Properties

Label 650.6.a.s.1.5
Level 650650
Weight 66
Character 650.1
Self dual yes
Analytic conductor 104.249104.249
Analytic rank 11
Dimension 66
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] = [650,6,Mod(1,650)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(650, 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("650.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 650=25213 650 = 2 \cdot 5^{2} \cdot 13
Weight: k k == 6 6
Character orbit: [χ][\chi] == 650.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: 104.249482878104.249482878
Analytic rank: 11
Dimension: 66
Coefficient field: Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x63x51033x4+1207x3+258312x2435604x11275680 x^{6} - 3x^{5} - 1033x^{4} + 1207x^{3} + 258312x^{2} - 435604x - 11275680 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 233252 2^{3}\cdot 3^{2}\cdot 5^{2}
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 19.7411-19.7411 of defining polynomial
Character χ\chi == 650.1

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) == q4.00000q2+18.7411q3+16.0000q474.9644q6+230.695q764.0000q8+108.229q9544.656q11+299.858q12169.000q13922.779q14+256.000q16+554.057q17432.917q182228.18q19+4323.47q21+2178.63q22+2915.01q231199.43q24+676.000q262525.75q27+3691.11q286864.22q296257.84q311024.00q3210207.5q332216.23q34+1731.67q365695.55q37+8912.71q383167.25q3911997.2q4117293.9q4215451.4q438714.50q4411660.0q46+16278.3q47+4797.72q48+36413.0q49+10383.6q512704.00q52+11052.3q53+10103.0q5414764.5q5641758.5q57+27456.9q5824145.9q5910681.8q61+25031.4q62+24967.9q63+4096.00q64+40829.9q6652777.4q67+8864.91q68+54630.5q6944162.3q716926.67q72+41761.3q73+22782.2q7435650.8q76125649.q77+12669.0q7859573.9q7973635.1q81+47988.7q8222640.6q83+69175.6q84+61805.8q86128643.q87+34858.0q88+129864.q8938987.4q91+46640.1q92117279.q9365113.1q9419190.9q9663287.9q97145652.q9858947.7q99+O(q100)q-4.00000 q^{2} +18.7411 q^{3} +16.0000 q^{4} -74.9644 q^{6} +230.695 q^{7} -64.0000 q^{8} +108.229 q^{9} -544.656 q^{11} +299.858 q^{12} -169.000 q^{13} -922.779 q^{14} +256.000 q^{16} +554.057 q^{17} -432.917 q^{18} -2228.18 q^{19} +4323.47 q^{21} +2178.63 q^{22} +2915.01 q^{23} -1199.43 q^{24} +676.000 q^{26} -2525.75 q^{27} +3691.11 q^{28} -6864.22 q^{29} -6257.84 q^{31} -1024.00 q^{32} -10207.5 q^{33} -2216.23 q^{34} +1731.67 q^{36} -5695.55 q^{37} +8912.71 q^{38} -3167.25 q^{39} -11997.2 q^{41} -17293.9 q^{42} -15451.4 q^{43} -8714.50 q^{44} -11660.0 q^{46} +16278.3 q^{47} +4797.72 q^{48} +36413.0 q^{49} +10383.6 q^{51} -2704.00 q^{52} +11052.3 q^{53} +10103.0 q^{54} -14764.5 q^{56} -41758.5 q^{57} +27456.9 q^{58} -24145.9 q^{59} -10681.8 q^{61} +25031.4 q^{62} +24967.9 q^{63} +4096.00 q^{64} +40829.9 q^{66} -52777.4 q^{67} +8864.91 q^{68} +54630.5 q^{69} -44162.3 q^{71} -6926.67 q^{72} +41761.3 q^{73} +22782.2 q^{74} -35650.8 q^{76} -125649. q^{77} +12669.0 q^{78} -59573.9 q^{79} -73635.1 q^{81} +47988.7 q^{82} -22640.6 q^{83} +69175.6 q^{84} +61805.8 q^{86} -128643. q^{87} +34858.0 q^{88} +129864. q^{89} -38987.4 q^{91} +46640.1 q^{92} -117279. q^{93} -65113.1 q^{94} -19190.9 q^{96} -63287.9 q^{97} -145652. q^{98} -58947.7 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q24q29q3+96q4+36q6+63q7384q8+629q9+370q11144q121014q13252q14+1536q16838q172516q181659q19+4322q21++386119q99+O(q100) 6 q - 24 q^{2} - 9 q^{3} + 96 q^{4} + 36 q^{6} + 63 q^{7} - 384 q^{8} + 629 q^{9} + 370 q^{11} - 144 q^{12} - 1014 q^{13} - 252 q^{14} + 1536 q^{16} - 838 q^{17} - 2516 q^{18} - 1659 q^{19} + 4322 q^{21}+ \cdots + 386119 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 −4.00000 −0.707107
33 18.7411 1.20224 0.601121 0.799158i 0.294721π-0.294721\pi
0.601121 + 0.799158i 0.294721π0.294721\pi
44 16.0000 0.500000
55 0 0
66 −74.9644 −0.850114
77 230.695 1.77948 0.889739 0.456470i 0.150887π-0.150887\pi
0.889739 + 0.456470i 0.150887π0.150887\pi
88 −64.0000 −0.353553
99 108.229 0.445388
1010 0 0
1111 −544.656 −1.35719 −0.678595 0.734512i 0.737411π-0.737411\pi
−0.678595 + 0.734512i 0.737411π0.737411\pi
1212 299.858 0.601121
1313 −169.000 −0.277350
1414 −922.779 −1.25828
1515 0 0
1616 256.000 0.250000
1717 554.057 0.464977 0.232489 0.972599i 0.425313π-0.425313\pi
0.232489 + 0.972599i 0.425313π0.425313\pi
1818 −432.917 −0.314937
1919 −2228.18 −1.41601 −0.708004 0.706208i 0.750404π-0.750404\pi
−0.708004 + 0.706208i 0.750404π0.750404\pi
2020 0 0
2121 4323.47 2.13936
2222 2178.63 0.959679
2323 2915.01 1.14900 0.574500 0.818505i 0.305197π-0.305197\pi
0.574500 + 0.818505i 0.305197π0.305197\pi
2424 −1199.43 −0.425057
2525 0 0
2626 676.000 0.196116
2727 −2525.75 −0.666779
2828 3691.11 0.889739
2929 −6864.22 −1.51564 −0.757820 0.652464i 0.773736π-0.773736\pi
−0.757820 + 0.652464i 0.773736π0.773736\pi
3030 0 0
3131 −6257.84 −1.16955 −0.584777 0.811194i 0.698818π-0.698818\pi
−0.584777 + 0.811194i 0.698818π0.698818\pi
3232 −1024.00 −0.176777
3333 −10207.5 −1.63167
3434 −2216.23 −0.328789
3535 0 0
3636 1731.67 0.222694
3737 −5695.55 −0.683961 −0.341980 0.939707i 0.611098π-0.611098\pi
−0.341980 + 0.939707i 0.611098π0.611098\pi
3838 8912.71 1.00127
3939 −3167.25 −0.333442
4040 0 0
4141 −11997.2 −1.11460 −0.557300 0.830311i 0.688163π-0.688163\pi
−0.557300 + 0.830311i 0.688163π0.688163\pi
4242 −17293.9 −1.51276
4343 −15451.4 −1.27438 −0.637189 0.770708i 0.719903π-0.719903\pi
−0.637189 + 0.770708i 0.719903π0.719903\pi
4444 −8714.50 −0.678595
4545 0 0
4646 −11660.0 −0.812466
4747 16278.3 1.07489 0.537445 0.843299i 0.319390π-0.319390\pi
0.537445 + 0.843299i 0.319390π0.319390\pi
4848 4797.72 0.300561
4949 36413.0 2.16654
5050 0 0
5151 10383.6 0.559016
5252 −2704.00 −0.138675
5353 11052.3 0.540462 0.270231 0.962796i 0.412900π-0.412900\pi
0.270231 + 0.962796i 0.412900π0.412900\pi
5454 10103.0 0.471484
5555 0 0
5656 −14764.5 −0.629140
5757 −41758.5 −1.70239
5858 27456.9 1.07172
5959 −24145.9 −0.903054 −0.451527 0.892257i 0.649121π-0.649121\pi
−0.451527 + 0.892257i 0.649121π0.649121\pi
6060 0 0
6161 −10681.8 −0.367552 −0.183776 0.982968i 0.558832π-0.558832\pi
−0.183776 + 0.982968i 0.558832π0.558832\pi
6262 25031.4 0.827000
6363 24967.9 0.792557
6464 4096.00 0.125000
6565 0 0
6666 40829.9 1.15377
6767 −52777.4 −1.43635 −0.718176 0.695861i 0.755023π-0.755023\pi
−0.718176 + 0.695861i 0.755023π0.755023\pi
6868 8864.91 0.232489
6969 54630.5 1.38138
7070 0 0
7171 −44162.3 −1.03970 −0.519848 0.854259i 0.674011π-0.674011\pi
−0.519848 + 0.854259i 0.674011π0.674011\pi
7272 −6926.67 −0.157468
7373 41761.3 0.917205 0.458602 0.888642i 0.348350π-0.348350\pi
0.458602 + 0.888642i 0.348350π0.348350\pi
7474 22782.2 0.483633
7575 0 0
7676 −35650.8 −0.708004
7777 −125649. −2.41509
7878 12669.0 0.235779
7979 −59573.9 −1.07396 −0.536980 0.843595i 0.680435π-0.680435\pi
−0.536980 + 0.843595i 0.680435π0.680435\pi
8080 0 0
8181 −73635.1 −1.24702
8282 47988.7 0.788141
8383 −22640.6 −0.360738 −0.180369 0.983599i 0.557729π-0.557729\pi
−0.180369 + 0.983599i 0.557729π0.557729\pi
8484 69175.6 1.06968
8585 0 0
8686 61805.8 0.901121
8787 −128643. −1.82217
8888 34858.0 0.479839
8989 129864. 1.73786 0.868930 0.494935i 0.164808π-0.164808\pi
0.868930 + 0.494935i 0.164808π0.164808\pi
9090 0 0
9191 −38987.4 −0.493538
9292 46640.1 0.574500
9393 −117279. −1.40609
9494 −65113.1 −0.760061
9595 0 0
9696 −19190.9 −0.212529
9797 −63287.9 −0.682953 −0.341477 0.939890i 0.610927π-0.610927\pi
−0.341477 + 0.939890i 0.610927π0.610927\pi
9898 −145652. −1.53197
9999 −58947.7 −0.604476
100100 0 0
101101 116458. 1.13596 0.567982 0.823041i 0.307724π-0.307724\pi
0.567982 + 0.823041i 0.307724π0.307724\pi
102102 −41534.6 −0.395284
103103 48487.1 0.450333 0.225166 0.974320i 0.427707π-0.427707\pi
0.225166 + 0.974320i 0.427707π0.427707\pi
104104 10816.0 0.0980581
105105 0 0
106106 −44209.4 −0.382164
107107 189220. 1.59775 0.798874 0.601499i 0.205430π-0.205430\pi
0.798874 + 0.601499i 0.205430π0.205430\pi
108108 −40412.1 −0.333389
109109 157628. 1.27077 0.635384 0.772197i 0.280842π-0.280842\pi
0.635384 + 0.772197i 0.280842π0.280842\pi
110110 0 0
111111 −106741. −0.822287
112112 59057.8 0.444869
113113 200949. 1.48044 0.740219 0.672365i 0.234722π-0.234722\pi
0.740219 + 0.672365i 0.234722π0.234722\pi
114114 167034. 1.20377
115115 0 0
116116 −109827. −0.757820
117117 −18290.7 −0.123528
118118 96583.7 0.638556
119119 127818. 0.827417
120120 0 0
121121 135600. 0.841966
122122 42727.1 0.259898
123123 −224840. −1.34002
124124 −100125. −0.584777
125125 0 0
126126 −99871.6 −0.560423
127127 −283395. −1.55913 −0.779565 0.626321i 0.784560π-0.784560\pi
−0.779565 + 0.626321i 0.784560π0.784560\pi
128128 −16384.0 −0.0883883
129129 −289577. −1.53211
130130 0 0
131131 −199352. −1.01494 −0.507472 0.861668i 0.669420π-0.669420\pi
−0.507472 + 0.861668i 0.669420π0.669420\pi
132132 −163319. −0.815836
133133 −514029. −2.51975
134134 211110. 1.01565
135135 0 0
136136 −35459.6 −0.164394
137137 265825. 1.21003 0.605013 0.796216i 0.293168π-0.293168\pi
0.605013 + 0.796216i 0.293168π0.293168\pi
138138 −218522. −0.976781
139139 985.292 0.00432541 0.00216271 0.999998i 0.499312π-0.499312\pi
0.00216271 + 0.999998i 0.499312π0.499312\pi
140140 0 0
141141 305073. 1.29228
142142 176649. 0.735176
143143 92046.9 0.376417
144144 27706.7 0.111347
145145 0 0
146146 −167045. −0.648562
147147 682420. 2.60471
148148 −91128.7 −0.341980
149149 −20636.5 −0.0761502 −0.0380751 0.999275i 0.512123π-0.512123\pi
−0.0380751 + 0.999275i 0.512123π0.512123\pi
150150 0 0
151151 31649.1 0.112959 0.0564793 0.998404i 0.482013π-0.482013\pi
0.0564793 + 0.998404i 0.482013π0.482013\pi
152152 142603. 0.500635
153153 59965.1 0.207095
154154 502597. 1.70773
155155 0 0
156156 −50676.0 −0.166721
157157 −475091. −1.53825 −0.769126 0.639097i 0.779308π-0.779308\pi
−0.769126 + 0.639097i 0.779308π0.779308\pi
158158 238296. 0.759405
159159 207133. 0.649766
160160 0 0
161161 672477. 2.04462
162162 294541. 0.881775
163163 368397. 1.08604 0.543022 0.839719i 0.317280π-0.317280\pi
0.543022 + 0.839719i 0.317280π0.317280\pi
164164 −191955. −0.557300
165165 0 0
166166 90562.2 0.255080
167167 −446876. −1.23993 −0.619963 0.784631i 0.712852π-0.712852\pi
−0.619963 + 0.784631i 0.712852π0.712852\pi
168168 −276702. −0.756379
169169 28561.0 0.0769231
170170 0 0
171171 −241154. −0.630673
172172 −247223. −0.637189
173173 −218403. −0.554810 −0.277405 0.960753i 0.589474π-0.589474\pi
−0.277405 + 0.960753i 0.589474π0.589474\pi
174174 514572. 1.28847
175175 0 0
176176 −139432. −0.339298
177177 −452521. −1.08569
178178 −519457. −1.22885
179179 338950. 0.790684 0.395342 0.918534i 0.370626π-0.370626\pi
0.395342 + 0.918534i 0.370626π0.370626\pi
180180 0 0
181181 −440716. −0.999915 −0.499957 0.866050i 0.666651π-0.666651\pi
−0.499957 + 0.866050i 0.666651π0.666651\pi
182182 155950. 0.348984
183183 −200188. −0.441887
184184 −186560. −0.406233
185185 0 0
186186 469116. 0.994255
187187 −301771. −0.631063
188188 260452. 0.537445
189189 −582678. −1.18652
190190 0 0
191191 643313. 1.27596 0.637982 0.770051i 0.279769π-0.279769\pi
0.637982 + 0.770051i 0.279769π0.279769\pi
192192 76763.6 0.150280
193193 −389679. −0.753033 −0.376517 0.926410i 0.622878π-0.622878\pi
−0.376517 + 0.926410i 0.622878π0.622878\pi
194194 253151. 0.482921
195195 0 0
196196 582608. 1.08327
197197 −326458. −0.599323 −0.299662 0.954046i 0.596874π-0.596874\pi
−0.299662 + 0.954046i 0.596874π0.596874\pi
198198 235791. 0.427429
199199 433426. 0.775858 0.387929 0.921689i 0.373191π-0.373191\pi
0.387929 + 0.921689i 0.373191π0.373191\pi
200200 0 0
201201 −989107. −1.72684
202202 −465830. −0.803247
203203 −1.58354e6 −2.69705
204204 166138. 0.279508
205205 0 0
206206 −193949. −0.318433
207207 315489. 0.511751
208208 −43264.0 −0.0693375
209209 1.21359e6 1.92179
210210 0 0
211211 −76110.5 −0.117690 −0.0588448 0.998267i 0.518742π-0.518742\pi
−0.0588448 + 0.998267i 0.518742π0.518742\pi
212212 176838. 0.270231
213213 −827651. −1.24997
214214 −756881. −1.12978
215215 0 0
216216 161648. 0.235742
217217 −1.44365e6 −2.08120
218218 −630510. −0.898568
219219 782652. 1.10270
220220 0 0
221221 −93635.6 −0.128962
222222 426963. 0.581444
223223 141163. 0.190090 0.0950450 0.995473i 0.469700π-0.469700\pi
0.0950450 + 0.995473i 0.469700π0.469700\pi
224224 −236231. −0.314570
225225 0 0
226226 −803797. −1.04683
227227 968458. 1.24743 0.623715 0.781652i 0.285623π-0.285623\pi
0.623715 + 0.781652i 0.285623π0.285623\pi
228228 −668136. −0.851193
229229 72887.3 0.0918466 0.0459233 0.998945i 0.485377π-0.485377\pi
0.0459233 + 0.998945i 0.485377π0.485377\pi
230230 0 0
231231 −2.35481e6 −2.90352
232232 439310. 0.535860
233233 −613692. −0.740561 −0.370280 0.928920i 0.620738π-0.620738\pi
−0.370280 + 0.928920i 0.620738π0.620738\pi
234234 73163.0 0.0873477
235235 0 0
236236 −386335. −0.451527
237237 −1.11648e6 −1.29116
238238 −511272. −0.585072
239239 −1.21444e6 −1.37525 −0.687626 0.726065i 0.741347π-0.741347\pi
−0.687626 + 0.726065i 0.741347π0.741347\pi
240240 0 0
241241 −1.78850e6 −1.98356 −0.991780 0.127957i 0.959158π-0.959158\pi
−0.991780 + 0.127957i 0.959158π0.959158\pi
242242 −542398. −0.595360
243243 −766246. −0.832439
244244 −170908. −0.183776
245245 0 0
246246 899361. 0.947537
247247 376562. 0.392730
248248 400502. 0.413500
249249 −424309. −0.433695
250250 0 0
251251 427715. 0.428519 0.214259 0.976777i 0.431266π-0.431266\pi
0.214259 + 0.976777i 0.431266π0.431266\pi
252252 399486. 0.396279
253253 −1.58768e6 −1.55941
254254 1.13358e6 1.10247
255255 0 0
256256 65536.0 0.0625000
257257 271022. 0.255960 0.127980 0.991777i 0.459151π-0.459151\pi
0.127980 + 0.991777i 0.459151π0.459151\pi
258258 1.15831e6 1.08337
259259 −1.31393e6 −1.21709
260260 0 0
261261 −742909. −0.675048
262262 797407. 0.717673
263263 1.31591e6 1.17310 0.586552 0.809912i 0.300485π-0.300485\pi
0.586552 + 0.809912i 0.300485π0.300485\pi
264264 653278. 0.576883
265265 0 0
266266 2.05611e6 1.78174
267267 2.43380e6 2.08933
268268 −844438. −0.718176
269269 −1.63605e6 −1.37853 −0.689266 0.724508i 0.742067π-0.742067\pi
−0.689266 + 0.724508i 0.742067π0.742067\pi
270270 0 0
271271 −1.41289e6 −1.16865 −0.584326 0.811519i 0.698641π-0.698641\pi
−0.584326 + 0.811519i 0.698641π0.698641\pi
272272 141839. 0.116244
273273 −730667. −0.593353
274274 −1.06330e6 −0.855617
275275 0 0
276276 874088. 0.690689
277277 −755228. −0.591397 −0.295698 0.955281i 0.595552π-0.595552\pi
−0.295698 + 0.955281i 0.595552π0.595552\pi
278278 −3941.17 −0.00305853
279279 −677282. −0.520905
280280 0 0
281281 −550427. −0.415848 −0.207924 0.978145i 0.566671π-0.566671\pi
−0.207924 + 0.978145i 0.566671π0.566671\pi
282282 −1.22029e6 −0.913778
283283 1.12011e6 0.831367 0.415683 0.909509i 0.363542π-0.363542\pi
0.415683 + 0.909509i 0.363542π0.363542\pi
284284 −706597. −0.519848
285285 0 0
286286 −368188. −0.266167
287287 −2.76768e6 −1.98341
288288 −110827. −0.0787342
289289 −1.11288e6 −0.783796
290290 0 0
291291 −1.18608e6 −0.821076
292292 668180. 0.458602
293293 1.47320e6 1.00252 0.501260 0.865297i 0.332870π-0.332870\pi
0.501260 + 0.865297i 0.332870π0.332870\pi
294294 −2.72968e6 −1.84181
295295 0 0
296296 364515. 0.241817
297297 1.37567e6 0.904946
298298 82546.1 0.0538463
299299 −492636. −0.318675
300300 0 0
301301 −3.56457e6 −2.26772
302302 −126596. −0.0798737
303303 2.18254e6 1.36570
304304 −570414. −0.354002
305305 0 0
306306 −239861. −0.146438
307307 −1.42452e6 −0.862623 −0.431312 0.902203i 0.641949π-0.641949\pi
−0.431312 + 0.902203i 0.641949π0.641949\pi
308308 −2.01039e6 −1.20754
309309 908703. 0.541409
310310 0 0
311311 −1.79196e6 −1.05058 −0.525288 0.850924i 0.676043π-0.676043\pi
−0.525288 + 0.850924i 0.676043π0.676043\pi
312312 202704. 0.117890
313313 2.93685e6 1.69442 0.847209 0.531260i 0.178281π-0.178281\pi
0.847209 + 0.531260i 0.178281π0.178281\pi
314314 1.90036e6 1.08771
315315 0 0
316316 −953182. −0.536980
317317 −390977. −0.218526 −0.109263 0.994013i 0.534849π-0.534849\pi
−0.109263 + 0.994013i 0.534849π0.534849\pi
318318 −828533. −0.459454
319319 3.73864e6 2.05701
320320 0 0
321321 3.54620e6 1.92088
322322 −2.68991e6 −1.44576
323323 −1.23454e6 −0.658412
324324 −1.17816e6 −0.623509
325325 0 0
326326 −1.47359e6 −0.767949
327327 2.95412e6 1.52777
328328 767819. 0.394071
329329 3.75531e6 1.91274
330330 0 0
331331 −2.78981e6 −1.39960 −0.699800 0.714339i 0.746728π-0.746728\pi
−0.699800 + 0.714339i 0.746728π0.746728\pi
332332 −362249. −0.180369
333333 −616425. −0.304628
334334 1.78750e6 0.876760
335335 0 0
336336 1.10681e6 0.534841
337337 −2.51413e6 −1.20591 −0.602953 0.797776i 0.706009π-0.706009\pi
−0.602953 + 0.797776i 0.706009π0.706009\pi
338338 −114244. −0.0543928
339339 3.76601e6 1.77985
340340 0 0
341341 3.40837e6 1.58731
342342 964616. 0.445953
343343 4.52300e6 2.07583
344344 988893. 0.450560
345345 0 0
346346 873614. 0.392310
347347 −310242. −0.138317 −0.0691587 0.997606i 0.522031π-0.522031\pi
−0.0691587 + 0.997606i 0.522031π0.522031\pi
348348 −2.05829e6 −0.911084
349349 −1.17835e6 −0.517859 −0.258929 0.965896i 0.583370π-0.583370\pi
−0.258929 + 0.965896i 0.583370π0.583370\pi
350350 0 0
351351 426852. 0.184931
352352 557728. 0.239920
353353 −1.34357e6 −0.573885 −0.286942 0.957948i 0.592639π-0.592639\pi
−0.286942 + 0.957948i 0.592639π0.592639\pi
354354 1.81009e6 0.767699
355355 0 0
356356 2.07783e6 0.868930
357357 2.39545e6 0.994756
358358 −1.35580e6 −0.559098
359359 −2.61851e6 −1.07230 −0.536152 0.844122i 0.680123π-0.680123\pi
−0.536152 + 0.844122i 0.680123π0.680123\pi
360360 0 0
361361 2.48868e6 1.00508
362362 1.76287e6 0.707046
363363 2.54129e6 1.01225
364364 −623798. −0.246769
365365 0 0
366366 800753. 0.312461
367367 −119818. −0.0464363 −0.0232182 0.999730i 0.507391π-0.507391\pi
−0.0232182 + 0.999730i 0.507391π0.507391\pi
368368 746242. 0.287250
369369 −1.29844e6 −0.496429
370370 0 0
371371 2.54972e6 0.961739
372372 −1.87646e6 −0.703044
373373 2.68734e6 1.00012 0.500058 0.865992i 0.333312π-0.333312\pi
0.500058 + 0.865992i 0.333312π0.333312\pi
374374 1.20708e6 0.446229
375375 0 0
376376 −1.04181e6 −0.380031
377377 1.16005e6 0.420363
378378 2.33071e6 0.838994
379379 1.16326e6 0.415988 0.207994 0.978130i 0.433307π-0.433307\pi
0.207994 + 0.978130i 0.433307π0.433307\pi
380380 0 0
381381 −5.31113e6 −1.87445
382382 −2.57325e6 −0.902243
383383 1.35360e6 0.471514 0.235757 0.971812i 0.424243π-0.424243\pi
0.235757 + 0.971812i 0.424243π0.424243\pi
384384 −307054. −0.106264
385385 0 0
386386 1.55872e6 0.532475
387387 −1.67230e6 −0.567592
388388 −1.01261e6 −0.341477
389389 1.64100e6 0.549839 0.274920 0.961467i 0.411349π-0.411349\pi
0.274920 + 0.961467i 0.411349π0.411349\pi
390390 0 0
391391 1.61508e6 0.534259
392392 −2.33043e6 −0.765987
393393 −3.73607e6 −1.22021
394394 1.30583e6 0.423786
395395 0 0
396396 −943164. −0.302238
397397 1.51737e6 0.483187 0.241593 0.970378i 0.422330π-0.422330\pi
0.241593 + 0.970378i 0.422330π0.422330\pi
398398 −1.73370e6 −0.548614
399399 −9.63347e6 −3.02936
400400 0 0
401401 −4.16517e6 −1.29352 −0.646758 0.762696i 0.723875π-0.723875\pi
−0.646758 + 0.762696i 0.723875π0.723875\pi
402402 3.95643e6 1.22106
403403 1.05758e6 0.324376
404404 1.86332e6 0.567982
405405 0 0
406406 6.33415e6 1.90710
407407 3.10212e6 0.928265
408408 −664553. −0.197642
409409 2.16258e6 0.639240 0.319620 0.947546i 0.396445π-0.396445\pi
0.319620 + 0.947546i 0.396445π0.396445\pi
410410 0 0
411411 4.98186e6 1.45474
412412 775794. 0.225166
413413 −5.57034e6 −1.60696
414414 −1.26196e6 −0.361862
415415 0 0
416416 173056. 0.0490290
417417 18465.5 0.00520020
418418 −4.85436e6 −1.35891
419419 −5.87037e6 −1.63354 −0.816772 0.576961i 0.804238π-0.804238\pi
−0.816772 + 0.576961i 0.804238π0.804238\pi
420420 0 0
421421 −2.14426e6 −0.589621 −0.294810 0.955556i 0.595256π-0.595256\pi
−0.294810 + 0.955556i 0.595256π0.595256\pi
422422 304442. 0.0832192
423423 1.76178e6 0.478742
424424 −707350. −0.191082
425425 0 0
426426 3.31061e6 0.883860
427427 −2.46423e6 −0.654050
428428 3.02752e6 0.798874
429429 1.72506e6 0.452545
430430 0 0
431431 2.56530e6 0.665189 0.332594 0.943070i 0.392076π-0.392076\pi
0.332594 + 0.943070i 0.392076π0.392076\pi
432432 −646593. −0.166695
433433 6.07499e6 1.55713 0.778567 0.627561i 0.215947π-0.215947\pi
0.778567 + 0.627561i 0.215947π0.215947\pi
434434 5.77460e6 1.47163
435435 0 0
436436 2.52204e6 0.635384
437437 −6.49515e6 −1.62699
438438 −3.13061e6 −0.779729
439439 7.17264e6 1.77631 0.888154 0.459547i 0.151988π-0.151988\pi
0.888154 + 0.459547i 0.151988π0.151988\pi
440440 0 0
441441 3.94095e6 0.964950
442442 374542. 0.0911896
443443 1.55350e6 0.376099 0.188049 0.982160i 0.439783π-0.439783\pi
0.188049 + 0.982160i 0.439783π0.439783\pi
444444 −1.70785e6 −0.411143
445445 0 0
446446 −564653. −0.134414
447447 −386751. −0.0915510
448448 944925. 0.222435
449449 −3.57322e6 −0.836456 −0.418228 0.908342i 0.637349π-0.637349\pi
−0.418228 + 0.908342i 0.637349π0.637349\pi
450450 0 0
451451 6.53433e6 1.51272
452452 3.21519e6 0.740219
453453 593139. 0.135804
454454 −3.87383e6 −0.882066
455455 0 0
456456 2.67255e6 0.601884
457457 8.13345e6 1.82173 0.910866 0.412703i 0.135415π-0.135415\pi
0.910866 + 0.412703i 0.135415π0.135415\pi
458458 −291549. −0.0649454
459459 −1.39941e6 −0.310037
460460 0 0
461461 −3.69923e6 −0.810697 −0.405349 0.914162i 0.632850π-0.632850\pi
−0.405349 + 0.914162i 0.632850π0.632850\pi
462462 9.41923e6 2.05310
463463 1.34127e6 0.290779 0.145389 0.989375i 0.453557π-0.453557\pi
0.145389 + 0.989375i 0.453557π0.453557\pi
464464 −1.75724e6 −0.378910
465465 0 0
466466 2.45477e6 0.523655
467467 −2.41068e6 −0.511501 −0.255751 0.966743i 0.582323π-0.582323\pi
−0.255751 + 0.966743i 0.582323π0.582323\pi
468468 −292652. −0.0617642
469469 −1.21755e7 −2.55596
470470 0 0
471471 −8.90373e6 −1.84935
472472 1.54534e6 0.319278
473473 8.41573e6 1.72957
474474 4.46592e6 0.912989
475475 0 0
476476 2.04509e6 0.413708
477477 1.19619e6 0.240715
478478 4.85777e6 0.972450
479479 18669.1 0.00371779 0.00185890 0.999998i 0.499408π-0.499408\pi
0.00185890 + 0.999998i 0.499408π0.499408\pi
480480 0 0
481481 962547. 0.189697
482482 7.15398e6 1.40259
483483 1.26030e7 2.45813
484484 2.16959e6 0.420983
485485 0 0
486486 3.06498e6 0.588623
487487 4.53165e6 0.865832 0.432916 0.901434i 0.357485π-0.357485\pi
0.432916 + 0.901434i 0.357485π0.357485\pi
488488 683633. 0.129949
489489 6.90417e6 1.30569
490490 0 0
491491 3.84989e6 0.720684 0.360342 0.932820i 0.382660π-0.382660\pi
0.360342 + 0.932820i 0.382660π0.382660\pi
492492 −3.59744e6 −0.670010
493493 −3.80317e6 −0.704739
494494 −1.50625e6 −0.277702
495495 0 0
496496 −1.60201e6 −0.292389
497497 −1.01880e7 −1.85011
498498 1.69724e6 0.306668
499499 2.18845e6 0.393445 0.196723 0.980459i 0.436970π-0.436970\pi
0.196723 + 0.980459i 0.436970π0.436970\pi
500500 0 0
501501 −8.37495e6 −1.49069
502502 −1.71086e6 −0.303009
503503 −1.37502e6 −0.242319 −0.121160 0.992633i 0.538661π-0.538661\pi
−0.121160 + 0.992633i 0.538661π0.538661\pi
504504 −1.59795e6 −0.280211
505505 0 0
506506 6.35071e6 1.10267
507507 535265. 0.0924802
508508 −4.53431e6 −0.779565
509509 7.64261e6 1.30752 0.653759 0.756703i 0.273191π-0.273191\pi
0.653759 + 0.756703i 0.273191π0.273191\pi
510510 0 0
511511 9.63410e6 1.63215
512512 −262144. −0.0441942
513513 5.62783e6 0.944164
514514 −1.08409e6 −0.180991
515515 0 0
516516 −4.63324e6 −0.766055
517517 −8.86606e6 −1.45883
518518 5.25573e6 0.860614
519519 −4.09312e6 −0.667016
520520 0 0
521521 1.17487e7 1.89625 0.948123 0.317903i 0.102979π-0.102979\pi
0.948123 + 0.317903i 0.102979π0.102979\pi
522522 2.97164e6 0.477331
523523 −5.40309e6 −0.863750 −0.431875 0.901933i 0.642148π-0.642148\pi
−0.431875 + 0.901933i 0.642148π0.642148\pi
524524 −3.18963e6 −0.507472
525525 0 0
526526 −5.26363e6 −0.829510
527527 −3.46720e6 −0.543817
528528 −2.61311e6 −0.407918
529529 2.06092e6 0.320201
530530 0 0
531531 −2.61330e6 −0.402209
532532 −8.22446e6 −1.25988
533533 2.02752e6 0.309134
534534 −9.73520e6 −1.47738
535535 0 0
536536 3.37775e6 0.507827
537537 6.35230e6 0.950594
538538 6.54422e6 0.974769
539539 −1.98326e7 −2.94041
540540 0 0
541541 −1.33517e7 −1.96129 −0.980646 0.195789i 0.937273π-0.937273\pi
−0.980646 + 0.195789i 0.937273π0.937273\pi
542542 5.65156e6 0.826362
543543 −8.25952e6 −1.20214
544544 −567354. −0.0821972
545545 0 0
546546 2.92267e6 0.419564
547547 −2.40834e6 −0.344152 −0.172076 0.985084i 0.555047π-0.555047\pi
−0.172076 + 0.985084i 0.555047π0.555047\pi
548548 4.25320e6 0.605013
549549 −1.15608e6 −0.163703
550550 0 0
551551 1.52947e7 2.14616
552552 −3.49635e6 −0.488391
553553 −1.37434e7 −1.91109
554554 3.02091e6 0.418180
555555 0 0
556556 15764.7 0.00216271
557557 1.52042e6 0.207647 0.103823 0.994596i 0.466892π-0.466892\pi
0.103823 + 0.994596i 0.466892π0.466892\pi
558558 2.70913e6 0.368336
559559 2.61129e6 0.353449
560560 0 0
561561 −5.65551e6 −0.758691
562562 2.20171e6 0.294049
563563 9.15496e6 1.21727 0.608633 0.793452i 0.291718π-0.291718\pi
0.608633 + 0.793452i 0.291718π0.291718\pi
564564 4.88117e6 0.646139
565565 0 0
566566 −4.48042e6 −0.587865
567567 −1.69872e7 −2.21904
568568 2.82639e6 0.367588
569569 1.18973e7 1.54052 0.770262 0.637727i 0.220125π-0.220125\pi
0.770262 + 0.637727i 0.220125π0.220125\pi
570570 0 0
571571 1.20642e7 1.54849 0.774245 0.632886i 0.218130π-0.218130\pi
0.774245 + 0.632886i 0.218130π0.218130\pi
572572 1.47275e6 0.188208
573573 1.20564e7 1.53402
574574 1.10707e7 1.40248
575575 0 0
576576 443307. 0.0556735
577577 1.38845e6 0.173616 0.0868081 0.996225i 0.472333π-0.472333\pi
0.0868081 + 0.996225i 0.472333π0.472333\pi
578578 4.45151e6 0.554227
579579 −7.30303e6 −0.905329
580580 0 0
581581 −5.22305e6 −0.641925
582582 4.74434e6 0.580588
583583 −6.01973e6 −0.733509
584584 −2.67272e6 −0.324281
585585 0 0
586586 −5.89280e6 −0.708888
587587 −5.80067e6 −0.694836 −0.347418 0.937710i 0.612942π-0.612942\pi
−0.347418 + 0.937710i 0.612942π0.612942\pi
588588 1.09187e7 1.30235
589589 1.39436e7 1.65610
590590 0 0
591591 −6.11818e6 −0.720532
592592 −1.45806e6 −0.170990
593593 1.06130e7 1.23937 0.619684 0.784852i 0.287261π-0.287261\pi
0.619684 + 0.784852i 0.287261π0.287261\pi
594594 −5.50267e6 −0.639893
595595 0 0
596596 −330184. −0.0380751
597597 8.12288e6 0.932770
598598 1.97054e6 0.225337
599599 −4.68069e6 −0.533020 −0.266510 0.963832i 0.585870π-0.585870\pi
−0.266510 + 0.963832i 0.585870π0.585870\pi
600600 0 0
601601 2.65345e6 0.299657 0.149828 0.988712i 0.452128π-0.452128\pi
0.149828 + 0.988712i 0.452128π0.452128\pi
602602 1.42583e7 1.60352
603603 −5.71206e6 −0.639734
604604 506386. 0.0564793
605605 0 0
606606 −8.73018e6 −0.965698
607607 6.58092e6 0.724962 0.362481 0.931991i 0.381930π-0.381930\pi
0.362481 + 0.931991i 0.381930π0.381930\pi
608608 2.28165e6 0.250317
609609 −2.96773e7 −3.24251
610610 0 0
611611 −2.75103e6 −0.298121
612612 959442. 0.103548
613613 8.28523e6 0.890540 0.445270 0.895396i 0.353108π-0.353108\pi
0.445270 + 0.895396i 0.353108π0.353108\pi
614614 5.69806e6 0.609967
615615 0 0
616616 8.04155e6 0.853863
617617 −5.42747e6 −0.573964 −0.286982 0.957936i 0.592652π-0.592652\pi
−0.286982 + 0.957936i 0.592652π0.592652\pi
618618 −3.63481e6 −0.382834
619619 −8.73793e6 −0.916604 −0.458302 0.888796i 0.651542π-0.651542\pi
−0.458302 + 0.888796i 0.651542π0.651542\pi
620620 0 0
621621 −7.36259e6 −0.766129
622622 7.16785e6 0.742870
623623 2.99590e7 3.09248
624624 −810815. −0.0833605
625625 0 0
626626 −1.17474e7 −1.19813
627627 2.27440e7 2.31046
628628 −7.60145e6 −0.769126
629629 −3.15566e6 −0.318026
630630 0 0
631631 −6.93247e6 −0.693130 −0.346565 0.938026i 0.612652π-0.612652\pi
−0.346565 + 0.938026i 0.612652π0.612652\pi
632632 3.81273e6 0.379702
633633 −1.42639e6 −0.141492
634634 1.56391e6 0.154521
635635 0 0
636636 3.31413e6 0.324883
637637 −6.15380e6 −0.600890
638638 −1.49546e7 −1.45453
639639 −4.77966e6 −0.463068
640640 0 0
641641 −9.65973e6 −0.928581 −0.464291 0.885683i 0.653691π-0.653691\pi
−0.464291 + 0.885683i 0.653691π0.653691\pi
642642 −1.41848e7 −1.35827
643643 −588572. −0.0561399 −0.0280700 0.999606i 0.508936π-0.508936\pi
−0.0280700 + 0.999606i 0.508936π0.508936\pi
644644 1.07596e7 1.02231
645645 0 0
646646 4.93815e6 0.465568
647647 7.53056e6 0.707240 0.353620 0.935389i 0.384951π-0.384951\pi
0.353620 + 0.935389i 0.384951π0.384951\pi
648648 4.71265e6 0.440887
649649 1.31512e7 1.22562
650650 0 0
651651 −2.70556e7 −2.50210
652652 5.89436e6 0.543022
653653 −9.16834e6 −0.841410 −0.420705 0.907197i 0.638217π-0.638217\pi
−0.420705 + 0.907197i 0.638217π0.638217\pi
654654 −1.18165e7 −1.08030
655655 0 0
656656 −3.07127e6 −0.278650
657657 4.51979e6 0.408512
658658 −1.50212e7 −1.35251
659659 −1.25416e7 −1.12496 −0.562482 0.826809i 0.690153π-0.690153\pi
−0.562482 + 0.826809i 0.690153π0.690153\pi
660660 0 0
661661 −2.80510e6 −0.249715 −0.124858 0.992175i 0.539847π-0.539847\pi
−0.124858 + 0.992175i 0.539847π0.539847\pi
662662 1.11592e7 0.989667
663663 −1.75483e6 −0.155043
664664 1.44900e6 0.127540
665665 0 0
666666 2.46570e6 0.215404
667667 −2.00092e7 −1.74147
668668 −7.15001e6 −0.619963
669669 2.64556e6 0.228534
670670 0 0
671671 5.81789e6 0.498838
672672 −4.42724e6 −0.378190
673673 −1.88930e7 −1.60792 −0.803958 0.594686i 0.797277π-0.797277\pi
−0.803958 + 0.594686i 0.797277π0.797277\pi
674674 1.00565e7 0.852705
675675 0 0
676676 456976. 0.0384615
677677 −7.43678e6 −0.623610 −0.311805 0.950146i 0.600934π-0.600934\pi
−0.311805 + 0.950146i 0.600934π0.600934\pi
678678 −1.50641e7 −1.25854
679679 −1.46002e7 −1.21530
680680 0 0
681681 1.81500e7 1.49971
682682 −1.36335e7 −1.12240
683683 −1.01428e7 −0.831967 −0.415984 0.909372i 0.636563π-0.636563\pi
−0.415984 + 0.909372i 0.636563π0.636563\pi
684684 −3.85846e6 −0.315336
685685 0 0
686686 −1.80920e7 −1.46783
687687 1.36599e6 0.110422
688688 −3.95557e6 −0.318594
689689 −1.86785e6 −0.149897
690690 0 0
691691 −2.15408e6 −0.171620 −0.0858098 0.996312i 0.527348π-0.527348\pi
−0.0858098 + 0.996312i 0.527348π0.527348\pi
692692 −3.49445e6 −0.277405
693693 −1.35989e7 −1.07565
694694 1.24097e6 0.0978051
695695 0 0
696696 8.23316e6 0.644234
697697 −6.64711e6 −0.518264
698698 4.71341e6 0.366181
699699 −1.15013e7 −0.890334
700700 0 0
701701 −6.90173e6 −0.530472 −0.265236 0.964183i 0.585450π-0.585450\pi
−0.265236 + 0.964183i 0.585450π0.585450\pi
702702 −1.70741e6 −0.130766
703703 1.26907e7 0.968494
704704 −2.23091e6 −0.169649
705705 0 0
706706 5.37429e6 0.405798
707707 2.68661e7 2.02142
708708 −7.24034e6 −0.542845
709709 1.62641e7 1.21511 0.607555 0.794278i 0.292150π-0.292150\pi
0.607555 + 0.794278i 0.292150π0.292150\pi
710710 0 0
711711 −6.44764e6 −0.478329
712712 −8.31131e6 −0.614426
713713 −1.82417e7 −1.34382
714714 −9.58180e6 −0.703399
715715 0 0
716716 5.42320e6 0.395342
717717 −2.27600e7 −1.65339
718718 1.04740e7 0.758233
719719 −6.59643e6 −0.475868 −0.237934 0.971281i 0.576470π-0.576470\pi
−0.237934 + 0.971281i 0.576470π0.576470\pi
720720 0 0
721721 1.11857e7 0.801357
722722 −9.95471e6 −0.710699
723723 −3.35184e7 −2.38472
724724 −7.05146e6 −0.499957
725725 0 0
726726 −1.01651e7 −0.715767
727727 2.19325e7 1.53905 0.769523 0.638620i 0.220494π-0.220494\pi
0.769523 + 0.638620i 0.220494π0.220494\pi
728728 2.49519e6 0.174492
729729 3.53304e6 0.246223
730730 0 0
731731 −8.56098e6 −0.592557
732732 −3.20301e6 −0.220943
733733 1.67003e7 1.14806 0.574028 0.818836i 0.305380π-0.305380\pi
0.574028 + 0.818836i 0.305380π0.305380\pi
734734 479273. 0.0328355
735735 0 0
736736 −2.98497e6 −0.203116
737737 2.87455e7 1.94940
738738 5.19378e6 0.351028
739739 −1.69875e6 −0.114425 −0.0572123 0.998362i 0.518221π-0.518221\pi
−0.0572123 + 0.998362i 0.518221π0.518221\pi
740740 0 0
741741 7.05719e6 0.472157
742742 −1.01989e7 −0.680052
743743 −1.82334e7 −1.21170 −0.605851 0.795578i 0.707167π-0.707167\pi
−0.605851 + 0.795578i 0.707167π0.707167\pi
744744 7.50585e6 0.497127
745745 0 0
746746 −1.07493e7 −0.707188
747747 −2.45037e6 −0.160668
748748 −4.82833e6 −0.315532
749749 4.36521e7 2.84315
750750 0 0
751751 −1.47109e6 −0.0951784 −0.0475892 0.998867i 0.515154π-0.515154\pi
−0.0475892 + 0.998867i 0.515154π0.515154\pi
752752 4.16724e6 0.268722
753753 8.01585e6 0.515184
754754 −4.64021e6 −0.297241
755755 0 0
756756 −9.32285e6 −0.593259
757757 −9.68714e6 −0.614407 −0.307203 0.951644i 0.599393π-0.599393\pi
−0.307203 + 0.951644i 0.599393π0.599393\pi
758758 −4.65306e6 −0.294148
759759 −2.97548e7 −1.87479
760760 0 0
761761 1.09169e7 0.683338 0.341669 0.939820i 0.389008π-0.389008\pi
0.341669 + 0.939820i 0.389008π0.389008\pi
762762 2.12445e7 1.32544
763763 3.63638e7 2.26130
764764 1.02930e7 0.637982
765765 0 0
766766 −5.41441e6 −0.333411
767767 4.08066e6 0.250462
768768 1.22822e6 0.0751402
769769 −1.70886e7 −1.04205 −0.521027 0.853540i 0.674451π-0.674451\pi
−0.521027 + 0.853540i 0.674451π0.674451\pi
770770 0 0
771771 5.07925e6 0.307726
772772 −6.23487e6 −0.376517
773773 −5.92288e6 −0.356520 −0.178260 0.983983i 0.557047π-0.557047\pi
−0.178260 + 0.983983i 0.557047π0.557047\pi
774774 6.68919e6 0.401348
775775 0 0
776776 4.05042e6 0.241461
777777 −2.46245e7 −1.46324
778778 −6.56402e6 −0.388795
779779 2.67318e7 1.57828
780780 0 0
781781 2.40533e7 1.41107
782782 −6.46032e6 −0.377778
783783 1.73373e7 1.01060
784784 9.32173e6 0.541635
785785 0 0
786786 1.49443e7 0.862818
787787 −2.75022e7 −1.58282 −0.791409 0.611288i 0.790652π-0.790652\pi
−0.791409 + 0.611288i 0.790652π0.790652\pi
788788 −5.22332e6 −0.299662
789789 2.46616e7 1.41036
790790 0 0
791791 4.63579e7 2.63441
792792 3.77265e6 0.213715
793793 1.80522e6 0.101941
794794 −6.06947e6 −0.341664
795795 0 0
796796 6.93481e6 0.387929
797797 1.29045e7 0.719606 0.359803 0.933028i 0.382844π-0.382844\pi
0.359803 + 0.933028i 0.382844π0.382844\pi
798798 3.85339e7 2.14208
799799 9.01909e6 0.499799
800800 0 0
801801 1.40551e7 0.774021
802802 1.66607e7 0.914653
803803 −2.27455e7 −1.24482
804804 −1.58257e7 −0.863422
805805 0 0
806806 −4.23030e6 −0.229369
807807 −3.06615e7 −1.65733
808808 −7.45329e6 −0.401624
809809 2.16172e7 1.16126 0.580628 0.814169i 0.302807π-0.302807\pi
0.580628 + 0.814169i 0.302807π0.302807\pi
810810 0 0
811811 −1.68933e7 −0.901906 −0.450953 0.892548i 0.648916π-0.648916\pi
−0.450953 + 0.892548i 0.648916π0.648916\pi
812812 −2.53366e7 −1.34852
813813 −2.64791e7 −1.40500
814814 −1.24085e7 −0.656382
815815 0 0
816816 2.65821e6 0.139754
817817 3.44286e7 1.80453
818818 −8.65032e6 −0.452011
819819 −4.21958e6 −0.219816
820820 0 0
821821 −7.06381e6 −0.365747 −0.182874 0.983136i 0.558540π-0.558540\pi
−0.182874 + 0.983136i 0.558540π0.558540\pi
822822 −1.99274e7 −1.02866
823823 −3.32953e7 −1.71350 −0.856748 0.515735i 0.827519π-0.827519\pi
−0.856748 + 0.515735i 0.827519π0.827519\pi
824824 −3.10318e6 −0.159217
825825 0 0
826826 2.22813e7 1.13630
827827 1.49348e7 0.759341 0.379670 0.925122i 0.376037π-0.376037\pi
0.379670 + 0.925122i 0.376037π0.376037\pi
828828 5.04782e6 0.255875
829829 1.10426e7 0.558065 0.279032 0.960282i 0.409986π-0.409986\pi
0.279032 + 0.960282i 0.409986π0.409986\pi
830830 0 0
831831 −1.41538e7 −0.711002
832832 −692224. −0.0346688
833833 2.01749e7 1.00739
834834 −73861.8 −0.00367710
835835 0 0
836836 1.94175e7 0.960897
837837 1.58058e7 0.779834
838838 2.34815e7 1.15509
839839 2.86322e7 1.40427 0.702133 0.712046i 0.252231π-0.252231\pi
0.702133 + 0.712046i 0.252231π0.252231\pi
840840 0 0
841841 2.66063e7 1.29717
842842 8.57705e6 0.416925
843843 −1.03156e7 −0.499950
844844 −1.21777e6 −0.0588448
845845 0 0
846846 −7.04714e6 −0.338522
847847 3.12821e7 1.49826
848848 2.82940e6 0.135115
849849 2.09920e7 0.999505
850850 0 0
851851 −1.66026e7 −0.785871
852852 −1.32424e7 −0.624983
853853 −1.71429e7 −0.806700 −0.403350 0.915046i 0.632154π-0.632154\pi
−0.403350 + 0.915046i 0.632154π0.632154\pi
854854 9.85691e6 0.462483
855855 0 0
856856 −1.21101e7 −0.564889
857857 −132094. −0.00614373 −0.00307186 0.999995i 0.500978π-0.500978\pi
−0.00307186 + 0.999995i 0.500978π0.500978\pi
858858 −6.90025e6 −0.319997
859859 3.33727e7 1.54315 0.771577 0.636136i 0.219468π-0.219468\pi
0.771577 + 0.636136i 0.219468π0.219468\pi
860860 0 0
861861 −5.18694e7 −2.38453
862862 −1.02612e7 −0.470359
863863 −1.01919e7 −0.465829 −0.232915 0.972497i 0.574826π-0.574826\pi
−0.232915 + 0.972497i 0.574826π0.574826\pi
864864 2.58637e6 0.117871
865865 0 0
866866 −2.43000e7 −1.10106
867867 −2.08566e7 −0.942313
868868 −2.30984e7 −1.04060
869869 3.24473e7 1.45757
870870 0 0
871871 8.91938e6 0.398372
872872 −1.00882e7 −0.449284
873873 −6.84960e6 −0.304179
874874 2.59806e7 1.15046
875875 0 0
876876 1.25224e7 0.551352
877877 −1.53857e6 −0.0675490 −0.0337745 0.999429i 0.510753π-0.510753\pi
−0.0337745 + 0.999429i 0.510753π0.510753\pi
878878 −2.86906e7 −1.25604
879879 2.76094e7 1.20527
880880 0 0
881881 −5.38590e6 −0.233786 −0.116893 0.993145i 0.537293π-0.537293\pi
−0.116893 + 0.993145i 0.537293π0.537293\pi
882882 −1.57638e7 −0.682323
883883 3.24054e7 1.39867 0.699336 0.714793i 0.253479π-0.253479\pi
0.699336 + 0.714793i 0.253479π0.253479\pi
884884 −1.49817e6 −0.0644808
885885 0 0
886886 −6.21400e6 −0.265942
887887 3.98506e7 1.70069 0.850346 0.526224i 0.176393π-0.176393\pi
0.850346 + 0.526224i 0.176393π0.176393\pi
888888 6.83142e6 0.290722
889889 −6.53776e7 −2.77444
890890 0 0
891891 4.01058e7 1.69244
892892 2.25861e6 0.0950450
893893 −3.62709e7 −1.52205
894894 1.54701e6 0.0647363
895895 0 0
896896 −3.77970e6 −0.157285
897897 −9.23255e6 −0.383125
898898 1.42929e7 0.591464
899899 4.29552e7 1.77262
900900 0 0
901901 6.12363e6 0.251303
902902 −2.61373e7 −1.06966
903903 −6.68039e7 −2.72636
904904 −1.28608e7 −0.523414
905905 0 0
906906 −2.37256e6 −0.0960276
907907 494733. 0.0199688 0.00998441 0.999950i 0.496822π-0.496822\pi
0.00998441 + 0.999950i 0.496822π0.496822\pi
908908 1.54953e7 0.623715
909909 1.26041e7 0.505944
910910 0 0
911911 1.03084e7 0.411526 0.205763 0.978602i 0.434032π-0.434032\pi
0.205763 + 0.978602i 0.434032π0.434032\pi
912912 −1.06902e7 −0.425597
913913 1.23313e7 0.489590
914914 −3.25338e7 −1.28816
915915 0 0
916916 1.16620e6 0.0459233
917917 −4.59894e7 −1.80607
918918 5.59764e6 0.219229
919919 3.06006e7 1.19520 0.597602 0.801793i 0.296120π-0.296120\pi
0.597602 + 0.801793i 0.296120π0.296120\pi
920920 0 0
921921 −2.66970e7 −1.03708
922922 1.47969e7 0.573250
923923 7.46344e6 0.288360
924924 −3.76769e7 −1.45176
925925 0 0
926926 −5.36507e6 −0.205612
927927 5.24772e6 0.200573
928928 7.02896e6 0.267930
929929 −4.45717e7 −1.69441 −0.847207 0.531263i 0.821718π-0.821718\pi
−0.847207 + 0.531263i 0.821718π0.821718\pi
930930 0 0
931931 −8.11347e7 −3.06784
932932 −9.81907e6 −0.370280
933933 −3.35833e7 −1.26305
934934 9.64271e6 0.361686
935935 0 0
936936 1.17061e6 0.0436739
937937 −4.43114e7 −1.64879 −0.824397 0.566012i 0.808485π-0.808485\pi
−0.824397 + 0.566012i 0.808485π0.808485\pi
938938 4.87019e7 1.80733
939939 5.50398e7 2.03710
940940 0 0
941941 1.48172e7 0.545498 0.272749 0.962085i 0.412067π-0.412067\pi
0.272749 + 0.962085i 0.412067π0.412067\pi
942942 3.56149e7 1.30769
943943 −3.49718e7 −1.28068
944944 −6.18136e6 −0.225764
945945 0 0
946946 −3.36629e7 −1.22299
947947 1.14497e7 0.414876 0.207438 0.978248i 0.433487π-0.433487\pi
0.207438 + 0.978248i 0.433487π0.433487\pi
948948 −1.78637e7 −0.645581
949949 −7.05765e6 −0.254387
950950 0 0
951951 −7.32734e6 −0.262721
952952 −8.18035e6 −0.292536
953953 3.21943e7 1.14828 0.574139 0.818758i 0.305337π-0.305337\pi
0.574139 + 0.818758i 0.305337π0.305337\pi
954954 −4.78475e6 −0.170211
955955 0 0
956956 −1.94311e7 −0.687626
957957 7.00663e7 2.47303
958958 −74676.5 −0.00262888
959959 6.13244e7 2.15321
960960 0 0
961961 1.05315e7 0.367858
962962 −3.85019e6 −0.134136
963963 2.04792e7 0.711617
964964 −2.86159e7 −0.991780
965965 0 0
966966 −5.04118e7 −1.73816
967967 −4.07255e7 −1.40055 −0.700277 0.713871i 0.746940π-0.746940\pi
−0.700277 + 0.713871i 0.746940π0.746940\pi
968968 −8.67837e6 −0.297680
969969 −2.31366e7 −0.791571
970970 0 0
971971 1.63928e7 0.557961 0.278980 0.960297i 0.410004π-0.410004\pi
0.278980 + 0.960297i 0.410004π0.410004\pi
972972 −1.22599e7 −0.416220
973973 227301. 0.00769698
974974 −1.81266e7 −0.612236
975975 0 0
976976 −2.73453e6 −0.0918880
977977 −4.03891e7 −1.35372 −0.676858 0.736114i 0.736659π-0.736659\pi
−0.676858 + 0.736114i 0.736659π0.736659\pi
978978 −2.76167e7 −0.923261
979979 −7.07314e7 −2.35861
980980 0 0
981981 1.70599e7 0.565984
982982 −1.53996e7 −0.509601
983983 −4.46121e7 −1.47254 −0.736272 0.676685i 0.763416π-0.763416\pi
−0.736272 + 0.676685i 0.763416π0.763416\pi
984984 1.43898e7 0.473769
985985 0 0
986986 1.52127e7 0.498325
987987 7.03787e7 2.29958
988988 6.02499e6 0.196365
989989 −4.50411e7 −1.46426
990990 0 0
991991 −2.35070e7 −0.760351 −0.380175 0.924914i 0.624136π-0.624136\pi
−0.380175 + 0.924914i 0.624136π0.624136\pi
992992 6.40803e6 0.206750
993993 −5.22841e7 −1.68266
994994 4.07521e7 1.30823
995995 0 0
996996 −6.78895e6 −0.216847
997997 −1.84154e6 −0.0586737 −0.0293369 0.999570i 0.509340π-0.509340\pi
−0.0293369 + 0.999570i 0.509340π0.509340\pi
998998 −8.75378e6 −0.278208
999999 1.43855e7 0.456050
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 650.6.a.s.1.5 6
5.2 odd 4 650.6.b.o.599.2 12
5.3 odd 4 650.6.b.o.599.11 12
5.4 even 2 650.6.a.t.1.2 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
650.6.a.s.1.5 6 1.1 even 1 trivial
650.6.a.t.1.2 yes 6 5.4 even 2
650.6.b.o.599.2 12 5.2 odd 4
650.6.b.o.599.11 12 5.3 odd 4