Properties

Label 1160.2.a.f.1.1
Level 11601160
Weight 22
Character 1160.1
Self dual yes
Analytic conductor 9.2639.263
Analytic rank 11
Dimension 33
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1160,2,Mod(1,1160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1160, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1160.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1160=23529 1160 = 2^{3} \cdot 5 \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1160.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: 9.262646634479.26264663447
Analytic rank: 11
Dimension: 33
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x23x+1 x^{3} - x^{2} - 3x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 0.3111080.311108 of defining polynomial
Character χ\chi == 1160.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q2.90321q3+1.00000q5+0.903212q7+5.42864q95.52543q110.622216q132.90321q15+3.52543q171.09679q192.62222q21+5.33185q23+1.00000q257.05086q271.00000q291.65878q31+16.0415q33+0.903212q352.28100q37+1.80642q397.67307q411.09679q43+5.42864q451.65878q476.18421q4910.2351q512.42864q535.52543q55+3.18421q57+9.28592q5910.9906q61+4.90321q630.622216q6511.1383q6715.4795q697.18421q71+11.9541q732.90321q754.99063q7715.3319q79+4.18421q817.95407q83+3.52543q85+2.90321q8716.6637q890.561993q91+4.81579q931.09679q9511.9541q9729.9956q99+O(q100)q-2.90321 q^{3} +1.00000 q^{5} +0.903212 q^{7} +5.42864 q^{9} -5.52543 q^{11} -0.622216 q^{13} -2.90321 q^{15} +3.52543 q^{17} -1.09679 q^{19} -2.62222 q^{21} +5.33185 q^{23} +1.00000 q^{25} -7.05086 q^{27} -1.00000 q^{29} -1.65878 q^{31} +16.0415 q^{33} +0.903212 q^{35} -2.28100 q^{37} +1.80642 q^{39} -7.67307 q^{41} -1.09679 q^{43} +5.42864 q^{45} -1.65878 q^{47} -6.18421 q^{49} -10.2351 q^{51} -2.42864 q^{53} -5.52543 q^{55} +3.18421 q^{57} +9.28592 q^{59} -10.9906 q^{61} +4.90321 q^{63} -0.622216 q^{65} -11.1383 q^{67} -15.4795 q^{69} -7.18421 q^{71} +11.9541 q^{73} -2.90321 q^{75} -4.99063 q^{77} -15.3319 q^{79} +4.18421 q^{81} -7.95407 q^{83} +3.52543 q^{85} +2.90321 q^{87} -16.6637 q^{89} -0.561993 q^{91} +4.81579 q^{93} -1.09679 q^{95} -11.9541 q^{97} -29.9956 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q2q3+3q54q7+3q910q112q132q15+4q1710q198q214q23+3q258q273q29+2q31+8q334q358q3910q41+30q99+O(q100) 3 q - 2 q^{3} + 3 q^{5} - 4 q^{7} + 3 q^{9} - 10 q^{11} - 2 q^{13} - 2 q^{15} + 4 q^{17} - 10 q^{19} - 8 q^{21} - 4 q^{23} + 3 q^{25} - 8 q^{27} - 3 q^{29} + 2 q^{31} + 8 q^{33} - 4 q^{35} - 8 q^{39} - 10 q^{41}+ \cdots - 30 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −2.90321 −1.67617 −0.838085 0.545540i 0.816325π-0.816325\pi
−0.838085 + 0.545540i 0.816325π0.816325\pi
44 0 0
55 1.00000 0.447214
66 0 0
77 0.903212 0.341382 0.170691 0.985325i 0.445400π-0.445400\pi
0.170691 + 0.985325i 0.445400π0.445400\pi
88 0 0
99 5.42864 1.80955
1010 0 0
1111 −5.52543 −1.66598 −0.832990 0.553289i 0.813373π-0.813373\pi
−0.832990 + 0.553289i 0.813373π0.813373\pi
1212 0 0
1313 −0.622216 −0.172572 −0.0862858 0.996270i 0.527500π-0.527500\pi
−0.0862858 + 0.996270i 0.527500π0.527500\pi
1414 0 0
1515 −2.90321 −0.749606
1616 0 0
1717 3.52543 0.855042 0.427521 0.904005i 0.359387π-0.359387\pi
0.427521 + 0.904005i 0.359387π0.359387\pi
1818 0 0
1919 −1.09679 −0.251620 −0.125810 0.992054i 0.540153π-0.540153\pi
−0.125810 + 0.992054i 0.540153π0.540153\pi
2020 0 0
2121 −2.62222 −0.572214
2222 0 0
2323 5.33185 1.11177 0.555884 0.831260i 0.312380π-0.312380\pi
0.555884 + 0.831260i 0.312380π0.312380\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 −7.05086 −1.35694
2828 0 0
2929 −1.00000 −0.185695
3030 0 0
3131 −1.65878 −0.297926 −0.148963 0.988843i 0.547593π-0.547593\pi
−0.148963 + 0.988843i 0.547593π0.547593\pi
3232 0 0
3333 16.0415 2.79246
3434 0 0
3535 0.903212 0.152671
3636 0 0
3737 −2.28100 −0.374993 −0.187497 0.982265i 0.560037π-0.560037\pi
−0.187497 + 0.982265i 0.560037π0.560037\pi
3838 0 0
3939 1.80642 0.289259
4040 0 0
4141 −7.67307 −1.19833 −0.599166 0.800625i 0.704501π-0.704501\pi
−0.599166 + 0.800625i 0.704501π0.704501\pi
4242 0 0
4343 −1.09679 −0.167259 −0.0836293 0.996497i 0.526651π-0.526651\pi
−0.0836293 + 0.996497i 0.526651π0.526651\pi
4444 0 0
4545 5.42864 0.809254
4646 0 0
4747 −1.65878 −0.241958 −0.120979 0.992655i 0.538603π-0.538603\pi
−0.120979 + 0.992655i 0.538603π0.538603\pi
4848 0 0
4949 −6.18421 −0.883458
5050 0 0
5151 −10.2351 −1.43320
5252 0 0
5353 −2.42864 −0.333599 −0.166800 0.985991i 0.553343π-0.553343\pi
−0.166800 + 0.985991i 0.553343π0.553343\pi
5454 0 0
5555 −5.52543 −0.745049
5656 0 0
5757 3.18421 0.421759
5858 0 0
5959 9.28592 1.20892 0.604462 0.796634i 0.293388π-0.293388\pi
0.604462 + 0.796634i 0.293388π0.293388\pi
6060 0 0
6161 −10.9906 −1.40721 −0.703603 0.710593i 0.748427π-0.748427\pi
−0.703603 + 0.710593i 0.748427π0.748427\pi
6262 0 0
6363 4.90321 0.617747
6464 0 0
6565 −0.622216 −0.0771764
6666 0 0
6767 −11.1383 −1.36076 −0.680378 0.732861i 0.738185π-0.738185\pi
−0.680378 + 0.732861i 0.738185π0.738185\pi
6868 0 0
6969 −15.4795 −1.86351
7070 0 0
7171 −7.18421 −0.852609 −0.426304 0.904580i 0.640185π-0.640185\pi
−0.426304 + 0.904580i 0.640185π0.640185\pi
7272 0 0
7373 11.9541 1.39912 0.699559 0.714575i 0.253380π-0.253380\pi
0.699559 + 0.714575i 0.253380π0.253380\pi
7474 0 0
7575 −2.90321 −0.335234
7676 0 0
7777 −4.99063 −0.568735
7878 0 0
7979 −15.3319 −1.72497 −0.862484 0.506084i 0.831092π-0.831092\pi
−0.862484 + 0.506084i 0.831092π0.831092\pi
8080 0 0
8181 4.18421 0.464912
8282 0 0
8383 −7.95407 −0.873072 −0.436536 0.899687i 0.643795π-0.643795\pi
−0.436536 + 0.899687i 0.643795π0.643795\pi
8484 0 0
8585 3.52543 0.382386
8686 0 0
8787 2.90321 0.311257
8888 0 0
8989 −16.6637 −1.76635 −0.883174 0.469045i 0.844598π-0.844598\pi
−0.883174 + 0.469045i 0.844598π0.844598\pi
9090 0 0
9191 −0.561993 −0.0589128
9292 0 0
9393 4.81579 0.499374
9494 0 0
9595 −1.09679 −0.112528
9696 0 0
9797 −11.9541 −1.21375 −0.606876 0.794797i 0.707577π-0.707577\pi
−0.606876 + 0.794797i 0.707577π0.707577\pi
9898 0 0
9999 −29.9956 −3.01467
100100 0 0
101101 8.66370 0.862071 0.431035 0.902335i 0.358148π-0.358148\pi
0.431035 + 0.902335i 0.358148π0.358148\pi
102102 0 0
103103 −17.6271 −1.73685 −0.868427 0.495817i 0.834868π-0.834868\pi
−0.868427 + 0.495817i 0.834868π0.834868\pi
104104 0 0
105105 −2.62222 −0.255902
106106 0 0
107107 3.95407 0.382254 0.191127 0.981565i 0.438786π-0.438786\pi
0.191127 + 0.981565i 0.438786π0.438786\pi
108108 0 0
109109 −2.81579 −0.269704 −0.134852 0.990866i 0.543056π-0.543056\pi
−0.134852 + 0.990866i 0.543056π0.543056\pi
110110 0 0
111111 6.62222 0.628553
112112 0 0
113113 14.7096 1.38377 0.691883 0.722010i 0.256781π-0.256781\pi
0.691883 + 0.722010i 0.256781π0.256781\pi
114114 0 0
115115 5.33185 0.497198
116116 0 0
117117 −3.37778 −0.312276
118118 0 0
119119 3.18421 0.291896
120120 0 0
121121 19.5303 1.77549
122122 0 0
123123 22.2766 2.00861
124124 0 0
125125 1.00000 0.0894427
126126 0 0
127127 −2.34122 −0.207750 −0.103875 0.994590i 0.533124π-0.533124\pi
−0.103875 + 0.994590i 0.533124π0.533124\pi
128128 0 0
129129 3.18421 0.280354
130130 0 0
131131 −5.65878 −0.494410 −0.247205 0.968963i 0.579512π-0.579512\pi
−0.247205 + 0.968963i 0.579512π0.579512\pi
132132 0 0
133133 −0.990632 −0.0858987
134134 0 0
135135 −7.05086 −0.606841
136136 0 0
137137 9.62714 0.822502 0.411251 0.911522i 0.365092π-0.365092\pi
0.411251 + 0.911522i 0.365092π0.365092\pi
138138 0 0
139139 6.66370 0.565208 0.282604 0.959237i 0.408802π-0.408802\pi
0.282604 + 0.959237i 0.408802π0.408802\pi
140140 0 0
141141 4.81579 0.405563
142142 0 0
143143 3.43801 0.287501
144144 0 0
145145 −1.00000 −0.0830455
146146 0 0
147147 17.9541 1.48083
148148 0 0
149149 −17.2257 −1.41118 −0.705592 0.708618i 0.749319π-0.749319\pi
−0.705592 + 0.708618i 0.749319π0.749319\pi
150150 0 0
151151 5.93978 0.483372 0.241686 0.970354i 0.422300π-0.422300\pi
0.241686 + 0.970354i 0.422300π0.422300\pi
152152 0 0
153153 19.1383 1.54724
154154 0 0
155155 −1.65878 −0.133236
156156 0 0
157157 −15.5669 −1.24238 −0.621188 0.783662i 0.713349π-0.713349\pi
−0.621188 + 0.783662i 0.713349π0.713349\pi
158158 0 0
159159 7.05086 0.559169
160160 0 0
161161 4.81579 0.379538
162162 0 0
163163 10.5161 0.823681 0.411841 0.911256i 0.364886π-0.364886\pi
0.411841 + 0.911256i 0.364886π0.364886\pi
164164 0 0
165165 16.0415 1.24883
166166 0 0
167167 12.6494 0.978841 0.489420 0.872048i 0.337208π-0.337208\pi
0.489420 + 0.872048i 0.337208π0.337208\pi
168168 0 0
169169 −12.6128 −0.970219
170170 0 0
171171 −5.95407 −0.455319
172172 0 0
173173 6.13335 0.466310 0.233155 0.972440i 0.425095π-0.425095\pi
0.233155 + 0.972440i 0.425095π0.425095\pi
174174 0 0
175175 0.903212 0.0682764
176176 0 0
177177 −26.9590 −2.02636
178178 0 0
179179 15.2257 1.13802 0.569011 0.822330i 0.307326π-0.307326\pi
0.569011 + 0.822330i 0.307326π0.307326\pi
180180 0 0
181181 3.93978 0.292841 0.146421 0.989222i 0.453225π-0.453225\pi
0.146421 + 0.989222i 0.453225π0.453225\pi
182182 0 0
183183 31.9081 2.35872
184184 0 0
185185 −2.28100 −0.167702
186186 0 0
187187 −19.4795 −1.42448
188188 0 0
189189 −6.36842 −0.463234
190190 0 0
191191 −7.06515 −0.511216 −0.255608 0.966781i 0.582276π-0.582276\pi
−0.255608 + 0.966781i 0.582276π0.582276\pi
192192 0 0
193193 1.98571 0.142935 0.0714673 0.997443i 0.477232π-0.477232\pi
0.0714673 + 0.997443i 0.477232π0.477232\pi
194194 0 0
195195 1.80642 0.129361
196196 0 0
197197 −16.2766 −1.15966 −0.579828 0.814739i 0.696880π-0.696880\pi
−0.579828 + 0.814739i 0.696880π0.696880\pi
198198 0 0
199199 22.5303 1.59713 0.798567 0.601906i 0.205592π-0.205592\pi
0.798567 + 0.601906i 0.205592π0.205592\pi
200200 0 0
201201 32.3368 2.28086
202202 0 0
203203 −0.903212 −0.0633930
204204 0 0
205205 −7.67307 −0.535911
206206 0 0
207207 28.9447 2.01180
208208 0 0
209209 6.06022 0.419194
210210 0 0
211211 −3.33185 −0.229374 −0.114687 0.993402i 0.536587π-0.536587\pi
−0.114687 + 0.993402i 0.536587π0.536587\pi
212212 0 0
213213 20.8573 1.42912
214214 0 0
215215 −1.09679 −0.0748003
216216 0 0
217217 −1.49823 −0.101707
218218 0 0
219219 −34.7052 −2.34516
220220 0 0
221221 −2.19358 −0.147556
222222 0 0
223223 −13.8938 −0.930401 −0.465200 0.885205i 0.654018π-0.654018\pi
−0.465200 + 0.885205i 0.654018π0.654018\pi
224224 0 0
225225 5.42864 0.361909
226226 0 0
227227 14.4558 0.959468 0.479734 0.877414i 0.340733π-0.340733\pi
0.479734 + 0.877414i 0.340733π0.340733\pi
228228 0 0
229229 15.3274 1.01286 0.506432 0.862280i 0.330964π-0.330964\pi
0.506432 + 0.862280i 0.330964π0.330964\pi
230230 0 0
231231 14.4889 0.953297
232232 0 0
233233 −11.7146 −0.767446 −0.383723 0.923448i 0.625358π-0.625358\pi
−0.383723 + 0.923448i 0.625358π0.625358\pi
234234 0 0
235235 −1.65878 −0.108207
236236 0 0
237237 44.5116 2.89134
238238 0 0
239239 −2.53035 −0.163675 −0.0818374 0.996646i 0.526079π-0.526079\pi
−0.0818374 + 0.996646i 0.526079π0.526079\pi
240240 0 0
241241 4.75557 0.306333 0.153167 0.988200i 0.451053π-0.451053\pi
0.153167 + 0.988200i 0.451053π0.451053\pi
242242 0 0
243243 9.00492 0.577666
244244 0 0
245245 −6.18421 −0.395095
246246 0 0
247247 0.682439 0.0434225
248248 0 0
249249 23.0923 1.46342
250250 0 0
251251 −6.76986 −0.427310 −0.213655 0.976909i 0.568537π-0.568537\pi
−0.213655 + 0.976909i 0.568537π0.568537\pi
252252 0 0
253253 −29.4608 −1.85218
254254 0 0
255255 −10.2351 −0.640945
256256 0 0
257257 −13.0923 −0.816678 −0.408339 0.912830i 0.633892π-0.633892\pi
−0.408339 + 0.912830i 0.633892π0.633892\pi
258258 0 0
259259 −2.06022 −0.128016
260260 0 0
261261 −5.42864 −0.336024
262262 0 0
263263 −10.1289 −0.624575 −0.312288 0.949988i 0.601095π-0.601095\pi
−0.312288 + 0.949988i 0.601095π0.601095\pi
264264 0 0
265265 −2.42864 −0.149190
266266 0 0
267267 48.3783 2.96070
268268 0 0
269269 −4.91750 −0.299825 −0.149913 0.988699i 0.547899π-0.547899\pi
−0.149913 + 0.988699i 0.547899π0.547899\pi
270270 0 0
271271 24.5763 1.49290 0.746451 0.665440i 0.231756π-0.231756\pi
0.746451 + 0.665440i 0.231756π0.231756\pi
272272 0 0
273273 1.63158 0.0987479
274274 0 0
275275 −5.52543 −0.333196
276276 0 0
277277 −24.7971 −1.48991 −0.744955 0.667114i 0.767529π-0.767529\pi
−0.744955 + 0.667114i 0.767529π0.767529\pi
278278 0 0
279279 −9.00492 −0.539111
280280 0 0
281281 −16.5303 −0.986118 −0.493059 0.869996i 0.664121π-0.664121\pi
−0.493059 + 0.869996i 0.664121π0.664121\pi
282282 0 0
283283 25.2400 1.50036 0.750181 0.661233i 0.229966π-0.229966\pi
0.750181 + 0.661233i 0.229966π0.229966\pi
284284 0 0
285285 3.18421 0.188616
286286 0 0
287287 −6.93041 −0.409089
288288 0 0
289289 −4.57136 −0.268904
290290 0 0
291291 34.7052 2.03445
292292 0 0
293293 8.63651 0.504550 0.252275 0.967656i 0.418821π-0.418821\pi
0.252275 + 0.967656i 0.418821π0.418821\pi
294294 0 0
295295 9.28592 0.540647
296296 0 0
297297 38.9590 2.26063
298298 0 0
299299 −3.31756 −0.191860
300300 0 0
301301 −0.990632 −0.0570991
302302 0 0
303303 −25.1526 −1.44498
304304 0 0
305305 −10.9906 −0.629322
306306 0 0
307307 14.6365 0.835350 0.417675 0.908597i 0.362845π-0.362845\pi
0.417675 + 0.908597i 0.362845π0.362845\pi
308308 0 0
309309 51.1753 2.91126
310310 0 0
311311 −1.65878 −0.0940608 −0.0470304 0.998893i 0.514976π-0.514976\pi
−0.0470304 + 0.998893i 0.514976π0.514976\pi
312312 0 0
313313 18.3368 1.03646 0.518228 0.855243i 0.326592π-0.326592\pi
0.518228 + 0.855243i 0.326592π0.326592\pi
314314 0 0
315315 4.90321 0.276265
316316 0 0
317317 22.5763 1.26801 0.634005 0.773329i 0.281410π-0.281410\pi
0.634005 + 0.773329i 0.281410π0.281410\pi
318318 0 0
319319 5.52543 0.309365
320320 0 0
321321 −11.4795 −0.640723
322322 0 0
323323 −3.86665 −0.215146
324324 0 0
325325 −0.622216 −0.0345143
326326 0 0
327327 8.17484 0.452070
328328 0 0
329329 −1.49823 −0.0826001
330330 0 0
331331 −35.1066 −1.92964 −0.964818 0.262920i 0.915314π-0.915314\pi
−0.964818 + 0.262920i 0.915314π0.915314\pi
332332 0 0
333333 −12.3827 −0.678568
334334 0 0
335335 −11.1383 −0.608549
336336 0 0
337337 −8.60793 −0.468904 −0.234452 0.972128i 0.575329π-0.575329\pi
−0.234452 + 0.972128i 0.575329π0.575329\pi
338338 0 0
339339 −42.7052 −2.31943
340340 0 0
341341 9.16547 0.496338
342342 0 0
343343 −11.9081 −0.642979
344344 0 0
345345 −15.4795 −0.833388
346346 0 0
347347 −18.6178 −0.999454 −0.499727 0.866183i 0.666566π-0.666566\pi
−0.499727 + 0.866183i 0.666566π0.666566\pi
348348 0 0
349349 −28.1017 −1.50425 −0.752125 0.659020i 0.770971π-0.770971\pi
−0.752125 + 0.659020i 0.770971π0.770971\pi
350350 0 0
351351 4.38715 0.234169
352352 0 0
353353 15.9398 0.848389 0.424194 0.905571i 0.360557π-0.360557\pi
0.424194 + 0.905571i 0.360557π0.360557\pi
354354 0 0
355355 −7.18421 −0.381298
356356 0 0
357357 −9.24443 −0.489267
358358 0 0
359359 21.5669 1.13826 0.569129 0.822248i 0.307280π-0.307280\pi
0.569129 + 0.822248i 0.307280π0.307280\pi
360360 0 0
361361 −17.7971 −0.936687
362362 0 0
363363 −56.7007 −2.97602
364364 0 0
365365 11.9541 0.625704
366366 0 0
367367 −15.3733 −0.802482 −0.401241 0.915973i 0.631421π-0.631421\pi
−0.401241 + 0.915973i 0.631421π0.631421\pi
368368 0 0
369369 −41.6543 −2.16844
370370 0 0
371371 −2.19358 −0.113885
372372 0 0
373373 −29.9081 −1.54858 −0.774292 0.632828i 0.781894π-0.781894\pi
−0.774292 + 0.632828i 0.781894π0.781894\pi
374374 0 0
375375 −2.90321 −0.149921
376376 0 0
377377 0.622216 0.0320457
378378 0 0
379379 −31.1195 −1.59850 −0.799252 0.600996i 0.794771π-0.794771\pi
−0.799252 + 0.600996i 0.794771π0.794771\pi
380380 0 0
381381 6.79706 0.348224
382382 0 0
383383 7.09679 0.362629 0.181314 0.983425i 0.441965π-0.441965\pi
0.181314 + 0.983425i 0.441965π0.441965\pi
384384 0 0
385385 −4.99063 −0.254346
386386 0 0
387387 −5.95407 −0.302662
388388 0 0
389389 33.0005 1.67319 0.836595 0.547821i 0.184543π-0.184543\pi
0.836595 + 0.547821i 0.184543π0.184543\pi
390390 0 0
391391 18.7971 0.950608
392392 0 0
393393 16.4286 0.828715
394394 0 0
395395 −15.3319 −0.771429
396396 0 0
397397 12.2766 0.616142 0.308071 0.951363i 0.400316π-0.400316\pi
0.308071 + 0.951363i 0.400316π0.400316\pi
398398 0 0
399399 2.87601 0.143981
400400 0 0
401401 30.6321 1.52969 0.764846 0.644213i 0.222815π-0.222815\pi
0.764846 + 0.644213i 0.222815π0.222815\pi
402402 0 0
403403 1.03212 0.0514135
404404 0 0
405405 4.18421 0.207915
406406 0 0
407407 12.6035 0.624731
408408 0 0
409409 −29.7462 −1.47085 −0.735427 0.677603i 0.763019π-0.763019\pi
−0.735427 + 0.677603i 0.763019π0.763019\pi
410410 0 0
411411 −27.9496 −1.37865
412412 0 0
413413 8.38715 0.412705
414414 0 0
415415 −7.95407 −0.390450
416416 0 0
417417 −19.3461 −0.947385
418418 0 0
419419 12.3368 0.602691 0.301345 0.953515i 0.402564π-0.402564\pi
0.301345 + 0.953515i 0.402564π0.402564\pi
420420 0 0
421421 −13.0094 −0.634038 −0.317019 0.948419i 0.602682π-0.602682\pi
−0.317019 + 0.948419i 0.602682π0.602682\pi
422422 0 0
423423 −9.00492 −0.437834
424424 0 0
425425 3.52543 0.171008
426426 0 0
427427 −9.92687 −0.480395
428428 0 0
429429 −9.98126 −0.481900
430430 0 0
431431 13.6316 0.656610 0.328305 0.944572i 0.393523π-0.393523\pi
0.328305 + 0.944572i 0.393523π0.393523\pi
432432 0 0
433433 21.8938 1.05215 0.526075 0.850438i 0.323663π-0.323663\pi
0.526075 + 0.850438i 0.323663π0.323663\pi
434434 0 0
435435 2.90321 0.139198
436436 0 0
437437 −5.84791 −0.279744
438438 0 0
439439 13.2573 0.632738 0.316369 0.948636i 0.397536π-0.397536\pi
0.316369 + 0.948636i 0.397536π0.397536\pi
440440 0 0
441441 −33.5718 −1.59866
442442 0 0
443443 −25.2716 −1.20069 −0.600346 0.799741i 0.704970π-0.704970\pi
−0.600346 + 0.799741i 0.704970π0.704970\pi
444444 0 0
445445 −16.6637 −0.789935
446446 0 0
447447 50.0098 2.36538
448448 0 0
449449 21.9496 1.03587 0.517933 0.855421i 0.326702π-0.326702\pi
0.517933 + 0.855421i 0.326702π0.326702\pi
450450 0 0
451451 42.3970 1.99640
452452 0 0
453453 −17.2444 −0.810214
454454 0 0
455455 −0.561993 −0.0263466
456456 0 0
457457 −9.45091 −0.442095 −0.221048 0.975263i 0.570948π-0.570948\pi
−0.221048 + 0.975263i 0.570948π0.570948\pi
458458 0 0
459459 −24.8573 −1.16024
460460 0 0
461461 24.3970 1.13628 0.568141 0.822931i 0.307663π-0.307663\pi
0.568141 + 0.822931i 0.307663π0.307663\pi
462462 0 0
463463 −8.17929 −0.380124 −0.190062 0.981772i 0.560869π-0.560869\pi
−0.190062 + 0.981772i 0.560869π0.560869\pi
464464 0 0
465465 4.81579 0.223327
466466 0 0
467467 −30.0370 −1.38995 −0.694974 0.719035i 0.744584π-0.744584\pi
−0.694974 + 0.719035i 0.744584π0.744584\pi
468468 0 0
469469 −10.0602 −0.464538
470470 0 0
471471 45.1941 2.08243
472472 0 0
473473 6.06022 0.278649
474474 0 0
475475 −1.09679 −0.0503241
476476 0 0
477477 −13.1842 −0.603663
478478 0 0
479479 21.3131 0.973821 0.486911 0.873452i 0.338124π-0.338124\pi
0.486911 + 0.873452i 0.338124π0.338124\pi
480480 0 0
481481 1.41927 0.0647132
482482 0 0
483483 −13.9813 −0.636170
484484 0 0
485485 −11.9541 −0.542806
486486 0 0
487487 2.14764 0.0973190 0.0486595 0.998815i 0.484505π-0.484505\pi
0.0486595 + 0.998815i 0.484505π0.484505\pi
488488 0 0
489489 −30.5303 −1.38063
490490 0 0
491491 −10.1289 −0.457111 −0.228556 0.973531i 0.573400π-0.573400\pi
−0.228556 + 0.973531i 0.573400π0.573400\pi
492492 0 0
493493 −3.52543 −0.158777
494494 0 0
495495 −29.9956 −1.34820
496496 0 0
497497 −6.48886 −0.291065
498498 0 0
499499 24.4701 1.09543 0.547717 0.836664i 0.315497π-0.315497\pi
0.547717 + 0.836664i 0.315497π0.315497\pi
500500 0 0
501501 −36.7239 −1.64070
502502 0 0
503503 37.5669 1.67503 0.837513 0.546417i 0.184009π-0.184009\pi
0.837513 + 0.546417i 0.184009π0.184009\pi
504504 0 0
505505 8.66370 0.385530
506506 0 0
507507 36.6178 1.62625
508508 0 0
509509 19.9398 0.883815 0.441908 0.897061i 0.354302π-0.354302\pi
0.441908 + 0.897061i 0.354302π0.354302\pi
510510 0 0
511511 10.7971 0.477634
512512 0 0
513513 7.73329 0.341433
514514 0 0
515515 −17.6271 −0.776744
516516 0 0
517517 9.16547 0.403097
518518 0 0
519519 −17.8064 −0.781615
520520 0 0
521521 19.5526 0.856616 0.428308 0.903633i 0.359110π-0.359110\pi
0.428308 + 0.903633i 0.359110π0.359110\pi
522522 0 0
523523 9.23999 0.404036 0.202018 0.979382i 0.435250π-0.435250\pi
0.202018 + 0.979382i 0.435250π0.435250\pi
524524 0 0
525525 −2.62222 −0.114443
526526 0 0
527527 −5.84791 −0.254739
528528 0 0
529529 5.42864 0.236028
530530 0 0
531531 50.4099 2.18760
532532 0 0
533533 4.77430 0.206798
534534 0 0
535535 3.95407 0.170949
536536 0 0
537537 −44.2034 −1.90752
538538 0 0
539539 34.1704 1.47182
540540 0 0
541541 6.56199 0.282122 0.141061 0.990001i 0.454949π-0.454949\pi
0.141061 + 0.990001i 0.454949π0.454949\pi
542542 0 0
543543 −11.4380 −0.490852
544544 0 0
545545 −2.81579 −0.120615
546546 0 0
547547 −11.3921 −0.487090 −0.243545 0.969890i 0.578310π-0.578310\pi
−0.243545 + 0.969890i 0.578310π0.578310\pi
548548 0 0
549549 −59.6642 −2.54641
550550 0 0
551551 1.09679 0.0467247
552552 0 0
553553 −13.8479 −0.588873
554554 0 0
555555 6.62222 0.281097
556556 0 0
557557 43.9813 1.86355 0.931773 0.363041i 0.118262π-0.118262\pi
0.931773 + 0.363041i 0.118262π0.118262\pi
558558 0 0
559559 0.682439 0.0288641
560560 0 0
561561 56.5531 2.38767
562562 0 0
563563 30.3323 1.27836 0.639178 0.769059i 0.279275π-0.279275\pi
0.639178 + 0.769059i 0.279275π0.279275\pi
564564 0 0
565565 14.7096 0.618839
566566 0 0
567567 3.77923 0.158713
568568 0 0
569569 −19.3778 −0.812359 −0.406179 0.913793i 0.633139π-0.633139\pi
−0.406179 + 0.913793i 0.633139π0.633139\pi
570570 0 0
571571 3.34614 0.140032 0.0700158 0.997546i 0.477695π-0.477695\pi
0.0700158 + 0.997546i 0.477695π0.477695\pi
572572 0 0
573573 20.5116 0.856885
574574 0 0
575575 5.33185 0.222354
576576 0 0
577577 −31.9956 −1.33199 −0.665996 0.745955i 0.731993π-0.731993\pi
−0.665996 + 0.745955i 0.731993π0.731993\pi
578578 0 0
579579 −5.76494 −0.239583
580580 0 0
581581 −7.18421 −0.298051
582582 0 0
583583 13.4193 0.555769
584584 0 0
585585 −3.37778 −0.139654
586586 0 0
587587 24.5575 1.01360 0.506799 0.862064i 0.330829π-0.330829\pi
0.506799 + 0.862064i 0.330829π0.330829\pi
588588 0 0
589589 1.81933 0.0749642
590590 0 0
591591 47.2543 1.94378
592592 0 0
593593 −16.7971 −0.689772 −0.344886 0.938645i 0.612082π-0.612082\pi
−0.344886 + 0.938645i 0.612082π0.612082\pi
594594 0 0
595595 3.18421 0.130540
596596 0 0
597597 −65.4104 −2.67707
598598 0 0
599599 25.9126 1.05876 0.529380 0.848385i 0.322425π-0.322425\pi
0.529380 + 0.848385i 0.322425π0.322425\pi
600600 0 0
601601 −30.8158 −1.25700 −0.628501 0.777809i 0.716331π-0.716331\pi
−0.628501 + 0.777809i 0.716331π0.716331\pi
602602 0 0
603603 −60.4657 −2.46235
604604 0 0
605605 19.5303 0.794022
606606 0 0
607607 −28.1476 −1.14248 −0.571239 0.820784i 0.693537π-0.693537\pi
−0.571239 + 0.820784i 0.693537π0.693537\pi
608608 0 0
609609 2.62222 0.106258
610610 0 0
611611 1.03212 0.0417551
612612 0 0
613613 37.5496 1.51661 0.758306 0.651898i 0.226027π-0.226027\pi
0.758306 + 0.651898i 0.226027π0.226027\pi
614614 0 0
615615 22.2766 0.898277
616616 0 0
617617 42.8212 1.72392 0.861958 0.506980i 0.169238π-0.169238\pi
0.861958 + 0.506980i 0.169238π0.169238\pi
618618 0 0
619619 −17.5540 −0.705555 −0.352778 0.935707i 0.614763π-0.614763\pi
−0.352778 + 0.935707i 0.614763π0.614763\pi
620620 0 0
621621 −37.5941 −1.50860
622622 0 0
623623 −15.0509 −0.603000
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 −17.5941 −0.702641
628628 0 0
629629 −8.04149 −0.320635
630630 0 0
631631 30.9304 1.23132 0.615660 0.788012i 0.288889π-0.288889\pi
0.615660 + 0.788012i 0.288889π0.288889\pi
632632 0 0
633633 9.67307 0.384470
634634 0 0
635635 −2.34122 −0.0929085
636636 0 0
637637 3.84791 0.152460
638638 0 0
639639 −39.0005 −1.54284
640640 0 0
641641 −37.1842 −1.46869 −0.734344 0.678778i 0.762510π-0.762510\pi
−0.734344 + 0.678778i 0.762510π0.762510\pi
642642 0 0
643643 −42.0054 −1.65653 −0.828266 0.560336i 0.810672π-0.810672\pi
−0.828266 + 0.560336i 0.810672π0.810672\pi
644644 0 0
645645 3.18421 0.125378
646646 0 0
647647 −30.6464 −1.20483 −0.602416 0.798182i 0.705795π-0.705795\pi
−0.602416 + 0.798182i 0.705795π0.705795\pi
648648 0 0
649649 −51.3087 −2.01404
650650 0 0
651651 4.34968 0.170477
652652 0 0
653653 1.85236 0.0724883 0.0362442 0.999343i 0.488461π-0.488461\pi
0.0362442 + 0.999343i 0.488461π0.488461\pi
654654 0 0
655655 −5.65878 −0.221107
656656 0 0
657657 64.8943 2.53177
658658 0 0
659659 −39.1985 −1.52696 −0.763478 0.645833i 0.776510π-0.776510\pi
−0.763478 + 0.645833i 0.776510π0.776510\pi
660660 0 0
661661 −43.6356 −1.69723 −0.848614 0.529012i 0.822562π-0.822562\pi
−0.848614 + 0.529012i 0.822562π0.822562\pi
662662 0 0
663663 6.36842 0.247329
664664 0 0
665665 −0.990632 −0.0384151
666666 0 0
667667 −5.33185 −0.206450
668668 0 0
669669 40.3368 1.55951
670670 0 0
671671 60.7279 2.34438
672672 0 0
673673 −36.8671 −1.42112 −0.710562 0.703635i 0.751559π-0.751559\pi
−0.710562 + 0.703635i 0.751559π0.751559\pi
674674 0 0
675675 −7.05086 −0.271388
676676 0 0
677677 −0.137799 −0.00529604 −0.00264802 0.999996i 0.500843π-0.500843\pi
−0.00264802 + 0.999996i 0.500843π0.500843\pi
678678 0 0
679679 −10.7971 −0.414353
680680 0 0
681681 −41.9684 −1.60823
682682 0 0
683683 −7.61729 −0.291468 −0.145734 0.989324i 0.546554π-0.546554\pi
−0.145734 + 0.989324i 0.546554π0.546554\pi
684684 0 0
685685 9.62714 0.367834
686686 0 0
687687 −44.4987 −1.69773
688688 0 0
689689 1.51114 0.0575698
690690 0 0
691691 19.4795 0.741035 0.370517 0.928826i 0.379180π-0.379180\pi
0.370517 + 0.928826i 0.379180π0.379180\pi
692692 0 0
693693 −27.0923 −1.02915
694694 0 0
695695 6.66370 0.252769
696696 0 0
697697 −27.0509 −1.02462
698698 0 0
699699 34.0098 1.28637
700700 0 0
701701 −37.0005 −1.39749 −0.698744 0.715371i 0.746257π-0.746257\pi
−0.698744 + 0.715371i 0.746257π0.746257\pi
702702 0 0
703703 2.50177 0.0943560
704704 0 0
705705 4.81579 0.181373
706706 0 0
707707 7.82516 0.294295
708708 0 0
709709 44.6133 1.67549 0.837744 0.546063i 0.183874π-0.183874\pi
0.837744 + 0.546063i 0.183874π0.183874\pi
710710 0 0
711711 −83.2311 −3.12141
712712 0 0
713713 −8.84437 −0.331224
714714 0 0
715715 3.43801 0.128574
716716 0 0
717717 7.34614 0.274347
718718 0 0
719719 −31.6543 −1.18051 −0.590254 0.807218i 0.700972π-0.700972\pi
−0.590254 + 0.807218i 0.700972π0.700972\pi
720720 0 0
721721 −15.9210 −0.592931
722722 0 0
723723 −13.8064 −0.513466
724724 0 0
725725 −1.00000 −0.0371391
726726 0 0
727727 −1.65878 −0.0615208 −0.0307604 0.999527i 0.509793π-0.509793\pi
−0.0307604 + 0.999527i 0.509793π0.509793\pi
728728 0 0
729729 −38.6958 −1.43318
730730 0 0
731731 −3.86665 −0.143013
732732 0 0
733733 44.9358 1.65974 0.829871 0.557955i 0.188414π-0.188414\pi
0.829871 + 0.557955i 0.188414π0.188414\pi
734734 0 0
735735 17.9541 0.662246
736736 0 0
737737 61.5437 2.26699
738738 0 0
739739 43.9639 1.61724 0.808619 0.588332i 0.200215π-0.200215\pi
0.808619 + 0.588332i 0.200215π0.200215\pi
740740 0 0
741741 −1.98126 −0.0727836
742742 0 0
743743 7.58565 0.278291 0.139145 0.990272i 0.455565π-0.455565\pi
0.139145 + 0.990272i 0.455565π0.455565\pi
744744 0 0
745745 −17.2257 −0.631101
746746 0 0
747747 −43.1798 −1.57986
748748 0 0
749749 3.57136 0.130495
750750 0 0
751751 −48.5259 −1.77074 −0.885368 0.464891i 0.846093π-0.846093\pi
−0.885368 + 0.464891i 0.846093π0.846093\pi
752752 0 0
753753 19.6543 0.716244
754754 0 0
755755 5.93978 0.216171
756756 0 0
757757 −20.9032 −0.759740 −0.379870 0.925040i 0.624031π-0.624031\pi
−0.379870 + 0.925040i 0.624031π0.624031\pi
758758 0 0
759759 85.5308 3.10457
760760 0 0
761761 −10.0000 −0.362500 −0.181250 0.983437i 0.558014π-0.558014\pi
−0.181250 + 0.983437i 0.558014π0.558014\pi
762762 0 0
763763 −2.54326 −0.0920721
764764 0 0
765765 19.1383 0.691946
766766 0 0
767767 −5.77784 −0.208626
768768 0 0
769769 15.5397 0.560377 0.280188 0.959945i 0.409603π-0.409603\pi
0.280188 + 0.959945i 0.409603π0.409603\pi
770770 0 0
771771 38.0098 1.36889
772772 0 0
773773 38.1891 1.37357 0.686784 0.726862i 0.259022π-0.259022\pi
0.686784 + 0.726862i 0.259022π0.259022\pi
774774 0 0
775775 −1.65878 −0.0595852
776776 0 0
777777 5.98126 0.214577
778778 0 0
779779 8.41573 0.301525
780780 0 0
781781 39.6958 1.42043
782782 0 0
783783 7.05086 0.251977
784784 0 0
785785 −15.5669 −0.555607
786786 0 0
787787 27.9541 0.996455 0.498227 0.867046i 0.333984π-0.333984\pi
0.498227 + 0.867046i 0.333984π0.333984\pi
788788 0 0
789789 29.4064 1.04689
790790 0 0
791791 13.2859 0.472393
792792 0 0
793793 6.83854 0.242844
794794 0 0
795795 7.05086 0.250068
796796 0 0
797797 2.50622 0.0887747 0.0443874 0.999014i 0.485866π-0.485866\pi
0.0443874 + 0.999014i 0.485866π0.485866\pi
798798 0 0
799799 −5.84791 −0.206884
800800 0 0
801801 −90.4612 −3.19629
802802 0 0
803803 −66.0513 −2.33090
804804 0 0
805805 4.81579 0.169734
806806 0 0
807807 14.2766 0.502558
808808 0 0
809809 −44.0928 −1.55022 −0.775110 0.631826i 0.782306π-0.782306\pi
−0.775110 + 0.631826i 0.782306π0.782306\pi
810810 0 0
811811 −29.8894 −1.04956 −0.524779 0.851238i 0.675852π-0.675852\pi
−0.524779 + 0.851238i 0.675852π0.675852\pi
812812 0 0
813813 −71.3502 −2.50236
814814 0 0
815815 10.5161 0.368362
816816 0 0
817817 1.20294 0.0420857
818818 0 0
819819 −3.05086 −0.106606
820820 0 0
821821 −6.65386 −0.232221 −0.116111 0.993236i 0.537043π-0.537043\pi
−0.116111 + 0.993236i 0.537043π0.537043\pi
822822 0 0
823823 36.7926 1.28251 0.641255 0.767328i 0.278414π-0.278414\pi
0.641255 + 0.767328i 0.278414π0.278414\pi
824824 0 0
825825 16.0415 0.558493
826826 0 0
827827 −42.8657 −1.49059 −0.745294 0.666736i 0.767691π-0.767691\pi
−0.745294 + 0.666736i 0.767691π0.767691\pi
828828 0 0
829829 41.5339 1.44253 0.721266 0.692658i 0.243561π-0.243561\pi
0.721266 + 0.692658i 0.243561π0.243561\pi
830830 0 0
831831 71.9911 2.49734
832832 0 0
833833 −21.8020 −0.755394
834834 0 0
835835 12.6494 0.437751
836836 0 0
837837 11.6958 0.404267
838838 0 0
839839 20.5763 0.710372 0.355186 0.934796i 0.384418π-0.384418\pi
0.355186 + 0.934796i 0.384418π0.384418\pi
840840 0 0
841841 1.00000 0.0344828
842842 0 0
843843 47.9911 1.65290
844844 0 0
845845 −12.6128 −0.433895
846846 0 0
847847 17.6400 0.606119
848848 0 0
849849 −73.2770 −2.51486
850850 0 0
851851 −12.1619 −0.416906
852852 0 0
853853 −57.1481 −1.95671 −0.978357 0.206923i 0.933655π-0.933655\pi
−0.978357 + 0.206923i 0.933655π0.933655\pi
854854 0 0
855855 −5.95407 −0.203625
856856 0 0
857857 −10.6035 −0.362208 −0.181104 0.983464i 0.557967π-0.557967\pi
−0.181104 + 0.983464i 0.557967π0.557967\pi
858858 0 0
859859 0.934855 0.0318968 0.0159484 0.999873i 0.494923π-0.494923\pi
0.0159484 + 0.999873i 0.494923π0.494923\pi
860860 0 0
861861 20.1204 0.685703
862862 0 0
863863 18.7096 0.636883 0.318442 0.947942i 0.396840π-0.396840\pi
0.318442 + 0.947942i 0.396840π0.396840\pi
864864 0 0
865865 6.13335 0.208540
866866 0 0
867867 13.2716 0.450728
868868 0 0
869869 84.7150 2.87376
870870 0 0
871871 6.93041 0.234828
872872 0 0
873873 −64.8943 −2.19634
874874 0 0
875875 0.903212 0.0305341
876876 0 0
877877 21.5714 0.728413 0.364207 0.931318i 0.381340π-0.381340\pi
0.364207 + 0.931318i 0.381340π0.381340\pi
878878 0 0
879879 −25.0736 −0.845712
880880 0 0
881881 24.2636 0.817463 0.408731 0.912655i 0.365971π-0.365971\pi
0.408731 + 0.912655i 0.365971π0.365971\pi
882882 0 0
883883 −35.1798 −1.18389 −0.591947 0.805977i 0.701640π-0.701640\pi
−0.591947 + 0.805977i 0.701640π0.701640\pi
884884 0 0
885885 −26.9590 −0.906217
886886 0 0
887887 −46.4242 −1.55877 −0.779386 0.626544i 0.784469π-0.784469\pi
−0.779386 + 0.626544i 0.784469π0.784469\pi
888888 0 0
889889 −2.11462 −0.0709220
890890 0 0
891891 −23.1195 −0.774534
892892 0 0
893893 1.81933 0.0608816
894894 0 0
895895 15.2257 0.508939
896896 0 0
897897 9.63158 0.321589
898898 0 0
899899 1.65878 0.0553234
900900 0 0
901901 −8.56199 −0.285241
902902 0 0
903903 2.87601 0.0957078
904904 0 0
905905 3.93978 0.130963
906906 0 0
907907 6.34122 0.210557 0.105278 0.994443i 0.466427π-0.466427\pi
0.105278 + 0.994443i 0.466427π0.466427\pi
908908 0 0
909909 47.0321 1.55996
910910 0 0
911911 −39.9353 −1.32312 −0.661558 0.749894i 0.730105π-0.730105\pi
−0.661558 + 0.749894i 0.730105π0.730105\pi
912912 0 0
913913 43.9496 1.45452
914914 0 0
915915 31.9081 1.05485
916916 0 0
917917 −5.11108 −0.168783
918918 0 0
919919 0.815792 0.0269105 0.0134552 0.999909i 0.495717π-0.495717\pi
0.0134552 + 0.999909i 0.495717π0.495717\pi
920920 0 0
921921 −42.4929 −1.40019
922922 0 0
923923 4.47013 0.147136
924924 0 0
925925 −2.28100 −0.0749987
926926 0 0
927927 −95.6914 −3.14292
928928 0 0
929929 11.4479 0.375592 0.187796 0.982208i 0.439866π-0.439866\pi
0.187796 + 0.982208i 0.439866π0.439866\pi
930930 0 0
931931 6.78277 0.222296
932932 0 0
933933 4.81579 0.157662
934934 0 0
935935 −19.4795 −0.637048
936936 0 0
937937 14.4286 0.471363 0.235682 0.971830i 0.424268π-0.424268\pi
0.235682 + 0.971830i 0.424268π0.424268\pi
938938 0 0
939939 −53.2355 −1.73728
940940 0 0
941941 −33.8163 −1.10238 −0.551189 0.834380i 0.685826π-0.685826\pi
−0.551189 + 0.834380i 0.685826π0.685826\pi
942942 0 0
943943 −40.9117 −1.33227
944944 0 0
945945 −6.36842 −0.207165
946946 0 0
947947 49.0879 1.59514 0.797571 0.603225i 0.206118π-0.206118\pi
0.797571 + 0.603225i 0.206118π0.206118\pi
948948 0 0
949949 −7.43801 −0.241448
950950 0 0
951951 −65.5437 −2.12540
952952 0 0
953953 32.1847 1.04256 0.521282 0.853384i 0.325454π-0.325454\pi
0.521282 + 0.853384i 0.325454π0.325454\pi
954954 0 0
955955 −7.06515 −0.228623
956956 0 0
957957 −16.0415 −0.518548
958958 0 0
959959 8.69535 0.280787
960960 0 0
961961 −28.2484 −0.911240
962962 0 0
963963 21.4652 0.691707
964964 0 0
965965 1.98571 0.0639223
966966 0 0
967967 −30.1003 −0.967961 −0.483981 0.875079i 0.660809π-0.660809\pi
−0.483981 + 0.875079i 0.660809π0.660809\pi
968968 0 0
969969 11.2257 0.360621
970970 0 0
971971 −61.0593 −1.95949 −0.979743 0.200257i 0.935822π-0.935822\pi
−0.979743 + 0.200257i 0.935822π0.935822\pi
972972 0 0
973973 6.01874 0.192952
974974 0 0
975975 1.80642 0.0578519
976976 0 0
977977 −37.6829 −1.20558 −0.602792 0.797899i 0.705945π-0.705945\pi
−0.602792 + 0.797899i 0.705945π0.705945\pi
978978 0 0
979979 92.0741 2.94270
980980 0 0
981981 −15.2859 −0.488042
982982 0 0
983983 59.0977 1.88493 0.942463 0.334312i 0.108504π-0.108504\pi
0.942463 + 0.334312i 0.108504π0.108504\pi
984984 0 0
985985 −16.2766 −0.518614
986986 0 0
987987 4.34968 0.138452
988988 0 0
989989 −5.84791 −0.185953
990990 0 0
991991 −36.3654 −1.15518 −0.577592 0.816326i 0.696007π-0.696007\pi
−0.577592 + 0.816326i 0.696007π0.696007\pi
992992 0 0
993993 101.922 3.23440
994994 0 0
995995 22.5303 0.714260
996996 0 0
997997 28.3412 0.897575 0.448788 0.893638i 0.351856π-0.351856\pi
0.448788 + 0.893638i 0.351856π0.351856\pi
998998 0 0
999999 16.0830 0.508843
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 1160.2.a.f.1.1 3
4.3 odd 2 2320.2.a.t.1.3 3
5.4 even 2 5800.2.a.s.1.3 3
8.3 odd 2 9280.2.a.bi.1.1 3
8.5 even 2 9280.2.a.bs.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1160.2.a.f.1.1 3 1.1 even 1 trivial
2320.2.a.t.1.3 3 4.3 odd 2
5800.2.a.s.1.3 3 5.4 even 2
9280.2.a.bi.1.1 3 8.3 odd 2
9280.2.a.bs.1.3 3 8.5 even 2