
338338 0 0
339339 12.0000 0.651751
340340 0 0
341341 12.0000 0.649836
342342 0 0
343343 13.0000 0.701934
344344 0 0
345345 0 0
346346 0 0
347347 −21.0000 −1.12734 −0.563670 0.826000i 0.690611π-0.690611\pi
−0.563670 + 0.826000i 0.690611π0.690611\pi
348348 0 0
349349 −17.0000 −0.909989 −0.454995 0.890494i 0.650359π-0.650359\pi
−0.454995 + 0.890494i 0.650359π0.650359\pi
350350 0 0
351351 −16.0000 −0.854017
352352 0 0
353353 −6.00000 −0.319348 −0.159674 0.987170i 0.551044π-0.551044\pi
−0.159674 + 0.987170i 0.551044π0.551044\pi
354354 0 0
355355 −18.0000 −0.955341
356356 0 0
357357 6.00000 0.317554
358358 0 0
359359 15.0000 0.791670 0.395835 0.918322i 0.370455π-0.370455\pi
0.395835 + 0.918322i 0.370455π0.370455\pi
360360 0 0
361361 1.00000 0.0526316
362362 0 0
363363 −4.00000 −0.209946
364364 0 0
365365 21.0000 1.09919
366366 0 0
367367 8.00000 0.417597 0.208798 0.977959i 0.433045π-0.433045\pi
0.208798 + 0.977959i 0.433045π0.433045\pi
368368 0 0
369369 −6.00000 −0.312348
370370 0 0
371371 12.0000 0.623009
372372 0 0
373373 4.00000 0.207112 0.103556 0.994624i 0.466978π-0.466978\pi
0.103556 + 0.994624i 0.466978π0.466978\pi
374374 0 0
375375 6.00000 0.309839
376376 0 0
377377 −24.0000 −1.23606
378378 0 0
379379 34.0000 1.74646 0.873231 0.487306i 0.162020π-0.162020\pi
0.873231 + 0.487306i 0.162020π0.162020\pi
380380 0 0
381381 4.00000 0.204926
382382 0 0
383383 12.0000 0.613171 0.306586 0.951843i 0.400813π-0.400813\pi
0.306586 + 0.951843i 0.400813π0.400813\pi
384384 0 0
385385 −9.00000 −0.458682
386386 0 0
387387 1.00000 0.0508329
388388 0 0
389389 −15.0000 −0.760530 −0.380265 0.924878i 0.624167π-0.624167\pi
−0.380265 + 0.924878i 0.624167π0.624167\pi
390390 0 0
391391 0 0
392392 0 0
393393 30.0000 1.51330
394394 0 0
395395 −24.0000 −1.20757
396396 0 0
397397 7.00000 0.351320 0.175660 0.984451i 0.443794π-0.443794\pi
0.175660 + 0.984451i 0.443794π0.443794\pi
398398 0 0
399399 2.00000 0.100125
400400 0 0
401401 12.0000 0.599251 0.299626 0.954057i 0.403138π-0.403138\pi
0.299626 + 0.954057i 0.403138π0.403138\pi
402402 0 0
403403 −16.0000 −0.797017
404404 0 0
405405 33.0000 1.63978
406406 0 0
407407 6.00000 0.297409
408408 0 0
409409 −4.00000 −0.197787 −0.0988936 0.995098i 0.531530π-0.531530\pi
−0.0988936 + 0.995098i 0.531530π0.531530\pi
410410 0 0
411411 −6.00000 −0.295958
412412 0 0
413413 −6.00000 −0.295241
414414 0 0
415415 36.0000 1.76717
416416 0 0
417417 26.0000 1.27323
418418 0 0
419419 12.0000 0.586238 0.293119 0.956076i 0.405307π-0.405307\pi
0.293119 + 0.956076i 0.405307π0.405307\pi
420420 0 0
421421 −8.00000 −0.389896 −0.194948 0.980814i 0.562454π-0.562454\pi
−0.194948 + 0.980814i 0.562454π0.562454\pi
422422 0 0
423423 −3.00000 −0.145865
424424 0 0
425425 −12.0000 −0.582086
426426 0 0
427427 −1.00000 −0.0483934
428428 0 0
429429 −24.0000 −1.15873
430430 0 0
431431 −24.0000 −1.15604 −0.578020 0.816023i 0.696174π-0.696174\pi
−0.578020 + 0.816023i 0.696174π0.696174\pi
432432 0 0
433433 2.00000 0.0961139 0.0480569 0.998845i 0.484697π-0.484697\pi
0.0480569 + 0.998845i 0.484697π0.484697\pi
434434 0 0
435435 36.0000 1.72607
436436 0 0
437437 0 0
438438 0 0
439439 −10.0000 −0.477274 −0.238637 0.971109i 0.576701π-0.576701\pi
−0.238637 + 0.971109i 0.576701π0.576701\pi
440440 0 0
441441 −6.00000 −0.285714
442442 0 0
443443 3.00000 0.142534 0.0712672 0.997457i 0.477296π-0.477296\pi
0.0712672 + 0.997457i 0.477296π0.477296\pi
444444 0 0
445445 −36.0000 −1.70656
446446 0 0
447447 −42.0000 −1.98653
448448 0 0
449449 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
450450 0 0
451451 18.0000 0.847587
452452 0 0
453453 −20.0000 −0.939682
454454 0 0
455455 12.0000 0.562569
456456 0 0
457457 −37.0000 −1.73079 −0.865393 0.501093i 0.832931π-0.832931\pi
−0.865393 + 0.501093i 0.832931π0.832931\pi
458458 0 0
459459 12.0000 0.560112
460460 0 0
461461 −9.00000 −0.419172 −0.209586 0.977790i 0.567212π-0.567212\pi
−0.209586 + 0.977790i 0.567212π0.567212\pi
462462 0 0
463463 −31.0000 −1.44069 −0.720346 0.693615i 0.756017π-0.756017\pi
−0.720346 + 0.693615i 0.756017π0.756017\pi
464464 0 0
465465 24.0000 1.11297
466466 0 0
467467 27.0000 1.24941 0.624705 0.780860i 0.285219π-0.285219\pi
0.624705 + 0.780860i 0.285219π0.285219\pi
468468 0 0
469469 −4.00000 −0.184703
470470 0 0
471471 −28.0000 −1.29017
472472 0 0
473473 −3.00000 −0.137940
474474 0 0
475475 −4.00000 −0.183533
476476 0 0
477477 −12.0000 −0.549442
478478 0 0
479479 −12.0000 −0.548294 −0.274147 0.961688i 0.588395π-0.588395\pi
−0.274147 + 0.961688i 0.588395π0.588395\pi
480480 0 0
481481 −8.00000 −0.364769
482482 0 0
483483 0 0
484484 0 0
485485 −24.0000 −1.08978
486486 0 0
487487 2.00000 0.0906287 0.0453143 0.998973i 0.485571π-0.485571\pi
0.0453143 + 0.998973i 0.485571π0.485571\pi
488488 0 0
489489 −40.0000 −1.80886
490490 0 0
491491 −12.0000 −0.541552 −0.270776 0.962642i 0.587280π-0.587280\pi
−0.270776 + 0.962642i 0.587280π0.587280\pi
492492 0 0
493493 18.0000 0.810679
494494 0 0
495495 9.00000 0.404520
496496 0 0
497497 −6.00000 −0.269137
498498 0 0
499499 −5.00000 −0.223831 −0.111915 0.993718i 0.535699π-0.535699\pi
−0.111915 + 0.993718i 0.535699π0.535699\pi
500500 0 0
501501 −36.0000 −1.60836
502502 0 0
503503 12.0000 0.535054 0.267527 0.963550i 0.413794π-0.413794\pi
0.267527 + 0.963550i 0.413794π0.413794\pi
504504 0 0
505505 18.0000 0.800989
506506 0 0
507507 6.00000 0.266469
508508 0 0
509509 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
510510 0 0
511511 7.00000 0.309662
512512 0 0
513513 4.00000 0.176604
514514 0 0
515515 −42.0000 −1.85074
516516 0 0
517517 9.00000 0.395820
518518 0 0
519519 36.0000 1.58022
520520 0 0
521521 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
522522 0 0
523523 −38.0000 −1.66162 −0.830812 0.556553i 0.812124π-0.812124\pi
−0.830812 + 0.556553i 0.812124π0.812124\pi
524524 0 0
525525 −8.00000 −0.349149
526526 0 0
527527 12.0000 0.522728
528528 0 0
529529 −23.0000 −1.00000
530530 0 0
531531 6.00000 0.260378
532532 0 0
533533 −24.0000 −1.03956
534534 0 0
535535 −54.0000 −2.33462
536536 0 0
537537 36.0000 1.55351
538538 0 0
539539 18.0000 0.775315
540540 0 0
541541 25.0000 1.07483 0.537417 0.843317i 0.319400π-0.319400\pi
0.537417 + 0.843317i 0.319400π0.319400\pi
542542 0 0
543543 −4.00000 −0.171656
544544 0 0
545545 −48.0000 −2.05609
546546 0 0
547547 28.0000 1.19719 0.598597 0.801050i 0.295725π-0.295725\pi
0.598597 + 0.801050i 0.295725π0.295725\pi
548548 0 0
549549 1.00000 0.0426790
550550 0 0
551551 6.00000 0.255609
552552 0 0
553553 −8.00000 −0.340195
554554 0 0
555555 12.0000 0.509372
556556 0 0
557557 −21.0000 −0.889799 −0.444899 0.895581i 0.646761π-0.646761\pi
−0.444899 + 0.895581i 0.646761π0.646761\pi
558558 0 0
559559 4.00000 0.169182
560560 0 0
561561 18.0000 0.759961
562562 0 0
563563 −6.00000 −0.252870 −0.126435 0.991975i 0.540353π-0.540353\pi
−0.126435 + 0.991975i 0.540353π0.540353\pi
564564 0 0
565565 −18.0000 −0.757266
566566 0 0
567567 11.0000 0.461957
568568 0 0
569569 −24.0000 −1.00613 −0.503066 0.864248i 0.667795π-0.667795\pi
−0.503066 + 0.864248i 0.667795π0.667795\pi
570570 0 0
571571 4.00000 0.167395 0.0836974 0.996491i 0.473327π-0.473327\pi
0.0836974 + 0.996491i 0.473327π0.473327\pi
572572 0 0
573573 6.00000 0.250654
574574 0 0
575575 0 0
576576 0 0
577577 11.0000 0.457936 0.228968 0.973434i 0.426465π-0.426465\pi
0.228968 + 0.973434i 0.426465π0.426465\pi
578578 0 0
579579 −8.00000 −0.332469
580580 0 0
581581 12.0000 0.497844
582582 0 0
583583 36.0000 1.49097
584584 0 0
585585 −12.0000 −0.496139
586586 0 0
587587 −45.0000 −1.85735 −0.928674 0.370896i 0.879051π-0.879051\pi
−0.928674 + 0.370896i 0.879051π0.879051\pi
588588 0 0
589589 4.00000 0.164817
590590 0 0
591591 −36.0000 −1.48084
592592 0 0
593593 −42.0000 −1.72473 −0.862367 0.506284i 0.831019π-0.831019\pi
−0.862367 + 0.506284i 0.831019π0.831019\pi
594594 0 0
595595 −9.00000 −0.368964
596596 0 0
597597 22.0000 0.900400
598598 0 0
599599 −36.0000 −1.47092 −0.735460 0.677568i 0.763034π-0.763034\pi
−0.735460 + 0.677568i 0.763034π0.763034\pi
600600 0 0
601601 26.0000 1.06056 0.530281 0.847822i 0.322086π-0.322086\pi
0.530281 + 0.847822i 0.322086π0.322086\pi
602602 0 0
603603 4.00000 0.162893
604604 0 0
605605 6.00000 0.243935
606606 0 0
607607 32.0000 1.29884 0.649420 0.760430i 0.275012π-0.275012\pi
0.649420 + 0.760430i 0.275012π0.275012\pi
608608 0 0
609609 12.0000 0.486265
610610 0 0
611611 −12.0000 −0.485468
612612 0 0
613613 −29.0000 −1.17130 −0.585649 0.810564i 0.699160π-0.699160\pi
−0.585649 + 0.810564i 0.699160π0.699160\pi
614614 0 0
615615 36.0000 1.45166
616616 0 0
617617 9.00000 0.362326 0.181163 0.983453i 0.442014π-0.442014\pi
0.181163 + 0.983453i 0.442014π0.442014\pi
618618 0 0
619619 −44.0000 −1.76851 −0.884255 0.467005i 0.845333π-0.845333\pi
−0.884255 + 0.467005i 0.845333π0.845333\pi
620620 0 0
621621 0 0
622622 0 0
623623 −12.0000 −0.480770
624624 0 0
625625 −29.0000 −1.16000
626626 0 0
627627 6.00000 0.239617
628628 0 0
629629 6.00000 0.239236
630630 0 0
631631 11.0000 0.437903 0.218952 0.975736i 0.429736π-0.429736\pi
0.218952 + 0.975736i 0.429736π0.429736\pi
632632 0 0
633633 −28.0000 −1.11290
634634 0 0
635635 −6.00000 −0.238103
636636 0 0
637637 −24.0000 −0.950915
638638 0 0
639639 6.00000 0.237356
640640 0 0
641641 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
642642 0 0
643643 13.0000 0.512670 0.256335 0.966588i 0.417485π-0.417485\pi
0.256335 + 0.966588i 0.417485π0.417485\pi
644644 0 0
645645 −6.00000 −0.236250
646646 0 0
647647 27.0000 1.06148 0.530740 0.847535i 0.321914π-0.321914\pi
0.530740 + 0.847535i 0.321914π0.321914\pi
648648 0 0
649649 −18.0000 −0.706562
650650 0 0
651651 8.00000 0.313545
652652 0 0
653653 39.0000 1.52619 0.763094 0.646288i 0.223679π-0.223679\pi
0.763094 + 0.646288i 0.223679π0.223679\pi
654654 0 0
655655 −45.0000 −1.75830
656656 0 0
657657 −7.00000 −0.273096
658658 0 0
659659 30.0000 1.16863 0.584317 0.811525i 0.301362π-0.301362\pi
0.584317 + 0.811525i 0.301362π0.301362\pi
660660 0 0
661661 −32.0000 −1.24466 −0.622328 0.782757i 0.713813π-0.713813\pi
−0.622328 + 0.782757i 0.713813π0.713813\pi
662662 0 0
663663 −24.0000 −0.932083
664664 0 0
665665 −3.00000 −0.116335
666666 0 0
667667 0 0
668668 0 0
669669 −20.0000 −0.773245
670670 0 0
671671 −3.00000 −0.115814
672672 0 0
673673 −10.0000 −0.385472 −0.192736 0.981251i 0.561736π-0.561736\pi
−0.192736 + 0.981251i 0.561736π0.561736\pi
674674 0 0
675675 −16.0000 −0.615840
676676 0 0
677677 42.0000 1.61419 0.807096 0.590421i 0.201038π-0.201038\pi
0.807096 + 0.590421i 0.201038π0.201038\pi
678678 0 0
679679 −8.00000 −0.307012
680680 0 0
681681 −24.0000 −0.919682
682682 0 0
683683 −36.0000 −1.37750 −0.688751 0.724998i 0.741841π-0.741841\pi
−0.688751 + 0.724998i 0.741841π0.741841\pi
684684 0 0
685685 9.00000 0.343872
686686 0 0
687687 −10.0000 −0.381524
688688 0 0
689689 −48.0000 −1.82865
690690 0 0
691691 −17.0000 −0.646710 −0.323355 0.946278i 0.604811π-0.604811\pi
−0.323355 + 0.946278i 0.604811π0.604811\pi
692692 0 0
693693 3.00000 0.113961
694694 0 0
695695 −39.0000 −1.47935
696696 0 0
697697 18.0000 0.681799
698698 0 0
699699 −42.0000 −1.58859
700700 0 0
701701 −6.00000 −0.226617 −0.113308 0.993560i 0.536145π-0.536145\pi
−0.113308 + 0.993560i 0.536145π0.536145\pi
702702 0 0
703703 2.00000 0.0754314
704704 0 0
705705 18.0000 0.677919
706706 0 0
707707 6.00000 0.225653
708708 0 0
709709 −26.0000 −0.976450 −0.488225 0.872718i 0.662356π-0.662356\pi
−0.488225 + 0.872718i 0.662356π0.662356\pi
710710 0 0
711711 8.00000 0.300023
712712 0 0
713713 0 0
714714 0 0
715715 36.0000 1.34632
716716 0 0
717717 30.0000 1.12037
718718 0 0
719719 15.0000 0.559406 0.279703 0.960087i 0.409764π-0.409764\pi
0.279703 + 0.960087i 0.409764π0.409764\pi
720720 0 0
721721 −14.0000 −0.521387
722722 0 0
723723 −20.0000 −0.743808
724724 0 0
725725 −24.0000 −0.891338
726726 0 0
727727 −19.0000 −0.704671 −0.352335 0.935874i 0.614612π-0.614612\pi
−0.352335 + 0.935874i 0.614612π0.614612\pi
728728 0 0
729729 13.0000 0.481481
730730 0 0
731731 −3.00000 −0.110959
732732 0 0
733733 22.0000 0.812589 0.406294 0.913742i 0.366821π-0.366821\pi
0.406294 + 0.913742i 0.366821π0.366821\pi
734734 0 0
735735 36.0000 1.32788
736736 0 0
737737 −12.0000 −0.442026
738738 0 0
739739 −11.0000 −0.404642 −0.202321 0.979319i 0.564848π-0.564848\pi
−0.202321 + 0.979319i 0.564848π0.564848\pi
740740 0 0
741741 −8.00000 −0.293887
742742 0 0
743743 −24.0000 −0.880475 −0.440237 0.897881i 0.645106π-0.645106\pi
−0.440237 + 0.897881i 0.645106π0.645106\pi
744744 0 0
745745 63.0000 2.30814
746746 0 0
747747 −12.0000 −0.439057
748748 0 0
749749 −18.0000 −0.657706
750750 0 0
751751 32.0000 1.16770 0.583848 0.811863i 0.301546π-0.301546\pi
0.583848 + 0.811863i 0.301546π0.301546\pi
752752 0 0
753753 −42.0000 −1.53057
754754 0 0
755755 30.0000 1.09181
756756 0 0
757757 25.0000 0.908640 0.454320 0.890838i 0.349882π-0.349882\pi
0.454320 + 0.890838i 0.349882π0.349882\pi
758758 0 0
759759 0 0
760760 0 0
761761 33.0000 1.19625 0.598125 0.801403i 0.295913π-0.295913\pi
0.598125 + 0.801403i 0.295913π0.295913\pi
762762 0 0
763763 −16.0000 −0.579239
764764 0 0
765765 9.00000 0.325396
766766 0 0
767767 24.0000 0.866590
768768 0 0
769769 23.0000 0.829401 0.414701 0.909958i 0.363886π-0.363886\pi
0.414701 + 0.909958i 0.363886π0.363886\pi
770770 0 0
771771 0 0
772772 0 0
773773 6.00000 0.215805 0.107903 0.994161i 0.465587π-0.465587\pi
0.107903 + 0.994161i 0.465587π0.465587\pi
774774 0 0
775775 −16.0000 −0.574737
776776 0 0
777777 4.00000 0.143499
778778 0 0
779779 6.00000 0.214972
780780 0 0
781781 −18.0000 −0.644091
782782 0 0
783783 24.0000 0.857690
784784 0 0
785785 42.0000 1.49904
786786 0 0
787787 4.00000 0.142585 0.0712923 0.997455i 0.477288π-0.477288\pi
0.0712923 + 0.997455i 0.477288π0.477288\pi
788788 0 0
789789 18.0000 0.640817
790790 0 0
791791 −6.00000 −0.213335
792792 0 0
793793 4.00000 0.142044
794794 0 0
795795 72.0000 2.55358
796796 0 0
797797 12.0000 0.425062 0.212531 0.977154i 0.431829π-0.431829\pi
0.212531 + 0.977154i 0.431829π0.431829\pi
798798 0 0
799799 9.00000 0.318397
800800 0 0
801801 12.0000 0.423999
802802 0 0
803803 21.0000 0.741074
804804 0 0
805805 0 0
806806 0 0
807807 −48.0000 −1.68968
808808 0 0
809809 −9.00000 −0.316423 −0.158212 0.987405i 0.550573π-0.550573\pi
−0.158212 + 0.987405i 0.550573π0.550573\pi
810810 0 0
811811 16.0000 0.561836 0.280918 0.959732i 0.409361π-0.409361\pi
0.280918 + 0.959732i 0.409361π0.409361\pi
812812 0 0
813813 −32.0000 −1.12229
814814 0 0
815815 60.0000 2.10171
816816 0 0
817817 −1.00000 −0.0349856
818818 0 0
819819 −4.00000 −0.139771
820820 0 0
821821 −33.0000 −1.15171 −0.575854 0.817553i 0.695330π-0.695330\pi
−0.575854 + 0.817553i 0.695330π0.695330\pi
822822 0 0
823823 −49.0000 −1.70803 −0.854016 0.520246i 0.825840π-0.825840\pi
−0.854016 + 0.520246i 0.825840π0.825840\pi
824824 0 0
825825 −24.0000 −0.835573
826826 0 0
827827 −12.0000 −0.417281 −0.208640 0.977992i 0.566904π-0.566904\pi
−0.208640 + 0.977992i 0.566904π0.566904\pi
828828 0 0
829829 16.0000 0.555703 0.277851 0.960624i 0.410378π-0.410378\pi
0.277851 + 0.960624i 0.410378π0.410378\pi
830830 0 0
831831 38.0000 1.31821
832832 0 0
833833 18.0000 0.623663
834834 0 0
835835 54.0000 1.86875
836836 0 0
837837 16.0000 0.553041
838838 0 0
839839 18.0000 0.621429 0.310715 0.950503i 0.399432π-0.399432\pi
0.310715 + 0.950503i 0.399432π0.399432\pi
840840 0 0
841841 7.00000 0.241379
842842 0 0
843843 12.0000 0.413302
844844 0 0
845845 −9.00000 −0.309609
846846 0 0
847847 2.00000 0.0687208
848848 0 0
849849 26.0000 0.892318
850850 0 0
851851 0 0
852852 0 0
853853 −26.0000 −0.890223 −0.445112 0.895475i 0.646836π-0.646836\pi
−0.445112 + 0.895475i 0.646836π0.646836\pi
854854 0 0
855855 3.00000 0.102598
856856 0 0
857857 18.0000 0.614868 0.307434 0.951569i 0.400530π-0.400530\pi
0.307434 + 0.951569i 0.400530π0.400530\pi
858858 0 0
859859 49.0000 1.67186 0.835929 0.548837i 0.184929π-0.184929\pi
0.835929 + 0.548837i 0.184929π0.184929\pi
860860 0 0
861861 12.0000 0.408959
862862 0 0
863863 18.0000 0.612727 0.306364 0.951915i 0.400888π-0.400888\pi
0.306364 + 0.951915i 0.400888π0.400888\pi
864864 0 0
865865 −54.0000 −1.83606
866866 0 0
867867 −16.0000 −0.543388
868868 0 0
869869 −24.0000 −0.814144
870870 0 0
871871 16.0000 0.542139
872872 0 0
873873 8.00000 0.270759
874874 0 0
875875 −3.00000 −0.101419
876876 0 0
877877 22.0000 0.742887 0.371444 0.928456i 0.378863π-0.378863\pi
0.371444 + 0.928456i 0.378863π0.378863\pi
878878 0 0
879879 24.0000 0.809500
880880 0 0
881881 −27.0000 −0.909653 −0.454827 0.890580i 0.650299π-0.650299\pi
−0.454827 + 0.890580i 0.650299π0.650299\pi
882882 0 0
883883 −47.0000 −1.58168 −0.790838 0.612026i 0.790355π-0.790355\pi
−0.790838 + 0.612026i 0.790355π0.790355\pi
884884 0 0
885885 −36.0000 −1.21013
886886 0 0
887887 18.0000 0.604381 0.302190 0.953248i 0.402282π-0.402282\pi
0.302190 + 0.953248i 0.402282π0.402282\pi
888888 0 0
889889 −2.00000 −0.0670778
890890 0 0
891891 33.0000 1.10554
892892 0 0
893893 3.00000 0.100391
894894 0 0
895895 −54.0000 −1.80502
896896 0 0
897897 0 0
898898 0 0
899899 24.0000 0.800445
900900 0 0
901901 36.0000 1.19933
902902 0 0
903903 −2.00000 −0.0665558
904904 0 0
905905 6.00000 0.199447
906906 0 0
907907 −8.00000 −0.265636 −0.132818 0.991140i 0.542403π-0.542403\pi
−0.132818 + 0.991140i 0.542403π0.542403\pi
908908 0 0
909909 −6.00000 −0.199007
910910 0 0
911911 −6.00000 −0.198789 −0.0993944 0.995048i 0.531691π-0.531691\pi
−0.0993944 + 0.995048i 0.531691π0.531691\pi
912912 0 0
913913 36.0000 1.19143
914914 0 0
915915 −6.00000 −0.198354
916916 0 0
917917 −15.0000 −0.495344
918918 0 0
919919 20.0000 0.659739 0.329870 0.944027i 0.392995π-0.392995\pi
0.329870 + 0.944027i 0.392995π0.392995\pi
920920 0 0
921921 −40.0000 −1.31804
922922 0 0
923923 24.0000 0.789970
924924 0 0
925925 −8.00000 −0.263038
926926 0 0
927927 14.0000 0.459820
928928 0 0
929929 −18.0000 −0.590561 −0.295280 0.955411i 0.595413π-0.595413\pi
−0.295280 + 0.955411i 0.595413π0.595413\pi
930930 0 0
931931 6.00000 0.196642
932932 0 0
933933 −6.00000 −0.196431
934934 0 0
935935 −27.0000 −0.882994
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 0 0
939939 −20.0000 −0.652675
940940 0 0
941941 18.0000 0.586783 0.293392 0.955992i 0.405216π-0.405216\pi
0.293392 + 0.955992i 0.405216π0.405216\pi
942942 0 0
943943 0 0
944944 0 0
945945 −12.0000 −0.390360
946946 0 0
947947 36.0000 1.16984 0.584921 0.811090i 0.301125π-0.301125\pi
0.584921 + 0.811090i 0.301125π0.301125\pi
948948 0 0
949949 −28.0000 −0.908918
950950 0 0
951951 −12.0000 −0.389127
952952 0 0
953953 −48.0000 −1.55487 −0.777436 0.628962i 0.783480π-0.783480\pi
−0.777436 + 0.628962i 0.783480π0.783480\pi
954954 0 0
955955 −9.00000 −0.291233
956956 0 0
957957 36.0000 1.16371
958958 0 0
959959 3.00000 0.0968751
960960 0 0
961961 −15.0000 −0.483871
962962 0 0
963963 18.0000 0.580042
964964 0 0
965965 12.0000 0.386294
966966 0 0
967967 −40.0000 −1.28631 −0.643157 0.765735i 0.722376π-0.722376\pi
−0.643157 + 0.765735i 0.722376π0.722376\pi
968968 0 0
969969 6.00000 0.192748
970970 0 0
971971 −60.0000 −1.92549 −0.962746 0.270408i 0.912841π-0.912841\pi
−0.962746 + 0.270408i 0.912841π0.912841\pi
972972 0 0
973973 −13.0000 −0.416761
974974 0 0
975975 32.0000 1.02482
976976 0 0
977977 24.0000 0.767828 0.383914 0.923369i 0.374576π-0.374576\pi
0.383914 + 0.923369i 0.374576π0.374576\pi
978978 0 0
979979 −36.0000 −1.15056
980980 0 0
981981 16.0000 0.510841
982982 0 0
983983 −36.0000 −1.14822 −0.574111 0.818778i 0.694652π-0.694652\pi
−0.574111 + 0.818778i 0.694652π0.694652\pi
984984 0 0
985985 54.0000 1.72058
986986 0 0
987987 6.00000 0.190982
988988 0 0
989989 0 0
990990 0 0
991991 −34.0000 −1.08005 −0.540023 0.841650i 0.681584π-0.681584\pi
−0.540023 + 0.841650i 0.681584π0.681584\pi
992992 0 0
993993 56.0000 1.77711
994994 0 0
995995 −33.0000 −1.04617
996996 0 0
997997 −17.0000 −0.538395 −0.269198 0.963085i 0.586759π-0.586759\pi
−0.269198 + 0.963085i 0.586759π0.586759\pi
998998 0 0
999999 8.00000 0.253109
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 1216.2.a.o.1.1 1
4.3 odd 2 1216.2.a.b.1.1 1
8.3 odd 2 304.2.a.f.1.1 1
8.5 even 2 19.2.a.a.1.1 1
24.5 odd 2 171.2.a.b.1.1 1
24.11 even 2 2736.2.a.c.1.1 1
40.13 odd 4 475.2.b.a.324.1 2
40.19 odd 2 7600.2.a.c.1.1 1
40.29 even 2 475.2.a.b.1.1 1
40.37 odd 4 475.2.b.a.324.2 2
56.5 odd 6 931.2.f.b.704.1 2
56.13 odd 2 931.2.a.a.1.1 1
56.37 even 6 931.2.f.c.704.1 2
56.45 odd 6 931.2.f.b.324.1 2
56.53 even 6 931.2.f.c.324.1 2
88.21 odd 2 2299.2.a.b.1.1 1
104.77 even 2 3211.2.a.a.1.1 1
120.29 odd 2 4275.2.a.i.1.1 1
136.101 even 2 5491.2.a.b.1.1 1
152.5 even 18 361.2.e.d.234.1 6
152.13 odd 18 361.2.e.e.245.1 6
152.21 odd 18 361.2.e.e.99.1 6
152.29 odd 18 361.2.e.e.62.1 6
152.37 odd 2 361.2.a.b.1.1 1
152.45 even 6 361.2.c.c.68.1 2
152.53 odd 18 361.2.e.e.54.1 6
152.61 even 18 361.2.e.d.54.1 6
152.69 odd 6 361.2.c.a.68.1 2
152.75 even 2 5776.2.a.c.1.1 1
152.85 even 18 361.2.e.d.62.1 6
152.93 even 18 361.2.e.d.99.1 6
152.101 even 18 361.2.e.d.245.1 6
152.109 odd 18 361.2.e.e.234.1 6
152.117 odd 18 361.2.e.e.28.1 6
152.125 even 6 361.2.c.c.292.1 2
152.141 odd 6 361.2.c.a.292.1 2
152.149 even 18 361.2.e.d.28.1 6
168.125 even 2 8379.2.a.j.1.1 1
456.341 even 2 3249.2.a.d.1.1 1
760.189 odd 2 9025.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.2.a.a.1.1 1 8.5 even 2
171.2.a.b.1.1 1 24.5 odd 2
304.2.a.f.1.1 1 8.3 odd 2
361.2.a.b.1.1 1 152.37 odd 2
361.2.c.a.68.1 2 152.69 odd 6
361.2.c.a.292.1 2 152.141 odd 6
361.2.c.c.68.1 2 152.45 even 6
361.2.c.c.292.1 2 152.125 even 6
361.2.e.d.28.1 6 152.149 even 18
361.2.e.d.54.1 6 152.61 even 18
361.2.e.d.62.1 6 152.85 even 18
361.2.e.d.99.1 6 152.93 even 18
361.2.e.d.234.1 6 152.5 even 18
361.2.e.d.245.1 6 152.101 even 18
361.2.e.e.28.1 6 152.117 odd 18
361.2.e.e.54.1 6 152.53 odd 18
361.2.e.e.62.1 6 152.29 odd 18
361.2.e.e.99.1 6 152.21 odd 18
361.2.e.e.234.1 6 152.109 odd 18
361.2.e.e.245.1 6 152.13 odd 18
475.2.a.b.1.1 1 40.29 even 2
475.2.b.a.324.1 2 40.13 odd 4
475.2.b.a.324.2 2 40.37 odd 4
931.2.a.a.1.1 1 56.13 odd 2
931.2.f.b.324.1 2 56.45 odd 6
931.2.f.b.704.1 2 56.5 odd 6
931.2.f.c.324.1 2 56.53 even 6
931.2.f.c.704.1 2 56.37 even 6
1216.2.a.b.1.1 1 4.3 odd 2
1216.2.a.o.1.1 1 1.1 even 1 trivial
2299.2.a.b.1.1 1 88.21 odd 2
2736.2.a.c.1.1 1 24.11 even 2
3211.2.a.a.1.1 1 104.77 even 2
3249.2.a.d.1.1 1 456.341 even 2
4275.2.a.i.1.1 1 120.29 odd 2
5491.2.a.b.1.1 1 136.101 even 2
5776.2.a.c.1.1 1 152.75 even 2
7600.2.a.c.1.1 1 40.19 odd 2
8379.2.a.j.1.1 1 168.125 even 2
9025.2.a.d.1.1 1 760.189 odd 2