Properties

Label 7569.2.a.bt.1.2
Level 75697569
Weight 22
Character 7569.1
Self dual yes
Analytic conductor 60.43960.439
Analytic rank 11
Dimension 1212
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [7569,2,Mod(1,7569)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7569, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("7569.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 7569=32292 7569 = 3^{2} \cdot 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7569.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,6,0,8,-2,0,-10,0,0,-20,14,0,-16,0,0,-4,22,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 60.438769289960.4387692899
Analytic rank: 11
Dimension: 1212
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x126x11+2x10+38x930x890x7+55x6+90x530x4++1 x^{12} - 6 x^{11} + 2 x^{10} + 38 x^{9} - 30 x^{8} - 90 x^{7} + 55 x^{6} + 90 x^{5} - 30 x^{4} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 87)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 2.907592.90759 of defining polynomial
Character χ\chi == 7569.1

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) == q1.90759q2+1.63890q4+1.71673q51.24174q7+0.688829q83.27481q102.54849q116.09491q13+2.36873q144.59181q16+1.70189q17+0.426606q19+2.81354q20+4.86148q22+5.66024q232.05286q25+11.6266q262.03509q28+1.85090q31+7.38163q323.24652q342.13172q357.56191q370.813789q38+1.18253q406.80500q41+10.4809q434.17672q4410.7974q46+12.0970q475.45809q49+3.91601q509.98896q52+3.20805q534.37506q550.855345q56+3.90939q59+14.5607q613.53077q624.89751q6410.4633q652.00896q67+2.78924q68+4.06646q70+11.3543q71+6.86914q73+14.4250q74+0.699164q76+3.16456q77+5.87993q797.88287q80+12.9812q826.66375q83+2.92168q8519.9932q861.75547q88+3.27600q89+7.56828q91+9.27658q9223.0761q94+0.732364q95+2.49744q97+10.4118q98+O(q100)q-1.90759 q^{2} +1.63890 q^{4} +1.71673 q^{5} -1.24174 q^{7} +0.688829 q^{8} -3.27481 q^{10} -2.54849 q^{11} -6.09491 q^{13} +2.36873 q^{14} -4.59181 q^{16} +1.70189 q^{17} +0.426606 q^{19} +2.81354 q^{20} +4.86148 q^{22} +5.66024 q^{23} -2.05286 q^{25} +11.6266 q^{26} -2.03509 q^{28} +1.85090 q^{31} +7.38163 q^{32} -3.24652 q^{34} -2.13172 q^{35} -7.56191 q^{37} -0.813789 q^{38} +1.18253 q^{40} -6.80500 q^{41} +10.4809 q^{43} -4.17672 q^{44} -10.7974 q^{46} +12.0970 q^{47} -5.45809 q^{49} +3.91601 q^{50} -9.98896 q^{52} +3.20805 q^{53} -4.37506 q^{55} -0.855345 q^{56} +3.90939 q^{59} +14.5607 q^{61} -3.53077 q^{62} -4.89751 q^{64} -10.4633 q^{65} -2.00896 q^{67} +2.78924 q^{68} +4.06646 q^{70} +11.3543 q^{71} +6.86914 q^{73} +14.4250 q^{74} +0.699164 q^{76} +3.16456 q^{77} +5.87993 q^{79} -7.88287 q^{80} +12.9812 q^{82} -6.66375 q^{83} +2.92168 q^{85} -19.9932 q^{86} -1.75547 q^{88} +3.27600 q^{89} +7.56828 q^{91} +9.27658 q^{92} -23.0761 q^{94} +0.732364 q^{95} +2.49744 q^{97} +10.4118 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+6q2+8q42q510q720q10+14q1116q134q16+22q1716q194q20+12q222q232q258q264q284q31+16q32++6q98+O(q100) 12 q + 6 q^{2} + 8 q^{4} - 2 q^{5} - 10 q^{7} - 20 q^{10} + 14 q^{11} - 16 q^{13} - 4 q^{16} + 22 q^{17} - 16 q^{19} - 4 q^{20} + 12 q^{22} - 2 q^{23} - 2 q^{25} - 8 q^{26} - 4 q^{28} - 4 q^{31} + 16 q^{32}+ \cdots + 6 q^{98}+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 −1.90759 −1.34887 −0.674435 0.738334i 0.735613π-0.735613\pi
−0.674435 + 0.738334i 0.735613π0.735613\pi
33 0 0
44 1.63890 0.819451
55 1.71673 0.767743 0.383871 0.923387i 0.374591π-0.374591\pi
0.383871 + 0.923387i 0.374591π0.374591\pi
66 0 0
77 −1.24174 −0.469333 −0.234666 0.972076i 0.575400π-0.575400\pi
−0.234666 + 0.972076i 0.575400π0.575400\pi
88 0.688829 0.243538
99 0 0
1010 −3.27481 −1.03559
1111 −2.54849 −0.768399 −0.384199 0.923250i 0.625522π-0.625522\pi
−0.384199 + 0.923250i 0.625522π0.625522\pi
1212 0 0
1313 −6.09491 −1.69042 −0.845212 0.534431i 0.820526π-0.820526\pi
−0.845212 + 0.534431i 0.820526π0.820526\pi
1414 2.36873 0.633069
1515 0 0
1616 −4.59181 −1.14795
1717 1.70189 0.412770 0.206385 0.978471i 0.433830π-0.433830\pi
0.206385 + 0.978471i 0.433830π0.433830\pi
1818 0 0
1919 0.426606 0.0978700 0.0489350 0.998802i 0.484417π-0.484417\pi
0.0489350 + 0.998802i 0.484417π0.484417\pi
2020 2.81354 0.629127
2121 0 0
2222 4.86148 1.03647
2323 5.66024 1.18024 0.590121 0.807315i 0.299080π-0.299080\pi
0.590121 + 0.807315i 0.299080π0.299080\pi
2424 0 0
2525 −2.05286 −0.410571
2626 11.6266 2.28016
2727 0 0
2828 −2.03509 −0.384595
2929 0 0
3030 0 0
3131 1.85090 0.332432 0.166216 0.986089i 0.446845π-0.446845\pi
0.166216 + 0.986089i 0.446845π0.446845\pi
3232 7.38163 1.30490
3333 0 0
3434 −3.24652 −0.556773
3535 −2.13172 −0.360327
3636 0 0
3737 −7.56191 −1.24317 −0.621585 0.783347i 0.713511π-0.713511\pi
−0.621585 + 0.783347i 0.713511π0.713511\pi
3838 −0.813789 −0.132014
3939 0 0
4040 1.18253 0.186974
4141 −6.80500 −1.06276 −0.531382 0.847133i 0.678327π-0.678327\pi
−0.531382 + 0.847133i 0.678327π0.678327\pi
4242 0 0
4343 10.4809 1.59832 0.799158 0.601120i 0.205279π-0.205279\pi
0.799158 + 0.601120i 0.205279π0.205279\pi
4444 −4.17672 −0.629665
4545 0 0
4646 −10.7974 −1.59199
4747 12.0970 1.76452 0.882262 0.470759i 0.156020π-0.156020\pi
0.882262 + 0.470759i 0.156020π0.156020\pi
4848 0 0
4949 −5.45809 −0.779727
5050 3.91601 0.553807
5151 0 0
5252 −9.98896 −1.38522
5353 3.20805 0.440660 0.220330 0.975425i 0.429287π-0.429287\pi
0.220330 + 0.975425i 0.429287π0.429287\pi
5454 0 0
5555 −4.37506 −0.589933
5656 −0.855345 −0.114300
5757 0 0
5858 0 0
5959 3.90939 0.508959 0.254479 0.967078i 0.418096π-0.418096\pi
0.254479 + 0.967078i 0.418096π0.418096\pi
6060 0 0
6161 14.5607 1.86430 0.932151 0.362069i 0.117930π-0.117930\pi
0.932151 + 0.362069i 0.117930π0.117930\pi
6262 −3.53077 −0.448408
6363 0 0
6464 −4.89751 −0.612188
6565 −10.4633 −1.29781
6666 0 0
6767 −2.00896 −0.245433 −0.122717 0.992442i 0.539161π-0.539161\pi
−0.122717 + 0.992442i 0.539161π0.539161\pi
6868 2.78924 0.338244
6969 0 0
7070 4.06646 0.486034
7171 11.3543 1.34751 0.673755 0.738955i 0.264680π-0.264680\pi
0.673755 + 0.738955i 0.264680π0.264680\pi
7272 0 0
7373 6.86914 0.803972 0.401986 0.915646i 0.368320π-0.368320\pi
0.401986 + 0.915646i 0.368320π0.368320\pi
7474 14.4250 1.67687
7575 0 0
7676 0.699164 0.0801996
7777 3.16456 0.360635
7878 0 0
7979 5.87993 0.661544 0.330772 0.943711i 0.392691π-0.392691\pi
0.330772 + 0.943711i 0.392691π0.392691\pi
8080 −7.88287 −0.881331
8181 0 0
8282 12.9812 1.43353
8383 −6.66375 −0.731441 −0.365721 0.930725i 0.619177π-0.619177\pi
−0.365721 + 0.930725i 0.619177π0.619177\pi
8484 0 0
8585 2.92168 0.316901
8686 −19.9932 −2.15592
8787 0 0
8888 −1.75547 −0.187134
8989 3.27600 0.347255 0.173628 0.984811i 0.444451π-0.444451\pi
0.173628 + 0.984811i 0.444451π0.444451\pi
9090 0 0
9191 7.56828 0.793372
9292 9.27658 0.967150
9393 0 0
9494 −23.0761 −2.38011
9595 0.732364 0.0751390
9696 0 0
9797 2.49744 0.253576 0.126788 0.991930i 0.459533π-0.459533\pi
0.126788 + 0.991930i 0.459533π0.459533\pi
9898 10.4118 1.05175
9999 0 0
100100 −3.36443 −0.336443
101101 17.2626 1.71770 0.858848 0.512230i 0.171181π-0.171181\pi
0.858848 + 0.512230i 0.171181π0.171181\pi
102102 0 0
103103 −17.6813 −1.74219 −0.871097 0.491112i 0.836591π-0.836591\pi
−0.871097 + 0.491112i 0.836591π0.836591\pi
104104 −4.19835 −0.411682
105105 0 0
106106 −6.11965 −0.594393
107107 −4.64732 −0.449273 −0.224637 0.974443i 0.572119π-0.572119\pi
−0.224637 + 0.974443i 0.572119π0.572119\pi
108108 0 0
109109 −0.941184 −0.0901491 −0.0450745 0.998984i 0.514353π-0.514353\pi
−0.0450745 + 0.998984i 0.514353π0.514353\pi
110110 8.34582 0.795742
111111 0 0
112112 5.70182 0.538771
113113 −7.30986 −0.687654 −0.343827 0.939033i 0.611723π-0.611723\pi
−0.343827 + 0.939033i 0.611723π0.611723\pi
114114 0 0
115115 9.71708 0.906123
116116 0 0
117117 0 0
118118 −7.45751 −0.686519
119119 −2.11331 −0.193727
120120 0 0
121121 −4.50520 −0.409563
122122 −27.7758 −2.51470
123123 0 0
124124 3.03345 0.272412
125125 −12.1078 −1.08296
126126 0 0
127127 −7.45690 −0.661693 −0.330846 0.943685i 0.607334π-0.607334\pi
−0.330846 + 0.943685i 0.607334π0.607334\pi
128128 −5.42081 −0.479137
129129 0 0
130130 19.9597 1.75058
131131 −12.2316 −1.06868 −0.534342 0.845268i 0.679441π-0.679441\pi
−0.534342 + 0.845268i 0.679441π0.679441\pi
132132 0 0
133133 −0.529732 −0.0459336
134134 3.83227 0.331057
135135 0 0
136136 1.17231 0.100525
137137 −6.61576 −0.565223 −0.282611 0.959234i 0.591201π-0.591201\pi
−0.282611 + 0.959234i 0.591201π0.591201\pi
138138 0 0
139139 8.30734 0.704620 0.352310 0.935883i 0.385396π-0.385396\pi
0.352310 + 0.935883i 0.385396π0.385396\pi
140140 −3.49368 −0.295270
141141 0 0
142142 −21.6594 −1.81762
143143 15.5328 1.29892
144144 0 0
145145 0 0
146146 −13.1035 −1.08445
147147 0 0
148148 −12.3932 −1.01872
149149 −20.9098 −1.71300 −0.856500 0.516147i 0.827366π-0.827366\pi
−0.856500 + 0.516147i 0.827366π0.827366\pi
150150 0 0
151151 −23.4397 −1.90750 −0.953748 0.300608i 0.902810π-0.902810\pi
−0.953748 + 0.300608i 0.902810π0.902810\pi
152152 0.293858 0.0238351
153153 0 0
154154 −6.03668 −0.486450
155155 3.17749 0.255222
156156 0 0
157157 −15.7821 −1.25955 −0.629775 0.776778i 0.716853π-0.716853\pi
−0.629775 + 0.776778i 0.716853π0.716853\pi
158158 −11.2165 −0.892337
159159 0 0
160160 12.6722 1.00183
161161 −7.02854 −0.553927
162162 0 0
163163 −10.0692 −0.788679 −0.394340 0.918965i 0.629027π-0.629027\pi
−0.394340 + 0.918965i 0.629027π0.629027\pi
164164 −11.1527 −0.870882
165165 0 0
166166 12.7117 0.986619
167167 −0.303139 −0.0234576 −0.0117288 0.999931i 0.503733π-0.503733\pi
−0.0117288 + 0.999931i 0.503733π0.503733\pi
168168 0 0
169169 24.1479 1.85753
170170 −5.57338 −0.427458
171171 0 0
172172 17.1771 1.30974
173173 −9.95056 −0.756527 −0.378264 0.925698i 0.623479π-0.623479\pi
−0.378264 + 0.925698i 0.623479π0.623479\pi
174174 0 0
175175 2.54911 0.192695
176176 11.7022 0.882084
177177 0 0
178178 −6.24927 −0.468402
179179 4.67839 0.349679 0.174839 0.984597i 0.444059π-0.444059\pi
0.174839 + 0.984597i 0.444059π0.444059\pi
180180 0 0
181181 −3.54773 −0.263700 −0.131850 0.991270i 0.542092π-0.542092\pi
−0.131850 + 0.991270i 0.542092π0.542092\pi
182182 −14.4372 −1.07016
183183 0 0
184184 3.89894 0.287434
185185 −12.9817 −0.954435
186186 0 0
187187 −4.33726 −0.317172
188188 19.8257 1.44594
189189 0 0
190190 −1.39705 −0.101353
191191 −4.17518 −0.302106 −0.151053 0.988526i 0.548266π-0.548266\pi
−0.151053 + 0.988526i 0.548266π0.548266\pi
192192 0 0
193193 −13.3631 −0.961894 −0.480947 0.876750i 0.659707π-0.659707\pi
−0.480947 + 0.876750i 0.659707π0.659707\pi
194194 −4.76408 −0.342041
195195 0 0
196196 −8.94526 −0.638947
197197 2.59538 0.184913 0.0924564 0.995717i 0.470528π-0.470528\pi
0.0924564 + 0.995717i 0.470528π0.470528\pi
198198 0 0
199199 −6.19886 −0.439425 −0.219713 0.975565i 0.570512π-0.570512\pi
−0.219713 + 0.975565i 0.570512π0.570512\pi
200200 −1.41407 −0.0999896
201201 0 0
202202 −32.9300 −2.31695
203203 0 0
204204 0 0
205205 −11.6823 −0.815929
206206 33.7287 2.34999
207207 0 0
208208 27.9866 1.94052
209209 −1.08720 −0.0752032
210210 0 0
211211 −20.9045 −1.43912 −0.719562 0.694428i 0.755658π-0.755658\pi
−0.719562 + 0.694428i 0.755658π0.755658\pi
212212 5.25768 0.361099
213213 0 0
214214 8.86518 0.606011
215215 17.9928 1.22710
216216 0 0
217217 −2.29834 −0.156021
218218 1.79539 0.121599
219219 0 0
220220 −7.17028 −0.483421
221221 −10.3729 −0.697756
222222 0 0
223223 22.2000 1.48662 0.743312 0.668945i 0.233254π-0.233254\pi
0.743312 + 0.668945i 0.233254π0.233254\pi
224224 −9.16605 −0.612432
225225 0 0
226226 13.9442 0.927556
227227 −4.91192 −0.326015 −0.163008 0.986625i 0.552120π-0.552120\pi
−0.163008 + 0.986625i 0.552120π0.552120\pi
228228 0 0
229229 21.6047 1.42768 0.713840 0.700309i 0.246955π-0.246955\pi
0.713840 + 0.700309i 0.246955π0.246955\pi
230230 −18.5362 −1.22224
231231 0 0
232232 0 0
233233 −21.5539 −1.41204 −0.706021 0.708191i 0.749512π-0.749512\pi
−0.706021 + 0.708191i 0.749512π0.749512\pi
234234 0 0
235235 20.7672 1.35470
236236 6.40710 0.417066
237237 0 0
238238 4.03132 0.261312
239239 −4.73822 −0.306490 −0.153245 0.988188i 0.548972π-0.548972\pi
−0.153245 + 0.988188i 0.548972π0.548972\pi
240240 0 0
241241 5.81935 0.374857 0.187429 0.982278i 0.439985π-0.439985\pi
0.187429 + 0.982278i 0.439985π0.439985\pi
242242 8.59407 0.552448
243243 0 0
244244 23.8635 1.52770
245245 −9.37003 −0.598629
246246 0 0
247247 −2.60012 −0.165442
248248 1.27496 0.0809598
249249 0 0
250250 23.0967 1.46077
251251 14.0940 0.889606 0.444803 0.895629i 0.353274π-0.353274\pi
0.444803 + 0.895629i 0.353274π0.353274\pi
252252 0 0
253253 −14.4251 −0.906897
254254 14.2247 0.892537
255255 0 0
256256 20.1357 1.25848
257257 8.61361 0.537302 0.268651 0.963238i 0.413422π-0.413422\pi
0.268651 + 0.963238i 0.413422π0.413422\pi
258258 0 0
259259 9.38991 0.583461
260260 −17.1483 −1.06349
261261 0 0
262262 23.3330 1.44152
263263 −7.52746 −0.464163 −0.232082 0.972696i 0.574554π-0.574554\pi
−0.232082 + 0.972696i 0.574554π0.574554\pi
264264 0 0
265265 5.50734 0.338313
266266 1.01051 0.0619585
267267 0 0
268268 −3.29248 −0.201120
269269 −13.3188 −0.812060 −0.406030 0.913860i 0.633087π-0.633087\pi
−0.406030 + 0.913860i 0.633087π0.633087\pi
270270 0 0
271271 16.1608 0.981696 0.490848 0.871245i 0.336687π-0.336687\pi
0.490848 + 0.871245i 0.336687π0.336687\pi
272272 −7.81476 −0.473840
273273 0 0
274274 12.6202 0.762412
275275 5.23168 0.315482
276276 0 0
277277 21.5548 1.29510 0.647552 0.762021i 0.275793π-0.275793\pi
0.647552 + 0.762021i 0.275793π0.275793\pi
278278 −15.8470 −0.950440
279279 0 0
280280 −1.46839 −0.0877533
281281 1.08043 0.0644528 0.0322264 0.999481i 0.489740π-0.489740\pi
0.0322264 + 0.999481i 0.489740π0.489740\pi
282282 0 0
283283 0.280757 0.0166893 0.00834464 0.999965i 0.497344π-0.497344\pi
0.00834464 + 0.999965i 0.497344π0.497344\pi
284284 18.6086 1.10422
285285 0 0
286286 −29.6303 −1.75207
287287 8.45004 0.498790
288288 0 0
289289 −14.1036 −0.829621
290290 0 0
291291 0 0
292292 11.2578 0.658816
293293 −1.28096 −0.0748342 −0.0374171 0.999300i 0.511913π-0.511913\pi
−0.0374171 + 0.999300i 0.511913π0.511913\pi
294294 0 0
295295 6.71134 0.390749
296296 −5.20886 −0.302759
297297 0 0
298298 39.8874 2.31061
299299 −34.4987 −1.99511
300300 0 0
301301 −13.0145 −0.750143
302302 44.7133 2.57296
303303 0 0
304304 −1.95889 −0.112350
305305 24.9967 1.43130
306306 0 0
307307 −9.48636 −0.541415 −0.270708 0.962662i 0.587258π-0.587258\pi
−0.270708 + 0.962662i 0.587258π0.587258\pi
308308 5.18640 0.295522
309309 0 0
310310 −6.06135 −0.344262
311311 −10.7333 −0.608632 −0.304316 0.952571i 0.598428π-0.598428\pi
−0.304316 + 0.952571i 0.598428π0.598428\pi
312312 0 0
313313 6.54110 0.369725 0.184862 0.982764i 0.440816π-0.440816\pi
0.184862 + 0.982764i 0.440816π0.440816\pi
314314 30.1058 1.69897
315315 0 0
316316 9.63663 0.542103
317317 10.5645 0.593359 0.296680 0.954977i 0.404121π-0.404121\pi
0.296680 + 0.954977i 0.404121π0.404121\pi
318318 0 0
319319 0 0
320320 −8.40767 −0.470003
321321 0 0
322322 13.4076 0.747175
323323 0.726037 0.0403978
324324 0 0
325325 12.5120 0.694039
326326 19.2079 1.06383
327327 0 0
328328 −4.68748 −0.258823
329329 −15.0213 −0.828149
330330 0 0
331331 −23.0562 −1.26728 −0.633641 0.773627i 0.718440π-0.718440\pi
−0.633641 + 0.773627i 0.718440π0.718440\pi
332332 −10.9212 −0.599380
333333 0 0
334334 0.578264 0.0316412
335335 −3.44883 −0.188429
336336 0 0
337337 −22.3538 −1.21769 −0.608844 0.793290i 0.708366π-0.708366\pi
−0.608844 + 0.793290i 0.708366π0.708366\pi
338338 −46.0644 −2.50557
339339 0 0
340340 4.78835 0.259685
341341 −4.71701 −0.255440
342342 0 0
343343 15.4697 0.835284
344344 7.21952 0.389251
345345 0 0
346346 18.9816 1.02046
347347 17.5923 0.944404 0.472202 0.881490i 0.343459π-0.343459\pi
0.472202 + 0.881490i 0.343459π0.343459\pi
348348 0 0
349349 −8.06121 −0.431507 −0.215753 0.976448i 0.569221π-0.569221\pi
−0.215753 + 0.976448i 0.569221π0.569221\pi
350350 −4.86266 −0.259920
351351 0 0
352352 −18.8120 −1.00268
353353 16.6752 0.887532 0.443766 0.896143i 0.353642π-0.353642\pi
0.443766 + 0.896143i 0.353642π0.353642\pi
354354 0 0
355355 19.4922 1.03454
356356 5.36904 0.284559
357357 0 0
358358 −8.92444 −0.471671
359359 −13.1953 −0.696419 −0.348210 0.937417i 0.613210π-0.613210\pi
−0.348210 + 0.937417i 0.613210π0.613210\pi
360360 0 0
361361 −18.8180 −0.990421
362362 6.76761 0.355698
363363 0 0
364364 12.4037 0.650129
365365 11.7924 0.617244
366366 0 0
367367 −1.47179 −0.0768269 −0.0384135 0.999262i 0.512230π-0.512230\pi
−0.0384135 + 0.999262i 0.512230π0.512230\pi
368368 −25.9907 −1.35486
369369 0 0
370370 24.7638 1.28741
371371 −3.98356 −0.206816
372372 0 0
373373 17.2512 0.893235 0.446617 0.894725i 0.352629π-0.352629\pi
0.446617 + 0.894725i 0.352629π0.352629\pi
374374 8.27371 0.427824
375375 0 0
376376 8.33274 0.429728
377377 0 0
378378 0 0
379379 −7.50752 −0.385635 −0.192818 0.981235i 0.561763π-0.561763\pi
−0.192818 + 0.981235i 0.561763π0.561763\pi
380380 1.20027 0.0615727
381381 0 0
382382 7.96454 0.407501
383383 −2.39899 −0.122583 −0.0612915 0.998120i 0.519522π-0.519522\pi
−0.0612915 + 0.998120i 0.519522π0.519522\pi
384384 0 0
385385 5.43268 0.276875
386386 25.4912 1.29747
387387 0 0
388388 4.09305 0.207793
389389 26.6147 1.34942 0.674709 0.738084i 0.264269π-0.264269\pi
0.674709 + 0.738084i 0.264269π0.264269\pi
390390 0 0
391391 9.63313 0.487168
392392 −3.75969 −0.189893
393393 0 0
394394 −4.95091 −0.249423
395395 10.0942 0.507896
396396 0 0
397397 −2.71330 −0.136176 −0.0680882 0.997679i 0.521690π-0.521690\pi
−0.0680882 + 0.997679i 0.521690π0.521690\pi
398398 11.8249 0.592728
399399 0 0
400400 9.42631 0.471316
401401 7.43927 0.371499 0.185750 0.982597i 0.440529π-0.440529\pi
0.185750 + 0.982597i 0.440529π0.440529\pi
402402 0 0
403403 −11.2811 −0.561951
404404 28.2917 1.40757
405405 0 0
406406 0 0
407407 19.2714 0.955250
408408 0 0
409409 −2.97967 −0.147335 −0.0736675 0.997283i 0.523470π-0.523470\pi
−0.0736675 + 0.997283i 0.523470π0.523470\pi
410410 22.2851 1.10058
411411 0 0
412412 −28.9780 −1.42764
413413 −4.85443 −0.238871
414414 0 0
415415 −11.4398 −0.561559
416416 −44.9904 −2.20583
417417 0 0
418418 2.07393 0.101439
419419 −35.1174 −1.71560 −0.857798 0.513987i 0.828168π-0.828168\pi
−0.857798 + 0.513987i 0.828168π0.828168\pi
420420 0 0
421421 −29.0918 −1.41785 −0.708923 0.705286i 0.750819π-0.750819\pi
−0.708923 + 0.705286i 0.750819π0.750819\pi
422422 39.8772 1.94119
423423 0 0
424424 2.20980 0.107317
425425 −3.49374 −0.169471
426426 0 0
427427 −18.0805 −0.874979
428428 −7.61649 −0.368157
429429 0 0
430430 −34.3228 −1.65519
431431 −20.9780 −1.01047 −0.505236 0.862981i 0.668595π-0.668595\pi
−0.505236 + 0.862981i 0.668595π0.668595\pi
432432 0 0
433433 −28.3258 −1.36125 −0.680626 0.732631i 0.738292π-0.738292\pi
−0.680626 + 0.732631i 0.738292π0.738292\pi
434434 4.38429 0.210452
435435 0 0
436436 −1.54251 −0.0738727
437437 2.41469 0.115510
438438 0 0
439439 −16.2271 −0.774475 −0.387238 0.921980i 0.626571π-0.626571\pi
−0.387238 + 0.921980i 0.626571π0.626571\pi
440440 −3.01367 −0.143671
441441 0 0
442442 19.7872 0.941182
443443 14.8967 0.707765 0.353882 0.935290i 0.384861π-0.384861\pi
0.353882 + 0.935290i 0.384861π0.384861\pi
444444 0 0
445445 5.62399 0.266603
446446 −42.3486 −2.00526
447447 0 0
448448 6.08142 0.287320
449449 6.90118 0.325687 0.162843 0.986652i 0.447933π-0.447933\pi
0.162843 + 0.986652i 0.447933π0.447933\pi
450450 0 0
451451 17.3425 0.816626
452452 −11.9801 −0.563499
453453 0 0
454454 9.36993 0.439752
455455 12.9927 0.609105
456456 0 0
457457 −36.5848 −1.71136 −0.855682 0.517503i 0.826862π-0.826862\pi
−0.855682 + 0.517503i 0.826862π0.826862\pi
458458 −41.2129 −1.92575
459459 0 0
460460 15.9253 0.742523
461461 −6.43285 −0.299608 −0.149804 0.988716i 0.547864π-0.547864\pi
−0.149804 + 0.988716i 0.547864π0.547864\pi
462462 0 0
463463 −5.95015 −0.276527 −0.138263 0.990395i 0.544152π-0.544152\pi
−0.138263 + 0.990395i 0.544152π0.544152\pi
464464 0 0
465465 0 0
466466 41.1160 1.90466
467467 −24.1307 −1.11663 −0.558317 0.829628i 0.688553π-0.688553\pi
−0.558317 + 0.829628i 0.688553π0.688553\pi
468468 0 0
469469 2.49460 0.115190
470470 −39.6152 −1.82731
471471 0 0
472472 2.69290 0.123951
473473 −26.7104 −1.22814
474474 0 0
475475 −0.875759 −0.0401826
476476 −3.46350 −0.158749
477477 0 0
478478 9.03859 0.413416
479479 −14.2737 −0.652182 −0.326091 0.945338i 0.605732π-0.605732\pi
−0.326091 + 0.945338i 0.605732π0.605732\pi
480480 0 0
481481 46.0891 2.10148
482482 −11.1009 −0.505634
483483 0 0
484484 −7.38357 −0.335617
485485 4.28741 0.194681
486486 0 0
487487 1.92761 0.0873482 0.0436741 0.999046i 0.486094π-0.486094\pi
0.0436741 + 0.999046i 0.486094π0.486094\pi
488488 10.0298 0.454028
489489 0 0
490490 17.8742 0.807473
491491 10.5430 0.475798 0.237899 0.971290i 0.423541π-0.423541\pi
0.237899 + 0.971290i 0.423541π0.423541\pi
492492 0 0
493493 0 0
494494 4.95997 0.223160
495495 0 0
496496 −8.49899 −0.381616
497497 −14.0991 −0.632431
498498 0 0
499499 −15.5558 −0.696373 −0.348186 0.937425i 0.613202π-0.613202\pi
−0.348186 + 0.937425i 0.613202π0.613202\pi
500500 −19.8435 −0.887429
501501 0 0
502502 −26.8856 −1.19996
503503 37.7207 1.68188 0.840941 0.541127i 0.182002π-0.182002\pi
0.840941 + 0.541127i 0.182002π0.182002\pi
504504 0 0
505505 29.6352 1.31875
506506 27.5171 1.22329
507507 0 0
508508 −12.2211 −0.542224
509509 −2.04844 −0.0907953 −0.0453977 0.998969i 0.514455π-0.514455\pi
−0.0453977 + 0.998969i 0.514455π0.514455\pi
510510 0 0
511511 −8.52968 −0.377331
512512 −27.5691 −1.21839
513513 0 0
514514 −16.4312 −0.724751
515515 −30.3540 −1.33756
516516 0 0
517517 −30.8290 −1.35586
518518 −17.9121 −0.787013
519519 0 0
520520 −7.20741 −0.316066
521521 −14.7934 −0.648109 −0.324055 0.946038i 0.605046π-0.605046\pi
−0.324055 + 0.946038i 0.605046π0.605046\pi
522522 0 0
523523 −39.6013 −1.73164 −0.865821 0.500354i 0.833203π-0.833203\pi
−0.865821 + 0.500354i 0.833203π0.833203\pi
524524 −20.0465 −0.875734
525525 0 0
526526 14.3593 0.626096
527527 3.15004 0.137218
528528 0 0
529529 9.03835 0.392972
530530 −10.5058 −0.456341
531531 0 0
532532 −0.868179 −0.0376403
533533 41.4759 1.79652
534534 0 0
535535 −7.97817 −0.344926
536536 −1.38383 −0.0597722
537537 0 0
538538 25.4068 1.09536
539539 13.9099 0.599141
540540 0 0
541541 16.1188 0.693003 0.346501 0.938049i 0.387370π-0.387370\pi
0.346501 + 0.938049i 0.387370π0.387370\pi
542542 −30.8281 −1.32418
543543 0 0
544544 12.5627 0.538623
545545 −1.61575 −0.0692113
546546 0 0
547547 0.445342 0.0190414 0.00952072 0.999955i 0.496969π-0.496969\pi
0.00952072 + 0.999955i 0.496969π0.496969\pi
548548 −10.8426 −0.463172
549549 0 0
550550 −9.97990 −0.425545
551551 0 0
552552 0 0
553553 −7.30134 −0.310484
554554 −41.1178 −1.74693
555555 0 0
556556 13.6149 0.577401
557557 42.0616 1.78221 0.891103 0.453802i 0.149933π-0.149933\pi
0.891103 + 0.453802i 0.149933π0.149933\pi
558558 0 0
559559 −63.8799 −2.70183
560560 9.78846 0.413638
561561 0 0
562562 −2.06101 −0.0869384
563563 −29.9081 −1.26048 −0.630239 0.776401i 0.717043π-0.717043\pi
−0.630239 + 0.776401i 0.717043π0.717043\pi
564564 0 0
565565 −12.5490 −0.527942
566566 −0.535570 −0.0225117
567567 0 0
568568 7.82119 0.328170
569569 −36.4098 −1.52638 −0.763189 0.646175i 0.776368π-0.776368\pi
−0.763189 + 0.646175i 0.776368π0.776368\pi
570570 0 0
571571 −42.0605 −1.76018 −0.880088 0.474810i 0.842517π-0.842517\pi
−0.880088 + 0.474810i 0.842517π0.842517\pi
572572 25.4568 1.06440
573573 0 0
574574 −16.1192 −0.672803
575575 −11.6197 −0.484573
576576 0 0
577577 20.2054 0.841162 0.420581 0.907255i 0.361826π-0.361826\pi
0.420581 + 0.907255i 0.361826π0.361826\pi
578578 26.9038 1.11905
579579 0 0
580580 0 0
581581 8.27463 0.343289
582582 0 0
583583 −8.17569 −0.338602
584584 4.73167 0.195798
585585 0 0
586586 2.44354 0.100942
587587 38.4897 1.58864 0.794319 0.607501i 0.207828π-0.207828\pi
0.794319 + 0.607501i 0.207828π0.207828\pi
588588 0 0
589589 0.789606 0.0325351
590590 −12.8025 −0.527070
591591 0 0
592592 34.7228 1.42710
593593 37.0241 1.52040 0.760198 0.649691i 0.225102π-0.225102\pi
0.760198 + 0.649691i 0.225102π0.225102\pi
594594 0 0
595595 −3.62797 −0.148732
596596 −34.2691 −1.40372
597597 0 0
598598 65.8093 2.69114
599599 −43.8397 −1.79124 −0.895621 0.444818i 0.853268π-0.853268\pi
−0.895621 + 0.444818i 0.853268π0.853268\pi
600600 0 0
601601 31.2193 1.27346 0.636731 0.771086i 0.280286π-0.280286\pi
0.636731 + 0.771086i 0.280286π0.280286\pi
602602 24.8263 1.01185
603603 0 0
604604 −38.4153 −1.56310
605605 −7.73419 −0.314439
606606 0 0
607607 0.493466 0.0200291 0.0100146 0.999950i 0.496812π-0.496812\pi
0.0100146 + 0.999950i 0.496812π0.496812\pi
608608 3.14904 0.127711
609609 0 0
610610 −47.6834 −1.93064
611611 −73.7299 −2.98279
612612 0 0
613613 −16.2384 −0.655864 −0.327932 0.944701i 0.606352π-0.606352\pi
−0.327932 + 0.944701i 0.606352π0.606352\pi
614614 18.0961 0.730299
615615 0 0
616616 2.17984 0.0878282
617617 25.7102 1.03506 0.517528 0.855666i 0.326852π-0.326852\pi
0.517528 + 0.855666i 0.326852π0.326852\pi
618618 0 0
619619 17.6792 0.710585 0.355293 0.934755i 0.384381π-0.384381\pi
0.355293 + 0.934755i 0.384381π0.384381\pi
620620 5.20759 0.209142
621621 0 0
622622 20.4748 0.820965
623623 −4.06794 −0.162978
624624 0 0
625625 −10.5215 −0.420860
626626 −12.4777 −0.498711
627627 0 0
628628 −25.8653 −1.03214
629629 −12.8696 −0.513143
630630 0 0
631631 −24.9109 −0.991688 −0.495844 0.868412i 0.665141π-0.665141\pi
−0.495844 + 0.868412i 0.665141π0.665141\pi
632632 4.05027 0.161111
633633 0 0
634634 −20.1527 −0.800365
635635 −12.8014 −0.508010
636636 0 0
637637 33.2665 1.31807
638638 0 0
639639 0 0
640640 −9.30605 −0.367854
641641 22.3113 0.881242 0.440621 0.897693i 0.354758π-0.354758\pi
0.440621 + 0.897693i 0.354758π0.354758\pi
642642 0 0
643643 −31.8680 −1.25675 −0.628375 0.777911i 0.716280π-0.716280\pi
−0.628375 + 0.777911i 0.716280π0.716280\pi
644644 −11.5191 −0.453915
645645 0 0
646646 −1.38498 −0.0544914
647647 39.4579 1.55125 0.775625 0.631194i 0.217435π-0.217435\pi
0.775625 + 0.631194i 0.217435π0.217435\pi
648648 0 0
649649 −9.96303 −0.391083
650650 −23.8677 −0.936169
651651 0 0
652652 −16.5024 −0.646284
653653 −3.48476 −0.136369 −0.0681845 0.997673i 0.521721π-0.521721\pi
−0.0681845 + 0.997673i 0.521721π0.521721\pi
654654 0 0
655655 −20.9984 −0.820475
656656 31.2473 1.22000
657657 0 0
658658 28.6544 1.11707
659659 22.3709 0.871446 0.435723 0.900081i 0.356493π-0.356493\pi
0.435723 + 0.900081i 0.356493π0.356493\pi
660660 0 0
661661 2.43331 0.0946449 0.0473225 0.998880i 0.484931π-0.484931\pi
0.0473225 + 0.998880i 0.484931π0.484931\pi
662662 43.9817 1.70940
663663 0 0
664664 −4.59018 −0.178134
665665 −0.909405 −0.0352652
666666 0 0
667667 0 0
668668 −0.496814 −0.0192223
669669 0 0
670670 6.57895 0.254167
671671 −37.1077 −1.43253
672672 0 0
673673 29.5001 1.13715 0.568573 0.822633i 0.307496π-0.307496\pi
0.568573 + 0.822633i 0.307496π0.307496\pi
674674 42.6418 1.64250
675675 0 0
676676 39.5761 1.52216
677677 −2.01910 −0.0776003 −0.0388002 0.999247i 0.512354π-0.512354\pi
−0.0388002 + 0.999247i 0.512354π0.512354\pi
678678 0 0
679679 −3.10116 −0.119012
680680 2.01254 0.0771774
681681 0 0
682682 8.99812 0.344556
683683 24.2990 0.929776 0.464888 0.885370i 0.346095π-0.346095\pi
0.464888 + 0.885370i 0.346095π0.346095\pi
684684 0 0
685685 −11.3574 −0.433946
686686 −29.5098 −1.12669
687687 0 0
688688 −48.1261 −1.83479
689689 −19.5528 −0.744902
690690 0 0
691691 −18.4208 −0.700758 −0.350379 0.936608i 0.613947π-0.613947\pi
−0.350379 + 0.936608i 0.613947π0.613947\pi
692692 −16.3080 −0.619937
693693 0 0
694694 −33.5589 −1.27388
695695 14.2614 0.540967
696696 0 0
697697 −11.5814 −0.438677
698698 15.3775 0.582047
699699 0 0
700700 4.17774 0.157904
701701 −22.7157 −0.857961 −0.428981 0.903314i 0.641127π-0.641127\pi
−0.428981 + 0.903314i 0.641127π0.641127\pi
702702 0 0
703703 −3.22595 −0.121669
704704 12.4812 0.470405
705705 0 0
706706 −31.8095 −1.19716
707707 −21.4357 −0.806171
708708 0 0
709709 41.0465 1.54153 0.770767 0.637117i 0.219873π-0.219873\pi
0.770767 + 0.637117i 0.219873π0.219873\pi
710710 −37.1832 −1.39546
711711 0 0
712712 2.25660 0.0845698
713713 10.4766 0.392350
714714 0 0
715715 26.6656 0.997236
716716 7.66741 0.286545
717717 0 0
718718 25.1712 0.939379
719719 9.71121 0.362167 0.181084 0.983468i 0.442040π-0.442040\pi
0.181084 + 0.983468i 0.442040π0.442040\pi
720720 0 0
721721 21.9556 0.817669
722722 35.8971 1.33595
723723 0 0
724724 −5.81437 −0.216089
725725 0 0
726726 0 0
727727 11.2890 0.418687 0.209344 0.977842i 0.432867π-0.432867\pi
0.209344 + 0.977842i 0.432867π0.432867\pi
728728 5.21325 0.193216
729729 0 0
730730 −22.4951 −0.832582
731731 17.8373 0.659737
732732 0 0
733733 8.47930 0.313190 0.156595 0.987663i 0.449948π-0.449948\pi
0.156595 + 0.987663i 0.449948π0.449948\pi
734734 2.80758 0.103630
735735 0 0
736736 41.7818 1.54010
737737 5.11981 0.188590
738738 0 0
739739 −11.4841 −0.422449 −0.211225 0.977438i 0.567745π-0.567745\pi
−0.211225 + 0.977438i 0.567745π0.567745\pi
740740 −21.2757 −0.782112
741741 0 0
742742 7.59900 0.278968
743743 −19.9907 −0.733387 −0.366694 0.930342i 0.619510π-0.619510\pi
−0.366694 + 0.930342i 0.619510π0.619510\pi
744744 0 0
745745 −35.8964 −1.31514
746746 −32.9083 −1.20486
747747 0 0
748748 −7.10834 −0.259907
749749 5.77075 0.210859
750750 0 0
751751 −24.5548 −0.896016 −0.448008 0.894030i 0.647866π-0.647866\pi
−0.448008 + 0.894030i 0.647866π0.647866\pi
752752 −55.5469 −2.02559
753753 0 0
754754 0 0
755755 −40.2395 −1.46447
756756 0 0
757757 −28.1411 −1.02281 −0.511403 0.859341i 0.670874π-0.670874\pi
−0.511403 + 0.859341i 0.670874π0.670874\pi
758758 14.3213 0.520172
759759 0 0
760760 0.504474 0.0182992
761761 −20.9629 −0.759904 −0.379952 0.925006i 0.624059π-0.624059\pi
−0.379952 + 0.925006i 0.624059π0.624059\pi
762762 0 0
763763 1.16870 0.0423099
764764 −6.84271 −0.247561
765765 0 0
766766 4.57630 0.165348
767767 −23.8274 −0.860356
768768 0 0
769769 −14.7809 −0.533014 −0.266507 0.963833i 0.585870π-0.585870\pi
−0.266507 + 0.963833i 0.585870π0.585870\pi
770770 −10.3633 −0.373468
771771 0 0
772772 −21.9007 −0.788224
773773 26.3677 0.948381 0.474190 0.880422i 0.342741π-0.342741\pi
0.474190 + 0.880422i 0.342741π0.342741\pi
774774 0 0
775775 −3.79964 −0.136487
776776 1.72031 0.0617554
777777 0 0
778778 −50.7699 −1.82019
779779 −2.90305 −0.104013
780780 0 0
781781 −28.9364 −1.03542
782782 −18.3761 −0.657127
783783 0 0
784784 25.0625 0.895088
785785 −27.0936 −0.967010
786786 0 0
787787 −2.71416 −0.0967493 −0.0483747 0.998829i 0.515404π-0.515404\pi
−0.0483747 + 0.998829i 0.515404π0.515404\pi
788788 4.25356 0.151527
789789 0 0
790790 −19.2557 −0.685085
791791 9.07694 0.322739
792792 0 0
793793 −88.7460 −3.15146
794794 5.17586 0.183684
795795 0 0
796796 −10.1593 −0.360087
797797 43.3542 1.53568 0.767841 0.640640i 0.221331π-0.221331\pi
0.767841 + 0.640640i 0.221331π0.221331\pi
798798 0 0
799799 20.5877 0.728342
800800 −15.1534 −0.535754
801801 0 0
802802 −14.1911 −0.501104
803803 −17.5059 −0.617771
804804 0 0
805805 −12.0661 −0.425273
806806 21.5197 0.757999
807807 0 0
808808 11.8910 0.418324
809809 10.8368 0.381000 0.190500 0.981687i 0.438989π-0.438989\pi
0.190500 + 0.981687i 0.438989π0.438989\pi
810810 0 0
811811 25.5684 0.897828 0.448914 0.893575i 0.351811π-0.351811\pi
0.448914 + 0.893575i 0.351811π0.351811\pi
812812 0 0
813813 0 0
814814 −36.7620 −1.28851
815815 −17.2860 −0.605503
816816 0 0
817817 4.47119 0.156427
818818 5.68399 0.198736
819819 0 0
820820 −19.1462 −0.668613
821821 32.2144 1.12429 0.562145 0.827039i 0.309976π-0.309976\pi
0.562145 + 0.827039i 0.309976π0.309976\pi
822822 0 0
823823 −28.8996 −1.00738 −0.503689 0.863885i 0.668024π-0.668024\pi
−0.503689 + 0.863885i 0.668024π0.668024\pi
824824 −12.1794 −0.424290
825825 0 0
826826 9.26027 0.322206
827827 −43.1409 −1.50016 −0.750078 0.661350i 0.769984π-0.769984\pi
−0.750078 + 0.661350i 0.769984π0.769984\pi
828828 0 0
829829 −4.73634 −0.164500 −0.0822500 0.996612i 0.526211π-0.526211\pi
−0.0822500 + 0.996612i 0.526211π0.526211\pi
830830 21.8225 0.757470
831831 0 0
832832 29.8499 1.03486
833833 −9.28908 −0.321848
834834 0 0
835835 −0.520405 −0.0180094
836836 −1.78181 −0.0616253
837837 0 0
838838 66.9896 2.31412
839839 −50.5499 −1.74517 −0.872587 0.488458i 0.837560π-0.837560\pi
−0.872587 + 0.488458i 0.837560π0.837560\pi
840840 0 0
841841 0 0
842842 55.4952 1.91249
843843 0 0
844844 −34.2604 −1.17929
845845 41.4554 1.42611
846846 0 0
847847 5.59428 0.192222
848848 −14.7308 −0.505856
849849 0 0
850850 6.66463 0.228595
851851 −42.8022 −1.46724
852852 0 0
853853 −16.6034 −0.568489 −0.284244 0.958752i 0.591743π-0.591743\pi
−0.284244 + 0.958752i 0.591743π0.591743\pi
854854 34.4903 1.18023
855855 0 0
856856 −3.20121 −0.109415
857857 −34.4467 −1.17668 −0.588338 0.808615i 0.700217π-0.700217\pi
−0.588338 + 0.808615i 0.700217π0.700217\pi
858858 0 0
859859 −17.1112 −0.583826 −0.291913 0.956445i 0.594292π-0.594292\pi
−0.291913 + 0.956445i 0.594292π0.594292\pi
860860 29.4884 1.00554
861861 0 0
862862 40.0174 1.36300
863863 −29.3576 −0.999344 −0.499672 0.866215i 0.666546π-0.666546\pi
−0.499672 + 0.866215i 0.666546π0.666546\pi
864864 0 0
865865 −17.0824 −0.580818
866866 54.0340 1.83615
867867 0 0
868868 −3.76675 −0.127852
869869 −14.9850 −0.508330
870870 0 0
871871 12.2444 0.414886
872872 −0.648315 −0.0219547
873873 0 0
874874 −4.60624 −0.155808
875875 15.0347 0.508267
876876 0 0
877877 51.3508 1.73399 0.866997 0.498314i 0.166047π-0.166047\pi
0.866997 + 0.498314i 0.166047π0.166047\pi
878878 30.9546 1.04467
879879 0 0
880880 20.0894 0.677214
881881 −16.0968 −0.542314 −0.271157 0.962535i 0.587406π-0.587406\pi
−0.271157 + 0.962535i 0.587406π0.587406\pi
882882 0 0
883883 −17.4335 −0.586683 −0.293341 0.956008i 0.594767π-0.594767\pi
−0.293341 + 0.956008i 0.594767π0.594767\pi
884884 −17.0001 −0.571777
885885 0 0
886886 −28.4169 −0.954683
887887 40.4547 1.35834 0.679168 0.733983i 0.262341π-0.262341\pi
0.679168 + 0.733983i 0.262341π0.262341\pi
888888 0 0
889889 9.25952 0.310554
890890 −10.7283 −0.359613
891891 0 0
892892 36.3836 1.21821
893893 5.16063 0.172694
894894 0 0
895895 8.03150 0.268463
896896 6.73123 0.224875
897897 0 0
898898 −13.1646 −0.439309
899899 0 0
900900 0 0
901901 5.45976 0.181891
902902 −33.0824 −1.10152
903903 0 0
904904 −5.03525 −0.167470
905905 −6.09047 −0.202454
906906 0 0
907907 38.0589 1.26373 0.631863 0.775080i 0.282291π-0.282291\pi
0.631863 + 0.775080i 0.282291π0.282291\pi
908908 −8.05015 −0.267153
909909 0 0
910910 −24.7847 −0.821604
911911 −1.63752 −0.0542534 −0.0271267 0.999632i 0.508636π-0.508636\pi
−0.0271267 + 0.999632i 0.508636π0.508636\pi
912912 0 0
913913 16.9825 0.562038
914914 69.7887 2.30841
915915 0 0
916916 35.4080 1.16991
917917 15.1885 0.501569
918918 0 0
919919 −7.82279 −0.258050 −0.129025 0.991641i 0.541185π-0.541185\pi
−0.129025 + 0.991641i 0.541185π0.541185\pi
920920 6.69341 0.220675
921921 0 0
922922 12.2712 0.404132
923923 −69.2036 −2.27786
924924 0 0
925925 15.5235 0.510409
926926 11.3504 0.372999
927927 0 0
928928 0 0
929929 −18.3159 −0.600926 −0.300463 0.953794i 0.597141π-0.597141\pi
−0.300463 + 0.953794i 0.597141π0.597141\pi
930930 0 0
931931 −2.32845 −0.0763119
932932 −35.3247 −1.15710
933933 0 0
934934 46.0314 1.50619
935935 −7.44588 −0.243506
936936 0 0
937937 0.405863 0.0132590 0.00662948 0.999978i 0.497890π-0.497890\pi
0.00662948 + 0.999978i 0.497890π0.497890\pi
938938 −4.75867 −0.155376
939939 0 0
940940 34.0353 1.11011
941941 −21.8792 −0.713242 −0.356621 0.934249i 0.616071π-0.616071\pi
−0.356621 + 0.934249i 0.616071π0.616071\pi
942942 0 0
943943 −38.5180 −1.25432
944944 −17.9511 −0.584260
945945 0 0
946946 50.9525 1.65661
947947 36.2764 1.17882 0.589412 0.807833i 0.299359π-0.299359\pi
0.589412 + 0.807833i 0.299359π0.299359\pi
948948 0 0
949949 −41.8668 −1.35905
950950 1.67059 0.0542011
951951 0 0
952952 −1.45571 −0.0471797
953953 −39.6858 −1.28555 −0.642775 0.766055i 0.722217π-0.722217\pi
−0.642775 + 0.766055i 0.722217π0.722217\pi
954954 0 0
955955 −7.16764 −0.231939
956956 −7.76548 −0.251154
957957 0 0
958958 27.2284 0.879708
959959 8.21505 0.265278
960960 0 0
961961 −27.5742 −0.889489
962962 −87.9192 −2.83463
963963 0 0
964964 9.53734 0.307177
965965 −22.9407 −0.738487
966966 0 0
967967 17.3969 0.559447 0.279723 0.960081i 0.409757π-0.409757\pi
0.279723 + 0.960081i 0.409757π0.409757\pi
968968 −3.10331 −0.0997442
969969 0 0
970970 −8.17862 −0.262600
971971 −48.7992 −1.56604 −0.783020 0.621996i 0.786322π-0.786322\pi
−0.783020 + 0.621996i 0.786322π0.786322\pi
972972 0 0
973973 −10.3155 −0.330701
974974 −3.67708 −0.117821
975975 0 0
976976 −66.8598 −2.14013
977977 51.9072 1.66066 0.830329 0.557274i 0.188153π-0.188153\pi
0.830329 + 0.557274i 0.188153π0.188153\pi
978978 0 0
979979 −8.34885 −0.266831
980980 −15.3566 −0.490547
981981 0 0
982982 −20.1117 −0.641790
983983 −16.0820 −0.512936 −0.256468 0.966553i 0.582559π-0.582559\pi
−0.256468 + 0.966553i 0.582559π0.582559\pi
984984 0 0
985985 4.45555 0.141966
986986 0 0
987987 0 0
988988 −4.26134 −0.135571
989989 59.3242 1.88640
990990 0 0
991991 −24.4350 −0.776202 −0.388101 0.921617i 0.626869π-0.626869\pi
−0.388101 + 0.921617i 0.626869π0.626869\pi
992992 13.6627 0.433790
993993 0 0
994994 26.8953 0.853067
995995 −10.6417 −0.337366
996996 0 0
997997 −55.5897 −1.76054 −0.880272 0.474469i 0.842640π-0.842640\pi
−0.880272 + 0.474469i 0.842640π0.842640\pi
998998 29.6741 0.939316
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 7569.2.a.bt.1.2 12
3.2 odd 2 2523.2.a.s.1.11 12
29.3 odd 28 261.2.o.b.154.2 24
29.10 odd 28 261.2.o.b.100.2 24
29.28 even 2 7569.2.a.bn.1.11 12
87.32 even 28 87.2.i.a.67.3 yes 24
87.68 even 28 87.2.i.a.13.3 24
87.86 odd 2 2523.2.a.v.1.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
87.2.i.a.13.3 24 87.68 even 28
87.2.i.a.67.3 yes 24 87.32 even 28
261.2.o.b.100.2 24 29.10 odd 28
261.2.o.b.154.2 24 29.3 odd 28
2523.2.a.s.1.11 12 3.2 odd 2
2523.2.a.v.1.2 12 87.86 odd 2
7569.2.a.bn.1.11 12 29.28 even 2
7569.2.a.bt.1.2 12 1.1 even 1 trivial