LMFDB - Embedded newform 234.2.l.c.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(127,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("234.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.l (of order $6$, degree $2$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	234.127
Dual form			234.2.l.c.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.267949i q^{5} +(0.633975 + 0.366025i) q^{7} +1.00000i q^{8} +(0.133975 + 0.232051i) q^{10} +(4.09808 - 2.36603i) q^{11} +(2.59808 + 2.50000i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.13397 - 1.96410i) q^{17} +(-1.09808 - 0.633975i) q^{19} +(-0.232051 - 0.133975i) q^{20} +(-2.36603 + 4.09808i) q^{22} +(3.09808 + 5.36603i) q^{23} +4.92820 q^{25} +(-3.50000 - 0.866025i) q^{26} +(0.633975 - 0.366025i) q^{28} +(1.23205 + 2.13397i) q^{29} -5.46410i q^{31} +(0.866025 + 0.500000i) q^{32} +2.26795i q^{34} +(0.0980762 - 0.169873i) q^{35} +(-9.06218 + 5.23205i) q^{37} +1.26795 q^{38} +0.267949 q^{40} +(-9.86603 + 5.69615i) q^{41} +(3.83013 - 6.63397i) q^{43} -4.73205i q^{44} +(-5.36603 - 3.09808i) q^{46} -8.19615i q^{47} +(-3.23205 - 5.59808i) q^{49} +(-4.26795 + 2.46410i) q^{50} +(3.46410 - 1.00000i) q^{52} -0.464102 q^{53} +(-0.633975 - 1.09808i) q^{55} +(-0.366025 + 0.633975i) q^{56} +(-2.13397 - 1.23205i) q^{58} +(-6.92820 - 4.00000i) q^{59} +(-0.598076 + 1.03590i) q^{61} +(2.73205 + 4.73205i) q^{62} -1.00000 q^{64} +(0.669873 - 0.696152i) q^{65} +(-9.63397 + 5.56218i) q^{67} +(-1.13397 - 1.96410i) q^{68} +0.196152i q^{70} +(1.09808 + 0.633975i) q^{71} +9.73205i q^{73} +(5.23205 - 9.06218i) q^{74} +(-1.09808 + 0.633975i) q^{76} +3.46410 q^{77} -9.46410 q^{79} +(-0.232051 + 0.133975i) q^{80} +(5.69615 - 9.86603i) q^{82} -10.1962i q^{83} +(-0.526279 - 0.303848i) q^{85} +7.66025i q^{86} +(2.36603 + 4.09808i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(0.732051 + 2.53590i) q^{91} +6.19615 q^{92} +(4.09808 + 7.09808i) q^{94} +(-0.169873 + 0.294229i) q^{95} +(5.19615 + 3.00000i) q^{97} +(5.59808 + 3.23205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 6 q^{7} + 4 q^{10} + 6 q^{11} + 4 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 2 q^{23} - 8 q^{25} - 14 q^{26} + 6 q^{28} - 2 q^{29} - 10 q^{35} - 12 q^{37} + 12 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^4 + 6 * q^7 + 4 * q^10 + 6 * q^11 + 4 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 2 * q^23 - 8 * q^25 - 14 * q^26 + 6 * q^28 - 2 * q^29 - 10 * q^35 - 12 * q^37 + 12 * q^38 + 8 * q^40 - 36 * q^41 - 2 * q^43 - 18 * q^46 - 6 * q^49 - 24 * q^50 + 12 * q^53 - 6 * q^55 + 2 * q^56 - 12 * q^58 + 8 * q^61 + 4 * q^62 - 4 * q^64 + 20 * q^65 - 42 * q^67 - 8 * q^68 - 6 * q^71 + 14 * q^74 + 6 * q^76 - 24 * q^79 + 6 * q^80 + 2 * q^82 + 36 * q^85 + 6 * q^88 + 12 * q^89 - 4 * q^91 + 4 * q^92 + 6 * q^94 - 18 * q^95 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	0.267949i		−	0.119831i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$		−	0.267949i		−	0.119831i	0.998203	−	0.0599153i	$-0.0190830\pi$
$6$		0			0
$7$	0.633975	+	0.366025i	0.239620	+	0.138345i	0.615002	−	0.788526i	$-0.289155\pi$
$7$	0.633975	+	0.366025i	0.239620	+	0.138345i	−0.375382	+	0.926870i	$0.622489\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.133975	+	0.232051i	0.0423665	+	0.0733809i
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.267421	−	0.963580i	$-0.413828\pi$
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.968195	+	0.250196i	$0.0804951\pi$
$12$		0			0
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$	−0.732051			−0.195649
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.13397	−	1.96410i	0.275029	−	0.476365i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	1.13397	−	1.96410i	0.275029	−	0.476365i	0.970143	+	0.242536i	$0.0779791\pi$
$18$		0			0
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	0.368725	−	0.929538i	$-0.379794\pi$
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	−0.620641	+	0.784095i	$0.713128\pi$
$20$	−0.232051	−	0.133975i	−0.0518881	−	0.0299576i
$21$		0			0
$22$	−2.36603	+	4.09808i	−0.504438	+	0.873713i
$23$	3.09808	+	5.36603i	0.645994	+	1.11889i	0.984071	+	0.177775i	$0.0568901\pi$
$23$	3.09808	+	5.36603i	0.645994	+	1.11889i	−0.338078	+	0.941118i	$0.609777\pi$
$24$		0			0
$25$	4.92820			0.985641
$26$	−3.50000	−	0.866025i	−0.686406	−	0.169842i
$27$		0			0
$28$	0.633975	−	0.366025i	0.119810	−	0.0691723i
$29$	1.23205	+	2.13397i	0.228786	+	0.396269i	0.957449	−	0.288604i	$-0.0931910\pi$
$29$	1.23205	+	2.13397i	0.228786	+	0.396269i	−0.728663	+	0.684873i	$0.759858\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			2.26795i			0.388950i
$35$	0.0980762	−	0.169873i	0.0165779	−	0.0287138i
$36$		0			0
$37$	−9.06218	+	5.23205i	−1.48981	+	0.860144i	−0.999932	−	0.0116456i	$-0.996293\pi$
$37$	−9.06218	+	5.23205i	−1.48981	+	0.860144i	−0.489881	+	0.871789i	$0.662960\pi$
$38$	1.26795			0.205689
$39$		0			0
$40$	0.267949			0.0423665
$41$	−9.86603	+	5.69615i	−1.54081	+	0.889590i	−0.542027	+	0.840361i	$0.682343\pi$
$41$	−9.86603	+	5.69615i	−1.54081	+	0.889590i	−0.998788	+	0.0492283i	$0.984324\pi$
$42$		0			0
$43$	3.83013	−	6.63397i	0.584089	−	1.01167i	−0.410899	−	0.911681i	$-0.634785\pi$
$43$	3.83013	−	6.63397i	0.584089	−	1.01167i	0.994988	−	0.0999910i	$-0.0318814\pi$
$44$		−	4.73205i		−	0.713384i
$45$		0			0
$46$	−5.36603	−	3.09808i	−0.791177	−	0.456786i
$47$		−	8.19615i		−	1.19553i	−0.801671	−	0.597766i	$-0.796055\pi$
$47$		−	8.19615i		−	1.19553i	0.801671	−	0.597766i	$-0.203945\pi$
$48$		0			0
$49$	−3.23205	−	5.59808i	−0.461722	−	0.799725i
$50$	−4.26795	+	2.46410i	−0.603579	+	0.348477i
$51$		0			0
$52$	3.46410	−	1.00000i	0.480384	−	0.138675i
$53$	−0.464102			−0.0637493			−0.0318746	−	0.999492i	$-0.510148\pi$
$53$	−0.464102			−0.0637493			−0.0318746	+	0.999492i	$0.510148\pi$
$54$		0			0
$55$	−0.633975	−	1.09808i	−0.0854851	−	0.148065i
$56$	−0.366025	+	0.633975i	−0.0489122	+	0.0847184i
$57$		0			0
$58$	−2.13397	−	1.23205i	−0.280205	−	0.161776i
$59$	−6.92820	−	4.00000i	−0.901975	−	0.520756i	−0.0241347	−	0.999709i	$-0.507683\pi$
$59$	−6.92820	−	4.00000i	−0.901975	−	0.520756i	−0.877841	+	0.478953i	$0.841016\pi$
$60$		0			0
$61$	−0.598076	+	1.03590i	−0.0765758	+	0.132633i	−0.901770	−	0.432215i	$-0.857732\pi$
$61$	−0.598076	+	1.03590i	−0.0765758	+	0.132633i	0.825195	+	0.564848i	$0.191065\pi$
$62$	2.73205	+	4.73205i	0.346971	+	0.600971i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.669873	−	0.696152i	0.0830875	−	0.0863471i
$66$		0			0
$67$	−9.63397	+	5.56218i	−1.17698	+	0.679528i	−0.955313	−	0.295595i	$-0.904482\pi$
$67$	−9.63397	+	5.56218i	−1.17698	+	0.679528i	−0.221664	+	0.975123i	$0.571149\pi$
$68$	−1.13397	−	1.96410i	−0.137515	−	0.238182i
$69$		0			0
$70$			0.196152i			0.0234447i
$71$	1.09808	+	0.633975i	0.130318	+	0.0752389i	0.563742	−	0.825951i	$-0.309361\pi$
$71$	1.09808	+	0.633975i	0.130318	+	0.0752389i	−0.433424	+	0.901190i	$0.642695\pi$
$72$		0			0
$73$			9.73205i			1.13905i	0.821974	+	0.569525i	$0.192873\pi$
$73$			9.73205i			1.13905i	−0.821974	+	0.569525i	$0.807127\pi$
$74$	5.23205	−	9.06218i	0.608214	−	1.05346i
$75$		0			0
$76$	−1.09808	+	0.633975i	−0.125958	+	0.0727219i
$77$	3.46410			0.394771
$78$		0			0
$79$	−9.46410			−1.06479			−0.532397	−	0.846495i	$-0.678709\pi$
$79$	−9.46410			−1.06479			−0.532397	+	0.846495i	$0.678709\pi$
$80$	−0.232051	+	0.133975i	−0.0259441	+	0.0149788i
$81$		0			0
$82$	5.69615	−	9.86603i	0.629035	−	1.08952i
$83$		−	10.1962i		−	1.11917i	−0.828772	−	0.559587i	$-0.810960\pi$
$83$		−	10.1962i		−	1.11917i	0.828772	−	0.559587i	$-0.189040\pi$
$84$		0			0
$85$	−0.526279	−	0.303848i	−0.0570830	−	0.0329569i
$86$			7.66025i			0.826026i
$87$		0			0
$88$	2.36603	+	4.09808i	0.252219	+	0.436856i
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	−0.611859	−	0.790967i	$-0.709578\pi$
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	0.379068	+	0.925369i	$0.376245\pi$
$90$		0			0
$91$	0.732051	+	2.53590i	0.0767398	+	0.265834i
$92$	6.19615			0.645994
$93$		0			0
$94$	4.09808	+	7.09808i	0.422684	+	0.732111i
$95$	−0.169873	+	0.294229i	−0.0174286	+	0.0301872i
$96$		0			0
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	0.740034	−	0.672569i	$-0.234809\pi$
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	−0.212445	+	0.977173i	$0.568143\pi$
$98$	5.59808	+	3.23205i	0.565491	+	0.326486i
$99$		0			0
$100$	2.46410	−	4.26795i	0.246410	−	0.426795i
$101$	5.96410	+	10.3301i	0.593450	+	1.02789i	0.993764	+	0.111508i	$0.0355680\pi$
$101$	5.96410	+	10.3301i	0.593450	+	1.02789i	−0.400313	+	0.916378i	$0.631099\pi$
$102$		0			0
$103$	18.7321			1.84572			0.922862	−	0.385131i	$-0.125844\pi$
$103$	18.7321			1.84572			0.922862	+	0.385131i	$0.125844\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$		0			0
$106$	0.401924	−	0.232051i	0.0390383	−	0.0225388i
$107$	−0.0980762	−	0.169873i	−0.00948139	−	0.0164222i	0.861246	−	0.508189i	$-0.169685\pi$
$107$	−0.0980762	−	0.169873i	−0.00948139	−	0.0164222i	−0.870727	+	0.491766i	$0.836351\pi$
$108$		0			0
$109$		−	5.46410i		−	0.523366i	−0.965154	−	0.261683i	$-0.915723\pi$
$109$		−	5.46410i		−	0.523366i	0.965154	−	0.261683i	$-0.0842775\pi$
$110$	1.09808	+	0.633975i	0.104697	+	0.0604471i
$111$		0			0
$112$		−	0.732051i		−	0.0691723i
$113$	−9.33013	+	16.1603i	−0.877705	+	1.52023i	−0.0238510	+	0.999716i	$0.507593\pi$
$113$	−9.33013	+	16.1603i	−0.877705	+	1.52023i	−0.853854	+	0.520513i	$0.825741\pi$
$114$		0			0
$115$	1.43782	−	0.830127i	0.134078	−	0.0774097i
$116$	2.46410			0.228786
$117$		0			0
$118$	8.00000			0.736460
$119$	1.43782	−	0.830127i	0.131805	−	0.0760976i
$120$		0			0
$121$	5.69615	−	9.86603i	0.517832	−	0.896911i
$122$		−	1.19615i		−	0.108295i
$123$		0			0
$124$	−4.73205	−	2.73205i	−0.424951	−	0.245345i
$125$		−	2.66025i		−	0.237940i
$126$		0			0
$127$	8.92820	+	15.4641i	0.792250	+	1.37222i	0.924571	+	0.381010i	$0.124424\pi$
$127$	8.92820	+	15.4641i	0.792250	+	1.37222i	−0.132321	+	0.991207i	$0.542243\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−0.232051	+	0.937822i	−0.0203522	+	0.0822524i
$131$	−13.4641			−1.17636			−0.588182	−	0.808729i	$-0.700156\pi$
$131$	−13.4641			−1.17636			−0.588182	+	0.808729i	$0.700156\pi$
$132$		0			0
$133$	−0.464102	−	0.803848i	−0.0402427	−	0.0697024i
$134$	5.56218	−	9.63397i	0.480499	−	0.832249i
$135$		0			0
$136$	1.96410	+	1.13397i	0.168420	+	0.0972375i
$137$	1.66987	+	0.964102i	0.142667	+	0.0823688i	0.569634	−	0.821898i	$-0.307085\pi$
$137$	1.66987	+	0.964102i	0.142667	+	0.0823688i	−0.426968	+	0.904267i	$0.640418\pi$
$138$		0			0
$139$	4.92820	−	8.53590i	0.418005	−	0.724005i	−0.577734	−	0.816225i	$-0.696063\pi$
$139$	4.92820	−	8.53590i	0.418005	−	0.724005i	0.995739	+	0.0922197i	$0.0293962\pi$
$140$	−0.0980762	−	0.169873i	−0.00828895	−	0.0143569i
$141$		0			0
$142$	−1.26795			−0.106404
$143$	16.5622	+	4.09808i	1.38500	+	0.342698i
$144$		0			0
$145$	0.571797	−	0.330127i	0.0474851	−	0.0274156i
$146$	−4.86603	−	8.42820i	−0.402715	−	0.697523i
$147$		0			0
$148$			10.4641i			0.860144i
$149$	2.42820	+	1.40192i	0.198926	+	0.114850i	0.596154	−	0.802870i	$-0.296695\pi$
$149$	2.42820	+	1.40192i	0.198926	+	0.114850i	−0.397228	+	0.917720i	$0.630028\pi$
$150$		0			0
$151$		−	3.26795i		−	0.265942i	−0.991120	−	0.132971i	$-0.957548\pi$
$151$		−	3.26795i		−	0.265942i	0.991120	−	0.132971i	$-0.0424517\pi$
$152$	0.633975	−	1.09808i	0.0514221	−	0.0890657i
$153$		0			0
$154$	−3.00000	+	1.73205i	−0.241747	+	0.139573i
$155$	−1.46410			−0.117599
$156$		0			0
$157$	−23.5885			−1.88256			−0.941282	−	0.337622i	$-0.890378\pi$
$157$	−23.5885			−1.88256			−0.941282	+	0.337622i	$0.890378\pi$
$158$	8.19615	−	4.73205i	0.652051	−	0.376462i
$159$		0			0
$160$	0.133975	−	0.232051i	0.0105916	−	0.0183452i
$161$			4.53590i			0.357479i
$162$		0			0
$163$	−5.66025	−	3.26795i	−0.443345	−	0.255966i	0.261670	−	0.965157i	$-0.415727\pi$
$163$	−5.66025	−	3.26795i	−0.443345	−	0.255966i	−0.705016	+	0.709192i	$0.749060\pi$
$164$			11.3923i			0.889590i
$165$		0			0
$166$	5.09808	+	8.83013i	0.395687	+	0.685351i
$167$	−2.19615	+	1.26795i	−0.169943	+	0.0981169i	−0.582559	−	0.812788i	$-0.697949\pi$
$167$	−2.19615	+	1.26795i	−0.169943	+	0.0981169i	0.412616	+	0.910905i	$0.364615\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	0.607695			0.0466081
$171$		0			0
$172$	−3.83013	−	6.63397i	−0.292044	−	0.505836i
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	−0.365755	−	0.930711i	$-0.619189\pi$
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	0.988897	−	0.148602i	$-0.0474774\pi$
$174$		0			0
$175$	3.12436	+	1.80385i	0.236179	+	0.136358i
$176$	−4.09808	−	2.36603i	−0.308904	−	0.178346i
$177$		0			0
$178$	1.26795	−	2.19615i	0.0950368	−	0.164609i
$179$	−11.0263	−	19.0981i	−0.824143	−	1.42746i	−0.902573	−	0.430538i	$-0.858324\pi$
$179$	−11.0263	−	19.0981i	−0.824143	−	1.42746i	0.0784298	−	0.996920i	$-0.475009\pi$
$180$		0			0
$181$	−8.80385			−0.654385			−0.327192	−	0.944958i	$-0.606103\pi$
$181$	−8.80385			−0.654385			−0.327192	+	0.944958i	$0.606103\pi$
$182$	−1.90192	−	1.83013i	−0.140980	−	0.135658i
$183$		0			0
$184$	−5.36603	+	3.09808i	−0.395589	+	0.228393i
$185$	1.40192	+	2.42820i	0.103071	+	0.178525i
$186$		0			0
$187$		−	10.7321i		−	0.784805i
$188$	−7.09808	−	4.09808i	−0.517680	−	0.298883i
$189$		0			0
$190$		−	0.339746i		−	0.0246478i
$191$	3.46410	−	6.00000i	0.250654	−	0.434145i	−0.713052	−	0.701111i	$-0.752688\pi$
$191$	3.46410	−	6.00000i	0.250654	−	0.434145i	0.963706	+	0.266966i	$0.0860212\pi$
$192$		0			0
$193$	7.16025	−	4.13397i	0.515406	−	0.297570i	−0.219647	−	0.975579i	$-0.570490\pi$
$193$	7.16025	−	4.13397i	0.515406	−	0.297570i	0.735053	+	0.678009i	$0.237157\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	−6.46410			−0.461722
$197$	−8.53590	+	4.92820i	−0.608158	+	0.351120i	−0.772244	−	0.635326i	$-0.780866\pi$
$197$	−8.53590	+	4.92820i	−0.608158	+	0.351120i	0.164086	+	0.986446i	$0.447532\pi$
$198$		0			0
$199$	−1.90192	+	3.29423i	−0.134824	+	0.233522i	−0.925530	−	0.378674i	$-0.876380\pi$
$199$	−1.90192	+	3.29423i	−0.134824	+	0.233522i	0.790706	+	0.612196i	$0.209714\pi$
$200$			4.92820i			0.348477i
$201$		0			0
$202$	−10.3301	−	5.96410i	−0.726825	−	0.419633i
$203$			1.80385i			0.126605i
$204$		0			0
$205$	1.52628	+	2.64359i	0.106600	+	0.184637i
$206$	−16.2224	+	9.36603i	−1.13027	+	0.652562i
$207$		0			0
$208$	0.866025	−	3.50000i	0.0600481	−	0.242681i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	2.19615	+	3.80385i	0.151189	+	0.261868i	0.931665	−	0.363319i	$-0.118356\pi$
$211$	2.19615	+	3.80385i	0.151189	+	0.261868i	−0.780476	+	0.625186i	$0.785023\pi$
$212$	−0.232051	+	0.401924i	−0.0159373	+	0.0276042i
$213$		0			0
$214$	0.169873	+	0.0980762i	0.0116123	+	0.00670435i
$215$	−1.77757	−	1.02628i	−0.121229	−	0.0699917i
$216$		0			0
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$	2.73205	+	4.73205i	0.185038	+	0.320495i
$219$		0			0
$220$	−1.26795			−0.0854851
$221$	7.85641	−	2.26795i	0.528479	−	0.152559i
$222$		0			0
$223$	−11.3205	+	6.53590i	−0.758077	+	0.437676i	−0.828605	−	0.559834i	$-0.810865\pi$
$223$	−11.3205	+	6.53590i	−0.758077	+	0.437676i	0.0705277	+	0.997510i	$0.477532\pi$
$224$	0.366025	+	0.633975i	0.0244561	+	0.0423592i
$225$		0			0
$226$		−	18.6603i		−	1.24126i
$227$	−1.56218	−	0.901924i	−0.103685	−	0.0598628i	0.447261	−	0.894404i	$-0.352400\pi$
$227$	−1.56218	−	0.901924i	−0.103685	−	0.0598628i	−0.550946	+	0.834541i	$0.685733\pi$
$228$		0			0
$229$		−	15.8564i		−	1.04782i	−0.851773	−	0.523910i	$-0.824473\pi$
$229$		−	15.8564i		−	1.04782i	0.851773	−	0.523910i	$-0.175527\pi$
$230$	−0.830127	+	1.43782i	−0.0547370	+	0.0948072i
$231$		0			0
$232$	−2.13397	+	1.23205i	−0.140102	+	0.0808881i
$233$	19.8564			1.30084			0.650418	−	0.759576i	$-0.274594\pi$
$233$	19.8564			1.30084			0.650418	+	0.759576i	$0.274594\pi$
$234$		0			0
$235$	−2.19615			−0.143261
$236$	−6.92820	+	4.00000i	−0.450988	+	0.260378i
$237$		0			0
$238$	−0.830127	+	1.43782i	−0.0538091	+	0.0932002i
$239$			9.66025i			0.624870i	0.949939	+	0.312435i	$0.101145\pi$
$239$			9.66025i			0.624870i	−0.949939	+	0.312435i	$0.898855\pi$
$240$		0			0
$241$	−15.2321	−	8.79423i	−0.981183	−	0.566486i	−0.0785557	−	0.996910i	$-0.525031\pi$
$241$	−15.2321	−	8.79423i	−0.981183	−	0.566486i	−0.902627	+	0.430424i	$0.858364\pi$
$242$			11.3923i			0.732325i
$243$		0			0
$244$	0.598076	+	1.03590i	0.0382879	+	0.0663166i
$245$	−1.50000	+	0.866025i	−0.0958315	+	0.0553283i
$246$		0			0
$247$	−1.26795	−	4.39230i	−0.0806777	−	0.279476i
$248$	5.46410			0.346971
$249$		0			0
$250$	1.33013	+	2.30385i	0.0841246	+	0.145708i
$251$	−3.26795	+	5.66025i	−0.206271	+	0.357272i	−0.950537	−	0.310611i	$-0.899466\pi$
$251$	−3.26795	+	5.66025i	−0.206271	+	0.357272i	0.744266	+	0.667883i	$0.232800\pi$
$252$		0			0
$253$	25.3923	+	14.6603i	1.59640	+	0.921682i
$254$	−15.4641	−	8.92820i	−0.970304	−	0.560205i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.3301	−	23.0885i	−0.831510	−	1.44022i	−0.896840	−	0.442355i	$-0.854143\pi$
$257$	−13.3301	−	23.0885i	−0.831510	−	1.44022i	0.0653297	−	0.997864i	$-0.479190\pi$
$258$		0			0
$259$	−7.66025			−0.475985
$260$	−0.267949	−	0.928203i	−0.0166175	−	0.0575647i
$261$		0			0
$262$	11.6603	−	6.73205i	0.720373	−	0.415907i
$263$	14.0263	+	24.2942i	0.864897	+	1.49805i	0.867149	+	0.498049i	$0.165950\pi$
$263$	14.0263	+	24.2942i	0.864897	+	1.49805i	−0.00225153	+	0.999997i	$0.500717\pi$
$264$		0			0
$265$			0.124356i			0.00763911i
$266$	0.803848	+	0.464102i	0.0492871	+	0.0284559i
$267$		0			0
$268$			11.1244i			0.679528i
$269$	−0.732051	+	1.26795i	−0.0446339	+	0.0773082i	−0.887479	−	0.460848i	$-0.847545\pi$
$269$	−0.732051	+	1.26795i	−0.0446339	+	0.0773082i	0.842845	+	0.538156i	$0.180879\pi$
$270$		0			0
$271$	−5.07180	+	2.92820i	−0.308090	+	0.177876i	−0.646071	−	0.763277i	$-0.723589\pi$
$271$	−5.07180	+	2.92820i	−0.308090	+	0.177876i	0.337982	+	0.941153i	$0.390256\pi$
$272$	−2.26795			−0.137515
$273$		0			0
$274$	−1.92820			−0.116487
$275$	20.1962	−	11.6603i	1.21787	−	0.703140i
$276$		0			0
$277$	−1.13397	+	1.96410i	−0.0681339	+	0.118011i	−0.898080	−	0.439832i	$-0.855038\pi$
$277$	−1.13397	+	1.96410i	−0.0681339	+	0.118011i	0.829946	+	0.557844i	$0.188371\pi$
$278$			9.85641i			0.591148i
$279$		0			0
$280$	0.169873	+	0.0980762i	0.0101519	+	0.00586117i
$281$		−	22.3205i		−	1.33153i	−0.746162	−	0.665765i	$-0.768105\pi$
$281$		−	22.3205i		−	1.33153i	0.746162	−	0.665765i	$-0.231895\pi$
$282$		0			0
$283$	4.16987	+	7.22243i	0.247873	+	0.429329i	0.962936	−	0.269732i	$-0.0869350\pi$
$283$	4.16987	+	7.22243i	0.247873	+	0.429329i	−0.715062	+	0.699061i	$0.753602\pi$
$284$	1.09808	−	0.633975i	0.0651588	−	0.0376195i
$285$		0			0
$286$	−16.3923	+	4.73205i	−0.969297	+	0.279812i
$287$	−8.33975			−0.492280
$288$		0			0
$289$	5.92820	+	10.2679i	0.348718	+	0.603997i
$290$	−0.330127	+	0.571797i	−0.0193857	+	0.0335771i
$291$		0			0
$292$	8.42820	+	4.86603i	0.493223	+	0.284763i
$293$	12.5718	+	7.25833i	0.734452	+	0.424036i	0.820049	−	0.572294i	$-0.193946\pi$
$293$	12.5718	+	7.25833i	0.734452	+	0.424036i	−0.0855965	+	0.996330i	$0.527280\pi$
$294$		0			0
$295$	−1.07180	+	1.85641i	−0.0624024	+	0.108084i
$296$	−5.23205	−	9.06218i	−0.304107	−	0.526728i
$297$		0			0
$298$	−2.80385			−0.162423
$299$	−5.36603	+	21.6865i	−0.310325	+	1.25416i
$300$		0			0
$301$	4.85641	−	2.80385i	0.279919	−	0.161611i
$302$	1.63397	+	2.83013i	0.0940247	+	0.162856i
$303$		0			0
$304$			1.26795i			0.0727219i
$305$	0.277568	+	0.160254i	0.0158935	+	0.00917612i
$306$		0			0
$307$		−	8.58846i		−	0.490169i	−0.969502	−	0.245085i	$-0.921184\pi$
$307$		−	8.58846i		−	0.490169i	0.969502	−	0.245085i	$-0.0788157\pi$
$308$	1.73205	−	3.00000i	0.0986928	−	0.170941i
$309$		0			0
$310$	1.26795	−	0.732051i	0.0720147	−	0.0415777i
$311$	15.6603			0.888012			0.444006	−	0.896024i	$-0.353557\pi$
$311$	15.6603			0.888012			0.444006	+	0.896024i	$0.353557\pi$
$312$		0			0
$313$	13.4641			0.761036			0.380518	−	0.924774i	$-0.375746\pi$
$313$	13.4641			0.761036			0.380518	+	0.924774i	$0.375746\pi$
$314$	20.4282	−	11.7942i	1.15283	−	0.665587i
$315$		0			0
$316$	−4.73205	+	8.19615i	−0.266199	+	0.461070i
$317$		−	3.33975i		−	0.187579i	−0.995592	−	0.0937894i	$-0.970102\pi$
$317$		−	3.33975i		−	0.187579i	0.995592	−	0.0937894i	$-0.0298980\pi$
$318$		0			0
$319$	10.0981	+	5.83013i	0.565384	+	0.326424i
$320$			0.267949i			0.0149788i
$321$		0			0
$322$	−2.26795	−	3.92820i	−0.126388	−	0.218910i
$323$	−2.49038	+	1.43782i	−0.138569	+	0.0800026i
$324$		0			0
$325$	12.8038	+	12.3205i	0.710230	+	0.683419i
$326$	6.53590			0.361990
$327$		0			0
$328$	−5.69615	−	9.86603i	−0.314517	−	0.544760i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.0583130	−	0.998298i	$-0.518572\pi$
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.893708	+	0.448649i	$0.851905\pi$
$332$	−8.83013	−	5.09808i	−0.484616	−	0.279793i
$333$		0			0
$334$	1.26795	−	2.19615i	0.0693791	−	0.120168i
$335$	1.49038	+	2.58142i	0.0814282	+	0.141038i
$336$		0			0
$337$	−6.85641			−0.373492			−0.186746	−	0.982408i	$-0.559794\pi$
$337$	−6.85641			−0.373492			−0.186746	+	0.982408i	$0.559794\pi$
$338$	−6.92820	−	11.0000i	−0.376845	−	0.598321i
$339$		0			0
$340$	−0.526279	+	0.303848i	−0.0285415	+	0.0164784i
$341$	−12.9282	−	22.3923i	−0.700101	−	1.21261i
$342$		0			0
$343$		−	9.85641i		−	0.532196i
$344$	6.63397	+	3.83013i	0.357680	+	0.206507i
$345$		0			0
$346$			16.3923i			0.881256i
$347$	4.43782	−	7.68653i	0.238235	−	0.412635i	−0.721973	−	0.691921i	$-0.756765\pi$
$347$	4.43782	−	7.68653i	0.238235	−	0.412635i	0.960208	+	0.279286i	$0.0900979\pi$
$348$		0			0
$349$	16.7321	−	9.66025i	0.895646	−	0.517102i	0.0198610	−	0.999803i	$-0.493678\pi$
$349$	16.7321	−	9.66025i	0.895646	−	0.517102i	0.875785	+	0.482701i	$0.160344\pi$
$350$	−3.60770			−0.192839
$351$		0			0
$352$	4.73205			0.252219
$353$	−17.1340	+	9.89230i	−0.911949	+	0.526514i	−0.881058	−	0.473008i	$-0.843168\pi$
$353$	−17.1340	+	9.89230i	−0.911949	+	0.526514i	−0.0308916	+	0.999523i	$0.509835\pi$
$354$		0			0
$355$	0.169873	−	0.294229i	0.00901592	−	0.0156160i
$356$			2.53590i			0.134402i
$357$		0			0
$358$	19.0981	+	11.0263i	1.00936	+	0.582757i
$359$			23.1244i			1.22046i	0.792226	+	0.610228i	$0.208922\pi$
$359$			23.1244i			1.22046i	−0.792226	+	0.610228i	$0.791078\pi$
$360$		0			0
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$	7.62436	−	4.40192i	0.400727	−	0.231360i
$363$		0			0
$364$	2.56218	+	0.633975i	0.134295	+	0.0332293i
$365$	2.60770			0.136493
$366$		0			0
$367$	7.36603	+	12.7583i	0.384503	+	0.665979i	0.991700	−	0.128572i	$-0.0410394\pi$
$367$	7.36603	+	12.7583i	0.384503	+	0.665979i	−0.607197	+	0.794551i	$0.707706\pi$
$368$	3.09808	−	5.36603i	0.161498	−	0.279723i
$369$		0			0
$370$	−2.42820	−	1.40192i	−0.126236	−	0.0728825i
$371$	−0.294229	−	0.169873i	−0.0152756	−	0.00881937i
$372$		0			0
$373$	5.13397	−	8.89230i	0.265827	−	0.460426i	−0.701953	−	0.712223i	$-0.747688\pi$
$373$	5.13397	−	8.89230i	0.265827	−	0.460426i	0.967780	+	0.251797i	$0.0810216\pi$
$374$	5.36603	+	9.29423i	0.277471	+	0.480593i
$375$		0			0
$376$	8.19615			0.422684
$377$	−2.13397	+	8.62436i	−0.109905	+	0.444177i
$378$		0			0
$379$	1.26795	−	0.732051i	0.0651302	−	0.0376029i	−0.467081	−	0.884214i	$-0.654694\pi$
$379$	1.26795	−	0.732051i	0.0651302	−	0.0376029i	0.532211	+	0.846611i	$0.321361\pi$
$380$	0.169873	+	0.294229i	0.00871430	+	0.0150936i
$381$		0			0
$382$			6.92820i			0.354478i
$383$	4.73205	+	2.73205i	0.241797	+	0.139601i	0.616002	−	0.787744i	$-0.288751\pi$
$383$	4.73205	+	2.73205i	0.241797	+	0.139601i	−0.374206	+	0.927346i	$0.622085\pi$
$384$		0			0
$385$		−	0.928203i		−	0.0473056i
$386$	−4.13397	+	7.16025i	−0.210414	+	0.364447i
$387$		0			0
$388$	5.19615	−	3.00000i	0.263795	−	0.152302i
$389$	−29.7846			−1.51014			−0.755070	−	0.655644i	$-0.772397\pi$
$389$	−29.7846			−1.51014			−0.755070	+	0.655644i	$0.772397\pi$
$390$		0			0
$391$	14.0526			0.710668
$392$	5.59808	−	3.23205i	0.282746	−	0.163243i
$393$		0			0
$394$	4.92820	−	8.53590i	0.248279	−	0.430032i
$395$			2.53590i			0.127595i
$396$		0			0
$397$	−0.339746	−	0.196152i	−0.0170514	−	0.00984461i	0.491450	−	0.870906i	$-0.336467\pi$
$397$	−0.339746	−	0.196152i	−0.0170514	−	0.00984461i	−0.508501	+	0.861061i	$0.669800\pi$
$398$		−	3.80385i		−	0.190670i
$399$		0			0
$400$	−2.46410	−	4.26795i	−0.123205	−	0.213397i
$401$	18.9904	−	10.9641i	0.948334	−	0.547521i	0.0557713	−	0.998444i	$-0.482238\pi$
$401$	18.9904	−	10.9641i	0.948334	−	0.547521i	0.892563	+	0.450922i	$0.148905\pi$
$402$		0			0
$403$	13.6603	−	14.1962i	0.680466	−	0.707161i
$404$	11.9282			0.593450
$405$		0			0
$406$	−0.901924	−	1.56218i	−0.0447617	−	0.0775296i
$407$	−24.7583	+	42.8827i	−1.22722	+	2.12562i
$408$		0			0
$409$	−12.3564	−	7.13397i	−0.610985	−	0.352752i	0.162366	−	0.986731i	$-0.448088\pi$
$409$	−12.3564	−	7.13397i	−0.610985	−	0.352752i	−0.773351	+	0.633978i	$0.781421\pi$
$410$	−2.64359	−	1.52628i	−0.130558	−	0.0753776i
$411$		0			0
$412$	9.36603	−	16.2224i	0.461431	−	0.799222i
$413$	−2.92820	−	5.07180i	−0.144087	−	0.249567i
$414$		0			0
$415$	−2.73205			−0.134111
$416$	1.00000	+	3.46410i	0.0490290	+	0.169842i
$417$		0			0
$418$	5.19615	−	3.00000i	0.254152	−	0.146735i
$419$	−5.26795	−	9.12436i	−0.257356	−	0.445754i	0.708177	−	0.706035i	$-0.249518\pi$
$419$	−5.26795	−	9.12436i	−0.257356	−	0.445754i	−0.965533	+	0.260281i	$0.916185\pi$
$420$		0			0
$421$			32.7128i			1.59432i	0.603765	+	0.797162i	$0.293667\pi$
$421$			32.7128i			1.59432i	−0.603765	+	0.797162i	$0.706333\pi$
$422$	−3.80385	−	2.19615i	−0.185168	−	0.106907i
$423$		0			0
$424$		−	0.464102i		−	0.0225388i
$425$	5.58846	−	9.67949i	0.271080	−	0.469524i
$426$		0			0
$427$	−0.758330	+	0.437822i	−0.0366982	+	0.0211877i
$428$	−0.196152			−0.00948139
$429$		0			0
$430$	2.05256			0.0989832
$431$	9.63397	−	5.56218i	0.464052	−	0.267921i	−0.249694	−	0.968325i	$-0.580330\pi$
$431$	9.63397	−	5.56218i	0.464052	−	0.267921i	0.713747	+	0.700404i	$0.246997\pi$
$432$		0			0
$433$	−7.42820	+	12.8660i	−0.356977	+	0.618302i	−0.987454	−	0.157906i	$-0.949526\pi$
$433$	−7.42820	+	12.8660i	−0.356977	+	0.618302i	0.630478	+	0.776208i	$0.282859\pi$
$434$			4.00000i			0.192006i
$435$		0			0
$436$	−4.73205	−	2.73205i	−0.226624	−	0.130842i
$437$		−	7.85641i		−	0.375823i
$438$		0			0
$439$	−8.83013	−	15.2942i	−0.421439	−	0.729954i	0.574642	−	0.818405i	$-0.305141\pi$
$439$	−8.83013	−	15.2942i	−0.421439	−	0.729954i	−0.996080	+	0.0884515i	$0.971808\pi$
$440$	1.09808	−	0.633975i	0.0523487	−	0.0302236i
$441$		0			0
$442$	−5.66987	+	5.89230i	−0.269688	+	0.280268i
$443$	−36.3923			−1.72905			−0.864525	−	0.502589i	$-0.832381\pi$
$443$	−36.3923			−1.72905			−0.864525	+	0.502589i	$0.832381\pi$
$444$		0			0
$445$	0.339746	+	0.588457i	0.0161055	+	0.0278955i
$446$	6.53590	−	11.3205i	0.309484	−	0.536042i
$447$		0			0
$448$	−0.633975	−	0.366025i	−0.0299525	−	0.0172931i
$449$	20.1962	+	11.6603i	0.953115	+	0.550281i	0.894047	−	0.447973i	$-0.147854\pi$
$449$	20.1962	+	11.6603i	0.953115	+	0.550281i	0.0590680	+	0.998254i	$0.481187\pi$
$450$		0			0
$451$	−26.9545	+	46.6865i	−1.26924	+	2.19838i
$452$	9.33013	+	16.1603i	0.438852	+	0.760114i
$453$		0			0
$454$	1.80385			0.0846588
$455$	0.679492	−	0.196152i	0.0318551	−	0.00919577i
$456$		0			0
$457$	16.1603	−	9.33013i	0.755945	−	0.436445i	−0.0718931	−	0.997412i	$-0.522904\pi$
$457$	16.1603	−	9.33013i	0.755945	−	0.436445i	0.827838	+	0.560967i	$0.189571\pi$
$458$	7.92820	+	13.7321i	0.370461	+	0.641657i
$459$		0			0
$460$		−	1.66025i		−	0.0774097i
$461$	22.2846	+	12.8660i	1.03790	+	0.599231i	0.919237	−	0.393704i	$-0.128807\pi$
$461$	22.2846	+	12.8660i	1.03790	+	0.599231i	0.118661	+	0.992935i	$0.462140\pi$
$462$		0			0
$463$			28.0526i			1.30371i	0.758342	+	0.651856i	$0.226010\pi$
$463$			28.0526i			1.30371i	−0.758342	+	0.651856i	$0.773990\pi$
$464$	1.23205	−	2.13397i	0.0571965	−	0.0990673i
$465$		0			0
$466$	−17.1962	+	9.92820i	−0.796596	+	0.459915i
$467$	−12.5885			−0.582524			−0.291262	−	0.956643i	$-0.594075\pi$
$467$	−12.5885			−0.582524			−0.291262	+	0.956643i	$0.594075\pi$
$468$		0			0
$469$	−8.14359			−0.376036
$470$	1.90192	−	1.09808i	0.0877292	−	0.0506505i
$471$		0			0
$472$	4.00000	−	6.92820i	0.184115	−	0.318896i
$473$		−	36.2487i		−	1.66672i
$474$		0			0
$475$	−5.41154	−	3.12436i	−0.248299	−	0.143355i
$476$		−	1.66025i		−	0.0760976i
$477$		0			0
$478$	−4.83013	−	8.36603i	−0.220925	−	0.382653i
$479$	22.9808	−	13.2679i	1.05002	−	0.606228i	0.127363	−	0.991856i	$-0.459349\pi$
$479$	22.9808	−	13.2679i	1.05002	−	0.606228i	0.922654	+	0.385628i	$0.126015\pi$
$480$		0			0
$481$	−36.6244	−	9.06218i	−1.66993	−	0.413200i
$482$	17.5885			0.801132
$483$		0			0
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	0.803848	−	1.39230i	0.0365008	−	0.0632213i
$486$		0			0
$487$	−18.2942	−	10.5622i	−0.828991	−	0.478618i	0.0245163	−	0.999699i	$-0.492195\pi$
$487$	−18.2942	−	10.5622i	−0.828991	−	0.478618i	−0.853507	+	0.521081i	$0.825529\pi$
$488$	−1.03590	−	0.598076i	−0.0468929	−	0.0270736i
$489$		0			0
$490$	0.866025	−	1.50000i	0.0391230	−	0.0677631i
$491$	−2.63397	−	4.56218i	−0.118870	−	0.205888i	0.800450	−	0.599399i	$-0.204594\pi$
$491$	−2.63397	−	4.56218i	−0.118870	−	0.205888i	−0.919320	+	0.393511i	$0.871260\pi$
$492$		0			0
$493$	5.58846			0.251691
$494$	3.29423	+	3.16987i	0.148214	+	0.142619i
$495$		0			0
$496$	−4.73205	+	2.73205i	−0.212475	+	0.122673i
$497$	0.464102	+	0.803848i	0.0208178	+	0.0360575i
$498$		0			0
$499$			32.0000i			1.43252i	0.697835	+	0.716258i	$0.254147\pi$
$499$			32.0000i			1.43252i	−0.697835	+	0.716258i	$0.745853\pi$
$500$	−2.30385	−	1.33013i	−0.103031	−	0.0594851i
$501$		0			0
$502$		−	6.53590i		−	0.291711i
$503$	−5.49038	+	9.50962i	−0.244804	+	0.424013i	−0.962076	−	0.272780i	$-0.912057\pi$
$503$	−5.49038	+	9.50962i	−0.244804	+	0.424013i	0.717272	+	0.696793i	$0.245390\pi$
$504$		0			0
$505$	2.76795	−	1.59808i	0.123172	−	0.0711135i
$506$	−29.3205			−1.30346
$507$		0			0
$508$	17.8564			0.792250
$509$	−8.89230	+	5.13397i	−0.394144	+	0.227559i	−0.683954	−	0.729525i	$-0.739741\pi$
$509$	−8.89230	+	5.13397i	−0.394144	+	0.227559i	0.289810	+	0.957084i	$0.406408\pi$
$510$		0			0
$511$	−3.56218	+	6.16987i	−0.157581	+	0.272939i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	23.0885	+	13.3301i	1.01839	+	0.587967i
$515$		−	5.01924i		−	0.221174i
$516$		0			0
$517$	−19.3923	−	33.5885i	−0.852873	−	1.47722i
$518$	6.63397	−	3.83013i	0.291480	−	0.168286i
$519$		0			0
$520$	0.696152	+	0.669873i	0.0305283	+	0.0293759i
$521$	17.4449			0.764273			0.382137	−	0.924106i	$-0.375188\pi$
$521$	17.4449			0.764273			0.382137	+	0.924106i	$0.375188\pi$
$522$		0			0
$523$	−18.2224	−	31.5622i	−0.796811	−	1.38012i	−0.921683	−	0.387945i	$-0.873185\pi$
$523$	−18.2224	−	31.5622i	−0.796811	−	1.38012i	0.124871	−	0.992173i	$-0.460148\pi$
$524$	−6.73205	+	11.6603i	−0.294091	+	0.509381i
$525$		0			0
$526$	−24.2942	−	14.0263i	−1.05928	−	0.611575i
$527$	−10.7321	−	6.19615i	−0.467495	−	0.269909i
$528$		0			0
$529$	−7.69615	+	13.3301i	−0.334615	+	0.579571i
$530$	−0.0621778	−	0.107695i	−0.00270083	−	0.00467798i
$531$		0			0
$532$	−0.928203			−0.0402427
$533$	−39.8731	−	9.86603i	−1.72709	−	0.427345i
$534$		0			0
$535$	−0.0455173	+	0.0262794i	−0.00196789	+	0.00113616i
$536$	−5.56218	−	9.63397i	−0.240249	−	0.416124i
$537$		0			0
$538$		−	1.46410i		−	0.0631219i
$539$	−26.4904	−	15.2942i	−1.14102	−	0.658769i
$540$		0			0
$541$		−	40.3205i		−	1.73351i	−0.498731	−	0.866757i	$-0.666200\pi$
$541$		−	40.3205i		−	1.73351i	0.498731	−	0.866757i	$-0.333800\pi$
$542$	2.92820	−	5.07180i	0.125777	−	0.217852i
$543$		0			0
$544$	1.96410	−	1.13397i	0.0842102	−	0.0486188i
$545$	−1.46410			−0.0627152
$546$		0			0
$547$	6.19615			0.264928			0.132464	−	0.991188i	$-0.457711\pi$
$547$	6.19615			0.264928			0.132464	+	0.991188i	$0.457711\pi$
$548$	1.66987	−	0.964102i	0.0713334	−	0.0411844i
$549$		0			0
$550$	−11.6603	+	20.1962i	−0.497195	+	0.861167i
$551$		−	3.12436i		−	0.133102i
$552$		0			0
$553$	−6.00000	−	3.46410i	−0.255146	−	0.147309i
$554$		−	2.26795i		−	0.0963559i
$555$		0			0
$556$	−4.92820	−	8.53590i	−0.209002	−	0.362003i
$557$	−26.3038	+	15.1865i	−1.11453	+	0.643474i	−0.939999	−	0.341178i	$-0.889174\pi$
$557$	−26.3038	+	15.1865i	−1.11453	+	0.643474i	−0.174531	+	0.984652i	$0.555841\pi$
$558$		0			0
$559$	26.5359	−	7.66025i	1.12235	−	0.323994i
$560$	−0.196152			−0.00828895
$561$		0			0
$562$	11.1603	+	19.3301i	0.470767	+	0.815392i
$563$	−10.5359	+	18.2487i	−0.444035	+	0.769091i	−0.997984	−	0.0634589i	$-0.979787\pi$
$563$	−10.5359	+	18.2487i	−0.444035	+	0.769091i	0.553949	+	0.832550i	$0.313120\pi$
$564$		0			0
$565$	4.33013	+	2.50000i	0.182170	+	0.105176i
$566$	−7.22243	−	4.16987i	−0.303581	−	0.175273i
$567$		0			0
$568$	−0.633975	+	1.09808i	−0.0266010	+	0.0460743i
$569$	19.3205	+	33.4641i	0.809958	+	1.40289i	0.912893	+	0.408200i	$0.133843\pi$
$569$	19.3205	+	33.4641i	0.809958	+	1.40289i	−0.102935	+	0.994688i	$0.532823\pi$
$570$		0			0
$571$	24.0526			1.00657			0.503284	−	0.864121i	$-0.332125\pi$
$571$	24.0526			1.00657			0.503284	+	0.864121i	$0.332125\pi$
$572$	11.8301	−	12.2942i	0.494642	−	0.514048i
$573$		0			0
$574$	7.22243	−	4.16987i	0.301458	−	0.174047i
$575$	15.2679	+	26.4449i	0.636717	+	1.10283i
$576$		0			0
$577$			0.267949i			0.0111549i	0.999984	+	0.00557744i	$0.00177536\pi$
$577$			0.267949i			0.0111549i	−0.999984	+	0.00557744i	$0.998225\pi$
$578$	−10.2679	−	5.92820i	−0.427090	−	0.246581i
$579$		0			0
$580$		−	0.660254i		−	0.0274156i
$581$	3.73205	−	6.46410i	0.154832	−	0.268176i
$582$		0			0
$583$	−1.90192	+	1.09808i	−0.0787696	+	0.0454777i
$584$	−9.73205			−0.402715
$585$		0			0
$586$	−14.5167			−0.599678
$587$	−13.8564	+	8.00000i	−0.571915	+	0.330195i	−0.757914	−	0.652355i	$-0.773781\pi$
$587$	−13.8564	+	8.00000i	−0.571915	+	0.330195i	0.185999	+	0.982550i	$0.440448\pi$
$588$		0			0
$589$	−3.46410	+	6.00000i	−0.142736	+	0.247226i
$590$		−	2.14359i		−	0.0882503i
$591$		0			0
$592$	9.06218	+	5.23205i	0.372453	+	0.215036i
$593$		−	36.8564i		−	1.51351i	−0.653698	−	0.756756i	$-0.726783\pi$
$593$		−	36.8564i		−	1.51351i	0.653698	−	0.756756i	$-0.273217\pi$
$594$		0			0
$595$	−0.222432	−	0.385263i	−0.00911882	−	0.0157943i
$596$	2.42820	−	1.40192i	0.0994631	−	0.0574250i
$597$		0			0
$598$	−6.19615	−	21.4641i	−0.253380	−	0.877732i
$599$	9.46410			0.386693			0.193346	−	0.981131i	$-0.438066\pi$
$599$	9.46410			0.386693			0.193346	+	0.981131i	$0.438066\pi$
$600$		0			0
$601$	2.96410	+	5.13397i	0.120908	+	0.209419i	0.920126	−	0.391622i	$-0.128086\pi$
$601$	2.96410	+	5.13397i	0.120908	+	0.209419i	−0.799218	+	0.601041i	$0.794753\pi$
$602$	−2.80385	+	4.85641i	−0.114276	+	0.197932i
$603$		0			0
$604$	−2.83013	−	1.63397i	−0.115156	−	0.0664855i
$605$	−2.64359	−	1.52628i	−0.107477	−	0.0620521i
$606$		0			0
$607$	−0.392305	+	0.679492i	−0.0159232	+	0.0275797i	−0.873877	−	0.486147i	$-0.838402\pi$
$607$	−0.392305	+	0.679492i	−0.0159232	+	0.0275797i	0.857954	+	0.513726i	$0.171735\pi$
$608$	−0.633975	−	1.09808i	−0.0257111	−	0.0445329i
$609$		0			0
$610$	−0.320508			−0.0129770
$611$	20.4904	−	21.2942i	0.828952	−	0.861472i
$612$		0			0
$613$	9.86603	−	5.69615i	0.398485	−	0.230065i	−0.287345	−	0.957827i	$-0.592773\pi$
$613$	9.86603	−	5.69615i	0.398485	−	0.230065i	0.685830	+	0.727762i	$0.259439\pi$
$614$	4.29423	+	7.43782i	0.173301	+	0.300166i
$615$		0			0
$616$			3.46410i			0.139573i
$617$	30.5263	+	17.6244i	1.22894	+	0.709530i	0.966809	−	0.255502i	$-0.0822407\pi$
$617$	30.5263	+	17.6244i	1.22894	+	0.709530i	0.262133	+	0.965032i	$0.415574\pi$
$618$		0			0
$619$		−	10.5359i		−	0.423474i	−0.977327	−	0.211737i	$-0.932088\pi$
$619$		−	10.5359i		−	0.423474i	0.977327	−	0.211737i	$-0.0679119\pi$
$620$	−0.732051	+	1.26795i	−0.0293999	+	0.0509221i
$621$		0			0
$622$	−13.5622	+	7.83013i	−0.543794	+	0.313959i
$623$	−1.85641			−0.0743754
$624$		0			0
$625$	23.9282			0.957128
$626$	−11.6603	+	6.73205i	−0.466037	+	0.269067i
$627$		0			0
$628$	−11.7942	+	20.4282i	−0.470641	+	0.815174i
$629$			23.7321i			0.946259i
$630$		0			0
$631$	41.3205	+	23.8564i	1.64494	+	0.949709i	0.979039	+	0.203671i	$0.0652874\pi$
$631$	41.3205	+	23.8564i	1.64494	+	0.949709i	0.665904	+	0.746037i	$0.268046\pi$
$632$		−	9.46410i		−	0.376462i
$633$		0			0
$634$	1.66987	+	2.89230i	0.0663191	+	0.114868i
$635$	4.14359	−	2.39230i	0.164433	−	0.0949357i
$636$		0			0
$637$	5.59808	−	22.6244i	0.221804	−	0.896410i
$638$	−11.6603			−0.461634
$639$		0			0
$640$	−0.133975	−	0.232051i	−0.00529581	−	0.00917261i
$641$	−12.9904	+	22.5000i	−0.513089	+	0.888697i	0.486796	+	0.873516i	$0.338166\pi$
$641$	−12.9904	+	22.5000i	−0.513089	+	0.888697i	−0.999885	+	0.0151806i	$0.995168\pi$
$642$		0			0
$643$	−12.0000	−	6.92820i	−0.473234	−	0.273222i	0.244359	−	0.969685i	$-0.421423\pi$
$643$	−12.0000	−	6.92820i	−0.473234	−	0.273222i	−0.717592	+	0.696463i	$0.754756\pi$
$644$	3.92820	+	2.26795i	0.154793	+	0.0893697i
$645$		0			0
$646$	1.43782	−	2.49038i	0.0565704	−	0.0979827i
$647$	−13.1244	−	22.7321i	−0.515972	−	0.893689i	−0.999828	−	0.0185417i	$-0.994098\pi$
$647$	−13.1244	−	22.7321i	−0.515972	−	0.893689i	0.483856	−	0.875147i	$-0.339236\pi$
$648$		0			0
$649$	−37.8564			−1.48599
$650$	−17.2487	−	4.26795i	−0.676550	−	0.167403i
$651$		0			0
$652$	−5.66025	+	3.26795i	−0.221673	+	0.127983i
$653$	−5.26795	−	9.12436i	−0.206151	−	0.357064i	0.744348	−	0.667792i	$-0.232760\pi$
$653$	−5.26795	−	9.12436i	−0.206151	−	0.357064i	−0.950499	+	0.310728i	$0.899427\pi$
$654$		0			0
$655$			3.60770i			0.140964i
$656$	9.86603	+	5.69615i	0.385204	+	0.222397i
$657$		0			0
$658$			6.00000i			0.233904i
$659$	19.1244	−	33.1244i	0.744979	−	1.29034i	−0.205225	−	0.978715i	$-0.565793\pi$
$659$	19.1244	−	33.1244i	0.744979	−	1.29034i	0.950205	−	0.311627i	$-0.100874\pi$
$660$		0			0
$661$	8.13397	−	4.69615i	0.316375	−	0.182659i	−0.333401	−	0.942785i	$-0.608196\pi$
$661$	8.13397	−	4.69615i	0.316375	−	0.182659i	0.649776	+	0.760126i	$0.274863\pi$
$662$	20.0000			0.777322
$663$		0			0
$664$	10.1962			0.395687
$665$	−0.215390	+	0.124356i	−0.00835248	+	0.00482231i
$666$		0			0
$667$	−7.63397	+	13.2224i	−0.295589	+	0.511975i
$668$			2.53590i			0.0981169i
$669$		0			0
$670$	−2.58142	−	1.49038i	−0.0997288	−	0.0575784i
$671$			5.66025i			0.218512i
$672$		0			0
$673$	7.03590	+	12.1865i	0.271214	+	0.469756i	0.969173	−	0.246381i	$-0.0792416\pi$
$673$	7.03590	+	12.1865i	0.271214	+	0.469756i	−0.697959	+	0.716138i	$0.745908\pi$
$674$	5.93782	−	3.42820i	0.228716	−	0.132049i
$675$		0			0
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	38.5359			1.48105			0.740527	−	0.672026i	$-0.234576\pi$
$677$	38.5359			1.48105			0.740527	+	0.672026i	$0.234576\pi$
$678$		0			0
$679$	2.19615	+	3.80385i	0.0842806	+	0.145978i
$680$	0.303848	−	0.526279i	0.0116520	−	0.0201819i
$681$		0			0
$682$	22.3923	+	12.9282i	0.857446	+	0.495046i
$683$	32.7846	+	18.9282i	1.25447	+	0.724268i	0.971994	−	0.235007i	$-0.0755114\pi$
$683$	32.7846	+	18.9282i	1.25447	+	0.724268i	0.282475	+	0.959275i	$0.408845\pi$
$684$		0			0
$685$	0.258330	−	0.447441i	0.00987029	−	0.0170958i
$686$	4.92820	+	8.53590i	0.188160	+	0.325902i
$687$		0			0
$688$	−7.66025			−0.292044
$689$	−1.20577	−	1.16025i	−0.0459362	−	0.0442022i
$690$		0			0
$691$	22.8109	−	13.1699i	0.867767	−	0.501006i	0.00116153	−	0.999999i	$-0.499630\pi$
$691$	22.8109	−	13.1699i	0.867767	−	0.501006i	0.866606	+	0.498994i	$0.166297\pi$
$692$	−8.19615	−	14.1962i	−0.311571	−	0.539657i
$693$		0			0
$694$			8.87564i			0.336915i
$695$	−2.28719	−	1.32051i	−0.0867580	−	0.0500897i
$696$		0			0
$697$			25.8372i			0.978653i
$698$	−9.66025	+	16.7321i	−0.365646	+	0.633317i
$699$		0			0
$700$	3.12436	−	1.80385i	0.118090	−	0.0681790i
$701$	31.3205			1.18296			0.591480	−	0.806320i	$-0.298544\pi$
$701$	31.3205			1.18296			0.591480	+	0.806320i	$0.298544\pi$
$702$		0			0
$703$	13.2679			0.500410
$704$	−4.09808	+	2.36603i	−0.154452	+	0.0891729i
$705$		0			0
$706$	9.89230	−	17.1340i	0.372302	−	0.644846i
$707$			8.73205i			0.328403i
$708$		0			0
$709$	35.3827	+	20.4282i	1.32882	+	0.767197i	0.985118	−	0.171880i	$-0.0549841\pi$
$709$	35.3827	+	20.4282i	1.32882	+	0.767197i	0.343707	+	0.939077i	$0.388317\pi$
$710$			0.339746i			0.0127504i
$711$		0			0
$712$	−1.26795	−	2.19615i	−0.0475184	−	0.0823043i
$713$	29.3205	−	16.9282i	1.09806	−	0.633966i
$714$		0			0
$715$	1.09808	−	4.43782i	0.0410657	−	0.165965i
$716$	−22.0526			−0.824143
$717$		0			0
$718$	−11.5622	−	20.0263i	−0.431497	−	0.747374i
$719$	11.2679	−	19.5167i	0.420224	−	0.727849i	−0.575737	−	0.817635i	$-0.695285\pi$
$719$	11.2679	−	19.5167i	0.420224	−	0.727849i	0.995961	+	0.0897860i	$0.0286183\pi$
$720$		0			0
$721$	11.8756	+	6.85641i	0.442272	+	0.255346i
$722$	15.0622	+	8.69615i	0.560556	+	0.323637i
$723$		0			0
$724$	−4.40192	+	7.62436i	−0.163596	+	0.283357i
$725$	6.07180	+	10.5167i	0.225501	+	0.390579i
$726$		0			0
$727$	−20.9808			−0.778133			−0.389067	−	0.921210i	$-0.627202\pi$
$727$	−20.9808			−0.778133			−0.389067	+	0.921210i	$0.627202\pi$
$728$	−2.53590	+	0.732051i	−0.0939866	+	0.0271316i
$729$		0			0
$730$	−2.25833	+	1.30385i	−0.0835846	+	0.0482576i
$731$	−8.68653	−	15.0455i	−0.321283	−	0.556479i
$732$		0			0
$733$			19.0000i			0.701781i	0.936416	+	0.350891i	$0.114121\pi$
$733$			19.0000i			0.701781i	−0.936416	+	0.350891i	$0.885879\pi$
$734$	−12.7583	−	7.36603i	−0.470919	−	0.271885i
$735$		0			0
$736$			6.19615i			0.228393i
$737$	−26.3205	+	45.5885i	−0.969528	+	1.67927i
$738$		0			0
$739$	9.46410	−	5.46410i	0.348143	−	0.201000i	−0.315724	−	0.948851i	$-0.602247\pi$
$739$	9.46410	−	5.46410i	0.348143	−	0.201000i	0.663867	+	0.747851i	$0.268914\pi$
$740$	2.80385			0.103071
$741$		0			0
$742$	0.339746			0.0124725
$743$	23.9090	−	13.8038i	0.877135	−	0.506414i	0.00742221	−	0.999972i	$-0.497637\pi$
$743$	23.9090	−	13.8038i	0.877135	−	0.506414i	0.869713	+	0.493558i	$0.164304\pi$
$744$		0			0
$745$	0.375644	−	0.650635i	0.0137625	−	0.0238374i
$746$			10.2679i			0.375936i
$747$		0			0
$748$	−9.29423	−	5.36603i	−0.339831	−	0.196201i
$749$		−	0.143594i		−	0.00524679i
$750$		0			0
$751$	7.95448	+	13.7776i	0.290263	+	0.502751i	0.973872	−	0.227098i	$-0.0729238\pi$
$751$	7.95448	+	13.7776i	0.290263	+	0.502751i	−0.683609	+	0.729849i	$0.739590\pi$
$752$	−7.09808	+	4.09808i	−0.258840	+	0.149441i
$753$		0			0
$754$	−2.46410	−	8.53590i	−0.0897373	−	0.310859i
$755$	−0.875644			−0.0318680
$756$		0			0
$757$	−3.53590	−	6.12436i	−0.128514	−	0.222593i	0.794587	−	0.607151i	$-0.207688\pi$
$757$	−3.53590	−	6.12436i	−0.128514	−	0.222593i	−0.923101	+	0.384557i	$0.874354\pi$
$758$	−0.732051	+	1.26795i	−0.0265893	+	0.0460540i
$759$		0			0
$760$	−0.294229	−	0.169873i	−0.0106728	−	0.00616194i
$761$	20.1962	+	11.6603i	0.732110	+	0.422684i	0.819194	−	0.573517i	$-0.194421\pi$
$761$	20.1962	+	11.6603i	0.732110	+	0.422684i	−0.0870836	+	0.996201i	$0.527755\pi$
$762$		0			0
$763$	2.00000	−	3.46410i	0.0724049	−	0.125409i
$764$	−3.46410	−	6.00000i	−0.125327	−	0.217072i
$765$		0			0
$766$	−5.46410			−0.197426
$767$	−8.00000	−	27.7128i	−0.288863	−	1.00065i
$768$		0			0
$769$	−13.9808	+	8.07180i	−0.504159	+	0.291076i	−0.730429	−	0.682988i	$-0.760680\pi$
$769$	−13.9808	+	8.07180i	−0.504159	+	0.291076i	0.226270	+	0.974065i	$0.427347\pi$
$770$	0.464102	+	0.803848i	0.0167251	+	0.0289687i
$771$		0			0
$772$		−	8.26795i		−	0.297570i
$773$	−30.3731	−	17.5359i	−1.09244	−	0.630722i	−0.158217	−	0.987404i	$-0.550575\pi$
$773$	−30.3731	−	17.5359i	−1.09244	−	0.630722i	−0.934226	+	0.356682i	$0.883908\pi$
$774$		0			0
$775$		−	26.9282i		−	0.967290i
$776$	−3.00000	+	5.19615i	−0.107694	+	0.186531i
$777$		0			0
$778$	25.7942	−	14.8923i	0.924768	−	0.533915i
$779$	14.4449			0.517541
$780$		0			0
$781$	6.00000			0.214697
$782$	−12.1699	+	7.02628i	−0.435194	+	0.251259i
$783$		0			0
$784$	−3.23205	+	5.59808i	−0.115430	+	0.199931i
$785$			6.32051i			0.225589i
$786$		0			0
$787$	34.0526	+	19.6603i	1.21384	+	0.700812i	0.963594	−	0.267369i	$-0.0861544\pi$
$787$	34.0526	+	19.6603i	1.21384	+	0.700812i	0.250248	+	0.968182i	$0.419488\pi$
$788$			9.85641i			0.351120i
$789$		0			0
$790$	−1.26795	−	2.19615i	−0.0451116	−	0.0781356i
$791$	−11.8301	+	6.83013i	−0.420631	+	0.242851i
$792$		0			0
$793$	−4.14359	+	1.19615i	−0.147143	+	0.0424766i
$794$	0.392305			0.0139224
$795$		0			0
$796$	1.90192	+	3.29423i	0.0674119	+	0.116761i
$797$	17.0000	−	29.4449i	0.602171	−	1.04299i	−0.390321	−	0.920679i	$-0.627636\pi$
$797$	17.0000	−	29.4449i	0.602171	−	1.04299i	0.992492	−	0.122312i	$-0.0390308\pi$
$798$		0			0
$799$	−16.0981	−	9.29423i	−0.569509	−	0.328806i
$800$	4.26795	+	2.46410i	0.150895	+	0.0871191i
$801$		0			0
$802$	−10.9641	+	18.9904i	−0.387156	+	0.670574i
$803$	23.0263	+	39.8827i	0.812580	+	1.40743i
$804$		0			0
$805$	1.21539			0.0428369
$806$	−4.73205	+	19.1244i	−0.166679	+	0.673627i
$807$		0			0
$808$	−10.3301	+	5.96410i	−0.363413	+	0.209816i
$809$	−11.2058	−	19.4090i	−0.393974	−	0.682383i	0.598996	−	0.800752i	$-0.295567\pi$
$809$	−11.2058	−	19.4090i	−0.393974	−	0.682383i	−0.992970	+	0.118369i	$0.962233\pi$
$810$		0			0
$811$		−	45.1769i		−	1.58638i	−0.608977	−	0.793188i	$-0.708420\pi$
$811$		−	45.1769i		−	1.58638i	0.608977	−	0.793188i	$-0.291580\pi$
$812$	1.56218	+	0.901924i	0.0548217	+	0.0316513i
$813$		0			0
$814$		−	49.5167i		−	1.73556i
$815$	−0.875644	+	1.51666i	−0.0306725	+	0.0531263i
$816$		0			0
$817$	−8.41154	+	4.85641i	−0.294283	+	0.169904i
$818$	14.2679			0.498867
$819$		0			0
$820$	3.05256			0.106600
$821$	−11.1962	+	6.46410i	−0.390748	+	0.225599i	−0.682484	−	0.730900i	$-0.739100\pi$
$821$	−11.1962	+	6.46410i	−0.390748	+	0.225599i	0.291736	+	0.956499i	$0.405767\pi$
$822$		0			0
$823$	−20.7846	+	36.0000i	−0.724506	+	1.25488i	0.234671	+	0.972075i	$0.424599\pi$
$823$	−20.7846	+	36.0000i	−0.724506	+	1.25488i	−0.959177	+	0.282806i	$0.908735\pi$
$824$			18.7321i			0.652562i
$825$		0			0
$826$	5.07180	+	2.92820i	0.176470	+	0.101885i
$827$			33.4641i			1.16366i	0.813310	+	0.581830i	$0.197663\pi$
$827$			33.4641i			1.16366i	−0.813310	+	0.581830i	$0.802337\pi$
$828$		0			0
$829$	6.06218	+	10.5000i	0.210548	+	0.364680i	0.951886	−	0.306452i	$-0.0991418\pi$
$829$	6.06218	+	10.5000i	0.210548	+	0.364680i	−0.741338	+	0.671132i	$0.765808\pi$
$830$	2.36603	−	1.36603i	0.0821259	−	0.0474154i
$831$		0			0
$832$	−2.59808	−	2.50000i	−0.0900721	−	0.0866719i
$833$	−14.6603			−0.507948
$834$		0			0
$835$	0.339746	+	0.588457i	0.0117574	+	0.0203644i
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$		0			0
$838$	9.12436	+	5.26795i	0.315196	+	0.181978i
$839$	−12.2487	−	7.07180i	−0.422872	−	0.244146i	0.273433	−	0.961891i	$-0.411841\pi$
$839$	−12.2487	−	7.07180i	−0.422872	−	0.244146i	−0.696306	+	0.717745i	$0.745174\pi$
$840$		0			0
$841$	11.4641	−	19.8564i	0.395314	−	0.684704i
$842$	−16.3564	−	28.3301i	−0.563679	−	0.976321i
$843$		0			0
$844$	4.39230			0.151189
$845$	3.48076	−	0.133975i	0.119742	−	0.00460887i
$846$		0			0
$847$	7.22243	−	4.16987i	0.248166	−	0.143279i
$848$	0.232051	+	0.401924i	0.00796866	+	0.0138021i
$849$		0			0
$850$			11.1769i			0.383365i
$851$	−56.1506	−	32.4186i	−1.92482	−	1.11129i
$852$		0			0
$853$		−	8.17691i		−	0.279972i	−0.990153	−	0.139986i	$-0.955294\pi$
$853$		−	8.17691i		−	0.279972i	0.990153	−	0.139986i	$-0.0447058\pi$
$854$	0.437822	−	0.758330i	0.0149820	−	0.0259495i
$855$		0			0
$856$	0.169873	−	0.0980762i	0.00580614	−	0.00335218i
$857$	−19.4449			−0.664224			−0.332112	−	0.943240i	$-0.607761\pi$
$857$	−19.4449			−0.664224			−0.332112	+	0.943240i	$0.607761\pi$
$858$		0			0
$859$	−22.8756			−0.780507			−0.390253	−	0.920707i	$-0.627613\pi$
$859$	−22.8756			−0.780507			−0.390253	+	0.920707i	$0.627613\pi$
$860$	−1.77757	+	1.02628i	−0.0606146	+	0.0349958i
$861$		0			0
$862$	−5.56218	+	9.63397i	−0.189449	+	0.328134i
$863$		−	7.12436i		−	0.242516i	−0.992621	−	0.121258i	$-0.961307\pi$
$863$		−	7.12436i		−	0.242516i	0.992621	−	0.121258i	$-0.0386928\pi$
$864$		0			0
$865$	−3.80385	−	2.19615i	−0.129335	−	0.0746714i
$866$		−	14.8564i		−	0.504841i
$867$		0			0
$868$	−2.00000	−	3.46410i	−0.0678844	−	0.117579i
$869$	−38.7846	+	22.3923i	−1.31568	+	0.759607i
$870$		0			0
$871$	−38.9352	−	9.63397i	−1.31927	−	0.326435i
$872$	5.46410			0.185038
$873$		0			0
$874$	3.92820	+	6.80385i	0.132873	+	0.230144i
$875$	0.973721	−	1.68653i	0.0329178	−	0.0570152i
$876$		0			0
$877$	−8.72243	−	5.03590i	−0.294536	−	0.170050i	0.345450	−	0.938437i	$-0.387726\pi$
$877$	−8.72243	−	5.03590i	−0.294536	−	0.170050i	−0.639985	+	0.768387i	$0.721060\pi$
$878$	15.2942	+	8.83013i	0.516155	+	0.298002i
$879$		0			0
$880$	−0.633975	+	1.09808i	−0.0213713	+	0.0370161i
$881$	−25.9186	−	44.8923i	−0.873219	−	1.51246i	−0.858648	−	0.512566i	$-0.828695\pi$
$881$	−25.9186	−	44.8923i	−0.873219	−	1.51246i	−0.0145717	−	0.999894i	$-0.504638\pi$
$882$		0			0
$883$	−29.0718			−0.978344			−0.489172	−	0.872187i	$-0.662701\pi$
$883$	−29.0718			−0.978344			−0.489172	+	0.872187i	$0.662701\pi$
$884$	1.96410	−	7.93782i	0.0660599	−	0.266978i
$885$		0			0
$886$	31.5167	−	18.1962i	1.05882	−	0.611312i
$887$	5.07180	+	8.78461i	0.170294	+	0.294958i	0.938523	−	0.345217i	$-0.112195\pi$
$887$	5.07180	+	8.78461i	0.170294	+	0.294958i	−0.768228	+	0.640176i	$0.778862\pi$
$888$		0			0
$889$			13.0718i			0.438414i
$890$	−0.588457	−	0.339746i	−0.0197251	−	0.0113883i
$891$		0			0
$892$			13.0718i			0.437676i
$893$	−5.19615	+	9.00000i	−0.173883	+	0.301174i
$894$		0			0
$895$	−5.11731	+	2.95448i	−0.171053	+	0.0987575i
$896$	0.732051			0.0244561
$897$		0			0
$898$	−23.3205			−0.778215
$899$	11.6603	−	6.73205i	0.388891	−	0.224526i
$900$		0			0
$901$	−0.526279	+	0.911543i	−0.0175329	+	0.0303679i
$902$		−	53.9090i		−	1.79497i
$903$		0			0
$904$	−16.1603	−	9.33013i	−0.537482	−	0.310315i
$905$			2.35898i			0.0784153i
$906$		0			0
$907$	7.80385	+	13.5167i	0.259123	+	0.448813i	0.966007	−	0.258516i	$-0.0832333\pi$
$907$	7.80385	+	13.5167i	0.259123	+	0.448813i	−0.706885	+	0.707329i	$0.749900\pi$
$908$	−1.56218	+	0.901924i	−0.0518427	+	0.0299314i
$909$		0			0
$910$	−0.490381	+	0.509619i	−0.0162560	+	0.0168937i
$911$	9.46410			0.313560			0.156780	−	0.987634i	$-0.449889\pi$
$911$	9.46410			0.313560			0.156780	+	0.987634i	$0.449889\pi$
$912$		0			0
$913$	−24.1244	−	41.7846i	−0.798400	−	1.38287i
$914$	−9.33013	+	16.1603i	−0.308613	+	0.534534i
$915$		0			0
$916$	−13.7321	−	7.92820i	−0.453720	−	0.261955i
$917$	−8.53590	−	4.92820i	−0.281880	−	0.162744i
$918$		0			0
$919$	28.9808	−	50.1962i	0.955987	−	1.65582i	0.223894	−	0.974613i	$-0.428123\pi$
$919$	28.9808	−	50.1962i	0.955987	−	1.65582i	0.732093	−	0.681205i	$-0.238544\pi$
$920$	0.830127	+	1.43782i	0.0273685	+	0.0474036i
$921$		0			0
$922$	−25.7321			−0.847440
$923$	1.26795	+	4.39230i	0.0417351	+	0.144574i
$924$		0			0
$925$	−44.6603	+	25.7846i	−1.46842	+	0.847793i
$926$	−14.0263	−	24.2942i	−0.460932	−	0.798358i
$927$		0			0
$928$			2.46410i			0.0808881i
$929$	8.00962	+	4.62436i	0.262787	+	0.151720i	0.625605	−	0.780140i	$-0.284852\pi$
$929$	8.00962	+	4.62436i	0.262787	+	0.151720i	−0.362818	+	0.931860i	$0.618185\pi$
$930$		0			0
$931$			8.19615i			0.268618i
$932$	9.92820	−	17.1962i	0.325209	−	0.563279i
$933$		0			0
$934$	10.9019	−	6.29423i	0.356722	−	0.205953i
$935$	−2.87564			−0.0940436
$936$		0			0
$937$	43.2487			1.41287			0.706437	−	0.707776i	$-0.250301\pi$
$937$	43.2487			1.41287			0.706437	+	0.707776i	$0.250301\pi$
$938$	7.05256	−	4.07180i	0.230274	−	0.132949i
$939$		0			0
$940$	−1.09808	+	1.90192i	−0.0358153	+	0.0620339i
$941$			56.6410i			1.84644i	0.384267	+	0.923222i	$0.374454\pi$
$941$			56.6410i			1.84644i	−0.384267	+	0.923222i	$0.625546\pi$
$942$		0			0
$943$	−61.1314	−	35.2942i	−1.99071	−	1.14934i
$944$			8.00000i			0.260378i
$945$		0			0
$946$	18.1244	+	31.3923i	0.589274	+	1.02065i
$947$	30.2487	−	17.4641i	0.982951	−	0.567507i	0.0797913	−	0.996812i	$-0.474575\pi$
$947$	30.2487	−	17.4641i	0.982951	−	0.567507i	0.903160	+	0.429305i	$0.141241\pi$
$948$		0			0
$949$	−24.3301	+	25.2846i	−0.789789	+	0.820773i
$950$	6.24871			0.202735
$951$		0			0
$952$	0.830127	+	1.43782i	0.0269046	+	0.0466001i
$953$	20.7846	−	36.0000i	0.673280	−	1.16615i	−0.303689	−	0.952771i	$-0.598218\pi$
$953$	20.7846	−	36.0000i	0.673280	−	1.16615i	0.976969	−	0.213383i	$-0.0684483\pi$
$954$		0			0
$955$	−1.60770	−	0.928203i	−0.0520238	−	0.0300360i
$956$	8.36603	+	4.83013i	0.270577	+	0.156217i
$957$		0			0
$958$	−13.2679	+	22.9808i	−0.428668	+	0.742475i
$959$	0.705771	+	1.22243i	0.0227905	+	0.0394744i
$960$		0			0
$961$	1.14359			0.0368901
$962$	36.2487	−	10.4641i	1.16871	−	0.337376i
$963$		0			0
$964$	−15.2321	+	8.79423i	−0.490591	+	0.283243i
$965$	−1.10770	−	1.91858i	−0.0356580	−	0.0617614i
$966$		0			0
$967$		−	18.8756i		−	0.607000i	−0.952831	−	0.303500i	$-0.901845\pi$
$967$		−	18.8756i		−	0.607000i	0.952831	−	0.303500i	$-0.0981552\pi$
$968$	9.86603	+	5.69615i	0.317106	+	0.183081i
$969$		0			0
$970$			1.60770i			0.0516200i
$971$	−9.12436	+	15.8038i	−0.292815	+	0.507170i	−0.974474	−	0.224500i	$-0.927925\pi$
$971$	−9.12436	+	15.8038i	−0.292815	+	0.507170i	0.681660	+	0.731669i	$0.261259\pi$
$972$		0			0
$973$	6.24871	−	3.60770i	0.200324	−	0.115657i
$974$	21.1244			0.676868
$975$		0			0
$976$	1.19615			0.0382879
$977$	−27.7750	+	16.0359i	−0.888601	+	0.513034i	−0.873485	−	0.486852i	$-0.838145\pi$
$977$	−27.7750	+	16.0359i	−0.888601	+	0.513034i	−0.0151161	+	0.999886i	$0.504812\pi$
$978$		0			0
$979$	−6.00000	+	10.3923i	−0.191761	+	0.332140i
$980$			1.73205i			0.0553283i
$981$		0			0
$982$	4.56218	+	2.63397i	0.145585	+	0.0840535i
$983$		−	20.7846i		−	0.662926i	−0.943468	−	0.331463i	$-0.892458\pi$
$983$		−	20.7846i		−	0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$984$		0			0
$985$	1.32051	+	2.28719i	0.0420749	+	0.0728758i
$986$	−4.83975	+	2.79423i	−0.154129	+	0.0889864i
$987$		0			0
$988$	−4.43782	−	1.09808i	−0.141186	−	0.0349345i
$989$	47.4641			1.50927
$990$		0			0
$991$	4.29423	+	7.43782i	0.136411	+	0.236270i	0.926135	−	0.377191i	$-0.123110\pi$
$991$	4.29423	+	7.43782i	0.136411	+	0.236270i	−0.789725	+	0.613461i	$0.789777\pi$
$992$	2.73205	−	4.73205i	0.0867427	−	0.150243i
$993$		0			0
$994$	−0.803848	−	0.464102i	−0.0254965	−	0.0147204i
$995$	0.882686	+	0.509619i	0.0279830	+	0.0161560i
$996$		0			0
$997$	−19.3301	+	33.4808i	−0.612191	+	1.06035i	0.378679	+	0.925528i	$0.376378\pi$
$997$	−19.3301	+	33.4808i	−0.612191	+	1.06035i	−0.990870	+	0.134818i	$0.956955\pi$
$998$	−16.0000	−	27.7128i	−0.506471	−	0.877234i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.l.c.127.1		4
3.2	odd	2		78.2.i.a.49.2	yes	4
4.3	odd	2		1872.2.by.h.1297.1		4
12.11	even	2		624.2.bv.e.49.2		4
13.2	odd	12		3042.2.a.p.1.2		2
13.3	even	3		3042.2.b.i.1351.2		4
13.4	even	6	inner	234.2.l.c.199.1		4
13.10	even	6		3042.2.b.i.1351.3		4
13.11	odd	12		3042.2.a.y.1.1		2
15.2	even	4		1950.2.y.g.49.1		4
15.8	even	4		1950.2.y.b.49.2		4
15.14	odd	2		1950.2.bc.d.751.1		4
39.2	even	12		1014.2.a.k.1.1		2
39.5	even	4		1014.2.e.g.991.1		4
39.8	even	4		1014.2.e.i.991.2		4
39.11	even	12		1014.2.a.i.1.2		2
39.17	odd	6		78.2.i.a.43.2	✓	4
39.20	even	12		1014.2.e.i.529.2		4
39.23	odd	6		1014.2.b.e.337.2		4
39.29	odd	6		1014.2.b.e.337.3		4
39.32	even	12		1014.2.e.g.529.1		4
39.35	odd	6		1014.2.i.a.823.1		4
39.38	odd	2		1014.2.i.a.361.1		4
52.43	odd	6		1872.2.by.h.433.2		4
156.11	odd	12		8112.2.a.bj.1.2		2
156.95	even	6		624.2.bv.e.433.1		4
156.119	odd	12		8112.2.a.bp.1.1		2
195.17	even	12		1950.2.y.b.199.2		4
195.134	odd	6		1950.2.bc.d.901.1		4
195.173	even	12		1950.2.y.g.199.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.2	✓	4	39.17	odd	6
78.2.i.a.49.2	yes	4	3.2	odd	2
234.2.l.c.127.1		4	1.1	even	1	trivial
234.2.l.c.199.1		4	13.4	even	6	inner
624.2.bv.e.49.2		4	12.11	even	2
624.2.bv.e.433.1		4	156.95	even	6
1014.2.a.i.1.2		2	39.11	even	12
1014.2.a.k.1.1		2	39.2	even	12
1014.2.b.e.337.2		4	39.23	odd	6
1014.2.b.e.337.3		4	39.29	odd	6
1014.2.e.g.529.1		4	39.32	even	12
1014.2.e.g.991.1		4	39.5	even	4
1014.2.e.i.529.2		4	39.20	even	12
1014.2.e.i.991.2		4	39.8	even	4
1014.2.i.a.361.1		4	39.38	odd	2
1014.2.i.a.823.1		4	39.35	odd	6
1872.2.by.h.433.2		4	52.43	odd	6
1872.2.by.h.1297.1		4	4.3	odd	2
1950.2.y.b.49.2		4	15.8	even	4
1950.2.y.b.199.2		4	195.17	even	12
1950.2.y.g.49.1		4	15.2	even	4
1950.2.y.g.199.1		4	195.173	even	12
1950.2.bc.d.751.1		4	15.14	odd	2
1950.2.bc.d.901.1		4	195.134	odd	6
3042.2.a.p.1.2		2	13.2	odd	12
3042.2.a.y.1.1		2	13.11	odd	12
3042.2.b.i.1351.2		4	13.3	even	3
3042.2.b.i.1351.3		4	13.10	even	6
8112.2.a.bj.1.2		2	156.11	odd	12
8112.2.a.bp.1.1		2	156.119	odd	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.267949i q^{5} +(0.633975 + 0.366025i) q^{7} +1.00000i q^{8} +(0.133975 + 0.232051i) q^{10} +(4.09808 - 2.36603i) q^{11} +(2.59808 + 2.50000i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.13397 - 1.96410i) q^{17} +(-1.09808 - 0.633975i) q^{19} +(-0.232051 - 0.133975i) q^{20} +(-2.36603 + 4.09808i) q^{22} +(3.09808 + 5.36603i) q^{23} +4.92820 q^{25} +(-3.50000 - 0.866025i) q^{26} +(0.633975 - 0.366025i) q^{28} +(1.23205 + 2.13397i) q^{29} -5.46410i q^{31} +(0.866025 + 0.500000i) q^{32} +2.26795i q^{34} +(0.0980762 - 0.169873i) q^{35} +(-9.06218 + 5.23205i) q^{37} +1.26795 q^{38} +0.267949 q^{40} +(-9.86603 + 5.69615i) q^{41} +(3.83013 - 6.63397i) q^{43} -4.73205i q^{44} +(-5.36603 - 3.09808i) q^{46} -8.19615i q^{47} +(-3.23205 - 5.59808i) q^{49} +(-4.26795 + 2.46410i) q^{50} +(3.46410 - 1.00000i) q^{52} -0.464102 q^{53} +(-0.633975 - 1.09808i) q^{55} +(-0.366025 + 0.633975i) q^{56} +(-2.13397 - 1.23205i) q^{58} +(-6.92820 - 4.00000i) q^{59} +(-0.598076 + 1.03590i) q^{61} +(2.73205 + 4.73205i) q^{62} -1.00000 q^{64} +(0.669873 - 0.696152i) q^{65} +(-9.63397 + 5.56218i) q^{67} +(-1.13397 - 1.96410i) q^{68} +0.196152i q^{70} +(1.09808 + 0.633975i) q^{71} +9.73205i q^{73} +(5.23205 - 9.06218i) q^{74} +(-1.09808 + 0.633975i) q^{76} +3.46410 q^{77} -9.46410 q^{79} +(-0.232051 + 0.133975i) q^{80} +(5.69615 - 9.86603i) q^{82} -10.1962i q^{83} +(-0.526279 - 0.303848i) q^{85} +7.66025i q^{86} +(2.36603 + 4.09808i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(0.732051 + 2.53590i) q^{91} +6.19615 q^{92} +(4.09808 + 7.09808i) q^{94} +(-0.169873 + 0.294229i) q^{95} +(5.19615 + 3.00000i) q^{97} +(5.59808 + 3.23205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 6 q^{7} + 4 q^{10} + 6 q^{11} + 4 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 2 q^{23} - 8 q^{25} - 14 q^{26} + 6 q^{28} - 2 q^{29} - 10 q^{35} - 12 q^{37} + 12 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^4 + 6 * q^7 + 4 * q^10 + 6 * q^11 + 4 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 2 * q^23 - 8 * q^25 - 14 * q^26 + 6 * q^28 - 2 * q^29 - 10 * q^35 - 12 * q^37 + 12 * q^38 + 8 * q^40 - 36 * q^41 - 2 * q^43 - 18 * q^46 - 6 * q^49 - 24 * q^50 + 12 * q^53 - 6 * q^55 + 2 * q^56 - 12 * q^58 + 8 * q^61 + 4 * q^62 - 4 * q^64 + 20 * q^65 - 42 * q^67 - 8 * q^68 - 6 * q^71 + 14 * q^74 + 6 * q^76 - 24 * q^79 + 6 * q^80 + 2 * q^82 + 36 * q^85 + 6 * q^88 + 12 * q^89 - 4 * q^91 + 4 * q^92 + 6 * q^94 - 18 * q^95 + 12 * q^98

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