Properties

Label 325.6.a.m.1.6
Level 325325
Weight 66
Character 325.1
Self dual yes
Analytic conductor 52.12552.125
Analytic rank 00
Dimension 1515
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: 1515
Coefficient field: Q[x]/(x15)\mathbb{Q}[x]/(x^{15} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x153x14356x13+802x12+49252x1178702x103324132x9++3541906480 x^{15} - 3 x^{14} - 356 x^{13} + 802 x^{12} + 49252 x^{11} - 78702 x^{10} - 3324132 x^{9} + \cdots + 3541906480 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 2756 2^{7}\cdot 5^{6}
Twist minimal: no (minimal twist has level 65)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.6
Root 4.301244.30124 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) == q3.30124q224.0437q321.1018q4+79.3742q6+91.7264q7+175.302q8+335.101q945.5406q11+507.366q12169.000q13302.811q14+96.5440q16+745.700q171106.25q18+306.010q192205.45q21+150.340q22+704.422q234214.91q24+557.910q262214.45q271935.59q286802.33q297605.25q315928.38q32+1094.97q332461.74q347071.24q36109.012q371010.21q38+4063.39q3913355.2q41+7280.71q42+4474.54q43+960.988q442325.47q46+4860.59q472321.28q488393.26q4917929.4q51+3566.21q52+40100.0q53+7310.45q54+16079.8q567357.62q57+22456.1q5829655.8q59+51545.6q61+25106.8q62+30737.6q63+16481.6q643614.75q6651877.6q6715735.6q6816936.9q69+42271.1q71+58743.9q72+45219.7q73+359.876q746457.36q764177.27q7713414.2q78+62532.7q7928185.8q81+44088.9q8246913.1q83+46538.9q8414771.5q86+163553.q877983.35q8863387.4q8915501.8q9114864.6q92+182859.q9316046.0q94+142540.q96132037.q97+27708.2q9815260.7q99+O(q100)q-3.30124 q^{2} -24.0437 q^{3} -21.1018 q^{4} +79.3742 q^{6} +91.7264 q^{7} +175.302 q^{8} +335.101 q^{9} -45.5406 q^{11} +507.366 q^{12} -169.000 q^{13} -302.811 q^{14} +96.5440 q^{16} +745.700 q^{17} -1106.25 q^{18} +306.010 q^{19} -2205.45 q^{21} +150.340 q^{22} +704.422 q^{23} -4214.91 q^{24} +557.910 q^{26} -2214.45 q^{27} -1935.59 q^{28} -6802.33 q^{29} -7605.25 q^{31} -5928.38 q^{32} +1094.97 q^{33} -2461.74 q^{34} -7071.24 q^{36} -109.012 q^{37} -1010.21 q^{38} +4063.39 q^{39} -13355.2 q^{41} +7280.71 q^{42} +4474.54 q^{43} +960.988 q^{44} -2325.47 q^{46} +4860.59 q^{47} -2321.28 q^{48} -8393.26 q^{49} -17929.4 q^{51} +3566.21 q^{52} +40100.0 q^{53} +7310.45 q^{54} +16079.8 q^{56} -7357.62 q^{57} +22456.1 q^{58} -29655.8 q^{59} +51545.6 q^{61} +25106.8 q^{62} +30737.6 q^{63} +16481.6 q^{64} -3614.75 q^{66} -51877.6 q^{67} -15735.6 q^{68} -16936.9 q^{69} +42271.1 q^{71} +58743.9 q^{72} +45219.7 q^{73} +359.876 q^{74} -6457.36 q^{76} -4177.27 q^{77} -13414.2 q^{78} +62532.7 q^{79} -28185.8 q^{81} +44088.9 q^{82} -46913.1 q^{83} +46538.9 q^{84} -14771.5 q^{86} +163553. q^{87} -7983.35 q^{88} -63387.4 q^{89} -15501.8 q^{91} -14864.6 q^{92} +182859. q^{93} -16046.0 q^{94} +142540. q^{96} -132037. q^{97} +27708.2 q^{98} -15260.7 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 15q+12q2+36q3+250q4202q6+306q7+576q8+963q9326q11+2702q122535q13+1334q14+6046q16+2722q17+2036q182624q19+3530q21+260488q99+O(q100) 15 q + 12 q^{2} + 36 q^{3} + 250 q^{4} - 202 q^{6} + 306 q^{7} + 576 q^{8} + 963 q^{9} - 326 q^{11} + 2702 q^{12} - 2535 q^{13} + 1334 q^{14} + 6046 q^{16} + 2722 q^{17} + 2036 q^{18} - 2624 q^{19} + 3530 q^{21}+ \cdots - 260488 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 −3.30124 −0.583583 −0.291791 0.956482i 0.594251π-0.594251\pi
−0.291791 + 0.956482i 0.594251π0.594251\pi
33 −24.0437 −1.54241 −0.771203 0.636589i 0.780345π-0.780345\pi
−0.771203 + 0.636589i 0.780345π0.780345\pi
44 −21.1018 −0.659431
55 0 0
66 79.3742 0.900121
77 91.7264 0.707537 0.353769 0.935333i 0.384900π-0.384900\pi
0.353769 + 0.935333i 0.384900π0.384900\pi
88 175.302 0.968415
99 335.101 1.37902
1010 0 0
1111 −45.5406 −0.113479 −0.0567397 0.998389i 0.518071π-0.518071\pi
−0.0567397 + 0.998389i 0.518071π0.518071\pi
1212 507.366 1.01711
1313 −169.000 −0.277350
1414 −302.811 −0.412906
1515 0 0
1616 96.5440 0.0942812
1717 745.700 0.625809 0.312905 0.949785i 0.398698π-0.398698\pi
0.312905 + 0.949785i 0.398698π0.398698\pi
1818 −1106.25 −0.804770
1919 306.010 0.194469 0.0972347 0.995261i 0.469000π-0.469000\pi
0.0972347 + 0.995261i 0.469000π0.469000\pi
2020 0 0
2121 −2205.45 −1.09131
2222 150.340 0.0662246
2323 704.422 0.277660 0.138830 0.990316i 0.455666π-0.455666\pi
0.138830 + 0.990316i 0.455666π0.455666\pi
2424 −4214.91 −1.49369
2525 0 0
2626 557.910 0.161857
2727 −2214.45 −0.584598
2828 −1935.59 −0.466572
2929 −6802.33 −1.50198 −0.750988 0.660316i 0.770422π-0.770422\pi
−0.750988 + 0.660316i 0.770422π0.770422\pi
3030 0 0
3131 −7605.25 −1.42138 −0.710689 0.703507i 0.751616π-0.751616\pi
−0.710689 + 0.703507i 0.751616π0.751616\pi
3232 −5928.38 −1.02344
3333 1094.97 0.175031
3434 −2461.74 −0.365211
3535 0 0
3636 −7071.24 −0.909367
3737 −109.012 −0.0130909 −0.00654547 0.999979i 0.502084π-0.502084\pi
−0.00654547 + 0.999979i 0.502084π0.502084\pi
3838 −1010.21 −0.113489
3939 4063.39 0.427787
4040 0 0
4141 −13355.2 −1.24077 −0.620386 0.784296i 0.713024π-0.713024\pi
−0.620386 + 0.784296i 0.713024π0.713024\pi
4242 7280.71 0.636869
4343 4474.54 0.369044 0.184522 0.982828i 0.440926π-0.440926\pi
0.184522 + 0.982828i 0.440926π0.440926\pi
4444 960.988 0.0748319
4545 0 0
4646 −2325.47 −0.162038
4747 4860.59 0.320955 0.160478 0.987039i 0.448697π-0.448697\pi
0.160478 + 0.987039i 0.448697π0.448697\pi
4848 −2321.28 −0.145420
4949 −8393.26 −0.499391
5050 0 0
5151 −17929.4 −0.965252
5252 3566.21 0.182893
5353 40100.0 1.96090 0.980448 0.196777i 0.0630473π-0.0630473\pi
0.980448 + 0.196777i 0.0630473π0.0630473\pi
5454 7310.45 0.341161
5555 0 0
5656 16079.8 0.685190
5757 −7357.62 −0.299951
5858 22456.1 0.876526
5959 −29655.8 −1.10912 −0.554561 0.832143i 0.687114π-0.687114\pi
−0.554561 + 0.832143i 0.687114π0.687114\pi
6060 0 0
6161 51545.6 1.77365 0.886823 0.462109i 0.152907π-0.152907\pi
0.886823 + 0.462109i 0.152907π0.152907\pi
6262 25106.8 0.829491
6363 30737.6 0.975706
6464 16481.6 0.502978
6565 0 0
6666 −3614.75 −0.102145
6767 −51877.6 −1.41186 −0.705932 0.708280i 0.749472π-0.749472\pi
−0.705932 + 0.708280i 0.749472π0.749472\pi
6868 −15735.6 −0.412678
6969 −16936.9 −0.428265
7070 0 0
7171 42271.1 0.995171 0.497585 0.867415i 0.334220π-0.334220\pi
0.497585 + 0.867415i 0.334220π0.334220\pi
7272 58743.9 1.33546
7373 45219.7 0.993162 0.496581 0.867990i 0.334588π-0.334588\pi
0.496581 + 0.867990i 0.334588π0.334588\pi
7474 359.876 0.00763964
7575 0 0
7676 −6457.36 −0.128239
7777 −4177.27 −0.0802909
7878 −13414.2 −0.249649
7979 62532.7 1.12730 0.563650 0.826014i 0.309397π-0.309397\pi
0.563650 + 0.826014i 0.309397π0.309397\pi
8080 0 0
8181 −28185.8 −0.477329
8282 44088.9 0.724093
8383 −46913.1 −0.747479 −0.373740 0.927534i 0.621925π-0.621925\pi
−0.373740 + 0.927534i 0.621925π0.621925\pi
8484 46538.9 0.719644
8585 0 0
8686 −14771.5 −0.215367
8787 163553. 2.31666
8888 −7983.35 −0.109895
8989 −63387.4 −0.848258 −0.424129 0.905602i 0.639420π-0.639420\pi
−0.424129 + 0.905602i 0.639420π0.639420\pi
9090 0 0
9191 −15501.8 −0.196236
9292 −14864.6 −0.183098
9393 182859. 2.19234
9494 −16046.0 −0.187304
9595 0 0
9696 142540. 1.57855
9797 −132037. −1.42484 −0.712421 0.701752i 0.752401π-0.752401\pi
−0.712421 + 0.701752i 0.752401π0.752401\pi
9898 27708.2 0.291436
9999 −15260.7 −0.156490
100100 0 0
101101 174161. 1.69882 0.849408 0.527736i 0.176959π-0.176959\pi
0.849408 + 0.527736i 0.176959π0.176959\pi
102102 59189.3 0.563304
103103 −41504.6 −0.385481 −0.192741 0.981250i 0.561738π-0.561738\pi
−0.192741 + 0.981250i 0.561738π0.561738\pi
104104 −29626.0 −0.268590
105105 0 0
106106 −132380. −1.14435
107107 7340.14 0.0619791 0.0309895 0.999520i 0.490134π-0.490134\pi
0.0309895 + 0.999520i 0.490134π0.490134\pi
108108 46729.0 0.385502
109109 51340.4 0.413898 0.206949 0.978352i 0.433647π-0.433647\pi
0.206949 + 0.978352i 0.433647π0.433647\pi
110110 0 0
111111 2621.06 0.0201915
112112 8855.63 0.0667075
113113 −145027. −1.06845 −0.534223 0.845344i 0.679396π-0.679396\pi
−0.534223 + 0.845344i 0.679396π0.679396\pi
114114 24289.3 0.175046
115115 0 0
116116 143541. 0.990450
117117 −56632.1 −0.382470
118118 97900.9 0.647264
119119 68400.4 0.442783
120120 0 0
121121 −158977. −0.987122
122122 −170164. −1.03507
123123 321110. 1.91378
124124 160485. 0.937301
125125 0 0
126126 −101472. −0.569405
127127 69448.0 0.382077 0.191038 0.981583i 0.438814π-0.438814\pi
0.191038 + 0.981583i 0.438814π0.438814\pi
128128 135298. 0.729907
129129 −107585. −0.569215
130130 0 0
131131 −264141. −1.34480 −0.672400 0.740188i 0.734736π-0.734736\pi
−0.672400 + 0.740188i 0.734736π0.734736\pi
132132 −23105.8 −0.115421
133133 28069.2 0.137594
134134 171260. 0.823939
135135 0 0
136136 130723. 0.606043
137137 −48840.0 −0.222318 −0.111159 0.993803i 0.535456π-0.535456\pi
−0.111159 + 0.993803i 0.535456π0.535456\pi
138138 55912.9 0.249928
139139 193453. 0.849255 0.424627 0.905368i 0.360405π-0.360405\pi
0.424627 + 0.905368i 0.360405π0.360405\pi
140140 0 0
141141 −116867. −0.495043
142142 −139547. −0.580764
143143 7696.36 0.0314735
144144 32352.0 0.130015
145145 0 0
146146 −149281. −0.579592
147147 201805. 0.770264
148148 2300.35 0.00863258
149149 −133014. −0.490830 −0.245415 0.969418i 0.578924π-0.578924\pi
−0.245415 + 0.969418i 0.578924π0.578924\pi
150150 0 0
151151 −310303. −1.10750 −0.553749 0.832684i 0.686803π-0.686803\pi
−0.553749 + 0.832684i 0.686803π0.686803\pi
152152 53644.1 0.188327
153153 249885. 0.863002
154154 13790.2 0.0468564
155155 0 0
156156 −85744.9 −0.282096
157157 −49697.8 −0.160912 −0.0804559 0.996758i 0.525638π-0.525638\pi
−0.0804559 + 0.996758i 0.525638π0.525638\pi
158158 −206436. −0.657873
159159 −964154. −3.02450
160160 0 0
161161 64614.1 0.196455
162162 93048.2 0.278561
163163 658943. 1.94258 0.971290 0.237899i 0.0764588π-0.0764588\pi
0.971290 + 0.237899i 0.0764588π0.0764588\pi
164164 281820. 0.818205
165165 0 0
166166 154872. 0.436216
167167 655469. 1.81870 0.909349 0.416034i 0.136580π-0.136580\pi
0.909349 + 0.416034i 0.136580π0.136580\pi
168168 −386619. −1.05684
169169 28561.0 0.0769231
170170 0 0
171171 102544. 0.268177
172172 −94420.9 −0.243359
173173 −280036. −0.711376 −0.355688 0.934605i 0.615753π-0.615753\pi
−0.355688 + 0.934605i 0.615753π0.615753\pi
174174 −539929. −1.35196
175175 0 0
176176 −4396.67 −0.0106990
177177 713036. 1.71072
178178 209257. 0.495028
179179 261227. 0.609377 0.304689 0.952452i 0.401448π-0.401448\pi
0.304689 + 0.952452i 0.401448π0.401448\pi
180180 0 0
181181 −112896. −0.256143 −0.128071 0.991765i 0.540879π-0.540879\pi
−0.128071 + 0.991765i 0.540879π0.540879\pi
182182 51175.1 0.114520
183183 −1.23935e6 −2.73568
184184 123486. 0.268890
185185 0 0
186186 −603660. −1.27941
187187 −33959.6 −0.0710164
188188 −102567. −0.211648
189189 −203124. −0.413625
190190 0 0
191191 790161. 1.56723 0.783614 0.621247i 0.213374π-0.213374\pi
0.783614 + 0.621247i 0.213374π0.213374\pi
192192 −396279. −0.775797
193193 272267. 0.526140 0.263070 0.964777i 0.415265π-0.415265\pi
0.263070 + 0.964777i 0.415265π0.415265\pi
194194 435887. 0.831513
195195 0 0
196196 177113. 0.329314
197197 −304065. −0.558215 −0.279107 0.960260i 0.590039π-0.590039\pi
−0.279107 + 0.960260i 0.590039π0.590039\pi
198198 50379.3 0.0913248
199199 291885. 0.522492 0.261246 0.965272i 0.415867π-0.415867\pi
0.261246 + 0.965272i 0.415867π0.415867\pi
200200 0 0
201201 1.24733e6 2.17767
202202 −574946. −0.991400
203203 −623953. −1.06270
204204 378343. 0.636518
205205 0 0
206206 137017. 0.224960
207207 236053. 0.382898
208208 −16315.9 −0.0261489
209209 −13935.9 −0.0220683
210210 0 0
211211 447521. 0.692003 0.346001 0.938234i 0.387539π-0.387539\pi
0.346001 + 0.938234i 0.387539π0.387539\pi
212212 −846182. −1.29308
213213 −1.01635e6 −1.53496
214214 −24231.6 −0.0361699
215215 0 0
216216 −388198. −0.566134
217217 −697603. −1.00568
218218 −169487. −0.241543
219219 −1.08725e6 −1.53186
220220 0 0
221221 −126023. −0.173568
222222 −8652.75 −0.0117834
223223 158.327 0.000213203 0 0.000106602 1.00000i 0.499966π-0.499966\pi
0.000106602 1.00000i 0.499966π0.499966\pi
224224 −543789. −0.724119
225225 0 0
226226 478769. 0.623526
227227 1.13950e6 1.46774 0.733870 0.679290i 0.237712π-0.237712\pi
0.733870 + 0.679290i 0.237712π0.237712\pi
228228 155259. 0.197797
229229 693287. 0.873624 0.436812 0.899553i 0.356108π-0.356108\pi
0.436812 + 0.899553i 0.356108π0.356108\pi
230230 0 0
231231 100437. 0.123841
232232 −1.19246e6 −1.45454
233233 −399786. −0.482434 −0.241217 0.970471i 0.577547π-0.577547\pi
−0.241217 + 0.970471i 0.577547π0.577547\pi
234234 186956. 0.223203
235235 0 0
236236 625791. 0.731390
237237 −1.50352e6 −1.73876
238238 −225806. −0.258401
239239 445444. 0.504427 0.252213 0.967672i 0.418842π-0.418842\pi
0.252213 + 0.967672i 0.418842π0.418842\pi
240240 0 0
241241 −1.23166e6 −1.36600 −0.682999 0.730420i 0.739324π-0.739324\pi
−0.682999 + 0.730420i 0.739324π0.739324\pi
242242 524822. 0.576067
243243 1.21580e6 1.32083
244244 −1.08771e6 −1.16960
245245 0 0
246246 −1.06006e6 −1.11685
247247 −51715.7 −0.0539361
248248 −1.33321e6 −1.37648
249249 1.12797e6 1.15292
250250 0 0
251251 615483. 0.616640 0.308320 0.951283i 0.400233π-0.400233\pi
0.308320 + 0.951283i 0.400233π0.400233\pi
252252 −648619. −0.643411
253253 −32079.8 −0.0315087
254254 −229265. −0.222973
255255 0 0
256256 −974063. −0.928939
257257 −844218. −0.797300 −0.398650 0.917103i 0.630521π-0.630521\pi
−0.398650 + 0.917103i 0.630521π0.630521\pi
258258 355163. 0.332184
259259 −9999.30 −0.00926233
260260 0 0
261261 −2.27947e6 −2.07125
262262 871993. 0.784802
263263 586640. 0.522976 0.261488 0.965207i 0.415787π-0.415787\pi
0.261488 + 0.965207i 0.415787π0.415787\pi
264264 191950. 0.169503
265265 0 0
266266 −92663.2 −0.0802977
267267 1.52407e6 1.30836
268268 1.09471e6 0.931027
269269 2.07403e6 1.74757 0.873786 0.486310i 0.161657π-0.161657\pi
0.873786 + 0.486310i 0.161657π0.161657\pi
270270 0 0
271271 1.92221e6 1.58993 0.794963 0.606658i 0.207490π-0.207490\pi
0.794963 + 0.606658i 0.207490π0.207490\pi
272272 71992.9 0.0590021
273273 372720. 0.302675
274274 161233. 0.129741
275275 0 0
276276 357400. 0.282411
277277 1.70508e6 1.33520 0.667599 0.744521i 0.267322π-0.267322\pi
0.667599 + 0.744521i 0.267322π0.267322\pi
278278 −638634. −0.495610
279279 −2.54853e6 −1.96010
280280 0 0
281281 −961277. −0.726244 −0.363122 0.931742i 0.618289π-0.618289\pi
−0.363122 + 0.931742i 0.618289π0.618289\pi
282282 385805. 0.288899
283283 −1.84545e6 −1.36973 −0.684867 0.728668i 0.740140π-0.740140\pi
−0.684867 + 0.728668i 0.740140π0.740140\pi
284284 −891996. −0.656247
285285 0 0
286286 −25407.5 −0.0183674
287287 −1.22503e6 −0.877893
288288 −1.98661e6 −1.41134
289289 −863788. −0.608363
290290 0 0
291291 3.17467e6 2.19769
292292 −954217. −0.654923
293293 425094. 0.289278 0.144639 0.989484i 0.453798π-0.453798\pi
0.144639 + 0.989484i 0.453798π0.453798\pi
294294 −666208. −0.449512
295295 0 0
296296 −19110.0 −0.0126775
297297 100848. 0.0663398
298298 439111. 0.286440
299299 −119047. −0.0770090
300300 0 0
301301 410434. 0.261112
302302 1.02438e6 0.646317
303303 −4.18747e6 −2.62027
304304 29543.4 0.0183348
305305 0 0
306306 −824931. −0.503633
307307 −669386. −0.405351 −0.202675 0.979246i 0.564964π-0.564964\pi
−0.202675 + 0.979246i 0.564964π0.564964\pi
308308 88148.0 0.0529463
309309 997926. 0.594569
310310 0 0
311311 −1.10103e6 −0.645506 −0.322753 0.946483i 0.604608π-0.604608\pi
−0.322753 + 0.946483i 0.604608π0.604608\pi
312312 712320. 0.414275
313313 698228. 0.402844 0.201422 0.979505i 0.435444π-0.435444\pi
0.201422 + 0.979505i 0.435444π0.435444\pi
314314 164064. 0.0939053
315315 0 0
316316 −1.31955e6 −0.743377
317317 −1.25102e6 −0.699226 −0.349613 0.936894i 0.613687π-0.613687\pi
−0.349613 + 0.936894i 0.613687π0.613687\pi
318318 3.18290e6 1.76504
319319 309782. 0.170443
320320 0 0
321321 −176484. −0.0955969
322322 −213307. −0.114648
323323 228192. 0.121701
324324 594771. 0.314766
325325 0 0
326326 −2.17533e6 −1.13366
327327 −1.23441e6 −0.638398
328328 −2.34120e6 −1.20158
329329 445845. 0.227088
330330 0 0
331331 −2.38101e6 −1.19452 −0.597258 0.802049i 0.703743π-0.703743\pi
−0.597258 + 0.802049i 0.703743π0.703743\pi
332332 989952. 0.492911
333333 −36530.1 −0.0180526
334334 −2.16386e6 −1.06136
335335 0 0
336336 −212923. −0.102890
337337 2.38010e6 1.14161 0.570807 0.821084i 0.306630π-0.306630\pi
0.570807 + 0.821084i 0.306630π0.306630\pi
338338 −94286.8 −0.0448910
339339 3.48699e6 1.64798
340340 0 0
341341 346348. 0.161297
342342 −338523. −0.156503
343343 −2.31153e6 −1.06088
344344 784396. 0.357387
345345 0 0
346346 924468. 0.415147
347347 3.45043e6 1.53833 0.769166 0.639049i 0.220672π-0.220672\pi
0.769166 + 0.639049i 0.220672π0.220672\pi
348348 −3.45127e6 −1.52768
349349 3.27121e6 1.43762 0.718811 0.695206i 0.244687π-0.244687\pi
0.718811 + 0.695206i 0.244687π0.244687\pi
350350 0 0
351351 374243. 0.162138
352352 269982. 0.116139
353353 4.08960e6 1.74680 0.873401 0.487001i 0.161909π-0.161909\pi
0.873401 + 0.487001i 0.161909π0.161909\pi
354354 −2.35390e6 −0.998345
355355 0 0
356356 1.33759e6 0.559368
357357 −1.64460e6 −0.682952
358358 −862375. −0.355622
359359 2.45540e6 1.00551 0.502754 0.864430i 0.332320π-0.332320\pi
0.502754 + 0.864430i 0.332320π0.332320\pi
360360 0 0
361361 −2.38246e6 −0.962182
362362 372697. 0.149480
363363 3.82240e6 1.52254
364364 327115. 0.129404
365365 0 0
366366 4.09139e6 1.59650
367367 −328555. −0.127333 −0.0636667 0.997971i 0.520279π-0.520279\pi
−0.0636667 + 0.997971i 0.520279π0.520279\pi
368368 68007.7 0.0261781
369369 −4.47536e6 −1.71105
370370 0 0
371371 3.67823e6 1.38741
372372 −3.85865e6 −1.44570
373373 5.17656e6 1.92650 0.963250 0.268606i 0.0865630π-0.0865630\pi
0.963250 + 0.268606i 0.0865630π0.0865630\pi
374374 112109. 0.0414439
375375 0 0
376376 852071. 0.310818
377377 1.14959e6 0.416573
378378 670561. 0.241384
379379 3.24314e6 1.15976 0.579880 0.814702i 0.303100π-0.303100\pi
0.579880 + 0.814702i 0.303100π0.303100\pi
380380 0 0
381381 −1.66979e6 −0.589318
382382 −2.60851e6 −0.914607
383383 4.53434e6 1.57949 0.789745 0.613435i 0.210213π-0.210213\pi
0.789745 + 0.613435i 0.210213π0.210213\pi
384384 −3.25308e6 −1.12581
385385 0 0
386386 −898819. −0.307046
387387 1.49942e6 0.508917
388388 2.78622e6 0.939586
389389 1.77865e6 0.595958 0.297979 0.954572i 0.403687π-0.403687\pi
0.297979 + 0.954572i 0.403687π0.403687\pi
390390 0 0
391391 525288. 0.173762
392392 −1.47135e6 −0.483618
393393 6.35094e6 2.07423
394394 1.00379e6 0.325764
395395 0 0
396396 322028. 0.103194
397397 5.19763e6 1.65512 0.827560 0.561378i 0.189729π-0.189729\pi
0.827560 + 0.561378i 0.189729π0.189729\pi
398398 −963583. −0.304917
399399 −674888. −0.212226
400400 0 0
401401 4.03901e6 1.25434 0.627168 0.778884i 0.284214π-0.284214\pi
0.627168 + 0.778884i 0.284214π0.284214\pi
402402 −4.11774e6 −1.27085
403403 1.28529e6 0.394219
404404 −3.67510e6 −1.12025
405405 0 0
406406 2.05982e6 0.620175
407407 4964.48 0.00148555
408408 −3.14306e6 −0.934765
409409 −2.23547e6 −0.660787 −0.330393 0.943843i 0.607181π-0.607181\pi
−0.330393 + 0.943843i 0.607181π0.607181\pi
410410 0 0
411411 1.17430e6 0.342904
412412 875823. 0.254199
413413 −2.72022e6 −0.784746
414414 −779267. −0.223452
415415 0 0
416416 1.00190e6 0.283850
417417 −4.65133e6 −1.30990
418418 46005.7 0.0128787
419419 1.52835e6 0.425291 0.212646 0.977129i 0.431792π-0.431792\pi
0.212646 + 0.977129i 0.431792π0.431792\pi
420420 0 0
421421 −2.80885e6 −0.772367 −0.386183 0.922422i 0.626207π-0.626207\pi
−0.386183 + 0.922422i 0.626207π0.626207\pi
422422 −1.47738e6 −0.403841
423423 1.62879e6 0.442603
424424 7.02961e6 1.89896
425425 0 0
426426 3.35523e6 0.895774
427427 4.72809e6 1.25492
428428 −154890. −0.0408710
429429 −185049. −0.0485449
430430 0 0
431431 −2.64484e6 −0.685813 −0.342906 0.939370i 0.611411π-0.611411\pi
−0.342906 + 0.939370i 0.611411π0.611411\pi
432432 −213792. −0.0551166
433433 −6.38548e6 −1.63672 −0.818359 0.574708i 0.805116π-0.805116\pi
−0.818359 + 0.574708i 0.805116π0.805116\pi
434434 2.30295e6 0.586896
435435 0 0
436436 −1.08337e6 −0.272937
437437 215560. 0.0539964
438438 3.58927e6 0.893967
439439 −1.84296e6 −0.456409 −0.228205 0.973613i 0.573286π-0.573286\pi
−0.228205 + 0.973613i 0.573286π0.573286\pi
440440 0 0
441441 −2.81259e6 −0.688669
442442 416033. 0.101291
443443 610862. 0.147888 0.0739442 0.997262i 0.476441π-0.476441\pi
0.0739442 + 0.997262i 0.476441π0.476441\pi
444444 −55309.1 −0.0133149
445445 0 0
446446 −522.676 −0.000124422 0
447447 3.19815e6 0.757059
448448 1.51180e6 0.355876
449449 −1.32831e6 −0.310945 −0.155473 0.987840i 0.549690π-0.549690\pi
−0.155473 + 0.987840i 0.549690π0.549690\pi
450450 0 0
451451 608206. 0.140802
452452 3.06033e6 0.704567
453453 7.46083e6 1.70821
454454 −3.76176e6 −0.856547
455455 0 0
456456 −1.28980e6 −0.290477
457457 −1.05715e6 −0.236780 −0.118390 0.992967i 0.537773π-0.537773\pi
−0.118390 + 0.992967i 0.537773π0.537773\pi
458458 −2.28871e6 −0.509832
459459 −1.65132e6 −0.365847
460460 0 0
461461 −88191.8 −0.0193275 −0.00966376 0.999953i 0.503076π-0.503076\pi
−0.00966376 + 0.999953i 0.503076π0.503076\pi
462462 −331568. −0.0722715
463463 −5.10298e6 −1.10630 −0.553148 0.833083i 0.686573π-0.686573\pi
−0.553148 + 0.833083i 0.686573π0.686573\pi
464464 −656724. −0.141608
465465 0 0
466466 1.31979e6 0.281540
467467 4.32926e6 0.918590 0.459295 0.888284i 0.348102π-0.348102\pi
0.459295 + 0.888284i 0.348102π0.348102\pi
468468 1.19504e6 0.252213
469469 −4.75855e6 −0.998946
470470 0 0
471471 1.19492e6 0.248191
472472 −5.19872e6 −1.07409
473473 −203773. −0.0418788
474474 4.96348e6 1.01471
475475 0 0
476476 −1.44337e6 −0.291985
477477 1.34376e7 2.70411
478478 −1.47052e6 −0.294375
479479 2.88997e6 0.575513 0.287756 0.957704i 0.407091π-0.407091\pi
0.287756 + 0.957704i 0.407091π0.407091\pi
480480 0 0
481481 18423.1 0.00363077
482482 4.06602e6 0.797172
483483 −1.55356e6 −0.303013
484484 3.35470e6 0.650940
485485 0 0
486486 −4.01366e6 −0.770815
487487 3.37347e6 0.644546 0.322273 0.946647i 0.395553π-0.395553\pi
0.322273 + 0.946647i 0.395553π0.395553\pi
488488 9.03604e6 1.71763
489489 −1.58434e7 −2.99625
490490 0 0
491491 5.24844e6 0.982486 0.491243 0.871023i 0.336543π-0.336543\pi
0.491243 + 0.871023i 0.336543π0.336543\pi
492492 −6.77600e6 −1.26200
493493 −5.07250e6 −0.939950
494494 170726. 0.0314762
495495 0 0
496496 −734241. −0.134009
497497 3.87738e6 0.704120
498498 −3.72369e6 −0.672822
499499 −3.51772e6 −0.632427 −0.316213 0.948688i 0.602412π-0.602412\pi
−0.316213 + 0.948688i 0.602412π0.602412\pi
500500 0 0
501501 −1.57599e7 −2.80517
502502 −2.03186e6 −0.359860
503503 8.97569e6 1.58179 0.790893 0.611954i 0.209616π-0.209616\pi
0.790893 + 0.611954i 0.209616π0.209616\pi
504504 5.38836e6 0.944889
505505 0 0
506506 105903. 0.0183879
507507 −686713. −0.118647
508508 −1.46548e6 −0.251953
509509 −9.09941e6 −1.55675 −0.778375 0.627800i 0.783955π-0.783955\pi
−0.778375 + 0.627800i 0.783955π0.783955\pi
510510 0 0
511511 4.14784e6 0.702700
512512 −1.11393e6 −0.187794
513513 −677645. −0.113686
514514 2.78697e6 0.465290
515515 0 0
516516 2.27023e6 0.375358
517517 −221354. −0.0364218
518518 33010.1 0.00540533
519519 6.73312e6 1.09723
520520 0 0
521521 5.26898e6 0.850418 0.425209 0.905095i 0.360201π-0.360201\pi
0.425209 + 0.905095i 0.360201π0.360201\pi
522522 7.52508e6 1.20874
523523 −4.16491e6 −0.665811 −0.332906 0.942960i 0.608029π-0.608029\pi
−0.332906 + 0.942960i 0.608029π0.608029\pi
524524 5.57385e6 0.886803
525525 0 0
526526 −1.93664e6 −0.305200
527527 −5.67124e6 −0.889511
528528 105712. 0.0165022
529529 −5.94013e6 −0.922905
530530 0 0
531531 −9.93769e6 −1.52950
532532 −592311. −0.0907341
533533 2.25704e6 0.344129
534534 −5.03132e6 −0.763535
535535 0 0
536536 −9.09424e6 −1.36727
537537 −6.28088e6 −0.939907
538538 −6.84689e6 −1.01985
539539 382234. 0.0566706
540540 0 0
541541 −3.03221e6 −0.445416 −0.222708 0.974885i 0.571490π-0.571490\pi
−0.222708 + 0.974885i 0.571490π0.571490\pi
542542 −6.34567e6 −0.927853
543543 2.71444e6 0.395076
544544 −4.42079e6 −0.640476
545545 0 0
546546 −1.23044e6 −0.176636
547547 −3.32454e6 −0.475076 −0.237538 0.971378i 0.576340π-0.576340\pi
−0.237538 + 0.971378i 0.576340π0.576340\pi
548548 1.03061e6 0.146603
549549 1.72730e7 2.44589
550550 0 0
551551 −2.08158e6 −0.292088
552552 −2.96908e6 −0.414738
553553 5.73590e6 0.797607
554554 −5.62888e6 −0.779198
555555 0 0
556556 −4.08220e6 −0.560025
557557 7.78685e6 1.06347 0.531733 0.846912i 0.321541π-0.321541\pi
0.531733 + 0.846912i 0.321541π0.321541\pi
558558 8.41331e6 1.14388
559559 −756198. −0.102354
560560 0 0
561561 816516. 0.109536
562562 3.17341e6 0.423824
563563 4.68638e6 0.623112 0.311556 0.950228i 0.399150π-0.399150\pi
0.311556 + 0.950228i 0.399150π0.399150\pi
564564 2.46610e6 0.326447
565565 0 0
566566 6.09227e6 0.799353
567567 −2.58538e6 −0.337728
568568 7.41020e6 0.963738
569569 −2.10415e6 −0.272456 −0.136228 0.990678i 0.543498π-0.543498\pi
−0.136228 + 0.990678i 0.543498π0.543498\pi
570570 0 0
571571 1.20728e7 1.54959 0.774796 0.632211i 0.217852π-0.217852\pi
0.774796 + 0.632211i 0.217852π0.217852\pi
572572 −162407. −0.0207546
573573 −1.89984e7 −2.41730
574574 4.04412e6 0.512323
575575 0 0
576576 5.52300e6 0.693615
577577 −1.02267e7 −1.27878 −0.639390 0.768883i 0.720813π-0.720813\pi
−0.639390 + 0.768883i 0.720813π0.720813\pi
578578 2.85157e6 0.355030
579579 −6.54631e6 −0.811522
580580 0 0
581581 −4.30317e6 −0.528869
582582 −1.04803e7 −1.28253
583583 −1.82618e6 −0.222521
584584 7.92709e6 0.961794
585585 0 0
586586 −1.40334e6 −0.168818
587587 −2.24352e6 −0.268741 −0.134371 0.990931i 0.542901π-0.542901\pi
−0.134371 + 0.990931i 0.542901π0.542901\pi
588588 −4.25846e6 −0.507936
589589 −2.32728e6 −0.276414
590590 0 0
591591 7.31086e6 0.860994
592592 −10524.5 −0.00123423
593593 590374. 0.0689430 0.0344715 0.999406i 0.489025π-0.489025\pi
0.0344715 + 0.999406i 0.489025π0.489025\pi
594594 −332922. −0.0387148
595595 0 0
596596 2.80683e6 0.323669
597597 −7.01801e6 −0.805894
598598 393004. 0.0449411
599599 2.71185e6 0.308815 0.154407 0.988007i 0.450653π-0.450653\pi
0.154407 + 0.988007i 0.450653π0.450653\pi
600600 0 0
601601 −9.99011e6 −1.12820 −0.564098 0.825708i 0.690776π-0.690776\pi
−0.564098 + 0.825708i 0.690776π0.690776\pi
602602 −1.35494e6 −0.152380
603603 −1.73842e7 −1.94698
604604 6.54795e6 0.730319
605605 0 0
606606 1.38239e7 1.52914
607607 −4.27804e6 −0.471273 −0.235637 0.971841i 0.575718π-0.575718\pi
−0.235637 + 0.971841i 0.575718π0.575718\pi
608608 −1.81414e6 −0.199027
609609 1.50022e7 1.63912
610610 0 0
611611 −821440. −0.0890170
612612 −5.27302e6 −0.569090
613613 −645645. −0.0693973 −0.0346986 0.999398i 0.511047π-0.511047\pi
−0.0346986 + 0.999398i 0.511047π0.511047\pi
614614 2.20981e6 0.236556
615615 0 0
616616 −732284. −0.0777549
617617 2.65549e6 0.280822 0.140411 0.990093i 0.455158π-0.455158\pi
0.140411 + 0.990093i 0.455158π0.455158\pi
618618 −3.29440e6 −0.346980
619619 −1.11716e7 −1.17190 −0.585948 0.810349i 0.699278π-0.699278\pi
−0.585948 + 0.810349i 0.699278π0.699278\pi
620620 0 0
621621 −1.55991e6 −0.162320
622622 3.63478e6 0.376706
623623 −5.81430e6 −0.600174
624624 392296. 0.0403322
625625 0 0
626626 −2.30502e6 −0.235092
627627 335070. 0.0340382
628628 1.04871e6 0.106110
629629 −81290.4 −0.00819243
630630 0 0
631631 −1.49550e6 −0.149525 −0.0747624 0.997201i 0.523820π-0.523820\pi
−0.0747624 + 0.997201i 0.523820π0.523820\pi
632632 1.09621e7 1.09169
633633 −1.07601e7 −1.06735
634634 4.12993e6 0.408056
635635 0 0
636636 2.03454e7 1.99445
637637 1.41846e6 0.138506
638638 −1.02267e6 −0.0994676
639639 1.41651e7 1.37236
640640 0 0
641641 9.23788e6 0.888030 0.444015 0.896019i 0.353554π-0.353554\pi
0.444015 + 0.896019i 0.353554π0.353554\pi
642642 582618. 0.0557887
643643 −3.69634e6 −0.352569 −0.176285 0.984339i 0.556408π-0.556408\pi
−0.176285 + 0.984339i 0.556408π0.556408\pi
644644 −1.36347e6 −0.129548
645645 0 0
646646 −753316. −0.0710225
647647 1.94037e7 1.82232 0.911159 0.412055i 0.135189π-0.135189\pi
0.911159 + 0.412055i 0.135189π0.135189\pi
648648 −4.94103e6 −0.462253
649649 1.35054e6 0.125862
650650 0 0
651651 1.67730e7 1.55116
652652 −1.39049e7 −1.28100
653653 −6.16635e6 −0.565907 −0.282953 0.959134i 0.591314π-0.591314\pi
−0.282953 + 0.959134i 0.591314π0.591314\pi
654654 4.07510e6 0.372558
655655 0 0
656656 −1.28937e6 −0.116982
657657 1.51532e7 1.36959
658658 −1.47184e6 −0.132525
659659 6.87190e6 0.616401 0.308200 0.951321i 0.400273π-0.400273\pi
0.308200 + 0.951321i 0.400273π0.400273\pi
660660 0 0
661661 −3.87812e6 −0.345237 −0.172618 0.984989i 0.555223π-0.555223\pi
−0.172618 + 0.984989i 0.555223π0.555223\pi
662662 7.86030e6 0.697099
663663 3.03007e6 0.267713
664664 −8.22396e6 −0.723870
665665 0 0
666666 120595. 0.0105352
667667 −4.79171e6 −0.417038
668668 −1.38316e7 −1.19931
669669 −3806.78 −0.000328846 0
670670 0 0
671671 −2.34742e6 −0.201272
672672 1.30747e7 1.11689
673673 −6.95400e6 −0.591830 −0.295915 0.955214i 0.595625π-0.595625\pi
−0.295915 + 0.955214i 0.595625π0.595625\pi
674674 −7.85727e6 −0.666227
675675 0 0
676676 −602689. −0.0507255
677677 −1.45095e7 −1.21669 −0.608345 0.793672i 0.708166π-0.708166\pi
−0.608345 + 0.793672i 0.708166π0.708166\pi
678678 −1.15114e7 −0.961731
679679 −1.21113e7 −1.00813
680680 0 0
681681 −2.73978e7 −2.26385
682682 −1.14338e6 −0.0941301
683683 1.77058e7 1.45232 0.726162 0.687524i 0.241302π-0.241302\pi
0.726162 + 0.687524i 0.241302π0.241302\pi
684684 −2.16387e6 −0.176844
685685 0 0
686686 7.63092e6 0.619108
687687 −1.66692e7 −1.34748
688688 431990. 0.0347939
689689 −6.77690e6 −0.543855
690690 0 0
691691 −8.82763e6 −0.703313 −0.351657 0.936129i 0.614382π-0.614382\pi
−0.351657 + 0.936129i 0.614382π0.614382\pi
692692 5.90927e6 0.469104
693693 −1.39981e6 −0.110722
694694 −1.13907e7 −0.897744
695695 0 0
696696 2.86712e7 2.24348
697697 −9.95901e6 −0.776487
698698 −1.07990e7 −0.838971
699699 9.61236e6 0.744110
700700 0 0
701701 1.38056e7 1.06111 0.530553 0.847652i 0.321984π-0.321984\pi
0.530553 + 0.847652i 0.321984π0.321984\pi
702702 −1.23547e6 −0.0946211
703703 −33358.8 −0.00254579
704704 −750581. −0.0570776
705705 0 0
706706 −1.35007e7 −1.01940
707707 1.59751e7 1.20198
708708 −1.50463e7 −1.12810
709709 2.05869e6 0.153806 0.0769032 0.997039i 0.475497π-0.475497\pi
0.0769032 + 0.997039i 0.475497π0.475497\pi
710710 0 0
711711 2.09548e7 1.55457
712712 −1.11119e7 −0.821466
713713 −5.35731e6 −0.394660
714714 5.42923e6 0.398559
715715 0 0
716716 −5.51237e6 −0.401842
717717 −1.07101e7 −0.778031
718718 −8.10585e6 −0.586797
719719 −7.96314e6 −0.574463 −0.287232 0.957861i 0.592735π-0.592735\pi
−0.287232 + 0.957861i 0.592735π0.592735\pi
720720 0 0
721721 −3.80707e6 −0.272743
722722 7.86507e6 0.561512
723723 2.96138e7 2.10692
724724 2.38231e6 0.168909
725725 0 0
726726 −1.26187e7 −0.888530
727727 −3.82952e6 −0.268725 −0.134363 0.990932i 0.542899π-0.542899\pi
−0.134363 + 0.990932i 0.542899π0.542899\pi
728728 −2.71749e6 −0.190037
729729 −2.23833e7 −1.55993
730730 0 0
731731 3.33667e6 0.230951
732732 2.61525e7 1.80400
733733 1.45934e7 1.00322 0.501611 0.865093i 0.332741π-0.332741\pi
0.501611 + 0.865093i 0.332741π0.332741\pi
734734 1.08464e6 0.0743096
735735 0 0
736736 −4.17608e6 −0.284167
737737 2.36254e6 0.160217
738738 1.47742e7 0.998537
739739 1.03685e7 0.698403 0.349202 0.937048i 0.386453π-0.386453\pi
0.349202 + 0.937048i 0.386453π0.386453\pi
740740 0 0
741741 1.24344e6 0.0831914
742742 −1.21427e7 −0.809667
743743 5.40170e6 0.358970 0.179485 0.983761i 0.442557π-0.442557\pi
0.179485 + 0.983761i 0.442557π0.442557\pi
744744 3.20555e7 2.12310
745745 0 0
746746 −1.70891e7 −1.12427
747747 −1.57206e7 −1.03079
748748 716609. 0.0468305
749749 673285. 0.0438525
750750 0 0
751751 −5.29620e6 −0.342661 −0.171330 0.985214i 0.554807π-0.554807\pi
−0.171330 + 0.985214i 0.554807π0.554807\pi
752752 469261. 0.0302601
753753 −1.47985e7 −0.951109
754754 −3.79509e6 −0.243105
755755 0 0
756756 4.28628e6 0.272757
757757 −8.87136e6 −0.562665 −0.281333 0.959610i 0.590776π-0.590776\pi
−0.281333 + 0.959610i 0.590776π0.590776\pi
758758 −1.07064e7 −0.676815
759759 771318. 0.0485992
760760 0 0
761761 −2.06961e7 −1.29547 −0.647734 0.761867i 0.724283π-0.724283\pi
−0.647734 + 0.761867i 0.724283π0.724283\pi
762762 5.51238e6 0.343916
763763 4.70927e6 0.292848
764764 −1.66738e7 −1.03348
765765 0 0
766766 −1.49689e7 −0.921763
767767 5.01183e6 0.307615
768768 2.34201e7 1.43280
769769 5.78756e6 0.352923 0.176461 0.984308i 0.443535π-0.443535\pi
0.176461 + 0.984308i 0.443535π0.443535\pi
770770 0 0
771771 2.02981e7 1.22976
772772 −5.74532e6 −0.346953
773773 1.74975e7 1.05324 0.526619 0.850101i 0.323459π-0.323459\pi
0.526619 + 0.850101i 0.323459π0.323459\pi
774774 −4.94996e6 −0.296995
775775 0 0
776776 −2.31464e7 −1.37984
777777 240420. 0.0142863
778778 −5.87175e6 −0.347791
779779 −4.08684e6 −0.241292
780780 0 0
781781 −1.92505e6 −0.112931
782782 −1.73410e6 −0.101405
783783 1.50635e7 0.878052
784784 −810319. −0.0470832
785785 0 0
786786 −2.09660e7 −1.21048
787787 1.50075e7 0.863719 0.431860 0.901941i 0.357858π-0.357858\pi
0.431860 + 0.901941i 0.357858π0.357858\pi
788788 6.41633e6 0.368104
789789 −1.41050e7 −0.806642
790790 0 0
791791 −1.33028e7 −0.755965
792792 −2.67523e6 −0.151547
793793 −8.71121e6 −0.491921
794794 −1.71586e7 −0.965899
795795 0 0
796796 −6.15930e6 −0.344547
797797 2.52578e7 1.40848 0.704240 0.709962i 0.251288π-0.251288\pi
0.704240 + 0.709962i 0.251288π0.251288\pi
798798 2.22797e6 0.123852
799799 3.62455e6 0.200857
800800 0 0
801801 −2.12412e7 −1.16976
802802 −1.33337e7 −0.732008
803803 −2.05933e6 −0.112703
804804 −2.63209e7 −1.43602
805805 0 0
806806 −4.24304e6 −0.230059
807807 −4.98675e7 −2.69547
808808 3.05307e7 1.64516
809809 4.92229e6 0.264421 0.132210 0.991222i 0.457793π-0.457793\pi
0.132210 + 0.991222i 0.457793π0.457793\pi
810810 0 0
811811 9.00480e6 0.480753 0.240376 0.970680i 0.422729π-0.422729\pi
0.240376 + 0.970680i 0.422729π0.422729\pi
812812 1.31665e7 0.700780
813813 −4.62170e7 −2.45231
814814 −16388.9 −0.000866942 0
815815 0 0
816816 −1.73098e6 −0.0910052
817817 1.36925e6 0.0717677
818818 7.37984e6 0.385624
819819 −5.19466e6 −0.270612
820820 0 0
821821 2.32720e7 1.20497 0.602486 0.798130i 0.294177π-0.294177\pi
0.602486 + 0.798130i 0.294177π0.294177\pi
822822 −3.87663e6 −0.200113
823823 2.00591e7 1.03232 0.516158 0.856493i 0.327362π-0.327362\pi
0.516158 + 0.856493i 0.327362π0.327362\pi
824824 −7.27584e6 −0.373306
825825 0 0
826826 8.98010e6 0.457964
827827 −9.70394e6 −0.493383 −0.246692 0.969094i 0.579343π-0.579343\pi
−0.246692 + 0.969094i 0.579343π0.579343\pi
828828 −4.98114e6 −0.252495
829829 −2.31044e7 −1.16764 −0.583819 0.811884i 0.698442π-0.698442\pi
−0.583819 + 0.811884i 0.698442π0.698442\pi
830830 0 0
831831 −4.09965e7 −2.05942
832832 −2.78539e6 −0.139501
833833 −6.25886e6 −0.312523
834834 1.53552e7 0.764432
835835 0 0
836836 294072. 0.0145525
837837 1.68415e7 0.830934
838838 −5.04544e6 −0.248193
839839 2.47020e6 0.121151 0.0605755 0.998164i 0.480706π-0.480706\pi
0.0605755 + 0.998164i 0.480706π0.480706\pi
840840 0 0
841841 2.57605e7 1.25593
842842 9.27270e6 0.450740
843843 2.31127e7 1.12016
844844 −9.44351e6 −0.456328
845845 0 0
846846 −5.37703e6 −0.258295
847847 −1.45824e7 −0.698426
848848 3.87141e6 0.184876
849849 4.43715e7 2.11269
850850 0 0
851851 −76790.6 −0.00363483
852852 2.14469e7 1.01220
853853 −2.26066e7 −1.06381 −0.531903 0.846805i 0.678523π-0.678523\pi
−0.531903 + 0.846805i 0.678523π0.678523\pi
854854 −1.56086e7 −0.732350
855855 0 0
856856 1.28674e6 0.0600215
857857 −352440. −0.0163920 −0.00819602 0.999966i 0.502609π-0.502609\pi
−0.00819602 + 0.999966i 0.502609π0.502609\pi
858858 610892. 0.0283300
859859 8.16362e6 0.377485 0.188743 0.982027i 0.439559π-0.439559\pi
0.188743 + 0.982027i 0.439559π0.439559\pi
860860 0 0
861861 2.94543e7 1.35407
862862 8.73124e6 0.400228
863863 2.20483e7 1.00774 0.503869 0.863780i 0.331910π-0.331910\pi
0.503869 + 0.863780i 0.331910π0.331910\pi
864864 1.31281e7 0.598299
865865 0 0
866866 2.10800e7 0.955160
867867 2.07687e7 0.938343
868868 1.47207e7 0.663175
869869 −2.84778e6 −0.127925
870870 0 0
871871 8.76731e6 0.391581
872872 9.00007e6 0.400825
873873 −4.42458e7 −1.96488
874874 −711616. −0.0315113
875875 0 0
876876 2.29429e7 1.01016
877877 −3.29930e7 −1.44852 −0.724258 0.689529i 0.757818π-0.757818\pi
−0.724258 + 0.689529i 0.757818π0.757818\pi
878878 6.08405e6 0.266352
879879 −1.02208e7 −0.446185
880880 0 0
881881 −2.33438e7 −1.01328 −0.506642 0.862156i 0.669114π-0.669114\pi
−0.506642 + 0.862156i 0.669114π0.669114\pi
882882 9.28504e6 0.401895
883883 3.71832e6 0.160489 0.0802444 0.996775i 0.474430π-0.474430\pi
0.0802444 + 0.996775i 0.474430π0.474430\pi
884884 2.65932e6 0.114456
885885 0 0
886886 −2.01660e6 −0.0863051
887887 5.38193e6 0.229683 0.114841 0.993384i 0.463364π-0.463364\pi
0.114841 + 0.993384i 0.463364π0.463364\pi
888888 459477. 0.0195538
889889 6.37022e6 0.270334
890890 0 0
891891 1.28360e6 0.0541670
892892 −3340.99 −0.000140593 0
893893 1.48739e6 0.0624160
894894 −1.05579e7 −0.441807
895895 0 0
896896 1.24104e7 0.516436
897897 2.86234e6 0.118779
898898 4.38507e6 0.181462
899899 5.17334e7 2.13487
900900 0 0
901901 2.99026e7 1.22715
902902 −2.00783e6 −0.0821697
903903 −9.86836e6 −0.402741
904904 −2.54235e7 −1.03470
905905 0 0
906906 −2.46300e7 −0.996883
907907 2.68436e7 1.08348 0.541742 0.840545i 0.317765π-0.317765\pi
0.541742 + 0.840545i 0.317765π0.317765\pi
908908 −2.40455e7 −0.967873
909909 5.83614e7 2.34270
910910 0 0
911911 1.10032e7 0.439260 0.219630 0.975583i 0.429515π-0.429515\pi
0.219630 + 0.975583i 0.429515π0.429515\pi
912912 −710334. −0.0282797
913913 2.13645e6 0.0848235
914914 3.48990e6 0.138181
915915 0 0
916916 −1.46296e7 −0.576095
917917 −2.42287e7 −0.951496
918918 5.45140e6 0.213502
919919 4.98823e7 1.94831 0.974153 0.225887i 0.0725282π-0.0725282\pi
0.974153 + 0.225887i 0.0725282π0.0725282\pi
920920 0 0
921921 1.60945e7 0.625215
922922 291143. 0.0112792
923923 −7.14381e6 −0.276011
924924 −2.11941e6 −0.0816647
925925 0 0
926926 1.68462e7 0.645615
927927 −1.39082e7 −0.531585
928928 4.03268e7 1.53718
929929 −4.09032e7 −1.55495 −0.777477 0.628911i 0.783501π-0.783501\pi
−0.777477 + 0.628911i 0.783501π0.783501\pi
930930 0 0
931931 −2.56842e6 −0.0971163
932932 8.43622e6 0.318132
933933 2.64730e7 0.995632
934934 −1.42919e7 −0.536073
935935 0 0
936936 −9.92771e6 −0.370390
937937 4.44775e7 1.65498 0.827488 0.561483i 0.189769π-0.189769\pi
0.827488 + 0.561483i 0.189769π0.189769\pi
938938 1.57091e7 0.582968
939939 −1.67880e7 −0.621348
940940 0 0
941941 8.18280e6 0.301251 0.150625 0.988591i 0.451871π-0.451871\pi
0.150625 + 0.988591i 0.451871π0.451871\pi
942942 −3.94472e6 −0.144840
943943 −9.40773e6 −0.344513
944944 −2.86309e6 −0.104569
945945 0 0
946946 672705. 0.0244397
947947 3.72825e7 1.35092 0.675461 0.737396i 0.263945π-0.263945\pi
0.675461 + 0.737396i 0.263945π0.263945\pi
948948 3.17270e7 1.14659
949949 −7.64213e6 −0.275454
950950 0 0
951951 3.00793e7 1.07849
952952 1.19907e7 0.428798
953953 4.11870e7 1.46902 0.734511 0.678597i 0.237412π-0.237412\pi
0.734511 + 0.678597i 0.237412π0.237412\pi
954954 −4.43606e7 −1.57807
955955 0 0
956956 −9.39967e6 −0.332635
957957 −7.44832e6 −0.262893
958958 −9.54050e6 −0.335859
959959 −4.47992e6 −0.157298
960960 0 0
961961 2.92107e7 1.02031
962962 −60819.0 −0.00211886
963963 2.45969e6 0.0854702
964964 2.59903e7 0.900781
965965 0 0
966966 5.12869e6 0.176833
967967 2.42760e7 0.834856 0.417428 0.908710i 0.362932π-0.362932\pi
0.417428 + 0.908710i 0.362932π0.362932\pi
968968 −2.78690e7 −0.955944
969969 −5.48658e6 −0.187712
970970 0 0
971971 −2.85115e6 −0.0970446 −0.0485223 0.998822i 0.515451π-0.515451\pi
−0.0485223 + 0.998822i 0.515451π0.515451\pi
972972 −2.56557e7 −0.870999
973973 1.77447e7 0.600879
974974 −1.11366e7 −0.376146
975975 0 0
976976 4.97642e6 0.167222
977977 3.23237e7 1.08339 0.541695 0.840575i 0.317783π-0.317783\pi
0.541695 + 0.840575i 0.317783π0.317783\pi
978978 5.23031e7 1.74856
979979 2.88670e6 0.0962597
980980 0 0
981981 1.72042e7 0.570772
982982 −1.73264e7 −0.573362
983983 1.56769e7 0.517461 0.258731 0.965950i 0.416696π-0.416696\pi
0.258731 + 0.965950i 0.416696π0.416696\pi
984984 5.62912e7 1.85333
985985 0 0
986986 1.67455e7 0.548538
987987 −1.07198e7 −0.350262
988988 1.09129e6 0.0355672
989989 3.15197e6 0.102469
990990 0 0
991991 5.10915e7 1.65259 0.826294 0.563239i 0.190445π-0.190445\pi
0.826294 + 0.563239i 0.190445π0.190445\pi
992992 4.50868e7 1.45469
993993 5.72485e7 1.84243
994994 −1.28002e7 −0.410912
995995 0 0
996996 −2.38021e7 −0.760269
997997 −5.33407e7 −1.69950 −0.849749 0.527188i 0.823247π-0.823247\pi
−0.849749 + 0.527188i 0.823247π0.823247\pi
998998 1.16129e7 0.369073
999999 241403. 0.00765294
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.m.1.6 15
5.2 odd 4 65.6.b.a.14.12 30
5.3 odd 4 65.6.b.a.14.19 yes 30
5.4 even 2 325.6.a.l.1.10 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.6.b.a.14.12 30 5.2 odd 4
65.6.b.a.14.19 yes 30 5.3 odd 4
325.6.a.l.1.10 15 5.4 even 2
325.6.a.m.1.6 15 1.1 even 1 trivial