Properties

Label 9280.2.a.bt.1.3
Level 92809280
Weight 22
Character 9280.1
Self dual yes
Analytic conductor 74.10174.101
Analytic rank 00
Dimension 33
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] = [9280,2,Mod(1,9280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("9280.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 9280=26529 9280 = 2^{6} \cdot 5 \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9280.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: 74.101173075774.1011730757
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x23x+1 x^{3} - x^{2} - 3x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 580)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 0.3111080.311108 of defining polynomial
Character χ\chi == 9280.1

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+2.90321q31.00000q5+1.52543q7+5.42864q91.52543q110.622216q132.90321q15+5.52543q17+2.90321q19+4.42864q21+2.90321q23+1.00000q25+7.05086q271.00000q29+2.90321q314.42864q331.52543q352.47457q371.80642q398.23506q415.65878q435.42864q45+4.70964q474.67307q49+16.0415q51+11.2859q53+1.52543q55+8.42864q57+10.2351q59+7.93978q61+8.28100q63+0.622216q652.90321q67+8.42864q697.47949q71+2.90321q73+2.90321q752.32693q77+16.5763q79+4.18421q816.76986q835.52543q852.90321q87+13.9081q890.949145q91+8.42864q932.90321q95+17.5669q978.28100q99+O(q100)q+2.90321 q^{3} -1.00000 q^{5} +1.52543 q^{7} +5.42864 q^{9} -1.52543 q^{11} -0.622216 q^{13} -2.90321 q^{15} +5.52543 q^{17} +2.90321 q^{19} +4.42864 q^{21} +2.90321 q^{23} +1.00000 q^{25} +7.05086 q^{27} -1.00000 q^{29} +2.90321 q^{31} -4.42864 q^{33} -1.52543 q^{35} -2.47457 q^{37} -1.80642 q^{39} -8.23506 q^{41} -5.65878 q^{43} -5.42864 q^{45} +4.70964 q^{47} -4.67307 q^{49} +16.0415 q^{51} +11.2859 q^{53} +1.52543 q^{55} +8.42864 q^{57} +10.2351 q^{59} +7.93978 q^{61} +8.28100 q^{63} +0.622216 q^{65} -2.90321 q^{67} +8.42864 q^{69} -7.47949 q^{71} +2.90321 q^{73} +2.90321 q^{75} -2.32693 q^{77} +16.5763 q^{79} +4.18421 q^{81} -6.76986 q^{83} -5.52543 q^{85} -2.90321 q^{87} +13.9081 q^{89} -0.949145 q^{91} +8.42864 q^{93} -2.90321 q^{95} +17.5669 q^{97} -8.28100 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+2q33q52q7+3q9+2q112q132q15+10q17+2q19+2q23+3q25+8q273q29+2q31+2q3514q37+8q39+2q4110q43+18q99+O(q100) 3 q + 2 q^{3} - 3 q^{5} - 2 q^{7} + 3 q^{9} + 2 q^{11} - 2 q^{13} - 2 q^{15} + 10 q^{17} + 2 q^{19} + 2 q^{23} + 3 q^{25} + 8 q^{27} - 3 q^{29} + 2 q^{31} + 2 q^{35} - 14 q^{37} + 8 q^{39} + 2 q^{41} - 10 q^{43}+ \cdots - 18 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 2.90321 1.67617 0.838085 0.545540i 0.183675π-0.183675\pi
0.838085 + 0.545540i 0.183675π0.183675\pi
44 0 0
55 −1.00000 −0.447214
66 0 0
77 1.52543 0.576557 0.288279 0.957547i 0.406917π-0.406917\pi
0.288279 + 0.957547i 0.406917π0.406917\pi
88 0 0
99 5.42864 1.80955
1010 0 0
1111 −1.52543 −0.459934 −0.229967 0.973198i 0.573862π-0.573862\pi
−0.229967 + 0.973198i 0.573862π0.573862\pi
1212 0 0
1313 −0.622216 −0.172572 −0.0862858 0.996270i 0.527500π-0.527500\pi
−0.0862858 + 0.996270i 0.527500π0.527500\pi
1414 0 0
1515 −2.90321 −0.749606
1616 0 0
1717 5.52543 1.34011 0.670057 0.742310i 0.266270π-0.266270\pi
0.670057 + 0.742310i 0.266270π0.266270\pi
1818 0 0
1919 2.90321 0.666042 0.333021 0.942919i 0.391932π-0.391932\pi
0.333021 + 0.942919i 0.391932π0.391932\pi
2020 0 0
2121 4.42864 0.966408
2222 0 0
2323 2.90321 0.605362 0.302681 0.953092i 0.402118π-0.402118\pi
0.302681 + 0.953092i 0.402118π0.402118\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 7.05086 1.35694
2828 0 0
2929 −1.00000 −0.185695
3030 0 0
3131 2.90321 0.521432 0.260716 0.965416i 0.416041π-0.416041\pi
0.260716 + 0.965416i 0.416041π0.416041\pi
3232 0 0
3333 −4.42864 −0.770927
3434 0 0
3535 −1.52543 −0.257844
3636 0 0
3737 −2.47457 −0.406817 −0.203409 0.979094i 0.565202π-0.565202\pi
−0.203409 + 0.979094i 0.565202π0.565202\pi
3838 0 0
3939 −1.80642 −0.289259
4040 0 0
4141 −8.23506 −1.28610 −0.643050 0.765824i 0.722331π-0.722331\pi
−0.643050 + 0.765824i 0.722331π0.722331\pi
4242 0 0
4343 −5.65878 −0.862956 −0.431478 0.902123i 0.642008π-0.642008\pi
−0.431478 + 0.902123i 0.642008π0.642008\pi
4444 0 0
4545 −5.42864 −0.809254
4646 0 0
4747 4.70964 0.686971 0.343485 0.939158i 0.388392π-0.388392\pi
0.343485 + 0.939158i 0.388392π0.388392\pi
4848 0 0
4949 −4.67307 −0.667582
5050 0 0
5151 16.0415 2.24626
5252 0 0
5353 11.2859 1.55024 0.775120 0.631814i 0.217689π-0.217689\pi
0.775120 + 0.631814i 0.217689π0.217689\pi
5454 0 0
5555 1.52543 0.205689
5656 0 0
5757 8.42864 1.11640
5858 0 0
5959 10.2351 1.33249 0.666246 0.745732i 0.267900π-0.267900\pi
0.666246 + 0.745732i 0.267900π0.267900\pi
6060 0 0
6161 7.93978 1.01658 0.508292 0.861185i 0.330277π-0.330277\pi
0.508292 + 0.861185i 0.330277π0.330277\pi
6262 0 0
6363 8.28100 1.04331
6464 0 0
6565 0.622216 0.0771764
6666 0 0
6767 −2.90321 −0.354684 −0.177342 0.984149i 0.556750π-0.556750\pi
−0.177342 + 0.984149i 0.556750π0.556750\pi
6868 0 0
6969 8.42864 1.01469
7070 0 0
7171 −7.47949 −0.887653 −0.443826 0.896113i 0.646379π-0.646379\pi
−0.443826 + 0.896113i 0.646379π0.646379\pi
7272 0 0
7373 2.90321 0.339795 0.169898 0.985462i 0.445656π-0.445656\pi
0.169898 + 0.985462i 0.445656π0.445656\pi
7474 0 0
7575 2.90321 0.335234
7676 0 0
7777 −2.32693 −0.265178
7878 0 0
7979 16.5763 1.86498 0.932489 0.361199i 0.117632π-0.117632\pi
0.932489 + 0.361199i 0.117632π0.117632\pi
8080 0 0
8181 4.18421 0.464912
8282 0 0
8383 −6.76986 −0.743089 −0.371544 0.928415i 0.621172π-0.621172\pi
−0.371544 + 0.928415i 0.621172π0.621172\pi
8484 0 0
8585 −5.52543 −0.599317
8686 0 0
8787 −2.90321 −0.311257
8888 0 0
8989 13.9081 1.47426 0.737130 0.675751i 0.236181π-0.236181\pi
0.737130 + 0.675751i 0.236181π0.236181\pi
9090 0 0
9191 −0.949145 −0.0994974
9292 0 0
9393 8.42864 0.874009
9494 0 0
9595 −2.90321 −0.297863
9696 0 0
9797 17.5669 1.78365 0.891825 0.452381i 0.149425π-0.149425\pi
0.891825 + 0.452381i 0.149425π0.149425\pi
9898 0 0
9999 −8.28100 −0.832271
100100 0 0
101101 −5.05086 −0.502579 −0.251289 0.967912i 0.580855π-0.580855\pi
−0.251289 + 0.967912i 0.580855π0.580855\pi
102102 0 0
103103 −9.56691 −0.942656 −0.471328 0.881958i 0.656225π-0.656225\pi
−0.471328 + 0.881958i 0.656225π0.656225\pi
104104 0 0
105105 −4.42864 −0.432191
106106 0 0
107107 −0.576283 −0.0557113 −0.0278557 0.999612i 0.508868π-0.508868\pi
−0.0278557 + 0.999612i 0.508868π0.508868\pi
108108 0 0
109109 −7.28592 −0.697864 −0.348932 0.937148i 0.613456π-0.613456\pi
−0.348932 + 0.937148i 0.613456π0.613456\pi
110110 0 0
111111 −7.18421 −0.681895
112112 0 0
113113 11.7605 1.10633 0.553167 0.833070i 0.313419π-0.313419\pi
0.553167 + 0.833070i 0.313419π0.313419\pi
114114 0 0
115115 −2.90321 −0.270726
116116 0 0
117117 −3.37778 −0.312276
118118 0 0
119119 8.42864 0.772652
120120 0 0
121121 −8.67307 −0.788461
122122 0 0
123123 −23.9081 −2.15572
124124 0 0
125125 −1.00000 −0.0894427
126126 0 0
127127 14.5161 1.28809 0.644046 0.764987i 0.277255π-0.277255\pi
0.644046 + 0.764987i 0.277255π0.277255\pi
128128 0 0
129129 −16.4286 −1.44646
130130 0 0
131131 −15.7605 −1.37700 −0.688500 0.725236i 0.741731π-0.741731\pi
−0.688500 + 0.725236i 0.741731π0.741731\pi
132132 0 0
133133 4.42864 0.384012
134134 0 0
135135 −7.05086 −0.606841
136136 0 0
137137 5.52543 0.472069 0.236035 0.971745i 0.424152π-0.424152\pi
0.236035 + 0.971745i 0.424152π0.424152\pi
138138 0 0
139139 −17.4193 −1.47748 −0.738742 0.673989i 0.764580π-0.764580\pi
−0.738742 + 0.673989i 0.764580π0.764580\pi
140140 0 0
141141 13.6731 1.15148
142142 0 0
143143 0.949145 0.0793715
144144 0 0
145145 1.00000 0.0830455
146146 0 0
147147 −13.5669 −1.11898
148148 0 0
149149 −2.00000 −0.163846 −0.0819232 0.996639i 0.526106π-0.526106\pi
−0.0819232 + 0.996639i 0.526106π0.526106\pi
150150 0 0
151151 5.37778 0.437638 0.218819 0.975765i 0.429780π-0.429780\pi
0.218819 + 0.975765i 0.429780π0.429780\pi
152152 0 0
153153 29.9956 2.42500
154154 0 0
155155 −2.90321 −0.233192
156156 0 0
157157 1.39207 0.111100 0.0555498 0.998456i 0.482309π-0.482309\pi
0.0555498 + 0.998456i 0.482309π0.482309\pi
158158 0 0
159159 32.7654 2.59847
160160 0 0
161161 4.42864 0.349026
162162 0 0
163163 7.19850 0.563830 0.281915 0.959439i 0.409030π-0.409030\pi
0.281915 + 0.959439i 0.409030π0.409030\pi
164164 0 0
165165 4.42864 0.344769
166166 0 0
167167 −15.7605 −1.21958 −0.609792 0.792562i 0.708747π-0.708747\pi
−0.609792 + 0.792562i 0.708747π0.708747\pi
168168 0 0
169169 −12.6128 −0.970219
170170 0 0
171171 15.7605 1.20523
172172 0 0
173173 −13.4795 −1.02483 −0.512413 0.858739i 0.671248π-0.671248\pi
−0.512413 + 0.858739i 0.671248π0.671248\pi
174174 0 0
175175 1.52543 0.115311
176176 0 0
177177 29.7146 2.23348
178178 0 0
179179 −0.266706 −0.0199346 −0.00996728 0.999950i 0.503173π-0.503173\pi
−0.00996728 + 0.999950i 0.503173π0.503173\pi
180180 0 0
181181 20.7971 1.54583 0.772916 0.634508i 0.218797π-0.218797\pi
0.772916 + 0.634508i 0.218797π0.218797\pi
182182 0 0
183183 23.0509 1.70397
184184 0 0
185185 2.47457 0.181934
186186 0 0
187187 −8.42864 −0.616363
188188 0 0
189189 10.7556 0.782353
190190 0 0
191191 9.43356 0.682589 0.341294 0.939956i 0.389135π-0.389135\pi
0.341294 + 0.939956i 0.389135π0.389135\pi
192192 0 0
193193 5.23014 0.376474 0.188237 0.982124i 0.439723π-0.439723\pi
0.188237 + 0.982124i 0.439723π0.439723\pi
194194 0 0
195195 1.80642 0.129361
196196 0 0
197197 −11.5397 −0.822171 −0.411085 0.911597i 0.634850π-0.634850\pi
−0.411085 + 0.911597i 0.634850π0.634850\pi
198198 0 0
199199 −8.33677 −0.590978 −0.295489 0.955346i 0.595483π-0.595483\pi
−0.295489 + 0.955346i 0.595483π0.595483\pi
200200 0 0
201201 −8.42864 −0.594510
202202 0 0
203203 −1.52543 −0.107064
204204 0 0
205205 8.23506 0.575162
206206 0 0
207207 15.7605 1.09543
208208 0 0
209209 −4.42864 −0.306335
210210 0 0
211211 9.79213 0.674118 0.337059 0.941483i 0.390568π-0.390568\pi
0.337059 + 0.941483i 0.390568π0.390568\pi
212212 0 0
213213 −21.7146 −1.48786
214214 0 0
215215 5.65878 0.385926
216216 0 0
217217 4.42864 0.300636
218218 0 0
219219 8.42864 0.569555
220220 0 0
221221 −3.43801 −0.231265
222222 0 0
223223 −16.0558 −1.07517 −0.537587 0.843208i 0.680664π-0.680664\pi
−0.537587 + 0.843208i 0.680664π0.680664\pi
224224 0 0
225225 5.42864 0.361909
226226 0 0
227227 19.1985 1.27425 0.637125 0.770761i 0.280124π-0.280124\pi
0.637125 + 0.770761i 0.280124π0.280124\pi
228228 0 0
229229 10.5906 0.699845 0.349922 0.936779i 0.386208π-0.386208\pi
0.349922 + 0.936779i 0.386208π0.386208\pi
230230 0 0
231231 −6.75557 −0.444484
232232 0 0
233233 23.1240 1.51490 0.757451 0.652892i 0.226444π-0.226444\pi
0.757451 + 0.652892i 0.226444π0.226444\pi
234234 0 0
235235 −4.70964 −0.307223
236236 0 0
237237 48.1245 3.12602
238238 0 0
239239 16.9906 1.09903 0.549516 0.835483i 0.314812π-0.314812\pi
0.549516 + 0.835483i 0.314812π0.314812\pi
240240 0 0
241241 0.368416 0.0237318 0.0118659 0.999930i 0.496223π-0.496223\pi
0.0118659 + 0.999930i 0.496223π0.496223\pi
242242 0 0
243243 −9.00492 −0.577666
244244 0 0
245245 4.67307 0.298552
246246 0 0
247247 −1.80642 −0.114940
248248 0 0
249249 −19.6543 −1.24554
250250 0 0
251251 15.7190 0.992175 0.496087 0.868273i 0.334770π-0.334770\pi
0.496087 + 0.868273i 0.334770π0.334770\pi
252252 0 0
253253 −4.42864 −0.278426
254254 0 0
255255 −16.0415 −1.00456
256256 0 0
257257 18.6035 1.16045 0.580227 0.814455i 0.302964π-0.302964\pi
0.580227 + 0.814455i 0.302964π0.302964\pi
258258 0 0
259259 −3.77478 −0.234553
260260 0 0
261261 −5.42864 −0.336024
262262 0 0
263263 12.7096 0.783710 0.391855 0.920027i 0.371834π-0.371834\pi
0.391855 + 0.920027i 0.371834π0.371834\pi
264264 0 0
265265 −11.2859 −0.693288
266266 0 0
267267 40.3783 2.47111
268268 0 0
269269 −21.7462 −1.32589 −0.662945 0.748668i 0.730694π-0.730694\pi
−0.662945 + 0.748668i 0.730694π0.730694\pi
270270 0 0
271271 18.3827 1.11667 0.558335 0.829616i 0.311440π-0.311440\pi
0.558335 + 0.829616i 0.311440π0.311440\pi
272272 0 0
273273 −2.75557 −0.166775
274274 0 0
275275 −1.52543 −0.0919867
276276 0 0
277277 −12.7971 −0.768901 −0.384450 0.923146i 0.625609π-0.625609\pi
−0.384450 + 0.923146i 0.625609π0.625609\pi
278278 0 0
279279 15.7605 0.943556
280280 0 0
281281 21.1842 1.26374 0.631872 0.775073i 0.282287π-0.282287\pi
0.631872 + 0.775073i 0.282287π0.282287\pi
282282 0 0
283283 −5.68736 −0.338079 −0.169039 0.985609i 0.554066π-0.554066\pi
−0.169039 + 0.985609i 0.554066π0.554066\pi
284284 0 0
285285 −8.42864 −0.499270
286286 0 0
287287 −12.5620 −0.741511
288288 0 0
289289 13.5303 0.795903
290290 0 0
291291 51.0005 2.98970
292292 0 0
293293 25.0879 1.46565 0.732825 0.680417i 0.238201π-0.238201\pi
0.732825 + 0.680417i 0.238201π0.238201\pi
294294 0 0
295295 −10.2351 −0.595908
296296 0 0
297297 −10.7556 −0.624101
298298 0 0
299299 −1.80642 −0.104468
300300 0 0
301301 −8.63206 −0.497544
302302 0 0
303303 −14.6637 −0.842408
304304 0 0
305305 −7.93978 −0.454630
306306 0 0
307307 30.8113 1.75850 0.879248 0.476364i 0.158046π-0.158046\pi
0.879248 + 0.476364i 0.158046π0.158046\pi
308308 0 0
309309 −27.7748 −1.58005
310310 0 0
311311 −30.0370 −1.70324 −0.851622 0.524156i 0.824381π-0.824381\pi
−0.851622 + 0.524156i 0.824381π0.824381\pi
312312 0 0
313313 −18.3368 −1.03646 −0.518228 0.855243i 0.673408π-0.673408\pi
−0.518228 + 0.855243i 0.673408π0.673408\pi
314314 0 0
315315 −8.28100 −0.466581
316316 0 0
317317 −20.4558 −1.14891 −0.574457 0.818535i 0.694787π-0.694787\pi
−0.574457 + 0.818535i 0.694787π0.694787\pi
318318 0 0
319319 1.52543 0.0854075
320320 0 0
321321 −1.67307 −0.0933817
322322 0 0
323323 16.0415 0.892572
324324 0 0
325325 −0.622216 −0.0345143
326326 0 0
327327 −21.1526 −1.16974
328328 0 0
329329 7.18421 0.396078
330330 0 0
331331 −12.0272 −0.661075 −0.330537 0.943793i 0.607230π-0.607230\pi
−0.330537 + 0.943793i 0.607230π0.607230\pi
332332 0 0
333333 −13.4336 −0.736155
334334 0 0
335335 2.90321 0.158619
336336 0 0
337337 −32.2306 −1.75571 −0.877857 0.478923i 0.841027π-0.841027\pi
−0.877857 + 0.478923i 0.841027π0.841027\pi
338338 0 0
339339 34.1432 1.85440
340340 0 0
341341 −4.42864 −0.239824
342342 0 0
343343 −17.8064 −0.961457
344344 0 0
345345 −8.42864 −0.453783
346346 0 0
347347 −29.9037 −1.60531 −0.802657 0.596441i 0.796581π-0.796581\pi
−0.802657 + 0.596441i 0.796581π0.796581\pi
348348 0 0
349349 −29.8163 −1.59603 −0.798014 0.602639i 0.794116π-0.794116\pi
−0.798014 + 0.602639i 0.794116π0.794116\pi
350350 0 0
351351 −4.38715 −0.234169
352352 0 0
353353 21.1842 1.12752 0.563761 0.825938i 0.309354π-0.309354\pi
0.563761 + 0.825938i 0.309354π0.309354\pi
354354 0 0
355355 7.47949 0.396970
356356 0 0
357357 24.4701 1.29510
358358 0 0
359359 −11.1985 −0.591034 −0.295517 0.955337i 0.595492π-0.595492\pi
−0.295517 + 0.955337i 0.595492π0.595492\pi
360360 0 0
361361 −10.5714 −0.556387
362362 0 0
363363 −25.1798 −1.32159
364364 0 0
365365 −2.90321 −0.151961
366366 0 0
367367 9.95407 0.519598 0.259799 0.965663i 0.416344π-0.416344\pi
0.259799 + 0.965663i 0.416344π0.416344\pi
368368 0 0
369369 −44.7052 −2.32726
370370 0 0
371371 17.2159 0.893802
372372 0 0
373373 −2.29529 −0.118845 −0.0594227 0.998233i 0.518926π-0.518926\pi
−0.0594227 + 0.998233i 0.518926π0.518926\pi
374374 0 0
375375 −2.90321 −0.149921
376376 0 0
377377 0.622216 0.0320457
378378 0 0
379379 9.61729 0.494007 0.247004 0.969015i 0.420554π-0.420554\pi
0.247004 + 0.969015i 0.420554π0.420554\pi
380380 0 0
381381 42.1432 2.15906
382382 0 0
383383 6.86172 0.350618 0.175309 0.984513i 0.443908π-0.443908\pi
0.175309 + 0.984513i 0.443908π0.443908\pi
384384 0 0
385385 2.32693 0.118591
386386 0 0
387387 −30.7195 −1.56156
388388 0 0
389389 −25.3590 −1.28575 −0.642877 0.765969i 0.722260π-0.722260\pi
−0.642877 + 0.765969i 0.722260π0.722260\pi
390390 0 0
391391 16.0415 0.811253
392392 0 0
393393 −45.7560 −2.30809
394394 0 0
395395 −16.5763 −0.834043
396396 0 0
397397 −24.2766 −1.21841 −0.609203 0.793015i 0.708510π-0.708510\pi
−0.609203 + 0.793015i 0.708510π0.708510\pi
398398 0 0
399399 12.8573 0.643669
400400 0 0
401401 5.30465 0.264902 0.132451 0.991190i 0.457715π-0.457715\pi
0.132451 + 0.991190i 0.457715π0.457715\pi
402402 0 0
403403 −1.80642 −0.0899844
404404 0 0
405405 −4.18421 −0.207915
406406 0 0
407407 3.77478 0.187109
408408 0 0
409409 0.714082 0.0353091 0.0176545 0.999844i 0.494380π-0.494380\pi
0.0176545 + 0.999844i 0.494380π0.494380\pi
410410 0 0
411411 16.0415 0.791268
412412 0 0
413413 15.6128 0.768258
414414 0 0
415415 6.76986 0.332319
416416 0 0
417417 −50.5718 −2.47651
418418 0 0
419419 −16.6321 −0.812529 −0.406265 0.913755i 0.633169π-0.633169\pi
−0.406265 + 0.913755i 0.633169π0.633169\pi
420420 0 0
421421 30.4286 1.48300 0.741501 0.670952i 0.234114π-0.234114\pi
0.741501 + 0.670952i 0.234114π0.234114\pi
422422 0 0
423423 25.5669 1.24311
424424 0 0
425425 5.52543 0.268023
426426 0 0
427427 12.1116 0.586119
428428 0 0
429429 2.75557 0.133040
430430 0 0
431431 31.2257 1.50409 0.752044 0.659112i 0.229068π-0.229068\pi
0.752044 + 0.659112i 0.229068π0.229068\pi
432432 0 0
433433 35.2400 1.69353 0.846763 0.531971i 0.178548π-0.178548\pi
0.846763 + 0.531971i 0.178548π0.178548\pi
434434 0 0
435435 2.90321 0.139198
436436 0 0
437437 8.42864 0.403197
438438 0 0
439439 −30.6133 −1.46109 −0.730547 0.682862i 0.760735π-0.760735\pi
−0.730547 + 0.682862i 0.760735π0.760735\pi
440440 0 0
441441 −25.3684 −1.20802
442442 0 0
443443 31.4938 1.49631 0.748157 0.663521i 0.230939π-0.230939\pi
0.748157 + 0.663521i 0.230939π0.230939\pi
444444 0 0
445445 −13.9081 −0.659309
446446 0 0
447447 −5.80642 −0.274634
448448 0 0
449449 −18.6321 −0.879301 −0.439651 0.898169i 0.644898π-0.644898\pi
−0.439651 + 0.898169i 0.644898π0.644898\pi
450450 0 0
451451 12.5620 0.591521
452452 0 0
453453 15.6128 0.733556
454454 0 0
455455 0.949145 0.0444966
456456 0 0
457457 −31.2859 −1.46349 −0.731747 0.681577i 0.761295π-0.761295\pi
−0.731747 + 0.681577i 0.761295π0.761295\pi
458458 0 0
459459 38.9590 1.81845
460460 0 0
461461 28.9304 1.34742 0.673712 0.738994i 0.264699π-0.264699\pi
0.673712 + 0.738994i 0.264699π0.264699\pi
462462 0 0
463463 14.1289 0.656626 0.328313 0.944569i 0.393520π-0.393520\pi
0.328313 + 0.944569i 0.393520π0.393520\pi
464464 0 0
465465 −8.42864 −0.390869
466466 0 0
467467 30.6909 1.42021 0.710103 0.704098i 0.248648π-0.248648\pi
0.710103 + 0.704098i 0.248648π0.248648\pi
468468 0 0
469469 −4.42864 −0.204496
470470 0 0
471471 4.04149 0.186222
472472 0 0
473473 8.63206 0.396903
474474 0 0
475475 2.90321 0.133208
476476 0 0
477477 61.2672 2.80523
478478 0 0
479479 −9.04641 −0.413341 −0.206670 0.978411i 0.566263π-0.566263\pi
−0.206670 + 0.978411i 0.566263π0.566263\pi
480480 0 0
481481 1.53972 0.0702051
482482 0 0
483483 12.8573 0.585026
484484 0 0
485485 −17.5669 −0.797673
486486 0 0
487487 14.6494 0.663828 0.331914 0.943310i 0.392306π-0.392306\pi
0.331914 + 0.943310i 0.392306π0.392306\pi
488488 0 0
489489 20.8988 0.945075
490490 0 0
491491 −22.1289 −0.998664 −0.499332 0.866411i 0.666421π-0.666421\pi
−0.499332 + 0.866411i 0.666421π0.666421\pi
492492 0 0
493493 −5.52543 −0.248853
494494 0 0
495495 8.28100 0.372203
496496 0 0
497497 −11.4094 −0.511783
498498 0 0
499499 29.9813 1.34215 0.671073 0.741391i 0.265834π-0.265834\pi
0.671073 + 0.741391i 0.265834π0.265834\pi
500500 0 0
501501 −45.7560 −2.04423
502502 0 0
503503 17.6874 0.788640 0.394320 0.918973i 0.370980π-0.370980\pi
0.394320 + 0.918973i 0.370980π0.370980\pi
504504 0 0
505505 5.05086 0.224760
506506 0 0
507507 −36.6178 −1.62625
508508 0 0
509509 −1.45091 −0.0643107 −0.0321553 0.999483i 0.510237π-0.510237\pi
−0.0321553 + 0.999483i 0.510237π0.510237\pi
510510 0 0
511511 4.42864 0.195911
512512 0 0
513513 20.4701 0.903778
514514 0 0
515515 9.56691 0.421569
516516 0 0
517517 −7.18421 −0.315961
518518 0 0
519519 −39.1338 −1.71778
520520 0 0
521521 −31.8765 −1.39653 −0.698267 0.715837i 0.746045π-0.746045\pi
−0.698267 + 0.715837i 0.746045π0.746045\pi
522522 0 0
523523 14.9032 0.651672 0.325836 0.945426i 0.394354π-0.394354\pi
0.325836 + 0.945426i 0.394354π0.394354\pi
524524 0 0
525525 4.42864 0.193282
526526 0 0
527527 16.0415 0.698778
528528 0 0
529529 −14.5714 −0.633537
530530 0 0
531531 55.5625 2.41121
532532 0 0
533533 5.12399 0.221944
534534 0 0
535535 0.576283 0.0249149
536536 0 0
537537 −0.774305 −0.0334137
538538 0 0
539539 7.12843 0.307043
540540 0 0
541541 12.7841 0.549633 0.274817 0.961497i 0.411383π-0.411383\pi
0.274817 + 0.961497i 0.411383π0.411383\pi
542542 0 0
543543 60.3783 2.59108
544544 0 0
545545 7.28592 0.312094
546546 0 0
547547 −18.8617 −0.806469 −0.403235 0.915097i 0.632114π-0.632114\pi
−0.403235 + 0.915097i 0.632114π0.632114\pi
548548 0 0
549549 43.1022 1.83956
550550 0 0
551551 −2.90321 −0.123681
552552 0 0
553553 25.2859 1.07527
554554 0 0
555555 7.18421 0.304953
556556 0 0
557557 15.6316 0.662331 0.331166 0.943573i 0.392558π-0.392558\pi
0.331166 + 0.943573i 0.392558π0.392558\pi
558558 0 0
559559 3.52098 0.148922
560560 0 0
561561 −24.4701 −1.03313
562562 0 0
563563 −1.18865 −0.0500958 −0.0250479 0.999686i 0.507974π-0.507974\pi
−0.0250479 + 0.999686i 0.507974π0.507974\pi
564564 0 0
565565 −11.7605 −0.494768
566566 0 0
567567 6.38271 0.268048
568568 0 0
569569 28.5303 1.19605 0.598027 0.801476i 0.295951π-0.295951\pi
0.598027 + 0.801476i 0.295951π0.295951\pi
570570 0 0
571571 −22.8385 −0.955763 −0.477882 0.878424i 0.658595π-0.658595\pi
−0.477882 + 0.878424i 0.658595π0.658595\pi
572572 0 0
573573 27.3876 1.14413
574574 0 0
575575 2.90321 0.121072
576576 0 0
577577 4.18913 0.174396 0.0871979 0.996191i 0.472209π-0.472209\pi
0.0871979 + 0.996191i 0.472209π0.472209\pi
578578 0 0
579579 15.1842 0.631034
580580 0 0
581581 −10.3269 −0.428433
582582 0 0
583583 −17.2159 −0.713008
584584 0 0
585585 3.37778 0.139654
586586 0 0
587587 39.2815 1.62132 0.810660 0.585517i 0.199109π-0.199109\pi
0.810660 + 0.585517i 0.199109π0.199109\pi
588588 0 0
589589 8.42864 0.347296
590590 0 0
591591 −33.5022 −1.37810
592592 0 0
593593 −21.4509 −0.880883 −0.440442 0.897781i 0.645178π-0.645178\pi
−0.440442 + 0.897781i 0.645178π0.645178\pi
594594 0 0
595595 −8.42864 −0.345541
596596 0 0
597597 −24.2034 −0.990580
598598 0 0
599599 −18.3827 −0.751097 −0.375549 0.926803i 0.622546π-0.622546\pi
−0.375549 + 0.926803i 0.622546π0.622546\pi
600600 0 0
601601 −12.3555 −0.503992 −0.251996 0.967728i 0.581087π-0.581087\pi
−0.251996 + 0.967728i 0.581087π0.581087\pi
602602 0 0
603603 −15.7605 −0.641817
604604 0 0
605605 8.67307 0.352610
606606 0 0
607607 −48.4340 −1.96588 −0.982938 0.183935i 0.941117π-0.941117\pi
−0.982938 + 0.183935i 0.941117π0.941117\pi
608608 0 0
609609 −4.42864 −0.179458
610610 0 0
611611 −2.93041 −0.118552
612612 0 0
613613 0.958989 0.0387332 0.0193666 0.999812i 0.493835π-0.493835\pi
0.0193666 + 0.999812i 0.493835π0.493835\pi
614614 0 0
615615 23.9081 0.964069
616616 0 0
617617 5.09679 0.205189 0.102594 0.994723i 0.467286π-0.467286\pi
0.102594 + 0.994723i 0.467286π0.467286\pi
618618 0 0
619619 0.0142901 0.000574368 0 0.000287184 1.00000i 0.499909π-0.499909\pi
0.000287184 1.00000i 0.499909π0.499909\pi
620620 0 0
621621 20.4701 0.821438
622622 0 0
623623 21.2159 0.849995
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 −12.8573 −0.513470
628628 0 0
629629 −13.6731 −0.545181
630630 0 0
631631 12.8859 0.512978 0.256489 0.966547i 0.417434π-0.417434\pi
0.256489 + 0.966547i 0.417434π0.417434\pi
632632 0 0
633633 28.4286 1.12994
634634 0 0
635635 −14.5161 −0.576052
636636 0 0
637637 2.90766 0.115206
638638 0 0
639639 −40.6035 −1.60625
640640 0 0
641641 −46.6865 −1.84400 −0.922002 0.387185i 0.873447π-0.873447\pi
−0.922002 + 0.387185i 0.873447π0.873447\pi
642642 0 0
643643 −28.1388 −1.10968 −0.554842 0.831956i 0.687221π-0.687221\pi
−0.554842 + 0.831956i 0.687221π0.687221\pi
644644 0 0
645645 16.4286 0.646877
646646 0 0
647647 47.5067 1.86768 0.933840 0.357690i 0.116436π-0.116436\pi
0.933840 + 0.357690i 0.116436π0.116436\pi
648648 0 0
649649 −15.6128 −0.612858
650650 0 0
651651 12.8573 0.503916
652652 0 0
653653 −25.5383 −0.999392 −0.499696 0.866201i 0.666555π-0.666555\pi
−0.499696 + 0.866201i 0.666555π0.666555\pi
654654 0 0
655655 15.7605 0.615813
656656 0 0
657657 15.7605 0.614875
658658 0 0
659659 11.4938 0.447734 0.223867 0.974620i 0.428132π-0.428132\pi
0.223867 + 0.974620i 0.428132π0.428132\pi
660660 0 0
661661 −48.4929 −1.88615 −0.943077 0.332574i 0.892083π-0.892083\pi
−0.943077 + 0.332574i 0.892083π0.892083\pi
662662 0 0
663663 −9.98126 −0.387640
664664 0 0
665665 −4.42864 −0.171735
666666 0 0
667667 −2.90321 −0.112413
668668 0 0
669669 −46.6133 −1.80218
670670 0 0
671671 −12.1116 −0.467561
672672 0 0
673673 −15.1526 −0.584088 −0.292044 0.956405i 0.594335π-0.594335\pi
−0.292044 + 0.956405i 0.594335π0.594335\pi
674674 0 0
675675 7.05086 0.271388
676676 0 0
677677 −38.8943 −1.49483 −0.747415 0.664357i 0.768705π-0.768705\pi
−0.747415 + 0.664357i 0.768705π0.768705\pi
678678 0 0
679679 26.7971 1.02838
680680 0 0
681681 55.7373 2.13586
682682 0 0
683683 11.3733 0.435189 0.217594 0.976039i 0.430179π-0.430179\pi
0.217594 + 0.976039i 0.430179π0.430179\pi
684684 0 0
685685 −5.52543 −0.211116
686686 0 0
687687 30.7467 1.17306
688688 0 0
689689 −7.02227 −0.267527
690690 0 0
691691 −29.4893 −1.12183 −0.560914 0.827874i 0.689550π-0.689550\pi
−0.560914 + 0.827874i 0.689550π0.689550\pi
692692 0 0
693693 −12.6321 −0.479852
694694 0 0
695695 17.4193 0.660751
696696 0 0
697697 −45.5022 −1.72352
698698 0 0
699699 67.1338 2.53923
700700 0 0
701701 −52.2895 −1.97495 −0.987473 0.157789i 0.949563π-0.949563\pi
−0.987473 + 0.157789i 0.949563π0.949563\pi
702702 0 0
703703 −7.18421 −0.270958
704704 0 0
705705 −13.6731 −0.514958
706706 0 0
707707 −7.70471 −0.289766
708708 0 0
709709 −9.18421 −0.344920 −0.172460 0.985017i 0.555172π-0.555172\pi
−0.172460 + 0.985017i 0.555172π0.555172\pi
710710 0 0
711711 89.9867 3.37476
712712 0 0
713713 8.42864 0.315655
714714 0 0
715715 −0.949145 −0.0354960
716716 0 0
717717 49.3274 1.84217
718718 0 0
719719 7.74620 0.288885 0.144442 0.989513i 0.453861π-0.453861\pi
0.144442 + 0.989513i 0.453861π0.453861\pi
720720 0 0
721721 −14.5936 −0.543495
722722 0 0
723723 1.06959 0.0397785
724724 0 0
725725 −1.00000 −0.0371391
726726 0 0
727727 −5.06821 −0.187969 −0.0939847 0.995574i 0.529960π-0.529960\pi
−0.0939847 + 0.995574i 0.529960π0.529960\pi
728728 0 0
729729 −38.6958 −1.43318
730730 0 0
731731 −31.2672 −1.15646
732732 0 0
733733 0.659257 0.0243502 0.0121751 0.999926i 0.496124π-0.496124\pi
0.0121751 + 0.999926i 0.496124π0.496124\pi
734734 0 0
735735 13.5669 0.500423
736736 0 0
737737 4.42864 0.163131
738738 0 0
739739 −7.07805 −0.260370 −0.130185 0.991490i 0.541557π-0.541557\pi
−0.130185 + 0.991490i 0.541557π0.541557\pi
740740 0 0
741741 −5.24443 −0.192659
742742 0 0
743743 26.3412 0.966366 0.483183 0.875519i 0.339481π-0.339481\pi
0.483183 + 0.875519i 0.339481π0.339481\pi
744744 0 0
745745 2.00000 0.0732743
746746 0 0
747747 −36.7511 −1.34465
748748 0 0
749749 −0.879077 −0.0321208
750750 0 0
751751 −4.92195 −0.179604 −0.0898022 0.995960i 0.528623π-0.528623\pi
−0.0898022 + 0.995960i 0.528623π0.528623\pi
752752 0 0
753753 45.6356 1.66305
754754 0 0
755755 −5.37778 −0.195718
756756 0 0
757757 −30.9032 −1.12320 −0.561598 0.827410i 0.689813π-0.689813\pi
−0.561598 + 0.827410i 0.689813π0.689813\pi
758758 0 0
759759 −12.8573 −0.466690
760760 0 0
761761 31.3274 1.13562 0.567809 0.823160i 0.307791π-0.307791\pi
0.567809 + 0.823160i 0.307791π0.307791\pi
762762 0 0
763763 −11.1141 −0.402359
764764 0 0
765765 −29.9956 −1.08449
766766 0 0
767767 −6.36842 −0.229950
768768 0 0
769769 −26.5620 −0.957850 −0.478925 0.877856i 0.658973π-0.658973\pi
−0.478925 + 0.877856i 0.658973π0.658973\pi
770770 0 0
771771 54.0098 1.94512
772772 0 0
773773 14.8528 0.534219 0.267110 0.963666i 0.413931π-0.413931\pi
0.267110 + 0.963666i 0.413931π0.413931\pi
774774 0 0
775775 2.90321 0.104286
776776 0 0
777777 −10.9590 −0.393152
778778 0 0
779779 −23.9081 −0.856598
780780 0 0
781781 11.4094 0.408261
782782 0 0
783783 −7.05086 −0.251977
784784 0 0
785785 −1.39207 −0.0496853
786786 0 0
787787 −25.5540 −0.910902 −0.455451 0.890261i 0.650522π-0.650522\pi
−0.455451 + 0.890261i 0.650522π0.650522\pi
788788 0 0
789789 36.8988 1.31363
790790 0 0
791791 17.9398 0.637865
792792 0 0
793793 −4.94025 −0.175434
794794 0 0
795795 −32.7654 −1.16207
796796 0 0
797797 10.2208 0.362038 0.181019 0.983480i 0.442060π-0.442060\pi
0.181019 + 0.983480i 0.442060π0.442060\pi
798798 0 0
799799 26.0228 0.920619
800800 0 0
801801 75.5022 2.66774
802802 0 0
803803 −4.42864 −0.156283
804804 0 0
805805 −4.42864 −0.156089
806806 0 0
807807 −63.1338 −2.22242
808808 0 0
809809 −2.44155 −0.0858402 −0.0429201 0.999079i 0.513666π-0.513666\pi
−0.0429201 + 0.999079i 0.513666π0.513666\pi
810810 0 0
811811 −2.33984 −0.0821628 −0.0410814 0.999156i 0.513080π-0.513080\pi
−0.0410814 + 0.999156i 0.513080π0.513080\pi
812812 0 0
813813 53.3689 1.87173
814814 0 0
815815 −7.19850 −0.252152
816816 0 0
817817 −16.4286 −0.574765
818818 0 0
819819 −5.15257 −0.180045
820820 0 0
821821 −14.6539 −0.511423 −0.255712 0.966753i 0.582310π-0.582310\pi
−0.255712 + 0.966753i 0.582310π0.582310\pi
822822 0 0
823823 −47.3733 −1.65133 −0.825665 0.564160i 0.809200π-0.809200\pi
−0.825665 + 0.564160i 0.809200π0.809200\pi
824824 0 0
825825 −4.42864 −0.154185
826826 0 0
827827 −18.3412 −0.637787 −0.318893 0.947791i 0.603311π-0.603311\pi
−0.318893 + 0.947791i 0.603311π0.603311\pi
828828 0 0
829829 −45.5625 −1.58245 −0.791225 0.611525i 0.790556π-0.790556\pi
−0.791225 + 0.611525i 0.790556π0.790556\pi
830830 0 0
831831 −37.1526 −1.28881
832832 0 0
833833 −25.8207 −0.894635
834834 0 0
835835 15.7605 0.545414
836836 0 0
837837 20.4701 0.707551
838838 0 0
839839 30.9733 1.06932 0.534658 0.845068i 0.320440π-0.320440\pi
0.534658 + 0.845068i 0.320440π0.320440\pi
840840 0 0
841841 1.00000 0.0344828
842842 0 0
843843 61.5022 2.11825
844844 0 0
845845 12.6128 0.433895
846846 0 0
847847 −13.2301 −0.454593
848848 0 0
849849 −16.5116 −0.566677
850850 0 0
851851 −7.18421 −0.246271
852852 0 0
853853 −25.4050 −0.869850 −0.434925 0.900467i 0.643225π-0.643225\pi
−0.434925 + 0.900467i 0.643225π0.643225\pi
854854 0 0
855855 −15.7605 −0.538997
856856 0 0
857857 −19.2573 −0.657818 −0.328909 0.944362i 0.606681π-0.606681\pi
−0.328909 + 0.944362i 0.606681π0.606681\pi
858858 0 0
859859 42.2623 1.44197 0.720985 0.692951i 0.243690π-0.243690\pi
0.720985 + 0.692951i 0.243690π0.243690\pi
860860 0 0
861861 −36.4701 −1.24290
862862 0 0
863863 9.88400 0.336455 0.168228 0.985748i 0.446196π-0.446196\pi
0.168228 + 0.985748i 0.446196π0.446196\pi
864864 0 0
865865 13.4795 0.458317
866866 0 0
867867 39.2815 1.33407
868868 0 0
869869 −25.2859 −0.857766
870870 0 0
871871 1.80642 0.0612083
872872 0 0
873873 95.3644 3.22760
874874 0 0
875875 −1.52543 −0.0515689
876876 0 0
877877 12.6508 0.427187 0.213594 0.976923i 0.431483π-0.431483\pi
0.213594 + 0.976923i 0.431483π0.431483\pi
878878 0 0
879879 72.8355 2.45668
880880 0 0
881881 −0.0888033 −0.00299186 −0.00149593 0.999999i 0.500476π-0.500476\pi
−0.00149593 + 0.999999i 0.500476π0.500476\pi
882882 0 0
883883 57.3131 1.92874 0.964370 0.264557i 0.0852258π-0.0852258\pi
0.964370 + 0.264557i 0.0852258π0.0852258\pi
884884 0 0
885885 −29.7146 −0.998844
886886 0 0
887887 −27.0781 −0.909192 −0.454596 0.890698i 0.650216π-0.650216\pi
−0.454596 + 0.890698i 0.650216π0.650216\pi
888888 0 0
889889 22.1432 0.742659
890890 0 0
891891 −6.38271 −0.213829
892892 0 0
893893 13.6731 0.457552
894894 0 0
895895 0.266706 0.00891500
896896 0 0
897897 −5.24443 −0.175106
898898 0 0
899899 −2.90321 −0.0968275
900900 0 0
901901 62.3595 2.07750
902902 0 0
903903 −25.0607 −0.833968
904904 0 0
905905 −20.7971 −0.691318
906906 0 0
907907 −38.6276 −1.28261 −0.641304 0.767287i 0.721606π-0.721606\pi
−0.641304 + 0.767287i 0.721606π0.721606\pi
908908 0 0
909909 −27.4193 −0.909440
910910 0 0
911911 −5.27163 −0.174657 −0.0873284 0.996180i 0.527833π-0.527833\pi
−0.0873284 + 0.996180i 0.527833π0.527833\pi
912912 0 0
913913 10.3269 0.341771
914914 0 0
915915 −23.0509 −0.762038
916916 0 0
917917 −24.0415 −0.793920
918918 0 0
919919 −11.6632 −0.384734 −0.192367 0.981323i 0.561616π-0.561616\pi
−0.192367 + 0.981323i 0.561616π0.561616\pi
920920 0 0
921921 89.4519 2.94754
922922 0 0
923923 4.65386 0.153184
924924 0 0
925925 −2.47457 −0.0813634
926926 0 0
927927 −51.9353 −1.70578
928928 0 0
929929 −46.8198 −1.53611 −0.768054 0.640385i 0.778775π-0.778775\pi
−0.768054 + 0.640385i 0.778775π0.778775\pi
930930 0 0
931931 −13.5669 −0.444638
932932 0 0
933933 −87.2039 −2.85493
934934 0 0
935935 8.42864 0.275646
936936 0 0
937937 4.44738 0.145289 0.0726447 0.997358i 0.476856π-0.476856\pi
0.0726447 + 0.997358i 0.476856π0.476856\pi
938938 0 0
939939 −53.2355 −1.73728
940940 0 0
941941 12.6726 0.413115 0.206557 0.978434i 0.433774π-0.433774\pi
0.206557 + 0.978434i 0.433774π0.433774\pi
942942 0 0
943943 −23.9081 −0.778556
944944 0 0
945945 −10.7556 −0.349879
946946 0 0
947947 −20.2306 −0.657407 −0.328703 0.944433i 0.606612π-0.606612\pi
−0.328703 + 0.944433i 0.606612π0.606612\pi
948948 0 0
949949 −1.80642 −0.0586390
950950 0 0
951951 −59.3876 −1.92578
952952 0 0
953953 −24.5718 −0.795960 −0.397980 0.917394i 0.630289π-0.630289\pi
−0.397980 + 0.917394i 0.630289π0.630289\pi
954954 0 0
955955 −9.43356 −0.305263
956956 0 0
957957 4.42864 0.143158
958958 0 0
959959 8.42864 0.272175
960960 0 0
961961 −22.5714 −0.728108
962962 0 0
963963 −3.12843 −0.100812
964964 0 0
965965 −5.23014 −0.168364
966966 0 0
967967 −52.9960 −1.70424 −0.852119 0.523349i 0.824683π-0.824683\pi
−0.852119 + 0.523349i 0.824683π0.824683\pi
968968 0 0
969969 46.5718 1.49610
970970 0 0
971971 4.02720 0.129239 0.0646195 0.997910i 0.479417π-0.479417\pi
0.0646195 + 0.997910i 0.479417π0.479417\pi
972972 0 0
973973 −26.5718 −0.851854
974974 0 0
975975 −1.80642 −0.0578519
976976 0 0
977977 13.2761 0.424739 0.212370 0.977189i 0.431882π-0.431882\pi
0.212370 + 0.977189i 0.431882π0.431882\pi
978978 0 0
979979 −21.2159 −0.678062
980980 0 0
981981 −39.5526 −1.26282
982982 0 0
983983 23.5857 0.752265 0.376133 0.926566i 0.377254π-0.377254\pi
0.376133 + 0.926566i 0.377254π0.377254\pi
984984 0 0
985985 11.5397 0.367686
986986 0 0
987987 20.8573 0.663895
988988 0 0
989989 −16.4286 −0.522400
990990 0 0
991991 −50.7882 −1.61334 −0.806670 0.591003i 0.798732π-0.798732\pi
−0.806670 + 0.591003i 0.798732π0.798732\pi
992992 0 0
993993 −34.9175 −1.10807
994994 0 0
995995 8.33677 0.264293
996996 0 0
997997 54.5705 1.72826 0.864132 0.503266i 0.167868π-0.167868\pi
0.864132 + 0.503266i 0.167868π0.167868\pi
998998 0 0
999999 −17.4479 −0.552026
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 9280.2.a.bt.1.3 3
4.3 odd 2 9280.2.a.bh.1.1 3
8.3 odd 2 580.2.a.d.1.3 3
8.5 even 2 2320.2.a.o.1.1 3
24.11 even 2 5220.2.a.w.1.1 3
40.3 even 4 2900.2.c.g.349.6 6
40.19 odd 2 2900.2.a.f.1.1 3
40.27 even 4 2900.2.c.g.349.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.2.a.d.1.3 3 8.3 odd 2
2320.2.a.o.1.1 3 8.5 even 2
2900.2.a.f.1.1 3 40.19 odd 2
2900.2.c.g.349.1 6 40.27 even 4
2900.2.c.g.349.6 6 40.3 even 4
5220.2.a.w.1.1 3 24.11 even 2
9280.2.a.bh.1.1 3 4.3 odd 2
9280.2.a.bt.1.3 3 1.1 even 1 trivial