Properties

Label 252.2.j.a.169.2
Level 252252
Weight 22
Character 252.169
Analytic conductor 2.0122.012
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,2,Mod(85,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
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")
 
//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

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: 2.012230130942.01223013094
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
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 169.2
Root 0.500000+2.05195i0.500000 + 2.05195i of defining polynomial
Character χ\chi == 252.169
Dual form 252.2.j.a.85.2

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+(0.9334631.45899i)q3+(1.230252.13086i)q5+(0.5000000.866025i)q7+(1.25729+2.72382i)q9+(2.32383+4.02499i)q11+(3.554086.15585i)q13+(1.96050+3.78400i)q154.51459q17+4.32743q19+(1.73025+0.0789082i)q21+(2.933465.08091i)q23+(0.527042+0.912864i)q25+(5.147660.708209i)q27+(3.487556.04061i)q29+(3.69076+6.39258i)q31+(8.041630.366739i)q332.46050q350.726654q37+(5.66372+10.9316i)q39+(0.1366730.236725i)q41+(2.417414.18708i)q43+(7.350870.671871i)q45+(1.83628+3.18054i)q47+(0.5000000.866025i)q49+(4.21420+6.58673i)q51+5.05408q53+11.4356q55+(4.039506.31367i)q57+(4.566547.90947i)q59+(6.9085611.9660i)q61+(1.73025+2.45076i)q63+(8.74484+15.1465i)q65+(0.663715+1.14959i)q67+(4.67471+9.02273i)q69+13.5218q714.32743q73+(1.823830.0831759i)q75+(2.32383+4.02499i)q77+(3.21780+5.57339i)q79+(5.838426.84929i)q81+(0.742705+1.28640i)q83+(5.55408+9.61996i)q85+(12.0687+0.550392i)q87+9.83482q897.10817q91+(5.8815111.3520i)q93+(5.323839.22115i)q95+(0.2463040.426611i)q97+(8.0416311.3903i)q99+O(q100)q+(-0.933463 - 1.45899i) q^{3} +(-1.23025 - 2.13086i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-1.25729 + 2.72382i) q^{9} +(-2.32383 + 4.02499i) q^{11} +(-3.55408 - 6.15585i) q^{13} +(-1.96050 + 3.78400i) q^{15} -4.51459 q^{17} +4.32743 q^{19} +(-1.73025 + 0.0789082i) q^{21} +(-2.93346 - 5.08091i) q^{23} +(-0.527042 + 0.912864i) q^{25} +(5.14766 - 0.708209i) q^{27} +(3.48755 - 6.04061i) q^{29} +(3.69076 + 6.39258i) q^{31} +(8.04163 - 0.366739i) q^{33} -2.46050 q^{35} -0.726654 q^{37} +(-5.66372 + 10.9316i) q^{39} +(-0.136673 - 0.236725i) q^{41} +(2.41741 - 4.18708i) q^{43} +(7.35087 - 0.671871i) q^{45} +(-1.83628 + 3.18054i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(4.21420 + 6.58673i) q^{51} +5.05408 q^{53} +11.4356 q^{55} +(-4.03950 - 6.31367i) q^{57} +(-4.56654 - 7.90947i) q^{59} +(6.90856 - 11.9660i) q^{61} +(1.73025 + 2.45076i) q^{63} +(-8.74484 + 15.1465i) q^{65} +(0.663715 + 1.14959i) q^{67} +(-4.67471 + 9.02273i) q^{69} +13.5218 q^{71} -4.32743 q^{73} +(1.82383 - 0.0831759i) q^{75} +(2.32383 + 4.02499i) q^{77} +(-3.21780 + 5.57339i) q^{79} +(-5.83842 - 6.84929i) q^{81} +(-0.742705 + 1.28640i) q^{83} +(5.55408 + 9.61996i) q^{85} +(-12.0687 + 0.550392i) q^{87} +9.83482 q^{89} -7.10817 q^{91} +(5.88151 - 11.3520i) q^{93} +(-5.32383 - 9.22115i) q^{95} +(0.246304 - 0.426611i) q^{97} +(-8.04163 - 11.3903i) 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(23)e\left(\frac{2}{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 −0.933463 1.45899i −0.538935 0.842347i
44 0 0
55 −1.23025 2.13086i −0.550186 0.952949i −0.998261 0.0589535i 0.981224π-0.981224\pi
0.448075 0.893996i 0.352110π-0.352110\pi
66 0 0
77 0.500000 0.866025i 0.188982 0.327327i
88 0 0
99 −1.25729 + 2.72382i −0.419098 + 0.907941i
1010 0 0
1111 −2.32383 + 4.02499i −0.700662 + 1.21358i 0.267573 + 0.963538i 0.413778π0.413778\pi
−0.968234 + 0.250044i 0.919555π0.919555\pi
1212 0 0
1313 −3.55408 6.15585i −0.985726 1.70733i −0.638667 0.769484i 0.720514π-0.720514\pi
−0.347059 0.937843i 0.612820π-0.612820\pi
1414 0 0
1515 −1.96050 + 3.78400i −0.506200 + 0.977025i
1616 0 0
1717 −4.51459 −1.09495 −0.547474 0.836822i 0.684411π-0.684411\pi
−0.547474 + 0.836822i 0.684411π0.684411\pi
1818 0 0
1919 4.32743 0.992781 0.496390 0.868099i 0.334658π-0.334658\pi
0.496390 + 0.868099i 0.334658π0.334658\pi
2020 0 0
2121 −1.73025 + 0.0789082i −0.377572 + 0.0172192i
2222 0 0
2323 −2.93346 5.08091i −0.611669 1.05944i −0.990959 0.134164i 0.957165π-0.957165\pi
0.379290 0.925278i 0.376168π-0.376168\pi
2424 0 0
2525 −0.527042 + 0.912864i −0.105408 + 0.182573i
2626 0 0
2727 5.14766 0.708209i 0.990668 0.136295i
2828 0 0
2929 3.48755 6.04061i 0.647621 1.12171i −0.336068 0.941838i 0.609097π-0.609097\pi
0.983689 0.179875i 0.0575694π-0.0575694\pi
3030 0 0
3131 3.69076 + 6.39258i 0.662880 + 1.14814i 0.979856 + 0.199708i 0.0639992π0.0639992\pi
−0.316976 + 0.948434i 0.602667π0.602667\pi
3232 0 0
3333 8.04163 0.366739i 1.39987 0.0638411i
3434 0 0
3535 −2.46050 −0.415901
3636 0 0
3737 −0.726654 −0.119461 −0.0597306 0.998215i 0.519024π-0.519024\pi
−0.0597306 + 0.998215i 0.519024π0.519024\pi
3838 0 0
3939 −5.66372 + 10.9316i −0.906920 + 1.75046i
4040 0 0
4141 −0.136673 0.236725i −0.0213448 0.0369702i 0.855156 0.518371i 0.173461π-0.173461\pi
−0.876500 + 0.481401i 0.840128π0.840128\pi
4242 0 0
4343 2.41741 4.18708i 0.368652 0.638524i −0.620703 0.784046i 0.713153π-0.713153\pi
0.989355 + 0.145522i 0.0464862π0.0464862\pi
4444 0 0
4545 7.35087 0.671871i 1.09580 0.100157i
4646 0 0
4747 −1.83628 + 3.18054i −0.267850 + 0.463929i −0.968306 0.249766i 0.919646π-0.919646\pi
0.700457 + 0.713695i 0.252980π0.252980\pi
4848 0 0
4949 −0.500000 0.866025i −0.0714286 0.123718i
5050 0 0
5151 4.21420 + 6.58673i 0.590106 + 0.922327i
5252 0 0
5353 5.05408 0.694232 0.347116 0.937822i 0.387161π-0.387161\pi
0.347116 + 0.937822i 0.387161π0.387161\pi
5454 0 0
5555 11.4356 1.54198
5656 0 0
5757 −4.03950 6.31367i −0.535044 0.836266i
5858 0 0
5959 −4.56654 7.90947i −0.594513 1.02973i −0.993615 0.112820i 0.964012π-0.964012\pi
0.399103 0.916906i 0.369322π-0.369322\pi
6060 0 0
6161 6.90856 11.9660i 0.884550 1.53209i 0.0383215 0.999265i 0.487799π-0.487799\pi
0.846228 0.532820i 0.178868π-0.178868\pi
6262 0 0
6363 1.73025 + 2.45076i 0.217991 + 0.308767i
6464 0 0
6565 −8.74484 + 15.1465i −1.08466 + 1.87869i
6666 0 0
6767 0.663715 + 1.14959i 0.0810857 + 0.140445i 0.903717 0.428131i 0.140828π-0.140828\pi
−0.822631 + 0.568576i 0.807495π0.807495\pi
6868 0 0
6969 −4.67471 + 9.02273i −0.562768 + 1.08621i
7070 0 0
7171 13.5218 1.60474 0.802370 0.596826i 0.203572π-0.203572\pi
0.802370 + 0.596826i 0.203572π0.203572\pi
7272 0 0
7373 −4.32743 −0.506487 −0.253244 0.967403i 0.581497π-0.581497\pi
−0.253244 + 0.967403i 0.581497π0.581497\pi
7474 0 0
7575 1.82383 0.0831759i 0.210598 0.00960433i
7676 0 0
7777 2.32383 + 4.02499i 0.264825 + 0.458691i
7878 0 0
7979 −3.21780 + 5.57339i −0.362031 + 0.627056i −0.988295 0.152555i 0.951250π-0.951250\pi
0.626264 + 0.779611i 0.284583π0.284583\pi
8080 0 0
8181 −5.83842 6.84929i −0.648713 0.761033i
8282 0 0
8383 −0.742705 + 1.28640i −0.0815225 + 0.141201i −0.903904 0.427735i 0.859312π-0.859312\pi
0.822382 + 0.568936i 0.192645π0.192645\pi
8484 0 0
8585 5.55408 + 9.61996i 0.602425 + 1.04343i
8686 0 0
8787 −12.0687 + 0.550392i −1.29390 + 0.0590083i
8888 0 0
8989 9.83482 1.04249 0.521245 0.853407i 0.325468π-0.325468\pi
0.521245 + 0.853407i 0.325468π0.325468\pi
9090 0 0
9191 −7.10817 −0.745139
9292 0 0
9393 5.88151 11.3520i 0.609885 1.17715i
9494 0 0
9595 −5.32383 9.22115i −0.546214 0.946070i
9696 0 0
9797 0.246304 0.426611i 0.0250084 0.0433158i −0.853250 0.521502i 0.825372π-0.825372\pi
0.878259 + 0.478186i 0.158705π0.158705\pi
9898 0 0
9999 −8.04163 11.3903i −0.808214 1.14477i
100100 0 0
101101 −1.70321 + 2.95005i −0.169476 + 0.293541i −0.938236 0.345997i 0.887541π-0.887541\pi
0.768760 + 0.639537i 0.220874π0.220874\pi
102102 0 0
103103 −2.58113 4.47064i −0.254326 0.440505i 0.710386 0.703812i 0.248520π-0.248520\pi
−0.964712 + 0.263307i 0.915187π0.915187\pi
104104 0 0
105105 2.29679 + 3.58985i 0.224144 + 0.350333i
106106 0 0
107107 −5.76303 −0.557133 −0.278567 0.960417i 0.589859π-0.589859\pi
−0.278567 + 0.960417i 0.589859π0.589859\pi
108108 0 0
109109 −8.98229 −0.860347 −0.430174 0.902746i 0.641548π-0.641548\pi
−0.430174 + 0.902746i 0.641548π0.641548\pi
110110 0 0
111111 0.678304 + 1.06018i 0.0643818 + 0.100628i
112112 0 0
113113 0.679767 + 1.17739i 0.0639471 + 0.110760i 0.896226 0.443597i 0.146298π-0.146298\pi
−0.832279 + 0.554356i 0.812964π0.812964\pi
114114 0 0
115115 −7.21780 + 12.5016i −0.673063 + 1.16578i
116116 0 0
117117 21.2360 1.94097i 1.96327 0.179443i
118118 0 0
119119 −2.25729 + 3.90975i −0.206926 + 0.358406i
120120 0 0
121121 −5.30039 9.18054i −0.481853 0.834595i
122122 0 0
123123 −0.217799 + 0.420378i −0.0196383 + 0.0379042i
124124 0 0
125125 −9.70895 −0.868394
126126 0 0
127127 −0.820039 −0.0727667 −0.0363833 0.999338i 0.511584π-0.511584\pi
−0.0363833 + 0.999338i 0.511584π0.511584\pi
128128 0 0
129129 −8.36546 + 0.381507i −0.736538 + 0.0335898i
130130 0 0
131131 −3.89397 6.74455i −0.340218 0.589274i 0.644255 0.764810i 0.277167π-0.277167\pi
−0.984473 + 0.175536i 0.943834π0.943834\pi
132132 0 0
133133 2.16372 3.74766i 0.187618 0.324964i
134134 0 0
135135 −7.84202 10.0977i −0.674934 0.869069i
136136 0 0
137137 1.49640 2.59184i 0.127846 0.221436i −0.794996 0.606615i 0.792527π-0.792527\pi
0.922842 + 0.385179i 0.125860π0.125860\pi
138138 0 0
139139 −3.16372 5.47972i −0.268343 0.464783i 0.700091 0.714053i 0.253143π-0.253143\pi
−0.968434 + 0.249270i 0.919809π0.919809\pi
140140 0 0
141141 6.35447 0.289796i 0.535143 0.0244052i
142142 0 0
143143 33.0364 2.76264
144144 0 0
145145 −17.1623 −1.42525
146146 0 0
147147 −0.796790 + 1.53790i −0.0657181 + 0.126844i
148148 0 0
149149 2.19076 + 3.79450i 0.179474 + 0.310858i 0.941700 0.336452i 0.109227π-0.109227\pi
−0.762227 + 0.647310i 0.775894π0.775894\pi
150150 0 0
151151 −3.30039 + 5.71644i −0.268582 + 0.465197i −0.968496 0.249030i 0.919888π-0.919888\pi
0.699914 + 0.714227i 0.253222π0.253222\pi
152152 0 0
153153 5.67617 12.2969i 0.458891 0.994149i
154154 0 0
155155 9.08113 15.7290i 0.729414 1.26338i
156156 0 0
157157 2.89037 + 5.00627i 0.230677 + 0.399544i 0.958007 0.286743i 0.0925727π-0.0925727\pi
−0.727331 + 0.686287i 0.759239π0.759239\pi
158158 0 0
159159 −4.71780 7.37385i −0.374146 0.584784i
160160 0 0
161161 −5.86693 −0.462379
162162 0 0
163163 7.32743 0.573929 0.286964 0.957941i 0.407354π-0.407354\pi
0.286964 + 0.957941i 0.407354π0.407354\pi
164164 0 0
165165 −10.6747 16.6844i −0.831025 1.29888i
166166 0 0
167167 6.01459 + 10.4176i 0.465423 + 0.806136i 0.999221 0.0394762i 0.0125689π-0.0125689\pi
−0.533798 + 0.845612i 0.679236π0.679236\pi
168168 0 0
169169 −18.7630 + 32.4985i −1.44331 + 2.49989i
170170 0 0
171171 −5.44085 + 11.7872i −0.416073 + 0.901386i
172172 0 0
173173 −2.44951 + 4.24268i −0.186233 + 0.322565i −0.943991 0.329970i 0.892961π-0.892961\pi
0.757758 + 0.652535i 0.226295π0.226295\pi
174174 0 0
175175 0.527042 + 0.912864i 0.0398406 + 0.0690060i
176176 0 0
177177 −7.27714 + 14.0457i −0.546983 + 1.05574i
178178 0 0
179179 −1.78074 −0.133099 −0.0665493 0.997783i 0.521199π-0.521199\pi
−0.0665493 + 0.997783i 0.521199π0.521199\pi
180180 0 0
181181 −16.9430 −1.25936 −0.629681 0.776854i 0.716815π-0.716815\pi
−0.629681 + 0.776854i 0.716815π0.716815\pi
182182 0 0
183183 −23.9071 + 1.09028i −1.76726 + 0.0805961i
184184 0 0
185185 0.893968 + 1.54840i 0.0657258 + 0.113840i
186186 0 0
187187 10.4911 18.1712i 0.767189 1.32881i
188188 0 0
189189 1.96050 4.81211i 0.142606 0.350030i
190190 0 0
191191 2.74484 4.75420i 0.198610 0.344002i −0.749468 0.662040i 0.769691π-0.769691\pi
0.948078 + 0.318038i 0.103024π0.103024\pi
192192 0 0
193193 2.75370 + 4.76954i 0.198215 + 0.343319i 0.947950 0.318420i 0.103152π-0.103152\pi
−0.749734 + 0.661739i 0.769819π0.769819\pi
194194 0 0
195195 30.2616 1.38008i 2.16708 0.0988296i
196196 0 0
197197 11.6300 0.828600 0.414300 0.910140i 0.364026π-0.364026\pi
0.414300 + 0.910140i 0.364026π0.364026\pi
198198 0 0
199199 −4.14747 −0.294006 −0.147003 0.989136i 0.546963π-0.546963\pi
−0.147003 + 0.989136i 0.546963π0.546963\pi
200200 0 0
201201 1.05768 2.04145i 0.0746032 0.143993i
202202 0 0
203203 −3.48755 6.04061i −0.244778 0.423968i
204204 0 0
205205 −0.336285 + 0.582462i −0.0234871 + 0.0406809i
206206 0 0
207207 17.5277 1.60204i 1.21826 0.111349i
208208 0 0
209209 −10.0562 + 17.4179i −0.695603 + 1.20482i
210210 0 0
211211 13.6082 + 23.5700i 0.936825 + 1.62263i 0.771347 + 0.636415i 0.219583π0.219583\pi
0.165478 + 0.986213i 0.447083π0.447083\pi
212212 0 0
213213 −12.6221 19.7281i −0.864851 1.35175i
214214 0 0
215215 −11.8961 −0.811308
216216 0 0
217217 7.38151 0.501090
218218 0 0
219219 4.03950 + 6.31367i 0.272964 + 0.426638i
220220 0 0
221221 16.0452 + 27.7912i 1.07932 + 1.86944i
222222 0 0
223223 1.60817 2.78543i 0.107691 0.186526i −0.807144 0.590355i 0.798988π-0.798988\pi
0.914834 + 0.403829i 0.132321π0.132321\pi
224224 0 0
225225 −1.82383 2.58331i −0.121589 0.172221i
226226 0 0
227227 −7.97296 + 13.8096i −0.529184 + 0.916573i 0.470237 + 0.882540i 0.344168π0.344168\pi
−0.999421 + 0.0340330i 0.989165π0.989165\pi
228228 0 0
229229 0.608168 + 1.05338i 0.0401889 + 0.0696092i 0.885420 0.464791i 0.153871π-0.153871\pi
−0.845231 + 0.534401i 0.820537π0.820537\pi
230230 0 0
231231 3.70321 7.14763i 0.243653 0.470279i
232232 0 0
233233 19.9722 1.30842 0.654210 0.756313i 0.273001π-0.273001\pi
0.654210 + 0.756313i 0.273001π0.273001\pi
234234 0 0
235235 9.03638 0.589468
236236 0 0
237237 11.1352 0.507822i 0.723310 0.0329866i
238238 0 0
239239 −3.00739 5.20896i −0.194532 0.336939i 0.752215 0.658918i 0.228985π-0.228985\pi
−0.946747 + 0.321978i 0.895652π0.895652\pi
240240 0 0
241241 9.30778 16.1215i 0.599567 1.03848i −0.393318 0.919402i 0.628673π-0.628673\pi
0.992885 0.119078i 0.0379938π-0.0379938\pi
242242 0 0
243243 −4.54309 + 14.9118i −0.291440 + 0.956589i
244244 0 0
245245 −1.23025 + 2.13086i −0.0785979 + 0.136136i
246246 0 0
247247 −15.3801 26.6390i −0.978609 1.69500i
248248 0 0
249249 2.57014 0.117211i 0.162876 0.00742796i
250250 0 0
251251 6.99707 0.441651 0.220826 0.975313i 0.429125π-0.429125\pi
0.220826 + 0.975313i 0.429125π0.429125\pi
252252 0 0
253253 27.2675 1.71429
254254 0 0
255255 8.85087 17.0832i 0.554263 1.06979i
256256 0 0
257257 8.88891 + 15.3960i 0.554475 + 0.960378i 0.997944 + 0.0640889i 0.0204141π0.0204141\pi
−0.443469 + 0.896289i 0.646253π0.646253\pi
258258 0 0
259259 −0.363327 + 0.629301i −0.0225760 + 0.0391028i
260260 0 0
261261 12.0687 + 17.0943i 0.747032 + 1.05811i
262262 0 0
263263 13.5993 23.5547i 0.838570 1.45245i −0.0525210 0.998620i 0.516726π-0.516726\pi
0.891091 0.453825i 0.149941π-0.149941\pi
264264 0 0
265265 −6.21780 10.7695i −0.381956 0.661568i
266266 0 0
267267 −9.18044 14.3489i −0.561834 0.878138i
268268 0 0
269269 23.8961 1.45697 0.728486 0.685061i 0.240225π-0.240225\pi
0.728486 + 0.685061i 0.240225π0.240225\pi
270270 0 0
271271 12.2733 0.745553 0.372776 0.927921i 0.378406π-0.378406\pi
0.372776 + 0.927921i 0.378406π0.378406\pi
272272 0 0
273273 6.63521 + 10.3707i 0.401581 + 0.627665i
274274 0 0
275275 −2.44951 4.24268i −0.147711 0.255843i
276276 0 0
277277 −6.39037 + 11.0684i −0.383960 + 0.665038i −0.991624 0.129156i 0.958773π-0.958773\pi
0.607664 + 0.794194i 0.292107π0.292107\pi
278278 0 0
279279 −22.0526 + 2.01561i −1.32026 + 0.120672i
280280 0 0
281281 14.2573 24.6944i 0.850519 1.47314i −0.0302219 0.999543i 0.509621π-0.509621\pi
0.880741 0.473599i 0.157045π-0.157045\pi
282282 0 0
283283 −0.363327 0.629301i −0.0215975 0.0374080i 0.855025 0.518587i 0.173542π-0.173542\pi
−0.876622 + 0.481179i 0.840209π0.840209\pi
284284 0 0
285285 −8.48395 + 16.3750i −0.502546 + 0.969972i
286286 0 0
287287 −0.273346 −0.0161351
288288 0 0
289289 3.38151 0.198913
290290 0 0
291291 −0.852336 + 0.0388708i −0.0499648 + 0.00227865i
292292 0 0
293293 −12.7901 22.1531i −0.747204 1.29420i −0.949158 0.314800i 0.898062π-0.898062\pi
0.201954 0.979395i 0.435271π-0.435271\pi
294294 0 0
295295 −11.2360 + 19.4613i −0.654184 + 1.13308i
296296 0 0
297297 −9.11177 + 22.3651i −0.528718 + 1.29775i
298298 0 0
299299 −20.8515 + 36.1159i −1.20588 + 2.08864i
300300 0 0
301301 −2.41741 4.18708i −0.139337 0.241339i
302302 0 0
303303 5.89397 0.268795i 0.338600 0.0154419i
304304 0 0
305305 −33.9971 −1.94667
306306 0 0
307307 −6.23405 −0.355796 −0.177898 0.984049i 0.556930π-0.556930\pi
−0.177898 + 0.984049i 0.556930π0.556930\pi
308308 0 0
309309 −4.11323 + 7.93901i −0.233993 + 0.451635i
310310 0 0
311311 −14.6192 25.3211i −0.828976 1.43583i −0.898842 0.438273i 0.855590π-0.855590\pi
0.0698655 0.997556i 0.477743π-0.477743\pi
312312 0 0
313313 −14.2434 + 24.6703i −0.805083 + 1.39445i 0.111151 + 0.993803i 0.464546π0.464546\pi
−0.916235 + 0.400642i 0.868787π0.868787\pi
314314 0 0
315315 3.09358 6.70198i 0.174303 0.377614i
316316 0 0
317317 −0.809243 + 1.40165i −0.0454516 + 0.0787245i −0.887856 0.460121i 0.847806π-0.847806\pi
0.842405 + 0.538846i 0.181139π0.181139\pi
318318 0 0
319319 16.2089 + 28.0747i 0.907527 + 1.57188i
320320 0 0
321321 5.37957 + 8.40819i 0.300258 + 0.469300i
322322 0 0
323323 −19.5366 −1.08704
324324 0 0
325325 7.49261 0.415615
326326 0 0
327327 8.38463 + 13.1051i 0.463671 + 0.724711i
328328 0 0
329329 1.83628 + 3.18054i 0.101238 + 0.175349i
330330 0 0
331331 6.99115 12.1090i 0.384268 0.665572i −0.607399 0.794397i 0.707787π-0.707787\pi
0.991667 + 0.128825i 0.0411205π0.0411205\pi
332332 0 0
333333 0.913618 1.97928i 0.0500660 0.108464i
334334 0 0
335335 1.63307 2.82857i 0.0892244 0.154541i
336336 0 0
337337 −13.8619 24.0095i −0.755104 1.30788i −0.945323 0.326137i 0.894253π-0.894253\pi
0.190219 0.981742i 0.439080π-0.439080\pi
338338 0 0
339339 1.08326 2.09082i 0.0588347 0.113558i
340340 0 0
341341 −34.3068 −1.85782
342342 0 0
343343 −1.00000 −0.0539949
344344 0 0
345345 24.9772 1.13909i 1.34473 0.0613264i
346346 0 0
347347 −3.76449 6.52029i −0.202089 0.350028i 0.747113 0.664697i 0.231440π-0.231440\pi
−0.949201 + 0.314670i 0.898106π0.898106\pi
348348 0 0
349349 15.0541 26.0744i 0.805827 1.39573i −0.109905 0.993942i 0.535055π-0.535055\pi
0.915732 0.401791i 0.131612π-0.131612\pi
350350 0 0
351351 −22.6549 29.1712i −1.20923 1.55705i
352352 0 0
353353 10.1819 17.6356i 0.541928 0.938647i −0.456865 0.889536i 0.651028π-0.651028\pi
0.998793 0.0491110i 0.0156388π-0.0156388\pi
354354 0 0
355355 −16.6352 28.8130i −0.882905 1.52924i
356356 0 0
357357 7.81138 0.356238i 0.413422 0.0188541i
358358 0 0
359359 −16.0263 −0.845833 −0.422917 0.906169i 0.638994π-0.638994\pi
−0.422917 + 0.906169i 0.638994π0.638994\pi
360360 0 0
361361 −0.273346 −0.0143866
362362 0 0
363363 −8.44659 + 16.3029i −0.443331 + 0.855680i
364364 0 0
365365 5.32383 + 9.22115i 0.278662 + 0.482657i
366366 0 0
367367 6.79893 11.7761i 0.354901 0.614707i −0.632200 0.774805i 0.717848π-0.717848\pi
0.987101 + 0.160099i 0.0511812π0.0511812\pi
368368 0 0
369369 0.816635 0.0746406i 0.0425123 0.00388563i
370370 0 0
371371 2.52704 4.37697i 0.131197 0.227241i
372372 0 0
373373 10.9641 + 18.9904i 0.567700 + 0.983285i 0.996793 + 0.0800246i 0.0254999π0.0254999\pi
−0.429093 + 0.903260i 0.641167π0.641167\pi
374374 0 0
375375 9.06294 + 14.1652i 0.468008 + 0.731490i
376376 0 0
377377 −49.5801 −2.55351
378378 0 0
379379 −29.7965 −1.53054 −0.765271 0.643708i 0.777395π-0.777395\pi
−0.765271 + 0.643708i 0.777395π0.777395\pi
380380 0 0
381381 0.765475 + 1.19643i 0.0392165 + 0.0612948i
382382 0 0
383383 0.0109905 + 0.0190361i 0.000561587 + 0.000972697i 0.866306 0.499514i 0.166488π-0.166488\pi
−0.865744 + 0.500486i 0.833155π0.833155\pi
384384 0 0
385385 5.71780 9.90352i 0.291406 0.504730i
386386 0 0
387387 8.36546 + 11.8490i 0.425240 + 0.602318i
388388 0 0
389389 17.6783 30.6197i 0.896326 1.55248i 0.0641702 0.997939i 0.479560π-0.479560\pi
0.832155 0.554543i 0.187107π-0.187107\pi
390390 0 0
391391 13.2434 + 22.9382i 0.669746 + 1.16003i
392392 0 0
393393 −6.20535 + 11.9770i −0.313018 + 0.604162i
394394 0 0
395395 15.8348 0.796736
396396 0 0
397397 −16.9430 −0.850344 −0.425172 0.905112i 0.639786π-0.639786\pi
−0.425172 + 0.905112i 0.639786π0.639786\pi
398398 0 0
399399 −7.48755 + 0.341470i −0.374846 + 0.0170949i
400400 0 0
401401 1.48181 + 2.56657i 0.0739982 + 0.128169i 0.900650 0.434545i 0.143091π-0.143091\pi
−0.826652 + 0.562713i 0.809757π0.809757\pi
402402 0 0
403403 26.2345 45.4395i 1.30683 2.26350i
404404 0 0
405405 −7.41216 + 20.8672i −0.368313 + 1.03690i
406406 0 0
407407 1.68862 2.92478i 0.0837018 0.144976i
408408 0 0
409409 7.32743 + 12.6915i 0.362318 + 0.627553i 0.988342 0.152251i 0.0486521π-0.0486521\pi
−0.626024 + 0.779804i 0.715319π0.715319\pi
410410 0 0
411411 −5.17830 + 0.236157i −0.255427 + 0.0116488i
412412 0 0
413413 −9.13307 −0.449409
414414 0 0
415415 3.65486 0.179410
416416 0 0
417417 −5.04163 + 9.73093i −0.246890 + 0.476526i
418418 0 0
419419 12.6352 + 21.8848i 0.617270 + 1.06914i 0.989982 + 0.141196i 0.0450949π0.0450949\pi
−0.372711 + 0.927947i 0.621572π0.621572\pi
420420 0 0
421421 7.99854 13.8539i 0.389825 0.675196i −0.602601 0.798043i 0.705869π-0.705869\pi
0.992426 + 0.122846i 0.0392022π0.0392022\pi
422422 0 0
423423 −6.35447 9.00059i −0.308965 0.437624i
424424 0 0
425425 2.37938 4.12120i 0.115417 0.199908i
426426 0 0
427427 −6.90856 11.9660i −0.334328 0.579074i
428428 0 0
429429 −30.8382 48.1997i −1.48888 2.32710i
430430 0 0
431431 13.0335 0.627799 0.313900 0.949456i 0.398364π-0.398364\pi
0.313900 + 0.949456i 0.398364π0.398364\pi
432432 0 0
433433 23.5467 1.13158 0.565791 0.824549i 0.308571π-0.308571\pi
0.565791 + 0.824549i 0.308571π0.308571\pi
434434 0 0
435435 16.0203 + 25.0395i 0.768116 + 1.20055i
436436 0 0
437437 −12.6944 21.9873i −0.607253 1.05179i
438438 0 0
439439 −3.35447 + 5.81012i −0.160100 + 0.277302i −0.934904 0.354900i 0.884515π-0.884515\pi
0.774804 + 0.632201i 0.217848π0.217848\pi
440440 0 0
441441 2.98755 0.273062i 0.142264 0.0130030i
442442 0 0
443443 −17.6228 + 30.5235i −0.837282 + 1.45022i 0.0548760 + 0.998493i 0.482524π0.482524\pi
−0.892158 + 0.451723i 0.850810π0.850810\pi
444444 0 0
445445 −12.0993 20.9566i −0.573562 0.993439i
446446 0 0
447447 3.49115 6.73832i 0.165126 0.318711i
448448 0 0
449449 −12.9387 −0.610616 −0.305308 0.952254i 0.598759π-0.598759\pi
−0.305308 + 0.952254i 0.598759π0.598759\pi
450450 0 0
451451 1.27042 0.0598218
452452 0 0
453453 11.4210 0.520856i 0.536606 0.0244719i
454454 0 0
455455 8.74484 + 15.1465i 0.409964 + 0.710079i
456456 0 0
457457 14.5993 25.2868i 0.682927 1.18286i −0.291156 0.956675i 0.594040π-0.594040\pi
0.974083 0.226189i 0.0726267π-0.0726267\pi
458458 0 0
459459 −23.2396 + 3.19727i −1.08473 + 0.149236i
460460 0 0
461461 9.34348 16.1834i 0.435169 0.753735i −0.562140 0.827042i 0.690022π-0.690022\pi
0.997309 + 0.0733066i 0.0233552π0.0233552\pi
462462 0 0
463463 19.1249 + 33.1253i 0.888809 + 1.53946i 0.841285 + 0.540593i 0.181800π0.181800\pi
0.0475247 + 0.998870i 0.484867π0.484867\pi
464464 0 0
465465 −31.4253 + 1.43315i −1.45731 + 0.0664608i
466466 0 0
467467 −15.2877 −0.707432 −0.353716 0.935353i 0.615082π-0.615082\pi
−0.353716 + 0.935353i 0.615082π0.615082\pi
468468 0 0
469469 1.32743 0.0612950
470470 0 0
471471 4.60603 8.89018i 0.212235 0.409638i
472472 0 0
473473 11.2353 + 19.4601i 0.516600 + 0.894778i
474474 0 0
475475 −2.28074 + 3.95035i −0.104647 + 0.181255i
476476 0 0
477477 −6.35447 + 13.7664i −0.290951 + 0.630322i
478478 0 0
479479 −5.51605 + 9.55408i −0.252035 + 0.436537i −0.964086 0.265591i 0.914433π-0.914433\pi
0.712051 + 0.702128i 0.247766π0.247766\pi
480480 0 0
481481 2.58259 + 4.47318i 0.117756 + 0.203959i
482482 0 0
483483 5.47656 + 8.55978i 0.249192 + 0.389483i
484484 0 0
485485 −1.21206 −0.0550370
486486 0 0
487487 16.6008 0.752253 0.376126 0.926568i 0.377256π-0.377256\pi
0.376126 + 0.926568i 0.377256π0.377256\pi
488488 0 0
489489 −6.83988 10.6906i −0.309310 0.483447i
490490 0 0
491491 13.3633 + 23.1460i 0.603079 + 1.04456i 0.992352 + 0.123440i 0.0393928π0.0393928\pi
−0.389273 + 0.921122i 0.627274π0.627274\pi
492492 0 0
493493 −15.7448 + 27.2709i −0.709112 + 1.22822i
494494 0 0
495495 −14.3779 + 31.1485i −0.646239 + 1.40002i
496496 0 0
497497 6.76089 11.7102i 0.303268 0.525275i
498498 0 0
499499 −0.618485 1.07125i −0.0276872 0.0479557i 0.851850 0.523786i 0.175481π-0.175481\pi
−0.879537 + 0.475830i 0.842148π0.842148\pi
500500 0 0
501501 9.58472 18.4996i 0.428214 0.826503i
502502 0 0
503503 −1.07179 −0.0477889 −0.0238944 0.999714i 0.507607π-0.507607\pi
−0.0238944 + 0.999714i 0.507607π0.507607\pi
504504 0 0
505505 8.38151 0.372973
506506 0 0
507507 64.9296 2.96112i 2.88362 0.131508i
508508 0 0
509509 −10.0344 17.3801i −0.444768 0.770362i 0.553268 0.833004i 0.313381π-0.313381\pi
−0.998036 + 0.0626420i 0.980047π0.980047\pi
510510 0 0
511511 −2.16372 + 3.74766i −0.0957171 + 0.165787i
512512 0 0
513513 22.2762 3.06472i 0.983516 0.135311i
514514 0 0
515515 −6.35087 + 11.0000i −0.279853 + 0.484720i
516516 0 0
517517 −8.53443 14.7821i −0.375344 0.650115i
518518 0 0
519519 8.47656 0.386574i 0.372080 0.0169687i
520520 0 0
521521 −30.8860 −1.35314 −0.676570 0.736379i 0.736534π-0.736534\pi
−0.676570 + 0.736379i 0.736534π0.736534\pi
522522 0 0
523523 −7.39922 −0.323545 −0.161773 0.986828i 0.551721π-0.551721\pi
−0.161773 + 0.986828i 0.551721π0.551721\pi
524524 0 0
525525 0.839883 1.62107i 0.0366555 0.0707494i
526526 0 0
527527 −16.6623 28.8599i −0.725819 1.25716i
528528 0 0
529529 −5.71041 + 9.89072i −0.248279 + 0.430031i
530530 0 0
531531 27.2855 2.49390i 1.18409 0.108226i
532532 0 0
533533 −0.971495 + 1.68268i −0.0420801 + 0.0728849i
534534 0 0
535535 7.08998 + 12.2802i 0.306527 + 0.530920i
536536 0 0
537537 1.66225 + 2.59808i 0.0717315 + 0.112115i
538538 0 0
539539 4.64766 0.200189
540540 0 0
541541 22.6696 0.974644 0.487322 0.873222i 0.337974π-0.337974\pi
0.487322 + 0.873222i 0.337974π0.337974\pi
542542 0 0
543543 15.8157 + 24.7196i 0.678715 + 1.06082i
544544 0 0
545545 11.0505 + 19.1400i 0.473351 + 0.819868i
546546 0 0
547547 3.07373 5.32386i 0.131423 0.227632i −0.792802 0.609479i 0.791379π-0.791379\pi
0.924225 + 0.381847i 0.124712π0.124712\pi
548548 0 0
549549 23.9071 + 33.8624i 1.02033 + 1.44521i
550550 0 0
551551 15.0921 26.1403i 0.642946 1.11361i
552552 0 0
553553 3.21780 + 5.57339i 0.136835 + 0.237005i
554554 0 0
555555 1.42461 2.74966i 0.0604713 0.116717i
556556 0 0
557557 29.6739 1.25732 0.628662 0.777679i 0.283603π-0.283603\pi
0.628662 + 0.777679i 0.283603π0.283603\pi
558558 0 0
559559 −34.3667 −1.45356
560560 0 0
561561 −36.3047 + 1.65568i −1.53278 + 0.0699027i
562562 0 0
563563 14.6555 + 25.3841i 0.617657 + 1.06981i 0.989912 + 0.141683i 0.0452514π0.0452514\pi
−0.372255 + 0.928131i 0.621415π0.621415\pi
564564 0 0
565565 1.67257 2.89698i 0.0703655 0.121877i
566566 0 0
567567 −8.85087 + 1.63157i −0.371702 + 0.0685196i
568568 0 0
569569 18.4430 31.9442i 0.773170 1.33917i −0.162647 0.986684i 0.552003π-0.552003\pi
0.935817 0.352486i 0.114664π-0.114664\pi
570570 0 0
571571 −16.1893 28.0407i −0.677501 1.17347i −0.975731 0.218972i 0.929730π-0.929730\pi
0.298230 0.954494i 0.403604π-0.403604\pi
572572 0 0
573573 −9.49854 + 0.433181i −0.396807 + 0.0180964i
574574 0 0
575575 6.18423 0.257900
576576 0 0
577577 23.0187 0.958280 0.479140 0.877739i 0.340949π-0.340949\pi
0.479140 + 0.877739i 0.340949π0.340949\pi
578578 0 0
579579 4.38823 8.46980i 0.182369 0.351993i
580580 0 0
581581 0.742705 + 1.28640i 0.0308126 + 0.0533690i
582582 0 0
583583 −11.7448 + 20.3427i −0.486422 + 0.842507i
584584 0 0
585585 −30.2616 42.8630i −1.25116 1.77217i
586586 0 0
587587 −2.87052 + 4.97189i −0.118479 + 0.205212i −0.919165 0.393872i 0.871135π-0.871135\pi
0.800686 + 0.599084i 0.204469π0.204469\pi
588588 0 0
589589 15.9715 + 27.6634i 0.658094 + 1.13985i
590590 0 0
591591 −10.8561 16.9680i −0.446562 0.697969i
592592 0 0
593593 27.7453 1.13936 0.569682 0.821865i 0.307066π-0.307066\pi
0.569682 + 0.821865i 0.307066π0.307066\pi
594594 0 0
595595 11.1082 0.455391
596596 0 0
597597 3.87151 + 6.05111i 0.158450 + 0.247655i
598598 0 0
599599 −2.05408 3.55778i −0.0839276 0.145367i 0.821006 0.570919i 0.193413π-0.193413\pi
−0.904934 + 0.425552i 0.860080π0.860080\pi
600600 0 0
601601 −7.80924 + 13.5260i −0.318546 + 0.551737i −0.980185 0.198085i 0.936528π-0.936528\pi
0.661639 + 0.749822i 0.269861π0.269861\pi
602602 0 0
603603 −3.96576 + 0.362471i −0.161498 + 0.0147610i
604604 0 0
605605 −13.0416 + 22.5888i −0.530218 + 0.918364i
606606 0 0
607607 0.280738 + 0.486253i 0.0113948 + 0.0197364i 0.871667 0.490099i 0.163040π-0.163040\pi
−0.860272 + 0.509836i 0.829706π0.829706\pi
608608 0 0
609609 −5.55768 + 10.7270i −0.225209 + 0.434679i
610610 0 0
611611 26.1052 1.05611
612612 0 0
613613 −20.2016 −0.815933 −0.407967 0.912997i 0.633762π-0.633762\pi
−0.407967 + 0.912997i 0.633762π0.633762\pi
614614 0 0
615615 1.16372 0.0530713i 0.0469255 0.00214004i
616616 0 0
617617 11.4569 + 19.8439i 0.461238 + 0.798887i 0.999023 0.0441948i 0.0140722π-0.0140722\pi
−0.537785 + 0.843082i 0.680739π0.680739\pi
618618 0 0
619619 −19.8515 + 34.3839i −0.797901 + 1.38201i 0.123080 + 0.992397i 0.460723π0.460723\pi
−0.920981 + 0.389608i 0.872610π0.872610\pi
620620 0 0
621621 −18.6988 24.0773i −0.750358 0.966188i
622622 0 0
623623 4.91741 8.51721i 0.197012 0.341235i
624624 0 0
625625 14.5797 + 25.2527i 0.583187 + 1.01011i
626626 0 0
627627 34.7996 1.58704i 1.38976 0.0633802i
628628 0 0
629629 3.28054 0.130804
630630 0 0
631631 −31.0364 −1.23554 −0.617769 0.786359i 0.711963π-0.711963\pi
−0.617769 + 0.786359i 0.711963π0.711963\pi
632632 0 0
633633 21.6857 41.8559i 0.861929 1.66362i
634634 0 0
635635 1.00885 + 1.74739i 0.0400352 + 0.0693429i
636636 0 0
637637 −3.55408 + 6.15585i −0.140818 + 0.243904i
638638 0 0
639639 −17.0009 + 36.8309i −0.672544 + 1.45701i
640640 0 0
641641 14.7932 25.6226i 0.584296 1.01203i −0.410667 0.911785i 0.634704π-0.634704\pi
0.994963 0.100245i 0.0319626π-0.0319626\pi
642642 0 0
643643 −12.8442 22.2467i −0.506524 0.877325i −0.999972 0.00754978i 0.997597π-0.997597\pi
0.493447 0.869776i 0.335737π-0.335737\pi
644644 0 0
645645 11.1046 + 17.3563i 0.437242 + 0.683403i
646646 0 0
647647 17.0177 0.669035 0.334518 0.942390i 0.391427π-0.391427\pi
0.334518 + 0.942390i 0.391427π0.391427\pi
648648 0 0
649649 42.4475 1.66621
650650 0 0
651651 −6.89037 10.7695i −0.270055 0.422092i
652652 0 0
653653 −0.735508 1.27394i −0.0287827 0.0498530i 0.851275 0.524719i 0.175830π-0.175830\pi
−0.880058 + 0.474866i 0.842496π0.842496\pi
654654 0 0
655655 −9.58113 + 16.5950i −0.374366 + 0.648420i
656656 0 0
657657 5.44085 11.7872i 0.212268 0.459861i
658658 0 0
659659 20.7003 35.8539i 0.806369 1.39667i −0.108995 0.994042i 0.534763π-0.534763\pi
0.915363 0.402629i 0.131904π-0.131904\pi
660660 0 0
661661 −19.1352 33.1432i −0.744273 1.28912i −0.950533 0.310622i 0.899463π-0.899463\pi
0.206260 0.978497i 0.433871π-0.433871\pi
662662 0 0
663663 25.5693 49.3518i 0.993031 1.91667i
664664 0 0
665665 −10.6477 −0.412899
666666 0 0
667667 −40.9224 −1.58452
668668 0 0
669669 −5.56507 + 0.253795i −0.215158 + 0.00981230i
670670 0 0
671671 32.1086 + 55.6138i 1.23954 + 2.14695i
672672 0 0
673673 15.2448 26.4048i 0.587645 1.01783i −0.406894 0.913475i 0.633388π-0.633388\pi
0.994540 0.104357i 0.0332783π-0.0332783\pi
674674 0 0
675675 −2.06654 + 5.07237i −0.0795411 + 0.195236i
676676 0 0
677677 −22.4626 + 38.9064i −0.863309 + 1.49530i 0.00540665 + 0.999985i 0.498279π0.498279\pi
−0.868716 + 0.495310i 0.835054π0.835054\pi
678678 0 0
679679 −0.246304 0.426611i −0.00945228 0.0163718i
680680 0 0
681681 27.5905 1.25826i 1.05727 0.0482168i
682682 0 0
683683 −48.3973 −1.85187 −0.925935 0.377683i 0.876721π-0.876721\pi
−0.925935 + 0.377683i 0.876721π0.876721\pi
684684 0 0
685685 −7.36381 −0.281357
686686 0 0
687687 0.969165 1.87060i 0.0369759 0.0713679i
688688 0 0
689689 −17.9626 31.1122i −0.684322 1.18528i
690690 0 0
691691 −9.19076 + 15.9189i −0.349633 + 0.605582i −0.986184 0.165652i 0.947027π-0.947027\pi
0.636551 + 0.771234i 0.280360π0.280360\pi
692692 0 0
693693 −13.8851 + 1.26910i −0.527452 + 0.0482092i
694694 0 0
695695 −7.78434 + 13.4829i −0.295277 + 0.511434i
696696 0 0
697697 0.617023 + 1.06871i 0.0233714 + 0.0404805i
698698 0 0
699699 −18.6433 29.1392i −0.705153 1.10214i
700700 0 0
701701 −27.0292 −1.02088 −0.510439 0.859914i 0.670517π-0.670517\pi
−0.510439 + 0.859914i 0.670517π0.670517\pi
702702 0 0
703703 −3.14454 −0.118599
704704 0 0
705705 −8.43512 13.1840i −0.317685 0.496537i
706706 0 0
707707 1.70321 + 2.95005i 0.0640558 + 0.110948i
708708 0 0
709709 −2.49261 + 4.31732i −0.0936119 + 0.162141i −0.909028 0.416734i 0.863175π-0.863175\pi
0.815417 + 0.578875i 0.196508π0.196508\pi
710710 0 0
711711 −11.1352 15.7721i −0.417603 0.591500i
712712 0 0
713713 21.6534 37.5048i 0.810926 1.40457i
714714 0 0
715715 −40.6431 70.3959i −1.51997 2.63266i
716716 0 0
717717 −4.79252 + 9.25012i −0.178980 + 0.345452i
718718 0 0
719719 15.6942 0.585293 0.292647 0.956221i 0.405464π-0.405464\pi
0.292647 + 0.956221i 0.405464π0.405464\pi
720720 0 0
721721 −5.16225 −0.192252
722722 0 0
723723 −32.2096 + 1.46892i −1.19789 + 0.0546298i
724724 0 0
725725 3.67617 + 6.36731i 0.136529 + 0.236476i
726726 0 0
727727 −10.9071 + 18.8916i −0.404522 + 0.700652i −0.994266 0.106938i 0.965895π-0.965895\pi
0.589744 + 0.807590i 0.299229π0.299229\pi
728728 0 0
729729 25.9969 7.29124i 0.962847 0.270046i
730730 0 0
731731 −10.9136 + 18.9029i −0.403655 + 0.699151i
732732 0 0
733733 12.0074 + 20.7974i 0.443503 + 0.768170i 0.997947 0.0640514i 0.0204022π-0.0204022\pi
−0.554443 + 0.832221i 0.687069π0.687069\pi
734734 0 0
735735 4.25729 0.194154i 0.157033 0.00716148i
736736 0 0
737737 −6.16945 −0.227255
738738 0 0
739739 18.7089 0.688220 0.344110 0.938929i 0.388181π-0.388181\pi
0.344110 + 0.938929i 0.388181π0.388181\pi
740740 0 0
741741 −24.5093 + 47.3059i −0.900373 + 1.73782i
742742 0 0
743743 20.1534 + 34.9067i 0.739356 + 1.28060i 0.952785 + 0.303644i 0.0982035π0.0982035\pi
−0.213429 + 0.976959i 0.568463π0.568463\pi
744744 0 0
745745 5.39037 9.33639i 0.197488 0.342059i
746746 0 0
747747 −2.57014 3.64039i −0.0940364 0.133195i
748748 0 0
749749 −2.88151 + 4.99093i −0.105288 + 0.182365i
750750 0 0
751751 10.5629 + 18.2955i 0.385447 + 0.667614i 0.991831 0.127558i 0.0407139π-0.0407139\pi
−0.606384 + 0.795172i 0.707381π0.707381\pi
752752 0 0
753753 −6.53151 10.2087i −0.238021 0.372024i
754754 0 0
755755 16.2412 0.591079
756756 0 0
757757 8.85934 0.321998 0.160999 0.986955i 0.448528π-0.448528\pi
0.160999 + 0.986955i 0.448528π0.448528\pi
758758 0 0
759759 −25.4532 39.7830i −0.923892 1.44403i
760760 0 0
761761 −0.694551 1.20300i −0.0251774 0.0436086i 0.853162 0.521646i 0.174682π-0.174682\pi
−0.878340 + 0.478037i 0.841348π0.841348\pi
762762 0 0
763763 −4.49115 + 7.77889i −0.162590 + 0.281615i
764764 0 0
765765 −33.1862 + 3.03322i −1.19985 + 0.109666i
766766 0 0
767767 −32.4597 + 56.2219i −1.17205 + 2.03005i
768768 0 0
769769 18.9626 + 32.8443i 0.683810 + 1.18439i 0.973809 + 0.227367i 0.0730118π0.0730118\pi
−0.289999 + 0.957027i 0.593655π0.593655\pi
770770 0 0
771771 14.1652 27.3404i 0.510146 0.984642i
772772 0 0
773773 1.31596 0.0473318 0.0236659 0.999720i 0.492466π-0.492466\pi
0.0236659 + 0.999720i 0.492466π0.492466\pi
774774 0 0
775775 −7.78074 −0.279492
776776 0 0
777777 1.25729 0.0573390i 0.0451052 0.00205702i
778778 0 0
779779 −0.591443 1.02441i −0.0211907 0.0367033i
780780 0 0
781781 −31.4224 + 54.4251i −1.12438 + 1.94748i
782782 0 0
783783 13.6747 33.5649i 0.488694 1.19951i
784784 0 0
785785 7.11177 12.3179i 0.253830 0.439646i
786786 0 0
787787 −6.12928 10.6162i −0.218485 0.378428i 0.735860 0.677134i 0.236778π-0.236778\pi
−0.954345 + 0.298706i 0.903445π0.903445\pi
788788 0 0
789789 −47.0605 + 2.14620i −1.67540 + 0.0764066i
790790 0 0
791791 1.35953 0.0483395
792792 0 0
793793 −98.2144 −3.48769
794794 0 0
795795 −9.90856 + 19.1247i −0.351420 + 0.678282i
796796 0 0
797797 −10.7178 18.5638i −0.379644 0.657563i 0.611366 0.791348i 0.290620π-0.290620\pi
−0.991010 + 0.133785i 0.957287π0.957287\pi
798798 0 0
799799 8.29007 14.3588i 0.293282 0.507979i
800800 0 0
801801 −12.3653 + 26.7883i −0.436905 + 0.946518i
802802 0 0
803803 10.0562 17.4179i 0.354876 0.614664i
804804 0 0
805805 7.21780 + 12.5016i 0.254394 + 0.440623i
806806 0 0
807807 −22.3061 34.8641i −0.785213 1.22728i
808808 0 0
809809 26.6955 0.938564 0.469282 0.883048i 0.344513π-0.344513\pi
0.469282 + 0.883048i 0.344513π0.344513\pi
810810 0 0
811811 38.2852 1.34438 0.672188 0.740381i 0.265355π-0.265355\pi
0.672188 + 0.740381i 0.265355π0.265355\pi
812812 0 0
813813 −11.4567 17.9067i −0.401804 0.628014i
814814 0 0
815815 −9.01459 15.6137i −0.315767 0.546925i
816816 0 0
817817 10.4612 18.1193i 0.365990 0.633914i
818818 0 0
819819 8.93706 19.3614i 0.312286 0.676542i
820820 0 0
821821 5.24990 9.09310i 0.183223 0.317351i −0.759753 0.650211i 0.774680π-0.774680\pi
0.942976 + 0.332860i 0.108014π0.108014\pi
822822 0 0
823823 −8.00000 13.8564i −0.278862 0.483004i 0.692240 0.721668i 0.256624π-0.256624\pi
−0.971102 + 0.238664i 0.923291π0.923291\pi
824824 0 0
825825 −3.90350 + 7.53420i −0.135902 + 0.262307i
826826 0 0
827827 −48.7817 −1.69631 −0.848153 0.529752i 0.822285π-0.822285\pi
−0.848153 + 0.529752i 0.822285π0.822285\pi
828828 0 0
829829 −6.21926 −0.216004 −0.108002 0.994151i 0.534445π-0.534445\pi
−0.108002 + 0.994151i 0.534445π0.534445\pi
830830 0 0
831831 22.1139 1.00851i 0.767123 0.0349847i
832832 0 0
833833 2.25729 + 3.90975i 0.0782106 + 0.135465i
834834 0 0
835835 14.7989 25.6325i 0.512138 0.887049i
836836 0 0
837837 23.5261 + 30.2930i 0.813180 + 1.04708i
838838 0 0
839839 21.0366 36.4364i 0.726263 1.25792i −0.232189 0.972671i 0.574589π-0.574589\pi
0.958452 0.285254i 0.0920779π-0.0920779\pi
840840 0 0
841841 −9.82597 17.0191i −0.338826 0.586865i
842842 0 0
843843 −49.3374 + 2.25004i −1.69927 + 0.0774954i
844844 0 0
845845 92.3330 3.17635
846846 0 0
847847 −10.6008 −0.364247
848848 0 0
849849 −0.578990 + 1.11752i −0.0198709 + 0.0383531i
850850 0 0
851851 2.13161 + 3.69206i 0.0730707 + 0.126562i
852852 0 0
853853 6.72519 11.6484i 0.230266 0.398833i −0.727620 0.685980i 0.759374π-0.759374\pi
0.957886 + 0.287147i 0.0927070π0.0927070\pi
854854 0 0
855855 31.8104 2.90748i 1.08789 0.0994336i
856856 0 0
857857 −20.6893 + 35.8349i −0.706733 + 1.22410i 0.259330 + 0.965789i 0.416498π0.416498\pi
−0.966063 + 0.258308i 0.916835π0.916835\pi
858858 0 0
859859 19.8815 + 34.4358i 0.678349 + 1.17493i 0.975478 + 0.220097i 0.0706374π0.0706374\pi
−0.297129 + 0.954837i 0.596029π0.596029\pi
860860 0 0
861861 0.255158 + 0.398809i 0.00869578 + 0.0135914i
862862 0 0
863863 53.3858 1.81727 0.908637 0.417588i 0.137124π-0.137124\pi
0.908637 + 0.417588i 0.137124π0.137124\pi
864864 0 0
865865 12.0541 0.409851
866866 0 0
867867 −3.15652 4.93359i −0.107201 0.167554i
868868 0 0
869869 −14.9552 25.9033i −0.507322 0.878708i
870870 0 0
871871 4.71780 8.17147i 0.159857 0.276880i
872872 0 0
873873 0.852336 + 1.20726i 0.0288472 + 0.0408597i
874874 0 0
875875 −4.85447 + 8.40819i −0.164111 + 0.284249i
876876 0 0
877877 3.42674 + 5.93530i 0.115713 + 0.200421i 0.918065 0.396431i 0.129751π-0.129751\pi
−0.802352 + 0.596852i 0.796418π0.796418\pi
878878 0 0
879879 −20.3820 + 39.3396i −0.687468 + 1.32689i
880880 0 0
881881 −12.5103 −0.421483 −0.210742 0.977542i 0.567588π-0.567588\pi
−0.210742 + 0.977542i 0.567588π0.567588\pi
882882 0 0
883883 6.69124 0.225178 0.112589 0.993642i 0.464086π-0.464086\pi
0.112589 + 0.993642i 0.464086π0.464086\pi
884884 0 0
885885 38.8822 1.77322i 1.30701 0.0596063i
886886 0 0
887887 −16.0708 27.8355i −0.539605 0.934623i −0.998925 0.0463524i 0.985240π-0.985240\pi
0.459320 0.888271i 0.348093π-0.348093\pi
888888 0 0
889889 −0.410019 + 0.710174i −0.0137516 + 0.0238185i
890890 0 0
891891 41.1359 7.58300i 1.37810 0.254040i
892892 0 0
893893 −7.94639 + 13.7636i −0.265916 + 0.460580i
894894 0 0
895895 2.19076 + 3.79450i 0.0732289 + 0.126836i
896896 0 0
897897 72.1569 3.29072i 2.40925 0.109874i
898898 0 0
899899 51.4868 1.71718
900900 0 0
901901 −22.8171 −0.760148
902902 0 0
903903 −3.85234 + 7.43546i −0.128198 + 0.247437i
904904 0 0
905905 20.8442 + 36.1031i 0.692883 + 1.20011i
906906 0 0
907907 15.7016 27.1959i 0.521362 0.903025i −0.478330 0.878180i 0.658758π-0.658758\pi
0.999691 0.0248444i 0.00790902π-0.00790902\pi
908908 0 0
909909 −5.89397 8.34832i −0.195491 0.276896i
910910 0 0
911911 −22.8982 + 39.6609i −0.758653 + 1.31402i 0.184885 + 0.982760i 0.440809π0.440809\pi
−0.943538 + 0.331265i 0.892525π0.892525\pi
912912 0 0
913913 −3.45185 5.97877i −0.114239 0.197868i
914914 0 0
915915 31.7350 + 49.6013i 1.04913 + 1.63977i
916916 0 0
917917 −7.78794 −0.257180
918918 0 0
919919 27.1800 0.896584 0.448292 0.893887i 0.352032π-0.352032\pi
0.448292 + 0.893887i 0.352032π0.352032\pi
920920 0 0
921921 5.81925 + 9.09540i 0.191751 + 0.299704i
922922 0 0
923923 −48.0576 83.2381i −1.58183 2.73982i
924924 0 0
925925 0.382977 0.663336i 0.0125922 0.0218104i
926926 0 0
927927 15.4225 1.40962i 0.506540 0.0462979i
928928 0 0
929929 20.3338 35.2192i 0.667132 1.15551i −0.311571 0.950223i 0.600855π-0.600855\pi
0.978703 0.205283i 0.0658115π-0.0658115\pi
930930 0 0
931931 −2.16372 3.74766i −0.0709129 0.122825i
932932 0 0
933933 −23.2968 + 44.9655i −0.762703 + 1.47210i
934934 0 0
935935 −51.6270 −1.68838
936936 0 0
937937 16.4150 0.536254 0.268127 0.963384i 0.413595π-0.413595\pi
0.268127 + 0.963384i 0.413595π0.413595\pi
938938 0 0
939939 49.2893 2.24784i 1.60849 0.0733555i
940940 0 0
941941 −3.66878 6.35451i −0.119599 0.207151i 0.800010 0.599987i 0.204827π-0.204827\pi
−0.919609 + 0.392836i 0.871494π0.871494\pi
942942 0 0
943943 −0.801851 + 1.38885i −0.0261119 + 0.0452271i
944944 0 0
945945 −12.6659 + 1.74255i −0.412020 + 0.0566852i
946946 0 0
947947 −29.5562 + 51.1929i −0.960448 + 1.66354i −0.239071 + 0.971002i 0.576843π0.576843\pi
−0.721377 + 0.692543i 0.756490π0.756490\pi
948948 0 0
949949 15.3801 + 26.6390i 0.499258 + 0.864740i
950950 0 0
951951 2.80039 0.127712i 0.0908088 0.00414134i
952952 0 0
953953 −16.9354 −0.548592 −0.274296 0.961645i 0.588445π-0.588445\pi
−0.274296 + 0.961645i 0.588445π0.588445\pi
954954 0 0
955955 −13.5074 −0.437089
956956 0 0
957957 25.8302 49.8554i 0.834973 1.61160i
958958 0 0
959959 −1.49640 2.59184i −0.0483213 0.0836950i
960960 0 0
961961 −11.7434 + 20.3401i −0.378819 + 0.656133i
962962 0 0
963963 7.24583 15.6975i 0.233493 0.505844i
964964 0 0
965965 6.77548 11.7355i 0.218110 0.377778i
966966 0 0
967967 3.55555 + 6.15839i 0.114339 + 0.198040i 0.917515 0.397701i 0.130192π-0.130192\pi
−0.803177 + 0.595741i 0.796858π0.796858\pi
968968 0 0
969969 18.2367 + 28.5036i 0.585846 + 0.915669i
970970 0 0
971971 −1.47102 −0.0472072 −0.0236036 0.999721i 0.507514π-0.507514\pi
−0.0236036 + 0.999721i 0.507514π0.507514\pi
972972 0 0
973973 −6.32743 −0.202848
974974 0 0
975975 −6.99407 10.9316i −0.223990 0.350092i
976976 0 0
977977 9.71634 + 16.8292i 0.310853 + 0.538413i 0.978547 0.206022i 0.0660519π-0.0660519\pi
−0.667694 + 0.744436i 0.732719π0.732719\pi
978978 0 0
979979 −22.8545 + 39.5851i −0.730432 + 1.26515i
980980 0 0
981981 11.2934 24.4662i 0.360570 0.781145i
982982 0 0
983983 −3.87218 + 6.70681i −0.123503 + 0.213914i −0.921147 0.389215i 0.872746π-0.872746\pi
0.797644 + 0.603129i 0.206080π0.206080\pi
984984 0 0
985985 −14.3078 24.7818i −0.455884 0.789614i
986986 0 0
987987 2.92627 5.64803i 0.0931441 0.179779i
988988 0 0
989989 −28.3655 −0.901972
990990 0 0
991991 −14.4710 −0.459687 −0.229843 0.973228i 0.573821π-0.573821\pi
−0.229843 + 0.973228i 0.573821π0.573821\pi
992992 0 0
993993 −24.1929 + 1.10332i −0.767738 + 0.0350127i
994994 0 0
995995 5.10243 + 8.83767i 0.161758 + 0.280173i
996996 0 0
997997 27.6549 47.8996i 0.875838 1.51700i 0.0199711 0.999801i 0.493643π-0.493643\pi
0.855867 0.517196i 0.173024π-0.173024\pi
998998 0 0
999999 −3.74057 + 0.514623i −0.118346 + 0.0162819i
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.169.2 yes 6
3.2 odd 2 756.2.j.b.505.3 6
4.3 odd 2 1008.2.r.j.673.2 6
7.2 even 3 1764.2.i.g.1537.3 6
7.3 odd 6 1764.2.l.f.961.2 6
7.4 even 3 1764.2.l.e.961.2 6
7.5 odd 6 1764.2.i.d.1537.1 6
7.6 odd 2 1764.2.j.e.1177.2 6
9.2 odd 6 2268.2.a.h.1.1 3
9.4 even 3 inner 252.2.j.a.85.2 6
9.5 odd 6 756.2.j.b.253.3 6
9.7 even 3 2268.2.a.i.1.3 3
12.11 even 2 3024.2.r.j.2017.3 6
21.2 odd 6 5292.2.i.f.2125.3 6
21.5 even 6 5292.2.i.e.2125.1 6
21.11 odd 6 5292.2.l.e.3313.1 6
21.17 even 6 5292.2.l.f.3313.3 6
21.20 even 2 5292.2.j.d.3529.1 6
36.7 odd 6 9072.2.a.by.1.3 3
36.11 even 6 9072.2.a.bv.1.1 3
36.23 even 6 3024.2.r.j.1009.3 6
36.31 odd 6 1008.2.r.j.337.2 6
63.4 even 3 1764.2.i.g.373.3 6
63.5 even 6 5292.2.l.f.361.3 6
63.13 odd 6 1764.2.j.e.589.2 6
63.23 odd 6 5292.2.l.e.361.1 6
63.31 odd 6 1764.2.i.d.373.1 6
63.32 odd 6 5292.2.i.f.1549.3 6
63.40 odd 6 1764.2.l.f.949.2 6
63.41 even 6 5292.2.j.d.1765.1 6
63.58 even 3 1764.2.l.e.949.2 6
63.59 even 6 5292.2.i.e.1549.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.j.a.85.2 6 9.4 even 3 inner
252.2.j.a.169.2 yes 6 1.1 even 1 trivial
756.2.j.b.253.3 6 9.5 odd 6
756.2.j.b.505.3 6 3.2 odd 2
1008.2.r.j.337.2 6 36.31 odd 6
1008.2.r.j.673.2 6 4.3 odd 2
1764.2.i.d.373.1 6 63.31 odd 6
1764.2.i.d.1537.1 6 7.5 odd 6
1764.2.i.g.373.3 6 63.4 even 3
1764.2.i.g.1537.3 6 7.2 even 3
1764.2.j.e.589.2 6 63.13 odd 6
1764.2.j.e.1177.2 6 7.6 odd 2
1764.2.l.e.949.2 6 63.58 even 3
1764.2.l.e.961.2 6 7.4 even 3
1764.2.l.f.949.2 6 63.40 odd 6
1764.2.l.f.961.2 6 7.3 odd 6
2268.2.a.h.1.1 3 9.2 odd 6
2268.2.a.i.1.3 3 9.7 even 3
3024.2.r.j.1009.3 6 36.23 even 6
3024.2.r.j.2017.3 6 12.11 even 2
5292.2.i.e.1549.1 6 63.59 even 6
5292.2.i.e.2125.1 6 21.5 even 6
5292.2.i.f.1549.3 6 63.32 odd 6
5292.2.i.f.2125.3 6 21.2 odd 6
5292.2.j.d.1765.1 6 63.41 even 6
5292.2.j.d.3529.1 6 21.20 even 2
5292.2.l.e.361.1 6 63.23 odd 6
5292.2.l.e.3313.1 6 21.11 odd 6
5292.2.l.f.361.3 6 63.5 even 6
5292.2.l.f.3313.3 6 21.17 even 6
9072.2.a.bv.1.1 3 36.11 even 6
9072.2.a.by.1.3 3 36.7 odd 6