Properties

Label 1458.2.a.e.1.3
Level 14581458
Weight 22
Character 1458.1
Self dual yes
Analytic conductor 11.64211.642
Analytic rank 11
Dimension 66
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1458,2,Mod(1,1458)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1458, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("1458.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1458=236 1458 = 2 \cdot 3^{6}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1458.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,-6,0,6,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 11.642188614711.6421886147
Analytic rank: 11
Dimension: 66
Coefficient field: Q(ζ36)+\Q(\zeta_{36})^+
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x66x4+9x23 x^{6} - 6x^{4} + 9x^{2} - 3 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 32 3^{2}
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 1.96962-1.96962 of defining polynomial
Character χ\chi == 1458.1

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) == q1.00000q2+1.00000q40.852666q5+1.37581q71.00000q8+0.852666q100.216780q11+1.95778q131.37581q14+1.00000q167.71783q176.12087q190.852666q20+0.216780q22+2.41293q234.27296q251.95778q26+1.37581q283.94668q29+8.84930q311.00000q32+7.71783q341.17310q35+6.63961q37+6.12087q38+0.852666q40+3.73396q4110.6495q430.216780q442.41293q46+1.52861q475.10716q49+4.27296q50+1.95778q5210.2304q53+0.184841q551.37581q56+3.94668q584.62382q59+5.24719q618.84930q62+1.00000q641.66933q65+4.45299q677.71783q68+1.17310q7015.8545q715.39860q736.63961q746.12087q760.298248q778.02895q790.852666q803.73396q82+12.0654q83+6.58073q85+10.6495q86+0.216780q883.61359q89+2.69352q91+2.41293q921.52861q94+5.21905q9510.6495q97+5.10716q98+O(q100)q-1.00000 q^{2} +1.00000 q^{4} -0.852666 q^{5} +1.37581 q^{7} -1.00000 q^{8} +0.852666 q^{10} -0.216780 q^{11} +1.95778 q^{13} -1.37581 q^{14} +1.00000 q^{16} -7.71783 q^{17} -6.12087 q^{19} -0.852666 q^{20} +0.216780 q^{22} +2.41293 q^{23} -4.27296 q^{25} -1.95778 q^{26} +1.37581 q^{28} -3.94668 q^{29} +8.84930 q^{31} -1.00000 q^{32} +7.71783 q^{34} -1.17310 q^{35} +6.63961 q^{37} +6.12087 q^{38} +0.852666 q^{40} +3.73396 q^{41} -10.6495 q^{43} -0.216780 q^{44} -2.41293 q^{46} +1.52861 q^{47} -5.10716 q^{49} +4.27296 q^{50} +1.95778 q^{52} -10.2304 q^{53} +0.184841 q^{55} -1.37581 q^{56} +3.94668 q^{58} -4.62382 q^{59} +5.24719 q^{61} -8.84930 q^{62} +1.00000 q^{64} -1.66933 q^{65} +4.45299 q^{67} -7.71783 q^{68} +1.17310 q^{70} -15.8545 q^{71} -5.39860 q^{73} -6.63961 q^{74} -6.12087 q^{76} -0.298248 q^{77} -8.02895 q^{79} -0.852666 q^{80} -3.73396 q^{82} +12.0654 q^{83} +6.58073 q^{85} +10.6495 q^{86} +0.216780 q^{88} -3.61359 q^{89} +2.69352 q^{91} +2.41293 q^{92} -1.52861 q^{94} +5.21905 q^{95} -10.6495 q^{97} +5.10716 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q6q2+6q46q56q8+6q106q11+6q13+6q1612q17+6q196q20+6q2212q23+6q256q266q296q316q32+12q34+6q98+O(q100) 6 q - 6 q^{2} + 6 q^{4} - 6 q^{5} - 6 q^{8} + 6 q^{10} - 6 q^{11} + 6 q^{13} + 6 q^{16} - 12 q^{17} + 6 q^{19} - 6 q^{20} + 6 q^{22} - 12 q^{23} + 6 q^{25} - 6 q^{26} - 6 q^{29} - 6 q^{31} - 6 q^{32} + 12 q^{34}+ \cdots - 6 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 −1.00000 −0.707107
33 0 0
44 1.00000 0.500000
55 −0.852666 −0.381324 −0.190662 0.981656i 0.561063π-0.561063\pi
−0.190662 + 0.981656i 0.561063π0.561063\pi
66 0 0
77 1.37581 0.520006 0.260003 0.965608i 0.416277π-0.416277\pi
0.260003 + 0.965608i 0.416277π0.416277\pi
88 −1.00000 −0.353553
99 0 0
1010 0.852666 0.269637
1111 −0.216780 −0.0653618 −0.0326809 0.999466i 0.510405π-0.510405\pi
−0.0326809 + 0.999466i 0.510405π0.510405\pi
1212 0 0
1313 1.95778 0.542991 0.271495 0.962440i 0.412482π-0.412482\pi
0.271495 + 0.962440i 0.412482π0.412482\pi
1414 −1.37581 −0.367699
1515 0 0
1616 1.00000 0.250000
1717 −7.71783 −1.87185 −0.935925 0.352200i 0.885434π-0.885434\pi
−0.935925 + 0.352200i 0.885434π0.885434\pi
1818 0 0
1919 −6.12087 −1.40422 −0.702111 0.712067i 0.747759π-0.747759\pi
−0.702111 + 0.712067i 0.747759π0.747759\pi
2020 −0.852666 −0.190662
2121 0 0
2222 0.216780 0.0462178
2323 2.41293 0.503131 0.251566 0.967840i 0.419055π-0.419055\pi
0.251566 + 0.967840i 0.419055π0.419055\pi
2424 0 0
2525 −4.27296 −0.854592
2626 −1.95778 −0.383952
2727 0 0
2828 1.37581 0.260003
2929 −3.94668 −0.732879 −0.366440 0.930442i 0.619423π-0.619423\pi
−0.366440 + 0.930442i 0.619423π0.619423\pi
3030 0 0
3131 8.84930 1.58938 0.794691 0.607015i 0.207633π-0.207633\pi
0.794691 + 0.607015i 0.207633π0.207633\pi
3232 −1.00000 −0.176777
3333 0 0
3434 7.71783 1.32360
3535 −1.17310 −0.198290
3636 0 0
3737 6.63961 1.09155 0.545773 0.837933i 0.316236π-0.316236\pi
0.545773 + 0.837933i 0.316236π0.316236\pi
3838 6.12087 0.992935
3939 0 0
4040 0.852666 0.134818
4141 3.73396 0.583146 0.291573 0.956549i 0.405821π-0.405821\pi
0.291573 + 0.956549i 0.405821π0.405821\pi
4242 0 0
4343 −10.6495 −1.62404 −0.812018 0.583632i 0.801631π-0.801631\pi
−0.812018 + 0.583632i 0.801631π0.801631\pi
4444 −0.216780 −0.0326809
4545 0 0
4646 −2.41293 −0.355768
4747 1.52861 0.222971 0.111485 0.993766i 0.464439π-0.464439\pi
0.111485 + 0.993766i 0.464439π0.464439\pi
4848 0 0
4949 −5.10716 −0.729594
5050 4.27296 0.604288
5151 0 0
5252 1.95778 0.271495
5353 −10.2304 −1.40525 −0.702624 0.711561i 0.747988π-0.747988\pi
−0.702624 + 0.711561i 0.747988π0.747988\pi
5454 0 0
5555 0.184841 0.0249240
5656 −1.37581 −0.183850
5757 0 0
5858 3.94668 0.518224
5959 −4.62382 −0.601971 −0.300985 0.953629i 0.597316π-0.597316\pi
−0.300985 + 0.953629i 0.597316π0.597316\pi
6060 0 0
6161 5.24719 0.671834 0.335917 0.941892i 0.390954π-0.390954\pi
0.335917 + 0.941892i 0.390954π0.390954\pi
6262 −8.84930 −1.12386
6363 0 0
6464 1.00000 0.125000
6565 −1.66933 −0.207055
6666 0 0
6767 4.45299 0.544020 0.272010 0.962294i 0.412312π-0.412312\pi
0.272010 + 0.962294i 0.412312π0.412312\pi
6868 −7.71783 −0.935925
6969 0 0
7070 1.17310 0.140213
7171 −15.8545 −1.88158 −0.940791 0.338987i 0.889916π-0.889916\pi
−0.940791 + 0.338987i 0.889916π0.889916\pi
7272 0 0
7373 −5.39860 −0.631858 −0.315929 0.948783i 0.602316π-0.602316\pi
−0.315929 + 0.948783i 0.602316π0.602316\pi
7474 −6.63961 −0.771840
7575 0 0
7676 −6.12087 −0.702111
7777 −0.298248 −0.0339885
7878 0 0
7979 −8.02895 −0.903328 −0.451664 0.892188i 0.649169π-0.649169\pi
−0.451664 + 0.892188i 0.649169π0.649169\pi
8080 −0.852666 −0.0953309
8181 0 0
8282 −3.73396 −0.412346
8383 12.0654 1.32435 0.662174 0.749350i 0.269634π-0.269634\pi
0.662174 + 0.749350i 0.269634π0.269634\pi
8484 0 0
8585 6.58073 0.713780
8686 10.6495 1.14837
8787 0 0
8888 0.216780 0.0231089
8989 −3.61359 −0.383040 −0.191520 0.981489i 0.561342π-0.561342\pi
−0.191520 + 0.981489i 0.561342π0.561342\pi
9090 0 0
9191 2.69352 0.282358
9292 2.41293 0.251566
9393 0 0
9494 −1.52861 −0.157664
9595 5.21905 0.535463
9696 0 0
9797 −10.6495 −1.08129 −0.540645 0.841251i 0.681820π-0.681820\pi
−0.540645 + 0.841251i 0.681820π0.681820\pi
9898 5.10716 0.515901
9999 0 0
100100 −4.27296 −0.427296
101101 13.3509 1.32846 0.664232 0.747527i 0.268759π-0.268759\pi
0.664232 + 0.747527i 0.268759π0.268759\pi
102102 0 0
103103 −14.3519 −1.41414 −0.707069 0.707145i 0.749983π-0.749983\pi
−0.707069 + 0.707145i 0.749983π0.749983\pi
104104 −1.95778 −0.191976
105105 0 0
106106 10.2304 0.993661
107107 −3.04925 −0.294782 −0.147391 0.989078i 0.547088π-0.547088\pi
−0.147391 + 0.989078i 0.547088π0.547088\pi
108108 0 0
109109 9.71567 0.930593 0.465296 0.885155i 0.345948π-0.345948\pi
0.465296 + 0.885155i 0.345948π0.345948\pi
110110 −0.184841 −0.0176239
111111 0 0
112112 1.37581 0.130001
113113 −9.26439 −0.871521 −0.435760 0.900063i 0.643521π-0.643521\pi
−0.435760 + 0.900063i 0.643521π0.643521\pi
114114 0 0
115115 −2.05742 −0.191856
116116 −3.94668 −0.366440
117117 0 0
118118 4.62382 0.425657
119119 −10.6182 −0.973372
120120 0 0
121121 −10.9530 −0.995728
122122 −5.24719 −0.475059
123123 0 0
124124 8.84930 0.794691
125125 7.90673 0.707200
126126 0 0
127127 −0.0235456 −0.00208933 −0.00104467 0.999999i 0.500333π-0.500333\pi
−0.00104467 + 0.999999i 0.500333π0.500333\pi
128128 −1.00000 −0.0883883
129129 0 0
130130 1.66933 0.146410
131131 −18.5654 −1.62206 −0.811031 0.585003i 0.801093π-0.801093\pi
−0.811031 + 0.585003i 0.801093π0.801093\pi
132132 0 0
133133 −8.42112 −0.730204
134134 −4.45299 −0.384680
135135 0 0
136136 7.71783 0.661799
137137 −7.47470 −0.638607 −0.319303 0.947653i 0.603449π-0.603449\pi
−0.319303 + 0.947653i 0.603449π0.603449\pi
138138 0 0
139139 −7.56904 −0.641998 −0.320999 0.947080i 0.604019π-0.604019\pi
−0.320999 + 0.947080i 0.604019π0.604019\pi
140140 −1.17310 −0.0991452
141141 0 0
142142 15.8545 1.33048
143143 −0.424409 −0.0354908
144144 0 0
145145 3.36519 0.279464
146146 5.39860 0.446791
147147 0 0
148148 6.63961 0.545773
149149 12.6704 1.03800 0.518998 0.854775i 0.326305π-0.326305\pi
0.518998 + 0.854775i 0.326305π0.326305\pi
150150 0 0
151151 3.98749 0.324498 0.162249 0.986750i 0.448125π-0.448125\pi
0.162249 + 0.986750i 0.448125π0.448125\pi
152152 6.12087 0.496468
153153 0 0
154154 0.298248 0.0240335
155155 −7.54549 −0.606069
156156 0 0
157157 0.523140 0.0417511 0.0208756 0.999782i 0.493355π-0.493355\pi
0.0208756 + 0.999782i 0.493355π0.493355\pi
158158 8.02895 0.638749
159159 0 0
160160 0.852666 0.0674091
161161 3.31973 0.261631
162162 0 0
163163 −18.0795 −1.41609 −0.708046 0.706166i 0.750423π-0.750423\pi
−0.708046 + 0.706166i 0.750423π0.750423\pi
164164 3.73396 0.291573
165165 0 0
166166 −12.0654 −0.936455
167167 19.7557 1.52874 0.764369 0.644779i 0.223050π-0.223050\pi
0.764369 + 0.644779i 0.223050π0.223050\pi
168168 0 0
169169 −9.16710 −0.705161
170170 −6.58073 −0.504719
171171 0 0
172172 −10.6495 −0.812018
173173 −18.5746 −1.41220 −0.706101 0.708112i 0.749547π-0.749547\pi
−0.706101 + 0.708112i 0.749547π0.749547\pi
174174 0 0
175175 −5.87876 −0.444393
176176 −0.216780 −0.0163404
177177 0 0
178178 3.61359 0.270850
179179 −10.1892 −0.761579 −0.380789 0.924662i 0.624348π-0.624348\pi
−0.380789 + 0.924662i 0.624348π0.624348\pi
180180 0 0
181181 3.19006 0.237115 0.118558 0.992947i 0.462173π-0.462173\pi
0.118558 + 0.992947i 0.462173π0.462173\pi
182182 −2.69352 −0.199657
183183 0 0
184184 −2.41293 −0.177884
185185 −5.66137 −0.416232
186186 0 0
187187 1.67308 0.122347
188188 1.52861 0.111485
189189 0 0
190190 −5.21905 −0.378630
191191 10.6274 0.768971 0.384485 0.923131i 0.374379π-0.374379\pi
0.384485 + 0.923131i 0.374379π0.374379\pi
192192 0 0
193193 −10.5447 −0.759026 −0.379513 0.925186i 0.623909π-0.623909\pi
−0.379513 + 0.925186i 0.623909π0.623909\pi
194194 10.6495 0.764588
195195 0 0
196196 −5.10716 −0.364797
197197 14.2848 1.01775 0.508873 0.860841i 0.330062π-0.330062\pi
0.508873 + 0.860841i 0.330062π0.330062\pi
198198 0 0
199199 −14.0693 −0.997348 −0.498674 0.866790i 0.666180π-0.666180\pi
−0.498674 + 0.866790i 0.666180π0.666180\pi
200200 4.27296 0.302144
201201 0 0
202202 −13.3509 −0.939366
203203 −5.42986 −0.381101
204204 0 0
205205 −3.18381 −0.222367
206206 14.3519 0.999946
207207 0 0
208208 1.95778 0.135748
209209 1.32688 0.0917825
210210 0 0
211211 21.1542 1.45632 0.728159 0.685408i 0.240376π-0.240376\pi
0.728159 + 0.685408i 0.240376π0.240376\pi
212212 −10.2304 −0.702624
213213 0 0
214214 3.04925 0.208443
215215 9.08048 0.619283
216216 0 0
217217 12.1749 0.826487
218218 −9.71567 −0.658028
219219 0 0
220220 0.184841 0.0124620
221221 −15.1098 −1.01640
222222 0 0
223223 −7.33082 −0.490908 −0.245454 0.969408i 0.578937π-0.578937\pi
−0.245454 + 0.969408i 0.578937π0.578937\pi
224224 −1.37581 −0.0919249
225225 0 0
226226 9.26439 0.616258
227227 −6.28319 −0.417030 −0.208515 0.978019i 0.566863π-0.566863\pi
−0.208515 + 0.978019i 0.566863π0.566863\pi
228228 0 0
229229 −0.0268956 −0.00177731 −0.000888656 1.00000i 0.500283π-0.500283\pi
−0.000888656 1.00000i 0.500283π0.500283\pi
230230 2.05742 0.135663
231231 0 0
232232 3.94668 0.259112
233233 23.8435 1.56204 0.781019 0.624508i 0.214700π-0.214700\pi
0.781019 + 0.624508i 0.214700π0.214700\pi
234234 0 0
235235 −1.30339 −0.0850240
236236 −4.62382 −0.300985
237237 0 0
238238 10.6182 0.688278
239239 15.3682 0.994088 0.497044 0.867725i 0.334419π-0.334419\pi
0.497044 + 0.867725i 0.334419π0.334419\pi
240240 0 0
241241 −0.964379 −0.0621211 −0.0310605 0.999518i 0.509888π-0.509888\pi
−0.0310605 + 0.999518i 0.509888π0.509888\pi
242242 10.9530 0.704086
243243 0 0
244244 5.24719 0.335917
245245 4.35470 0.278212
246246 0 0
247247 −11.9833 −0.762480
248248 −8.84930 −0.561931
249249 0 0
250250 −7.90673 −0.500066
251251 18.2157 1.14977 0.574884 0.818235i 0.305047π-0.305047\pi
0.574884 + 0.818235i 0.305047π0.305047\pi
252252 0 0
253253 −0.523077 −0.0328856
254254 0.0235456 0.00147738
255255 0 0
256256 1.00000 0.0625000
257257 16.3732 1.02133 0.510665 0.859780i 0.329399π-0.329399\pi
0.510665 + 0.859780i 0.329399π0.329399\pi
258258 0 0
259259 9.13482 0.567610
260260 −1.66933 −0.103528
261261 0 0
262262 18.5654 1.14697
263263 13.4275 0.827977 0.413989 0.910282i 0.364135π-0.364135\pi
0.413989 + 0.910282i 0.364135π0.364135\pi
264264 0 0
265265 8.72308 0.535854
266266 8.42112 0.516332
267267 0 0
268268 4.45299 0.272010
269269 −1.91176 −0.116562 −0.0582809 0.998300i 0.518562π-0.518562\pi
−0.0582809 + 0.998300i 0.518562π0.518562\pi
270270 0 0
271271 −4.71707 −0.286542 −0.143271 0.989684i 0.545762π-0.545762\pi
−0.143271 + 0.989684i 0.545762π0.545762\pi
272272 −7.71783 −0.467962
273273 0 0
274274 7.47470 0.451563
275275 0.926295 0.0558577
276276 0 0
277277 −21.8798 −1.31463 −0.657316 0.753615i 0.728308π-0.728308\pi
−0.657316 + 0.753615i 0.728308π0.728308\pi
278278 7.56904 0.453961
279279 0 0
280280 1.17310 0.0701063
281281 23.7942 1.41945 0.709723 0.704481i 0.248820π-0.248820\pi
0.709723 + 0.704481i 0.248820π0.248820\pi
282282 0 0
283283 6.28259 0.373461 0.186731 0.982411i 0.440211π-0.440211\pi
0.186731 + 0.982411i 0.440211π0.440211\pi
284284 −15.8545 −0.940791
285285 0 0
286286 0.424409 0.0250958
287287 5.13720 0.303239
288288 0 0
289289 42.5650 2.50382
290290 −3.36519 −0.197611
291291 0 0
292292 −5.39860 −0.315929
293293 −2.73672 −0.159881 −0.0799404 0.996800i 0.525473π-0.525473\pi
−0.0799404 + 0.996800i 0.525473π0.525473\pi
294294 0 0
295295 3.94258 0.229546
296296 −6.63961 −0.385920
297297 0 0
298298 −12.6704 −0.733974
299299 4.72399 0.273196
300300 0 0
301301 −14.6517 −0.844508
302302 −3.98749 −0.229454
303303 0 0
304304 −6.12087 −0.351056
305305 −4.47410 −0.256186
306306 0 0
307307 −28.4426 −1.62331 −0.811654 0.584139i 0.801432π-0.801432\pi
−0.811654 + 0.584139i 0.801432π0.801432\pi
308308 −0.298248 −0.0169942
309309 0 0
310310 7.54549 0.428555
311311 −29.0437 −1.64692 −0.823458 0.567377i 0.807958π-0.807958\pi
−0.823458 + 0.567377i 0.807958π0.807958\pi
312312 0 0
313313 16.6720 0.942357 0.471178 0.882038i 0.343829π-0.343829\pi
0.471178 + 0.882038i 0.343829π0.343829\pi
314314 −0.523140 −0.0295225
315315 0 0
316316 −8.02895 −0.451664
317317 −13.1666 −0.739511 −0.369756 0.929129i 0.620559π-0.620559\pi
−0.369756 + 0.929129i 0.620559π0.620559\pi
318318 0 0
319319 0.855562 0.0479023
320320 −0.852666 −0.0476655
321321 0 0
322322 −3.31973 −0.185001
323323 47.2398 2.62849
324324 0 0
325325 −8.36552 −0.464036
326326 18.0795 1.00133
327327 0 0
328328 −3.73396 −0.206173
329329 2.10307 0.115946
330330 0 0
331331 −23.6804 −1.30159 −0.650795 0.759253i 0.725564π-0.725564\pi
−0.650795 + 0.759253i 0.725564π0.725564\pi
332332 12.0654 0.662174
333333 0 0
334334 −19.7557 −1.08098
335335 −3.79691 −0.207448
336336 0 0
337337 26.5282 1.44508 0.722542 0.691327i 0.242973π-0.242973\pi
0.722542 + 0.691327i 0.242973π0.242973\pi
338338 9.16710 0.498624
339339 0 0
340340 6.58073 0.356890
341341 −1.91836 −0.103885
342342 0 0
343343 −16.6571 −0.899399
344344 10.6495 0.574183
345345 0 0
346346 18.5746 0.998577
347347 13.8715 0.744660 0.372330 0.928100i 0.378559π-0.378559\pi
0.372330 + 0.928100i 0.378559π0.378559\pi
348348 0 0
349349 23.7682 1.27228 0.636142 0.771572i 0.280529π-0.280529\pi
0.636142 + 0.771572i 0.280529π0.280529\pi
350350 5.87876 0.314233
351351 0 0
352352 0.216780 0.0115544
353353 −31.9264 −1.69927 −0.849636 0.527369i 0.823179π-0.823179\pi
−0.849636 + 0.527369i 0.823179π0.823179\pi
354354 0 0
355355 13.5186 0.717492
356356 −3.61359 −0.191520
357357 0 0
358358 10.1892 0.538518
359359 35.0803 1.85147 0.925734 0.378174i 0.123448π-0.123448\pi
0.925734 + 0.378174i 0.123448π0.123448\pi
360360 0 0
361361 18.4650 0.971842
362362 −3.19006 −0.167666
363363 0 0
364364 2.69352 0.141179
365365 4.60320 0.240943
366366 0 0
367367 −14.5368 −0.758813 −0.379407 0.925230i 0.623872π-0.623872\pi
−0.379407 + 0.925230i 0.623872π0.623872\pi
368368 2.41293 0.125783
369369 0 0
370370 5.66137 0.294321
371371 −14.0750 −0.730737
372372 0 0
373373 23.2530 1.20400 0.601998 0.798497i 0.294371π-0.294371\pi
0.601998 + 0.798497i 0.294371π0.294371\pi
374374 −1.67308 −0.0865127
375375 0 0
376376 −1.52861 −0.0788320
377377 −7.72672 −0.397946
378378 0 0
379379 −8.25841 −0.424206 −0.212103 0.977247i 0.568031π-0.568031\pi
−0.212103 + 0.977247i 0.568031π0.568031\pi
380380 5.21905 0.267732
381381 0 0
382382 −10.6274 −0.543745
383383 −9.20617 −0.470413 −0.235207 0.971945i 0.575577π-0.575577\pi
−0.235207 + 0.971945i 0.575577π0.575577\pi
384384 0 0
385385 0.254306 0.0129606
386386 10.5447 0.536713
387387 0 0
388388 −10.6495 −0.540645
389389 34.8315 1.76603 0.883014 0.469348i 0.155511π-0.155511\pi
0.883014 + 0.469348i 0.155511π0.155511\pi
390390 0 0
391391 −18.6226 −0.941786
392392 5.10716 0.257950
393393 0 0
394394 −14.2848 −0.719655
395395 6.84601 0.344460
396396 0 0
397397 30.4492 1.52820 0.764100 0.645097i 0.223183π-0.223183\pi
0.764100 + 0.645097i 0.223183π0.223183\pi
398398 14.0693 0.705232
399399 0 0
400400 −4.27296 −0.213648
401401 6.84345 0.341745 0.170873 0.985293i 0.445341π-0.445341\pi
0.170873 + 0.985293i 0.445341π0.445341\pi
402402 0 0
403403 17.3250 0.863019
404404 13.3509 0.664232
405405 0 0
406406 5.42986 0.269479
407407 −1.43934 −0.0713454
408408 0 0
409409 16.2080 0.801435 0.400717 0.916202i 0.368761π-0.368761\pi
0.400717 + 0.916202i 0.368761π0.368761\pi
410410 3.18381 0.157237
411411 0 0
412412 −14.3519 −0.707069
413413 −6.36148 −0.313028
414414 0 0
415415 −10.2877 −0.505005
416416 −1.95778 −0.0959881
417417 0 0
418418 −1.32688 −0.0649000
419419 12.1019 0.591215 0.295608 0.955309i 0.404478π-0.404478\pi
0.295608 + 0.955309i 0.404478π0.404478\pi
420420 0 0
421421 25.4767 1.24166 0.620830 0.783945i 0.286796π-0.286796\pi
0.620830 + 0.783945i 0.286796π0.286796\pi
422422 −21.1542 −1.02977
423423 0 0
424424 10.2304 0.496830
425425 32.9780 1.59967
426426 0 0
427427 7.21912 0.349358
428428 −3.04925 −0.147391
429429 0 0
430430 −9.08048 −0.437899
431431 −10.5220 −0.506828 −0.253414 0.967358i 0.581554π-0.581554\pi
−0.253414 + 0.967358i 0.581554π0.581554\pi
432432 0 0
433433 6.89705 0.331451 0.165726 0.986172i 0.447003π-0.447003\pi
0.165726 + 0.986172i 0.447003π0.447003\pi
434434 −12.1749 −0.584415
435435 0 0
436436 9.71567 0.465296
437437 −14.7692 −0.706508
438438 0 0
439439 13.8072 0.658981 0.329491 0.944159i 0.393123π-0.393123\pi
0.329491 + 0.944159i 0.393123π0.393123\pi
440440 −0.184841 −0.00881196
441441 0 0
442442 15.1098 0.718701
443443 3.20767 0.152401 0.0762005 0.997093i 0.475721π-0.475721\pi
0.0762005 + 0.997093i 0.475721π0.475721\pi
444444 0 0
445445 3.08119 0.146062
446446 7.33082 0.347124
447447 0 0
448448 1.37581 0.0650007
449449 26.3248 1.24235 0.621173 0.783673i 0.286656π-0.286656\pi
0.621173 + 0.783673i 0.286656π0.286656\pi
450450 0 0
451451 −0.809449 −0.0381154
452452 −9.26439 −0.435760
453453 0 0
454454 6.28319 0.294885
455455 −2.29668 −0.107670
456456 0 0
457457 −3.98002 −0.186177 −0.0930887 0.995658i 0.529674π-0.529674\pi
−0.0930887 + 0.995658i 0.529674π0.529674\pi
458458 0.0268956 0.00125675
459459 0 0
460460 −2.05742 −0.0959279
461461 −7.93927 −0.369769 −0.184884 0.982760i 0.559191π-0.559191\pi
−0.184884 + 0.982760i 0.559191π0.559191\pi
462462 0 0
463463 −27.6106 −1.28317 −0.641587 0.767050i 0.721724π-0.721724\pi
−0.641587 + 0.767050i 0.721724π0.721724\pi
464464 −3.94668 −0.183220
465465 0 0
466466 −23.8435 −1.10453
467467 −20.6638 −0.956207 −0.478103 0.878304i 0.658676π-0.658676\pi
−0.478103 + 0.878304i 0.658676π0.658676\pi
468468 0 0
469469 6.12645 0.282893
470470 1.30339 0.0601210
471471 0 0
472472 4.62382 0.212829
473473 2.30861 0.106150
474474 0 0
475475 26.1542 1.20004
476476 −10.6182 −0.486686
477477 0 0
478478 −15.3682 −0.702926
479479 −30.4658 −1.39202 −0.696009 0.718033i 0.745043π-0.745043\pi
−0.696009 + 0.718033i 0.745043π0.745043\pi
480480 0 0
481481 12.9989 0.592699
482482 0.964379 0.0439262
483483 0 0
484484 −10.9530 −0.497864
485485 9.08044 0.412322
486486 0 0
487487 −11.9590 −0.541912 −0.270956 0.962592i 0.587340π-0.587340\pi
−0.270956 + 0.962592i 0.587340π0.587340\pi
488488 −5.24719 −0.237529
489489 0 0
490490 −4.35470 −0.196725
491491 40.9377 1.84749 0.923745 0.383007i 0.125111π-0.125111\pi
0.923745 + 0.383007i 0.125111π0.125111\pi
492492 0 0
493493 30.4598 1.37184
494494 11.9833 0.539155
495495 0 0
496496 8.84930 0.397345
497497 −21.8127 −0.978433
498498 0 0
499499 6.69932 0.299903 0.149951 0.988693i 0.452088π-0.452088\pi
0.149951 + 0.988693i 0.452088π0.452088\pi
500500 7.90673 0.353600
501501 0 0
502502 −18.2157 −0.813009
503503 −33.2407 −1.48213 −0.741065 0.671433i 0.765679π-0.765679\pi
−0.741065 + 0.671433i 0.765679π0.765679\pi
504504 0 0
505505 −11.3839 −0.506575
506506 0.523077 0.0232536
507507 0 0
508508 −0.0235456 −0.00104467
509509 11.8539 0.525414 0.262707 0.964876i 0.415385π-0.415385\pi
0.262707 + 0.964876i 0.415385π0.415385\pi
510510 0 0
511511 −7.42742 −0.328570
512512 −1.00000 −0.0441942
513513 0 0
514514 −16.3732 −0.722189
515515 12.2374 0.539244
516516 0 0
517517 −0.331373 −0.0145738
518518 −9.13482 −0.401361
519519 0 0
520520 1.66933 0.0732050
521521 −4.70898 −0.206304 −0.103152 0.994666i 0.532893π-0.532893\pi
−0.103152 + 0.994666i 0.532893π0.532893\pi
522522 0 0
523523 −16.4344 −0.718624 −0.359312 0.933217i 0.616989π-0.616989\pi
−0.359312 + 0.933217i 0.616989π0.616989\pi
524524 −18.5654 −0.811031
525525 0 0
526526 −13.4275 −0.585468
527527 −68.2974 −2.97508
528528 0 0
529529 −17.1778 −0.746859
530530 −8.72308 −0.378906
531531 0 0
532532 −8.42112 −0.365102
533533 7.31026 0.316643
534534 0 0
535535 2.59999 0.112407
536536 −4.45299 −0.192340
537537 0 0
538538 1.91176 0.0824216
539539 1.10713 0.0476876
540540 0 0
541541 26.0900 1.12170 0.560849 0.827918i 0.310475π-0.310475\pi
0.560849 + 0.827918i 0.310475π0.310475\pi
542542 4.71707 0.202616
543543 0 0
544544 7.71783 0.330899
545545 −8.28422 −0.354857
546546 0 0
547547 28.3476 1.21205 0.606027 0.795444i 0.292762π-0.292762\pi
0.606027 + 0.795444i 0.292762π0.292762\pi
548548 −7.47470 −0.319303
549549 0 0
550550 −0.926295 −0.0394973
551551 24.1571 1.02913
552552 0 0
553553 −11.0463 −0.469736
554554 21.8798 0.929585
555555 0 0
556556 −7.56904 −0.320999
557557 29.2139 1.23783 0.618916 0.785457i 0.287572π-0.287572\pi
0.618916 + 0.785457i 0.287572π0.287572\pi
558558 0 0
559559 −20.8494 −0.881836
560560 −1.17310 −0.0495726
561561 0 0
562562 −23.7942 −1.00370
563563 2.30342 0.0970776 0.0485388 0.998821i 0.484544π-0.484544\pi
0.0485388 + 0.998821i 0.484544π0.484544\pi
564564 0 0
565565 7.89943 0.332332
566566 −6.28259 −0.264077
567567 0 0
568568 15.8545 0.665240
569569 4.26971 0.178996 0.0894978 0.995987i 0.471474π-0.471474\pi
0.0894978 + 0.995987i 0.471474π0.471474\pi
570570 0 0
571571 19.1153 0.799950 0.399975 0.916526i 0.369019π-0.369019\pi
0.399975 + 0.916526i 0.369019π0.369019\pi
572572 −0.424409 −0.0177454
573573 0 0
574574 −5.13720 −0.214422
575575 −10.3104 −0.429972
576576 0 0
577577 8.31584 0.346193 0.173096 0.984905i 0.444623π-0.444623\pi
0.173096 + 0.984905i 0.444623π0.444623\pi
578578 −42.5650 −1.77047
579579 0 0
580580 3.36519 0.139732
581581 16.5996 0.688668
582582 0 0
583583 2.21774 0.0918495
584584 5.39860 0.223396
585585 0 0
586586 2.73672 0.113053
587587 −36.5516 −1.50865 −0.754324 0.656502i 0.772035π-0.772035\pi
−0.754324 + 0.656502i 0.772035π0.772035\pi
588588 0 0
589589 −54.1654 −2.23185
590590 −3.94258 −0.162313
591591 0 0
592592 6.63961 0.272886
593593 −22.4408 −0.921535 −0.460768 0.887521i 0.652426π-0.652426\pi
−0.460768 + 0.887521i 0.652426π0.652426\pi
594594 0 0
595595 9.05381 0.371170
596596 12.6704 0.518998
597597 0 0
598598 −4.72399 −0.193178
599599 19.3129 0.789105 0.394553 0.918873i 0.370900π-0.370900\pi
0.394553 + 0.918873i 0.370900π0.370900\pi
600600 0 0
601601 −8.68146 −0.354124 −0.177062 0.984200i 0.556659π-0.556659\pi
−0.177062 + 0.984200i 0.556659π0.556659\pi
602602 14.6517 0.597157
603603 0 0
604604 3.98749 0.162249
605605 9.33925 0.379695
606606 0 0
607607 8.27174 0.335740 0.167870 0.985809i 0.446311π-0.446311\pi
0.167870 + 0.985809i 0.446311π0.446311\pi
608608 6.12087 0.248234
609609 0 0
610610 4.47410 0.181151
611611 2.99268 0.121071
612612 0 0
613613 −15.0384 −0.607394 −0.303697 0.952769i 0.598221π-0.598221\pi
−0.303697 + 0.952769i 0.598221π0.598221\pi
614614 28.4426 1.14785
615615 0 0
616616 0.298248 0.0120167
617617 −32.6891 −1.31601 −0.658006 0.753012i 0.728600π-0.728600\pi
−0.658006 + 0.753012i 0.728600π0.728600\pi
618618 0 0
619619 −29.2318 −1.17493 −0.587463 0.809251i 0.699873π-0.699873\pi
−0.587463 + 0.809251i 0.699873π0.699873\pi
620620 −7.54549 −0.303034
621621 0 0
622622 29.0437 1.16455
623623 −4.97160 −0.199183
624624 0 0
625625 14.6230 0.584920
626626 −16.6720 −0.666347
627627 0 0
628628 0.523140 0.0208756
629629 −51.2434 −2.04321
630630 0 0
631631 37.6857 1.50024 0.750121 0.661300i 0.229995π-0.229995\pi
0.750121 + 0.661300i 0.229995π0.229995\pi
632632 8.02895 0.319375
633633 0 0
634634 13.1666 0.522913
635635 0.0200765 0.000796713 0
636636 0 0
637637 −9.99870 −0.396163
638638 −0.855562 −0.0338720
639639 0 0
640640 0.852666 0.0337046
641641 −8.66494 −0.342244 −0.171122 0.985250i 0.554739π-0.554739\pi
−0.171122 + 0.985250i 0.554739π0.554739\pi
642642 0 0
643643 −10.0722 −0.397210 −0.198605 0.980080i 0.563641π-0.563641\pi
−0.198605 + 0.980080i 0.563641π0.563641\pi
644644 3.31973 0.130816
645645 0 0
646646 −47.2398 −1.85863
647647 −25.0736 −0.985745 −0.492873 0.870101i 0.664053π-0.664053\pi
−0.492873 + 0.870101i 0.664053π0.664053\pi
648648 0 0
649649 1.00235 0.0393459
650650 8.36552 0.328123
651651 0 0
652652 −18.0795 −0.708046
653653 −12.3050 −0.481530 −0.240765 0.970583i 0.577398π-0.577398\pi
−0.240765 + 0.970583i 0.577398π0.577398\pi
654654 0 0
655655 15.8300 0.618531
656656 3.73396 0.145786
657657 0 0
658658 −2.10307 −0.0819862
659659 −29.0125 −1.13017 −0.565084 0.825033i 0.691156π-0.691156\pi
−0.565084 + 0.825033i 0.691156π0.691156\pi
660660 0 0
661661 −40.9322 −1.59208 −0.796039 0.605245i 0.793075π-0.793075\pi
−0.796039 + 0.605245i 0.793075π0.793075\pi
662662 23.6804 0.920364
663663 0 0
664664 −12.0654 −0.468228
665665 7.18040 0.278444
666666 0 0
667667 −9.52306 −0.368734
668668 19.7557 0.764369
669669 0 0
670670 3.79691 0.146688
671671 −1.13749 −0.0439123
672672 0 0
673673 10.9601 0.422482 0.211241 0.977434i 0.432249π-0.432249\pi
0.211241 + 0.977434i 0.432249π0.432249\pi
674674 −26.5282 −1.02183
675675 0 0
676676 −9.16710 −0.352581
677677 −29.9509 −1.15111 −0.575554 0.817764i 0.695214π-0.695214\pi
−0.575554 + 0.817764i 0.695214π0.695214\pi
678678 0 0
679679 −14.6516 −0.562277
680680 −6.58073 −0.252360
681681 0 0
682682 1.91836 0.0734576
683683 −41.8638 −1.60187 −0.800937 0.598749i 0.795665π-0.795665\pi
−0.800937 + 0.598749i 0.795665π0.795665\pi
684684 0 0
685685 6.37342 0.243516
686686 16.6571 0.635971
687687 0 0
688688 −10.6495 −0.406009
689689 −20.0288 −0.763037
690690 0 0
691691 16.0023 0.608758 0.304379 0.952551i 0.401551π-0.401551\pi
0.304379 + 0.952551i 0.401551π0.401551\pi
692692 −18.5746 −0.706101
693693 0 0
694694 −13.8715 −0.526554
695695 6.45386 0.244809
696696 0 0
697697 −28.8180 −1.09156
698698 −23.7682 −0.899640
699699 0 0
700700 −5.87876 −0.222196
701701 −31.8940 −1.20462 −0.602309 0.798263i 0.705753π-0.705753\pi
−0.602309 + 0.798263i 0.705753π0.705753\pi
702702 0 0
703703 −40.6402 −1.53277
704704 −0.216780 −0.00817022
705705 0 0
706706 31.9264 1.20157
707707 18.3682 0.690809
708708 0 0
709709 28.5427 1.07194 0.535972 0.844236i 0.319945π-0.319945\pi
0.535972 + 0.844236i 0.319945π0.319945\pi
710710 −13.5186 −0.507343
711711 0 0
712712 3.61359 0.135425
713713 21.3528 0.799668
714714 0 0
715715 0.361879 0.0135335
716716 −10.1892 −0.380789
717717 0 0
718718 −35.0803 −1.30919
719719 −26.5082 −0.988590 −0.494295 0.869294i 0.664574π-0.664574\pi
−0.494295 + 0.869294i 0.664574π0.664574\pi
720720 0 0
721721 −19.7455 −0.735359
722722 −18.4650 −0.687196
723723 0 0
724724 3.19006 0.118558
725725 16.8640 0.626313
726726 0 0
727727 37.9038 1.40577 0.702887 0.711302i 0.251894π-0.251894\pi
0.702887 + 0.711302i 0.251894π0.251894\pi
728728 −2.69352 −0.0998287
729729 0 0
730730 −4.60320 −0.170372
731731 82.1912 3.03995
732732 0 0
733733 18.3195 0.676647 0.338324 0.941030i 0.390140π-0.390140\pi
0.338324 + 0.941030i 0.390140π0.390140\pi
734734 14.5368 0.536562
735735 0 0
736736 −2.41293 −0.0889419
737737 −0.965322 −0.0355581
738738 0 0
739739 −6.16227 −0.226683 −0.113341 0.993556i 0.536155π-0.536155\pi
−0.113341 + 0.993556i 0.536155π0.536155\pi
740740 −5.66137 −0.208116
741741 0 0
742742 14.0750 0.516709
743743 −0.542730 −0.0199108 −0.00995542 0.999950i 0.503169π-0.503169\pi
−0.00995542 + 0.999950i 0.503169π0.503169\pi
744744 0 0
745745 −10.8036 −0.395812
746746 −23.2530 −0.851354
747747 0 0
748748 1.67308 0.0611737
749749 −4.19518 −0.153288
750750 0 0
751751 −39.9221 −1.45678 −0.728389 0.685164i 0.759730π-0.759730\pi
−0.728389 + 0.685164i 0.759730π0.759730\pi
752752 1.52861 0.0557427
753753 0 0
754754 7.72672 0.281391
755755 −3.40000 −0.123739
756756 0 0
757757 24.6220 0.894903 0.447452 0.894308i 0.352332π-0.352332\pi
0.447452 + 0.894308i 0.352332π0.352332\pi
758758 8.25841 0.299959
759759 0 0
760760 −5.21905 −0.189315
761761 18.8199 0.682221 0.341111 0.940023i 0.389197π-0.389197\pi
0.341111 + 0.940023i 0.389197π0.389197\pi
762762 0 0
763763 13.3669 0.483913
764764 10.6274 0.384485
765765 0 0
766766 9.20617 0.332632
767767 −9.05243 −0.326864
768768 0 0
769769 10.2179 0.368468 0.184234 0.982882i 0.441020π-0.441020\pi
0.184234 + 0.982882i 0.441020π0.441020\pi
770770 −0.254306 −0.00916454
771771 0 0
772772 −10.5447 −0.379513
773773 19.8681 0.714605 0.357302 0.933989i 0.383697π-0.383697\pi
0.357302 + 0.933989i 0.383697π0.383697\pi
774774 0 0
775775 −37.8127 −1.35827
776776 10.6495 0.382294
777777 0 0
778778 −34.8315 −1.24877
779779 −22.8550 −0.818867
780780 0 0
781781 3.43694 0.122984
782782 18.6226 0.665943
783783 0 0
784784 −5.10716 −0.182399
785785 −0.446063 −0.0159207
786786 0 0
787787 31.9487 1.13885 0.569424 0.822044i 0.307166π-0.307166\pi
0.569424 + 0.822044i 0.307166π0.307166\pi
788788 14.2848 0.508873
789789 0 0
790790 −6.84601 −0.243570
791791 −12.7460 −0.453196
792792 0 0
793793 10.2729 0.364800
794794 −30.4492 −1.08060
795795 0 0
796796 −14.0693 −0.498674
797797 9.66226 0.342255 0.171127 0.985249i 0.445259π-0.445259\pi
0.171127 + 0.985249i 0.445259π0.445259\pi
798798 0 0
799799 −11.7976 −0.417368
800800 4.27296 0.151072
801801 0 0
802802 −6.84345 −0.241651
803803 1.17031 0.0412994
804804 0 0
805805 −2.83062 −0.0997661
806806 −17.3250 −0.610247
807807 0 0
808808 −13.3509 −0.469683
809809 −10.0580 −0.353621 −0.176811 0.984245i 0.556578π-0.556578\pi
−0.176811 + 0.984245i 0.556578π0.556578\pi
810810 0 0
811811 5.87482 0.206293 0.103146 0.994666i 0.467109π-0.467109\pi
0.103146 + 0.994666i 0.467109π0.467109\pi
812812 −5.42986 −0.190551
813813 0 0
814814 1.43934 0.0504488
815815 15.4157 0.539989
816816 0 0
817817 65.1843 2.28051
818818 −16.2080 −0.566700
819819 0 0
820820 −3.18381 −0.111184
821821 24.8647 0.867785 0.433893 0.900965i 0.357140π-0.357140\pi
0.433893 + 0.900965i 0.357140π0.357140\pi
822822 0 0
823823 −7.16718 −0.249832 −0.124916 0.992167i 0.539866π-0.539866\pi
−0.124916 + 0.992167i 0.539866π0.539866\pi
824824 14.3519 0.499973
825825 0 0
826826 6.36148 0.221344
827827 −10.5317 −0.366223 −0.183112 0.983092i 0.558617π-0.558617\pi
−0.183112 + 0.983092i 0.558617π0.558617\pi
828828 0 0
829829 20.5499 0.713728 0.356864 0.934156i 0.383846π-0.383846\pi
0.356864 + 0.934156i 0.383846π0.383846\pi
830830 10.2877 0.357092
831831 0 0
832832 1.95778 0.0678738
833833 39.4162 1.36569
834834 0 0
835835 −16.8450 −0.582944
836836 1.32688 0.0458912
837837 0 0
838838 −12.1019 −0.418052
839839 −42.6483 −1.47238 −0.736192 0.676773i 0.763378π-0.763378\pi
−0.736192 + 0.676773i 0.763378π0.763378\pi
840840 0 0
841841 −13.4238 −0.462888
842842 −25.4767 −0.877986
843843 0 0
844844 21.1542 0.728159
845845 7.81647 0.268895
846846 0 0
847847 −15.0692 −0.517784
848848 −10.2304 −0.351312
849849 0 0
850850 −32.9780 −1.13114
851851 16.0209 0.549191
852852 0 0
853853 −21.3810 −0.732071 −0.366036 0.930601i 0.619285π-0.619285\pi
−0.366036 + 0.930601i 0.619285π0.619285\pi
854854 −7.21912 −0.247033
855855 0 0
856856 3.04925 0.104221
857857 2.73552 0.0934434 0.0467217 0.998908i 0.485123π-0.485123\pi
0.0467217 + 0.998908i 0.485123π0.485123\pi
858858 0 0
859859 11.9332 0.407156 0.203578 0.979059i 0.434743π-0.434743\pi
0.203578 + 0.979059i 0.434743π0.434743\pi
860860 9.08048 0.309642
861861 0 0
862862 10.5220 0.358382
863863 −9.23050 −0.314210 −0.157105 0.987582i 0.550216π-0.550216\pi
−0.157105 + 0.987582i 0.550216π0.550216\pi
864864 0 0
865865 15.8379 0.538506
866866 −6.89705 −0.234371
867867 0 0
868868 12.1749 0.413244
869869 1.74052 0.0590431
870870 0 0
871871 8.71798 0.295397
872872 −9.71567 −0.329014
873873 0 0
874874 14.7692 0.499577
875875 10.8781 0.367748
876876 0 0
877877 32.0380 1.08185 0.540924 0.841072i 0.318075π-0.318075\pi
0.540924 + 0.841072i 0.318075π0.318075\pi
878878 −13.8072 −0.465970
879879 0 0
880880 0.184841 0.00623100
881881 −20.5135 −0.691116 −0.345558 0.938397i 0.612310π-0.612310\pi
−0.345558 + 0.938397i 0.612310π0.612310\pi
882882 0 0
883883 2.02711 0.0682176 0.0341088 0.999418i 0.489141π-0.489141\pi
0.0341088 + 0.999418i 0.489141π0.489141\pi
884884 −15.1098 −0.508198
885885 0 0
886886 −3.20767 −0.107764
887887 −0.862252 −0.0289516 −0.0144758 0.999895i 0.504608π-0.504608\pi
−0.0144758 + 0.999895i 0.504608π0.504608\pi
888888 0 0
889889 −0.0323942 −0.00108647
890890 −3.08119 −0.103282
891891 0 0
892892 −7.33082 −0.245454
893893 −9.35642 −0.313101
894894 0 0
895895 8.68801 0.290408
896896 −1.37581 −0.0459624
897897 0 0
898898 −26.3248 −0.878472
899899 −34.9253 −1.16482
900900 0 0
901901 78.9562 2.63041
902902 0.809449 0.0269517
903903 0 0
904904 9.26439 0.308129
905905 −2.72005 −0.0904176
906906 0 0
907907 −21.7579 −0.722458 −0.361229 0.932477i 0.617643π-0.617643\pi
−0.361229 + 0.932477i 0.617643π0.617643\pi
908908 −6.28319 −0.208515
909909 0 0
910910 2.29668 0.0761341
911911 49.0649 1.62559 0.812797 0.582547i 0.197944π-0.197944\pi
0.812797 + 0.582547i 0.197944π0.197944\pi
912912 0 0
913913 −2.61554 −0.0865617
914914 3.98002 0.131647
915915 0 0
916916 −0.0268956 −0.000888656 0
917917 −25.5423 −0.843482
918918 0 0
919919 20.1308 0.664053 0.332026 0.943270i 0.392268π-0.392268\pi
0.332026 + 0.943270i 0.392268π0.392268\pi
920920 2.05742 0.0678313
921921 0 0
922922 7.93927 0.261466
923923 −31.0396 −1.02168
924924 0 0
925925 −28.3708 −0.932827
926926 27.6106 0.907341
927927 0 0
928928 3.94668 0.129556
929929 7.60365 0.249468 0.124734 0.992190i 0.460192π-0.460192\pi
0.124734 + 0.992190i 0.460192π0.460192\pi
930930 0 0
931931 31.2602 1.02451
932932 23.8435 0.781019
933933 0 0
934934 20.6638 0.676140
935935 −1.42657 −0.0466540
936936 0 0
937937 22.0037 0.718830 0.359415 0.933178i 0.382976π-0.382976\pi
0.359415 + 0.933178i 0.382976π0.382976\pi
938938 −6.12645 −0.200036
939939 0 0
940940 −1.30339 −0.0425120
941941 −32.1377 −1.04766 −0.523830 0.851823i 0.675497π-0.675497\pi
−0.523830 + 0.851823i 0.675497π0.675497\pi
942942 0 0
943943 9.00978 0.293399
944944 −4.62382 −0.150493
945945 0 0
946946 −2.30861 −0.0750593
947947 −2.73709 −0.0889435 −0.0444717 0.999011i 0.514160π-0.514160\pi
−0.0444717 + 0.999011i 0.514160π0.514160\pi
948948 0 0
949949 −10.5693 −0.343093
950950 −26.1542 −0.848555
951951 0 0
952952 10.6182 0.344139
953953 −32.8770 −1.06499 −0.532495 0.846433i 0.678746π-0.678746\pi
−0.532495 + 0.846433i 0.678746π0.678746\pi
954954 0 0
955955 −9.06161 −0.293227
956956 15.3682 0.497044
957957 0 0
958958 30.4658 0.984306
959959 −10.2837 −0.332079
960960 0 0
961961 47.3101 1.52613
962962 −12.9989 −0.419102
963963 0 0
964964 −0.964379 −0.0310605
965965 8.99113 0.289435
966966 0 0
967967 −18.4425 −0.593071 −0.296535 0.955022i 0.595831π-0.595831\pi
−0.296535 + 0.955022i 0.595831π0.595831\pi
968968 10.9530 0.352043
969969 0 0
970970 −9.08044 −0.291555
971971 57.1595 1.83434 0.917168 0.398500i 0.130469π-0.130469\pi
0.917168 + 0.398500i 0.130469π0.130469\pi
972972 0 0
973973 −10.4135 −0.333842
974974 11.9590 0.383190
975975 0 0
976976 5.24719 0.167959
977977 3.67102 0.117446 0.0587232 0.998274i 0.481297π-0.481297\pi
0.0587232 + 0.998274i 0.481297π0.481297\pi
978978 0 0
979979 0.783356 0.0250362
980980 4.35470 0.139106
981981 0 0
982982 −40.9377 −1.30637
983983 −6.68787 −0.213310 −0.106655 0.994296i 0.534014π-0.534014\pi
−0.106655 + 0.994296i 0.534014π0.534014\pi
984984 0 0
985985 −12.1801 −0.388091
986986 −30.4598 −0.970037
987987 0 0
988988 −11.9833 −0.381240
989989 −25.6966 −0.817103
990990 0 0
991991 −51.4790 −1.63528 −0.817642 0.575728i 0.804719π-0.804719\pi
−0.817642 + 0.575728i 0.804719π0.804719\pi
992992 −8.84930 −0.280966
993993 0 0
994994 21.8127 0.691857
995995 11.9964 0.380313
996996 0 0
997997 −44.2781 −1.40230 −0.701150 0.713014i 0.747330π-0.747330\pi
−0.701150 + 0.713014i 0.747330π0.747330\pi
998998 −6.69932 −0.212063
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 1458.2.a.e.1.3 6
3.2 odd 2 1458.2.a.h.1.4 yes 6
9.2 odd 6 1458.2.c.e.973.3 12
9.4 even 3 1458.2.c.h.487.4 12
9.5 odd 6 1458.2.c.e.487.3 12
9.7 even 3 1458.2.c.h.973.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1458.2.a.e.1.3 6 1.1 even 1 trivial
1458.2.a.h.1.4 yes 6 3.2 odd 2
1458.2.c.e.487.3 12 9.5 odd 6
1458.2.c.e.973.3 12 9.2 odd 6
1458.2.c.h.487.4 12 9.4 even 3
1458.2.c.h.973.4 12 9.7 even 3