LMFDB - Embedded newform 33.8.d.b.32.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,8,Mod(32,33)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("33.32");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.d (of order $2$, degree $1$, 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:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			32.20
Character	$\chi$	$=$	33.32
Dual form			33.8.d.b.32.19

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+15.1340 q^{2} +(46.1737 + 7.41559i) q^{3} +101.039 q^{4} +382.367i q^{5} +(698.794 + 112.228i) q^{6} +606.007i q^{7} -408.027 q^{8} +(2077.02 + 684.810i) q^{9} +O(q^{10})$	\(q+15.1340 q^{2} +(46.1737 + 7.41559i) q^{3} +101.039 q^{4} +382.367i q^{5} +(698.794 + 112.228i) q^{6} +606.007i q^{7} -408.027 q^{8} +(2077.02 + 684.810i) q^{9} +5786.75i q^{10} +(2661.25 - 3522.06i) q^{11} +(4665.35 + 749.265i) q^{12} -11997.6i q^{13} +9171.33i q^{14} +(-2835.48 + 17655.3i) q^{15} -19108.1 q^{16} +11561.6 q^{17} +(31433.7 + 10363.9i) q^{18} -39675.5i q^{19} +38634.0i q^{20} +(-4493.90 + 27981.6i) q^{21} +(40275.5 - 53303.0i) q^{22} +65113.4i q^{23} +(-18840.1 - 3025.76i) q^{24} -68079.3 q^{25} -181573. i q^{26} +(90825.3 + 47022.5i) q^{27} +61230.4i q^{28} +106136. q^{29} +(-42912.2 + 267196. i) q^{30} -50369.3 q^{31} -236955. q^{32} +(148998. - 142892. i) q^{33} +174973. q^{34} -231717. q^{35} +(209860. + 69192.6i) q^{36} -487955. q^{37} -600451. i q^{38} +(88969.6 - 553975. i) q^{39} -156016. i q^{40} -386270. q^{41} +(-68010.9 + 423474. i) q^{42} -385905. i q^{43} +(268891. - 355866. i) q^{44} +(-261849. + 794183. i) q^{45} +985428. i q^{46} -578092. i q^{47} +(-882292. - 141698. i) q^{48} +456299. q^{49} -1.03032e6 q^{50} +(533840. + 85735.9i) q^{51} -1.21223e6i q^{52} +424648. i q^{53} +(1.37455e6 + 711641. i) q^{54} +(1.34672e6 + 1.01757e6i) q^{55} -247267. i q^{56} +(294218. - 1.83197e6i) q^{57} +1.60626e6 q^{58} +979885. i q^{59} +(-286494. + 1.78387e6i) q^{60} +3.28548e6i q^{61} -762290. q^{62} +(-415000. + 1.25869e6i) q^{63} -1.14025e6 q^{64} +4.58750e6 q^{65} +(2.25494e6 - 2.16253e6i) q^{66} +990302. q^{67} +1.16817e6 q^{68} +(-482854. + 3.00652e6i) q^{69} -3.50681e6 q^{70} -126653. i q^{71} +(-847480. - 279421. i) q^{72} -1.59343e6i q^{73} -7.38472e6 q^{74} +(-3.14347e6 - 504849. i) q^{75} -4.00878e6i q^{76} +(2.13439e6 + 1.61274e6i) q^{77} +(1.34647e6 - 8.38388e6i) q^{78} -3.65952e6i q^{79} -7.30630e6i q^{80} +(3.84504e6 + 2.84473e6i) q^{81} -5.84583e6 q^{82} -9.71525e6 q^{83} +(-454060. + 2.82723e6i) q^{84} +4.42076e6i q^{85} -5.84031e6i q^{86} +(4.90067e6 + 787058. i) q^{87} +(-1.08586e6 + 1.43710e6i) q^{88} +1.86398e6i q^{89} +(-3.96283e6 + 1.20192e7i) q^{90} +7.27065e6 q^{91} +6.57900e6i q^{92} +(-2.32573e6 - 373518. i) q^{93} -8.74886e6i q^{94} +1.51706e7 q^{95} +(-1.09411e7 - 1.75716e6i) q^{96} +4.20959e6 q^{97} +6.90564e6 q^{98} +(7.93941e6 - 5.49293e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9}+O(q^{10}) $ 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9	$ 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37} - 100296 q^{42} - 1854252 q^{45} + 3172548 q^{48} - 1169304 q^{49} - 4401936 q^{55} - 2920440 q^{58} + 1981452 q^{60} + 14578596 q^{64} + 2895156 q^{66} + 7729200 q^{67} - 4614108 q^{69} - 6924504 q^{70} - 4375800 q^{75} - 26237448 q^{78} + 22367340 q^{81} - 23600232 q^{82} - 25179660 q^{88} + 9380640 q^{91} + 25396908 q^{93} + 72948360 q^{97} + 53650080 q^{99}+O(q^{100}) $ 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	15.1340			1.33767			0.668836	−	0.743410i	$-0.266793\pi$
$2$	15.1340			1.33767			0.668836	+	0.743410i	$0.266793\pi$
$3$	46.1737	+	7.41559i	0.987348	+	0.158570i
$3$	46.1737	+	7.41559i	0.987348	+	0.158570i
$4$	101.039			0.789368
$5$			382.367i			1.36800i	0.729483	+	0.683998i	$0.239761\pi$
$5$			382.367i			1.36800i	−0.729483	+	0.683998i	$0.760239\pi$
$6$	698.794	+	112.228i	1.32075	+	0.212115i
$7$			606.007i			0.667782i	0.942612	+	0.333891i	$0.108362\pi$
$7$			606.007i			0.667782i	−0.942612	+	0.333891i	$0.891638\pi$
$8$	−408.027			−0.281757
$9$	2077.02	+	684.810i	0.949711	+	0.313128i
$10$			5786.75i			1.82993i
$11$	2661.25	−	3522.06i	0.602853	−	0.797852i
$11$	2661.25	−	3522.06i	0.602853	−	0.797852i
$12$	4665.35	+	749.265i	0.779381	+	0.125170i
$13$		−	11997.6i		−	1.51459i	−0.653076	−	0.757293i	$-0.726522\pi$
$13$		−	11997.6i		−	1.51459i	0.653076	−	0.757293i	$-0.273478\pi$
$14$			9171.33i			0.893273i
$15$	−2835.48	+	17655.3i	−0.216924	+	1.35069i
$16$	−19108.1			−1.16627
$17$	11561.6			0.570750			0.285375	−	0.958416i	$-0.407882\pi$
$17$	11561.6			0.570750			0.285375	+	0.958416i	$0.407882\pi$
$18$	31433.7	+	10363.9i	1.27040	+	0.418862i
$19$		−	39675.5i		−	1.32704i	−0.748157	−	0.663522i	$-0.769061\pi$
$19$		−	39675.5i		−	1.32704i	0.748157	−	0.663522i	$-0.230939\pi$
$20$			38634.0i			1.07985i
$21$	−4493.90	+	27981.6i	−0.105890	+	0.659333i
$22$	40275.5	−	53303.0i	0.806420	−	1.06726i
$23$			65113.4i			1.11589i	0.829877	+	0.557947i	$0.188411\pi$
$23$			65113.4i			1.11589i	−0.829877	+	0.557947i	$0.811589\pi$
$24$	−18840.1	−	3025.76i	−0.278192	−	0.0446782i
$25$	−68079.3			−0.871416
$26$		−	181573.i		−	2.02602i
$27$	90825.3	+	47022.5i	0.888042	+	0.459762i
$28$			61230.4i			0.527125i
$29$	106136.			0.808105			0.404052	−	0.914736i	$-0.367601\pi$
$29$	106136.			0.808105			0.404052	+	0.914736i	$0.367601\pi$
$30$	−42912.2	+	267196.i	−0.290173	+	1.80678i
$31$	−50369.3			−0.303668			−0.151834	−	0.988406i	$-0.548518\pi$
$31$	−50369.3			−0.303668			−0.151834	+	0.988406i	$0.548518\pi$
$32$	−236955.			−1.27833
$33$	148998.	−	142892.i	0.721741	−	0.692163i
$34$	174973.			0.763476
$35$	−231717.			−0.913523
$36$	209860.	+	69192.6i	0.749671	+	0.247173i
$37$	−487955.			−1.58370			−0.791851	−	0.610714i	$-0.790882\pi$
$37$	−487955.			−1.58370			−0.791851	+	0.610714i	$0.790882\pi$
$38$		−	600451.i		−	1.77515i
$39$	88969.6	−	553975.i	0.240168	−	1.49542i
$40$		−	156016.i		−	0.385442i
$41$	−386270.			−0.875281			−0.437641	−	0.899150i	$-0.644186\pi$
$41$	−386270.			−0.875281			−0.437641	+	0.899150i	$0.644186\pi$
$42$	−68010.9	+	423474.i	−0.141646	+	0.881971i
$43$		−	385905.i		−	0.740187i	−0.928995	−	0.370093i	$-0.879326\pi$
$43$		−	385905.i		−	0.740187i	0.928995	−	0.370093i	$-0.120674\pi$
$44$	268891.	−	355866.i	0.475873	−	0.629799i
$45$	−261849.	+	794183.i	−0.428358	+	1.29920i
$46$			985428.i			1.49270i
$47$		−	578092.i		−	0.812184i	−0.913832	−	0.406092i	$-0.866891\pi$
$47$		−	578092.i		−	0.812184i	0.913832	−	0.406092i	$-0.133109\pi$
$48$	−882292.	−	141698.i	−1.15151	−	0.184935i
$49$	456299.			0.554068
$50$	−1.03032e6			−1.16567
$51$	533840.	+	85735.9i	0.563528	+	0.0905039i
$52$		−	1.21223e6i		−	1.19557i
$53$			424648.i			0.391799i	0.980624	+	0.195900i	$0.0627627\pi$
$53$			424648.i			0.391799i	−0.980624	+	0.195900i	$0.937237\pi$
$54$	1.37455e6	+	711641.i	1.18791	+	0.615011i
$55$	1.34672e6	+	1.01757e6i	1.09146	+	0.824702i
$56$		−	247267.i		−	0.188152i
$57$	294218.	−	1.83197e6i	0.210430	−	1.31025i
$58$	1.60626e6			1.08098
$59$			979885.i			0.621145i	0.950550	+	0.310572i	$0.100521\pi$
$59$			979885.i			0.621145i	−0.950550	+	0.310572i	$0.899479\pi$
$60$	−286494.	+	1.78387e6i	−0.171232	+	1.06619i
$61$			3.28548e6i			1.85329i	0.375935	+	0.926646i	$0.377321\pi$
$61$			3.28548e6i			1.85329i	−0.375935	+	0.926646i	$0.622679\pi$
$62$	−762290.			−0.406209
$63$	−415000.	+	1.25869e6i	−0.209101	+	0.634200i
$64$	−1.14025e6			−0.543715
$65$	4.58750e6			2.07195
$66$	2.25494e6	−	2.16253e6i	0.965454	−	0.925887i
$67$	990302.			0.402259			0.201130	−	0.979565i	$-0.435539\pi$
$67$	990302.			0.402259			0.201130	+	0.979565i	$0.435539\pi$
$68$	1.16817e6			0.450531
$69$	−482854.	+	3.00652e6i	−0.176947	+	1.10177i
$70$	−3.50681e6			−1.22199
$71$		−	126653.i		−	0.0419963i	−0.999780	−	0.0209981i	$-0.993316\pi$
$71$		−	126653.i		−	0.0419963i	0.999780	−	0.0209981i	$-0.00668440\pi$
$72$	−847480.	−	279421.i	−0.267587	−	0.0882258i
$73$		−	1.59343e6i		−	0.479405i	−0.970846	−	0.239702i	$-0.922950\pi$
$73$		−	1.59343e6i		−	0.479405i	0.970846	−	0.239702i	$-0.0770499\pi$
$74$	−7.38472e6			−2.11847
$75$	−3.14347e6	−	504849.i	−0.860390	−	0.138181i
$76$		−	4.00878e6i		−	1.04753i
$77$	2.13439e6	+	1.61274e6i	0.532791	+	0.402574i
$78$	1.34647e6	−	8.38388e6i	0.321266	−	2.00039i
$79$		−	3.65952e6i		−	0.835082i	−0.908658	−	0.417541i	$-0.862892\pi$
$79$		−	3.65952e6i		−	0.835082i	0.908658	−	0.417541i	$-0.137108\pi$
$80$		−	7.30630e6i		−	1.59545i
$81$	3.84504e6	+	2.84473e6i	0.803902	+	0.594762i
$82$	−5.84583e6			−1.17084
$83$	−9.71525e6			−1.86501			−0.932504	−	0.361161i	$-0.882381\pi$
$83$	−9.71525e6			−1.86501			−0.932504	+	0.361161i	$0.882381\pi$
$84$	−454060.	+	2.82723e6i	−0.0835864	+	0.520456i
$85$			4.42076e6i			0.780784i
$86$		−	5.84031e6i		−	0.990128i
$87$	4.90067e6	+	787058.i	0.797880	+	0.128141i
$88$	−1.08586e6	+	1.43710e6i	−0.169858	+	0.224800i
$89$			1.86398e6i			0.280270i	0.990132	+	0.140135i	$0.0447536\pi$
$89$			1.86398e6i			0.280270i	−0.990132	+	0.140135i	$0.955246\pi$
$90$	−3.96283e6	+	1.20192e7i	−0.573003	+	1.73791i
$91$	7.27065e6			1.01141
$92$			6.57900e6i			0.880850i
$93$	−2.32573e6	−	373518.i	−0.299826	−	0.0481528i
$94$		−	8.74886e6i		−	1.08644i
$95$	1.51706e7			1.81539
$96$	−1.09411e7	−	1.75716e6i	−1.26215	−	0.202704i
$97$	4.20959e6			0.468316			0.234158	−	0.972199i	$-0.424767\pi$
$97$	4.20959e6			0.468316			0.234158	+	0.972199i	$0.424767\pi$
$98$	6.90564e6			0.741161
$99$	7.93941e6	−	5.49293e6i	0.822366	−	0.568959i
$100$	−6.87868e6			−0.687868
$101$	−3.32486e6			−0.321106			−0.160553	−	0.987027i	$-0.551328\pi$
$101$	−3.32486e6			−0.321106			−0.160553	+	0.987027i	$0.551328\pi$
$102$	8.07916e6	+	1.29753e6i	0.753816	+	0.121065i
$103$	5.64268e6			0.508810			0.254405	−	0.967098i	$-0.418120\pi$
$103$	5.64268e6			0.508810			0.254405	+	0.967098i	$0.418120\pi$
$104$			4.89536e6i			0.426745i
$105$	−1.06992e7	−	1.71832e6i	−0.901965	−	0.144858i
$106$			6.42664e6i			0.524099i
$107$	−1.43410e7			−1.13171			−0.565855	−	0.824505i	$-0.691454\pi$
$107$	−1.43410e7			−1.13171			−0.565855	+	0.824505i	$0.691454\pi$
$108$	9.17691e6	+	4.75112e6i	0.700992	+	0.362921i
$109$			5.92621e6i			0.438313i	0.975690	+	0.219157i	$0.0703306\pi$
$109$			5.92621e6i			0.438313i	−0.975690	+	0.219157i	$0.929669\pi$
$110$	2.03813e7	+	1.54000e7i	1.46001	+	1.10318i
$111$	−2.25307e7	−	3.61847e6i	−1.56366	−	0.251128i
$112$		−	1.15796e7i		−	0.778811i
$113$			756050.i			0.0492919i	0.999696	+	0.0246460i	$0.00784585\pi$
$113$			756050.i			0.0492919i	−0.999696	+	0.0246460i	$0.992154\pi$
$114$	4.45270e6	−	2.77250e7i	0.281486	−	1.75269i
$115$	−2.48972e7			−1.52654
$116$	1.07238e7			0.637892
$117$	8.21610e6	−	2.49193e7i	0.474259	−	1.43842i
$118$			1.48296e7i			0.830889i
$119$			7.00639e6i			0.381136i
$120$	1.15695e6	−	7.20384e6i	0.0611196	−	0.380566i
$121$	−5.32264e6	−	1.87462e7i	−0.273136	−	0.961976i
$122$			4.97225e7i			2.47910i
$123$	−1.78355e7	−	2.86442e6i	−0.864207	−	0.138793i
$124$	−5.08927e6			−0.239706
$125$			3.84113e6i			0.175903i
$126$	−6.28062e6	+	1.90490e7i	−0.279709	+	0.848351i
$127$			2.18761e7i			0.947671i	0.880613	+	0.473836i	$0.157131\pi$
$127$			2.18761e7i			0.947671i	−0.880613	+	0.473836i	$0.842869\pi$
$128$	1.30736e7			0.551013
$129$	2.86172e6	−	1.78187e7i	0.117372	−	0.730822i
$130$	6.94273e7			2.77159
$131$	1.71518e7			0.666591			0.333296	−	0.942822i	$-0.391839\pi$
$131$	1.71518e7			0.666591			0.333296	+	0.942822i	$0.391839\pi$
$132$	1.50546e7	−	1.44376e7i	0.569720	−	0.546371i
$133$	2.40437e7			0.886176
$134$	1.49873e7			0.538091
$135$	−1.79799e7	+	3.47286e7i	−0.628953	+	1.21484i
$136$	−4.71744e6			−0.160812
$137$		−	5.26626e7i		−	1.74977i	−0.484332	−	0.874884i	$-0.660937\pi$
$137$		−	5.26626e7i		−	1.74977i	0.484332	−	0.874884i	$-0.339063\pi$
$138$	−7.30753e6	+	4.55008e7i	−0.236698	+	1.47381i
$139$			2.14303e7i			0.676826i	0.940998	+	0.338413i	$0.109890\pi$
$139$			2.14303e7i			0.676826i	−0.940998	+	0.338413i	$0.890110\pi$
$140$	−2.34125e7			−0.721106
$141$	4.28689e6	−	2.66926e7i	0.128788	−	0.801908i
$142$		−	1.91677e6i		−	0.0561773i
$143$	−4.22564e7	−	3.19287e7i	−1.20841	−	0.913073i
$144$	−3.96879e7	−	1.30854e7i	−1.10762	−	0.365190i
$145$			4.05827e7i			1.10548i
$146$		−	2.41150e7i		−	0.641287i
$147$	2.10690e7	+	3.38372e6i	0.547057	+	0.0878586i
$148$	−4.93025e7			−1.25012
$149$	−3.44443e7			−0.853031			−0.426516	−	0.904480i	$-0.640259\pi$
$149$	−3.44443e7			−0.853031			−0.426516	+	0.904480i	$0.640259\pi$
$150$	−4.75735e7	−	7.64040e6i	−1.15092	−	0.184840i
$151$		−	2.84478e7i		−	0.672402i	−0.941790	−	0.336201i	$-0.890858\pi$
$151$		−	2.84478e7i		−	0.672402i	0.941790	−	0.336201i	$-0.109142\pi$
$152$			1.61887e7i			0.373904i
$153$	2.40136e7	+	7.91748e6i	0.542047	+	0.178718i
$154$	3.23020e7	+	2.44072e7i	0.712700	+	0.538513i
$155$		−	1.92595e7i		−	0.415418i
$156$	8.98940e6	−	5.59731e7i	0.189581	−	1.18044i
$157$	−2.23238e7			−0.460384			−0.230192	−	0.973145i	$-0.573935\pi$
$157$	−2.23238e7			−0.460384			−0.230192	+	0.973145i	$0.573935\pi$
$158$		−	5.53833e7i		−	1.11707i
$159$	−3.14902e6	+	1.96076e7i	−0.0621277	+	0.386842i
$160$		−	9.06038e7i		−	1.74875i
$161$	−3.94591e7			−0.745173
$162$	5.81910e7	+	4.30522e7i	1.07536	+	0.795597i
$163$	9.48313e7			1.71512			0.857561	−	0.514382i	$-0.171979\pi$
$163$	9.48313e7			1.71512			0.857561	+	0.514382i	$0.171979\pi$
$164$	−3.90284e7			−0.690919
$165$	5.46370e7	+	5.69719e7i	0.946877	+	0.987340i
$166$	−1.47031e8			−2.49477
$167$	5.58180e7			0.927399			0.463700	−	0.885992i	$-0.346522\pi$
$167$	5.58180e7			0.927399			0.463700	+	0.885992i	$0.346522\pi$
$168$	1.83363e6	−	1.14172e7i	0.0298353	−	0.185771i
$169$	−8.11946e7			−1.29397
$170$			6.69039e7i			1.04443i
$171$	2.71702e7	−	8.24068e7i	0.415534	−	1.26031i
$172$		−	3.89915e7i		−	0.584280i
$173$	1.32874e7			0.195110			0.0975550	−	0.995230i	$-0.468898\pi$
$173$	1.32874e7			0.195110			0.0975550	+	0.995230i	$0.468898\pi$
$174$	7.41669e7	+	1.19114e7i	1.06730	+	0.171411i
$175$		−	4.12566e7i		−	0.581915i
$176$	−5.08515e7	+	6.72999e7i	−0.703088	+	0.930508i
$177$	−7.26643e6	+	4.52449e7i	−0.0984951	+	0.613286i
$178$			2.82095e7i			0.374909i
$179$		−	2.71120e7i		−	0.353326i	−0.984271	−	0.176663i	$-0.943470\pi$
$179$		−	2.71120e7i		−	0.353326i	0.984271	−	0.176663i	$-0.0565302\pi$
$180$	−2.64570e7	+	8.02435e7i	−0.338132	+	1.02555i
$181$	−8.79660e7			−1.10266			−0.551328	−	0.834289i	$-0.685879\pi$
$181$	−8.79660e7			−1.10266			−0.551328	+	0.834289i	$0.685879\pi$
$182$	1.10034e8			1.35294
$183$	−2.43637e7	+	1.51702e8i	−0.293877	+	1.82984i
$184$		−	2.65680e7i		−	0.314410i
$185$		−	1.86578e8i		−	2.16650i
$186$	−3.51978e7	−	5.65284e6i	−0.401070	−	0.0644126i
$187$	3.07683e7	−	4.07205e7i	0.344078	−	0.455374i
$188$		−	5.84099e7i		−	0.641112i
$189$	−2.84960e7	+	5.50408e7i	−0.307021	+	0.593018i
$190$	2.29593e8			2.42840
$191$			1.72566e8i			1.79200i	0.444054	+	0.896000i	$0.353540\pi$
$191$			1.72566e8i			1.79200i	−0.444054	+	0.896000i	$0.646460\pi$
$192$	−5.26497e7	−	8.45565e6i	−0.536836	−	0.0862170i
$193$			1.61614e8i			1.61819i	0.587681	+	0.809093i	$0.300041\pi$
$193$			1.61614e8i			1.61819i	−0.587681	+	0.809093i	$0.699959\pi$
$194$	6.37082e7			0.626454
$195$	2.11822e8	+	3.40190e7i	2.04573	+	0.328549i
$196$	4.61040e7			0.437363
$197$	−2.02825e8			−1.89012			−0.945062	−	0.326892i	$-0.893999\pi$
$197$	−2.02825e8			−1.89012			−0.945062	+	0.326892i	$0.893999\pi$
$198$	1.20155e8	−	8.31302e7i	1.10006	−	0.761080i
$199$	5.49997e7			0.494737			0.247369	−	0.968921i	$-0.420434\pi$
$199$	5.49997e7			0.494737			0.247369	+	0.968921i	$0.420434\pi$
$200$	2.77782e7			0.245527
$201$	4.57259e7	+	7.34368e6i	0.397170	+	0.0637863i
$202$	−5.03185e7			−0.429534
$203$			6.43189e7i			0.539638i
$204$	5.39387e7	+	8.66268e6i	0.444831	+	0.0714408i
$205$		−	1.47697e8i		−	1.19738i
$206$	8.53966e7			0.680621
$207$	−4.45903e7	+	1.35242e8i	−0.349417	+	1.05978i
$208$			2.29252e8i			1.76641i
$209$	−1.39740e8	−	1.05587e8i	−1.05878	−	0.800013i
$210$	−1.61922e8	−	2.60051e7i	−1.20653	−	0.193772i
$211$		−	1.81015e8i		−	1.32656i	−0.748372	−	0.663280i	$-0.769164\pi$
$211$		−	1.81015e8i		−	1.32656i	0.748372	−	0.663280i	$-0.230836\pi$
$212$			4.29060e7i			0.309274i
$213$	939206.	−	5.84803e6i	0.00665935	−	0.0414649i
$214$	−2.17037e8			−1.51386
$215$	1.47557e8			1.01257
$216$	−3.70592e7	−	1.91865e7i	−0.250212	−	0.129541i
$217$		−	3.05241e7i		−	0.202784i
$218$			8.96876e7i			0.586320i
$219$	1.18162e7	−	7.35744e7i	0.0760193	−	0.473339i
$220$	1.36071e8	+	1.02815e8i	0.861563	+	0.650993i
$221$		−	1.38711e8i		−	0.864449i
$222$	−3.40980e8	−	5.47621e7i	−2.09167	−	0.335927i
$223$	2.06351e7			0.124606			0.0623031	−	0.998057i	$-0.480155\pi$
$223$	2.06351e7			0.124606			0.0623031	+	0.998057i	$0.480155\pi$
$224$		−	1.43597e8i		−	0.853642i
$225$	−1.41402e8	−	4.66214e7i	−0.827593	−	0.272864i
$226$			1.14421e7i			0.0659364i
$227$	−1.06944e7			−0.0606829			−0.0303414	−	0.999540i	$-0.509659\pi$
$227$	−1.06944e7			−0.0606829			−0.0303414	+	0.999540i	$0.509659\pi$
$228$	2.97275e7	−	1.85100e8i	0.166106	−	1.03427i
$229$	−9.93165e7			−0.546509			−0.273255	−	0.961942i	$-0.588100\pi$
$229$	−9.93165e7			−0.546509			−0.273255	+	0.961942i	$0.588100\pi$
$230$	−3.76795e8			−2.04201
$231$	8.65934e7	+	9.02938e7i	0.462214	+	0.481966i
$232$	−4.33062e7			−0.227689
$233$	2.80466e8			1.45256			0.726281	−	0.687398i	$-0.241247\pi$
$233$	2.80466e8			1.45256			0.726281	+	0.687398i	$0.241247\pi$
$234$	1.24343e8	−	3.77130e8i	0.634403	−	1.92413i
$235$	2.21043e8			1.11106
$236$			9.90067e7i			0.490312i
$237$	2.71375e7	−	1.68973e8i	0.132419	−	0.824516i
$238$			1.06035e8i			0.509835i
$239$	−9.28076e7			−0.439735			−0.219868	−	0.975530i	$-0.570563\pi$
$239$	−9.28076e7			−0.439735			−0.219868	+	0.975530i	$0.570563\pi$
$240$	5.41806e7	−	3.37359e8i	0.252991	−	1.57526i
$241$		−	9.40748e6i		−	0.0432926i	−0.999766	−	0.0216463i	$-0.993109\pi$
$241$		−	9.40748e6i		−	0.0432926i	0.999766	−	0.0216463i	$-0.00689077\pi$
$242$	−8.05530e7	−	2.83705e8i	−0.365366	−	1.28681i
$243$	1.56444e8	+	1.59865e8i	0.699419	+	0.714712i
$244$			3.31961e8i			1.46293i
$245$			1.74473e8i			0.757963i
$246$	−2.69923e8	−	4.33503e7i	−1.15603	−	0.185660i
$247$	−4.76013e8			−2.00992
$248$	2.05520e7			0.0855606
$249$	−4.48589e8	−	7.20443e7i	−1.84141	−	0.295734i
$250$			5.81317e7i			0.235301i
$251$			4.16559e8i			1.66272i	0.555736	+	0.831359i	$0.312437\pi$
$251$			4.16559e8i			1.66272i	−0.555736	+	0.831359i	$0.687563\pi$
$252$	−4.19312e7	+	1.27177e8i	−0.165058	+	0.500617i
$253$	2.29333e8	+	1.73283e8i	0.890318	+	0.672720i
$254$			3.31074e8i			1.26767i
$255$	−3.27826e7	+	2.04123e8i	−0.123809	+	0.770905i
$256$	3.43809e8			1.28079
$257$		−	3.77472e8i		−	1.38713i	−0.720392	−	0.693567i	$-0.756038\pi$
$257$		−	3.77472e8i		−	1.38713i	0.720392	−	0.693567i	$-0.243962\pi$
$258$	4.33093e7	−	2.69669e8i	0.157005	−	0.977600i
$259$		−	2.95704e8i		−	1.05757i
$260$	4.63516e8			1.63553
$261$	2.20445e8	+	7.26827e7i	0.767466	+	0.253040i
$262$	2.59576e8			0.891681
$263$	4.16350e8			1.41128			0.705641	−	0.708570i	$-0.250659\pi$
$263$	4.16350e8			1.41128			0.705641	+	0.708570i	$0.250659\pi$
$264$	−6.07952e7	+	5.83037e7i	−0.203355	+	0.195021i
$265$	−1.62371e8			−0.535980
$266$	3.63878e8			1.18541
$267$	−1.38225e7	+	8.60668e7i	−0.0444424	+	0.276724i
$268$	1.00059e8			0.317530
$269$			2.30270e8i			0.721279i	0.932705	+	0.360640i	$0.117442\pi$
$269$			2.30270e8i			0.721279i	−0.932705	+	0.360640i	$0.882558\pi$
$270$	−2.72108e8	+	5.25584e8i	−0.841333	+	1.62506i
$271$			1.66406e8i			0.507897i	0.967218	+	0.253948i	$0.0817294\pi$
$271$			1.66406e8i			0.507897i	−0.967218	+	0.253948i	$0.918271\pi$
$272$	−2.20920e8			−0.665646
$273$	3.35713e8	+	5.39162e7i	0.998616	+	0.160380i
$274$		−	7.96998e8i		−	2.34062i
$275$	−1.81176e8	+	2.39780e8i	−0.525336	+	0.695261i
$276$	−4.87872e7	+	3.03776e8i	−0.139677	+	0.869706i
$277$		−	3.84003e8i		−	1.08556i	−0.839873	−	0.542782i	$-0.817371\pi$
$277$		−	3.84003e8i		−	1.08556i	0.839873	−	0.542782i	$-0.182629\pi$
$278$			3.24328e8i			0.905372i
$279$	−1.04618e8	−	3.44934e7i	−0.288397	−	0.0950870i
$280$	9.45468e7			0.257391
$281$	−1.37459e8			−0.369573			−0.184787	−	0.982779i	$-0.559159\pi$
$281$	−1.37459e8			−0.369573			−0.184787	+	0.982779i	$0.559159\pi$
$282$	6.48780e7	−	4.03967e8i	0.172276	−	1.07269i
$283$			2.65986e8i			0.697600i	0.937197	+	0.348800i	$0.113411\pi$
$283$			2.65986e8i			0.697600i	−0.937197	+	0.348800i	$0.886589\pi$
$284$		−	1.27969e7i		−	0.0331505i
$285$	7.00483e8	+	1.12499e8i	1.79242	+	0.287867i
$286$	−6.39510e8	−	4.83211e8i	−1.61646	−	1.22139i
$287$		−	2.34082e8i		−	0.584497i
$288$	−4.92160e8	−	1.62269e8i	−1.21404	−	0.400279i
$289$	−2.76669e8			−0.674245
$290$			6.14180e8i			1.47878i
$291$	1.94372e8	+	3.12166e7i	0.462391	+	0.0742610i
$292$		−	1.60999e8i		−	0.378427i
$293$	−2.48141e8			−0.576318			−0.288159	−	0.957583i	$-0.593043\pi$
$293$	−2.48141e8			−0.576318			−0.288159	+	0.957583i	$0.593043\pi$
$294$	3.18859e8	+	5.12094e7i	0.731784	+	0.117526i
$295$	−3.74675e8			−0.849724
$296$	1.99099e8			0.446219
$297$	4.07325e8	−	1.94753e8i	0.902181	−	0.431357i
$298$	−5.21281e8			−1.14108
$299$	7.81206e8			1.69012
$300$	−3.17614e8	−	5.10095e7i	−0.679164	−	0.109075i
$301$	2.33861e8			0.494283
$302$		−	4.30530e8i		−	0.899453i
$303$	−1.53521e8	−	2.46558e7i	−0.317043	−	0.0509178i
$304$			7.58125e8i			1.54769i
$305$	−1.25626e9			−2.53530
$306$	3.63423e8	+	1.19824e8i	0.725082	+	0.239066i
$307$			5.70569e8i			1.12544i	0.826646	+	0.562722i	$0.190246\pi$
$307$			5.70569e8i			1.12544i	−0.826646	+	0.562722i	$0.809754\pi$
$308$	2.15657e8	+	1.62950e8i	0.420568	+	0.317779i
$309$	2.60543e8	+	4.18438e7i	0.502372	+	0.0806821i
$310$		−	2.91475e8i		−	0.555693i
$311$		−	2.54680e8i		−	0.480102i	−0.970760	−	0.240051i	$-0.922836\pi$
$311$		−	2.54680e8i		−	0.480102i	0.970760	−	0.240051i	$-0.0771641\pi$
$312$	−3.63020e7	+	2.26037e8i	−0.0676690	+	0.421345i
$313$	9.21228e8			1.69809			0.849047	−	0.528317i	$-0.177177\pi$
$313$	9.21228e8			1.69809			0.849047	+	0.528317i	$0.177177\pi$
$314$	−3.37850e8			−0.615843
$315$	−4.81280e8	−	1.58682e8i	−0.867583	−	0.286050i
$316$		−	3.69754e8i		−	0.659187i
$317$		−	8.45935e8i		−	1.49152i	−0.666214	−	0.745761i	$-0.732086\pi$
$317$		−	8.45935e8i		−	1.49152i	0.666214	−	0.745761i	$-0.267914\pi$
$318$	−4.76573e7	+	2.96742e8i	−0.0831065	+	0.517468i
$319$	2.82453e8	−	3.73816e8i	0.487169	−	0.644748i
$320$		−	4.35995e8i		−	0.743800i
$321$	−6.62175e8	−	1.06347e8i	−1.11739	−	0.179455i
$322$	−5.97176e8			−0.996798
$323$		−	4.58712e8i		−	0.757410i
$324$	3.88499e8	+	2.87429e8i	0.634574	+	0.469486i
$325$			8.16791e8i			1.31983i
$326$	1.43518e9			2.29427
$327$	−4.39464e7	+	2.73635e8i	−0.0695034	+	0.432768i
$328$	1.57609e8			0.246616
$329$	3.50328e8			0.542361
$330$	8.26879e8	+	8.62215e8i	1.26661	+	1.32074i
$331$	1.31406e8			0.199167			0.0995834	−	0.995029i	$-0.468249\pi$
$331$	1.31406e8			0.199167			0.0995834	+	0.995029i	$0.468249\pi$
$332$	−9.81620e8			−1.47218
$333$	−1.01349e9	−	3.34156e8i	−1.50406	−	0.495901i
$334$	8.44752e8			1.24056
$335$			3.78659e8i			0.550289i
$336$	8.58699e7	−	5.34675e8i	0.123496	−	0.768957i
$337$		−	8.76185e7i		−	0.124707i	−0.998054	−	0.0623535i	$-0.980139\pi$
$337$		−	8.76185e7i		−	0.124707i	0.998054	−	0.0623535i	$-0.0198606\pi$
$338$	−1.22880e9			−1.73091
$339$	−5.60656e6	+	3.49096e7i	−0.00781623	+	0.0486683i
$340$			4.46670e8i			0.616326i
$341$	−1.34045e8	+	1.77404e8i	−0.183068	+	0.242283i
$342$	4.11195e8	−	1.24715e9i	0.555849	−	1.68588i
$343$			7.75593e8i			1.03778i
$344$			1.57460e8i			0.208553i
$345$	−1.14959e9	−	1.84627e8i	−1.50722	−	0.242063i
$346$	2.01092e8			0.260993
$347$	−8.75736e8			−1.12517			−0.562587	−	0.826738i	$-0.690194\pi$
$347$	−8.75736e8			−1.12517			−0.562587	+	0.826738i	$0.690194\pi$
$348$	4.95159e8	+	7.95236e7i	0.629821	+	0.101151i
$349$		−	3.54252e8i		−	0.446091i	−0.974808	−	0.223046i	$-0.928400\pi$
$349$		−	3.54252e8i		−	0.446091i	0.974808	−	0.223046i	$-0.0715999\pi$
$350$		−	6.24378e8i		−	0.778412i
$351$	5.64159e8	−	1.08969e9i	0.696349	−	1.34502i
$352$	−6.30598e8	+	8.34571e8i	−0.770643	+	1.01991i
$353$		−	3.09997e8i		−	0.375099i	−0.982255	−	0.187549i	$-0.939946\pi$
$353$		−	3.09997e8i		−	0.375099i	0.982255	−	0.187549i	$-0.0600544\pi$
$354$	−1.09970e8	+	6.84738e8i	−0.131754	+	0.820376i
$355$	4.84278e7			0.0574508
$356$			1.88335e8i			0.221236i
$357$	−5.19565e7	+	3.23511e8i	−0.0604368	+	0.376314i
$358$		−	4.10313e8i		−	0.472634i
$359$	3.09686e8			0.353257			0.176629	−	0.984278i	$-0.443481\pi$
$359$	3.09686e8			0.353257			0.176629	+	0.984278i	$0.443481\pi$
$360$	1.06841e8	−	3.24048e8i	0.120693	−	0.366059i
$361$	−6.80277e8			−0.761046
$362$	−1.33128e9			−1.47499
$363$	−1.06752e8	−	9.05051e8i	−0.117139	−	0.993116i
$364$	7.34620e8			0.798377
$365$	6.09274e8			0.655824
$366$	−3.68722e8	+	2.29587e9i	−0.393111	+	2.44773i
$367$	8.64807e8			0.913246			0.456623	−	0.889660i	$-0.349059\pi$
$367$	8.64807e8			0.913246			0.456623	+	0.889660i	$0.349059\pi$
$368$		−	1.24419e9i		−	1.30143i
$369$	−8.02290e8	−	2.64522e8i	−0.831264	−	0.274075i
$370$		−	2.82367e9i		−	2.89807i
$371$	−2.57340e8			−0.261636
$372$	−2.34990e8	−	3.77399e7i	−0.236673	−	0.0380103i
$373$		−	1.14954e9i		−	1.14695i	−0.819224	−	0.573473i	$-0.805596\pi$
$373$		−	1.14954e9i		−	1.14695i	0.819224	−	0.573473i	$-0.194404\pi$
$374$	4.65648e8	−	6.16266e8i	0.460264	−	0.609141i
$375$	−2.84842e7	+	1.77359e8i	−0.0278930	+	0.173678i
$376$			2.35877e8i			0.228838i
$377$		−	1.27337e9i		−	1.22394i
$378$	−4.31259e8	+	8.32989e8i	−0.410693	+	0.793264i
$379$	−5.12297e8			−0.483376			−0.241688	−	0.970354i	$-0.577701\pi$
$379$	−5.12297e8			−0.483376			−0.241688	+	0.970354i	$0.577701\pi$
$380$	1.53282e9			1.43301
$381$	−1.62225e8	+	1.01010e9i	−0.150272	+	0.935681i
$382$			2.61162e9i			2.39711i
$383$			8.66254e8i			0.787861i	0.919140	+	0.393930i	$0.128885\pi$
$383$			8.66254e8i			0.787861i	−0.919140	+	0.393930i	$0.871115\pi$
$384$	6.03658e8	+	9.69488e7i	0.544041	+	0.0873742i
$385$	−6.16657e8	+	8.16121e8i	−0.550721	+	0.728856i
$386$			2.44587e9i			2.16460i
$387$	2.64272e8	−	8.01533e8i	0.231773	−	0.702964i
$388$	4.25334e8			0.369674
$389$			1.29053e9i			1.11159i	0.831319	+	0.555795i	$0.187586\pi$
$389$			1.29053e9i			1.11159i	−0.831319	+	0.555795i	$0.812414\pi$
$390$	3.20572e9	+	5.14845e8i	2.73652	+	0.439491i
$391$			7.52813e8i			0.636896i
$392$	−1.86182e8			−0.156112
$393$	7.91961e8	+	1.27191e8i	0.658157	+	0.105701i
$394$	−3.06956e9			−2.52837
$395$	1.39928e9			1.14239
$396$	8.02191e8	−	5.55000e8i	0.649150	−	0.449118i
$397$	1.65887e9			1.33060			0.665298	−	0.746578i	$-0.268305\pi$
$397$	1.65887e9			1.33060			0.665298	+	0.746578i	$0.268305\pi$
$398$	8.32368e8			0.661796
$399$	1.11018e9	+	1.78298e8i	0.874964	+	0.140521i
$400$	1.30087e9			1.01630
$401$		−	1.24108e8i		−	0.0961160i	−0.998845	−	0.0480580i	$-0.984697\pi$
$401$		−	1.24108e8i		−	0.0961160i	0.998845	−	0.0480580i	$-0.0153032\pi$
$402$	6.92017e8	+	1.11139e8i	0.531283	+	0.0853252i
$403$			6.04312e8i			0.459932i
$404$	−3.35941e8			−0.253471
$405$	−1.08773e9	+	1.47021e9i	−0.813632	+	1.09974i
$406$			9.73404e8i			0.721858i
$407$	−1.29857e9	+	1.71861e9i	−0.954740	+	1.26356i
$408$	−2.17821e8	−	3.49826e7i	−0.158778	−	0.0255001i
$409$		−	8.58759e7i		−	0.0620640i	−0.999518	−	0.0310320i	$-0.990121\pi$
$409$		−	8.58759e7i		−	0.0620640i	0.999518	−	0.0310320i	$-0.00987938\pi$
$410$		−	2.23525e9i		−	1.60170i
$411$	3.90525e8	−	2.43163e9i	0.277461	−	1.72763i
$412$	5.70132e8			0.401638
$413$	−5.93817e8			−0.414789
$414$	−6.74831e8	+	2.04675e9i	−0.467406	+	1.41763i
$415$		−	3.71479e9i		−	2.55132i
$416$			2.84290e9i			1.93613i
$417$	−1.58919e8	+	9.89518e8i	−0.107324	+	0.668263i
$418$	−2.11483e9	−	1.59795e9i	−1.41631	−	1.07016i
$419$		−	7.66377e8i		−	0.508971i	−0.967077	−	0.254486i	$-0.918094\pi$
$419$		−	7.66377e8i		−	0.508971i	0.967077	−	0.254486i	$-0.0819062\pi$
$420$	−1.08104e9	−	1.73617e8i	−0.711982	−	0.114346i
$421$	1.82292e9			1.19064			0.595319	−	0.803489i	$-0.297026\pi$
$421$	1.82292e9			1.19064			0.595319	+	0.803489i	$0.297026\pi$
$422$		−	2.73949e9i		−	1.77450i
$423$	3.95883e8	−	1.20071e9i	0.254317	−	0.771340i
$424$		−	1.73268e8i		−	0.110392i
$425$	−7.87104e8			−0.497360
$426$	1.42140e7	−	8.85043e7i	0.00890804	−	0.0554665i
$427$	−1.99102e9			−1.23759
$428$	−1.44900e9			−0.893335
$429$	−1.71436e9	−	1.78762e9i	−1.04834	−	1.09314i
$430$	2.23314e9			1.35449
$431$	1.49167e9			0.897432			0.448716	−	0.893674i	$-0.351882\pi$
$431$	1.49167e9			0.897432			0.448716	+	0.893674i	$0.351882\pi$
$432$	−1.73550e9	−	8.98512e8i	−1.03569	−	0.536205i
$433$	−1.96513e9			−1.16328			−0.581639	−	0.813447i	$-0.697588\pi$
$433$	−1.96513e9			−1.16328			−0.581639	+	0.813447i	$0.697588\pi$
$434$		−	4.61953e8i		−	0.271259i
$435$	−3.00945e8	+	1.87385e9i	−0.175297	+	1.09150i
$436$			5.98779e8i			0.345990i
$437$	2.58341e9			1.48084
$438$	1.78827e8	−	1.11348e9i	0.101689	−	0.633173i
$439$			8.06558e8i			0.454998i	0.973778	+	0.227499i	$0.0730549\pi$
$439$			8.06558e8i			0.454998i	−0.973778	+	0.227499i	$0.926945\pi$
$440$	−5.49498e8	−	4.15198e8i	−0.307526	−	0.232365i
$441$	9.47740e8	+	3.12478e8i	0.526204	+	0.173494i
$442$		−	2.09926e9i		−	1.15635i
$443$			3.09404e9i			1.69088i	0.534070	+	0.845440i	$0.320662\pi$
$443$			3.09404e9i			1.69088i	−0.534070	+	0.845440i	$0.679338\pi$
$444$	−2.27648e9	−	3.65607e8i	−1.23431	−	0.198232i
$445$	−7.12724e8			−0.383408
$446$	3.12292e8			0.166682
$447$	−1.59042e9	−	2.55425e8i	−0.842239	−	0.135265i
$448$		−	6.91001e8i		−	0.363083i
$449$		−	1.71204e9i		−	0.892588i	−0.894886	−	0.446294i	$-0.852744\pi$
$449$		−	1.71204e9i		−	0.892588i	0.894886	−	0.446294i	$-0.147256\pi$
$450$	−2.13998e9	−	7.05571e8i	−1.10705	−	0.365003i
$451$	−1.02796e9	+	1.36047e9i	−0.527666	+	0.698345i
$452$			7.63906e7i			0.0389095i
$453$	2.10957e8	−	1.31354e9i	0.106623	−	0.663894i
$454$	−1.61850e8			−0.0811739
$455$			2.78005e9i			1.38361i
$456$	−1.20049e8	+	7.47492e8i	−0.0592899	+	0.369173i
$457$		−	2.67186e9i		−	1.30951i	−0.755843	−	0.654753i	$-0.772773\pi$
$457$		−	2.67186e9i		−	1.30951i	0.755843	−	0.654753i	$-0.227227\pi$
$458$	−1.50306e9			−0.731050
$459$	1.05008e9	+	5.43654e8i	0.506850	+	0.262409i
$460$	−2.51559e9			−1.20500
$461$	2.06832e9			0.983251			0.491626	−	0.870807i	$-0.336403\pi$
$461$	2.06832e9			0.983251			0.491626	+	0.870807i	$0.336403\pi$
$462$	1.31051e9	+	1.36651e9i	0.618290	+	0.644712i
$463$	1.09223e9			0.511423			0.255712	−	0.966753i	$-0.417690\pi$
$463$	1.09223e9			0.511423			0.255712	+	0.966753i	$0.417690\pi$
$464$	−2.02805e9			−0.942465
$465$	1.42821e8	−	8.89284e8i	0.0658728	−	0.410162i
$466$	4.24458e9			1.94305
$467$		−	8.98527e8i		−	0.408246i	−0.978945	−	0.204123i	$-0.934566\pi$
$467$		−	8.98527e8i		−	0.408246i	0.978945	−	0.204123i	$-0.0654343\pi$
$468$	8.30148e8	−	2.51782e9i	0.374365	−	1.13544i
$469$			6.00130e8i			0.268621i
$470$	3.34527e9			1.48624
$471$	−1.03077e9	−	1.65544e8i	−0.454559	−	0.0730031i
$472$		−	3.99820e8i		−	0.175012i
$473$	−1.35918e9	−	1.02699e9i	−0.590560	−	0.446224i
$474$	4.10700e8	−	2.55725e9i	0.177133	−	1.10293i
$475$			2.70109e9i			1.15641i
$476$			7.07920e8i			0.300857i
$477$	−2.90803e8	+	8.82001e8i	−0.122683	+	0.372096i
$478$	−1.40455e9			−0.588222
$479$	1.89271e9			0.786883			0.393442	−	0.919350i	$-0.371284\pi$
$479$	1.89271e9			0.786883			0.393442	+	0.919350i	$0.371284\pi$
$480$	6.71881e8	−	4.18351e9i	0.277299	−	1.72662i
$481$			5.85430e9i			2.39865i
$482$		−	1.42373e8i		−	0.0579113i
$483$	−1.82197e9	−	2.92613e8i	−0.735745	−	0.118162i
$484$	−5.37795e8	−	1.89410e9i	−0.215604	−	0.759353i
$485$			1.60961e9i			0.640655i
$486$	2.36763e9	+	2.41940e9i	0.935594	+	0.956050i
$487$	2.99056e9			1.17328			0.586640	−	0.809848i	$-0.300451\pi$
$487$	2.99056e9			1.17328			0.586640	+	0.809848i	$0.300451\pi$
$488$		−	1.34056e9i		−	0.522177i
$489$	4.37871e9	+	7.03230e8i	1.69342	+	0.271967i
$490$			2.64049e9i			1.01391i
$491$	−7.55508e8			−0.288041			−0.144020	−	0.989575i	$-0.546003\pi$
$491$	−7.55508e8			−0.288041			−0.144020	+	0.989575i	$0.546003\pi$
$492$	−1.80208e9	−	2.89419e8i	−0.682177	−	0.109559i
$493$	1.22709e9			0.461225
$494$	−7.20399e9			−2.68862
$495$	2.10031e9	+	3.03577e9i	0.778334	+	1.12499i
$496$	9.62461e8			0.354158
$497$	7.67525e7			0.0280443
$498$	−6.78896e9	−	1.09032e9i	−2.46320	−	0.395596i
$499$	−9.08032e8			−0.327152			−0.163576	−	0.986531i	$-0.552303\pi$
$499$	−9.08032e8			−0.327152			−0.163576	+	0.986531i	$0.552303\pi$
$500$			3.88104e8i			0.138852i
$501$	2.57732e9	+	4.13924e8i	0.915666	+	0.147058i
$502$			6.30422e9i			2.22417i
$503$	3.77001e9			1.32085			0.660427	−	0.750891i	$-0.270375\pi$
$503$	3.77001e9			1.32085			0.660427	+	0.750891i	$0.270375\pi$
$504$	1.69331e8	−	5.13579e8i	0.0589156	−	0.178690i
$505$		−	1.27131e9i		−	0.439272i
$506$	3.47074e9	+	2.62247e9i	1.19095	+	0.899879i
$507$	−3.74906e9	−	6.02106e8i	−1.27760	−	0.205185i
$508$			2.21035e9i			0.748061i
$509$		−	6.07753e8i		−	0.204275i	−0.994770	−	0.102137i	$-0.967432\pi$
$509$		−	6.07753e8i		−	0.204275i	0.994770	−	0.102137i	$-0.0325682\pi$
$510$	−4.96132e8	+	3.08920e9i	−0.165616	+	1.03122i
$511$	9.65628e8			0.320138
$512$	3.52980e9			1.16226
$513$	1.86565e9	−	3.60354e9i	0.610124	−	1.17847i
$514$		−	5.71267e9i		−	1.85553i
$515$			2.15757e9i			0.696050i
$516$	2.89145e8	−	1.80038e9i	0.0926493	−	0.576887i
$517$	−2.03607e9	−	1.53845e9i	−0.648002	−	0.489628i
$518$		−	4.47519e9i		−	1.41468i
$519$	6.13529e8	+	9.85342e7i	0.192641	+	0.0309386i
$520$	−1.87182e9			−0.583785
$521$			4.87416e9i			1.50997i	0.655743	+	0.754984i	$0.272355\pi$
$521$			4.87416e9i			1.50997i	−0.655743	+	0.754984i	$0.727645\pi$
$522$	3.33623e9	+	1.09998e9i	1.02662	+	0.338485i
$523$		−	3.37254e9i		−	1.03086i	−0.856931	−	0.515432i	$-0.827632\pi$
$523$		−	3.37254e9i		−	1.03086i	0.856931	−	0.515432i	$-0.172368\pi$
$524$	1.73300e9			0.526186
$525$	3.05942e8	−	1.90497e9i	0.0922744	−	0.574553i
$526$	6.30106e9			1.88783
$527$	−5.82348e8			−0.173319
$528$	−2.84707e9	+	2.73039e9i	−0.841743	+	0.807246i
$529$	−8.34924e8			−0.245218
$530$	−2.45733e9			−0.716966
$531$	−6.71035e8	+	2.03524e9i	−0.194498	+	0.589908i
$532$	2.42935e9			0.699519
$533$			4.63433e9i			1.32569i
$534$	−2.09190e8	+	1.30254e9i	−0.0594494	+	0.370166i
$535$		−	5.48351e9i		−	1.54817i
$536$	−4.04070e8			−0.113339
$537$	2.01051e8	−	1.25186e9i	0.0560269	−	0.348855i
$538$			3.48491e9i			0.964836i
$539$	1.21433e9	−	1.60711e9i	0.334022	−	0.442064i
$540$	−1.81667e9	+	3.50894e9i	−0.496475	+	0.958955i
$541$		−	4.79936e9i		−	1.30315i	−0.758586	−	0.651573i	$-0.774109\pi$
$541$		−	4.79936e9i		−	1.30315i	0.758586	−	0.651573i	$-0.225891\pi$
$542$			2.51839e9i			0.679400i
$543$	−4.06171e9	−	6.52320e8i	−1.08870	−	0.174848i
$544$	−2.73958e9			−0.729604
$545$	−2.26599e9			−0.599611
$546$	5.08069e9	+	8.15969e8i	1.33582	+	0.214536i
$547$		−	1.48406e8i		−	0.0387699i	−0.999812	−	0.0193850i	$-0.993829\pi$
$547$		−	1.48406e8i		−	0.0387699i	0.999812	−	0.0193850i	$-0.00617081\pi$
$548$		−	5.32098e9i		−	1.38121i
$549$	−2.24993e9	+	6.82399e9i	−0.580317	+	1.76009i
$550$	−2.74193e9	+	3.62883e9i	−0.702727	+	0.930031i
$551$		−	4.21098e9i		−	1.07239i
$552$	1.97018e8	−	1.22674e9i	0.0498561	−	0.310432i
$553$	2.21769e9			0.557652
$554$		−	5.81152e9i		−	1.45213i
$555$	1.38358e9	−	8.61498e9i	0.343542	−	2.13909i
$556$			2.16530e9i			0.534265i
$557$	−4.68987e9			−1.14992			−0.574960	−	0.818182i	$-0.694982\pi$
$557$	−4.68987e9			−1.14992			−0.574960	+	0.818182i	$0.694982\pi$
$558$	−1.58329e9	−	5.22024e8i	−0.385781	−	0.127195i
$559$	−4.62995e9			−1.12108
$560$	4.42767e9			1.06541
$561$	1.72265e9	−	1.65205e9i	0.411934	−	0.395052i
$562$	−2.08031e9			−0.494368
$563$	−4.80760e9			−1.13540			−0.567700	−	0.823236i	$-0.692167\pi$
$563$	−4.80760e9			−1.13540			−0.567700	+	0.823236i	$0.692167\pi$
$564$	4.33144e8	−	2.69700e9i	0.101661	−	0.633000i
$565$	−2.89088e8			−0.0674312
$566$			4.02545e9i			0.933161i
$567$	−1.72392e9	+	2.33012e9i	−0.397171	+	0.536831i
$568$			5.16778e7i			0.0118327i
$569$	−1.05756e9			−0.240665			−0.120333	−	0.992734i	$-0.538396\pi$
$569$	−1.05756e9			−0.240665			−0.120333	+	0.992734i	$0.538396\pi$
$570$	1.06011e10	+	1.70257e9i	2.39768	+	0.385072i
$571$		−	3.25606e9i		−	0.731924i	−0.930630	−	0.365962i	$-0.880740\pi$
$571$		−	3.25606e9i		−	0.731924i	0.930630	−	0.365962i	$-0.119260\pi$
$572$	−4.26955e9	−	3.22605e9i	−0.953884	−	0.720751i
$573$	−1.27968e9	+	7.96800e9i	−0.284158	+	1.76933i
$574$		−	3.54261e9i		−	0.781865i
$575$		−	4.43287e9i		−	0.972407i
$576$	−2.36833e9	−	7.80857e8i	−0.516372	−	0.170252i
$577$	−5.67316e9			−1.22945			−0.614724	−	0.788743i	$-0.710732\pi$
$577$	−5.67316e9			−1.22945			−0.614724	+	0.788743i	$0.710732\pi$
$578$	−4.18712e9			−0.901919
$579$	−1.19846e9	+	7.46231e9i	−0.256596	+	1.59771i
$580$			4.10044e9i			0.872634i
$581$		−	5.88751e9i		−	1.24542i
$582$	2.94164e9	+	4.72434e8i	0.618528	+	0.0993369i
$583$	1.49564e9	+	1.13010e9i	0.312598	+	0.236197i
$584$			6.50162e8i			0.135075i
$585$	9.52831e9	+	3.14157e9i	1.96775	+	0.648785i
$586$	−3.75538e9			−0.770924
$587$		−	3.98491e9i		−	0.813177i	−0.913611	−	0.406588i	$-0.866718\pi$
$587$		−	3.98491e9i		−	0.813177i	0.913611	−	0.406588i	$-0.133282\pi$
$588$	2.12879e9	+	3.41888e8i	0.431830	+	0.0693528i
$589$			1.99843e9i			0.402981i
$590$	−5.67035e9			−1.13665
$591$	−9.36519e9	−	1.50407e9i	−1.86621	−	0.299717i
$592$	9.32389e9			1.84702
$593$	5.04623e9			0.993747			0.496874	−	0.867823i	$-0.334481\pi$
$593$	5.04623e9			0.993747			0.496874	+	0.867823i	$0.334481\pi$
$594$	6.16448e9	−	2.94740e9i	1.20682	−	0.577015i
$595$	−2.67901e9			−0.521393
$596$	−3.48022e9			−0.673356
$597$	2.53954e9	+	4.07855e8i	0.488478	+	0.0784506i
$598$	1.18228e10			2.26082
$599$		−	8.72470e9i		−	1.65866i	−0.558761	−	0.829329i	$-0.688723\pi$
$599$		−	8.72470e9i		−	1.65866i	0.558761	−	0.829329i	$-0.311277\pi$
$600$	1.28262e9	+	2.05992e8i	0.242421	+	0.0389333i
$601$			2.99758e9i			0.563262i	0.959523	+	0.281631i	$0.0908754\pi$
$601$			2.99758e9i			0.563262i	−0.959523	+	0.281631i	$0.909125\pi$
$602$	3.53927e9			0.661189
$603$	2.05688e9	+	6.78169e8i	0.382030	+	0.125959i
$604$		−	2.87434e9i		−	0.530772i
$605$	7.16792e9	−	2.03520e9i	1.31598	−	0.373649i
$606$	−2.32339e9	−	3.73142e8i	−0.424100	−	0.0681113i
$607$			6.36897e8i			0.115587i	0.998329	+	0.0577935i	$0.0184065\pi$
$607$			6.36897e8i			0.115587i	−0.998329	+	0.0577935i	$0.981594\pi$
$608$			9.40133e9i			1.69639i
$609$	−4.76962e8	+	2.96984e9i	−0.0855704	+	0.532810i
$610$	−1.90122e10			−3.39140
$611$	−6.93573e9			−1.23012
$612$	2.42631e9	+	7.99975e8i	0.427875	+	0.141074i
$613$			2.70849e9i			0.474915i	0.971398	+	0.237458i	$0.0763141\pi$
$613$			2.70849e9i			0.474915i	−0.971398	+	0.237458i	$0.923686\pi$
$614$			8.63502e9i			1.50548i
$615$	1.09526e9	−	6.81971e9i	0.189869	−	1.18223i
$616$	−8.70890e8	−	6.58041e8i	−0.150117	−	0.113428i
$617$			1.73717e9i			0.297744i	0.988856	+	0.148872i	$0.0475643\pi$
$617$			1.73717e9i			0.297744i	−0.988856	+	0.148872i	$0.952436\pi$
$618$	3.94308e9	+	6.33266e8i	0.672009	+	0.107926i
$619$	9.10177e9			1.54244			0.771221	−	0.636568i	$-0.219647\pi$
$619$	9.10177e9			1.54244			0.771221	+	0.636568i	$0.219647\pi$
$620$		−	1.94597e9i		−	0.327917i
$621$	−3.06180e9	+	5.91394e9i	−0.513045	+	0.990960i
$622$		−	3.85433e9i		−	0.642219i
$623$	−1.12958e9			−0.187159
$624$	−1.70004e9	+	1.05854e10i	−0.280100	+	1.74406i
$625$	−6.78742e9			−1.11205
$626$	1.39419e10			2.27149
$627$	−5.66931e9	−	5.91158e9i	−0.918530	−	0.957783i
$628$	−2.25558e9			−0.363412
$629$	−5.64152e9			−0.903897
$630$	−7.28371e9	−	2.40150e9i	−1.16054	−	0.382641i
$631$	2.99440e9			0.474468			0.237234	−	0.971453i	$-0.423759\pi$
$631$	2.99440e9			0.474468			0.237234	+	0.971453i	$0.423759\pi$
$632$			1.49318e9i			0.235290i
$633$	1.34234e9	−	8.35814e9i	0.210353	−	1.30978i
$634$		−	1.28024e10i		−	1.99517i
$635$	−8.36471e9			−1.29641
$636$	−3.18174e8	+	1.98113e9i	−0.0490416	+	0.305361i
$637$		−	5.47450e9i		−	0.839183i
$638$	4.27466e9	−	5.65734e9i	0.651672	−	0.862462i
$639$	8.67332e7	−	2.63060e8i	0.0131502	−	0.0398843i
$640$			4.99893e9i			0.753784i
$641$		−	1.55901e7i		−	0.00233801i	−0.999999	−	0.00116900i	$-0.999628\pi$
$641$		−	1.55901e7i		−	0.00233801i	0.999999	−	0.00116900i	$-0.000372106\pi$
$642$	−1.00214e10	−	1.60946e9i	−1.49470	−	0.240053i
$643$	−1.60059e9			−0.237433			−0.118717	−	0.992928i	$-0.537878\pi$
$643$	−1.60059e9			−0.237433			−0.118717	+	0.992928i	$0.537878\pi$
$644$	−3.98692e9			−0.588216
$645$	6.81327e9	+	1.09423e9i	0.999762	+	0.160564i
$646$		−	6.94216e9i		−	1.01317i
$647$			6.36604e9i			0.924068i	0.886862	+	0.462034i	$0.152880\pi$
$647$			6.36604e9i			0.924068i	−0.886862	+	0.462034i	$0.847120\pi$
$648$	−1.56888e9	−	1.16073e9i	−0.226505	−	0.167578i
$649$	3.45121e9	+	2.60772e9i	0.495582	+	0.374459i
$650$			1.23613e10i			1.76550i
$651$	2.26355e8	−	1.40941e9i	0.0321555	−	0.200219i
$652$	9.58167e9			1.35386
$653$		−	4.85301e9i		−	0.682048i	−0.940055	−	0.341024i	$-0.889226\pi$
$653$		−	4.85301e9i		−	0.682048i	0.940055	−	0.341024i	$-0.110774\pi$
$654$	−6.65086e8	+	4.14120e9i	−0.0929728	+	0.578901i
$655$			6.55827e9i			0.911895i
$656$	7.38089e9			1.02081
$657$	1.09120e9	−	3.30958e9i	0.150115	−	0.455296i
$658$	5.30187e9			0.725502
$659$	3.42393e9			0.466044			0.233022	−	0.972472i	$-0.425139\pi$
$659$	3.42393e9			0.466044			0.233022	+	0.972472i	$0.425139\pi$
$660$	5.52048e9	+	5.75639e9i	0.747434	+	0.779375i
$661$	3.67996e9			0.495607			0.247804	−	0.968810i	$-0.420291\pi$
$661$	3.67996e9			0.495607			0.247804	+	0.968810i	$0.420291\pi$
$662$	1.98870e9			0.266420
$663$	1.02863e9	−	6.40482e9i	0.137076	−	0.853512i
$664$	3.96408e9			0.525478
$665$			9.19350e9i			1.21229i
$666$	−1.53382e10	−	5.05714e9i	−2.01194	−	0.663353i
$667$			6.91084e9i			0.901759i
$668$	5.63980e9			0.732059
$669$	9.52798e8	+	1.53021e8i	0.123030	+	0.0197588i
$670$			5.73063e9i			0.736107i
$671$	1.15716e10	+	8.74348e9i	1.47865	+	1.11726i
$672$	1.06485e9	−	6.63038e9i	0.135362	−	0.842842i
$673$			7.41545e9i			0.937745i	0.883266	+	0.468872i	$0.155340\pi$
$673$			7.41545e9i			0.937745i	−0.883266	+	0.468872i	$0.844660\pi$
$674$		−	1.32602e9i		−	0.166817i
$675$	−6.18333e9	−	3.20126e9i	−0.773854	−	0.400644i
$676$	−8.20383e9			−1.02142
$677$	4.64683e9			0.575568			0.287784	−	0.957695i	$-0.407082\pi$
$677$	4.64683e9			0.575568			0.287784	+	0.957695i	$0.407082\pi$
$678$	−8.48498e7	+	5.28323e8i	−0.0104556	+	0.0651022i
$679$			2.55104e9i			0.312733i
$680$		−	1.80379e9i		−	0.219991i
$681$	−4.93800e8	−	7.93054e7i	−0.0599151	−	0.00962250i
$682$	−2.02865e9	+	2.68483e9i	−0.244884	+	0.324095i
$683$		−	7.59585e9i		−	0.912229i	−0.889921	−	0.456115i	$-0.849241\pi$
$683$		−	7.59585e9i		−	0.912229i	0.889921	−	0.456115i	$-0.150759\pi$
$684$	2.74526e9	−	8.32631e9i	0.328010	−	0.994847i
$685$	2.01364e10			2.39368
$686$			1.17379e10i			1.38821i
$687$	−4.58581e9	−	7.36491e8i	−0.539594	−	0.0866600i
$688$			7.37392e9i			0.863255i
$689$	5.09477e9			0.593413
$690$	−1.73980e10	−	2.79416e9i	−2.01617	−	0.323802i
$691$	−2.32902e9			−0.268534			−0.134267	−	0.990945i	$-0.542868\pi$
$691$	−2.32902e9			−0.268534			−0.134267	+	0.990945i	$0.542868\pi$
$692$	1.34255e9			0.154014
$693$	3.32875e9	+	4.81134e9i	0.379940	+	0.549161i
$694$	−1.32534e10			−1.50511
$695$	−8.19425e9			−0.925896
$696$	−1.99961e9	−	3.21141e8i	−0.224808	−	0.0361047i
$697$	−4.46589e9			−0.499566
$698$		−	5.36127e9i		−	0.596724i
$699$	1.29501e10	+	2.07982e9i	1.43418	+	0.230333i
$700$		−	4.16853e9i		−	0.459345i
$701$	−1.17453e10			−1.28781			−0.643903	−	0.765107i	$-0.722686\pi$
$701$	−1.17453e10			−1.28781			−0.643903	+	0.765107i	$0.722686\pi$
$702$	8.53801e9	−	1.64914e10i	0.931486	−	1.79919i
$703$			1.93599e10i			2.10164i
$704$	−3.03450e9	+	4.01604e9i	−0.327780	+	0.433804i
$705$	1.02064e10	+	1.63917e9i	1.09701	+	0.176182i
$706$		−	4.69150e9i		−	0.501759i
$707$		−	2.01489e9i		−	0.214429i
$708$	−7.34193e8	+	4.57150e9i	−0.0777488	+	0.484108i
$709$	−5.57081e9			−0.587025			−0.293512	−	0.955955i	$-0.594824\pi$
$709$	−5.57081e9			−0.587025			−0.293512	+	0.955955i	$0.594824\pi$
$710$	7.32909e8			0.0768503
$711$	2.50608e9	−	7.60089e9i	0.261487	−	0.793087i
$712$		−	7.60555e8i		−	0.0789679i
$713$		−	3.27971e9i		−	0.338862i
$714$	−7.86312e8	+	4.89603e9i	−0.0808447	+	0.503385i
$715$	1.22085e10	−	1.61574e10i	1.24908	−	1.65311i
$716$		−	2.73937e9i		−	0.278904i
$717$	−4.28527e9	−	6.88224e8i	−0.434171	−	0.0697289i
$718$	4.68680e9			0.472543
$719$			1.15940e10i			1.16327i	0.813449	+	0.581636i	$0.197587\pi$
$719$			1.15940e10i			1.16327i	−0.813449	+	0.581636i	$0.802413\pi$
$720$	5.00343e9	−	1.51753e10i	0.499579	−	1.51522i
$721$			3.41951e9i			0.339774i
$722$	−1.02953e10			−1.01803
$723$	6.97620e7	−	4.34378e8i	0.00686491	−	0.0427448i
$724$	−8.88800e9			−0.870401
$725$	−7.22564e9			−0.704195
$726$	−1.61559e9	−	1.36971e10i	−0.156694	−	1.32846i
$727$	−1.47621e10			−1.42488			−0.712441	−	0.701732i	$-0.752411\pi$
$727$	−1.47621e10			−1.42488			−0.712441	+	0.701732i	$0.752411\pi$
$728$	−2.96662e9			−0.284972
$729$	6.03811e9	+	8.54167e9i	0.577238	+	0.816576i
$730$	9.22077e9			0.877278
$731$		−	4.46167e9i		−	0.422461i
$732$	−2.46169e9	+	1.53279e10i	−0.231977	+	1.44442i
$733$			1.52975e9i			0.143469i	0.997424	+	0.0717343i	$0.0228534\pi$
$733$			1.52975e9i			0.143469i	−0.997424	+	0.0717343i	$0.977147\pi$
$734$	1.30880e10			1.22162
$735$	−1.29382e9	+	8.05608e9i	−0.120190	+	0.748373i
$736$		−	1.54290e10i		−	1.42647i
$737$	2.63544e9	−	3.48790e9i	0.242503	−	0.320943i
$738$	−1.21419e10	−	4.00328e9i	−1.11196	−	0.366622i
$739$		−	4.37940e9i		−	0.399171i	−0.979880	−	0.199586i	$-0.936040\pi$
$739$		−	4.37940e9i		−	0.399171i	0.979880	−	0.199586i	$-0.0639596\pi$
$740$		−	1.88516e10i		−	1.71017i
$741$	−2.19793e10	−	3.52992e9i	−1.98449	−	0.318714i
$742$	−3.89459e9			−0.349984
$743$	3.28720e9			0.294012			0.147006	−	0.989136i	$-0.453036\pi$
$743$	3.28720e9			0.294012			0.147006	+	0.989136i	$0.453036\pi$
$744$	9.48963e8	+	1.52406e8i	0.0844781	+	0.0135674i
$745$		−	1.31703e10i		−	1.16694i
$746$		−	1.73972e10i		−	1.53424i
$747$	−2.01787e10	−	6.65310e9i	−1.77122	−	0.583986i
$748$	3.10880e9	−	4.11437e9i	0.271604	−	0.359457i
$749$		−	8.69072e9i		−	0.755735i
$750$	−4.31081e8	+	2.68416e9i	−0.0373117	+	0.232324i
$751$	−1.01289e10			−0.872619			−0.436309	−	0.899797i	$-0.643715\pi$
$751$	−1.01289e10			−0.872619			−0.436309	+	0.899797i	$0.643715\pi$
$752$			1.10462e10i			0.947222i
$753$	−3.08903e9	+	1.92341e10i	−0.263658	+	1.64168i
$754$		−	1.92713e10i		−	1.63724i
$755$	1.08775e10			0.919844
$756$	−2.87921e9	+	5.56127e9i	−0.242352	+	0.468110i
$757$	−8.59174e9			−0.719856			−0.359928	−	0.932980i	$-0.617199\pi$
$757$	−8.59174e9			−0.719856			−0.359928	+	0.932980i	$0.617199\pi$
$758$	−7.75313e9			−0.646598
$759$	9.30416e9	+	9.70176e9i	0.772380	+	0.805386i
$760$	−6.19002e9			−0.511499
$761$	−6.60203e9			−0.543039			−0.271520	−	0.962433i	$-0.587526\pi$
$761$	−6.60203e9			−0.543039			−0.271520	+	0.962433i	$0.587526\pi$
$762$	−2.45511e9	+	1.52869e10i	−0.201015	+	1.25163i
$763$	−3.59133e9			−0.292698
$764$			1.74359e10i			1.41455i
$765$	−3.02738e9	+	9.18200e9i	−0.244485	+	0.741519i
$766$			1.31099e10i			1.05390i
$767$	1.17563e10			0.940777
$768$	1.58749e10	+	2.54955e9i	1.26459	+	0.203095i
$769$		−	7.24411e9i		−	0.574437i	−0.957865	−	0.287219i	$-0.907269\pi$
$769$		−	7.24411e9i		−	0.574437i	0.957865	−	0.287219i	$-0.0927306\pi$
$770$	−9.33251e9	+	1.23512e10i	−0.736684	+	0.974971i
$771$	2.79918e9	−	1.74293e10i	0.219958	−	1.36958i
$772$			1.63293e10i			1.27734i
$773$		−	1.29614e10i		−	1.00931i	−0.863321	−	0.504655i	$-0.831620\pi$
$773$		−	1.29614e10i		−	1.00931i	0.863321	−	0.504655i	$-0.168380\pi$
$774$	3.99950e9	−	1.21304e10i	0.310036	−	0.940335i
$775$	3.42911e9			0.264621
$776$	−1.71763e9			−0.131951
$777$	2.19282e9	−	1.36537e10i	0.167699	−	1.04419i
$778$			1.95309e10i			1.48694i
$779$			1.53255e10i			1.16154i
$780$	2.14023e10	+	3.43725e9i	1.61484	+	0.259346i
$781$	−4.46079e8	−	3.37055e8i	−0.0335068	−	0.0253176i
$782$			1.13931e10i			0.851958i
$783$	9.63979e9	+	4.99076e9i	0.717631	+	0.371536i
$784$	−8.71900e9			−0.646190
$785$		−	8.53589e9i		−	0.629804i
$786$	1.19856e10	+	1.92491e9i	0.880399	+	0.141394i
$787$		−	2.11439e10i		−	1.54623i	−0.634267	−	0.773114i	$-0.718698\pi$
$787$		−	2.11439e10i		−	1.54623i	0.634267	−	0.773114i	$-0.281302\pi$
$788$	−2.04933e10			−1.49200
$789$	1.92244e10	+	3.08748e9i	1.39343	+	0.223787i
$790$	2.11767e10			1.52814
$791$	−4.58171e8			−0.0329162
$792$	−3.23950e9	+	2.24126e9i	−0.231707	+	0.160308i
$793$	3.94179e10			2.80697
$794$	2.51054e10			1.77990
$795$	−7.49728e9	−	1.20408e9i	−0.529199	−	0.0849905i
$796$	5.55712e9			0.390530
$797$			3.51717e8i			0.0246088i	0.999924	+	0.0123044i	$0.00391670\pi$
$797$			3.51717e8i			0.0246088i	−0.999924	+	0.0123044i	$0.996083\pi$
$798$	1.68016e10	+	2.69837e9i	1.17041	+	0.187971i
$799$		−	6.68365e9i		−	0.463553i
$800$	1.61318e10			1.11395
$801$	−1.27647e9	+	3.87152e9i	−0.0877602	+	0.266175i
$802$		−	1.87826e9i		−	0.128572i
$803$	−5.61215e9	−	4.24051e9i	−0.382494	−	0.289011i
$804$	4.62010e9	+	7.41999e8i	0.313513	+	0.0503509i
$805$		−	1.50879e10i		−	1.01939i
$806$			9.14568e9i			0.615238i
$807$	−1.70759e9	+	1.06324e10i	−0.114373	+	0.712154i
$808$	1.35663e9			0.0904737
$809$	−2.78790e9			−0.185122			−0.0925608	−	0.995707i	$-0.529505\pi$
$809$	−2.78790e9			−0.185122			−0.0925608	+	0.995707i	$0.529505\pi$
$810$	−1.64617e10	+	2.22503e10i	−1.08837	+	1.47109i
$811$			2.13556e10i			1.40585i	0.711264	+	0.702925i	$0.248123\pi$
$811$			2.13556e10i			1.40585i	−0.711264	+	0.702925i	$0.751877\pi$
$812$			6.49872e9i			0.425973i
$813$	−1.23400e9	+	7.68356e9i	−0.0805373	+	0.501471i
$814$	−1.96526e10	+	2.60094e10i	−1.27713	+	1.69023i
$815$			3.62603e10i			2.34628i
$816$	−1.02007e10	−	1.63825e9i	−0.657224	−	0.105552i
$817$	−1.53110e10			−0.982261
$818$		−	1.29965e9i		−	0.0830213i
$819$	1.51013e10	+	4.97902e9i	0.960549	+	0.316701i
$820$		−	1.49232e10i		−	0.945175i
$821$	6.51373e8			0.0410798			0.0205399	−	0.999789i	$-0.493461\pi$
$821$	6.51373e8			0.0410798			0.0205399	+	0.999789i	$0.493461\pi$
$822$	5.91021e9	−	3.68003e10i	0.371152	−	2.31100i
$823$	−1.09450e10			−0.684410			−0.342205	−	0.939625i	$-0.611174\pi$
$823$	−1.09450e10			−0.684410			−0.342205	+	0.939625i	$0.611174\pi$
$824$	−2.30237e9			−0.143361
$825$	−1.01437e10	+	9.72797e9i	−0.628937	+	0.603161i
$826$	−8.98685e9			−0.554852
$827$	5.95619e9			0.366184			0.183092	−	0.983096i	$-0.441389\pi$
$827$	5.95619e9			0.366184			0.183092	+	0.983096i	$0.441389\pi$
$828$	−4.50536e9	+	1.36647e10i	−0.275819	+	0.836553i
$829$	−2.22272e8			−0.0135501			−0.00677507	−	0.999977i	$-0.502157\pi$
$829$	−2.22272e8			−0.0135501			−0.00677507	+	0.999977i	$0.502157\pi$
$830$		−	5.62197e10i		−	3.41284i
$831$	2.84761e9	−	1.77308e10i	0.172138	−	1.07183i
$832$			1.36803e10i			0.823503i
$833$	5.27553e9			0.316234
$834$	−2.40508e9	+	1.49754e10i	−0.143565	+	0.893917i
$835$			2.13430e10i			1.26868i
$836$	−1.41192e10	−	1.06684e10i	−0.835771	−	0.631505i
$837$	−4.57480e9	−	2.36849e9i	−0.269670	−	0.139615i
$838$		−	1.15984e10i		−	0.680837i
$839$			2.43099e10i			1.42107i	0.703660	+	0.710537i	$0.251548\pi$
$839$			2.43099e10i			1.42107i	−0.703660	+	0.710537i	$0.748452\pi$
$840$	4.36557e9	+	7.01121e8i	0.254135	+	0.0408146i
$841$	−5.98513e9			−0.346967
$842$	2.75881e10			1.59268
$843$	−6.34698e9	−	1.01934e9i	−0.364897	−	0.0586033i
$844$		−	1.82896e10i		−	1.04714i
$845$		−	3.10461e10i		−	1.77015i
$846$	5.99131e9	−	1.81715e10i	0.340193	−	1.03180i
$847$	1.13603e10	−	3.22556e9i	0.642390	−	0.182395i
$848$		−	8.11422e9i		−	0.456942i
$849$	−1.97245e9	+	1.22816e10i	−0.110619	+	0.688774i
$850$	−1.19121e10			−0.665305
$851$		−	3.17724e10i		−	1.76724i
$852$	9.48965e7	−	5.90879e8i	0.00525668	−	0.0327311i
$853$			2.82318e10i			1.55746i	0.627359	+	0.778730i	$0.284136\pi$
$853$			2.82318e10i			1.55746i	−0.627359	+	0.778730i	$0.715864\pi$
$854$	−3.01322e10			−1.65550
$855$	3.15096e10	+	1.03890e10i	1.72410	+	0.568450i
$856$	5.85150e9			0.318867
$857$	−3.30439e10			−1.79332			−0.896661	−	0.442718i	$-0.854014\pi$
$857$	−3.30439e10			−1.79332			−0.896661	+	0.442718i	$0.854014\pi$
$858$	−2.59452e10	−	2.70540e10i	−1.40234	−	1.46226i
$859$	−9.51468e9			−0.512175			−0.256087	−	0.966654i	$-0.582433\pi$
$859$	−9.51468e9			−0.512175			−0.256087	+	0.966654i	$0.582433\pi$
$860$	1.49091e10			0.799293
$861$	1.73586e9	−	1.08084e10i	0.0926837	−	0.577101i
$862$	2.25749e10			1.20047
$863$			1.54359e10i			0.817512i	0.912644	+	0.408756i	$0.134037\pi$
$863$			1.54359e10i			0.817512i	−0.912644	+	0.408756i	$0.865963\pi$
$864$	−2.15215e10	−	1.11422e10i	−1.13521	−	0.587725i
$865$			5.08067e9i			0.266910i
$866$	−2.97403e10			−1.55608
$867$	−1.27748e10	−	2.05166e9i	−0.665714	−	0.106915i
$868$		−	3.08413e9i		−	0.160071i
$869$	−1.28890e10	−	9.73890e9i	−0.666272	−	0.503432i
$870$	−4.55451e9	+	2.83590e10i	−0.234490	+	1.46007i
$871$		−	1.18813e10i		−	0.609256i
$872$		−	2.41806e9i		−	0.123498i
$873$	8.74340e9	+	2.88277e9i	0.444765	+	0.146643i
$874$	3.90974e10			1.98088
$875$	−2.32775e9			−0.117465
$876$	1.19390e9	−	7.43389e9i	0.0600072	−	0.373639i
$877$		−	3.34863e10i		−	1.67636i	−0.545390	−	0.838182i	$-0.683618\pi$
$877$		−	3.34863e10i		−	1.67636i	0.545390	−	0.838182i	$-0.316382\pi$
$878$			1.22065e10i			0.608639i
$879$	−1.14576e10	−	1.84011e9i	−0.569026	−	0.0913868i
$880$	−2.57332e10	−	1.94439e10i	−1.27293	−	0.961822i
$881$			3.25171e9i			0.160213i	0.996786	+	0.0801063i	$0.0255260\pi$
$881$			3.25171e9i			0.160213i	−0.996786	+	0.0801063i	$0.974474\pi$
$882$	1.43431e10	+	4.72905e9i	0.703889	+	0.232078i
$883$	2.98788e10			1.46050			0.730250	−	0.683180i	$-0.239404\pi$
$883$	2.98788e10			1.46050			0.730250	+	0.683180i	$0.239404\pi$
$884$		−	1.40153e10i		−	0.682368i
$885$	−1.73001e10	−	2.77844e9i	−0.838973	−	0.134741i
$886$			4.68253e10i			2.26184i
$887$	3.84104e10			1.84806			0.924030	−	0.382320i	$-0.124875\pi$
$887$	3.84104e10			1.84806			0.924030	+	0.382320i	$0.124875\pi$
$888$	9.19312e9	+	1.47644e9i	0.440573	+	0.0707570i
$889$	−1.32571e10			−0.632837
$890$	−1.07864e10			−0.512875
$891$	2.02519e10	−	5.97192e9i	0.959167	−	0.282841i
$892$	2.08495e9			0.0983601
$893$	−2.29361e10			−1.07780
$894$	−2.40695e10	−	3.86561e9i	−1.12664	−	0.180941i
$895$	1.03667e10			0.483348
$896$			7.92272e9i			0.367956i
$897$	3.60712e10	+	5.79311e9i	1.66873	+	0.268002i
$898$		−	2.59100e10i		−	1.19399i
$899$	−5.34597e9			−0.245396
$900$	−1.42871e10	−	4.71059e9i	−0.653275	−	0.215390i
$901$			4.90960e9i			0.223619i
$902$	−1.55572e10	+	2.05893e10i	−0.705845	+	0.934157i
$903$	1.07982e10	+	1.73422e9i	0.488029	+	0.0783786i
$904$		−	3.08489e8i		−	0.0138883i
$905$		−	3.36353e10i		−	1.50843i
$906$	3.19263e9	−	1.98791e10i	0.142626	−	0.888073i
$907$	4.02910e9			0.179301			0.0896505	−	0.995973i	$-0.471425\pi$
$907$	4.02910e9			0.179301			0.0896505	+	0.995973i	$0.471425\pi$
$908$	−1.08055e9			−0.0479011
$909$	−6.90579e9	−	2.27690e9i	−0.304958	−	0.100547i
$910$			4.20734e10i			1.85082i
$911$			2.56115e10i			1.12233i	0.827704	+	0.561164i	$0.189646\pi$
$911$			2.56115e10i			1.12233i	−0.827704	+	0.561164i	$0.810354\pi$
$912$	−5.62194e9	+	3.50054e10i	−0.245417	+	1.52810i
$913$	−2.58547e10	+	3.42177e10i	−1.12433	+	1.48800i
$914$		−	4.04361e10i		−	1.75169i
$915$	−5.80060e10	−	9.31589e9i	−2.50322	−	0.402023i
$916$	−1.00349e10			−0.431397
$917$			1.03941e10i			0.445137i
$918$	1.58920e10	+	8.22769e9i	0.677999	+	0.351017i
$919$			8.55430e9i			0.363563i	0.983339	+	0.181782i	$0.0581864\pi$
$919$			8.55430e9i			0.363563i	−0.983339	+	0.181782i	$0.941814\pi$
$920$	1.01587e10			0.430112
$921$	−4.23111e9	+	2.63453e10i	−0.178462	+	1.11121i
$922$	3.13020e10			1.31527
$923$	−1.51953e9			−0.0636069
$924$	8.74932e9	+	9.12321e9i	0.364857	+	0.380448i
$925$	3.32196e10			1.38006
$926$	1.65298e10			0.684117
$927$	1.17200e10	+	3.86417e9i	0.483222	+	0.159322i
$928$	−2.51494e10			−1.03302
$929$		−	3.68827e10i		−	1.50927i	−0.656143	−	0.754637i	$-0.727813\pi$
$929$		−	3.68827e10i		−	1.50927i	0.656143	−	0.754637i	$-0.272187\pi$
$930$	2.16146e9	−	1.34585e10i	0.0881163	−	0.548662i
$931$		−	1.81039e10i		−	0.735272i
$932$	2.83380e10			1.14661
$933$	1.88860e9	−	1.17595e10i	0.0761298	−	0.474027i
$934$		−	1.35983e10i		−	0.546099i
$935$	1.55702e10	+	1.17648e10i	0.622950	+	0.470698i
$936$	−3.35239e9	+	1.01678e10i	−0.133626	+	0.405284i
$937$			2.59288e10i			1.02966i	0.857292	+	0.514830i	$0.172145\pi$
$937$			2.59288e10i			1.02966i	−0.857292	+	0.514830i	$0.827855\pi$
$938$			9.08239e9i			0.359327i
$939$	4.25365e10	+	6.83145e9i	1.67661	+	0.269267i
$940$	2.23340e10			0.877039
$941$	−1.62160e10			−0.634426			−0.317213	−	0.948354i	$-0.602747\pi$
$941$	−1.62160e10			−0.634426			−0.317213	+	0.948354i	$0.602747\pi$
$942$	−1.55998e10	−	2.50536e9i	−0.608051	−	0.0976543i
$943$		−	2.51513e10i		−	0.976720i
$944$		−	1.87237e10i		−	0.724420i
$945$	−2.10458e10	−	1.08959e10i	−0.811247	−	0.420003i
$946$	−2.05699e10	−	1.55425e10i	−0.789975	−	0.596902i
$947$		−	2.75380e10i		−	1.05368i	−0.849965	−	0.526839i	$-0.823377\pi$
$947$		−	2.75380e10i		−	1.05368i	0.849965	−	0.526839i	$-0.176623\pi$
$948$	2.74195e9	−	1.70729e10i	0.104527	−	0.650847i
$949$	−1.91174e10			−0.726099
$950$			4.08783e10i			1.54689i
$951$	6.27311e9	−	3.90599e10i	0.236511	−	1.47265i
$952$		−	2.85880e9i		−	0.107388i
$953$	3.49124e10			1.30663			0.653317	−	0.757084i	$-0.273377\pi$
$953$	3.49124e10			1.30663			0.653317	+	0.757084i	$0.273377\pi$
$954$	−4.40103e9	+	1.33482e10i	−0.164110	+	0.497743i
$955$	−6.59834e10			−2.45145
$956$	−9.37720e9			−0.347113
$957$	1.58140e10	−	1.51659e10i	0.583243	−	0.559340i
$958$	2.86444e10			1.05259
$959$	3.19139e10			1.16846
$960$	3.23316e9	−	2.01315e10i	0.117945	−	0.734390i
$961$	−2.49756e10			−0.907785
$962$			8.85992e10i			3.20861i
$963$	−2.97864e10	−	9.82084e9i	−1.07480	−	0.354370i
$964$		−	9.50523e8i		−	0.0341738i
$965$	−6.17958e10			−2.21367
$966$	−2.75738e10	−	4.42842e9i	−0.984186	−	0.158062i
$967$		−	2.14498e10i		−	0.762835i	−0.924403	−	0.381417i	$-0.875436\pi$
$967$		−	2.14498e10i		−	0.762835i	0.924403	−	0.381417i	$-0.124564\pi$
$968$	2.17178e9	+	7.64895e9i	0.0769578	+	0.271043i
$969$	3.40162e9	−	2.11804e10i	0.120103	−	0.747827i
$970$			2.43599e10i			0.856987i
$971$			3.76213e10i			1.31876i	0.751809	+	0.659381i	$0.229181\pi$
$971$			3.76213e10i			1.31876i	−0.751809	+	0.659381i	$0.770819\pi$
$972$	1.58070e10	+	1.61526e10i	0.552099	+	0.564170i
$973$	−1.29869e10			−0.451972
$974$	4.52593e10			1.56946
$975$	−6.05699e9	+	3.77142e10i	−0.209286	+	1.30313i
$976$		−	6.27792e10i		−	2.16143i
$977$			4.62339e10i			1.58610i	0.609159	+	0.793048i	$0.291507\pi$
$977$			4.62339e10i			1.58610i	−0.609159	+	0.793048i	$0.708493\pi$
$978$	6.62676e10	+	1.06427e10i	2.26524	+	0.363803i
$979$	6.56505e9	+	4.96052e9i	0.223614	+	0.168962i
$980$			1.76286e10i			0.598312i
$981$	−4.05833e9	+	1.23089e10i	−0.137248	+	0.416271i
$982$	−1.14339e10			−0.385304
$983$		−	9.79841e8i		−	0.0329017i	−0.999865	−	0.0164508i	$-0.994763\pi$
$983$		−	9.79841e8i		−	0.0329017i	0.999865	−	0.0164508i	$-0.00523670\pi$
$984$	7.27737e9	+	1.16876e9i	0.243496	+	0.0391060i
$985$		−	7.75536e10i		−	2.58568i
$986$	1.85709e10			0.616969
$987$	1.61759e10	+	2.59789e9i	0.535499	+	0.0860023i
$988$	−4.80959e10			−1.58657
$989$	2.51276e10			0.825969
$990$	3.17862e10	+	4.59434e10i	1.04116	+	1.50487i
$991$	2.36532e10			0.772027			0.386014	−	0.922493i	$-0.373852\pi$
$991$	2.36532e10			0.772027			0.386014	+	0.922493i	$0.373852\pi$
$992$	1.19353e10			0.388187
$993$	6.06750e9	+	9.74453e8i	0.196647	+	0.0315819i
$994$	1.16158e9			0.0375141
$995$			2.10301e10i			0.676799i
$996$	−4.53250e10	−	7.27929e9i	−1.45355	−	0.233443i
$997$			1.40793e10i			0.449934i	0.974366	+	0.224967i	$0.0722274\pi$
$997$			1.40793e10i			0.449934i	−0.974366	+	0.224967i	$0.927773\pi$
$998$	−1.37422e10			−0.437622
$999$	−4.43186e10	−	2.29449e10i	−1.40639	−	0.728126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.d.b.32.20	yes	24
3.2	odd	2	inner	33.8.d.b.32.5	✓	24
11.10	odd	2	inner	33.8.d.b.32.6	yes	24
33.32	even	2	inner	33.8.d.b.32.19	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.d.b.32.5	✓	24	3.2	odd	2	inner
33.8.d.b.32.6	yes	24	11.10	odd	2	inner
33.8.d.b.32.19	yes	24	33.32	even	2	inner
33.8.d.b.32.20	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+15.1340 q^{2} +(46.1737 + 7.41559i) q^{3} +101.039 q^{4} +382.367i q^{5} +(698.794 + 112.228i) q^{6} +606.007i q^{7} -408.027 q^{8} +(2077.02 + 684.810i) q^{9} +O(q^{10})\)	\(q+15.1340 q^{2} +(46.1737 + 7.41559i) q^{3} +101.039 q^{4} +382.367i q^{5} +(698.794 + 112.228i) q^{6} +606.007i q^{7} -408.027 q^{8} +(2077.02 + 684.810i) q^{9} +5786.75i q^{10} +(2661.25 - 3522.06i) q^{11} +(4665.35 + 749.265i) q^{12} -11997.6i q^{13} +9171.33i q^{14} +(-2835.48 + 17655.3i) q^{15} -19108.1 q^{16} +11561.6 q^{17} +(31433.7 + 10363.9i) q^{18} -39675.5i q^{19} +38634.0i q^{20} +(-4493.90 + 27981.6i) q^{21} +(40275.5 - 53303.0i) q^{22} +65113.4i q^{23} +(-18840.1 - 3025.76i) q^{24} -68079.3 q^{25} -181573. i q^{26} +(90825.3 + 47022.5i) q^{27} +61230.4i q^{28} +106136. q^{29} +(-42912.2 + 267196. i) q^{30} -50369.3 q^{31} -236955. q^{32} +(148998. - 142892. i) q^{33} +174973. q^{34} -231717. q^{35} +(209860. + 69192.6i) q^{36} -487955. q^{37} -600451. i q^{38} +(88969.6 - 553975. i) q^{39} -156016. i q^{40} -386270. q^{41} +(-68010.9 + 423474. i) q^{42} -385905. i q^{43} +(268891. - 355866. i) q^{44} +(-261849. + 794183. i) q^{45} +985428. i q^{46} -578092. i q^{47} +(-882292. - 141698. i) q^{48} +456299. q^{49} -1.03032e6 q^{50} +(533840. + 85735.9i) q^{51} -1.21223e6i q^{52} +424648. i q^{53} +(1.37455e6 + 711641. i) q^{54} +(1.34672e6 + 1.01757e6i) q^{55} -247267. i q^{56} +(294218. - 1.83197e6i) q^{57} +1.60626e6 q^{58} +979885. i q^{59} +(-286494. + 1.78387e6i) q^{60} +3.28548e6i q^{61} -762290. q^{62} +(-415000. + 1.25869e6i) q^{63} -1.14025e6 q^{64} +4.58750e6 q^{65} +(2.25494e6 - 2.16253e6i) q^{66} +990302. q^{67} +1.16817e6 q^{68} +(-482854. + 3.00652e6i) q^{69} -3.50681e6 q^{70} -126653. i q^{71} +(-847480. - 279421. i) q^{72} -1.59343e6i q^{73} -7.38472e6 q^{74} +(-3.14347e6 - 504849. i) q^{75} -4.00878e6i q^{76} +(2.13439e6 + 1.61274e6i) q^{77} +(1.34647e6 - 8.38388e6i) q^{78} -3.65952e6i q^{79} -7.30630e6i q^{80} +(3.84504e6 + 2.84473e6i) q^{81} -5.84583e6 q^{82} -9.71525e6 q^{83} +(-454060. + 2.82723e6i) q^{84} +4.42076e6i q^{85} -5.84031e6i q^{86} +(4.90067e6 + 787058. i) q^{87} +(-1.08586e6 + 1.43710e6i) q^{88} +1.86398e6i q^{89} +(-3.96283e6 + 1.20192e7i) q^{90} +7.27065e6 q^{91} +6.57900e6i q^{92} +(-2.32573e6 - 373518. i) q^{93} -8.74886e6i q^{94} +1.51706e7 q^{95} +(-1.09411e7 - 1.75716e6i) q^{96} +4.20959e6 q^{97} +6.90564e6 q^{98} +(7.93941e6 - 5.49293e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9}+O(q^{10}) \) 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9	\( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37} - 100296 q^{42} - 1854252 q^{45} + 3172548 q^{48} - 1169304 q^{49} - 4401936 q^{55} - 2920440 q^{58} + 1981452 q^{60} + 14578596 q^{64} + 2895156 q^{66} + 7729200 q^{67} - 4614108 q^{69} - 6924504 q^{70} - 4375800 q^{75} - 26237448 q^{78} + 22367340 q^{81} - 23600232 q^{82} - 25179660 q^{88} + 9380640 q^{91} + 25396908 q^{93} + 72948360 q^{97} + 53650080 q^{99}+O(q^{100}) \) 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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