Properties

Label 252.2.j.a.85.3
Level 252252
Weight 22
Character 252.85
Analytic conductor 2.0122.012
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [252,2,Mod(85,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.85"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 252=22327 252 = 2^{2} \cdot 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 252.j (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.012230130942.01223013094
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 6.0.309123.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x63x5+10x415x3+19x212x+3 x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 85.3
Root 0.5000000.224437i0.500000 - 0.224437i of defining polynomial
Character χ\chi == 252.85
Dual form 252.2.j.a.169.3

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.64400+0.545231i)q3+(0.8498141.47192i)q5+(0.500000+0.866025i)q7+(2.40545+1.79272i)q9+(1.238552.14523i)q11+(0.388736+0.673310i)q13+(2.199631.95649i)q15+2.81089q174.98762q19+(0.349814+1.69636i)q21+(0.356004+0.616617i)q23+(1.05563+1.82841i)q25+(2.97710+4.25874i)q27+(2.255263.90623i)q29+(2.54944+4.41576i)q31+(0.8665244.20205i)q33+1.69963q356.87636q37+(1.00619+0.894969i)q39+(2.938185.08907i)q41+(2.32691+4.03033i)q43+(4.682922.01715i)q45+(6.4938111.2476i)q47+(0.500000+0.866025i)q49+(4.62110+1.53259i)q51+1.88874q534.21015q55+(8.199632.71941i)q57+(7.14400+12.3738i)q59+(7.1545212.3920i)q61+(0.349814+2.97954i)q63+(0.660706+1.14438i)q65+(3.99381+6.91748i)q67+(0.921468+0.819611i)q6910.2632q71+4.98762q73+(0.738550+3.58146i)q75+(1.238552.14523i)q77+(4.60507+7.97622i)q79+(2.57234+8.62456i)q81+(4.405457.63046i)q83+(2.388744.13741i)q85+(1.577847.65146i)q87+9.65383q890.777472q91+(6.59888+5.86946i)q93+(4.23855+7.34138i)q95+(4.320727.48371i)q97+(0.8665247.38061i)q99+O(q100)q+(1.64400 + 0.545231i) q^{3} +(0.849814 - 1.47192i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.40545 + 1.79272i) q^{9} +(-1.23855 - 2.14523i) q^{11} +(-0.388736 + 0.673310i) q^{13} +(2.19963 - 1.95649i) q^{15} +2.81089 q^{17} -4.98762 q^{19} +(0.349814 + 1.69636i) q^{21} +(-0.356004 + 0.616617i) q^{23} +(1.05563 + 1.82841i) q^{25} +(2.97710 + 4.25874i) q^{27} +(-2.25526 - 3.90623i) q^{29} +(-2.54944 + 4.41576i) q^{31} +(-0.866524 - 4.20205i) q^{33} +1.69963 q^{35} -6.87636 q^{37} +(-1.00619 + 0.894969i) q^{39} +(2.93818 - 5.08907i) q^{41} +(2.32691 + 4.03033i) q^{43} +(4.68292 - 2.01715i) q^{45} +(-6.49381 - 11.2476i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(4.62110 + 1.53259i) q^{51} +1.88874 q^{53} -4.21015 q^{55} +(-8.19963 - 2.71941i) q^{57} +(-7.14400 + 12.3738i) q^{59} +(-7.15452 - 12.3920i) q^{61} +(-0.349814 + 2.97954i) q^{63} +(0.660706 + 1.14438i) q^{65} +(-3.99381 + 6.91748i) q^{67} +(-0.921468 + 0.819611i) q^{69} -10.2632 q^{71} +4.98762 q^{73} +(0.738550 + 3.58146i) q^{75} +(1.23855 - 2.14523i) q^{77} +(4.60507 + 7.97622i) q^{79} +(2.57234 + 8.62456i) q^{81} +(-4.40545 - 7.63046i) q^{83} +(2.38874 - 4.13741i) q^{85} +(-1.57784 - 7.65146i) q^{87} +9.65383 q^{89} -0.777472 q^{91} +(-6.59888 + 5.86946i) q^{93} +(-4.23855 + 7.34138i) q^{95} +(-4.32072 - 7.48371i) q^{97} +(0.866524 - 7.38061i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q2q3q5+3q7+8q92q113q13+q15+4q17+6q194q2114q23+6q25+7q27q29+3q31+8q332q356q3724q39+8q99+O(q100) 6 q - 2 q^{3} - q^{5} + 3 q^{7} + 8 q^{9} - 2 q^{11} - 3 q^{13} + q^{15} + 4 q^{17} + 6 q^{19} - 4 q^{21} - 14 q^{23} + 6 q^{25} + 7 q^{27} - q^{29} + 3 q^{31} + 8 q^{33} - 2 q^{35} - 6 q^{37} - 24 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/252Z)×\left(\mathbb{Z}/252\mathbb{Z}\right)^\times.

nn 2929 7373 127127
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11 11

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 1.64400 + 0.545231i 0.949162 + 0.314789i
44 0 0
55 0.849814 1.47192i 0.380048 0.658263i −0.611020 0.791615i 0.709241π-0.709241\pi
0.991069 + 0.133352i 0.0425740π0.0425740\pi
66 0 0
77 0.500000 + 0.866025i 0.188982 + 0.327327i
88 0 0
99 2.40545 + 1.79272i 0.801815 + 0.597572i
1010 0 0
1111 −1.23855 2.14523i −0.373437 0.646812i 0.616655 0.787234i 0.288487π-0.288487\pi
−0.990092 + 0.140422i 0.955154π0.955154\pi
1212 0 0
1313 −0.388736 + 0.673310i −0.107816 + 0.186743i −0.914885 0.403714i 0.867719π-0.867719\pi
0.807069 + 0.590457i 0.201052π0.201052\pi
1414 0 0
1515 2.19963 1.95649i 0.567942 0.505163i
1616 0 0
1717 2.81089 0.681742 0.340871 0.940110i 0.389278π-0.389278\pi
0.340871 + 0.940110i 0.389278π0.389278\pi
1818 0 0
1919 −4.98762 −1.14424 −0.572119 0.820170i 0.693879π-0.693879\pi
−0.572119 + 0.820170i 0.693879π0.693879\pi
2020 0 0
2121 0.349814 + 1.69636i 0.0763357 + 0.370176i
2222 0 0
2323 −0.356004 + 0.616617i −0.0742320 + 0.128574i −0.900752 0.434334i 0.856984π-0.856984\pi
0.826520 + 0.562907i 0.190317π0.190317\pi
2424 0 0
2525 1.05563 + 1.82841i 0.211126 + 0.365682i
2626 0 0
2727 2.97710 + 4.25874i 0.572943 + 0.819595i
2828 0 0
2929 −2.25526 3.90623i −0.418791 0.725368i 0.577027 0.816725i 0.304213π-0.304213\pi
−0.995818 + 0.0913573i 0.970879π0.970879\pi
3030 0 0
3131 −2.54944 + 4.41576i −0.457893 + 0.793095i −0.998849 0.0479563i 0.984729π-0.984729\pi
0.540956 + 0.841051i 0.318063π0.318063\pi
3232 0 0
3333 −0.866524 4.20205i −0.150843 0.731483i
3434 0 0
3535 1.69963 0.287290
3636 0 0
3737 −6.87636 −1.13047 −0.565233 0.824931i 0.691214π-0.691214\pi
−0.565233 + 0.824931i 0.691214π0.691214\pi
3838 0 0
3939 −1.00619 + 0.894969i −0.161119 + 0.143310i
4040 0 0
4141 2.93818 5.08907i 0.458866 0.794780i −0.540035 0.841643i 0.681589π-0.681589\pi
0.998901 + 0.0468628i 0.0149223π0.0149223\pi
4242 0 0
4343 2.32691 + 4.03033i 0.354851 + 0.614620i 0.987092 0.160151i 0.0511982π-0.0511982\pi
−0.632241 + 0.774771i 0.717865π0.717865\pi
4444 0 0
4545 4.68292 2.01715i 0.698088 0.300699i
4646 0 0
4747 −6.49381 11.2476i −0.947220 1.64063i −0.751245 0.660023i 0.770546π-0.770546\pi
−0.195975 0.980609i 0.562787π-0.562787\pi
4848 0 0
4949 −0.500000 + 0.866025i −0.0714286 + 0.123718i
5050 0 0
5151 4.62110 + 1.53259i 0.647083 + 0.214605i
5252 0 0
5353 1.88874 0.259438 0.129719 0.991551i 0.458593π-0.458593\pi
0.129719 + 0.991551i 0.458593π0.458593\pi
5454 0 0
5555 −4.21015 −0.567696
5656 0 0
5757 −8.19963 2.71941i −1.08607 0.360194i
5858 0 0
5959 −7.14400 + 12.3738i −0.930069 + 1.61093i −0.146870 + 0.989156i 0.546920π0.546920\pi
−0.783199 + 0.621771i 0.786413π0.786413\pi
6060 0 0
6161 −7.15452 12.3920i −0.916042 1.58663i −0.805369 0.592774i 0.798033π-0.798033\pi
−0.110673 0.993857i 0.535301π-0.535301\pi
6262 0 0
6363 −0.349814 + 2.97954i −0.0440724 + 0.375386i
6464 0 0
6565 0.660706 + 1.14438i 0.0819505 + 0.141942i
6666 0 0
6767 −3.99381 + 6.91748i −0.487922 + 0.845105i −0.999904 0.0138913i 0.995578π-0.995578\pi
0.511982 + 0.858996i 0.328911π0.328911\pi
6868 0 0
6969 −0.921468 + 0.819611i −0.110932 + 0.0986696i
7070 0 0
7171 −10.2632 −1.21802 −0.609011 0.793162i 0.708433π-0.708433\pi
−0.609011 + 0.793162i 0.708433π0.708433\pi
7272 0 0
7373 4.98762 0.583757 0.291878 0.956455i 0.405720π-0.405720\pi
0.291878 + 0.956455i 0.405720π0.405720\pi
7474 0 0
7575 0.738550 + 3.58146i 0.0852804 + 0.413551i
7676 0 0
7777 1.23855 2.14523i 0.141146 0.244472i
7878 0 0
7979 4.60507 + 7.97622i 0.518111 + 0.897395i 0.999779 + 0.0210410i 0.00669805π0.00669805\pi
−0.481667 + 0.876354i 0.659969π0.659969\pi
8080 0 0
8181 2.57234 + 8.62456i 0.285816 + 0.958285i
8282 0 0
8383 −4.40545 7.63046i −0.483561 0.837551i 0.516261 0.856431i 0.327323π-0.327323\pi
−0.999822 + 0.0188798i 0.993990π0.993990\pi
8484 0 0
8585 2.38874 4.13741i 0.259095 0.448765i
8686 0 0
8787 −1.57784 7.65146i −0.169163 0.820322i
8888 0 0
8989 9.65383 1.02330 0.511652 0.859193i 0.329034π-0.329034\pi
0.511652 + 0.859193i 0.329034π0.329034\pi
9090 0 0
9191 −0.777472 −0.0815012
9292 0 0
9393 −6.59888 + 5.86946i −0.684272 + 0.608635i
9494 0 0
9595 −4.23855 + 7.34138i −0.434866 + 0.753210i
9696 0 0
9797 −4.32072 7.48371i −0.438703 0.759856i 0.558887 0.829244i 0.311229π-0.311229\pi
−0.997590 + 0.0693880i 0.977895π0.977895\pi
9898 0 0
9999 0.866524 7.38061i 0.0870890 0.741779i
100100 0 0
101101 −1.20582 2.08854i −0.119983 0.207817i 0.799777 0.600297i 0.204951π-0.204951\pi
−0.919761 + 0.392479i 0.871617π0.871617\pi
102102 0 0
103103 2.16690 3.75317i 0.213511 0.369811i −0.739300 0.673376i 0.764844π-0.764844\pi
0.952811 + 0.303565i 0.0981769π0.0981769\pi
104104 0 0
105105 2.79418 + 0.926690i 0.272684 + 0.0904357i
106106 0 0
107107 19.1978 1.85592 0.927959 0.372682i 0.121562π-0.121562\pi
0.927959 + 0.372682i 0.121562π0.121562\pi
108108 0 0
109109 18.9629 1.81631 0.908156 0.418631i 0.137490π-0.137490\pi
0.908156 + 0.418631i 0.137490π0.137490\pi
110110 0 0
111111 −11.3047 3.74920i −1.07299 0.355859i
112112 0 0
113113 −6.46472 + 11.1972i −0.608150 + 1.05335i 0.383395 + 0.923584i 0.374755π0.374755\pi
−0.991545 + 0.129762i 0.958579π0.958579\pi
114114 0 0
115115 0.605074 + 1.04802i 0.0564235 + 0.0977283i
116116 0 0
117117 −2.14214 + 0.922719i −0.198041 + 0.0853054i
118118 0 0
119119 1.40545 + 2.43430i 0.128837 + 0.223152i
120120 0 0
121121 2.43199 4.21233i 0.221090 0.382939i
122122 0 0
123123 7.60507 6.76443i 0.685726 0.609928i
124124 0 0
125125 12.0865 1.08105
126126 0 0
127127 17.6291 1.56433 0.782163 0.623073i 0.214116π-0.214116\pi
0.782163 + 0.623073i 0.214116π0.214116\pi
128128 0 0
129129 1.62797 + 7.89456i 0.143335 + 0.695077i
130130 0 0
131131 2.84362 4.92530i 0.248449 0.430326i −0.714647 0.699485i 0.753413π-0.753413\pi
0.963096 + 0.269160i 0.0867460π0.0867460\pi
132132 0 0
133133 −2.49381 4.31941i −0.216241 0.374540i
134134 0 0
135135 8.79851 0.762918i 0.757255 0.0656615i
136136 0 0
137137 9.72617 + 16.8462i 0.830963 + 1.43927i 0.897276 + 0.441471i 0.145543π0.145543\pi
−0.0663128 + 0.997799i 0.521124π0.521124\pi
138138 0 0
139139 1.49381 2.58736i 0.126703 0.219457i −0.795694 0.605699i 0.792894π-0.792894\pi
0.922397 + 0.386242i 0.126227π0.126227\pi
140140 0 0
141141 −4.54325 22.0317i −0.382611 1.85540i
142142 0 0
143143 1.92587 0.161050
144144 0 0
145145 −7.66621 −0.636644
146146 0 0
147147 −1.29418 + 1.15113i −0.106742 + 0.0949433i
148148 0 0
149149 −4.04944 + 7.01384i −0.331743 + 0.574596i −0.982854 0.184387i 0.940970π-0.940970\pi
0.651111 + 0.758983i 0.274303π0.274303\pi
150150 0 0
151151 4.43199 + 7.67643i 0.360670 + 0.624699i 0.988071 0.153997i 0.0492147π-0.0492147\pi
−0.627401 + 0.778696i 0.715881π0.715881\pi
152152 0 0
153153 6.76145 + 5.03913i 0.546631 + 0.407390i
154154 0 0
155155 4.33310 + 7.50516i 0.348043 + 0.602829i
156156 0 0
157157 4.38255 7.59079i 0.349765 0.605811i −0.636442 0.771324i 0.719595π-0.719595\pi
0.986208 + 0.165513i 0.0529280π0.0529280\pi
158158 0 0
159159 3.10507 + 1.02980i 0.246248 + 0.0816683i
160160 0 0
161161 −0.712008 −0.0561141
162162 0 0
163163 −1.98762 −0.155682 −0.0778412 0.996966i 0.524803π-0.524803\pi
−0.0778412 + 0.996966i 0.524803π0.524803\pi
164164 0 0
165165 −6.92147 2.29550i −0.538836 0.178705i
166166 0 0
167167 −1.31089 + 2.27053i −0.101440 + 0.175699i −0.912278 0.409571i 0.865678π-0.865678\pi
0.810838 + 0.585270i 0.199012π0.199012\pi
168168 0 0
169169 6.19777 + 10.7349i 0.476751 + 0.825758i
170170 0 0
171171 −11.9975 8.94138i −0.917468 0.683765i
172172 0 0
173173 2.61491 + 4.52915i 0.198808 + 0.344345i 0.948142 0.317847i 0.102960π-0.102960\pi
−0.749334 + 0.662192i 0.769626π0.769626\pi
174174 0 0
175175 −1.05563 + 1.82841i −0.0797983 + 0.138215i
176176 0 0
177177 −18.4913 + 16.4473i −1.38989 + 1.23625i
178178 0 0
179179 −4.76509 −0.356160 −0.178080 0.984016i 0.556989π-0.556989\pi
−0.178080 + 0.984016i 0.556989π0.556989\pi
180180 0 0
181181 −10.4313 −0.775352 −0.387676 0.921796i 0.626722π-0.626722\pi
−0.387676 + 0.921796i 0.626722π0.626722\pi
182182 0 0
183183 −5.00550 24.2732i −0.370017 1.79433i
184184 0 0
185185 −5.84362 + 10.1215i −0.429632 + 0.744144i
186186 0 0
187187 −3.48143 6.03001i −0.254587 0.440958i
188188 0 0
189189 −2.19963 + 4.70761i −0.159999 + 0.342429i
190190 0 0
191191 −6.66071 11.5367i −0.481952 0.834765i 0.517834 0.855481i 0.326739π-0.326739\pi
−0.999785 + 0.0207164i 0.993405π0.993405\pi
192192 0 0
193193 7.32072 12.6799i 0.526957 0.912717i −0.472549 0.881304i 0.656666π-0.656666\pi
0.999507 0.0314125i 0.0100005π-0.0100005\pi
194194 0 0
195195 0.462249 + 2.24159i 0.0331023 + 0.160524i
196196 0 0
197197 −18.4858 −1.31706 −0.658528 0.752556i 0.728821π-0.728821\pi
−0.658528 + 0.752556i 0.728821π0.728821\pi
198198 0 0
199199 23.6167 1.67414 0.837071 0.547094i 0.184266π-0.184266\pi
0.837071 + 0.547094i 0.184266π0.184266\pi
200200 0 0
201201 −10.3374 + 9.19476i −0.729146 + 0.648549i
202202 0 0
203203 2.25526 3.90623i 0.158288 0.274163i
204204 0 0
205205 −4.99381 8.64953i −0.348783 0.604110i
206206 0 0
207207 −1.96177 + 0.845025i −0.136352 + 0.0587333i
208208 0 0
209209 6.17742 + 10.6996i 0.427301 + 0.740107i
210210 0 0
211211 7.27747 12.6050i 0.501002 0.867761i −0.498998 0.866603i 0.666298π-0.666298\pi
0.999999 0.00115718i 0.000368342π-0.000368342\pi
212212 0 0
213213 −16.8727 5.59583i −1.15610 0.383420i
214214 0 0
215215 7.90978 0.539442
216216 0 0
217217 −5.09888 −0.346135
218218 0 0
219219 8.19963 + 2.71941i 0.554080 + 0.183760i
220220 0 0
221221 −1.09269 + 1.89260i −0.0735026 + 0.127310i
222222 0 0
223223 −4.72253 8.17966i −0.316244 0.547750i 0.663457 0.748214i 0.269088π-0.269088\pi
−0.979701 + 0.200464i 0.935755π0.935755\pi
224224 0 0
225225 −0.738550 + 6.29059i −0.0492367 + 0.419372i
226226 0 0
227227 −9.55563 16.5508i −0.634230 1.09852i −0.986678 0.162687i 0.947984π-0.947984\pi
0.352448 0.935831i 0.385349π-0.385349\pi
228228 0 0
229229 −5.72253 + 9.91171i −0.378155 + 0.654984i −0.990794 0.135379i 0.956775π-0.956775\pi
0.612639 + 0.790363i 0.290108π0.290108\pi
230230 0 0
231231 3.20582 2.85146i 0.210927 0.187612i
232232 0 0
233233 −1.19049 −0.0779913 −0.0389956 0.999239i 0.512416π-0.512416\pi
−0.0389956 + 0.999239i 0.512416π0.512416\pi
234234 0 0
235235 −22.0741 −1.43996
236236 0 0
237237 3.22184 + 15.6237i 0.209281 + 1.01487i
238238 0 0
239239 −12.1414 + 21.0296i −0.785365 + 1.36029i 0.143416 + 0.989663i 0.454191π0.454191\pi
−0.928781 + 0.370630i 0.879142π0.879142\pi
240240 0 0
241241 10.7095 + 18.5493i 0.689857 + 1.19487i 0.971884 + 0.235461i 0.0756599π0.0756599\pi
−0.282027 + 0.959406i 0.591007π0.591007\pi
242242 0 0
243243 −0.473458 + 15.5813i −0.0303723 + 0.999539i
244244 0 0
245245 0.849814 + 1.47192i 0.0542926 + 0.0940376i
246246 0 0
247247 1.93887 3.35822i 0.123367 0.213678i
248248 0 0
249249 −3.08217 14.9464i −0.195325 0.947191i
250250 0 0
251251 −2.67996 −0.169158 −0.0845789 0.996417i 0.526955π-0.526955\pi
−0.0845789 + 0.996417i 0.526955π0.526955\pi
252252 0 0
253253 1.76371 0.110884
254254 0 0
255255 6.18292 5.49948i 0.387189 0.344391i
256256 0 0
257257 5.54256 9.60000i 0.345736 0.598832i −0.639752 0.768582i 0.720963π-0.720963\pi
0.985487 + 0.169750i 0.0542961π0.0542961\pi
258258 0 0
259259 −3.43818 5.95510i −0.213638 0.370032i
260260 0 0
261261 1.57784 13.4393i 0.0976661 0.831869i
262262 0 0
263263 −6.70396 11.6116i −0.413384 0.716002i 0.581873 0.813279i 0.302320π-0.302320\pi
−0.995257 + 0.0972776i 0.968987π0.968987\pi
264264 0 0
265265 1.60507 2.78007i 0.0985989 0.170778i
266266 0 0
267267 15.8709 + 5.26357i 0.971281 + 0.322125i
268268 0 0
269269 4.09022 0.249385 0.124693 0.992195i 0.460206π-0.460206\pi
0.124693 + 0.992195i 0.460206π0.460206\pi
270270 0 0
271271 6.12364 0.371985 0.185992 0.982551i 0.440450π-0.440450\pi
0.185992 + 0.982551i 0.440450π0.440450\pi
272272 0 0
273273 −1.27816 0.423902i −0.0773578 0.0256557i
274274 0 0
275275 2.61491 4.52915i 0.157685 0.273118i
276276 0 0
277277 −7.88255 13.6530i −0.473616 0.820327i 0.525928 0.850529i 0.323718π-0.323718\pi
−0.999544 + 0.0302019i 0.990385π0.990385\pi
278278 0 0
279279 −14.0488 + 6.05146i −0.841077 + 0.362291i
280280 0 0
281281 10.5946 + 18.3503i 0.632018 + 1.09469i 0.987139 + 0.159867i 0.0511065π0.0511065\pi
−0.355120 + 0.934821i 0.615560π0.615560\pi
282282 0 0
283283 −3.43818 + 5.95510i −0.204378 + 0.353994i −0.949935 0.312449i 0.898851π-0.898851\pi
0.745556 + 0.666443i 0.232184π0.232184\pi
284284 0 0
285285 −10.9709 + 9.75822i −0.649861 + 0.578027i
286286 0 0
287287 5.87636 0.346870
288288 0 0
289289 −9.09888 −0.535228
290290 0 0
291291 −3.02290 14.6590i −0.177206 0.859325i
292292 0 0
293293 13.7534 23.8216i 0.803482 1.39167i −0.113829 0.993500i 0.536311π-0.536311\pi
0.917311 0.398172i 0.130355π-0.130355\pi
294294 0 0
295295 12.1421 + 21.0308i 0.706943 + 1.22446i
296296 0 0
297297 5.44870 11.6612i 0.316166 0.676653i
298298 0 0
299299 −0.276783 0.479402i −0.0160068 0.0277245i
300300 0 0
301301 −2.32691 + 4.03033i −0.134121 + 0.232305i
302302 0 0
303303 −0.843624 4.09100i −0.0484649 0.235022i
304304 0 0
305305 −24.3200 −1.39256
306306 0 0
307307 −21.5178 −1.22809 −0.614043 0.789273i 0.710458π-0.710458\pi
−0.614043 + 0.789273i 0.710458π0.710458\pi
308308 0 0
309309 5.60872 4.98874i 0.319069 0.283800i
310310 0 0
311311 −9.19275 + 15.9223i −0.521273 + 0.902871i 0.478421 + 0.878131i 0.341209π0.341209\pi
−0.999694 + 0.0247407i 0.992124π0.992124\pi
312312 0 0
313313 0.000688709 0.00119288i 3.89281e−5 6.74255e-5i 0.866045 0.499966i 0.166654π-0.166654\pi
−0.866006 + 0.500034i 0.833321π0.833321\pi
314314 0 0
315315 4.08836 + 3.04695i 0.230353 + 0.171676i
316316 0 0
317317 −7.04944 12.2100i −0.395936 0.685781i 0.597284 0.802030i 0.296247π-0.296247\pi
−0.993220 + 0.116248i 0.962913π0.962913\pi
318318 0 0
319319 −5.58650 + 9.67611i −0.312784 + 0.541758i
320320 0 0
321321 31.5611 + 10.4672i 1.76157 + 0.584223i
322322 0 0
323323 −14.0197 −0.780075
324324 0 0
325325 −1.64145 −0.0910512
326326 0 0
327327 31.1749 + 10.3391i 1.72397 + 0.571756i
328328 0 0
329329 6.49381 11.2476i 0.358015 0.620101i
330330 0 0
331331 −6.98143 12.0922i −0.383734 0.664647i 0.607859 0.794045i 0.292029π-0.292029\pi
−0.991593 + 0.129398i 0.958695π0.958695\pi
332332 0 0
333333 −16.5407 12.3274i −0.906425 0.675535i
334334 0 0
335335 6.78799 + 11.7571i 0.370868 + 0.642362i
336336 0 0
337337 −12.0982 + 20.9547i −0.659031 + 1.14147i 0.321836 + 0.946795i 0.395700π0.395700\pi
−0.980867 + 0.194679i 0.937633π0.937633\pi
338338 0 0
339339 −16.7330 + 14.8834i −0.908814 + 0.808357i
340340 0 0
341341 12.6304 0.683977
342342 0 0
343343 −1.00000 −0.0539949
344344 0 0
345345 0.423327 + 2.05285i 0.0227912 + 0.110521i
346346 0 0
347347 16.3578 28.3325i 0.878132 1.52097i 0.0247435 0.999694i 0.492123π-0.492123\pi
0.853389 0.521275i 0.174544π-0.174544\pi
348348 0 0
349349 11.8887 + 20.5919i 0.636389 + 1.10226i 0.986219 + 0.165445i 0.0529062π0.0529062\pi
−0.349830 + 0.936813i 0.613760π0.613760\pi
350350 0 0
351351 −4.02476 + 0.348986i −0.214826 + 0.0186275i
352352 0 0
353353 −10.0309 17.3740i −0.533889 0.924724i −0.999216 0.0395847i 0.987396π-0.987396\pi
0.465327 0.885139i 0.345937π-0.345937\pi
354354 0 0
355355 −8.72184 + 15.1067i −0.462907 + 0.801779i
356356 0 0
357357 0.983290 + 4.76828i 0.0520412 + 0.252364i
358358 0 0
359359 8.30175 0.438150 0.219075 0.975708i 0.429696π-0.429696\pi
0.219075 + 0.975708i 0.429696π0.429696\pi
360360 0 0
361361 5.87636 0.309282
362362 0 0
363363 6.29487 5.59905i 0.330395 0.293874i
364364 0 0
365365 4.23855 7.34138i 0.221856 0.384266i
366366 0 0
367367 −5.77197 9.99735i −0.301294 0.521857i 0.675135 0.737694i 0.264085π-0.264085\pi
−0.976429 + 0.215837i 0.930752π0.930752\pi
368368 0 0
369369 16.1909 6.97418i 0.842864 0.363061i
370370 0 0
371371 0.944368 + 1.63569i 0.0490291 + 0.0849210i
372372 0 0
373373 −1.42580 + 2.46956i −0.0738250 + 0.127869i −0.900575 0.434701i 0.856854π-0.856854\pi
0.826750 + 0.562570i 0.190187π0.190187\pi
374374 0 0
375375 19.8702 + 6.58994i 1.02609 + 0.340303i
376376 0 0
377377 3.50680 0.180609
378378 0 0
379379 35.9519 1.84672 0.923361 0.383932i 0.125430π-0.125430\pi
0.923361 + 0.383932i 0.125430π0.125430\pi
380380 0 0
381381 28.9821 + 9.61192i 1.48480 + 0.492433i
382382 0 0
383383 0.915278 1.58531i 0.0467685 0.0810054i −0.841694 0.539956i 0.818441π-0.818441\pi
0.888462 + 0.458950i 0.151774π0.151774\pi
384384 0 0
385385 −2.10507 3.64610i −0.107285 0.185822i
386386 0 0
387387 −1.62797 + 13.8662i −0.0827546 + 0.704861i
388388 0 0
389389 5.69530 + 9.86454i 0.288763 + 0.500152i 0.973515 0.228624i 0.0734227π-0.0734227\pi
−0.684752 + 0.728776i 0.740089π0.740089\pi
390390 0 0
391391 −1.00069 + 1.73324i −0.0506070 + 0.0876539i
392392 0 0
393393 7.36033 6.54674i 0.371280 0.330240i
394394 0 0
395395 15.6538 0.787630
396396 0 0
397397 −10.4313 −0.523532 −0.261766 0.965131i 0.584305π-0.584305\pi
−0.261766 + 0.965131i 0.584305π0.584305\pi
398398 0 0
399399 −1.74474 8.46079i −0.0873462 0.423569i
400400 0 0
401401 17.0371 29.5091i 0.850790 1.47361i −0.0297058 0.999559i 0.509457π-0.509457\pi
0.880496 0.474053i 0.157210π-0.157210\pi
402402 0 0
403403 −1.98212 3.43313i −0.0987364 0.171016i
404404 0 0
405405 14.8807 + 3.54299i 0.739427 + 0.176053i
406406 0 0
407407 8.51671 + 14.7514i 0.422158 + 0.731199i
408408 0 0
409409 −1.98762 + 3.44266i −0.0982815 + 0.170229i −0.910973 0.412465i 0.864668π-0.864668\pi
0.812692 + 0.582694i 0.198001π0.198001\pi
410410 0 0
411411 6.80470 + 32.9981i 0.335651 + 1.62768i
412412 0 0
413413 −14.2880 −0.703066
414414 0 0
415415 −14.9752 −0.735106
416416 0 0
417417 3.86652 3.43913i 0.189345 0.168415i
418418 0 0
419419 4.72184 8.17847i 0.230677 0.399544i −0.727331 0.686287i 0.759239π-0.759239\pi
0.958008 + 0.286743i 0.0925726π0.0925726\pi
420420 0 0
421421 3.16002 + 5.47331i 0.154010 + 0.266753i 0.932698 0.360658i 0.117448π-0.117448\pi
−0.778688 + 0.627411i 0.784115π0.784115\pi
422422 0 0
423423 4.54325 38.6971i 0.220900 1.88152i
424424 0 0
425425 2.96727 + 5.13946i 0.143934 + 0.249300i
426426 0 0
427427 7.15452 12.3920i 0.346231 0.599690i
428428 0 0
429429 3.16613 + 1.05005i 0.152862 + 0.0506967i
430430 0 0
431431 −27.7541 −1.33687 −0.668434 0.743772i 0.733035π-0.733035\pi
−0.668434 + 0.743772i 0.733035π0.733035\pi
432432 0 0
433433 11.2473 0.540510 0.270255 0.962789i 0.412892π-0.412892\pi
0.270255 + 0.962789i 0.412892π0.412892\pi
434434 0 0
435435 −12.6032 4.17985i −0.604278 0.200409i
436436 0 0
437437 1.77561 3.07545i 0.0849391 0.147119i
438438 0 0
439439 7.54325 + 13.0653i 0.360020 + 0.623573i 0.987964 0.154686i 0.0494366π-0.0494366\pi
−0.627944 + 0.778259i 0.716103π0.716103\pi
440440 0 0
441441 −2.75526 + 1.18682i −0.131203 + 0.0565152i
442442 0 0
443443 −3.96658 6.87032i −0.188458 0.326419i 0.756278 0.654250i 0.227016π-0.227016\pi
−0.944736 + 0.327831i 0.893682π0.893682\pi
444444 0 0
445445 8.20396 14.2097i 0.388905 0.673603i
446446 0 0
447447 −10.4814 + 9.32284i −0.495755 + 0.440955i
448448 0 0
449449 −32.5636 −1.53677 −0.768386 0.639987i 0.778940π-0.778940\pi
−0.768386 + 0.639987i 0.778940π0.778940\pi
450450 0 0
451451 −14.5563 −0.685430
452452 0 0
453453 3.10074 + 15.0365i 0.145686 + 0.706475i
454454 0 0
455455 −0.660706 + 1.14438i −0.0309744 + 0.0536492i
456456 0 0
457457 −5.70396 9.87955i −0.266820 0.462146i 0.701219 0.712946i 0.252640π-0.252640\pi
−0.968039 + 0.250800i 0.919306π0.919306\pi
458458 0 0
459459 8.36831 + 11.9709i 0.390599 + 0.558752i
460460 0 0
461461 −2.45853 4.25830i −0.114505 0.198329i 0.803077 0.595876i 0.203195π-0.203195\pi
−0.917582 + 0.397547i 0.869862π0.869862\pi
462462 0 0
463463 −7.59957 + 13.1628i −0.353182 + 0.611729i −0.986805 0.161913i 0.948234π-0.948234\pi
0.633623 + 0.773642i 0.281567π0.281567\pi
464464 0 0
465465 3.03156 + 14.7010i 0.140585 + 0.681742i
466466 0 0
467467 23.7810 1.10046 0.550228 0.835015i 0.314541π-0.314541\pi
0.550228 + 0.835015i 0.314541π0.314541\pi
468468 0 0
469469 −7.98762 −0.368834
470470 0 0
471471 11.3436 10.0897i 0.522687 0.464910i
472472 0 0
473473 5.76400 9.98354i 0.265029 0.459044i
474474 0 0
475475 −5.26509 9.11941i −0.241579 0.418427i
476476 0 0
477477 4.54325 + 3.38597i 0.208021 + 0.155033i
478478 0 0
479479 −3.02909 5.24654i −0.138403 0.239720i 0.788489 0.615048i 0.210863π-0.210863\pi
−0.926892 + 0.375328i 0.877530π0.877530\pi
480480 0 0
481481 2.67309 4.62992i 0.121882 0.211106i
482482 0 0
483483 −1.17054 0.388209i −0.0532613 0.0176641i
484484 0 0
485485 −14.6872 −0.666914
486486 0 0
487487 1.13602 0.0514781 0.0257391 0.999669i 0.491806π-0.491806\pi
0.0257391 + 0.999669i 0.491806π0.491806\pi
488488 0 0
489489 −3.26764 1.08371i −0.147768 0.0490072i
490490 0 0
491491 16.4382 28.4718i 0.741845 1.28491i −0.209810 0.977742i 0.567285π-0.567285\pi
0.951655 0.307170i 0.0993821π-0.0993821\pi
492492 0 0
493493 −6.33929 10.9800i −0.285507 0.494513i
494494 0 0
495495 −10.1273 7.54760i −0.455188 0.339239i
496496 0 0
497497 −5.13162 8.88822i −0.230184 0.398691i
498498 0 0
499499 −13.0989 + 22.6879i −0.586387 + 1.01565i 0.408314 + 0.912841i 0.366117π0.366117\pi
−0.994701 + 0.102810i 0.967217π0.967217\pi
500500 0 0
501501 −3.39307 + 3.01801i −0.151591 + 0.134835i
502502 0 0
503503 −25.8516 −1.15267 −0.576333 0.817215i 0.695517π-0.695517\pi
−0.576333 + 0.817215i 0.695517π0.695517\pi
504504 0 0
505505 −4.09888 −0.182398
506506 0 0
507507 4.33613 + 21.0273i 0.192574 + 0.933854i
508508 0 0
509509 −17.5858 + 30.4595i −0.779478 + 1.35009i 0.152766 + 0.988262i 0.451182π0.451182\pi
−0.932243 + 0.361832i 0.882151π0.882151\pi
510510 0 0
511511 2.49381 + 4.31941i 0.110320 + 0.191079i
512512 0 0
513513 −14.8486 21.2410i −0.655584 0.937812i
514514 0 0
515515 −3.68292 6.37900i −0.162289 0.281092i
516516 0 0
517517 −16.0858 + 27.8615i −0.707453 + 1.22535i
518518 0 0
519519 1.82946 + 8.87163i 0.0803045 + 0.389421i
520520 0 0
521521 −17.8626 −0.782575 −0.391287 0.920269i 0.627970π-0.627970\pi
−0.391287 + 0.920269i 0.627970π0.627970\pi
522522 0 0
523523 −22.8640 −0.999772 −0.499886 0.866091i 0.666625π-0.666625\pi
−0.499886 + 0.866091i 0.666625π0.666625\pi
524524 0 0
525525 −2.73236 + 2.43033i −0.119250 + 0.106068i
526526 0 0
527527 −7.16621 + 12.4122i −0.312165 + 0.540685i
528528 0 0
529529 11.2465 + 19.4795i 0.488979 + 0.846937i
530530 0 0
531531 −39.3671 + 16.9573i −1.70839 + 0.735883i
532532 0 0
533533 2.28435 + 3.95661i 0.0989462 + 0.171380i
534534 0 0
535535 16.3145 28.2576i 0.705339 1.22168i
536536 0 0
537537 −7.83379 2.59808i −0.338053 0.112115i
538538 0 0
539539 2.47710 0.106696
540540 0 0
541541 22.3077 0.959081 0.479541 0.877520i 0.340803π-0.340803\pi
0.479541 + 0.877520i 0.340803π0.340803\pi
542542 0 0
543543 −17.1490 5.68747i −0.735935 0.244073i
544544 0 0
545545 16.1149 27.9118i 0.690287 1.19561i
546546 0 0
547547 −10.8083 18.7206i −0.462131 0.800435i 0.536936 0.843623i 0.319582π-0.319582\pi
−0.999067 + 0.0431882i 0.986249π0.986249\pi
548548 0 0
549549 5.00550 42.6343i 0.213630 1.81959i
550550 0 0
551551 11.2484 + 19.4828i 0.479197 + 0.829994i
552552 0 0
553553 −4.60507 + 7.97622i −0.195828 + 0.339183i
554554 0 0
555555 −15.1254 + 13.4535i −0.642039 + 0.571069i
556556 0 0
557557 3.17535 0.134544 0.0672720 0.997735i 0.478570π-0.478570\pi
0.0672720 + 0.997735i 0.478570π0.478570\pi
558558 0 0
559559 −3.61822 −0.153034
560560 0 0
561561 −2.43571 11.8115i −0.102836 0.498682i
562562 0 0
563563 −21.8814 + 37.8997i −0.922190 + 1.59728i −0.126171 + 0.992009i 0.540269π0.540269\pi
−0.796019 + 0.605271i 0.793065π0.793065\pi
564564 0 0
565565 10.9876 + 19.0311i 0.462253 + 0.800645i
566566 0 0
567567 −6.18292 + 6.53999i −0.259658 + 0.274654i
568568 0 0
569569 11.9313 + 20.6656i 0.500186 + 0.866348i 1.00000 0.000214897i 6.84039e5π6.84039e-5\pi
−0.499814 + 0.866133i 0.666598π0.666598\pi
570570 0 0
571571 −5.11058 + 8.85178i −0.213871 + 0.370435i −0.952923 0.303213i 0.901941π-0.901941\pi
0.739052 + 0.673649i 0.235274π0.235274\pi
572572 0 0
573573 −4.66002 22.5979i −0.194675 0.944040i
574574 0 0
575575 −1.50324 −0.0626893
576576 0 0
577577 −36.0370 −1.50024 −0.750120 0.661302i 0.770004π-0.770004\pi
−0.750120 + 0.661302i 0.770004π0.770004\pi
578578 0 0
579579 18.9487 16.8542i 0.787481 0.700435i
580580 0 0
581581 4.40545 7.63046i 0.182769 0.316565i
582582 0 0
583583 −2.33929 4.05178i −0.0968836 0.167807i
584584 0 0
585585 −0.462249 + 3.93720i −0.0191116 + 0.162783i
586586 0 0
587587 10.5142 + 18.2111i 0.433966 + 0.751651i 0.997211 0.0746391i 0.0237805π-0.0237805\pi
−0.563245 + 0.826290i 0.690447π0.690447\pi
588588 0 0
589589 12.7156 22.0242i 0.523939 0.907489i
590590 0 0
591591 −30.3905 10.0790i −1.25010 0.414595i
592592 0 0
593593 −25.1606 −1.03322 −0.516612 0.856220i 0.672807π-0.672807\pi
−0.516612 + 0.856220i 0.672807π0.672807\pi
594594 0 0
595595 4.77747 0.195857
596596 0 0
597597 38.8257 + 12.8766i 1.58903 + 0.527002i
598598 0 0
599599 1.11126 1.92477i 0.0454050 0.0786438i −0.842430 0.538806i 0.818875π-0.818875\pi
0.887835 + 0.460162i 0.152209π0.152209\pi
600600 0 0
601601 −14.0494 24.3343i −0.573089 0.992619i −0.996246 0.0865627i 0.972412π-0.972412\pi
0.423158 0.906056i 0.360922π-0.360922\pi
602602 0 0
603603 −22.0080 + 9.47987i −0.896234 + 0.386050i
604604 0 0
605605 −4.13348 7.15939i −0.168050 0.291071i
606606 0 0
607607 3.26509 5.65531i 0.132526 0.229542i −0.792124 0.610361i 0.791025π-0.791025\pi
0.924650 + 0.380819i 0.124358π0.124358\pi
608608 0 0
609609 5.83743 5.19218i 0.236545 0.210398i
610610 0 0
611611 10.0975 0.408501
612612 0 0
613613 10.7280 0.433298 0.216649 0.976250i 0.430487π-0.430487\pi
0.216649 + 0.976250i 0.430487π0.430487\pi
614614 0 0
615615 −3.49381 16.9426i −0.140884 0.683191i
616616 0 0
617617 15.5265 26.8928i 0.625075 1.08266i −0.363451 0.931613i 0.618402π-0.618402\pi
0.988526 0.151049i 0.0482650π-0.0482650\pi
618618 0 0
619619 0.723217 + 1.25265i 0.0290685 + 0.0503482i 0.880194 0.474615i 0.157413π-0.157413\pi
−0.851125 + 0.524963i 0.824079π0.824079\pi
620620 0 0
621621 −3.68587 + 0.319601i −0.147909 + 0.0128252i
622622 0 0
623623 4.82691 + 8.36046i 0.193386 + 0.334955i
624624 0 0
625625 4.99312 8.64834i 0.199725 0.345934i
626626 0 0
627627 4.32189 + 20.9582i 0.172600 + 0.836991i
628628 0 0
629629 −19.3287 −0.770686
630630 0 0
631631 0.0741250 0.00295087 0.00147544 0.999999i 0.499530π-0.499530\pi
0.00147544 + 0.999999i 0.499530π0.499530\pi
632632 0 0
633633 18.8367 16.7546i 0.748693 0.665935i
634634 0 0
635635 14.9814 25.9486i 0.594520 1.02974i
636636 0 0
637637 −0.388736 0.673310i −0.0154023 0.0266775i
638638 0 0
639639 −24.6877 18.3991i −0.976628 0.727855i
640640 0 0
641641 23.5204 + 40.7384i 0.928998 + 1.60907i 0.785002 + 0.619494i 0.212662π0.212662\pi
0.143996 + 0.989578i 0.454005π0.454005\pi
642642 0 0
643643 16.8647 29.2105i 0.665077 1.15195i −0.314187 0.949361i 0.601732π-0.601732\pi
0.979264 0.202587i 0.0649348π-0.0649348\pi
644644 0 0
645645 13.0036 + 4.31266i 0.512018 + 0.169811i
646646 0 0
647647 44.9629 1.76767 0.883836 0.467796i 0.154952π-0.154952\pi
0.883836 + 0.467796i 0.154952π0.154952\pi
648648 0 0
649649 35.3928 1.38929
650650 0 0
651651 −8.38255 2.78007i −0.328538 0.108960i
652652 0 0
653653 −20.8578 + 36.1267i −0.816228 + 1.41375i 0.0922143 + 0.995739i 0.470606π0.470606\pi
−0.908443 + 0.418010i 0.862728π0.862728\pi
654654 0 0
655655 −4.83310 8.37118i −0.188845 0.327089i
656656 0 0
657657 11.9975 + 8.94138i 0.468065 + 0.348837i
658658 0 0
659659 10.5259 + 18.2313i 0.410029 + 0.710191i 0.994892 0.100941i 0.0321852π-0.0321852\pi
−0.584863 + 0.811132i 0.698852π0.698852\pi
660660 0 0
661661 −11.2218 + 19.4368i −0.436479 + 0.756004i −0.997415 0.0718553i 0.977108π-0.977108\pi
0.560936 + 0.827859i 0.310441π0.310441\pi
662662 0 0
663663 −2.82829 + 2.51566i −0.109842 + 0.0977001i
664664 0 0
665665 −8.47710 −0.328728
666666 0 0
667667 3.21153 0.124351
668668 0 0
669669 −3.30401 16.0222i −0.127741 0.619454i
670670 0 0
671671 −17.7225 + 30.6962i −0.684168 + 1.18501i
672672 0 0
673673 5.83929 + 10.1140i 0.225088 + 0.389864i 0.956346 0.292237i 0.0943996π-0.0943996\pi
−0.731258 + 0.682101i 0.761066π0.761066\pi
674674 0 0
675675 −4.64400 + 9.93902i −0.178747 + 0.382553i
676676 0 0
677677 −5.23422 9.06593i −0.201167 0.348432i 0.747737 0.663995i 0.231140π-0.231140\pi
−0.948905 + 0.315562i 0.897807π0.897807\pi
678678 0 0
679679 4.32072 7.48371i 0.165814 0.287199i
680680 0 0
681681 −6.68539 32.4195i −0.256185 1.24232i
682682 0 0
683683 32.8158 1.25566 0.627832 0.778349i 0.283943π-0.283943\pi
0.627832 + 0.778349i 0.283943π0.283943\pi
684684 0 0
685685 33.0617 1.26322
686686 0 0
687687 −14.8120 + 13.1747i −0.565113 + 0.502647i
688688 0 0
689689 −0.734219 + 1.27171i −0.0279715 + 0.0484481i
690690 0 0
691691 −2.95056 5.11052i −0.112245 0.194413i 0.804430 0.594047i 0.202471π-0.202471\pi
−0.916675 + 0.399634i 0.869137π0.869137\pi
692692 0 0
693693 6.82505 2.93987i 0.259262 0.111676i
694694 0 0
695695 −2.53892 4.39754i −0.0963068 0.166808i
696696 0 0
697697 8.25890 14.3048i 0.312828 0.541834i
698698 0 0
699699 −1.95715 0.649089i −0.0740263 0.0245508i
700700 0 0
701701 −12.3782 −0.467519 −0.233759 0.972294i 0.575103π-0.575103\pi
−0.233759 + 0.972294i 0.575103π0.575103\pi
702702 0 0
703703 34.2967 1.29352
704704 0 0
705705 −36.2898 12.0355i −1.36675 0.453283i
706706 0 0
707707 1.20582 2.08854i 0.0453495 0.0785476i
708708 0 0
709709 6.64145 + 11.5033i 0.249425 + 0.432016i 0.963366 0.268189i 0.0864251π-0.0864251\pi
−0.713942 + 0.700205i 0.753092π0.753092\pi
710710 0 0
711711 −3.22184 + 27.4420i −0.120828 + 1.02915i
712712 0 0
713713 −1.81522 3.14406i −0.0679806 0.117746i
714714 0 0
715715 1.63664 2.83474i 0.0612067 0.106013i
716716 0 0
717717 −31.4265 + 27.9527i −1.17364 + 1.04391i
718718 0 0
719719 −24.3694 −0.908825 −0.454413 0.890791i 0.650151π-0.650151\pi
−0.454413 + 0.890791i 0.650151π0.650151\pi
720720 0 0
721721 4.33379 0.161399
722722 0 0
723723 7.49264 + 36.3342i 0.278654 + 1.35128i
724724 0 0
725725 4.76145 8.24707i 0.176836 0.306289i
726726 0 0
727727 7.99450 + 13.8469i 0.296500 + 0.513552i 0.975333 0.220740i 0.0708473π-0.0708473\pi
−0.678833 + 0.734293i 0.737514π0.737514\pi
728728 0 0
729729 −9.27375 + 25.3574i −0.343472 + 0.939163i
730730 0 0
731731 6.54070 + 11.3288i 0.241917 + 0.419012i
732732 0 0
733733 21.1414 36.6181i 0.780877 1.35252i −0.150554 0.988602i 0.548106π-0.548106\pi
0.931431 0.363917i 0.118561π-0.118561\pi
734734 0 0
735735 0.594554 + 2.88318i 0.0219304 + 0.106348i
736736 0 0
737737 19.7861 0.728832
738738 0 0
739739 −3.08650 −0.113539 −0.0567695 0.998387i 0.518080π-0.518080\pi
−0.0567695 + 0.998387i 0.518080π0.518080\pi
740740 0 0
741741 5.01849 4.46376i 0.184359 0.163980i
742742 0 0
743743 −3.31522 + 5.74213i −0.121624 + 0.210658i −0.920408 0.390959i 0.872143π-0.872143\pi
0.798784 + 0.601617i 0.205477π0.205477\pi
744744 0 0
745745 6.88255 + 11.9209i 0.252157 + 0.436749i
746746 0 0
747747 3.08217 26.2524i 0.112771 0.960524i
748748 0 0
749749 9.59888 + 16.6258i 0.350736 + 0.607492i
750750 0 0
751751 21.3702 37.0142i 0.779808 1.35067i −0.152243 0.988343i 0.548650π-0.548650\pi
0.932052 0.362325i 0.118017π-0.118017\pi
752752 0 0
753753 −4.40585 1.46120i −0.160558 0.0532491i
754754 0 0
755755 15.0655 0.548288
756756 0 0
757757 −31.0232 −1.12756 −0.563779 0.825926i 0.690653π-0.690653\pi
−0.563779 + 0.825926i 0.690653π0.690653\pi
758758 0 0
759759 2.89954 + 0.961632i 0.105247 + 0.0349050i
760760 0 0
761761 −11.8182 + 20.4697i −0.428409 + 0.742025i −0.996732 0.0807799i 0.974259π-0.974259\pi
0.568323 + 0.822805i 0.307592π0.307592\pi
762762 0 0
763763 9.48143 + 16.4223i 0.343251 + 0.594528i
764764 0 0
765765 13.1632 5.67000i 0.475916 0.204999i
766766 0 0
767767 −5.55425 9.62025i −0.200553 0.347367i
768768 0 0
769769 1.73422 3.00376i 0.0625375 0.108318i −0.833061 0.553180i 0.813414π-0.813414\pi
0.895599 + 0.444862i 0.146747π0.146747\pi
770770 0 0
771771 14.3462 12.7604i 0.516665 0.459554i
772772 0 0
773773 34.5970 1.24437 0.622184 0.782871i 0.286245π-0.286245\pi
0.622184 + 0.782871i 0.286245π0.286245\pi
774774 0 0
775775 −10.7651 −0.386694
776776 0 0
777777 −2.40545 11.6648i −0.0862949 0.418471i
778778 0 0
779779 −14.6545 + 25.3824i −0.525053 + 0.909418i
780780 0 0
781781 12.7115 + 22.0170i 0.454854 + 0.787831i
782782 0 0
783783 9.92147 21.2338i 0.354564 0.758834i
784784 0 0
785785 −7.44870 12.9015i −0.265855 0.460475i
786786 0 0
787787 6.07963 10.5302i 0.216715 0.375362i −0.737087 0.675798i 0.763799π-0.763799\pi
0.953802 + 0.300437i 0.0971323π0.0971323\pi
788788 0 0
789789 −4.69028 22.7446i −0.166978 0.809730i
790790 0 0
791791 −12.9294 −0.459718
792792 0 0
793793 11.1249 0.395056
794794 0 0
795795 4.15452 3.69529i 0.147346 0.131058i
796796 0 0
797797 −2.89493 + 5.01416i −0.102544 + 0.177611i −0.912732 0.408559i 0.866031π-0.866031\pi
0.810188 + 0.586170i 0.199365π0.199365\pi
798798 0 0
799799 −18.2534 31.6158i −0.645759 1.11849i
800800 0 0
801801 23.2218 + 17.3066i 0.820501 + 0.611497i
802802 0 0
803803 −6.17742 10.6996i −0.217996 0.377581i
804804 0 0
805805 −0.605074 + 1.04802i −0.0213261 + 0.0369378i
806806 0 0
807807 6.72431 + 2.23012i 0.236707 + 0.0785038i
808808 0 0
809809 −49.1817 −1.72914 −0.864568 0.502516i 0.832408π-0.832408\pi
−0.864568 + 0.502516i 0.832408π0.832408\pi
810810 0 0
811811 40.7266 1.43010 0.715052 0.699072i 0.246403π-0.246403\pi
0.715052 + 0.699072i 0.246403π0.246403\pi
812812 0 0
813813 10.0672 + 3.33880i 0.353074 + 0.117097i
814814 0 0
815815 −1.68911 + 2.92562i −0.0591669 + 0.102480i
816816 0 0
817817 −11.6058 20.1018i −0.406034 0.703272i
818818 0 0
819819 −1.87017 1.39379i −0.0653489 0.0487028i
820820 0 0
821821 −7.54689 13.0716i −0.263388 0.456202i 0.703752 0.710446i 0.251507π-0.251507\pi
−0.967140 + 0.254244i 0.918173π0.918173\pi
822822 0 0
823823 −8.00000 + 13.8564i −0.278862 + 0.483004i −0.971102 0.238664i 0.923291π-0.923291\pi
0.692240 + 0.721668i 0.256624π0.256624\pi
824824 0 0
825825 6.76833 6.02018i 0.235643 0.209596i
826826 0 0
827827 35.2348 1.22523 0.612616 0.790381i 0.290117π-0.290117\pi
0.612616 + 0.790381i 0.290117π0.290117\pi
828828 0 0
829829 −3.23491 −0.112353 −0.0561765 0.998421i 0.517891π-0.517891\pi
−0.0561765 + 0.998421i 0.517891π0.517891\pi
830830 0 0
831831 −5.51485 26.7432i −0.191308 0.927713i
832832 0 0
833833 −1.40545 + 2.43430i −0.0486958 + 0.0843436i
834834 0 0
835835 2.22803 + 3.85906i 0.0771041 + 0.133548i
836836 0 0
837837 −26.3955 + 2.28875i −0.912363 + 0.0791109i
838838 0 0
839839 15.5197 + 26.8808i 0.535798 + 0.928030i 0.999124 + 0.0418419i 0.0133226π0.0133226\pi
−0.463326 + 0.886188i 0.653344π0.653344\pi
840840 0 0
841841 4.32760 7.49563i 0.149228 0.258470i
842842 0 0
843843 7.41225 + 35.9443i 0.255291 + 1.23799i
844844 0 0
845845 21.0678 0.724755
846846 0 0
847847 4.86398 0.167128
848848 0 0
849849 −8.89926 + 7.91556i −0.305422 + 0.271661i
850850 0 0
851851 2.44801 4.24008i 0.0839167 0.145348i
852852 0 0
853853 8.03637 + 13.9194i 0.275160 + 0.476591i 0.970176 0.242403i 0.0779358π-0.0779358\pi
−0.695015 + 0.718995i 0.744602π0.744602\pi
854854 0 0
855855 −23.3566 + 10.0608i −0.798779 + 0.344072i
856856 0 0
857857 −9.61058 16.6460i −0.328291 0.568617i 0.653882 0.756597i 0.273139π-0.273139\pi
−0.982173 + 0.187980i 0.939806π0.939806\pi
858858 0 0
859859 7.40112 12.8191i 0.252523 0.437382i −0.711697 0.702487i 0.752073π-0.752073\pi
0.964220 + 0.265104i 0.0854064π0.0854064\pi
860860 0 0
861861 9.66071 + 3.20397i 0.329236 + 0.109191i
862862 0 0
863863 14.7688 0.502736 0.251368 0.967892i 0.419120π-0.419120\pi
0.251368 + 0.967892i 0.419120π0.419120\pi
864864 0 0
865865 8.88874 0.302226
866866 0 0
867867 −14.9585 4.96099i −0.508018 0.168484i
868868 0 0
869869 11.4072 19.7579i 0.386964 0.670241i
870870 0 0
871871 −3.10507 5.37815i −0.105211 0.182232i
872872 0 0
873873 3.02290 25.7475i 0.102310 0.871421i
874874 0 0
875875 6.04325 + 10.4672i 0.204299 + 0.353857i
876876 0 0
877877 −26.1916 + 45.3651i −0.884427 + 1.53187i −0.0380575 + 0.999276i 0.512117π0.512117\pi
−0.846369 + 0.532597i 0.821216π0.821216\pi
878878 0 0
879879 35.5988 31.6638i 1.20072 1.06799i
880880 0 0
881881 −31.3214 −1.05525 −0.527623 0.849479i 0.676916π-0.676916\pi
−0.527623 + 0.849479i 0.676916π0.676916\pi
882882 0 0
883883 −43.0494 −1.44873 −0.724363 0.689419i 0.757866π-0.757866\pi
−0.724363 + 0.689419i 0.757866π0.757866\pi
884884 0 0
885885 8.49498 + 41.1948i 0.285556 + 1.38475i
886886 0 0
887887 7.48831 12.9701i 0.251433 0.435494i −0.712488 0.701685i 0.752432π-0.752432\pi
0.963921 + 0.266190i 0.0857649π0.0857649\pi
888888 0 0
889889 8.81453 + 15.2672i 0.295630 + 0.512046i
890890 0 0
891891 15.3157 16.2002i 0.513095 0.542728i
892892 0 0
893893 32.3887 + 56.0988i 1.08385 + 1.87727i
894894 0 0
895895 −4.04944 + 7.01384i −0.135358 + 0.234447i
896896 0 0
897897 −0.193645 0.939046i −0.00646562 0.0313538i
898898 0 0
899899 22.9986 0.767047
900900 0 0
901901 5.30903 0.176870
902902 0 0
903903 −6.02290 + 5.35715i −0.200430 + 0.178275i
904904 0 0
905905 −8.86467 + 15.3541i −0.294671 + 0.510386i
906906 0 0
907907 −15.2280 26.3756i −0.505636 0.875787i −0.999979 0.00652002i 0.997925π-0.997925\pi
0.494343 0.869267i 0.335409π-0.335409\pi
908908 0 0
909909 0.843624 7.18555i 0.0279812 0.238330i
910910 0 0
911911 9.97593 + 17.2788i 0.330517 + 0.572473i 0.982613 0.185664i 0.0594435π-0.0594435\pi
−0.652096 + 0.758136i 0.726110π0.726110\pi
912912 0 0
913913 −10.9127 + 18.9014i −0.361159 + 0.625545i
914914 0 0
915915 −39.9820 13.2600i −1.32177 0.438363i
916916 0 0
917917 5.68725 0.187809
918918 0 0
919919 45.6291 1.50516 0.752582 0.658498i 0.228808π-0.228808\pi
0.752582 + 0.658498i 0.228808π0.228808\pi
920920 0 0
921921 −35.3752 11.7322i −1.16565 0.386588i
922922 0 0
923923 3.98969 6.91034i 0.131322 0.227457i
924924 0 0
925925 −7.25890 12.5728i −0.238671 0.413391i
926926 0 0
927927 11.9407 5.14343i 0.392185 0.168932i
928928 0 0
929929 −28.1861 48.8197i −0.924755 1.60172i −0.791954 0.610580i 0.790936π-0.790936\pi
−0.132801 0.991143i 0.542397π-0.542397\pi
930930 0 0
931931 2.49381 4.31941i 0.0817313 0.141563i
932932 0 0
933933 −23.7942 + 21.1640i −0.778987 + 0.692880i
934934 0 0
935935 −11.8343 −0.387022
936936 0 0
937937 −36.8530 −1.20393 −0.601967 0.798521i 0.705616π-0.705616\pi
−0.601967 + 0.798521i 0.705616π0.705616\pi
938938 0 0
939939 0.000481840 0.00233659i 1.57243e−5 7.62519e-5i
940940 0 0
941941 4.38000 7.58638i 0.142784 0.247309i −0.785760 0.618531i 0.787728π-0.787728\pi
0.928544 + 0.371223i 0.121061π0.121061\pi
942942 0 0
943943 2.09201 + 3.62346i 0.0681251 + 0.117996i
944944 0 0
945945 5.05996 + 7.23828i 0.164601 + 0.235461i
946946 0 0
947947 −13.3226 23.0754i −0.432926 0.749849i 0.564198 0.825640i 0.309185π-0.309185\pi
−0.997124 + 0.0757901i 0.975852π0.975852\pi
948948 0 0
949949 −1.93887 + 3.35822i −0.0629383 + 0.109012i
950950 0 0
951951 −4.93199 23.9168i −0.159931 0.775554i
952952 0 0
953953 24.3039 0.787282 0.393641 0.919264i 0.371215π-0.371215\pi
0.393641 + 0.919264i 0.371215π0.371215\pi
954954 0 0
955955 −22.6414 −0.732660
956956 0 0
957957 −14.4599 + 12.8616i −0.467422 + 0.415755i
958958 0 0
959959 −9.72617 + 16.8462i −0.314074 + 0.543993i
960960 0 0
961961 2.50069 + 4.33132i 0.0806674 + 0.139720i
962962 0 0
963963 46.1792 + 34.4161i 1.48810 + 1.10904i
964964 0 0
965965 −12.4425 21.5511i −0.400539 0.693753i
966966 0 0
967967 5.22872 9.05641i 0.168144 0.291234i −0.769623 0.638498i 0.779556π-0.779556\pi
0.937767 + 0.347264i 0.112889π0.112889\pi
968968 0 0
969969 −23.0483 7.64396i −0.740417 0.245559i
970970 0 0
971971 −41.7156 −1.33872 −0.669358 0.742940i 0.733431π-0.733431\pi
−0.669358 + 0.742940i 0.733431π0.733431\pi
972972 0 0
973973 2.98762 0.0957787
974974 0 0
975975 −2.69853 0.894969i −0.0864223 0.0286619i
976976 0 0
977977 −2.94506 + 5.10099i −0.0942207 + 0.163195i −0.909283 0.416178i 0.863369π-0.863369\pi
0.815062 + 0.579373i 0.196703π0.196703\pi
978978 0 0
979979 −11.9567 20.7097i −0.382139 0.661885i
980980 0 0
981981 45.6141 + 33.9950i 1.45635 + 1.08538i
982982 0 0
983983 −20.9196 36.2338i −0.667232 1.15568i −0.978675 0.205415i 0.934146π-0.934146\pi
0.311443 0.950265i 0.399188π-0.399188\pi
984984 0 0
985985 −15.7095 + 27.2096i −0.500545 + 0.866969i
986986 0 0
987987 16.8083 14.9504i 0.535015 0.475876i
988988 0 0
989989 −3.31356 −0.105365
990990 0 0
991991 −54.7156 −1.73810 −0.869049 0.494726i 0.835268π-0.835268\pi
−0.869049 + 0.494726i 0.835268π0.835268\pi
992992 0 0
993993 −4.88441 23.6860i −0.155002 0.751653i
994994 0 0
995995 20.0698 34.7619i 0.636255 1.10203i
996996 0 0
997997 9.02476 + 15.6313i 0.285817 + 0.495050i 0.972807 0.231617i 0.0744017π-0.0744017\pi
−0.686990 + 0.726667i 0.741068π0.741068\pi
998998 0 0
999999 −20.4716 29.2846i −0.647693 0.926524i
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 252.2.j.a.85.3 6
3.2 odd 2 756.2.j.b.253.1 6
4.3 odd 2 1008.2.r.j.337.1 6
7.2 even 3 1764.2.l.e.949.1 6
7.3 odd 6 1764.2.i.d.373.3 6
7.4 even 3 1764.2.i.g.373.1 6
7.5 odd 6 1764.2.l.f.949.3 6
7.6 odd 2 1764.2.j.e.589.1 6
9.2 odd 6 756.2.j.b.505.1 6
9.4 even 3 2268.2.a.i.1.1 3
9.5 odd 6 2268.2.a.h.1.3 3
9.7 even 3 inner 252.2.j.a.169.3 yes 6
12.11 even 2 3024.2.r.j.1009.1 6
21.2 odd 6 5292.2.l.e.361.3 6
21.5 even 6 5292.2.l.f.361.1 6
21.11 odd 6 5292.2.i.f.1549.1 6
21.17 even 6 5292.2.i.e.1549.3 6
21.20 even 2 5292.2.j.d.1765.3 6
36.7 odd 6 1008.2.r.j.673.1 6
36.11 even 6 3024.2.r.j.2017.1 6
36.23 even 6 9072.2.a.bv.1.3 3
36.31 odd 6 9072.2.a.by.1.1 3
63.2 odd 6 5292.2.i.f.2125.1 6
63.11 odd 6 5292.2.l.e.3313.3 6
63.16 even 3 1764.2.i.g.1537.1 6
63.20 even 6 5292.2.j.d.3529.3 6
63.25 even 3 1764.2.l.e.961.1 6
63.34 odd 6 1764.2.j.e.1177.1 6
63.38 even 6 5292.2.l.f.3313.1 6
63.47 even 6 5292.2.i.e.2125.3 6
63.52 odd 6 1764.2.l.f.961.3 6
63.61 odd 6 1764.2.i.d.1537.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.j.a.85.3 6 1.1 even 1 trivial
252.2.j.a.169.3 yes 6 9.7 even 3 inner
756.2.j.b.253.1 6 3.2 odd 2
756.2.j.b.505.1 6 9.2 odd 6
1008.2.r.j.337.1 6 4.3 odd 2
1008.2.r.j.673.1 6 36.7 odd 6
1764.2.i.d.373.3 6 7.3 odd 6
1764.2.i.d.1537.3 6 63.61 odd 6
1764.2.i.g.373.1 6 7.4 even 3
1764.2.i.g.1537.1 6 63.16 even 3
1764.2.j.e.589.1 6 7.6 odd 2
1764.2.j.e.1177.1 6 63.34 odd 6
1764.2.l.e.949.1 6 7.2 even 3
1764.2.l.e.961.1 6 63.25 even 3
1764.2.l.f.949.3 6 7.5 odd 6
1764.2.l.f.961.3 6 63.52 odd 6
2268.2.a.h.1.3 3 9.5 odd 6
2268.2.a.i.1.1 3 9.4 even 3
3024.2.r.j.1009.1 6 12.11 even 2
3024.2.r.j.2017.1 6 36.11 even 6
5292.2.i.e.1549.3 6 21.17 even 6
5292.2.i.e.2125.3 6 63.47 even 6
5292.2.i.f.1549.1 6 21.11 odd 6
5292.2.i.f.2125.1 6 63.2 odd 6
5292.2.j.d.1765.3 6 21.20 even 2
5292.2.j.d.3529.3 6 63.20 even 6
5292.2.l.e.361.3 6 21.2 odd 6
5292.2.l.e.3313.3 6 63.11 odd 6
5292.2.l.f.361.1 6 21.5 even 6
5292.2.l.f.3313.1 6 63.38 even 6
9072.2.a.bv.1.3 3 36.23 even 6
9072.2.a.by.1.1 3 36.31 odd 6