Properties

Label 1216.2.s.g.31.3
Level 12161216
Weight 22
Character 1216.31
Analytic conductor 9.7109.710
Analytic rank 00
Dimension 1212
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1216,2,Mod(31,1216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1216.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1216=2619 1216 = 2^{6} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1216.s (of order 66, degree 22, 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: 9.709808885799.70980888579
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x126x11+18x1018x9+11x836x7+180x6120x5+31x4++9 x^{12} - 6 x^{11} + 18 x^{10} - 18 x^{9} + 11 x^{8} - 36 x^{7} + 180 x^{6} - 120 x^{5} + 31 x^{4} + \cdots + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 2632 2^{6}\cdot 3^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 31.3
Root 1.649011.64901i1.64901 - 1.64901i of defining polynomial
Character χ\chi == 1216.31
Dual form 1216.2.s.g.863.3

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+(0.121621+0.0702177i)q3+(1.50000+0.866025i)q5+2.00000iq7+(1.49014+2.58100i)q9+(2.130573.69026i)q13+(0.1216210.210653i)q15+(1.99014+3.44702i)q17+(4.313050.630574i)q19+(0.1404350.243241i)q21+(6.409963.70079i)q23+(1.00000+1.73205i)q250.839843iq27+(1.99014+3.44702i)q298.62609q31+(1.732053.00000i)q357.26115q37+0.598416iq39+(6.39172+3.69026i)q41+(6.1667210.6811i)q435.16199iq45+(0.364862+0.210653i)q47+3.00000q49+(0.4840840.279486i)q51+(5.48028+9.49212i)q53+(0.480278+0.379543i)q57+(1.213810.700792i)q59+(1.92131+1.10927i)q61+(5.161992.98028i)q63+7.38053iq65+(1.81951+1.05050i)q67+1.03944q69+(0.9705661.68107i)q71+(2.50000+4.33013i)q730.280871iq75+(2.70262+4.68107i)q79+(4.411457.64085i)q818.62609q83+(5.970423.44702i)q850.558972iq87+(14.5491+8.39993i)q89+(7.38053+4.26115i)q91+(1.049110.605704i)q93+(5.92348+4.68107i)q95+(6.39172+3.69026i)q97+O(q100)q+(-0.121621 + 0.0702177i) q^{3} +(-1.50000 + 0.866025i) q^{5} +2.00000i q^{7} +(-1.49014 + 2.58100i) q^{9} +(2.13057 - 3.69026i) q^{13} +(0.121621 - 0.210653i) q^{15} +(1.99014 + 3.44702i) q^{17} +(4.31305 - 0.630574i) q^{19} +(-0.140435 - 0.243241i) q^{21} +(-6.40996 - 3.70079i) q^{23} +(-1.00000 + 1.73205i) q^{25} -0.839843i q^{27} +(-1.99014 + 3.44702i) q^{29} -8.62609 q^{31} +(-1.73205 - 3.00000i) q^{35} -7.26115 q^{37} +0.598416i q^{39} +(-6.39172 + 3.69026i) q^{41} +(-6.16672 - 10.6811i) q^{43} -5.16199i q^{45} +(0.364862 + 0.210653i) q^{47} +3.00000 q^{49} +(-0.484084 - 0.279486i) q^{51} +(-5.48028 + 9.49212i) q^{53} +(-0.480278 + 0.379543i) q^{57} +(1.21381 - 0.700792i) q^{59} +(1.92131 + 1.10927i) q^{61} +(-5.16199 - 2.98028i) q^{63} +7.38053i q^{65} +(1.81951 + 1.05050i) q^{67} +1.03944 q^{69} +(-0.970566 - 1.68107i) q^{71} +(2.50000 + 4.33013i) q^{73} -0.280871i q^{75} +(2.70262 + 4.68107i) q^{79} +(-4.41145 - 7.64085i) q^{81} -8.62609 q^{83} +(-5.97042 - 3.44702i) q^{85} -0.558972i q^{87} +(14.5491 + 8.39993i) q^{89} +(7.38053 + 4.26115i) q^{91} +(1.04911 - 0.605704i) q^{93} +(-5.92348 + 4.68107i) q^{95} +(-6.39172 + 3.69026i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q18q5+12q92q136q174q2112q25+6q2932q37+6q41+36q496q53+54q57+30q61+132q69+30q7330q81+18q85++6q97+O(q100) 12 q - 18 q^{5} + 12 q^{9} - 2 q^{13} - 6 q^{17} - 4 q^{21} - 12 q^{25} + 6 q^{29} - 32 q^{37} + 6 q^{41} + 36 q^{49} - 6 q^{53} + 54 q^{57} + 30 q^{61} + 132 q^{69} + 30 q^{73} - 30 q^{81} + 18 q^{85}+ \cdots + 6 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1216Z)×\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times.

nn 191191 705705 837837
χ(n)\chi(n) 1-1 e(56)e\left(\frac{5}{6}\right) 1-1

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
33 −0.121621 + 0.0702177i −0.0702177 + 0.0405402i −0.534698 0.845043i 0.679575π-0.679575\pi
0.464480 + 0.885584i 0.346241π0.346241\pi
44 0 0
55 −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i 0.793258π-0.793258\pi
0.125567 + 0.992085i 0.459925π0.459925\pi
66 0 0
77 2.00000i 0.755929i 0.925820 + 0.377964i 0.123376π0.123376\pi
−0.925820 + 0.377964i 0.876624π0.876624\pi
88 0 0
99 −1.49014 + 2.58100i −0.496713 + 0.860332i
1010 0 0
1111 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1212 0 0
1313 2.13057 3.69026i 0.590915 1.02349i −0.403194 0.915114i 0.632100π-0.632100\pi
0.994109 0.108380i 0.0345665π-0.0345665\pi
1414 0 0
1515 0.121621 0.210653i 0.0314023 0.0543904i
1616 0 0
1717 1.99014 + 3.44702i 0.482680 + 0.836026i 0.999802 0.0198857i 0.00633024π-0.00633024\pi
−0.517123 + 0.855911i 0.672997π0.672997\pi
1818 0 0
1919 4.31305 0.630574i 0.989481 0.144664i
2020 0 0
2121 −0.140435 0.243241i −0.0306455 0.0530796i
2222 0 0
2323 −6.40996 3.70079i −1.33657 0.771668i −0.350272 0.936648i 0.613911π-0.613911\pi
−0.986297 + 0.164980i 0.947244π0.947244\pi
2424 0 0
2525 −1.00000 + 1.73205i −0.200000 + 0.346410i
2626 0 0
2727 0.839843i 0.161628i
2828 0 0
2929 −1.99014 + 3.44702i −0.369560 + 0.640096i −0.989497 0.144556i 0.953825π-0.953825\pi
0.619937 + 0.784651i 0.287158π0.287158\pi
3030 0 0
3131 −8.62609 −1.54929 −0.774646 0.632395i 0.782072π-0.782072\pi
−0.774646 + 0.632395i 0.782072π0.782072\pi
3232 0 0
3333 0 0
3434 0 0
3535 −1.73205 3.00000i −0.292770 0.507093i
3636 0 0
3737 −7.26115 −1.19373 −0.596863 0.802343i 0.703586π-0.703586\pi
−0.596863 + 0.802343i 0.703586π0.703586\pi
3838 0 0
3939 0.598416i 0.0958232i
4040 0 0
4141 −6.39172 + 3.69026i −0.998219 + 0.576322i −0.907721 0.419574i 0.862179π-0.862179\pi
−0.0904984 + 0.995897i 0.528846π0.528846\pi
4242 0 0
4343 −6.16672 10.6811i −0.940416 1.62885i −0.764680 0.644411i 0.777103π-0.777103\pi
−0.175736 0.984437i 0.556231π-0.556231\pi
4444 0 0
4545 5.16199i 0.769504i
4646 0 0
4747 0.364862 + 0.210653i 0.0532206 + 0.0307269i 0.526374 0.850253i 0.323551π-0.323551\pi
−0.473154 + 0.880980i 0.656884π0.656884\pi
4848 0 0
4949 3.00000 0.428571
5050 0 0
5151 −0.484084 0.279486i −0.0677853 0.0391359i
5252 0 0
5353 −5.48028 + 9.49212i −0.752774 + 1.30384i 0.193699 + 0.981061i 0.437951π0.437951\pi
−0.946473 + 0.322782i 0.895382π0.895382\pi
5454 0 0
5555 0 0
5656 0 0
5757 −0.480278 + 0.379543i −0.0636144 + 0.0502717i
5858 0 0
5959 1.21381 0.700792i 0.158024 0.0912353i −0.418903 0.908031i 0.637585π-0.637585\pi
0.576927 + 0.816796i 0.304252π0.304252\pi
6060 0 0
6161 1.92131 + 1.10927i 0.245998 + 0.142027i 0.617930 0.786233i 0.287971π-0.287971\pi
−0.371932 + 0.928260i 0.621305π0.621305\pi
6262 0 0
6363 −5.16199 2.98028i −0.650350 0.375480i
6464 0 0
6565 7.38053i 0.915442i
6666 0 0
6767 1.81951 + 1.05050i 0.222289 + 0.128338i 0.607010 0.794695i 0.292369π-0.292369\pi
−0.384721 + 0.923033i 0.625702π0.625702\pi
6868 0 0
6969 1.03944 0.125134
7070 0 0
7171 −0.970566 1.68107i −0.115185 0.199506i 0.802669 0.596425i 0.203413π-0.203413\pi
−0.917854 + 0.396919i 0.870079π0.870079\pi
7272 0 0
7373 2.50000 + 4.33013i 0.292603 + 0.506803i 0.974424 0.224716i 0.0721453π-0.0721453\pi
−0.681822 + 0.731519i 0.738812π0.738812\pi
7474 0 0
7575 0.280871i 0.0324322i
7676 0 0
7777 0 0
7878 0 0
7979 2.70262 + 4.68107i 0.304068 + 0.526662i 0.977053 0.212994i 0.0683216π-0.0683216\pi
−0.672985 + 0.739656i 0.734988π0.734988\pi
8080 0 0
8181 −4.41145 7.64085i −0.490161 0.848983i
8282 0 0
8383 −8.62609 −0.946837 −0.473418 0.880838i 0.656980π-0.656980\pi
−0.473418 + 0.880838i 0.656980π0.656980\pi
8484 0 0
8585 −5.97042 3.44702i −0.647583 0.373882i
8686 0 0
8787 0.558972i 0.0599281i
8888 0 0
8989 14.5491 + 8.39993i 1.54220 + 0.890391i 0.998699 + 0.0509840i 0.0162358π0.0162358\pi
0.543503 + 0.839407i 0.317098π0.317098\pi
9090 0 0
9191 7.38053 + 4.26115i 0.773689 + 0.446690i
9292 0 0
9393 1.04911 0.605704i 0.108788 0.0628086i
9494 0 0
9595 −5.92348 + 4.68107i −0.607736 + 0.480268i
9696 0 0
9797 −6.39172 + 3.69026i −0.648981 + 0.374689i −0.788066 0.615591i 0.788917π-0.788917\pi
0.139085 + 0.990280i 0.455584π0.455584\pi
9898 0 0
9999 0 0
100100 0 0
101101 0.0295831 + 0.0170798i 0.00294363 + 0.00169951i 0.501471 0.865174i 0.332792π-0.332792\pi
−0.498527 + 0.866874i 0.666126π0.666126\pi
102102 0 0
103103 −3.95058 −0.389263 −0.194631 0.980876i 0.562351π-0.562351\pi
−0.194631 + 0.980876i 0.562351π0.562351\pi
104104 0 0
105105 0.421306 + 0.243241i 0.0411153 + 0.0237379i
106106 0 0
107107 7.96056i 0.769576i 0.923005 + 0.384788i 0.125725π0.125725\pi
−0.923005 + 0.384788i 0.874275π0.874275\pi
108108 0 0
109109 −7.70927 13.3528i −0.738414 1.27897i −0.953209 0.302311i 0.902242π-0.902242\pi
0.214795 0.976659i 0.431092π-0.431092\pi
110110 0 0
111111 0.883105 0.509861i 0.0838206 0.0483939i
112112 0 0
113113 13.0632i 1.22888i 0.788964 + 0.614439i 0.210618π0.210618\pi
−0.788964 + 0.614439i 0.789382π0.789382\pi
114114 0 0
115115 12.8199 1.19546
116116 0 0
117117 6.34970 + 10.9980i 0.587030 + 1.01677i
118118 0 0
119119 −6.89404 + 3.98028i −0.631976 + 0.364871i
120120 0 0
121121 −11.0000 −1.00000
122122 0 0
123123 0.518243 0.897624i 0.0467284 0.0809360i
124124 0 0
125125 12.1244i 1.08444i
126126 0 0
127127 6.40996 11.1024i 0.568792 0.985177i −0.427894 0.903829i 0.640744π-0.640744\pi
0.996686 0.0813476i 0.0259224π-0.0259224\pi
128128 0 0
129129 1.50000 + 0.866025i 0.132068 + 0.0762493i
130130 0 0
131131 −8.99096 15.5728i −0.785543 1.36060i −0.928674 0.370897i 0.879050π-0.879050\pi
0.143130 0.989704i 0.454283π-0.454283\pi
132132 0 0
133133 1.26115 + 8.62609i 0.109355 + 0.747977i
134134 0 0
135135 0.727325 + 1.25976i 0.0625982 + 0.108423i
136136 0 0
137137 7.99014 13.8393i 0.682644 1.18237i −0.291527 0.956562i 0.594163π-0.594163\pi
0.974171 0.225811i 0.0725032π-0.0725032\pi
138138 0 0
139139 −2.45938 + 4.25976i −0.208602 + 0.361308i −0.951274 0.308346i 0.900225π-0.900225\pi
0.742673 + 0.669655i 0.233558π0.233558\pi
140140 0 0
141141 −0.0591663 −0.00498270
142142 0 0
143143 0 0
144144 0 0
145145 6.89404i 0.572519i
146146 0 0
147147 −0.364862 + 0.210653i −0.0300933 + 0.0173744i
148148 0 0
149149 0.0295831 0.0170798i 0.00242355 0.00139923i −0.498788 0.866724i 0.666221π-0.666221\pi
0.501211 + 0.865325i 0.332888π0.332888\pi
150150 0 0
151151 9.90582 0.806124 0.403062 0.915173i 0.367946π-0.367946\pi
0.403062 + 0.915173i 0.367946π0.367946\pi
152152 0 0
153153 −11.8623 −0.959013
154154 0 0
155155 12.9391 7.47042i 1.03930 0.600038i
156156 0 0
157157 16.8621 9.73536i 1.34575 0.776966i 0.358102 0.933683i 0.383424π-0.383424\pi
0.987644 + 0.156716i 0.0500908π0.0500908\pi
158158 0 0
159159 1.53925i 0.122070i
160160 0 0
161161 7.40158 12.8199i 0.583327 1.01035i
162162 0 0
163163 2.97762 0.233225 0.116613 0.993177i 0.462796π-0.462796\pi
0.116613 + 0.993177i 0.462796π0.462796\pi
164164 0 0
165165 0 0
166166 0 0
167167 0.121621 0.210653i 0.00941128 0.0163008i −0.861281 0.508128i 0.830338π-0.830338\pi
0.870693 + 0.491827i 0.163671π0.163671\pi
168168 0 0
169169 −2.57869 4.46643i −0.198361 0.343571i
170170 0 0
171171 −4.79953 + 12.0716i −0.367029 + 0.923139i
172172 0 0
173173 1.50000 + 2.59808i 0.114043 + 0.197528i 0.917397 0.397974i 0.130287π-0.130287\pi
−0.803354 + 0.595502i 0.796953π0.796953\pi
174174 0 0
175175 −3.46410 2.00000i −0.261861 0.151186i
176176 0 0
177177 −0.0984160 + 0.170461i −0.00739740 + 0.0128127i
178178 0 0
179179 11.1574i 0.833942i 0.908920 + 0.416971i 0.136908π0.136908\pi
−0.908920 + 0.416971i 0.863092π0.863092\pi
180180 0 0
181181 −5.76115 + 9.97860i −0.428223 + 0.741704i −0.996715 0.0809848i 0.974193π-0.974193\pi
0.568493 + 0.822688i 0.307527π0.307527\pi
182182 0 0
183183 −0.311561 −0.0230312
184184 0 0
185185 10.8917 6.28834i 0.800775 0.462328i
186186 0 0
187187 0 0
188188 0 0
189189 1.67969 0.122179
190190 0 0
191191 13.1179i 0.949181i 0.880207 + 0.474591i 0.157404π0.157404\pi
−0.880207 + 0.474591i 0.842596π0.842596\pi
192192 0 0
193193 2.34261 1.35251i 0.168625 0.0973556i −0.413312 0.910589i 0.635628π-0.635628\pi
0.581937 + 0.813234i 0.302295π0.302295\pi
194194 0 0
195195 −0.518243 0.897624i −0.0371122 0.0642802i
196196 0 0
197197 12.0902i 0.861391i 0.902497 + 0.430695i 0.141732π0.141732\pi
−0.902497 + 0.430695i 0.858268π0.858268\pi
198198 0 0
199199 −0.637465 0.368041i −0.0451887 0.0260897i 0.477235 0.878775i 0.341639π-0.341639\pi
−0.522424 + 0.852686i 0.674972π0.674972\pi
200200 0 0
201201 −0.295053 −0.0208115
202202 0 0
203203 −6.89404 3.98028i −0.483867 0.279361i
204204 0 0
205205 6.39172 11.0708i 0.446417 0.773217i
206206 0 0
207207 19.1035 11.0294i 1.32778 0.766596i
208208 0 0
209209 0 0
210210 0 0
211211 −18.1377 + 10.4718i −1.24865 + 0.720909i −0.970840 0.239727i 0.922942π-0.922942\pi
−0.277810 + 0.960636i 0.589609π0.589609\pi
212212 0 0
213213 0.236082 + 0.136302i 0.0161760 + 0.00933925i
214214 0 0
215215 18.5002 + 10.6811i 1.26170 + 0.728443i
216216 0 0
217217 17.2522i 1.17115i
218218 0 0
219219 −0.608103 0.351088i −0.0410918 0.0237244i
220220 0 0
221221 16.9606 1.14089
222222 0 0
223223 5.52685 + 9.57279i 0.370106 + 0.641042i 0.989581 0.143974i 0.0459882π-0.0459882\pi
−0.619476 + 0.785016i 0.712655π0.712655\pi
224224 0 0
225225 −2.98028 5.16199i −0.198685 0.344133i
226226 0 0
227227 19.9606i 1.32483i 0.749138 + 0.662414i 0.230468π0.230468\pi
−0.749138 + 0.662414i 0.769532π0.769532\pi
228228 0 0
229229 11.1172i 0.734647i 0.930093 + 0.367324i 0.119726π0.119726\pi
−0.930093 + 0.367324i 0.880274π0.880274\pi
230230 0 0
231231 0 0
232232 0 0
233233 6.39172 + 11.0708i 0.418736 + 0.725271i 0.995813 0.0914183i 0.0291400π-0.0291400\pi
−0.577077 + 0.816690i 0.695807π0.695807\pi
234234 0 0
235235 −0.729724 −0.0476019
236236 0 0
237237 −0.657388 0.379543i −0.0427019 0.0246540i
238238 0 0
239239 17.7440i 1.14776i 0.818938 + 0.573882i 0.194563π0.194563\pi
−0.818938 + 0.573882i 0.805437π0.805437\pi
240240 0 0
241241 −3.81303 2.20145i −0.245619 0.141808i 0.372138 0.928178i 0.378625π-0.378625\pi
−0.617756 + 0.786369i 0.711958π0.711958\pi
242242 0 0
243243 3.25502 + 1.87929i 0.208810 + 0.120556i
244244 0 0
245245 −4.50000 + 2.59808i −0.287494 + 0.165985i
246246 0 0
247247 6.86228 17.2598i 0.436637 1.09821i
248248 0 0
249249 1.04911 0.605704i 0.0664847 0.0383850i
250250 0 0
251251 8.14201 14.1024i 0.513919 0.890134i −0.485950 0.873986i 0.661526π-0.661526\pi
0.999870 0.0161477i 0.00514021π-0.00514021\pi
252252 0 0
253253 0 0
254254 0 0
255255 0.968168 0.0606290
256256 0 0
257257 −13.0787 7.55099i −0.815827 0.471018i 0.0331486 0.999450i 0.489447π-0.489447\pi
−0.848975 + 0.528433i 0.822780π0.822780\pi
258258 0 0
259259 14.5223i 0.902372i
260260 0 0
261261 −5.93117 10.2731i −0.367130 0.635888i
262262 0 0
263263 10.0274 5.78935i 0.618319 0.356986i −0.157895 0.987456i 0.550471π-0.550471\pi
0.776214 + 0.630469i 0.217138π0.217138\pi
264264 0 0
265265 18.9842i 1.16619i
266266 0 0
267267 −2.35930 −0.144387
268268 0 0
269269 9.39172 + 16.2669i 0.572623 + 0.991813i 0.996295 + 0.0859972i 0.0274076π0.0274076\pi
−0.423672 + 0.905816i 0.639259π0.639259\pi
270270 0 0
271271 24.5111 14.1515i 1.48894 0.859642i 0.489023 0.872271i 0.337354π-0.337354\pi
0.999920 + 0.0126295i 0.00402019π0.00402019\pi
272272 0 0
273273 −1.19683 −0.0724356
274274 0 0
275275 0 0
276276 0 0
277277 3.15734i 0.189706i 0.995491 + 0.0948530i 0.0302381π0.0302381\pi
−0.995491 + 0.0948530i 0.969762π0.969762\pi
278278 0 0
279279 12.8541 22.2639i 0.769554 1.33291i
280280 0 0
281281 −5.34261 3.08456i −0.318714 0.184009i 0.332105 0.943242i 0.392241π-0.392241\pi
−0.650819 + 0.759233i 0.725574π0.725574\pi
282282 0 0
283283 7.25891 + 12.5728i 0.431497 + 0.747375i 0.997002 0.0773697i 0.0246522π-0.0246522\pi
−0.565505 + 0.824745i 0.691319π0.691319\pi
284284 0 0
285285 0.391723 0.985247i 0.0232037 0.0583610i
286286 0 0
287287 −7.38053 12.7834i −0.435659 0.754583i
288288 0 0
289289 0.578694 1.00233i 0.0340408 0.0589604i
290290 0 0
291291 0.518243 0.897624i 0.0303800 0.0526196i
292292 0 0
293293 −30.5866 −1.78689 −0.893445 0.449174i 0.851718π-0.851718\pi
−0.893445 + 0.449174i 0.851718π0.851718\pi
294294 0 0
295295 −1.21381 + 2.10238i −0.0706706 + 0.122405i
296296 0 0
297297 0 0
298298 0 0
299299 −27.3138 + 15.7696i −1.57960 + 0.911981i
300300 0 0
301301 21.3621 12.3334i 1.23129 0.710888i
302302 0 0
303303 −0.00479723 −0.000275593
304304 0 0
305305 −3.84261 −0.220027
306306 0 0
307307 14.8611 8.58008i 0.848170 0.489691i −0.0118632 0.999930i 0.503776π-0.503776\pi
0.860033 + 0.510239i 0.170443π0.170443\pi
308308 0 0
309309 0.480472 0.277401i 0.0273331 0.0157808i
310310 0 0
311311 29.7440i 1.68663i 0.537421 + 0.843314i 0.319398π0.319398\pi
−0.537421 + 0.843314i 0.680602π0.680602\pi
312312 0 0
313313 5.81303 10.0685i 0.328572 0.569103i −0.653657 0.756791i 0.726766π-0.726766\pi
0.982229 + 0.187688i 0.0600994π0.0600994\pi
314314 0 0
315315 10.3240 0.581691
316316 0 0
317317 8.41145 14.5691i 0.472434 0.818279i −0.527069 0.849823i 0.676709π-0.676709\pi
0.999502 + 0.0315434i 0.0100422π0.0100422\pi
318318 0 0
319319 0 0
320320 0 0
321321 −0.558972 0.968168i −0.0311988 0.0540378i
322322 0 0
323323 10.7572 + 13.6122i 0.598545 + 0.757405i
324324 0 0
325325 4.26115 + 7.38053i 0.236366 + 0.409398i
326326 0 0
327327 1.87521 + 1.08265i 0.103699 + 0.0598709i
328328 0 0
329329 −0.421306 + 0.729724i −0.0232274 + 0.0402310i
330330 0 0
331331 33.3594i 1.83360i 0.399350 + 0.916798i 0.369236π0.369236\pi
−0.399350 + 0.916798i 0.630764π0.630764\pi
332332 0 0
333333 10.8201 18.7410i 0.592939 1.02700i
334334 0 0
335335 −3.63902 −0.198821
336336 0 0
337337 −11.5491 + 6.66788i −0.629120 + 0.363223i −0.780411 0.625267i 0.784990π-0.784990\pi
0.151291 + 0.988489i 0.451657π0.451657\pi
338338 0 0
339339 −0.917265 1.58875i −0.0498190 0.0862890i
340340 0 0
341341 0 0
342342 0 0
343343 20.0000i 1.07990i
344344 0 0
345345 −1.55917 + 0.900185i −0.0839427 + 0.0484643i
346346 0 0
347347 −3.98235 6.89762i −0.213783 0.370284i 0.739112 0.673582i 0.235245π-0.235245\pi
−0.952896 + 0.303299i 0.901912π0.901912\pi
348348 0 0
349349 6.13496i 0.328397i 0.986427 + 0.164198i 0.0525037π0.0525037\pi
−0.986427 + 0.164198i 0.947496π0.947496\pi
350350 0 0
351351 −3.09924 1.78935i −0.165425 0.0955083i
352352 0 0
353353 12.9803 0.690870 0.345435 0.938443i 0.387731π-0.387731\pi
0.345435 + 0.938443i 0.387731π0.387731\pi
354354 0 0
355355 2.91170 + 1.68107i 0.154537 + 0.0892219i
356356 0 0
357357 0.558972 0.968168i 0.0295839 0.0512409i
358358 0 0
359359 −23.4746 + 13.5531i −1.23894 + 0.715304i −0.968878 0.247539i 0.920378π-0.920378\pi
−0.270064 + 0.962842i 0.587045π0.587045\pi
360360 0 0
361361 18.2048 5.43939i 0.958145 0.286284i
362362 0 0
363363 1.33783 0.772395i 0.0702177 0.0405402i
364364 0 0
365365 −7.50000 4.33013i −0.392568 0.226649i
366366 0 0
367367 3.82896 + 2.21065i 0.199870 + 0.115395i 0.596595 0.802542i 0.296520π-0.296520\pi
−0.396725 + 0.917938i 0.629853π0.629853\pi
368368 0 0
369369 21.9960i 1.14507i
370370 0 0
371371 −18.9842 10.9606i −0.985613 0.569044i
372372 0 0
373373 13.6797 0.708307 0.354154 0.935187i 0.384769π-0.384769\pi
0.354154 + 0.935187i 0.384769π0.384769\pi
374374 0 0
375375 0.851344 + 1.47457i 0.0439632 + 0.0761465i
376376 0 0
377377 8.48028 + 14.6883i 0.436757 + 0.756485i
378378 0 0
379379 23.0446i 1.18372i −0.806040 0.591861i 0.798394π-0.798394\pi
0.806040 0.591861i 0.201606π-0.201606\pi
380380 0 0
381381 1.80037i 0.0922358i
382382 0 0
383383 3.98235 + 6.89762i 0.203488 + 0.352452i 0.949650 0.313313i 0.101439π-0.101439\pi
−0.746162 + 0.665765i 0.768105π0.768105\pi
384384 0 0
385385 0 0
386386 0 0
387387 36.7571 1.86847
388388 0 0
389389 17.7048 + 10.2218i 0.897667 + 0.518268i 0.876442 0.481507i 0.159910π-0.159910\pi
0.0212242 + 0.999775i 0.493244π0.493244\pi
390390 0 0
391391 29.4604i 1.48987i
392392 0 0
393393 2.18697 + 1.26265i 0.110318 + 0.0636922i
394394 0 0
395395 −8.10785 4.68107i −0.407950 0.235530i
396396 0 0
397397 13.0787 7.55099i 0.656401 0.378973i −0.134503 0.990913i 0.542944π-0.542944\pi
0.790904 + 0.611940i 0.209611π0.209611\pi
398398 0 0
399399 −0.759086 0.960556i −0.0380018 0.0480879i
400400 0 0
401401 26.9113 15.5372i 1.34388 0.775892i 0.356509 0.934292i 0.383967π-0.383967\pi
0.987375 + 0.158400i 0.0506337π0.0506337\pi
402402 0 0
403403 −18.3785 + 31.8326i −0.915500 + 1.58569i
404404 0 0
405405 13.2343 + 7.64085i 0.657619 + 0.379677i
406406 0 0
407407 0 0
408408 0 0
409409 1.13786 + 0.656944i 0.0562636 + 0.0324838i 0.527868 0.849326i 0.322992π-0.322992\pi
−0.471604 + 0.881810i 0.656325π0.656325\pi
410410 0 0
411411 2.24420i 0.110698i
412412 0 0
413413 1.40158 + 2.42761i 0.0689674 + 0.119455i
414414 0 0
415415 12.9391 7.47042i 0.635157 0.366708i
416416 0 0
417417 0.690767i 0.0338270i
418418 0 0
419419 15.2475 0.744891 0.372445 0.928054i 0.378519π-0.378519\pi
0.372445 + 0.928054i 0.378519π0.378519\pi
420420 0 0
421421 6.23885 + 10.8060i 0.304063 + 0.526653i 0.977052 0.213000i 0.0683233π-0.0683233\pi
−0.672989 + 0.739652i 0.734990π0.734990\pi
422422 0 0
423423 −1.08739 + 0.627805i −0.0528707 + 0.0305249i
424424 0 0
425425 −7.96056 −0.386144
426426 0 0
427427 −2.21853 + 3.84261i −0.107362 + 0.185957i
428428 0 0
429429 0 0
430430 0 0
431431 −12.8175 + 22.2006i −0.617398 + 1.06937i 0.372560 + 0.928008i 0.378480π0.378480\pi
−0.989959 + 0.141357i 0.954853π0.954853\pi
432432 0 0
433433 −2.76392 1.59575i −0.132825 0.0766868i 0.432115 0.901819i 0.357767π-0.357767\pi
−0.564940 + 0.825132i 0.691101π0.691101\pi
434434 0 0
435435 0.484084 + 0.838458i 0.0232100 + 0.0402010i
436436 0 0
437437 −29.9801 11.9197i −1.43414 0.570198i
438438 0 0
439439 −1.24797 2.16154i −0.0595622 0.103165i 0.834707 0.550695i 0.185637π-0.185637\pi
−0.894269 + 0.447530i 0.852304π0.852304\pi
440440 0 0
441441 −4.47042 + 7.74299i −0.212877 + 0.368714i
442442 0 0
443443 14.3063 24.7793i 0.679714 1.17730i −0.295353 0.955388i 0.595437π-0.595437\pi
0.975067 0.221911i 0.0712296π-0.0712296\pi
444444 0 0
445445 −29.0982 −1.37939
446446 0 0
447447 −0.00239861 + 0.00415452i −0.000113450 + 0.000196502i
448448 0 0
449449 5.58016i 0.263344i 0.991293 + 0.131672i 0.0420345π0.0420345\pi
−0.991293 + 0.131672i 0.957965π0.957965\pi
450450 0 0
451451 0 0
452452 0 0
453453 −1.20475 + 0.695564i −0.0566042 + 0.0326804i
454454 0 0
455455 −14.7611 −0.692009
456456 0 0
457457 −38.7243 −1.81145 −0.905723 0.423871i 0.860671π-0.860671\pi
−0.905723 + 0.423871i 0.860671π0.860671\pi
458458 0 0
459459 2.89496 1.67140i 0.135125 0.0780144i
460460 0 0
461461 −13.1752 + 7.60669i −0.613629 + 0.354279i −0.774384 0.632716i 0.781940π-0.781940\pi
0.160756 + 0.986994i 0.448607π0.448607\pi
462462 0 0
463463 11.7834i 0.547623i −0.961783 0.273812i 0.911716π-0.911716\pi
0.961783 0.273812i 0.0882845π-0.0882845\pi
464464 0 0
465465 −1.04911 + 1.81711i −0.0486513 + 0.0842666i
466466 0 0
467467 −36.0321 −1.66737 −0.833684 0.552241i 0.813773π-0.813773\pi
−0.833684 + 0.552241i 0.813773π0.813773\pi
468468 0 0
469469 −2.10099 + 3.63902i −0.0970148 + 0.168034i
470470 0 0
471471 −1.36719 + 2.36804i −0.0629967 + 0.109114i
472472 0 0
473473 0 0
474474 0 0
475475 −3.22086 + 8.10099i −0.147783 + 0.371699i
476476 0 0
477477 −16.3328 28.2892i −0.747825 1.29527i
478478 0 0
479479 9.29772 + 5.36804i 0.424824 + 0.245272i 0.697139 0.716936i 0.254456π-0.254456\pi
−0.272315 + 0.962208i 0.587789π0.587789\pi
480480 0 0
481481 −15.4704 + 26.7955i −0.705390 + 1.22177i
482482 0 0
483483 2.07889i 0.0945927i
484484 0 0
485485 6.39172 11.0708i 0.290233 0.502699i
486486 0 0
487487 28.5491 1.29368 0.646842 0.762624i 0.276089π-0.276089\pi
0.646842 + 0.762624i 0.276089π0.276089\pi
488488 0 0
489489 −0.362140 + 0.209082i −0.0163765 + 0.00945499i
490490 0 0
491491 −17.6171 30.5136i −0.795046 1.37706i −0.922810 0.385256i 0.874113π-0.874113\pi
0.127763 0.991805i 0.459220π-0.459220\pi
492492 0 0
493493 −15.8426 −0.713515
494494 0 0
495495 0 0
496496 0 0
497497 3.36214 1.94113i 0.150813 0.0870717i
498498 0 0
499499 −6.16672 10.6811i −0.276060 0.478150i 0.694342 0.719645i 0.255696π-0.255696\pi
−0.970402 + 0.241495i 0.922362π0.922362\pi
500500 0 0
501501 0.0341597i 0.00152614i
502502 0 0
503503 −20.1980 11.6613i −0.900586 0.519954i −0.0231960 0.999731i 0.507384π-0.507384\pi
−0.877390 + 0.479777i 0.840718π0.840718\pi
504504 0 0
505505 −0.0591663 −0.00263286
506506 0 0
507507 0.627245 + 0.362140i 0.0278569 + 0.0160832i
508508 0 0
509509 −17.5491 + 30.3960i −0.777851 + 1.34728i 0.155328 + 0.987863i 0.450357π0.450357\pi
−0.933178 + 0.359414i 0.882977π0.882977\pi
510510 0 0
511511 −8.66025 + 5.00000i −0.383107 + 0.221187i
512512 0 0
513513 −0.529583 3.62228i −0.0233817 0.159928i
514514 0 0
515515 5.92588 3.42131i 0.261125 0.150761i
516516 0 0
517517 0 0
518518 0 0
519519 −0.364862 0.210653i −0.0160157 0.00924664i
520520 0 0
521521 29.5221i 1.29339i 0.762750 + 0.646693i 0.223849π0.223849\pi
−0.762750 + 0.646693i 0.776151π0.776151\pi
522522 0 0
523523 1.19227 + 0.688356i 0.0521342 + 0.0300997i 0.525841 0.850583i 0.323751π-0.323751\pi
−0.473706 + 0.880683i 0.657084π0.657084\pi
524524 0 0
525525 0.561741 0.0245164
526526 0 0
527527 −17.1671 29.7343i −0.747812 1.29525i
528528 0 0
529529 15.8917 + 27.5253i 0.690944 + 1.19675i
530530 0 0
531531 4.17711i 0.181271i
532532 0 0
533533 31.4495i 1.36223i
534534 0 0
535535 −6.89404 11.9408i −0.298055 0.516247i
536536 0 0
537537 −0.783446 1.35697i −0.0338082 0.0585575i
538538 0 0
539539 0 0
540540 0 0
541541 −0.450889 0.260321i −0.0193852 0.0111921i 0.490276 0.871567i 0.336896π-0.336896\pi
−0.509661 + 0.860375i 0.670229π0.670229\pi
542542 0 0
543543 1.61814i 0.0694410i
544544 0 0
545545 23.1278 + 13.3528i 0.990686 + 0.571973i
546546 0 0
547547 9.66498 + 5.58008i 0.413245 + 0.238587i 0.692183 0.721722i 0.256649π-0.256649\pi
−0.278938 + 0.960309i 0.589982π0.589982\pi
548548 0 0
549549 −5.72603 + 3.30592i −0.244381 + 0.141093i
550550 0 0
551551 −6.40996 + 16.1221i −0.273073 + 0.686824i
552552 0 0
553553 −9.36214 + 5.40523i −0.398119 + 0.229854i
554554 0 0
555555 −0.883105 + 1.52958i −0.0374857 + 0.0649272i
556556 0 0
557557 27.1769 + 15.6906i 1.15152 + 0.664832i 0.949258 0.314499i 0.101836π-0.101836\pi
0.202265 + 0.979331i 0.435170π0.435170\pi
558558 0 0
559559 −52.5546 −2.22282
560560 0 0
561561 0 0
562562 0 0
563563 42.7243i 1.80061i −0.435256 0.900307i 0.643342π-0.643342\pi
0.435256 0.900307i 0.356658π-0.356658\pi
564564 0 0
565565 −11.3130 19.5947i −0.475943 0.824357i
566566 0 0
567567 15.2817 8.82289i 0.641771 0.370527i
568568 0 0
569569 19.8547i 0.832353i 0.909284 + 0.416177i 0.136630π0.136630\pi
−0.909284 + 0.416177i 0.863370π0.863370\pi
570570 0 0
571571 39.0098 1.63251 0.816254 0.577693i 0.196047π-0.196047\pi
0.816254 + 0.577693i 0.196047π0.196047\pi
572572 0 0
573573 −0.921112 1.59541i −0.0384800 0.0666493i
574574 0 0
575575 12.8199 7.40158i 0.534628 0.308667i
576576 0 0
577577 −12.0982 −0.503656 −0.251828 0.967772i 0.581032π-0.581032\pi
−0.251828 + 0.967772i 0.581032π0.581032\pi
578578 0 0
579579 −0.189940 + 0.328986i −0.00789363 + 0.0136722i
580580 0 0
581581 17.2522i 0.715741i
582582 0 0
583583 0 0
584584 0 0
585585 −19.0491 10.9980i −0.787584 0.454712i
586586 0 0
587587 6.56334 + 11.3680i 0.270898 + 0.469209i 0.969092 0.246699i 0.0793460π-0.0793460\pi
−0.698194 + 0.715909i 0.746013π0.746013\pi
588588 0 0
589589 −37.2048 + 5.43939i −1.53300 + 0.224126i
590590 0 0
591591 −0.848946 1.47042i −0.0349210 0.0604849i
592592 0 0
593593 −3.39172 + 5.87464i −0.139281 + 0.241242i −0.927225 0.374505i 0.877813π-0.877813\pi
0.787943 + 0.615748i 0.211146π0.211146\pi
594594 0 0
595595 6.89404 11.9408i 0.282628 0.489526i
596596 0 0
597597 0.103372 0.00423073
598598 0 0
599599 −11.1196 + 19.2598i −0.454336 + 0.786933i −0.998650 0.0519490i 0.983457π-0.983457\pi
0.544314 + 0.838882i 0.316790π0.316790\pi
600600 0 0
601601 25.9466i 1.05838i 0.848502 + 0.529192i 0.177505π0.177505\pi
−0.848502 + 0.529192i 0.822495π0.822495\pi
602602 0 0
603603 −5.42265 + 3.13077i −0.220827 + 0.127495i
604604 0 0
605605 16.5000 9.52628i 0.670820 0.387298i
606606 0 0
607607 −12.8834 −0.522923 −0.261461 0.965214i 0.584204π-0.584204\pi
−0.261461 + 0.965214i 0.584204π0.584204\pi
608608 0 0
609609 1.11794 0.0453014
610610 0 0
611611 1.55473 0.897624i 0.0628977 0.0363140i
612612 0 0
613613 26.9704 15.5714i 1.08932 0.628922i 0.155928 0.987768i 0.450163π-0.450163\pi
0.933397 + 0.358846i 0.116830π0.116830\pi
614614 0 0
615615 1.79525i 0.0723914i
616616 0 0
617617 −8.54911 + 14.8075i −0.344174 + 0.596127i −0.985203 0.171389i 0.945174π-0.945174\pi
0.641029 + 0.767517i 0.278508π0.278508\pi
618618 0 0
619619 −42.4055 −1.70442 −0.852211 0.523198i 0.824739π-0.824739\pi
−0.852211 + 0.523198i 0.824739π0.824739\pi
620620 0 0
621621 −3.10808 + 5.38336i −0.124723 + 0.216027i
622622 0 0
623623 −16.7999 + 29.0982i −0.673072 + 1.16580i
624624 0 0
625625 5.50000 + 9.52628i 0.220000 + 0.381051i
626626 0 0
627627 0 0
628628 0 0
629629 −14.4507 25.0293i −0.576187 0.997985i
630630 0 0
631631 −29.4346 16.9941i −1.17177 0.676524i −0.217677 0.976021i 0.569848π-0.569848\pi
−0.954097 + 0.299496i 0.903181π0.903181\pi
632632 0 0
633633 1.47061 2.54717i 0.0584516 0.101241i
634634 0 0
635635 22.2048i 0.881169i
636636 0 0
637637 6.39172 11.0708i 0.253249 0.438641i
638638 0 0
639639 5.78511 0.228856
640640 0 0
641641 25.8621 14.9315i 1.02149 0.589759i 0.106957 0.994264i 0.465889π-0.465889\pi
0.914536 + 0.404504i 0.132556π0.132556\pi
642642 0 0
643643 −22.7233 39.3580i −0.896121 1.55213i −0.832411 0.554159i 0.813040π-0.813040\pi
−0.0637103 0.997968i 0.520293π-0.520293\pi
644644 0 0
645645 −3.00000 −0.118125
646646 0 0
647647 2.35422i 0.0925539i 0.998929 + 0.0462770i 0.0147357π0.0147357\pi
−0.998929 + 0.0462770i 0.985264π0.985264\pi
648648 0 0
649649 0 0
650650 0 0
651651 1.21141 + 2.09822i 0.0474789 + 0.0822358i
652652 0 0
653653 27.9513i 1.09382i 0.837192 + 0.546909i 0.184195π0.184195\pi
−0.837192 + 0.546909i 0.815805π0.815805\pi
654654 0 0
655655 26.9729 + 15.5728i 1.05392 + 0.608479i
656656 0 0
657657 −14.9014 −0.581359
658658 0 0
659659 −16.9215 9.76962i −0.659168 0.380571i 0.132792 0.991144i 0.457606π-0.457606\pi
−0.791960 + 0.610573i 0.790939π0.790939\pi
660660 0 0
661661 −1.29073 + 2.23561i −0.0502036 + 0.0869553i −0.890035 0.455892i 0.849320π-0.849320\pi
0.839832 + 0.542847i 0.182654π0.182654\pi
662662 0 0
663663 −2.06275 + 1.19093i −0.0801107 + 0.0462519i
664664 0 0
665665 −9.36214 11.8470i −0.363048 0.459405i
666666 0 0
667667 25.5134 14.7302i 0.987884 0.570355i
668668 0 0
669669 −1.34436 0.776166i −0.0519759 0.0300083i
670670 0 0
671671 0 0
672672 0 0
673673 36.8254i 1.41951i −0.704446 0.709757i 0.748805π-0.748805\pi
0.704446 0.709757i 0.251195π-0.251195\pi
674674 0 0
675675 1.45465 + 0.839843i 0.0559895 + 0.0323256i
676676 0 0
677677 −31.8229 −1.22305 −0.611527 0.791224i 0.709444π-0.709444\pi
−0.611527 + 0.791224i 0.709444π0.709444\pi
678678 0 0
679679 −7.38053 12.7834i −0.283239 0.490584i
680680 0 0
681681 −1.40158 2.42761i −0.0537088 0.0930264i
682682 0 0
683683 27.7834i 1.06310i 0.847026 + 0.531552i 0.178391π0.178391\pi
−0.847026 + 0.531552i 0.821609π0.821609\pi
684684 0 0
685685 27.6787i 1.05755i
686686 0 0
687687 −0.780626 1.35208i −0.0297827 0.0515852i
688688 0 0
689689 23.3523 + 40.4473i 0.889651 + 1.54092i
690690 0 0
691691 20.7846 0.790684 0.395342 0.918534i 0.370626π-0.370626\pi
0.395342 + 0.918534i 0.370626π0.370626\pi
692692 0 0
693693 0 0
694694 0 0
695695 8.51953i 0.323164i
696696 0 0
697697 −25.4408 14.6883i −0.963640 0.556358i
698698 0 0
699699 −1.55473 0.897624i −0.0588053 0.0339513i
700700 0 0
701701 −23.4391 + 13.5326i −0.885282 + 0.511118i −0.872396 0.488799i 0.837435π-0.837435\pi
−0.0128857 + 0.999917i 0.504102π0.504102\pi
702702 0 0
703703 −31.3177 + 4.57869i −1.18117 + 0.172689i
704704 0 0
705705 0.0887494 0.0512395i 0.00334250 0.00192979i
706706 0 0
707707 −0.0341597 + 0.0591663i −0.00128471 + 0.00222518i
708708 0 0
709709 10.8621 + 6.27126i 0.407936 + 0.235522i 0.689903 0.723902i 0.257653π-0.257653\pi
−0.281966 + 0.959424i 0.590987π0.590987\pi
710710 0 0
711711 −16.1091 −0.604138
712712 0 0
713713 55.2929 + 31.9234i 2.07074 + 1.19554i
714714 0 0
715715 0 0
716716 0 0
717717 −1.24594 2.15804i −0.0465306 0.0805933i
718718 0 0
719719 −14.1529 + 8.17121i −0.527816 + 0.304735i −0.740127 0.672468i 0.765234π-0.765234\pi
0.212311 + 0.977202i 0.431901π0.431901\pi
720720 0 0
721721 7.90117i 0.294255i
722722 0 0
723723 0.618324 0.0229957
724724 0 0
725725 −3.98028 6.89404i −0.147824 0.256038i
726726 0 0
727727 −34.6308 + 19.9941i −1.28439 + 0.741540i −0.977647 0.210254i 0.932571π-0.932571\pi
−0.306738 + 0.951794i 0.599238π0.599238\pi
728728 0 0
729729 25.9408 0.960772
730730 0 0
731731 24.5453 42.5136i 0.907839 1.57242i
732732 0 0
733733 6.55312i 0.242045i −0.992650 0.121023i 0.961383π-0.961383\pi
0.992650 0.121023i 0.0386173π-0.0386173\pi
734734 0 0
735735 0.364862 0.631959i 0.0134581 0.0233102i
736736 0 0
737737 0 0
738738 0 0
739739 2.66846 + 4.62190i 0.0981608 + 0.170019i 0.910923 0.412576i 0.135371π-0.135371\pi
−0.812763 + 0.582595i 0.802037π0.802037\pi
740740 0 0
741741 0.377346 + 2.58100i 0.0138621 + 0.0948153i
742742 0 0
743743 10.2707 + 17.7893i 0.376795 + 0.652628i 0.990594 0.136834i 0.0436928π-0.0436928\pi
−0.613799 + 0.789462i 0.710360π0.710360\pi
744744 0 0
745745 −0.0295831 + 0.0512395i −0.00108384 + 0.00187727i
746746 0 0
747747 12.8541 22.2639i 0.470306 0.814594i
748748 0 0
749749 −15.9211 −0.581745
750750 0 0
751751 15.5225 26.8858i 0.566425 0.981078i −0.430490 0.902595i 0.641659π-0.641659\pi
0.996916 0.0784823i 0.0250074π-0.0250074\pi
752752 0 0
753753 2.28685i 0.0833375i
754754 0 0
755755 −14.8587 + 8.57869i −0.540765 + 0.312211i
756756 0 0
757757 44.1651 25.4987i 1.60521 0.926767i 0.614786 0.788694i 0.289242π-0.289242\pi
0.990422 0.138074i 0.0440911π-0.0440911\pi
758758 0 0
759759 0 0
760760 0 0
761761 13.7046 0.496790 0.248395 0.968659i 0.420097π-0.420097\pi
0.248395 + 0.968659i 0.420097π0.420097\pi
762762 0 0
763763 26.7057 15.4185i 0.966811 0.558188i
764764 0 0
765765 17.7935 10.2731i 0.643325 0.371424i
766766 0 0
767767 5.97236i 0.215649i
768768 0 0
769769 −21.8621 + 37.8663i −0.788369 + 1.36550i 0.138597 + 0.990349i 0.455741π0.455741\pi
−0.926966 + 0.375146i 0.877593π0.877593\pi
770770 0 0
771771 2.12085 0.0763806
772772 0 0
773773 21.4606 37.1708i 0.771883 1.33694i −0.164648 0.986352i 0.552649π-0.552649\pi
0.936530 0.350587i 0.114018π-0.114018\pi
774774 0 0
775775 8.62609 14.9408i 0.309858 0.536691i
776776 0 0
777777 1.01972 + 1.76621i 0.0365823 + 0.0633624i
778778 0 0
779779 −25.2408 + 19.9467i −0.904346 + 0.714666i
780780 0 0
781781 0 0
782782 0 0
783783 2.89496 + 1.67140i 0.103457 + 0.0597311i
784784 0 0
785785 −16.8621 + 29.2061i −0.601836 + 1.04241i
786786 0 0
787787 25.6797i 0.915382i 0.889111 + 0.457691i 0.151323π0.151323\pi
−0.889111 + 0.457691i 0.848677π0.848677\pi
788788 0 0
789789 −0.813029 + 1.40821i −0.0289446 + 0.0501335i
790790 0 0
791791 −26.1263 −0.928945
792792 0 0
793793 8.18697 4.72675i 0.290728 0.167852i
794794 0 0
795795 1.33303 + 2.30887i 0.0472777 + 0.0818873i
796796 0 0
797797 −1.70456 −0.0603785 −0.0301893 0.999544i 0.509611π-0.509611\pi
−0.0301893 + 0.999544i 0.509611π0.509611\pi
798798 0 0
799799 1.67692i 0.0593250i
800800 0 0
801801 −43.3604 + 25.0341i −1.53206 + 0.884538i
802802 0 0
803803 0 0
804804 0 0
805805 25.6398i 0.903686i
806806 0 0
807807 −2.28445 1.31893i −0.0804166 0.0464285i
808808 0 0
809809 4.17711 0.146859 0.0734297 0.997300i 0.476606π-0.476606\pi
0.0734297 + 0.997300i 0.476606π0.476606\pi
810810 0 0
811811 −42.6590 24.6292i −1.49796 0.864848i −0.497963 0.867198i 0.665919π-0.665919\pi
−0.999997 + 0.00235039i 0.999252π0.999252\pi
812812 0 0
813813 −1.98737 + 3.44222i −0.0697001 + 0.120724i
814814 0 0
815815 −4.46643 + 2.57869i −0.156452 + 0.0903277i
816816 0 0
817817 −33.3326 42.1794i −1.16616 1.47567i
818818 0 0
819819 −21.9960 + 12.6994i −0.768603 + 0.443753i
820820 0 0
821821 −43.1752 24.9272i −1.50682 0.869965i −0.999969 0.00793394i 0.997475π-0.997475\pi
−0.506855 0.862031i 0.669192π-0.669192\pi
822822 0 0
823823 24.6136 + 14.2107i 0.857975 + 0.495352i 0.863334 0.504633i 0.168372π-0.168372\pi
−0.00535850 + 0.999986i 0.501706π0.501706\pi
824824 0 0
825825 0 0
826826 0 0
827827 32.0498 + 18.5040i 1.11448 + 0.643446i 0.939986 0.341212i 0.110838π-0.110838\pi
0.174494 + 0.984658i 0.444171π0.444171\pi
828828 0 0
829829 −23.0446 −0.800372 −0.400186 0.916434i 0.631054π-0.631054\pi
−0.400186 + 0.916434i 0.631054π0.631054\pi
830830 0 0
831831 −0.221701 0.383997i −0.00769072 0.0133207i
832832 0 0
833833 5.97042 + 10.3411i 0.206863 + 0.358297i
834834 0 0
835835 0.421306i 0.0145799i
836836 0 0
837837 7.24456i 0.250409i
838838 0 0
839839 24.5453 + 42.5136i 0.847396 + 1.46773i 0.883524 + 0.468386i 0.155164π0.155164\pi
−0.0361276 + 0.999347i 0.511502π0.511502\pi
840840 0 0
841841 6.57869 + 11.3946i 0.226852 + 0.392918i
842842 0 0
843843 0.866362 0.0298391
844844 0 0
845845 7.73608 + 4.46643i 0.266129 + 0.153650i
846846 0 0
847847 22.0000i 0.755929i
848848 0 0
849849 −1.76566 1.01941i −0.0605975 0.0349860i
850850 0 0
851851 46.5437 + 26.8720i 1.59550 + 0.921160i
852852 0 0
853853 7.92131 4.57337i 0.271220 0.156589i −0.358222 0.933637i 0.616617π-0.616617\pi
0.629442 + 0.777047i 0.283283π0.283283\pi
854854 0 0
855855 −3.25502 22.2639i −0.111319 0.761410i
856856 0 0
857857 −4.50000 + 2.59808i −0.153717 + 0.0887486i −0.574886 0.818234i 0.694953π-0.694953\pi
0.421168 + 0.906982i 0.361620π0.361620\pi
858858 0 0
859859 1.85367 3.21065i 0.0632465 0.109546i −0.832668 0.553772i 0.813188π-0.813188\pi
0.895915 + 0.444226i 0.146521π0.146521\pi
860860 0 0
861861 1.79525 + 1.03649i 0.0611819 + 0.0353234i
862862 0 0
863863 2.67086 0.0909170 0.0454585 0.998966i 0.485525π-0.485525\pi
0.0454585 + 0.998966i 0.485525π0.485525\pi
864864 0 0
865865 −4.50000 2.59808i −0.153005 0.0883372i
866866 0 0
867867 0.162538i 0.00552009i
868868 0 0
869869 0 0
870870 0 0
871871 7.75321 4.47632i 0.262707 0.151674i
872872 0 0
873873 21.9960i 0.744452i
874874 0 0
875875 24.2487 0.819756
876876 0 0
877877 7.71204 + 13.3576i 0.260417 + 0.451056i 0.966353 0.257220i 0.0828066π-0.0828066\pi
−0.705936 + 0.708276i 0.749473π0.749473\pi
878878 0 0
879879 3.71996 2.14772i 0.125471 0.0724408i
880880 0 0
881881 −11.4687 −0.386389 −0.193195 0.981160i 0.561885π-0.561885\pi
−0.193195 + 0.981160i 0.561885π0.561885\pi
882882 0 0
883883 −19.9890 + 34.6219i −0.672682 + 1.16512i 0.304458 + 0.952526i 0.401525π0.401525\pi
−0.977141 + 0.212594i 0.931809π0.931809\pi
884884 0 0
885885 0.340923i 0.0114600i
886886 0 0
887887 29.2549 50.6710i 0.982284 1.70137i 0.328851 0.944382i 0.393339π-0.393339\pi
0.653433 0.756984i 0.273328π-0.273328\pi
888888 0 0
889889 22.2048 + 12.8199i 0.744723 + 0.429966i
890890 0 0
891891 0 0
892892 0 0
893893 1.70650 + 0.678484i 0.0571058 + 0.0227046i
894894 0 0
895895 −9.66258 16.7361i −0.322984 0.559426i
896896 0 0
897897 2.21461 3.83582i 0.0739438 0.128074i
898898 0 0
899899 17.1671 29.7343i 0.572556 0.991696i
900900 0 0
901901 −43.6261 −1.45339
902902 0 0
903903 −1.73205 + 3.00000i −0.0576390 + 0.0998337i
904904 0 0
905905 19.9572i 0.663400i
906906 0 0
907907 −45.9356 + 26.5209i −1.52527 + 0.880612i −0.525714 + 0.850661i 0.676202π0.676202\pi
−0.999551 + 0.0299511i 0.990465π0.990465\pi
908908 0 0
909909 −0.0881660 + 0.0509027i −0.00292428 + 0.00168833i
910910 0 0
911911 −30.6904 −1.01682 −0.508410 0.861115i 0.669766π-0.669766\pi
−0.508410 + 0.861115i 0.669766π0.669766\pi
912912 0 0
913913 0 0
914914 0 0
915915 0.467341 0.269819i 0.0154498 0.00891995i
916916 0 0
917917 31.1456 17.9819i 1.02852 0.593815i
918918 0 0
919919 32.8426i 1.08338i 0.840579 + 0.541689i 0.182215π0.182215\pi
−0.840579 + 0.541689i 0.817785π0.817785\pi
920920 0 0
921921 −1.20495 + 2.08703i −0.0397043 + 0.0687699i
922922 0 0
923923 −8.27145 −0.272258
924924 0 0
925925 7.26115 12.5767i 0.238745 0.413519i
926926 0 0
927927 5.88692 10.1964i 0.193352 0.334895i
928928 0 0
929929 −6.88186 11.9197i −0.225787 0.391074i 0.730769 0.682625i 0.239162π-0.239162\pi
−0.956555 + 0.291551i 0.905829π0.905829\pi
930930 0 0
931931 12.9391 1.89172i 0.424063 0.0619987i
932932 0 0
933933 −2.08855 3.61748i −0.0683762 0.118431i
934934 0 0
935935 0 0
936936 0 0
937937 21.2243 36.7615i 0.693367 1.20095i −0.277361 0.960766i 0.589460π-0.589460\pi
0.970728 0.240181i 0.0772068π-0.0772068\pi
938938 0 0
939939 1.63271i 0.0532815i
940940 0 0
941941 −28.2440 + 48.9200i −0.920728 + 1.59475i −0.122437 + 0.992476i 0.539071π0.539071\pi
−0.798291 + 0.602272i 0.794262π0.794262\pi
942942 0 0
943943 54.6276 1.77892
944944 0 0
945945 −2.51953 + 1.45465i −0.0819602 + 0.0473198i
946946 0 0
947947 −19.5366 33.8385i −0.634856 1.09960i −0.986546 0.163486i 0.947726π-0.947726\pi
0.351690 0.936116i 0.385607π-0.385607\pi
948948 0 0
949949 21.3057 0.691614
950950 0 0
951951 2.36253i 0.0766102i
952952 0 0
953953 −15.1769 + 8.76240i −0.491629 + 0.283842i −0.725250 0.688486i 0.758276π-0.758276\pi
0.233621 + 0.972328i 0.424942π0.424942\pi
954954 0 0
955955 −11.3605 19.6769i −0.367616 0.636730i
956956 0 0
957957 0 0
958958 0 0
959959 27.6787 + 15.9803i 0.893790 + 0.516030i
960960 0 0
961961 43.4095 1.40031
962962 0 0
963963 −20.5462 11.8623i −0.662091 0.382258i
964964 0 0
965965 −2.34261 + 4.05752i −0.0754114 + 0.130616i
966966 0 0
967967 18.1251 10.4645i 0.582863 0.336516i −0.179407 0.983775i 0.557418π-0.557418\pi
0.762270 + 0.647259i 0.224085π0.224085\pi
968968 0 0
969969 −2.26411 0.900185i −0.0727338 0.0289181i
970970 0 0
971971 −41.3715 + 23.8858i −1.32767 + 0.766533i −0.984939 0.172900i 0.944686π-0.944686\pi
−0.342734 + 0.939433i 0.611353π0.611353\pi
972972 0 0
973973 −8.51953 4.91875i −0.273124 0.157688i
974974 0 0
975975 −1.03649 0.598416i −0.0331941 0.0191646i
976976 0 0
977977 48.1223i 1.53957i −0.638303 0.769785i 0.720363π-0.720363\pi
0.638303 0.769785i 0.279637π-0.279637\pi
978978 0 0
979979 0 0
980980 0 0
981981 45.9515 1.46712
982982 0 0
983983 −18.9866 32.8858i −0.605580 1.04889i −0.991960 0.126555i 0.959608π-0.959608\pi
0.386380 0.922340i 0.373725π-0.373725\pi
984984 0 0
985985 −10.4704 18.1353i −0.333615 0.577839i
986986 0 0
987987 0.118333i 0.00376657i
988988 0 0
989989 91.2870i 2.90276i
990990 0 0
991991 22.4166 + 38.8267i 0.712086 + 1.23337i 0.964073 + 0.265639i 0.0855828π0.0855828\pi
−0.251987 + 0.967731i 0.581084π0.581084\pi
992992 0 0
993993 −2.34242 4.05719i −0.0743344 0.128751i
994994 0 0
995995 1.27493 0.0404180
996996 0 0
997997 −12.6574 7.30775i −0.400863 0.231439i 0.285993 0.958232i 0.407677π-0.407677\pi
−0.686856 + 0.726793i 0.741010π0.741010\pi
998998 0 0
999999 6.09822i 0.192939i
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 1216.2.s.g.31.3 12
4.3 odd 2 inner 1216.2.s.g.31.4 yes 12
8.3 odd 2 1216.2.s.h.31.3 yes 12
8.5 even 2 1216.2.s.h.31.4 yes 12
19.8 odd 6 1216.2.s.h.863.3 yes 12
76.27 even 6 1216.2.s.h.863.4 yes 12
152.27 even 6 inner 1216.2.s.g.863.3 yes 12
152.141 odd 6 inner 1216.2.s.g.863.4 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1216.2.s.g.31.3 12 1.1 even 1 trivial
1216.2.s.g.31.4 yes 12 4.3 odd 2 inner
1216.2.s.g.863.3 yes 12 152.27 even 6 inner
1216.2.s.g.863.4 yes 12 152.141 odd 6 inner
1216.2.s.h.31.3 yes 12 8.3 odd 2
1216.2.s.h.31.4 yes 12 8.5 even 2
1216.2.s.h.863.3 yes 12 19.8 odd 6
1216.2.s.h.863.4 yes 12 76.27 even 6