Properties

Label 7744.2.a.dv.1.3
Level 77447744
Weight 22
Character 7744.1
Self dual yes
Analytic conductor 61.83661.836
Analytic rank 11
Dimension 66
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7744,2,Mod(1,7744)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7744, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("7744.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7744=26112 7744 = 2^{6} \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7744.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: 61.836151325361.8361513253
Analytic rank: 11
Dimension: 66
Coefficient field: 6.6.19898000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x510x4+7x3+24x215x5 x^{6} - x^{5} - 10x^{4} + 7x^{3} + 24x^{2} - 15x - 5 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 352)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 0.9356830.935683 of defining polynomial
Character χ\chi == 7744.1

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+0.0643165q32.31301q5+1.63066q72.99586q9+1.15644q130.148765q15+3.36056q17+5.83478q19+0.104878q217.86209q23+0.350020q250.385633q27+5.92691q293.61053q313.77174q35+0.362348q37+0.0743784q394.40970q415.15478q43+6.92946q451.15852q474.34095q49+0.216140q516.14411q53+0.375273q57+8.12241q59+8.82601q614.88524q632.67486q65+12.6763q670.505662q6915.0072q71+13.0022q73+0.0225121q75+2.07633q79+8.96279q818.94922q837.77302q85+0.381198q87+13.9653q89+1.88577q910.232217q9313.4959q95+0.00798799q97+O(q100)q+0.0643165 q^{3} -2.31301 q^{5} +1.63066 q^{7} -2.99586 q^{9} +1.15644 q^{13} -0.148765 q^{15} +3.36056 q^{17} +5.83478 q^{19} +0.104878 q^{21} -7.86209 q^{23} +0.350020 q^{25} -0.385633 q^{27} +5.92691 q^{29} -3.61053 q^{31} -3.77174 q^{35} +0.362348 q^{37} +0.0743784 q^{39} -4.40970 q^{41} -5.15478 q^{43} +6.92946 q^{45} -1.15852 q^{47} -4.34095 q^{49} +0.216140 q^{51} -6.14411 q^{53} +0.375273 q^{57} +8.12241 q^{59} +8.82601 q^{61} -4.88524 q^{63} -2.67486 q^{65} +12.6763 q^{67} -0.505662 q^{69} -15.0072 q^{71} +13.0022 q^{73} +0.0225121 q^{75} +2.07633 q^{79} +8.96279 q^{81} -8.94922 q^{83} -7.77302 q^{85} +0.381198 q^{87} +13.9653 q^{89} +1.88577 q^{91} -0.232217 q^{93} -13.4959 q^{95} +0.00798799 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+5q32q7+7q94q138q159q17+5q1912q216q23+4q25+26q2710q2912q3126q35+12q372q3917q41+11q43+21q97+O(q100) 6 q + 5 q^{3} - 2 q^{7} + 7 q^{9} - 4 q^{13} - 8 q^{15} - 9 q^{17} + 5 q^{19} - 12 q^{21} - 6 q^{23} + 4 q^{25} + 26 q^{27} - 10 q^{29} - 12 q^{31} - 26 q^{35} + 12 q^{37} - 2 q^{39} - 17 q^{41} + 11 q^{43}+ \cdots - 21 q^{97}+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 0.0643165 0.0371332 0.0185666 0.999828i 0.494090π-0.494090\pi
0.0185666 + 0.999828i 0.494090π0.494090\pi
44 0 0
55 −2.31301 −1.03441 −0.517205 0.855862i 0.673028π-0.673028\pi
−0.517205 + 0.855862i 0.673028π0.673028\pi
66 0 0
77 1.63066 0.616332 0.308166 0.951333i 0.400285π-0.400285\pi
0.308166 + 0.951333i 0.400285π0.400285\pi
88 0 0
99 −2.99586 −0.998621
1010 0 0
1111 0 0
1212 0 0
1313 1.15644 0.320739 0.160370 0.987057i 0.448731π-0.448731\pi
0.160370 + 0.987057i 0.448731π0.448731\pi
1414 0 0
1515 −0.148765 −0.0384109
1616 0 0
1717 3.36056 0.815057 0.407528 0.913193i 0.366391π-0.366391\pi
0.407528 + 0.913193i 0.366391π0.366391\pi
1818 0 0
1919 5.83478 1.33859 0.669295 0.742996i 0.266596π-0.266596\pi
0.669295 + 0.742996i 0.266596π0.266596\pi
2020 0 0
2121 0.104878 0.0228863
2222 0 0
2323 −7.86209 −1.63936 −0.819680 0.572822i 0.805848π-0.805848\pi
−0.819680 + 0.572822i 0.805848π0.805848\pi
2424 0 0
2525 0.350020 0.0700040
2626 0 0
2727 −0.385633 −0.0742151
2828 0 0
2929 5.92691 1.10060 0.550300 0.834967i 0.314513π-0.314513\pi
0.550300 + 0.834967i 0.314513π0.314513\pi
3030 0 0
3131 −3.61053 −0.648470 −0.324235 0.945977i 0.605107π-0.605107\pi
−0.324235 + 0.945977i 0.605107π0.605107\pi
3232 0 0
3333 0 0
3434 0 0
3535 −3.77174 −0.637540
3636 0 0
3737 0.362348 0.0595696 0.0297848 0.999556i 0.490518π-0.490518\pi
0.0297848 + 0.999556i 0.490518π0.490518\pi
3838 0 0
3939 0.0743784 0.0119101
4040 0 0
4141 −4.40970 −0.688679 −0.344340 0.938845i 0.611897π-0.611897\pi
−0.344340 + 0.938845i 0.611897π0.611897\pi
4242 0 0
4343 −5.15478 −0.786097 −0.393049 0.919518i 0.628580π-0.628580\pi
−0.393049 + 0.919518i 0.628580π0.628580\pi
4444 0 0
4545 6.92946 1.03298
4646 0 0
4747 −1.15852 −0.168988 −0.0844941 0.996424i 0.526927π-0.526927\pi
−0.0844941 + 0.996424i 0.526927π0.526927\pi
4848 0 0
4949 −4.34095 −0.620135
5050 0 0
5151 0.216140 0.0302656
5252 0 0
5353 −6.14411 −0.843959 −0.421980 0.906605i 0.638665π-0.638665\pi
−0.421980 + 0.906605i 0.638665π0.638665\pi
5454 0 0
5555 0 0
5656 0 0
5757 0.375273 0.0497061
5858 0 0
5959 8.12241 1.05745 0.528724 0.848794i 0.322671π-0.322671\pi
0.528724 + 0.848794i 0.322671π0.322671\pi
6060 0 0
6161 8.82601 1.13005 0.565027 0.825072i 0.308866π-0.308866\pi
0.565027 + 0.825072i 0.308866π0.308866\pi
6262 0 0
6363 −4.88524 −0.615482
6464 0 0
6565 −2.67486 −0.331776
6666 0 0
6767 12.6763 1.54865 0.774326 0.632787i 0.218089π-0.218089\pi
0.774326 + 0.632787i 0.218089π0.218089\pi
6868 0 0
6969 −0.505662 −0.0608746
7070 0 0
7171 −15.0072 −1.78103 −0.890515 0.454955i 0.849656π-0.849656\pi
−0.890515 + 0.454955i 0.849656π0.849656\pi
7272 0 0
7373 13.0022 1.52179 0.760896 0.648874i 0.224760π-0.224760\pi
0.760896 + 0.648874i 0.224760π0.224760\pi
7474 0 0
7575 0.0225121 0.00259947
7676 0 0
7777 0 0
7878 0 0
7979 2.07633 0.233606 0.116803 0.993155i 0.462735π-0.462735\pi
0.116803 + 0.993155i 0.462735π0.462735\pi
8080 0 0
8181 8.96279 0.995865
8282 0 0
8383 −8.94922 −0.982305 −0.491152 0.871074i 0.663424π-0.663424\pi
−0.491152 + 0.871074i 0.663424π0.663424\pi
8484 0 0
8585 −7.77302 −0.843103
8686 0 0
8787 0.381198 0.0408687
8888 0 0
8989 13.9653 1.48032 0.740160 0.672431i 0.234750π-0.234750\pi
0.740160 + 0.672431i 0.234750π0.234750\pi
9090 0 0
9191 1.88577 0.197682
9292 0 0
9393 −0.232217 −0.0240797
9494 0 0
9595 −13.4959 −1.38465
9696 0 0
9797 0.00798799 0.000811057 0 0.000405529 1.00000i 0.499871π-0.499871\pi
0.000405529 1.00000i 0.499871π0.499871\pi
9898 0 0
9999 0 0
100100 0 0
101101 −10.0557 −1.00058 −0.500292 0.865857i 0.666774π-0.666774\pi
−0.500292 + 0.865857i 0.666774π0.666774\pi
102102 0 0
103103 −4.87601 −0.480447 −0.240224 0.970718i 0.577221π-0.577221\pi
−0.240224 + 0.970718i 0.577221π0.577221\pi
104104 0 0
105105 −0.242585 −0.0236739
106106 0 0
107107 5.65316 0.546512 0.273256 0.961941i 0.411899π-0.411899\pi
0.273256 + 0.961941i 0.411899π0.411899\pi
108108 0 0
109109 −8.01561 −0.767756 −0.383878 0.923384i 0.625412π-0.625412\pi
−0.383878 + 0.923384i 0.625412π0.625412\pi
110110 0 0
111111 0.0233050 0.00221201
112112 0 0
113113 −9.62436 −0.905384 −0.452692 0.891667i 0.649536π-0.649536\pi
−0.452692 + 0.891667i 0.649536π0.649536\pi
114114 0 0
115115 18.1851 1.69577
116116 0 0
117117 −3.46454 −0.320297
118118 0 0
119119 5.47994 0.502345
120120 0 0
121121 0 0
122122 0 0
123123 −0.283616 −0.0255728
124124 0 0
125125 10.7555 0.961997
126126 0 0
127127 20.6659 1.83380 0.916900 0.399116i 0.130683π-0.130683\pi
0.916900 + 0.399116i 0.130683π0.130683\pi
128128 0 0
129129 −0.331538 −0.0291903
130130 0 0
131131 17.9382 1.56727 0.783633 0.621224i 0.213364π-0.213364\pi
0.783633 + 0.621224i 0.213364π0.213364\pi
132132 0 0
133133 9.51455 0.825016
134134 0 0
135135 0.891973 0.0767688
136136 0 0
137137 −4.44854 −0.380064 −0.190032 0.981778i 0.560859π-0.560859\pi
−0.190032 + 0.981778i 0.560859π0.560859\pi
138138 0 0
139139 5.52337 0.468486 0.234243 0.972178i 0.424739π-0.424739\pi
0.234243 + 0.972178i 0.424739π0.424739\pi
140140 0 0
141141 −0.0745123 −0.00627506
142142 0 0
143143 0 0
144144 0 0
145145 −13.7090 −1.13847
146146 0 0
147147 −0.279195 −0.0230276
148148 0 0
149149 −12.1307 −0.993788 −0.496894 0.867811i 0.665526π-0.665526\pi
−0.496894 + 0.867811i 0.665526π0.665526\pi
150150 0 0
151151 −15.1453 −1.23251 −0.616255 0.787547i 0.711351π-0.711351\pi
−0.616255 + 0.787547i 0.711351π0.711351\pi
152152 0 0
153153 −10.0678 −0.813933
154154 0 0
155155 8.35119 0.670784
156156 0 0
157157 −16.4555 −1.31329 −0.656646 0.754199i 0.728026π-0.728026\pi
−0.656646 + 0.754199i 0.728026π0.728026\pi
158158 0 0
159159 −0.395168 −0.0313389
160160 0 0
161161 −12.8204 −1.01039
162162 0 0
163163 −12.4470 −0.974924 −0.487462 0.873144i 0.662077π-0.662077\pi
−0.487462 + 0.873144i 0.662077π0.662077\pi
164164 0 0
165165 0 0
166166 0 0
167167 15.8104 1.22344 0.611722 0.791073i 0.290477π-0.290477\pi
0.611722 + 0.791073i 0.290477π0.290477\pi
168168 0 0
169169 −11.6626 −0.897126
170170 0 0
171171 −17.4802 −1.33675
172172 0 0
173173 −0.828750 −0.0630087 −0.0315044 0.999504i 0.510030π-0.510030\pi
−0.0315044 + 0.999504i 0.510030π0.510030\pi
174174 0 0
175175 0.570764 0.0431457
176176 0 0
177177 0.522405 0.0392664
178178 0 0
179179 −16.8994 −1.26312 −0.631561 0.775326i 0.717585π-0.717585\pi
−0.631561 + 0.775326i 0.717585π0.717585\pi
180180 0 0
181181 −11.2573 −0.836747 −0.418374 0.908275i 0.637400π-0.637400\pi
−0.418374 + 0.908275i 0.637400π0.637400\pi
182182 0 0
183183 0.567658 0.0419625
184184 0 0
185185 −0.838115 −0.0616194
186186 0 0
187187 0 0
188188 0 0
189189 −0.628837 −0.0457411
190190 0 0
191191 −25.9575 −1.87822 −0.939108 0.343622i 0.888346π-0.888346\pi
−0.939108 + 0.343622i 0.888346π0.888346\pi
192192 0 0
193193 0.630257 0.0453669 0.0226835 0.999743i 0.492779π-0.492779\pi
0.0226835 + 0.999743i 0.492779π0.492779\pi
194194 0 0
195195 −0.172038 −0.0123199
196196 0 0
197197 −22.7866 −1.62348 −0.811741 0.584018i 0.801480π-0.801480\pi
−0.811741 + 0.584018i 0.801480π0.801480\pi
198198 0 0
199199 −17.6443 −1.25077 −0.625386 0.780316i 0.715058π-0.715058\pi
−0.625386 + 0.780316i 0.715058π0.715058\pi
200200 0 0
201201 0.815293 0.0575063
202202 0 0
203203 9.66478 0.678334
204204 0 0
205205 10.1997 0.712377
206206 0 0
207207 23.5537 1.63710
208208 0 0
209209 0 0
210210 0 0
211211 −8.73572 −0.601392 −0.300696 0.953720i 0.597219π-0.597219\pi
−0.300696 + 0.953720i 0.597219π0.597219\pi
212212 0 0
213213 −0.965212 −0.0661352
214214 0 0
215215 11.9231 0.813147
216216 0 0
217217 −5.88755 −0.399673
218218 0 0
219219 0.836256 0.0565089
220220 0 0
221221 3.88630 0.261421
222222 0 0
223223 8.23913 0.551733 0.275867 0.961196i 0.411035π-0.411035\pi
0.275867 + 0.961196i 0.411035π0.411035\pi
224224 0 0
225225 −1.04861 −0.0699074
226226 0 0
227227 3.16827 0.210285 0.105143 0.994457i 0.466470π-0.466470\pi
0.105143 + 0.994457i 0.466470π0.466470\pi
228228 0 0
229229 8.01670 0.529758 0.264879 0.964282i 0.414668π-0.414668\pi
0.264879 + 0.964282i 0.414668π0.414668\pi
230230 0 0
231231 0 0
232232 0 0
233233 −18.3572 −1.20262 −0.601311 0.799015i 0.705355π-0.705355\pi
−0.601311 + 0.799015i 0.705355π0.705355\pi
234234 0 0
235235 2.67968 0.174803
236236 0 0
237237 0.133543 0.00867452
238238 0 0
239239 −14.9536 −0.967266 −0.483633 0.875271i 0.660683π-0.660683\pi
−0.483633 + 0.875271i 0.660683π0.660683\pi
240240 0 0
241241 −24.4586 −1.57552 −0.787758 0.615984i 0.788758π-0.788758\pi
−0.787758 + 0.615984i 0.788758π0.788758\pi
242242 0 0
243243 1.73335 0.111195
244244 0 0
245245 10.0407 0.641474
246246 0 0
247247 6.74759 0.429339
248248 0 0
249249 −0.575583 −0.0364761
250250 0 0
251251 7.09048 0.447547 0.223773 0.974641i 0.428162π-0.428162\pi
0.223773 + 0.974641i 0.428162π0.428162\pi
252252 0 0
253253 0 0
254254 0 0
255255 −0.499934 −0.0313071
256256 0 0
257257 19.0829 1.19036 0.595181 0.803592i 0.297080π-0.297080\pi
0.595181 + 0.803592i 0.297080π0.297080\pi
258258 0 0
259259 0.590867 0.0367147
260260 0 0
261261 −17.7562 −1.09908
262262 0 0
263263 −16.3340 −1.00720 −0.503598 0.863938i 0.667991π-0.667991\pi
−0.503598 + 0.863938i 0.667991π0.667991\pi
264264 0 0
265265 14.2114 0.873000
266266 0 0
267267 0.898200 0.0549689
268268 0 0
269269 −17.7091 −1.07974 −0.539871 0.841748i 0.681527π-0.681527\pi
−0.539871 + 0.841748i 0.681527π0.681527\pi
270270 0 0
271271 9.21399 0.559710 0.279855 0.960042i 0.409714π-0.409714\pi
0.279855 + 0.960042i 0.409714π0.409714\pi
272272 0 0
273273 0.121286 0.00734055
274274 0 0
275275 0 0
276276 0 0
277277 −29.7217 −1.78581 −0.892903 0.450249i 0.851335π-0.851335\pi
−0.892903 + 0.450249i 0.851335π0.851335\pi
278278 0 0
279279 10.8167 0.647576
280280 0 0
281281 −14.4799 −0.863797 −0.431898 0.901922i 0.642156π-0.642156\pi
−0.431898 + 0.901922i 0.642156π0.642156\pi
282282 0 0
283283 22.3729 1.32993 0.664965 0.746875i 0.268447π-0.268447\pi
0.664965 + 0.746875i 0.268447π0.268447\pi
284284 0 0
285285 −0.868010 −0.0514165
286286 0 0
287287 −7.19072 −0.424455
288288 0 0
289289 −5.70661 −0.335683
290290 0 0
291291 0.000513759 0 3.01171e−5 0
292292 0 0
293293 −23.2823 −1.36017 −0.680084 0.733134i 0.738057π-0.738057\pi
−0.680084 + 0.733134i 0.738057π0.738057\pi
294294 0 0
295295 −18.7872 −1.09384
296296 0 0
297297 0 0
298298 0 0
299299 −9.09206 −0.525807
300300 0 0
301301 −8.40570 −0.484497
302302 0 0
303303 −0.646750 −0.0371548
304304 0 0
305305 −20.4147 −1.16894
306306 0 0
307307 −23.0645 −1.31636 −0.658179 0.752861i 0.728673π-0.728673\pi
−0.658179 + 0.752861i 0.728673π0.728673\pi
308308 0 0
309309 −0.313608 −0.0178405
310310 0 0
311311 2.61858 0.148486 0.0742431 0.997240i 0.476346π-0.476346\pi
0.0742431 + 0.997240i 0.476346π0.476346\pi
312312 0 0
313313 −31.5910 −1.78563 −0.892815 0.450424i 0.851273π-0.851273\pi
−0.892815 + 0.450424i 0.851273π0.851273\pi
314314 0 0
315315 11.2996 0.636661
316316 0 0
317317 11.4254 0.641715 0.320857 0.947128i 0.396029π-0.396029\pi
0.320857 + 0.947128i 0.396029π0.396029\pi
318318 0 0
319319 0 0
320320 0 0
321321 0.363592 0.0202937
322322 0 0
323323 19.6082 1.09103
324324 0 0
325325 0.404778 0.0224530
326326 0 0
327327 −0.515536 −0.0285092
328328 0 0
329329 −1.88916 −0.104153
330330 0 0
331331 19.5632 1.07529 0.537645 0.843171i 0.319314π-0.319314\pi
0.537645 + 0.843171i 0.319314π0.319314\pi
332332 0 0
333333 −1.08555 −0.0594875
334334 0 0
335335 −29.3203 −1.60194
336336 0 0
337337 −3.95997 −0.215713 −0.107857 0.994166i 0.534399π-0.534399\pi
−0.107857 + 0.994166i 0.534399π0.534399\pi
338338 0 0
339339 −0.619006 −0.0336198
340340 0 0
341341 0 0
342342 0 0
343343 −18.4932 −0.998541
344344 0 0
345345 1.16960 0.0629693
346346 0 0
347347 1.89515 0.101737 0.0508686 0.998705i 0.483801π-0.483801\pi
0.0508686 + 0.998705i 0.483801π0.483801\pi
348348 0 0
349349 27.5241 1.47333 0.736664 0.676258i 0.236400π-0.236400\pi
0.736664 + 0.676258i 0.236400π0.236400\pi
350350 0 0
351351 −0.445962 −0.0238037
352352 0 0
353353 −17.3853 −0.925325 −0.462663 0.886534i 0.653106π-0.653106\pi
−0.462663 + 0.886534i 0.653106π0.653106\pi
354354 0 0
355355 34.7119 1.84231
356356 0 0
357357 0.352451 0.0186537
358358 0 0
359359 0.964744 0.0509172 0.0254586 0.999676i 0.491895π-0.491895\pi
0.0254586 + 0.999676i 0.491895π0.491895\pi
360360 0 0
361361 15.0447 0.791825
362362 0 0
363363 0 0
364364 0 0
365365 −30.0742 −1.57416
366366 0 0
367367 20.7760 1.08450 0.542249 0.840218i 0.317573π-0.317573\pi
0.542249 + 0.840218i 0.317573π0.317573\pi
368368 0 0
369369 13.2109 0.687729
370370 0 0
371371 −10.0190 −0.520159
372372 0 0
373373 2.62662 0.136001 0.0680006 0.997685i 0.478338π-0.478338\pi
0.0680006 + 0.997685i 0.478338π0.478338\pi
374374 0 0
375375 0.691753 0.0357220
376376 0 0
377377 6.85413 0.353006
378378 0 0
379379 4.79962 0.246540 0.123270 0.992373i 0.460662π-0.460662\pi
0.123270 + 0.992373i 0.460662π0.460662\pi
380380 0 0
381381 1.32916 0.0680948
382382 0 0
383383 −17.1461 −0.876125 −0.438062 0.898945i 0.644335π-0.644335\pi
−0.438062 + 0.898945i 0.644335π0.644335\pi
384384 0 0
385385 0 0
386386 0 0
387387 15.4430 0.785013
388388 0 0
389389 15.4901 0.785379 0.392690 0.919671i 0.371545π-0.371545\pi
0.392690 + 0.919671i 0.371545π0.371545\pi
390390 0 0
391391 −26.4211 −1.33617
392392 0 0
393393 1.15372 0.0581975
394394 0 0
395395 −4.80258 −0.241644
396396 0 0
397397 15.5364 0.779750 0.389875 0.920868i 0.372518π-0.372518\pi
0.389875 + 0.920868i 0.372518π0.372518\pi
398398 0 0
399399 0.611943 0.0306354
400400 0 0
401401 −18.7515 −0.936403 −0.468202 0.883622i 0.655098π-0.655098\pi
−0.468202 + 0.883622i 0.655098π0.655098\pi
402402 0 0
403403 −4.17537 −0.207990
404404 0 0
405405 −20.7310 −1.03013
406406 0 0
407407 0 0
408408 0 0
409409 −36.7959 −1.81944 −0.909719 0.415224i 0.863703π-0.863703\pi
−0.909719 + 0.415224i 0.863703π0.863703\pi
410410 0 0
411411 −0.286115 −0.0141130
412412 0 0
413413 13.2449 0.651739
414414 0 0
415415 20.6996 1.01611
416416 0 0
417417 0.355244 0.0173964
418418 0 0
419419 −18.6797 −0.912565 −0.456283 0.889835i 0.650819π-0.650819\pi
−0.456283 + 0.889835i 0.650819π0.650819\pi
420420 0 0
421421 1.81263 0.0883420 0.0441710 0.999024i 0.485935π-0.485935\pi
0.0441710 + 0.999024i 0.485935π0.485935\pi
422422 0 0
423423 3.47078 0.168755
424424 0 0
425425 1.17626 0.0570572
426426 0 0
427427 14.3922 0.696488
428428 0 0
429429 0 0
430430 0 0
431431 19.8525 0.956260 0.478130 0.878289i 0.341315π-0.341315\pi
0.478130 + 0.878289i 0.341315π0.341315\pi
432432 0 0
433433 16.6917 0.802153 0.401076 0.916045i 0.368636π-0.368636\pi
0.401076 + 0.916045i 0.368636π0.368636\pi
434434 0 0
435435 −0.881715 −0.0422750
436436 0 0
437437 −45.8736 −2.19443
438438 0 0
439439 33.3999 1.59409 0.797044 0.603921i 0.206396π-0.206396\pi
0.797044 + 0.603921i 0.206396π0.206396\pi
440440 0 0
441441 13.0049 0.619280
442442 0 0
443443 9.09056 0.431906 0.215953 0.976404i 0.430714π-0.430714\pi
0.215953 + 0.976404i 0.430714π0.430714\pi
444444 0 0
445445 −32.3019 −1.53126
446446 0 0
447447 −0.780206 −0.0369025
448448 0 0
449449 −5.13109 −0.242151 −0.121076 0.992643i 0.538634π-0.538634\pi
−0.121076 + 0.992643i 0.538634π0.538634\pi
450450 0 0
451451 0 0
452452 0 0
453453 −0.974095 −0.0457670
454454 0 0
455455 −4.36180 −0.204484
456456 0 0
457457 −3.72570 −0.174281 −0.0871404 0.996196i 0.527773π-0.527773\pi
−0.0871404 + 0.996196i 0.527773π0.527773\pi
458458 0 0
459459 −1.29594 −0.0604895
460460 0 0
461461 0.439230 0.0204570 0.0102285 0.999948i 0.496744π-0.496744\pi
0.0102285 + 0.999948i 0.496744π0.496744\pi
462462 0 0
463463 −26.8109 −1.24601 −0.623003 0.782219i 0.714088π-0.714088\pi
−0.623003 + 0.782219i 0.714088π0.714088\pi
464464 0 0
465465 0.537120 0.0249083
466466 0 0
467467 −16.9363 −0.783720 −0.391860 0.920025i 0.628168π-0.628168\pi
−0.391860 + 0.920025i 0.628168π0.628168\pi
468468 0 0
469469 20.6707 0.954483
470470 0 0
471471 −1.05836 −0.0487667
472472 0 0
473473 0 0
474474 0 0
475475 2.04229 0.0937067
476476 0 0
477477 18.4069 0.842795
478478 0 0
479479 −3.56180 −0.162743 −0.0813715 0.996684i 0.525930π-0.525930\pi
−0.0813715 + 0.996684i 0.525930π0.525930\pi
480480 0 0
481481 0.419035 0.0191063
482482 0 0
483483 −0.824563 −0.0375189
484484 0 0
485485 −0.0184763 −0.000838966 0
486486 0 0
487487 −17.9696 −0.814280 −0.407140 0.913366i 0.633474π-0.633474\pi
−0.407140 + 0.913366i 0.633474π0.633474\pi
488488 0 0
489489 −0.800548 −0.0362020
490490 0 0
491491 −12.2524 −0.552941 −0.276471 0.961022i 0.589165π-0.589165\pi
−0.276471 + 0.961022i 0.589165π0.589165\pi
492492 0 0
493493 19.9178 0.897051
494494 0 0
495495 0 0
496496 0 0
497497 −24.4717 −1.09770
498498 0 0
499499 −20.2052 −0.904508 −0.452254 0.891889i 0.649380π-0.649380\pi
−0.452254 + 0.891889i 0.649380π0.649380\pi
500500 0 0
501501 1.01687 0.0454304
502502 0 0
503503 16.3770 0.730214 0.365107 0.930966i 0.381032π-0.381032\pi
0.365107 + 0.930966i 0.381032π0.381032\pi
504504 0 0
505505 23.2590 1.03501
506506 0 0
507507 −0.750100 −0.0333131
508508 0 0
509509 −4.61829 −0.204702 −0.102351 0.994748i 0.532637π-0.532637\pi
−0.102351 + 0.994748i 0.532637π0.532637\pi
510510 0 0
511511 21.2022 0.937928
512512 0 0
513513 −2.25008 −0.0993437
514514 0 0
515515 11.2783 0.496979
516516 0 0
517517 0 0
518518 0 0
519519 −0.0533023 −0.00233971
520520 0 0
521521 −11.5905 −0.507789 −0.253894 0.967232i 0.581712π-0.581712\pi
−0.253894 + 0.967232i 0.581712π0.581712\pi
522522 0 0
523523 29.8079 1.30341 0.651705 0.758472i 0.274054π-0.274054\pi
0.651705 + 0.758472i 0.274054π0.274054\pi
524524 0 0
525525 0.0367095 0.00160213
526526 0 0
527527 −12.1334 −0.528540
528528 0 0
529529 38.8125 1.68750
530530 0 0
531531 −24.3336 −1.05599
532532 0 0
533533 −5.09956 −0.220887
534534 0 0
535535 −13.0758 −0.565317
536536 0 0
537537 −1.08691 −0.0469037
538538 0 0
539539 0 0
540540 0 0
541541 2.41990 0.104039 0.0520197 0.998646i 0.483434π-0.483434\pi
0.0520197 + 0.998646i 0.483434π0.483434\pi
542542 0 0
543543 −0.724029 −0.0310711
544544 0 0
545545 18.5402 0.794174
546546 0 0
547547 13.4096 0.573352 0.286676 0.958028i 0.407450π-0.407450\pi
0.286676 + 0.958028i 0.407450π0.407450\pi
548548 0 0
549549 −26.4415 −1.12850
550550 0 0
551551 34.5822 1.47325
552552 0 0
553553 3.38580 0.143979
554554 0 0
555555 −0.0539046 −0.00228812
556556 0 0
557557 −7.54076 −0.319512 −0.159756 0.987157i 0.551071π-0.551071\pi
−0.159756 + 0.987157i 0.551071π0.551071\pi
558558 0 0
559559 −5.96121 −0.252132
560560 0 0
561561 0 0
562562 0 0
563563 1.22795 0.0517519 0.0258759 0.999665i 0.491763π-0.491763\pi
0.0258759 + 0.999665i 0.491763π0.491763\pi
564564 0 0
565565 22.2613 0.936538
566566 0 0
567567 14.6153 0.613783
568568 0 0
569569 13.4679 0.564605 0.282303 0.959325i 0.408902π-0.408902\pi
0.282303 + 0.959325i 0.408902π0.408902\pi
570570 0 0
571571 11.8746 0.496935 0.248467 0.968640i 0.420073π-0.420073\pi
0.248467 + 0.968640i 0.420073π0.420073\pi
572572 0 0
573573 −1.66949 −0.0697441
574574 0 0
575575 −2.75189 −0.114762
576576 0 0
577577 20.3792 0.848397 0.424199 0.905569i 0.360556π-0.360556\pi
0.424199 + 0.905569i 0.360556π0.360556\pi
578578 0 0
579579 0.0405359 0.00168462
580580 0 0
581581 −14.5931 −0.605425
582582 0 0
583583 0 0
584584 0 0
585585 8.01353 0.331319
586586 0 0
587587 −23.7047 −0.978399 −0.489199 0.872172i 0.662711π-0.662711\pi
−0.489199 + 0.872172i 0.662711π0.662711\pi
588588 0 0
589589 −21.0666 −0.868036
590590 0 0
591591 −1.46556 −0.0602850
592592 0 0
593593 −40.7647 −1.67400 −0.837002 0.547199i 0.815694π-0.815694\pi
−0.837002 + 0.547199i 0.815694π0.815694\pi
594594 0 0
595595 −12.6752 −0.519631
596596 0 0
597597 −1.13482 −0.0464451
598598 0 0
599599 23.4038 0.956252 0.478126 0.878291i 0.341316π-0.341316\pi
0.478126 + 0.878291i 0.341316π0.341316\pi
600600 0 0
601601 32.3471 1.31947 0.659733 0.751500i 0.270669π-0.270669\pi
0.659733 + 0.751500i 0.270669π0.270669\pi
602602 0 0
603603 −37.9763 −1.54652
604604 0 0
605605 0 0
606606 0 0
607607 −28.0266 −1.13757 −0.568783 0.822488i 0.692586π-0.692586\pi
−0.568783 + 0.822488i 0.692586π0.692586\pi
608608 0 0
609609 0.621605 0.0251887
610610 0 0
611611 −1.33977 −0.0542012
612612 0 0
613613 −2.36787 −0.0956373 −0.0478186 0.998856i 0.515227π-0.515227\pi
−0.0478186 + 0.998856i 0.515227π0.515227\pi
614614 0 0
615615 0.656008 0.0264528
616616 0 0
617617 −10.4196 −0.419477 −0.209738 0.977758i 0.567261π-0.567261\pi
−0.209738 + 0.977758i 0.567261π0.567261\pi
618618 0 0
619619 −32.8611 −1.32080 −0.660400 0.750914i 0.729613π-0.729613\pi
−0.660400 + 0.750914i 0.729613π0.729613\pi
620620 0 0
621621 3.03188 0.121665
622622 0 0
623623 22.7727 0.912368
624624 0 0
625625 −26.6276 −1.06510
626626 0 0
627627 0 0
628628 0 0
629629 1.21769 0.0485526
630630 0 0
631631 −20.7502 −0.826050 −0.413025 0.910720i 0.635528π-0.635528\pi
−0.413025 + 0.910720i 0.635528π0.635528\pi
632632 0 0
633633 −0.561851 −0.0223316
634634 0 0
635635 −47.8004 −1.89690
636636 0 0
637637 −5.02006 −0.198902
638638 0 0
639639 44.9596 1.77857
640640 0 0
641641 −0.977465 −0.0386075 −0.0193038 0.999814i 0.506145π-0.506145\pi
−0.0193038 + 0.999814i 0.506145π0.506145\pi
642642 0 0
643643 −38.2108 −1.50689 −0.753443 0.657514i 0.771608π-0.771608\pi
−0.753443 + 0.657514i 0.771608π0.771608\pi
644644 0 0
645645 0.766850 0.0301947
646646 0 0
647647 34.9743 1.37498 0.687491 0.726193i 0.258712π-0.258712\pi
0.687491 + 0.726193i 0.258712π0.258712\pi
648648 0 0
649649 0 0
650650 0 0
651651 −0.378666 −0.0148411
652652 0 0
653653 −35.3919 −1.38499 −0.692496 0.721422i 0.743489π-0.743489\pi
−0.692496 + 0.721422i 0.743489π0.743489\pi
654654 0 0
655655 −41.4912 −1.62120
656656 0 0
657657 −38.9528 −1.51969
658658 0 0
659659 23.8852 0.930437 0.465219 0.885196i 0.345976π-0.345976\pi
0.465219 + 0.885196i 0.345976π0.345976\pi
660660 0 0
661661 28.4658 1.10719 0.553596 0.832785i 0.313255π-0.313255\pi
0.553596 + 0.832785i 0.313255π0.313255\pi
662662 0 0
663663 0.249953 0.00970738
664664 0 0
665665 −22.0073 −0.853405
666666 0 0
667667 −46.5979 −1.80428
668668 0 0
669669 0.529912 0.0204876
670670 0 0
671671 0 0
672672 0 0
673673 44.7473 1.72488 0.862440 0.506159i 0.168935π-0.168935\pi
0.862440 + 0.506159i 0.168935π0.168935\pi
674674 0 0
675675 −0.134979 −0.00519535
676676 0 0
677677 5.90113 0.226799 0.113399 0.993549i 0.463826π-0.463826\pi
0.113399 + 0.993549i 0.463826π0.463826\pi
678678 0 0
679679 0.0130257 0.000499880 0
680680 0 0
681681 0.203772 0.00780856
682682 0 0
683683 −35.5174 −1.35904 −0.679518 0.733659i 0.737811π-0.737811\pi
−0.679518 + 0.733659i 0.737811π0.737811\pi
684684 0 0
685685 10.2895 0.393142
686686 0 0
687687 0.515606 0.0196716
688688 0 0
689689 −7.10532 −0.270691
690690 0 0
691691 21.1563 0.804824 0.402412 0.915459i 0.368172π-0.368172\pi
0.402412 + 0.915459i 0.368172π0.368172\pi
692692 0 0
693693 0 0
694694 0 0
695695 −12.7756 −0.484607
696696 0 0
697697 −14.8191 −0.561312
698698 0 0
699699 −1.18067 −0.0446571
700700 0 0
701701 19.3398 0.730455 0.365228 0.930918i 0.380991π-0.380991\pi
0.365228 + 0.930918i 0.380991π0.380991\pi
702702 0 0
703703 2.11422 0.0797394
704704 0 0
705705 0.172348 0.00649099
706706 0 0
707707 −16.3975 −0.616692
708708 0 0
709709 26.6296 1.00009 0.500047 0.865998i 0.333316π-0.333316\pi
0.500047 + 0.865998i 0.333316π0.333316\pi
710710 0 0
711711 −6.22041 −0.233284
712712 0 0
713713 28.3863 1.06308
714714 0 0
715715 0 0
716716 0 0
717717 −0.961761 −0.0359176
718718 0 0
719719 34.2435 1.27707 0.638533 0.769594i 0.279541π-0.279541\pi
0.638533 + 0.769594i 0.279541π0.279541\pi
720720 0 0
721721 −7.95111 −0.296115
722722 0 0
723723 −1.57309 −0.0585039
724724 0 0
725725 2.07454 0.0770463
726726 0 0
727727 38.7547 1.43733 0.718666 0.695355i 0.244753π-0.244753\pi
0.718666 + 0.695355i 0.244753π0.244753\pi
728728 0 0
729729 −26.7769 −0.991736
730730 0 0
731731 −17.3230 −0.640714
732732 0 0
733733 27.9567 1.03260 0.516301 0.856407i 0.327308π-0.327308\pi
0.516301 + 0.856407i 0.327308π0.327308\pi
734734 0 0
735735 0.645780 0.0238200
736736 0 0
737737 0 0
738738 0 0
739739 −0.0393633 −0.00144800 −0.000724001 1.00000i 0.500230π-0.500230\pi
−0.000724001 1.00000i 0.500230π0.500230\pi
740740 0 0
741741 0.433981 0.0159427
742742 0 0
743743 26.1740 0.960231 0.480116 0.877205i 0.340595π-0.340595\pi
0.480116 + 0.877205i 0.340595π0.340595\pi
744744 0 0
745745 28.0585 1.02798
746746 0 0
747747 26.8106 0.980950
748748 0 0
749749 9.21839 0.336833
750750 0 0
751751 −19.2932 −0.704017 −0.352009 0.935997i 0.614501π-0.614501\pi
−0.352009 + 0.935997i 0.614501π0.614501\pi
752752 0 0
753753 0.456035 0.0166188
754754 0 0
755755 35.0313 1.27492
756756 0 0
757757 −45.7863 −1.66413 −0.832065 0.554678i 0.812841π-0.812841\pi
−0.832065 + 0.554678i 0.812841π0.812841\pi
758758 0 0
759759 0 0
760760 0 0
761761 −13.2108 −0.478891 −0.239445 0.970910i 0.576966π-0.576966\pi
−0.239445 + 0.970910i 0.576966π0.576966\pi
762762 0 0
763763 −13.0707 −0.473192
764764 0 0
765765 23.2869 0.841940
766766 0 0
767767 9.39311 0.339165
768768 0 0
769769 −3.36696 −0.121416 −0.0607078 0.998156i 0.519336π-0.519336\pi
−0.0607078 + 0.998156i 0.519336π0.519336\pi
770770 0 0
771771 1.22735 0.0442019
772772 0 0
773773 −48.2075 −1.73390 −0.866952 0.498392i 0.833924π-0.833924\pi
−0.866952 + 0.498392i 0.833924π0.833924\pi
774774 0 0
775775 −1.26376 −0.0453955
776776 0 0
777777 0.0380025 0.00136333
778778 0 0
779779 −25.7296 −0.921860
780780 0 0
781781 0 0
782782 0 0
783783 −2.28561 −0.0816811
784784 0 0
785785 38.0618 1.35848
786786 0 0
787787 25.8460 0.921310 0.460655 0.887579i 0.347615π-0.347615\pi
0.460655 + 0.887579i 0.347615π0.347615\pi
788788 0 0
789789 −1.05054 −0.0374004
790790 0 0
791791 −15.6941 −0.558017
792792 0 0
793793 10.2068 0.362453
794794 0 0
795795 0.914028 0.0324172
796796 0 0
797797 −0.215683 −0.00763990 −0.00381995 0.999993i 0.501216π-0.501216\pi
−0.00381995 + 0.999993i 0.501216π0.501216\pi
798798 0 0
799799 −3.89330 −0.137735
800800 0 0
801801 −41.8382 −1.47828
802802 0 0
803803 0 0
804804 0 0
805805 29.6537 1.04516
806806 0 0
807807 −1.13899 −0.0400942
808808 0 0
809809 −23.6384 −0.831082 −0.415541 0.909574i 0.636408π-0.636408\pi
−0.415541 + 0.909574i 0.636408π0.636408\pi
810810 0 0
811811 −37.8284 −1.32834 −0.664168 0.747584i 0.731214π-0.731214\pi
−0.664168 + 0.747584i 0.731214π0.731214\pi
812812 0 0
813813 0.592612 0.0207838
814814 0 0
815815 28.7901 1.00847
816816 0 0
817817 −30.0770 −1.05226
818818 0 0
819819 −5.64950 −0.197409
820820 0 0
821821 −26.7163 −0.932404 −0.466202 0.884678i 0.654378π-0.654378\pi
−0.466202 + 0.884678i 0.654378π0.654378\pi
822822 0 0
823823 −19.5534 −0.681589 −0.340794 0.940138i 0.610696π-0.610696\pi
−0.340794 + 0.940138i 0.610696π0.610696\pi
824824 0 0
825825 0 0
826826 0 0
827827 26.7772 0.931133 0.465567 0.885013i 0.345851π-0.345851\pi
0.465567 + 0.885013i 0.345851π0.345851\pi
828828 0 0
829829 −34.5078 −1.19851 −0.599253 0.800560i 0.704536π-0.704536\pi
−0.599253 + 0.800560i 0.704536π0.704536\pi
830830 0 0
831831 −1.91160 −0.0663126
832832 0 0
833833 −14.5880 −0.505445
834834 0 0
835835 −36.5696 −1.26554
836836 0 0
837837 1.39234 0.0481263
838838 0 0
839839 32.8263 1.13329 0.566645 0.823962i 0.308241π-0.308241\pi
0.566645 + 0.823962i 0.308241π0.308241\pi
840840 0 0
841841 6.12824 0.211319
842842 0 0
843843 −0.931295 −0.0320755
844844 0 0
845845 26.9758 0.927996
846846 0 0
847847 0 0
848848 0 0
849849 1.43895 0.0493845
850850 0 0
851851 −2.84881 −0.0976560
852852 0 0
853853 30.2939 1.03724 0.518621 0.855004i 0.326446π-0.326446\pi
0.518621 + 0.855004i 0.326446π0.326446\pi
854854 0 0
855855 40.4319 1.38274
856856 0 0
857857 −22.7328 −0.776538 −0.388269 0.921546i 0.626927π-0.626927\pi
−0.388269 + 0.921546i 0.626927π0.626927\pi
858858 0 0
859859 −18.4958 −0.631068 −0.315534 0.948914i 0.602184π-0.602184\pi
−0.315534 + 0.948914i 0.602184π0.602184\pi
860860 0 0
861861 −0.462482 −0.0157613
862862 0 0
863863 39.8463 1.35638 0.678192 0.734884i 0.262764π-0.262764\pi
0.678192 + 0.734884i 0.262764π0.262764\pi
864864 0 0
865865 1.91691 0.0651769
866866 0 0
867867 −0.367029 −0.0124650
868868 0 0
869869 0 0
870870 0 0
871871 14.6594 0.496714
872872 0 0
873873 −0.0239309 −0.000809939 0
874874 0 0
875875 17.5385 0.592909
876876 0 0
877877 −0.181186 −0.00611822 −0.00305911 0.999995i 0.500974π-0.500974\pi
−0.00305911 + 0.999995i 0.500974π0.500974\pi
878878 0 0
879879 −1.49744 −0.0505073
880880 0 0
881881 −2.32439 −0.0783108 −0.0391554 0.999233i 0.512467π-0.512467\pi
−0.0391554 + 0.999233i 0.512467π0.512467\pi
882882 0 0
883883 57.5471 1.93661 0.968307 0.249764i 0.0803530π-0.0803530\pi
0.968307 + 0.249764i 0.0803530π0.0803530\pi
884884 0 0
885885 −1.20833 −0.0406175
886886 0 0
887887 −9.19676 −0.308797 −0.154398 0.988009i 0.549344π-0.549344\pi
−0.154398 + 0.988009i 0.549344π0.549344\pi
888888 0 0
889889 33.6990 1.13023
890890 0 0
891891 0 0
892892 0 0
893893 −6.75974 −0.226206
894894 0 0
895895 39.0885 1.30659
896896 0 0
897897 −0.584769 −0.0195249
898898 0 0
899899 −21.3993 −0.713706
900900 0 0
901901 −20.6477 −0.687874
902902 0 0
903903 −0.540626 −0.0179909
904904 0 0
905905 26.0382 0.865540
906906 0 0
907907 −21.3640 −0.709379 −0.354689 0.934984i 0.615413π-0.615413\pi
−0.354689 + 0.934984i 0.615413π0.615413\pi
908908 0 0
909909 30.1256 0.999204
910910 0 0
911911 7.88751 0.261325 0.130662 0.991427i 0.458290π-0.458290\pi
0.130662 + 0.991427i 0.458290π0.458290\pi
912912 0 0
913913 0 0
914914 0 0
915915 −1.31300 −0.0434064
916916 0 0
917917 29.2511 0.965956
918918 0 0
919919 −44.1977 −1.45795 −0.728974 0.684541i 0.760003π-0.760003\pi
−0.728974 + 0.684541i 0.760003π0.760003\pi
920920 0 0
921921 −1.48343 −0.0488806
922922 0 0
923923 −17.3550 −0.571246
924924 0 0
925925 0.126829 0.00417011
926926 0 0
927927 14.6078 0.479785
928928 0 0
929929 37.4330 1.22814 0.614069 0.789253i 0.289532π-0.289532\pi
0.614069 + 0.789253i 0.289532π0.289532\pi
930930 0 0
931931 −25.3285 −0.830107
932932 0 0
933933 0.168418 0.00551376
934934 0 0
935935 0 0
936936 0 0
937937 39.0621 1.27610 0.638051 0.769994i 0.279741π-0.279741\pi
0.638051 + 0.769994i 0.279741π0.279741\pi
938938 0 0
939939 −2.03182 −0.0663060
940940 0 0
941941 −57.6873 −1.88055 −0.940277 0.340412i 0.889434π-0.889434\pi
−0.940277 + 0.340412i 0.889434π0.889434\pi
942942 0 0
943943 34.6694 1.12899
944944 0 0
945945 1.45451 0.0473151
946946 0 0
947947 −28.2809 −0.919007 −0.459503 0.888176i 0.651973π-0.651973\pi
−0.459503 + 0.888176i 0.651973π0.651973\pi
948948 0 0
949949 15.0363 0.488099
950950 0 0
951951 0.734842 0.0238289
952952 0 0
953953 −7.80122 −0.252706 −0.126353 0.991985i 0.540327π-0.540327\pi
−0.126353 + 0.991985i 0.540327π0.540327\pi
954954 0 0
955955 60.0399 1.94285
956956 0 0
957957 0 0
958958 0 0
959959 −7.25406 −0.234246
960960 0 0
961961 −17.9641 −0.579487
962962 0 0
963963 −16.9361 −0.545758
964964 0 0
965965 −1.45779 −0.0469280
966966 0 0
967967 21.5958 0.694475 0.347237 0.937777i 0.387120π-0.387120\pi
0.347237 + 0.937777i 0.387120π0.387120\pi
968968 0 0
969969 1.26113 0.0405133
970970 0 0
971971 30.4357 0.976729 0.488364 0.872640i 0.337594π-0.337594\pi
0.488364 + 0.872640i 0.337594π0.337594\pi
972972 0 0
973973 9.00674 0.288743
974974 0 0
975975 0.0260339 0.000833752 0
976976 0 0
977977 −29.2066 −0.934403 −0.467201 0.884151i 0.654738π-0.654738\pi
−0.467201 + 0.884151i 0.654738π0.654738\pi
978978 0 0
979979 0 0
980980 0 0
981981 24.0137 0.766697
982982 0 0
983983 5.42324 0.172975 0.0864873 0.996253i 0.472436π-0.472436\pi
0.0864873 + 0.996253i 0.472436π0.472436\pi
984984 0 0
985985 52.7058 1.67935
986986 0 0
987987 −0.121504 −0.00386752
988988 0 0
989989 40.5274 1.28870
990990 0 0
991991 −27.9224 −0.886985 −0.443492 0.896278i 0.646261π-0.646261\pi
−0.443492 + 0.896278i 0.646261π0.646261\pi
992992 0 0
993993 1.25824 0.0399289
994994 0 0
995995 40.8115 1.29381
996996 0 0
997997 −12.8037 −0.405496 −0.202748 0.979231i 0.564987π-0.564987\pi
−0.202748 + 0.979231i 0.564987π0.564987\pi
998998 0 0
999999 −0.139733 −0.00442097
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 7744.2.a.dv.1.3 6
4.3 odd 2 7744.2.a.du.1.4 6
8.3 odd 2 3872.2.a.bq.1.3 6
8.5 even 2 3872.2.a.bn.1.4 6
11.3 even 5 704.2.m.n.449.2 12
11.4 even 5 704.2.m.n.577.2 12
11.10 odd 2 7744.2.a.dw.1.3 6
44.3 odd 10 704.2.m.m.449.2 12
44.15 odd 10 704.2.m.m.577.2 12
44.43 even 2 7744.2.a.dt.1.4 6
88.3 odd 10 352.2.m.e.97.2 12
88.21 odd 2 3872.2.a.bo.1.4 6
88.37 even 10 352.2.m.f.225.2 yes 12
88.43 even 2 3872.2.a.bp.1.3 6
88.59 odd 10 352.2.m.e.225.2 yes 12
88.69 even 10 352.2.m.f.97.2 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
352.2.m.e.97.2 12 88.3 odd 10
352.2.m.e.225.2 yes 12 88.59 odd 10
352.2.m.f.97.2 yes 12 88.69 even 10
352.2.m.f.225.2 yes 12 88.37 even 10
704.2.m.m.449.2 12 44.3 odd 10
704.2.m.m.577.2 12 44.15 odd 10
704.2.m.n.449.2 12 11.3 even 5
704.2.m.n.577.2 12 11.4 even 5
3872.2.a.bn.1.4 6 8.5 even 2
3872.2.a.bo.1.4 6 88.21 odd 2
3872.2.a.bp.1.3 6 88.43 even 2
3872.2.a.bq.1.3 6 8.3 odd 2
7744.2.a.dt.1.4 6 44.43 even 2
7744.2.a.du.1.4 6 4.3 odd 2
7744.2.a.dv.1.3 6 1.1 even 1 trivial
7744.2.a.dw.1.3 6 11.10 odd 2