Properties

Label 4368.2.a.n.1.1
Level 43684368
Weight 22
Character 4368.1
Self dual yes
Analytic conductor 34.87934.879
Analytic rank 00
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [4368,2,Mod(1,4368)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4368, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4368.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 4368=243713 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4368.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,1,0,-3,0,-1,0,1,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 34.878655602934.8786556029
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 2184)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 4368.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.00000q33.00000q51.00000q7+1.00000q9+5.00000q111.00000q133.00000q15+3.00000q17+1.00000q191.00000q211.00000q23+4.00000q25+1.00000q275.00000q29+8.00000q31+5.00000q33+3.00000q35+1.00000q371.00000q3912.0000q4111.0000q433.00000q458.00000q47+1.00000q49+3.00000q51+10.0000q5315.0000q55+1.00000q57+8.00000q59+13.0000q611.00000q63+3.00000q652.00000q671.00000q698.00000q71+11.0000q73+4.00000q755.00000q772.00000q79+1.00000q81+18.0000q839.00000q855.00000q87+18.0000q89+1.00000q91+8.00000q933.00000q95+10.0000q97+5.00000q99+O(q100)q+1.00000 q^{3} -3.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} +5.00000 q^{11} -1.00000 q^{13} -3.00000 q^{15} +3.00000 q^{17} +1.00000 q^{19} -1.00000 q^{21} -1.00000 q^{23} +4.00000 q^{25} +1.00000 q^{27} -5.00000 q^{29} +8.00000 q^{31} +5.00000 q^{33} +3.00000 q^{35} +1.00000 q^{37} -1.00000 q^{39} -12.0000 q^{41} -11.0000 q^{43} -3.00000 q^{45} -8.00000 q^{47} +1.00000 q^{49} +3.00000 q^{51} +10.0000 q^{53} -15.0000 q^{55} +1.00000 q^{57} +8.00000 q^{59} +13.0000 q^{61} -1.00000 q^{63} +3.00000 q^{65} -2.00000 q^{67} -1.00000 q^{69} -8.00000 q^{71} +11.0000 q^{73} +4.00000 q^{75} -5.00000 q^{77} -2.00000 q^{79} +1.00000 q^{81} +18.0000 q^{83} -9.00000 q^{85} -5.00000 q^{87} +18.0000 q^{89} +1.00000 q^{91} +8.00000 q^{93} -3.00000 q^{95} +10.0000 q^{97} +5.00000 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 1.00000 0.577350
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
88 0 0
99 1.00000 0.333333
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 −1.00000 −0.277350
1414 0 0
1515 −3.00000 −0.774597
1616 0 0
1717 3.00000 0.727607 0.363803 0.931476i 0.381478π-0.381478\pi
0.363803 + 0.931476i 0.381478π0.381478\pi
1818 0 0
1919 1.00000 0.229416 0.114708 0.993399i 0.463407π-0.463407\pi
0.114708 + 0.993399i 0.463407π0.463407\pi
2020 0 0
2121 −1.00000 −0.218218
2222 0 0
2323 −1.00000 −0.208514 −0.104257 0.994550i 0.533247π-0.533247\pi
−0.104257 + 0.994550i 0.533247π0.533247\pi
2424 0 0
2525 4.00000 0.800000
2626 0 0
2727 1.00000 0.192450
2828 0 0
2929 −5.00000 −0.928477 −0.464238 0.885710i 0.653672π-0.653672\pi
−0.464238 + 0.885710i 0.653672π0.653672\pi
3030 0 0
3131 8.00000 1.43684 0.718421 0.695608i 0.244865π-0.244865\pi
0.718421 + 0.695608i 0.244865π0.244865\pi
3232 0 0
3333 5.00000 0.870388
3434 0 0
3535 3.00000 0.507093
3636 0 0
3737 1.00000 0.164399 0.0821995 0.996616i 0.473806π-0.473806\pi
0.0821995 + 0.996616i 0.473806π0.473806\pi
3838 0 0
3939 −1.00000 −0.160128
4040 0 0
4141 −12.0000 −1.87409 −0.937043 0.349215i 0.886448π-0.886448\pi
−0.937043 + 0.349215i 0.886448π0.886448\pi
4242 0 0
4343 −11.0000 −1.67748 −0.838742 0.544529i 0.816708π-0.816708\pi
−0.838742 + 0.544529i 0.816708π0.816708\pi
4444 0 0
4545 −3.00000 −0.447214
4646 0 0
4747 −8.00000 −1.16692 −0.583460 0.812142i 0.698301π-0.698301\pi
−0.583460 + 0.812142i 0.698301π0.698301\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 3.00000 0.420084
5252 0 0
5353 10.0000 1.37361 0.686803 0.726844i 0.259014π-0.259014\pi
0.686803 + 0.726844i 0.259014π0.259014\pi
5454 0 0
5555 −15.0000 −2.02260
5656 0 0
5757 1.00000 0.132453
5858 0 0
5959 8.00000 1.04151 0.520756 0.853706i 0.325650π-0.325650\pi
0.520756 + 0.853706i 0.325650π0.325650\pi
6060 0 0
6161 13.0000 1.66448 0.832240 0.554416i 0.187058π-0.187058\pi
0.832240 + 0.554416i 0.187058π0.187058\pi
6262 0 0
6363 −1.00000 −0.125988
6464 0 0
6565 3.00000 0.372104
6666 0 0
6767 −2.00000 −0.244339 −0.122169 0.992509i 0.538985π-0.538985\pi
−0.122169 + 0.992509i 0.538985π0.538985\pi
6868 0 0
6969 −1.00000 −0.120386
7070 0 0
7171 −8.00000 −0.949425 −0.474713 0.880141i 0.657448π-0.657448\pi
−0.474713 + 0.880141i 0.657448π0.657448\pi
7272 0 0
7373 11.0000 1.28745 0.643726 0.765256i 0.277388π-0.277388\pi
0.643726 + 0.765256i 0.277388π0.277388\pi
7474 0 0
7575 4.00000 0.461880
7676 0 0
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 1.00000 0.111111
8282 0 0
8383 18.0000 1.97576 0.987878 0.155230i 0.0496119π-0.0496119\pi
0.987878 + 0.155230i 0.0496119π0.0496119\pi
8484 0 0
8585 −9.00000 −0.976187
8686 0 0
8787 −5.00000 −0.536056
8888 0 0
8989 18.0000 1.90800 0.953998 0.299813i 0.0969242π-0.0969242\pi
0.953998 + 0.299813i 0.0969242π0.0969242\pi
9090 0 0
9191 1.00000 0.104828
9292 0 0
9393 8.00000 0.829561
9494 0 0
9595 −3.00000 −0.307794
9696 0 0
9797 10.0000 1.01535 0.507673 0.861550i 0.330506π-0.330506\pi
0.507673 + 0.861550i 0.330506π0.330506\pi
9898 0 0
9999 5.00000 0.502519
100100 0 0
101101 −16.0000 −1.59206 −0.796030 0.605257i 0.793070π-0.793070\pi
−0.796030 + 0.605257i 0.793070π0.793070\pi
102102 0 0
103103 −5.00000 −0.492665 −0.246332 0.969185i 0.579225π-0.579225\pi
−0.246332 + 0.969185i 0.579225π0.579225\pi
104104 0 0
105105 3.00000 0.292770
106106 0 0
107107 10.0000 0.966736 0.483368 0.875417i 0.339413π-0.339413\pi
0.483368 + 0.875417i 0.339413π0.339413\pi
108108 0 0
109109 3.00000 0.287348 0.143674 0.989625i 0.454108π-0.454108\pi
0.143674 + 0.989625i 0.454108π0.454108\pi
110110 0 0
111111 1.00000 0.0949158
112112 0 0
113113 18.0000 1.69330 0.846649 0.532152i 0.178617π-0.178617\pi
0.846649 + 0.532152i 0.178617π0.178617\pi
114114 0 0
115115 3.00000 0.279751
116116 0 0
117117 −1.00000 −0.0924500
118118 0 0
119119 −3.00000 −0.275010
120120 0 0
121121 14.0000 1.27273
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 −11.0000 −0.968496
130130 0 0
131131 −11.0000 −0.961074 −0.480537 0.876974i 0.659558π-0.659558\pi
−0.480537 + 0.876974i 0.659558π0.659558\pi
132132 0 0
133133 −1.00000 −0.0867110
134134 0 0
135135 −3.00000 −0.258199
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 12.0000 1.01783 0.508913 0.860818i 0.330047π-0.330047\pi
0.508913 + 0.860818i 0.330047π0.330047\pi
140140 0 0
141141 −8.00000 −0.673722
142142 0 0
143143 −5.00000 −0.418121
144144 0 0
145145 15.0000 1.24568
146146 0 0
147147 1.00000 0.0824786
148148 0 0
149149 12.0000 0.983078 0.491539 0.870855i 0.336434π-0.336434\pi
0.491539 + 0.870855i 0.336434π0.336434\pi
150150 0 0
151151 3.00000 0.244137 0.122068 0.992522i 0.461047π-0.461047\pi
0.122068 + 0.992522i 0.461047π0.461047\pi
152152 0 0
153153 3.00000 0.242536
154154 0 0
155155 −24.0000 −1.92773
156156 0 0
157157 17.0000 1.35675 0.678374 0.734717i 0.262685π-0.262685\pi
0.678374 + 0.734717i 0.262685π0.262685\pi
158158 0 0
159159 10.0000 0.793052
160160 0 0
161161 1.00000 0.0788110
162162 0 0
163163 −10.0000 −0.783260 −0.391630 0.920123i 0.628089π-0.628089\pi
−0.391630 + 0.920123i 0.628089π0.628089\pi
164164 0 0
165165 −15.0000 −1.16775
166166 0 0
167167 15.0000 1.16073 0.580367 0.814355i 0.302909π-0.302909\pi
0.580367 + 0.814355i 0.302909π0.302909\pi
168168 0 0
169169 1.00000 0.0769231
170170 0 0
171171 1.00000 0.0764719
172172 0 0
173173 2.00000 0.152057 0.0760286 0.997106i 0.475776π-0.475776\pi
0.0760286 + 0.997106i 0.475776π0.475776\pi
174174 0 0
175175 −4.00000 −0.302372
176176 0 0
177177 8.00000 0.601317
178178 0 0
179179 −4.00000 −0.298974 −0.149487 0.988764i 0.547762π-0.547762\pi
−0.149487 + 0.988764i 0.547762π0.547762\pi
180180 0 0
181181 14.0000 1.04061 0.520306 0.853980i 0.325818π-0.325818\pi
0.520306 + 0.853980i 0.325818π0.325818\pi
182182 0 0
183183 13.0000 0.960988
184184 0 0
185185 −3.00000 −0.220564
186186 0 0
187187 15.0000 1.09691
188188 0 0
189189 −1.00000 −0.0727393
190190 0 0
191191 −25.0000 −1.80894 −0.904468 0.426541i 0.859732π-0.859732\pi
−0.904468 + 0.426541i 0.859732π0.859732\pi
192192 0 0
193193 8.00000 0.575853 0.287926 0.957653i 0.407034π-0.407034\pi
0.287926 + 0.957653i 0.407034π0.407034\pi
194194 0 0
195195 3.00000 0.214834
196196 0 0
197197 16.0000 1.13995 0.569976 0.821661i 0.306952π-0.306952\pi
0.569976 + 0.821661i 0.306952π0.306952\pi
198198 0 0
199199 17.0000 1.20510 0.602549 0.798082i 0.294152π-0.294152\pi
0.602549 + 0.798082i 0.294152π0.294152\pi
200200 0 0
201201 −2.00000 −0.141069
202202 0 0
203203 5.00000 0.350931
204204 0 0
205205 36.0000 2.51435
206206 0 0
207207 −1.00000 −0.0695048
208208 0 0
209209 5.00000 0.345857
210210 0 0
211211 15.0000 1.03264 0.516321 0.856395i 0.327301π-0.327301\pi
0.516321 + 0.856395i 0.327301π0.327301\pi
212212 0 0
213213 −8.00000 −0.548151
214214 0 0
215215 33.0000 2.25058
216216 0 0
217217 −8.00000 −0.543075
218218 0 0
219219 11.0000 0.743311
220220 0 0
221221 −3.00000 −0.201802
222222 0 0
223223 10.0000 0.669650 0.334825 0.942280i 0.391323π-0.391323\pi
0.334825 + 0.942280i 0.391323π0.391323\pi
224224 0 0
225225 4.00000 0.266667
226226 0 0
227227 10.0000 0.663723 0.331862 0.943328i 0.392323π-0.392323\pi
0.331862 + 0.943328i 0.392323π0.392323\pi
228228 0 0
229229 14.0000 0.925146 0.462573 0.886581i 0.346926π-0.346926\pi
0.462573 + 0.886581i 0.346926π0.346926\pi
230230 0 0
231231 −5.00000 −0.328976
232232 0 0
233233 −8.00000 −0.524097 −0.262049 0.965055i 0.584398π-0.584398\pi
−0.262049 + 0.965055i 0.584398π0.584398\pi
234234 0 0
235235 24.0000 1.56559
236236 0 0
237237 −2.00000 −0.129914
238238 0 0
239239 −20.0000 −1.29369 −0.646846 0.762620i 0.723912π-0.723912\pi
−0.646846 + 0.762620i 0.723912π0.723912\pi
240240 0 0
241241 10.0000 0.644157 0.322078 0.946713i 0.395619π-0.395619\pi
0.322078 + 0.946713i 0.395619π0.395619\pi
242242 0 0
243243 1.00000 0.0641500
244244 0 0
245245 −3.00000 −0.191663
246246 0 0
247247 −1.00000 −0.0636285
248248 0 0
249249 18.0000 1.14070
250250 0 0
251251 −15.0000 −0.946792 −0.473396 0.880850i 0.656972π-0.656972\pi
−0.473396 + 0.880850i 0.656972π0.656972\pi
252252 0 0
253253 −5.00000 −0.314347
254254 0 0
255255 −9.00000 −0.563602
256256 0 0
257257 −14.0000 −0.873296 −0.436648 0.899632i 0.643834π-0.643834\pi
−0.436648 + 0.899632i 0.643834π0.643834\pi
258258 0 0
259259 −1.00000 −0.0621370
260260 0 0
261261 −5.00000 −0.309492
262262 0 0
263263 −12.0000 −0.739952 −0.369976 0.929041i 0.620634π-0.620634\pi
−0.369976 + 0.929041i 0.620634π0.620634\pi
264264 0 0
265265 −30.0000 −1.84289
266266 0 0
267267 18.0000 1.10158
268268 0 0
269269 −26.0000 −1.58525 −0.792624 0.609711i 0.791286π-0.791286\pi
−0.792624 + 0.609711i 0.791286π0.791286\pi
270270 0 0
271271 22.0000 1.33640 0.668202 0.743980i 0.267064π-0.267064\pi
0.668202 + 0.743980i 0.267064π0.267064\pi
272272 0 0
273273 1.00000 0.0605228
274274 0 0
275275 20.0000 1.20605
276276 0 0
277277 22.0000 1.32185 0.660926 0.750451i 0.270164π-0.270164\pi
0.660926 + 0.750451i 0.270164π0.270164\pi
278278 0 0
279279 8.00000 0.478947
280280 0 0
281281 −22.0000 −1.31241 −0.656205 0.754583i 0.727839π-0.727839\pi
−0.656205 + 0.754583i 0.727839π0.727839\pi
282282 0 0
283283 4.00000 0.237775 0.118888 0.992908i 0.462067π-0.462067\pi
0.118888 + 0.992908i 0.462067π0.462067\pi
284284 0 0
285285 −3.00000 −0.177705
286286 0 0
287287 12.0000 0.708338
288288 0 0
289289 −8.00000 −0.470588
290290 0 0
291291 10.0000 0.586210
292292 0 0
293293 −6.00000 −0.350524 −0.175262 0.984522i 0.556077π-0.556077\pi
−0.175262 + 0.984522i 0.556077π0.556077\pi
294294 0 0
295295 −24.0000 −1.39733
296296 0 0
297297 5.00000 0.290129
298298 0 0
299299 1.00000 0.0578315
300300 0 0
301301 11.0000 0.634029
302302 0 0
303303 −16.0000 −0.919176
304304 0 0
305305 −39.0000 −2.23313
306306 0 0
307307 16.0000 0.913168 0.456584 0.889680i 0.349073π-0.349073\pi
0.456584 + 0.889680i 0.349073π0.349073\pi
308308 0 0
309309 −5.00000 −0.284440
310310 0 0
311311 −30.0000 −1.70114 −0.850572 0.525859i 0.823744π-0.823744\pi
−0.850572 + 0.525859i 0.823744π0.823744\pi
312312 0 0
313313 −12.0000 −0.678280 −0.339140 0.940736i 0.610136π-0.610136\pi
−0.339140 + 0.940736i 0.610136π0.610136\pi
314314 0 0
315315 3.00000 0.169031
316316 0 0
317317 −28.0000 −1.57264 −0.786318 0.617822i 0.788015π-0.788015\pi
−0.786318 + 0.617822i 0.788015π0.788015\pi
318318 0 0
319319 −25.0000 −1.39973
320320 0 0
321321 10.0000 0.558146
322322 0 0
323323 3.00000 0.166924
324324 0 0
325325 −4.00000 −0.221880
326326 0 0
327327 3.00000 0.165900
328328 0 0
329329 8.00000 0.441054
330330 0 0
331331 −26.0000 −1.42909 −0.714545 0.699590i 0.753366π-0.753366\pi
−0.714545 + 0.699590i 0.753366π0.753366\pi
332332 0 0
333333 1.00000 0.0547997
334334 0 0
335335 6.00000 0.327815
336336 0 0
337337 −13.0000 −0.708155 −0.354078 0.935216i 0.615205π-0.615205\pi
−0.354078 + 0.935216i 0.615205π0.615205\pi
338338 0 0
339339 18.0000 0.977626
340340 0 0
341341 40.0000 2.16612
342342 0 0
343343 −1.00000 −0.0539949
344344 0 0
345345 3.00000 0.161515
346346 0 0
347347 16.0000 0.858925 0.429463 0.903085i 0.358703π-0.358703\pi
0.429463 + 0.903085i 0.358703π0.358703\pi
348348 0 0
349349 −6.00000 −0.321173 −0.160586 0.987022i 0.551338π-0.551338\pi
−0.160586 + 0.987022i 0.551338π0.551338\pi
350350 0 0
351351 −1.00000 −0.0533761
352352 0 0
353353 −10.0000 −0.532246 −0.266123 0.963939i 0.585743π-0.585743\pi
−0.266123 + 0.963939i 0.585743π0.585743\pi
354354 0 0
355355 24.0000 1.27379
356356 0 0
357357 −3.00000 −0.158777
358358 0 0
359359 −8.00000 −0.422224 −0.211112 0.977462i 0.567708π-0.567708\pi
−0.211112 + 0.977462i 0.567708π0.567708\pi
360360 0 0
361361 −18.0000 −0.947368
362362 0 0
363363 14.0000 0.734809
364364 0 0
365365 −33.0000 −1.72730
366366 0 0
367367 16.0000 0.835193 0.417597 0.908633i 0.362873π-0.362873\pi
0.417597 + 0.908633i 0.362873π0.362873\pi
368368 0 0
369369 −12.0000 −0.624695
370370 0 0
371371 −10.0000 −0.519174
372372 0 0
373373 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
374374 0 0
375375 3.00000 0.154919
376376 0 0
377377 5.00000 0.257513
378378 0 0
379379 −12.0000 −0.616399 −0.308199 0.951322i 0.599726π-0.599726\pi
−0.308199 + 0.951322i 0.599726π0.599726\pi
380380 0 0
381381 2.00000 0.102463
382382 0 0
383383 15.0000 0.766464 0.383232 0.923652i 0.374811π-0.374811\pi
0.383232 + 0.923652i 0.374811π0.374811\pi
384384 0 0
385385 15.0000 0.764471
386386 0 0
387387 −11.0000 −0.559161
388388 0 0
389389 18.0000 0.912636 0.456318 0.889817i 0.349168π-0.349168\pi
0.456318 + 0.889817i 0.349168π0.349168\pi
390390 0 0
391391 −3.00000 −0.151717
392392 0 0
393393 −11.0000 −0.554877
394394 0 0
395395 6.00000 0.301893
396396 0 0
397397 18.0000 0.903394 0.451697 0.892171i 0.350819π-0.350819\pi
0.451697 + 0.892171i 0.350819π0.350819\pi
398398 0 0
399399 −1.00000 −0.0500626
400400 0 0
401401 34.0000 1.69788 0.848939 0.528490i 0.177242π-0.177242\pi
0.848939 + 0.528490i 0.177242π0.177242\pi
402402 0 0
403403 −8.00000 −0.398508
404404 0 0
405405 −3.00000 −0.149071
406406 0 0
407407 5.00000 0.247841
408408 0 0
409409 −7.00000 −0.346128 −0.173064 0.984911i 0.555367π-0.555367\pi
−0.173064 + 0.984911i 0.555367π0.555367\pi
410410 0 0
411411 −3.00000 −0.147979
412412 0 0
413413 −8.00000 −0.393654
414414 0 0
415415 −54.0000 −2.65076
416416 0 0
417417 12.0000 0.587643
418418 0 0
419419 15.0000 0.732798 0.366399 0.930458i 0.380591π-0.380591\pi
0.366399 + 0.930458i 0.380591π0.380591\pi
420420 0 0
421421 14.0000 0.682318 0.341159 0.940006i 0.389181π-0.389181\pi
0.341159 + 0.940006i 0.389181π0.389181\pi
422422 0 0
423423 −8.00000 −0.388973
424424 0 0
425425 12.0000 0.582086
426426 0 0
427427 −13.0000 −0.629114
428428 0 0
429429 −5.00000 −0.241402
430430 0 0
431431 −2.00000 −0.0963366 −0.0481683 0.998839i 0.515338π-0.515338\pi
−0.0481683 + 0.998839i 0.515338π0.515338\pi
432432 0 0
433433 16.0000 0.768911 0.384455 0.923144i 0.374389π-0.374389\pi
0.384455 + 0.923144i 0.374389π0.374389\pi
434434 0 0
435435 15.0000 0.719195
436436 0 0
437437 −1.00000 −0.0478365
438438 0 0
439439 −1.00000 −0.0477274 −0.0238637 0.999715i 0.507597π-0.507597\pi
−0.0238637 + 0.999715i 0.507597π0.507597\pi
440440 0 0
441441 1.00000 0.0476190
442442 0 0
443443 −18.0000 −0.855206 −0.427603 0.903967i 0.640642π-0.640642\pi
−0.427603 + 0.903967i 0.640642π0.640642\pi
444444 0 0
445445 −54.0000 −2.55985
446446 0 0
447447 12.0000 0.567581
448448 0 0
449449 9.00000 0.424736 0.212368 0.977190i 0.431882π-0.431882\pi
0.212368 + 0.977190i 0.431882π0.431882\pi
450450 0 0
451451 −60.0000 −2.82529
452452 0 0
453453 3.00000 0.140952
454454 0 0
455455 −3.00000 −0.140642
456456 0 0
457457 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
458458 0 0
459459 3.00000 0.140028
460460 0 0
461461 −17.0000 −0.791769 −0.395884 0.918300i 0.629562π-0.629562\pi
−0.395884 + 0.918300i 0.629562π0.629562\pi
462462 0 0
463463 −5.00000 −0.232370 −0.116185 0.993228i 0.537067π-0.537067\pi
−0.116185 + 0.993228i 0.537067π0.537067\pi
464464 0 0
465465 −24.0000 −1.11297
466466 0 0
467467 −31.0000 −1.43451 −0.717254 0.696811i 0.754601π-0.754601\pi
−0.717254 + 0.696811i 0.754601π0.754601\pi
468468 0 0
469469 2.00000 0.0923514
470470 0 0
471471 17.0000 0.783319
472472 0 0
473473 −55.0000 −2.52890
474474 0 0
475475 4.00000 0.183533
476476 0 0
477477 10.0000 0.457869
478478 0 0
479479 −27.0000 −1.23366 −0.616831 0.787096i 0.711584π-0.711584\pi
−0.616831 + 0.787096i 0.711584π0.711584\pi
480480 0 0
481481 −1.00000 −0.0455961
482482 0 0
483483 1.00000 0.0455016
484484 0 0
485485 −30.0000 −1.36223
486486 0 0
487487 8.00000 0.362515 0.181257 0.983436i 0.441983π-0.441983\pi
0.181257 + 0.983436i 0.441983π0.441983\pi
488488 0 0
489489 −10.0000 −0.452216
490490 0 0
491491 −6.00000 −0.270776 −0.135388 0.990793i 0.543228π-0.543228\pi
−0.135388 + 0.990793i 0.543228π0.543228\pi
492492 0 0
493493 −15.0000 −0.675566
494494 0 0
495495 −15.0000 −0.674200
496496 0 0
497497 8.00000 0.358849
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 15.0000 0.670151
502502 0 0
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 48.0000 2.13597
506506 0 0
507507 1.00000 0.0444116
508508 0 0
509509 7.00000 0.310270 0.155135 0.987893i 0.450419π-0.450419\pi
0.155135 + 0.987893i 0.450419π0.450419\pi
510510 0 0
511511 −11.0000 −0.486611
512512 0 0
513513 1.00000 0.0441511
514514 0 0
515515 15.0000 0.660979
516516 0 0
517517 −40.0000 −1.75920
518518 0 0
519519 2.00000 0.0877903
520520 0 0
521521 −39.0000 −1.70862 −0.854311 0.519763i 0.826020π-0.826020\pi
−0.854311 + 0.519763i 0.826020π0.826020\pi
522522 0 0
523523 20.0000 0.874539 0.437269 0.899331i 0.355946π-0.355946\pi
0.437269 + 0.899331i 0.355946π0.355946\pi
524524 0 0
525525 −4.00000 −0.174574
526526 0 0
527527 24.0000 1.04546
528528 0 0
529529 −22.0000 −0.956522
530530 0 0
531531 8.00000 0.347170
532532 0 0
533533 12.0000 0.519778
534534 0 0
535535 −30.0000 −1.29701
536536 0 0
537537 −4.00000 −0.172613
538538 0 0
539539 5.00000 0.215365
540540 0 0
541541 3.00000 0.128980 0.0644900 0.997918i 0.479458π-0.479458\pi
0.0644900 + 0.997918i 0.479458π0.479458\pi
542542 0 0
543543 14.0000 0.600798
544544 0 0
545545 −9.00000 −0.385518
546546 0 0
547547 −20.0000 −0.855138 −0.427569 0.903983i 0.640630π-0.640630\pi
−0.427569 + 0.903983i 0.640630π0.640630\pi
548548 0 0
549549 13.0000 0.554826
550550 0 0
551551 −5.00000 −0.213007
552552 0 0
553553 2.00000 0.0850487
554554 0 0
555555 −3.00000 −0.127343
556556 0 0
557557 8.00000 0.338971 0.169485 0.985533i 0.445789π-0.445789\pi
0.169485 + 0.985533i 0.445789π0.445789\pi
558558 0 0
559559 11.0000 0.465250
560560 0 0
561561 15.0000 0.633300
562562 0 0
563563 21.0000 0.885044 0.442522 0.896758i 0.354084π-0.354084\pi
0.442522 + 0.896758i 0.354084π0.354084\pi
564564 0 0
565565 −54.0000 −2.27180
566566 0 0
567567 −1.00000 −0.0419961
568568 0 0
569569 −10.0000 −0.419222 −0.209611 0.977785i 0.567220π-0.567220\pi
−0.209611 + 0.977785i 0.567220π0.567220\pi
570570 0 0
571571 40.0000 1.67395 0.836974 0.547243i 0.184323π-0.184323\pi
0.836974 + 0.547243i 0.184323π0.184323\pi
572572 0 0
573573 −25.0000 −1.04439
574574 0 0
575575 −4.00000 −0.166812
576576 0 0
577577 18.0000 0.749350 0.374675 0.927156i 0.377754π-0.377754\pi
0.374675 + 0.927156i 0.377754π0.377754\pi
578578 0 0
579579 8.00000 0.332469
580580 0 0
581581 −18.0000 −0.746766
582582 0 0
583583 50.0000 2.07079
584584 0 0
585585 3.00000 0.124035
586586 0 0
587587 −18.0000 −0.742940 −0.371470 0.928445i 0.621146π-0.621146\pi
−0.371470 + 0.928445i 0.621146π0.621146\pi
588588 0 0
589589 8.00000 0.329634
590590 0 0
591591 16.0000 0.658152
592592 0 0
593593 22.0000 0.903432 0.451716 0.892162i 0.350812π-0.350812\pi
0.451716 + 0.892162i 0.350812π0.350812\pi
594594 0 0
595595 9.00000 0.368964
596596 0 0
597597 17.0000 0.695764
598598 0 0
599599 9.00000 0.367730 0.183865 0.982952i 0.441139π-0.441139\pi
0.183865 + 0.982952i 0.441139π0.441139\pi
600600 0 0
601601 −40.0000 −1.63163 −0.815817 0.578310i 0.803712π-0.803712\pi
−0.815817 + 0.578310i 0.803712π0.803712\pi
602602 0 0
603603 −2.00000 −0.0814463
604604 0 0
605605 −42.0000 −1.70754
606606 0 0
607607 −1.00000 −0.0405887 −0.0202944 0.999794i 0.506460π-0.506460\pi
−0.0202944 + 0.999794i 0.506460π0.506460\pi
608608 0 0
609609 5.00000 0.202610
610610 0 0
611611 8.00000 0.323645
612612 0 0
613613 19.0000 0.767403 0.383701 0.923457i 0.374649π-0.374649\pi
0.383701 + 0.923457i 0.374649π0.374649\pi
614614 0 0
615615 36.0000 1.45166
616616 0 0
617617 15.0000 0.603877 0.301939 0.953327i 0.402366π-0.402366\pi
0.301939 + 0.953327i 0.402366π0.402366\pi
618618 0 0
619619 17.0000 0.683288 0.341644 0.939829i 0.389016π-0.389016\pi
0.341644 + 0.939829i 0.389016π0.389016\pi
620620 0 0
621621 −1.00000 −0.0401286
622622 0 0
623623 −18.0000 −0.721155
624624 0 0
625625 −29.0000 −1.16000
626626 0 0
627627 5.00000 0.199681
628628 0 0
629629 3.00000 0.119618
630630 0 0
631631 −9.00000 −0.358284 −0.179142 0.983823i 0.557332π-0.557332\pi
−0.179142 + 0.983823i 0.557332π0.557332\pi
632632 0 0
633633 15.0000 0.596196
634634 0 0
635635 −6.00000 −0.238103
636636 0 0
637637 −1.00000 −0.0396214
638638 0 0
639639 −8.00000 −0.316475
640640 0 0
641641 −10.0000 −0.394976 −0.197488 0.980305i 0.563278π-0.563278\pi
−0.197488 + 0.980305i 0.563278π0.563278\pi
642642 0 0
643643 −49.0000 −1.93237 −0.966186 0.257847i 0.916987π-0.916987\pi
−0.966186 + 0.257847i 0.916987π0.916987\pi
644644 0 0
645645 33.0000 1.29937
646646 0 0
647647 −32.0000 −1.25805 −0.629025 0.777385i 0.716546π-0.716546\pi
−0.629025 + 0.777385i 0.716546π0.716546\pi
648648 0 0
649649 40.0000 1.57014
650650 0 0
651651 −8.00000 −0.313545
652652 0 0
653653 45.0000 1.76099 0.880493 0.474059i 0.157212π-0.157212\pi
0.880493 + 0.474059i 0.157212π0.157212\pi
654654 0 0
655655 33.0000 1.28942
656656 0 0
657657 11.0000 0.429151
658658 0 0
659659 2.00000 0.0779089 0.0389545 0.999241i 0.487597π-0.487597\pi
0.0389545 + 0.999241i 0.487597π0.487597\pi
660660 0 0
661661 10.0000 0.388955 0.194477 0.980907i 0.437699π-0.437699\pi
0.194477 + 0.980907i 0.437699π0.437699\pi
662662 0 0
663663 −3.00000 −0.116510
664664 0 0
665665 3.00000 0.116335
666666 0 0
667667 5.00000 0.193601
668668 0 0
669669 10.0000 0.386622
670670 0 0
671671 65.0000 2.50930
672672 0 0
673673 31.0000 1.19496 0.597481 0.801883i 0.296168π-0.296168\pi
0.597481 + 0.801883i 0.296168π0.296168\pi
674674 0 0
675675 4.00000 0.153960
676676 0 0
677677 14.0000 0.538064 0.269032 0.963131i 0.413296π-0.413296\pi
0.269032 + 0.963131i 0.413296π0.413296\pi
678678 0 0
679679 −10.0000 −0.383765
680680 0 0
681681 10.0000 0.383201
682682 0 0
683683 39.0000 1.49229 0.746147 0.665782i 0.231902π-0.231902\pi
0.746147 + 0.665782i 0.231902π0.231902\pi
684684 0 0
685685 9.00000 0.343872
686686 0 0
687687 14.0000 0.534133
688688 0 0
689689 −10.0000 −0.380970
690690 0 0
691691 −4.00000 −0.152167 −0.0760836 0.997101i 0.524242π-0.524242\pi
−0.0760836 + 0.997101i 0.524242π0.524242\pi
692692 0 0
693693 −5.00000 −0.189934
694694 0 0
695695 −36.0000 −1.36556
696696 0 0
697697 −36.0000 −1.36360
698698 0 0
699699 −8.00000 −0.302588
700700 0 0
701701 22.0000 0.830929 0.415464 0.909610i 0.363619π-0.363619\pi
0.415464 + 0.909610i 0.363619π0.363619\pi
702702 0 0
703703 1.00000 0.0377157
704704 0 0
705705 24.0000 0.903892
706706 0 0
707707 16.0000 0.601742
708708 0 0
709709 −18.0000 −0.676004 −0.338002 0.941145i 0.609751π-0.609751\pi
−0.338002 + 0.941145i 0.609751π0.609751\pi
710710 0 0
711711 −2.00000 −0.0750059
712712 0 0
713713 −8.00000 −0.299602
714714 0 0
715715 15.0000 0.560968
716716 0 0
717717 −20.0000 −0.746914
718718 0 0
719719 −10.0000 −0.372937 −0.186469 0.982461i 0.559704π-0.559704\pi
−0.186469 + 0.982461i 0.559704π0.559704\pi
720720 0 0
721721 5.00000 0.186210
722722 0 0
723723 10.0000 0.371904
724724 0 0
725725 −20.0000 −0.742781
726726 0 0
727727 −49.0000 −1.81731 −0.908655 0.417548i 0.862889π-0.862889\pi
−0.908655 + 0.417548i 0.862889π0.862889\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −33.0000 −1.22055
732732 0 0
733733 44.0000 1.62518 0.812589 0.582838i 0.198058π-0.198058\pi
0.812589 + 0.582838i 0.198058π0.198058\pi
734734 0 0
735735 −3.00000 −0.110657
736736 0 0
737737 −10.0000 −0.368355
738738 0 0
739739 10.0000 0.367856 0.183928 0.982940i 0.441119π-0.441119\pi
0.183928 + 0.982940i 0.441119π0.441119\pi
740740 0 0
741741 −1.00000 −0.0367359
742742 0 0
743743 10.0000 0.366864 0.183432 0.983032i 0.441279π-0.441279\pi
0.183432 + 0.983032i 0.441279π0.441279\pi
744744 0 0
745745 −36.0000 −1.31894
746746 0 0
747747 18.0000 0.658586
748748 0 0
749749 −10.0000 −0.365392
750750 0 0
751751 −32.0000 −1.16770 −0.583848 0.811863i 0.698454π-0.698454\pi
−0.583848 + 0.811863i 0.698454π0.698454\pi
752752 0 0
753753 −15.0000 −0.546630
754754 0 0
755755 −9.00000 −0.327544
756756 0 0
757757 −6.00000 −0.218074 −0.109037 0.994038i 0.534777π-0.534777\pi
−0.109037 + 0.994038i 0.534777π0.534777\pi
758758 0 0
759759 −5.00000 −0.181489
760760 0 0
761761 12.0000 0.435000 0.217500 0.976060i 0.430210π-0.430210\pi
0.217500 + 0.976060i 0.430210π0.430210\pi
762762 0 0
763763 −3.00000 −0.108607
764764 0 0
765765 −9.00000 −0.325396
766766 0 0
767767 −8.00000 −0.288863
768768 0 0
769769 49.0000 1.76699 0.883493 0.468445i 0.155186π-0.155186\pi
0.883493 + 0.468445i 0.155186π0.155186\pi
770770 0 0
771771 −14.0000 −0.504198
772772 0 0
773773 −25.0000 −0.899188 −0.449594 0.893233i 0.648431π-0.648431\pi
−0.449594 + 0.893233i 0.648431π0.648431\pi
774774 0 0
775775 32.0000 1.14947
776776 0 0
777777 −1.00000 −0.0358748
778778 0 0
779779 −12.0000 −0.429945
780780 0 0
781781 −40.0000 −1.43131
782782 0 0
783783 −5.00000 −0.178685
784784 0 0
785785 −51.0000 −1.82027
786786 0 0
787787 17.0000 0.605985 0.302992 0.952993i 0.402014π-0.402014\pi
0.302992 + 0.952993i 0.402014π0.402014\pi
788788 0 0
789789 −12.0000 −0.427211
790790 0 0
791791 −18.0000 −0.640006
792792 0 0
793793 −13.0000 −0.461644
794794 0 0
795795 −30.0000 −1.06399
796796 0 0
797797 48.0000 1.70025 0.850124 0.526583i 0.176527π-0.176527\pi
0.850124 + 0.526583i 0.176527π0.176527\pi
798798 0 0
799799 −24.0000 −0.849059
800800 0 0
801801 18.0000 0.635999
802802 0 0
803803 55.0000 1.94091
804804 0 0
805805 −3.00000 −0.105736
806806 0 0
807807 −26.0000 −0.915243
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 −51.0000 −1.79085 −0.895426 0.445210i 0.853129π-0.853129\pi
−0.895426 + 0.445210i 0.853129π0.853129\pi
812812 0 0
813813 22.0000 0.771574
814814 0 0
815815 30.0000 1.05085
816816 0 0
817817 −11.0000 −0.384841
818818 0 0
819819 1.00000 0.0349428
820820 0 0
821821 −24.0000 −0.837606 −0.418803 0.908077i 0.637550π-0.637550\pi
−0.418803 + 0.908077i 0.637550π0.637550\pi
822822 0 0
823823 −4.00000 −0.139431 −0.0697156 0.997567i 0.522209π-0.522209\pi
−0.0697156 + 0.997567i 0.522209π0.522209\pi
824824 0 0
825825 20.0000 0.696311
826826 0 0
827827 45.0000 1.56480 0.782402 0.622774i 0.213994π-0.213994\pi
0.782402 + 0.622774i 0.213994π0.213994\pi
828828 0 0
829829 53.0000 1.84077 0.920383 0.391018i 0.127877π-0.127877\pi
0.920383 + 0.391018i 0.127877π0.127877\pi
830830 0 0
831831 22.0000 0.763172
832832 0 0
833833 3.00000 0.103944
834834 0 0
835835 −45.0000 −1.55729
836836 0 0
837837 8.00000 0.276520
838838 0 0
839839 −20.0000 −0.690477 −0.345238 0.938515i 0.612202π-0.612202\pi
−0.345238 + 0.938515i 0.612202π0.612202\pi
840840 0 0
841841 −4.00000 −0.137931
842842 0 0
843843 −22.0000 −0.757720
844844 0 0
845845 −3.00000 −0.103203
846846 0 0
847847 −14.0000 −0.481046
848848 0 0
849849 4.00000 0.137280
850850 0 0
851851 −1.00000 −0.0342796
852852 0 0
853853 4.00000 0.136957 0.0684787 0.997653i 0.478185π-0.478185\pi
0.0684787 + 0.997653i 0.478185π0.478185\pi
854854 0 0
855855 −3.00000 −0.102598
856856 0 0
857857 −18.0000 −0.614868 −0.307434 0.951569i 0.599470π-0.599470\pi
−0.307434 + 0.951569i 0.599470π0.599470\pi
858858 0 0
859859 20.0000 0.682391 0.341196 0.939992i 0.389168π-0.389168\pi
0.341196 + 0.939992i 0.389168π0.389168\pi
860860 0 0
861861 12.0000 0.408959
862862 0 0
863863 10.0000 0.340404 0.170202 0.985409i 0.445558π-0.445558\pi
0.170202 + 0.985409i 0.445558π0.445558\pi
864864 0 0
865865 −6.00000 −0.204006
866866 0 0
867867 −8.00000 −0.271694
868868 0 0
869869 −10.0000 −0.339227
870870 0 0
871871 2.00000 0.0677674
872872 0 0
873873 10.0000 0.338449
874874 0 0
875875 −3.00000 −0.101419
876876 0 0
877877 14.0000 0.472746 0.236373 0.971662i 0.424041π-0.424041\pi
0.236373 + 0.971662i 0.424041π0.424041\pi
878878 0 0
879879 −6.00000 −0.202375
880880 0 0
881881 3.00000 0.101073 0.0505363 0.998722i 0.483907π-0.483907\pi
0.0505363 + 0.998722i 0.483907π0.483907\pi
882882 0 0
883883 −19.0000 −0.639401 −0.319700 0.947519i 0.603582π-0.603582\pi
−0.319700 + 0.947519i 0.603582π0.603582\pi
884884 0 0
885885 −24.0000 −0.806751
886886 0 0
887887 −52.0000 −1.74599 −0.872995 0.487730i 0.837825π-0.837825\pi
−0.872995 + 0.487730i 0.837825π0.837825\pi
888888 0 0
889889 −2.00000 −0.0670778
890890 0 0
891891 5.00000 0.167506
892892 0 0
893893 −8.00000 −0.267710
894894 0 0
895895 12.0000 0.401116
896896 0 0
897897 1.00000 0.0333890
898898 0 0
899899 −40.0000 −1.33407
900900 0 0
901901 30.0000 0.999445
902902 0 0
903903 11.0000 0.366057
904904 0 0
905905 −42.0000 −1.39613
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 0 0
909909 −16.0000 −0.530687
910910 0 0
911911 −15.0000 −0.496972 −0.248486 0.968635i 0.579933π-0.579933\pi
−0.248486 + 0.968635i 0.579933π0.579933\pi
912912 0 0
913913 90.0000 2.97857
914914 0 0
915915 −39.0000 −1.28930
916916 0 0
917917 11.0000 0.363252
918918 0 0
919919 18.0000 0.593765 0.296883 0.954914i 0.404053π-0.404053\pi
0.296883 + 0.954914i 0.404053π0.404053\pi
920920 0 0
921921 16.0000 0.527218
922922 0 0
923923 8.00000 0.263323
924924 0 0
925925 4.00000 0.131519
926926 0 0
927927 −5.00000 −0.164222
928928 0 0
929929 44.0000 1.44359 0.721797 0.692105i 0.243317π-0.243317\pi
0.721797 + 0.692105i 0.243317π0.243317\pi
930930 0 0
931931 1.00000 0.0327737
932932 0 0
933933 −30.0000 −0.982156
934934 0 0
935935 −45.0000 −1.47166
936936 0 0
937937 −34.0000 −1.11073 −0.555366 0.831606i 0.687422π-0.687422\pi
−0.555366 + 0.831606i 0.687422π0.687422\pi
938938 0 0
939939 −12.0000 −0.391605
940940 0 0
941941 −18.0000 −0.586783 −0.293392 0.955992i 0.594784π-0.594784\pi
−0.293392 + 0.955992i 0.594784π0.594784\pi
942942 0 0
943943 12.0000 0.390774
944944 0 0
945945 3.00000 0.0975900
946946 0 0
947947 −39.0000 −1.26733 −0.633665 0.773608i 0.718450π-0.718450\pi
−0.633665 + 0.773608i 0.718450π0.718450\pi
948948 0 0
949949 −11.0000 −0.357075
950950 0 0
951951 −28.0000 −0.907962
952952 0 0
953953 48.0000 1.55487 0.777436 0.628962i 0.216520π-0.216520\pi
0.777436 + 0.628962i 0.216520π0.216520\pi
954954 0 0
955955 75.0000 2.42694
956956 0 0
957957 −25.0000 −0.808135
958958 0 0
959959 3.00000 0.0968751
960960 0 0
961961 33.0000 1.06452
962962 0 0
963963 10.0000 0.322245
964964 0 0
965965 −24.0000 −0.772587
966966 0 0
967967 33.0000 1.06121 0.530604 0.847620i 0.321965π-0.321965\pi
0.530604 + 0.847620i 0.321965π0.321965\pi
968968 0 0
969969 3.00000 0.0963739
970970 0 0
971971 −24.0000 −0.770197 −0.385098 0.922876i 0.625832π-0.625832\pi
−0.385098 + 0.922876i 0.625832π0.625832\pi
972972 0 0
973973 −12.0000 −0.384702
974974 0 0
975975 −4.00000 −0.128103
976976 0 0
977977 19.0000 0.607864 0.303932 0.952694i 0.401700π-0.401700\pi
0.303932 + 0.952694i 0.401700π0.401700\pi
978978 0 0
979979 90.0000 2.87641
980980 0 0
981981 3.00000 0.0957826
982982 0 0
983983 −51.0000 −1.62665 −0.813324 0.581811i 0.802344π-0.802344\pi
−0.813324 + 0.581811i 0.802344π0.802344\pi
984984 0 0
985985 −48.0000 −1.52941
986986 0 0
987987 8.00000 0.254643
988988 0 0
989989 11.0000 0.349780
990990 0 0
991991 −30.0000 −0.952981 −0.476491 0.879180i 0.658091π-0.658091\pi
−0.476491 + 0.879180i 0.658091π0.658091\pi
992992 0 0
993993 −26.0000 −0.825085
994994 0 0
995995 −51.0000 −1.61681
996996 0 0
997997 14.0000 0.443384 0.221692 0.975117i 0.428842π-0.428842\pi
0.221692 + 0.975117i 0.428842π0.428842\pi
998998 0 0
999999 1.00000 0.0316386
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 4368.2.a.n.1.1 1
4.3 odd 2 2184.2.a.a.1.1 1
12.11 even 2 6552.2.a.z.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2184.2.a.a.1.1 1 4.3 odd 2
4368.2.a.n.1.1 1 1.1 even 1 trivial
6552.2.a.z.1.1 1 12.11 even 2