Properties

Label 128.4.a.e.1.2
Level 128128
Weight 44
Character 128.1
Self dual yes
Analytic conductor 7.5527.552
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] = [128,4,Mod(1,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, 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("128.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 128=27 128 = 2^{7}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 128.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: 7.552244480737.55224448073
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ12)+\Q(\zeta_{12})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x23 x^{2} - 3 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.732051.73205 of defining polynomial
Character χ\chi == 128.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+4.92820q315.8564q517.8564q72.71281q952.9282q118.43078q1378.1436q15+129.138q1750.4974q1988.0000q21+128.708q23+126.426q25146.431q27111.282q29302.851q31260.841q33+283.138q35+182.995q3741.5486q3994.5744q41184.641q43+43.0155q45+296.841q4724.1487q49+636.420q51+102.995q53+839.251q55248.862q57+93.3693q59+338.974q61+48.4411q63+133.682q65489.041q67+634.297q6986.9845q71154.267q73+623.051q75+945.108q77449.415q79648.395q81383.933q832047.67q85548.420q87517.672q89+150.543q911492.51q93+800.708q95+1739.39q97+143.584q99+O(q100)q+4.92820 q^{3} -15.8564 q^{5} -17.8564 q^{7} -2.71281 q^{9} -52.9282 q^{11} -8.43078 q^{13} -78.1436 q^{15} +129.138 q^{17} -50.4974 q^{19} -88.0000 q^{21} +128.708 q^{23} +126.426 q^{25} -146.431 q^{27} -111.282 q^{29} -302.851 q^{31} -260.841 q^{33} +283.138 q^{35} +182.995 q^{37} -41.5486 q^{39} -94.5744 q^{41} -184.641 q^{43} +43.0155 q^{45} +296.841 q^{47} -24.1487 q^{49} +636.420 q^{51} +102.995 q^{53} +839.251 q^{55} -248.862 q^{57} +93.3693 q^{59} +338.974 q^{61} +48.4411 q^{63} +133.682 q^{65} -489.041 q^{67} +634.297 q^{69} -86.9845 q^{71} -154.267 q^{73} +623.051 q^{75} +945.108 q^{77} -449.415 q^{79} -648.395 q^{81} -383.933 q^{83} -2047.67 q^{85} -548.420 q^{87} -517.672 q^{89} +150.543 q^{91} -1492.51 q^{93} +800.708 q^{95} +1739.39 q^{97} +143.584 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q4q34q58q7+50q992q11100q13184q15+92q174q19176q21+8q23+142q25376q2784q29384q31+88q33+400q35+1916q99+O(q100) 2 q - 4 q^{3} - 4 q^{5} - 8 q^{7} + 50 q^{9} - 92 q^{11} - 100 q^{13} - 184 q^{15} + 92 q^{17} - 4 q^{19} - 176 q^{21} + 8 q^{23} + 142 q^{25} - 376 q^{27} - 84 q^{29} - 384 q^{31} + 88 q^{33} + 400 q^{35}+ \cdots - 1916 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 4.92820 0.948433 0.474217 0.880408i 0.342731π-0.342731\pi
0.474217 + 0.880408i 0.342731π0.342731\pi
44 0 0
55 −15.8564 −1.41824 −0.709120 0.705088i 0.750908π-0.750908\pi
−0.709120 + 0.705088i 0.750908π0.750908\pi
66 0 0
77 −17.8564 −0.964155 −0.482078 0.876128i 0.660118π-0.660118\pi
−0.482078 + 0.876128i 0.660118π0.660118\pi
88 0 0
99 −2.71281 −0.100475
1010 0 0
1111 −52.9282 −1.45077 −0.725384 0.688344i 0.758338π-0.758338\pi
−0.725384 + 0.688344i 0.758338π0.758338\pi
1212 0 0
1313 −8.43078 −0.179868 −0.0899338 0.995948i 0.528666π-0.528666\pi
−0.0899338 + 0.995948i 0.528666π0.528666\pi
1414 0 0
1515 −78.1436 −1.34511
1616 0 0
1717 129.138 1.84239 0.921196 0.389098i 0.127213π-0.127213\pi
0.921196 + 0.389098i 0.127213π0.127213\pi
1818 0 0
1919 −50.4974 −0.609732 −0.304866 0.952395i 0.598612π-0.598612\pi
−0.304866 + 0.952395i 0.598612π0.598612\pi
2020 0 0
2121 −88.0000 −0.914437
2222 0 0
2323 128.708 1.16684 0.583422 0.812169i 0.301713π-0.301713\pi
0.583422 + 0.812169i 0.301713π0.301713\pi
2424 0 0
2525 126.426 1.01141
2626 0 0
2727 −146.431 −1.04373
2828 0 0
2929 −111.282 −0.712571 −0.356285 0.934377i 0.615957π-0.615957\pi
−0.356285 + 0.934377i 0.615957π0.615957\pi
3030 0 0
3131 −302.851 −1.75464 −0.877318 0.479910i 0.840669π-0.840669\pi
−0.877318 + 0.479910i 0.840669π0.840669\pi
3232 0 0
3333 −260.841 −1.37596
3434 0 0
3535 283.138 1.36740
3636 0 0
3737 182.995 0.813086 0.406543 0.913632i 0.366734π-0.366734\pi
0.406543 + 0.913632i 0.366734π0.366734\pi
3838 0 0
3939 −41.5486 −0.170592
4040 0 0
4141 −94.5744 −0.360245 −0.180122 0.983644i 0.557649π-0.557649\pi
−0.180122 + 0.983644i 0.557649π0.557649\pi
4242 0 0
4343 −184.641 −0.654825 −0.327413 0.944881i 0.606177π-0.606177\pi
−0.327413 + 0.944881i 0.606177π0.606177\pi
4444 0 0
4545 43.0155 0.142497
4646 0 0
4747 296.841 0.921249 0.460624 0.887595i 0.347625π-0.347625\pi
0.460624 + 0.887595i 0.347625π0.347625\pi
4848 0 0
4949 −24.1487 −0.0704045
5050 0 0
5151 636.420 1.74739
5252 0 0
5353 102.995 0.266933 0.133466 0.991053i 0.457389π-0.457389\pi
0.133466 + 0.991053i 0.457389π0.457389\pi
5454 0 0
5555 839.251 2.05754
5656 0 0
5757 −248.862 −0.578290
5858 0 0
5959 93.3693 0.206028 0.103014 0.994680i 0.467151π-0.467151\pi
0.103014 + 0.994680i 0.467151π0.467151\pi
6060 0 0
6161 338.974 0.711495 0.355748 0.934582i 0.384226π-0.384226\pi
0.355748 + 0.934582i 0.384226π0.384226\pi
6262 0 0
6363 48.4411 0.0968731
6464 0 0
6565 133.682 0.255095
6666 0 0
6767 −489.041 −0.891729 −0.445865 0.895100i 0.647104π-0.647104\pi
−0.445865 + 0.895100i 0.647104π0.647104\pi
6868 0 0
6969 634.297 1.10667
7070 0 0
7171 −86.9845 −0.145397 −0.0726983 0.997354i 0.523161π-0.523161\pi
−0.0726983 + 0.997354i 0.523161π0.523161\pi
7272 0 0
7373 −154.267 −0.247336 −0.123668 0.992324i 0.539466π-0.539466\pi
−0.123668 + 0.992324i 0.539466π0.539466\pi
7474 0 0
7575 623.051 0.959250
7676 0 0
7777 945.108 1.39877
7878 0 0
7979 −449.415 −0.640040 −0.320020 0.947411i 0.603690π-0.603690\pi
−0.320020 + 0.947411i 0.603690π0.603690\pi
8080 0 0
8181 −648.395 −0.889430
8282 0 0
8383 −383.933 −0.507737 −0.253868 0.967239i 0.581703π-0.581703\pi
−0.253868 + 0.967239i 0.581703π0.581703\pi
8484 0 0
8585 −2047.67 −2.61295
8686 0 0
8787 −548.420 −0.675826
8888 0 0
8989 −517.672 −0.616551 −0.308276 0.951297i 0.599752π-0.599752\pi
−0.308276 + 0.951297i 0.599752π0.599752\pi
9090 0 0
9191 150.543 0.173420
9292 0 0
9393 −1492.51 −1.66415
9494 0 0
9595 800.708 0.864746
9696 0 0
9797 1739.39 1.82071 0.910355 0.413829i 0.135809π-0.135809\pi
0.910355 + 0.413829i 0.135809π0.135809\pi
9898 0 0
9999 143.584 0.145765
100100 0 0
101101 1158.99 1.14182 0.570912 0.821011i 0.306590π-0.306590\pi
0.570912 + 0.821011i 0.306590π0.306590\pi
102102 0 0
103103 −1635.01 −1.56410 −0.782048 0.623218i 0.785825π-0.785825\pi
−0.782048 + 0.623218i 0.785825π0.785825\pi
104104 0 0
105105 1395.36 1.29689
106106 0 0
107107 −282.589 −0.255317 −0.127659 0.991818i 0.540746π-0.540746\pi
−0.127659 + 0.991818i 0.540746π0.540746\pi
108108 0 0
109109 −1004.98 −0.883120 −0.441560 0.897232i 0.645575π-0.645575\pi
−0.441560 + 0.897232i 0.645575π0.645575\pi
110110 0 0
111111 901.836 0.771157
112112 0 0
113113 −567.108 −0.472115 −0.236057 0.971739i 0.575855π-0.575855\pi
−0.236057 + 0.971739i 0.575855π0.575855\pi
114114 0 0
115115 −2040.84 −1.65486
116116 0 0
117117 22.8711 0.0180721
118118 0 0
119119 −2305.95 −1.77635
120120 0 0
121121 1470.39 1.10473
122122 0 0
123123 −466.082 −0.341668
124124 0 0
125125 −22.6053 −0.0161750
126126 0 0
127127 −496.616 −0.346988 −0.173494 0.984835i 0.555506π-0.555506\pi
−0.173494 + 0.984835i 0.555506π0.555506\pi
128128 0 0
129129 −909.948 −0.621058
130130 0 0
131131 −1658.72 −1.10628 −0.553142 0.833087i 0.686571π-0.686571\pi
−0.553142 + 0.833087i 0.686571π0.686571\pi
132132 0 0
133133 901.703 0.587876
134134 0 0
135135 2321.87 1.48025
136136 0 0
137137 −432.872 −0.269947 −0.134974 0.990849i 0.543095π-0.543095\pi
−0.134974 + 0.990849i 0.543095π0.543095\pi
138138 0 0
139139 146.148 0.0891809 0.0445904 0.999005i 0.485802π-0.485802\pi
0.0445904 + 0.999005i 0.485802π0.485802\pi
140140 0 0
141141 1462.89 0.873743
142142 0 0
143143 446.226 0.260946
144144 0 0
145145 1764.53 1.01060
146146 0 0
147147 −119.010 −0.0667740
148148 0 0
149149 −3556.29 −1.95532 −0.977659 0.210198i 0.932589π-0.932589\pi
−0.977659 + 0.210198i 0.932589π0.932589\pi
150150 0 0
151151 −1320.32 −0.711562 −0.355781 0.934569i 0.615785π-0.615785\pi
−0.355781 + 0.934569i 0.615785π0.615785\pi
152152 0 0
153153 −350.328 −0.185114
154154 0 0
155155 4802.13 2.48849
156156 0 0
157157 −2040.43 −1.03722 −0.518612 0.855010i 0.673551π-0.673551\pi
−0.518612 + 0.855010i 0.673551π0.673551\pi
158158 0 0
159159 507.580 0.253168
160160 0 0
161161 −2298.26 −1.12502
162162 0 0
163163 2392.21 1.14952 0.574762 0.818321i 0.305095π-0.305095\pi
0.574762 + 0.818321i 0.305095π0.305095\pi
164164 0 0
165165 4136.00 1.95144
166166 0 0
167167 2068.34 0.958400 0.479200 0.877706i 0.340927π-0.340927\pi
0.479200 + 0.877706i 0.340927π0.340927\pi
168168 0 0
169169 −2125.92 −0.967648
170170 0 0
171171 136.990 0.0612625
172172 0 0
173173 2441.87 1.07313 0.536566 0.843859i 0.319721π-0.319721\pi
0.536566 + 0.843859i 0.319721π0.319721\pi
174174 0 0
175175 −2257.51 −0.975152
176176 0 0
177177 460.143 0.195404
178178 0 0
179179 2430.84 1.01502 0.507512 0.861645i 0.330565π-0.330565\pi
0.507512 + 0.861645i 0.330565π0.330565\pi
180180 0 0
181181 −1928.96 −0.792148 −0.396074 0.918219i 0.629628π-0.629628\pi
−0.396074 + 0.918219i 0.629628π0.629628\pi
182182 0 0
183183 1670.53 0.674806
184184 0 0
185185 −2901.64 −1.15315
186186 0 0
187187 −6835.07 −2.67288
188188 0 0
189189 2614.73 1.00631
190190 0 0
191191 4087.34 1.54843 0.774214 0.632924i 0.218145π-0.218145\pi
0.774214 + 0.632924i 0.218145π0.218145\pi
192192 0 0
193193 −1156.52 −0.431339 −0.215669 0.976466i 0.569193π-0.569193\pi
−0.215669 + 0.976466i 0.569193π0.569193\pi
194194 0 0
195195 658.811 0.241941
196196 0 0
197197 2658.44 0.961452 0.480726 0.876871i 0.340373π-0.340373\pi
0.480726 + 0.876871i 0.340373π0.340373\pi
198198 0 0
199199 −742.369 −0.264448 −0.132224 0.991220i 0.542212π-0.542212\pi
−0.132224 + 0.991220i 0.542212π0.542212\pi
200200 0 0
201201 −2410.09 −0.845745
202202 0 0
203203 1987.10 0.687029
204204 0 0
205205 1499.61 0.510914
206206 0 0
207207 −349.160 −0.117238
208208 0 0
209209 2672.74 0.884580
210210 0 0
211211 3838.30 1.25232 0.626160 0.779694i 0.284626π-0.284626\pi
0.626160 + 0.779694i 0.284626π0.284626\pi
212212 0 0
213213 −428.677 −0.137899
214214 0 0
215215 2927.74 0.928700
216216 0 0
217217 5407.84 1.69174
218218 0 0
219219 −760.257 −0.234582
220220 0 0
221221 −1088.74 −0.331387
222222 0 0
223223 −3418.34 −1.02650 −0.513249 0.858240i 0.671558π-0.671558\pi
−0.513249 + 0.858240i 0.671558π0.671558\pi
224224 0 0
225225 −342.969 −0.101620
226226 0 0
227227 −515.729 −0.150793 −0.0753967 0.997154i 0.524022π-0.524022\pi
−0.0753967 + 0.997154i 0.524022π0.524022\pi
228228 0 0
229229 −1595.26 −0.460340 −0.230170 0.973150i 0.573928π-0.573928\pi
−0.230170 + 0.973150i 0.573928π0.573928\pi
230230 0 0
231231 4657.68 1.32664
232232 0 0
233233 5251.27 1.47649 0.738245 0.674533i 0.235655π-0.235655\pi
0.738245 + 0.674533i 0.235655π0.235655\pi
234234 0 0
235235 −4706.83 −1.30655
236236 0 0
237237 −2214.81 −0.607035
238238 0 0
239239 −2029.27 −0.549216 −0.274608 0.961556i 0.588548π-0.588548\pi
−0.274608 + 0.961556i 0.588548π0.588548\pi
240240 0 0
241241 −4615.72 −1.23371 −0.616856 0.787076i 0.711594π-0.711594\pi
−0.616856 + 0.787076i 0.711594π0.711594\pi
242242 0 0
243243 758.210 0.200161
244244 0 0
245245 382.912 0.0998505
246246 0 0
247247 425.733 0.109671
248248 0 0
249249 −1892.10 −0.481554
250250 0 0
251251 2702.52 0.679607 0.339804 0.940496i 0.389639π-0.389639\pi
0.339804 + 0.940496i 0.389639π0.389639\pi
252252 0 0
253253 −6812.27 −1.69282
254254 0 0
255255 −10091.3 −2.47821
256256 0 0
257257 991.785 0.240723 0.120362 0.992730i 0.461595π-0.461595\pi
0.120362 + 0.992730i 0.461595π0.461595\pi
258258 0 0
259259 −3267.63 −0.783941
260260 0 0
261261 301.887 0.0715952
262262 0 0
263263 −7430.74 −1.74220 −0.871101 0.491105i 0.836593π-0.836593\pi
−0.871101 + 0.491105i 0.836593π0.836593\pi
264264 0 0
265265 −1633.13 −0.378575
266266 0 0
267267 −2551.19 −0.584758
268268 0 0
269269 −3281.50 −0.743778 −0.371889 0.928277i 0.621290π-0.621290\pi
−0.371889 + 0.928277i 0.621290π0.621290\pi
270270 0 0
271271 −221.518 −0.0496542 −0.0248271 0.999692i 0.507904π-0.507904\pi
−0.0248271 + 0.999692i 0.507904π0.507904\pi
272272 0 0
273273 741.909 0.164477
274274 0 0
275275 −6691.48 −1.46731
276276 0 0
277277 −1106.28 −0.239963 −0.119982 0.992776i 0.538284π-0.538284\pi
−0.119982 + 0.992776i 0.538284π0.538284\pi
278278 0 0
279279 821.579 0.176296
280280 0 0
281281 −2372.52 −0.503676 −0.251838 0.967769i 0.581035π-0.581035\pi
−0.251838 + 0.967769i 0.581035π0.581035\pi
282282 0 0
283283 −2549.89 −0.535602 −0.267801 0.963474i 0.586297π-0.586297\pi
−0.267801 + 0.963474i 0.586297π0.586297\pi
284284 0 0
285285 3946.05 0.820154
286286 0 0
287287 1688.76 0.347332
288288 0 0
289289 11763.7 2.39441
290290 0 0
291291 8572.09 1.72682
292292 0 0
293293 −130.319 −0.0259840 −0.0129920 0.999916i 0.504136π-0.504136\pi
−0.0129920 + 0.999916i 0.504136π0.504136\pi
294294 0 0
295295 −1480.50 −0.292197
296296 0 0
297297 7750.32 1.51421
298298 0 0
299299 −1085.11 −0.209877
300300 0 0
301301 3297.03 0.631353
302302 0 0
303303 5711.76 1.08294
304304 0 0
305305 −5374.91 −1.00907
306306 0 0
307307 62.1182 0.0115481 0.00577406 0.999983i 0.498162π-0.498162\pi
0.00577406 + 0.999983i 0.498162π0.498162\pi
308308 0 0
309309 −8057.64 −1.48344
310310 0 0
311311 −593.837 −0.108275 −0.0541373 0.998533i 0.517241π-0.517241\pi
−0.0541373 + 0.998533i 0.517241π0.517241\pi
312312 0 0
313313 3669.69 0.662694 0.331347 0.943509i 0.392497π-0.392497\pi
0.331347 + 0.943509i 0.392497π0.392497\pi
314314 0 0
315315 −768.102 −0.137389
316316 0 0
317317 −374.339 −0.0663249 −0.0331625 0.999450i 0.510558π-0.510558\pi
−0.0331625 + 0.999450i 0.510558π0.510558\pi
318318 0 0
319319 5889.96 1.03378
320320 0 0
321321 −1392.66 −0.242151
322322 0 0
323323 −6521.16 −1.12337
324324 0 0
325325 −1065.87 −0.181919
326326 0 0
327327 −4952.77 −0.837580
328328 0 0
329329 −5300.51 −0.888227
330330 0 0
331331 5871.13 0.974945 0.487472 0.873138i 0.337919π-0.337919\pi
0.487472 + 0.873138i 0.337919π0.337919\pi
332332 0 0
333333 −496.431 −0.0816944
334334 0 0
335335 7754.43 1.26469
336336 0 0
337337 1047.83 0.169373 0.0846865 0.996408i 0.473011π-0.473011\pi
0.0846865 + 0.996408i 0.473011π0.473011\pi
338338 0 0
339339 −2794.82 −0.447769
340340 0 0
341341 16029.4 2.54557
342342 0 0
343343 6555.96 1.03204
344344 0 0
345345 −10057.7 −1.56953
346346 0 0
347347 3921.88 0.606737 0.303368 0.952873i 0.401889π-0.401889\pi
0.303368 + 0.952873i 0.401889π0.401889\pi
348348 0 0
349349 11604.9 1.77993 0.889966 0.456027i 0.150728π-0.150728\pi
0.889966 + 0.456027i 0.150728π0.150728\pi
350350 0 0
351351 1234.53 0.187733
352352 0 0
353353 −1530.22 −0.230724 −0.115362 0.993324i 0.536803π-0.536803\pi
−0.115362 + 0.993324i 0.536803π0.536803\pi
354354 0 0
355355 1379.26 0.206207
356356 0 0
357357 −11364.2 −1.68475
358358 0 0
359359 −10764.0 −1.58246 −0.791231 0.611518i 0.790559π-0.790559\pi
−0.791231 + 0.611518i 0.790559π0.790559\pi
360360 0 0
361361 −4309.01 −0.628227
362362 0 0
363363 7246.40 1.04776
364364 0 0
365365 2446.11 0.350782
366366 0 0
367367 −10713.0 −1.52374 −0.761869 0.647731i 0.775718π-0.775718\pi
−0.761869 + 0.647731i 0.775718π0.775718\pi
368368 0 0
369369 256.563 0.0361954
370370 0 0
371371 −1839.12 −0.257365
372372 0 0
373373 9186.32 1.27520 0.637600 0.770368i 0.279927π-0.279927\pi
0.637600 + 0.770368i 0.279927π0.279927\pi
374374 0 0
375375 −111.404 −0.0153409
376376 0 0
377377 938.194 0.128168
378378 0 0
379379 14201.0 1.92468 0.962342 0.271842i 0.0876327π-0.0876327\pi
0.962342 + 0.271842i 0.0876327π0.0876327\pi
380380 0 0
381381 −2447.42 −0.329095
382382 0 0
383383 9691.24 1.29295 0.646474 0.762936i 0.276243π-0.276243\pi
0.646474 + 0.762936i 0.276243π0.276243\pi
384384 0 0
385385 −14986.0 −1.98379
386386 0 0
387387 500.897 0.0657933
388388 0 0
389389 −6358.79 −0.828801 −0.414400 0.910095i 0.636009π-0.636009\pi
−0.414400 + 0.910095i 0.636009π0.636009\pi
390390 0 0
391391 16621.1 2.14978
392392 0 0
393393 −8174.52 −1.04924
394394 0 0
395395 7126.11 0.907731
396396 0 0
397397 −13034.2 −1.64778 −0.823888 0.566752i 0.808200π-0.808200\pi
−0.823888 + 0.566752i 0.808200π0.808200\pi
398398 0 0
399399 4443.77 0.557561
400400 0 0
401401 6705.06 0.834999 0.417499 0.908677i 0.362907π-0.362907\pi
0.417499 + 0.908677i 0.362907π0.362907\pi
402402 0 0
403403 2553.27 0.315602
404404 0 0
405405 10281.2 1.26143
406406 0 0
407407 −9685.59 −1.17960
408408 0 0
409409 10967.8 1.32598 0.662988 0.748630i 0.269288π-0.269288\pi
0.662988 + 0.748630i 0.269288π0.269288\pi
410410 0 0
411411 −2133.28 −0.256027
412412 0 0
413413 −1667.24 −0.198643
414414 0 0
415415 6087.80 0.720093
416416 0 0
417417 720.249 0.0845821
418418 0 0
419419 −13686.0 −1.59571 −0.797856 0.602849i 0.794032π-0.794032\pi
−0.797856 + 0.602849i 0.794032π0.794032\pi
420420 0 0
421421 8552.92 0.990128 0.495064 0.868857i 0.335145π-0.335145\pi
0.495064 + 0.868857i 0.335145π0.335145\pi
422422 0 0
423423 −805.274 −0.0925621
424424 0 0
425425 16326.4 1.86340
426426 0 0
427427 −6052.86 −0.685992
428428 0 0
429429 2199.09 0.247490
430430 0 0
431431 12187.6 1.36208 0.681039 0.732247i 0.261528π-0.261528\pi
0.681039 + 0.732247i 0.261528π0.261528\pi
432432 0 0
433433 −8906.35 −0.988480 −0.494240 0.869326i 0.664554π-0.664554\pi
−0.494240 + 0.869326i 0.664554π0.664554\pi
434434 0 0
435435 8695.98 0.958483
436436 0 0
437437 −6499.41 −0.711462
438438 0 0
439439 −4655.21 −0.506107 −0.253054 0.967452i 0.581435π-0.581435\pi
−0.253054 + 0.967452i 0.581435π0.581435\pi
440440 0 0
441441 65.5110 0.00707386
442442 0 0
443443 −10008.8 −1.07343 −0.536716 0.843763i 0.680335π-0.680335\pi
−0.536716 + 0.843763i 0.680335π0.680335\pi
444444 0 0
445445 8208.41 0.874418
446446 0 0
447447 −17526.1 −1.85449
448448 0 0
449449 −3373.71 −0.354600 −0.177300 0.984157i 0.556736π-0.556736\pi
−0.177300 + 0.984157i 0.556736π0.556736\pi
450450 0 0
451451 5005.65 0.522632
452452 0 0
453453 −6506.79 −0.674869
454454 0 0
455455 −2387.08 −0.245952
456456 0 0
457457 −13600.4 −1.39212 −0.696060 0.717984i 0.745065π-0.745065\pi
−0.696060 + 0.717984i 0.745065π0.745065\pi
458458 0 0
459459 −18909.8 −1.92295
460460 0 0
461461 3559.45 0.359609 0.179805 0.983702i 0.442453π-0.442453\pi
0.179805 + 0.983702i 0.442453π0.442453\pi
462462 0 0
463463 −8019.14 −0.804926 −0.402463 0.915436i 0.631846π-0.631846\pi
−0.402463 + 0.915436i 0.631846π0.631846\pi
464464 0 0
465465 23665.9 2.36017
466466 0 0
467467 2066.14 0.204731 0.102365 0.994747i 0.467359π-0.467359\pi
0.102365 + 0.994747i 0.467359π0.467359\pi
468468 0 0
469469 8732.51 0.859765
470470 0 0
471471 −10055.7 −0.983737
472472 0 0
473473 9772.72 0.950000
474474 0 0
475475 −6384.17 −0.616686
476476 0 0
477477 −279.406 −0.0268199
478478 0 0
479479 −3679.26 −0.350960 −0.175480 0.984483i 0.556148π-0.556148\pi
−0.175480 + 0.984483i 0.556148π0.556148\pi
480480 0 0
481481 −1542.79 −0.146248
482482 0 0
483483 −11326.3 −1.06700
484484 0 0
485485 −27580.5 −2.58220
486486 0 0
487487 10884.4 1.01277 0.506386 0.862307i 0.330981π-0.330981\pi
0.506386 + 0.862307i 0.330981π0.330981\pi
488488 0 0
489489 11789.3 1.09025
490490 0 0
491491 14548.9 1.33723 0.668616 0.743608i 0.266887π-0.266887\pi
0.668616 + 0.743608i 0.266887π0.266887\pi
492492 0 0
493493 −14370.8 −1.31284
494494 0 0
495495 −2276.73 −0.206730
496496 0 0
497497 1553.23 0.140185
498498 0 0
499499 −8461.92 −0.759134 −0.379567 0.925164i 0.623927π-0.623927\pi
−0.379567 + 0.925164i 0.623927π0.623927\pi
500500 0 0
501501 10193.2 0.908978
502502 0 0
503503 −983.702 −0.0871990 −0.0435995 0.999049i 0.513883π-0.513883\pi
−0.0435995 + 0.999049i 0.513883π0.513883\pi
504504 0 0
505505 −18377.5 −1.61938
506506 0 0
507507 −10477.0 −0.917749
508508 0 0
509509 −14472.5 −1.26028 −0.630140 0.776481i 0.717003π-0.717003\pi
−0.630140 + 0.776481i 0.717003π0.717003\pi
510510 0 0
511511 2754.65 0.238470
512512 0 0
513513 7394.38 0.636393
514514 0 0
515515 25925.3 2.21826
516516 0 0
517517 −15711.3 −1.33652
518518 0 0
519519 12034.0 1.01779
520520 0 0
521521 −10761.8 −0.904959 −0.452480 0.891775i 0.649460π-0.649460\pi
−0.452480 + 0.891775i 0.649460π0.649460\pi
522522 0 0
523523 1516.67 0.126806 0.0634029 0.997988i 0.479805π-0.479805\pi
0.0634029 + 0.997988i 0.479805π0.479805\pi
524524 0 0
525525 −11125.5 −0.924866
526526 0 0
527527 −39109.7 −3.23273
528528 0 0
529529 4398.66 0.361524
530530 0 0
531531 −253.293 −0.0207006
532532 0 0
533533 797.336 0.0647963
534534 0 0
535535 4480.85 0.362101
536536 0 0
537537 11979.7 0.962682
538538 0 0
539539 1278.15 0.102141
540540 0 0
541541 22541.9 1.79141 0.895704 0.444652i 0.146673π-0.146673\pi
0.895704 + 0.444652i 0.146673π0.146673\pi
542542 0 0
543543 −9506.33 −0.751299
544544 0 0
545545 15935.4 1.25248
546546 0 0
547547 10202.0 0.797448 0.398724 0.917071i 0.369453π-0.369453\pi
0.398724 + 0.917071i 0.369453π0.369453\pi
548548 0 0
549549 −919.574 −0.0714872
550550 0 0
551551 5619.46 0.434477
552552 0 0
553553 8024.94 0.617098
554554 0 0
555555 −14299.9 −1.09369
556556 0 0
557557 7139.06 0.543073 0.271536 0.962428i 0.412468π-0.412468\pi
0.271536 + 0.962428i 0.412468π0.412468\pi
558558 0 0
559559 1556.67 0.117782
560560 0 0
561561 −33684.6 −2.53505
562562 0 0
563563 −19558.0 −1.46407 −0.732034 0.681268i 0.761429π-0.761429\pi
−0.732034 + 0.681268i 0.761429π0.761429\pi
564564 0 0
565565 8992.29 0.669572
566566 0 0
567567 11578.0 0.857549
568568 0 0
569569 −5835.86 −0.429969 −0.214984 0.976617i 0.568970π-0.568970\pi
−0.214984 + 0.976617i 0.568970π0.568970\pi
570570 0 0
571571 9820.65 0.719757 0.359879 0.932999i 0.382818π-0.382818\pi
0.359879 + 0.932999i 0.382818π0.382818\pi
572572 0 0
573573 20143.3 1.46858
574574 0 0
575575 16271.9 1.18015
576576 0 0
577577 451.231 0.0325563 0.0162782 0.999868i 0.494818π-0.494818\pi
0.0162782 + 0.999868i 0.494818π0.494818\pi
578578 0 0
579579 −5699.58 −0.409096
580580 0 0
581581 6855.67 0.489537
582582 0 0
583583 −5451.33 −0.387257
584584 0 0
585585 −362.654 −0.0256306
586586 0 0
587587 −24775.7 −1.74208 −0.871042 0.491209i 0.836555π-0.836555\pi
−0.871042 + 0.491209i 0.836555π0.836555\pi
588588 0 0
589589 15293.2 1.06986
590590 0 0
591591 13101.3 0.911873
592592 0 0
593593 −4207.64 −0.291378 −0.145689 0.989330i 0.546540π-0.546540\pi
−0.145689 + 0.989330i 0.546540π0.546540\pi
594594 0 0
595595 36564.1 2.51929
596596 0 0
597597 −3658.54 −0.250811
598598 0 0
599599 1916.32 0.130715 0.0653577 0.997862i 0.479181π-0.479181\pi
0.0653577 + 0.997862i 0.479181π0.479181\pi
600600 0 0
601601 −19361.1 −1.31407 −0.657034 0.753861i 0.728189π-0.728189\pi
−0.657034 + 0.753861i 0.728189π0.728189\pi
602602 0 0
603603 1326.68 0.0895961
604604 0 0
605605 −23315.2 −1.56677
606606 0 0
607607 6097.02 0.407694 0.203847 0.979003i 0.434655π-0.434655\pi
0.203847 + 0.979003i 0.434655π0.434655\pi
608608 0 0
609609 9792.82 0.651601
610610 0 0
611611 −2502.60 −0.165703
612612 0 0
613613 13837.7 0.911743 0.455872 0.890046i 0.349328π-0.349328\pi
0.455872 + 0.890046i 0.349328π0.349328\pi
614614 0 0
615615 7390.38 0.484567
616616 0 0
617617 11959.1 0.780318 0.390159 0.920747i 0.372420π-0.372420\pi
0.390159 + 0.920747i 0.372420π0.372420\pi
618618 0 0
619619 8385.02 0.544463 0.272231 0.962232i 0.412238π-0.412238\pi
0.272231 + 0.962232i 0.412238π0.412238\pi
620620 0 0
621621 −18846.8 −1.21787
622622 0 0
623623 9243.75 0.594451
624624 0 0
625625 −15444.8 −0.988465
626626 0 0
627627 13171.8 0.838965
628628 0 0
629629 23631.7 1.49802
630630 0 0
631631 13592.1 0.857513 0.428757 0.903420i 0.358952π-0.358952\pi
0.428757 + 0.903420i 0.358952π0.358952\pi
632632 0 0
633633 18915.9 1.18774
634634 0 0
635635 7874.54 0.492113
636636 0 0
637637 203.593 0.0126635
638638 0 0
639639 235.973 0.0146087
640640 0 0
641641 −18123.4 −1.11674 −0.558371 0.829591i 0.688573π-0.688573\pi
−0.558371 + 0.829591i 0.688573π0.688573\pi
642642 0 0
643643 25042.1 1.53587 0.767935 0.640528i 0.221284π-0.221284\pi
0.767935 + 0.640528i 0.221284π0.221284\pi
644644 0 0
645645 14428.5 0.880809
646646 0 0
647647 −6022.08 −0.365923 −0.182962 0.983120i 0.558568π-0.558568\pi
−0.182962 + 0.983120i 0.558568π0.558568\pi
648648 0 0
649649 −4941.87 −0.298899
650650 0 0
651651 26650.9 1.60450
652652 0 0
653653 14093.8 0.844617 0.422308 0.906452i 0.361220π-0.361220\pi
0.422308 + 0.906452i 0.361220π0.361220\pi
654654 0 0
655655 26301.4 1.56898
656656 0 0
657657 418.496 0.0248510
658658 0 0
659659 −17240.7 −1.01912 −0.509562 0.860434i 0.670193π-0.670193\pi
−0.509562 + 0.860434i 0.670193π0.670193\pi
660660 0 0
661661 −20209.5 −1.18920 −0.594598 0.804023i 0.702689π-0.702689\pi
−0.594598 + 0.804023i 0.702689π0.702689\pi
662662 0 0
663663 −5365.52 −0.314298
664664 0 0
665665 −14297.8 −0.833749
666666 0 0
667667 −14322.8 −0.831459
668668 0 0
669669 −16846.3 −0.973564
670670 0 0
671671 −17941.3 −1.03221
672672 0 0
673673 6838.55 0.391689 0.195845 0.980635i 0.437255π-0.437255\pi
0.195845 + 0.980635i 0.437255π0.437255\pi
674674 0 0
675675 −18512.6 −1.05563
676676 0 0
677677 187.425 0.0106401 0.00532003 0.999986i 0.498307π-0.498307\pi
0.00532003 + 0.999986i 0.498307π0.498307\pi
678678 0 0
679679 −31059.3 −1.75545
680680 0 0
681681 −2541.62 −0.143018
682682 0 0
683683 23476.0 1.31520 0.657601 0.753367i 0.271571π-0.271571\pi
0.657601 + 0.753367i 0.271571π0.271571\pi
684684 0 0
685685 6863.79 0.382850
686686 0 0
687687 −7861.77 −0.436602
688688 0 0
689689 −868.327 −0.0480125
690690 0 0
691691 −6309.92 −0.347382 −0.173691 0.984800i 0.555569π-0.555569\pi
−0.173691 + 0.984800i 0.555569π0.555569\pi
692692 0 0
693693 −2563.90 −0.140540
694694 0 0
695695 −2317.39 −0.126480
696696 0 0
697697 −12213.2 −0.663712
698698 0 0
699699 25879.3 1.40035
700700 0 0
701701 24920.4 1.34270 0.671348 0.741142i 0.265716π-0.265716\pi
0.671348 + 0.741142i 0.265716π0.265716\pi
702702 0 0
703703 −9240.77 −0.495764
704704 0 0
705705 −23196.2 −1.23918
706706 0 0
707707 −20695.5 −1.10090
708708 0 0
709709 −14478.9 −0.766949 −0.383474 0.923551i 0.625273π-0.625273\pi
−0.383474 + 0.923551i 0.625273π0.625273\pi
710710 0 0
711711 1219.18 0.0643077
712712 0 0
713713 −38979.3 −2.04738
714714 0 0
715715 −7075.54 −0.370084
716716 0 0
717717 −10000.7 −0.520895
718718 0 0
719719 6411.30 0.332547 0.166273 0.986080i 0.446827π-0.446827\pi
0.166273 + 0.986080i 0.446827π0.446827\pi
720720 0 0
721721 29195.3 1.50803
722722 0 0
723723 −22747.2 −1.17009
724724 0 0
725725 −14068.9 −0.720698
726726 0 0
727727 20626.3 1.05225 0.526126 0.850407i 0.323644π-0.323644\pi
0.526126 + 0.850407i 0.323644π0.323644\pi
728728 0 0
729729 21243.3 1.07927
730730 0 0
731731 −23844.3 −1.20645
732732 0 0
733733 −5732.29 −0.288850 −0.144425 0.989516i 0.546133π-0.546133\pi
−0.144425 + 0.989516i 0.546133π0.546133\pi
734734 0 0
735735 1887.07 0.0947015
736736 0 0
737737 25884.1 1.29369
738738 0 0
739739 −36336.0 −1.80872 −0.904359 0.426773i 0.859650π-0.859650\pi
−0.904359 + 0.426773i 0.859650π0.859650\pi
740740 0 0
741741 2098.10 0.104016
742742 0 0
743743 −4363.83 −0.215469 −0.107734 0.994180i 0.534360π-0.534360\pi
−0.107734 + 0.994180i 0.534360π0.534360\pi
744744 0 0
745745 56389.9 2.77311
746746 0 0
747747 1041.54 0.0510146
748748 0 0
749749 5046.03 0.246166
750750 0 0
751751 16162.7 0.785334 0.392667 0.919681i 0.371552π-0.371552\pi
0.392667 + 0.919681i 0.371552π0.371552\pi
752752 0 0
753753 13318.6 0.644562
754754 0 0
755755 20935.5 1.00917
756756 0 0
757757 −4411.92 −0.211828 −0.105914 0.994375i 0.533777π-0.533777\pi
−0.105914 + 0.994375i 0.533777π0.533777\pi
758758 0 0
759759 −33572.2 −1.60553
760760 0 0
761761 28281.8 1.34719 0.673597 0.739099i 0.264749π-0.264749\pi
0.673597 + 0.739099i 0.264749π0.264749\pi
762762 0 0
763763 17945.4 0.851465
764764 0 0
765765 5554.95 0.262535
766766 0 0
767767 −787.176 −0.0370577
768768 0 0
769769 −15016.8 −0.704186 −0.352093 0.935965i 0.614530π-0.614530\pi
−0.352093 + 0.935965i 0.614530π0.614530\pi
770770 0 0
771771 4887.72 0.228310
772772 0 0
773773 −8674.11 −0.403604 −0.201802 0.979426i 0.564680π-0.564680\pi
−0.201802 + 0.979426i 0.564680π0.564680\pi
774774 0 0
775775 −38288.2 −1.77465
776776 0 0
777777 −16103.5 −0.743515
778778 0 0
779779 4775.76 0.219653
780780 0 0
781781 4603.94 0.210937
782782 0 0
783783 16295.1 0.743729
784784 0 0
785785 32353.9 1.47103
786786 0 0
787787 −23660.2 −1.07166 −0.535829 0.844327i 0.680001π-0.680001\pi
−0.535829 + 0.844327i 0.680001π0.680001\pi
788788 0 0
789789 −36620.2 −1.65236
790790 0 0
791791 10126.5 0.455192
792792 0 0
793793 −2857.82 −0.127975
794794 0 0
795795 −8048.39 −0.359053
796796 0 0
797797 −35432.5 −1.57476 −0.787380 0.616468i 0.788563π-0.788563\pi
−0.787380 + 0.616468i 0.788563π0.788563\pi
798798 0 0
799799 38333.6 1.69730
800800 0 0
801801 1404.35 0.0619477
802802 0 0
803803 8165.05 0.358827
804804 0 0
805805 36442.1 1.59555
806806 0 0
807807 −16171.9 −0.705424
808808 0 0
809809 −14005.5 −0.608664 −0.304332 0.952566i 0.598433π-0.598433\pi
−0.304332 + 0.952566i 0.598433π0.598433\pi
810810 0 0
811811 −22580.8 −0.977706 −0.488853 0.872366i 0.662584π-0.662584\pi
−0.488853 + 0.872366i 0.662584π0.662584\pi
812812 0 0
813813 −1091.69 −0.0470937
814814 0 0
815815 −37931.8 −1.63030
816816 0 0
817817 9323.90 0.399268
818818 0 0
819819 −408.396 −0.0174243
820820 0 0
821821 −21308.9 −0.905827 −0.452914 0.891554i 0.649615π-0.649615\pi
−0.452914 + 0.891554i 0.649615π0.649615\pi
822822 0 0
823823 −13571.4 −0.574810 −0.287405 0.957809i 0.592793π-0.592793\pi
−0.287405 + 0.957809i 0.592793π0.592793\pi
824824 0 0
825825 −32977.0 −1.39165
826826 0 0
827827 −19295.2 −0.811318 −0.405659 0.914025i 0.632958π-0.632958\pi
−0.405659 + 0.914025i 0.632958π0.632958\pi
828828 0 0
829829 −28752.7 −1.20461 −0.602306 0.798265i 0.705751π-0.705751\pi
−0.602306 + 0.798265i 0.705751π0.705751\pi
830830 0 0
831831 −5451.96 −0.227589
832832 0 0
833833 −3118.53 −0.129713
834834 0 0
835835 −32796.4 −1.35924
836836 0 0
837837 44346.7 1.83136
838838 0 0
839839 566.927 0.0233284 0.0116642 0.999932i 0.496287π-0.496287\pi
0.0116642 + 0.999932i 0.496287π0.496287\pi
840840 0 0
841841 −12005.3 −0.492243
842842 0 0
843843 −11692.3 −0.477703
844844 0 0
845845 33709.5 1.37236
846846 0 0
847847 −26256.0 −1.06513
848848 0 0
849849 −12566.4 −0.507983
850850 0 0
851851 23552.8 0.948744
852852 0 0
853853 −34698.1 −1.39278 −0.696389 0.717665i 0.745211π-0.745211\pi
−0.696389 + 0.717665i 0.745211π0.745211\pi
854854 0 0
855855 −2172.17 −0.0868850
856856 0 0
857857 37362.0 1.48922 0.744610 0.667500i 0.232636π-0.232636\pi
0.744610 + 0.667500i 0.232636π0.232636\pi
858858 0 0
859859 29572.2 1.17461 0.587305 0.809366i 0.300189π-0.300189\pi
0.587305 + 0.809366i 0.300189π0.300189\pi
860860 0 0
861861 8322.54 0.329421
862862 0 0
863863 11636.5 0.458994 0.229497 0.973309i 0.426292π-0.426292\pi
0.229497 + 0.973309i 0.426292π0.426292\pi
864864 0 0
865865 −38719.2 −1.52196
866866 0 0
867867 57974.1 2.27094
868868 0 0
869869 23786.7 0.928550
870870 0 0
871871 4123.00 0.160393
872872 0 0
873873 −4718.65 −0.182935
874874 0 0
875875 403.649 0.0155952
876876 0 0
877877 −19878.2 −0.765380 −0.382690 0.923877i 0.625002π-0.625002\pi
−0.382690 + 0.923877i 0.625002π0.625002\pi
878878 0 0
879879 −642.238 −0.0246441
880880 0 0
881881 −36460.3 −1.39430 −0.697150 0.716926i 0.745549π-0.745549\pi
−0.697150 + 0.716926i 0.745549π0.745549\pi
882882 0 0
883883 −28119.9 −1.07170 −0.535849 0.844314i 0.680009π-0.680009\pi
−0.535849 + 0.844314i 0.680009π0.680009\pi
884884 0 0
885885 −7296.21 −0.277129
886886 0 0
887887 41888.4 1.58565 0.792826 0.609448i 0.208609π-0.208609\pi
0.792826 + 0.609448i 0.208609π0.208609\pi
888888 0 0
889889 8867.77 0.334551
890890 0 0
891891 34318.4 1.29036
892892 0 0
893893 −14989.7 −0.561715
894894 0 0
895895 −38544.3 −1.43955
896896 0 0
897897 −5347.62 −0.199055
898898 0 0
899899 33701.9 1.25030
900900 0 0
901901 13300.6 0.491795
902902 0 0
903903 16248.4 0.598796
904904 0 0
905905 30586.4 1.12346
906906 0 0
907907 12575.3 0.460371 0.230185 0.973147i 0.426067π-0.426067\pi
0.230185 + 0.973147i 0.426067π0.426067\pi
908908 0 0
909909 −3144.14 −0.114724
910910 0 0
911911 39814.7 1.44799 0.723995 0.689805i 0.242304π-0.242304\pi
0.723995 + 0.689805i 0.242304π0.242304\pi
912912 0 0
913913 20320.9 0.736609
914914 0 0
915915 −26488.7 −0.957036
916916 0 0
917917 29618.8 1.06663
918918 0 0
919919 −8987.93 −0.322616 −0.161308 0.986904i 0.551571π-0.551571\pi
−0.161308 + 0.986904i 0.551571π0.551571\pi
920920 0 0
921921 306.131 0.0109526
922922 0 0
923923 733.348 0.0261521
924924 0 0
925925 23135.2 0.822359
926926 0 0
927927 4435.46 0.157152
928928 0 0
929929 234.252 0.00827293 0.00413647 0.999991i 0.498683π-0.498683\pi
0.00413647 + 0.999991i 0.498683π0.498683\pi
930930 0 0
931931 1219.45 0.0429279
932932 0 0
933933 −2926.55 −0.102691
934934 0 0
935935 108380. 3.79079
936936 0 0
937937 17624.6 0.614483 0.307241 0.951632i 0.400594π-0.400594\pi
0.307241 + 0.951632i 0.400594π0.400594\pi
938938 0 0
939939 18085.0 0.628521
940940 0 0
941941 30532.1 1.05772 0.528861 0.848708i 0.322619π-0.322619\pi
0.528861 + 0.848708i 0.322619π0.322619\pi
942942 0 0
943943 −12172.4 −0.420349
944944 0 0
945945 −41460.2 −1.42720
946946 0 0
947947 42092.8 1.44438 0.722192 0.691692i 0.243135π-0.243135\pi
0.722192 + 0.691692i 0.243135π0.243135\pi
948948 0 0
949949 1300.59 0.0444877
950950 0 0
951951 −1844.82 −0.0629048
952952 0 0
953953 −48641.0 −1.65334 −0.826672 0.562683i 0.809769π-0.809769\pi
−0.826672 + 0.562683i 0.809769π0.809769\pi
954954 0 0
955955 −64810.6 −2.19604
956956 0 0
957957 29026.9 0.980467
958958 0 0
959959 7729.54 0.260271
960960 0 0
961961 61927.9 2.07874
962962 0 0
963963 766.612 0.0256529
964964 0 0
965965 18338.3 0.611742
966966 0 0
967967 53000.5 1.76254 0.881272 0.472609i 0.156688π-0.156688\pi
0.881272 + 0.472609i 0.156688π0.156688\pi
968968 0 0
969969 −32137.6 −1.06544
970970 0 0
971971 −26286.3 −0.868761 −0.434381 0.900729i 0.643033π-0.643033\pi
−0.434381 + 0.900729i 0.643033π0.643033\pi
972972 0 0
973973 −2609.68 −0.0859842
974974 0 0
975975 −5252.81 −0.172538
976976 0 0
977977 −30508.0 −0.999014 −0.499507 0.866310i 0.666486π-0.666486\pi
−0.499507 + 0.866310i 0.666486π0.666486\pi
978978 0 0
979979 27399.4 0.894473
980980 0 0
981981 2726.34 0.0887311
982982 0 0
983983 −37044.3 −1.20196 −0.600982 0.799263i 0.705224π-0.705224\pi
−0.600982 + 0.799263i 0.705224π0.705224\pi
984984 0 0
985985 −42153.3 −1.36357
986986 0 0
987987 −26122.0 −0.842424
988988 0 0
989989 −23764.7 −0.764079
990990 0 0
991991 −47803.5 −1.53232 −0.766160 0.642650i 0.777835π-0.777835\pi
−0.766160 + 0.642650i 0.777835π0.777835\pi
992992 0 0
993993 28934.1 0.924670
994994 0 0
995995 11771.3 0.375051
996996 0 0
997997 13478.1 0.428140 0.214070 0.976818i 0.431328π-0.431328\pi
0.214070 + 0.976818i 0.431328π0.431328\pi
998998 0 0
999999 −26796.1 −0.848639
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 128.4.a.e.1.2 2
3.2 odd 2 1152.4.a.s.1.2 2
4.3 odd 2 128.4.a.g.1.1 yes 2
8.3 odd 2 128.4.a.f.1.2 yes 2
8.5 even 2 128.4.a.h.1.1 yes 2
12.11 even 2 1152.4.a.t.1.2 2
16.3 odd 4 256.4.b.h.129.2 4
16.5 even 4 256.4.b.i.129.2 4
16.11 odd 4 256.4.b.h.129.3 4
16.13 even 4 256.4.b.i.129.3 4
24.5 odd 2 1152.4.a.q.1.1 2
24.11 even 2 1152.4.a.r.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.4.a.e.1.2 2 1.1 even 1 trivial
128.4.a.f.1.2 yes 2 8.3 odd 2
128.4.a.g.1.1 yes 2 4.3 odd 2
128.4.a.h.1.1 yes 2 8.5 even 2
256.4.b.h.129.2 4 16.3 odd 4
256.4.b.h.129.3 4 16.11 odd 4
256.4.b.i.129.2 4 16.5 even 4
256.4.b.i.129.3 4 16.13 even 4
1152.4.a.q.1.1 2 24.5 odd 2
1152.4.a.r.1.1 2 24.11 even 2
1152.4.a.s.1.2 2 3.2 odd 2
1152.4.a.t.1.2 2 12.11 even 2