Properties

Label 2475.2.a.y.1.3
Level 24752475
Weight 22
Character 2475.1
Self dual yes
Analytic conductor 19.76319.763
Analytic rank 00
Dimension 33
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] = [2475,2,Mod(1,2475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2475, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2475.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2475=325211 2475 = 3^{2} \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2475.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-3,0,5,0,0,8,-9,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 19.762974500319.7629745003
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.148.1
Copy content comment:defining polynomial
 
Copy content 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]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 165)
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 == 2475.1

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+1.21432q20.525428q4+4.90321q73.06668q8+1.00000q11+4.14764q13+5.95407q142.67307q16+5.33185q175.18421q19+1.21432q224.00000q23+5.03657q262.57628q281.80642q29+2.62222q31+2.88739q32+6.47457q34+5.80642q376.29529q381.80642q41+4.90321q430.525428q444.85728q467.05086q47+17.0415q492.17929q52+7.18421q5315.0366q562.19358q581.67307q59+0.755569q61+3.18421q62+8.85236q644.85728q672.80150q680.428639q71+12.7096q73+7.05086q74+2.72393q76+4.90321q776.42864q792.19358q82+2.90321q83+5.95407q863.06668q880.622216q89+20.3368q91+2.10171q928.56199q942.75557q97+20.6938q98+O(q100)q+1.21432 q^{2} -0.525428 q^{4} +4.90321 q^{7} -3.06668 q^{8} +1.00000 q^{11} +4.14764 q^{13} +5.95407 q^{14} -2.67307 q^{16} +5.33185 q^{17} -5.18421 q^{19} +1.21432 q^{22} -4.00000 q^{23} +5.03657 q^{26} -2.57628 q^{28} -1.80642 q^{29} +2.62222 q^{31} +2.88739 q^{32} +6.47457 q^{34} +5.80642 q^{37} -6.29529 q^{38} -1.80642 q^{41} +4.90321 q^{43} -0.525428 q^{44} -4.85728 q^{46} -7.05086 q^{47} +17.0415 q^{49} -2.17929 q^{52} +7.18421 q^{53} -15.0366 q^{56} -2.19358 q^{58} -1.67307 q^{59} +0.755569 q^{61} +3.18421 q^{62} +8.85236 q^{64} -4.85728 q^{67} -2.80150 q^{68} -0.428639 q^{71} +12.7096 q^{73} +7.05086 q^{74} +2.72393 q^{76} +4.90321 q^{77} -6.42864 q^{79} -2.19358 q^{82} +2.90321 q^{83} +5.95407 q^{86} -3.06668 q^{88} -0.622216 q^{89} +20.3368 q^{91} +2.10171 q^{92} -8.56199 q^{94} -2.75557 q^{97} +20.6938 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q3q2+5q4+8q79q8+3q11+6q132q14+5q164q172q193q2212q23+8q26+12q28+8q29+8q3111q32+26q34++29q98+O(q100) 3 q - 3 q^{2} + 5 q^{4} + 8 q^{7} - 9 q^{8} + 3 q^{11} + 6 q^{13} - 2 q^{14} + 5 q^{16} - 4 q^{17} - 2 q^{19} - 3 q^{22} - 12 q^{23} + 8 q^{26} + 12 q^{28} + 8 q^{29} + 8 q^{31} - 11 q^{32} + 26 q^{34}+ \cdots + 29 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 1.21432 0.858654 0.429327 0.903149i 0.358751π-0.358751\pi
0.429327 + 0.903149i 0.358751π0.358751\pi
33 0 0
44 −0.525428 −0.262714
55 0 0
66 0 0
77 4.90321 1.85324 0.926620 0.375999i 0.122700π-0.122700\pi
0.926620 + 0.375999i 0.122700π0.122700\pi
88 −3.06668 −1.08423
99 0 0
1010 0 0
1111 1.00000 0.301511
1212 0 0
1313 4.14764 1.15035 0.575175 0.818031i 0.304934π-0.304934\pi
0.575175 + 0.818031i 0.304934π0.304934\pi
1414 5.95407 1.59129
1515 0 0
1616 −2.67307 −0.668268
1717 5.33185 1.29316 0.646582 0.762845i 0.276198π-0.276198\pi
0.646582 + 0.762845i 0.276198π0.276198\pi
1818 0 0
1919 −5.18421 −1.18934 −0.594669 0.803970i 0.702717π-0.702717\pi
−0.594669 + 0.803970i 0.702717π0.702717\pi
2020 0 0
2121 0 0
2222 1.21432 0.258894
2323 −4.00000 −0.834058 −0.417029 0.908893i 0.636929π-0.636929\pi
−0.417029 + 0.908893i 0.636929π0.636929\pi
2424 0 0
2525 0 0
2626 5.03657 0.987752
2727 0 0
2828 −2.57628 −0.486872
2929 −1.80642 −0.335444 −0.167722 0.985834i 0.553641π-0.553641\pi
−0.167722 + 0.985834i 0.553641π0.553641\pi
3030 0 0
3131 2.62222 0.470964 0.235482 0.971879i 0.424333π-0.424333\pi
0.235482 + 0.971879i 0.424333π0.424333\pi
3232 2.88739 0.510423
3333 0 0
3434 6.47457 1.11038
3535 0 0
3636 0 0
3737 5.80642 0.954570 0.477285 0.878749i 0.341621π-0.341621\pi
0.477285 + 0.878749i 0.341621π0.341621\pi
3838 −6.29529 −1.02123
3939 0 0
4040 0 0
4141 −1.80642 −0.282116 −0.141058 0.990001i 0.545050π-0.545050\pi
−0.141058 + 0.990001i 0.545050π0.545050\pi
4242 0 0
4343 4.90321 0.747733 0.373866 0.927483i 0.378032π-0.378032\pi
0.373866 + 0.927483i 0.378032π0.378032\pi
4444 −0.525428 −0.0792112
4545 0 0
4646 −4.85728 −0.716167
4747 −7.05086 −1.02847 −0.514236 0.857648i 0.671925π-0.671925\pi
−0.514236 + 0.857648i 0.671925π0.671925\pi
4848 0 0
4949 17.0415 2.43450
5050 0 0
5151 0 0
5252 −2.17929 −0.302213
5353 7.18421 0.986827 0.493413 0.869795i 0.335749π-0.335749\pi
0.493413 + 0.869795i 0.335749π0.335749\pi
5454 0 0
5555 0 0
5656 −15.0366 −2.00935
5757 0 0
5858 −2.19358 −0.288031
5959 −1.67307 −0.217815 −0.108908 0.994052i 0.534735π-0.534735\pi
−0.108908 + 0.994052i 0.534735π0.534735\pi
6060 0 0
6161 0.755569 0.0967407 0.0483703 0.998829i 0.484597π-0.484597\pi
0.0483703 + 0.998829i 0.484597π0.484597\pi
6262 3.18421 0.404395
6363 0 0
6464 8.85236 1.10654
6565 0 0
6666 0 0
6767 −4.85728 −0.593411 −0.296706 0.954969i 0.595888π-0.595888\pi
−0.296706 + 0.954969i 0.595888π0.595888\pi
6868 −2.80150 −0.339732
6969 0 0
7070 0 0
7171 −0.428639 −0.0508701 −0.0254351 0.999676i 0.508097π-0.508097\pi
−0.0254351 + 0.999676i 0.508097π0.508097\pi
7272 0 0
7373 12.7096 1.48755 0.743775 0.668430i 0.233033π-0.233033\pi
0.743775 + 0.668430i 0.233033π0.233033\pi
7474 7.05086 0.819645
7575 0 0
7676 2.72393 0.312456
7777 4.90321 0.558773
7878 0 0
7979 −6.42864 −0.723278 −0.361639 0.932318i 0.617783π-0.617783\pi
−0.361639 + 0.932318i 0.617783π0.617783\pi
8080 0 0
8181 0 0
8282 −2.19358 −0.242240
8383 2.90321 0.318669 0.159334 0.987225i 0.449065π-0.449065\pi
0.159334 + 0.987225i 0.449065π0.449065\pi
8484 0 0
8585 0 0
8686 5.95407 0.642044
8787 0 0
8888 −3.06668 −0.326909
8989 −0.622216 −0.0659547 −0.0329774 0.999456i 0.510499π-0.510499\pi
−0.0329774 + 0.999456i 0.510499π0.510499\pi
9090 0 0
9191 20.3368 2.13187
9292 2.10171 0.219118
9393 0 0
9494 −8.56199 −0.883102
9595 0 0
9696 0 0
9797 −2.75557 −0.279786 −0.139893 0.990167i 0.544676π-0.544676\pi
−0.139893 + 0.990167i 0.544676π0.544676\pi
9898 20.6938 2.09039
9999 0 0
100100 0 0
101101 17.8064 1.77181 0.885903 0.463871i 0.153540π-0.153540\pi
0.885903 + 0.463871i 0.153540π0.153540\pi
102102 0 0
103103 4.94914 0.487654 0.243827 0.969819i 0.421597π-0.421597\pi
0.243827 + 0.969819i 0.421597π0.421597\pi
104104 −12.7195 −1.24725
105105 0 0
106106 8.72393 0.847343
107107 −11.1985 −1.08260 −0.541300 0.840830i 0.682068π-0.682068\pi
−0.541300 + 0.840830i 0.682068π0.682068\pi
108108 0 0
109109 15.7146 1.50518 0.752591 0.658488i 0.228804π-0.228804\pi
0.752591 + 0.658488i 0.228804π0.228804\pi
110110 0 0
111111 0 0
112112 −13.1066 −1.23846
113113 1.76494 0.166031 0.0830156 0.996548i 0.473545π-0.473545\pi
0.0830156 + 0.996548i 0.473545π0.473545\pi
114114 0 0
115115 0 0
116116 0.949145 0.0881259
117117 0 0
118118 −2.03164 −0.187028
119119 26.1432 2.39654
120120 0 0
121121 1.00000 0.0909091
122122 0.917502 0.0830667
123123 0 0
124124 −1.37778 −0.123729
125125 0 0
126126 0 0
127127 18.7096 1.66021 0.830106 0.557606i 0.188280π-0.188280\pi
0.830106 + 0.557606i 0.188280π0.188280\pi
128128 4.97481 0.439715
129129 0 0
130130 0 0
131131 1.24443 0.108726 0.0543632 0.998521i 0.482687π-0.482687\pi
0.0543632 + 0.998521i 0.482687π0.482687\pi
132132 0 0
133133 −25.4193 −2.20413
134134 −5.89829 −0.509535
135135 0 0
136136 −16.3511 −1.40209
137137 −18.7971 −1.60594 −0.802970 0.596019i 0.796748π-0.796748\pi
−0.802970 + 0.596019i 0.796748π0.796748\pi
138138 0 0
139139 14.0415 1.19098 0.595492 0.803361i 0.296957π-0.296957\pi
0.595492 + 0.803361i 0.296957π0.296957\pi
140140 0 0
141141 0 0
142142 −0.520505 −0.0436798
143143 4.14764 0.346843
144144 0 0
145145 0 0
146146 15.4336 1.27729
147147 0 0
148148 −3.05086 −0.250779
149149 3.05086 0.249936 0.124968 0.992161i 0.460117π-0.460117\pi
0.124968 + 0.992161i 0.460117π0.460117\pi
150150 0 0
151151 −0.326929 −0.0266051 −0.0133026 0.999912i 0.504234π-0.504234\pi
−0.0133026 + 0.999912i 0.504234π0.504234\pi
152152 15.8983 1.28952
153153 0 0
154154 5.95407 0.479792
155155 0 0
156156 0 0
157157 −19.9081 −1.58884 −0.794421 0.607367i 0.792226π-0.792226\pi
−0.794421 + 0.607367i 0.792226π0.792226\pi
158158 −7.80642 −0.621046
159159 0 0
160160 0 0
161161 −19.6128 −1.54571
162162 0 0
163163 12.1748 0.953607 0.476804 0.879010i 0.341795π-0.341795\pi
0.476804 + 0.879010i 0.341795π0.341795\pi
164164 0.949145 0.0741158
165165 0 0
166166 3.52543 0.273626
167167 −13.0049 −1.00635 −0.503176 0.864184i 0.667835π-0.667835\pi
−0.503176 + 0.864184i 0.667835π0.667835\pi
168168 0 0
169169 4.20294 0.323303
170170 0 0
171171 0 0
172172 −2.57628 −0.196440
173173 −13.8938 −1.05633 −0.528165 0.849142i 0.677120π-0.677120\pi
−0.528165 + 0.849142i 0.677120π0.677120\pi
174174 0 0
175175 0 0
176176 −2.67307 −0.201490
177177 0 0
178178 −0.755569 −0.0566323
179179 −12.8573 −0.960998 −0.480499 0.876995i 0.659544π-0.659544\pi
−0.480499 + 0.876995i 0.659544π0.659544\pi
180180 0 0
181181 0.917502 0.0681974 0.0340987 0.999418i 0.489144π-0.489144\pi
0.0340987 + 0.999418i 0.489144π0.489144\pi
182182 24.6953 1.83054
183183 0 0
184184 12.2667 0.904314
185185 0 0
186186 0 0
187187 5.33185 0.389904
188188 3.70471 0.270194
189189 0 0
190190 0 0
191191 −14.3684 −1.03966 −0.519831 0.854269i 0.674005π-0.674005\pi
−0.519831 + 0.854269i 0.674005π0.674005\pi
192192 0 0
193193 −11.7605 −0.846539 −0.423269 0.906004i 0.639118π-0.639118\pi
−0.423269 + 0.906004i 0.639118π0.639118\pi
194194 −3.34614 −0.240239
195195 0 0
196196 −8.95407 −0.639576
197197 3.82071 0.272215 0.136107 0.990694i 0.456541π-0.456541\pi
0.136107 + 0.990694i 0.456541π0.456541\pi
198198 0 0
199199 −13.7146 −0.972199 −0.486100 0.873903i 0.661581π-0.661581\pi
−0.486100 + 0.873903i 0.661581π0.661581\pi
200200 0 0
201201 0 0
202202 21.6227 1.52137
203203 −8.85728 −0.621659
204204 0 0
205205 0 0
206206 6.00984 0.418726
207207 0 0
208208 −11.0869 −0.768741
209209 −5.18421 −0.358599
210210 0 0
211211 1.95851 0.134830 0.0674148 0.997725i 0.478525π-0.478525\pi
0.0674148 + 0.997725i 0.478525π0.478525\pi
212212 −3.77478 −0.259253
213213 0 0
214214 −13.5986 −0.929578
215215 0 0
216216 0 0
217217 12.8573 0.872809
218218 19.0825 1.29243
219219 0 0
220220 0 0
221221 22.1146 1.48759
222222 0 0
223223 −26.0098 −1.74175 −0.870874 0.491506i 0.836446π-0.836446\pi
−0.870874 + 0.491506i 0.836446π0.836446\pi
224224 14.1575 0.945937
225225 0 0
226226 2.14320 0.142563
227227 6.34122 0.420882 0.210441 0.977607i 0.432510π-0.432510\pi
0.210441 + 0.977607i 0.432510π0.432510\pi
228228 0 0
229229 −23.3274 −1.54152 −0.770759 0.637127i 0.780123π-0.780123\pi
−0.770759 + 0.637127i 0.780123π0.780123\pi
230230 0 0
231231 0 0
232232 5.53972 0.363700
233233 1.42372 0.0932708 0.0466354 0.998912i 0.485150π-0.485150\pi
0.0466354 + 0.998912i 0.485150π0.485150\pi
234234 0 0
235235 0 0
236236 0.879077 0.0572231
237237 0 0
238238 31.7462 2.05780
239239 18.9590 1.22636 0.613178 0.789945i 0.289891π-0.289891\pi
0.613178 + 0.789945i 0.289891π0.289891\pi
240240 0 0
241241 −1.34614 −0.0867126 −0.0433563 0.999060i 0.513805π-0.513805\pi
−0.0433563 + 0.999060i 0.513805π0.513805\pi
242242 1.21432 0.0780594
243243 0 0
244244 −0.396997 −0.0254151
245245 0 0
246246 0 0
247247 −21.5022 −1.36816
248248 −8.04149 −0.510635
249249 0 0
250250 0 0
251251 −1.08250 −0.0683267 −0.0341633 0.999416i 0.510877π-0.510877\pi
−0.0341633 + 0.999416i 0.510877π0.510877\pi
252252 0 0
253253 −4.00000 −0.251478
254254 22.7195 1.42555
255255 0 0
256256 −11.6637 −0.728981
257257 0.133353 0.00831834 0.00415917 0.999991i 0.498676π-0.498676\pi
0.00415917 + 0.999991i 0.498676π0.498676\pi
258258 0 0
259259 28.4701 1.76905
260260 0 0
261261 0 0
262262 1.51114 0.0933584
263263 0.147643 0.00910407 0.00455203 0.999990i 0.498551π-0.498551\pi
0.00455203 + 0.999990i 0.498551π0.498551\pi
264264 0 0
265265 0 0
266266 −30.8671 −1.89258
267267 0 0
268268 2.55215 0.155897
269269 26.8573 1.63752 0.818759 0.574138i 0.194663π-0.194663\pi
0.818759 + 0.574138i 0.194663π0.194663\pi
270270 0 0
271271 3.08250 0.187248 0.0936242 0.995608i 0.470155π-0.470155\pi
0.0936242 + 0.995608i 0.470155π0.470155\pi
272272 −14.2524 −0.864180
273273 0 0
274274 −22.8256 −1.37895
275275 0 0
276276 0 0
277277 −8.70964 −0.523311 −0.261656 0.965161i 0.584268π-0.584268\pi
−0.261656 + 0.965161i 0.584268π0.584268\pi
278278 17.0509 1.02264
279279 0 0
280280 0 0
281281 20.3783 1.21567 0.607833 0.794065i 0.292039π-0.292039\pi
0.607833 + 0.794065i 0.292039π0.292039\pi
282282 0 0
283283 −6.32248 −0.375833 −0.187916 0.982185i 0.560173π-0.560173\pi
−0.187916 + 0.982185i 0.560173π0.560173\pi
284284 0.225219 0.0133643
285285 0 0
286286 5.03657 0.297818
287287 −8.85728 −0.522829
288288 0 0
289289 11.4286 0.672273
290290 0 0
291291 0 0
292292 −6.67799 −0.390800
293293 −16.6780 −0.974339 −0.487169 0.873308i 0.661971π-0.661971\pi
−0.487169 + 0.873308i 0.661971π0.661971\pi
294294 0 0
295295 0 0
296296 −17.8064 −1.03498
297297 0 0
298298 3.70471 0.214608
299299 −16.5906 −0.959458
300300 0 0
301301 24.0415 1.38573
302302 −0.396997 −0.0228446
303303 0 0
304304 13.8578 0.794797
305305 0 0
306306 0 0
307307 −9.58565 −0.547082 −0.273541 0.961860i 0.588195π-0.588195\pi
−0.273541 + 0.961860i 0.588195π0.588195\pi
308308 −2.57628 −0.146797
309309 0 0
310310 0 0
311311 −14.5303 −0.823941 −0.411970 0.911197i 0.635159π-0.635159\pi
−0.411970 + 0.911197i 0.635159π0.635159\pi
312312 0 0
313313 −21.0321 −1.18881 −0.594403 0.804167i 0.702612π-0.702612\pi
−0.594403 + 0.804167i 0.702612π0.702612\pi
314314 −24.1748 −1.36427
315315 0 0
316316 3.37778 0.190015
317317 0.990632 0.0556394 0.0278197 0.999613i 0.491144π-0.491144\pi
0.0278197 + 0.999613i 0.491144π0.491144\pi
318318 0 0
319319 −1.80642 −0.101140
320320 0 0
321321 0 0
322322 −23.8163 −1.32723
323323 −27.6414 −1.53801
324324 0 0
325325 0 0
326326 14.7841 0.818818
327327 0 0
328328 5.53972 0.305880
329329 −34.5718 −1.90601
330330 0 0
331331 −17.5812 −0.966350 −0.483175 0.875524i 0.660517π-0.660517\pi
−0.483175 + 0.875524i 0.660517π0.660517\pi
332332 −1.52543 −0.0837187
333333 0 0
334334 −15.7921 −0.864107
335335 0 0
336336 0 0
337337 −3.16992 −0.172676 −0.0863382 0.996266i 0.527517π-0.527517\pi
−0.0863382 + 0.996266i 0.527517π0.527517\pi
338338 5.10372 0.277606
339339 0 0
340340 0 0
341341 2.62222 0.142001
342342 0 0
343343 49.2355 2.65847
344344 −15.0366 −0.810717
345345 0 0
346346 −16.8716 −0.907021
347347 −4.97634 −0.267144 −0.133572 0.991039i 0.542645π-0.542645\pi
−0.133572 + 0.991039i 0.542645π0.542645\pi
348348 0 0
349349 18.2034 0.974407 0.487203 0.873289i 0.338017π-0.338017\pi
0.487203 + 0.873289i 0.338017π0.338017\pi
350350 0 0
351351 0 0
352352 2.88739 0.153898
353353 −22.4099 −1.19276 −0.596379 0.802703i 0.703395π-0.703395\pi
−0.596379 + 0.802703i 0.703395π0.703395\pi
354354 0 0
355355 0 0
356356 0.326929 0.0173272
357357 0 0
358358 −15.6128 −0.825165
359359 −21.3274 −1.12562 −0.562809 0.826587i 0.690279π-0.690279\pi
−0.562809 + 0.826587i 0.690279π0.690279\pi
360360 0 0
361361 7.87601 0.414527
362362 1.11414 0.0585579
363363 0 0
364364 −10.6855 −0.560072
365365 0 0
366366 0 0
367367 35.1338 1.83397 0.916985 0.398921i 0.130615π-0.130615\pi
0.916985 + 0.398921i 0.130615π0.130615\pi
368368 10.6923 0.557374
369369 0 0
370370 0 0
371371 35.2257 1.82883
372372 0 0
373373 −17.0049 −0.880481 −0.440241 0.897880i 0.645107π-0.645107\pi
−0.440241 + 0.897880i 0.645107π0.645107\pi
374374 6.47457 0.334792
375375 0 0
376376 21.6227 1.11511
377377 −7.49240 −0.385878
378378 0 0
379379 2.36842 0.121657 0.0608287 0.998148i 0.480626π-0.480626\pi
0.0608287 + 0.998148i 0.480626π0.480626\pi
380380 0 0
381381 0 0
382382 −17.4479 −0.892710
383383 −1.21585 −0.0621271 −0.0310635 0.999517i 0.509889π-0.509889\pi
−0.0310635 + 0.999517i 0.509889π0.509889\pi
384384 0 0
385385 0 0
386386 −14.2810 −0.726884
387387 0 0
388388 1.44785 0.0735035
389389 −2.26671 −0.114927 −0.0574633 0.998348i 0.518301π-0.518301\pi
−0.0574633 + 0.998348i 0.518301π0.518301\pi
390390 0 0
391391 −21.3274 −1.07857
392392 −52.2607 −2.63957
393393 0 0
394394 4.63957 0.233738
395395 0 0
396396 0 0
397397 −18.4889 −0.927929 −0.463965 0.885854i 0.653574π-0.653574\pi
−0.463965 + 0.885854i 0.653574π0.653574\pi
398398 −16.6539 −0.834782
399399 0 0
400400 0 0
401401 −17.5625 −0.877028 −0.438514 0.898724i 0.644495π-0.644495\pi
−0.438514 + 0.898724i 0.644495π0.644495\pi
402402 0 0
403403 10.8760 0.541773
404404 −9.35599 −0.465478
405405 0 0
406406 −10.7556 −0.533790
407407 5.80642 0.287814
408408 0 0
409409 −21.3461 −1.05550 −0.527749 0.849400i 0.676964π-0.676964\pi
−0.527749 + 0.849400i 0.676964π0.676964\pi
410410 0 0
411411 0 0
412412 −2.60042 −0.128113
413413 −8.20342 −0.403664
414414 0 0
415415 0 0
416416 11.9759 0.587165
417417 0 0
418418 −6.29529 −0.307913
419419 −28.8573 −1.40977 −0.704885 0.709321i 0.749001π-0.749001\pi
−0.704885 + 0.709321i 0.749001π0.749001\pi
420420 0 0
421421 −35.4893 −1.72964 −0.864822 0.502078i 0.832569π-0.832569\pi
−0.864822 + 0.502078i 0.832569π0.832569\pi
422422 2.37826 0.115772
423423 0 0
424424 −22.0316 −1.06995
425425 0 0
426426 0 0
427427 3.70471 0.179284
428428 5.88400 0.284414
429429 0 0
430430 0 0
431431 −9.24443 −0.445289 −0.222644 0.974900i 0.571469π-0.571469\pi
−0.222644 + 0.974900i 0.571469π0.571469\pi
432432 0 0
433433 −6.28544 −0.302059 −0.151030 0.988529i 0.548259π-0.548259\pi
−0.151030 + 0.988529i 0.548259π0.548259\pi
434434 15.6128 0.749441
435435 0 0
436436 −8.25686 −0.395432
437437 20.7368 0.991977
438438 0 0
439439 −36.5303 −1.74350 −0.871749 0.489952i 0.837014π-0.837014\pi
−0.871749 + 0.489952i 0.837014π0.837014\pi
440440 0 0
441441 0 0
442442 26.8542 1.27732
443443 38.2766 1.81857 0.909287 0.416170i 0.136628π-0.136628\pi
0.909287 + 0.416170i 0.136628π0.136628\pi
444444 0 0
445445 0 0
446446 −31.5843 −1.49556
447447 0 0
448448 43.4050 2.05069
449449 31.8479 1.50300 0.751498 0.659735i 0.229332π-0.229332\pi
0.751498 + 0.659735i 0.229332π0.229332\pi
450450 0 0
451451 −1.80642 −0.0850612
452452 −0.927346 −0.0436187
453453 0 0
454454 7.70027 0.361391
455455 0 0
456456 0 0
457457 1.39207 0.0651185 0.0325592 0.999470i 0.489634π-0.489634\pi
0.0325592 + 0.999470i 0.489634π0.489634\pi
458458 −28.3269 −1.32363
459459 0 0
460460 0 0
461461 7.70471 0.358844 0.179422 0.983772i 0.442577π-0.442577\pi
0.179422 + 0.983772i 0.442577π0.442577\pi
462462 0 0
463463 4.68244 0.217611 0.108806 0.994063i 0.465297π-0.465297\pi
0.108806 + 0.994063i 0.465297π0.465297\pi
464464 4.82870 0.224167
465465 0 0
466466 1.72885 0.0800873
467467 −12.8573 −0.594964 −0.297482 0.954727i 0.596147π-0.596147\pi
−0.297482 + 0.954727i 0.596147π0.596147\pi
468468 0 0
469469 −23.8163 −1.09973
470470 0 0
471471 0 0
472472 5.13077 0.236163
473473 4.90321 0.225450
474474 0 0
475475 0 0
476476 −13.7364 −0.629605
477477 0 0
478478 23.0223 1.05301
479479 −8.38715 −0.383219 −0.191609 0.981471i 0.561371π-0.561371\pi
−0.191609 + 0.981471i 0.561371π0.561371\pi
480480 0 0
481481 24.0830 1.09809
482482 −1.63465 −0.0744561
483483 0 0
484484 −0.525428 −0.0238831
485485 0 0
486486 0 0
487487 9.83500 0.445667 0.222833 0.974857i 0.428469π-0.428469\pi
0.222833 + 0.974857i 0.428469π0.428469\pi
488488 −2.31708 −0.104890
489489 0 0
490490 0 0
491491 32.9403 1.48657 0.743286 0.668973i 0.233266π-0.233266\pi
0.743286 + 0.668973i 0.233266π0.233266\pi
492492 0 0
493493 −9.63158 −0.433785
494494 −26.1106 −1.17477
495495 0 0
496496 −7.00937 −0.314730
497497 −2.10171 −0.0942746
498498 0 0
499499 −1.63158 −0.0730397 −0.0365199 0.999333i 0.511627π-0.511627\pi
−0.0365199 + 0.999333i 0.511627π0.511627\pi
500500 0 0
501501 0 0
502502 −1.31450 −0.0586689
503503 −41.8622 −1.86654 −0.933272 0.359171i 0.883059π-0.883059\pi
−0.933272 + 0.359171i 0.883059π0.883059\pi
504504 0 0
505505 0 0
506506 −4.85728 −0.215932
507507 0 0
508508 −9.83056 −0.436160
509509 38.8573 1.72232 0.861159 0.508335i 0.169739π-0.169739\pi
0.861159 + 0.508335i 0.169739π0.169739\pi
510510 0 0
511511 62.3180 2.75679
512512 −24.1131 −1.06566
513513 0 0
514514 0.161933 0.00714257
515515 0 0
516516 0 0
517517 −7.05086 −0.310096
518518 34.5718 1.51900
519519 0 0
520520 0 0
521521 −11.1111 −0.486785 −0.243393 0.969928i 0.578260π-0.578260\pi
−0.243393 + 0.969928i 0.578260π0.578260\pi
522522 0 0
523523 27.3002 1.19375 0.596877 0.802332i 0.296408π-0.296408\pi
0.596877 + 0.802332i 0.296408π0.296408\pi
524524 −0.653858 −0.0285639
525525 0 0
526526 0.179286 0.00781724
527527 13.9813 0.609033
528528 0 0
529529 −7.00000 −0.304348
530530 0 0
531531 0 0
532532 13.3560 0.579055
533533 −7.49240 −0.324532
534534 0 0
535535 0 0
536536 14.8957 0.643396
537537 0 0
538538 32.6133 1.40606
539539 17.0415 0.734029
540540 0 0
541541 −16.1017 −0.692267 −0.346133 0.938185i 0.612506π-0.612506\pi
−0.346133 + 0.938185i 0.612506π0.612506\pi
542542 3.74314 0.160782
543543 0 0
544544 15.3951 0.660061
545545 0 0
546546 0 0
547547 40.0370 1.71186 0.855930 0.517091i 0.172985π-0.172985\pi
0.855930 + 0.517091i 0.172985π0.172985\pi
548548 9.87649 0.421903
549549 0 0
550550 0 0
551551 9.36488 0.398957
552552 0 0
553553 −31.5210 −1.34041
554554 −10.5763 −0.449343
555555 0 0
556556 −7.37778 −0.312888
557557 28.2908 1.19872 0.599361 0.800479i 0.295422π-0.295422\pi
0.599361 + 0.800479i 0.295422π0.295422\pi
558558 0 0
559559 20.3368 0.860154
560560 0 0
561561 0 0
562562 24.7457 1.04384
563563 32.7926 1.38204 0.691022 0.722834i 0.257161π-0.257161\pi
0.691022 + 0.722834i 0.257161π0.257161\pi
564564 0 0
565565 0 0
566566 −7.67752 −0.322710
567567 0 0
568568 1.31450 0.0551551
569569 8.88586 0.372515 0.186257 0.982501i 0.440364π-0.440364\pi
0.186257 + 0.982501i 0.440364π0.440364\pi
570570 0 0
571571 −10.6953 −0.447586 −0.223793 0.974637i 0.571844π-0.571844\pi
−0.223793 + 0.974637i 0.571844π0.571844\pi
572572 −2.17929 −0.0911205
573573 0 0
574574 −10.7556 −0.448929
575575 0 0
576576 0 0
577577 −27.1338 −1.12960 −0.564798 0.825229i 0.691046π-0.691046\pi
−0.564798 + 0.825229i 0.691046π0.691046\pi
578578 13.8780 0.577250
579579 0 0
580580 0 0
581581 14.2351 0.590570
582582 0 0
583583 7.18421 0.297540
584584 −38.9763 −1.61285
585585 0 0
586586 −20.2524 −0.836620
587587 10.9590 0.452326 0.226163 0.974089i 0.427382π-0.427382\pi
0.226163 + 0.974089i 0.427382π0.427382\pi
588588 0 0
589589 −13.5941 −0.560136
590590 0 0
591591 0 0
592592 −15.5210 −0.637908
593593 23.7003 0.973253 0.486627 0.873610i 0.338227π-0.338227\pi
0.486627 + 0.873610i 0.338227π0.338227\pi
594594 0 0
595595 0 0
596596 −1.60300 −0.0656616
597597 0 0
598598 −20.1463 −0.823842
599599 −41.7146 −1.70441 −0.852205 0.523208i 0.824735π-0.824735\pi
−0.852205 + 0.523208i 0.824735π0.824735\pi
600600 0 0
601601 14.5906 0.595162 0.297581 0.954697i 0.403820π-0.403820\pi
0.297581 + 0.954697i 0.403820π0.403820\pi
602602 29.1941 1.18986
603603 0 0
604604 0.171778 0.00698953
605605 0 0
606606 0 0
607607 −19.9826 −0.811071 −0.405535 0.914079i 0.632915π-0.632915\pi
−0.405535 + 0.914079i 0.632915π0.632915\pi
608608 −14.9688 −0.607066
609609 0 0
610610 0 0
611611 −29.2444 −1.18310
612612 0 0
613613 19.0781 0.770555 0.385278 0.922801i 0.374106π-0.374106\pi
0.385278 + 0.922801i 0.374106π0.374106\pi
614614 −11.6400 −0.469754
615615 0 0
616616 −15.0366 −0.605840
617617 39.3590 1.58454 0.792268 0.610174i 0.208900π-0.208900\pi
0.792268 + 0.610174i 0.208900π0.208900\pi
618618 0 0
619619 −23.0923 −0.928160 −0.464080 0.885793i 0.653615π-0.653615\pi
−0.464080 + 0.885793i 0.653615π0.653615\pi
620620 0 0
621621 0 0
622622 −17.6445 −0.707480
623623 −3.05086 −0.122230
624624 0 0
625625 0 0
626626 −25.5397 −1.02077
627627 0 0
628628 10.4603 0.417411
629629 30.9590 1.23442
630630 0 0
631631 −25.5111 −1.01558 −0.507791 0.861480i 0.669538π-0.669538\pi
−0.507791 + 0.861480i 0.669538π0.669538\pi
632632 19.7146 0.784203
633633 0 0
634634 1.20294 0.0477750
635635 0 0
636636 0 0
637637 70.6820 2.80052
638638 −2.19358 −0.0868445
639639 0 0
640640 0 0
641641 6.25380 0.247010 0.123505 0.992344i 0.460586π-0.460586\pi
0.123505 + 0.992344i 0.460586π0.460586\pi
642642 0 0
643643 6.84743 0.270036 0.135018 0.990843i 0.456891π-0.456891\pi
0.135018 + 0.990843i 0.456891π0.456891\pi
644644 10.3051 0.406079
645645 0 0
646646 −33.5655 −1.32062
647647 −20.2953 −0.797890 −0.398945 0.916975i 0.630624π-0.630624\pi
−0.398945 + 0.916975i 0.630624π0.630624\pi
648648 0 0
649649 −1.67307 −0.0656738
650650 0 0
651651 0 0
652652 −6.39700 −0.250526
653653 10.6222 0.415679 0.207840 0.978163i 0.433357π-0.433357\pi
0.207840 + 0.978163i 0.433357π0.433357\pi
654654 0 0
655655 0 0
656656 4.82870 0.188529
657657 0 0
658658 −41.9813 −1.63660
659659 −10.1017 −0.393507 −0.196753 0.980453i 0.563040π-0.563040\pi
−0.196753 + 0.980453i 0.563040π0.563040\pi
660660 0 0
661661 21.6128 0.840642 0.420321 0.907375i 0.361917π-0.361917\pi
0.420321 + 0.907375i 0.361917π0.361917\pi
662662 −21.3492 −0.829760
663663 0 0
664664 −8.90321 −0.345512
665665 0 0
666666 0 0
667667 7.22570 0.279780
668668 6.83314 0.264382
669669 0 0
670670 0 0
671671 0.755569 0.0291684
672672 0 0
673673 10.2208 0.393982 0.196991 0.980405i 0.436883π-0.436883\pi
0.196991 + 0.980405i 0.436883π0.436883\pi
674674 −3.84929 −0.148269
675675 0 0
676676 −2.20834 −0.0849363
677677 −13.9224 −0.535082 −0.267541 0.963546i 0.586211π-0.586211\pi
−0.267541 + 0.963546i 0.586211π0.586211\pi
678678 0 0
679679 −13.5111 −0.518510
680680 0 0
681681 0 0
682682 3.18421 0.121930
683683 10.3970 0.397830 0.198915 0.980017i 0.436258π-0.436258\pi
0.198915 + 0.980017i 0.436258π0.436258\pi
684684 0 0
685685 0 0
686686 59.7877 2.28270
687687 0 0
688688 −13.1066 −0.499686
689689 29.7975 1.13520
690690 0 0
691691 −0.977725 −0.0371944 −0.0185972 0.999827i 0.505920π-0.505920\pi
−0.0185972 + 0.999827i 0.505920π0.505920\pi
692692 7.30021 0.277512
693693 0 0
694694 −6.04287 −0.229384
695695 0 0
696696 0 0
697697 −9.63158 −0.364822
698698 22.1048 0.836678
699699 0 0
700700 0 0
701701 −48.9688 −1.84953 −0.924764 0.380542i 0.875737π-0.875737\pi
−0.924764 + 0.380542i 0.875737π0.875737\pi
702702 0 0
703703 −30.1017 −1.13531
704704 8.85236 0.333636
705705 0 0
706706 −27.2128 −1.02417
707707 87.3087 3.28358
708708 0 0
709709 −37.2672 −1.39960 −0.699799 0.714340i 0.746727π-0.746727\pi
−0.699799 + 0.714340i 0.746727π0.746727\pi
710710 0 0
711711 0 0
712712 1.90813 0.0715103
713713 −10.4889 −0.392811
714714 0 0
715715 0 0
716716 6.75557 0.252467
717717 0 0
718718 −25.8983 −0.966516
719719 −5.83500 −0.217609 −0.108804 0.994063i 0.534702π-0.534702\pi
−0.108804 + 0.994063i 0.534702π0.534702\pi
720720 0 0
721721 24.2667 0.903739
722722 9.56400 0.355935
723723 0 0
724724 −0.482081 −0.0179164
725725 0 0
726726 0 0
727727 −46.8385 −1.73715 −0.868573 0.495562i 0.834962π-0.834962\pi
−0.868573 + 0.495562i 0.834962π0.834962\pi
728728 −62.3663 −2.31145
729729 0 0
730730 0 0
731731 26.1432 0.966941
732732 0 0
733733 −45.2083 −1.66981 −0.834904 0.550395i 0.814477π-0.814477\pi
−0.834904 + 0.550395i 0.814477π0.814477\pi
734734 42.6637 1.57475
735735 0 0
736736 −11.5496 −0.425723
737737 −4.85728 −0.178920
738738 0 0
739739 5.65433 0.207998 0.103999 0.994577i 0.466836π-0.466836\pi
0.103999 + 0.994577i 0.466836π0.466836\pi
740740 0 0
741741 0 0
742742 42.7753 1.57033
743743 −4.50622 −0.165317 −0.0826585 0.996578i 0.526341π-0.526341\pi
−0.0826585 + 0.996578i 0.526341π0.526341\pi
744744 0 0
745745 0 0
746746 −20.6494 −0.756029
747747 0 0
748748 −2.80150 −0.102433
749749 −54.9086 −2.00632
750750 0 0
751751 47.5121 1.73374 0.866870 0.498534i 0.166128π-0.166128\pi
0.866870 + 0.498534i 0.166128π0.166128\pi
752752 18.8474 0.687295
753753 0 0
754754 −9.09817 −0.331336
755755 0 0
756756 0 0
757757 −46.6637 −1.69602 −0.848011 0.529979i 0.822200π-0.822200\pi
−0.848011 + 0.529979i 0.822200π0.822200\pi
758758 2.87601 0.104462
759759 0 0
760760 0 0
761761 −14.9304 −0.541227 −0.270613 0.962688i 0.587227π-0.587227\pi
−0.270613 + 0.962688i 0.587227π0.587227\pi
762762 0 0
763763 77.0518 2.78946
764764 7.54956 0.273134
765765 0 0
766766 −1.47643 −0.0533457
767767 −6.93930 −0.250564
768768 0 0
769769 38.8573 1.40123 0.700615 0.713540i 0.252909π-0.252909\pi
0.700615 + 0.713540i 0.252909π0.252909\pi
770770 0 0
771771 0 0
772772 6.17929 0.222397
773773 36.3368 1.30694 0.653471 0.756951i 0.273312π-0.273312\pi
0.653471 + 0.756951i 0.273312π0.273312\pi
774774 0 0
775775 0 0
776776 8.45044 0.303353
777777 0 0
778778 −2.75251 −0.0986821
779779 9.36488 0.335532
780780 0 0
781781 −0.428639 −0.0153379
782782 −25.8983 −0.926121
783783 0 0
784784 −45.5531 −1.62690
785785 0 0
786786 0 0
787787 −33.5482 −1.19586 −0.597932 0.801547i 0.704011π-0.704011\pi
−0.597932 + 0.801547i 0.704011π0.704011\pi
788788 −2.00751 −0.0715145
789789 0 0
790790 0 0
791791 8.65386 0.307696
792792 0 0
793793 3.13383 0.111286
794794 −22.4514 −0.796770
795795 0 0
796796 7.20601 0.255410
797797 16.1334 0.571473 0.285736 0.958308i 0.407762π-0.407762\pi
0.285736 + 0.958308i 0.407762π0.407762\pi
798798 0 0
799799 −37.5941 −1.32998
800800 0 0
801801 0 0
802802 −21.3265 −0.753063
803803 12.7096 0.448513
804804 0 0
805805 0 0
806806 13.2070 0.465195
807807 0 0
808808 −54.6065 −1.92105
809809 −25.7431 −0.905081 −0.452540 0.891744i 0.649482π-0.649482\pi
−0.452540 + 0.891744i 0.649482π0.649482\pi
810810 0 0
811811 13.4509 0.472325 0.236163 0.971714i 0.424110π-0.424110\pi
0.236163 + 0.971714i 0.424110π0.424110\pi
812812 4.65386 0.163318
813813 0 0
814814 7.05086 0.247132
815815 0 0
816816 0 0
817817 −25.4193 −0.889308
818818 −25.9210 −0.906308
819819 0 0
820820 0 0
821821 −24.1748 −0.843708 −0.421854 0.906664i 0.638620π-0.638620\pi
−0.421854 + 0.906664i 0.638620π0.638620\pi
822822 0 0
823823 −40.9117 −1.42609 −0.713046 0.701118i 0.752685π-0.752685\pi
−0.713046 + 0.701118i 0.752685π0.752685\pi
824824 −15.1774 −0.528731
825825 0 0
826826 −9.96158 −0.346608
827827 20.1476 0.700602 0.350301 0.936637i 0.386079π-0.386079\pi
0.350301 + 0.936637i 0.386079π0.386079\pi
828828 0 0
829829 31.4322 1.09168 0.545842 0.837888i 0.316210π-0.316210\pi
0.545842 + 0.837888i 0.316210π0.316210\pi
830830 0 0
831831 0 0
832832 36.7164 1.27291
833833 90.8627 3.14821
834834 0 0
835835 0 0
836836 2.72393 0.0942089
837837 0 0
838838 −35.0420 −1.21050
839839 52.8988 1.82627 0.913134 0.407659i 0.133655π-0.133655\pi
0.913134 + 0.407659i 0.133655π0.133655\pi
840840 0 0
841841 −25.7368 −0.887477
842842 −43.0954 −1.48517
843843 0 0
844844 −1.02906 −0.0354216
845845 0 0
846846 0 0
847847 4.90321 0.168476
848848 −19.2039 −0.659465
849849 0 0
850850 0 0
851851 −23.2257 −0.796167
852852 0 0
853853 −46.9229 −1.60661 −0.803305 0.595568i 0.796927π-0.796927\pi
−0.803305 + 0.595568i 0.796927π0.796927\pi
854854 4.49871 0.153943
855855 0 0
856856 34.3422 1.17379
857857 25.1481 0.859043 0.429522 0.903057i 0.358682π-0.358682\pi
0.429522 + 0.903057i 0.358682π0.358682\pi
858858 0 0
859859 1.84791 0.0630499 0.0315250 0.999503i 0.489964π-0.489964\pi
0.0315250 + 0.999503i 0.489964π0.489964\pi
860860 0 0
861861 0 0
862862 −11.2257 −0.382349
863863 −32.6824 −1.11252 −0.556262 0.831007i 0.687765π-0.687765\pi
−0.556262 + 0.831007i 0.687765π0.687765\pi
864864 0 0
865865 0 0
866866 −7.63254 −0.259364
867867 0 0
868868 −6.75557 −0.229299
869869 −6.42864 −0.218077
870870 0 0
871871 −20.1463 −0.682630
872872 −48.1915 −1.63197
873873 0 0
874874 25.1811 0.851765
875875 0 0
876876 0 0
877877 49.1798 1.66068 0.830341 0.557255i 0.188145π-0.188145\pi
0.830341 + 0.557255i 0.188145π0.188145\pi
878878 −44.3595 −1.49706
879879 0 0
880880 0 0
881881 −33.8163 −1.13930 −0.569650 0.821888i 0.692921π-0.692921\pi
−0.569650 + 0.821888i 0.692921π0.692921\pi
882882 0 0
883883 24.7368 0.832461 0.416230 0.909259i 0.363351π-0.363351\pi
0.416230 + 0.909259i 0.363351π0.363351\pi
884884 −11.6196 −0.390810
885885 0 0
886886 46.4800 1.56153
887887 −7.64004 −0.256528 −0.128264 0.991740i 0.540940π-0.540940\pi
−0.128264 + 0.991740i 0.540940π0.540940\pi
888888 0 0
889889 91.7373 3.07677
890890 0 0
891891 0 0
892892 13.6663 0.457581
893893 36.5531 1.22320
894894 0 0
895895 0 0
896896 24.3926 0.814898
897897 0 0
898898 38.6735 1.29055
899899 −4.73683 −0.157982
900900 0 0
901901 38.3051 1.27613
902902 −2.19358 −0.0730381
903903 0 0
904904 −5.41249 −0.180017
905905 0 0
906906 0 0
907907 −30.3970 −1.00932 −0.504658 0.863319i 0.668381π-0.668381\pi
−0.504658 + 0.863319i 0.668381π0.668381\pi
908908 −3.33185 −0.110571
909909 0 0
910910 0 0
911911 45.3274 1.50176 0.750882 0.660436i 0.229629π-0.229629\pi
0.750882 + 0.660436i 0.229629π0.229629\pi
912912 0 0
913913 2.90321 0.0960823
914914 1.69042 0.0559142
915915 0 0
916916 12.2569 0.404978
917917 6.10171 0.201496
918918 0 0
919919 −16.3269 −0.538576 −0.269288 0.963060i 0.586788π-0.586788\pi
−0.269288 + 0.963060i 0.586788π0.586788\pi
920920 0 0
921921 0 0
922922 9.35599 0.308123
923923 −1.77784 −0.0585184
924924 0 0
925925 0 0
926926 5.68598 0.186853
927927 0 0
928928 −5.21585 −0.171219
929929 29.6128 0.971566 0.485783 0.874079i 0.338535π-0.338535\pi
0.485783 + 0.874079i 0.338535π0.338535\pi
930930 0 0
931931 −88.3466 −2.89544
932932 −0.748060 −0.0245035
933933 0 0
934934 −15.6128 −0.510868
935935 0 0
936936 0 0
937937 8.92195 0.291467 0.145734 0.989324i 0.453446π-0.453446\pi
0.145734 + 0.989324i 0.453446π0.453446\pi
938938 −28.9206 −0.944290
939939 0 0
940940 0 0
941941 22.2766 0.726195 0.363097 0.931751i 0.381719π-0.381719\pi
0.363097 + 0.931751i 0.381719π0.381719\pi
942942 0 0
943943 7.22570 0.235301
944944 4.47224 0.145559
945945 0 0
946946 5.95407 0.193583
947947 −44.4612 −1.44480 −0.722398 0.691477i 0.756960π-0.756960\pi
−0.722398 + 0.691477i 0.756960π0.756960\pi
948948 0 0
949949 52.7150 1.71120
950950 0 0
951951 0 0
952952 −80.1727 −2.59841
953953 −20.5575 −0.665924 −0.332962 0.942940i 0.608048π-0.608048\pi
−0.332962 + 0.942940i 0.608048π0.608048\pi
954954 0 0
955955 0 0
956956 −9.96158 −0.322180
957957 0 0
958958 −10.1847 −0.329052
959959 −92.1659 −2.97619
960960 0 0
961961 −24.1240 −0.778193
962962 29.2444 0.942878
963963 0 0
964964 0.707300 0.0227806
965965 0 0
966966 0 0
967967 27.4839 0.883824 0.441912 0.897058i 0.354300π-0.354300\pi
0.441912 + 0.897058i 0.354300π0.354300\pi
968968 −3.06668 −0.0985667
969969 0 0
970970 0 0
971971 5.81532 0.186622 0.0933112 0.995637i 0.470255π-0.470255\pi
0.0933112 + 0.995637i 0.470255π0.470255\pi
972972 0 0
973973 68.8484 2.20718
974974 11.9428 0.382673
975975 0 0
976976 −2.01969 −0.0646487
977977 −48.3912 −1.54817 −0.774085 0.633081i 0.781790π-0.781790\pi
−0.774085 + 0.633081i 0.781790π0.781790\pi
978978 0 0
979979 −0.622216 −0.0198861
980980 0 0
981981 0 0
982982 40.0000 1.27645
983983 49.9724 1.59387 0.796936 0.604064i 0.206453π-0.206453\pi
0.796936 + 0.604064i 0.206453π0.206453\pi
984984 0 0
985985 0 0
986986 −11.6958 −0.372471
987987 0 0
988988 11.2979 0.359433
989989 −19.6128 −0.623652
990990 0 0
991991 −7.35905 −0.233768 −0.116884 0.993146i 0.537291π-0.537291\pi
−0.116884 + 0.993146i 0.537291π0.537291\pi
992992 7.57136 0.240391
993993 0 0
994994 −2.55215 −0.0809492
995995 0 0
996996 0 0
997997 −4.33138 −0.137176 −0.0685880 0.997645i 0.521849π-0.521849\pi
−0.0685880 + 0.997645i 0.521849π0.521849\pi
998998 −1.98126 −0.0627158
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 2475.2.a.y.1.3 3
3.2 odd 2 825.2.a.n.1.1 3
5.2 odd 4 495.2.c.d.199.4 6
5.3 odd 4 495.2.c.d.199.3 6
5.4 even 2 2475.2.a.be.1.1 3
15.2 even 4 165.2.c.a.34.3 6
15.8 even 4 165.2.c.a.34.4 yes 6
15.14 odd 2 825.2.a.h.1.3 3
33.32 even 2 9075.2.a.cc.1.3 3
60.23 odd 4 2640.2.d.i.529.5 6
60.47 odd 4 2640.2.d.i.529.2 6
165.32 odd 4 1815.2.c.d.364.4 6
165.98 odd 4 1815.2.c.d.364.3 6
165.164 even 2 9075.2.a.ck.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.c.a.34.3 6 15.2 even 4
165.2.c.a.34.4 yes 6 15.8 even 4
495.2.c.d.199.3 6 5.3 odd 4
495.2.c.d.199.4 6 5.2 odd 4
825.2.a.h.1.3 3 15.14 odd 2
825.2.a.n.1.1 3 3.2 odd 2
1815.2.c.d.364.3 6 165.98 odd 4
1815.2.c.d.364.4 6 165.32 odd 4
2475.2.a.y.1.3 3 1.1 even 1 trivial
2475.2.a.be.1.1 3 5.4 even 2
2640.2.d.i.529.2 6 60.47 odd 4
2640.2.d.i.529.5 6 60.23 odd 4
9075.2.a.cc.1.3 3 33.32 even 2
9075.2.a.ck.1.1 3 165.164 even 2