Properties

Label 448.2.z.a.47.10
Level 448448
Weight 22
Character 448.47
Analytic conductor 3.5773.577
Analytic rank 00
Dimension 5656
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [448,2,Mod(47,448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(448, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("448.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 448=267 448 = 2^{6} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 448.z (of order 1212, degree 44, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.577298010553.57729801055
Analytic rank: 00
Dimension: 5656
Relative dimension: 1414 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 47.10
Character χ\chi == 448.47
Dual form 448.2.z.a.143.10

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+(0.2825071.05433i)q3+(1.39922+0.374919i)q5+(0.298614+2.62885i)q7+(1.56627+0.904287i)q9+(1.42219+5.30770i)q11+(1.84531+1.84531i)q13+1.58116iq15+(5.694243.28757i)q17+(3.244530.869370i)q19+(2.85604+0.427830i)q21+(0.2561730.443704i)q23+(2.51288+1.45081i)q25+(3.711373.71137i)q27+(2.302632.30263i)q29+(3.79637+6.57551i)q31+(5.19429+2.99893i)q33+(1.403433.56637i)q35+(1.07603+4.01582i)q37+(1.42426+2.46689i)q390.453189q41+(3.408423.40842i)q43+(2.530590.678070i)q45+(1.714682.96992i)q47+(6.82166+1.57002i)q49+(1.857536.93238i)q51+(1.372260.367696i)q537.95984iq553.66642iq57+(6.575601.76193i)q59+(1.30846+4.88324i)q61+(1.90952+4.38752i)q63+(1.890153.27384i)q65+(6.19818+1.66080i)q67+(0.3954410.395441i)q696.44865q71+(7.43995+12.8864i)q73+(0.819730+3.05927i)q75+(14.37782.15377i)q77+(3.33780+1.92708i)q79+(0.1516680.262697i)q81+(2.440512.44051i)q83+(6.73491+6.73491i)q85+(3.07824+1.77722i)q87+(3.813446.60506i)q89+(5.402084.30001i)q91+(8.005272.14500i)q93+(4.21387+2.43288i)q9511.2152iq97+(7.02722+7.02722i)q99+O(q100)q+(0.282507 - 1.05433i) q^{3} +(-1.39922 + 0.374919i) q^{5} +(0.298614 + 2.62885i) q^{7} +(1.56627 + 0.904287i) q^{9} +(-1.42219 + 5.30770i) q^{11} +(-1.84531 + 1.84531i) q^{13} +1.58116i q^{15} +(5.69424 - 3.28757i) q^{17} +(3.24453 - 0.869370i) q^{19} +(2.85604 + 0.427830i) q^{21} +(0.256173 - 0.443704i) q^{23} +(-2.51288 + 1.45081i) q^{25} +(3.71137 - 3.71137i) q^{27} +(-2.30263 - 2.30263i) q^{29} +(3.79637 + 6.57551i) q^{31} +(5.19429 + 2.99893i) q^{33} +(-1.40343 - 3.56637i) q^{35} +(1.07603 + 4.01582i) q^{37} +(1.42426 + 2.46689i) q^{39} -0.453189 q^{41} +(-3.40842 - 3.40842i) q^{43} +(-2.53059 - 0.678070i) q^{45} +(1.71468 - 2.96992i) q^{47} +(-6.82166 + 1.57002i) q^{49} +(-1.85753 - 6.93238i) q^{51} +(-1.37226 - 0.367696i) q^{53} -7.95984i q^{55} -3.66642i q^{57} +(-6.57560 - 1.76193i) q^{59} +(1.30846 + 4.88324i) q^{61} +(-1.90952 + 4.38752i) q^{63} +(1.89015 - 3.27384i) q^{65} +(6.19818 + 1.66080i) q^{67} +(-0.395441 - 0.395441i) q^{69} -6.44865 q^{71} +(7.43995 + 12.8864i) q^{73} +(0.819730 + 3.05927i) q^{75} +(-14.3778 - 2.15377i) q^{77} +(3.33780 + 1.92708i) q^{79} +(-0.151668 - 0.262697i) q^{81} +(-2.44051 - 2.44051i) q^{83} +(-6.73491 + 6.73491i) q^{85} +(-3.07824 + 1.77722i) q^{87} +(3.81344 - 6.60506i) q^{89} +(-5.40208 - 4.30001i) q^{91} +(8.00527 - 2.14500i) q^{93} +(-4.21387 + 2.43288i) q^{95} -11.2152i q^{97} +(-7.02722 + 7.02722i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 56q+6q36q5+8q72q1112q17+6q1910q21+12q2324q2912q33+2q35+6q37+4q39+12q458q49+34q51+6q5342q59++16q99+O(q100) 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} - 10 q^{21} + 12 q^{23} - 24 q^{29} - 12 q^{33} + 2 q^{35} + 6 q^{37} + 4 q^{39} + 12 q^{45} - 8 q^{49} + 34 q^{51} + 6 q^{53} - 42 q^{59}+ \cdots + 16 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/448Z)×\left(\mathbb{Z}/448\mathbb{Z}\right)^\times.

nn 127127 129129 197197
χ(n)\chi(n) 1-1 e(56)e\left(\frac{5}{6}\right) e(34)e\left(\frac{3}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.282507 1.05433i 0.163106 0.608719i −0.835169 0.549994i 0.814630π-0.814630\pi
0.998274 0.0587246i 0.0187034π-0.0187034\pi
44 0 0
55 −1.39922 + 0.374919i −0.625749 + 0.167669i −0.557740 0.830016i 0.688331π-0.688331\pi
−0.0680093 + 0.997685i 0.521665π0.521665\pi
66 0 0
77 0.298614 + 2.62885i 0.112866 + 0.993610i
88 0 0
99 1.56627 + 0.904287i 0.522090 + 0.301429i
1010 0 0
1111 −1.42219 + 5.30770i −0.428807 + 1.60033i 0.326658 + 0.945143i 0.394077π0.394077\pi
−0.755465 + 0.655189i 0.772589π0.772589\pi
1212 0 0
1313 −1.84531 + 1.84531i −0.511798 + 0.511798i −0.915077 0.403279i 0.867870π-0.867870\pi
0.403279 + 0.915077i 0.367870π0.367870\pi
1414 0 0
1515 1.58116i 0.408253i
1616 0 0
1717 5.69424 3.28757i 1.38106 0.797353i 0.388771 0.921334i 0.372900π-0.372900\pi
0.992285 + 0.123982i 0.0395664π0.0395664\pi
1818 0 0
1919 3.24453 0.869370i 0.744347 0.199447i 0.133338 0.991071i 0.457431π-0.457431\pi
0.611009 + 0.791624i 0.290764π0.290764\pi
2020 0 0
2121 2.85604 + 0.427830i 0.623238 + 0.0933601i
2222 0 0
2323 0.256173 0.443704i 0.0534157 0.0925187i −0.838081 0.545546i 0.816322π-0.816322\pi
0.891497 + 0.453027i 0.149656π0.149656\pi
2424 0 0
2525 −2.51288 + 1.45081i −0.502576 + 0.290162i
2626 0 0
2727 3.71137 3.71137i 0.714254 0.714254i
2828 0 0
2929 −2.30263 2.30263i −0.427587 0.427587i 0.460219 0.887806i 0.347771π-0.347771\pi
−0.887806 + 0.460219i 0.847771π0.847771\pi
3030 0 0
3131 3.79637 + 6.57551i 0.681848 + 1.18100i 0.974416 + 0.224751i 0.0721568π0.0721568\pi
−0.292568 + 0.956245i 0.594510π0.594510\pi
3232 0 0
3333 5.19429 + 2.99893i 0.904211 + 0.522046i
3434 0 0
3535 −1.40343 3.56637i −0.237223 0.602827i
3636 0 0
3737 1.07603 + 4.01582i 0.176899 + 0.660196i 0.996220 + 0.0868615i 0.0276838π0.0276838\pi
−0.819321 + 0.573334i 0.805650π0.805650\pi
3838 0 0
3939 1.42426 + 2.46689i 0.228064 + 0.395018i
4040 0 0
4141 −0.453189 −0.0707762 −0.0353881 0.999374i 0.511267π-0.511267\pi
−0.0353881 + 0.999374i 0.511267π0.511267\pi
4242 0 0
4343 −3.40842 3.40842i −0.519779 0.519779i 0.397726 0.917504i 0.369800π-0.369800\pi
−0.917504 + 0.397726i 0.869800π0.869800\pi
4444 0 0
4545 −2.53059 0.678070i −0.377238 0.101081i
4646 0 0
4747 1.71468 2.96992i 0.250112 0.433207i −0.713444 0.700712i 0.752866π-0.752866\pi
0.963556 + 0.267505i 0.0861992π0.0861992\pi
4848 0 0
4949 −6.82166 + 1.57002i −0.974523 + 0.224289i
5050 0 0
5151 −1.85753 6.93238i −0.260106 0.970727i
5252 0 0
5353 −1.37226 0.367696i −0.188495 0.0505070i 0.163337 0.986570i 0.447774π-0.447774\pi
−0.351831 + 0.936063i 0.614441π0.614441\pi
5454 0 0
5555 7.95984i 1.07330i
5656 0 0
5757 3.66642i 0.485629i
5858 0 0
5959 −6.57560 1.76193i −0.856070 0.229383i −0.196015 0.980601i 0.562800π-0.562800\pi
−0.660055 + 0.751218i 0.729467π0.729467\pi
6060 0 0
6161 1.30846 + 4.88324i 0.167531 + 0.625235i 0.997704 + 0.0677284i 0.0215751π0.0215751\pi
−0.830173 + 0.557506i 0.811758π0.811758\pi
6262 0 0
6363 −1.90952 + 4.38752i −0.240577 + 0.552775i
6464 0 0
6565 1.89015 3.27384i 0.234445 0.406070i
6666 0 0
6767 6.19818 + 1.66080i 0.757229 + 0.202899i 0.616722 0.787181i 0.288460π-0.288460\pi
0.140507 + 0.990080i 0.455127π0.455127\pi
6868 0 0
6969 −0.395441 0.395441i −0.0476055 0.0476055i
7070 0 0
7171 −6.44865 −0.765314 −0.382657 0.923890i 0.624991π-0.624991\pi
−0.382657 + 0.923890i 0.624991π0.624991\pi
7272 0 0
7373 7.43995 + 12.8864i 0.870780 + 1.50823i 0.861191 + 0.508281i 0.169719π0.169719\pi
0.00958835 + 0.999954i 0.496948π0.496948\pi
7474 0 0
7575 0.819730 + 3.05927i 0.0946543 + 0.353255i
7676 0 0
7777 −14.3778 2.15377i −1.63850 0.245445i
7878 0 0
7979 3.33780 + 1.92708i 0.375532 + 0.216813i 0.675873 0.737019i 0.263767π-0.263767\pi
−0.300341 + 0.953832i 0.597100π0.597100\pi
8080 0 0
8181 −0.151668 0.262697i −0.0168520 0.0291886i
8282 0 0
8383 −2.44051 2.44051i −0.267881 0.267881i 0.560365 0.828246i 0.310661π-0.310661\pi
−0.828246 + 0.560365i 0.810661π0.810661\pi
8484 0 0
8585 −6.73491 + 6.73491i −0.730503 + 0.730503i
8686 0 0
8787 −3.07824 + 1.77722i −0.330022 + 0.190538i
8888 0 0
8989 3.81344 6.60506i 0.404223 0.700135i −0.590007 0.807398i 0.700875π-0.700875\pi
0.994231 + 0.107262i 0.0342085π0.0342085\pi
9090 0 0
9191 −5.40208 4.30001i −0.566292 0.450763i
9292 0 0
9393 8.00527 2.14500i 0.830107 0.222427i
9494 0 0
9595 −4.21387 + 2.43288i −0.432334 + 0.249608i
9696 0 0
9797 11.2152i 1.13873i −0.822085 0.569365i 0.807189π-0.807189\pi
0.822085 0.569365i 0.192811π-0.192811\pi
9898 0 0
9999 −7.02722 + 7.02722i −0.706263 + 0.706263i
100100 0 0
101101 5.03457 18.7893i 0.500959 1.86960i 0.00725520 0.999974i 0.497691π-0.497691\pi
0.493704 0.869630i 0.335643π-0.335643\pi
102102 0 0
103103 −6.15035 3.55091i −0.606012 0.349881i 0.165391 0.986228i 0.447111π-0.447111\pi
−0.771403 + 0.636347i 0.780445π0.780445\pi
104104 0 0
105105 −4.15662 + 0.472156i −0.405645 + 0.0460777i
106106 0 0
107107 11.5830 3.10366i 1.11977 0.300042i 0.348981 0.937130i 0.386528π-0.386528\pi
0.770791 + 0.637088i 0.219861π0.219861\pi
108108 0 0
109109 2.68591 10.0240i 0.257264 0.960122i −0.709553 0.704652i 0.751103π-0.751103\pi
0.966817 0.255470i 0.0822302π-0.0822302\pi
110110 0 0
111111 4.53799 0.430727
112112 0 0
113113 −13.4601 −1.26622 −0.633109 0.774062i 0.718222π-0.718222\pi
−0.633109 + 0.774062i 0.718222π0.718222\pi
114114 0 0
115115 −0.192088 + 0.716883i −0.0179123 + 0.0668497i
116116 0 0
117117 −4.55896 + 1.22157i −0.421476 + 0.112934i
118118 0 0
119119 10.3429 + 13.9876i 0.948132 + 1.28224i
120120 0 0
121121 −16.6227 9.59715i −1.51116 0.872468i
122122 0 0
123123 −0.128029 + 0.477811i −0.0115440 + 0.0430828i
124124 0 0
125125 8.09362 8.09362i 0.723916 0.723916i
126126 0 0
127127 13.7356i 1.21884i −0.792849 0.609418i 0.791403π-0.791403\pi
0.792849 0.609418i 0.208597π-0.208597\pi
128128 0 0
129129 −4.55651 + 2.63070i −0.401178 + 0.231620i
130130 0 0
131131 −2.81460 + 0.754169i −0.245912 + 0.0658920i −0.379670 0.925122i 0.623962π-0.623962\pi
0.133757 + 0.991014i 0.457296π0.457296\pi
132132 0 0
133133 3.25430 + 8.26977i 0.282184 + 0.717080i
134134 0 0
135135 −3.80156 + 6.58449i −0.327186 + 0.566703i
136136 0 0
137137 6.25695 3.61245i 0.534568 0.308633i −0.208307 0.978064i 0.566795π-0.566795\pi
0.742874 + 0.669431i 0.233462π0.233462\pi
138138 0 0
139139 −0.708981 + 0.708981i −0.0601350 + 0.0601350i −0.736535 0.676400i 0.763539π-0.763539\pi
0.676400 + 0.736535i 0.263539π0.263539\pi
140140 0 0
141141 −2.64687 2.64687i −0.222906 0.222906i
142142 0 0
143143 −7.16997 12.4188i −0.599583 1.03851i
144144 0 0
145145 4.08518 + 2.35858i 0.339255 + 0.195869i
146146 0 0
147147 −0.271845 + 7.63583i −0.0224214 + 0.629793i
148148 0 0
149149 2.46397 + 9.19566i 0.201856 + 0.753338i 0.990385 + 0.138340i 0.0441766π0.0441766\pi
−0.788529 + 0.614998i 0.789157π0.789157\pi
150150 0 0
151151 −3.55073 6.15004i −0.288954 0.500483i 0.684606 0.728913i 0.259974π-0.259974\pi
−0.973560 + 0.228430i 0.926641π0.926641\pi
152152 0 0
153153 11.8916 0.961381
154154 0 0
155155 −7.77723 7.77723i −0.624683 0.624683i
156156 0 0
157157 8.47741 + 2.27152i 0.676571 + 0.181287i 0.580713 0.814108i 0.302774π-0.302774\pi
0.0958582 + 0.995395i 0.469440π0.469440\pi
158158 0 0
159159 −0.775348 + 1.34294i −0.0614891 + 0.106502i
160160 0 0
161161 1.24293 + 0.540942i 0.0979563 + 0.0426322i
162162 0 0
163163 3.28686 + 12.2667i 0.257447 + 0.960805i 0.966713 + 0.255864i 0.0823600π0.0823600\pi
−0.709266 + 0.704941i 0.750973π0.750973\pi
164164 0 0
165165 −8.39231 2.24871i −0.653340 0.175062i
166166 0 0
167167 21.5280i 1.66588i −0.553361 0.832942i 0.686655π-0.686655\pi
0.553361 0.832942i 0.313345π-0.313345\pi
168168 0 0
169169 6.18963i 0.476126i
170170 0 0
171171 5.86798 + 1.57232i 0.448736 + 0.120238i
172172 0 0
173173 5.18431 + 19.3481i 0.394156 + 1.47101i 0.823213 + 0.567733i 0.192179π0.192179\pi
−0.429057 + 0.903278i 0.641154π0.641154\pi
174174 0 0
175175 −4.56434 6.17274i −0.345032 0.466615i
176176 0 0
177177 −3.71531 + 6.43510i −0.279260 + 0.483692i
178178 0 0
179179 6.57967 + 1.76302i 0.491787 + 0.131774i 0.496186 0.868216i 0.334733π-0.334733\pi
−0.00439858 + 0.999990i 0.501400π0.501400\pi
180180 0 0
181181 −6.32019 6.32019i −0.469776 0.469776i 0.432066 0.901842i 0.357785π-0.357785\pi
−0.901842 + 0.432066i 0.857785π0.857785\pi
182182 0 0
183183 5.51821 0.407917
184184 0 0
185185 −3.01121 5.21558i −0.221389 0.383457i
186186 0 0
187187 9.35112 + 34.8989i 0.683822 + 2.55206i
188188 0 0
189189 10.8649 + 8.64836i 0.790305 + 0.629076i
190190 0 0
191191 −11.5374 6.66112i −0.834817 0.481982i 0.0206820 0.999786i 0.493416π-0.493416\pi
−0.855499 + 0.517804i 0.826750π0.826750\pi
192192 0 0
193193 5.25772 + 9.10664i 0.378459 + 0.655511i 0.990838 0.135054i 0.0431207π-0.0431207\pi
−0.612379 + 0.790564i 0.709787π0.709787\pi
194194 0 0
195195 −2.91773 2.91773i −0.208943 0.208943i
196196 0 0
197197 14.0642 14.0642i 1.00203 1.00203i 0.00203129 0.999998i 0.499353π-0.499353\pi
0.999998 0.00203129i 0.000646580π-0.000646580\pi
198198 0 0
199199 20.9503 12.0957i 1.48513 0.857439i 0.485272 0.874363i 0.338721π-0.338721\pi
0.999857 + 0.0169240i 0.00538734π0.00538734\pi
200200 0 0
201201 3.50206 6.06575i 0.247017 0.427845i
202202 0 0
203203 5.36565 6.74085i 0.376595 0.473115i
204204 0 0
205205 0.634110 0.169909i 0.0442882 0.0118670i
206206 0 0
207207 0.802472 0.463307i 0.0557757 0.0322021i
208208 0 0
209209 18.4574i 1.27673i
210210 0 0
211211 −8.81296 + 8.81296i −0.606709 + 0.606709i −0.942085 0.335375i 0.891137π-0.891137\pi
0.335375 + 0.942085i 0.391137π0.391137\pi
212212 0 0
213213 −1.82179 + 6.79902i −0.124827 + 0.465861i
214214 0 0
215215 6.04700 + 3.49124i 0.412402 + 0.238101i
216216 0 0
217217 −16.1523 + 11.9436i −1.09649 + 0.810785i
218218 0 0
219219 15.6883 4.20368i 1.06012 0.284058i
220220 0 0
221221 −4.44106 + 16.5743i −0.298738 + 1.11490i
222222 0 0
223223 5.44902 0.364893 0.182447 0.983216i 0.441598π-0.441598\pi
0.182447 + 0.983216i 0.441598π0.441598\pi
224224 0 0
225225 −5.24780 −0.349853
226226 0 0
227227 −0.389502 + 1.45364i −0.0258521 + 0.0964815i −0.977647 0.210255i 0.932570π-0.932570\pi
0.951794 + 0.306737i 0.0992371π0.0992371\pi
228228 0 0
229229 4.77902 1.28054i 0.315807 0.0846202i −0.0974340 0.995242i 0.531063π-0.531063\pi
0.413241 + 0.910622i 0.364397π0.364397\pi
230230 0 0
231231 −6.33263 + 14.5505i −0.416656 + 0.957354i
232232 0 0
233233 −10.7652 6.21528i −0.705251 0.407177i 0.104049 0.994572i 0.466820π-0.466820\pi
−0.809300 + 0.587395i 0.800153π0.800153\pi
234234 0 0
235235 −1.28574 + 4.79843i −0.0838721 + 0.313015i
236236 0 0
237237 2.97474 2.97474i 0.193230 0.193230i
238238 0 0
239239 7.34038i 0.474810i 0.971411 + 0.237405i 0.0762968π0.0762968\pi
−0.971411 + 0.237405i 0.923703π0.923703\pi
240240 0 0
241241 −8.98405 + 5.18694i −0.578713 + 0.334120i −0.760622 0.649195i 0.775106π-0.775106\pi
0.181909 + 0.983315i 0.441773π0.441773\pi
242242 0 0
243243 14.8897 3.98968i 0.955173 0.255938i
244244 0 0
245245 8.95636 4.75438i 0.572201 0.303746i
246246 0 0
247247 −4.38292 + 7.59144i −0.278879 + 0.483032i
248248 0 0
249249 −3.26257 + 1.88365i −0.206757 + 0.119371i
250250 0 0
251251 0.401720 0.401720i 0.0253563 0.0253563i −0.694315 0.719671i 0.744293π-0.744293\pi
0.719671 + 0.694315i 0.244293π0.244293\pi
252252 0 0
253253 1.99072 + 1.99072i 0.125156 + 0.125156i
254254 0 0
255255 5.19817 + 9.00349i 0.325522 + 0.563820i
256256 0 0
257257 7.92211 + 4.57383i 0.494168 + 0.285308i 0.726302 0.687376i 0.241237π-0.241237\pi
−0.232134 + 0.972684i 0.574571π0.574571\pi
258258 0 0
259259 −10.2356 + 4.02791i −0.636012 + 0.250282i
260260 0 0
261261 −1.52430 5.68877i −0.0943519 0.352126i
262262 0 0
263263 2.29116 + 3.96841i 0.141279 + 0.244703i 0.927979 0.372634i 0.121545π-0.121545\pi
−0.786699 + 0.617336i 0.788212π0.788212\pi
264264 0 0
265265 2.05795 0.126419
266266 0 0
267267 −5.88661 5.88661i −0.360254 0.360254i
268268 0 0
269269 −9.22279 2.47124i −0.562323 0.150674i −0.0335497 0.999437i 0.510681π-0.510681\pi
−0.528773 + 0.848763i 0.677348π0.677348\pi
270270 0 0
271271 −3.64178 + 6.30775i −0.221223 + 0.383169i −0.955179 0.296027i 0.904338π-0.904338\pi
0.733957 + 0.679196i 0.237671π0.237671\pi
272272 0 0
273273 −6.05976 + 4.48080i −0.366754 + 0.271190i
274274 0 0
275275 −4.12667 15.4009i −0.248848 0.928712i
276276 0 0
277277 31.2724 + 8.37942i 1.87898 + 0.503470i 0.999627 + 0.0272931i 0.00868875π0.00868875\pi
0.879349 + 0.476177i 0.157978π0.157978\pi
278278 0 0
279279 13.7320i 0.822115i
280280 0 0
281281 4.09880i 0.244514i −0.992498 0.122257i 0.960987π-0.960987\pi
0.992498 0.122257i 0.0390132π-0.0390132\pi
282282 0 0
283283 −13.1954 3.53570i −0.784387 0.210176i −0.155669 0.987809i 0.549753π-0.549753\pi
−0.628718 + 0.777633i 0.716420π0.716420\pi
284284 0 0
285285 1.37461 + 5.13012i 0.0814249 + 0.303882i
286286 0 0
287287 −0.135329 1.19136i −0.00798819 0.0703239i
288288 0 0
289289 13.1162 22.7180i 0.771543 1.33635i
290290 0 0
291291 −11.8245 3.16838i −0.693167 0.185733i
292292 0 0
293293 −16.6941 16.6941i −0.975280 0.975280i 0.0244213 0.999702i 0.492226π-0.492226\pi
−0.999702 + 0.0244213i 0.992226π0.992226\pi
294294 0 0
295295 9.86128 0.574146
296296 0 0
297297 14.4206 + 24.9771i 0.836766 + 1.44932i
298298 0 0
299299 0.346054 + 1.29149i 0.0200128 + 0.0746889i
300300 0 0
301301 7.94240 9.97801i 0.457792 0.575123i
302302 0 0
303303 −18.3878 10.6162i −1.05635 0.609886i
304304 0 0
305305 −3.66164 6.34215i −0.209665 0.363151i
306306 0 0
307307 16.7590 + 16.7590i 0.956484 + 0.956484i 0.999092 0.0426074i 0.0135665π-0.0135665\pi
−0.0426074 + 0.999092i 0.513566π0.513566\pi
308308 0 0
309309 −5.48135 + 5.48135i −0.311823 + 0.311823i
310310 0 0
311311 18.6053 10.7418i 1.05501 0.609111i 0.130963 0.991387i 0.458193π-0.458193\pi
0.924048 + 0.382277i 0.124860π0.124860\pi
312312 0 0
313313 10.4249 18.0565i 0.589253 1.02062i −0.405078 0.914282i 0.632756π-0.632756\pi
0.994331 0.106334i 0.0339111π-0.0339111\pi
314314 0 0
315315 1.02687 6.85501i 0.0578576 0.386236i
316316 0 0
317317 14.3981 3.85795i 0.808676 0.216684i 0.169287 0.985567i 0.445854π-0.445854\pi
0.639390 + 0.768883i 0.279187π0.279187\pi
318318 0 0
319319 15.4964 8.94686i 0.867633 0.500928i
320320 0 0
321321 13.0891i 0.730565i
322322 0 0
323323 15.6170 15.6170i 0.868955 0.868955i
324324 0 0
325325 1.95985 7.31425i 0.108713 0.405722i
326326 0 0
327327 −9.80980 5.66369i −0.542483 0.313203i
328328 0 0
329329 8.31948 + 3.62078i 0.458668 + 0.199620i
330330 0 0
331331 −2.89002 + 0.774378i −0.158850 + 0.0425637i −0.337367 0.941373i 0.609536π-0.609536\pi
0.178518 + 0.983937i 0.442870π0.442870\pi
332332 0 0
333333 −1.94609 + 7.26290i −0.106645 + 0.398005i
334334 0 0
335335 −9.29528 −0.507855
336336 0 0
337337 −20.5605 −1.12000 −0.560000 0.828493i 0.689199π-0.689199\pi
−0.560000 + 0.828493i 0.689199π0.689199\pi
338338 0 0
339339 −3.80257 + 14.1914i −0.206527 + 0.770771i
340340 0 0
341341 −40.3000 + 10.7983i −2.18237 + 0.584763i
342342 0 0
343343 −6.16439 17.4643i −0.332846 0.942981i
344344 0 0
345345 0.701566 + 0.405049i 0.0377711 + 0.0218071i
346346 0 0
347347 1.55085 5.78787i 0.0832542 0.310709i −0.911724 0.410804i 0.865248π-0.865248\pi
0.994978 + 0.100095i 0.0319147π0.0319147\pi
348348 0 0
349349 3.15549 3.15549i 0.168909 0.168909i −0.617590 0.786500i 0.711891π-0.711891\pi
0.786500 + 0.617590i 0.211891π0.211891\pi
350350 0 0
351351 13.6973i 0.731108i
352352 0 0
353353 6.03486 3.48423i 0.321203 0.185447i −0.330726 0.943727i 0.607293π-0.607293\pi
0.651929 + 0.758280i 0.273960π0.273960\pi
354354 0 0
355355 9.02307 2.41773i 0.478895 0.128320i
356356 0 0
357357 17.6695 6.95325i 0.935168 0.368005i
358358 0 0
359359 −18.6187 + 32.2485i −0.982656 + 1.70201i −0.330735 + 0.943724i 0.607297π0.607297\pi
−0.651921 + 0.758287i 0.726037π0.726037\pi
360360 0 0
361361 −6.68329 + 3.85860i −0.351752 + 0.203084i
362362 0 0
363363 −14.8146 + 14.8146i −0.777566 + 0.777566i
364364 0 0
365365 −15.2415 15.2415i −0.797774 0.797774i
366366 0 0
367367 13.0391 + 22.5844i 0.680637 + 1.17890i 0.974787 + 0.223138i 0.0716300π0.0716300\pi
−0.294150 + 0.955759i 0.595037π0.595037\pi
368368 0 0
369369 −0.709816 0.409813i −0.0369516 0.0213340i
370370 0 0
371371 0.556840 3.71726i 0.0289097 0.192991i
372372 0 0
373373 9.46676 + 35.3304i 0.490170 + 1.82934i 0.555555 + 0.831480i 0.312506π0.312506\pi
−0.0653850 + 0.997860i 0.520828π0.520828\pi
374374 0 0
375375 −6.24686 10.8199i −0.322586 0.558736i
376376 0 0
377377 8.49813 0.437676
378378 0 0
379379 0.261074 + 0.261074i 0.0134105 + 0.0134105i 0.713780 0.700370i 0.246982π-0.246982\pi
−0.700370 + 0.713780i 0.746982π0.746982\pi
380380 0 0
381381 −14.4819 3.88041i −0.741929 0.198799i
382382 0 0
383383 8.76848 15.1875i 0.448048 0.776043i −0.550211 0.835026i 0.685453π-0.685453\pi
0.998259 + 0.0589834i 0.0187859π0.0187859\pi
384384 0 0
385385 20.9252 2.37692i 1.06645 0.121139i
386386 0 0
387387 −2.25632 8.42070i −0.114695 0.428048i
388388 0 0
389389 −21.5199 5.76625i −1.09110 0.292361i −0.331967 0.943291i 0.607712π-0.607712\pi
−0.759137 + 0.650930i 0.774379π0.774379\pi
390390 0 0
391391 3.36874i 0.170365i
392392 0 0
393393 3.18058i 0.160439i
394394 0 0
395395 −5.39281 1.44500i −0.271342 0.0727058i
396396 0 0
397397 −6.12529 22.8599i −0.307419 1.14730i −0.930843 0.365420i 0.880925π-0.880925\pi
0.623424 0.781884i 0.285741π-0.285741\pi
398398 0 0
399399 9.63844 1.09484i 0.482526 0.0548108i
400400 0 0
401401 −3.87231 + 6.70703i −0.193374 + 0.334933i −0.946366 0.323096i 0.895276π-0.895276\pi
0.752992 + 0.658029i 0.228610π0.228610\pi
402402 0 0
403403 −19.1394 5.12838i −0.953400 0.255463i
404404 0 0
405405 0.310707 + 0.310707i 0.0154392 + 0.0154392i
406406 0 0
407407 −22.8451 −1.13239
408408 0 0
409409 −15.9651 27.6524i −0.789425 1.36732i −0.926320 0.376739i 0.877045π-0.877045\pi
0.136894 0.990586i 0.456288π-0.456288\pi
410410 0 0
411411 −2.04109 7.61745i −0.100680 0.375741i
412412 0 0
413413 2.66827 17.8124i 0.131297 0.876489i
414414 0 0
415415 4.32981 + 2.49981i 0.212542 + 0.122711i
416416 0 0
417417 0.547209 + 0.947793i 0.0267969 + 0.0464136i
418418 0 0
419419 −6.96449 6.96449i −0.340238 0.340238i 0.516219 0.856457i 0.327339π-0.327339\pi
−0.856457 + 0.516219i 0.827339π0.827339\pi
420420 0 0
421421 6.31935 6.31935i 0.307986 0.307986i −0.536142 0.844128i 0.680119π-0.680119\pi
0.844128 + 0.536142i 0.180119π0.180119\pi
422422 0 0
423423 5.37132 3.10113i 0.261162 0.150782i
424424 0 0
425425 −9.53929 + 16.5225i −0.462724 + 0.801461i
426426 0 0
427427 −12.4466 + 4.89795i −0.602331 + 0.237028i
428428 0 0
429429 −15.1191 + 4.05114i −0.729955 + 0.195591i
430430 0 0
431431 −5.61569 + 3.24222i −0.270498 + 0.156172i −0.629114 0.777313i 0.716582π-0.716582\pi
0.358616 + 0.933485i 0.383249π0.383249\pi
432432 0 0
433433 17.1718i 0.825223i −0.910907 0.412612i 0.864617π-0.864617\pi
0.910907 0.412612i 0.135383π-0.135383\pi
434434 0 0
435435 3.64081 3.64081i 0.174564 0.174564i
436436 0 0
437437 0.445418 1.66232i 0.0213072 0.0795196i
438438 0 0
439439 −27.1054 15.6493i −1.29367 0.746900i −0.314366 0.949302i 0.601792π-0.601792\pi
−0.979302 + 0.202402i 0.935125π0.935125\pi
440440 0 0
441441 −12.1043 3.70966i −0.576396 0.176650i
442442 0 0
443443 11.7094 3.13752i 0.556330 0.149068i 0.0303104 0.999541i 0.490350π-0.490350\pi
0.526020 + 0.850472i 0.323684π0.323684\pi
444444 0 0
445445 −2.85946 + 10.6717i −0.135552 + 0.505885i
446446 0 0
447447 10.3914 0.491495
448448 0 0
449449 33.4968 1.58081 0.790406 0.612583i 0.209869π-0.209869\pi
0.790406 + 0.612583i 0.209869π0.209869\pi
450450 0 0
451451 0.644522 2.40539i 0.0303494 0.113265i
452452 0 0
453453 −7.48729 + 2.00621i −0.351783 + 0.0942601i
454454 0 0
455455 9.17085 + 3.99130i 0.429936 + 0.187115i
456456 0 0
457457 −2.60908 1.50635i −0.122047 0.0704641i 0.437733 0.899105i 0.355781π-0.355781\pi
−0.559781 + 0.828641i 0.689115π0.689115\pi
458458 0 0
459459 8.93205 33.3349i 0.416912 1.55594i
460460 0 0
461461 −20.6763 + 20.6763i −0.962993 + 0.962993i −0.999339 0.0363467i 0.988428π-0.988428\pi
0.0363467 + 0.999339i 0.488428π0.488428\pi
462462 0 0
463463 11.6775i 0.542697i 0.962481 + 0.271349i 0.0874696π0.0874696\pi
−0.962481 + 0.271349i 0.912530π0.912530\pi
464464 0 0
465465 −10.3969 + 6.00266i −0.482145 + 0.278367i
466466 0 0
467467 −9.80739 + 2.62788i −0.453832 + 0.121604i −0.478492 0.878092i 0.658816π-0.658816\pi
0.0246599 + 0.999696i 0.492150π0.492150\pi
468468 0 0
469469 −2.51512 + 16.7900i −0.116137 + 0.775290i
470470 0 0
471471 4.78986 8.29629i 0.220705 0.382273i
472472 0 0
473473 22.9383 13.2434i 1.05470 0.608933i
474474 0 0
475475 −6.89183 + 6.89183i −0.316219 + 0.316219i
476476 0 0
477477 −1.81683 1.81683i −0.0831870 0.0831870i
478478 0 0
479479 −5.72312 9.91273i −0.261496 0.452924i 0.705144 0.709064i 0.250882π-0.250882\pi
−0.966640 + 0.256140i 0.917549π0.917549\pi
480480 0 0
481481 −9.39606 5.42482i −0.428424 0.247350i
482482 0 0
483483 0.921468 1.15764i 0.0419283 0.0526743i
484484 0 0
485485 4.20479 + 15.6925i 0.190930 + 0.712560i
486486 0 0
487487 −4.85037 8.40108i −0.219791 0.380689i 0.734953 0.678118i 0.237204π-0.237204\pi
−0.954744 + 0.297429i 0.903871π0.903871\pi
488488 0 0
489489 13.8618 0.626851
490490 0 0
491491 11.4667 + 11.4667i 0.517483 + 0.517483i 0.916809 0.399326i 0.130756π-0.130756\pi
−0.399326 + 0.916809i 0.630756π0.630756\pi
492492 0 0
493493 −20.6817 5.54166i −0.931459 0.249584i
494494 0 0
495495 7.19798 12.4673i 0.323525 0.560362i
496496 0 0
497497 −1.92566 16.9525i −0.0863776 0.760424i
498498 0 0
499499 −4.93931 18.4338i −0.221114 0.825209i −0.983924 0.178586i 0.942848π-0.942848\pi
0.762810 0.646623i 0.223819π-0.223819\pi
500500 0 0
501501 −22.6976 6.08181i −1.01405 0.271715i
502502 0 0
503503 22.4043i 0.998960i 0.866325 + 0.499480i 0.166476π0.166476\pi
−0.866325 + 0.499480i 0.833524π0.833524\pi
504504 0 0
505505 28.1779i 1.25390i
506506 0 0
507507 6.52593 + 1.74862i 0.289827 + 0.0776588i
508508 0 0
509509 −3.91534 14.6122i −0.173544 0.647676i −0.996795 0.0799982i 0.974509π-0.974509\pi
0.823251 0.567678i 0.192158π-0.192158\pi
510510 0 0
511511 −31.6546 + 23.4065i −1.40032 + 1.03544i
512512 0 0
513513 8.81512 15.2682i 0.389197 0.674109i
514514 0 0
515515 9.93698 + 2.66261i 0.437876 + 0.117328i
516516 0 0
517517 13.3248 + 13.3248i 0.586025 + 0.586025i
518518 0 0
519519 21.8639 0.959721
520520 0 0
521521 3.63800 + 6.30121i 0.159384 + 0.276061i 0.934647 0.355578i 0.115716π-0.115716\pi
−0.775263 + 0.631639i 0.782383π0.782383\pi
522522 0 0
523523 −4.66897 17.4249i −0.204160 0.761936i −0.989704 0.143130i 0.954283π-0.954283\pi
0.785544 0.618806i 0.212383π-0.212383\pi
524524 0 0
525525 −7.79758 + 3.06849i −0.340314 + 0.133920i
526526 0 0
527527 43.2349 + 24.9617i 1.88334 + 1.08735i
528528 0 0
529529 11.3688 + 19.6913i 0.494294 + 0.856141i
530530 0 0
531531 −8.70588 8.70588i −0.377803 0.377803i
532532 0 0
533533 0.836275 0.836275i 0.0362231 0.0362231i
534534 0 0
535535 −15.0435 + 8.68540i −0.650389 + 0.375502i
536536 0 0
537537 3.71761 6.43909i 0.160427 0.277867i
538538 0 0
539539 1.36852 38.4402i 0.0589463 1.65574i
540540 0 0
541541 −2.61709 + 0.701247i −0.112518 + 0.0301490i −0.314638 0.949212i 0.601883π-0.601883\pi
0.202121 + 0.979361i 0.435217π0.435217\pi
542542 0 0
543543 −8.44907 + 4.87808i −0.362585 + 0.209338i
544544 0 0
545545 15.0327i 0.643931i
546546 0 0
547547 20.4366 20.4366i 0.873807 0.873807i −0.119078 0.992885i 0.537994π-0.537994\pi
0.992885 + 0.119078i 0.0379937π0.0379937\pi
548548 0 0
549549 −2.36645 + 8.83170i −0.100998 + 0.376928i
550550 0 0
551551 −9.47278 5.46911i −0.403554 0.232992i
552552 0 0
553553 −4.06928 + 9.35002i −0.173043 + 0.397603i
554554 0 0
555555 −6.34964 + 1.70138i −0.269527 + 0.0722196i
556556 0 0
557557 1.22222 4.56137i 0.0517869 0.193271i −0.935186 0.354156i 0.884768π-0.884768\pi
0.986973 + 0.160885i 0.0514348π0.0514348\pi
558558 0 0
559559 12.5792 0.532044
560560 0 0
561561 39.4367 1.66502
562562 0 0
563563 1.89945 7.08884i 0.0800522 0.298759i −0.914279 0.405085i 0.867242π-0.867242\pi
0.994331 + 0.106326i 0.0339087π0.0339087\pi
564564 0 0
565565 18.8336 5.04645i 0.792335 0.212306i
566566 0 0
567567 0.645300 0.477158i 0.0271001 0.0200387i
568568 0 0
569569 10.8006 + 6.23575i 0.452787 + 0.261416i 0.709006 0.705202i 0.249144π-0.249144\pi
−0.256220 + 0.966619i 0.582477π0.582477\pi
570570 0 0
571571 −9.94080 + 37.0996i −0.416010 + 1.55257i 0.366795 + 0.930302i 0.380455π0.380455\pi
−0.782805 + 0.622267i 0.786212π0.786212\pi
572572 0 0
573573 −10.2824 + 10.2824i −0.429555 + 0.429555i
574574 0 0
575575 1.48663i 0.0619969i
576576 0 0
577577 −16.4040 + 9.47084i −0.682906 + 0.394276i −0.800949 0.598732i 0.795671π-0.795671\pi
0.118043 + 0.993009i 0.462338π0.462338\pi
578578 0 0
579579 11.0868 2.97069i 0.460750 0.123458i
580580 0 0
581581 5.68696 7.14450i 0.235935 0.296404i
582582 0 0
583583 3.90324 6.76062i 0.161656 0.279996i
584584 0 0
585585 5.92098 3.41848i 0.244803 0.141337i
586586 0 0
587587 −7.54134 + 7.54134i −0.311264 + 0.311264i −0.845399 0.534135i 0.820637π-0.820637\pi
0.534135 + 0.845399i 0.320637π0.320637\pi
588588 0 0
589589 18.0340 + 18.0340i 0.743078 + 0.743078i
590590 0 0
591591 −10.8551 18.8015i −0.446517 0.773391i
592592 0 0
593593 −10.2804 5.93539i −0.422165 0.243737i 0.273838 0.961776i 0.411707π-0.411707\pi
−0.696003 + 0.718039i 0.745040π0.745040\pi
594594 0 0
595595 −19.7162 15.6939i −0.808284 0.643387i
596596 0 0
597597 −6.83423 25.5057i −0.279706 1.04388i
598598 0 0
599599 10.9170 + 18.9089i 0.446058 + 0.772595i 0.998125 0.0612043i 0.0194941π-0.0194941\pi
−0.552067 + 0.833800i 0.686161π0.686161\pi
600600 0 0
601601 −37.4893 −1.52922 −0.764610 0.644493i 0.777068π-0.777068\pi
−0.764610 + 0.644493i 0.777068π0.777068\pi
602602 0 0
603603 8.20620 + 8.20620i 0.334182 + 0.334182i
604604 0 0
605605 26.8570 + 7.19631i 1.09189 + 0.292572i
606606 0 0
607607 2.33958 4.05227i 0.0949605 0.164476i −0.814632 0.579979i 0.803061π-0.803061\pi
0.909592 + 0.415502i 0.136394π0.136394\pi
608608 0 0
609609 −5.59125 7.56151i −0.226569 0.306408i
610610 0 0
611611 2.31630 + 8.64456i 0.0937075 + 0.349721i
612612 0 0
613613 −4.89703 1.31216i −0.197789 0.0529975i 0.158564 0.987349i 0.449313π-0.449313\pi
−0.356354 + 0.934351i 0.615980π0.615980\pi
614614 0 0
615615 0.716563i 0.0288946i
616616 0 0
617617 16.4696i 0.663041i 0.943448 + 0.331520i 0.107562π0.107562\pi
−0.943448 + 0.331520i 0.892438π0.892438\pi
618618 0 0
619619 −14.6852 3.93490i −0.590249 0.158157i −0.0486822 0.998814i 0.515502π-0.515502\pi
−0.541567 + 0.840657i 0.682169π0.682169\pi
620620 0 0
621621 −0.696000 2.59751i −0.0279295 0.104234i
622622 0 0
623623 18.5024 + 8.05257i 0.741285 + 0.322619i
624624 0 0
625625 −1.03623 + 1.79481i −0.0414493 + 0.0717922i
626626 0 0
627627 19.4602 + 5.21435i 0.777167 + 0.208241i
628628 0 0
629629 19.3295 + 19.3295i 0.770717 + 0.770717i
630630 0 0
631631 6.82302 0.271620 0.135810 0.990735i 0.456636π-0.456636\pi
0.135810 + 0.990735i 0.456636π0.456636\pi
632632 0 0
633633 6.80206 + 11.7815i 0.270357 + 0.468273i
634634 0 0
635635 5.14974 + 19.2191i 0.204361 + 0.762686i
636636 0 0
637637 9.69092 15.4853i 0.383968 0.613549i
638638 0 0
639639 −10.1003 5.83143i −0.399563 0.230688i
640640 0 0
641641 −16.5379 28.6446i −0.653210 1.13139i −0.982339 0.187108i 0.940089π-0.940089\pi
0.329130 0.944285i 0.393245π-0.393245\pi
642642 0 0
643643 14.7445 + 14.7445i 0.581464 + 0.581464i 0.935306 0.353841i 0.115125π-0.115125\pi
−0.353841 + 0.935306i 0.615125π0.615125\pi
644644 0 0
645645 5.38925 5.38925i 0.212201 0.212201i
646646 0 0
647647 −9.62533 + 5.55719i −0.378411 + 0.218476i −0.677127 0.735867i 0.736775π-0.736775\pi
0.298716 + 0.954342i 0.403442π0.403442\pi
648648 0 0
649649 18.7035 32.3955i 0.734178 1.27163i
650650 0 0
651651 8.02937 + 20.4041i 0.314696 + 0.799699i
652652 0 0
653653 16.2451 4.35285i 0.635718 0.170340i 0.0734551 0.997299i 0.476597π-0.476597\pi
0.562263 + 0.826958i 0.309931π0.309931\pi
654654 0 0
655655 3.65548 2.11049i 0.142831 0.0824638i
656656 0 0
657657 26.9114i 1.04991i
658658 0 0
659659 −32.5839 + 32.5839i −1.26929 + 1.26929i −0.322834 + 0.946455i 0.604636π0.604636\pi
−0.946455 + 0.322834i 0.895364π0.895364\pi
660660 0 0
661661 4.53812 16.9365i 0.176512 0.658753i −0.819777 0.572683i 0.805903π-0.805903\pi
0.996289 0.0860697i 0.0274308π-0.0274308\pi
662662 0 0
663663 16.2201 + 9.36470i 0.629938 + 0.363695i
664664 0 0
665665 −7.65398 10.3511i −0.296809 0.401399i
666666 0 0
667667 −1.61155 + 0.431815i −0.0623996 + 0.0167199i
668668 0 0
669669 1.53939 5.74507i 0.0595162 0.222117i
670670 0 0
671671 −27.7796 −1.07242
672672 0 0
673673 11.0728 0.426827 0.213413 0.976962i 0.431542π-0.431542\pi
0.213413 + 0.976962i 0.431542π0.431542\pi
674674 0 0
675675 −3.94173 + 14.7107i −0.151717 + 0.566217i
676676 0 0
677677 5.69655 1.52639i 0.218936 0.0586638i −0.147684 0.989035i 0.547182π-0.547182\pi
0.366620 + 0.930371i 0.380515π0.380515\pi
678678 0 0
679679 29.4830 3.34902i 1.13145 0.128523i
680680 0 0
681681 1.42258 + 0.821328i 0.0545135 + 0.0314734i
682682 0 0
683683 0.824476 3.07699i 0.0315477 0.117738i −0.948356 0.317207i 0.897255π-0.897255\pi
0.979904 + 0.199469i 0.0639218π0.0639218\pi
684684 0 0
685685 −7.40047 + 7.40047i −0.282757 + 0.282757i
686686 0 0
687687 5.40044i 0.206040i
688688 0 0
689689 3.21077 1.85374i 0.122321 0.0706218i
690690 0 0
691691 20.4319 5.47470i 0.777265 0.208267i 0.151686 0.988429i 0.451530π-0.451530\pi
0.625578 + 0.780161i 0.284863π0.284863\pi
692692 0 0
693693 −20.5719 16.3751i −0.781462 0.622037i
694694 0 0
695695 0.726208 1.25783i 0.0275466 0.0477122i
696696 0 0
697697 −2.58056 + 1.48989i −0.0977458 + 0.0564336i
698698 0 0
699699 −9.59422 + 9.59422i −0.362887 + 0.362887i
700700 0 0
701701 19.0687 + 19.0687i 0.720214 + 0.720214i 0.968649 0.248435i 0.0799162π-0.0799162\pi
−0.248435 + 0.968649i 0.579916π0.579916\pi
702702 0 0
703703 6.98246 + 12.0940i 0.263348 + 0.456133i
704704 0 0
705705 4.69591 + 2.71118i 0.176858 + 0.102109i
706706 0 0
707707 50.8975 + 7.62437i 1.91420 + 0.286744i
708708 0 0
709709 −9.03837 33.7317i −0.339443 1.26682i −0.898971 0.438008i 0.855684π-0.855684\pi
0.559528 0.828812i 0.310982π-0.310982\pi
710710 0 0
711711 3.48527 + 6.03666i 0.130708 + 0.226392i
712712 0 0
713713 3.89011 0.145686
714714 0 0
715715 14.6884 + 14.6884i 0.549315 + 0.549315i
716716 0 0
717717 7.73920 + 2.07371i 0.289026 + 0.0774442i
718718 0 0
719719 −25.7551 + 44.6092i −0.960505 + 1.66364i −0.239268 + 0.970953i 0.576908π0.576908\pi
−0.721236 + 0.692689i 0.756426π0.756426\pi
720720 0 0
721721 7.49820 17.2287i 0.279248 0.641629i
722722 0 0
723723 2.93070 + 10.9375i 0.108994 + 0.406771i
724724 0 0
725725 9.12690 + 2.44555i 0.338965 + 0.0908253i
726726 0 0
727727 10.3415i 0.383546i 0.981439 + 0.191773i 0.0614237π0.0614237\pi
−0.981439 + 0.191773i 0.938576π0.938576\pi
728728 0 0
729729 17.7358i 0.656881i
730730 0 0
731731 −30.6138 8.20293i −1.13229 0.303396i
732732 0 0
733733 5.21156 + 19.4498i 0.192493 + 0.718395i 0.992901 + 0.118940i 0.0379495π0.0379495\pi
−0.800408 + 0.599455i 0.795384π0.795384\pi
734734 0 0
735735 −2.48245 10.7861i −0.0915666 0.397852i
736736 0 0
737737 −17.6300 + 30.5361i −0.649411 + 1.12481i
738738 0 0
739739 −29.5182 7.90938i −1.08584 0.290951i −0.328856 0.944380i 0.606663π-0.606663\pi
−0.756988 + 0.653429i 0.773330π0.773330\pi
740740 0 0
741741 6.76569 + 6.76569i 0.248544 + 0.248544i
742742 0 0
743743 36.5659 1.34147 0.670735 0.741697i 0.265979π-0.265979\pi
0.670735 + 0.741697i 0.265979π0.265979\pi
744744 0 0
745745 −6.89526 11.9429i −0.252623 0.437556i
746746 0 0
747747 −1.61558 6.02943i −0.0591110 0.220605i
748748 0 0
749749 11.6179 + 29.5232i 0.424509 + 1.07875i
750750 0 0
751751 −30.5955 17.6643i −1.11644 0.644580i −0.175954 0.984398i 0.556301π-0.556301\pi
−0.940491 + 0.339819i 0.889634π0.889634\pi
752752 0 0
753753 −0.310057 0.537034i −0.0112991 0.0195706i
754754 0 0
755755 7.27401 + 7.27401i 0.264728 + 0.264728i
756756 0 0
757757 −1.06021 + 1.06021i −0.0385339 + 0.0385339i −0.726111 0.687577i 0.758674π-0.758674\pi
0.687577 + 0.726111i 0.258674π0.258674\pi
758758 0 0
759759 2.66127 1.53649i 0.0965981 0.0557709i
760760 0 0
761761 −15.2003 + 26.3277i −0.551010 + 0.954378i 0.447192 + 0.894438i 0.352424π0.352424\pi
−0.998202 + 0.0599396i 0.980909π0.980909\pi
762762 0 0
763763 27.1535 + 4.06755i 0.983023 + 0.147255i
764764 0 0
765765 −16.6390 + 4.45840i −0.601584 + 0.161194i
766766 0 0
767767 15.3853 8.88274i 0.555533 0.320737i
768768 0 0
769769 38.0523i 1.37220i 0.727507 + 0.686101i 0.240679π0.240679\pi
−0.727507 + 0.686101i 0.759321π0.759321\pi
770770 0 0
771771 7.06039 7.06039i 0.254274 0.254274i
772772 0 0
773773 −4.02680 + 15.0282i −0.144834 + 0.540528i 0.854929 + 0.518746i 0.173601π0.173601\pi
−0.999763 + 0.0217825i 0.993066π0.993066\pi
774774 0 0
775775 −19.0796 11.0156i −0.685361 0.395693i
776776 0 0
777777 1.35511 + 11.9297i 0.0486142 + 0.427975i
778778 0 0
779779 −1.47039 + 0.393989i −0.0526820 + 0.0141161i
780780 0 0
781781 9.17123 34.2275i 0.328172 1.22476i
782782 0 0
783783 −17.0918 −0.610812
784784 0 0
785785 −12.7134 −0.453760
786786 0 0
787787 −4.32518 + 16.1418i −0.154176 + 0.575393i 0.844998 + 0.534769i 0.179601π0.179601\pi
−0.999175 + 0.0406241i 0.987065π0.987065\pi
788788 0 0
789789 4.83129 1.29454i 0.171998 0.0460868i
790790 0 0
791791 −4.01937 35.3845i −0.142912 1.25813i
792792 0 0
793793 −11.4256 6.59659i −0.405736 0.234252i
794794 0 0
795795 0.581386 2.16976i 0.0206196 0.0769535i
796796 0 0
797797 −6.46029 + 6.46029i −0.228835 + 0.228835i −0.812206 0.583371i 0.801733π-0.801733\pi
0.583371 + 0.812206i 0.301733π0.301733\pi
798798 0 0
799799 22.5486i 0.797710i
800800 0 0
801801 11.9457 6.89688i 0.422082 0.243689i
802802 0 0
803803 −78.9780 + 21.1621i −2.78707 + 0.746794i
804804 0 0
805805 −1.94194 0.290899i −0.0684442 0.0102528i
806806 0 0
807807 −5.21101 + 9.02573i −0.183436 + 0.317721i
808808 0 0
809809 −24.9554 + 14.4080i −0.877386 + 0.506559i −0.869796 0.493412i 0.835750π-0.835750\pi
−0.00759061 + 0.999971i 0.502416π0.502416\pi
810810 0 0
811811 32.3761 32.3761i 1.13688 1.13688i 0.147873 0.989006i 0.452757π-0.452757\pi
0.989006 0.147873i 0.0472427π-0.0472427\pi
812812 0 0
813813 5.62163 + 5.62163i 0.197159 + 0.197159i
814814 0 0
815815 −9.19808 15.9315i −0.322195 0.558058i
816816 0 0
817817 −14.0219 8.09555i −0.490564 0.283227i
818818 0 0
819819 −4.57268 11.6200i −0.159782 0.406036i
820820 0 0
821821 7.00094 + 26.1279i 0.244334 + 0.911869i 0.973717 + 0.227762i 0.0731409π0.0731409\pi
−0.729382 + 0.684106i 0.760192π0.760192\pi
822822 0 0
823823 12.1699 + 21.0790i 0.424218 + 0.734767i 0.996347 0.0853968i 0.0272158π-0.0272158\pi
−0.572129 + 0.820163i 0.693882π0.693882\pi
824824 0 0
825825 −17.4035 −0.605913
826826 0 0
827827 31.7583 + 31.7583i 1.10435 + 1.10435i 0.993880 + 0.110466i 0.0352344π0.0352344\pi
0.110466 + 0.993880i 0.464766π0.464766\pi
828828 0 0
829829 39.6910 + 10.6352i 1.37853 + 0.369375i 0.870586 0.492017i 0.163740π-0.163740\pi
0.507941 + 0.861392i 0.330407π0.330407\pi
830830 0 0
831831 17.6694 30.6042i 0.612944 1.06165i
832832 0 0
833833 −33.6826 + 31.3668i −1.16703 + 1.08679i
834834 0 0
835835 8.07125 + 30.1223i 0.279317 + 1.04243i
836836 0 0
837837 38.4939 + 10.3144i 1.33054 + 0.356518i
838838 0 0
839839 12.4384i 0.429423i 0.976678 + 0.214711i 0.0688811π0.0688811\pi
−0.976678 + 0.214711i 0.931119π0.931119\pi
840840 0 0
841841 18.3958i 0.634339i
842842 0 0
843843 −4.32149 1.15794i −0.148840 0.0398816i
844844 0 0
845845 −2.32061 8.66065i −0.0798316 0.297935i
846846 0 0
847847 20.2656 46.5645i 0.696335 1.59997i
848848 0 0
849849 −7.45561 + 12.9135i −0.255876 + 0.443190i
850850 0 0
851851 2.05748 + 0.551301i 0.0705297 + 0.0188984i
852852 0 0
853853 −11.8456 11.8456i −0.405585 0.405585i 0.474611 0.880196i 0.342589π-0.342589\pi
−0.880196 + 0.474611i 0.842589π0.842589\pi
854854 0 0
855855 −8.80008 −0.300956
856856 0 0
857857 7.54656 + 13.0710i 0.257786 + 0.446498i 0.965648 0.259852i 0.0836738π-0.0836738\pi
−0.707863 + 0.706350i 0.750340π0.750340\pi
858858 0 0
859859 −11.8045 44.0551i −0.402765 1.50314i −0.808141 0.588990i 0.799526π-0.799526\pi
0.405375 0.914150i 0.367141π-0.367141\pi
860860 0 0
861861 −1.29432 0.193888i −0.0441104 0.00660767i
862862 0 0
863863 23.4497 + 13.5387i 0.798237 + 0.460862i 0.842854 0.538142i 0.180874π-0.180874\pi
−0.0446175 + 0.999004i 0.514207π0.514207\pi
864864 0 0
865865 −14.5080 25.1285i −0.493286 0.854396i
866866 0 0
867867 −20.2469 20.2469i −0.687619 0.687619i
868868 0 0
869869 −14.9754 + 14.9754i −0.508004 + 0.508004i
870870 0 0
871871 −14.5023 + 8.37290i −0.491391 + 0.283705i
872872 0 0
873873 10.1418 17.5660i 0.343246 0.594520i
874874 0 0
875875 23.6938 + 18.8600i 0.800995 + 0.637585i
876876 0 0
877877 −8.80425 + 2.35909i −0.297298 + 0.0796609i −0.404385 0.914589i 0.632514π-0.632514\pi
0.107087 + 0.994250i 0.465848π0.465848\pi
878878 0 0
879879 −22.3173 + 12.8849i −0.752745 + 0.434598i
880880 0 0
881881 0.723819i 0.0243861i −0.999926 0.0121930i 0.996119π-0.996119\pi
0.999926 0.0121930i 0.00388126π-0.00388126\pi
882882 0 0
883883 21.2381 21.2381i 0.714718 0.714718i −0.252800 0.967518i 0.581352π-0.581352\pi
0.967518 + 0.252800i 0.0813516π0.0813516\pi
884884 0 0
885885 2.78588 10.3971i 0.0936464 0.349493i
886886 0 0
887887 −17.5247 10.1179i −0.588422 0.339726i 0.176051 0.984381i 0.443668π-0.443668\pi
−0.764473 + 0.644655i 0.777001π0.777001\pi
888888 0 0
889889 36.1088 4.10164i 1.21105 0.137565i
890890 0 0
891891 1.61002 0.431403i 0.0539377 0.0144526i
892892 0 0
893893 2.98139 11.1267i 0.0997683 0.372340i
894894 0 0
895895 −9.86738 −0.329830
896896 0 0
897897 1.45942 0.0487288
898898 0 0
899899 6.39931 23.8825i 0.213429 0.796528i
900900 0 0
901901 −9.02281 + 2.41766i −0.300594 + 0.0805438i
902902 0 0
903903 −8.27634 11.1928i −0.275419 0.372473i
904904 0 0
905905 11.2129 + 6.47376i 0.372729 + 0.215195i
906906 0 0
907907 −3.46515 + 12.9321i −0.115058 + 0.429404i −0.999291 0.0376423i 0.988015π-0.988015\pi
0.884233 + 0.467046i 0.154682π0.154682\pi
908908 0 0
909909 24.8764 24.8764i 0.825099 0.825099i
910910 0 0
911911 34.5549i 1.14485i −0.819955 0.572427i 0.806002π-0.806002\pi
0.819955 0.572427i 0.193998π-0.193998\pi
912912 0 0
913913 16.4244 9.48262i 0.543568 0.313829i
914914 0 0
915915 −7.72117 + 2.06888i −0.255254 + 0.0683951i
916916 0 0
917917 −2.82307 7.17393i −0.0932260 0.236904i
918918 0 0
919919 26.7589 46.3478i 0.882695 1.52887i 0.0343626 0.999409i 0.489060π-0.489060\pi
0.848333 0.529464i 0.177607π-0.177607\pi
920920 0 0
921921 22.4040 12.9350i 0.738238 0.426222i
922922 0 0
923923 11.8998 11.8998i 0.391686 0.391686i
924924 0 0
925925 −8.53014 8.53014i −0.280469 0.280469i
926926 0 0
927927 −6.42208 11.1234i −0.210929 0.365339i
928928 0 0
929929 −0.0427340 0.0246725i −0.00140206 0.000809477i 0.499299 0.866430i 0.333591π-0.333591\pi
−0.500701 + 0.865620i 0.666924π0.666924\pi
930930 0 0
931931 −20.7682 + 11.0245i −0.680649 + 0.361314i
932932 0 0
933933 −6.06927 22.6508i −0.198699 0.741554i
934934 0 0
935935 −26.1685 45.3252i −0.855802 1.48229i
936936 0 0
937937 −0.977039 −0.0319185 −0.0159592 0.999873i 0.505080π-0.505080\pi
−0.0159592 + 0.999873i 0.505080π0.505080\pi
938938 0 0
939939 −16.0925 16.0925i −0.525157 0.525157i
940940 0 0
941941 −37.6344 10.0841i −1.22685 0.328733i −0.413496 0.910506i 0.635693π-0.635693\pi
−0.813351 + 0.581773i 0.802359π0.802359\pi
942942 0 0
943943 −0.116095 + 0.201082i −0.00378056 + 0.00654812i
944944 0 0
945945 −18.4448 8.02748i −0.600010 0.261134i
946946 0 0
947947 5.93312 + 22.1427i 0.192801 + 0.719541i 0.992825 + 0.119574i 0.0381530π0.0381530\pi
−0.800025 + 0.599967i 0.795180π0.795180\pi
948948 0 0
949949 −37.5084 10.0504i −1.21757 0.326248i
950950 0 0
951951 16.2702i 0.527599i
952952 0 0
953953 34.2308i 1.10884i −0.832235 0.554422i 0.812939π-0.812939\pi
0.832235 0.554422i 0.187061π-0.187061\pi
954954 0 0
955955 18.6407 + 4.99477i 0.603200 + 0.161627i
956956 0 0
957957 −5.05511 18.8659i −0.163408 0.609849i
958958 0 0
959959 11.3650 + 15.3698i 0.366995 + 0.496318i
960960 0 0
961961 −13.3248 + 23.0793i −0.429834 + 0.744494i
962962 0 0
963963 20.9487 + 5.61320i 0.675064 + 0.180883i
964964 0 0
965965 −10.7710 10.7710i −0.346729 0.346729i
966966 0 0
967967 −21.2761 −0.684193 −0.342096 0.939665i 0.611137π-0.611137\pi
−0.342096 + 0.939665i 0.611137π0.611137\pi
968968 0 0
969969 −12.0536 20.8775i −0.387218 0.670680i
970970 0 0
971971 −7.74616 28.9091i −0.248586 0.927736i −0.971547 0.236847i 0.923886π-0.923886\pi
0.722961 0.690889i 0.242781π-0.242781\pi
972972 0 0
973973 −2.07551 1.65209i −0.0665379 0.0529635i
974974 0 0
975975 −7.15798 4.13266i −0.229239 0.132351i
976976 0 0
977977 1.50722 + 2.61058i 0.0482201 + 0.0835197i 0.889128 0.457659i 0.151312π-0.151312\pi
−0.840908 + 0.541178i 0.817978π0.817978\pi
978978 0 0
979979 29.6342 + 29.6342i 0.947115 + 0.947115i
980980 0 0
981981 13.2714 13.2714i 0.423724 0.423724i
982982 0 0
983983 −35.2886 + 20.3739i −1.12553 + 0.649826i −0.942807 0.333339i 0.891825π-0.891825\pi
−0.182724 + 0.983164i 0.558491π0.558491\pi
984984 0 0
985985 −14.4059 + 24.9517i −0.459010 + 0.795029i
986986 0 0
987987 6.16781 7.74860i 0.196324 0.246641i
988988 0 0
989989 −2.38547 + 0.639186i −0.0758536 + 0.0203249i
990990 0 0
991991 21.1944 12.2366i 0.673262 0.388708i −0.124049 0.992276i 0.539588π-0.539588\pi
0.797312 + 0.603568i 0.206255π0.206255\pi
992992 0 0
993993 3.26581i 0.103637i
994994 0 0
995995 −24.7792 + 24.7792i −0.785552 + 0.785552i
996996 0 0
997997 −11.1506 + 41.6146i −0.353143 + 1.31795i 0.529662 + 0.848209i 0.322319π0.322319\pi
−0.882805 + 0.469740i 0.844348π0.844348\pi
998998 0 0
999999 18.8978 + 10.9106i 0.597899 + 0.345197i
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 448.2.z.a.47.10 56
4.3 odd 2 112.2.v.a.19.12 yes 56
7.3 odd 6 inner 448.2.z.a.367.10 56
8.3 odd 2 896.2.z.b.607.10 56
8.5 even 2 896.2.z.a.607.5 56
16.3 odd 4 896.2.z.a.159.5 56
16.5 even 4 112.2.v.a.75.3 yes 56
16.11 odd 4 inner 448.2.z.a.271.10 56
16.13 even 4 896.2.z.b.159.10 56
28.3 even 6 112.2.v.a.3.3 56
28.11 odd 6 784.2.w.f.227.3 56
28.19 even 6 784.2.j.a.195.14 56
28.23 odd 6 784.2.j.a.195.13 56
28.27 even 2 784.2.w.f.19.12 56
56.3 even 6 896.2.z.b.479.10 56
56.45 odd 6 896.2.z.a.479.5 56
112.3 even 12 896.2.z.a.31.5 56
112.5 odd 12 784.2.j.a.587.13 56
112.37 even 12 784.2.j.a.587.14 56
112.45 odd 12 896.2.z.b.31.10 56
112.53 even 12 784.2.w.f.619.12 56
112.59 even 12 inner 448.2.z.a.143.10 56
112.69 odd 4 784.2.w.f.411.3 56
112.101 odd 12 112.2.v.a.59.12 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.v.a.3.3 56 28.3 even 6
112.2.v.a.19.12 yes 56 4.3 odd 2
112.2.v.a.59.12 yes 56 112.101 odd 12
112.2.v.a.75.3 yes 56 16.5 even 4
448.2.z.a.47.10 56 1.1 even 1 trivial
448.2.z.a.143.10 56 112.59 even 12 inner
448.2.z.a.271.10 56 16.11 odd 4 inner
448.2.z.a.367.10 56 7.3 odd 6 inner
784.2.j.a.195.13 56 28.23 odd 6
784.2.j.a.195.14 56 28.19 even 6
784.2.j.a.587.13 56 112.5 odd 12
784.2.j.a.587.14 56 112.37 even 12
784.2.w.f.19.12 56 28.27 even 2
784.2.w.f.227.3 56 28.11 odd 6
784.2.w.f.411.3 56 112.69 odd 4
784.2.w.f.619.12 56 112.53 even 12
896.2.z.a.31.5 56 112.3 even 12
896.2.z.a.159.5 56 16.3 odd 4
896.2.z.a.479.5 56 56.45 odd 6
896.2.z.a.607.5 56 8.5 even 2
896.2.z.b.31.10 56 112.45 odd 12
896.2.z.b.159.10 56 16.13 even 4
896.2.z.b.479.10 56 56.3 even 6
896.2.z.b.607.10 56 8.3 odd 2