Properties

Label 352.6.a.b.1.5
Level 352352
Weight 66
Character 352.1
Self dual yes
Analytic conductor 56.45556.455
Analytic rank 11
Dimension 66
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [352,6,Mod(1,352)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(352, 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("352.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 352=2511 352 = 2^{5} \cdot 11
Weight: k k == 6 6
Character orbit: [χ][\chi] == 352.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 56.455104574256.4551045742
Analytic rank: 11
Dimension: 66
Coefficient field: Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x63x5492x4880x3+32838x2+13500x442908 x^{6} - 3x^{5} - 492x^{4} - 880x^{3} + 32838x^{2} + 13500x - 442908 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 211 2^{11}
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 16.7550-16.7550 of defining polynomial
Character χ\chi == 352.1

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+16.0835q3100.636q5+99.5357q7+15.6776q9121.000q11+1129.85q131618.58q15+5.49747q17576.534q19+1600.88q21961.905q23+7002.66q253656.13q272010.70q29+5682.00q311946.10q3310016.9q357369.08q37+18171.9q3918926.0q4121955.7q431577.74q4520022.7q476899.64q49+88.4183q519830.41q53+12177.0q559272.67q57+3365.53q59+28629.3q61+1560.49q63113704.q6542601.9q6715470.8q69+34117.8q715606.36q73+112627.q7512043.8q7721585.3q7962612.9q8182926.3q83553.245q8532338.9q87+104138.q89+112461.q91+91386.3q93+58020.3q95+12807.1q971896.99q99+O(q100)q+16.0835 q^{3} -100.636 q^{5} +99.5357 q^{7} +15.6776 q^{9} -121.000 q^{11} +1129.85 q^{13} -1618.58 q^{15} +5.49747 q^{17} -576.534 q^{19} +1600.88 q^{21} -961.905 q^{23} +7002.66 q^{25} -3656.13 q^{27} -2010.70 q^{29} +5682.00 q^{31} -1946.10 q^{33} -10016.9 q^{35} -7369.08 q^{37} +18171.9 q^{39} -18926.0 q^{41} -21955.7 q^{43} -1577.74 q^{45} -20022.7 q^{47} -6899.64 q^{49} +88.4183 q^{51} -9830.41 q^{53} +12177.0 q^{55} -9272.67 q^{57} +3365.53 q^{59} +28629.3 q^{61} +1560.49 q^{63} -113704. q^{65} -42601.9 q^{67} -15470.8 q^{69} +34117.8 q^{71} -5606.36 q^{73} +112627. q^{75} -12043.8 q^{77} -21585.3 q^{79} -62612.9 q^{81} -82926.3 q^{83} -553.245 q^{85} -32338.9 q^{87} +104138. q^{89} +112461. q^{91} +91386.3 q^{93} +58020.3 q^{95} +12807.1 q^{97} -1896.99 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q9q389q5+196q7+595q9726q111032q13+655q151614q17826q19420q21+1507q23+10547q2510647q272146q29+9471q31+1089q33+71995q99+O(q100) 6 q - 9 q^{3} - 89 q^{5} + 196 q^{7} + 595 q^{9} - 726 q^{11} - 1032 q^{13} + 655 q^{15} - 1614 q^{17} - 826 q^{19} - 420 q^{21} + 1507 q^{23} + 10547 q^{25} - 10647 q^{27} - 2146 q^{29} + 9471 q^{31} + 1089 q^{33}+ \cdots - 71995 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 16.0835 1.03175 0.515877 0.856663i 0.327466π-0.327466\pi
0.515877 + 0.856663i 0.327466π0.327466\pi
44 0 0
55 −100.636 −1.80024 −0.900118 0.435645i 0.856520π-0.856520\pi
−0.900118 + 0.435645i 0.856520π0.856520\pi
66 0 0
77 99.5357 0.767775 0.383887 0.923380i 0.374585π-0.374585\pi
0.383887 + 0.923380i 0.374585π0.374585\pi
88 0 0
99 15.6776 0.0645170
1010 0 0
1111 −121.000 −0.301511
1212 0 0
1313 1129.85 1.85423 0.927114 0.374780i 0.122282π-0.122282\pi
0.927114 + 0.374780i 0.122282π0.122282\pi
1414 0 0
1515 −1618.58 −1.85740
1616 0 0
1717 5.49747 0.00461360 0.00230680 0.999997i 0.499266π-0.499266\pi
0.00230680 + 0.999997i 0.499266π0.499266\pi
1818 0 0
1919 −576.534 −0.366388 −0.183194 0.983077i 0.558644π-0.558644\pi
−0.183194 + 0.983077i 0.558644π0.558644\pi
2020 0 0
2121 1600.88 0.792155
2222 0 0
2323 −961.905 −0.379151 −0.189576 0.981866i 0.560711π-0.560711\pi
−0.189576 + 0.981866i 0.560711π0.560711\pi
2424 0 0
2525 7002.66 2.24085
2626 0 0
2727 −3656.13 −0.965189
2828 0 0
2929 −2010.70 −0.443968 −0.221984 0.975050i 0.571253π-0.571253\pi
−0.221984 + 0.975050i 0.571253π0.571253\pi
3030 0 0
3131 5682.00 1.06193 0.530967 0.847393i 0.321829π-0.321829\pi
0.530967 + 0.847393i 0.321829π0.321829\pi
3232 0 0
3333 −1946.10 −0.311086
3434 0 0
3535 −10016.9 −1.38218
3636 0 0
3737 −7369.08 −0.884930 −0.442465 0.896786i 0.645896π-0.645896\pi
−0.442465 + 0.896786i 0.645896π0.645896\pi
3838 0 0
3939 18171.9 1.91311
4040 0 0
4141 −18926.0 −1.75833 −0.879163 0.476521i 0.841897π-0.841897\pi
−0.879163 + 0.476521i 0.841897π0.841897\pi
4242 0 0
4343 −21955.7 −1.81083 −0.905413 0.424532i 0.860439π-0.860439\pi
−0.905413 + 0.424532i 0.860439π0.860439\pi
4444 0 0
4545 −1577.74 −0.116146
4646 0 0
4747 −20022.7 −1.32214 −0.661071 0.750323i 0.729898π-0.729898\pi
−0.661071 + 0.750323i 0.729898π0.729898\pi
4848 0 0
4949 −6899.64 −0.410522
5050 0 0
5151 88.4183 0.00476011
5252 0 0
5353 −9830.41 −0.480709 −0.240354 0.970685i 0.577264π-0.577264\pi
−0.240354 + 0.970685i 0.577264π0.577264\pi
5454 0 0
5555 12177.0 0.542792
5656 0 0
5757 −9272.67 −0.378022
5858 0 0
5959 3365.53 0.125870 0.0629352 0.998018i 0.479954π-0.479954\pi
0.0629352 + 0.998018i 0.479954π0.479954\pi
6060 0 0
6161 28629.3 0.985114 0.492557 0.870280i 0.336062π-0.336062\pi
0.492557 + 0.870280i 0.336062π0.336062\pi
6262 0 0
6363 1560.49 0.0495346
6464 0 0
6565 −113704. −3.33805
6666 0 0
6767 −42601.9 −1.15942 −0.579712 0.814821i 0.696835π-0.696835\pi
−0.579712 + 0.814821i 0.696835π0.696835\pi
6868 0 0
6969 −15470.8 −0.391191
7070 0 0
7171 34117.8 0.803221 0.401611 0.915810i 0.368450π-0.368450\pi
0.401611 + 0.915810i 0.368450π0.368450\pi
7272 0 0
7373 −5606.36 −0.123133 −0.0615664 0.998103i 0.519610π-0.519610\pi
−0.0615664 + 0.998103i 0.519610π0.519610\pi
7474 0 0
7575 112627. 2.31201
7676 0 0
7777 −12043.8 −0.231493
7878 0 0
7979 −21585.3 −0.389127 −0.194563 0.980890i 0.562329π-0.562329\pi
−0.194563 + 0.980890i 0.562329π0.562329\pi
8080 0 0
8181 −62612.9 −1.06035
8282 0 0
8383 −82926.3 −1.32129 −0.660643 0.750700i 0.729716π-0.729716\pi
−0.660643 + 0.750700i 0.729716π0.729716\pi
8484 0 0
8585 −553.245 −0.00830558
8686 0 0
8787 −32338.9 −0.458065
8888 0 0
8989 104138. 1.39358 0.696792 0.717273i 0.254610π-0.254610\pi
0.696792 + 0.717273i 0.254610π0.254610\pi
9090 0 0
9191 112461. 1.42363
9292 0 0
9393 91386.3 1.09565
9494 0 0
9595 58020.3 0.659585
9696 0 0
9797 12807.1 0.138205 0.0691024 0.997610i 0.477986π-0.477986\pi
0.0691024 + 0.997610i 0.477986π0.477986\pi
9898 0 0
9999 −1896.99 −0.0194526
100100 0 0
101101 −90924.3 −0.886903 −0.443452 0.896298i 0.646246π-0.646246\pi
−0.443452 + 0.896298i 0.646246π0.646246\pi
102102 0 0
103103 167606. 1.55667 0.778336 0.627848i 0.216064π-0.216064\pi
0.778336 + 0.627848i 0.216064π0.216064\pi
104104 0 0
105105 −161107. −1.42607
106106 0 0
107107 131979. 1.11441 0.557206 0.830374i 0.311873π-0.311873\pi
0.557206 + 0.830374i 0.311873π0.311873\pi
108108 0 0
109109 −47254.7 −0.380960 −0.190480 0.981691i 0.561004π-0.561004\pi
−0.190480 + 0.981691i 0.561004π0.561004\pi
110110 0 0
111111 −118520. −0.913031
112112 0 0
113113 10173.1 0.0749476 0.0374738 0.999298i 0.488069π-0.488069\pi
0.0374738 + 0.999298i 0.488069π0.488069\pi
114114 0 0
115115 96802.6 0.682562
116116 0 0
117117 17713.4 0.119629
118118 0 0
119119 547.194 0.00354221
120120 0 0
121121 14641.0 0.0909091
122122 0 0
123123 −304396. −1.81416
124124 0 0
125125 −390234. −2.23383
126126 0 0
127127 −121460. −0.668225 −0.334113 0.942533i 0.608437π-0.608437\pi
−0.334113 + 0.942533i 0.608437π0.608437\pi
128128 0 0
129129 −353124. −1.86833
130130 0 0
131131 −322828. −1.64359 −0.821794 0.569785i 0.807027π-0.807027\pi
−0.821794 + 0.569785i 0.807027π0.807027\pi
132132 0 0
133133 −57385.8 −0.281303
134134 0 0
135135 367939. 1.73757
136136 0 0
137137 −415124. −1.88963 −0.944814 0.327608i 0.893758π-0.893758\pi
−0.944814 + 0.327608i 0.893758π0.893758\pi
138138 0 0
139139 96216.7 0.422390 0.211195 0.977444i 0.432265π-0.432265\pi
0.211195 + 0.977444i 0.432265π0.432265\pi
140140 0 0
141141 −322035. −1.36413
142142 0 0
143143 −136712. −0.559071
144144 0 0
145145 202349. 0.799247
146146 0 0
147147 −110970. −0.423557
148148 0 0
149149 9994.87 0.0368817 0.0184409 0.999830i 0.494130π-0.494130\pi
0.0184409 + 0.999830i 0.494130π0.494130\pi
150150 0 0
151151 −486380. −1.73593 −0.867967 0.496621i 0.834574π-0.834574\pi
−0.867967 + 0.496621i 0.834574π0.834574\pi
152152 0 0
153153 86.1873 0.000297656 0
154154 0 0
155155 −571816. −1.91173
156156 0 0
157157 −150199. −0.486315 −0.243158 0.969987i 0.578183π-0.578183\pi
−0.243158 + 0.969987i 0.578183π0.578183\pi
158158 0 0
159159 −158107. −0.495973
160160 0 0
161161 −95743.9 −0.291103
162162 0 0
163163 339066. 0.999573 0.499787 0.866148i 0.333412π-0.333412\pi
0.499787 + 0.866148i 0.333412π0.333412\pi
164164 0 0
165165 195848. 0.560028
166166 0 0
167167 464673. 1.28931 0.644653 0.764475i 0.277002π-0.277002\pi
0.644653 + 0.764475i 0.277002π0.277002\pi
168168 0 0
169169 905271. 2.43816
170170 0 0
171171 −9038.69 −0.0236383
172172 0 0
173173 −124921. −0.317338 −0.158669 0.987332i 0.550720π-0.550720\pi
−0.158669 + 0.987332i 0.550720π0.550720\pi
174174 0 0
175175 697015. 1.72047
176176 0 0
177177 54129.4 0.129867
178178 0 0
179179 −391469. −0.913198 −0.456599 0.889673i 0.650933π-0.650933\pi
−0.456599 + 0.889673i 0.650933π0.650933\pi
180180 0 0
181181 −555178. −1.25961 −0.629805 0.776753i 0.716865π-0.716865\pi
−0.629805 + 0.776753i 0.716865π0.716865\pi
182182 0 0
183183 460459. 1.01640
184184 0 0
185185 741597. 1.59308
186186 0 0
187187 −665.194 −0.00139105
188188 0 0
189189 −363916. −0.741048
190190 0 0
191191 874483. 1.73447 0.867237 0.497896i 0.165894π-0.165894\pi
0.867237 + 0.497896i 0.165894π0.165894\pi
192192 0 0
193193 29380.7 0.0567765 0.0283883 0.999597i 0.490963π-0.490963\pi
0.0283883 + 0.999597i 0.490963π0.490963\pi
194194 0 0
195195 −1.82875e6 −3.44405
196196 0 0
197197 103525. 0.190056 0.0950278 0.995475i 0.469706π-0.469706\pi
0.0950278 + 0.995475i 0.469706π0.469706\pi
198198 0 0
199199 −163131. −0.292014 −0.146007 0.989284i 0.546642π-0.546642\pi
−0.146007 + 0.989284i 0.546642π0.546642\pi
200200 0 0
201201 −685187. −1.19624
202202 0 0
203203 −200136. −0.340867
204204 0 0
205205 1.90464e6 3.16540
206206 0 0
207207 −15080.4 −0.0244617
208208 0 0
209209 69760.7 0.110470
210210 0 0
211211 −848872. −1.31261 −0.656306 0.754495i 0.727882π-0.727882\pi
−0.656306 + 0.754495i 0.727882π0.727882\pi
212212 0 0
213213 548732. 0.828727
214214 0 0
215215 2.20954e6 3.25991
216216 0 0
217217 565562. 0.815326
218218 0 0
219219 −90169.6 −0.127043
220220 0 0
221221 6211.32 0.00855467
222222 0 0
223223 382088. 0.514519 0.257260 0.966342i 0.417180π-0.417180\pi
0.257260 + 0.966342i 0.417180π0.417180\pi
224224 0 0
225225 109785. 0.144573
226226 0 0
227227 850742. 1.09581 0.547903 0.836542i 0.315426π-0.315426\pi
0.547903 + 0.836542i 0.315426π0.315426\pi
228228 0 0
229229 461501. 0.581545 0.290773 0.956792i 0.406088π-0.406088\pi
0.290773 + 0.956792i 0.406088π0.406088\pi
230230 0 0
231231 −193706. −0.238844
232232 0 0
233233 874178. 1.05490 0.527449 0.849587i 0.323149π-0.323149\pi
0.527449 + 0.849587i 0.323149π0.323149\pi
234234 0 0
235235 2.01501e6 2.38017
236236 0 0
237237 −347167. −0.401483
238238 0 0
239239 −1.22182e6 −1.38360 −0.691802 0.722087i 0.743183π-0.743183\pi
−0.691802 + 0.722087i 0.743183π0.743183\pi
240240 0 0
241241 385792. 0.427869 0.213935 0.976848i 0.431372π-0.431372\pi
0.213935 + 0.976848i 0.431372π0.431372\pi
242242 0 0
243243 −118592. −0.128837
244244 0 0
245245 694354. 0.739036
246246 0 0
247247 −651398. −0.679366
248248 0 0
249249 −1.33374e6 −1.36324
250250 0 0
251251 −283850. −0.284384 −0.142192 0.989839i 0.545415π-0.545415\pi
−0.142192 + 0.989839i 0.545415π0.545415\pi
252252 0 0
253253 116391. 0.114318
254254 0 0
255255 −8898.09 −0.00856932
256256 0 0
257257 −1.57262e6 −1.48522 −0.742610 0.669724i 0.766412π-0.766412\pi
−0.742610 + 0.669724i 0.766412π0.766412\pi
258258 0 0
259259 −733487. −0.679427
260260 0 0
261261 −31522.9 −0.0286435
262262 0 0
263263 282196. 0.251571 0.125786 0.992057i 0.459855π-0.459855\pi
0.125786 + 0.992057i 0.459855π0.459855\pi
264264 0 0
265265 989296. 0.865389
266266 0 0
267267 1.67489e6 1.43784
268268 0 0
269269 −1.58865e6 −1.33859 −0.669297 0.742995i 0.733405π-0.733405\pi
−0.669297 + 0.742995i 0.733405π0.733405\pi
270270 0 0
271271 1.26811e6 1.04890 0.524448 0.851443i 0.324272π-0.324272\pi
0.524448 + 0.851443i 0.324272π0.324272\pi
272272 0 0
273273 1.80876e6 1.46884
274274 0 0
275275 −847322. −0.675642
276276 0 0
277277 −716430. −0.561015 −0.280507 0.959852i 0.590503π-0.590503\pi
−0.280507 + 0.959852i 0.590503π0.590503\pi
278278 0 0
279279 89080.4 0.0685128
280280 0 0
281281 1.80960e6 1.36715 0.683576 0.729880i 0.260424π-0.260424\pi
0.683576 + 0.729880i 0.260424π0.260424\pi
282282 0 0
283283 −972811. −0.722042 −0.361021 0.932558i 0.617572π-0.617572\pi
−0.361021 + 0.932558i 0.617572π0.617572\pi
284284 0 0
285285 933167. 0.680530
286286 0 0
287287 −1.88381e6 −1.35000
288288 0 0
289289 −1.41983e6 −0.999979
290290 0 0
291291 205983. 0.142593
292292 0 0
293293 1.32696e6 0.903000 0.451500 0.892271i 0.350889π-0.350889\pi
0.451500 + 0.892271i 0.350889π0.350889\pi
294294 0 0
295295 −338694. −0.226596
296296 0 0
297297 442392. 0.291015
298298 0 0
299299 −1.08681e6 −0.703033
300300 0 0
301301 −2.18538e6 −1.39031
302302 0 0
303303 −1.46238e6 −0.915066
304304 0 0
305305 −2.88115e6 −1.77344
306306 0 0
307307 564125. 0.341609 0.170805 0.985305i 0.445363π-0.445363\pi
0.170805 + 0.985305i 0.445363π0.445363\pi
308308 0 0
309309 2.69569e6 1.60610
310310 0 0
311311 2.99389e6 1.75523 0.877617 0.479363i 0.159132π-0.159132\pi
0.877617 + 0.479363i 0.159132π0.159132\pi
312312 0 0
313313 2.69271e6 1.55356 0.776781 0.629771i 0.216851π-0.216851\pi
0.776781 + 0.629771i 0.216851π0.216851\pi
314314 0 0
315315 −157041. −0.0891739
316316 0 0
317317 671680. 0.375417 0.187709 0.982225i 0.439894π-0.439894\pi
0.187709 + 0.982225i 0.439894π0.439894\pi
318318 0 0
319319 243294. 0.133861
320320 0 0
321321 2.12268e6 1.14980
322322 0 0
323323 −3169.48 −0.00169037
324324 0 0
325325 7.91197e6 4.15505
326326 0 0
327327 −760019. −0.393057
328328 0 0
329329 −1.99298e6 −1.01511
330330 0 0
331331 −618419. −0.310251 −0.155125 0.987895i 0.549578π-0.549578\pi
−0.155125 + 0.987895i 0.549578π0.549578\pi
332332 0 0
333333 −115530. −0.0570931
334334 0 0
335335 4.28730e6 2.08724
336336 0 0
337337 1.62745e6 0.780606 0.390303 0.920686i 0.372370π-0.372370\pi
0.390303 + 0.920686i 0.372370π0.372370\pi
338338 0 0
339339 163619. 0.0773275
340340 0 0
341341 −687522. −0.320185
342342 0 0
343343 −2.35966e6 −1.08296
344344 0 0
345345 1.55692e6 0.704236
346346 0 0
347347 −1.80110e6 −0.802996 −0.401498 0.915860i 0.631510π-0.631510\pi
−0.401498 + 0.915860i 0.631510π0.631510\pi
348348 0 0
349349 2.29014e6 1.00647 0.503233 0.864151i 0.332144π-0.332144\pi
0.503233 + 0.864151i 0.332144π0.332144\pi
350350 0 0
351351 −4.13088e6 −1.78968
352352 0 0
353353 −2.59156e6 −1.10694 −0.553470 0.832869i 0.686697π-0.686697\pi
−0.553470 + 0.832869i 0.686697π0.686697\pi
354354 0 0
355355 −3.43349e6 −1.44599
356356 0 0
357357 8800.78 0.00365469
358358 0 0
359359 −1.04765e6 −0.429024 −0.214512 0.976721i 0.568816π-0.568816\pi
−0.214512 + 0.976721i 0.568816π0.568816\pi
360360 0 0
361361 −2.14371e6 −0.865760
362362 0 0
363363 235478. 0.0937958
364364 0 0
365365 564203. 0.221668
366366 0 0
367367 3.72232e6 1.44261 0.721304 0.692618i 0.243543π-0.243543\pi
0.721304 + 0.692618i 0.243543π0.243543\pi
368368 0 0
369369 −296715. −0.113442
370370 0 0
371371 −978477. −0.369076
372372 0 0
373373 −4.97449e6 −1.85130 −0.925650 0.378381i 0.876481π-0.876481\pi
−0.925650 + 0.378381i 0.876481π0.876481\pi
374374 0 0
375375 −6.27631e6 −2.30476
376376 0 0
377377 −2.27179e6 −0.823217
378378 0 0
379379 −1.49702e6 −0.535341 −0.267670 0.963511i 0.586254π-0.586254\pi
−0.267670 + 0.963511i 0.586254π0.586254\pi
380380 0 0
381381 −1.95349e6 −0.689444
382382 0 0
383383 5.26503e6 1.83402 0.917009 0.398866i 0.130596π-0.130596\pi
0.917009 + 0.398866i 0.130596π0.130596\pi
384384 0 0
385385 1.21205e6 0.416742
386386 0 0
387387 −344214. −0.116829
388388 0 0
389389 −3.47145e6 −1.16315 −0.581576 0.813492i 0.697564π-0.697564\pi
−0.581576 + 0.813492i 0.697564π0.697564\pi
390390 0 0
391391 −5288.04 −0.00174925
392392 0 0
393393 −5.19219e6 −1.69578
394394 0 0
395395 2.17227e6 0.700521
396396 0 0
397397 −5.69270e6 −1.81277 −0.906383 0.422456i 0.861168π-0.861168\pi
−0.906383 + 0.422456i 0.861168π0.861168\pi
398398 0 0
399399 −922962. −0.290236
400400 0 0
401401 1.32139e6 0.410364 0.205182 0.978724i 0.434221π-0.434221\pi
0.205182 + 0.978724i 0.434221π0.434221\pi
402402 0 0
403403 6.41982e6 1.96907
404404 0 0
405405 6.30113e6 1.90889
406406 0 0
407407 891659. 0.266817
408408 0 0
409409 147690. 0.0436558 0.0218279 0.999762i 0.493051π-0.493051\pi
0.0218279 + 0.999762i 0.493051π0.493051\pi
410410 0 0
411411 −6.67663e6 −1.94963
412412 0 0
413413 334991. 0.0966401
414414 0 0
415415 8.34539e6 2.37863
416416 0 0
417417 1.54750e6 0.435803
418418 0 0
419419 3.96934e6 1.10454 0.552272 0.833664i 0.313761π-0.313761\pi
0.552272 + 0.833664i 0.313761π0.313761\pi
420420 0 0
421421 −4.22916e6 −1.16292 −0.581459 0.813576i 0.697518π-0.697518\pi
−0.581459 + 0.813576i 0.697518π0.697518\pi
422422 0 0
423423 −313909. −0.0853007
424424 0 0
425425 38496.9 0.0103384
426426 0 0
427427 2.84964e6 0.756346
428428 0 0
429429 −2.19880e6 −0.576823
430430 0 0
431431 2.80166e6 0.726479 0.363239 0.931696i 0.381671π-0.381671\pi
0.363239 + 0.931696i 0.381671π0.381671\pi
432432 0 0
433433 −4.99859e6 −1.28123 −0.640615 0.767862i 0.721321π-0.721321\pi
−0.640615 + 0.767862i 0.721321π0.721321\pi
434434 0 0
435435 3.25447e6 0.824626
436436 0 0
437437 554571. 0.138916
438438 0 0
439439 617298. 0.152874 0.0764370 0.997074i 0.475646π-0.475646\pi
0.0764370 + 0.997074i 0.475646π0.475646\pi
440440 0 0
441441 −108170. −0.0264856
442442 0 0
443443 3.10619e6 0.752002 0.376001 0.926619i 0.377299π-0.377299\pi
0.376001 + 0.926619i 0.377299π0.377299\pi
444444 0 0
445445 −1.04800e7 −2.50878
446446 0 0
447447 160752. 0.0380529
448448 0 0
449449 5.73212e6 1.34184 0.670919 0.741531i 0.265900π-0.265900\pi
0.670919 + 0.741531i 0.265900π0.265900\pi
450450 0 0
451451 2.29005e6 0.530155
452452 0 0
453453 −7.82267e6 −1.79106
454454 0 0
455455 −1.13176e7 −2.56287
456456 0 0
457457 −481316. −0.107805 −0.0539026 0.998546i 0.517166π-0.517166\pi
−0.0539026 + 0.998546i 0.517166π0.517166\pi
458458 0 0
459459 −20099.5 −0.00445300
460460 0 0
461461 4.21739e6 0.924254 0.462127 0.886814i 0.347086π-0.347086\pi
0.462127 + 0.886814i 0.347086π0.347086\pi
462462 0 0
463463 −989813. −0.214586 −0.107293 0.994227i 0.534218π-0.534218\pi
−0.107293 + 0.994227i 0.534218π0.534218\pi
464464 0 0
465465 −9.19678e6 −1.97244
466466 0 0
467467 2.02797e6 0.430298 0.215149 0.976581i 0.430976π-0.430976\pi
0.215149 + 0.976581i 0.430976π0.430976\pi
468468 0 0
469469 −4.24042e6 −0.890177
470470 0 0
471471 −2.41572e6 −0.501758
472472 0 0
473473 2.65664e6 0.545984
474474 0 0
475475 −4.03728e6 −0.821021
476476 0 0
477477 −154118. −0.0310139
478478 0 0
479479 3.70289e6 0.737398 0.368699 0.929549i 0.379803π-0.379803\pi
0.368699 + 0.929549i 0.379803π0.379803\pi
480480 0 0
481481 −8.32597e6 −1.64086
482482 0 0
483483 −1.53989e6 −0.300347
484484 0 0
485485 −1.28886e6 −0.248801
486486 0 0
487487 −8.22043e6 −1.57062 −0.785311 0.619101i 0.787497π-0.787497\pi
−0.785311 + 0.619101i 0.787497π0.787497\pi
488488 0 0
489489 5.45335e6 1.03131
490490 0 0
491491 977146. 0.182918 0.0914588 0.995809i 0.470847π-0.470847\pi
0.0914588 + 0.995809i 0.470847π0.470847\pi
492492 0 0
493493 −11053.7 −0.00204829
494494 0 0
495495 190906. 0.0350193
496496 0 0
497497 3.39594e6 0.616693
498498 0 0
499499 8.97522e6 1.61359 0.806796 0.590830i 0.201200π-0.201200\pi
0.806796 + 0.590830i 0.201200π0.201200\pi
500500 0 0
501501 7.47355e6 1.33025
502502 0 0
503503 1.40004e6 0.246729 0.123365 0.992361i 0.460632π-0.460632\pi
0.123365 + 0.992361i 0.460632π0.460632\pi
504504 0 0
505505 9.15028e6 1.59664
506506 0 0
507507 1.45599e7 2.51558
508508 0 0
509509 −2.68974e6 −0.460167 −0.230083 0.973171i 0.573900π-0.573900\pi
−0.230083 + 0.973171i 0.573900π0.573900\pi
510510 0 0
511511 −558033. −0.0945382
512512 0 0
513513 2.10788e6 0.353633
514514 0 0
515515 −1.68673e7 −2.80238
516516 0 0
517517 2.42275e6 0.398641
518518 0 0
519519 −2.00917e6 −0.327415
520520 0 0
521521 6.78645e6 1.09534 0.547670 0.836695i 0.315515π-0.315515\pi
0.547670 + 0.836695i 0.315515π0.315515\pi
522522 0 0
523523 202631. 0.0323931 0.0161965 0.999869i 0.494844π-0.494844\pi
0.0161965 + 0.999869i 0.494844π0.494844\pi
524524 0 0
525525 1.12104e7 1.77510
526526 0 0
527527 31236.6 0.00489934
528528 0 0
529529 −5.51108e6 −0.856244
530530 0 0
531531 52763.6 0.00812078
532532 0 0
533533 −2.13836e7 −3.26034
534534 0 0
535535 −1.32819e7 −2.00621
536536 0 0
537537 −6.29618e6 −0.942196
538538 0 0
539539 834856. 0.123777
540540 0 0
541541 3.08517e6 0.453196 0.226598 0.973988i 0.427240π-0.427240\pi
0.226598 + 0.973988i 0.427240π0.427240\pi
542542 0 0
543543 −8.92919e6 −1.29961
544544 0 0
545545 4.75554e6 0.685817
546546 0 0
547547 5.25255e6 0.750589 0.375294 0.926906i 0.377542π-0.377542\pi
0.375294 + 0.926906i 0.377542π0.377542\pi
548548 0 0
549549 448840. 0.0635566
550550 0 0
551551 1.15923e6 0.162664
552552 0 0
553553 −2.14851e6 −0.298762
554554 0 0
555555 1.19274e7 1.64367
556556 0 0
557557 3.43928e6 0.469709 0.234855 0.972030i 0.424539π-0.424539\pi
0.234855 + 0.972030i 0.424539π0.424539\pi
558558 0 0
559559 −2.48067e7 −3.35768
560560 0 0
561561 −10698.6 −0.00143523
562562 0 0
563563 1.10226e7 1.46559 0.732796 0.680448i 0.238215π-0.238215\pi
0.732796 + 0.680448i 0.238215π0.238215\pi
564564 0 0
565565 −1.02378e6 −0.134923
566566 0 0
567567 −6.23222e6 −0.814114
568568 0 0
569569 −2.65040e6 −0.343187 −0.171593 0.985168i 0.554892π-0.554892\pi
−0.171593 + 0.985168i 0.554892π0.554892\pi
570570 0 0
571571 8.31534e6 1.06731 0.533654 0.845703i 0.320818π-0.320818\pi
0.533654 + 0.845703i 0.320818π0.320818\pi
572572 0 0
573573 1.40647e7 1.78955
574574 0 0
575575 −6.73590e6 −0.849622
576576 0 0
577577 6.23879e6 0.780119 0.390060 0.920790i 0.372454π-0.372454\pi
0.390060 + 0.920790i 0.372454π0.372454\pi
578578 0 0
579579 472543. 0.0585794
580580 0 0
581581 −8.25413e6 −1.01445
582582 0 0
583583 1.18948e6 0.144939
584584 0 0
585585 −1.78261e6 −0.215361
586586 0 0
587587 −9.45705e6 −1.13282 −0.566409 0.824124i 0.691668π-0.691668\pi
−0.566409 + 0.824124i 0.691668π0.691668\pi
588588 0 0
589589 −3.27587e6 −0.389080
590590 0 0
591591 1.66504e6 0.196091
592592 0 0
593593 −1.24162e7 −1.44995 −0.724973 0.688778i 0.758148π-0.758148\pi
−0.724973 + 0.688778i 0.758148π0.758148\pi
594594 0 0
595595 −55067.6 −0.00637682
596596 0 0
597597 −2.62371e6 −0.301287
598598 0 0
599599 2.42313e6 0.275937 0.137969 0.990437i 0.455943π-0.455943\pi
0.137969 + 0.990437i 0.455943π0.455943\pi
600600 0 0
601601 −8.03836e6 −0.907781 −0.453890 0.891057i 0.649964π-0.649964\pi
−0.453890 + 0.891057i 0.649964π0.649964\pi
602602 0 0
603603 −667898. −0.0748026
604604 0 0
605605 −1.47342e6 −0.163658
606606 0 0
607607 2.56220e6 0.282255 0.141127 0.989991i 0.454927π-0.454927\pi
0.141127 + 0.989991i 0.454927π0.454927\pi
608608 0 0
609609 −3.21888e6 −0.351691
610610 0 0
611611 −2.26227e7 −2.45155
612612 0 0
613613 2.69197e6 0.289347 0.144673 0.989479i 0.453787π-0.453787\pi
0.144673 + 0.989479i 0.453787π0.453787\pi
614614 0 0
615615 3.06332e7 3.26592
616616 0 0
617617 −1.39002e7 −1.46997 −0.734984 0.678084i 0.762811π-0.762811\pi
−0.734984 + 0.678084i 0.762811π0.762811\pi
618618 0 0
619619 1.63082e6 0.171072 0.0855360 0.996335i 0.472740π-0.472740\pi
0.0855360 + 0.996335i 0.472740π0.472740\pi
620620 0 0
621621 3.51685e6 0.365953
622622 0 0
623623 1.03654e7 1.06996
624624 0 0
625625 1.73883e7 1.78057
626626 0 0
627627 1.12199e6 0.113978
628628 0 0
629629 −40511.3 −0.00408272
630630 0 0
631631 −7.26684e6 −0.726561 −0.363280 0.931680i 0.618343π-0.618343\pi
−0.363280 + 0.931680i 0.618343π0.618343\pi
632632 0 0
633633 −1.36528e7 −1.35429
634634 0 0
635635 1.22233e7 1.20296
636636 0 0
637637 −7.79556e6 −0.761200
638638 0 0
639639 534887. 0.0518215
640640 0 0
641641 −2.03214e6 −0.195347 −0.0976737 0.995218i 0.531140π-0.531140\pi
−0.0976737 + 0.995218i 0.531140π0.531140\pi
642642 0 0
643643 −8.46142e6 −0.807079 −0.403539 0.914962i 0.632220π-0.632220\pi
−0.403539 + 0.914962i 0.632220π0.632220\pi
644644 0 0
645645 3.55371e7 3.36343
646646 0 0
647647 −1.72450e7 −1.61958 −0.809788 0.586722i 0.800418π-0.800418\pi
−0.809788 + 0.586722i 0.800418π0.800418\pi
648648 0 0
649649 −407229. −0.0379513
650650 0 0
651651 9.09620e6 0.841216
652652 0 0
653653 218182. 0.0200233 0.0100116 0.999950i 0.496813π-0.496813\pi
0.0100116 + 0.999950i 0.496813π0.496813\pi
654654 0 0
655655 3.24882e7 2.95885
656656 0 0
657657 −87894.4 −0.00794416
658658 0 0
659659 −1.09287e7 −0.980287 −0.490143 0.871642i 0.663056π-0.663056\pi
−0.490143 + 0.871642i 0.663056π0.663056\pi
660660 0 0
661661 −1.01145e6 −0.0900413 −0.0450206 0.998986i 0.514335π-0.514335\pi
−0.0450206 + 0.998986i 0.514335π0.514335\pi
662662 0 0
663663 99899.5 0.00882632
664664 0 0
665665 5.77509e6 0.506413
666666 0 0
667667 1.93410e6 0.168331
668668 0 0
669669 6.14530e6 0.530857
670670 0 0
671671 −3.46415e6 −0.297023
672672 0 0
673673 1.74638e7 1.48628 0.743142 0.669134i 0.233335π-0.233335\pi
0.743142 + 0.669134i 0.233335π0.233335\pi
674674 0 0
675675 −2.56026e7 −2.16285
676676 0 0
677677 7.41726e6 0.621974 0.310987 0.950414i 0.399340π-0.399340\pi
0.310987 + 0.950414i 0.399340π0.399340\pi
678678 0 0
679679 1.27477e6 0.106110
680680 0 0
681681 1.36829e7 1.13060
682682 0 0
683683 1.42076e7 1.16538 0.582691 0.812694i 0.302000π-0.302000\pi
0.582691 + 0.812694i 0.302000π0.302000\pi
684684 0 0
685685 4.17765e7 3.40178
686686 0 0
687687 7.42253e6 0.600012
688688 0 0
689689 −1.11069e7 −0.891343
690690 0 0
691691 −6.44515e6 −0.513497 −0.256749 0.966478i 0.582651π-0.582651\pi
−0.256749 + 0.966478i 0.582651π0.582651\pi
692692 0 0
693693 −188819. −0.0149352
694694 0 0
695695 −9.68289e6 −0.760402
696696 0 0
697697 −104045. −0.00811222
698698 0 0
699699 1.40598e7 1.08839
700700 0 0
701701 −1.64220e7 −1.26221 −0.631105 0.775697i 0.717398π-0.717398\pi
−0.631105 + 0.775697i 0.717398π0.717398\pi
702702 0 0
703703 4.24853e6 0.324228
704704 0 0
705705 3.24084e7 2.45575
706706 0 0
707707 −9.05021e6 −0.680942
708708 0 0
709709 2.34022e7 1.74840 0.874200 0.485566i 0.161386π-0.161386\pi
0.874200 + 0.485566i 0.161386π0.161386\pi
710710 0 0
711711 −338407. −0.0251053
712712 0 0
713713 −5.46555e6 −0.402633
714714 0 0
715715 1.37582e7 1.00646
716716 0 0
717717 −1.96511e7 −1.42754
718718 0 0
719719 −512196. −0.0369500 −0.0184750 0.999829i 0.505881π-0.505881\pi
−0.0184750 + 0.999829i 0.505881π0.505881\pi
720720 0 0
721721 1.66828e7 1.19517
722722 0 0
723723 6.20488e6 0.441456
724724 0 0
725725 −1.40802e7 −0.994866
726726 0 0
727727 2.41905e6 0.169750 0.0848749 0.996392i 0.472951π-0.472951\pi
0.0848749 + 0.996392i 0.472951π0.472951\pi
728728 0 0
729729 1.33076e7 0.927427
730730 0 0
731731 −120701. −0.00835443
732732 0 0
733733 2.52577e6 0.173633 0.0868167 0.996224i 0.472331π-0.472331\pi
0.0868167 + 0.996224i 0.472331π0.472331\pi
734734 0 0
735735 1.11676e7 0.762504
736736 0 0
737737 5.15484e6 0.349580
738738 0 0
739739 −2.14494e7 −1.44479 −0.722393 0.691483i 0.756958π-0.756958\pi
−0.722393 + 0.691483i 0.756958π0.756958\pi
740740 0 0
741741 −1.04767e7 −0.700939
742742 0 0
743743 −5.97440e6 −0.397029 −0.198514 0.980098i 0.563612π-0.563612\pi
−0.198514 + 0.980098i 0.563612π0.563612\pi
744744 0 0
745745 −1.00585e6 −0.0663959
746746 0 0
747747 −1.30009e6 −0.0852455
748748 0 0
749749 1.31366e7 0.855618
750750 0 0
751751 −1.90539e7 −1.23277 −0.616387 0.787443i 0.711404π-0.711404\pi
−0.616387 + 0.787443i 0.711404π0.711404\pi
752752 0 0
753753 −4.56530e6 −0.293414
754754 0 0
755755 4.89475e7 3.12509
756756 0 0
757757 1.24379e7 0.788874 0.394437 0.918923i 0.370940π-0.370940\pi
0.394437 + 0.918923i 0.370940π0.370940\pi
758758 0 0
759759 1.87196e6 0.117949
760760 0 0
761761 7.50491e6 0.469768 0.234884 0.972023i 0.424529π-0.424529\pi
0.234884 + 0.972023i 0.424529π0.424529\pi
762762 0 0
763763 −4.70353e6 −0.292491
764764 0 0
765765 −8673.57 −0.000535851 0
766766 0 0
767767 3.80255e6 0.233392
768768 0 0
769769 −1.13597e7 −0.692710 −0.346355 0.938104i 0.612581π-0.612581\pi
−0.346355 + 0.938104i 0.612581π0.612581\pi
770770 0 0
771771 −2.52932e7 −1.53238
772772 0 0
773773 −1.57906e7 −0.950493 −0.475247 0.879853i 0.657641π-0.657641\pi
−0.475247 + 0.879853i 0.657641π0.657641\pi
774774 0 0
775775 3.97892e7 2.37964
776776 0 0
777777 −1.17970e7 −0.701002
778778 0 0
779779 1.09115e7 0.644229
780780 0 0
781781 −4.12826e6 −0.242180
782782 0 0
783783 7.35136e6 0.428512
784784 0 0
785785 1.51155e7 0.875483
786786 0 0
787787 −5.96895e6 −0.343527 −0.171764 0.985138i 0.554946π-0.554946\pi
−0.171764 + 0.985138i 0.554946π0.554946\pi
788788 0 0
789789 4.53868e6 0.259560
790790 0 0
791791 1.01259e6 0.0575429
792792 0 0
793793 3.23469e7 1.82663
794794 0 0
795795 1.59113e7 0.892869
796796 0 0
797797 2.04962e7 1.14295 0.571476 0.820619i 0.306371π-0.306371\pi
0.571476 + 0.820619i 0.306371π0.306371\pi
798798 0 0
799799 −110074. −0.00609984
800800 0 0
801801 1.63263e6 0.0899099
802802 0 0
803803 678369. 0.0371259
804804 0 0
805805 9.63531e6 0.524054
806806 0 0
807807 −2.55511e7 −1.38110
808808 0 0
809809 −3.68444e7 −1.97925 −0.989625 0.143674i 0.954108π-0.954108\pi
−0.989625 + 0.143674i 0.954108π0.954108\pi
810810 0 0
811811 −2.94791e7 −1.57384 −0.786922 0.617053i 0.788326π-0.788326\pi
−0.786922 + 0.617053i 0.788326π0.788326\pi
812812 0 0
813813 2.03955e7 1.08220
814814 0 0
815815 −3.41223e7 −1.79947
816816 0 0
817817 1.26582e7 0.663465
818818 0 0
819819 1.76312e6 0.0918483
820820 0 0
821821 −1.59725e7 −0.827020 −0.413510 0.910500i 0.635697π-0.635697\pi
−0.413510 + 0.910500i 0.635697π0.635697\pi
822822 0 0
823823 4.71603e6 0.242704 0.121352 0.992610i 0.461277π-0.461277\pi
0.121352 + 0.992610i 0.461277π0.461277\pi
824824 0 0
825825 −1.36279e7 −0.697097
826826 0 0
827827 −1.07195e7 −0.545016 −0.272508 0.962154i 0.587853π-0.587853\pi
−0.272508 + 0.962154i 0.587853π0.587853\pi
828828 0 0
829829 3.14806e7 1.59095 0.795475 0.605987i 0.207222π-0.207222\pi
0.795475 + 0.605987i 0.207222π0.207222\pi
830830 0 0
831831 −1.15227e7 −0.578829
832832 0 0
833833 −37930.5 −0.00189398
834834 0 0
835835 −4.67630e7 −2.32106
836836 0 0
837837 −2.07741e7 −1.02497
838838 0 0
839839 6.69007e6 0.328115 0.164057 0.986451i 0.447542π-0.447542\pi
0.164057 + 0.986451i 0.447542π0.447542\pi
840840 0 0
841841 −1.64683e7 −0.802893
842842 0 0
843843 2.91046e7 1.41056
844844 0 0
845845 −9.11031e7 −4.38926
846846 0 0
847847 1.45730e6 0.0697977
848848 0 0
849849 −1.56462e7 −0.744970
850850 0 0
851851 7.08836e6 0.335522
852852 0 0
853853 −2.91412e7 −1.37131 −0.685654 0.727928i 0.740484π-0.740484\pi
−0.685654 + 0.727928i 0.740484π0.740484\pi
854854 0 0
855855 909621. 0.0425545
856856 0 0
857857 −2.11821e7 −0.985184 −0.492592 0.870260i 0.663950π-0.663950\pi
−0.492592 + 0.870260i 0.663950π0.663950\pi
858858 0 0
859859 −9.16226e6 −0.423662 −0.211831 0.977306i 0.567943π-0.567943\pi
−0.211831 + 0.977306i 0.567943π0.567943\pi
860860 0 0
861861 −3.02982e7 −1.39287
862862 0 0
863863 3.11789e7 1.42506 0.712532 0.701640i 0.247548π-0.247548\pi
0.712532 + 0.701640i 0.247548π0.247548\pi
864864 0 0
865865 1.25716e7 0.571283
866866 0 0
867867 −2.28357e7 −1.03173
868868 0 0
869869 2.61183e6 0.117326
870870 0 0
871871 −4.81339e7 −2.14984
872872 0 0
873873 200786. 0.00891656
874874 0 0
875875 −3.88422e7 −1.71508
876876 0 0
877877 4.32059e7 1.89690 0.948449 0.316931i 0.102652π-0.102652\pi
0.948449 + 0.316931i 0.102652π0.102652\pi
878878 0 0
879879 2.13420e7 0.931674
880880 0 0
881881 −2.40150e7 −1.04242 −0.521210 0.853428i 0.674519π-0.674519\pi
−0.521210 + 0.853428i 0.674519π0.674519\pi
882882 0 0
883883 2.76263e7 1.19240 0.596200 0.802836i 0.296677π-0.296677\pi
0.596200 + 0.802836i 0.296677π0.296677\pi
884884 0 0
885885 −5.44738e6 −0.233792
886886 0 0
887887 −1.53944e7 −0.656984 −0.328492 0.944507i 0.606540π-0.606540\pi
−0.328492 + 0.944507i 0.606540π0.606540\pi
888888 0 0
889889 −1.20896e7 −0.513047
890890 0 0
891891 7.57616e6 0.319709
892892 0 0
893893 1.15438e7 0.484417
894894 0 0
895895 3.93960e7 1.64397
896896 0 0
897897 −1.74797e7 −0.725357
898898 0 0
899899 −1.14248e7 −0.471464
900900 0 0
901901 −54042.3 −0.00221780
902902 0 0
903903 −3.51485e7 −1.43445
904904 0 0
905905 5.58711e7 2.26760
906906 0 0
907907 1.15688e7 0.466951 0.233475 0.972363i 0.424990π-0.424990\pi
0.233475 + 0.972363i 0.424990π0.424990\pi
908908 0 0
909909 −1.42548e6 −0.0572204
910910 0 0
911911 2.43936e6 0.0973824 0.0486912 0.998814i 0.484495π-0.484495\pi
0.0486912 + 0.998814i 0.484495π0.484495\pi
912912 0 0
913913 1.00341e7 0.398383
914914 0 0
915915 −4.63389e7 −1.82975
916916 0 0
917917 −3.21329e7 −1.26191
918918 0 0
919919 4.19368e7 1.63797 0.818986 0.573814i 0.194537π-0.194537\pi
0.818986 + 0.573814i 0.194537π0.194537\pi
920920 0 0
921921 9.07309e6 0.352457
922922 0 0
923923 3.85481e7 1.48936
924924 0 0
925925 −5.16032e7 −1.98300
926926 0 0
927927 2.62767e6 0.100432
928928 0 0
929929 −2.44846e7 −0.930796 −0.465398 0.885101i 0.654089π-0.654089\pi
−0.465398 + 0.885101i 0.654089π0.654089\pi
930930 0 0
931931 3.97788e6 0.150410
932932 0 0
933933 4.81521e7 1.81097
934934 0 0
935935 66942.6 0.00250423
936936 0 0
937937 1.50232e7 0.559002 0.279501 0.960145i 0.409831π-0.409831\pi
0.279501 + 0.960145i 0.409831π0.409831\pi
938938 0 0
939939 4.33081e7 1.60289
940940 0 0
941941 −2.07793e7 −0.764990 −0.382495 0.923957i 0.624935π-0.624935\pi
−0.382495 + 0.923957i 0.624935π0.624935\pi
942942 0 0
943943 1.82050e7 0.666672
944944 0 0
945945 3.66231e7 1.33406
946946 0 0
947947 −4.09922e7 −1.48534 −0.742670 0.669657i 0.766441π-0.766441\pi
−0.742670 + 0.669657i 0.766441π0.766441\pi
948948 0 0
949949 −6.33435e6 −0.228316
950950 0 0
951951 1.08029e7 0.387338
952952 0 0
953953 −1.32155e7 −0.471359 −0.235680 0.971831i 0.575732π-0.575732\pi
−0.235680 + 0.971831i 0.575732π0.575732\pi
954954 0 0
955955 −8.80047e7 −3.12246
956956 0 0
957957 3.91301e6 0.138112
958958 0 0
959959 −4.13197e7 −1.45081
960960 0 0
961961 3.65602e6 0.127703
962962 0 0
963963 2.06912e6 0.0718986
964964 0 0
965965 −2.95676e6 −0.102211
966966 0 0
967967 −2.42092e7 −0.832557 −0.416279 0.909237i 0.636666π-0.636666\pi
−0.416279 + 0.909237i 0.636666π0.636666\pi
968968 0 0
969969 −50976.2 −0.00174405
970970 0 0
971971 4.87361e7 1.65883 0.829417 0.558630i 0.188673π-0.188673\pi
0.829417 + 0.558630i 0.188673π0.188673\pi
972972 0 0
973973 9.57700e6 0.324300
974974 0 0
975975 1.27252e8 4.28699
976976 0 0
977977 8.53236e6 0.285978 0.142989 0.989724i 0.454329π-0.454329\pi
0.142989 + 0.989724i 0.454329π0.454329\pi
978978 0 0
979979 −1.26007e7 −0.420181
980980 0 0
981981 −740842. −0.0245784
982982 0 0
983983 −1.37548e7 −0.454015 −0.227008 0.973893i 0.572894π-0.572894\pi
−0.227008 + 0.973893i 0.572894π0.572894\pi
984984 0 0
985985 −1.04184e7 −0.342145
986986 0 0
987987 −3.20539e7 −1.04734
988988 0 0
989989 2.11193e7 0.686577
990990 0 0
991991 −7.12861e6 −0.230580 −0.115290 0.993332i 0.536780π-0.536780\pi
−0.115290 + 0.993332i 0.536780π0.536780\pi
992992 0 0
993993 −9.94631e6 −0.320102
994994 0 0
995995 1.64169e7 0.525694
996996 0 0
997997 −1.71603e7 −0.546746 −0.273373 0.961908i 0.588139π-0.588139\pi
−0.273373 + 0.961908i 0.588139π0.588139\pi
998998 0 0
999999 2.69423e7 0.854125
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 352.6.a.b.1.5 6
4.3 odd 2 352.6.a.d.1.2 yes 6
8.3 odd 2 704.6.a.ba.1.5 6
8.5 even 2 704.6.a.bc.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
352.6.a.b.1.5 6 1.1 even 1 trivial
352.6.a.d.1.2 yes 6 4.3 odd 2
704.6.a.ba.1.5 6 8.3 odd 2
704.6.a.bc.1.2 6 8.5 even 2