Properties

Label 4275.2.a.bo.1.4
Level 42754275
Weight 22
Character 4275.1
Self dual yes
Analytic conductor 34.13634.136
Analytic rank 11
Dimension 44
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [4275,2,Mod(1,4275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4275.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 4275=325219 4275 = 3^{2} \cdot 5^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4275.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,-2,0,8,0,0,-4,-12,0,0,-4,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 34.136046864134.1360468641
Analytic rank: 11
Dimension: 44
Coefficient field: 4.4.11344.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x42x34x2+4x+3 x^{4} - 2x^{3} - 4x^{2} + 4x + 3 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 95)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 2.781652.78165 of defining polynomial
Character χ\chi == 4275.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.95594q2+1.82571q4+3.56331q70.340899q85.56331q115.26647q13+6.96962q144.31820q16+1.40632q17+1.00000q1910.8815q226.96962q2310.3009q26+6.50557q281.40632q29+1.75489q317.76435q32+2.75067q343.61504q37+1.95594q384.34858q41+3.56331q4310.1570q4413.6322q468.26046q47+5.69716q499.61504q527.61504q531.21473q562.75067q589.47519q59+9.21473q61+3.43247q626.55023q64+4.76090q67+2.56753q68+14.0689q716.59368q737.07082q74+1.82571q7619.8238q77+5.47519q798.50557q824.15699q83+6.96962q86+1.89653q88+9.23009q8918.7660q9112.7245q9216.1570q9411.5116q97+11.1433q98+O(q100)q+1.95594 q^{2} +1.82571 q^{4} +3.56331 q^{7} -0.340899 q^{8} -5.56331 q^{11} -5.26647 q^{13} +6.96962 q^{14} -4.31820 q^{16} +1.40632 q^{17} +1.00000 q^{19} -10.8815 q^{22} -6.96962 q^{23} -10.3009 q^{26} +6.50557 q^{28} -1.40632 q^{29} +1.75489 q^{31} -7.76435 q^{32} +2.75067 q^{34} -3.61504 q^{37} +1.95594 q^{38} -4.34858 q^{41} +3.56331 q^{43} -10.1570 q^{44} -13.6322 q^{46} -8.26046 q^{47} +5.69716 q^{49} -9.61504 q^{52} -7.61504 q^{53} -1.21473 q^{56} -2.75067 q^{58} -9.47519 q^{59} +9.21473 q^{61} +3.43247 q^{62} -6.55023 q^{64} +4.76090 q^{67} +2.56753 q^{68} +14.0689 q^{71} -6.59368 q^{73} -7.07082 q^{74} +1.82571 q^{76} -19.8238 q^{77} +5.47519 q^{79} -8.50557 q^{82} -4.15699 q^{83} +6.96962 q^{86} +1.89653 q^{88} +9.23009 q^{89} -18.7660 q^{91} -12.7245 q^{92} -16.1570 q^{94} -11.5116 q^{97} +11.1433 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q2q2+8q44q712q84q112q13+8q14+4q16+4q17+4q194q228q234q26+8q284q29+4q316q324q34+6q37++38q98+O(q100) 4 q - 2 q^{2} + 8 q^{4} - 4 q^{7} - 12 q^{8} - 4 q^{11} - 2 q^{13} + 8 q^{14} + 4 q^{16} + 4 q^{17} + 4 q^{19} - 4 q^{22} - 8 q^{23} - 4 q^{26} + 8 q^{28} - 4 q^{29} + 4 q^{31} - 6 q^{32} - 4 q^{34} + 6 q^{37}+ \cdots + 38 q^{98}+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 1.95594 1.38306 0.691530 0.722348i 0.256937π-0.256937\pi
0.691530 + 0.722348i 0.256937π0.256937\pi
33 0 0
44 1.82571 0.912855
55 0 0
66 0 0
77 3.56331 1.34680 0.673402 0.739277i 0.264832π-0.264832\pi
0.673402 + 0.739277i 0.264832π0.264832\pi
88 −0.340899 −0.120526
99 0 0
1010 0 0
1111 −5.56331 −1.67740 −0.838700 0.544594i 0.816684π-0.816684\pi
−0.838700 + 0.544594i 0.816684π0.816684\pi
1212 0 0
1313 −5.26647 −1.46065 −0.730327 0.683097i 0.760632π-0.760632\pi
−0.730327 + 0.683097i 0.760632π0.760632\pi
1414 6.96962 1.86271
1515 0 0
1616 −4.31820 −1.07955
1717 1.40632 0.341082 0.170541 0.985351i 0.445448π-0.445448\pi
0.170541 + 0.985351i 0.445448π0.445448\pi
1818 0 0
1919 1.00000 0.229416
2020 0 0
2121 0 0
2222 −10.8815 −2.31995
2323 −6.96962 −1.45327 −0.726633 0.687025i 0.758916π-0.758916\pi
−0.726633 + 0.687025i 0.758916π0.758916\pi
2424 0 0
2525 0 0
2626 −10.3009 −2.02017
2727 0 0
2828 6.50557 1.22944
2929 −1.40632 −0.261146 −0.130573 0.991439i 0.541682π-0.541682\pi
−0.130573 + 0.991439i 0.541682π0.541682\pi
3030 0 0
3131 1.75489 0.315188 0.157594 0.987504i 0.449626π-0.449626\pi
0.157594 + 0.987504i 0.449626π0.449626\pi
3232 −7.76435 −1.37256
3333 0 0
3434 2.75067 0.471737
3535 0 0
3636 0 0
3737 −3.61504 −0.594309 −0.297155 0.954829i 0.596038π-0.596038\pi
−0.297155 + 0.954829i 0.596038π0.596038\pi
3838 1.95594 0.317296
3939 0 0
4040 0 0
4141 −4.34858 −0.679134 −0.339567 0.940582i 0.610280π-0.610280\pi
−0.339567 + 0.940582i 0.610280π0.610280\pi
4242 0 0
4343 3.56331 0.543399 0.271700 0.962382i 0.412414π-0.412414\pi
0.271700 + 0.962382i 0.412414π0.412414\pi
4444 −10.1570 −1.53122
4545 0 0
4646 −13.6322 −2.00996
4747 −8.26046 −1.20491 −0.602456 0.798152i 0.705811π-0.705811\pi
−0.602456 + 0.798152i 0.705811π0.705811\pi
4848 0 0
4949 5.69716 0.813879
5050 0 0
5151 0 0
5252 −9.61504 −1.33337
5353 −7.61504 −1.04601 −0.523003 0.852331i 0.675188π-0.675188\pi
−0.523003 + 0.852331i 0.675188π0.675188\pi
5454 0 0
5555 0 0
5656 −1.21473 −0.162325
5757 0 0
5858 −2.75067 −0.361181
5959 −9.47519 −1.23356 −0.616782 0.787134i 0.711564π-0.711564\pi
−0.616782 + 0.787134i 0.711564π0.711564\pi
6060 0 0
6161 9.21473 1.17983 0.589913 0.807467i 0.299162π-0.299162\pi
0.589913 + 0.807467i 0.299162π0.299162\pi
6262 3.43247 0.435924
6363 0 0
6464 −6.55023 −0.818779
6565 0 0
6666 0 0
6767 4.76090 0.581636 0.290818 0.956778i 0.406073π-0.406073\pi
0.290818 + 0.956778i 0.406073π0.406073\pi
6868 2.56753 0.311358
6969 0 0
7070 0 0
7171 14.0689 1.66967 0.834834 0.550502i 0.185563π-0.185563\pi
0.834834 + 0.550502i 0.185563π0.185563\pi
7272 0 0
7373 −6.59368 −0.771732 −0.385866 0.922555i 0.626097π-0.626097\pi
−0.385866 + 0.922555i 0.626097π0.626097\pi
7474 −7.07082 −0.821966
7575 0 0
7676 1.82571 0.209423
7777 −19.8238 −2.25913
7878 0 0
7979 5.47519 0.616007 0.308004 0.951385i 0.400339π-0.400339\pi
0.308004 + 0.951385i 0.400339π0.400339\pi
8080 0 0
8181 0 0
8282 −8.50557 −0.939283
8383 −4.15699 −0.456289 −0.228144 0.973627i 0.573266π-0.573266\pi
−0.228144 + 0.973627i 0.573266π0.573266\pi
8484 0 0
8585 0 0
8686 6.96962 0.751554
8787 0 0
8888 1.89653 0.202171
8989 9.23009 0.978387 0.489194 0.872175i 0.337291π-0.337291\pi
0.489194 + 0.872175i 0.337291π0.337291\pi
9090 0 0
9191 −18.7660 −1.96721
9292 −12.7245 −1.32662
9393 0 0
9494 −16.1570 −1.66647
9595 0 0
9696 0 0
9797 −11.5116 −1.16882 −0.584411 0.811457i 0.698675π-0.698675\pi
−0.584411 + 0.811457i 0.698675π0.698675\pi
9898 11.1433 1.12564
9999 0 0
100100 0 0
101101 11.8511 1.17923 0.589616 0.807684i 0.299279π-0.299279\pi
0.589616 + 0.807684i 0.299279π0.299279\pi
102102 0 0
103103 −1.35458 −0.133471 −0.0667354 0.997771i 0.521258π-0.521258\pi
−0.0667354 + 0.997771i 0.521258π0.521258\pi
104104 1.79533 0.176047
105105 0 0
106106 −14.8946 −1.44669
107107 −7.06287 −0.682794 −0.341397 0.939919i 0.610900π-0.610900\pi
−0.341397 + 0.939919i 0.610900π0.610900\pi
108108 0 0
109109 10.1844 0.975484 0.487742 0.872988i 0.337821π-0.337821\pi
0.487742 + 0.872988i 0.337821π0.337821\pi
110110 0 0
111111 0 0
112112 −15.3871 −1.45394
113113 1.86015 0.174988 0.0874940 0.996165i 0.472114π-0.472114\pi
0.0874940 + 0.996165i 0.472114π0.472114\pi
114114 0 0
115115 0 0
116116 −2.56753 −0.238389
117117 0 0
118118 −18.5329 −1.70609
119119 5.01114 0.459370
120120 0 0
121121 19.9504 1.81367
122122 18.0235 1.63177
123123 0 0
124124 3.20393 0.287721
125125 0 0
126126 0 0
127127 4.89053 0.433964 0.216982 0.976176i 0.430379π-0.430379\pi
0.216982 + 0.976176i 0.430379π0.430379\pi
128128 2.71684 0.240137
129129 0 0
130130 0 0
131131 −2.81263 −0.245741 −0.122870 0.992423i 0.539210π-0.539210\pi
−0.122870 + 0.992423i 0.539210π0.539210\pi
132132 0 0
133133 3.56331 0.308978
134134 9.31204 0.804438
135135 0 0
136136 −0.479412 −0.0411093
137137 9.23009 0.788579 0.394290 0.918986i 0.370991π-0.370991\pi
0.394290 + 0.918986i 0.370991π0.370991\pi
138138 0 0
139139 −3.67878 −0.312030 −0.156015 0.987755i 0.549865π-0.549865\pi
−0.156015 + 0.987755i 0.549865π0.549865\pi
140140 0 0
141141 0 0
142142 27.5179 2.30925
143143 29.2990 2.45010
144144 0 0
145145 0 0
146146 −12.8969 −1.06735
147147 0 0
148148 −6.60002 −0.542519
149149 −7.09925 −0.581593 −0.290797 0.956785i 0.593920π-0.593920\pi
−0.290797 + 0.956785i 0.593920π0.593920\pi
150150 0 0
151151 −18.3567 −1.49385 −0.746924 0.664910i 0.768470π-0.768470\pi
−0.746924 + 0.664910i 0.768470π0.768470\pi
152152 −0.340899 −0.0276506
153153 0 0
154154 −38.7742 −3.12451
155155 0 0
156156 0 0
157157 −17.2301 −1.37511 −0.687555 0.726132i 0.741316π-0.741316\pi
−0.687555 + 0.726132i 0.741316π0.741316\pi
158158 10.7092 0.851975
159159 0 0
160160 0 0
161161 −24.8349 −1.95726
162162 0 0
163163 −10.8662 −0.851103 −0.425551 0.904934i 0.639920π-0.639920\pi
−0.425551 + 0.904934i 0.639920π0.639920\pi
164164 −7.93925 −0.619951
165165 0 0
166166 −8.13083 −0.631075
167167 2.82977 0.218974 0.109487 0.993988i 0.465079π-0.465079\pi
0.109487 + 0.993988i 0.465079π0.465079\pi
168168 0 0
169169 14.7357 1.13351
170170 0 0
171171 0 0
172172 6.50557 0.496045
173173 −9.26647 −0.704516 −0.352258 0.935903i 0.614586π-0.614586\pi
−0.352258 + 0.935903i 0.614586π0.614586\pi
174174 0 0
175175 0 0
176176 24.0235 1.81084
177177 0 0
178178 18.0535 1.35317
179179 3.59067 0.268379 0.134190 0.990956i 0.457157π-0.457157\pi
0.134190 + 0.990956i 0.457157π0.457157\pi
180180 0 0
181181 −19.7630 −1.46897 −0.734487 0.678623i 0.762577π-0.762577\pi
−0.734487 + 0.678623i 0.762577π0.762577\pi
182182 −36.7053 −2.72078
183183 0 0
184184 2.37594 0.175157
185185 0 0
186186 0 0
187187 −7.82377 −0.572131
188188 −15.0812 −1.09991
189189 0 0
190190 0 0
191191 −8.31398 −0.601579 −0.300789 0.953691i 0.597250π-0.597250\pi
−0.300789 + 0.953691i 0.597250π0.597250\pi
192192 0 0
193193 22.2514 1.60169 0.800847 0.598869i 0.204383π-0.204383\pi
0.800847 + 0.598869i 0.204383π0.204383\pi
194194 −22.5160 −1.61655
195195 0 0
196196 10.4014 0.742954
197197 −8.81263 −0.627874 −0.313937 0.949444i 0.601648π-0.601648\pi
−0.313937 + 0.949444i 0.601648π0.601648\pi
198198 0 0
199199 21.0659 1.49332 0.746660 0.665206i 0.231656π-0.231656\pi
0.746660 + 0.665206i 0.231656π0.231656\pi
200200 0 0
201201 0 0
202202 23.1801 1.63095
203203 −5.01114 −0.351713
204204 0 0
205205 0 0
206206 −2.64948 −0.184598
207207 0 0
208208 22.7417 1.57685
209209 −5.56331 −0.384822
210210 0 0
211211 5.34556 0.368004 0.184002 0.982926i 0.441095π-0.441095\pi
0.184002 + 0.982926i 0.441095π0.441095\pi
212212 −13.9029 −0.954853
213213 0 0
214214 −13.8146 −0.944345
215215 0 0
216216 0 0
217217 6.25323 0.424497
218218 19.9200 1.34915
219219 0 0
220220 0 0
221221 −7.40632 −0.498203
222222 0 0
223223 3.10947 0.208226 0.104113 0.994565i 0.466800π-0.466800\pi
0.104113 + 0.994565i 0.466800π0.466800\pi
224224 −27.6668 −1.84856
225225 0 0
226226 3.63834 0.242019
227227 14.4692 0.960354 0.480177 0.877172i 0.340572π-0.340572\pi
0.480177 + 0.877172i 0.340572π0.340572\pi
228228 0 0
229229 −5.21473 −0.344599 −0.172299 0.985045i 0.555120π-0.555120\pi
−0.172299 + 0.985045i 0.555120π0.555120\pi
230230 0 0
231231 0 0
232232 0.479412 0.0314750
233233 −3.18737 −0.208811 −0.104406 0.994535i 0.533294π-0.533294\pi
−0.104406 + 0.994535i 0.533294π0.533294\pi
234234 0 0
235235 0 0
236236 −17.2990 −1.12607
237237 0 0
238238 9.80150 0.635337
239239 −16.5209 −1.06865 −0.534325 0.845279i 0.679434π-0.679434\pi
−0.534325 + 0.845279i 0.679434π0.679434\pi
240240 0 0
241241 −12.2271 −0.787615 −0.393807 0.919193i 0.628842π-0.628842\pi
−0.393807 + 0.919193i 0.628842π0.628842\pi
242242 39.0218 2.50842
243243 0 0
244244 16.8234 1.07701
245245 0 0
246246 0 0
247247 −5.26647 −0.335097
248248 −0.598242 −0.0379884
249249 0 0
250250 0 0
251251 −4.52093 −0.285358 −0.142679 0.989769i 0.545572π-0.545572\pi
−0.142679 + 0.989769i 0.545572π0.545572\pi
252252 0 0
253253 38.7742 2.43771
254254 9.56559 0.600198
255255 0 0
256256 18.4144 1.15090
257257 15.9290 0.993625 0.496813 0.867858i 0.334504π-0.334504\pi
0.496813 + 0.867858i 0.334504π0.334504\pi
258258 0 0
259259 −12.8815 −0.800418
260260 0 0
261261 0 0
262262 −5.50135 −0.339874
263263 0.854147 0.0526689 0.0263345 0.999653i 0.491617π-0.491617\pi
0.0263345 + 0.999653i 0.491617π0.491617\pi
264264 0 0
265265 0 0
266266 6.96962 0.427335
267267 0 0
268268 8.69202 0.530950
269269 −10.3913 −0.633569 −0.316784 0.948498i 0.602603π-0.602603\pi
−0.316784 + 0.948498i 0.602603π0.602603\pi
270270 0 0
271271 −8.19971 −0.498097 −0.249048 0.968491i 0.580118π-0.580118\pi
−0.249048 + 0.968491i 0.580118π0.580118\pi
272272 −6.07276 −0.368215
273273 0 0
274274 18.0535 1.09065
275275 0 0
276276 0 0
277277 −14.6484 −0.880137 −0.440069 0.897964i 0.645046π-0.645046\pi
−0.440069 + 0.897964i 0.645046π0.645046\pi
278278 −7.19549 −0.431557
279279 0 0
280280 0 0
281281 31.6129 1.88587 0.942935 0.332977i 0.108053π-0.108053\pi
0.942935 + 0.332977i 0.108053π0.108053\pi
282282 0 0
283283 −24.7326 −1.47020 −0.735101 0.677957i 0.762865π-0.762865\pi
−0.735101 + 0.677957i 0.762865π0.762865\pi
284284 25.6857 1.52417
285285 0 0
286286 57.3071 3.38864
287287 −15.4953 −0.914660
288288 0 0
289289 −15.0223 −0.883663
290290 0 0
291291 0 0
292292 −12.0382 −0.704480
293293 30.2857 1.76931 0.884655 0.466245i 0.154394π-0.154394\pi
0.884655 + 0.466245i 0.154394π0.154394\pi
294294 0 0
295295 0 0
296296 1.23237 0.0716298
297297 0 0
298298 −13.8857 −0.804379
299299 36.7053 2.12272
300300 0 0
301301 12.6972 0.731852
302302 −35.9046 −2.06608
303303 0 0
304304 −4.31820 −0.247666
305305 0 0
306306 0 0
307307 23.0629 1.31627 0.658134 0.752901i 0.271346π-0.271346\pi
0.658134 + 0.752901i 0.271346π0.271346\pi
308308 −36.1925 −2.06226
309309 0 0
310310 0 0
311311 10.3152 0.584921 0.292460 0.956278i 0.405526π-0.405526\pi
0.292460 + 0.956278i 0.405526π0.405526\pi
312312 0 0
313313 4.95038 0.279812 0.139906 0.990165i 0.455320π-0.455320\pi
0.139906 + 0.990165i 0.455320π0.455320\pi
314314 −33.7011 −1.90186
315315 0 0
316316 9.99612 0.562326
317317 −14.2433 −0.799985 −0.399992 0.916518i 0.630987π-0.630987\pi
−0.399992 + 0.916518i 0.630987π0.630987\pi
318318 0 0
319319 7.82377 0.438047
320320 0 0
321321 0 0
322322 −48.5756 −2.70702
323323 1.40632 0.0782495
324324 0 0
325325 0 0
326326 −21.2536 −1.17713
327327 0 0
328328 1.48243 0.0818534
329329 −29.4346 −1.62278
330330 0 0
331331 2.04272 0.112278 0.0561390 0.998423i 0.482121π-0.482121\pi
0.0561390 + 0.998423i 0.482121π0.482121\pi
332332 −7.58946 −0.416526
333333 0 0
334334 5.53487 0.302855
335335 0 0
336336 0 0
337337 −34.6951 −1.88996 −0.944980 0.327128i 0.893919π-0.893919\pi
−0.944980 + 0.327128i 0.893919π0.893919\pi
338338 28.8221 1.56772
339339 0 0
340340 0 0
341341 −9.76302 −0.528697
342342 0 0
343343 −4.64243 −0.250668
344344 −1.21473 −0.0654938
345345 0 0
346346 −18.1247 −0.974388
347347 7.35280 0.394719 0.197359 0.980331i 0.436763π-0.436763\pi
0.197359 + 0.980331i 0.436763π0.436763\pi
348348 0 0
349349 −31.7630 −1.70024 −0.850118 0.526593i 0.823469π-0.823469\pi
−0.850118 + 0.526593i 0.823469π0.823469\pi
350350 0 0
351351 0 0
352352 43.1955 2.30233
353353 −7.52179 −0.400345 −0.200172 0.979761i 0.564150π-0.564150\pi
−0.200172 + 0.979761i 0.564150π0.564150\pi
354354 0 0
355355 0 0
356356 16.8515 0.893126
357357 0 0
358358 7.02314 0.371185
359359 30.3982 1.60436 0.802178 0.597085i 0.203674π-0.203674\pi
0.802178 + 0.597085i 0.203674π0.203674\pi
360360 0 0
361361 1.00000 0.0526316
362362 −38.6553 −2.03168
363363 0 0
364364 −34.2613 −1.79578
365365 0 0
366366 0 0
367367 −3.91577 −0.204401 −0.102201 0.994764i 0.532588π-0.532588\pi
−0.102201 + 0.994764i 0.532588π0.532588\pi
368368 30.0962 1.56887
369369 0 0
370370 0 0
371371 −27.1347 −1.40877
372372 0 0
373373 −26.7759 −1.38641 −0.693203 0.720743i 0.743801π-0.743801\pi
−0.693203 + 0.720743i 0.743801π0.743801\pi
374374 −15.3028 −0.791291
375375 0 0
376376 2.81599 0.145223
377377 7.40632 0.381445
378378 0 0
379379 14.9504 0.767950 0.383975 0.923344i 0.374555π-0.374555\pi
0.383975 + 0.923344i 0.374555π0.374555\pi
380380 0 0
381381 0 0
382382 −16.2617 −0.832019
383383 −27.9910 −1.43027 −0.715136 0.698985i 0.753635π-0.753635\pi
−0.715136 + 0.698985i 0.753635π0.753635\pi
384384 0 0
385385 0 0
386386 43.5225 2.21524
387387 0 0
388388 −21.0168 −1.06697
389389 35.2036 1.78489 0.892447 0.451152i 0.148987π-0.148987\pi
0.892447 + 0.451152i 0.148987π0.148987\pi
390390 0 0
391391 −9.80150 −0.495683
392392 −1.94216 −0.0980937
393393 0 0
394394 −17.2370 −0.868388
395395 0 0
396396 0 0
397397 35.9735 1.80546 0.902730 0.430208i 0.141560π-0.141560\pi
0.902730 + 0.430208i 0.141560π0.141560\pi
398398 41.2036 2.06535
399399 0 0
400400 0 0
401401 −23.2421 −1.16065 −0.580327 0.814383i 0.697075π-0.697075\pi
−0.580327 + 0.814383i 0.697075π0.697075\pi
402402 0 0
403403 −9.24209 −0.460381
404404 21.6367 1.07647
405405 0 0
406406 −9.80150 −0.486440
407407 20.1116 0.996895
408408 0 0
409409 −31.8926 −1.57699 −0.788495 0.615041i 0.789139π-0.789139\pi
−0.788495 + 0.615041i 0.789139π0.789139\pi
410410 0 0
411411 0 0
412412 −2.47307 −0.121840
413413 −33.7630 −1.66137
414414 0 0
415415 0 0
416416 40.8907 2.00483
417417 0 0
418418 −10.8815 −0.532232
419419 −31.8238 −1.55469 −0.777346 0.629073i 0.783435π-0.783435\pi
−0.777346 + 0.629073i 0.783435π0.783435\pi
420420 0 0
421421 0.348578 0.0169887 0.00849433 0.999964i 0.497296π-0.497296\pi
0.00849433 + 0.999964i 0.497296π0.497296\pi
422422 10.4556 0.508971
423423 0 0
424424 2.59596 0.126071
425425 0 0
426426 0 0
427427 32.8349 1.58899
428428 −12.8948 −0.623292
429429 0 0
430430 0 0
431431 −29.2764 −1.41019 −0.705097 0.709111i 0.749096π-0.749096\pi
−0.705097 + 0.709111i 0.749096π0.749096\pi
432432 0 0
433433 0.883290 0.0424482 0.0212241 0.999775i 0.493244π-0.493244\pi
0.0212241 + 0.999775i 0.493244π0.493244\pi
434434 12.2310 0.587105
435435 0 0
436436 18.5937 0.890476
437437 −6.96962 −0.333402
438438 0 0
439439 −13.8584 −0.661424 −0.330712 0.943732i 0.607289π-0.607289\pi
−0.330712 + 0.943732i 0.607289π0.607289\pi
440440 0 0
441441 0 0
442442 −14.4863 −0.689044
443443 −13.5753 −0.644982 −0.322491 0.946572i 0.604520π-0.604520\pi
−0.322491 + 0.946572i 0.604520π0.604520\pi
444444 0 0
445445 0 0
446446 6.08195 0.287989
447447 0 0
448448 −23.3405 −1.10273
449449 15.6334 0.737785 0.368893 0.929472i 0.379737π-0.379737\pi
0.368893 + 0.929472i 0.379737π0.379737\pi
450450 0 0
451451 24.1925 1.13918
452452 3.39609 0.159739
453453 0 0
454454 28.3009 1.32823
455455 0 0
456456 0 0
457457 −5.30284 −0.248057 −0.124028 0.992279i 0.539581π-0.539581\pi
−0.124028 + 0.992279i 0.539581π0.539581\pi
458458 −10.1997 −0.476601
459459 0 0
460460 0 0
461461 −0.374734 −0.0174531 −0.00872656 0.999962i 0.502778π-0.502778\pi
−0.00872656 + 0.999962i 0.502778π0.502778\pi
462462 0 0
463463 −6.65564 −0.309314 −0.154657 0.987968i 0.549427π-0.549427\pi
−0.154657 + 0.987968i 0.549427π0.549427\pi
464464 6.07276 0.281921
465465 0 0
466466 −6.23431 −0.288799
467467 −0.854147 −0.0395252 −0.0197626 0.999805i 0.506291π-0.506291\pi
−0.0197626 + 0.999805i 0.506291π0.506291\pi
468468 0 0
469469 16.9645 0.783349
470470 0 0
471471 0 0
472472 3.23009 0.148677
473473 −19.8238 −0.911498
474474 0 0
475475 0 0
476476 9.14889 0.419339
477477 0 0
478478 −32.3140 −1.47801
479479 17.0731 0.780090 0.390045 0.920796i 0.372460π-0.372460\pi
0.390045 + 0.920796i 0.372460π0.372460\pi
480480 0 0
481481 19.0385 0.868081
482482 −23.9154 −1.08932
483483 0 0
484484 36.4236 1.65562
485485 0 0
486486 0 0
487487 −12.8259 −0.581197 −0.290598 0.956845i 0.593854π-0.593854\pi
−0.290598 + 0.956845i 0.593854π0.593854\pi
488488 −3.14129 −0.142200
489489 0 0
490490 0 0
491491 10.4054 0.469591 0.234796 0.972045i 0.424558π-0.424558\pi
0.234796 + 0.972045i 0.424558π0.424558\pi
492492 0 0
493493 −1.97773 −0.0890723
494494 −10.3009 −0.463460
495495 0 0
496496 −7.57799 −0.340262
497497 50.1317 2.24872
498498 0 0
499499 36.1612 1.61880 0.809399 0.587258i 0.199793π-0.199793\pi
0.809399 + 0.587258i 0.199793π0.199793\pi
500500 0 0
501501 0 0
502502 −8.84267 −0.394668
503503 33.2536 1.48270 0.741352 0.671117i 0.234185π-0.234185\pi
0.741352 + 0.671117i 0.234185π0.234185\pi
504504 0 0
505505 0 0
506506 75.8400 3.37150
507507 0 0
508508 8.92869 0.396146
509509 −7.29084 −0.323161 −0.161580 0.986860i 0.551659π-0.551659\pi
−0.161580 + 0.986860i 0.551659π0.551659\pi
510510 0 0
511511 −23.4953 −1.03937
512512 30.5839 1.35163
513513 0 0
514514 31.1563 1.37424
515515 0 0
516516 0 0
517517 45.9555 2.02112
518518 −25.1955 −1.10703
519519 0 0
520520 0 0
521521 9.87849 0.432785 0.216392 0.976306i 0.430571π-0.430571\pi
0.216392 + 0.976306i 0.430571π0.430571\pi
522522 0 0
523523 11.1925 0.489414 0.244707 0.969597i 0.421308π-0.421308\pi
0.244707 + 0.969597i 0.421308π0.421308\pi
524524 −5.13505 −0.224326
525525 0 0
526526 1.67066 0.0728443
527527 2.46794 0.107505
528528 0 0
529529 25.5756 1.11198
530530 0 0
531531 0 0
532532 6.50557 0.282052
533533 22.9016 0.991980
534534 0 0
535535 0 0
536536 −1.62299 −0.0701023
537537 0 0
538538 −20.3248 −0.876263
539539 −31.6950 −1.36520
540540 0 0
541541 2.22587 0.0956974 0.0478487 0.998855i 0.484763π-0.484763\pi
0.0478487 + 0.998855i 0.484763π0.484763\pi
542542 −16.0382 −0.688898
543543 0 0
544544 −10.9191 −0.468154
545545 0 0
546546 0 0
547547 34.9675 1.49510 0.747552 0.664204i 0.231229π-0.231229\pi
0.747552 + 0.664204i 0.231229π0.231229\pi
548548 16.8515 0.719859
549549 0 0
550550 0 0
551551 −1.40632 −0.0599111
552552 0 0
553553 19.5098 0.829641
554554 −28.6514 −1.21728
555555 0 0
556556 −6.71640 −0.284839
557557 −8.88539 −0.376486 −0.188243 0.982122i 0.560279π-0.560279\pi
−0.188243 + 0.982122i 0.560279π0.560279\pi
558558 0 0
559559 −18.7660 −0.793719
560560 0 0
561561 0 0
562562 61.8331 2.60827
563563 −29.6767 −1.25072 −0.625362 0.780335i 0.715048π-0.715048\pi
−0.625362 + 0.780335i 0.715048π0.715048\pi
564564 0 0
565565 0 0
566566 −48.3756 −2.03338
567567 0 0
568568 −4.79607 −0.201239
569569 22.1152 0.927116 0.463558 0.886067i 0.346573π-0.346573\pi
0.463558 + 0.886067i 0.346573π0.346573\pi
570570 0 0
571571 −33.2656 −1.39212 −0.696060 0.717983i 0.745065π-0.745065\pi
−0.696060 + 0.717983i 0.745065π0.745065\pi
572572 53.4914 2.23659
573573 0 0
574574 −30.3080 −1.26503
575575 0 0
576576 0 0
577577 −0.934140 −0.0388887 −0.0194444 0.999811i 0.506190π-0.506190\pi
−0.0194444 + 0.999811i 0.506190π0.506190\pi
578578 −29.3827 −1.22216
579579 0 0
580580 0 0
581581 −14.8126 −0.614532
582582 0 0
583583 42.3648 1.75457
584584 2.24778 0.0930139
585585 0 0
586586 59.2371 2.44706
587587 1.57531 0.0650200 0.0325100 0.999471i 0.489650π-0.489650\pi
0.0325100 + 0.999471i 0.489650π0.489650\pi
588588 0 0
589589 1.75489 0.0723092
590590 0 0
591591 0 0
592592 15.6105 0.641587
593593 26.0162 1.06836 0.534180 0.845371i 0.320621π-0.320621\pi
0.534180 + 0.845371i 0.320621π0.320621\pi
594594 0 0
595595 0 0
596596 −12.9612 −0.530911
597597 0 0
598598 71.7934 2.93585
599599 −19.5359 −0.798217 −0.399109 0.916904i 0.630680π-0.630680\pi
−0.399109 + 0.916904i 0.630680π0.630680\pi
600600 0 0
601601 43.5299 1.77562 0.887811 0.460208i 0.152225π-0.152225\pi
0.887811 + 0.460208i 0.152225π0.152225\pi
602602 24.8349 1.01220
603603 0 0
604604 −33.5140 −1.36367
605605 0 0
606606 0 0
607607 12.5847 0.510796 0.255398 0.966836i 0.417794π-0.417794\pi
0.255398 + 0.966836i 0.417794π0.417794\pi
608608 −7.76435 −0.314886
609609 0 0
610610 0 0
611611 43.5034 1.75996
612612 0 0
613613 18.2412 0.736756 0.368378 0.929676i 0.379913π-0.379913\pi
0.368378 + 0.929676i 0.379913π0.379913\pi
614614 45.1097 1.82048
615615 0 0
616616 6.75791 0.272284
617617 26.7314 1.07617 0.538084 0.842892i 0.319148π-0.319148\pi
0.538084 + 0.842892i 0.319148π0.319148\pi
618618 0 0
619619 2.92690 0.117642 0.0588211 0.998269i 0.481266π-0.481266\pi
0.0588211 + 0.998269i 0.481266π0.481266\pi
620620 0 0
621621 0 0
622622 20.1759 0.808980
623623 32.8896 1.31770
624624 0 0
625625 0 0
626626 9.68267 0.386997
627627 0 0
628628 −31.4572 −1.25528
629629 −5.08389 −0.202708
630630 0 0
631631 −13.2493 −0.527447 −0.263724 0.964598i 0.584951π-0.584951\pi
−0.263724 + 0.964598i 0.584951π0.584951\pi
632632 −1.86649 −0.0742450
633633 0 0
634634 −27.8591 −1.10643
635635 0 0
636636 0 0
637637 −30.0039 −1.18880
638638 15.3028 0.605845
639639 0 0
640640 0 0
641641 −6.93026 −0.273729 −0.136864 0.990590i 0.543702π-0.543702\pi
−0.136864 + 0.990590i 0.543702π0.543702\pi
642642 0 0
643643 −14.4794 −0.571012 −0.285506 0.958377i 0.592162π-0.592162\pi
−0.285506 + 0.958377i 0.592162π0.592162\pi
644644 −45.3414 −1.78670
645645 0 0
646646 2.75067 0.108224
647647 6.35549 0.249860 0.124930 0.992166i 0.460129π-0.460129\pi
0.124930 + 0.992166i 0.460129π0.460129\pi
648648 0 0
649649 52.7134 2.06918
650650 0 0
651651 0 0
652652 −19.8385 −0.776934
653653 −34.4030 −1.34629 −0.673146 0.739509i 0.735058π-0.735058\pi
−0.673146 + 0.739509i 0.735058π0.735058\pi
654654 0 0
655655 0 0
656656 18.7780 0.733159
657657 0 0
658658 −57.5723 −2.24440
659659 19.6214 0.764341 0.382170 0.924092i 0.375177π-0.375177\pi
0.382170 + 0.924092i 0.375177π0.375177\pi
660660 0 0
661661 39.8054 1.54825 0.774126 0.633032i 0.218190π-0.218190\pi
0.774126 + 0.633032i 0.218190π0.218190\pi
662662 3.99544 0.155287
663663 0 0
664664 1.41712 0.0549947
665665 0 0
666666 0 0
667667 9.80150 0.379515
668668 5.16635 0.199892
669669 0 0
670670 0 0
671671 −51.2644 −1.97904
672672 0 0
673673 8.90374 0.343214 0.171607 0.985166i 0.445104π-0.445104\pi
0.171607 + 0.985166i 0.445104π0.445104\pi
674674 −67.8615 −2.61393
675675 0 0
676676 26.9030 1.03473
677677 22.2695 0.855886 0.427943 0.903806i 0.359238π-0.359238\pi
0.427943 + 0.903806i 0.359238π0.359238\pi
678678 0 0
679679 −41.0193 −1.57417
680680 0 0
681681 0 0
682682 −19.0959 −0.731220
683683 15.4054 0.589472 0.294736 0.955579i 0.404768π-0.404768\pi
0.294736 + 0.955579i 0.404768π0.404768\pi
684684 0 0
685685 0 0
686686 −9.08033 −0.346689
687687 0 0
688688 −15.3871 −0.586627
689689 40.1044 1.52785
690690 0 0
691691 −17.8773 −0.680084 −0.340042 0.940410i 0.610441π-0.610441\pi
−0.340042 + 0.940410i 0.610441π0.610441\pi
692692 −16.9179 −0.643122
693693 0 0
694694 14.3817 0.545920
695695 0 0
696696 0 0
697697 −6.11548 −0.231640
698698 −62.1266 −2.35153
699699 0 0
700700 0 0
701701 −35.3609 −1.33556 −0.667782 0.744357i 0.732756π-0.732756\pi
−0.667782 + 0.744357i 0.732756π0.732756\pi
702702 0 0
703703 −3.61504 −0.136344
704704 36.4409 1.37342
705705 0 0
706706 −14.7122 −0.553701
707707 42.2292 1.58819
708708 0 0
709709 6.90410 0.259289 0.129644 0.991561i 0.458616π-0.458616\pi
0.129644 + 0.991561i 0.458616π0.458616\pi
710710 0 0
711711 0 0
712712 −3.14653 −0.117921
713713 −12.2310 −0.458053
714714 0 0
715715 0 0
716716 6.55552 0.244991
717717 0 0
718718 59.4572 2.21892
719719 38.9431 1.45233 0.726167 0.687518i 0.241300π-0.241300\pi
0.726167 + 0.687518i 0.241300π0.241300\pi
720720 0 0
721721 −4.82678 −0.179759
722722 1.95594 0.0727926
723723 0 0
724724 −36.0816 −1.34096
725725 0 0
726726 0 0
727727 6.18347 0.229332 0.114666 0.993404i 0.463420π-0.463420\pi
0.114666 + 0.993404i 0.463420π0.463420\pi
728728 6.39733 0.237101
729729 0 0
730730 0 0
731731 5.01114 0.185344
732732 0 0
733733 0.688715 0.0254383 0.0127191 0.999919i 0.495951π-0.495951\pi
0.0127191 + 0.999919i 0.495951π0.495951\pi
734734 −7.65902 −0.282699
735735 0 0
736736 54.1146 1.99469
737737 −26.4863 −0.975636
738738 0 0
739739 −26.2532 −0.965741 −0.482870 0.875692i 0.660406π-0.660406\pi
−0.482870 + 0.875692i 0.660406π0.660406\pi
740740 0 0
741741 0 0
742742 −53.0740 −1.94841
743743 −32.5688 −1.19483 −0.597416 0.801931i 0.703806π-0.703806\pi
−0.597416 + 0.801931i 0.703806π0.703806\pi
744744 0 0
745745 0 0
746746 −52.3722 −1.91748
747747 0 0
748748 −14.2839 −0.522273
749749 −25.1672 −0.919589
750750 0 0
751751 45.4833 1.65971 0.829855 0.557979i 0.188423π-0.188423\pi
0.829855 + 0.557979i 0.188423π0.188423\pi
752752 35.6703 1.30076
753753 0 0
754754 14.4863 0.527561
755755 0 0
756756 0 0
757757 −2.74947 −0.0999311 −0.0499656 0.998751i 0.515911π-0.515911\pi
−0.0499656 + 0.998751i 0.515911π0.515911\pi
758758 29.2421 1.06212
759759 0 0
760760 0 0
761761 33.2978 1.20704 0.603521 0.797347i 0.293764π-0.293764\pi
0.603521 + 0.797347i 0.293764π0.293764\pi
762762 0 0
763763 36.2900 1.31379
764764 −15.1789 −0.549154
765765 0 0
766766 −54.7488 −1.97815
767767 49.9008 1.80181
768768 0 0
769769 −19.1540 −0.690710 −0.345355 0.938472i 0.612241π-0.612241\pi
−0.345355 + 0.938472i 0.612241π0.612241\pi
770770 0 0
771771 0 0
772772 40.6247 1.46212
773773 0.569309 0.0204766 0.0102383 0.999948i 0.496741π-0.496741\pi
0.0102383 + 0.999948i 0.496741π0.496741\pi
774774 0 0
775775 0 0
776776 3.92429 0.140874
777777 0 0
778778 68.8562 2.46862
779779 −4.34858 −0.155804
780780 0 0
781781 −78.2695 −2.80070
782782 −19.1712 −0.685559
783783 0 0
784784 −24.6015 −0.878624
785785 0 0
786786 0 0
787787 −15.9991 −0.570307 −0.285153 0.958482i 0.592044π-0.592044\pi
−0.285153 + 0.958482i 0.592044π0.592044\pi
788788 −16.0893 −0.573158
789789 0 0
790790 0 0
791791 6.62828 0.235675
792792 0 0
793793 −48.5290 −1.72332
794794 70.3621 2.49706
795795 0 0
796796 38.4602 1.36318
797797 −35.7528 −1.26643 −0.633214 0.773976i 0.718265π-0.718265\pi
−0.633214 + 0.773976i 0.718265π0.718265\pi
798798 0 0
799799 −11.6168 −0.410974
800800 0 0
801801 0 0
802802 −45.4602 −1.60526
803803 36.6827 1.29450
804804 0 0
805805 0 0
806806 −18.0770 −0.636735
807807 0 0
808808 −4.04004 −0.142128
809809 −23.2036 −0.815796 −0.407898 0.913028i 0.633738π-0.633738\pi
−0.407898 + 0.913028i 0.633738π0.633738\pi
810810 0 0
811811 −21.7549 −0.763918 −0.381959 0.924179i 0.624750π-0.624750\pi
−0.381959 + 0.924179i 0.624750π0.624750\pi
812812 −9.14889 −0.321063
813813 0 0
814814 39.3371 1.37877
815815 0 0
816816 0 0
817817 3.56331 0.124664
818818 −62.3802 −2.18107
819819 0 0
820820 0 0
821821 −52.2532 −1.82365 −0.911825 0.410579i 0.865327π-0.865327\pi
−0.911825 + 0.410579i 0.865327π0.865327\pi
822822 0 0
823823 9.44783 0.329331 0.164665 0.986349i 0.447346π-0.447346\pi
0.164665 + 0.986349i 0.447346π0.447346\pi
824824 0.461775 0.0160867
825825 0 0
826826 −66.0385 −2.29777
827827 −50.2216 −1.74638 −0.873188 0.487383i 0.837952π-0.837952\pi
−0.873188 + 0.487383i 0.837952π0.837952\pi
828828 0 0
829829 44.2066 1.53536 0.767680 0.640834i 0.221411π-0.221411\pi
0.767680 + 0.640834i 0.221411π0.221411\pi
830830 0 0
831831 0 0
832832 34.4966 1.19595
833833 8.01200 0.277599
834834 0 0
835835 0 0
836836 −10.1570 −0.351287
837837 0 0
838838 −62.2455 −2.15023
839839 30.4033 1.04964 0.524819 0.851214i 0.324133π-0.324133\pi
0.524819 + 0.851214i 0.324133π0.324133\pi
840840 0 0
841841 −27.0223 −0.931803
842842 0.681799 0.0234963
843843 0 0
844844 9.75945 0.335934
845845 0 0
846846 0 0
847847 71.0893 2.44266
848848 32.8833 1.12922
849849 0 0
850850 0 0
851851 25.1955 0.863690
852852 0 0
853853 −3.93925 −0.134877 −0.0674386 0.997723i 0.521483π-0.521483\pi
−0.0674386 + 0.997723i 0.521483π0.521483\pi
854854 64.2232 2.19767
855855 0 0
856856 2.40773 0.0822945
857857 27.4388 0.937292 0.468646 0.883386i 0.344742π-0.344742\pi
0.468646 + 0.883386i 0.344742π0.344742\pi
858858 0 0
859859 32.4517 1.10724 0.553619 0.832770i 0.313246π-0.313246\pi
0.553619 + 0.832770i 0.313246π0.313246\pi
860860 0 0
861861 0 0
862862 −57.2629 −1.95038
863863 −2.10861 −0.0717778 −0.0358889 0.999356i 0.511426π-0.511426\pi
−0.0358889 + 0.999356i 0.511426π0.511426\pi
864864 0 0
865865 0 0
866866 1.72766 0.0587084
867867 0 0
868868 11.4166 0.387504
869869 −30.4602 −1.03329
870870 0 0
871871 −25.0731 −0.849569
872872 −3.47184 −0.117571
873873 0 0
874874 −13.6322 −0.461115
875875 0 0
876876 0 0
877877 37.6613 1.27173 0.635866 0.771799i 0.280643π-0.280643\pi
0.635866 + 0.771799i 0.280643π0.280643\pi
878878 −27.1062 −0.914789
879879 0 0
880880 0 0
881881 39.8818 1.34365 0.671827 0.740708i 0.265510π-0.265510\pi
0.671827 + 0.740708i 0.265510π0.265510\pi
882882 0 0
883883 −36.0458 −1.21304 −0.606518 0.795070i 0.707434π-0.707434\pi
−0.606518 + 0.795070i 0.707434π0.707434\pi
884884 −13.5218 −0.454787
885885 0 0
886886 −26.5525 −0.892050
887887 −26.2057 −0.879902 −0.439951 0.898022i 0.645004π-0.645004\pi
−0.439951 + 0.898022i 0.645004π0.645004\pi
888888 0 0
889889 17.4264 0.584464
890890 0 0
891891 0 0
892892 5.67700 0.190080
893893 −8.26046 −0.276426
894894 0 0
895895 0 0
896896 9.68093 0.323417
897897 0 0
898898 30.5780 1.02040
899899 −2.46794 −0.0823103
900900 0 0
901901 −10.7092 −0.356774
902902 47.3191 1.57555
903903 0 0
904904 −0.634123 −0.0210906
905905 0 0
906906 0 0
907907 22.8036 0.757182 0.378591 0.925564i 0.376409π-0.376409\pi
0.378591 + 0.925564i 0.376409π0.376409\pi
908908 26.4166 0.876664
909909 0 0
910910 0 0
911911 −4.44146 −0.147152 −0.0735761 0.997290i 0.523441π-0.523441\pi
−0.0735761 + 0.997290i 0.523441π0.523441\pi
912912 0 0
913913 23.1266 0.765379
914914 −10.3721 −0.343077
915915 0 0
916916 −9.52059 −0.314569
917917 −10.0223 −0.330965
918918 0 0
919919 37.0111 1.22088 0.610442 0.792061i 0.290992π-0.290992\pi
0.610442 + 0.792061i 0.290992π0.290992\pi
920920 0 0
921921 0 0
922922 −0.732959 −0.0241387
923923 −74.0932 −2.43881
924924 0 0
925925 0 0
926926 −13.0181 −0.427800
927927 0 0
928928 10.9191 0.358438
929929 3.04185 0.0997999 0.0499000 0.998754i 0.484110π-0.484110\pi
0.0499000 + 0.998754i 0.484110π0.484110\pi
930930 0 0
931931 5.69716 0.186717
932932 −5.81921 −0.190615
933933 0 0
934934 −1.67066 −0.0546657
935935 0 0
936936 0 0
937937 −38.6099 −1.26133 −0.630666 0.776055i 0.717218π-0.717218\pi
−0.630666 + 0.776055i 0.717218π0.717218\pi
938938 33.1817 1.08342
939939 0 0
940940 0 0
941941 −2.69716 −0.0879248 −0.0439624 0.999033i 0.513998π-0.513998\pi
−0.0439624 + 0.999033i 0.513998π0.513998\pi
942942 0 0
943943 30.3080 0.986963
944944 40.9158 1.33170
945945 0 0
946946 −38.7742 −1.26066
947947 −20.1877 −0.656012 −0.328006 0.944676i 0.606377π-0.606377\pi
−0.328006 + 0.944676i 0.606377π0.606377\pi
948948 0 0
949949 34.7254 1.12723
950950 0 0
951951 0 0
952952 −1.70829 −0.0553661
953953 5.18559 0.167978 0.0839888 0.996467i 0.473234π-0.473234\pi
0.0839888 + 0.996467i 0.473234π0.473234\pi
954954 0 0
955955 0 0
956956 −30.1624 −0.975523
957957 0 0
958958 33.3940 1.07891
959959 32.8896 1.06206
960960 0 0
961961 −27.9203 −0.900656
962962 37.2382 1.20061
963963 0 0
964964 −22.3231 −0.718979
965965 0 0
966966 0 0
967967 −58.0054 −1.86533 −0.932665 0.360744i 0.882523π-0.882523\pi
−0.932665 + 0.360744i 0.882523π0.882523\pi
968968 −6.80107 −0.218595
969969 0 0
970970 0 0
971971 24.3221 0.780533 0.390267 0.920702i 0.372383π-0.372383\pi
0.390267 + 0.920702i 0.372383π0.372383\pi
972972 0 0
973973 −13.1086 −0.420244
974974 −25.0867 −0.803830
975975 0 0
976976 −39.7911 −1.27368
977977 −36.1134 −1.15537 −0.577685 0.816260i 0.696044π-0.696044\pi
−0.577685 + 0.816260i 0.696044π0.696044\pi
978978 0 0
979979 −51.3498 −1.64115
980980 0 0
981981 0 0
982982 20.3525 0.649473
983983 21.1603 0.674909 0.337455 0.941342i 0.390434π-0.390434\pi
0.337455 + 0.941342i 0.390434π0.390434\pi
984984 0 0
985985 0 0
986986 −3.86832 −0.123192
987987 0 0
988988 −9.61504 −0.305895
989989 −24.8349 −0.789704
990990 0 0
991991 20.2652 0.643746 0.321873 0.946783i 0.395688π-0.395688\pi
0.321873 + 0.946783i 0.395688π0.395688\pi
992992 −13.6256 −0.432614
993993 0 0
994994 98.0548 3.11011
995995 0 0
996996 0 0
997997 −24.2875 −0.769193 −0.384597 0.923085i 0.625659π-0.625659\pi
−0.384597 + 0.923085i 0.625659π0.625659\pi
998998 70.7293 2.23890
999999 0 0
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 4275.2.a.bo.1.4 4
3.2 odd 2 475.2.a.i.1.1 4
5.4 even 2 855.2.a.m.1.1 4
12.11 even 2 7600.2.a.cf.1.2 4
15.2 even 4 475.2.b.e.324.3 8
15.8 even 4 475.2.b.e.324.6 8
15.14 odd 2 95.2.a.b.1.4 4
57.56 even 2 9025.2.a.bf.1.4 4
60.59 even 2 1520.2.a.t.1.3 4
105.104 even 2 4655.2.a.y.1.4 4
120.29 odd 2 6080.2.a.cc.1.3 4
120.59 even 2 6080.2.a.ch.1.2 4
285.284 even 2 1805.2.a.p.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.a.b.1.4 4 15.14 odd 2
475.2.a.i.1.1 4 3.2 odd 2
475.2.b.e.324.3 8 15.2 even 4
475.2.b.e.324.6 8 15.8 even 4
855.2.a.m.1.1 4 5.4 even 2
1520.2.a.t.1.3 4 60.59 even 2
1805.2.a.p.1.1 4 285.284 even 2
4275.2.a.bo.1.4 4 1.1 even 1 trivial
4655.2.a.y.1.4 4 105.104 even 2
6080.2.a.cc.1.3 4 120.29 odd 2
6080.2.a.ch.1.2 4 120.59 even 2
7600.2.a.cf.1.2 4 12.11 even 2
9025.2.a.bf.1.4 4 57.56 even 2