LMFDB - Embedded newform 672.2.bb.a.271.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(271,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("672.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.15
Character	$\chi$	$=$	672.271
Dual form			672.2.bb.a.367.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{3} +(1.44142 - 2.49662i) q^{5} +(2.63862 - 0.194181i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{3} +(1.44142 - 2.49662i) q^{5} +(2.63862 - 0.194181i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.91340 - 5.04616i) q^{11} +1.04841 q^{13} -2.88284i q^{15} +(-5.91062 + 3.41250i) q^{17} +(0.589961 + 0.340614i) q^{19} +(2.18802 - 1.48747i) q^{21} +(1.85937 + 1.07351i) q^{23} +(-1.65540 - 2.86723i) q^{25} -1.00000i q^{27} +6.61515i q^{29} +(1.91558 + 3.31788i) q^{31} +(-5.04616 - 2.91340i) q^{33} +(3.31857 - 6.86751i) q^{35} +(-2.06185 - 1.19041i) q^{37} +(0.907949 - 0.524204i) q^{39} -1.19919i q^{41} -1.34319 q^{43} +(-1.44142 - 2.49662i) q^{45} +(5.52670 - 9.57253i) q^{47} +(6.92459 - 1.02474i) q^{49} +(-3.41250 + 5.91062i) q^{51} +(6.99615 - 4.03923i) q^{53} -16.7978 q^{55} +0.681229 q^{57} +(-6.81625 + 3.93537i) q^{59} +(1.63471 - 2.83140i) q^{61} +(1.15114 - 2.38220i) q^{63} +(1.51120 - 2.61747i) q^{65} +(6.65629 + 11.5290i) q^{67} +2.14701 q^{69} -1.08533i q^{71} +(4.88878 - 2.82254i) q^{73} +(-2.86723 - 1.65540i) q^{75} +(-8.66721 - 12.7491i) q^{77} +(10.9630 + 6.32946i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.482042i q^{83} +19.6754i q^{85} +(3.30757 + 5.72889i) q^{87} +(10.7308 + 6.19543i) q^{89} +(2.76635 - 0.203581i) q^{91} +(3.31788 + 1.91558i) q^{93} +(1.70077 - 0.981939i) q^{95} -3.63532i q^{97} -5.82680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^9	$ 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	1.44142	−	2.49662i	0.644624	−	1.11652i	−0.339765	−	0.940511i	$-0.610347\pi$
$5$	1.44142	−	2.49662i	0.644624	−	1.11652i	0.984388	−	0.176010i	$-0.0563193\pi$
$6$		0			0
$7$	2.63862	−	0.194181i	0.997303	−	0.0733933i
$7$	2.63862	−	0.194181i	0.997303	−	0.0733933i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−2.91340	−	5.04616i	−0.878423	−	1.52147i	−0.853071	−	0.521795i	$-0.825262\pi$
$11$	−2.91340	−	5.04616i	−0.878423	−	1.52147i	−0.0253527	−	0.999679i	$-0.508071\pi$
$12$		0			0
$13$	1.04841			0.290776			0.145388	−	0.989375i	$-0.453557\pi$
$13$	1.04841			0.290776			0.145388	+	0.989375i	$0.453557\pi$
$14$		0			0
$15$		−	2.88284i		−	0.744347i
$16$		0			0
$17$	−5.91062	+	3.41250i	−1.43354	+	0.827652i	−0.997388	−	0.0722232i	$-0.976991\pi$
$17$	−5.91062	+	3.41250i	−1.43354	+	0.827652i	−0.436147	+	0.899875i	$0.643657\pi$
$18$		0			0
$19$	0.589961	+	0.340614i	0.135346	+	0.0781423i	0.566144	−	0.824306i	$-0.308434\pi$
$19$	0.589961	+	0.340614i	0.135346	+	0.0781423i	−0.430798	+	0.902448i	$0.641768\pi$
$20$		0			0
$21$	2.18802	−	1.48747i	0.477465	−	0.324593i
$22$		0			0
$23$	1.85937	+	1.07351i	0.387705	+	0.223841i	0.681165	−	0.732130i	$-0.261474\pi$
$23$	1.85937	+	1.07351i	0.387705	+	0.223841i	−0.293460	+	0.955971i	$0.594807\pi$
$24$		0			0
$25$	−1.65540	−	2.86723i	−0.331079	−	0.573446i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			6.61515i			1.22840i	0.789149	+	0.614201i	$0.210522\pi$
$29$			6.61515i			1.22840i	−0.789149	+	0.614201i	$0.789478\pi$
$30$		0			0
$31$	1.91558	+	3.31788i	0.344048	+	0.595909i	0.985180	−	0.171522i	$-0.0548684\pi$
$31$	1.91558	+	3.31788i	0.344048	+	0.595909i	−0.641132	+	0.767430i	$0.721535\pi$
$32$		0			0
$33$	−5.04616	−	2.91340i	−0.878423	−	0.507158i
$34$		0			0
$35$	3.31857	−	6.86751i	0.560940	−	1.16082i
$36$		0			0
$37$	−2.06185	−	1.19041i	−0.338966	−	0.195702i	0.320849	−	0.947130i	$-0.396032\pi$
$37$	−2.06185	−	1.19041i	−0.338966	−	0.195702i	−0.659814	+	0.751429i	$0.729365\pi$
$38$		0			0
$39$	0.907949	−	0.524204i	0.145388	−	0.0839399i
$40$		0			0
$41$		−	1.19919i		−	0.187281i	−0.995606	−	0.0936407i	$-0.970149\pi$
$41$		−	1.19919i		−	0.187281i	0.995606	−	0.0936407i	$-0.0298505\pi$
$42$		0			0
$43$	−1.34319			−0.204835			−0.102418	−	0.994741i	$-0.532658\pi$
$43$	−1.34319			−0.204835			−0.102418	+	0.994741i	$0.532658\pi$
$44$		0			0
$45$	−1.44142	−	2.49662i	−0.214875	−	0.372174i
$46$		0			0
$47$	5.52670	−	9.57253i	0.806152	−	1.39630i	−0.109359	−	0.994002i	$-0.534880\pi$
$47$	5.52670	−	9.57253i	0.806152	−	1.39630i	0.915511	−	0.402294i	$-0.131787\pi$
$48$		0			0
$49$	6.92459	−	1.02474i	0.989227	−	0.146391i
$50$		0			0
$51$	−3.41250	+	5.91062i	−0.477845	+	0.827652i
$52$		0			0
$53$	6.99615	−	4.03923i	0.960995	−	0.554830i	0.0645156	−	0.997917i	$-0.479450\pi$
$53$	6.99615	−	4.03923i	0.960995	−	0.554830i	0.896479	+	0.443086i	$0.146116\pi$
$54$		0			0
$55$	−16.7978			−2.26501
$56$		0			0
$57$	0.681229			0.0902310
$58$		0			0
$59$	−6.81625	+	3.93537i	−0.887400	+	0.512341i	−0.873091	−	0.487557i	$-0.837888\pi$
$59$	−6.81625	+	3.93537i	−0.887400	+	0.512341i	−0.0143092	+	0.999898i	$0.504555\pi$
$60$		0			0
$61$	1.63471	−	2.83140i	0.209303	−	0.362524i	−0.742192	−	0.670187i	$-0.766214\pi$
$61$	1.63471	−	2.83140i	0.209303	−	0.362524i	0.951495	+	0.307663i	$0.0995471\pi$
$62$		0			0
$63$	1.15114	−	2.38220i	0.145030	−	0.300129i
$64$		0			0
$65$	1.51120	−	2.61747i	0.187441	−	0.324658i
$66$		0			0
$67$	6.65629	+	11.5290i	0.813195	+	1.40850i	0.910617	+	0.413252i	$0.135607\pi$
$67$	6.65629	+	11.5290i	0.813195	+	1.40850i	−0.0974214	+	0.995243i	$0.531059\pi$
$68$		0			0
$69$	2.14701			0.258470
$70$		0			0
$71$		−	1.08533i		−	0.128805i	−0.997924	−	0.0644027i	$-0.979486\pi$
$71$		−	1.08533i		−	0.128805i	0.997924	−	0.0644027i	$-0.0205142\pi$
$72$		0			0
$73$	4.88878	−	2.82254i	0.572188	−	0.330353i	−0.185835	−	0.982581i	$-0.559499\pi$
$73$	4.88878	−	2.82254i	0.572188	−	0.330353i	0.758023	+	0.652228i	$0.226166\pi$
$74$		0			0
$75$	−2.86723	−	1.65540i	−0.331079	−	0.191149i
$76$		0			0
$77$	−8.66721	−	12.7491i	−0.987720	−	1.45290i
$78$		0			0
$79$	10.9630	+	6.32946i	1.23343	+	0.712120i	0.967743	−	0.251939i	$-0.0810684\pi$
$79$	10.9630	+	6.32946i	1.23343	+	0.712120i	0.265686	+	0.964060i	$0.414402\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	0.482042i		−	0.0529110i	−0.999650	−	0.0264555i	$-0.991578\pi$
$83$		−	0.482042i		−	0.0529110i	0.999650	−	0.0264555i	$-0.00842203\pi$
$84$		0			0
$85$			19.6754i			2.13410i
$86$		0			0
$87$	3.30757	+	5.72889i	0.354609	+	0.614201i
$88$		0			0
$89$	10.7308	+	6.19543i	1.13746	+	0.656714i	0.945801	−	0.324747i	$-0.105279\pi$
$89$	10.7308	+	6.19543i	1.13746	+	0.656714i	0.191661	+	0.981461i	$0.438612\pi$
$90$		0			0
$91$	2.76635	−	0.203581i	0.289992	−	0.0213410i
$92$		0			0
$93$	3.31788	+	1.91558i	0.344048	+	0.198636i
$94$		0			0
$95$	1.70077	−	0.981939i	0.174495	−	0.100745i
$96$		0			0
$97$		−	3.63532i		−	0.369111i	−0.982822	−	0.184556i	$-0.940915\pi$
$97$		−	3.63532i		−	0.369111i	0.982822	−	0.184556i	$-0.0590846\pi$
$98$		0			0
$99$	−5.82680			−0.585616
$100$		0			0
$101$	−1.25234	−	2.16911i	−0.124612	−	0.215835i	0.796969	−	0.604020i	$-0.206435\pi$
$101$	−1.25234	−	2.16911i	−0.124612	−	0.215835i	−0.921581	+	0.388185i	$0.873102\pi$
$102$		0			0
$103$	−2.31322	+	4.00661i	−0.227928	+	0.394783i	−0.957194	−	0.289447i	$-0.906529\pi$
$103$	−2.31322	+	4.00661i	−0.227928	+	0.394783i	0.729266	+	0.684231i	$0.239862\pi$
$104$		0			0
$105$	−0.559792	−	7.60672i	−0.0546301	−	0.742340i
$106$		0			0
$107$	−3.03473	+	5.25631i	−0.293378	+	0.508146i	−0.974606	−	0.223925i	$-0.928113\pi$
$107$	−3.03473	+	5.25631i	−0.293378	+	0.508146i	0.681228	+	0.732071i	$0.261446\pi$
$108$		0			0
$109$	−12.6132	+	7.28224i	−1.20813	+	0.697513i	−0.962350	−	0.271814i	$-0.912377\pi$
$109$	−12.6132	+	7.28224i	−1.20813	+	0.697513i	−0.245777	+	0.969326i	$0.579043\pi$
$110$		0			0
$111$	−2.38082			−0.225977
$112$		0			0
$113$	−3.82875			−0.360179			−0.180089	−	0.983650i	$-0.557639\pi$
$113$	−3.82875			−0.360179			−0.180089	+	0.983650i	$0.557639\pi$
$114$		0			0
$115$	5.36027	−	3.09475i	0.499847	−	0.288587i
$116$		0			0
$117$	0.524204	−	0.907949i	0.0484627	−	0.0839399i
$118$		0			0
$119$	−14.9332	+	10.1520i	−1.36893	+	0.930632i
$120$		0			0
$121$	−11.4758	+	19.8767i	−1.04326	+	1.80697i
$122$		0			0
$123$	−0.599593	−	1.03853i	−0.0540635	−	0.0936407i
$124$		0			0
$125$	4.86972			0.435561
$126$		0			0
$127$		−	0.550415i		−	0.0488415i	−0.999702	−	0.0244207i	$-0.992226\pi$
$127$		−	0.550415i		−	0.0488415i	0.999702	−	0.0244207i	$-0.00777413\pi$
$128$		0			0
$129$	−1.16324	+	0.671597i	−0.102418	+	0.0591308i
$130$		0			0
$131$	2.42818	+	1.40191i	0.212151	+	0.122486i	0.602311	−	0.798262i	$-0.294247\pi$
$131$	2.42818	+	1.40191i	0.212151	+	0.122486i	−0.390159	+	0.920747i	$0.627580\pi$
$132$		0			0
$133$	1.62282	+	0.784192i	0.140717	+	0.0679980i
$134$		0			0
$135$	−2.49662	−	1.44142i	−0.214875	−	0.124058i
$136$		0			0
$137$	−6.38148	−	11.0530i	−0.545206	−	0.944325i	−0.998594	−	0.0530118i	$-0.983118\pi$
$137$	−6.38148	−	11.0530i	−0.545206	−	0.944325i	0.453387	−	0.891314i	$-0.350215\pi$
$138$		0			0
$139$		−	6.11761i		−	0.518889i	−0.965758	−	0.259444i	$-0.916461\pi$
$139$		−	6.11761i		−	0.518889i	0.965758	−	0.259444i	$-0.0835394\pi$
$140$		0			0
$141$		−	11.0534i		−	0.930864i
$142$		0			0
$143$	−3.05443	−	5.29044i	−0.255425	−	0.442408i
$144$		0			0
$145$	16.5155	+	9.53522i	1.37154	+	0.791857i
$146$		0			0
$147$	5.48450	−	4.34974i	0.452354	−	0.358761i
$148$		0			0
$149$	1.75163	+	1.01130i	0.143499	+	0.0828491i	0.570030	−	0.821624i	$-0.306931\pi$
$149$	1.75163	+	1.01130i	0.143499	+	0.0828491i	−0.426532	+	0.904473i	$0.640265\pi$
$150$		0			0
$151$	−12.1833	+	7.03404i	−0.991464	+	0.572422i	−0.905712	−	0.423895i	$-0.860663\pi$
$151$	−12.1833	+	7.03404i	−0.991464	+	0.572422i	−0.0857523	+	0.996316i	$0.527329\pi$
$152$		0			0
$153$			6.82499i			0.551768i
$154$		0			0
$155$	11.0446			0.887126
$156$		0			0
$157$	2.61739	+	4.53344i	0.208890	+	0.361808i	0.951365	−	0.308065i	$-0.0996816\pi$
$157$	2.61739	+	4.53344i	0.208890	+	0.361808i	−0.742475	+	0.669874i	$0.766348\pi$
$158$		0			0
$159$	4.03923	−	6.99615i	0.320332	−	0.554830i
$160$		0			0
$161$	5.11461	+	2.47152i	0.403088	+	0.194783i
$162$		0			0
$163$	0.488212	−	0.845609i	0.0382397	−	0.0662332i	−0.846272	−	0.532751i	$-0.821158\pi$
$163$	0.488212	−	0.845609i	0.0382397	−	0.0662332i	0.884512	+	0.466518i	$0.154492\pi$
$164$		0			0
$165$	−14.5473	+	8.39888i	−1.13251	+	0.653852i
$166$		0			0
$167$	2.08267			0.161162			0.0805808	−	0.996748i	$-0.474322\pi$
$167$	2.08267			0.161162			0.0805808	+	0.996748i	$0.474322\pi$
$168$		0			0
$169$	−11.9008			−0.915449
$170$		0			0
$171$	0.589961	−	0.340614i	0.0451155	−	0.0260474i
$172$		0			0
$173$	−10.6732	+	18.4864i	−0.811465	+	1.40550i	0.100374	+	0.994950i	$0.467996\pi$
$173$	−10.6732	+	18.4864i	−0.811465	+	1.40550i	−0.911839	+	0.410548i	$0.865337\pi$
$174$		0			0
$175$	−4.92472	−	7.24408i	−0.372274	−	0.547601i
$176$		0			0
$177$	−3.93537	+	6.81625i	−0.295800	+	0.512341i
$178$		0			0
$179$	−3.47487	−	6.01865i	−0.259724	−	0.449855i	0.706444	−	0.707769i	$-0.250298\pi$
$179$	−3.47487	−	6.01865i	−0.259724	−	0.449855i	−0.966168	+	0.257914i	$0.916965\pi$
$180$		0			0
$181$	−7.67619			−0.570566			−0.285283	−	0.958443i	$-0.592088\pi$
$181$	−7.67619			−0.570566			−0.285283	+	0.958443i	$0.592088\pi$
$182$		0			0
$183$		−	3.26942i		−	0.241683i
$184$		0			0
$185$	−5.94398	+	3.43176i	−0.437010	+	0.252308i
$186$		0			0
$187$	34.4400	+	19.8839i	2.51850	+	1.45406i
$188$		0			0
$189$	−0.194181	−	2.63862i	−0.0141246	−	0.191931i
$190$		0			0
$191$	15.4238	+	8.90495i	1.11603	+	0.644340i	0.940384	−	0.340114i	$-0.110466\pi$
$191$	15.4238	+	8.90495i	1.11603	+	0.644340i	0.175645	+	0.984454i	$0.443799\pi$
$192$		0			0
$193$	6.89797	+	11.9476i	0.496527	+	0.860010i	0.999992	−	0.00400574i	$-0.00127507\pi$
$193$	6.89797	+	11.9476i	0.496527	+	0.860010i	−0.503465	+	0.864016i	$0.667942\pi$
$194$		0			0
$195$		−	3.02240i		−	0.216439i
$196$		0			0
$197$			1.13180i			0.0806374i	0.999187	+	0.0403187i	$0.0128373\pi$
$197$			1.13180i			0.0806374i	−0.999187	+	0.0403187i	$0.987163\pi$
$198$		0			0
$199$	4.26593	+	7.38881i	0.302404	+	0.523779i	0.976680	−	0.214701i	$-0.0688776\pi$
$199$	4.26593	+	7.38881i	0.302404	+	0.523779i	−0.674276	+	0.738479i	$0.735544\pi$
$200$		0			0
$201$	11.5290	+	6.65629i	0.813195	+	0.469498i
$202$		0			0
$203$	1.28453	+	17.4548i	0.0901566	+	1.22509i
$204$		0			0
$205$	−2.99391	−	1.72853i	−0.209104	−	0.120726i
$206$		0			0
$207$	1.85937	−	1.07351i	0.129235	−	0.0746138i
$208$		0			0
$209$		−	3.96939i		−	0.274568i
$210$		0			0
$211$	−21.2436			−1.46247			−0.731237	−	0.682124i	$-0.761056\pi$
$211$	−21.2436			−1.46247			−0.731237	+	0.682124i	$0.761056\pi$
$212$		0			0
$213$	−0.542667	−	0.939926i	−0.0371829	−	0.0644027i
$214$		0			0
$215$	−1.93611	+	3.35344i	−0.132042	+	0.228703i
$216$		0			0
$217$	5.69874	+	8.38264i	0.386856	+	0.569051i
$218$		0			0
$219$	2.82254	−	4.88878i	0.190729	−	0.330353i
$220$		0			0
$221$	−6.19674	+	3.57769i	−0.416838	+	0.240662i
$222$		0			0
$223$	−3.12207			−0.209069			−0.104535	−	0.994521i	$-0.533335\pi$
$223$	−3.12207			−0.209069			−0.104535	+	0.994521i	$0.533335\pi$
$224$		0			0
$225$	−3.31079			−0.220720
$226$		0			0
$227$	−4.52649	+	2.61337i	−0.300434	+	0.173456i	−0.642638	−	0.766170i	$-0.722160\pi$
$227$	−4.52649	+	2.61337i	−0.300434	+	0.173456i	0.342204	+	0.939626i	$0.388827\pi$
$228$		0			0
$229$	14.2129	−	24.6175i	0.939215	−	1.62677i	0.172276	−	0.985049i	$-0.444888\pi$
$229$	14.2129	−	24.6175i	0.939215	−	1.62677i	0.766939	−	0.641720i	$-0.221779\pi$
$230$		0			0
$231$	−13.8806	−	6.70748i	−0.913276	−	0.441320i
$232$		0			0
$233$	−3.05971	+	5.29957i	−0.200448	+	0.347186i	−0.948673	−	0.316259i	$-0.897573\pi$
$233$	−3.05971	+	5.29957i	−0.200448	+	0.347186i	0.748225	+	0.663445i	$0.230906\pi$
$234$		0			0
$235$	−15.9326	−	27.5961i	−1.03933	−	1.80017i
$236$		0			0
$237$	12.6589			0.822286
$238$		0			0
$239$		−	8.83528i		−	0.571507i	−0.958303	−	0.285753i	$-0.907756\pi$
$239$		−	8.83528i		−	0.571507i	0.958303	−	0.285753i	$-0.0922439\pi$
$240$		0			0
$241$	5.15757	−	2.97772i	0.332228	−	0.191812i	−0.324602	−	0.945851i	$-0.605230\pi$
$241$	5.15757	−	2.97772i	0.332228	−	0.191812i	0.656830	+	0.754039i	$0.271897\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	7.42288	−	18.7651i	0.474231	−	1.19886i
$246$		0			0
$247$	0.618521	+	0.357103i	0.0393555	+	0.0227219i
$248$		0			0
$249$	−0.241021	−	0.417461i	−0.0152741	−	0.0264555i
$250$		0			0
$251$			2.13955i			0.135047i	0.997718	+	0.0675235i	$0.0215098\pi$
$251$			2.13955i			0.135047i	−0.997718	+	0.0675235i	$0.978490\pi$
$252$		0			0
$253$		−	12.5102i		−	0.786510i
$254$		0			0
$255$	9.83770	+	17.0394i	0.616061	+	1.06705i
$256$		0			0
$257$	−16.7030	−	9.64346i	−1.04190	−	0.601543i	−0.121531	−	0.992588i	$-0.538780\pi$
$257$	−16.7030	−	9.64346i	−1.04190	−	0.601543i	−0.920372	+	0.391045i	$0.872114\pi$
$258$		0			0
$259$	−5.67158	−	2.74066i	−0.352415	−	0.170296i
$260$		0			0
$261$	5.72889	+	3.30757i	0.354609	+	0.204734i
$262$		0			0
$263$	−21.0740	+	12.1671i	−1.29948	+	0.750254i	−0.980314	−	0.197446i	$-0.936735\pi$
$263$	−21.0740	+	12.1671i	−1.29948	+	0.750254i	−0.319164	+	0.947699i	$0.603402\pi$
$264$		0			0
$265$		−	23.2889i		−	1.43063i
$266$		0			0
$267$	12.3909			0.758308
$268$		0			0
$269$	10.4505	+	18.1007i	0.637176	+	1.10362i	0.986050	+	0.166452i	$0.0532310\pi$
$269$	10.4505	+	18.1007i	0.637176	+	1.10362i	−0.348873	+	0.937170i	$0.613436\pi$
$270$		0			0
$271$	9.99697	−	17.3153i	0.607273	−	1.05183i	−0.384415	−	0.923160i	$-0.625597\pi$
$271$	9.99697	−	17.3153i	0.607273	−	1.05183i	0.991688	−	0.128667i	$-0.0410698\pi$
$272$		0			0
$273$	2.29394	−	1.55948i	0.138835	−	0.0943840i
$274$		0			0
$275$	−9.64567	+	16.7068i	−0.581656	+	1.00746i
$276$		0			0
$277$	−13.2433	+	7.64600i	−0.795710	+	0.459404i	−0.841969	−	0.539526i	$-0.818604\pi$
$277$	−13.2433	+	7.64600i	−0.795710	+	0.459404i	0.0462586	+	0.998929i	$0.485270\pi$
$278$		0			0
$279$	3.83116			0.229365
$280$		0			0
$281$	5.59802			0.333950			0.166975	−	0.985961i	$-0.446600\pi$
$281$	5.59802			0.333950			0.166975	+	0.985961i	$0.446600\pi$
$282$		0			0
$283$	−9.72911	+	5.61710i	−0.578335	+	0.333902i	−0.760472	−	0.649371i	$-0.775032\pi$
$283$	−9.72911	+	5.61710i	−0.578335	+	0.333902i	0.182136	+	0.983273i	$0.441699\pi$
$284$		0			0
$285$	0.981939	−	1.70077i	0.0581650	−	0.100745i
$286$		0			0
$287$	−0.232859	−	3.16419i	−0.0137452	−	0.186776i
$288$		0			0
$289$	14.7903	−	25.6175i	0.870016	−	1.50691i
$290$		0			0
$291$	−1.81766	−	3.14828i	−0.106553	−	0.184556i
$292$		0			0
$293$	−17.7212			−1.03528			−0.517642	−	0.855598i	$-0.673190\pi$
$293$	−17.7212			−1.03528			−0.517642	+	0.855598i	$0.673190\pi$
$294$		0			0
$295$			22.6901i			1.32107i
$296$		0			0
$297$	−5.04616	+	2.91340i	−0.292808	+	0.169053i
$298$		0			0
$299$	1.94938	+	1.12547i	0.112735	+	0.0650878i
$300$		0			0
$301$	−3.54417	+	0.260822i	−0.204283	+	0.0150335i
$302$		0			0
$303$	−2.16911	−	1.25234i	−0.124612	−	0.0719449i
$304$		0			0
$305$	−4.71262	−	8.16250i	−0.269844	−	0.467383i
$306$		0			0
$307$		−	20.3724i		−	1.16271i	−0.813649	−	0.581357i	$-0.802522\pi$
$307$		−	20.3724i		−	1.16271i	0.813649	−	0.581357i	$-0.197478\pi$
$308$		0			0
$309$			4.62644i			0.263189i
$310$		0			0
$311$	−14.4363	−	25.0045i	−0.818610	−	1.41787i	−0.906706	−	0.421762i	$-0.861412\pi$
$311$	−14.4363	−	25.0045i	−0.818610	−	1.41787i	0.0880964	−	0.996112i	$-0.471922\pi$
$312$		0			0
$313$	−4.08718	−	2.35974i	−0.231021	−	0.133380i	0.380022	−	0.924978i	$-0.375916\pi$
$313$	−4.08718	−	2.35974i	−0.231021	−	0.133380i	−0.611043	+	0.791597i	$0.709250\pi$
$314$		0			0
$315$	−4.28815	−	6.30772i	−0.241610	−	0.355400i
$316$		0			0
$317$	22.0349	+	12.7218i	1.23760	+	0.714529i	0.968603	−	0.248612i	$-0.0799743\pi$
$317$	22.0349	+	12.7218i	1.23760	+	0.714529i	0.268998	+	0.963141i	$0.413308\pi$
$318$		0			0
$319$	33.3811	−	19.2726i	1.86898	−	1.07906i
$320$		0			0
$321$			6.06946i			0.338764i
$322$		0			0
$323$	−4.64938			−0.258699
$324$		0			0
$325$	−1.73553	−	3.00603i	−0.0962700	−	0.166745i
$326$		0			0
$327$	−7.28224	+	12.6132i	−0.402709	+	0.697513i
$328$		0			0
$329$	12.7240	−	26.3314i	0.701499	−	1.45170i
$330$		0			0
$331$	−9.85929	+	17.0768i	−0.541916	+	0.938625i	0.456878	+	0.889529i	$0.348967\pi$
$331$	−9.85929	+	17.0768i	−0.541916	+	0.938625i	−0.998794	+	0.0490963i	$0.984366\pi$
$332$		0			0
$333$	−2.06185	+	1.19041i	−0.112989	+	0.0652339i
$334$		0			0
$335$	38.3781			2.09682
$336$		0			0
$337$	−24.7720			−1.34942			−0.674709	−	0.738084i	$-0.735731\pi$
$337$	−24.7720			−1.34942			−0.674709	+	0.738084i	$0.735731\pi$
$338$		0			0
$339$	−3.31580	+	1.91438i	−0.180089	+	0.103975i
$340$		0			0
$341$	11.1617	−	19.3326i	0.604440	−	1.04692i
$342$		0			0
$343$	18.0723	−	4.04850i	0.975815	−	0.218599i
$344$		0			0
$345$	3.09475	−	5.36027i	0.166616	−	0.288587i
$346$		0			0
$347$	−7.49413	−	12.9802i	−0.402306	−	0.696815i	0.591698	−	0.806160i	$-0.298458\pi$
$347$	−7.49413	−	12.9802i	−0.402306	−	0.696815i	−0.994004	+	0.109345i	$0.965125\pi$
$348$		0			0
$349$	27.4546			1.46961			0.734806	−	0.678278i	$-0.237273\pi$
$349$	27.4546			1.46961			0.734806	+	0.678278i	$0.237273\pi$
$350$		0			0
$351$		−	1.04841i		−	0.0559599i
$352$		0			0
$353$	20.7884	−	12.0022i	1.10645	−	0.638811i	0.168544	−	0.985694i	$-0.446093\pi$
$353$	20.7884	−	12.0022i	1.10645	−	0.638811i	0.937908	+	0.346883i	$0.112760\pi$
$354$		0			0
$355$	−2.70966	−	1.56442i	−0.143814	−	0.0830310i
$356$		0			0
$357$	−7.85654	+	16.2585i	−0.415812	+	0.860491i
$358$		0			0
$359$	11.8249	+	6.82714i	0.624097	+	0.360322i	0.778462	−	0.627691i	$-0.216000\pi$
$359$	11.8249	+	6.82714i	0.624097	+	0.360322i	−0.154366	+	0.988014i	$0.549333\pi$
$360$		0			0
$361$	−9.26796	−	16.0526i	−0.487788	−	0.844873i
$362$		0			0
$363$			22.9516i			1.20465i
$364$		0			0
$365$		−	16.2739i		−	0.851813i
$366$		0			0
$367$	−17.3424	−	30.0379i	−0.905264	−	1.56796i	−0.820562	−	0.571557i	$-0.806340\pi$
$367$	−17.3424	−	30.0379i	−0.905264	−	1.56796i	−0.0847016	−	0.996406i	$-0.526994\pi$
$368$		0			0
$369$	−1.03853	−	0.599593i	−0.0540635	−	0.0312136i
$370$		0			0
$371$	17.6758	−	12.0165i	0.917682	−	0.623865i
$372$		0			0
$373$	5.26744	+	3.04116i	0.272738	+	0.157465i	0.630131	−	0.776489i	$-0.283001\pi$
$373$	5.26744	+	3.04116i	0.272738	+	0.157465i	−0.357393	+	0.933954i	$0.616334\pi$
$374$		0			0
$375$	4.21730	−	2.43486i	0.217780	−	0.125736i
$376$		0			0
$377$			6.93538i			0.357190i
$378$		0			0
$379$	−19.0628			−0.979189			−0.489594	−	0.871950i	$-0.662855\pi$
$379$	−19.0628			−0.979189			−0.489594	+	0.871950i	$0.662855\pi$
$380$		0			0
$381$	−0.275208	−	0.476674i	−0.0140993	−	0.0244207i
$382$		0			0
$383$	4.12501	−	7.14473i	0.210778	−	0.365079i	−0.741180	−	0.671306i	$-0.765733\pi$
$383$	4.12501	−	7.14473i	0.210778	−	0.365079i	0.951958	+	0.306228i	$0.0990668\pi$
$384$		0			0
$385$	−44.3228	+	3.26180i	−2.25890	+	0.166237i
$386$		0			0
$387$	−0.671597	+	1.16324i	−0.0341392	+	0.0591308i
$388$		0			0
$389$	16.9926	−	9.81070i	0.861560	−	0.497422i	−0.00297421	−	0.999996i	$-0.500947\pi$
$389$	16.9926	−	9.81070i	0.861560	−	0.497422i	0.864534	+	0.502574i	$0.167613\pi$
$390$		0			0
$391$	−14.6533			−0.741051
$392$		0			0
$393$	2.80383			0.141434
$394$		0			0
$395$	31.6045	−	18.2469i	1.59019	−	0.918099i
$396$		0			0
$397$	15.6816	−	27.1613i	0.787035	−	1.36318i	−0.140741	−	0.990047i	$-0.544948\pi$
$397$	15.6816	−	27.1613i	0.787035	−	1.36318i	0.927776	−	0.373138i	$-0.121718\pi$
$398$		0			0
$399$	1.79750	−	0.132281i	0.0899876	−	0.00662235i
$400$		0			0
$401$	−17.4562	+	30.2350i	−0.871722	+	1.50987i	−0.0115069	+	0.999934i	$0.503663\pi$
$401$	−17.4562	+	30.2350i	−0.871722	+	1.50987i	−0.860215	+	0.509932i	$0.829670\pi$
$402$		0			0
$403$	2.00831	+	3.47849i	0.100041	+	0.173276i
$404$		0			0
$405$	−2.88284			−0.143250
$406$		0			0
$407$			13.8725i			0.687636i
$408$		0			0
$409$	11.8182	−	6.82325i	0.584373	−	0.337388i	−0.178496	−	0.983941i	$-0.557123\pi$
$409$	11.8182	−	6.82325i	0.584373	−	0.337388i	0.762869	+	0.646553i	$0.223790\pi$
$410$		0			0
$411$	−11.0530	−	6.38148i	−0.545206	−	0.314775i
$412$		0			0
$413$	−17.2213	+	11.7075i	−0.847405	+	0.576088i
$414$		0			0
$415$	−1.20348	−	0.694827i	−0.0590763	−	0.0341077i
$416$		0			0
$417$	−3.05880	−	5.29800i	−0.149790	−	0.259444i
$418$		0			0
$419$			4.22322i			0.206318i	0.994665	+	0.103159i	$0.0328950\pi$
$419$			4.22322i			0.206318i	−0.994665	+	0.103159i	$0.967105\pi$
$420$		0			0
$421$			11.6892i			0.569697i	0.958573	+	0.284849i	$0.0919433\pi$
$421$			11.6892i			0.569697i	−0.958573	+	0.284849i	$0.908057\pi$
$422$		0			0
$423$	−5.52670	−	9.57253i	−0.268717	−	0.465432i
$424$		0			0
$425$	19.5688	+	11.2981i	0.949228	+	0.548037i
$426$		0			0
$427$	3.76357	−	7.78842i	0.182132	−	0.376908i
$428$		0			0
$429$	−5.29044	−	3.05443i	−0.255425	−	0.147469i
$430$		0			0
$431$	−29.7064	+	17.1510i	−1.43091	+	0.826136i	−0.997190	−	0.0749129i	$-0.976132\pi$
$431$	−29.7064	+	17.1510i	−1.43091	+	0.826136i	−0.433719	+	0.901048i	$0.642799\pi$
$432$		0			0
$433$			14.1884i			0.681853i	0.940090	+	0.340926i	$0.110741\pi$
$433$			14.1884i			0.681853i	−0.940090	+	0.340926i	$0.889259\pi$
$434$		0			0
$435$	19.0704			0.914358
$436$		0			0
$437$	0.731303	+	1.26665i	0.0349830	+	0.0605923i
$438$		0			0
$439$	14.0252	−	24.2923i	0.669386	−	1.15941i	−0.308691	−	0.951163i	$-0.599891\pi$
$439$	14.0252	−	24.2923i	0.669386	−	1.15941i	0.978076	−	0.208247i	$-0.0667759\pi$
$440$		0			0
$441$	2.57485	−	6.50924i	0.122612	−	0.309964i
$442$		0			0
$443$	5.51040	−	9.54430i	0.261807	−	0.453463i	−0.704915	−	0.709292i	$-0.749015\pi$
$443$	5.51040	−	9.54430i	0.261807	−	0.453463i	0.966722	+	0.255828i	$0.0823482\pi$
$444$		0			0
$445$	30.9352	−	17.8605i	1.46647	−	0.846667i
$446$		0			0
$447$	2.02260			0.0956659
$448$		0			0
$449$	30.2270			1.42650			0.713250	−	0.700910i	$-0.247222\pi$
$449$	30.2270			1.42650			0.713250	+	0.700910i	$0.247222\pi$
$450$		0			0
$451$	−6.05128	+	3.49371i	−0.284944	+	0.164512i
$452$		0			0
$453$	−7.03404	+	12.1833i	−0.330488	+	0.572422i
$454$		0			0
$455$	3.47921	−	7.19996i	0.163108	−	0.337539i
$456$		0			0
$457$	−12.7386	+	22.0639i	−0.595887	+	1.03211i	0.397534	+	0.917587i	$0.369866\pi$
$457$	−12.7386	+	22.0639i	−0.595887	+	1.03211i	−0.993421	+	0.114519i	$0.963467\pi$
$458$		0			0
$459$	3.41250	+	5.91062i	0.159282	+	0.275884i
$460$		0			0
$461$	−27.9292			−1.30079			−0.650395	−	0.759596i	$-0.725397\pi$
$461$	−27.9292			−1.30079			−0.650395	+	0.759596i	$0.725397\pi$
$462$		0			0
$463$			19.4232i			0.902674i	0.892354	+	0.451337i	$0.149053\pi$
$463$			19.4232i			0.902674i	−0.892354	+	0.451337i	$0.850947\pi$
$464$		0			0
$465$	9.56493	−	5.52232i	0.443563	−	0.256091i
$466$		0			0
$467$	1.30760	+	0.754943i	0.0605085	+	0.0349346i	0.529949	−	0.848029i	$-0.322211\pi$
$467$	1.30760	+	0.754943i	0.0605085	+	0.0349346i	−0.469441	+	0.882964i	$0.655544\pi$
$468$		0			0
$469$	19.8021	+	29.1282i	0.914376	+	1.34501i
$470$		0			0
$471$	4.53344	+	2.61739i	0.208890	+	0.120603i
$472$		0			0
$473$	3.91326	+	6.77797i	0.179932	+	0.311651i
$474$		0			0
$475$		−	2.25541i		−	0.103485i
$476$		0			0
$477$		−	8.07845i		−	0.369887i
$478$		0			0
$479$	7.12030	+	12.3327i	0.325335	+	0.563496i	0.981580	−	0.191051i	$-0.0611897\pi$
$479$	7.12030	+	12.3327i	0.325335	+	0.563496i	−0.656245	+	0.754548i	$0.727856\pi$
$480$		0			0
$481$	−2.16166	−	1.24803i	−0.0985631	−	0.0569054i
$482$		0			0
$483$	5.66514	−	0.416908i	0.257773	−	0.0189700i
$484$		0			0
$485$	−9.07601	−	5.24004i	−0.412120	−	0.237938i
$486$		0			0
$487$	−6.40076	+	3.69548i	−0.290046	+	0.167458i	−0.637963	−	0.770067i	$-0.720223\pi$
$487$	−6.40076	+	3.69548i	−0.290046	+	0.167458i	0.347916	+	0.937526i	$0.386889\pi$
$488$		0			0
$489$		−	0.976425i		−	0.0441555i
$490$		0			0
$491$	−14.0578			−0.634420			−0.317210	−	0.948355i	$-0.602746\pi$
$491$	−14.0578			−0.634420			−0.317210	+	0.948355i	$0.602746\pi$
$492$		0			0
$493$	−22.5742	−	39.0996i	−1.01669	−	1.76096i
$494$		0			0
$495$	−8.39888	+	14.5473i	−0.377502	+	0.653852i
$496$		0			0
$497$	−0.210751	−	2.86378i	−0.00945346	−	0.128458i
$498$		0			0
$499$	13.4960	−	23.3757i	0.604162	−	1.04644i	−0.388021	−	0.921651i	$-0.626841\pi$
$499$	13.4960	−	23.3757i	0.604162	−	1.04644i	0.992183	−	0.124789i	$-0.0398255\pi$
$500$		0			0
$501$	1.80364	−	1.04133i	0.0805808	−	0.0465233i
$502$		0			0
$503$	3.15505			0.140677			0.0703384	−	0.997523i	$-0.477592\pi$
$503$	3.15505			0.140677			0.0703384	+	0.997523i	$0.477592\pi$
$504$		0			0
$505$	−7.22059			−0.321312
$506$		0			0
$507$	−10.3064	+	5.95042i	−0.457725	+	0.264267i
$508$		0			0
$509$	−10.8815	+	18.8473i	−0.482315	+	0.835394i	−0.999794	−	0.0203019i	$-0.993537\pi$
$509$	−10.8815	+	18.8473i	−0.482315	+	0.835394i	0.517479	+	0.855696i	$0.326871\pi$
$510$		0			0
$511$	12.3515	−	8.39689i	0.546399	−	0.371457i
$512$		0			0
$513$	0.340614	−	0.589961i	0.0150385	−	0.0260474i
$514$		0			0
$515$	6.66865	+	11.5504i	0.293856	+	0.508973i
$516$		0			0
$517$	−64.4060			−2.83257
$518$		0			0
$519$			21.3463i			0.936999i
$520$		0			0
$521$	−34.9828	+	20.1973i	−1.53262	+	0.884860i	−0.533383	+	0.845874i	$0.679080\pi$
$521$	−34.9828	+	20.1973i	−1.53262	+	0.884860i	−0.999240	+	0.0389867i	$0.987587\pi$
$522$		0			0
$523$	−25.4468	−	14.6917i	−1.11271	−	0.642424i	−0.173181	−	0.984890i	$-0.555405\pi$
$523$	−25.4468	−	14.6917i	−1.11271	−	0.642424i	−0.939530	+	0.342466i	$0.888738\pi$
$524$		0			0
$525$	−7.88697	−	3.81120i	−0.344216	−	0.166334i
$526$		0			0
$527$	−22.6445	−	13.0738i	−0.986410	−	0.569504i
$528$		0			0
$529$	−9.19517	−	15.9265i	−0.399790	−	0.692457i
$530$		0			0
$531$			7.87073i			0.341561i
$532$		0			0
$533$		−	1.25724i		−	0.0544570i
$534$		0			0
$535$	8.74866	+	15.1531i	0.378237	+	0.655126i
$536$		0			0
$537$	−6.01865	−	3.47487i	−0.259724	−	0.149952i
$538$		0			0
$539$	−25.3451	−	31.9571i	−1.09169	−	1.37649i
$540$		0			0
$541$	26.5848	+	15.3487i	1.14297	+	0.659893i	0.947164	−	0.320749i	$-0.103935\pi$
$541$	26.5848	+	15.3487i	1.14297	+	0.659893i	0.195805	+	0.980643i	$0.437268\pi$
$542$		0			0
$543$	−6.64777	+	3.83809i	−0.285283	+	0.164708i
$544$		0			0
$545$			41.9872i			1.79853i
$546$		0			0
$547$	15.7691			0.674240			0.337120	−	0.941462i	$-0.390547\pi$
$547$	15.7691			0.674240			0.337120	+	0.941462i	$0.390547\pi$
$548$		0			0
$549$	−1.63471	−	2.83140i	−0.0697678	−	0.120841i
$550$		0			0
$551$	−2.25322	+	3.90268i	−0.0959902	+	0.166260i
$552$		0			0
$553$	30.1561	+	14.5722i	1.28237	+	0.619674i
$554$		0			0
$555$	−3.43176	+	5.94398i	−0.145670	+	0.252308i
$556$		0			0
$557$	−19.2427	+	11.1098i	−0.815340	+	0.470737i	−0.848807	−	0.528703i	$-0.822679\pi$
$557$	−19.2427	+	11.1098i	−0.815340	+	0.470737i	0.0334668	+	0.999440i	$0.489345\pi$
$558$		0			0
$559$	−1.40822			−0.0595612
$560$		0			0
$561$	39.7679			1.67900
$562$		0			0
$563$	−20.7809	+	11.9978i	−0.875809	+	0.505648i	−0.869274	−	0.494330i	$-0.835413\pi$
$563$	−20.7809	+	11.9978i	−0.875809	+	0.505648i	−0.00653450	+	0.999979i	$0.502080\pi$
$564$		0			0
$565$	−5.51885	+	9.55893i	−0.232180	+	0.402147i
$566$		0			0
$567$	−1.48747	−	2.18802i	−0.0624680	−	0.0918881i
$568$		0			0
$569$	−0.631897	+	1.09448i	−0.0264905	+	0.0458829i	−0.878967	−	0.476883i	$-0.841767\pi$
$569$	−0.631897	+	1.09448i	−0.0264905	+	0.0458829i	0.852476	+	0.522766i	$0.175100\pi$
$570$		0			0
$571$	10.3555	+	17.9363i	0.433365	+	0.750611i	0.997161	−	0.0753037i	$-0.0239926\pi$
$571$	10.3555	+	17.9363i	0.433365	+	0.750611i	−0.563795	+	0.825915i	$0.690659\pi$
$572$		0			0
$573$	17.8099			0.744019
$574$		0			0
$575$		−	7.10831i		−	0.296437i
$576$		0			0
$577$	−27.2402	+	15.7271i	−1.13402	+	0.654728i	−0.944943	−	0.327234i	$-0.893884\pi$
$577$	−27.2402	+	15.7271i	−1.13402	+	0.654728i	−0.189079	+	0.981962i	$0.560550\pi$
$578$		0			0
$579$	11.9476	+	6.89797i	0.496527	+	0.286670i
$580$		0			0
$581$	−0.0936032	−	1.27192i	−0.00388332	−	0.0527683i
$582$		0			0
$583$	−40.7652	−	23.5358i	−1.68832	−	0.974752i
$584$		0			0
$585$	−1.51120	−	2.61747i	−0.0624804	−	0.108219i
$586$		0			0
$587$			5.93391i			0.244919i	0.992474	+	0.122459i	$0.0390781\pi$
$587$			5.93391i			0.244919i	−0.992474	+	0.122459i	$0.960922\pi$
$588$		0			0
$589$			2.60989i			0.107539i
$590$		0			0
$591$	0.565900	+	0.980167i	0.0232780	+	0.0403187i
$592$		0			0
$593$	−13.6001	−	7.85199i	−0.558487	−	0.322443i	0.194051	−	0.980991i	$-0.437837\pi$
$593$	−13.6001	−	7.85199i	−0.558487	−	0.322443i	−0.752538	+	0.658549i	$0.771171\pi$
$594$		0			0
$595$	3.82058	+	51.9158i	0.156628	+	2.12834i
$596$		0			0
$597$	7.38881	+	4.26593i	0.302404	+	0.174593i
$598$		0			0
$599$	−15.0452	+	8.68632i	−0.614728	+	0.354914i	−0.774814	−	0.632190i	$-0.782156\pi$
$599$	−15.0452	+	8.68632i	−0.614728	+	0.354914i	0.160085	+	0.987103i	$0.448823\pi$
$600$		0			0
$601$		−	43.6846i		−	1.78193i	−0.454069	−	0.890966i	$-0.650028\pi$
$601$		−	43.6846i		−	1.78193i	0.454069	−	0.890966i	$-0.349972\pi$
$602$		0			0
$603$	13.3126			0.542130
$604$		0			0
$605$	33.0830	+	57.3014i	1.34501	+	2.32963i
$606$		0			0
$607$	−9.60046	+	16.6285i	−0.389671	+	0.674929i	−0.992405	−	0.123012i	$-0.960745\pi$
$607$	−9.60046	+	16.6285i	−0.389671	+	0.674929i	0.602734	+	0.797942i	$0.294078\pi$
$608$		0			0
$609$	9.83986	+	14.4741i	0.398731	+	0.586519i
$610$		0			0
$611$	5.79424	−	10.0359i	0.234410	−	0.406010i
$612$		0			0
$613$	14.8672	−	8.58358i	0.600480	−	0.346688i	−0.168750	−	0.985659i	$-0.553973\pi$
$613$	14.8672	−	8.58358i	0.600480	−	0.346688i	0.769231	+	0.638971i	$0.220640\pi$
$614$		0			0
$615$	−3.45707			−0.139402
$616$		0			0
$617$	−16.8150			−0.676946			−0.338473	−	0.940976i	$-0.609910\pi$
$617$	−16.8150			−0.676946			−0.338473	+	0.940976i	$0.609910\pi$
$618$		0			0
$619$	30.1572	−	17.4113i	1.21212	−	0.699818i	0.248899	−	0.968529i	$-0.419931\pi$
$619$	30.1572	−	17.4113i	1.21212	−	0.699818i	0.963221	+	0.268712i	$0.0865979\pi$
$620$		0			0
$621$	1.07351	−	1.85937i	0.0430783	−	0.0746138i
$622$		0			0
$623$	29.5175	+	14.2636i	1.18259	+	0.571461i
$624$		0			0
$625$	15.2963	−	26.4940i	0.611852	−	1.05976i
$626$		0			0
$627$	−1.98469	−	3.43759i	−0.0792610	−	0.137284i
$628$		0			0
$629$	16.2491			0.647892
$630$		0			0
$631$		−	11.8869i		−	0.473210i	−0.971606	−	0.236605i	$-0.923965\pi$
$631$		−	11.8869i		−	0.473210i	0.971606	−	0.236605i	$-0.0760346\pi$
$632$		0			0
$633$	−18.3975	+	10.6218i	−0.731237	+	0.422180i
$634$		0			0
$635$	−1.37418	−	0.793381i	−0.0545325	−	0.0314844i
$636$		0			0
$637$	7.25980	−	1.07434i	0.287644	−	0.0425670i
$638$		0			0
$639$	−0.939926	−	0.542667i	−0.0371829	−	0.0214676i
$640$		0			0
$641$	18.4447	+	31.9472i	0.728523	+	1.26184i	0.957507	+	0.288409i	$0.0931263\pi$
$641$	18.4447	+	31.9472i	0.728523	+	1.26184i	−0.228984	+	0.973430i	$0.573540\pi$
$642$		0			0
$643$		−	10.0475i		−	0.396235i	−0.980178	−	0.198117i	$-0.936517\pi$
$643$		−	10.0475i		−	0.396235i	0.980178	−	0.198117i	$-0.0634827\pi$
$644$		0			0
$645$			3.87222i			0.152469i
$646$		0			0
$647$	19.5824	+	33.9177i	0.769862	+	1.33344i	0.937637	+	0.347615i	$0.113008\pi$
$647$	19.5824	+	33.9177i	0.769862	+	1.33344i	−0.167775	+	0.985825i	$0.553658\pi$
$648$		0			0
$649$	39.7169	+	22.9306i	1.55903	+	0.900104i
$650$		0			0
$651$	9.12658	+	4.41021i	0.357699	+	0.172850i
$652$		0			0
$653$	−35.9422	−	20.7512i	−1.40653	−	0.812058i	−0.411475	−	0.911421i	$-0.634986\pi$
$653$	−35.9422	−	20.7512i	−1.40653	−	0.812058i	−0.995051	+	0.0993632i	$0.968319\pi$
$654$		0			0
$655$	7.00008	−	4.04150i	0.273516	−	0.157914i
$656$		0			0
$657$		−	5.64507i		−	0.220235i
$658$		0			0
$659$	35.4347			1.38034			0.690170	−	0.723647i	$-0.257536\pi$
$659$	35.4347			1.38034			0.690170	+	0.723647i	$0.257536\pi$
$660$		0			0
$661$	−11.8165	−	20.4668i	−0.459610	−	0.796067i	0.539330	−	0.842094i	$-0.318677\pi$
$661$	−11.8165	−	20.4668i	−0.459610	−	0.796067i	−0.998940	+	0.0460268i	$0.985344\pi$
$662$		0			0
$663$	−3.57769	+	6.19674i	−0.138946	+	0.240662i
$664$		0			0
$665$	4.29700	−	2.92121i	0.166630	−	0.113280i
$666$		0			0
$667$	−7.10140	+	12.3000i	−0.274967	+	0.476257i
$668$		0			0
$669$	−2.70379	+	1.56104i	−0.104535	+	0.0603531i
$670$		0			0
$671$	−19.0503			−0.735428
$672$		0			0
$673$	8.69720			0.335253			0.167626	−	0.985851i	$-0.446390\pi$
$673$	8.69720			0.335253			0.167626	+	0.985851i	$0.446390\pi$
$674$		0			0
$675$	−2.86723	+	1.65540i	−0.110360	+	0.0637163i
$676$		0			0
$677$	5.45947	−	9.45608i	0.209825	−	0.363427i	−0.741835	−	0.670583i	$-0.766044\pi$
$677$	5.45947	−	9.45608i	0.209825	−	0.363427i	0.951659	+	0.307156i	$0.0993774\pi$
$678$		0			0
$679$	−0.705909	−	9.59223i	−0.0270903	−	0.368116i
$680$		0			0
$681$	−2.61337	+	4.52649i	−0.100145	+	0.173456i
$682$		0			0
$683$	18.2758	+	31.6547i	0.699305	+	1.21123i	0.968708	+	0.248204i	$0.0798405\pi$
$683$	18.2758	+	31.6547i	0.699305	+	1.21123i	−0.269402	+	0.963028i	$0.586826\pi$
$684$		0			0
$685$	−36.7936			−1.40581
$686$		0			0
$687$		−	28.4258i		−	1.08451i
$688$		0			0
$689$	7.33482	−	4.23476i	0.279434	−	0.161332i
$690$		0			0
$691$	4.59821	+	2.65478i	0.174924	+	0.100993i	0.584906	−	0.811101i	$-0.301131\pi$
$691$	4.59821	+	2.65478i	0.174924	+	0.100993i	−0.409981	+	0.912094i	$0.634465\pi$
$692$		0			0
$693$	−15.3747	+	1.13145i	−0.584036	+	0.0429803i
$694$		0			0
$695$	−15.2733	−	8.81806i	−0.579350	−	0.334488i
$696$		0			0
$697$	4.09222	+	7.08793i	0.155004	+	0.268475i
$698$		0			0
$699$			6.11941i			0.231457i
$700$		0			0
$701$			6.16681i			0.232917i	0.993196	+	0.116459i	$0.0371542\pi$
$701$			6.16681i			0.232917i	−0.993196	+	0.116459i	$0.962846\pi$
$702$		0			0
$703$	−0.810940	−	1.40459i	−0.0305852	−	0.0529751i
$704$		0			0
$705$	−27.5961	−	15.9326i	−1.03933	−	0.600057i
$706$		0			0
$707$	−3.72564	−	5.48028i	−0.140117	−	0.206107i
$708$		0			0
$709$	1.73062	+	0.999172i	0.0649947	+	0.0375247i	0.532145	−	0.846653i	$-0.321386\pi$
$709$	1.73062	+	0.999172i	0.0649947	+	0.0375247i	−0.467151	+	0.884178i	$0.654719\pi$
$710$		0			0
$711$	10.9630	−	6.32946i	0.411143	−	0.237373i
$712$		0			0
$713$			8.22554i			0.308049i
$714$		0			0
$715$	−17.6109			−0.658611
$716$		0			0
$717$	−4.41764	−	7.65158i	−0.164980	−	0.285753i
$718$		0			0
$719$	−6.72446	+	11.6471i	−0.250780	+	0.434364i	−0.963741	−	0.266840i	$-0.914020\pi$
$719$	−6.72446	+	11.6471i	−0.250780	+	0.434364i	0.712961	+	0.701204i	$0.247354\pi$
$720$		0			0
$721$	−5.32569	+	11.0211i	−0.198339	+	0.410447i
$722$		0			0
$723$	2.97772	−	5.15757i	0.110743	−	0.191812i
$724$		0			0
$725$	18.9672	−	10.9507i	0.704423	−	0.406699i
$726$		0			0
$727$	19.6532			0.728897			0.364448	−	0.931224i	$-0.381258\pi$
$727$	19.6532			0.728897			0.364448	+	0.931224i	$0.381258\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	7.93911	−	4.58365i	0.293639	−	0.169532i
$732$		0			0
$733$	−12.6139	+	21.8480i	−0.465907	+	0.806974i	−0.999242	−	0.0389298i	$-0.987605\pi$
$733$	−12.6139	+	21.8480i	−0.465907	+	0.806974i	0.533335	+	0.845904i	$0.320938\pi$
$734$		0			0
$735$	−2.95415	−	19.9625i	−0.108966	−	0.736328i
$736$		0			0
$737$	38.7849	−	67.1774i	1.42866	−	2.47451i
$738$		0			0
$739$	3.35478	+	5.81064i	0.123407	+	0.213748i	0.921109	−	0.389304i	$-0.127284\pi$
$739$	3.35478	+	5.81064i	0.123407	+	0.213748i	−0.797702	+	0.603052i	$0.793951\pi$
$740$		0			0
$741$	0.714206			0.0262370
$742$		0			0
$743$		−	26.0661i		−	0.956273i	−0.878286	−	0.478137i	$-0.841312\pi$
$743$		−	26.0661i		−	0.956273i	0.878286	−	0.478137i	$-0.158688\pi$
$744$		0			0
$745$	5.04967	−	2.91543i	0.185005	−	0.106813i
$746$		0			0
$747$	−0.417461	−	0.241021i	−0.0152741	−	0.00881850i
$748$		0			0
$749$	−6.98682	+	14.4587i	−0.255293	+	0.528308i
$750$		0			0
$751$	−4.94762	−	2.85651i	−0.180541	−	0.104236i	0.407006	−	0.913426i	$-0.366573\pi$
$751$	−4.94762	−	2.85651i	−0.180541	−	0.104236i	−0.587547	+	0.809190i	$0.699906\pi$
$752$		0			0
$753$	1.06977	+	1.85290i	0.0389847	+	0.0675235i
$754$		0			0
$755$			40.5561i			1.47599i
$756$		0			0
$757$			4.75364i			0.172774i	0.996262	+	0.0863869i	$0.0275321\pi$
$757$			4.75364i			0.172774i	−0.996262	+	0.0863869i	$0.972468\pi$
$758$		0			0
$759$	−6.25511	−	10.8342i	−0.227046	−	0.393255i
$760$		0			0
$761$	−23.6671	−	13.6642i	−0.857931	−	0.495327i	0.00538774	−	0.999985i	$-0.498285\pi$
$761$	−23.6671	−	13.6642i	−0.857931	−	0.495327i	−0.863319	+	0.504659i	$0.831618\pi$
$762$		0			0
$763$	−31.8674	+	21.6643i	−1.15368	+	0.784300i
$764$		0			0
$765$	17.0394	+	9.83770i	0.616061	+	0.355683i
$766$		0			0
$767$	−7.14622	+	4.12587i	−0.258035	+	0.148977i
$768$		0			0
$769$		−	22.7151i		−	0.819127i	−0.912282	−	0.409564i	$-0.865681\pi$
$769$		−	22.7151i		−	0.819127i	0.912282	−	0.409564i	$-0.134319\pi$
$770$		0			0
$771$	−19.2869			−0.694602
$772$		0			0
$773$	−9.05937	−	15.6913i	−0.325843	−	0.564376i	0.655840	−	0.754900i	$-0.272315\pi$
$773$	−9.05937	−	15.6913i	−0.325843	−	0.564376i	−0.981683	+	0.190524i	$0.938981\pi$
$774$		0			0
$775$	6.34209	−	10.9848i	0.227814	−	0.394586i
$776$		0			0
$777$	−6.28206	+	0.462308i	−0.225368	+	0.0165852i
$778$		0			0
$779$	0.408460	−	0.707474i	0.0146346	−	0.0253479i
$780$		0			0
$781$	−5.47676	+	3.16201i	−0.195974	+	0.113146i
$782$		0			0
$783$	6.61515			0.236406
$784$		0			0
$785$	15.0910			0.538622
$786$		0			0
$787$	−4.25358	+	2.45581i	−0.151624	+	0.0875400i	−0.573892	−	0.818931i	$-0.694567\pi$
$787$	−4.25358	+	2.45581i	−0.151624	+	0.0875400i	0.422269	+	0.906471i	$0.361234\pi$
$788$		0			0
$789$	−12.1671	+	21.0740i	−0.433159	+	0.750254i
$790$		0			0
$791$	−10.1026	+	0.743469i	−0.359207	+	0.0264347i
$792$		0			0
$793$	1.71385	−	2.96847i	0.0608604	−	0.105413i
$794$		0			0
$795$	−11.6445	−	20.1688i	−0.412987	−	0.715314i
$796$		0			0
$797$	23.8384			0.844398			0.422199	−	0.906503i	$-0.361258\pi$
$797$	23.8384			0.844398			0.422199	+	0.906503i	$0.361258\pi$
$798$		0			0
$799$			75.4394i			2.66885i
$800$		0			0
$801$	10.7308	−	6.19543i	0.379154	−	0.218905i
$802$		0			0
$803$	−28.4859	−	16.4464i	−1.00525	−	0.580379i
$804$		0			0
$805$	13.5427	−	9.20672i	0.477319	−	0.324494i
$806$		0			0
$807$	18.1007	+	10.4505i	0.637176	+	0.367874i
$808$		0			0
$809$	0.597915	+	1.03562i	0.0210216	+	0.0364104i	0.876345	−	0.481684i	$-0.159975\pi$
$809$	0.597915	+	1.03562i	0.0210216	+	0.0364104i	−0.855323	+	0.518095i	$0.826641\pi$
$810$		0			0
$811$			6.44559i			0.226335i	0.993576	+	0.113168i	$0.0360997\pi$
$811$			6.44559i			0.226335i	−0.993576	+	0.113168i	$0.963900\pi$
$812$		0			0
$813$		−	19.9939i		−	0.701218i
$814$		0			0
$815$	−1.40744	−	2.43776i	−0.0493005	−	0.0853910i
$816$		0			0
$817$	−0.792433	−	0.457511i	−0.0277237	−	0.0160063i
$818$		0			0
$819$	1.20687	−	2.49752i	0.0421714	−	0.0872703i
$820$		0			0
$821$	−1.87701	−	1.08369i	−0.0655079	−	0.0378210i	0.466888	−	0.884316i	$-0.345375\pi$
$821$	−1.87701	−	1.08369i	−0.0655079	−	0.0378210i	−0.532396	+	0.846495i	$0.678708\pi$
$822$		0			0
$823$	−5.19529	+	2.99950i	−0.181096	+	0.104556i	−0.587808	−	0.809001i	$-0.700009\pi$
$823$	−5.19529	+	2.99950i	−0.181096	+	0.104556i	0.406711	+	0.913557i	$0.366675\pi$
$824$		0			0
$825$			19.2913i			0.671638i
$826$		0			0
$827$	−21.0143			−0.730738			−0.365369	−	0.930863i	$-0.619057\pi$
$827$	−21.0143			−0.730738			−0.365369	+	0.930863i	$0.619057\pi$
$828$		0			0
$829$	6.59891	+	11.4296i	0.229190	+	0.396968i	0.957568	−	0.288207i	$-0.0930591\pi$
$829$	6.59891	+	11.4296i	0.229190	+	0.396968i	−0.728379	+	0.685175i	$0.759726\pi$
$830$		0			0
$831$	−7.64600	+	13.2433i	−0.265237	+	0.459404i
$832$		0			0
$833$	−37.4317	+	29.6870i	−1.29693	+	1.02859i
$834$		0			0
$835$	3.00200	−	5.19962i	0.103889	−	0.179940i
$836$		0			0
$837$	3.31788	−	1.91558i	0.114683	−	0.0662121i
$838$		0			0
$839$	33.8661			1.16919			0.584594	−	0.811326i	$-0.301254\pi$
$839$	33.8661			1.16919			0.584594	+	0.811326i	$0.301254\pi$
$840$		0			0
$841$	−14.7602			−0.508973
$842$		0			0
$843$	4.84803	−	2.79901i	0.166975	−	0.0964031i
$844$		0			0
$845$	−17.1541	+	29.7118i	−0.590120	+	1.02212i
$846$		0			0
$847$	−26.4206	+	54.6753i	−0.907822	+	1.87867i
$848$		0			0
$849$	−5.61710	+	9.72911i	−0.192778	+	0.333902i
$850$		0			0
$851$	−2.55582	−	4.42681i	−0.0876124	−	0.151749i
$852$		0			0
$853$	50.0832			1.71482			0.857408	−	0.514638i	$-0.172074\pi$
$853$	50.0832			1.71482			0.857408	+	0.514638i	$0.172074\pi$
$854$		0			0
$855$		−	1.96388i		−	0.0671632i
$856$		0			0
$857$	42.6628	−	24.6314i	1.45734	−	0.841393i	0.458455	−	0.888717i	$-0.348403\pi$
$857$	42.6628	−	24.6314i	1.45734	−	0.841393i	0.998880	+	0.0473246i	$0.0150695\pi$
$858$		0			0
$859$	3.38667	+	1.95530i	0.115552	+	0.0667139i	0.556662	−	0.830739i	$-0.312082\pi$
$859$	3.38667	+	1.95530i	0.115552	+	0.0667139i	−0.441110	+	0.897453i	$0.645415\pi$
$860$		0			0
$861$	−1.78376	−	2.62384i	−0.0607903	−	0.0894203i
$862$		0			0
$863$	−37.4230	−	21.6062i	−1.27390	−	0.735484i	−0.298176	−	0.954511i	$-0.596378\pi$
$863$	−37.4230	−	21.6062i	−1.27390	−	0.735484i	−0.975719	+	0.219027i	$0.929712\pi$
$864$		0			0
$865$	30.7690	+	53.2935i	1.04618	+	1.81203i
$866$		0			0
$867$		−	29.5806i		−	1.00461i
$868$		0			0
$869$		−	73.7611i		−	2.50217i
$870$		0			0
$871$	6.97851	+	12.0871i	0.236458	+	0.409557i
$872$		0			0
$873$	−3.14828	−	1.81766i	−0.106553	−	0.0615185i
$874$		0			0
$875$	12.8493	−	0.945604i	0.434386	−	0.0319673i
$876$		0			0
$877$	−18.3069	−	10.5695i	−0.618182	−	0.356907i	0.157979	−	0.987442i	$-0.449502\pi$
$877$	−18.3069	−	10.5695i	−0.618182	−	0.356907i	−0.776161	+	0.630535i	$0.782835\pi$
$878$		0			0
$879$	−15.3470	+	8.86060i	−0.517642	+	0.298860i
$880$		0			0
$881$		−	49.1167i		−	1.65478i	−0.561625	−	0.827392i	$-0.689823\pi$
$881$		−	49.1167i		−	1.65478i	0.561625	−	0.827392i	$-0.310177\pi$
$882$		0			0
$883$	−37.8457			−1.27361			−0.636804	−	0.771025i	$-0.719744\pi$
$883$	−37.8457			−1.27361			−0.636804	+	0.771025i	$0.719744\pi$
$884$		0			0
$885$	11.3450	+	19.6502i	0.381360	+	0.660534i
$886$		0			0
$887$	−8.97039	+	15.5372i	−0.301196	+	0.521687i	−0.976407	−	0.215937i	$-0.930719\pi$
$887$	−8.97039	+	15.5372i	−0.301196	+	0.521687i	0.675211	+	0.737625i	$0.264053\pi$
$888$		0			0
$889$	−0.106880	−	1.45233i	−0.00358464	−	0.0487097i
$890$		0			0
$891$	−2.91340	+	5.04616i	−0.0976026	+	0.169053i
$892$		0			0
$893$	6.52108	−	3.76495i	0.218220	−	0.125989i
$894$		0			0
$895$	−20.0350			−0.669697
$896$		0			0
$897$	2.25095			0.0751569
$898$		0			0
$899$	−21.9483	+	12.6718i	−0.732016	+	0.422629i
$900$		0			0
$901$	−27.5677	+	47.7487i	−0.918413	+	1.59074i
$902$		0			0
$903$	−2.93893	+	1.99797i	−0.0978016	+	0.0664881i
$904$		0			0
$905$	−11.0646	+	19.1645i	−0.367801	+	0.637049i
$906$		0			0
$907$	11.0887	+	19.2062i	0.368194	+	0.637730i	0.989283	−	0.146009i	$-0.0466430\pi$
$907$	11.0887	+	19.2062i	0.368194	+	0.637730i	−0.621089	+	0.783740i	$0.713310\pi$
$908$		0			0
$909$	−2.50468			−0.0830748
$910$		0			0
$911$		−	35.2495i		−	1.16787i	−0.811801	−	0.583934i	$-0.801513\pi$
$911$		−	35.2495i		−	1.16787i	0.811801	−	0.583934i	$-0.198487\pi$
$912$		0			0
$913$	−2.43246	+	1.40438i	−0.0805027	+	0.0464783i
$914$		0			0
$915$	−8.16250	−	4.71262i	−0.269844	−	0.155794i
$916$		0			0
$917$	6.67927	+	3.22760i	0.220569	+	0.106585i
$918$		0			0
$919$	15.1837	+	8.76632i	0.500864	+	0.289174i	0.729070	−	0.684439i	$-0.239953\pi$
$919$	15.1837	+	8.76632i	0.500864	+	0.289174i	−0.228206	+	0.973613i	$0.573286\pi$
$920$		0			0
$921$	−10.1862	−	17.6430i	−0.335647	−	0.581357i
$922$		0			0
$923$		−	1.13787i		−	0.0374535i
$924$		0			0
$925$			7.88239i			0.259171i
$926$		0			0
$927$	2.31322	+	4.00661i	0.0759761	+	0.131594i
$928$		0			0
$929$	−44.9106	−	25.9292i	−1.47347	−	0.850708i	−0.473916	−	0.880570i	$-0.657160\pi$
$929$	−44.9106	−	25.9292i	−1.47347	−	0.850708i	−0.999554	+	0.0298619i	$0.990493\pi$
$930$		0			0
$931$	4.43428	+	1.75406i	0.145328	+	0.0574870i
$932$		0			0
$933$	−25.0045	−	14.4363i	−0.818610	−	0.472625i
$934$		0			0
$935$	99.2852	−	57.3223i	3.24697	−	1.87464i
$936$		0			0
$937$			36.9665i			1.20764i	0.797120	+	0.603821i	$0.206356\pi$
$937$			36.9665i			1.20764i	−0.797120	+	0.603821i	$0.793644\pi$
$938$		0			0
$939$	−4.71947			−0.154014
$940$		0			0
$941$	−26.2751	−	45.5098i	−0.856544	−	1.48358i	−0.875206	−	0.483751i	$-0.839274\pi$
$941$	−26.2751	−	45.5098i	−0.856544	−	1.48358i	0.0186621	−	0.999826i	$-0.494059\pi$
$942$		0			0
$943$	1.28733	−	2.22973i	0.0419214	−	0.0726099i
$944$		0			0
$945$	−6.86751	−	3.31857i	−0.223400	−	0.107953i
$946$		0			0
$947$	13.4671	−	23.3256i	0.437621	−	0.757982i	−0.559885	−	0.828571i	$-0.689155\pi$
$947$	13.4671	−	23.3256i	0.437621	−	0.757982i	0.997505	+	0.0705889i	$0.0224879\pi$
$948$		0			0
$949$	5.12543	−	2.95917i	0.166379	−	0.0960588i
$950$		0			0
$951$	25.4437			0.825067
$952$		0			0
$953$	−31.5488			−1.02196			−0.510982	−	0.859591i	$-0.670718\pi$
$953$	−31.5488			−1.02196			−0.510982	+	0.859591i	$0.670718\pi$
$954$		0			0
$955$	44.4645	−	25.6716i	1.43884	−	0.830713i
$956$		0			0
$957$	19.2726	−	33.3811i	0.622994	−	1.07906i
$958$		0			0
$959$	−18.9846	−	27.9256i	−0.613043	−	0.901764i
$960$		0			0
$961$	8.16112	−	14.1355i	0.263262	−	0.455983i
$962$		0			0
$963$	3.03473	+	5.25631i	0.0977928	+	0.169382i
$964$		0			0
$965$	39.7716			1.28029
$966$		0			0
$967$		−	60.7635i		−	1.95402i	−0.213187	−	0.977011i	$-0.568384\pi$
$967$		−	60.7635i		−	1.95402i	0.213187	−	0.977011i	$-0.431616\pi$
$968$		0			0
$969$	−4.02648	+	2.32469i	−0.129349	+	0.0746799i
$970$		0			0
$971$	13.9382	+	8.04723i	0.447299	+	0.258248i	0.706689	−	0.707525i	$-0.250188\pi$
$971$	13.9382	+	8.04723i	0.447299	+	0.258248i	−0.259390	+	0.965773i	$0.583521\pi$
$972$		0			0
$973$	−1.18792	−	16.1420i	−0.0380830	−	0.517489i
$974$		0			0
$975$	−3.00603	−	1.73553i	−0.0962700	−	0.0555815i
$976$		0			0
$977$	16.3583	+	28.3334i	0.523349	+	0.906467i	0.999631	+	0.0271741i	$0.00865086\pi$
$977$	16.3583	+	28.3334i	0.523349	+	0.906467i	−0.476282	+	0.879293i	$0.658016\pi$
$978$		0			0
$979$		−	72.1991i		−	2.30749i
$980$		0			0
$981$			14.5645i			0.465008i
$982$		0			0
$983$	−18.5785	−	32.1789i	−0.592561	−	1.02635i	−0.993886	−	0.110410i	$-0.964783\pi$
$983$	−18.5785	−	32.1789i	−0.592561	−	1.02635i	0.401325	−	0.915936i	$-0.368550\pi$
$984$		0			0
$985$	2.82567	+	1.63140i	0.0900333	+	0.0519808i
$986$		0			0
$987$	−2.14636	−	29.1657i	−0.0683192	−	0.928354i
$988$		0			0
$989$	−2.49749	−	1.44193i	−0.0794156	−	0.0458506i
$990$		0			0
$991$	38.2912	−	22.1074i	1.21636	−	0.702266i	0.252223	−	0.967669i	$-0.418838\pi$
$991$	38.2912	−	22.1074i	1.21636	−	0.702266i	0.964137	+	0.265403i	$0.0855051\pi$
$992$		0			0
$993$			19.7186i			0.625750i
$994$		0			0
$995$	24.5960			0.779747
$996$		0			0
$997$	13.3432	+	23.1110i	0.422582	+	0.731934i	0.996191	−	0.0871953i	$-0.0277904\pi$
$997$	13.3432	+	23.1110i	0.422582	+	0.731934i	−0.573609	+	0.819129i	$0.694457\pi$
$998$		0			0
$999$	−1.19041	+	2.06185i	−0.0376628	+	0.0652339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bb.a.271.15		32
3.2	odd	2		2016.2.bs.c.271.3		32
4.3	odd	2		168.2.t.a.19.14	yes	32
7.2	even	3		4704.2.p.a.3919.26		32
7.3	odd	6	inner	672.2.bb.a.367.10		32
7.5	odd	6		4704.2.p.a.3919.29		32
8.3	odd	2	inner	672.2.bb.a.271.10		32
8.5	even	2		168.2.t.a.19.9	✓	32
12.11	even	2		504.2.bk.c.19.3		32
21.17	even	6		2016.2.bs.c.1711.14		32
24.5	odd	2		504.2.bk.c.19.8		32
24.11	even	2		2016.2.bs.c.271.14		32
28.3	even	6		168.2.t.a.115.9	yes	32
28.19	even	6		1176.2.p.a.979.5		32
28.23	odd	6		1176.2.p.a.979.6		32
56.3	even	6	inner	672.2.bb.a.367.15		32
56.5	odd	6		1176.2.p.a.979.8		32
56.19	even	6		4704.2.p.a.3919.25		32
56.37	even	6		1176.2.p.a.979.7		32
56.45	odd	6		168.2.t.a.115.14	yes	32
56.51	odd	6		4704.2.p.a.3919.30		32
84.59	odd	6		504.2.bk.c.451.8		32
168.59	odd	6		2016.2.bs.c.1711.3		32
168.101	even	6		504.2.bk.c.451.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.9	✓	32	8.5	even	2
168.2.t.a.19.14	yes	32	4.3	odd	2
168.2.t.a.115.9	yes	32	28.3	even	6
168.2.t.a.115.14	yes	32	56.45	odd	6
504.2.bk.c.19.3		32	12.11	even	2
504.2.bk.c.19.8		32	24.5	odd	2
504.2.bk.c.451.3		32	168.101	even	6
504.2.bk.c.451.8		32	84.59	odd	6
672.2.bb.a.271.10		32	8.3	odd	2	inner
672.2.bb.a.271.15		32	1.1	even	1	trivial
672.2.bb.a.367.10		32	7.3	odd	6	inner
672.2.bb.a.367.15		32	56.3	even	6	inner
1176.2.p.a.979.5		32	28.19	even	6
1176.2.p.a.979.6		32	28.23	odd	6
1176.2.p.a.979.7		32	56.37	even	6
1176.2.p.a.979.8		32	56.5	odd	6
2016.2.bs.c.271.3		32	3.2	odd	2
2016.2.bs.c.271.14		32	24.11	even	2
2016.2.bs.c.1711.3		32	168.59	odd	6
2016.2.bs.c.1711.14		32	21.17	even	6
4704.2.p.a.3919.25		32	56.19	even	6
4704.2.p.a.3919.26		32	7.2	even	3
4704.2.p.a.3919.29		32	7.5	odd	6
4704.2.p.a.3919.30		32	56.51	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(1.44142 - 2.49662i) q^{5} +(2.63862 - 0.194181i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{3} +(1.44142 - 2.49662i) q^{5} +(2.63862 - 0.194181i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.91340 - 5.04616i) q^{11} +1.04841 q^{13} -2.88284i q^{15} +(-5.91062 + 3.41250i) q^{17} +(0.589961 + 0.340614i) q^{19} +(2.18802 - 1.48747i) q^{21} +(1.85937 + 1.07351i) q^{23} +(-1.65540 - 2.86723i) q^{25} -1.00000i q^{27} +6.61515i q^{29} +(1.91558 + 3.31788i) q^{31} +(-5.04616 - 2.91340i) q^{33} +(3.31857 - 6.86751i) q^{35} +(-2.06185 - 1.19041i) q^{37} +(0.907949 - 0.524204i) q^{39} -1.19919i q^{41} -1.34319 q^{43} +(-1.44142 - 2.49662i) q^{45} +(5.52670 - 9.57253i) q^{47} +(6.92459 - 1.02474i) q^{49} +(-3.41250 + 5.91062i) q^{51} +(6.99615 - 4.03923i) q^{53} -16.7978 q^{55} +0.681229 q^{57} +(-6.81625 + 3.93537i) q^{59} +(1.63471 - 2.83140i) q^{61} +(1.15114 - 2.38220i) q^{63} +(1.51120 - 2.61747i) q^{65} +(6.65629 + 11.5290i) q^{67} +2.14701 q^{69} -1.08533i q^{71} +(4.88878 - 2.82254i) q^{73} +(-2.86723 - 1.65540i) q^{75} +(-8.66721 - 12.7491i) q^{77} +(10.9630 + 6.32946i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.482042i q^{83} +19.6754i q^{85} +(3.30757 + 5.72889i) q^{87} +(10.7308 + 6.19543i) q^{89} +(2.76635 - 0.203581i) q^{91} +(3.31788 + 1.91558i) q^{93} +(1.70077 - 0.981939i) q^{95} -3.63532i q^{97} -5.82680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^9	\( 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Introduction

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