Properties

Label 140.6.a.d.1.2
Level 140140
Weight 66
Character 140.1
Self dual yes
Analytic conductor 22.45422.454
Analytic rank 00
Dimension 33
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] = [140,6,Mod(1,140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(140, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("140.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 140=2257 140 = 2^{2} \cdot 5 \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 140.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: 22.453734773822.4537347738
Analytic rank: 00
Dimension: 33
Coefficient field: Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3499x210 x^{3} - 499x - 210 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 0.420991-0.420991 of defining polynomial
Character χ\chi == 140.1

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+1.57901q3+25.0000q5+49.0000q7240.507q9+322.771q11+657.331q13+39.4752q15+665.753q172215.14q19+77.3714q21+1586.87q23+625.000q25763.461q27+6386.70q29+7712.24q31+509.658q33+1225.00q35+3433.65q37+1037.93q396537.24q41+16611.0q436012.67q45+12516.9q47+2401.00q49+1051.23q51+4240.34q53+8069.27q553497.73q57+26156.3q59+32683.8q6111784.8q63+16433.3q656153.18q67+2505.68q6933827.2q7182194.4q73+986.880q75+15815.8q7735205.3q79+57237.6q81+17529.6q83+16643.8q85+10084.7q8772867.8q89+32209.2q91+12177.7q9355378.5q95166047.q9777628.6q99+O(q100)q+1.57901 q^{3} +25.0000 q^{5} +49.0000 q^{7} -240.507 q^{9} +322.771 q^{11} +657.331 q^{13} +39.4752 q^{15} +665.753 q^{17} -2215.14 q^{19} +77.3714 q^{21} +1586.87 q^{23} +625.000 q^{25} -763.461 q^{27} +6386.70 q^{29} +7712.24 q^{31} +509.658 q^{33} +1225.00 q^{35} +3433.65 q^{37} +1037.93 q^{39} -6537.24 q^{41} +16611.0 q^{43} -6012.67 q^{45} +12516.9 q^{47} +2401.00 q^{49} +1051.23 q^{51} +4240.34 q^{53} +8069.27 q^{55} -3497.73 q^{57} +26156.3 q^{59} +32683.8 q^{61} -11784.8 q^{63} +16433.3 q^{65} -6153.18 q^{67} +2505.68 q^{69} -33827.2 q^{71} -82194.4 q^{73} +986.880 q^{75} +15815.8 q^{77} -35205.3 q^{79} +57237.6 q^{81} +17529.6 q^{83} +16643.8 q^{85} +10084.7 q^{87} -72867.8 q^{89} +32209.2 q^{91} +12177.7 q^{93} -55378.5 q^{95} -166047. q^{97} -77628.6 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+6q3+75q5+147q7+281q914q114q13+150q15+44q17+2328q19+294q21+3676q23+1875q25+3726q27+4092q29+5888q31+11318q33+114368q99+O(q100) 3 q + 6 q^{3} + 75 q^{5} + 147 q^{7} + 281 q^{9} - 14 q^{11} - 4 q^{13} + 150 q^{15} + 44 q^{17} + 2328 q^{19} + 294 q^{21} + 3676 q^{23} + 1875 q^{25} + 3726 q^{27} + 4092 q^{29} + 5888 q^{31} + 11318 q^{33}+ \cdots - 114368 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 1.57901 0.101293 0.0506467 0.998717i 0.483872π-0.483872\pi
0.0506467 + 0.998717i 0.483872π0.483872\pi
44 0 0
55 25.0000 0.447214
66 0 0
77 49.0000 0.377964
88 0 0
99 −240.507 −0.989740
1010 0 0
1111 322.771 0.804290 0.402145 0.915576i 0.368265π-0.368265\pi
0.402145 + 0.915576i 0.368265π0.368265\pi
1212 0 0
1313 657.331 1.07876 0.539381 0.842062i 0.318658π-0.318658\pi
0.539381 + 0.842062i 0.318658π0.318658\pi
1414 0 0
1515 39.4752 0.0452998
1616 0 0
1717 665.753 0.558715 0.279358 0.960187i 0.409878π-0.409878\pi
0.279358 + 0.960187i 0.409878π0.409878\pi
1818 0 0
1919 −2215.14 −1.40772 −0.703862 0.710337i 0.748543π-0.748543\pi
−0.703862 + 0.710337i 0.748543π0.748543\pi
2020 0 0
2121 77.3714 0.0382853
2222 0 0
2323 1586.87 0.625492 0.312746 0.949837i 0.398751π-0.398751\pi
0.312746 + 0.949837i 0.398751π0.398751\pi
2424 0 0
2525 625.000 0.200000
2626 0 0
2727 −763.461 −0.201548
2828 0 0
2929 6386.70 1.41020 0.705102 0.709106i 0.250901π-0.250901\pi
0.705102 + 0.709106i 0.250901π0.250901\pi
3030 0 0
3131 7712.24 1.44137 0.720686 0.693262i 0.243827π-0.243827\pi
0.720686 + 0.693262i 0.243827π0.243827\pi
3232 0 0
3333 509.658 0.0814693
3434 0 0
3535 1225.00 0.169031
3636 0 0
3737 3433.65 0.412337 0.206169 0.978517i 0.433900π-0.433900\pi
0.206169 + 0.978517i 0.433900π0.433900\pi
3838 0 0
3939 1037.93 0.109272
4040 0 0
4141 −6537.24 −0.607344 −0.303672 0.952777i 0.598213π-0.598213\pi
−0.303672 + 0.952777i 0.598213π0.598213\pi
4242 0 0
4343 16611.0 1.37001 0.685007 0.728536i 0.259799π-0.259799\pi
0.685007 + 0.728536i 0.259799π0.259799\pi
4444 0 0
4545 −6012.67 −0.442625
4646 0 0
4747 12516.9 0.826515 0.413257 0.910614i 0.364391π-0.364391\pi
0.413257 + 0.910614i 0.364391π0.364391\pi
4848 0 0
4949 2401.00 0.142857
5050 0 0
5151 1051.23 0.0565942
5252 0 0
5353 4240.34 0.207353 0.103677 0.994611i 0.466939π-0.466939\pi
0.103677 + 0.994611i 0.466939π0.466939\pi
5454 0 0
5555 8069.27 0.359689
5656 0 0
5757 −3497.73 −0.142593
5858 0 0
5959 26156.3 0.978243 0.489122 0.872216i 0.337317π-0.337317\pi
0.489122 + 0.872216i 0.337317π0.337317\pi
6060 0 0
6161 32683.8 1.12463 0.562313 0.826924i 0.309911π-0.309911\pi
0.562313 + 0.826924i 0.309911π0.309911\pi
6262 0 0
6363 −11784.8 −0.374086
6464 0 0
6565 16433.3 0.482437
6666 0 0
6767 −6153.18 −0.167461 −0.0837303 0.996488i 0.526683π-0.526683\pi
−0.0837303 + 0.996488i 0.526683π0.526683\pi
6868 0 0
6969 2505.68 0.0633583
7070 0 0
7171 −33827.2 −0.796379 −0.398190 0.917303i 0.630361π-0.630361\pi
−0.398190 + 0.917303i 0.630361π0.630361\pi
7272 0 0
7373 −82194.4 −1.80524 −0.902621 0.430437i 0.858360π-0.858360\pi
−0.902621 + 0.430437i 0.858360π0.858360\pi
7474 0 0
7575 986.880 0.0202587
7676 0 0
7777 15815.8 0.303993
7878 0 0
7979 −35205.3 −0.634659 −0.317329 0.948315i 0.602786π-0.602786\pi
−0.317329 + 0.948315i 0.602786π0.602786\pi
8080 0 0
8181 57237.6 0.969324
8282 0 0
8383 17529.6 0.279304 0.139652 0.990201i 0.455402π-0.455402\pi
0.139652 + 0.990201i 0.455402π0.455402\pi
8484 0 0
8585 16643.8 0.249865
8686 0 0
8787 10084.7 0.142844
8888 0 0
8989 −72867.8 −0.975126 −0.487563 0.873088i 0.662114π-0.662114\pi
−0.487563 + 0.873088i 0.662114π0.662114\pi
9090 0 0
9191 32209.2 0.407734
9292 0 0
9393 12177.7 0.146002
9494 0 0
9595 −55378.5 −0.629553
9696 0 0
9797 −166047. −1.79185 −0.895927 0.444202i 0.853487π-0.853487\pi
−0.895927 + 0.444202i 0.853487π0.853487\pi
9898 0 0
9999 −77628.6 −0.796038
100100 0 0
101101 19577.2 0.190963 0.0954813 0.995431i 0.469561π-0.469561\pi
0.0954813 + 0.995431i 0.469561π0.469561\pi
102102 0 0
103103 83864.5 0.778906 0.389453 0.921046i 0.372664π-0.372664\pi
0.389453 + 0.921046i 0.372664π0.372664\pi
104104 0 0
105105 1934.29 0.0171217
106106 0 0
107107 −105704. −0.892547 −0.446273 0.894897i 0.647249π-0.647249\pi
−0.446273 + 0.894897i 0.647249π0.647249\pi
108108 0 0
109109 −114386. −0.922160 −0.461080 0.887359i 0.652538π-0.652538\pi
−0.461080 + 0.887359i 0.652538π0.652538\pi
110110 0 0
111111 5421.77 0.0417670
112112 0 0
113113 −95123.1 −0.700793 −0.350396 0.936601i 0.613953π-0.613953\pi
−0.350396 + 0.936601i 0.613953π0.613953\pi
114114 0 0
115115 39671.8 0.279729
116116 0 0
117117 −158092. −1.06769
118118 0 0
119119 32621.9 0.211175
120120 0 0
121121 −56870.0 −0.353118
122122 0 0
123123 −10322.4 −0.0615199
124124 0 0
125125 15625.0 0.0894427
126126 0 0
127127 97854.5 0.538358 0.269179 0.963090i 0.413248π-0.413248\pi
0.269179 + 0.963090i 0.413248π0.413248\pi
128128 0 0
129129 26228.9 0.138773
130130 0 0
131131 −31926.2 −0.162543 −0.0812715 0.996692i 0.525898π-0.525898\pi
−0.0812715 + 0.996692i 0.525898π0.525898\pi
132132 0 0
133133 −108542. −0.532070
134134 0 0
135135 −19086.5 −0.0901348
136136 0 0
137137 22595.8 0.102855 0.0514276 0.998677i 0.483623π-0.483623\pi
0.0514276 + 0.998677i 0.483623π0.483623\pi
138138 0 0
139139 287232. 1.26094 0.630472 0.776212i 0.282861π-0.282861\pi
0.630472 + 0.776212i 0.282861π0.282861\pi
140140 0 0
141141 19764.2 0.0837205
142142 0 0
143143 212167. 0.867637
144144 0 0
145145 159668. 0.630662
146146 0 0
147147 3791.20 0.0144705
148148 0 0
149149 −437546. −1.61458 −0.807288 0.590158i 0.799065π-0.799065\pi
−0.807288 + 0.590158i 0.799065π0.799065\pi
150150 0 0
151151 505868. 1.80549 0.902744 0.430179i 0.141550π-0.141550\pi
0.902744 + 0.430179i 0.141550π0.141550\pi
152152 0 0
153153 −160118. −0.552983
154154 0 0
155155 192806. 0.644601
156156 0 0
157157 −214333. −0.693967 −0.346984 0.937871i 0.612794π-0.612794\pi
−0.346984 + 0.937871i 0.612794π0.612794\pi
158158 0 0
159159 6695.54 0.0210035
160160 0 0
161161 77756.7 0.236414
162162 0 0
163163 −587081. −1.73073 −0.865364 0.501143i 0.832913π-0.832913\pi
−0.865364 + 0.501143i 0.832913π0.832913\pi
164164 0 0
165165 12741.5 0.0364342
166166 0 0
167167 −387234. −1.07444 −0.537220 0.843442i 0.680525π-0.680525\pi
−0.537220 + 0.843442i 0.680525π0.680525\pi
168168 0 0
169169 60790.6 0.163727
170170 0 0
171171 532757. 1.39328
172172 0 0
173173 610438. 1.55069 0.775347 0.631535i 0.217575π-0.217575\pi
0.775347 + 0.631535i 0.217575π0.217575\pi
174174 0 0
175175 30625.0 0.0755929
176176 0 0
177177 41301.1 0.0990897
178178 0 0
179179 169505. 0.395412 0.197706 0.980261i 0.436651π-0.436651\pi
0.197706 + 0.980261i 0.436651π0.436651\pi
180180 0 0
181181 305167. 0.692374 0.346187 0.938166i 0.387476π-0.387476\pi
0.346187 + 0.938166i 0.387476π0.387476\pi
182182 0 0
183183 51608.1 0.113917
184184 0 0
185185 85841.4 0.184403
186186 0 0
187187 214886. 0.449369
188188 0 0
189189 −37409.6 −0.0761778
190190 0 0
191191 941471. 1.86734 0.933670 0.358134i 0.116587π-0.116587\pi
0.933670 + 0.358134i 0.116587π0.116587\pi
192192 0 0
193193 385057. 0.744101 0.372051 0.928212i 0.378655π-0.378655\pi
0.372051 + 0.928212i 0.378655π0.378655\pi
194194 0 0
195195 25948.3 0.0488677
196196 0 0
197197 −1.03718e6 −1.90410 −0.952048 0.305948i 0.901026π-0.901026\pi
−0.952048 + 0.305948i 0.901026π0.901026\pi
198198 0 0
199199 410855. 0.735455 0.367727 0.929934i 0.380136π-0.380136\pi
0.367727 + 0.929934i 0.380136π0.380136\pi
200200 0 0
201201 −9715.93 −0.0169627
202202 0 0
203203 312949. 0.533007
204204 0 0
205205 −163431. −0.271612
206206 0 0
207207 −381653. −0.619075
208208 0 0
209209 −714983. −1.13222
210210 0 0
211211 442714. 0.684568 0.342284 0.939597i 0.388799π-0.388799\pi
0.342284 + 0.939597i 0.388799π0.388799\pi
212212 0 0
213213 −53413.4 −0.0806680
214214 0 0
215215 415275. 0.612689
216216 0 0
217217 377900. 0.544787
218218 0 0
219219 −129786. −0.182859
220220 0 0
221221 437620. 0.602721
222222 0 0
223223 93933.5 0.126491 0.0632453 0.997998i 0.479855π-0.479855\pi
0.0632453 + 0.997998i 0.479855π0.479855\pi
224224 0 0
225225 −150317. −0.197948
226226 0 0
227227 234538. 0.302099 0.151049 0.988526i 0.451735π-0.451735\pi
0.151049 + 0.988526i 0.451735π0.451735\pi
228228 0 0
229229 239032. 0.301208 0.150604 0.988594i 0.451878π-0.451878\pi
0.150604 + 0.988594i 0.451878π0.451878\pi
230230 0 0
231231 24973.2 0.0307925
232232 0 0
233233 −1.47330e6 −1.77788 −0.888939 0.458025i 0.848557π-0.848557\pi
−0.888939 + 0.458025i 0.848557π0.848557\pi
234234 0 0
235235 312921. 0.369629
236236 0 0
237237 −55589.5 −0.0642868
238238 0 0
239239 −1.31478e6 −1.48887 −0.744436 0.667694i 0.767282π-0.767282\pi
−0.744436 + 0.667694i 0.767282π0.767282\pi
240240 0 0
241241 1.20810e6 1.33986 0.669932 0.742423i 0.266323π-0.266323\pi
0.669932 + 0.742423i 0.266323π0.266323\pi
242242 0 0
243243 275900. 0.299734
244244 0 0
245245 60025.0 0.0638877
246246 0 0
247247 −1.45608e6 −1.51860
248248 0 0
249249 27679.4 0.0282916
250250 0 0
251251 −518940. −0.519916 −0.259958 0.965620i 0.583709π-0.583709\pi
−0.259958 + 0.965620i 0.583709π0.583709\pi
252252 0 0
253253 512196. 0.503077
254254 0 0
255255 26280.7 0.0253097
256256 0 0
257257 −566825. −0.535324 −0.267662 0.963513i 0.586251π-0.586251\pi
−0.267662 + 0.963513i 0.586251π0.586251\pi
258258 0 0
259259 168249. 0.155849
260260 0 0
261261 −1.53605e6 −1.39573
262262 0 0
263263 −1.27389e6 −1.13564 −0.567822 0.823151i 0.692214π-0.692214\pi
−0.567822 + 0.823151i 0.692214π0.692214\pi
264264 0 0
265265 106009. 0.0927313
266266 0 0
267267 −115059. −0.0987738
268268 0 0
269269 −445770. −0.375604 −0.187802 0.982207i 0.560136π-0.560136\pi
−0.187802 + 0.982207i 0.560136π0.560136\pi
270270 0 0
271271 1.26776e6 1.04861 0.524306 0.851530i 0.324325π-0.324325\pi
0.524306 + 0.851530i 0.324325π0.324325\pi
272272 0 0
273273 50858.6 0.0413007
274274 0 0
275275 201732. 0.160858
276276 0 0
277277 −309948. −0.242711 −0.121355 0.992609i 0.538724π-0.538724\pi
−0.121355 + 0.992609i 0.538724π0.538724\pi
278278 0 0
279279 −1.85484e6 −1.42658
280280 0 0
281281 291247. 0.220037 0.110018 0.993930i 0.464909π-0.464909\pi
0.110018 + 0.993930i 0.464909π0.464909\pi
282282 0 0
283283 723026. 0.536646 0.268323 0.963329i 0.413531π-0.413531\pi
0.268323 + 0.963329i 0.413531π0.413531\pi
284284 0 0
285285 −87443.2 −0.0637696
286286 0 0
287287 −320325. −0.229554
288288 0 0
289289 −976630. −0.687837
290290 0 0
291291 −262190. −0.181503
292292 0 0
293293 −1.19632e6 −0.814098 −0.407049 0.913406i 0.633442π-0.633442\pi
−0.407049 + 0.913406i 0.633442π0.633442\pi
294294 0 0
295295 653908. 0.437484
296296 0 0
297297 −246423. −0.162103
298298 0 0
299299 1.04310e6 0.674757
300300 0 0
301301 813940. 0.517817
302302 0 0
303303 30912.6 0.0193433
304304 0 0
305305 817096. 0.502948
306306 0 0
307307 −1.95349e6 −1.18295 −0.591475 0.806324i 0.701454π-0.701454\pi
−0.591475 + 0.806324i 0.701454π0.701454\pi
308308 0 0
309309 132423. 0.0788981
310310 0 0
311311 794401. 0.465735 0.232868 0.972508i 0.425189π-0.425189\pi
0.232868 + 0.972508i 0.425189π0.425189\pi
312312 0 0
313313 −118598. −0.0684255 −0.0342127 0.999415i 0.510892π-0.510892\pi
−0.0342127 + 0.999415i 0.510892π0.510892\pi
314314 0 0
315315 −294621. −0.167297
316316 0 0
317317 −2.78228e6 −1.55508 −0.777540 0.628833i 0.783533π-0.783533\pi
−0.777540 + 0.628833i 0.783533π0.783533\pi
318318 0 0
319319 2.06144e6 1.13421
320320 0 0
321321 −166907. −0.0904092
322322 0 0
323323 −1.47474e6 −0.786517
324324 0 0
325325 410832. 0.215752
326326 0 0
327327 −180616. −0.0934088
328328 0 0
329329 613326. 0.312393
330330 0 0
331331 −2.38160e6 −1.19481 −0.597404 0.801940i 0.703801π-0.703801\pi
−0.597404 + 0.801940i 0.703801π0.703801\pi
332332 0 0
333333 −825817. −0.408106
334334 0 0
335335 −153830. −0.0748907
336336 0 0
337337 270123. 0.129565 0.0647823 0.997899i 0.479365π-0.479365\pi
0.0647823 + 0.997899i 0.479365π0.479365\pi
338338 0 0
339339 −150200. −0.0709857
340340 0 0
341341 2.48929e6 1.15928
342342 0 0
343343 117649. 0.0539949
344344 0 0
345345 62642.1 0.0283347
346346 0 0
347347 3.58739e6 1.59939 0.799696 0.600405i 0.204994π-0.204994\pi
0.799696 + 0.600405i 0.204994π0.204994\pi
348348 0 0
349349 −1.13696e6 −0.499666 −0.249833 0.968289i 0.580376π-0.580376\pi
−0.249833 + 0.968289i 0.580376π0.580376\pi
350350 0 0
351351 −501847. −0.217422
352352 0 0
353353 3.49344e6 1.49216 0.746081 0.665855i 0.231933π-0.231933\pi
0.746081 + 0.665855i 0.231933π0.231933\pi
354354 0 0
355355 −845680. −0.356152
356356 0 0
357357 51510.2 0.0213906
358358 0 0
359359 −986571. −0.404010 −0.202005 0.979384i 0.564746π-0.564746\pi
−0.202005 + 0.979384i 0.564746π0.564746\pi
360360 0 0
361361 2.43075e6 0.981687
362362 0 0
363363 −89798.2 −0.0357685
364364 0 0
365365 −2.05486e6 −0.807329
366366 0 0
367367 3.28626e6 1.27361 0.636805 0.771025i 0.280255π-0.280255\pi
0.636805 + 0.771025i 0.280255π0.280255\pi
368368 0 0
369369 1.57225e6 0.601112
370370 0 0
371371 207777. 0.0783722
372372 0 0
373373 3.67518e6 1.36775 0.683874 0.729600i 0.260294π-0.260294\pi
0.683874 + 0.729600i 0.260294π0.260294\pi
374374 0 0
375375 24672.0 0.00905996
376376 0 0
377377 4.19818e6 1.52127
378378 0 0
379379 −1.18583e6 −0.424059 −0.212029 0.977263i 0.568007π-0.568007\pi
−0.212029 + 0.977263i 0.568007π0.568007\pi
380380 0 0
381381 154513. 0.0545322
382382 0 0
383383 −2.67224e6 −0.930846 −0.465423 0.885088i 0.654098π-0.654098\pi
−0.465423 + 0.885088i 0.654098π0.654098\pi
384384 0 0
385385 395394. 0.135950
386386 0 0
387387 −3.99506e6 −1.35596
388388 0 0
389389 −2.60515e6 −0.872890 −0.436445 0.899731i 0.643763π-0.643763\pi
−0.436445 + 0.899731i 0.643763π0.643763\pi
390390 0 0
391391 1.05646e6 0.349472
392392 0 0
393393 −50411.7 −0.0164646
394394 0 0
395395 −880133. −0.283828
396396 0 0
397397 4.59840e6 1.46430 0.732151 0.681142i 0.238517π-0.238517\pi
0.732151 + 0.681142i 0.238517π0.238517\pi
398398 0 0
399399 −171389. −0.0538952
400400 0 0
401401 −2.14418e6 −0.665887 −0.332943 0.942947i 0.608042π-0.608042\pi
−0.332943 + 0.942947i 0.608042π0.608042\pi
402402 0 0
403403 5.06949e6 1.55490
404404 0 0
405405 1.43094e6 0.433495
406406 0 0
407407 1.10828e6 0.331639
408408 0 0
409409 4.01508e6 1.18682 0.593411 0.804900i 0.297781π-0.297781\pi
0.593411 + 0.804900i 0.297781π0.297781\pi
410410 0 0
411411 35679.0 0.0104186
412412 0 0
413413 1.28166e6 0.369741
414414 0 0
415415 438240. 0.124908
416416 0 0
417417 453542. 0.127725
418418 0 0
419419 2.05677e6 0.572335 0.286168 0.958180i 0.407619π-0.407619\pi
0.286168 + 0.958180i 0.407619π0.407619\pi
420420 0 0
421421 −536575. −0.147545 −0.0737726 0.997275i 0.523504π-0.523504\pi
−0.0737726 + 0.997275i 0.523504π0.523504\pi
422422 0 0
423423 −3.01039e6 −0.818034
424424 0 0
425425 416096. 0.111743
426426 0 0
427427 1.60151e6 0.425069
428428 0 0
429429 335014. 0.0878860
430430 0 0
431431 −5.57365e6 −1.44526 −0.722631 0.691234i 0.757067π-0.757067\pi
−0.722631 + 0.691234i 0.757067π0.757067\pi
432432 0 0
433433 −600292. −0.153866 −0.0769331 0.997036i 0.524513π-0.524513\pi
−0.0769331 + 0.997036i 0.524513π0.524513\pi
434434 0 0
435435 252117. 0.0638820
436436 0 0
437437 −3.51514e6 −0.880521
438438 0 0
439439 4.08074e6 1.01060 0.505298 0.862945i 0.331383π-0.331383\pi
0.505298 + 0.862945i 0.331383π0.331383\pi
440440 0 0
441441 −577457. −0.141391
442442 0 0
443443 −6.45140e6 −1.56187 −0.780935 0.624612i 0.785257π-0.785257\pi
−0.780935 + 0.624612i 0.785257π0.785257\pi
444444 0 0
445445 −1.82169e6 −0.436089
446446 0 0
447447 −690889. −0.163546
448448 0 0
449449 3.62778e6 0.849230 0.424615 0.905374i 0.360409π-0.360409\pi
0.424615 + 0.905374i 0.360409π0.360409\pi
450450 0 0
451451 −2.11003e6 −0.488480
452452 0 0
453453 798769. 0.182884
454454 0 0
455455 805230. 0.182344
456456 0 0
457457 5.12392e6 1.14766 0.573828 0.818976i 0.305458π-0.305458\pi
0.573828 + 0.818976i 0.305458π0.305458\pi
458458 0 0
459459 −508277. −0.112608
460460 0 0
461461 −3.96610e6 −0.869184 −0.434592 0.900627i 0.643107π-0.643107\pi
−0.434592 + 0.900627i 0.643107π0.643107\pi
462462 0 0
463463 310011. 0.0672085 0.0336043 0.999435i 0.489301π-0.489301\pi
0.0336043 + 0.999435i 0.489301π0.489301\pi
464464 0 0
465465 304442. 0.0652939
466466 0 0
467467 −1.07130e6 −0.227311 −0.113655 0.993520i 0.536256π-0.536256\pi
−0.113655 + 0.993520i 0.536256π0.536256\pi
468468 0 0
469469 −301506. −0.0632942
470470 0 0
471471 −338433. −0.0702943
472472 0 0
473473 5.36155e6 1.10189
474474 0 0
475475 −1.38446e6 −0.281545
476476 0 0
477477 −1.01983e6 −0.205226
478478 0 0
479479 5.62151e6 1.11947 0.559737 0.828670i 0.310902π-0.310902\pi
0.559737 + 0.828670i 0.310902π0.310902\pi
480480 0 0
481481 2.25705e6 0.444813
482482 0 0
483483 122778. 0.0239472
484484 0 0
485485 −4.15118e6 −0.801341
486486 0 0
487487 −4.04558e6 −0.772962 −0.386481 0.922297i 0.626309π-0.626309\pi
−0.386481 + 0.922297i 0.626309π0.626309\pi
488488 0 0
489489 −927006. −0.175312
490490 0 0
491491 −4.15461e6 −0.777727 −0.388863 0.921295i 0.627132π-0.627132\pi
−0.388863 + 0.921295i 0.627132π0.627132\pi
492492 0 0
493493 4.25197e6 0.787903
494494 0 0
495495 −1.94071e6 −0.355999
496496 0 0
497497 −1.65753e6 −0.301003
498498 0 0
499499 −2.79365e6 −0.502251 −0.251125 0.967955i 0.580801π-0.580801\pi
−0.251125 + 0.967955i 0.580801π0.580801\pi
500500 0 0
501501 −611445. −0.108834
502502 0 0
503503 −6.95171e6 −1.22510 −0.612551 0.790431i 0.709856π-0.709856\pi
−0.612551 + 0.790431i 0.709856π0.709856\pi
504504 0 0
505505 489431. 0.0854010
506506 0 0
507507 95988.9 0.0165845
508508 0 0
509509 −7.84503e6 −1.34215 −0.671073 0.741391i 0.734166π-0.734166\pi
−0.671073 + 0.741391i 0.734166π0.734166\pi
510510 0 0
511511 −4.02753e6 −0.682317
512512 0 0
513513 1.69118e6 0.283723
514514 0 0
515515 2.09661e6 0.348337
516516 0 0
517517 4.04008e6 0.664758
518518 0 0
519519 963887. 0.157075
520520 0 0
521521 −6.03460e6 −0.973989 −0.486995 0.873405i 0.661907π-0.661907\pi
−0.486995 + 0.873405i 0.661907π0.661907\pi
522522 0 0
523523 −1.59256e6 −0.254590 −0.127295 0.991865i 0.540629π-0.540629\pi
−0.127295 + 0.991865i 0.540629π0.540629\pi
524524 0 0
525525 48357.1 0.00765707
526526 0 0
527527 5.13444e6 0.805317
528528 0 0
529529 −3.91818e6 −0.608759
530530 0 0
531531 −6.29078e6 −0.968206
532532 0 0
533533 −4.29713e6 −0.655179
534534 0 0
535535 −2.64259e6 −0.399159
536536 0 0
537537 267650. 0.0400526
538538 0 0
539539 774973. 0.114899
540540 0 0
541541 −1.73741e6 −0.255217 −0.127608 0.991825i 0.540730π-0.540730\pi
−0.127608 + 0.991825i 0.540730π0.540730\pi
542542 0 0
543543 481861. 0.0701330
544544 0 0
545545 −2.85965e6 −0.412402
546546 0 0
547547 1.14309e7 1.63348 0.816738 0.577009i 0.195780π-0.195780\pi
0.816738 + 0.577009i 0.195780π0.195780\pi
548548 0 0
549549 −7.86068e6 −1.11309
550550 0 0
551551 −1.41475e7 −1.98518
552552 0 0
553553 −1.72506e6 −0.239879
554554 0 0
555555 135544. 0.0186788
556556 0 0
557557 1.08461e7 1.48127 0.740635 0.671908i 0.234525π-0.234525\pi
0.740635 + 0.671908i 0.234525π0.234525\pi
558558 0 0
559559 1.09189e7 1.47792
560560 0 0
561561 339306. 0.0455182
562562 0 0
563563 203287. 0.0270295 0.0135148 0.999909i 0.495698π-0.495698\pi
0.0135148 + 0.999909i 0.495698π0.495698\pi
564564 0 0
565565 −2.37808e6 −0.313404
566566 0 0
567567 2.80464e6 0.366370
568568 0 0
569569 1.04184e7 1.34903 0.674514 0.738262i 0.264353π-0.264353\pi
0.674514 + 0.738262i 0.264353π0.264353\pi
570570 0 0
571571 −4.44964e6 −0.571129 −0.285565 0.958359i 0.592181π-0.592181\pi
−0.285565 + 0.958359i 0.592181π0.592181\pi
572572 0 0
573573 1.48659e6 0.189149
574574 0 0
575575 991794. 0.125098
576576 0 0
577577 −4.10826e6 −0.513711 −0.256855 0.966450i 0.582686π-0.582686\pi
−0.256855 + 0.966450i 0.582686π0.582686\pi
578578 0 0
579579 608009. 0.0753726
580580 0 0
581581 858950. 0.105567
582582 0 0
583583 1.36866e6 0.166772
584584 0 0
585585 −3.95231e6 −0.477487
586586 0 0
587587 −1.10539e7 −1.32409 −0.662047 0.749463i 0.730312π-0.730312\pi
−0.662047 + 0.749463i 0.730312π0.730312\pi
588588 0 0
589589 −1.70837e7 −2.02905
590590 0 0
591591 −1.63772e6 −0.192872
592592 0 0
593593 1.01113e7 1.18078 0.590390 0.807118i 0.298974π-0.298974\pi
0.590390 + 0.807118i 0.298974π0.298974\pi
594594 0 0
595595 815547. 0.0944402
596596 0 0
597597 648744. 0.0744968
598598 0 0
599599 −1.10092e6 −0.125369 −0.0626845 0.998033i 0.519966π-0.519966\pi
−0.0626845 + 0.998033i 0.519966π0.519966\pi
600600 0 0
601601 2.03055e6 0.229312 0.114656 0.993405i 0.463423π-0.463423\pi
0.114656 + 0.993405i 0.463423π0.463423\pi
602602 0 0
603603 1.47988e6 0.165742
604604 0 0
605605 −1.42175e6 −0.157919
606606 0 0
607607 4.20572e6 0.463307 0.231654 0.972798i 0.425586π-0.425586\pi
0.231654 + 0.972798i 0.425586π0.425586\pi
608608 0 0
609609 494148. 0.0539901
610610 0 0
611611 8.22771e6 0.891612
612612 0 0
613613 −1.34913e7 −1.45012 −0.725060 0.688686i 0.758188π-0.758188\pi
−0.725060 + 0.688686i 0.758188π0.758188\pi
614614 0 0
615615 −258059. −0.0275126
616616 0 0
617617 9.26037e6 0.979299 0.489650 0.871919i 0.337125π-0.337125\pi
0.489650 + 0.871919i 0.337125π0.337125\pi
618618 0 0
619619 1.11560e7 1.17026 0.585131 0.810939i 0.301043π-0.301043\pi
0.585131 + 0.810939i 0.301043π0.301043\pi
620620 0 0
621621 −1.21151e6 −0.126067
622622 0 0
623623 −3.57052e6 −0.368563
624624 0 0
625625 390625. 0.0400000
626626 0 0
627627 −1.12896e6 −0.114686
628628 0 0
629629 2.28597e6 0.230379
630630 0 0
631631 8.72868e6 0.872721 0.436360 0.899772i 0.356267π-0.356267\pi
0.436360 + 0.899772i 0.356267π0.356267\pi
632632 0 0
633633 699049. 0.0693423
634634 0 0
635635 2.44636e6 0.240761
636636 0 0
637637 1.57825e6 0.154109
638638 0 0
639639 8.13566e6 0.788208
640640 0 0
641641 646402. 0.0621380 0.0310690 0.999517i 0.490109π-0.490109\pi
0.0310690 + 0.999517i 0.490109π0.490109\pi
642642 0 0
643643 1.36895e7 1.30575 0.652873 0.757468i 0.273564π-0.273564\pi
0.652873 + 0.757468i 0.273564π0.273564\pi
644644 0 0
645645 655723. 0.0620614
646646 0 0
647647 −1.12743e7 −1.05884 −0.529418 0.848361i 0.677590π-0.677590\pi
−0.529418 + 0.848361i 0.677590π0.677590\pi
648648 0 0
649649 8.44250e6 0.786791
650650 0 0
651651 596707. 0.0551834
652652 0 0
653653 1.23867e7 1.13677 0.568384 0.822763i 0.307569π-0.307569\pi
0.568384 + 0.822763i 0.307569π0.307569\pi
654654 0 0
655655 −798154. −0.0726915
656656 0 0
657657 1.97683e7 1.78672
658658 0 0
659659 9.93495e6 0.891153 0.445576 0.895244i 0.352999π-0.352999\pi
0.445576 + 0.895244i 0.352999π0.352999\pi
660660 0 0
661661 −4.30434e6 −0.383181 −0.191590 0.981475i 0.561364π-0.561364\pi
−0.191590 + 0.981475i 0.561364π0.561364\pi
662662 0 0
663663 691005. 0.0610517
664664 0 0
665665 −2.71355e6 −0.237949
666666 0 0
667667 1.01349e7 0.882072
668668 0 0
669669 148322. 0.0128127
670670 0 0
671671 1.05494e7 0.904526
672672 0 0
673673 −252232. −0.0214665 −0.0107333 0.999942i 0.503417π-0.503417\pi
−0.0107333 + 0.999942i 0.503417π0.503417\pi
674674 0 0
675675 −477163. −0.0403095
676676 0 0
677677 −1.06012e7 −0.888960 −0.444480 0.895789i 0.646612π-0.646612\pi
−0.444480 + 0.895789i 0.646612π0.646612\pi
678678 0 0
679679 −8.13632e6 −0.677257
680680 0 0
681681 370338. 0.0306006
682682 0 0
683683 −1.30105e7 −1.06719 −0.533594 0.845741i 0.679159π-0.679159\pi
−0.533594 + 0.845741i 0.679159π0.679159\pi
684684 0 0
685685 564895. 0.0459983
686686 0 0
687687 377433. 0.0305104
688688 0 0
689689 2.78731e6 0.223685
690690 0 0
691691 −9.67711e6 −0.770993 −0.385496 0.922709i 0.625970π-0.625970\pi
−0.385496 + 0.922709i 0.625970π0.625970\pi
692692 0 0
693693 −3.80380e6 −0.300874
694694 0 0
695695 7.18080e6 0.563911
696696 0 0
697697 −4.35218e6 −0.339332
698698 0 0
699699 −2.32636e6 −0.180087
700700 0 0
701701 −1.63711e7 −1.25829 −0.629147 0.777286i 0.716596π-0.716596\pi
−0.629147 + 0.777286i 0.716596π0.716596\pi
702702 0 0
703703 −7.60603e6 −0.580457
704704 0 0
705705 494106. 0.0374410
706706 0 0
707707 959285. 0.0721771
708708 0 0
709709 7.10343e6 0.530704 0.265352 0.964152i 0.414512π-0.414512\pi
0.265352 + 0.964152i 0.414512π0.414512\pi
710710 0 0
711711 8.46711e6 0.628147
712712 0 0
713713 1.22383e7 0.901567
714714 0 0
715715 5.30418e6 0.388019
716716 0 0
717717 −2.07604e6 −0.150813
718718 0 0
719719 −6.87623e6 −0.496053 −0.248027 0.968753i 0.579782π-0.579782\pi
−0.248027 + 0.968753i 0.579782π0.579782\pi
720720 0 0
721721 4.10936e6 0.294399
722722 0 0
723723 1.90760e6 0.135719
724724 0 0
725725 3.99169e6 0.282041
726726 0 0
727727 9.71330e6 0.681602 0.340801 0.940136i 0.389302π-0.389302\pi
0.340801 + 0.940136i 0.389302π0.389302\pi
728728 0 0
729729 −1.34731e7 −0.938963
730730 0 0
731731 1.10588e7 0.765448
732732 0 0
733733 −1.14783e7 −0.789070 −0.394535 0.918881i 0.629094π-0.629094\pi
−0.394535 + 0.918881i 0.629094π0.629094\pi
734734 0 0
735735 94780.0 0.00647140
736736 0 0
737737 −1.98607e6 −0.134687
738738 0 0
739739 1.55073e7 1.04454 0.522270 0.852780i 0.325085π-0.325085\pi
0.522270 + 0.852780i 0.325085π0.325085\pi
740740 0 0
741741 −2.29916e6 −0.153824
742742 0 0
743743 2.49648e7 1.65904 0.829520 0.558477i 0.188614π-0.188614\pi
0.829520 + 0.558477i 0.188614π0.188614\pi
744744 0 0
745745 −1.09387e7 −0.722060
746746 0 0
747747 −4.21599e6 −0.276438
748748 0 0
749749 −5.17949e6 −0.337351
750750 0 0
751751 1.59690e6 0.103319 0.0516593 0.998665i 0.483549π-0.483549\pi
0.0516593 + 0.998665i 0.483549π0.483549\pi
752752 0 0
753753 −819411. −0.0526641
754754 0 0
755755 1.26467e7 0.807438
756756 0 0
757757 −8.30133e6 −0.526512 −0.263256 0.964726i 0.584796π-0.584796\pi
−0.263256 + 0.964726i 0.584796π0.584796\pi
758758 0 0
759759 808762. 0.0509584
760760 0 0
761761 911464. 0.0570529 0.0285265 0.999593i 0.490919π-0.490919\pi
0.0285265 + 0.999593i 0.490919π0.490919\pi
762762 0 0
763763 −5.60491e6 −0.348544
764764 0 0
765765 −4.00295e6 −0.247301
766766 0 0
767767 1.71934e7 1.05529
768768 0 0
769769 −2.51616e7 −1.53434 −0.767171 0.641442i 0.778336π-0.778336\pi
−0.767171 + 0.641442i 0.778336π0.778336\pi
770770 0 0
771771 −895022. −0.0542248
772772 0 0
773773 −4.10309e6 −0.246980 −0.123490 0.992346i 0.539409π-0.539409\pi
−0.123490 + 0.992346i 0.539409π0.539409\pi
774774 0 0
775775 4.82015e6 0.288274
776776 0 0
777777 265667. 0.0157865
778778 0 0
779779 1.44809e7 0.854972
780780 0 0
781781 −1.09184e7 −0.640520
782782 0 0
783783 −4.87600e6 −0.284223
784784 0 0
785785 −5.35831e6 −0.310352
786786 0 0
787787 −2.32406e7 −1.33755 −0.668777 0.743463i 0.733182π-0.733182\pi
−0.668777 + 0.743463i 0.733182π0.733182\pi
788788 0 0
789789 −2.01148e6 −0.115033
790790 0 0
791791 −4.66103e6 −0.264875
792792 0 0
793793 2.14841e7 1.21320
794794 0 0
795795 167388. 0.00939307
796796 0 0
797797 −9.23259e6 −0.514846 −0.257423 0.966299i 0.582873π-0.582873\pi
−0.257423 + 0.966299i 0.582873π0.582873\pi
798798 0 0
799799 8.33313e6 0.461787
800800 0 0
801801 1.75252e7 0.965120
802802 0 0
803803 −2.65300e7 −1.45194
804804 0 0
805805 1.94392e6 0.105728
806806 0 0
807807 −703874. −0.0380462
808808 0 0
809809 −3.27151e7 −1.75743 −0.878714 0.477349i 0.841598π-0.841598\pi
−0.878714 + 0.477349i 0.841598π0.841598\pi
810810 0 0
811811 −1.01835e7 −0.543681 −0.271840 0.962342i 0.587632π-0.587632\pi
−0.271840 + 0.962342i 0.587632π0.587632\pi
812812 0 0
813813 2.00181e6 0.106218
814814 0 0
815815 −1.46770e7 −0.774005
816816 0 0
817817 −3.67958e7 −1.92860
818818 0 0
819819 −7.74653e6 −0.403550
820820 0 0
821821 3.37256e7 1.74623 0.873116 0.487512i 0.162096π-0.162096\pi
0.873116 + 0.487512i 0.162096π0.162096\pi
822822 0 0
823823 −1.33753e7 −0.688343 −0.344171 0.938907i 0.611840π-0.611840\pi
−0.344171 + 0.938907i 0.611840π0.611840\pi
824824 0 0
825825 318536. 0.0162939
826826 0 0
827827 1.05590e7 0.536856 0.268428 0.963300i 0.413496π-0.413496\pi
0.268428 + 0.963300i 0.413496π0.413496\pi
828828 0 0
829829 −3.01166e7 −1.52202 −0.761009 0.648741i 0.775296π-0.775296\pi
−0.761009 + 0.648741i 0.775296π0.775296\pi
830830 0 0
831831 −489410. −0.0245850
832832 0 0
833833 1.59847e6 0.0798165
834834 0 0
835835 −9.68084e6 −0.480504
836836 0 0
837837 −5.88799e6 −0.290505
838838 0 0
839839 2.47935e6 0.121600 0.0607998 0.998150i 0.480635π-0.480635\pi
0.0607998 + 0.998150i 0.480635π0.480635\pi
840840 0 0
841841 2.02788e7 0.988674
842842 0 0
843843 459881. 0.0222883
844844 0 0
845845 1.51977e6 0.0732208
846846 0 0
847847 −2.78663e6 −0.133466
848848 0 0
849849 1.14166e6 0.0543587
850850 0 0
851851 5.44877e6 0.257914
852852 0 0
853853 −1.23084e6 −0.0579199 −0.0289600 0.999581i 0.509220π-0.509220\pi
−0.0289600 + 0.999581i 0.509220π0.509220\pi
854854 0 0
855855 1.33189e7 0.623094
856856 0 0
857857 −2.75099e7 −1.27949 −0.639746 0.768586i 0.720961π-0.720961\pi
−0.639746 + 0.768586i 0.720961π0.720961\pi
858858 0 0
859859 −1.28833e7 −0.595722 −0.297861 0.954609i 0.596273π-0.596273\pi
−0.297861 + 0.954609i 0.596273π0.596273\pi
860860 0 0
861861 −505795. −0.0232524
862862 0 0
863863 −1.57981e7 −0.722067 −0.361033 0.932553i 0.617576π-0.617576\pi
−0.361033 + 0.932553i 0.617576π0.617576\pi
864864 0 0
865865 1.52610e7 0.693492
866866 0 0
867867 −1.54211e6 −0.0696734
868868 0 0
869869 −1.13632e7 −0.510450
870870 0 0
871871 −4.04468e6 −0.180650
872872 0 0
873873 3.99355e7 1.77347
874874 0 0
875875 765625. 0.0338062
876876 0 0
877877 −3.99471e7 −1.75383 −0.876913 0.480649i 0.840401π-0.840401\pi
−0.876913 + 0.480649i 0.840401π0.840401\pi
878878 0 0
879879 −1.88899e6 −0.0824628
880880 0 0
881881 4.20714e7 1.82620 0.913098 0.407740i 0.133683π-0.133683\pi
0.913098 + 0.407740i 0.133683π0.133683\pi
882882 0 0
883883 −2.82226e7 −1.21813 −0.609067 0.793118i 0.708456π-0.708456\pi
−0.609067 + 0.793118i 0.708456π0.708456\pi
884884 0 0
885885 1.03253e6 0.0443142
886886 0 0
887887 −1.26687e7 −0.540658 −0.270329 0.962768i 0.587132π-0.587132\pi
−0.270329 + 0.962768i 0.587132π0.587132\pi
888888 0 0
889889 4.79487e6 0.203480
890890 0 0
891891 1.84746e7 0.779618
892892 0 0
893893 −2.77266e7 −1.16350
894894 0 0
895895 4.23762e6 0.176833
896896 0 0
897897 1.64706e6 0.0683485
898898 0 0
899899 4.92558e7 2.03263
900900 0 0
901901 2.82302e6 0.115852
902902 0 0
903903 1.28522e6 0.0524514
904904 0 0
905905 7.62917e6 0.309639
906906 0 0
907907 −1.50368e7 −0.606928 −0.303464 0.952843i 0.598143π-0.598143\pi
−0.303464 + 0.952843i 0.598143π0.598143\pi
908908 0 0
909909 −4.70846e6 −0.189003
910910 0 0
911911 −1.13882e7 −0.454630 −0.227315 0.973821i 0.572995π-0.572995\pi
−0.227315 + 0.973821i 0.572995π0.572995\pi
912912 0 0
913913 5.65804e6 0.224641
914914 0 0
915915 1.29020e6 0.0509454
916916 0 0
917917 −1.56438e6 −0.0614355
918918 0 0
919919 1.66749e7 0.651292 0.325646 0.945492i 0.394418π-0.394418\pi
0.325646 + 0.945492i 0.394418π0.394418\pi
920920 0 0
921921 −3.08458e6 −0.119825
922922 0 0
923923 −2.22356e7 −0.859103
924924 0 0
925925 2.14603e6 0.0824674
926926 0 0
927927 −2.01700e7 −0.770914
928928 0 0
929929 3.13311e7 1.19107 0.595534 0.803330i 0.296941π-0.296941\pi
0.595534 + 0.803330i 0.296941π0.296941\pi
930930 0 0
931931 −5.31856e6 −0.201103
932932 0 0
933933 1.25437e6 0.0471759
934934 0 0
935935 5.37214e6 0.200964
936936 0 0
937937 4.22607e7 1.57249 0.786245 0.617914i 0.212022π-0.212022\pi
0.786245 + 0.617914i 0.212022π0.212022\pi
938938 0 0
939939 −187268. −0.00693105
940940 0 0
941941 −2.46633e7 −0.907980 −0.453990 0.891007i 0.650000π-0.650000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
942942 0 0
943943 −1.03738e7 −0.379889
944944 0 0
945945 −935240. −0.0340678
946946 0 0
947947 −1.33679e7 −0.484383 −0.242191 0.970229i 0.577866π-0.577866\pi
−0.242191 + 0.970229i 0.577866π0.577866\pi
948948 0 0
949949 −5.40289e7 −1.94743
950950 0 0
951951 −4.39325e6 −0.157519
952952 0 0
953953 −2.17678e7 −0.776395 −0.388198 0.921576i 0.626902π-0.626902\pi
−0.388198 + 0.921576i 0.626902π0.626902\pi
954954 0 0
955955 2.35368e7 0.835100
956956 0 0
957957 3.25504e6 0.114888
958958 0 0
959959 1.10719e6 0.0388756
960960 0 0
961961 3.08494e7 1.07755
962962 0 0
963963 2.54225e7 0.883389
964964 0 0
965965 9.62643e6 0.332772
966966 0 0
967967 2.58647e7 0.889491 0.444746 0.895657i 0.353294π-0.353294\pi
0.444746 + 0.895657i 0.353294π0.353294\pi
968968 0 0
969969 −2.32862e6 −0.0796691
970970 0 0
971971 3.76225e7 1.28056 0.640280 0.768142i 0.278819π-0.278819\pi
0.640280 + 0.768142i 0.278819π0.278819\pi
972972 0 0
973973 1.40744e7 0.476592
974974 0 0
975975 648707. 0.0218543
976976 0 0
977977 4.22400e7 1.41575 0.707876 0.706336i 0.249653π-0.249653\pi
0.707876 + 0.706336i 0.249653π0.249653\pi
978978 0 0
979979 −2.35196e7 −0.784284
980980 0 0
981981 2.75106e7 0.912698
982982 0 0
983983 2.18464e7 0.721100 0.360550 0.932740i 0.382589π-0.382589\pi
0.360550 + 0.932740i 0.382589π0.382589\pi
984984 0 0
985985 −2.59295e7 −0.851538
986986 0 0
987987 968447. 0.0316434
988988 0 0
989989 2.63595e7 0.856933
990990 0 0
991991 4.62904e6 0.149729 0.0748646 0.997194i 0.476148π-0.476148\pi
0.0748646 + 0.997194i 0.476148π0.476148\pi
992992 0 0
993993 −3.76056e6 −0.121026
994994 0 0
995995 1.02714e7 0.328905
996996 0 0
997997 −4.99110e7 −1.59023 −0.795113 0.606462i 0.792588π-0.792588\pi
−0.795113 + 0.606462i 0.792588π0.792588\pi
998998 0 0
999999 −2.62146e6 −0.0831055
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 140.6.a.d.1.2 3
4.3 odd 2 560.6.a.t.1.2 3
5.2 odd 4 700.6.e.g.449.3 6
5.3 odd 4 700.6.e.g.449.4 6
5.4 even 2 700.6.a.i.1.2 3
7.6 odd 2 980.6.a.h.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.6.a.d.1.2 3 1.1 even 1 trivial
560.6.a.t.1.2 3 4.3 odd 2
700.6.a.i.1.2 3 5.4 even 2
700.6.e.g.449.3 6 5.2 odd 4
700.6.e.g.449.4 6 5.3 odd 4
980.6.a.h.1.2 3 7.6 odd 2