Properties

Label 392.2.e.e.195.4
Level 392392
Weight 22
Character 392.195
Analytic conductor 3.1303.130
Analytic rank 00
Dimension 1212
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,2,Mod(195,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.195");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 392=2372 392 = 2^{3} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 392.e (of order 22, degree 11, 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: 3.130135759233.13013575923
Analytic rank: 00
Dimension: 1212
Coefficient field: 12.0.144054149089536.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x123x11+x9+48x8189x7+431x6654x5+624x4340x3+96x212x+4 x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 28 2^{8}
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 195.4
Root 2.002330.854000i2.00233 - 0.854000i of defining polynomial
Character χ\chi == 392.195
Dual form 392.2.e.e.195.1

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+(1.30084+0.554812i)q2+0.480901iq3+(1.384371.44344i)q4+3.19427q5+(0.2668100.625575i)q6+(1.00000+2.64575i)q8+2.76873q9+(4.15523+1.77222i)q101.60168q11+(0.694153+0.665743i)q12+1.38831q13+1.53613iq15+(0.1670553.99651i)q164.02534iq17+(3.60168+1.53613i)q185.27649iq19+(4.422044.61075i)q20+(2.083530.888631i)q22+4.42301iq23+(1.272340.480901i)q24+5.20336q25+(1.80596+0.770249i)q26+2.77419iq27+5.10613iq29+(0.8522621.99826i)q300.115962q31+(2.43462+5.10613i)q320.770249iq33+(2.23331+5.23632i)q34+(3.832943.99651i)q36+5.34727iq37+(2.92746+6.86387i)q38+0.667638iq39+(3.19427+8.45124i)q404.21689iq41+(2.21731+2.31193i)q44+8.84408q45+(2.453945.75363i)q46+10.1164q47+(1.921930.0803370i)q48+(6.76873+2.88689i)q50+1.93579q51+(1.921932.00394i)q52+7.08425iq53+(1.539153.60878i)q545.11619q55+2.53747q57+(2.832946.64226i)q58+5.06748iq59+(2.21731+2.12656i)q608.42643q61+(0.1508480.0643370i)q62+(6.000005.29150i)q64+4.43462q65+(0.427343+1.00197i)q6610.0363q67+(5.810355.57255i)q682.12703q695.29150iq71+(2.76873+7.32538i)q7210.7445iq73+(2.966736.95594i)q74+2.50230iq75+(7.616317.30460i)q76+(0.3704130.868490i)q7811.9338iq79+(0.53361912.7659i)q80+6.97209q81+(2.33958+5.48550i)q82+14.9789iq8312.8580iq852.45554q87+(1.601684.23764i)q88+1.73205iq89+(11.5047+4.90680i)q90+(6.38437+6.12307i)q920.0557662iq93+(13.1598+5.61272i)q9416.8545iq95+(2.45554+1.17081i)q962.87198iq974.43462q99+O(q100)q+(-1.30084 + 0.554812i) q^{2} +0.480901i q^{3} +(1.38437 - 1.44344i) q^{4} +3.19427 q^{5} +(-0.266810 - 0.625575i) q^{6} +(-1.00000 + 2.64575i) q^{8} +2.76873 q^{9} +(-4.15523 + 1.77222i) q^{10} -1.60168 q^{11} +(0.694153 + 0.665743i) q^{12} +1.38831 q^{13} +1.53613i q^{15} +(-0.167055 - 3.99651i) q^{16} -4.02534i q^{17} +(-3.60168 + 1.53613i) q^{18} -5.27649i q^{19} +(4.42204 - 4.61075i) q^{20} +(2.08353 - 0.888631i) q^{22} +4.42301i q^{23} +(-1.27234 - 0.480901i) q^{24} +5.20336 q^{25} +(-1.80596 + 0.770249i) q^{26} +2.77419i q^{27} +5.10613i q^{29} +(-0.852262 - 1.99826i) q^{30} -0.115962 q^{31} +(2.43462 + 5.10613i) q^{32} -0.770249i q^{33} +(2.23331 + 5.23632i) q^{34} +(3.83294 - 3.99651i) q^{36} +5.34727i q^{37} +(2.92746 + 6.86387i) q^{38} +0.667638i q^{39} +(-3.19427 + 8.45124i) q^{40} -4.21689i q^{41} +(-2.21731 + 2.31193i) q^{44} +8.84408 q^{45} +(-2.45394 - 5.75363i) q^{46} +10.1164 q^{47} +(1.92193 - 0.0803370i) q^{48} +(-6.76873 + 2.88689i) q^{50} +1.93579 q^{51} +(1.92193 - 2.00394i) q^{52} +7.08425i q^{53} +(-1.53915 - 3.60878i) q^{54} -5.11619 q^{55} +2.53747 q^{57} +(-2.83294 - 6.64226i) q^{58} +5.06748i q^{59} +(2.21731 + 2.12656i) q^{60} -8.42643 q^{61} +(0.150848 - 0.0643370i) q^{62} +(-6.00000 - 5.29150i) q^{64} +4.43462 q^{65} +(0.427343 + 1.00197i) q^{66} -10.0363 q^{67} +(-5.81035 - 5.57255i) q^{68} -2.12703 q^{69} -5.29150i q^{71} +(-2.76873 + 7.32538i) q^{72} -10.7445i q^{73} +(-2.96673 - 6.95594i) q^{74} +2.50230i q^{75} +(-7.61631 - 7.30460i) q^{76} +(-0.370413 - 0.868490i) q^{78} -11.9338i q^{79} +(-0.533619 - 12.7659i) q^{80} +6.97209 q^{81} +(2.33958 + 5.48550i) q^{82} +14.9789i q^{83} -12.8580i q^{85} -2.45554 q^{87} +(1.60168 - 4.23764i) q^{88} +1.73205i q^{89} +(-11.5047 + 4.90680i) q^{90} +(6.38437 + 6.12307i) q^{92} -0.0557662i q^{93} +(-13.1598 + 5.61272i) q^{94} -16.8545i q^{95} +(-2.45554 + 1.17081i) q^{96} -2.87198i q^{97} -4.43462 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q12q8+12q1112q18+24q22+24q30+48q3612q44+36q4648q5012q5136q5736q58+12q6072q64+24q6560q6724q74+24q99+O(q100) 12 q - 12 q^{8} + 12 q^{11} - 12 q^{18} + 24 q^{22} + 24 q^{30} + 48 q^{36} - 12 q^{44} + 36 q^{46} - 48 q^{50} - 12 q^{51} - 36 q^{57} - 36 q^{58} + 12 q^{60} - 72 q^{64} + 24 q^{65} - 60 q^{67} - 24 q^{74}+ \cdots - 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/392Z)×\left(\mathbb{Z}/392\mathbb{Z}\right)^\times.

nn 197197 295295 297297
χ(n)\chi(n) 1-1 1-1 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 −1.30084 + 0.554812i −0.919832 + 0.392311i
33 0.480901i 0.277648i 0.990317 + 0.138824i 0.0443323π0.0443323\pi
−0.990317 + 0.138824i 0.955668π0.955668\pi
44 1.38437 1.44344i 0.692184 0.721721i
55 3.19427 1.42852 0.714260 0.699880i 0.246763π-0.246763\pi
0.714260 + 0.699880i 0.246763π0.246763\pi
66 −0.266810 0.625575i −0.108925 0.255390i
77 0 0
88 −1.00000 + 2.64575i −0.353553 + 0.935414i
99 2.76873 0.922911
1010 −4.15523 + 1.77222i −1.31400 + 0.560425i
1111 −1.60168 −0.482924 −0.241462 0.970410i 0.577627π-0.577627\pi
−0.241462 + 0.970410i 0.577627π0.577627\pi
1212 0.694153 + 0.665743i 0.200385 + 0.192184i
1313 1.38831 0.385047 0.192523 0.981292i 0.438333π-0.438333\pi
0.192523 + 0.981292i 0.438333π0.438333\pi
1414 0 0
1515 1.53613i 0.396626i
1616 −0.167055 3.99651i −0.0417638 0.999128i
1717 4.02534i 0.976288i −0.872763 0.488144i 0.837674π-0.837674\pi
0.872763 0.488144i 0.162326π-0.162326\pi
1818 −3.60168 + 1.53613i −0.848924 + 0.362069i
1919 5.27649i 1.21051i −0.796032 0.605255i 0.793071π-0.793071\pi
0.796032 0.605255i 0.206929π-0.206929\pi
2020 4.42204 4.61075i 0.988799 1.03099i
2121 0 0
2222 2.08353 0.888631i 0.444210 0.189457i
2323 4.42301i 0.922262i 0.887332 + 0.461131i 0.152556π0.152556\pi
−0.887332 + 0.461131i 0.847444π0.847444\pi
2424 −1.27234 0.480901i −0.259716 0.0981635i
2525 5.20336 1.04067
2626 −1.80596 + 0.770249i −0.354179 + 0.151058i
2727 2.77419i 0.533893i
2828 0 0
2929 5.10613i 0.948185i 0.880475 + 0.474093i 0.157224π0.157224\pi
−0.880475 + 0.474093i 0.842776π0.842776\pi
3030 −0.852262 1.99826i −0.155601 0.364830i
3131 −0.115962 −0.0208274 −0.0104137 0.999946i 0.503315π-0.503315\pi
−0.0104137 + 0.999946i 0.503315π0.503315\pi
3232 2.43462 + 5.10613i 0.430385 + 0.902646i
3333 0.770249i 0.134083i
3434 2.23331 + 5.23632i 0.383009 + 0.898022i
3535 0 0
3636 3.83294 3.99651i 0.638824 0.666085i
3737 5.34727i 0.879086i 0.898222 + 0.439543i 0.144860π0.144860\pi
−0.898222 + 0.439543i 0.855140π0.855140\pi
3838 2.92746 + 6.86387i 0.474897 + 1.11347i
3939 0.667638i 0.106908i
4040 −3.19427 + 8.45124i −0.505058 + 1.33626i
4141 4.21689i 0.658568i −0.944231 0.329284i 0.893193π-0.893193\pi
0.944231 0.329284i 0.106807π-0.106807\pi
4242 0 0
4343 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4444 −2.21731 + 2.31193i −0.334272 + 0.348537i
4545 8.84408 1.31840
4646 −2.45394 5.75363i −0.361814 0.848327i
4747 10.1164 1.47563 0.737816 0.675002i 0.235857π-0.235857\pi
0.737816 + 0.675002i 0.235857π0.235857\pi
4848 1.92193 0.0803370i 0.277406 0.0115956i
4949 0 0
5050 −6.76873 + 2.88689i −0.957244 + 0.408267i
5151 1.93579 0.271065
5252 1.92193 2.00394i 0.266523 0.277897i
5353 7.08425i 0.973096i 0.873654 + 0.486548i 0.161744π0.161744\pi
−0.873654 + 0.486548i 0.838256π0.838256\pi
5454 −1.53915 3.60878i −0.209452 0.491092i
5555 −5.11619 −0.689868
5656 0 0
5757 2.53747 0.336096
5858 −2.83294 6.64226i −0.371984 0.872172i
5959 5.06748i 0.659729i 0.944028 + 0.329865i 0.107003π0.107003\pi
−0.944028 + 0.329865i 0.892997π0.892997\pi
6060 2.21731 + 2.12656i 0.286254 + 0.274538i
6161 −8.42643 −1.07889 −0.539447 0.842020i 0.681367π-0.681367\pi
−0.539447 + 0.842020i 0.681367π0.681367\pi
6262 0.150848 0.0643370i 0.0191577 0.00817081i
6363 0 0
6464 −6.00000 5.29150i −0.750000 0.661438i
6565 4.43462 0.550047
6666 0.427343 + 1.00197i 0.0526023 + 0.123334i
6767 −10.0363 −1.22613 −0.613065 0.790033i 0.710064π-0.710064\pi
−0.613065 + 0.790033i 0.710064π0.710064\pi
6868 −5.81035 5.57255i −0.704608 0.675771i
6969 −2.12703 −0.256064
7070 0 0
7171 5.29150i 0.627986i −0.949425 0.313993i 0.898333π-0.898333\pi
0.949425 0.313993i 0.101667π-0.101667\pi
7272 −2.76873 + 7.32538i −0.326298 + 0.863305i
7373 10.7445i 1.25755i −0.777586 0.628776i 0.783556π-0.783556\pi
0.777586 0.628776i 0.216444π-0.216444\pi
7474 −2.96673 6.95594i −0.344875 0.808611i
7575 2.50230i 0.288941i
7676 −7.61631 7.30460i −0.873651 0.837895i
7777 0 0
7878 −0.370413 0.868490i −0.0419411 0.0983371i
7979 11.9338i 1.34265i −0.741162 0.671327i 0.765725π-0.765725\pi
0.741162 0.671327i 0.234275π-0.234275\pi
8080 −0.533619 12.7659i −0.0596604 1.42727i
8181 6.97209 0.774677
8282 2.33958 + 5.48550i 0.258364 + 0.605772i
8383 14.9789i 1.64415i 0.569382 + 0.822073i 0.307182π0.307182\pi
−0.569382 + 0.822073i 0.692818π0.692818\pi
8484 0 0
8585 12.8580i 1.39465i
8686 0 0
8787 −2.45554 −0.263262
8888 1.60168 4.23764i 0.170740 0.451734i
8989 1.73205i 0.183597i 0.995778 + 0.0917985i 0.0292616π0.0292616\pi
−0.995778 + 0.0917985i 0.970738π0.970738\pi
9090 −11.5047 + 4.90680i −1.21271 + 0.517223i
9191 0 0
9292 6.38437 + 6.12307i 0.665616 + 0.638375i
9393 0.0557662i 0.00578268i
9494 −13.1598 + 5.61272i −1.35733 + 0.578907i
9595 16.8545i 1.72924i
9696 −2.45554 + 1.17081i −0.250618 + 0.119496i
9797 2.87198i 0.291606i −0.989314 0.145803i 0.953423π-0.953423\pi
0.989314 0.145803i 0.0465765π-0.0465765\pi
9898 0 0
9999 −4.43462 −0.445696
100100 7.20336 7.51075i 0.720336 0.751075i
101101 −6.80620 −0.677242 −0.338621 0.940923i 0.609960π-0.609960\pi
−0.338621 + 0.940923i 0.609960π0.609960\pi
102102 −2.51815 + 1.07400i −0.249334 + 0.106342i
103103 −14.0494 −1.38433 −0.692165 0.721739i 0.743343π-0.743343\pi
−0.692165 + 0.721739i 0.743343π0.743343\pi
104104 −1.38831 + 3.67311i −0.136135 + 0.360178i
105105 0 0
106106 −3.93043 9.21547i −0.381757 0.895086i
107107 −5.13915 −0.496820 −0.248410 0.968655i 0.579908π-0.579908\pi
−0.248410 + 0.968655i 0.579908π0.579908\pi
108108 4.00438 + 3.84050i 0.385322 + 0.369552i
109109 2.83112i 0.271172i −0.990766 0.135586i 0.956708π-0.956708\pi
0.990766 0.135586i 0.0432917π-0.0432917\pi
110110 6.65535 2.83853i 0.634563 0.270643i
111111 −2.57151 −0.244077
112112 0 0
113113 −1.43695 −0.135177 −0.0675887 0.997713i 0.521531π-0.521531\pi
−0.0675887 + 0.997713i 0.521531π0.521531\pi
114114 −3.30084 + 1.40782i −0.309152 + 0.131854i
115115 14.1283i 1.31747i
116116 7.37041 + 7.06876i 0.684326 + 0.656318i
117117 3.84385 0.355364
118118 −2.81150 6.59198i −0.258819 0.606841i
119119 0 0
120120 −4.06421 1.53613i −0.371010 0.140229i
121121 −8.43462 −0.766784
122122 10.9614 4.67508i 0.992401 0.423262i
123123 2.02791 0.182850
124124 −0.160534 + 0.167384i −0.0144164 + 0.0150316i
125125 0.649581 0.0581003
126126 0 0
127127 4.92077i 0.436647i 0.975876 + 0.218324i 0.0700589π0.0700589\pi
−0.975876 + 0.218324i 0.929941π0.929941\pi
128128 10.7408 + 3.55452i 0.949364 + 0.314178i
129129 0 0
130130 −5.76873 + 2.46038i −0.505951 + 0.215790i
131131 3.94500i 0.344676i −0.985038 0.172338i 0.944868π-0.944868\pi
0.985038 0.172338i 0.0551322π-0.0551322\pi
132132 −1.11181 1.06631i −0.0967707 0.0928101i
133133 0 0
134134 13.0556 5.56826i 1.12783 0.481025i
135135 8.86151i 0.762677i
136136 10.6500 + 4.02534i 0.913234 + 0.345170i
137137 −0.102845 −0.00878661 −0.00439331 0.999990i 0.501398π-0.501398\pi
−0.00439331 + 0.999990i 0.501398π0.501398\pi
138138 2.76693 1.18010i 0.235536 0.100457i
139139 14.9789i 1.27049i −0.772310 0.635246i 0.780899π-0.780899\pi
0.772310 0.635246i 0.219101π-0.219101\pi
140140 0 0
141141 4.86500i 0.409707i
142142 2.93579 + 6.88340i 0.246366 + 0.577642i
143143 −2.22362 −0.185949
144144 −0.462531 11.0653i −0.0385443 0.922106i
145145 16.3104i 1.35450i
146146 5.96120 + 13.9769i 0.493352 + 1.15674i
147147 0 0
148148 7.71848 + 7.40258i 0.634455 + 0.608489i
149149 11.3064i 0.926257i −0.886291 0.463129i 0.846727π-0.846727\pi
0.886291 0.463129i 0.153273π-0.153273\pi
150150 −1.38831 3.25509i −0.113355 0.265777i
151151 14.8206i 1.20609i 0.797708 + 0.603044i 0.206046π0.206046\pi
−0.797708 + 0.603044i 0.793954π0.793954\pi
152152 13.9603 + 5.27649i 1.13233 + 0.427980i
153153 11.1451i 0.901028i
154154 0 0
155155 −0.370413 −0.0297523
156156 0.963697 + 0.924256i 0.0771575 + 0.0739997i
157157 −0.738725 −0.0589567 −0.0294783 0.999565i 0.509385π-0.509385\pi
−0.0294783 + 0.999565i 0.509385π0.509385\pi
158158 6.62100 + 15.5239i 0.526738 + 1.23502i
159159 −3.40682 −0.270179
160160 7.77685 + 16.3104i 0.614814 + 1.28945i
161161 0 0
162162 −9.06957 + 3.86820i −0.712573 + 0.303915i
163163 −8.70452 −0.681791 −0.340895 0.940101i 0.610730π-0.610730\pi
−0.340895 + 0.940101i 0.610730π0.610730\pi
164164 −6.08684 5.83773i −0.475303 0.455850i
165165 2.46038i 0.191541i
166166 −8.31046 19.4851i −0.645017 1.51234i
167167 1.38831 0.107430 0.0537152 0.998556i 0.482894π-0.482894\pi
0.0537152 + 0.998556i 0.482894π0.482894\pi
168168 0 0
169169 −11.0726 −0.851739
170170 7.13378 + 16.7262i 0.547136 + 1.28284i
171171 14.6092i 1.11719i
172172 0 0
173173 0.970649 0.0737971 0.0368985 0.999319i 0.488252π-0.488252\pi
0.0368985 + 0.999319i 0.488252π0.488252\pi
174174 3.19427 1.36237i 0.242157 0.103281i
175175 0 0
176176 0.267569 + 6.40113i 0.0201688 + 0.482503i
177177 −2.43695 −0.183173
178178 −0.960963 2.25312i −0.0720272 0.168879i
179179 −14.2699 −1.06658 −0.533291 0.845932i 0.679045π-0.679045\pi
−0.533291 + 0.845932i 0.679045π0.679045\pi
180180 12.2435 12.7659i 0.912574 0.951516i
181181 15.3218 1.13886 0.569429 0.822041i 0.307164π-0.307164\pi
0.569429 + 0.822041i 0.307164π0.307164\pi
182182 0 0
183183 4.05228i 0.299553i
184184 −11.7022 4.42301i −0.862697 0.326069i
185185 17.0806i 1.25579i
186186 0.0309397 + 0.0725428i 0.00226861 + 0.00531910i
187187 6.44730i 0.471473i
188188 14.0049 14.6025i 1.02141 1.06500i
189189 0 0
190190 9.35110 + 21.9250i 0.678400 + 1.59061i
191191 2.50067i 0.180942i −0.995899 0.0904709i 0.971163π-0.971163\pi
0.995899 0.0904709i 0.0288372π-0.0288372\pi
192192 2.54469 2.88541i 0.183647 0.208236i
193193 −3.10051 −0.223180 −0.111590 0.993754i 0.535594π-0.535594\pi
−0.111590 + 0.993754i 0.535594π0.535594\pi
194194 1.59341 + 3.73599i 0.114400 + 0.268229i
195195 2.13261i 0.152720i
196196 0 0
197197 15.6891i 1.11780i 0.829233 + 0.558902i 0.188777π0.188777\pi
−0.829233 + 0.558902i 0.811223π0.811223\pi
198198 5.76873 2.46038i 0.409966 0.174852i
199199 −11.8258 −0.838309 −0.419154 0.907915i 0.637673π-0.637673\pi
−0.419154 + 0.907915i 0.637673π0.637673\pi
200200 −5.20336 + 13.7668i −0.367933 + 0.973459i
201201 4.82647i 0.340433i
202202 8.85377 3.77616i 0.622949 0.265690i
203203 0 0
204204 2.67984 2.79420i 0.187627 0.195633i
205205 13.4699i 0.940778i
206206 18.2760 7.79479i 1.27335 0.543089i
207207 12.2461i 0.851166i
208208 −0.231924 5.54838i −0.0160810 0.384711i
209209 8.45124i 0.584585i
210210 0 0
211211 10.0726 0.693427 0.346713 0.937971i 0.387298π-0.387298\pi
0.346713 + 0.937971i 0.387298π0.387298\pi
212212 10.2257 + 9.80720i 0.702304 + 0.673561i
213213 2.54469 0.174359
214214 6.68521 2.85126i 0.456991 0.194908i
215215 0 0
216216 −7.33982 2.77419i −0.499411 0.188760i
217217 0 0
218218 1.57074 + 3.68283i 0.106384 + 0.249433i
219219 5.16706 0.349157
220220 −7.08269 + 7.38494i −0.477515 + 0.497892i
221221 5.58840i 0.375917i
222222 3.34512 1.42670i 0.224510 0.0957540i
223223 24.3086 1.62783 0.813913 0.580987i 0.197333π-0.197333\pi
0.813913 + 0.580987i 0.197333π0.197333\pi
224224 0 0
225225 14.4067 0.960448
226226 1.86925 0.797240i 0.124341 0.0530316i
227227 14.3239i 0.950710i 0.879794 + 0.475355i 0.157680π0.157680\pi
−0.879794 + 0.475355i 0.842320π0.842320\pi
228228 3.51279 3.66269i 0.232640 0.242568i
229229 −10.6500 −0.703775 −0.351887 0.936042i 0.614460π-0.614460\pi
−0.351887 + 0.936042i 0.614460π0.614460\pi
230230 −7.83855 18.3786i −0.516859 1.21185i
231231 0 0
232232 −13.5096 5.10613i −0.886946 0.335234i
233233 −0.637982 −0.0417956 −0.0208978 0.999782i 0.506652π-0.506652\pi
−0.0208978 + 0.999782i 0.506652π0.506652\pi
234234 −5.00023 + 2.13261i −0.326875 + 0.139413i
235235 32.3146 2.10797
236236 7.31462 + 7.01525i 0.476141 + 0.456654i
237237 5.73896 0.372785
238238 0 0
239239 4.73540i 0.306307i −0.988202 0.153154i 0.951057π-0.951057\pi
0.988202 0.153154i 0.0489430π-0.0489430\pi
240240 6.13915 0.256618i 0.396280 0.0165646i
241241 11.7063i 0.754071i 0.926199 + 0.377036i 0.123057π0.123057\pi
−0.926199 + 0.377036i 0.876943π0.876943\pi
242242 10.9721 4.67963i 0.705313 0.300818i
243243 11.6755i 0.748981i
244244 −11.6653 + 12.1631i −0.746792 + 0.778661i
245245 0 0
246246 −2.63798 + 1.12511i −0.168192 + 0.0717342i
247247 7.32538i 0.466103i
248248 0.115962 0.306806i 0.00736359 0.0194822i
249249 −7.20336 −0.456494
250250 −0.845001 + 0.360395i −0.0534425 + 0.0227934i
251251 11.5631i 0.729858i −0.931035 0.364929i 0.881093π-0.881093\pi
0.931035 0.364929i 0.118907π-0.118907\pi
252252 0 0
253253 7.08425i 0.445383i
254254 −2.73010 6.40113i −0.171302 0.401642i
255255 6.18343 0.387222
256256 −15.9442 + 1.33528i −0.996512 + 0.0834547i
257257 23.5908i 1.47155i −0.677224 0.735777i 0.736817π-0.736817\pi
0.677224 0.735777i 0.263183π-0.263183\pi
258258 0 0
259259 0 0
260260 6.13915 6.40113i 0.380734 0.396981i
261261 14.1375i 0.875091i
262262 2.18873 + 5.13182i 0.135220 + 0.317045i
263263 10.6791i 0.658499i −0.944243 0.329249i 0.893204π-0.893204\pi
0.944243 0.329249i 0.106796π-0.106796\pi
264264 2.03789 + 0.770249i 0.125423 + 0.0474055i
265265 22.6290i 1.39009i
266266 0 0
267267 −0.832945 −0.0509754
268268 −13.8939 + 14.4868i −0.848707 + 0.884924i
269269 −23.3380 −1.42294 −0.711471 0.702716i 0.751971π-0.751971\pi
−0.711471 + 0.702716i 0.751971π0.751971\pi
270270 −4.91647 11.5274i −0.299207 0.701535i
271271 13.6392 0.828523 0.414262 0.910158i 0.364040π-0.364040\pi
0.414262 + 0.910158i 0.364040π0.364040\pi
272272 −16.0873 + 0.672454i −0.975436 + 0.0407735i
273273 0 0
274274 0.133784 0.0570595i 0.00808221 0.00344709i
275275 −8.33411 −0.502566
276276 −2.94459 + 3.07025i −0.177244 + 0.184807i
277277 0.457470i 0.0274867i −0.999906 0.0137433i 0.995625π-0.995625\pi
0.999906 0.0137433i 0.00437478π-0.00437478\pi
278278 8.31046 + 19.4851i 0.498429 + 1.16864i
279279 −0.321068 −0.0192218
280280 0 0
281281 1.43695 0.0857215 0.0428608 0.999081i 0.486353π-0.486353\pi
0.0428608 + 0.999081i 0.486353π0.486353\pi
282282 −2.69916 6.32858i −0.160733 0.376862i
283283 31.2264i 1.85622i −0.372312 0.928108i 0.621435π-0.621435\pi
0.372312 0.928108i 0.378565π-0.378565\pi
284284 −7.63798 7.32538i −0.453231 0.434681i
285285 8.10536 0.480120
286286 2.89257 1.23369i 0.171041 0.0729497i
287287 0 0
288288 6.74083 + 14.1375i 0.397207 + 0.833062i
289289 0.796642 0.0468613
290290 −9.04919 21.2172i −0.531387 1.24592i
291291 1.38114 0.0809639
292292 −15.5091 14.8744i −0.907603 0.870457i
293293 −31.3006 −1.82860 −0.914299 0.405040i 0.867258π-0.867258\pi
−0.914299 + 0.405040i 0.867258π0.867258\pi
294294 0 0
295295 16.1869i 0.942437i
296296 −14.1475 5.34727i −0.822309 0.310804i
297297 4.44336i 0.257830i
298298 6.27293 + 14.7078i 0.363381 + 0.852001i
299299 6.14050i 0.355114i
300300 3.61193 + 3.46410i 0.208535 + 0.200000i
301301 0 0
302302 −8.22268 19.2793i −0.473162 1.10940i
303303 3.27311i 0.188035i
304304 −21.0875 + 0.881465i −1.20945 + 0.0505555i
305305 −26.9163 −1.54122
306306 6.18343 + 14.4980i 0.353483 + 0.828794i
307307 14.7215i 0.840202i −0.907477 0.420101i 0.861995π-0.861995\pi
0.907477 0.420101i 0.138005π-0.138005\pi
308308 0 0
309309 6.75638i 0.384357i
310310 0.481848 0.205510i 0.0273672 0.0116722i
311311 15.5805 0.883490 0.441745 0.897141i 0.354360π-0.354360\pi
0.441745 + 0.897141i 0.354360π0.354360\pi
312312 −1.76640 0.667638i −0.100003 0.0377975i
313313 13.0862i 0.739673i 0.929097 + 0.369837i 0.120586π0.120586\pi
−0.929097 + 0.369837i 0.879414π0.879414\pi
314314 0.960963 0.409854i 0.0542303 0.0231294i
315315 0 0
316316 −17.2257 16.5207i −0.969022 0.929363i
317317 23.5526i 1.32284i 0.750014 + 0.661422i 0.230047π0.230047\pi
−0.750014 + 0.661422i 0.769953π0.769953\pi
318318 4.43173 1.89015i 0.248519 0.105994i
319319 8.17839i 0.457902i
320320 −19.1656 16.9025i −1.07139 0.944878i
321321 2.47142i 0.137941i
322322 0 0
323323 −21.2397 −1.18181
324324 9.65194 10.0638i 0.536219 0.559101i
325325 7.22385 0.400707
326326 11.3232 4.82937i 0.627133 0.267474i
327327 1.36149 0.0752905
328328 11.1568 + 4.21689i 0.616034 + 0.232839i
329329 0 0
330330 1.36505 + 3.20056i 0.0751435 + 0.176185i
331331 33.0554 1.81689 0.908445 0.418004i 0.137270π-0.137270\pi
0.908445 + 0.418004i 0.137270π0.137270\pi
332332 21.6212 + 20.7363i 1.18662 + 1.13805i
333333 14.8052i 0.811318i
334334 −1.80596 + 0.770249i −0.0988179 + 0.0421461i
335335 −32.0587 −1.75155
336336 0 0
337337 −15.5096 −0.844860 −0.422430 0.906396i 0.638823π-0.638823\pi
−0.422430 + 0.906396i 0.638823π0.638823\pi
338338 14.4037 6.14322i 0.783457 0.334147i
339339 0.691033i 0.0375318i
340340 −18.5598 17.8002i −1.00655 0.965352i
341341 0.185734 0.0100580
342342 8.10536 + 19.0042i 0.438288 + 1.02763i
343343 0 0
344344 0 0
345345 −6.79431 −0.365793
346346 −1.26266 + 0.538528i −0.0678809 + 0.0289514i
347347 22.4988 1.20780 0.603900 0.797060i 0.293612π-0.293612\pi
0.603900 + 0.797060i 0.293612π0.293612\pi
348348 −3.39938 + 3.54444i −0.182226 + 0.190002i
349349 −28.4735 −1.52415 −0.762077 0.647486i 0.775820π-0.775820\pi
−0.762077 + 0.647486i 0.775820π0.775820\pi
350350 0 0
351351 3.85142i 0.205574i
352352 −3.89949 8.17839i −0.207843 0.435910i
353353 9.57372i 0.509558i 0.966999 + 0.254779i 0.0820027π0.0820027\pi
−0.966999 + 0.254779i 0.917997π0.917997\pi
354354 3.17009 1.35205i 0.168488 0.0718608i
355355 16.9025i 0.897091i
356356 2.50012 + 2.39779i 0.132506 + 0.127083i
357357 0 0
358358 18.5629 7.91711i 0.981077 0.418432i
359359 3.75538i 0.198201i −0.995077 0.0991006i 0.968403π-0.968403\pi
0.995077 0.0991006i 0.0315966π-0.0315966\pi
360360 −8.84408 + 23.3992i −0.466124 + 1.23325i
361361 −8.84134 −0.465334
362362 −19.9312 + 8.50070i −1.04756 + 0.446787i
363363 4.05622i 0.212896i
364364 0 0
365365 34.3209i 1.79644i
366366 2.24825 + 5.27136i 0.117518 + 0.275538i
367367 16.8260 0.878312 0.439156 0.898411i 0.355278π-0.355278\pi
0.439156 + 0.898411i 0.355278π0.355278\pi
368368 17.6766 0.738887i 0.921457 0.0385172i
369369 11.6755i 0.607800i
370370 −9.47653 22.2191i −0.492661 1.15512i
371371 0 0
372372 −0.0804953 0.0772008i −0.00417349 0.00400268i
373373 12.8580i 0.665763i −0.942969 0.332882i 0.891979π-0.891979\pi
0.942969 0.332882i 0.108021π-0.108021\pi
374374 −3.57704 8.38691i −0.184964 0.433677i
375375 0.312384i 0.0161314i
376376 −10.1164 + 26.7656i −0.521715 + 1.38033i
377377 7.08888i 0.365096i
378378 0 0
379379 25.5822 1.31407 0.657034 0.753861i 0.271811π-0.271811\pi
0.657034 + 0.753861i 0.271811π0.271811\pi
380380 −24.3286 23.3329i −1.24803 1.19695i
381381 −2.36640 −0.121234
382382 1.38740 + 3.25296i 0.0709855 + 0.166436i
383383 −26.9693 −1.37807 −0.689033 0.724730i 0.741964π-0.741964\pi
−0.689033 + 0.724730i 0.741964π0.741964\pi
384384 −1.70937 + 5.16527i −0.0872311 + 0.263589i
385385 0 0
386386 4.03327 1.72020i 0.205288 0.0875560i
387387 0 0
388388 −4.14555 3.97588i −0.210458 0.201845i
389389 31.9902i 1.62197i −0.585070 0.810983i 0.698933π-0.698933\pi
0.585070 0.810983i 0.301067π-0.301067\pi
390390 −1.18320 2.77419i −0.0599137 0.140477i
391391 17.8041 0.900394
392392 0 0
393393 1.89716 0.0956988
394394 −8.70452 20.4091i −0.438528 1.02819i
395395 38.1197i 1.91801i
396396 −6.13915 + 6.40113i −0.308504 + 0.321669i
397397 17.0386 0.855142 0.427571 0.903982i 0.359369π-0.359369\pi
0.427571 + 0.903982i 0.359369π0.359369\pi
398398 15.3835 6.56110i 0.771104 0.328878i
399399 0 0
400400 −0.869248 20.7953i −0.0434624 1.03976i
401401 −5.89716 −0.294490 −0.147245 0.989100i 0.547041π-0.547041\pi
−0.147245 + 0.989100i 0.547041π0.547041\pi
402402 2.67778 + 6.27846i 0.133556 + 0.313141i
403403 −0.160991 −0.00801951
404404 −9.42228 + 9.82436i −0.468776 + 0.488780i
405405 22.2707 1.10664
406406 0 0
407407 8.56461i 0.424532i
408408 −1.93579 + 5.12162i −0.0958359 + 0.253558i
409409 0.239890i 0.0118618i 0.999982 + 0.00593090i 0.00188787π0.00188787\pi
−0.999982 + 0.00593090i 0.998112π0.998112\pi
410410 7.47326 + 17.5222i 0.369078 + 0.865358i
411411 0.0494581i 0.00243959i
412412 −19.4496 + 20.2795i −0.958211 + 0.999101i
413413 0 0
414414 −6.79431 15.9303i −0.333922 0.782930i
415415 47.8466i 2.34870i
416416 3.38000 + 7.08888i 0.165718 + 0.347561i
417417 7.20336 0.352750
418418 −4.68885 10.9937i −0.229339 0.537720i
419419 29.4140i 1.43697i 0.695544 + 0.718484i 0.255163π0.255163\pi
−0.695544 + 0.718484i 0.744837π0.744837\pi
420420 0 0
421421 32.1265i 1.56575i 0.622180 + 0.782874i 0.286247π0.286247\pi
−0.622180 + 0.782874i 0.713753π0.713753\pi
422422 −13.1028 + 5.58840i −0.637836 + 0.272039i
423423 28.0097 1.36188
424424 −18.7432 7.08425i −0.910248 0.344041i
425425 20.9453i 1.01600i
426426 −3.31023 + 1.41182i −0.160381 + 0.0684031i
427427 0 0
428428 −7.11447 + 7.41807i −0.343891 + 0.358566i
429429 1.06934i 0.0516283i
430430 0 0
431431 37.8352i 1.82246i 0.411902 + 0.911228i 0.364865π0.364865\pi
−0.411902 + 0.911228i 0.635135π0.635135\pi
432432 11.0871 0.463443i 0.533427 0.0222974i
433433 25.4835i 1.22466i 0.790602 + 0.612330i 0.209768π0.209768\pi
−0.790602 + 0.612330i 0.790232π0.790232\pi
434434 0 0
435435 −7.84367 −0.376075
436436 −4.08656 3.91931i −0.195711 0.187701i
437437 23.3380 1.11641
438438 −6.72151 + 2.86674i −0.321166 + 0.136978i
439439 23.9607 1.14358 0.571792 0.820399i 0.306248π-0.306248\pi
0.571792 + 0.820399i 0.306248π0.306248\pi
440440 5.11619 13.5362i 0.243905 0.645312i
441441 0 0
442442 3.10051 + 7.26962i 0.147476 + 0.345780i
443443 10.2699 0.487938 0.243969 0.969783i 0.421551π-0.421551\pi
0.243969 + 0.969783i 0.421551π0.421551\pi
444444 −3.55991 + 3.71182i −0.168946 + 0.176155i
445445 5.53264i 0.262272i
446446 −31.6216 + 13.4867i −1.49733 + 0.638615i
447447 5.43726 0.257174
448448 0 0
449449 11.5096 0.543170 0.271585 0.962414i 0.412452π-0.412452\pi
0.271585 + 0.962414i 0.412452π0.412452\pi
450450 −18.7408 + 7.99302i −0.883451 + 0.376795i
451451 6.75411i 0.318039i
452452 −1.98927 + 2.07416i −0.0935675 + 0.0975604i
453453 −7.12726 −0.334868
454454 −7.94707 18.6331i −0.372974 0.874494i
455455 0 0
456456 −2.53747 + 6.71351i −0.118828 + 0.314389i
457457 30.6101 1.43188 0.715939 0.698162i 0.245999π-0.245999\pi
0.715939 + 0.698162i 0.245999π0.245999\pi
458458 13.8540 5.90877i 0.647355 0.276099i
459459 11.1671 0.521233
460460 20.3934 + 19.5587i 0.950847 + 0.911931i
461461 17.3671 0.808866 0.404433 0.914568i 0.367469π-0.367469\pi
0.404433 + 0.914568i 0.367469π0.367469\pi
462462 0 0
463463 21.7288i 1.00983i −0.863171 0.504913i 0.831525π-0.831525\pi
0.863171 0.504913i 0.168475π-0.168475\pi
464464 20.4067 0.853006i 0.947358 0.0395998i
465465 0.178132i 0.00826068i
466466 0.829913 0.353960i 0.0384450 0.0163969i
467467 0.676491i 0.0313043i −0.999877 0.0156521i 0.995018π-0.995018\pi
0.999877 0.0156521i 0.00498243π-0.00498243\pi
468468 5.32130 5.54838i 0.245977 0.256474i
469469 0 0
470470 −42.0361 + 17.9285i −1.93898 + 0.826981i
471471 0.355254i 0.0163692i
472472 −13.4073 5.06748i −0.617120 0.233250i
473473 0 0
474474 −7.46546 + 3.18404i −0.342900 + 0.146248i
475475 27.4555i 1.25974i
476476 0 0
477477 19.6144i 0.898082i
478478 2.62726 + 6.15999i 0.120168 + 0.281751i
479479 −28.7678 −1.31443 −0.657217 0.753701i 0.728267π-0.728267\pi
−0.657217 + 0.753701i 0.728267π0.728267\pi
480480 −7.84367 + 3.73989i −0.358013 + 0.170702i
481481 7.42365i 0.338489i
482482 −6.49482 15.2281i −0.295831 0.693619i
483483 0 0
484484 −11.6766 + 12.1749i −0.530755 + 0.553404i
485485 9.17389i 0.416565i
486486 −6.47768 15.1879i −0.293834 0.688937i
487487 1.83303i 0.0830624i 0.999137 + 0.0415312i 0.0132236π0.0132236\pi
−0.999137 + 0.0415312i 0.986776π0.986776\pi
488488 8.42643 22.2942i 0.381446 1.00921i
489489 4.18601i 0.189298i
490490 0 0
491491 13.4370 0.606401 0.303201 0.952927i 0.401945π-0.401945\pi
0.303201 + 0.952927i 0.401945π0.401945\pi
492492 2.80737 2.92717i 0.126566 0.131967i
493493 20.5539 0.925702
494494 4.06421 + 9.52915i 0.182857 + 0.428737i
495495 −14.1654 −0.636687
496496 0.0193720 + 0.463443i 0.000869830 + 0.0208092i
497497 0 0
498498 9.37041 3.99651i 0.419898 0.179088i
499499 −11.3681 −0.508905 −0.254453 0.967085i 0.581895π-0.581895\pi
−0.254453 + 0.967085i 0.581895π0.581895\pi
500500 0.899259 0.937633i 0.0402161 0.0419322i
501501 0.667638i 0.0298279i
502502 6.41536 + 15.0418i 0.286331 + 0.671347i
503503 −13.2022 −0.588656 −0.294328 0.955704i 0.595096π-0.595096\pi
−0.294328 + 0.955704i 0.595096π0.595096\pi
504504 0 0
505505 −21.7408 −0.967454
506506 3.93043 + 9.21547i 0.174729 + 0.409678i
507507 5.32483i 0.236484i
508508 7.10284 + 6.81215i 0.315138 + 0.302240i
509509 26.4357 1.17174 0.585870 0.810405i 0.300753π-0.300753\pi
0.585870 + 0.810405i 0.300753π0.300753\pi
510510 −8.04365 + 3.43064i −0.356179 + 0.151911i
511511 0 0
512512 20.0000 10.5830i 0.883883 0.467707i
513513 14.6380 0.646283
514514 13.0885 + 30.6878i 0.577307 + 1.35358i
515515 −44.8776 −1.97755
516516 0 0
517517 −16.2033 −0.712619
518518 0 0
519519 0.466786i 0.0204896i
520520 −4.43462 + 11.7329i −0.194471 + 0.514522i
521521 12.0277i 0.526942i 0.964667 + 0.263471i 0.0848674π0.0848674\pi
−0.964667 + 0.263471i 0.915133π0.915133\pi
522522 −7.84367 18.3907i −0.343308 0.804937i
523523 2.80911i 0.122834i 0.998112 + 0.0614168i 0.0195619π0.0195619\pi
−0.998112 + 0.0614168i 0.980438π0.980438\pi
524524 −5.69439 5.46133i −0.248760 0.238579i
525525 0 0
526526 5.92487 + 13.8917i 0.258337 + 0.605708i
527527 0.466786i 0.0203335i
528528 −3.07831 + 0.128674i −0.133966 + 0.00559982i
529529 3.43695 0.149433
530530 −12.5548 29.4367i −0.545347 1.27865i
531531 14.0305i 0.608872i
532532 0 0
533533 5.85434i 0.253580i
534534 1.08353 0.462128i 0.0468888 0.0199982i
535535 −16.4158 −0.709718
536536 10.0363 26.5536i 0.433502 1.14694i
537537 6.86241i 0.296135i
538538 30.3590 12.9482i 1.30887 0.558236i
539539 0 0
540540 12.7911 + 12.2676i 0.550441 + 0.527913i
541541 1.94715i 0.0837144i 0.999124 + 0.0418572i 0.0133275π0.0133275\pi
−0.999124 + 0.0418572i 0.986673π0.986673\pi
542542 −17.7424 + 7.56720i −0.762102 + 0.325039i
543543 7.36825i 0.316202i
544544 20.5539 9.80019i 0.881242 0.420180i
545545 9.04336i 0.387375i
546546 0 0
547547 28.4561 1.21669 0.608347 0.793671i 0.291833π-0.291833\pi
0.608347 + 0.793671i 0.291833π0.291833\pi
548548 −0.142375 + 0.148450i −0.00608195 + 0.00634149i
549549 −23.3305 −0.995723
550550 10.8413 4.62386i 0.462276 0.197162i
551551 26.9425 1.14779
552552 2.12703 5.62760i 0.0905325 0.239526i
553553 0 0
554554 0.253810 + 0.595095i 0.0107833 + 0.0252832i
555555 −8.21408 −0.348668
556556 −21.6212 20.7363i −0.916942 0.879414i
557557 9.19869i 0.389761i −0.980827 0.194881i 0.937568π-0.937568\pi
0.980827 0.194881i 0.0624319π-0.0624319\pi
558558 0.417657 0.178132i 0.0176808 0.00754094i
559559 0 0
560560 0 0
561561 −3.10051 −0.130904
562562 −1.86925 + 0.797240i −0.0788495 + 0.0336295i
563563 27.1970i 1.14622i 0.819480 + 0.573108i 0.194263π0.194263\pi
−0.819480 + 0.573108i 0.805737π0.805737\pi
564564 7.02235 + 6.73495i 0.295694 + 0.283592i
565565 −4.59002 −0.193104
566566 17.3248 + 40.6205i 0.728214 + 1.70741i
567567 0 0
568568 14.0000 + 5.29150i 0.587427 + 0.222027i
569569 −23.5398 −0.986840 −0.493420 0.869791i 0.664253π-0.664253\pi
−0.493420 + 0.869791i 0.664253π0.664253\pi
570570 −10.5438 + 4.49695i −0.441630 + 0.188357i
571571 30.3425 1.26979 0.634897 0.772597i 0.281042π-0.281042\pi
0.634897 + 0.772597i 0.281042π0.281042\pi
572572 −3.07831 + 3.20967i −0.128711 + 0.134203i
573573 1.20257 0.0502382
574574 0 0
575575 23.0145i 0.959772i
576576 −16.6124 14.6508i −0.692184 0.610449i
577577 28.6088i 1.19100i −0.803355 0.595500i 0.796954π-0.796954\pi
0.803355 0.595500i 0.203046π-0.203046\pi
578578 −1.03630 + 0.441986i −0.0431045 + 0.0183842i
579579 1.49104i 0.0619655i
580580 23.5431 + 22.5795i 0.977574 + 0.937564i
581581 0 0
582582 −1.79664 + 0.766273i −0.0744732 + 0.0317630i
583583 11.3467i 0.469932i
584584 28.4274 + 10.7445i 1.17633 + 0.444612i
585585 12.2783 0.507645
586586 40.7170 17.3659i 1.68200 0.717380i
587587 15.2362i 0.628867i −0.949280 0.314433i 0.898186π-0.898186\pi
0.949280 0.314433i 0.101814π-0.101814\pi
588588 0 0
589589 0.611872i 0.0252117i
590590 −8.98068 21.0565i −0.369729 0.866884i
591591 −7.54492 −0.310357
592592 21.3704 0.893289i 0.878319 0.0367139i
593593 21.1234i 0.867435i 0.901049 + 0.433717i 0.142798π0.142798\pi
−0.901049 + 0.433717i 0.857202π0.857202\pi
594594 2.46523 + 5.78010i 0.101150 + 0.237160i
595595 0 0
596596 −16.3202 15.6522i −0.668500 0.641140i
597597 5.68704i 0.232755i
598598 −3.40682 7.98780i −0.139315 0.326645i
599599 33.6936i 1.37668i −0.725387 0.688341i 0.758339π-0.758339\pi
0.725387 0.688341i 0.241661π-0.241661\pi
600600 −6.62046 2.50230i −0.270279 0.102156i
601601 24.3960i 0.995132i −0.867426 0.497566i 0.834227π-0.834227\pi
0.867426 0.497566i 0.165773π-0.165773\pi
602602 0 0
603603 −27.7879 −1.13161
604604 21.3928 + 20.5172i 0.870459 + 0.834834i
605605 −26.9425 −1.09537
606606 1.81596 + 4.25779i 0.0737683 + 0.172961i
607607 −8.17513 −0.331818 −0.165909 0.986141i 0.553056π-0.553056\pi
−0.165909 + 0.986141i 0.553056π0.553056\pi
608608 26.9425 12.8463i 1.09266 0.520985i
609609 0 0
610610 35.0138 14.9335i 1.41767 0.604639i
611611 14.0447 0.568188
612612 −16.0873 15.4289i −0.650291 0.623676i
613613 16.9996i 0.686608i 0.939224 + 0.343304i 0.111546π0.111546\pi
−0.939224 + 0.343304i 0.888454π0.888454\pi
614614 8.16768 + 19.1504i 0.329621 + 0.772845i
615615 6.47768 0.261205
616616 0 0
617617 39.6548 1.59644 0.798221 0.602365i 0.205775π-0.205775\pi
0.798221 + 0.602365i 0.205775π0.205775\pi
618618 3.74852 + 8.78897i 0.150788 + 0.353544i
619619 14.4013i 0.578837i 0.957203 + 0.289419i 0.0934620π0.0934620\pi
−0.957203 + 0.289419i 0.906538π0.906538\pi
620620 −0.512788 + 0.534671i −0.0205941 + 0.0214729i
621621 −12.2703 −0.492389
622622 −20.2677 + 8.64425i −0.812662 + 0.346603i
623623 0 0
624624 2.66822 0.111532i 0.106814 0.00446487i
625625 −23.9419 −0.957674
626626 −7.26036 17.0230i −0.290182 0.680376i
627627 −4.06421 −0.162309
628628 −1.02267 + 1.06631i −0.0408088 + 0.0425503i
629629 21.5246 0.858241
630630 0 0
631631 36.6698i 1.45980i 0.683553 + 0.729900i 0.260434π0.260434\pi
−0.683553 + 0.729900i 0.739566π0.739566\pi
632632 31.5738 + 11.9338i 1.25594 + 0.474700i
633633 4.84393i 0.192529i
634634 −13.0672 30.6381i −0.518967 1.21679i
635635 15.7183i 0.623760i
636636 −4.71629 + 4.91755i −0.187013 + 0.194994i
637637 0 0
638638 4.53747 + 10.6388i 0.179640 + 0.421193i
639639 14.6508i 0.579575i
640640 34.3091 + 11.3541i 1.35619 + 0.448810i
641641 18.2760 0.721857 0.360929 0.932593i 0.382460π-0.382460\pi
0.360929 + 0.932593i 0.382460π0.382460\pi
642642 1.37117 + 3.21492i 0.0541159 + 0.126883i
643643 13.6340i 0.537671i 0.963186 + 0.268836i 0.0866389π0.0866389\pi
−0.963186 + 0.268836i 0.913361π0.913361\pi
644644 0 0
645645 0 0
646646 27.6294 11.7840i 1.08706 0.463636i
647647 −17.4831 −0.687330 −0.343665 0.939092i 0.611668π-0.611668\pi
−0.343665 + 0.939092i 0.611668π0.611668\pi
648648 −6.97209 + 18.4464i −0.273890 + 0.724644i
649649 8.11647i 0.318599i
650650 −9.39708 + 4.00788i −0.368584 + 0.157202i
651651 0 0
652652 −12.0503 + 12.5645i −0.471924 + 0.492063i
653653 9.70520i 0.379794i 0.981804 + 0.189897i 0.0608154π0.0608154\pi
−0.981804 + 0.189897i 0.939185π0.939185\pi
654654 −1.77108 + 0.755370i −0.0692546 + 0.0295373i
655655 12.6014i 0.492378i
656656 −16.8529 + 0.704454i −0.657993 + 0.0275043i
657657 29.7488i 1.16061i
658658 0 0
659659 −28.9465 −1.12760 −0.563798 0.825913i 0.690660π-0.690660\pi
−0.563798 + 0.825913i 0.690660π0.690660\pi
660660 −3.55142 3.40607i −0.138239 0.132581i
661661 −12.8737 −0.500728 −0.250364 0.968152i 0.580550π-0.580550\pi
−0.250364 + 0.968152i 0.580550π0.580550\pi
662662 −42.9998 + 18.3395i −1.67123 + 0.712787i
663663 2.68747 0.104373
664664 −39.6304 14.9789i −1.53796 0.581293i
665665 0 0
666666 −8.21408 19.2591i −0.318289 0.746277i
667667 −22.5845 −0.874475
668668 1.92193 2.00394i 0.0743615 0.0775348i
669669 11.6900i 0.451963i
670670 41.7032 17.7865i 1.61113 0.687154i
671671 13.4964 0.521024
672672 0 0
673673 −23.6548 −0.911825 −0.455912 0.890025i 0.650687π-0.650687\pi
−0.455912 + 0.890025i 0.650687π0.650687\pi
674674 20.1755 8.60489i 0.777129 0.331448i
675675 14.4351i 0.555607i
676676 −15.3286 + 15.9827i −0.589560 + 0.614718i
677677 −3.60448 −0.138531 −0.0692657 0.997598i 0.522066π-0.522066\pi
−0.0692657 + 0.997598i 0.522066π0.522066\pi
678678 0.383393 + 0.898923i 0.0147241 + 0.0345229i
679679 0 0
680680 34.0191 + 12.8580i 1.30457 + 0.493083i
681681 −6.88837 −0.263963
682682 −0.241610 + 0.103047i −0.00925171 + 0.00394588i
683683 −7.61847 −0.291513 −0.145756 0.989321i 0.546562π-0.546562\pi
−0.145756 + 0.989321i 0.546562π0.546562\pi
684684 −21.0875 20.2245i −0.806302 0.773303i
685685 −0.328514 −0.0125519
686686 0 0
687687 5.12162i 0.195402i
688688 0 0
689689 9.83510i 0.374688i
690690 8.83831 3.76957i 0.336469 0.143505i
691691 51.9277i 1.97542i −0.156285 0.987712i 0.549952π-0.549952\pi
0.156285 0.987712i 0.450048π-0.450048\pi
692692 1.34373 1.40108i 0.0510811 0.0532609i
693693 0 0
694694 −29.2674 + 12.4826i −1.11097 + 0.473834i
695695 47.8466i 1.81492i
696696 2.45554 6.49676i 0.0930772 0.246259i
697697 −16.9744 −0.642952
698698 37.0395 15.7975i 1.40197 0.597943i
699699 0.306806i 0.0116045i
700700 0 0
701701 0.741474i 0.0280051i −0.999902 0.0140025i 0.995543π-0.995543\pi
0.999902 0.0140025i 0.00445729π-0.00445729\pi
702702 −2.13682 5.01009i −0.0806489 0.189093i
703703 28.2148 1.06414
704704 9.61007 + 8.47529i 0.362193 + 0.319424i
705705 15.5401i 0.585275i
706706 −5.31161 12.4539i −0.199905 0.468708i
707707 0 0
708708 −3.37364 + 3.51761i −0.126789 + 0.132200i
709709 41.1640i 1.54595i 0.634438 + 0.772974i 0.281232π0.281232\pi
−0.634438 + 0.772974i 0.718768π0.718768\pi
710710 9.37770 + 21.9874i 0.351939 + 0.825173i
711711 33.0414i 1.23915i
712712 −4.58258 1.73205i −0.171739 0.0649113i
713713 0.512901i 0.0192083i
714714 0 0
715715 −7.10284 −0.265631
716716 −19.7548 + 20.5978i −0.738271 + 0.769775i
717717 2.27726 0.0850457
718718 2.08353 + 4.88514i 0.0777566 + 0.182312i
719719 −14.0494 −0.523955 −0.261978 0.965074i 0.584375π-0.584375\pi
−0.261978 + 0.965074i 0.584375π0.584375\pi
720720 −1.47745 35.3455i −0.0550613 1.31725i
721721 0 0
722722 11.5012 4.90528i 0.428029 0.182556i
723723 −5.62959 −0.209367
724724 21.2110 22.1161i 0.788299 0.821938i
725725 26.5690i 0.986750i
726726 2.25044 + 5.27649i 0.0835216 + 0.195829i
727727 13.2022 0.489642 0.244821 0.969568i 0.421271π-0.421271\pi
0.244821 + 0.969568i 0.421271π0.421271\pi
728728 0 0
729729 15.3015 0.566724
730730 19.0417 + 44.6460i 0.704764 + 1.65242i
731731 0 0
732732 −5.84923 5.60984i −0.216194 0.207346i
733733 −49.9594 −1.84529 −0.922646 0.385648i 0.873978π-0.873978\pi
−0.922646 + 0.385648i 0.873978π0.873978\pi
734734 −21.8880 + 9.33529i −0.807900 + 0.344572i
735735 0 0
736736 −22.5845 + 10.7684i −0.832476 + 0.396928i
737737 16.0749 0.592128
738738 6.47768 + 15.1879i 0.238447 + 0.559074i
739739 −36.5435 −1.34428 −0.672138 0.740426i 0.734624π-0.734624\pi
−0.672138 + 0.740426i 0.734624π0.734624\pi
740740 24.6549 + 23.6458i 0.906332 + 0.869239i
741741 3.52278 0.129413
742742 0 0
743743 15.1330i 0.555177i −0.960700 0.277589i 0.910465π-0.910465\pi
0.960700 0.277589i 0.0895352π-0.0895352\pi
744744 0.147543 + 0.0557662i 0.00540920 + 0.00204449i
745745 36.1157i 1.32318i
746746 7.13378 + 16.7262i 0.261186 + 0.612390i
747747 41.4725i 1.51740i
748748 9.30631 + 8.92543i 0.340273 + 0.326346i
749749 0 0
750750 −0.173314 0.406362i −0.00632855 0.0148382i
751751 13.8561i 0.505617i 0.967516 + 0.252808i 0.0813542π0.0813542\pi
−0.967516 + 0.252808i 0.918646π0.918646\pi
752752 −1.69000 40.4304i −0.0616280 1.47435i
753753 5.56071 0.202644
754754 −3.93299 9.22149i −0.143231 0.335827i
755755 47.3412i 1.72292i
756756 0 0
757757 46.6967i 1.69722i −0.529019 0.848610i 0.677440π-0.677440\pi
0.529019 0.848610i 0.322560π-0.322560\pi
758758 −33.2783 + 14.1933i −1.20872 + 0.515524i
759759 3.40682 0.123660
760760 44.5929 + 16.8545i 1.61755 + 0.611378i
761761 47.1001i 1.70738i 0.520783 + 0.853689i 0.325640π0.325640\pi
−0.520783 + 0.853689i 0.674360π0.674360\pi
762762 3.07831 1.31291i 0.111515 0.0475616i
763763 0 0
764764 −3.60957 3.46184i −0.130590 0.125245i
765765 35.6004i 1.28714i
766766 35.0827 14.9629i 1.26759 0.540631i
767767 7.03521i 0.254027i
768768 −0.642135 7.66757i −0.0231711 0.276680i
769769 17.3071i 0.624110i 0.950064 + 0.312055i 0.101017π0.101017\pi
−0.950064 + 0.312055i 0.898983π0.898983\pi
770770 0 0
771771 11.3448 0.408574
772772 −4.29225 + 4.47541i −0.154481 + 0.161074i
773773 27.0778 0.973921 0.486960 0.873424i 0.338106π-0.338106\pi
0.486960 + 0.873424i 0.338106π0.338106\pi
774774 0 0
775775 −0.603391 −0.0216744
776776 7.59856 + 2.87198i 0.272772 + 0.103098i
777777 0 0
778778 17.7485 + 41.6141i 0.636315 + 1.49194i
779779 −22.2504 −0.797203
780780 3.07831 + 2.95232i 0.110221 + 0.105710i
781781 8.47529i 0.303270i
782782 −23.1603 + 9.87795i −0.828211 + 0.353235i
783783 −14.1654 −0.506230
784784 0 0
785785 −2.35969 −0.0842208
786786 −2.46789 + 1.05256i −0.0880269 + 0.0375437i
787787 54.2344i 1.93325i 0.256197 + 0.966624i 0.417530π0.417530\pi
−0.256197 + 0.966624i 0.582470π0.582470\pi
788788 22.6464 + 21.7195i 0.806744 + 0.773726i
789789 5.13557 0.182831
790790 21.1492 + 49.5876i 0.752456 + 1.76425i
791791 0 0
792792 4.43462 11.7329i 0.157578 0.416911i
793793 −11.6985 −0.415424
794794 −22.1645 + 9.45321i −0.786588 + 0.335482i
795795 −10.8823 −0.385956
796796 −16.3713 + 17.0699i −0.580264 + 0.605026i
797797 20.1437 0.713527 0.356763 0.934195i 0.383880π-0.383880\pi
0.356763 + 0.934195i 0.383880π0.383880\pi
798798 0 0
799799 40.7221i 1.44064i
800800 12.6682 + 26.5690i 0.447889 + 0.939358i
801801 4.79559i 0.169444i
802802 7.67125 3.27181i 0.270881 0.115532i
803803 17.2093i 0.607303i
804804 −6.96673 6.68160i −0.245698 0.235642i
805805 0 0
806806 0.209423 0.0893195i 0.00737661 0.00314615i
807807 11.2233i 0.395077i
808808 6.80620 18.0075i 0.239441 0.633502i
809809 34.5543 1.21486 0.607432 0.794372i 0.292200π-0.292200\pi
0.607432 + 0.794372i 0.292200π0.292200\pi
810810 −28.9707 + 12.3561i −1.01793 + 0.434148i
811811 13.6340i 0.478754i −0.970927 0.239377i 0.923057π-0.923057\pi
0.970927 0.239377i 0.0769431π-0.0769431\pi
812812 0 0
813813 6.55911i 0.230038i
814814 4.75175 + 11.1412i 0.166549 + 0.390498i
815815 −27.8046 −0.973953
816816 −0.323384 7.73640i −0.0113207 0.270828i
817817 0 0
818818 −0.133094 0.312058i −0.00465352 0.0109109i
819819 0 0
820820 −19.4430 18.6473i −0.678980 0.651191i
821821 32.0211i 1.11754i −0.829321 0.558772i 0.811273π-0.811273\pi
0.829321 0.558772i 0.188727π-0.188727\pi
822822 0.0274399 + 0.0643370i 0.000957078 + 0.00224401i
823823 30.9921i 1.08032i 0.841564 + 0.540158i 0.181635π0.181635\pi
−0.841564 + 0.540158i 0.818365π0.818365\pi
824824 14.0494 37.1713i 0.489435 1.29492i
825825 4.00788i 0.139537i
826826 0 0
827827 −11.0191 −0.383172 −0.191586 0.981476i 0.561363π-0.561363\pi
−0.191586 + 0.981476i 0.561363π0.561363\pi
828828 17.6766 + 16.9532i 0.614305 + 0.589163i
829829 37.9672 1.31866 0.659328 0.751856i 0.270841π-0.270841\pi
0.659328 + 0.751856i 0.270841π0.270841\pi
830830 −26.5459 62.2407i −0.921420 2.16041i
831831 0.219998 0.00763163
832832 −8.32984 7.34623i −0.288785 0.254685i
833833 0 0
834834 −9.37041 + 3.99651i −0.324471 + 0.138388i
835835 4.43462 0.153466
836836 12.1989 + 11.6996i 0.421907 + 0.404640i
837837 0.321700i 0.0111196i
838838 −16.3192 38.2629i −0.563739 1.32177i
839839 −8.32984 −0.287578 −0.143789 0.989608i 0.545929π-0.545929\pi
−0.143789 + 0.989608i 0.545929π0.545929\pi
840840 0 0
841841 2.92739 0.100945
842842 −17.8242 41.7914i −0.614261 1.44023i
843843 0.691033i 0.0238004i
844844 13.9442 14.5392i 0.479979 0.500461i
845845 −35.3689 −1.21673
846846 −36.4361 + 15.5401i −1.25270 + 0.534280i
847847 0 0
848848 28.3123 1.18346i 0.972247 0.0406402i
849849 15.0168 0.515375
850850 11.6207 + 27.2465i 0.398587 + 0.934546i
851851 −23.6510 −0.810747
852852 3.52278 3.67311i 0.120689 0.125839i
853853 −6.94153 −0.237673 −0.118837 0.992914i 0.537917π-0.537917\pi
−0.118837 + 0.992914i 0.537917π0.537917\pi
854854 0 0
855855 46.6657i 1.59593i
856856 5.13915 13.5969i 0.175652 0.464733i
857857 2.21407i 0.0756313i −0.999285 0.0378156i 0.987960π-0.987960\pi
0.999285 0.0378156i 0.0120400π-0.0120400\pi
858858 0.593283 + 1.39104i 0.0202544 + 0.0474894i
859859 6.07762i 0.207366i 0.994610 + 0.103683i 0.0330627π0.0330627\pi
−0.994610 + 0.103683i 0.966937π0.966937\pi
860860 0 0
861861 0 0
862862 −20.9914 49.2175i −0.714970 1.67635i
863863 8.83054i 0.300595i −0.988641 0.150298i 0.951977π-0.951977\pi
0.988641 0.150298i 0.0480232π-0.0480232\pi
864864 −14.1654 + 6.75411i −0.481916 + 0.229779i
865865 3.10051 0.105421
866866 −14.1386 33.1500i −0.480448 1.12648i
867867 0.383106i 0.0130110i
868868 0 0
869869 19.1141i 0.648400i
870870 10.2034 4.35176i 0.345926 0.147539i
871871 −13.9335 −0.472117
872872 7.49044 + 2.83112i 0.253658 + 0.0958738i
873873 7.95176i 0.269126i
874874 −30.3590 + 12.9482i −1.02691 + 0.437979i
875875 0 0
876876 7.15310 7.45835i 0.241681 0.251994i
877877 11.9002i 0.401842i −0.979607 0.200921i 0.935607π-0.935607\pi
0.979607 0.200921i 0.0643934π-0.0643934\pi
878878 −31.1691 + 13.2937i −1.05191 + 0.448641i
879879 15.0525i 0.507707i
880880 0.854687 + 20.4469i 0.0288115 + 0.689266i
881881 53.9142i 1.81642i −0.418519 0.908208i 0.637451π-0.637451\pi
0.418519 0.908208i 0.362549π-0.362549\pi
882882 0 0
883883 11.1987 0.376866 0.188433 0.982086i 0.439659π-0.439659\pi
0.188433 + 0.982086i 0.439659π0.439659\pi
884884 −8.06654 7.73640i −0.271307 0.260203i
885885 −7.78429 −0.261666
886886 −13.3595 + 5.69786i −0.448821 + 0.191423i
887887 −36.3664 −1.22106 −0.610531 0.791992i 0.709044π-0.709044\pi
−0.610531 + 0.791992i 0.709044π0.709044\pi
888888 2.57151 6.80357i 0.0862941 0.228313i
889889 0 0
890890 −3.06957 7.19707i −0.102892 0.241246i
891891 −11.1671 −0.374110
892892 33.6521 35.0881i 1.12675 1.17484i
893893 53.3792i 1.78627i
894894 −7.07301 + 3.01666i −0.236557 + 0.100892i
895895 −45.5819 −1.52364
896896 0 0
897897 −2.95297 −0.0985968
898898 −14.9721 + 6.38564i −0.499625 + 0.213092i
899899 0.592117i 0.0197482i
900900 19.9442 20.7953i 0.664806 0.693176i
901901 28.5165 0.950022
902902 −3.74726 8.78601i −0.124770 0.292542i
903903 0 0
904904 1.43695 3.80183i 0.0477924 0.126447i
905905 48.9419 1.62688
906906 9.27143 3.95429i 0.308023 0.131373i
907907 −17.8474 −0.592613 −0.296307 0.955093i 0.595755π-0.595755\pi
−0.296307 + 0.955093i 0.595755π0.595755\pi
908908 20.6757 + 19.8295i 0.686148 + 0.658066i
909909 −18.8446 −0.625034
910910 0 0
911911 11.1458i 0.369278i 0.982806 + 0.184639i 0.0591116π0.0591116\pi
−0.982806 + 0.184639i 0.940888π0.940888\pi
912912 −0.423897 10.1410i −0.0140366 0.335803i
913913 23.9914i 0.793998i
914914 −39.8188 + 16.9828i −1.31709 + 0.561742i
915915 12.9441i 0.427918i
916916 −14.7436 + 15.3727i −0.487141 + 0.507929i
917917 0 0
918918 −14.5265 + 6.19562i −0.479448 + 0.204486i
919919 32.6552i 1.07720i 0.842563 + 0.538598i 0.181046π0.181046\pi
−0.842563 + 0.538598i 0.818954π0.818954\pi
920920 −37.3800 14.1283i −1.23238 0.465796i
921921 7.07960 0.233281
922922 −22.5918 + 9.63548i −0.744022 + 0.317328i
923923 7.34623i 0.241804i
924924 0 0
925925 27.8238i 0.914839i
926926 12.0554 + 28.2657i 0.396166 + 0.928870i
927927 −38.8991 −1.27761
928928 −26.0726 + 12.4315i −0.855875 + 0.408085i
929929 26.9076i 0.882811i −0.897308 0.441406i 0.854480π-0.854480\pi
0.897308 0.441406i 0.145520π-0.145520\pi
930930 0.0988299 + 0.231721i 0.00324076 + 0.00759844i
931931 0 0
932932 −0.883202 + 0.920891i −0.0289302 + 0.0301648i
933933 7.49268i 0.245299i
934934 0.375326 + 0.880007i 0.0122810 + 0.0287947i
935935 20.5944i 0.673510i
936936 −3.84385 + 10.1699i −0.125640 + 0.332413i
937937 32.6476i 1.06655i 0.845942 + 0.533275i 0.179039π0.179039\pi
−0.845942 + 0.533275i 0.820961π0.820961\pi
938938 0 0
939939 −6.29315 −0.205369
940940 44.7353 46.6443i 1.45910 1.52137i
941941 12.6417 0.412109 0.206055 0.978541i 0.433938π-0.433938\pi
0.206055 + 0.978541i 0.433938π0.433938\pi
942942 0.197099 + 0.462128i 0.00642183 + 0.0150569i
943943 18.6514 0.607372
944944 20.2522 0.846548i 0.659154 0.0275528i
945945 0 0
946946 0 0
947947 −42.2541 −1.37307 −0.686537 0.727095i 0.740870π-0.740870\pi
−0.686537 + 0.727095i 0.740870π0.740870\pi
948948 7.94483 8.28386i 0.258036 0.269047i
949949 14.9167i 0.484217i
950950 15.2326 + 35.7152i 0.494212 + 1.15875i
951951 −11.3264 −0.367285
952952 0 0
953953 −44.4561 −1.44007 −0.720037 0.693936i 0.755875π-0.755875\pi
−0.720037 + 0.693936i 0.755875π0.755875\pi
954954 −10.8823 25.5152i −0.352328 0.826085i
955955 7.98780i 0.258479i
956956 −6.83528 6.55553i −0.221069 0.212021i
957957 3.93299 0.127136
958958 37.4223 15.9607i 1.20906 0.515668i
959959 0 0
960960 8.12842 9.21676i 0.262344 0.297470i
961961 −30.9866 −0.999566
962962 −4.11873 9.65697i −0.132793 0.311353i
963963 −14.2289 −0.458521
964964 16.8974 + 16.2059i 0.544229 + 0.521956i
965965 −9.90388 −0.318817
966966 0 0
967967 25.7160i 0.826972i 0.910510 + 0.413486i 0.135689π0.135689\pi
−0.910510 + 0.413486i 0.864311π0.864311\pi
968968 8.43462 22.3159i 0.271099 0.717261i
969969 10.2142i 0.328127i
970970 5.08979 + 11.9338i 0.163423 + 0.383170i
971971 46.5051i 1.49242i −0.665711 0.746210i 0.731871π-0.731871\pi
0.665711 0.746210i 0.268129π-0.268129\pi
972972 16.8529 + 16.1631i 0.540556 + 0.518432i
973973 0 0
974974 −1.01699 2.38448i −0.0325863 0.0764035i
975975 3.47396i 0.111256i
976976 1.40768 + 33.6763i 0.0450587 + 1.07795i
977977 34.2695 1.09638 0.548189 0.836354i 0.315317π-0.315317\pi
0.548189 + 0.836354i 0.315317π0.315317\pi
978978 2.32245 + 5.44533i 0.0742638 + 0.174123i
979979 2.77419i 0.0886635i
980980 0 0
981981 7.83862i 0.250268i
982982 −17.4793 + 7.45498i −0.557788 + 0.237898i
983983 1.55467 0.0495862 0.0247931 0.999693i 0.492107π-0.492107\pi
0.0247931 + 0.999693i 0.492107π0.492107\pi
984984 −2.02791 + 5.36534i −0.0646473 + 0.171041i
985985 50.1153i 1.59681i
986986 −26.7374 + 11.4036i −0.851491 + 0.363163i
987987 0 0
988988 −10.5738 10.1410i −0.336396 0.322629i
989989 0 0
990990 18.4269 7.85913i 0.585645 0.249779i
991991 26.1519i 0.830741i −0.909652 0.415371i 0.863652π-0.863652\pi
0.909652 0.415371i 0.136348π-0.136348\pi
992992 −0.282324 0.592117i −0.00896378 0.0187997i
993993 15.8964i 0.504457i
994994 0 0
995995 −37.7748 −1.19754
996996 −9.97209 + 10.3976i −0.315978 + 0.329462i
997997 −36.2933 −1.14942 −0.574711 0.818356i 0.694886π-0.694886\pi
−0.574711 + 0.818356i 0.694886π0.694886\pi
998998 14.7881 6.30715i 0.468108 0.199649i
999999 −14.8343 −0.469338
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 392.2.e.e.195.4 12
4.3 odd 2 1568.2.e.e.783.6 12
7.2 even 3 56.2.m.a.3.6 yes 12
7.3 odd 6 56.2.m.a.19.3 yes 12
7.4 even 3 392.2.m.g.19.3 12
7.5 odd 6 392.2.m.g.227.6 12
7.6 odd 2 inner 392.2.e.e.195.3 12
8.3 odd 2 inner 392.2.e.e.195.2 12
8.5 even 2 1568.2.e.e.783.5 12
21.2 odd 6 504.2.bk.a.451.1 12
21.17 even 6 504.2.bk.a.19.4 12
28.3 even 6 224.2.q.a.47.4 12
28.11 odd 6 1568.2.q.g.1391.3 12
28.19 even 6 1568.2.q.g.815.4 12
28.23 odd 6 224.2.q.a.143.3 12
28.27 even 2 1568.2.e.e.783.7 12
56.3 even 6 56.2.m.a.19.5 yes 12
56.5 odd 6 1568.2.q.g.815.3 12
56.11 odd 6 392.2.m.g.19.5 12
56.13 odd 2 1568.2.e.e.783.8 12
56.19 even 6 392.2.m.g.227.4 12
56.27 even 2 inner 392.2.e.e.195.1 12
56.37 even 6 224.2.q.a.143.4 12
56.45 odd 6 224.2.q.a.47.3 12
56.51 odd 6 56.2.m.a.3.4 12
56.53 even 6 1568.2.q.g.1391.4 12
84.23 even 6 2016.2.bs.a.1711.6 12
84.59 odd 6 2016.2.bs.a.271.1 12
168.59 odd 6 504.2.bk.a.19.2 12
168.101 even 6 2016.2.bs.a.271.6 12
168.107 even 6 504.2.bk.a.451.3 12
168.149 odd 6 2016.2.bs.a.1711.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.m.a.3.4 12 56.51 odd 6
56.2.m.a.3.6 yes 12 7.2 even 3
56.2.m.a.19.3 yes 12 7.3 odd 6
56.2.m.a.19.5 yes 12 56.3 even 6
224.2.q.a.47.3 12 56.45 odd 6
224.2.q.a.47.4 12 28.3 even 6
224.2.q.a.143.3 12 28.23 odd 6
224.2.q.a.143.4 12 56.37 even 6
392.2.e.e.195.1 12 56.27 even 2 inner
392.2.e.e.195.2 12 8.3 odd 2 inner
392.2.e.e.195.3 12 7.6 odd 2 inner
392.2.e.e.195.4 12 1.1 even 1 trivial
392.2.m.g.19.3 12 7.4 even 3
392.2.m.g.19.5 12 56.11 odd 6
392.2.m.g.227.4 12 56.19 even 6
392.2.m.g.227.6 12 7.5 odd 6
504.2.bk.a.19.2 12 168.59 odd 6
504.2.bk.a.19.4 12 21.17 even 6
504.2.bk.a.451.1 12 21.2 odd 6
504.2.bk.a.451.3 12 168.107 even 6
1568.2.e.e.783.5 12 8.5 even 2
1568.2.e.e.783.6 12 4.3 odd 2
1568.2.e.e.783.7 12 28.27 even 2
1568.2.e.e.783.8 12 56.13 odd 2
1568.2.q.g.815.3 12 56.5 odd 6
1568.2.q.g.815.4 12 28.19 even 6
1568.2.q.g.1391.3 12 28.11 odd 6
1568.2.q.g.1391.4 12 56.53 even 6
2016.2.bs.a.271.1 12 84.59 odd 6
2016.2.bs.a.271.6 12 168.101 even 6
2016.2.bs.a.1711.1 12 168.149 odd 6
2016.2.bs.a.1711.6 12 84.23 even 6