LMFDB - Embedded newform 525.2.bf.d.32.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(32,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("525.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bf (of order $12$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	525.32
Dual form			525.2.bf.d.443.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(-1.62484 - 0.599900i) q^{3} +(-2.00000 - 1.41421i) q^{6} +(1.15539 + 2.38014i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.28024 + 1.94949i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(-1.62484 - 0.599900i) q^{3} +(-2.00000 - 1.41421i) q^{6} +(1.15539 + 2.38014i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.28024 + 1.94949i) q^{9} +(3.67423 + 2.12132i) q^{11} +(3.53553 - 3.53553i) q^{13} +(0.707107 + 3.67423i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-0.366025 - 1.36603i) q^{17} +(2.40130 + 3.49768i) q^{18} +(6.06218 - 3.50000i) q^{19} +(-0.449490 - 4.56048i) q^{21} +(4.24264 + 4.24264i) q^{22} +(-1.09808 + 4.09808i) q^{23} +(2.04989 + 4.44949i) q^{24} +(6.12372 - 3.53553i) q^{26} +(-2.53553 - 4.53553i) q^{27} +7.07107 q^{29} +(0.500000 - 0.866025i) q^{31} +(-4.69748 - 5.65099i) q^{33} -2.00000i q^{34} +(0.258819 - 0.965926i) q^{37} +(9.56218 - 2.56218i) q^{38} +(-7.86566 + 3.62372i) q^{39} +7.07107i q^{41} +(1.05524 - 6.39425i) q^{42} +(-3.53553 + 3.53553i) q^{43} +(-3.00000 + 5.19615i) q^{46} +(-5.46410 - 1.46410i) q^{47} +(1.17157 + 6.82843i) q^{48} +(-4.33013 + 5.50000i) q^{49} +(-0.224745 + 2.43916i) q^{51} +(-2.73205 + 0.732051i) q^{53} +(-1.80348 - 7.12372i) q^{54} +(2.44949 - 7.07107i) q^{56} +(-11.9497 + 2.05025i) q^{57} +(9.65926 + 2.58819i) q^{58} +(0.707107 - 1.22474i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(1.00000 - 1.00000i) q^{62} +(-2.00548 + 7.67972i) q^{63} +8.00000i q^{64} +(-4.34847 - 9.43879i) q^{66} +(0.965926 - 0.258819i) q^{67} +(4.24264 - 6.00000i) q^{69} +7.07107i q^{71} +(-0.661498 - 8.45946i) q^{72} +(-1.81173 - 6.76148i) q^{73} +(0.707107 - 1.22474i) q^{74} +(-0.803848 + 11.1962i) q^{77} +(-12.0711 + 2.07107i) q^{78} +(6.06218 - 3.50000i) q^{79} +(1.39898 + 8.89060i) q^{81} +(-2.58819 + 9.65926i) q^{82} +(1.00000 + 1.00000i) q^{83} +(-6.12372 + 3.53553i) q^{86} +(-11.4894 - 4.24194i) q^{87} +(-3.10583 - 11.5911i) q^{88} +(-7.77817 - 13.4722i) q^{89} +(12.5000 + 4.33013i) q^{91} +(-1.33195 + 1.10721i) q^{93} +(-6.92820 - 4.00000i) q^{94} +(7.07107 + 7.07107i) q^{97} +(-7.92820 + 5.92820i) q^{98} +(4.24264 + 12.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{3} - 16 q^{6} - 16 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^3 - 16 * q^6 - 16 * q^8	$ 8 q + 4 q^{2} - 4 q^{3} - 16 q^{6} - 16 q^{8} - 16 q^{16} + 4 q^{17} + 4 q^{18} + 16 q^{21} + 12 q^{23} + 8 q^{27} + 4 q^{31} - 12 q^{33} + 28 q^{38} + 20 q^{42} - 24 q^{46} - 16 q^{47} + 32 q^{48} + 8 q^{51} - 8 q^{53} - 56 q^{57} - 16 q^{61} + 8 q^{62} + 8 q^{63} + 24 q^{66} - 8 q^{72} - 48 q^{77} - 40 q^{78} - 28 q^{81} + 8 q^{83} + 20 q^{87} + 100 q^{91} + 4 q^{93} - 8 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^3 - 16 * q^6 - 16 * q^8 - 16 * q^16 + 4 * q^17 + 4 * q^18 + 16 * q^21 + 12 * q^23 + 8 * q^27 + 4 * q^31 - 12 * q^33 + 28 * q^38 + 20 * q^42 - 24 * q^46 - 16 * q^47 + 32 * q^48 + 8 * q^51 - 8 * q^53 - 56 * q^57 - 16 * q^61 + 8 * q^62 + 8 * q^63 + 24 * q^66 - 8 * q^72 - 48 * q^77 - 40 * q^78 - 28 * q^81 + 8 * q^83 + 20 * q^87 + 100 * q^91 + 4 * q^93 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.36603	+	0.366025i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$2$	1.36603	+	0.366025i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$3$	−1.62484	−	0.599900i	−0.938104	−	0.346353i
$3$	−1.62484	−	0.599900i	−0.938104	−	0.346353i
$4$		0			0
$5$		0			0
$5$		0			0
$6$	−2.00000	−	1.41421i	−0.816497	−	0.577350i
$7$	1.15539	+	2.38014i	0.436698	+	0.899608i
$7$	1.15539	+	2.38014i	0.436698	+	0.899608i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	2.28024	+	1.94949i	0.760080	+	0.649830i
$10$		0			0
$11$	3.67423	+	2.12132i	1.10782	+	0.639602i	0.938265	−	0.345918i	$-0.112432\pi$
$11$	3.67423	+	2.12132i	1.10782	+	0.639602i	0.169559	+	0.985520i	$0.445766\pi$
$12$		0			0
$13$	3.53553	−	3.53553i	0.980581	−	0.980581i	−0.0192343	−	0.999815i	$-0.506123\pi$
$13$	3.53553	−	3.53553i	0.980581	−	0.980581i	0.999815	+	0.0192343i	$0.00612285\pi$
$14$	0.707107	+	3.67423i	0.188982	+	0.981981i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−0.366025	−	1.36603i	−0.0887742	−	0.331310i	0.907228	−	0.420639i	$-0.138194\pi$
$17$	−0.366025	−	1.36603i	−0.0887742	−	0.331310i	−0.996002	+	0.0893296i	$0.971528\pi$
$18$	2.40130	+	3.49768i	0.565992	+	0.824411i
$19$	6.06218	−	3.50000i	1.39076	−	0.802955i	0.397360	−	0.917663i	$-0.369927\pi$
$19$	6.06218	−	3.50000i	1.39076	−	0.802955i	0.993399	+	0.114708i	$0.0365932\pi$
$20$		0			0
$21$	−0.449490	−	4.56048i	−0.0980867	−	0.995178i
$22$	4.24264	+	4.24264i	0.904534	+	0.904534i
$23$	−1.09808	+	4.09808i	−0.228965	+	0.854508i	0.751812	+	0.659377i	$0.229180\pi$
$23$	−1.09808	+	4.09808i	−0.228965	+	0.854508i	−0.980777	+	0.195131i	$0.937487\pi$
$24$	2.04989	+	4.44949i	0.418432	+	0.908248i
$25$		0			0
$26$	6.12372	−	3.53553i	1.20096	−	0.693375i
$27$	−2.53553	−	4.53553i	−0.487964	−	0.872864i
$28$		0			0
$29$	7.07107			1.31306			0.656532	−	0.754298i	$-0.272023\pi$
$29$	7.07107			1.31306			0.656532	+	0.754298i	$0.272023\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$		0			0
$33$	−4.69748	−	5.65099i	−0.817726	−	0.983711i
$34$		−	2.00000i		−	0.342997i
$35$		0			0
$36$		0			0
$37$	0.258819	−	0.965926i	0.0425496	−	0.158797i	−0.941382	−	0.337342i	$-0.890472\pi$
$37$	0.258819	−	0.965926i	0.0425496	−	0.158797i	0.983932	+	0.178545i	$0.0571389\pi$
$38$	9.56218	−	2.56218i	1.55119	−	0.415640i
$39$	−7.86566	+	3.62372i	−1.25951	+	0.580260i
$40$		0			0
$41$			7.07107i			1.10432i	0.833740	+	0.552158i	$0.186195\pi$
$41$			7.07107i			1.10432i	−0.833740	+	0.552158i	$0.813805\pi$
$42$	1.05524	−	6.39425i	0.162827	−	0.986655i
$43$	−3.53553	+	3.53553i	−0.539164	+	0.539164i	−0.923283	−	0.384120i	$-0.874505\pi$
$43$	−3.53553	+	3.53553i	−0.539164	+	0.539164i	0.384120	+	0.923283i	$0.374505\pi$
$44$		0			0
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−5.46410	−	1.46410i	−0.797021	−	0.213561i	−0.162745	−	0.986668i	$-0.552035\pi$
$47$	−5.46410	−	1.46410i	−0.797021	−	0.213561i	−0.634276	+	0.773107i	$0.718702\pi$
$48$	1.17157	+	6.82843i	0.169102	+	0.985599i
$49$	−4.33013	+	5.50000i	−0.618590	+	0.785714i
$50$		0			0
$51$	−0.224745	+	2.43916i	−0.0314706	+	0.341550i
$52$		0			0
$53$	−2.73205	+	0.732051i	−0.375276	+	0.100555i	−0.441527	−	0.897248i	$-0.645563\pi$
$53$	−2.73205	+	0.732051i	−0.375276	+	0.100555i	0.0662507	+	0.997803i	$0.478896\pi$
$54$	−1.80348	−	7.12372i	−0.245423	−	0.969416i
$55$		0			0
$56$	2.44949	−	7.07107i	0.327327	−	0.944911i
$57$	−11.9497	+	2.05025i	−1.58278	+	0.271563i
$58$	9.65926	+	2.58819i	1.26832	+	0.339846i
$59$	0.707107	−	1.22474i	0.0920575	−	0.159448i	−0.816319	−	0.577601i	$-0.803989\pi$
$59$	0.707107	−	1.22474i	0.0920575	−	0.159448i	0.908377	+	0.418153i	$0.137322\pi$
$60$		0			0
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$	1.00000	−	1.00000i	0.127000	−	0.127000i
$63$	−2.00548	+	7.67972i	−0.252667	+	0.967553i
$64$			8.00000i			1.00000i
$65$		0			0
$66$	−4.34847	−	9.43879i	−0.535260	−	1.16184i
$67$	0.965926	−	0.258819i	0.118007	−	0.0316198i	−0.199332	−	0.979932i	$-0.563877\pi$
$67$	0.965926	−	0.258819i	0.118007	−	0.0316198i	0.317339	+	0.948312i	$0.397211\pi$
$68$		0			0
$69$	4.24264	−	6.00000i	0.510754	−	0.722315i
$70$		0			0
$71$			7.07107i			0.839181i	0.907713	+	0.419591i	$0.137826\pi$
$71$			7.07107i			0.839181i	−0.907713	+	0.419591i	$0.862174\pi$
$72$	−0.661498	−	8.45946i	−0.0779583	−	0.996957i
$73$	−1.81173	−	6.76148i	−0.212047	−	0.791371i	−0.987185	−	0.159579i	$-0.948986\pi$
$73$	−1.81173	−	6.76148i	−0.212047	−	0.791371i	0.775138	−	0.631792i	$-0.217680\pi$
$74$	0.707107	−	1.22474i	0.0821995	−	0.142374i
$75$		0			0
$76$		0			0
$77$	−0.803848	+	11.1962i	−0.0916069	+	1.27592i
$78$	−12.0711	+	2.07107i	−1.36678	+	0.234502i
$79$	6.06218	−	3.50000i	0.682048	−	0.393781i	−0.118578	−	0.992945i	$-0.537834\pi$
$79$	6.06218	−	3.50000i	0.682048	−	0.393781i	0.800626	+	0.599164i	$0.204500\pi$
$80$		0			0
$81$	1.39898	+	8.89060i	0.155442	+	0.987845i
$82$	−2.58819	+	9.65926i	−0.285818	+	1.06669i
$83$	1.00000	+	1.00000i	0.109764	+	0.109764i	0.759856	−	0.650092i	$-0.225269\pi$
$83$	1.00000	+	1.00000i	0.109764	+	0.109764i	−0.650092	+	0.759856i	$0.725269\pi$
$84$		0			0
$85$		0			0
$86$	−6.12372	+	3.53553i	−0.660338	+	0.381246i
$87$	−11.4894	−	4.24194i	−1.23179	−	0.454783i
$88$	−3.10583	−	11.5911i	−0.331082	−	1.23562i
$89$	−7.77817	−	13.4722i	−0.824485	−	1.42805i	−0.902312	−	0.431083i	$-0.858132\pi$
$89$	−7.77817	−	13.4722i	−0.824485	−	1.42805i	0.0778275	−	0.996967i	$-0.475202\pi$
$90$		0			0
$91$	12.5000	+	4.33013i	1.31036	+	0.453921i
$92$		0			0
$93$	−1.33195	+	1.10721i	−0.138117	+	0.114812i
$94$	−6.92820	−	4.00000i	−0.714590	−	0.412568i
$95$		0			0
$96$		0			0
$97$	7.07107	+	7.07107i	0.717958	+	0.717958i	0.968187	−	0.250229i	$-0.0805058\pi$
$97$	7.07107	+	7.07107i	0.717958	+	0.717958i	−0.250229	+	0.968187i	$0.580506\pi$
$98$	−7.92820	+	5.92820i	−0.800869	+	0.598839i
$99$	4.24264	+	12.0000i	0.426401	+	1.20605i
$100$		0			0
$101$	−8.57321	−	4.94975i	−0.853067	−	0.492518i	0.00861771	−	0.999963i	$-0.497257\pi$
$101$	−8.57321	−	4.94975i	−0.853067	−	0.492518i	−0.861684	+	0.507445i	$0.830590\pi$
$102$	−1.19980	+	3.24969i	−0.118798	+	0.321767i
$103$	2.89778	+	0.776457i	0.285526	+	0.0765066i	0.398740	−	0.917064i	$-0.369448\pi$
$103$	2.89778	+	0.776457i	0.285526	+	0.0765066i	−0.113213	+	0.993571i	$0.536114\pi$
$104$	−14.1421			−1.38675
$105$		0			0
$106$	−4.00000			−0.388514
$107$	15.0263	+	4.02628i	1.45265	+	0.389235i	0.896943	−	0.442146i	$-0.145783\pi$
$107$	15.0263	+	4.02628i	1.45265	+	0.389235i	0.555702	+	0.831381i	$0.312449\pi$
$108$		0			0
$109$	−14.7224	−	8.50000i	−1.41015	−	0.814152i	−0.414751	−	0.909935i	$-0.636131\pi$
$109$	−14.7224	−	8.50000i	−1.41015	−	0.814152i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$	−1.00000	+	1.41421i	−0.0949158	+	0.134231i
$112$	5.93426	−	8.76268i	0.560734	−	0.827996i
$113$	−14.0000	−	14.0000i	−1.31701	−	1.31701i	−0.916132	−	0.400878i	$-0.868705\pi$
$113$	−14.0000	−	14.0000i	−1.31701	−	1.31701i	−0.400878	−	0.916132i	$-0.631295\pi$
$114$	−17.0741	−	1.57321i	−1.59914	−	0.147345i
$115$		0			0
$116$		0			0
$117$	14.9543	−	1.16938i	1.38253	−	0.108109i
$118$	1.41421	−	1.41421i	0.130189	−	0.130189i
$119$	2.82843	−	2.44949i	0.259281	−	0.224544i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.46410	−	5.46410i	−0.132554	−	0.494697i
$123$	4.24194	−	11.4894i	0.382483	−	1.03596i
$124$		0			0
$125$		0			0
$126$	−5.55051	+	9.75663i	−0.494479	+	0.869190i
$127$	10.6066	+	10.6066i	0.941184	+	0.941184i	0.998364	−	0.0571802i	$-0.0182109\pi$
$127$	10.6066	+	10.6066i	0.941184	+	0.941184i	−0.0571802	+	0.998364i	$0.518211\pi$
$128$	−2.92820	+	10.9282i	−0.258819	+	0.965926i
$129$	7.86566	−	3.62372i	0.692533	−	0.319051i
$130$		0			0
$131$	−14.6969	+	8.48528i	−1.28408	+	0.741362i	−0.977591	−	0.210513i	$-0.932487\pi$
$131$	−14.6969	+	8.48528i	−1.28408	+	0.741362i	−0.306486	+	0.951875i	$0.599153\pi$
$132$		0			0
$133$	15.3347	+	10.3849i	1.32969	+	0.900489i
$134$	1.41421			0.122169
$135$		0			0
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	−4.02628	−	15.0263i	−0.343988	−	1.28378i	−0.893790	−	0.448486i	$-0.851963\pi$
$137$	−4.02628	−	15.0263i	−0.343988	−	1.28378i	0.549801	−	0.835295i	$-0.314703\pi$
$138$	7.99171	−	6.64324i	0.680299	−	0.565510i
$139$			11.0000i			0.933008i	0.884519	+	0.466504i	$0.154487\pi$
$139$			11.0000i			0.933008i	−0.884519	+	0.466504i	$0.845513\pi$
$140$		0			0
$141$	8.00000	+	5.65685i	0.673722	+	0.476393i
$142$	−2.58819	+	9.65926i	−0.217196	+	0.810587i
$143$	20.4904	−	5.49038i	1.71349	−	0.459129i
$144$	2.19275	−	11.7980i	0.182729	−	0.983163i
$145$		0			0
$146$		−	9.89949i		−	0.819288i
$147$	10.3352	−	6.33900i	0.852436	−	0.522832i
$148$		0			0
$149$	−4.24264	−	7.34847i	−0.347571	−	0.602010i	0.638247	−	0.769832i	$-0.279660\pi$
$149$	−4.24264	−	7.34847i	−0.347571	−	0.602010i	−0.985817	+	0.167822i	$0.946327\pi$
$150$		0			0
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	−0.717752	−	0.696299i	$-0.754829\pi$
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	0.961888	+	0.273442i	$0.0881622\pi$
$152$	−19.1244	−	5.12436i	−1.55119	−	0.415640i
$153$	1.82843	−	3.82843i	0.147820	−	0.309510i
$154$	−5.19615	+	15.0000i	−0.418718	+	1.20873i
$155$		0			0
$156$		0			0
$157$	−3.86370	+	1.03528i	−0.308357	+	0.0826240i	−0.409679	−	0.912230i	$-0.634359\pi$
$157$	−3.86370	+	1.03528i	−0.308357	+	0.0826240i	0.101322	+	0.994854i	$0.467693\pi$
$158$	9.56218	−	2.56218i	0.760726	−	0.203836i
$159$	4.87832	+	0.449490i	0.386876	+	0.0356469i
$160$		0			0
$161$	−11.0227	+	2.12132i	−0.868711	+	0.167183i
$162$	−1.34315	+	12.6569i	−0.105527	+	0.994416i
$163$	−1.93185	−	0.517638i	−0.151314	−	0.0405445i	0.182367	−	0.983231i	$-0.441624\pi$
$163$	−1.93185	−	0.517638i	−0.151314	−	0.0405445i	−0.333681	+	0.942686i	$0.608291\pi$
$164$		0			0
$165$		0			0
$166$	1.00000	+	1.73205i	0.0776151	+	0.134433i
$167$	7.00000	−	7.00000i	0.541676	−	0.541676i	−0.382344	−	0.924020i	$-0.624883\pi$
$167$	7.00000	−	7.00000i	0.541676	−	0.541676i	0.924020	+	0.382344i	$0.124883\pi$
$168$	−8.22198	+	10.0199i	−0.634339	+	0.773055i
$169$		−	12.0000i		−	0.923077i
$170$		0			0
$171$	20.6464	+	3.83732i	1.57887	+	0.293447i
$172$		0			0
$173$	0.732051	−	2.73205i	0.0556568	−	0.207714i	−0.932498	−	0.361176i	$-0.882375\pi$
$173$	0.732051	−	2.73205i	0.0556568	−	0.207714i	0.988155	+	0.153462i	$0.0490422\pi$
$174$	−14.1421	−	10.0000i	−1.07211	−	0.758098i
$175$		0			0
$176$		−	16.9706i		−	1.27920i
$177$	−1.88366	+	1.56583i	−0.141585	+	0.117695i
$178$	−5.69402	−	21.2504i	−0.426785	−	1.59278i
$179$	−9.89949	+	17.1464i	−0.739923	+	1.28158i	0.212607	+	0.977138i	$0.431805\pi$
$179$	−9.89949	+	17.1464i	−0.739923	+	1.28158i	−0.952529	+	0.304446i	$0.901529\pi$
$180$		0			0
$181$	−3.00000			−0.222988			−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000			−0.222988			−0.111494	+	0.993765i	$0.535564\pi$
$182$	15.4904	+	10.4904i	1.14822	+	0.777599i
$183$	1.17157	+	6.82843i	0.0866052	+	0.504772i
$184$	10.3923	−	6.00000i	0.766131	−	0.442326i
$185$		0			0
$186$	−2.22474	+	1.02494i	−0.163126	+	0.0751525i
$187$	1.55291	−	5.79555i	0.113560	−	0.423813i
$188$		0			0
$189$	7.86566	−	11.2753i	0.572143	−	0.820154i
$190$		0			0
$191$	9.79796	−	5.65685i	0.708955	−	0.409316i	−0.101719	−	0.994813i	$-0.532434\pi$
$191$	9.79796	−	5.65685i	0.708955	−	0.409316i	0.810674	+	0.585498i	$0.199101\pi$
$192$	4.79920	−	12.9988i	0.346353	−	0.938104i
$193$	5.95284	+	22.2163i	0.428495	+	1.59916i	0.756171	+	0.654374i	$0.227068\pi$
$193$	5.95284	+	22.2163i	0.428495	+	1.59916i	−0.327677	+	0.944790i	$0.606266\pi$
$194$	7.07107	+	12.2474i	0.507673	+	0.879316i
$195$		0			0
$196$		0			0
$197$	−3.00000	+	3.00000i	−0.213741	+	0.213741i	−0.805855	−	0.592113i	$-0.798294\pi$
$197$	−3.00000	+	3.00000i	−0.213741	+	0.213741i	0.592113	+	0.805855i	$0.298294\pi$
$198$	1.40325	+	17.9452i	0.0997246	+	1.27531i
$199$	−1.73205	−	1.00000i	−0.122782	−	0.0708881i	0.437351	−	0.899291i	$-0.355917\pi$
$199$	−1.73205	−	1.00000i	−0.122782	−	0.0708881i	−0.560133	+	0.828403i	$0.689250\pi$
$200$		0			0
$201$	−1.72474	−	0.158919i	−0.121654	−	0.0112093i
$202$	−9.89949	−	9.89949i	−0.696526	−	0.696526i
$203$	8.16987	+	16.8301i	0.573413	+	1.18124i
$204$		0			0
$205$		0			0
$206$	3.67423	+	2.12132i	0.255996	+	0.147799i
$207$	−10.4930	+	7.20390i	−0.729316	+	0.500706i
$208$	−19.3185	−	5.17638i	−1.33950	−	0.358917i
$209$	29.6985			2.05429
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$		0			0
$213$	4.24194	−	11.4894i	0.290653	−	0.787240i
$214$	19.0526	+	11.0000i	1.30241	+	0.751945i
$215$		0			0
$216$	−4.00000	+	14.1421i	−0.272166	+	0.962250i
$217$	2.63896	+	0.189469i	0.179144	+	0.0128620i
$218$	−17.0000	−	17.0000i	−1.15139	−	1.15139i
$219$	−1.11243	+	12.0732i	−0.0751711	+	0.815832i
$220$		0			0
$221$	−6.12372	−	3.53553i	−0.411926	−	0.237826i
$222$	−1.88366	+	1.56583i	−0.126423	+	0.105091i
$223$	−7.07107	+	7.07107i	−0.473514	+	0.473514i	−0.903050	−	0.429536i	$-0.858677\pi$
$223$	−7.07107	+	7.07107i	−0.473514	+	0.473514i	0.429536	+	0.903050i	$0.358677\pi$
$224$		0			0
$225$		0			0
$226$	−14.0000	−	24.2487i	−0.931266	−	1.61300i
$227$	3.29423	+	12.2942i	0.218646	+	0.815997i	0.984851	+	0.173401i	$0.0554757\pi$
$227$	3.29423	+	12.2942i	0.218646	+	0.815997i	−0.766206	+	0.642595i	$0.777858\pi$
$228$		0			0
$229$	−2.59808	+	1.50000i	−0.171686	+	0.0991228i	−0.583380	−	0.812199i	$-0.698270\pi$
$229$	−2.59808	+	1.50000i	−0.171686	+	0.0991228i	0.411695	+	0.911322i	$0.364937\pi$
$230$		0			0
$231$	8.02270	−	17.7098i	0.527855	−	1.16522i
$232$	−14.1421	−	14.1421i	−0.928477	−	0.928477i
$233$	0.732051	−	2.73205i	0.0479582	−	0.178983i	−0.937792	−	0.347197i	$-0.887133\pi$
$233$	0.732051	−	2.73205i	0.0479582	−	0.178983i	0.985750	+	0.168215i	$0.0538001\pi$
$234$	20.8560	+	3.87628i	1.36340	+	0.253400i
$235$		0			0
$236$		0			0
$237$	−11.9497	+	2.05025i	−0.776220	+	0.133178i
$238$	4.76028	−	2.31079i	0.308563	−	0.149786i
$239$	−28.2843			−1.82956			−0.914779	−	0.403955i	$-0.867635\pi$
$239$	−28.2843			−1.82956			−0.914779	+	0.403955i	$0.867635\pi$
$240$		0			0
$241$	−12.0000	+	20.7846i	−0.772988	+	1.33885i	0.162930	+	0.986638i	$0.447905\pi$
$241$	−12.0000	+	20.7846i	−0.772988	+	1.33885i	−0.935918	+	0.352217i	$0.885428\pi$
$242$	2.56218	+	9.56218i	0.164703	+	0.614680i
$243$	3.06035	−	15.2851i	0.196322	−	0.980540i
$244$		0			0
$245$		0			0
$246$	10.0000	−	14.1421i	0.637577	−	0.901670i
$247$	9.05867	−	33.8074i	0.576389	−	2.15111i
$248$	−2.73205	+	0.732051i	−0.173485	+	0.0464853i
$249$	−1.02494	−	2.22474i	−0.0649532	−	0.140987i
$250$		0			0
$251$		−	7.07107i		−	0.446322i	−0.974782	−	0.223161i	$-0.928362\pi$
$251$		−	7.07107i		−	0.446322i	0.974782	−	0.223161i	$-0.0716375\pi$
$252$		0			0
$253$	−12.7279	+	12.7279i	−0.800198	+	0.800198i
$254$	10.6066	+	18.3712i	0.665517	+	1.15271i
$255$		0			0
$256$		0			0
$257$	−12.2942	−	3.29423i	−0.766893	−	0.205488i	−0.145894	−	0.989300i	$-0.546606\pi$
$257$	−12.2942	−	3.29423i	−0.766893	−	0.205488i	−0.620998	+	0.783812i	$0.713273\pi$
$258$	12.0711	−	2.07107i	0.751512	−	0.128939i
$259$	2.59808	−	0.500000i	0.161437	−	0.0310685i
$260$		0			0
$261$	16.1237	+	13.7850i	0.998033	+	0.853268i
$262$	−23.1822	+	6.21166i	−1.43220	+	0.383757i
$263$	−16.3923	+	4.39230i	−1.01079	+	0.270841i	−0.725961	−	0.687736i	$-0.758605\pi$
$263$	−16.3923	+	4.39230i	−1.01079	+	0.270841i	−0.284832	+	0.958577i	$0.591938\pi$
$264$	−1.90702	+	20.6969i	−0.117369	+	1.27381i
$265$		0			0
$266$	17.1464	+	19.7990i	1.05131	+	1.21395i
$267$	4.55635	+	26.5563i	0.278844	+	1.62522i
$268$		0			0
$269$	−2.82843	+	4.89898i	−0.172452	+	0.298696i	−0.939277	−	0.343161i	$-0.888502\pi$
$269$	−2.82843	+	4.89898i	−0.172452	+	0.298696i	0.766824	+	0.641857i	$0.221836\pi$
$270$		0			0
$271$	−7.00000	−	12.1244i	−0.425220	−	0.736502i	0.571221	−	0.820796i	$-0.306470\pi$
$271$	−7.00000	−	12.1244i	−0.425220	−	0.736502i	−0.996441	+	0.0842940i	$0.973137\pi$
$272$	−4.00000	+	4.00000i	−0.242536	+	0.242536i
$273$	−17.7129	−	14.5345i	−1.07203	−	0.879670i
$274$		−	22.0000i		−	1.32907i
$275$		0			0
$276$		0			0
$277$	−8.69333	+	2.32937i	−0.522332	+	0.139958i	−0.510345	−	0.859970i	$-0.670482\pi$
$277$	−8.69333	+	2.32937i	−0.522332	+	0.139958i	−0.0119868	+	0.999928i	$0.503816\pi$
$278$	−4.02628	+	15.0263i	−0.241480	+	0.901216i
$279$	2.82843	−	1.00000i	0.169334	−	0.0598684i
$280$		0			0
$281$		−	14.1421i		−	0.843649i	−0.906677	−	0.421825i	$-0.861390\pi$
$281$		−	14.1421i		−	0.843649i	0.906677	−	0.421825i	$-0.138610\pi$
$282$	8.85765	+	10.6556i	0.527465	+	0.634532i
$283$	5.95284	+	22.2163i	0.353859	+	1.32062i	0.881914	+	0.471411i	$0.156255\pi$
$283$	5.95284	+	22.2163i	0.353859	+	1.32062i	−0.528054	+	0.849211i	$0.677078\pi$
$284$		0			0
$285$		0			0
$286$	30.0000			1.77394
$287$	−16.8301	+	8.16987i	−0.993451	+	0.482252i
$288$		0			0
$289$	12.9904	−	7.50000i	0.764140	−	0.441176i
$290$		0			0
$291$	−7.24745	−	15.7313i	−0.424853	−	0.922186i
$292$		0			0
$293$	16.0000	+	16.0000i	0.934730	+	0.934730i	0.997997	−	0.0632667i	$-0.0201519\pi$
$293$	16.0000	+	16.0000i	0.934730	+	0.934730i	−0.0632667	+	0.997997i	$0.520152\pi$
$294$	16.4384	−	4.87628i	0.958709	−	0.284390i
$295$		0			0
$296$	−2.44949	+	1.41421i	−0.142374	+	0.0821995i
$297$	0.305174	−	22.0433i	0.0177080	−	1.27908i
$298$	−3.10583	−	11.5911i	−0.179916	−	0.671455i
$299$	10.6066	+	18.3712i	0.613396	+	1.06243i
$300$		0			0
$301$	−12.5000	−	4.33013i	−0.720488	−	0.249584i
$302$	6.00000	−	6.00000i	0.345261	−	0.345261i
$303$	10.9608	+	13.1856i	0.629681	+	0.757495i
$304$	−24.2487	−	14.0000i	−1.39076	−	0.802955i
$305$		0			0
$306$	3.89898	−	4.56048i	0.222890	−	0.260705i
$307$	−10.6066	−	10.6066i	−0.605351	−	0.605351i	0.336377	−	0.941727i	$-0.390798\pi$
$307$	−10.6066	−	10.6066i	−0.605351	−	0.605351i	−0.941727	+	0.336377i	$0.890798\pi$
$308$		0			0
$309$	−4.24264	−	3.00000i	−0.241355	−	0.170664i
$310$		0			0
$311$	28.1691	+	16.2635i	1.59732	+	0.922216i	0.992000	+	0.126237i	$0.0402901\pi$
$311$	28.1691	+	16.2635i	1.59732	+	0.922216i	0.605325	+	0.795979i	$0.293043\pi$
$312$	22.9788	+	8.48387i	1.30092	+	0.480305i
$313$	−16.4207	−	4.39992i	−0.928155	−	0.248698i	−0.237087	−	0.971488i	$-0.576193\pi$
$313$	−16.4207	−	4.39992i	−0.928155	−	0.248698i	−0.691068	+	0.722790i	$0.742859\pi$
$314$	−5.65685			−0.319235
$315$		0			0
$316$		0			0
$317$	1.36603	+	0.366025i	0.0767236	+	0.0205580i	0.296977	−	0.954885i	$-0.404022\pi$
$317$	1.36603	+	0.366025i	0.0767236	+	0.0205580i	−0.220253	+	0.975443i	$0.570688\pi$
$318$	6.49938	+	2.39960i	0.364467	+	0.134563i
$319$	25.9808	+	15.0000i	1.45464	+	0.839839i
$320$		0			0
$321$	−22.0000	−	15.5563i	−1.22792	−	0.868271i
$322$	−15.8338	−	1.13681i	−0.882380	−	0.0633521i
$323$	−7.00000	−	7.00000i	−0.389490	−	0.389490i
$324$		0			0
$325$		0			0
$326$	−2.44949	−	1.41421i	−0.135665	−	0.0783260i
$327$	18.8225	+	22.6432i	1.04089	+	1.25217i
$328$	14.1421	−	14.1421i	0.780869	−	0.780869i
$329$	−2.82843	−	14.6969i	−0.155936	−	0.810268i
$330$		0			0
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	0.879440	−	0.476011i	$-0.157918\pi$
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	−0.851957	+	0.523612i	$0.824584\pi$
$332$		0			0
$333$	2.47323	−	1.69798i	0.135532	−	0.0930485i
$334$	12.1244	−	7.00000i	0.663415	−	0.383023i
$335$		0			0
$336$	−14.8990	+	10.6780i	−0.812806	+	0.582535i
$337$	3.53553	+	3.53553i	0.192593	+	0.192593i	0.796815	−	0.604223i	$-0.206516\pi$
$337$	3.53553	+	3.53553i	0.192593	+	0.192593i	−0.604223	+	0.796815i	$0.706516\pi$
$338$	4.39230	−	16.3923i	0.238910	−	0.891624i
$339$	14.3492	+	31.1464i	0.779342	+	1.69164i
$340$		0			0
$341$	3.67423	−	2.12132i	0.198971	−	0.114876i
$342$	26.7990	+	12.7990i	1.44912	+	0.692090i
$343$	−18.0938	−	3.95164i	−0.976972	−	0.213368i
$344$	14.1421			0.762493
$345$		0			0
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	−5.85641	−	21.8564i	−0.314388	−	1.17331i	−0.924558	−	0.381042i	$-0.875565\pi$
$347$	−5.85641	−	21.8564i	−0.314388	−	1.17331i	0.610169	−	0.792271i	$-0.291101\pi$
$348$		0			0
$349$			26.0000i			1.39175i	0.718164	+	0.695874i	$0.244983\pi$
$349$			26.0000i			1.39175i	−0.718164	+	0.695874i	$0.755017\pi$
$350$		0			0
$351$	−25.0000	−	7.07107i	−1.33440	−	0.377426i
$352$		0			0
$353$	4.09808	−	1.09808i	0.218119	−	0.0584447i	−0.148105	−	0.988972i	$-0.547317\pi$
$353$	4.09808	−	1.09808i	0.218119	−	0.0584447i	0.366223	+	0.930527i	$0.380651\pi$
$354$	−3.14626	+	1.44949i	−0.167222	+	0.0770395i
$355$		0			0
$356$		0			0
$357$	−6.06520	+	2.28327i	−0.321005	+	0.120843i
$358$	−19.7990	+	19.7990i	−1.04641	+	1.04641i
$359$	−0.707107	−	1.22474i	−0.0373197	−	0.0646396i	0.846762	−	0.531971i	$-0.178549\pi$
$359$	−0.707107	−	1.22474i	−0.0373197	−	0.0646396i	−0.884082	+	0.467332i	$0.845215\pi$
$360$		0			0
$361$	15.0000	−	25.9808i	0.789474	−	1.36741i
$362$	−4.09808	−	1.09808i	−0.215390	−	0.0577136i
$363$	−2.05025	−	11.9497i	−0.107610	−	0.627199i
$364$		0			0
$365$		0			0
$366$	−0.898979	+	9.75663i	−0.0469904	+	0.509987i
$367$	20.2844	−	5.43520i	1.05884	−	0.283715i	0.312939	−	0.949773i	$-0.398686\pi$
$367$	20.2844	−	5.43520i	1.05884	−	0.283715i	0.745900	+	0.666058i	$0.232020\pi$
$368$	16.3923	−	4.39230i	0.854508	−	0.228965i
$369$	−13.7850	+	16.1237i	−0.717617	+	0.839368i
$370$		0			0
$371$	−4.89898	−	5.65685i	−0.254342	−	0.293689i
$372$		0			0
$373$	22.2163	+	5.95284i	1.15032	+	0.308226i	0.783092	−	0.621906i	$-0.213641\pi$
$373$	22.2163	+	5.95284i	1.15032	+	0.308226i	0.367224	+	0.930132i	$0.380308\pi$
$374$	4.24264	−	7.34847i	0.219382	−	0.379980i
$375$		0			0
$376$	8.00000	+	13.8564i	0.412568	+	0.714590i
$377$	25.0000	−	25.0000i	1.28757	−	1.28757i
$378$	14.8717	−	12.5233i	0.764919	−	0.644127i
$379$		−	9.00000i		−	0.462299i	−0.972918	−	0.231149i	$-0.925751\pi$
$379$		−	9.00000i		−	0.462299i	0.972918	−	0.231149i	$-0.0742486\pi$
$380$		0			0
$381$	−10.8712	−	23.5970i	−0.556947	−	1.20891i
$382$	15.4548	−	4.14110i	0.790737	−	0.211877i
$383$	4.39230	−	16.3923i	0.224436	−	0.837608i	−0.758193	−	0.652030i	$-0.773918\pi$
$383$	4.39230	−	16.3923i	0.224436	−	0.837608i	0.982630	−	0.185578i	$-0.0594157\pi$
$384$	11.3137	−	16.0000i	0.577350	−	0.816497i
$385$		0			0
$386$			32.5269i			1.65558i
$387$	−14.9543	+	1.16938i	−0.760172	+	0.0594427i
$388$		0			0
$389$	14.8492	−	25.7196i	0.752886	−	1.30404i	−0.193532	−	0.981094i	$-0.561994\pi$
$389$	14.8492	−	25.7196i	0.752886	−	1.30404i	0.946418	−	0.322944i	$-0.104672\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	19.6603	−	2.33975i	0.992993	−	0.118175i
$393$	28.9706	−	4.97056i	1.46137	−	0.250732i
$394$	−5.19615	+	3.00000i	−0.261778	+	0.151138i
$395$		0			0
$396$		0			0
$397$	0.258819	−	0.965926i	0.0129898	−	0.0484784i	−0.959127	−	0.282977i	$-0.908678\pi$
$397$	0.258819	−	0.965926i	0.0129898	−	0.0484784i	0.972117	+	0.234498i	$0.0753447\pi$
$398$	−2.00000	−	2.00000i	−0.100251	−	0.100251i
$399$	−18.6866	−	26.0732i	−0.935498	−	1.30529i
$400$		0			0
$401$	22.0454	−	12.7279i	1.10090	−	0.635602i	0.164439	−	0.986387i	$-0.447419\pi$
$401$	22.0454	−	12.7279i	1.10090	−	0.635602i	0.936456	+	0.350785i	$0.114085\pi$
$402$	−2.29788	−	0.848387i	−0.114608	−	0.0423137i
$403$	−1.29410	−	4.82963i	−0.0644635	−	0.240581i
$404$		0			0
$405$		0			0
$406$	5.00000	+	25.9808i	0.248146	+	1.28940i
$407$	3.00000	−	3.00000i	0.148704	−	0.148704i
$408$	5.32780	−	4.42883i	0.263766	−	0.219260i
$409$	−32.0429	−	18.5000i	−1.58442	−	0.914766i	−0.994203	−	0.107523i	$-0.965708\pi$
$409$	−32.0429	−	18.5000i	−1.58442	−	0.914766i	−0.590219	−	0.807243i	$-0.700959\pi$
$410$		0			0
$411$	−2.47219	+	26.8307i	−0.121944	+	1.32346i
$412$		0			0
$413$	3.73205	+	0.267949i	0.183642	+	0.0131849i
$414$	−16.9706	+	6.00000i	−0.834058	+	0.294884i
$415$		0			0
$416$		0			0
$417$	6.59890	−	17.8733i	0.323150	−	0.875259i
$418$	40.5689	+	10.8704i	1.98429	+	0.531689i
$419$	−14.1421			−0.690889			−0.345444	−	0.938439i	$-0.612272\pi$
$419$	−14.1421			−0.690889			−0.345444	+	0.938439i	$0.612272\pi$
$420$		0			0
$421$	−23.0000			−1.12095			−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000			−1.12095			−0.560476	+	0.828171i	$0.689382\pi$
$422$	2.73205	+	0.732051i	0.132994	+	0.0356357i
$423$	−9.60521	−	13.9907i	−0.467021	−	0.680252i
$424$	6.92820	+	4.00000i	0.336463	+	0.194257i
$425$		0			0
$426$	10.0000	−	14.1421i	0.484502	−	0.685189i
$427$	5.93426	−	8.76268i	0.287179	−	0.424056i
$428$		0			0
$429$	−36.5874	−	3.37117i	−1.76645	−	0.162762i
$430$		0			0
$431$	−2.44949	−	1.41421i	−0.117988	−	0.0681203i	0.439845	−	0.898074i	$-0.355033\pi$
$431$	−2.44949	−	1.41421i	−0.117988	−	0.0681203i	−0.557832	+	0.829954i	$0.688367\pi$
$432$	−10.6405	+	17.8544i	−0.511940	+	0.859021i
$433$	−10.6066	+	10.6066i	−0.509721	+	0.509721i	−0.914441	−	0.404720i	$-0.867369\pi$
$433$	−10.6066	+	10.6066i	−0.509721	+	0.509721i	0.404720	+	0.914441i	$0.367369\pi$
$434$	3.53553	+	1.22474i	0.169711	+	0.0587896i
$435$		0			0
$436$		0			0
$437$	7.68653	+	28.6865i	0.367697	+	1.37226i
$438$	−5.93871	+	16.0851i	−0.283763	+	0.768578i
$439$	−32.9090	+	19.0000i	−1.57066	+	0.906821i	−0.574571	+	0.818455i	$0.694831\pi$
$439$	−32.9090	+	19.0000i	−1.57066	+	0.906821i	−0.996088	+	0.0883659i	$0.971836\pi$
$440$		0			0
$441$	−20.5959	+	4.09978i	−0.980758	+	0.195227i
$442$	−7.07107	−	7.07107i	−0.336336	−	0.336336i
$443$	−2.92820	+	10.9282i	−0.139123	+	0.519215i	0.860824	+	0.508903i	$0.169949\pi$
$443$	−2.92820	+	10.9282i	−0.139123	+	0.519215i	−0.999947	+	0.0103113i	$0.996718\pi$
$444$		0			0
$445$		0			0
$446$	−12.2474	+	7.07107i	−0.579934	+	0.334825i
$447$	2.48528	+	14.4853i	0.117550	+	0.685130i
$448$	−19.0411	+	9.24316i	−0.899608	+	0.436698i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	−15.0000	+	25.9808i	−0.706322	+	1.22339i
$452$		0			0
$453$	−7.99171	+	6.64324i	−0.375483	+	0.312127i
$454$			18.0000i			0.844782i
$455$		0			0
$456$	28.0000	+	19.7990i	1.31122	+	0.927173i
$457$	−7.50575	+	28.0118i	−0.351104	+	1.31034i	0.534212	+	0.845350i	$0.320608\pi$
$457$	−7.50575	+	28.0118i	−0.351104	+	1.31034i	−0.885317	+	0.464989i	$0.846058\pi$
$458$	−4.09808	+	1.09808i	−0.191491	+	0.0513097i
$459$	−5.26758	+	5.12372i	−0.245870	+	0.239155i
$460$		0			0
$461$			7.07107i			0.329332i	0.986349	+	0.164666i	$0.0526547\pi$
$461$			7.07107i			0.329332i	−0.986349	+	0.164666i	$0.947345\pi$
$462$	17.4414	−	21.2555i	0.811449	−	0.988895i
$463$	17.6777	−	17.6777i	0.821551	−	0.821551i	−0.164779	−	0.986330i	$-0.552691\pi$
$463$	17.6777	−	17.6777i	0.821551	−	0.821551i	0.986330	+	0.164779i	$0.0526912\pi$
$464$	−14.1421	−	24.4949i	−0.656532	−	1.13715i
$465$		0			0
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	−5.46410	−	1.46410i	−0.252848	−	0.0677505i	0.130168	−	0.991492i	$-0.458448\pi$
$467$	−5.46410	−	1.46410i	−0.252848	−	0.0677505i	−0.383017	+	0.923741i	$0.625115\pi$
$468$		0			0
$469$	1.73205	+	2.00000i	0.0799787	+	0.0923514i
$470$		0			0
$471$	6.89898	+	0.635674i	0.317888	+	0.0292903i
$472$	−3.86370	+	1.03528i	−0.177841	+	0.0476524i
$473$	−20.4904	+	5.49038i	−0.942149	+	0.252448i
$474$	−17.0741	−	1.57321i	−0.784240	−	0.0722601i
$475$		0			0
$476$		0			0
$477$	−7.65685	−	3.65685i	−0.350583	−	0.167436i
$478$	−38.6370	−	10.3528i	−1.76722	−	0.473524i
$479$	4.24264	−	7.34847i	0.193851	−	0.335760i	−0.752672	−	0.658396i	$-0.771235\pi$
$479$	4.24264	−	7.34847i	0.193851	−	0.335760i	0.946523	+	0.322635i	$0.104569\pi$
$480$		0			0
$481$	−2.50000	−	4.33013i	−0.113990	−	0.197437i
$482$	−24.0000	+	24.0000i	−1.09317	+	1.09317i
$483$	19.1828	+	3.16571i	0.872846	+	0.144045i
$484$		0			0
$485$		0			0
$486$	9.77526	−	19.7597i	0.443415	−	0.896317i
$487$	−28.0118	+	7.50575i	−1.26934	+	0.340118i	−0.829777	−	0.558095i	$-0.811533\pi$
$487$	−28.0118	+	7.50575i	−1.26934	+	0.340118i	−0.439561	+	0.898213i	$0.644866\pi$
$488$	−2.92820	+	10.9282i	−0.132554	+	0.494697i
$489$	2.82843	+	2.00000i	0.127906	+	0.0904431i
$490$		0			0
$491$			14.1421i			0.638226i	0.947717	+	0.319113i	$0.103385\pi$
$491$			14.1421i			0.638226i	−0.947717	+	0.319113i	$0.896615\pi$
$492$		0			0
$493$	−2.58819	−	9.65926i	−0.116566	−	0.435031i
$494$	24.7487	−	42.8661i	1.11350	−	1.92864i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−16.8301	+	8.16987i	−0.754934	+	0.366469i
$498$	−0.585786	−	3.41421i	−0.0262497	−	0.152995i
$499$	23.3827	−	13.5000i	1.04675	−	0.604343i	0.125014	−	0.992155i	$-0.460102\pi$
$499$	23.3827	−	13.5000i	1.04675	−	0.604343i	0.921739	+	0.387812i	$0.126769\pi$
$500$		0			0
$501$	−15.5732	+	7.17461i	−0.695760	+	0.320538i
$502$	2.58819	−	9.65926i	0.115517	−	0.431114i
$503$	−24.0000	−	24.0000i	−1.07011	−	1.07011i	−0.997350	−	0.0727574i	$-0.976820\pi$
$503$	−24.0000	−	24.0000i	−1.07011	−	1.07011i	−0.0727574	−	0.997350i	$-0.523180\pi$
$504$	19.3704	−	11.3485i	0.862826	−	0.505501i
$505$		0			0
$506$	−22.0454	+	12.7279i	−0.980038	+	0.565825i
$507$	−7.19881	+	19.4981i	−0.319710	+	0.865943i
$508$		0			0
$509$	−4.24264	−	7.34847i	−0.188052	−	0.325715i	0.756549	−	0.653937i	$-0.226884\pi$
$509$	−4.24264	−	7.34847i	−0.188052	−	0.325715i	−0.944601	+	0.328222i	$0.893551\pi$
$510$		0			0
$511$	14.0000	−	12.1244i	0.619324	−	0.536350i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	−31.2452	−	18.6208i	−1.37951	−	0.822130i
$514$	−15.5885	−	9.00000i	−0.687577	−	0.396973i
$515$		0			0
$516$		0			0
$517$	−16.9706	−	16.9706i	−0.746364	−	0.746364i
$518$	3.73205	+	0.267949i	0.163977	+	0.0117730i
$519$	−2.82843	+	4.00000i	−0.124154	+	0.175581i
$520$		0			0
$521$	−26.9444	−	15.5563i	−1.18046	−	0.681536i	−0.224335	−	0.974512i	$-0.572021\pi$
$521$	−26.9444	−	15.5563i	−1.18046	−	0.681536i	−0.956120	+	0.292976i	$0.905354\pi$
$522$	16.9798	+	24.7323i	0.743184	+	1.08250i
$523$	−6.76148	−	1.81173i	−0.295659	−	0.0792216i	0.107941	−	0.994157i	$-0.465574\pi$
$523$	−6.76148	−	1.81173i	−0.295659	−	0.0792216i	−0.403599	+	0.914936i	$0.632241\pi$
$524$		0			0
$525$		0			0
$526$	−24.0000			−1.04645
$527$	−1.36603	−	0.366025i	−0.0595050	−	0.0159443i
$528$	−10.1806	+	27.5745i	−0.443056	+	1.20003i
$529$	4.33013	+	2.50000i	0.188266	+	0.108696i
$530$		0			0
$531$	4.00000	−	1.41421i	0.173585	−	0.0613716i
$532$		0			0
$533$	25.0000	+	25.0000i	1.08287	+	1.08287i
$534$	−3.49621	+	37.9444i	−0.151296	+	1.64201i
$535$		0			0
$536$	−2.44949	−	1.41421i	−0.105802	−	0.0610847i
$537$	26.3713	−	21.9216i	1.13801	−	0.945985i
$538$	−5.65685	+	5.65685i	−0.243884	+	0.243884i
$539$	−27.5772	+	11.0227i	−1.18783	+	0.474781i
$540$		0			0
$541$	5.50000	+	9.52628i	0.236463	+	0.409567i	0.959697	−	0.281037i	$-0.0906783\pi$
$541$	5.50000	+	9.52628i	0.236463	+	0.409567i	−0.723234	+	0.690604i	$0.757345\pi$
$542$	−5.12436	−	19.1244i	−0.220110	−	0.821461i
$543$	4.87453	+	1.79970i	0.209186	+	0.0772326i
$544$		0			0
$545$		0			0
$546$	−18.8763	−	26.3379i	−0.807830	−	1.12716i
$547$	−7.07107	−	7.07107i	−0.302337	−	0.302337i	0.539591	−	0.841928i	$-0.318579\pi$
$547$	−7.07107	−	7.07107i	−0.302337	−	0.302337i	−0.841928	+	0.539591i	$0.818579\pi$
$548$		0			0
$549$	2.19275	−	11.7980i	0.0935844	−	0.503525i
$550$		0			0
$551$	42.8661	−	24.7487i	1.82616	−	1.05433i
$552$	−20.4853	+	3.51472i	−0.871911	+	0.149596i
$553$	15.3347	+	10.3849i	0.652098	+	0.441613i
$554$	−12.7279			−0.540758
$555$		0			0
$556$		0			0
$557$	5.12436	+	19.1244i	0.217126	+	0.810325i	0.985407	+	0.170213i	$0.0544455\pi$
$557$	5.12436	+	19.1244i	0.217126	+	0.810325i	−0.768281	+	0.640112i	$0.778888\pi$
$558$	4.22973	−	0.330749i	0.179059	−	0.0140017i
$559$			25.0000i			1.05739i
$560$		0			0
$561$	−6.00000	+	8.48528i	−0.253320	+	0.358249i
$562$	5.17638	−	19.3185i	0.218352	−	0.814902i
$563$	−30.0526	+	8.05256i	−1.26656	+	0.339375i	−0.828714	−	0.559673i	$-0.810927\pi$
$563$	−30.0526	+	8.05256i	−1.26656	+	0.339375i	−0.437851	+	0.899048i	$0.644260\pi$
$564$		0			0
$565$		0			0
$566$			32.5269i			1.36721i
$567$	−19.5445	+	13.6019i	−0.820792	+	0.571227i
$568$	14.1421	−	14.1421i	0.593391	−	0.593391i
$569$	−0.707107	−	1.22474i	−0.0296435	−	0.0513440i	0.850823	−	0.525452i	$-0.176104\pi$
$569$	−0.707107	−	1.22474i	−0.0296435	−	0.0513440i	−0.880467	+	0.474108i	$0.842771\pi$
$570$		0			0
$571$	0.500000	−	0.866025i	0.0209243	−	0.0362420i	−0.855374	−	0.518012i	$-0.826672\pi$
$571$	0.500000	−	0.866025i	0.0209243	−	0.0362420i	0.876298	+	0.481770i	$0.160006\pi$
$572$		0			0
$573$	−19.3137	+	3.31371i	−0.806842	+	0.138432i
$574$	−25.9808	+	5.00000i	−1.08442	+	0.208696i
$575$		0			0
$576$	−15.5959	+	18.2419i	−0.649830	+	0.760080i
$577$	10.6252	−	2.84701i	0.442332	−	0.118523i	−0.0307771	−	0.999526i	$-0.509798\pi$
$577$	10.6252	−	2.84701i	0.442332	−	0.118523i	0.473109	+	0.881004i	$0.343132\pi$
$578$	20.4904	−	5.49038i	0.852287	−	0.228370i
$579$	3.65513	−	39.6691i	0.151902	−	1.64859i
$580$		0			0
$581$	−1.22474	+	3.53553i	−0.0508110	+	0.146679i
$582$	−4.14214	−	24.1421i	−0.171697	−	1.00072i
$583$	−11.5911	−	3.10583i	−0.480055	−	0.128630i
$584$	−9.89949	+	17.1464i	−0.409644	+	0.709524i
$585$		0			0
$586$	16.0000	+	27.7128i	0.660954	+	1.14481i
$587$	−13.0000	+	13.0000i	−0.536567	+	0.536567i	−0.922519	−	0.385952i	$-0.873873\pi$
$587$	−13.0000	+	13.0000i	−0.536567	+	0.536567i	0.385952	+	0.922519i	$0.373873\pi$
$588$		0			0
$589$		−	7.00000i		−	0.288430i
$590$		0			0
$591$	6.67423	−	3.07483i	0.274541	−	0.126482i
$592$	−3.86370	+	1.03528i	−0.158797	+	0.0425496i
$593$	−4.75833	+	17.7583i	−0.195401	+	0.729247i	0.796761	+	0.604294i	$0.206545\pi$
$593$	−4.75833	+	17.7583i	−0.195401	+	0.729247i	−0.992163	+	0.124953i	$0.960122\pi$
$594$	8.48528	−	30.0000i	0.348155	−	1.23091i
$595$		0			0
$596$		0			0
$597$	2.21441	+	2.66390i	0.0906299	+	0.109026i
$598$	7.76457	+	28.9778i	0.317517	+	1.18499i
$599$	−9.89949	+	17.1464i	−0.404482	+	0.700584i	−0.994261	−	0.106981i	$-0.965882\pi$
$599$	−9.89949	+	17.1464i	−0.404482	+	0.700584i	0.589779	+	0.807565i	$0.299215\pi$
$600$		0			0
$601$	7.00000			0.285536			0.142768	−	0.989756i	$-0.454400\pi$
$601$	7.00000			0.285536			0.142768	+	0.989756i	$0.454400\pi$
$602$	−15.4904	−	10.4904i	−0.631341	−	0.427556i
$603$	2.70711	+	1.29289i	0.110242	+	0.0526507i
$604$		0			0
$605$		0			0
$606$	10.1464	+	22.0239i	0.412170	+	0.894658i
$607$	10.6116	−	39.6030i	0.430711	−	1.60743i	−0.320416	−	0.947277i	$-0.603823\pi$
$607$	10.6116	−	39.6030i	0.430711	−	1.60743i	0.751127	−	0.660158i	$-0.229511\pi$
$608$		0			0
$609$	−3.17837	−	32.2474i	−0.128794	−	1.30673i
$610$		0			0
$611$	−24.4949	+	14.1421i	−0.990957	+	0.572130i
$612$		0			0
$613$	−0.517638	−	1.93185i	−0.0209072	−	0.0780268i	0.954684	−	0.297621i	$-0.0961932\pi$
$613$	−0.517638	−	1.93185i	−0.0209072	−	0.0780268i	−0.975591	+	0.219594i	$0.929527\pi$
$614$	−10.6066	−	18.3712i	−0.428048	−	0.741400i
$615$		0			0
$616$	24.0000	−	20.7846i	0.966988	−	0.837436i
$617$	−8.00000	+	8.00000i	−0.322068	+	0.322068i	−0.849560	−	0.527492i	$-0.823132\pi$
$617$	−8.00000	+	8.00000i	−0.322068	+	0.322068i	0.527492	+	0.849560i	$0.323132\pi$
$618$	−4.69748	−	5.65099i	−0.188960	−	0.227316i
$619$	2.59808	+	1.50000i	0.104425	+	0.0602901i	0.551303	−	0.834305i	$-0.314131\pi$
$619$	2.59808	+	1.50000i	0.104425	+	0.0602901i	−0.446878	+	0.894595i	$0.647464\pi$
$620$		0			0
$621$	21.3712	−	5.41045i	0.857596	−	0.217114i
$622$	32.5269	+	32.5269i	1.30421	+	1.30421i
$623$	23.0788	−	34.0788i	0.924634	−	1.36534i
$624$	28.2843	+	20.0000i	1.13228	+	0.800641i
$625$		0			0
$626$	−20.8207	−	12.0208i	−0.832161	−	0.480448i
$627$	−48.2554	−	17.8161i	−1.92714	−	0.711508i
$628$		0			0
$629$	−1.41421			−0.0563884
$630$		0			0
$631$	12.0000			0.477712			0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000			0.477712			0.238856	+	0.971055i	$0.423228\pi$
$632$	−19.1244	−	5.12436i	−0.760726	−	0.203836i
$633$	−3.24969	−	1.19980i	−0.129164	−	0.0476878i
$634$	1.73205	+	1.00000i	0.0687885	+	0.0397151i
$635$		0			0
$636$		0			0
$637$	4.13613	+	34.7547i	0.163879	+	1.37703i
$638$	30.0000	+	30.0000i	1.18771	+	1.18771i
$639$	−13.7850	+	16.1237i	−0.545325	+	0.637845i
$640$		0			0
$641$	−8.57321	−	4.94975i	−0.338622	−	0.195503i	0.321041	−	0.947065i	$-0.395967\pi$
$641$	−8.57321	−	4.94975i	−0.338622	−	0.195503i	−0.659662	+	0.751562i	$0.729301\pi$
$642$	−24.3585	−	29.3029i	−0.961355	−	1.15649i
$643$	−17.6777	+	17.6777i	−0.697139	+	0.697139i	−0.963793	−	0.266653i	$-0.914082\pi$
$643$	−17.6777	+	17.6777i	−0.697139	+	0.697139i	0.266653	+	0.963793i	$0.414082\pi$
$644$		0			0
$645$		0			0
$646$	−7.00000	−	12.1244i	−0.275411	−	0.477026i
$647$	−0.366025	−	1.36603i	−0.0143899	−	0.0537040i	0.958358	−	0.285571i	$-0.0921832\pi$
$647$	−0.366025	−	1.36603i	−0.0143899	−	0.0537040i	−0.972747	+	0.231867i	$0.925517\pi$
$648$	14.9833	−	20.5792i	0.588598	−	0.808426i
$649$	5.19615	−	3.00000i	0.203967	−	0.117760i
$650$		0			0
$651$	−4.17423	−	1.89097i	−0.163601	−	0.0741129i
$652$		0			0
$653$	9.88269	−	36.8827i	0.386739	−	1.44333i	−0.448667	−	0.893699i	$-0.648101\pi$
$653$	9.88269	−	36.8827i	0.386739	−	1.44333i	0.835407	−	0.549632i	$-0.185232\pi$
$654$	17.4240	+	37.8207i	0.681334	+	1.47890i
$655$		0			0
$656$	24.4949	−	14.1421i	0.956365	−	0.552158i
$657$	9.05025	−	18.9497i	0.353084	−	0.739300i
$658$	1.51575	−	21.1117i	0.0590901	−	0.823018i
$659$	28.2843			1.10180			0.550899	−	0.834572i	$-0.314285\pi$
$659$	28.2843			1.10180			0.550899	+	0.834572i	$0.314285\pi$
$660$		0			0
$661$	−9.50000	+	16.4545i	−0.369507	+	0.640005i	−0.989489	−	0.144611i	$-0.953807\pi$
$661$	−9.50000	+	16.4545i	−0.369507	+	0.640005i	0.619981	+	0.784617i	$0.287140\pi$
$662$	0.366025	+	1.36603i	0.0142260	+	0.0530921i
$663$	7.82913	+	9.41832i	0.304058	+	0.365777i
$664$		−	4.00000i		−	0.155230i
$665$		0			0
$666$	4.00000	−	1.41421i	0.154997	−	0.0547997i
$667$	−7.76457	+	28.9778i	−0.300645	+	1.12202i
$668$		0			0
$669$	15.7313	−	7.24745i	0.608208	−	0.280203i
$670$		0			0
$671$		−	16.9706i		−	0.655141i
$672$		0			0
$673$	17.6777	−	17.6777i	0.681424	−	0.681424i	−0.278897	−	0.960321i	$-0.589969\pi$
$673$	17.6777	−	17.6777i	0.681424	−	0.681424i	0.960321	+	0.278897i	$0.0899688\pi$
$674$	3.53553	+	6.12372i	0.136184	+	0.235877i
$675$		0			0
$676$		0			0
$677$	42.3468	+	11.3468i	1.62752	+	0.436092i	0.953198	−	0.302346i	$-0.0977698\pi$
$677$	42.3468	+	11.3468i	1.62752	+	0.436092i	0.674321	+	0.738438i	$0.264436\pi$
$678$	8.20101	+	47.7990i	0.314958	+	1.83571i
$679$	−8.66025	+	25.0000i	−0.332350	+	0.959412i
$680$		0			0
$681$	2.02270	−	21.9524i	0.0775102	−	0.841218i
$682$	5.79555	−	1.55291i	0.221923	−	0.0594642i
$683$	−23.2224	+	6.22243i	−0.888582	+	0.238095i	−0.674106	−	0.738635i	$-0.735471\pi$
$683$	−23.2224	+	6.22243i	−0.888582	+	0.238095i	−0.214476	+	0.976729i	$0.568804\pi$
$684$		0			0
$685$		0			0
$686$	−23.2702	−	12.0208i	−0.888459	−	0.458957i
$687$	5.12132	−	0.878680i	0.195391	−	0.0335237i
$688$	19.3185	+	5.17638i	0.736512	+	0.197348i
$689$	−7.07107	+	12.2474i	−0.269386	+	0.466591i
$690$		0			0
$691$	−14.5000	−	25.1147i	−0.551606	−	0.955410i	−0.998159	−	0.0606524i	$-0.980682\pi$
$691$	−14.5000	−	25.1147i	−0.551606	−	0.955410i	0.446553	−	0.894757i	$-0.352651\pi$
$692$		0			0
$693$	−23.6597	+	23.9628i	−0.898760	+	0.910272i
$694$		−	32.0000i		−	1.21470i
$695$		0			0
$696$	14.4949	+	31.4626i	0.549428	+	1.19259i
$697$	9.65926	−	2.58819i	0.365870	−	0.0980347i
$698$	−9.51666	+	35.5167i	−0.360211	+	1.34433i
$699$	−2.82843	+	4.00000i	−0.106981	+	0.151294i
$700$		0			0
$701$		−	21.2132i		−	0.801212i	−0.916250	−	0.400606i	$-0.868800\pi$
$701$		−	21.2132i		−	0.801212i	0.916250	−	0.400606i	$-0.131200\pi$
$702$	−31.5624	−	18.8099i	−1.19125	−	0.709934i
$703$	−1.81173	−	6.76148i	−0.0683308	−	0.255014i
$704$	−16.9706	+	29.3939i	−0.639602	+	1.10782i
$705$		0			0
$706$	6.00000			0.225813
$707$	1.87564	−	26.1244i	0.0705409	−	0.982508i
$708$		0			0
$709$	27.7128	−	16.0000i	1.04078	−	0.600893i	0.120723	−	0.992686i	$-0.461479\pi$
$709$	27.7128	−	16.0000i	1.04078	−	0.600893i	0.920053	+	0.391794i	$0.128145\pi$
$710$		0			0
$711$	20.6464	+	3.83732i	0.774302	+	0.143911i
$712$	−11.3880	+	42.5007i	−0.426785	+	1.59278i
$713$	3.00000	+	3.00000i	0.112351	+	0.112351i
$714$	−9.12096	+	0.898979i	−0.341343	+	0.0336435i
$715$		0			0
$716$		0			0
$717$	45.9575	+	16.9677i	1.71632	+	0.633672i
$718$	−0.517638	−	1.93185i	−0.0193181	−	0.0720961i
$719$	9.89949	+	17.1464i	0.369189	+	0.639454i	0.989439	−	0.144950i	$-0.0463022\pi$
$719$	9.89949	+	17.1464i	0.369189	+	0.639454i	−0.620250	+	0.784404i	$0.712969\pi$
$720$		0			0
$721$	1.50000	+	7.79423i	0.0558629	+	0.290272i
$722$	30.0000	−	30.0000i	1.11648	−	1.11648i
$723$	31.9668	−	26.5730i	1.18886	−	0.988259i
$724$		0			0
$725$		0			0
$726$	1.57321	−	17.0741i	0.0583875	−	0.633679i
$727$	17.6777	+	17.6777i	0.655628	+	0.655628i	0.954343	−	0.298714i	$-0.0965577\pi$
$727$	17.6777	+	17.6777i	0.655628	+	0.655628i	−0.298714	+	0.954343i	$0.596558\pi$
$728$	−16.3397	−	33.6603i	−0.605591	−	1.24753i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$		0			0
$731$	6.12372	+	3.53553i	0.226494	+	0.130766i
$732$		0			0
$733$	31.8756	+	8.54103i	1.17735	+	0.315470i	0.793875	−	0.608081i	$-0.208060\pi$
$733$	31.8756	+	8.54103i	1.17735	+	0.315470i	0.383475	+	0.923551i	$0.374727\pi$
$734$	29.6985			1.09619
$735$		0			0
$736$		0			0
$737$	4.09808	+	1.09808i	0.150955	+	0.0404482i
$738$	−24.7323	+	16.9798i	−0.910409	+	0.625034i
$739$	−6.06218	−	3.50000i	−0.223001	−	0.128750i	0.384338	−	0.923192i	$-0.374430\pi$
$739$	−6.06218	−	3.50000i	−0.223001	−	0.128750i	−0.607339	+	0.794443i	$0.707763\pi$
$740$		0			0
$741$	−35.0000	+	49.4975i	−1.28576	+	1.81834i
$742$	−4.62158	−	9.52056i	−0.169663	−	0.349511i
$743$	11.0000	+	11.0000i	0.403551	+	0.403551i	0.879482	−	0.475931i	$-0.157889\pi$
$743$	11.0000	+	11.0000i	0.403551	+	0.403551i	−0.475931	+	0.879482i	$0.657889\pi$
$744$	4.87832	+	0.449490i	0.178848	+	0.0164791i
$745$		0			0
$746$	28.1691	+	16.2635i	1.03135	+	0.595447i
$747$	0.330749	+	4.22973i	0.0121015	+	0.154758i
$748$		0			0
$749$	7.77817	+	40.4166i	0.284208	+	1.47679i
$750$		0			0
$751$	−19.5000	−	33.7750i	−0.711565	−	1.23247i	−0.964269	−	0.264923i	$-0.914653\pi$
$751$	−19.5000	−	33.7750i	−0.711565	−	1.23247i	0.252704	−	0.967544i	$-0.418680\pi$
$752$	5.85641	+	21.8564i	0.213561	+	0.797021i
$753$	−4.24194	+	11.4894i	−0.154585	+	0.418696i
$754$	43.3013	−	25.0000i	1.57694	−	0.910446i
$755$		0			0
$756$		0			0
$757$	14.1421	+	14.1421i	0.514005	+	0.514005i	0.915751	−	0.401746i	$-0.131597\pi$
$757$	14.1421	+	14.1421i	0.514005	+	0.514005i	−0.401746	+	0.915751i	$0.631597\pi$
$758$	3.29423	−	12.2942i	0.119652	−	0.446546i
$759$	28.3164	−	13.0454i	1.02782	−	0.473518i
$760$		0			0
$761$	−20.8207	+	12.0208i	−0.754748	+	0.435754i	−0.827407	−	0.561603i	$-0.810185\pi$
$761$	−20.8207	+	12.0208i	−0.754748	+	0.435754i	0.0726586	+	0.997357i	$0.476852\pi$
$762$	−6.21320	−	36.2132i	−0.225081	−	1.31187i
$763$	3.22097	−	44.8623i	0.116607	−	1.62412i
$764$		0			0
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	−1.83013	−	6.83013i	−0.0660821	−	0.246622i
$768$		0			0
$769$		−	29.0000i		−	1.04577i	−0.852404	−	0.522883i	$-0.824856\pi$
$769$		−	29.0000i		−	1.04577i	0.852404	−	0.522883i	$-0.175144\pi$
$770$		0			0
$771$	18.0000	+	12.7279i	0.648254	+	0.458385i
$772$		0			0
$773$	17.7583	−	4.75833i	0.638723	−	0.171145i	0.0750979	−	0.997176i	$-0.476073\pi$
$773$	17.7583	−	4.75833i	0.638723	−	0.171145i	0.563625	+	0.826031i	$0.309406\pi$
$774$	−20.8560	−	3.87628i	−0.749655	−	0.139330i
$775$		0			0
$776$		−	28.2843i		−	1.01535i
$777$	−4.52142	−	0.746165i	−0.162205	−	0.0267685i
$778$	29.6985	−	29.6985i	1.06474	−	1.06474i
$779$	24.7487	+	42.8661i	0.886716	+	1.53584i
$780$		0			0
$781$	−15.0000	+	25.9808i	−0.536742	+	0.929665i
$782$	8.19615	+	2.19615i	0.293094	+	0.0785343i
$783$	−17.9289	−	32.0711i	−0.640728	−	1.14613i
$784$	27.7128	+	4.00000i	0.989743	+	0.142857i
$785$		0			0
$786$	41.3939	+	3.81405i	1.47647	+	0.136043i
$787$	25.1141	−	6.72930i	0.895220	−	0.239873i	0.218258	−	0.975891i	$-0.429963\pi$
$787$	25.1141	−	6.72930i	0.895220	−	0.239873i	0.676962	+	0.736018i	$0.263296\pi$
$788$		0			0
$789$	29.2699	+	2.69694i	1.04204	+	0.0960136i
$790$		0			0
$791$	17.1464	−	49.4975i	0.609657	−	1.75993i
$792$	15.5147	−	32.4853i	0.551292	−	1.15431i
$793$	−19.3185	−	5.17638i	−0.686021	−	0.183819i
$794$	0.707107	−	1.22474i	0.0250943	−	0.0434646i
$795$		0			0
$796$		0			0
$797$	17.0000	−	17.0000i	0.602171	−	0.602171i	−0.338717	−	0.940888i	$-0.609993\pi$
$797$	17.0000	−	17.0000i	0.602171	−	0.602171i	0.940888	+	0.338717i	$0.109993\pi$
$798$	−15.9829	−	42.4564i	−0.565787	−	1.50294i
$799$			8.00000i			0.283020i
$800$		0			0
$801$	8.52781	−	45.8833i	0.301315	−	1.62121i
$802$	34.7733	−	9.31749i	1.22789	−	0.329012i
$803$	7.68653	−	28.6865i	0.271252	−	1.01233i
$804$		0			0
$805$		0			0
$806$		−	7.07107i		−	0.249068i
$807$	7.53465	−	6.26330i	0.265232	−	0.220479i
$808$	7.24693	+	27.0459i	0.254946	+	0.951472i
$809$	−9.89949	+	17.1464i	−0.348048	+	0.602836i	−0.985903	−	0.167320i	$-0.946489\pi$
$809$	−9.89949	+	17.1464i	−0.348048	+	0.602836i	0.637855	+	0.770157i	$0.279822\pi$
$810$		0			0
$811$	−18.0000			−0.632065			−0.316033	−	0.948748i	$-0.602351\pi$
$811$	−18.0000			−0.632065			−0.316033	+	0.948748i	$0.602351\pi$
$812$		0			0
$813$	4.10051	+	23.8995i	0.143811	+	0.838192i
$814$	5.19615	−	3.00000i	0.182125	−	0.105150i
$815$		0			0
$816$	8.89898	−	4.09978i	0.311527	−	0.143521i
$817$	−9.05867	+	33.8074i	−0.316923	+	1.18277i
$818$	−37.0000	−	37.0000i	−1.29367	−	1.29367i
$819$	20.0614	+	34.2423i	0.701004	+	1.19652i
$820$		0			0
$821$	15.9217	−	9.19239i	0.555671	−	0.320817i	−0.195735	−	0.980657i	$-0.562709\pi$
$821$	15.9217	−	9.19239i	0.555671	−	0.320817i	0.751406	+	0.659840i	$0.229376\pi$
$822$	−13.1978	+	35.7466i	−0.460326	+	1.24681i
$823$	7.24693	+	27.0459i	0.252612	+	0.942762i	0.969403	+	0.245474i	$0.0789435\pi$
$823$	7.24693	+	27.0459i	0.252612	+	0.942762i	−0.716791	+	0.697288i	$0.754390\pi$
$824$	−4.24264	−	7.34847i	−0.147799	−	0.255996i
$825$		0			0
$826$	5.00000	+	1.73205i	0.173972	+	0.0602658i
$827$	−18.0000	+	18.0000i	−0.625921	+	0.625921i	−0.947039	−	0.321118i	$-0.895941\pi$
$827$	−18.0000	+	18.0000i	−0.625921	+	0.625921i	0.321118	+	0.947039i	$0.395941\pi$
$828$		0			0
$829$	−6.06218	−	3.50000i	−0.210548	−	0.121560i	0.391018	−	0.920383i	$-0.372123\pi$
$829$	−6.06218	−	3.50000i	−0.210548	−	0.121560i	−0.601566	+	0.798823i	$0.705456\pi$
$830$		0			0
$831$	15.5227	+	1.43027i	0.538477	+	0.0496154i
$832$	28.2843	+	28.2843i	0.980581	+	0.980581i
$833$	9.09808	+	3.90192i	0.315230	+	0.135194i
$834$	15.5563	−	22.0000i	0.538672	−	0.761798i
$835$		0			0
$836$		0			0
$837$	−5.19565	−	0.0719302i	−0.179588	−	0.00248627i
$838$	−19.3185	−	5.17638i	−0.667347	−	0.178815i
$839$	−35.3553			−1.22060			−0.610301	−	0.792170i	$-0.708951\pi$
$839$	−35.3553			−1.22060			−0.610301	+	0.792170i	$0.708951\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$	−31.4186	−	8.41858i	−1.08276	−	0.290124i
$843$	−8.48387	+	22.9788i	−0.292200	+	0.791431i
$844$		0			0
$845$		0			0
$846$	−8.00000	−	22.6274i	−0.275046	−	0.777947i
$847$	−10.3849	+	15.3347i	−0.356831	+	0.526906i
$848$	8.00000	+	8.00000i	0.274721	+	0.274721i
$849$	3.65513	−	39.6691i	0.125444	−	1.36144i
$850$		0			0
$851$	3.67423	+	2.12132i	0.125951	+	0.0727179i
$852$		0			0
$853$	38.8909	−	38.8909i	1.33160	−	1.33160i	0.427657	−	0.903941i	$-0.359339\pi$
$853$	38.8909	−	38.8909i	1.33160	−	1.33160i	0.903941	−	0.427657i	$-0.140661\pi$
$854$	11.3137	−	9.79796i	0.387147	−	0.335279i
$855$		0			0
$856$	−22.0000	−	38.1051i	−0.751945	−	1.30241i
$857$	−7.68653	−	28.6865i	−0.262567	−	0.979913i	−0.963723	−	0.266905i	$-0.913999\pi$
$857$	−7.68653	−	28.6865i	−0.262567	−	0.979913i	0.701156	−	0.713008i	$-0.252668\pi$
$858$	−48.7453	−	17.9970i	−1.66414	−	0.614408i
$859$	19.0526	−	11.0000i	0.650065	−	0.375315i	−0.138416	−	0.990374i	$-0.544201\pi$
$859$	19.0526	−	11.0000i	0.650065	−	0.375315i	0.788481	+	0.615059i	$0.210868\pi$
$860$		0			0
$861$	32.2474	−	3.17837i	1.09899	−	0.108319i
$862$	−2.82843	−	2.82843i	−0.0963366	−	0.0963366i
$863$	−10.2487	+	38.2487i	−0.348870	+	1.30200i	0.539155	+	0.842207i	$0.318744\pi$
$863$	−10.2487	+	38.2487i	−0.348870	+	1.30200i	−0.888025	+	0.459795i	$0.847923\pi$
$864$		0			0
$865$		0			0
$866$	−18.3712	+	10.6066i	−0.624278	+	0.360427i
$867$	−25.6066	+	4.39340i	−0.869646	+	0.149208i
$868$		0			0
$869$	29.6985			1.00745
$870$		0			0
$871$	2.50000	−	4.33013i	0.0847093	−	0.146721i
$872$	12.4449	+	46.4449i	0.421436	+	1.57282i
$873$	2.33875	+	29.9087i	0.0791547	+	1.01226i
$874$			42.0000i			1.42067i
$875$		0			0
$876$		0			0
$877$	−6.21166	+	23.1822i	−0.209753	+	0.782808i	0.778195	+	0.628022i	$0.216135\pi$
$877$	−6.21166	+	23.1822i	−0.209753	+	0.782808i	−0.987948	+	0.154786i	$0.950531\pi$
$878$	−51.9090	+	13.9090i	−1.75184	+	0.469405i
$879$	−16.3991	−	35.5959i	−0.553128	−	1.20062i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−29.6352	−	1.93823i	−0.997868	−	0.0652636i
$883$	10.6066	−	10.6066i	0.356941	−	0.356941i	−0.505743	−	0.862684i	$-0.668782\pi$
$883$	10.6066	−	10.6066i	0.356941	−	0.356941i	0.862684	+	0.505743i	$0.168782\pi$
$884$		0			0
$885$		0			0
$886$	−8.00000	+	13.8564i	−0.268765	+	0.465515i
$887$	28.6865	+	7.68653i	0.963200	+	0.258089i	0.705954	−	0.708258i	$-0.250518\pi$
$887$	28.6865	+	7.68653i	0.963200	+	0.258089i	0.257245	+	0.966346i	$0.417185\pi$
$888$	4.82843	−	0.828427i	0.162031	−	0.0278002i
$889$	−12.9904	+	37.5000i	−0.435683	+	1.25771i
$890$		0			0
$891$	−13.7196	+	35.6339i	−0.459625	+	1.19378i
$892$		0			0
$893$	−38.2487	+	10.2487i	−1.27994	+	0.342960i
$894$	−1.90702	+	20.6969i	−0.0637804	+	0.692209i
$895$		0			0
$896$	−29.3939	+	5.65685i	−0.981981	+	0.188982i
$897$	−6.21320	−	36.2132i	−0.207453	−	1.20912i
$898$		0			0
$899$	3.53553	−	6.12372i	0.117917	−	0.204238i
$900$		0			0
$901$	2.00000	+	3.46410i	0.0666297	+	0.115406i
$902$	−30.0000	+	30.0000i	−0.998891	+	0.998891i
$903$	17.7129	+	14.5345i	0.589449	+	0.483679i
$904$			56.0000i			1.86253i
$905$		0			0
$906$	−13.3485	+	6.14966i	−0.443473	+	0.204309i
$907$	49.2622	−	13.1998i	1.63573	−	0.438291i	0.680158	−	0.733065i	$-0.261911\pi$
$907$	49.2622	−	13.1998i	1.63573	−	0.438291i	0.955567	+	0.294774i	$0.0952444\pi$
$908$		0			0
$909$	−9.89949	−	28.0000i	−0.328346	−	0.928701i
$910$		0			0
$911$			35.3553i			1.17137i	0.810537	+	0.585687i	$0.199175\pi$
$911$			35.3553i			1.17137i	−0.810537	+	0.585687i	$0.800825\pi$
$912$	31.0018	+	37.2946i	1.02657	+	1.23495i
$913$	1.55291	+	5.79555i	0.0513940	+	0.191805i
$914$	−20.5061	+	35.5176i	−0.678281	+	1.17482i
$915$		0			0
$916$		0			0
$917$	−37.1769	−	25.1769i	−1.22769	−	0.831415i
$918$	−9.07107	+	5.07107i	−0.299390	+	0.167370i
$919$	−11.2583	+	6.50000i	−0.371378	+	0.214415i	−0.674060	−	0.738676i	$-0.735451\pi$
$919$	−11.2583	+	6.50000i	−0.371378	+	0.214415i	0.302682	+	0.953092i	$0.402118\pi$
$920$		0			0
$921$	10.8712	+	23.5970i	0.358217	+	0.777547i
$922$	−2.58819	+	9.65926i	−0.0852375	+	0.318111i
$923$	25.0000	+	25.0000i	0.822885	+	0.822885i
$924$		0			0
$925$		0			0
$926$	30.6186	−	17.6777i	1.00619	−	0.580924i
$927$	5.09393	+	7.41970i	0.167307	+	0.243695i
$928$		0			0
$929$	−7.77817	−	13.4722i	−0.255194	−	0.442008i	0.709754	−	0.704449i	$-0.248806\pi$
$929$	−7.77817	−	13.4722i	−0.255194	−	0.442008i	−0.964948	+	0.262441i	$0.915473\pi$
$930$		0			0
$931$	−7.00000	+	48.4974i	−0.229416	+	1.58944i
$932$		0			0
$933$	−36.0140	−	43.3243i	−1.17905	−	1.41837i
$934$	−6.92820	−	4.00000i	−0.226698	−	0.130884i
$935$		0			0
$936$	−32.2474	−	27.5699i	−1.05404	−	0.901152i
$937$	−10.6066	−	10.6066i	−0.346503	−	0.346503i	0.512302	−	0.858805i	$-0.328793\pi$
$937$	−10.6066	−	10.6066i	−0.346503	−	0.346503i	−0.858805	+	0.512302i	$0.828793\pi$
$938$	1.63397	+	3.36603i	0.0533512	+	0.109905i
$939$	24.0416	+	17.0000i	0.784569	+	0.554774i
$940$		0			0
$941$	15.9217	+	9.19239i	0.519032	+	0.299663i	0.736539	−	0.676396i	$-0.236459\pi$
$941$	15.9217	+	9.19239i	0.519032	+	0.299663i	−0.217506	+	0.976059i	$0.569792\pi$
$942$	9.19151	+	3.39355i	0.299476	+	0.110568i
$943$	−28.9778	−	7.76457i	−0.943646	−	0.252849i
$944$	−5.65685			−0.184115
$945$		0			0
$946$	−30.0000			−0.975384
$947$	15.0263	+	4.02628i	0.488288	+	0.130837i	0.494559	−	0.869144i	$-0.335329\pi$
$947$	15.0263	+	4.02628i	0.488288	+	0.130837i	−0.00627092	+	0.999980i	$0.501996\pi$
$948$		0			0
$949$	−30.3109	−	17.5000i	−0.983933	−	0.568074i
$950$		0			0
$951$	−2.00000	−	1.41421i	−0.0648544	−	0.0458590i
$952$	−10.5558	−	0.757875i	−0.342117	−	0.0245629i
$953$	36.0000	+	36.0000i	1.16615	+	1.16615i	0.983103	+	0.183051i	$0.0585973\pi$
$953$	36.0000	+	36.0000i	1.16615	+	1.16615i	0.183051	+	0.983103i	$0.441403\pi$
$954$	−9.12096	−	7.79796i	−0.295302	−	0.252468i
$955$		0			0
$956$		0			0
$957$	−33.2162	−	39.9585i	−1.07373	−	1.29168i
$958$	8.48528	−	8.48528i	0.274147	−	0.274147i
$959$	31.1127	−	26.9444i	1.00468	−	0.870080i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	−1.83013	−	6.83013i	−0.0590057	−	0.220212i
$963$	26.4143	+	38.4745i	0.851189	+	1.23982i
$964$		0			0
$965$		0			0
$966$	25.0454	+	11.3458i	0.805823	+	0.365046i
$967$	−24.7487	−	24.7487i	−0.795866	−	0.795866i	0.186575	−	0.982441i	$-0.440261\pi$
$967$	−24.7487	−	24.7487i	−0.795866	−	0.795866i	−0.982441	+	0.186575i	$0.940261\pi$
$968$	5.12436	−	19.1244i	0.164703	−	0.614680i
$969$	7.17461	+	15.5732i	0.230482	+	0.500284i
$970$		0			0
$971$	−39.1918	+	22.6274i	−1.25773	+	0.726148i	−0.972632	−	0.232351i	$-0.925358\pi$
$971$	−39.1918	+	22.6274i	−1.25773	+	0.726148i	−0.285094	+	0.958500i	$0.592025\pi$
$972$		0			0
$973$	−26.1815	+	12.7093i	−0.839341	+	0.407443i
$974$	−41.0122			−1.31412
$975$		0			0
$976$	−8.00000	+	13.8564i	−0.256074	+	0.443533i
$977$	−4.02628	−	15.0263i	−0.128812	−	0.480733i	0.871135	−	0.491044i	$-0.163385\pi$
$977$	−4.02628	−	15.0263i	−0.128812	−	0.480733i	−0.999947	+	0.0103108i	$0.996718\pi$
$978$	3.13165	+	3.76733i	0.100139	+	0.120466i
$979$		−	66.0000i		−	2.10937i
$980$		0			0
$981$	−17.0000	−	48.0833i	−0.542768	−	1.53518i
$982$	−5.17638	+	19.3185i	−0.165185	+	0.616479i
$983$	−36.8827	+	9.88269i	−1.17637	+	0.315209i	−0.793488	−	0.608586i	$-0.791737\pi$
$983$	−36.8827	+	9.88269i	−1.17637	+	0.315209i	−0.382887	+	0.923795i	$0.625070\pi$
$984$	−31.4626	+	14.4949i	−1.00299	+	0.462080i
$985$		0			0
$986$		−	14.1421i		−	0.450377i
$987$	−4.22095	+	25.5770i	−0.134354	+	0.814125i
$988$		0			0
$989$	−10.6066	−	18.3712i	−0.337270	−	0.584169i
$990$		0			0
$991$	20.5000	−	35.5070i	0.651204	−	1.12792i	−0.331627	−	0.943411i	$-0.607598\pi$
$991$	20.5000	−	35.5070i	0.651204	−	1.12792i	0.982831	−	0.184508i	$-0.0590691\pi$
$992$		0			0
$993$	−0.292893	−	1.70711i	−0.00929469	−	0.0541734i
$994$	−25.9808	+	5.00000i	−0.824060	+	0.158590i
$995$		0			0
$996$		0			0
$997$	−37.6711	+	10.0939i	−1.19306	+	0.319678i	−0.800093	−	0.599876i	$-0.795217\pi$
$997$	−37.6711	+	10.0939i	−1.19306	+	0.319678i	−0.392963	+	0.919554i	$0.628550\pi$
$998$	36.8827	−	9.88269i	1.16750	−	0.312831i
$999$	−5.03723	+	1.27526i	−0.159371	+	0.0403473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bf.d.32.1	yes	8
3.2	odd	2		525.2.bf.a.32.1	✓	8
5.2	odd	4	inner	525.2.bf.d.368.1	yes	8
5.3	odd	4		525.2.bf.a.368.2	yes	8
5.4	even	2		525.2.bf.a.32.2	yes	8
7.2	even	3	inner	525.2.bf.d.107.2	yes	8
15.2	even	4		525.2.bf.a.368.1	yes	8
15.8	even	4	inner	525.2.bf.d.368.2	yes	8
15.14	odd	2	inner	525.2.bf.d.32.2	yes	8
21.2	odd	6		525.2.bf.a.107.2	yes	8
35.2	odd	12	inner	525.2.bf.d.443.2	yes	8
35.9	even	6		525.2.bf.a.107.1	yes	8
35.23	odd	12		525.2.bf.a.443.1	yes	8
105.2	even	12		525.2.bf.a.443.2	yes	8
105.23	even	12	inner	525.2.bf.d.443.1	yes	8
105.44	odd	6	inner	525.2.bf.d.107.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bf.a.32.1	✓	8	3.2	odd	2
525.2.bf.a.32.2	yes	8	5.4	even	2
525.2.bf.a.107.1	yes	8	35.9	even	6
525.2.bf.a.107.2	yes	8	21.2	odd	6
525.2.bf.a.368.1	yes	8	15.2	even	4
525.2.bf.a.368.2	yes	8	5.3	odd	4
525.2.bf.a.443.1	yes	8	35.23	odd	12
525.2.bf.a.443.2	yes	8	105.2	even	12
525.2.bf.d.32.1	yes	8	1.1	even	1	trivial
525.2.bf.d.32.2	yes	8	15.14	odd	2	inner
525.2.bf.d.107.1	yes	8	105.44	odd	6	inner
525.2.bf.d.107.2	yes	8	7.2	even	3	inner
525.2.bf.d.368.1	yes	8	5.2	odd	4	inner
525.2.bf.d.368.2	yes	8	15.8	even	4	inner
525.2.bf.d.443.1	yes	8	105.23	even	12	inner
525.2.bf.d.443.2	yes	8	35.2	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.62484 - 0.599900i) q^{3} +(-2.00000 - 1.41421i) q^{6} +(1.15539 + 2.38014i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.28024 + 1.94949i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.62484 - 0.599900i) q^{3} +(-2.00000 - 1.41421i) q^{6} +(1.15539 + 2.38014i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.28024 + 1.94949i) q^{9} +(3.67423 + 2.12132i) q^{11} +(3.53553 - 3.53553i) q^{13} +(0.707107 + 3.67423i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-0.366025 - 1.36603i) q^{17} +(2.40130 + 3.49768i) q^{18} +(6.06218 - 3.50000i) q^{19} +(-0.449490 - 4.56048i) q^{21} +(4.24264 + 4.24264i) q^{22} +(-1.09808 + 4.09808i) q^{23} +(2.04989 + 4.44949i) q^{24} +(6.12372 - 3.53553i) q^{26} +(-2.53553 - 4.53553i) q^{27} +7.07107 q^{29} +(0.500000 - 0.866025i) q^{31} +(-4.69748 - 5.65099i) q^{33} -2.00000i q^{34} +(0.258819 - 0.965926i) q^{37} +(9.56218 - 2.56218i) q^{38} +(-7.86566 + 3.62372i) q^{39} +7.07107i q^{41} +(1.05524 - 6.39425i) q^{42} +(-3.53553 + 3.53553i) q^{43} +(-3.00000 + 5.19615i) q^{46} +(-5.46410 - 1.46410i) q^{47} +(1.17157 + 6.82843i) q^{48} +(-4.33013 + 5.50000i) q^{49} +(-0.224745 + 2.43916i) q^{51} +(-2.73205 + 0.732051i) q^{53} +(-1.80348 - 7.12372i) q^{54} +(2.44949 - 7.07107i) q^{56} +(-11.9497 + 2.05025i) q^{57} +(9.65926 + 2.58819i) q^{58} +(0.707107 - 1.22474i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(1.00000 - 1.00000i) q^{62} +(-2.00548 + 7.67972i) q^{63} +8.00000i q^{64} +(-4.34847 - 9.43879i) q^{66} +(0.965926 - 0.258819i) q^{67} +(4.24264 - 6.00000i) q^{69} +7.07107i q^{71} +(-0.661498 - 8.45946i) q^{72} +(-1.81173 - 6.76148i) q^{73} +(0.707107 - 1.22474i) q^{74} +(-0.803848 + 11.1962i) q^{77} +(-12.0711 + 2.07107i) q^{78} +(6.06218 - 3.50000i) q^{79} +(1.39898 + 8.89060i) q^{81} +(-2.58819 + 9.65926i) q^{82} +(1.00000 + 1.00000i) q^{83} +(-6.12372 + 3.53553i) q^{86} +(-11.4894 - 4.24194i) q^{87} +(-3.10583 - 11.5911i) q^{88} +(-7.77817 - 13.4722i) q^{89} +(12.5000 + 4.33013i) q^{91} +(-1.33195 + 1.10721i) q^{93} +(-6.92820 - 4.00000i) q^{94} +(7.07107 + 7.07107i) q^{97} +(-7.92820 + 5.92820i) q^{98} +(4.24264 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{3} - 16 q^{6} - 16 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^3 - 16 * q^6 - 16 * q^8	\( 8 q + 4 q^{2} - 4 q^{3} - 16 q^{6} - 16 q^{8} - 16 q^{16} + 4 q^{17} + 4 q^{18} + 16 q^{21} + 12 q^{23} + 8 q^{27} + 4 q^{31} - 12 q^{33} + 28 q^{38} + 20 q^{42} - 24 q^{46} - 16 q^{47} + 32 q^{48} + 8 q^{51} - 8 q^{53} - 56 q^{57} - 16 q^{61} + 8 q^{62} + 8 q^{63} + 24 q^{66} - 8 q^{72} - 48 q^{77} - 40 q^{78} - 28 q^{81} + 8 q^{83} + 20 q^{87} + 100 q^{91} + 4 q^{93} - 8 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^3 - 16 * q^6 - 16 * q^8 - 16 * q^16 + 4 * q^17 + 4 * q^18 + 16 * q^21 + 12 * q^23 + 8 * q^27 + 4 * q^31 - 12 * q^33 + 28 * q^38 + 20 * q^42 - 24 * q^46 - 16 * q^47 + 32 * q^48 + 8 * q^51 - 8 * q^53 - 56 * q^57 - 16 * q^61 + 8 * q^62 + 8 * q^63 + 24 * q^66 - 8 * q^72 - 48 * q^77 - 40 * q^78 - 28 * q^81 + 8 * q^83 + 20 * q^87 + 100 * q^91 + 4 * q^93 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more