Properties

Label 7728.2.a.ce.1.1
Level 77287728
Weight 22
Character 7728.1
Self dual yes
Analytic conductor 61.70861.708
Analytic rank 00
Dimension 44
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] = [7728,2,Mod(1,7728)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7728.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7728=243723 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7728.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: 61.708390682061.7083906820
Analytic rank: 00
Dimension: 44
Coefficient field: 4.4.15317.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x42x34x2+5x+2 x^{4} - 2x^{3} - 4x^{2} + 5x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 483)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.329731.32973 of defining polynomial
Character χ\chi == 7728.1

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+1.00000q32.73589q5+1.00000q7+1.00000q9+2.50407q11+1.48511q132.73589q15+0.902098q172.50407q19+1.00000q211.00000q23+2.48511q25+1.00000q27+6.68466q291.09790q31+2.50407q332.73589q35+9.91023q37+1.48511q392.30826q415.83380q432.73589q45+6.74671q47+1.00000q49+0.902098q514.91648q536.85086q552.50407q57+7.32973q591.00625q61+1.00000q634.06311q6511.2929q671.00000q69+0.362008q715.34411q73+2.48511q75+2.50407q7710.4672q79+1.00000q817.59946q832.46805q85+6.68466q87+10.6245q89+1.48511q911.09790q93+6.85086q95+13.9102q97+2.50407q99+O(q100)q+1.00000 q^{3} -2.73589 q^{5} +1.00000 q^{7} +1.00000 q^{9} +2.50407 q^{11} +1.48511 q^{13} -2.73589 q^{15} +0.902098 q^{17} -2.50407 q^{19} +1.00000 q^{21} -1.00000 q^{23} +2.48511 q^{25} +1.00000 q^{27} +6.68466 q^{29} -1.09790 q^{31} +2.50407 q^{33} -2.73589 q^{35} +9.91023 q^{37} +1.48511 q^{39} -2.30826 q^{41} -5.83380 q^{43} -2.73589 q^{45} +6.74671 q^{47} +1.00000 q^{49} +0.902098 q^{51} -4.91648 q^{53} -6.85086 q^{55} -2.50407 q^{57} +7.32973 q^{59} -1.00625 q^{61} +1.00000 q^{63} -4.06311 q^{65} -11.2929 q^{67} -1.00000 q^{69} +0.362008 q^{71} -5.34411 q^{73} +2.48511 q^{75} +2.50407 q^{77} -10.4672 q^{79} +1.00000 q^{81} -7.59946 q^{83} -2.46805 q^{85} +6.68466 q^{87} +10.6245 q^{89} +1.48511 q^{91} -1.09790 q^{93} +6.85086 q^{95} +13.9102 q^{97} +2.50407 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q3+5q5+4q7+4q9q11+7q13+5q15+2q17+q19+4q214q23+11q25+4q27+2q296q31q33+5q35+16q37+7q39+q99+O(q100) 4 q + 4 q^{3} + 5 q^{5} + 4 q^{7} + 4 q^{9} - q^{11} + 7 q^{13} + 5 q^{15} + 2 q^{17} + q^{19} + 4 q^{21} - 4 q^{23} + 11 q^{25} + 4 q^{27} + 2 q^{29} - 6 q^{31} - q^{33} + 5 q^{35} + 16 q^{37} + 7 q^{39}+ \cdots - 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 1.00000 0.577350
44 0 0
55 −2.73589 −1.22353 −0.611764 0.791040i 0.709540π-0.709540\pi
−0.611764 + 0.791040i 0.709540π0.709540\pi
66 0 0
77 1.00000 0.377964
88 0 0
99 1.00000 0.333333
1010 0 0
1111 2.50407 0.755005 0.377502 0.926009i 0.376783π-0.376783\pi
0.377502 + 0.926009i 0.376783π0.376783\pi
1212 0 0
1313 1.48511 0.411896 0.205948 0.978563i 0.433972π-0.433972\pi
0.205948 + 0.978563i 0.433972π0.433972\pi
1414 0 0
1515 −2.73589 −0.706405
1616 0 0
1717 0.902098 0.218791 0.109396 0.993998i 0.465108π-0.465108\pi
0.109396 + 0.993998i 0.465108π0.465108\pi
1818 0 0
1919 −2.50407 −0.574473 −0.287236 0.957860i 0.592736π-0.592736\pi
−0.287236 + 0.957860i 0.592736π0.592736\pi
2020 0 0
2121 1.00000 0.218218
2222 0 0
2323 −1.00000 −0.208514
2424 0 0
2525 2.48511 0.497023
2626 0 0
2727 1.00000 0.192450
2828 0 0
2929 6.68466 1.24131 0.620655 0.784084i 0.286867π-0.286867\pi
0.620655 + 0.784084i 0.286867π0.286867\pi
3030 0 0
3131 −1.09790 −0.197189 −0.0985945 0.995128i 0.531435π-0.531435\pi
−0.0985945 + 0.995128i 0.531435π0.531435\pi
3232 0 0
3333 2.50407 0.435902
3434 0 0
3535 −2.73589 −0.462450
3636 0 0
3737 9.91023 1.62923 0.814616 0.580000i 0.196948π-0.196948\pi
0.814616 + 0.580000i 0.196948π0.196948\pi
3838 0 0
3939 1.48511 0.237808
4040 0 0
4141 −2.30826 −0.360490 −0.180245 0.983622i 0.557689π-0.557689\pi
−0.180245 + 0.983622i 0.557689π0.557689\pi
4242 0 0
4343 −5.83380 −0.889645 −0.444823 0.895619i 0.646733π-0.646733\pi
−0.444823 + 0.895619i 0.646733π0.646733\pi
4444 0 0
4545 −2.73589 −0.407843
4646 0 0
4747 6.74671 0.984109 0.492055 0.870564i 0.336246π-0.336246\pi
0.492055 + 0.870564i 0.336246π0.336246\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 0.902098 0.126319
5252 0 0
5353 −4.91648 −0.675331 −0.337666 0.941266i 0.609637π-0.609637\pi
−0.337666 + 0.941266i 0.609637π0.609637\pi
5454 0 0
5555 −6.85086 −0.923770
5656 0 0
5757 −2.50407 −0.331672
5858 0 0
5959 7.32973 0.954249 0.477125 0.878836i 0.341679π-0.341679\pi
0.477125 + 0.878836i 0.341679π0.341679\pi
6060 0 0
6161 −1.00625 −0.128837 −0.0644185 0.997923i 0.520519π-0.520519\pi
−0.0644185 + 0.997923i 0.520519π0.520519\pi
6262 0 0
6363 1.00000 0.125988
6464 0 0
6565 −4.06311 −0.503967
6666 0 0
6767 −11.2929 −1.37964 −0.689822 0.723979i 0.742311π-0.742311\pi
−0.689822 + 0.723979i 0.742311π0.742311\pi
6868 0 0
6969 −1.00000 −0.120386
7070 0 0
7171 0.362008 0.0429624 0.0214812 0.999769i 0.493162π-0.493162\pi
0.0214812 + 0.999769i 0.493162π0.493162\pi
7272 0 0
7373 −5.34411 −0.625481 −0.312741 0.949839i 0.601247π-0.601247\pi
−0.312741 + 0.949839i 0.601247π0.601247\pi
7474 0 0
7575 2.48511 0.286956
7676 0 0
7777 2.50407 0.285365
7878 0 0
7979 −10.4672 −1.17765 −0.588827 0.808259i 0.700410π-0.700410\pi
−0.588827 + 0.808259i 0.700410π0.700410\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 −7.59946 −0.834149 −0.417075 0.908872i 0.636945π-0.636945\pi
−0.417075 + 0.908872i 0.636945π0.636945\pi
8484 0 0
8585 −2.46805 −0.267697
8686 0 0
8787 6.68466 0.716671
8888 0 0
8989 10.6245 1.12619 0.563097 0.826391i 0.309610π-0.309610\pi
0.563097 + 0.826391i 0.309610π0.309610\pi
9090 0 0
9191 1.48511 0.155682
9292 0 0
9393 −1.09790 −0.113847
9494 0 0
9595 6.85086 0.702884
9696 0 0
9797 13.9102 1.41237 0.706185 0.708027i 0.250415π-0.250415\pi
0.706185 + 0.708027i 0.250415π0.250415\pi
9898 0 0
9999 2.50407 0.251668
100100 0 0
101101 1.81502 0.180601 0.0903004 0.995915i 0.471217π-0.471217\pi
0.0903004 + 0.995915i 0.471217π0.471217\pi
102102 0 0
103103 16.6605 1.64161 0.820805 0.571209i 0.193525π-0.193525\pi
0.820805 + 0.571209i 0.193525π0.193525\pi
104104 0 0
105105 −2.73589 −0.266996
106106 0 0
107107 −1.68092 −0.162500 −0.0812502 0.996694i 0.525891π-0.525891\pi
−0.0812502 + 0.996694i 0.525891π0.525891\pi
108108 0 0
109109 11.4333 1.09511 0.547554 0.836771i 0.315559π-0.315559\pi
0.547554 + 0.836771i 0.315559π0.315559\pi
110110 0 0
111111 9.91023 0.940638
112112 0 0
113113 3.14914 0.296246 0.148123 0.988969i 0.452677π-0.452677\pi
0.148123 + 0.988969i 0.452677π0.452677\pi
114114 0 0
115115 2.73589 0.255123
116116 0 0
117117 1.48511 0.137299
118118 0 0
119119 0.902098 0.0826952
120120 0 0
121121 −4.72964 −0.429968
122122 0 0
123123 −2.30826 −0.208129
124124 0 0
125125 6.88046 0.615407
126126 0 0
127127 −0.449266 −0.0398659 −0.0199329 0.999801i 0.506345π-0.506345\pi
−0.0199329 + 0.999801i 0.506345π0.506345\pi
128128 0 0
129129 −5.83380 −0.513637
130130 0 0
131131 19.9759 1.74530 0.872649 0.488347i 0.162400π-0.162400\pi
0.872649 + 0.488347i 0.162400π0.162400\pi
132132 0 0
133133 −2.50407 −0.217130
134134 0 0
135135 −2.73589 −0.235468
136136 0 0
137137 0.270356 0.0230981 0.0115490 0.999933i 0.496324π-0.496324\pi
0.0115490 + 0.999933i 0.496324π0.496324\pi
138138 0 0
139139 −4.42512 −0.375334 −0.187667 0.982233i 0.560093π-0.560093\pi
−0.187667 + 0.982233i 0.560093π0.560093\pi
140140 0 0
141141 6.74671 0.568176
142142 0 0
143143 3.71883 0.310984
144144 0 0
145145 −18.2885 −1.51878
146146 0 0
147147 1.00000 0.0824786
148148 0 0
149149 −3.69530 −0.302731 −0.151365 0.988478i 0.548367π-0.548367\pi
−0.151365 + 0.988478i 0.548367π0.548367\pi
150150 0 0
151151 −8.63174 −0.702441 −0.351221 0.936293i 0.614233π-0.614233\pi
−0.351221 + 0.936293i 0.614233π0.614233\pi
152152 0 0
153153 0.902098 0.0729303
154154 0 0
155155 3.00374 0.241266
156156 0 0
157157 9.93438 0.792850 0.396425 0.918067i 0.370251π-0.370251\pi
0.396425 + 0.918067i 0.370251π0.370251\pi
158158 0 0
159159 −4.91648 −0.389903
160160 0 0
161161 −1.00000 −0.0788110
162162 0 0
163163 −14.7082 −1.15203 −0.576017 0.817438i 0.695394π-0.695394\pi
−0.576017 + 0.817438i 0.695394π0.695394\pi
164164 0 0
165165 −6.85086 −0.533339
166166 0 0
167167 5.47430 0.423614 0.211807 0.977312i 0.432065π-0.432065\pi
0.211807 + 0.977312i 0.432065π0.432065\pi
168168 0 0
169169 −10.7944 −0.830341
170170 0 0
171171 −2.50407 −0.191491
172172 0 0
173173 18.1727 1.38165 0.690823 0.723024i 0.257248π-0.257248\pi
0.690823 + 0.723024i 0.257248π0.257248\pi
174174 0 0
175175 2.48511 0.187857
176176 0 0
177177 7.32973 0.550936
178178 0 0
179179 −10.1860 −0.761341 −0.380670 0.924711i 0.624307π-0.624307\pi
−0.380670 + 0.924711i 0.624307π0.624307\pi
180180 0 0
181181 13.5186 1.00483 0.502416 0.864626i 0.332445π-0.332445\pi
0.502416 + 0.864626i 0.332445π0.332445\pi
182182 0 0
183183 −1.00625 −0.0743841
184184 0 0
185185 −27.1133 −1.99341
186186 0 0
187187 2.25892 0.165188
188188 0 0
189189 1.00000 0.0727393
190190 0 0
191191 0.631742 0.0457113 0.0228556 0.999739i 0.492724π-0.492724\pi
0.0228556 + 0.999739i 0.492724π0.492724\pi
192192 0 0
193193 1.36826 0.0984893 0.0492447 0.998787i 0.484319π-0.484319\pi
0.0492447 + 0.998787i 0.484319π0.484319\pi
194194 0 0
195195 −4.06311 −0.290966
196196 0 0
197197 24.7611 1.76416 0.882078 0.471104i 0.156144π-0.156144\pi
0.882078 + 0.471104i 0.156144π0.156144\pi
198198 0 0
199199 −1.44470 −0.102412 −0.0512059 0.998688i 0.516306π-0.516306\pi
−0.0512059 + 0.998688i 0.516306π0.516306\pi
200200 0 0
201201 −11.2929 −0.796538
202202 0 0
203203 6.68466 0.469171
204204 0 0
205205 6.31517 0.441070
206206 0 0
207207 −1.00000 −0.0695048
208208 0 0
209209 −6.27036 −0.433730
210210 0 0
211211 23.0990 1.59020 0.795099 0.606480i 0.207419π-0.207419\pi
0.795099 + 0.606480i 0.207419π0.207419\pi
212212 0 0
213213 0.362008 0.0248044
214214 0 0
215215 15.9606 1.08851
216216 0 0
217217 −1.09790 −0.0745304
218218 0 0
219219 −5.34411 −0.361122
220220 0 0
221221 1.33972 0.0901192
222222 0 0
223223 18.6497 1.24888 0.624438 0.781074i 0.285328π-0.285328\pi
0.624438 + 0.781074i 0.285328π0.285328\pi
224224 0 0
225225 2.48511 0.165674
226226 0 0
227227 −20.6334 −1.36949 −0.684744 0.728783i 0.740086π-0.740086\pi
−0.684744 + 0.728783i 0.740086π0.740086\pi
228228 0 0
229229 14.9544 0.988214 0.494107 0.869401i 0.335495π-0.335495\pi
0.494107 + 0.869401i 0.335495π0.335495\pi
230230 0 0
231231 2.50407 0.164756
232232 0 0
233233 28.1052 1.84123 0.920617 0.390467i 0.127687π-0.127687\pi
0.920617 + 0.390467i 0.127687π0.127687\pi
234234 0 0
235235 −18.4583 −1.20409
236236 0 0
237237 −10.4672 −0.679919
238238 0 0
239239 −25.8536 −1.67233 −0.836166 0.548476i 0.815208π-0.815208\pi
−0.836166 + 0.548476i 0.815208π0.815208\pi
240240 0 0
241241 −14.8311 −0.955356 −0.477678 0.878535i 0.658521π-0.658521\pi
−0.477678 + 0.878535i 0.658521π0.658521\pi
242242 0 0
243243 1.00000 0.0641500
244244 0 0
245245 −2.73589 −0.174790
246246 0 0
247247 −3.71883 −0.236623
248248 0 0
249249 −7.59946 −0.481596
250250 0 0
251251 16.2841 1.02784 0.513922 0.857837i 0.328192π-0.328192\pi
0.513922 + 0.857837i 0.328192π0.328192\pi
252252 0 0
253253 −2.50407 −0.157429
254254 0 0
255255 −2.46805 −0.154555
256256 0 0
257257 22.9446 1.43125 0.715623 0.698486i 0.246143π-0.246143\pi
0.715623 + 0.698486i 0.246143π0.246143\pi
258258 0 0
259259 9.91023 0.615792
260260 0 0
261261 6.68466 0.413770
262262 0 0
263263 0.776932 0.0479077 0.0239538 0.999713i 0.492375π-0.492375\pi
0.0239538 + 0.999713i 0.492375π0.492375\pi
264264 0 0
265265 13.4510 0.826287
266266 0 0
267267 10.6245 0.650208
268268 0 0
269269 3.05937 0.186533 0.0932666 0.995641i 0.470269π-0.470269\pi
0.0932666 + 0.995641i 0.470269π0.470269\pi
270270 0 0
271271 16.0631 0.975765 0.487882 0.872909i 0.337770π-0.337770\pi
0.487882 + 0.872909i 0.337770π0.337770\pi
272272 0 0
273273 1.48511 0.0898832
274274 0 0
275275 6.22289 0.375255
276276 0 0
277277 −11.6103 −0.697594 −0.348797 0.937198i 0.613410π-0.613410\pi
−0.348797 + 0.937198i 0.613410π0.613410\pi
278278 0 0
279279 −1.09790 −0.0657296
280280 0 0
281281 9.89753 0.590437 0.295219 0.955430i 0.404608π-0.404608\pi
0.295219 + 0.955430i 0.404608π0.404608\pi
282282 0 0
283283 −13.9994 −0.832177 −0.416088 0.909324i 0.636599π-0.636599\pi
−0.416088 + 0.909324i 0.636599π0.636599\pi
284284 0 0
285285 6.85086 0.405810
286286 0 0
287287 −2.30826 −0.136253
288288 0 0
289289 −16.1862 −0.952130
290290 0 0
291291 13.9102 0.815432
292292 0 0
293293 −8.14038 −0.475566 −0.237783 0.971318i 0.576421π-0.576421\pi
−0.237783 + 0.971318i 0.576421π0.576421\pi
294294 0 0
295295 −20.0534 −1.16755
296296 0 0
297297 2.50407 0.145301
298298 0 0
299299 −1.48511 −0.0858863
300300 0 0
301301 −5.83380 −0.336254
302302 0 0
303303 1.81502 0.104270
304304 0 0
305305 2.75299 0.157636
306306 0 0
307307 −13.5095 −0.771027 −0.385514 0.922702i 0.625976π-0.625976\pi
−0.385514 + 0.922702i 0.625976π0.625976\pi
308308 0 0
309309 16.6605 0.947783
310310 0 0
311311 24.3035 1.37813 0.689063 0.724701i 0.258022π-0.258022\pi
0.689063 + 0.724701i 0.258022π0.258022\pi
312312 0 0
313313 −33.7836 −1.90956 −0.954782 0.297308i 0.903911π-0.903911\pi
−0.954782 + 0.297308i 0.903911π0.903911\pi
314314 0 0
315315 −2.73589 −0.154150
316316 0 0
317317 32.1594 1.80625 0.903126 0.429376i 0.141267π-0.141267\pi
0.903126 + 0.429376i 0.141267π0.141267\pi
318318 0 0
319319 16.7388 0.937195
320320 0 0
321321 −1.68092 −0.0938196
322322 0 0
323323 −2.25892 −0.125689
324324 0 0
325325 3.69068 0.204722
326326 0 0
327327 11.4333 0.632261
328328 0 0
329329 6.74671 0.371958
330330 0 0
331331 4.84004 0.266033 0.133016 0.991114i 0.457534π-0.457534\pi
0.133016 + 0.991114i 0.457534π0.457534\pi
332332 0 0
333333 9.91023 0.543077
334334 0 0
335335 30.8961 1.68803
336336 0 0
337337 −2.59195 −0.141192 −0.0705962 0.997505i 0.522490π-0.522490\pi
−0.0705962 + 0.997505i 0.522490π0.522490\pi
338338 0 0
339339 3.14914 0.171038
340340 0 0
341341 −2.74922 −0.148879
342342 0 0
343343 1.00000 0.0539949
344344 0 0
345345 2.73589 0.147296
346346 0 0
347347 15.9390 0.855651 0.427825 0.903861i 0.359280π-0.359280\pi
0.427825 + 0.903861i 0.359280π0.359280\pi
348348 0 0
349349 −8.02603 −0.429624 −0.214812 0.976655i 0.568914π-0.568914\pi
−0.214812 + 0.976655i 0.568914π0.568914\pi
350350 0 0
351351 1.48511 0.0792695
352352 0 0
353353 10.7871 0.574141 0.287070 0.957909i 0.407319π-0.407319\pi
0.287070 + 0.957909i 0.407319π0.407319\pi
354354 0 0
355355 −0.990415 −0.0525658
356356 0 0
357357 0.902098 0.0477441
358358 0 0
359359 2.17891 0.114998 0.0574992 0.998346i 0.481687π-0.481687\pi
0.0574992 + 0.998346i 0.481687π0.481687\pi
360360 0 0
361361 −12.7296 −0.669981
362362 0 0
363363 −4.72964 −0.248242
364364 0 0
365365 14.6209 0.765294
366366 0 0
367367 −27.0388 −1.41141 −0.705707 0.708504i 0.749370π-0.749370\pi
−0.705707 + 0.708504i 0.749370π0.749370\pi
368368 0 0
369369 −2.30826 −0.120163
370370 0 0
371371 −4.91648 −0.255251
372372 0 0
373373 16.4189 0.850140 0.425070 0.905161i 0.360249π-0.360249\pi
0.425070 + 0.905161i 0.360249π0.360249\pi
374374 0 0
375375 6.88046 0.355306
376376 0 0
377377 9.92748 0.511291
378378 0 0
379379 34.6399 1.77933 0.889667 0.456610i 0.150936π-0.150936\pi
0.889667 + 0.456610i 0.150936π0.150936\pi
380380 0 0
381381 −0.449266 −0.0230166
382382 0 0
383383 10.6722 0.545322 0.272661 0.962110i 0.412096π-0.412096\pi
0.272661 + 0.962110i 0.412096π0.412096\pi
384384 0 0
385385 −6.85086 −0.349152
386386 0 0
387387 −5.83380 −0.296548
388388 0 0
389389 0.0302201 0.00153222 0.000766110 1.00000i 0.499756π-0.499756\pi
0.000766110 1.00000i 0.499756π0.499756\pi
390390 0 0
391391 −0.902098 −0.0456211
392392 0 0
393393 19.9759 1.00765
394394 0 0
395395 28.6372 1.44089
396396 0 0
397397 20.4749 1.02761 0.513803 0.857908i 0.328236π-0.328236\pi
0.513803 + 0.857908i 0.328236π0.328236\pi
398398 0 0
399399 −2.50407 −0.125360
400400 0 0
401401 −36.4304 −1.81925 −0.909623 0.415435i 0.863629π-0.863629\pi
−0.909623 + 0.415435i 0.863629π0.863629\pi
402402 0 0
403403 −1.63051 −0.0812214
404404 0 0
405405 −2.73589 −0.135948
406406 0 0
407407 24.8159 1.23008
408408 0 0
409409 37.4054 1.84958 0.924790 0.380479i 0.124241π-0.124241\pi
0.924790 + 0.380479i 0.124241π0.124241\pi
410410 0 0
411411 0.270356 0.0133357
412412 0 0
413413 7.32973 0.360672
414414 0 0
415415 20.7913 1.02061
416416 0 0
417417 −4.42512 −0.216699
418418 0 0
419419 37.2017 1.81742 0.908710 0.417428i 0.137068π-0.137068\pi
0.908710 + 0.417428i 0.137068π0.137068\pi
420420 0 0
421421 27.6326 1.34673 0.673366 0.739309i 0.264848π-0.264848\pi
0.673366 + 0.739309i 0.264848π0.264848\pi
422422 0 0
423423 6.74671 0.328036
424424 0 0
425425 2.24182 0.108744
426426 0 0
427427 −1.00625 −0.0486958
428428 0 0
429429 3.71883 0.179547
430430 0 0
431431 −35.0676 −1.68915 −0.844573 0.535441i 0.820145π-0.820145\pi
−0.844573 + 0.535441i 0.820145π0.820145\pi
432432 0 0
433433 −1.00708 −0.0483970 −0.0241985 0.999707i 0.507703π-0.507703\pi
−0.0241985 + 0.999707i 0.507703π0.507703\pi
434434 0 0
435435 −18.2885 −0.876867
436436 0 0
437437 2.50407 0.119786
438438 0 0
439439 4.04649 0.193129 0.0965643 0.995327i 0.469215π-0.469215\pi
0.0965643 + 0.995327i 0.469215π0.469215\pi
440440 0 0
441441 1.00000 0.0476190
442442 0 0
443443 29.3947 1.39659 0.698293 0.715812i 0.253943π-0.253943\pi
0.698293 + 0.715812i 0.253943π0.253943\pi
444444 0 0
445445 −29.0675 −1.37793
446446 0 0
447447 −3.69530 −0.174782
448448 0 0
449449 −4.87627 −0.230126 −0.115063 0.993358i 0.536707π-0.536707\pi
−0.115063 + 0.993358i 0.536707π0.536707\pi
450450 0 0
451451 −5.78005 −0.272172
452452 0 0
453453 −8.63174 −0.405555
454454 0 0
455455 −4.06311 −0.190482
456456 0 0
457457 −35.5212 −1.66161 −0.830806 0.556562i 0.812120π-0.812120\pi
−0.830806 + 0.556562i 0.812120π0.812120\pi
458458 0 0
459459 0.902098 0.0421064
460460 0 0
461461 −18.9442 −0.882319 −0.441160 0.897429i 0.645433π-0.645433\pi
−0.441160 + 0.897429i 0.645433π0.645433\pi
462462 0 0
463463 −14.1933 −0.659618 −0.329809 0.944048i 0.606984π-0.606984\pi
−0.329809 + 0.944048i 0.606984π0.606984\pi
464464 0 0
465465 3.00374 0.139295
466466 0 0
467467 31.0355 1.43615 0.718075 0.695966i 0.245024π-0.245024\pi
0.718075 + 0.695966i 0.245024π0.245024\pi
468468 0 0
469469 −11.2929 −0.521457
470470 0 0
471471 9.93438 0.457752
472472 0 0
473473 −14.6082 −0.671687
474474 0 0
475475 −6.22289 −0.285526
476476 0 0
477477 −4.91648 −0.225110
478478 0 0
479479 −10.5214 −0.480735 −0.240367 0.970682i 0.577268π-0.577268\pi
−0.240367 + 0.970682i 0.577268π0.577268\pi
480480 0 0
481481 14.7178 0.671075
482482 0 0
483483 −1.00000 −0.0455016
484484 0 0
485485 −38.0569 −1.72808
486486 0 0
487487 31.7378 1.43818 0.719089 0.694918i 0.244559π-0.244559\pi
0.719089 + 0.694918i 0.244559π0.244559\pi
488488 0 0
489489 −14.7082 −0.665127
490490 0 0
491491 31.8788 1.43867 0.719336 0.694662i 0.244446π-0.244446\pi
0.719336 + 0.694662i 0.244446π0.244446\pi
492492 0 0
493493 6.03022 0.271587
494494 0 0
495495 −6.85086 −0.307923
496496 0 0
497497 0.362008 0.0162383
498498 0 0
499499 39.4279 1.76503 0.882517 0.470280i 0.155847π-0.155847\pi
0.882517 + 0.470280i 0.155847π0.155847\pi
500500 0 0
501501 5.47430 0.244573
502502 0 0
503503 −24.4589 −1.09057 −0.545284 0.838251i 0.683578π-0.683578\pi
−0.545284 + 0.838251i 0.683578π0.683578\pi
504504 0 0
505505 −4.96569 −0.220970
506506 0 0
507507 −10.7944 −0.479398
508508 0 0
509509 20.3927 0.903889 0.451944 0.892046i 0.350731π-0.350731\pi
0.451944 + 0.892046i 0.350731π0.350731\pi
510510 0 0
511511 −5.34411 −0.236410
512512 0 0
513513 −2.50407 −0.110557
514514 0 0
515515 −45.5814 −2.00856
516516 0 0
517517 16.8942 0.743007
518518 0 0
519519 18.1727 0.797694
520520 0 0
521521 26.3058 1.15248 0.576238 0.817282i 0.304520π-0.304520\pi
0.576238 + 0.817282i 0.304520π0.304520\pi
522522 0 0
523523 40.4256 1.76769 0.883843 0.467783i 0.154947π-0.154947\pi
0.883843 + 0.467783i 0.154947π0.154947\pi
524524 0 0
525525 2.48511 0.108459
526526 0 0
527527 −0.990415 −0.0431432
528528 0 0
529529 1.00000 0.0434783
530530 0 0
531531 7.32973 0.318083
532532 0 0
533533 −3.42804 −0.148485
534534 0 0
535535 4.59881 0.198824
536536 0 0
537537 −10.1860 −0.439560
538538 0 0
539539 2.50407 0.107858
540540 0 0
541541 0.360122 0.0154828 0.00774142 0.999970i 0.497536π-0.497536\pi
0.00774142 + 0.999970i 0.497536π0.497536\pi
542542 0 0
543543 13.5186 0.580140
544544 0 0
545545 −31.2802 −1.33990
546546 0 0
547547 −20.2023 −0.863789 −0.431894 0.901924i 0.642155π-0.642155\pi
−0.431894 + 0.901924i 0.642155π0.642155\pi
548548 0 0
549549 −1.00625 −0.0429457
550550 0 0
551551 −16.7388 −0.713099
552552 0 0
553553 −10.4672 −0.445111
554554 0 0
555555 −27.1133 −1.15090
556556 0 0
557557 9.71086 0.411463 0.205731 0.978609i 0.434043π-0.434043\pi
0.205731 + 0.978609i 0.434043π0.434043\pi
558558 0 0
559559 −8.66385 −0.366442
560560 0 0
561561 2.25892 0.0953715
562562 0 0
563563 −27.2789 −1.14967 −0.574835 0.818269i 0.694934π-0.694934\pi
−0.574835 + 0.818269i 0.694934π0.694934\pi
564564 0 0
565565 −8.61570 −0.362465
566566 0 0
567567 1.00000 0.0419961
568568 0 0
569569 19.6132 0.822229 0.411115 0.911584i 0.365140π-0.365140\pi
0.411115 + 0.911584i 0.365140π0.365140\pi
570570 0 0
571571 −21.1859 −0.886601 −0.443301 0.896373i 0.646193π-0.646193\pi
−0.443301 + 0.896373i 0.646193π0.646193\pi
572572 0 0
573573 0.631742 0.0263914
574574 0 0
575575 −2.48511 −0.103636
576576 0 0
577577 −12.4079 −0.516547 −0.258273 0.966072i 0.583154π-0.583154\pi
−0.258273 + 0.966072i 0.583154π0.583154\pi
578578 0 0
579579 1.36826 0.0568629
580580 0 0
581581 −7.59946 −0.315279
582582 0 0
583583 −12.3112 −0.509878
584584 0 0
585585 −4.06311 −0.167989
586586 0 0
587587 9.35493 0.386119 0.193060 0.981187i 0.438159π-0.438159\pi
0.193060 + 0.981187i 0.438159π0.438159\pi
588588 0 0
589589 2.74922 0.113280
590590 0 0
591591 24.7611 1.01854
592592 0 0
593593 −16.7836 −0.689218 −0.344609 0.938746i 0.611989π-0.611989\pi
−0.344609 + 0.938746i 0.611989π0.611989\pi
594594 0 0
595595 −2.46805 −0.101180
596596 0 0
597597 −1.44470 −0.0591275
598598 0 0
599599 16.0512 0.655836 0.327918 0.944706i 0.393653π-0.393653\pi
0.327918 + 0.944706i 0.393653π0.393653\pi
600600 0 0
601601 −24.4364 −0.996781 −0.498390 0.866953i 0.666075π-0.666075\pi
−0.498390 + 0.866953i 0.666075π0.666075\pi
602602 0 0
603603 −11.2929 −0.459882
604604 0 0
605605 12.9398 0.526078
606606 0 0
607607 −28.2329 −1.14594 −0.572969 0.819577i 0.694208π-0.694208\pi
−0.572969 + 0.819577i 0.694208π0.694208\pi
608608 0 0
609609 6.68466 0.270876
610610 0 0
611611 10.0196 0.405351
612612 0 0
613613 17.9873 0.726500 0.363250 0.931692i 0.381667π-0.381667\pi
0.363250 + 0.931692i 0.381667π0.381667\pi
614614 0 0
615615 6.31517 0.254652
616616 0 0
617617 12.9998 0.523353 0.261677 0.965156i 0.415725π-0.415725\pi
0.261677 + 0.965156i 0.415725π0.415725\pi
618618 0 0
619619 1.26266 0.0507505 0.0253752 0.999678i 0.491922π-0.491922\pi
0.0253752 + 0.999678i 0.491922π0.491922\pi
620620 0 0
621621 −1.00000 −0.0401286
622622 0 0
623623 10.6245 0.425661
624624 0 0
625625 −31.2498 −1.24999
626626 0 0
627627 −6.27036 −0.250414
628628 0 0
629629 8.94001 0.356461
630630 0 0
631631 24.4568 0.973611 0.486806 0.873510i 0.338162π-0.338162\pi
0.486806 + 0.873510i 0.338162π0.338162\pi
632632 0 0
633633 23.0990 0.918101
634634 0 0
635635 1.22914 0.0487771
636636 0 0
637637 1.48511 0.0588423
638638 0 0
639639 0.362008 0.0143208
640640 0 0
641641 −1.29037 −0.0509665 −0.0254833 0.999675i 0.508112π-0.508112\pi
−0.0254833 + 0.999675i 0.508112π0.508112\pi
642642 0 0
643643 −34.3110 −1.35309 −0.676547 0.736399i 0.736524π-0.736524\pi
−0.676547 + 0.736399i 0.736524π0.736524\pi
644644 0 0
645645 15.9606 0.628450
646646 0 0
647647 2.62092 0.103039 0.0515196 0.998672i 0.483594π-0.483594\pi
0.0515196 + 0.998672i 0.483594π0.483594\pi
648648 0 0
649649 18.3541 0.720463
650650 0 0
651651 −1.09790 −0.0430302
652652 0 0
653653 7.53697 0.294944 0.147472 0.989066i 0.452886π-0.452886\pi
0.147472 + 0.989066i 0.452886π0.452886\pi
654654 0 0
655655 −54.6518 −2.13542
656656 0 0
657657 −5.34411 −0.208494
658658 0 0
659659 −22.8213 −0.888990 −0.444495 0.895781i 0.646617π-0.646617\pi
−0.444495 + 0.895781i 0.646617π0.646617\pi
660660 0 0
661661 27.3668 1.06445 0.532223 0.846604i 0.321357π-0.321357\pi
0.532223 + 0.846604i 0.321357π0.321357\pi
662662 0 0
663663 1.33972 0.0520304
664664 0 0
665665 6.85086 0.265665
666666 0 0
667667 −6.68466 −0.258831
668668 0 0
669669 18.6497 0.721039
670670 0 0
671671 −2.51972 −0.0972726
672672 0 0
673673 22.9790 0.885774 0.442887 0.896577i 0.353954π-0.353954\pi
0.442887 + 0.896577i 0.353954π0.353954\pi
674674 0 0
675675 2.48511 0.0956521
676676 0 0
677677 −8.80814 −0.338524 −0.169262 0.985571i 0.554138π-0.554138\pi
−0.169262 + 0.985571i 0.554138π0.554138\pi
678678 0 0
679679 13.9102 0.533826
680680 0 0
681681 −20.6334 −0.790674
682682 0 0
683683 −34.4889 −1.31968 −0.659840 0.751406i 0.729376π-0.729376\pi
−0.659840 + 0.751406i 0.729376π0.729376\pi
684684 0 0
685685 −0.739666 −0.0282612
686686 0 0
687687 14.9544 0.570546
688688 0 0
689689 −7.30154 −0.278166
690690 0 0
691691 −37.6110 −1.43079 −0.715395 0.698721i 0.753753π-0.753753\pi
−0.715395 + 0.698721i 0.753753π0.753753\pi
692692 0 0
693693 2.50407 0.0951217
694694 0 0
695695 12.1067 0.459232
696696 0 0
697697 −2.08228 −0.0788721
698698 0 0
699699 28.1052 1.06304
700700 0 0
701701 −47.5348 −1.79536 −0.897682 0.440644i 0.854750π-0.854750\pi
−0.897682 + 0.440644i 0.854750π0.854750\pi
702702 0 0
703703 −24.8159 −0.935949
704704 0 0
705705 −18.4583 −0.695179
706706 0 0
707707 1.81502 0.0682607
708708 0 0
709709 −41.1332 −1.54479 −0.772395 0.635143i 0.780941π-0.780941\pi
−0.772395 + 0.635143i 0.780941π0.780941\pi
710710 0 0
711711 −10.4672 −0.392551
712712 0 0
713713 1.09790 0.0411167
714714 0 0
715715 −10.1743 −0.380498
716716 0 0
717717 −25.8536 −0.965522
718718 0 0
719719 −8.25857 −0.307993 −0.153996 0.988071i 0.549214π-0.549214\pi
−0.153996 + 0.988071i 0.549214π0.549214\pi
720720 0 0
721721 16.6605 0.620470
722722 0 0
723723 −14.8311 −0.551575
724724 0 0
725725 16.6121 0.616959
726726 0 0
727727 −0.985235 −0.0365403 −0.0182702 0.999833i 0.505816π-0.505816\pi
−0.0182702 + 0.999833i 0.505816π0.505816\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −5.26266 −0.194646
732732 0 0
733733 27.7847 1.02625 0.513125 0.858314i 0.328488π-0.328488\pi
0.513125 + 0.858314i 0.328488π0.328488\pi
734734 0 0
735735 −2.73589 −0.100915
736736 0 0
737737 −28.2781 −1.04164
738738 0 0
739739 −30.0540 −1.10555 −0.552777 0.833329i 0.686432π-0.686432\pi
−0.552777 + 0.833329i 0.686432π0.686432\pi
740740 0 0
741741 −3.71883 −0.136614
742742 0 0
743743 −40.1617 −1.47339 −0.736695 0.676225i 0.763615π-0.763615\pi
−0.736695 + 0.676225i 0.763615π0.763615\pi
744744 0 0
745745 10.1100 0.370400
746746 0 0
747747 −7.59946 −0.278050
748748 0 0
749749 −1.68092 −0.0614194
750750 0 0
751751 2.15350 0.0785823 0.0392912 0.999228i 0.487490π-0.487490\pi
0.0392912 + 0.999228i 0.487490π0.487490\pi
752752 0 0
753753 16.2841 0.593426
754754 0 0
755755 23.6155 0.859457
756756 0 0
757757 −32.0577 −1.16516 −0.582579 0.812774i 0.697956π-0.697956\pi
−0.582579 + 0.812774i 0.697956π0.697956\pi
758758 0 0
759759 −2.50407 −0.0908919
760760 0 0
761761 0.669651 0.0242748 0.0121374 0.999926i 0.496136π-0.496136\pi
0.0121374 + 0.999926i 0.496136π0.496136\pi
762762 0 0
763763 11.4333 0.413912
764764 0 0
765765 −2.46805 −0.0892324
766766 0 0
767767 10.8855 0.393052
768768 0 0
769769 43.5115 1.56906 0.784532 0.620089i 0.212903π-0.212903\pi
0.784532 + 0.620089i 0.212903π0.212903\pi
770770 0 0
771771 22.9446 0.826331
772772 0 0
773773 21.0046 0.755482 0.377741 0.925911i 0.376701π-0.376701\pi
0.377741 + 0.925911i 0.376701π0.376701\pi
774774 0 0
775775 −2.72841 −0.0980074
776776 0 0
777777 9.91023 0.355528
778778 0 0
779779 5.78005 0.207092
780780 0 0
781781 0.906493 0.0324369
782782 0 0
783783 6.68466 0.238890
784784 0 0
785785 −27.1794 −0.970075
786786 0 0
787787 −22.1975 −0.791255 −0.395627 0.918411i 0.629473π-0.629473\pi
−0.395627 + 0.918411i 0.629473π0.629473\pi
788788 0 0
789789 0.776932 0.0276595
790790 0 0
791791 3.14914 0.111970
792792 0 0
793793 −1.49440 −0.0530675
794794 0 0
795795 13.4510 0.477057
796796 0 0
797797 22.8502 0.809397 0.404699 0.914450i 0.367376π-0.367376\pi
0.404699 + 0.914450i 0.367376π0.367376\pi
798798 0 0
799799 6.08620 0.215314
800800 0 0
801801 10.6245 0.375398
802802 0 0
803803 −13.3820 −0.472241
804804 0 0
805805 2.73589 0.0964276
806806 0 0
807807 3.05937 0.107695
808808 0 0
809809 −38.0621 −1.33819 −0.669097 0.743175i 0.733319π-0.733319\pi
−0.669097 + 0.743175i 0.733319π0.733319\pi
810810 0 0
811811 −21.0208 −0.738142 −0.369071 0.929401i 0.620324π-0.620324\pi
−0.369071 + 0.929401i 0.620324π0.620324\pi
812812 0 0
813813 16.0631 0.563358
814814 0 0
815815 40.2400 1.40955
816816 0 0
817817 14.6082 0.511077
818818 0 0
819819 1.48511 0.0518941
820820 0 0
821821 −10.4132 −0.363425 −0.181712 0.983352i 0.558164π-0.558164\pi
−0.181712 + 0.983352i 0.558164π0.558164\pi
822822 0 0
823823 −30.0396 −1.04711 −0.523557 0.851991i 0.675395π-0.675395\pi
−0.523557 + 0.851991i 0.675395π0.675395\pi
824824 0 0
825825 6.22289 0.216653
826826 0 0
827827 −28.6978 −0.997920 −0.498960 0.866625i 0.666285π-0.666285\pi
−0.498960 + 0.866625i 0.666285π0.666285\pi
828828 0 0
829829 16.4384 0.570931 0.285465 0.958389i 0.407852π-0.407852\pi
0.285465 + 0.958389i 0.407852π0.407852\pi
830830 0 0
831831 −11.6103 −0.402756
832832 0 0
833833 0.902098 0.0312559
834834 0 0
835835 −14.9771 −0.518304
836836 0 0
837837 −1.09790 −0.0379490
838838 0 0
839839 12.5437 0.433055 0.216528 0.976277i 0.430527π-0.430527\pi
0.216528 + 0.976277i 0.430527π0.430527\pi
840840 0 0
841841 15.6847 0.540850
842842 0 0
843843 9.89753 0.340889
844844 0 0
845845 29.5324 1.01595
846846 0 0
847847 −4.72964 −0.162512
848848 0 0
849849 −13.9994 −0.480457
850850 0 0
851851 −9.91023 −0.339718
852852 0 0
853853 −22.0613 −0.755365 −0.377683 0.925935i 0.623279π-0.623279\pi
−0.377683 + 0.925935i 0.623279π0.623279\pi
854854 0 0
855855 6.85086 0.234295
856856 0 0
857857 6.15359 0.210203 0.105101 0.994462i 0.466483π-0.466483\pi
0.105101 + 0.994462i 0.466483π0.466483\pi
858858 0 0
859859 −23.0698 −0.787131 −0.393566 0.919296i 0.628759π-0.628759\pi
−0.393566 + 0.919296i 0.628759π0.628759\pi
860860 0 0
861861 −2.30826 −0.0786655
862862 0 0
863863 5.22145 0.177740 0.0888702 0.996043i 0.471674π-0.471674\pi
0.0888702 + 0.996043i 0.471674π0.471674\pi
864864 0 0
865865 −49.7186 −1.69048
866866 0 0
867867 −16.1862 −0.549713
868868 0 0
869869 −26.2106 −0.889135
870870 0 0
871871 −16.7712 −0.568271
872872 0 0
873873 13.9102 0.470790
874874 0 0
875875 6.88046 0.232602
876876 0 0
877877 49.8716 1.68404 0.842022 0.539443i 0.181365π-0.181365\pi
0.842022 + 0.539443i 0.181365π0.181365\pi
878878 0 0
879879 −8.14038 −0.274568
880880 0 0
881881 −20.3054 −0.684107 −0.342053 0.939681i 0.611122π-0.611122\pi
−0.342053 + 0.939681i 0.611122π0.611122\pi
882882 0 0
883883 50.3500 1.69441 0.847206 0.531265i 0.178283π-0.178283\pi
0.847206 + 0.531265i 0.178283π0.178283\pi
884884 0 0
885885 −20.0534 −0.674086
886886 0 0
887887 −47.2694 −1.58715 −0.793576 0.608471i 0.791783π-0.791783\pi
−0.793576 + 0.608471i 0.791783π0.791783\pi
888888 0 0
889889 −0.449266 −0.0150679
890890 0 0
891891 2.50407 0.0838894
892892 0 0
893893 −16.8942 −0.565344
894894 0 0
895895 27.8679 0.931522
896896 0 0
897897 −1.48511 −0.0495865
898898 0 0
899899 −7.33910 −0.244773
900900 0 0
901901 −4.43515 −0.147756
902902 0 0
903903 −5.83380 −0.194137
904904 0 0
905905 −36.9855 −1.22944
906906 0 0
907907 5.65035 0.187617 0.0938084 0.995590i 0.470096π-0.470096\pi
0.0938084 + 0.995590i 0.470096π0.470096\pi
908908 0 0
909909 1.81502 0.0602003
910910 0 0
911911 −18.2196 −0.603641 −0.301820 0.953365i 0.597594π-0.597594\pi
−0.301820 + 0.953365i 0.597594π0.597594\pi
912912 0 0
913913 −19.0296 −0.629787
914914 0 0
915915 2.75299 0.0910111
916916 0 0
917917 19.9759 0.659661
918918 0 0
919919 −7.79561 −0.257154 −0.128577 0.991700i 0.541041π-0.541041\pi
−0.128577 + 0.991700i 0.541041π0.541041\pi
920920 0 0
921921 −13.5095 −0.445153
922922 0 0
923923 0.537623 0.0176961
924924 0 0
925925 24.6281 0.809766
926926 0 0
927927 16.6605 0.547203
928928 0 0
929929 11.5912 0.380293 0.190147 0.981756i 0.439104π-0.439104\pi
0.190147 + 0.981756i 0.439104π0.439104\pi
930930 0 0
931931 −2.50407 −0.0820675
932932 0 0
933933 24.3035 0.795662
934934 0 0
935935 −6.18015 −0.202113
936936 0 0
937937 −32.0050 −1.04556 −0.522778 0.852469i 0.675105π-0.675105\pi
−0.522778 + 0.852469i 0.675105π0.675105\pi
938938 0 0
939939 −33.7836 −1.10249
940940 0 0
941941 11.1090 0.362141 0.181071 0.983470i 0.442044π-0.442044\pi
0.181071 + 0.983470i 0.442044π0.442044\pi
942942 0 0
943943 2.30826 0.0751674
944944 0 0
945945 −2.73589 −0.0889986
946946 0 0
947947 12.1262 0.394049 0.197025 0.980399i 0.436872π-0.436872\pi
0.197025 + 0.980399i 0.436872π0.436872\pi
948948 0 0
949949 −7.93661 −0.257633
950950 0 0
951951 32.1594 1.04284
952952 0 0
953953 27.6645 0.896140 0.448070 0.893999i 0.352112π-0.352112\pi
0.448070 + 0.893999i 0.352112π0.352112\pi
954954 0 0
955955 −1.72838 −0.0559291
956956 0 0
957957 16.7388 0.541090
958958 0 0
959959 0.270356 0.00873026
960960 0 0
961961 −29.7946 −0.961117
962962 0 0
963963 −1.68092 −0.0541668
964964 0 0
965965 −3.74341 −0.120505
966966 0 0
967967 56.1838 1.80675 0.903374 0.428853i 0.141082π-0.141082\pi
0.903374 + 0.428853i 0.141082π0.141082\pi
968968 0 0
969969 −2.25892 −0.0725668
970970 0 0
971971 43.9884 1.41166 0.705828 0.708383i 0.250575π-0.250575\pi
0.705828 + 0.708383i 0.250575π0.250575\pi
972972 0 0
973973 −4.42512 −0.141863
974974 0 0
975975 3.69068 0.118196
976976 0 0
977977 −6.47804 −0.207251 −0.103625 0.994616i 0.533044π-0.533044\pi
−0.103625 + 0.994616i 0.533044π0.533044\pi
978978 0 0
979979 26.6044 0.850282
980980 0 0
981981 11.4333 0.365036
982982 0 0
983983 −37.8961 −1.20870 −0.604349 0.796720i 0.706567π-0.706567\pi
−0.604349 + 0.796720i 0.706567π0.706567\pi
984984 0 0
985985 −67.7437 −2.15849
986986 0 0
987987 6.74671 0.214750
988988 0 0
989989 5.83380 0.185504
990990 0 0
991991 −53.3499 −1.69472 −0.847358 0.531022i 0.821808π-0.821808\pi
−0.847358 + 0.531022i 0.821808π0.821808\pi
992992 0 0
993993 4.84004 0.153594
994994 0 0
995995 3.95254 0.125304
996996 0 0
997997 24.8754 0.787813 0.393907 0.919150i 0.371123π-0.371123\pi
0.393907 + 0.919150i 0.371123π0.371123\pi
998998 0 0
999999 9.91023 0.313546
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 7728.2.a.ce.1.1 4
4.3 odd 2 483.2.a.j.1.2 4
12.11 even 2 1449.2.a.o.1.3 4
28.27 even 2 3381.2.a.x.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.a.j.1.2 4 4.3 odd 2
1449.2.a.o.1.3 4 12.11 even 2
3381.2.a.x.1.2 4 28.27 even 2
7728.2.a.ce.1.1 4 1.1 even 1 trivial