Properties

Label 1521.4.a.r.1.1
Level 15211521
Weight 44
Character 1521.1
Self dual yes
Analytic conductor 89.74289.742
Analytic rank 11
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1521,4,Mod(1,1521)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1521.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 1521=32132 1521 = 3^{2} \cdot 13^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1521.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: 89.741905118789.7419051187
Analytic rank: 11
Dimension: 22
Coefficient field: Q(17)\Q(\sqrt{17})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x4 x^{2} - x - 4 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 13)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.56155-1.56155 of defining polynomial
Character χ\chi == 1521.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.56155q25.56155q43.56155q5+27.1771q7+21.1771q8+5.56155q10+15.2614q1142.4384q14+11.4233q1644.5464q1723.9697q19+19.8078q2023.8314q22122.739q23112.315q25151.147q28+219.909q2927.0928q31187.255q32+69.5616q3496.7926q3594.1922q37+37.4299q3875.4233q40160.354q41151.302q4384.8769q44+191.663q46+466.948q47+395.594q49+175.386q50+120.847q5354.3542q55+575.531q56343.400q58439.633q59137.305q61+42.3068q62+201.022q64512.280q67+247.747q68+151.147q70+410.719q71+308.004q73+147.086q74+133.309q76+414.759q77586.462q7940.6847q80+250.401q82+1354.20q83+158.654q85+236.266q86+323.191q88+439.882q89+682.617q92729.164q94+85.3693q95+1511.27q97617.740q98+O(q100)q-1.56155 q^{2} -5.56155 q^{4} -3.56155 q^{5} +27.1771 q^{7} +21.1771 q^{8} +5.56155 q^{10} +15.2614 q^{11} -42.4384 q^{14} +11.4233 q^{16} -44.5464 q^{17} -23.9697 q^{19} +19.8078 q^{20} -23.8314 q^{22} -122.739 q^{23} -112.315 q^{25} -151.147 q^{28} +219.909 q^{29} -27.0928 q^{31} -187.255 q^{32} +69.5616 q^{34} -96.7926 q^{35} -94.1922 q^{37} +37.4299 q^{38} -75.4233 q^{40} -160.354 q^{41} -151.302 q^{43} -84.8769 q^{44} +191.663 q^{46} +466.948 q^{47} +395.594 q^{49} +175.386 q^{50} +120.847 q^{53} -54.3542 q^{55} +575.531 q^{56} -343.400 q^{58} -439.633 q^{59} -137.305 q^{61} +42.3068 q^{62} +201.022 q^{64} -512.280 q^{67} +247.747 q^{68} +151.147 q^{70} +410.719 q^{71} +308.004 q^{73} +147.086 q^{74} +133.309 q^{76} +414.759 q^{77} -586.462 q^{79} -40.6847 q^{80} +250.401 q^{82} +1354.20 q^{83} +158.654 q^{85} +236.266 q^{86} +323.191 q^{88} +439.882 q^{89} +682.617 q^{92} -729.164 q^{94} +85.3693 q^{95} +1511.27 q^{97} -617.740 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q27q43q5+9q73q8+7q10+80q1189q1439q1619q17+84q19+19q20+142q22196q23237q25125q28+44q29+86q31+650q98+O(q100) 2 q + q^{2} - 7 q^{4} - 3 q^{5} + 9 q^{7} - 3 q^{8} + 7 q^{10} + 80 q^{11} - 89 q^{14} - 39 q^{16} - 19 q^{17} + 84 q^{19} + 19 q^{20} + 142 q^{22} - 196 q^{23} - 237 q^{25} - 125 q^{28} + 44 q^{29} + 86 q^{31}+ \cdots - 650 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 −1.56155 −0.552092 −0.276046 0.961144i 0.589024π-0.589024\pi
−0.276046 + 0.961144i 0.589024π0.589024\pi
33 0 0
44 −5.56155 −0.695194
55 −3.56155 −0.318555 −0.159277 0.987234i 0.550916π-0.550916\pi
−0.159277 + 0.987234i 0.550916π0.550916\pi
66 0 0
77 27.1771 1.46742 0.733712 0.679460i 0.237786π-0.237786\pi
0.733712 + 0.679460i 0.237786π0.237786\pi
88 21.1771 0.935904
99 0 0
1010 5.56155 0.175872
1111 15.2614 0.418316 0.209158 0.977882i 0.432928π-0.432928\pi
0.209158 + 0.977882i 0.432928π0.432928\pi
1212 0 0
1313 0 0
1414 −42.4384 −0.810154
1515 0 0
1616 11.4233 0.178489
1717 −44.5464 −0.635535 −0.317767 0.948169i 0.602933π-0.602933\pi
−0.317767 + 0.948169i 0.602933π0.602933\pi
1818 0 0
1919 −23.9697 −0.289422 −0.144711 0.989474i 0.546225π-0.546225\pi
−0.144711 + 0.989474i 0.546225π0.546225\pi
2020 19.8078 0.221458
2121 0 0
2222 −23.8314 −0.230949
2323 −122.739 −1.11273 −0.556365 0.830938i 0.687804π-0.687804\pi
−0.556365 + 0.830938i 0.687804π0.687804\pi
2424 0 0
2525 −112.315 −0.898523
2626 0 0
2727 0 0
2828 −151.147 −1.02014
2929 219.909 1.40814 0.704071 0.710130i 0.251364π-0.251364\pi
0.704071 + 0.710130i 0.251364π0.251364\pi
3030 0 0
3131 −27.0928 −0.156968 −0.0784840 0.996915i 0.525008π-0.525008\pi
−0.0784840 + 0.996915i 0.525008π0.525008\pi
3232 −187.255 −1.03445
3333 0 0
3434 69.5616 0.350874
3535 −96.7926 −0.467455
3636 0 0
3737 −94.1922 −0.418516 −0.209258 0.977860i 0.567105π-0.567105\pi
−0.209258 + 0.977860i 0.567105π0.567105\pi
3838 37.4299 0.159788
3939 0 0
4040 −75.4233 −0.298137
4141 −160.354 −0.610808 −0.305404 0.952223i 0.598791π-0.598791\pi
−0.305404 + 0.952223i 0.598791π0.598791\pi
4242 0 0
4343 −151.302 −0.536589 −0.268295 0.963337i 0.586460π-0.586460\pi
−0.268295 + 0.963337i 0.586460π0.586460\pi
4444 −84.8769 −0.290811
4545 0 0
4646 191.663 0.614329
4747 466.948 1.44918 0.724589 0.689181i 0.242030π-0.242030\pi
0.724589 + 0.689181i 0.242030π0.242030\pi
4848 0 0
4949 395.594 1.15333
5050 175.386 0.496067
5151 0 0
5252 0 0
5353 120.847 0.313199 0.156600 0.987662i 0.449947π-0.449947\pi
0.156600 + 0.987662i 0.449947π0.449947\pi
5454 0 0
5555 −54.3542 −0.133257
5656 575.531 1.37337
5757 0 0
5858 −343.400 −0.777424
5959 −439.633 −0.970090 −0.485045 0.874489i 0.661197π-0.661197\pi
−0.485045 + 0.874489i 0.661197π0.661197\pi
6060 0 0
6161 −137.305 −0.288198 −0.144099 0.989563i 0.546028π-0.546028\pi
−0.144099 + 0.989563i 0.546028π0.546028\pi
6262 42.3068 0.0866609
6363 0 0
6464 201.022 0.392621
6565 0 0
6666 0 0
6767 −512.280 −0.934104 −0.467052 0.884230i 0.654684π-0.654684\pi
−0.467052 + 0.884230i 0.654684π0.654684\pi
6868 247.747 0.441820
6969 0 0
7070 151.147 0.258078
7171 410.719 0.686526 0.343263 0.939239i 0.388468π-0.388468\pi
0.343263 + 0.939239i 0.388468π0.388468\pi
7272 0 0
7373 308.004 0.493823 0.246912 0.969038i 0.420584π-0.420584\pi
0.246912 + 0.969038i 0.420584π0.420584\pi
7474 147.086 0.231060
7575 0 0
7676 133.309 0.201205
7777 414.759 0.613847
7878 0 0
7979 −586.462 −0.835217 −0.417608 0.908627i 0.637132π-0.637132\pi
−0.417608 + 0.908627i 0.637132π0.637132\pi
8080 −40.6847 −0.0568585
8181 0 0
8282 250.401 0.337222
8383 1354.20 1.79088 0.895440 0.445182i 0.146861π-0.146861\pi
0.895440 + 0.445182i 0.146861π0.146861\pi
8484 0 0
8585 158.654 0.202453
8686 236.266 0.296247
8787 0 0
8888 323.191 0.391503
8989 439.882 0.523904 0.261952 0.965081i 0.415634π-0.415634\pi
0.261952 + 0.965081i 0.415634π0.415634\pi
9090 0 0
9191 0 0
9292 682.617 0.773563
9393 0 0
9494 −729.164 −0.800080
9595 85.3693 0.0921969
9696 0 0
9797 1511.27 1.58192 0.790959 0.611869i 0.209582π-0.209582\pi
0.790959 + 0.611869i 0.209582π0.209582\pi
9898 −617.740 −0.636747
9999 0 0
100100 624.648 0.624648
101101 −336.260 −0.331278 −0.165639 0.986186i 0.552969π-0.552969\pi
−0.165639 + 0.986186i 0.552969π0.552969\pi
102102 0 0
103103 322.712 0.308716 0.154358 0.988015i 0.450669π-0.450669\pi
0.154358 + 0.988015i 0.450669π0.450669\pi
104104 0 0
105105 0 0
106106 −188.708 −0.172915
107107 −1434.62 −1.29617 −0.648083 0.761570i 0.724429π-0.724429\pi
−0.648083 + 0.761570i 0.724429π0.724429\pi
108108 0 0
109109 −849.147 −0.746179 −0.373089 0.927795i 0.621702π-0.621702\pi
−0.373089 + 0.927795i 0.621702π0.621702\pi
110110 84.8769 0.0735699
111111 0 0
112112 310.452 0.261919
113113 −1614.53 −1.34409 −0.672044 0.740511i 0.734583π-0.734583\pi
−0.672044 + 0.740511i 0.734583π0.734583\pi
114114 0 0
115115 437.140 0.354465
116116 −1223.04 −0.978931
117117 0 0
118118 686.509 0.535579
119119 −1210.64 −0.932599
120120 0 0
121121 −1098.09 −0.825012
122122 214.409 0.159112
123123 0 0
124124 150.678 0.109123
125125 845.211 0.604784
126126 0 0
127127 865.174 0.604502 0.302251 0.953228i 0.402262π-0.402262\pi
0.302251 + 0.953228i 0.402262π0.402262\pi
128128 1184.13 0.817683
129129 0 0
130130 0 0
131131 281.400 0.187680 0.0938400 0.995587i 0.470086π-0.470086\pi
0.0938400 + 0.995587i 0.470086π0.470086\pi
132132 0 0
133133 −651.426 −0.424705
134134 799.953 0.515712
135135 0 0
136136 −943.363 −0.594799
137137 −2641.43 −1.64725 −0.823624 0.567137i 0.808051π-0.808051\pi
−0.823624 + 0.567137i 0.808051π0.808051\pi
138138 0 0
139139 −1998.64 −1.21958 −0.609791 0.792562i 0.708747π-0.708747\pi
−0.609791 + 0.792562i 0.708747π0.708747\pi
140140 538.317 0.324972
141141 0 0
142142 −641.359 −0.379026
143143 0 0
144144 0 0
145145 −783.218 −0.448570
146146 −480.964 −0.272636
147147 0 0
148148 523.855 0.290950
149149 −1752.98 −0.963824 −0.481912 0.876220i 0.660058π-0.660058\pi
−0.481912 + 0.876220i 0.660058π0.660058\pi
150150 0 0
151151 2794.64 1.50613 0.753063 0.657949i 0.228576π-0.228576\pi
0.753063 + 0.657949i 0.228576π0.228576\pi
152152 −507.608 −0.270871
153153 0 0
154154 −647.669 −0.338900
155155 96.4924 0.0500030
156156 0 0
157157 3244.87 1.64949 0.824743 0.565508i 0.191320π-0.191320\pi
0.824743 + 0.565508i 0.191320π0.191320\pi
158158 915.792 0.461117
159159 0 0
160160 666.918 0.329528
161161 −3335.68 −1.63285
162162 0 0
163163 −3281.47 −1.57684 −0.788418 0.615139i 0.789100π-0.789100\pi
−0.788418 + 0.615139i 0.789100π0.789100\pi
164164 891.818 0.424630
165165 0 0
166166 −2114.66 −0.988731
167167 −3126.52 −1.44873 −0.724364 0.689418i 0.757866π-0.757866\pi
−0.724364 + 0.689418i 0.757866π0.757866\pi
168168 0 0
169169 0 0
170170 −247.747 −0.111773
171171 0 0
172172 841.474 0.373034
173173 −97.5698 −0.0428792 −0.0214396 0.999770i 0.506825π-0.506825\pi
−0.0214396 + 0.999770i 0.506825π0.506825\pi
174174 0 0
175175 −3052.40 −1.31851
176176 174.335 0.0746648
177177 0 0
178178 −686.900 −0.289243
179179 34.7150 0.0144956 0.00724782 0.999974i 0.497693π-0.497693\pi
0.00724782 + 0.999974i 0.497693π0.497693\pi
180180 0 0
181181 −1229.35 −0.504843 −0.252422 0.967617i 0.581227π-0.581227\pi
−0.252422 + 0.967617i 0.581227π0.581227\pi
182182 0 0
183183 0 0
184184 −2599.25 −1.04141
185185 335.471 0.133320
186186 0 0
187187 −679.839 −0.265854
188188 −2596.96 −1.00746
189189 0 0
190190 −133.309 −0.0509012
191191 −4280.80 −1.62172 −0.810858 0.585243i 0.800999π-0.800999\pi
−0.810858 + 0.585243i 0.800999π0.800999\pi
192192 0 0
193193 −472.320 −0.176157 −0.0880786 0.996114i 0.528073π-0.528073\pi
−0.0880786 + 0.996114i 0.528073π0.528073\pi
194194 −2359.93 −0.873365
195195 0 0
196196 −2200.12 −0.801791
197197 −4484.37 −1.62182 −0.810908 0.585173i 0.801026π-0.801026\pi
−0.810908 + 0.585173i 0.801026π0.801026\pi
198198 0 0
199199 −366.240 −0.130463 −0.0652314 0.997870i 0.520779π-0.520779\pi
−0.0652314 + 0.997870i 0.520779π0.520779\pi
200200 −2378.51 −0.840931
201201 0 0
202202 525.087 0.182896
203203 5976.49 2.06634
204204 0 0
205205 571.110 0.194576
206206 −503.932 −0.170440
207207 0 0
208208 0 0
209209 −365.810 −0.121070
210210 0 0
211211 2122.55 0.692524 0.346262 0.938138i 0.387451π-0.387451\pi
0.346262 + 0.938138i 0.387451π0.387451\pi
212212 −672.095 −0.217734
213213 0 0
214214 2240.23 0.715603
215215 538.870 0.170933
216216 0 0
217217 −736.303 −0.230339
218218 1325.99 0.411960
219219 0 0
220220 302.294 0.0926392
221221 0 0
222222 0 0
223223 5926.42 1.77965 0.889826 0.456301i 0.150826π-0.150826\pi
0.889826 + 0.456301i 0.150826π0.150826\pi
224224 −5089.04 −1.51797
225225 0 0
226226 2521.17 0.742060
227227 −895.661 −0.261881 −0.130941 0.991390i 0.541800π-0.541800\pi
−0.130941 + 0.991390i 0.541800π0.541800\pi
228228 0 0
229229 −627.717 −0.181138 −0.0905692 0.995890i 0.528869π-0.528869\pi
−0.0905692 + 0.995890i 0.528869π0.528869\pi
230230 −682.617 −0.195698
231231 0 0
232232 4657.03 1.31788
233233 −2303.72 −0.647734 −0.323867 0.946103i 0.604983π-0.604983\pi
−0.323867 + 0.946103i 0.604983π0.604983\pi
234234 0 0
235235 −1663.06 −0.461643
236236 2445.04 0.674401
237237 0 0
238238 1890.48 0.514881
239239 544.622 0.147400 0.0737001 0.997280i 0.476519π-0.476519\pi
0.0737001 + 0.997280i 0.476519π0.476519\pi
240240 0 0
241241 −5426.10 −1.45031 −0.725157 0.688584i 0.758233π-0.758233\pi
−0.725157 + 0.688584i 0.758233π0.758233\pi
242242 1714.73 0.455483
243243 0 0
244244 763.629 0.200354
245245 −1408.93 −0.367400
246246 0 0
247247 0 0
248248 −573.746 −0.146907
249249 0 0
250250 −1319.84 −0.333897
251251 5221.22 1.31299 0.656494 0.754331i 0.272039π-0.272039\pi
0.656494 + 0.754331i 0.272039π0.272039\pi
252252 0 0
253253 −1873.16 −0.465472
254254 −1351.02 −0.333741
255255 0 0
256256 −3457.26 −0.844057
257257 −658.206 −0.159758 −0.0798789 0.996805i 0.525453π-0.525453\pi
−0.0798789 + 0.996805i 0.525453π0.525453\pi
258258 0 0
259259 −2559.87 −0.614141
260260 0 0
261261 0 0
262262 −439.422 −0.103617
263263 −3246.45 −0.761160 −0.380580 0.924748i 0.624276π-0.624276\pi
−0.380580 + 0.924748i 0.624276π0.624276\pi
264264 0 0
265265 −430.401 −0.0997711
266266 1017.24 0.234477
267267 0 0
268268 2849.07 0.649384
269269 2585.80 0.586093 0.293047 0.956098i 0.405331π-0.405331\pi
0.293047 + 0.956098i 0.405331π0.405331\pi
270270 0 0
271271 −988.933 −0.221673 −0.110836 0.993839i 0.535353π-0.535353\pi
−0.110836 + 0.993839i 0.535353π0.535353\pi
272272 −508.867 −0.113436
273273 0 0
274274 4124.74 0.909433
275275 −1714.09 −0.375866
276276 0 0
277277 8142.40 1.76617 0.883086 0.469211i 0.155462π-0.155462\pi
0.883086 + 0.469211i 0.155462π0.155462\pi
278278 3120.97 0.673322
279279 0 0
280280 −2049.78 −0.437493
281281 1534.21 0.325705 0.162853 0.986650i 0.447930π-0.447930\pi
0.162853 + 0.986650i 0.447930π0.447930\pi
282282 0 0
283283 −6965.00 −1.46299 −0.731495 0.681847i 0.761177π-0.761177\pi
−0.731495 + 0.681847i 0.761177π0.761177\pi
284284 −2284.23 −0.477269
285285 0 0
286286 0 0
287287 −4357.96 −0.896314
288288 0 0
289289 −2928.62 −0.596096
290290 1223.04 0.247652
291291 0 0
292292 −1712.98 −0.343303
293293 640.029 0.127614 0.0638070 0.997962i 0.479676π-0.479676\pi
0.0638070 + 0.997962i 0.479676π0.479676\pi
294294 0 0
295295 1565.77 0.309027
296296 −1994.72 −0.391691
297297 0 0
298298 2737.37 0.532120
299299 0 0
300300 0 0
301301 −4111.95 −0.787404
302302 −4363.99 −0.831520
303303 0 0
304304 −273.813 −0.0516587
305305 489.019 0.0918070
306306 0 0
307307 100.406 0.0186660 0.00933299 0.999956i 0.497029π-0.497029\pi
0.00933299 + 0.999956i 0.497029π0.497029\pi
308308 −2306.71 −0.426743
309309 0 0
310310 −150.678 −0.0276062
311311 3878.92 0.707245 0.353623 0.935388i 0.384950π-0.384950\pi
0.353623 + 0.935388i 0.384950π0.384950\pi
312312 0 0
313313 −3789.39 −0.684311 −0.342155 0.939643i 0.611157π-0.611157\pi
−0.342155 + 0.939643i 0.611157π0.611157\pi
314314 −5067.04 −0.910668
315315 0 0
316316 3261.64 0.580638
317317 4406.81 0.780791 0.390396 0.920647i 0.372338π-0.372338\pi
0.390396 + 0.920647i 0.372338π0.372338\pi
318318 0 0
319319 3356.11 0.589048
320320 −715.950 −0.125071
321321 0 0
322322 5208.84 0.901482
323323 1067.76 0.183938
324324 0 0
325325 0 0
326326 5124.19 0.870559
327327 0 0
328328 −3395.83 −0.571657
329329 12690.3 2.12656
330330 0 0
331331 4131.49 0.686064 0.343032 0.939324i 0.388546π-0.388546\pi
0.343032 + 0.939324i 0.388546π0.388546\pi
332332 −7531.47 −1.24501
333333 0 0
334334 4882.23 0.799831
335335 1824.51 0.297564
336336 0 0
337337 −4560.82 −0.737221 −0.368611 0.929584i 0.620166π-0.620166\pi
−0.368611 + 0.929584i 0.620166π0.620166\pi
338338 0 0
339339 0 0
340340 −882.365 −0.140744
341341 −413.473 −0.0656622
342342 0 0
343343 1429.34 0.225007
344344 −3204.14 −0.502196
345345 0 0
346346 152.360 0.0236733
347347 −10069.4 −1.55779 −0.778896 0.627153i 0.784220π-0.784220\pi
−0.778896 + 0.627153i 0.784220π0.784220\pi
348348 0 0
349349 −5879.32 −0.901757 −0.450878 0.892585i 0.648889π-0.648889\pi
−0.450878 + 0.892585i 0.648889π0.648889\pi
350350 4766.49 0.727942
351351 0 0
352352 −2857.76 −0.432725
353353 −9142.56 −1.37850 −0.689249 0.724525i 0.742059π-0.742059\pi
−0.689249 + 0.724525i 0.742059π0.742059\pi
354354 0 0
355355 −1462.80 −0.218696
356356 −2446.43 −0.364215
357357 0 0
358358 −54.2093 −0.00800293
359359 −2754.32 −0.404924 −0.202462 0.979290i 0.564894π-0.564894\pi
−0.202462 + 0.979290i 0.564894π0.564894\pi
360360 0 0
361361 −6284.45 −0.916235
362362 1919.69 0.278720
363363 0 0
364364 0 0
365365 −1096.97 −0.157310
366366 0 0
367367 3040.19 0.432416 0.216208 0.976347i 0.430631π-0.430631\pi
0.216208 + 0.976347i 0.430631π0.430631\pi
368368 −1402.08 −0.198610
369369 0 0
370370 −523.855 −0.0736052
371371 3284.26 0.459596
372372 0 0
373373 −5384.72 −0.747481 −0.373740 0.927533i 0.621925π-0.621925\pi
−0.373740 + 0.927533i 0.621925π0.621925\pi
374374 1061.60 0.146776
375375 0 0
376376 9888.59 1.35629
377377 0 0
378378 0 0
379379 3424.27 0.464097 0.232049 0.972704i 0.425457π-0.425457\pi
0.232049 + 0.972704i 0.425457π0.425457\pi
380380 −474.786 −0.0640948
381381 0 0
382382 6684.69 0.895336
383383 −382.985 −0.0510956 −0.0255478 0.999674i 0.508133π-0.508133\pi
−0.0255478 + 0.999674i 0.508133π0.508133\pi
384384 0 0
385385 −1477.19 −0.195544
386386 737.553 0.0972551
387387 0 0
388388 −8405.00 −1.09974
389389 −8588.34 −1.11940 −0.559699 0.828696i 0.689083π-0.689083\pi
−0.559699 + 0.828696i 0.689083π0.689083\pi
390390 0 0
391391 5467.56 0.707178
392392 8377.52 1.07941
393393 0 0
394394 7002.57 0.895392
395395 2088.72 0.266063
396396 0 0
397397 7239.16 0.915171 0.457586 0.889166i 0.348714π-0.348714\pi
0.457586 + 0.889166i 0.348714π0.348714\pi
398398 571.904 0.0720275
399399 0 0
400400 −1283.01 −0.160376
401401 4269.62 0.531708 0.265854 0.964013i 0.414346π-0.414346\pi
0.265854 + 0.964013i 0.414346π0.414346\pi
402402 0 0
403403 0 0
404404 1870.12 0.230302
405405 0 0
406406 −9332.60 −1.14081
407407 −1437.50 −0.175072
408408 0 0
409409 −13562.5 −1.63967 −0.819834 0.572602i 0.805934π-0.805934\pi
−0.819834 + 0.572602i 0.805934π0.805934\pi
410410 −891.818 −0.107424
411411 0 0
412412 −1794.78 −0.214618
413413 −11947.9 −1.42353
414414 0 0
415415 −4823.06 −0.570494
416416 0 0
417417 0 0
418418 571.232 0.0668418
419419 14576.9 1.69959 0.849794 0.527114i 0.176726π-0.176726\pi
0.849794 + 0.527114i 0.176726π0.176726\pi
420420 0 0
421421 −15848.4 −1.83469 −0.917343 0.398099i 0.869670π-0.869670\pi
−0.917343 + 0.398099i 0.869670π0.869670\pi
422422 −3314.48 −0.382337
423423 0 0
424424 2559.18 0.293124
425425 5003.24 0.571042
426426 0 0
427427 −3731.55 −0.422909
428428 7978.70 0.901087
429429 0 0
430430 −841.474 −0.0943709
431431 10694.7 1.19524 0.597618 0.801781i 0.296114π-0.296114\pi
0.597618 + 0.801781i 0.296114π0.296114\pi
432432 0 0
433433 −16079.0 −1.78454 −0.892272 0.451498i 0.850890π-0.850890\pi
−0.892272 + 0.451498i 0.850890π0.850890\pi
434434 1149.78 0.127168
435435 0 0
436436 4722.57 0.518739
437437 2942.01 0.322049
438438 0 0
439439 6035.80 0.656203 0.328101 0.944643i 0.393591π-0.393591\pi
0.328101 + 0.944643i 0.393591π0.393591\pi
440440 −1151.06 −0.124715
441441 0 0
442442 0 0
443443 −10201.3 −1.09409 −0.547043 0.837105i 0.684247π-0.684247\pi
−0.547043 + 0.837105i 0.684247π0.684247\pi
444444 0 0
445445 −1566.66 −0.166892
446446 −9254.41 −0.982532
447447 0 0
448448 5463.19 0.576141
449449 −5822.54 −0.611988 −0.305994 0.952033i 0.598989π-0.598989\pi
−0.305994 + 0.952033i 0.598989π0.598989\pi
450450 0 0
451451 −2447.22 −0.255511
452452 8979.27 0.934402
453453 0 0
454454 1398.62 0.144583
455455 0 0
456456 0 0
457457 −4621.60 −0.473062 −0.236531 0.971624i 0.576010π-0.576010\pi
−0.236531 + 0.971624i 0.576010π0.576010\pi
458458 980.213 0.100005
459459 0 0
460460 −2431.18 −0.246422
461461 5127.77 0.518056 0.259028 0.965870i 0.416598π-0.416598\pi
0.259028 + 0.965870i 0.416598π0.416598\pi
462462 0 0
463463 −6486.27 −0.651064 −0.325532 0.945531i 0.605543π-0.605543\pi
−0.325532 + 0.945531i 0.605543π0.605543\pi
464464 2512.09 0.251338
465465 0 0
466466 3597.39 0.357609
467467 −12978.0 −1.28598 −0.642990 0.765875i 0.722306π-0.722306\pi
−0.642990 + 0.765875i 0.722306π0.722306\pi
468468 0 0
469469 −13922.3 −1.37073
470470 2596.96 0.254869
471471 0 0
472472 −9310.13 −0.907910
473473 −2309.08 −0.224464
474474 0 0
475475 2692.16 0.260053
476476 6733.04 0.648337
477477 0 0
478478 −850.456 −0.0813786
479479 −5808.96 −0.554109 −0.277055 0.960854i 0.589358π-0.589358\pi
−0.277055 + 0.960854i 0.589358π0.589358\pi
480480 0 0
481481 0 0
482482 8473.14 0.800707
483483 0 0
484484 6107.09 0.573543
485485 −5382.46 −0.503928
486486 0 0
487487 5387.14 0.501262 0.250631 0.968083i 0.419362π-0.419362\pi
0.250631 + 0.968083i 0.419362π0.419362\pi
488488 −2907.72 −0.269726
489489 0 0
490490 2200.12 0.202839
491491 −15259.1 −1.40251 −0.701255 0.712911i 0.747376π-0.747376\pi
−0.701255 + 0.712911i 0.747376π0.747376\pi
492492 0 0
493493 −9796.16 −0.894922
494494 0 0
495495 0 0
496496 −309.489 −0.0280171
497497 11162.1 1.00742
498498 0 0
499499 −1856.04 −0.166509 −0.0832544 0.996528i 0.526531π-0.526531\pi
−0.0832544 + 0.996528i 0.526531π0.526531\pi
500500 −4700.69 −0.420442
501501 0 0
502502 −8153.20 −0.724891
503503 −1049.46 −0.0930283 −0.0465142 0.998918i 0.514811π-0.514811\pi
−0.0465142 + 0.998918i 0.514811π0.514811\pi
504504 0 0
505505 1197.61 0.105530
506506 2925.04 0.256984
507507 0 0
508508 −4811.71 −0.420246
509509 −551.106 −0.0479909 −0.0239954 0.999712i 0.507639π-0.507639\pi
−0.0239954 + 0.999712i 0.507639π0.507639\pi
510510 0 0
511511 8370.64 0.724649
512512 −4074.36 −0.351686
513513 0 0
514514 1027.82 0.0882010
515515 −1149.36 −0.0983431
516516 0 0
517517 7126.26 0.606214
518518 3997.37 0.339063
519519 0 0
520520 0 0
521521 8995.30 0.756413 0.378206 0.925721i 0.376541π-0.376541\pi
0.378206 + 0.925721i 0.376541π0.376541\pi
522522 0 0
523523 2663.91 0.222724 0.111362 0.993780i 0.464479π-0.464479\pi
0.111362 + 0.993780i 0.464479π0.464479\pi
524524 −1565.02 −0.130474
525525 0 0
526526 5069.51 0.420230
527527 1206.89 0.0997586
528528 0 0
529529 2897.77 0.238167
530530 672.095 0.0550829
531531 0 0
532532 3622.94 0.295253
533533 0 0
534534 0 0
535535 5109.47 0.412900
536536 −10848.6 −0.874232
537537 0 0
538538 −4037.86 −0.323577
539539 6037.30 0.482458
540540 0 0
541541 6169.23 0.490270 0.245135 0.969489i 0.421168π-0.421168\pi
0.245135 + 0.969489i 0.421168π0.421168\pi
542542 1544.27 0.122384
543543 0 0
544544 8341.52 0.657426
545545 3024.28 0.237699
546546 0 0
547547 5140.42 0.401807 0.200904 0.979611i 0.435612π-0.435612\pi
0.200904 + 0.979611i 0.435612π0.435612\pi
548548 14690.5 1.14516
549549 0 0
550550 2676.64 0.207513
551551 −5271.15 −0.407547
552552 0 0
553553 −15938.3 −1.22562
554554 −12714.8 −0.975090
555555 0 0
556556 11115.5 0.847847
557557 2778.56 0.211367 0.105683 0.994400i 0.466297π-0.466297\pi
0.105683 + 0.994400i 0.466297π0.466297\pi
558558 0 0
559559 0 0
560560 −1105.69 −0.0834356
561561 0 0
562562 −2395.75 −0.179819
563563 −4906.14 −0.367263 −0.183632 0.982995i 0.558785π-0.558785\pi
−0.183632 + 0.982995i 0.558785π0.558785\pi
564564 0 0
565565 5750.22 0.428166
566566 10876.2 0.807706
567567 0 0
568568 8697.82 0.642522
569569 9363.15 0.689849 0.344924 0.938631i 0.387905π-0.387905\pi
0.344924 + 0.938631i 0.387905π0.387905\pi
570570 0 0
571571 7199.32 0.527640 0.263820 0.964572i 0.415018π-0.415018\pi
0.263820 + 0.964572i 0.415018π0.415018\pi
572572 0 0
573573 0 0
574574 6805.18 0.494848
575575 13785.4 0.999813
576576 0 0
577577 11449.6 0.826086 0.413043 0.910711i 0.364466π-0.364466\pi
0.413043 + 0.910711i 0.364466π0.364466\pi
578578 4573.19 0.329100
579579 0 0
580580 4355.91 0.311843
581581 36803.3 2.62798
582582 0 0
583583 1844.28 0.131016
584584 6522.62 0.462171
585585 0 0
586586 −999.439 −0.0704547
587587 −5439.39 −0.382466 −0.191233 0.981545i 0.561249π-0.561249\pi
−0.191233 + 0.981545i 0.561249π0.561249\pi
588588 0 0
589589 649.406 0.0454301
590590 −2445.04 −0.170611
591591 0 0
592592 −1075.99 −0.0747006
593593 −28405.8 −1.96709 −0.983547 0.180651i 0.942180π-0.942180\pi
−0.983547 + 0.180651i 0.942180π0.942180\pi
594594 0 0
595595 4311.76 0.297084
596596 9749.30 0.670045
597597 0 0
598598 0 0
599599 10482.3 0.715020 0.357510 0.933909i 0.383626π-0.383626\pi
0.357510 + 0.933909i 0.383626π0.383626\pi
600600 0 0
601601 3199.54 0.217158 0.108579 0.994088i 0.465370π-0.465370\pi
0.108579 + 0.994088i 0.465370π0.465370\pi
602602 6421.02 0.434720
603603 0 0
604604 −15542.6 −1.04705
605605 3910.91 0.262812
606606 0 0
607607 11342.8 0.758468 0.379234 0.925301i 0.376188π-0.376188\pi
0.379234 + 0.925301i 0.376188π0.376188\pi
608608 4488.44 0.299392
609609 0 0
610610 −763.629 −0.0506859
611611 0 0
612612 0 0
613613 −14385.4 −0.947831 −0.473916 0.880570i 0.657160π-0.657160\pi
−0.473916 + 0.880570i 0.657160π0.657160\pi
614614 −156.789 −0.0103053
615615 0 0
616616 8783.39 0.574502
617617 22056.8 1.43918 0.719588 0.694401i 0.244331π-0.244331\pi
0.719588 + 0.694401i 0.244331π0.244331\pi
618618 0 0
619619 −13621.4 −0.884477 −0.442238 0.896898i 0.645815π-0.645815\pi
−0.442238 + 0.896898i 0.645815π0.645815\pi
620620 −536.648 −0.0347618
621621 0 0
622622 −6057.14 −0.390465
623623 11954.7 0.768789
624624 0 0
625625 11029.2 0.705866
626626 5917.34 0.377803
627627 0 0
628628 −18046.5 −1.14671
629629 4195.92 0.265982
630630 0 0
631631 18737.5 1.18214 0.591068 0.806622i 0.298707π-0.298707\pi
0.591068 + 0.806622i 0.298707π0.298707\pi
632632 −12419.6 −0.781683
633633 0 0
634634 −6881.46 −0.431069
635635 −3081.36 −0.192567
636636 0 0
637637 0 0
638638 −5240.75 −0.325209
639639 0 0
640640 −4217.35 −0.260477
641641 −29798.7 −1.83616 −0.918081 0.396394i 0.870261π-0.870261\pi
−0.918081 + 0.396394i 0.870261π0.870261\pi
642642 0 0
643643 22983.5 1.40961 0.704807 0.709399i 0.251034π-0.251034\pi
0.704807 + 0.709399i 0.251034π0.251034\pi
644644 18551.5 1.13515
645645 0 0
646646 −1667.37 −0.101551
647647 24905.4 1.51334 0.756672 0.653794i 0.226824π-0.226824\pi
0.756672 + 0.653794i 0.226824π0.226824\pi
648648 0 0
649649 −6709.39 −0.405804
650650 0 0
651651 0 0
652652 18250.1 1.09621
653653 −10077.8 −0.603946 −0.301973 0.953316i 0.597645π-0.597645\pi
−0.301973 + 0.953316i 0.597645π0.597645\pi
654654 0 0
655655 −1002.22 −0.0597864
656656 −1831.77 −0.109022
657657 0 0
658658 −19816.5 −1.17406
659659 −12334.6 −0.729116 −0.364558 0.931181i 0.618780π-0.618780\pi
−0.364558 + 0.931181i 0.618780π0.618780\pi
660660 0 0
661661 12749.1 0.750202 0.375101 0.926984i 0.377608π-0.377608\pi
0.375101 + 0.926984i 0.377608π0.377608\pi
662662 −6451.54 −0.378771
663663 0 0
664664 28678.1 1.67609
665665 2320.09 0.135292
666666 0 0
667667 −26991.3 −1.56688
668668 17388.3 1.00715
669669 0 0
670670 −2849.07 −0.164283
671671 −2095.46 −0.120558
672672 0 0
673673 −13618.2 −0.780007 −0.390004 0.920813i 0.627526π-0.627526\pi
−0.390004 + 0.920813i 0.627526π0.627526\pi
674674 7121.96 0.407014
675675 0 0
676676 0 0
677677 −9655.67 −0.548150 −0.274075 0.961708i 0.588372π-0.588372\pi
−0.274075 + 0.961708i 0.588372π0.588372\pi
678678 0 0
679679 41071.9 2.32135
680680 3359.84 0.189476
681681 0 0
682682 645.660 0.0362516
683683 16316.8 0.914119 0.457060 0.889436i 0.348903π-0.348903\pi
0.457060 + 0.889436i 0.348903π0.348903\pi
684684 0 0
685685 9407.61 0.524739
686686 −2232.00 −0.124225
687687 0 0
688688 −1728.37 −0.0957753
689689 0 0
690690 0 0
691691 −2350.84 −0.129421 −0.0647106 0.997904i 0.520612π-0.520612\pi
−0.0647106 + 0.997904i 0.520612π0.520612\pi
692692 542.640 0.0298093
693693 0 0
694694 15723.9 0.860045
695695 7118.24 0.388504
696696 0 0
697697 7143.20 0.388189
698698 9180.88 0.497853
699699 0 0
700700 16976.1 0.916623
701701 8076.90 0.435179 0.217589 0.976040i 0.430181π-0.430181\pi
0.217589 + 0.976040i 0.430181π0.430181\pi
702702 0 0
703703 2257.76 0.121128
704704 3067.87 0.164239
705705 0 0
706706 14276.6 0.761058
707707 −9138.55 −0.486125
708708 0 0
709709 13624.9 0.721712 0.360856 0.932622i 0.382485π-0.382485\pi
0.360856 + 0.932622i 0.382485π0.382485\pi
710710 2284.23 0.120741
711711 0 0
712712 9315.43 0.490324
713713 3325.33 0.174663
714714 0 0
715715 0 0
716716 −193.069 −0.0100773
717717 0 0
718718 4301.02 0.223555
719719 −16235.8 −0.842131 −0.421066 0.907030i 0.638344π-0.638344\pi
−0.421066 + 0.907030i 0.638344π0.638344\pi
720720 0 0
721721 8770.37 0.453018
722722 9813.51 0.505846
723723 0 0
724724 6837.08 0.350964
725725 −24699.2 −1.26525
726726 0 0
727727 24181.2 1.23361 0.616803 0.787118i 0.288428π-0.288428\pi
0.616803 + 0.787118i 0.288428π0.288428\pi
728728 0 0
729729 0 0
730730 1712.98 0.0868496
731731 6739.96 0.341021
732732 0 0
733733 −3053.70 −0.153876 −0.0769379 0.997036i 0.524514π-0.524514\pi
−0.0769379 + 0.997036i 0.524514π0.524514\pi
734734 −4747.41 −0.238733
735735 0 0
736736 22983.4 1.15106
737737 −7818.10 −0.390751
738738 0 0
739739 8033.62 0.399894 0.199947 0.979807i 0.435923π-0.435923\pi
0.199947 + 0.979807i 0.435923π0.435923\pi
740740 −1865.74 −0.0926836
741741 0 0
742742 −5128.54 −0.253739
743743 −16139.6 −0.796912 −0.398456 0.917187i 0.630454π-0.630454\pi
−0.398456 + 0.917187i 0.630454π0.630454\pi
744744 0 0
745745 6243.33 0.307031
746746 8408.53 0.412678
747747 0 0
748748 3780.96 0.184820
749749 −38988.7 −1.90202
750750 0 0
751751 −18491.1 −0.898469 −0.449235 0.893414i 0.648303π-0.648303\pi
−0.449235 + 0.893414i 0.648303π0.648303\pi
752752 5334.08 0.258662
753753 0 0
754754 0 0
755755 −9953.28 −0.479784
756756 0 0
757757 160.630 0.00771227 0.00385613 0.999993i 0.498773π-0.498773\pi
0.00385613 + 0.999993i 0.498773π0.498773\pi
758758 −5347.17 −0.256224
759759 0 0
760760 1807.87 0.0862874
761761 26799.1 1.27656 0.638282 0.769803i 0.279645π-0.279645\pi
0.638282 + 0.769803i 0.279645π0.279645\pi
762762 0 0
763763 −23077.3 −1.09496
764764 23807.9 1.12741
765765 0 0
766766 598.052 0.0282095
767767 0 0
768768 0 0
769769 5145.82 0.241304 0.120652 0.992695i 0.461501π-0.461501\pi
0.120652 + 0.992695i 0.461501π0.461501\pi
770770 2306.71 0.107958
771771 0 0
772772 2626.83 0.122463
773773 12810.6 0.596072 0.298036 0.954555i 0.403668π-0.403668\pi
0.298036 + 0.954555i 0.403668π0.403668\pi
774774 0 0
775775 3042.94 0.141039
776776 32004.3 1.48052
777777 0 0
778778 13411.1 0.618011
779779 3843.64 0.176781
780780 0 0
781781 6268.13 0.287185
782782 −8537.89 −0.390428
783783 0 0
784784 4518.98 0.205857
785785 −11556.8 −0.525452
786786 0 0
787787 −28073.0 −1.27153 −0.635764 0.771883i 0.719315π-0.719315\pi
−0.635764 + 0.771883i 0.719315π0.719315\pi
788788 24940.0 1.12748
789789 0 0
790790 −3261.64 −0.146891
791791 −43878.1 −1.97235
792792 0 0
793793 0 0
794794 −11304.3 −0.505259
795795 0 0
796796 2036.87 0.0906970
797797 −30093.1 −1.33746 −0.668729 0.743507i 0.733161π-0.733161\pi
−0.668729 + 0.743507i 0.733161π0.733161\pi
798798 0 0
799799 −20800.8 −0.921003
800800 21031.6 0.929473
801801 0 0
802802 −6667.24 −0.293552
803803 4700.56 0.206574
804804 0 0
805805 11880.2 0.520151
806806 0 0
807807 0 0
808808 −7120.99 −0.310044
809809 24337.1 1.05766 0.528831 0.848727i 0.322631π-0.322631\pi
0.528831 + 0.848727i 0.322631π0.322631\pi
810810 0 0
811811 −19078.7 −0.826071 −0.413035 0.910715i 0.635531π-0.635531\pi
−0.413035 + 0.910715i 0.635531π0.635531\pi
812812 −33238.5 −1.43651
813813 0 0
814814 2244.74 0.0966559
815815 11687.1 0.502309
816816 0 0
817817 3626.66 0.155301
818818 21178.6 0.905248
819819 0 0
820820 −3176.26 −0.135268
821821 2013.92 0.0856104 0.0428052 0.999083i 0.486371π-0.486371\pi
0.0428052 + 0.999083i 0.486371π0.486371\pi
822822 0 0
823823 −7692.10 −0.325795 −0.162898 0.986643i 0.552084π-0.552084\pi
−0.162898 + 0.986643i 0.552084π0.552084\pi
824824 6834.10 0.288929
825825 0 0
826826 18657.3 0.785922
827827 −4762.76 −0.200263 −0.100131 0.994974i 0.531926π-0.531926\pi
−0.100131 + 0.994974i 0.531926π0.531926\pi
828828 0 0
829829 19977.7 0.836976 0.418488 0.908222i 0.362560π-0.362560\pi
0.418488 + 0.908222i 0.362560π0.362560\pi
830830 7531.47 0.314965
831831 0 0
832832 0 0
833833 −17622.3 −0.732984
834834 0 0
835835 11135.3 0.461499
836836 2034.47 0.0841671
837837 0 0
838838 −22762.6 −0.938330
839839 −30615.8 −1.25980 −0.629901 0.776676i 0.716905π-0.716905\pi
−0.629901 + 0.776676i 0.716905π0.716905\pi
840840 0 0
841841 23971.0 0.982861
842842 24748.1 1.01292
843843 0 0
844844 −11804.7 −0.481439
845845 0 0
846846 0 0
847847 −29842.9 −1.21064
848848 1380.47 0.0559026
849849 0 0
850850 −7812.83 −0.315268
851851 11561.0 0.465696
852852 0 0
853853 −5660.88 −0.227227 −0.113614 0.993525i 0.536243π-0.536243\pi
−0.113614 + 0.993525i 0.536243π0.536243\pi
854854 5827.01 0.233485
855855 0 0
856856 −30381.0 −1.21309
857857 −41346.1 −1.64802 −0.824012 0.566572i 0.808269π-0.808269\pi
−0.824012 + 0.566572i 0.808269π0.808269\pi
858858 0 0
859859 −34810.5 −1.38268 −0.691339 0.722530i 0.742979π-0.742979\pi
−0.691339 + 0.722530i 0.742979π0.742979\pi
860860 −2996.96 −0.118832
861861 0 0
862862 −16700.4 −0.659880
863863 −8360.51 −0.329774 −0.164887 0.986312i 0.552726π-0.552726\pi
−0.164887 + 0.986312i 0.552726π0.552726\pi
864864 0 0
865865 347.500 0.0136594
866866 25108.2 0.985233
867867 0 0
868868 4094.99 0.160130
869869 −8950.21 −0.349385
870870 0 0
871871 0 0
872872 −17982.4 −0.698352
873873 0 0
874874 −4594.10 −0.177801
875875 22970.4 0.887475
876876 0 0
877877 40579.3 1.56245 0.781223 0.624251i 0.214596π-0.214596\pi
0.781223 + 0.624251i 0.214596π0.214596\pi
878878 −9425.22 −0.362285
879879 0 0
880880 −620.903 −0.0237848
881881 −10445.2 −0.399442 −0.199721 0.979853i 0.564004π-0.564004\pi
−0.199721 + 0.979853i 0.564004π0.564004\pi
882882 0 0
883883 18227.6 0.694685 0.347343 0.937738i 0.387084π-0.387084\pi
0.347343 + 0.937738i 0.387084π0.387084\pi
884884 0 0
885885 0 0
886886 15929.9 0.604036
887887 23517.7 0.890245 0.445122 0.895470i 0.353160π-0.353160\pi
0.445122 + 0.895470i 0.353160π0.353160\pi
888888 0 0
889889 23512.9 0.887061
890890 2446.43 0.0921399
891891 0 0
892892 −32960.1 −1.23720
893893 −11192.6 −0.419424
894894 0 0
895895 −123.639 −0.00461766
896896 32181.2 1.19989
897897 0 0
898898 9092.21 0.337874
899899 −5957.95 −0.221033
900900 0 0
901901 −5383.28 −0.199049
902902 3821.47 0.141065
903903 0 0
904904 −34191.0 −1.25794
905905 4378.38 0.160820
906906 0 0
907907 −30564.6 −1.11894 −0.559471 0.828850i 0.688996π-0.688996\pi
−0.559471 + 0.828850i 0.688996π0.688996\pi
908908 4981.26 0.182058
909909 0 0
910910 0 0
911911 32766.5 1.19166 0.595831 0.803110i 0.296823π-0.296823\pi
0.595831 + 0.803110i 0.296823π0.296823\pi
912912 0 0
913913 20667.0 0.749154
914914 7216.87 0.261174
915915 0 0
916916 3491.08 0.125926
917917 7647.64 0.275406
918918 0 0
919919 20686.7 0.742538 0.371269 0.928525i 0.378923π-0.378923\pi
0.371269 + 0.928525i 0.378923π0.378923\pi
920920 9257.35 0.331745
921921 0 0
922922 −8007.28 −0.286015
923923 0 0
924924 0 0
925925 10579.2 0.376047
926926 10128.6 0.359447
927927 0 0
928928 −41179.0 −1.45665
929929 45632.2 1.61156 0.805782 0.592212i 0.201745π-0.201745\pi
0.805782 + 0.592212i 0.201745π0.201745\pi
930930 0 0
931931 −9482.26 −0.333801
932932 12812.3 0.450301
933933 0 0
934934 20265.9 0.709979
935935 2421.28 0.0846892
936936 0 0
937937 −17761.4 −0.619253 −0.309626 0.950858i 0.600204π-0.600204\pi
−0.309626 + 0.950858i 0.600204π0.600204\pi
938938 21740.4 0.756768
939939 0 0
940940 9249.19 0.320931
941941 −44888.3 −1.55507 −0.777534 0.628841i 0.783530π-0.783530\pi
−0.777534 + 0.628841i 0.783530π0.783530\pi
942942 0 0
943943 19681.7 0.679664
944944 −5022.05 −0.173150
945945 0 0
946946 3605.74 0.123925
947947 16069.6 0.551415 0.275708 0.961242i 0.411088π-0.411088\pi
0.275708 + 0.961242i 0.411088π0.411088\pi
948948 0 0
949949 0 0
950950 −4203.96 −0.143573
951951 0 0
952952 −25637.8 −0.872823
953953 −3512.03 −0.119377 −0.0596883 0.998217i 0.519011π-0.519011\pi
−0.0596883 + 0.998217i 0.519011π0.519011\pi
954954 0 0
955955 15246.3 0.516605
956956 −3028.94 −0.102472
957957 0 0
958958 9071.00 0.305919
959959 −71786.5 −2.41721
960960 0 0
961961 −29057.0 −0.975361
962962 0 0
963963 0 0
964964 30177.5 1.00825
965965 1682.19 0.0561158
966966 0 0
967967 37011.9 1.23084 0.615421 0.788199i 0.288986π-0.288986\pi
0.615421 + 0.788199i 0.288986π0.288986\pi
968968 −23254.4 −0.772132
969969 0 0
970970 8405.00 0.278215
971971 −19532.3 −0.645542 −0.322771 0.946477i 0.604614π-0.604614\pi
−0.322771 + 0.946477i 0.604614π0.604614\pi
972972 0 0
973973 −54317.1 −1.78965
974974 −8412.30 −0.276743
975975 0 0
976976 −1568.47 −0.0514402
977977 30201.2 0.988970 0.494485 0.869186i 0.335357π-0.335357\pi
0.494485 + 0.869186i 0.335357π0.335357\pi
978978 0 0
979979 6713.21 0.219157
980980 7835.83 0.255415
981981 0 0
982982 23827.8 0.774315
983983 −38774.9 −1.25812 −0.629058 0.777359i 0.716559π-0.716559\pi
−0.629058 + 0.777359i 0.716559π0.716559\pi
984984 0 0
985985 15971.3 0.516638
986986 15297.2 0.494080
987987 0 0
988988 0 0
989989 18570.6 0.597079
990990 0 0
991991 −27728.9 −0.888838 −0.444419 0.895819i 0.646590π-0.646590\pi
−0.444419 + 0.895819i 0.646590π0.646590\pi
992992 5073.25 0.162375
993993 0 0
994994 −17430.3 −0.556192
995995 1304.38 0.0415596
996996 0 0
997997 −48918.2 −1.55392 −0.776958 0.629552i 0.783239π-0.783239\pi
−0.776958 + 0.629552i 0.783239π0.783239\pi
998998 2898.31 0.0919283
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 1521.4.a.r.1.1 2
3.2 odd 2 169.4.a.g.1.2 2
13.12 even 2 117.4.a.d.1.2 2
39.2 even 12 169.4.e.f.147.3 8
39.5 even 4 169.4.b.f.168.2 4
39.8 even 4 169.4.b.f.168.3 4
39.11 even 12 169.4.e.f.147.2 8
39.17 odd 6 169.4.c.g.146.2 4
39.20 even 12 169.4.e.f.23.3 8
39.23 odd 6 169.4.c.g.22.2 4
39.29 odd 6 169.4.c.j.22.1 4
39.32 even 12 169.4.e.f.23.2 8
39.35 odd 6 169.4.c.j.146.1 4
39.38 odd 2 13.4.a.b.1.1 2
52.51 odd 2 1872.4.a.bb.1.2 2
156.155 even 2 208.4.a.h.1.1 2
195.38 even 4 325.4.b.e.274.3 4
195.77 even 4 325.4.b.e.274.2 4
195.194 odd 2 325.4.a.f.1.2 2
273.272 even 2 637.4.a.b.1.1 2
312.77 odd 2 832.4.a.s.1.1 2
312.155 even 2 832.4.a.z.1.2 2
429.428 even 2 1573.4.a.b.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.a.b.1.1 2 39.38 odd 2
117.4.a.d.1.2 2 13.12 even 2
169.4.a.g.1.2 2 3.2 odd 2
169.4.b.f.168.2 4 39.5 even 4
169.4.b.f.168.3 4 39.8 even 4
169.4.c.g.22.2 4 39.23 odd 6
169.4.c.g.146.2 4 39.17 odd 6
169.4.c.j.22.1 4 39.29 odd 6
169.4.c.j.146.1 4 39.35 odd 6
169.4.e.f.23.2 8 39.32 even 12
169.4.e.f.23.3 8 39.20 even 12
169.4.e.f.147.2 8 39.11 even 12
169.4.e.f.147.3 8 39.2 even 12
208.4.a.h.1.1 2 156.155 even 2
325.4.a.f.1.2 2 195.194 odd 2
325.4.b.e.274.2 4 195.77 even 4
325.4.b.e.274.3 4 195.38 even 4
637.4.a.b.1.1 2 273.272 even 2
832.4.a.s.1.1 2 312.77 odd 2
832.4.a.z.1.2 2 312.155 even 2
1521.4.a.r.1.1 2 1.1 even 1 trivial
1573.4.a.b.1.2 2 429.428 even 2
1872.4.a.bb.1.2 2 52.51 odd 2