LMFDB - Embedded newform 308.2.n.a.263.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(219,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("308.219");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.n (of order $6$, degree $2$, 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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.2
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	308.263
Dual form			308.2.n.a.219.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.895644 - 1.09445i) q^{2} +(2.29129 + 1.32288i) q^{3} +(-0.395644 - 1.96048i) q^{4} +(3.50000 - 1.32288i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-2.50000 - 1.32288i) q^{8} +(2.00000 + 3.46410i) q^{9} +(3.29129 - 0.409175i) q^{11} +(1.68693 - 5.01540i) q^{12} -2.64575i q^{13} +(2.39564 + 2.87418i) q^{14} +(-3.68693 + 1.55130i) q^{16} +(-4.58258 - 2.64575i) q^{17} +(5.58258 + 0.913701i) q^{18} +(-4.58258 + 5.29150i) q^{21} +(2.50000 - 3.96863i) q^{22} +(-4.58258 + 2.64575i) q^{23} +(-3.97822 - 6.33828i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-2.89564 - 2.36965i) q^{26} +2.64575i q^{27} +(5.29129 - 0.0476751i) q^{28} +7.93725i q^{29} +(-9.16515 - 5.29150i) q^{31} +(-1.60436 + 5.42458i) q^{32} +(8.08258 + 3.41643i) q^{33} +(-7.00000 + 2.64575i) q^{34} +(6.00000 - 5.29150i) q^{36} +(4.00000 + 6.92820i) q^{37} +(3.50000 - 6.06218i) q^{39} +(1.68693 + 9.75470i) q^{42} +2.00000 q^{43} +(-2.10436 - 6.29060i) q^{44} +(-1.20871 + 7.38505i) q^{46} +(-10.5000 - 1.32288i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.50000 - 6.61438i) q^{50} +(-7.00000 - 12.1244i) q^{51} +(-5.18693 + 1.04678i) q^{52} +(2.00000 - 3.46410i) q^{53} +(2.89564 + 2.36965i) q^{54} +(4.68693 - 5.83375i) q^{56} +(8.68693 + 7.10895i) q^{58} +(-2.29129 - 1.32288i) q^{59} +(2.29129 - 1.32288i) q^{61} +(-14.0000 + 5.29150i) q^{62} +(-10.0000 + 3.46410i) q^{63} +(4.50000 + 6.61438i) q^{64} +(10.9782 - 5.78608i) q^{66} +(-2.29129 - 1.32288i) q^{67} +(-3.37386 + 10.0308i) q^{68} -14.0000 q^{69} -5.29150i q^{71} +(-0.417424 - 11.3060i) q^{72} +(9.16515 + 5.29150i) q^{73} +(11.1652 + 1.82740i) q^{74} +(11.4564 - 6.61438i) q^{75} +(-0.582576 + 8.75560i) q^{77} +(-3.50000 - 9.26013i) q^{78} +(6.50000 + 11.2583i) q^{79} +(2.50000 - 4.33013i) q^{81} +(12.1869 + 6.89048i) q^{84} +(1.79129 - 2.18890i) q^{86} +(-10.5000 + 18.1865i) q^{87} +(-8.76951 - 3.33103i) q^{88} +(7.00000 + 12.1244i) q^{89} +(6.87386 + 1.32288i) q^{91} +(7.00000 + 7.93725i) q^{92} +(-14.0000 - 24.2487i) q^{93} +(-10.8521 + 10.3069i) q^{96} +7.00000 q^{97} +(-8.66515 + 4.78698i) q^{98} +(8.00000 + 10.5830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 3 q^{4} + 14 q^{6} - 2 q^{7} - 10 q^{8} + 8 q^{9} + 4 q^{11} - 7 q^{12} + 5 q^{14} - q^{16} + 4 q^{18} + 10 q^{22} + 7 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{28} - 11 q^{32} + 14 q^{33} - 28 q^{34}+ \cdots + 32 q^{99}+O(q^{100}) $ 4 * q - q^2 + 3 * q^4 + 14 * q^6 - 2 * q^7 - 10 * q^8 + 8 * q^9 + 4 * q^11 - 7 * q^12 + 5 * q^14 - q^16 + 4 * q^18 + 10 * q^22 + 7 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^28 - 11 * q^32 + 14 * q^33 - 28 * q^34 + 24 * q^36 + 16 * q^37 + 14 * q^39 - 7 * q^42 + 8 * q^43 - 13 * q^44 - 14 * q^46 - 42 * q^48 - 26 * q^49 - 10 * q^50 - 28 * q^51 - 7 * q^52 + 8 * q^53 + 7 * q^54 + 5 * q^56 + 21 * q^58 - 56 * q^62 - 40 * q^63 + 18 * q^64 + 21 * q^66 + 14 * q^68 - 56 * q^69 - 20 * q^72 + 8 * q^74 + 16 * q^77 - 14 * q^78 + 26 * q^79 + 10 * q^81 + 35 * q^84 - 2 * q^86 - 42 * q^87 - 3 * q^88 + 28 * q^89 + 28 * q^92 - 56 * q^93 + 7 * q^96 + 28 * q^97 + 2 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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 $

$2$	0.895644	−	1.09445i	0.633316	−	0.773893i
$2$	0.895644	−	1.09445i	0.633316	−	0.773893i
$3$	2.29129	+	1.32288i	1.32288	+	0.763763i	0.984186	−	0.177136i	$-0.0566831\pi$
$3$	2.29129	+	1.32288i	1.32288	+	0.763763i	0.338689	+	0.940898i	$0.390016\pi$
$4$	−0.395644	−	1.96048i	−0.197822	−	0.980238i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	3.50000	−	1.32288i	1.42887	−	0.540062i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−2.50000	−	1.32288i	−0.883883	−	0.467707i
$9$	2.00000	+	3.46410i	0.666667	+	1.15470i
$10$		0			0
$11$	3.29129	−	0.409175i	0.992361	−	0.123371i
$11$	3.29129	−	0.409175i	0.992361	−	0.123371i
$12$	1.68693	−	5.01540i	0.486975	−	1.44782i
$13$		−	2.64575i		−	0.733799i	−0.930261	−	0.366900i	$-0.880419\pi$
$13$		−	2.64575i		−	0.733799i	0.930261	−	0.366900i	$-0.119581\pi$
$14$	2.39564	+	2.87418i	0.640263	+	0.768156i
$15$		0			0
$16$	−3.68693	+	1.55130i	−0.921733	+	0.387825i
$17$	−4.58258	−	2.64575i	−1.11144	−	0.641689i	−0.172236	−	0.985056i	$-0.555099\pi$
$17$	−4.58258	−	2.64575i	−1.11144	−	0.641689i	−0.939201	+	0.343367i	$0.888433\pi$
$18$	5.58258	+	0.913701i	1.31583	+	0.215361i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$	−4.58258	+	5.29150i	−1.00000	+	1.15470i
$22$	2.50000	−	3.96863i	0.533002	−	0.846114i
$23$	−4.58258	+	2.64575i	−0.955533	+	0.551677i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.58258	+	2.64575i	−0.955533	+	0.551677i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$	−3.97822	−	6.33828i	−0.812051	−	1.29380i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	−2.89564	−	2.36965i	−0.567882	−	0.464727i
$27$			2.64575i			0.509175i
$28$	5.29129	−	0.0476751i	0.999959	−	0.00900975i
$29$			7.93725i			1.47391i	0.675941	+	0.736956i	$0.263737\pi$
$29$			7.93725i			1.47391i	−0.675941	+	0.736956i	$0.736263\pi$
$30$		0			0
$31$	−9.16515	−	5.29150i	−1.64611	−	0.950382i	−0.978598	−	0.205783i	$-0.934026\pi$
$31$	−9.16515	−	5.29150i	−1.64611	−	0.950382i	−0.667512	−	0.744599i	$-0.732641\pi$
$32$	−1.60436	+	5.42458i	−0.283613	+	0.958939i
$33$	8.08258	+	3.41643i	1.40700	+	0.594724i
$34$	−7.00000	+	2.64575i	−1.20049	+	0.453743i
$35$		0			0
$36$	6.00000	−	5.29150i	1.00000	−	0.881917i
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$		0			0
$39$	3.50000	−	6.06218i	0.560449	−	0.970725i
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	1.68693	+	9.75470i	0.260299	+	1.50518i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−2.10436	−	6.29060i	−0.317244	−	0.948344i
$45$		0			0
$46$	−1.20871	+	7.38505i	−0.178215	+	1.08887i
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$	−10.5000	−	1.32288i	−1.51554	−	0.190941i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	−2.50000	−	6.61438i	−0.353553	−	0.935414i
$51$	−7.00000	−	12.1244i	−0.980196	−	1.69775i
$52$	−5.18693	+	1.04678i	−0.719298	+	0.145162i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$	2.89564	+	2.36965i	0.394047	+	0.322469i
$55$		0			0
$56$	4.68693	−	5.83375i	0.626318	−	0.779568i
$57$		0			0
$58$	8.68693	+	7.10895i	1.14065	+	0.933451i
$59$	−2.29129	−	1.32288i	−0.298300	−	0.172224i	0.343379	−	0.939197i	$-0.388429\pi$
$59$	−2.29129	−	1.32288i	−0.298300	−	0.172224i	−0.641679	+	0.766973i	$0.721762\pi$
$60$		0			0
$61$	2.29129	−	1.32288i	0.293369	−	0.169377i	−0.346091	−	0.938201i	$-0.612491\pi$
$61$	2.29129	−	1.32288i	0.293369	−	0.169377i	0.639460	+	0.768824i	$0.279158\pi$
$62$	−14.0000	+	5.29150i	−1.77800	+	0.672022i
$63$	−10.0000	+	3.46410i	−1.25988	+	0.436436i
$64$	4.50000	+	6.61438i	0.562500	+	0.826797i
$65$		0			0
$66$	10.9782	−	5.78608i	1.35133	−	0.712217i
$67$	−2.29129	−	1.32288i	−0.279925	−	0.161615i	0.353464	−	0.935448i	$-0.385004\pi$
$67$	−2.29129	−	1.32288i	−0.279925	−	0.161615i	−0.633390	+	0.773833i	$0.718337\pi$
$68$	−3.37386	+	10.0308i	−0.409141	+	1.21641i
$69$	−14.0000			−1.68540
$70$		0			0
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$	−0.417424	−	11.3060i	−0.0491939	−	1.33243i
$73$	9.16515	+	5.29150i	1.07270	+	0.619324i	0.928918	−	0.370286i	$-0.120740\pi$
$73$	9.16515	+	5.29150i	1.07270	+	0.619324i	0.143782	+	0.989609i	$0.454074\pi$
$74$	11.1652	+	1.82740i	1.29792	+	0.212431i
$75$	11.4564	−	6.61438i	1.32288	−	0.763763i
$76$		0			0
$77$	−0.582576	+	8.75560i	−0.0663907	+	0.997794i
$78$	−3.50000	−	9.26013i	−0.396297	−	1.04850i
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	0.956325	+	0.292306i	$0.0944227\pi$
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	12.1869	+	6.89048i	1.32970	+	0.751813i
$85$		0			0
$86$	1.79129	−	2.18890i	0.193160	−	0.236035i
$87$	−10.5000	+	18.1865i	−1.12572	+	1.94980i
$88$	−8.76951	−	3.33103i	−0.934833	−	0.355089i
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	0.951584	+	0.307389i	$0.0994552\pi$
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	−0.209585	+	0.977790i	$0.567211\pi$
$90$		0			0
$91$	6.87386	+	1.32288i	0.720577	+	0.138675i
$92$	7.00000	+	7.93725i	0.729800	+	0.827516i
$93$	−14.0000	−	24.2487i	−1.45173	−	2.51447i
$94$		0			0
$95$		0			0
$96$	−10.8521	+	10.3069i	−1.10759	+	1.05194i
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	−8.66515	+	4.78698i	−0.875312	+	0.483558i
$99$	8.00000	+	10.5830i	0.804030	+	1.06363i
$100$	−9.47822	−	3.18800i	−0.947822	−	0.318800i
$101$	−6.87386	−	3.96863i	−0.683975	−	0.394893i	0.117376	−	0.993088i	$-0.462552\pi$
$101$	−6.87386	−	3.96863i	−0.683975	−	0.394893i	−0.801351	+	0.598194i	$0.795885\pi$
$102$	−19.5390	−	3.19795i	−1.93465	−	0.316644i
$103$	4.58258	−	2.64575i	0.451535	−	0.260694i	−0.256943	−	0.966426i	$-0.582715\pi$
$103$	4.58258	−	2.64575i	0.451535	−	0.260694i	0.708478	+	0.705733i	$0.249382\pi$
$104$	−3.50000	+	6.61438i	−0.343203	+	0.648593i
$105$		0			0
$106$	−2.00000	−	5.29150i	−0.194257	−	0.513956i
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	0.992003	−	0.126217i	$-0.0402834\pi$
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	−0.605308	+	0.795991i	$0.706950\pi$
$108$	5.18693	−	1.04678i	0.499113	−	0.100726i
$109$	−9.16515	−	5.29150i	−0.877862	−	0.506834i	−0.00790932	−	0.999969i	$-0.502518\pi$
$109$	−9.16515	−	5.29150i	−0.877862	−	0.506834i	−0.869953	+	0.493135i	$0.835851\pi$
$110$		0			0
$111$			21.1660i			2.00899i
$112$	−2.18693	−	10.3546i	−0.206646	−	0.978416i
$113$	−19.0000			−1.78737			−0.893685	−	0.448695i	$-0.851889\pi$
$113$	−19.0000			−1.78737			−0.893685	+	0.448695i	$0.851889\pi$
$114$		0			0
$115$		0			0
$116$	15.5608	−	3.14033i	1.44478	−	0.291572i
$117$	9.16515	−	5.29150i	0.847319	−	0.489200i
$118$	−3.50000	+	1.32288i	−0.322201	+	0.121781i
$119$	9.16515	−	10.5830i	0.840168	−	0.970143i
$120$		0			0
$121$	10.6652	−	2.69343i	0.969559	−	0.244857i
$122$	0.604356	−	3.69253i	0.0547158	−	0.334306i
$123$		0			0
$124$	−6.74773	+	20.0616i	−0.605964	+	1.80159i
$125$		0			0
$126$	−5.16515	+	14.0471i	−0.460148	+	1.25142i
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	11.2695	+	0.999100i	0.996093	+	0.0883088i
$129$	4.58258	+	2.64575i	0.403473	+	0.232945i
$130$		0			0
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$	3.50000	−	17.1974i	0.304636	−	1.49684i
$133$		0			0
$134$	−3.50000	+	1.32288i	−0.302354	+	0.114279i
$135$		0			0
$136$	7.95644	+	12.6766i	0.682259	+	1.08701i
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$	−12.5390	+	15.3223i	−1.06739	+	1.30432i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$		0			0
$142$	−5.79129	−	4.73930i	−0.485994	−	0.397713i
$143$	−1.08258	−	8.70793i	−0.0905295	−	0.728194i
$144$	−12.7477	−	9.66930i	−1.06231	−	0.805775i
$145$		0			0
$146$	14.0000	−	5.29150i	1.15865	−	0.437928i
$147$	−11.4564	−	14.5516i	−0.944911	−	1.20020i
$148$	12.0000	−	10.5830i	0.986394	−	0.869918i
$149$	9.16515	−	5.29150i	0.750838	−	0.433497i	−0.0751583	−	0.997172i	$-0.523946\pi$
$149$	9.16515	−	5.29150i	0.750838	−	0.433497i	0.825997	+	0.563675i	$0.190613\pi$
$150$	3.02178	−	18.4626i	0.246727	−	1.50747i
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	−0.279554	−	0.960130i	$-0.590186\pi$
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	0.971274	−	0.237964i	$-0.0764802\pi$
$152$		0			0
$153$		−	21.1660i		−	1.71117i
$154$	9.06080	+	8.47950i	0.730140	+	0.683298i
$155$		0			0
$156$	−13.2695	−	4.46320i	−1.06241	−	0.357342i
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	18.1434	+	2.96953i	1.44341	+	0.236243i
$159$	9.16515	−	5.29150i	0.726844	−	0.419643i
$160$		0			0
$161$	−4.58258	−	13.2288i	−0.361158	−	1.04257i
$162$	−2.50000	−	6.61438i	−0.196419	−	0.519675i
$163$	2.29129	−	1.32288i	0.179468	−	0.103616i	−0.407575	−	0.913172i	$-0.633625\pi$
$163$	2.29129	−	1.32288i	0.179468	−	0.103616i	0.587042	+	0.809556i	$0.300292\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−21.0000			−1.62503			−0.812514	−	0.582941i	$-0.801902\pi$
$167$	−21.0000			−1.62503			−0.812514	+	0.582941i	$0.801902\pi$
$168$	18.4564	−	7.16658i	1.42395	−	0.552914i
$169$	6.00000			0.461538
$170$		0			0
$171$		0			0
$172$	−0.791288	−	3.92095i	−0.0603351	−	0.298970i
$173$	−11.4564	+	6.61438i	−0.871017	+	0.502882i	−0.867686	−	0.497113i	$-0.834394\pi$
$173$	−11.4564	+	6.61438i	−0.871017	+	0.502882i	−0.00333090	+	0.999994i	$0.501060\pi$
$174$	10.5000	+	27.7804i	0.796003	+	2.10603i
$175$	10.0000	+	8.66025i	0.755929	+	0.654654i
$176$	−11.5000	+	6.61438i	−0.866845	+	0.498578i
$177$	−3.50000	−	6.06218i	−0.263076	−	0.455661i
$178$	19.5390	+	3.19795i	1.46451	+	0.239697i
$179$	6.87386	+	3.96863i	0.513777	+	0.296629i	0.734385	−	0.678733i	$-0.237471\pi$
$179$	6.87386	+	3.96863i	0.513777	+	0.296629i	−0.220608	+	0.975363i	$0.570804\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	7.60436	−	6.33828i	0.563672	−	0.469824i
$183$	7.00000			0.517455
$184$	14.9564	−	0.552200i	1.10260	−	0.0407088i
$185$		0			0
$186$	−39.0780	−	6.39590i	−2.86534	−	0.468970i
$187$	−16.1652	−	6.83285i	−1.18211	−	0.499668i
$188$		0			0
$189$	−6.87386	−	1.32288i	−0.500000	−	0.0962250i
$190$		0			0
$191$	−9.16515	+	5.29150i	−0.663167	+	0.382880i	−0.793483	−	0.608593i	$-0.791734\pi$
$191$	−9.16515	+	5.29150i	−0.663167	+	0.382880i	0.130316	+	0.991473i	$0.458401\pi$
$192$	1.56080	+	21.1084i	0.112641	+	1.52337i
$193$	18.3303	+	10.5830i	1.31944	+	0.761781i	0.983639	−	0.180150i	$-0.0576584\pi$
$193$	18.3303	+	10.5830i	1.31944	+	0.761781i	0.335805	+	0.941932i	$0.390992\pi$
$194$	6.26951	−	7.66115i	0.450124	−	0.550039i
$195$		0			0
$196$	−2.52178	+	13.7710i	−0.180127	+	0.983643i
$197$			7.93725i			0.565506i	0.959193	+	0.282753i	$0.0912477\pi$
$197$			7.93725i			0.565506i	−0.959193	+	0.282753i	$0.908752\pi$
$198$	18.7477	+	0.723000i	1.33234	+	0.0513814i
$199$	9.16515	+	5.29150i	0.649700	+	0.375105i	0.788341	−	0.615238i	$-0.210940\pi$
$199$	9.16515	+	5.29150i	0.649700	+	0.375105i	−0.138641	+	0.990343i	$0.544273\pi$
$200$	−11.9782	+	7.51813i	−0.846988	+	0.531612i
$201$	−3.50000	−	6.06218i	−0.246871	−	0.427593i
$202$	−10.5000	+	3.96863i	−0.738777	+	0.279232i
$203$	−20.6216	−	3.96863i	−1.44735	−	0.278543i
$204$	−21.0000	+	18.5203i	−1.47029	+	1.29668i
$205$		0			0
$206$	1.20871	−	7.38505i	0.0842150	−	0.514541i
$207$	−18.3303	−	10.5830i	−1.27404	−	0.735570i
$208$	4.10436	+	9.75470i	0.284586	+	0.676367i
$209$		0			0
$210$		0			0
$211$	−2.00000			−0.137686			−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$	−7.58258	−	2.55040i	−0.520773	−	0.175162i
$213$	7.00000	−	12.1244i	0.479632	−	0.830747i
$214$	11.1652	+	1.82740i	0.763234	+	0.124919i
$215$		0			0
$216$	3.50000	−	6.61438i	0.238145	−	0.450051i
$217$	18.3303	−	21.1660i	1.24434	−	1.43684i
$218$	−14.0000	+	5.29150i	−0.948200	+	0.358386i
$219$	14.0000	+	24.2487i	0.946032	+	1.63858i
$220$		0			0
$221$	−7.00000	+	12.1244i	−0.470871	+	0.815572i
$222$	23.1652	+	18.9572i	1.55474	+	1.27232i
$223$			15.8745i			1.06304i	0.847047	+	0.531518i	$0.178378\pi$
$223$			15.8745i			1.06304i	−0.847047	+	0.531518i	$0.821622\pi$
$224$	−13.2913	−	6.88053i	−0.888062	−	0.459725i
$225$	20.0000			1.33333
$226$	−17.0172	+	20.7946i	−1.13197	+	1.38323i
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	−0.534577	−	0.845120i	$-0.679529\pi$
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	0.999184	+	0.0403978i	$0.0128625\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$	−12.9174	+	19.2909i	−0.849904	+	1.26925i
$232$	10.5000	−	19.8431i	0.689359	−	1.30277i
$233$	−13.7477	+	7.93725i	−0.900644	+	0.519987i	−0.877409	−	0.479743i	$-0.840730\pi$
$233$	−13.7477	+	7.93725i	−0.900644	+	0.519987i	−0.0232346	+	0.999730i	$0.507396\pi$
$234$	2.41742	−	14.7701i	0.158032	−	0.965552i
$235$		0			0
$236$	−1.68693	+	5.01540i	−0.109810	+	0.326475i
$237$			34.3948i			2.23418i
$238$	−3.37386	−	19.5094i	−0.218695	−	1.26461i
$239$	19.0000			1.22901			0.614504	−	0.788914i	$-0.289356\pi$
$239$	19.0000			1.22901			0.614504	+	0.788914i	$0.289356\pi$
$240$		0			0
$241$	−4.58258	−	2.64575i	−0.295190	−	0.170428i	0.345090	−	0.938570i	$-0.387848\pi$
$241$	−4.58258	−	2.64575i	−0.295190	−	0.170428i	−0.640280	+	0.768142i	$0.721182\pi$
$242$	6.60436	−	14.0848i	0.424544	−	0.905407i
$243$	18.3303	−	10.5830i	1.17589	−	0.678900i
$244$	−3.50000	−	3.96863i	−0.224065	−	0.254065i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	15.9129	+	25.3531i	1.01047	+	1.60992i
$249$		0			0
$250$		0			0
$251$		−	15.8745i		−	1.00199i	−0.865450	−	0.500995i	$-0.832967\pi$
$251$		−	15.8745i		−	1.00199i	0.865450	−	0.500995i	$-0.167033\pi$
$252$	10.7477	+	18.2342i	0.677043	+	1.14865i
$253$	−14.0000	+	10.5830i	−0.880172	+	0.665348i
$254$	4.47822	−	5.47225i	0.280988	−	0.343360i
$255$		0			0
$256$	11.1869	−	11.4391i	0.699183	−	0.714943i
$257$	3.50000	+	6.06218i	0.218324	+	0.378148i	0.954296	−	0.298864i	$-0.0966077\pi$
$257$	3.50000	+	6.06218i	0.218324	+	0.378148i	−0.735972	+	0.677012i	$0.763274\pi$
$258$	7.00000	−	2.64575i	0.435801	−	0.164717i
$259$	−20.0000	+	6.92820i	−1.24274	+	0.430498i
$260$		0			0
$261$	−27.4955	+	15.8745i	−1.70193	+	0.982607i
$262$	−19.5390	−	3.19795i	−1.20712	−	0.197570i
$263$	5.50000	−	9.52628i	0.339145	−	0.587416i	−0.645128	−	0.764075i	$-0.723196\pi$
$263$	5.50000	−	9.52628i	0.339145	−	0.587416i	0.984272	+	0.176659i	$0.0565291\pi$
$264$	−15.6869	−	19.2333i	−0.965464	−	1.18373i
$265$		0			0
$266$		0			0
$267$			37.0405i			2.26684i
$268$	−1.68693	+	5.01540i	−0.103046	+	0.306364i
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	0.0243472	+	0.999704i	$0.492249\pi$
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	−0.877942	+	0.478766i	$0.841084\pi$
$270$		0			0
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	0.739921	−	0.672694i	$-0.234863\pi$
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	−0.952531	+	0.304443i	$0.901530\pi$
$272$	21.0000	+	2.64575i	1.27331	+	0.160422i
$273$	14.0000	+	12.1244i	0.847319	+	0.733799i
$274$	1.50000	+	3.96863i	0.0906183	+	0.239754i
$275$	6.45644	−	15.2746i	0.389338	−	0.921095i
$276$	5.53901	+	27.4467i	0.333410	+	1.65209i
$277$	11.4564	+	6.61438i	0.688351	+	0.397419i	0.802994	−	0.595987i	$-0.203239\pi$
$277$	11.4564	+	6.61438i	0.688351	+	0.397419i	−0.114643	+	0.993407i	$0.536572\pi$
$278$	12.5390	−	15.3223i	0.752040	−	0.918971i
$279$		−	42.3320i		−	2.53435i
$280$		0			0
$281$		−	15.8745i		−	0.946994i	−0.880795	−	0.473497i	$-0.842992\pi$
$281$		−	15.8745i		−	0.946994i	0.880795	−	0.473497i	$-0.157008\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$	−10.3739	+	2.09355i	−0.615576	+	0.124229i
$285$		0			0
$286$	−10.5000	−	6.61438i	−0.620878	−	0.391116i
$287$		0			0
$288$	−22.0000	+	5.29150i	−1.29636	+	0.311805i
$289$	5.50000	+	9.52628i	0.323529	+	0.560369i
$290$		0			0
$291$	16.0390	+	9.26013i	0.940224	+	0.542838i
$292$	6.74773	−	20.0616i	0.394881	−	1.17402i
$293$		−	21.1660i		−	1.23653i	−0.785969	−	0.618266i	$-0.787836\pi$
$293$		−	21.1660i		−	1.23653i	0.785969	−	0.618266i	$-0.212164\pi$
$294$	−26.1869	−	0.494575i	−1.52725	−	0.0288442i
$295$		0			0
$296$	−0.834849	−	22.6120i	−0.0485246	−	1.31430i
$297$	1.08258	+	8.70793i	0.0628174	+	0.505285i
$298$	2.41742	−	14.7701i	0.140038	−	0.855609i
$299$	7.00000	+	12.1244i	0.404820	+	0.701170i
$300$	−17.5000	−	19.8431i	−1.01036	−	1.14564i
$301$	−1.00000	+	5.19615i	−0.0576390	+	0.299501i
$302$	−8.50000	−	22.4889i	−0.489120	−	1.29409i
$303$	−10.5000	−	18.1865i	−0.603209	−	1.04479i
$304$		0			0
$305$		0			0
$306$	−23.1652	−	18.9572i	−1.32426	−	1.08371i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	17.3956	−	2.32198i	0.991209	−	0.132307i
$309$	14.0000			0.796432
$310$		0			0
$311$	9.16515	+	5.29150i	0.519708	+	0.300054i	0.736815	−	0.676094i	$-0.236329\pi$
$311$	9.16515	+	5.29150i	0.519708	+	0.300054i	−0.217107	+	0.976148i	$0.569662\pi$
$312$	−16.7695	+	10.5254i	−0.949386	+	0.595882i
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	0.993757	+	0.111563i	$0.0355857\pi$
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	−0.400262	+	0.916401i	$0.631081\pi$
$314$	−7.00000	−	18.5203i	−0.395033	−	1.04516i
$315$		0			0
$316$	19.5000	−	17.1974i	1.09696	−	0.967428i
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$	2.41742	−	14.7701i	0.135562	−	0.828266i
$319$	3.24773	+	26.1238i	0.181838	+	1.46265i
$320$		0			0
$321$			21.1660i			1.18137i
$322$	−18.5826	−	6.83285i	−1.03557	−	0.380780i
$323$		0			0
$324$	−9.47822	−	3.18800i	−0.526568	−	0.177111i
$325$	−11.4564	−	6.61438i	−0.635489	−	0.366900i
$326$	0.604356	−	3.69253i	0.0334722	−	0.204510i
$327$	−14.0000	−	24.2487i	−0.774202	−	1.34096i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−20.6216	+	11.9059i	−1.13347	+	0.654406i	−0.944804	−	0.327636i	$-0.893748\pi$
$331$	−20.6216	+	11.9059i	−1.13347	+	0.654406i	−0.188661	+	0.982042i	$0.560415\pi$
$332$		0			0
$333$	−16.0000	+	27.7128i	−0.876795	+	1.51865i
$334$	−18.8085	+	22.9835i	−1.02916	+	1.25760i
$335$		0			0
$336$	8.68693	−	26.6184i	0.473911	−	1.45215i
$337$			15.8745i			0.864740i	0.901696	+	0.432370i	$0.142322\pi$
$337$			15.8745i			0.864740i	−0.901696	+	0.432370i	$0.857678\pi$
$338$	5.37386	−	6.56670i	0.292300	−	0.357182i
$339$	−43.5345	−	25.1346i	−2.36447	−	1.36513i
$340$		0			0
$341$	−32.3303	−	13.6657i	−1.75078	−	0.740039i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−5.00000	−	2.64575i	−0.269582	−	0.142649i
$345$		0			0
$346$	−3.02178	+	18.4626i	−0.162452	+	0.992557i
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$	39.8085	+	13.3896i	2.13396	+	0.717758i
$349$			10.5830i			0.566495i	0.959047	+	0.283248i	$0.0914118\pi$
$349$			10.5830i			0.566495i	−0.959047	+	0.283248i	$0.908588\pi$
$350$	18.4347	−	3.18800i	0.985374	−	0.170406i
$351$	7.00000			0.373632
$352$	−3.06080	+	18.5103i	−0.163141	+	0.986603i
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	−0.989960	−	0.141344i	$-0.954858\pi$
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	0.617388	+	0.786659i	$0.288191\pi$
$354$	−9.76951	−	1.59898i	−0.519243	−	0.0849846i
$355$		0			0
$356$	21.0000	−	18.5203i	1.11300	−	0.981572i
$357$	35.0000	−	12.1244i	1.85240	−	0.641689i
$358$	10.5000	−	3.96863i	0.554942	−	0.209748i
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	0.597372	−	0.801964i	$-0.296211\pi$
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	−0.993207	+	0.116358i	$0.962878\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$		0			0
$363$	28.0000	+	7.93725i	1.46962	+	0.416598i
$364$	−0.126136	−	13.9994i	−0.00661135	−	0.733770i
$365$		0			0
$366$	6.26951	−	7.66115i	0.327712	−	0.400455i
$367$	13.7477	+	7.93725i	0.717626	+	0.414321i	0.813878	−	0.581036i	$-0.197352\pi$
$367$	13.7477	+	7.93725i	0.717626	+	0.414321i	−0.0962526	+	0.995357i	$0.530686\pi$
$368$	12.7913	−	16.8637i	0.666792	−	0.879079i
$369$		0			0
$370$		0			0
$371$	8.00000	+	6.92820i	0.415339	+	0.359694i
$372$	−42.0000	+	37.0405i	−2.17760	+	1.92046i
$373$	−20.6216	+	11.9059i	−1.06775	+	0.616463i	−0.927565	−	0.373663i	$-0.878102\pi$
$373$	−20.6216	+	11.9059i	−1.06775	+	0.616463i	−0.140181	+	0.990126i	$0.544768\pi$
$374$	−21.9564	+	11.5722i	−1.13534	+	0.598382i
$375$		0			0
$376$		0			0
$377$	21.0000			1.08156
$378$	−7.60436	+	6.33828i	−0.391126	+	0.326006i
$379$		−	18.5203i		−	0.951322i	−0.879629	−	0.475661i	$-0.842209\pi$
$379$		−	18.5203i		−	0.951322i	0.879629	−	0.475661i	$-0.157791\pi$
$380$		0			0
$381$	11.4564	+	6.61438i	0.586931	+	0.338865i
$382$	−2.41742	+	14.7701i	−0.123686	+	0.755704i
$383$	−13.7477	+	7.93725i	−0.702476	+	0.405575i	−0.808269	−	0.588813i	$-0.799595\pi$
$383$	−13.7477	+	7.93725i	−0.702476	+	0.405575i	0.105793	+	0.994388i	$0.466262\pi$
$384$	24.5000	+	17.1974i	1.25026	+	0.877600i
$385$		0			0
$386$	28.0000	−	10.5830i	1.42516	−	0.538661i
$387$	4.00000	+	6.92820i	0.203331	+	0.352180i
$388$	−2.76951	−	13.7233i	−0.140600	−	0.696697i
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	28.0000			1.41602
$392$	12.8131	+	15.0939i	0.647158	+	0.762356i
$393$		−	37.0405i		−	1.86845i
$394$	8.68693	+	7.10895i	0.437641	+	0.358144i
$395$		0			0
$396$	17.5826	−	19.8709i	0.883558	−	0.998551i
$397$	−14.0000	−	24.2487i	−0.702640	−	1.21701i	−0.967537	−	0.252731i	$-0.918671\pi$
$397$	−14.0000	−	24.2487i	−0.702640	−	1.21701i	0.264897	−	0.964277i	$-0.414662\pi$
$398$	14.0000	−	5.29150i	0.701757	−	0.265239i
$399$		0			0
$400$	−2.50000	+	19.8431i	−0.125000	+	0.992157i
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$	−9.76951	−	1.59898i	−0.487259	−	0.0797497i
$403$	−14.0000	+	24.2487i	−0.697390	+	1.20791i
$404$	−5.06080	+	15.0462i	−0.251784	+	0.748577i
$405$		0			0
$406$	−22.8131	+	19.0148i	−1.13219	+	0.943690i
$407$	16.0000	+	21.1660i	0.793091	+	1.04916i
$408$	1.46099	+	39.5710i	0.0723295	+	1.95906i
$409$	−32.0780	−	18.5203i	−1.58616	−	0.915768i	−0.993932	−	0.109995i	$-0.964917\pi$
$409$	−32.0780	−	18.5203i	−1.58616	−	0.915768i	−0.592224	−	0.805773i	$-0.701750\pi$
$410$		0			0
$411$	−6.87386	+	3.96863i	−0.339063	+	0.195758i
$412$	−7.00000	−	7.93725i	−0.344865	−	0.391040i
$413$	4.58258	−	5.29150i	0.225494	−	0.260378i
$414$	−28.0000	+	10.5830i	−1.37612	+	0.520126i
$415$		0			0
$416$	14.3521	+	4.24473i	0.703669	+	0.208115i
$417$	32.0780	+	18.5203i	1.57087	+	0.906941i
$418$		0			0
$419$			5.29150i			0.258507i	0.991612	+	0.129253i	$0.0412581\pi$
$419$			5.29150i			0.258507i	−0.991612	+	0.129253i	$0.958742\pi$
$420$		0			0
$421$	12.0000			0.584844			0.292422	−	0.956289i	$-0.405539\pi$
$421$	12.0000			0.584844			0.292422	+	0.956289i	$0.405539\pi$
$422$	−1.79129	+	2.18890i	−0.0871985	+	0.106554i
$423$		0			0
$424$	−9.58258	+	6.01450i	−0.465371	+	0.292090i
$425$	−22.9129	+	13.2288i	−1.11144	+	0.641689i
$426$	−7.00000	−	18.5203i	−0.339151	−	0.897309i
$427$	2.29129	+	6.61438i	0.110883	+	0.320092i
$428$	12.0000	−	10.5830i	0.580042	−	0.511549i
$429$	9.03901	−	21.3845i	0.436408	−	1.03245i
$430$		0			0
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	−0.827636	−	0.561266i	$-0.810315\pi$
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$432$	−4.10436	−	9.75470i	−0.197471	−	0.469323i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−6.74773	−	39.0188i	−0.323901	−	1.87296i
$435$		0			0
$436$	−6.74773	+	20.0616i	−0.323158	+	0.960777i
$437$		0			0
$438$	39.0780	+	6.39590i	1.86722	+	0.305608i
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$		0			0
$441$	−4.00000	−	27.7128i	−0.190476	−	1.31966i
$442$	7.00000	+	18.5203i	0.332956	+	0.880919i
$443$	−32.0780	+	18.5203i	−1.52407	+	0.879924i	−0.524479	+	0.851423i	$0.675740\pi$
$443$	−32.0780	+	18.5203i	−1.52407	+	0.879924i	−0.999594	+	0.0285009i	$0.990927\pi$
$444$	41.4955	−	8.37420i	1.96929	−	0.397422i
$445$		0			0
$446$	17.3739	+	14.2179i	0.822676	+	0.673237i
$447$	28.0000			1.32435
$448$	−19.4347	+	8.38415i	−0.918201	+	0.396114i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	17.9129	−	21.8890i	0.844421	−	1.03186i
$451$		0			0
$452$	7.51723	+	37.2490i	0.353581	+	1.75205i
$453$	38.9519	−	22.4889i	1.83012	−	1.05662i
$454$	−7.00000	−	18.5203i	−0.328526	−	0.869199i
$455$		0			0
$456$		0			0
$457$	−4.58258	+	2.64575i	−0.214364	+	0.123763i	−0.603338	−	0.797486i	$-0.706163\pi$
$457$	−4.58258	+	2.64575i	−0.214364	+	0.123763i	0.388974	+	0.921249i	$0.372830\pi$
$458$	−19.5390	−	3.19795i	−0.912998	−	0.149430i
$459$	7.00000	−	12.1244i	0.326732	−	0.565916i
$460$		0			0
$461$		−	7.93725i		−	0.369675i	−0.982769	−	0.184837i	$-0.940824\pi$
$461$		−	7.93725i		−	0.369675i	0.982769	−	0.184837i	$-0.0591758\pi$
$462$	9.54356	+	31.4153i	0.444007	+	1.46157i
$463$		−	21.1660i		−	0.983668i	−0.870689	−	0.491834i	$-0.836327\pi$
$463$		−	21.1660i		−	0.983668i	0.870689	−	0.491834i	$-0.163673\pi$
$464$	−12.3131	−	29.2641i	−0.571620	−	1.35855i
$465$		0			0
$466$	−3.62614	+	22.1552i	−0.167978	+	1.02632i
$467$	13.7477	−	7.93725i	0.636169	−	0.367292i	−0.146968	−	0.989141i	$-0.546952\pi$
$467$	13.7477	−	7.93725i	0.636169	−	0.367292i	0.783137	+	0.621849i	$0.213618\pi$
$468$	−14.0000	−	15.8745i	−0.647150	−	0.733799i
$469$	4.58258	−	5.29150i	0.211604	−	0.244339i
$470$		0			0
$471$	32.0780	−	18.5203i	1.47808	−	0.853368i
$472$	3.97822	+	6.33828i	0.183112	+	0.291743i
$473$	6.58258	−	0.818350i	0.302667	−	0.0376278i
$474$	37.6434	+	30.8055i	1.72902	+	1.41494i
$475$		0			0
$476$	−24.3739	−	13.7810i	−1.11717	−	0.631649i
$477$	16.0000			0.732590
$478$	17.0172	−	20.7946i	0.778350	−	0.951121i
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	−0.519973	−	0.854183i	$-0.674058\pi$
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	0.999730	+	0.0232187i	$0.00739140\pi$
$480$		0			0
$481$	18.3303	−	10.5830i	0.835790	−	0.482544i
$482$	−7.00000	+	2.64575i	−0.318841	+	0.120511i
$483$	7.00000	−	36.3731i	0.318511	−	1.65503i
$484$	−9.50000	−	19.8431i	−0.431818	−	0.901961i
$485$		0			0
$486$	4.83485	−	29.5402i	0.219313	−	1.33997i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$	−7.47822	+	0.276100i	−0.338523	+	0.0124985i
$489$	7.00000			0.316551
$490$		0			0
$491$	−26.0000			−1.17336			−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000			−1.17336			−0.586682	+	0.809818i	$0.699566\pi$
$492$		0			0
$493$	21.0000	−	36.3731i	0.945792	−	1.63816i
$494$		0			0
$495$		0			0
$496$	42.0000	+	5.29150i	1.88586	+	0.237595i
$497$	13.7477	+	2.64575i	0.616670	+	0.118678i
$498$		0			0
$499$	22.9129	−	13.2288i	1.02572	−	0.592200i	0.109965	−	0.993935i	$-0.464926\pi$
$499$	22.9129	−	13.2288i	1.02572	−	0.592200i	0.915756	+	0.401735i	$0.131593\pi$
$500$		0			0
$501$	−48.1170	−	27.7804i	−2.14971	−	1.24114i
$502$	−17.3739	−	14.2179i	−0.775433	−	0.634576i
$503$	−7.00000			−0.312115			−0.156057	−	0.987748i	$-0.549878\pi$
$503$	−7.00000			−0.312115			−0.156057	+	0.987748i	$0.549878\pi$
$504$	29.5826	+	4.56850i	1.31771	+	0.203497i
$505$		0			0
$506$	−0.956439	+	24.8009i	−0.0425189	+	1.10254i
$507$	13.7477	+	7.93725i	0.610558	+	0.352506i
$508$	−1.97822	−	9.80238i	−0.0877693	−	0.434910i
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	0.978421	−	0.206623i	$-0.0662474\pi$
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	−0.668151	+	0.744026i	$0.732914\pi$
$510$		0			0
$511$	−18.3303	+	21.1660i	−0.810885	+	0.936329i
$512$	−2.50000	−	22.4889i	−0.110485	−	0.993878i
$513$		0			0
$514$	9.76951	+	1.59898i	0.430915	+	0.0705278i
$515$		0			0
$516$	3.37386	−	10.0308i	0.148526	−	0.441582i
$517$		0			0
$518$	−10.3303	+	28.0942i	−0.453887	+	1.23439i
$519$	−35.0000			−1.53633
$520$		0			0
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.120656	−	0.992694i	$-0.461500\pi$
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.799370	−	0.600839i	$-0.205167\pi$
$522$	−7.25227	+	44.3103i	−0.317423	+	1.93941i
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	0.977503	−	0.210921i	$-0.0676463\pi$
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	−0.671414	+	0.741082i	$0.734313\pi$
$524$	−21.0000	+	18.5203i	−0.917389	+	0.809061i
$525$	11.4564	+	33.0719i	0.500000	+	1.44338i
$526$	−5.50000	−	14.5516i	−0.239811	−	0.634481i
$527$	28.0000	+	48.4974i	1.21970	+	2.11258i
$528$	−35.0998	−	0.0576255i	−1.52752	−	0.00250783i
$529$	2.50000	−	4.33013i	0.108696	−	0.188266i
$530$		0			0
$531$		−	10.5830i		−	0.459263i
$532$		0			0
$533$		0			0
$534$	40.5390	+	33.1751i	1.75429	+	1.43563i
$535$		0			0
$536$	3.97822	+	6.33828i	0.171833	+	0.273772i
$537$	10.5000	+	18.1865i	0.453108	+	0.784807i
$538$	14.0000	+	37.0405i	0.603583	+	1.59693i
$539$	−22.4564	−	5.89138i	−0.967267	−	0.253760i
$540$		0			0
$541$	20.6216	−	11.9059i	0.886591	−	0.511874i	0.0137654	−	0.999905i	$-0.495618\pi$
$541$	20.6216	−	11.9059i	0.886591	−	0.511874i	0.872826	+	0.488031i	$0.162285\pi$
$542$	−9.76951	−	1.59898i	−0.419636	−	0.0686819i
$543$		0			0
$544$	21.7042	−	20.6138i	0.930558	−	0.883810i
$545$		0			0
$546$	25.8085	−	4.46320i	1.10450	−	0.191007i
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	5.68693	+	1.91280i	0.242934	+	0.0817108i
$549$	9.16515	+	5.29150i	0.391159	+	0.225836i
$550$	−10.9347	−	20.7469i	−0.466255	−	0.884650i
$551$		0			0
$552$	35.0000	+	18.5203i	1.48970	+	0.788275i
$553$	−32.5000	+	11.2583i	−1.38204	+	0.478753i
$554$	17.5000	−	6.61438i	0.743504	−	0.281018i
$555$		0			0
$556$	−5.53901	−	27.4467i	−0.234907	−	1.16400i
$557$	−9.16515	−	5.29150i	−0.388340	−	0.224208i	0.293101	−	0.956082i	$-0.405313\pi$
$557$	−9.16515	−	5.29150i	−0.388340	−	0.224208i	−0.681441	+	0.731873i	$0.738646\pi$
$558$	−46.3303	−	37.9144i	−1.96132	−	1.60505i
$559$		−	5.29150i		−	0.223807i
$560$		0			0
$561$	−28.0000	−	37.0405i	−1.18216	−	1.56385i
$562$	−17.3739	−	14.2179i	−0.732872	−	0.599746i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$		0			0
$566$	14.0000	+	37.0405i	0.588464	+	1.55693i
$567$	10.0000	+	8.66025i	0.419961	+	0.363696i
$568$	−7.00000	+	13.2288i	−0.293713	+	0.555066i
$569$	27.4955	−	15.8745i	1.15267	−	0.665494i	0.203133	−	0.979151i	$-0.434888\pi$
$569$	27.4955	−	15.8745i	1.15267	−	0.665494i	0.949536	+	0.313657i	$0.101554\pi$
$570$		0			0
$571$	9.00000	−	15.5885i	0.376638	−	0.652357i	−0.613933	−	0.789359i	$-0.710413\pi$
$571$	9.00000	−	15.5885i	0.376638	−	0.652357i	0.990571	+	0.137002i	$0.0437466\pi$
$572$	−16.6434	+	5.56760i	−0.695894	+	0.232793i
$573$	−28.0000			−1.16972
$574$		0			0
$575$			26.4575i			1.10335i
$576$	−13.9129	+	28.8172i	−0.579703	+	1.20072i
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	0.228968	+	0.973434i	$0.426465\pi$
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	15.3521	+	2.51268i	0.638562	+	0.104514i
$579$	28.0000	+	48.4974i	1.16364	+	2.01548i
$580$		0			0
$581$		0			0
$582$	24.5000	−	9.26013i	1.01556	−	0.383845i
$583$	5.16515	−	12.2197i	0.213919	−	0.506089i
$584$	−15.9129	−	25.3531i	−0.658480	−	1.04912i
$585$		0			0
$586$	−23.1652	−	18.9572i	−0.956944	−	0.783115i
$587$		−	7.93725i		−	0.327606i	−0.986493	−	0.163803i	$-0.947624\pi$
$587$		−	7.93725i		−	0.327606i	0.986493	−	0.163803i	$-0.0523761\pi$
$588$	−23.9955	+	28.2173i	−0.989556	+	1.16366i
$589$		0			0
$590$		0			0
$591$	−10.5000	+	18.1865i	−0.431912	+	0.748094i
$592$	−25.4955	−	19.3386i	−1.04786	−	0.794812i
$593$	−13.7477	+	7.93725i	−0.564551	+	0.325944i	−0.754970	−	0.655759i	$-0.772349\pi$
$593$	−13.7477	+	7.93725i	−0.564551	+	0.325944i	0.190419	+	0.981703i	$0.439015\pi$
$594$	10.5000	+	6.61438i	0.430820	+	0.271391i
$595$		0			0
$596$	−14.0000	−	15.8745i	−0.573462	−	0.650245i
$597$	14.0000	+	24.2487i	0.572982	+	0.992434i
$598$	19.5390	+	3.19795i	0.799010	+	0.130774i
$599$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$599$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$600$	−37.3911	+	1.38050i	−1.52649	+	0.0563587i
$601$			42.3320i			1.72676i	0.504555	+	0.863380i	$0.331657\pi$
$601$			42.3320i			1.72676i	−0.504555	+	0.863380i	$0.668343\pi$
$602$	4.79129	+	5.74835i	0.195278	+	0.234285i
$603$		−	10.5830i		−	0.430973i
$604$	−32.2259	−	10.8392i	−1.31126	−	0.441041i
$605$		0			0
$606$	−29.3085	−	4.79693i	−1.19058	−	0.194862i
$607$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$607$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$608$		0			0
$609$	−42.0000	−	36.3731i	−1.70193	−	1.47391i
$610$		0			0
$611$		0			0
$612$	−41.4955	+	8.37420i	−1.67735	+	0.338507i
$613$	−36.6606	−	21.1660i	−1.48071	−	0.854887i	−0.480947	−	0.876750i	$-0.659707\pi$
$613$	−36.6606	−	21.1660i	−1.48071	−	0.854887i	−0.999761	+	0.0218626i	$0.993040\pi$
$614$	−25.0780	+	30.6446i	−1.01207	+	1.23672i
$615$		0			0
$616$	13.0390	−	21.1183i	0.525357	−	0.850882i
$617$	−23.0000			−0.925945			−0.462973	−	0.886373i	$-0.653217\pi$
$617$	−23.0000			−0.925945			−0.462973	+	0.886373i	$0.653217\pi$
$618$	12.5390	−	15.3223i	0.504393	−	0.616354i
$619$	4.58258	+	2.64575i	0.184189	+	0.106342i	0.589259	−	0.807944i	$-0.299420\pi$
$619$	4.58258	+	2.64575i	0.184189	+	0.106342i	−0.405070	+	0.914286i	$0.632753\pi$
$620$		0			0
$621$	−7.00000	−	12.1244i	−0.280900	−	0.486534i
$622$	14.0000	−	5.29150i	0.561349	−	0.212170i
$623$	−35.0000	+	12.1244i	−1.40225	+	0.485752i
$624$	−3.50000	+	27.7804i	−0.140112	+	1.11211i
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	29.3085	+	4.79693i	1.17140	+	0.191724i
$627$		0			0
$628$	−26.5390	−	8.92640i	−1.05902	−	0.356202i
$629$		−	42.3320i		−	1.68789i
$630$		0			0
$631$		−	26.4575i		−	1.05326i	−0.850096	−	0.526628i	$-0.823456\pi$
$631$		−	26.4575i		−	1.05326i	0.850096	−	0.526628i	$-0.176544\pi$
$632$	−1.35663	−	36.7445i	−0.0539638	−	1.46162i
$633$	−4.58258	−	2.64575i	−0.182141	−	0.105159i
$634$	8.37386	+	1.37055i	0.332569	+	0.0544315i
$635$		0			0
$636$	−14.0000	−	15.8745i	−0.555136	−	0.629465i
$637$	−6.87386	+	17.1974i	−0.272352	+	0.681385i
$638$	31.5000	+	19.8431i	1.24710	+	0.785597i
$639$	18.3303	−	10.5830i	0.725136	−	0.418657i
$640$		0			0
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	−0.736725	−	0.676192i	$-0.763629\pi$
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	0.953962	+	0.299927i	$0.0969622\pi$
$642$	23.1652	+	18.9572i	0.914256	+	0.748181i
$643$			18.5203i			0.730368i	0.930935	+	0.365184i	$0.118994\pi$
$643$			18.5203i			0.730368i	−0.930935	+	0.365184i	$0.881006\pi$
$644$	−24.1216	+	14.2179i	−0.950524	+	0.560264i
$645$		0			0
$646$		0			0
$647$	27.4955	+	15.8745i	1.08096	+	0.624091i	0.931155	−	0.364625i	$-0.118803\pi$
$647$	27.4955	+	15.8745i	1.08096	+	0.624091i	0.149803	+	0.988716i	$0.452136\pi$
$648$	−11.9782	+	7.51813i	−0.470549	+	0.295340i
$649$	−8.08258	−	3.41643i	−0.317269	−	0.134106i
$650$	−17.5000	+	6.61438i	−0.686406	+	0.259437i
$651$	70.0000	−	24.2487i	2.74352	−	0.950382i
$652$	−3.50000	−	3.96863i	−0.137071	−	0.155423i
$653$	−4.00000	−	6.92820i	−0.156532	−	0.271122i	0.777084	−	0.629397i	$-0.216698\pi$
$653$	−4.00000	−	6.92820i	−0.156532	−	0.271122i	−0.933616	+	0.358276i	$0.883365\pi$
$654$	−39.0780	−	6.39590i	−1.52807	−	0.250100i
$655$		0			0
$656$		0			0
$657$			42.3320i			1.65153i
$658$		0			0
$659$	−26.0000			−1.01282			−0.506408	−	0.862294i	$-0.669027\pi$
$659$	−26.0000			−1.01282			−0.506408	+	0.862294i	$0.669027\pi$
$660$		0			0
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$	−5.43920	+	33.2327i	−0.211401	+	1.29163i
$663$	−32.0780	+	18.5203i	−1.24581	+	0.719267i
$664$		0			0
$665$		0			0
$666$	16.0000	+	42.3320i	0.619987	+	1.64033i
$667$	−21.0000	−	36.3731i	−0.813123	−	1.40837i
$668$	8.30852	+	41.1700i	0.321466	+	1.59291i
$669$	−21.0000	+	36.3731i	−0.811907	+	1.40626i
$670$		0			0
$671$	7.00000	−	5.29150i	0.270232	−	0.204276i
$672$	−21.3521	−	33.3480i	−0.823674	−	1.28643i
$673$			31.7490i			1.22383i	0.790922	+	0.611917i	$0.209601\pi$
$673$			31.7490i			1.22383i	−0.790922	+	0.611917i	$0.790399\pi$
$674$	17.3739	+	14.2179i	0.669216	+	0.547653i
$675$	11.4564	+	6.61438i	0.440959	+	0.254588i
$676$	−2.37386	−	11.7629i	−0.0913024	−	0.452418i
$677$	27.4955	−	15.8745i	1.05674	−	0.610107i	0.132209	−	0.991222i	$-0.457793\pi$
$677$	27.4955	−	15.8745i	1.05674	−	0.610107i	0.924528	+	0.381115i	$0.124460\pi$
$678$	−66.5000	+	25.1346i	−2.55392	+	0.965290i
$679$	−3.50000	+	18.1865i	−0.134318	+	0.697935i
$680$		0			0
$681$	32.0780	−	18.5203i	1.22923	−	0.709698i
$682$	−43.9129	+	23.1443i	−1.68151	+	0.886241i
$683$	20.6216	+	11.9059i	0.789063	+	0.455566i	0.839633	−	0.543155i	$-0.182770\pi$
$683$	20.6216	+	11.9059i	0.789063	+	0.455566i	−0.0505694	+	0.998721i	$0.516104\pi$
$684$		0			0
$685$		0			0
$686$	−8.10436	−	24.9062i	−0.309426	−	0.950924i
$687$		−	37.0405i		−	1.41318i
$688$	−7.37386	+	3.10260i	−0.281126	+	0.118286i
$689$	−9.16515	−	5.29150i	−0.349164	−	0.201590i
$690$		0			0
$691$	−2.29129	+	1.32288i	−0.0871647	+	0.0503246i	−0.542949	−	0.839766i	$-0.682692\pi$
$691$	−2.29129	+	1.32288i	−0.0871647	+	0.0503246i	0.455784	+	0.890090i	$0.349359\pi$
$692$	17.5000	+	19.8431i	0.665250	+	0.754323i
$693$	−31.4955	+	15.4931i	−1.19641	+	0.588534i
$694$	9.00000	+	23.8118i	0.341635	+	0.903882i
$695$		0			0
$696$	50.3085	−	31.5761i	1.90694	−	1.19689i
$697$		0			0
$698$	11.5826	+	9.47860i	0.438407	+	0.358770i
$699$	−42.0000			−1.58859
$700$	13.0218	−	23.0311i	0.492177	−	0.870495i
$701$			34.3948i			1.29907i	0.760331	+	0.649536i	$0.225037\pi$
$701$			34.3948i			1.29907i	−0.760331	+	0.649536i	$0.774963\pi$
$702$	6.26951	−	7.66115i	0.236627	−	0.289152i
$703$		0			0
$704$	17.5172	+	19.9285i	0.660206	+	0.751085i
$705$		0			0
$706$	7.00000	+	18.5203i	0.263448	+	0.697019i
$707$	13.7477	−	15.8745i	0.517036	−	0.597022i
$708$	−10.5000	+	9.26013i	−0.394614	+	0.348017i
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	0.781086	−	0.624423i	$-0.214666\pi$
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	−0.931309	+	0.364229i	$0.881333\pi$
$710$		0			0
$711$	−26.0000	+	45.0333i	−0.975076	+	1.68888i
$712$	−1.46099	−	39.5710i	−0.0547527	−	1.48299i
$713$	56.0000			2.09722
$714$	18.0780	−	49.1649i	0.676553	−	1.83995i
$715$		0			0
$716$	5.06080	−	15.0462i	0.189131	−	0.562303i
$717$	43.5345	+	25.1346i	1.62582	+	0.938670i
$718$	−20.9347	−	3.42638i	−0.781275	−	0.127871i
$719$	−27.4955	+	15.8745i	−1.02541	+	0.592019i	−0.915666	−	0.401941i	$-0.868336\pi$
$719$	−27.4955	+	15.8745i	−1.02541	+	0.592019i	−0.109742	+	0.993960i	$0.535002\pi$
$720$		0			0
$721$	4.58258	+	13.2288i	0.170664	+	0.492665i
$722$	−9.50000	−	25.1346i	−0.353553	−	0.935414i
$723$	−7.00000	−	12.1244i	−0.260333	−	0.450910i
$724$		0			0
$725$	34.3693	+	19.8431i	1.27644	+	0.736956i
$726$	33.7650	−	23.5357i	1.25314	−	0.873490i
$727$		−	21.1660i		−	0.785004i	−0.919751	−	0.392502i	$-0.871610\pi$
$727$		−	21.1660i		−	0.785004i	0.919751	−	0.392502i	$-0.128390\pi$
$728$	−15.4347	−	12.4005i	−0.572047	−	0.459591i
$729$	41.0000			1.51852
$730$		0			0
$731$	−9.16515	−	5.29150i	−0.338985	−	0.195713i
$732$	−2.76951	−	13.7233i	−0.102364	−	0.507229i
$733$	11.4564	−	6.61438i	0.423153	−	0.244308i	−0.273272	−	0.961937i	$-0.588106\pi$
$733$	11.4564	−	6.61438i	0.423153	−	0.244308i	0.696426	+	0.717629i	$0.254773\pi$
$734$	21.0000	−	7.93725i	0.775124	−	0.292969i
$735$		0			0
$736$	−7.00000	−	29.1033i	−0.258023	−	1.07276i
$737$	−8.08258	−	3.41643i	−0.297726	−	0.125846i
$738$		0			0
$739$	23.0000	−	39.8372i	0.846069	−	1.46543i	−0.0386212	−	0.999254i	$-0.512297\pi$
$739$	23.0000	−	39.8372i	0.846069	−	1.46543i	0.884690	−	0.466180i	$-0.154370\pi$
$740$		0			0
$741$		0			0
$742$	14.7477	−	2.55040i	0.541406	−	0.0936282i
$743$	12.0000			0.440237			0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000			0.440237			0.220119	+	0.975473i	$0.429356\pi$
$744$	2.92197	+	79.1420i	0.107125	+	2.90149i
$745$		0			0
$746$	−5.43920	+	33.2327i	−0.199143	+	1.21674i
$747$		0			0
$748$	−7.00000	+	34.3948i	−0.255945	+	1.25760i
$749$	−20.0000	+	6.92820i	−0.730784	+	0.253151i
$750$		0			0
$751$	41.2432	−	23.8118i	1.50499	−	0.868904i	0.505002	−	0.863118i	$-0.331492\pi$
$751$	41.2432	−	23.8118i	1.50499	−	0.868904i	0.999983	−	0.00578524i	$-0.00184151\pi$
$752$		0			0
$753$	21.0000	−	36.3731i	0.765283	−	1.32551i
$754$	18.8085	−	22.9835i	0.684966	−	0.837008i
$755$		0			0
$756$	0.126136	+	13.9994i	0.00458754	+	0.509154i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−20.2695	−	16.5876i	−0.736222	−	0.602487i
$759$	−46.0780	+	5.72845i	−1.67253	+	0.207930i
$760$		0			0
$761$	−13.7477	+	7.93725i	−0.498355	+	0.287725i	−0.728034	−	0.685541i	$-0.759566\pi$
$761$	−13.7477	+	7.93725i	−0.498355	+	0.287725i	0.229679	+	0.973266i	$0.426232\pi$
$762$	17.5000	−	6.61438i	0.633958	−	0.239614i
$763$	18.3303	−	21.1660i	0.663602	−	0.766261i
$764$	14.0000	+	15.8745i	0.506502	+	0.574320i
$765$		0			0
$766$	−3.62614	+	22.1552i	−0.131018	+	0.800498i
$767$	−3.50000	+	6.06218i	−0.126378	+	0.218893i
$768$	40.7650	−	11.4113i	1.47098	−	0.411770i
$769$		−	47.6235i		−	1.71735i	−0.512522	−	0.858674i	$-0.671289\pi$
$769$		−	47.6235i		−	1.71735i	0.512522	−	0.858674i	$-0.328711\pi$
$770$		0			0
$771$			18.5203i			0.666991i
$772$	13.4955	−	40.1232i	0.485712	−	1.44407i
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	−0.712241	−	0.701935i	$-0.752320\pi$
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	0.964014	+	0.265852i	$0.0856532\pi$
$774$	11.1652	+	1.82740i	0.401323	+	0.0656846i
$775$	−45.8258	+	26.4575i	−1.64611	+	0.950382i
$776$	−17.5000	−	9.26013i	−0.628213	−	0.332419i
$777$	−54.9909	−	10.5830i	−1.97279	−	0.379663i
$778$	9.00000	+	23.8118i	0.322666	+	0.853693i
$779$		0			0
$780$		0			0
$781$	−2.16515	−	17.4159i	−0.0774752	−	0.623188i
$782$	25.0780	−	30.6446i	0.896789	−	1.09585i
$783$	−21.0000			−0.750479
$784$	27.9955	−	0.504525i	0.999838	−	0.0180188i
$785$		0			0
$786$	−40.5390	−	33.1751i	−1.44598	−	1.18332i
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	−0.713871	−	0.700278i	$-0.753059\pi$
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	0.963394	+	0.268091i	$0.0863928\pi$
$788$	15.5608	−	3.14033i	0.554330	−	0.111869i
$789$	25.2042	−	14.5516i	0.897292	−	0.518052i
$790$		0			0
$791$	9.50000	−	49.3634i	0.337781	−	1.75516i
$792$	−6.00000	−	37.0405i	−0.213201	−	1.31618i
$793$	−3.50000	−	6.06218i	−0.124289	−	0.215274i
$794$	−39.0780	−	6.39590i	−1.38683	−	0.226982i
$795$		0			0
$796$	6.74773	−	20.0616i	0.239167	−	0.711065i
$797$	14.0000			0.495905			0.247953	−	0.968772i	$-0.420242\pi$
$797$	14.0000			0.495905			0.247953	+	0.968772i	$0.420242\pi$
$798$		0			0
$799$		0			0
$800$	19.4782	+	20.5085i	0.688659	+	0.725085i
$801$	−28.0000	+	48.4974i	−0.989331	+	1.71357i
$802$	37.6824	+	6.16748i	1.33061	+	0.217781i
$803$	32.3303	+	13.6657i	1.14091	+	0.482252i
$804$	−10.5000	+	9.26013i	−0.370306	+	0.326580i
$805$		0			0
$806$	14.0000	+	37.0405i	0.493129	+	1.30470i
$807$	−64.1561	+	37.0405i	−2.25840	+	1.30389i
$808$	11.9347	+	19.0148i	0.419860	+	0.668940i
$809$	−27.4955	−	15.8745i	−0.966689	−	0.558118i	−0.0684635	−	0.997654i	$-0.521810\pi$
$809$	−27.4955	−	15.8745i	−0.966689	−	0.558118i	−0.898225	+	0.439536i	$0.855143\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	0.378409	+	41.9983i	0.0132796	+	1.47385i
$813$		−	18.5203i		−	0.649534i
$814$	37.4955	+	1.44600i	1.31421	+	0.0506823i
$815$		0			0
$816$	44.6170	+	33.8426i	1.56191	+	1.18473i
$817$		0			0
$818$	−49.0000	+	18.5203i	−1.71324	+	0.647546i
$819$	9.16515	+	26.4575i	0.320256	+	0.924500i
$820$		0			0
$821$	29.7867	−	17.1974i	1.03956	−	0.600193i	0.119855	−	0.992791i	$-0.461757\pi$
$821$	29.7867	−	17.1974i	1.03956	−	0.600193i	0.919710	+	0.392599i	$0.128424\pi$
$822$	−1.81307	+	11.0776i	−0.0632380	+	0.386375i
$823$	−9.16515	−	5.29150i	−0.319477	−	0.184450i	0.331682	−	0.943391i	$-0.392384\pi$
$823$	−9.16515	−	5.29150i	−0.319477	−	0.184450i	−0.651159	+	0.758941i	$0.725717\pi$
$824$	−14.9564	+	0.552200i	−0.521032	+	0.0192368i
$825$	35.0000	−	26.4575i	1.21854	−	0.921132i
$826$	−1.68693	−	9.75470i	−0.0586959	−	0.339410i
$827$	−26.0000			−0.904109			−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000			−0.904109			−0.452054	+	0.891990i	$0.649309\pi$
$828$	−13.4955	+	40.1232i	−0.468999	+	1.39438i
$829$	−21.0000	+	36.3731i	−0.729360	+	1.26329i	0.227794	+	0.973709i	$0.426849\pi$
$829$	−21.0000	+	36.3731i	−0.729360	+	1.26329i	−0.957154	+	0.289579i	$0.906485\pi$
$830$		0			0
$831$	17.5000	+	30.3109i	0.607068	+	1.05147i
$832$	17.5000	−	11.9059i	0.606703	−	0.412762i
$833$	22.9129	+	29.1033i	0.793884	+	1.00837i
$834$	49.0000	−	18.5203i	1.69673	−	0.641304i
$835$		0			0
$836$		0			0
$837$	14.0000	−	24.2487i	0.483911	−	0.838158i
$838$	5.79129	+	4.73930i	0.200057	+	0.163716i
$839$		0			0		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$		0			0
$841$	−34.0000			−1.17241
$842$	10.7477	−	13.1334i	0.370391	−	0.452607i
$843$	21.0000	−	36.3731i	0.723278	−	1.25275i
$844$	0.791288	+	3.92095i	0.0272373	+	0.134965i
$845$		0			0
$846$		0			0
$847$	1.66515	+	29.0556i	0.0572153	+	0.998362i
$848$	−2.00000	+	15.8745i	−0.0686803	+	0.545133i
$849$	−64.1561	+	37.0405i	−2.20183	+	1.27123i
$850$	−6.04356	+	36.9253i	−0.207292	+	1.26653i
$851$	−36.6606	−	21.1660i	−1.25671	−	0.725561i
$852$	−26.5390	−	8.92640i	−0.909212	−	0.305814i
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	9.29129	+	3.41643i	0.317941	+	0.116908i
$855$		0			0
$856$	−0.834849	−	22.6120i	−0.0285345	−	0.772863i
$857$	18.3303	+	10.5830i	0.626151	+	0.361509i	0.779260	−	0.626701i	$-0.215595\pi$
$857$	18.3303	+	10.5830i	0.626151	+	0.361509i	−0.153109	+	0.988209i	$0.548928\pi$
$858$	−15.3085	−	29.0456i	−0.522624	−	0.991602i
$859$	−16.0390	+	9.26013i	−0.547244	+	0.315952i	−0.748010	−	0.663688i	$-0.768990\pi$
$859$	−16.0390	+	9.26013i	−0.547244	+	0.315952i	0.200766	+	0.979639i	$0.435657\pi$
$860$		0			0
$861$		0			0
$862$	−1.50000	−	3.96863i	−0.0510902	−	0.135172i
$863$	13.7477	−	7.93725i	0.467978	−	0.270187i	−0.247415	−	0.968910i	$-0.579581\pi$
$863$	13.7477	−	7.93725i	0.467978	−	0.270187i	0.715393	+	0.698722i	$0.246248\pi$
$864$	−14.3521	−	4.24473i	−0.488268	−	0.144409i
$865$		0			0
$866$	−12.5390	+	15.3223i	−0.426093	+	0.520673i
$867$			29.1033i			0.988399i
$868$	−48.7477	−	27.5619i	−1.65461	−	0.935512i
$869$	26.0000	+	34.3948i	0.881990	+	1.16676i
$870$		0			0
$871$	−3.50000	+	6.06218i	−0.118593	+	0.205409i
$872$	15.9129	+	25.3531i	0.538878	+	0.858565i
$873$	14.0000	+	24.2487i	0.473828	+	0.820695i
$874$		0			0
$875$		0			0
$876$	42.0000	−	37.0405i	1.41905	−	1.25148i
$877$	−11.4564	+	6.61438i	−0.386856	+	0.223352i	−0.680797	−	0.732472i	$-0.738367\pi$
$877$	−11.4564	+	6.61438i	−0.386856	+	0.223352i	0.293941	+	0.955824i	$0.405033\pi$
$878$	−48.8475	−	7.99488i	−1.64852	−	0.269814i
$879$	28.0000	−	48.4974i	0.944417	−	1.63578i
$880$		0			0
$881$	7.00000			0.235836			0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000			0.235836			0.117918	+	0.993023i	$0.462378\pi$
$882$	−33.9129	−	20.4430i	−1.14191	−	0.688352i
$883$		−	34.3948i		−	1.15748i	−0.815514	−	0.578738i	$-0.803545\pi$
$883$		−	34.3948i		−	1.15748i	0.815514	−	0.578738i	$-0.196455\pi$
$884$	26.5390	+	8.92640i	0.892604	+	0.300227i
$885$		0			0
$886$	−8.46099	+	51.6954i	−0.284252	+	1.73674i
$887$	24.5000	+	42.4352i	0.822629	+	1.42484i	0.903718	+	0.428129i	$0.140827\pi$
$887$	24.5000	+	42.4352i	0.822629	+	1.42484i	−0.0810881	+	0.996707i	$0.525840\pi$
$888$	28.0000	−	52.9150i	0.939618	−	1.77571i
$889$	−2.50000	+	12.9904i	−0.0838473	+	0.435683i
$890$		0			0
$891$	6.45644	−	15.2746i	0.216299	−	0.511719i
$892$	31.1216	−	6.28065i	1.04203	−	0.210292i
$893$		0			0
$894$	25.0780	−	30.6446i	0.838735	−	1.02491i
$895$		0			0
$896$	−8.23049	+	28.7795i	−0.274961	+	0.961455i
$897$			37.0405i			1.23675i
$898$	−26.8693	+	32.8335i	−0.896641	+	1.09567i
$899$	42.0000	−	72.7461i	1.40078	−	2.42622i
$900$	−7.91288	−	39.2095i	−0.263763	−	1.30698i
$901$	−18.3303	+	10.5830i	−0.610671	+	0.352571i
$902$		0			0
$903$	−9.16515	+	10.5830i	−0.304997	+	0.352180i
$904$	47.5000	+	25.1346i	1.57983	+	0.835966i
$905$		0			0
$906$	10.2741	−	62.7730i	0.341333	−	2.08549i
$907$	−4.58258	−	2.64575i	−0.152162	−	0.0878507i	0.421986	−	0.906602i	$-0.361333\pi$
$907$	−4.58258	−	2.64575i	−0.152162	−	0.0878507i	−0.574148	+	0.818752i	$0.694667\pi$
$908$	−26.5390	−	8.92640i	−0.880728	−	0.296233i
$909$		−	31.7490i		−	1.05305i
$910$		0			0
$911$		−	15.8745i		−	0.525946i	−0.964803	−	0.262973i	$-0.915297\pi$
$911$		−	15.8745i		−	0.525946i	0.964803	−	0.262973i	$-0.0847030\pi$
$912$		0			0
$913$		0			0
$914$	−1.20871	+	7.38505i	−0.0399806	+	0.244276i
$915$		0			0
$916$	−21.0000	+	18.5203i	−0.693860	+	0.611927i
$917$	35.0000	−	12.1244i	1.15580	−	0.400381i
$918$	−7.00000	−	18.5203i	−0.231034	−	0.611260i
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	0.924427	−	0.381358i	$-0.124544\pi$
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	−0.792480	+	0.609898i	$0.791210\pi$
$920$		0			0
$921$	−64.1561	−	37.0405i	−2.11401	−	1.22053i
$922$	−8.68693	−	7.10895i	−0.286089	−	0.234121i
$923$	−14.0000			−0.460816
$924$	42.9301	+	17.6920i	1.41230	+	0.582023i
$925$	40.0000			1.31519
$926$	−23.1652	−	18.9572i	−0.761254	−	0.622973i
$927$	18.3303	+	10.5830i	0.602046	+	0.347591i
$928$	−43.0562	−	12.7342i	−1.41339	−	0.418020i
$929$	−17.5000	−	30.3109i	−0.574156	−	0.994468i	−0.996133	−	0.0878612i	$-0.971997\pi$
$929$	−17.5000	−	30.3109i	−0.574156	−	0.994468i	0.421976	−	0.906607i	$-0.361337\pi$
$930$		0			0
$931$		0			0
$932$	21.0000	+	23.8118i	0.687878	+	0.779980i
$933$	14.0000	+	24.2487i	0.458339	+	0.793867i
$934$	3.62614	−	22.1552i	0.118651	−	0.724939i
$935$		0			0
$936$	−29.9129	+	1.10440i	−0.977733	+	0.0360985i
$937$			26.4575i			0.864329i	0.901795	+	0.432165i	$0.142250\pi$
$937$			26.4575i			0.864329i	−0.901795	+	0.432165i	$0.857750\pi$
$938$	−1.68693	−	9.75470i	−0.0550803	−	0.318502i
$939$			55.5608i			1.81316i
$940$		0			0
$941$	48.1170	+	27.7804i	1.56857	+	0.905615i	0.996336	+	0.0855250i	$0.0272567\pi$
$941$	48.1170	+	27.7804i	1.56857	+	0.905615i	0.572235	+	0.820090i	$0.306077\pi$
$942$	8.46099	−	51.6954i	0.275674	−	1.68433i
$943$		0			0
$944$	10.5000	+	1.32288i	0.341746	+	0.0430559i
$945$		0			0
$946$	5.00000	−	7.93725i	0.162564	−	0.258062i
$947$	−13.7477	+	7.93725i	−0.446741	+	0.257926i	−0.706453	−	0.707760i	$-0.749706\pi$
$947$	−13.7477	+	7.93725i	−0.446741	+	0.257926i	0.259712	+	0.965686i	$0.416372\pi$
$948$	67.4301	−	13.6081i	2.19003	−	0.441970i
$949$	14.0000	−	24.2487i	0.454459	−	0.787146i
$950$		0			0
$951$			15.8745i			0.514766i
$952$	−36.9129	+	14.3332i	−1.19635	+	0.464540i
$953$		−	15.8745i		−	0.514226i	−0.966381	−	0.257113i	$-0.917229\pi$
$953$		−	15.8745i		−	0.514226i	0.966381	−	0.257113i	$-0.0827712\pi$
$954$	14.3303	−	17.5112i	0.463961	−	0.566946i
$955$		0			0
$956$	−7.51723	−	37.2490i	−0.243125	−	1.20472i
$957$	−27.1170	+	64.1535i	−0.876570	+	2.07379i
$958$	−10.5000	−	27.7804i	−0.339240	−	0.897544i
$959$	−6.00000	−	5.19615i	−0.193750	−	0.167793i
$960$		0			0
$961$	40.5000	+	70.1481i	1.30645	+	2.26284i
$962$	4.83485	−	29.5402i	0.155882	−	0.952415i
$963$	−16.0000	+	27.7128i	−0.515593	+	0.893033i
$964$	−3.37386	+	10.0308i	−0.108665	+	0.323070i
$965$		0			0
$966$	−33.5390	−	40.2385i	−1.07910	−	1.29465i
$967$	16.0000			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$968$	−30.2259	−	7.37510i	−0.971499	−	0.237045i
$969$		0			0
$970$		0			0
$971$	25.2042	−	14.5516i	0.808840	−	0.466984i	−0.0377128	−	0.999289i	$-0.512007\pi$
$971$	25.2042	−	14.5516i	0.808840	−	0.466984i	0.846553	+	0.532305i	$0.178674\pi$
$972$	−28.0000	−	31.7490i	−0.898100	−	1.01835i
$973$	−7.00000	+	36.3731i	−0.224410	+	1.16607i
$974$		0			0
$975$	−17.5000	−	30.3109i	−0.560449	−	0.970725i
$976$	−6.39564	+	8.43183i	−0.204720	+	0.269896i
$977$	19.0000	−	32.9090i	0.607864	−	1.05285i	−0.383728	−	0.923446i	$-0.625360\pi$
$977$	19.0000	−	32.9090i	0.607864	−	1.05285i	0.991592	−	0.129405i	$-0.0413067\pi$
$978$	6.26951	−	7.66115i	0.200477	−	0.244977i
$979$	28.0000	+	37.0405i	0.894884	+	1.18382i
$980$		0			0
$981$		−	42.3320i		−	1.35156i
$982$	−23.2867	+	28.4557i	−0.743110	+	0.908058i
$983$	41.2432	+	23.8118i	1.31545	+	0.759477i	0.982994	−	0.183640i	$-0.0587881\pi$
$983$	41.2432	+	23.8118i	1.31545	+	0.759477i	0.332460	+	0.943117i	$0.392121\pi$
$984$		0			0
$985$		0			0
$986$	−21.0000	−	55.5608i	−0.668776	−	1.76942i
$987$		0			0
$988$		0			0
$989$	−9.16515	+	5.29150i	−0.291435	+	0.168260i
$990$		0			0
$991$	−18.3303	−	10.5830i	−0.582281	−	0.336180i	0.179758	−	0.983711i	$-0.442468\pi$
$991$	−18.3303	−	10.5830i	−0.582281	−	0.336180i	−0.762039	+	0.647531i	$0.775802\pi$
$992$	43.4083	−	41.2276i	1.37822	−	1.30898i
$993$	−63.0000			−1.99924
$994$	15.2087	−	12.6766i	0.482391	−	0.402076i
$995$		0			0
$996$		0			0
$997$	−45.8258	−	26.4575i	−1.45132	−	0.837918i	−0.452760	−	0.891632i	$-0.649561\pi$
$997$	−45.8258	−	26.4575i	−1.45132	−	0.837918i	−0.998556	+	0.0537146i	$0.982894\pi$
$998$	6.04356	−	36.9253i	0.191306	−	1.16885i
$999$	−18.3303	+	10.5830i	−0.579945	+	0.334831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.n.a.263.2	yes	4
4.3	odd	2		308.2.n.b.263.2	yes	4
7.2	even	3	inner	308.2.n.a.219.1	✓	4
11.10	odd	2		308.2.n.b.263.1	yes	4
28.23	odd	6		308.2.n.b.219.1	yes	4
44.43	even	2	inner	308.2.n.a.263.1	yes	4
77.65	odd	6		308.2.n.b.219.2	yes	4
308.219	even	6	inner	308.2.n.a.219.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.n.a.219.1	✓	4	7.2	even	3	inner
308.2.n.a.219.2	yes	4	308.219	even	6	inner
308.2.n.a.263.1	yes	4	44.43	even	2	inner
308.2.n.a.263.2	yes	4	1.1	even	1	trivial
308.2.n.b.219.1	yes	4	28.23	odd	6
308.2.n.b.219.2	yes	4	77.65	odd	6
308.2.n.b.263.1	yes	4	11.10	odd	2
308.2.n.b.263.2	yes	4	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.895644 - 1.09445i) q^{2} +(2.29129 + 1.32288i) q^{3} +(-0.395644 - 1.96048i) q^{4} +(3.50000 - 1.32288i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-2.50000 - 1.32288i) q^{8} +(2.00000 + 3.46410i) q^{9} +(3.29129 - 0.409175i) q^{11} +(1.68693 - 5.01540i) q^{12} -2.64575i q^{13} +(2.39564 + 2.87418i) q^{14} +(-3.68693 + 1.55130i) q^{16} +(-4.58258 - 2.64575i) q^{17} +(5.58258 + 0.913701i) q^{18} +(-4.58258 + 5.29150i) q^{21} +(2.50000 - 3.96863i) q^{22} +(-4.58258 + 2.64575i) q^{23} +(-3.97822 - 6.33828i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-2.89564 - 2.36965i) q^{26} +2.64575i q^{27} +(5.29129 - 0.0476751i) q^{28} +7.93725i q^{29} +(-9.16515 - 5.29150i) q^{31} +(-1.60436 + 5.42458i) q^{32} +(8.08258 + 3.41643i) q^{33} +(-7.00000 + 2.64575i) q^{34} +(6.00000 - 5.29150i) q^{36} +(4.00000 + 6.92820i) q^{37} +(3.50000 - 6.06218i) q^{39} +(1.68693 + 9.75470i) q^{42} +2.00000 q^{43} +(-2.10436 - 6.29060i) q^{44} +(-1.20871 + 7.38505i) q^{46} +(-10.5000 - 1.32288i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.50000 - 6.61438i) q^{50} +(-7.00000 - 12.1244i) q^{51} +(-5.18693 + 1.04678i) q^{52} +(2.00000 - 3.46410i) q^{53} +(2.89564 + 2.36965i) q^{54} +(4.68693 - 5.83375i) q^{56} +(8.68693 + 7.10895i) q^{58} +(-2.29129 - 1.32288i) q^{59} +(2.29129 - 1.32288i) q^{61} +(-14.0000 + 5.29150i) q^{62} +(-10.0000 + 3.46410i) q^{63} +(4.50000 + 6.61438i) q^{64} +(10.9782 - 5.78608i) q^{66} +(-2.29129 - 1.32288i) q^{67} +(-3.37386 + 10.0308i) q^{68} -14.0000 q^{69} -5.29150i q^{71} +(-0.417424 - 11.3060i) q^{72} +(9.16515 + 5.29150i) q^{73} +(11.1652 + 1.82740i) q^{74} +(11.4564 - 6.61438i) q^{75} +(-0.582576 + 8.75560i) q^{77} +(-3.50000 - 9.26013i) q^{78} +(6.50000 + 11.2583i) q^{79} +(2.50000 - 4.33013i) q^{81} +(12.1869 + 6.89048i) q^{84} +(1.79129 - 2.18890i) q^{86} +(-10.5000 + 18.1865i) q^{87} +(-8.76951 - 3.33103i) q^{88} +(7.00000 + 12.1244i) q^{89} +(6.87386 + 1.32288i) q^{91} +(7.00000 + 7.93725i) q^{92} +(-14.0000 - 24.2487i) q^{93} +(-10.8521 + 10.3069i) q^{96} +7.00000 q^{97} +(-8.66515 + 4.78698i) q^{98} +(8.00000 + 10.5830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 3 q^{4} + 14 q^{6} - 2 q^{7} - 10 q^{8} + 8 q^{9} + 4 q^{11} - 7 q^{12} + 5 q^{14} - q^{16} + 4 q^{18} + 10 q^{22} + 7 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{28} - 11 q^{32} + 14 q^{33} - 28 q^{34}+ \cdots + 32 q^{99}+O(q^{100}) \) 4 * q - q^2 + 3 * q^4 + 14 * q^6 - 2 * q^7 - 10 * q^8 + 8 * q^9 + 4 * q^11 - 7 * q^12 + 5 * q^14 - q^16 + 4 * q^18 + 10 * q^22 + 7 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^28 - 11 * q^32 + 14 * q^33 - 28 * q^34 + 24 * q^36 + 16 * q^37 + 14 * q^39 - 7 * q^42 + 8 * q^43 - 13 * q^44 - 14 * q^46 - 42 * q^48 - 26 * q^49 - 10 * q^50 - 28 * q^51 - 7 * q^52 + 8 * q^53 + 7 * q^54 + 5 * q^56 + 21 * q^58 - 56 * q^62 - 40 * q^63 + 18 * q^64 + 21 * q^66 + 14 * q^68 - 56 * q^69 - 20 * q^72 + 8 * q^74 + 16 * q^77 - 14 * q^78 + 26 * q^79 + 10 * q^81 + 35 * q^84 - 2 * q^86 - 42 * q^87 - 3 * q^88 + 28 * q^89 + 28 * q^92 - 56 * q^93 + 7 * q^96 + 28 * q^97 + 2 * q^98 + 32 * q^99

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