Properties

Label 476.4.a.b.1.4
Level 476476
Weight 44
Character 476.1
Self dual yes
Analytic conductor 28.08528.085
Analytic rank 00
Dimension 66
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [476,4,Mod(1,476)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(476, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("476.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 476=22717 476 = 2^{2} \cdot 7 \cdot 17
Weight: k k == 4 4
Character orbit: [χ][\chi] == 476.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: 28.084909162728.0849091627
Analytic rank: 00
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: x62x571x432x3+547x2+268x720 x^{6} - 2x^{5} - 71x^{4} - 32x^{3} + 547x^{2} + 268x - 720 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 24 2^{4}
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 1.009201.00920 of defining polynomial
Character χ\chi == 476.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+1.00920q3+15.3947q57.00000q725.9815q9+25.7348q11+16.0232q13+15.5364q15+17.0000q17+157.385q197.06441q21152.339q23+111.998q2553.4690q27+293.792q29+246.190q31+25.9715q33107.763q35102.495q37+16.1707q3980.0959q41311.232q43399.979q45+449.527q47+49.0000q49+17.1564q51518.705q53+396.180q55+158.833q57+810.255q59+101.071q61+181.871q63+246.673q65233.289q67153.740q69+981.570q71274.218q73+113.029q75180.143q77218.065q79+647.540q81+432.623q83+261.711q85+296.495q87+1019.40q89112.163q91+248.456q93+2422.91q95+466.343q97668.628q99+O(q100)q+1.00920 q^{3} +15.3947 q^{5} -7.00000 q^{7} -25.9815 q^{9} +25.7348 q^{11} +16.0232 q^{13} +15.5364 q^{15} +17.0000 q^{17} +157.385 q^{19} -7.06441 q^{21} -152.339 q^{23} +111.998 q^{25} -53.4690 q^{27} +293.792 q^{29} +246.190 q^{31} +25.9715 q^{33} -107.763 q^{35} -102.495 q^{37} +16.1707 q^{39} -80.0959 q^{41} -311.232 q^{43} -399.979 q^{45} +449.527 q^{47} +49.0000 q^{49} +17.1564 q^{51} -518.705 q^{53} +396.180 q^{55} +158.833 q^{57} +810.255 q^{59} +101.071 q^{61} +181.871 q^{63} +246.673 q^{65} -233.289 q^{67} -153.740 q^{69} +981.570 q^{71} -274.218 q^{73} +113.029 q^{75} -180.143 q^{77} -218.065 q^{79} +647.540 q^{81} +432.623 q^{83} +261.711 q^{85} +296.495 q^{87} +1019.40 q^{89} -112.163 q^{91} +248.456 q^{93} +2422.91 q^{95} +466.343 q^{97} -668.628 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+2q314q542q716q92q11+8q1316q15+102q17+170q1914q21+102q23+140q25+422q27+278q29+380q31+98q33+98q35++450q99+O(q100) 6 q + 2 q^{3} - 14 q^{5} - 42 q^{7} - 16 q^{9} - 2 q^{11} + 8 q^{13} - 16 q^{15} + 102 q^{17} + 170 q^{19} - 14 q^{21} + 102 q^{23} + 140 q^{25} + 422 q^{27} + 278 q^{29} + 380 q^{31} + 98 q^{33} + 98 q^{35}+ \cdots + 450 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 1.00920 0.194221 0.0971104 0.995274i 0.469040π-0.469040\pi
0.0971104 + 0.995274i 0.469040π0.469040\pi
44 0 0
55 15.3947 1.37695 0.688474 0.725261i 0.258281π-0.258281\pi
0.688474 + 0.725261i 0.258281π0.258281\pi
66 0 0
77 −7.00000 −0.377964
88 0 0
99 −25.9815 −0.962278
1010 0 0
1111 25.7348 0.705393 0.352696 0.935738i 0.385265π-0.385265\pi
0.352696 + 0.935738i 0.385265π0.385265\pi
1212 0 0
1313 16.0232 0.341849 0.170925 0.985284i 0.445324π-0.445324\pi
0.170925 + 0.985284i 0.445324π0.445324\pi
1414 0 0
1515 15.5364 0.267432
1616 0 0
1717 17.0000 0.242536
1818 0 0
1919 157.385 1.90035 0.950175 0.311717i 0.100904π-0.100904\pi
0.950175 + 0.311717i 0.100904π0.100904\pi
2020 0 0
2121 −7.06441 −0.0734086
2222 0 0
2323 −152.339 −1.38108 −0.690540 0.723294i 0.742627π-0.742627\pi
−0.690540 + 0.723294i 0.742627π0.742627\pi
2424 0 0
2525 111.998 0.895985
2626 0 0
2727 −53.4690 −0.381115
2828 0 0
2929 293.792 1.88124 0.940618 0.339466i 0.110246π-0.110246\pi
0.940618 + 0.339466i 0.110246π0.110246\pi
3030 0 0
3131 246.190 1.42636 0.713179 0.700982i 0.247255π-0.247255\pi
0.713179 + 0.700982i 0.247255π0.247255\pi
3232 0 0
3333 25.9715 0.137002
3434 0 0
3535 −107.763 −0.520437
3636 0 0
3737 −102.495 −0.455405 −0.227703 0.973731i 0.573121π-0.573121\pi
−0.227703 + 0.973731i 0.573121π0.573121\pi
3838 0 0
3939 16.1707 0.0663943
4040 0 0
4141 −80.0959 −0.305094 −0.152547 0.988296i 0.548748π-0.548748\pi
−0.152547 + 0.988296i 0.548748π0.548748\pi
4242 0 0
4343 −311.232 −1.10378 −0.551889 0.833918i 0.686093π-0.686093\pi
−0.551889 + 0.833918i 0.686093π0.686093\pi
4444 0 0
4545 −399.979 −1.32501
4646 0 0
4747 449.527 1.39511 0.697556 0.716530i 0.254271π-0.254271\pi
0.697556 + 0.716530i 0.254271π0.254271\pi
4848 0 0
4949 49.0000 0.142857
5050 0 0
5151 17.1564 0.0471055
5252 0 0
5353 −518.705 −1.34433 −0.672167 0.740400i 0.734636π-0.734636\pi
−0.672167 + 0.740400i 0.734636π0.734636\pi
5454 0 0
5555 396.180 0.971289
5656 0 0
5757 158.833 0.369088
5858 0 0
5959 810.255 1.78790 0.893951 0.448164i 0.147922π-0.147922\pi
0.893951 + 0.448164i 0.147922π0.147922\pi
6060 0 0
6161 101.071 0.212144 0.106072 0.994358i 0.466173π-0.466173\pi
0.106072 + 0.994358i 0.466173π0.466173\pi
6262 0 0
6363 181.871 0.363707
6464 0 0
6565 246.673 0.470709
6666 0 0
6767 −233.289 −0.425385 −0.212693 0.977119i 0.568223π-0.568223\pi
−0.212693 + 0.977119i 0.568223π0.568223\pi
6868 0 0
6969 −153.740 −0.268234
7070 0 0
7171 981.570 1.64072 0.820358 0.571850i 0.193774π-0.193774\pi
0.820358 + 0.571850i 0.193774π0.193774\pi
7272 0 0
7373 −274.218 −0.439654 −0.219827 0.975539i 0.570549π-0.570549\pi
−0.219827 + 0.975539i 0.570549π0.570549\pi
7474 0 0
7575 113.029 0.174019
7676 0 0
7777 −180.143 −0.266613
7878 0 0
7979 −218.065 −0.310560 −0.155280 0.987870i 0.549628π-0.549628\pi
−0.155280 + 0.987870i 0.549628π0.549628\pi
8080 0 0
8181 647.540 0.888258
8282 0 0
8383 432.623 0.572127 0.286064 0.958211i 0.407653π-0.407653\pi
0.286064 + 0.958211i 0.407653π0.407653\pi
8484 0 0
8585 261.711 0.333959
8686 0 0
8787 296.495 0.365375
8888 0 0
8989 1019.40 1.21412 0.607058 0.794657i 0.292349π-0.292349\pi
0.607058 + 0.794657i 0.292349π0.292349\pi
9090 0 0
9191 −112.163 −0.129207
9292 0 0
9393 248.456 0.277028
9494 0 0
9595 2422.91 2.61668
9696 0 0
9797 466.343 0.488144 0.244072 0.969757i 0.421517π-0.421517\pi
0.244072 + 0.969757i 0.421517π0.421517\pi
9898 0 0
9999 −668.628 −0.678784
100100 0 0
101101 317.874 0.313165 0.156583 0.987665i 0.449952π-0.449952\pi
0.156583 + 0.987665i 0.449952π0.449952\pi
102102 0 0
103103 659.029 0.630447 0.315224 0.949017i 0.397920π-0.397920\pi
0.315224 + 0.949017i 0.397920π0.397920\pi
104104 0 0
105105 −108.755 −0.101080
106106 0 0
107107 −471.704 −0.426181 −0.213091 0.977032i 0.568353π-0.568353\pi
−0.213091 + 0.977032i 0.568353π0.568353\pi
108108 0 0
109109 −500.205 −0.439550 −0.219775 0.975551i 0.570532π-0.570532\pi
−0.219775 + 0.975551i 0.570532π0.570532\pi
110110 0 0
111111 −103.438 −0.0884492
112112 0 0
113113 −123.992 −0.103223 −0.0516115 0.998667i 0.516436π-0.516436\pi
−0.0516115 + 0.998667i 0.516436π0.516436\pi
114114 0 0
115115 −2345.22 −1.90167
116116 0 0
117117 −416.308 −0.328954
118118 0 0
119119 −119.000 −0.0916698
120120 0 0
121121 −668.722 −0.502421
122122 0 0
123123 −80.8328 −0.0592557
124124 0 0
125125 −200.161 −0.143224
126126 0 0
127127 −1011.83 −0.706974 −0.353487 0.935439i 0.615004π-0.615004\pi
−0.353487 + 0.935439i 0.615004π0.615004\pi
128128 0 0
129129 −314.096 −0.214377
130130 0 0
131131 686.919 0.458140 0.229070 0.973410i 0.426431π-0.426431\pi
0.229070 + 0.973410i 0.426431π0.426431\pi
132132 0 0
133133 −1101.70 −0.718265
134134 0 0
135135 −823.141 −0.524776
136136 0 0
137137 −2091.92 −1.30456 −0.652279 0.757979i 0.726187π-0.726187\pi
−0.652279 + 0.757979i 0.726187π0.726187\pi
138138 0 0
139139 1372.65 0.837605 0.418802 0.908077i 0.362450π-0.362450\pi
0.418802 + 0.908077i 0.362450π0.362450\pi
140140 0 0
141141 453.663 0.270960
142142 0 0
143143 412.354 0.241138
144144 0 0
145145 4522.86 2.59036
146146 0 0
147147 49.4508 0.0277458
148148 0 0
149149 −2399.64 −1.31937 −0.659684 0.751543i 0.729310π-0.729310\pi
−0.659684 + 0.751543i 0.729310π0.729310\pi
150150 0 0
151151 −3143.05 −1.69389 −0.846946 0.531678i 0.821562π-0.821562\pi
−0.846946 + 0.531678i 0.821562π0.821562\pi
152152 0 0
153153 −441.686 −0.233387
154154 0 0
155155 3790.04 1.96402
156156 0 0
157157 −167.866 −0.0853323 −0.0426662 0.999089i 0.513585π-0.513585\pi
−0.0426662 + 0.999089i 0.513585π0.513585\pi
158158 0 0
159159 −523.478 −0.261097
160160 0 0
161161 1066.37 0.521999
162162 0 0
163163 4127.67 1.98346 0.991729 0.128346i 0.0409669π-0.0409669\pi
0.991729 + 0.128346i 0.0409669π0.0409669\pi
164164 0 0
165165 399.825 0.188645
166166 0 0
167167 −1829.02 −0.847507 −0.423753 0.905778i 0.639288π-0.639288\pi
−0.423753 + 0.905778i 0.639288π0.639288\pi
168168 0 0
169169 −1940.26 −0.883139
170170 0 0
171171 −4089.11 −1.82867
172172 0 0
173173 −1930.68 −0.848481 −0.424240 0.905550i 0.639459π-0.639459\pi
−0.424240 + 0.905550i 0.639459π0.639459\pi
174174 0 0
175175 −783.987 −0.338650
176176 0 0
177177 817.710 0.347248
178178 0 0
179179 −1322.13 −0.552069 −0.276034 0.961148i 0.589020π-0.589020\pi
−0.276034 + 0.961148i 0.589020π0.589020\pi
180180 0 0
181181 494.916 0.203242 0.101621 0.994823i 0.467597π-0.467597\pi
0.101621 + 0.994823i 0.467597π0.467597\pi
182182 0 0
183183 102.001 0.0412027
184184 0 0
185185 −1577.88 −0.627069
186186 0 0
187187 437.491 0.171083
188188 0 0
189189 374.283 0.144048
190190 0 0
191191 124.336 0.0471028 0.0235514 0.999723i 0.492503π-0.492503\pi
0.0235514 + 0.999723i 0.492503π0.492503\pi
192192 0 0
193193 2718.16 1.01377 0.506884 0.862014i 0.330797π-0.330797\pi
0.506884 + 0.862014i 0.330797π0.330797\pi
194194 0 0
195195 248.943 0.0914215
196196 0 0
197197 −3498.30 −1.26520 −0.632598 0.774481i 0.718011π-0.718011\pi
−0.632598 + 0.774481i 0.718011π0.718011\pi
198198 0 0
199199 1175.36 0.418688 0.209344 0.977842i 0.432867π-0.432867\pi
0.209344 + 0.977842i 0.432867π0.432867\pi
200200 0 0
201201 −235.436 −0.0826187
202202 0 0
203203 −2056.55 −0.711041
204204 0 0
205205 −1233.06 −0.420099
206206 0 0
207207 3957.99 1.32898
208208 0 0
209209 4050.27 1.34049
210210 0 0
211211 −3063.75 −0.999608 −0.499804 0.866138i 0.666595π-0.666595\pi
−0.499804 + 0.866138i 0.666595π0.666595\pi
212212 0 0
213213 990.601 0.318661
214214 0 0
215215 −4791.34 −1.51984
216216 0 0
217217 −1723.33 −0.539113
218218 0 0
219219 −276.741 −0.0853900
220220 0 0
221221 272.395 0.0829107
222222 0 0
223223 −3458.24 −1.03848 −0.519239 0.854629i 0.673785π-0.673785\pi
−0.519239 + 0.854629i 0.673785π0.673785\pi
224224 0 0
225225 −2909.88 −0.862187
226226 0 0
227227 −1731.27 −0.506205 −0.253102 0.967439i 0.581451π-0.581451\pi
−0.253102 + 0.967439i 0.581451π0.581451\pi
228228 0 0
229229 −4666.12 −1.34649 −0.673245 0.739420i 0.735100π-0.735100\pi
−0.673245 + 0.739420i 0.735100π0.735100\pi
230230 0 0
231231 −181.801 −0.0517819
232232 0 0
233233 6137.20 1.72559 0.862793 0.505558i 0.168713π-0.168713\pi
0.862793 + 0.505558i 0.168713π0.168713\pi
234234 0 0
235235 6920.35 1.92100
236236 0 0
237237 −220.072 −0.0603172
238238 0 0
239239 −1399.51 −0.378774 −0.189387 0.981903i 0.560650π-0.560650\pi
−0.189387 + 0.981903i 0.560650π0.560650\pi
240240 0 0
241241 1160.08 0.310072 0.155036 0.987909i 0.450451π-0.450451\pi
0.155036 + 0.987909i 0.450451π0.450451\pi
242242 0 0
243243 2097.16 0.553633
244244 0 0
245245 754.342 0.196707
246246 0 0
247247 2521.82 0.649634
248248 0 0
249249 436.604 0.111119
250250 0 0
251251 −7093.95 −1.78393 −0.891965 0.452105i 0.850673π-0.850673\pi
−0.891965 + 0.452105i 0.850673π0.850673\pi
252252 0 0
253253 −3920.40 −0.974204
254254 0 0
255255 264.119 0.0648618
256256 0 0
257257 −6646.89 −1.61331 −0.806657 0.591019i 0.798726π-0.798726\pi
−0.806657 + 0.591019i 0.798726π0.798726\pi
258258 0 0
259259 717.462 0.172127
260260 0 0
261261 −7633.17 −1.81027
262262 0 0
263263 7548.59 1.76983 0.884916 0.465751i 0.154216π-0.154216\pi
0.884916 + 0.465751i 0.154216π0.154216\pi
264264 0 0
265265 −7985.33 −1.85108
266266 0 0
267267 1028.78 0.235807
268268 0 0
269269 −7286.99 −1.65166 −0.825828 0.563922i 0.809292π-0.809292\pi
−0.825828 + 0.563922i 0.809292π0.809292\pi
270270 0 0
271271 3457.10 0.774922 0.387461 0.921886i 0.373352π-0.373352\pi
0.387461 + 0.921886i 0.373352π0.373352\pi
272272 0 0
273273 −113.195 −0.0250947
274274 0 0
275275 2882.24 0.632021
276276 0 0
277277 −2279.17 −0.494377 −0.247188 0.968967i 0.579507π-0.579507\pi
−0.247188 + 0.968967i 0.579507π0.579507\pi
278278 0 0
279279 −6396.40 −1.37255
280280 0 0
281281 −5833.37 −1.23840 −0.619199 0.785234i 0.712543π-0.712543\pi
−0.619199 + 0.785234i 0.712543π0.712543\pi
282282 0 0
283283 5449.45 1.14465 0.572325 0.820027i 0.306042π-0.306042\pi
0.572325 + 0.820027i 0.306042π0.306042\pi
284284 0 0
285285 2445.20 0.508214
286286 0 0
287287 560.671 0.115315
288288 0 0
289289 289.000 0.0588235
290290 0 0
291291 470.634 0.0948077
292292 0 0
293293 2639.75 0.526334 0.263167 0.964750i 0.415233π-0.415233\pi
0.263167 + 0.964750i 0.415233π0.415233\pi
294294 0 0
295295 12473.7 2.46185
296296 0 0
297297 −1376.01 −0.268836
298298 0 0
299299 −2440.96 −0.472121
300300 0 0
301301 2178.63 0.417189
302302 0 0
303303 320.799 0.0608232
304304 0 0
305305 1555.96 0.292111
306306 0 0
307307 −6167.27 −1.14653 −0.573265 0.819370i 0.694323π-0.694323\pi
−0.573265 + 0.819370i 0.694323π0.694323\pi
308308 0 0
309309 665.093 0.122446
310310 0 0
311311 6519.01 1.18862 0.594308 0.804238i 0.297426π-0.297426\pi
0.594308 + 0.804238i 0.297426π0.297426\pi
312312 0 0
313313 −10196.8 −1.84140 −0.920702 0.390267i 0.872383π-0.872383\pi
−0.920702 + 0.390267i 0.872383π0.872383\pi
314314 0 0
315315 2799.85 0.500805
316316 0 0
317317 −5456.49 −0.966773 −0.483387 0.875407i 0.660593π-0.660593\pi
−0.483387 + 0.875407i 0.660593π0.660593\pi
318318 0 0
319319 7560.67 1.32701
320320 0 0
321321 −476.045 −0.0827733
322322 0 0
323323 2675.55 0.460903
324324 0 0
325325 1794.57 0.306292
326326 0 0
327327 −504.807 −0.0853697
328328 0 0
329329 −3146.69 −0.527303
330330 0 0
331331 42.4952 0.00705663 0.00352832 0.999994i 0.498877π-0.498877\pi
0.00352832 + 0.999994i 0.498877π0.498877\pi
332332 0 0
333333 2662.96 0.438227
334334 0 0
335335 −3591.43 −0.585733
336336 0 0
337337 −9804.74 −1.58486 −0.792431 0.609962i 0.791185π-0.791185\pi
−0.792431 + 0.609962i 0.791185π0.791185\pi
338338 0 0
339339 −125.133 −0.0200480
340340 0 0
341341 6335.65 1.00614
342342 0 0
343343 −343.000 −0.0539949
344344 0 0
345345 −2366.79 −0.369345
346346 0 0
347347 −6842.22 −1.05853 −0.529265 0.848457i 0.677532π-0.677532\pi
−0.529265 + 0.848457i 0.677532π0.677532\pi
348348 0 0
349349 10649.2 1.63335 0.816674 0.577099i 0.195815π-0.195815\pi
0.816674 + 0.577099i 0.195815π0.195815\pi
350350 0 0
351351 −856.746 −0.130284
352352 0 0
353353 −1594.80 −0.240461 −0.120231 0.992746i 0.538363π-0.538363\pi
−0.120231 + 0.992746i 0.538363π0.538363\pi
354354 0 0
355355 15111.0 2.25918
356356 0 0
357357 −120.095 −0.0178042
358358 0 0
359359 4241.38 0.623542 0.311771 0.950157i 0.399078π-0.399078\pi
0.311771 + 0.950157i 0.399078π0.399078\pi
360360 0 0
361361 17911.1 2.61133
362362 0 0
363363 −674.875 −0.0975806
364364 0 0
365365 −4221.51 −0.605381
366366 0 0
367367 6814.84 0.969296 0.484648 0.874709i 0.338948π-0.338948\pi
0.484648 + 0.874709i 0.338948π0.338948\pi
368368 0 0
369369 2081.01 0.293586
370370 0 0
371371 3630.94 0.508110
372372 0 0
373373 1982.82 0.275245 0.137623 0.990485i 0.456054π-0.456054\pi
0.137623 + 0.990485i 0.456054π0.456054\pi
374374 0 0
375375 −202.003 −0.0278170
376376 0 0
377377 4707.50 0.643100
378378 0 0
379379 −3805.19 −0.515725 −0.257862 0.966182i 0.583018π-0.583018\pi
−0.257862 + 0.966182i 0.583018π0.583018\pi
380380 0 0
381381 −1021.14 −0.137309
382382 0 0
383383 9577.05 1.27771 0.638857 0.769325i 0.279408π-0.279408\pi
0.638857 + 0.769325i 0.279408π0.279408\pi
384384 0 0
385385 −2773.26 −0.367113
386386 0 0
387387 8086.28 1.06214
388388 0 0
389389 10499.8 1.36854 0.684269 0.729229i 0.260121π-0.260121\pi
0.684269 + 0.729229i 0.260121π0.260121\pi
390390 0 0
391391 −2589.76 −0.334961
392392 0 0
393393 693.239 0.0889804
394394 0 0
395395 −3357.06 −0.427625
396396 0 0
397397 6497.20 0.821373 0.410687 0.911777i 0.365289π-0.365289\pi
0.410687 + 0.911777i 0.365289π0.365289\pi
398398 0 0
399399 −1111.83 −0.139502
400400 0 0
401401 6028.66 0.750766 0.375383 0.926870i 0.377511π-0.377511\pi
0.375383 + 0.926870i 0.377511π0.377511\pi
402402 0 0
403403 3944.76 0.487600
404404 0 0
405405 9968.71 1.22308
406406 0 0
407407 −2637.67 −0.321240
408408 0 0
409409 −4053.69 −0.490079 −0.245039 0.969513i 0.578801π-0.578801\pi
−0.245039 + 0.969513i 0.578801π0.578801\pi
410410 0 0
411411 −2111.16 −0.253372
412412 0 0
413413 −5671.79 −0.675764
414414 0 0
415415 6660.12 0.787789
416416 0 0
417417 1385.28 0.162680
418418 0 0
419419 −3771.70 −0.439760 −0.219880 0.975527i 0.570567π-0.570567\pi
−0.219880 + 0.975527i 0.570567π0.570567\pi
420420 0 0
421421 7683.30 0.889457 0.444728 0.895666i 0.353300π-0.353300\pi
0.444728 + 0.895666i 0.353300π0.353300\pi
422422 0 0
423423 −11679.4 −1.34249
424424 0 0
425425 1903.97 0.217308
426426 0 0
427427 −707.495 −0.0801828
428428 0 0
429429 416.148 0.0468341
430430 0 0
431431 −2810.92 −0.314146 −0.157073 0.987587i 0.550206π-0.550206\pi
−0.157073 + 0.987587i 0.550206π0.550206\pi
432432 0 0
433433 −12675.1 −1.40676 −0.703380 0.710814i 0.748327π-0.748327\pi
−0.703380 + 0.710814i 0.748327π0.748327\pi
434434 0 0
435435 4564.47 0.503103
436436 0 0
437437 −23975.9 −2.62453
438438 0 0
439439 3256.34 0.354024 0.177012 0.984209i 0.443357π-0.443357\pi
0.177012 + 0.984209i 0.443357π0.443357\pi
440440 0 0
441441 −1273.09 −0.137468
442442 0 0
443443 −4751.27 −0.509570 −0.254785 0.966998i 0.582005π-0.582005\pi
−0.254785 + 0.966998i 0.582005π0.582005\pi
444444 0 0
445445 15693.4 1.67177
446446 0 0
447447 −2421.72 −0.256249
448448 0 0
449449 −13214.1 −1.38889 −0.694445 0.719546i 0.744350π-0.744350\pi
−0.694445 + 0.719546i 0.744350π0.744350\pi
450450 0 0
451451 −2061.25 −0.215211
452452 0 0
453453 −3171.97 −0.328989
454454 0 0
455455 −1726.71 −0.177911
456456 0 0
457457 8864.12 0.907322 0.453661 0.891174i 0.350118π-0.350118\pi
0.453661 + 0.891174i 0.350118π0.350118\pi
458458 0 0
459459 −908.973 −0.0924340
460460 0 0
461461 −17544.6 −1.77252 −0.886261 0.463186i 0.846706π-0.846706\pi
−0.886261 + 0.463186i 0.846706π0.846706\pi
462462 0 0
463463 −6190.68 −0.621394 −0.310697 0.950509i 0.600562π-0.600562\pi
−0.310697 + 0.950509i 0.600562π0.600562\pi
464464 0 0
465465 3824.91 0.381454
466466 0 0
467467 12097.8 1.19876 0.599381 0.800464i 0.295414π-0.295414\pi
0.599381 + 0.800464i 0.295414π0.295414\pi
468468 0 0
469469 1633.02 0.160781
470470 0 0
471471 −169.411 −0.0165733
472472 0 0
473473 −8009.48 −0.778597
474474 0 0
475475 17626.8 1.70268
476476 0 0
477477 13476.7 1.29362
478478 0 0
479479 −2134.03 −0.203562 −0.101781 0.994807i 0.532454π-0.532454\pi
−0.101781 + 0.994807i 0.532454π0.532454\pi
480480 0 0
481481 −1642.29 −0.155680
482482 0 0
483483 1076.18 0.101383
484484 0 0
485485 7179.23 0.672149
486486 0 0
487487 10374.0 0.965278 0.482639 0.875820i 0.339678π-0.339678\pi
0.482639 + 0.875820i 0.339678π0.339678\pi
488488 0 0
489489 4165.64 0.385229
490490 0 0
491491 −7307.57 −0.671662 −0.335831 0.941922i 0.609017π-0.609017\pi
−0.335831 + 0.941922i 0.609017π0.609017\pi
492492 0 0
493493 4994.47 0.456267
494494 0 0
495495 −10293.4 −0.934650
496496 0 0
497497 −6870.99 −0.620133
498498 0 0
499499 7833.65 0.702770 0.351385 0.936231i 0.385711π-0.385711\pi
0.351385 + 0.936231i 0.385711π0.385711\pi
500500 0 0
501501 −1845.85 −0.164603
502502 0 0
503503 −15051.0 −1.33418 −0.667090 0.744977i 0.732460π-0.732460\pi
−0.667090 + 0.744977i 0.732460π0.732460\pi
504504 0 0
505505 4893.59 0.431212
506506 0 0
507507 −1958.11 −0.171524
508508 0 0
509509 −299.106 −0.0260464 −0.0130232 0.999915i 0.504146π-0.504146\pi
−0.0130232 + 0.999915i 0.504146π0.504146\pi
510510 0 0
511511 1919.52 0.166174
512512 0 0
513513 −8415.23 −0.724253
514514 0 0
515515 10145.6 0.868093
516516 0 0
517517 11568.5 0.984102
518518 0 0
519519 −1948.45 −0.164793
520520 0 0
521521 13064.5 1.09859 0.549297 0.835627i 0.314896π-0.314896\pi
0.549297 + 0.835627i 0.314896π0.314896\pi
522522 0 0
523523 −11621.2 −0.971623 −0.485812 0.874064i 0.661476π-0.661476\pi
−0.485812 + 0.874064i 0.661476π0.661476\pi
524524 0 0
525525 −791.200 −0.0657730
526526 0 0
527527 4185.24 0.345943
528528 0 0
529529 11040.1 0.907380
530530 0 0
531531 −21051.7 −1.72046
532532 0 0
533533 −1283.39 −0.104296
534534 0 0
535535 −7261.77 −0.586829
536536 0 0
537537 −1334.29 −0.107223
538538 0 0
539539 1261.00 0.100770
540540 0 0
541541 −552.394 −0.0438988 −0.0219494 0.999759i 0.506987π-0.506987\pi
−0.0219494 + 0.999759i 0.506987π0.506987\pi
542542 0 0
543543 499.470 0.0394739
544544 0 0
545545 −7700.53 −0.605237
546546 0 0
547547 3714.09 0.290316 0.145158 0.989408i 0.453631π-0.453631\pi
0.145158 + 0.989408i 0.453631π0.453631\pi
548548 0 0
549549 −2625.97 −0.204141
550550 0 0
551551 46238.6 3.57501
552552 0 0
553553 1526.46 0.117381
554554 0 0
555555 −1592.39 −0.121790
556556 0 0
557557 9082.21 0.690890 0.345445 0.938439i 0.387728π-0.387728\pi
0.345445 + 0.938439i 0.387728π0.387728\pi
558558 0 0
559559 −4986.94 −0.377326
560560 0 0
561561 441.516 0.0332279
562562 0 0
563563 13260.3 0.992640 0.496320 0.868140i 0.334684π-0.334684\pi
0.496320 + 0.868140i 0.334684π0.334684\pi
564564 0 0
565565 −1908.83 −0.142133
566566 0 0
567567 −4532.78 −0.335730
568568 0 0
569569 16130.1 1.18842 0.594208 0.804312i 0.297466π-0.297466\pi
0.594208 + 0.804312i 0.297466π0.297466\pi
570570 0 0
571571 −10919.8 −0.800316 −0.400158 0.916446i 0.631045π-0.631045\pi
−0.400158 + 0.916446i 0.631045π0.631045\pi
572572 0 0
573573 125.480 0.00914835
574574 0 0
575575 −17061.7 −1.23743
576576 0 0
577577 −13205.7 −0.952790 −0.476395 0.879231i 0.658057π-0.658057\pi
−0.476395 + 0.879231i 0.658057π0.658057\pi
578578 0 0
579579 2743.17 0.196895
580580 0 0
581581 −3028.36 −0.216244
582582 0 0
583583 −13348.8 −0.948283
584584 0 0
585585 −6408.95 −0.452953
586586 0 0
587587 11464.8 0.806136 0.403068 0.915170i 0.367944π-0.367944\pi
0.403068 + 0.915170i 0.367944π0.367944\pi
588588 0 0
589589 38746.7 2.71058
590590 0 0
591591 −3530.49 −0.245727
592592 0 0
593593 10524.3 0.728807 0.364404 0.931241i 0.381273π-0.381273\pi
0.364404 + 0.931241i 0.381273π0.381273\pi
594594 0 0
595595 −1831.97 −0.126225
596596 0 0
597597 1186.17 0.0813179
598598 0 0
599599 −21190.3 −1.44543 −0.722715 0.691146i 0.757106π-0.757106\pi
−0.722715 + 0.691146i 0.757106π0.757106\pi
600600 0 0
601601 −17924.2 −1.21654 −0.608272 0.793729i 0.708137π-0.708137\pi
−0.608272 + 0.793729i 0.708137π0.708137\pi
602602 0 0
603603 6061.21 0.409339
604604 0 0
605605 −10294.8 −0.691807
606606 0 0
607607 11521.8 0.770438 0.385219 0.922825i 0.374126π-0.374126\pi
0.385219 + 0.922825i 0.374126π0.374126\pi
608608 0 0
609609 −2075.47 −0.138099
610610 0 0
611611 7202.87 0.476918
612612 0 0
613613 8052.51 0.530567 0.265284 0.964170i 0.414534π-0.414534\pi
0.265284 + 0.964170i 0.414534π0.414534\pi
614614 0 0
615615 −1244.40 −0.0815920
616616 0 0
617617 −21023.6 −1.37176 −0.685882 0.727713i 0.740583π-0.740583\pi
−0.685882 + 0.727713i 0.740583π0.740583\pi
618618 0 0
619619 −29039.3 −1.88560 −0.942802 0.333354i 0.891819π-0.891819\pi
−0.942802 + 0.333354i 0.891819π0.891819\pi
620620 0 0
621621 8145.40 0.526350
622622 0 0
623623 −7135.81 −0.458893
624624 0 0
625625 −17081.2 −1.09320
626626 0 0
627627 4087.54 0.260352
628628 0 0
629629 −1742.41 −0.110452
630630 0 0
631631 −8671.86 −0.547102 −0.273551 0.961857i 0.588198π-0.588198\pi
−0.273551 + 0.961857i 0.588198π0.588198\pi
632632 0 0
633633 −3091.94 −0.194145
634634 0 0
635635 −15576.9 −0.973467
636636 0 0
637637 785.138 0.0488356
638638 0 0
639639 −25502.7 −1.57883
640640 0 0
641641 −17252.9 −1.06310 −0.531551 0.847026i 0.678391π-0.678391\pi
−0.531551 + 0.847026i 0.678391π0.678391\pi
642642 0 0
643643 16000.1 0.981309 0.490655 0.871354i 0.336758π-0.336758\pi
0.490655 + 0.871354i 0.336758π0.336758\pi
644644 0 0
645645 −4835.42 −0.295185
646646 0 0
647647 −4349.51 −0.264292 −0.132146 0.991230i 0.542187π-0.542187\pi
−0.132146 + 0.991230i 0.542187π0.542187\pi
648648 0 0
649649 20851.7 1.26117
650650 0 0
651651 −1739.19 −0.104707
652652 0 0
653653 15497.9 0.928761 0.464380 0.885636i 0.346277π-0.346277\pi
0.464380 + 0.885636i 0.346277π0.346277\pi
654654 0 0
655655 10574.9 0.630835
656656 0 0
657657 7124.59 0.423070
658658 0 0
659659 1040.36 0.0614970 0.0307485 0.999527i 0.490211π-0.490211\pi
0.0307485 + 0.999527i 0.490211π0.490211\pi
660660 0 0
661661 10737.2 0.631814 0.315907 0.948790i 0.397691π-0.397691\pi
0.315907 + 0.948790i 0.397691π0.397691\pi
662662 0 0
663663 274.901 0.0161030
664664 0 0
665665 −16960.3 −0.989013
666666 0 0
667667 −44756.0 −2.59814
668668 0 0
669669 −3490.05 −0.201694
670670 0 0
671671 2601.03 0.149645
672672 0 0
673673 21103.1 1.20871 0.604357 0.796713i 0.293430π-0.293430\pi
0.604357 + 0.796713i 0.293430π0.293430\pi
674674 0 0
675675 −5988.43 −0.341473
676676 0 0
677677 −8460.36 −0.480292 −0.240146 0.970737i 0.577195π-0.577195\pi
−0.240146 + 0.970737i 0.577195π0.577195\pi
678678 0 0
679679 −3264.40 −0.184501
680680 0 0
681681 −1747.20 −0.0983155
682682 0 0
683683 −8550.65 −0.479036 −0.239518 0.970892i 0.576989π-0.576989\pi
−0.239518 + 0.970892i 0.576989π0.576989\pi
684684 0 0
685685 −32204.5 −1.79631
686686 0 0
687687 −4709.05 −0.261516
688688 0 0
689689 −8311.33 −0.459560
690690 0 0
691691 9246.17 0.509032 0.254516 0.967069i 0.418084π-0.418084\pi
0.254516 + 0.967069i 0.418084π0.418084\pi
692692 0 0
693693 4680.40 0.256556
694694 0 0
695695 21131.7 1.15334
696696 0 0
697697 −1361.63 −0.0739963
698698 0 0
699699 6193.67 0.335145
700700 0 0
701701 1138.54 0.0613438 0.0306719 0.999530i 0.490235π-0.490235\pi
0.0306719 + 0.999530i 0.490235π0.490235\pi
702702 0 0
703703 −16131.1 −0.865430
704704 0 0
705705 6984.03 0.373097
706706 0 0
707707 −2225.12 −0.118365
708708 0 0
709709 −7742.45 −0.410118 −0.205059 0.978750i 0.565739π-0.565739\pi
−0.205059 + 0.978750i 0.565739π0.565739\pi
710710 0 0
711711 5665.66 0.298845
712712 0 0
713713 −37504.3 −1.96991
714714 0 0
715715 6348.08 0.332035
716716 0 0
717717 −1412.39 −0.0735657
718718 0 0
719719 −33796.7 −1.75300 −0.876498 0.481406i 0.840126π-0.840126\pi
−0.876498 + 0.481406i 0.840126π0.840126\pi
720720 0 0
721721 −4613.21 −0.238287
722722 0 0
723723 1170.75 0.0602224
724724 0 0
725725 32904.2 1.68556
726726 0 0
727727 27370.1 1.39629 0.698144 0.715958i 0.254010π-0.254010\pi
0.698144 + 0.715958i 0.254010π0.254010\pi
728728 0 0
729729 −15367.1 −0.780731
730730 0 0
731731 −5290.95 −0.267706
732732 0 0
733733 20572.5 1.03665 0.518324 0.855184i 0.326556π-0.326556\pi
0.518324 + 0.855184i 0.326556π0.326556\pi
734734 0 0
735735 761.283 0.0382046
736736 0 0
737737 −6003.64 −0.300064
738738 0 0
739739 7596.57 0.378138 0.189069 0.981964i 0.439453π-0.439453\pi
0.189069 + 0.981964i 0.439453π0.439453\pi
740740 0 0
741741 2545.02 0.126172
742742 0 0
743743 −10034.0 −0.495441 −0.247721 0.968831i 0.579682π-0.579682\pi
−0.247721 + 0.968831i 0.579682π0.579682\pi
744744 0 0
745745 −36941.8 −1.81670
746746 0 0
747747 −11240.2 −0.550546
748748 0 0
749749 3301.93 0.161081
750750 0 0
751751 29250.6 1.42126 0.710632 0.703564i 0.248409π-0.248409\pi
0.710632 + 0.703564i 0.248409π0.248409\pi
752752 0 0
753753 −7159.22 −0.346476
754754 0 0
755755 −48386.5 −2.33240
756756 0 0
757757 −40135.6 −1.92702 −0.963509 0.267676i 0.913744π-0.913744\pi
−0.963509 + 0.267676i 0.913744π0.913744\pi
758758 0 0
759759 −3956.47 −0.189211
760760 0 0
761761 5811.28 0.276818 0.138409 0.990375i 0.455801π-0.455801\pi
0.138409 + 0.990375i 0.455801π0.455801\pi
762762 0 0
763763 3501.43 0.166134
764764 0 0
765765 −6799.64 −0.321361
766766 0 0
767767 12982.9 0.611194
768768 0 0
769769 32588.3 1.52817 0.764086 0.645114i 0.223190π-0.223190\pi
0.764086 + 0.645114i 0.223190π0.223190\pi
770770 0 0
771771 −6708.05 −0.313339
772772 0 0
773773 34681.7 1.61373 0.806865 0.590737i 0.201163π-0.201163\pi
0.806865 + 0.590737i 0.201163π0.201163\pi
774774 0 0
775775 27572.9 1.27799
776776 0 0
777777 724.063 0.0334307
778778 0 0
779779 −12605.9 −0.579786
780780 0 0
781781 25260.5 1.15735
782782 0 0
783783 −15708.8 −0.716968
784784 0 0
785785 −2584.26 −0.117498
786786 0 0
787787 −14570.5 −0.659953 −0.329976 0.943989i 0.607041π-0.607041\pi
−0.329976 + 0.943989i 0.607041π0.607041\pi
788788 0 0
789789 7618.04 0.343738
790790 0 0
791791 867.944 0.0390146
792792 0 0
793793 1619.48 0.0725212
794794 0 0
795795 −8058.81 −0.359518
796796 0 0
797797 20881.3 0.928047 0.464023 0.885823i 0.346405π-0.346405\pi
0.464023 + 0.885823i 0.346405π0.346405\pi
798798 0 0
799799 7641.96 0.338364
800800 0 0
801801 −26485.6 −1.16832
802802 0 0
803803 −7056.93 −0.310129
804804 0 0
805805 16416.5 0.718765
806806 0 0
807807 −7354.03 −0.320786
808808 0 0
809809 −5971.77 −0.259526 −0.129763 0.991545i 0.541422π-0.541422\pi
−0.129763 + 0.991545i 0.541422π0.541422\pi
810810 0 0
811811 −41435.5 −1.79408 −0.897039 0.441951i 0.854286π-0.854286\pi
−0.897039 + 0.441951i 0.854286π0.854286\pi
812812 0 0
813813 3488.91 0.150506
814814 0 0
815815 63544.4 2.73112
816816 0 0
817817 −48983.4 −2.09756
818818 0 0
819819 2914.15 0.124333
820820 0 0
821821 1088.07 0.0462531 0.0231266 0.999733i 0.492638π-0.492638\pi
0.0231266 + 0.999733i 0.492638π0.492638\pi
822822 0 0
823823 14637.7 0.619973 0.309987 0.950741i 0.399675π-0.399675\pi
0.309987 + 0.950741i 0.399675π0.399675\pi
824824 0 0
825825 2908.76 0.122752
826826 0 0
827827 3434.72 0.144422 0.0722110 0.997389i 0.476994π-0.476994\pi
0.0722110 + 0.997389i 0.476994π0.476994\pi
828828 0 0
829829 34138.8 1.43027 0.715133 0.698988i 0.246366π-0.246366\pi
0.715133 + 0.698988i 0.246366π0.246366\pi
830830 0 0
831831 −2300.14 −0.0960182
832832 0 0
833833 833.000 0.0346479
834834 0 0
835835 −28157.3 −1.16697
836836 0 0
837837 −13163.6 −0.543607
838838 0 0
839839 −4742.97 −0.195168 −0.0975838 0.995227i 0.531111π-0.531111\pi
−0.0975838 + 0.995227i 0.531111π0.531111\pi
840840 0 0
841841 61924.9 2.53905
842842 0 0
843843 −5887.05 −0.240523
844844 0 0
845845 −29869.7 −1.21604
846846 0 0
847847 4681.06 0.189897
848848 0 0
849849 5499.59 0.222315
850850 0 0
851851 15613.9 0.628951
852852 0 0
853853 10776.5 0.432569 0.216284 0.976330i 0.430606π-0.430606\pi
0.216284 + 0.976330i 0.430606π0.430606\pi
854854 0 0
855855 −62950.8 −2.51798
856856 0 0
857857 901.774 0.0359440 0.0179720 0.999838i 0.494279π-0.494279\pi
0.0179720 + 0.999838i 0.494279π0.494279\pi
858858 0 0
859859 2052.46 0.0815240 0.0407620 0.999169i 0.487021π-0.487021\pi
0.0407620 + 0.999169i 0.487021π0.487021\pi
860860 0 0
861861 565.830 0.0223965
862862 0 0
863863 7560.61 0.298223 0.149111 0.988820i 0.452359π-0.452359\pi
0.149111 + 0.988820i 0.452359π0.452359\pi
864864 0 0
865865 −29722.4 −1.16831
866866 0 0
867867 291.659 0.0114248
868868 0 0
869869 −5611.85 −0.219067
870870 0 0
871871 −3738.05 −0.145418
872872 0 0
873873 −12116.3 −0.469730
874874 0 0
875875 1401.13 0.0541334
876876 0 0
877877 26675.1 1.02709 0.513543 0.858064i 0.328333π-0.328333\pi
0.513543 + 0.858064i 0.328333π0.328333\pi
878878 0 0
879879 2664.04 0.102225
880880 0 0
881881 13711.6 0.524354 0.262177 0.965020i 0.415560π-0.415560\pi
0.262177 + 0.965020i 0.415560π0.415560\pi
882882 0 0
883883 29386.2 1.11996 0.559980 0.828506i 0.310809π-0.310809\pi
0.559980 + 0.828506i 0.310809π0.310809\pi
884884 0 0
885885 12588.4 0.478142
886886 0 0
887887 15162.6 0.573969 0.286985 0.957935i 0.407347π-0.407347\pi
0.286985 + 0.957935i 0.407347π0.407347\pi
888888 0 0
889889 7082.84 0.267211
890890 0 0
891891 16664.3 0.626571
892892 0 0
893893 70748.9 2.65120
894894 0 0
895895 −20353.8 −0.760170
896896 0 0
897897 −2463.42 −0.0916958
898898 0 0
899899 72328.8 2.68332
900900 0 0
901901 −8817.99 −0.326049
902902 0 0
903903 2198.67 0.0810268
904904 0 0
905905 7619.11 0.279854
906906 0 0
907907 30643.4 1.12183 0.560914 0.827874i 0.310450π-0.310450\pi
0.560914 + 0.827874i 0.310450π0.310450\pi
908908 0 0
909909 −8258.86 −0.301352
910910 0 0
911911 −28467.4 −1.03531 −0.517655 0.855589i 0.673195π-0.673195\pi
−0.517655 + 0.855589i 0.673195π0.673195\pi
912912 0 0
913913 11133.5 0.403574
914914 0 0
915915 1570.27 0.0567340
916916 0 0
917917 −4808.43 −0.173161
918918 0 0
919919 15469.7 0.555275 0.277637 0.960686i 0.410449π-0.410449\pi
0.277637 + 0.960686i 0.410449π0.410449\pi
920920 0 0
921921 −6224.01 −0.222680
922922 0 0
923923 15727.9 0.560878
924924 0 0
925925 −11479.2 −0.408036
926926 0 0
927927 −17122.6 −0.606666
928928 0 0
929929 24954.0 0.881286 0.440643 0.897682i 0.354750π-0.354750\pi
0.440643 + 0.897682i 0.354750π0.354750\pi
930930 0 0
931931 7711.88 0.271479
932932 0 0
933933 6578.99 0.230854
934934 0 0
935935 6735.06 0.235572
936936 0 0
937937 53097.7 1.85125 0.925627 0.378438i 0.123539π-0.123539\pi
0.925627 + 0.378438i 0.123539π0.123539\pi
938938 0 0
939939 −10290.7 −0.357639
940940 0 0
941941 −31108.6 −1.07770 −0.538848 0.842403i 0.681140π-0.681140\pi
−0.538848 + 0.842403i 0.681140π0.681140\pi
942942 0 0
943943 12201.7 0.421360
944944 0 0
945945 5761.99 0.198347
946946 0 0
947947 −37184.9 −1.27597 −0.637987 0.770047i 0.720233π-0.720233\pi
−0.637987 + 0.770047i 0.720233π0.720233\pi
948948 0 0
949949 −4393.85 −0.150296
950950 0 0
951951 −5506.70 −0.187767
952952 0 0
953953 −29917.1 −1.01690 −0.508452 0.861090i 0.669782π-0.669782\pi
−0.508452 + 0.861090i 0.669782π0.669782\pi
954954 0 0
955955 1914.12 0.0648581
956956 0 0
957957 7630.24 0.257733
958958 0 0
959959 14643.4 0.493077
960960 0 0
961961 30818.7 1.03450
962962 0 0
963963 12255.6 0.410105
964964 0 0
965965 41845.3 1.39591
966966 0 0
967967 −49683.9 −1.65225 −0.826126 0.563485i 0.809460π-0.809460\pi
−0.826126 + 0.563485i 0.809460π0.809460\pi
968968 0 0
969969 2700.17 0.0895169
970970 0 0
971971 −38044.4 −1.25737 −0.628684 0.777661i 0.716406π-0.716406\pi
−0.628684 + 0.777661i 0.716406π0.716406\pi
972972 0 0
973973 −9608.58 −0.316585
974974 0 0
975975 1811.08 0.0594883
976976 0 0
977977 −45796.0 −1.49964 −0.749818 0.661644i 0.769859π-0.769859\pi
−0.749818 + 0.661644i 0.769859π0.769859\pi
978978 0 0
979979 26234.1 0.856429
980980 0 0
981981 12996.1 0.422969
982982 0 0
983983 −10.6433 −0.000345340 0 −0.000172670 1.00000i 0.500055π-0.500055\pi
−0.000172670 1.00000i 0.500055π0.500055\pi
984984 0 0
985985 −53855.4 −1.74211
986986 0 0
987987 −3175.64 −0.102413
988988 0 0
989989 47412.7 1.52441
990990 0 0
991991 −6252.30 −0.200415 −0.100207 0.994967i 0.531951π-0.531951\pi
−0.100207 + 0.994967i 0.531951π0.531951\pi
992992 0 0
993993 42.8862 0.00137055
994994 0 0
995995 18094.3 0.576511
996996 0 0
997997 −11851.0 −0.376453 −0.188227 0.982126i 0.560274π-0.560274\pi
−0.188227 + 0.982126i 0.560274π0.560274\pi
998998 0 0
999999 5480.28 0.173562
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 476.4.a.b.1.4 6
4.3 odd 2 1904.4.a.m.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
476.4.a.b.1.4 6 1.1 even 1 trivial
1904.4.a.m.1.3 6 4.3 odd 2