Properties

Label 312.4.a.d.1.1
Level 312312
Weight 44
Character 312.1
Self dual yes
Analytic conductor 18.40918.409
Analytic rank 11
Dimension 22
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] = [312,4,Mod(1,312)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(312, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("312.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 312=23313 312 = 2^{3} \cdot 3 \cdot 13
Weight: k k == 4 4
Character orbit: [χ][\chi] == 312.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: 18.408595921818.4085959218
Analytic rank: 11
Dimension: 22
Coefficient field: Q(17)\Q(\sqrt{17})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x4 x^{2} - x - 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 2.561552.56155 of defining polynomial
Character χ\chi == 312.1

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+3.00000q313.1231q5+15.6155q7+9.00000q955.7235q11+13.0000q1339.3693q15+23.4773q1725.6458q19+46.8466q21189.477q23+47.2159q25+27.0000q27236.739q29+47.0625q31167.170q33204.924q35154.648q37+39.0000q3934.6610q41398.833q43118.108q45+582.773q4799.1553q49+70.4318q51361.015q53+731.265q5576.9375q57+396.985q59211.322q61+140.540q63170.600q65+85.8277q67568.432q69651.602q71+927.329q73+141.648q75870.152q771117.98q79+81.0000q81+391.629q83308.095q85710.216q87745.960q89+203.002q91+141.187q93+336.553q95173.231q97501.511q99+O(q100)q+3.00000 q^{3} -13.1231 q^{5} +15.6155 q^{7} +9.00000 q^{9} -55.7235 q^{11} +13.0000 q^{13} -39.3693 q^{15} +23.4773 q^{17} -25.6458 q^{19} +46.8466 q^{21} -189.477 q^{23} +47.2159 q^{25} +27.0000 q^{27} -236.739 q^{29} +47.0625 q^{31} -167.170 q^{33} -204.924 q^{35} -154.648 q^{37} +39.0000 q^{39} -34.6610 q^{41} -398.833 q^{43} -118.108 q^{45} +582.773 q^{47} -99.1553 q^{49} +70.4318 q^{51} -361.015 q^{53} +731.265 q^{55} -76.9375 q^{57} +396.985 q^{59} -211.322 q^{61} +140.540 q^{63} -170.600 q^{65} +85.8277 q^{67} -568.432 q^{69} -651.602 q^{71} +927.329 q^{73} +141.648 q^{75} -870.152 q^{77} -1117.98 q^{79} +81.0000 q^{81} +391.629 q^{83} -308.095 q^{85} -710.216 q^{87} -745.960 q^{89} +203.002 q^{91} +141.187 q^{93} +336.553 q^{95} -173.231 q^{97} -501.511 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+6q318q510q7+18q9+4q11+26q1354q1552q17142q1930q21280q2354q25+54q27424q29178q31+12q3380q35++36q99+O(q100) 2 q + 6 q^{3} - 18 q^{5} - 10 q^{7} + 18 q^{9} + 4 q^{11} + 26 q^{13} - 54 q^{15} - 52 q^{17} - 142 q^{19} - 30 q^{21} - 280 q^{23} - 54 q^{25} + 54 q^{27} - 424 q^{29} - 178 q^{31} + 12 q^{33} - 80 q^{35}+ \cdots + 36 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 3.00000 0.577350
44 0 0
55 −13.1231 −1.17377 −0.586883 0.809672i 0.699645π-0.699645\pi
−0.586883 + 0.809672i 0.699645π0.699645\pi
66 0 0
77 15.6155 0.843159 0.421580 0.906791i 0.361476π-0.361476\pi
0.421580 + 0.906791i 0.361476π0.361476\pi
88 0 0
99 9.00000 0.333333
1010 0 0
1111 −55.7235 −1.52739 −0.763694 0.645579i 0.776616π-0.776616\pi
−0.763694 + 0.645579i 0.776616π0.776616\pi
1212 0 0
1313 13.0000 0.277350
1414 0 0
1515 −39.3693 −0.677674
1616 0 0
1717 23.4773 0.334946 0.167473 0.985877i 0.446439π-0.446439\pi
0.167473 + 0.985877i 0.446439π0.446439\pi
1818 0 0
1919 −25.6458 −0.309661 −0.154830 0.987941i 0.549483π-0.549483\pi
−0.154830 + 0.987941i 0.549483π0.549483\pi
2020 0 0
2121 46.8466 0.486798
2222 0 0
2323 −189.477 −1.71777 −0.858886 0.512167i 0.828843π-0.828843\pi
−0.858886 + 0.512167i 0.828843π0.828843\pi
2424 0 0
2525 47.2159 0.377727
2626 0 0
2727 27.0000 0.192450
2828 0 0
2929 −236.739 −1.51591 −0.757953 0.652309i 0.773800π-0.773800\pi
−0.757953 + 0.652309i 0.773800π0.773800\pi
3030 0 0
3131 47.0625 0.272667 0.136333 0.990663i 0.456468π-0.456468\pi
0.136333 + 0.990663i 0.456468π0.456468\pi
3232 0 0
3333 −167.170 −0.881838
3434 0 0
3535 −204.924 −0.989672
3636 0 0
3737 −154.648 −0.687133 −0.343567 0.939128i 0.611635π-0.611635\pi
−0.343567 + 0.939128i 0.611635π0.611635\pi
3838 0 0
3939 39.0000 0.160128
4040 0 0
4141 −34.6610 −0.132028 −0.0660139 0.997819i 0.521028π-0.521028\pi
−0.0660139 + 0.997819i 0.521028π0.521028\pi
4242 0 0
4343 −398.833 −1.41445 −0.707227 0.706987i 0.750054π-0.750054\pi
−0.707227 + 0.706987i 0.750054π0.750054\pi
4444 0 0
4545 −118.108 −0.391255
4646 0 0
4747 582.773 1.80864 0.904321 0.426854i 0.140378π-0.140378\pi
0.904321 + 0.426854i 0.140378π0.140378\pi
4848 0 0
4949 −99.1553 −0.289082
5050 0 0
5151 70.4318 0.193381
5252 0 0
5353 −361.015 −0.935646 −0.467823 0.883822i 0.654962π-0.654962\pi
−0.467823 + 0.883822i 0.654962π0.654962\pi
5454 0 0
5555 731.265 1.79280
5656 0 0
5757 −76.9375 −0.178783
5858 0 0
5959 396.985 0.875983 0.437992 0.898979i 0.355690π-0.355690\pi
0.437992 + 0.898979i 0.355690π0.355690\pi
6060 0 0
6161 −211.322 −0.443558 −0.221779 0.975097i 0.571186π-0.571186\pi
−0.221779 + 0.975097i 0.571186π0.571186\pi
6262 0 0
6363 140.540 0.281053
6464 0 0
6565 −170.600 −0.325544
6666 0 0
6767 85.8277 0.156500 0.0782502 0.996934i 0.475067π-0.475067\pi
0.0782502 + 0.996934i 0.475067π0.475067\pi
6868 0 0
6969 −568.432 −0.991756
7070 0 0
7171 −651.602 −1.08917 −0.544584 0.838706i 0.683313π-0.683313\pi
−0.544584 + 0.838706i 0.683313π0.683313\pi
7272 0 0
7373 927.329 1.48679 0.743395 0.668852i 0.233214π-0.233214\pi
0.743395 + 0.668852i 0.233214π0.233214\pi
7474 0 0
7575 141.648 0.218081
7676 0 0
7777 −870.152 −1.28783
7878 0 0
7979 −1117.98 −1.59218 −0.796090 0.605178i 0.793102π-0.793102\pi
−0.796090 + 0.605178i 0.793102π0.793102\pi
8080 0 0
8181 81.0000 0.111111
8282 0 0
8383 391.629 0.517914 0.258957 0.965889i 0.416621π-0.416621\pi
0.258957 + 0.965889i 0.416621π0.416621\pi
8484 0 0
8585 −308.095 −0.393148
8686 0 0
8787 −710.216 −0.875208
8888 0 0
8989 −745.960 −0.888445 −0.444223 0.895916i 0.646520π-0.646520\pi
−0.444223 + 0.895916i 0.646520π0.646520\pi
9090 0 0
9191 203.002 0.233850
9292 0 0
9393 141.187 0.157424
9494 0 0
9595 336.553 0.363470
9696 0 0
9797 −173.231 −0.181329 −0.0906647 0.995881i 0.528899π-0.528899\pi
−0.0906647 + 0.995881i 0.528899π0.528899\pi
9898 0 0
9999 −501.511 −0.509129
100100 0 0
101101 −1263.45 −1.24473 −0.622367 0.782726i 0.713829π-0.713829\pi
−0.622367 + 0.782726i 0.713829π0.713829\pi
102102 0 0
103103 874.401 0.836479 0.418240 0.908337i 0.362647π-0.362647\pi
0.418240 + 0.908337i 0.362647π0.362647\pi
104104 0 0
105105 −614.773 −0.571387
106106 0 0
107107 1591.89 1.43826 0.719128 0.694877i 0.244541π-0.244541\pi
0.719128 + 0.694877i 0.244541π0.244541\pi
108108 0 0
109109 371.788 0.326705 0.163352 0.986568i 0.447769π-0.447769\pi
0.163352 + 0.986568i 0.447769π0.447769\pi
110110 0 0
111111 −463.943 −0.396716
112112 0 0
113113 1173.98 0.977335 0.488667 0.872470i 0.337483π-0.337483\pi
0.488667 + 0.872470i 0.337483π0.337483\pi
114114 0 0
115115 2486.53 2.01626
116116 0 0
117117 117.000 0.0924500
118118 0 0
119119 366.610 0.282412
120120 0 0
121121 1774.11 1.33291
122122 0 0
123123 −103.983 −0.0762263
124124 0 0
125125 1020.77 0.730403
126126 0 0
127127 739.360 0.516595 0.258298 0.966065i 0.416839π-0.416839\pi
0.258298 + 0.966065i 0.416839π0.416839\pi
128128 0 0
129129 −1196.50 −0.816635
130130 0 0
131131 2131.58 1.42166 0.710829 0.703365i 0.248320π-0.248320\pi
0.710829 + 0.703365i 0.248320π0.248320\pi
132132 0 0
133133 −400.473 −0.261094
134134 0 0
135135 −354.324 −0.225891
136136 0 0
137137 −256.934 −0.160229 −0.0801144 0.996786i 0.525529π-0.525529\pi
−0.0801144 + 0.996786i 0.525529π0.525529\pi
138138 0 0
139139 437.443 0.266931 0.133466 0.991053i 0.457389π-0.457389\pi
0.133466 + 0.991053i 0.457389π0.457389\pi
140140 0 0
141141 1748.32 1.04422
142142 0 0
143143 −724.405 −0.423621
144144 0 0
145145 3106.75 1.77932
146146 0 0
147147 −297.466 −0.166902
148148 0 0
149149 −3406.65 −1.87304 −0.936522 0.350609i 0.885975π-0.885975\pi
−0.936522 + 0.350609i 0.885975π0.885975\pi
150150 0 0
151151 3275.77 1.76542 0.882710 0.469918i 0.155717π-0.155717\pi
0.882710 + 0.469918i 0.155717π0.155717\pi
152152 0 0
153153 211.295 0.111649
154154 0 0
155155 −617.606 −0.320047
156156 0 0
157157 1074.34 0.546128 0.273064 0.961996i 0.411963π-0.411963\pi
0.273064 + 0.961996i 0.411963π0.411963\pi
158158 0 0
159159 −1083.05 −0.540196
160160 0 0
161161 −2958.79 −1.44835
162162 0 0
163163 2031.49 0.976186 0.488093 0.872792i 0.337693π-0.337693\pi
0.488093 + 0.872792i 0.337693π0.337693\pi
164164 0 0
165165 2193.80 1.03507
166166 0 0
167167 299.697 0.138870 0.0694349 0.997586i 0.477880π-0.477880\pi
0.0694349 + 0.997586i 0.477880π0.477880\pi
168168 0 0
169169 169.000 0.0769231
170170 0 0
171171 −230.813 −0.103220
172172 0 0
173173 2371.16 1.04206 0.521028 0.853540i 0.325549π-0.325549\pi
0.521028 + 0.853540i 0.325549π0.325549\pi
174174 0 0
175175 737.301 0.318484
176176 0 0
177177 1190.95 0.505749
178178 0 0
179179 −249.613 −0.104229 −0.0521145 0.998641i 0.516596π-0.516596\pi
−0.0521145 + 0.998641i 0.516596π0.516596\pi
180180 0 0
181181 −3151.45 −1.29417 −0.647087 0.762416i 0.724013π-0.724013\pi
−0.647087 + 0.762416i 0.724013π0.724013\pi
182182 0 0
183183 −633.966 −0.256088
184184 0 0
185185 2029.46 0.806534
186186 0 0
187187 −1308.24 −0.511592
188188 0 0
189189 421.619 0.162266
190190 0 0
191191 −4739.45 −1.79547 −0.897735 0.440535i 0.854789π-0.854789\pi
−0.897735 + 0.440535i 0.854789π0.854789\pi
192192 0 0
193193 636.818 0.237509 0.118754 0.992924i 0.462110π-0.462110\pi
0.118754 + 0.992924i 0.462110π0.462110\pi
194194 0 0
195195 −511.801 −0.187953
196196 0 0
197197 −3001.13 −1.08539 −0.542695 0.839930i 0.682596π-0.682596\pi
−0.542695 + 0.839930i 0.682596π0.682596\pi
198198 0 0
199199 −648.958 −0.231173 −0.115587 0.993297i 0.536875π-0.536875\pi
−0.115587 + 0.993297i 0.536875π0.536875\pi
200200 0 0
201201 257.483 0.0903555
202202 0 0
203203 −3696.80 −1.27815
204204 0 0
205205 454.860 0.154970
206206 0 0
207207 −1705.30 −0.572590
208208 0 0
209209 1429.08 0.472972
210210 0 0
211211 −240.114 −0.0783418 −0.0391709 0.999233i 0.512472π-0.512472\pi
−0.0391709 + 0.999233i 0.512472π0.512472\pi
212212 0 0
213213 −1954.81 −0.628832
214214 0 0
215215 5233.93 1.66024
216216 0 0
217217 734.906 0.229902
218218 0 0
219219 2781.99 0.858399
220220 0 0
221221 305.204 0.0928972
222222 0 0
223223 −1104.37 −0.331633 −0.165816 0.986157i 0.553026π-0.553026\pi
−0.165816 + 0.986157i 0.553026π0.553026\pi
224224 0 0
225225 424.943 0.125909
226226 0 0
227227 497.034 0.145327 0.0726636 0.997357i 0.476850π-0.476850\pi
0.0726636 + 0.997357i 0.476850π0.476850\pi
228228 0 0
229229 2879.05 0.830800 0.415400 0.909639i 0.363642π-0.363642\pi
0.415400 + 0.909639i 0.363642π0.363642\pi
230230 0 0
231231 −2610.45 −0.743529
232232 0 0
233233 −3846.91 −1.08163 −0.540814 0.841142i 0.681884π-0.681884\pi
−0.540814 + 0.841142i 0.681884π0.681884\pi
234234 0 0
235235 −7647.79 −2.12292
236236 0 0
237237 −3353.93 −0.919246
238238 0 0
239239 2903.25 0.785755 0.392877 0.919591i 0.371480π-0.371480\pi
0.392877 + 0.919591i 0.371480π0.371480\pi
240240 0 0
241241 −4801.06 −1.28325 −0.641626 0.767018i 0.721740π-0.721740\pi
−0.641626 + 0.767018i 0.721740π0.721740\pi
242242 0 0
243243 243.000 0.0641500
244244 0 0
245245 1301.23 0.339315
246246 0 0
247247 −333.396 −0.0858845
248248 0 0
249249 1174.89 0.299018
250250 0 0
251251 4768.20 1.19907 0.599534 0.800350i 0.295353π-0.295353\pi
0.599534 + 0.800350i 0.295353π0.295353\pi
252252 0 0
253253 10558.3 2.62370
254254 0 0
255255 −924.284 −0.226984
256256 0 0
257257 6002.18 1.45683 0.728415 0.685136i 0.240257π-0.240257\pi
0.728415 + 0.685136i 0.240257π0.240257\pi
258258 0 0
259259 −2414.91 −0.579363
260260 0 0
261261 −2130.65 −0.505302
262262 0 0
263263 −3268.33 −0.766289 −0.383145 0.923688i 0.625159π-0.625159\pi
−0.383145 + 0.923688i 0.625159π0.625159\pi
264264 0 0
265265 4737.64 1.09823
266266 0 0
267267 −2237.88 −0.512944
268268 0 0
269269 −8690.14 −1.96969 −0.984846 0.173431i 0.944515π-0.944515\pi
−0.984846 + 0.173431i 0.944515π0.944515\pi
270270 0 0
271271 −3239.17 −0.726073 −0.363036 0.931775i 0.618260π-0.618260\pi
−0.363036 + 0.931775i 0.618260π0.618260\pi
272272 0 0
273273 609.006 0.135014
274274 0 0
275275 −2631.03 −0.576936
276276 0 0
277277 −220.091 −0.0477400 −0.0238700 0.999715i 0.507599π-0.507599\pi
−0.0238700 + 0.999715i 0.507599π0.507599\pi
278278 0 0
279279 423.562 0.0908889
280280 0 0
281281 587.233 0.124667 0.0623334 0.998055i 0.480146π-0.480146\pi
0.0623334 + 0.998055i 0.480146π0.480146\pi
282282 0 0
283283 −8274.09 −1.73796 −0.868981 0.494845i 0.835225π-0.835225\pi
−0.868981 + 0.494845i 0.835225π0.835225\pi
284284 0 0
285285 1009.66 0.209849
286286 0 0
287287 −541.250 −0.111320
288288 0 0
289289 −4361.82 −0.887812
290290 0 0
291291 −519.693 −0.104691
292292 0 0
293293 −5382.07 −1.07312 −0.536559 0.843863i 0.680276π-0.680276\pi
−0.536559 + 0.843863i 0.680276π0.680276\pi
294294 0 0
295295 −5209.67 −1.02820
296296 0 0
297297 −1504.53 −0.293946
298298 0 0
299299 −2463.20 −0.476424
300300 0 0
301301 −6227.99 −1.19261
302302 0 0
303303 −3790.35 −0.718647
304304 0 0
305305 2773.20 0.520633
306306 0 0
307307 −3095.92 −0.575549 −0.287774 0.957698i 0.592915π-0.592915\pi
−0.287774 + 0.957698i 0.592915π0.592915\pi
308308 0 0
309309 2623.20 0.482941
310310 0 0
311311 3474.58 0.633521 0.316761 0.948506i 0.397405π-0.397405\pi
0.316761 + 0.948506i 0.397405π0.397405\pi
312312 0 0
313313 −3523.92 −0.636370 −0.318185 0.948029i 0.603073π-0.603073\pi
−0.318185 + 0.948029i 0.603073π0.603073\pi
314314 0 0
315315 −1844.32 −0.329891
316316 0 0
317317 −323.396 −0.0572988 −0.0286494 0.999590i 0.509121π-0.509121\pi
−0.0286494 + 0.999590i 0.509121π0.509121\pi
318318 0 0
319319 13191.9 2.31537
320320 0 0
321321 4775.66 0.830378
322322 0 0
323323 −602.094 −0.103720
324324 0 0
325325 613.807 0.104763
326326 0 0
327327 1115.36 0.188623
328328 0 0
329329 9100.30 1.52497
330330 0 0
331331 −1057.74 −0.175646 −0.0878228 0.996136i 0.527991π-0.527991\pi
−0.0878228 + 0.996136i 0.527991π0.527991\pi
332332 0 0
333333 −1391.83 −0.229044
334334 0 0
335335 −1126.33 −0.183695
336336 0 0
337337 11538.4 1.86510 0.932550 0.361041i 0.117578π-0.117578\pi
0.932550 + 0.361041i 0.117578π0.117578\pi
338338 0 0
339339 3521.94 0.564265
340340 0 0
341341 −2622.49 −0.416468
342342 0 0
343343 −6904.49 −1.08690
344344 0 0
345345 7459.59 1.16409
346346 0 0
347347 5211.75 0.806286 0.403143 0.915137i 0.367918π-0.367918\pi
0.403143 + 0.915137i 0.367918π0.367918\pi
348348 0 0
349349 −2369.81 −0.363476 −0.181738 0.983347i 0.558172π-0.558172\pi
−0.181738 + 0.983347i 0.558172π0.558172\pi
350350 0 0
351351 351.000 0.0533761
352352 0 0
353353 −8997.40 −1.35661 −0.678305 0.734780i 0.737285π-0.737285\pi
−0.678305 + 0.734780i 0.737285π0.737285\pi
354354 0 0
355355 8551.05 1.27843
356356 0 0
357357 1099.83 0.163051
358358 0 0
359359 10863.4 1.59707 0.798537 0.601946i 0.205608π-0.205608\pi
0.798537 + 0.601946i 0.205608π0.205608\pi
360360 0 0
361361 −6201.29 −0.904110
362362 0 0
363363 5322.32 0.769557
364364 0 0
365365 −12169.4 −1.74514
366366 0 0
367367 −13552.2 −1.92757 −0.963785 0.266682i 0.914073π-0.914073\pi
−0.963785 + 0.266682i 0.914073π0.914073\pi
368368 0 0
369369 −311.949 −0.0440092
370370 0 0
371371 −5637.44 −0.788899
372372 0 0
373373 2255.64 0.313118 0.156559 0.987669i 0.449960π-0.449960\pi
0.156559 + 0.987669i 0.449960π0.449960\pi
374374 0 0
375375 3062.31 0.421698
376376 0 0
377377 −3077.60 −0.420437
378378 0 0
379379 −7698.92 −1.04345 −0.521724 0.853114i 0.674711π-0.674711\pi
−0.521724 + 0.853114i 0.674711π0.674711\pi
380380 0 0
381381 2218.08 0.298256
382382 0 0
383383 211.235 0.0281818 0.0140909 0.999901i 0.495515π-0.495515\pi
0.0140909 + 0.999901i 0.495515π0.495515\pi
384384 0 0
385385 11419.1 1.51161
386386 0 0
387387 −3589.50 −0.471485
388388 0 0
389389 3515.25 0.458175 0.229088 0.973406i 0.426426π-0.426426\pi
0.229088 + 0.973406i 0.426426π0.426426\pi
390390 0 0
391391 −4448.41 −0.575360
392392 0 0
393393 6394.75 0.820795
394394 0 0
395395 14671.3 1.86885
396396 0 0
397397 −10968.8 −1.38667 −0.693337 0.720613i 0.743860π-0.743860\pi
−0.693337 + 0.720613i 0.743860π0.743860\pi
398398 0 0
399399 −1201.42 −0.150742
400400 0 0
401401 6508.24 0.810488 0.405244 0.914208i 0.367187π-0.367187\pi
0.405244 + 0.914208i 0.367187π0.367187\pi
402402 0 0
403403 611.812 0.0756242
404404 0 0
405405 −1062.97 −0.130418
406406 0 0
407407 8617.51 1.04952
408408 0 0
409409 9363.46 1.13201 0.566006 0.824401i 0.308488π-0.308488\pi
0.566006 + 0.824401i 0.308488π0.308488\pi
410410 0 0
411411 −770.801 −0.0925081
412412 0 0
413413 6199.13 0.738594
414414 0 0
415415 −5139.39 −0.607910
416416 0 0
417417 1312.33 0.154113
418418 0 0
419419 −12057.8 −1.40588 −0.702940 0.711249i 0.748130π-0.748130\pi
−0.702940 + 0.711249i 0.748130π0.748130\pi
420420 0 0
421421 −15937.1 −1.84496 −0.922479 0.386047i 0.873840π-0.873840\pi
−0.922479 + 0.386047i 0.873840π0.873840\pi
422422 0 0
423423 5244.95 0.602880
424424 0 0
425425 1108.50 0.126518
426426 0 0
427427 −3299.90 −0.373990
428428 0 0
429429 −2173.22 −0.244578
430430 0 0
431431 6792.37 0.759111 0.379556 0.925169i 0.376077π-0.376077\pi
0.379556 + 0.925169i 0.376077π0.376077\pi
432432 0 0
433433 −3338.00 −0.370471 −0.185235 0.982694i 0.559305π-0.559305\pi
−0.185235 + 0.982694i 0.559305π0.559305\pi
434434 0 0
435435 9320.24 1.02729
436436 0 0
437437 4859.30 0.531927
438438 0 0
439439 13313.1 1.44738 0.723688 0.690127i 0.242445π-0.242445\pi
0.723688 + 0.690127i 0.242445π0.242445\pi
440440 0 0
441441 −892.398 −0.0963608
442442 0 0
443443 5175.32 0.555050 0.277525 0.960718i 0.410486π-0.410486\pi
0.277525 + 0.960718i 0.410486π0.410486\pi
444444 0 0
445445 9789.31 1.04283
446446 0 0
447447 −10219.9 −1.08140
448448 0 0
449449 −4090.57 −0.429947 −0.214973 0.976620i 0.568966π-0.568966\pi
−0.214973 + 0.976620i 0.568966π0.568966\pi
450450 0 0
451451 1931.43 0.201658
452452 0 0
453453 9827.31 1.01927
454454 0 0
455455 −2664.01 −0.274486
456456 0 0
457457 −4300.78 −0.440224 −0.220112 0.975475i 0.570642π-0.570642\pi
−0.220112 + 0.975475i 0.570642π0.570642\pi
458458 0 0
459459 633.886 0.0644603
460460 0 0
461461 −2578.07 −0.260461 −0.130231 0.991484i 0.541572π-0.541572\pi
−0.130231 + 0.991484i 0.541572π0.541572\pi
462462 0 0
463463 −4529.58 −0.454660 −0.227330 0.973818i 0.573000π-0.573000\pi
−0.227330 + 0.973818i 0.573000π0.573000\pi
464464 0 0
465465 −1852.82 −0.184779
466466 0 0
467467 4761.89 0.471850 0.235925 0.971771i 0.424188π-0.424188\pi
0.235925 + 0.971771i 0.424188π0.424188\pi
468468 0 0
469469 1340.24 0.131955
470470 0 0
471471 3223.03 0.315307
472472 0 0
473473 22224.4 2.16042
474474 0 0
475475 −1210.89 −0.116967
476476 0 0
477477 −3249.14 −0.311882
478478 0 0
479479 11621.4 1.10855 0.554275 0.832333i 0.312995π-0.312995\pi
0.554275 + 0.832333i 0.312995π0.312995\pi
480480 0 0
481481 −2010.42 −0.190576
482482 0 0
483483 −8876.36 −0.836208
484484 0 0
485485 2273.33 0.212838
486486 0 0
487487 7836.62 0.729181 0.364590 0.931168i 0.381209π-0.381209\pi
0.364590 + 0.931168i 0.381209π0.381209\pi
488488 0 0
489489 6094.46 0.563601
490490 0 0
491491 −14163.9 −1.30185 −0.650925 0.759142i 0.725619π-0.725619\pi
−0.650925 + 0.759142i 0.725619π0.725619\pi
492492 0 0
493493 −5557.98 −0.507746
494494 0 0
495495 6581.39 0.597599
496496 0 0
497497 −10175.1 −0.918342
498498 0 0
499499 −811.953 −0.0728417 −0.0364208 0.999337i 0.511596π-0.511596\pi
−0.0364208 + 0.999337i 0.511596π0.511596\pi
500500 0 0
501501 899.091 0.0801765
502502 0 0
503503 9718.41 0.861476 0.430738 0.902477i 0.358253π-0.358253\pi
0.430738 + 0.902477i 0.358253π0.358253\pi
504504 0 0
505505 16580.4 1.46103
506506 0 0
507507 507.000 0.0444116
508508 0 0
509509 −10546.5 −0.918403 −0.459201 0.888332i 0.651864π-0.651864\pi
−0.459201 + 0.888332i 0.651864π0.651864\pi
510510 0 0
511511 14480.7 1.25360
512512 0 0
513513 −692.438 −0.0595943
514514 0 0
515515 −11474.9 −0.981831
516516 0 0
517517 −32474.1 −2.76250
518518 0 0
519519 7113.47 0.601631
520520 0 0
521521 1157.10 0.0973005 0.0486503 0.998816i 0.484508π-0.484508\pi
0.0486503 + 0.998816i 0.484508π0.484508\pi
522522 0 0
523523 19193.0 1.60468 0.802342 0.596865i 0.203587π-0.203587\pi
0.802342 + 0.596865i 0.203587π0.203587\pi
524524 0 0
525525 2211.90 0.183877
526526 0 0
527527 1104.90 0.0913285
528528 0 0
529529 23734.6 1.95074
530530 0 0
531531 3572.86 0.291994
532532 0 0
533533 −450.593 −0.0366179
534534 0 0
535535 −20890.5 −1.68818
536536 0 0
537537 −748.840 −0.0601766
538538 0 0
539539 5525.28 0.441541
540540 0 0
541541 −7809.48 −0.620620 −0.310310 0.950635i 0.600433π-0.600433\pi
−0.310310 + 0.950635i 0.600433π0.600433\pi
542542 0 0
543543 −9454.35 −0.747192
544544 0 0
545545 −4879.01 −0.383475
546546 0 0
547547 4979.12 0.389199 0.194599 0.980883i 0.437659π-0.437659\pi
0.194599 + 0.980883i 0.437659π0.437659\pi
548548 0 0
549549 −1901.90 −0.147853
550550 0 0
551551 6071.36 0.469417
552552 0 0
553553 −17457.8 −1.34246
554554 0 0
555555 6088.37 0.465652
556556 0 0
557557 24508.2 1.86435 0.932176 0.362005i 0.117908π-0.117908\pi
0.932176 + 0.362005i 0.117908π0.117908\pi
558558 0 0
559559 −5184.83 −0.392299
560560 0 0
561561 −3924.71 −0.295368
562562 0 0
563563 14957.3 1.11967 0.559836 0.828604i 0.310864π-0.310864\pi
0.559836 + 0.828604i 0.310864π0.310864\pi
564564 0 0
565565 −15406.3 −1.14716
566566 0 0
567567 1264.86 0.0936844
568568 0 0
569569 5756.83 0.424146 0.212073 0.977254i 0.431979π-0.431979\pi
0.212073 + 0.977254i 0.431979π0.431979\pi
570570 0 0
571571 −7292.96 −0.534502 −0.267251 0.963627i 0.586115π-0.586115\pi
−0.267251 + 0.963627i 0.586115π0.586115\pi
572572 0 0
573573 −14218.4 −1.03662
574574 0 0
575575 −8946.34 −0.648849
576576 0 0
577577 20749.7 1.49709 0.748544 0.663085i 0.230753π-0.230753\pi
0.748544 + 0.663085i 0.230753π0.230753\pi
578578 0 0
579579 1910.46 0.137126
580580 0 0
581581 6115.49 0.436684
582582 0 0
583583 20117.0 1.42909
584584 0 0
585585 −1535.40 −0.108515
586586 0 0
587587 2046.37 0.143889 0.0719444 0.997409i 0.477080π-0.477080\pi
0.0719444 + 0.997409i 0.477080π0.477080\pi
588588 0 0
589589 −1206.96 −0.0844343
590590 0 0
591591 −9003.39 −0.626650
592592 0 0
593593 12664.1 0.876988 0.438494 0.898734i 0.355512π-0.355512\pi
0.438494 + 0.898734i 0.355512π0.355512\pi
594594 0 0
595595 −4811.06 −0.331486
596596 0 0
597597 −1946.87 −0.133468
598598 0 0
599599 5788.48 0.394843 0.197421 0.980319i 0.436743π-0.436743\pi
0.197421 + 0.980319i 0.436743π0.436743\pi
600600 0 0
601601 −19622.2 −1.33179 −0.665897 0.746044i 0.731951π-0.731951\pi
−0.665897 + 0.746044i 0.731951π0.731951\pi
602602 0 0
603603 772.449 0.0521668
604604 0 0
605605 −23281.8 −1.56453
606606 0 0
607607 −11386.5 −0.761389 −0.380695 0.924701i 0.624315π-0.624315\pi
−0.380695 + 0.924701i 0.624315π0.624315\pi
608608 0 0
609609 −11090.4 −0.737940
610610 0 0
611611 7576.04 0.501627
612612 0 0
613613 −16046.0 −1.05725 −0.528623 0.848857i 0.677291π-0.677291\pi
−0.528623 + 0.848857i 0.677291π0.677291\pi
614614 0 0
615615 1364.58 0.0894718
616616 0 0
617617 −25943.8 −1.69280 −0.846402 0.532545i 0.821236π-0.821236\pi
−0.846402 + 0.532545i 0.821236π0.821236\pi
618618 0 0
619619 22044.1 1.43139 0.715693 0.698415i 0.246111π-0.246111\pi
0.715693 + 0.698415i 0.246111π0.246111\pi
620620 0 0
621621 −5115.89 −0.330585
622622 0 0
623623 −11648.6 −0.749101
624624 0 0
625625 −19297.6 −1.23505
626626 0 0
627627 4287.23 0.273071
628628 0 0
629629 −3630.71 −0.230152
630630 0 0
631631 −6948.74 −0.438392 −0.219196 0.975681i 0.570343π-0.570343\pi
−0.219196 + 0.975681i 0.570343π0.570343\pi
632632 0 0
633633 −720.341 −0.0452306
634634 0 0
635635 −9702.70 −0.606362
636636 0 0
637637 −1289.02 −0.0801770
638638 0 0
639639 −5864.42 −0.363056
640640 0 0
641641 −17916.9 −1.10402 −0.552009 0.833838i 0.686139π-0.686139\pi
−0.552009 + 0.833838i 0.686139π0.686139\pi
642642 0 0
643643 10248.9 0.628581 0.314290 0.949327i 0.398233π-0.398233\pi
0.314290 + 0.949327i 0.398233π0.398233\pi
644644 0 0
645645 15701.8 0.958539
646646 0 0
647647 −13034.7 −0.792035 −0.396018 0.918243i 0.629608π-0.629608\pi
−0.396018 + 0.918243i 0.629608π0.629608\pi
648648 0 0
649649 −22121.4 −1.33797
650650 0 0
651651 2204.72 0.132734
652652 0 0
653653 5517.54 0.330656 0.165328 0.986239i 0.447132π-0.447132\pi
0.165328 + 0.986239i 0.447132π0.447132\pi
654654 0 0
655655 −27973.0 −1.66869
656656 0 0
657657 8345.97 0.495597
658658 0 0
659659 −31919.9 −1.88683 −0.943416 0.331610i 0.892408π-0.892408\pi
−0.943416 + 0.331610i 0.892408π0.892408\pi
660660 0 0
661661 −3517.33 −0.206972 −0.103486 0.994631i 0.533000π-0.533000\pi
−0.103486 + 0.994631i 0.533000π0.533000\pi
662662 0 0
663663 915.613 0.0536342
664664 0 0
665665 5255.45 0.306463
666666 0 0
667667 44856.6 2.60398
668668 0 0
669669 −3313.11 −0.191468
670670 0 0
671671 11775.6 0.677484
672672 0 0
673673 −33399.0 −1.91298 −0.956490 0.291766i 0.905757π-0.905757\pi
−0.956490 + 0.291766i 0.905757π0.905757\pi
674674 0 0
675675 1274.83 0.0726936
676676 0 0
677677 −15843.8 −0.899450 −0.449725 0.893167i 0.648478π-0.648478\pi
−0.449725 + 0.893167i 0.648478π0.648478\pi
678678 0 0
679679 −2705.09 −0.152890
680680 0 0
681681 1491.10 0.0839047
682682 0 0
683683 −10145.6 −0.568392 −0.284196 0.958766i 0.591727π-0.591727\pi
−0.284196 + 0.958766i 0.591727π0.591727\pi
684684 0 0
685685 3371.77 0.188071
686686 0 0
687687 8637.16 0.479663
688688 0 0
689689 −4693.20 −0.259502
690690 0 0
691691 18650.9 1.02679 0.513396 0.858152i 0.328387π-0.328387\pi
0.513396 + 0.858152i 0.328387π0.328387\pi
692692 0 0
693693 −7831.36 −0.429277
694694 0 0
695695 −5740.61 −0.313315
696696 0 0
697697 −813.745 −0.0442221
698698 0 0
699699 −11540.7 −0.624478
700700 0 0
701701 25182.9 1.35684 0.678420 0.734675i 0.262665π-0.262665\pi
0.678420 + 0.734675i 0.262665π0.262665\pi
702702 0 0
703703 3966.07 0.212778
704704 0 0
705705 −22943.4 −1.22567
706706 0 0
707707 −19729.4 −1.04951
708708 0 0
709709 16697.6 0.884473 0.442236 0.896899i 0.354185π-0.354185\pi
0.442236 + 0.896899i 0.354185π0.354185\pi
710710 0 0
711711 −10061.8 −0.530727
712712 0 0
713713 −8917.27 −0.468379
714714 0 0
715715 9506.45 0.497232
716716 0 0
717717 8709.74 0.453656
718718 0 0
719719 22657.4 1.17521 0.587606 0.809147i 0.300070π-0.300070\pi
0.587606 + 0.809147i 0.300070π0.300070\pi
720720 0 0
721721 13654.2 0.705285
722722 0 0
723723 −14403.2 −0.740886
724724 0 0
725725 −11177.8 −0.572599
726726 0 0
727727 −32052.8 −1.63518 −0.817588 0.575803i 0.804690π-0.804690\pi
−0.817588 + 0.575803i 0.804690π0.804690\pi
728728 0 0
729729 729.000 0.0370370
730730 0 0
731731 −9363.52 −0.473765
732732 0 0
733733 22728.1 1.14527 0.572634 0.819811i 0.305922π-0.305922\pi
0.572634 + 0.819811i 0.305922π0.305922\pi
734734 0 0
735735 3903.68 0.195904
736736 0 0
737737 −4782.62 −0.239037
738738 0 0
739739 3741.58 0.186247 0.0931234 0.995655i 0.470315π-0.470315\pi
0.0931234 + 0.995655i 0.470315π0.470315\pi
740740 0 0
741741 −1000.19 −0.0495854
742742 0 0
743743 −23932.4 −1.18169 −0.590844 0.806786i 0.701205π-0.701205\pi
−0.590844 + 0.806786i 0.701205π0.701205\pi
744744 0 0
745745 44705.8 2.19852
746746 0 0
747747 3524.66 0.172638
748748 0 0
749749 24858.1 1.21268
750750 0 0
751751 −15777.6 −0.766623 −0.383311 0.923619i 0.625216π-0.625216\pi
−0.383311 + 0.923619i 0.625216π0.625216\pi
752752 0 0
753753 14304.6 0.692282
754754 0 0
755755 −42988.3 −2.07219
756756 0 0
757757 32474.4 1.55919 0.779593 0.626287i 0.215426π-0.215426\pi
0.779593 + 0.626287i 0.215426π0.215426\pi
758758 0 0
759759 31675.0 1.51480
760760 0 0
761761 24471.4 1.16569 0.582844 0.812584i 0.301940π-0.301940\pi
0.582844 + 0.812584i 0.301940π0.301940\pi
762762 0 0
763763 5805.66 0.275464
764764 0 0
765765 −2772.85 −0.131049
766766 0 0
767767 5160.80 0.242954
768768 0 0
769769 5185.33 0.243157 0.121578 0.992582i 0.461204π-0.461204\pi
0.121578 + 0.992582i 0.461204π0.461204\pi
770770 0 0
771771 18006.5 0.841102
772772 0 0
773773 6218.64 0.289352 0.144676 0.989479i 0.453786π-0.453786\pi
0.144676 + 0.989479i 0.453786π0.453786\pi
774774 0 0
775775 2222.10 0.102994
776776 0 0
777777 −7244.72 −0.334495
778778 0 0
779779 888.910 0.0408838
780780 0 0
781781 36309.5 1.66358
782782 0 0
783783 −6391.94 −0.291736
784784 0 0
785785 −14098.7 −0.641026
786786 0 0
787787 −15933.8 −0.721702 −0.360851 0.932623i 0.617514π-0.617514\pi
−0.360851 + 0.932623i 0.617514π0.617514\pi
788788 0 0
789789 −9805.00 −0.442417
790790 0 0
791791 18332.3 0.824049
792792 0 0
793793 −2747.19 −0.123021
794794 0 0
795795 14212.9 0.634063
796796 0 0
797797 −825.379 −0.0366831 −0.0183415 0.999832i 0.505839π-0.505839\pi
−0.0183415 + 0.999832i 0.505839π0.505839\pi
798798 0 0
799799 13681.9 0.605796
800800 0 0
801801 −6713.64 −0.296148
802802 0 0
803803 −51674.0 −2.27090
804804 0 0
805805 38828.5 1.70003
806806 0 0
807807 −26070.4 −1.13720
808808 0 0
809809 23981.8 1.04222 0.521110 0.853490i 0.325518π-0.325518\pi
0.521110 + 0.853490i 0.325518π0.325518\pi
810810 0 0
811811 −1359.77 −0.0588753 −0.0294376 0.999567i 0.509372π-0.509372\pi
−0.0294376 + 0.999567i 0.509372π0.509372\pi
812812 0 0
813813 −9717.52 −0.419198
814814 0 0
815815 −26659.4 −1.14581
816816 0 0
817817 10228.4 0.438001
818818 0 0
819819 1827.02 0.0779501
820820 0 0
821821 −29276.9 −1.24455 −0.622273 0.782801i 0.713791π-0.713791\pi
−0.622273 + 0.782801i 0.713791π0.713791\pi
822822 0 0
823823 −3971.15 −0.168196 −0.0840982 0.996457i 0.526801π-0.526801\pi
−0.0840982 + 0.996457i 0.526801π0.526801\pi
824824 0 0
825825 −7893.10 −0.333094
826826 0 0
827827 −18920.5 −0.795564 −0.397782 0.917480i 0.630220π-0.630220\pi
−0.397782 + 0.917480i 0.630220π0.630220\pi
828828 0 0
829829 29902.3 1.25277 0.626387 0.779512i 0.284533π-0.284533\pi
0.626387 + 0.779512i 0.284533π0.284533\pi
830830 0 0
831831 −660.273 −0.0275627
832832 0 0
833833 −2327.90 −0.0968269
834834 0 0
835835 −3932.95 −0.163001
836836 0 0
837837 1270.69 0.0524748
838838 0 0
839839 41125.0 1.69224 0.846121 0.532991i 0.178932π-0.178932\pi
0.846121 + 0.532991i 0.178932π0.178932\pi
840840 0 0
841841 31656.2 1.29797
842842 0 0
843843 1761.70 0.0719765
844844 0 0
845845 −2217.80 −0.0902897
846846 0 0
847847 27703.6 1.12386
848848 0 0
849849 −24822.3 −1.00341
850850 0 0
851851 29302.2 1.18034
852852 0 0
853853 2252.79 0.0904266 0.0452133 0.998977i 0.485603π-0.485603\pi
0.0452133 + 0.998977i 0.485603π0.485603\pi
854854 0 0
855855 3028.98 0.121157
856856 0 0
857857 16608.6 0.662005 0.331002 0.943630i 0.392613π-0.392613\pi
0.331002 + 0.943630i 0.392613π0.392613\pi
858858 0 0
859859 −14112.0 −0.560529 −0.280265 0.959923i 0.590422π-0.590422\pi
−0.280265 + 0.959923i 0.590422π0.590422\pi
860860 0 0
861861 −1623.75 −0.0642709
862862 0 0
863863 40154.6 1.58387 0.791934 0.610607i 0.209075π-0.209075\pi
0.791934 + 0.610607i 0.209075π0.209075\pi
864864 0 0
865865 −31116.9 −1.22313
866866 0 0
867867 −13085.5 −0.512578
868868 0 0
869869 62297.6 2.43188
870870 0 0
871871 1115.76 0.0434054
872872 0 0
873873 −1559.08 −0.0604431
874874 0 0
875875 15939.8 0.615846
876876 0 0
877877 −22495.6 −0.866161 −0.433080 0.901355i 0.642573π-0.642573\pi
−0.433080 + 0.901355i 0.642573π0.642573\pi
878878 0 0
879879 −16146.2 −0.619565
880880 0 0
881881 −42296.3 −1.61748 −0.808740 0.588166i 0.799850π-0.799850\pi
−0.808740 + 0.588166i 0.799850π0.799850\pi
882882 0 0
883883 −37440.9 −1.42694 −0.713469 0.700687i 0.752877π-0.752877\pi
−0.713469 + 0.700687i 0.752877π0.752877\pi
884884 0 0
885885 −15629.0 −0.593631
886886 0 0
887887 3372.82 0.127675 0.0638377 0.997960i 0.479666π-0.479666\pi
0.0638377 + 0.997960i 0.479666π0.479666\pi
888888 0 0
889889 11545.5 0.435572
890890 0 0
891891 −4513.60 −0.169710
892892 0 0
893893 −14945.7 −0.560066
894894 0 0
895895 3275.70 0.122340
896896 0 0
897897 −7389.61 −0.275064
898898 0 0
899899 −11141.5 −0.413337
900900 0 0
901901 −8475.65 −0.313390
902902 0 0
903903 −18684.0 −0.688554
904904 0 0
905905 41356.8 1.51906
906906 0 0
907907 30130.3 1.10304 0.551522 0.834160i 0.314047π-0.314047\pi
0.551522 + 0.834160i 0.314047π0.314047\pi
908908 0 0
909909 −11371.1 −0.414911
910910 0 0
911911 −26089.9 −0.948844 −0.474422 0.880297i 0.657343π-0.657343\pi
−0.474422 + 0.880297i 0.657343π0.657343\pi
912912 0 0
913913 −21822.9 −0.791055
914914 0 0
915915 8319.60 0.300588
916916 0 0
917917 33285.8 1.19868
918918 0 0
919919 −5142.55 −0.184589 −0.0922944 0.995732i 0.529420π-0.529420\pi
−0.0922944 + 0.995732i 0.529420π0.529420\pi
920920 0 0
921921 −9287.76 −0.332293
922922 0 0
923923 −8470.83 −0.302081
924924 0 0
925925 −7301.83 −0.259549
926926 0 0
927927 7869.61 0.278826
928928 0 0
929929 23311.6 0.823282 0.411641 0.911346i 0.364956π-0.364956\pi
0.411641 + 0.911346i 0.364956π0.364956\pi
930930 0 0
931931 2542.92 0.0895176
932932 0 0
933933 10423.7 0.365764
934934 0 0
935935 17168.1 0.600489
936936 0 0
937937 −17214.9 −0.600199 −0.300099 0.953908i 0.597020π-0.597020\pi
−0.300099 + 0.953908i 0.597020π0.597020\pi
938938 0 0
939939 −10571.8 −0.367409
940940 0 0
941941 −27871.2 −0.965541 −0.482770 0.875747i 0.660369π-0.660369\pi
−0.482770 + 0.875747i 0.660369π0.660369\pi
942942 0 0
943943 6567.47 0.226793
944944 0 0
945945 −5532.95 −0.190462
946946 0 0
947947 −14956.7 −0.513227 −0.256614 0.966514i 0.582607π-0.582607\pi
−0.256614 + 0.966514i 0.582607π0.582607\pi
948948 0 0
949949 12055.3 0.412361
950950 0 0
951951 −970.188 −0.0330815
952952 0 0
953953 −2056.14 −0.0698898 −0.0349449 0.999389i 0.511126π-0.511126\pi
−0.0349449 + 0.999389i 0.511126π0.511126\pi
954954 0 0
955955 62196.4 2.10746
956956 0 0
957957 39575.7 1.33678
958958 0 0
959959 −4012.16 −0.135098
960960 0 0
961961 −27576.1 −0.925653
962962 0 0
963963 14327.0 0.479419
964964 0 0
965965 −8357.03 −0.278780
966966 0 0
967967 25282.1 0.840764 0.420382 0.907347i 0.361896π-0.361896\pi
0.420382 + 0.907347i 0.361896π0.361896\pi
968968 0 0
969969 −1806.28 −0.0598825
970970 0 0
971971 22919.6 0.757493 0.378747 0.925500i 0.376355π-0.376355\pi
0.378747 + 0.925500i 0.376355π0.376355\pi
972972 0 0
973973 6830.91 0.225066
974974 0 0
975975 1841.42 0.0604848
976976 0 0
977977 42964.8 1.40693 0.703463 0.710732i 0.251636π-0.251636\pi
0.703463 + 0.710732i 0.251636π0.251636\pi
978978 0 0
979979 41567.5 1.35700
980980 0 0
981981 3346.09 0.108902
982982 0 0
983983 −53757.9 −1.74426 −0.872132 0.489271i 0.837263π-0.837263\pi
−0.872132 + 0.489271i 0.837263π0.837263\pi
984984 0 0
985985 39384.2 1.27399
986986 0 0
987987 27300.9 0.880443
988988 0 0
989989 75569.8 2.42971
990990 0 0
991991 −28021.7 −0.898224 −0.449112 0.893475i 0.648260π-0.648260\pi
−0.449112 + 0.893475i 0.648260π0.648260\pi
992992 0 0
993993 −3173.22 −0.101409
994994 0 0
995995 8516.35 0.271343
996996 0 0
997997 7057.01 0.224170 0.112085 0.993699i 0.464247π-0.464247\pi
0.112085 + 0.993699i 0.464247π0.464247\pi
998998 0 0
999999 −4175.49 −0.132239
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 312.4.a.d.1.1 2
3.2 odd 2 936.4.a.j.1.2 2
4.3 odd 2 624.4.a.j.1.1 2
8.3 odd 2 2496.4.a.bj.1.2 2
8.5 even 2 2496.4.a.ba.1.2 2
12.11 even 2 1872.4.a.bi.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
312.4.a.d.1.1 2 1.1 even 1 trivial
624.4.a.j.1.1 2 4.3 odd 2
936.4.a.j.1.2 2 3.2 odd 2
1872.4.a.bi.1.2 2 12.11 even 2
2496.4.a.ba.1.2 2 8.5 even 2
2496.4.a.bj.1.2 2 8.3 odd 2