Properties

Label 325.6.a.b.1.2
Level 325325
Weight 66
Character 325.1
Self dual yes
Analytic conductor 52.12552.125
Analytic rank 00
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] = [325,6,Mod(1,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 325=5213 325 = 5^{2} \cdot 13
Weight: k k == 6 6
Character orbit: [χ][\chi] == 325.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: 52.124741439252.1247414392
Analytic rank: 00
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 1.2
Root 1.56155-1.56155 of defining polynomial
Character χ\chi == 325.1

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+4.56155q2+1.63068q311.1922q4+7.43845q6126.309q7197.024q8240.341q914.8296q1118.2510q12+169.000q13576.164q14540.582q16+1051.12q171096.33q18213.723q19205.969q2167.6458q22+4231.16q23321.283q24+770.902q26788.176q27+1413.68q28504.955q29+4783.58q31+3838.86q3224.1823q33+4794.75q34+2689.95q36+4635.74q37974.911q38+275.585q39+7944.15q41939.541q42+8516.41q43+165.976q44+19300.7q4624921.2q47881.518q48853.113q49+1714.05q511891.49q52+7808.46q533595.31q54+24885.8q56348.515q572303.38q5837337.5q5918172.2q61+21820.5q62+30357.1q63+34809.8q64110.309q66+34559.9q6711764.4q68+6899.68q69+41255.7q71+47352.8q72+1056.42q73+21146.2q74+2392.04q76+1873.10q77+1257.10q7847719.3q79+57117.6q81+36237.7q82+74799.0q83+2305.26q84+38848.0q86823.421q87+2921.78q88+9799.26q8921346.2q9147356.1q92+7800.50q93113679.q94+6259.97q96+138432.q973891.52q98+3564.15q99+O(q100)q+4.56155 q^{2} +1.63068 q^{3} -11.1922 q^{4} +7.43845 q^{6} -126.309 q^{7} -197.024 q^{8} -240.341 q^{9} -14.8296 q^{11} -18.2510 q^{12} +169.000 q^{13} -576.164 q^{14} -540.582 q^{16} +1051.12 q^{17} -1096.33 q^{18} -213.723 q^{19} -205.969 q^{21} -67.6458 q^{22} +4231.16 q^{23} -321.283 q^{24} +770.902 q^{26} -788.176 q^{27} +1413.68 q^{28} -504.955 q^{29} +4783.58 q^{31} +3838.86 q^{32} -24.1823 q^{33} +4794.75 q^{34} +2689.95 q^{36} +4635.74 q^{37} -974.911 q^{38} +275.585 q^{39} +7944.15 q^{41} -939.541 q^{42} +8516.41 q^{43} +165.976 q^{44} +19300.7 q^{46} -24921.2 q^{47} -881.518 q^{48} -853.113 q^{49} +1714.05 q^{51} -1891.49 q^{52} +7808.46 q^{53} -3595.31 q^{54} +24885.8 q^{56} -348.515 q^{57} -2303.38 q^{58} -37337.5 q^{59} -18172.2 q^{61} +21820.5 q^{62} +30357.1 q^{63} +34809.8 q^{64} -110.309 q^{66} +34559.9 q^{67} -11764.4 q^{68} +6899.68 q^{69} +41255.7 q^{71} +47352.8 q^{72} +1056.42 q^{73} +21146.2 q^{74} +2392.04 q^{76} +1873.10 q^{77} +1257.10 q^{78} -47719.3 q^{79} +57117.6 q^{81} +36237.7 q^{82} +74799.0 q^{83} +2305.26 q^{84} +38848.0 q^{86} -823.421 q^{87} +2921.78 q^{88} +9799.26 q^{89} -21346.2 q^{91} -47356.1 q^{92} +7800.50 q^{93} -113679. q^{94} +6259.97 q^{96} +138432. q^{97} -3891.52 q^{98} +3564.15 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+5q2+28q343q4+19q6+36q7225q8+212q9376q11857q12+338q13505q14+465q16+2630q17898q18312q19+4074q21226q22+159808q99+O(q100) 2 q + 5 q^{2} + 28 q^{3} - 43 q^{4} + 19 q^{6} + 36 q^{7} - 225 q^{8} + 212 q^{9} - 376 q^{11} - 857 q^{12} + 338 q^{13} - 505 q^{14} + 465 q^{16} + 2630 q^{17} - 898 q^{18} - 312 q^{19} + 4074 q^{21} - 226 q^{22}+ \cdots - 159808 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 4.56155 0.806376 0.403188 0.915117i 0.367902π-0.367902\pi
0.403188 + 0.915117i 0.367902π0.367902\pi
33 1.63068 0.104608 0.0523042 0.998631i 0.483343π-0.483343\pi
0.0523042 + 0.998631i 0.483343π0.483343\pi
44 −11.1922 −0.349757
55 0 0
66 7.43845 0.0843537
77 −126.309 −0.974290 −0.487145 0.873321i 0.661962π-0.661962\pi
−0.487145 + 0.873321i 0.661962π0.661962\pi
88 −197.024 −1.08841
99 −240.341 −0.989057
1010 0 0
1111 −14.8296 −0.0369527 −0.0184764 0.999829i 0.505882π-0.505882\pi
−0.0184764 + 0.999829i 0.505882π0.505882\pi
1212 −18.2510 −0.0365875
1313 169.000 0.277350
1414 −576.164 −0.785644
1515 0 0
1616 −540.582 −0.527912
1717 1051.12 0.882126 0.441063 0.897476i 0.354602π-0.354602\pi
0.441063 + 0.897476i 0.354602π0.354602\pi
1818 −1096.33 −0.797552
1919 −213.723 −0.135821 −0.0679107 0.997691i 0.521633π-0.521633\pi
−0.0679107 + 0.997691i 0.521633π0.521633\pi
2020 0 0
2121 −205.969 −0.101919
2222 −67.6458 −0.0297978
2323 4231.16 1.66778 0.833892 0.551928i 0.186108π-0.186108\pi
0.833892 + 0.551928i 0.186108π0.186108\pi
2424 −321.283 −0.113857
2525 0 0
2626 770.902 0.223649
2727 −788.176 −0.208072
2828 1413.68 0.340765
2929 −504.955 −0.111495 −0.0557477 0.998445i 0.517754π-0.517754\pi
−0.0557477 + 0.998445i 0.517754π0.517754\pi
3030 0 0
3131 4783.58 0.894022 0.447011 0.894528i 0.352488π-0.352488\pi
0.447011 + 0.894528i 0.352488π0.352488\pi
3232 3838.86 0.662716
3333 −24.1823 −0.00386557
3434 4794.75 0.711325
3535 0 0
3636 2689.95 0.345930
3737 4635.74 0.556692 0.278346 0.960481i 0.410214π-0.410214\pi
0.278346 + 0.960481i 0.410214π0.410214\pi
3838 −974.911 −0.109523
3939 275.585 0.0290131
4040 0 0
4141 7944.15 0.738054 0.369027 0.929419i 0.379691π-0.379691\pi
0.369027 + 0.929419i 0.379691π0.379691\pi
4242 −939.541 −0.0821850
4343 8516.41 0.702401 0.351201 0.936300i 0.385774π-0.385774\pi
0.351201 + 0.936300i 0.385774π0.385774\pi
4444 165.976 0.0129245
4545 0 0
4646 19300.7 1.34486
4747 −24921.2 −1.64560 −0.822801 0.568330i 0.807590π-0.807590\pi
−0.822801 + 0.568330i 0.807590π0.807590\pi
4848 −881.518 −0.0552241
4949 −853.113 −0.0507594
5050 0 0
5151 1714.05 0.0922777
5252 −1891.49 −0.0970052
5353 7808.46 0.381835 0.190917 0.981606i 0.438854π-0.438854\pi
0.190917 + 0.981606i 0.438854π0.438854\pi
5454 −3595.31 −0.167784
5555 0 0
5656 24885.8 1.06043
5757 −348.515 −0.0142081
5858 −2303.38 −0.0899073
5959 −37337.5 −1.39642 −0.698209 0.715894i 0.746020π-0.746020\pi
−0.698209 + 0.715894i 0.746020π0.746020\pi
6060 0 0
6161 −18172.2 −0.625292 −0.312646 0.949870i 0.601215π-0.601215\pi
−0.312646 + 0.949870i 0.601215π0.601215\pi
6262 21820.5 0.720918
6363 30357.1 0.963628
6464 34809.8 1.06231
6565 0 0
6666 −110.309 −0.00311710
6767 34559.9 0.940559 0.470279 0.882518i 0.344153π-0.344153\pi
0.470279 + 0.882518i 0.344153π0.344153\pi
6868 −11764.4 −0.308530
6969 6899.68 0.174464
7070 0 0
7171 41255.7 0.971265 0.485632 0.874163i 0.338589π-0.338589\pi
0.485632 + 0.874163i 0.338589π0.338589\pi
7272 47352.8 1.07650
7373 1056.42 0.0232022 0.0116011 0.999933i 0.496307π-0.496307\pi
0.0116011 + 0.999933i 0.496307π0.496307\pi
7474 21146.2 0.448903
7575 0 0
7676 2392.04 0.0475045
7777 1873.10 0.0360027
7878 1257.10 0.0233955
7979 −47719.3 −0.860253 −0.430126 0.902769i 0.641531π-0.641531\pi
−0.430126 + 0.902769i 0.641531π0.641531\pi
8080 0 0
8181 57117.6 0.967291
8282 36237.7 0.595149
8383 74799.0 1.19179 0.595896 0.803061i 0.296797π-0.296797\pi
0.595896 + 0.803061i 0.296797π0.296797\pi
8484 2305.26 0.0356469
8585 0 0
8686 38848.0 0.566400
8787 −823.421 −0.0116634
8888 2921.78 0.0402198
8989 9799.26 0.131135 0.0655675 0.997848i 0.479114π-0.479114\pi
0.0655675 + 0.997848i 0.479114π0.479114\pi
9090 0 0
9191 −21346.2 −0.270219
9292 −47356.1 −0.583320
9393 7800.50 0.0935222
9494 −113679. −1.32697
9595 0 0
9696 6259.97 0.0693257
9797 138432. 1.49385 0.746927 0.664906i 0.231528π-0.231528\pi
0.746927 + 0.664906i 0.231528π0.231528\pi
9898 −3891.52 −0.0409312
9999 3564.15 0.0365484
100100 0 0
101101 139151. 1.35733 0.678663 0.734450i 0.262560π-0.262560\pi
0.678663 + 0.734450i 0.262560π0.262560\pi
102102 7818.71 0.0744106
103103 −98512.2 −0.914950 −0.457475 0.889223i 0.651246π-0.651246\pi
−0.457475 + 0.889223i 0.651246π0.651246\pi
104104 −33297.0 −0.301871
105105 0 0
106106 35618.7 0.307902
107107 26848.4 0.226704 0.113352 0.993555i 0.463841π-0.463841\pi
0.113352 + 0.993555i 0.463841π0.463841\pi
108108 8821.45 0.0727747
109109 −63220.9 −0.509676 −0.254838 0.966984i 0.582022π-0.582022\pi
−0.254838 + 0.966984i 0.582022π0.582022\pi
110110 0 0
111111 7559.43 0.0582346
112112 68280.2 0.514340
113113 −114434. −0.843058 −0.421529 0.906815i 0.638506π-0.638506\pi
−0.421529 + 0.906815i 0.638506π0.638506\pi
114114 −1589.77 −0.0114570
115115 0 0
116116 5651.57 0.0389964
117117 −40617.6 −0.274315
118118 −170317. −1.12604
119119 −132766. −0.859446
120120 0 0
121121 −160831. −0.998634
122122 −82893.4 −0.504221
123123 12954.4 0.0772066
124124 −53538.9 −0.312691
125125 0 0
126126 138476. 0.777047
127127 248871. 1.36919 0.684596 0.728922i 0.259978π-0.259978\pi
0.684596 + 0.728922i 0.259978π0.259978\pi
128128 35943.2 0.193906
129129 13887.6 0.0734770
130130 0 0
131131 102963. 0.524205 0.262102 0.965040i 0.415584π-0.415584\pi
0.262102 + 0.965040i 0.415584π0.415584\pi
132132 270.654 0.00135201
133133 26995.1 0.132329
134134 157647. 0.758444
135135 0 0
136136 −207096. −0.960117
137137 36037.4 0.164041 0.0820204 0.996631i 0.473863π-0.473863\pi
0.0820204 + 0.996631i 0.473863π0.473863\pi
138138 31473.3 0.140684
139139 152655. 0.670151 0.335076 0.942191i 0.391238π-0.391238\pi
0.335076 + 0.942191i 0.391238π0.391238\pi
140140 0 0
141141 −40638.6 −0.172144
142142 188190. 0.783205
143143 −2506.20 −0.0102488
144144 129924. 0.522136
145145 0 0
146146 4818.92 0.0187097
147147 −1391.16 −0.00530986
148148 −51884.3 −0.194707
149149 72547.1 0.267704 0.133852 0.991001i 0.457265π-0.457265\pi
0.133852 + 0.991001i 0.457265π0.457265\pi
150150 0 0
151151 489021. 1.74536 0.872681 0.488291i 0.162379π-0.162379\pi
0.872681 + 0.488291i 0.162379π0.162379\pi
152152 42108.6 0.147830
153153 −252627. −0.872473
154154 8544.26 0.0290317
155155 0 0
156156 −3084.42 −0.0101476
157157 −89467.9 −0.289680 −0.144840 0.989455i 0.546267π-0.546267\pi
−0.144840 + 0.989455i 0.546267π0.546267\pi
158158 −217674. −0.693687
159159 12733.1 0.0399431
160160 0 0
161161 −534432. −1.62490
162162 260545. 0.780000
163163 225668. 0.665275 0.332637 0.943055i 0.392061π-0.392061\pi
0.332637 + 0.943055i 0.392061π0.392061\pi
164164 −88912.8 −0.258140
165165 0 0
166166 341200. 0.961033
167167 −209528. −0.581367 −0.290683 0.956819i 0.593883π-0.593883\pi
−0.290683 + 0.956819i 0.593883π0.593883\pi
168168 40580.9 0.110930
169169 28561.0 0.0769231
170170 0 0
171171 51366.5 0.134335
172172 −95317.6 −0.245670
173173 465184. 1.18171 0.590853 0.806779i 0.298791π-0.298791\pi
0.590853 + 0.806779i 0.298791π0.298791\pi
174174 −3756.08 −0.00940506
175175 0 0
176176 8016.60 0.0195078
177177 −60885.7 −0.146077
178178 44699.9 0.105744
179179 −472573. −1.10239 −0.551197 0.834375i 0.685829π-0.685829\pi
−0.551197 + 0.834375i 0.685829π0.685829\pi
180180 0 0
181181 −74099.4 −0.168120 −0.0840598 0.996461i 0.526789π-0.526789\pi
−0.0840598 + 0.996461i 0.526789π0.526789\pi
182182 −97371.7 −0.217898
183183 −29633.1 −0.0654108
184184 −833638. −1.81524
185185 0 0
186186 35582.4 0.0754141
187187 −15587.7 −0.0325970
188188 278924. 0.575561
189189 99553.5 0.202722
190190 0 0
191191 −224128. −0.444543 −0.222271 0.974985i 0.571347π-0.571347\pi
−0.222271 + 0.974985i 0.571347π0.571347\pi
192192 56763.8 0.111127
193193 662265. 1.27979 0.639895 0.768463i 0.278978π-0.278978\pi
0.639895 + 0.768463i 0.278978π0.278978\pi
194194 631467. 1.20461
195195 0 0
196196 9548.24 0.0177535
197197 −666464. −1.22352 −0.611760 0.791043i 0.709538π-0.709538\pi
−0.611760 + 0.791043i 0.709538π0.709538\pi
198198 16258.1 0.0294717
199199 645720. 1.15588 0.577938 0.816081i 0.303858π-0.303858\pi
0.577938 + 0.816081i 0.303858π0.303858\pi
200200 0 0
201201 56356.3 0.0983903
202202 634746. 1.09451
203203 63780.1 0.108629
204204 −19184.0 −0.0322748
205205 0 0
206206 −449369. −0.737794
207207 −1.01692e6 −1.64953
208208 −91358.4 −0.146417
209209 3169.43 0.00501897
210210 0 0
211211 −868021. −1.34222 −0.671110 0.741357i 0.734182π-0.734182\pi
−0.671110 + 0.741357i 0.734182π0.734182\pi
212212 −87394.1 −0.133550
213213 67274.9 0.101602
214214 122470. 0.182808
215215 0 0
216216 155289. 0.226468
217217 −604207. −0.871037
218218 −288385. −0.410991
219219 1722.69 0.00242715
220220 0 0
221221 177639. 0.244658
222222 34482.7 0.0469590
223223 58342.9 0.0785644 0.0392822 0.999228i 0.487493π-0.487493\pi
0.0392822 + 0.999228i 0.487493π0.487493\pi
224224 −484882. −0.645678
225225 0 0
226226 −521995. −0.679822
227227 −111768. −0.143964 −0.0719820 0.997406i 0.522932π-0.522932\pi
−0.0719820 + 0.997406i 0.522932π0.522932\pi
228228 3900.67 0.00496937
229229 1.14984e6 1.44893 0.724467 0.689309i 0.242086π-0.242086\pi
0.724467 + 0.689309i 0.242086π0.242086\pi
230230 0 0
231231 3054.44 0.00376618
232232 99488.0 0.121353
233233 −630470. −0.760807 −0.380404 0.924821i 0.624215π-0.624215\pi
−0.380404 + 0.924821i 0.624215π0.624215\pi
234234 −185279. −0.221201
235235 0 0
236236 417891. 0.488408
237237 −77815.0 −0.0899897
238238 −605618. −0.693037
239239 −165628. −0.187559 −0.0937797 0.995593i 0.529895π-0.529895\pi
−0.0937797 + 0.995593i 0.529895π0.529895\pi
240240 0 0
241241 690968. 0.766329 0.383165 0.923680i 0.374834π-0.374834\pi
0.383165 + 0.923680i 0.374834π0.374834\pi
242242 −733639. −0.805275
243243 284667. 0.309259
244244 203387. 0.218700
245245 0 0
246246 59092.1 0.0622575
247247 −36119.3 −0.0376701
248248 −942478. −0.973065
249249 121974. 0.124671
250250 0 0
251251 −386887. −0.387615 −0.193807 0.981040i 0.562084π-0.562084\pi
−0.193807 + 0.981040i 0.562084π0.562084\pi
252252 −339764. −0.337036
253253 −62746.2 −0.0616292
254254 1.13524e6 1.10408
255255 0 0
256256 −949957. −0.905950
257257 −258260. −0.243907 −0.121953 0.992536i 0.538916π-0.538916\pi
−0.121953 + 0.992536i 0.538916π0.538916\pi
258258 63348.8 0.0592501
259259 −585535. −0.542379
260260 0 0
261261 121361. 0.110275
262262 469669. 0.422706
263263 1.19053e6 1.06133 0.530665 0.847582i 0.321942π-0.321942\pi
0.530665 + 0.847582i 0.321942π0.321942\pi
264264 4764.49 0.00420733
265265 0 0
266266 123140. 0.106707
267267 15979.5 0.0137178
268268 −386803. −0.328967
269269 850968. 0.717022 0.358511 0.933525i 0.383285π-0.383285\pi
0.358511 + 0.933525i 0.383285π0.383285\pi
270270 0 0
271271 −40926.1 −0.0338514 −0.0169257 0.999857i 0.505388π-0.505388\pi
−0.0169257 + 0.999857i 0.505388π0.505388\pi
272272 −568218. −0.465685
273273 −34808.8 −0.0282672
274274 164387. 0.132279
275275 0 0
276276 −77222.8 −0.0610201
277277 −1.00054e6 −0.783490 −0.391745 0.920074i 0.628128π-0.628128\pi
−0.391745 + 0.920074i 0.628128π0.628128\pi
278278 696342. 0.540394
279279 −1.14969e6 −0.884239
280280 0 0
281281 −1.73596e6 −1.31151 −0.655757 0.754972i 0.727650π-0.727650\pi
−0.655757 + 0.754972i 0.727650π0.727650\pi
282282 −185375. −0.138813
283283 1.27363e6 0.945319 0.472660 0.881245i 0.343294π-0.343294\pi
0.472660 + 0.881245i 0.343294π0.343294\pi
284284 −461743. −0.339707
285285 0 0
286286 −11432.1 −0.00826443
287287 −1.00342e6 −0.719078
288288 −922636. −0.655464
289289 −315001. −0.221854
290290 0 0
291291 225739. 0.156270
292292 −11823.7 −0.00811515
293293 2043.70 0.00139075 0.000695374 1.00000i 0.499779π-0.499779\pi
0.000695374 1.00000i 0.499779π0.499779\pi
294294 −6345.84 −0.00428174
295295 0 0
296296 −913351. −0.605910
297297 11688.3 0.00768883
298298 330927. 0.215870
299299 715066. 0.462560
300300 0 0
301301 −1.07570e6 −0.684342
302302 2.23070e6 1.40742
303303 226912. 0.141988
304304 115535. 0.0717018
305305 0 0
306306 −1.15237e6 −0.703541
307307 401308. 0.243014 0.121507 0.992591i 0.461227π-0.461227\pi
0.121507 + 0.992591i 0.461227π0.461227\pi
308308 −20964.2 −0.0125922
309309 −160642. −0.0957114
310310 0 0
311311 −1.92628e6 −1.12933 −0.564663 0.825322i 0.690994π-0.690994\pi
−0.564663 + 0.825322i 0.690994π0.690994\pi
312312 −54296.9 −0.0315783
313313 −1.64519e6 −0.949196 −0.474598 0.880203i 0.657407π-0.657407\pi
−0.474598 + 0.880203i 0.657407π0.657407\pi
314314 −408113. −0.233591
315315 0 0
316316 534085. 0.300880
317317 1.99476e6 1.11492 0.557459 0.830205i 0.311777π-0.311777\pi
0.557459 + 0.830205i 0.311777π0.311777\pi
318318 58082.8 0.0322092
319319 7488.26 0.00412006
320320 0 0
321321 43781.2 0.0237151
322322 −2.43784e6 −1.31028
323323 −224649. −0.119812
324324 −639273. −0.338317
325325 0 0
326326 1.02940e6 0.536462
327327 −103093. −0.0533164
328328 −1.56519e6 −0.803306
329329 3.14777e6 1.60329
330330 0 0
331331 −675924. −0.339100 −0.169550 0.985522i 0.554231π-0.554231\pi
−0.169550 + 0.985522i 0.554231π0.554231\pi
332332 −837168. −0.416838
333333 −1.11416e6 −0.550600
334334 −955772. −0.468800
335335 0 0
336336 111343. 0.0538042
337337 2.13552e6 1.02430 0.512152 0.858895i 0.328848π-0.328848\pi
0.512152 + 0.858895i 0.328848π0.328848\pi
338338 130283. 0.0620289
339339 −186605. −0.0881909
340340 0 0
341341 −70938.3 −0.0330366
342342 234311. 0.108325
343343 2.23063e6 1.02374
344344 −1.67793e6 −0.764502
345345 0 0
346346 2.12196e6 0.952899
347347 2.57257e6 1.14695 0.573473 0.819225i 0.305596π-0.305596\pi
0.573473 + 0.819225i 0.305596π0.305596\pi
348348 9215.92 0.00407935
349349 2.02363e6 0.889339 0.444670 0.895695i 0.353321π-0.353321\pi
0.444670 + 0.895695i 0.353321π0.353321\pi
350350 0 0
351351 −133202. −0.0577088
352352 −56928.7 −0.0244892
353353 −2.04810e6 −0.874810 −0.437405 0.899265i 0.644102π-0.644102\pi
−0.437405 + 0.899265i 0.644102π0.644102\pi
354354 −277733. −0.117793
355355 0 0
356356 −109676. −0.0458654
357357 −216499. −0.0899053
358358 −2.15567e6 −0.888944
359359 −1.59901e6 −0.654808 −0.327404 0.944885i 0.606174π-0.606174\pi
−0.327404 + 0.944885i 0.606174π0.606174\pi
360360 0 0
361361 −2.43042e6 −0.981553
362362 −338008. −0.135568
363363 −262265. −0.104466
364364 238911. 0.0945112
365365 0 0
366366 −135173. −0.0527457
367367 3.86389e6 1.49747 0.748737 0.662867i 0.230661π-0.230661\pi
0.748737 + 0.662867i 0.230661π0.230661\pi
368368 −2.28729e6 −0.880444
369369 −1.90930e6 −0.729977
370370 0 0
371371 −986276. −0.372018
372372 −87305.0 −0.0327101
373373 1.56702e6 0.583179 0.291589 0.956544i 0.405816π-0.405816\pi
0.291589 + 0.956544i 0.405816π0.405816\pi
374374 −71104.0 −0.0262854
375375 0 0
376376 4.91007e6 1.79109
377377 −85337.3 −0.0309233
378378 454118. 0.163471
379379 3.19239e6 1.14161 0.570805 0.821086i 0.306631π-0.306631\pi
0.570805 + 0.821086i 0.306631π0.306631\pi
380380 0 0
381381 405829. 0.143229
382382 −1.02237e6 −0.358469
383383 −400432. −0.139486 −0.0697432 0.997565i 0.522218π-0.522218\pi
−0.0697432 + 0.997565i 0.522218π0.522218\pi
384384 58611.9 0.0202842
385385 0 0
386386 3.02096e6 1.03199
387387 −2.04684e6 −0.694715
388388 −1.54937e6 −0.522487
389389 413440. 0.138528 0.0692642 0.997598i 0.477935π-0.477935\pi
0.0692642 + 0.997598i 0.477935π0.477935\pi
390390 0 0
391391 4.44746e6 1.47120
392392 168083. 0.0552471
393393 167899. 0.0548362
394394 −3.04011e6 −0.986618
395395 0 0
396396 −39890.8 −0.0127831
397397 102926. 0.0327753 0.0163877 0.999866i 0.494783π-0.494783\pi
0.0163877 + 0.999866i 0.494783π0.494783\pi
398398 2.94548e6 0.932071
399399 44020.5 0.0138428
400400 0 0
401401 2.23365e6 0.693671 0.346836 0.937926i 0.387256π-0.387256\pi
0.346836 + 0.937926i 0.387256π0.387256\pi
402402 257072. 0.0793396
403403 808424. 0.247957
404404 −1.55741e6 −0.474734
405405 0 0
406406 290937. 0.0875958
407407 −68746.0 −0.0205713
408408 −337708. −0.100436
409409 −4.46150e6 −1.31878 −0.659390 0.751801i 0.729185π-0.729185\pi
−0.659390 + 0.751801i 0.729185π0.729185\pi
410410 0 0
411411 58765.6 0.0171600
412412 1.10257e6 0.320010
413413 4.71606e6 1.36052
414414 −4.63874e6 −1.33014
415415 0 0
416416 648768. 0.183804
417417 248931. 0.0701034
418418 14457.5 0.00404718
419419 4.22792e6 1.17650 0.588250 0.808679i 0.299817π-0.299817\pi
0.588250 + 0.808679i 0.299817π0.299817\pi
420420 0 0
421421 4.11791e6 1.13233 0.566163 0.824293i 0.308427π-0.308427\pi
0.566163 + 0.824293i 0.308427π0.308427\pi
422422 −3.95952e6 −1.08233
423423 5.98959e6 1.62759
424424 −1.53845e6 −0.415594
425425 0 0
426426 306878. 0.0819298
427427 2.29531e6 0.609216
428428 −300493. −0.0792912
429429 −4086.81 −0.00107212
430430 0 0
431431 1.15324e6 0.299038 0.149519 0.988759i 0.452227π-0.452227\pi
0.149519 + 0.988759i 0.452227π0.452227\pi
432432 426074. 0.109844
433433 33734.3 0.00864673 0.00432337 0.999991i 0.498624π-0.498624\pi
0.00432337 + 0.999991i 0.498624π0.498624\pi
434434 −2.75612e6 −0.702383
435435 0 0
436436 707583. 0.178263
437437 −904298. −0.226521
438438 7858.13 0.00195719
439439 7.48363e6 1.85332 0.926661 0.375898i 0.122666π-0.122666\pi
0.926661 + 0.375898i 0.122666π0.122666\pi
440440 0 0
441441 205038. 0.0502039
442442 810312. 0.197286
443443 3.28028e6 0.794148 0.397074 0.917786i 0.370026π-0.370026\pi
0.397074 + 0.917786i 0.370026π0.370026\pi
444444 −84606.9 −0.0203680
445445 0 0
446446 266134. 0.0633525
447447 118301. 0.0280040
448448 −4.39678e6 −1.03500
449449 7.95356e6 1.86185 0.930927 0.365205i 0.119001π-0.119001\pi
0.930927 + 0.365205i 0.119001π0.119001\pi
450450 0 0
451451 −117808. −0.0272731
452452 1.28077e6 0.294866
453453 797439. 0.182579
454454 −509837. −0.116089
455455 0 0
456456 68665.8 0.0154642
457457 3.35187e6 0.750753 0.375377 0.926872i 0.377513π-0.377513\pi
0.375377 + 0.926872i 0.377513π0.377513\pi
458458 5.24506e6 1.16839
459459 −828468. −0.183546
460460 0 0
461461 4.68627e6 1.02701 0.513505 0.858086i 0.328347π-0.328347\pi
0.513505 + 0.858086i 0.328347π0.328347\pi
462462 13933.0 0.00303696
463463 −6.64697e6 −1.44102 −0.720512 0.693442i 0.756093π-0.756093\pi
−0.720512 + 0.693442i 0.756093π0.756093\pi
464464 272969. 0.0588599
465465 0 0
466466 −2.87592e6 −0.613497
467467 3.14141e6 0.666549 0.333275 0.942830i 0.391846π-0.391846\pi
0.333275 + 0.942830i 0.391846π0.391846\pi
468468 454602. 0.0959437
469469 −4.36522e6 −0.916377
470470 0 0
471471 −145894. −0.0303029
472472 7.35638e6 1.51988
473473 −126295. −0.0259556
474474 −354957. −0.0725655
475475 0 0
476476 1.48595e6 0.300598
477477 −1.87669e6 −0.377656
478478 −755521. −0.151243
479479 −6.68286e6 −1.33083 −0.665416 0.746473i 0.731746π-0.731746\pi
−0.665416 + 0.746473i 0.731746π0.731746\pi
480480 0 0
481481 783441. 0.154399
482482 3.15189e6 0.617950
483483 −871489. −0.169979
484484 1.80006e6 0.349280
485485 0 0
486486 1.29853e6 0.249379
487487 4.06478e6 0.776631 0.388316 0.921526i 0.373057π-0.373057\pi
0.388316 + 0.921526i 0.373057π0.373057\pi
488488 3.58035e6 0.680575
489489 367993. 0.0695933
490490 0 0
491491 −2.10434e6 −0.393923 −0.196962 0.980411i 0.563107π-0.563107\pi
−0.196962 + 0.980411i 0.563107π0.563107\pi
492492 −144989. −0.0270036
493493 −530768. −0.0983530
494494 −164760. −0.0303763
495495 0 0
496496 −2.58592e6 −0.471966
497497 −5.21095e6 −0.946293
498498 556389. 0.100532
499499 5.96715e6 1.07279 0.536396 0.843966i 0.319785π-0.319785\pi
0.536396 + 0.843966i 0.319785π0.319785\pi
500500 0 0
501501 −341673. −0.0608158
502502 −1.76481e6 −0.312563
503503 1.00144e7 1.76483 0.882417 0.470467i 0.155915π-0.155915\pi
0.882417 + 0.470467i 0.155915π0.155915\pi
504504 −5.98108e6 −1.04882
505505 0 0
506506 −286220. −0.0496963
507507 46573.9 0.00804680
508508 −2.78542e6 −0.478885
509509 −8.47321e6 −1.44962 −0.724809 0.688950i 0.758072π-0.758072\pi
−0.724809 + 0.688950i 0.758072π0.758072\pi
510510 0 0
511511 −133435. −0.0226057
512512 −5.48346e6 −0.924442
513513 168452. 0.0282606
514514 −1.17807e6 −0.196681
515515 0 0
516516 −155433. −0.0256991
517517 369571. 0.0608095
518518 −2.67095e6 −0.437362
519519 758567. 0.123616
520520 0 0
521521 −197614. −0.0318951 −0.0159476 0.999873i 0.505076π-0.505076\pi
−0.0159476 + 0.999873i 0.505076π0.505076\pi
522522 553596. 0.0889235
523523 −8.27263e6 −1.32248 −0.661240 0.750174i 0.729970π-0.729970\pi
−0.661240 + 0.750174i 0.729970π0.729970\pi
524524 −1.15238e6 −0.183345
525525 0 0
526526 5.43066e6 0.855831
527527 5.02812e6 0.788640
528528 13072.5 0.00204068
529529 1.14664e7 1.78150
530530 0 0
531531 8.97374e6 1.38114
532532 −302136. −0.0462832
533533 1.34256e6 0.204699
534534 72891.3 0.0110617
535535 0 0
536536 −6.80913e6 −1.02372
537537 −770618. −0.115320
538538 3.88174e6 0.578190
539539 12651.3 0.00187570
540540 0 0
541541 363216. 0.0533546 0.0266773 0.999644i 0.491507π-0.491507\pi
0.0266773 + 0.999644i 0.491507π0.491507\pi
542542 −186686. −0.0272970
543543 −120833. −0.0175867
544544 4.03511e6 0.584599
545545 0 0
546546 −158782. −0.0227940
547547 620452. 0.0886624 0.0443312 0.999017i 0.485884π-0.485884\pi
0.0443312 + 0.999017i 0.485884π0.485884\pi
548548 −403339. −0.0573745
549549 4.36752e6 0.618449
550550 0 0
551551 107921. 0.0151435
552552 −1.35940e6 −0.189889
553553 6.02736e6 0.838136
554554 −4.56400e6 −0.631788
555555 0 0
556556 −1.70855e6 −0.234390
557557 −3.89737e6 −0.532272 −0.266136 0.963935i 0.585747π-0.585747\pi
−0.266136 + 0.963935i 0.585747π0.585747\pi
558558 −5.24437e6 −0.713029
559559 1.43927e6 0.194811
560560 0 0
561561 −25418.5 −0.00340992
562562 −7.91865e6 −1.05757
563563 −510725. −0.0679073 −0.0339536 0.999423i 0.510810π-0.510810\pi
−0.0339536 + 0.999423i 0.510810π0.510810\pi
564564 454837. 0.0602085
565565 0 0
566566 5.80975e6 0.762283
567567 −7.21445e6 −0.942422
568568 −8.12834e6 −1.05714
569569 9.75625e6 1.26329 0.631644 0.775259i 0.282381π-0.282381\pi
0.631644 + 0.775259i 0.282381π0.282381\pi
570570 0 0
571571 −1.41952e7 −1.82201 −0.911006 0.412393i 0.864693π-0.864693\pi
−0.911006 + 0.412393i 0.864693π0.864693\pi
572572 28049.9 0.00358461
573573 −365482. −0.0465029
574574 −4.57713e6 −0.579847
575575 0 0
576576 −8.36622e6 −1.05069
577577 1.16423e6 0.145579 0.0727896 0.997347i 0.476810π-0.476810\pi
0.0727896 + 0.997347i 0.476810π0.476810\pi
578578 −1.43689e6 −0.178898
579579 1.07994e6 0.133877
580580 0 0
581581 −9.44777e6 −1.16115
582582 1.02972e6 0.126012
583583 −115796. −0.0141098
584584 −208140. −0.0252536
585585 0 0
586586 9322.45 0.00112147
587587 −6.58038e6 −0.788234 −0.394117 0.919060i 0.628950π-0.628950\pi
−0.394117 + 0.919060i 0.628950π0.628950\pi
588588 15570.2 0.00185716
589589 −1.02236e6 −0.121427
590590 0 0
591591 −1.08679e6 −0.127991
592592 −2.50600e6 −0.293885
593593 1.91423e6 0.223541 0.111771 0.993734i 0.464348π-0.464348\pi
0.111771 + 0.993734i 0.464348π0.464348\pi
594594 53316.8 0.00620009
595595 0 0
596596 −811964. −0.0936313
597597 1.05296e6 0.120914
598598 3.26181e6 0.372997
599599 −2.33678e6 −0.266104 −0.133052 0.991109i 0.542478π-0.542478\pi
−0.133052 + 0.991109i 0.542478π0.542478\pi
600600 0 0
601601 1.04273e7 1.17757 0.588786 0.808289i 0.299606π-0.299606\pi
0.588786 + 0.808289i 0.299606π0.299606\pi
602602 −4.90684e6 −0.551837
603603 −8.30617e6 −0.930266
604604 −5.47324e6 −0.610453
605605 0 0
606606 1.03507e6 0.114495
607607 120274. 0.0132495 0.00662474 0.999978i 0.497891π-0.497891\pi
0.00662474 + 0.999978i 0.497891π0.497891\pi
608608 −820455. −0.0900111
609609 104005. 0.0113635
610610 0 0
611611 −4.21169e6 −0.456408
612612 2.82747e6 0.305154
613613 −1.34576e7 −1.44649 −0.723245 0.690592i 0.757350π-0.757350\pi
−0.723245 + 0.690592i 0.757350π0.757350\pi
614614 1.83059e6 0.195961
615615 0 0
616616 −369046. −0.0391858
617617 6.84879e6 0.724270 0.362135 0.932126i 0.382048π-0.382048\pi
0.362135 + 0.932126i 0.382048π0.382048\pi
618618 −732778. −0.0771794
619619 −5.40663e6 −0.567153 −0.283577 0.958950i 0.591521π-0.591521\pi
−0.283577 + 0.958950i 0.591521π0.591521\pi
620620 0 0
621621 −3.33490e6 −0.347019
622622 −8.78684e6 −0.910661
623623 −1.23773e6 −0.127763
624624 −148977. −0.0153164
625625 0 0
626626 −7.50463e6 −0.765409
627627 5168.33 0.000525027 0
628628 1.00135e6 0.101318
629629 4.87273e6 0.491072
630630 0 0
631631 −9.62552e6 −0.962390 −0.481195 0.876614i 0.659797π-0.659797\pi
−0.481195 + 0.876614i 0.659797π0.659797\pi
632632 9.40183e6 0.936310
633633 −1.41547e6 −0.140408
634634 9.09920e6 0.899043
635635 0 0
636636 −142512. −0.0139704
637637 −144176. −0.0140781
638638 34158.1 0.00332232
639639 −9.91542e6 −0.960636
640640 0 0
641641 −1.58752e7 −1.52607 −0.763037 0.646355i 0.776293π-0.776293\pi
−0.763037 + 0.646355i 0.776293π0.776293\pi
642642 199710. 0.0191233
643643 −1.57235e7 −1.49976 −0.749880 0.661574i 0.769889π-0.769889\pi
−0.749880 + 0.661574i 0.769889π0.769889\pi
644644 5.98149e6 0.568322
645645 0 0
646646 −1.02475e6 −0.0966132
647647 1.58173e7 1.48549 0.742747 0.669572i 0.233523π-0.233523\pi
0.742747 + 0.669572i 0.233523π0.233523\pi
648648 −1.12535e7 −1.05281
649649 553699. 0.0516015
650650 0 0
651651 −985270. −0.0911178
652652 −2.52573e6 −0.232685
653653 −5.31229e6 −0.487527 −0.243763 0.969835i 0.578382π-0.578382\pi
−0.243763 + 0.969835i 0.578382π0.578382\pi
654654 −470265. −0.0429931
655655 0 0
656656 −4.29447e6 −0.389628
657657 −253901. −0.0229483
658658 1.43587e7 1.29286
659659 9.90554e6 0.888514 0.444257 0.895899i 0.353468π-0.353468\pi
0.444257 + 0.895899i 0.353468π0.353468\pi
660660 0 0
661661 −1.29988e7 −1.15717 −0.578587 0.815621i 0.696396π-0.696396\pi
−0.578587 + 0.815621i 0.696396π0.696396\pi
662662 −3.08326e6 −0.273442
663663 289674. 0.0255932
664664 −1.47372e7 −1.29716
665665 0 0
666666 −5.08229e6 −0.443991
667667 −2.13654e6 −0.185950
668668 2.34508e6 0.203337
669669 95138.8 0.00821850
670670 0 0
671671 269486. 0.0231062
672672 −790688. −0.0675433
673673 1.32503e7 1.12769 0.563844 0.825881i 0.309322π-0.309322\pi
0.563844 + 0.825881i 0.309322π0.309322\pi
674674 9.74129e6 0.825975
675675 0 0
676676 −319661. −0.0269044
677677 −2.23310e7 −1.87257 −0.936284 0.351245i 0.885758π-0.885758\pi
−0.936284 + 0.351245i 0.885758π0.885758\pi
678678 −851208. −0.0711151
679679 −1.74852e7 −1.45545
680680 0 0
681681 −182259. −0.0150598
682682 −323589. −0.0266399
683683 1.40049e7 1.14876 0.574380 0.818588i 0.305243π-0.305243\pi
0.574380 + 0.818588i 0.305243π0.305243\pi
684684 −574906. −0.0469847
685685 0 0
686686 1.01751e7 0.825523
687687 1.87502e6 0.151571
688688 −4.60382e6 −0.370806
689689 1.31963e6 0.105902
690690 0 0
691691 −5.24817e6 −0.418132 −0.209066 0.977902i 0.567042π-0.567042\pi
−0.209066 + 0.977902i 0.567042π0.567042\pi
692692 −5.20645e6 −0.413310
693693 −450183. −0.0356087
694694 1.17349e7 0.924870
695695 0 0
696696 162233. 0.0126945
697697 8.35027e6 0.651056
698698 9.23090e6 0.717142
699699 −1.02810e6 −0.0795868
700700 0 0
701701 −2.13994e7 −1.64477 −0.822386 0.568930i 0.807358π-0.807358\pi
−0.822386 + 0.568930i 0.807358π0.807358\pi
702702 −607607. −0.0465350
703703 −990767. −0.0756107
704704 −516214. −0.0392553
705705 0 0
706706 −9.34250e6 −0.705426
707707 −1.75760e7 −1.32243
708708 681447. 0.0510915
709709 4.35333e6 0.325242 0.162621 0.986689i 0.448005π-0.448005\pi
0.162621 + 0.986689i 0.448005π0.448005\pi
710710 0 0
711711 1.14689e7 0.850839
712712 −1.93069e6 −0.142729
713713 2.02401e7 1.49104
714714 −987571. −0.0724975
715715 0 0
716716 5.28915e6 0.385570
717717 −270087. −0.0196203
718718 −7.29395e6 −0.528021
719719 2.21389e7 1.59710 0.798552 0.601926i 0.205600π-0.205600\pi
0.798552 + 0.601926i 0.205600π0.205600\pi
720720 0 0
721721 1.24430e7 0.891426
722722 −1.10865e7 −0.791501
723723 1.12675e6 0.0801645
724724 829338. 0.0588010
725725 0 0
726726 −1.19633e6 −0.0842385
727727 4.83218e6 0.339084 0.169542 0.985523i 0.445771π-0.445771\pi
0.169542 + 0.985523i 0.445771π0.445771\pi
728728 4.20570e6 0.294110
729729 −1.34154e7 −0.934940
730730 0 0
731731 8.95178e6 0.619606
732732 331661. 0.0228779
733733 2.47827e7 1.70368 0.851840 0.523803i 0.175487π-0.175487\pi
0.851840 + 0.523803i 0.175487π0.175487\pi
734734 1.76253e7 1.20753
735735 0 0
736736 1.62428e7 1.10527
737737 −512509. −0.0347562
738738 −8.70939e6 −0.588636
739739 7.09289e6 0.477762 0.238881 0.971049i 0.423219π-0.423219\pi
0.238881 + 0.971049i 0.423219π0.423219\pi
740740 0 0
741741 −58899.1 −0.00394061
742742 −4.49895e6 −0.299986
743743 −1.95117e7 −1.29665 −0.648327 0.761362i 0.724531π-0.724531\pi
−0.648327 + 0.761362i 0.724531π0.724531\pi
744744 −1.53688e6 −0.101791
745745 0 0
746746 7.14803e6 0.470262
747747 −1.79773e7 −1.17875
748748 174461. 0.0114010
749749 −3.39118e6 −0.220875
750750 0 0
751751 1.66103e7 1.07468 0.537339 0.843366i 0.319430π-0.319430\pi
0.537339 + 0.843366i 0.319430π0.319430\pi
752752 1.34720e7 0.868733
753753 −630891. −0.0405477
754754 −389271. −0.0249358
755755 0 0
756756 −1.11423e6 −0.0709037
757757 −1.22902e6 −0.0779508 −0.0389754 0.999240i 0.512409π-0.512409\pi
−0.0389754 + 0.999240i 0.512409π0.512409\pi
758758 1.45622e7 0.920567
759759 −102319. −0.00644693
760760 0 0
761761 1.37482e7 0.860569 0.430284 0.902693i 0.358413π-0.358413\pi
0.430284 + 0.902693i 0.358413π0.358413\pi
762762 1.85121e6 0.115496
763763 7.98535e6 0.496572
764764 2.50850e6 0.155482
765765 0 0
766766 −1.82659e6 −0.112478
767767 −6.31004e6 −0.387297
768768 −1.54908e6 −0.0947699
769769 −1.01549e7 −0.619240 −0.309620 0.950860i 0.600202π-0.600202\pi
−0.309620 + 0.950860i 0.600202π0.600202\pi
770770 0 0
771771 −421140. −0.0255147
772772 −7.41222e6 −0.447616
773773 −1.41511e7 −0.851807 −0.425903 0.904769i 0.640044π-0.640044\pi
−0.425903 + 0.904769i 0.640044π0.640044\pi
774774 −9.33677e6 −0.560202
775775 0 0
776776 −2.72745e7 −1.62593
777777 −954821. −0.0567374
778778 1.88593e6 0.111706
779779 −1.69785e6 −0.100243
780780 0 0
781781 −611803. −0.0358909
782782 2.02873e7 1.18634
783783 397993. 0.0231991
784784 461178. 0.0267965
785785 0 0
786786 765882. 0.0442186
787787 1.03095e6 0.0593338 0.0296669 0.999560i 0.490555π-0.490555\pi
0.0296669 + 0.999560i 0.490555π0.490555\pi
788788 7.45923e6 0.427935
789789 1.94137e6 0.111024
790790 0 0
791791 1.44540e7 0.821383
792792 −702222. −0.0397797
793793 −3.07110e6 −0.173425
794794 469500. 0.0264292
795795 0 0
796796 −7.22705e6 −0.404276
797797 1.43337e7 0.799303 0.399651 0.916667i 0.369131π-0.369131\pi
0.399651 + 0.916667i 0.369131π0.369131\pi
798798 200802. 0.0111625
799799 −2.61952e7 −1.45163
800800 0 0
801801 −2.35516e6 −0.129700
802802 1.01889e7 0.559360
803803 −15666.3 −0.000857386 0
804804 −630753. −0.0344127
805805 0 0
806806 3.68767e6 0.199947
807807 1.38766e6 0.0750065
808808 −2.74161e7 −1.47733
809809 1.55020e7 0.832751 0.416376 0.909193i 0.363300π-0.363300\pi
0.416376 + 0.909193i 0.363300π0.363300\pi
810810 0 0
811811 2.45861e7 1.31261 0.656307 0.754494i 0.272118π-0.272118\pi
0.656307 + 0.754494i 0.272118π0.272118\pi
812812 −713842. −0.0379938
813813 −66737.5 −0.00354114
814814 −313589. −0.0165882
815815 0 0
816816 −926583. −0.0487146
817817 −1.82016e6 −0.0954011
818818 −2.03513e7 −1.06343
819819 5.13036e6 0.267262
820820 0 0
821821 −3.33396e6 −0.172624 −0.0863122 0.996268i 0.527508π-0.527508\pi
−0.0863122 + 0.996268i 0.527508π0.527508\pi
822822 268062. 0.0138375
823823 −3.08787e6 −0.158913 −0.0794564 0.996838i 0.525318π-0.525318\pi
−0.0794564 + 0.996838i 0.525318π0.525318\pi
824824 1.94092e7 0.995842
825825 0 0
826826 2.15125e7 1.09709
827827 −6.89555e6 −0.350595 −0.175297 0.984516i 0.556089π-0.556089\pi
−0.175297 + 0.984516i 0.556089π0.556089\pi
828828 1.13816e7 0.576936
829829 −2.00007e7 −1.01078 −0.505391 0.862890i 0.668652π-0.668652\pi
−0.505391 + 0.862890i 0.668652π0.668652\pi
830830 0 0
831831 −1.63156e6 −0.0819596
832832 5.88286e6 0.294632
833833 −896725. −0.0447762
834834 1.13551e6 0.0565297
835835 0 0
836836 −35473.0 −0.00175542
837837 −3.77030e6 −0.186021
838838 1.92859e7 0.948701
839839 5.23988e6 0.256990 0.128495 0.991710i 0.458985π-0.458985\pi
0.128495 + 0.991710i 0.458985π0.458985\pi
840840 0 0
841841 −2.02562e7 −0.987569
842842 1.87841e7 0.913081
843843 −2.83079e6 −0.137195
844844 9.71509e6 0.469452
845845 0 0
846846 2.73218e7 1.31245
847847 2.03144e7 0.972959
848848 −4.22111e6 −0.201575
849849 2.07689e6 0.0988883
850850 0 0
851851 1.96146e7 0.928442
852852 −752957. −0.0355362
853853 1.32853e7 0.625170 0.312585 0.949890i 0.398805π-0.398805\pi
0.312585 + 0.949890i 0.398805π0.398805\pi
854854 1.04702e7 0.491257
855855 0 0
856856 −5.28976e6 −0.246747
857857 8.34473e6 0.388115 0.194057 0.980990i 0.437835π-0.437835\pi
0.194057 + 0.980990i 0.437835π0.437835\pi
858858 −18642.2 −0.000864528 0
859859 −4.07521e7 −1.88437 −0.942187 0.335088i 0.891234π-0.891234\pi
−0.942187 + 0.335088i 0.891234π0.891234\pi
860860 0 0
861861 −1.63625e6 −0.0752216
862862 5.26056e6 0.241137
863863 1.73853e7 0.794614 0.397307 0.917686i 0.369945π-0.369945\pi
0.397307 + 0.917686i 0.369945π0.369945\pi
864864 −3.02570e6 −0.137893
865865 0 0
866866 153881. 0.00697252
867867 −513667. −0.0232078
868868 6.76243e6 0.304652
869869 707656. 0.0317887
870870 0 0
871871 5.84063e6 0.260864
872872 1.24560e7 0.554738
873873 −3.32710e7 −1.47751
874874 −4.12500e6 −0.182661
875875 0 0
876876 −19280.7 −0.000848912 0
877877 −2.58279e6 −0.113394 −0.0566971 0.998391i 0.518057π-0.518057\pi
−0.0566971 + 0.998391i 0.518057π0.518057\pi
878878 3.41370e7 1.49447
879879 3332.63 0.000145484 0
880880 0 0
881881 −1.66814e7 −0.724090 −0.362045 0.932161i 0.617921π-0.617921\pi
−0.362045 + 0.932161i 0.617921π0.617921\pi
882882 935291. 0.0404833
883883 −2.36384e7 −1.02027 −0.510137 0.860093i 0.670405π-0.670405\pi
−0.510137 + 0.860093i 0.670405π0.670405\pi
884884 −1.98818e6 −0.0855708
885885 0 0
886886 1.49632e7 0.640382
887887 5.25660e6 0.224334 0.112167 0.993689i 0.464221π-0.464221\pi
0.112167 + 0.993689i 0.464221π0.464221\pi
888888 −1.48939e6 −0.0633833
889889 −3.14345e7 −1.33399
890890 0 0
891891 −847029. −0.0357441
892892 −652988. −0.0274785
893893 5.32625e6 0.223508
894894 539638. 0.0225818
895895 0 0
896896 −4.53994e6 −0.188921
897897 1.16605e6 0.0483876
898898 3.62806e7 1.50135
899899 −2.41549e6 −0.0996795
900900 0 0
901901 8.20763e6 0.336826
902902 −537389. −0.0219924
903903 −1.75412e6 −0.0715879
904904 2.25461e7 0.917595
905905 0 0
906906 3.63756e6 0.147228
907907 −3.22789e7 −1.30287 −0.651435 0.758705i 0.725833π-0.725833\pi
−0.651435 + 0.758705i 0.725833π0.725833\pi
908908 1.25094e6 0.0503525
909909 −3.34438e7 −1.34247
910910 0 0
911911 4.20975e7 1.68058 0.840292 0.542134i 0.182383π-0.182383\pi
0.840292 + 0.542134i 0.182383π0.182383\pi
912912 188401. 0.00750061
913913 −1.10924e6 −0.0440400
914914 1.52897e7 0.605389
915915 0 0
916916 −1.28693e7 −0.506775
917917 −1.30051e7 −0.510728
918918 −3.77910e6 −0.148007
919919 −2.19460e7 −0.857168 −0.428584 0.903502i 0.640987π-0.640987\pi
−0.428584 + 0.903502i 0.640987π0.640987\pi
920920 0 0
921921 654407. 0.0254213
922922 2.13767e7 0.828157
923923 6.97221e6 0.269380
924924 −34186.0 −0.00131725
925925 0 0
926926 −3.03205e7 −1.16201
927927 2.36765e7 0.904937
928928 −1.93845e6 −0.0738899
929929 −1.35921e7 −0.516710 −0.258355 0.966050i 0.583180π-0.583180\pi
−0.258355 + 0.966050i 0.583180π0.583180\pi
930930 0 0
931931 182330. 0.00689421
932932 7.05637e6 0.266098
933933 −3.14116e6 −0.118137
934934 1.43297e7 0.537489
935935 0 0
936936 8.00263e6 0.298568
937937 −3.01018e7 −1.12007 −0.560033 0.828470i 0.689212π-0.689212\pi
−0.560033 + 0.828470i 0.689212π0.689212\pi
938938 −1.99122e7 −0.738944
939939 −2.68279e6 −0.0992938
940940 0 0
941941 −1.06275e7 −0.391252 −0.195626 0.980679i 0.562674π-0.562674\pi
−0.195626 + 0.980679i 0.562674π0.562674\pi
942942 −665503. −0.0244356
943943 3.36130e7 1.23091
944944 2.01840e7 0.737187
945945 0 0
946946 −576099. −0.0209300
947947 2.41709e7 0.875826 0.437913 0.899017i 0.355718π-0.355718\pi
0.437913 + 0.899017i 0.355718π0.355718\pi
948948 870924. 0.0314745
949949 178535. 0.00643514
950950 0 0
951951 3.25282e6 0.116630
952952 2.61580e7 0.935432
953953 −4.27043e7 −1.52314 −0.761569 0.648084i 0.775570π-0.775570\pi
−0.761569 + 0.648084i 0.775570π0.775570\pi
954954 −8.56063e6 −0.304533
955955 0 0
956956 1.85375e6 0.0656003
957957 12211.0 0.000430993 0
958958 −3.04842e7 −1.07315
959959 −4.55184e6 −0.159823
960960 0 0
961961 −5.74655e6 −0.200724
962962 3.57371e6 0.124503
963963 −6.45276e6 −0.224223
964964 −7.73348e6 −0.268029
965965 0 0
966966 −3.97535e6 −0.137067
967967 4.42692e7 1.52242 0.761211 0.648504i 0.224605π-0.224605\pi
0.761211 + 0.648504i 0.224605π0.224605\pi
968968 3.16875e7 1.08693
969969 −366332. −0.0125333
970970 0 0
971971 3.88962e7 1.32391 0.661956 0.749542i 0.269726π-0.269726\pi
0.661956 + 0.749542i 0.269726π0.269726\pi
972972 −3.18606e6 −0.108166
973973 −1.92816e7 −0.652922
974974 1.85417e7 0.626257
975975 0 0
976976 9.82357e6 0.330099
977977 2.71611e7 0.910354 0.455177 0.890401i 0.349576π-0.349576\pi
0.455177 + 0.890401i 0.349576π0.349576\pi
978978 1.67862e6 0.0561184
979979 −145319. −0.00484580
980980 0 0
981981 1.51946e7 0.504099
982982 −9.59904e6 −0.317650
983983 1.98048e7 0.653714 0.326857 0.945074i 0.394011π-0.394011\pi
0.326857 + 0.945074i 0.394011π0.394011\pi
984984 −2.55232e6 −0.0840326
985985 0 0
986986 −2.42113e6 −0.0793096
987987 5.13301e6 0.167718
988988 404255. 0.0131754
989989 3.60343e7 1.17145
990990 0 0
991991 −1.44104e7 −0.466115 −0.233057 0.972463i 0.574873π-0.574873\pi
−0.233057 + 0.972463i 0.574873π0.574873\pi
992992 1.83635e7 0.592483
993993 −1.10222e6 −0.0354727
994994 −2.37700e7 −0.763068
995995 0 0
996996 −1.36516e6 −0.0436048
997997 −3.16635e7 −1.00884 −0.504418 0.863459i 0.668293π-0.668293\pi
−0.504418 + 0.863459i 0.668293π0.668293\pi
998998 2.72195e7 0.865074
999999 −3.65378e6 −0.115832
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 325.6.a.b.1.2 2
5.2 odd 4 325.6.b.b.274.4 4
5.3 odd 4 325.6.b.b.274.1 4
5.4 even 2 13.6.a.a.1.1 2
15.14 odd 2 117.6.a.c.1.2 2
20.19 odd 2 208.6.a.h.1.1 2
35.34 odd 2 637.6.a.a.1.1 2
40.19 odd 2 832.6.a.i.1.2 2
40.29 even 2 832.6.a.p.1.1 2
65.34 odd 4 169.6.b.a.168.1 4
65.44 odd 4 169.6.b.a.168.4 4
65.64 even 2 169.6.a.a.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.6.a.a.1.1 2 5.4 even 2
117.6.a.c.1.2 2 15.14 odd 2
169.6.a.a.1.2 2 65.64 even 2
169.6.b.a.168.1 4 65.34 odd 4
169.6.b.a.168.4 4 65.44 odd 4
208.6.a.h.1.1 2 20.19 odd 2
325.6.a.b.1.2 2 1.1 even 1 trivial
325.6.b.b.274.1 4 5.3 odd 4
325.6.b.b.274.4 4 5.2 odd 4
637.6.a.a.1.1 2 35.34 odd 2
832.6.a.i.1.2 2 40.19 odd 2
832.6.a.p.1.1 2 40.29 even 2