Properties

Label 784.6.a.bi.1.2
Level 784784
Weight 66
Character 784.1
Self dual yes
Analytic conductor 125.741125.741
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [784,6,Mod(1,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 6, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.1"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Level: N N == 784=2472 784 = 2^{4} \cdot 7^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 784.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,0,0,0,0,1480] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 125.740914733125.740914733
Analytic rank: 00
Dimension: 44
Coefficient field: Q(2,1177)\Q(\sqrt{2}, \sqrt{1177})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x42x3591x2+592x+85262 x^{4} - 2x^{3} - 591x^{2} + 592x + 85262 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 272 2\cdot 7^{2}
Twist minimal: no (minimal twist has level 196)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 16.239516.2395 of defining polynomial
Character χ\chi == 784.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q19.3093q3+49.9872q5+129.848q9+351.152q11+853.910q13965.216q15+2267.40q17201.628q19+1069.22q23626.281q25+2184.88q27+6862.06q295402.82q316780.49q33+9917.10q3716488.4q399383.43q41+22378.6q43+6490.74q45+6792.94q4743781.9q51+3494.13q53+17553.1q55+3893.29q5727543.5q5928901.8q61+42684.6q6570459.7q6720645.8q6924149.9q71+62230.6q73+12093.0q75+79757.9q7973741.6q816356.40q83+113341.q85132501.q8760189.5q89+104324.q9310078.8q953180.12q97+45596.4q99+O(q100)q-19.3093 q^{3} +49.9872 q^{5} +129.848 q^{9} +351.152 q^{11} +853.910 q^{13} -965.216 q^{15} +2267.40 q^{17} -201.628 q^{19} +1069.22 q^{23} -626.281 q^{25} +2184.88 q^{27} +6862.06 q^{29} -5402.82 q^{31} -6780.49 q^{33} +9917.10 q^{37} -16488.4 q^{39} -9383.43 q^{41} +22378.6 q^{43} +6490.74 q^{45} +6792.94 q^{47} -43781.9 q^{51} +3494.13 q^{53} +17553.1 q^{55} +3893.29 q^{57} -27543.5 q^{59} -28901.8 q^{61} +42684.6 q^{65} -70459.7 q^{67} -20645.8 q^{69} -24149.9 q^{71} +62230.6 q^{73} +12093.0 q^{75} +79757.9 q^{79} -73741.6 q^{81} -6356.40 q^{83} +113341. q^{85} -132501. q^{87} -60189.5 q^{89} +104324. q^{93} -10078.8 q^{95} -3180.12 q^{97} +45596.4 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+1480q9+444q11+3824q153408q23+11904q25+20724q29+13732q3725608q39+28996q43181852q51+528q53+89540q57+110220q65195384q67+66412q99+O(q100) 4 q + 1480 q^{9} + 444 q^{11} + 3824 q^{15} - 3408 q^{23} + 11904 q^{25} + 20724 q^{29} + 13732 q^{37} - 25608 q^{39} + 28996 q^{43} - 181852 q^{51} + 528 q^{53} + 89540 q^{57} + 110220 q^{65} - 195384 q^{67}+ \cdots - 66412 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 −19.3093 −1.23869 −0.619345 0.785119i 0.712602π-0.712602\pi
−0.619345 + 0.785119i 0.712602π0.712602\pi
44 0 0
55 49.9872 0.894198 0.447099 0.894484i 0.352457π-0.352457\pi
0.447099 + 0.894484i 0.352457π0.352457\pi
66 0 0
77 0 0
88 0 0
99 129.848 0.534354
1010 0 0
1111 351.152 0.875011 0.437505 0.899216i 0.355862π-0.355862\pi
0.437505 + 0.899216i 0.355862π0.355862\pi
1212 0 0
1313 853.910 1.40137 0.700687 0.713469i 0.252877π-0.252877\pi
0.700687 + 0.713469i 0.252877π0.252877\pi
1414 0 0
1515 −965.216 −1.10763
1616 0 0
1717 2267.40 1.90286 0.951430 0.307866i 0.0996147π-0.0996147\pi
0.951430 + 0.307866i 0.0996147π0.0996147\pi
1818 0 0
1919 −201.628 −0.128135 −0.0640674 0.997946i 0.520407π-0.520407\pi
−0.0640674 + 0.997946i 0.520407π0.520407\pi
2020 0 0
2121 0 0
2222 0 0
2323 1069.22 0.421450 0.210725 0.977545i 0.432418π-0.432418\pi
0.210725 + 0.977545i 0.432418π0.432418\pi
2424 0 0
2525 −626.281 −0.200410
2626 0 0
2727 2184.88 0.576791
2828 0 0
2929 6862.06 1.51516 0.757582 0.652740i 0.226380π-0.226380\pi
0.757582 + 0.652740i 0.226380π0.226380\pi
3030 0 0
3131 −5402.82 −1.00975 −0.504877 0.863191i 0.668462π-0.668462\pi
−0.504877 + 0.863191i 0.668462π0.668462\pi
3232 0 0
3333 −6780.49 −1.08387
3434 0 0
3535 0 0
3636 0 0
3737 9917.10 1.19091 0.595457 0.803387i 0.296971π-0.296971\pi
0.595457 + 0.803387i 0.296971π0.296971\pi
3838 0 0
3939 −16488.4 −1.73587
4040 0 0
4141 −9383.43 −0.871770 −0.435885 0.900002i 0.643565π-0.643565\pi
−0.435885 + 0.900002i 0.643565π0.643565\pi
4242 0 0
4343 22378.6 1.84570 0.922851 0.385158i 0.125853π-0.125853\pi
0.922851 + 0.385158i 0.125853π0.125853\pi
4444 0 0
4545 6490.74 0.477818
4646 0 0
4747 6792.94 0.448552 0.224276 0.974526i 0.427998π-0.427998\pi
0.224276 + 0.974526i 0.427998π0.427998\pi
4848 0 0
4949 0 0
5050 0 0
5151 −43781.9 −2.35705
5252 0 0
5353 3494.13 0.170863 0.0854317 0.996344i 0.472773π-0.472773\pi
0.0854317 + 0.996344i 0.472773π0.472773\pi
5454 0 0
5555 17553.1 0.782433
5656 0 0
5757 3893.29 0.158719
5858 0 0
5959 −27543.5 −1.03012 −0.515062 0.857153i 0.672231π-0.672231\pi
−0.515062 + 0.857153i 0.672231π0.672231\pi
6060 0 0
6161 −28901.8 −0.994490 −0.497245 0.867610i 0.665655π-0.665655\pi
−0.497245 + 0.867610i 0.665655π0.665655\pi
6262 0 0
6363 0 0
6464 0 0
6565 42684.6 1.25311
6666 0 0
6767 −70459.7 −1.91758 −0.958790 0.284114i 0.908300π-0.908300\pi
−0.958790 + 0.284114i 0.908300π0.908300\pi
6868 0 0
6969 −20645.8 −0.522046
7070 0 0
7171 −24149.9 −0.568550 −0.284275 0.958743i 0.591753π-0.591753\pi
−0.284275 + 0.958743i 0.591753π0.591753\pi
7272 0 0
7373 62230.6 1.36677 0.683387 0.730056i 0.260506π-0.260506\pi
0.683387 + 0.730056i 0.260506π0.260506\pi
7474 0 0
7575 12093.0 0.248246
7676 0 0
7777 0 0
7878 0 0
7979 79757.9 1.43783 0.718913 0.695100i 0.244640π-0.244640\pi
0.718913 + 0.695100i 0.244640π0.244640\pi
8080 0 0
8181 −73741.6 −1.24882
8282 0 0
8383 −6356.40 −0.101278 −0.0506391 0.998717i 0.516126π-0.516126\pi
−0.0506391 + 0.998717i 0.516126π0.516126\pi
8484 0 0
8585 113341. 1.70153
8686 0 0
8787 −132501. −1.87682
8888 0 0
8989 −60189.5 −0.805464 −0.402732 0.915318i 0.631939π-0.631939\pi
−0.402732 + 0.915318i 0.631939π0.631939\pi
9090 0 0
9191 0 0
9292 0 0
9393 104324. 1.25077
9494 0 0
9595 −10078.8 −0.114578
9696 0 0
9797 −3180.12 −0.0343174 −0.0171587 0.999853i 0.505462π-0.505462\pi
−0.0171587 + 0.999853i 0.505462π0.505462\pi
9898 0 0
9999 45596.4 0.467565
100100 0 0
101101 −115219. −1.12388 −0.561941 0.827177i 0.689945π-0.689945\pi
−0.561941 + 0.827177i 0.689945π0.689945\pi
102102 0 0
103103 −122065. −1.13370 −0.566852 0.823820i 0.691839π-0.691839\pi
−0.566852 + 0.823820i 0.691839π0.691839\pi
104104 0 0
105105 0 0
106106 0 0
107107 54130.9 0.457074 0.228537 0.973535i 0.426606π-0.426606\pi
0.228537 + 0.973535i 0.426606π0.426606\pi
108108 0 0
109109 39838.5 0.321171 0.160586 0.987022i 0.448662π-0.448662\pi
0.160586 + 0.987022i 0.448662π0.448662\pi
110110 0 0
111111 −191492. −1.47517
112112 0 0
113113 −68432.6 −0.504159 −0.252079 0.967707i 0.581114π-0.581114\pi
−0.252079 + 0.967707i 0.581114π0.581114\pi
114114 0 0
115115 53447.1 0.376860
116116 0 0
117117 110879. 0.748829
118118 0 0
119119 0 0
120120 0 0
121121 −37743.2 −0.234356
122122 0 0
123123 181187. 1.07985
124124 0 0
125125 −187516. −1.07340
126126 0 0
127127 256765. 1.41262 0.706312 0.707901i 0.250358π-0.250358\pi
0.706312 + 0.707901i 0.250358π0.250358\pi
128128 0 0
129129 −432114. −2.28625
130130 0 0
131131 222523. 1.13291 0.566457 0.824091i 0.308314π-0.308314\pi
0.566457 + 0.824091i 0.308314π0.308314\pi
132132 0 0
133133 0 0
134134 0 0
135135 109216. 0.515766
136136 0 0
137137 88409.0 0.402434 0.201217 0.979547i 0.435510π-0.435510\pi
0.201217 + 0.979547i 0.435510π0.435510\pi
138138 0 0
139139 105621. 0.463674 0.231837 0.972755i 0.425526π-0.425526\pi
0.231837 + 0.972755i 0.425526π0.425526\pi
140140 0 0
141141 −131167. −0.555618
142142 0 0
143143 299852. 1.22622
144144 0 0
145145 343015. 1.35486
146146 0 0
147147 0 0
148148 0 0
149149 −449212. −1.65762 −0.828811 0.559528i 0.810982π-0.810982\pi
−0.828811 + 0.559528i 0.810982π0.810982\pi
150150 0 0
151151 −12824.7 −0.0457727 −0.0228863 0.999738i 0.507286π-0.507286\pi
−0.0228863 + 0.999738i 0.507286π0.507286\pi
152152 0 0
153153 294418. 1.01680
154154 0 0
155155 −270072. −0.902921
156156 0 0
157157 −155429. −0.503249 −0.251624 0.967825i 0.580965π-0.580965\pi
−0.251624 + 0.967825i 0.580965π0.580965\pi
158158 0 0
159159 −67469.1 −0.211647
160160 0 0
161161 0 0
162162 0 0
163163 474063. 1.39755 0.698774 0.715342i 0.253729π-0.253729\pi
0.698774 + 0.715342i 0.253729π0.253729\pi
164164 0 0
165165 −338938. −0.969192
166166 0 0
167167 −308200. −0.855147 −0.427574 0.903981i 0.640632π-0.640632\pi
−0.427574 + 0.903981i 0.640632π0.640632\pi
168168 0 0
169169 357870. 0.963847
170170 0 0
171171 −26181.0 −0.0684693
172172 0 0
173173 474941. 1.20649 0.603245 0.797556i 0.293874π-0.293874\pi
0.603245 + 0.797556i 0.293874π0.293874\pi
174174 0 0
175175 0 0
176176 0 0
177177 531846. 1.27601
178178 0 0
179179 619706. 1.44562 0.722808 0.691049i 0.242851π-0.242851\pi
0.722808 + 0.691049i 0.242851π0.242851\pi
180180 0 0
181181 −108568. −0.246324 −0.123162 0.992387i 0.539303π-0.539303\pi
−0.123162 + 0.992387i 0.539303π0.539303\pi
182182 0 0
183183 558073. 1.23187
184184 0 0
185185 495728. 1.06491
186186 0 0
187187 796204. 1.66502
188188 0 0
189189 0 0
190190 0 0
191191 244317. 0.484585 0.242293 0.970203i 0.422101π-0.422101\pi
0.242293 + 0.970203i 0.422101π0.422101\pi
192192 0 0
193193 64918.4 0.125451 0.0627255 0.998031i 0.480021π-0.480021\pi
0.0627255 + 0.998031i 0.480021π0.480021\pi
194194 0 0
195195 −824208. −1.55221
196196 0 0
197197 876652. 1.60939 0.804696 0.593687i 0.202328π-0.202328\pi
0.804696 + 0.593687i 0.202328π0.202328\pi
198198 0 0
199199 −82565.9 −0.147798 −0.0738989 0.997266i 0.523544π-0.523544\pi
−0.0738989 + 0.997266i 0.523544π0.523544\pi
200200 0 0
201201 1.36053e6 2.37529
202202 0 0
203203 0 0
204204 0 0
205205 −469051. −0.779535
206206 0 0
207207 138836. 0.225203
208208 0 0
209209 −70802.1 −0.112119
210210 0 0
211211 271448. 0.419740 0.209870 0.977729i 0.432696π-0.432696\pi
0.209870 + 0.977729i 0.432696π0.432696\pi
212212 0 0
213213 466316. 0.704257
214214 0 0
215215 1.11864e6 1.65042
216216 0 0
217217 0 0
218218 0 0
219219 −1.20163e6 −1.69301
220220 0 0
221221 1.93616e6 2.66662
222222 0 0
223223 1.33163e6 1.79316 0.896582 0.442878i 0.146043π-0.146043\pi
0.896582 + 0.442878i 0.146043π0.146043\pi
224224 0 0
225225 −81321.3 −0.107090
226226 0 0
227227 551492. 0.710354 0.355177 0.934799i 0.384421π-0.384421\pi
0.355177 + 0.934799i 0.384421π0.384421\pi
228228 0 0
229229 −759511. −0.957074 −0.478537 0.878067i 0.658833π-0.658833\pi
−0.478537 + 0.878067i 0.658833π0.658833\pi
230230 0 0
231231 0 0
232232 0 0
233233 806195. 0.972860 0.486430 0.873720i 0.338299π-0.338299\pi
0.486430 + 0.873720i 0.338299π0.338299\pi
234234 0 0
235235 339560. 0.401095
236236 0 0
237237 −1.54007e6 −1.78102
238238 0 0
239239 798850. 0.904629 0.452315 0.891858i 0.350598π-0.350598\pi
0.452315 + 0.891858i 0.350598π0.350598\pi
240240 0 0
241241 −73687.9 −0.0817247 −0.0408624 0.999165i 0.513011π-0.513011\pi
−0.0408624 + 0.999165i 0.513011π0.513011\pi
242242 0 0
243243 892969. 0.970110
244244 0 0
245245 0 0
246246 0 0
247247 −172172. −0.179565
248248 0 0
249249 122737. 0.125452
250250 0 0
251251 −25091.9 −0.0251391 −0.0125696 0.999921i 0.504001π-0.504001\pi
−0.0125696 + 0.999921i 0.504001π0.504001\pi
252252 0 0
253253 375457. 0.368773
254254 0 0
255255 −2.18854e6 −2.10767
256256 0 0
257257 363530. 0.343326 0.171663 0.985156i 0.445086π-0.445086\pi
0.171663 + 0.985156i 0.445086π0.445086\pi
258258 0 0
259259 0 0
260260 0 0
261261 891025. 0.809634
262262 0 0
263263 −2.10649e6 −1.87789 −0.938946 0.344064i 0.888196π-0.888196\pi
−0.938946 + 0.344064i 0.888196π0.888196\pi
264264 0 0
265265 174662. 0.152786
266266 0 0
267267 1.16222e6 0.997720
268268 0 0
269269 −736198. −0.620318 −0.310159 0.950685i 0.600382π-0.600382\pi
−0.310159 + 0.950685i 0.600382π0.600382\pi
270270 0 0
271271 565623. 0.467847 0.233924 0.972255i 0.424843π-0.424843\pi
0.233924 + 0.972255i 0.424843π0.424843\pi
272272 0 0
273273 0 0
274274 0 0
275275 −219920. −0.175361
276276 0 0
277277 −512229. −0.401111 −0.200555 0.979682i 0.564275π-0.564275\pi
−0.200555 + 0.979682i 0.564275π0.564275\pi
278278 0 0
279279 −701545. −0.539566
280280 0 0
281281 541721. 0.409270 0.204635 0.978838i 0.434399π-0.434399\pi
0.204635 + 0.978838i 0.434399π0.434399\pi
282282 0 0
283283 −1.65919e6 −1.23149 −0.615744 0.787946i 0.711144π-0.711144\pi
−0.615744 + 0.787946i 0.711144π0.711144\pi
284284 0 0
285285 194615. 0.141927
286286 0 0
287287 0 0
288288 0 0
289289 3.72127e6 2.62088
290290 0 0
291291 61405.8 0.0425086
292292 0 0
293293 −130633. −0.0888962 −0.0444481 0.999012i 0.514153π-0.514153\pi
−0.0444481 + 0.999012i 0.514153π0.514153\pi
294294 0 0
295295 −1.37682e6 −0.921136
296296 0 0
297297 767226. 0.504699
298298 0 0
299299 913015. 0.590609
300300 0 0
301301 0 0
302302 0 0
303303 2.22480e6 1.39214
304304 0 0
305305 −1.44472e6 −0.889271
306306 0 0
307307 −789634. −0.478167 −0.239084 0.970999i 0.576847π-0.576847\pi
−0.239084 + 0.970999i 0.576847π0.576847\pi
308308 0 0
309309 2.35699e6 1.40431
310310 0 0
311311 −1.93597e6 −1.13500 −0.567502 0.823372i 0.692090π-0.692090\pi
−0.567502 + 0.823372i 0.692090π0.692090\pi
312312 0 0
313313 1.82834e6 1.05486 0.527430 0.849598i 0.323156π-0.323156\pi
0.527430 + 0.849598i 0.323156π0.323156\pi
314314 0 0
315315 0 0
316316 0 0
317317 −1.68315e6 −0.940751 −0.470376 0.882466i 0.655882π-0.655882\pi
−0.470376 + 0.882466i 0.655882π0.655882\pi
318318 0 0
319319 2.40963e6 1.32579
320320 0 0
321321 −1.04523e6 −0.566173
322322 0 0
323323 −457173. −0.243823
324324 0 0
325325 −534787. −0.280849
326326 0 0
327327 −769252. −0.397832
328328 0 0
329329 0 0
330330 0 0
331331 2.98161e6 1.49582 0.747912 0.663798i 0.231057π-0.231057\pi
0.747912 + 0.663798i 0.231057π0.231057\pi
332332 0 0
333333 1.28772e6 0.636370
334334 0 0
335335 −3.52208e6 −1.71470
336336 0 0
337337 −1.45801e6 −0.699335 −0.349668 0.936874i 0.613705π-0.613705\pi
−0.349668 + 0.936874i 0.613705π0.613705\pi
338338 0 0
339339 1.32138e6 0.624496
340340 0 0
341341 −1.89721e6 −0.883547
342342 0 0
343343 0 0
344344 0 0
345345 −1.03202e6 −0.466812
346346 0 0
347347 −3.34680e6 −1.49213 −0.746065 0.665873i 0.768059π-0.768059\pi
−0.746065 + 0.665873i 0.768059π0.768059\pi
348348 0 0
349349 −3.49755e6 −1.53709 −0.768546 0.639794i 0.779020π-0.779020\pi
−0.768546 + 0.639794i 0.779020π0.779020\pi
350350 0 0
351351 1.86569e6 0.808300
352352 0 0
353353 −3.00600e6 −1.28396 −0.641981 0.766721i 0.721887π-0.721887\pi
−0.641981 + 0.766721i 0.721887π0.721887\pi
354354 0 0
355355 −1.20718e6 −0.508396
356356 0 0
357357 0 0
358358 0 0
359359 −1.23247e6 −0.504708 −0.252354 0.967635i 0.581205π-0.581205\pi
−0.252354 + 0.967635i 0.581205π0.581205\pi
360360 0 0
361361 −2.43545e6 −0.983581
362362 0 0
363363 728795. 0.290294
364364 0 0
365365 3.11073e6 1.22217
366366 0 0
367367 2.16047e6 0.837305 0.418653 0.908146i 0.362502π-0.362502\pi
0.418653 + 0.908146i 0.362502π0.362502\pi
368368 0 0
369369 −1.21842e6 −0.465834
370370 0 0
371371 0 0
372372 0 0
373373 −1.33520e6 −0.496908 −0.248454 0.968644i 0.579922π-0.579922\pi
−0.248454 + 0.968644i 0.579922π0.579922\pi
374374 0 0
375375 3.62080e6 1.32962
376376 0 0
377377 5.85959e6 2.12331
378378 0 0
379379 3.68471e6 1.31767 0.658834 0.752289i 0.271050π-0.271050\pi
0.658834 + 0.752289i 0.271050π0.271050\pi
380380 0 0
381381 −4.95795e6 −1.74980
382382 0 0
383383 −4.01114e6 −1.39724 −0.698620 0.715493i 0.746202π-0.746202\pi
−0.698620 + 0.715493i 0.746202π0.746202\pi
384384 0 0
385385 0 0
386386 0 0
387387 2.90581e6 0.986257
388388 0 0
389389 −1.80717e6 −0.605515 −0.302757 0.953068i 0.597907π-0.597907\pi
−0.302757 + 0.953068i 0.597907π0.597907\pi
390390 0 0
391391 2.42435e6 0.801960
392392 0 0
393393 −4.29676e6 −1.40333
394394 0 0
395395 3.98687e6 1.28570
396396 0 0
397397 3.28328e6 1.04552 0.522759 0.852480i 0.324903π-0.324903\pi
0.522759 + 0.852480i 0.324903π0.324903\pi
398398 0 0
399399 0 0
400400 0 0
401401 3.09097e6 0.959918 0.479959 0.877291i 0.340652π-0.340652\pi
0.479959 + 0.877291i 0.340652π0.340652\pi
402402 0 0
403403 −4.61352e6 −1.41504
404404 0 0
405405 −3.68613e6 −1.11669
406406 0 0
407407 3.48241e6 1.04206
408408 0 0
409409 −416847. −0.123216 −0.0616082 0.998100i 0.519623π-0.519623\pi
−0.0616082 + 0.998100i 0.519623π0.519623\pi
410410 0 0
411411 −1.70711e6 −0.498492
412412 0 0
413413 0 0
414414 0 0
415415 −317739. −0.0905628
416416 0 0
417417 −2.03946e6 −0.574348
418418 0 0
419419 −4.70440e6 −1.30909 −0.654544 0.756024i 0.727139π-0.727139\pi
−0.654544 + 0.756024i 0.727139π0.727139\pi
420420 0 0
421421 −2.75525e6 −0.757626 −0.378813 0.925473i 0.623668π-0.623668\pi
−0.378813 + 0.925473i 0.623668π0.623668\pi
422422 0 0
423423 882050. 0.239686
424424 0 0
425425 −1.42003e6 −0.381352
426426 0 0
427427 0 0
428428 0 0
429429 −5.78993e6 −1.51890
430430 0 0
431431 249909. 0.0648022 0.0324011 0.999475i 0.489685π-0.489685\pi
0.0324011 + 0.999475i 0.489685π0.489685\pi
432432 0 0
433433 7.61708e6 1.95240 0.976199 0.216875i 0.0695864π-0.0695864\pi
0.976199 + 0.216875i 0.0695864π0.0695864\pi
434434 0 0
435435 −6.62338e6 −1.67825
436436 0 0
437437 −215584. −0.0540024
438438 0 0
439439 3.30848e6 0.819345 0.409672 0.912233i 0.365643π-0.365643\pi
0.409672 + 0.912233i 0.365643π0.365643\pi
440440 0 0
441441 0 0
442442 0 0
443443 −1.39077e6 −0.336703 −0.168351 0.985727i 0.553844π-0.553844\pi
−0.168351 + 0.985727i 0.553844π0.553844\pi
444444 0 0
445445 −3.00871e6 −0.720244
446446 0 0
447447 8.67396e6 2.05328
448448 0 0
449449 7.39368e6 1.73079 0.865396 0.501089i 0.167067π-0.167067\pi
0.865396 + 0.501089i 0.167067π0.167067\pi
450450 0 0
451451 −3.29501e6 −0.762809
452452 0 0
453453 247636. 0.0566982
454454 0 0
455455 0 0
456456 0 0
457457 −3.54533e6 −0.794085 −0.397042 0.917800i 0.629963π-0.629963\pi
−0.397042 + 0.917800i 0.629963π0.629963\pi
458458 0 0
459459 4.95402e6 1.09755
460460 0 0
461461 4.59122e6 1.00618 0.503090 0.864234i 0.332196π-0.332196\pi
0.503090 + 0.864234i 0.332196π0.332196\pi
462462 0 0
463463 183800. 0.0398468 0.0199234 0.999802i 0.493658π-0.493658\pi
0.0199234 + 0.999802i 0.493658π0.493658\pi
464464 0 0
465465 5.21489e6 1.11844
466466 0 0
467467 2.58361e6 0.548194 0.274097 0.961702i 0.411621π-0.411621\pi
0.274097 + 0.961702i 0.411621π0.411621\pi
468468 0 0
469469 0 0
470470 0 0
471471 3.00122e6 0.623370
472472 0 0
473473 7.85828e6 1.61501
474474 0 0
475475 126276. 0.0256795
476476 0 0
477477 453705. 0.0913015
478478 0 0
479479 7.30745e6 1.45522 0.727608 0.685993i 0.240632π-0.240632\pi
0.727608 + 0.685993i 0.240632π0.240632\pi
480480 0 0
481481 8.46832e6 1.66892
482482 0 0
483483 0 0
484484 0 0
485485 −158965. −0.0306866
486486 0 0
487487 5.08456e6 0.971473 0.485737 0.874105i 0.338551π-0.338551\pi
0.485737 + 0.874105i 0.338551π0.338551\pi
488488 0 0
489489 −9.15381e6 −1.73113
490490 0 0
491491 −5.83908e6 −1.09305 −0.546526 0.837442i 0.684050π-0.684050\pi
−0.546526 + 0.837442i 0.684050π0.684050\pi
492492 0 0
493493 1.55591e7 2.88315
494494 0 0
495495 2.27923e6 0.418096
496496 0 0
497497 0 0
498498 0 0
499499 −8.78201e6 −1.57886 −0.789428 0.613843i 0.789623π-0.789623\pi
−0.789428 + 0.613843i 0.789623π0.789623\pi
500500 0 0
501501 5.95111e6 1.05926
502502 0 0
503503 −2.64568e6 −0.466248 −0.233124 0.972447i 0.574895π-0.574895\pi
−0.233124 + 0.972447i 0.574895π0.574895\pi
504504 0 0
505505 −5.75948e6 −1.00497
506506 0 0
507507 −6.91020e6 −1.19391
508508 0 0
509509 −1.11720e7 −1.91134 −0.955668 0.294445i 0.904865π-0.904865\pi
−0.955668 + 0.294445i 0.904865π0.904865\pi
510510 0 0
511511 0 0
512512 0 0
513513 −440534. −0.0739071
514514 0 0
515515 −6.10171e6 −1.01376
516516 0 0
517517 2.38535e6 0.392488
518518 0 0
519519 −9.17076e6 −1.49447
520520 0 0
521521 2.17607e6 0.351219 0.175610 0.984460i 0.443810π-0.443810\pi
0.175610 + 0.984460i 0.443810π0.443810\pi
522522 0 0
523523 −7.26978e6 −1.16216 −0.581082 0.813845i 0.697370π-0.697370\pi
−0.581082 + 0.813845i 0.697370π0.697370\pi
524524 0 0
525525 0 0
526526 0 0
527527 −1.22504e7 −1.92142
528528 0 0
529529 −5.29312e6 −0.822380
530530 0 0
531531 −3.57647e6 −0.550451
532532 0 0
533533 −8.01261e6 −1.22168
534534 0 0
535535 2.70585e6 0.408714
536536 0 0
537537 −1.19661e7 −1.79067
538538 0 0
539539 0 0
540540 0 0
541541 3.66943e6 0.539021 0.269510 0.962998i 0.413138π-0.413138\pi
0.269510 + 0.962998i 0.413138π0.413138\pi
542542 0 0
543543 2.09637e6 0.305119
544544 0 0
545545 1.99141e6 0.287191
546546 0 0
547547 2.30515e6 0.329406 0.164703 0.986343i 0.447333π-0.447333\pi
0.164703 + 0.986343i 0.447333π0.447333\pi
548548 0 0
549549 −3.75284e6 −0.531410
550550 0 0
551551 −1.38359e6 −0.194145
552552 0 0
553553 0 0
554554 0 0
555555 −9.57215e6 −1.31910
556556 0 0
557557 1.13750e7 1.55350 0.776752 0.629807i 0.216866π-0.216866\pi
0.776752 + 0.629807i 0.216866π0.216866\pi
558558 0 0
559559 1.91093e7 2.58652
560560 0 0
561561 −1.53741e7 −2.06245
562562 0 0
563563 3.48375e6 0.463208 0.231604 0.972810i 0.425603π-0.425603\pi
0.231604 + 0.972810i 0.425603π0.425603\pi
564564 0 0
565565 −3.42076e6 −0.450818
566566 0 0
567567 0 0
568568 0 0
569569 4.96029e6 0.642283 0.321142 0.947031i 0.395933π-0.395933\pi
0.321142 + 0.947031i 0.395933π0.395933\pi
570570 0 0
571571 −1.08592e7 −1.39382 −0.696912 0.717156i 0.745443π-0.745443\pi
−0.696912 + 0.717156i 0.745443π0.745443\pi
572572 0 0
573573 −4.71758e6 −0.600251
574574 0 0
575575 −669629. −0.0844627
576576 0 0
577577 5.84580e6 0.730978 0.365489 0.930816i 0.380902π-0.380902\pi
0.365489 + 0.930816i 0.380902π0.380902\pi
578578 0 0
579579 −1.25353e6 −0.155395
580580 0 0
581581 0 0
582582 0 0
583583 1.22697e6 0.149507
584584 0 0
585585 5.54251e6 0.669602
586586 0 0
587587 −4.30716e6 −0.515936 −0.257968 0.966153i 0.583053π-0.583053\pi
−0.257968 + 0.966153i 0.583053π0.583053\pi
588588 0 0
589589 1.08936e6 0.129385
590590 0 0
591591 −1.69275e7 −1.99354
592592 0 0
593593 1.98311e6 0.231585 0.115792 0.993273i 0.463059π-0.463059\pi
0.115792 + 0.993273i 0.463059π0.463059\pi
594594 0 0
595595 0 0
596596 0 0
597597 1.59429e6 0.183076
598598 0 0
599599 5.16092e6 0.587706 0.293853 0.955851i 0.405062π-0.405062\pi
0.293853 + 0.955851i 0.405062π0.405062\pi
600600 0 0
601601 −9.35142e6 −1.05607 −0.528033 0.849224i 0.677070π-0.677070\pi
−0.528033 + 0.849224i 0.677070π0.677070\pi
602602 0 0
603603 −9.14905e6 −1.02467
604604 0 0
605605 −1.88668e6 −0.209561
606606 0 0
607607 4.99700e6 0.550475 0.275237 0.961376i 0.411244π-0.411244\pi
0.275237 + 0.961376i 0.411244π0.411244\pi
608608 0 0
609609 0 0
610610 0 0
611611 5.80056e6 0.628589
612612 0 0
613613 −3.63239e6 −0.390428 −0.195214 0.980761i 0.562540π-0.562540\pi
−0.195214 + 0.980761i 0.562540π0.562540\pi
614614 0 0
615615 9.05704e6 0.965603
616616 0 0
617617 8.56763e6 0.906041 0.453021 0.891500i 0.350346π-0.350346\pi
0.453021 + 0.891500i 0.350346π0.350346\pi
618618 0 0
619619 1.70312e7 1.78656 0.893282 0.449497i 0.148397π-0.148397\pi
0.893282 + 0.449497i 0.148397π0.148397\pi
620620 0 0
621621 2.33611e6 0.243089
622622 0 0
623623 0 0
624624 0 0
625625 −7.41627e6 −0.759426
626626 0 0
627627 1.36714e6 0.138881
628628 0 0
629629 2.24861e7 2.26614
630630 0 0
631631 −5.97254e6 −0.597153 −0.298576 0.954386i 0.596512π-0.596512\pi
−0.298576 + 0.954386i 0.596512π0.596512\pi
632632 0 0
633633 −5.24146e6 −0.519928
634634 0 0
635635 1.28350e7 1.26317
636636 0 0
637637 0 0
638638 0 0
639639 −3.13581e6 −0.303807
640640 0 0
641641 6.39027e6 0.614291 0.307146 0.951663i 0.400626π-0.400626\pi
0.307146 + 0.951663i 0.400626π0.400626\pi
642642 0 0
643643 4.19353e6 0.399993 0.199996 0.979797i 0.435907π-0.435907\pi
0.199996 + 0.979797i 0.435907π0.435907\pi
644644 0 0
645645 −2.16002e7 −2.04436
646646 0 0
647647 −9.03770e6 −0.848784 −0.424392 0.905478i 0.639512π-0.639512\pi
−0.424392 + 0.905478i 0.639512π0.639512\pi
648648 0 0
649649 −9.67197e6 −0.901370
650650 0 0
651651 0 0
652652 0 0
653653 −8.76742e6 −0.804616 −0.402308 0.915504i 0.631792π-0.631792\pi
−0.402308 + 0.915504i 0.631792π0.631792\pi
654654 0 0
655655 1.11233e7 1.01305
656656 0 0
657657 8.08051e6 0.730341
658658 0 0
659659 −1.87668e7 −1.68336 −0.841680 0.539977i 0.818433π-0.818433\pi
−0.841680 + 0.539977i 0.818433π0.818433\pi
660660 0 0
661661 7.01945e6 0.624884 0.312442 0.949937i 0.398853π-0.398853\pi
0.312442 + 0.949937i 0.398853π0.398853\pi
662662 0 0
663663 −3.73858e7 −3.30311
664664 0 0
665665 0 0
666666 0 0
667667 7.33703e6 0.638566
668668 0 0
669669 −2.57127e7 −2.22117
670670 0 0
671671 −1.01489e7 −0.870190
672672 0 0
673673 1.21574e7 1.03468 0.517338 0.855781i 0.326923π-0.326923\pi
0.517338 + 0.855781i 0.326923π0.326923\pi
674674 0 0
675675 −1.36835e6 −0.115595
676676 0 0
677677 −890977. −0.0747127 −0.0373564 0.999302i 0.511894π-0.511894\pi
−0.0373564 + 0.999302i 0.511894π0.511894\pi
678678 0 0
679679 0 0
680680 0 0
681681 −1.06489e7 −0.879909
682682 0 0
683683 −1.97098e7 −1.61670 −0.808351 0.588700i 0.799640π-0.799640\pi
−0.808351 + 0.588700i 0.799640π0.799640\pi
684684 0 0
685685 4.41932e6 0.359856
686686 0 0
687687 1.46656e7 1.18552
688688 0 0
689689 2.98367e6 0.239444
690690 0 0
691691 −1.37488e7 −1.09539 −0.547697 0.836677i 0.684495π-0.684495\pi
−0.547697 + 0.836677i 0.684495π0.684495\pi
692692 0 0
693693 0 0
694694 0 0
695695 5.27969e6 0.414616
696696 0 0
697697 −2.12760e7 −1.65886
698698 0 0
699699 −1.55670e7 −1.20507
700700 0 0
701701 1.40261e7 1.07806 0.539031 0.842286i 0.318791π-0.318791\pi
0.539031 + 0.842286i 0.318791π0.318791\pi
702702 0 0
703703 −1.99957e6 −0.152598
704704 0 0
705705 −6.55666e6 −0.496832
706706 0 0
707707 0 0
708708 0 0
709709 1.19993e7 0.896479 0.448239 0.893914i 0.352051π-0.352051\pi
0.448239 + 0.893914i 0.352051π0.352051\pi
710710 0 0
711711 1.03564e7 0.768307
712712 0 0
713713 −5.77678e6 −0.425561
714714 0 0
715715 1.49888e7 1.09648
716716 0 0
717717 −1.54252e7 −1.12056
718718 0 0
719719 −2.31346e7 −1.66894 −0.834470 0.551054i 0.814226π-0.814226\pi
−0.834470 + 0.551054i 0.814226π0.814226\pi
720720 0 0
721721 0 0
722722 0 0
723723 1.42286e6 0.101232
724724 0 0
725725 −4.29758e6 −0.303654
726726 0 0
727727 −117783. −0.00826505 −0.00413252 0.999991i 0.501315π-0.501315\pi
−0.00413252 + 0.999991i 0.501315π0.501315\pi
728728 0 0
729729 676615. 0.0471545
730730 0 0
731731 5.07413e7 3.51211
732732 0 0
733733 −1.09660e7 −0.753854 −0.376927 0.926243i 0.623019π-0.623019\pi
−0.376927 + 0.926243i 0.623019π0.623019\pi
734734 0 0
735735 0 0
736736 0 0
737737 −2.47421e7 −1.67790
738738 0 0
739739 −4.66161e6 −0.313996 −0.156998 0.987599i 0.550182π-0.550182\pi
−0.156998 + 0.987599i 0.550182π0.550182\pi
740740 0 0
741741 3.32452e6 0.222425
742742 0 0
743743 1.32766e7 0.882296 0.441148 0.897434i 0.354571π-0.354571\pi
0.441148 + 0.897434i 0.354571π0.354571\pi
744744 0 0
745745 −2.24549e7 −1.48224
746746 0 0
747747 −825366. −0.0541184
748748 0 0
749749 0 0
750750 0 0
751751 1.26804e7 0.820412 0.410206 0.911993i 0.365457π-0.365457\pi
0.410206 + 0.911993i 0.365457π0.365457\pi
752752 0 0
753753 484507. 0.0311396
754754 0 0
755755 −641073. −0.0409298
756756 0 0
757757 −9.32262e6 −0.591287 −0.295643 0.955298i 0.595534π-0.595534\pi
−0.295643 + 0.955298i 0.595534π0.595534\pi
758758 0 0
759759 −7.24981e6 −0.456796
760760 0 0
761761 −1.89841e7 −1.18831 −0.594153 0.804352i 0.702513π-0.702513\pi
−0.594153 + 0.804352i 0.702513π0.702513\pi
762762 0 0
763763 0 0
764764 0 0
765765 1.47171e7 0.909221
766766 0 0
767767 −2.35197e7 −1.44359
768768 0 0
769769 −9.22276e6 −0.562400 −0.281200 0.959649i 0.590732π-0.590732\pi
−0.281200 + 0.959649i 0.590732π0.590732\pi
770770 0 0
771771 −7.01949e6 −0.425275
772772 0 0
773773 7.55017e6 0.454473 0.227236 0.973840i 0.427031π-0.427031\pi
0.227236 + 0.973840i 0.427031π0.427031\pi
774774 0 0
775775 3.38368e6 0.202365
776776 0 0
777777 0 0
778778 0 0
779779 1.89196e6 0.111704
780780 0 0
781781 −8.48027e6 −0.497488
782782 0 0
783783 1.49928e7 0.873934
784784 0 0
785785 −7.76946e6 −0.450004
786786 0 0
787787 −5.66483e6 −0.326024 −0.163012 0.986624i 0.552121π-0.552121\pi
−0.163012 + 0.986624i 0.552121π0.552121\pi
788788 0 0
789789 4.06748e7 2.32613
790790 0 0
791791 0 0
792792 0 0
793793 −2.46796e7 −1.39365
794794 0 0
795795 −3.37259e6 −0.189254
796796 0 0
797797 −2.25166e6 −0.125561 −0.0627807 0.998027i 0.519997π-0.519997\pi
−0.0627807 + 0.998027i 0.519997π0.519997\pi
798798 0 0
799799 1.54023e7 0.853532
800800 0 0
801801 −7.81549e6 −0.430403
802802 0 0
803803 2.18524e7 1.19594
804804 0 0
805805 0 0
806806 0 0
807807 1.42155e7 0.768381
808808 0 0
809809 1.19636e7 0.642675 0.321338 0.946965i 0.395868π-0.395868\pi
0.321338 + 0.946965i 0.395868π0.395868\pi
810810 0 0
811811 958303. 0.0511624 0.0255812 0.999673i 0.491856π-0.491856\pi
0.0255812 + 0.999673i 0.491856π0.491856\pi
812812 0 0
813813 −1.09218e7 −0.579518
814814 0 0
815815 2.36971e7 1.24969
816816 0 0
817817 −4.51215e6 −0.236499
818818 0 0
819819 0 0
820820 0 0
821821 2.56029e7 1.32566 0.662828 0.748772i 0.269356π-0.269356\pi
0.662828 + 0.748772i 0.269356π0.269356\pi
822822 0 0
823823 1.15955e7 0.596748 0.298374 0.954449i 0.403556π-0.403556\pi
0.298374 + 0.954449i 0.403556π0.403556\pi
824824 0 0
825825 4.24649e6 0.217218
826826 0 0
827827 4.22668e6 0.214900 0.107450 0.994211i 0.465731π-0.465731\pi
0.107450 + 0.994211i 0.465731π0.465731\pi
828828 0 0
829829 −1.33000e7 −0.672148 −0.336074 0.941836i 0.609099π-0.609099\pi
−0.336074 + 0.941836i 0.609099π0.609099\pi
830830 0 0
831831 9.89076e6 0.496852
832832 0 0
833833 0 0
834834 0 0
835835 −1.54060e7 −0.764671
836836 0 0
837837 −1.18045e7 −0.582418
838838 0 0
839839 3.03054e7 1.48633 0.743166 0.669107i 0.233323π-0.233323\pi
0.743166 + 0.669107i 0.233323π0.233323\pi
840840 0 0
841841 2.65768e7 1.29572
842842 0 0
843843 −1.04602e7 −0.506959
844844 0 0
845845 1.78889e7 0.861870
846846 0 0
847847 0 0
848848 0 0
849849 3.20378e7 1.52543
850850 0 0
851851 1.06035e7 0.501911
852852 0 0
853853 1.04047e7 0.489616 0.244808 0.969572i 0.421275π-0.421275\pi
0.244808 + 0.969572i 0.421275π0.421275\pi
854854 0 0
855855 −1.30872e6 −0.0612251
856856 0 0
857857 2.19500e7 1.02090 0.510448 0.859909i 0.329480π-0.329480\pi
0.510448 + 0.859909i 0.329480π0.329480\pi
858858 0 0
859859 9.08936e6 0.420291 0.210146 0.977670i 0.432606π-0.432606\pi
0.210146 + 0.977670i 0.432606π0.432606\pi
860860 0 0
861861 0 0
862862 0 0
863863 −1.82502e6 −0.0834141 −0.0417071 0.999130i 0.513280π-0.513280\pi
−0.0417071 + 0.999130i 0.513280π0.513280\pi
864864 0 0
865865 2.37409e7 1.07884
866866 0 0
867867 −7.18550e7 −3.24645
868868 0 0
869869 2.80072e7 1.25811
870870 0 0
871871 −6.01662e7 −2.68725
872872 0 0
873873 −412932. −0.0183376
874874 0 0
875875 0 0
876876 0 0
877877 −1.49949e7 −0.658331 −0.329166 0.944272i 0.606767π-0.606767\pi
−0.329166 + 0.944272i 0.606767π0.606767\pi
878878 0 0
879879 2.52242e6 0.110115
880880 0 0
881881 1.71560e6 0.0744692 0.0372346 0.999307i 0.488145π-0.488145\pi
0.0372346 + 0.999307i 0.488145π0.488145\pi
882882 0 0
883883 −3.86989e7 −1.67031 −0.835155 0.550015i 0.814622π-0.814622\pi
−0.835155 + 0.550015i 0.814622π0.814622\pi
884884 0 0
885885 2.65855e7 1.14100
886886 0 0
887887 5.82614e6 0.248641 0.124320 0.992242i 0.460325π-0.460325\pi
0.124320 + 0.992242i 0.460325π0.460325\pi
888888 0 0
889889 0 0
890890 0 0
891891 −2.58945e7 −1.09273
892892 0 0
893893 −1.36965e6 −0.0574752
894894 0 0
895895 3.09774e7 1.29267
896896 0 0
897897 −1.76297e7 −0.731581
898898 0 0
899899 −3.70745e7 −1.52994
900900 0 0
901901 7.92260e6 0.325129
902902 0 0
903903 0 0
904904 0 0
905905 −5.42702e6 −0.220262
906906 0 0
907907 −9.83957e6 −0.397153 −0.198577 0.980085i 0.563632π-0.563632\pi
−0.198577 + 0.980085i 0.563632π0.563632\pi
908908 0 0
909909 −1.49610e7 −0.600551
910910 0 0
911911 2.53673e7 1.01269 0.506347 0.862330i 0.330996π-0.330996\pi
0.506347 + 0.862330i 0.330996π0.330996\pi
912912 0 0
913913 −2.23206e6 −0.0886196
914914 0 0
915915 2.78965e7 1.10153
916916 0 0
917917 0 0
918918 0 0
919919 5.85847e6 0.228821 0.114410 0.993434i 0.463502π-0.463502\pi
0.114410 + 0.993434i 0.463502π0.463502\pi
920920 0 0
921921 1.52472e7 0.592301
922922 0 0
923923 −2.06218e7 −0.796751
924924 0 0
925925 −6.21089e6 −0.238671
926926 0 0
927927 −1.58500e7 −0.605799
928928 0 0
929929 −18528.6 −0.000704374 0 −0.000352187 1.00000i 0.500112π-0.500112\pi
−0.000352187 1.00000i 0.500112π0.500112\pi
930930 0 0
931931 0 0
932932 0 0
933933 3.73821e7 1.40592
934934 0 0
935935 3.98000e7 1.48886
936936 0 0
937937 −3.91119e7 −1.45533 −0.727663 0.685935i 0.759394π-0.759394\pi
−0.727663 + 0.685935i 0.759394π0.759394\pi
938938 0 0
939939 −3.53038e7 −1.30665
940940 0 0
941941 8.90516e6 0.327844 0.163922 0.986473i 0.447585π-0.447585\pi
0.163922 + 0.986473i 0.447585π0.447585\pi
942942 0 0
943943 −1.00329e7 −0.367408
944944 0 0
945945 0 0
946946 0 0
947947 7.43836e6 0.269527 0.134764 0.990878i 0.456973π-0.456973\pi
0.134764 + 0.990878i 0.456973π0.456973\pi
948948 0 0
949949 5.31393e7 1.91536
950950 0 0
951951 3.25004e7 1.16530
952952 0 0
953953 3.87886e7 1.38348 0.691739 0.722148i 0.256845π-0.256845\pi
0.691739 + 0.722148i 0.256845π0.256845\pi
954954 0 0
955955 1.22127e7 0.433315
956956 0 0
957957 −4.65282e7 −1.64224
958958 0 0
959959 0 0
960960 0 0
961961 561277. 0.0196051
962962 0 0
963963 7.02879e6 0.244239
964964 0 0
965965 3.24509e6 0.112178
966966 0 0
967967 2.80184e7 0.963557 0.481779 0.876293i 0.339991π-0.339991\pi
0.481779 + 0.876293i 0.339991π0.339991\pi
968968 0 0
969969 8.82767e6 0.302021
970970 0 0
971971 4.45242e7 1.51547 0.757736 0.652561i 0.226305π-0.226305\pi
0.757736 + 0.652561i 0.226305π0.226305\pi
972972 0 0
973973 0 0
974974 0 0
975975 1.03264e7 0.347885
976976 0 0
977977 922043. 0.0309040 0.0154520 0.999881i 0.495081π-0.495081\pi
0.0154520 + 0.999881i 0.495081π0.495081\pi
978978 0 0
979979 −2.11357e7 −0.704790
980980 0 0
981981 5.17294e6 0.171619
982982 0 0
983983 −4.12706e6 −0.136225 −0.0681125 0.997678i 0.521698π-0.521698\pi
−0.0681125 + 0.997678i 0.521698π0.521698\pi
984984 0 0
985985 4.38214e7 1.43912
986986 0 0
987987 0 0
988988 0 0
989989 2.39275e7 0.777871
990990 0 0
991991 −3.49392e6 −0.113013 −0.0565065 0.998402i 0.517996π-0.517996\pi
−0.0565065 + 0.998402i 0.517996π0.517996\pi
992992 0 0
993993 −5.75726e7 −1.85286
994994 0 0
995995 −4.12724e6 −0.132161
996996 0 0
997997 1.16105e7 0.369924 0.184962 0.982746i 0.440784π-0.440784\pi
0.184962 + 0.982746i 0.440784π0.440784\pi
998998 0 0
999999 2.16677e7 0.686909
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 784.6.a.bi.1.2 4
4.3 odd 2 196.6.a.k.1.3 yes 4
7.6 odd 2 inner 784.6.a.bi.1.3 4
28.3 even 6 196.6.e.l.177.3 8
28.11 odd 6 196.6.e.l.177.2 8
28.19 even 6 196.6.e.l.165.3 8
28.23 odd 6 196.6.e.l.165.2 8
28.27 even 2 196.6.a.k.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
196.6.a.k.1.2 4 28.27 even 2
196.6.a.k.1.3 yes 4 4.3 odd 2
196.6.e.l.165.2 8 28.23 odd 6
196.6.e.l.165.3 8 28.19 even 6
196.6.e.l.177.2 8 28.11 odd 6
196.6.e.l.177.3 8 28.3 even 6
784.6.a.bi.1.2 4 1.1 even 1 trivial
784.6.a.bi.1.3 4 7.6 odd 2 inner