LMFDB - Embedded newform 735.2.i.n.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(226,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.226"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,4,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1534132224.10
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} - 8x^{5} + 34x^{4} - 24x^{3} + 28x^{2} + 8x + 4 $ x^8 + 6x^6 - 8x^5 + 34x^4 - 24x^3 + 28x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.874559 - 1.51478i$ of defining polynomial
Character	$\chi$	$=$	735.226
Dual form			735.2.i.n.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37456 + 2.38081i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.77882 - 4.81306i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.74912 q^{6} +9.78039 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.37456 - 2.38081i) q^{10} +(2.22274 + 3.84990i) q^{11} +(2.77882 - 4.81306i) q^{12} +3.61706 q^{13} -1.00000 q^{15} +(-7.88607 + 13.6591i) q^{16} +(2.47363 + 4.28445i) q^{17} +(-1.37456 - 2.38081i) q^{18} +(-1.37220 + 2.37672i) q^{19} +5.55765 q^{20} -12.2212 q^{22} +(2.18073 - 3.77714i) q^{23} +(4.89020 + 8.47007i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-4.97186 + 8.61152i) q^{26} -1.00000 q^{27} +0.660384 q^{29} +(1.37456 - 2.38081i) q^{30} +(-0.627797 - 1.08738i) q^{31} +(-11.8994 - 20.6103i) q^{32} +(-2.22274 + 3.84990i) q^{33} -13.6006 q^{34} +5.55765 q^{36} +(1.08402 - 1.87758i) q^{37} +(-3.77235 - 6.53390i) q^{38} +(1.80853 + 3.13247i) q^{39} +(-4.89020 + 8.47007i) q^{40} -5.77568 q^{41} -9.11529 q^{43} +(12.3532 - 21.3964i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(5.99509 + 10.3838i) q^{46} +(-3.24264 + 5.61642i) q^{47} -15.7721 q^{48} +2.74912 q^{50} +(-2.47363 + 4.28445i) q^{51} +(-10.0512 - 17.4091i) q^{52} +(-3.51564 - 6.08926i) q^{53} +(1.37456 - 2.38081i) q^{54} -4.44549 q^{55} -2.74441 q^{57} +(-0.907737 + 1.57225i) q^{58} +(6.91245 + 11.9727i) q^{59} +(2.77882 + 4.81306i) q^{60} +(-4.70711 + 8.15295i) q^{61} +3.45178 q^{62} +33.8812 q^{64} +(-1.80853 + 3.13247i) q^{65} +(-6.11058 - 10.5838i) q^{66} +(-1.53304 - 2.65530i) q^{67} +(13.7475 - 23.8114i) q^{68} +4.36147 q^{69} +0.277444 q^{71} +(-4.89020 + 8.47007i) q^{72} +(5.30676 + 9.19159i) q^{73} +(2.98010 + 5.16169i) q^{74} +(0.500000 - 0.866025i) q^{75} +15.2524 q^{76} -9.94372 q^{78} +(2.76901 - 4.79607i) q^{79} +(-7.88607 - 13.6591i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.93901 - 13.7508i) q^{82} -7.17157 q^{83} -4.94725 q^{85} +(12.5295 - 21.7017i) q^{86} +(0.330192 + 0.571909i) q^{87} +(21.7393 + 37.6536i) q^{88} +(0.414214 - 0.717439i) q^{89} +2.74912 q^{90} -24.2395 q^{92} +(0.627797 - 1.08738i) q^{93} +(-8.91440 - 15.4402i) q^{94} +(-1.37220 - 2.37672i) q^{95} +(11.8994 - 20.6103i) q^{96} +6.20784 q^{97} -4.44549 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} - 4 q^{9} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 8 q^{15} - 12 q^{16} + 8 q^{17} - 4 q^{18} - 8 q^{19} + 16 q^{20} + 12 q^{24} - 4 q^{25} - 8 q^{27}+ \cdots + 16 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 - 4 * q^9 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 8 * q^15 - 12 * q^16 + 8 * q^17 - 4 * q^18 - 8 * q^19 + 16 * q^20 + 12 * q^24 - 4 * q^25 - 8 * q^27 + 16 * q^29 + 4 * q^30 - 8 * q^31 - 28 * q^32 + 8 * q^33 + 16 * q^34 + 16 * q^36 - 8 * q^37 + 4 * q^38 - 12 * q^40 - 16 * q^43 + 16 * q^44 - 4 * q^45 - 12 * q^46 + 8 * q^47 - 24 * q^48 + 8 * q^50 - 8 * q^51 - 32 * q^52 - 8 * q^53 + 4 * q^54 + 16 * q^55 - 16 * q^57 + 24 * q^58 + 16 * q^59 + 8 * q^60 - 32 * q^61 + 40 * q^62 + 48 * q^64 + 24 * q^68 - 16 * q^71 - 12 * q^72 + 32 * q^74 + 4 * q^75 - 16 * q^76 - 12 * q^80 - 4 * q^81 - 8 * q^82 - 80 * q^83 - 16 * q^85 + 32 * q^86 + 8 * q^87 + 40 * q^88 - 8 * q^89 + 8 * q^90 - 16 * q^92 + 8 * q^93 - 16 * q^94 - 8 * q^95 + 28 * q^96 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−1.37456	+	2.38081i	−0.971960	+	1.68348i	−0.282337	+	0.959315i	$0.591110\pi$
$2$	−1.37456	+	2.38081i	−0.971960	+	1.68348i	−0.689623	+	0.724168i	$0.742224\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.77882	−	4.81306i	−1.38941	−	2.40653i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−2.74912			−1.12232
$7$		0			0
$7$		0			0
$8$	9.78039			3.45789
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.37456	−	2.38081i	−0.434674	−	0.752877i
$11$	2.22274	+	3.84990i	0.670182	+	1.16079i	0.977852	+	0.209297i	$0.0671174\pi$
$11$	2.22274	+	3.84990i	0.670182	+	1.16079i	−0.307670	+	0.951493i	$0.599549\pi$
$12$	2.77882	−	4.81306i	0.802177	−	1.38941i
$13$	3.61706			1.00319			0.501596	−	0.865102i	$-0.332746\pi$
$13$	3.61706			1.00319			0.501596	+	0.865102i	$0.332746\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	−7.88607	+	13.6591i	−1.97152	+	3.41477i
$17$	2.47363	+	4.28445i	0.599942	+	1.03913i	0.992829	+	0.119544i	$0.0381432\pi$
$17$	2.47363	+	4.28445i	0.599942	+	1.03913i	−0.392887	+	0.919587i	$0.628523\pi$
$18$	−1.37456	−	2.38081i	−0.323987	−	0.561161i
$19$	−1.37220	+	2.37672i	−0.314805	+	0.545258i	−0.979396	−	0.201949i	$-0.935272\pi$
$19$	−1.37220	+	2.37672i	−0.314805	+	0.545258i	0.664591	+	0.747207i	$0.268606\pi$
$20$	5.55765			1.24273
$21$		0			0
$22$	−12.2212			−2.60556
$23$	2.18073	−	3.77714i	0.454714	−	0.787588i	−0.543958	−	0.839113i	$-0.683075\pi$
$23$	2.18073	−	3.77714i	0.454714	−	0.787588i	0.998672	+	0.0515247i	$0.0164081\pi$
$24$	4.89020	+	8.47007i	0.998207	+	1.72895i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−4.97186	+	8.61152i	−0.975062	+	1.68886i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	0.660384			0.122630			0.0613151	−	0.998118i	$-0.480471\pi$
$29$	0.660384			0.122630			0.0613151	+	0.998118i	$0.480471\pi$
$30$	1.37456	−	2.38081i	0.250959	−	0.434674i
$31$	−0.627797	−	1.08738i	−0.112756	−	0.195299i	0.804125	−	0.594461i	$-0.202634\pi$
$31$	−0.627797	−	1.08738i	−0.112756	−	0.195299i	−0.916880	+	0.399162i	$0.869301\pi$
$32$	−11.8994	−	20.6103i	−2.10353	−	3.64342i
$33$	−2.22274	+	3.84990i	−0.386930	+	0.670182i
$34$	−13.6006			−2.33248
$35$		0			0
$36$	5.55765			0.926275
$37$	1.08402	−	1.87758i	0.178212	−	0.308672i	−0.763056	−	0.646332i	$-0.776302\pi$
$37$	1.08402	−	1.87758i	0.178212	−	0.308672i	0.941268	+	0.337660i	$0.109635\pi$
$38$	−3.77235	−	6.53390i	−0.611955	−	1.05994i
$39$	1.80853	+	3.13247i	0.289597	+	0.501596i
$40$	−4.89020	+	8.47007i	−0.773208	+	1.33924i
$41$	−5.77568			−0.902009			−0.451005	−	0.892522i	$-0.648934\pi$
$41$	−5.77568			−0.902009			−0.451005	+	0.892522i	$0.648934\pi$
$42$		0			0
$43$	−9.11529			−1.39007			−0.695035	−	0.718976i	$-0.744611\pi$
$43$	−9.11529			−1.39007			−0.695035	+	0.718976i	$0.744611\pi$
$44$	12.3532	−	21.3964i	1.86232	−	3.22563i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	5.99509	+	10.3838i	0.883928	+	1.53101i
$47$	−3.24264	+	5.61642i	−0.472988	+	0.819239i	−0.999522	−	0.0309151i	$-0.990158\pi$
$47$	−3.24264	+	5.61642i	−0.472988	+	0.819239i	0.526534	+	0.850154i	$0.323491\pi$
$48$	−15.7721			−2.27651
$49$		0			0
$50$	2.74912			0.388784
$51$	−2.47363	+	4.28445i	−0.346377	+	0.599942i
$52$	−10.0512	−	17.4091i	−1.39385	−	2.41421i
$53$	−3.51564	−	6.08926i	−0.482910	−	0.836424i	0.516898	−	0.856047i	$-0.327087\pi$
$53$	−3.51564	−	6.08926i	−0.482910	−	0.836424i	−0.999807	+	0.0196229i	$0.993753\pi$
$54$	1.37456	−	2.38081i	0.187054	−	0.323987i
$55$	−4.44549			−0.599429
$56$		0			0
$57$	−2.74441			−0.363505
$58$	−0.907737	+	1.57225i	−0.119192	+	0.206446i
$59$	6.91245	+	11.9727i	0.899924	+	1.55871i	0.827589	+	0.561334i	$0.189712\pi$
$59$	6.91245	+	11.9727i	0.899924	+	1.55871i	0.0723348	+	0.997380i	$0.476955\pi$
$60$	2.77882	+	4.81306i	0.358745	+	0.621364i
$61$	−4.70711	+	8.15295i	−0.602683	+	1.04388i	0.389730	+	0.920929i	$0.372568\pi$
$61$	−4.70711	+	8.15295i	−0.602683	+	1.04388i	−0.992413	+	0.122949i	$0.960765\pi$
$62$	3.45178			0.438376
$63$		0			0
$64$	33.8812			4.23514
$65$	−1.80853	+	3.13247i	−0.224321	+	0.388535i
$66$	−6.11058	−	10.5838i	−0.752161	−	1.30278i
$67$	−1.53304	−	2.65530i	−0.187290	−	0.324396i	0.757056	−	0.653351i	$-0.226637\pi$
$67$	−1.53304	−	2.65530i	−0.187290	−	0.324396i	−0.944346	+	0.328954i	$0.893304\pi$
$68$	13.7475	−	23.8114i	1.66713	−	2.88756i
$69$	4.36147			0.525059
$70$		0			0
$71$	0.277444			0.0329265			0.0164632	−	0.999864i	$-0.494759\pi$
$71$	0.277444			0.0329265			0.0164632	+	0.999864i	$0.494759\pi$
$72$	−4.89020	+	8.47007i	−0.576315	+	0.998207i
$73$	5.30676	+	9.19159i	0.621110	+	1.07579i	0.989279	+	0.146035i	$0.0466513\pi$
$73$	5.30676	+	9.19159i	0.621110	+	1.07579i	−0.368170	+	0.929759i	$0.620015\pi$
$74$	2.98010	+	5.16169i	0.346430	+	0.600034i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	15.2524			1.74957
$77$		0			0
$78$	−9.94372			−1.12590
$79$	2.76901	−	4.79607i	0.311539	−	0.539601i	−0.667157	−	0.744917i	$-0.732489\pi$
$79$	2.76901	−	4.79607i	0.311539	−	0.539601i	0.978696	+	0.205316i	$0.0658224\pi$
$80$	−7.88607	−	13.6591i	−0.881690	−	1.52713i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.93901	−	13.7508i	0.876717	−	1.51852i
$83$	−7.17157			−0.787182			−0.393591	−	0.919286i	$-0.628767\pi$
$83$	−7.17157			−0.787182			−0.393591	+	0.919286i	$0.628767\pi$
$84$		0			0
$85$	−4.94725			−0.536605
$86$	12.5295	−	21.7017i	1.35109	−	2.34016i
$87$	0.330192	+	0.571909i	0.0354003	+	0.0613151i
$88$	21.7393	+	37.6536i	2.31742	+	4.01388i
$89$	0.414214	−	0.717439i	0.0439065	−	0.0760484i	−0.843237	−	0.537542i	$-0.819353\pi$
$89$	0.414214	−	0.717439i	0.0439065	−	0.0760484i	0.887144	+	0.461494i	$0.152686\pi$
$90$	2.74912			0.289782
$91$		0			0
$92$	−24.2395			−2.52714
$93$	0.627797	−	1.08738i	0.0650995	−	0.112756i
$94$	−8.91440	−	15.4402i	−0.919450	−	1.59253i
$95$	−1.37220	−	2.37672i	−0.140785	−	0.243847i
$96$	11.8994	−	20.6103i	1.21447	−	2.10353i
$97$	6.20784			0.630310			0.315155	−	0.949040i	$-0.397943\pi$
$97$	6.20784			0.630310			0.315155	+	0.949040i	$0.397943\pi$
$98$		0			0
$99$	−4.44549			−0.446788
$100$	−2.77882	+	4.81306i	−0.277882	+	0.481306i
$101$	−2.05941	−	3.56701i	−0.204919	−	0.354930i	0.745188	−	0.666855i	$-0.232360\pi$
$101$	−2.05941	−	3.56701i	−0.204919	−	0.354930i	−0.950107	+	0.311924i	$0.899026\pi$
$102$	−6.80029	−	11.7784i	−0.673329	−	1.16624i
$103$	4.08402	−	7.07373i	0.402411	−	0.696996i	−0.591606	−	0.806227i	$-0.701506\pi$
$103$	4.08402	−	7.07373i	0.402411	−	0.696996i	0.994016	+	0.109232i	$0.0348391\pi$
$104$	35.3763			3.46893
$105$		0			0
$106$	19.3298			1.87748
$107$	4.26475	−	7.38677i	0.412289	−	0.714106i	−0.582850	−	0.812580i	$-0.698063\pi$
$107$	4.26475	−	7.38677i	0.412289	−	0.714106i	0.995140	+	0.0984734i	$0.0313960\pi$
$108$	2.77882	+	4.81306i	0.267392	+	0.463137i
$109$	1.82843	+	3.16693i	0.175132	+	0.303337i	0.940207	−	0.340604i	$-0.110632\pi$
$109$	1.82843	+	3.16693i	0.175132	+	0.303337i	−0.765075	+	0.643941i	$0.777298\pi$
$110$	6.11058	−	10.5838i	0.582621	−	1.00913i
$111$	2.16804			0.205782
$112$		0			0
$113$	12.6085			1.18611			0.593056	−	0.805161i	$-0.297921\pi$
$113$	12.6085			1.18611			0.593056	+	0.805161i	$0.297921\pi$
$114$	3.77235	−	6.53390i	0.353313	−	0.611955i
$115$	2.18073	+	3.77714i	0.203354	+	0.352220i
$116$	−1.83509	−	3.17847i	−0.170384	−	0.295114i
$117$	−1.80853	+	3.13247i	−0.167199	+	0.289597i
$118$	−38.0063			−3.49876
$119$		0			0
$120$	−9.78039			−0.892823
$121$	−4.38118	+	7.58842i	−0.398289	+	0.689856i
$122$	−12.9404	−	22.4134i	−1.17157	−	2.02922i
$123$	−2.88784	−	5.00188i	−0.260388	−	0.451005i
$124$	−3.48908	+	6.04326i	−0.313328	+	0.542700i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−0.0562783			−0.00499389			−0.00249695	−	0.999997i	$-0.500795\pi$
$127$	−0.0562783			−0.00499389			−0.00249695	+	0.999997i	$0.500795\pi$
$128$	−22.7729	+	39.4439i	−2.01286	+	3.48638i
$129$	−4.55765	−	7.89408i	−0.401278	−	0.695035i
$130$	−4.97186	−	8.61152i	−0.436061	−	0.755280i
$131$	−9.83156	+	17.0288i	−0.858987	+	1.48781i	0.0139083	+	0.999903i	$0.495573\pi$
$131$	−9.83156	+	17.0288i	−0.858987	+	1.48781i	−0.872896	+	0.487907i	$0.837761\pi$
$132$	24.7064			2.15042
$133$		0			0
$134$	8.42900			0.728155
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	24.1930	+	41.9036i	2.07453	+	3.59320i
$137$	9.37534	+	16.2386i	0.800989	+	1.38735i	0.918966	+	0.394337i	$0.129026\pi$
$137$	9.37534	+	16.2386i	0.800989	+	1.38735i	−0.117977	+	0.993016i	$0.537641\pi$
$138$	−5.99509	+	10.3838i	−0.510336	+	0.883928i
$139$	−6.14657			−0.521345			−0.260673	−	0.965427i	$-0.583944\pi$
$139$	−6.14657			−0.521345			−0.260673	+	0.965427i	$0.583944\pi$
$140$		0			0
$141$	−6.48528			−0.546159
$142$	−0.381362	+	0.660539i	−0.0320032	+	0.0554312i
$143$	8.03979	+	13.9253i	0.672321	+	1.16449i
$144$	−7.88607	−	13.6591i	−0.657173	−	1.13826i
$145$	−0.330192	+	0.571909i	−0.0274210	+	0.0474945i
$146$	−29.1778			−2.41478
$147$		0			0
$148$	−12.0492			−0.990440
$149$	−10.1153	+	17.5202i	−0.828677	+	1.43531i	0.0703990	+	0.997519i	$0.477573\pi$
$149$	−10.1153	+	17.5202i	−0.828677	+	1.43531i	−0.899076	+	0.437792i	$0.855761\pi$
$150$	1.37456	+	2.38081i	0.112232	+	0.194392i
$151$	−10.5541	−	18.2803i	−0.858882	−	1.48763i	−0.872996	−	0.487727i	$-0.837826\pi$
$151$	−10.5541	−	18.2803i	−0.858882	−	1.48763i	0.0141145	−	0.999900i	$-0.495507\pi$
$152$	−13.4207	+	23.2453i	−1.08856	+	1.88544i
$153$	−4.94725			−0.399962
$154$		0			0
$155$	1.25559			0.100852
$156$	10.0512	−	17.4091i	0.804738	−	1.39385i
$157$	−0.980103	−	1.69759i	−0.0782207	−	0.135482i	0.824262	−	0.566209i	$-0.191591\pi$
$157$	−0.980103	−	1.69759i	−0.0782207	−	0.135482i	−0.902482	+	0.430727i	$0.858257\pi$
$158$	7.61235	+	13.1850i	0.605606	+	1.04894i
$159$	3.51564	−	6.08926i	0.278808	−	0.482910i
$160$	23.7987			1.88145
$161$		0			0
$162$	2.74912			0.215991
$163$	4.09069	−	7.08527i	0.320407	−	0.554962i	−0.660165	−	0.751121i	$-0.729514\pi$
$163$	4.09069	−	7.08527i	0.320407	−	0.554962i	0.980572	+	0.196159i	$0.0628469\pi$
$164$	16.0496	+	27.7987i	1.25326	+	2.17071i
$165$	−2.22274	−	3.84990i	−0.173040	−	0.299715i
$166$	9.85775	−	17.0741i	0.765110	−	1.32521i
$167$	−3.76235			−0.291139			−0.145570	−	0.989348i	$-0.546502\pi$
$167$	−3.76235			−0.291139			−0.145570	+	0.989348i	$0.546502\pi$
$168$		0			0
$169$	0.0831193			0.00639379
$170$	6.80029	−	11.7784i	0.521558	−	0.903365i
$171$	−1.37220	−	2.37672i	−0.104935	−	0.181753i
$172$	25.3298	+	43.8725i	1.93138	+	3.34525i
$173$	7.85304	−	13.6019i	0.597055	−	1.03413i	−0.396198	−	0.918165i	$-0.629671\pi$
$173$	7.85304	−	13.6019i	0.597055	−	1.03413i	0.993253	−	0.115965i	$-0.0369961\pi$
$174$	−1.81547			−0.137631
$175$		0			0
$176$	−70.1149			−5.28511
$177$	−6.91245	+	11.9727i	−0.519571	+	0.899924i
$178$	1.13872	+	1.97232i	0.0853508	+	0.147832i
$179$	0.640487	+	1.10936i	0.0478722	+	0.0829171i	0.888969	−	0.457968i	$-0.151423\pi$
$179$	0.640487	+	1.10936i	0.0478722	+	0.0829171i	−0.841096	+	0.540885i	$0.818089\pi$
$180$	−2.77882	+	4.81306i	−0.207121	+	0.358745i
$181$	16.5599			1.23089			0.615443	−	0.788181i	$-0.288977\pi$
$181$	16.5599			1.23089			0.615443	+	0.788181i	$0.288977\pi$
$182$		0			0
$183$	−9.41421			−0.695919
$184$	21.3284	−	36.9419i	1.57235	−	2.72339i
$185$	1.08402	+	1.87758i	0.0796988	+	0.138042i
$186$	1.72589	+	2.98933i	0.126548	+	0.219188i
$187$	−10.9965	+	19.0464i	−0.804142	+	1.39281i
$188$	36.0429			2.62870
$189$		0			0
$190$	7.54469			0.547350
$191$	−4.38136	+	7.58874i	−0.317024	+	0.549102i	−0.979866	−	0.199658i	$-0.936017\pi$
$191$	−4.38136	+	7.58874i	−0.317024	+	0.549102i	0.662841	+	0.748760i	$0.269350\pi$
$192$	16.9406	+	29.3419i	1.22258	+	2.11757i
$193$	−13.2493	−	22.9485i	−0.953706	−	1.65187i	−0.737302	−	0.675563i	$-0.763901\pi$
$193$	−13.2493	−	22.9485i	−0.953706	−	1.65187i	−0.216403	−	0.976304i	$-0.569433\pi$
$194$	−8.53304	+	14.7797i	−0.612636	+	1.06112i
$195$	−3.61706			−0.259023
$196$		0			0
$197$	4.11439			0.293138			0.146569	−	0.989200i	$-0.453177\pi$
$197$	4.11439			0.293138			0.146569	+	0.989200i	$0.453177\pi$
$198$	6.11058	−	10.5838i	0.434260	−	0.752161i
$199$	3.81769	+	6.61243i	0.270629	+	0.468743i	0.969023	−	0.246970i	$-0.0794351\pi$
$199$	3.81769	+	6.61243i	0.270629	+	0.468743i	−0.698394	+	0.715713i	$0.746102\pi$
$200$	−4.89020	−	8.47007i	−0.345789	−	0.598924i
$201$	1.53304	−	2.65530i	0.108132	−	0.187290i
$202$	11.3231			0.796693
$203$		0			0
$204$	27.4951			1.92504
$205$	2.88784	−	5.00188i	0.201695	−	0.349347i
$206$	11.2275	+	19.4465i	0.782254	+	1.35490i
$207$	2.18073	+	3.77714i	0.151571	+	0.262529i
$208$	−28.5244	+	49.4057i	−1.97781	+	3.42567i
$209$	−12.2002			−0.843907
$210$		0			0
$211$	−0.317238			−0.0218396			−0.0109198	−	0.999940i	$-0.503476\pi$
$211$	−0.317238			−0.0218396			−0.0109198	+	0.999940i	$0.503476\pi$
$212$	−19.5387	+	33.8420i	−1.34192	+	2.32428i
$213$	0.138722	+	0.240273i	0.00950506	+	0.0164632i
$214$	11.7243	+	20.3071i	0.801457	+	1.38816i
$215$	4.55765	−	7.89408i	0.310829	−	0.538372i
$216$	−9.78039			−0.665471
$217$		0			0
$218$	−10.0531			−0.680883
$219$	−5.30676	+	9.19159i	−0.358598	+	0.621110i
$220$	12.3532	+	21.3964i	0.832854	+	1.44255i
$221$	8.94725	+	15.4971i	0.601857	+	1.04245i
$222$	−2.98010	+	5.16169i	−0.200011	+	0.346430i
$223$	29.0590			1.94594			0.972968	−	0.230941i	$-0.0741803\pi$
$223$	29.0590			1.94594			0.972968	+	0.230941i	$0.0741803\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−17.3312	+	30.0185i	−1.15285	+	1.99680i
$227$	10.4455	+	18.0921i	0.693291	+	1.20082i	0.970753	+	0.240079i	$0.0771734\pi$
$227$	10.4455	+	18.0921i	0.693291	+	1.20082i	−0.277462	+	0.960737i	$0.589493\pi$
$228$	7.62622	+	13.2090i	0.505059	+	0.874787i
$229$	−2.46447	+	4.26858i	−0.162857	+	0.282076i	−0.935892	−	0.352287i	$-0.885404\pi$
$229$	−2.46447	+	4.26858i	−0.162857	+	0.282076i	0.773036	+	0.634363i	$0.218737\pi$
$230$	−11.9902			−0.790609
$231$		0			0
$232$	6.45881			0.424042
$233$	0.546910	−	0.947275i	0.0358292	−	0.0620581i	−0.847555	−	0.530708i	$-0.821926\pi$
$233$	0.546910	−	0.947275i	0.0358292	−	0.0620581i	0.883384	+	0.468650i	$0.155259\pi$
$234$	−4.97186	−	8.61152i	−0.325021	−	0.562952i
$235$	−3.24264	−	5.61642i	−0.211527	−	0.366375i
$236$	38.4170	−	66.5401i	2.50073	−	4.33139i
$237$	5.53803			0.359734
$238$		0			0
$239$	25.6725			1.66062			0.830309	−	0.557303i	$-0.188164\pi$
$239$	25.6725			1.66062			0.830309	+	0.557303i	$0.188164\pi$
$240$	7.88607	−	13.6591i	0.509044	−	0.881690i
$241$	−12.3734	−	21.4313i	−0.797040	−	1.38051i	−0.921536	−	0.388293i	$-0.873065\pi$
$241$	−12.3734	−	21.4313i	−0.797040	−	1.38051i	0.124496	−	0.992220i	$-0.460269\pi$
$242$	−12.0444	−	20.8615i	−0.774241	−	1.34103i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	52.3209			3.34950
$245$		0			0
$246$	15.8780			1.01235
$247$	−4.96334	+	8.59676i	−0.315810	+	0.546998i
$248$	−6.14010	−	10.6350i	−0.389897	−	0.675321i
$249$	−3.58579	−	6.21076i	−0.227240	−	0.393591i
$250$	−1.37456	+	2.38081i	−0.0869347	+	0.150575i
$251$	0.405692			0.0256070			0.0128035	−	0.999918i	$-0.495924\pi$
$251$	0.405692			0.0256070			0.0128035	+	0.999918i	$0.495924\pi$
$252$		0			0
$253$	19.3888			1.21897
$254$	0.0773578	−	0.133988i	0.00485386	−	0.00840713i
$255$	−2.47363	−	4.28445i	−0.154904	−	0.268302i
$256$	−28.7243	−	49.7519i	−1.79527	−	3.10950i
$257$	5.44549	−	9.43186i	0.339680	−	0.588343i	−0.644692	−	0.764442i	$-0.723015\pi$
$257$	5.44549	−	9.43186i	0.339680	−	0.588343i	0.984372	+	0.176099i	$0.0563479\pi$
$258$	25.0590			1.56011
$259$		0			0
$260$	20.1023			1.24669
$261$	−0.330192	+	0.571909i	−0.0204384	+	0.0354003i
$262$	−27.0281	−	46.8141i	−1.66980	−	2.89218i
$263$	−4.38358	−	7.59258i	−0.270303	−	0.468179i	0.698636	−	0.715477i	$-0.253791\pi$
$263$	−4.38358	−	7.59258i	−0.270303	−	0.468179i	−0.968939	+	0.247298i	$0.920457\pi$
$264$	−21.7393	+	37.6536i	−1.33796	+	2.31742i
$265$	7.03127			0.431928
$266$		0			0
$267$	0.828427			0.0506989
$268$	−8.52008	+	14.7572i	−0.520447	+	0.901441i
$269$	−11.4173	−	19.7754i	−0.696128	−	1.20573i	−0.969799	−	0.243906i	$-0.921571\pi$
$269$	−11.4173	−	19.7754i	−0.696128	−	1.20573i	0.273671	−	0.961823i	$-0.411762\pi$
$270$	1.37456	+	2.38081i	0.0836530	+	0.144891i
$271$	−5.33740	+	9.24465i	−0.324224	+	0.561572i	−0.981355	−	0.192204i	$-0.938436\pi$
$271$	−5.33740	+	9.24465i	−0.324224	+	0.561572i	0.657131	+	0.753776i	$0.271770\pi$
$272$	−78.0288			−4.73119
$273$		0			0
$274$	−51.5478			−3.11412
$275$	2.22274	−	3.84990i	0.134036	−	0.232158i
$276$	−12.1197	−	20.9920i	−0.729523	−	1.26357i
$277$	6.21803	+	10.7699i	0.373605	+	0.647103i	0.990117	−	0.140242i	$-0.0447881\pi$
$277$	6.21803	+	10.7699i	0.373605	+	0.647103i	−0.616512	+	0.787346i	$0.711455\pi$
$278$	8.44882	−	14.6338i	0.506726	−	0.877676i
$279$	1.25559			0.0751705
$280$		0			0
$281$	12.9169			0.770556			0.385278	−	0.922800i	$-0.374105\pi$
$281$	12.9169			0.770556			0.385278	+	0.922800i	$0.374105\pi$
$282$	8.91440	−	15.4402i	0.530845	−	0.919450i
$283$	−12.8070	−	22.1823i	−0.761294	−	1.31860i	−0.942184	−	0.335097i	$-0.891231\pi$
$283$	−12.8070	−	22.1823i	−0.761294	−	1.31860i	0.180889	−	0.983503i	$-0.442102\pi$
$284$	−0.770967	−	1.33535i	−0.0457485	−	0.0792387i
$285$	1.37220	−	2.37672i	0.0812823	−	0.140785i
$286$	−44.2047			−2.61388
$287$		0			0
$288$	23.7987			1.40235
$289$	−3.73765	+	6.47380i	−0.219862	+	0.380812i
$290$	−0.907737	−	1.57225i	−0.0533041	−	0.0923255i
$291$	3.10392	+	5.37615i	0.181955	+	0.315155i
$292$	29.4931	−	51.0836i	1.72595	−	2.98944i
$293$	−1.68276			−0.0983080			−0.0491540	−	0.998791i	$-0.515653\pi$
$293$	−1.68276			−0.0983080			−0.0491540	+	0.998791i	$0.515653\pi$
$294$		0			0
$295$	−13.8249			−0.804917
$296$	10.6022	−	18.3635i	0.616238	−	1.06735i
$297$	−2.22274	−	3.84990i	−0.128977	−	0.223394i
$298$	−27.8081	−	48.1651i	−1.61088	−	2.79013i
$299$	7.88784	−	13.6621i	0.456166	−	0.790102i
$300$	−5.55765			−0.320871
$301$		0			0
$302$	58.0290			3.33919
$303$	2.05941	−	3.56701i	0.118310	−	0.204919i
$304$	−21.6426	−	37.4861i	−1.24129	−	2.14997i
$305$	−4.70711	−	8.15295i	−0.269528	−	0.466836i
$306$	6.80029	−	11.7784i	0.388747	−	0.673329i
$307$	−7.31371			−0.417415			−0.208708	−	0.977978i	$-0.566926\pi$
$307$	−7.31371			−0.417415			−0.208708	+	0.977978i	$0.566926\pi$
$308$		0			0
$309$	8.16804			0.464664
$310$	−1.72589	+	2.98933i	−0.0980239	+	0.169782i
$311$	−5.60097	−	9.70117i	−0.317602	−	0.550103i	0.662385	−	0.749163i	$-0.269544\pi$
$311$	−5.60097	−	9.70117i	−0.317602	−	0.550103i	−0.979987	+	0.199061i	$0.936211\pi$
$312$	17.6881	+	30.6367i	1.00139	+	1.73446i
$313$	15.7428	−	27.2674i	0.889837	−	1.54124i	0.0497702	−	0.998761i	$-0.484151\pi$
$313$	15.7428	−	27.2674i	0.889837	−	1.54124i	0.840067	−	0.542483i	$-0.182516\pi$
$314$	5.38883			0.304110
$315$		0			0
$316$	−30.7784			−1.73142
$317$	−4.22524	+	7.31833i	−0.237313	+	0.411038i	−0.959942	−	0.280197i	$-0.909600\pi$
$317$	−4.22524	+	7.31833i	−0.237313	+	0.411038i	0.722629	+	0.691236i	$0.242933\pi$
$318$	9.66490	+	16.7401i	0.541981	+	0.938738i
$319$	1.46786	+	2.54242i	0.0821846	+	0.142348i
$320$	−16.9406	+	29.3419i	−0.947007	+	1.64026i
$321$	8.52951			0.476071
$322$		0			0
$323$	−13.5773			−0.755459
$324$	−2.77882	+	4.81306i	−0.154379	+	0.267392i
$325$	−1.80853	−	3.13247i	−0.100319	−	0.173758i
$326$	11.2458	+	19.4783i	0.622846	+	1.07880i
$327$	−1.82843	+	3.16693i	−0.101112	+	0.175132i
$328$	−56.4884			−3.11905
$329$		0			0
$330$	12.2212			0.672753
$331$	−8.32666	+	14.4222i	−0.457675	+	0.792716i	−0.998838	−	0.0482019i	$-0.984651\pi$
$331$	−8.32666	+	14.4222i	−0.457675	+	0.792716i	0.541163	+	0.840918i	$0.317984\pi$
$332$	19.9285	+	34.5172i	1.09372	+	1.89438i
$333$	1.08402	+	1.87758i	0.0594040	+	0.102891i
$334$	5.17157	−	8.95743i	0.282976	−	0.490129i
$335$	3.06608			0.167518
$336$		0			0
$337$	31.9178			1.73867			0.869337	−	0.494220i	$-0.164546\pi$
$337$	31.9178			1.73867			0.869337	+	0.494220i	$0.164546\pi$
$338$	−0.114252	+	0.197891i	−0.00621451	+	0.0107639i
$339$	6.30427	+	10.9193i	0.342401	+	0.593056i
$340$	13.7475	+	23.8114i	0.745565	+	1.29136i
$341$	2.79086	−	4.83392i	0.151134	−	0.261771i
$342$	7.54469			0.407970
$343$		0			0
$344$	−89.1511			−4.80671
$345$	−2.18073	+	3.77714i	−0.117407	+	0.203354i
$346$	21.5889	+	37.3931i	1.16063	+	2.01027i
$347$	3.95641	+	6.85271i	0.212391	+	0.367872i	0.952462	−	0.304656i	$-0.0985415\pi$
$347$	3.95641	+	6.85271i	0.212391	+	0.367872i	−0.740071	+	0.672529i	$0.765208\pi$
$348$	1.83509	−	3.17847i	0.0983712	−	0.170384i
$349$	25.1525			1.34638			0.673190	−	0.739469i	$-0.264924\pi$
$349$	25.1525			1.34638			0.673190	+	0.739469i	$0.264924\pi$
$350$		0			0
$351$	−3.61706			−0.193064
$352$	52.8984	−	91.6228i	2.81950	−	4.88351i
$353$	10.2833	+	17.8113i	0.547327	+	0.947998i	0.998456	+	0.0555395i	$0.0176879\pi$
$353$	10.2833	+	17.8113i	0.547327	+	0.947998i	−0.451130	+	0.892458i	$0.648979\pi$
$354$	−19.0031	−	32.9144i	−1.01001	−	1.74938i
$355$	−0.138722	+	0.240273i	−0.00736259	+	0.0127524i
$356$	−4.60411			−0.244017
$357$		0			0
$358$	−3.52155			−0.186120
$359$	7.05117	−	12.2130i	0.372147	−	0.644577i	−0.617749	−	0.786375i	$-0.711955\pi$
$359$	7.05117	−	12.2130i	0.372147	−	0.644577i	0.989896	+	0.141799i	$0.0452885\pi$
$360$	−4.89020	−	8.47007i	−0.257736	−	0.446412i
$361$	5.73412	+	9.93179i	0.301796	+	0.522726i
$362$	−22.7625	+	39.4259i	−1.19637	+	2.07218i
$363$	−8.76235			−0.459904
$364$		0			0
$365$	−10.6135			−0.555538
$366$	12.9404	−	22.4134i	0.676405	−	1.17157i
$367$	−0.193422	−	0.335017i	−0.0100965	−	0.0174877i	0.860933	−	0.508718i	$-0.169881\pi$
$367$	−0.193422	−	0.335017i	−0.0100965	−	0.0174877i	−0.871030	+	0.491231i	$0.836547\pi$
$368$	34.3948	+	59.5736i	1.79295	+	3.10549i
$369$	2.88784	−	5.00188i	0.150335	−	0.260388i
$370$	−5.96021			−0.309856
$371$		0			0
$372$	−6.97815			−0.361800
$373$	5.31724	−	9.20973i	0.275316	−	0.476862i	−0.694899	−	0.719108i	$-0.744551\pi$
$373$	5.31724	−	9.20973i	0.275316	−	0.476862i	0.970215	+	0.242246i	$0.0778841\pi$
$374$	−30.2306	−	52.3609i	−1.56319	−	2.70752i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−31.7143	+	54.9308i	−1.63554	+	2.83284i
$377$	2.38865			0.123022
$378$		0			0
$379$	−26.4290			−1.35757			−0.678783	−	0.734339i	$-0.737492\pi$
$379$	−26.4290			−1.35757			−0.678783	+	0.734339i	$0.737492\pi$
$380$	−7.62622	+	13.2090i	−0.391217	+	0.677607i
$381$	−0.0281391	−	0.0487384i	−0.00144161	−	0.00249695i
$382$	−12.0449	−	20.8623i	−0.616270	−	1.06741i
$383$	−2.57283	+	4.45628i	−0.131466	+	0.227705i	−0.924242	−	0.381808i	$-0.875302\pi$
$383$	−2.57283	+	4.45628i	−0.131466	+	0.227705i	0.792776	+	0.609513i	$0.208635\pi$
$384$	−45.5459			−2.32425
$385$		0			0
$386$	72.8478			3.70785
$387$	4.55765	−	7.89408i	0.231678	−	0.401278i
$388$	−17.2505	−	29.8787i	−0.875761	−	1.51686i
$389$	6.45401	+	11.1787i	0.327231	+	0.566781i	0.981961	−	0.189082i	$-0.0605511\pi$
$389$	6.45401	+	11.1787i	0.327231	+	0.566781i	−0.654730	+	0.755863i	$0.727218\pi$
$390$	4.97186	−	8.61152i	0.251760	−	0.436061i
$391$	21.5773			1.09121
$392$		0			0
$393$	−19.6631			−0.991873
$394$	−5.65547	+	9.79557i	−0.284919	+	0.493494i
$395$	2.76901	+	4.79607i	0.139324	+	0.241317i
$396$	12.3532	+	21.3964i	0.620773	+	1.07521i
$397$	11.3814	−	19.7131i	0.571214	−	0.989372i	−0.425227	−	0.905087i	$-0.639806\pi$
$397$	11.3814	−	19.7131i	0.571214	−	0.989372i	0.996442	−	0.0842855i	$-0.0268608\pi$
$398$	−20.9906			−1.05216
$399$		0			0
$400$	15.7721			0.788607
$401$	4.92540	−	8.53105i	0.245963	−	0.426020i	−0.716439	−	0.697650i	$-0.754229\pi$
$401$	4.92540	−	8.53105i	0.245963	−	0.426020i	0.962402	+	0.271630i	$0.0875625\pi$
$402$	4.21450	+	7.29973i	0.210200	+	0.364077i
$403$	−2.27078	−	3.93311i	−0.113116	−	0.195922i
$404$	−11.4455	+	19.8242i	−0.569434	+	0.986289i
$405$	1.00000			0.0496904
$406$		0			0
$407$	9.63801			0.477738
$408$	−24.1930	+	41.9036i	−1.19773	+	2.07453i
$409$	7.33712	+	12.7083i	0.362797	+	0.628383i	0.988420	−	0.151742i	$-0.0484884\pi$
$409$	7.33712	+	12.7083i	0.362797	+	0.628383i	−0.625623	+	0.780126i	$0.715155\pi$
$410$	7.93901	+	13.7508i	0.392080	+	0.679102i
$411$	−9.37534	+	16.2386i	−0.462451	+	0.800989i
$412$	−45.3951			−2.23646
$413$		0			0
$414$	−11.9902			−0.589285
$415$	3.58579	−	6.21076i	0.176019	−	0.304874i
$416$	−43.0407	−	74.5486i	−2.11024	−	3.65505i
$417$	−3.07328	−	5.32308i	−0.150499	−	0.260673i
$418$	16.7699	−	29.0463i	0.820243	−	1.42070i
$419$	−9.89450			−0.483378			−0.241689	−	0.970354i	$-0.577701\pi$
$419$	−9.89450			−0.483378			−0.241689	+	0.970354i	$0.577701\pi$
$420$		0			0
$421$	35.4388			1.72718			0.863591	−	0.504193i	$-0.168210\pi$
$421$	35.4388			1.72718			0.863591	+	0.504193i	$0.168210\pi$
$422$	0.436063	−	0.755283i	0.0212272	−	0.0367666i
$423$	−3.24264	−	5.61642i	−0.157663	−	0.273080i
$424$	−34.3843	−	59.5554i	−1.66985	−	2.89226i
$425$	2.47363	−	4.28445i	0.119988	−	0.207826i
$426$	−0.762725			−0.0369541
$427$		0			0
$428$	−47.4040			−2.29136
$429$	−8.03979	+	13.9253i	−0.388165	+	0.672321i
$430$	12.5295	+	21.7017i	0.604227	+	1.04655i
$431$	8.34656	+	14.4567i	0.402040	+	0.696353i	0.993972	−	0.109635i	$-0.0349681\pi$
$431$	8.34656	+	14.4567i	0.402040	+	0.696353i	−0.591932	+	0.805988i	$0.701635\pi$
$432$	7.88607	−	13.6591i	0.379419	−	0.657173i
$433$	−13.0363			−0.626483			−0.313241	−	0.949674i	$-0.601415\pi$
$433$	−13.0363			−0.626483			−0.313241	+	0.949674i	$0.601415\pi$
$434$		0			0
$435$	−0.660384			−0.0316630
$436$	10.1618	−	17.6007i	0.486660	−	0.842919i
$437$	5.98481	+	10.3660i	0.286293	+	0.495873i
$438$	−14.5889	−	25.2688i	−0.697086	−	1.20739i
$439$	−11.3557	+	19.6687i	−0.541979	+	0.938735i	0.456811	+	0.889564i	$0.348991\pi$
$439$	−11.3557	+	19.6687i	−0.541979	+	0.938735i	−0.998790	+	0.0491715i	$0.984342\pi$
$440$	−43.4786			−2.07276
$441$		0			0
$442$	−49.1941			−2.33992
$443$	−4.12445	+	7.14376i	−0.195959	+	0.339410i	−0.947214	−	0.320601i	$-0.896115\pi$
$443$	−4.12445	+	7.14376i	−0.195959	+	0.339410i	0.751256	+	0.660011i	$0.229449\pi$
$444$	−6.02461	−	10.4349i	−0.285915	−	0.495220i
$445$	0.414214	+	0.717439i	0.0196356	+	0.0340099i
$446$	−39.9433	+	69.1839i	−1.89137	+	3.27595i
$447$	−20.2306			−0.956874
$448$		0			0
$449$	24.5212			1.15723			0.578613	−	0.815602i	$-0.303594\pi$
$449$	24.5212			1.15723			0.578613	+	0.815602i	$0.303594\pi$
$450$	−1.37456	+	2.38081i	−0.0647973	+	0.112232i
$451$	−12.8379	−	22.2358i	−0.604511	−	1.04704i
$452$	−35.0369	−	60.6857i	−1.64800	−	2.85442i
$453$	10.5541	−	18.2803i	0.495876	−	0.858882i
$454$	−57.4317			−2.69541
$455$		0			0
$456$	−26.8414			−1.25696
$457$	14.1734	−	24.5491i	0.663004	−	1.14836i	−0.316818	−	0.948486i	$-0.602615\pi$
$457$	14.1734	−	24.5491i	0.663004	−	1.14836i	0.979822	−	0.199871i	$-0.0640521\pi$
$458$	−6.77511	−	11.7348i	−0.316580	−	0.548333i
$459$	−2.47363	−	4.28445i	−0.115459	−	0.199981i
$460$	12.1197	−	20.9920i	0.565086	−	0.978757i
$461$	38.3727			1.78720			0.893598	−	0.448868i	$-0.148173\pi$
$461$	38.3727			1.78720			0.893598	+	0.448868i	$0.148173\pi$
$462$		0			0
$463$	2.38530			0.110855			0.0554273	−	0.998463i	$-0.482348\pi$
$463$	2.38530			0.110855			0.0554273	+	0.998463i	$0.482348\pi$
$464$	−5.20784	+	9.02024i	−0.241768	+	0.418754i
$465$	0.627797	+	1.08738i	0.0291134	+	0.0504259i
$466$	1.50352	+	2.60417i	0.0696492	+	0.120636i
$467$	9.90393	−	17.1541i	0.458299	−	0.793797i	−0.540572	−	0.841298i	$-0.681792\pi$
$467$	9.90393	−	17.1541i	0.458299	−	0.793797i	0.998871	+	0.0475004i	$0.0151255\pi$
$468$	20.1023			0.929231
$469$		0			0
$470$	17.8288			0.822381
$471$	0.980103	−	1.69759i	0.0451607	−	0.0782207i
$472$	67.6064	+	117.098i	3.11184	+	5.38986i
$473$	−20.2610	−	35.0930i	−0.931600	−	1.61358i
$474$	−7.61235	+	13.1850i	−0.349647	+	0.605606i
$475$	2.74441			0.125922
$476$		0			0
$477$	7.03127			0.321940
$478$	−35.2884	+	61.1213i	−1.61405	+	2.79563i
$479$	1.71980	+	2.97877i	0.0785795	+	0.136104i	0.902637	−	0.430402i	$-0.141628\pi$
$479$	1.71980	+	2.97877i	0.0785795	+	0.136104i	−0.824058	+	0.566506i	$0.808295\pi$
$480$	11.8994	+	20.6103i	0.543129	+	0.940727i
$481$	3.92097	−	6.79132i	0.178781	−	0.309658i
$482$	68.0318			3.09876
$483$		0			0
$484$	48.6981			2.21355
$485$	−3.10392	+	5.37615i	−0.140942	+	0.244118i
$486$	1.37456	+	2.38081i	0.0623513	+	0.107996i
$487$	3.56118	+	6.16814i	0.161372	+	0.279505i	0.935361	−	0.353694i	$-0.115075\pi$
$487$	3.56118	+	6.16814i	0.161372	+	0.279505i	−0.773989	+	0.633199i	$0.781741\pi$
$488$	−46.0373	+	79.7390i	−2.08401	+	3.60962i
$489$	8.18137			0.369974
$490$		0			0
$491$	−31.6896			−1.43013			−0.715066	−	0.699057i	$-0.753603\pi$
$491$	−31.6896			−1.43013			−0.715066	+	0.699057i	$0.753603\pi$
$492$	−16.0496	+	27.7987i	−0.723572	+	1.25326i
$493$	1.63354	+	2.82938i	0.0735711	+	0.127429i
$494$	−13.6448	−	23.6335i	−0.613909	−	1.06332i
$495$	2.22274	−	3.84990i	0.0999049	−	0.173040i
$496$	19.8034			0.889200
$497$		0			0
$498$	19.7155			0.883473
$499$	19.5014	−	33.7774i	0.873001	−	1.51208i	0.0141243	−	0.999900i	$-0.495504\pi$
$499$	19.5014	−	33.7774i	0.873001	−	1.51208i	0.858877	−	0.512182i	$-0.171163\pi$
$500$	−2.77882	−	4.81306i	−0.124273	−	0.215247i
$501$	−1.88118	−	3.25829i	−0.0840447	−	0.145570i
$502$	−0.557647	+	0.965873i	−0.0248890	+	0.0431090i
$503$	−18.5308			−0.826247			−0.413123	−	0.910675i	$-0.635562\pi$
$503$	−18.5308			−0.826247			−0.413123	+	0.910675i	$0.635562\pi$
$504$		0			0
$505$	4.11882			0.183285
$506$	−26.6511	+	46.1610i	−1.18479	+	2.05211i
$507$	0.0415597	+	0.0719835i	0.00184573	+	0.00319690i
$508$	0.156387	+	0.270871i	0.00693857	+	0.0120180i
$509$	19.9026	−	34.4724i	0.882169	−	1.52796i	0.0332436	−	0.999447i	$-0.489416\pi$
$509$	19.9026	−	34.4724i	0.882169	−	1.52796i	0.848925	−	0.528513i	$-0.177250\pi$
$510$	13.6006			0.602244
$511$		0			0
$512$	66.8412			2.95399
$513$	1.37220	−	2.37672i	0.0605842	−	0.104935i
$514$	14.9703	+	25.9293i	0.660311	+	1.14369i
$515$	4.08402	+	7.07373i	0.179963	+	0.311706i
$516$	−25.3298	+	43.8725i	−1.11508	+	1.93138i
$517$	−28.8302			−1.26795
$518$		0			0
$519$	15.7061			0.689420
$520$	−17.6881	+	30.6367i	−0.775676	+	1.34351i
$521$	−13.1797	−	22.8279i	−0.577413	−	1.00011i	−0.995775	−	0.0918283i	$-0.970729\pi$
$521$	−13.1797	−	22.8279i	−0.577413	−	1.00011i	0.418362	−	0.908280i	$-0.362604\pi$
$522$	−0.907737	−	1.57225i	−0.0397306	−	0.0688153i
$523$	12.1864	−	21.1074i	0.532872	−	0.922962i	−0.466391	−	0.884579i	$-0.654446\pi$
$523$	12.1864	−	21.1074i	0.532872	−	0.922962i	0.999263	−	0.0383833i	$-0.0122208\pi$
$524$	109.281			4.77395
$525$		0			0
$526$	24.1019			1.05089
$527$	3.10587	−	5.37953i	0.135294	−	0.234336i
$528$	−35.0574	−	60.7213i	−1.52568	−	2.64255i
$529$	1.98881	+	3.44472i	0.0864701	+	0.149771i
$530$	−9.66490	+	16.7401i	−0.419816	+	0.727143i
$531$	−13.8249			−0.599949
$532$		0			0
$533$	−20.8910			−0.904888
$534$	−1.13872	+	1.97232i	−0.0492773	+	0.0853508i
$535$	4.26475	+	7.38677i	0.184381	+	0.319358i
$536$	−14.9937	−	25.9699i	−0.647630	−	1.12173i
$537$	−0.640487	+	1.10936i	−0.0276390	+	0.0478722i
$538$	62.7753			2.70643
$539$		0			0
$540$	−5.55765			−0.239163
$541$	−12.1814	+	21.0988i	−0.523718	+	0.907106i	0.475901	+	0.879499i	$0.342122\pi$
$541$	−12.1814	+	21.0988i	−0.523718	+	0.907106i	−0.999619	+	0.0276073i	$0.991211\pi$
$542$	−14.6731	−	25.4146i	−0.630265	−	1.09165i
$543$	8.27994	+	14.3413i	0.355326	+	0.615443i
$544$	58.8691	−	101.964i	2.52399	−	4.37168i
$545$	−3.65685			−0.156642
$546$		0			0
$547$	10.1421			0.433646			0.216823	−	0.976211i	$-0.430430\pi$
$547$	10.1421			0.433646			0.216823	+	0.976211i	$0.430430\pi$
$548$	52.1048	−	90.2482i	2.22581	−	3.85521i
$549$	−4.70711	−	8.15295i	−0.200894	−	0.347959i
$550$	6.11058	+	10.5838i	0.260556	+	0.451296i
$551$	−0.906181	+	1.56955i	−0.0386046	+	0.0668651i
$552$	42.6568			1.81560
$553$		0			0
$554$	−34.1882			−1.45252
$555$	−1.08402	+	1.87758i	−0.0460142	+	0.0796988i
$556$	17.0802	+	29.5838i	0.724363	+	1.25463i
$557$	7.27799	+	12.6058i	0.308378	+	0.534127i	0.978008	−	0.208569i	$-0.0668804\pi$
$557$	7.27799	+	12.6058i	0.308378	+	0.534127i	−0.669630	+	0.742695i	$0.733547\pi$
$558$	−1.72589	+	2.98933i	−0.0730627	+	0.126548i
$559$	−32.9706			−1.39451
$560$		0			0
$561$	−21.9929			−0.928543
$562$	−17.7550	+	30.7526i	−0.748950	+	1.29722i
$563$	18.2922	+	31.6831i	0.770926	+	1.33528i	0.937056	+	0.349179i	$0.113539\pi$
$563$	18.2922	+	31.6831i	0.770926	+	1.33528i	−0.166130	+	0.986104i	$0.553127\pi$
$564$	18.0215	+	31.2141i	0.758840	+	1.31435i
$565$	−6.30427	+	10.9193i	−0.265223	+	0.459379i
$566$	70.4156			2.95979
$567$		0			0
$568$	2.71351			0.113856
$569$	1.82344	−	3.15828i	0.0764424	−	0.132402i	−0.825270	−	0.564738i	$-0.808977\pi$
$569$	1.82344	−	3.15828i	0.0764424	−	0.132402i	0.901713	+	0.432336i	$0.142311\pi$
$570$	3.77235	+	6.53390i	0.158006	+	0.273675i
$571$	19.2967	+	33.4228i	0.807540	+	1.39870i	0.914563	+	0.404444i	$0.132535\pi$
$571$	19.2967	+	33.4228i	0.807540	+	1.39870i	−0.107022	+	0.994257i	$0.534132\pi$
$572$	44.6823	−	77.3921i	1.86826	−	3.23593i
$573$	−8.76272			−0.366068
$574$		0			0
$575$	−4.36147			−0.181886
$576$	−16.9406	+	29.3419i	−0.705857	+	1.22258i
$577$	−7.02617	−	12.1697i	−0.292503	−	0.506630i	0.681898	−	0.731447i	$-0.261155\pi$
$577$	−7.02617	−	12.1697i	−0.292503	−	0.506630i	−0.974401	+	0.224817i	$0.927822\pi$
$578$	−10.2752	−	17.7972i	−0.427393	−	0.740267i
$579$	13.2493	−	22.9485i	0.550622	−	0.953706i
$580$	3.67018			0.152396
$581$		0			0
$582$	−17.0661			−0.707412
$583$	15.6287	−	27.0697i	0.647275	−	1.12111i
$584$	51.9022	+	89.8973i	2.14773	+	3.71998i
$585$	−1.80853	−	3.13247i	−0.0747735	−	0.129512i
$586$	2.31305	−	4.00633i	0.0955514	−	0.165500i
$587$	−27.0402			−1.11607			−0.558034	−	0.829818i	$-0.688444\pi$
$587$	−27.0402			−1.11607			−0.558034	+	0.829818i	$0.688444\pi$
$588$		0			0
$589$	3.44586			0.141984
$590$	19.0031	−	32.9144i	0.782347	−	1.35506i
$591$	2.05720	+	3.56317i	0.0846217	+	0.146569i
$592$	17.0973	+	29.6135i	0.702697	+	1.21711i
$593$	−10.8382	+	18.7724i	−0.445073	+	0.770888i	−0.998057	−	0.0623031i	$-0.980155\pi$
$593$	−10.8382	+	18.7724i	−0.445073	+	0.770888i	0.552985	+	0.833191i	$0.313489\pi$
$594$	12.2212			0.501440
$595$		0			0
$596$	112.434			4.60550
$597$	−3.81769	+	6.61243i	−0.156248	+	0.270629i
$598$	21.6846	+	37.5588i	0.886749	+	1.53589i
$599$	−12.9949	−	22.5078i	−0.530957	−	0.919644i	−0.999347	−	0.0361227i	$-0.988499\pi$
$599$	−12.9949	−	22.5078i	−0.530957	−	0.919644i	0.468390	−	0.883522i	$-0.344834\pi$
$600$	4.89020	−	8.47007i	0.199641	−	0.345789i
$601$	12.0746			0.492533			0.246267	−	0.969202i	$-0.420796\pi$
$601$	12.0746			0.492533			0.246267	+	0.969202i	$0.420796\pi$
$602$		0			0
$603$	3.06608			0.124860
$604$	−58.6561	+	101.595i	−2.38668	+	4.13385i
$605$	−4.38118	−	7.58842i	−0.178120	−	0.308513i
$606$	5.66157	+	9.80612i	0.229985	+	0.398346i
$607$	−20.8695	+	36.1470i	−0.847067	+	1.46716i	0.0367474	+	0.999325i	$0.488300\pi$
$607$	−20.8695	+	36.1470i	−0.847067	+	1.46716i	−0.883814	+	0.467838i	$0.845033\pi$
$608$	65.3133			2.64880
$609$		0			0
$610$	25.8808			1.04788
$611$	−11.7288	+	20.3149i	−0.474497	+	0.821854i
$612$	13.7475	+	23.8114i	0.555711	+	0.962520i
$613$	5.90079	+	10.2205i	0.238331	+	0.412801i	0.960235	−	0.279192i	$-0.0900664\pi$
$613$	5.90079	+	10.2205i	0.238331	+	0.412801i	−0.721905	+	0.691993i	$0.756733\pi$
$614$	10.0531	−	17.4125i	0.405711	−	0.702712i
$615$	5.77568			0.232898
$616$		0			0
$617$	12.2913			0.494829			0.247415	−	0.968910i	$-0.420419\pi$
$617$	12.2913			0.494829			0.247415	+	0.968910i	$0.420419\pi$
$618$	−11.2275	+	19.4465i	−0.451634	+	0.782254i
$619$	−12.1886	−	21.1112i	−0.489900	−	0.848532i	0.510032	−	0.860155i	$-0.329634\pi$
$619$	−12.1886	−	21.1112i	−0.489900	−	0.848532i	−0.999932	+	0.0116231i	$0.996300\pi$
$620$	−3.48908	−	6.04326i	−0.140125	−	0.242703i
$621$	−2.18073	+	3.77714i	−0.0875098	+	0.151571i
$622$	30.7955			1.23479
$623$		0			0
$624$	−57.0488			−2.28378
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	43.2789	+	74.9612i	1.72977	+	2.99605i
$627$	−6.10011	−	10.5657i	−0.243615	−	0.421953i
$628$	−5.44706	+	9.43459i	−0.217362	+	0.376481i
$629$	10.7259			0.427668
$630$		0			0
$631$	−43.3200			−1.72454			−0.862271	−	0.506448i	$-0.830958\pi$
$631$	−43.3200			−1.72454			−0.862271	+	0.506448i	$0.830958\pi$
$632$	27.0820	−	46.9075i	1.07727	−	1.86588i
$633$	−0.158619	−	0.274736i	−0.00630455	−	0.0109198i
$634$	−11.6157	−	20.1189i	−0.461318	−	0.799025i
$635$	0.0281391	−	0.0487384i	0.00111667	−	0.00193413i
$636$	−39.0773			−1.54952
$637$		0			0
$638$	−8.07066			−0.319521
$639$	−0.138722	+	0.240273i	−0.00548775	+	0.00950506i
$640$	−22.7729	−	39.4439i	−0.900179	−	1.55916i
$641$	−9.27038	−	16.0568i	−0.366158	−	0.634205i	0.622803	−	0.782379i	$-0.285994\pi$
$641$	−9.27038	−	16.0568i	−0.366158	−	0.634205i	−0.988961	+	0.148174i	$0.952660\pi$
$642$	−11.7243	+	20.3071i	−0.462722	+	0.801457i
$643$	8.55489			0.337372			0.168686	−	0.985670i	$-0.446048\pi$
$643$	8.55489			0.337372			0.168686	+	0.985670i	$0.446048\pi$
$644$		0			0
$645$	9.11529			0.358914
$646$	18.6627	−	32.3248i	0.734276	−	1.27180i
$647$	−21.5443	−	37.3158i	−0.846994	−	1.46704i	−0.883878	−	0.467717i	$-0.845077\pi$
$647$	−21.5443	−	37.3158i	−0.846994	−	1.46704i	0.0368847	−	0.999320i	$-0.488257\pi$
$648$	−4.89020	−	8.47007i	−0.192105	−	0.332736i
$649$	−30.7292	+	53.2245i	−1.20623	+	2.08925i
$650$	9.94372			0.390025
$651$		0			0
$652$	−45.4692			−1.78071
$653$	7.01387	−	12.1484i	0.274474	−	0.475403i	−0.695528	−	0.718499i	$-0.744830\pi$
$653$	7.01387	−	12.1484i	0.274474	−	0.475403i	0.970002	+	0.243096i	$0.0781629\pi$
$654$	−5.02656	−	8.70626i	−0.196554	−	0.340442i
$655$	−9.83156	−	17.0288i	−0.384151	−	0.665369i
$656$	45.5474	−	78.8905i	1.77833	−	3.08016i
$657$	−10.6135			−0.414073
$658$		0			0
$659$	−19.1488			−0.745932			−0.372966	−	0.927845i	$-0.621659\pi$
$659$	−19.1488			−0.745932			−0.372966	+	0.927845i	$0.621659\pi$
$660$	−12.3532	+	21.3964i	−0.480849	+	0.832854i
$661$	13.2858	+	23.0117i	0.516759	+	0.895053i	0.999811	+	0.0194610i	$0.00619502\pi$
$661$	13.2858	+	23.0117i	0.516759	+	0.895053i	−0.483052	+	0.875592i	$0.660472\pi$
$662$	−22.8910	−	39.6483i	−0.889683	−	1.54098i
$663$	−8.94725	+	15.4971i	−0.347482	+	0.601857i
$664$	−70.1408			−2.72199
$665$		0			0
$666$	−5.96021			−0.230953
$667$	1.44012	−	2.49436i	0.0557617	−	0.0965821i
$668$	10.4549	+	18.1084i	0.404513	+	0.700636i
$669$	14.5295	+	25.1658i	0.561743	+	0.972968i
$670$	−4.21450	+	7.29973i	−0.162820	+	0.282013i
$671$	−41.8508			−1.61563
$672$		0			0
$673$	46.6900			1.79977			0.899883	−	0.436132i	$-0.143652\pi$
$673$	46.6900			1.79977			0.899883	+	0.436132i	$0.143652\pi$
$674$	−43.8729	+	75.9901i	−1.68992	+	2.92703i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−0.230974	−	0.400059i	−0.00888361	−	0.0153869i
$677$	−20.8476	+	36.1092i	−0.801240	+	1.38779i	0.117560	+	0.993066i	$0.462493\pi$
$677$	−20.8476	+	36.1092i	−0.801240	+	1.38779i	−0.918800	+	0.394723i	$0.870841\pi$
$678$	−34.6624			−1.33120
$679$		0			0
$680$	−48.3861			−1.85552
$681$	−10.4455	+	18.0921i	−0.400272	+	0.693291i
$682$	7.67241	+	13.2890i	0.293792	+	0.508862i
$683$	10.7715	+	18.6568i	0.412160	+	0.713883i	0.995126	−	0.0986143i	$-0.0314410\pi$
$683$	10.7715	+	18.6568i	0.412160	+	0.713883i	−0.582965	+	0.812497i	$0.698108\pi$
$684$	−7.62622	+	13.2090i	−0.291596	+	0.505059i
$685$	−18.7507			−0.716426
$686$		0			0
$687$	−4.92893			−0.188050
$688$	71.8839	−	124.507i	2.74055	−	4.74677i
$689$	−12.7163	−	22.0252i	−0.484451	−	0.839094i
$690$	−5.99509	−	10.3838i	−0.228229	−	0.395305i
$691$	−11.4612	+	19.8514i	−0.436005	+	0.755183i	−0.997377	−	0.0723805i	$-0.976940\pi$
$691$	−11.4612	+	19.8514i	−0.436005	+	0.755183i	0.561372	+	0.827564i	$0.310274\pi$
$692$	−87.2888			−3.31822
$693$		0			0
$694$	−21.7533			−0.825743
$695$	3.07328	−	5.32308i	0.116576	−	0.201916i
$696$	3.22941	+	5.59350i	0.122410	+	0.212021i
$697$	−14.2869	−	24.7456i	−0.541154	−	0.937306i
$698$	−34.5735	+	59.8831i	−1.30863	+	2.26661i
$699$	1.09382			0.0413720
$700$		0			0
$701$	−51.4317			−1.94255			−0.971275	−	0.237960i	$-0.923521\pi$
$701$	−51.4317			−1.94255			−0.971275	+	0.237960i	$0.923521\pi$
$702$	4.97186	−	8.61152i	0.187651	−	0.325021i
$703$	2.97499	+	5.15284i	0.112204	+	0.194343i
$704$	75.3091	+	130.439i	2.83832	+	4.91611i
$705$	3.24264	−	5.61642i	0.122125	−	0.211527i
$706$	−56.5402			−2.12792
$707$		0			0
$708$	76.8339			2.88759
$709$	17.2341	−	29.8504i	0.647241	−	1.12105i	−0.336538	−	0.941670i	$-0.609256\pi$
$709$	17.2341	−	29.8504i	0.647241	−	1.12105i	0.983779	−	0.179384i	$-0.0574106\pi$
$710$	−0.381362	−	0.660539i	−0.0143123	−	0.0247896i
$711$	2.76901	+	4.79607i	0.103846	+	0.179867i
$712$	4.05117	−	7.01683i	0.151824	−	0.262967i
$713$	−5.47623			−0.205086
$714$		0			0
$715$	−16.0796			−0.601343
$716$	3.55960	−	6.16541i	0.133028	−	0.230412i
$717$	12.8363	+	22.2331i	0.479379	+	0.830309i
$718$	19.3845	+	33.5749i	0.723423	+	1.25301i
$719$	−21.0375	+	36.4381i	−0.784568	+	1.35891i	0.144689	+	0.989477i	$0.453782\pi$
$719$	−21.0375	+	36.4381i	−0.784568	+	1.35891i	−0.929257	+	0.369434i	$0.879551\pi$
$720$	15.7721			0.587793
$721$		0			0
$722$	−31.5275			−1.17333
$723$	12.3734	−	21.4313i	0.460171	−	0.797040i
$724$	−46.0170	−	79.7038i	−1.71021	−	2.96217i
$725$	−0.330192	−	0.571909i	−0.0122630	−	0.0212402i
$726$	12.0444	−	20.8615i	0.447008	−	0.774241i
$727$	36.6722			1.36010			0.680048	−	0.733168i	$-0.261959\pi$
$727$	36.6722			1.36010			0.680048	+	0.733168i	$0.261959\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	14.5889	−	25.2688i	0.539960	−	0.935238i
$731$	−22.5478	−	39.0540i	−0.833962	−	1.44446i
$732$	26.1604	+	45.3112i	0.966918	+	1.67475i
$733$	23.1848	−	40.1572i	0.856350	−	1.48324i	−0.0190378	−	0.999819i	$-0.506060\pi$
$733$	23.1848	−	40.1572i	0.856350	−	1.48324i	0.875387	−	0.483422i	$-0.160606\pi$
$734$	1.06348			0.0392538
$735$		0			0
$736$	−103.797			−3.82602
$737$	6.81510	−	11.8041i	0.251037	−	0.434810i
$738$	7.93901	+	13.7508i	0.292239	+	0.506173i
$739$	−0.679232	−	1.17646i	−0.0249859	−	0.0432769i	0.853262	−	0.521482i	$-0.174621\pi$
$739$	−0.679232	−	1.17646i	−0.0249859	−	0.0432769i	−0.878248	+	0.478205i	$0.841287\pi$
$740$	6.02461	−	10.4349i	0.221469	−	0.383596i
$741$	−9.92668			−0.364666
$742$		0			0
$743$	−26.2748			−0.963930			−0.481965	−	0.876191i	$-0.660077\pi$
$743$	−26.2748			−0.963930			−0.481965	+	0.876191i	$0.660077\pi$
$744$	6.14010	−	10.6350i	0.225107	−	0.389897i
$745$	−10.1153	−	17.5202i	−0.370596	−	0.641891i
$746$	14.6177	+	25.3186i	0.535193	+	0.926981i
$747$	3.58579	−	6.21076i	0.131197	−	0.227240i
$748$	122.229			4.46914
$749$		0			0
$750$	−2.74912			−0.100384
$751$	12.6135	−	21.8473i	0.460274	−	0.797218i	−0.538700	−	0.842498i	$-0.681084\pi$
$751$	12.6135	−	21.8473i	0.460274	−	0.797218i	0.998974	+	0.0452792i	$0.0144178\pi$
$752$	−51.1434	−	88.5830i	−1.86501	−	3.23029i
$753$	0.202846	+	0.351339i	0.00739212	+	0.0128035i
$754$	−3.28334	+	5.68691i	−0.119572	+	0.207105i
$755$	21.1082			0.768207
$756$		0			0
$757$	6.02331			0.218921			0.109460	−	0.993991i	$-0.465088\pi$
$757$	6.02331			0.218921			0.109460	+	0.993991i	$0.465088\pi$
$758$	36.3282	−	62.9223i	1.31950	−	2.28544i
$759$	9.69442	+	16.7912i	0.351885	+	0.609483i
$760$	−13.4207	−	23.2453i	−0.486819	−	0.843196i
$761$	15.4107	−	26.6921i	0.558637	−	0.967587i	−0.438974	−	0.898500i	$-0.644658\pi$
$761$	15.4107	−	26.6921i	0.558637	−	0.967587i	0.997611	−	0.0690875i	$-0.0220088\pi$
$762$	0.154716			0.00560476
$763$		0			0
$764$	48.7001			1.76191
$765$	2.47363	−	4.28445i	0.0894341	−	0.154904i
$766$	−7.07302	−	12.2508i	−0.255559	−	0.442640i
$767$	25.0027	+	43.3060i	0.902797	+	1.56369i
$768$	28.7243	−	49.7519i	1.03650	−	1.79527i
$769$	−31.8736			−1.14939			−0.574695	−	0.818367i	$-0.694879\pi$
$769$	−31.8736			−1.14939			−0.574695	+	0.818367i	$0.694879\pi$
$770$		0			0
$771$	10.8910			0.392229
$772$	−73.6350	+	127.539i	−2.65018	+	4.59025i
$773$	−8.54560	−	14.8014i	−0.307364	−	0.532370i	0.670421	−	0.741981i	$-0.266113\pi$
$773$	−8.54560	−	14.8014i	−0.307364	−	0.532370i	−0.977785	+	0.209611i	$0.932780\pi$
$774$	12.5295	+	21.7017i	0.450364	+	0.780053i
$775$	−0.627797	+	1.08738i	−0.0225511	+	0.0390597i
$776$	60.7151			2.17954
$777$		0			0
$778$	−35.4857			−1.27222
$779$	7.92540	−	13.7272i	0.283957	−	0.491828i
$780$	10.0512	+	17.4091i	0.359890	+	0.623347i
$781$	0.616686	+	1.06813i	0.0220668	+	0.0382207i
$782$	−29.6592	+	51.3713i	−1.06061	+	1.83703i
$783$	−0.660384			−0.0236002
$784$		0			0
$785$	1.96021			0.0699627
$786$	27.0281	−	46.8141i	0.964061	−	1.66980i
$787$	14.0809	+	24.3888i	0.501929	+	0.869366i	0.999998	+	0.00222844i	$0.000709335\pi$
$787$	14.0809	+	24.3888i	0.501929	+	0.869366i	−0.498069	+	0.867137i	$0.665957\pi$
$788$	−11.4332	−	19.8028i	−0.407290	−	0.705447i
$789$	4.38358	−	7.59258i	0.156060	−	0.270303i
$790$	−15.2247			−0.541670
$791$		0			0
$792$	−43.4786			−1.54494
$793$	−17.0259	+	29.4897i	−0.604607	+	1.04721i
$794$	31.2887	+	54.1936i	1.11039	+	1.92326i
$795$	3.51564	+	6.08926i	0.124687	+	0.215964i
$796$	21.2174	−	36.7496i	0.752030	−	1.30255i
$797$	9.60058			0.340070			0.170035	−	0.985438i	$-0.445612\pi$
$797$	9.60058			0.340070			0.170035	+	0.985438i	$0.445612\pi$
$798$		0			0
$799$	−32.0843			−1.13506
$800$	−11.8994	+	20.6103i	−0.420706	+	0.728684i
$801$	0.414214	+	0.717439i	0.0146355	+	0.0253495i
$802$	13.5405	+	23.4529i	0.478132	+	0.828149i
$803$	−23.5912	+	40.8611i	−0.832514	+	1.44196i
$804$	−17.0402			−0.600960
$805$		0			0
$806$	12.4853			0.439775
$807$	11.4173	−	19.7754i	0.401910	−	0.696128i
$808$	−20.1419	−	34.8867i	−0.708588	−	1.22731i
$809$	10.5166	+	18.2152i	0.369742	+	0.640413i	0.989525	−	0.144361i	$-0.0461126\pi$
$809$	10.5166	+	18.2152i	0.369742	+	0.640413i	−0.619783	+	0.784773i	$0.712779\pi$
$810$	−1.37456	+	2.38081i	−0.0482971	+	0.0836530i
$811$	0.770313			0.0270493			0.0135247	−	0.999909i	$-0.495695\pi$
$811$	0.770313			0.0270493			0.0135247	+	0.999909i	$0.495695\pi$
$812$		0			0
$813$	−10.6748			−0.374382
$814$	−13.2480	+	22.9462i	−0.464342	+	0.804265i
$815$	4.09069	+	7.08527i	0.143290	+	0.248186i
$816$	−39.0144	−	67.5749i	−1.36578	−	2.36560i
$817$	12.5080	−	21.6645i	0.437601	−	0.757947i
$818$	−40.3412			−1.41050
$819$		0			0
$820$	−32.0992			−1.12095
$821$	8.23911	−	14.2706i	0.287547	−	0.498046i	−0.685677	−	0.727906i	$-0.740494\pi$
$821$	8.23911	−	14.2706i	0.287547	−	0.498046i	0.973224	+	0.229860i	$0.0738269\pi$
$822$	−25.7739	−	44.6417i	−0.898968	−	1.55706i
$823$	8.02814	+	13.9051i	0.279843	+	0.484703i	0.971346	−	0.237671i	$-0.0763841\pi$
$823$	8.02814	+	13.9051i	0.279843	+	0.484703i	−0.691502	+	0.722374i	$0.743051\pi$
$824$	39.9433	−	69.1839i	1.39149	−	2.41013i
$825$	4.44549			0.154772
$826$		0			0
$827$	−1.11736			−0.0388545			−0.0194272	−	0.999811i	$-0.506184\pi$
$827$	−1.11736			−0.0388545			−0.0194272	+	0.999811i	$0.506184\pi$
$828$	12.1197	−	20.9920i	0.421190	−	0.729523i
$829$	26.2862	+	45.5290i	0.912958	+	1.58129i	0.809864	+	0.586617i	$0.199541\pi$
$829$	26.2862	+	45.5290i	0.912958	+	1.58129i	0.103094	+	0.994672i	$0.467126\pi$
$830$	9.85775	+	17.0741i	0.342167	+	0.592651i
$831$	−6.21803	+	10.7699i	−0.215701	+	0.373605i
$832$	122.550			4.24866
$833$		0			0
$834$	16.8976			0.585117
$835$	1.88118	−	3.25829i	0.0651008	−	0.112758i
$836$	33.9023	+	58.7204i	1.17253	+	2.03089i
$837$	0.627797	+	1.08738i	0.0216998	+	0.0375852i
$838$	13.6006	−	23.5569i	0.469824	−	0.813759i
$839$	8.65667			0.298861			0.149431	−	0.988772i	$-0.452256\pi$
$839$	8.65667			0.298861			0.149431	+	0.988772i	$0.452256\pi$
$840$		0			0
$841$	−28.5639			−0.984962
$842$	−48.7127	+	84.3729i	−1.67875	+	2.90768i
$843$	6.45844	+	11.1863i	0.222441	+	0.385278i
$844$	0.881549	+	1.52689i	0.0303442	+	0.0525577i
$845$	−0.0415597	+	0.0719835i	−0.00142970	+	0.00247631i
$846$	17.8288			0.612967
$847$		0			0
$848$	110.898			3.80826
$849$	12.8070	−	22.1823i	0.439533	−	0.761294i
$850$	6.80029	+	11.7784i	0.233248	+	0.403997i
$851$	−4.72792	−	8.18900i	−0.162071	−	0.280715i
$852$	0.770967	−	1.33535i	0.0264129	−	0.0457485i
$853$	−21.9361			−0.751078			−0.375539	−	0.926807i	$-0.622542\pi$
$853$	−21.9361			−0.751078			−0.375539	+	0.926807i	$0.622542\pi$
$854$		0			0
$855$	2.74441			0.0938567
$856$	41.7110	−	72.2455i	1.42565	−	2.46930i
$857$	−12.5626	−	21.7591i	−0.429132	−	0.743278i	0.567665	−	0.823260i	$-0.307847\pi$
$857$	−12.5626	−	21.7591i	−0.429132	−	0.743278i	−0.996796	+	0.0799821i	$0.974514\pi$
$858$	−22.1023	−	38.2824i	−0.754561	−	1.30694i
$859$	−4.04591	+	7.00773i	−0.138045	+	0.239101i	−0.926756	−	0.375663i	$-0.877415\pi$
$859$	−4.04591	+	7.00773i	−0.138045	+	0.239101i	0.788712	+	0.614763i	$0.210748\pi$
$860$	−50.6596			−1.72748
$861$		0			0
$862$	−45.8913			−1.56307
$863$	−11.5337	+	19.9769i	−0.392611	+	0.680022i	−0.992793	−	0.119841i	$-0.961761\pi$
$863$	−11.5337	+	19.9769i	−0.392611	+	0.680022i	0.600182	+	0.799863i	$0.295095\pi$
$864$	11.8994	+	20.6103i	0.404824	+	0.701176i
$865$	7.85304	+	13.6019i	0.267011	+	0.462477i
$866$	17.9191	−	31.0368i	0.608916	−	1.05467i
$867$	−7.47530			−0.253874
$868$		0			0
$869$	24.6192			0.835150
$870$	0.907737	−	1.57225i	0.0307752	−	0.0533041i
$871$	−5.54509	−	9.60438i	−0.187888	−	0.325432i
$872$	17.8827	+	30.9738i	0.605586	+	1.04891i
$873$	−3.10392	+	5.37615i	−0.105052	+	0.181955i
$874$	−32.9059			−1.11306
$875$		0			0
$876$	58.9863			1.99296
$877$	2.16175	−	3.74427i	0.0729972	−	0.126435i	−0.827216	−	0.561884i	$-0.810077\pi$
$877$	2.16175	−	3.74427i	0.0729972	−	0.126435i	0.900214	+	0.435449i	$0.143410\pi$
$878$	−31.2182	−	54.0715i	−1.05356	−	1.82483i
$879$	−0.841381	−	1.45731i	−0.0283791	−	0.0491540i
$880$	35.0574	−	60.7213i	1.18179	−	2.04691i
$881$	−19.9929			−0.673579			−0.336790	−	0.941580i	$-0.609341\pi$
$881$	−19.9929			−0.673579			−0.336790	+	0.941580i	$0.609341\pi$
$882$		0			0
$883$	1.89450			0.0637551			0.0318776	−	0.999492i	$-0.489851\pi$
$883$	1.89450			0.0637551			0.0318776	+	0.999492i	$0.489851\pi$
$884$	49.7257	−	86.1274i	1.67246	−	2.89678i
$885$	−6.91245	−	11.9727i	−0.232359	−	0.402458i
$886$	−11.3386	−	19.6390i	−0.380928	−	0.659787i
$887$	2.61263	−	4.52520i	0.0877234	−	0.151941i	−0.818825	−	0.574043i	$-0.805374\pi$
$887$	2.61263	−	4.52520i	0.0877234	−	0.151941i	0.906548	+	0.422102i	$0.138707\pi$
$888$	21.2043			0.711570
$889$		0			0
$890$	−2.27744			−0.0763401
$891$	2.22274	−	3.84990i	0.0744647	−	0.128977i
$892$	−80.7499	−	139.863i	−2.70371	−	4.68296i
$893$	−8.89912	−	15.4137i	−0.297798	−	0.515801i
$894$	27.8081	−	48.1651i	0.930043	−	1.61088i
$895$	−1.28097			−0.0428182
$896$		0			0
$897$	15.7757			0.526735
$898$	−33.7058	+	58.3801i	−1.12478	+	1.94817i
$899$	−0.414587	−	0.718086i	−0.0138273	−	0.0239495i
$900$	−2.77882	−	4.81306i	−0.0926275	−	0.160435i
$901$	17.3927	−	30.1251i	0.579436	−	1.00361i
$902$	70.5855			2.35024
$903$		0			0
$904$	123.316			4.10144
$905$	−8.27994	+	14.3413i	−0.275235	+	0.476720i
$906$	29.0145	+	50.2546i	0.963943	+	1.66960i
$907$	2.70960	+	4.69317i	0.0899709	+	0.155834i	0.907499	−	0.420055i	$-0.137989\pi$
$907$	2.70960	+	4.69317i	0.0899709	+	0.155834i	−0.817528	+	0.575889i	$0.804656\pi$
$908$	58.0523	−	100.550i	1.92653	−	3.33686i
$909$	4.11882			0.136613
$910$		0			0
$911$	0.226686			0.00751043			0.00375522	−	0.999993i	$-0.498805\pi$
$911$	0.226686			0.00751043			0.00375522	+	0.999993i	$0.498805\pi$
$912$	21.6426	−	37.4861i	0.716658	−	1.24129i
$913$	−15.9406	−	27.6099i	−0.527556	−	0.913753i
$914$	38.9644	+	67.4883i	1.28883	+	2.23231i
$915$	4.70711	−	8.15295i	0.155612	−	0.269528i
$916$	27.3933			0.905099
$917$		0			0
$918$	13.6006			0.448886
$919$	4.05312	−	7.02021i	0.133700	−	0.231575i	−0.791400	−	0.611299i	$-0.790647\pi$
$919$	4.05312	−	7.02021i	0.133700	−	0.231575i	0.925100	+	0.379723i	$0.123981\pi$
$920$	21.3284	+	36.9419i	0.703177	+	1.21794i
$921$	−3.65685	−	6.33386i	−0.120497	−	0.208708i
$922$	−52.7456	+	91.3580i	−1.73708	+	3.00872i
$923$	1.00353			0.0330316
$924$		0			0
$925$	−2.16804			−0.0712848
$926$	−3.27874	+	5.67895i	−0.107746	+	0.186622i
$927$	4.08402	+	7.07373i	0.134137	+	0.232332i
$928$	−7.85814	−	13.6107i	−0.257956	−	0.446793i
$929$	−1.14972	+	1.99138i	−0.0377212	+	0.0653351i	−0.884270	−	0.466977i	$-0.845343\pi$
$929$	−1.14972	+	1.99138i	−0.0377212	+	0.0653351i	0.846548	+	0.532312i	$0.178677\pi$
$930$	−3.45178			−0.113188
$931$		0			0
$932$	−6.07906			−0.199126
$933$	5.60097	−	9.70117i	0.183368	−	0.317602i
$934$	27.2271	+	47.1587i	0.890897	+	1.54308i
$935$	−10.9965	−	19.0464i	−0.359623	−	0.622885i
$936$	−17.6881	+	30.6367i	−0.578155	+	1.00139i
$937$	−16.1023			−0.526041			−0.263020	−	0.964790i	$-0.584719\pi$
$937$	−16.1023			−0.526041			−0.263020	+	0.964790i	$0.584719\pi$
$938$		0			0
$939$	31.4857			1.02750
$940$	−18.0215	+	31.2141i	−0.587795	+	1.01809i
$941$	−6.76235	−	11.7127i	−0.220446	−	0.381824i	0.734497	−	0.678612i	$-0.237418\pi$
$941$	−6.76235	−	11.7127i	−0.220446	−	0.381824i	−0.954944	+	0.296787i	$0.904085\pi$
$942$	2.69442	+	4.66687i	0.0877889	+	0.152055i
$943$	−12.5952	+	21.8155i	−0.410156	+	0.710412i
$944$	−218.048			−7.09687
$945$		0			0
$946$	111.400			3.62191
$947$	−3.42690	+	5.93557i	−0.111359	+	0.192880i	−0.916319	−	0.400450i	$-0.868854\pi$
$947$	−3.42690	+	5.93557i	−0.111359	+	0.192880i	0.804959	+	0.593330i	$0.202187\pi$
$948$	−15.3892	−	26.6549i	−0.499818	−	0.865711i
$949$	19.1949	+	33.2465i	0.623092	+	1.07923i
$950$	−3.77235	+	6.53390i	−0.122391	+	0.211988i
$951$	−8.45048			−0.274026
$952$		0			0
$953$	−44.9483			−1.45602			−0.728009	−	0.685568i	$-0.759554\pi$
$953$	−44.9483			−1.45602			−0.728009	+	0.685568i	$0.759554\pi$
$954$	−9.66490	+	16.7401i	−0.312913	+	0.541981i
$955$	−4.38136	−	7.58874i	−0.141778	−	0.245566i
$956$	−71.3395	−	123.564i	−2.30728	−	3.99633i
$957$	−1.46786	+	2.54242i	−0.0474493	+	0.0821846i
$958$	−9.45584			−0.305504
$959$		0			0
$960$	−33.8812			−1.09351
$961$	14.7117	−	25.4815i	0.474572	−	0.821983i
$962$	10.7792	+	18.6701i	0.347536	+	0.601949i
$963$	4.26475	+	7.38677i	0.137430	+	0.238035i
$964$	−68.7669	+	119.108i	−2.21483	+	3.83620i
$965$	26.4986			0.853020
$966$		0			0
$967$	12.4245			0.399546			0.199773	−	0.979842i	$-0.435979\pi$
$967$	12.4245			0.399546			0.199773	+	0.979842i	$0.435979\pi$
$968$	−42.8496	+	74.2177i	−1.37724	+	2.38545i
$969$	−6.78863	−	11.7583i	−0.218082	−	0.377730i
$970$	−8.53304	−	14.7797i	−0.273979	−	0.474546i
$971$	−10.4079	+	18.0271i	−0.334006	+	0.578516i	−0.983293	−	0.182028i	$-0.941734\pi$
$971$	−10.4079	+	18.0271i	−0.334006	+	0.578516i	0.649287	+	0.760543i	$0.275067\pi$
$972$	−5.55765			−0.178262
$973$		0			0
$974$	−19.5802			−0.627390
$975$	1.80853	−	3.13247i	0.0579193	−	0.100319i
$976$	−74.2412	−	128.590i	−2.37640	−	4.11605i
$977$	−21.3709	−	37.0155i	−0.683716	−	1.18423i	−0.973839	−	0.227241i	$-0.927029\pi$
$977$	−21.3709	−	37.0155i	−0.683716	−	1.18423i	0.290123	−	0.956989i	$-0.406304\pi$
$978$	−11.2458	+	19.4783i	−0.359600	+	0.622846i
$979$	3.68276			0.117702
$980$		0			0
$981$	−3.65685			−0.116754
$982$	43.5592	−	75.4468i	1.39003	−	2.40760i
$983$	−2.84491	−	4.92753i	−0.0907386	−	0.157164i	0.817084	−	0.576519i	$-0.195589\pi$
$983$	−2.84491	−	4.92753i	−0.0907386	−	0.157164i	−0.907822	+	0.419355i	$0.862256\pi$
$984$	−28.2442	−	48.9204i	−0.900392	−	1.55952i
$985$	−2.05720	+	3.56317i	−0.0655477	+	0.113532i
$986$	−8.98160			−0.286033
$987$		0			0
$988$	55.1690			1.75516
$989$	−19.8780	+	34.4297i	−0.632084	+	1.09480i
$990$	6.11058	+	10.5838i	0.194207	+	0.336377i
$991$	−29.5608	−	51.2008i	−0.939029	−	1.62645i	−0.767287	−	0.641304i	$-0.778394\pi$
$991$	−29.5608	−	51.2008i	−0.939029	−	1.62645i	−0.171743	−	0.985142i	$-0.554940\pi$
$992$	−14.9408	+	25.8782i	−0.474370	+	0.821632i
$993$	−16.6533			−0.528477
$994$		0			0
$995$	−7.63538			−0.242058
$996$	−19.9285	+	34.5172i	−0.631460	+	1.09372i
$997$	22.7647	+	39.4296i	0.720965	+	1.24875i	0.960614	+	0.277888i	$0.0896343\pi$
$997$	22.7647	+	39.4296i	0.720965	+	1.24875i	−0.239649	+	0.970860i	$0.577032\pi$
$998$	53.6116	+	92.8579i	1.69704	+	2.93937i
$999$	−1.08402	+	1.87758i	−0.0342969	+	0.0594040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.i.n.226.1		8
7.2	even	3		735.2.a.n.1.4	✓	4
7.3	odd	6		735.2.i.m.361.1		8
7.4	even	3	inner	735.2.i.n.361.1		8
7.5	odd	6		735.2.a.o.1.4	yes	4
7.6	odd	2		735.2.i.m.226.1		8
21.2	odd	6		2205.2.a.bf.1.1		4
21.5	even	6		2205.2.a.bg.1.1		4
35.9	even	6		3675.2.a.bl.1.1		4
35.19	odd	6		3675.2.a.bk.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.a.n.1.4	✓	4	7.2	even	3
735.2.a.o.1.4	yes	4	7.5	odd	6
735.2.i.m.226.1		8	7.6	odd	2
735.2.i.m.361.1		8	7.3	odd	6
735.2.i.n.226.1		8	1.1	even	1	trivial
735.2.i.n.361.1		8	7.4	even	3	inner
2205.2.a.bf.1.1		4	21.2	odd	6
2205.2.a.bg.1.1		4	21.5	even	6
3675.2.a.bk.1.1		4	35.19	odd	6
3675.2.a.bl.1.1		4	35.9	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.37456 + 2.38081i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.77882 - 4.81306i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.74912 q^{6} +9.78039 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.37456 - 2.38081i) q^{10} +(2.22274 + 3.84990i) q^{11} +(2.77882 - 4.81306i) q^{12} +3.61706 q^{13} -1.00000 q^{15} +(-7.88607 + 13.6591i) q^{16} +(2.47363 + 4.28445i) q^{17} +(-1.37456 - 2.38081i) q^{18} +(-1.37220 + 2.37672i) q^{19} +5.55765 q^{20} -12.2212 q^{22} +(2.18073 - 3.77714i) q^{23} +(4.89020 + 8.47007i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-4.97186 + 8.61152i) q^{26} -1.00000 q^{27} +0.660384 q^{29} +(1.37456 - 2.38081i) q^{30} +(-0.627797 - 1.08738i) q^{31} +(-11.8994 - 20.6103i) q^{32} +(-2.22274 + 3.84990i) q^{33} -13.6006 q^{34} +5.55765 q^{36} +(1.08402 - 1.87758i) q^{37} +(-3.77235 - 6.53390i) q^{38} +(1.80853 + 3.13247i) q^{39} +(-4.89020 + 8.47007i) q^{40} -5.77568 q^{41} -9.11529 q^{43} +(12.3532 - 21.3964i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(5.99509 + 10.3838i) q^{46} +(-3.24264 + 5.61642i) q^{47} -15.7721 q^{48} +2.74912 q^{50} +(-2.47363 + 4.28445i) q^{51} +(-10.0512 - 17.4091i) q^{52} +(-3.51564 - 6.08926i) q^{53} +(1.37456 - 2.38081i) q^{54} -4.44549 q^{55} -2.74441 q^{57} +(-0.907737 + 1.57225i) q^{58} +(6.91245 + 11.9727i) q^{59} +(2.77882 + 4.81306i) q^{60} +(-4.70711 + 8.15295i) q^{61} +3.45178 q^{62} +33.8812 q^{64} +(-1.80853 + 3.13247i) q^{65} +(-6.11058 - 10.5838i) q^{66} +(-1.53304 - 2.65530i) q^{67} +(13.7475 - 23.8114i) q^{68} +4.36147 q^{69} +0.277444 q^{71} +(-4.89020 + 8.47007i) q^{72} +(5.30676 + 9.19159i) q^{73} +(2.98010 + 5.16169i) q^{74} +(0.500000 - 0.866025i) q^{75} +15.2524 q^{76} -9.94372 q^{78} +(2.76901 - 4.79607i) q^{79} +(-7.88607 - 13.6591i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.93901 - 13.7508i) q^{82} -7.17157 q^{83} -4.94725 q^{85} +(12.5295 - 21.7017i) q^{86} +(0.330192 + 0.571909i) q^{87} +(21.7393 + 37.6536i) q^{88} +(0.414214 - 0.717439i) q^{89} +2.74912 q^{90} -24.2395 q^{92} +(0.627797 - 1.08738i) q^{93} +(-8.91440 - 15.4402i) q^{94} +(-1.37220 - 2.37672i) q^{95} +(11.8994 - 20.6103i) q^{96} +6.20784 q^{97} -4.44549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} - 4 q^{9} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 8 q^{15} - 12 q^{16} + 8 q^{17} - 4 q^{18} - 8 q^{19} + 16 q^{20} + 12 q^{24} - 4 q^{25} - 8 q^{27}+ \cdots + 16 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 - 4 * q^9 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 8 * q^15 - 12 * q^16 + 8 * q^17 - 4 * q^18 - 8 * q^19 + 16 * q^20 + 12 * q^24 - 4 * q^25 - 8 * q^27 + 16 * q^29 + 4 * q^30 - 8 * q^31 - 28 * q^32 + 8 * q^33 + 16 * q^34 + 16 * q^36 - 8 * q^37 + 4 * q^38 - 12 * q^40 - 16 * q^43 + 16 * q^44 - 4 * q^45 - 12 * q^46 + 8 * q^47 - 24 * q^48 + 8 * q^50 - 8 * q^51 - 32 * q^52 - 8 * q^53 + 4 * q^54 + 16 * q^55 - 16 * q^57 + 24 * q^58 + 16 * q^59 + 8 * q^60 - 32 * q^61 + 40 * q^62 + 48 * q^64 + 24 * q^68 - 16 * q^71 - 12 * q^72 + 32 * q^74 + 4 * q^75 - 16 * q^76 - 12 * q^80 - 4 * q^81 - 8 * q^82 - 80 * q^83 - 16 * q^85 + 32 * q^86 + 8 * q^87 + 40 * q^88 - 8 * q^89 + 8 * q^90 - 16 * q^92 + 8 * q^93 - 16 * q^94 - 8 * q^95 + 28 * q^96 + 16 * q^99

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