LMFDB - Embedded newform 768.2.o.a.287.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.o (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			287.6
Character	$\chi$	$=$	768.287
Dual form			768.2.o.a.479.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.641495 - 1.60888i) q^{3} +(-0.296199 + 0.715088i) q^{5} +(-2.77714 + 2.77714i) q^{7} +(-2.17697 + 2.06417i) q^{9} +O(q^{10})$	\(q+(-0.641495 - 1.60888i) q^{3} +(-0.296199 + 0.715088i) q^{5} +(-2.77714 + 2.77714i) q^{7} +(-2.17697 + 2.06417i) q^{9} +(0.829014 - 2.00142i) q^{11} +(3.73669 - 1.54779i) q^{13} +(1.34050 + 0.0178227i) q^{15} +5.19928 q^{17} +(-0.814726 - 1.96692i) q^{19} +(6.24959 + 2.68655i) q^{21} +(4.13184 - 4.13184i) q^{23} +(3.11192 + 3.11192i) q^{25} +(4.71751 + 2.17832i) q^{27} +(3.45738 - 1.43209i) q^{29} +0.343074i q^{31} +(-3.75184 - 0.0498828i) q^{33} +(-1.16331 - 2.80849i) q^{35} +(-4.31781 - 1.78850i) q^{37} +(-4.88727 - 5.01898i) q^{39} +(3.37894 + 3.37894i) q^{41} +(9.15044 + 3.79024i) q^{43} +(-0.831249 - 2.16813i) q^{45} -4.84842i q^{47} -8.42499i q^{49} +(-3.33531 - 8.36500i) q^{51} +(-4.15435 - 1.72079i) q^{53} +(1.18564 + 1.18564i) q^{55} +(-2.64189 + 2.57256i) q^{57} +(-8.08629 - 3.34945i) q^{59} +(2.47236 + 5.96880i) q^{61} +(0.313252 - 11.7782i) q^{63} +3.13052i q^{65} +(-5.45025 + 2.25757i) q^{67} +(-9.29818 - 3.99707i) q^{69} +(6.23395 + 6.23395i) q^{71} +(-1.44956 + 1.44956i) q^{73} +(3.01041 - 7.00297i) q^{75} +(3.25592 + 7.86050i) q^{77} +13.2460 q^{79} +(0.478386 - 8.98728i) q^{81} +(6.19358 - 2.56547i) q^{83} +(-1.54002 + 3.71795i) q^{85} +(-4.52195 - 4.64382i) q^{87} +(9.26892 - 9.26892i) q^{89} +(-6.07889 + 14.6757i) q^{91} +(0.551964 - 0.220080i) q^{93} +1.64784 q^{95} +9.56950 q^{97} +(2.32653 + 6.06825i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9	$ 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9} + 8 q^{13} + 8 q^{15} - 8 q^{19} + 4 q^{21} - 8 q^{25} - 28 q^{27} - 8 q^{33} + 8 q^{37} + 28 q^{39} - 8 q^{43} + 4 q^{45} - 16 q^{51} - 24 q^{55} - 4 q^{57} + 40 q^{61} + 56 q^{67} + 4 q^{69} - 8 q^{73} + 16 q^{75} - 16 q^{79} + 48 q^{85} - 52 q^{87} + 40 q^{91} - 8 q^{93} - 16 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9 + 8 * q^13 + 8 * q^15 - 8 * q^19 + 4 * q^21 - 8 * q^25 - 28 * q^27 - 8 * q^33 + 8 * q^37 + 28 * q^39 - 8 * q^43 + 4 * q^45 - 16 * q^51 - 24 * q^55 - 4 * q^57 + 40 * q^61 + 56 * q^67 + 4 * q^69 - 8 * q^73 + 16 * q^75 - 16 * q^79 + 48 * q^85 - 52 * q^87 + 40 * q^91 - 8 * q^93 - 16 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

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			0
$2$		0			0
$3$	−0.641495	−	1.60888i	−0.370367	−	0.928885i
$3$	−0.641495	−	1.60888i	−0.370367	−	0.928885i
$4$		0			0
$5$	−0.296199	+	0.715088i	−0.132464	+	0.319797i	−0.976169	−	0.217010i	$-0.930370\pi$
$5$	−0.296199	+	0.715088i	−0.132464	+	0.319797i	0.843705	+	0.536807i	$0.180370\pi$
$6$		0			0
$7$	−2.77714	+	2.77714i	−1.04966	+	1.04966i	−0.0509588	+	0.998701i	$0.516228\pi$
$7$	−2.77714	+	2.77714i	−1.04966	+	1.04966i	−0.998701	+	0.0509588i	$0.983772\pi$
$8$		0			0
$9$	−2.17697	+	2.06417i	−0.725656	+	0.688057i
$10$		0			0
$11$	0.829014	−	2.00142i	0.249957	−	0.603450i	−0.748243	−	0.663425i	$-0.769102\pi$
$11$	0.829014	−	2.00142i	0.249957	−	0.603450i	0.998200	+	0.0599753i	$0.0191022\pi$
$12$		0			0
$13$	3.73669	−	1.54779i	1.03637	−	0.429279i	0.201363	−	0.979517i	$-0.435463\pi$
$13$	3.73669	−	1.54779i	1.03637	−	0.429279i	0.835008	+	0.550237i	$0.185463\pi$
$14$		0			0
$15$	1.34050	+	0.0178227i	0.346115	+	0.00460179i
$16$		0			0
$17$	5.19928			1.26101			0.630506	−	0.776185i	$-0.282848\pi$
$17$	5.19928			1.26101			0.630506	+	0.776185i	$0.282848\pi$
$18$		0			0
$19$	−0.814726	−	1.96692i	−0.186911	−	0.451243i	0.802451	−	0.596718i	$-0.203529\pi$
$19$	−0.814726	−	1.96692i	−0.186911	−	0.451243i	−0.989362	+	0.145475i	$0.953529\pi$
$20$		0			0
$21$	6.24959	+	2.68655i	1.36377	+	0.586254i
$22$		0			0
$23$	4.13184	−	4.13184i	0.861549	−	0.861549i	−0.129969	−	0.991518i	$-0.541488\pi$
$23$	4.13184	−	4.13184i	0.861549	−	0.861549i	0.991518	+	0.129969i	$0.0414878\pi$
$24$		0			0
$25$	3.11192	+	3.11192i	0.622383	+	0.622383i
$26$		0			0
$27$	4.71751	+	2.17832i	0.907886	+	0.419218i
$28$		0			0
$29$	3.45738	−	1.43209i	0.642019	−	0.265933i	−0.0378308	−	0.999284i	$-0.512045\pi$
$29$	3.45738	−	1.43209i	0.642019	−	0.265933i	0.679850	+	0.733351i	$0.262045\pi$
$30$		0			0
$31$			0.343074i			0.0616180i	0.999525	+	0.0308090i	$0.00980836\pi$
$31$			0.343074i			0.0616180i	−0.999525	+	0.0308090i	$0.990192\pi$
$32$		0			0
$33$	−3.75184	−	0.0498828i	−0.653112	−	0.00868348i
$34$		0			0
$35$	−1.16331	−	2.80849i	−0.196636	−	0.474721i
$36$		0			0
$37$	−4.31781	−	1.78850i	−0.709844	−	0.294027i	−0.00160386	−	0.999999i	$-0.500511\pi$
$37$	−4.31781	−	1.78850i	−0.709844	−	0.294027i	−0.708240	+	0.705972i	$0.750511\pi$
$38$		0			0
$39$	−4.88727	−	5.01898i	−0.782589	−	0.803680i
$40$		0			0
$41$	3.37894	+	3.37894i	0.527702	+	0.527702i	0.919887	−	0.392184i	$-0.128280\pi$
$41$	3.37894	+	3.37894i	0.527702	+	0.527702i	−0.392184	+	0.919887i	$0.628280\pi$
$42$		0			0
$43$	9.15044	+	3.79024i	1.39543	+	0.578005i	0.948561	−	0.316595i	$-0.102539\pi$
$43$	9.15044	+	3.79024i	1.39543	+	0.578005i	0.446868	+	0.894600i	$0.352539\pi$
$44$		0			0
$45$	−0.831249	−	2.16813i	−0.123915	−	0.323206i
$46$		0			0
$47$		−	4.84842i		−	0.707215i	−0.935394	−	0.353608i	$-0.884955\pi$
$47$		−	4.84842i		−	0.707215i	0.935394	−	0.353608i	$-0.115045\pi$
$48$		0			0
$49$		−	8.42499i		−	1.20357i
$50$		0			0
$51$	−3.33531	−	8.36500i	−0.467037	−	1.17133i
$52$		0			0
$53$	−4.15435	−	1.72079i	−0.570644	−	0.236369i	0.0786546	−	0.996902i	$-0.474938\pi$
$53$	−4.15435	−	1.72079i	−0.570644	−	0.236369i	−0.649299	+	0.760533i	$0.724938\pi$
$54$		0			0
$55$	1.18564	+	1.18564i	0.159871	+	0.159871i
$56$		0			0
$57$	−2.64189	+	2.57256i	−0.349927	+	0.340744i
$58$		0			0
$59$	−8.08629	−	3.34945i	−1.05275	−	0.436062i	−0.211875	−	0.977297i	$-0.567957\pi$
$59$	−8.08629	−	3.34945i	−1.05275	−	0.436062i	−0.840871	+	0.541235i	$0.817957\pi$
$60$		0			0
$61$	2.47236	+	5.96880i	0.316553	+	0.764227i	0.999432	+	0.0336954i	$0.0107276\pi$
$61$	2.47236	+	5.96880i	0.316553	+	0.764227i	−0.682879	+	0.730531i	$0.739272\pi$
$62$		0			0
$63$	0.313252	−	11.7782i	0.0394660	−	1.48392i
$64$		0			0
$65$			3.13052i			0.388293i
$66$		0			0
$67$	−5.45025	+	2.25757i	−0.665854	+	0.275806i	−0.689900	−	0.723905i	$-0.742345\pi$
$67$	−5.45025	+	2.25757i	−0.665854	+	0.275806i	0.0240453	+	0.999711i	$0.492345\pi$
$68$		0			0
$69$	−9.29818	−	3.99707i	−1.11937	−	0.481191i
$70$		0			0
$71$	6.23395	+	6.23395i	0.739834	+	0.739834i	0.972546	−	0.232712i	$-0.0747598\pi$
$71$	6.23395	+	6.23395i	0.739834	+	0.739834i	−0.232712	+	0.972546i	$0.574760\pi$
$72$		0			0
$73$	−1.44956	+	1.44956i	−0.169658	+	0.169658i	−0.786829	−	0.617171i	$-0.788279\pi$
$73$	−1.44956	+	1.44956i	−0.169658	+	0.169658i	0.617171	+	0.786829i	$0.288279\pi$
$74$		0			0
$75$	3.01041	−	7.00297i	0.347612	−	0.808633i
$76$		0			0
$77$	3.25592	+	7.86050i	0.371047	+	0.895787i
$78$		0			0
$79$	13.2460			1.49029			0.745144	−	0.666904i	$-0.232381\pi$
$79$	13.2460			1.49029			0.745144	+	0.666904i	$0.232381\pi$
$80$		0			0
$81$	0.478386	−	8.98728i	0.0531540	−	0.998586i
$82$		0			0
$83$	6.19358	−	2.56547i	0.679834	−	0.281596i	−0.0159235	−	0.999873i	$-0.505069\pi$
$83$	6.19358	−	2.56547i	0.679834	−	0.281596i	0.695758	+	0.718277i	$0.255069\pi$
$84$		0			0
$85$	−1.54002	+	3.71795i	−0.167039	+	0.403268i
$86$		0			0
$87$	−4.52195	−	4.64382i	−0.484804	−	0.497870i
$88$		0			0
$89$	9.26892	−	9.26892i	0.982503	−	0.982503i	−0.0173462	−	0.999850i	$-0.505522\pi$
$89$	9.26892	−	9.26892i	0.982503	−	0.982503i	0.999850	+	0.0173462i	$0.00552174\pi$
$90$		0			0
$91$	−6.07889	+	14.6757i	−0.637240	+	1.53843i
$92$		0			0
$93$	0.551964	−	0.220080i	0.0572360	−	0.0228213i
$94$		0			0
$95$	1.64784			0.169065
$96$		0			0
$97$	9.56950			0.971635			0.485818	−	0.874060i	$-0.338522\pi$
$97$	9.56950			0.971635			0.485818	+	0.874060i	$0.338522\pi$
$98$		0			0
$99$	2.32653	+	6.06825i	0.233825	+	0.609882i
$100$		0			0
$101$	1.02241	−	2.46831i	0.101733	−	0.245606i	−0.864815	−	0.502091i	$-0.832564\pi$
$101$	1.02241	−	2.46831i	0.101733	−	0.245606i	0.966548	+	0.256485i	$0.0825643\pi$
$102$		0			0
$103$	−7.61434	+	7.61434i	−0.750263	+	0.750263i	−0.974528	−	0.224265i	$-0.928002\pi$
$103$	−7.61434	+	7.61434i	−0.750263	+	0.750263i	0.224265	+	0.974528i	$0.428002\pi$
$104$		0			0
$105$	−3.77225	+	3.67326i	−0.368134	+	0.358473i
$106$		0			0
$107$	−4.84555	+	11.6982i	−0.468437	+	1.13091i	0.496409	+	0.868089i	$0.334652\pi$
$107$	−4.84555	+	11.6982i	−0.468437	+	1.13091i	−0.964846	+	0.262817i	$0.915348\pi$
$108$		0			0
$109$	13.7600	−	5.69956i	1.31796	−	0.545919i	0.390766	−	0.920490i	$-0.372210\pi$
$109$	13.7600	−	5.69956i	1.31796	−	0.545919i	0.927198	+	0.374571i	$0.122210\pi$
$110$		0			0
$111$	−0.107616	+	8.09414i	−0.0102145	+	0.768262i
$112$		0			0
$113$	−15.8596			−1.49195			−0.745974	−	0.665975i	$-0.768016\pi$
$113$	−15.8596			−1.49195			−0.745974	+	0.665975i	$0.768016\pi$
$114$		0			0
$115$	1.73078	+	4.17848i	0.161396	+	0.389645i
$116$		0			0
$117$	−4.93976	+	11.0827i	−0.456681	+	1.02459i
$118$		0			0
$119$	−14.4391	+	14.4391i	−1.32363	+	1.32363i
$120$		0			0
$121$	4.45977	+	4.45977i	0.405434	+	0.405434i
$122$		0			0
$123$	3.26873	−	7.60388i	0.294731	−	0.685618i
$124$		0			0
$125$	−6.72248	+	2.78454i	−0.601277	+	0.249057i
$126$		0			0
$127$		−	2.27121i		−	0.201537i	−0.994910	−	0.100769i	$-0.967870\pi$
$127$		−	2.27121i		−	0.201537i	0.994910	−	0.100769i	$-0.0321301\pi$
$128$		0			0
$129$	0.228063	−	17.1533i	0.0200798	−	1.51027i
$130$		0			0
$131$	2.57445	+	6.21528i	0.224931	+	0.543032i	0.995547	−	0.0942683i	$-0.0300512\pi$
$131$	2.57445	+	6.21528i	0.224931	+	0.543032i	−0.770616	+	0.637300i	$0.780051\pi$
$132$		0			0
$133$	7.72502	+	3.19981i	0.669844	+	0.277459i
$134$		0			0
$135$	−2.95501	+	2.72822i	−0.254327	+	0.234808i
$136$		0			0
$137$	−8.23933	−	8.23933i	−0.703934	−	0.703934i	0.261319	−	0.965252i	$-0.415843\pi$
$137$	−8.23933	−	8.23933i	−0.703934	−	0.703934i	−0.965252	+	0.261319i	$0.915843\pi$
$138$		0			0
$139$	−4.47443	−	1.85337i	−0.379516	−	0.157201i	0.184766	−	0.982782i	$-0.440847\pi$
$139$	−4.47443	−	1.85337i	−0.379516	−	0.157201i	−0.564283	+	0.825582i	$0.690847\pi$
$140$		0			0
$141$	−7.80052	+	3.11024i	−0.656922	+	0.261929i
$142$		0			0
$143$		−	8.76181i		−	0.732700i
$144$		0			0
$145$			2.89652i			0.240543i
$146$		0			0
$147$	−13.5548	+	5.40459i	−1.11798	+	0.445763i
$148$		0			0
$149$	−14.7806	−	6.12233i	−1.21087	−	0.501561i	−0.316377	−	0.948634i	$-0.602466\pi$
$149$	−14.7806	−	6.12233i	−1.21087	−	0.501561i	−0.894497	+	0.447073i	$0.852466\pi$
$150$		0			0
$151$	6.48300	+	6.48300i	0.527579	+	0.527579i	0.919850	−	0.392271i	$-0.128310\pi$
$151$	6.48300	+	6.48300i	0.527579	+	0.527579i	−0.392271	+	0.919850i	$0.628310\pi$
$152$		0			0
$153$	−11.3187	+	10.7322i	−0.915061	+	0.867648i
$154$		0			0
$155$	−0.245328	−	0.101618i	−0.0197053	−	0.00816218i
$156$		0			0
$157$	−0.376399	−	0.908707i	−0.0300399	−	0.0725227i	0.908148	−	0.418650i	$-0.137497\pi$
$157$	−0.376399	−	0.908707i	−0.0300399	−	0.0725227i	−0.938188	+	0.346127i	$0.887497\pi$
$158$		0			0
$159$	−0.103542	+	7.78772i	−0.00821142	+	0.617606i
$160$		0			0
$161$			22.9494i			1.80867i
$162$		0			0
$163$	−1.44038	+	0.596624i	−0.112819	+	0.0467312i	−0.438379	−	0.898790i	$-0.644447\pi$
$163$	−1.44038	+	0.596624i	−0.112819	+	0.0467312i	0.325560	+	0.945521i	$0.394447\pi$
$164$		0			0
$165$	1.14696	−	2.66812i	0.0892909	−	0.207713i
$166$		0			0
$167$	3.06006	+	3.06006i	0.236795	+	0.236795i	0.815522	−	0.578727i	$-0.196450\pi$
$167$	3.06006	+	3.06006i	0.236795	+	0.236795i	−0.578727	+	0.815522i	$0.696450\pi$
$168$		0			0
$169$	2.37482	−	2.37482i	0.182679	−	0.182679i
$170$		0			0
$171$	5.83370	+	2.60019i	0.446114	+	0.198842i
$172$		0			0
$173$	−4.07676	−	9.84216i	−0.309950	−	0.748286i	−0.999706	−	0.0242438i	$-0.992282\pi$
$173$	−4.07676	−	9.84216i	−0.309950	−	0.748286i	0.689756	−	0.724042i	$-0.257718\pi$
$174$		0			0
$175$	−17.2844			−1.30658
$176$		0			0
$177$	−0.201541	+	15.1585i	−0.0151487	+	1.13938i
$178$		0			0
$179$	4.90033	−	2.02978i	0.366268	−	0.151713i	−0.191956	−	0.981404i	$-0.561483\pi$
$179$	4.90033	−	2.02978i	0.366268	−	0.151713i	0.558224	+	0.829690i	$0.311483\pi$
$180$		0			0
$181$	7.21135	−	17.4097i	0.536016	−	1.29406i	−0.391468	−	0.920192i	$-0.628033\pi$
$181$	7.21135	−	17.4097i	0.536016	−	1.29406i	0.927483	−	0.373864i	$-0.121967\pi$
$182$		0			0
$183$	8.01706	−	7.80668i	0.592638	−	0.577086i
$184$		0			0
$185$	2.55787	−	2.55787i	0.188058	−	0.188058i
$186$		0			0
$187$	4.31028	−	10.4059i	0.315199	−	0.760957i
$188$		0			0
$189$	−19.1507	+	7.05169i	−1.39301	+	0.512935i
$190$		0			0
$191$	−5.45750			−0.394891			−0.197446	−	0.980314i	$-0.563265\pi$
$191$	−5.45750			−0.394891			−0.197446	+	0.980314i	$0.563265\pi$
$192$		0			0
$193$	−10.5440			−0.758971			−0.379486	−	0.925198i	$-0.623899\pi$
$193$	−10.5440			−0.758971			−0.379486	+	0.925198i	$0.623899\pi$
$194$		0			0
$195$	5.03662	−	2.00821i	0.360680	−	0.143811i
$196$		0			0
$197$	−0.0524216	+	0.126557i	−0.00373489	+	0.00901681i	−0.925736	−	0.378170i	$-0.876553\pi$
$197$	−0.0524216	+	0.126557i	−0.00373489	+	0.00901681i	0.922001	+	0.387187i	$0.126553\pi$
$198$		0			0
$199$	6.64709	−	6.64709i	0.471200	−	0.471200i	−0.431103	−	0.902303i	$-0.641875\pi$
$199$	6.64709	−	6.64709i	0.471200	−	0.471200i	0.902303	+	0.431103i	$0.141875\pi$
$200$		0			0
$201$	7.12846	+	7.32057i	0.502803	+	0.516353i
$202$		0			0
$203$	−5.62450	+	13.5787i	−0.394763	+	0.953041i
$204$		0			0
$205$	−3.41708	+	1.41540i	−0.238659	+	0.0988560i
$206$		0			0
$207$	−0.466058	+	17.5237i	−0.0323932	+	1.21798i
$208$		0			0
$209$	−4.61205			−0.319022
$210$		0			0
$211$	−2.88401	−	6.96261i	−0.198543	−	0.479326i	0.792981	−	0.609246i	$-0.208528\pi$
$211$	−2.88401	−	6.96261i	−0.198543	−	0.479326i	−0.991524	+	0.129920i	$0.958528\pi$
$212$		0			0
$213$	6.03061	−	14.0287i	0.413211	−	0.961232i
$214$		0			0
$215$	−5.42071	+	5.42071i	−0.369689	+	0.369689i
$216$		0			0
$217$	−0.952765	−	0.952765i	−0.0646779	−	0.0646779i
$218$		0			0
$219$	3.26204	+	1.40228i	0.220429	+	0.0947570i
$220$		0			0
$221$	19.4281	−	8.04739i	1.30688	−	0.541326i
$222$		0			0
$223$			16.6352i			1.11398i	0.830520	+	0.556988i	$0.188043\pi$
$223$			16.6352i			1.11398i	−0.830520	+	0.556988i	$0.811957\pi$
$224$		0			0
$225$	−13.1981	−	0.351013i	−0.879872	−	0.0234009i
$226$		0			0
$227$	1.09433	+	2.64195i	0.0726335	+	0.175353i	0.956027	−	0.293280i	$-0.0947468\pi$
$227$	1.09433	+	2.64195i	0.0726335	+	0.175353i	−0.883393	+	0.468633i	$0.844747\pi$
$228$		0			0
$229$	1.48780	+	0.616268i	0.0983167	+	0.0407241i	0.431300	−	0.902209i	$-0.358055\pi$
$229$	1.48780	+	0.616268i	0.0983167	+	0.0407241i	−0.332983	+	0.942933i	$0.608055\pi$
$230$		0			0
$231$	10.5579	−	10.2808i	0.694659	−	0.676430i
$232$		0			0
$233$	−14.1523	−	14.1523i	−0.927150	−	0.927150i	0.0703713	−	0.997521i	$-0.477582\pi$
$233$	−14.1523	−	14.1523i	−0.927150	−	0.927150i	−0.997521	+	0.0703713i	$0.977582\pi$
$234$		0			0
$235$	3.46705	+	1.43610i	0.226165	+	0.0936808i
$236$		0			0
$237$	−8.49722	−	21.3111i	−0.551953	−	1.38431i
$238$		0			0
$239$			5.75051i			0.371969i	0.982553	+	0.185985i	$0.0595475\pi$
$239$			5.75051i			0.371969i	−0.982553	+	0.185985i	$0.940453\pi$
$240$		0			0
$241$			0.404801i			0.0260755i	0.999915	+	0.0130378i	$0.00415016\pi$
$241$			0.404801i			0.0260755i	−0.999915	+	0.0130378i	$0.995850\pi$
$242$		0			0
$243$	−14.7663	+	4.99563i	−0.947259	+	0.320470i
$244$		0			0
$245$	6.02461	+	2.49548i	0.384898	+	0.159430i
$246$		0			0
$247$	−6.08876	−	6.08876i	−0.387418	−	0.387418i
$248$		0			0
$249$	−8.10067	−	8.31898i	−0.513359	−	0.527194i
$250$		0			0
$251$	10.1825	+	4.21772i	0.642712	+	0.266220i	0.680143	−	0.733079i	$-0.261917\pi$
$251$	10.1825	+	4.21772i	0.642712	+	0.266220i	−0.0374311	+	0.999299i	$0.511917\pi$
$252$		0			0
$253$	−4.84418	−	11.6949i	−0.304551	−	0.735252i
$254$		0			0
$255$	6.96963	+	0.0926651i	0.436455	+	0.00580291i
$256$		0			0
$257$		−	27.0174i		−	1.68530i	−0.538460	−	0.842651i	$-0.680994\pi$
$257$		−	27.0174i		−	1.68530i	0.538460	−	0.842651i	$-0.319006\pi$
$258$		0			0
$259$	16.9581	−	7.02426i	1.05372	−	0.436466i
$260$		0			0
$261$	−4.57052	+	10.2543i	−0.282908	+	0.634722i
$262$		0			0
$263$	−0.0909901	−	0.0909901i	−0.00561069	−	0.00561069i	0.704296	−	0.709907i	$-0.251263\pi$
$263$	−0.0909901	−	0.0909901i	−0.00561069	−	0.00561069i	−0.709907	+	0.704296i	$0.751263\pi$
$264$		0			0
$265$	2.46103	−	2.46103i	0.151180	−	0.151180i
$266$		0			0
$267$	−20.8585	−	8.96658i	−1.27652	−	0.548746i
$268$		0			0
$269$	8.83071	+	21.3192i	0.538418	+	1.29986i	0.925827	+	0.377948i	$0.123370\pi$
$269$	8.83071	+	21.3192i	0.538418	+	1.29986i	−0.387409	+	0.921908i	$0.626630\pi$
$270$		0			0
$271$	2.82777			0.171775			0.0858874	−	0.996305i	$-0.472627\pi$
$271$	2.82777			0.171775			0.0858874	+	0.996305i	$0.472627\pi$
$272$		0			0
$273$	27.5110	+	0.365774i	1.66504	+	0.0221377i
$274$		0			0
$275$	8.80806	−	3.64842i	0.531146	−	0.220008i
$276$		0			0
$277$	−5.81789	+	14.0456i	−0.349563	+	0.843920i	0.647108	+	0.762398i	$0.275978\pi$
$277$	−5.81789	+	14.0456i	−0.349563	+	0.843920i	−0.996672	+	0.0815223i	$0.974022\pi$
$278$		0			0
$279$	−0.708164	−	0.746862i	−0.0423967	−	0.0447135i
$280$		0			0
$281$	−11.3239	+	11.3239i	−0.675530	+	0.675530i	−0.958985	−	0.283455i	$-0.908519\pi$
$281$	−11.3239	+	11.3239i	−0.675530	+	0.675530i	0.283455	+	0.958985i	$0.408519\pi$
$282$		0			0
$283$	3.05059	−	7.36479i	0.181339	−	0.437791i	−0.806904	−	0.590683i	$-0.798859\pi$
$283$	3.05059	−	7.36479i	0.181339	−	0.437791i	0.988243	+	0.152892i	$0.0488585\pi$
$284$		0			0
$285$	−1.05708	−	2.65118i	−0.0626162	−	0.157042i
$286$		0			0
$287$	−18.7676			−1.10782
$288$		0			0
$289$	10.0325			0.590149
$290$		0			0
$291$	−6.13878	−	15.3961i	−0.359862	−	0.902538i
$292$		0			0
$293$	−4.77629	+	11.5310i	−0.279034	+	0.673648i	−0.999809	−	0.0195210i	$-0.993786\pi$
$293$	−4.77629	+	11.5310i	−0.279034	+	0.673648i	0.720775	+	0.693169i	$0.243786\pi$
$294$		0			0
$295$	4.79031	−	4.79031i	0.278903	−	0.278903i
$296$		0			0
$297$	8.27061	−	7.63585i	0.479909	−	0.443077i
$298$		0			0
$299$	9.04421	−	21.8346i	0.523040	−	1.26273i
$300$		0			0
$301$	−35.9380	+	14.8860i	−2.07143	+	0.858016i
$302$		0			0
$303$	−4.62708	−	0.0615196i	−0.265819	−	0.00353421i
$304$		0			0
$305$	−5.00053			−0.286330
$306$		0			0
$307$	12.3306	+	29.7687i	0.703744	+	1.69899i	0.715071	+	0.699052i	$0.246394\pi$
$307$	12.3306	+	29.7687i	0.703744	+	1.69899i	−0.0113269	+	0.999936i	$0.503606\pi$
$308$		0			0
$309$	17.1351	+	7.36597i	0.974781	+	0.419035i
$310$		0			0
$311$	22.2380	−	22.2380i	1.26100	−	1.26100i	0.310392	−	0.950609i	$-0.399540\pi$
$311$	22.2380	−	22.2380i	1.26100	−	1.26100i	0.950609	−	0.310392i	$-0.100460\pi$
$312$		0			0
$313$	−13.4230	−	13.4230i	−0.758713	−	0.758713i	0.217375	−	0.976088i	$-0.430250\pi$
$313$	−13.4230	−	13.4230i	−0.758713	−	0.758713i	−0.976088	+	0.217375i	$0.930250\pi$
$314$		0			0
$315$	8.32969	+	3.71271i	0.469325	+	0.209187i
$316$		0			0
$317$	−0.947076	+	0.392292i	−0.0531931	+	0.0220333i	−0.409121	−	0.912480i	$-0.634165\pi$
$317$	−0.947076	+	0.392292i	−0.0531931	+	0.0220333i	0.355928	+	0.934513i	$0.384165\pi$
$318$		0			0
$319$		−	8.10688i		−	0.453898i
$320$		0			0
$321$	21.9293	+	0.291562i	1.22398	+	0.0162734i
$322$		0			0
$323$	−4.23599	−	10.2266i	−0.235697	−	0.569022i
$324$		0			0
$325$	16.4449	+	6.81168i	0.912197	+	0.377844i
$326$		0			0
$327$	−17.9968	−	18.4818i	−0.995227	−	1.02205i
$328$		0			0
$329$	13.4647	+	13.4647i	0.742335	+	0.742335i
$330$		0			0
$331$	−20.7914	−	8.61208i	−1.14280	−	0.473363i	−0.270686	−	0.962668i	$-0.587251\pi$
$331$	−20.7914	−	8.61208i	−1.14280	−	0.473363i	−0.872113	+	0.489305i	$0.837251\pi$
$332$		0			0
$333$	13.0915	−	5.01921i	0.717410	−	0.275051i
$334$		0			0
$335$		−	4.56610i		−	0.249473i
$336$		0			0
$337$			29.6373i			1.61444i	0.590248	+	0.807222i	$0.299030\pi$
$337$			29.6373i			1.61444i	−0.590248	+	0.807222i	$0.700970\pi$
$338$		0			0
$339$	10.1739	+	25.5162i	0.552569	+	1.38585i
$340$		0			0
$341$	0.686634	+	0.284413i	0.0371833	+	0.0154018i
$342$		0			0
$343$	3.95740	+	3.95740i	0.213680	+	0.213680i
$344$		0			0
$345$	5.61237	−	5.46509i	0.302160	−	0.294231i
$346$		0			0
$347$	−21.8544	−	9.05241i	−1.17321	−	0.485959i	−0.290956	−	0.956736i	$-0.593973\pi$
$347$	−21.8544	−	9.05241i	−1.17321	−	0.485959i	−0.882252	+	0.470778i	$0.843973\pi$
$348$		0			0
$349$	−0.170032	−	0.410493i	−0.00910160	−	0.0219732i	0.919263	−	0.393643i	$-0.128785\pi$
$349$	−0.170032	−	0.410493i	−0.00910160	−	0.0219732i	−0.928365	+	0.371670i	$0.878785\pi$
$350$		0			0
$351$	20.9995	+	0.837993i	1.12087	+	0.0447288i
$352$		0			0
$353$			23.1851i			1.23402i	0.786956	+	0.617010i	$0.211656\pi$
$353$			23.1851i			1.23402i	−0.786956	+	0.617010i	$0.788344\pi$
$354$		0			0
$355$	−6.30432	+	2.61133i	−0.334599	+	0.138595i
$356$		0			0
$357$	32.4934	+	13.9681i	1.71973	+	0.739273i
$358$		0			0
$359$	7.59655	+	7.59655i	0.400930	+	0.400930i	0.878561	−	0.477630i	$-0.158504\pi$
$359$	7.59655	+	7.59655i	0.400930	+	0.400930i	−0.477630	+	0.878561i	$0.658504\pi$
$360$		0			0
$361$	10.2300	−	10.2300i	0.538422	−	0.538422i
$362$		0			0
$363$	4.31430	−	10.0361i	0.226442	−	0.526761i
$364$		0			0
$365$	−0.607204	−	1.46592i	−0.0317825	−	0.0767298i
$366$		0			0
$367$	−14.4269			−0.753079			−0.376540	−	0.926401i	$-0.622886\pi$
$367$	−14.4269			−0.753079			−0.376540	+	0.926401i	$0.622886\pi$
$368$		0			0
$369$	−14.3306	−	0.381133i	−0.746020	−	0.0198410i
$370$		0			0
$371$	16.3161	−	6.75834i	0.847089	−	0.350876i
$372$		0			0
$373$	−4.38447	+	10.5851i	−0.227019	+	0.548073i	−0.995812	−	0.0914248i	$-0.970858\pi$
$373$	−4.38447	+	10.5851i	−0.227019	+	0.548073i	0.768793	+	0.639498i	$0.220858\pi$
$374$		0			0
$375$	8.79243	+	9.02938i	0.454039	+	0.466275i
$376$		0			0
$377$	10.7026	−	10.7026i	0.551211	−	0.551211i
$378$		0			0
$379$	1.10789	−	2.67468i	0.0569084	−	0.137389i	−0.892868	−	0.450319i	$-0.851310\pi$
$379$	1.10789	−	2.67468i	0.0569084	−	0.137389i	0.949776	+	0.312930i	$0.101310\pi$
$380$		0			0
$381$	−3.65409	+	1.45697i	−0.187205	+	0.0746427i
$382$		0			0
$383$	−3.50037			−0.178861			−0.0894304	−	0.995993i	$-0.528505\pi$
$383$	−3.50037			−0.178861			−0.0894304	+	0.995993i	$0.528505\pi$
$384$		0			0
$385$	−6.58535			−0.335621
$386$		0			0
$387$	−27.7439	+	10.6369i	−1.41030	+	0.540702i
$388$		0			0
$389$	10.6893	−	25.8063i	0.541969	−	1.30843i	−0.381362	−	0.924426i	$-0.624545\pi$
$389$	10.6893	−	25.8063i	0.541969	−	1.30843i	0.923332	−	0.384004i	$-0.125455\pi$
$390$		0			0
$391$	21.4826	−	21.4826i	1.08642	−	1.08642i
$392$		0			0
$393$	8.34813	−	8.12905i	0.421107	−	0.410056i
$394$		0			0
$395$	−3.92344	+	9.47203i	−0.197410	+	0.476590i
$396$		0			0
$397$	−11.8148	+	4.89383i	−0.592966	+	0.245614i	−0.658926	−	0.752208i	$-0.728989\pi$
$397$	−11.8148	+	4.89383i	−0.592966	+	0.245614i	0.0659602	+	0.997822i	$0.478989\pi$
$398$		0			0
$399$	0.192536	−	14.4813i	0.00963887	−	0.724970i
$400$		0			0
$401$	37.4682			1.87107			0.935537	−	0.353229i	$-0.114916\pi$
$401$	37.4682			1.87107			0.935537	+	0.353229i	$0.114916\pi$
$402$		0			0
$403$	0.531006	+	1.28196i	0.0264513	+	0.0638591i
$404$		0			0
$405$	6.28500	+	3.00411i	0.312304	+	0.149276i
$406$		0			0
$407$	−7.15905	+	7.15905i	−0.354861	+	0.354861i
$408$		0			0
$409$	−9.85216	−	9.85216i	−0.487158	−	0.487158i	0.420250	−	0.907408i	$-0.361942\pi$
$409$	−9.85216	−	9.85216i	−0.487158	−	0.487158i	−0.907408	+	0.420250i	$0.861942\pi$
$410$		0			0
$411$	−7.97058	+	18.5416i	−0.393160	+	0.914587i
$412$		0			0
$413$	31.7586	−	13.1549i	1.56274	−	0.647308i
$414$		0			0
$415$			5.18885i			0.254710i
$416$		0			0
$417$	−0.111520	+	8.38774i	−0.00546114	+	0.410749i
$418$		0			0
$419$	5.45030	+	13.1582i	0.266264	+	0.642819i	0.999302	−	0.0373695i	$-0.0118979\pi$
$419$	5.45030	+	13.1582i	0.266264	+	0.642819i	−0.733037	+	0.680189i	$0.761898\pi$
$420$		0			0
$421$	−13.4081	−	5.55381i	−0.653470	−	0.270676i	0.0312176	−	0.999513i	$-0.490062\pi$
$421$	−13.4081	−	5.55381i	−0.653470	−	0.270676i	−0.684688	+	0.728836i	$0.740062\pi$
$422$		0			0
$423$	10.0080	+	10.5549i	0.486605	+	0.513195i
$424$		0			0
$425$	16.1797	+	16.1797i	0.784832	+	0.784832i
$426$		0			0
$427$	−23.4423	−	9.71011i	−1.13445	−	0.469905i
$428$		0			0
$429$	−14.0967	+	5.62066i	−0.680594	+	0.271368i
$430$		0			0
$431$		−	37.0767i		−	1.78592i	−0.450133	−	0.892962i	$-0.648623\pi$
$431$		−	37.0767i		−	1.78592i	0.450133	−	0.892962i	$-0.351377\pi$
$432$		0			0
$433$		−	0.656469i		−	0.0315479i	−0.999876	−	0.0157739i	$-0.994979\pi$
$433$		−	0.656469i		−	0.0315479i	0.999876	−	0.0157739i	$-0.00502121\pi$
$434$		0			0
$435$	4.66014	−	1.85810i	0.223437	−	0.0890891i
$436$		0			0
$437$	−11.4933	−	4.76069i	−0.549801	−	0.227735i
$438$		0			0
$439$	−14.8613	−	14.8613i	−0.709293	−	0.709293i	0.257093	−	0.966387i	$-0.417235\pi$
$439$	−14.8613	−	14.8613i	−0.709293	−	0.709293i	−0.966387	+	0.257093i	$0.917235\pi$
$440$		0			0
$441$	17.3906	+	18.3409i	0.828125	+	0.873378i
$442$		0			0
$443$	5.86331	+	2.42866i	0.278574	+	0.115389i	0.517596	−	0.855625i	$-0.326827\pi$
$443$	5.86331	+	2.42866i	0.278574	+	0.115389i	−0.239022	+	0.971014i	$0.576827\pi$
$444$		0			0
$445$	3.88265	+	9.37354i	0.184055	+	0.444348i
$446$		0			0
$447$	−0.368388	+	27.7076i	−0.0174241	+	1.31053i
$448$		0			0
$449$			0.964596i			0.0455221i	0.999741	+	0.0227611i	$0.00724569\pi$
$449$			0.964596i			0.0455221i	−0.999741	+	0.0227611i	$0.992754\pi$
$450$		0			0
$451$	9.56386	−	3.96148i	0.450345	−	0.186539i
$452$		0			0
$453$	6.27154	−	14.5892i	0.294662	−	0.685458i
$454$		0			0
$455$	−8.69388	−	8.69388i	−0.407575	−	0.407575i
$456$		0			0
$457$	8.65709	−	8.65709i	0.404962	−	0.404962i	−0.475016	−	0.879977i	$-0.657558\pi$
$457$	8.65709	−	8.65709i	0.404962	−	0.404962i	0.879977	+	0.475016i	$0.157558\pi$
$458$		0			0
$459$	24.5277	+	11.3257i	1.14485	+	0.528638i
$460$		0			0
$461$	12.4022	+	29.9416i	0.577628	+	1.39452i	0.894936	+	0.446195i	$0.147221\pi$
$461$	12.4022	+	29.9416i	0.577628	+	1.39452i	−0.317308	+	0.948323i	$0.602779\pi$
$462$		0			0
$463$	−18.0597			−0.839306			−0.419653	−	0.907685i	$-0.637848\pi$
$463$	−18.0597			−0.839306			−0.419653	+	0.907685i	$0.637848\pi$
$464$		0			0
$465$	−0.00611450	+	0.459891i	−0.000283553	+	0.0213269i
$466$		0			0
$467$	−3.41999	+	1.41660i	−0.158258	+	0.0655526i	−0.460406	−	0.887708i	$-0.652296\pi$
$467$	−3.41999	+	1.41660i	−0.158258	+	0.0655526i	0.302148	+	0.953261i	$0.402296\pi$
$468$		0			0
$469$	8.86653	−	21.4057i	0.409418	−	0.988423i
$470$		0			0
$471$	−1.22054	+	1.18851i	−0.0562395	+	0.0547636i
$472$		0			0
$473$	15.1717	−	15.1717i	0.697594	−	0.697594i
$474$		0			0
$475$	3.58554	−	8.65625i	0.164516	−	0.397176i
$476$		0			0
$477$	12.5959	−	4.82920i	0.576727	−	0.221114i
$478$		0			0
$479$	22.0035			1.00537			0.502684	−	0.864470i	$-0.332346\pi$
$479$	22.0035			1.00537			0.502684	+	0.864470i	$0.332346\pi$
$480$		0			0
$481$	−18.9025			−0.861882
$482$		0			0
$483$	36.9228	−	14.7219i	1.68004	−	0.669871i
$484$		0			0
$485$	−2.83448	+	6.84304i	−0.128707	+	0.310726i
$486$		0			0
$487$	4.12841	−	4.12841i	0.187076	−	0.187076i	−0.607355	−	0.794431i	$-0.707769\pi$
$487$	4.12841	−	4.12841i	0.187076	−	0.187076i	0.794431	+	0.607355i	$0.207769\pi$
$488$		0			0
$489$	1.88389	+	1.93466i	0.0851924	+	0.0874882i
$490$		0			0
$491$	5.44901	−	13.1551i	0.245911	−	0.593681i	−0.751939	−	0.659233i	$-0.770881\pi$
$491$	5.44901	−	13.1551i	0.245911	−	0.593681i	0.997849	+	0.0655526i	$0.0208810\pi$
$492$		0			0
$493$	17.9759	−	7.44586i	0.809594	−	0.335345i
$494$		0			0
$495$	−5.02845	−	0.133736i	−0.226012	−	0.00601097i
$496$		0			0
$497$	−34.6251			−1.55315
$498$		0			0
$499$	−14.4361	−	34.8519i	−0.646250	−	1.56018i	−0.818109	−	0.575063i	$-0.804978\pi$
$499$	−14.4361	−	34.8519i	−0.646250	−	1.56018i	0.171860	−	0.985121i	$-0.445022\pi$
$500$		0			0
$501$	2.96025	−	6.88628i	0.132254	−	0.307656i
$502$		0			0
$503$	−2.95140	+	2.95140i	−0.131596	+	0.131596i	−0.769837	−	0.638241i	$-0.779662\pi$
$503$	−2.95140	+	2.95140i	−0.131596	+	0.131596i	0.638241	+	0.769837i	$0.279662\pi$
$504$		0			0
$505$	1.46222	+	1.46222i	0.0650681	+	0.0650681i
$506$		0			0
$507$	−5.34424	−	2.29736i	−0.237346	−	0.102029i
$508$		0			0
$509$	−40.0107	+	16.5730i	−1.77344	+	0.734584i	−0.779281	+	0.626675i	$0.784415\pi$
$509$	−40.0107	+	16.5730i	−1.77344	+	0.734584i	−0.994161	+	0.107909i	$0.965585\pi$
$510$		0			0
$511$		−	8.05125i		−	0.356166i
$512$		0			0
$513$	0.441103	−	11.0537i	0.0194752	−	0.488033i
$514$		0			0
$515$	−3.18956	−	7.70028i	−0.140549	−	0.339315i
$516$		0			0
$517$	−9.70371	−	4.01941i	−0.426769	−	0.176773i
$518$		0			0
$519$	−13.2196	+	12.8727i	−0.580276	+	0.565049i
$520$		0			0
$521$	−9.10873	−	9.10873i	−0.399061	−	0.399061i	0.478841	−	0.877902i	$-0.341057\pi$
$521$	−9.10873	−	9.10873i	−0.399061	−	0.399061i	−0.877902	+	0.478841i	$0.841057\pi$
$522$		0			0
$523$	18.7797	+	7.77882i	0.821181	+	0.340144i	0.753405	−	0.657556i	$-0.228410\pi$
$523$	18.7797	+	7.77882i	0.821181	+	0.340144i	0.0677753	+	0.997701i	$0.478410\pi$
$524$		0			0
$525$	11.0879	+	27.8085i	0.483915	+	1.21366i
$526$		0			0
$527$			1.78374i			0.0777009i
$528$		0			0
$529$		−	11.1443i		−	0.484534i
$530$		0			0
$531$	24.5175	−	9.39985i	1.06397	−	0.407919i
$532$		0			0
$533$	17.8560	+	7.39618i	0.773427	+	0.320364i
$534$		0			0
$535$	−6.92999	−	6.92999i	−0.299609	−	0.299609i
$536$		0			0
$537$	−6.40921	−	6.58194i	−0.276578	−	0.284032i
$538$		0			0
$539$	−16.8619	−	6.98443i	−0.726294	−	0.300841i
$540$		0			0
$541$	−4.91944	−	11.8766i	−0.211503	−	0.510614i	0.782151	−	0.623088i	$-0.214122\pi$
$541$	−4.91944	−	11.8766i	−0.211503	−	0.510614i	−0.993655	+	0.112475i	$0.964122\pi$
$542$		0			0
$543$	−32.6362	−	0.433916i	−1.40055	−	0.0186211i
$544$		0			0
$545$			11.5278i			0.493796i
$546$		0			0
$547$	−19.4330	+	8.04942i	−0.830896	+	0.344168i	−0.757257	−	0.653117i	$-0.773461\pi$
$547$	−19.4330	+	8.04942i	−0.830896	+	0.344168i	−0.0736387	+	0.997285i	$0.523461\pi$
$548$		0			0
$549$	−17.7029	−	7.89052i	−0.755541	−	0.336759i
$550$		0			0
$551$	−5.63363	−	5.63363i	−0.240001	−	0.240001i
$552$		0			0
$553$	−36.7859	+	36.7859i	−1.56429	+	1.56429i
$554$		0			0
$555$	−5.75615	−	2.47443i	−0.244335	−	0.105034i
$556$		0			0
$557$	−14.3258	−	34.5854i	−0.607002	−	1.46543i	−0.866245	−	0.499620i	$-0.833473\pi$
$557$	−14.3258	−	34.5854i	−0.607002	−	1.46543i	0.259243	−	0.965812i	$-0.416527\pi$
$558$		0			0
$559$	40.0588			1.69431
$560$		0			0
$561$	−19.5069	−	0.259355i	−0.823581	−	0.0109500i
$562$		0			0
$563$	−14.4215	+	5.97357i	−0.607793	+	0.251756i	−0.665284	−	0.746590i	$-0.731690\pi$
$563$	−14.4215	+	5.97357i	−0.607793	+	0.251756i	0.0574918	+	0.998346i	$0.481690\pi$
$564$		0			0
$565$	4.69761	−	11.3410i	0.197630	−	0.477121i
$566$		0			0
$567$	23.6304	+	26.2875i	0.992382	+	1.10397i
$568$		0			0
$569$	−3.11604	+	3.11604i	−0.130631	+	0.130631i	−0.769399	−	0.638768i	$-0.779444\pi$
$569$	−3.11604	+	3.11604i	−0.130631	+	0.130631i	0.638768	+	0.769399i	$0.279444\pi$
$570$		0			0
$571$	4.75950	−	11.4904i	0.199179	−	0.480860i	−0.792457	−	0.609928i	$-0.791198\pi$
$571$	4.75950	−	11.4904i	0.199179	−	0.480860i	0.991636	+	0.129068i	$0.0411984\pi$
$572$		0			0
$573$	3.50096	+	8.78045i	0.146255	+	0.366809i
$574$		0			0
$575$	25.7159			1.07243
$576$		0			0
$577$	−18.4677			−0.768820			−0.384410	−	0.923163i	$-0.625595\pi$
$577$	−18.4677			−0.768820			−0.384410	+	0.923163i	$0.625595\pi$
$578$		0			0
$579$	6.76390	+	16.9639i	0.281098	+	0.704997i
$580$		0			0
$581$	−10.0758	+	24.3251i	−0.418014	+	1.00917i
$582$		0			0
$583$	−6.88803	+	6.88803i	−0.285273	+	0.285273i
$584$		0			0
$585$	−6.46193	−	6.81504i	−0.267168	−	0.281767i
$586$		0			0
$587$	2.04862	−	4.94582i	0.0845558	−	0.204136i	−0.875946	−	0.482409i	$-0.839762\pi$
$587$	2.04862	−	4.94582i	0.0845558	−	0.204136i	0.960502	+	0.278273i	$0.0897620\pi$
$588$		0			0
$589$	0.674800	−	0.279511i	0.0278047	−	0.0115171i
$590$		0			0
$591$	0.237243	+	0.00315427i	0.00975886	+	0.000129749i
$592$		0			0
$593$	26.6090			1.09270			0.546351	−	0.837556i	$-0.316016\pi$
$593$	26.6090			1.09270			0.546351	+	0.837556i	$0.316016\pi$
$594$		0			0
$595$	−6.04839	−	14.6021i	−0.247960	−	0.598628i
$596$		0			0
$597$	−14.9584	−	6.43027i	−0.612207	−	0.263174i
$598$		0			0
$599$	−12.7251	+	12.7251i	−0.519933	+	0.519933i	−0.917551	−	0.397618i	$-0.869837\pi$
$599$	−12.7251	+	12.7251i	−0.519933	+	0.519933i	0.397618	+	0.917551i	$0.369837\pi$
$600$		0			0
$601$	−6.45474	−	6.45474i	−0.263294	−	0.263294i	0.563097	−	0.826391i	$-0.309610\pi$
$601$	−6.45474	−	6.45474i	−0.263294	−	0.263294i	−0.826391	+	0.563097i	$0.809610\pi$
$602$		0			0
$603$	7.20502	−	16.1649i	0.293411	−	0.658286i
$604$		0			0
$605$	−4.51011	+	1.86815i	−0.183362	+	0.0759511i
$606$		0			0
$607$		−	30.2504i		−	1.22783i	−0.789373	−	0.613914i	$-0.789594\pi$
$607$		−	30.2504i		−	1.22783i	0.789373	−	0.613914i	$-0.210406\pi$
$608$		0			0
$609$	25.4546	+	0.338433i	1.03147	+	0.0137140i
$610$		0			0
$611$	−7.50433	−	18.1171i	−0.303593	−	0.732938i
$612$		0			0
$613$	2.29750	+	0.951656i	0.0927952	+	0.0384370i	0.428598	−	0.903495i	$-0.359008\pi$
$613$	2.29750	+	0.951656i	0.0927952	+	0.0384370i	−0.335803	+	0.941932i	$0.609008\pi$
$614$		0			0
$615$	4.46925	+	4.58969i	0.180217	+	0.185074i
$616$		0			0
$617$	−3.87504	−	3.87504i	−0.156003	−	0.156003i	0.624790	−	0.780793i	$-0.285185\pi$
$617$	−3.87504	−	3.87504i	−0.156003	−	0.156003i	−0.780793	+	0.624790i	$0.785185\pi$
$618$		0			0
$619$	7.55208	+	3.12818i	0.303544	+	0.125732i	0.529256	−	0.848462i	$-0.322471\pi$
$619$	7.55208	+	3.12818i	0.303544	+	0.125732i	−0.225712	+	0.974194i	$0.572471\pi$
$620$		0			0
$621$	28.4925	−	10.4916i	1.14336	−	0.421012i
$622$		0			0
$623$			51.4821i			2.06259i
$624$		0			0
$625$			16.3726i			0.654905i
$626$		0			0
$627$	2.95860	+	7.42022i	0.118155	+	0.296335i
$628$		0			0
$629$	−22.4495	−	9.29889i	−0.895121	−	0.370771i
$630$		0			0
$631$	3.02275	+	3.02275i	0.120334	+	0.120334i	0.764709	−	0.644375i	$-0.222883\pi$
$631$	3.02275	+	3.02275i	0.120334	+	0.120334i	−0.644375	+	0.764709i	$0.722883\pi$
$632$		0			0
$633$	−9.35190	+	9.10648i	−0.371705	+	0.361950i
$634$		0			0
$635$	1.62411	+	0.672730i	0.0644510	+	0.0266965i
$636$		0			0
$637$	−13.0401	−	31.4816i	−0.516668	−	1.24735i
$638$		0			0
$639$	−26.4391	−	0.703168i	−1.04591	−	0.0278169i
$640$		0			0
$641$		−	30.4562i		−	1.20295i	−0.798893	−	0.601473i	$-0.794581\pi$
$641$		−	30.4562i		−	1.20295i	0.798893	−	0.601473i	$-0.205419\pi$
$642$		0			0
$643$	18.0821	−	7.48986i	0.713089	−	0.295371i	0.00350703	−	0.999994i	$-0.498884\pi$
$643$	18.0821	−	7.48986i	0.713089	−	0.295371i	0.709582	+	0.704623i	$0.248884\pi$
$644$		0			0
$645$	12.1986	+	5.24389i	0.480319	+	0.206478i
$646$		0			0
$647$	28.1003	+	28.1003i	1.10474	+	1.10474i	0.993831	+	0.110905i	$0.0353748\pi$
$647$	28.1003	+	28.1003i	1.10474	+	1.10474i	0.110905	+	0.993831i	$0.464625\pi$
$648$		0			0
$649$	−13.4073	+	13.4073i	−0.526282	+	0.526282i
$650$		0			0
$651$	−0.921687	+	2.14407i	−0.0361238	+	0.0840329i
$652$		0			0
$653$	−6.44946	−	15.5704i	−0.252387	−	0.609316i	0.746009	−	0.665936i	$-0.231968\pi$
$653$	−6.44946	−	15.5704i	−0.252387	−	0.609316i	−0.998396	+	0.0566202i	$0.981968\pi$
$654$		0			0
$655$	−5.20703			−0.203455
$656$		0			0
$657$	0.163505	−	6.14778i	0.00637894	−	0.239848i
$658$		0			0
$659$	−30.0479	+	12.4463i	−1.17050	+	0.484838i	−0.881358	−	0.472448i	$-0.843370\pi$
$659$	−30.0479	+	12.4463i	−1.17050	+	0.484838i	−0.289143	+	0.957286i	$0.593370\pi$
$660$		0			0
$661$	−16.0509	+	38.7503i	−0.624308	+	1.50721i	0.222290	+	0.974981i	$0.428647\pi$
$661$	−16.0509	+	38.7503i	−0.624308	+	1.50721i	−0.846598	+	0.532233i	$0.821353\pi$
$662$		0			0
$663$	−25.4103	−	26.0951i	−0.986854	−	1.01345i
$664$		0			0
$665$	−4.57629	+	4.57629i	−0.177461	+	0.177461i
$666$		0			0
$667$	8.36817	−	20.2025i	0.324017	−	0.782246i
$668$		0			0
$669$	26.7640	−	10.6714i	1.03476	−	0.412580i
$670$		0			0
$671$	13.9957			0.540297
$672$		0			0
$673$	1.07753			0.0415357			0.0207678	−	0.999784i	$-0.493389\pi$
$673$	1.07753			0.0415357			0.0207678	+	0.999784i	$0.493389\pi$
$674$		0			0
$675$	7.90176	+	21.4593i	0.304139	+	0.825967i
$676$		0			0
$677$	12.6041	−	30.4289i	0.484414	−	1.16948i	−0.473078	−	0.881021i	$-0.656857\pi$
$677$	12.6041	−	30.4289i	0.484414	−	1.16948i	0.957492	−	0.288459i	$-0.0931429\pi$
$678$		0			0
$679$	−26.5758	+	26.5758i	−1.01989	+	1.01989i
$680$		0			0
$681$	3.54857	−	3.45545i	0.135981	−	0.132413i
$682$		0			0
$683$	−19.7550	+	47.6928i	−0.755904	+	1.82491i	−0.233120	+	0.972448i	$0.574893\pi$
$683$	−19.7550	+	47.6928i	−0.755904	+	1.82491i	−0.522784	+	0.852465i	$0.675107\pi$
$684$		0			0
$685$	8.33233	−	3.45136i	0.318362	−	0.131870i
$686$		0			0
$687$	0.0370816	−	2.78902i	0.00141475	−	0.106408i
$688$		0			0
$689$	−18.1870			−0.692868
$690$		0			0
$691$	4.23089	+	10.2143i	0.160951	+	0.388569i	0.983696	−	0.179842i	$-0.0575585\pi$
$691$	4.23089	+	10.2143i	0.160951	+	0.388569i	−0.822745	+	0.568411i	$0.807559\pi$
$692$		0			0
$693$	−23.3135	−	10.3913i	−0.885605	−	0.394732i
$694$		0			0
$695$	2.65065	−	2.65065i	0.100545	−	0.100545i
$696$		0			0
$697$	17.5681	+	17.5681i	0.665438	+	0.665438i
$698$		0			0
$699$	−13.6907	+	31.8480i	−0.517830	+	1.20460i
$700$		0			0
$701$	−22.1122	+	9.15919i	−0.835168	+	0.345938i	−0.758946	−	0.651153i	$-0.774286\pi$
$701$	−22.1122	+	9.15919i	−0.835168	+	0.345938i	−0.0762214	+	0.997091i	$0.524286\pi$
$702$		0			0
$703$			9.94993i			0.375269i
$704$		0			0
$705$	0.0864119	−	6.49931i	0.00325446	−	0.244778i
$706$		0			0
$707$	4.01547	+	9.69421i	0.151017	+	0.364588i
$708$		0			0
$709$	−28.2667	−	11.7085i	−1.06158	−	0.439721i	−0.217568	−	0.976045i	$-0.569812\pi$
$709$	−28.2667	−	11.7085i	−1.06158	−	0.439721i	−0.844012	+	0.536325i	$0.819812\pi$
$710$		0			0
$711$	−28.8360	+	27.3419i	−1.08144	+	1.02540i
$712$		0			0
$713$	1.41753	+	1.41753i	0.0530869	+	0.0530869i
$714$		0			0
$715$	6.26547	+	2.59524i	0.234315	+	0.0970566i
$716$		0			0
$717$	9.25186	−	3.68892i	0.345517	−	0.137765i
$718$		0			0
$719$			19.8341i			0.739687i	0.929094	+	0.369843i	$0.120589\pi$
$719$			19.8341i			0.739687i	−0.929094	+	0.369843i	$0.879411\pi$
$720$		0			0
$721$		−	42.2921i		−	1.57504i
$722$		0			0
$723$	0.651275	−	0.259678i	0.0242212	−	0.00965751i
$724$		0			0
$725$	15.2156	+	6.30252i	0.565095	+	0.234070i
$726$		0			0
$727$	21.1914	+	21.1914i	0.785946	+	0.785946i	0.980827	−	0.194881i	$-0.0624321\pi$
$727$	21.1914	+	21.1914i	0.785946	+	0.785946i	−0.194881	+	0.980827i	$0.562432\pi$
$728$		0			0
$729$	17.5099	+	20.5525i	0.648513	+	0.761203i
$730$		0			0
$731$	47.5757	+	19.7065i	1.75965	+	0.728871i
$732$		0			0
$733$	18.2396	+	44.0342i	0.673694	+	1.62644i	0.775283	+	0.631614i	$0.217607\pi$
$733$	18.2396	+	44.0342i	0.673694	+	1.62644i	−0.101589	+	0.994826i	$0.532393\pi$
$734$		0			0
$735$	0.150156	−	11.2937i	0.00553858	−	0.416574i
$736$		0			0
$737$			12.7798i			0.470749i
$738$		0			0
$739$	−14.9807	+	6.20519i	−0.551073	+	0.228262i	−0.640804	−	0.767704i	$-0.721399\pi$
$739$	−14.9807	+	6.20519i	−0.551073	+	0.228262i	0.0897317	+	0.995966i	$0.471399\pi$
$740$		0			0
$741$	−5.89015	+	13.7020i	−0.216380	+	0.503354i
$742$		0			0
$743$	−22.8633	−	22.8633i	−0.838773	−	0.838773i	0.149925	−	0.988697i	$-0.452097\pi$
$743$	−22.8633	−	22.8633i	−0.838773	−	0.838773i	−0.988697	+	0.149925i	$0.952097\pi$
$744$		0			0
$745$	8.75601	−	8.75601i	0.320795	−	0.320795i
$746$		0			0
$747$	−8.18767	+	18.3696i	−0.299571	+	0.672107i
$748$		0			0
$749$	−19.0307	−	45.9442i	−0.695367	−	1.67877i
$750$		0			0
$751$	25.4070			0.927116			0.463558	−	0.886067i	$-0.346573\pi$
$751$	25.4070			0.927116			0.463558	+	0.886067i	$0.346573\pi$
$752$		0			0
$753$	0.253785	−	19.0880i	0.00924845	−	0.695605i
$754$		0			0
$755$	−6.55618	+	2.71566i	−0.238604	+	0.0988329i
$756$		0			0
$757$	−12.3294	+	29.7658i	−0.448120	+	1.08186i	0.524906	+	0.851160i	$0.324101\pi$
$757$	−12.3294	+	29.7658i	−0.448120	+	1.08186i	−0.973026	+	0.230697i	$0.925899\pi$
$758$		0			0
$759$	−15.7081	+	15.2959i	−0.570169	+	0.555206i
$760$		0			0
$761$	−23.7667	+	23.7667i	−0.861542	+	0.861542i	−0.991517	−	0.129975i	$-0.958510\pi$
$761$	−23.7667	+	23.7667i	−0.861542	+	0.861542i	0.129975	+	0.991517i	$0.458510\pi$
$762$		0			0
$763$	−22.3848	+	54.0418i	−0.810385	+	1.95644i
$764$		0			0
$765$	−4.32190	−	11.2727i	−0.156258	−	0.407566i
$766$		0			0
$767$	−35.4002			−1.27823
$768$		0			0
$769$	20.4960			0.739104			0.369552	−	0.929210i	$-0.379511\pi$
$769$	20.4960			0.739104			0.369552	+	0.929210i	$0.379511\pi$
$770$		0			0
$771$	−43.4677	+	17.3315i	−1.56545	+	0.624180i
$772$		0			0
$773$	−17.8280	+	43.0405i	−0.641228	+	1.54806i	0.183797	+	0.982964i	$0.441161\pi$
$773$	−17.8280	+	43.0405i	−0.641228	+	1.54806i	−0.825025	+	0.565097i	$0.808839\pi$
$774$		0			0
$775$	−1.06762	+	1.06762i	−0.0383500	+	0.0383500i
$776$		0			0
$777$	−22.1797	−	22.7774i	−0.795691	−	0.817135i
$778$		0			0
$779$	3.89320	−	9.39903i	0.139489	−	0.336755i
$780$		0			0
$781$	17.6448	−	7.30870i	0.631380	−	0.261526i
$782$		0			0
$783$	19.4298	+	0.775355i	0.694364	+	0.0277089i
$784$		0			0
$785$	0.761295			0.0271718
$786$		0			0
$787$	−9.25890	−	22.3530i	−0.330044	−	0.796797i	−0.998588	−	0.0531241i	$-0.983082\pi$
$787$	−9.25890	−	22.3530i	−0.330044	−	0.796797i	0.668544	−	0.743673i	$-0.266918\pi$
$788$		0			0
$789$	−0.0880222	+	0.204762i	−0.00313367	+	0.00728970i
$790$		0			0
$791$	44.0444	−	44.0444i	1.56604	−	1.56604i
$792$		0			0
$793$	18.4769	+	18.4769i	0.656133	+	0.656133i
$794$		0			0
$795$	−5.53824	−	2.38076i	−0.196421	−	0.0844368i
$796$		0			0
$797$	−21.1390	+	8.75605i	−0.748781	+	0.310155i	−0.724244	−	0.689544i	$-0.757811\pi$
$797$	−21.1390	+	8.75605i	−0.748781	+	0.310155i	−0.0245368	+	0.999699i	$0.507811\pi$
$798$		0			0
$799$		−	25.2083i		−	0.891806i
$800$		0			0
$801$	−1.04550	+	39.3108i	−0.0369410	+	1.38898i
$802$		0			0
$803$	1.69947	+	4.10287i	0.0599728	+	0.144787i
$804$		0			0
$805$	−16.4108	−	6.79760i	−0.578406	−	0.239584i
$806$		0			0
$807$	28.6352	−	27.8837i	1.00801	−	0.981553i
$808$		0			0
$809$	−13.3483	−	13.3483i	−0.469301	−	0.469301i	0.432387	−	0.901688i	$-0.357671\pi$
$809$	−13.3483	−	13.3483i	−0.469301	−	0.469301i	−0.901688	+	0.432387i	$0.857671\pi$
$810$		0			0
$811$	18.1422	+	7.51474i	0.637058	+	0.263878i	0.677749	−	0.735294i	$-0.262956\pi$
$811$	18.1422	+	7.51474i	0.637058	+	0.263878i	−0.0406904	+	0.999172i	$0.512956\pi$
$812$		0			0
$813$	−1.81400	−	4.54953i	−0.0636198	−	0.159559i
$814$		0			0
$815$		−	1.20672i		−	0.0422694i
$816$		0			0
$817$		−	21.0862i		−	0.737713i
$818$		0			0
$819$	−17.0597	−	44.4965i	−0.596114	−	1.55483i
$820$		0			0
$821$	27.9756	+	11.5879i	0.976355	+	0.404420i	0.813074	−	0.582160i	$-0.197792\pi$
$821$	27.9756	+	11.5879i	0.976355	+	0.404420i	0.163281	+	0.986580i	$0.447792\pi$
$822$		0			0
$823$	−29.0608	−	29.0608i	−1.01300	−	1.01300i	−0.999914	−	0.0130818i	$-0.995836\pi$
$823$	−29.0608	−	29.0608i	−1.01300	−	1.01300i	−0.0130818	−	0.999914i	$-0.504164\pi$
$824$		0			0
$825$	−11.5202	−	11.8306i	−0.401081	−	0.411890i
$826$		0			0
$827$	−2.28063	−	0.944670i	−0.0793054	−	0.0328494i	0.342678	−	0.939453i	$-0.388666\pi$
$827$	−2.28063	−	0.944670i	−0.0793054	−	0.0328494i	−0.421984	+	0.906604i	$0.638666\pi$
$828$		0			0
$829$	19.1205	+	46.1610i	0.664082	+	1.60324i	0.791346	+	0.611368i	$0.209380\pi$
$829$	19.1205	+	46.1610i	0.664082	+	1.60324i	−0.127264	+	0.991869i	$0.540620\pi$
$830$		0			0
$831$	26.3298	+	0.350070i	0.913372	+	0.0121438i
$832$		0			0
$833$		−	43.8039i		−	1.51772i
$834$		0			0
$835$	−3.09460	+	1.28183i	−0.107093	+	0.0443595i
$836$		0			0
$837$	−0.747325	+	1.61846i	−0.0258313	+	0.0559421i
$838$		0			0
$839$	−26.7898	−	26.7898i	−0.924887	−	0.924887i	0.0724830	−	0.997370i	$-0.476908\pi$
$839$	−26.7898	−	26.7898i	−0.924887	−	0.924887i	−0.997370	+	0.0724830i	$0.976908\pi$
$840$		0			0
$841$	−10.6035	+	10.6035i	−0.365638	+	0.365638i
$842$		0			0
$843$	25.4831	+	10.9546i	0.877684	+	0.377296i
$844$		0			0
$845$	0.994788	+	2.40163i	0.0342217	+	0.0826186i
$846$		0			0
$847$	−24.7708			−0.851135
$848$		0			0
$849$	−13.8060	−	0.183558i	−0.473820	−	0.00629969i
$850$		0			0
$851$	−25.2303	+	10.4507i	−0.864884	+	0.358247i
$852$		0			0
$853$	16.6540	−	40.2063i	0.570222	−	1.37664i	−0.331145	−	0.943580i	$-0.607435\pi$
$853$	16.6540	−	40.2063i	0.570222	−	1.37664i	0.901366	−	0.433057i	$-0.142565\pi$
$854$		0			0
$855$	−3.58730	+	3.40143i	−0.122683	+	0.116327i
$856$		0			0
$857$	−26.3920	+	26.3920i	−0.901532	+	0.901532i	−0.995569	−	0.0940369i	$-0.970023\pi$
$857$	−26.3920	+	26.3920i	−0.901532	+	0.901532i	0.0940369	+	0.995569i	$0.470023\pi$
$858$		0			0
$859$	−10.8177	+	26.1163i	−0.369096	+	0.891077i	0.624803	+	0.780782i	$0.285179\pi$
$859$	−10.8177	+	26.1163i	−0.369096	+	0.891077i	−0.993899	+	0.110294i	$0.964821\pi$
$860$		0			0
$861$	12.0393	+	30.1947i	0.410298	+	1.02903i
$862$		0			0
$863$	−30.4203			−1.03552			−0.517760	−	0.855526i	$-0.673234\pi$
$863$	−30.4203			−1.03552			−0.517760	+	0.855526i	$0.673234\pi$
$864$		0			0
$865$	8.24555			0.280357
$866$		0			0
$867$	−6.43582	−	16.1411i	−0.218572	−	0.548181i
$868$		0			0
$869$	10.9811	−	26.5107i	0.372508	−	0.899313i
$870$		0			0
$871$	−16.8717	+	16.8717i	−0.571675	+	0.571675i
$872$		0			0
$873$	−20.8325	+	19.7531i	−0.705073	+	0.668541i
$874$		0			0
$875$	10.9362	−	26.4023i	0.369711	−	0.892562i
$876$		0			0
$877$	−17.8161	+	7.37968i	−0.601608	+	0.249194i	−0.662636	−	0.748942i	$-0.730562\pi$
$877$	−17.8161	+	7.37968i	−0.601608	+	0.249194i	0.0610277	+	0.998136i	$0.480562\pi$
$878$		0			0
$879$	21.6159	+	0.287395i	0.729087	+	0.00969361i
$880$		0			0
$881$	18.0163			0.606984			0.303492	−	0.952834i	$-0.401847\pi$
$881$	18.0163			0.606984			0.303492	+	0.952834i	$0.401847\pi$
$882$		0			0
$883$	1.13662	+	2.74405i	0.0382504	+	0.0923447i	0.941850	−	0.336033i	$-0.109085\pi$
$883$	1.13662	+	2.74405i	0.0382504	+	0.0923447i	−0.903600	+	0.428378i	$0.859085\pi$
$884$		0			0
$885$	−10.7800	−	4.63406i	−0.362365	−	0.155772i
$886$		0			0
$887$	−33.9649	+	33.9649i	−1.14043	+	1.14043i	−0.152060	+	0.988371i	$0.548591\pi$
$887$	−33.9649	+	33.9649i	−1.14043	+	1.14043i	−0.988371	+	0.152060i	$0.951409\pi$
$888$		0			0
$889$	6.30746	+	6.30746i	0.211545	+	0.211545i
$890$		0			0
$891$	−17.5907	−	8.40803i	−0.589310	−	0.281679i
$892$		0			0
$893$	−9.53647	+	3.95013i	−0.319126	+	0.132186i
$894$		0			0
$895$			4.10539i			0.137228i
$896$		0			0
$897$	−40.9311	−	0.544201i	−1.36665	−	0.0181703i
$898$		0			0
$899$	0.491315	+	1.18614i	0.0163863	+	0.0395599i
$900$		0			0
$901$	−21.5997	−	8.94687i	−0.719589	−	0.298063i
$902$		0			0
$903$	47.0038	+	48.2706i	1.56419	+	1.60634i
$904$		0			0
$905$	10.3135	+	10.3135i	0.342833	+	0.342833i
$906$		0			0
$907$	43.9663	+	18.2114i	1.45988	+	0.604701i	0.964525	−	0.263991i	$-0.0850391\pi$
$907$	43.9663	+	18.2114i	1.45988	+	0.604701i	0.495352	+	0.868692i	$0.335039\pi$
$908$		0			0
$909$	2.86927	+	7.48386i	0.0951677	+	0.248224i
$910$		0			0
$911$			30.0744i			0.996410i	0.867059	+	0.498205i	$0.166007\pi$
$911$			30.0744i			0.996410i	−0.867059	+	0.498205i	$0.833993\pi$
$912$		0			0
$913$		−	14.5227i		−	0.480633i
$914$		0			0
$915$	3.20782	+	8.04524i	0.106047	+	0.265967i
$916$		0			0
$917$	−24.4103	−	10.1111i	−0.806100	−	0.333897i
$918$		0			0
$919$	21.8072	+	21.8072i	0.719352	+	0.719352i	0.968472	−	0.249121i	$-0.0801416\pi$
$919$	21.8072	+	21.8072i	0.719352	+	0.719352i	−0.249121	+	0.968472i	$0.580142\pi$
$920$		0			0
$921$	39.9841	−	38.9348i	1.31752	−	1.28295i
$922$		0			0
$923$	32.9432	+	13.6455i	1.08434	+	0.449148i
$924$		0			0
$925$	−7.87102	−	19.0023i	−0.258798	−	0.624792i
$926$		0			0
$927$	0.858871	−	32.2935i	0.0282090	−	1.06066i
$928$		0			0
$929$		−	31.8839i		−	1.04608i	−0.852309	−	0.523038i	$-0.824798\pi$
$929$		−	31.8839i		−	1.04608i	0.852309	−	0.523038i	$-0.175202\pi$
$930$		0			0
$931$	−16.5713	+	6.86406i	−0.543102	+	0.224960i
$932$		0			0
$933$	−50.0437	−	21.5126i	−1.63836	−	0.704292i
$934$		0			0
$935$	6.16446	+	6.16446i	0.201599	+	0.201599i
$936$		0			0
$937$	36.2485	−	36.2485i	1.18419	−	1.18419i	0.205536	−	0.978650i	$-0.434106\pi$
$937$	36.2485	−	36.2485i	1.18419	−	1.18419i	0.978650	−	0.205536i	$-0.0658936\pi$
$938$		0			0
$939$	−12.9852	+	30.2067i	−0.423755	+	0.985760i
$940$		0			0
$941$	6.43068	+	15.5250i	0.209634	+	0.506102i	0.993366	−	0.114998i	$-0.0366862\pi$
$941$	6.43068	+	15.5250i	0.209634	+	0.506102i	−0.783731	+	0.621100i	$0.786686\pi$
$942$		0			0
$943$	27.9225			0.909283
$944$		0			0
$945$	0.629833	−	15.7831i	0.0204885	−	0.513425i
$946$		0			0
$947$	−16.2355	+	6.72498i	−0.527584	+	0.218532i	−0.630545	−	0.776153i	$-0.717168\pi$
$947$	−16.2355	+	6.72498i	−0.527584	+	0.218532i	0.102961	+	0.994685i	$0.467168\pi$
$948$		0			0
$949$	−3.17294	+	7.66016i	−0.102998	+	0.248659i
$950$		0			0
$951$	1.23869	+	1.27208i	0.0401674	+	0.0412499i
$952$		0			0
$953$	0.946267	−	0.946267i	0.0306526	−	0.0306526i	−0.691614	−	0.722267i	$-0.743100\pi$
$953$	0.946267	−	0.946267i	0.0306526	−	0.0306526i	0.722267	+	0.691614i	$0.243100\pi$
$954$		0			0
$955$	1.61651	−	3.90260i	0.0523090	−	0.126285i
$956$		0			0
$957$	−13.0430	+	5.20052i	−0.421620	+	0.168109i
$958$		0			0
$959$	45.7635			1.47778
$960$		0			0
$961$	30.8823			0.996203
$962$		0			0
$963$	−13.5985	−	35.4686i	−0.438204	−	1.14296i
$964$		0			0
$965$	3.12311	−	7.53987i	0.100537	−	0.242717i
$966$		0			0
$967$	19.1657	−	19.1657i	0.616326	−	0.616326i	−0.328261	−	0.944587i	$-0.606463\pi$
$967$	19.1657	−	19.1657i	0.616326	−	0.616326i	0.944587	+	0.328261i	$0.106463\pi$
$968$		0			0
$969$	−13.7359	+	13.3755i	−0.441262	+	0.429682i
$970$		0			0
$971$	13.7803	−	33.2686i	0.442231	−	1.06764i	−0.532933	−	0.846158i	$-0.678910\pi$
$971$	13.7803	−	33.2686i	0.442231	−	1.06764i	0.975164	−	0.221483i	$-0.0710899\pi$
$972$		0			0
$973$	17.5732	−	7.27905i	0.563370	−	0.233356i
$974$		0			0
$975$	0.409867	−	30.8274i	0.0131263	−	0.987267i
$976$		0			0
$977$	22.7166			0.726769			0.363384	−	0.931639i	$-0.381621\pi$
$977$	22.7166			0.726769			0.363384	+	0.931639i	$0.381621\pi$
$978$		0			0
$979$	−10.8669	−	26.2350i	−0.347308	−	0.838475i
$980$		0			0
$981$	−18.1901	+	40.8107i	−0.580766	+	1.30298i
$982$		0			0
$983$	−0.832934	+	0.832934i	−0.0265665	+	0.0265665i	−0.720265	−	0.693699i	$-0.755980\pi$
$983$	−0.832934	+	0.832934i	−0.0265665	+	0.0265665i	0.693699	+	0.720265i	$0.255980\pi$
$984$		0			0
$985$	−0.0749722	−	0.0749722i	−0.00238881	−	0.00238881i
$986$		0			0
$987$	13.0255	−	30.3007i	0.414608	−	0.964481i
$988$		0			0
$989$	53.4688	−	22.1475i	1.70021	−	0.704250i
$990$		0			0
$991$		−	3.31878i		−	0.105425i	−0.998610	−	0.0527123i	$-0.983213\pi$
$991$		−	3.31878i		−	0.105425i	0.998610	−	0.0527123i	$-0.0167866\pi$
$992$		0			0
$993$	−0.518200	+	38.9754i	−0.0164446	+	1.23685i
$994$		0			0
$995$	2.78439	+	6.72212i	0.0882712	+	0.213105i
$996$		0			0
$997$	48.7016	+	20.1729i	1.54240	+	0.638881i	0.981921	−	0.189290i	$-0.0606187\pi$
$997$	48.7016	+	20.1729i	1.54240	+	0.638881i	0.560475	+	0.828172i	$0.310619\pi$
$998$		0			0
$999$	−16.4734	−	17.8428i	−0.521196	−	0.564522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.a.287.6		56
3.2	odd	2	inner	768.2.o.a.287.10		56
4.3	odd	2		768.2.o.b.287.9		56
8.3	odd	2		96.2.o.a.59.5	✓	56
8.5	even	2		384.2.o.a.143.9		56
12.11	even	2		768.2.o.b.287.5		56
24.5	odd	2		384.2.o.a.143.5		56
24.11	even	2		96.2.o.a.59.10	yes	56
32.3	odd	8		384.2.o.a.239.5		56
32.13	even	8		768.2.o.b.479.5		56
32.19	odd	8	inner	768.2.o.a.479.10		56
32.29	even	8		96.2.o.a.83.10	yes	56
96.29	odd	8		96.2.o.a.83.5	yes	56
96.35	even	8		384.2.o.a.239.9		56
96.77	odd	8		768.2.o.b.479.9		56
96.83	even	8	inner	768.2.o.a.479.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.59.5	✓	56	8.3	odd	2
96.2.o.a.59.10	yes	56	24.11	even	2
96.2.o.a.83.5	yes	56	96.29	odd	8
96.2.o.a.83.10	yes	56	32.29	even	8
384.2.o.a.143.5		56	24.5	odd	2
384.2.o.a.143.9		56	8.5	even	2
384.2.o.a.239.5		56	32.3	odd	8
384.2.o.a.239.9		56	96.35	even	8
768.2.o.a.287.6		56	1.1	even	1	trivial
768.2.o.a.287.10		56	3.2	odd	2	inner
768.2.o.a.479.6		56	96.83	even	8	inner
768.2.o.a.479.10		56	32.19	odd	8	inner
768.2.o.b.287.5		56	12.11	even	2
768.2.o.b.287.9		56	4.3	odd	2
768.2.o.b.479.5		56	32.13	even	8
768.2.o.b.479.9		56	96.77	odd	8

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.641495 - 1.60888i) q^{3} +(-0.296199 + 0.715088i) q^{5} +(-2.77714 + 2.77714i) q^{7} +(-2.17697 + 2.06417i) q^{9} +O(q^{10})\)	\(q+(-0.641495 - 1.60888i) q^{3} +(-0.296199 + 0.715088i) q^{5} +(-2.77714 + 2.77714i) q^{7} +(-2.17697 + 2.06417i) q^{9} +(0.829014 - 2.00142i) q^{11} +(3.73669 - 1.54779i) q^{13} +(1.34050 + 0.0178227i) q^{15} +5.19928 q^{17} +(-0.814726 - 1.96692i) q^{19} +(6.24959 + 2.68655i) q^{21} +(4.13184 - 4.13184i) q^{23} +(3.11192 + 3.11192i) q^{25} +(4.71751 + 2.17832i) q^{27} +(3.45738 - 1.43209i) q^{29} +0.343074i q^{31} +(-3.75184 - 0.0498828i) q^{33} +(-1.16331 - 2.80849i) q^{35} +(-4.31781 - 1.78850i) q^{37} +(-4.88727 - 5.01898i) q^{39} +(3.37894 + 3.37894i) q^{41} +(9.15044 + 3.79024i) q^{43} +(-0.831249 - 2.16813i) q^{45} -4.84842i q^{47} -8.42499i q^{49} +(-3.33531 - 8.36500i) q^{51} +(-4.15435 - 1.72079i) q^{53} +(1.18564 + 1.18564i) q^{55} +(-2.64189 + 2.57256i) q^{57} +(-8.08629 - 3.34945i) q^{59} +(2.47236 + 5.96880i) q^{61} +(0.313252 - 11.7782i) q^{63} +3.13052i q^{65} +(-5.45025 + 2.25757i) q^{67} +(-9.29818 - 3.99707i) q^{69} +(6.23395 + 6.23395i) q^{71} +(-1.44956 + 1.44956i) q^{73} +(3.01041 - 7.00297i) q^{75} +(3.25592 + 7.86050i) q^{77} +13.2460 q^{79} +(0.478386 - 8.98728i) q^{81} +(6.19358 - 2.56547i) q^{83} +(-1.54002 + 3.71795i) q^{85} +(-4.52195 - 4.64382i) q^{87} +(9.26892 - 9.26892i) q^{89} +(-6.07889 + 14.6757i) q^{91} +(0.551964 - 0.220080i) q^{93} +1.64784 q^{95} +9.56950 q^{97} +(2.32653 + 6.06825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9} + 8 q^{13} + 8 q^{15} - 8 q^{19} + 4 q^{21} - 8 q^{25} - 28 q^{27} - 8 q^{33} + 8 q^{37} + 28 q^{39} - 8 q^{43} + 4 q^{45} - 16 q^{51} - 24 q^{55} - 4 q^{57} + 40 q^{61} + 56 q^{67} + 4 q^{69} - 8 q^{73} + 16 q^{75} - 16 q^{79} + 48 q^{85} - 52 q^{87} + 40 q^{91} - 8 q^{93} - 16 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9 + 8 * q^13 + 8 * q^15 - 8 * q^19 + 4 * q^21 - 8 * q^25 - 28 * q^27 - 8 * q^33 + 8 * q^37 + 28 * q^39 - 8 * q^43 + 4 * q^45 - 16 * q^51 - 24 * q^55 - 4 * q^57 + 40 * q^61 + 56 * q^67 + 4 * q^69 - 8 * q^73 + 16 * q^75 - 16 * q^79 + 48 * q^85 - 52 * q^87 + 40 * q^91 - 8 * q^93 - 16 * q^97 + 60 * q^99

Introduction

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