Properties

Label 350.6.a.z.1.3
Level 350350
Weight 66
Character 350.1
Self dual yes
Analytic conductor 56.13456.134
Analytic rank 00
Dimension 55
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] = [350,6,Mod(1,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, 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("350.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 350=2527 350 = 2 \cdot 5^{2} \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 350.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: 56.134336934556.1343369345
Analytic rank: 00
Dimension: 55
Coefficient field: Q[x]/(x5)\mathbb{Q}[x]/(x^{5} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x5x4915x32649x2+122688x432576 x^{5} - x^{4} - 915x^{3} - 2649x^{2} + 122688x - 432576 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 22353 2^{2}\cdot 3\cdot 5^{3}
Twist minimal: no (minimal twist has level 70)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 4.912344.91234 of defining polynomial
Character χ\chi == 350.1

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+4.00000q21.91234q3+16.0000q47.64937q6+49.0000q7+64.0000q8239.343q9780.137q1130.5975q12+869.410q13+196.000q14+256.000q16+326.997q17957.372q18+1768.20q1993.7048q213120.55q22+1898.23q23122.390q24+3477.64q26+922.405q27+784.000q28+4858.54q29+5436.97q31+1024.00q32+1491.89q33+1307.99q343829.49q36+4411.45q37+7072.79q381662.61q399886.32q41374.819q4215658.3q4312482.2q44+7592.94q46+16840.3q47489.560q48+2401.00q49625.329q51+13910.6q5222056.0q53+3689.62q54+3136.00q563381.40q57+19434.2q58+40053.7q59+21919.3q61+21747.9q6211727.8q63+4096.00q64+5967.55q66+50458.1q67+5231.94q683630.07q6928254.7q7115317.9q72+85457.9q73+17645.8q74+28291.2q7638226.7q776650.44q78+67249.4q79+56396.4q8139545.3q82+18647.1q831499.28q8462633.2q869291.19q8749928.8q8859853.7q89+42601.1q91+30371.7q9210397.3q93+67361.3q941958.24q9646061.0q97+9604.00q98+186720.q99+O(q100)q+4.00000 q^{2} -1.91234 q^{3} +16.0000 q^{4} -7.64937 q^{6} +49.0000 q^{7} +64.0000 q^{8} -239.343 q^{9} -780.137 q^{11} -30.5975 q^{12} +869.410 q^{13} +196.000 q^{14} +256.000 q^{16} +326.997 q^{17} -957.372 q^{18} +1768.20 q^{19} -93.7048 q^{21} -3120.55 q^{22} +1898.23 q^{23} -122.390 q^{24} +3477.64 q^{26} +922.405 q^{27} +784.000 q^{28} +4858.54 q^{29} +5436.97 q^{31} +1024.00 q^{32} +1491.89 q^{33} +1307.99 q^{34} -3829.49 q^{36} +4411.45 q^{37} +7072.79 q^{38} -1662.61 q^{39} -9886.32 q^{41} -374.819 q^{42} -15658.3 q^{43} -12482.2 q^{44} +7592.94 q^{46} +16840.3 q^{47} -489.560 q^{48} +2401.00 q^{49} -625.329 q^{51} +13910.6 q^{52} -22056.0 q^{53} +3689.62 q^{54} +3136.00 q^{56} -3381.40 q^{57} +19434.2 q^{58} +40053.7 q^{59} +21919.3 q^{61} +21747.9 q^{62} -11727.8 q^{63} +4096.00 q^{64} +5967.55 q^{66} +50458.1 q^{67} +5231.94 q^{68} -3630.07 q^{69} -28254.7 q^{71} -15317.9 q^{72} +85457.9 q^{73} +17645.8 q^{74} +28291.2 q^{76} -38226.7 q^{77} -6650.44 q^{78} +67249.4 q^{79} +56396.4 q^{81} -39545.3 q^{82} +18647.1 q^{83} -1499.28 q^{84} -62633.2 q^{86} -9291.19 q^{87} -49928.8 q^{88} -59853.7 q^{89} +42601.1 q^{91} +30371.7 q^{92} -10397.3 q^{93} +67361.3 q^{94} -1958.24 q^{96} -46061.0 q^{97} +9604.00 q^{98} +186720. q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 5q+20q2+14q3+80q4+56q6+245q7+320q8+655q9+748q11+224q12+456q13+980q14+1280q16+780q17+2620q18256q19+686q21++575944q99+O(q100) 5 q + 20 q^{2} + 14 q^{3} + 80 q^{4} + 56 q^{6} + 245 q^{7} + 320 q^{8} + 655 q^{9} + 748 q^{11} + 224 q^{12} + 456 q^{13} + 980 q^{14} + 1280 q^{16} + 780 q^{17} + 2620 q^{18} - 256 q^{19} + 686 q^{21}+ \cdots + 575944 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 −1.91234 −0.122677 −0.0613384 0.998117i 0.519537π-0.519537\pi
−0.0613384 + 0.998117i 0.519537π0.519537\pi
44 16.0000 0.500000
55 0 0
66 −7.64937 −0.0867456
77 49.0000 0.377964
88 64.0000 0.353553
99 −239.343 −0.984950
1010 0 0
1111 −780.137 −1.94397 −0.971984 0.235048i 0.924475π-0.924475\pi
−0.971984 + 0.235048i 0.924475π0.924475\pi
1212 −30.5975 −0.0613384
1313 869.410 1.42681 0.713405 0.700752i 0.247152π-0.247152\pi
0.713405 + 0.700752i 0.247152π0.247152\pi
1414 196.000 0.267261
1515 0 0
1616 256.000 0.250000
1717 326.997 0.274423 0.137212 0.990542i 0.456186π-0.456186\pi
0.137212 + 0.990542i 0.456186π0.456186\pi
1818 −957.372 −0.696465
1919 1768.20 1.12369 0.561845 0.827242i 0.310092π-0.310092\pi
0.561845 + 0.827242i 0.310092π0.310092\pi
2020 0 0
2121 −93.7048 −0.0463675
2222 −3120.55 −1.37459
2323 1898.23 0.748221 0.374111 0.927384i 0.377948π-0.377948\pi
0.374111 + 0.927384i 0.377948π0.377948\pi
2424 −122.390 −0.0433728
2525 0 0
2626 3477.64 1.00891
2727 922.405 0.243507
2828 784.000 0.188982
2929 4858.54 1.07278 0.536390 0.843970i 0.319788π-0.319788\pi
0.536390 + 0.843970i 0.319788π0.319788\pi
3030 0 0
3131 5436.97 1.01614 0.508069 0.861316i 0.330359π-0.330359\pi
0.508069 + 0.861316i 0.330359π0.330359\pi
3232 1024.00 0.176777
3333 1491.89 0.238480
3434 1307.99 0.194047
3535 0 0
3636 −3829.49 −0.492475
3737 4411.45 0.529757 0.264879 0.964282i 0.414668π-0.414668\pi
0.264879 + 0.964282i 0.414668π0.414668\pi
3838 7072.79 0.794569
3939 −1662.61 −0.175036
4040 0 0
4141 −9886.32 −0.918492 −0.459246 0.888309i 0.651880π-0.651880\pi
−0.459246 + 0.888309i 0.651880π0.651880\pi
4242 −374.819 −0.0327868
4343 −15658.3 −1.29144 −0.645719 0.763575i 0.723442π-0.723442\pi
−0.645719 + 0.763575i 0.723442π0.723442\pi
4444 −12482.2 −0.971984
4545 0 0
4646 7592.94 0.529072
4747 16840.3 1.11200 0.556002 0.831181i 0.312335π-0.312335\pi
0.556002 + 0.831181i 0.312335π0.312335\pi
4848 −489.560 −0.0306692
4949 2401.00 0.142857
5050 0 0
5151 −625.329 −0.0336654
5252 13910.6 0.713405
5353 −22056.0 −1.07854 −0.539271 0.842132i 0.681300π-0.681300\pi
−0.539271 + 0.842132i 0.681300π0.681300\pi
5454 3689.62 0.172186
5555 0 0
5656 3136.00 0.133631
5757 −3381.40 −0.137851
5858 19434.2 0.758570
5959 40053.7 1.49800 0.749002 0.662568i 0.230534π-0.230534\pi
0.749002 + 0.662568i 0.230534π0.230534\pi
6060 0 0
6161 21919.3 0.754229 0.377114 0.926167i 0.376916π-0.376916\pi
0.377114 + 0.926167i 0.376916π0.376916\pi
6262 21747.9 0.718518
6363 −11727.8 −0.372276
6464 4096.00 0.125000
6565 0 0
6666 5967.55 0.168631
6767 50458.1 1.37323 0.686616 0.727020i 0.259095π-0.259095\pi
0.686616 + 0.727020i 0.259095π0.259095\pi
6868 5231.94 0.137212
6969 −3630.07 −0.0917894
7070 0 0
7171 −28254.7 −0.665189 −0.332594 0.943070i 0.607924π-0.607924\pi
−0.332594 + 0.943070i 0.607924π0.607924\pi
7272 −15317.9 −0.348233
7373 85457.9 1.87692 0.938458 0.345393i 0.112254π-0.112254\pi
0.938458 + 0.345393i 0.112254π0.112254\pi
7474 17645.8 0.374595
7575 0 0
7676 28291.2 0.561845
7777 −38226.7 −0.734751
7878 −6650.44 −0.123769
7979 67249.4 1.21233 0.606164 0.795339i 0.292707π-0.292707\pi
0.606164 + 0.795339i 0.292707π0.292707\pi
8080 0 0
8181 56396.4 0.955078
8282 −39545.3 −0.649472
8383 18647.1 0.297110 0.148555 0.988904i 0.452538π-0.452538\pi
0.148555 + 0.988904i 0.452538π0.452538\pi
8484 −1499.28 −0.0231837
8585 0 0
8686 −62633.2 −0.913184
8787 −9291.19 −0.131605
8888 −49928.8 −0.687296
8989 −59853.7 −0.800969 −0.400485 0.916303i 0.631158π-0.631158\pi
−0.400485 + 0.916303i 0.631158π0.631158\pi
9090 0 0
9191 42601.1 0.539284
9292 30371.7 0.374111
9393 −10397.3 −0.124657
9494 67361.3 0.786305
9595 0 0
9696 −1958.24 −0.0216864
9797 −46061.0 −0.497054 −0.248527 0.968625i 0.579947π-0.579947\pi
−0.248527 + 0.968625i 0.579947π0.579947\pi
9898 9604.00 0.101015
9999 186720. 1.91471
100100 0 0
101101 −71113.3 −0.693661 −0.346831 0.937928i 0.612742π-0.612742\pi
−0.346831 + 0.937928i 0.612742π0.612742\pi
102102 −2501.32 −0.0238050
103103 5051.27 0.0469146 0.0234573 0.999725i 0.492533π-0.492533\pi
0.0234573 + 0.999725i 0.492533π0.492533\pi
104104 55642.2 0.504454
105105 0 0
106106 −88224.0 −0.762645
107107 −71370.8 −0.602644 −0.301322 0.953522i 0.597428π-0.597428\pi
−0.301322 + 0.953522i 0.597428π0.597428\pi
108108 14758.5 0.121754
109109 138106. 1.11339 0.556695 0.830717i 0.312069π-0.312069\pi
0.556695 + 0.830717i 0.312069π0.312069\pi
110110 0 0
111111 −8436.20 −0.0649889
112112 12544.0 0.0944911
113113 −158667. −1.16894 −0.584468 0.811417i 0.698697π-0.698697\pi
−0.584468 + 0.811417i 0.698697π0.698697\pi
114114 −13525.6 −0.0974752
115115 0 0
116116 77736.6 0.536390
117117 −208087. −1.40534
118118 160215. 1.05925
119119 16022.8 0.103722
120120 0 0
121121 447562. 2.77901
122122 87677.4 0.533320
123123 18906.0 0.112678
124124 86991.5 0.508069
125125 0 0
126126 −46911.2 −0.263239
127127 67468.8 0.371188 0.185594 0.982627i 0.440579π-0.440579\pi
0.185594 + 0.982627i 0.440579π0.440579\pi
128128 16384.0 0.0883883
129129 29944.0 0.158429
130130 0 0
131131 158205. 0.805457 0.402729 0.915319i 0.368062π-0.368062\pi
0.402729 + 0.915319i 0.368062π0.368062\pi
132132 23870.2 0.119240
133133 86641.7 0.424715
134134 201832. 0.971021
135135 0 0
136136 20927.8 0.0970233
137137 200407. 0.912243 0.456122 0.889917i 0.349238π-0.349238\pi
0.456122 + 0.889917i 0.349238π0.349238\pi
138138 −14520.3 −0.0649049
139139 −191630. −0.841252 −0.420626 0.907234i 0.638190π-0.638190\pi
−0.420626 + 0.907234i 0.638190π0.638190\pi
140140 0 0
141141 −32204.5 −0.136417
142142 −113019. −0.470360
143143 −678259. −2.77367
144144 −61271.8 −0.246238
145145 0 0
146146 341831. 1.32718
147147 −4591.53 −0.0175253
148148 70583.2 0.264879
149149 33501.4 0.123622 0.0618112 0.998088i 0.480312π-0.480312\pi
0.0618112 + 0.998088i 0.480312π0.480312\pi
150150 0 0
151151 −485524. −1.73288 −0.866439 0.499282i 0.833597π-0.833597\pi
−0.866439 + 0.499282i 0.833597π0.833597\pi
152152 113165. 0.397285
153153 −78264.3 −0.270293
154154 −152907. −0.519547
155155 0 0
156156 −26601.7 −0.0875182
157157 −493697. −1.59850 −0.799248 0.601001i 0.794769π-0.794769\pi
−0.799248 + 0.601001i 0.794769π0.794769\pi
158158 268997. 0.857246
159159 42178.6 0.132312
160160 0 0
161161 93013.5 0.282801
162162 225586. 0.675342
163163 −192313. −0.566943 −0.283472 0.958981i 0.591486π-0.591486\pi
−0.283472 + 0.958981i 0.591486π0.591486\pi
164164 −158181. −0.459246
165165 0 0
166166 74588.5 0.210088
167167 36326.5 0.100794 0.0503968 0.998729i 0.483951π-0.483951\pi
0.0503968 + 0.998729i 0.483951π0.483951\pi
168168 −5997.10 −0.0163934
169169 384581. 1.03579
170170 0 0
171171 −423206. −1.10678
172172 −250533. −0.645719
173173 27050.2 0.0687156 0.0343578 0.999410i 0.489061π-0.489061\pi
0.0343578 + 0.999410i 0.489061π0.489061\pi
174174 −37164.7 −0.0930589
175175 0 0
176176 −199715. −0.485992
177177 −76596.4 −0.183770
178178 −239415. −0.566371
179179 123119. 0.287206 0.143603 0.989635i 0.454131π-0.454131\pi
0.143603 + 0.989635i 0.454131π0.454131\pi
180180 0 0
181181 −135382. −0.307159 −0.153580 0.988136i 0.549080π-0.549080\pi
−0.153580 + 0.988136i 0.549080π0.549080\pi
182182 170404. 0.381331
183183 −41917.3 −0.0925263
184184 121487. 0.264536
185185 0 0
186186 −41589.4 −0.0881455
187187 −255102. −0.533470
188188 269445. 0.556002
189189 45197.8 0.0920371
190190 0 0
191191 189708. 0.376272 0.188136 0.982143i 0.439755π-0.439755\pi
0.188136 + 0.982143i 0.439755π0.439755\pi
192192 −7832.95 −0.0153346
193193 362697. 0.700891 0.350445 0.936583i 0.386030π-0.386030\pi
0.350445 + 0.936583i 0.386030π0.386030\pi
194194 −184244. −0.351470
195195 0 0
196196 38416.0 0.0714286
197197 828304. 1.52063 0.760316 0.649554i 0.225044π-0.225044\pi
0.760316 + 0.649554i 0.225044π0.225044\pi
198198 746881. 1.35391
199199 864115. 1.54682 0.773409 0.633908i 0.218550π-0.218550\pi
0.773409 + 0.633908i 0.218550π0.218550\pi
200200 0 0
201201 −96493.1 −0.168464
202202 −284453. −0.490493
203203 238068. 0.405473
204204 −10005.3 −0.0168327
205205 0 0
206206 20205.1 0.0331736
207207 −454329. −0.736961
208208 222569. 0.356703
209209 −1.37944e6 −2.18442
210210 0 0
211211 −446374. −0.690229 −0.345114 0.938561i 0.612160π-0.612160\pi
−0.345114 + 0.938561i 0.612160π0.612160\pi
212212 −352896. −0.539271
213213 54032.7 0.0816032
214214 −285483. −0.426134
215215 0 0
216216 59033.9 0.0860928
217217 266412. 0.384064
218218 552426. 0.787286
219219 −163425. −0.230254
220220 0 0
221221 284294. 0.391550
222222 −33744.8 −0.0459541
223223 −615894. −0.829362 −0.414681 0.909967i 0.636107π-0.636107\pi
−0.414681 + 0.909967i 0.636107π0.636107\pi
224224 50176.0 0.0668153
225225 0 0
226226 −634669. −0.826563
227227 143815. 0.185242 0.0926210 0.995701i 0.470475π-0.470475\pi
0.0926210 + 0.995701i 0.470475π0.470475\pi
228228 −54102.4 −0.0689254
229229 −547130. −0.689449 −0.344724 0.938704i 0.612028π-0.612028\pi
−0.344724 + 0.938704i 0.612028π0.612028\pi
230230 0 0
231231 73102.5 0.0901369
232232 310946. 0.379285
233233 −624672. −0.753811 −0.376905 0.926252i 0.623012π-0.623012\pi
−0.376905 + 0.926252i 0.623012π0.623012\pi
234234 −832349. −0.993724
235235 0 0
236236 640859. 0.749002
237237 −128604. −0.148725
238238 64091.3 0.0733427
239239 −711873. −0.806136 −0.403068 0.915170i 0.632056π-0.632056\pi
−0.403068 + 0.915170i 0.632056π0.632056\pi
240240 0 0
241241 546788. 0.606424 0.303212 0.952923i 0.401941π-0.401941\pi
0.303212 + 0.952923i 0.401941π0.401941\pi
242242 1.79025e6 1.96506
243243 −331993. −0.360673
244244 350709. 0.377114
245245 0 0
246246 75624.1 0.0796751
247247 1.53729e6 1.60329
248248 347966. 0.359259
249249 −35659.7 −0.0364485
250250 0 0
251251 −232147. −0.232583 −0.116292 0.993215i 0.537101π-0.537101\pi
−0.116292 + 0.993215i 0.537101π0.537101\pi
252252 −187645. −0.186138
253253 −1.48088e6 −1.45452
254254 269875. 0.262469
255255 0 0
256256 65536.0 0.0625000
257257 −574030. −0.542128 −0.271064 0.962561i 0.587375π-0.587375\pi
−0.271064 + 0.962561i 0.587375π0.587375\pi
258258 119776. 0.112026
259259 216161. 0.200229
260260 0 0
261261 −1.16286e6 −1.05663
262262 632821. 0.569544
263263 −312043. −0.278180 −0.139090 0.990280i 0.544418π-0.544418\pi
−0.139090 + 0.990280i 0.544418π0.544418\pi
264264 95480.9 0.0843153
265265 0 0
266266 346567. 0.300319
267267 114461. 0.0982603
268268 807329. 0.686616
269269 −2.18449e6 −1.84064 −0.920322 0.391161i 0.872074π-0.872074\pi
−0.920322 + 0.391161i 0.872074π0.872074\pi
270270 0 0
271271 951923. 0.787370 0.393685 0.919246i 0.371200π-0.371200\pi
0.393685 + 0.919246i 0.371200π0.371200\pi
272272 83711.1 0.0686058
273273 −81467.8 −0.0661576
274274 801626. 0.645053
275275 0 0
276276 −58081.2 −0.0458947
277277 −1.07542e6 −0.842126 −0.421063 0.907031i 0.638343π-0.638343\pi
−0.421063 + 0.907031i 0.638343π0.638343\pi
278278 −766519. −0.594855
279279 −1.30130e6 −1.00085
280280 0 0
281281 689287. 0.520756 0.260378 0.965507i 0.416153π-0.416153\pi
0.260378 + 0.965507i 0.416153π0.416153\pi
282282 −128818. −0.0964614
283283 2.04961e6 1.52127 0.760635 0.649180i 0.224888π-0.224888\pi
0.760635 + 0.649180i 0.224888π0.224888\pi
284284 −452075. −0.332594
285285 0 0
286286 −2.71303e6 −1.96128
287287 −484430. −0.347157
288288 −245087. −0.174116
289289 −1.31293e6 −0.924692
290290 0 0
291291 88084.4 0.0609770
292292 1.36733e6 0.938458
293293 −303846. −0.206769 −0.103384 0.994641i 0.532967π-0.532967\pi
−0.103384 + 0.994641i 0.532967π0.532967\pi
294294 −18366.1 −0.0123922
295295 0 0
296296 282333. 0.187297
297297 −719602. −0.473370
298298 134006. 0.0874142
299299 1.65034e6 1.06757
300300 0 0
301301 −767256. −0.488117
302302 −1.94210e6 −1.22533
303303 135993. 0.0850962
304304 452659. 0.280923
305305 0 0
306306 −313057. −0.191126
307307 482206. 0.292002 0.146001 0.989284i 0.453360π-0.453360\pi
0.146001 + 0.989284i 0.453360π0.453360\pi
308308 −611627. −0.367375
309309 −9659.76 −0.00575533
310310 0 0
311311 −1.44282e6 −0.845886 −0.422943 0.906156i 0.639003π-0.639003\pi
−0.422943 + 0.906156i 0.639003π0.639003\pi
312312 −106407. −0.0618847
313313 −826161. −0.476655 −0.238327 0.971185i 0.576599π-0.576599\pi
−0.238327 + 0.971185i 0.576599π0.576599\pi
314314 −1.97479e6 −1.13031
315315 0 0
316316 1.07599e6 0.606164
317317 −1.34244e6 −0.750318 −0.375159 0.926960i 0.622412π-0.622412\pi
−0.375159 + 0.926960i 0.622412π0.622412\pi
318318 168715. 0.0935588
319319 −3.79032e6 −2.08545
320320 0 0
321321 136485. 0.0739305
322322 372054. 0.199971
323323 578194. 0.308367
324324 902342. 0.477539
325325 0 0
326326 −769252. −0.400890
327327 −264107. −0.136587
328328 −632725. −0.324736
329329 825176. 0.420298
330330 0 0
331331 2.62883e6 1.31884 0.659420 0.751775i 0.270802π-0.270802\pi
0.659420 + 0.751775i 0.270802π0.270802\pi
332332 298354. 0.148555
333333 −1.05585e6 −0.521784
334334 145306. 0.0712718
335335 0 0
336336 −23988.4 −0.0115919
337337 −3.77083e6 −1.80868 −0.904342 0.426809i 0.859638π-0.859638\pi
−0.904342 + 0.426809i 0.859638π0.859638\pi
338338 1.53832e6 0.732412
339339 303426. 0.143401
340340 0 0
341341 −4.24158e6 −1.97534
342342 −1.69282e6 −0.782611
343343 117649. 0.0539949
344344 −1.00213e6 −0.456592
345345 0 0
346346 108201. 0.0485892
347347 1.16777e6 0.520636 0.260318 0.965523i 0.416173π-0.416173\pi
0.260318 + 0.965523i 0.416173π0.416173\pi
348348 −148659. −0.0658026
349349 2.40057e6 1.05499 0.527497 0.849557i 0.323131π-0.323131\pi
0.527497 + 0.849557i 0.323131π0.323131\pi
350350 0 0
351351 801948. 0.347439
352352 −798860. −0.343648
353353 3.78830e6 1.61811 0.809054 0.587734i 0.199980π-0.199980\pi
0.809054 + 0.587734i 0.199980π0.199980\pi
354354 −306386. −0.129945
355355 0 0
356356 −957659. −0.400485
357357 −30641.1 −0.0127243
358358 492477. 0.203085
359359 3.69702e6 1.51396 0.756981 0.653437i 0.226673π-0.226673\pi
0.756981 + 0.653437i 0.226673π0.226673\pi
360360 0 0
361361 650423. 0.262680
362362 −541527. −0.217194
363363 −855892. −0.340920
364364 681617. 0.269642
365365 0 0
366366 −167669. −0.0654260
367367 −1.13137e6 −0.438468 −0.219234 0.975672i 0.570356π-0.570356\pi
−0.219234 + 0.975672i 0.570356π0.570356\pi
368368 485948. 0.187055
369369 2.36622e6 0.904669
370370 0 0
371371 −1.08074e6 −0.407651
372372 −166358. −0.0623283
373373 −3.59413e6 −1.33759 −0.668793 0.743449i 0.733189π-0.733189\pi
−0.668793 + 0.743449i 0.733189π0.733189\pi
374374 −1.02041e6 −0.377220
375375 0 0
376376 1.07778e6 0.393153
377377 4.22406e6 1.53065
378378 180791. 0.0650801
379379 −1.36485e6 −0.488076 −0.244038 0.969766i 0.578472π-0.578472\pi
−0.244038 + 0.969766i 0.578472π0.578472\pi
380380 0 0
381381 −129023. −0.0455361
382382 758832. 0.266065
383383 −4.95361e6 −1.72554 −0.862770 0.505596i 0.831273π-0.831273\pi
−0.862770 + 0.505596i 0.831273π0.831273\pi
384384 −31331.8 −0.0108432
385385 0 0
386386 1.45079e6 0.495605
387387 3.74770e6 1.27200
388388 −736976. −0.248527
389389 2.34235e6 0.784834 0.392417 0.919787i 0.371639π-0.371639\pi
0.392417 + 0.919787i 0.371639π0.371639\pi
390390 0 0
391391 620716. 0.205329
392392 153664. 0.0505076
393393 −302542. −0.0988109
394394 3.31321e6 1.07525
395395 0 0
396396 2.98752e6 0.957356
397397 −1.54459e6 −0.491853 −0.245927 0.969288i 0.579092π-0.579092\pi
−0.245927 + 0.969288i 0.579092π0.579092\pi
398398 3.45646e6 1.09376
399399 −165688. −0.0521027
400400 0 0
401401 429318. 0.133327 0.0666636 0.997776i 0.478765π-0.478765\pi
0.0666636 + 0.997776i 0.478765π0.478765\pi
402402 −385972. −0.119122
403403 4.72696e6 1.44984
404404 −1.13781e6 −0.346831
405405 0 0
406406 952273. 0.286712
407407 −3.44153e6 −1.02983
408408 −40021.1 −0.0119025
409409 −282665. −0.0835533 −0.0417767 0.999127i 0.513302π-0.513302\pi
−0.0417767 + 0.999127i 0.513302π0.513302\pi
410410 0 0
411411 −383246. −0.111911
412412 80820.3 0.0234573
413413 1.96263e6 0.566192
414414 −1.81732e6 −0.521110
415415 0 0
416416 890276. 0.252227
417417 366462. 0.103202
418418 −5.51774e6 −1.54462
419419 −3.15372e6 −0.877582 −0.438791 0.898589i 0.644593π-0.644593\pi
−0.438791 + 0.898589i 0.644593π0.644593\pi
420420 0 0
421421 3.80804e6 1.04712 0.523560 0.851989i 0.324604π-0.324604\pi
0.523560 + 0.851989i 0.324604π0.324604\pi
422422 −1.78550e6 −0.488065
423423 −4.03062e6 −1.09527
424424 −1.41158e6 −0.381322
425425 0 0
426426 216131. 0.0577022
427427 1.07405e6 0.285072
428428 −1.14193e6 −0.301322
429429 1.29706e6 0.340265
430430 0 0
431431 −1.88084e6 −0.487708 −0.243854 0.969812i 0.578412π-0.578412\pi
−0.243854 + 0.969812i 0.578412π0.578412\pi
432432 236136. 0.0608768
433433 −5.01618e6 −1.28574 −0.642871 0.765975i 0.722257π-0.722257\pi
−0.642871 + 0.765975i 0.722257π0.722257\pi
434434 1.06565e6 0.271574
435435 0 0
436436 2.20970e6 0.556695
437437 3.35645e6 0.840769
438438 −653699. −0.162814
439439 2.64450e6 0.654911 0.327456 0.944867i 0.393809π-0.393809\pi
0.327456 + 0.944867i 0.393809π0.393809\pi
440440 0 0
441441 −574662. −0.140707
442442 1.13718e6 0.276868
443443 7.38758e6 1.78852 0.894258 0.447552i 0.147704π-0.147704\pi
0.894258 + 0.447552i 0.147704π0.147704\pi
444444 −134979. −0.0324945
445445 0 0
446446 −2.46358e6 −0.586447
447447 −64066.1 −0.0151656
448448 200704. 0.0472456
449449 4.20191e6 0.983628 0.491814 0.870700i 0.336334π-0.336334\pi
0.491814 + 0.870700i 0.336334π0.336334\pi
450450 0 0
451451 7.71269e6 1.78552
452452 −2.53867e6 −0.584468
453453 928488. 0.212584
454454 575260. 0.130986
455455 0 0
456456 −216409. −0.0487376
457457 3.84060e6 0.860217 0.430109 0.902777i 0.358475π-0.358475\pi
0.430109 + 0.902777i 0.358475π0.358475\pi
458458 −2.18852e6 −0.487514
459459 301623. 0.0668241
460460 0 0
461461 −2.56922e6 −0.563052 −0.281526 0.959554i 0.590841π-0.590841\pi
−0.281526 + 0.959554i 0.590841π0.590841\pi
462462 292410. 0.0637364
463463 3.49589e6 0.757889 0.378944 0.925419i 0.376287π-0.376287\pi
0.378944 + 0.925419i 0.376287π0.376287\pi
464464 1.24379e6 0.268195
465465 0 0
466466 −2.49869e6 −0.533025
467467 −15357.9 −0.00325867 −0.00162933 0.999999i 0.500519π-0.500519\pi
−0.00162933 + 0.999999i 0.500519π0.500519\pi
468468 −3.32939e6 −0.702669
469469 2.47245e6 0.519033
470470 0 0
471471 944118. 0.196098
472472 2.56344e6 0.529624
473473 1.22156e7 2.51051
474474 −514415. −0.105164
475475 0 0
476476 256365. 0.0518611
477477 5.27895e6 1.06231
478478 −2.84749e6 −0.570024
479479 2.48585e6 0.495036 0.247518 0.968883i 0.420385π-0.420385\pi
0.247518 + 0.968883i 0.420385π0.420385\pi
480480 0 0
481481 3.83536e6 0.755863
482482 2.18715e6 0.428807
483483 −177874. −0.0346931
484484 7.16100e6 1.38951
485485 0 0
486486 −1.32797e6 −0.255034
487487 1.01652e6 0.194219 0.0971096 0.995274i 0.469040π-0.469040\pi
0.0971096 + 0.995274i 0.469040π0.469040\pi
488488 1.40284e6 0.266660
489489 367768. 0.0695508
490490 0 0
491491 −802250. −0.150178 −0.0750890 0.997177i 0.523924π-0.523924\pi
−0.0750890 + 0.997177i 0.523924π0.523924\pi
492492 302497. 0.0563388
493493 1.58872e6 0.294396
494494 6.14915e6 1.13370
495495 0 0
496496 1.39186e6 0.254035
497497 −1.38448e6 −0.251418
498498 −142639. −0.0257730
499499 3.00612e6 0.540450 0.270225 0.962797i 0.412902π-0.412902\pi
0.270225 + 0.962797i 0.412902π0.412902\pi
500500 0 0
501501 −69468.8 −0.0123650
502502 −928587. −0.164461
503503 6.02092e6 1.06107 0.530534 0.847664i 0.321991π-0.321991\pi
0.530534 + 0.847664i 0.321991π0.321991\pi
504504 −750579. −0.131620
505505 0 0
506506 −5.92353e6 −1.02850
507507 −735450. −0.127067
508508 1.07950e6 0.185594
509509 8.24891e6 1.41124 0.705622 0.708588i 0.250668π-0.250668\pi
0.705622 + 0.708588i 0.250668π0.250668\pi
510510 0 0
511511 4.18744e6 0.709408
512512 262144. 0.0441942
513513 1.63099e6 0.273627
514514 −2.29612e6 −0.383342
515515 0 0
516516 479104. 0.0792147
517517 −1.31378e7 −2.16170
518518 864644. 0.141584
519519 −51729.2 −0.00842981
520520 0 0
521521 −3.69104e6 −0.595736 −0.297868 0.954607i 0.596276π-0.596276\pi
−0.297868 + 0.954607i 0.596276π0.596276\pi
522522 −4.65143e6 −0.747154
523523 −5.00116e6 −0.799496 −0.399748 0.916625i 0.630902π-0.630902\pi
−0.399748 + 0.916625i 0.630902π0.630902\pi
524524 2.53128e6 0.402729
525525 0 0
526526 −1.24817e6 −0.196703
527527 1.77787e6 0.278852
528528 381923. 0.0596199
529529 −2.83305e6 −0.440165
530530 0 0
531531 −9.58657e6 −1.47546
532532 1.38627e6 0.212358
533533 −8.59527e6 −1.31051
534534 457843. 0.0694806
535535 0 0
536536 3.22932e6 0.485511
537537 −235446. −0.0352335
538538 −8.73797e6 −1.30153
539539 −1.87311e6 −0.277710
540540 0 0
541541 −6.07709e6 −0.892694 −0.446347 0.894860i 0.647275π-0.647275\pi
−0.446347 + 0.894860i 0.647275π0.647275\pi
542542 3.80769e6 0.556754
543543 258896. 0.0376813
544544 334844. 0.0485116
545545 0 0
546546 −325871. −0.0467805
547547 2.13370e6 0.304905 0.152453 0.988311i 0.451283π-0.451283\pi
0.152453 + 0.988311i 0.451283π0.451283\pi
548548 3.20651e6 0.456122
549549 −5.24624e6 −0.742878
550550 0 0
551551 8.59085e6 1.20547
552552 −232325. −0.0324525
553553 3.29522e6 0.458217
554554 −4.30167e6 −0.595473
555555 0 0
556556 −3.06608e6 −0.420626
557557 2.95091e6 0.403012 0.201506 0.979487i 0.435417π-0.435417\pi
0.201506 + 0.979487i 0.435417π0.435417\pi
558558 −5.20520e6 −0.707705
559559 −1.36135e7 −1.84264
560560 0 0
561561 487842. 0.0654444
562562 2.75715e6 0.368230
563563 1.19591e7 1.59011 0.795057 0.606534i 0.207441π-0.207441\pi
0.795057 + 0.606534i 0.207441π0.207441\pi
564564 −515272. −0.0682085
565565 0 0
566566 8.19846e6 1.07570
567567 2.76342e6 0.360985
568568 −1.80830e6 −0.235180
569569 −7.83827e6 −1.01494 −0.507469 0.861670i 0.669419π-0.669419\pi
−0.507469 + 0.861670i 0.669419π0.669419\pi
570570 0 0
571571 −6.60771e6 −0.848126 −0.424063 0.905633i 0.639397π-0.639397\pi
−0.424063 + 0.905633i 0.639397π0.639397\pi
572572 −1.08521e7 −1.38684
573573 −362786. −0.0461599
574574 −1.93772e6 −0.245477
575575 0 0
576576 −980349. −0.123119
577577 4.77589e6 0.597193 0.298596 0.954380i 0.403482π-0.403482\pi
0.298596 + 0.954380i 0.403482π0.403482\pi
578578 −5.25172e6 −0.653856
579579 −693600. −0.0859830
580580 0 0
581581 913709. 0.112297
582582 352337. 0.0431173
583583 1.72067e7 2.09665
584584 5.46930e6 0.663590
585585 0 0
586586 −1.21539e6 −0.146208
587587 7.01821e6 0.840681 0.420340 0.907367i 0.361911π-0.361911\pi
0.420340 + 0.907367i 0.361911π0.361911\pi
588588 −73464.5 −0.00876263
589589 9.61364e6 1.14183
590590 0 0
591591 −1.58400e6 −0.186546
592592 1.12933e6 0.132439
593593 −1.10510e7 −1.29052 −0.645261 0.763962i 0.723251π-0.723251\pi
−0.645261 + 0.763962i 0.723251π0.723251\pi
594594 −2.87841e6 −0.334723
595595 0 0
596596 536022. 0.0618112
597597 −1.65248e6 −0.189759
598598 6.60137e6 0.754886
599599 −1.64477e6 −0.187300 −0.0936501 0.995605i 0.529853π-0.529853\pi
−0.0936501 + 0.995605i 0.529853π0.529853\pi
600600 0 0
601601 1.53175e7 1.72982 0.864911 0.501925i 0.167375π-0.167375\pi
0.864911 + 0.501925i 0.167375π0.167375\pi
602602 −3.06903e6 −0.345151
603603 −1.20768e7 −1.35257
604604 −7.76838e6 −0.866439
605605 0 0
606606 543972. 0.0601721
607607 3.55348e6 0.391455 0.195728 0.980658i 0.437293π-0.437293\pi
0.195728 + 0.980658i 0.437293π0.437293\pi
608608 1.81063e6 0.198642
609609 −455268. −0.0497421
610610 0 0
611611 1.46412e7 1.58662
612612 −1.25223e6 −0.135147
613613 −5.87140e6 −0.631088 −0.315544 0.948911i 0.602187π-0.602187\pi
−0.315544 + 0.948911i 0.602187π0.602187\pi
614614 1.92882e6 0.206477
615615 0 0
616616 −2.44651e6 −0.259774
617617 −1.11324e7 −1.17727 −0.588636 0.808398i 0.700335π-0.700335\pi
−0.588636 + 0.808398i 0.700335π0.700335\pi
618618 −38639.0 −0.00406963
619619 1.76747e7 1.85407 0.927034 0.374977i 0.122349π-0.122349\pi
0.927034 + 0.374977i 0.122349π0.122349\pi
620620 0 0
621621 1.75094e6 0.182197
622622 −5.77129e6 −0.598132
623623 −2.93283e6 −0.302738
624624 −425628. −0.0437591
625625 0 0
626626 −3.30464e6 −0.337046
627627 2.63795e6 0.267977
628628 −7.89916e6 −0.799248
629629 1.44253e6 0.145378
630630 0 0
631631 −1.19809e7 −1.19789 −0.598945 0.800790i 0.704413π-0.704413\pi
−0.598945 + 0.800790i 0.704413π0.704413\pi
632632 4.30396e6 0.428623
633633 853620. 0.0846750
634634 −5.36975e6 −0.530555
635635 0 0
636636 674858. 0.0661561
637637 2.08745e6 0.203830
638638 −1.51613e7 −1.47464
639639 6.76257e6 0.655178
640640 0 0
641641 −1.88873e6 −0.181562 −0.0907809 0.995871i 0.528936π-0.528936\pi
−0.0907809 + 0.995871i 0.528936π0.528936\pi
642642 545942. 0.0522768
643643 −6.75118e6 −0.643950 −0.321975 0.946748i 0.604347π-0.604347\pi
−0.321975 + 0.946748i 0.604347π0.604347\pi
644644 1.48822e6 0.141401
645645 0 0
646646 2.31278e6 0.218048
647647 9.88165e6 0.928045 0.464022 0.885823i 0.346406π-0.346406\pi
0.464022 + 0.885823i 0.346406π0.346406\pi
648648 3.60937e6 0.337671
649649 −3.12474e7 −2.91207
650650 0 0
651651 −509470. −0.0471158
652652 −3.07701e6 −0.283472
653653 1.45036e7 1.33104 0.665522 0.746378i 0.268209π-0.268209\pi
0.665522 + 0.746378i 0.268209π0.268209\pi
654654 −1.05643e6 −0.0965817
655655 0 0
656656 −2.53090e6 −0.229623
657657 −2.04537e7 −1.84867
658658 3.30071e6 0.297195
659659 2.12571e6 0.190674 0.0953370 0.995445i 0.469607π-0.469607\pi
0.0953370 + 0.995445i 0.469607π0.469607\pi
660660 0 0
661661 2.52280e6 0.224584 0.112292 0.993675i 0.464181π-0.464181\pi
0.112292 + 0.993675i 0.464181π0.464181\pi
662662 1.05153e7 0.932560
663663 −543667. −0.0480341
664664 1.19342e6 0.105044
665665 0 0
666666 −4.22340e6 −0.368957
667667 9.22264e6 0.802677
668668 581225. 0.0503968
669669 1.17780e6 0.101743
670670 0 0
671671 −1.71001e7 −1.46620
672672 −95953.7 −0.00819669
673673 −1.19058e7 −1.01326 −0.506630 0.862164i 0.669109π-0.669109\pi
−0.506630 + 0.862164i 0.669109π0.669109\pi
674674 −1.50833e7 −1.27893
675675 0 0
676676 6.15329e6 0.517894
677677 −1.67013e7 −1.40048 −0.700241 0.713907i 0.746924π-0.746924\pi
−0.700241 + 0.713907i 0.746924π0.746924\pi
678678 1.21370e6 0.101400
679679 −2.25699e6 −0.187869
680680 0 0
681681 −275023. −0.0227249
682682 −1.69663e7 −1.39678
683683 5.59510e6 0.458940 0.229470 0.973316i 0.426301π-0.426301\pi
0.229470 + 0.973316i 0.426301π0.426301\pi
684684 −6.77129e6 −0.553390
685685 0 0
686686 470596. 0.0381802
687687 1.04630e6 0.0845794
688688 −4.00852e6 −0.322859
689689 −1.91757e7 −1.53888
690690 0 0
691691 1.65131e6 0.131563 0.0657815 0.997834i 0.479046π-0.479046\pi
0.0657815 + 0.997834i 0.479046π0.479046\pi
692692 432803. 0.0343578
693693 9.14929e6 0.723693
694694 4.67108e6 0.368145
695695 0 0
696696 −594636. −0.0465295
697697 −3.23279e6 −0.252055
698698 9.60226e6 0.745994
699699 1.19459e6 0.0924751
700700 0 0
701701 −1.74041e7 −1.33770 −0.668848 0.743400i 0.733212π-0.733212\pi
−0.668848 + 0.743400i 0.733212π0.733212\pi
702702 3.20779e6 0.245676
703703 7.80031e6 0.595283
704704 −3.19544e6 −0.242996
705705 0 0
706706 1.51532e7 1.14418
707707 −3.48455e6 −0.262179
708708 −1.22554e6 −0.0918851
709709 1.15661e7 0.864113 0.432057 0.901846i 0.357788π-0.357788\pi
0.432057 + 0.901846i 0.357788π0.357788\pi
710710 0 0
711711 −1.60957e7 −1.19408
712712 −3.83064e6 −0.283185
713713 1.03206e7 0.760296
714714 −122565. −0.00899745
715715 0 0
716716 1.96991e6 0.143603
717717 1.36135e6 0.0988941
718718 1.47881e7 1.07053
719719 −1.14902e7 −0.828904 −0.414452 0.910071i 0.636027π-0.636027\pi
−0.414452 + 0.910071i 0.636027π0.636027\pi
720720 0 0
721721 247512. 0.0177320
722722 2.60169e6 0.185743
723723 −1.04565e6 −0.0743942
724724 −2.16611e6 −0.153580
725725 0 0
726726 −3.42357e6 −0.241067
727727 2.00113e7 1.40423 0.702117 0.712062i 0.252238π-0.252238\pi
0.702117 + 0.712062i 0.252238π0.252238\pi
728728 2.72647e6 0.190666
729729 −1.30694e7 −0.910831
730730 0 0
731731 −5.12021e6 −0.354400
732732 −670676. −0.0462632
733733 −2.53634e7 −1.74360 −0.871800 0.489862i 0.837047π-0.837047\pi
−0.871800 + 0.489862i 0.837047π0.837047\pi
734734 −4.52546e6 −0.310044
735735 0 0
736736 1.94379e6 0.132268
737737 −3.93642e7 −2.66952
738738 9.46489e6 0.639697
739739 −9.76419e6 −0.657696 −0.328848 0.944383i 0.606660π-0.606660\pi
−0.328848 + 0.944383i 0.606660π0.606660\pi
740740 0 0
741741 −2.93982e6 −0.196687
742742 −4.32298e6 −0.288253
743743 6.62984e6 0.440586 0.220293 0.975434i 0.429299π-0.429299\pi
0.220293 + 0.975434i 0.429299π0.429299\pi
744744 −665430. −0.0440728
745745 0 0
746746 −1.43765e7 −0.945815
747747 −4.46306e6 −0.292638
748748 −4.08163e6 −0.266735
749749 −3.49717e6 −0.227778
750750 0 0
751751 3.02375e6 0.195635 0.0978174 0.995204i 0.468814π-0.468814\pi
0.0978174 + 0.995204i 0.468814π0.468814\pi
752752 4.31113e6 0.278001
753753 443944. 0.0285326
754754 1.68962e7 1.08234
755755 0 0
756756 723165. 0.0460186
757757 4.32091e6 0.274053 0.137027 0.990567i 0.456245π-0.456245\pi
0.137027 + 0.990567i 0.456245π0.456245\pi
758758 −5.45941e6 −0.345122
759759 2.83195e6 0.178436
760760 0 0
761761 −8.52278e6 −0.533482 −0.266741 0.963768i 0.585947π-0.585947\pi
−0.266741 + 0.963768i 0.585947π0.585947\pi
762762 −516094. −0.0321989
763763 6.76721e6 0.420822
764764 3.03533e6 0.188136
765765 0 0
766766 −1.98145e7 −1.22014
767767 3.48231e7 2.13737
768768 −125327. −0.00766730
769769 1.93335e7 1.17895 0.589475 0.807787i 0.299335π-0.299335\pi
0.589475 + 0.807787i 0.299335π0.299335\pi
770770 0 0
771771 1.09774e6 0.0665065
772772 5.80315e6 0.350445
773773 −1.85205e7 −1.11482 −0.557408 0.830239i 0.688204π-0.688204\pi
−0.557408 + 0.830239i 0.688204π0.688204\pi
774774 1.49908e7 0.899441
775775 0 0
776776 −2.94790e6 −0.175735
777777 −413374. −0.0245635
778778 9.36941e6 0.554962
779779 −1.74810e7 −1.03210
780780 0 0
781781 2.20425e7 1.29311
782782 2.48286e6 0.145190
783783 4.48154e6 0.261230
784784 614656. 0.0357143
785785 0 0
786786 −1.21017e6 −0.0698699
787787 927171. 0.0533609 0.0266804 0.999644i 0.491506π-0.491506\pi
0.0266804 + 0.999644i 0.491506π0.491506\pi
788788 1.32529e7 0.760316
789789 596733. 0.0341262
790790 0 0
791791 −7.77469e6 −0.441816
792792 1.19501e7 0.676953
793793 1.90569e7 1.07614
794794 −6.17834e6 −0.347793
795795 0 0
796796 1.38258e7 0.773409
797797 8.55917e6 0.477294 0.238647 0.971106i 0.423296π-0.423296\pi
0.238647 + 0.971106i 0.423296π0.423296\pi
798798 −662754. −0.0368422
799799 5.50673e6 0.305159
800800 0 0
801801 1.43256e7 0.788915
802802 1.71727e6 0.0942765
803803 −6.66688e7 −3.64866
804804 −1.54389e6 −0.0842318
805805 0 0
806806 1.89078e7 1.02519
807807 4.17750e6 0.225804
808808 −4.55125e6 −0.245246
809809 2.67123e6 0.143496 0.0717481 0.997423i 0.477142π-0.477142\pi
0.0717481 + 0.997423i 0.477142π0.477142\pi
810810 0 0
811811 1.47660e7 0.788334 0.394167 0.919039i 0.371033π-0.371033\pi
0.394167 + 0.919039i 0.371033π0.371033\pi
812812 3.80909e6 0.202736
813813 −1.82040e6 −0.0965920
814814 −1.37661e7 −0.728200
815815 0 0
816816 −160084. −0.00841634
817817 −2.76870e7 −1.45118
818818 −1.13066e6 −0.0590811
819819 −1.01963e7 −0.531168
820820 0 0
821821 −9.07572e6 −0.469919 −0.234960 0.972005i 0.575496π-0.575496\pi
−0.234960 + 0.972005i 0.575496π0.575496\pi
822822 −1.53298e6 −0.0791331
823823 3.06337e7 1.57652 0.788262 0.615340i 0.210981π-0.210981\pi
0.788262 + 0.615340i 0.210981π0.210981\pi
824824 323281. 0.0165868
825825 0 0
826826 7.85053e6 0.400358
827827 5.77395e6 0.293568 0.146784 0.989169i 0.453108π-0.453108\pi
0.146784 + 0.989169i 0.453108π0.453108\pi
828828 −7.26926e6 −0.368480
829829 7.67908e6 0.388082 0.194041 0.980993i 0.437841π-0.437841\pi
0.194041 + 0.980993i 0.437841π0.437841\pi
830830 0 0
831831 2.05656e6 0.103309
832832 3.56110e6 0.178351
833833 785119. 0.0392033
834834 1.46585e6 0.0729749
835835 0 0
836836 −2.20710e7 −1.09221
837837 5.01509e6 0.247437
838838 −1.26149e7 −0.620544
839839 1.46555e6 0.0718782 0.0359391 0.999354i 0.488558π-0.488558\pi
0.0359391 + 0.999354i 0.488558π0.488558\pi
840840 0 0
841841 3.09424e6 0.150856
842842 1.52322e7 0.740426
843843 −1.31815e6 −0.0638847
844844 −7.14199e6 −0.345114
845845 0 0
846846 −1.61225e7 −0.774471
847847 2.19306e7 1.05037
848848 −5.64634e6 −0.269636
849849 −3.91956e6 −0.186624
850850 0 0
851851 8.37396e6 0.396376
852852 864523. 0.0408016
853853 −1.31222e7 −0.617496 −0.308748 0.951144i 0.599910π-0.599910\pi
−0.308748 + 0.951144i 0.599910π0.599910\pi
854854 4.29619e6 0.201576
855855 0 0
856856 −4.56773e6 −0.213067
857857 −3.79938e6 −0.176710 −0.0883549 0.996089i 0.528161π-0.528161\pi
−0.0883549 + 0.996089i 0.528161π0.528161\pi
858858 5.18825e6 0.240604
859859 −3.76559e6 −0.174120 −0.0870602 0.996203i 0.527747π-0.527747\pi
−0.0870602 + 0.996203i 0.527747π0.527747\pi
860860 0 0
861861 926396. 0.0425881
862862 −7.52338e6 −0.344862
863863 −9.96098e6 −0.455276 −0.227638 0.973746i 0.573100π-0.573100\pi
−0.227638 + 0.973746i 0.573100π0.573100\pi
864864 944542. 0.0430464
865865 0 0
866866 −2.00647e7 −0.909156
867867 2.51077e6 0.113438
868868 4.26259e6 0.192032
869869 −5.24637e7 −2.35673
870870 0 0
871871 4.38688e7 1.95934
872872 8.83881e6 0.393643
873873 1.10244e7 0.489574
874874 1.34258e7 0.594514
875875 0 0
876876 −2.61479e6 −0.115127
877877 1.25571e7 0.551304 0.275652 0.961258i 0.411106π-0.411106\pi
0.275652 + 0.961258i 0.411106π0.411106\pi
878878 1.05780e7 0.463092
879879 581058. 0.0253657
880880 0 0
881881 1.86084e7 0.807735 0.403868 0.914817i 0.367666π-0.367666\pi
0.403868 + 0.914817i 0.367666π0.367666\pi
882882 −2.29865e6 −0.0994950
883883 1.31567e7 0.567866 0.283933 0.958844i 0.408361π-0.408361\pi
0.283933 + 0.958844i 0.408361π0.408361\pi
884884 4.54870e6 0.195775
885885 0 0
886886 2.95503e7 1.26467
887887 6.52618e6 0.278516 0.139258 0.990256i 0.455528π-0.455528\pi
0.139258 + 0.990256i 0.455528π0.455528\pi
888888 −539917. −0.0229770
889889 3.30597e6 0.140296
890890 0 0
891891 −4.39969e7 −1.85664
892892 −9.85431e6 −0.414681
893893 2.97770e7 1.24955
894894 −256264. −0.0107237
895895 0 0
896896 802816. 0.0334077
897897 −3.15602e6 −0.130966
898898 1.68076e7 0.695530
899899 2.64157e7 1.09009
900900 0 0
901901 −7.21224e6 −0.295977
902902 3.08507e7 1.26255
903903 1.46726e6 0.0598807
904904 −1.01547e7 −0.413281
905905 0 0
906906 3.71395e6 0.150320
907907 −2.06271e7 −0.832570 −0.416285 0.909234i 0.636668π-0.636668\pi
−0.416285 + 0.909234i 0.636668π0.636668\pi
908908 2.30104e6 0.0926210
909909 1.70205e7 0.683222
910910 0 0
911911 −6.80945e6 −0.271842 −0.135921 0.990720i 0.543399π-0.543399\pi
−0.135921 + 0.990720i 0.543399π0.543399\pi
912912 −865638. −0.0344627
913913 −1.45473e7 −0.577572
914914 1.53624e7 0.608265
915915 0 0
916916 −8.75408e6 −0.344724
917917 7.75206e6 0.304434
918918 1.20649e6 0.0472518
919919 2.32177e7 0.906841 0.453420 0.891297i 0.350204π-0.350204\pi
0.453420 + 0.891297i 0.350204π0.350204\pi
920920 0 0
921921 −922142. −0.0358219
922922 −1.02769e7 −0.398138
923923 −2.45649e7 −0.949098
924924 1.16964e6 0.0450684
925925 0 0
926926 1.39836e7 0.535908
927927 −1.20899e6 −0.0462085
928928 4.97514e6 0.189642
929929 4.68022e7 1.77921 0.889604 0.456733i 0.150981π-0.150981\pi
0.889604 + 0.456733i 0.150981π0.150981\pi
930930 0 0
931931 4.24544e6 0.160527
932932 −9.99475e6 −0.376905
933933 2.75917e6 0.103771
934934 −61431.7 −0.00230423
935935 0 0
936936 −1.33176e7 −0.496862
937937 −1.22112e7 −0.454368 −0.227184 0.973852i 0.572952π-0.572952\pi
−0.227184 + 0.973852i 0.572952π0.572952\pi
938938 9.88979e6 0.367012
939939 1.57990e6 0.0584745
940940 0 0
941941 3.96195e7 1.45860 0.729298 0.684196i 0.239847π-0.239847\pi
0.729298 + 0.684196i 0.239847π0.239847\pi
942942 3.77647e6 0.138662
943943 −1.87666e7 −0.687235
944944 1.02538e7 0.374501
945945 0 0
946946 4.88624e7 1.77520
947947 −1.31421e7 −0.476200 −0.238100 0.971241i 0.576525π-0.576525\pi
−0.238100 + 0.971241i 0.576525π0.576525\pi
948948 −2.05766e6 −0.0743623
949949 7.42979e7 2.67800
950950 0 0
951951 2.56720e6 0.0920466
952952 1.02546e6 0.0366713
953953 −5.17474e7 −1.84568 −0.922839 0.385185i 0.874138π-0.874138\pi
−0.922839 + 0.385185i 0.874138π0.874138\pi
954954 2.11158e7 0.751167
955955 0 0
956956 −1.13900e7 −0.403068
957957 7.24840e6 0.255836
958958 9.94341e6 0.350043
959959 9.81992e6 0.344795
960960 0 0
961961 931510. 0.0325371
962962 1.53414e7 0.534476
963963 1.70821e7 0.593575
964964 8.74861e6 0.303212
965965 0 0
966966 −711494. −0.0245317
967967 −5.60278e7 −1.92680 −0.963401 0.268063i 0.913616π-0.913616\pi
−0.963401 + 0.268063i 0.913616π0.913616\pi
968968 2.86440e7 0.982529
969969 −1.10571e6 −0.0378294
970970 0 0
971971 −1.07082e7 −0.364475 −0.182237 0.983255i 0.558334π-0.558334\pi
−0.182237 + 0.983255i 0.558334π0.558334\pi
972972 −5.31190e6 −0.180337
973973 −9.38986e6 −0.317963
974974 4.06607e6 0.137334
975975 0 0
976976 5.61135e6 0.188557
977977 −2.02350e7 −0.678214 −0.339107 0.940748i 0.610125π-0.610125\pi
−0.339107 + 0.940748i 0.610125π0.610125\pi
978978 1.47107e6 0.0491798
979979 4.66941e7 1.55706
980980 0 0
981981 −3.30548e7 −1.09663
982982 −3.20900e6 −0.106192
983983 1.65832e7 0.547375 0.273688 0.961819i 0.411757π-0.411757\pi
0.273688 + 0.961819i 0.411757π0.411757\pi
984984 1.20999e6 0.0398376
985985 0 0
986986 6.35490e6 0.208169
987987 −1.57802e6 −0.0515608
988988 2.45966e7 0.801647
989989 −2.97231e7 −0.966281
990990 0 0
991991 2.58044e6 0.0834660 0.0417330 0.999129i 0.486712π-0.486712\pi
0.0417330 + 0.999129i 0.486712π0.486712\pi
992992 5.56746e6 0.179630
993993 −5.02721e6 −0.161791
994994 −5.53792e6 −0.177779
995995 0 0
996996 −570555. −0.0182242
997997 −3.95431e7 −1.25989 −0.629945 0.776640i 0.716923π-0.716923\pi
−0.629945 + 0.776640i 0.716923π0.716923\pi
998998 1.20245e7 0.382156
999999 4.06914e6 0.129000
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 350.6.a.z.1.3 5
5.2 odd 4 70.6.c.d.29.8 yes 10
5.3 odd 4 70.6.c.d.29.3 10
5.4 even 2 350.6.a.y.1.3 5
15.2 even 4 630.6.g.h.379.4 10
15.8 even 4 630.6.g.h.379.9 10
20.3 even 4 560.6.g.d.449.6 10
20.7 even 4 560.6.g.d.449.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.6.c.d.29.3 10 5.3 odd 4
70.6.c.d.29.8 yes 10 5.2 odd 4
350.6.a.y.1.3 5 5.4 even 2
350.6.a.z.1.3 5 1.1 even 1 trivial
560.6.g.d.449.5 10 20.7 even 4
560.6.g.d.449.6 10 20.3 even 4
630.6.g.h.379.4 10 15.2 even 4
630.6.g.h.379.9 10 15.8 even 4