LMFDB - Embedded newform 350.3.k.e.101.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,3,Mod(101,350)] 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("350.101"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	350.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.53680925261$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 42x^{14} + 1322x^{12} - 17616x^{10} + 175407x^{8} - 205392x^{6} + 203018x^{4} - 23226x^{2} + 2401 $ x^16 - 42x^14 + 1322x^12 - 17616x^10 + 175407x^8 - 205392x^6 + 203018x^4 - 23226*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Root			$-0.898665 - 0.518845i$ of defining polynomial
Character	$\chi$	$=$	350.101
Dual form			350.3.k.e.201.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(-0.898665 - 0.518845i) q^{3} +(-1.00000 + 1.73205i) q^{4} -1.46751i q^{6} +(2.09417 + 6.67941i) q^{7} -2.82843 q^{8} +(-3.96160 - 6.86169i) q^{9} +(-6.23704 + 10.8029i) q^{11} +(1.79733 - 1.03769i) q^{12} +0.748223i q^{13} +(-6.69977 + 7.28787i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-10.0032 - 5.77534i) q^{17} +(5.60255 - 9.70390i) q^{18} +(-13.0948 + 7.56027i) q^{19} +(1.58362 - 7.08910i) q^{21} -17.6410 q^{22} +(18.1566 + 31.4481i) q^{23} +(2.54181 + 1.46751i) q^{24} +(-0.916382 + 0.529074i) q^{26} +17.5610i q^{27} +(-13.6632 - 3.05220i) q^{28} -50.5846 q^{29} +(-40.4989 - 23.3820i) q^{31} +(2.82843 - 4.89898i) q^{32} +(11.2100 - 6.47211i) q^{33} -16.3351i q^{34} +15.8464 q^{36} +(5.86915 + 10.1657i) q^{37} +(-18.5188 - 10.6918i) q^{38} +(0.388211 - 0.672402i) q^{39} +12.7397i q^{41} +(9.80212 - 3.07322i) q^{42} -26.2604 q^{43} +(-12.4741 - 21.6057i) q^{44} +(-25.6773 + 44.4743i) q^{46} +(35.0296 - 20.2244i) q^{47} +4.15076i q^{48} +(-40.2289 + 27.9756i) q^{49} +(5.99301 + 10.3802i) q^{51} +(-1.29596 - 0.748223i) q^{52} +(-13.1861 + 22.8390i) q^{53} +(-21.5078 + 12.4175i) q^{54} +(-5.92320 - 18.8922i) q^{56} +15.6904 q^{57} +(-35.7687 - 61.9532i) q^{58} +(68.4898 + 39.5426i) q^{59} +(45.2611 - 26.1315i) q^{61} -66.1344i q^{62} +(37.5358 - 40.8307i) q^{63} +8.00000 q^{64} +(15.8534 + 9.15294i) q^{66} +(17.3504 - 30.0519i) q^{67} +(20.0064 - 11.5507i) q^{68} -37.6817i q^{69} +14.6636 q^{71} +(11.2051 + 19.4078i) q^{72} +(87.6124 + 50.5830i) q^{73} +(-8.30023 + 14.3764i) q^{74} -30.2411i q^{76} +(-85.2182 - 19.0367i) q^{77} +1.09803 q^{78} +(-17.8625 - 30.9387i) q^{79} +(-26.5430 + 45.9738i) q^{81} +(-15.6029 + 9.00833i) q^{82} +80.8664i q^{83} +(10.6951 + 9.83200i) q^{84} +(-18.5689 - 32.1623i) q^{86} +(45.4586 + 26.2455i) q^{87} +(17.6410 - 30.5551i) q^{88} +(117.103 - 67.6093i) q^{89} +(-4.99769 + 1.56690i) q^{91} -72.6263 q^{92} +(24.2633 + 42.0252i) q^{93} +(49.5394 + 28.6016i) q^{94} +(-5.08362 + 2.93503i) q^{96} +91.4185i q^{97} +(-62.7091 - 29.4884i) q^{98} +98.8347 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 12 q^{9} - 12 q^{11} - 32 q^{14} - 32 q^{16} + 12 q^{19} - 8 q^{21} + 24 q^{24} - 48 q^{26} + 136 q^{29} + 84 q^{31} - 48 q^{36} - 312 q^{39} - 24 q^{44} - 68 q^{46} - 296 q^{49} - 76 q^{51}+ \cdots - 176 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 12 * q^9 - 12 * q^11 - 32 * q^14 - 32 * q^16 + 12 * q^19 - 8 * q^21 + 24 * q^24 - 48 * q^26 + 136 * q^29 + 84 * q^31 - 48 * q^36 - 312 * q^39 - 24 * q^44 - 68 * q^46 - 296 * q^49 - 76 * q^51 + 108 * q^54 + 56 * q^56 + 372 * q^59 + 348 * q^61 + 128 * q^64 + 480 * q^66 - 384 * q^71 - 208 * q^74 - 148 * q^79 - 140 * q^81 - 256 * q^84 - 188 * q^86 + 912 * q^89 - 616 * q^91 + 600 * q^94 - 48 * q^96 - 176 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	−0.898665	−	0.518845i	−0.299555	−	0.172948i	0.342688	−	0.939449i	$-0.388663\pi$
$3$	−0.898665	−	0.518845i	−0.299555	−	0.172948i	−0.642243	+	0.766501i	$0.721996\pi$
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		−	1.46751i		−	0.244586i
$7$	2.09417	+	6.67941i	0.299167	+	0.954201i
$7$	2.09417	+	6.67941i	0.299167	+	0.954201i
$8$	−2.82843			−0.353553
$9$	−3.96160	−	6.86169i	−0.440178	−	0.762410i
$10$		0			0
$11$	−6.23704	+	10.8029i	−0.567004	+	0.982079i	0.429856	+	0.902897i	$0.358564\pi$
$11$	−6.23704	+	10.8029i	−0.567004	+	0.982079i	−0.996860	+	0.0791820i	$0.974769\pi$
$12$	1.79733	−	1.03769i	0.149778	−	0.0864741i
$13$			0.748223i			0.0575556i	0.999586	+	0.0287778i	$0.00916153\pi$
$13$			0.748223i			0.0575556i	−0.999586	+	0.0287778i	$0.990838\pi$
$14$	−6.69977	+	7.28787i	−0.478555	+	0.520562i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−10.0032	−	5.77534i	−0.588422	−	0.339726i	0.176051	−	0.984381i	$-0.443668\pi$
$17$	−10.0032	−	5.77534i	−0.588422	−	0.339726i	−0.764473	+	0.644655i	$0.777001\pi$
$18$	5.60255	−	9.70390i	0.311253	−	0.539106i
$19$	−13.0948	+	7.56027i	−0.689198	+	0.397909i	−0.803312	−	0.595559i	$-0.796931\pi$
$19$	−13.0948	+	7.56027i	−0.689198	+	0.397909i	0.114113	+	0.993468i	$0.463597\pi$
$20$		0			0
$21$	1.58362	−	7.08910i	0.0754104	−	0.337576i
$22$	−17.6410			−0.801864
$23$	18.1566	+	31.4481i	0.789416	+	1.36731i	0.926325	+	0.376725i	$0.122950\pi$
$23$	18.1566	+	31.4481i	0.789416	+	1.36731i	−0.136909	+	0.990584i	$0.543717\pi$
$24$	2.54181	+	1.46751i	0.105909	+	0.0611464i
$25$		0			0
$26$	−0.916382	+	0.529074i	−0.0352455	+	0.0203490i
$27$			17.5610i			0.650408i
$28$	−13.6632	−	3.05220i	−0.487973	−	0.109007i
$29$	−50.5846			−1.74430			−0.872148	−	0.489243i	$-0.837273\pi$
$29$	−50.5846			−1.74430			−0.872148	+	0.489243i	$0.837273\pi$
$30$		0			0
$31$	−40.4989	−	23.3820i	−1.30642	−	0.754259i	−0.324919	−	0.945742i	$-0.605337\pi$
$31$	−40.4989	−	23.3820i	−1.30642	−	0.754259i	−0.981496	+	0.191483i	$0.938670\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	11.2100	−	6.47211i	0.339698	−	0.196125i
$34$		−	16.3351i		−	0.480445i
$35$		0			0
$36$	15.8464			0.440178
$37$	5.86915	+	10.1657i	0.158626	+	0.274748i	0.934373	−	0.356296i	$-0.115960\pi$
$37$	5.86915	+	10.1657i	0.158626	+	0.274748i	−0.775748	+	0.631043i	$0.782627\pi$
$38$	−18.5188	−	10.6918i	−0.487337	−	0.281364i
$39$	0.388211	−	0.672402i	0.00995414	−	0.0172411i
$40$		0			0
$41$			12.7397i			0.310724i	0.987858	+	0.155362i	$0.0496545\pi$
$41$			12.7397i			0.310724i	−0.987858	+	0.155362i	$0.950346\pi$
$42$	9.80212	−	3.07322i	0.233384	−	0.0731719i
$43$	−26.2604			−0.610706			−0.305353	−	0.952239i	$-0.598774\pi$
$43$	−26.2604			−0.610706			−0.305353	+	0.952239i	$0.598774\pi$
$44$	−12.4741	−	21.6057i	−0.283502	−	0.491040i
$45$		0			0
$46$	−25.6773	+	44.4743i	−0.558201	+	0.966833i
$47$	35.0296	−	20.2244i	0.745311	−	0.430305i	−0.0786862	−	0.996899i	$-0.525073\pi$
$47$	35.0296	−	20.2244i	0.745311	−	0.430305i	0.823997	+	0.566594i	$0.191739\pi$
$48$			4.15076i			0.0864741i
$49$	−40.2289	+	27.9756i	−0.820998	+	0.570930i
$50$		0			0
$51$	5.99301	+	10.3802i	0.117510	+	0.203533i
$52$	−1.29596	−	0.748223i	−0.0249223	−	0.0143889i
$53$	−13.1861	+	22.8390i	−0.248794	+	0.430924i	−0.963191	−	0.268816i	$-0.913368\pi$
$53$	−13.1861	+	22.8390i	−0.248794	+	0.430924i	0.714398	+	0.699740i	$0.246701\pi$
$54$	−21.5078	+	12.4175i	−0.398292	+	0.229954i
$55$		0			0
$56$	−5.92320	−	18.8922i	−0.105771	−	0.337361i
$57$	15.6904			0.275270
$58$	−35.7687	−	61.9532i	−0.616702	−	1.06816i
$59$	68.4898	+	39.5426i	1.16084	+	0.670214i	0.951506	−	0.307630i	$-0.0995358\pi$
$59$	68.4898	+	39.5426i	1.16084	+	0.670214i	0.209338	+	0.977843i	$0.432869\pi$
$60$		0			0
$61$	45.2611	−	26.1315i	0.741985	−	0.428385i	−0.0808056	−	0.996730i	$-0.525749\pi$
$61$	45.2611	−	26.1315i	0.741985	−	0.428385i	0.822791	+	0.568345i	$0.192416\pi$
$62$		−	66.1344i		−	1.06668i
$63$	37.5358	−	40.8307i	0.595806	−	0.648106i
$64$	8.00000			0.125000
$65$		0			0
$66$	15.8534	+	9.15294i	0.240202	+	0.138681i
$67$	17.3504	−	30.0519i	0.258962	−	0.448535i	−0.707002	−	0.707211i	$-0.749953\pi$
$67$	17.3504	−	30.0519i	0.258962	−	0.448535i	0.965964	+	0.258676i	$0.0832863\pi$
$68$	20.0064	−	11.5507i	0.294211	−	0.169863i
$69$		−	37.6817i		−	0.546112i
$70$		0			0
$71$	14.6636			0.206530			0.103265	−	0.994654i	$-0.467071\pi$
$71$	14.6636			0.206530			0.103265	+	0.994654i	$0.467071\pi$
$72$	11.2051	+	19.4078i	0.155626	+	0.269553i
$73$	87.6124	+	50.5830i	1.20017	+	0.692918i	0.960593	−	0.277959i	$-0.0896581\pi$
$73$	87.6124	+	50.5830i	1.20017	+	0.692918i	0.239577	+	0.970877i	$0.422991\pi$
$74$	−8.30023	+	14.3764i	−0.112165	+	0.194276i
$75$		0			0
$76$		−	30.2411i		−	0.397909i
$77$	−85.2182	−	19.0367i	−1.10673	−	0.247230i
$78$	1.09803			0.0140773
$79$	−17.8625	−	30.9387i	−0.226107	−	0.391629i	0.730544	−	0.682866i	$-0.239267\pi$
$79$	−17.8625	−	30.9387i	−0.226107	−	0.391629i	−0.956651	+	0.291237i	$0.905933\pi$
$80$		0			0
$81$	−26.5430	+	45.9738i	−0.327691	+	0.567577i
$82$	−15.6029	+	9.00833i	−0.190279	+	0.109858i
$83$			80.8664i			0.974293i	0.873320	+	0.487147i	$0.161962\pi$
$83$			80.8664i			0.974293i	−0.873320	+	0.487147i	$0.838038\pi$
$84$	10.6951	+	9.83200i	0.127322	+	0.117048i
$85$		0			0
$86$	−18.5689	−	32.1623i	−0.215917	−	0.373980i
$87$	45.4586	+	26.2455i	0.522512	+	0.301673i
$88$	17.6410	−	30.5551i	0.200466	−	0.347217i
$89$	117.103	−	67.6093i	1.31576	−	0.759655i	0.332717	−	0.943027i	$-0.392035\pi$
$89$	117.103	−	67.6093i	1.31576	−	0.759655i	0.983044	+	0.183372i	$0.0587012\pi$
$90$		0			0
$91$	−4.99769	+	1.56690i	−0.0549196	+	0.0172187i
$92$	−72.6263			−0.789416
$93$	24.2633	+	42.0252i	0.260895	+	0.451884i
$94$	49.5394	+	28.6016i	0.527014	+	0.304272i
$95$		0			0
$96$	−5.08362	+	2.93503i	−0.0529543	+	0.0305732i
$97$			91.4185i			0.942459i	0.882011	+	0.471230i	$0.156190\pi$
$97$			91.4185i			0.942459i	−0.882011	+	0.471230i	$0.843810\pi$
$98$	−62.7091	−	29.4884i	−0.639889	−	0.300902i
$99$	98.8347			0.998330
$100$		0			0
$101$	76.2197	+	44.0054i	0.754650	+	0.435698i	0.827372	−	0.561655i	$-0.189835\pi$
$101$	76.2197	+	44.0054i	0.754650	+	0.435698i	−0.0727215	+	0.997352i	$0.523168\pi$
$102$	−8.47539	+	14.6798i	−0.0830921	+	0.143920i
$103$	97.5104	−	56.2976i	0.946703	−	0.546579i	0.0546475	−	0.998506i	$-0.482596\pi$
$103$	97.5104	−	56.2976i	0.946703	−	0.546579i	0.892055	+	0.451927i	$0.149263\pi$
$104$		−	2.11629i		−	0.0203490i
$105$		0			0
$106$	−37.2959			−0.351848
$107$	−1.43644	−	2.48799i	−0.0134247	−	0.0232523i	0.859235	−	0.511581i	$-0.170940\pi$
$107$	−1.43644	−	2.48799i	−0.0134247	−	0.0232523i	−0.872660	+	0.488329i	$0.837607\pi$
$108$	−30.4166	−	17.5610i	−0.281635	−	0.162602i
$109$	−42.6084	+	73.8000i	−0.390903	+	0.677064i	−0.992569	−	0.121684i	$-0.961171\pi$
$109$	−42.6084	+	73.8000i	−0.390903	+	0.677064i	0.601666	+	0.798748i	$0.294504\pi$
$110$		0			0
$111$		−	12.1807i		−	0.109736i
$112$	18.9498	−	20.6132i	0.169195	−	0.184047i
$113$	−211.525			−1.87190			−0.935950	−	0.352132i	$-0.885457\pi$
$113$	−211.525			−1.87190			−0.935950	+	0.352132i	$0.885457\pi$
$114$	11.0948	+	19.2168i	0.0973228	+	0.168568i
$115$		0			0
$116$	50.5846	−	87.6150i	0.436074	−	0.755302i
$117$	5.13408	−	2.96416i	0.0438810	−	0.0253347i
$118$			111.843i			0.947825i
$119$	17.6275	−	78.9098i	0.148130	−	0.663108i
$120$		0			0
$121$	−17.3014	−	29.9668i	−0.142986	−	0.247660i
$122$	64.0088	+	36.9555i	0.524663	+	0.302914i
$123$	6.60993	−	11.4487i	0.0537392	−	0.0930791i
$124$	80.9977	−	46.7641i	0.653208	−	0.377130i
$125$		0			0
$126$	76.5490	+	17.1001i	0.607531	+	0.135715i
$127$	52.2434			0.411366			0.205683	−	0.978619i	$-0.434058\pi$
$127$	52.2434			0.411366			0.205683	+	0.978619i	$0.434058\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	23.5993	+	13.6250i	0.182940	+	0.105621i
$130$		0			0
$131$	81.3342	−	46.9583i	0.620872	−	0.358461i	−0.156336	−	0.987704i	$-0.549968\pi$
$131$	81.3342	−	46.9583i	0.620872	−	0.358461i	0.777208	+	0.629243i	$0.216635\pi$
$132$			25.8884i			0.196125i
$133$	−77.9207	−	71.6328i	−0.585870	−	0.538592i
$134$	49.0745			0.366227
$135$		0			0
$136$	28.2933	+	16.3351i	0.208039	+	0.120111i
$137$	−58.4189	+	101.185i	−0.426415	+	0.738573i	−0.996551	−	0.0829771i	$-0.973557\pi$
$137$	−58.4189	+	101.185i	−0.426415	+	0.738573i	0.570136	+	0.821550i	$0.306891\pi$
$138$	46.1505	−	26.6450i	0.334424	−	0.193080i
$139$		−	67.8796i		−	0.488342i	−0.969732	−	0.244171i	$-0.921484\pi$
$139$		−	67.8796i		−	0.488342i	0.969732	−	0.244171i	$-0.0785159\pi$
$140$		0			0
$141$	−41.9732			−0.297682
$142$	10.3687	+	17.9592i	0.0730193	+	0.126473i
$143$	−8.08296	−	4.66670i	−0.0565242	−	0.0326343i
$144$	−15.8464	+	27.4468i	−0.110044	+	0.190603i
$145$		0			0
$146$			143.070i			0.979934i
$147$	50.6673	−	4.26813i	0.344676	−	0.0290349i
$148$	−23.4766			−0.158626
$149$	86.0779	+	149.091i	0.577704	+	1.00061i	0.995742	+	0.0921836i	$0.0293847\pi$
$149$	86.0779	+	149.091i	0.577704	+	1.00061i	−0.418038	+	0.908430i	$0.637282\pi$
$150$		0			0
$151$	55.1081	−	95.4500i	0.364954	−	0.632119i	−0.623815	−	0.781572i	$-0.714418\pi$
$151$	55.1081	−	95.4500i	0.364954	−	0.632119i	0.988769	+	0.149453i	$0.0477514\pi$
$152$	37.0376	−	21.3837i	0.243668	−	0.140682i
$153$			91.5184i			0.598159i
$154$	−36.9432	−	117.831i	−0.239891	−	0.765140i
$155$		0			0
$156$	0.776423	+	1.34480i	0.00497707	+	0.00862054i
$157$	−176.811	−	102.082i	−1.12618	−	0.650201i	−0.183210	−	0.983074i	$-0.558649\pi$
$157$	−176.811	−	102.082i	−1.12618	−	0.650201i	−0.942972	+	0.332873i	$0.891982\pi$
$158$	25.2613	−	43.7539i	0.159882	−	0.276924i
$159$	23.6997	−	13.6830i	0.149055	−	0.0860569i
$160$		0			0
$161$	−172.032	+	187.133i	−1.06852	+	1.16231i
$162$	−75.0748			−0.463425
$163$	48.9358	+	84.7593i	0.300220	+	0.519996i	0.976186	−	0.216937i	$-0.0696067\pi$
$163$	48.9358	+	84.7593i	0.300220	+	0.519996i	−0.675966	+	0.736933i	$0.736273\pi$
$164$	−22.0658	−	12.7397i	−0.134548	−	0.0776811i
$165$		0			0
$166$	−99.0407	+	57.1811i	−0.596630	+	0.344465i
$167$			97.1736i			0.581878i	0.956742	+	0.290939i	$0.0939676\pi$
$167$			97.1736i			0.581878i	−0.956742	+	0.290939i	$0.906032\pi$
$168$	−4.47915	+	20.0510i	−0.0266616	+	0.119351i
$169$	168.440			0.996687
$170$		0			0
$171$	103.752	+	59.9015i	0.606740	+	0.350301i
$172$	26.2604	−	45.4843i	0.152677	−	0.264444i
$173$	53.5699	−	30.9286i	0.309652	−	0.178778i	−0.337118	−	0.941462i	$-0.609452\pi$
$173$	53.5699	−	30.9286i	0.309652	−	0.178778i	0.646771	+	0.762684i	$0.276119\pi$
$174$			74.2336i			0.426630i
$175$		0			0
$176$	49.8963			0.283502
$177$	−41.0329	−	71.0711i	−0.231824	−	0.401532i
$178$	165.608	+	95.6140i	0.930383	+	0.537157i
$179$	−112.111	+	194.181i	−0.626316	+	1.08481i	0.361968	+	0.932190i	$0.382105\pi$
$179$	−112.111	+	194.181i	−0.626316	+	1.08481i	−0.988285	+	0.152622i	$0.951228\pi$
$180$		0			0
$181$		−	329.246i		−	1.81904i	−0.415659	−	0.909520i	$-0.636449\pi$
$181$		−	329.246i		−	1.81904i	0.415659	−	0.909520i	$-0.363551\pi$
$182$	−5.45296	−	5.01292i	−0.0299613	−	0.0275435i
$183$	−54.2327			−0.296354
$184$	−51.3545	−	88.9486i	−0.279101	−	0.483416i
$185$		0			0
$186$	−34.3135	+	59.4327i	−0.184481	+	0.319530i
$187$	124.781	−	72.0421i	0.667275	−	0.385252i
$188$			80.8974i			0.430305i
$189$	−117.297	+	36.7757i	−0.620620	+	0.194581i
$190$		0			0
$191$	33.1175	+	57.3612i	0.173390	+	0.300320i	0.939603	−	0.342266i	$-0.111195\pi$
$191$	33.1175	+	57.3612i	0.173390	+	0.300320i	−0.766213	+	0.642587i	$0.777861\pi$
$192$	−7.18932	−	4.15076i	−0.0374444	−	0.0216185i
$193$	126.728	−	219.500i	0.656623	−	1.13730i	−0.324861	−	0.945762i	$-0.605318\pi$
$193$	126.728	−	219.500i	0.656623	−	1.13730i	0.981484	−	0.191543i	$-0.0613491\pi$
$194$	−111.964	+	64.6427i	−0.577136	+	0.333210i
$195$		0			0
$196$	−8.22623	−	97.6541i	−0.0419706	−	0.498235i
$197$	−191.330			−0.971217			−0.485608	−	0.874176i	$-0.661402\pi$
$197$	−191.330			−0.971217			−0.485608	+	0.874176i	$0.661402\pi$
$198$	69.8867	+	121.047i	0.352963	+	0.611350i
$199$	−195.609	−	112.935i	−0.982960	−	0.567512i	−0.0797973	−	0.996811i	$-0.525427\pi$
$199$	−195.609	−	112.935i	−0.982960	−	0.567512i	−0.903162	+	0.429299i	$0.858761\pi$
$200$		0			0
$201$	−31.1845	+	18.0044i	−0.155147	+	0.0895740i
$202$			124.466i			0.616169i
$203$	−105.933	−	337.875i	−0.521835	−	1.66441i
$204$	−23.9720			−0.117510
$205$		0			0
$206$	137.900	+	79.6169i	0.669420	+	0.386490i
$207$	143.858	−	249.170i	0.694967	−	1.20372i
$208$	2.59192	−	1.49645i	0.0124612	−	0.00719445i
$209$		−	188.615i		−	0.902463i
$210$		0			0
$211$	−186.816			−0.885386			−0.442693	−	0.896673i	$-0.645977\pi$
$211$	−186.816			−0.885386			−0.442693	+	0.896673i	$0.645977\pi$
$212$	−26.3722	−	45.6779i	−0.124397	−	0.215462i
$213$	−13.1777	−	7.60814i	−0.0618670	−	0.0357190i
$214$	2.03144	−	3.51855i	0.00949270	−	0.0164418i
$215$		0			0
$216$		−	49.6701i		−	0.229954i
$217$	71.3667	−	319.474i	0.328879	−	1.47223i
$218$	−120.515			−0.552821
$219$	−52.4894	−	90.9144i	−0.239678	−	0.415134i
$220$		0			0
$221$	4.32124	−	7.48461i	0.0195531	−	0.0338670i
$222$	14.9183	−	8.61306i	0.0671994	−	0.0387976i
$223$			194.106i			0.870431i	0.900326	+	0.435215i	$0.143328\pi$
$223$			194.106i			0.870431i	−0.900326	+	0.435215i	$0.856672\pi$
$224$	38.6455	+	8.63293i	0.172524	+	0.0385399i
$225$		0			0
$226$	−149.571	−	259.064i	−0.661817	−	1.14630i
$227$	304.630	+	175.878i	1.34198	+	0.774795i	0.987098	−	0.160115i	$-0.0511864\pi$
$227$	304.630	+	175.878i	1.34198	+	0.774795i	0.354886	+	0.934910i	$0.384520\pi$
$228$	−15.6904	+	27.1766i	−0.0688176	+	0.119196i
$229$	−162.993	+	94.1041i	−0.711760	+	0.410935i	−0.811712	−	0.584057i	$-0.801464\pi$
$229$	−162.993	+	94.1041i	−0.711760	+	0.410935i	0.0999523	+	0.994992i	$0.468131\pi$
$230$		0			0
$231$	66.7055	+	61.3226i	0.288768	+	0.265466i
$232$	143.075			0.616702
$233$	−157.040	−	272.001i	−0.673991	−	1.16739i	−0.976763	−	0.214324i	$-0.931245\pi$
$233$	−157.040	−	272.001i	−0.673991	−	1.16739i	0.302772	−	0.953063i	$-0.402088\pi$
$234$	7.26068	+	4.19196i	0.0310286	+	0.0179143i
$235$		0			0
$236$	−136.980	+	79.0852i	−0.580422	+	0.335107i
$237$			37.0714i			0.156419i
$238$	109.109	−	34.2085i	0.458441	−	0.143733i
$239$	−336.269			−1.40699			−0.703493	−	0.710703i	$-0.748377\pi$
$239$	−336.269			−1.40699			−0.703493	+	0.710703i	$0.748377\pi$
$240$		0			0
$241$	−331.276	−	191.262i	−1.37459	−	0.793619i	−0.383086	−	0.923713i	$-0.625139\pi$
$241$	−331.276	−	191.262i	−1.37459	−	0.793619i	−0.991502	+	0.130094i	$0.958472\pi$
$242$	24.4678	−	42.3795i	0.101107	−	0.175122i
$243$	184.581	−	106.568i	0.759593	−	0.438551i
$244$			104.526i			0.428385i
$245$		0			0
$246$	18.6957			0.0759988
$247$	−5.65677	−	9.79781i	−0.0229019	−	0.0396672i
$248$	114.548	+	66.1344i	0.461887	+	0.266671i
$249$	41.9571	−	72.6718i	0.168502	−	0.291855i
$250$		0			0
$251$			302.072i			1.20347i	0.798695	+	0.601736i	$0.205524\pi$
$251$			302.072i			1.20347i	−0.798695	+	0.601736i	$0.794476\pi$
$252$	33.1850	+	105.845i	0.131687	+	0.420018i
$253$	−452.973			−1.79041
$254$	36.9417	+	63.9849i	0.145440	+	0.251909i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−177.257	+	102.339i	−0.689717	+	0.398208i	−0.803506	−	0.595297i	$-0.797034\pi$
$257$	−177.257	+	102.339i	−0.689717	+	0.398208i	0.113789	+	0.993505i	$0.463701\pi$
$258$			38.5375i			0.149370i
$259$	−55.6096	+	60.4911i	−0.214709	+	0.233556i
$260$		0			0
$261$	200.396	+	347.096i	0.767800	+	1.32987i
$262$	115.024	+	66.4091i	0.439023	+	0.253470i
$263$	−48.7155	+	84.3776i	−0.185230	+	0.320828i	−0.943654	−	0.330934i	$-0.892636\pi$
$263$	−48.7155	+	84.3776i	−0.185230	+	0.320828i	0.758424	+	0.651761i	$0.225970\pi$
$264$	−31.7067	+	18.3059i	−0.120101	+	0.0693405i
$265$		0			0
$266$	32.6336	−	146.085i	0.122683	−	0.549192i
$267$	−140.315			−0.525524
$268$	34.7009	+	60.1037i	0.129481	+	0.224268i
$269$	−83.6084	−	48.2713i	−0.310812	−	0.179447i	0.336478	−	0.941691i	$-0.390764\pi$
$269$	−83.6084	−	48.2713i	−0.310812	−	0.179447i	−0.647290	+	0.762244i	$0.724098\pi$
$270$		0			0
$271$	−72.4056	+	41.8034i	−0.267179	+	0.154256i	−0.627605	−	0.778532i	$-0.715965\pi$
$271$	−72.4056	+	41.8034i	−0.267179	+	0.154256i	0.360426	+	0.932788i	$0.382631\pi$
$272$			46.2027i			0.169863i
$273$	5.30423	+	1.18490i	0.0194294	+	0.00434029i
$274$	−165.234			−0.603043
$275$		0			0
$276$	65.2667	+	37.6817i	0.236473	+	0.136528i
$277$	−192.867	+	334.055i	−0.696271	+	1.20598i	0.273480	+	0.961878i	$0.411825\pi$
$277$	−192.867	+	334.055i	−0.696271	+	1.20598i	−0.969750	+	0.244098i	$0.921508\pi$
$278$	83.1352	−	47.9981i	0.299047	−	0.172655i
$279$			370.521i			1.32803i
$280$		0			0
$281$	243.459			0.866402			0.433201	−	0.901297i	$-0.357384\pi$
$281$	243.459			0.866402			0.433201	+	0.901297i	$0.357384\pi$
$282$	−29.6795	−	51.4064i	−0.105247	−	0.182292i
$283$	89.0540	+	51.4153i	0.314678	+	0.181680i	0.649018	−	0.760773i	$-0.275180\pi$
$283$	89.0540	+	51.4153i	0.314678	+	0.181680i	−0.334340	+	0.942453i	$0.608513\pi$
$284$	−14.6636	+	25.3981i	−0.0516324	+	0.0894300i
$285$		0			0
$286$		−	13.1994i		−	0.0461518i
$287$	−85.0936	+	26.6791i	−0.296494	+	0.0929585i
$288$	−44.8204			−0.155626
$289$	−77.7909	−	134.738i	−0.269173	−	0.466221i
$290$		0			0
$291$	47.4320	−	82.1547i	0.162997	−	0.282318i
$292$	−175.225	+	101.166i	−0.600085	+	0.346459i
$293$			440.610i			1.50379i	0.659284	+	0.751894i	$0.270859\pi$
$293$			440.610i			1.50379i	−0.659284	+	0.751894i	$0.729141\pi$
$294$	41.0546	+	59.0365i	0.139641	+	0.200804i
$295$		0			0
$296$	−16.6005	−	28.7528i	−0.0560827	−	0.0971380i
$297$	−189.709	−	109.529i	−0.638752	−	0.368784i
$298$	−121.733	+	210.847i	−0.408499	+	0.707540i
$299$	−23.5302	+	13.5852i	−0.0786963	+	0.0454353i
$300$		0			0
$301$	−54.9936	−	175.404i	−0.182703	−	0.582736i
$302$	155.869			0.516123
$303$	−45.6640	−	79.0923i	−0.150706	−	0.261031i
$304$	52.3791	+	30.2411i	0.172300	+	0.0994772i
$305$		0			0
$306$	−112.087	+	64.7133i	−0.366296	+	0.211481i
$307$		−	247.192i		−	0.805185i	−0.915379	−	0.402592i	$-0.868109\pi$
$307$		−	247.192i		−	0.805185i	0.915379	−	0.402592i	$-0.131891\pi$
$308$	118.191	−	128.566i	0.383736	−	0.417420i
$309$	−116.839			−0.378119
$310$		0			0
$311$	−369.117	−	213.110i	−1.18687	−	0.685240i	−0.229276	−	0.973361i	$-0.573636\pi$
$311$	−369.117	−	213.110i	−1.18687	−	0.685240i	−0.957594	+	0.288121i	$0.906969\pi$
$312$	−1.09803	+	1.90184i	−0.00351932	+	0.00609564i
$313$	116.025	−	66.9870i	0.370686	−	0.214016i	−0.303072	−	0.952968i	$-0.598012\pi$
$313$	116.025	−	66.9870i	0.370686	−	0.214016i	0.673758	+	0.738952i	$0.264679\pi$
$314$		−	288.730i		−	0.919523i
$315$		0			0
$316$	71.4499			0.226107
$317$	160.983	+	278.831i	0.507833	+	0.879593i	0.999959	+	0.00906850i	$0.00288663\pi$
$317$	160.983	+	278.831i	0.507833	+	0.879593i	−0.492126	+	0.870524i	$0.663780\pi$
$318$	33.5165	+	19.3508i	0.105398	+	0.0608514i
$319$	315.498	−	546.459i	0.989022	−	1.71304i
$320$		0			0
$321$			2.98116i			0.00928711i
$322$	−350.834	−	78.3721i	−1.08955	−	0.243392i
$323$	174.652			0.540720
$324$	−53.0859	−	91.9475i	−0.163845	−	0.283789i
$325$		0			0
$326$	−69.2057	+	119.868i	−0.212287	+	0.367693i
$327$	76.5814	−	44.2143i	0.234194	−	0.135212i
$328$		−	36.0333i		−	0.109858i
$329$	208.445	+	191.624i	0.633570	+	0.582443i
$330$		0			0
$331$	117.402	+	203.347i	0.354690	+	0.614342i	0.987065	−	0.160321i	$-0.0512530\pi$
$331$	117.402	+	203.347i	0.354690	+	0.614342i	−0.632375	+	0.774663i	$0.717920\pi$
$332$	−140.065	−	80.8664i	−0.421881	−	0.243573i
$333$	46.5025	−	80.5446i	0.139647	−	0.241876i
$334$	−119.013	+	68.7121i	−0.356326	+	0.205725i
$335$		0			0
$336$	−27.7246	+	8.69238i	−0.0825136	+	0.0258702i
$337$	−217.706			−0.646012			−0.323006	−	0.946397i	$-0.604693\pi$
$337$	−217.706			−0.646012			−0.323006	+	0.946397i	$0.604693\pi$
$338$	119.105	+	206.296i	0.352382	+	0.610344i
$339$	190.090	+	109.748i	0.560737	+	0.323742i
$340$		0			0
$341$	505.186	−	291.669i	1.48148	−	0.855335i
$342$			169.427i			0.495401i
$343$	−271.106	−	210.120i	−0.790398	−	0.612594i
$344$	74.2755			0.215917
$345$		0			0
$346$	75.7593	+	43.7396i	0.218957	+	0.126415i
$347$	93.1157	−	161.281i	0.268345	−	0.464787i	−0.700090	−	0.714055i	$-0.746857\pi$
$347$	93.1157	−	161.281i	0.268345	−	0.464787i	0.968435	+	0.249268i	$0.0801899\pi$
$348$	−90.9172	+	52.4911i	−0.261256	+	0.150836i
$349$			81.7368i			0.234203i	0.993120	+	0.117101i	$0.0373603\pi$
$349$			81.7368i			0.234203i	−0.993120	+	0.117101i	$0.962640\pi$
$350$		0			0
$351$	−13.1396			−0.0374347
$352$	35.2820	+	61.1103i	0.100233	+	0.173609i
$353$	93.4757	+	53.9682i	0.264804	+	0.152884i	0.626524	−	0.779402i	$-0.284477\pi$
$353$	93.4757	+	53.9682i	0.264804	+	0.152884i	−0.361720	+	0.932287i	$0.617810\pi$
$354$	58.0293	−	100.510i	0.163925	−	0.283926i
$355$		0			0
$356$			270.437i			0.759655i
$357$	−56.7832	+	61.7676i	−0.159056	+	0.173018i
$358$	−317.097			−0.885745
$359$	301.930	+	522.957i	0.841029	+	1.45671i	0.889025	+	0.457858i	$0.151383\pi$
$359$	301.930	+	522.957i	0.841029	+	1.45671i	−0.0479959	+	0.998848i	$0.515283\pi$
$360$		0			0
$361$	−66.1847	+	114.635i	−0.183337	+	0.317549i
$362$	403.243	−	232.812i	1.11393	−	0.643128i
$363$			35.9069i			0.0989169i
$364$	2.28373	−	10.2232i	0.00627398	−	0.0280856i
$365$		0			0
$366$	−38.3483	−	66.4213i	−0.104777	−	0.181479i
$367$	470.710	+	271.765i	1.28259	+	0.740503i	0.977321	−	0.211763i	$-0.0679205\pi$
$367$	470.710	+	271.765i	1.28259	+	0.740503i	0.305268	+	0.952266i	$0.401254\pi$
$368$	72.6263	−	125.792i	0.197354	−	0.341827i
$369$	87.4159	−	50.4696i	0.236900	−	0.136774i
$370$		0			0
$371$	−180.165	−	40.2466i	−0.485619	−	0.108481i
$372$	−97.0531			−0.260895
$373$	41.6452	+	72.1316i	0.111649	+	0.193382i	0.916435	−	0.400183i	$-0.131053\pi$
$373$	41.6452	+	72.1316i	0.111649	+	0.193382i	−0.804786	+	0.593565i	$0.797720\pi$
$374$	176.466	+	101.883i	0.471835	+	0.272414i
$375$		0			0
$376$	−99.0787	+	57.2031i	−0.263507	+	0.152136i
$377$		−	37.8485i		−	0.100394i
$378$	−127.983	−	117.655i	−0.338578	−	0.311256i
$379$	30.4409			0.0803189			0.0401595	−	0.999193i	$-0.487213\pi$
$379$	30.4409			0.0803189			0.0401595	+	0.999193i	$0.487213\pi$
$380$		0			0
$381$	−46.9493	−	27.1062i	−0.123227	−	0.0711449i
$382$	−46.8352	+	81.1209i	−0.122605	+	0.212358i
$383$	255.925	−	147.759i	0.668213	−	0.385793i	−0.127186	−	0.991879i	$-0.540595\pi$
$383$	255.925	−	147.759i	0.668213	−	0.385793i	0.795399	+	0.606086i	$0.207261\pi$
$384$		−	11.7401i		−	0.0305732i
$385$		0			0
$386$	358.442			0.928605
$387$	104.033	+	180.191i	0.268819	+	0.465609i
$388$	−158.342	−	91.4185i	−0.408097	−	0.235615i
$389$	214.388	−	371.330i	0.551125	−	0.954577i	−0.447069	−	0.894500i	$-0.647532\pi$
$389$	214.388	−	371.330i	0.551125	−	0.954577i	0.998194	−	0.0600771i	$-0.0191347\pi$
$390$		0			0
$391$		−	419.441i		−	1.07274i
$392$	113.785	−	79.1269i	0.290267	−	0.201854i
$393$	−97.4563			−0.247980
$394$	−135.291	−	234.330i	−0.343377	−	0.594746i
$395$		0			0
$396$	−98.8347	+	171.187i	−0.249582	+	0.432290i
$397$	277.807	−	160.392i	0.699765	−	0.404009i	−0.107495	−	0.994206i	$-0.534283\pi$
$397$	277.807	−	160.392i	0.699765	−	0.404009i	0.807260	+	0.590196i	$0.200950\pi$
$398$		−	319.428i		−	0.802583i
$399$	32.8584	+	104.803i	0.0823518	+	0.262663i
$400$		0			0
$401$	118.854	+	205.861i	0.296394	+	0.513370i	0.975308	−	0.220848i	$-0.0708824\pi$
$401$	118.854	+	205.861i	0.296394	+	0.513370i	−0.678914	+	0.734218i	$0.737549\pi$
$402$	−44.1015	−	25.4620i	−0.109705	−	0.0633384i
$403$	17.4950	−	30.3022i	0.0434119	−	0.0751915i
$404$	−152.439	+	88.0109i	−0.377325	+	0.217849i
$405$		0			0
$406$	338.905	−	368.654i	0.834741	−	0.908015i
$407$	−146.425			−0.359765
$408$	−16.9508	−	29.3596i	−0.0415460	−	0.0719598i
$409$	−171.560	−	99.0500i	−0.419461	−	0.242176i	0.275386	−	0.961334i	$-0.411194\pi$
$409$	−171.560	−	99.0500i	−0.419461	−	0.242176i	−0.694847	+	0.719158i	$0.744528\pi$
$410$		0			0
$411$	104.998	−	60.6207i	0.255470	−	0.147496i
$412$			225.191i			0.546579i
$413$	−120.692	+	540.280i	−0.292232	+	1.30818i
$414$	406.892			0.982831
$415$		0			0
$416$	3.66553	+	2.11629i	0.00881137	+	0.00508725i
$417$	−35.2189	+	61.0010i	−0.0844579	+	0.146285i
$418$	231.005	−	133.371i	0.552644	−	0.319069i
$419$			56.6448i			0.135190i	0.997713	+	0.0675952i	$0.0215326\pi$
$419$			56.6448i			0.135190i	−0.997713	+	0.0675952i	$0.978467\pi$
$420$		0			0
$421$	−220.350			−0.523396			−0.261698	−	0.965150i	$-0.584282\pi$
$421$	−220.350			−0.523396			−0.261698	+	0.965150i	$0.584282\pi$
$422$	−132.099	−	228.802i	−0.313031	−	0.542186i
$423$	−277.547	−	160.242i	−0.656139	−	0.378822i
$424$	37.2959	−	64.5983i	0.0879619	−	0.152355i
$425$		0			0
$426$		−	21.5191i		−	0.0505142i
$427$	269.327	+	247.593i	0.630743	+	0.579844i
$428$	5.74577			0.0134247
$429$	4.84258	+	8.38760i	0.0112881	+	0.0195515i
$430$		0			0
$431$	136.661	−	236.704i	0.317079	−	0.549197i	−0.662798	−	0.748798i	$-0.730631\pi$
$431$	136.661	−	236.704i	0.317079	−	0.549197i	0.979877	+	0.199601i	$0.0639646\pi$
$432$	60.8332	−	35.1220i	0.140818	−	0.0813010i
$433$		−	201.926i		−	0.466342i	−0.972436	−	0.233171i	$-0.925090\pi$
$433$		−	201.926i		−	0.466342i	0.972436	−	0.233171i	$-0.0749102\pi$
$434$	441.738	−	138.496i	1.01783	−	0.319116i
$435$		0			0
$436$	−85.2169	−	147.600i	−0.195452	−	0.338532i
$437$	−475.512	−	274.537i	−1.08813	−	0.628231i
$438$	74.2313	−	128.572i	0.169478	−	0.293544i
$439$	527.183	−	304.370i	1.20087	−	0.693325i	0.240124	−	0.970742i	$-0.422812\pi$
$439$	527.183	−	304.370i	1.20087	−	0.693325i	0.960749	+	0.277418i	$0.0894786\pi$
$440$		0			0
$441$	351.331	+	165.210i	0.796669	+	0.374627i
$442$	12.2223			0.0276523
$443$	389.685	+	674.954i	0.879650	+	1.52360i	0.851726	+	0.523988i	$0.175556\pi$
$443$	389.685	+	674.954i	0.879650	+	1.52360i	0.0279237	+	0.999610i	$0.491110\pi$
$444$	21.0976	+	12.1807i	0.0475171	+	0.0274340i
$445$		0			0
$446$	−237.730	+	137.254i	−0.533028	+	0.307744i
$447$		−	178.644i		−	0.399652i
$448$	16.7533	+	53.4352i	0.0373959	+	0.119275i
$449$	8.03323			0.0178914			0.00894569	−	0.999960i	$-0.497152\pi$
$449$	8.03323			0.0178914			0.00894569	+	0.999960i	$0.497152\pi$
$450$		0			0
$451$	−137.625	−	79.4580i	−0.305156	−	0.176182i
$452$	211.525	−	366.372i	0.467975	−	0.810557i
$453$	−99.0474	+	57.1850i	−0.218648	+	0.126236i
$454$			497.459i			1.09573i
$455$		0			0
$456$	−44.3792			−0.0973228
$457$	−249.654	−	432.413i	−0.546289	−	0.946200i	−0.998525	−	0.0543016i	$-0.982707\pi$
$457$	−249.654	−	432.413i	−0.546289	−	0.946200i	0.452236	−	0.891898i	$-0.350627\pi$
$458$	−230.507	−	133.083i	−0.503290	−	0.290575i
$459$	101.421	−	175.666i	0.220960	−	0.382715i
$460$		0			0
$461$			690.386i			1.49758i	0.662805	+	0.748792i	$0.269366\pi$
$461$			690.386i			1.49758i	−0.662805	+	0.748792i	$0.730634\pi$
$462$	−27.9366	+	125.059i	−0.0604689	+	0.270690i
$463$	615.045			1.32839			0.664195	−	0.747559i	$-0.268774\pi$
$463$	615.045			1.32839			0.664195	+	0.747559i	$0.268774\pi$
$464$	101.169	+	175.230i	0.218037	+	0.377651i
$465$		0			0
$466$	222.088	−	384.668i	0.476584	−	0.825467i
$467$	−41.4549	+	23.9340i	−0.0887686	+	0.0512506i	−0.543727	−	0.839262i	$-0.682987\pi$
$467$	−41.4549	+	23.9340i	−0.0887686	+	0.0512506i	0.454959	+	0.890513i	$0.349654\pi$
$468$			11.8566i			0.0253347i
$469$	237.063	+	52.9570i	0.505465	+	0.112915i
$470$		0			0
$471$	105.929	+	183.474i	0.224902	+	0.389542i
$472$	−193.718	−	111.843i	−0.410420	−	0.236956i
$473$	163.787	−	283.687i	0.346273	−	0.599762i
$474$	−45.4030	+	26.2134i	−0.0957869	+	0.0553026i
$475$		0			0
$476$	119.048	+	109.442i	0.250102	+	0.229919i
$477$	208.952			0.438054
$478$	−237.778	−	411.844i	−0.497444	−	0.861599i
$479$	−116.614	−	67.3269i	−0.243452	−	0.140557i	0.373310	−	0.927707i	$-0.378223\pi$
$479$	−116.614	−	67.3269i	−0.243452	−	0.140557i	−0.616762	+	0.787149i	$0.711556\pi$
$480$		0			0
$481$	−7.60619	+	4.39143i	−0.0158133	+	0.00912980i
$482$		−	540.971i		−	1.12235i
$483$	251.692	−	78.9119i	0.521101	−	0.163379i
$484$	69.2054			0.142986
$485$		0			0
$486$	261.037	+	150.710i	0.537113	+	0.310103i
$487$	223.414	−	386.964i	0.458755	−	0.794588i	−0.540140	−	0.841575i	$-0.681629\pi$
$487$	223.414	−	386.964i	0.458755	−	0.794588i	0.998895	+	0.0469875i	$0.0149621\pi$
$488$	−128.018	+	73.9110i	−0.262331	+	0.151457i
$489$		−	101.560i		−	0.207690i
$490$		0			0
$491$	−119.125			−0.242617			−0.121309	−	0.992615i	$-0.538709\pi$
$491$	−119.125			−0.242617			−0.121309	+	0.992615i	$0.538709\pi$
$492$	13.2199	+	22.8975i	0.0268696	+	0.0465395i
$493$	506.007	+	292.143i	1.02638	+	0.592582i
$494$	7.99988	−	13.8562i	0.0161941	−	0.0280490i
$495$		0			0
$496$			187.056i			0.377130i
$497$	30.7081	+	97.9442i	0.0617869	+	0.197071i
$498$	118.673			0.238298
$499$	42.1210	+	72.9558i	0.0844109	+	0.146204i	0.905140	−	0.425114i	$-0.139766\pi$
$499$	42.1210	+	72.9558i	0.0844109	+	0.146204i	−0.820729	+	0.571318i	$0.806432\pi$
$500$		0			0
$501$	50.4180	−	87.3265i	0.100635	−	0.174304i
$502$	−369.961	+	213.597i	−0.736973	+	0.425492i
$503$			388.428i			0.772223i	0.922452	+	0.386111i	$0.126182\pi$
$503$			388.428i			0.772223i	−0.922452	+	0.386111i	$0.873818\pi$
$504$	−106.167	+	115.487i	−0.210649	+	0.229140i
$505$		0			0
$506$	−320.300	−	554.776i	−0.633004	−	1.09640i
$507$	−151.371	−	87.3943i	−0.298563	−	0.172375i
$508$	−52.2434	+	90.4883i	−0.102841	+	0.178127i
$509$	−68.8518	+	39.7516i	−0.135269	+	0.0780975i	−0.566107	−	0.824332i	$-0.691551\pi$
$509$	−68.8518	+	39.7516i	−0.135269	+	0.0780975i	0.430838	+	0.902429i	$0.358218\pi$
$510$		0			0
$511$	−154.390	+	691.128i	−0.302132	+	1.35250i
$512$	−22.6274			−0.0441942
$513$	−132.766	−	229.957i	−0.258803	−	0.448260i
$514$	−250.680	−	144.730i	−0.487703	−	0.281576i
$515$		0			0
$516$	−47.1986	+	27.2501i	−0.0914701	+	0.0528103i
$517$			504.561i			0.975939i
$518$	−113.408	−	25.3340i	−0.218934	−	0.0489073i
$519$	−64.1885			−0.123677
$520$		0			0
$521$	69.7252	+	40.2559i	0.133830	+	0.0772666i	0.565420	−	0.824803i	$-0.308714\pi$
$521$	69.7252	+	40.2559i	0.133830	+	0.0772666i	−0.431590	+	0.902070i	$0.642047\pi$
$522$	−283.403	+	490.868i	−0.542917	+	0.940359i
$523$	−703.527	+	406.182i	−1.34518	+	0.776638i	−0.987562	−	0.157231i	$-0.949743\pi$
$523$	−703.527	+	406.182i	−1.34518	+	0.776638i	−0.357615	+	0.933869i	$0.616410\pi$
$524$			187.833i			0.358461i
$525$		0			0
$526$	−137.788			−0.261955
$527$	270.078	+	467.789i	0.512483	+	0.887646i
$528$	−44.8401	−	25.8884i	−0.0849244	−	0.0490311i
$529$	−394.822	+	683.851i	−0.746355	+	1.29272i
$530$		0			0
$531$		−	626.608i		−	1.18005i
$532$	201.992	−	63.3299i	0.379685	−	0.119041i
$533$	−9.53214			−0.0178839
$534$	−99.2176	−	171.850i	−0.185801	−	0.321816i
$535$		0			0
$536$	−49.0745	+	84.9995i	−0.0915569	+	0.158581i
$537$	201.500	−	116.336i	0.375233	−	0.216641i
$538$		−	136.532i		−	0.253777i
$539$	−51.3073	−	609.073i	−0.0951898	−	1.13001i
$540$		0			0
$541$	−141.664	−	245.370i	−0.261857	−	0.453549i	0.704879	−	0.709328i	$-0.251001\pi$
$541$	−141.664	−	245.370i	−0.261857	−	0.453549i	−0.966735	+	0.255779i	$0.917668\pi$
$542$	−102.397	−	59.1190i	−0.188924	−	0.109076i
$543$	−170.828	+	295.882i	−0.314600	+	0.544903i
$544$	−56.5865	+	32.6703i	−0.104019	+	0.0600556i
$545$		0			0
$546$	2.29945	+	7.33417i	0.00421146	+	0.0134326i
$547$	51.6110			0.0943529			0.0471764	−	0.998887i	$-0.484978\pi$
$547$	51.6110			0.0943529			0.0471764	+	0.998887i	$0.484978\pi$
$548$	−116.838	−	202.369i	−0.213208	−	0.369287i
$549$	−358.613	−	207.045i	−0.653211	−	0.377131i
$550$		0			0
$551$	662.393	−	382.433i	1.20217	−	0.694070i
$552$			106.580i			0.193080i
$553$	169.245	−	184.101i	0.306049	−	0.332914i
$554$	−545.510			−0.984675
$555$		0			0
$556$	117.571	+	67.8796i	0.211458	+	0.122086i
$557$	−117.878	+	204.171i	−0.211631	+	0.366555i	−0.952225	−	0.305397i	$-0.901211\pi$
$557$	−117.878	+	204.171i	−0.211631	+	0.366555i	0.740594	+	0.671953i	$0.234544\pi$
$558$	−453.794	+	261.998i	−0.813251	+	0.469530i
$559$		−	19.6486i		−	0.0351496i
$560$		0			0
$561$	−149.515			−0.266514
$562$	172.151	+	298.175i	0.306319	+	0.530561i
$563$	−230.044	−	132.816i	−0.408604	−	0.235907i	0.281586	−	0.959536i	$-0.409140\pi$
$563$	−230.044	−	132.816i	−0.408604	−	0.235907i	−0.690190	+	0.723629i	$0.742473\pi$
$564$	41.9732	−	72.6997i	0.0744205	−	0.128900i
$565$		0			0
$566$			145.425i			0.256934i
$567$	−362.663	−	81.0145i	−0.639617	−	0.142883i
$568$	−41.4750			−0.0730193
$569$	−13.0381	−	22.5826i	−0.0229141	−	0.0396883i	0.854341	−	0.519713i	$-0.173961\pi$
$569$	−13.0381	−	22.5826i	−0.0229141	−	0.0396883i	−0.877255	+	0.480025i	$0.840628\pi$
$570$		0			0
$571$	−147.312	+	255.152i	−0.257989	+	0.446851i	−0.965703	−	0.259649i	$-0.916393\pi$
$571$	−147.312	+	255.152i	−0.257989	+	0.446851i	0.707714	+	0.706499i	$0.249727\pi$
$572$	16.1659	−	9.33340i	0.0282621	−	0.0163171i
$573$		−	68.7313i		−	0.119950i
$574$	−92.8454	−	85.3530i	−0.161751	−	0.148699i
$575$		0			0
$576$	−31.6928	−	54.8935i	−0.0550222	−	0.0953013i
$577$	498.049	+	287.549i	0.863170	+	0.498351i	0.865072	−	0.501647i	$-0.167272\pi$
$577$	498.049	+	287.549i	0.863170	+	0.498351i	−0.00190285	+	0.999998i	$0.500606\pi$
$578$	110.013	−	190.548i	0.190334	−	0.329668i
$579$	−227.773	+	131.505i	−0.393389	+	0.227124i
$580$		0			0
$581$	−540.139	+	169.348i	−0.929672	+	0.291476i
$582$	134.158			0.230512
$583$	−164.484	−	284.895i	−0.282134	−	0.488671i
$584$	−247.805	−	143.070i	−0.424324	−	0.244984i
$585$		0			0
$586$	−539.635	+	311.558i	−0.920878	+	0.531669i
$587$			509.360i			0.867734i	0.900977	+	0.433867i	$0.142851\pi$
$587$			509.360i			0.867734i	−0.900977	+	0.433867i	$0.857149\pi$
$588$	−43.2747	+	92.0265i	−0.0735964	+	0.156508i
$589$	707.098			1.20051
$590$		0			0
$591$	171.941	+	99.2704i	0.290933	+	0.167970i
$592$	23.4766	−	40.6627i	0.0396564	−	0.0686869i
$593$	185.975	−	107.373i	0.313618	−	0.181067i	−0.334926	−	0.942244i	$-0.608711\pi$
$593$	185.975	−	107.373i	0.313618	−	0.181067i	0.648544	+	0.761177i	$0.275378\pi$
$594$		−	309.794i		−	0.521539i
$595$		0			0
$596$	−344.312			−0.577704
$597$	117.191	+	202.981i	0.196300	+	0.340002i
$598$	−33.2767	−	19.2123i	−0.0556467	−	0.0321276i
$599$	−477.250	+	826.621i	−0.796744	+	1.38000i	0.124982	+	0.992159i	$0.460113\pi$
$599$	−477.250	+	826.621i	−0.796744	+	1.38000i	−0.921726	+	0.387842i	$0.873221\pi$
$600$		0			0
$601$		−	851.298i		−	1.41647i	−0.705977	−	0.708234i	$-0.749492\pi$
$601$		−	851.298i		−	1.41647i	0.705977	−	0.708234i	$-0.250508\pi$
$602$	175.938	−	191.382i	0.292256	−	0.317911i
$603$	−274.942			−0.455957
$604$	110.216	+	190.900i	0.182477	+	0.316059i
$605$		0			0
$606$	64.5786	−	111.853i	0.106565	−	0.184577i
$607$	−909.818	+	525.284i	−1.49888	+	0.865377i	−0.999999	−	0.00129613i	$-0.999587\pi$
$607$	−909.818	+	525.284i	−1.49888	+	0.865377i	−0.498877	+	0.866673i	$0.666254\pi$
$608$			85.5347i			0.140682i
$609$	−80.1066	+	358.599i	−0.131538	+	0.588832i
$610$		0			0
$611$	15.1323	+	26.2100i	0.0247665	+	0.0428968i
$612$	−158.514	−	91.5184i	−0.259011	−	0.149540i
$613$	−506.057	+	876.517i	−0.825542	+	1.42988i	0.0759624	+	0.997111i	$0.475797\pi$
$613$	−506.057	+	876.517i	−0.825542	+	1.42988i	−0.901504	+	0.432770i	$0.857536\pi$
$614$	302.747	−	174.791i	0.493073	−	0.284676i
$615$		0			0
$616$	241.033	+	53.8439i	0.391288	+	0.0874090i
$617$	706.409			1.14491			0.572454	−	0.819937i	$-0.305991\pi$
$617$	706.409			1.14491			0.572454	+	0.819937i	$0.305991\pi$
$618$	−82.6176	−	143.098i	−0.133685	−	0.231550i
$619$	−681.409	−	393.412i	−1.10082	−	0.635560i	−0.164385	−	0.986396i	$-0.552564\pi$
$619$	−681.409	−	393.412i	−1.10082	−	0.635560i	−0.936437	+	0.350836i	$0.885897\pi$
$620$		0			0
$621$	−552.261	+	318.848i	−0.889309	+	0.513443i
$622$		−	602.765i		−	0.969076i
$623$	696.823	+	640.591i	1.11850	+	1.02824i
$624$	−3.10569			−0.00497707
$625$		0			0
$626$	164.084	+	94.7339i	0.262115	+	0.151332i
$627$	−97.8617	+	169.502i	−0.156079	+	0.270337i
$628$	353.621	−	204.163i	0.563091	−	0.325101i
$629$		−	135.585i		−	0.215557i
$630$		0			0
$631$	−218.755			−0.346680			−0.173340	−	0.984862i	$-0.555456\pi$
$631$	−218.755			−0.346680			−0.173340	+	0.984862i	$0.555456\pi$
$632$	50.5227	+	87.5079i	0.0799410	+	0.138462i
$633$	167.885	+	96.9287i	0.265222	+	0.153126i
$634$	−227.664	+	394.326i	−0.359092	+	0.621966i
$635$		0			0
$636$			54.7322i			0.0860569i
$637$	−20.9320	−	30.1002i	−0.0328603	−	0.0472531i
$638$	892.363			1.39869
$639$	−58.0914	−	100.617i	−0.0909098	−	0.157460i
$640$		0			0
$641$	304.336	−	527.125i	0.474783	−	0.822348i	−0.524800	−	0.851225i	$-0.675860\pi$
$641$	304.336	−	527.125i	0.474783	−	0.822348i	0.999583	+	0.0288778i	$0.00919336\pi$
$642$	−3.65116	+	2.10800i	−0.00568717	+	0.00328349i
$643$		−	1184.38i		−	1.84196i	−0.389614	−	0.920978i	$-0.627392\pi$
$643$		−	1184.38i		−	1.84196i	0.389614	−	0.920978i	$-0.372608\pi$
$644$	−152.092	−	485.100i	−0.236167	−	0.753261i
$645$		0			0
$646$	123.498	+	213.905i	0.191173	+	0.331122i
$647$	−197.111	−	113.802i	−0.304653	−	0.175892i	0.339878	−	0.940470i	$-0.389614\pi$
$647$	−197.111	−	113.802i	−0.304653	−	0.175892i	−0.644531	+	0.764578i	$0.722948\pi$
$648$	75.0748	−	130.033i	0.115856	−	0.200669i
$649$	−854.347	+	493.258i	−1.31641	+	0.760027i
$650$		0			0
$651$	−229.892	+	250.072i	−0.353137	+	0.384135i
$652$	−195.743			−0.300220
$653$	−115.332	−	199.761i	−0.176619	−	0.305912i	0.764102	−	0.645096i	$-0.223183\pi$
$653$	−115.332	−	199.761i	−0.176619	−	0.305912i	−0.940720	+	0.339183i	$0.889849\pi$
$654$	108.303	+	62.5285i	0.165600	+	0.0956093i
$655$		0			0
$656$	44.1316	−	25.4794i	0.0672738	−	0.0388406i
$657$		−	801.559i		−	1.22003i
$658$	−87.2977	+	390.790i	−0.132671	+	0.593906i
$659$	−726.539			−1.10249			−0.551244	−	0.834344i	$-0.685847\pi$
$659$	−726.539			−1.10249			−0.551244	+	0.834344i	$0.685847\pi$
$660$		0			0
$661$	−214.930	−	124.090i	−0.325159	−	0.187731i	0.328531	−	0.944493i	$-0.393447\pi$
$661$	−214.930	−	124.090i	−0.325159	−	0.187731i	−0.653690	+	0.756763i	$0.726780\pi$
$662$	−166.032	+	287.576i	−0.250804	+	0.434405i
$663$	−7.76670	+	4.48411i	−0.0117145	+	0.00676336i
$664$		−	228.725i		−	0.344465i
$665$		0			0
$666$	131.529			0.197491
$667$	−918.442	−	1590.79i	−1.37697	−	2.38499i
$668$	−168.310	−	97.1736i	−0.251960	−	0.145469i
$669$	100.711	−	174.436i	0.150539	−	0.260742i
$670$		0			0
$671$			651.933i			0.971584i
$672$	−30.2502	−	27.8091i	−0.0450152	−	0.0413826i
$673$	835.990			1.24218			0.621092	−	0.783738i	$-0.286689\pi$
$673$	835.990			1.24218			0.621092	+	0.783738i	$0.286689\pi$
$674$	−153.941	−	266.634i	−0.228400	−	0.395600i
$675$		0			0
$676$	−168.440	+	291.747i	−0.249172	+	0.431578i
$677$	−327.468	+	189.063i	−0.483704	+	0.279267i	−0.721959	−	0.691936i	$-0.756758\pi$
$677$	−327.468	+	189.063i	−0.483704	+	0.279267i	0.238255	+	0.971203i	$0.423425\pi$
$678$			310.416i			0.457840i
$679$	−610.622	+	191.446i	−0.899295	+	0.281953i
$680$		0			0
$681$	−182.507	−	316.112i	−0.267999	−	0.464188i
$682$	714.441	+	412.483i	1.04757	+	0.604813i
$683$	96.6649	−	167.429i	0.141530	−	0.245137i	−0.786543	−	0.617535i	$-0.788131\pi$
$683$	96.6649	−	167.429i	0.141530	−	0.245137i	0.928073	+	0.372399i	$0.121465\pi$
$684$	−207.505	+	119.803i	−0.303370	+	0.175151i
$685$		0			0
$686$	65.6418	−	480.613i	0.0956878	−	0.700602i
$687$	195.302			0.284282
$688$	52.5207	+	90.9686i	0.0763383	+	0.132222i
$689$	−17.0886	−	9.86613i	−0.0248021	−	0.0143195i
$690$		0			0
$691$	501.502	−	289.542i	0.725763	−	0.419019i	−0.0911074	−	0.995841i	$-0.529041\pi$
$691$	501.502	−	289.542i	0.725763	−	0.419019i	0.816870	+	0.576822i	$0.195707\pi$
$692$			123.714i			0.178778i
$693$	206.976	+	660.157i	0.298667	+	0.952607i
$694$	263.371			0.379497
$695$		0			0
$696$	−128.576	−	74.2336i	−0.184736	−	0.106657i
$697$	73.5761	−	127.438i	0.105561	−	0.182837i
$698$	−100.107	+	57.7966i	−0.143419	+	0.0828032i
$699$			325.917i			0.466262i
$700$		0			0
$701$	−516.871			−0.737334			−0.368667	−	0.929562i	$-0.620186\pi$
$701$	−516.871			−0.737334			−0.368667	+	0.929562i	$0.620186\pi$
$702$	−9.29107	−	16.0926i	−0.0132351	−	0.0229239i
$703$	−153.710	−	88.7447i	−0.218649	−	0.126237i
$704$	−49.8963	+	86.4230i	−0.0708755	+	0.122760i
$705$		0			0
$706$			152.645i			0.216211i
$707$	−134.313	+	601.257i	−0.189977	+	0.850434i
$708$	164.132			0.231824
$709$	29.9375	+	51.8533i	0.0422250	+	0.0731359i	0.886366	−	0.462986i	$-0.153222\pi$
$709$	29.9375	+	51.8533i	0.0422250	+	0.0731359i	−0.844141	+	0.536122i	$0.819889\pi$
$710$		0			0
$711$	−141.528	+	245.134i	−0.199055	+	0.344773i
$712$	−331.216	+	191.228i	−0.465192	+	0.268579i
$713$		−	1698.15i		−	2.38170i
$714$	−115.801	−	25.8686i	−0.162187	−	0.0362305i
$715$		0			0
$716$	−224.221	−	388.363i	−0.313158	−	0.542406i
$717$	302.194	+	174.472i	0.421470	+	0.243336i
$718$	−426.993	+	739.573i	−0.594698	+	1.03005i
$719$	1072.53	−	619.228i	1.49170	−	0.861235i	0.491748	−	0.870738i	$-0.336358\pi$
$719$	1072.53	−	619.228i	1.49170	−	0.861235i	0.999955	+	0.00950279i	$0.00302488\pi$
$720$		0			0
$721$	580.238	+	533.415i	0.804768	+	0.739826i
$722$	−187.199			−0.259278
$723$	198.471	+	343.761i	0.274510	+	0.475465i
$724$	570.271	+	329.246i	0.787668	+	0.454760i
$725$		0			0
$726$	−43.9767	+	25.3900i	−0.0605740	+	0.0349724i
$727$		−	387.549i		−	0.533080i	−0.963824	−	0.266540i	$-0.914120\pi$
$727$		−	387.549i		−	0.533080i	0.963824	−	0.266540i	$-0.0858805\pi$
$728$	14.1356	−	4.43188i	0.0194170	−	0.00608774i
$729$	256.605			0.351995
$730$		0			0
$731$	262.687	+	151.663i	0.359353	+	0.207473i
$732$	54.2327	−	93.9339i	0.0740884	−	0.128325i
$733$	−912.012	+	526.551i	−1.24422	+	0.718350i	−0.969950	−	0.243303i	$-0.921769\pi$
$733$	−912.012	+	526.551i	−1.24422	+	0.718350i	−0.274269	+	0.961653i	$0.588436\pi$
$734$			768.667i			1.04723i
$735$		0			0
$736$	205.418			0.279101
$737$	216.431	+	374.869i	0.293665	+	0.508642i
$738$	123.625	+	71.3748i	0.167513	+	0.0967138i
$739$	123.560	−	214.013i	0.167199	−	0.289598i	−0.770235	−	0.637760i	$-0.779861\pi$
$739$	123.560	−	214.013i	0.167199	−	0.289598i	0.937434	+	0.348163i	$0.113194\pi$
$740$		0			0
$741$			11.7399i			0.0158434i
$742$	−78.1038	−	249.114i	−0.105261	−	0.335733i
$743$	−189.686			−0.255298			−0.127649	−	0.991819i	$-0.540743\pi$
$743$	−189.686			−0.255298			−0.127649	+	0.991819i	$0.540743\pi$
$744$	−68.6269	−	118.865i	−0.0922405	−	0.159765i
$745$		0			0
$746$	−58.8952	+	102.010i	−0.0789480	+	0.136742i
$747$	554.880	−	320.360i	0.742811	−	0.428862i
$748$			288.168i			0.385252i
$749$	13.6102	−	14.8049i	0.0181711	−	0.0197662i
$750$		0			0
$751$	400.319	+	693.373i	0.533048	+	0.923267i	0.999255	+	0.0385908i	$0.0122869\pi$
$751$	400.319	+	693.373i	0.533048	+	0.923267i	−0.466207	+	0.884676i	$0.654380\pi$
$752$	−140.118	−	80.8974i	−0.186328	−	0.107576i
$753$	156.728	−	271.461i	0.208138	−	0.360506i
$754$	46.3548	−	26.7630i	0.0614785	−	0.0354946i
$755$		0			0
$756$	53.5998	−	239.940i	0.0708992	−	0.317382i
$757$	809.069			1.06878			0.534392	−	0.845237i	$-0.320541\pi$
$757$	809.069			1.06878			0.534392	+	0.845237i	$0.320541\pi$
$758$	21.5249	+	37.2823i	0.0283970	+	0.0491851i
$759$	407.071	+	235.023i	0.536325	+	0.309648i
$760$		0			0
$761$	−213.647	+	123.349i	−0.280745	+	0.162088i	−0.633761	−	0.773529i	$-0.718490\pi$
$761$	−213.647	+	123.349i	−0.280745	+	0.162088i	0.353016	+	0.935617i	$0.385156\pi$
$762$		−	76.6680i		−	0.100614i
$763$	−582.169	−	130.050i	−0.763000	−	0.170445i
$764$	−132.470			−0.173390
$765$		0			0
$766$	361.933	+	208.962i	0.472498	+	0.272797i
$767$	−29.5867	+	51.2456i	−0.0385746	+	0.0668131i
$768$	14.3786	−	8.30151i	0.0187222	−	0.0108093i
$769$		−	851.221i		−	1.10692i	−0.832876	−	0.553460i	$-0.813307\pi$
$769$		−	851.221i		−	1.10692i	0.832876	−	0.553460i	$-0.186693\pi$
$770$		0			0
$771$	212.393			0.275478
$772$	253.457	+	439.000i	0.328312	+	0.568652i
$773$	−771.684	−	445.532i	−0.998298	−	0.576368i	−0.0905537	−	0.995892i	$-0.528864\pi$
$773$	−771.684	−	445.532i	−0.998298	−	0.576368i	−0.907744	+	0.419524i	$0.862197\pi$
$774$	−147.125	+	254.828i	−0.190084	+	0.329235i
$775$		0			0
$776$		−	258.571i		−	0.333210i
$777$	81.3599	−	25.5084i	0.104710	−	0.0328294i
$778$	606.380			0.779409
$779$	−96.3156	−	166.823i	−0.123640	−	0.214151i
$780$		0			0
$781$	−91.4576	+	158.409i	−0.117103	+	0.202829i
$782$	513.709	−	296.590i	0.656916	−	0.379271i
$783$		−	888.317i		−	1.13450i
$784$	177.368	+	83.4059i	0.226235	+	0.106385i
$785$		0			0
$786$	−68.9120	−	119.359i	−0.0876743	−	0.151856i
$787$	−425.522	−	245.676i	−0.540689	−	0.312167i	0.204669	−	0.978831i	$-0.434388\pi$
$787$	−425.522	−	245.676i	−0.540689	−	0.312167i	−0.745358	+	0.666664i	$0.767722\pi$
$788$	191.330	−	331.393i	0.242804	−	0.420549i
$789$	87.5578	−	50.5515i	0.110973	−	0.0640703i
$790$		0			0
$791$	−442.968	−	1412.86i	−0.560011	−	1.78617i
$792$	−279.547			−0.352963
$793$	19.5522	+	33.8654i	0.0246560	+	0.0427054i
$794$	392.878	+	226.828i	0.494808	+	0.285678i
$795$		0			0
$796$	391.218	−	225.870i	0.491480	−	0.283756i
$797$		−	68.9206i		−	0.0864751i	−0.999065	−	0.0432375i	$-0.986233\pi$
$797$		−	68.9206i		−	0.0864751i	0.999065	−	0.0432375i	$-0.0137672\pi$
$798$	−105.122	+	114.350i	−0.131732	+	0.143295i
$799$	−467.210			−0.584744
$800$		0			0
$801$	−927.828	−	535.682i	−1.15834	−	0.668766i
$802$	−168.085	+	291.132i	−0.209582	+	0.363007i
$803$	−1092.88	+	630.977i	−1.36100	+	0.785774i
$804$		−	72.0175i		−	0.0895740i
$805$		0			0
$806$	49.4833			0.0613936
$807$	50.0906	+	86.7595i	0.0620702	+	0.107509i
$808$	−215.582	−	124.466i	−0.266809	−	0.154042i
$809$	−19.0763	+	33.0411i	−0.0235801	+	0.0408419i	−0.877575	−	0.479440i	$-0.840840\pi$
$809$	−19.0763	+	33.0411i	−0.0235801	+	0.0408419i	0.853995	+	0.520282i	$0.174173\pi$
$810$		0			0
$811$			763.676i			0.941648i	0.882227	+	0.470824i	$0.156043\pi$
$811$			763.676i			0.941648i	−0.882227	+	0.470824i	$0.843957\pi$
$812$	691.149	+	154.394i	0.851169	+	0.190141i
$813$	86.7579			0.106713
$814$	−103.538	−	179.333i	−0.127196	−	0.220310i
$815$		0			0
$816$	23.9720	−	41.5208i	0.0293775	−	0.0508833i
$817$	343.873	−	198.535i	0.420898	−	0.243005i
$818$		−	280.156i		−	0.342489i
$819$	30.5505	+	28.0851i	0.0373021	+	0.0342920i
$820$		0			0
$821$	204.439	+	354.099i	0.249013	+	0.431302i	0.963252	−	0.268599i	$-0.0865606\pi$
$821$	204.439	+	354.099i	0.249013	+	0.431302i	−0.714240	+	0.699901i	$0.753227\pi$
$822$	148.490	+	85.7306i	0.180644	+	0.104295i
$823$	76.8529	−	133.113i	0.0933814	−	0.161741i	−0.815551	−	0.578686i	$-0.803566\pi$
$823$	76.8529	−	133.113i	0.0933814	−	0.161741i	0.908932	+	0.416945i	$0.136899\pi$
$824$	−275.801	+	159.234i	−0.334710	+	0.193245i
$825$		0			0
$826$	−747.047	+	234.219i	−0.904416	+	0.283558i
$827$	−571.706			−0.691301			−0.345650	−	0.938363i	$-0.612342\pi$
$827$	−571.706			−0.691301			−0.345650	+	0.938363i	$0.612342\pi$
$828$	287.716	+	498.339i	0.347483	+	0.601859i
$829$	1099.69	+	634.905i	1.32652	+	0.765869i	0.984760	−	0.173918i	$-0.0556426\pi$
$829$	1099.69	+	634.905i	1.32652	+	0.765869i	0.341763	+	0.939786i	$0.388976\pi$
$830$		0			0
$831$	346.646	−	200.136i	0.417143	−	0.240838i
$832$			5.98578i			0.00719445i
$833$	563.986	−	47.5093i	0.677054	−	0.0570339i
$834$	−99.6142			−0.119442
$835$		0			0
$836$	326.690	+	188.615i	0.390778	+	0.225616i
$837$	410.612	−	711.202i	0.490576	−	0.849703i
$838$	−69.3754	+	40.0539i	−0.0827869	+	0.0477970i
$839$		−	732.075i		−	0.872556i	−0.899812	−	0.436278i	$-0.856296\pi$
$839$		−	732.075i		−	0.872556i	0.899812	−	0.436278i	$-0.143704\pi$
$840$		0			0
$841$	1717.80			2.04257
$842$	−155.811	−	269.872i	−0.185048	−	0.320513i
$843$	−218.788	−	126.317i	−0.259535	−	0.149843i
$844$	186.816	−	323.575i	0.221346	−	0.383383i
$845$		0			0
$846$		−	453.232i		−	0.535735i
$847$	163.929	−	178.318i	0.193540	−	0.210529i
$848$	105.489			0.124397
$849$	−53.3531	−	92.4103i	−0.0628423	−	0.108846i
$850$		0			0
$851$	−213.127	+	369.147i	−0.250443	+	0.433780i
$852$	26.3554	−	15.2163i	0.0309335	−	0.0178595i
$853$			193.304i			0.226617i	0.993560	+	0.113308i	$0.0361448\pi$
$853$			193.304i			0.226617i	−0.993560	+	0.113308i	$0.963855\pi$
$854$	−112.796	+	504.932i	−0.132079	+	0.591255i
$855$		0			0
$856$	4.06287	+	7.03710i	0.00474635	+	0.00822092i
$857$	−410.336	−	236.907i	−0.478805	−	0.276438i	0.241113	−	0.970497i	$-0.422487\pi$
$857$	−410.336	−	236.907i	−0.478805	−	0.276438i	−0.719918	+	0.694059i	$0.755821\pi$
$858$	−6.84844	+	11.8619i	−0.00798187	+	0.0138250i
$859$	760.044	−	438.811i	0.884801	−	0.510840i	0.0125624	−	0.999921i	$-0.496001\pi$
$859$	760.044	−	438.811i	0.884801	−	0.510840i	0.872238	+	0.489081i	$0.162668\pi$
$860$		0			0
$861$	90.3130	+	20.1748i	0.104893	+	0.0234318i
$862$	386.536			0.448417
$863$	−451.797	−	782.535i	−0.523519	−	0.906761i	−0.999625	−	0.0273737i	$-0.991286\pi$
$863$	−451.797	−	782.535i	−0.523519	−	0.906761i	0.476106	−	0.879388i	$-0.342048\pi$
$864$	86.0311	+	49.6701i	0.0995730	+	0.0574885i
$865$		0			0
$866$	247.308	−	142.783i	0.285575	−	0.164877i
$867$			161.446i			0.186212i
$868$	481.979	+	443.085i	0.555275	+	0.510467i
$869$	445.636			0.512814
$870$		0			0
$871$	22.4855	+	12.9820i	0.0258157	+	0.0149047i
$872$	120.515	−	208.738i	0.138205	−	0.239378i
$873$	627.286	−	362.164i	0.718541	−	0.414850i
$874$		−	776.508i		−	0.888453i
$875$		0			0
$876$	209.958			0.239678
$877$	−651.867	−	1129.07i	−0.743292	−	1.28742i	−0.950988	−	0.309226i	$-0.899930\pi$
$877$	−651.867	−	1129.07i	−0.743292	−	1.28742i	0.207696	−	0.978193i	$-0.433403\pi$
$878$	745.550	+	430.443i	0.849146	+	0.490255i
$879$	228.608	−	395.961i	0.260077	−	0.450467i
$880$		0			0
$881$		−	796.338i		−	0.903902i	−0.892043	−	0.451951i	$-0.850728\pi$
$881$		−	796.338i		−	0.903902i	0.892043	−	0.451951i	$-0.149272\pi$
$882$	46.0879	+	547.112i	0.0522538	+	0.620308i
$883$	1253.73			1.41985			0.709927	−	0.704276i	$-0.248728\pi$
$883$	1253.73			1.41985			0.709927	+	0.704276i	$0.248728\pi$
$884$	8.64249	+	14.9692i	0.00977657	+	0.0169335i
$885$		0			0
$886$	−551.097	+	954.529i	−0.622006	+	1.07735i
$887$	−848.034	+	489.613i	−0.956070	+	0.551987i	−0.894961	−	0.446144i	$-0.852797\pi$
$887$	−848.034	+	489.613i	−0.956070	+	0.551987i	−0.0611090	+	0.998131i	$0.519464\pi$
$888$			34.4522i			0.0387976i
$889$	109.407	+	348.955i	0.123067	+	0.392525i
$890$		0			0
$891$	−331.099	−	573.480i	−0.371604	−	0.643637i
$892$	−336.202	−	194.106i	−0.376908	−	0.217608i
$893$	−305.803	+	529.666i	−0.342445	+	0.593132i
$894$	218.794	−	126.321i	0.244736	−	0.141298i
$895$		0			0
$896$	−53.5981	+	58.3030i	−0.0598194	+	0.0650703i
$897$	28.1943			0.0314318
$898$	5.68035	+	9.83866i	0.00632556	+	0.0109562i
$899$	2048.62	+	1182.77i	2.27877	+	1.31565i
$900$		0			0
$901$	263.805	−	152.308i	0.292792	−	0.169043i
$902$		−	224.741i		−	0.249159i
$903$	−41.5864	+	186.162i	−0.0460536	+	0.206160i
$904$	598.282			0.661817
$905$		0			0
$906$	−140.074	−	80.8718i	−0.154607	−	0.0892625i
$907$	−825.386	+	1429.61i	−0.910017	+	1.57620i	−0.0959807	+	0.995383i	$0.530599\pi$
$907$	−825.386	+	1429.61i	−0.910017	+	1.57620i	−0.814037	+	0.580813i	$0.802735\pi$
$908$	−609.261	+	351.757i	−0.670992	+	0.387398i
$909$		−	697.328i		−	0.767138i
$910$		0			0
$911$	−736.949			−0.808945			−0.404472	−	0.914550i	$-0.632545\pi$
$911$	−736.949			−0.808945			−0.404472	+	0.914550i	$0.632545\pi$
$912$	−31.3808	−	54.3532i	−0.0344088	−	0.0595978i
$913$	−873.589	−	504.367i	−0.956833	−	0.552428i
$914$	353.064	−	611.525i	0.386285	−	0.669064i
$915$		0			0
$916$		−	376.416i		−	0.410935i
$917$	483.981	+	444.926i	0.527788	+	0.485197i
$918$	286.862			0.312485
$919$	432.226	+	748.637i	0.470322	+	0.814621i	0.999424	−	0.0339368i	$-0.0108045\pi$
$919$	432.226	+	748.637i	0.470322	+	0.814621i	−0.529102	+	0.848558i	$0.677471\pi$
$920$		0			0
$921$	−128.254	+	222.143i	−0.139255	+	0.241197i
$922$	−845.547	+	488.177i	−0.917080	+	0.529476i
$923$			10.9717i			0.0118870i
$924$	−172.919	+	54.2147i	−0.187142	+	0.0586740i
$925$		0			0
$926$	434.902	+	753.273i	0.469657	+	0.813470i
$927$	−772.594	−	446.058i	−0.833435	−	0.481184i
$928$	−143.075	+	247.813i	−0.154175	+	0.267040i
$929$	−515.059	+	297.370i	−0.554423	+	0.320096i	−0.750904	−	0.660411i	$-0.770382\pi$
$929$	−515.059	+	297.370i	−0.554423	+	0.320096i	0.196481	+	0.980508i	$0.437049\pi$
$930$		0			0
$931$	315.285	−	670.475i	0.338652	−	0.720167i
$932$	628.160			0.673991
$933$	221.142	+	383.028i	0.237022	+	0.410534i
$934$	−58.6261	−	33.8478i	−0.0627689	−	0.0362396i
$935$		0			0
$936$	−14.5214	+	8.38391i	−0.0155143	+	0.00895717i
$937$			312.979i			0.334022i	0.985955	+	0.167011i	$0.0534116\pi$
$937$			312.979i			0.334022i	−0.985955	+	0.167011i	$0.946588\pi$
$938$	102.770	+	327.788i	0.109563	+	0.349455i
$939$	−139.023			−0.148055
$940$		0			0
$941$	45.2375	+	26.1179i	0.0480738	+	0.0277554i	0.523844	−	0.851814i	$-0.324497\pi$
$941$	45.2375	+	26.1179i	0.0480738	+	0.0277554i	−0.475770	+	0.879569i	$0.657831\pi$
$942$	−149.806	+	259.472i	−0.159030	+	0.275448i
$943$	−400.639	+	231.309i	−0.424856	+	0.245291i
$944$		−	316.341i		−	0.335107i
$945$		0			0
$946$	463.260			0.489704
$947$	281.247	+	487.134i	0.296987	+	0.514397i	0.975445	−	0.220242i	$-0.0706847\pi$
$947$	281.247	+	487.134i	0.296987	+	0.514397i	−0.678458	+	0.734639i	$0.737351\pi$
$948$	−64.2095	−	37.0714i	−0.0677315	−	0.0391048i
$949$	−37.8474	+	65.5536i	−0.0398813	+	0.0690765i
$950$		0			0
$951$		−	334.101i		−	0.351315i
$952$	−49.8581	+	223.191i	−0.0523719	+	0.234444i
$953$	786.616			0.825411			0.412705	−	0.910865i	$-0.364584\pi$
$953$	786.616			0.825411			0.412705	+	0.910865i	$0.364584\pi$
$954$	147.751	+	255.913i	0.154876	+	0.268252i
$955$		0			0
$956$	336.269	−	582.436i	0.351746	−	0.609243i
$957$	−567.054	+	327.389i	−0.592533	+	0.342099i
$958$		−	190.429i		−	0.198778i
$959$	−798.192	−	178.306i	−0.832317	−	0.185929i
$960$		0			0
$961$	612.939	+	1061.64i	0.637814	+	1.10473i
$962$	−10.7568	−	6.21043i	−0.0111817	−	0.00645574i
$963$	−11.3812	+	19.7129i	−0.0118185	+	0.0204703i
$964$	662.551	−	382.524i	0.687294	−	0.396809i
$965$		0			0
$966$	274.620	+	252.459i	0.284285	+	0.261345i
$967$	372.034			0.384730			0.192365	−	0.981323i	$-0.438384\pi$
$967$	372.034			0.384730			0.192365	+	0.981323i	$0.438384\pi$
$968$	48.9356	+	84.7590i	0.0505533	+	0.0875609i
$969$	−156.954	−	90.6175i	−0.161975	−	0.0935165i
$970$		0			0
$971$	−463.408	+	267.549i	−0.477248	+	0.275539i	−0.719269	−	0.694732i	$-0.755523\pi$
$971$	−463.408	+	267.549i	−0.477248	+	0.275539i	0.242021	+	0.970271i	$0.422190\pi$
$972$			426.272i			0.438551i
$973$	453.395	−	142.151i	0.465977	−	0.146096i
$974$	631.910			0.648778
$975$		0			0
$976$	−181.044	−	104.526i	−0.185496	−	0.107096i
$977$	401.956	−	696.209i	0.411419	−	0.712599i	−0.583626	−	0.812023i	$-0.698367\pi$
$977$	401.956	−	696.209i	0.411419	−	0.712599i	0.995045	+	0.0994238i	$0.0316999\pi$
$978$	124.385	−	71.8140i	0.127184	−	0.0734294i
$979$			1686.73i			1.72291i
$980$		0			0
$981$	675.191			0.688268
$982$	−84.2342	−	145.898i	−0.0857782	−	0.148572i
$983$	205.321	+	118.542i	0.208872	+	0.120592i	0.600787	−	0.799409i	$-0.294854\pi$
$983$	205.321	+	118.542i	0.208872	+	0.120592i	−0.391915	+	0.920001i	$0.628187\pi$
$984$	−18.6957	+	32.3819i	−0.0189997	+	0.0329084i
$985$		0			0
$986$			826.305i			0.838038i
$987$	−87.8989	−	280.356i	−0.0890566	−	0.284049i
$988$	22.6271			0.0229019
$989$	−476.798	−	825.838i	−0.482101	−	0.835024i
$990$		0			0
$991$	211.092	−	365.622i	0.213009	−	0.368942i	−0.739646	−	0.672996i	$-0.765007\pi$
$991$	211.092	−	365.622i	0.213009	−	0.368942i	0.952655	+	0.304054i	$0.0983403\pi$
$992$	−229.096	+	132.269i	−0.230944	+	0.133335i
$993$		−	243.655i		−	0.245372i
$994$	−98.2428	+	106.867i	−0.0988358	+	0.107512i
$995$		0			0
$996$	83.9141	+	145.344i	0.0842511	+	0.145927i
$997$	1344.88	+	776.469i	1.34893	+	0.778806i	0.988098	−	0.153825i	$-0.0491591\pi$
$997$	1344.88	+	776.469i	1.34893	+	0.778806i	0.360833	+	0.932630i	$0.382492\pi$
$998$	−59.5681	+	103.175i	−0.0596875	+	0.103382i
$999$	−178.519	+	103.068i	−0.178698	+	0.103171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.3.k.e.101.6		16
5.2	odd	4		70.3.h.a.59.2	yes	16
5.3	odd	4		70.3.h.a.59.7	yes	16
5.4	even	2	inner	350.3.k.e.101.3		16
7.5	odd	6	inner	350.3.k.e.201.6		16
15.2	even	4		630.3.bc.a.199.6		16
15.8	even	4		630.3.bc.a.199.4		16
20.3	even	4		560.3.br.b.129.3		16
20.7	even	4		560.3.br.b.129.6		16
35.2	odd	12		490.3.h.b.19.6		16
35.3	even	12		490.3.d.a.489.14		16
35.12	even	12		70.3.h.a.19.7	yes	16
35.13	even	4		490.3.h.b.129.6		16
35.17	even	12		490.3.d.a.489.3		16
35.18	odd	12		490.3.d.a.489.11		16
35.19	odd	6	inner	350.3.k.e.201.3		16
35.23	odd	12		490.3.h.b.19.3		16
35.27	even	4		490.3.h.b.129.3		16
35.32	odd	12		490.3.d.a.489.6		16
35.33	even	12		70.3.h.a.19.2	✓	16
105.47	odd	12		630.3.bc.a.19.4		16
105.68	odd	12		630.3.bc.a.19.6		16
140.47	odd	12		560.3.br.b.369.3		16
140.103	odd	12		560.3.br.b.369.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.h.a.19.2	✓	16	35.33	even	12
70.3.h.a.19.7	yes	16	35.12	even	12
70.3.h.a.59.2	yes	16	5.2	odd	4
70.3.h.a.59.7	yes	16	5.3	odd	4
350.3.k.e.101.3		16	5.4	even	2	inner
350.3.k.e.101.6		16	1.1	even	1	trivial
350.3.k.e.201.3		16	35.19	odd	6	inner
350.3.k.e.201.6		16	7.5	odd	6	inner
490.3.d.a.489.3		16	35.17	even	12
490.3.d.a.489.6		16	35.32	odd	12
490.3.d.a.489.11		16	35.18	odd	12
490.3.d.a.489.14		16	35.3	even	12
490.3.h.b.19.3		16	35.23	odd	12
490.3.h.b.19.6		16	35.2	odd	12
490.3.h.b.129.3		16	35.27	even	4
490.3.h.b.129.6		16	35.13	even	4
560.3.br.b.129.3		16	20.3	even	4
560.3.br.b.129.6		16	20.7	even	4
560.3.br.b.369.3		16	140.47	odd	12
560.3.br.b.369.6		16	140.103	odd	12
630.3.bc.a.19.4		16	105.47	odd	12
630.3.bc.a.19.6		16	105.68	odd	12
630.3.bc.a.199.4		16	15.8	even	4
630.3.bc.a.199.6		16	15.2	even	4

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-0.898665 - 0.518845i) q^{3} +(-1.00000 + 1.73205i) q^{4} -1.46751i q^{6} +(2.09417 + 6.67941i) q^{7} -2.82843 q^{8} +(-3.96160 - 6.86169i) q^{9} +(-6.23704 + 10.8029i) q^{11} +(1.79733 - 1.03769i) q^{12} +0.748223i q^{13} +(-6.69977 + 7.28787i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-10.0032 - 5.77534i) q^{17} +(5.60255 - 9.70390i) q^{18} +(-13.0948 + 7.56027i) q^{19} +(1.58362 - 7.08910i) q^{21} -17.6410 q^{22} +(18.1566 + 31.4481i) q^{23} +(2.54181 + 1.46751i) q^{24} +(-0.916382 + 0.529074i) q^{26} +17.5610i q^{27} +(-13.6632 - 3.05220i) q^{28} -50.5846 q^{29} +(-40.4989 - 23.3820i) q^{31} +(2.82843 - 4.89898i) q^{32} +(11.2100 - 6.47211i) q^{33} -16.3351i q^{34} +15.8464 q^{36} +(5.86915 + 10.1657i) q^{37} +(-18.5188 - 10.6918i) q^{38} +(0.388211 - 0.672402i) q^{39} +12.7397i q^{41} +(9.80212 - 3.07322i) q^{42} -26.2604 q^{43} +(-12.4741 - 21.6057i) q^{44} +(-25.6773 + 44.4743i) q^{46} +(35.0296 - 20.2244i) q^{47} +4.15076i q^{48} +(-40.2289 + 27.9756i) q^{49} +(5.99301 + 10.3802i) q^{51} +(-1.29596 - 0.748223i) q^{52} +(-13.1861 + 22.8390i) q^{53} +(-21.5078 + 12.4175i) q^{54} +(-5.92320 - 18.8922i) q^{56} +15.6904 q^{57} +(-35.7687 - 61.9532i) q^{58} +(68.4898 + 39.5426i) q^{59} +(45.2611 - 26.1315i) q^{61} -66.1344i q^{62} +(37.5358 - 40.8307i) q^{63} +8.00000 q^{64} +(15.8534 + 9.15294i) q^{66} +(17.3504 - 30.0519i) q^{67} +(20.0064 - 11.5507i) q^{68} -37.6817i q^{69} +14.6636 q^{71} +(11.2051 + 19.4078i) q^{72} +(87.6124 + 50.5830i) q^{73} +(-8.30023 + 14.3764i) q^{74} -30.2411i q^{76} +(-85.2182 - 19.0367i) q^{77} +1.09803 q^{78} +(-17.8625 - 30.9387i) q^{79} +(-26.5430 + 45.9738i) q^{81} +(-15.6029 + 9.00833i) q^{82} +80.8664i q^{83} +(10.6951 + 9.83200i) q^{84} +(-18.5689 - 32.1623i) q^{86} +(45.4586 + 26.2455i) q^{87} +(17.6410 - 30.5551i) q^{88} +(117.103 - 67.6093i) q^{89} +(-4.99769 + 1.56690i) q^{91} -72.6263 q^{92} +(24.2633 + 42.0252i) q^{93} +(49.5394 + 28.6016i) q^{94} +(-5.08362 + 2.93503i) q^{96} +91.4185i q^{97} +(-62.7091 - 29.4884i) q^{98} +98.8347 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 12 q^{9} - 12 q^{11} - 32 q^{14} - 32 q^{16} + 12 q^{19} - 8 q^{21} + 24 q^{24} - 48 q^{26} + 136 q^{29} + 84 q^{31} - 48 q^{36} - 312 q^{39} - 24 q^{44} - 68 q^{46} - 296 q^{49} - 76 q^{51}+ \cdots - 176 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 12 * q^9 - 12 * q^11 - 32 * q^14 - 32 * q^16 + 12 * q^19 - 8 * q^21 + 24 * q^24 - 48 * q^26 + 136 * q^29 + 84 * q^31 - 48 * q^36 - 312 * q^39 - 24 * q^44 - 68 * q^46 - 296 * q^49 - 76 * q^51 + 108 * q^54 + 56 * q^56 + 372 * q^59 + 348 * q^61 + 128 * q^64 + 480 * q^66 - 384 * q^71 - 208 * q^74 - 148 * q^79 - 140 * q^81 - 256 * q^84 - 188 * q^86 + 912 * q^89 - 616 * q^91 + 600 * q^94 - 48 * q^96 - 176 * q^99

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