LMFDB - Embedded newform 552.2.f.d.277.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 2x^17 + x^16 - 4x^15 + 16x^14 - 24x^13 + 32x^12 - 16x^11 - 16x^10 - 32x^9 + 128x^8 - 192x^7 + 256x^6 - 128x^5 + 64x^4 - 256x^3 + 512x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.11
Root			$-0.133806 + 1.40787i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.d.277.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.133806 - 1.40787i) q^{2} -1.00000i q^{3} +(-1.96419 - 0.376764i) q^{4} +2.81880i q^{5} +(-1.40787 - 0.133806i) q^{6} +1.52994 q^{7} +(-0.793255 + 2.71491i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.133806 - 1.40787i) q^{2} -1.00000i q^{3} +(-1.96419 - 0.376764i) q^{4} +2.81880i q^{5} +(-1.40787 - 0.133806i) q^{6} +1.52994 q^{7} +(-0.793255 + 2.71491i) q^{8} -1.00000 q^{9} +(3.96850 + 0.377173i) q^{10} +5.55573i q^{11} +(-0.376764 + 1.96419i) q^{12} -1.85412i q^{13} +(0.204715 - 2.15395i) q^{14} +2.81880 q^{15} +(3.71610 + 1.48007i) q^{16} +5.32371 q^{17} +(-0.133806 + 1.40787i) q^{18} +3.73947i q^{19} +(1.06202 - 5.53666i) q^{20} -1.52994i q^{21} +(7.82174 + 0.743392i) q^{22} +1.00000 q^{23} +(2.71491 + 0.793255i) q^{24} -2.94563 q^{25} +(-2.61036 - 0.248093i) q^{26} +1.00000i q^{27} +(-3.00509 - 0.576424i) q^{28} +0.0915052i q^{29} +(0.377173 - 3.96850i) q^{30} -5.72298 q^{31} +(2.58098 - 5.03374i) q^{32} +5.55573 q^{33} +(0.712347 - 7.49509i) q^{34} +4.31258i q^{35} +(1.96419 + 0.376764i) q^{36} -4.54395i q^{37} +(5.26468 + 0.500364i) q^{38} -1.85412 q^{39} +(-7.65279 - 2.23603i) q^{40} +6.21826 q^{41} +(-2.15395 - 0.204715i) q^{42} +10.1600i q^{43} +(2.09320 - 10.9125i) q^{44} -2.81880i q^{45} +(0.133806 - 1.40787i) q^{46} +5.98791 q^{47} +(1.48007 - 3.71610i) q^{48} -4.65930 q^{49} +(-0.394144 + 4.14706i) q^{50} -5.32371i q^{51} +(-0.698566 + 3.64185i) q^{52} -6.56499i q^{53} +(1.40787 + 0.133806i) q^{54} -15.6605 q^{55} +(-1.21363 + 4.15364i) q^{56} +3.73947 q^{57} +(0.128827 + 0.0122440i) q^{58} +3.88850i q^{59} +(-5.53666 - 1.06202i) q^{60} +7.32041i q^{61} +(-0.765771 + 8.05721i) q^{62} -1.52994 q^{63} +(-6.74149 - 4.30724i) q^{64} +5.22640 q^{65} +(0.743392 - 7.82174i) q^{66} -15.8956i q^{67} +(-10.4568 - 2.00578i) q^{68} -1.00000i q^{69} +(6.07155 + 0.577050i) q^{70} -11.1353 q^{71} +(0.793255 - 2.71491i) q^{72} -0.668457 q^{73} +(-6.39729 - 0.608010i) q^{74} +2.94563i q^{75} +(1.40889 - 7.34503i) q^{76} +8.49991i q^{77} +(-0.248093 + 2.61036i) q^{78} +8.30751 q^{79} +(-4.17202 + 10.4749i) q^{80} +1.00000 q^{81} +(0.832042 - 8.75450i) q^{82} +1.52866i q^{83} +(-0.576424 + 3.00509i) q^{84} +15.0065i q^{85} +(14.3039 + 1.35947i) q^{86} +0.0915052 q^{87} +(-15.0833 - 4.40711i) q^{88} +6.22475 q^{89} +(-3.96850 - 0.377173i) q^{90} -2.83669i q^{91} +(-1.96419 - 0.376764i) q^{92} +5.72298i q^{93} +(0.801220 - 8.43019i) q^{94} -10.5408 q^{95} +(-5.03374 - 2.58098i) q^{96} +8.93385 q^{97} +(-0.623444 + 6.55968i) q^{98} -5.55573i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	0.133806	−	1.40787i	0.0946153	−	0.995514i
$2$	0.133806	−	1.40787i	0.0946153	−	0.995514i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.96419	−	0.376764i	−0.982096	−	0.188382i
$5$			2.81880i			1.26061i	0.776350	+	0.630303i	$0.217069\pi$
$5$			2.81880i			1.26061i	−0.776350	+	0.630303i	$0.782931\pi$
$6$	−1.40787	−	0.133806i	−0.574760	−	0.0546262i
$7$	1.52994			0.578261			0.289131	−	0.957290i	$-0.406634\pi$
$7$	1.52994			0.578261			0.289131	+	0.957290i	$0.406634\pi$
$8$	−0.793255	+	2.71491i	−0.280458	+	0.959866i
$9$	−1.00000			−0.333333
$10$	3.96850	+	0.377173i	1.25495	+	0.119273i
$11$			5.55573i			1.67512i	0.546349	+	0.837558i	$0.316017\pi$
$11$			5.55573i			1.67512i	−0.546349	+	0.837558i	$0.683983\pi$
$12$	−0.376764	+	1.96419i	−0.108762	+	0.567013i
$13$		−	1.85412i		−	0.514241i	−0.966379	−	0.257121i	$-0.917226\pi$
$13$		−	1.85412i		−	0.514241i	0.966379	−	0.257121i	$-0.0827738\pi$
$14$	0.204715	−	2.15395i	0.0547124	−	0.575667i
$15$	2.81880			0.727811
$16$	3.71610	+	1.48007i	0.929025	+	0.370018i
$17$	5.32371			1.29119			0.645595	−	0.763680i	$-0.276609\pi$
$17$	5.32371			1.29119			0.645595	+	0.763680i	$0.276609\pi$
$18$	−0.133806	+	1.40787i	−0.0315384	+	0.331838i
$19$			3.73947i			0.857892i	0.903330	+	0.428946i	$0.141115\pi$
$19$			3.73947i			0.857892i	−0.903330	+	0.428946i	$0.858885\pi$
$20$	1.06202	−	5.53666i	0.237475	−	1.23804i
$21$		−	1.52994i		−	0.333859i
$22$	7.82174	+	0.743392i	1.66760	+	0.158492i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	2.71491	+	0.793255i	0.554179	+	0.161923i
$25$	−2.94563			−0.589126
$26$	−2.61036	−	0.248093i	−0.511934	−	0.0486551i
$27$			1.00000i			0.192450i
$28$	−3.00509	−	0.576424i	−0.567908	−	0.108934i
$29$			0.0915052i			0.0169921i	0.999964	+	0.00849605i	$0.00270441\pi$
$29$			0.0915052i			0.0169921i	−0.999964	+	0.00849605i	$0.997296\pi$
$30$	0.377173	−	3.96850i	0.0688621	−	0.724546i
$31$	−5.72298			−1.02788			−0.513939	−	0.857827i	$-0.671814\pi$
$31$	−5.72298			−1.02788			−0.513939	+	0.857827i	$0.671814\pi$
$32$	2.58098	−	5.03374i	0.456258	−	0.889848i
$33$	5.55573			0.967129
$34$	0.712347	−	7.49509i	0.122166	−	1.28540i
$35$			4.31258i			0.728959i
$36$	1.96419	+	0.376764i	0.327365	+	0.0627939i
$37$		−	4.54395i		−	0.747022i	−0.927626	−	0.373511i	$-0.878154\pi$
$37$		−	4.54395i		−	0.747022i	0.927626	−	0.373511i	$-0.121846\pi$
$38$	5.26468	+	0.500364i	0.854044	+	0.0811698i
$39$	−1.85412			−0.296897
$40$	−7.65279	−	2.23603i	−1.21001	−	0.353547i
$41$	6.21826			0.971129			0.485565	−	0.874201i	$-0.338614\pi$
$41$	6.21826			0.971129			0.485565	+	0.874201i	$0.338614\pi$
$42$	−2.15395	−	0.204715i	−0.332361	−	0.0315882i
$43$			10.1600i			1.54938i	0.632340	+	0.774691i	$0.282095\pi$
$43$			10.1600i			1.54938i	−0.632340	+	0.774691i	$0.717905\pi$
$44$	2.09320	−	10.9125i	0.315561	−	1.64512i
$45$		−	2.81880i		−	0.420202i
$46$	0.133806	−	1.40787i	0.0197287	−	0.207579i
$47$	5.98791			0.873426			0.436713	−	0.899601i	$-0.356143\pi$
$47$	5.98791			0.873426			0.436713	+	0.899601i	$0.356143\pi$
$48$	1.48007	−	3.71610i	0.213630	−	0.536373i
$49$	−4.65930			−0.665614
$50$	−0.394144	+	4.14706i	−0.0557403	+	0.586483i
$51$		−	5.32371i		−	0.745469i
$52$	−0.698566	+	3.64185i	−0.0968737	+	0.505034i
$53$		−	6.56499i		−	0.901771i	−0.892582	−	0.450885i	$-0.851108\pi$
$53$		−	6.56499i		−	0.901771i	0.892582	−	0.450885i	$-0.148892\pi$
$54$	1.40787	+	0.133806i	0.191587	+	0.0182087i
$55$	−15.6605			−2.11166
$56$	−1.21363	+	4.15364i	−0.162178	+	0.555053i
$57$	3.73947			0.495304
$58$	0.128827	+	0.0122440i	0.0169159	+	0.00160771i
$59$			3.88850i			0.506239i	0.967435	+	0.253119i	$0.0814566\pi$
$59$			3.88850i			0.506239i	−0.967435	+	0.253119i	$0.918543\pi$
$60$	−5.53666	−	1.06202i	−0.714780	−	0.137106i
$61$			7.32041i			0.937283i	0.883388	+	0.468641i	$0.155256\pi$
$61$			7.32041i			0.937283i	−0.883388	+	0.468641i	$0.844744\pi$
$62$	−0.765771	+	8.05721i	−0.0972530	+	1.02327i
$63$	−1.52994			−0.192754
$64$	−6.74149	−	4.30724i	−0.842687	−	0.538404i
$65$	5.22640			0.648255
$66$	0.743392	−	7.82174i	0.0915052	−	0.962790i
$67$		−	15.8956i		−	1.94196i	−0.239170	−	0.970978i	$-0.576875\pi$
$67$		−	15.8956i		−	1.94196i	0.239170	−	0.970978i	$-0.423125\pi$
$68$	−10.4568	−	2.00578i	−1.26807	−	0.243237i
$69$		−	1.00000i		−	0.120386i
$70$	6.07155	+	0.577050i	0.725689	+	0.0689707i
$71$	−11.1353			−1.32152			−0.660758	−	0.750599i	$-0.729765\pi$
$71$	−11.1353			−1.32152			−0.660758	+	0.750599i	$0.729765\pi$
$72$	0.793255	−	2.71491i	0.0934860	−	0.319955i
$73$	−0.668457			−0.0782370			−0.0391185	−	0.999235i	$-0.512455\pi$
$73$	−0.668457			−0.0782370			−0.0391185	+	0.999235i	$0.512455\pi$
$74$	−6.39729	−	0.608010i	−0.743670	−	0.0706797i
$75$			2.94563i			0.340132i
$76$	1.40889	−	7.34503i	0.161611	−	0.842533i
$77$			8.49991i			0.968654i
$78$	−0.248093	+	2.61036i	−0.0280910	+	0.295565i
$79$	8.30751			0.934668			0.467334	−	0.884081i	$-0.345215\pi$
$79$	8.30751			0.934668			0.467334	+	0.884081i	$0.345215\pi$
$80$	−4.17202	+	10.4749i	−0.466447	+	1.17113i
$81$	1.00000			0.111111
$82$	0.832042	−	8.75450i	0.0918837	−	0.966773i
$83$			1.52866i			0.167792i	0.996475	+	0.0838961i	$0.0267364\pi$
$83$			1.52866i			0.167792i	−0.996475	+	0.0838961i	$0.973264\pi$
$84$	−0.576424	+	3.00509i	−0.0628930	+	0.327882i
$85$			15.0065i			1.62768i
$86$	14.3039	+	1.35947i	1.54243	+	0.146595i
$87$	0.0915052			0.00981039
$88$	−15.0833	−	4.40711i	−1.60789	−	0.469800i
$89$	6.22475			0.659822			0.329911	−	0.944012i	$-0.392981\pi$
$89$	6.22475			0.659822			0.329911	+	0.944012i	$0.392981\pi$
$90$	−3.96850	−	0.377173i	−0.418317	−	0.0397575i
$91$		−	2.83669i		−	0.297366i
$92$	−1.96419	−	0.376764i	−0.204781	−	0.0392803i
$93$			5.72298i			0.593446i
$94$	0.801220	−	8.43019i	0.0826395	−	0.869508i
$95$	−10.5408			−1.08146
$96$	−5.03374	−	2.58098i	−0.513754	−	0.263421i
$97$	8.93385			0.907095			0.453547	−	0.891232i	$-0.350158\pi$
$97$	8.93385			0.907095			0.453547	+	0.891232i	$0.350158\pi$
$98$	−0.623444	+	6.55968i	−0.0629773	+	0.662628i
$99$		−	5.55573i		−	0.558372i
$100$	5.78578	+	1.10981i	0.578578	+	0.110981i
$101$			4.50947i			0.448709i	0.974508	+	0.224354i	$0.0720273\pi$
$101$			4.50947i			0.448709i	−0.974508	+	0.224354i	$0.927973\pi$
$102$	−7.49509	−	0.712347i	−0.742125	−	0.0705328i
$103$	−9.79414			−0.965045			−0.482523	−	0.875883i	$-0.660279\pi$
$103$	−9.79414			−0.965045			−0.482523	+	0.875883i	$0.660279\pi$
$104$	5.03378	+	1.47079i	0.493603	+	0.144223i
$105$	4.31258			0.420865
$106$	−9.24265	−	0.878437i	−0.897725	−	0.0853214i
$107$			11.6186i			1.12321i	0.827405	+	0.561606i	$0.189816\pi$
$107$			11.6186i			1.12321i	−0.827405	+	0.561606i	$0.810184\pi$
$108$	0.376764	−	1.96419i	0.0362541	−	0.189004i
$109$			5.00563i			0.479452i	0.970841	+	0.239726i	$0.0770576\pi$
$109$			5.00563i			0.479452i	−0.970841	+	0.239726i	$0.922942\pi$
$110$	−2.09547	+	22.0479i	−0.199795	+	2.10219i
$111$	−4.54395			−0.431293
$112$	5.68539	+	2.26441i	0.537219	+	0.213967i
$113$	14.1914			1.33502			0.667510	−	0.744601i	$-0.267360\pi$
$113$	14.1914			1.33502			0.667510	+	0.744601i	$0.267360\pi$
$114$	0.500364	−	5.26468i	0.0468634	−	0.493082i
$115$			2.81880i			0.262854i
$116$	0.0344758	−	0.179734i	0.00320100	−	0.0166879i
$117$			1.85412i			0.171414i
$118$	5.47449	+	0.520305i	0.503968	+	0.0478980i
$119$	8.14494			0.746645
$120$	−2.23603	+	7.65279i	−0.204120	+	0.698601i
$121$	−19.8661			−1.80601
$122$	10.3062	+	0.979517i	0.933078	+	0.0886813i
$123$		−	6.21826i		−	0.560682i
$124$	11.2410	+	2.15621i	1.00947	+	0.193633i
$125$			5.79086i			0.517950i
$126$	−0.204715	+	2.15395i	−0.0182375	+	0.191889i
$127$	14.2301			1.26271			0.631356	−	0.775493i	$-0.282498\pi$
$127$	14.2301			1.26271			0.631356	+	0.775493i	$0.282498\pi$
$128$	−6.96608	+	8.91481i	−0.615720	+	0.787965i
$129$	10.1600			0.894536
$130$	0.699325	−	7.35809i	0.0613349	−	0.645347i
$131$			4.13233i			0.361043i	0.983571	+	0.180522i	$0.0577786\pi$
$131$			4.13233i			0.361043i	−0.983571	+	0.180522i	$0.942221\pi$
$132$	−10.9125	−	2.09320i	−0.949813	−	0.182189i
$133$			5.72114i			0.496086i
$134$	−22.3789	−	2.12693i	−1.93324	−	0.183739i
$135$	−2.81880			−0.242604
$136$	−4.22306	+	14.4534i	−0.362125	+	1.23937i
$137$	−16.8321			−1.43806			−0.719031	−	0.694978i	$-0.755414\pi$
$137$	−16.8321			−1.43806			−0.719031	+	0.694978i	$0.755414\pi$
$138$	−1.40787	−	0.133806i	−0.119846	−	0.0113903i
$139$		−	16.6671i		−	1.41368i	−0.707372	−	0.706842i	$-0.750119\pi$
$139$		−	16.6671i		−	1.41368i	0.707372	−	0.706842i	$-0.249881\pi$
$140$	1.62482	−	8.47073i	0.137323	−	0.715908i
$141$		−	5.98791i		−	0.504273i
$142$	−1.48997	+	15.6770i	−0.125036	+	1.31559i
$143$	10.3010			0.861413
$144$	−3.71610	−	1.48007i	−0.309675	−	0.123339i
$145$	−0.257935			−0.0214203
$146$	−0.0894438	+	0.941100i	−0.00740242	+	0.0778860i
$147$			4.65930i			0.384292i
$148$	−1.71200	+	8.92520i	−0.140725	+	0.733647i
$149$		−	11.8772i		−	0.973020i	−0.873675	−	0.486510i	$-0.838270\pi$
$149$		−	11.8772i		−	0.973020i	0.873675	−	0.486510i	$-0.161730\pi$
$150$	4.14706	+	0.394144i	0.338606	+	0.0321817i
$151$	−13.0504			−1.06203			−0.531014	−	0.847363i	$-0.678189\pi$
$151$	−13.0504			−1.06203			−0.531014	+	0.847363i	$0.678189\pi$
$152$	−10.1523	−	2.96635i	−0.823462	−	0.240603i
$153$	−5.32371			−0.430397
$154$	11.9668	+	1.13734i	0.964309	+	0.0916496i
$155$		−	16.1319i		−	1.29575i
$156$	3.64185	+	0.698566i	0.291582	+	0.0559300i
$157$		−	19.0690i		−	1.52187i	−0.648825	−	0.760937i	$-0.724739\pi$
$157$		−	19.0690i		−	1.52187i	0.648825	−	0.760937i	$-0.275261\pi$
$158$	1.11160	−	11.6959i	0.0884340	−	0.930475i
$159$	−6.56499			−0.520638
$160$	14.1891	+	7.27528i	1.12175	+	0.575161i
$161$	1.52994			0.120576
$162$	0.133806	−	1.40787i	0.0105128	−	0.110613i
$163$		−	13.9343i		−	1.09142i	−0.837975	−	0.545709i	$-0.816260\pi$
$163$		−	13.9343i		−	1.09142i	0.837975	−	0.545709i	$-0.183740\pi$
$164$	−12.2139	−	2.34281i	−0.953742	−	0.182943i
$165$			15.6605i			1.21917i
$166$	2.15215	+	0.204544i	0.167040	+	0.0158757i
$167$	−8.17083			−0.632277			−0.316139	−	0.948713i	$-0.602387\pi$
$167$	−8.17083			−0.632277			−0.316139	+	0.948713i	$0.602387\pi$
$168$	4.15364	+	1.21363i	0.320460	+	0.0936335i
$169$	9.56223			0.735556
$170$	21.1272	+	2.00796i	1.62038	+	0.154004i
$171$		−	3.73947i		−	0.285964i
$172$	3.82791	−	19.9561i	0.291875	−	1.52164i
$173$		−	19.0700i		−	1.44986i	−0.688821	−	0.724932i	$-0.741871\pi$
$173$		−	19.0700i		−	1.44986i	0.688821	−	0.724932i	$-0.258129\pi$
$174$	0.0122440	−	0.128827i	0.000928213	−	0.00976638i
$175$	−4.50662			−0.340668
$176$	−8.22288	+	20.6456i	−0.619823	+	1.55622i
$177$	3.88850			0.292277
$178$	0.832910	−	8.76363i	0.0624293	−	0.656862i
$179$			17.0651i			1.27550i	0.770241	+	0.637752i	$0.220136\pi$
$179$			17.0651i			1.27550i	−0.770241	+	0.637752i	$0.779864\pi$
$180$	−1.06202	+	5.53666i	−0.0791584	+	0.412678i
$181$		−	0.189248i		−	0.0140667i	−0.999975	−	0.00703334i	$-0.997761\pi$
$181$		−	0.189248i		−	0.0140667i	0.999975	−	0.00703334i	$-0.00223880\pi$
$182$	−3.99369	−	0.379567i	−0.296032	−	0.0281354i
$183$	7.32041			0.541141
$184$	−0.793255	+	2.71491i	−0.0584795	+	0.200146i
$185$	12.8085			0.941699
$186$	8.05721	+	0.765771i	0.590783	+	0.0561491i
$187$			29.5771i			2.16289i
$188$	−11.7614	−	2.25603i	−0.857788	−	0.164538i
$189$			1.52994i			0.111286i
$190$	−1.41043	+	14.8401i	−0.102323	+	1.07661i
$191$	−13.1592			−0.952167			−0.476083	−	0.879400i	$-0.657944\pi$
$191$	−13.1592			−0.952167			−0.476083	+	0.879400i	$0.657944\pi$
$192$	−4.30724	+	6.74149i	−0.310848	+	0.486525i
$193$	2.95455			0.212673			0.106337	−	0.994330i	$-0.466088\pi$
$193$	2.95455			0.212673			0.106337	+	0.994330i	$0.466088\pi$
$194$	1.19541	−	12.5777i	0.0858251	−	0.903026i
$195$		−	5.22640i		−	0.374270i
$196$	9.15176	+	1.75545i	0.653697	+	0.125390i
$197$		−	25.5436i		−	1.81990i	−0.414715	−	0.909951i	$-0.636119\pi$
$197$		−	25.5436i		−	1.81990i	0.414715	−	0.909951i	$-0.363881\pi$
$198$	−7.82174	−	0.743392i	−0.555867	−	0.0528306i
$199$	−7.92928			−0.562092			−0.281046	−	0.959694i	$-0.590681\pi$
$199$	−7.92928			−0.562092			−0.281046	+	0.959694i	$0.590681\pi$
$200$	2.33663	−	7.99712i	0.165225	−	0.565482i
$201$	−15.8956			−1.12119
$202$	6.34874	+	0.603395i	0.446696	+	0.0424547i
$203$			0.139997i			0.00982587i
$204$	−2.00578	+	10.4568i	−0.140433	+	0.732122i
$205$			17.5280i			1.22421i
$206$	−1.31052	+	13.7889i	−0.0913081	+	0.960716i
$207$	−1.00000			−0.0695048
$208$	2.74423	−	6.89010i	0.190278	−	0.477743i
$209$	−20.7755			−1.43707
$210$	0.577050	−	6.07155i	0.0398203	−	0.418977i
$211$		−	16.8478i		−	1.15985i	−0.814671	−	0.579924i	$-0.803082\pi$
$211$		−	16.8478i		−	1.15985i	0.814671	−	0.579924i	$-0.196918\pi$
$212$	−2.47345	+	12.8949i	−0.169877	+	0.885625i
$213$			11.1353i			0.762978i
$214$	16.3575	+	1.55464i	1.11817	+	0.106273i
$215$	−28.6389			−1.95316
$216$	−2.71491	−	0.793255i	−0.184726	−	0.0539742i
$217$	−8.75579			−0.594382
$218$	7.04727	+	0.669784i	0.477301	+	0.0453635i
$219$			0.668457i			0.0451702i
$220$	30.7602	+	5.90030i	2.07385	+	0.397798i
$221$		−	9.87082i		−	0.663983i
$222$	−0.608010	+	6.39729i	−0.0408069	+	0.429358i
$223$	−14.5247			−0.972643			−0.486322	−	0.873780i	$-0.661662\pi$
$223$	−14.5247			−0.972643			−0.486322	+	0.873780i	$0.661662\pi$
$224$	3.94874	−	7.70129i	0.263836	−	0.514564i
$225$	2.94563			0.196375
$226$	1.89891	−	19.9797i	0.126313	−	1.32903i
$227$			17.2251i			1.14327i	0.820508	+	0.571635i	$0.193691\pi$
$227$			17.2251i			1.14327i	−0.820508	+	0.571635i	$0.806309\pi$
$228$	−7.34503	−	1.40889i	−0.486436	−	0.0933063i
$229$		−	25.1934i		−	1.66483i	−0.554155	−	0.832414i	$-0.686958\pi$
$229$		−	25.1934i		−	1.66483i	0.554155	−	0.832414i	$-0.313042\pi$
$230$	3.96850	+	0.377173i	0.261675	+	0.0248701i
$231$	8.49991			0.559253
$232$	−0.248429	−	0.0725870i	−0.0163101	−	0.00476557i
$233$	−11.4444			−0.749748			−0.374874	−	0.927076i	$-0.622314\pi$
$233$	−11.4444			−0.749748			−0.374874	+	0.927076i	$0.622314\pi$
$234$	2.61036	+	0.248093i	0.170645	+	0.0162184i
$235$			16.8787i			1.10105i
$236$	1.46504	−	7.63775i	0.0953662	−	0.497175i
$237$		−	8.30751i		−	0.539631i
$238$	1.08984	−	11.4670i	0.0706441	−	0.743296i
$239$	17.4459			1.12848			0.564241	−	0.825610i	$-0.309169\pi$
$239$	17.4459			1.12848			0.564241	+	0.825610i	$0.309169\pi$
$240$	10.4749	+	4.17202i	0.676154	+	0.269303i
$241$	−12.6268			−0.813365			−0.406683	−	0.913570i	$-0.633314\pi$
$241$	−12.6268			−0.813365			−0.406683	+	0.913570i	$0.633314\pi$
$242$	−2.65822	+	27.9689i	−0.170877	+	1.79791i
$243$		−	1.00000i		−	0.0641500i
$244$	2.75806	−	14.3787i	0.176567	−	0.920502i
$245$		−	13.1336i		−	0.839077i
$246$	−8.75450	−	0.832042i	−0.558166	−	0.0530491i
$247$	6.93343			0.441164
$248$	4.53978	−	15.5374i	0.288277	−	0.986625i
$249$	1.52866			0.0968749
$250$	8.15278	+	0.774854i	0.515627	+	0.0490061i
$251$		−	23.9732i		−	1.51317i	−0.653893	−	0.756587i	$-0.726865\pi$
$251$		−	23.9732i		−	1.51317i	0.653893	−	0.756587i	$-0.273135\pi$
$252$	3.00509	+	0.576424i	0.189303	+	0.0363113i
$253$			5.55573i			0.349286i
$254$	1.90407	−	20.0341i	0.119472	−	1.25705i
$255$	15.0065			0.939742
$256$	11.6188	+	11.0002i	0.726173	+	0.687512i
$257$	18.8926			1.17849			0.589245	−	0.807954i	$-0.299425\pi$
$257$	18.8926			1.17849			0.589245	+	0.807954i	$0.299425\pi$
$258$	1.35947	−	14.3039i	0.0846368	−	0.890523i
$259$		−	6.95196i		−	0.431973i
$260$	−10.2657	−	1.96912i	−0.636649	−	0.122119i
$261$		−	0.0915052i		−	0.00566403i
$262$	5.81778	+	0.552932i	0.359424	+	0.0341602i
$263$	27.1212			1.67237			0.836184	−	0.548450i	$-0.184782\pi$
$263$	27.1212			1.67237			0.836184	+	0.548450i	$0.184782\pi$
$264$	−4.40711	+	15.0833i	−0.271239	+	0.928314i
$265$	18.5054			1.13678
$266$	8.05462	+	0.765525i	0.493860	+	0.0469373i
$267$		−	6.22475i		−	0.380948i
$268$	−5.98888	+	31.2220i	−0.365829	+	1.90719i
$269$			3.89996i			0.237785i	0.992907	+	0.118892i	$0.0379343\pi$
$269$			3.89996i			0.237785i	−0.992907	+	0.118892i	$0.962066\pi$
$270$	−0.377173	+	3.96850i	−0.0229540	+	0.241515i
$271$	1.16444			0.0707346			0.0353673	−	0.999374i	$-0.488740\pi$
$271$	1.16444			0.0707346			0.0353673	+	0.999374i	$0.488740\pi$
$272$	19.7834	+	7.87948i	1.19955	+	0.477764i
$273$	−2.83669			−0.171684
$274$	−2.25224	+	23.6974i	−0.136063	+	1.43161i
$275$		−	16.3651i		−	0.986854i
$276$	−0.376764	+	1.96419i	−0.0226785	+	0.118230i
$277$		−	3.23458i		−	0.194347i	−0.995267	−	0.0971735i	$-0.969020\pi$
$277$		−	3.23458i		−	0.194347i	0.995267	−	0.0971735i	$-0.0309802\pi$
$278$	−23.4651	−	2.23016i	−1.40734	−	0.133756i
$279$	5.72298			0.342626
$280$	−11.7083	−	3.42098i	−0.699703	−	0.204442i
$281$	4.50603			0.268807			0.134404	−	0.990927i	$-0.457088\pi$
$281$	4.50603			0.268807			0.134404	+	0.990927i	$0.457088\pi$
$282$	−8.43019	−	0.801220i	−0.502011	−	0.0477119i
$283$			7.11533i			0.422962i	0.977382	+	0.211481i	$0.0678287\pi$
$283$			7.11533i			0.422962i	−0.977382	+	0.211481i	$0.932171\pi$
$284$	21.8718	+	4.19537i	1.29786	+	0.248950i
$285$			10.5408i			0.624383i
$286$	1.37834	−	14.5025i	0.0815029	−	0.857549i
$287$	9.51353			0.561566
$288$	−2.58098	+	5.03374i	−0.152086	+	0.296616i
$289$	11.3419			0.667173
$290$	−0.0345133	+	0.363139i	−0.00202669	+	0.0213242i
$291$		−	8.93385i		−	0.523712i
$292$	1.31298	+	0.251850i	0.0768362	+	0.0147384i
$293$		−	28.2506i		−	1.65042i	−0.564828	−	0.825208i	$-0.691058\pi$
$293$		−	28.2506i		−	1.65042i	0.564828	−	0.825208i	$-0.308942\pi$
$294$	6.55968	+	0.623444i	0.382569	+	0.0363600i
$295$	−10.9609			−0.638167
$296$	12.3364	+	3.60451i	0.717041	+	0.209508i
$297$	−5.55573			−0.322376
$298$	−16.7216	−	1.58925i	−0.968655	−	0.0920626i
$299$		−	1.85412i		−	0.107227i
$300$	1.10981	−	5.78578i	0.0640746	−	0.334042i
$301$			15.5441i			0.895947i
$302$	−1.74623	+	18.3733i	−0.100484	+	1.05726i
$303$	4.50947			0.259062
$304$	−5.53468	+	13.8962i	−0.317436	+	0.797003i
$305$	−20.6348			−1.18154
$306$	−0.712347	+	7.49509i	−0.0407221	+	0.428466i
$307$		−	16.1187i		−	0.919940i	−0.887934	−	0.459970i	$-0.847860\pi$
$307$		−	16.1187i		−	0.919940i	0.887934	−	0.459970i	$-0.152140\pi$
$308$	3.20246	−	16.6954i	0.182477	−	0.951311i
$309$			9.79414i			0.557169i
$310$	−22.7117	−	2.15855i	−1.28994	−	0.122598i
$311$	6.43010			0.364618			0.182309	−	0.983241i	$-0.441643\pi$
$311$	6.43010			0.364618			0.182309	+	0.983241i	$0.441643\pi$
$312$	1.47079	−	5.03378i	0.0832672	−	0.284982i
$313$	32.1758			1.81869			0.909343	−	0.416048i	$-0.136585\pi$
$313$	32.1758			1.81869			0.909343	+	0.416048i	$0.136585\pi$
$314$	−26.8467	−	2.55156i	−1.51505	−	0.143993i
$315$		−	4.31258i		−	0.242986i
$316$	−16.3175	−	3.12997i	−0.917934	−	0.176074i
$317$		−	0.934992i		−	0.0525144i	−0.999655	−	0.0262572i	$-0.991641\pi$
$317$		−	0.934992i		−	0.0525144i	0.999655	−	0.0262572i	$-0.00835889\pi$
$318$	−0.878437	+	9.24265i	−0.0492603	+	0.518302i
$319$	−0.508378			−0.0284637
$320$	12.1412	−	19.0029i	0.678715	−	1.06230i
$321$	11.6186			0.648487
$322$	0.204715	−	2.15395i	0.0114083	−	0.120035i
$323$			19.9079i			1.10770i
$324$	−1.96419	−	0.376764i	−0.109122	−	0.0209313i
$325$			5.46156i			0.302953i
$326$	−19.6177	−	1.86450i	−1.08652	−	0.103265i
$327$	5.00563			0.276812
$328$	−4.93267	+	16.8820i	−0.272361	+	0.932154i
$329$	9.16111			0.505068
$330$	22.0479	+	2.09547i	1.21370	+	0.115352i
$331$		−	26.8197i		−	1.47415i	−0.675813	−	0.737073i	$-0.736208\pi$
$331$		−	26.8197i		−	1.47415i	0.675813	−	0.737073i	$-0.263792\pi$
$332$	0.575944	−	3.00258i	0.0316090	−	0.164788i
$333$			4.54395i			0.249007i
$334$	−1.09331	+	11.5035i	−0.0598231	+	0.629441i
$335$	44.8065			2.44804
$336$	2.26441	−	5.68539i	0.123534	−	0.310163i
$337$	6.40889			0.349114			0.174557	−	0.984647i	$-0.444151\pi$
$337$	6.40889			0.349114			0.174557	+	0.984647i	$0.444151\pi$
$338$	1.27949	−	13.4624i	0.0695949	−	0.732256i
$339$		−	14.1914i		−	0.770774i
$340$	5.65390	−	29.4756i	0.306626	−	1.59854i
$341$		−	31.7953i		−	1.72181i
$342$	−5.26468	−	0.500364i	−0.284681	−	0.0270566i
$343$	−17.8380			−0.963160
$344$	−27.5834	−	8.05945i	−1.48720	−	0.434537i
$345$	2.81880			0.151759
$346$	−26.8480	−	2.55168i	−1.44336	−	0.137179i
$347$			19.0891i			1.02476i	0.858760	+	0.512378i	$0.171235\pi$
$347$			19.0891i			1.02476i	−0.858760	+	0.512378i	$0.828765\pi$
$348$	−0.179734	−	0.0344758i	−0.00963474	−	0.00184810i
$349$		−	19.3421i		−	1.03536i	−0.855574	−	0.517680i	$-0.826796\pi$
$349$		−	19.3421i		−	1.03536i	0.855574	−	0.517680i	$-0.173204\pi$
$350$	−0.603014	+	6.34473i	−0.0322325	+	0.339140i
$351$	1.85412			0.0989658
$352$	27.9661	+	14.3393i	1.49060	+	0.764285i
$353$	−25.2351			−1.34313			−0.671563	−	0.740947i	$-0.734377\pi$
$353$	−25.2351			−1.34313			−0.671563	+	0.740947i	$0.734377\pi$
$354$	0.520305	−	5.47449i	0.0276539	−	0.290966i
$355$		−	31.3881i		−	1.66591i
$356$	−12.2266	−	2.34526i	−0.648008	−	0.124298i
$357$		−	8.14494i		−	0.431076i
$358$	24.0254	+	2.28342i	1.26978	+	0.120682i
$359$	17.5256			0.924964			0.462482	−	0.886629i	$-0.346959\pi$
$359$	17.5256			0.924964			0.462482	+	0.886629i	$0.346959\pi$
$360$	7.65279	+	2.23603i	0.403337	+	0.117849i
$361$	5.01639			0.264021
$362$	−0.266436	−	0.0253225i	−0.0140036	−	0.00133092i
$363$			19.8661i			1.04270i
$364$	−1.06876	+	5.57180i	−0.0560183	+	0.292042i
$365$		−	1.88425i		−	0.0986260i
$366$	0.979517	−	10.3062i	0.0512002	−	0.538713i
$367$	−10.9963			−0.574000			−0.287000	−	0.957931i	$-0.592658\pi$
$367$	−10.9963			−0.574000			−0.287000	+	0.957931i	$0.592658\pi$
$368$	3.71610	+	1.48007i	0.193715	+	0.0771541i
$369$	−6.21826			−0.323710
$370$	1.71386	−	18.0327i	0.0890992	−	0.937475i
$371$		−	10.0440i		−	0.521459i
$372$	2.15621	−	11.2410i	0.111794	−	0.582820i
$373$			27.9245i			1.44588i	0.690912	+	0.722939i	$0.257209\pi$
$373$			27.9245i			1.44588i	−0.690912	+	0.722939i	$0.742791\pi$
$374$	41.6407	+	3.95761i	2.15319	+	0.204643i
$375$	5.79086			0.299039
$376$	−4.74994	+	16.2566i	−0.244959	+	0.838372i
$377$	0.169662			0.00873803
$378$	2.15395	+	0.204715i	0.110787	+	0.0105294i
$379$			13.4810i			0.692471i	0.938148	+	0.346236i	$0.112540\pi$
$379$			13.4810i			0.692471i	−0.938148	+	0.346236i	$0.887460\pi$
$380$	20.7042	+	3.97139i	1.06210	+	0.203728i
$381$		−	14.2301i		−	0.729028i
$382$	−1.76078	+	18.5264i	−0.0900896	+	0.947895i
$383$	−33.1873			−1.69579			−0.847897	−	0.530162i	$-0.822131\pi$
$383$	−33.1873			−1.69579			−0.847897	+	0.530162i	$0.822131\pi$
$384$	8.91481	+	6.96608i	0.454932	+	0.355486i
$385$	−23.9595			−1.22109
$386$	0.395337	−	4.15962i	0.0201221	−	0.211719i
$387$		−	10.1600i		−	0.516461i
$388$	−17.5478	−	3.36595i	−0.890854	−	0.170880i
$389$			34.0806i			1.72795i	0.503532	+	0.863977i	$0.332034\pi$
$389$			34.0806i			1.72795i	−0.503532	+	0.863977i	$0.667966\pi$
$390$	−7.35809	−	0.699325i	−0.372591	−	0.0354117i
$391$	5.32371			0.269232
$392$	3.69601	−	12.6496i	0.186677	−	0.638901i
$393$	4.13233			0.208448
$394$	−35.9620	−	3.41789i	−1.81174	−	0.172191i
$395$			23.4172i			1.17825i
$396$	−2.09320	+	10.9125i	−0.105187	+	0.548375i
$397$		−	4.70480i		−	0.236127i	−0.993006	−	0.118064i	$-0.962331\pi$
$397$		−	4.70480i		−	0.236127i	0.993006	−	0.118064i	$-0.0376687\pi$
$398$	−1.06099	+	11.1634i	−0.0531825	+	0.559570i
$399$	5.72114			0.286415
$400$	−10.9462	−	4.35974i	−0.547312	−	0.217987i
$401$	3.66859			0.183200			0.0916002	−	0.995796i	$-0.470802\pi$
$401$	3.66859			0.183200			0.0916002	+	0.995796i	$0.470802\pi$
$402$	−2.12693	+	22.3789i	−0.106082	+	1.11616i
$403$			10.6111i			0.528577i
$404$	1.69900	−	8.85746i	0.0845286	−	0.440675i
$405$			2.81880i			0.140067i
$406$	0.197098	+	0.0187325i	0.00978179	+	0.000929678i
$407$	25.2450			1.25135
$408$	14.4534	+	4.22306i	0.715551	+	0.209073i
$409$	−8.30192			−0.410504			−0.205252	−	0.978709i	$-0.565801\pi$
$409$	−8.30192			−0.410504			−0.205252	+	0.978709i	$0.565801\pi$
$410$	24.6772	+	2.34536i	1.21872	+	0.115829i
$411$			16.8321i			0.830265i
$412$	19.2376	+	3.69008i	0.947767	+	0.181797i
$413$			5.94915i			0.292738i
$414$	−0.133806	+	1.40787i	−0.00657622	+	0.0691930i
$415$	−4.30899			−0.211520
$416$	−9.33317	−	4.78546i	−0.457596	−	0.234627i
$417$	−16.6671			−0.816190
$418$	−2.77989	+	29.2491i	−0.135969	+	1.43062i
$419$		−	23.6822i		−	1.15695i	−0.815700	−	0.578475i	$-0.803648\pi$
$419$		−	23.6822i		−	1.15695i	0.815700	−	0.578475i	$-0.196352\pi$
$420$	−8.47073	−	1.62482i	−0.413329	−	0.0792832i
$421$			11.2041i			0.546052i	0.962007	+	0.273026i	$0.0880245\pi$
$421$			11.2041i			0.546052i	−0.962007	+	0.273026i	$0.911975\pi$
$422$	−23.7195	−	2.25434i	−1.15464	−	0.109739i
$423$	−5.98791			−0.291142
$424$	17.8234	+	5.20771i	0.865579	+	0.252909i
$425$	−15.6817			−0.760673
$426$	15.6770	+	1.48997i	0.759555	+	0.0721894i
$427$			11.1998i			0.541994i
$428$	4.37746	−	22.8212i	0.211593	−	1.10310i
$429$		−	10.3010i		−	0.497337i
$430$	−3.83207	+	40.3199i	−0.184799	+	1.94440i
$431$	−13.3705			−0.644035			−0.322017	−	0.946734i	$-0.604361\pi$
$431$	−13.3705			−0.644035			−0.322017	+	0.946734i	$0.604361\pi$
$432$	−1.48007	+	3.71610i	−0.0712100	+	0.178791i
$433$	−20.0457			−0.963334			−0.481667	−	0.876354i	$-0.659968\pi$
$433$	−20.0457			−0.963334			−0.481667	+	0.876354i	$0.659968\pi$
$434$	−1.17158	+	12.3270i	−0.0562376	+	0.591715i
$435$			0.257935i			0.0123670i
$436$	1.88594	−	9.83201i	0.0903200	−	0.470868i
$437$			3.73947i			0.178883i
$438$	0.941100	+	0.0894438i	0.0449675	+	0.00427379i
$439$	39.1958			1.87072			0.935358	−	0.353703i	$-0.115078\pi$
$439$	39.1958			1.87072			0.935358	+	0.353703i	$0.115078\pi$
$440$	12.4228	−	42.5168i	0.592232	−	2.02691i
$441$	4.65930			0.221871
$442$	−13.8968	−	1.32078i	−0.661005	−	0.0628230i
$443$			41.1184i			1.95359i	0.214172	+	0.976796i	$0.431295\pi$
$443$			41.1184i			1.95359i	−0.214172	+	0.976796i	$0.568705\pi$
$444$	8.92520	+	1.71200i	0.423571	+	0.0812478i
$445$			17.5463i			0.831775i
$446$	−1.94349	+	20.4488i	−0.0920270	+	0.968280i
$447$	−11.8772			−0.561773
$448$	−10.3140	−	6.58979i	−0.487293	−	0.311338i
$449$	29.3251			1.38393			0.691967	−	0.721929i	$-0.256744\pi$
$449$	29.3251			1.38393			0.691967	+	0.721929i	$0.256744\pi$
$450$	0.394144	−	4.14706i	0.0185801	−	0.195494i
$451$			34.5470i			1.62675i
$452$	−27.8747	−	5.34682i	−1.31112	−	0.251493i
$453$			13.0504i			0.613162i
$454$	24.2507	+	2.30483i	1.13814	+	0.108171i
$455$	7.99605			0.374861
$456$	−2.96635	+	10.1523i	−0.138912	+	0.475426i
$457$	−26.1327			−1.22244			−0.611218	−	0.791462i	$-0.709320\pi$
$457$	−26.1327			−1.22244			−0.611218	+	0.791462i	$0.709320\pi$
$458$	−35.4690	−	3.37104i	−1.65736	−	0.157518i
$459$			5.32371i			0.248490i
$460$	1.06202	−	5.53666i	0.0495170	−	0.258148i
$461$			23.1531i			1.07835i	0.842195	+	0.539173i	$0.181263\pi$
$461$			23.1531i			1.07835i	−0.842195	+	0.539173i	$0.818737\pi$
$462$	1.13734	−	11.9668i	0.0529139	−	0.556744i
$463$	24.9290			1.15855			0.579273	−	0.815133i	$-0.303336\pi$
$463$	24.9290			1.15855			0.579273	+	0.815133i	$0.303336\pi$
$464$	−0.135434	+	0.340042i	−0.00628738	+	0.0157861i
$465$	−16.1319			−0.748101
$466$	−1.53133	+	16.1122i	−0.0709377	+	0.746385i
$467$			11.4965i			0.531993i	0.963974	+	0.265996i	$0.0857009\pi$
$467$			11.4965i			0.531993i	−0.963974	+	0.265996i	$0.914299\pi$
$468$	0.698566	−	3.64185i	0.0322912	−	0.168345i
$469$		−	24.3192i		−	1.12296i
$470$	23.7630	+	2.25848i	1.09611	+	0.104176i
$471$	−19.0690			−0.878655
$472$	−10.5569	−	3.08457i	−0.485922	−	0.141979i
$473$	−56.4461			−2.59539
$474$	−11.6959	−	1.11160i	−0.537210	−	0.0510574i
$475$		−	11.0151i		−	0.505406i
$476$	−15.9982	−	3.06872i	−0.733277	−	0.140654i
$477$			6.56499i			0.300590i
$478$	2.33437	−	24.5616i	0.106772	−	1.12342i
$479$	5.55752			0.253930			0.126965	−	0.991907i	$-0.459476\pi$
$479$	5.55752			0.253930			0.126965	+	0.991907i	$0.459476\pi$
$480$	7.27528	−	14.1891i	0.332069	−	0.647641i
$481$	−8.42505			−0.384149
$482$	−1.68955	+	17.7769i	−0.0769568	+	0.809716i
$483$		−	1.52994i		−	0.0696145i
$484$	39.0209	+	7.48484i	1.77368	+	0.340220i
$485$			25.1827i			1.14349i
$486$	−1.40787	−	0.133806i	−0.0638622	−	0.00606958i
$487$	42.0409			1.90506			0.952529	−	0.304449i	$-0.0984724\pi$
$487$	42.0409			1.90506			0.952529	+	0.304449i	$0.0984724\pi$
$488$	−19.8743	−	5.80695i	−0.899666	−	0.262868i
$489$	−13.9343			−0.630130
$490$	−18.4904	−	1.75736i	−0.835312	−	0.0793895i
$491$			12.6548i			0.571105i	0.958363	+	0.285553i	$0.0921771\pi$
$491$			12.6548i			0.571105i	−0.958363	+	0.285553i	$0.907823\pi$
$492$	−2.34281	+	12.2139i	−0.105622	+	0.550643i
$493$			0.487148i			0.0219400i
$494$	0.927737	−	9.76136i	0.0417408	−	0.439184i
$495$	15.6605			0.703887
$496$	−21.2672	−	8.47042i	−0.954924	−	0.380333i
$497$	−17.0363			−0.764181
$498$	0.204544	−	2.15215i	0.00916585	−	0.0964403i
$499$		−	3.86760i		−	0.173138i	−0.996246	−	0.0865688i	$-0.972410\pi$
$499$		−	3.86760i		−	0.173138i	0.996246	−	0.0865688i	$-0.0275902\pi$
$500$	2.18179	−	11.3744i	0.0975724	−	0.508677i
$501$			8.17083i			0.365046i
$502$	−33.7511	−	3.20776i	−1.50639	−	0.143170i
$503$	−15.3553			−0.684660			−0.342330	−	0.939580i	$-0.611216\pi$
$503$	−15.3553			−0.684660			−0.342330	+	0.939580i	$0.611216\pi$
$504$	1.21363	−	4.15364i	0.0540593	−	0.185018i
$505$	−12.7113			−0.565645
$506$	7.82174	+	0.743392i	0.347719	+	0.0330478i
$507$		−	9.56223i		−	0.424673i
$508$	−27.9506	−	5.36137i	−1.24011	−	0.237872i
$509$		−	20.3187i		−	0.900612i	−0.892874	−	0.450306i	$-0.851315\pi$
$509$		−	20.3187i		−	0.900612i	0.892874	−	0.450306i	$-0.148685\pi$
$510$	2.00796	−	21.1272i	0.0889140	−	0.935527i
$511$	−1.02270			−0.0452414
$512$	17.0415	−	14.8858i	0.753134	−	0.657867i
$513$	−3.73947			−0.165101
$514$	2.52795	−	26.5984i	0.111503	−	1.17320i
$515$		−	27.6077i		−	1.21654i
$516$	−19.9561	−	3.82791i	−0.878520	−	0.168514i
$517$			33.2672i			1.46309i
$518$	−9.78744	−	0.930215i	−0.430036	−	0.0408713i
$519$	−19.0700			−0.837079
$520$	−4.14587	+	14.1892i	−0.181808	+	0.622238i
$521$	11.0890			0.485817			0.242909	−	0.970049i	$-0.421899\pi$
$521$	11.0890			0.485817			0.242909	+	0.970049i	$0.421899\pi$
$522$	−0.128827	−	0.0122440i	−0.00563862	−	0.000535904i
$523$			10.9043i			0.476813i	0.971165	+	0.238407i	$0.0766251\pi$
$523$			10.9043i			0.476813i	−0.971165	+	0.238407i	$0.923375\pi$
$524$	1.55691	−	8.11669i	0.0680140	−	0.354579i
$525$			4.50662i			0.196685i
$526$	3.62899	−	38.1832i	0.158232	−	1.66486i
$527$	−30.4675			−1.32719
$528$	20.6456	+	8.22288i	0.898486	+	0.357855i
$529$	1.00000			0.0434783
$530$	2.47614	−	26.0532i	0.107557	−	1.13168i
$531$		−	3.88850i		−	0.168746i
$532$	2.15552	−	11.2374i	0.0934535	−	0.487204i
$533$		−	11.5294i		−	0.499395i
$534$	−8.76363	−	0.832910i	−0.379239	−	0.0360436i
$535$	−32.7505			−1.41593
$536$	43.1551	+	12.6093i	1.86402	+	0.544637i
$537$	17.0651			0.736413
$538$	5.49063	+	0.521839i	0.236718	+	0.0224981i
$539$		−	25.8858i		−	1.11498i
$540$	5.53666	+	1.06202i	0.238260	+	0.0457021i
$541$		−	16.9651i		−	0.729386i	−0.931128	−	0.364693i	$-0.881174\pi$
$541$		−	16.9651i		−	0.729386i	0.931128	−	0.364693i	$-0.118826\pi$
$542$	0.155809	−	1.63938i	0.00669257	−	0.0704172i
$543$	−0.189248			−0.00812140
$544$	13.7404	−	26.7982i	0.589116	−	1.14896i
$545$	−14.1099			−0.604400
$546$	−0.379567	+	3.99369i	−0.0162440	+	0.170914i
$547$		−	0.100554i		−	0.00429938i	−0.999998	−	0.00214969i	$-0.999316\pi$
$547$		−	0.100554i		−	0.00429938i	0.999998	−	0.00214969i	$-0.000684269\pi$
$548$	33.0614	+	6.34171i	1.41231	+	0.270905i
$549$		−	7.32041i		−	0.312428i
$550$	−23.0399	−	2.18976i	−0.982426	−	0.0933715i
$551$	−0.342181			−0.0145774
$552$	2.71491	+	0.793255i	0.115554	+	0.0337632i
$553$	12.7100			0.540482
$554$	−4.55386	−	0.432807i	−0.193475	−	0.0183882i
$555$		−	12.8085i		−	0.543690i
$556$	−6.27955	+	32.7373i	−0.266312	+	1.38837i
$557$			17.7403i			0.751682i	0.926684	+	0.375841i	$0.122646\pi$
$557$			17.7403i			0.751682i	−0.926684	+	0.375841i	$0.877354\pi$
$558$	0.765771	−	8.05721i	0.0324177	−	0.341089i
$559$	18.8378			0.796756
$560$	−6.38293	+	16.0260i	−0.269728	+	0.677221i
$561$	29.5771			1.24875
$562$	0.602935	−	6.34390i	0.0254333	−	0.267601i
$563$			2.28914i			0.0964758i	0.998836	+	0.0482379i	$0.0153606\pi$
$563$			2.28914i			0.0964758i	−0.998836	+	0.0482379i	$0.984639\pi$
$564$	−2.25603	+	11.7614i	−0.0949958	+	0.495244i
$565$			40.0028i			1.68293i
$566$	10.0175	+	0.952076i	0.421065	+	0.0400187i
$567$	1.52994			0.0642512
$568$	8.83313	−	30.2313i	0.370630	−	1.26848i
$569$	34.6267			1.45163			0.725813	−	0.687892i	$-0.241464\pi$
$569$	34.6267			1.45163			0.725813	+	0.687892i	$0.241464\pi$
$570$	14.8401	+	1.41043i	0.621582	+	0.0590762i
$571$			6.94347i			0.290575i	0.989389	+	0.145288i	$0.0464107\pi$
$571$			6.94347i			0.290575i	−0.989389	+	0.145288i	$0.953589\pi$
$572$	−20.2332	−	3.88104i	−0.845991	−	0.162275i
$573$			13.1592i			0.549734i
$574$	1.27297	−	13.3938i	0.0531328	−	0.559047i
$575$	−2.94563			−0.122841
$576$	6.74149	+	4.30724i	0.280896	+	0.179468i
$577$	2.27958			0.0949001			0.0474501	−	0.998874i	$-0.484891\pi$
$577$	2.27958			0.0949001			0.0474501	+	0.998874i	$0.484891\pi$
$578$	1.51762	−	15.9680i	0.0631248	−	0.664180i
$579$		−	2.95455i		−	0.122787i
$580$	0.506633	+	0.0971804i	0.0210368	+	0.00403520i
$581$			2.33875i			0.0970278i
$582$	−12.5777	−	1.19541i	−0.521362	−	0.0495511i
$583$	36.4733			1.51057
$584$	0.530257	−	1.81480i	0.0219422	−	0.0750971i
$585$	−5.22640			−0.216085
$586$	−39.7731	−	3.78011i	−1.64301	−	0.156155i
$587$		−	11.0925i		−	0.457835i	−0.973446	−	0.228917i	$-0.926481\pi$
$587$		−	11.0925i		−	0.457835i	0.973446	−	0.228917i	$-0.0735186\pi$
$588$	1.75545	−	9.15176i	0.0723937	−	0.377412i
$589$		−	21.4009i		−	0.881809i
$590$	−1.46664	+	15.4315i	−0.0603804	+	0.635305i
$591$	−25.5436			−1.05072
$592$	6.72538	−	16.8858i	0.276411	−	0.694001i
$593$	−25.2170			−1.03554			−0.517768	−	0.855521i	$-0.673237\pi$
$593$	−25.2170			−1.03554			−0.517768	+	0.855521i	$0.673237\pi$
$594$	−0.743392	+	7.82174i	−0.0305017	+	0.320930i
$595$			22.9589i			0.941225i
$596$	−4.47490	+	23.3291i	−0.183299	+	0.955599i
$597$			7.92928i			0.324524i
$598$	−2.61036	−	0.248093i	−0.106746	−	0.0101453i
$599$	−23.9192			−0.977313			−0.488656	−	0.872476i	$-0.662513\pi$
$599$	−23.9192			−0.977313			−0.488656	+	0.872476i	$0.662513\pi$
$600$	−7.99712	−	2.33663i	−0.326481	−	0.0953927i
$601$	6.35494			0.259223			0.129612	−	0.991565i	$-0.458627\pi$
$601$	6.35494			0.259223			0.129612	+	0.991565i	$0.458627\pi$
$602$	21.8841	+	2.07990i	0.891928	+	0.0847704i
$603$			15.8956i			0.647318i
$604$	25.6335	+	4.91692i	1.04301	+	0.200067i
$605$		−	55.9987i		−	2.27667i
$606$	0.603395	−	6.34874i	0.0245113	−	0.257900i
$607$	24.4834			0.993749			0.496874	−	0.867823i	$-0.334481\pi$
$607$	24.4834			0.993749			0.496874	+	0.867823i	$0.334481\pi$
$608$	18.8235	+	9.65151i	0.763393	+	0.391420i
$609$	0.139997			0.00567297
$610$	−2.76106	+	29.0511i	−0.111792	+	1.17624i
$611$		−	11.1023i		−	0.449152i
$612$	10.4568	+	2.00578i	0.422691	+	0.0810789i
$613$			29.7865i			1.20307i	0.798848	+	0.601533i	$0.205443\pi$
$613$			29.7865i			1.20307i	−0.798848	+	0.601533i	$0.794557\pi$
$614$	−22.6930	−	2.15678i	−0.915813	−	0.0870405i
$615$	17.5280			0.706798
$616$	−23.0765	−	6.74259i	−0.929779	−	0.271667i
$617$	−34.6826			−1.39627			−0.698134	−	0.715967i	$-0.745986\pi$
$617$	−34.6826			−1.39627			−0.698134	+	0.715967i	$0.745986\pi$
$618$	13.7889	+	1.31052i	0.554670	+	0.0527168i
$619$			0.261110i			0.0104949i	0.999986	+	0.00524745i	$0.00167032\pi$
$619$			0.261110i			0.0104949i	−0.999986	+	0.00524745i	$0.998330\pi$
$620$	−6.07793	+	31.6862i	−0.244095	+	1.27255i
$621$			1.00000i			0.0401286i
$622$	0.860388	−	9.05275i	0.0344984	−	0.362982i
$623$	9.52346			0.381549
$624$	−6.89010	−	2.74423i	−0.275825	−	0.109857i
$625$	−31.0514			−1.24206
$626$	4.30533	−	45.2994i	0.172076	−	1.81053i
$627$			20.7755i			0.829692i
$628$	−7.18452	+	37.4552i	−0.286693	+	1.49463i
$629$		−	24.1907i		−	0.964547i
$630$	−6.07155	−	0.577050i	−0.241896	−	0.0229902i
$631$	9.58039			0.381389			0.190695	−	0.981649i	$-0.438926\pi$
$631$	9.58039			0.381389			0.190695	+	0.981649i	$0.438926\pi$
$632$	−6.58998	+	22.5542i	−0.262135	+	0.897156i
$633$	−16.8478			−0.669639
$634$	−1.31635	−	0.125108i	−0.0522788	−	0.00496867i
$635$			40.1117i			1.59178i
$636$	12.8949	+	2.47345i	0.511316	+	0.0980787i
$637$			8.63891i			0.342286i
$638$	−0.0680242	+	0.715730i	−0.00269310	+	0.0283360i
$639$	11.1353			0.440505
$640$	−25.1290	−	19.6360i	−0.993313	−	0.776180i
$641$	32.4751			1.28269			0.641345	−	0.767253i	$-0.278377\pi$
$641$	32.4751			1.28269			0.641345	+	0.767253i	$0.278377\pi$
$642$	1.55464	−	16.3575i	0.0613568	−	0.645578i
$643$		−	45.8079i		−	1.80649i	−0.429127	−	0.903244i	$-0.641179\pi$
$643$		−	45.8079i		−	1.80649i	0.429127	−	0.903244i	$-0.358821\pi$
$644$	−3.00509	−	0.576424i	−0.118417	−	0.0227143i
$645$			28.6389i			1.12766i
$646$	28.0277	+	2.66380i	1.10273	+	0.104806i
$647$	−19.7514			−0.776508			−0.388254	−	0.921552i	$-0.626922\pi$
$647$	−19.7514			−0.776508			−0.388254	+	0.921552i	$0.626922\pi$
$648$	−0.793255	+	2.71491i	−0.0311620	+	0.106652i
$649$	−21.6034			−0.848009
$650$	7.68916	+	0.730791i	0.301594	+	0.0286640i
$651$			8.75579i			0.343167i
$652$	−5.24993	+	27.3696i	−0.205603	+	1.07188i
$653$			32.1246i			1.25713i	0.777757	+	0.628565i	$0.216358\pi$
$653$			32.1246i			1.25713i	−0.777757	+	0.628565i	$0.783642\pi$
$654$	0.669784	−	7.04727i	0.0261906	−	0.275570i
$655$	−11.6482			−0.455133
$656$	23.1077	+	9.20347i	0.902203	+	0.359335i
$657$	0.668457			0.0260790
$658$	1.22581	−	12.8976i	0.0477872	−	0.502803i
$659$		−	22.8155i		−	0.888767i	−0.895837	−	0.444383i	$-0.853423\pi$
$659$		−	22.8155i		−	0.888767i	0.895837	−	0.444383i	$-0.146577\pi$
$660$	5.90030	−	30.7602i	0.229669	−	1.19734i
$661$		−	11.5069i		−	0.447566i	−0.974639	−	0.223783i	$-0.928159\pi$
$661$		−	11.5069i		−	0.447566i	0.974639	−	0.223783i	$-0.0718408\pi$
$662$	−37.7587	−	3.58865i	−1.46753	−	0.139477i
$663$	−9.87082			−0.383351
$664$	−4.15018	−	1.21262i	−0.161058	−	0.0470587i
$665$	−16.1267			−0.625368
$666$	6.39729	+	0.608010i	0.247890	+	0.0235599i
$667$			0.0915052i			0.00354310i
$668$	16.0491	+	3.07847i	0.620957	+	0.119110i
$669$			14.5247i			0.561556i
$670$	5.99539	−	63.0817i	0.231622	−	2.43706i
$671$	−40.6702			−1.57006
$672$	−7.70129	−	3.94874i	−0.297084	−	0.152326i
$673$	7.03361			0.271126			0.135563	−	0.990769i	$-0.456716\pi$
$673$	7.03361			0.271126			0.135563	+	0.990769i	$0.456716\pi$
$674$	0.857549	−	9.02287i	0.0330316	−	0.347548i
$675$		−	2.94563i		−	0.113377i
$676$	−18.7821	−	3.60270i	−0.722387	−	0.138565i
$677$		−	24.7211i		−	0.950111i	−0.879956	−	0.475055i	$-0.842428\pi$
$677$		−	24.7211i		−	0.950111i	0.879956	−	0.475055i	$-0.157572\pi$
$678$	−19.9797	−	1.89891i	−0.767316	−	0.0729270i
$679$	13.6682			0.524538
$680$	−40.7413	−	11.9040i	−1.56236	−	0.456496i
$681$	17.2251			0.660067
$682$	−44.7637	−	4.25442i	−1.71409	−	0.162910i
$683$		−	8.39929i		−	0.321390i	−0.987004	−	0.160695i	$-0.948626\pi$
$683$		−	8.39929i		−	0.321390i	0.987004	−	0.160695i	$-0.0513735\pi$
$684$	−1.40889	+	7.34503i	−0.0538704	+	0.280844i
$685$		−	47.4462i		−	1.81283i
$686$	−2.38683	+	25.1135i	−0.0911297	+	0.958839i
$687$	−25.1934			−0.961188
$688$	−15.0375	+	37.7555i	−0.573299	+	1.43941i
$689$	−12.1723			−0.463728
$690$	0.377173	−	3.96850i	0.0143587	−	0.151078i
$691$			8.26581i			0.314446i	0.987563	+	0.157223i	$0.0502542\pi$
$691$			8.26581i			0.314446i	−0.987563	+	0.157223i	$0.949746\pi$
$692$	−7.18487	+	37.4571i	−0.273128	+	1.42391i
$693$		−	8.49991i		−	0.322885i
$694$	26.8749	+	2.55424i	1.02016	+	0.0969577i
$695$	46.9811			1.78210
$696$	−0.0725870	+	0.248429i	−0.00275140	+	0.00941666i
$697$	33.1042			1.25391
$698$	−27.2312	−	2.58810i	−1.03072	−	0.0979610i
$699$			11.4444i			0.432867i
$700$	8.85186	+	1.69793i	0.334569	+	0.0641757i
$701$			14.1213i			0.533353i	0.963786	+	0.266677i	$0.0859256\pi$
$701$			14.1213i			0.533353i	−0.963786	+	0.266677i	$0.914074\pi$
$702$	0.248093	−	2.61036i	0.00936368	−	0.0985218i
$703$	16.9920			0.640864
$704$	23.9298	−	37.4539i	0.901890	−	1.41160i
$705$	16.8787			0.635689
$706$	−3.37661	+	35.5277i	−0.127080	+	1.33710i
$707$			6.89919i			0.259471i
$708$	−7.63775	−	1.46504i	−0.287044	−	0.0550597i
$709$			23.8735i			0.896589i	0.893886	+	0.448294i	$0.147968\pi$
$709$			23.8735i			0.896589i	−0.893886	+	0.448294i	$0.852032\pi$
$710$	−44.1904	−	4.19993i	−1.65844	−	0.157621i
$711$	−8.30751			−0.311556
$712$	−4.93781	+	16.8996i	−0.185052	+	0.633341i
$713$	−5.72298			−0.214327
$714$	−11.4670	−	1.08984i	−0.429142	−	0.0407864i
$715$			29.0365i			1.08590i
$716$	6.42951	−	33.5191i	0.240282	−	1.25267i
$717$		−	17.4459i		−	0.651529i
$718$	2.34503	−	24.6737i	0.0875158	−	0.920815i
$719$	10.6369			0.396690			0.198345	−	0.980132i	$-0.436443\pi$
$719$	10.6369			0.396690			0.198345	+	0.980132i	$0.436443\pi$
$720$	4.17202	−	10.4749i	0.155482	−	0.390378i
$721$	−14.9844			−0.558048
$722$	0.671225	−	7.06242i	0.0249804	−	0.262836i
$723$			12.6268i			0.469597i
$724$	−0.0713016	+	0.371719i	−0.00264990	+	0.0138148i
$725$		−	0.269540i		−	0.0100105i
$726$	27.9689	+	2.65822i	1.03802	+	0.0986556i
$727$	22.6114			0.838611			0.419306	−	0.907845i	$-0.362274\pi$
$727$	22.6114			0.838611			0.419306	+	0.907845i	$0.362274\pi$
$728$	7.70136	+	2.25022i	0.285431	+	0.0833986i
$729$	−1.00000			−0.0370370
$730$	−2.65277	−	0.252124i	−0.0981835	−	0.00933153i
$731$			54.0888i			2.00055i
$732$	−14.3787	−	2.75806i	−0.531452	−	0.101941i
$733$			32.7106i			1.20819i	0.796911	+	0.604097i	$0.206466\pi$
$733$			32.7106i			1.20819i	−0.796911	+	0.604097i	$0.793534\pi$
$734$	−1.47137	+	15.4813i	−0.0543092	+	0.571425i
$735$	−13.1336			−0.484441
$736$	2.58098	−	5.03374i	0.0951364	−	0.185546i
$737$	88.3116			3.25300
$738$	−0.832042	+	8.75450i	−0.0306279	+	0.322258i
$739$			14.6584i			0.539217i	0.962970	+	0.269608i	$0.0868943\pi$
$739$			14.6584i			0.539217i	−0.962970	+	0.269608i	$0.913106\pi$
$740$	−25.1583	−	4.82577i	−0.924839	−	0.177399i
$741$		−	6.93343i		−	0.254706i
$742$	−14.1407	−	1.34395i	−0.519120	−	0.0493380i
$743$	−14.2374			−0.522320			−0.261160	−	0.965296i	$-0.584105\pi$
$743$	−14.2374			−0.522320			−0.261160	+	0.965296i	$0.584105\pi$
$744$	−15.5374	−	4.53978i	−0.569628	−	0.166437i
$745$	33.4795			1.22659
$746$	39.3141	+	3.73648i	1.43939	+	0.136802i
$747$		−	1.52866i		−	0.0559308i
$748$	11.1436	−	58.0951i	0.407450	−	2.12417i
$749$			17.7757i			0.649510i
$750$	0.774854	−	8.15278i	0.0282937	−	0.297697i
$751$	23.9489			0.873907			0.436953	−	0.899484i	$-0.356057\pi$
$751$	23.9489			0.873907			0.436953	+	0.899484i	$0.356057\pi$
$752$	22.2517	+	8.86253i	0.811434	+	0.323183i
$753$	−23.9732			−0.873632
$754$	0.0227018	−	0.238862i	0.000826752	−	0.00869883i
$755$		−	36.7865i		−	1.33880i
$756$	0.576424	−	3.00509i	0.0209643	−	0.109294i
$757$		−	50.2861i		−	1.82768i	−0.406074	−	0.913840i	$-0.633102\pi$
$757$		−	50.2861i		−	1.82768i	0.406074	−	0.913840i	$-0.366898\pi$
$758$	18.9795	+	1.80384i	0.689365	+	0.0655184i
$759$	5.55573			0.201660
$760$	8.36155	−	28.6174i	0.303305	−	1.03806i
$761$	−16.3787			−0.593726			−0.296863	−	0.954920i	$-0.595941\pi$
$761$	−16.3787			−0.593726			−0.296863	+	0.954920i	$0.595941\pi$
$762$	−20.0341	−	1.90407i	−0.725757	−	0.0689772i
$763$			7.65828i			0.277248i
$764$	25.8472	+	4.95791i	0.935119	+	0.179371i
$765$		−	15.0065i		−	0.542561i
$766$	−4.44067	+	46.7234i	−0.160448	+	1.68819i
$767$	7.20975			0.260329
$768$	11.0002	−	11.6188i	0.396935	−	0.419256i
$769$	12.4062			0.447378			0.223689	−	0.974661i	$-0.428190\pi$
$769$	12.4062			0.447378			0.223689	+	0.974661i	$0.428190\pi$
$770$	−3.20594	+	33.7319i	−0.115534	+	1.21561i
$771$		−	18.8926i		−	0.680402i
$772$	−5.80330	−	1.11317i	−0.208865	−	0.0400637i
$773$			34.8269i			1.25264i	0.779568	+	0.626318i	$0.215439\pi$
$773$			34.8269i			1.25264i	−0.779568	+	0.626318i	$0.784561\pi$
$774$	−14.3039	−	1.35947i	−0.514144	−	0.0488651i
$775$	16.8578			0.605549
$776$	−7.08682	+	24.2546i	−0.254402	+	0.870690i
$777$	−6.95196			−0.249400
$778$	47.9810	+	4.56020i	1.72020	+	0.163491i
$779$			23.2530i			0.833124i
$780$	−1.96912	+	10.2657i	−0.0705057	+	0.367569i
$781$		−	61.8647i		−	2.21369i
$782$	0.712347	−	7.49509i	0.0254735	−	0.268024i
$783$	−0.0915052			−0.00327013
$784$	−17.3144	−	6.89610i	−0.618372	−	0.246289i
$785$	53.7518			1.91848
$786$	0.552932	−	5.81778i	0.0197224	−	0.207513i
$787$		−	10.0090i		−	0.356781i	−0.983960	−	0.178391i	$-0.942911\pi$
$787$		−	10.0090i		−	0.356781i	0.983960	−	0.178391i	$-0.0570891\pi$
$788$	−9.62388	+	50.1724i	−0.342837	+	1.78732i
$789$		−	27.1212i		−	0.965542i
$790$	32.9684	+	3.13337i	1.17296	+	0.111480i
$791$	21.7120			0.771990
$792$	15.0833	+	4.40711i	0.535962	+	0.156600i
$793$	13.5729			0.481989
$794$	−6.62375	−	0.629532i	−0.235068	−	0.0223413i
$795$		−	18.5054i		−	0.656319i
$796$	15.5746	+	2.98746i	0.552028	+	0.105888i
$797$			31.6394i			1.12072i	0.828248	+	0.560362i	$0.189338\pi$
$797$			31.6394i			1.12072i	−0.828248	+	0.560362i	$0.810662\pi$
$798$	0.765525	−	8.05462i	0.0270993	−	0.285130i
$799$	31.8779			1.12776
$800$	−7.60262	+	14.8275i	−0.268793	+	0.524232i
$801$	−6.22475			−0.219941
$802$	0.490880	−	5.16489i	0.0173336	−	0.182379i
$803$		−	3.71377i		−	0.131056i
$804$	31.2220	+	5.98888i	1.10111	+	0.211211i
$805$			4.31258i			0.151998i
$806$	14.9391	+	1.41983i	0.526206	+	0.0500115i
$807$	3.89996			0.137285
$808$	−12.2428	−	3.57716i	−0.430701	−	0.125844i
$809$	−37.7471			−1.32712			−0.663558	−	0.748125i	$-0.730954\pi$
$809$	−37.7471			−1.32712			−0.663558	+	0.748125i	$0.730954\pi$
$810$	3.96850	+	0.377173i	0.139439	+	0.0132525i
$811$		−	45.4845i		−	1.59718i	−0.601876	−	0.798589i	$-0.705580\pi$
$811$		−	45.4845i		−	1.59718i	0.601876	−	0.798589i	$-0.294420\pi$
$812$	0.0527458	−	0.274981i	0.00185101	−	0.00964994i
$813$		−	1.16444i		−	0.0408386i
$814$	3.37794	−	35.5416i	0.118397	−	1.24573i
$815$	39.2780			1.37585
$816$	7.87948	−	19.7834i	0.275837	−	0.692559i
$817$	−37.9929			−1.32920
$818$	−1.11085	+	11.6880i	−0.0388399	+	0.408662i
$819$			2.83669i			0.0991219i
$820$	6.60392	−	34.4284i	0.230619	−	1.20229i
$821$		−	46.4403i		−	1.62078i	−0.585892	−	0.810389i	$-0.699256\pi$
$821$		−	46.4403i		−	1.62078i	0.585892	−	0.810389i	$-0.300744\pi$
$822$	23.6974	+	2.25224i	0.826541	+	0.0785558i
$823$	−7.01352			−0.244476			−0.122238	−	0.992501i	$-0.539007\pi$
$823$	−7.01352			−0.244476			−0.122238	+	0.992501i	$0.539007\pi$
$824$	7.76925	−	26.5902i	0.270655	−	0.926314i
$825$	−16.3651			−0.569760
$826$	8.37562	+	0.796033i	0.291425	+	0.0276975i
$827$			25.7743i			0.896262i	0.893968	+	0.448131i	$0.147910\pi$
$827$			25.7743i			0.896262i	−0.893968	+	0.448131i	$0.852090\pi$
$828$	1.96419	+	0.376764i	0.0682604	+	0.0130934i
$829$			27.5652i			0.957379i	0.877984	+	0.478689i	$0.158888\pi$
$829$			27.5652i			0.957379i	−0.877984	+	0.478689i	$0.841112\pi$
$830$	−0.576570	+	6.06649i	−0.0200130	+	0.210571i
$831$	−3.23458			−0.112206
$832$	−7.98614	+	12.4996i	−0.276870	+	0.433344i
$833$	−24.8048			−0.859435
$834$	−2.23016	+	23.4651i	−0.0772241	+	0.812529i
$835$		−	23.0319i		−	0.797052i
$836$	40.8070	+	7.82744i	1.41134	+	0.270718i
$837$		−	5.72298i		−	0.197815i
$838$	−33.3414	−	3.16882i	−1.15176	−	0.109465i
$839$	18.0347			0.622626			0.311313	−	0.950307i	$-0.399231\pi$
$839$	18.0347			0.622626			0.311313	+	0.950307i	$0.399231\pi$
$840$	−3.42098	+	11.7083i	−0.118035	+	0.403974i
$841$	28.9916			0.999711
$842$	15.7738	+	1.49917i	0.543602	+	0.0516649i
$843$		−	4.50603i		−	0.155196i
$844$	−6.34762	+	33.0922i	−0.218494	+	1.13908i
$845$			26.9540i			0.927246i
$846$	−0.801220	+	8.43019i	−0.0275465	+	0.289836i
$847$	−30.3939			−1.04435
$848$	9.71666	−	24.3962i	0.333671	−	0.837767i
$849$	7.11533			0.244197
$850$	−2.09831	+	22.0778i	−0.0719714	+	0.757261i
$851$		−	4.54395i		−	0.155765i
$852$	4.19537	−	21.8718i	0.143731	−	0.749317i
$853$			30.8777i			1.05723i	0.848861	+	0.528616i	$0.177289\pi$
$853$			30.8777i			1.05723i	−0.848861	+	0.528616i	$0.822711\pi$
$854$	15.7678	+	1.49860i	0.539563	+	0.0512810i
$855$	10.5408			0.360488
$856$	−31.5435	−	9.21651i	−1.07813	−	0.315014i
$857$	−19.2629			−0.658007			−0.329003	−	0.944329i	$-0.606713\pi$
$857$	−19.2629			−0.658007			−0.329003	+	0.944329i	$0.606713\pi$
$858$	−14.5025	−	1.37834i	−0.495106	−	0.0470557i
$859$			3.36054i			0.114660i	0.998355	+	0.0573301i	$0.0182587\pi$
$859$			3.36054i			0.114660i	−0.998355	+	0.0573301i	$0.981741\pi$
$860$	56.2524	+	10.7901i	1.91819	+	0.367940i
$861$		−	9.51353i		−	0.324220i
$862$	−1.78906	+	18.8239i	−0.0609356	+	0.641146i
$863$	−28.4323			−0.967847			−0.483923	−	0.875110i	$-0.660789\pi$
$863$	−28.4323			−0.967847			−0.483923	+	0.875110i	$0.660789\pi$
$864$	5.03374	+	2.58098i	0.171251	+	0.0878069i
$865$	53.7544			1.82771
$866$	−2.68224	+	28.2217i	−0.0911461	+	0.959012i
$867$		−	11.3419i		−	0.385192i
$868$	17.1981	+	3.29886i	0.583740	+	0.111971i
$869$			46.1543i			1.56568i
$870$	0.363139	+	0.0345133i	0.0123115	+	0.00117011i
$871$	−29.4724			−0.998633
$872$	−13.5898	−	3.97074i	−0.460210	−	0.134466i
$873$	−8.93385			−0.302365
$874$	5.26468	+	0.500364i	0.178080	+	0.0169251i
$875$			8.85964i			0.299511i
$876$	0.251850	−	1.31298i	0.00850923	−	0.0443614i
$877$			5.93724i			0.200486i	0.994963	+	0.100243i	$0.0319621\pi$
$877$			5.93724i			0.200486i	−0.994963	+	0.100243i	$0.968038\pi$
$878$	5.24465	−	55.1826i	0.176998	−	1.86232i
$879$	−28.2506			−0.952869
$880$	−58.1959	−	23.1786i	−1.96178	−	0.781352i
$881$	54.6858			1.84241			0.921206	−	0.389076i	$-0.127206\pi$
$881$	54.6858			1.84241			0.921206	+	0.389076i	$0.127206\pi$
$882$	0.623444	−	6.55968i	0.0209924	−	0.220876i
$883$		−	45.4971i		−	1.53110i	−0.643376	−	0.765550i	$-0.722467\pi$
$883$		−	45.4971i		−	1.53110i	0.643376	−	0.765550i	$-0.277533\pi$
$884$	−3.71897	+	19.3882i	−0.125082	+	0.652095i
$885$			10.9609i			0.368446i
$886$	57.8893	+	5.50190i	1.94483	+	0.184840i
$887$	32.1231			1.07859			0.539295	−	0.842117i	$-0.318691\pi$
$887$	32.1231			1.07859			0.539295	+	0.842117i	$0.318691\pi$
$888$	3.60451	−	12.3364i	0.120960	−	0.413984i
$889$	21.7711			0.730178
$890$	24.7029	+	2.34781i	0.828043	+	0.0786987i
$891$			5.55573i			0.186124i
$892$	28.5292	+	5.47236i	0.955229	+	0.183228i
$893$			22.3916i			0.749306i
$894$	−1.58925	+	16.7216i	−0.0531524	+	0.559253i
$895$	−48.1031			−1.60791
$896$	−10.6576	+	13.6391i	−0.356047	+	0.455649i
$897$	−1.85412			−0.0619074
$898$	3.92388	−	41.2858i	0.130941	−	1.37773i
$899$		−	0.523683i		−	0.0174658i
$900$	−5.78578	−	1.10981i	−0.192859	−	0.0369935i
$901$		−	34.9501i		−	1.16436i
$902$	48.6376	+	4.62260i	1.61946	+	0.153916i
$903$	15.5441			0.517275
$904$	−11.2574	+	38.5285i	−0.374417	+	1.28144i
$905$	0.533451			0.0177325
$906$	18.3733	+	1.74623i	0.610412	+	0.0580146i
$907$		−	14.2346i		−	0.472653i	−0.971674	−	0.236327i	$-0.924056\pi$
$907$		−	14.2346i		−	0.472653i	0.971674	−	0.236327i	$-0.0759435\pi$
$908$	6.48979	−	33.8334i	0.215371	−	1.12280i
$909$		−	4.50947i		−	0.149570i
$910$	1.06992	−	11.2574i	0.0354676	−	0.373179i
$911$	−49.6913			−1.64635			−0.823173	−	0.567791i	$-0.807798\pi$
$911$	−49.6913			−1.64635			−0.823173	+	0.567791i	$0.807798\pi$
$912$	13.8962	+	5.53468i	0.460150	+	0.183272i
$913$	−8.49283			−0.281072
$914$	−3.49672	+	36.7914i	−0.115661	+	1.21695i
$915$			20.6348i			0.682165i
$916$	−9.49196	+	49.4847i	−0.313623	+	1.63502i
$917$			6.32220i			0.208777i
$918$	7.49509	+	0.712347i	0.247375	+	0.0235109i
$919$	−4.33854			−0.143115			−0.0715576	−	0.997436i	$-0.522797\pi$
$919$	−4.33854			−0.143115			−0.0715576	+	0.997436i	$0.522797\pi$
$920$	−7.65279	−	2.23603i	−0.252305	−	0.0737196i
$921$	−16.1187			−0.531128
$922$	32.5965	+	3.09803i	1.07351	+	0.102028i
$923$			20.6462i			0.679578i
$924$	−16.6954	−	3.20246i	−0.549240	−	0.105353i
$925$			13.3848i			0.440089i
$926$	3.33565	−	35.0967i	0.109616	−	1.15335i
$927$	9.79414			0.321682
$928$	0.460613	+	0.236174i	0.0151204	+	0.00775278i
$929$	−17.9366			−0.588479			−0.294240	−	0.955732i	$-0.595066\pi$
$929$	−17.9366			−0.588479			−0.294240	+	0.955732i	$0.595066\pi$
$930$	−2.15855	+	22.7117i	−0.0707818	+	0.744745i
$931$		−	17.4233i		−	0.571025i
$932$	22.4790	+	4.31184i	0.736325	+	0.141239i
$933$		−	6.43010i		−	0.210512i
$934$	16.1855	+	1.53830i	0.529606	+	0.0503347i
$935$	−83.3720			−2.72656
$936$	−5.03378	−	1.47079i	−0.164534	−	0.0480744i
$937$	−31.5865			−1.03189			−0.515943	−	0.856623i	$-0.672558\pi$
$937$	−31.5865			−1.03189			−0.515943	+	0.856623i	$0.672558\pi$
$938$	−34.2383	−	3.25406i	−1.11792	−	0.106249i
$939$		−	32.1758i		−	1.05002i
$940$	6.35928	−	33.1530i	0.207417	−	1.08133i
$941$		−	8.30639i		−	0.270780i	−0.990792	−	0.135390i	$-0.956771\pi$
$941$		−	8.30639i		−	0.270780i	0.990792	−	0.135390i	$-0.0432288\pi$
$942$	−2.55156	+	26.8467i	−0.0831342	+	0.874713i
$943$	6.21826			0.202494
$944$	−5.75525	+	14.4500i	−0.187317	+	0.470308i
$945$	−4.31258			−0.140288
$946$	−7.55284	+	79.4687i	−0.245564	+	2.58375i
$947$		−	23.4557i		−	0.762209i	−0.924532	−	0.381105i	$-0.875544\pi$
$947$		−	23.4557i		−	0.762209i	0.924532	−	0.381105i	$-0.124456\pi$
$948$	−3.12997	+	16.3175i	−0.101657	+	0.529969i
$949$			1.23940i			0.0402327i
$950$	−15.5078	−	1.47389i	−0.503139	−	0.0478192i
$951$	−0.934992			−0.0303192
$952$	−6.46101	+	22.1128i	−0.209403	+	0.716680i
$953$	22.3020			0.722433			0.361216	−	0.932482i	$-0.382362\pi$
$953$	22.3020			0.722433			0.361216	+	0.932482i	$0.382362\pi$
$954$	9.24265	+	0.878437i	0.299242	+	0.0284405i
$955$		−	37.0932i		−	1.20031i
$956$	−34.2671	−	6.57298i	−1.10828	−	0.212585i
$957$			0.508378i			0.0164335i
$958$	0.743631	−	7.82426i	0.0240256	−	0.252790i
$959$	−25.7520			−0.831575
$960$	−19.0029	−	12.1412i	−0.613316	−	0.391857i
$961$	1.75253			0.0565331
$962$	−1.12732	+	11.8614i	−0.0363464	+	0.382426i
$963$		−	11.6186i		−	0.374404i
$964$	24.8015	+	4.75733i	0.798802	+	0.153223i
$965$			8.32828i			0.268097i
$966$	−2.15395	−	0.204715i	−0.0693022	−	0.00658660i
$967$	−7.41291			−0.238383			−0.119192	−	0.992871i	$-0.538030\pi$
$967$	−7.41291			−0.238383			−0.119192	+	0.992871i	$0.538030\pi$
$968$	15.7589	−	53.9348i	0.506511	−	1.73353i
$969$	19.9079			0.639532
$970$	35.4540	+	3.36961i	1.13836	+	0.108192i
$971$			21.2617i			0.682320i	0.940005	+	0.341160i	$0.110820\pi$
$971$			21.2617i			0.682320i	−0.940005	+	0.341160i	$0.889180\pi$
$972$	−0.376764	+	1.96419i	−0.0120847	+	0.0630015i
$973$		−	25.4995i		−	0.817478i
$974$	5.62534	−	59.1882i	0.180248	−	1.89651i
$975$	5.46156			0.174910
$976$	−10.8347	+	27.2034i	−0.346811	+	0.870759i
$977$	−15.9600			−0.510606			−0.255303	−	0.966861i	$-0.582175\pi$
$977$	−15.9600			−0.510606			−0.255303	+	0.966861i	$0.582175\pi$
$978$	−1.86450	+	19.6177i	−0.0596200	+	0.627304i
$979$			34.5830i			1.10528i
$980$	−4.94827	+	25.7970i	−0.158067	+	0.824054i
$981$		−	5.00563i		−	0.159817i
$982$	17.8164	+	1.69330i	0.568543	+	0.0540353i
$983$	3.18078			0.101451			0.0507256	−	0.998713i	$-0.483847\pi$
$983$	3.18078			0.101451			0.0507256	+	0.998713i	$0.483847\pi$
$984$	16.8820	+	4.93267i	0.538179	+	0.157248i
$985$	72.0022			2.29418
$986$	0.685840	+	0.0651834i	0.0218416	+	0.00207586i
$987$		−	9.16111i		−	0.291601i
$988$	−13.6186	−	2.61226i	−0.433265	−	0.0831072i
$989$			10.1600i			0.323068i
$990$	2.09547	−	22.0479i	0.0665985	−	0.700729i
$991$	4.08113			0.129641			0.0648207	−	0.997897i	$-0.479352\pi$
$991$	4.08113			0.129641			0.0648207	+	0.997897i	$0.479352\pi$
$992$	−14.7709	+	28.8080i	−0.468978	+	0.914655i
$993$	−26.8197			−0.851098
$994$	−2.27956	+	23.9848i	−0.0723033	+	0.760753i
$995$		−	22.3511i		−	0.708576i
$996$	−3.00258	−	0.575944i	−0.0951405	−	0.0182495i
$997$		−	47.2738i		−	1.49718i	−0.663036	−	0.748588i	$-0.730732\pi$
$997$		−	47.2738i		−	1.49718i	0.663036	−	0.748588i	$-0.269268\pi$
$998$	−5.44507	−	0.517509i	−0.172361	−	0.0163815i
$999$	4.54395			0.143764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.d.277.11	✓	20
4.3	odd	2		2208.2.f.d.1105.19		20
8.3	odd	2		2208.2.f.d.1105.2		20
8.5	even	2	inner	552.2.f.d.277.12	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.d.277.11	✓	20	1.1	even	1	trivial
552.2.f.d.277.12	yes	20	8.5	even	2	inner
2208.2.f.d.1105.2		20	8.3	odd	2
2208.2.f.d.1105.19		20	4.3	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.133806 - 1.40787i) q^{2} -1.00000i q^{3} +(-1.96419 - 0.376764i) q^{4} +2.81880i q^{5} +(-1.40787 - 0.133806i) q^{6} +1.52994 q^{7} +(-0.793255 + 2.71491i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.133806 - 1.40787i) q^{2} -1.00000i q^{3} +(-1.96419 - 0.376764i) q^{4} +2.81880i q^{5} +(-1.40787 - 0.133806i) q^{6} +1.52994 q^{7} +(-0.793255 + 2.71491i) q^{8} -1.00000 q^{9} +(3.96850 + 0.377173i) q^{10} +5.55573i q^{11} +(-0.376764 + 1.96419i) q^{12} -1.85412i q^{13} +(0.204715 - 2.15395i) q^{14} +2.81880 q^{15} +(3.71610 + 1.48007i) q^{16} +5.32371 q^{17} +(-0.133806 + 1.40787i) q^{18} +3.73947i q^{19} +(1.06202 - 5.53666i) q^{20} -1.52994i q^{21} +(7.82174 + 0.743392i) q^{22} +1.00000 q^{23} +(2.71491 + 0.793255i) q^{24} -2.94563 q^{25} +(-2.61036 - 0.248093i) q^{26} +1.00000i q^{27} +(-3.00509 - 0.576424i) q^{28} +0.0915052i q^{29} +(0.377173 - 3.96850i) q^{30} -5.72298 q^{31} +(2.58098 - 5.03374i) q^{32} +5.55573 q^{33} +(0.712347 - 7.49509i) q^{34} +4.31258i q^{35} +(1.96419 + 0.376764i) q^{36} -4.54395i q^{37} +(5.26468 + 0.500364i) q^{38} -1.85412 q^{39} +(-7.65279 - 2.23603i) q^{40} +6.21826 q^{41} +(-2.15395 - 0.204715i) q^{42} +10.1600i q^{43} +(2.09320 - 10.9125i) q^{44} -2.81880i q^{45} +(0.133806 - 1.40787i) q^{46} +5.98791 q^{47} +(1.48007 - 3.71610i) q^{48} -4.65930 q^{49} +(-0.394144 + 4.14706i) q^{50} -5.32371i q^{51} +(-0.698566 + 3.64185i) q^{52} -6.56499i q^{53} +(1.40787 + 0.133806i) q^{54} -15.6605 q^{55} +(-1.21363 + 4.15364i) q^{56} +3.73947 q^{57} +(0.128827 + 0.0122440i) q^{58} +3.88850i q^{59} +(-5.53666 - 1.06202i) q^{60} +7.32041i q^{61} +(-0.765771 + 8.05721i) q^{62} -1.52994 q^{63} +(-6.74149 - 4.30724i) q^{64} +5.22640 q^{65} +(0.743392 - 7.82174i) q^{66} -15.8956i q^{67} +(-10.4568 - 2.00578i) q^{68} -1.00000i q^{69} +(6.07155 + 0.577050i) q^{70} -11.1353 q^{71} +(0.793255 - 2.71491i) q^{72} -0.668457 q^{73} +(-6.39729 - 0.608010i) q^{74} +2.94563i q^{75} +(1.40889 - 7.34503i) q^{76} +8.49991i q^{77} +(-0.248093 + 2.61036i) q^{78} +8.30751 q^{79} +(-4.17202 + 10.4749i) q^{80} +1.00000 q^{81} +(0.832042 - 8.75450i) q^{82} +1.52866i q^{83} +(-0.576424 + 3.00509i) q^{84} +15.0065i q^{85} +(14.3039 + 1.35947i) q^{86} +0.0915052 q^{87} +(-15.0833 - 4.40711i) q^{88} +6.22475 q^{89} +(-3.96850 - 0.377173i) q^{90} -2.83669i q^{91} +(-1.96419 - 0.376764i) q^{92} +5.72298i q^{93} +(0.801220 - 8.43019i) q^{94} -10.5408 q^{95} +(-5.03374 - 2.58098i) q^{96} +8.93385 q^{97} +(-0.623444 + 6.55968i) q^{98} -5.55573i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Introduction

L-functions

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