Properties

Label 700.6.a.k.1.4
Level 700700
Weight 66
Character 700.1
Self dual yes
Analytic conductor 112.269112.269
Analytic rank 11
Dimension 44
CM no
Inner twists 11

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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] = [700,6,Mod(1,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, 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("700.1"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Level: N N == 700=22527 700 = 2^{2} \cdot 5^{2} \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 700.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,-22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 112.268673869112.268673869
Analytic rank: 11
Dimension: 44
Coefficient field: Q[x]/(x4)\mathbb{Q}[x]/(x^{4} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x42x3393x21002x+16596 x^{4} - 2x^{3} - 393x^{2} - 1002x + 16596 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 225 2^{2}\cdot 5
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 21.105221.1052 of defining polynomial
Character χ\chi == 700.1

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) == q+15.1052q349.0000q714.8337q9+332.519q11+395.417q1315.8479q171508.76q19740.153q213178.50q233894.62q274488.23q29+3120.60q31+5022.76q33+15890.5q37+5972.84q39+3364.92q41102.425q4315905.5q47+2401.00q49239.385q5140865.2q5322790.1q5722450.3q59+24435.9q61+726.853q63+2260.27q6748011.8q69+25552.6q7125552.9q7316293.4q7766958.4q7955224.4q8126284.5q8367795.5q87+40585.1q8919375.4q91+47137.2q9357800.0q974932.50q99+O(q100)q+15.1052 q^{3} -49.0000 q^{7} -14.8337 q^{9} +332.519 q^{11} +395.417 q^{13} -15.8479 q^{17} -1508.76 q^{19} -740.153 q^{21} -3178.50 q^{23} -3894.62 q^{27} -4488.23 q^{29} +3120.60 q^{31} +5022.76 q^{33} +15890.5 q^{37} +5972.84 q^{39} +3364.92 q^{41} -102.425 q^{43} -15905.5 q^{47} +2401.00 q^{49} -239.385 q^{51} -40865.2 q^{53} -22790.1 q^{57} -22450.3 q^{59} +24435.9 q^{61} +726.853 q^{63} +2260.27 q^{67} -48011.8 q^{69} +25552.6 q^{71} -25552.9 q^{73} -16293.4 q^{77} -66958.4 q^{79} -55224.4 q^{81} -26284.5 q^{83} -67795.5 q^{87} +40585.1 q^{89} -19375.4 q^{91} +47137.2 q^{93} -57800.0 q^{97} -4932.50 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q22q3196q762q9+48q11+430q13+1286q17384q19+1078q211256q23+1196q274994q29+4618q31+15268q33+16922q37+3200q39+170416q99+O(q100) 4 q - 22 q^{3} - 196 q^{7} - 62 q^{9} + 48 q^{11} + 430 q^{13} + 1286 q^{17} - 384 q^{19} + 1078 q^{21} - 1256 q^{23} + 1196 q^{27} - 4994 q^{29} + 4618 q^{31} + 15268 q^{33} + 16922 q^{37} + 3200 q^{39}+ \cdots - 170416 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 15.1052 0.968997 0.484499 0.874792i 0.339002π-0.339002\pi
0.484499 + 0.874792i 0.339002π0.339002\pi
44 0 0
55 0 0
66 0 0
77 −49.0000 −0.377964
88 0 0
99 −14.8337 −0.0610442
1010 0 0
1111 332.519 0.828581 0.414290 0.910145i 0.364030π-0.364030\pi
0.414290 + 0.910145i 0.364030π0.364030\pi
1212 0 0
1313 395.417 0.648928 0.324464 0.945898i 0.394816π-0.394816\pi
0.324464 + 0.945898i 0.394816π0.394816\pi
1414 0 0
1515 0 0
1616 0 0
1717 −15.8479 −0.0132999 −0.00664996 0.999978i 0.502117π-0.502117\pi
−0.00664996 + 0.999978i 0.502117π0.502117\pi
1818 0 0
1919 −1508.76 −0.958817 −0.479409 0.877592i 0.659149π-0.659149\pi
−0.479409 + 0.877592i 0.659149π0.659149\pi
2020 0 0
2121 −740.153 −0.366247
2222 0 0
2323 −3178.50 −1.25286 −0.626431 0.779477i 0.715485π-0.715485\pi
−0.626431 + 0.779477i 0.715485π0.715485\pi
2424 0 0
2525 0 0
2626 0 0
2727 −3894.62 −1.02815
2828 0 0
2929 −4488.23 −0.991015 −0.495508 0.868604i 0.665018π-0.665018\pi
−0.495508 + 0.868604i 0.665018π0.665018\pi
3030 0 0
3131 3120.60 0.583222 0.291611 0.956537i 0.405809π-0.405809\pi
0.291611 + 0.956537i 0.405809π0.405809\pi
3232 0 0
3333 5022.76 0.802892
3434 0 0
3535 0 0
3636 0 0
3737 15890.5 1.90824 0.954118 0.299431i 0.0967967π-0.0967967\pi
0.954118 + 0.299431i 0.0967967π0.0967967\pi
3838 0 0
3939 5972.84 0.628810
4040 0 0
4141 3364.92 0.312619 0.156309 0.987708i 0.450040π-0.450040\pi
0.156309 + 0.987708i 0.450040π0.450040\pi
4242 0 0
4343 −102.425 −0.00844763 −0.00422381 0.999991i 0.501344π-0.501344\pi
−0.00422381 + 0.999991i 0.501344π0.501344\pi
4444 0 0
4545 0 0
4646 0 0
4747 −15905.5 −1.05027 −0.525137 0.851018i 0.675986π-0.675986\pi
−0.525137 + 0.851018i 0.675986π0.675986\pi
4848 0 0
4949 2401.00 0.142857
5050 0 0
5151 −239.385 −0.0128876
5252 0 0
5353 −40865.2 −1.99832 −0.999158 0.0410244i 0.986938π-0.986938\pi
−0.999158 + 0.0410244i 0.986938π0.986938\pi
5454 0 0
5555 0 0
5656 0 0
5757 −22790.1 −0.929091
5858 0 0
5959 −22450.3 −0.839638 −0.419819 0.907608i 0.637906π-0.637906\pi
−0.419819 + 0.907608i 0.637906π0.637906\pi
6060 0 0
6161 24435.9 0.840821 0.420411 0.907334i 0.361886π-0.361886\pi
0.420411 + 0.907334i 0.361886π0.361886\pi
6262 0 0
6363 726.853 0.0230725
6464 0 0
6565 0 0
6666 0 0
6767 2260.27 0.0615139 0.0307569 0.999527i 0.490208π-0.490208\pi
0.0307569 + 0.999527i 0.490208π0.490208\pi
6868 0 0
6969 −48011.8 −1.21402
7070 0 0
7171 25552.6 0.601575 0.300788 0.953691i 0.402750π-0.402750\pi
0.300788 + 0.953691i 0.402750π0.402750\pi
7272 0 0
7373 −25552.9 −0.561219 −0.280610 0.959822i 0.590537π-0.590537\pi
−0.280610 + 0.959822i 0.590537π0.590537\pi
7474 0 0
7575 0 0
7676 0 0
7777 −16293.4 −0.313174
7878 0 0
7979 −66958.4 −1.20708 −0.603541 0.797332i 0.706244π-0.706244\pi
−0.603541 + 0.797332i 0.706244π0.706244\pi
8080 0 0
8181 −55224.4 −0.935229
8282 0 0
8383 −26284.5 −0.418798 −0.209399 0.977830i 0.567151π-0.567151\pi
−0.209399 + 0.977830i 0.567151π0.567151\pi
8484 0 0
8585 0 0
8686 0 0
8787 −67795.5 −0.960291
8888 0 0
8989 40585.1 0.543114 0.271557 0.962422i 0.412461π-0.412461\pi
0.271557 + 0.962422i 0.412461π0.412461\pi
9090 0 0
9191 −19375.4 −0.245272
9292 0 0
9393 47137.2 0.565141
9494 0 0
9595 0 0
9696 0 0
9797 −57800.0 −0.623732 −0.311866 0.950126i 0.600954π-0.600954\pi
−0.311866 + 0.950126i 0.600954π0.600954\pi
9898 0 0
9999 −4932.50 −0.0505800
100100 0 0
101101 −21958.1 −0.214186 −0.107093 0.994249i 0.534154π-0.534154\pi
−0.107093 + 0.994249i 0.534154π0.534154\pi
102102 0 0
103103 −39562.2 −0.367441 −0.183720 0.982979i 0.558814π-0.558814\pi
−0.183720 + 0.982979i 0.558814π0.558814\pi
104104 0 0
105105 0 0
106106 0 0
107107 −21102.7 −0.178188 −0.0890941 0.996023i 0.528397π-0.528397\pi
−0.0890941 + 0.996023i 0.528397π0.528397\pi
108108 0 0
109109 −221229. −1.78351 −0.891756 0.452517i 0.850526π-0.850526\pi
−0.891756 + 0.452517i 0.850526π0.850526\pi
110110 0 0
111111 240028. 1.84908
112112 0 0
113113 110973. 0.817562 0.408781 0.912633i 0.365954π-0.365954\pi
0.408781 + 0.912633i 0.365954π0.365954\pi
114114 0 0
115115 0 0
116116 0 0
117117 −5865.51 −0.0396133
118118 0 0
119119 776.547 0.00502690
120120 0 0
121121 −50482.1 −0.313454
122122 0 0
123123 50827.7 0.302927
124124 0 0
125125 0 0
126126 0 0
127127 144389. 0.794376 0.397188 0.917737i 0.369986π-0.369986\pi
0.397188 + 0.917737i 0.369986π0.369986\pi
128128 0 0
129129 −1547.15 −0.00818573
130130 0 0
131131 −275842. −1.40437 −0.702186 0.711994i 0.747792π-0.747792\pi
−0.702186 + 0.711994i 0.747792π0.747792\pi
132132 0 0
133133 73929.2 0.362399
134134 0 0
135135 0 0
136136 0 0
137137 −120194. −0.547118 −0.273559 0.961855i 0.588201π-0.588201\pi
−0.273559 + 0.961855i 0.588201π0.588201\pi
138138 0 0
139139 −110020. −0.482986 −0.241493 0.970403i 0.577637π-0.577637\pi
−0.241493 + 0.970403i 0.577637π0.577637\pi
140140 0 0
141141 −240255. −1.01771
142142 0 0
143143 131484. 0.537689
144144 0 0
145145 0 0
146146 0 0
147147 36267.5 0.138428
148148 0 0
149149 138049. 0.509412 0.254706 0.967019i 0.418021π-0.418021\pi
0.254706 + 0.967019i 0.418021π0.418021\pi
150150 0 0
151151 −73709.8 −0.263077 −0.131538 0.991311i 0.541992π-0.541992\pi
−0.131538 + 0.991311i 0.541992π0.541992\pi
152152 0 0
153153 235.084 0.000811883 0
154154 0 0
155155 0 0
156156 0 0
157157 −156298. −0.506062 −0.253031 0.967458i 0.581427π-0.581427\pi
−0.253031 + 0.967458i 0.581427π0.581427\pi
158158 0 0
159159 −617276. −1.93636
160160 0 0
161161 155747. 0.473537
162162 0 0
163163 437524. 1.28983 0.644916 0.764253i 0.276892π-0.276892\pi
0.644916 + 0.764253i 0.276892π0.276892\pi
164164 0 0
165165 0 0
166166 0 0
167167 −229449. −0.636642 −0.318321 0.947983i 0.603119π-0.603119\pi
−0.318321 + 0.947983i 0.603119π0.603119\pi
168168 0 0
169169 −214939. −0.578892
170170 0 0
171171 22380.5 0.0585302
172172 0 0
173173 690255. 1.75345 0.876727 0.480988i 0.159722π-0.159722\pi
0.876727 + 0.480988i 0.159722π0.159722\pi
174174 0 0
175175 0 0
176176 0 0
177177 −339116. −0.813607
178178 0 0
179179 −48336.8 −0.112757 −0.0563787 0.998409i 0.517955π-0.517955\pi
−0.0563787 + 0.998409i 0.517955π0.517955\pi
180180 0 0
181181 −645264. −1.46400 −0.732000 0.681305i 0.761413π-0.761413\pi
−0.732000 + 0.681305i 0.761413π0.761413\pi
182182 0 0
183183 369108. 0.814754
184184 0 0
185185 0 0
186186 0 0
187187 −5269.72 −0.0110201
188188 0 0
189189 190837. 0.388604
190190 0 0
191191 −361005. −0.716028 −0.358014 0.933716i 0.616546π-0.616546\pi
−0.358014 + 0.933716i 0.616546π0.616546\pi
192192 0 0
193193 187639. 0.362601 0.181301 0.983428i 0.441969π-0.441969\pi
0.181301 + 0.983428i 0.441969π0.441969\pi
194194 0 0
195195 0 0
196196 0 0
197197 −461114. −0.846531 −0.423265 0.906006i 0.639116π-0.639116\pi
−0.423265 + 0.906006i 0.639116π0.639116\pi
198198 0 0
199199 −567995. −1.01675 −0.508373 0.861137i 0.669753π-0.669753\pi
−0.508373 + 0.861137i 0.669753π0.669753\pi
200200 0 0
201201 34141.7 0.0596068
202202 0 0
203203 219923. 0.374569
204204 0 0
205205 0 0
206206 0 0
207207 47149.1 0.0764799
208208 0 0
209209 −501691. −0.794457
210210 0 0
211211 −891786. −1.37897 −0.689484 0.724301i 0.742163π-0.742163\pi
−0.689484 + 0.724301i 0.742163π0.742163\pi
212212 0 0
213213 385977. 0.582925
214214 0 0
215215 0 0
216216 0 0
217217 −152910. −0.220437
218218 0 0
219219 −385981. −0.543820
220220 0 0
221221 −6266.52 −0.00863070
222222 0 0
223223 530560. 0.714451 0.357225 0.934018i 0.383723π-0.383723\pi
0.357225 + 0.934018i 0.383723π0.383723\pi
224224 0 0
225225 0 0
226226 0 0
227227 593649. 0.764655 0.382327 0.924027i 0.375123π-0.375123\pi
0.382327 + 0.924027i 0.375123π0.375123\pi
228228 0 0
229229 757698. 0.954789 0.477394 0.878689i 0.341581π-0.341581\pi
0.477394 + 0.878689i 0.341581π0.341581\pi
230230 0 0
231231 −246115. −0.303465
232232 0 0
233233 59250.9 0.0714999 0.0357499 0.999361i 0.488618π-0.488618\pi
0.0357499 + 0.999361i 0.488618π0.488618\pi
234234 0 0
235235 0 0
236236 0 0
237237 −1.01142e6 −1.16966
238238 0 0
239239 −962045. −1.08943 −0.544717 0.838620i 0.683363π-0.683363\pi
−0.544717 + 0.838620i 0.683363π0.683363\pi
240240 0 0
241241 −298605. −0.331172 −0.165586 0.986195i 0.552952π-0.552952\pi
−0.165586 + 0.986195i 0.552952π0.552952\pi
242242 0 0
243243 112220. 0.121914
244244 0 0
245245 0 0
246246 0 0
247247 −596589. −0.622204
248248 0 0
249249 −397032. −0.405815
250250 0 0
251251 943473. 0.945247 0.472624 0.881264i 0.343307π-0.343307\pi
0.472624 + 0.881264i 0.343307π0.343307\pi
252252 0 0
253253 −1.05691e6 −1.03810
254254 0 0
255255 0 0
256256 0 0
257257 −685001. −0.646931 −0.323466 0.946240i 0.604848π-0.604848\pi
−0.323466 + 0.946240i 0.604848π0.604848\pi
258258 0 0
259259 −778632. −0.721245
260260 0 0
261261 66577.3 0.0604957
262262 0 0
263263 517012. 0.460905 0.230452 0.973084i 0.425979π-0.425979\pi
0.230452 + 0.973084i 0.425979π0.425979\pi
264264 0 0
265265 0 0
266266 0 0
267267 613044. 0.526276
268268 0 0
269269 −2.00093e6 −1.68597 −0.842987 0.537934i 0.819205π-0.819205\pi
−0.842987 + 0.537934i 0.819205π0.819205\pi
270270 0 0
271271 2.05219e6 1.69744 0.848720 0.528842i 0.177374π-0.177374\pi
0.848720 + 0.528842i 0.177374π0.177374\pi
272272 0 0
273273 −292669. −0.237668
274274 0 0
275275 0 0
276276 0 0
277277 −1.03018e6 −0.806700 −0.403350 0.915046i 0.632154π-0.632154\pi
−0.403350 + 0.915046i 0.632154π0.632154\pi
278278 0 0
279279 −46290.2 −0.0356023
280280 0 0
281281 −348383. −0.263204 −0.131602 0.991303i 0.542012π-0.542012\pi
−0.131602 + 0.991303i 0.542012π0.542012\pi
282282 0 0
283283 −777820. −0.577315 −0.288658 0.957432i 0.593209π-0.593209\pi
−0.288658 + 0.957432i 0.593209π0.593209\pi
284284 0 0
285285 0 0
286286 0 0
287287 −164881. −0.118159
288288 0 0
289289 −1.41961e6 −0.999823
290290 0 0
291291 −873078. −0.604395
292292 0 0
293293 1.57096e6 1.06905 0.534524 0.845153i 0.320491π-0.320491\pi
0.534524 + 0.845153i 0.320491π0.320491\pi
294294 0 0
295295 0 0
296296 0 0
297297 −1.29504e6 −0.851904
298298 0 0
299299 −1.25683e6 −0.813017
300300 0 0
301301 5018.82 0.00319290
302302 0 0
303303 −331681. −0.207546
304304 0 0
305305 0 0
306306 0 0
307307 1.47525e6 0.893347 0.446673 0.894697i 0.352609π-0.352609\pi
0.446673 + 0.894697i 0.352609π0.352609\pi
308308 0 0
309309 −597594. −0.356049
310310 0 0
311311 −3.31797e6 −1.94523 −0.972617 0.232416i 0.925337π-0.925337\pi
−0.972617 + 0.232416i 0.925337π0.925337\pi
312312 0 0
313313 94950.8 0.0547820 0.0273910 0.999625i 0.491280π-0.491280\pi
0.0273910 + 0.999625i 0.491280π0.491280\pi
314314 0 0
315315 0 0
316316 0 0
317317 −392081. −0.219143 −0.109572 0.993979i 0.534948π-0.534948\pi
−0.109572 + 0.993979i 0.534948π0.534948\pi
318318 0 0
319319 −1.49242e6 −0.821136
320320 0 0
321321 −318760. −0.172664
322322 0 0
323323 23910.6 0.0127522
324324 0 0
325325 0 0
326326 0 0
327327 −3.34170e6 −1.72822
328328 0 0
329329 779369. 0.396966
330330 0 0
331331 3.72431e6 1.86842 0.934212 0.356719i 0.116105π-0.116105\pi
0.934212 + 0.356719i 0.116105π0.116105\pi
332332 0 0
333333 −235715. −0.116487
334334 0 0
335335 0 0
336336 0 0
337337 736373. 0.353202 0.176601 0.984283i 0.443490π-0.443490\pi
0.176601 + 0.984283i 0.443490π0.443490\pi
338338 0 0
339339 1.67626e6 0.792215
340340 0 0
341341 1.03766e6 0.483247
342342 0 0
343343 −117649. −0.0539949
344344 0 0
345345 0 0
346346 0 0
347347 1.84485e6 0.822504 0.411252 0.911522i 0.365092π-0.365092\pi
0.411252 + 0.911522i 0.365092π0.365092\pi
348348 0 0
349349 795830. 0.349749 0.174875 0.984591i 0.444048π-0.444048\pi
0.174875 + 0.984591i 0.444048π0.444048\pi
350350 0 0
351351 −1.54000e6 −0.667195
352352 0 0
353353 −2.87945e6 −1.22991 −0.614954 0.788563i 0.710826π-0.710826\pi
−0.614954 + 0.788563i 0.710826π0.710826\pi
354354 0 0
355355 0 0
356356 0 0
357357 11729.9 0.00487105
358358 0 0
359359 −137690. −0.0563854 −0.0281927 0.999603i 0.508975π-0.508975\pi
−0.0281927 + 0.999603i 0.508975π0.508975\pi
360360 0 0
361361 −199745. −0.0806694
362362 0 0
363363 −762541. −0.303736
364364 0 0
365365 0 0
366366 0 0
367367 621992. 0.241057 0.120528 0.992710i 0.461541π-0.461541\pi
0.120528 + 0.992710i 0.461541π0.461541\pi
368368 0 0
369369 −49914.4 −0.0190836
370370 0 0
371371 2.00240e6 0.755293
372372 0 0
373373 75865.9 0.0282341 0.0141171 0.999900i 0.495506π-0.495506\pi
0.0141171 + 0.999900i 0.495506π0.495506\pi
374374 0 0
375375 0 0
376376 0 0
377377 −1.77472e6 −0.643098
378378 0 0
379379 −2.81997e6 −1.00843 −0.504216 0.863578i 0.668218π-0.668218\pi
−0.504216 + 0.863578i 0.668218π0.668218\pi
380380 0 0
381381 2.18103e6 0.769748
382382 0 0
383383 1.06476e6 0.370899 0.185449 0.982654i 0.440626π-0.440626\pi
0.185449 + 0.982654i 0.440626π0.440626\pi
384384 0 0
385385 0 0
386386 0 0
387387 1519.35 0.000515679 0
388388 0 0
389389 3.73180e6 1.25039 0.625194 0.780469i 0.285020π-0.285020\pi
0.625194 + 0.780469i 0.285020π0.285020\pi
390390 0 0
391391 50372.6 0.0166630
392392 0 0
393393 −4.16664e6 −1.36083
394394 0 0
395395 0 0
396396 0 0
397397 −826618. −0.263226 −0.131613 0.991301i 0.542016π-0.542016\pi
−0.131613 + 0.991301i 0.542016π0.542016\pi
398398 0 0
399399 1.11671e6 0.351164
400400 0 0
401401 542752. 0.168554 0.0842772 0.996442i 0.473142π-0.473142\pi
0.0842772 + 0.996442i 0.473142π0.473142\pi
402402 0 0
403403 1.23394e6 0.378470
404404 0 0
405405 0 0
406406 0 0
407407 5.28388e6 1.58113
408408 0 0
409409 3.01368e6 0.890819 0.445409 0.895327i 0.353058π-0.353058\pi
0.445409 + 0.895327i 0.353058π0.353058\pi
410410 0 0
411411 −1.81555e6 −0.530156
412412 0 0
413413 1.10006e6 0.317353
414414 0 0
415415 0 0
416416 0 0
417417 −1.66187e6 −0.468012
418418 0 0
419419 3.17741e6 0.884175 0.442088 0.896972i 0.354238π-0.354238\pi
0.442088 + 0.896972i 0.354238π0.354238\pi
420420 0 0
421421 −5.99161e6 −1.64755 −0.823774 0.566919i 0.808135π-0.808135\pi
−0.823774 + 0.566919i 0.808135π0.808135\pi
422422 0 0
423423 235938. 0.0641131
424424 0 0
425425 0 0
426426 0 0
427427 −1.19736e6 −0.317801
428428 0 0
429429 1.98608e6 0.521020
430430 0 0
431431 −934600. −0.242344 −0.121172 0.992632i 0.538665π-0.538665\pi
−0.121172 + 0.992632i 0.538665π0.538665\pi
432432 0 0
433433 7.40221e6 1.89733 0.948663 0.316289i 0.102437π-0.102437\pi
0.948663 + 0.316289i 0.102437π0.102437\pi
434434 0 0
435435 0 0
436436 0 0
437437 4.79559e6 1.20126
438438 0 0
439439 3.34676e6 0.828827 0.414413 0.910089i 0.363987π-0.363987\pi
0.414413 + 0.910089i 0.363987π0.363987\pi
440440 0 0
441441 −35615.8 −0.00872060
442442 0 0
443443 −1.12131e6 −0.271467 −0.135734 0.990745i 0.543339π-0.543339\pi
−0.135734 + 0.990745i 0.543339π0.543339\pi
444444 0 0
445445 0 0
446446 0 0
447447 2.08526e6 0.493619
448448 0 0
449449 2.30290e6 0.539088 0.269544 0.962988i 0.413127π-0.413127\pi
0.269544 + 0.962988i 0.413127π0.413127\pi
450450 0 0
451451 1.11890e6 0.259030
452452 0 0
453453 −1.11340e6 −0.254921
454454 0 0
455455 0 0
456456 0 0
457457 −33146.7 −0.00742420 −0.00371210 0.999993i 0.501182π-0.501182\pi
−0.00371210 + 0.999993i 0.501182π0.501182\pi
458458 0 0
459459 61721.6 0.0136743
460460 0 0
461461 6.51273e6 1.42729 0.713643 0.700510i 0.247044π-0.247044\pi
0.713643 + 0.700510i 0.247044π0.247044\pi
462462 0 0
463463 −3.05694e6 −0.662726 −0.331363 0.943503i 0.607508π-0.607508\pi
−0.331363 + 0.943503i 0.607508π0.607508\pi
464464 0 0
465465 0 0
466466 0 0
467467 7.90495e6 1.67729 0.838643 0.544681i 0.183349π-0.183349\pi
0.838643 + 0.544681i 0.183349π0.183349\pi
468468 0 0
469469 −110753. −0.0232501
470470 0 0
471471 −2.36091e6 −0.490373
472472 0 0
473473 −34058.2 −0.00699954
474474 0 0
475475 0 0
476476 0 0
477477 606184. 0.121986
478478 0 0
479479 −8.46668e6 −1.68607 −0.843033 0.537862i 0.819232π-0.819232\pi
−0.843033 + 0.537862i 0.819232π0.819232\pi
480480 0 0
481481 6.28335e6 1.23831
482482 0 0
483483 2.35258e6 0.458856
484484 0 0
485485 0 0
486486 0 0
487487 7.59849e6 1.45179 0.725897 0.687803i 0.241425π-0.241425\pi
0.725897 + 0.687803i 0.241425π0.241425\pi
488488 0 0
489489 6.60888e6 1.24984
490490 0 0
491491 −7.44368e6 −1.39343 −0.696713 0.717350i 0.745355π-0.745355\pi
−0.696713 + 0.717350i 0.745355π0.745355\pi
492492 0 0
493493 71129.0 0.0131804
494494 0 0
495495 0 0
496496 0 0
497497 −1.25208e6 −0.227374
498498 0 0
499499 7.49430e6 1.34735 0.673674 0.739029i 0.264715π-0.264715\pi
0.673674 + 0.739029i 0.264715π0.264715\pi
500500 0 0
501501 −3.46587e6 −0.616904
502502 0 0
503503 −4.74622e6 −0.836427 −0.418213 0.908349i 0.637344π-0.637344\pi
−0.418213 + 0.908349i 0.637344π0.637344\pi
504504 0 0
505505 0 0
506506 0 0
507507 −3.24668e6 −0.560945
508508 0 0
509509 7.65723e6 1.31002 0.655009 0.755621i 0.272665π-0.272665\pi
0.655009 + 0.755621i 0.272665π0.272665\pi
510510 0 0
511511 1.25209e6 0.212121
512512 0 0
513513 5.87605e6 0.985807
514514 0 0
515515 0 0
516516 0 0
517517 −5.28888e6 −0.870236
518518 0 0
519519 1.04264e7 1.69909
520520 0 0
521521 754861. 0.121835 0.0609176 0.998143i 0.480597π-0.480597\pi
0.0609176 + 0.998143i 0.480597π0.480597\pi
522522 0 0
523523 182962. 0.0292487 0.0146243 0.999893i 0.495345π-0.495345\pi
0.0146243 + 0.999893i 0.495345π0.495345\pi
524524 0 0
525525 0 0
526526 0 0
527527 −49455.0 −0.00775682
528528 0 0
529529 3.66653e6 0.569661
530530 0 0
531531 333022. 0.0512550
532532 0 0
533533 1.33055e6 0.202867
534534 0 0
535535 0 0
536536 0 0
537537 −730135. −0.109262
538538 0 0
539539 798378. 0.118369
540540 0 0
541541 1.09713e7 1.61163 0.805813 0.592170i 0.201729π-0.201729\pi
0.805813 + 0.592170i 0.201729π0.201729\pi
542542 0 0
543543 −9.74682e6 −1.41861
544544 0 0
545545 0 0
546546 0 0
547547 8.47830e6 1.21155 0.605773 0.795637i 0.292864π-0.292864\pi
0.605773 + 0.795637i 0.292864π0.292864\pi
548548 0 0
549549 −362476. −0.0513273
550550 0 0
551551 6.77166e6 0.950202
552552 0 0
553553 3.28096e6 0.456234
554554 0 0
555555 0 0
556556 0 0
557557 1.00722e7 1.37558 0.687791 0.725909i 0.258581π-0.258581\pi
0.687791 + 0.725909i 0.258581π0.258581\pi
558558 0 0
559559 −40500.6 −0.00548190
560560 0 0
561561 −79600.1 −0.0106784
562562 0 0
563563 −1.41582e7 −1.88251 −0.941254 0.337699i 0.890352π-0.890352\pi
−0.941254 + 0.337699i 0.890352π0.890352\pi
564564 0 0
565565 0 0
566566 0 0
567567 2.70599e6 0.353483
568568 0 0
569569 2.86677e6 0.371204 0.185602 0.982625i 0.440577π-0.440577\pi
0.185602 + 0.982625i 0.440577π0.440577\pi
570570 0 0
571571 −4.30611e6 −0.552707 −0.276354 0.961056i 0.589126π-0.589126\pi
−0.276354 + 0.961056i 0.589126π0.589126\pi
572572 0 0
573573 −5.45305e6 −0.693829
574574 0 0
575575 0 0
576576 0 0
577577 1.38465e7 1.73141 0.865703 0.500558i 0.166872π-0.166872\pi
0.865703 + 0.500558i 0.166872π0.166872\pi
578578 0 0
579579 2.83432e6 0.351360
580580 0 0
581581 1.28794e6 0.158291
582582 0 0
583583 −1.35885e7 −1.65577
584584 0 0
585585 0 0
586586 0 0
587587 −3.82239e6 −0.457867 −0.228934 0.973442i 0.573524π-0.573524\pi
−0.228934 + 0.973442i 0.573524π0.573524\pi
588588 0 0
589589 −4.70824e6 −0.559204
590590 0 0
591591 −6.96521e6 −0.820286
592592 0 0
593593 4.69083e6 0.547789 0.273894 0.961760i 0.411688π-0.411688\pi
0.273894 + 0.961760i 0.411688π0.411688\pi
594594 0 0
595595 0 0
596596 0 0
597597 −8.57967e6 −0.985223
598598 0 0
599599 −2.58012e6 −0.293814 −0.146907 0.989150i 0.546932π-0.546932\pi
−0.146907 + 0.989150i 0.546932π0.546932\pi
600600 0 0
601601 1.23938e7 1.39965 0.699825 0.714314i 0.253261π-0.253261\pi
0.699825 + 0.714314i 0.253261π0.253261\pi
602602 0 0
603603 −33528.2 −0.00375506
604604 0 0
605605 0 0
606606 0 0
607607 −1.42413e7 −1.56884 −0.784421 0.620229i 0.787040π-0.787040\pi
−0.784421 + 0.620229i 0.787040π0.787040\pi
608608 0 0
609609 3.32198e6 0.362956
610610 0 0
611611 −6.28930e6 −0.681552
612612 0 0
613613 −5.67108e6 −0.609557 −0.304779 0.952423i 0.598583π-0.598583\pi
−0.304779 + 0.952423i 0.598583π0.598583\pi
614614 0 0
615615 0 0
616616 0 0
617617 6.62397e6 0.700495 0.350248 0.936657i 0.386097π-0.386097\pi
0.350248 + 0.936657i 0.386097π0.386097\pi
618618 0 0
619619 1.22073e7 1.28054 0.640269 0.768151i 0.278823π-0.278823\pi
0.640269 + 0.768151i 0.278823π0.278823\pi
620620 0 0
621621 1.23791e7 1.28813
622622 0 0
623623 −1.98867e6 −0.205278
624624 0 0
625625 0 0
626626 0 0
627627 −7.57813e6 −0.769827
628628 0 0
629629 −251830. −0.0253794
630630 0 0
631631 −1.02556e7 −1.02538 −0.512691 0.858573i 0.671351π-0.671351\pi
−0.512691 + 0.858573i 0.671351π0.671351\pi
632632 0 0
633633 −1.34706e7 −1.33622
634634 0 0
635635 0 0
636636 0 0
637637 949396. 0.0927041
638638 0 0
639639 −379041. −0.0367227
640640 0 0
641641 2.59811e6 0.249754 0.124877 0.992172i 0.460146π-0.460146\pi
0.124877 + 0.992172i 0.460146π0.460146\pi
642642 0 0
643643 8.91060e6 0.849923 0.424962 0.905211i 0.360288π-0.360288\pi
0.424962 + 0.905211i 0.360288π0.360288\pi
644644 0 0
645645 0 0
646646 0 0
647647 −1.22375e7 −1.14929 −0.574647 0.818402i 0.694860π-0.694860\pi
−0.574647 + 0.818402i 0.694860π0.694860\pi
648648 0 0
649649 −7.46515e6 −0.695708
650650 0 0
651651 −2.30972e6 −0.213603
652652 0 0
653653 3.70630e6 0.340140 0.170070 0.985432i 0.445601π-0.445601\pi
0.170070 + 0.985432i 0.445601π0.445601\pi
654654 0 0
655655 0 0
656656 0 0
657657 379045. 0.0342592
658658 0 0
659659 −9.92944e6 −0.890658 −0.445329 0.895367i 0.646913π-0.646913\pi
−0.445329 + 0.895367i 0.646913π0.646913\pi
660660 0 0
661661 1.22697e7 1.09227 0.546137 0.837696i 0.316098π-0.316098\pi
0.546137 + 0.837696i 0.316098π0.316098\pi
662662 0 0
663663 −94656.9 −0.00836312
664664 0 0
665665 0 0
666666 0 0
667667 1.42659e7 1.24160
668668 0 0
669669 8.01420e6 0.692301
670670 0 0
671671 8.12540e6 0.696688
672672 0 0
673673 5.84674e6 0.497595 0.248798 0.968555i 0.419965π-0.419965\pi
0.248798 + 0.968555i 0.419965π0.419965\pi
674674 0 0
675675 0 0
676676 0 0
677677 −3.17692e6 −0.266400 −0.133200 0.991089i 0.542525π-0.542525\pi
−0.133200 + 0.991089i 0.542525π0.542525\pi
678678 0 0
679679 2.83220e6 0.235749
680680 0 0
681681 8.96718e6 0.740948
682682 0 0
683683 1.32512e7 1.08693 0.543467 0.839431i 0.317111π-0.317111\pi
0.543467 + 0.839431i 0.317111π0.317111\pi
684684 0 0
685685 0 0
686686 0 0
687687 1.14452e7 0.925188
688688 0 0
689689 −1.61588e7 −1.29676
690690 0 0
691691 −7.46243e6 −0.594546 −0.297273 0.954793i 0.596077π-0.596077\pi
−0.297273 + 0.954793i 0.596077π0.596077\pi
692692 0 0
693693 241692. 0.0191175
694694 0 0
695695 0 0
696696 0 0
697697 −53326.9 −0.00415781
698698 0 0
699699 894995. 0.0692832
700700 0 0
701701 −1.03333e7 −0.794224 −0.397112 0.917770i 0.629988π-0.629988\pi
−0.397112 + 0.917770i 0.629988π0.629988\pi
702702 0 0
703703 −2.39749e7 −1.82965
704704 0 0
705705 0 0
706706 0 0
707707 1.07595e6 0.0809548
708708 0 0
709709 −1.29564e7 −0.967988 −0.483994 0.875071i 0.660814π-0.660814\pi
−0.483994 + 0.875071i 0.660814π0.660814\pi
710710 0 0
711711 993243. 0.0736854
712712 0 0
713713 −9.91884e6 −0.730697
714714 0 0
715715 0 0
716716 0 0
717717 −1.45319e7 −1.05566
718718 0 0
719719 202068. 0.0145773 0.00728863 0.999973i 0.497680π-0.497680\pi
0.00728863 + 0.999973i 0.497680π0.497680\pi
720720 0 0
721721 1.93855e6 0.138880
722722 0 0
723723 −4.51047e6 −0.320905
724724 0 0
725725 0 0
726726 0 0
727727 8.61730e6 0.604693 0.302347 0.953198i 0.402230π-0.402230\pi
0.302347 + 0.953198i 0.402230π0.402230\pi
728728 0 0
729729 1.51146e7 1.05336
730730 0 0
731731 1623.22 0.000112353 0
732732 0 0
733733 −1.50161e6 −0.103228 −0.0516140 0.998667i 0.516437π-0.516437\pi
−0.0516140 + 0.998667i 0.516437π0.516437\pi
734734 0 0
735735 0 0
736736 0 0
737737 751582. 0.0509692
738738 0 0
739739 −1.26282e7 −0.850608 −0.425304 0.905051i 0.639833π-0.639833\pi
−0.425304 + 0.905051i 0.639833π0.639833\pi
740740 0 0
741741 −9.01158e6 −0.602914
742742 0 0
743743 −2.71651e7 −1.80526 −0.902630 0.430418i 0.858366π-0.858366\pi
−0.902630 + 0.430418i 0.858366π0.858366\pi
744744 0 0
745745 0 0
746746 0 0
747747 389898. 0.0255652
748748 0 0
749749 1.03403e6 0.0673488
750750 0 0
751751 6.85890e6 0.443767 0.221883 0.975073i 0.428780π-0.428780\pi
0.221883 + 0.975073i 0.428780π0.428780\pi
752752 0 0
753753 1.42513e7 0.915942
754754 0 0
755755 0 0
756756 0 0
757757 −5.02373e6 −0.318630 −0.159315 0.987228i 0.550929π-0.550929\pi
−0.159315 + 0.987228i 0.550929π0.550929\pi
758758 0 0
759759 −1.59648e7 −1.00591
760760 0 0
761761 1.11417e7 0.697412 0.348706 0.937232i 0.386621π-0.386621\pi
0.348706 + 0.937232i 0.386621π0.386621\pi
762762 0 0
763763 1.08402e7 0.674104
764764 0 0
765765 0 0
766766 0 0
767767 −8.87723e6 −0.544865
768768 0 0
769769 3.94087e6 0.240312 0.120156 0.992755i 0.461660π-0.461660\pi
0.120156 + 0.992755i 0.461660π0.461660\pi
770770 0 0
771771 −1.03471e7 −0.626875
772772 0 0
773773 1.57423e7 0.947588 0.473794 0.880636i 0.342884π-0.342884\pi
0.473794 + 0.880636i 0.342884π0.342884\pi
774774 0 0
775775 0 0
776776 0 0
777777 −1.17614e7 −0.698885
778778 0 0
779779 −5.07686e6 −0.299744
780780 0 0
781781 8.49674e6 0.498454
782782 0 0
783783 1.74800e7 1.01891
784784 0 0
785785 0 0
786786 0 0
787787 1.28875e7 0.741709 0.370854 0.928691i 0.379065π-0.379065\pi
0.370854 + 0.928691i 0.379065π0.379065\pi
788788 0 0
789789 7.80955e6 0.446615
790790 0 0
791791 −5.43767e6 −0.309009
792792 0 0
793793 9.66236e6 0.545633
794794 0 0
795795 0 0
796796 0 0
797797 2.13128e7 1.18849 0.594243 0.804286i 0.297452π-0.297452\pi
0.594243 + 0.804286i 0.297452π0.297452\pi
798798 0 0
799799 252069. 0.0139686
800800 0 0
801801 −602028. −0.0331540
802802 0 0
803803 −8.49682e6 −0.465015
804804 0 0
805805 0 0
806806 0 0
807807 −3.02244e7 −1.63370
808808 0 0
809809 1.59293e7 0.855709 0.427854 0.903848i 0.359270π-0.359270\pi
0.427854 + 0.903848i 0.359270π0.359270\pi
810810 0 0
811811 −3.28642e7 −1.75457 −0.877286 0.479967i 0.840648π-0.840648\pi
−0.877286 + 0.479967i 0.840648π0.840648\pi
812812 0 0
813813 3.09987e7 1.64482
814814 0 0
815815 0 0
816816 0 0
817817 154535. 0.00809973
818818 0 0
819819 287410. 0.0149724
820820 0 0
821821 2.62592e7 1.35964 0.679820 0.733379i 0.262058π-0.262058\pi
0.679820 + 0.733379i 0.262058π0.262058\pi
822822 0 0
823823 2.10397e7 1.08278 0.541388 0.840773i 0.317899π-0.317899\pi
0.541388 + 0.840773i 0.317899π0.317899\pi
824824 0 0
825825 0 0
826826 0 0
827827 6.90340e6 0.350994 0.175497 0.984480i 0.443847π-0.443847\pi
0.175497 + 0.984480i 0.443847π0.443847\pi
828828 0 0
829829 −2.14263e7 −1.08283 −0.541417 0.840754i 0.682112π-0.682112\pi
−0.541417 + 0.840754i 0.682112π0.682112\pi
830830 0 0
831831 −1.55610e7 −0.781690
832832 0 0
833833 −38050.8 −0.00189999
834834 0 0
835835 0 0
836836 0 0
837837 −1.21536e7 −0.599640
838838 0 0
839839 −4.08576e6 −0.200386 −0.100193 0.994968i 0.531946π-0.531946\pi
−0.100193 + 0.994968i 0.531946π0.531946\pi
840840 0 0
841841 −366923. −0.0178890
842842 0 0
843843 −5.26239e6 −0.255044
844844 0 0
845845 0 0
846846 0 0
847847 2.47362e6 0.118475
848848 0 0
849849 −1.17491e7 −0.559417
850850 0 0
851851 −5.05079e7 −2.39075
852852 0 0
853853 3.80900e7 1.79242 0.896208 0.443634i 0.146311π-0.146311\pi
0.896208 + 0.443634i 0.146311π0.146311\pi
854854 0 0
855855 0 0
856856 0 0
857857 −1.83479e7 −0.853362 −0.426681 0.904402i 0.640317π-0.640317\pi
−0.426681 + 0.904402i 0.640317π0.640317\pi
858858 0 0
859859 −1.26840e7 −0.586508 −0.293254 0.956035i 0.594738π-0.594738\pi
−0.293254 + 0.956035i 0.594738π0.594738\pi
860860 0 0
861861 −2.49056e6 −0.114496
862862 0 0
863863 4.70445e6 0.215022 0.107511 0.994204i 0.465712π-0.465712\pi
0.107511 + 0.994204i 0.465712π0.465712\pi
864864 0 0
865865 0 0
866866 0 0
867867 −2.14434e7 −0.968826
868868 0 0
869869 −2.22649e7 −1.00017
870870 0 0
871871 893748. 0.0399181
872872 0 0
873873 857390. 0.0380752
874874 0 0
875875 0 0
876876 0 0
877877 −6.84823e6 −0.300663 −0.150331 0.988636i 0.548034π-0.548034\pi
−0.150331 + 0.988636i 0.548034π0.548034\pi
878878 0 0
879879 2.37297e7 1.03590
880880 0 0
881881 −1.99909e7 −0.867748 −0.433874 0.900974i 0.642854π-0.642854\pi
−0.433874 + 0.900974i 0.642854π0.642854\pi
882882 0 0
883883 3.08647e7 1.33217 0.666087 0.745874i 0.267968π-0.267968\pi
0.666087 + 0.745874i 0.267968π0.267968\pi
884884 0 0
885885 0 0
886886 0 0
887887 1.34136e7 0.572447 0.286224 0.958163i 0.407600π-0.407600\pi
0.286224 + 0.958163i 0.407600π0.407600\pi
888888 0 0
889889 −7.07508e6 −0.300246
890890 0 0
891891 −1.83631e7 −0.774913
892892 0 0
893893 2.39976e7 1.00702
894894 0 0
895895 0 0
896896 0 0
897897 −1.89847e7 −0.787811
898898 0 0
899899 −1.40060e7 −0.577982
900900 0 0
901901 647628. 0.0265775
902902 0 0
903903 75810.2 0.00309391
904904 0 0
905905 0 0
906906 0 0
907907 2.38108e7 0.961070 0.480535 0.876975i 0.340442π-0.340442\pi
0.480535 + 0.876975i 0.340442π0.340442\pi
908908 0 0
909909 325721. 0.0130748
910910 0 0
911911 −1.99857e7 −0.797856 −0.398928 0.916982i 0.630618π-0.630618\pi
−0.398928 + 0.916982i 0.630618π0.630618\pi
912912 0 0
913913 −8.74011e6 −0.347008
914914 0 0
915915 0 0
916916 0 0
917917 1.35163e7 0.530802
918918 0 0
919919 −1.92392e7 −0.751446 −0.375723 0.926732i 0.622606π-0.622606\pi
−0.375723 + 0.926732i 0.622606π0.622606\pi
920920 0 0
921921 2.22839e7 0.865651
922922 0 0
923923 1.01039e7 0.390379
924924 0 0
925925 0 0
926926 0 0
927927 586855. 0.0224301
928928 0 0
929929 −3.35236e7 −1.27442 −0.637208 0.770692i 0.719911π-0.719911\pi
−0.637208 + 0.770692i 0.719911π0.719911\pi
930930 0 0
931931 −3.62253e6 −0.136974
932932 0 0
933933 −5.01185e7 −1.88493
934934 0 0
935935 0 0
936936 0 0
937937 −4.49418e7 −1.67225 −0.836125 0.548539i 0.815184π-0.815184\pi
−0.836125 + 0.548539i 0.815184π0.815184\pi
938938 0 0
939939 1.43425e6 0.0530836
940940 0 0
941941 3.75307e7 1.38170 0.690848 0.723000i 0.257238π-0.257238\pi
0.690848 + 0.723000i 0.257238π0.257238\pi
942942 0 0
943943 −1.06954e7 −0.391668
944944 0 0
945945 0 0
946946 0 0
947947 −5.77961e6 −0.209423 −0.104711 0.994503i 0.533392π-0.533392\pi
−0.104711 + 0.994503i 0.533392π0.533392\pi
948948 0 0
949949 −1.01040e7 −0.364191
950950 0 0
951951 −5.92245e6 −0.212349
952952 0 0
953953 4.60167e7 1.64128 0.820642 0.571443i 0.193616π-0.193616\pi
0.820642 + 0.571443i 0.193616π0.193616\pi
954954 0 0
955955 0 0
956956 0 0
957957 −2.25433e7 −0.795678
958958 0 0
959959 5.88950e6 0.206791
960960 0 0
961961 −1.88910e7 −0.659852
962962 0 0
963963 313032. 0.0108774
964964 0 0
965965 0 0
966966 0 0
967967 −1.78796e7 −0.614883 −0.307441 0.951567i 0.599473π-0.599473\pi
−0.307441 + 0.951567i 0.599473π0.599473\pi
968968 0 0
969969 361175. 0.0123568
970970 0 0
971971 −1.22974e7 −0.418568 −0.209284 0.977855i 0.567113π-0.567113\pi
−0.209284 + 0.977855i 0.567113π0.567113\pi
972972 0 0
973973 5.39097e6 0.182551
974974 0 0
975975 0 0
976976 0 0
977977 3.07260e7 1.02984 0.514920 0.857238i 0.327822π-0.327822\pi
0.514920 + 0.857238i 0.327822π0.327822\pi
978978 0 0
979979 1.34953e7 0.450014
980980 0 0
981981 3.28165e6 0.108873
982982 0 0
983983 −3.81863e7 −1.26044 −0.630222 0.776415i 0.717036π-0.717036\pi
−0.630222 + 0.776415i 0.717036π0.717036\pi
984984 0 0
985985 0 0
986986 0 0
987987 1.17725e7 0.384659
988988 0 0
989989 325558. 0.0105837
990990 0 0
991991 −5.23079e6 −0.169193 −0.0845966 0.996415i 0.526960π-0.526960\pi
−0.0845966 + 0.996415i 0.526960π0.526960\pi
992992 0 0
993993 5.62563e7 1.81050
994994 0 0
995995 0 0
996996 0 0
997997 −4.72487e7 −1.50540 −0.752700 0.658363i 0.771249π-0.771249\pi
−0.752700 + 0.658363i 0.771249π0.771249\pi
998998 0 0
999999 −6.18874e7 −1.96195
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 700.6.a.k.1.4 4
5.2 odd 4 700.6.e.j.449.3 8
5.3 odd 4 700.6.e.j.449.6 8
5.4 even 2 700.6.a.n.1.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
700.6.a.k.1.4 4 1.1 even 1 trivial
700.6.a.n.1.1 yes 4 5.4 even 2
700.6.e.j.449.3 8 5.2 odd 4
700.6.e.j.449.6 8 5.3 odd 4