LMFDB - Embedded newform 525.2.bf.a.368.1

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			368.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	525.368
Dual form			525.2.bf.a.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(-2.00000 + 1.41421i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(2.00000 - 2.00000i) q^{8} +(0.548188 + 2.94949i) q^{9} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(-2.00000 + 1.41421i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(2.00000 - 2.00000i) q^{8} +(0.548188 + 2.94949i) q^{9} +(-3.67423 - 2.12132i) q^{11} +(-3.53553 - 3.53553i) q^{13} +(0.707107 + 3.67423i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-1.36603 + 0.366025i) q^{17} +(4.22973 + 0.330749i) q^{18} +(-6.06218 + 3.50000i) q^{19} +(4.44949 + 1.09638i) q^{21} +(-4.24264 + 4.24264i) q^{22} +(-4.09808 - 1.09808i) q^{23} +(-4.87832 + 0.449490i) q^{24} +(-6.12372 + 3.53553i) q^{26} +(2.53553 - 4.53553i) q^{27} +7.07107 q^{29} +(0.500000 - 0.866025i) q^{31} +(2.54516 + 6.89363i) q^{33} +2.00000i q^{34} +(0.965926 + 0.258819i) q^{37} +(2.56218 + 9.56218i) q^{38} +(0.794593 + 8.62372i) q^{39} -7.07107i q^{41} +(3.12630 - 5.67681i) q^{42} +(3.53553 + 3.53553i) q^{43} +(-3.00000 + 5.19615i) q^{46} +(-1.46410 + 5.46410i) q^{47} +(-1.17157 + 6.82843i) q^{48} +(4.33013 - 5.50000i) q^{49} +(2.22474 + 1.02494i) q^{51} +(-0.732051 - 2.73205i) q^{53} +(-5.26758 - 5.12372i) q^{54} +(-2.44949 + 7.07107i) q^{56} +(11.9497 + 2.05025i) q^{57} +(2.58819 - 9.65926i) q^{58} +(0.707107 - 1.22474i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(-1.00000 - 1.00000i) q^{62} +(-4.71259 - 6.38682i) q^{63} -8.00000i q^{64} +(10.3485 - 0.953512i) q^{66} +(0.258819 + 0.965926i) q^{67} +(4.24264 + 6.00000i) q^{69} -7.07107i q^{71} +(6.99536 + 4.80260i) q^{72} +(-6.76148 + 1.81173i) q^{73} +(0.707107 - 1.22474i) q^{74} +(11.1962 + 0.803848i) q^{77} +(12.0711 + 2.07107i) q^{78} +(-6.06218 + 3.50000i) q^{79} +(-8.39898 + 3.23375i) q^{81} +(-9.65926 - 2.58819i) q^{82} +(-1.00000 + 1.00000i) q^{83} +(6.12372 - 3.53553i) q^{86} +(-9.41832 - 7.82913i) q^{87} +(-11.5911 + 3.10583i) q^{88} +(-7.77817 - 13.4722i) q^{89} +(12.5000 + 4.33013i) q^{91} +(-1.62484 + 0.599900i) q^{93} +(6.92820 + 4.00000i) q^{94} +(-7.07107 + 7.07107i) q^{97} +(-5.92820 - 7.92820i) q^{98} +(4.24264 - 12.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$	−1.33195	−	1.10721i	−0.769002	−	0.639246i
$3$	−1.33195	−	1.10721i	−0.769002	−	0.639246i
$4$		0			0
$5$		0			0
$5$		0			0
$6$	−2.00000	+	1.41421i	−0.816497	+	0.577350i
$7$	−2.38014	+	1.15539i	−0.899608	+	0.436698i
$7$	−2.38014	+	1.15539i	−0.899608	+	0.436698i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	0.548188	+	2.94949i	0.182729	+	0.983163i
$10$		0			0
$11$	−3.67423	−	2.12132i	−1.10782	−	0.639602i	−0.169559	−	0.985520i	$-0.554234\pi$
$11$	−3.67423	−	2.12132i	−1.10782	−	0.639602i	−0.938265	+	0.345918i	$0.887568\pi$
$12$		0			0
$13$	−3.53553	−	3.53553i	−0.980581	−	0.980581i	0.0192343	−	0.999815i	$-0.493877\pi$
$13$	−3.53553	−	3.53553i	−0.980581	−	0.980581i	−0.999815	+	0.0192343i	$0.993877\pi$
$14$	0.707107	+	3.67423i	0.188982	+	0.981981i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−1.36603	+	0.366025i	−0.331310	+	0.0887742i	−0.420639	−	0.907228i	$-0.638194\pi$
$17$	−1.36603	+	0.366025i	−0.331310	+	0.0887742i	0.0893296	+	0.996002i	$0.471528\pi$
$18$	4.22973	+	0.330749i	0.996957	+	0.0779583i
$19$	−6.06218	+	3.50000i	−1.39076	+	0.802955i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$	−6.06218	+	3.50000i	−1.39076	+	0.802955i	−0.397360	+	0.917663i	$0.630073\pi$
$20$		0			0
$21$	4.44949	+	1.09638i	0.970958	+	0.239249i
$22$	−4.24264	+	4.24264i	−0.904534	+	0.904534i
$23$	−4.09808	−	1.09808i	−0.854508	−	0.228965i	−0.195131	−	0.980777i	$-0.562513\pi$
$23$	−4.09808	−	1.09808i	−0.854508	−	0.228965i	−0.659377	+	0.751812i	$0.729180\pi$
$24$	−4.87832	+	0.449490i	−0.995782	+	0.0917517i
$25$		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
$33$	2.54516	+	6.89363i	0.443056	+	1.20003i
$34$			2.00000i			0.342997i
$35$		0			0
$36$		0			0
$37$	0.965926	+	0.258819i	0.158797	+	0.0425496i	0.337342	−	0.941382i	$-0.390472\pi$
$37$	0.965926	+	0.258819i	0.158797	+	0.0425496i	−0.178545	+	0.983932i	$0.557139\pi$
$38$	2.56218	+	9.56218i	0.415640	+	1.55119i
$39$	0.794593	+	8.62372i	0.127237	+	1.38090i
$40$		0			0
$41$		−	7.07107i		−	1.10432i	−0.833740	−	0.552158i	$-0.813805\pi$
$41$		−	7.07107i		−	1.10432i	0.833740	−	0.552158i	$-0.186195\pi$
$42$	3.12630	−	5.67681i	0.482399	−	0.875951i
$43$	3.53553	+	3.53553i	0.539164	+	0.539164i	0.923283	−	0.384120i	$-0.125495\pi$
$43$	3.53553	+	3.53553i	0.539164	+	0.539164i	−0.384120	+	0.923283i	$0.625495\pi$
$44$		0			0
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−1.46410	+	5.46410i	−0.213561	+	0.797021i	0.773107	+	0.634276i	$0.218702\pi$
$47$	−1.46410	+	5.46410i	−0.213561	+	0.797021i	−0.986668	+	0.162745i	$0.947965\pi$
$48$	−1.17157	+	6.82843i	−0.169102	+	0.985599i
$49$	4.33013	−	5.50000i	0.618590	−	0.785714i
$50$		0			0
$51$	2.22474	+	1.02494i	0.311527	+	0.143521i
$52$		0			0
$53$	−0.732051	−	2.73205i	−0.100555	−	0.375276i	0.897248	−	0.441527i	$-0.145563\pi$
$53$	−0.732051	−	2.73205i	−0.100555	−	0.375276i	−0.997803	+	0.0662507i	$0.978896\pi$
$54$	−5.26758	−	5.12372i	−0.716827	−	0.697251i
$55$		0			0
$56$	−2.44949	+	7.07107i	−0.327327	+	0.944911i
$57$	11.9497	+	2.05025i	1.58278	+	0.271563i
$58$	2.58819	−	9.65926i	0.339846	−	1.26832i
$59$	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
$63$	−4.71259	−	6.38682i	−0.593730	−	0.804664i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	10.3485	−	0.953512i	1.27381	−	0.117369i
$67$	0.258819	+	0.965926i	0.0316198	+	0.118007i	0.979932	−	0.199332i	$-0.0638774\pi$
$67$	0.258819	+	0.965926i	0.0316198	+	0.118007i	−0.948312	+	0.317339i	$0.897211\pi$
$68$		0			0
$69$	4.24264	+	6.00000i	0.510754	+	0.722315i
$70$		0			0
$71$		−	7.07107i		−	0.839181i	−0.907713	−	0.419591i	$-0.862174\pi$
$71$		−	7.07107i		−	0.839181i	0.907713	−	0.419591i	$-0.137826\pi$
$72$	6.99536	+	4.80260i	0.824411	+	0.565992i
$73$	−6.76148	+	1.81173i	−0.791371	+	0.212047i	−0.631792	−	0.775138i	$-0.717680\pi$
$73$	−6.76148	+	1.81173i	−0.791371	+	0.212047i	−0.159579	+	0.987185i	$0.551014\pi$
$74$	0.707107	−	1.22474i	0.0821995	−	0.142374i
$75$		0			0
$76$		0			0
$77$	11.1962	+	0.803848i	1.27592	+	0.0916069i
$78$	12.0711	+	2.07107i	1.36678	+	0.234502i
$79$	−6.06218	+	3.50000i	−0.682048	+	0.393781i	−0.800626	−	0.599164i	$-0.795500\pi$
$79$	−6.06218	+	3.50000i	−0.682048	+	0.393781i	0.118578	+	0.992945i	$0.462166\pi$
$80$		0			0
$81$	−8.39898	+	3.23375i	−0.933220	+	0.359306i
$82$	−9.65926	−	2.58819i	−1.06669	−	0.285818i
$83$	−1.00000	+	1.00000i	−0.109764	+	0.109764i	−0.759856	−	0.650092i	$-0.774731\pi$
$83$	−1.00000	+	1.00000i	−0.109764	+	0.109764i	0.650092	+	0.759856i	$0.274731\pi$
$84$		0			0
$85$		0			0
$86$	6.12372	−	3.53553i	0.660338	−	0.381246i
$87$	−9.41832	−	7.82913i	−1.00975	−	0.839371i
$88$	−11.5911	+	3.10583i	−1.23562	+	0.331082i
$89$	−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
$93$	−1.62484	+	0.599900i	−0.168489	+	0.0622068i
$94$	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	$-0.919494\pi$
$97$	−7.07107	+	7.07107i	−0.717958	+	0.717958i	0.250229	+	0.968187i	$0.419494\pi$
$98$	−5.92820	−	7.92820i	−0.598839	−	0.800869i
$99$	4.24264	−	12.0000i	0.426401	−	1.20605i
$100$		0			0
$101$	8.57321	+	4.94975i	0.853067	+	0.492518i	0.861684	−	0.507445i	$-0.169410\pi$
$101$	8.57321	+	4.94975i	0.853067	+	0.492518i	−0.00861771	+	0.999963i	$0.502743\pi$
$102$	2.21441	−	2.66390i	0.219260	−	0.263766i
$103$	0.776457	−	2.89778i	0.0765066	−	0.285526i	−0.917064	−	0.398740i	$-0.869448\pi$
$103$	0.776457	−	2.89778i	0.0765066	−	0.285526i	0.993571	+	0.113213i	$0.0361143\pi$
$104$	−14.1421			−1.38675
$105$		0			0
$106$	−4.00000			−0.388514
$107$	4.02628	−	15.0263i	0.389235	−	1.45265i	−0.442146	−	0.896943i	$-0.645783\pi$
$107$	4.02628	−	15.0263i	0.389235	−	1.45265i	0.831381	−	0.555702i	$-0.187551\pi$
$108$		0			0
$109$	14.7224	+	8.50000i	1.41015	+	0.814152i	0.995402	−	0.0957826i	$-0.0305354\pi$
$109$	14.7224	+	8.50000i	1.41015	+	0.814152i	0.414751	+	0.909935i	$0.363869\pi$
$110$		0			0
$111$	−1.00000	−	1.41421i	−0.0949158	−	0.134231i
$112$	8.76268	+	5.93426i	0.827996	+	0.560734i
$113$	14.0000	−	14.0000i	1.31701	−	1.31701i	0.400878	−	0.916132i	$-0.368705\pi$
$113$	14.0000	−	14.0000i	1.31701	−	1.31701i	0.916132	−	0.400878i	$-0.131295\pi$
$114$	7.17461	−	15.5732i	0.671964	−	1.45857i
$115$		0			0
$116$		0			0
$117$	8.48988	−	12.3662i	0.784890	−	1.14325i
$118$	−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
$122$	−5.46410	+	1.46410i	−0.494697	+	0.132554i
$123$	−7.82913	+	9.41832i	−0.705929	+	0.849221i
$124$		0			0
$125$		0			0
$126$	−10.4495	+	4.09978i	−0.930915	+	0.365237i
$127$	−10.6066	+	10.6066i	−0.941184	+	0.941184i	−0.998364	−	0.0571802i	$-0.981789\pi$
$127$	−10.6066	+	10.6066i	−0.941184	+	0.941184i	0.0571802	+	0.998364i	$0.481789\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$	−0.794593	−	8.62372i	−0.0699600	−	0.759277i
$130$		0			0
$131$	14.6969	−	8.48528i	1.28408	−	0.741362i	0.306486	−	0.951875i	$-0.400847\pi$
$131$	14.6969	−	8.48528i	1.28408	−	0.741362i	0.977591	+	0.210513i	$0.0675133\pi$
$132$		0			0
$133$	10.3849	−	15.3347i	0.900489	−	1.32969i
$134$	1.41421			0.122169
$135$		0			0
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	−15.0263	+	4.02628i	−1.28378	+	0.343988i	−0.835295	−	0.549801i	$-0.814703\pi$
$137$	−15.0263	+	4.02628i	−1.28378	+	0.343988i	−0.448486	+	0.893790i	$0.648037\pi$
$138$	9.74907	−	3.59940i	0.829896	−	0.306401i
$139$		−	11.0000i		−	0.933008i	−0.884519	−	0.466504i	$-0.845513\pi$
$139$		−	11.0000i		−	0.933008i	0.884519	−	0.466504i	$-0.154487\pi$
$140$		0			0
$141$	8.00000	−	5.65685i	0.673722	−	0.476393i
$142$	−9.65926	−	2.58819i	−0.810587	−	0.217196i
$143$	5.49038	+	20.4904i	0.459129	+	1.71349i
$144$	9.12096	−	7.79796i	0.760080	−	0.649830i
$145$		0			0
$146$			9.89949i			0.819288i
$147$	−11.8572	+	2.53139i	−0.977961	+	0.208785i
$148$		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	$0.0881622\pi$
$152$	−5.12436	+	19.1244i	−0.415640	+	1.55119i
$153$	−1.82843	−	3.82843i	−0.147820	−	0.309510i
$154$	5.19615	−	15.0000i	0.418718	−	1.20873i
$155$		0			0
$156$		0			0
$157$	−1.03528	−	3.86370i	−0.0826240	−	0.308357i	0.912230	−	0.409679i	$-0.134359\pi$
$157$	−1.03528	−	3.86370i	−0.0826240	−	0.308357i	−0.994854	+	0.101322i	$0.967693\pi$
$158$	2.56218	+	9.56218i	0.203836	+	0.760726i
$159$	−2.04989	+	4.44949i	−0.162567	+	0.352867i
$160$		0			0
$161$	11.0227	−	2.12132i	0.868711	−	0.167183i
$162$	1.34315	+	12.6569i	0.105527	+	0.994416i
$163$	−0.517638	+	1.93185i	−0.0405445	+	0.151314i	−0.983231	−	0.182367i	$-0.941624\pi$
$163$	−0.517638	+	1.93185i	−0.0405445	+	0.151314i	0.942686	+	0.333681i	$0.108291\pi$
$164$		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	$-0.375117\pi$
$167$	−7.00000	−	7.00000i	−0.541676	−	0.541676i	−0.924020	+	0.382344i	$0.875117\pi$
$168$	11.0917	−	6.70623i	0.855746	−	0.517397i
$169$			12.0000i			0.923077i
$170$		0			0
$171$	−13.6464	−	15.9617i	−1.04357	−	1.22062i
$172$		0			0
$173$	2.73205	+	0.732051i	0.207714	+	0.0556568i	0.361176	−	0.932498i	$-0.382375\pi$
$173$	2.73205	+	0.732051i	0.207714	+	0.0556568i	−0.153462	+	0.988155i	$0.549042\pi$
$174$	−14.1421	+	10.0000i	−1.07211	+	0.758098i
$175$		0			0
$176$			16.9706i			1.27920i
$177$	−2.29788	+	0.848387i	−0.172719	+	0.0637687i
$178$	−21.2504	+	5.69402i	−1.59278	+	0.426785i
$179$	−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	$0.535564\pi$
$182$	10.4904	−	15.4904i	0.777599	−	1.14822i
$183$	−1.17157	+	6.82843i	−0.0866052	+	0.504772i
$184$	−10.3923	+	6.00000i	−0.766131	+	0.442326i
$185$		0			0
$186$	0.224745	+	2.43916i	0.0164791	+	0.178848i
$187$	5.79555	+	1.55291i	0.423813	+	0.113560i
$188$		0			0
$189$	−0.794593	+	13.7247i	−0.0577981	+	0.998328i
$190$		0			0
$191$	−9.79796	+	5.65685i	−0.708955	+	0.409316i	−0.810674	−	0.585498i	$-0.800899\pi$
$191$	−9.79796	+	5.65685i	−0.708955	+	0.409316i	0.101719	+	0.994813i	$0.467566\pi$
$192$	−8.85765	+	10.6556i	−0.639246	+	0.769002i
$193$	22.2163	−	5.95284i	1.59916	−	0.428495i	0.654374	−	0.756171i	$-0.272932\pi$
$193$	22.2163	−	5.95284i	1.59916	−	0.428495i	0.944790	+	0.327677i	$0.106266\pi$
$194$	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	$-0.201706\pi$
$197$	3.00000	+	3.00000i	0.213741	+	0.213741i	−0.592113	+	0.805855i	$0.701706\pi$
$198$	−14.8394	−	10.1879i	−1.05459	−	0.724020i
$199$	1.73205	+	1.00000i	0.122782	+	0.0708881i	0.560133	−	0.828403i	$-0.310750\pi$
$199$	1.73205	+	1.00000i	0.122782	+	0.0708881i	−0.437351	+	0.899291i	$0.644083\pi$
$200$		0			0
$201$	0.724745	−	1.57313i	0.0511196	−	0.110960i
$202$	9.89949	−	9.89949i	0.696526	−	0.696526i
$203$	−16.8301	+	8.16987i	−1.18124	+	0.573413i
$204$		0			0
$205$		0			0
$206$	−3.67423	−	2.12132i	−0.255996	−	0.147799i
$207$	0.992248	−	12.6892i	0.0689660	−	0.881959i
$208$	−5.17638	+	19.3185i	−0.358917	+	1.33950i
$209$	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
$213$	−7.82913	+	9.41832i	−0.536443	+	0.645332i
$214$	−19.0526	−	11.0000i	−1.30241	−	0.751945i
$215$		0			0
$216$	−4.00000	−	14.1421i	−0.272166	−	0.962250i
$217$	−0.189469	+	2.63896i	−0.0128620	+	0.179144i
$218$	17.0000	−	17.0000i	1.15139	−	1.15139i
$219$	11.0119	+	5.07321i	0.744117	+	0.342816i
$220$		0			0
$221$	6.12372	+	3.53553i	0.411926	+	0.237826i
$222$	−2.29788	+	0.848387i	−0.154223	+	0.0569400i
$223$	7.07107	+	7.07107i	0.473514	+	0.473514i	0.903050	−	0.429536i	$-0.141323\pi$
$223$	7.07107	+	7.07107i	0.473514	+	0.473514i	−0.429536	+	0.903050i	$0.641323\pi$
$224$		0			0
$225$		0			0
$226$	−14.0000	−	24.2487i	−0.931266	−	1.61300i
$227$	12.2942	−	3.29423i	0.815997	−	0.218646i	0.173401	−	0.984851i	$-0.444524\pi$
$227$	12.2942	−	3.29423i	0.815997	−	0.218646i	0.642595	+	0.766206i	$0.277858\pi$
$228$		0			0
$229$	2.59808	−	1.50000i	0.171686	−	0.0991228i	−0.411695	−	0.911322i	$-0.635063\pi$
$229$	2.59808	−	1.50000i	0.171686	−	0.0991228i	0.583380	+	0.812199i	$0.301730\pi$
$230$		0			0
$231$	−14.0227	−	13.4671i	−0.922626	−	0.886073i
$232$	14.1421	−	14.1421i	0.928477	−	0.928477i
$233$	2.73205	+	0.732051i	0.178983	+	0.0479582i	0.347197	−	0.937792i	$-0.387133\pi$
$233$	2.73205	+	0.732051i	0.178983	+	0.0479582i	−0.168215	+	0.985750i	$0.553800\pi$
$234$	−13.7850	−	16.1237i	−0.901152	−	1.05404i
$235$		0			0
$236$		0			0
$237$	11.9497	+	2.05025i	0.776220	+	0.133178i
$238$	−2.31079	−	4.76028i	−0.149786	−	0.308563i
$239$	−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	$0.885428\pi$
$242$	9.56218	−	2.56218i	0.614680	−	0.164703i
$243$	14.7675	+	4.99221i	0.947333	+	0.320250i
$244$		0			0
$245$		0			0
$246$	10.0000	+	14.1421i	0.637577	+	0.901670i
$247$	33.8074	+	9.05867i	2.15111	+	0.576389i
$248$	−0.732051	−	2.73205i	−0.0464853	−	0.173485i
$249$	2.43916	−	0.224745i	0.154575	−	0.0142426i
$250$		0			0
$251$			7.07107i			0.446322i	0.974782	+	0.223161i	$0.0716375\pi$
$251$			7.07107i			0.446322i	−0.974782	+	0.223161i	$0.928362\pi$
$252$		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
$257$	−3.29423	+	12.2942i	−0.205488	+	0.766893i	0.783812	+	0.620998i	$0.213273\pi$
$257$	−3.29423	+	12.2942i	−0.205488	+	0.766893i	−0.989300	+	0.145894i	$0.953394\pi$
$258$	−12.0711	−	2.07107i	−0.751512	−	0.128939i
$259$	−2.59808	+	0.500000i	−0.161437	+	0.0310685i
$260$		0			0
$261$	3.87628	+	20.8560i	0.239935	+	1.29096i
$262$	−6.21166	−	23.1822i	−0.383757	−	1.43220i
$263$	−4.39230	−	16.3923i	−0.270841	−	1.01079i	−0.958577	−	0.284832i	$-0.908062\pi$
$263$	−4.39230	−	16.3923i	−0.270841	−	1.01079i	0.687736	−	0.725961i	$-0.258605\pi$
$264$	18.8776	+	8.69694i	1.16184	+	0.535260i
$265$		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
$273$	−11.8550	−	19.6076i	−0.717500	−	1.18671i
$274$			22.0000i			1.32907i
$275$		0			0
$276$		0			0
$277$	−2.32937	−	8.69333i	−0.139958	−	0.522332i	−0.999928	−	0.0119868i	$-0.996184\pi$
$277$	−2.32937	−	8.69333i	−0.139958	−	0.522332i	0.859970	−	0.510345i	$-0.170482\pi$
$278$	−15.0263	−	4.02628i	−0.901216	−	0.241480i
$279$	2.82843	+	1.00000i	0.169334	+	0.0598684i
$280$		0			0
$281$			14.1421i			0.843649i	0.906677	+	0.421825i	$0.138610\pi$
$281$			14.1421i			0.843649i	−0.906677	+	0.421825i	$0.861390\pi$
$282$	−4.79920	−	12.9988i	−0.285788	−	0.774065i
$283$	22.2163	−	5.95284i	1.32062	−	0.353859i	0.471411	−	0.881914i	$-0.343745\pi$
$283$	22.2163	−	5.95284i	1.32062	−	0.353859i	0.849211	+	0.528054i	$0.177078\pi$
$284$		0			0
$285$		0			0
$286$	30.0000			1.77394
$287$	8.16987	+	16.8301i	0.482252	+	0.993451i
$288$		0			0
$289$	−12.9904	+	7.50000i	−0.764140	+	0.441176i
$290$		0			0
$291$	17.2474	−	1.58919i	1.01106	−	0.0931597i
$292$		0			0
$293$	−16.0000	+	16.0000i	−0.934730	+	0.934730i	−0.997997	−	0.0632667i	$-0.979848\pi$
$293$	−16.0000	+	16.0000i	−0.934730	+	0.934730i	0.0632667	+	0.997997i	$0.479848\pi$
$294$	−0.882079	+	17.1237i	−0.0514439	+	0.998676i
$295$		0			0
$296$	2.44949	−	1.41421i	0.142374	−	0.0821995i
$297$	−18.9375	+	11.2859i	−1.09886	+	0.654876i
$298$	−11.5911	+	3.10583i	−0.671455	+	0.179916i
$299$	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
$303$	−5.93871	−	16.0851i	−0.341170	−	0.924067i
$304$	24.2487	+	14.0000i	1.39076	+	0.802955i
$305$		0			0
$306$	−5.89898	+	1.09638i	−0.337222	+	0.0626757i
$307$	10.6066	−	10.6066i	0.605351	−	0.605351i	−0.336377	−	0.941727i	$-0.609202\pi$
$307$	10.6066	−	10.6066i	0.605351	−	0.605351i	0.941727	+	0.336377i	$0.109202\pi$
$308$		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	$-0.959710\pi$
$311$	−28.1691	−	16.2635i	−1.59732	−	0.922216i	−0.605325	−	0.795979i	$-0.706957\pi$
$312$	18.8366	+	15.6583i	1.06641	+	0.886475i
$313$	−4.39992	+	16.4207i	−0.248698	+	0.928155i	0.722790	+	0.691068i	$0.242859\pi$
$313$	−4.39992	+	16.4207i	−0.248698	+	0.928155i	−0.971488	+	0.237087i	$0.923807\pi$
$314$	−5.65685			−0.319235
$315$		0			0
$316$		0			0
$317$	0.366025	−	1.36603i	0.0205580	−	0.0767236i	−0.954885	−	0.296977i	$-0.904022\pi$
$317$	0.366025	−	1.36603i	0.0205580	−	0.0767236i	0.975443	+	0.220253i	$0.0706883\pi$
$318$	5.32780	+	4.42883i	0.298768	+	0.248356i
$319$	−25.9808	−	15.0000i	−1.45464	−	0.839839i
$320$		0			0
$321$	−22.0000	+	15.5563i	−1.22792	+	0.868271i
$322$	1.13681	−	15.8338i	0.0633521	−	0.882380i
$323$	7.00000	−	7.00000i	0.389490	−	0.389490i
$324$		0			0
$325$		0			0
$326$	2.44949	+	1.41421i	0.135665	+	0.0783260i
$327$	−10.1983	−	27.6224i	−0.563968	−	1.52752i
$328$	−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
$333$	−0.233875	+	2.99087i	−0.0128163	+	0.163899i
$334$	−12.1244	+	7.00000i	−0.663415	+	0.383023i
$335$		0			0
$336$	−5.10102	−	17.6062i	−0.278283	−	0.960499i
$337$	−3.53553	+	3.53553i	−0.192593	+	0.192593i	−0.796815	−	0.604223i	$-0.793484\pi$
$337$	−3.53553	+	3.53553i	−0.192593	+	0.192593i	0.604223	+	0.796815i	$0.293484\pi$
$338$	16.3923	+	4.39230i	0.891624	+	0.238910i
$339$	−34.1482	+	3.14643i	−1.85468	+	0.170891i
$340$		0			0
$341$	−3.67423	+	2.12132i	−0.198971	+	0.114876i
$342$	−26.7990	+	12.7990i	−1.44912	+	0.692090i
$343$	−3.95164	+	18.0938i	−0.213368	+	0.976972i
$344$	14.1421			0.762493
$345$		0			0
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	−21.8564	+	5.85641i	−1.17331	+	0.314388i	−0.792271	−	0.610169i	$-0.791101\pi$
$347$	−21.8564	+	5.85641i	−1.17331	+	0.314388i	−0.381042	+	0.924558i	$0.624435\pi$
$348$		0			0
$349$		−	26.0000i		−	1.39175i	−0.718164	−	0.695874i	$-0.755017\pi$
$349$		−	26.0000i		−	1.39175i	0.718164	−	0.695874i	$-0.244983\pi$
$350$		0			0
$351$	−25.0000	+	7.07107i	−1.33440	+	0.377426i
$352$		0			0
$353$	1.09808	+	4.09808i	0.0584447	+	0.218119i	0.988972	−	0.148105i	$-0.0473173\pi$
$353$	1.09808	+	4.09808i	0.0584447	+	0.218119i	−0.930527	+	0.366223i	$0.880651\pi$
$354$	0.317837	+	3.44949i	0.0168929	+	0.183338i
$355$		0			0
$356$		0			0
$357$	−6.47942	+	0.130948i	−0.342927	+	0.00693052i
$358$	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
$362$	−1.09808	+	4.09808i	−0.0577136	+	0.215390i
$363$	2.05025	−	11.9497i	0.107610	−	0.627199i
$364$		0			0
$365$		0			0
$366$	8.89898	+	4.09978i	0.465157	+	0.214299i
$367$	5.43520	+	20.2844i	0.283715	+	1.05884i	0.949773	+	0.312939i	$0.101314\pi$
$367$	5.43520	+	20.2844i	0.283715	+	1.05884i	−0.666058	+	0.745900i	$0.732020\pi$
$368$	4.39230	+	16.3923i	0.228965	+	0.854508i
$369$	20.8560	−	3.87628i	1.08572	−	0.201791i
$370$		0			0
$371$	4.89898	+	5.65685i	0.254342	+	0.293689i
$372$		0			0
$373$	5.95284	−	22.2163i	0.308226	−	1.15032i	−0.621906	−	0.783092i	$-0.713641\pi$
$373$	5.95284	−	22.2163i	0.308226	−	1.15032i	0.930132	−	0.367224i	$-0.119692\pi$
$374$	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
$378$	18.4575	+	6.10904i	0.949352	+	0.314215i
$379$			9.00000i			0.462299i	0.972918	+	0.231149i	$0.0742486\pi$
$379$			9.00000i			0.462299i	−0.972918	+	0.231149i	$0.925751\pi$
$380$		0			0
$381$	25.8712	−	2.38378i	1.32542	−	0.122125i
$382$	4.14110	+	15.4548i	0.211877	+	0.790737i
$383$	16.3923	+	4.39230i	0.837608	+	0.224436i	0.652030	−	0.758193i	$-0.273918\pi$
$383$	16.3923	+	4.39230i	0.837608	+	0.224436i	0.185578	+	0.982630i	$0.440584\pi$
$384$	11.3137	+	16.0000i	0.577350	+	0.816497i
$385$		0			0
$386$		−	32.5269i		−	1.65558i
$387$	−8.48988	+	12.3662i	−0.431565	+	0.628607i
$388$		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
$392$	−2.33975	−	19.6603i	−0.118175	−	0.992993i
$393$	−28.9706	−	4.97056i	−1.46137	−	0.250732i
$394$	5.19615	−	3.00000i	0.261778	−	0.151138i
$395$		0			0
$396$		0			0
$397$	0.965926	+	0.258819i	0.0484784	+	0.0129898i	0.282977	−	0.959127i	$-0.408678\pi$
$397$	0.965926	+	0.258819i	0.0484784	+	0.0129898i	−0.234498	+	0.972117i	$0.575345\pi$
$398$	2.00000	−	2.00000i	0.100251	−	0.100251i
$399$	−30.8109	+	8.92679i	−1.54248	+	0.446898i
$400$		0			0
$401$	−22.0454	+	12.7279i	−1.10090	+	0.635602i	−0.936456	−	0.350785i	$-0.885915\pi$
$401$	−22.0454	+	12.7279i	−1.10090	+	0.635602i	−0.164439	+	0.986387i	$0.552581\pi$
$402$	−1.88366	−	1.56583i	−0.0939486	−	0.0780963i
$403$	−4.82963	+	1.29410i	−0.240581	+	0.0644635i
$404$		0			0
$405$		0			0
$406$	5.00000	+	25.9808i	0.248146	+	1.28940i
$407$	−3.00000	−	3.00000i	−0.148704	−	0.148704i
$408$	6.49938	−	2.39960i	0.321767	−	0.118798i
$409$	32.0429	+	18.5000i	1.58442	+	0.914766i	0.994203	+	0.107523i	$0.0342919\pi$
$409$	32.0429	+	18.5000i	1.58442	+	0.914766i	0.590219	+	0.807243i	$0.299041\pi$
$410$		0			0
$411$	24.4722	+	11.2744i	1.20712	+	0.556124i
$412$		0			0
$413$	−0.267949	+	3.73205i	−0.0131849	+	0.183642i
$414$	−16.9706	−	6.00000i	−0.834058	−	0.294884i
$415$		0			0
$416$		0			0
$417$	−12.1793	+	14.6515i	−0.596421	+	0.717485i
$418$	10.8704	−	40.5689i	0.531689	−	1.98429i
$419$	−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	$0.689382\pi$
$422$	0.732051	−	2.73205i	0.0356357	−	0.132994i
$423$	−16.9189	−	1.32300i	−0.822626	−	0.0643263i
$424$	−6.92820	−	4.00000i	−0.336463	−	0.194257i
$425$		0			0
$426$	10.0000	+	14.1421i	0.484502	+	0.685189i
$427$	8.76268	+	5.93426i	0.424056	+	0.287179i
$428$		0			0
$429$	15.3742	−	33.3712i	0.742271	−	1.61118i
$430$		0			0
$431$	2.44949	+	1.41421i	0.117988	+	0.0681203i	0.557832	−	0.829954i	$-0.311633\pi$
$431$	2.44949	+	1.41421i	0.117988	+	0.0681203i	−0.439845	+	0.898074i	$0.644967\pi$
$432$	−20.7826	+	0.287721i	−0.999904	+	0.0138430i
$433$	10.6066	+	10.6066i	0.509721	+	0.509721i	0.914441	−	0.404720i	$-0.132631\pi$
$433$	10.6066	+	10.6066i	0.509721	+	0.509721i	−0.404720	+	0.914441i	$0.632631\pi$
$434$	3.53553	+	1.22474i	0.169711	+	0.0587896i
$435$		0			0
$436$		0			0
$437$	28.6865	−	7.68653i	1.37226	−	0.367697i
$438$	10.9608	−	13.1856i	0.523727	−	0.630034i
$439$	32.9090	−	19.0000i	1.57066	−	0.906821i	0.574571	−	0.818455i	$-0.305169\pi$
$439$	32.9090	−	19.0000i	1.57066	−	0.906821i	0.996088	−	0.0883659i	$-0.0281645\pi$
$440$		0			0
$441$	18.5959	+	9.75663i	0.885520	+	0.464601i
$442$	7.07107	−	7.07107i	0.336336	−	0.336336i
$443$	−10.9282	−	2.92820i	−0.519215	−	0.139123i	−0.0103113	−	0.999947i	$-0.503282\pi$
$443$	−10.9282	−	2.92820i	−0.519215	−	0.139123i	−0.508903	+	0.860824i	$0.669949\pi$
$444$		0			0
$445$		0			0
$446$	12.2474	−	7.07107i	0.579934	−	0.334825i
$447$	−2.48528	+	14.4853i	−0.117550	+	0.685130i
$448$	9.24316	+	19.0411i	0.436698	+	0.899608i
$449$		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
$453$	−9.74907	+	3.59940i	−0.458051	+	0.169115i
$454$		−	18.0000i		−	0.844782i
$455$		0			0
$456$	28.0000	−	19.7990i	1.31122	−	0.927173i
$457$	−28.0118	−	7.50575i	−1.31034	−	0.351104i	−0.464989	−	0.885317i	$-0.653942\pi$
$457$	−28.0118	−	7.50575i	−1.31034	−	0.351104i	−0.845350	+	0.534212i	$0.820608\pi$
$458$	−1.09808	−	4.09808i	−0.0513097	−	0.191491i
$459$	−1.80348	+	7.12372i	−0.0841794	+	0.332507i
$460$		0			0
$461$		−	7.07107i		−	0.329332i	−0.986349	−	0.164666i	$-0.947345\pi$
$461$		−	7.07107i		−	0.329332i	0.986349	−	0.164666i	$-0.0526547\pi$
$462$	−23.5291	+	14.2261i	−1.09467	+	0.661856i
$463$	−17.6777	−	17.6777i	−0.821551	−	0.821551i	0.164779	−	0.986330i	$-0.447309\pi$
$463$	−17.6777	−	17.6777i	−0.821551	−	0.821551i	−0.986330	+	0.164779i	$0.947309\pi$
$464$	−14.1421	−	24.4949i	−0.656532	−	1.13715i
$465$		0			0
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	−1.46410	+	5.46410i	−0.0677505	+	0.252848i	−0.991492	−	0.130168i	$-0.958448\pi$
$467$	−1.46410	+	5.46410i	−0.0677505	+	0.252848i	0.923741	+	0.383017i	$0.125115\pi$
$468$		0			0
$469$	−1.73205	−	2.00000i	−0.0799787	−	0.0923514i
$470$		0			0
$471$	−2.89898	+	6.29253i	−0.133578	+	0.289944i
$472$	−1.03528	−	3.86370i	−0.0476524	−	0.177841i
$473$	−5.49038	−	20.4904i	−0.252448	−	0.942149i
$474$	7.17461	−	15.5732i	0.329541	−	0.715301i
$475$		0			0
$476$		0			0
$477$	7.65685	−	3.65685i	0.350583	−	0.167436i
$478$	−10.3528	+	38.6370i	−0.473524	+	1.76722i
$479$	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
$483$	−17.0304	−	9.37891i	−0.774912	−	0.426755i
$484$		0			0
$485$		0			0
$486$	12.2247	−	18.3455i	0.554526	−	0.832167i
$487$	−7.50575	−	28.0118i	−0.340118	−	1.26934i	−0.898213	−	0.439561i	$-0.855134\pi$
$487$	−7.50575	−	28.0118i	−0.340118	−	1.26934i	0.558095	−	0.829777i	$-0.311533\pi$
$488$	−10.9282	−	2.92820i	−0.494697	−	0.132554i
$489$	2.82843	−	2.00000i	0.127906	−	0.0904431i
$490$		0			0
$491$		−	14.1421i		−	0.638226i	−0.947717	−	0.319113i	$-0.896615\pi$
$491$		−	14.1421i		−	0.638226i	0.947717	−	0.319113i	$-0.103385\pi$
$492$		0			0
$493$	−9.65926	+	2.58819i	−0.435031	+	0.116566i
$494$	24.7487	−	42.8661i	1.11350	−	1.92864i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	8.16987	+	16.8301i	0.366469	+	0.754934i
$498$	0.585786	−	3.41421i	0.0262497	−	0.152995i
$499$	−23.3827	+	13.5000i	−1.04675	+	0.604343i	−0.921739	−	0.387812i	$-0.873231\pi$
$499$	−23.3827	+	13.5000i	−1.04675	+	0.604343i	−0.125014	+	0.992155i	$0.539898\pi$
$500$		0			0
$501$	1.57321	+	17.0741i	0.0702860	+	0.762815i
$502$	9.65926	+	2.58819i	0.431114	+	0.115517i
$503$	24.0000	−	24.0000i	1.07011	−	1.07011i	0.0727574	−	0.997350i	$-0.476820\pi$
$503$	24.0000	−	24.0000i	1.07011	−	1.07011i	0.997350	−	0.0727574i	$-0.0231799\pi$
$504$	−22.1988	−	3.34847i	−0.988814	−	0.149153i
$505$		0			0
$506$	22.0454	−	12.7279i	0.980038	−	0.565825i
$507$	13.2865	−	15.9834i	0.590073	−	0.709848i
$508$		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
$513$	0.503511	+	36.3696i	0.0222306	+	1.60576i
$514$	15.5885	+	9.00000i	0.687577	+	0.396973i
$515$		0			0
$516$		0			0
$517$	16.9706	−	16.9706i	0.746364	−	0.746364i
$518$	−0.267949	+	3.73205i	−0.0117730	+	0.163977i
$519$	−2.82843	−	4.00000i	−0.124154	−	0.175581i
$520$		0			0
$521$	26.9444	+	15.5563i	1.18046	+	0.681536i	0.956120	−	0.292976i	$-0.0946456\pi$
$521$	26.9444	+	15.5563i	1.18046	+	0.681536i	0.224335	+	0.974512i	$0.427979\pi$
$522$	29.9087	+	2.33875i	1.30907	+	0.102364i
$523$	−1.81173	+	6.76148i	−0.0792216	+	0.295659i	−0.994157	−	0.107941i	$-0.965574\pi$
$523$	−1.81173	+	6.76148i	−0.0792216	+	0.295659i	0.914936	+	0.403599i	$0.132241\pi$
$524$		0			0
$525$		0			0
$526$	−24.0000			−1.04645
$527$	−0.366025	+	1.36603i	−0.0159443	+	0.0595050i
$528$	18.7899	−	22.6040i	0.817726	−	0.983711i
$529$	−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
$534$	34.6089	+	15.9444i	1.49767	+	0.689981i
$535$		0			0
$536$	2.44949	+	1.41421i	0.105802	+	0.0610847i
$537$	32.1703	−	11.8774i	1.38825	−	0.512549i
$538$	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	$0.757345\pi$
$542$	−19.1244	+	5.12436i	−0.821461	+	0.220110i
$543$	3.99585	+	3.32162i	0.171478	+	0.142544i
$544$		0			0
$545$		0			0
$546$	−31.1237	+	9.01742i	−1.33197	+	0.385910i
$547$	7.07107	−	7.07107i	0.302337	−	0.302337i	−0.539591	−	0.841928i	$-0.681421\pi$
$547$	7.07107	−	7.07107i	0.302337	−	0.302337i	0.841928	+	0.539591i	$0.181421\pi$
$548$		0			0
$549$	9.12096	−	7.79796i	0.389273	−	0.332809i
$550$		0			0
$551$	−42.8661	+	24.7487i	−1.82616	+	1.05433i
$552$	20.4853	+	3.51472i	0.871911	+	0.149596i
$553$	10.3849	−	15.3347i	0.441613	−	0.652098i
$554$	−12.7279			−0.540758
$555$		0			0
$556$		0			0
$557$	19.1244	−	5.12436i	0.810325	−	0.217126i	0.170213	−	0.985407i	$-0.445555\pi$
$557$	19.1244	−	5.12436i	0.810325	−	0.217126i	0.640112	+	0.768281i	$0.278888\pi$
$558$	2.40130	−	3.49768i	0.101655	−	0.148069i
$559$		−	25.0000i		−	1.05739i
$560$		0			0
$561$	−6.00000	−	8.48528i	−0.253320	−	0.358249i
$562$	19.3185	+	5.17638i	0.814902	+	0.218352i
$563$	−8.05256	−	30.0526i	−0.339375	−	1.26656i	−0.899048	−	0.437851i	$-0.855740\pi$
$563$	−8.05256	−	30.0526i	−0.339375	−	1.26656i	0.559673	−	0.828714i	$-0.310927\pi$
$564$		0			0
$565$		0			0
$566$		−	32.5269i		−	1.36721i
$567$	16.2545	−	17.4009i	0.682624	−	0.730770i
$568$	−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
$576$	23.5959	−	4.38551i	0.983163	−	0.182729i
$577$	2.84701	+	10.6252i	0.118523	+	0.442332i	0.999526	−	0.0307771i	$-0.00979822\pi$
$577$	2.84701	+	10.6252i	0.118523	+	0.442332i	−0.881004	+	0.473109i	$0.843132\pi$
$578$	5.49038	+	20.4904i	0.228370	+	0.852287i
$579$	−36.1820	−	16.6691i	−1.50367	−	0.692745i
$580$		0			0
$581$	1.22474	−	3.53553i	0.0508110	−	0.146679i
$582$	4.14214	−	24.1421i	0.171697	−	1.00072i
$583$	−3.10583	+	11.5911i	−0.128630	+	0.480055i
$584$	−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	$-0.126127\pi$
$587$	13.0000	+	13.0000i	0.536567	+	0.536567i	−0.385952	+	0.922519i	$0.626127\pi$
$588$		0			0
$589$			7.00000i			0.288430i
$590$		0			0
$591$	−0.674235	−	7.31747i	−0.0277343	−	0.301001i
$592$	−1.03528	−	3.86370i	−0.0425496	−	0.158797i
$593$	−17.7583	−	4.75833i	−0.729247	−	0.195401i	−0.124953	−	0.992163i	$-0.539878\pi$
$593$	−17.7583	−	4.75833i	−0.729247	−	0.195401i	−0.604294	+	0.796761i	$0.706545\pi$
$594$	8.48528	+	30.0000i	0.348155	+	1.23091i
$595$		0			0
$596$		0			0
$597$	−1.19980	−	3.24969i	−0.0491046	−	0.133001i
$598$	28.9778	−	7.76457i	1.18499	−	0.317517i
$599$	−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	$0.454400\pi$
$602$	−10.4904	+	15.4904i	−0.427556	+	0.631341i
$603$	−2.70711	+	1.29289i	−0.110242	+	0.0526507i
$604$		0			0
$605$		0			0
$606$	−24.1464	+	2.22486i	−0.980882	+	0.0903788i
$607$	39.6030	+	10.6116i	1.60743	+	0.430711i	0.947277	−	0.320416i	$-0.103823\pi$
$607$	39.6030	+	10.6116i	1.60743	+	0.430711i	0.660158	+	0.751127i	$0.270489\pi$
$608$		0			0
$609$	31.4626	+	7.75255i	1.27493	+	0.314149i
$610$		0			0
$611$	24.4949	−	14.1421i	0.990957	−	0.572130i
$612$		0			0
$613$	−1.93185	+	0.517638i	−0.0780268	+	0.0209072i	−0.297621	−	0.954684i	$-0.596193\pi$
$613$	−1.93185	+	0.517638i	−0.0780268	+	0.0209072i	0.219594	+	0.975591i	$0.429527\pi$
$614$	−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	$-0.176868\pi$
$617$	8.00000	+	8.00000i	0.322068	+	0.322068i	−0.527492	+	0.849560i	$0.676868\pi$
$618$	2.54516	+	6.89363i	0.102381	+	0.277303i
$619$	−2.59808	−	1.50000i	−0.104425	−	0.0602901i	0.446878	−	0.894595i	$-0.352536\pi$
$619$	−2.59808	−	1.50000i	−0.104425	−	0.0602901i	−0.551303	+	0.834305i	$0.685869\pi$
$620$		0			0
$621$	−15.3712	+	15.8028i	−0.616824	+	0.634143i
$622$	−32.5269	+	32.5269i	−1.30421	+	1.30421i
$623$	34.0788	+	23.0788i	1.36534	+	0.924634i
$624$	28.2843	−	20.0000i	1.13228	−	0.800641i
$625$		0			0
$626$	20.8207	+	12.0208i	0.832161	+	0.480448i
$627$	−39.5569	−	32.8824i	−1.57975	−	1.31319i
$628$		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	$0.423228\pi$
$632$	−5.12436	+	19.1244i	−0.203836	+	0.760726i
$633$	−2.66390	−	2.21441i	−0.105881	−	0.0880150i
$634$	−1.73205	−	1.00000i	−0.0687885	−	0.0397151i
$635$		0			0
$636$		0			0
$637$	−34.7547	+	4.13613i	−1.37703	+	0.163879i
$638$	−30.0000	+	30.0000i	−1.18771	+	1.18771i
$639$	20.8560	−	3.87628i	0.825052	−	0.153343i
$640$		0			0
$641$	8.57321	+	4.94975i	0.338622	+	0.195503i	0.659662	−	0.751562i	$-0.270699\pi$
$641$	8.57321	+	4.94975i	0.338622	+	0.195503i	−0.321041	+	0.947065i	$0.604033\pi$
$642$	13.1978	+	35.7466i	0.520876	+	1.41080i
$643$	17.6777	+	17.6777i	0.697139	+	0.697139i	0.963793	−	0.266653i	$-0.0859179\pi$
$643$	17.6777	+	17.6777i	0.697139	+	0.697139i	−0.266653	+	0.963793i	$0.585918\pi$
$644$		0			0
$645$		0			0
$646$	−7.00000	−	12.1244i	−0.275411	−	0.477026i
$647$	−1.36603	+	0.366025i	−0.0537040	+	0.0143899i	−0.285571	−	0.958358i	$-0.592183\pi$
$647$	−1.36603	+	0.366025i	−0.0537040	+	0.0143899i	0.231867	+	0.972747i	$0.425517\pi$
$648$	−10.3305	+	23.2655i	−0.405819	+	0.913954i
$649$	−5.19615	+	3.00000i	−0.203967	+	0.117760i
$650$		0			0
$651$	3.17423	−	3.30518i	0.124408	−	0.129540i
$652$		0			0
$653$	36.8827	+	9.88269i	1.44333	+	0.386739i	0.893699	−	0.448667i	$-0.148101\pi$
$653$	36.8827	+	9.88269i	1.44333	+	0.386739i	0.549632	+	0.835407i	$0.314768\pi$
$654$	−41.4657	+	3.82066i	−1.62144	+	0.149400i
$655$		0			0
$656$	−24.4949	+	14.1421i	−0.956365	+	0.552158i
$657$	−9.05025	−	18.9497i	−0.353084	−	0.739300i
$658$	−21.1117	−	1.51575i	−0.823018	−	0.0590901i
$659$	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	$0.287140\pi$
$662$	1.36603	−	0.366025i	0.0530921	−	0.0142260i
$663$	−4.24194	−	11.4894i	−0.164743	−	0.446211i
$664$			4.00000i			0.155230i
$665$		0			0
$666$	4.00000	+	1.41421i	0.154997	+	0.0547997i
$667$	−28.9778	−	7.76457i	−1.12202	−	0.300645i
$668$		0			0
$669$	−1.58919	−	17.2474i	−0.0614415	−	0.666825i
$670$		0			0
$671$			16.9706i			0.655141i
$672$		0			0
$673$	−17.6777	−	17.6777i	−0.681424	−	0.681424i	0.278897	−	0.960321i	$-0.410031\pi$
$673$	−17.6777	−	17.6777i	−0.681424	−	0.681424i	−0.960321	+	0.278897i	$0.910031\pi$
$674$	3.53553	+	6.12372i	0.136184	+	0.235877i
$675$		0			0
$676$		0			0
$677$	11.3468	−	42.3468i	0.436092	−	1.62752i	−0.302346	−	0.953198i	$-0.597770\pi$
$677$	11.3468	−	42.3468i	0.436092	−	1.62752i	0.738438	−	0.674321i	$-0.235564\pi$
$678$	−8.20101	+	47.7990i	−0.314958	+	1.83571i
$679$	8.66025	−	25.0000i	0.332350	−	0.959412i
$680$		0			0
$681$	−20.0227	−	9.22450i	−0.767272	−	0.353483i
$682$	1.55291	+	5.79555i	0.0594642	+	0.221923i
$683$	−6.22243	−	23.2224i	−0.238095	−	0.888582i	−0.976729	−	0.214476i	$-0.931196\pi$
$683$	−6.22243	−	23.2224i	−0.238095	−	0.888582i	0.738635	−	0.674106i	$-0.235471\pi$
$684$		0			0
$685$		0			0
$686$	23.2702	+	12.0208i	0.888459	+	0.458957i
$687$	−5.12132	−	0.878680i	−0.195391	−	0.0335237i
$688$	5.17638	−	19.3185i	0.197348	−	0.736512i
$689$	−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
$693$	3.76666	+	33.4636i	0.143084	+	1.27118i
$694$			32.0000i			1.21470i
$695$		0			0
$696$	−34.4949	+	3.17837i	−1.30753	+	0.120476i
$697$	2.58819	+	9.65926i	0.0980347	+	0.365870i
$698$	−35.5167	−	9.51666i	−1.34433	−	0.360211i
$699$	−2.82843	−	4.00000i	−0.106981	−	0.151294i
$700$		0			0
$701$			21.2132i			0.801212i	0.916250	+	0.400606i	$0.131200\pi$
$701$			21.2132i			0.801212i	−0.916250	+	0.400606i	$0.868800\pi$
$702$	0.508623	+	36.7388i	0.0191967	+	1.38662i
$703$	−6.76148	+	1.81173i	−0.255014	+	0.0683308i
$704$	−16.9706	+	29.3939i	−0.639602	+	1.10782i
$705$		0			0
$706$	6.00000			0.225813
$707$	−26.1244	−	1.87564i	−0.982508	−	0.0705409i
$708$		0			0
$709$	−27.7128	+	16.0000i	−1.04078	+	0.600893i	−0.920053	−	0.391794i	$-0.871855\pi$
$709$	−27.7128	+	16.0000i	−1.04078	+	0.600893i	−0.120723	+	0.992686i	$0.538521\pi$
$710$		0			0
$711$	−13.6464	−	15.9617i	−0.511781	−	0.598609i
$712$	−42.5007	−	11.3880i	−1.59278	−	0.426785i
$713$	−3.00000	+	3.00000i	−0.112351	+	0.112351i
$714$	−2.19275	+	8.89898i	−0.0820617	+	0.333036i
$715$		0			0
$716$		0			0
$717$	37.6733	+	31.3165i	1.40693	+	1.16954i
$718$	−1.93185	+	0.517638i	−0.0720961	+	0.0193181i
$719$	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
$723$	38.9963	−	14.3976i	1.45029	−	0.535453i
$724$		0			0
$725$		0			0
$726$	−15.5732	−	7.17461i	−0.577976	−	0.266275i
$727$	−17.6777	+	17.6777i	−0.655628	+	0.655628i	−0.954343	−	0.298714i	$-0.903442\pi$
$727$	−17.6777	+	17.6777i	−0.655628	+	0.655628i	0.298714	+	0.954343i	$0.403442\pi$
$728$	33.6603	−	16.3397i	1.24753	−	0.605591i
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$		0			0
$731$	−6.12372	−	3.53553i	−0.226494	−	0.130766i
$732$		0			0
$733$	8.54103	−	31.8756i	0.315470	−	1.17735i	−0.608081	−	0.793875i	$-0.708060\pi$
$733$	8.54103	−	31.8756i	0.315470	−	1.17735i	0.923551	−	0.383475i	$-0.125273\pi$
$734$	29.6985			1.09619
$735$		0			0
$736$		0			0
$737$	1.09808	−	4.09808i	0.0404482	−	0.150955i
$738$	2.33875	−	29.9087i	0.0860906	−	1.10095i
$739$	6.06218	+	3.50000i	0.223001	+	0.128750i	0.607339	−	0.794443i	$-0.292237\pi$
$739$	6.06218	+	3.50000i	0.223001	+	0.128750i	−0.384338	+	0.923192i	$0.625570\pi$
$740$		0			0
$741$	−35.0000	−	49.4975i	−1.28576	−	1.81834i
$742$	9.52056	−	4.62158i	0.349511	−	0.169663i
$743$	−11.0000	+	11.0000i	−0.403551	+	0.403551i	−0.879482	−	0.475931i	$-0.842111\pi$
$743$	−11.0000	+	11.0000i	−0.403551	+	0.403551i	0.475931	+	0.879482i	$0.342111\pi$
$744$	−2.04989	+	4.44949i	−0.0751525	+	0.163126i
$745$		0			0
$746$	−28.1691	−	16.2635i	−1.03135	−	0.595447i
$747$	−3.49768	−	2.40130i	−0.127973	−	0.0878590i
$748$		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	$-0.418680\pi$
$752$	21.8564	−	5.85641i	0.797021	−	0.213561i
$753$	7.82913	−	9.41832i	0.285309	−	0.343223i
$754$	−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	$-0.868403\pi$
$757$	−14.1421	+	14.1421i	−0.514005	+	0.514005i	0.401746	+	0.915751i	$0.368403\pi$
$758$	12.2942	+	3.29423i	0.446546	+	0.119652i
$759$	−2.86054	−	31.0454i	−0.103831	−	1.12688i
$760$		0			0
$761$	20.8207	−	12.0208i	0.754748	−	0.435754i	−0.0726586	−	0.997357i	$-0.523148\pi$
$761$	20.8207	−	12.0208i	0.754748	−	0.435754i	0.827407	+	0.561603i	$0.189815\pi$
$762$	6.21320	−	36.2132i	0.225081	−	1.31187i
$763$	−44.8623	−	3.22097i	−1.62412	−	0.116607i
$764$		0			0
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	−6.83013	+	1.83013i	−0.246622	+	0.0660821i
$768$		0			0
$769$			29.0000i			1.04577i	0.852404	+	0.522883i	$0.175144\pi$
$769$			29.0000i			1.04577i	−0.852404	+	0.522883i	$0.824856\pi$
$770$		0			0
$771$	18.0000	−	12.7279i	0.648254	−	0.458385i
$772$		0			0
$773$	4.75833	+	17.7583i	0.171145	+	0.638723i	0.997176	+	0.0750979i	$0.0239269\pi$
$773$	4.75833	+	17.7583i	0.171145	+	0.638723i	−0.826031	+	0.563625i	$0.809406\pi$
$774$	13.7850	+	16.1237i	0.495491	+	0.579555i
$775$		0			0
$776$			28.2843i			1.01535i
$777$	4.01411	+	2.21063i	0.144006	+	0.0793059i
$778$	−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
$782$	2.19615	−	8.19615i	0.0785343	−	0.293094i
$783$	17.9289	−	32.0711i	0.640728	−	1.14613i
$784$	−27.7128	−	4.00000i	−0.989743	−	0.142857i
$785$		0			0
$786$	−17.3939	+	37.7552i	−0.620419	+	1.34668i
$787$	6.72930	+	25.1141i	0.239873	+	0.895220i	0.975891	+	0.218258i	$0.0700373\pi$
$787$	6.72930	+	25.1141i	0.239873	+	0.895220i	−0.736018	+	0.676962i	$0.763296\pi$
$788$		0			0
$789$	−12.2993	+	26.6969i	−0.437868	+	0.950436i
$790$		0			0
$791$	−17.1464	+	49.4975i	−0.609657	+	1.75993i
$792$	−15.5147	−	32.4853i	−0.551292	−	1.15431i
$793$	−5.17638	+	19.3185i	−0.183819	+	0.686021i
$794$	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	$-0.390007\pi$
$797$	−17.0000	−	17.0000i	−0.602171	−	0.602171i	−0.940888	+	0.338717i	$0.890007\pi$
$798$	0.916639	+	45.3559i	0.0324487	+	1.60558i
$799$		−	8.00000i		−	0.283020i
$800$		0			0
$801$	35.4722	−	30.3269i	1.25335	−	1.07155i
$802$	9.31749	+	34.7733i	0.329012	+	1.22789i
$803$	28.6865	+	7.68653i	1.01233	+	0.271252i
$804$		0			0
$805$		0			0
$806$			7.07107i			0.249068i
$807$	9.19151	−	3.39355i	0.323556	−	0.119459i
$808$	27.0459	−	7.24693i	0.951472	−	0.254946i
$809$	−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
$816$	−0.898979	−	9.75663i	−0.0314706	−	0.341550i
$817$	−33.8074	−	9.05867i	−1.18277	−	0.316923i
$818$	37.0000	−	37.0000i	1.29367	−	1.29367i
$819$	−5.91931	+	39.2423i	−0.206838	+	1.37124i
$820$		0			0
$821$	−15.9217	+	9.19239i	−0.555671	+	0.320817i	−0.751406	−	0.659840i	$-0.770624\pi$
$821$	−15.9217	+	9.19239i	−0.555671	+	0.320817i	0.195735	+	0.980657i	$0.437291\pi$
$822$	24.3585	−	29.3029i	0.849602	−	1.02206i
$823$	27.0459	−	7.24693i	0.942762	−	0.252612i	0.245474	−	0.969403i	$-0.421057\pi$
$823$	27.0459	−	7.24693i	0.942762	−	0.252612i	0.697288	+	0.716791i	$0.254390\pi$
$824$	−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	$-0.104059\pi$
$827$	18.0000	+	18.0000i	0.625921	+	0.625921i	−0.321118	+	0.947039i	$0.604059\pi$
$828$		0			0
$829$	6.06218	+	3.50000i	0.210548	+	0.121560i	0.601566	−	0.798823i	$-0.294544\pi$
$829$	6.06218	+	3.50000i	0.210548	+	0.121560i	−0.391018	+	0.920383i	$0.627877\pi$
$830$		0			0
$831$	−6.52270	+	14.1582i	−0.226270	+	0.491142i
$832$	−28.2843	+	28.2843i	−0.980581	+	0.980581i
$833$	−3.90192	+	9.09808i	−0.135194	+	0.315230i
$834$	15.5563	+	22.0000i	0.538672	+	0.761798i
$835$		0			0
$836$		0			0
$837$	−2.66012	−	4.46360i	−0.0919472	−	0.154285i
$838$	−5.17638	+	19.3185i	−0.178815	+	0.667347i
$839$	−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
$842$	−8.41858	+	31.4186i	−0.290124	+	1.08276i
$843$	15.6583	−	18.8366i	0.539299	−	0.648768i
$844$		0			0
$845$		0			0
$846$	−8.00000	+	22.6274i	−0.275046	+	0.777947i
$847$	−15.3347	−	10.3849i	−0.526906	−	0.356831i
$848$	−8.00000	+	8.00000i	−0.274721	+	0.274721i
$849$	−36.1820	−	16.6691i	−1.24176	−	0.572083i
$850$		0			0
$851$	−3.67423	−	2.12132i	−0.125951	−	0.0727179i
$852$		0			0
$853$	−38.8909	−	38.8909i	−1.33160	−	1.33160i	−0.903941	−	0.427657i	$-0.859339\pi$
$853$	−38.8909	−	38.8909i	−1.33160	−	1.33160i	−0.427657	−	0.903941i	$-0.640661\pi$
$854$	11.3137	−	9.79796i	0.387147	−	0.335279i
$855$		0			0
$856$	−22.0000	−	38.1051i	−0.751945	−	1.30241i
$857$	−28.6865	+	7.68653i	−0.979913	+	0.262567i	−0.713008	−	0.701156i	$-0.752668\pi$
$857$	−28.6865	+	7.68653i	−0.979913	+	0.262567i	−0.266905	+	0.963723i	$0.586001\pi$
$858$	−39.9585	−	33.2162i	−1.36416	−	1.13398i
$859$	−19.0526	+	11.0000i	−0.650065	+	0.375315i	−0.788481	−	0.615059i	$-0.789132\pi$
$859$	−19.0526	+	11.0000i	−0.650065	+	0.375315i	0.138416	+	0.990374i	$0.455799\pi$
$860$		0			0
$861$	7.75255	−	31.4626i	0.264206	−	1.07224i
$862$	2.82843	−	2.82843i	0.0963366	−	0.0963366i
$863$	−38.2487	−	10.2487i	−1.30200	−	0.348870i	−0.459795	−	0.888025i	$-0.652077\pi$
$863$	−38.2487	−	10.2487i	−1.30200	−	0.348870i	−0.842207	+	0.539155i	$0.818744\pi$
$864$		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
$872$	46.4449	−	12.4449i	1.57282	−	0.421436i
$873$	−24.7323	−	16.9798i	−0.837062	−	0.574678i
$874$		−	42.0000i		−	1.42067i
$875$		0			0
$876$		0			0
$877$	−23.1822	−	6.21166i	−0.782808	−	0.209753i	−0.154786	−	0.987948i	$-0.549469\pi$
$877$	−23.1822	−	6.21166i	−0.782808	−	0.209753i	−0.628022	+	0.778195i	$0.716135\pi$
$878$	−13.9090	−	51.9090i	−0.469405	−	1.75184i
$879$	39.0265	−	3.59592i	1.31633	−	0.121287i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	20.1344	−	21.8313i	0.677960	−	0.735099i
$883$	−10.6066	−	10.6066i	−0.356941	−	0.356941i	0.505743	−	0.862684i	$-0.331218\pi$
$883$	−10.6066	−	10.6066i	−0.356941	−	0.356941i	−0.862684	+	0.505743i	$0.831218\pi$
$884$		0			0
$885$		0			0
$886$	−8.00000	+	13.8564i	−0.268765	+	0.465515i
$887$	7.68653	−	28.6865i	0.258089	−	0.963200i	−0.708258	−	0.705954i	$-0.750518\pi$
$887$	7.68653	−	28.6865i	0.258089	−	0.963200i	0.966346	−	0.257245i	$-0.0828149\pi$
$888$	−4.82843	−	0.828427i	−0.162031	−	0.0278002i
$889$	12.9904	−	37.5000i	0.435683	−	1.25771i
$890$		0			0
$891$	37.7196	+	5.93537i	1.26366	+	0.198842i
$892$		0			0
$893$	−10.2487	−	38.2487i	−0.342960	−	1.27994i
$894$	18.8776	+	8.69694i	0.631361	+	0.290869i
$895$		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
$903$	11.8550	+	19.6076i	0.394511	+	0.652500i
$904$		−	56.0000i		−	1.86253i
$905$		0			0
$906$	1.34847	+	14.6349i	0.0447999	+	0.486213i
$907$	13.1998	+	49.2622i	0.438291	+	1.63573i	0.733065	+	0.680158i	$0.238089\pi$
$907$	13.1998	+	49.2622i	0.438291	+	1.63573i	−0.294774	+	0.955567i	$0.595244\pi$
$908$		0			0
$909$	−9.89949	+	28.0000i	−0.328346	+	0.928701i
$910$		0			0
$911$		−	35.3553i		−	1.17137i	−0.810537	−	0.585687i	$-0.800825\pi$
$911$		−	35.3553i		−	1.17137i	0.810537	−	0.585687i	$-0.199175\pi$
$912$	−16.7972	−	45.4956i	−0.556211	−	1.50651i
$913$	5.79555	−	1.55291i	0.191805	−	0.0513940i
$914$	−20.5061	+	35.5176i	−0.678281	+	1.17482i
$915$		0			0
$916$		0			0
$917$	−25.1769	+	37.1769i	−0.831415	+	1.22769i
$918$	9.07107	+	5.07107i	0.299390	+	0.167370i
$919$	11.2583	−	6.50000i	0.371378	−	0.214415i	−0.302682	−	0.953092i	$-0.597882\pi$
$919$	11.2583	−	6.50000i	0.371378	−	0.214415i	0.674060	+	0.738676i	$0.264549\pi$
$920$		0			0
$921$	−25.8712	+	2.38378i	−0.852484	+	0.0785482i
$922$	−9.65926	−	2.58819i	−0.318111	−	0.0852375i
$923$	−25.0000	+	25.0000i	−0.822885	+	0.822885i
$924$		0			0
$925$		0			0
$926$	−30.6186	+	17.6777i	−1.00619	+	0.580924i
$927$	8.97261	+	0.701625i	0.294699	+	0.0230444i
$928$		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
$933$	19.5129	+	52.8512i	0.638824	+	1.73027i
$934$	6.92820	+	4.00000i	0.226698	+	0.130884i
$935$		0			0
$936$	−7.75255	−	41.7121i	−0.253400	−	1.36340i
$937$	10.6066	−	10.6066i	0.346503	−	0.346503i	−0.512302	−	0.858805i	$-0.671207\pi$
$937$	10.6066	−	10.6066i	0.346503	−	0.346503i	0.858805	+	0.512302i	$0.171207\pi$
$938$	−3.36603	+	1.63397i	−0.109905	+	0.0533512i
$939$	24.0416	−	17.0000i	0.784569	−	0.554774i
$940$		0			0
$941$	−15.9217	−	9.19239i	−0.519032	−	0.299663i	0.217506	−	0.976059i	$-0.430208\pi$
$941$	−15.9217	−	9.19239i	−0.519032	−	0.299663i	−0.736539	+	0.676396i	$0.763541\pi$
$942$	7.53465	+	6.26330i	0.245492	+	0.204070i
$943$	−7.76457	+	28.9778i	−0.252849	+	0.943646i
$944$	−5.65685			−0.184115
$945$		0			0
$946$	−30.0000			−0.975384
$947$	4.02628	−	15.0263i	0.130837	−	0.488288i	−0.869144	−	0.494559i	$-0.835329\pi$
$947$	4.02628	−	15.0263i	0.130837	−	0.488288i	0.999980	+	0.00627092i	$0.00199611\pi$
$948$		0			0
$949$	30.3109	+	17.5000i	0.983933	+	0.568074i
$950$		0			0
$951$	−2.00000	+	1.41421i	−0.0648544	+	0.0458590i
$952$	0.757875	−	10.5558i	0.0245629	−	0.342117i
$953$	−36.0000	+	36.0000i	−1.16615	+	1.16615i	−0.183051	+	0.983103i	$0.558597\pi$
$953$	−36.0000	+	36.0000i	−1.16615	+	1.16615i	−0.983103	+	0.183051i	$0.941403\pi$
$954$	−2.19275	−	11.7980i	−0.0709930	−	0.381973i
$955$		0			0
$956$		0			0
$957$	17.9970	+	48.7453i	0.581761	+	1.57571i
$958$	−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
$962$	−6.83013	+	1.83013i	−0.220212	+	0.0590057i
$963$	46.5270	+	3.63824i	1.49931	+	0.117241i
$964$		0			0
$965$		0			0
$966$	−19.0454	+	19.8311i	−0.612776	+	0.638055i
$967$	24.7487	−	24.7487i	0.795866	−	0.795866i	−0.186575	−	0.982441i	$-0.559739\pi$
$967$	24.7487	−	24.7487i	0.795866	−	0.795866i	0.982441	+	0.186575i	$0.0597387\pi$
$968$	19.1244	+	5.12436i	0.614680	+	0.164703i
$969$	−17.0741	+	1.57321i	−0.548499	+	0.0505389i
$970$		0			0
$971$	39.1918	−	22.6274i	1.25773	−	0.726148i	0.285094	−	0.958500i	$-0.407975\pi$
$971$	39.1918	−	22.6274i	1.25773	−	0.726148i	0.972632	+	0.232351i	$0.0746419\pi$
$972$		0			0
$973$	12.7093	+	26.1815i	0.407443	+	0.839341i
$974$	−41.0122			−1.31412
$975$		0			0
$976$	−8.00000	+	13.8564i	−0.256074	+	0.443533i
$977$	−15.0263	+	4.02628i	−0.480733	+	0.128812i	−0.491044	−	0.871135i	$-0.663385\pi$
$977$	−15.0263	+	4.02628i	−0.480733	+	0.128812i	0.0103108	+	0.999947i	$0.496718\pi$
$978$	−1.69677	−	4.59575i	−0.0542569	−	0.146956i
$979$			66.0000i			2.10937i
$980$		0			0
$981$	−17.0000	+	48.0833i	−0.542768	+	1.53518i
$982$	−19.3185	−	5.17638i	−0.616479	−	0.165185i
$983$	−9.88269	−	36.8827i	−0.315209	−	1.17637i	−0.923795	−	0.382887i	$-0.874930\pi$
$983$	−9.88269	−	36.8827i	−0.315209	−	1.17637i	0.608586	−	0.793488i	$-0.291737\pi$
$984$	3.17837	+	34.4949i	0.101323	+	1.09966i
$985$		0			0
$986$			14.1421i			0.450377i
$987$	−12.5052	+	22.7073i	−0.398045	+	0.722780i
$988$		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
$997$	−10.0939	−	37.6711i	−0.319678	−	1.19306i	−0.919554	−	0.392963i	$-0.871450\pi$
$997$	−10.0939	−	37.6711i	−0.319678	−	1.19306i	0.599876	−	0.800093i	$-0.295217\pi$
$998$	9.88269	+	36.8827i	0.312831	+	1.16750i
$999$	3.62302	−	3.72474i	0.114627	−	0.117846i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(-2.00000 + 1.41421i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(2.00000 - 2.00000i) q^{8} +(0.548188 + 2.94949i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(-2.00000 + 1.41421i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(2.00000 - 2.00000i) q^{8} +(0.548188 + 2.94949i) q^{9} +(-3.67423 - 2.12132i) q^{11} +(-3.53553 - 3.53553i) q^{13} +(0.707107 + 3.67423i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-1.36603 + 0.366025i) q^{17} +(4.22973 + 0.330749i) q^{18} +(-6.06218 + 3.50000i) q^{19} +(4.44949 + 1.09638i) q^{21} +(-4.24264 + 4.24264i) q^{22} +(-4.09808 - 1.09808i) q^{23} +(-4.87832 + 0.449490i) q^{24} +(-6.12372 + 3.53553i) q^{26} +(2.53553 - 4.53553i) q^{27} +7.07107 q^{29} +(0.500000 - 0.866025i) q^{31} +(2.54516 + 6.89363i) q^{33} +2.00000i q^{34} +(0.965926 + 0.258819i) q^{37} +(2.56218 + 9.56218i) q^{38} +(0.794593 + 8.62372i) q^{39} -7.07107i q^{41} +(3.12630 - 5.67681i) q^{42} +(3.53553 + 3.53553i) q^{43} +(-3.00000 + 5.19615i) q^{46} +(-1.46410 + 5.46410i) q^{47} +(-1.17157 + 6.82843i) q^{48} +(4.33013 - 5.50000i) q^{49} +(2.22474 + 1.02494i) q^{51} +(-0.732051 - 2.73205i) q^{53} +(-5.26758 - 5.12372i) q^{54} +(-2.44949 + 7.07107i) q^{56} +(11.9497 + 2.05025i) q^{57} +(2.58819 - 9.65926i) q^{58} +(0.707107 - 1.22474i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(-1.00000 - 1.00000i) q^{62} +(-4.71259 - 6.38682i) q^{63} -8.00000i q^{64} +(10.3485 - 0.953512i) q^{66} +(0.258819 + 0.965926i) q^{67} +(4.24264 + 6.00000i) q^{69} -7.07107i q^{71} +(6.99536 + 4.80260i) q^{72} +(-6.76148 + 1.81173i) q^{73} +(0.707107 - 1.22474i) q^{74} +(11.1962 + 0.803848i) q^{77} +(12.0711 + 2.07107i) q^{78} +(-6.06218 + 3.50000i) q^{79} +(-8.39898 + 3.23375i) q^{81} +(-9.65926 - 2.58819i) q^{82} +(-1.00000 + 1.00000i) q^{83} +(6.12372 - 3.53553i) q^{86} +(-9.41832 - 7.82913i) q^{87} +(-11.5911 + 3.10583i) q^{88} +(-7.77817 - 13.4722i) q^{89} +(12.5000 + 4.33013i) q^{91} +(-1.62484 + 0.599900i) q^{93} +(6.92820 + 4.00000i) q^{94} +(-7.07107 + 7.07107i) q^{97} +(-5.92820 - 7.92820i) q^{98} +(4.24264 - 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{3} - 16 q^{6} + 16 q^{8}+O(q^{10}) \) 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