Properties

Label 702.2.j.b.593.4
Level 702702
Weight 22
Character 702.593
Analytic conductor 5.6055.605
Analytic rank 00
Dimension 2424
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [702,2,Mod(161,702)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(702, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("702.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 702=23313 702 = 2 \cdot 3^{3} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 702.j (of order 44, 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: 5.605498221895.60549822189
Analytic rank: 00
Dimension: 2424
Relative dimension: 1212 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 593.4
Character χ\chi == 702.593
Dual form 702.2.j.b.161.4

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+(0.707107+0.707107i)q21.00000iq4+(0.7309530.730953i)q5+(2.49696+2.49696i)q7+(0.707107+0.707107i)q8+1.03372iq10+(1.95374+1.95374i)q11+(3.21489+1.63232i)q133.53123iq141.00000q16+5.44078q17+(5.990765.99076i)q19+(0.7309530.730953i)q202.76300q225.11422q23+3.93142iq25+(1.119053.42750i)q26+(2.49696+2.49696i)q28+8.51991iq29+(3.53068+3.53068i)q31+(0.7071070.707107i)q32+(3.84721+3.84721i)q34+3.65032iq35+(7.78749+7.78749i)q37+8.47222q38+1.03372q40+(1.061811.06181i)q41+3.79673iq43+(1.953741.95374i)q44+(3.616303.61630i)q46+(7.809317.80931i)q475.46960iq49+(2.779932.77993i)q50+(1.63232+3.21489i)q52+11.7290iq53+2.85618q553.53123q56+(6.024496.02449i)q58+(1.861851.86185i)q59+6.42979q614.99314q62+1.00000iq64+(1.15679+3.54308i)q65+(0.887018+0.887018i)q675.44078iq68+(2.581162.58116i)q70+(3.17883+3.17883i)q71+(2.31653+2.31653i)q7311.0132iq74+(5.99076+5.99076i)q769.75681q775.29836q79+(0.730953+0.730953i)q80+1.50163iq82+(4.777714.77771i)q83+(3.976953.97695i)q85+(2.684692.68469i)q86+2.76300iq88+(0.144930+0.144930i)q89+(3.9516312.1033i)q91+5.11422iq92+11.0440q948.75793q95+(4.665004.66500i)q97+(3.86759+3.86759i)q98+O(q100)q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.730953 - 0.730953i) q^{5} +(-2.49696 + 2.49696i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.03372i q^{10} +(1.95374 + 1.95374i) q^{11} +(-3.21489 + 1.63232i) q^{13} -3.53123i q^{14} -1.00000 q^{16} +5.44078 q^{17} +(-5.99076 - 5.99076i) q^{19} +(-0.730953 - 0.730953i) q^{20} -2.76300 q^{22} -5.11422 q^{23} +3.93142i q^{25} +(1.11905 - 3.42750i) q^{26} +(2.49696 + 2.49696i) q^{28} +8.51991i q^{29} +(3.53068 + 3.53068i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.84721 + 3.84721i) q^{34} +3.65032i q^{35} +(-7.78749 + 7.78749i) q^{37} +8.47222 q^{38} +1.03372 q^{40} +(1.06181 - 1.06181i) q^{41} +3.79673i q^{43} +(1.95374 - 1.95374i) q^{44} +(3.61630 - 3.61630i) q^{46} +(-7.80931 - 7.80931i) q^{47} -5.46960i q^{49} +(-2.77993 - 2.77993i) q^{50} +(1.63232 + 3.21489i) q^{52} +11.7290i q^{53} +2.85618 q^{55} -3.53123 q^{56} +(-6.02449 - 6.02449i) q^{58} +(-1.86185 - 1.86185i) q^{59} +6.42979 q^{61} -4.99314 q^{62} +1.00000i q^{64} +(-1.15679 + 3.54308i) q^{65} +(0.887018 + 0.887018i) q^{67} -5.44078i q^{68} +(-2.58116 - 2.58116i) q^{70} +(-3.17883 + 3.17883i) q^{71} +(-2.31653 + 2.31653i) q^{73} -11.0132i q^{74} +(-5.99076 + 5.99076i) q^{76} -9.75681 q^{77} -5.29836 q^{79} +(-0.730953 + 0.730953i) q^{80} +1.50163i q^{82} +(4.77771 - 4.77771i) q^{83} +(3.97695 - 3.97695i) q^{85} +(-2.68469 - 2.68469i) q^{86} +2.76300i q^{88} +(0.144930 + 0.144930i) q^{89} +(3.95163 - 12.1033i) q^{91} +5.11422i q^{92} +11.0440 q^{94} -8.75793 q^{95} +(-4.66500 - 4.66500i) q^{97} +(3.86759 + 3.86759i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q24q1624q19+24q34+24q37+24q46+48q7024q7324q7624q7924q91+72q94+96q97+O(q100) 24 q - 24 q^{16} - 24 q^{19} + 24 q^{34} + 24 q^{37} + 24 q^{46} + 48 q^{70} - 24 q^{73} - 24 q^{76} - 24 q^{79} - 24 q^{91} + 72 q^{94} + 96 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/702Z)×\left(\mathbb{Z}/702\mathbb{Z}\right)^\times.

nn 379379 677677
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right) 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.707107 + 0.707107i −0.500000 + 0.500000i
33 0 0
44 1.00000i 0.500000i
55 0.730953 0.730953i 0.326892 0.326892i −0.524511 0.851403i 0.675752π-0.675752\pi
0.851403 + 0.524511i 0.175752π0.175752\pi
66 0 0
77 −2.49696 + 2.49696i −0.943761 + 0.943761i −0.998501 0.0547394i 0.982567π-0.982567\pi
0.0547394 + 0.998501i 0.482567π0.482567\pi
88 0.707107 + 0.707107i 0.250000 + 0.250000i
99 0 0
1010 1.03372i 0.326892i
1111 1.95374 + 1.95374i 0.589075 + 0.589075i 0.937381 0.348306i 0.113243π-0.113243\pi
−0.348306 + 0.937381i 0.613243π0.613243\pi
1212 0 0
1313 −3.21489 + 1.63232i −0.891651 + 0.452723i
1414 3.53123i 0.943761i
1515 0 0
1616 −1.00000 −0.250000
1717 5.44078 1.31958 0.659791 0.751449i 0.270645π-0.270645\pi
0.659791 + 0.751449i 0.270645π0.270645\pi
1818 0 0
1919 −5.99076 5.99076i −1.37438 1.37438i −0.853840 0.520536i 0.825732π-0.825732\pi
−0.520536 0.853840i 0.674268π-0.674268\pi
2020 −0.730953 0.730953i −0.163446 0.163446i
2121 0 0
2222 −2.76300 −0.589075
2323 −5.11422 −1.06639 −0.533194 0.845993i 0.679009π-0.679009\pi
−0.533194 + 0.845993i 0.679009π0.679009\pi
2424 0 0
2525 3.93142i 0.786283i
2626 1.11905 3.42750i 0.219464 0.672187i
2727 0 0
2828 2.49696 + 2.49696i 0.471881 + 0.471881i
2929 8.51991i 1.58211i 0.611746 + 0.791054i 0.290467π0.290467\pi
−0.611746 + 0.791054i 0.709533π0.709533\pi
3030 0 0
3131 3.53068 + 3.53068i 0.634129 + 0.634129i 0.949101 0.314972i 0.101995π-0.101995\pi
−0.314972 + 0.949101i 0.601995π0.601995\pi
3232 0.707107 0.707107i 0.125000 0.125000i
3333 0 0
3434 −3.84721 + 3.84721i −0.659791 + 0.659791i
3535 3.65032i 0.617016i
3636 0 0
3737 −7.78749 + 7.78749i −1.28026 + 1.28026i −0.339734 + 0.940521i 0.610337π0.610337\pi
−0.940521 + 0.339734i 0.889663π0.889663\pi
3838 8.47222 1.37438
3939 0 0
4040 1.03372 0.163446
4141 1.06181 1.06181i 0.165827 0.165827i −0.619315 0.785142i 0.712590π-0.712590\pi
0.785142 + 0.619315i 0.212590π0.212590\pi
4242 0 0
4343 3.79673i 0.578996i 0.957179 + 0.289498i 0.0934883π0.0934883\pi
−0.957179 + 0.289498i 0.906512π0.906512\pi
4444 1.95374 1.95374i 0.294537 0.294537i
4545 0 0
4646 3.61630 3.61630i 0.533194 0.533194i
4747 −7.80931 7.80931i −1.13910 1.13910i −0.988611 0.150493i 0.951914π-0.951914\pi
−0.150493 0.988611i 0.548086π-0.548086\pi
4848 0 0
4949 5.46960i 0.781371i
5050 −2.77993 2.77993i −0.393142 0.393142i
5151 0 0
5252 1.63232 + 3.21489i 0.226362 + 0.445826i
5353 11.7290i 1.61111i 0.592522 + 0.805554i 0.298132π0.298132\pi
−0.592522 + 0.805554i 0.701868π0.701868\pi
5454 0 0
5555 2.85618 0.385128
5656 −3.53123 −0.471881
5757 0 0
5858 −6.02449 6.02449i −0.791054 0.791054i
5959 −1.86185 1.86185i −0.242393 0.242393i 0.575447 0.817839i 0.304828π-0.304828\pi
−0.817839 + 0.575447i 0.804828π0.804828\pi
6060 0 0
6161 6.42979 0.823250 0.411625 0.911353i 0.364961π-0.364961\pi
0.411625 + 0.911353i 0.364961π0.364961\pi
6262 −4.99314 −0.634129
6363 0 0
6464 1.00000i 0.125000i
6565 −1.15679 + 3.54308i −0.143482 + 0.439465i
6666 0 0
6767 0.887018 + 0.887018i 0.108367 + 0.108367i 0.759211 0.650845i 0.225585π-0.225585\pi
−0.650845 + 0.759211i 0.725585π0.725585\pi
6868 5.44078i 0.659791i
6969 0 0
7070 −2.58116 2.58116i −0.308508 0.308508i
7171 −3.17883 + 3.17883i −0.377258 + 0.377258i −0.870112 0.492854i 0.835954π-0.835954\pi
0.492854 + 0.870112i 0.335954π0.335954\pi
7272 0 0
7373 −2.31653 + 2.31653i −0.271129 + 0.271129i −0.829555 0.558425i 0.811406π-0.811406\pi
0.558425 + 0.829555i 0.311406π0.311406\pi
7474 11.0132i 1.28026i
7575 0 0
7676 −5.99076 + 5.99076i −0.687188 + 0.687188i
7777 −9.75681 −1.11189
7878 0 0
7979 −5.29836 −0.596112 −0.298056 0.954548i 0.596338π-0.596338\pi
−0.298056 + 0.954548i 0.596338π0.596338\pi
8080 −0.730953 + 0.730953i −0.0817230 + 0.0817230i
8181 0 0
8282 1.50163i 0.165827i
8383 4.77771 4.77771i 0.524422 0.524422i −0.394482 0.918904i 0.629076π-0.629076\pi
0.918904 + 0.394482i 0.129076π0.129076\pi
8484 0 0
8585 3.97695 3.97695i 0.431361 0.431361i
8686 −2.68469 2.68469i −0.289498 0.289498i
8787 0 0
8888 2.76300i 0.294537i
8989 0.144930 + 0.144930i 0.0153625 + 0.0153625i 0.714746 0.699384i 0.246542π-0.246542\pi
−0.699384 + 0.714746i 0.746542π0.746542\pi
9090 0 0
9191 3.95163 12.1033i 0.414243 1.26877i
9292 5.11422i 0.533194i
9393 0 0
9494 11.0440 1.13910
9595 −8.75793 −0.898545
9696 0 0
9797 −4.66500 4.66500i −0.473659 0.473659i 0.429438 0.903097i 0.358712π-0.358712\pi
−0.903097 + 0.429438i 0.858712π0.858712\pi
9898 3.86759 + 3.86759i 0.390685 + 0.390685i
9999 0 0
100100 3.93142 0.393142
101101 16.6680 1.65853 0.829266 0.558855i 0.188759π-0.188759\pi
0.829266 + 0.558855i 0.188759π0.188759\pi
102102 0 0
103103 1.83045i 0.180360i −0.995925 0.0901799i 0.971256π-0.971256\pi
0.995925 0.0901799i 0.0287442π-0.0287442\pi
104104 −3.42750 1.11905i −0.336094 0.109732i
105105 0 0
106106 −8.29369 8.29369i −0.805554 0.805554i
107107 9.43019i 0.911651i 0.890069 + 0.455825i 0.150656π0.150656\pi
−0.890069 + 0.455825i 0.849344π0.849344\pi
108108 0 0
109109 −6.65317 6.65317i −0.637259 0.637259i 0.312620 0.949878i 0.398793π-0.398793\pi
−0.949878 + 0.312620i 0.898793π0.898793\pi
110110 −2.01963 + 2.01963i −0.192564 + 0.192564i
111111 0 0
112112 2.49696 2.49696i 0.235940 0.235940i
113113 13.5909i 1.27852i −0.768989 0.639262i 0.779240π-0.779240\pi
0.768989 0.639262i 0.220760π-0.220760\pi
114114 0 0
115115 −3.73825 + 3.73825i −0.348594 + 0.348594i
116116 8.51991 0.791054
117117 0 0
118118 2.63306 0.242393
119119 −13.5854 + 13.5854i −1.24537 + 1.24537i
120120 0 0
121121 3.36580i 0.305982i
122122 −4.54655 + 4.54655i −0.411625 + 0.411625i
123123 0 0
124124 3.53068 3.53068i 0.317065 0.317065i
125125 6.52844 + 6.52844i 0.583922 + 0.583922i
126126 0 0
127127 11.0838i 0.983531i 0.870728 + 0.491766i 0.163648π0.163648\pi
−0.870728 + 0.491766i 0.836352π0.836352\pi
128128 −0.707107 0.707107i −0.0625000 0.0625000i
129129 0 0
130130 −1.68736 3.32331i −0.147992 0.291474i
131131 12.1356i 1.06029i −0.847906 0.530146i 0.822137π-0.822137\pi
0.847906 0.530146i 0.177863π-0.177863\pi
132132 0 0
133133 29.9174 2.59416
134134 −1.25443 −0.108367
135135 0 0
136136 3.84721 + 3.84721i 0.329896 + 0.329896i
137137 9.00744 + 9.00744i 0.769558 + 0.769558i 0.978029 0.208471i 0.0668486π-0.0668486\pi
−0.208471 + 0.978029i 0.566849π0.566849\pi
138138 0 0
139139 3.26746 0.277142 0.138571 0.990352i 0.455749π-0.455749\pi
0.138571 + 0.990352i 0.455749π0.455749\pi
140140 3.65032 0.308508
141141 0 0
142142 4.49554i 0.377258i
143143 −9.47019 3.09194i −0.791937 0.258561i
144144 0 0
145145 6.22765 + 6.22765i 0.517178 + 0.517178i
146146 3.27607i 0.271129i
147147 0 0
148148 7.78749 + 7.78749i 0.640128 + 0.640128i
149149 10.6695 10.6695i 0.874082 0.874082i −0.118832 0.992914i 0.537915π-0.537915\pi
0.992914 + 0.118832i 0.0379150π0.0379150\pi
150150 0 0
151151 10.4284 10.4284i 0.848649 0.848649i −0.141316 0.989965i 0.545133π-0.545133\pi
0.989965 + 0.141316i 0.0451332π0.0451332\pi
152152 8.47222i 0.687188i
153153 0 0
154154 6.89911 6.89911i 0.555946 0.555946i
155155 5.16152 0.414583
156156 0 0
157157 9.82931 0.784465 0.392232 0.919866i 0.371703π-0.371703\pi
0.392232 + 0.919866i 0.371703π0.371703\pi
158158 3.74650 3.74650i 0.298056 0.298056i
159159 0 0
160160 1.03372i 0.0817230i
161161 12.7700 12.7700i 1.00642 1.00642i
162162 0 0
163163 −0.658684 + 0.658684i −0.0515921 + 0.0515921i −0.732432 0.680840i 0.761615π-0.761615\pi
0.680840 + 0.732432i 0.261615π0.261615\pi
164164 −1.06181 1.06181i −0.0829136 0.0829136i
165165 0 0
166166 6.75670i 0.524422i
167167 12.5357 + 12.5357i 0.970041 + 0.970041i 0.999564 0.0295232i 0.00939889π-0.00939889\pi
−0.0295232 + 0.999564i 0.509399π0.509399\pi
168168 0 0
169169 7.67108 10.4955i 0.590083 0.807342i
170170 5.62426i 0.431361i
171171 0 0
172172 3.79673 0.289498
173173 −3.87945 −0.294949 −0.147475 0.989066i 0.547115π-0.547115\pi
−0.147475 + 0.989066i 0.547115π0.547115\pi
174174 0 0
175175 −9.81658 9.81658i −0.742064 0.742064i
176176 −1.95374 1.95374i −0.147269 0.147269i
177177 0 0
178178 −0.204962 −0.0153625
179179 −5.10968 −0.381916 −0.190958 0.981598i 0.561159π-0.561159\pi
−0.190958 + 0.981598i 0.561159π0.561159\pi
180180 0 0
181181 4.01356i 0.298326i −0.988813 0.149163i 0.952342π-0.952342\pi
0.988813 0.149163i 0.0476579π-0.0476579\pi
182182 5.76409 + 11.3525i 0.427263 + 0.841506i
183183 0 0
184184 −3.61630 3.61630i −0.266597 0.266597i
185185 11.3846i 0.837011i
186186 0 0
187187 10.6299 + 10.6299i 0.777332 + 0.777332i
188188 −7.80931 + 7.80931i −0.569552 + 0.569552i
189189 0 0
190190 6.19279 6.19279i 0.449272 0.449272i
191191 22.1476i 1.60254i 0.598302 + 0.801271i 0.295842π0.295842\pi
−0.598302 + 0.801271i 0.704158π0.704158\pi
192192 0 0
193193 −2.20149 + 2.20149i −0.158467 + 0.158467i −0.781887 0.623420i 0.785743π-0.785743\pi
0.623420 + 0.781887i 0.285743π0.285743\pi
194194 6.59730 0.473659
195195 0 0
196196 −5.46960 −0.390685
197197 2.43748 2.43748i 0.173663 0.173663i −0.614923 0.788587i 0.710813π-0.710813\pi
0.788587 + 0.614923i 0.210813π0.210813\pi
198198 0 0
199199 8.47213i 0.600573i −0.953849 0.300287i 0.902918π-0.902918\pi
0.953849 0.300287i 0.0970823π-0.0970823\pi
200200 −2.77993 + 2.77993i −0.196571 + 0.196571i
201201 0 0
202202 −11.7861 + 11.7861i −0.829266 + 0.829266i
203203 −21.2739 21.2739i −1.49313 1.49313i
204204 0 0
205205 1.55227i 0.108415i
206206 1.29432 + 1.29432i 0.0901799 + 0.0901799i
207207 0 0
208208 3.21489 1.63232i 0.222913 0.113181i
209209 23.4088i 1.61922i
210210 0 0
211211 4.56205 0.314064 0.157032 0.987594i 0.449807π-0.449807\pi
0.157032 + 0.987594i 0.449807π0.449807\pi
212212 11.7290 0.805554
213213 0 0
214214 −6.66815 6.66815i −0.455825 0.455825i
215215 2.77523 + 2.77523i 0.189269 + 0.189269i
216216 0 0
217217 −17.6319 −1.19693
218218 9.40901 0.637259
219219 0 0
220220 2.85618i 0.192564i
221221 −17.4915 + 8.88107i −1.17661 + 0.597406i
222222 0 0
223223 2.22483 + 2.22483i 0.148985 + 0.148985i 0.777665 0.628679i 0.216404π-0.216404\pi
−0.628679 + 0.777665i 0.716404π0.716404\pi
224224 3.53123i 0.235940i
225225 0 0
226226 9.61022 + 9.61022i 0.639262 + 0.639262i
227227 1.28867 1.28867i 0.0855323 0.0855323i −0.663046 0.748578i 0.730737π-0.730737\pi
0.748578 + 0.663046i 0.230737π0.230737\pi
228228 0 0
229229 −9.06136 + 9.06136i −0.598792 + 0.598792i −0.939991 0.341199i 0.889167π-0.889167\pi
0.341199 + 0.939991i 0.389167π0.389167\pi
230230 5.28669i 0.348594i
231231 0 0
232232 −6.02449 + 6.02449i −0.395527 + 0.395527i
233233 5.22631 0.342387 0.171193 0.985237i 0.445238π-0.445238\pi
0.171193 + 0.985237i 0.445238π0.445238\pi
234234 0 0
235235 −11.4165 −0.744728
236236 −1.86185 + 1.86185i −0.121196 + 0.121196i
237237 0 0
238238 19.2126i 1.24537i
239239 7.28487 7.28487i 0.471219 0.471219i −0.431090 0.902309i 0.641871π-0.641871\pi
0.902309 + 0.431090i 0.141871π0.141871\pi
240240 0 0
241241 −18.8070 + 18.8070i −1.21147 + 1.21147i −0.240923 + 0.970544i 0.577450π0.577450\pi
−0.970544 + 0.240923i 0.922550π0.922550\pi
242242 2.37998 + 2.37998i 0.152991 + 0.152991i
243243 0 0
244244 6.42979i 0.411625i
245245 −3.99802 3.99802i −0.255424 0.255424i
246246 0 0
247247 29.0385 + 9.48085i 1.84768 + 0.603252i
248248 4.99314i 0.317065i
249249 0 0
250250 −9.23261 −0.583922
251251 14.2652 0.900408 0.450204 0.892926i 0.351351π-0.351351\pi
0.450204 + 0.892926i 0.351351π0.351351\pi
252252 0 0
253253 −9.99186 9.99186i −0.628183 0.628183i
254254 −7.83746 7.83746i −0.491766 0.491766i
255255 0 0
256256 1.00000 0.0625000
257257 7.06194 0.440512 0.220256 0.975442i 0.429311π-0.429311\pi
0.220256 + 0.975442i 0.429311π0.429311\pi
258258 0 0
259259 38.8901i 2.41651i
260260 3.54308 + 1.15679i 0.219733 + 0.0717410i
261261 0 0
262262 8.58116 + 8.58116i 0.530146 + 0.530146i
263263 24.5931i 1.51648i −0.651977 0.758239i 0.726060π-0.726060\pi
0.651977 0.758239i 0.273940π-0.273940\pi
264264 0 0
265265 8.57338 + 8.57338i 0.526658 + 0.526658i
266266 −21.1548 + 21.1548i −1.29708 + 1.29708i
267267 0 0
268268 0.887018 0.887018i 0.0541833 0.0541833i
269269 13.0138i 0.793464i −0.917934 0.396732i 0.870144π-0.870144\pi
0.917934 0.396732i 0.129856π-0.129856\pi
270270 0 0
271271 2.41921 2.41921i 0.146956 0.146956i −0.629801 0.776757i 0.716863π-0.716863\pi
0.776757 + 0.629801i 0.216863π0.216863\pi
272272 −5.44078 −0.329896
273273 0 0
274274 −12.7384 −0.769558
275275 −7.68096 + 7.68096i −0.463180 + 0.463180i
276276 0 0
277277 25.0593i 1.50567i −0.658211 0.752833i 0.728687π-0.728687\pi
0.658211 0.752833i 0.271313π-0.271313\pi
278278 −2.31044 + 2.31044i −0.138571 + 0.138571i
279279 0 0
280280 −2.58116 + 2.58116i −0.154254 + 0.154254i
281281 −9.20333 9.20333i −0.549024 0.549024i 0.377134 0.926159i 0.376910π-0.376910\pi
−0.926159 + 0.377134i 0.876910π0.876910\pi
282282 0 0
283283 31.0477i 1.84559i 0.385289 + 0.922796i 0.374102π0.374102\pi
−0.385289 + 0.922796i 0.625898π0.625898\pi
284284 3.17883 + 3.17883i 0.188629 + 0.188629i
285285 0 0
286286 8.88277 4.51010i 0.525249 0.266688i
287287 5.30260i 0.313002i
288288 0 0
289289 12.6021 0.741298
290290 −8.80723 −0.517178
291291 0 0
292292 2.31653 + 2.31653i 0.135565 + 0.135565i
293293 19.8206 + 19.8206i 1.15793 + 1.15793i 0.984920 + 0.173009i 0.0553490π0.0553490\pi
0.173009 + 0.984920i 0.444651π0.444651\pi
294294 0 0
295295 −2.72185 −0.158473
296296 −11.0132 −0.640128
297297 0 0
298298 15.0890i 0.874082i
299299 16.4417 8.34803i 0.950847 0.482779i
300300 0 0
301301 −9.48027 9.48027i −0.546434 0.546434i
302302 14.7479i 0.848649i
303303 0 0
304304 5.99076 + 5.99076i 0.343594 + 0.343594i
305305 4.69987 4.69987i 0.269114 0.269114i
306306 0 0
307307 −12.6972 + 12.6972i −0.724668 + 0.724668i −0.969552 0.244885i 0.921250π-0.921250\pi
0.244885 + 0.969552i 0.421250π0.421250\pi
308308 9.75681i 0.555946i
309309 0 0
310310 −3.64975 + 3.64975i −0.207292 + 0.207292i
311311 −12.3667 −0.701250 −0.350625 0.936516i 0.614031π-0.614031\pi
−0.350625 + 0.936516i 0.614031π0.614031\pi
312312 0 0
313313 −10.4672 −0.591639 −0.295820 0.955244i 0.595593π-0.595593\pi
−0.295820 + 0.955244i 0.595593π0.595593\pi
314314 −6.95037 + 6.95037i −0.392232 + 0.392232i
315315 0 0
316316 5.29836i 0.298056i
317317 −10.8423 + 10.8423i −0.608967 + 0.608967i −0.942676 0.333709i 0.891700π-0.891700\pi
0.333709 + 0.942676i 0.391700π0.391700\pi
318318 0 0
319319 −16.6457 + 16.6457i −0.931980 + 0.931980i
320320 0.730953 + 0.730953i 0.0408615 + 0.0408615i
321321 0 0
322322 18.0595i 1.00642i
323323 −32.5944 32.5944i −1.81360 1.81360i
324324 0 0
325325 −6.41732 12.6391i −0.355969 0.701090i
326326 0.931520i 0.0515921i
327327 0 0
328328 1.50163 0.0829136
329329 38.9990 2.15009
330330 0 0
331331 19.4823 + 19.4823i 1.07084 + 1.07084i 0.997291 + 0.0735518i 0.0234334π0.0234334\pi
0.0735518 + 0.997291i 0.476567π0.476567\pi
332332 −4.77771 4.77771i −0.262211 0.262211i
333333 0 0
334334 −17.7281 −0.970041
335335 1.29674 0.0708483
336336 0 0
337337 22.0991i 1.20381i −0.798566 0.601907i 0.794408π-0.794408\pi
0.798566 0.601907i 0.205592π-0.205592\pi
338338 1.99713 + 12.8457i 0.108629 + 0.698713i
339339 0 0
340340 −3.97695 3.97695i −0.215680 0.215680i
341341 13.7961i 0.747099i
342342 0 0
343343 −3.82136 3.82136i −0.206334 0.206334i
344344 −2.68469 + 2.68469i −0.144749 + 0.144749i
345345 0 0
346346 2.74319 2.74319i 0.147475 0.147475i
347347 2.56427i 0.137657i −0.997629 0.0688285i 0.978074π-0.978074\pi
0.997629 0.0688285i 0.0219261π-0.0219261\pi
348348 0 0
349349 −25.9102 + 25.9102i −1.38694 + 1.38694i −0.555276 + 0.831666i 0.687387π0.687387\pi
−0.831666 + 0.555276i 0.812613π0.812613\pi
350350 13.8827 0.742064
351351 0 0
352352 2.76300 0.147269
353353 4.90973 4.90973i 0.261319 0.261319i −0.564271 0.825590i 0.690843π-0.690843\pi
0.825590 + 0.564271i 0.190843π0.190843\pi
354354 0 0
355355 4.64715i 0.246645i
356356 0.144930 0.144930i 0.00768126 0.00768126i
357357 0 0
358358 3.61309 3.61309i 0.190958 0.190958i
359359 −17.3664 17.3664i −0.916563 0.916563i 0.0802151 0.996778i 0.474439π-0.474439\pi
−0.996778 + 0.0802151i 0.974439π0.974439\pi
360360 0 0
361361 52.7785i 2.77782i
362362 2.83802 + 2.83802i 0.149163 + 0.149163i
363363 0 0
364364 −12.1033 3.95163i −0.634384 0.207122i
365365 3.38655i 0.177260i
366366 0 0
367367 3.21535 0.167840 0.0839199 0.996473i 0.473256π-0.473256\pi
0.0839199 + 0.996473i 0.473256π0.473256\pi
368368 5.11422 0.266597
369369 0 0
370370 −8.05011 8.05011i −0.418505 0.418505i
371371 −29.2869 29.2869i −1.52050 1.52050i
372372 0 0
373373 23.0464 1.19330 0.596648 0.802503i 0.296499π-0.296499\pi
0.596648 + 0.802503i 0.296499π0.296499\pi
374374 −15.0329 −0.777332
375375 0 0
376376 11.0440i 0.569552i
377377 −13.9072 27.3906i −0.716257 1.41069i
378378 0 0
379379 −12.6790 12.6790i −0.651276 0.651276i 0.302024 0.953300i 0.402338π-0.402338\pi
−0.953300 + 0.302024i 0.902338π0.902338\pi
380380 8.75793i 0.449272i
381381 0 0
382382 −15.6607 15.6607i −0.801271 0.801271i
383383 2.64413 2.64413i 0.135109 0.135109i −0.636318 0.771427i 0.719543π-0.719543\pi
0.771427 + 0.636318i 0.219543π0.219543\pi
384384 0 0
385385 −7.13177 + 7.13177i −0.363469 + 0.363469i
386386 3.11337i 0.158467i
387387 0 0
388388 −4.66500 + 4.66500i −0.236829 + 0.236829i
389389 22.7276 1.15234 0.576169 0.817331i 0.304547π-0.304547\pi
0.576169 + 0.817331i 0.304547π0.304547\pi
390390 0 0
391391 −27.8253 −1.40719
392392 3.86759 3.86759i 0.195343 0.195343i
393393 0 0
394394 3.44712i 0.173663i
395395 −3.87285 + 3.87285i −0.194864 + 0.194864i
396396 0 0
397397 −5.15592 + 5.15592i −0.258768 + 0.258768i −0.824553 0.565785i 0.808573π-0.808573\pi
0.565785 + 0.824553i 0.308573π0.308573\pi
398398 5.99070 + 5.99070i 0.300287 + 0.300287i
399399 0 0
400400 3.93142i 0.196571i
401401 −13.8525 13.8525i −0.691763 0.691763i 0.270857 0.962620i 0.412693π-0.412693\pi
−0.962620 + 0.270857i 0.912693π0.912693\pi
402402 0 0
403403 −17.1140 5.58757i −0.852507 0.278337i
404404 16.6680i 0.829266i
405405 0 0
406406 30.0858 1.49313
407407 −30.4295 −1.50833
408408 0 0
409409 −11.1285 11.1285i −0.550269 0.550269i 0.376249 0.926519i 0.377214π-0.377214\pi
−0.926519 + 0.376249i 0.877214π0.877214\pi
410410 1.09762 + 1.09762i 0.0542076 + 0.0542076i
411411 0 0
412412 −1.83045 −0.0901799
413413 9.29794 0.457522
414414 0 0
415415 6.98456i 0.342859i
416416 −1.11905 + 3.42750i −0.0548660 + 0.168047i
417417 0 0
418418 16.5525 + 16.5525i 0.809610 + 0.809610i
419419 28.7408i 1.40408i 0.712137 + 0.702041i 0.247728π0.247728\pi
−0.712137 + 0.702041i 0.752272π0.752272\pi
420420 0 0
421421 15.4602 + 15.4602i 0.753484 + 0.753484i 0.975128 0.221643i 0.0711421π-0.0711421\pi
−0.221643 + 0.975128i 0.571142π0.571142\pi
422422 −3.22585 + 3.22585i −0.157032 + 0.157032i
423423 0 0
424424 −8.29369 + 8.29369i −0.402777 + 0.402777i
425425 21.3900i 1.03757i
426426 0 0
427427 −16.0549 + 16.0549i −0.776951 + 0.776951i
428428 9.43019 0.455825
429429 0 0
430430 −3.92477 −0.189269
431431 −3.04773 + 3.04773i −0.146804 + 0.146804i −0.776689 0.629885i 0.783102π-0.783102\pi
0.629885 + 0.776689i 0.283102π0.283102\pi
432432 0 0
433433 10.5849i 0.508676i 0.967115 + 0.254338i 0.0818575π0.0818575\pi
−0.967115 + 0.254338i 0.918142π0.918142\pi
434434 12.4677 12.4677i 0.598466 0.598466i
435435 0 0
436436 −6.65317 + 6.65317i −0.318629 + 0.318629i
437437 30.6381 + 30.6381i 1.46562 + 1.46562i
438438 0 0
439439 0.756908i 0.0361252i 0.999837 + 0.0180626i 0.00574982π0.00574982\pi
−0.999837 + 0.0180626i 0.994250π0.994250\pi
440440 2.01963 + 2.01963i 0.0962819 + 0.0962819i
441441 0 0
442442 6.08851 18.6482i 0.289601 0.887006i
443443 36.7332i 1.74525i 0.488393 + 0.872624i 0.337583π0.337583\pi
−0.488393 + 0.872624i 0.662417π0.662417\pi
444444 0 0
445445 0.211874 0.0100438
446446 −3.14638 −0.148985
447447 0 0
448448 −2.49696 2.49696i −0.117970 0.117970i
449449 16.5702 + 16.5702i 0.781996 + 0.781996i 0.980167 0.198172i 0.0635003π-0.0635003\pi
−0.198172 + 0.980167i 0.563500π0.563500\pi
450450 0 0
451451 4.14901 0.195369
452452 −13.5909 −0.639262
453453 0 0
454454 1.82246i 0.0855323i
455455 −5.95847 11.7354i −0.279337 0.550163i
456456 0 0
457457 −0.692812 0.692812i −0.0324084 0.0324084i 0.690717 0.723125i 0.257295π-0.257295\pi
−0.723125 + 0.690717i 0.757295π0.757295\pi
458458 12.8147i 0.598792i
459459 0 0
460460 3.73825 + 3.73825i 0.174297 + 0.174297i
461461 8.54391 8.54391i 0.397930 0.397930i −0.479573 0.877502i 0.659208π-0.659208\pi
0.877502 + 0.479573i 0.159208π0.159208\pi
462462 0 0
463463 −10.8803 + 10.8803i −0.505650 + 0.505650i −0.913188 0.407538i 0.866387π-0.866387\pi
0.407538 + 0.913188i 0.366387π0.366387\pi
464464 8.51991i 0.395527i
465465 0 0
466466 −3.69556 + 3.69556i −0.171193 + 0.171193i
467467 −18.8587 −0.872678 −0.436339 0.899782i 0.643725π-0.643725\pi
−0.436339 + 0.899782i 0.643725π0.643725\pi
468468 0 0
469469 −4.42970 −0.204544
470470 8.07266 8.07266i 0.372364 0.372364i
471471 0 0
472472 2.63306i 0.121196i
473473 −7.41782 + 7.41782i −0.341072 + 0.341072i
474474 0 0
475475 23.5522 23.5522i 1.08065 1.08065i
476476 13.5854 + 13.5854i 0.622685 + 0.622685i
477477 0 0
478478 10.3024i 0.471219i
479479 −10.5691 10.5691i −0.482915 0.482915i 0.423146 0.906061i 0.360926π-0.360926\pi
−0.906061 + 0.423146i 0.860926π0.860926\pi
480480 0 0
481481 12.3243 37.7476i 0.561940 1.72114i
482482 26.5972i 1.21147i
483483 0 0
484484 −3.36580 −0.152991
485485 −6.81979 −0.309671
486486 0 0
487487 −20.2191 20.2191i −0.916214 0.916214i 0.0805378 0.996752i 0.474336π-0.474336\pi
−0.996752 + 0.0805378i 0.974336π0.974336\pi
488488 4.54655 + 4.54655i 0.205812 + 0.205812i
489489 0 0
490490 5.65405 0.255424
491491 28.8492 1.30195 0.650973 0.759101i 0.274361π-0.274361\pi
0.650973 + 0.759101i 0.274361π0.274361\pi
492492 0 0
493493 46.3549i 2.08772i
494494 −27.2373 + 13.8293i −1.22546 + 0.622212i
495495 0 0
496496 −3.53068 3.53068i −0.158532 0.158532i
497497 15.8748i 0.712082i
498498 0 0
499499 10.5258 + 10.5258i 0.471199 + 0.471199i 0.902303 0.431103i 0.141876π-0.141876\pi
−0.431103 + 0.902303i 0.641876π0.641876\pi
500500 6.52844 6.52844i 0.291961 0.291961i
501501 0 0
502502 −10.0870 + 10.0870i −0.450204 + 0.450204i
503503 8.87705i 0.395808i −0.980221 0.197904i 0.936587π-0.936587\pi
0.980221 0.197904i 0.0634134π-0.0634134\pi
504504 0 0
505505 12.1835 12.1835i 0.542161 0.542161i
506506 14.1306 0.628183
507507 0 0
508508 11.0838 0.491766
509509 17.5845 17.5845i 0.779418 0.779418i −0.200314 0.979732i 0.564196π-0.564196\pi
0.979732 + 0.200314i 0.0641962π0.0641962\pi
510510 0 0
511511 11.5686i 0.511763i
512512 −0.707107 + 0.707107i −0.0312500 + 0.0312500i
513513 0 0
514514 −4.99355 + 4.99355i −0.220256 + 0.220256i
515515 −1.33797 1.33797i −0.0589582 0.0589582i
516516 0 0
517517 30.5147i 1.34204i
518518 27.4994 + 27.4994i 1.20826 + 1.20826i
519519 0 0
520520 −3.32331 + 1.68736i −0.145737 + 0.0739958i
521521 7.10124i 0.311111i 0.987827 + 0.155556i 0.0497168π0.0497168\pi
−0.987827 + 0.155556i 0.950283π0.950283\pi
522522 0 0
523523 28.9433 1.26560 0.632801 0.774314i 0.281905π-0.281905\pi
0.632801 + 0.774314i 0.281905π0.281905\pi
524524 −12.1356 −0.530146
525525 0 0
526526 17.3900 + 17.3900i 0.758239 + 0.758239i
527527 19.2096 + 19.2096i 0.836785 + 0.836785i
528528 0 0
529529 3.15525 0.137185
530530 −12.1246 −0.526658
531531 0 0
532532 29.9174i 1.29708i
533533 −1.68040 + 5.14683i −0.0727862 + 0.222934i
534534 0 0
535535 6.89302 + 6.89302i 0.298011 + 0.298011i
536536 1.25443i 0.0541833i
537537 0 0
538538 9.20213 + 9.20213i 0.396732 + 0.396732i
539539 10.6862 10.6862i 0.460286 0.460286i
540540 0 0
541541 9.21585 9.21585i 0.396221 0.396221i −0.480677 0.876898i 0.659609π-0.659609\pi
0.876898 + 0.480677i 0.159609π0.159609\pi
542542 3.42128i 0.146956i
543543 0 0
544544 3.84721 3.84721i 0.164948 0.164948i
545545 −9.72631 −0.416629
546546 0 0
547547 −8.53557 −0.364955 −0.182477 0.983210i 0.558412π-0.558412\pi
−0.182477 + 0.983210i 0.558412π0.558412\pi
548548 9.00744 9.00744i 0.384779 0.384779i
549549 0 0
550550 10.8625i 0.463180i
551551 51.0408 51.0408i 2.17441 2.17441i
552552 0 0
553553 13.2298 13.2298i 0.562587 0.562587i
554554 17.7196 + 17.7196i 0.752833 + 0.752833i
555555 0 0
556556 3.26746i 0.138571i
557557 10.9056 + 10.9056i 0.462083 + 0.462083i 0.899338 0.437255i 0.144049π-0.144049\pi
−0.437255 + 0.899338i 0.644049π0.644049\pi
558558 0 0
559559 −6.19746 12.2061i −0.262125 0.516262i
560560 3.65032i 0.154254i
561561 0 0
562562 13.0155 0.549024
563563 −6.06531 −0.255622 −0.127811 0.991799i 0.540795π-0.540795\pi
−0.127811 + 0.991799i 0.540795π0.540795\pi
564564 0 0
565565 −9.93430 9.93430i −0.417939 0.417939i
566566 −21.9540 21.9540i −0.922796 0.922796i
567567 0 0
568568 −4.49554 −0.188629
569569 14.3081 0.599827 0.299913 0.953966i 0.403042π-0.403042\pi
0.299913 + 0.953966i 0.403042π0.403042\pi
570570 0 0
571571 5.93459i 0.248355i 0.992260 + 0.124177i 0.0396292π0.0396292\pi
−0.992260 + 0.124177i 0.960371π0.960371\pi
572572 −3.09194 + 9.47019i −0.129281 + 0.395968i
573573 0 0
574574 −3.74950 3.74950i −0.156501 0.156501i
575575 20.1061i 0.838484i
576576 0 0
577577 20.4971 + 20.4971i 0.853304 + 0.853304i 0.990539 0.137235i 0.0438215π-0.0438215\pi
−0.137235 + 0.990539i 0.543821π0.543821\pi
578578 −8.91100 + 8.91100i −0.370649 + 0.370649i
579579 0 0
580580 6.22765 6.22765i 0.258589 0.258589i
581581 23.8595i 0.989858i
582582 0 0
583583 −22.9155 + 22.9155i −0.949063 + 0.949063i
584584 −3.27607 −0.135565
585585 0 0
586586 −28.0305 −1.15793
587587 −27.9522 + 27.9522i −1.15371 + 1.15371i −0.167907 + 0.985803i 0.553701π0.553701\pi
−0.985803 + 0.167907i 0.946299π0.946299\pi
588588 0 0
589589 42.3030i 1.74306i
590590 1.92464 1.92464i 0.0792363 0.0792363i
591591 0 0
592592 7.78749 7.78749i 0.320064 0.320064i
593593 −21.8876 21.8876i −0.898816 0.898816i 0.0965155 0.995331i 0.469230π-0.469230\pi
−0.995331 + 0.0965155i 0.969230π0.969230\pi
594594 0 0
595595 19.8606i 0.814203i
596596 −10.6695 10.6695i −0.437041 0.437041i
597597 0 0
598598 −5.72307 + 17.5290i −0.234034 + 0.716813i
599599 30.4677i 1.24488i 0.782668 + 0.622439i 0.213858π0.213858\pi
−0.782668 + 0.622439i 0.786142π0.786142\pi
600600 0 0
601601 10.5012 0.428354 0.214177 0.976795i 0.431293π-0.431293\pi
0.214177 + 0.976795i 0.431293π0.431293\pi
602602 13.4071 0.546434
603603 0 0
604604 −10.4284 10.4284i −0.424325 0.424325i
605605 −2.46024 2.46024i −0.100023 0.100023i
606606 0 0
607607 16.5851 0.673168 0.336584 0.941653i 0.390728π-0.390728\pi
0.336584 + 0.941653i 0.390728π0.390728\pi
608608 −8.47222 −0.343594
609609 0 0
610610 6.64662i 0.269114i
611611 37.8534 + 12.3588i 1.53138 + 0.499985i
612612 0 0
613613 13.3912 + 13.3912i 0.540866 + 0.540866i 0.923783 0.382917i 0.125080π-0.125080\pi
−0.382917 + 0.923783i 0.625080π0.625080\pi
614614 17.9566i 0.724668i
615615 0 0
616616 −6.89911 6.89911i −0.277973 0.277973i
617617 −5.96507 + 5.96507i −0.240145 + 0.240145i −0.816910 0.576765i 0.804315π-0.804315\pi
0.576765 + 0.816910i 0.304315π0.304315\pi
618618 0 0
619619 8.99098 8.99098i 0.361378 0.361378i −0.502942 0.864320i 0.667749π-0.667749\pi
0.864320 + 0.502942i 0.167749π0.167749\pi
620620 5.16152i 0.207292i
621621 0 0
622622 8.74456 8.74456i 0.350625 0.350625i
623623 −0.723767 −0.0289971
624624 0 0
625625 −10.1131 −0.404525
626626 7.40140 7.40140i 0.295820 0.295820i
627627 0 0
628628 9.82931i 0.392232i
629629 −42.3700 + 42.3700i −1.68940 + 1.68940i
630630 0 0
631631 13.1946 13.1946i 0.525267 0.525267i −0.393890 0.919157i 0.628871π-0.628871\pi
0.919157 + 0.393890i 0.128871π0.128871\pi
632632 −3.74650 3.74650i −0.149028 0.149028i
633633 0 0
634634 15.3334i 0.608967i
635635 8.10176 + 8.10176i 0.321509 + 0.321509i
636636 0 0
637637 8.92811 + 17.5842i 0.353745 + 0.696710i
638638 23.5406i 0.931980i
639639 0 0
640640 −1.03372 −0.0408615
641641 −2.95203 −0.116598 −0.0582992 0.998299i 0.518568π-0.518568\pi
−0.0582992 + 0.998299i 0.518568π0.518568\pi
642642 0 0
643643 −23.5471 23.5471i −0.928607 0.928607i 0.0690092 0.997616i 0.478016π-0.478016\pi
−0.997616 + 0.0690092i 0.978016π0.978016\pi
644644 −12.7700 12.7700i −0.503208 0.503208i
645645 0 0
646646 46.0955 1.81360
647647 21.5988 0.849138 0.424569 0.905396i 0.360426π-0.360426\pi
0.424569 + 0.905396i 0.360426π0.360426\pi
648648 0 0
649649 7.27516i 0.285575i
650650 13.4749 + 4.39945i 0.528529 + 0.172561i
651651 0 0
652652 0.658684 + 0.658684i 0.0257961 + 0.0257961i
653653 5.01350i 0.196194i 0.995177 + 0.0980968i 0.0312755π0.0312755\pi
−0.995177 + 0.0980968i 0.968725π0.968725\pi
654654 0 0
655655 −8.87055 8.87055i −0.346601 0.346601i
656656 −1.06181 + 1.06181i −0.0414568 + 0.0414568i
657657 0 0
658658 −27.5765 + 27.5765i −1.07504 + 1.07504i
659659 21.4750i 0.836546i 0.908321 + 0.418273i 0.137364π0.137364\pi
−0.908321 + 0.418273i 0.862636π0.862636\pi
660660 0 0
661661 −7.22887 + 7.22887i −0.281171 + 0.281171i −0.833576 0.552405i 0.813710π-0.813710\pi
0.552405 + 0.833576i 0.313710π0.313710\pi
662662 −27.5521 −1.07084
663663 0 0
664664 6.75670 0.262211
665665 21.8682 21.8682i 0.848012 0.848012i
666666 0 0
667667 43.5727i 1.68714i
668668 12.5357 12.5357i 0.485020 0.485020i
669669 0 0
670670 −0.916932 + 0.916932i −0.0354242 + 0.0354242i
671671 12.5621 + 12.5621i 0.484956 + 0.484956i
672672 0 0
673673 18.2056i 0.701774i −0.936418 0.350887i 0.885880π-0.885880\pi
0.936418 0.350887i 0.114120π-0.114120\pi
674674 15.6264 + 15.6264i 0.601907 + 0.601907i
675675 0 0
676676 −10.4955 7.67108i −0.403671 0.295042i
677677 14.3760i 0.552515i 0.961084 + 0.276257i 0.0890942π0.0890942\pi
−0.961084 + 0.276257i 0.910906π0.910906\pi
678678 0 0
679679 23.2966 0.894042
680680 5.62426 0.215680
681681 0 0
682682 −9.75529 9.75529i −0.373549 0.373549i
683683 11.7572 + 11.7572i 0.449877 + 0.449877i 0.895313 0.445437i 0.146952π-0.146952\pi
−0.445437 + 0.895313i 0.646952π0.646952\pi
684684 0 0
685685 13.1680 0.503125
686686 5.40421 0.206334
687687 0 0
688688 3.79673i 0.144749i
689689 −19.1455 37.7076i −0.729386 1.43655i
690690 0 0
691691 14.9559 + 14.9559i 0.568948 + 0.568948i 0.931834 0.362886i 0.118209π-0.118209\pi
−0.362886 + 0.931834i 0.618209π0.618209\pi
692692 3.87945i 0.147475i
693693 0 0
694694 1.81321 + 1.81321i 0.0688285 + 0.0688285i
695695 2.38836 2.38836i 0.0905956 0.0905956i
696696 0 0
697697 5.77708 5.77708i 0.218823 0.218823i
698698 36.6426i 1.38694i
699699 0 0
700700 −9.81658 + 9.81658i −0.371032 + 0.371032i
701701 −45.3798 −1.71397 −0.856985 0.515342i 0.827665π-0.827665\pi
−0.856985 + 0.515342i 0.827665π0.827665\pi
702702 0 0
703703 93.3061 3.51910
704704 −1.95374 + 1.95374i −0.0736343 + 0.0736343i
705705 0 0
706706 6.94341i 0.261319i
707707 −41.6194 + 41.6194i −1.56526 + 1.56526i
708708 0 0
709709 −24.8489 + 24.8489i −0.933218 + 0.933218i −0.997906 0.0646873i 0.979395π-0.979395\pi
0.0646873 + 0.997906i 0.479395π0.479395\pi
710710 −3.28603 3.28603i −0.123323 0.123323i
711711 0 0
712712 0.204962i 0.00768126i
713713 −18.0567 18.0567i −0.676228 0.676228i
714714 0 0
715715 −9.18232 + 4.66219i −0.343399 + 0.174356i
716716 5.10968i 0.190958i
717717 0 0
718718 24.5598 0.916563
719719 −34.3801 −1.28216 −0.641081 0.767473i 0.721514π-0.721514\pi
−0.641081 + 0.767473i 0.721514π0.721514\pi
720720 0 0
721721 4.57056 + 4.57056i 0.170217 + 0.170217i
722722 −37.3200 37.3200i −1.38891 1.38891i
723723 0 0
724724 −4.01356 −0.149163
725725 −33.4953 −1.24398
726726 0 0
727727 7.44017i 0.275941i −0.990436 0.137970i 0.955942π-0.955942\pi
0.990436 0.137970i 0.0440579π-0.0440579\pi
728728 11.3525 5.76409i 0.420753 0.213631i
729729 0 0
730730 −2.39465 2.39465i −0.0886300 0.0886300i
731731 20.6572i 0.764032i
732732 0 0
733733 36.0059 + 36.0059i 1.32991 + 1.32991i 0.905446 + 0.424460i 0.139536π0.139536\pi
0.424460 + 0.905446i 0.360464π0.360464\pi
734734 −2.27359 + 2.27359i −0.0839199 + 0.0839199i
735735 0 0
736736 −3.61630 + 3.61630i −0.133299 + 0.133299i
737737 3.46601i 0.127672i
738738 0 0
739739 17.8745 17.8745i 0.657525 0.657525i −0.297269 0.954794i 0.596076π-0.596076\pi
0.954794 + 0.297269i 0.0960757π0.0960757\pi
740740 11.3846 0.418505
741741 0 0
742742 41.4180 1.52050
743743 6.18249 6.18249i 0.226814 0.226814i −0.584547 0.811360i 0.698728π-0.698728\pi
0.811360 + 0.584547i 0.198728π0.198728\pi
744744 0 0
745745 15.5979i 0.571461i
746746 −16.2962 + 16.2962i −0.596648 + 0.596648i
747747 0 0
748748 10.6299 10.6299i 0.388666 0.388666i
749749 −23.5468 23.5468i −0.860381 0.860381i
750750 0 0
751751 18.2839i 0.667189i 0.942717 + 0.333594i 0.108262π0.108262\pi
−0.942717 + 0.333594i 0.891738π0.891738\pi
752752 7.80931 + 7.80931i 0.284776 + 0.284776i
753753 0 0
754754 29.2020 + 9.53421i 1.06347 + 0.347216i
755755 15.2453i 0.554833i
756756 0 0
757757 −7.47864 −0.271816 −0.135908 0.990721i 0.543395π-0.543395\pi
−0.135908 + 0.990721i 0.543395π0.543395\pi
758758 17.9308 0.651276
759759 0 0
760760 −6.19279 6.19279i −0.224636 0.224636i
761761 2.80360 + 2.80360i 0.101630 + 0.101630i 0.756094 0.654463i 0.227105π-0.227105\pi
−0.654463 + 0.756094i 0.727105π0.727105\pi
762762 0 0
763763 33.2254 1.20284
764764 22.1476 0.801271
765765 0 0
766766 3.73937i 0.135109i
767767 9.02480 + 2.94653i 0.325867 + 0.106393i
768768 0 0
769769 −0.486296 0.486296i −0.0175363 0.0175363i 0.698284 0.715821i 0.253947π-0.253947\pi
−0.715821 + 0.698284i 0.753947π0.753947\pi
770770 10.0858i 0.363469i
771771 0 0
772772 2.20149 + 2.20149i 0.0792333 + 0.0792333i
773773 −15.2154 + 15.2154i −0.547261 + 0.547261i −0.925648 0.378387i 0.876479π-0.876479\pi
0.378387 + 0.925648i 0.376479π0.376479\pi
774774 0 0
775775 −13.8806 + 13.8806i −0.498605 + 0.498605i
776776 6.59730i 0.236829i
777777 0 0
778778 −16.0709 + 16.0709i −0.576169 + 0.576169i
779779 −12.7221 −0.455818
780780 0 0
781781 −12.4212 −0.444466
782782 19.6755 19.6755i 0.703594 0.703594i
783783 0 0
784784 5.46960i 0.195343i
785785 7.18476 7.18476i 0.256435 0.256435i
786786 0 0
787787 0.495643 0.495643i 0.0176678 0.0176678i −0.698218 0.715885i 0.746023π-0.746023\pi
0.715885 + 0.698218i 0.246023π0.246023\pi
788788 −2.43748 2.43748i −0.0868317 0.0868317i
789789 0 0
790790 5.47703i 0.194864i
791791 33.9359 + 33.9359i 1.20662 + 1.20662i
792792 0 0
793793 −20.6711 + 10.4955i −0.734052 + 0.372704i
794794 7.29157i 0.258768i
795795 0 0
796796 −8.47213 −0.300287
797797 17.9090 0.634369 0.317185 0.948364i 0.397263π-0.397263\pi
0.317185 + 0.948364i 0.397263π0.397263\pi
798798 0 0
799799 −42.4887 42.4887i −1.50314 1.50314i
800800 2.77993 + 2.77993i 0.0982854 + 0.0982854i
801801 0 0
802802 19.5904 0.691763
803803 −9.05179 −0.319431
804804 0 0
805805 18.6685i 0.657979i
806806 16.0524 8.15038i 0.565422 0.287085i
807807 0 0
808808 11.7861 + 11.7861i 0.414633 + 0.414633i
809809 27.2029i 0.956402i −0.878250 0.478201i 0.841289π-0.841289\pi
0.878250 0.478201i 0.158711π-0.158711\pi
810810 0 0
811811 −31.6498 31.6498i −1.11138 1.11138i −0.992965 0.118412i 0.962220π-0.962220\pi
−0.118412 0.992965i 0.537780π-0.537780\pi
812812 −21.2739 + 21.2739i −0.746566 + 0.746566i
813813 0 0
814814 21.5169 21.5169i 0.754166 0.754166i
815815 0.962934i 0.0337301i
816816 0 0
817817 22.7453 22.7453i 0.795757 0.795757i
818818 15.7381 0.550269
819819 0 0
820820 −1.55227 −0.0542076
821821 −32.8949 + 32.8949i −1.14804 + 1.14804i −0.161104 + 0.986937i 0.551505π0.551505\pi
−0.986937 + 0.161104i 0.948495π0.948495\pi
822822 0 0
823823 6.29469i 0.219419i 0.993964 + 0.109710i 0.0349921π0.0349921\pi
−0.993964 + 0.109710i 0.965008π0.965008\pi
824824 1.29432 1.29432i 0.0450899 0.0450899i
825825 0 0
826826 −6.57464 + 6.57464i −0.228761 + 0.228761i
827827 23.3955 + 23.3955i 0.813543 + 0.813543i 0.985163 0.171620i 0.0549002π-0.0549002\pi
−0.171620 + 0.985163i 0.554900π0.554900\pi
828828 0 0
829829 3.14079i 0.109084i −0.998511 0.0545421i 0.982630π-0.982630\pi
0.998511 0.0545421i 0.0173699π-0.0173699\pi
830830 4.93883 + 4.93883i 0.171429 + 0.171429i
831831 0 0
832832 −1.63232 3.21489i −0.0565904 0.111456i
833833 29.7589i 1.03108i
834834 0 0
835835 18.3260 0.634197
836836 −23.4088 −0.809610
837837 0 0
838838 −20.3228 20.3228i −0.702041 0.702041i
839839 28.0370 + 28.0370i 0.967944 + 0.967944i 0.999502 0.0315577i 0.0100468π-0.0100468\pi
−0.0315577 + 0.999502i 0.510047π0.510047\pi
840840 0 0
841841 −43.5889 −1.50307
842842 −21.8640 −0.753484
843843 0 0
844844 4.56205i 0.157032i
845845 −2.06448 13.2789i −0.0710202 0.456807i
846846 0 0
847847 8.40427 + 8.40427i 0.288774 + 0.288774i
848848 11.7290i 0.402777i
849849 0 0
850850 −15.1250 15.1250i −0.518783 0.518783i
851851 39.8270 39.8270i 1.36525 1.36525i
852852 0 0
853853 −5.31816 + 5.31816i −0.182090 + 0.182090i −0.792266 0.610176i 0.791099π-0.791099\pi
0.610176 + 0.792266i 0.291099π0.291099\pi
854854 22.7051i 0.776951i
855855 0 0
856856 −6.66815 + 6.66815i −0.227913 + 0.227913i
857857 13.1601 0.449540 0.224770 0.974412i 0.427837π-0.427837\pi
0.224770 + 0.974412i 0.427837π0.427837\pi
858858 0 0
859859 −39.9763 −1.36397 −0.681987 0.731365i 0.738884π-0.738884\pi
−0.681987 + 0.731365i 0.738884π0.738884\pi
860860 2.77523 2.77523i 0.0946345 0.0946345i
861861 0 0
862862 4.31015i 0.146804i
863863 −19.5420 + 19.5420i −0.665217 + 0.665217i −0.956605 0.291388i 0.905883π-0.905883\pi
0.291388 + 0.956605i 0.405883π0.405883\pi
864864 0 0
865865 −2.83570 + 2.83570i −0.0964166 + 0.0964166i
866866 −7.48462 7.48462i −0.254338 0.254338i
867867 0 0
868868 17.6319i 0.598466i
869869 −10.3516 10.3516i −0.351154 0.351154i
870870 0 0
871871 −4.29957 1.40377i −0.145685 0.0475651i
872872 9.40901i 0.318629i
873873 0 0
874874 −43.3288 −1.46562
875875 −32.6025 −1.10217
876876 0 0
877877 10.6502 + 10.6502i 0.359633 + 0.359633i 0.863678 0.504045i 0.168155π-0.168155\pi
−0.504045 + 0.863678i 0.668155π0.668155\pi
878878 −0.535215 0.535215i −0.0180626 0.0180626i
879879 0 0
880880 −2.85618 −0.0962819
881881 −5.09673 −0.171713 −0.0858567 0.996307i 0.527363π-0.527363\pi
−0.0858567 + 0.996307i 0.527363π0.527363\pi
882882 0 0
883883 43.6345i 1.46842i 0.678924 + 0.734209i 0.262447π0.262447\pi
−0.678924 + 0.734209i 0.737553π0.737553\pi
884884 8.88107 + 17.4915i 0.298703 + 0.588304i
885885 0 0
886886 −25.9743 25.9743i −0.872624 0.872624i
887887 53.9013i 1.80983i −0.425593 0.904915i 0.639934π-0.639934\pi
0.425593 0.904915i 0.360066π-0.360066\pi
888888 0 0
889889 −27.6759 27.6759i −0.928219 0.928219i
890890 −0.149817 + 0.149817i −0.00502189 + 0.00502189i
891891 0 0
892892 2.22483 2.22483i 0.0744927 0.0744927i
893893 93.5674i 3.13111i
894894 0 0
895895 −3.73494 + 3.73494i −0.124845 + 0.124845i
896896 3.53123 0.117970
897897 0 0
898898 −23.4338 −0.781996
899899 −30.0811 + 30.0811i −1.00326 + 1.00326i
900900 0 0
901901 63.8151i 2.12599i
902902 −2.93379 + 2.93379i −0.0976846 + 0.0976846i
903903 0 0
904904 9.61022 9.61022i 0.319631 0.319631i
905905 −2.93372 2.93372i −0.0975203 0.0975203i
906906 0 0
907907 7.07627i 0.234964i 0.993075 + 0.117482i 0.0374822π0.0374822\pi
−0.993075 + 0.117482i 0.962518π0.962518\pi
908908 −1.28867 1.28867i −0.0427661 0.0427661i
909909 0 0
910910 12.5114 + 4.08489i 0.414750 + 0.135413i
911911 20.6283i 0.683447i 0.939801 + 0.341723i 0.111011π0.111011\pi
−0.939801 + 0.341723i 0.888989π0.888989\pi
912912 0 0
913913 18.6688 0.617847
914914 0.979785 0.0324084
915915 0 0
916916 9.06136 + 9.06136i 0.299396 + 0.299396i
917917 30.3021 + 30.3021i 1.00066 + 1.00066i
918918 0 0
919919 −27.6811 −0.913115 −0.456558 0.889694i 0.650918π-0.650918\pi
−0.456558 + 0.889694i 0.650918π0.650918\pi
920920 −5.28669 −0.174297
921921 0 0
922922 12.0829i 0.397930i
923923 5.03074 15.4085i 0.165589 0.507176i
924924 0 0
925925 −30.6159 30.6159i −1.00664 1.00664i
926926 15.3871i 0.505650i
927927 0 0
928928 6.02449 + 6.02449i 0.197763 + 0.197763i
929929 19.1542 19.1542i 0.628430 0.628430i −0.319243 0.947673i 0.603429π-0.603429\pi
0.947673 + 0.319243i 0.103429π0.103429\pi
930930 0 0
931931 −32.7671 + 32.7671i −1.07390 + 1.07390i
932932 5.22631i 0.171193i
933933 0 0
934934 13.3351 13.3351i 0.436339 0.436339i
935935 15.5399 0.508208
936936 0 0
937937 −14.2237 −0.464668 −0.232334 0.972636i 0.574636π-0.574636\pi
−0.232334 + 0.972636i 0.574636π0.574636\pi
938938 3.13227 3.13227i 0.102272 0.102272i
939939 0 0
940940 11.4165i 0.372364i
941941 −25.7864 + 25.7864i −0.840613 + 0.840613i −0.988939 0.148325i 0.952612π-0.952612\pi
0.148325 + 0.988939i 0.452612π0.452612\pi
942942 0 0
943943 −5.43034 + 5.43034i −0.176836 + 0.176836i
944944 1.86185 + 1.86185i 0.0605982 + 0.0605982i
945945 0 0
946946 10.4904i 0.341072i
947947 −5.61473 5.61473i −0.182454 0.182454i 0.609970 0.792424i 0.291181π-0.291181\pi
−0.792424 + 0.609970i 0.791181π0.791181\pi
948948 0 0
949949 3.66609 11.2287i 0.119006 0.364499i
950950 33.3078i 1.08065i
951951 0 0
952952 −19.2126 −0.622685
953953 35.0177 1.13434 0.567168 0.823602i 0.308039π-0.308039\pi
0.567168 + 0.823602i 0.308039π0.308039\pi
954954 0 0
955955 16.1888 + 16.1888i 0.523858 + 0.523858i
956956 −7.28487 7.28487i −0.235609 0.235609i
957957 0 0
958958 14.9470 0.482915
959959 −44.9824 −1.45256
960960 0 0
961961 6.06858i 0.195761i
962962 17.9770 + 35.4062i 0.579602 + 1.14154i
963963 0 0
964964 18.8070 + 18.8070i 0.605734 + 0.605734i
965965 3.21837i 0.103603i
966966 0 0
967967 28.4024 + 28.4024i 0.913361 + 0.913361i 0.996535 0.0831742i 0.0265058π-0.0265058\pi
−0.0831742 + 0.996535i 0.526506π0.526506\pi
968968 2.37998 2.37998i 0.0764955 0.0764955i
969969 0 0
970970 4.82232 4.82232i 0.154835 0.154835i
971971 18.0510i 0.579283i −0.957135 0.289642i 0.906464π-0.906464\pi
0.957135 0.289642i 0.0935361π-0.0935361\pi
972972 0 0
973973 −8.15871 + 8.15871i −0.261556 + 0.261556i
974974 28.5941 0.916214
975975 0 0
976976 −6.42979 −0.205812
977977 8.94926 8.94926i 0.286312 0.286312i −0.549308 0.835620i 0.685109π-0.685109\pi
0.835620 + 0.549308i 0.185109π0.185109\pi
978978 0 0
979979 0.566310i 0.0180994i
980980 −3.99802 + 3.99802i −0.127712 + 0.127712i
981981 0 0
982982 −20.3995 + 20.3995i −0.650973 + 0.650973i
983983 27.8757 + 27.8757i 0.889098 + 0.889098i 0.994436 0.105338i 0.0335925π-0.0335925\pi
−0.105338 + 0.994436i 0.533593π0.533593\pi
984984 0 0
985985 3.56337i 0.113538i
986986 −32.7779 32.7779i −1.04386 1.04386i
987987 0 0
988988 9.48085 29.0385i 0.301626 0.923838i
989989 19.4173i 0.617434i
990990 0 0
991991 10.8811 0.345649 0.172825 0.984953i 0.444711π-0.444711\pi
0.172825 + 0.984953i 0.444711π0.444711\pi
992992 4.99314 0.158532
993993 0 0
994994 11.2252 + 11.2252i 0.356041 + 0.356041i
995995 −6.19272 6.19272i −0.196323 0.196323i
996996 0 0
997997 −10.4383 −0.330585 −0.165292 0.986245i 0.552857π-0.552857\pi
−0.165292 + 0.986245i 0.552857π0.552857\pi
998998 −14.8857 −0.471199
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 702.2.j.b.593.4 yes 24
3.2 odd 2 inner 702.2.j.b.593.9 yes 24
13.5 odd 4 inner 702.2.j.b.161.9 yes 24
39.5 even 4 inner 702.2.j.b.161.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
702.2.j.b.161.4 24 39.5 even 4 inner
702.2.j.b.161.9 yes 24 13.5 odd 4 inner
702.2.j.b.593.4 yes 24 1.1 even 1 trivial
702.2.j.b.593.9 yes 24 3.2 odd 2 inner