Properties

Label 729.2.a.a.1.4
Level 729729
Weight 22
Character 729.1
Self dual yes
Analytic conductor 5.8215.821
Analytic rank 11
Dimension 66
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(1,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 729=36 729 = 3^{6}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 729.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 5.821094307355.82109430735
Analytic rank: 11
Dimension: 66
Coefficient field: 6.6.1397493.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x63x53x4+10x3+3x26x+1 x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 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 27)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 1.11662-1.11662 of defining polynomial
Character χ\chi == 729.1

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) == q0.415466q21.82739q4+2.21519q51.31963q7+1.59015q80.920335q105.21519q110.0180585q13+0.548261q14+2.99412q163.13280q17+0.417352q194.04801q20+2.16673q221.03439q230.0929475q25+0.00750270q26+2.41147q287.80722q29+3.72966q314.42426q32+1.30157q342.92322q35+4.42476q370.173396q38+3.52248q403.67494q418.30787q43+9.53017q44+0.429753q467.09791q475.25858q49+0.0386165q50+0.0329999q521.30057q5311.5526q552.09841q56+3.24364q583.70181q59+6.91424q611.54955q624.15011q640.0400030q6511.0268q67+5.72483q68+1.21450q706.08428q710.546973q731.83834q740.762665q76+6.88211q77+0.489144q79+6.63254q80+1.52681q82+4.61367q836.93973q85+3.45164q868.29293q883.37307q89+0.0238305q91+1.89023q92+2.94894q94+0.924513q95+9.94136q97+2.18476q98+O(q100)q-0.415466 q^{2} -1.82739 q^{4} +2.21519 q^{5} -1.31963 q^{7} +1.59015 q^{8} -0.920335 q^{10} -5.21519 q^{11} -0.0180585 q^{13} +0.548261 q^{14} +2.99412 q^{16} -3.13280 q^{17} +0.417352 q^{19} -4.04801 q^{20} +2.16673 q^{22} -1.03439 q^{23} -0.0929475 q^{25} +0.00750270 q^{26} +2.41147 q^{28} -7.80722 q^{29} +3.72966 q^{31} -4.42426 q^{32} +1.30157 q^{34} -2.92322 q^{35} +4.42476 q^{37} -0.173396 q^{38} +3.52248 q^{40} -3.67494 q^{41} -8.30787 q^{43} +9.53017 q^{44} +0.429753 q^{46} -7.09791 q^{47} -5.25858 q^{49} +0.0386165 q^{50} +0.0329999 q^{52} -1.30057 q^{53} -11.5526 q^{55} -2.09841 q^{56} +3.24364 q^{58} -3.70181 q^{59} +6.91424 q^{61} -1.54955 q^{62} -4.15011 q^{64} -0.0400030 q^{65} -11.0268 q^{67} +5.72483 q^{68} +1.21450 q^{70} -6.08428 q^{71} -0.546973 q^{73} -1.83834 q^{74} -0.762665 q^{76} +6.88211 q^{77} +0.489144 q^{79} +6.63254 q^{80} +1.52681 q^{82} +4.61367 q^{83} -6.93973 q^{85} +3.45164 q^{86} -8.29293 q^{88} -3.37307 q^{89} +0.0238305 q^{91} +1.89023 q^{92} +2.94894 q^{94} +0.924513 q^{95} +9.94136 q^{97} +2.18476 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q3q2+3q46q56q8+3q1012q116q143q169q17+3q196q20+6q2215q236q2515q266q2812q2912q35++45q98+O(q100) 6 q - 3 q^{2} + 3 q^{4} - 6 q^{5} - 6 q^{8} + 3 q^{10} - 12 q^{11} - 6 q^{14} - 3 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} + 6 q^{22} - 15 q^{23} - 6 q^{25} - 15 q^{26} - 6 q^{28} - 12 q^{29} - 12 q^{35}+ \cdots + 45 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 −0.415466 −0.293779 −0.146889 0.989153i 0.546926π-0.546926\pi
−0.146889 + 0.989153i 0.546926π0.546926\pi
33 0 0
44 −1.82739 −0.913694
55 2.21519 0.990662 0.495331 0.868704i 0.335047π-0.335047\pi
0.495331 + 0.868704i 0.335047π0.335047\pi
66 0 0
77 −1.31963 −0.498773 −0.249386 0.968404i 0.580229π-0.580229\pi
−0.249386 + 0.968404i 0.580229π0.580229\pi
88 1.59015 0.562203
99 0 0
1010 −0.920335 −0.291036
1111 −5.21519 −1.57244 −0.786219 0.617948i 0.787964π-0.787964\pi
−0.786219 + 0.617948i 0.787964π0.787964\pi
1212 0 0
1313 −0.0180585 −0.00500853 −0.00250427 0.999997i 0.500797π-0.500797\pi
−0.00250427 + 0.999997i 0.500797π0.500797\pi
1414 0.548261 0.146529
1515 0 0
1616 2.99412 0.748530
1717 −3.13280 −0.759814 −0.379907 0.925025i 0.624044π-0.624044\pi
−0.379907 + 0.925025i 0.624044π0.624044\pi
1818 0 0
1919 0.417352 0.0957472 0.0478736 0.998853i 0.484756π-0.484756\pi
0.0478736 + 0.998853i 0.484756π0.484756\pi
2020 −4.04801 −0.905162
2121 0 0
2222 2.16673 0.461949
2323 −1.03439 −0.215684 −0.107842 0.994168i 0.534394π-0.534394\pi
−0.107842 + 0.994168i 0.534394π0.534394\pi
2424 0 0
2525 −0.0929475 −0.0185895
2626 0.00750270 0.00147140
2727 0 0
2828 2.41147 0.455726
2929 −7.80722 −1.44976 −0.724882 0.688873i 0.758106π-0.758106\pi
−0.724882 + 0.688873i 0.758106π0.758106\pi
3030 0 0
3131 3.72966 0.669868 0.334934 0.942242i 0.391286π-0.391286\pi
0.334934 + 0.942242i 0.391286π0.391286\pi
3232 −4.42426 −0.782106
3333 0 0
3434 1.30157 0.223218
3535 −2.92322 −0.494115
3636 0 0
3737 4.42476 0.727426 0.363713 0.931511i 0.381509π-0.381509\pi
0.363713 + 0.931511i 0.381509π0.381509\pi
3838 −0.173396 −0.0281285
3939 0 0
4040 3.52248 0.556953
4141 −3.67494 −0.573929 −0.286965 0.957941i 0.592646π-0.592646\pi
−0.286965 + 0.957941i 0.592646π0.592646\pi
4242 0 0
4343 −8.30787 −1.26694 −0.633469 0.773768i 0.718370π-0.718370\pi
−0.633469 + 0.773768i 0.718370π0.718370\pi
4444 9.53017 1.43673
4545 0 0
4646 0.429753 0.0633636
4747 −7.09791 −1.03534 −0.517668 0.855581i 0.673200π-0.673200\pi
−0.517668 + 0.855581i 0.673200π0.673200\pi
4848 0 0
4949 −5.25858 −0.751226
5050 0.0386165 0.00546120
5151 0 0
5252 0.0329999 0.00457627
5353 −1.30057 −0.178648 −0.0893238 0.996003i 0.528471π-0.528471\pi
−0.0893238 + 0.996003i 0.528471π0.528471\pi
5454 0 0
5555 −11.5526 −1.55775
5656 −2.09841 −0.280412
5757 0 0
5858 3.24364 0.425910
5959 −3.70181 −0.481935 −0.240967 0.970533i 0.577465π-0.577465\pi
−0.240967 + 0.970533i 0.577465π0.577465\pi
6060 0 0
6161 6.91424 0.885277 0.442639 0.896700i 0.354042π-0.354042\pi
0.442639 + 0.896700i 0.354042π0.354042\pi
6262 −1.54955 −0.196793
6363 0 0
6464 −4.15011 −0.518764
6565 −0.0400030 −0.00496176
6666 0 0
6767 −11.0268 −1.34714 −0.673569 0.739125i 0.735239π-0.735239\pi
−0.673569 + 0.739125i 0.735239π0.735239\pi
6868 5.72483 0.694238
6969 0 0
7070 1.21450 0.145161
7171 −6.08428 −0.722071 −0.361035 0.932552i 0.617577π-0.617577\pi
−0.361035 + 0.932552i 0.617577π0.617577\pi
7272 0 0
7373 −0.546973 −0.0640183 −0.0320092 0.999488i 0.510191π-0.510191\pi
−0.0320092 + 0.999488i 0.510191π0.510191\pi
7474 −1.83834 −0.213702
7575 0 0
7676 −0.762665 −0.0874836
7777 6.88211 0.784289
7878 0 0
7979 0.489144 0.0550330 0.0275165 0.999621i 0.491240π-0.491240\pi
0.0275165 + 0.999621i 0.491240π0.491240\pi
8080 6.63254 0.741540
8181 0 0
8282 1.52681 0.168608
8383 4.61367 0.506416 0.253208 0.967412i 0.418514π-0.418514\pi
0.253208 + 0.967412i 0.418514π0.418514\pi
8484 0 0
8585 −6.93973 −0.752719
8686 3.45164 0.372200
8787 0 0
8888 −8.29293 −0.884029
8989 −3.37307 −0.357544 −0.178772 0.983891i 0.557212π-0.557212\pi
−0.178772 + 0.983891i 0.557212π0.557212\pi
9090 0 0
9191 0.0238305 0.00249812
9292 1.89023 0.197070
9393 0 0
9494 2.94894 0.304160
9595 0.924513 0.0948531
9696 0 0
9797 9.94136 1.00939 0.504696 0.863297i 0.331605π-0.331605\pi
0.504696 + 0.863297i 0.331605π0.331605\pi
9898 2.18476 0.220694
9999 0 0
100100 0.169851 0.0169851
101101 13.7995 1.37310 0.686550 0.727082i 0.259124π-0.259124\pi
0.686550 + 0.727082i 0.259124π0.259124\pi
102102 0 0
103103 4.56512 0.449815 0.224907 0.974380i 0.427792π-0.427792\pi
0.224907 + 0.974380i 0.427792π0.427792\pi
104104 −0.0287158 −0.00281581
105105 0 0
106106 0.540345 0.0524829
107107 −11.2965 −1.09207 −0.546035 0.837762i 0.683864π-0.683864\pi
−0.546035 + 0.837762i 0.683864π0.683864\pi
108108 0 0
109109 14.5032 1.38915 0.694577 0.719419i 0.255592π-0.255592\pi
0.694577 + 0.719419i 0.255592π0.255592\pi
110110 4.79972 0.457635
111111 0 0
112112 −3.95113 −0.373347
113113 12.5584 1.18140 0.590699 0.806892i 0.298852π-0.298852\pi
0.590699 + 0.806892i 0.298852π0.298852\pi
114114 0 0
115115 −2.29136 −0.213670
116116 14.2668 1.32464
117117 0 0
118118 1.53798 0.141582
119119 4.13413 0.378975
120120 0 0
121121 16.1982 1.47256
122122 −2.87263 −0.260076
123123 0 0
124124 −6.81554 −0.612054
125125 −11.2818 −1.00908
126126 0 0
127127 −8.39499 −0.744935 −0.372467 0.928045i 0.621488π-0.621488\pi
−0.372467 + 0.928045i 0.621488π0.621488\pi
128128 10.5727 0.934508
129129 0 0
130130 0.0166199 0.00145766
131131 −15.5349 −1.35729 −0.678645 0.734466i 0.737433π-0.737433\pi
−0.678645 + 0.734466i 0.737433π0.737433\pi
132132 0 0
133133 −0.550750 −0.0477561
134134 4.58126 0.395761
135135 0 0
136136 −4.98162 −0.427170
137137 12.0074 1.02586 0.512930 0.858430i 0.328560π-0.328560\pi
0.512930 + 0.858430i 0.328560π0.328560\pi
138138 0 0
139139 6.14512 0.521222 0.260611 0.965444i 0.416076π-0.416076\pi
0.260611 + 0.965444i 0.416076π0.416076\pi
140140 5.34187 0.451470
141141 0 0
142142 2.52781 0.212129
143143 0.0941785 0.00787561
144144 0 0
145145 −17.2945 −1.43623
146146 0.227249 0.0188072
147147 0 0
148148 −8.08575 −0.664644
149149 0.882820 0.0723235 0.0361617 0.999346i 0.488487π-0.488487\pi
0.0361617 + 0.999346i 0.488487π0.488487\pi
150150 0 0
151151 8.22547 0.669379 0.334690 0.942328i 0.391368π-0.391368\pi
0.334690 + 0.942328i 0.391368π0.391368\pi
152152 0.663653 0.0538294
153153 0 0
154154 −2.85929 −0.230408
155155 8.26190 0.663612
156156 0 0
157157 12.5598 1.00238 0.501192 0.865336i 0.332895π-0.332895\pi
0.501192 + 0.865336i 0.332895π0.332895\pi
158158 −0.203223 −0.0161675
159159 0 0
160160 −9.80056 −0.774802
161161 1.36501 0.107578
162162 0 0
163163 3.31466 0.259624 0.129812 0.991539i 0.458563π-0.458563\pi
0.129812 + 0.991539i 0.458563π0.458563\pi
164164 6.71554 0.524396
165165 0 0
166166 −1.91682 −0.148774
167167 −20.5630 −1.59121 −0.795606 0.605815i 0.792847π-0.792847\pi
−0.795606 + 0.605815i 0.792847π0.792847\pi
168168 0 0
169169 −12.9997 −0.999975
170170 2.88322 0.221133
171171 0 0
172172 15.1817 1.15759
173173 14.0333 1.06693 0.533465 0.845822i 0.320890π-0.320890\pi
0.533465 + 0.845822i 0.320890π0.320890\pi
174174 0 0
175175 0.122656 0.00927194
176176 −15.6149 −1.17702
177177 0 0
178178 1.40139 0.105039
179179 10.1900 0.761636 0.380818 0.924650i 0.375642π-0.375642\pi
0.380818 + 0.924650i 0.375642π0.375642\pi
180180 0 0
181181 24.0547 1.78797 0.893987 0.448093i 0.147897π-0.147897\pi
0.893987 + 0.448093i 0.147897π0.147897\pi
182182 −0.00990079 −0.000733895 0
183183 0 0
184184 −1.64483 −0.121258
185185 9.80166 0.720633
186186 0 0
187187 16.3381 1.19476
188188 12.9706 0.945981
189189 0 0
190190 −0.384104 −0.0278658
191191 10.9464 0.792052 0.396026 0.918239i 0.370389π-0.370389\pi
0.396026 + 0.918239i 0.370389π0.370389\pi
192192 0 0
193193 −10.8060 −0.777830 −0.388915 0.921274i 0.627150π-0.627150\pi
−0.388915 + 0.921274i 0.627150π0.627150\pi
194194 −4.13030 −0.296538
195195 0 0
196196 9.60946 0.686390
197197 −22.0734 −1.57266 −0.786331 0.617806i 0.788022π-0.788022\pi
−0.786331 + 0.617806i 0.788022π0.788022\pi
198198 0 0
199199 12.8868 0.913518 0.456759 0.889590i 0.349010π-0.349010\pi
0.456759 + 0.889590i 0.349010π0.349010\pi
200200 −0.147801 −0.0104511
201201 0 0
202202 −5.73322 −0.403388
203203 10.3026 0.723103
204204 0 0
205205 −8.14068 −0.568570
206206 −1.89665 −0.132146
207207 0 0
208208 −0.0540694 −0.00374904
209209 −2.17657 −0.150557
210210 0 0
211211 −23.9956 −1.65193 −0.825964 0.563723i 0.809368π-0.809368\pi
−0.825964 + 0.563723i 0.809368π0.809368\pi
212212 2.37665 0.163229
213213 0 0
214214 4.69330 0.320827
215215 −18.4035 −1.25511
216216 0 0
217217 −4.92177 −0.334112
218218 −6.02558 −0.408104
219219 0 0
220220 21.1111 1.42331
221221 0.0565736 0.00380555
222222 0 0
223223 21.6622 1.45061 0.725303 0.688430i 0.241700π-0.241700\pi
0.725303 + 0.688430i 0.241700π0.241700\pi
224224 5.83838 0.390093
225225 0 0
226226 −5.21760 −0.347070
227227 21.6419 1.43642 0.718211 0.695826i 0.244961π-0.244961\pi
0.718211 + 0.695826i 0.244961π0.244961\pi
228228 0 0
229229 −10.8054 −0.714038 −0.357019 0.934097i 0.616207π-0.616207\pi
−0.357019 + 0.934097i 0.616207π0.616207\pi
230230 0.951982 0.0627719
231231 0 0
232232 −12.4147 −0.815062
233233 7.63900 0.500447 0.250224 0.968188i 0.419496π-0.419496\pi
0.250224 + 0.968188i 0.419496π0.419496\pi
234234 0 0
235235 −15.7232 −1.02567
236236 6.76465 0.440341
237237 0 0
238238 −1.71759 −0.111335
239239 −3.23149 −0.209028 −0.104514 0.994523i 0.533329π-0.533329\pi
−0.104514 + 0.994523i 0.533329π0.533329\pi
240240 0 0
241241 −26.5449 −1.70991 −0.854955 0.518702i 0.826415π-0.826415\pi
−0.854955 + 0.518702i 0.826415π0.826415\pi
242242 −6.72979 −0.432608
243243 0 0
244244 −12.6350 −0.808873
245245 −11.6487 −0.744210
246246 0 0
247247 −0.00753676 −0.000479553 0
248248 5.93073 0.376602
249249 0 0
250250 4.68722 0.296446
251251 −4.49930 −0.283993 −0.141997 0.989867i 0.545352π-0.545352\pi
−0.141997 + 0.989867i 0.545352π0.545352\pi
252252 0 0
253253 5.39452 0.339150
254254 3.48783 0.218846
255255 0 0
256256 3.90761 0.244226
257257 13.7354 0.856792 0.428396 0.903591i 0.359079π-0.359079\pi
0.428396 + 0.903591i 0.359079π0.359079\pi
258258 0 0
259259 −5.83904 −0.362820
260260 0.0731010 0.00453353
261261 0 0
262262 6.45423 0.398743
263263 −24.2026 −1.49239 −0.746197 0.665725i 0.768122π-0.768122\pi
−0.746197 + 0.665725i 0.768122π0.768122\pi
264264 0 0
265265 −2.88101 −0.176979
266266 0.228818 0.0140297
267267 0 0
268268 20.1502 1.23087
269269 12.0062 0.732032 0.366016 0.930609i 0.380722π-0.380722\pi
0.366016 + 0.930609i 0.380722π0.380722\pi
270270 0 0
271271 3.71777 0.225839 0.112919 0.993604i 0.463980π-0.463980\pi
0.112919 + 0.993604i 0.463980π0.463980\pi
272272 −9.37997 −0.568744
273273 0 0
274274 −4.98867 −0.301376
275275 0.484739 0.0292308
276276 0 0
277277 −23.4831 −1.41096 −0.705482 0.708728i 0.749269π-0.749269\pi
−0.705482 + 0.708728i 0.749269π0.749269\pi
278278 −2.55309 −0.153124
279279 0 0
280280 −4.64837 −0.277793
281281 −20.3717 −1.21528 −0.607638 0.794214i 0.707883π-0.707883\pi
−0.607638 + 0.794214i 0.707883π0.707883\pi
282282 0 0
283283 11.5999 0.689545 0.344772 0.938686i 0.387956π-0.387956\pi
0.344772 + 0.938686i 0.387956π0.387956\pi
284284 11.1183 0.659752
285285 0 0
286286 −0.0391280 −0.00231369
287287 4.84956 0.286260
288288 0 0
289289 −7.18559 −0.422682
290290 7.18526 0.421933
291291 0 0
292292 0.999532 0.0584932
293293 31.5742 1.84458 0.922291 0.386496i 0.126315π-0.126315\pi
0.922291 + 0.386496i 0.126315π0.126315\pi
294294 0 0
295295 −8.20020 −0.477434
296296 7.03603 0.408961
297297 0 0
298298 −0.366782 −0.0212471
299299 0.0186795 0.00108026
300300 0 0
301301 10.9633 0.631915
302302 −3.41741 −0.196650
303303 0 0
304304 1.24960 0.0716697
305305 15.3163 0.877010
306306 0 0
307307 −8.12054 −0.463464 −0.231732 0.972780i 0.574439π-0.574439\pi
−0.231732 + 0.972780i 0.574439π0.574439\pi
308308 −12.5763 −0.716601
309309 0 0
310310 −3.43254 −0.194955
311311 −23.8486 −1.35233 −0.676164 0.736751i 0.736359π-0.736359\pi
−0.676164 + 0.736751i 0.736359π0.736359\pi
312312 0 0
313313 26.9105 1.52107 0.760535 0.649297i 0.224937π-0.224937\pi
0.760535 + 0.649297i 0.224937π0.224937\pi
314314 −5.21818 −0.294479
315315 0 0
316316 −0.893856 −0.0502833
317317 −8.33233 −0.467990 −0.233995 0.972238i 0.575180π-0.575180\pi
−0.233995 + 0.972238i 0.575180π0.575180\pi
318318 0 0
319319 40.7161 2.27967
320320 −9.19328 −0.513920
321321 0 0
322322 −0.567114 −0.0316040
323323 −1.30748 −0.0727501
324324 0 0
325325 0.00167849 9.31061e−5 0
326326 −1.37713 −0.0762721
327327 0 0
328328 −5.84371 −0.322665
329329 9.36661 0.516398
330330 0 0
331331 −6.42026 −0.352889 −0.176445 0.984311i 0.556460π-0.556460\pi
−0.176445 + 0.984311i 0.556460π0.556460\pi
332332 −8.43096 −0.462709
333333 0 0
334334 8.54322 0.467464
335335 −24.4264 −1.33456
336336 0 0
337337 7.47489 0.407183 0.203592 0.979056i 0.434739π-0.434739\pi
0.203592 + 0.979056i 0.434739π0.434739\pi
338338 5.40093 0.293772
339339 0 0
340340 12.6816 0.687755
341341 −19.4509 −1.05333
342342 0 0
343343 16.1768 0.873464
344344 −13.2108 −0.712277
345345 0 0
346346 −5.83035 −0.313442
347347 −31.4545 −1.68857 −0.844283 0.535898i 0.819973π-0.819973\pi
−0.844283 + 0.535898i 0.819973π0.819973\pi
348348 0 0
349349 11.8529 0.634474 0.317237 0.948346i 0.397245π-0.397245\pi
0.317237 + 0.948346i 0.397245π0.397245\pi
350350 −0.0509595 −0.00272390
351351 0 0
352352 23.0733 1.22981
353353 −8.20708 −0.436819 −0.218409 0.975857i 0.570087π-0.570087\pi
−0.218409 + 0.975857i 0.570087π0.570087\pi
354354 0 0
355355 −13.4778 −0.715328
356356 6.16390 0.326686
357357 0 0
358358 −4.23360 −0.223753
359359 17.7273 0.935611 0.467806 0.883831i 0.345045π-0.345045\pi
0.467806 + 0.883831i 0.345045π0.345045\pi
360360 0 0
361361 −18.8258 −0.990832
362362 −9.99393 −0.525269
363363 0 0
364364 −0.0435477 −0.00228252
365365 −1.21165 −0.0634205
366366 0 0
367367 −20.3195 −1.06067 −0.530335 0.847788i 0.677934π-0.677934\pi
−0.530335 + 0.847788i 0.677934π0.677934\pi
368368 −3.09708 −0.161446
369369 0 0
370370 −4.07226 −0.211707
371371 1.71628 0.0891046
372372 0 0
373373 −9.68144 −0.501286 −0.250643 0.968080i 0.580642π-0.580642\pi
−0.250643 + 0.968080i 0.580642π0.580642\pi
374374 −6.78793 −0.350996
375375 0 0
376376 −11.2867 −0.582069
377377 0.140987 0.00726119
378378 0 0
379379 −4.12905 −0.212095 −0.106048 0.994361i 0.533820π-0.533820\pi
−0.106048 + 0.994361i 0.533820π0.533820\pi
380380 −1.68944 −0.0866667
381381 0 0
382382 −4.54785 −0.232688
383383 4.75018 0.242723 0.121362 0.992608i 0.461274π-0.461274\pi
0.121362 + 0.992608i 0.461274π0.461274\pi
384384 0 0
385385 15.2452 0.776966
386386 4.48951 0.228510
387387 0 0
388388 −18.1667 −0.922275
389389 −21.8133 −1.10598 −0.552990 0.833188i 0.686513π-0.686513\pi
−0.552990 + 0.833188i 0.686513π0.686513\pi
390390 0 0
391391 3.24052 0.163880
392392 −8.36193 −0.422341
393393 0 0
394394 9.17074 0.462015
395395 1.08355 0.0545191
396396 0 0
397397 −34.8490 −1.74902 −0.874512 0.485005i 0.838818π-0.838818\pi
−0.874512 + 0.485005i 0.838818π0.838818\pi
398398 −5.35401 −0.268373
399399 0 0
400400 −0.278296 −0.0139148
401401 −18.8261 −0.940130 −0.470065 0.882632i 0.655769π-0.655769\pi
−0.470065 + 0.882632i 0.655769π0.655769\pi
402402 0 0
403403 −0.0673522 −0.00335505
404404 −25.2170 −1.25459
405405 0 0
406406 −4.28040 −0.212433
407407 −23.0759 −1.14383
408408 0 0
409409 −6.35996 −0.314480 −0.157240 0.987560i 0.550260π-0.550260\pi
−0.157240 + 0.987560i 0.550260π0.550260\pi
410410 3.38218 0.167034
411411 0 0
412412 −8.34224 −0.410993
413413 4.88502 0.240376
414414 0 0
415415 10.2201 0.501687
416416 0.0798955 0.00391720
417417 0 0
418418 0.904291 0.0442303
419419 −24.3180 −1.18801 −0.594005 0.804461i 0.702454π-0.702454\pi
−0.594005 + 0.804461i 0.702454π0.702454\pi
420420 0 0
421421 −7.99004 −0.389411 −0.194705 0.980862i 0.562375π-0.562375\pi
−0.194705 + 0.980862i 0.562375π0.562375\pi
422422 9.96937 0.485302
423423 0 0
424424 −2.06811 −0.100436
425425 0.291185 0.0141246
426426 0 0
427427 −9.12423 −0.441552
428428 20.6430 0.997818
429429 0 0
430430 7.64603 0.368724
431431 9.87124 0.475481 0.237740 0.971329i 0.423593π-0.423593\pi
0.237740 + 0.971329i 0.423593π0.423593\pi
432432 0 0
433433 −6.10369 −0.293325 −0.146662 0.989187i 0.546853π-0.546853\pi
−0.146662 + 0.989187i 0.546853π0.546853\pi
434434 2.04483 0.0981550
435435 0 0
436436 −26.5029 −1.26926
437437 −0.431704 −0.0206512
438438 0 0
439439 −15.1340 −0.722308 −0.361154 0.932506i 0.617617π-0.617617\pi
−0.361154 + 0.932506i 0.617617π0.617617\pi
440440 −18.3704 −0.875774
441441 0 0
442442 −0.0235044 −0.00111799
443443 −0.722793 −0.0343410 −0.0171705 0.999853i 0.505466π-0.505466\pi
−0.0171705 + 0.999853i 0.505466π0.505466\pi
444444 0 0
445445 −7.47197 −0.354205
446446 −8.99990 −0.426158
447447 0 0
448448 5.47661 0.258746
449449 1.66845 0.0787389 0.0393695 0.999225i 0.487465π-0.487465\pi
0.0393695 + 0.999225i 0.487465π0.487465\pi
450450 0 0
451451 19.1655 0.902468
452452 −22.9491 −1.07944
453453 0 0
454454 −8.99147 −0.421991
455455 0.0527891 0.00247479
456456 0 0
457457 11.0834 0.518462 0.259231 0.965815i 0.416531π-0.416531\pi
0.259231 + 0.965815i 0.416531π0.416531\pi
458458 4.48926 0.209769
459459 0 0
460460 4.18720 0.195229
461461 −21.8844 −1.01926 −0.509629 0.860394i 0.670217π-0.670217\pi
−0.509629 + 0.860394i 0.670217π0.670217\pi
462462 0 0
463463 24.8517 1.15496 0.577479 0.816406i 0.304037π-0.304037\pi
0.577479 + 0.816406i 0.304037π0.304037\pi
464464 −23.3758 −1.08519
465465 0 0
466466 −3.17375 −0.147021
467467 −11.8355 −0.547683 −0.273842 0.961775i 0.588294π-0.588294\pi
−0.273842 + 0.961775i 0.588294π0.588294\pi
468468 0 0
469469 14.5513 0.671916
470470 6.53246 0.301320
471471 0 0
472472 −5.88644 −0.270945
473473 43.3271 1.99218
474474 0 0
475475 −0.0387919 −0.00177989
476476 −7.55465 −0.346267
477477 0 0
478478 1.34258 0.0614080
479479 2.88735 0.131926 0.0659632 0.997822i 0.478988π-0.478988\pi
0.0659632 + 0.997822i 0.478988π0.478988\pi
480480 0 0
481481 −0.0799046 −0.00364333
482482 11.0285 0.502336
483483 0 0
484484 −29.6003 −1.34547
485485 22.0220 0.999966
486486 0 0
487487 8.75903 0.396910 0.198455 0.980110i 0.436408π-0.436408\pi
0.198455 + 0.980110i 0.436408π0.436408\pi
488488 10.9947 0.497706
489489 0 0
490490 4.83966 0.218633
491491 −22.5730 −1.01871 −0.509354 0.860557i 0.670115π-0.670115\pi
−0.509354 + 0.860557i 0.670115π0.670115\pi
492492 0 0
493493 24.4584 1.10155
494494 0.00313127 0.000140883 0
495495 0 0
496496 11.1671 0.501416
497497 8.02899 0.360149
498498 0 0
499499 −25.3328 −1.13405 −0.567026 0.823700i 0.691906π-0.691906\pi
−0.567026 + 0.823700i 0.691906π0.691906\pi
500500 20.6163 0.921988
501501 0 0
502502 1.86931 0.0834312
503503 3.74414 0.166943 0.0834714 0.996510i 0.473399π-0.473399\pi
0.0834714 + 0.996510i 0.473399π0.473399\pi
504504 0 0
505505 30.5684 1.36028
506506 −2.24124 −0.0996353
507507 0 0
508508 15.3409 0.680642
509509 24.3499 1.07929 0.539645 0.841893i 0.318559π-0.318559\pi
0.539645 + 0.841893i 0.318559π0.318559\pi
510510 0 0
511511 0.721801 0.0319306
512512 −22.7690 −1.00626
513513 0 0
514514 −5.70660 −0.251707
515515 10.1126 0.445614
516516 0 0
517517 37.0169 1.62800
518518 2.42592 0.106589
519519 0 0
520520 −0.0636108 −0.00278952
521521 19.6209 0.859608 0.429804 0.902922i 0.358583π-0.358583\pi
0.429804 + 0.902922i 0.358583π0.358583\pi
522522 0 0
523523 20.8154 0.910194 0.455097 0.890442i 0.349605π-0.349605\pi
0.455097 + 0.890442i 0.349605π0.349605\pi
524524 28.3883 1.24015
525525 0 0
526526 10.0553 0.438434
527527 −11.6843 −0.508975
528528 0 0
529529 −21.9300 −0.953480
530530 1.19696 0.0519928
531531 0 0
532532 1.00643 0.0436345
533533 0.0663640 0.00287454
534534 0 0
535535 −25.0238 −1.08187
536536 −17.5343 −0.757365
537537 0 0
538538 −4.98818 −0.215056
539539 27.4245 1.18126
540540 0 0
541541 −30.6272 −1.31676 −0.658382 0.752684i 0.728759π-0.728759\pi
−0.658382 + 0.752684i 0.728759π0.728759\pi
542542 −1.54461 −0.0663467
543543 0 0
544544 13.8603 0.594255
545545 32.1273 1.37618
546546 0 0
547547 22.6477 0.968345 0.484172 0.874973i 0.339121π-0.339121\pi
0.484172 + 0.874973i 0.339121π0.339121\pi
548548 −21.9422 −0.937323
549549 0 0
550550 −0.201393 −0.00858741
551551 −3.25836 −0.138811
552552 0 0
553553 −0.645489 −0.0274490
554554 9.75644 0.414512
555555 0 0
556556 −11.2295 −0.476237
557557 36.4518 1.54451 0.772256 0.635311i 0.219128π-0.219128\pi
0.772256 + 0.635311i 0.219128π0.219128\pi
558558 0 0
559559 0.150028 0.00634550
560560 −8.75249 −0.369860
561561 0 0
562562 8.46377 0.357023
563563 26.5162 1.11753 0.558763 0.829327i 0.311276π-0.311276\pi
0.558763 + 0.829327i 0.311276π0.311276\pi
564564 0 0
565565 27.8193 1.17037
566566 −4.81938 −0.202574
567567 0 0
568568 −9.67492 −0.405950
569569 22.9674 0.962844 0.481422 0.876489i 0.340121π-0.340121\pi
0.481422 + 0.876489i 0.340121π0.340121\pi
570570 0 0
571571 −4.79801 −0.200790 −0.100395 0.994948i 0.532011π-0.532011\pi
−0.100395 + 0.994948i 0.532011π0.532011\pi
572572 −0.172101 −0.00719589
573573 0 0
574574 −2.01483 −0.0840973
575575 0.0961436 0.00400947
576576 0 0
577577 −4.31333 −0.179566 −0.0897831 0.995961i 0.528617π-0.528617\pi
−0.0897831 + 0.995961i 0.528617π0.528617\pi
578578 2.98537 0.124175
579579 0 0
580580 31.6037 1.31227
581581 −6.08833 −0.252587
582582 0 0
583583 6.78274 0.280912
584584 −0.869769 −0.0359913
585585 0 0
586586 −13.1180 −0.541899
587587 41.8222 1.72619 0.863094 0.505044i 0.168524π-0.168524\pi
0.863094 + 0.505044i 0.168524π0.168524\pi
588588 0 0
589589 1.55658 0.0641379
590590 3.40691 0.140260
591591 0 0
592592 13.2483 0.544500
593593 −31.5370 −1.29507 −0.647536 0.762035i 0.724200π-0.724200\pi
−0.647536 + 0.762035i 0.724200π0.724200\pi
594594 0 0
595595 9.15786 0.375436
596596 −1.61326 −0.0660815
597597 0 0
598598 −0.00776070 −0.000317358 0
599599 −12.6303 −0.516060 −0.258030 0.966137i 0.583073π-0.583073\pi
−0.258030 + 0.966137i 0.583073π0.583073\pi
600600 0 0
601601 20.5430 0.837965 0.418983 0.907994i 0.362387π-0.362387\pi
0.418983 + 0.907994i 0.362387π0.362387\pi
602602 −4.55489 −0.185643
603603 0 0
604604 −15.0311 −0.611608
605605 35.8820 1.45881
606606 0 0
607607 12.9126 0.524105 0.262052 0.965054i 0.415601π-0.415601\pi
0.262052 + 0.965054i 0.415601π0.415601\pi
608608 −1.84647 −0.0748844
609609 0 0
610610 −6.36342 −0.257647
611611 0.128178 0.00518552
612612 0 0
613613 −31.1598 −1.25853 −0.629265 0.777191i 0.716644π-0.716644\pi
−0.629265 + 0.777191i 0.716644π0.716644\pi
614614 3.37381 0.136156
615615 0 0
616616 10.9436 0.440930
617617 −7.14078 −0.287477 −0.143739 0.989616i 0.545912π-0.545912\pi
−0.143739 + 0.989616i 0.545912π0.545912\pi
618618 0 0
619619 −10.0309 −0.403176 −0.201588 0.979470i 0.564610π-0.564610\pi
−0.201588 + 0.979470i 0.564610π0.564610\pi
620620 −15.0977 −0.606338
621621 0 0
622622 9.90827 0.397285
623623 4.45119 0.178333
624624 0 0
625625 −24.5266 −0.981065
626626 −11.1804 −0.446858
627627 0 0
628628 −22.9517 −0.915871
629629 −13.8619 −0.552708
630630 0 0
631631 −7.07560 −0.281675 −0.140838 0.990033i 0.544980π-0.544980\pi
−0.140838 + 0.990033i 0.544980π0.544980\pi
632632 0.777813 0.0309397
633633 0 0
634634 3.46180 0.137486
635635 −18.5965 −0.737978
636636 0 0
637637 0.0949621 0.00376254
638638 −16.9162 −0.669718
639639 0 0
640640 23.4206 0.925781
641641 −5.01121 −0.197931 −0.0989655 0.995091i 0.531553π-0.531553\pi
−0.0989655 + 0.995091i 0.531553π0.531553\pi
642642 0 0
643643 1.63840 0.0646123 0.0323062 0.999478i 0.489715π-0.489715\pi
0.0323062 + 0.999478i 0.489715π0.489715\pi
644644 −2.49440 −0.0982930
645645 0 0
646646 0.543213 0.0213724
647647 34.4927 1.35605 0.678024 0.735040i 0.262836π-0.262836\pi
0.678024 + 0.735040i 0.262836π0.262836\pi
648648 0 0
649649 19.3056 0.757813
650650 −0.000697358 0 −2.73526e−5 0
651651 0 0
652652 −6.05717 −0.237217
653653 38.7606 1.51682 0.758410 0.651778i 0.225977π-0.225977\pi
0.758410 + 0.651778i 0.225977π0.225977\pi
654654 0 0
655655 −34.4127 −1.34462
656656 −11.0032 −0.429604
657657 0 0
658658 −3.89151 −0.151707
659659 9.39192 0.365857 0.182929 0.983126i 0.441442π-0.441442\pi
0.182929 + 0.983126i 0.441442π0.441442\pi
660660 0 0
661661 −24.1474 −0.939226 −0.469613 0.882872i 0.655607π-0.655607\pi
−0.469613 + 0.882872i 0.655607π0.655607\pi
662662 2.66740 0.103671
663663 0 0
664664 7.33643 0.284709
665665 −1.22001 −0.0473101
666666 0 0
667667 8.07569 0.312692
668668 37.5765 1.45388
669669 0 0
670670 10.1483 0.392065
671671 −36.0590 −1.39204
672672 0 0
673673 −26.4661 −1.02019 −0.510097 0.860117i 0.670391π-0.670391\pi
−0.510097 + 0.860117i 0.670391π0.670391\pi
674674 −3.10557 −0.119622
675675 0 0
676676 23.7554 0.913671
677677 31.0668 1.19400 0.596998 0.802243i 0.296360π-0.296360\pi
0.596998 + 0.802243i 0.296360π0.296360\pi
678678 0 0
679679 −13.1189 −0.503457
680680 −11.0352 −0.423181
681681 0 0
682682 8.08119 0.309445
683683 38.1361 1.45924 0.729619 0.683854i 0.239697π-0.239697\pi
0.729619 + 0.683854i 0.239697π0.239697\pi
684684 0 0
685685 26.5986 1.01628
686686 −6.72090 −0.256605
687687 0 0
688688 −24.8748 −0.948342
689689 0.0234864 0.000894762 0
690690 0 0
691691 32.9295 1.25270 0.626349 0.779543i 0.284548π-0.284548\pi
0.626349 + 0.779543i 0.284548π0.284548\pi
692692 −25.6442 −0.974847
693693 0 0
694694 13.0683 0.496065
695695 13.6126 0.516355
696696 0 0
697697 11.5128 0.436080
698698 −4.92450 −0.186395
699699 0 0
700700 −0.224140 −0.00847171
701701 −2.30710 −0.0871381 −0.0435690 0.999050i 0.513873π-0.513873\pi
−0.0435690 + 0.999050i 0.513873π0.513873\pi
702702 0 0
703703 1.84668 0.0696490
704704 21.6436 0.815725
705705 0 0
706706 3.40977 0.128328
707707 −18.2102 −0.684865
708708 0 0
709709 −11.1521 −0.418825 −0.209412 0.977827i 0.567155π-0.567155\pi
−0.209412 + 0.977827i 0.567155π0.567155\pi
710710 5.59958 0.210148
711711 0 0
712712 −5.36368 −0.201012
713713 −3.85791 −0.144480
714714 0 0
715715 0.208623 0.00780206
716716 −18.6211 −0.695902
717717 0 0
718718 −7.36510 −0.274863
719719 −32.1700 −1.19974 −0.599869 0.800098i 0.704781π-0.704781\pi
−0.599869 + 0.800098i 0.704781π0.704781\pi
720720 0 0
721721 −6.02426 −0.224355
722722 7.82149 0.291086
723723 0 0
724724 −43.9573 −1.63366
725725 0.725662 0.0269504
726726 0 0
727727 −5.36551 −0.198996 −0.0994979 0.995038i 0.531724π-0.531724\pi
−0.0994979 + 0.995038i 0.531724π0.531724\pi
728728 0.0378942 0.00140445
729729 0 0
730730 0.503399 0.0186316
731731 26.0269 0.962638
732732 0 0
733733 −14.5964 −0.539129 −0.269564 0.962982i 0.586880π-0.586880\pi
−0.269564 + 0.962982i 0.586880π0.586880\pi
734734 8.44208 0.311603
735735 0 0
736736 4.57639 0.168688
737737 57.5068 2.11829
738738 0 0
739739 −43.2165 −1.58975 −0.794873 0.606776i 0.792463π-0.792463\pi
−0.794873 + 0.606776i 0.792463π0.792463\pi
740740 −17.9114 −0.658438
741741 0 0
742742 −0.713055 −0.0261771
743743 8.11221 0.297608 0.148804 0.988867i 0.452458π-0.452458\pi
0.148804 + 0.988867i 0.452458π0.452458\pi
744744 0 0
745745 1.95561 0.0716481
746746 4.02231 0.147267
747747 0 0
748748 −29.8561 −1.09165
749749 14.9071 0.544695
750750 0 0
751751 8.75545 0.319491 0.159746 0.987158i 0.448933π-0.448933\pi
0.159746 + 0.987158i 0.448933π0.448933\pi
752752 −21.2520 −0.774981
753753 0 0
754754 −0.0585753 −0.00213319
755755 18.2210 0.663129
756756 0 0
757757 −32.1511 −1.16855 −0.584276 0.811555i 0.698622π-0.698622\pi
−0.584276 + 0.811555i 0.698622π0.698622\pi
758758 1.71548 0.0623091
759759 0 0
760760 1.47012 0.0533267
761761 −24.5459 −0.889789 −0.444894 0.895583i 0.646759π-0.646759\pi
−0.444894 + 0.895583i 0.646759π0.646759\pi
762762 0 0
763763 −19.1388 −0.692872
764764 −20.0033 −0.723693
765765 0 0
766766 −1.97354 −0.0713069
767767 0.0668492 0.00241379
768768 0 0
769769 31.4144 1.13283 0.566416 0.824119i 0.308330π-0.308330\pi
0.566416 + 0.824119i 0.308330π0.308330\pi
770770 −6.33385 −0.228256
771771 0 0
772772 19.7467 0.710699
773773 28.7145 1.03279 0.516395 0.856351i 0.327274π-0.327274\pi
0.516395 + 0.856351i 0.327274π0.327274\pi
774774 0 0
775775 −0.346663 −0.0124525
776776 15.8083 0.567483
777777 0 0
778778 9.06270 0.324913
779779 −1.53374 −0.0549521
780780 0 0
781781 31.7306 1.13541
782782 −1.34633 −0.0481446
783783 0 0
784784 −15.7448 −0.562315
785785 27.8224 0.993022
786786 0 0
787787 −38.8160 −1.38364 −0.691821 0.722069i 0.743191π-0.743191\pi
−0.691821 + 0.722069i 0.743191π0.743191\pi
788788 40.3366 1.43693
789789 0 0
790790 −0.450177 −0.0160166
791791 −16.5725 −0.589249
792792 0 0
793793 −0.124861 −0.00443394
794794 14.4786 0.513826
795795 0 0
796796 −23.5491 −0.834676
797797 −4.03410 −0.142895 −0.0714476 0.997444i 0.522762π-0.522762\pi
−0.0714476 + 0.997444i 0.522762π0.522762\pi
798798 0 0
799799 22.2363 0.786664
800800 0.411224 0.0145390
801801 0 0
802802 7.82160 0.276190
803803 2.85257 0.100665
804804 0 0
805805 3.02374 0.106573
806806 0.0279826 0.000985644 0
807807 0 0
808808 21.9433 0.771961
809809 −29.9454 −1.05283 −0.526413 0.850229i 0.676463π-0.676463\pi
−0.526413 + 0.850229i 0.676463π0.676463\pi
810810 0 0
811811 20.2173 0.709927 0.354963 0.934880i 0.384493π-0.384493\pi
0.354963 + 0.934880i 0.384493π0.384493\pi
812812 −18.8269 −0.660695
813813 0 0
814814 9.58727 0.336034
815815 7.34259 0.257200
816816 0 0
817817 −3.46731 −0.121306
818818 2.64235 0.0923875
819819 0 0
820820 14.8762 0.519499
821821 26.8736 0.937896 0.468948 0.883226i 0.344633π-0.344633\pi
0.468948 + 0.883226i 0.344633π0.344633\pi
822822 0 0
823823 23.0543 0.803623 0.401812 0.915722i 0.368381π-0.368381\pi
0.401812 + 0.915722i 0.368381π0.368381\pi
824824 7.25923 0.252887
825825 0 0
826826 −2.02956 −0.0706174
827827 −5.10953 −0.177676 −0.0888378 0.996046i 0.528315π-0.528315\pi
−0.0888378 + 0.996046i 0.528315π0.528315\pi
828828 0 0
829829 −30.5982 −1.06272 −0.531360 0.847146i 0.678319π-0.678319\pi
−0.531360 + 0.847146i 0.678319π0.678319\pi
830830 −4.24612 −0.147385
831831 0 0
832832 0.0749449 0.00259825
833833 16.4741 0.570792
834834 0 0
835835 −45.5508 −1.57635
836836 3.97744 0.137563
837837 0 0
838838 10.1033 0.349013
839839 −56.3087 −1.94399 −0.971996 0.234997i 0.924492π-0.924492\pi
−0.971996 + 0.234997i 0.924492π0.924492\pi
840840 0 0
841841 31.9527 1.10182
842842 3.31959 0.114401
843843 0 0
844844 43.8493 1.50936
845845 −28.7967 −0.990637
846846 0 0
847847 −21.3756 −0.734474
848848 −3.89408 −0.133723
849849 0 0
850850 −0.120978 −0.00414950
851851 −4.57691 −0.156894
852852 0 0
853853 −45.5450 −1.55943 −0.779715 0.626134i 0.784636π-0.784636\pi
−0.779715 + 0.626134i 0.784636π0.784636\pi
854854 3.79081 0.129719
855855 0 0
856856 −17.9631 −0.613966
857857 −17.4892 −0.597419 −0.298709 0.954344i 0.596556π-0.596556\pi
−0.298709 + 0.954344i 0.596556π0.596556\pi
858858 0 0
859859 18.3460 0.625958 0.312979 0.949760i 0.398673π-0.398673\pi
0.312979 + 0.949760i 0.398673π0.398673\pi
860860 33.6303 1.14678
861861 0 0
862862 −4.10117 −0.139686
863863 4.65373 0.158415 0.0792073 0.996858i 0.474761π-0.474761\pi
0.0792073 + 0.996858i 0.474761π0.474761\pi
864864 0 0
865865 31.0863 1.05697
866866 2.53588 0.0861726
867867 0 0
868868 8.99399 0.305276
869869 −2.55098 −0.0865360
870870 0 0
871871 0.199128 0.00674718
872872 23.0622 0.780986
873873 0 0
874874 0.179358 0.00606688
875875 14.8878 0.503301
876876 0 0
877877 −3.66710 −0.123829 −0.0619145 0.998081i 0.519721π-0.519721\pi
−0.0619145 + 0.998081i 0.519721π0.519721\pi
878878 6.28768 0.212199
879879 0 0
880880 −34.5899 −1.16603
881881 38.3008 1.29039 0.645193 0.764020i 0.276777π-0.276777\pi
0.645193 + 0.764020i 0.276777π0.276777\pi
882882 0 0
883883 22.6142 0.761027 0.380513 0.924775i 0.375747π-0.375747\pi
0.380513 + 0.924775i 0.375747π0.375747\pi
884884 −0.103382 −0.00347711
885885 0 0
886886 0.300296 0.0100887
887887 −1.89656 −0.0636802 −0.0318401 0.999493i 0.510137π-0.510137\pi
−0.0318401 + 0.999493i 0.510137π0.510137\pi
888888 0 0
889889 11.0783 0.371553
890890 3.10435 0.104058
891891 0 0
892892 −39.5852 −1.32541
893893 −2.96233 −0.0991306
894894 0 0
895895 22.5727 0.754523
896896 −13.9521 −0.466107
897897 0 0
898898 −0.693184 −0.0231318
899899 −29.1183 −0.971150
900900 0 0
901901 4.07443 0.135739
902902 −7.96262 −0.265126
903903 0 0
904904 19.9698 0.664185
905905 53.2857 1.77128
906906 0 0
907907 6.53094 0.216856 0.108428 0.994104i 0.465418π-0.465418\pi
0.108428 + 0.994104i 0.465418π0.465418\pi
908908 −39.5481 −1.31245
909909 0 0
910910 −0.0219321 −0.000727042 0
911911 −43.0371 −1.42588 −0.712942 0.701223i 0.752638π-0.752638\pi
−0.712942 + 0.701223i 0.752638π0.752638\pi
912912 0 0
913913 −24.0612 −0.796308
914914 −4.60480 −0.152313
915915 0 0
916916 19.7456 0.652412
917917 20.5003 0.676980
918918 0 0
919919 −16.7911 −0.553887 −0.276943 0.960886i 0.589321π-0.589321\pi
−0.276943 + 0.960886i 0.589321π0.589321\pi
920920 −3.64361 −0.120126
921921 0 0
922922 9.09222 0.299436
923923 0.109873 0.00361652
924924 0 0
925925 −0.411270 −0.0135225
926926 −10.3251 −0.339302
927927 0 0
928928 34.5412 1.13387
929929 −11.6000 −0.380584 −0.190292 0.981728i 0.560943π-0.560943\pi
−0.190292 + 0.981728i 0.560943π0.560943\pi
930930 0 0
931931 −2.19468 −0.0719277
932932 −13.9594 −0.457256
933933 0 0
934934 4.91727 0.160898
935935 36.1920 1.18360
936936 0 0
937937 47.7953 1.56140 0.780702 0.624904i 0.214862π-0.214862\pi
0.780702 + 0.624904i 0.214862π0.214862\pi
938938 −6.04557 −0.197395
939939 0 0
940940 28.7324 0.937147
941941 11.2604 0.367077 0.183538 0.983013i 0.441245π-0.441245\pi
0.183538 + 0.983013i 0.441245π0.441245\pi
942942 0 0
943943 3.80131 0.123788
944944 −11.0837 −0.360743
945945 0 0
946946 −18.0010 −0.585261
947947 7.33189 0.238255 0.119127 0.992879i 0.461990π-0.461990\pi
0.119127 + 0.992879i 0.461990π0.461990\pi
948948 0 0
949949 0.00987752 0.000320638 0
950950 0.0161167 0.000522895 0
951951 0 0
952952 6.57388 0.213061
953953 −24.8753 −0.805791 −0.402895 0.915246i 0.631996π-0.631996\pi
−0.402895 + 0.915246i 0.631996π0.631996\pi
954954 0 0
955955 24.2483 0.784655
956956 5.90519 0.190987
957957 0 0
958958 −1.19960 −0.0387572
959959 −15.8453 −0.511672
960960 0 0
961961 −17.0896 −0.551277
962962 0.0331976 0.00107034
963963 0 0
964964 48.5079 1.56233
965965 −23.9372 −0.770567
966966 0 0
967967 −34.0300 −1.09433 −0.547165 0.837025i 0.684293π-0.684293\pi
−0.547165 + 0.837025i 0.684293π0.684293\pi
968968 25.7575 0.827878
969969 0 0
970970 −9.14938 −0.293769
971971 −34.2476 −1.09906 −0.549530 0.835474i 0.685193π-0.685193\pi
−0.549530 + 0.835474i 0.685193π0.685193\pi
972972 0 0
973973 −8.10928 −0.259971
974974 −3.63908 −0.116604
975975 0 0
976976 20.7021 0.662657
977977 −23.4173 −0.749186 −0.374593 0.927189i 0.622218π-0.622218\pi
−0.374593 + 0.927189i 0.622218π0.622218\pi
978978 0 0
979979 17.5912 0.562216
980980 21.2868 0.679980
981981 0 0
982982 9.37834 0.299275
983983 −33.2031 −1.05902 −0.529508 0.848305i 0.677623π-0.677623\pi
−0.529508 + 0.848305i 0.677623π0.677623\pi
984984 0 0
985985 −48.8966 −1.55798
986986 −10.1617 −0.323613
987987 0 0
988988 0.0137726 0.000438165 0
989989 8.59355 0.273259
990990 0 0
991991 −28.1806 −0.895187 −0.447594 0.894237i 0.647719π-0.647719\pi
−0.447594 + 0.894237i 0.647719π0.647719\pi
992992 −16.5010 −0.523907
993993 0 0
994994 −3.33577 −0.105804
995995 28.5466 0.904988
996996 0 0
997997 −44.9507 −1.42360 −0.711802 0.702381i 0.752120π-0.752120\pi
−0.711802 + 0.702381i 0.752120π0.752120\pi
998998 10.5249 0.333161
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 729.2.a.a.1.4 6
3.2 odd 2 729.2.a.d.1.3 6
9.2 odd 6 729.2.c.b.244.4 12
9.4 even 3 729.2.c.e.487.3 12
9.5 odd 6 729.2.c.b.487.4 12
9.7 even 3 729.2.c.e.244.3 12
27.2 odd 18 243.2.e.b.190.2 12
27.4 even 9 27.2.e.a.16.2 12
27.5 odd 18 243.2.e.a.217.1 12
27.7 even 9 27.2.e.a.22.2 yes 12
27.11 odd 18 243.2.e.a.28.1 12
27.13 even 9 243.2.e.c.55.1 12
27.14 odd 18 243.2.e.b.55.2 12
27.16 even 9 243.2.e.d.28.2 12
27.20 odd 18 81.2.e.a.37.1 12
27.22 even 9 243.2.e.d.217.2 12
27.23 odd 18 81.2.e.a.46.1 12
27.25 even 9 243.2.e.c.190.1 12
108.7 odd 18 432.2.u.c.49.1 12
108.31 odd 18 432.2.u.c.97.1 12
135.4 even 18 675.2.l.c.151.1 12
135.7 odd 36 675.2.u.b.49.2 24
135.34 even 18 675.2.l.c.76.1 12
135.58 odd 36 675.2.u.b.124.2 24
135.88 odd 36 675.2.u.b.49.3 24
135.112 odd 36 675.2.u.b.124.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.16.2 12 27.4 even 9
27.2.e.a.22.2 yes 12 27.7 even 9
81.2.e.a.37.1 12 27.20 odd 18
81.2.e.a.46.1 12 27.23 odd 18
243.2.e.a.28.1 12 27.11 odd 18
243.2.e.a.217.1 12 27.5 odd 18
243.2.e.b.55.2 12 27.14 odd 18
243.2.e.b.190.2 12 27.2 odd 18
243.2.e.c.55.1 12 27.13 even 9
243.2.e.c.190.1 12 27.25 even 9
243.2.e.d.28.2 12 27.16 even 9
243.2.e.d.217.2 12 27.22 even 9
432.2.u.c.49.1 12 108.7 odd 18
432.2.u.c.97.1 12 108.31 odd 18
675.2.l.c.76.1 12 135.34 even 18
675.2.l.c.151.1 12 135.4 even 18
675.2.u.b.49.2 24 135.7 odd 36
675.2.u.b.49.3 24 135.88 odd 36
675.2.u.b.124.2 24 135.58 odd 36
675.2.u.b.124.3 24 135.112 odd 36
729.2.a.a.1.4 6 1.1 even 1 trivial
729.2.a.d.1.3 6 3.2 odd 2
729.2.c.b.244.4 12 9.2 odd 6
729.2.c.b.487.4 12 9.5 odd 6
729.2.c.e.244.3 12 9.7 even 3
729.2.c.e.487.3 12 9.4 even 3