LMFDB - Embedded newform 768.2.o.b.479.5

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			479.5
Character	$\chi$	$=$	768.479
Dual form			768.2.o.b.287.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.684042 + 1.59125i) q^{3} +(0.296199 + 0.715088i) q^{5} +(2.77714 + 2.77714i) q^{7} +(-2.06417 - 2.17697i) q^{9} +O(q^{10})$	\(q+(-0.684042 + 1.59125i) q^{3} +(0.296199 + 0.715088i) q^{5} +(2.77714 + 2.77714i) q^{7} +(-2.06417 - 2.17697i) q^{9} +(0.829014 + 2.00142i) q^{11} +(3.73669 + 1.54779i) q^{13} +(-1.34050 - 0.0178227i) q^{15} -5.19928 q^{17} +(0.814726 - 1.96692i) q^{19} +(-6.31881 + 2.51945i) q^{21} +(4.13184 + 4.13184i) q^{23} +(3.11192 - 3.11192i) q^{25} +(4.87609 - 1.79548i) q^{27} +(-3.45738 - 1.43209i) q^{29} +0.343074i q^{31} +(-3.75184 - 0.0498828i) q^{33} +(-1.16331 + 2.80849i) q^{35} +(-4.31781 + 1.78850i) q^{37} +(-5.01898 + 4.88727i) q^{39} +(-3.37894 + 3.37894i) q^{41} +(-9.15044 + 3.79024i) q^{43} +(0.945319 - 2.12088i) q^{45} +4.84842i q^{47} +8.42499i q^{49} +(3.55653 - 8.27337i) q^{51} +(4.15435 - 1.72079i) q^{53} +(-1.18564 + 1.18564i) q^{55} +(2.57256 + 2.64189i) q^{57} +(-8.08629 + 3.34945i) q^{59} +(2.47236 - 5.96880i) q^{61} +(0.313252 - 11.7782i) q^{63} +3.13052i q^{65} +(5.45025 + 2.25757i) q^{67} +(-9.40117 + 3.74845i) q^{69} +(6.23395 - 6.23395i) q^{71} +(-1.44956 - 1.44956i) q^{73} +(2.82316 + 7.08053i) q^{75} +(-3.25592 + 7.86050i) q^{77} -13.2460 q^{79} +(-0.478386 + 8.98728i) q^{81} +(6.19358 + 2.56547i) q^{83} +(-1.54002 - 3.71795i) q^{85} +(4.64382 - 4.52195i) q^{87} +(-9.26892 - 9.26892i) q^{89} +(6.07889 + 14.6757i) q^{91} +(-0.545918 - 0.234677i) q^{93} +1.64784 q^{95} +9.56950 q^{97} +(2.64579 - 5.93600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

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
$3$	−0.684042	+	1.59125i	−0.394932	+	0.918710i
$3$	−0.684042	+	1.59125i	−0.394932	+	0.918710i
$4$		0			0
$5$	0.296199	+	0.715088i	0.132464	+	0.319797i	0.976169	−	0.217010i	$-0.0696303\pi$
$5$	0.296199	+	0.715088i	0.132464	+	0.319797i	−0.843705	+	0.536807i	$0.819630\pi$
$6$		0			0
$7$	2.77714	+	2.77714i	1.04966	+	1.04966i	0.998701	+	0.0509588i	$0.0162277\pi$
$7$	2.77714	+	2.77714i	1.04966	+	1.04966i	0.0509588	+	0.998701i	$0.483772\pi$
$8$		0			0
$9$	−2.06417	−	2.17697i	−0.688057	−	0.725656i
$10$		0			0
$11$	0.829014	+	2.00142i	0.249957	+	0.603450i	0.998200	−	0.0599753i	$-0.0191022\pi$
$11$	0.829014	+	2.00142i	0.249957	+	0.603450i	−0.748243	+	0.663425i	$0.769102\pi$
$12$		0			0
$13$	3.73669	+	1.54779i	1.03637	+	0.429279i	0.835008	−	0.550237i	$-0.185463\pi$
$13$	3.73669	+	1.54779i	1.03637	+	0.429279i	0.201363	+	0.979517i	$0.435463\pi$
$14$		0			0
$15$	−1.34050	−	0.0178227i	−0.346115	−	0.00460179i
$16$		0			0
$17$	−5.19928			−1.26101			−0.630506	−	0.776185i	$-0.717152\pi$
$17$	−5.19928			−1.26101			−0.630506	+	0.776185i	$0.717152\pi$
$18$		0			0
$19$	0.814726	−	1.96692i	0.186911	−	0.451243i	−0.802451	−	0.596718i	$-0.796471\pi$
$19$	0.814726	−	1.96692i	0.186911	−	0.451243i	0.989362	+	0.145475i	$0.0464711\pi$
$20$		0			0
$21$	−6.31881	+	2.51945i	−1.37888	+	0.549789i
$22$		0			0
$23$	4.13184	+	4.13184i	0.861549	+	0.861549i	0.991518	−	0.129969i	$-0.0414878\pi$
$23$	4.13184	+	4.13184i	0.861549	+	0.861549i	−0.129969	+	0.991518i	$0.541488\pi$
$24$		0			0
$25$	3.11192	−	3.11192i	0.622383	−	0.622383i
$26$		0			0
$27$	4.87609	−	1.79548i	0.938404	−	0.345541i
$28$		0			0
$29$	−3.45738	−	1.43209i	−0.642019	−	0.265933i	0.0378308	−	0.999284i	$-0.487955\pi$
$29$	−3.45738	−	1.43209i	−0.642019	−	0.265933i	−0.679850	+	0.733351i	$0.737955\pi$
$30$		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	−0.708240	−	0.705972i	$-0.750511\pi$
$37$	−4.31781	+	1.78850i	−0.709844	+	0.294027i	−0.00160386	+	0.999999i	$0.500511\pi$
$38$		0			0
$39$	−5.01898	+	4.88727i	−0.803680	+	0.782589i
$40$		0			0
$41$	−3.37894	+	3.37894i	−0.527702	+	0.527702i	−0.919887	−	0.392184i	$-0.871720\pi$
$41$	−3.37894	+	3.37894i	−0.527702	+	0.527702i	0.392184	+	0.919887i	$0.371720\pi$
$42$		0			0
$43$	−9.15044	+	3.79024i	−1.39543	+	0.578005i	−0.948561	−	0.316595i	$-0.897461\pi$
$43$	−9.15044	+	3.79024i	−1.39543	+	0.578005i	−0.446868	+	0.894600i	$0.647461\pi$
$44$		0			0
$45$	0.945319	−	2.12088i	0.140920	−	0.316162i
$46$		0			0
$47$			4.84842i			0.707215i	0.935394	+	0.353608i	$0.115045\pi$
$47$			4.84842i			0.707215i	−0.935394	+	0.353608i	$0.884955\pi$
$48$		0			0
$49$			8.42499i			1.20357i
$50$		0			0
$51$	3.55653	−	8.27337i	0.498014	−	1.15850i
$52$		0			0
$53$	4.15435	−	1.72079i	0.570644	−	0.236369i	−0.0786546	−	0.996902i	$-0.525062\pi$
$53$	4.15435	−	1.72079i	0.570644	−	0.236369i	0.649299	+	0.760533i	$0.275062\pi$
$54$		0			0
$55$	−1.18564	+	1.18564i	−0.159871	+	0.159871i
$56$		0			0
$57$	2.57256	+	2.64189i	0.340744	+	0.349927i
$58$		0			0
$59$	−8.08629	+	3.34945i	−1.05275	+	0.436062i	−0.840871	−	0.541235i	$-0.817957\pi$
$59$	−8.08629	+	3.34945i	−1.05275	+	0.436062i	−0.211875	+	0.977297i	$0.567957\pi$
$60$		0			0
$61$	2.47236	−	5.96880i	0.316553	−	0.764227i	−0.682879	−	0.730531i	$-0.739272\pi$
$61$	2.47236	−	5.96880i	0.316553	−	0.764227i	0.999432	−	0.0336954i	$-0.0107276\pi$
$62$		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	$-0.257655\pi$
$67$	5.45025	+	2.25757i	0.665854	+	0.275806i	−0.0240453	+	0.999711i	$0.507655\pi$
$68$		0			0
$69$	−9.40117	+	3.74845i	−1.13177	+	0.451261i
$70$		0			0
$71$	6.23395	−	6.23395i	0.739834	−	0.739834i	−0.232712	−	0.972546i	$-0.574760\pi$
$71$	6.23395	−	6.23395i	0.739834	−	0.739834i	0.972546	+	0.232712i	$0.0747598\pi$
$72$		0			0
$73$	−1.44956	−	1.44956i	−0.169658	−	0.169658i	0.617171	−	0.786829i	$-0.288279\pi$
$73$	−1.44956	−	1.44956i	−0.169658	−	0.169658i	−0.786829	+	0.617171i	$0.788279\pi$
$74$		0			0
$75$	2.82316	+	7.08053i	0.325991	+	0.817589i
$76$		0			0
$77$	−3.25592	+	7.86050i	−0.371047	+	0.895787i
$78$		0			0
$79$	−13.2460			−1.49029			−0.745144	−	0.666904i	$-0.767619\pi$
$79$	−13.2460			−1.49029			−0.745144	+	0.666904i	$0.767619\pi$
$80$		0			0
$81$	−0.478386	+	8.98728i	−0.0531540	+	0.998586i
$82$		0			0
$83$	6.19358	+	2.56547i	0.679834	+	0.281596i	0.695758	−	0.718277i	$-0.255069\pi$
$83$	6.19358	+	2.56547i	0.679834	+	0.281596i	−0.0159235	+	0.999873i	$0.505069\pi$
$84$		0			0
$85$	−1.54002	−	3.71795i	−0.167039	−	0.403268i
$86$		0			0
$87$	4.64382	−	4.52195i	0.497870	−	0.484804i
$88$		0			0
$89$	−9.26892	−	9.26892i	−0.982503	−	0.982503i	0.0173462	−	0.999850i	$-0.494478\pi$
$89$	−9.26892	−	9.26892i	−0.982503	−	0.982503i	−0.999850	+	0.0173462i	$0.994478\pi$
$90$		0			0
$91$	6.07889	+	14.6757i	0.637240	+	1.53843i
$92$		0			0
$93$	−0.545918	−	0.234677i	−0.0566091	−	0.0243349i
$94$		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
$99$	2.64579	−	5.93600i	0.265912	−	0.596591i
$100$		0			0
$101$	−1.02241	−	2.46831i	−0.101733	−	0.245606i	0.864815	−	0.502091i	$-0.167436\pi$
$101$	−1.02241	−	2.46831i	−0.101733	−	0.245606i	−0.966548	+	0.256485i	$0.917436\pi$
$102$		0			0
$103$	7.61434	+	7.61434i	0.750263	+	0.750263i	0.974528	−	0.224265i	$-0.0719982\pi$
$103$	7.61434	+	7.61434i	0.750263	+	0.750263i	−0.224265	+	0.974528i	$0.571998\pi$
$104$		0			0
$105$	−3.67326	−	3.77225i	−0.358473	−	0.368134i
$106$		0			0
$107$	−4.84555	−	11.6982i	−0.468437	−	1.13091i	−0.964846	−	0.262817i	$-0.915348\pi$
$107$	−4.84555	−	11.6982i	−0.468437	−	1.13091i	0.496409	−	0.868089i	$-0.334652\pi$
$108$		0			0
$109$	13.7600	+	5.69956i	1.31796	+	0.545919i	0.927198	−	0.374571i	$-0.122210\pi$
$109$	13.7600	+	5.69956i	1.31796	+	0.545919i	0.390766	+	0.920490i	$0.372210\pi$
$110$		0			0
$111$	0.107616	−	8.09414i	0.0102145	−	0.768262i
$112$		0			0
$113$	15.8596			1.49195			0.745974	−	0.665975i	$-0.231984\pi$
$113$	15.8596			1.49195			0.745974	+	0.665975i	$0.231984\pi$
$114$		0			0
$115$	−1.73078	+	4.17848i	−0.161396	+	0.389645i
$116$		0			0
$117$	−4.34369	−	11.3296i	−0.401574	−	1.04742i
$118$		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
$123$	−3.06541	−	7.68809i	−0.276399	−	0.693212i
$124$		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	−0.770616	−	0.637300i	$-0.780051\pi$
$131$	2.57445	−	6.21528i	0.224931	−	0.543032i	0.995547	+	0.0942683i	$0.0300512\pi$
$132$		0			0
$133$	7.72502	−	3.19981i	0.669844	−	0.277459i
$134$		0			0
$135$	2.72822	+	2.95501i	0.234808	+	0.254327i
$136$		0			0
$137$	8.23933	−	8.23933i	0.703934	−	0.703934i	−0.261319	−	0.965252i	$-0.584157\pi$
$137$	8.23933	−	8.23933i	0.703934	−	0.703934i	0.965252	+	0.261319i	$0.0841574\pi$
$138$		0			0
$139$	4.47443	−	1.85337i	0.379516	−	0.157201i	−0.184766	−	0.982782i	$-0.559153\pi$
$139$	4.47443	−	1.85337i	0.379516	−	0.157201i	0.564283	+	0.825582i	$0.309153\pi$
$140$		0			0
$141$	−7.71507	−	3.31653i	−0.649726	−	0.279302i
$142$		0			0
$143$			8.76181i			0.732700i
$144$		0			0
$145$		−	2.89652i		−	0.240543i
$146$		0			0
$147$	−13.4063	−	5.76305i	−1.10573	−	0.475328i
$148$		0			0
$149$	14.7806	−	6.12233i	1.21087	−	0.501561i	0.316377	−	0.948634i	$-0.397534\pi$
$149$	14.7806	−	6.12233i	1.21087	−	0.501561i	0.894497	+	0.447073i	$0.147534\pi$
$150$		0			0
$151$	−6.48300	+	6.48300i	−0.527579	+	0.527579i	−0.919850	−	0.392271i	$-0.871690\pi$
$151$	−6.48300	+	6.48300i	−0.527579	+	0.527579i	0.392271	+	0.919850i	$0.371690\pi$
$152$		0			0
$153$	10.7322	+	11.3187i	0.867648	+	0.915061i
$154$		0			0
$155$	−0.245328	+	0.101618i	−0.0197053	+	0.00816218i
$156$		0			0
$157$	−0.376399	+	0.908707i	−0.0300399	+	0.0725227i	−0.938188	−	0.346127i	$-0.887497\pi$
$157$	−0.376399	+	0.908707i	−0.0300399	+	0.0725227i	0.908148	+	0.418650i	$0.137497\pi$
$158$		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	$-0.355553\pi$
$163$	1.44038	+	0.596624i	0.112819	+	0.0467312i	−0.325560	+	0.945521i	$0.605553\pi$
$164$		0			0
$165$	−1.07562	−	2.69767i	−0.0837370	−	0.210013i
$166$		0			0
$167$	3.06006	−	3.06006i	0.236795	−	0.236795i	−0.578727	−	0.815522i	$-0.696450\pi$
$167$	3.06006	−	3.06006i	0.236795	−	0.236795i	0.815522	+	0.578727i	$0.196450\pi$
$168$		0			0
$169$	2.37482	+	2.37482i	0.182679	+	0.182679i
$170$		0			0
$171$	−5.96366	+	2.28643i	−0.456053	+	0.174848i
$172$		0			0
$173$	4.07676	−	9.84216i	0.309950	−	0.748286i	−0.689756	−	0.724042i	$-0.742282\pi$
$173$	4.07676	−	9.84216i	0.309950	−	0.748286i	0.999706	−	0.0242438i	$-0.00771779\pi$
$174$		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	0.558224	−	0.829690i	$-0.311483\pi$
$179$	4.90033	+	2.02978i	0.366268	+	0.151713i	−0.191956	+	0.981404i	$0.561483\pi$
$180$		0			0
$181$	7.21135	+	17.4097i	0.536016	+	1.29406i	0.927483	+	0.373864i	$0.121967\pi$
$181$	7.21135	+	17.4097i	0.536016	+	1.29406i	−0.391468	+	0.920192i	$0.628033\pi$
$182$		0			0
$183$	7.80668	+	8.01706i	0.577086	+	0.592638i
$184$		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
$189$	18.5279	+	8.55527i	1.34770	+	0.622305i
$190$		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
$195$	−4.98145	−	2.14141i	−0.356729	−	0.153349i
$196$		0			0
$197$	0.0524216	+	0.126557i	0.00373489	+	0.00901681i	0.925736	−	0.378170i	$-0.123447\pi$
$197$	0.0524216	+	0.126557i	0.00373489	+	0.00901681i	−0.922001	+	0.387187i	$0.873447\pi$
$198$		0			0
$199$	−6.64709	−	6.64709i	−0.471200	−	0.471200i	0.431103	−	0.902303i	$-0.358125\pi$
$199$	−6.64709	−	6.64709i	−0.471200	−	0.471200i	−0.902303	+	0.431103i	$0.858125\pi$
$200$		0			0
$201$	−7.32057	+	7.12846i	−0.516353	+	0.502803i
$202$		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	$-0.791472\pi$
$211$	2.88401	−	6.96261i	0.198543	−	0.479326i	0.991524	+	0.129920i	$0.0414722\pi$
$212$		0			0
$213$	5.65551	+	14.1841i	0.387509	+	0.971878i
$214$		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
$219$	3.29817	−	1.31505i	0.222870	−	0.0888632i
$220$		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	−0.883393	−	0.468633i	$-0.844747\pi$
$227$	1.09433	−	2.64195i	0.0726335	−	0.175353i	0.956027	+	0.293280i	$0.0947468\pi$
$228$		0			0
$229$	1.48780	−	0.616268i	0.0983167	−	0.0407241i	−0.332983	−	0.942933i	$-0.608055\pi$
$229$	1.48780	−	0.616268i	0.0983167	−	0.0407241i	0.431300	+	0.902209i	$0.358055\pi$
$230$		0			0
$231$	−10.2808	−	10.5579i	−0.676430	−	0.694659i
$232$		0			0
$233$	14.1523	−	14.1523i	0.927150	−	0.927150i	−0.0703713	−	0.997521i	$-0.522418\pi$
$233$	14.1523	−	14.1523i	0.927150	−	0.927150i	0.997521	+	0.0703713i	$0.0224184\pi$
$234$		0			0
$235$	−3.46705	+	1.43610i	−0.226165	+	0.0936808i
$236$		0			0
$237$	9.06080	−	21.0777i	0.588562	−	1.36914i
$238$		0			0
$239$		−	5.75051i		−	0.371969i	−0.982553	−	0.185985i	$-0.940453\pi$
$239$		−	5.75051i		−	0.371969i	0.982553	−	0.185985i	$-0.0595475\pi$
$240$		0			0
$241$		−	0.404801i		−	0.0260755i	−0.999915	−	0.0130378i	$-0.995850\pi$
$241$		−	0.404801i		−	0.0260755i	0.999915	−	0.0130378i	$-0.00415016\pi$
$242$		0			0
$243$	−13.9738	−	6.90891i	−0.896419	−	0.443207i
$244$		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
$249$	−8.31898	+	8.10067i	−0.527194	+	0.513359i
$250$		0			0
$251$	10.1825	−	4.21772i	0.642712	−	0.266220i	−0.0374311	−	0.999299i	$-0.511917\pi$
$251$	10.1825	−	4.21772i	0.642712	−	0.266220i	0.680143	+	0.733079i	$0.261917\pi$
$252$		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
$261$	4.01901	+	10.4827i	0.248770	+	0.648863i
$262$		0			0
$263$	−0.0909901	+	0.0909901i	−0.00561069	+	0.00561069i	−0.709907	−	0.704296i	$-0.751263\pi$
$263$	−0.0909901	+	0.0909901i	−0.00561069	+	0.00561069i	0.704296	+	0.709907i	$0.251263\pi$
$264$		0			0
$265$	2.46103	+	2.46103i	0.151180	+	0.151180i
$266$		0			0
$267$	21.0895	−	8.40886i	1.29066	−	0.514614i
$268$		0			0
$269$	−8.83071	+	21.3192i	−0.538418	+	1.29986i	0.387409	+	0.921908i	$0.373370\pi$
$269$	−8.83071	+	21.3192i	−0.538418	+	1.29986i	−0.925827	+	0.377948i	$0.876630\pi$
$270$		0			0
$271$	−2.82777			−0.171775			−0.0858874	−	0.996305i	$-0.527373\pi$
$271$	−2.82777			−0.171775			−0.0858874	+	0.996305i	$0.527373\pi$
$272$		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	−0.996672	−	0.0815223i	$-0.974022\pi$
$277$	−5.81789	−	14.0456i	−0.349563	−	0.843920i	0.647108	−	0.762398i	$-0.275978\pi$
$278$		0			0
$279$	0.746862	−	0.708164i	0.0447135	−	0.0423967i
$280$		0			0
$281$	11.3239	+	11.3239i	0.675530	+	0.675530i	0.958985	−	0.283455i	$-0.0914808\pi$
$281$	11.3239	+	11.3239i	0.675530	+	0.675530i	−0.283455	+	0.958985i	$0.591481\pi$
$282$		0			0
$283$	−3.05059	−	7.36479i	−0.181339	−	0.437791i	0.806904	−	0.590683i	$-0.201141\pi$
$283$	−3.05059	−	7.36479i	−0.181339	−	0.437791i	−0.988243	+	0.152892i	$0.951141\pi$
$284$		0			0
$285$	−1.12719	+	2.62214i	−0.0667693	+	0.155322i
$286$		0			0
$287$	−18.7676			−1.10782
$288$		0			0
$289$	10.0325			0.590149
$290$		0			0
$291$	−6.54594	+	15.2275i	−0.383730	+	0.892652i
$292$		0			0
$293$	4.77629	+	11.5310i	0.279034	+	0.673648i	0.999809	−	0.0195210i	$-0.00621412\pi$
$293$	4.77629	+	11.5310i	0.279034	+	0.673648i	−0.720775	+	0.693169i	$0.756214\pi$
$294$		0			0
$295$	−4.79031	−	4.79031i	−0.278903	−	0.278903i
$296$		0			0
$297$	7.63585	+	8.27061i	0.443077	+	0.479909i
$298$		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	0.0113269	+	0.999936i	$0.496394\pi$
$307$	−12.3306	+	29.7687i	−0.703744	+	1.69899i	−0.715071	+	0.699052i	$0.753606\pi$
$308$		0			0
$309$	−17.3249	+	6.90781i	−0.985577	+	0.392971i
$310$		0			0
$311$	22.2380	+	22.2380i	1.26100	+	1.26100i	0.950609	+	0.310392i	$0.100460\pi$
$311$	22.2380	+	22.2380i	1.26100	+	1.26100i	0.310392	+	0.950609i	$0.399540\pi$
$312$		0			0
$313$	−13.4230	+	13.4230i	−0.758713	+	0.758713i	−0.976088	−	0.217375i	$-0.930250\pi$
$313$	−13.4230	+	13.4230i	−0.758713	+	0.758713i	0.217375	+	0.976088i	$0.430250\pi$
$314$		0			0
$315$	8.51526	−	3.26470i	0.479781	−	0.183945i
$316$		0			0
$317$	0.947076	+	0.392292i	0.0531931	+	0.0220333i	0.409121	−	0.912480i	$-0.365835\pi$
$317$	0.947076	+	0.392292i	0.0531931	+	0.0220333i	−0.355928	+	0.934513i	$0.615835\pi$
$318$		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
$327$	−18.4818	+	17.9968i	−1.02205	+	0.995227i
$328$		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	$-0.412749\pi$
$331$	20.7914	−	8.61208i	1.14280	−	0.473363i	0.872113	+	0.489305i	$0.162749\pi$
$332$		0			0
$333$	12.8062	+	5.70798i	0.701776	+	0.312795i
$334$		0			0
$335$			4.56610i			0.249473i
$336$		0			0
$337$		−	29.6373i		−	1.61444i	−0.590248	−	0.807222i	$-0.700970\pi$
$337$		−	29.6373i		−	1.61444i	0.590248	−	0.807222i	$-0.299030\pi$
$338$		0			0
$339$	−10.8487	+	25.2367i	−0.589218	+	1.37067i
$340$		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
$345$	−5.46509	−	5.61237i	−0.294231	−	0.302160i
$346$		0			0
$347$	−21.8544	+	9.05241i	−1.17321	+	0.485959i	−0.882252	−	0.470778i	$-0.843973\pi$
$347$	−21.8544	+	9.05241i	−1.17321	+	0.485959i	−0.290956	+	0.956736i	$0.593973\pi$
$348$		0			0
$349$	−0.170032	+	0.410493i	−0.00910160	+	0.0219732i	−0.928365	−	0.371670i	$-0.878785\pi$
$349$	−0.170032	+	0.410493i	−0.00910160	+	0.0219732i	0.919263	+	0.393643i	$0.128785\pi$
$350$		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
$357$	32.8533	−	13.0993i	1.73878	−	0.693290i
$358$		0			0
$359$	7.59655	−	7.59655i	0.400930	−	0.400930i	−0.477630	−	0.878561i	$-0.658504\pi$
$359$	7.59655	−	7.59655i	0.400930	−	0.400930i	0.878561	+	0.477630i	$0.158504\pi$
$360$		0			0
$361$	10.2300	+	10.2300i	0.538422	+	0.538422i
$362$		0			0
$363$	4.04595	+	10.1473i	0.212357	+	0.532595i
$364$		0			0
$365$	0.607204	−	1.46592i	0.0317825	−	0.0767298i
$366$		0			0
$367$	14.4269			0.753079			0.376540	−	0.926401i	$-0.377114\pi$
$367$	14.4269			0.753079			0.376540	+	0.926401i	$0.377114\pi$
$368$		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	0.768793	−	0.639498i	$-0.220858\pi$
$373$	−4.38447	−	10.5851i	−0.227019	−	0.548073i	−0.995812	+	0.0914248i	$0.970858\pi$
$374$		0			0
$375$	−9.02938	+	8.79243i	−0.466275	+	0.454039i
$376$		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	$-0.148690\pi$
$379$	−1.10789	−	2.67468i	−0.0569084	−	0.137389i	−0.949776	+	0.312930i	$0.898690\pi$
$380$		0			0
$381$	3.61406	+	1.55360i	0.185154	+	0.0795934i
$382$		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
$387$	27.1393	+	12.0965i	1.37957	+	0.614901i
$388$		0			0
$389$	−10.6893	−	25.8063i	−0.541969	−	1.30843i	−0.923332	−	0.384004i	$-0.874545\pi$
$389$	−10.6893	−	25.8063i	−0.541969	−	1.30843i	0.381362	−	0.924426i	$-0.375455\pi$
$390$		0			0
$391$	−21.4826	−	21.4826i	−1.08642	−	1.08642i
$392$		0			0
$393$	8.12905	+	8.34813i	0.410056	+	0.421107i
$394$		0			0
$395$	−3.92344	−	9.47203i	−0.197410	−	0.476590i
$396$		0			0
$397$	−11.8148	−	4.89383i	−0.592966	−	0.245614i	0.0659602	−	0.997822i	$-0.478989\pi$
$397$	−11.8148	−	4.89383i	−0.592966	−	0.245614i	−0.658926	+	0.752208i	$0.728989\pi$
$398$		0			0
$399$	−0.192536	+	14.4813i	−0.00963887	+	0.724970i
$400$		0			0
$401$	−37.4682			−1.87107			−0.935537	−	0.353229i	$-0.885084\pi$
$401$	−37.4682			−1.87107			−0.935537	+	0.353229i	$0.885084\pi$
$402$		0			0
$403$	−0.531006	+	1.28196i	−0.0264513	+	0.0638591i
$404$		0			0
$405$	−6.56839	+	2.31994i	−0.326386	+	0.115279i
$406$		0			0
$407$	−7.15905	−	7.15905i	−0.354861	−	0.354861i
$408$		0			0
$409$	−9.85216	+	9.85216i	−0.487158	+	0.487158i	−0.907408	−	0.420250i	$-0.861942\pi$
$409$	−9.85216	+	9.85216i	−0.487158	+	0.487158i	0.420250	+	0.907408i	$0.361942\pi$
$410$		0			0
$411$	7.47481	+	18.7469i	0.368705	+	0.924717i
$412$		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	−0.733037	−	0.680189i	$-0.761898\pi$
$419$	5.45030	−	13.1582i	0.266264	−	0.642819i	0.999302	+	0.0373695i	$0.0118979\pi$
$420$		0			0
$421$	−13.4081	+	5.55381i	−0.653470	+	0.270676i	−0.684688	−	0.728836i	$-0.740062\pi$
$421$	−13.4081	+	5.55381i	−0.653470	+	0.270676i	0.0312176	+	0.999513i	$0.490062\pi$
$422$		0			0
$423$	10.5549	−	10.0080i	0.513195	−	0.486605i
$424$		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
$429$	−13.9423	−	5.99345i	−0.673139	−	0.289367i
$430$		0			0
$431$			37.0767i			1.78592i	0.450133	+	0.892962i	$0.351377\pi$
$431$			37.0767i			1.78592i	−0.450133	+	0.892962i	$0.648623\pi$
$432$		0			0
$433$			0.656469i			0.0315479i	0.999876	+	0.0157739i	$0.00502121\pi$
$433$			0.656469i			0.0315479i	−0.999876	+	0.0157739i	$0.994979\pi$
$434$		0			0
$435$	4.60909	+	1.98134i	0.220989	+	0.0949980i
$436$		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	$-0.582765\pi$
$439$	14.8613	−	14.8613i	0.709293	−	0.709293i	0.966387	+	0.257093i	$0.0827648\pi$
$440$		0			0
$441$	18.3409	−	17.3906i	0.873378	−	0.828125i
$442$		0			0
$443$	5.86331	−	2.42866i	0.278574	−	0.115389i	−0.239022	−	0.971014i	$-0.576827\pi$
$443$	5.86331	−	2.42866i	0.278574	−	0.115389i	0.517596	+	0.855625i	$0.326827\pi$
$444$		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
$453$	−5.88145	−	14.7507i	−0.276334	−	0.693050i
$454$		0			0
$455$	−8.69388	+	8.69388i	−0.407575	+	0.407575i
$456$		0			0
$457$	8.65709	+	8.65709i	0.404962	+	0.404962i	0.879977	−	0.475016i	$-0.157558\pi$
$457$	8.65709	+	8.65709i	0.404962	+	0.404962i	−0.475016	+	0.879977i	$0.657558\pi$
$458$		0			0
$459$	−25.3522	+	9.33521i	−1.18334	+	0.435730i
$460$		0			0
$461$	−12.4022	+	29.9416i	−0.577628	+	1.39452i	0.317308	+	0.948323i	$0.397221\pi$
$461$	−12.4022	+	29.9416i	−0.577628	+	1.39452i	−0.894936	+	0.446195i	$0.852779\pi$
$462$		0			0
$463$	18.0597			0.839306			0.419653	−	0.907685i	$-0.362152\pi$
$463$	18.0597			0.839306			0.419653	+	0.907685i	$0.362152\pi$
$464$		0			0
$465$	0.00611450	−	0.459891i	0.000283553	−	0.0213269i
$466$		0			0
$467$	−3.41999	−	1.41660i	−0.158258	−	0.0655526i	0.302148	−	0.953261i	$-0.402296\pi$
$467$	−3.41999	−	1.41660i	−0.158258	−	0.0655526i	−0.460406	+	0.887708i	$0.652296\pi$
$468$		0			0
$469$	8.86653	+	21.4057i	0.409418	+	0.988423i
$470$		0			0
$471$	−1.18851	−	1.22054i	−0.0547636	−	0.0562395i
$472$		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
$477$	−12.3214	−	5.49189i	−0.564158	−	0.251456i
$478$		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
$483$	−36.5183	−	15.6984i	−1.66164	−	0.714300i
$484$		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	$-0.292231\pi$
$487$	−4.12841	−	4.12841i	−0.187076	−	0.187076i	−0.794431	+	0.607355i	$0.792231\pi$
$488$		0			0
$489$	−1.93466	+	1.88389i	−0.0874882	+	0.0851924i
$490$		0			0
$491$	5.44901	+	13.1551i	0.245911	+	0.593681i	0.997849	−	0.0655526i	$-0.0208810\pi$
$491$	5.44901	+	13.1551i	0.245911	+	0.593681i	−0.751939	+	0.659233i	$0.770881\pi$
$492$		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	−0.171860	−	0.985121i	$-0.554978\pi$
$499$	14.4361	−	34.8519i	0.646250	−	1.56018i	0.818109	−	0.575063i	$-0.195022\pi$
$500$		0			0
$501$	2.77612	+	6.96255i	0.124028	+	0.311064i
$502$		0			0
$503$	−2.95140	−	2.95140i	−0.131596	−	0.131596i	0.638241	−	0.769837i	$-0.279662\pi$
$503$	−2.95140	−	2.95140i	−0.131596	−	0.131596i	−0.769837	+	0.638241i	$0.779662\pi$
$504$		0			0
$505$	1.46222	−	1.46222i	0.0650681	−	0.0650681i
$506$		0			0
$507$	−5.40343	+	2.15447i	−0.239975	+	0.0956832i
$508$		0			0
$509$	40.0107	+	16.5730i	1.77344	+	0.734584i	0.994161	+	0.107909i	$0.0344154\pi$
$509$	40.0107	+	16.5730i	1.77344	+	0.734584i	0.779281	+	0.626675i	$0.215585\pi$
$510$		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
$519$	12.8727	+	13.2196i	0.565049	+	0.580276i
$520$		0			0
$521$	9.10873	−	9.10873i	0.399061	−	0.399061i	−0.478841	−	0.877902i	$-0.658943\pi$
$521$	9.10873	−	9.10873i	0.399061	−	0.399061i	0.877902	+	0.478841i	$0.158943\pi$
$522$		0			0
$523$	−18.7797	+	7.77882i	−0.821181	+	0.340144i	−0.753405	−	0.657556i	$-0.771590\pi$
$523$	−18.7797	+	7.77882i	−0.821181	+	0.340144i	−0.0677753	+	0.997701i	$0.521590\pi$
$524$		0			0
$525$	−11.8233	+	27.5039i	−0.516011	+	1.20037i
$526$		0			0
$527$		−	1.78374i		−	0.0777009i
$528$		0			0
$529$			11.1443i			0.484534i
$530$		0			0
$531$	23.9832	+	10.6898i	1.04078	+	0.463896i
$532$		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
$537$	−6.58194	+	6.40921i	−0.284032	+	0.276578i
$538$		0			0
$539$	−16.8619	+	6.98443i	−0.726294	+	0.300841i
$540$		0			0
$541$	−4.91944	+	11.8766i	−0.211503	+	0.510614i	−0.993655	−	0.112475i	$-0.964122\pi$
$541$	−4.91944	+	11.8766i	−0.211503	+	0.510614i	0.782151	+	0.623088i	$0.214122\pi$
$542$		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	$-0.226539\pi$
$547$	19.4330	+	8.04942i	0.830896	+	0.344168i	0.0736387	+	0.997285i	$0.476539\pi$
$548$		0			0
$549$	−18.0973	+	6.93839i	−0.772373	+	0.296123i
$550$		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
$555$	5.81990	−	2.32052i	0.247041	−	0.0985007i
$556$		0			0
$557$	14.3258	−	34.5854i	0.607002	−	1.46543i	−0.259243	−	0.965812i	$-0.583473\pi$
$557$	14.3258	−	34.5854i	0.607002	−	1.46543i	0.866245	−	0.499620i	$-0.166527\pi$
$558$		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	0.0574918	−	0.998346i	$-0.481690\pi$
$563$	−14.4215	−	5.97357i	−0.607793	−	0.251756i	−0.665284	+	0.746590i	$0.731690\pi$
$564$		0			0
$565$	4.69761	+	11.3410i	0.197630	+	0.477121i
$566$		0			0
$567$	−26.2875	+	23.6304i	−1.10397	+	0.992382i
$568$		0			0
$569$	3.11604	+	3.11604i	0.130631	+	0.130631i	0.769399	−	0.638768i	$-0.220556\pi$
$569$	3.11604	+	3.11604i	0.130631	+	0.130631i	−0.638768	+	0.769399i	$0.720556\pi$
$570$		0			0
$571$	−4.75950	−	11.4904i	−0.199179	−	0.480860i	0.792457	−	0.609928i	$-0.208802\pi$
$571$	−4.75950	−	11.4904i	−0.199179	−	0.480860i	−0.991636	+	0.129068i	$0.958802\pi$
$572$		0			0
$573$	3.73316	−	8.68427i	0.155955	−	0.362791i
$574$		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
$579$	7.21252	−	16.7781i	0.299742	−	0.697275i
$580$		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
$585$	6.81504	−	6.46193i	0.281767	−	0.267168i
$586$		0			0
$587$	2.04862	+	4.94582i	0.0845558	+	0.204136i	0.960502	−	0.278273i	$-0.0897620\pi$
$587$	2.04862	+	4.94582i	0.0845558	+	0.204136i	−0.875946	+	0.482409i	$0.839762\pi$
$588$		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	$-0.683984\pi$
$593$	−26.6090			−1.09270			−0.546351	+	0.837556i	$0.683984\pi$
$594$		0			0
$595$	6.04839	−	14.6021i	0.247960	−	0.598628i
$596$		0			0
$597$	15.1241	−	6.03031i	0.618988	−	0.246804i
$598$		0			0
$599$	−12.7251	−	12.7251i	−0.519933	−	0.519933i	0.397618	−	0.917551i	$-0.369837\pi$
$599$	−12.7251	−	12.7251i	−0.519933	−	0.519933i	−0.917551	+	0.397618i	$0.869837\pi$
$600$		0			0
$601$	−6.45474	+	6.45474i	−0.263294	+	0.263294i	−0.826391	−	0.563097i	$-0.809610\pi$
$601$	−6.45474	+	6.45474i	−0.263294	+	0.263294i	0.563097	+	0.826391i	$0.309610\pi$
$602$		0			0
$603$	−6.33560	−	16.5250i	−0.258006	−	0.672952i
$604$		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	−0.335803	−	0.941932i	$-0.609008\pi$
$613$	2.29750	−	0.951656i	0.0927952	−	0.0384370i	0.428598	+	0.903495i	$0.359008\pi$
$614$		0			0
$615$	4.58969	−	4.46925i	0.185074	−	0.180217i
$616$		0			0
$617$	3.87504	−	3.87504i	0.156003	−	0.156003i	−0.624790	−	0.780793i	$-0.714815\pi$
$617$	3.87504	−	3.87504i	0.156003	−	0.156003i	0.780793	+	0.624790i	$0.214815\pi$
$618$		0			0
$619$	−7.55208	+	3.12818i	−0.303544	+	0.125732i	−0.529256	−	0.848462i	$-0.677529\pi$
$619$	−7.55208	+	3.12818i	−0.303544	+	0.125732i	0.225712	+	0.974194i	$0.427529\pi$
$620$		0			0
$621$	27.5659	+	12.7286i	1.10618	+	0.510781i
$622$		0			0
$623$		−	51.4821i		−	2.06259i
$624$		0			0
$625$		−	16.3726i		−	0.654905i
$626$		0			0
$627$	−3.15484	+	7.33894i	−0.125992	+	0.293089i
$628$		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	$-0.777117\pi$
$631$	−3.02275	+	3.02275i	−0.120334	+	0.120334i	0.644375	+	0.764709i	$0.277117\pi$
$632$		0			0
$633$	9.10648	+	9.35190i	0.361950	+	0.371705i
$634$		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	$-0.501116\pi$
$643$	−18.0821	−	7.48986i	−0.713089	−	0.295371i	−0.709582	+	0.704623i	$0.751116\pi$
$644$		0			0
$645$	12.3337	−	4.91772i	0.485639	−	0.193635i
$646$		0			0
$647$	28.1003	−	28.1003i	1.10474	−	1.10474i	0.110905	−	0.993831i	$-0.464625\pi$
$647$	28.1003	−	28.1003i	1.10474	−	1.10474i	0.993831	−	0.110905i	$-0.0353748\pi$
$648$		0			0
$649$	−13.4073	−	13.4073i	−0.526282	−	0.526282i
$650$		0			0
$651$	−0.864358	−	2.16782i	−0.0338769	−	0.0849636i
$652$		0			0
$653$	6.44946	−	15.5704i	0.252387	−	0.609316i	−0.746009	−	0.665936i	$-0.768032\pi$
$653$	6.44946	−	15.5704i	0.252387	−	0.609316i	0.998396	+	0.0566202i	$0.0180324\pi$
$654$		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	−0.289143	−	0.957286i	$-0.593370\pi$
$659$	−30.0479	−	12.4463i	−1.17050	−	0.484838i	−0.881358	+	0.472448i	$0.843370\pi$
$660$		0			0
$661$	−16.0509	−	38.7503i	−0.624308	−	1.50721i	−0.846598	−	0.532233i	$-0.821353\pi$
$661$	−16.0509	−	38.7503i	−0.624308	−	1.50721i	0.222290	−	0.974981i	$-0.428647\pi$
$662$		0			0
$663$	26.0951	−	25.4103i	1.01345	−	0.986854i
$664$		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
$669$	−26.4708	−	11.3792i	−1.02342	−	0.439945i
$670$		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
$675$	9.58659	−	20.7614i	0.368988	−	0.799106i
$676$		0			0
$677$	−12.6041	−	30.4289i	−0.484414	−	1.16948i	−0.957492	−	0.288459i	$-0.906857\pi$
$677$	−12.6041	−	30.4289i	−0.484414	−	1.16948i	0.473078	−	0.881021i	$-0.343143\pi$
$678$		0			0
$679$	26.5758	+	26.5758i	1.01989	+	1.01989i
$680$		0			0
$681$	3.45545	+	3.54857i	0.132413	+	0.135981i
$682$		0			0
$683$	−19.7550	−	47.6928i	−0.755904	−	1.82491i	−0.522784	−	0.852465i	$-0.675107\pi$
$683$	−19.7550	−	47.6928i	−0.755904	−	1.82491i	−0.233120	−	0.972448i	$-0.574893\pi$
$684$		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	$-0.942441\pi$
$691$	−4.23089	+	10.2143i	−0.160951	+	0.388569i	0.822745	+	0.568411i	$0.192441\pi$
$692$		0			0
$693$	23.8328	−	9.13737i	0.905335	−	0.347100i
$694$		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
$699$	12.8391	+	32.2007i	0.485621	+	1.21794i
$700$		0			0
$701$	22.1122	+	9.15919i	0.835168	+	0.345938i	0.758946	−	0.651153i	$-0.225714\pi$
$701$	22.1122	+	9.15919i	0.835168	+	0.345938i	0.0762214	+	0.997091i	$0.475714\pi$
$702$		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	−0.844012	−	0.536325i	$-0.819812\pi$
$709$	−28.2667	+	11.7085i	−1.06158	+	0.439721i	−0.217568	+	0.976045i	$0.569812\pi$
$710$		0			0
$711$	27.3419	+	28.8360i	1.02540	+	1.08144i
$712$		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
$717$	9.15051	+	3.93359i	0.341732	+	0.146903i
$718$		0			0
$719$		−	19.8341i		−	0.739687i	−0.929094	−	0.369843i	$-0.879411\pi$
$719$		−	19.8341i		−	0.739687i	0.929094	−	0.369843i	$-0.120589\pi$
$720$		0			0
$721$			42.2921i			1.57504i
$722$		0			0
$723$	0.644140	+	0.276901i	0.0239558	+	0.0102981i
$724$		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	$-0.937568\pi$
$727$	−21.1914	+	21.1914i	−0.785946	+	0.785946i	0.194881	+	0.980827i	$0.437568\pi$
$728$		0			0
$729$	20.5525	−	17.5099i	0.761203	−	0.648513i
$730$		0			0
$731$	47.5757	−	19.7065i	1.75965	−	0.728871i
$732$		0			0
$733$	18.2396	−	44.0342i	0.673694	−	1.62644i	−0.101589	−	0.994826i	$-0.532393\pi$
$733$	18.2396	−	44.0342i	0.673694	−	1.62644i	0.775283	−	0.631614i	$-0.217607\pi$
$734$		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	$-0.278601\pi$
$739$	14.9807	+	6.20519i	0.551073	+	0.228262i	−0.0897317	+	0.995966i	$0.528601\pi$
$740$		0			0
$741$	5.52378	+	13.8537i	0.202921	+	0.508929i
$742$		0			0
$743$	−22.8633	+	22.8633i	−0.838773	+	0.838773i	−0.988697	−	0.149925i	$-0.952097\pi$
$743$	−22.8633	+	22.8633i	−0.838773	+	0.838773i	0.149925	+	0.988697i	$0.452097\pi$
$744$		0			0
$745$	8.75601	+	8.75601i	0.320795	+	0.320795i
$746$		0			0
$747$	−7.19968	−	18.7788i	−0.263423	−	0.687080i
$748$		0			0
$749$	19.0307	−	45.9442i	0.695367	−	1.67877i
$750$		0			0
$751$	−25.4070			−0.927116			−0.463558	−	0.886067i	$-0.653427\pi$
$751$	−25.4070			−0.927116			−0.463558	+	0.886067i	$0.653427\pi$
$752$		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	−0.973026	−	0.230697i	$-0.925899\pi$
$757$	−12.3294	−	29.7658i	−0.448120	−	1.08186i	0.524906	−	0.851160i	$-0.324101\pi$
$758$		0			0
$759$	−15.2959	−	15.7081i	−0.555206	−	0.570169i
$760$		0			0
$761$	23.7667	+	23.7667i	0.861542	+	0.861542i	0.991517	−	0.129975i	$-0.0414898\pi$
$761$	23.7667	+	23.7667i	0.861542	+	0.861542i	−0.129975	+	0.991517i	$0.541490\pi$
$762$		0			0
$763$	22.3848	+	54.0418i	0.810385	+	1.95644i
$764$		0			0
$765$	−4.91498	+	11.0271i	−0.177701	+	0.398684i
$766$		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
$771$	42.9916	+	18.4811i	1.54830	+	0.665580i
$772$		0			0
$773$	17.8280	+	43.0405i	0.641228	+	1.54806i	0.825025	+	0.565097i	$0.191161\pi$
$773$	17.8280	+	43.0405i	0.641228	+	1.54806i	−0.183797	+	0.982964i	$0.558839\pi$
$774$		0			0
$775$	1.06762	+	1.06762i	0.0383500	+	0.0383500i
$776$		0			0
$777$	22.7774	−	22.1797i	0.817135	−	0.795691i
$778$		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	−0.668544	−	0.743673i	$-0.733082\pi$
$787$	9.25890	−	22.3530i	0.330044	−	0.796797i	0.998588	−	0.0531241i	$-0.0169179\pi$
$788$		0			0
$789$	−0.0825472	−	0.207029i	−0.00293876	−	0.00737044i
$790$		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
$795$	−5.59958	+	2.23268i	−0.198596	+	0.0791848i
$796$		0			0
$797$	21.1390	+	8.75605i	0.748781	+	0.310155i	0.724244	−	0.689544i	$-0.242189\pi$
$797$	21.1390	+	8.75605i	0.748781	+	0.310155i	0.0245368	+	0.999699i	$0.492189\pi$
$798$		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
$807$	−27.8837	−	28.6352i	−0.981553	−	1.00801i
$808$		0			0
$809$	13.3483	−	13.3483i	0.469301	−	0.469301i	−0.432387	−	0.901688i	$-0.642329\pi$
$809$	13.3483	−	13.3483i	0.469301	−	0.469301i	0.901688	+	0.432387i	$0.142329\pi$
$810$		0			0
$811$	−18.1422	+	7.51474i	−0.637058	+	0.263878i	−0.677749	−	0.735294i	$-0.737044\pi$
$811$	−18.1422	+	7.51474i	−0.637058	+	0.263878i	0.0406904	+	0.999172i	$0.487044\pi$
$812$		0			0
$813$	1.93431	−	4.49970i	0.0678394	−	0.157811i
$814$		0			0
$815$			1.20672i			0.0422694i
$816$		0			0
$817$			21.0862i			0.737713i
$818$		0			0
$819$	19.4007	−	43.5268i	0.677917	−	1.52095i
$820$		0			0
$821$	−27.9756	+	11.5879i	−0.976355	+	0.404420i	−0.813074	−	0.582160i	$-0.802208\pi$
$821$	−27.9756	+	11.5879i	−0.976355	+	0.404420i	−0.163281	+	0.986580i	$0.552208\pi$
$822$		0			0
$823$	29.0608	−	29.0608i	1.01300	−	1.01300i	0.0130818	−	0.999914i	$-0.495836\pi$
$823$	29.0608	−	29.0608i	1.01300	−	1.01300i	0.999914	−	0.0130818i	$-0.00416419\pi$
$824$		0			0
$825$	−11.8306	+	11.5202i	−0.411890	+	0.401081i
$826$		0			0
$827$	−2.28063	+	0.944670i	−0.0793054	+	0.0328494i	−0.421984	−	0.906604i	$-0.638666\pi$
$827$	−2.28063	+	0.944670i	−0.0793054	+	0.0328494i	0.342678	+	0.939453i	$0.388666\pi$
$828$		0			0
$829$	19.1205	−	46.1610i	0.664082	−	1.60324i	−0.127264	−	0.991869i	$-0.540620\pi$
$829$	19.1205	−	46.1610i	0.664082	−	1.60324i	0.791346	−	0.611368i	$-0.209380\pi$
$830$		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
$837$	0.615984	+	1.67286i	0.0212915	+	0.0578225i
$838$		0			0
$839$	−26.7898	+	26.7898i	−0.924887	+	0.924887i	−0.997370	−	0.0724830i	$-0.976908\pi$
$839$	−26.7898	+	26.7898i	−0.924887	+	0.924887i	0.0724830	+	0.997370i	$0.476908\pi$
$840$		0			0
$841$	−10.6035	−	10.6035i	−0.365638	−	0.365638i
$842$		0			0
$843$	−25.7653	+	10.2732i	−0.887405	+	0.353828i
$844$		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	0.901366	+	0.433057i	$0.142565\pi$
$853$	16.6540	+	40.2063i	0.570222	+	1.37664i	−0.331145	+	0.943580i	$0.607435\pi$
$854$		0			0
$855$	−3.40143	−	3.58730i	−0.116327	−	0.122683i
$856$		0			0
$857$	26.3920	+	26.3920i	0.901532	+	0.901532i	0.995569	−	0.0940369i	$-0.0299772\pi$
$857$	26.3920	+	26.3920i	0.901532	+	0.901532i	−0.0940369	+	0.995569i	$0.529977\pi$
$858$		0			0
$859$	10.8177	+	26.1163i	0.369096	+	0.891077i	0.993899	+	0.110294i	$0.0351793\pi$
$859$	10.8177	+	26.1163i	0.369096	+	0.891077i	−0.624803	+	0.780782i	$0.714821\pi$
$860$		0			0
$861$	12.8378	−	29.8640i	0.437512	−	1.01776i
$862$		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
$867$	−6.86267	+	15.9643i	−0.233069	+	0.542176i
$868$		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
$873$	−19.7531	−	20.8325i	−0.668541	−	0.705073i
$874$		0			0
$875$	10.9362	+	26.4023i	0.369711	+	0.892562i
$876$		0			0
$877$	−17.8161	−	7.37968i	−0.601608	−	0.249194i	0.0610277	−	0.998136i	$-0.480562\pi$
$877$	−17.8161	−	7.37968i	−0.601608	−	0.249194i	−0.662636	+	0.748942i	$0.730562\pi$
$878$		0			0
$879$	−21.6159	−	0.287395i	−0.729087	−	0.00969361i
$880$		0			0
$881$	−18.0163			−0.606984			−0.303492	−	0.952834i	$-0.598153\pi$
$881$	−18.0163			−0.606984			−0.303492	+	0.952834i	$0.598153\pi$
$882$		0			0
$883$	−1.13662	+	2.74405i	−0.0382504	+	0.0923447i	−0.941850	−	0.336033i	$-0.890915\pi$
$883$	−1.13662	+	2.74405i	−0.0382504	+	0.0923447i	0.903600	+	0.428378i	$0.140915\pi$
$884$		0			0
$885$	10.8994	−	4.34582i	0.366378	−	0.146083i
$886$		0			0
$887$	−33.9649	−	33.9649i	−1.14043	−	1.14043i	−0.988371	−	0.152060i	$-0.951409\pi$
$887$	−33.9649	−	33.9649i	−1.14043	−	1.14043i	−0.152060	−	0.988371i	$-0.548591\pi$
$888$		0			0
$889$	6.30746	−	6.30746i	0.211545	−	0.211545i
$890$		0			0
$891$	−18.3839	+	6.49313i	−0.615883	+	0.217528i
$892$		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
$903$	48.2706	−	47.0038i	1.60634	−	1.56419i
$904$		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	$-0.914961\pi$
$907$	−43.9663	+	18.2114i	−1.45988	+	0.604701i	−0.495352	+	0.868692i	$0.664961\pi$
$908$		0			0
$909$	−3.26301	+	7.32077i	−0.108227	+	0.242815i
$910$		0			0
$911$		−	30.0744i		−	0.996410i	−0.867059	−	0.498205i	$-0.833993\pi$
$911$		−	30.0744i		−	0.996410i	0.867059	−	0.498205i	$-0.166007\pi$
$912$		0			0
$913$			14.5227i			0.480633i
$914$		0			0
$915$	−3.42058	+	7.95711i	−0.113081	+	0.263054i
$916$		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	$-0.919858\pi$
$919$	−21.8072	+	21.8072i	−0.719352	+	0.719352i	0.249121	+	0.968472i	$0.419858\pi$
$920$		0			0
$921$	−38.9348	−	39.9841i	−1.28295	−	1.31752i
$922$		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
$933$	−50.5980	+	20.1745i	−1.65650	+	0.660485i
$934$		0			0
$935$	6.16446	−	6.16446i	0.201599	−	0.201599i
$936$		0			0
$937$	36.2485	+	36.2485i	1.18419	+	1.18419i	0.978650	+	0.205536i	$0.0658936\pi$
$937$	36.2485	+	36.2485i	1.18419	+	1.18419i	0.205536	+	0.978650i	$0.434106\pi$
$938$		0			0
$939$	−12.1775	−	30.5413i	−0.397397	−	0.996677i
$940$		0			0
$941$	−6.43068	+	15.5250i	−0.209634	+	0.506102i	−0.993366	−	0.114998i	$-0.963314\pi$
$941$	−6.43068	+	15.5250i	−0.209634	+	0.506102i	0.783731	+	0.621100i	$0.213314\pi$
$942$		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	0.102961	−	0.994685i	$-0.467168\pi$
$947$	−16.2355	−	6.72498i	−0.527584	−	0.218532i	−0.630545	+	0.776153i	$0.717168\pi$
$948$		0			0
$949$	−3.17294	−	7.66016i	−0.102998	−	0.248659i
$950$		0			0
$951$	−1.27208	+	1.23869i	−0.0412499	+	0.0401674i
$952$		0			0
$953$	−0.946267	−	0.946267i	−0.0306526	−	0.0306526i	0.691614	−	0.722267i	$-0.256900\pi$
$953$	−0.946267	−	0.946267i	−0.0306526	−	0.0306526i	−0.722267	+	0.691614i	$0.756900\pi$
$954$		0			0
$955$	−1.61651	−	3.90260i	−0.0523090	−	0.126285i
$956$		0			0
$957$	12.9001	+	5.54545i	0.417001	+	0.179259i
$958$		0			0
$959$	45.7635			1.47778
$960$		0			0
$961$	30.8823			0.996203
$962$		0			0
$963$	−15.4645	+	34.6957i	−0.498338	+	1.11805i
$964$		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	$-0.393537\pi$
$967$	−19.1657	−	19.1657i	−0.616326	−	0.616326i	−0.944587	+	0.328261i	$0.893537\pi$
$968$		0			0
$969$	−13.3755	−	13.7359i	−0.429682	−	0.441262i
$970$		0			0
$971$	13.7803	+	33.2686i	0.442231	+	1.06764i	0.975164	+	0.221483i	$0.0710899\pi$
$971$	13.7803	+	33.2686i	0.442231	+	1.06764i	−0.532933	+	0.846158i	$0.678910\pi$
$972$		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	$-0.618379\pi$
$977$	−22.7166			−0.726769			−0.363384	+	0.931639i	$0.618379\pi$
$978$		0			0
$979$	10.8669	−	26.2350i	0.347308	−	0.838475i
$980$		0			0
$981$	−15.9951	−	41.7199i	−0.510686	−	1.33201i
$982$		0			0
$983$	−0.832934	−	0.832934i	−0.0265665	−	0.0265665i	0.693699	−	0.720265i	$-0.255980\pi$
$983$	−0.832934	−	0.832934i	−0.0265665	−	0.0265665i	−0.720265	+	0.693699i	$0.755980\pi$
$984$		0			0
$985$	−0.0749722	+	0.0749722i	−0.00238881	+	0.00238881i
$986$		0			0
$987$	−12.2154	−	30.6363i	−0.388819	−	0.975163i
$988$		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	0.560475	−	0.828172i	$-0.310619\pi$
$997$	48.7016	−	20.1729i	1.54240	−	0.638881i	0.981921	+	0.189290i	$0.0606187\pi$
$998$		0			0
$999$	−17.8428	+	16.4734i	−0.564522	+	0.521196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.b.479.5		56
3.2	odd	2	inner	768.2.o.b.479.9		56
4.3	odd	2		768.2.o.a.479.10		56
8.3	odd	2		384.2.o.a.239.5		56
8.5	even	2		96.2.o.a.83.10	yes	56
12.11	even	2		768.2.o.a.479.6		56
24.5	odd	2		96.2.o.a.83.5	yes	56
24.11	even	2		384.2.o.a.239.9		56
32.5	even	8		768.2.o.a.287.6		56
32.11	odd	8		96.2.o.a.59.5	✓	56
32.21	even	8		384.2.o.a.143.9		56
32.27	odd	8	inner	768.2.o.b.287.9		56
96.5	odd	8		768.2.o.a.287.10		56
96.11	even	8		96.2.o.a.59.10	yes	56
96.53	odd	8		384.2.o.a.143.5		56
96.59	even	8	inner	768.2.o.b.287.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.59.5	✓	56	32.11	odd	8
96.2.o.a.59.10	yes	56	96.11	even	8
96.2.o.a.83.5	yes	56	24.5	odd	2
96.2.o.a.83.10	yes	56	8.5	even	2
384.2.o.a.143.5		56	96.53	odd	8
384.2.o.a.143.9		56	32.21	even	8
384.2.o.a.239.5		56	8.3	odd	2
384.2.o.a.239.9		56	24.11	even	2
768.2.o.a.287.6		56	32.5	even	8
768.2.o.a.287.10		56	96.5	odd	8
768.2.o.a.479.6		56	12.11	even	2
768.2.o.a.479.10		56	4.3	odd	2
768.2.o.b.287.5		56	96.59	even	8	inner
768.2.o.b.287.9		56	32.27	odd	8	inner
768.2.o.b.479.5		56	1.1	even	1	trivial
768.2.o.b.479.9		56	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.684042 + 1.59125i) q^{3} +(0.296199 + 0.715088i) q^{5} +(2.77714 + 2.77714i) q^{7} +(-2.06417 - 2.17697i) q^{9} +O(q^{10})\)	\(q+(-0.684042 + 1.59125i) q^{3} +(0.296199 + 0.715088i) q^{5} +(2.77714 + 2.77714i) q^{7} +(-2.06417 - 2.17697i) q^{9} +(0.829014 + 2.00142i) q^{11} +(3.73669 + 1.54779i) q^{13} +(-1.34050 - 0.0178227i) q^{15} -5.19928 q^{17} +(0.814726 - 1.96692i) q^{19} +(-6.31881 + 2.51945i) q^{21} +(4.13184 + 4.13184i) q^{23} +(3.11192 - 3.11192i) q^{25} +(4.87609 - 1.79548i) q^{27} +(-3.45738 - 1.43209i) q^{29} +0.343074i q^{31} +(-3.75184 - 0.0498828i) q^{33} +(-1.16331 + 2.80849i) q^{35} +(-4.31781 + 1.78850i) q^{37} +(-5.01898 + 4.88727i) q^{39} +(-3.37894 + 3.37894i) q^{41} +(-9.15044 + 3.79024i) q^{43} +(0.945319 - 2.12088i) q^{45} +4.84842i q^{47} +8.42499i q^{49} +(3.55653 - 8.27337i) q^{51} +(4.15435 - 1.72079i) q^{53} +(-1.18564 + 1.18564i) q^{55} +(2.57256 + 2.64189i) q^{57} +(-8.08629 + 3.34945i) q^{59} +(2.47236 - 5.96880i) q^{61} +(0.313252 - 11.7782i) q^{63} +3.13052i q^{65} +(5.45025 + 2.25757i) q^{67} +(-9.40117 + 3.74845i) q^{69} +(6.23395 - 6.23395i) q^{71} +(-1.44956 - 1.44956i) q^{73} +(2.82316 + 7.08053i) q^{75} +(-3.25592 + 7.86050i) q^{77} -13.2460 q^{79} +(-0.478386 + 8.98728i) q^{81} +(6.19358 + 2.56547i) q^{83} +(-1.54002 - 3.71795i) q^{85} +(4.64382 - 4.52195i) q^{87} +(-9.26892 - 9.26892i) q^{89} +(6.07889 + 14.6757i) q^{91} +(-0.545918 - 0.234677i) q^{93} +1.64784 q^{95} +9.56950 q^{97} +(2.64579 - 5.93600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more