LMFDB - Embedded newform 1078.2.e.v.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1078.67
Dual form			1078.2.e.v.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} +2.64575 q^{6} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} +2.64575 q^{6} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +(0.822876 - 1.42526i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.32288 + 2.29129i) q^{12} -5.00000 q^{13} -4.35425 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{18} +(-2.82288 - 4.88936i) q^{19} +1.64575 q^{20} -1.00000 q^{22} +(-0.822876 - 1.42526i) q^{23} +(-1.32288 + 2.29129i) q^{24} +(1.14575 - 1.98450i) q^{25} +(-2.50000 - 4.33013i) q^{26} -2.64575 q^{27} +6.29150 q^{29} +(-2.17712 - 3.77089i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.32288 + 2.29129i) q^{33} +6.00000 q^{34} +4.00000 q^{36} +(-1.82288 - 3.15731i) q^{37} +(2.82288 - 4.88936i) q^{38} +(-6.61438 + 11.4564i) q^{39} +(0.822876 + 1.42526i) q^{40} -10.9373 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.29150 + 5.70105i) q^{45} +(0.822876 - 1.42526i) q^{46} +(1.35425 + 2.34563i) q^{47} -2.64575 q^{48} +2.29150 q^{50} +(-7.93725 - 13.7477i) q^{51} +(2.50000 - 4.33013i) q^{52} +(-0.822876 + 1.42526i) q^{53} +(-1.32288 - 2.29129i) q^{54} +1.64575 q^{55} -14.9373 q^{57} +(3.14575 + 5.44860i) q^{58} +(2.32288 - 4.02334i) q^{59} +(2.17712 - 3.77089i) q^{60} +(7.14575 + 12.3768i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(4.11438 + 7.12631i) q^{65} +(-1.32288 + 2.29129i) q^{66} +(5.96863 - 10.3380i) q^{67} +(3.00000 + 5.19615i) q^{68} -4.35425 q^{69} +4.35425 q^{71} +(2.00000 + 3.46410i) q^{72} +(0.177124 - 0.306788i) q^{73} +(1.82288 - 3.15731i) q^{74} +(-3.03137 - 5.25049i) q^{75} +5.64575 q^{76} -13.2288 q^{78} +(1.32288 + 2.29129i) q^{79} +(-0.822876 + 1.42526i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-5.46863 - 9.47194i) q^{82} -2.70850 q^{83} -9.87451 q^{85} +(-2.00000 - 3.46410i) q^{86} +(8.32288 - 14.4156i) q^{87} +(0.500000 - 0.866025i) q^{88} +(3.29150 + 5.70105i) q^{89} -6.58301 q^{90} +1.64575 q^{92} +(5.29150 + 9.16515i) q^{93} +(-1.35425 + 2.34563i) q^{94} +(-4.64575 + 8.04668i) q^{95} +(-1.32288 - 2.29129i) q^{96} +16.2915 q^{97} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^8 - 8 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} - 8 q^{9} - 2 q^{10} - 2 q^{11} - 20 q^{13} - 28 q^{15} - 2 q^{16} + 12 q^{17} + 8 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{22} + 2 q^{23} - 6 q^{25} - 10 q^{26} + 4 q^{29} - 14 q^{30} - 8 q^{31} + 2 q^{32} + 24 q^{34} + 16 q^{36} - 2 q^{37} + 6 q^{38} - 2 q^{40} - 12 q^{41} - 16 q^{43} - 2 q^{44} + 8 q^{45} - 2 q^{46} + 16 q^{47} - 12 q^{50} + 10 q^{52} + 2 q^{53} - 4 q^{55} - 28 q^{57} + 2 q^{58} + 4 q^{59} + 14 q^{60} + 18 q^{61} - 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} + 12 q^{68} - 28 q^{69} + 28 q^{71} + 8 q^{72} + 6 q^{73} + 2 q^{74} - 28 q^{75} + 12 q^{76} + 2 q^{80} + 10 q^{81} - 6 q^{82} - 32 q^{83} + 24 q^{85} - 8 q^{86} + 28 q^{87} + 2 q^{88} - 8 q^{89} + 16 q^{90} - 4 q^{92} - 16 q^{94} - 8 q^{95} + 44 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^8 - 8 * q^9 - 2 * q^10 - 2 * q^11 - 20 * q^13 - 28 * q^15 - 2 * q^16 + 12 * q^17 + 8 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^22 + 2 * q^23 - 6 * q^25 - 10 * q^26 + 4 * q^29 - 14 * q^30 - 8 * q^31 + 2 * q^32 + 24 * q^34 + 16 * q^36 - 2 * q^37 + 6 * q^38 - 2 * q^40 - 12 * q^41 - 16 * q^43 - 2 * q^44 + 8 * q^45 - 2 * q^46 + 16 * q^47 - 12 * q^50 + 10 * q^52 + 2 * q^53 - 4 * q^55 - 28 * q^57 + 2 * q^58 + 4 * q^59 + 14 * q^60 + 18 * q^61 - 16 * q^62 + 4 * q^64 - 10 * q^65 + 8 * q^67 + 12 * q^68 - 28 * q^69 + 28 * q^71 + 8 * q^72 + 6 * q^73 + 2 * q^74 - 28 * q^75 + 12 * q^76 + 2 * q^80 + 10 * q^81 - 6 * q^82 - 32 * q^83 + 24 * q^85 - 8 * q^86 + 28 * q^87 + 2 * q^88 - 8 * q^89 + 16 * q^90 - 4 * q^92 - 16 * q^94 - 8 * q^95 + 44 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.32288	−	2.29129i	0.763763	−	1.32288i	−0.177136	−	0.984186i	$-0.556683\pi$
$3$	1.32288	−	2.29129i	0.763763	−	1.32288i	0.940898	−	0.338689i	$-0.109984\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	0.621252	−	0.783611i	$-0.286624\pi$
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	−0.989253	+	0.146214i	$0.953291\pi$
$6$	2.64575			1.08012
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.00000	−	3.46410i	−0.666667	−	1.15470i
$10$	0.822876	−	1.42526i	0.260216	−	0.450708i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	1.32288	+	2.29129i	0.381881	+	0.661438i
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	−4.35425			−1.12426
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	2.00000	−	3.46410i	0.471405	−	0.816497i
$19$	−2.82288	−	4.88936i	−0.647612	−	1.12170i	−0.983692	−	0.179863i	$-0.942434\pi$
$19$	−2.82288	−	4.88936i	−0.647612	−	1.12170i	0.336080	−	0.941834i	$-0.390899\pi$
$20$	1.64575			0.368001
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−0.822876	−	1.42526i	−0.171581	−	0.297188i	0.767391	−	0.641179i	$-0.221554\pi$
$23$	−0.822876	−	1.42526i	−0.171581	−	0.297188i	−0.938973	+	0.343991i	$0.888221\pi$
$24$	−1.32288	+	2.29129i	−0.270031	+	0.467707i
$25$	1.14575	−	1.98450i	0.229150	−	0.396900i
$26$	−2.50000	−	4.33013i	−0.490290	−	0.849208i
$27$	−2.64575			−0.509175
$28$		0			0
$29$	6.29150			1.16830			0.584151	−	0.811645i	$-0.301427\pi$
$29$	6.29150			1.16830			0.584151	+	0.811645i	$0.301427\pi$
$30$	−2.17712	−	3.77089i	−0.397487	−	0.688467i
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.32288	+	2.29129i	0.230283	+	0.398862i
$34$	6.00000			1.02899
$35$		0			0
$36$	4.00000			0.666667
$37$	−1.82288	−	3.15731i	−0.299679	−	0.519059i	0.676384	−	0.736550i	$-0.263546\pi$
$37$	−1.82288	−	3.15731i	−0.299679	−	0.519059i	−0.976062	+	0.217491i	$0.930213\pi$
$38$	2.82288	−	4.88936i	0.457931	−	0.793160i
$39$	−6.61438	+	11.4564i	−1.05915	+	1.83450i
$40$	0.822876	+	1.42526i	0.130108	+	0.225354i
$41$	−10.9373			−1.70811			−0.854056	−	0.520181i	$-0.825864\pi$
$41$	−10.9373			−1.70811			−0.854056	+	0.520181i	$0.825864\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	−3.29150	+	5.70105i	−0.490668	+	0.849862i
$46$	0.822876	−	1.42526i	0.121326	−	0.210143i
$47$	1.35425	+	2.34563i	0.197537	+	0.342145i	0.947729	−	0.319075i	$-0.103372\pi$
$47$	1.35425	+	2.34563i	0.197537	+	0.342145i	−0.750192	+	0.661220i	$0.770039\pi$
$48$	−2.64575			−0.381881
$49$		0			0
$50$	2.29150			0.324067
$51$	−7.93725	−	13.7477i	−1.11144	−	1.92507i
$52$	2.50000	−	4.33013i	0.346688	−	0.600481i
$53$	−0.822876	+	1.42526i	−0.113031	+	0.195775i	−0.916991	−	0.398908i	$-0.869389\pi$
$53$	−0.822876	+	1.42526i	−0.113031	+	0.195775i	0.803960	+	0.594683i	$0.202722\pi$
$54$	−1.32288	−	2.29129i	−0.180021	−	0.311805i
$55$	1.64575			0.221913
$56$		0			0
$57$	−14.9373			−1.97849
$58$	3.14575	+	5.44860i	0.413057	+	0.715436i
$59$	2.32288	−	4.02334i	0.302413	−	0.523794i	−0.674269	−	0.738486i	$-0.735541\pi$
$59$	2.32288	−	4.02334i	0.302413	−	0.523794i	0.976682	+	0.214692i	$0.0688746\pi$
$60$	2.17712	−	3.77089i	0.281066	−	0.486820i
$61$	7.14575	+	12.3768i	0.914920	+	1.58469i	0.807019	+	0.590526i	$0.201080\pi$
$61$	7.14575	+	12.3768i	0.914920	+	1.58469i	0.107901	+	0.994162i	$0.465587\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	4.11438	+	7.12631i	0.510326	+	0.883910i
$66$	−1.32288	+	2.29129i	−0.162835	+	0.282038i
$67$	5.96863	−	10.3380i	0.729184	−	1.26298i	−0.228045	−	0.973651i	$-0.573233\pi$
$67$	5.96863	−	10.3380i	0.729184	−	1.26298i	0.957229	−	0.289333i	$-0.0934334\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$	−4.35425			−0.524190
$70$		0			0
$71$	4.35425			0.516754			0.258377	−	0.966044i	$-0.416812\pi$
$71$	4.35425			0.516754			0.258377	+	0.966044i	$0.416812\pi$
$72$	2.00000	+	3.46410i	0.235702	+	0.408248i
$73$	0.177124	−	0.306788i	0.0207308	−	0.0359069i	−0.855474	−	0.517846i	$-0.826734\pi$
$73$	0.177124	−	0.306788i	0.0207308	−	0.0359069i	0.876205	+	0.481939i	$0.160067\pi$
$74$	1.82288	−	3.15731i	0.211905	−	0.367030i
$75$	−3.03137	−	5.25049i	−0.350033	−	0.606275i
$76$	5.64575			0.647612
$77$		0			0
$78$	−13.2288			−1.49786
$79$	1.32288	+	2.29129i	0.148835	+	0.257790i	0.930797	−	0.365536i	$-0.119114\pi$
$79$	1.32288	+	2.29129i	0.148835	+	0.257790i	−0.781962	+	0.623326i	$0.785781\pi$
$80$	−0.822876	+	1.42526i	−0.0920003	+	0.159349i
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	−5.46863	−	9.47194i	−0.603909	−	1.04600i
$83$	−2.70850			−0.297296			−0.148648	−	0.988890i	$-0.547492\pi$
$83$	−2.70850			−0.297296			−0.148648	+	0.988890i	$0.547492\pi$
$84$		0			0
$85$	−9.87451			−1.07104
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	8.32288	−	14.4156i	0.892306	−	1.54552i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	3.29150	+	5.70105i	0.348899	+	0.604310i	0.986054	−	0.166425i	$-0.0532224\pi$
$89$	3.29150	+	5.70105i	0.348899	+	0.604310i	−0.637156	+	0.770735i	$0.719889\pi$
$90$	−6.58301			−0.693910
$91$		0			0
$92$	1.64575			0.171581
$93$	5.29150	+	9.16515i	0.548703	+	0.950382i
$94$	−1.35425	+	2.34563i	−0.139680	+	0.241933i
$95$	−4.64575	+	8.04668i	−0.476644	+	0.825572i
$96$	−1.32288	−	2.29129i	−0.135015	−	0.233854i
$97$	16.2915			1.65415			0.827076	−	0.562090i	$-0.190003\pi$
$97$	16.2915			1.65415			0.827076	+	0.562090i	$0.190003\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$	1.14575	+	1.98450i	0.114575	+	0.198450i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$	7.93725	−	13.7477i	0.785905	−	1.36123i
$103$	−1.46863	−	2.54374i	−0.144708	−	0.250642i	0.784556	−	0.620058i	$-0.212891\pi$
$103$	−1.46863	−	2.54374i	−0.144708	−	0.250642i	−0.929264	+	0.369416i	$0.879558\pi$
$104$	5.00000			0.490290
$105$		0			0
$106$	−1.64575			−0.159849
$107$	5.46863	+	9.47194i	0.528672	+	0.915687i	0.999441	+	0.0334304i	$0.0106432\pi$
$107$	5.46863	+	9.47194i	0.528672	+	0.915687i	−0.470769	+	0.882257i	$0.656023\pi$
$108$	1.32288	−	2.29129i	0.127294	−	0.220479i
$109$	5.29150	−	9.16515i	0.506834	−	0.877862i	−0.493135	−	0.869953i	$-0.664149\pi$
$109$	5.29150	−	9.16515i	0.506834	−	0.877862i	0.999969	−	0.00790932i	$-0.00251764\pi$
$110$	0.822876	+	1.42526i	0.0784581	+	0.135893i
$111$	−9.64575			−0.915534
$112$		0			0
$113$	−18.2915			−1.72072			−0.860360	−	0.509687i	$-0.829761\pi$
$113$	−18.2915			−1.72072			−0.860360	+	0.509687i	$0.829761\pi$
$114$	−7.46863	−	12.9360i	−0.699501	−	1.21157i
$115$	−1.35425	+	2.34563i	−0.126284	+	0.218731i
$116$	−3.14575	+	5.44860i	−0.292076	+	0.505890i
$117$	10.0000	+	17.3205i	0.924500	+	1.60128i
$118$	4.64575			0.427676
$119$		0			0
$120$	4.35425			0.397487
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−7.14575	+	12.3768i	−0.646946	+	1.12054i
$123$	−14.4686	+	25.0604i	−1.30459	+	2.25962i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	15.9373			1.41420			0.707101	−	0.707112i	$-0.250002\pi$
$127$	15.9373			1.41420			0.707101	+	0.707112i	$0.250002\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−5.29150	+	9.16515i	−0.465891	+	0.806947i
$130$	−4.11438	+	7.12631i	−0.360855	+	0.625019i
$131$	5.17712	+	8.96704i	0.452327	+	0.783454i	0.998530	−	0.0541989i	$-0.0172605\pi$
$131$	5.17712	+	8.96704i	0.452327	+	0.783454i	−0.546203	+	0.837653i	$0.683927\pi$
$132$	−2.64575			−0.230283
$133$		0			0
$134$	11.9373			1.03122
$135$	2.17712	+	3.77089i	0.187377	+	0.324547i
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	6.43725	−	11.1497i	0.549972	−	0.952579i	−0.448304	−	0.893881i	$-0.647972\pi$
$137$	6.43725	−	11.1497i	0.549972	−	0.952579i	0.998276	−	0.0586978i	$-0.0186948\pi$
$138$	−2.17712	−	3.77089i	−0.185329	−	0.320999i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	7.16601			0.603487
$142$	2.17712	+	3.77089i	0.182700	+	0.316446i
$143$	2.50000	−	4.33013i	0.209061	−	0.362103i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	−5.17712	−	8.96704i	−0.429937	−	0.744672i
$146$	0.354249			0.0293178
$147$		0			0
$148$	3.64575			0.299679
$149$	7.64575	+	13.2428i	0.626364	+	1.08489i	0.988275	+	0.152682i	$0.0487911\pi$
$149$	7.64575	+	13.2428i	0.626364	+	1.08489i	−0.361911	+	0.932213i	$0.617876\pi$
$150$	3.03137	−	5.25049i	0.247511	−	0.428701i
$151$	4.32288	−	7.48744i	0.351791	−	0.609319i	−0.634773	−	0.772699i	$-0.718906\pi$
$151$	4.32288	−	7.48744i	0.351791	−	0.609319i	0.986563	+	0.163380i	$0.0522396\pi$
$152$	2.82288	+	4.88936i	0.228965	+	0.396580i
$153$	−24.0000			−1.94029
$154$		0			0
$155$	6.58301			0.528760
$156$	−6.61438	−	11.4564i	−0.529574	−	0.917249i
$157$	10.5830	−	18.3303i	0.844616	−	1.46292i	−0.0413387	−	0.999145i	$-0.513162\pi$
$157$	10.5830	−	18.3303i	0.844616	−	1.46292i	0.885954	−	0.463772i	$-0.153504\pi$
$158$	−1.32288	+	2.29129i	−0.105242	+	0.182285i
$159$	2.17712	+	3.77089i	0.172657	+	0.299051i
$160$	−1.64575			−0.130108
$161$		0			0
$162$	5.00000			0.392837
$163$	−0.322876	−	0.559237i	−0.0252896	−	0.0438028i	0.853104	−	0.521741i	$-0.174717\pi$
$163$	−0.322876	−	0.559237i	−0.0252896	−	0.0438028i	−0.878393	+	0.477939i	$0.841384\pi$
$164$	5.46863	−	9.47194i	0.427028	−	0.739634i
$165$	2.17712	−	3.77089i	0.169489	−	0.293563i
$166$	−1.35425	−	2.34563i	−0.105110	−	0.182056i
$167$	11.2288			0.868907			0.434454	−	0.900694i	$-0.356941\pi$
$167$	11.2288			0.868907			0.434454	+	0.900694i	$0.356941\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	−4.93725	−	8.55157i	−0.378670	−	0.655876i
$171$	−11.2915	+	19.5575i	−0.863483	+	1.49560i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−0.145751	−	0.252449i	−0.0110813	−	0.0191933i	0.860432	−	0.509566i	$-0.170194\pi$
$173$	−0.145751	−	0.252449i	−0.0110813	−	0.0191933i	−0.871513	+	0.490373i	$0.836861\pi$
$174$	16.6458			1.26191
$175$		0			0
$176$	1.00000			0.0753778
$177$	−6.14575	−	10.6448i	−0.461943	−	0.800109i
$178$	−3.29150	+	5.70105i	−0.246709	+	0.427312i
$179$	9.96863	−	17.2662i	0.745090	−	1.29053i	−0.205062	−	0.978749i	$-0.565740\pi$
$179$	9.96863	−	17.2662i	0.745090	−	1.29053i	0.950153	−	0.311785i	$-0.100927\pi$
$180$	−3.29150	−	5.70105i	−0.245334	−	0.424931i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	37.8118			2.79513
$184$	0.822876	+	1.42526i	0.0606632	+	0.105072i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$	−5.29150	+	9.16515i	−0.387992	+	0.672022i
$187$	3.00000	+	5.19615i	0.219382	+	0.379980i
$188$	−2.70850			−0.197537
$189$		0			0
$190$	−9.29150			−0.674076
$191$	1.35425	+	2.34563i	0.0979900	+	0.169724i	0.910853	−	0.412732i	$-0.135425\pi$
$191$	1.35425	+	2.34563i	0.0979900	+	0.169724i	−0.812863	+	0.582456i	$0.802092\pi$
$192$	1.32288	−	2.29129i	0.0954703	−	0.165359i
$193$	−12.7601	+	22.1012i	−0.918494	+	1.59088i	−0.116791	+	0.993157i	$0.537261\pi$
$193$	−12.7601	+	22.1012i	−0.918494	+	1.59088i	−0.801703	+	0.597722i	$0.796073\pi$
$194$	8.14575	+	14.1089i	0.584831	+	1.01296i
$195$	21.7712			1.55907
$196$		0			0
$197$	−12.8745			−0.917271			−0.458635	−	0.888625i	$-0.651662\pi$
$197$	−12.8745			−0.917271			−0.458635	+	0.888625i	$0.651662\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	2.11438	−	3.66221i	0.149884	−	0.259607i	−0.781300	−	0.624155i	$-0.785443\pi$
$199$	2.11438	−	3.66221i	0.149884	−	0.259607i	0.931185	+	0.364548i	$0.118777\pi$
$200$	−1.14575	+	1.98450i	−0.0810169	+	0.140325i
$201$	−15.7915	−	27.3517i	−1.11385	−	1.92924i
$202$	3.00000			0.211079
$203$		0			0
$204$	15.8745			1.11144
$205$	9.00000	+	15.5885i	0.628587	+	1.08875i
$206$	1.46863	−	2.54374i	0.102324	−	0.177231i
$207$	−3.29150	+	5.70105i	−0.228775	+	0.396250i
$208$	2.50000	+	4.33013i	0.173344	+	0.300240i
$209$	5.64575			0.390525
$210$		0			0
$211$	0.937254			0.0645232			0.0322616	−	0.999479i	$-0.489729\pi$
$211$	0.937254			0.0645232			0.0322616	+	0.999479i	$0.489729\pi$
$212$	−0.822876	−	1.42526i	−0.0565153	−	0.0978874i
$213$	5.76013	−	9.97684i	0.394678	−	0.683602i
$214$	−5.46863	+	9.47194i	−0.373828	+	0.647488i
$215$	3.29150	+	5.70105i	0.224479	+	0.388808i
$216$	2.64575			0.180021
$217$		0			0
$218$	10.5830			0.716772
$219$	−0.468627	−	0.811686i	−0.0316669	−	0.0548486i
$220$	−0.822876	+	1.42526i	−0.0554783	+	0.0960912i
$221$	−15.0000	+	25.9808i	−1.00901	+	1.74766i
$222$	−4.82288	−	8.35347i	−0.323690	−	0.560648i
$223$	17.6458			1.18165			0.590823	−	0.806801i	$-0.298803\pi$
$223$	17.6458			1.18165			0.590823	+	0.806801i	$0.298803\pi$
$224$		0			0
$225$	−9.16601			−0.611067
$226$	−9.14575	−	15.8409i	−0.608366	−	1.05372i
$227$	−1.35425	+	2.34563i	−0.0898846	+	0.155685i	−0.907462	−	0.420134i	$-0.861983\pi$
$227$	−1.35425	+	2.34563i	−0.0898846	+	0.155685i	0.817578	+	0.575818i	$0.195317\pi$
$228$	7.46863	−	12.9360i	0.494622	−	0.856710i
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	−0.999442	−	0.0334101i	$-0.989363\pi$
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	0.470787	−	0.882247i	$-0.343970\pi$
$230$	−2.70850			−0.178593
$231$		0			0
$232$	−6.29150			−0.413057
$233$	−0.531373	−	0.920365i	−0.0348114	−	0.0602951i	0.848095	−	0.529845i	$-0.177750\pi$
$233$	−0.531373	−	0.920365i	−0.0348114	−	0.0602951i	−0.882906	+	0.469549i	$0.844416\pi$
$234$	−10.0000	+	17.3205i	−0.653720	+	1.13228i
$235$	2.22876	−	3.86032i	0.145388	−	0.251819i
$236$	2.32288	+	4.02334i	0.151206	+	0.261897i
$237$	7.00000			0.454699
$238$		0			0
$239$	−17.2288			−1.11444			−0.557218	−	0.830366i	$-0.688131\pi$
$239$	−17.2288			−1.11444			−0.557218	+	0.830366i	$0.688131\pi$
$240$	2.17712	+	3.77089i	0.140533	+	0.243410i
$241$	−12.4059	+	21.4876i	−0.799133	+	1.38414i	0.121048	+	0.992647i	$0.461374\pi$
$241$	−12.4059	+	21.4876i	−0.799133	+	1.38414i	−0.920181	+	0.391492i	$0.871959\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$	−10.5830	−	18.3303i	−0.678900	−	1.17589i
$244$	−14.2915			−0.914920
$245$		0			0
$246$	−28.9373			−1.84497
$247$	14.1144	+	24.4468i	0.898076	+	1.55551i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$	−3.58301	+	6.20595i	−0.227064	+	0.393286i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	3.29150			0.207758			0.103879	−	0.994590i	$-0.466875\pi$
$251$	3.29150			0.207758			0.103879	+	0.994590i	$0.466875\pi$
$252$		0			0
$253$	1.64575			0.103467
$254$	7.96863	+	13.8021i	0.499996	+	0.866019i
$255$	−13.0627	+	22.6253i	−0.818021	+	1.41685i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.7915	−	18.6914i	−0.673155	−	1.16594i	−0.977004	−	0.213219i	$-0.931605\pi$
$257$	−10.7915	−	18.6914i	−0.673155	−	1.16594i	0.303849	−	0.952720i	$-0.401728\pi$
$258$	−10.5830			−0.658869
$259$		0			0
$260$	−8.22876			−0.510326
$261$	−12.5830	−	21.7944i	−0.778868	−	1.34904i
$262$	−5.17712	+	8.96704i	−0.319844	+	0.553986i
$263$	−9.96863	+	17.2662i	−0.614692	+	1.06468i	0.375747	+	0.926722i	$0.377386\pi$
$263$	−9.96863	+	17.2662i	−0.614692	+	1.06468i	−0.990438	+	0.137955i	$0.955947\pi$
$264$	−1.32288	−	2.29129i	−0.0814174	−	0.141019i
$265$	2.70850			0.166382
$266$		0			0
$267$	17.4170			1.06590
$268$	5.96863	+	10.3380i	0.364592	+	0.631492i
$269$	2.70850	−	4.69126i	0.165140	−	0.286031i	−0.771565	−	0.636151i	$-0.780526\pi$
$269$	2.70850	−	4.69126i	0.165140	−	0.286031i	0.936705	+	0.350120i	$0.113859\pi$
$270$	−2.17712	+	3.77089i	−0.132496	+	0.229489i
$271$	−1.03137	−	1.78639i	−0.0626514	−	0.108515i	0.832998	−	0.553275i	$-0.186622\pi$
$271$	−1.03137	−	1.78639i	−0.0626514	−	0.108515i	−0.895650	+	0.444760i	$0.853289\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	12.8745			0.777777
$275$	1.14575	+	1.98450i	0.0690914	+	0.119670i
$276$	2.17712	−	3.77089i	0.131047	−	0.226981i
$277$	11.1458	−	19.3050i	0.669683	−	1.15993i	−0.308309	−	0.951286i	$-0.599763\pi$
$277$	11.1458	−	19.3050i	0.669683	−	1.15993i	0.977993	−	0.208639i	$-0.0669035\pi$
$278$	2.00000	+	3.46410i	0.119952	+	0.207763i
$279$	16.0000			0.957895
$280$		0			0
$281$	−22.9373			−1.36832			−0.684161	−	0.729331i	$-0.739831\pi$
$281$	−22.9373			−1.36832			−0.684161	+	0.729331i	$0.739831\pi$
$282$	3.58301	+	6.20595i	0.213365	+	0.369559i
$283$	−1.17712	+	2.03884i	−0.0699728	+	0.121196i	−0.898889	−	0.438176i	$-0.855625\pi$
$283$	−1.17712	+	2.03884i	−0.0699728	+	0.121196i	0.828916	+	0.559373i	$0.188958\pi$
$284$	−2.17712	+	3.77089i	−0.129189	+	0.223761i
$285$	12.2915	+	21.2895i	0.728086	+	1.26108i
$286$	5.00000			0.295656
$287$		0			0
$288$	−4.00000			−0.235702
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	5.17712	−	8.96704i	0.304011	−	0.526563i
$291$	21.5516	−	37.3285i	1.26338	−	2.18824i
$292$	0.177124	+	0.306788i	0.0103654	+	0.0179534i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$		0			0
$295$	−7.64575			−0.445153
$296$	1.82288	+	3.15731i	0.105952	+	0.183515i
$297$	1.32288	−	2.29129i	0.0767610	−	0.132954i
$298$	−7.64575	+	13.2428i	−0.442906	+	0.767137i
$299$	4.11438	+	7.12631i	0.237941	+	0.412125i
$300$	6.06275			0.350033
$301$		0			0
$302$	8.64575			0.497507
$303$	−3.96863	−	6.87386i	−0.227992	−	0.394893i
$304$	−2.82288	+	4.88936i	−0.161903	+	0.280424i
$305$	11.7601	−	20.3691i	0.673383	−	1.16633i
$306$	−12.0000	−	20.7846i	−0.685994	−	1.18818i
$307$	−22.2288			−1.26866			−0.634331	−	0.773062i	$-0.718724\pi$
$307$	−22.2288			−1.26866			−0.634331	+	0.773062i	$0.718724\pi$
$308$		0			0
$309$	−7.77124			−0.442091
$310$	3.29150	+	5.70105i	0.186945	+	0.323798i
$311$	0.531373	−	0.920365i	0.0301314	−	0.0521891i	−0.850566	−	0.525868i	$-0.823741\pi$
$311$	0.531373	−	0.920365i	0.0301314	−	0.0521891i	0.880698	+	0.473678i	$0.157074\pi$
$312$	6.61438	−	11.4564i	0.374465	−	0.648593i
$313$	11.7915	+	20.4235i	0.666495	+	1.15440i	0.978878	+	0.204447i	$0.0655396\pi$
$313$	11.7915	+	20.4235i	0.666495	+	1.15440i	−0.312382	+	0.949956i	$0.601127\pi$
$314$	21.1660			1.19447
$315$		0			0
$316$	−2.64575			−0.148835
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$	−2.17712	+	3.77089i	−0.122087	+	0.211461i
$319$	−3.14575	+	5.44860i	−0.176128	+	0.305063i
$320$	−0.822876	−	1.42526i	−0.0460001	−	0.0796746i
$321$	28.9373			1.61512
$322$		0			0
$323$	−33.8745			−1.88483
$324$	2.50000	+	4.33013i	0.138889	+	0.240563i
$325$	−5.72876	+	9.92250i	−0.317774	+	0.550401i
$326$	0.322876	−	0.559237i	0.0178824	−	0.0309733i
$327$	−14.0000	−	24.2487i	−0.774202	−	1.34096i
$328$	10.9373			0.603909
$329$		0			0
$330$	4.35425			0.239694
$331$	10.3229	+	17.8797i	0.567397	+	0.982760i	0.996822	+	0.0796575i	$0.0253827\pi$
$331$	10.3229	+	17.8797i	0.567397	+	0.982760i	−0.429426	+	0.903102i	$0.641284\pi$
$332$	1.35425	−	2.34563i	0.0743241	−	0.128733i
$333$	−7.29150	+	12.6293i	−0.399572	+	0.692079i
$334$	5.61438	+	9.72439i	0.307205	+	0.532095i
$335$	−19.6458			−1.07336
$336$		0			0
$337$	9.06275			0.493679			0.246840	−	0.969056i	$-0.420608\pi$
$337$	9.06275			0.493679			0.246840	+	0.969056i	$0.420608\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	−24.1974	+	41.9111i	−1.31422	+	2.27630i
$340$	4.93725	−	8.55157i	0.267760	−	0.463774i
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$	−22.5830			−1.22115
$343$		0			0
$344$	4.00000			0.215666
$345$	3.58301	+	6.20595i	0.192903	+	0.334117i
$346$	0.145751	−	0.252449i	0.00783564	−	0.0135717i
$347$	10.4059	−	18.0235i	0.558617	−	0.967553i	−0.438995	−	0.898489i	$-0.644666\pi$
$347$	10.4059	−	18.0235i	0.558617	−	0.967553i	0.997612	−	0.0690636i	$-0.0220011\pi$
$348$	8.32288	+	14.4156i	0.446153	+	0.772760i
$349$	1.87451			0.100340			0.0501701	−	0.998741i	$-0.484024\pi$
$349$	1.87451			0.100340			0.0501701	+	0.998741i	$0.484024\pi$
$350$		0			0
$351$	13.2288			0.706099
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	3.58301	−	6.20595i	0.190704	−	0.330309i	−0.754780	−	0.655978i	$-0.772256\pi$
$353$	3.58301	−	6.20595i	0.190704	−	0.330309i	0.945484	+	0.325669i	$0.105590\pi$
$354$	6.14575	−	10.6448i	0.326643	−	0.565762i
$355$	−3.58301	−	6.20595i	−0.190166	−	0.329377i
$356$	−6.58301			−0.348899
$357$		0			0
$358$	19.9373			1.05372
$359$	12.9686	+	22.4623i	0.684458	+	1.18552i	0.973607	+	0.228232i	$0.0732944\pi$
$359$	12.9686	+	22.4623i	0.684458	+	1.18552i	−0.289149	+	0.957284i	$0.593372\pi$
$360$	3.29150	−	5.70105i	0.173477	−	0.300472i
$361$	−6.43725	+	11.1497i	−0.338803	+	0.586824i
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$	−2.64575			−0.138866
$364$		0			0
$365$	−0.583005			−0.0305159
$366$	18.9059	+	32.7459i	0.988226	+	1.71166i
$367$	−18.1144	+	31.3750i	−0.945563	+	1.63776i	−0.190943	+	0.981601i	$0.561154\pi$
$367$	−18.1144	+	31.3750i	−0.945563	+	1.63776i	−0.754620	+	0.656162i	$0.772179\pi$
$368$	−0.822876	+	1.42526i	−0.0428954	+	0.0742969i
$369$	21.8745	+	37.8878i	1.13874	+	1.97236i
$370$	−6.00000			−0.311925
$371$		0			0
$372$	−10.5830			−0.548703
$373$	−10.4373	−	18.0779i	−0.540421	−	0.936036i	−0.998880	−	0.0473204i	$-0.984932\pi$
$373$	−10.4373	−	18.0779i	−0.540421	−	0.936036i	0.458459	−	0.888715i	$-0.348402\pi$
$374$	−3.00000	+	5.19615i	−0.155126	+	0.268687i
$375$	−15.8745	+	27.4955i	−0.819756	+	1.41986i
$376$	−1.35425	−	2.34563i	−0.0698400	−	0.120967i
$377$	−31.4575			−1.62014
$378$		0			0
$379$	6.06275			0.311422			0.155711	−	0.987803i	$-0.450233\pi$
$379$	6.06275			0.311422			0.155711	+	0.987803i	$0.450233\pi$
$380$	−4.64575	−	8.04668i	−0.238322	−	0.412786i
$381$	21.0830	−	36.5168i	1.08012	−	1.87081i
$382$	−1.35425	+	2.34563i	−0.0692894	+	0.120013i
$383$	12.0516	+	20.8740i	0.615810	+	1.06661i	0.990242	+	0.139359i	$0.0445043\pi$
$383$	12.0516	+	20.8740i	0.615810	+	1.06661i	−0.374432	+	0.927254i	$0.622162\pi$
$384$	2.64575			0.135015
$385$		0			0
$386$	−25.5203			−1.29895
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	−8.14575	+	14.1089i	−0.413538	+	0.716269i
$389$	−13.4059	+	23.2197i	−0.679705	+	1.17728i	0.295364	+	0.955385i	$0.404559\pi$
$389$	−13.4059	+	23.2197i	−0.679705	+	1.17728i	−0.975070	+	0.221899i	$0.928774\pi$
$390$	10.8856	+	18.8544i	0.551215	+	0.954732i
$391$	−9.87451			−0.499375
$392$		0			0
$393$	27.3948			1.38188
$394$	−6.43725	−	11.1497i	−0.324304	−	0.561711i
$395$	2.17712	−	3.77089i	0.109543	−	0.189734i
$396$	−2.00000	+	3.46410i	−0.100504	+	0.174078i
$397$	−5.58301	−	9.67005i	−0.280203	−	0.485326i	0.691232	−	0.722633i	$-0.257068\pi$
$397$	−5.58301	−	9.67005i	−0.280203	−	0.485326i	−0.971435	+	0.237307i	$0.923735\pi$
$398$	4.22876			0.211968
$399$		0			0
$400$	−2.29150			−0.114575
$401$	−10.7915	−	18.6914i	−0.538902	−	0.933406i	−0.998963	−	0.0455185i	$-0.985506\pi$
$401$	−10.7915	−	18.6914i	−0.538902	−	0.933406i	0.460062	−	0.887887i	$-0.347827\pi$
$402$	15.7915	−	27.3517i	0.787609	−	1.36418i
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$	−8.22876			−0.408890
$406$		0			0
$407$	3.64575			0.180713
$408$	7.93725	+	13.7477i	0.392953	+	0.680614i
$409$	1.53137	−	2.65242i	0.0757215	−	0.131154i	−0.825678	−	0.564141i	$-0.809207\pi$
$409$	1.53137	−	2.65242i	0.0757215	−	0.131154i	0.901400	+	0.432988i	$0.142541\pi$
$410$	−9.00000	+	15.5885i	−0.444478	+	0.769859i
$411$	−17.0314	−	29.4992i	−0.840096	−	1.45509i
$412$	2.93725			0.144708
$413$		0			0
$414$	−6.58301			−0.323537
$415$	2.22876	+	3.86032i	0.109405	+	0.189496i
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$	5.29150	−	9.16515i	0.259126	−	0.448819i
$418$	2.82288	+	4.88936i	0.138071	+	0.239147i
$419$	9.87451			0.482401			0.241201	−	0.970475i	$-0.422459\pi$
$419$	9.87451			0.482401			0.241201	+	0.970475i	$0.422459\pi$
$420$		0			0
$421$	9.16601			0.446724			0.223362	−	0.974736i	$-0.428297\pi$
$421$	9.16601			0.446724			0.223362	+	0.974736i	$0.428297\pi$
$422$	0.468627	+	0.811686i	0.0228124	+	0.0395122i
$423$	5.41699	−	9.38251i	0.263383	−	0.456193i
$424$	0.822876	−	1.42526i	0.0399624	−	0.0692169i
$425$	−6.87451	−	11.9070i	−0.333463	−	0.577574i
$426$	11.5203			0.558158
$427$		0			0
$428$	−10.9373			−0.528672
$429$	−6.61438	−	11.4564i	−0.319345	−	0.553122i
$430$	−3.29150	+	5.70105i	−0.158730	+	0.274929i
$431$	−14.6144	+	25.3128i	−0.703950	+	1.21928i	0.263119	+	0.964763i	$0.415249\pi$
$431$	−14.6144	+	25.3128i	−0.703950	+	1.21928i	−0.967069	+	0.254514i	$0.918085\pi$
$432$	1.32288	+	2.29129i	0.0636469	+	0.110240i
$433$	16.0000			0.768911			0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000			0.768911			0.384455	+	0.923144i	$0.374389\pi$
$434$		0			0
$435$	−27.3948			−1.31348
$436$	5.29150	+	9.16515i	0.253417	+	0.438931i
$437$	−4.64575	+	8.04668i	−0.222236	+	0.384925i
$438$	0.468627	−	0.811686i	0.0223919	−	0.0387838i
$439$	1.96863	+	3.40976i	0.0939574	+	0.162739i	0.909173	−	0.416419i	$-0.136715\pi$
$439$	1.96863	+	3.40976i	0.0939574	+	0.162739i	−0.815216	+	0.579158i	$0.803382\pi$
$440$	−1.64575			−0.0784581
$441$		0			0
$442$	−30.0000			−1.42695
$443$	−17.2288	−	29.8411i	−0.818563	−	1.41779i	−0.906741	−	0.421688i	$-0.861438\pi$
$443$	−17.2288	−	29.8411i	−0.818563	−	1.41779i	0.0881781	−	0.996105i	$-0.471896\pi$
$444$	4.82288	−	8.35347i	0.228884	−	0.396438i
$445$	5.41699	−	9.38251i	0.256790	−	0.444774i
$446$	8.82288	+	15.2817i	0.417775	+	0.723608i
$447$	40.4575			1.91357
$448$		0			0
$449$	−21.8745			−1.03232			−0.516161	−	0.856492i	$-0.672639\pi$
$449$	−21.8745			−1.03232			−0.516161	+	0.856492i	$0.672639\pi$
$450$	−4.58301	−	7.93800i	−0.216045	−	0.374201i
$451$	5.46863	−	9.47194i	0.257508	−	0.446016i
$452$	9.14575	−	15.8409i	0.430180	−	0.745094i
$453$	−11.4373	−	19.8099i	−0.537369	−	0.930751i
$454$	−2.70850			−0.127116
$455$		0			0
$456$	14.9373			0.699501
$457$	−1.58301	−	2.74185i	−0.0740499	−	0.128258i	0.826623	−	0.562756i	$-0.190259\pi$
$457$	−1.58301	−	2.74185i	−0.0740499	−	0.128258i	−0.900673	+	0.434498i	$0.856926\pi$
$458$	8.00000	−	13.8564i	0.373815	−	0.647467i
$459$	−7.93725	+	13.7477i	−0.370479	+	0.641689i
$460$	−1.35425	−	2.34563i	−0.0631422	−	0.109365i
$461$	−10.1660			−0.473478			−0.236739	−	0.971573i	$-0.576079\pi$
$461$	−10.1660			−0.473478			−0.236739	+	0.971573i	$0.576079\pi$
$462$		0			0
$463$	30.4575			1.41548			0.707740	−	0.706473i	$-0.249715\pi$
$463$	30.4575			1.41548			0.707740	+	0.706473i	$0.249715\pi$
$464$	−3.14575	−	5.44860i	−0.146038	−	0.252945i
$465$	8.70850	−	15.0836i	0.403847	−	0.699483i
$466$	0.531373	−	0.920365i	0.0246154	−	0.0426351i
$467$	10.6458	+	18.4390i	0.492627	+	0.853254i	0.999964	−	0.00849322i	$-0.00270351\pi$
$467$	10.6458	+	18.4390i	0.492627	+	0.853254i	−0.507337	+	0.861748i	$0.669370\pi$
$468$	−20.0000			−0.924500
$469$		0			0
$470$	4.45751			0.205610
$471$	−28.0000	−	48.4974i	−1.29017	−	2.23464i
$472$	−2.32288	+	4.02334i	−0.106919	+	0.185189i
$473$	2.00000	−	3.46410i	0.0919601	−	0.159280i
$474$	3.50000	+	6.06218i	0.160760	+	0.278445i
$475$	−12.9373			−0.593602
$476$		0			0
$477$	6.58301			0.301415
$478$	−8.61438	−	14.9205i	−0.394012	−	0.682450i
$479$	−5.03137	+	8.71459i	−0.229889	+	0.398180i	−0.957775	−	0.287518i	$-0.907170\pi$
$479$	−5.03137	+	8.71459i	−0.229889	+	0.398180i	0.727886	+	0.685698i	$0.240503\pi$
$480$	−2.17712	+	3.77089i	−0.0993717	+	0.172117i
$481$	9.11438	+	15.7866i	0.415580	+	0.719805i
$482$	−24.8118			−1.13014
$483$		0			0
$484$	1.00000			0.0454545
$485$	−13.4059	−	23.2197i	−0.608730	−	1.05435i
$486$	10.5830	−	18.3303i	0.480055	−	0.831479i
$487$	4.70850	−	8.15536i	0.213362	−	0.369554i	−0.739402	−	0.673264i	$-0.764892\pi$
$487$	4.70850	−	8.15536i	0.213362	−	0.369554i	0.952765	+	0.303709i	$0.0982252\pi$
$488$	−7.14575	−	12.3768i	−0.323473	−	0.560272i
$489$	−1.70850			−0.0772609
$490$		0			0
$491$	21.2915			0.960872			0.480436	−	0.877030i	$-0.340478\pi$
$491$	21.2915			0.960872			0.480436	+	0.877030i	$0.340478\pi$
$492$	−14.4686	−	25.0604i	−0.652296	−	1.12981i
$493$	18.8745	−	32.6916i	0.850065	−	1.47236i
$494$	−14.1144	+	24.4468i	−0.635036	+	1.09991i
$495$	−3.29150	−	5.70105i	−0.147942	−	0.256243i
$496$	4.00000			0.179605
$497$		0			0
$498$	−7.16601			−0.321117
$499$	6.93725	+	12.0157i	0.310554	+	0.537896i	0.978482	−	0.206330i	$-0.0661521\pi$
$499$	6.93725	+	12.0157i	0.310554	+	0.537896i	−0.667928	+	0.744226i	$0.732819\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$	14.8542	−	25.7283i	0.663639	−	1.14946i
$502$	1.64575	+	2.85052i	0.0734535	+	0.127225i
$503$	4.06275			0.181149			0.0905744	−	0.995890i	$-0.471130\pi$
$503$	4.06275			0.181149			0.0905744	+	0.995890i	$0.471130\pi$
$504$		0			0
$505$	−4.93725			−0.219705
$506$	0.822876	+	1.42526i	0.0365813	+	0.0633606i
$507$	15.8745	−	27.4955i	0.705012	−	1.22112i
$508$	−7.96863	+	13.8021i	−0.353551	+	0.612368i
$509$	−0.291503	−	0.504897i	−0.0129206	−	0.0223792i	0.859493	−	0.511148i	$-0.170780\pi$
$509$	−0.291503	−	0.504897i	−0.0129206	−	0.0223792i	−0.872413	+	0.488769i	$0.837446\pi$
$510$	−26.1255			−1.15686
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	7.46863	+	12.9360i	0.329748	+	0.571140i
$514$	10.7915	−	18.6914i	0.475993	−	0.824444i
$515$	−2.41699	+	4.18636i	−0.106506	+	0.184473i
$516$	−5.29150	−	9.16515i	−0.232945	−	0.403473i
$517$	−2.70850			−0.119120
$518$		0			0
$519$	−0.771243			−0.0338538
$520$	−4.11438	−	7.12631i	−0.180427	−	0.312509i
$521$	−16.9373	+	29.3362i	−0.742035	+	1.28524i	0.209533	+	0.977802i	$0.432806\pi$
$521$	−16.9373	+	29.3362i	−0.742035	+	1.28524i	−0.951567	+	0.307440i	$0.900528\pi$
$522$	12.5830	−	21.7944i	0.550743	−	0.953915i
$523$	−10.7601	−	18.6371i	−0.470508	−	0.814943i	0.528923	−	0.848670i	$-0.322596\pi$
$523$	−10.7601	−	18.6371i	−0.470508	−	0.814943i	−0.999431	+	0.0337264i	$0.989263\pi$
$524$	−10.3542			−0.452327
$525$		0			0
$526$	−19.9373			−0.869306
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$	1.32288	−	2.29129i	0.0575708	−	0.0997155i
$529$	10.1458	−	17.5730i	0.441120	−	0.764042i
$530$	1.35425	+	2.34563i	0.0588248	+	0.101888i
$531$	−18.5830			−0.806434
$532$		0			0
$533$	54.6863			2.36873
$534$	8.70850	+	15.0836i	0.376854	+	0.652729i
$535$	9.00000	−	15.5885i	0.389104	−	0.673948i
$536$	−5.96863	+	10.3380i	−0.257805	+	0.446532i
$537$	−26.3745	−	45.6820i	−1.13814	−	1.97132i
$538$	5.41699			0.233543
$539$		0			0
$540$	−4.35425			−0.187377
$541$	−1.14575	−	1.98450i	−0.0492597	−	0.0853203i	0.840344	−	0.542053i	$-0.182353\pi$
$541$	−1.14575	−	1.98450i	−0.0492597	−	0.0853203i	−0.889604	+	0.456733i	$0.849020\pi$
$542$	1.03137	−	1.78639i	0.0443013	−	0.0767320i
$543$	13.2288	−	22.9129i	0.567700	−	0.983286i
$544$	−3.00000	−	5.19615i	−0.128624	−	0.222783i
$545$	−17.4170			−0.746062
$546$		0			0
$547$	−9.52026			−0.407057			−0.203528	−	0.979069i	$-0.565241\pi$
$547$	−9.52026			−0.407057			−0.203528	+	0.979069i	$0.565241\pi$
$548$	6.43725	+	11.1497i	0.274986	+	0.476289i
$549$	28.5830	−	49.5072i	1.21989	−	2.11292i
$550$	−1.14575	+	1.98450i	−0.0488550	+	0.0846193i
$551$	−17.7601	−	30.7614i	−0.756607	−	1.31048i
$552$	4.35425			0.185329
$553$		0			0
$554$	22.2915			0.947075
$555$	7.93725	+	13.7477i	0.336918	+	0.583559i
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	15.8745	−	27.4955i	0.672624	−	1.16502i	−0.304533	−	0.952502i	$-0.598500\pi$
$557$	15.8745	−	27.4955i	0.672624	−	1.16502i	0.977157	−	0.212518i	$-0.0681664\pi$
$558$	8.00000	+	13.8564i	0.338667	+	0.586588i
$559$	20.0000			0.845910
$560$		0			0
$561$	15.8745			0.670222
$562$	−11.4686	−	19.8642i	−0.483775	−	0.837923i
$563$	14.4686	−	25.0604i	0.609780	−	1.05617i	−0.381496	−	0.924370i	$-0.624591\pi$
$563$	14.4686	−	25.0604i	0.609780	−	1.05617i	0.991276	−	0.131800i	$-0.0420755\pi$
$564$	−3.58301	+	6.20595i	−0.150872	+	0.261318i
$565$	15.0516	+	26.0702i	0.633227	+	1.09678i
$566$	−2.35425			−0.0989565
$567$		0			0
$568$	−4.35425			−0.182700
$569$	−0.583005	−	1.00979i	−0.0244409	−	0.0423328i	0.853546	−	0.521017i	$-0.174447\pi$
$569$	−0.583005	−	1.00979i	−0.0244409	−	0.0423328i	−0.877987	+	0.478684i	$0.841114\pi$
$570$	−12.2915	+	21.2895i	−0.514834	+	0.891719i
$571$	14.5314	−	25.1691i	0.608119	−	1.05329i	−0.383431	−	0.923569i	$-0.625258\pi$
$571$	14.5314	−	25.1691i	0.608119	−	1.05329i	0.991550	−	0.129724i	$-0.0414090\pi$
$572$	2.50000	+	4.33013i	0.104530	+	0.181052i
$573$	7.16601			0.299364
$574$		0			0
$575$	−3.77124			−0.157272
$576$	−2.00000	−	3.46410i	−0.0833333	−	0.144338i
$577$	13.7288	−	23.7789i	0.571536	−	0.989929i	−0.424873	−	0.905253i	$-0.639681\pi$
$577$	13.7288	−	23.7789i	0.571536	−	0.989929i	0.996409	−	0.0846757i	$-0.0269854\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$	33.7601	+	58.4743i	1.40302	+	2.43011i
$580$	10.3542			0.429937
$581$		0			0
$582$	43.1033			1.78669
$583$	−0.822876	−	1.42526i	−0.0340800	−	0.0590283i
$584$	−0.177124	+	0.306788i	−0.00732946	+	0.0126950i
$585$	16.4575	−	28.5052i	0.680434	−	1.17855i
$586$	−6.00000	−	10.3923i	−0.247858	−	0.429302i
$587$	−7.93725			−0.327606			−0.163803	−	0.986493i	$-0.552376\pi$
$587$	−7.93725			−0.327606			−0.163803	+	0.986493i	$0.552376\pi$
$588$		0			0
$589$	22.5830			0.930517
$590$	−3.82288	−	6.62141i	−0.157385	−	0.272599i
$591$	−17.0314	+	29.4992i	−0.700577	+	1.21344i
$592$	−1.82288	+	3.15731i	−0.0749197	+	0.129765i
$593$	3.53137	+	6.11652i	0.145016	+	0.251175i	0.929379	−	0.369127i	$-0.120343\pi$
$593$	3.53137	+	6.11652i	0.145016	+	0.251175i	−0.784363	+	0.620302i	$0.787010\pi$
$594$	2.64575			0.108556
$595$		0			0
$596$	−15.2915			−0.626364
$597$	−5.59412	−	9.68930i	−0.228952	−	0.396557i
$598$	−4.11438	+	7.12631i	−0.168249	+	0.291417i
$599$	−21.8745	+	37.8878i	−0.893768	+	1.54805i	−0.0584464	+	0.998291i	$0.518615\pi$
$599$	−21.8745	+	37.8878i	−0.893768	+	1.54805i	−0.835322	+	0.549761i	$0.814719\pi$
$600$	3.03137	+	5.25049i	0.123755	+	0.214350i
$601$	3.41699			0.139382			0.0696911	−	0.997569i	$-0.477799\pi$
$601$	3.41699			0.139382			0.0696911	+	0.997569i	$0.477799\pi$
$602$		0			0
$603$	−47.7490			−1.94449
$604$	4.32288	+	7.48744i	0.175895	+	0.304660i
$605$	−0.822876	+	1.42526i	−0.0334547	+	0.0579452i
$606$	3.96863	−	6.87386i	0.161214	−	0.279232i
$607$	5.35425	+	9.27383i	0.217322	+	0.376413i	0.953988	−	0.299843i	$-0.0969344\pi$
$607$	5.35425	+	9.27383i	0.217322	+	0.376413i	−0.736666	+	0.676257i	$0.763601\pi$
$608$	−5.64575			−0.228965
$609$		0			0
$610$	23.5203			0.952307
$611$	−6.77124	−	11.7281i	−0.273935	−	0.474470i
$612$	12.0000	−	20.7846i	0.485071	−	0.840168i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	−11.1144	−	19.2507i	−0.448540	−	0.776894i
$615$	47.6235			1.92037
$616$		0			0
$617$	−5.70850			−0.229815			−0.114908	−	0.993376i	$-0.536657\pi$
$617$	−5.70850			−0.229815			−0.114908	+	0.993376i	$0.536657\pi$
$618$	−3.88562	−	6.73009i	−0.156303	−	0.270724i
$619$	6.70850	−	11.6195i	0.269637	−	0.467025i	−0.699131	−	0.714994i	$-0.746430\pi$
$619$	6.70850	−	11.6195i	0.269637	−	0.467025i	0.968768	+	0.247968i	$0.0797629\pi$
$620$	−3.29150	+	5.70105i	−0.132190	+	0.228960i
$621$	2.17712	+	3.77089i	0.0873650	+	0.151321i
$622$	1.06275			0.0426122
$623$		0			0
$624$	13.2288			0.529574
$625$	4.14575	+	7.18065i	0.165830	+	0.287226i
$626$	−11.7915	+	20.4235i	−0.471283	+	0.816286i
$627$	7.46863	−	12.9360i	0.298268	−	0.516616i
$628$	10.5830	+	18.3303i	0.422308	+	0.731459i
$629$	−21.8745			−0.872194
$630$		0			0
$631$	−12.8118			−0.510028			−0.255014	−	0.966937i	$-0.582080\pi$
$631$	−12.8118			−0.510028			−0.255014	+	0.966937i	$0.582080\pi$
$632$	−1.32288	−	2.29129i	−0.0526212	−	0.0911425i
$633$	1.23987	−	2.14752i	0.0492804	−	0.0853562i
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$	−13.1144	−	22.7148i	−0.520428	−	0.901408i
$636$	−4.35425			−0.172657
$637$		0			0
$638$	−6.29150			−0.249083
$639$	−8.70850	−	15.0836i	−0.344503	−	0.596696i
$640$	0.822876	−	1.42526i	0.0325270	−	0.0563384i
$641$	−6.43725	+	11.1497i	−0.254256	+	0.440385i	−0.964693	−	0.263376i	$-0.915164\pi$
$641$	−6.43725	+	11.1497i	−0.254256	+	0.440385i	0.710437	+	0.703761i	$0.248497\pi$
$642$	14.4686	+	25.0604i	0.571031	+	0.989055i
$643$	30.5203			1.20360			0.601801	−	0.798646i	$-0.294450\pi$
$643$	30.5203			1.20360			0.601801	+	0.798646i	$0.294450\pi$
$644$		0			0
$645$	17.4170			0.685793
$646$	−16.9373	−	29.3362i	−0.666387	−	1.15422i
$647$	−4.40588	+	7.63121i	−0.173213	+	0.300014i	−0.939541	−	0.342435i	$-0.888748\pi$
$647$	−4.40588	+	7.63121i	−0.173213	+	0.300014i	0.766328	+	0.642449i	$0.222082\pi$
$648$	−2.50000	+	4.33013i	−0.0982093	+	0.170103i
$649$	2.32288	+	4.02334i	0.0911808	+	0.157930i
$650$	−11.4575			−0.449401
$651$		0			0
$652$	0.645751			0.0252896
$653$	−3.82288	−	6.62141i	−0.149601	−	0.259116i	0.781479	−	0.623931i	$-0.214465\pi$
$653$	−3.82288	−	6.62141i	−0.149601	−	0.259116i	−0.931080	+	0.364815i	$0.881132\pi$
$654$	14.0000	−	24.2487i	0.547443	−	0.948200i
$655$	8.52026	−	14.7575i	0.332914	−	0.576624i
$656$	5.46863	+	9.47194i	0.213514	+	0.369817i
$657$	−1.41699			−0.0552822
$658$		0			0
$659$	−6.58301			−0.256437			−0.128219	−	0.991746i	$-0.540926\pi$
$659$	−6.58301			−0.256437			−0.128219	+	0.991746i	$0.540926\pi$
$660$	2.17712	+	3.77089i	0.0847445	+	0.146782i
$661$	3.70850	−	6.42331i	0.144244	−	0.249838i	−0.784847	−	0.619690i	$-0.787258\pi$
$661$	3.70850	−	6.42331i	0.144244	−	0.249838i	0.929091	+	0.369852i	$0.120592\pi$
$662$	−10.3229	+	17.8797i	−0.401210	+	0.694916i
$663$	39.6863	+	68.7386i	1.54129	+	2.66959i
$664$	2.70850			0.105110
$665$		0			0
$666$	−14.5830			−0.565080
$667$	−5.17712	−	8.96704i	−0.200459	−	0.347205i
$668$	−5.61438	+	9.72439i	−0.217227	+	0.376248i
$669$	23.3431	−	40.4315i	0.902498	−	1.56317i
$670$	−9.82288	−	17.0137i	−0.379491	−	0.657297i
$671$	−14.2915			−0.551717
$672$		0			0
$673$	0.937254			0.0361285			0.0180642	−	0.999837i	$-0.494250\pi$
$673$	0.937254			0.0361285			0.0180642	+	0.999837i	$0.494250\pi$
$674$	4.53137	+	7.84857i	0.174542	+	0.302316i
$675$	−3.03137	+	5.25049i	−0.116678	+	0.202092i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	−16.9373	−	29.3362i	−0.650952	−	1.12748i	−0.982892	−	0.184181i	$-0.941037\pi$
$677$	−16.9373	−	29.3362i	−0.650952	−	1.12748i	0.331941	−	0.943300i	$-0.392297\pi$
$678$	−48.3948			−1.85859
$679$		0			0
$680$	9.87451			0.378670
$681$	3.58301	+	6.20595i	0.137301	+	0.237812i
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	−0.968627	+	1.67771i	−0.0370635	+	0.0641958i	−0.883962	−	0.467559i	$-0.845134\pi$
$683$	−0.968627	+	1.67771i	−0.0370635	+	0.0641958i	0.846899	+	0.531754i	$0.178467\pi$
$684$	−11.2915	−	19.5575i	−0.431741	−	0.747798i
$685$	−21.1882			−0.809561
$686$		0			0
$687$	−42.3320			−1.61507
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	4.11438	−	7.12631i	0.156745	−	0.271491i
$690$	−3.58301	+	6.20595i	−0.136403	+	0.236256i
$691$	−22.6144	−	39.1693i	−0.860291	−	1.49007i	−0.871648	−	0.490133i	$-0.836948\pi$
$691$	−22.6144	−	39.1693i	−0.860291	−	1.49007i	0.0113561	−	0.999936i	$-0.496385\pi$
$692$	0.291503			0.0110813
$693$		0			0
$694$	20.8118			0.790004
$695$	−3.29150	−	5.70105i	−0.124854	−	0.216253i
$696$	−8.32288	+	14.4156i	−0.315478	+	0.546424i
$697$	−32.8118	+	56.8316i	−1.24283	+	2.15265i
$698$	0.937254	+	1.62337i	0.0354756	+	0.0614455i
$699$	−2.81176			−0.106351
$700$		0			0
$701$	24.8745			0.939497			0.469749	−	0.882800i	$-0.344345\pi$
$701$	24.8745			0.939497			0.469749	+	0.882800i	$0.344345\pi$
$702$	6.61438	+	11.4564i	0.249644	+	0.432395i
$703$	−10.2915	+	17.8254i	−0.388151	+	0.672298i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	−5.89674	−	10.2134i	−0.222084	−	0.384661i
$706$	7.16601			0.269696
$707$		0			0
$708$	12.2915			0.461943
$709$	−20.4059	−	35.3440i	−0.766359	−	1.32737i	−0.939525	−	0.342480i	$-0.888733\pi$
$709$	−20.4059	−	35.3440i	−0.766359	−	1.32737i	0.173166	−	0.984893i	$-0.444600\pi$
$710$	3.58301	−	6.20595i	0.134468	−	0.232905i
$711$	5.29150	−	9.16515i	0.198447	−	0.343720i
$712$	−3.29150	−	5.70105i	−0.123354	−	0.213656i
$713$	6.58301			0.246535
$714$		0			0
$715$	−8.22876			−0.307738
$716$	9.96863	+	17.2662i	0.372545	+	0.645267i
$717$	−22.7915	+	39.4760i	−0.851164	+	1.47426i
$718$	−12.9686	+	22.4623i	−0.483985	+	0.838286i
$719$	13.9373	+	24.1400i	0.519772	+	0.900271i	0.999736	+	0.0229831i	$0.00731639\pi$
$719$	13.9373	+	24.1400i	0.519772	+	0.900271i	−0.479964	+	0.877288i	$0.659350\pi$
$720$	6.58301			0.245334
$721$		0			0
$722$	−12.8745			−0.479140
$723$	32.8229	+	56.8509i	1.22070	+	2.11431i
$724$	−5.00000	+	8.66025i	−0.185824	+	0.321856i
$725$	7.20850	−	12.4855i	0.267717	−	0.463699i
$726$	−1.32288	−	2.29129i	−0.0490965	−	0.0850377i
$727$	6.70850			0.248804			0.124402	−	0.992232i	$-0.460299\pi$
$727$	6.70850			0.248804			0.124402	+	0.992232i	$0.460299\pi$
$728$		0			0
$729$	−41.0000			−1.51852
$730$	−0.291503	−	0.504897i	−0.0107890	−	0.0186871i
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$	−18.9059	+	32.7459i	−0.698781	+	1.21033i
$733$	−5.72876	−	9.92250i	−0.211596	−	0.366496i	0.740618	−	0.671926i	$-0.234533\pi$
$733$	−5.72876	−	9.92250i	−0.211596	−	0.366496i	−0.952214	+	0.305431i	$0.901200\pi$
$734$	−36.2288			−1.33723
$735$		0			0
$736$	−1.64575			−0.0606632
$737$	5.96863	+	10.3380i	0.219857	+	0.380804i
$738$	−21.8745	+	37.8878i	−0.805212	+	1.39467i
$739$	−11.9373	+	20.6759i	−0.439119	+	0.760576i	−0.997622	−	0.0689263i	$-0.978043\pi$
$739$	−11.9373	+	20.6759i	−0.439119	+	0.760576i	0.558503	+	0.829503i	$0.311376\pi$
$740$	−3.00000	−	5.19615i	−0.110282	−	0.191014i
$741$	74.6863			2.74367
$742$		0			0
$743$	−45.2915			−1.66158			−0.830792	−	0.556583i	$-0.812112\pi$
$743$	−45.2915			−1.66158			−0.830792	+	0.556583i	$0.812112\pi$
$744$	−5.29150	−	9.16515i	−0.193996	−	0.336011i
$745$	12.5830	−	21.7944i	0.461006	−	0.798485i
$746$	10.4373	−	18.0779i	0.382135	−	0.661877i
$747$	5.41699	+	9.38251i	0.198197	+	0.343288i
$748$	−6.00000			−0.219382
$749$		0			0
$750$	−31.7490			−1.15931
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	1.35425	−	2.34563i	0.0493844	−	0.0855362i
$753$	4.35425	−	7.54178i	0.158678	−	0.274838i
$754$	−15.7288	−	27.2430i	−0.572808	−	0.992132i
$755$	−14.2288			−0.517837
$756$		0			0
$757$	−23.1660			−0.841983			−0.420991	−	0.907065i	$-0.638318\pi$
$757$	−23.1660			−0.841983			−0.420991	+	0.907065i	$0.638318\pi$
$758$	3.03137	+	5.25049i	0.110104	+	0.190706i
$759$	2.17712	−	3.77089i	0.0790246	−	0.136875i
$760$	4.64575	−	8.04668i	0.168519	−	0.291884i
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$	42.1660			1.52751
$763$		0			0
$764$	−2.70850			−0.0979900
$765$	19.7490	+	34.2063i	0.714027	+	1.23673i
$766$	−12.0516	+	20.8740i	−0.435443	+	0.754210i
$767$	−11.6144	+	20.1167i	−0.419371	+	0.726372i
$768$	1.32288	+	2.29129i	0.0477352	+	0.0826797i
$769$	−27.1660			−0.979631			−0.489816	−	0.871826i	$-0.662936\pi$
$769$	−27.1660			−0.979631			−0.489816	+	0.871826i	$0.662936\pi$
$770$		0			0
$771$	−57.1033			−2.05652
$772$	−12.7601	−	22.1012i	−0.459247	−	0.795439i
$773$	−9.29150	+	16.0934i	−0.334192	+	0.578838i	−0.983329	−	0.181834i	$-0.941797\pi$
$773$	−9.29150	+	16.0934i	−0.334192	+	0.578838i	0.649137	+	0.760671i	$0.275130\pi$
$774$	−8.00000	+	13.8564i	−0.287554	+	0.498058i
$775$	4.58301	+	7.93800i	0.164626	+	0.285141i
$776$	−16.2915			−0.584831
$777$		0			0
$778$	−26.8118			−0.961248
$779$	30.8745	+	53.4762i	1.10619	+	1.91598i
$780$	−10.8856	+	18.8544i	−0.389768	+	0.675098i
$781$	−2.17712	+	3.77089i	−0.0779036	+	0.134933i
$782$	−4.93725	−	8.55157i	−0.176556	−	0.305804i
$783$	−16.6458			−0.594871
$784$		0			0
$785$	−34.8340			−1.24328
$786$	13.6974	+	23.7246i	0.488569	+	0.846227i
$787$	23.4059	−	40.5402i	0.834330	−	1.44510i	−0.0602456	−	0.998184i	$-0.519188\pi$
$787$	23.4059	−	40.5402i	0.834330	−	1.44510i	0.894575	−	0.446918i	$-0.147478\pi$
$788$	6.43725	−	11.1497i	0.229318	−	0.397190i
$789$	26.3745	+	45.6820i	0.938957	+	1.62632i
$790$	4.35425			0.154917
$791$		0			0
$792$	−4.00000			−0.142134
$793$	−35.7288	−	61.8840i	−1.26877	−	2.19757i
$794$	5.58301	−	9.67005i	0.198133	−	0.343177i
$795$	3.58301	−	6.20595i	0.127076	−	0.220102i
$796$	2.11438	+	3.66221i	0.0749422	+	0.129804i
$797$	−7.16601			−0.253833			−0.126917	−	0.991913i	$-0.540508\pi$
$797$	−7.16601			−0.253833			−0.126917	+	0.991913i	$0.540508\pi$
$798$		0			0
$799$	16.2510			0.574918
$800$	−1.14575	−	1.98450i	−0.0405084	−	0.0701627i
$801$	13.1660	−	22.8042i	0.465198	−	0.805747i
$802$	10.7915	−	18.6914i	0.381061	−	0.660017i
$803$	0.177124	+	0.306788i	0.00625058	+	0.0108263i
$804$	31.5830			1.11385
$805$		0			0
$806$	20.0000			0.704470
$807$	−7.16601	−	12.4119i	−0.252256	−	0.436919i
$808$	−1.50000	+	2.59808i	−0.0527698	+	0.0914000i
$809$	−14.7085	+	25.4759i	−0.517123	+	0.895684i	0.482679	+	0.875797i	$0.339664\pi$
$809$	−14.7085	+	25.4759i	−0.517123	+	0.895684i	−0.999802	+	0.0198864i	$0.993670\pi$
$810$	−4.11438	−	7.12631i	−0.144565	−	0.250393i
$811$	35.7490			1.25532			0.627659	−	0.778489i	$-0.284013\pi$
$811$	35.7490			1.25532			0.627659	+	0.778489i	$0.284013\pi$
$812$		0			0
$813$	−5.45751			−0.191403
$814$	1.82288	+	3.15731i	0.0638918	+	0.110664i
$815$	−0.531373	+	0.920365i	−0.0186132	+	0.0322390i
$816$	−7.93725	+	13.7477i	−0.277859	+	0.481267i
$817$	11.2915	+	19.5575i	0.395040	+	0.684229i
$818$	3.06275			0.107086
$819$		0			0
$820$	−18.0000			−0.628587
$821$	9.14575	+	15.8409i	0.319189	+	0.552851i	0.980319	−	0.197420i	$-0.0632562\pi$
$821$	9.14575	+	15.8409i	0.319189	+	0.552851i	−0.661130	+	0.750271i	$0.729923\pi$
$822$	17.0314	−	29.4992i	0.594037	−	1.02890i
$823$	6.06275	−	10.5010i	0.211334	−	0.366041i	−0.740798	−	0.671728i	$-0.765553\pi$
$823$	6.06275	−	10.5010i	0.211334	−	0.366041i	0.952132	+	0.305686i	$0.0988859\pi$
$824$	1.46863	+	2.54374i	0.0511620	+	0.0886153i
$825$	6.06275			0.211078
$826$		0			0
$827$	33.3948			1.16125			0.580625	−	0.814171i	$-0.302808\pi$
$827$	33.3948			1.16125			0.580625	+	0.814171i	$0.302808\pi$
$828$	−3.29150	−	5.70105i	−0.114388	−	0.198125i
$829$	−12.6974	+	21.9925i	−0.440998	+	0.763832i	−0.997764	−	0.0668382i	$-0.978709\pi$
$829$	−12.6974	+	21.9925i	−0.440998	+	0.763832i	0.556765	+	0.830670i	$0.312042\pi$
$830$	−2.22876	+	3.86032i	−0.0773613	+	0.133994i
$831$	−29.4889	−	51.0762i	−1.02296	−	1.77182i
$832$	−5.00000			−0.173344
$833$		0			0
$834$	10.5830			0.366460
$835$	−9.23987	−	16.0039i	−0.319759	−	0.553839i
$836$	−2.82288	+	4.88936i	−0.0976312	+	0.169102i
$837$	5.29150	−	9.16515i	0.182901	−	0.316794i
$838$	4.93725	+	8.55157i	0.170555	+	0.295409i
$839$	3.87451			0.133763			0.0668814	−	0.997761i	$-0.478695\pi$
$839$	3.87451			0.133763			0.0668814	+	0.997761i	$0.478695\pi$
$840$		0			0
$841$	10.5830			0.364931
$842$	4.58301	+	7.93800i	0.157941	+	0.273561i
$843$	−30.3431	+	52.5559i	−1.04507	+	1.81012i
$844$	−0.468627	+	0.811686i	−0.0161308	+	0.0279394i
$845$	−9.87451	−	17.1031i	−0.339693	−	0.588366i
$846$	10.8340			0.372480
$847$		0			0
$848$	1.64575			0.0565153
$849$	3.11438	+	5.39426i	0.106885	+	0.185131i
$850$	6.87451	−	11.9070i	0.235794	−	0.408407i
$851$	−3.00000	+	5.19615i	−0.102839	+	0.178122i
$852$	5.76013	+	9.97684i	0.197339	+	0.341801i
$853$	−39.1660			−1.34102			−0.670509	−	0.741901i	$-0.733924\pi$
$853$	−39.1660			−1.34102			−0.670509	+	0.741901i	$0.733924\pi$
$854$		0			0
$855$	37.1660			1.27105
$856$	−5.46863	−	9.47194i	−0.186914	−	0.323744i
$857$	18.0000	−	31.1769i	0.614868	−	1.06498i	−0.375539	−	0.926806i	$-0.622542\pi$
$857$	18.0000	−	31.1769i	0.614868	−	1.06498i	0.990408	−	0.138177i	$-0.0441242\pi$
$858$	6.61438	−	11.4564i	0.225811	−	0.391116i
$859$	−4.90588	−	8.49723i	−0.167386	−	0.289922i	0.770114	−	0.637907i	$-0.220199\pi$
$859$	−4.90588	−	8.49723i	−0.167386	−	0.289922i	−0.937500	+	0.347985i	$0.886866\pi$
$860$	−6.58301			−0.224479
$861$		0			0
$862$	−29.2288			−0.995535
$863$	6.23987	+	10.8078i	0.212408	+	0.367901i	0.952468	−	0.304640i	$-0.0985362\pi$
$863$	6.23987	+	10.8078i	0.212408	+	0.367901i	−0.740060	+	0.672541i	$0.765203\pi$
$864$	−1.32288	+	2.29129i	−0.0450051	+	0.0779512i
$865$	−0.239870	+	0.415468i	−0.00815584	+	0.0141263i
$866$	8.00000	+	13.8564i	0.271851	+	0.470860i
$867$	−50.2693			−1.70723
$868$		0			0
$869$	−2.64575			−0.0897510
$870$	−13.6974	−	23.7246i	−0.464385	−	0.804338i
$871$	−29.8431	+	51.6898i	−1.01120	+	1.75144i
$872$	−5.29150	+	9.16515i	−0.179193	+	0.310371i
$873$	−32.5830	−	56.4354i	−1.10277	−	1.91005i
$874$	−9.29150			−0.314290
$875$		0			0
$876$	0.937254			0.0316669
$877$	11.4373	+	19.8099i	0.386209	+	0.668933i	0.991936	−	0.126739i	$-0.0404511\pi$
$877$	11.4373	+	19.8099i	0.386209	+	0.668933i	−0.605727	+	0.795672i	$0.707118\pi$
$878$	−1.96863	+	3.40976i	−0.0664379	+	0.115074i
$879$	−15.8745	+	27.4955i	−0.535434	+	0.927399i
$880$	−0.822876	−	1.42526i	−0.0277391	−	0.0480456i
$881$	24.8745			0.838043			0.419022	−	0.907976i	$-0.362373\pi$
$881$	24.8745			0.838043			0.419022	+	0.907976i	$0.362373\pi$
$882$		0			0
$883$	21.9373			0.738247			0.369124	−	0.929380i	$-0.379658\pi$
$883$	21.9373			0.738247			0.369124	+	0.929380i	$0.379658\pi$
$884$	−15.0000	−	25.9808i	−0.504505	−	0.873828i
$885$	−10.1144	+	17.5186i	−0.339991	+	0.588882i
$886$	17.2288	−	29.8411i	0.578811	−	1.00253i
$887$	22.5516	+	39.0606i	0.757210	+	1.31153i	0.944268	+	0.329177i	$0.106771\pi$
$887$	22.5516	+	39.0606i	0.757210	+	1.31153i	−0.187059	+	0.982349i	$0.559895\pi$
$888$	9.64575			0.323690
$889$		0			0
$890$	10.8340			0.363156
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$	−8.82288	+	15.2817i	−0.295412	+	0.511668i
$893$	7.64575	−	13.2428i	0.255855	−	0.443154i
$894$	20.2288	+	35.0372i	0.676551	+	1.17182i
$895$	−32.8118			−1.09678
$896$		0			0
$897$	21.7712			0.726921
$898$	−10.9373	−	18.9439i	−0.364981	−	0.632165i
$899$	−12.5830	+	21.7944i	−0.419667	+	0.726884i
$900$	4.58301	−	7.93800i	0.152767	−	0.264600i
$901$	4.93725	+	8.55157i	0.164484	+	0.284894i
$902$	10.9373			0.364171
$903$		0			0
$904$	18.2915			0.608366
$905$	−8.22876	−	14.2526i	−0.273533	−	0.473773i
$906$	11.4373	−	19.8099i	0.379977	−	0.658140i
$907$	−21.2288	+	36.7693i	−0.704889	+	1.22090i	0.261842	+	0.965111i	$0.415670\pi$
$907$	−21.2288	+	36.7693i	−0.704889	+	1.22090i	−0.966731	+	0.255793i	$0.917663\pi$
$908$	−1.35425	−	2.34563i	−0.0449423	−	0.0778424i
$909$	−12.0000			−0.398015
$910$		0			0
$911$	9.29150			0.307841			0.153921	−	0.988083i	$-0.450810\pi$
$911$	9.29150			0.307841			0.153921	+	0.988083i	$0.450810\pi$
$912$	7.46863	+	12.9360i	0.247311	+	0.428355i
$913$	1.35425	−	2.34563i	0.0448191	−	0.0776289i
$914$	1.58301	−	2.74185i	0.0523612	−	0.0906922i
$915$	−31.1144	−	53.8917i	−1.02861	−	1.78160i
$916$	16.0000			0.528655
$917$		0			0
$918$	−15.8745			−0.523937
$919$	12.3542	+	21.3982i	0.407529	+	0.705861i	0.994612	−	0.103666i	$-0.0330572\pi$
$919$	12.3542	+	21.3982i	0.407529	+	0.705861i	−0.587083	+	0.809527i	$0.699724\pi$
$920$	1.35425	−	2.34563i	0.0446483	−	0.0773330i
$921$	−29.4059	+	50.9325i	−0.968957	+	1.67828i
$922$	−5.08301	−	8.80402i	−0.167400	−	0.289945i
$923$	−21.7712			−0.716609
$924$		0			0
$925$	−8.35425			−0.274686
$926$	15.2288	+	26.3770i	0.500448	+	0.866801i
$927$	−5.87451	+	10.1749i	−0.192944	+	0.334189i
$928$	3.14575	−	5.44860i	0.103264	−	0.178859i
$929$	7.20850	+	12.4855i	0.236503	+	0.409635i	0.959708	−	0.280998i	$-0.0906653\pi$
$929$	7.20850	+	12.4855i	0.236503	+	0.409635i	−0.723205	+	0.690633i	$0.757332\pi$
$930$	17.4170			0.571126
$931$		0			0
$932$	1.06275			0.0348114
$933$	−1.40588	−	2.43506i	−0.0460265	−	0.0797202i
$934$	−10.6458	+	18.4390i	−0.348340	+	0.603342i
$935$	4.93725	−	8.55157i	0.161465	−	0.279666i
$936$	−10.0000	−	17.3205i	−0.326860	−	0.566139i
$937$	−32.6863			−1.06781			−0.533907	−	0.845543i	$-0.679277\pi$
$937$	−32.6863			−1.06781			−0.533907	+	0.845543i	$0.679277\pi$
$938$		0			0
$939$	62.3948			2.03618
$940$	2.22876	+	3.86032i	0.0726940	+	0.125910i
$941$	25.3118	−	43.8413i	0.825140	−	1.42918i	−0.0766725	−	0.997056i	$-0.524430\pi$
$941$	25.3118	−	43.8413i	0.825140	−	1.42918i	0.901812	−	0.432128i	$-0.142237\pi$
$942$	28.0000	−	48.4974i	0.912289	−	1.58013i
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$	−4.64575			−0.151206
$945$		0			0
$946$	4.00000			0.130051
$947$	1.06275	+	1.84073i	0.0345346	+	0.0598157i	0.882776	−	0.469794i	$-0.155672\pi$
$947$	1.06275	+	1.84073i	0.0345346	+	0.0598157i	−0.848242	+	0.529610i	$0.822338\pi$
$948$	−3.50000	+	6.06218i	−0.113675	+	0.196890i
$949$	−0.885622	+	1.53394i	−0.0287485	+	0.0497939i
$950$	−6.46863	−	11.2040i	−0.209870	−	0.363505i
$951$	−31.7490			−1.02953
$952$		0			0
$953$	11.5203			0.373178			0.186589	−	0.982438i	$-0.440257\pi$
$953$	11.5203			0.373178			0.186589	+	0.982438i	$0.440257\pi$
$954$	3.29150	+	5.70105i	0.106566	+	0.184578i
$955$	2.22876	−	3.86032i	0.0721209	−	0.124917i
$956$	8.61438	−	14.9205i	0.278609	−	0.482565i
$957$	8.32288	+	14.4156i	0.269040	+	0.465992i
$958$	−10.0627			−0.325113
$959$		0			0
$960$	−4.35425			−0.140533
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−9.11438	+	15.7866i	−0.293859	+	0.508979i
$963$	21.8745	−	37.8878i	0.704896	−	1.22092i
$964$	−12.4059	−	21.4876i	−0.399567	−	0.692070i
$965$	42.0000			1.35203
$966$		0			0
$967$	58.3320			1.87583			0.937916	−	0.346863i	$-0.112753\pi$
$967$	58.3320			1.87583			0.937916	+	0.346863i	$0.112753\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$	−44.8118	+	77.6162i	−1.43956	+	2.49339i
$970$	13.4059	−	23.2197i	0.430437	−	0.745539i
$971$	−5.03137	−	8.71459i	−0.161464	−	0.279665i	0.773930	−	0.633272i	$-0.218288\pi$
$971$	−5.03137	−	8.71459i	−0.161464	−	0.279665i	−0.935394	+	0.353607i	$0.884955\pi$
$972$	21.1660			0.678900
$973$		0			0
$974$	9.41699			0.301740
$975$	15.1569	+	26.2525i	0.485408	+	0.840752i
$976$	7.14575	−	12.3768i	0.228730	−	0.396172i
$977$	8.22876	−	14.2526i	0.263261	−	0.455982i	−0.703845	−	0.710353i	$-0.748535\pi$
$977$	8.22876	−	14.2526i	0.263261	−	0.455982i	0.967107	+	0.254371i	$0.0818685\pi$
$978$	−0.854249	−	1.47960i	−0.0273159	−	0.0473125i
$979$	−6.58301			−0.210394
$980$		0			0
$981$	−42.3320			−1.35156
$982$	10.6458	+	18.4390i	0.339720	+	0.588412i
$983$	−13.3542	+	23.1302i	−0.425934	+	0.737740i	−0.996507	−	0.0835070i	$-0.973388\pi$
$983$	−13.3542	+	23.1302i	−0.425934	+	0.737740i	0.570573	+	0.821247i	$0.306721\pi$
$984$	14.4686	−	25.0604i	0.461243	−	0.798896i
$985$	10.5941	+	18.3496i	0.337557	+	0.584665i
$986$	37.7490			1.20217
$987$		0			0
$988$	−28.2288			−0.898076
$989$	3.29150	+	5.70105i	0.104664	+	0.181283i
$990$	3.29150	−	5.70105i	0.104611	−	0.181191i
$991$	11.3431	−	19.6469i	0.360327	−	0.624104i	−0.627688	−	0.778465i	$-0.715999\pi$
$991$	11.3431	−	19.6469i	0.360327	−	0.624104i	0.988014	+	0.154361i	$0.0493319\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	54.6235			1.73343
$994$		0			0
$995$	−6.95948			−0.220630
$996$	−3.58301	−	6.20595i	−0.113532	−	0.196643i
$997$	−10.7085	+	18.5477i	−0.339142	+	0.587410i	−0.984271	−	0.176663i	$-0.943470\pi$
$997$	−10.7085	+	18.5477i	−0.339142	+	0.587410i	0.645130	+	0.764073i	$0.276803\pi$
$998$	−6.93725	+	12.0157i	−0.219595	+	0.380350i
$999$	4.82288	+	8.35347i	0.152589	+	0.264292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.v.67.2		4
7.2	even	3	inner	1078.2.e.v.177.2		4
7.3	odd	6		1078.2.a.s.1.2		2
7.4	even	3		1078.2.a.n.1.1		2
7.5	odd	6		154.2.e.f.23.1	✓	4
7.6	odd	2		154.2.e.f.67.1	yes	4
21.5	even	6		1386.2.k.s.793.1		4
21.11	odd	6		9702.2.a.dr.1.1		2
21.17	even	6		9702.2.a.cz.1.2		2
21.20	even	2		1386.2.k.s.991.1		4
28.3	even	6		8624.2.a.ca.1.1		2
28.11	odd	6		8624.2.a.bk.1.2		2
28.19	even	6		1232.2.q.g.177.2		4
28.27	even	2		1232.2.q.g.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.f.23.1	✓	4	7.5	odd	6
154.2.e.f.67.1	yes	4	7.6	odd	2
1078.2.a.n.1.1		2	7.4	even	3
1078.2.a.s.1.2		2	7.3	odd	6
1078.2.e.v.67.2		4	1.1	even	1	trivial
1078.2.e.v.177.2		4	7.2	even	3	inner
1232.2.q.g.177.2		4	28.19	even	6
1232.2.q.g.529.2		4	28.27	even	2
1386.2.k.s.793.1		4	21.5	even	6
1386.2.k.s.991.1		4	21.20	even	2
8624.2.a.bk.1.2		2	28.11	odd	6
8624.2.a.ca.1.1		2	28.3	even	6
9702.2.a.cz.1.2		2	21.17	even	6
9702.2.a.dr.1.1		2	21.11	odd	6

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} +2.64575 q^{6} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} +2.64575 q^{6} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +(0.822876 - 1.42526i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.32288 + 2.29129i) q^{12} -5.00000 q^{13} -4.35425 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{18} +(-2.82288 - 4.88936i) q^{19} +1.64575 q^{20} -1.00000 q^{22} +(-0.822876 - 1.42526i) q^{23} +(-1.32288 + 2.29129i) q^{24} +(1.14575 - 1.98450i) q^{25} +(-2.50000 - 4.33013i) q^{26} -2.64575 q^{27} +6.29150 q^{29} +(-2.17712 - 3.77089i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.32288 + 2.29129i) q^{33} +6.00000 q^{34} +4.00000 q^{36} +(-1.82288 - 3.15731i) q^{37} +(2.82288 - 4.88936i) q^{38} +(-6.61438 + 11.4564i) q^{39} +(0.822876 + 1.42526i) q^{40} -10.9373 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.29150 + 5.70105i) q^{45} +(0.822876 - 1.42526i) q^{46} +(1.35425 + 2.34563i) q^{47} -2.64575 q^{48} +2.29150 q^{50} +(-7.93725 - 13.7477i) q^{51} +(2.50000 - 4.33013i) q^{52} +(-0.822876 + 1.42526i) q^{53} +(-1.32288 - 2.29129i) q^{54} +1.64575 q^{55} -14.9373 q^{57} +(3.14575 + 5.44860i) q^{58} +(2.32288 - 4.02334i) q^{59} +(2.17712 - 3.77089i) q^{60} +(7.14575 + 12.3768i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(4.11438 + 7.12631i) q^{65} +(-1.32288 + 2.29129i) q^{66} +(5.96863 - 10.3380i) q^{67} +(3.00000 + 5.19615i) q^{68} -4.35425 q^{69} +4.35425 q^{71} +(2.00000 + 3.46410i) q^{72} +(0.177124 - 0.306788i) q^{73} +(1.82288 - 3.15731i) q^{74} +(-3.03137 - 5.25049i) q^{75} +5.64575 q^{76} -13.2288 q^{78} +(1.32288 + 2.29129i) q^{79} +(-0.822876 + 1.42526i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-5.46863 - 9.47194i) q^{82} -2.70850 q^{83} -9.87451 q^{85} +(-2.00000 - 3.46410i) q^{86} +(8.32288 - 14.4156i) q^{87} +(0.500000 - 0.866025i) q^{88} +(3.29150 + 5.70105i) q^{89} -6.58301 q^{90} +1.64575 q^{92} +(5.29150 + 9.16515i) q^{93} +(-1.35425 + 2.34563i) q^{94} +(-4.64575 + 8.04668i) q^{95} +(-1.32288 - 2.29129i) q^{96} +16.2915 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^8 - 8 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} - 8 q^{9} - 2 q^{10} - 2 q^{11} - 20 q^{13} - 28 q^{15} - 2 q^{16} + 12 q^{17} + 8 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{22} + 2 q^{23} - 6 q^{25} - 10 q^{26} + 4 q^{29} - 14 q^{30} - 8 q^{31} + 2 q^{32} + 24 q^{34} + 16 q^{36} - 2 q^{37} + 6 q^{38} - 2 q^{40} - 12 q^{41} - 16 q^{43} - 2 q^{44} + 8 q^{45} - 2 q^{46} + 16 q^{47} - 12 q^{50} + 10 q^{52} + 2 q^{53} - 4 q^{55} - 28 q^{57} + 2 q^{58} + 4 q^{59} + 14 q^{60} + 18 q^{61} - 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} + 12 q^{68} - 28 q^{69} + 28 q^{71} + 8 q^{72} + 6 q^{73} + 2 q^{74} - 28 q^{75} + 12 q^{76} + 2 q^{80} + 10 q^{81} - 6 q^{82} - 32 q^{83} + 24 q^{85} - 8 q^{86} + 28 q^{87} + 2 q^{88} - 8 q^{89} + 16 q^{90} - 4 q^{92} - 16 q^{94} - 8 q^{95} + 44 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^8 - 8 * q^9 - 2 * q^10 - 2 * q^11 - 20 * q^13 - 28 * q^15 - 2 * q^16 + 12 * q^17 + 8 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^22 + 2 * q^23 - 6 * q^25 - 10 * q^26 + 4 * q^29 - 14 * q^30 - 8 * q^31 + 2 * q^32 + 24 * q^34 + 16 * q^36 - 2 * q^37 + 6 * q^38 - 2 * q^40 - 12 * q^41 - 16 * q^43 - 2 * q^44 + 8 * q^45 - 2 * q^46 + 16 * q^47 - 12 * q^50 + 10 * q^52 + 2 * q^53 - 4 * q^55 - 28 * q^57 + 2 * q^58 + 4 * q^59 + 14 * q^60 + 18 * q^61 - 16 * q^62 + 4 * q^64 - 10 * q^65 + 8 * q^67 + 12 * q^68 - 28 * q^69 + 28 * q^71 + 8 * q^72 + 6 * q^73 + 2 * q^74 - 28 * q^75 + 12 * q^76 + 2 * q^80 + 10 * q^81 - 6 * q^82 - 32 * q^83 + 24 * q^85 - 8 * q^86 + 28 * q^87 + 2 * q^88 - 8 * q^89 + 16 * q^90 - 4 * q^92 - 16 * q^94 - 8 * q^95 + 44 * q^97 + 16 * q^99

Introduction

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