LMFDB - Embedded newform 630.2.bv.c.523.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(73,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("630.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bv (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			523.2
Root			$0.144868 + 1.25092i$ of defining polynomial
Character	$\chi$	$=$	630.523
Dual form			630.2.bv.c.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.82591 + 1.29076i) q^{5} +(-1.90155 - 1.83959i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.82591 + 1.29076i) q^{5} +(-1.90155 - 1.83959i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.774197 - 2.09777i) q^{10} +(-2.01999 - 3.49872i) q^{11} +(-0.204875 + 0.204875i) q^{13} +(-1.28475 + 2.31288i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.527924 - 1.97024i) q^{17} +(3.10166 - 5.37224i) q^{19} +(-2.22666 - 0.204875i) q^{20} +(-2.85669 + 2.85669i) q^{22} +(4.38350 - 1.17456i) q^{23} +(1.66789 + 4.71361i) q^{25} +(0.250919 + 0.144868i) q^{26} +(2.56659 + 0.642357i) q^{28} -7.15869i q^{29} +(6.33287 - 3.65628i) q^{31} +(-0.965926 - 0.258819i) q^{32} -2.03974 q^{34} +(-1.09759 - 5.81337i) q^{35} +(1.19723 + 4.46814i) q^{37} +(-5.99195 - 1.60554i) q^{38} +(0.378409 + 2.20382i) q^{40} -2.58745i q^{41} +(-4.97801 - 4.97801i) q^{43} +(3.49872 + 2.01999i) q^{44} +(-2.26907 - 3.93014i) q^{46} +(0.304388 - 0.0815604i) q^{47} +(0.231803 + 6.99616i) q^{49} +(4.12132 - 2.83103i) q^{50} +(0.0749894 - 0.279864i) q^{52} +(-2.14370 + 8.00039i) q^{53} +(0.827689 - 8.99566i) q^{55} +(-0.0438127 - 2.64539i) q^{56} +(-6.91477 + 1.85281i) q^{58} +(0.427702 + 0.740802i) q^{59} +(-5.99356 - 3.46038i) q^{61} +(-5.17076 - 5.17076i) q^{62} +1.00000i q^{64} +(-0.638527 + 0.109639i) q^{65} +(3.05106 + 0.817530i) q^{67} +(0.527924 + 1.97024i) q^{68} +(-5.33121 + 2.56480i) q^{70} -7.12240 q^{71} +(-11.1331 - 2.98311i) q^{73} +(4.00603 - 2.31288i) q^{74} +6.20333i q^{76} +(-2.59511 + 10.3690i) q^{77} +(4.39618 + 2.53813i) q^{79} +(2.03078 - 0.935904i) q^{80} +(-2.49929 + 0.669683i) q^{82} +(-3.85372 + 3.85372i) q^{83} +(3.50704 - 2.91605i) q^{85} +(-3.51999 + 6.09680i) q^{86} +(1.04562 - 3.90231i) q^{88} +(-1.53615 + 2.66069i) q^{89} +(0.766467 - 0.0126942i) q^{91} +(-3.20895 + 3.20895i) q^{92} +(-0.157563 - 0.272906i) q^{94} +(12.5976 - 5.80572i) q^{95} +(6.63103 + 6.63103i) q^{97} +(6.69778 - 2.03464i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 + 8 * q^7	$ 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47} + 32 q^{50} + 28 q^{53} + 4 q^{56} - 32 q^{58} - 12 q^{61} + 8 q^{65} + 32 q^{67} + 36 q^{68} - 12 q^{70} - 16 q^{71} - 12 q^{73} - 16 q^{77} + 12 q^{80} - 48 q^{82} + 24 q^{85} - 12 q^{86} - 4 q^{88} - 16 q^{91} - 8 q^{92} - 20 q^{95} - 40 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.82591	+	1.29076i	0.816571	+	0.577245i
$5$	1.82591	+	1.29076i	0.816571	+	0.577245i
$6$		0			0
$7$	−1.90155	−	1.83959i	−0.718719	−	0.695300i
$7$	−1.90155	−	1.83959i	−0.718719	−	0.695300i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	0.774197	−	2.09777i	0.244822	−	0.663372i
$11$	−2.01999	−	3.49872i	−0.609049	−	1.05490i	−0.991397	−	0.130886i	$-0.958218\pi$
$11$	−2.01999	−	3.49872i	−0.609049	−	1.05490i	0.382349	−	0.924018i	$-0.375115\pi$
$12$		0			0
$13$	−0.204875	+	0.204875i	−0.0568221	+	0.0568221i	−0.734947	−	0.678125i	$-0.762793\pi$
$13$	−0.204875	+	0.204875i	−0.0568221	+	0.0568221i	0.678125	+	0.734947i	$0.262793\pi$
$14$	−1.28475	+	2.31288i	−0.343364	+	0.618143i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.527924	−	1.97024i	0.128040	−	0.477853i	−0.871890	−	0.489703i	$-0.837105\pi$
$17$	0.527924	−	1.97024i	0.128040	−	0.477853i	0.999930	+	0.0118498i	$0.00377201\pi$
$18$		0			0
$19$	3.10166	−	5.37224i	0.711571	−	1.23248i	−0.252697	−	0.967545i	$-0.581318\pi$
$19$	3.10166	−	5.37224i	0.711571	−	1.23248i	0.964267	−	0.264931i	$-0.0853491\pi$
$20$	−2.22666	−	0.204875i	−0.497897	−	0.0458114i
$21$		0			0
$22$	−2.85669	+	2.85669i	−0.609049	+	0.609049i
$23$	4.38350	−	1.17456i	0.914023	−	0.244912i	0.228994	−	0.973428i	$-0.426456\pi$
$23$	4.38350	−	1.17456i	0.914023	−	0.244912i	0.685029	+	0.728516i	$0.259790\pi$
$24$		0			0
$25$	1.66789	+	4.71361i	0.333577	+	0.942723i
$26$	0.250919	+	0.144868i	0.0492094	+	0.0284110i
$27$		0			0
$28$	2.56659	+	0.642357i	0.485040	+	0.121394i
$29$		−	7.15869i		−	1.32934i	−0.747139	−	0.664668i	$-0.768573\pi$
$29$		−	7.15869i		−	1.32934i	0.747139	−	0.664668i	$-0.231427\pi$
$30$		0			0
$31$	6.33287	−	3.65628i	1.13742	−	0.656688i	0.191627	−	0.981468i	$-0.438624\pi$
$31$	6.33287	−	3.65628i	1.13742	−	0.656688i	0.945790	+	0.324780i	$0.105290\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		0			0
$34$	−2.03974			−0.349813
$35$	−1.09759	−	5.81337i	−0.185527	−	0.982639i
$36$		0			0
$37$	1.19723	+	4.46814i	0.196824	+	0.734558i	0.991787	+	0.127900i	$0.0408236\pi$
$37$	1.19723	+	4.46814i	0.196824	+	0.734558i	−0.794963	+	0.606658i	$0.792510\pi$
$38$	−5.99195	−	1.60554i	−0.972023	−	0.260453i
$39$		0			0
$40$	0.378409	+	2.20382i	0.0598317	+	0.348454i
$41$		−	2.58745i		−	0.404093i	−0.979376	−	0.202046i	$-0.935241\pi$
$41$		−	2.58745i		−	0.404093i	0.979376	−	0.202046i	$-0.0647591\pi$
$42$		0			0
$43$	−4.97801	−	4.97801i	−0.759140	−	0.759140i	0.217026	−	0.976166i	$-0.430364\pi$
$43$	−4.97801	−	4.97801i	−0.759140	−	0.759140i	−0.976166	+	0.217026i	$0.930364\pi$
$44$	3.49872	+	2.01999i	0.527452	+	0.304524i
$45$		0			0
$46$	−2.26907	−	3.93014i	−0.334556	−	0.579468i
$47$	0.304388	−	0.0815604i	0.0443995	−	0.0118968i	−0.236551	−	0.971619i	$-0.576017\pi$
$47$	0.304388	−	0.0815604i	0.0443995	−	0.0118968i	0.280950	+	0.959722i	$0.409350\pi$
$48$		0			0
$49$	0.231803	+	6.99616i	0.0331148	+	0.999452i
$50$	4.12132	−	2.83103i	0.582843	−	0.400368i
$51$		0			0
$52$	0.0749894	−	0.279864i	0.0103992	−	0.0388102i
$53$	−2.14370	+	8.00039i	−0.294460	+	1.09894i	0.647186	+	0.762332i	$0.275946\pi$
$53$	−2.14370	+	8.00039i	−0.294460	+	1.09894i	−0.941646	+	0.336606i	$0.890721\pi$
$54$		0			0
$55$	0.827689	−	8.99566i	0.111606	−	1.21297i
$56$	−0.0438127	−	2.64539i	−0.00585472	−	0.353505i
$57$		0			0
$58$	−6.91477	+	1.85281i	−0.907953	+	0.243285i
$59$	0.427702	+	0.740802i	0.0556821	+	0.0964442i	0.892523	−	0.451002i	$-0.148933\pi$
$59$	0.427702	+	0.740802i	0.0556821	+	0.0964442i	−0.836841	+	0.547446i	$0.815600\pi$
$60$		0			0
$61$	−5.99356	−	3.46038i	−0.767397	−	0.443057i	0.0645484	−	0.997915i	$-0.479439\pi$
$61$	−5.99356	−	3.46038i	−0.767397	−	0.443057i	−0.831945	+	0.554858i	$0.812773\pi$
$62$	−5.17076	−	5.17076i	−0.656688	−	0.656688i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.638527	+	0.109639i	−0.0791995	+	0.0135990i
$66$		0			0
$67$	3.05106	+	0.817530i	0.372747	+	0.0998772i	0.440329	−	0.897837i	$-0.354862\pi$
$67$	3.05106	+	0.817530i	0.372747	+	0.0998772i	−0.0675822	+	0.997714i	$0.521528\pi$
$68$	0.527924	+	1.97024i	0.0640201	+	0.238926i
$69$		0			0
$70$	−5.33121	+	2.56480i	−0.637201	+	0.306553i
$71$	−7.12240			−0.845273			−0.422637	−	0.906299i	$-0.638895\pi$
$71$	−7.12240			−0.845273			−0.422637	+	0.906299i	$0.638895\pi$
$72$		0			0
$73$	−11.1331	−	2.98311i	−1.30303	−	0.349147i	−0.460438	−	0.887692i	$-0.652307\pi$
$73$	−11.1331	−	2.98311i	−1.30303	−	0.349147i	−0.842597	+	0.538545i	$0.818974\pi$
$74$	4.00603	−	2.31288i	0.465691	−	0.268867i
$75$		0			0
$76$			6.20333i			0.711571i
$77$	−2.59511	+	10.3690i	−0.295740	+	1.18165i
$78$		0			0
$79$	4.39618	+	2.53813i	0.494609	+	0.285562i	0.726484	−	0.687183i	$-0.241153\pi$
$79$	4.39618	+	2.53813i	0.494609	+	0.285562i	−0.231876	+	0.972745i	$0.574486\pi$
$80$	2.03078	−	0.935904i	0.227049	−	0.104637i
$81$		0			0
$82$	−2.49929	+	0.669683i	−0.276000	+	0.0739541i
$83$	−3.85372	+	3.85372i	−0.423001	+	0.423001i	−0.886236	−	0.463235i	$-0.846689\pi$
$83$	−3.85372	+	3.85372i	−0.423001	+	0.423001i	0.463235	+	0.886236i	$0.346689\pi$
$84$		0			0
$85$	3.50704	−	2.91605i	0.380392	−	0.316290i
$86$	−3.51999	+	6.09680i	−0.379570	+	0.657434i
$87$		0			0
$88$	1.04562	−	3.90231i	0.111464	−	0.415988i
$89$	−1.53615	+	2.66069i	−0.162832	+	0.282033i	−0.935883	−	0.352310i	$-0.885396\pi$
$89$	−1.53615	+	2.66069i	−0.162832	+	0.282033i	0.773051	+	0.634343i	$0.218729\pi$
$90$		0			0
$91$	0.766467	−	0.0126942i	0.0803475	−	0.00133071i
$92$	−3.20895	+	3.20895i	−0.334556	+	0.334556i
$93$		0			0
$94$	−0.157563	−	0.272906i	−0.0162513	−	0.0281481i
$95$	12.5976	−	5.80572i	1.29249	−	0.595655i
$96$		0			0
$97$	6.63103	+	6.63103i	0.673279	+	0.673279i	0.958471	−	0.285191i	$-0.0920572\pi$
$97$	6.63103	+	6.63103i	0.673279	+	0.673279i	−0.285191	+	0.958471i	$0.592057\pi$
$98$	6.69778	−	2.03464i	0.676578	−	0.205530i
$99$		0			0
$100$	−3.80124	−	3.24817i	−0.380124	−	0.324817i
$101$	8.56364	−	4.94422i	0.852114	−	0.491968i	−0.00924966	−	0.999957i	$-0.502944\pi$
$101$	8.56364	−	4.94422i	0.852114	−	0.491968i	0.861364	+	0.507989i	$0.169611\pi$
$102$		0			0
$103$	1.10827	+	4.13612i	0.109201	+	0.407544i	0.998788	−	0.0492221i	$-0.0156742\pi$
$103$	1.10827	+	4.13612i	0.109201	+	0.407544i	−0.889587	+	0.456766i	$0.849008\pi$
$104$	−0.289737			−0.0284110
$105$		0			0
$106$	8.28261			0.804479
$107$	3.84918	+	14.3653i	0.372114	+	1.38875i	0.857516	+	0.514457i	$0.172007\pi$
$107$	3.84918	+	14.3653i	0.372114	+	1.38875i	−0.485402	+	0.874291i	$0.661327\pi$
$108$		0			0
$109$	11.4586	−	6.61564i	1.09754	−	0.633664i	0.161964	−	0.986797i	$-0.448217\pi$
$109$	11.4586	−	6.61564i	1.09754	−	0.633664i	0.935573	+	0.353133i	$0.114884\pi$
$110$	−8.90336	+	1.52876i	−0.848902	+	0.145762i
$111$		0			0
$112$	−2.54391	+	0.726997i	−0.240377	+	0.0686947i
$113$	−9.75336	−	9.75336i	−0.917519	−	0.917519i	0.0793296	−	0.996848i	$-0.474722\pi$
$113$	−9.75336	−	9.75336i	−0.917519	−	0.917519i	−0.996848	+	0.0793296i	$0.974722\pi$
$114$		0			0
$115$	9.51994	+	3.51341i	0.887739	+	0.327627i
$116$	3.57935	+	6.19961i	0.332334	+	0.575619i
$117$		0			0
$118$	0.604862	−	0.604862i	0.0556821	−	0.0556821i
$119$	−4.62831	+	2.77535i	−0.424276	+	0.254416i
$120$		0			0
$121$	−2.66069	+	4.60846i	−0.241881	+	0.418951i
$122$	−1.79123	+	6.68495i	−0.162170	+	0.605227i
$123$		0			0
$124$	−3.65628	+	6.33287i	−0.328344	+	0.568708i
$125$	−3.03873	+	10.7595i	−0.271792	+	0.962356i
$126$		0			0
$127$	−2.19984	+	2.19984i	−0.195204	+	0.195204i	−0.797940	−	0.602736i	$-0.794077\pi$
$127$	−2.19984	+	2.19984i	−0.195204	+	0.195204i	0.602736	+	0.797940i	$0.294077\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	0.271166	+	0.588393i	0.0237828	+	0.0516055i
$131$	6.32091	+	3.64938i	0.552260	+	0.318848i	0.750033	−	0.661400i	$-0.230037\pi$
$131$	6.32091	+	3.64938i	0.552260	+	0.318848i	−0.197773	+	0.980248i	$0.563371\pi$
$132$		0			0
$133$	−15.7807	+	4.50980i	−1.36836	+	0.391049i
$134$		−	3.15869i		−	0.272870i
$135$		0			0
$136$	1.76647	−	1.01987i	0.151473	−	0.0874531i
$137$	6.93431	+	1.85804i	0.592438	+	0.158743i	0.542567	−	0.840012i	$-0.317452\pi$
$137$	6.93431	+	1.85804i	0.592438	+	0.158743i	0.0498710	+	0.998756i	$0.484119\pi$
$138$		0			0
$139$	−12.4172			−1.05321			−0.526605	−	0.850110i	$-0.676535\pi$
$139$	−12.4172			−1.05321			−0.526605	+	0.850110i	$0.676535\pi$
$140$	3.85723	+	4.48573i	0.325995	+	0.379113i
$141$		0			0
$142$	1.84341	+	6.87971i	0.154696	+	0.577332i
$143$	1.13064	+	0.302955i	0.0945492	+	0.0253344i
$144$		0			0
$145$	9.24014	−	13.0711i	0.767352	−	1.08550i
$146$			11.5259i			0.953887i
$147$		0			0
$148$	−3.27091	−	3.27091i	−0.268867	−	0.268867i
$149$	20.7399	+	11.9742i	1.69908	+	0.980963i	0.946637	+	0.322302i	$0.104457\pi$
$149$	20.7399	+	11.9742i	1.69908	+	0.980963i	0.752440	+	0.658661i	$0.228877\pi$
$150$		0			0
$151$	1.77167	+	3.06862i	0.144176	+	0.249721i	0.929065	−	0.369916i	$-0.120613\pi$
$151$	1.77167	+	3.06862i	0.144176	+	0.249721i	−0.784889	+	0.619636i	$0.787280\pi$
$152$	5.99195	−	1.60554i	0.486012	−	0.130226i
$153$		0			0
$154$	10.6873	−	0.177002i	0.861207	−	0.0142632i
$155$	16.2826	+	1.49816i	1.30785	+	0.120335i
$156$		0			0
$157$	−1.58462	+	5.91389i	−0.126467	+	0.471980i	−0.999888	−	0.0149859i	$-0.995230\pi$
$157$	−1.58462	+	5.91389i	−0.126467	+	0.471980i	0.873421	+	0.486966i	$0.161896\pi$
$158$	1.31384	−	4.90330i	0.104523	−	0.390086i
$159$		0			0
$160$	−1.42962	−	1.71936i	−0.113021	−	0.135927i
$161$	−10.4962	−	5.83037i	−0.827213	−	0.459498i
$162$		0			0
$163$	15.9937	−	4.28549i	1.25272	−	0.335666i	0.429334	−	0.903146i	$-0.358748\pi$
$163$	15.9937	−	4.28549i	1.25272	−	0.335666i	0.823387	+	0.567480i	$0.192082\pi$
$164$	1.29373	+	2.24080i	0.101023	+	0.174977i
$165$		0			0
$166$	4.71983	+	2.72499i	0.366329	+	0.211500i
$167$	−10.2873	−	10.2873i	−0.796056	−	0.796056i	0.186415	−	0.982471i	$-0.440313\pi$
$167$	−10.2873	−	10.2873i	−0.796056	−	0.796056i	−0.982471	+	0.186415i	$0.940313\pi$
$168$		0			0
$169$			12.9161i			0.993543i
$170$	−3.72438	−	2.63281i	−0.285647	−	0.201927i
$171$		0			0
$172$	6.80009	+	1.82208i	0.518502	+	0.138932i
$173$	−2.01155	−	7.50720i	−0.152935	−	0.570762i	−0.999273	−	0.0381159i	$-0.987864\pi$
$173$	−2.01155	−	7.50720i	−0.152935	−	0.570762i	0.846338	−	0.532646i	$-0.178802\pi$
$174$		0			0
$175$	5.49955	−	12.0314i	0.415727	−	0.909489i
$176$	−4.03997			−0.304524
$177$		0			0
$178$	2.96762	+	0.795171i	0.222432	+	0.0596006i
$179$	3.34695	−	1.93236i	0.250163	−	0.144431i	−0.369676	−	0.929161i	$-0.620531\pi$
$179$	3.34695	−	1.93236i	0.250163	−	0.144431i	0.619839	+	0.784729i	$0.287198\pi$
$180$		0			0
$181$		−	6.99107i		−	0.519642i	−0.965657	−	0.259821i	$-0.916336\pi$
$181$		−	6.99107i		−	0.519642i	0.965657	−	0.259821i	$-0.0836636\pi$
$182$	−0.210638	−	0.737064i	−0.0156135	−	0.0546348i
$183$		0			0
$184$	3.93014	+	2.26907i	0.289734	+	0.167278i
$185$	−3.58125	+	9.70376i	−0.263299	+	0.713435i
$186$		0			0
$187$	−7.95971	+	2.13280i	−0.582071	+	0.155966i
$188$	−0.222827	+	0.222827i	−0.0162513	+	0.0162513i
$189$		0			0
$190$	−8.86840	−	10.6657i	−0.643381	−	0.773774i
$191$	2.23721	−	3.87496i	0.161879	−	0.280383i	−0.773664	−	0.633597i	$-0.781578\pi$
$191$	2.23721	−	3.87496i	0.161879	−	0.280383i	0.935543	+	0.353214i	$0.114911\pi$
$192$		0			0
$193$	−5.19573	+	19.3907i	−0.373997	+	1.39577i	0.480809	+	0.876825i	$0.340343\pi$
$193$	−5.19573	+	19.3907i	−0.373997	+	1.39577i	−0.854805	+	0.518949i	$0.826324\pi$
$194$	4.68885	−	8.12132i	0.336640	−	0.583077i
$195$		0			0
$196$	−3.69883	−	5.94295i	−0.264202	−	0.424497i
$197$	7.84901	−	7.84901i	0.559219	−	0.559219i	−0.369866	−	0.929085i	$-0.620596\pi$
$197$	7.84901	−	7.84901i	0.559219	−	0.559219i	0.929085	+	0.369866i	$0.120596\pi$
$198$		0			0
$199$	5.40103	+	9.35485i	0.382869	+	0.663148i	0.991471	−	0.130327i	$-0.0416028\pi$
$199$	5.40103	+	9.35485i	0.382869	+	0.663148i	−0.608602	+	0.793475i	$0.708270\pi$
$200$	−2.15365	+	4.51240i	−0.152286	+	0.319075i
$201$		0			0
$202$	−6.99218	−	6.99218i	−0.491968	−	0.491968i
$203$	−13.1691	+	13.6126i	−0.924288	+	0.955419i
$204$		0			0
$205$	3.33978	−	4.72446i	0.233260	−	0.329970i
$206$	3.70835	−	2.14101i	0.258373	−	0.149172i
$207$		0			0
$208$	0.0749894	+	0.279864i	0.00519958	+	0.0194051i
$209$	−25.0613			−1.73353
$210$		0			0
$211$	7.56555			0.520834			0.260417	−	0.965496i	$-0.416140\pi$
$211$	7.56555			0.520834			0.260417	+	0.965496i	$0.416140\pi$
$212$	−2.14370	−	8.00039i	−0.147230	−	0.549469i
$213$		0			0
$214$	12.8796	−	7.43604i	0.880431	−	0.508317i
$215$	−2.66399	−	15.5148i	−0.181682	−	1.05810i
$216$		0			0
$217$	−18.7683	−	4.69728i	−1.27408	−	0.318872i
$218$	−9.35593	−	9.35593i	−0.633664	−	0.633664i
$219$		0			0
$220$	3.78103	+	8.20431i	0.254917	+	0.553135i
$221$	0.295494	+	0.511811i	0.0198771	+	0.0344281i
$222$		0			0
$223$	−9.35230	+	9.35230i	−0.626277	+	0.626277i	−0.947129	−	0.320853i	$-0.896031\pi$
$223$	−9.35230	+	9.35230i	−0.626277	+	0.626277i	0.320853	+	0.947129i	$0.396031\pi$
$224$	1.36064	+	2.26907i	0.0909114	+	0.151608i
$225$		0			0
$226$	−6.89667	+	11.9454i	−0.458759	+	0.794595i
$227$	−4.19127	+	15.6420i	−0.278184	+	1.03820i	0.675493	+	0.737367i	$0.263931\pi$
$227$	−4.19127	+	15.6420i	−0.278184	+	1.03820i	−0.953677	+	0.300832i	$0.902736\pi$
$228$		0			0
$229$	−5.88820	+	10.1987i	−0.389103	+	0.673947i	−0.992329	−	0.123624i	$-0.960548\pi$
$229$	−5.88820	+	10.1987i	−0.389103	+	0.673947i	0.603226	+	0.797570i	$0.293882\pi$
$230$	0.929750	−	10.1049i	0.0613059	−	0.666297i
$231$		0			0
$232$	5.06196	−	5.06196i	0.332334	−	0.332334i
$233$	−5.52920	+	1.48154i	−0.362230	+	0.0970591i	−0.435343	−	0.900264i	$-0.643373\pi$
$233$	−5.52920	+	1.48154i	−0.362230	+	0.0970591i	0.0731138	+	0.997324i	$0.476706\pi$
$234$		0			0
$235$	0.661059	+	0.243969i	0.0431227	+	0.0159148i
$236$	−0.740802	−	0.427702i	−0.0482221	−	0.0278410i
$237$		0			0
$238$	3.87867	+	3.75229i	0.251417	+	0.243225i
$239$			8.33794i			0.539337i	0.962953	+	0.269668i	$0.0869141\pi$
$239$			8.33794i			0.539337i	−0.962953	+	0.269668i	$0.913086\pi$
$240$		0			0
$241$	2.56723	−	1.48219i	0.165370	−	0.0954763i	−0.415031	−	0.909807i	$-0.636229\pi$
$241$	2.56723	−	1.48219i	0.165370	−	0.0954763i	0.580401	+	0.814331i	$0.302896\pi$
$242$	5.14006	+	1.37728i	0.330416	+	0.0885347i
$243$		0			0
$244$	6.92077			0.443057
$245$	−8.60710	+	13.0736i	−0.549887	+	0.835239i
$246$		0			0
$247$	0.465184	+	1.73609i	0.0295989	+	0.110465i
$248$	7.06340	+	1.89263i	0.448526	+	0.120182i
$249$		0			0
$250$	11.1793	+	0.150429i	0.707043	+	0.00951396i
$251$		−	16.1800i		−	1.02127i	−0.859796	−	0.510637i	$-0.829410\pi$
$251$		−	16.1800i		−	1.02127i	0.859796	−	0.510637i	$-0.170590\pi$
$252$		0			0
$253$	−12.9641	−	12.9641i	−0.815043	−	0.815043i
$254$	2.69424	+	1.55552i	0.169052	+	0.0976020i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.62621	−	1.50754i	0.350954	−	0.0940377i	−0.0790355	−	0.996872i	$-0.525184\pi$
$257$	5.62621	−	1.50754i	0.350954	−	0.0940377i	0.429989	+	0.902834i	$0.358517\pi$
$258$		0			0
$259$	5.94295	−	10.6988i	0.369277	−	0.664793i
$260$	0.498161	−	0.414214i	0.0308946	−	0.0256884i
$261$		0			0
$262$	1.88906	−	7.05006i	0.116706	−	0.435554i
$263$	−0.449601	+	1.67793i	−0.0277236	+	0.103466i	−0.978401	−	0.206715i	$-0.933723\pi$
$263$	−0.449601	+	1.67793i	−0.0277236	+	0.103466i	0.950678	+	0.310180i	$0.100389\pi$
$264$		0			0
$265$	−14.2408	+	11.8410i	−0.874803	+	0.727386i
$266$	8.44048	+	14.0758i	0.517519	+	0.863041i
$267$		0			0
$268$	−3.05106	+	0.817530i	−0.186373	+	0.0499386i
$269$	−1.89169	−	3.27650i	−0.115338	−	0.199772i	0.802577	−	0.596549i	$-0.203462\pi$
$269$	−1.89169	−	3.27650i	−0.115338	−	0.199772i	−0.917915	+	0.396777i	$0.870128\pi$
$270$		0			0
$271$	−18.4029	−	10.6249i	−1.11789	−	0.645416i	−0.177032	−	0.984205i	$-0.556649\pi$
$271$	−18.4029	−	10.6249i	−1.11789	−	0.645416i	−0.940862	+	0.338789i	$0.889983\pi$
$272$	−1.44231	−	1.44231i	−0.0874531	−	0.0874531i
$273$		0			0
$274$		−	7.17893i		−	0.433695i
$275$	13.1225	−	15.3569i	0.791317	−	0.926056i
$276$		0			0
$277$	4.72353	+	1.26567i	0.283810	+	0.0760465i	0.397916	−	0.917422i	$-0.369734\pi$
$277$	4.72353	+	1.26567i	0.283810	+	0.0760465i	−0.114106	+	0.993469i	$0.536400\pi$
$278$	3.21380	+	11.9941i	0.192751	+	0.719356i
$279$		0			0
$280$	3.33456	−	4.88679i	0.199278	−	0.292042i
$281$	29.4776			1.75849			0.879243	−	0.476373i	$-0.158049\pi$
$281$	29.4776			1.75849			0.879243	+	0.476373i	$0.158049\pi$
$282$		0			0
$283$	−10.8991	−	2.92041i	−0.647886	−	0.173601i	−0.0801133	−	0.996786i	$-0.525528\pi$
$283$	−10.8991	−	2.92041i	−0.647886	−	0.173601i	−0.567773	+	0.823185i	$0.692195\pi$
$284$	6.16818	−	3.56120i	0.366014	−	0.211318i
$285$		0			0
$286$		−	1.17053i		−	0.0692148i
$287$	−4.75986	+	4.92018i	−0.280966	+	0.290429i
$288$		0			0
$289$	11.1193	+	6.41973i	0.654076	+	0.377631i
$290$	−15.0173	−	5.54224i	−0.881844	−	0.325451i
$291$		0			0
$292$	11.1331	−	2.98311i	0.651517	−	0.174573i
$293$	−7.23407	+	7.23407i	−0.422619	+	0.422619i	−0.886105	−	0.463485i	$-0.846599\pi$
$293$	−7.23407	+	7.23407i	−0.422619	+	0.422619i	0.463485	+	0.886105i	$0.346599\pi$
$294$		0			0
$295$	−0.175251	+	1.90470i	−0.0102035	+	0.110896i
$296$	−2.31288	+	4.00603i	−0.134433	+	0.232846i
$297$		0			0
$298$	6.19829	−	23.1323i	0.359057	−	1.34002i
$299$	−0.657432	+	1.13871i	−0.0380203	+	0.0658531i
$300$		0			0
$301$	0.308440	+	18.6235i	0.0177782	+	1.07344i
$302$	2.50552	−	2.50552i	0.144176	−	0.144176i
$303$		0			0
$304$	−3.10166	−	5.37224i	−0.177893	−	0.308119i
$305$	−6.47718	−	14.0546i	−0.370882	−	0.804763i
$306$		0			0
$307$	1.07859	+	1.07859i	0.0615584	+	0.0615584i	0.737216	−	0.675657i	$-0.236140\pi$
$307$	1.07859	+	1.07859i	0.0615584	+	0.0615584i	−0.675657	+	0.737216i	$0.736140\pi$
$308$	−2.93705	−	10.2773i	−0.167354	−	0.585605i
$309$		0			0
$310$	−2.76714	−	16.1156i	−0.157163	−	0.915302i
$311$	8.33830	−	4.81412i	0.472821	−	0.272984i	−0.244599	−	0.969624i	$-0.578656\pi$
$311$	8.33830	−	4.81412i	0.472821	−	0.272984i	0.717420	+	0.696641i	$0.245323\pi$
$312$		0			0
$313$	0.783378	+	2.92361i	0.0442791	+	0.165252i	0.984525	−	0.175244i	$-0.0560716\pi$
$313$	0.783378	+	2.92361i	0.0442791	+	0.165252i	−0.940246	+	0.340496i	$0.889405\pi$
$314$	6.12251			0.345513
$315$		0			0
$316$	−5.07627			−0.285562
$317$	−0.504353	−	1.88227i	−0.0283273	−	0.105719i	0.950315	−	0.311291i	$-0.100761\pi$
$317$	−0.504353	−	1.88227i	−0.0283273	−	0.105719i	−0.978642	+	0.205572i	$0.934095\pi$
$318$		0			0
$319$	−25.0463	+	14.4605i	−1.40232	+	0.809631i
$320$	−1.29076	+	1.82591i	−0.0721556	+	0.102071i
$321$		0			0
$322$	−2.91510	+	11.6475i	−0.162452	+	0.649091i
$323$	−8.94715	−	8.94715i	−0.497833	−	0.497833i
$324$		0			0
$325$	−1.30741	−	0.623993i	−0.0725220	−	0.0346129i
$326$	−8.27894	−	14.3395i	−0.458528	−	0.794194i
$327$		0			0
$328$	1.82961	−	1.82961i	0.101023	−	0.101023i
$329$	−0.728847	−	0.404858i	−0.0401826	−	0.0223205i
$330$		0			0
$331$	14.4468	−	25.0225i	0.794066	−	1.37536i	−0.129365	−	0.991597i	$-0.541294\pi$
$331$	14.4468	−	25.0225i	0.794066	−	1.37536i	0.923431	−	0.383765i	$-0.125373\pi$
$332$	1.41056	−	5.26428i	0.0774145	−	0.288915i
$333$		0			0
$334$	−7.27423	+	12.5993i	−0.398028	+	0.689405i
$335$	4.51573	+	5.43092i	0.246721	+	0.296723i
$336$		0			0
$337$	−0.823226	+	0.823226i	−0.0448440	+	0.0448440i	−0.729173	−	0.684329i	$-0.760095\pi$
$337$	−0.823226	+	0.823226i	−0.0448440	+	0.0448440i	0.684329	+	0.729173i	$0.260095\pi$
$338$	12.4759	−	3.34292i	0.678602	−	0.181831i
$339$		0			0
$340$	−1.57916	+	4.27890i	−0.0856420	+	0.232056i
$341$	−25.5846	−	14.7713i	−1.38548	−	0.799910i
$342$		0			0
$343$	12.4293	−	13.7300i	0.671119	−	0.741350i
$344$		−	7.03997i		−	0.379570i
$345$		0			0
$346$	−6.73077	+	3.88601i	−0.361849	+	0.208913i
$347$	−16.1350	−	4.32336i	−0.866172	−	0.232090i	−0.201740	−	0.979439i	$-0.564660\pi$
$347$	−16.1350	−	4.32336i	−0.866172	−	0.232090i	−0.664432	+	0.747349i	$0.731326\pi$
$348$		0			0
$349$	−36.7146			−1.96529			−0.982644	−	0.185503i	$-0.940608\pi$
$349$	−36.7146			−1.96529			−0.982644	+	0.185503i	$0.940608\pi$
$350$	−13.0448	−	2.19820i	−0.697276	−	0.117499i
$351$		0			0
$352$	1.04562	+	3.90231i	0.0557318	+	0.207994i
$353$	13.7845	+	3.69356i	0.733677	+	0.196588i	0.606266	−	0.795262i	$-0.292667\pi$
$353$	13.7845	+	3.69356i	0.733677	+	0.196588i	0.127411	+	0.991850i	$0.459333\pi$
$354$		0			0
$355$	−13.0048	−	9.19329i	−0.690226	−	0.487929i
$356$		−	3.07230i		−	0.162832i
$357$		0			0
$358$	−2.73277	−	2.73277i	−0.144431	−	0.144431i
$359$	−23.4596	−	13.5444i	−1.23815	−	0.714847i	−0.269435	−	0.963019i	$-0.586837\pi$
$359$	−23.4596	−	13.5444i	−1.23815	−	0.714847i	−0.968716	+	0.248172i	$0.920170\pi$
$360$		0			0
$361$	−9.74064	−	16.8713i	−0.512665	−	0.887962i
$362$	−6.75285	+	1.80942i	−0.354922	+	0.0951011i
$363$		0			0
$364$	−0.657432	+	0.394227i	−0.0344588	+	0.0206631i
$365$	−16.4776	−	19.8171i	−0.862477	−	1.03727i
$366$		0			0
$367$	5.86782	−	21.8990i	0.306298	−	1.14312i	−0.625525	−	0.780204i	$-0.715115\pi$
$367$	5.86782	−	21.8990i	0.306298	−	1.14312i	0.931823	−	0.362914i	$-0.118218\pi$
$368$	1.17456	−	4.38350i	0.0612279	−	0.228506i
$369$		0			0
$370$	10.3000	+	0.947702i	0.535472	+	0.0492687i
$371$	18.7938	−	11.2696i	0.975726	−	0.585090i
$372$		0			0
$373$	12.3984	−	3.32215i	0.641966	−	0.172014i	0.0768720	−	0.997041i	$-0.475507\pi$
$373$	12.3984	−	3.32215i	0.641966	−	0.172014i	0.565094	+	0.825027i	$0.308840\pi$
$374$	4.12025	+	7.13648i	0.213053	+	0.369019i
$375$		0			0
$376$	0.272906	+	0.157563i	0.0140741	+	0.00812567i
$377$	1.46664	+	1.46664i	0.0755356	+	0.0755356i
$378$		0			0
$379$		−	14.4739i		−	0.743476i	−0.928338	−	0.371738i	$-0.878762\pi$
$379$		−	14.4739i		−	0.743476i	0.928338	−	0.371738i	$-0.121238\pi$
$380$	−8.00700	+	11.3267i	−0.410750	+	0.581048i
$381$		0			0
$382$	−4.32196	−	1.15807i	−0.221131	−	0.0592518i
$383$	−0.453341	−	1.69189i	−0.0231647	−	0.0864517i	0.953376	−	0.301786i	$-0.0975827\pi$
$383$	−0.453341	−	1.69189i	−0.0231647	−	0.0864517i	−0.976540	+	0.215334i	$0.930916\pi$
$384$		0			0
$385$	−18.1222	+	15.5831i	−0.923595	+	0.794189i
$386$	20.0747			1.02178
$387$		0			0
$388$	−9.05816	−	2.42713i	−0.459858	−	0.123219i
$389$	−2.40954	+	1.39115i	−0.122169	+	0.0705341i	−0.559839	−	0.828601i	$-0.689137\pi$
$389$	−2.40954	+	1.39115i	−0.122169	+	0.0705341i	0.437670	+	0.899135i	$0.355804\pi$
$390$		0			0
$391$		−	9.25661i		−	0.468127i
$392$	−4.78312	+	5.11094i	−0.241584	+	0.258142i
$393$		0			0
$394$	−9.61304	−	5.55009i	−0.484298	−	0.279610i
$395$	4.75090	+	10.3088i	0.239044	+	0.518692i
$396$		0			0
$397$	38.3163	−	10.2668i	1.92304	−	0.515277i	0.936828	−	0.349791i	$-0.113747\pi$
$397$	38.3163	−	10.2668i	1.92304	−	0.515277i	0.986212	−	0.165486i	$-0.0529193\pi$
$398$	7.63821	−	7.63821i	0.382869	−	0.382869i
$399$		0			0
$400$	4.91605	+	0.912375i	0.245803	+	0.0456187i
$401$	−9.98528	+	17.2950i	−0.498641	+	0.863672i	−0.999999	−	0.00156835i	$-0.999501\pi$
$401$	−9.98528	+	17.2950i	−0.498641	+	0.863672i	0.501358	+	0.865240i	$0.332834\pi$
$402$		0			0
$403$	−0.548365	+	2.04653i	−0.0273160	+	0.101945i
$404$	−4.94422	+	8.56364i	−0.245984	+	0.426057i
$405$		0			0
$406$	16.5572	+	9.19714i	0.821720	+	0.456446i
$407$	13.2144	−	13.2144i	0.655012	−	0.655012i
$408$		0			0
$409$	7.65280	+	13.2550i	0.378407	+	0.655419i	0.990831	−	0.135110i	$-0.0431388\pi$
$409$	7.65280	+	13.2550i	0.378407	+	0.655419i	−0.612424	+	0.790529i	$0.709805\pi$
$410$	−5.42787	−	2.00320i	−0.268064	−	0.0989309i
$411$		0			0
$412$	−3.02785	−	3.02785i	−0.149172	−	0.149172i
$413$	0.549475	−	2.19547i	0.0270379	−	0.108032i
$414$		0			0
$415$	−12.0108	+	2.06232i	−0.589585	+	0.101235i
$416$	0.250919	−	0.144868i	0.0123023	−	0.00710276i
$417$		0			0
$418$	6.48634	+	24.2073i	0.317257	+	1.18402i
$419$	−27.7027			−1.35337			−0.676684	−	0.736274i	$-0.736584\pi$
$419$	−27.7027			−1.35337			−0.676684	+	0.736274i	$0.736584\pi$
$420$		0			0
$421$	33.0159			1.60910			0.804549	−	0.593887i	$-0.202407\pi$
$421$	33.0159			1.60910			0.804549	+	0.593887i	$0.202407\pi$
$422$	−1.95811	−	7.30776i	−0.0953192	−	0.355736i
$423$		0			0
$424$	−7.17295	+	4.14131i	−0.348349	+	0.201120i
$425$	10.1675	−	0.797705i	0.493194	−	0.0386944i
$426$		0			0
$427$	5.03138	+	17.6058i	0.243485	+	0.852005i
$428$	−10.5161	−	10.5161i	−0.508317	−	0.508317i
$429$		0			0
$430$	−14.2967	+	6.58874i	−0.689446	+	0.317737i
$431$	11.9586	+	20.7129i	0.576027	+	0.997708i	0.995929	+	0.0901384i	$0.0287309\pi$
$431$	11.9586	+	20.7129i	0.576027	+	0.997708i	−0.419902	+	0.907569i	$0.637936\pi$
$432$		0			0
$433$	13.2515	−	13.2515i	0.636829	−	0.636829i	−0.312943	−	0.949772i	$-0.601315\pi$
$433$	13.2515	−	13.2515i	0.636829	−	0.636829i	0.949772	+	0.312943i	$0.101315\pi$
$434$	0.320383	+	19.3446i	0.0153789	+	0.928569i
$435$		0			0
$436$	−6.61564	+	11.4586i	−0.316832	+	0.548769i
$437$	7.28615	−	27.1923i	0.348544	−	1.30078i
$438$		0			0
$439$	7.05383	−	12.2176i	0.336661	−	0.583114i	−0.647141	−	0.762370i	$-0.724036\pi$
$439$	7.05383	−	12.2176i	0.336661	−	0.583114i	0.983802	+	0.179256i	$0.0573690\pi$
$440$	6.94616	−	5.77563i	0.331145	−	0.275342i
$441$		0			0
$442$	0.417892	−	0.417892i	0.0198771	−	0.0198771i
$443$	20.3457	−	5.45161i	0.966652	−	0.259014i	0.259238	−	0.965813i	$-0.416528\pi$
$443$	20.3457	−	5.45161i	0.966652	−	0.259014i	0.707414	+	0.706800i	$0.249862\pi$
$444$		0			0
$445$	−6.23919	+	2.87538i	−0.295766	+	0.136306i
$446$	11.4542	+	6.61308i	0.542371	+	0.313138i
$447$		0			0
$448$	1.83959	−	1.90155i	0.0869125	−	0.0898399i
$449$			31.3247i			1.47831i	0.673538	+	0.739153i	$0.264774\pi$
$449$			31.3247i			1.47831i	−0.673538	+	0.739153i	$0.735226\pi$
$450$		0			0
$451$	−9.05278	+	5.22662i	−0.426279	+	0.246112i
$452$	13.3233	+	3.56998i	0.626677	+	0.167918i
$453$		0			0
$454$	16.1938			0.760014
$455$	1.41588	+	0.966145i	0.0663776	+	0.0452936i
$456$		0			0
$457$	−0.740622	−	2.76404i	−0.0346448	−	0.129296i	0.946438	−	0.322887i	$-0.104653\pi$
$457$	−0.740622	−	2.76404i	−0.0346448	−	0.129296i	−0.981082	+	0.193591i	$0.937987\pi$
$458$	11.3751	+	3.04796i	0.531525	+	0.142422i
$459$		0			0
$460$	−10.0012	+	1.71727i	−0.466309	+	0.0800681i
$461$			3.02674i			0.140969i	0.997513	+	0.0704846i	$0.0224546\pi$
$461$			3.02674i			0.140969i	−0.997513	+	0.0704846i	$0.977545\pi$
$462$		0			0
$463$	19.2889	+	19.2889i	0.896431	+	0.896431i	0.995118	−	0.0986876i	$-0.0314644\pi$
$463$	19.2889	+	19.2889i	0.896431	+	0.896431i	−0.0986876	+	0.995118i	$0.531464\pi$
$464$	−6.19961	−	3.57935i	−0.287810	−	0.166167i
$465$		0			0
$466$	2.86212	+	4.95734i	0.132585	+	0.229644i
$467$	24.2727	−	6.50385i	1.12321	−	0.300962i	0.351026	−	0.936366i	$-0.385833\pi$
$467$	24.2727	−	6.50385i	1.12321	−	0.300962i	0.772180	+	0.635403i	$0.219166\pi$
$468$		0			0
$469$	−4.29784	−	7.16729i	−0.198456	−	0.330955i
$470$	0.0645612	−	0.701677i	0.00297799	−	0.0323660i
$471$		0			0
$472$	−0.221395	+	0.826257i	−0.0101905	+	0.0380316i
$473$	−7.36115	+	27.4722i	−0.338466	+	1.26317i
$474$		0			0
$475$	30.4959	+	5.65976i	1.39925	+	0.259688i
$476$	2.62056	−	4.71767i	0.120113	−	0.216234i
$477$		0			0
$478$	8.05384	−	2.15802i	0.368374	−	0.0987055i
$479$	−4.14346	−	7.17668i	−0.189319	−	0.327911i	0.755704	−	0.654913i	$-0.227295\pi$
$479$	−4.14346	−	7.17668i	−0.189319	−	0.327911i	−0.945024	+	0.327002i	$0.893961\pi$
$480$		0			0
$481$	−1.16069	−	0.670127i	−0.0529231	−	0.0305551i
$482$	−2.09613	−	2.09613i	−0.0954763	−	0.0954763i
$483$		0			0
$484$		−	5.32139i		−	0.241881i
$485$	3.54860	+	20.6667i	0.161134	+	0.938427i
$486$		0			0
$487$	−10.3144	−	2.76375i	−0.467392	−	0.125237i	0.0174340	−	0.999848i	$-0.494450\pi$
$487$	−10.3144	−	2.76375i	−0.467392	−	0.125237i	−0.484826	+	0.874611i	$0.661117\pi$
$488$	−1.79123	−	6.68495i	−0.0810850	−	0.302613i
$489$		0			0
$490$	14.8558	+	4.93014i	0.671115	+	0.222721i
$491$	−25.7259			−1.16100			−0.580498	−	0.814262i	$-0.697142\pi$
$491$	−25.7259			−1.16100			−0.580498	+	0.814262i	$0.697142\pi$
$492$		0			0
$493$	−14.1043	−	3.77924i	−0.635227	−	0.170209i
$494$	1.55654	−	0.898666i	0.0700319	−	0.0404329i
$495$		0			0
$496$		−	7.31256i		−	0.328344i
$497$	13.5436	+	13.1023i	0.607514	+	0.587719i
$498$		0			0
$499$	12.6429	+	7.29940i	0.565975	+	0.326766i	0.755540	−	0.655102i	$-0.227374\pi$
$499$	12.6429	+	7.29940i	0.565975	+	0.326766i	−0.189565	+	0.981868i	$0.560708\pi$
$500$	−2.74812	−	10.8373i	−0.122900	−	0.484660i
$501$		0			0
$502$	−15.6287	+	4.18770i	−0.697543	+	0.186906i
$503$	13.9891	−	13.9891i	0.623744	−	0.623744i	−0.322743	−	0.946487i	$-0.604605\pi$
$503$	13.9891	−	13.9891i	0.623744	−	0.623744i	0.946487	+	0.322743i	$0.104605\pi$
$504$		0			0
$505$	22.0182	+	2.02589i	0.979798	+	0.0901510i
$506$	−9.16697	+	15.8777i	−0.407522	+	0.705848i
$507$		0			0
$508$	0.805197	−	3.00504i	0.0357248	−	0.133327i
$509$	1.42883	−	2.47481i	0.0633319	−	0.109694i	−0.832621	−	0.553843i	$-0.813161\pi$
$509$	1.42883	−	2.47481i	0.0633319	−	0.109694i	0.895953	+	0.444149i	$0.146494\pi$
$510$		0			0
$511$	15.6825	+	26.1530i	0.693754	+	1.15694i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−2.91234	−	5.04433i	−0.128458	−	0.222496i
$515$	−3.31513	+	8.98269i	−0.146082	+	0.395825i
$516$		0			0
$517$	−0.900216	−	0.900216i	−0.0395914	−	0.0395914i
$518$	−11.8724	−	2.97139i	−0.521644	−	0.130555i
$519$		0			0
$520$	−0.529033	−	0.373980i	−0.0231996	−	0.0164001i
$521$	−24.7917	+	14.3135i	−1.08614	+	0.627084i	−0.932547	−	0.361049i	$-0.882419\pi$
$521$	−24.7917	+	14.3135i	−1.08614	+	0.627084i	−0.153595	+	0.988134i	$0.549085\pi$
$522$		0			0
$523$	8.17429	+	30.5069i	0.357437	+	1.33397i	0.877390	+	0.479777i	$0.159283\pi$
$523$	8.17429	+	30.5069i	0.357437	+	1.33397i	−0.519954	+	0.854195i	$0.674051\pi$
$524$	−7.29876			−0.318848
$525$		0			0
$526$	1.73712			0.0757422
$527$	−3.86048	−	14.4075i	−0.168165	−	0.627600i
$528$		0			0
$529$	−2.08308	+	1.20267i	−0.0905687	+	0.0522899i
$530$	15.1233	+	10.6909i	0.656914	+	0.464381i
$531$		0			0
$532$	11.4116	−	11.7960i	0.494755	−	0.511419i
$533$	0.530105	+	0.530105i	0.0229614	+	0.0229614i
$534$		0			0
$535$	−11.5139	+	31.1981i	−0.497790	+	1.34881i
$536$	1.57935	+	2.73551i	0.0682174	+	0.118156i
$537$		0			0
$538$	−2.67525	+	2.67525i	−0.115338	+	0.115338i
$539$	24.0094	−	14.9432i	1.03416	−	0.643648i
$540$		0			0
$541$	−18.4994	+	32.0420i	−0.795353	+	1.37759i	0.127262	+	0.991869i	$0.459381\pi$
$541$	−18.4994	+	32.0420i	−0.795353	+	1.37759i	−0.922615	+	0.385722i	$0.873952\pi$
$542$	−5.49985	+	20.5257i	−0.236239	+	0.881655i
$543$		0			0
$544$	−1.01987	+	1.76647i	−0.0437266	+	0.0757366i
$545$	29.4616	+	2.71076i	1.26200	+	0.116116i
$546$		0			0
$547$	−20.0765	+	20.0765i	−0.858409	+	0.858409i	−0.991151	−	0.132742i	$-0.957622\pi$
$547$	−20.0765	+	20.0765i	−0.858409	+	0.858409i	0.132742	+	0.991151i	$0.457622\pi$
$548$	−6.93431	+	1.85804i	−0.296219	+	0.0793717i
$549$		0			0
$550$	−18.2300	−	8.70071i	−0.777329	−	0.370999i
$551$	−38.4582	−	22.2039i	−1.63838	−	0.945916i
$552$		0			0
$553$	−3.69043	−	12.9136i	−0.156933	−	0.549141i
$554$		−	4.89016i		−	0.207763i
$555$		0			0
$556$	10.7536	−	6.20859i	0.456054	−	0.263303i
$557$	−24.8367	−	6.65499i	−1.05237	−	0.281981i	−0.309137	−	0.951017i	$-0.600040\pi$
$557$	−24.8367	−	6.65499i	−1.05237	−	0.281981i	−0.743229	+	0.669037i	$0.766707\pi$
$558$		0			0
$559$	2.03974			0.0862718
$560$	−5.58332	−	1.95614i	−0.235939	−	0.0826621i
$561$		0			0
$562$	−7.62937	−	28.4732i	−0.321825	−	1.20107i
$563$	−5.18407	−	1.38907i	−0.218482	−	0.0585422i	0.147917	−	0.989000i	$-0.452743\pi$
$563$	−5.18407	−	1.38907i	−0.218482	−	0.0585422i	−0.366400	+	0.930458i	$0.619410\pi$
$564$		0			0
$565$	−5.21952	−	30.3980i	−0.219587	−	1.27885i
$566$			11.2836i			0.474286i
$567$		0			0
$568$	−5.03630	−	5.03630i	−0.211318	−	0.211318i
$569$	22.0839	+	12.7502i	0.925806	+	0.534514i	0.885483	−	0.464672i	$-0.153828\pi$
$569$	22.0839	+	12.7502i	0.925806	+	0.534514i	0.0403234	+	0.999187i	$0.487161\pi$
$570$		0			0
$571$	−7.95235	−	13.7739i	−0.332795	−	0.576419i	0.650263	−	0.759709i	$-0.274659\pi$
$571$	−7.95235	−	13.7739i	−0.332795	−	0.576419i	−0.983059	+	0.183290i	$0.941325\pi$
$572$	−1.13064	+	0.302955i	−0.0472746	+	0.0126672i
$573$		0			0
$574$	5.98447	+	3.32424i	0.249787	+	0.138751i
$575$	12.8476	+	18.7031i	0.535781	+	0.779973i
$576$		0			0
$577$	−5.96565	+	22.2641i	−0.248353	+	0.926867i	0.723315	+	0.690518i	$0.242617\pi$
$577$	−5.96565	+	22.2641i	−0.248353	+	0.926867i	−0.971668	+	0.236349i	$0.924049\pi$
$578$	3.32310	−	12.4020i	0.138223	−	0.515854i
$579$		0			0
$580$	−1.46664	+	15.9400i	−0.0608988	+	0.661872i
$581$	14.4173	−	0.238779i	0.598132	−	0.00990621i
$582$		0			0
$583$	32.3214	−	8.66048i	1.33861	−	0.358681i
$584$	−5.76293	−	9.98169i	−0.238472	−	0.413045i
$585$		0			0
$586$	8.85989	+	5.11526i	0.365999	+	0.211310i
$587$	28.2277	+	28.2277i	1.16508	+	1.16508i	0.983348	+	0.181734i	$0.0581711\pi$
$587$	28.2277	+	28.2277i	1.16508	+	1.16508i	0.181734	+	0.983348i	$0.441829\pi$
$588$		0			0
$589$		−	45.3622i		−	1.86912i
$590$	1.88515	−	0.323692i	0.0776105	−	0.0133262i
$591$		0			0
$592$	4.46814	+	1.19723i	0.183639	+	0.0492060i
$593$	9.16977	+	34.2220i	0.376557	+	1.40533i	0.851056	+	0.525075i	$0.175963\pi$
$593$	9.16977	+	34.2220i	0.376557	+	1.40533i	−0.474499	+	0.880256i	$0.657371\pi$
$594$		0			0
$595$	−12.0332	−	0.906496i	−0.493312	−	0.0371627i
$596$	−23.9483			−0.980963
$597$		0			0
$598$	1.27006	+	0.340312i	0.0519367	+	0.0139164i
$599$	14.5339	−	8.39115i	0.593839	−	0.342853i	−0.172775	−	0.984961i	$-0.555273\pi$
$599$	14.5339	−	8.39115i	0.593839	−	0.342853i	0.766614	+	0.642108i	$0.221940\pi$
$600$		0			0
$601$		−	1.73528i		−	0.0707833i	−0.999374	−	0.0353917i	$-0.988732\pi$
$601$		−	1.73528i		−	0.0707833i	0.999374	−	0.0353917i	$-0.0112679\pi$
$602$	17.9091	−	5.11804i	0.729919	−	0.208596i
$603$		0			0
$604$	−3.06862	−	1.77167i	−0.124860	−	0.0720881i
$605$	−10.8066	+	4.98031i	−0.439350	+	0.202478i
$606$		0			0
$607$	38.0930	−	10.2070i	1.54615	−	0.414288i	0.617900	−	0.786257i	$-0.287984\pi$
$607$	38.0930	−	10.2070i	1.54615	−	0.414288i	0.928245	+	0.371968i	$0.121317\pi$
$608$	−4.38642	+	4.38642i	−0.177893	+	0.177893i
$609$		0			0
$610$	−11.8993	+	9.89407i	−0.481787	+	0.400599i
$611$	−0.0456517	+	0.0790711i	−0.00184687	+	0.00319887i
$612$		0			0
$613$	0.0885018	−	0.330293i	0.00357455	−	0.0133404i	−0.964116	−	0.265483i	$-0.914469\pi$
$613$	0.0885018	−	0.330293i	0.00357455	−	0.0133404i	0.967690	+	0.252143i	$0.0811352\pi$
$614$	0.762678	−	1.32100i	0.0307792	−	0.0533111i
$615$		0			0
$616$	−9.16697	+	5.49694i	−0.369348	+	0.221478i
$617$	−11.1876	+	11.1876i	−0.450397	+	0.450397i	−0.895486	−	0.445089i	$-0.853172\pi$
$617$	−11.1876	+	11.1876i	−0.450397	+	0.450397i	0.445089	+	0.895486i	$0.353172\pi$
$618$		0			0
$619$	−18.2682	−	31.6414i	−0.734260	−	1.27178i	−0.955047	−	0.296454i	$-0.904196\pi$
$619$	−18.2682	−	31.6414i	−0.734260	−	1.27178i	0.220787	−	0.975322i	$-0.429138\pi$
$620$	−14.8502	+	6.84386i	−0.596400	+	0.274856i
$621$		0			0
$622$	−6.80819	−	6.80819i	−0.272984	−	0.272984i
$623$	7.81566	−	2.23356i	0.313128	−	0.0894855i
$624$		0			0
$625$	−19.4363	+	15.7235i	−0.777452	+	0.628942i
$626$	2.62123	−	1.51337i	0.104766	−	0.0604864i
$627$		0			0
$628$	−1.58462	−	5.91389i	−0.0632333	−	0.235990i
$629$	9.43535			0.376212
$630$		0			0
$631$	−35.8189			−1.42593			−0.712964	−	0.701201i	$-0.752648\pi$
$631$	−35.8189			−1.42593			−0.712964	+	0.701201i	$0.752648\pi$
$632$	1.31384	+	4.90330i	0.0522616	+	0.195043i
$633$		0			0
$634$	−1.68760	+	0.974335i	−0.0670231	+	0.0386958i
$635$	−6.85616	+	1.17725i	−0.272079	+	0.0467176i
$636$		0			0
$637$	−1.48083	−	1.38585i	−0.0586726	−	0.0549093i
$638$	20.4502	+	20.4502i	0.809631	+	0.809631i
$639$		0			0
$640$	2.09777	+	0.774197i	0.0829215	+	0.0306028i
$641$	−7.16573	−	12.4114i	−0.283029	−	0.490221i	0.689100	−	0.724666i	$-0.258006\pi$
$641$	−7.16573	−	12.4114i	−0.283029	−	0.490221i	−0.972129	+	0.234445i	$0.924673\pi$
$642$		0			0
$643$	−7.65201	+	7.65201i	−0.301766	+	0.301766i	−0.841704	−	0.539939i	$-0.818447\pi$
$643$	−7.65201	+	7.65201i	−0.301766	+	0.301766i	0.539939	+	0.841704i	$0.318447\pi$
$644$	12.0051	−	0.198828i	0.473068	−	0.00783492i
$645$		0			0
$646$	−6.32659	+	10.9580i	−0.248916	+	0.431136i
$647$	−8.37254	+	31.2468i	−0.329159	+	1.22844i	0.580906	+	0.813971i	$0.302698\pi$
$647$	−8.37254	+	31.2468i	−0.329159	+	1.22844i	−0.910065	+	0.414466i	$0.863968\pi$
$648$		0			0
$649$	1.72791	−	2.99282i	0.0678262	−	0.117478i
$650$	−0.264349	+	1.42436i	−0.0103686	+	0.0558681i
$651$		0			0
$652$	−11.7082	+	11.7082i	−0.458528	+	0.458528i
$653$	−0.494788	+	0.132578i	−0.0193625	+	0.00518818i	−0.268487	−	0.963283i	$-0.586524\pi$
$653$	−0.494788	+	0.132578i	−0.0193625	+	0.00518818i	0.249125	+	0.968471i	$0.419857\pi$
$654$		0			0
$655$	6.83094	+	14.8222i	0.266907	+	0.579151i
$656$	−2.24080	−	1.29373i	−0.0874886	−	0.0505116i
$657$		0			0
$658$	−0.202423	+	0.808797i	−0.00789127	+	0.0315302i
$659$			19.5542i			0.761723i	0.924632	+	0.380862i	$0.124373\pi$
$659$			19.5542i			0.761723i	−0.924632	+	0.380862i	$0.875627\pi$
$660$		0			0
$661$	34.0324	−	19.6486i	1.32371	−	0.764242i	0.339388	−	0.940647i	$-0.389780\pi$
$661$	34.0324	−	19.6486i	1.32371	−	0.764242i	0.984318	+	0.176405i	$0.0564468\pi$
$662$	−27.9090	−	7.47819i	−1.08471	−	0.290648i
$663$		0			0
$664$	−5.44998			−0.211500
$665$	−34.6352	−	12.1346i	−1.34310	−	0.470559i
$666$		0			0
$667$	−8.40828	−	31.3801i	−0.325570	−	1.21504i
$668$	14.0527	+	3.76542i	0.543716	+	0.145688i
$669$		0			0
$670$	4.07711	−	5.76749i	0.157512	−	0.222817i
$671$			27.9597i			1.07937i
$672$		0			0
$673$	18.4813	+	18.4813i	0.712401	+	0.712401i	0.967037	−	0.254636i	$-0.0819556\pi$
$673$	18.4813	+	18.4813i	0.712401	+	0.712401i	−0.254636	+	0.967037i	$0.581956\pi$
$674$	1.00824	+	0.582108i	0.0388360	+	0.0224220i
$675$		0			0
$676$	−6.45803	−	11.1856i	−0.248386	−	0.430217i
$677$	39.7951	−	10.6631i	1.52945	−	0.409815i	0.606611	−	0.794999i	$-0.292528\pi$
$677$	39.7951	−	10.6631i	1.52945	−	0.409815i	0.922840	+	0.385183i	$0.125862\pi$
$678$		0			0
$679$	−0.410862	−	24.8076i	−0.0157674	−	0.952030i
$680$	4.54181	+	0.417892i	0.174171	+	0.0160254i
$681$		0			0
$682$	−7.64618	+	28.5359i	−0.292787	+	1.09270i
$683$	2.36248	−	8.81689i	0.0903978	−	0.337369i	−0.905884	−	0.423526i	$-0.860792\pi$
$683$	2.36248	−	8.81689i	0.0903978	−	0.337369i	0.996282	+	0.0861573i	$0.0274588\pi$
$684$		0			0
$685$	10.2631	+	12.3431i	0.392134	+	0.471607i
$686$	−16.4791	−	8.45219i	−0.629175	−	0.322706i
$687$		0			0
$688$	−6.80009	+	1.82208i	−0.259251	+	0.0694661i
$689$	−1.19989	−	2.07827i	−0.0457121	−	0.0791758i
$690$		0			0
$691$	−41.9971	−	24.2470i	−1.59765	−	0.922401i	−0.991940	−	0.126712i	$-0.959558\pi$
$691$	−41.9971	−	24.2470i	−1.59765	−	0.922401i	−0.605706	−	0.795689i	$-0.707109\pi$
$692$	5.49565	+	5.49565i	0.208913	+	0.208913i
$693$		0			0
$694$			16.7042i			0.634082i
$695$	−22.6726	−	16.0276i	−0.860022	−	0.607960i
$696$		0			0
$697$	−5.09790	−	1.36598i	−0.193097	−	0.0517401i
$698$	9.50244	+	35.4636i	0.359673	+	1.34232i
$699$		0			0
$700$	1.25296	+	13.1693i	0.0473573	+	0.497752i
$701$	30.8898			1.16669			0.583347	−	0.812223i	$-0.301743\pi$
$701$	30.8898			1.16669			0.583347	+	0.812223i	$0.301743\pi$
$702$		0			0
$703$	27.7173	+	7.42684i	1.04538	+	0.280109i
$704$	3.49872	−	2.01999i	0.131863	−	0.0761311i
$705$		0			0
$706$		−	14.2708i		−	0.537089i
$707$	−25.3796	−	6.35191i	−0.954496	−	0.238888i
$708$		0			0
$709$	12.7354	+	7.35277i	0.478287	+	0.276139i	0.719702	−	0.694283i	$-0.244278\pi$
$709$	12.7354	+	7.35277i	0.478287	+	0.276139i	−0.241416	+	0.970422i	$0.577612\pi$
$710$	−5.51414	+	14.9411i	−0.206942	+	0.560730i
$711$		0			0
$712$	−2.96762	+	0.795171i	−0.111216	+	0.0298003i
$713$	23.4656	−	23.4656i	0.878795	−	0.878795i
$714$		0			0
$715$	1.67341	+	2.01256i	0.0625821	+	0.0752654i
$716$	−1.93236	+	3.34695i	−0.0722157	+	0.125081i
$717$		0			0
$718$	−7.01110	+	26.1658i	−0.261652	+	0.976499i
$719$	11.7360	−	20.3273i	0.437679	−	0.758082i	−0.559831	−	0.828607i	$-0.689134\pi$
$719$	11.7360	−	20.3273i	0.437679	−	0.758082i	0.997510	+	0.0705247i	$0.0224674\pi$
$720$		0			0
$721$	5.50134	−	9.90382i	0.204881	−	0.368837i
$722$	−13.7753	+	13.7753i	−0.512665	+	0.512665i
$723$		0			0
$724$	3.49553	+	6.05444i	0.129911	+	0.225012i
$725$	33.7433	−	11.9399i	1.25320	−	0.443436i
$726$		0			0
$727$	14.1380	+	14.1380i	0.524349	+	0.524349i	0.918882	−	0.394533i	$-0.129093\pi$
$727$	14.1380	+	14.1380i	0.524349	+	0.524349i	−0.394533	+	0.918882i	$0.629093\pi$
$728$	0.550950	+	0.532998i	0.0204196	+	0.0197542i
$729$		0			0
$730$	−14.8771	+	21.0452i	−0.550626	+	0.778917i
$731$	−12.4359	+	7.17986i	−0.459958	+	0.265557i
$732$		0			0
$733$	−7.17859	−	26.7908i	−0.265147	−	0.989543i	−0.962160	−	0.272484i	$-0.912155\pi$
$733$	−7.17859	−	26.7908i	−0.265147	−	0.989543i	0.697013	−	0.717058i	$-0.254512\pi$
$734$	−22.6715			−0.836821
$735$		0			0
$736$	−4.53813			−0.167278
$737$	−3.30280	−	12.3262i	−0.121660	−	0.454042i
$738$		0			0
$739$	11.7451	−	6.78102i	0.432050	−	0.249444i	−0.268170	−	0.963372i	$-0.586419\pi$
$739$	11.7451	−	6.78102i	0.432050	−	0.249444i	0.700219	+	0.713928i	$0.253085\pi$
$740$	−1.75043	−	10.1943i	−0.0643470	−	0.374751i
$741$		0			0
$742$	−15.7498	−	15.2366i	−0.578194	−	0.559354i
$743$	−13.5961	−	13.5961i	−0.498791	−	0.498791i	0.412270	−	0.911062i	$-0.364736\pi$
$743$	−13.5961	−	13.5961i	−0.498791	−	0.498791i	−0.911062	+	0.412270i	$0.864736\pi$
$744$		0			0
$745$	22.4134	+	48.6339i	0.821162	+	1.78181i
$746$	−6.41789	−	11.1161i	−0.234976	−	0.406990i
$747$		0			0
$748$	5.82691	−	5.82691i	0.213053	−	0.213053i
$749$	19.1069	−	34.3973i	0.698152	−	1.25685i
$750$		0			0
$751$	−21.8309	+	37.8123i	−0.796622	+	1.37979i	0.125182	+	0.992134i	$0.460049\pi$
$751$	−21.8309	+	37.8123i	−0.796622	+	1.37979i	−0.921804	+	0.387656i	$0.873285\pi$
$752$	0.0815604	−	0.304388i	0.00297420	−	0.0110999i
$753$		0			0
$754$	1.03707	−	1.79626i	0.0377678	−	0.0654158i
$755$	−0.725941	+	7.88981i	−0.0264197	+	0.287140i
$756$		0			0
$757$	7.88896	−	7.88896i	0.286729	−	0.286729i	−0.549056	−	0.835785i	$-0.685013\pi$
$757$	7.88896	−	7.88896i	0.286729	−	0.286729i	0.835785	+	0.549056i	$0.185013\pi$
$758$	−13.9807	+	3.74613i	−0.507803	+	0.136065i
$759$		0			0
$760$	13.0131	+	4.80260i	0.472036	+	0.174208i
$761$	1.70923	+	0.986825i	0.0619596	+	0.0357724i	0.530660	−	0.847585i	$-0.321944\pi$
$761$	1.70923	+	0.986825i	0.0619596	+	0.0357724i	−0.468700	+	0.883357i	$0.655278\pi$
$762$		0			0
$763$	−33.9593	−	8.49921i	−1.22941	−	0.307692i
$764$			4.47442i			0.161879i
$765$		0			0
$766$	−1.51691	+	0.875788i	−0.0548082	+	0.0316435i
$767$	−0.239397	−	0.0641463i	−0.00864413	−	0.00231619i
$768$		0			0
$769$	17.4914			0.630756			0.315378	−	0.948966i	$-0.397869\pi$
$769$	17.4914			0.630756			0.315378	+	0.948966i	$0.397869\pi$
$770$	19.7425	+	13.4715i	0.711470	+	0.485480i
$771$		0			0
$772$	−5.19573	−	19.3907i	−0.186998	−	0.697887i
$773$	−43.1933	−	11.5736i	−1.55355	−	0.416274i	−0.622939	−	0.782271i	$-0.714061\pi$
$773$	−43.1933	−	11.5736i	−1.55355	−	0.416274i	−0.930616	+	0.365997i	$0.880728\pi$
$774$		0			0
$775$	27.7968	+	23.7524i	0.998491	+	0.853212i
$776$			9.37769i			0.336640i
$777$		0			0
$778$	1.96738	+	1.96738i	0.0705341	+	0.0705341i
$779$	−13.9004	−	8.02542i	−0.498035	−	0.287540i
$780$		0			0
$781$	14.3871	+	24.9193i	0.514813	+	0.891682i
$782$	−8.94120	+	2.39579i	−0.319737	+	0.0856732i
$783$		0			0
$784$	6.17475	+	3.29733i	0.220527	+	0.117762i
$785$	−10.5268	+	8.75286i	−0.375717	+	0.312403i
$786$		0			0
$787$	6.71595	−	25.0643i	0.239398	−	0.893445i	−0.736719	−	0.676199i	$-0.763626\pi$
$787$	6.71595	−	25.0643i	0.239398	−	0.893445i	0.976117	−	0.217246i	$-0.0697074\pi$
$788$	−2.87294	+	10.7220i	−0.102344	+	0.381954i
$789$		0			0
$790$	8.72792	−	7.25713i	0.310525	−	0.258197i
$791$	0.604323	+	36.4887i	0.0214873	+	1.29739i
$792$		0			0
$793$	1.93688	−	0.518984i	0.0687805	−	0.0184297i
$794$	−19.8340	−	34.3535i	−0.703881	−	1.21916i
$795$		0			0
$796$	−9.35485	−	5.40103i	−0.331574	−	0.191434i
$797$	−37.3374	−	37.3374i	−1.32256	−	1.32256i	−0.911698	−	0.410861i	$-0.865228\pi$
$797$	−37.3374	−	37.3374i	−1.32256	−	1.32256i	−0.410861	−	0.911698i	$-0.634772\pi$
$798$		0			0
$799$		−	0.642773i		−	0.0227397i
$800$	−0.391082	−	4.98468i	−0.0138268	−	0.176235i
$801$		0			0
$802$	19.2901	+	5.16876i	0.681156	+	0.182515i
$803$	12.0517	+	44.9776i	0.425295	+	1.58722i
$804$		0			0
$805$	−11.6394	−	24.1937i	−0.410236	−	0.852717i
$806$	2.11872			0.0746287
$807$		0			0
$808$	9.55150	+	2.55932i	0.336021	+	0.0900364i
$809$	−13.9001	+	8.02525i	−0.488703	+	0.282153i	−0.724036	−	0.689762i	$-0.757715\pi$
$809$	−13.9001	+	8.02525i	−0.488703	+	0.282153i	0.235333	+	0.971915i	$0.424382\pi$
$810$		0			0
$811$			35.4040i			1.24320i	0.783334	+	0.621602i	$0.213518\pi$
$811$			35.4040i			1.24320i	−0.783334	+	0.621602i	$0.786482\pi$
$812$	4.59844	−	18.3734i	0.161374	−	0.644781i
$813$		0			0
$814$	−16.1842	−	9.34397i	−0.567257	−	0.327506i
$815$	34.7345	+	12.8190i	1.21670	+	0.449032i
$816$		0			0
$817$	−42.1832	+	11.3030i	−1.47580	+	0.395440i
$818$	10.8227	−	10.8227i	0.378407	−	0.378407i
$819$		0			0
$820$	−0.530105	+	5.76139i	−0.0185121	+	0.201196i
$821$	13.4231	−	23.2495i	0.468469	−	0.811412i	−0.530881	−	0.847446i	$-0.678139\pi$
$821$	13.4231	−	23.2495i	0.468469	−	0.811412i	0.999351	+	0.0360337i	$0.0114724\pi$
$822$		0			0
$823$	7.24225	−	27.0285i	0.252449	−	0.942153i	−0.717043	−	0.697029i	$-0.754505\pi$
$823$	7.24225	−	27.0285i	0.252449	−	0.942153i	0.969492	−	0.245124i	$-0.0788286\pi$
$824$	−2.14101	+	3.70835i	−0.0745858	+	0.129186i
$825$		0			0
$826$	−2.26288	+	0.0374776i	−0.0787355	+	0.00130401i
$827$	−16.8901	+	16.8901i	−0.587325	+	0.587325i	−0.936906	−	0.349581i	$-0.886324\pi$
$827$	−16.8901	+	16.8901i	−0.587325	+	0.587325i	0.349581	+	0.936906i	$0.386324\pi$
$828$		0			0
$829$	−7.08412	−	12.2701i	−0.246042	−	0.426157i	0.716382	−	0.697708i	$-0.245797\pi$
$829$	−7.08412	−	12.2701i	−0.246042	−	0.426157i	−0.962424	+	0.271551i	$0.912463\pi$
$830$	5.10066	+	11.0677i	0.177047	+	0.384167i
$831$		0			0
$832$	−0.204875	−	0.204875i	−0.00710276	−	0.00710276i
$833$	13.9065	+	3.23673i	0.481831	+	0.112146i
$834$		0			0
$835$	−5.50526	−	32.0621i	−0.190517	−	1.10956i
$836$	21.7037	−	12.5306i	0.750638	−	0.433381i
$837$		0			0
$838$	7.17000	+	26.7588i	0.247683	+	0.924367i
$839$	18.1874			0.627900			0.313950	−	0.949439i	$-0.398348\pi$
$839$	18.1874			0.627900			0.313950	+	0.949439i	$0.398348\pi$
$840$		0			0
$841$	−22.2469			−0.767134
$842$	−8.54515	−	31.8909i	−0.294485	−	1.09903i
$843$		0			0
$844$	−6.55196	+	3.78278i	−0.225528	+	0.130209i
$845$	−16.6715	+	23.5835i	−0.573517	+	0.811298i
$846$		0			0
$847$	13.5371	−	3.86863i	0.465141	−	0.132928i
$848$	5.85669	+	5.85669i	0.201120	+	0.201120i
$849$		0			0
$850$	−3.40206	−	9.61455i	−0.116690	−	0.329776i
$851$	10.4962	+	18.1799i	0.359804	+	0.623198i
$852$		0			0
$853$	17.4820	−	17.4820i	0.598574	−	0.598574i	−0.341359	−	0.939933i	$-0.610887\pi$
$853$	17.4820	−	17.4820i	0.598574	−	0.598574i	0.939933	+	0.341359i	$0.110887\pi$
$854$	15.7037	−	9.41665i	0.537369	−	0.322231i
$855$		0			0
$856$	−7.43604	+	12.8796i	−0.254159	+	0.440216i
$857$	6.76932	−	25.2634i	0.231235	−	0.862982i	−0.748574	−	0.663051i	$-0.769261\pi$
$857$	6.76932	−	25.2634i	0.231235	−	0.862982i	0.979810	−	0.199932i	$-0.0640720\pi$
$858$		0			0
$859$	−24.4126	+	42.2838i	−0.832946	+	1.44271i	0.0627455	+	0.998030i	$0.480014\pi$
$859$	−24.4126	+	42.2838i	−0.832946	+	1.44271i	−0.895692	+	0.444676i	$0.853319\pi$
$860$	10.0645	+	12.1042i	0.343196	+	0.412751i
$861$		0			0
$862$	16.9121	−	16.9121i	0.576027	−	0.576027i
$863$	14.8258	−	3.97256i	0.504676	−	0.135228i	0.00250685	−	0.999997i	$-0.499202\pi$
$863$	14.8258	−	3.97256i	0.504676	−	0.135228i	0.502169	+	0.864769i	$0.332535\pi$
$864$		0			0
$865$	6.01708	−	16.3039i	0.204587	−	0.554349i
$866$	−16.2298	−	9.37026i	−0.551510	−	0.318414i
$867$		0			0
$868$	18.6025	−	5.31621i	0.631410	−	0.180444i
$869$		−	20.5080i		−	0.695686i
$870$		0			0
$871$	−0.792578	+	0.457595i	−0.0268555	+	0.0155050i
$872$	12.7804	+	3.42451i	0.432800	+	0.115968i
$873$		0			0
$874$	−28.1515			−0.952240
$875$	25.5713	−	14.8697i	0.864469	−	0.502687i
$876$		0			0
$877$	−10.2134	−	38.1169i	−0.344882	−	1.28712i	−0.892750	−	0.450552i	$-0.851227\pi$
$877$	−10.2134	−	38.1169i	−0.344882	−	1.28712i	0.547868	−	0.836565i	$-0.315440\pi$
$878$	−13.6270	−	3.65133i	−0.459888	−	0.123227i
$879$		0			0
$880$	−7.37662	−	5.21463i	−0.248666	−	0.175785i
$881$		−	52.5926i		−	1.77189i	−0.463791	−	0.885945i	$-0.653511\pi$
$881$		−	52.5926i		−	1.77189i	0.463791	−	0.885945i	$-0.346489\pi$
$882$		0			0
$883$	13.0940	+	13.0940i	0.440649	+	0.440649i	0.892230	−	0.451581i	$-0.149140\pi$
$883$	13.0940	+	13.0940i	0.440649	+	0.440649i	−0.451581	+	0.892230i	$0.649140\pi$
$884$	−0.511811	−	0.295494i	−0.0172141	−	0.00993854i
$885$		0			0
$886$	−10.5317	−	18.2414i	−0.353819	−	0.612833i
$887$	−35.6990	+	9.56553i	−1.19866	+	0.321179i	−0.802302	−	0.596919i	$-0.796391\pi$
$887$	−35.6990	+	9.56553i	−1.19866	+	0.321179i	−0.396354	+	0.918098i	$0.629725\pi$
$888$		0			0
$889$	8.22991	−	0.136303i	0.276022	−	0.00457146i
$890$	4.39223	+	5.28239i	0.147228	+	0.177066i
$891$		0			0
$892$	3.42318	−	12.7755i	0.114617	−	0.427755i
$893$	0.505946	−	1.88822i	0.0169308	−	0.0631867i
$894$		0			0
$895$	8.60543	+	0.791785i	0.287648	+	0.0264664i
$896$	−2.31288	−	1.28475i	−0.0772679	−	0.0429205i
$897$		0			0
$898$	30.2574	−	8.10744i	1.00970	−	0.270549i
$899$	−26.1742	−	45.3351i	−0.872959	−	1.51201i
$900$		0			0
$901$	14.6310	+	8.44719i	0.487428	+	0.281417i
$902$	7.39156	+	7.39156i	0.246112	+	0.246112i
$903$		0			0
$904$		−	13.7933i		−	0.458759i
$905$	9.02378	−	12.7651i	0.299961	−	0.424325i
$906$		0			0
$907$	16.0061	+	4.28883i	0.531474	+	0.142408i	0.514569	−	0.857449i	$-0.327952\pi$
$907$	16.0061	+	4.28883i	0.531474	+	0.142408i	0.0169054	+	0.999857i	$0.494619\pi$
$908$	−4.19127	−	15.6420i	−0.139092	−	0.519099i
$909$		0			0
$910$	0.566767	−	1.61769i	0.0187881	−	0.0536261i
$911$	1.46770			0.0486270			0.0243135	−	0.999704i	$-0.492260\pi$
$911$	1.46770			0.0486270			0.0243135	+	0.999704i	$0.492260\pi$
$912$		0			0
$913$	21.2676	+	5.69862i	0.703853	+	0.188597i
$914$	−2.47817	+	1.43077i	−0.0819705	+	0.0473257i
$915$		0			0
$916$		−	11.7764i		−	0.389103i
$917$	−5.30617	−	18.5674i	−0.175225	−	0.613149i
$918$		0			0
$919$	−24.1523	−	13.9443i	−0.796710	−	0.459981i	0.0456096	−	0.998959i	$-0.485477\pi$
$919$	−24.1523	−	13.9443i	−0.796710	−	0.459981i	−0.842319	+	0.538979i	$0.818810\pi$
$920$	4.24726	+	9.21597i	0.140028	+	0.303842i
$921$		0			0
$922$	2.92361	−	0.783378i	0.0962838	−	0.0257992i
$923$	1.45920	−	1.45920i	0.0480302	−	0.0480302i
$924$		0			0
$925$	−19.0642	+	13.0957i	−0.626828	+	0.430582i
$926$	13.6393	−	23.6240i	0.448215	−	0.776332i
$927$		0			0
$928$	−1.85281	+	6.91477i	−0.0608213	+	0.226988i
$929$	−16.6468	+	28.8331i	−0.546164	+	0.945984i	0.452368	+	0.891831i	$0.350579\pi$
$929$	−16.6468	+	28.8331i	−0.546164	+	0.945984i	−0.998533	+	0.0541530i	$0.982754\pi$
$930$		0			0
$931$	38.3040	+	20.4544i	1.25536	+	0.670367i
$932$	4.04765	−	4.04765i	0.132585	−	0.132585i
$933$		0			0
$934$	−12.5645	−	21.7623i	−0.411122	−	0.712084i
$935$	−17.2866	−	6.37976i	−0.565333	−	0.208641i
$936$		0			0
$937$	−25.6651	−	25.6651i	−0.838442	−	0.838442i	0.150212	−	0.988654i	$-0.452004\pi$
$937$	−25.6651	−	25.6651i	−0.838442	−	0.838442i	−0.988654	+	0.150212i	$0.952004\pi$
$938$	−5.81071	+	6.00642i	−0.189726	+	0.196117i
$939$		0			0
$940$	−0.694478	+	0.119246i	−0.0226514	+	0.00388938i
$941$	21.0732	−	12.1666i	0.686967	−	0.396621i	−0.115508	−	0.993307i	$-0.536849\pi$
$941$	21.0732	−	12.1666i	0.686967	−	0.396621i	0.802475	+	0.596686i	$0.203516\pi$
$942$		0			0
$943$	−3.03911	−	11.3421i	−0.0989670	−	0.369350i
$944$	0.855404			0.0278410
$945$		0			0
$946$	28.4413			0.924707
$947$	0.556477	+	2.07680i	0.0180831	+	0.0674869i	0.974378	−	0.224918i	$-0.0722113\pi$
$947$	0.556477	+	2.07680i	0.0180831	+	0.0674869i	−0.956295	+	0.292405i	$0.905545\pi$
$948$		0			0
$949$	2.89206	−	1.66973i	0.0938804	−	0.0542019i
$950$	−2.42601	−	30.9216i	−0.0787101	−	1.00323i
$951$		0			0
$952$	−5.23517	−	1.31024i	−0.169673	−	0.0424652i
$953$	13.1863	+	13.1863i	0.427146	+	0.427146i	0.887655	−	0.460509i	$-0.152333\pi$
$953$	13.1863	+	13.1863i	0.427146	+	0.427146i	−0.460509	+	0.887655i	$0.652333\pi$
$954$		0			0
$955$	9.08659	−	4.18763i	0.294035	−	0.135509i
$956$	−4.16897	−	7.22087i	−0.134834	−	0.233540i
$957$		0			0
$958$	−5.85973	+	5.85973i	−0.189319	+	0.189319i
$959$	−9.76792	−	16.2895i	−0.315423	−	0.526015i
$960$		0			0
$961$	11.2368	−	19.4627i	0.362477	−	0.627829i
$962$	−0.346883	+	1.29459i	−0.0111840	+	0.0417391i
$963$		0			0
$964$	−1.48219	+	2.56723i	−0.0477381	+	0.0826849i
$965$	−34.5156	+	28.6993i	−1.11110	+	0.923862i
$966$		0			0
$967$	−27.7931	+	27.7931i	−0.893766	+	0.893766i	−0.994875	−	0.101109i	$-0.967761\pi$
$967$	−27.7931	+	27.7931i	−0.893766	+	0.893766i	0.101109	+	0.994875i	$0.467761\pi$
$968$	−5.14006	+	1.37728i	−0.165208	+	0.0442673i
$969$		0			0
$970$	19.0441	−	8.77662i	0.611468	−	0.281800i
$971$	−12.1029	−	6.98760i	−0.388400	−	0.224243i	0.293067	−	0.956092i	$-0.405324\pi$
$971$	−12.1029	−	6.98760i	−0.388400	−	0.224243i	−0.681467	+	0.731849i	$0.738658\pi$
$972$		0			0
$973$	23.6119	+	22.8425i	0.756963	+	0.732298i
$974$			10.6783i			0.342155i
$975$		0			0
$976$	−5.99356	+	3.46038i	−0.191849	+	0.110764i
$977$	8.06456	+	2.16089i	0.258008	+	0.0691331i	0.385505	−	0.922706i	$-0.374027\pi$
$977$	8.06456	+	2.16089i	0.258008	+	0.0691331i	−0.127496	+	0.991839i	$0.540694\pi$
$978$		0			0
$979$	12.4120			0.396690
$980$	0.917190	−	15.6256i	0.0292986	−	0.499141i
$981$		0			0
$982$	6.65836	+	24.8494i	0.212477	+	0.792975i
$983$	23.5262	+	6.30383i	0.750370	+	0.201061i	0.613682	−	0.789553i	$-0.289688\pi$
$983$	23.5262	+	6.30383i	0.750370	+	0.201061i	0.136688	+	0.990614i	$0.456354\pi$
$984$		0			0
$985$	24.4628	−	4.20041i	0.779449	−	0.133836i
$986$			14.6019i			0.465018i
$987$		0			0
$988$	−1.27091	−	1.27091i	−0.0404329	−	0.0404329i
$989$	−27.6681	−	15.9742i	−0.879794	−	0.507949i
$990$		0			0
$991$	−8.72002	−	15.1035i	−0.277000	−	0.479779i	0.693637	−	0.720324i	$-0.256007\pi$
$991$	−8.72002	−	15.1035i	−0.277000	−	0.479779i	−0.970638	+	0.240545i	$0.922674\pi$
$992$	−7.06340	+	1.89263i	−0.224263	+	0.0600911i
$993$		0			0
$994$	9.15051	−	16.4733i	0.290237	−	0.522500i
$995$	−2.21307	+	24.0525i	−0.0701590	+	0.762516i
$996$		0			0
$997$	6.77324	−	25.2781i	0.214511	−	0.800565i	−0.771827	−	0.635832i	$-0.780657\pi$
$997$	6.77324	−	25.2781i	0.214511	−	0.800565i	0.986338	−	0.164733i	$-0.0526762\pi$
$998$	3.77845	−	14.1014i	0.119605	−	0.446371i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.c.523.2		16
3.2	odd	2		70.2.k.a.33.4	yes	16
5.2	odd	4	inner	630.2.bv.c.397.4		16
7.3	odd	6	inner	630.2.bv.c.73.4		16
12.11	even	2		560.2.ci.c.33.1		16
15.2	even	4		70.2.k.a.47.2	yes	16
15.8	even	4		350.2.o.c.257.3		16
15.14	odd	2		350.2.o.c.243.1		16
21.2	odd	6		490.2.g.c.293.5		16
21.5	even	6		490.2.g.c.293.8		16
21.11	odd	6		490.2.l.c.423.1		16
21.17	even	6		70.2.k.a.3.2	✓	16
21.20	even	2		490.2.l.c.313.3		16
35.17	even	12	inner	630.2.bv.c.577.2		16
60.47	odd	4		560.2.ci.c.257.1		16
84.59	odd	6		560.2.ci.c.353.1		16
105.2	even	12		490.2.g.c.97.8		16
105.17	odd	12		70.2.k.a.17.4	yes	16
105.32	even	12		490.2.l.c.227.3		16
105.38	odd	12		350.2.o.c.157.1		16
105.47	odd	12		490.2.g.c.97.5		16
105.59	even	6		350.2.o.c.143.3		16
105.62	odd	4		490.2.l.c.117.1		16
420.227	even	12		560.2.ci.c.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.2	✓	16	21.17	even	6
70.2.k.a.17.4	yes	16	105.17	odd	12
70.2.k.a.33.4	yes	16	3.2	odd	2
70.2.k.a.47.2	yes	16	15.2	even	4
350.2.o.c.143.3		16	105.59	even	6
350.2.o.c.157.1		16	105.38	odd	12
350.2.o.c.243.1		16	15.14	odd	2
350.2.o.c.257.3		16	15.8	even	4
490.2.g.c.97.5		16	105.47	odd	12
490.2.g.c.97.8		16	105.2	even	12
490.2.g.c.293.5		16	21.2	odd	6
490.2.g.c.293.8		16	21.5	even	6
490.2.l.c.117.1		16	105.62	odd	4
490.2.l.c.227.3		16	105.32	even	12
490.2.l.c.313.3		16	21.20	even	2
490.2.l.c.423.1		16	21.11	odd	6
560.2.ci.c.17.1		16	420.227	even	12
560.2.ci.c.33.1		16	12.11	even	2
560.2.ci.c.257.1		16	60.47	odd	4
560.2.ci.c.353.1		16	84.59	odd	6
630.2.bv.c.73.4		16	7.3	odd	6	inner
630.2.bv.c.397.4		16	5.2	odd	4	inner
630.2.bv.c.523.2		16	1.1	even	1	trivial
630.2.bv.c.577.2		16	35.17	even	12	inner

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.82591 + 1.29076i) q^{5} +(-1.90155 - 1.83959i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.82591 + 1.29076i) q^{5} +(-1.90155 - 1.83959i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.774197 - 2.09777i) q^{10} +(-2.01999 - 3.49872i) q^{11} +(-0.204875 + 0.204875i) q^{13} +(-1.28475 + 2.31288i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.527924 - 1.97024i) q^{17} +(3.10166 - 5.37224i) q^{19} +(-2.22666 - 0.204875i) q^{20} +(-2.85669 + 2.85669i) q^{22} +(4.38350 - 1.17456i) q^{23} +(1.66789 + 4.71361i) q^{25} +(0.250919 + 0.144868i) q^{26} +(2.56659 + 0.642357i) q^{28} -7.15869i q^{29} +(6.33287 - 3.65628i) q^{31} +(-0.965926 - 0.258819i) q^{32} -2.03974 q^{34} +(-1.09759 - 5.81337i) q^{35} +(1.19723 + 4.46814i) q^{37} +(-5.99195 - 1.60554i) q^{38} +(0.378409 + 2.20382i) q^{40} -2.58745i q^{41} +(-4.97801 - 4.97801i) q^{43} +(3.49872 + 2.01999i) q^{44} +(-2.26907 - 3.93014i) q^{46} +(0.304388 - 0.0815604i) q^{47} +(0.231803 + 6.99616i) q^{49} +(4.12132 - 2.83103i) q^{50} +(0.0749894 - 0.279864i) q^{52} +(-2.14370 + 8.00039i) q^{53} +(0.827689 - 8.99566i) q^{55} +(-0.0438127 - 2.64539i) q^{56} +(-6.91477 + 1.85281i) q^{58} +(0.427702 + 0.740802i) q^{59} +(-5.99356 - 3.46038i) q^{61} +(-5.17076 - 5.17076i) q^{62} +1.00000i q^{64} +(-0.638527 + 0.109639i) q^{65} +(3.05106 + 0.817530i) q^{67} +(0.527924 + 1.97024i) q^{68} +(-5.33121 + 2.56480i) q^{70} -7.12240 q^{71} +(-11.1331 - 2.98311i) q^{73} +(4.00603 - 2.31288i) q^{74} +6.20333i q^{76} +(-2.59511 + 10.3690i) q^{77} +(4.39618 + 2.53813i) q^{79} +(2.03078 - 0.935904i) q^{80} +(-2.49929 + 0.669683i) q^{82} +(-3.85372 + 3.85372i) q^{83} +(3.50704 - 2.91605i) q^{85} +(-3.51999 + 6.09680i) q^{86} +(1.04562 - 3.90231i) q^{88} +(-1.53615 + 2.66069i) q^{89} +(0.766467 - 0.0126942i) q^{91} +(-3.20895 + 3.20895i) q^{92} +(-0.157563 - 0.272906i) q^{94} +(12.5976 - 5.80572i) q^{95} +(6.63103 + 6.63103i) q^{97} +(6.69778 - 2.03464i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 + 8 * q^7	\( 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47} + 32 q^{50} + 28 q^{53} + 4 q^{56} - 32 q^{58} - 12 q^{61} + 8 q^{65} + 32 q^{67} + 36 q^{68} - 12 q^{70} - 16 q^{71} - 12 q^{73} - 16 q^{77} + 12 q^{80} - 48 q^{82} + 24 q^{85} - 12 q^{86} - 4 q^{88} - 16 q^{91} - 8 q^{92} - 20 q^{95} - 40 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

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