Properties

Label 399.2.cb.a.320.1
Level 399399
Weight 22
Character 399.320
Analytic conductor 3.1863.186
Analytic rank 00
Dimension 66
CM discriminant -3
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [399,2,Mod(5,399)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(399, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 15, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("399.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 399=3719 399 = 3 \cdot 7 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 399.cb (of order 1818, degree 66, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.186031040653.18603104065
Analytic rank: 00
Dimension: 66
Coefficient field: Q(ζ18)\Q(\zeta_{18})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x3+1 x^{6} - x^{3} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: U(1)[D18]\mathrm{U}(1)[D_{18}]

Embedding invariants

Embedding label 320.1
Root 0.7660440.642788i-0.766044 - 0.642788i of defining polynomial
Character χ\chi == 399.320
Dual form 399.2.cb.a.101.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.11334+1.32683i)q3+(1.532091.28558i)q4+(1.286992.31164i)q7+(0.5209452.95442i)q9+3.46410iq12+(1.992735.47497i)q13+(0.6945933.93923i)q16+(0.500000+4.33013i)q19+(4.50000+0.866025i)q21+(0.8682414.92404i)q25+(4.50000+2.59808i)q27+(4.943561.88711i)q28+(7.27244+4.19875i)q31+(4.596273.85673i)q36+(2.543234.40501i)q37+(5.04576+8.73951i)q39+(1.535968.71086i)q43+(4.45336+5.30731i)q48+(3.68732+5.95010i)q49+(3.9854510.9499i)q52+(5.188665.48432i)q57+(4.30406+11.8253i)q61+(6.15910+5.00654i)q63+(4.000006.92820i)q64+(0.5949220.216534i)q67+(10.5680+12.5945i)q73+(7.50000+4.33013i)q75+(4.80066+7.27693i)q76+(2.46538+13.9819i)q79+(8.45723+3.07818i)q81+(8.007744.45826i)q84+(15.2208+2.43977i)q91+(13.6677+4.97464i)q93+(12.246714.5951i)q97+O(q100)q+(-1.11334 + 1.32683i) q^{3} +(1.53209 - 1.28558i) q^{4} +(-1.28699 - 2.31164i) q^{7} +(-0.520945 - 2.95442i) q^{9} +3.46410i q^{12} +(1.99273 - 5.47497i) q^{13} +(0.694593 - 3.93923i) q^{16} +(-0.500000 + 4.33013i) q^{19} +(4.50000 + 0.866025i) q^{21} +(-0.868241 - 4.92404i) q^{25} +(4.50000 + 2.59808i) q^{27} +(-4.94356 - 1.88711i) q^{28} +(7.27244 + 4.19875i) q^{31} +(-4.59627 - 3.85673i) q^{36} +(2.54323 - 4.40501i) q^{37} +(5.04576 + 8.73951i) q^{39} +(1.53596 - 8.71086i) q^{43} +(4.45336 + 5.30731i) q^{48} +(-3.68732 + 5.95010i) q^{49} +(-3.98545 - 10.9499i) q^{52} +(-5.18866 - 5.48432i) q^{57} +(-4.30406 + 11.8253i) q^{61} +(-6.15910 + 5.00654i) q^{63} +(-4.00000 - 6.92820i) q^{64} +(-0.594922 - 0.216534i) q^{67} +(-10.5680 + 12.5945i) q^{73} +(7.50000 + 4.33013i) q^{75} +(4.80066 + 7.27693i) q^{76} +(-2.46538 + 13.9819i) q^{79} +(-8.45723 + 3.07818i) q^{81} +(8.00774 - 4.45826i) q^{84} +(-15.2208 + 2.43977i) q^{91} +(-13.6677 + 4.97464i) q^{93} +(12.2467 - 14.5951i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q6q133q19+27q21+27q2724q43+12q5239q6124q64+15q6721q73+45q7539q7951q9154q93+O(q100) 6 q - 6 q^{13} - 3 q^{19} + 27 q^{21} + 27 q^{27} - 24 q^{43} + 12 q^{52} - 39 q^{61} - 24 q^{64} + 15 q^{67} - 21 q^{73} + 45 q^{75} - 39 q^{79} - 51 q^{91} - 54 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/399Z)×\left(\mathbb{Z}/399\mathbb{Z}\right)^\times.

nn 115115 134134 211211
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 1-1 e(29)e\left(\frac{2}{9}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
33 −1.11334 + 1.32683i −0.642788 + 0.766044i
44 1.53209 1.28558i 0.766044 0.642788i
55 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
66 0 0
77 −1.28699 2.31164i −0.486436 0.873716i
88 0 0
99 −0.520945 2.95442i −0.173648 0.984808i
1010 0 0
1111 0 0 1.00000 00
−1.00000 π\pi
1212 3.46410i 1.00000i
1313 1.99273 5.47497i 0.552683 1.51848i −0.277350 0.960769i 0.589456π-0.589456\pi
0.830033 0.557714i 0.188322π-0.188322\pi
1414 0 0
1515 0 0
1616 0.694593 3.93923i 0.173648 0.984808i
1717 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
1818 0 0
1919 −0.500000 + 4.33013i −0.114708 + 0.993399i
2020 0 0
2121 4.50000 + 0.866025i 0.981981 + 0.188982i
2222 0 0
2323 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
2424 0 0
2525 −0.868241 4.92404i −0.173648 0.984808i
2626 0 0
2727 4.50000 + 2.59808i 0.866025 + 0.500000i
2828 −4.94356 1.88711i −0.934246 0.356630i
2929 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
3030 0 0
3131 7.27244 + 4.19875i 1.30617 + 0.754117i 0.981455 0.191695i 0.0613985π-0.0613985\pi
0.324714 + 0.945812i 0.394732π0.394732\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 −4.59627 3.85673i −0.766044 0.642788i
3737 2.54323 4.40501i 0.418105 0.724179i −0.577644 0.816289i 0.696028π-0.696028\pi
0.995749 + 0.0921098i 0.0293611π0.0293611\pi
3838 0 0
3939 5.04576 + 8.73951i 0.807968 + 1.39944i
4040 0 0
4141 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
4242 0 0
4343 1.53596 8.71086i 0.234232 1.32839i −0.609994 0.792406i 0.708828π-0.708828\pi
0.844226 0.535988i 0.180061π-0.180061\pi
4444 0 0
4545 0 0
4646 0 0
4747 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
4848 4.45336 + 5.30731i 0.642788 + 0.766044i
4949 −3.68732 + 5.95010i −0.526760 + 0.850014i
5050 0 0
5151 0 0
5252 −3.98545 10.9499i −0.552683 1.51848i
5353 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
5454 0 0
5555 0 0
5656 0 0
5757 −5.18866 5.48432i −0.687255 0.726416i
5858 0 0
5959 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
6060 0 0
6161 −4.30406 + 11.8253i −0.551079 + 1.51408i 0.281161 + 0.959661i 0.409281π0.409281\pi
−0.832240 + 0.554416i 0.812942π0.812942\pi
6262 0 0
6363 −6.15910 + 5.00654i −0.775974 + 0.630765i
6464 −4.00000 6.92820i −0.500000 0.866025i
6565 0 0
6666 0 0
6767 −0.594922 0.216534i −0.0726813 0.0264538i 0.305424 0.952217i 0.401202π-0.401202\pi
−0.378105 + 0.925763i 0.623424π0.623424\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
7272 0 0
7373 −10.5680 + 12.5945i −1.23690 + 1.47408i −0.409644 + 0.912245i 0.634347π0.634347\pi
−0.827252 + 0.561830i 0.810097π0.810097\pi
7474 0 0
7575 7.50000 + 4.33013i 0.866025 + 0.500000i
7676 4.80066 + 7.27693i 0.550673 + 0.834721i
7777 0 0
7878 0 0
7979 −2.46538 + 13.9819i −0.277377 + 1.57309i 0.453930 + 0.891038i 0.350022π0.350022\pi
−0.731307 + 0.682048i 0.761089π0.761089\pi
8080 0 0
8181 −8.45723 + 3.07818i −0.939693 + 0.342020i
8282 0 0
8383 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
8484 8.00774 4.45826i 0.873716 0.486436i
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
9090 0 0
9191 −15.2208 + 2.43977i −1.59557 + 0.255757i
9292 0 0
9393 −13.6677 + 4.97464i −1.41728 + 0.515846i
9494 0 0
9595 0 0
9696 0 0
9797 12.2467 14.5951i 1.24347 1.48191i 0.427284 0.904117i 0.359470π-0.359470\pi
0.816185 0.577791i 0.196085π-0.196085\pi
9898 0 0
9999 0 0
100100 −7.66044 6.42788i −0.766044 0.642788i
101101 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
102102 0 0
103103 −13.4315 + 7.75470i −1.32345 + 0.764094i −0.984277 0.176631i 0.943480π-0.943480\pi
−0.339172 + 0.940724i 0.610147π0.610147\pi
104104 0 0
105105 0 0
106106 0 0
107107 0 0 1.00000 00
−1.00000 π\pi
108108 10.2344 1.80460i 0.984808 0.173648i
109109 1.87939 0.684040i 0.180012 0.0655192i −0.250441 0.968132i 0.580576π-0.580576\pi
0.430454 + 0.902613i 0.358354π0.358354\pi
110110 0 0
111111 3.01320 + 8.27871i 0.286001 + 0.785780i
112112 −10.0000 + 3.46410i −0.944911 + 0.327327i
113113 0 0 1.00000 00
−1.00000 π\pi
114114 0 0
115115 0 0
116116 0 0
117117 −17.2135 3.03520i −1.59139 0.280604i
118118 0 0
119119 0 0
120120 0 0
121121 11.0000 1.00000
122122 0 0
123123 0 0
124124 16.5398 2.91642i 1.48532 0.261902i
125125 0 0
126126 0 0
127127 17.8542 + 6.49838i 1.58430 + 0.576638i 0.976134 0.217171i 0.0696829π-0.0696829\pi
0.608167 + 0.793809i 0.291905π0.291905\pi
128128 0 0
129129 9.84776 + 11.7361i 0.867047 + 1.03331i
130130 0 0
131131 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
132132 0 0
133133 10.6532 4.41701i 0.923747 0.383003i
134134 0 0
135135 0 0
136136 0 0
137137 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
138138 0 0
139139 8.05556 22.1325i 0.683264 1.87725i 0.296866 0.954919i 0.404058π-0.404058\pi
0.386398 0.922332i 0.373719π-0.373719\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 −12.0000 −1.00000
145145 0 0
146146 0 0
147147 −3.78952 11.5169i −0.312554 0.949900i
148148 −1.76651 10.0184i −0.145206 0.823506i
149149 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
150150 0 0
151151 11.5000 + 19.9186i 0.935857 + 1.62095i 0.773099 + 0.634285i 0.218706π0.218706\pi
0.162758 + 0.986666i 0.447961π0.447961\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 18.9659 + 6.90301i 1.51848 + 0.552683i
157157 −5.04236 13.8538i −0.402424 1.10565i −0.961085 0.276254i 0.910907π-0.910907\pi
0.558661 0.829396i 0.311315π-0.311315\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 11.2456 + 19.4779i 0.880821 + 1.52563i 0.850430 + 0.526088i 0.176342π0.176342\pi
0.0303908 + 0.999538i 0.490325π0.490325\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
168168 0 0
169169 −16.0458 13.4640i −1.23429 1.03569i
170170 0 0
171171 13.0535 0.778544i 0.998226 0.0595368i
172172 −8.84524 15.3204i −0.674443 1.16817i
173173 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
174174 0 0
175175 −10.2652 + 8.34424i −0.775974 + 0.630765i
176176 0 0
177177 0 0
178178 0 0
179179 0 0 1.00000 00
−1.00000 π\pi
180180 0 0
181181 −4.45336 5.30731i −0.331016 0.394489i 0.574707 0.818359i 0.305116π-0.305116\pi
−0.905723 + 0.423870i 0.860671π0.860671\pi
182182 0 0
183183 −10.8983 18.8764i −0.805623 1.39538i
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 0.214355 13.7461i 0.0155920 0.999878i
190190 0 0
191191 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
192192 13.6459 + 2.40614i 0.984808 + 0.173648i
193193 −5.82114 4.88451i −0.419015 0.351595i 0.408773 0.912636i 0.365957π-0.365957\pi
−0.827788 + 0.561041i 0.810401π0.810401\pi
194194 0 0
195195 0 0
196196 2.00000 + 13.8564i 0.142857 + 0.989743i
197197 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
198198 0 0
199199 −5.24809 + 14.4190i −0.372027 + 1.02214i 0.602549 + 0.798082i 0.294152π0.294152\pi
−0.974576 + 0.224055i 0.928070π0.928070\pi
200200 0 0
201201 0.949655 0.548284i 0.0669835 0.0386729i
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 −20.1830 11.6527i −1.39944 0.807968i
209209 0 0
210210 0 0
211211 21.3293 + 17.8974i 1.46837 + 1.23211i 0.917630 + 0.397436i 0.130100π0.130100\pi
0.550743 + 0.834675i 0.314345π0.314345\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 0.346419 22.2150i 0.0235165 1.50805i
218218 0 0
219219 −4.94491 28.0440i −0.334146 1.89504i
220220 0 0
221221 0 0
222222 0 0
223223 0.186137 + 0.0328209i 0.0124646 + 0.00219785i 0.179877 0.983689i 0.442430π-0.442430\pi
−0.167412 + 0.985887i 0.553541π0.553541\pi
224224 0 0
225225 −14.0954 + 5.13030i −0.939693 + 0.342020i
226226 0 0
227227 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
228228 −15.0000 1.73205i −0.993399 0.114708i
229229 10.3981 + 6.00335i 0.687126 + 0.396713i 0.802535 0.596606i 0.203484π-0.203484\pi
−0.115408 + 0.993318i 0.536818π0.536818\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
234234 0 0
235235 0 0
236236 0 0
237237 −15.8068 18.8378i −1.02676 1.22364i
238238 0 0
239239 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
240240 0 0
241241 30.3614 5.35354i 1.95575 0.344852i 0.957309 0.289066i 0.0933448π-0.0933448\pi
0.998443 0.0557856i 0.0177663π-0.0177663\pi
242242 0 0
243243 5.33157 14.6484i 0.342020 0.939693i
244244 8.60813 + 23.6506i 0.551079 + 1.51408i
245245 0 0
246246 0 0
247247 22.7110 + 11.3662i 1.44506 + 0.723217i
248248 0 0
249249 0 0
250250 0 0
251251 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
252252 −3.00000 + 15.5885i −0.188982 + 0.981981i
253253 0 0
254254 0 0
255255 0 0
256256 −15.0351 5.47232i −0.939693 0.342020i
257257 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
258258 0 0
259259 −13.4559 0.209830i −0.836108 0.0130382i
260260 0 0
261261 0 0
262262 0 0
263263 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 −1.18984 + 0.433068i −0.0726813 + 0.0264538i
269269 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
270270 0 0
271271 10.0201 11.9415i 0.608676 0.725391i −0.370403 0.928871i 0.620781π-0.620781\pi
0.979079 + 0.203479i 0.0652250π0.0652250\pi
272272 0 0
273273 13.7087 22.9116i 0.829690 1.38667i
274274 0 0
275275 0 0
276276 0 0
277277 26.0000 1.56219 0.781094 0.624413i 0.214662π-0.214662\pi
0.781094 + 0.624413i 0.214662π0.214662\pi
278278 0 0
279279 8.61633 23.6732i 0.515846 1.41728i
280280 0 0
281281 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
282282 0 0
283283 −32.4090 5.71458i −1.92652 0.339697i −0.927130 0.374741i 0.877732π-0.877732\pi
−0.999386 + 0.0350443i 0.988843π0.988843\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 15.9748 + 5.81434i 0.939693 + 0.342020i
290290 0 0
291291 5.73039 + 32.4987i 0.335921 + 1.90510i
292292 32.8819i 1.92427i
293293 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 17.0574 3.00767i 0.984808 0.173648i
301301 −22.1131 + 7.66020i −1.27458 + 0.441527i
302302 0 0
303303 0 0
304304 16.7101 + 4.97729i 0.958388 + 0.285467i
305305 0 0
306306 0 0
307307 10.6631 + 29.2967i 0.608577 + 1.67205i 0.733337 + 0.679865i 0.237962π0.237962\pi
−0.124760 + 0.992187i 0.539816π0.539816\pi
308308 0 0
309309 4.66473 26.4550i 0.265367 1.50497i
310310 0 0
311311 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
312312 0 0
313313 27.2918 4.81228i 1.54262 0.272006i 0.663345 0.748314i 0.269136π-0.269136\pi
0.879279 + 0.476308i 0.158025π0.158025\pi
314314 0 0
315315 0 0
316316 14.1976 + 24.5909i 0.798677 + 1.38335i
317317 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
318318 0 0
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 0 0
324324 −9.00000 + 15.5885i −0.500000 + 0.866025i
325325 −28.6891 5.05867i −1.59139 0.280604i
326326 0 0
327327 −1.18479 + 3.25519i −0.0655192 + 0.180012i
328328 0 0
329329 0 0
330330 0 0
331331 −17.9971 31.1718i −0.989208 1.71336i −0.621492 0.783420i 0.713473π-0.713473\pi
−0.367716 0.929938i 0.619860π-0.619860\pi
332332 0 0
333333 −14.3391 5.21902i −0.785780 0.286001i
334334 0 0
335335 0 0
336336 6.53714 17.1250i 0.356630 0.934246i
337337 −4.72503 + 26.7970i −0.257389 + 1.45973i 0.532476 + 0.846445i 0.321262π0.321262\pi
−0.789865 + 0.613280i 0.789850π0.789850\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 18.5000 + 0.866025i 0.998906 + 0.0467610i
344344 0 0
345345 0 0
346346 0 0
347347 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
348348 0 0
349349 −15.1879 + 8.76877i −0.812992 + 0.469381i −0.847994 0.530006i 0.822190π-0.822190\pi
0.0350017 + 0.999387i 0.488856π0.488856\pi
350350 0 0
351351 23.1917 19.4601i 1.23788 1.03870i
352352 0 0
353353 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
360360 0 0
361361 −18.5000 4.33013i −0.973684 0.227901i
362362 0 0
363363 −12.2467 + 14.5951i −0.642788 + 0.766044i
364364 −20.1830 + 23.3054i −1.05788 + 1.22153i
365365 0 0
366366 0 0
367367 −36.6104 + 6.45540i −1.91105 + 0.336969i −0.997555 0.0698862i 0.977736π-0.977736\pi
−0.913493 + 0.406855i 0.866625π0.866625\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 −14.5449 + 25.1925i −0.754117 + 1.30617i
373373 −25.0000 −1.29445 −0.647225 0.762299i 0.724071π-0.724071\pi
−0.647225 + 0.762299i 0.724071π0.724071\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 −30.6219 −1.57294 −0.786469 0.617629i 0.788093π-0.788093\pi
−0.786469 + 0.617629i 0.788093π0.788093\pi
380380 0 0
381381 −28.5000 + 16.4545i −1.46010 + 0.842989i
382382 0 0
383383 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
384384 0 0
385385 0 0
386386 0 0
387387 −26.5357 −1.34889
388388 38.1051i 1.93449i
389389 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 2.02915 + 5.57505i 0.101840 + 0.279804i 0.980140 0.198307i 0.0635442π-0.0635442\pi
−0.878300 + 0.478110i 0.841322π0.841322\pi
398398 0 0
399399 −6.00000 + 19.0526i −0.300376 + 0.953821i
400400 −20.0000 −1.00000
401401 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
402402 0 0
403403 37.4800 31.4494i 1.86701 1.56661i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 −8.88594 + 24.4139i −0.439382 + 1.20719i 0.500514 + 0.865729i 0.333144π0.333144\pi
−0.939895 + 0.341463i 0.889078π0.889078\pi
410410 0 0
411411 0 0
412412 −10.6091 + 29.1482i −0.522671 + 1.43603i
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 20.3974 + 35.3293i 0.998865 + 1.73008i
418418 0 0
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 0 0
421421 17.8542 6.49838i 0.870159 0.316712i 0.131927 0.991259i 0.457883π-0.457883\pi
0.738231 + 0.674548i 0.235661π0.235661\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 32.8751 5.26963i 1.59094 0.255015i
428428 0 0
429429 0 0
430430 0 0
431431 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
432432 13.3601 15.9219i 0.642788 0.766044i
433433 −30.0940 + 5.30639i −1.44623 + 0.255009i −0.840996 0.541041i 0.818030π-0.818030\pi
−0.605231 + 0.796050i 0.706919π0.706919\pi
434434 0 0
435435 0 0
436436 2.00000 3.46410i 0.0957826 0.165900i
437437 0 0
438438 0 0
439439 7.57944 + 20.8243i 0.361747 + 0.993892i 0.978412 + 0.206666i 0.0662612π0.0662612\pi
−0.616665 + 0.787226i 0.711517π0.711517\pi
440440 0 0
441441 19.5000 + 7.79423i 0.928571 + 0.371154i
442442 0 0
443443 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
444444 15.2594 + 8.81002i 0.724179 + 0.418105i
445445 0 0
446446 0 0
447447 0 0
448448 −10.8675 + 18.1631i −0.513442 + 0.858124i
449449 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
450450 0 0
451451 0 0
452452 0 0
453453 −39.2320 6.91765i −1.84328 0.325020i
454454 0 0
455455 0 0
456456 0 0
457457 19.6006 33.9492i 0.916878 1.58808i 0.112749 0.993624i 0.464034π-0.464034\pi
0.804129 0.594455i 0.202632π-0.202632\pi
458458 0 0
459459 0 0
460460 0 0
461461 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
462462 0 0
463463 4.58630 + 7.94371i 0.213144 + 0.369176i 0.952697 0.303923i 0.0982964π-0.0982964\pi
−0.739553 + 0.673098i 0.764963π0.764963\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
468468 −30.2746 + 17.4790i −1.39944 + 0.807968i
469469 0.265111 + 1.65392i 0.0122417 + 0.0763710i
470470 0 0
471471 23.9954 + 8.73362i 1.10565 + 0.402424i
472472 0 0
473473 0 0
474474 0 0
475475 21.7558 1.29757i 0.998226 0.0595368i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
480480 0 0
481481 −19.0493 22.7021i −0.868574 1.03513i
482482 0 0
483483 0 0
484484 16.8530 14.1413i 0.766044 0.642788i
485485 0 0
486486 0 0
487487 22.0000 38.1051i 0.996915 1.72671i 0.430486 0.902597i 0.358342π-0.358342\pi
0.566429 0.824110i 0.308325π-0.308325\pi
488488 0 0
489489 −38.3640 6.76460i −1.73488 0.305906i
490490 0 0
491491 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 21.5912 25.7314i 0.969474 1.15537i
497497 0 0
498498 0 0
499499 −34.1300 28.6385i −1.52787 1.28203i −0.811610 0.584199i 0.801409π-0.801409\pi
−0.716258 0.697835i 0.754147π-0.754147\pi
500500 0 0
501501 0 0
502502 0 0
503503 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
504504 0 0
505505 0 0
506506 0 0
507507 35.7288 6.29995i 1.58677 0.279791i
508508 35.7083 12.9968i 1.58430 0.576638i
509509 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
510510 0 0
511511 42.7149 + 8.22048i 1.88959 + 0.363653i
512512 0 0
513513 −13.5000 + 18.1865i −0.596040 + 0.802955i
514514 0 0
515515 0 0
516516 30.1753 + 5.32072i 1.32839 + 0.234232i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
522522 0 0
523523 −15.4599 + 2.72600i −0.676015 + 0.119200i −0.501107 0.865385i 0.667074π-0.667074\pi
−0.174908 + 0.984585i 0.555963π0.555963\pi
524524 0 0
525525 0.357259 22.9101i 0.0155920 0.999878i
526526 0 0
527527 0 0
528528 0 0
529529 17.6190 + 14.7841i 0.766044 + 0.642788i
530530 0 0
531531 0 0
532532 10.6432 20.4627i 0.461442 0.887171i
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 −0.202277 1.14717i −0.00869658 0.0493207i 0.980151 0.198254i 0.0635271π-0.0635271\pi
−0.988847 + 0.148933i 0.952416π0.952416\pi
542542 0 0
543543 12.0000 0.514969
544544 0 0
545545 0 0
546546 0 0
547547 7.96720 + 45.1842i 0.340653 + 1.93194i 0.362031 + 0.932166i 0.382083π0.382083\pi
−0.0213785 + 0.999771i 0.506805π0.506805\pi
548548 0 0
549549 37.1792 + 6.55569i 1.58677 + 0.279790i
550550 0 0
551551 0 0
552552 0 0
553553 35.4940 12.2955i 1.50936 0.522857i
554554 0 0
555555 0 0
556556 −16.1111 44.2649i −0.683264 1.87725i
557557 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
558558 0 0
559559 −44.6309 25.7677i −1.88769 1.08986i
560560 0 0
561561 0 0
562562 0 0
563563 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
564564 0 0
565565 0 0
566566 0 0
567567 18.0000 + 15.5885i 0.755929 + 0.654654i
568568 0 0
569569 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
570570 0 0
571571 −15.2187 26.3595i −0.636882 1.10311i −0.986113 0.166076i 0.946890π-0.946890\pi
0.349231 0.937037i 0.386443π-0.386443\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 −18.3851 + 15.4269i −0.766044 + 0.642788i
577577 28.5000 + 16.4545i 1.18647 + 0.685009i 0.957503 0.288425i 0.0931316π-0.0931316\pi
0.228968 + 0.973434i 0.426465π0.426465\pi
578578 0 0
579579 12.9618 2.28552i 0.538675 0.0949829i
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
588588 −20.6117 12.7732i −0.850014 0.526760i
589589 −21.8173 + 29.3912i −0.898967 + 1.21104i
590590 0 0
591591 0 0
592592 −15.5858 13.0781i −0.640574 0.537505i
593593 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
594594 0 0
595595 0 0
596596 0 0
597597 −13.2886 23.0166i −0.543868 0.942007i
598598 0 0
599599 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
600600 0 0
601601 13.1042 7.56570i 0.534530 0.308611i −0.208329 0.978059i 0.566802π-0.566802\pi
0.742859 + 0.669448i 0.233469π0.233469\pi
602602 0 0
603603 −0.329812 + 1.87046i −0.0134310 + 0.0761708i
604604 43.2259 + 15.7329i 1.75884 + 0.640164i
605605 0 0
606606 0 0
607607 −41.0091 23.6766i −1.66451 0.961005i −0.970520 0.241020i 0.922518π-0.922518\pi
−0.693990 0.719985i 0.744149π-0.744149\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 −44.1656 + 16.0749i −1.78383 + 0.649261i −0.784245 + 0.620451i 0.786949π0.786949\pi
−0.999585 + 0.0288097i 0.990828π0.990828\pi
614614 0 0
615615 0 0
616616 0 0
617617 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
618618 0 0
619619 49.7594i 2.00000i −0.000400419 1.00000i 0.500127π-0.500127\pi
0.000400419 1.00000i 0.499873π-0.499873\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 37.9317 13.8060i 1.51848 0.552683i
625625 −23.4923 + 8.55050i −0.939693 + 0.342020i
626626 0 0
627627 0 0
628628 −25.5354 14.7429i −1.01897 0.588304i
629629 0 0
630630 0 0
631631 8.55959 + 48.5439i 0.340752 + 1.93250i 0.360657 + 0.932699i 0.382553π0.382553\pi
−0.0199047 + 0.999802i 0.506336π0.506336\pi
632632 0 0
633633 −47.4937 + 8.37441i −1.88770 + 0.332853i
634634 0 0
635635 0 0
636636 0 0
637637 25.2288 + 32.0449i 0.999601 + 1.26966i
638638 0 0
639639 0 0
640640 0 0
641641 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
642642 0 0
643643 −11.6213 31.9293i −0.458301 1.25917i −0.926750 0.375680i 0.877409π-0.877409\pi
0.468449 0.883491i 0.344813π-0.344813\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
648648 0 0
649649 0 0
650650 0 0
651651 29.0898 + 25.1925i 1.14012 + 0.987371i
652652 42.2695 + 15.3848i 1.65540 + 0.602517i
653653 0 0 1.00000 00
−1.00000 π\pi
654654 0 0
655655 0 0
656656 0 0
657657 42.7149 + 24.6614i 1.66647 + 0.962135i
658658 0 0
659659 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
660660 0 0
661661 −32.2869 38.4780i −1.25581 1.49662i −0.791783 0.610802i 0.790847π-0.790847\pi
−0.464031 0.885819i 0.653597π-0.653597\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −0.250781 + 0.210430i −0.00969577 + 0.00813571i
670670 0 0
671671 0 0
672672 0 0
673673 14.6977 25.4572i 0.566557 0.981305i −0.430346 0.902664i 0.641609π-0.641609\pi
0.996903 0.0786409i 0.0250581π-0.0250581\pi
674674 0 0
675675 8.88594 24.4139i 0.342020 0.939693i
676676 −41.8925 −1.61125
677677 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
678678 0 0
679679 −49.5000 9.52628i −1.89964 0.365585i
680680 0 0
681681 0 0
682682 0 0
683683 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
684684 18.9982 17.9741i 0.726416 0.687255i
685685 0 0
686686 0 0
687687 −19.5421 + 7.11272i −0.745576 + 0.271367i
688688 −33.2472 12.1010i −1.26754 0.461346i
689689 0 0
690690 0 0
691691 51.9615i 1.97671i −0.152167 0.988355i 0.548625π-0.548625\pi
0.152167 0.988355i 0.451375π-0.451375\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 −5.00000 + 25.9808i −0.188982 + 0.981981i
701701 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
702702 0 0
703703 17.8026 + 13.2150i 0.671439 + 0.498414i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 39.5133 33.1556i 1.48395 1.24518i 0.582115 0.813107i 0.302225π-0.302225\pi
0.901837 0.432077i 0.142219π-0.142219\pi
710710 0 0
711711 42.5928 1.59735
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
720720 0 0
721721 35.2123 + 21.0686i 1.31137 + 0.784636i
722722 0 0
723723 −26.6994 + 46.2447i −0.992961 + 1.71986i
724724 −13.6459 2.40614i −0.507146 0.0894235i
725725 0 0
726726 0 0
727727 14.0314 + 2.47411i 0.520395 + 0.0917597i 0.427675 0.903933i 0.359333π-0.359333\pi
0.0927199 + 0.995692i 0.470444π0.470444\pi
728728 0 0
729729 13.5000 + 23.3827i 0.500000 + 0.866025i
730730 0 0
731731 0 0
732732 −40.9641 14.9097i −1.51408 0.551079i
733733 18.0000 10.3923i 0.664845 0.383849i −0.129275 0.991609i 0.541265π-0.541265\pi
0.794121 + 0.607760i 0.207932π0.207932\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 3.67153 20.8223i 0.135060 0.765961i −0.839759 0.542960i 0.817304π-0.817304\pi
0.974818 0.223001i 0.0715853π-0.0715853\pi
740740 0 0
741741 −40.3661 + 17.4790i −1.48288 + 0.642108i
742742 0 0
743743 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 8.85045 + 50.1934i 0.322958 + 1.83158i 0.523655 + 0.851930i 0.324568π0.324568\pi
−0.200698 + 0.979653i 0.564321π0.564321\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 −17.3432 21.3357i −0.630765 0.775974i
757757 −10.5775 + 3.84991i −0.384447 + 0.139927i −0.527011 0.849858i 0.676688π-0.676688\pi
0.142564 + 0.989786i 0.454465π0.454465\pi
758758 0 0
759759 0 0
760760 0 0
761761 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
762762 0 0
763763 −4.00000 3.46410i −0.144810 0.125409i
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 24.0000 13.8564i 0.866025 0.500000i
769769 −26.4654 31.5403i −0.954368 1.13737i −0.990429 0.138022i 0.955925π-0.955925\pi
0.0360609 0.999350i 0.488519π-0.488519\pi
770770 0 0
771771 0 0
772772 −15.1979 −0.546985
773773 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
774774 0 0
775775 14.3606 39.4553i 0.515846 1.41728i
776776 0 0
777777 15.2594 17.6200i 0.547428 0.632115i
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 20.8776 + 18.6581i 0.745630 + 0.666361i
785785 0 0
786786 0 0
787787 55.7508i 1.98730i 0.112514 + 0.993650i 0.464110π0.464110\pi
−0.112514 + 0.993650i 0.535890π0.535890\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 56.1664 + 47.1292i 1.99453 + 1.67361i
794794 0 0
795795 0 0
796796 10.4962 + 28.8380i 0.372027 + 1.02214i
797797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
798798 0 0
799799 0 0
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 0.750096 2.06087i 0.0264538 0.0726813i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 0 0 1.00000 00
−1.00000 π\pi
810810 0 0
811811 −14.8099 + 40.6899i −0.520046 + 1.42882i 0.350423 + 0.936592i 0.386038π0.386038\pi
−0.870469 + 0.492223i 0.836184π0.836184\pi
812812 0 0
813813 4.68850 + 26.5898i 0.164433 + 0.932545i
814814 0 0
815815 0 0
816816 0 0
817817 36.9511 + 11.0063i 1.29276 + 0.385063i
818818 0 0
819819 15.1373 + 43.6976i 0.528939 + 1.52692i
820820 0 0
821821 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
822822 0 0
823823 0.868241 + 4.92404i 0.0302650 + 0.171641i 0.996194 0.0871670i 0.0277814π-0.0277814\pi
−0.965929 + 0.258808i 0.916670π0.916670\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
828828 0 0
829829 2.62551 + 1.51584i 0.0911876 + 0.0526472i 0.544900 0.838501i 0.316567π-0.316567\pi
−0.453713 + 0.891148i 0.649901π0.649901\pi
830830 0 0
831831 −28.9469 + 34.4975i −1.00416 + 1.19671i
832832 −45.9026 + 8.09387i −1.59139 + 0.280604i
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 21.8173 + 37.7887i 0.754117 + 1.30617i
838838 0 0
839839 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
840840 0 0
841841 5.03580 28.5594i 0.173648 0.984808i
842842 0 0
843843 0 0
844844 55.6870 1.91682
845845 0 0
846846 0 0
847847 −14.1569 25.4280i −0.486436 0.873716i
848848 0 0
849849 43.6645 36.6389i 1.49856 1.25744i
850850 0 0
851851 0 0
852852 0 0
853853 −35.9420 + 42.8340i −1.23063 + 1.46661i −0.393753 + 0.919216i 0.628823π0.628823\pi
−0.836877 + 0.547391i 0.815621π0.815621\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
858858 0 0
859859 −0.984052 + 2.70366i −0.0335754 + 0.0922477i −0.955348 0.295484i 0.904519π-0.904519\pi
0.921772 + 0.387732i 0.126741π0.126741\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
864864 0 0
865865 0 0
866866 0 0
867867 −25.5000 + 14.7224i −0.866025 + 0.500000i
868868 −28.0283 34.4807i −0.951342 1.17035i
869869 0 0
870870 0 0
871871 −2.37104 + 2.82569i −0.0803395 + 0.0957448i
872872 0 0
873873 −49.5000 28.5788i −1.67532 0.967247i
874874 0 0
875875 0 0
876876 −43.6287 36.6088i −1.47408 1.23690i
877877 2.66766 15.1291i 0.0900805 0.510872i −0.906064 0.423141i 0.860927π-0.860927\pi
0.996144 0.0877308i 0.0279615π-0.0279615\pi
878878 0 0
879879 0 0
880880 0 0
881881 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
882882 0 0
883883 −45.4910 + 38.1715i −1.53089 + 1.28457i −0.740055 + 0.672546i 0.765201π0.765201\pi
−0.790838 + 0.612026i 0.790355π0.790355\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
888888 0 0
889889 −7.95621 49.6357i −0.266843 1.66473i
890890 0 0
891891 0 0
892892 0.327372 0.189008i 0.0109612 0.00632846i
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 −15.0000 + 25.9808i −0.500000 + 0.866025i
901901 0 0
902902 0 0
903903 14.4556 37.8687i 0.481054 1.26019i
904904 0 0
905905 0 0
906906 0 0
907907 −37.5877 + 13.6808i −1.24808 + 0.454264i −0.879752 0.475433i 0.842292π-0.842292\pi
−0.368327 + 0.929696i 0.620069π0.620069\pi
908908 0 0
909909 0 0
910910 0 0
911911 0 0 1.00000 00
−1.00000 π\pi
912912 −25.2080 + 16.6300i −0.834721 + 0.550673i
913913 0 0
914914 0 0
915915 0 0
916916 23.6486 4.16988i 0.781371 0.137777i
917917 0 0
918918 0 0
919919 −59.5271 −1.96362 −0.981810 0.189867i 0.939194π-0.939194\pi
−0.981810 + 0.189867i 0.939194π0.939194\pi
920920 0 0
921921 −50.7434 18.4691i −1.67205 0.608577i
922922 0 0
923923 0 0
924924 0 0
925925 −23.8986 8.69837i −0.785780 0.286001i
926926 0 0
927927 29.9078 + 35.6427i 0.982300 + 1.17066i
928928 0 0
929929 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
930930 0 0
931931 −23.9210 18.9416i −0.783980 0.620786i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 −8.80566 + 24.1933i −0.287668 + 0.790362i 0.708723 + 0.705487i 0.249271π0.249271\pi
−0.996392 + 0.0848755i 0.972951π0.972951\pi
938938 0 0
939939 −24.0000 + 41.5692i −0.783210 + 1.35656i
940940 0 0
941941 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
948948 −48.4347 8.54034i −1.57309 0.277377i
949949 47.8953 + 82.9572i 1.55475 + 2.69290i
950950 0 0
951951 0 0
952952 0 0
953953 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 19.7589 + 34.2235i 0.637385 + 1.10398i
962962 0 0
963963 0 0
964964 39.6340 47.2340i 1.27653 1.52130i
965965 0 0
966966 0 0
967967 1.03234 + 0.866234i 0.0331977 + 0.0278562i 0.659236 0.751936i 0.270880π-0.270880\pi
−0.626038 + 0.779793i 0.715324π0.715324\pi
968968 0 0
969969 0 0
970970 0 0
971971 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
972972 −10.6631 29.2967i −0.342020 0.939693i
973973 −61.5296 + 9.86272i −1.97255 + 0.316184i
974974 0 0
975975 38.6528 32.4335i 1.23788 1.03870i
976976 43.5931 + 25.1685i 1.39538 + 0.805623i
977977 0 0 1.00000 00
−1.00000 π\pi
978978 0 0
979979 0 0
980980 0 0
981981 −3.00000 5.19615i −0.0957826 0.165900i
982982 0 0
983983 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 49.4074 11.7825i 1.57186 0.374853i
989989 0 0
990990 0 0
991991 19.8744 + 16.6766i 0.631331 + 0.529749i 0.901342 0.433108i 0.142583π-0.142583\pi
−0.270011 + 0.962857i 0.587027π0.587027\pi
992992 0 0
993993 61.3965 + 10.8259i 1.94836 + 0.343548i
994994 0 0
995995 0 0
996996 0 0
997997 −7.07151 + 19.4288i −0.223957 + 0.615317i −0.999880 0.0155113i 0.995062π-0.995062\pi
0.775923 + 0.630828i 0.217285π0.217285\pi
998998 0 0
999999 22.8891 13.2150i 0.724179 0.418105i
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 399.2.cb.a.320.1 yes 6
3.2 odd 2 CM 399.2.cb.a.320.1 yes 6
7.3 odd 6 399.2.ci.a.206.1 yes 6
19.6 even 9 399.2.ci.a.215.1 yes 6
21.17 even 6 399.2.ci.a.206.1 yes 6
57.44 odd 18 399.2.ci.a.215.1 yes 6
133.101 odd 18 inner 399.2.cb.a.101.1 6
399.101 even 18 inner 399.2.cb.a.101.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
399.2.cb.a.101.1 6 133.101 odd 18 inner
399.2.cb.a.101.1 6 399.101 even 18 inner
399.2.cb.a.320.1 yes 6 1.1 even 1 trivial
399.2.cb.a.320.1 yes 6 3.2 odd 2 CM
399.2.ci.a.206.1 yes 6 7.3 odd 6
399.2.ci.a.206.1 yes 6 21.17 even 6
399.2.ci.a.215.1 yes 6 19.6 even 9
399.2.ci.a.215.1 yes 6 57.44 odd 18